LMFDB - Embedded newform 154.2.e.f.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(23,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("154.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.e (of order $3$, 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:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	154.67
Dual form			154.2.e.f.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} -2.64575 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} -2.64575 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(-0.822876 + 1.42526i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.32288 - 2.29129i) q^{12} +5.00000 q^{13} +(1.32288 - 2.29129i) q^{14} -4.35425 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{18} +(2.82288 + 4.88936i) q^{19} -1.64575 q^{20} +7.00000 q^{21} -1.00000 q^{22} +(-0.822876 - 1.42526i) q^{23} +(1.32288 - 2.29129i) q^{24} +(1.14575 - 1.98450i) q^{25} +(2.50000 + 4.33013i) q^{26} +2.64575 q^{27} +2.64575 q^{28} +6.29150 q^{29} +(-2.17712 - 3.77089i) q^{30} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.32288 - 2.29129i) q^{33} -6.00000 q^{34} +(2.17712 - 3.77089i) q^{35} +4.00000 q^{36} +(-1.82288 - 3.15731i) q^{37} +(-2.82288 + 4.88936i) q^{38} +(-6.61438 + 11.4564i) q^{39} +(-0.822876 - 1.42526i) q^{40} +10.9373 q^{41} +(3.50000 + 6.06218i) q^{42} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(3.29150 - 5.70105i) q^{45} +(0.822876 - 1.42526i) q^{46} +(-1.35425 - 2.34563i) q^{47} +2.64575 q^{48} +(-3.50000 + 6.06218i) q^{49} +2.29150 q^{50} +(-7.93725 - 13.7477i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(-0.822876 + 1.42526i) q^{53} +(1.32288 + 2.29129i) q^{54} -1.64575 q^{55} +(1.32288 + 2.29129i) q^{56} -14.9373 q^{57} +(3.14575 + 5.44860i) q^{58} +(-2.32288 + 4.02334i) q^{59} +(2.17712 - 3.77089i) q^{60} +(-7.14575 - 12.3768i) q^{61} +4.00000 q^{62} +(-5.29150 + 9.16515i) q^{63} +1.00000 q^{64} +(4.11438 + 7.12631i) q^{65} +(1.32288 - 2.29129i) q^{66} +(5.96863 - 10.3380i) q^{67} +(-3.00000 - 5.19615i) q^{68} +4.35425 q^{69} +4.35425 q^{70} +4.35425 q^{71} +(2.00000 + 3.46410i) q^{72} +(-0.177124 + 0.306788i) q^{73} +(1.82288 - 3.15731i) q^{74} +(3.03137 + 5.25049i) q^{75} -5.64575 q^{76} +2.64575 q^{77} -13.2288 q^{78} +(1.32288 + 2.29129i) q^{79} +(0.822876 - 1.42526i) q^{80} +(2.50000 - 4.33013i) q^{81} +(5.46863 + 9.47194i) q^{82} +2.70850 q^{83} +(-3.50000 + 6.06218i) q^{84} -9.87451 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-8.32288 + 14.4156i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-3.29150 - 5.70105i) q^{89} +6.58301 q^{90} +(-6.61438 - 11.4564i) q^{91} +1.64575 q^{92} +(5.29150 + 9.16515i) q^{93} +(1.35425 - 2.34563i) q^{94} +(-4.64575 + 8.04668i) q^{95} +(1.32288 + 2.29129i) q^{96} -16.2915 q^{97} -7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 8 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 28 q^{15} - 2 q^{16} - 12 q^{17} + 8 q^{18} + 6 q^{19} + 4 q^{20} + 28 q^{21} - 4 q^{22} + 2 q^{23} - 6 q^{25} + 10 q^{26} + 4 q^{29} - 14 q^{30} + 8 q^{31} + 2 q^{32} - 24 q^{34} + 14 q^{35} + 16 q^{36} - 2 q^{37} - 6 q^{38} + 2 q^{40} + 12 q^{41} + 14 q^{42} - 16 q^{43} - 2 q^{44} - 8 q^{45} - 2 q^{46} - 16 q^{47} - 14 q^{49} - 12 q^{50} - 10 q^{52} + 2 q^{53} + 4 q^{55} - 28 q^{57} + 2 q^{58} - 4 q^{59} + 14 q^{60} - 18 q^{61} + 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} - 12 q^{68} + 28 q^{69} + 28 q^{70} + 28 q^{71} + 8 q^{72} - 6 q^{73} + 2 q^{74} + 28 q^{75} - 12 q^{76} - 2 q^{80} + 10 q^{81} + 6 q^{82} + 32 q^{83} - 14 q^{84} + 24 q^{85} - 8 q^{86} - 28 q^{87} + 2 q^{88} + 8 q^{89} - 16 q^{90} - 4 q^{92} + 16 q^{94} - 8 q^{95} - 44 q^{97} - 28 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 8 * q^9 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 28 * q^15 - 2 * q^16 - 12 * q^17 + 8 * q^18 + 6 * q^19 + 4 * q^20 + 28 * q^21 - 4 * q^22 + 2 * q^23 - 6 * q^25 + 10 * q^26 + 4 * q^29 - 14 * q^30 + 8 * q^31 + 2 * q^32 - 24 * q^34 + 14 * q^35 + 16 * q^36 - 2 * q^37 - 6 * q^38 + 2 * q^40 + 12 * q^41 + 14 * q^42 - 16 * q^43 - 2 * q^44 - 8 * q^45 - 2 * q^46 - 16 * q^47 - 14 * q^49 - 12 * q^50 - 10 * q^52 + 2 * q^53 + 4 * q^55 - 28 * q^57 + 2 * q^58 - 4 * q^59 + 14 * q^60 - 18 * q^61 + 16 * q^62 + 4 * q^64 - 10 * q^65 + 8 * q^67 - 12 * q^68 + 28 * q^69 + 28 * q^70 + 28 * q^71 + 8 * q^72 - 6 * q^73 + 2 * q^74 + 28 * q^75 - 12 * q^76 - 2 * q^80 + 10 * q^81 + 6 * q^82 + 32 * q^83 - 14 * q^84 + 24 * q^85 - 8 * q^86 - 28 * q^87 + 2 * q^88 + 8 * q^89 - 16 * q^90 - 4 * q^92 + 16 * q^94 - 8 * q^95 - 44 * q^97 - 28 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.32288	+	2.29129i	−0.763763	+	1.32288i	0.177136	+	0.984186i	$0.443317\pi$
$3$	−1.32288	+	2.29129i	−0.763763	+	1.32288i	−0.940898	+	0.338689i	$0.890016\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.822876	+	1.42526i	0.368001	+	0.637397i	0.989253	−	0.146214i	$-0.0467089\pi$
$5$	0.822876	+	1.42526i	0.368001	+	0.637397i	−0.621252	+	0.783611i	$0.713376\pi$
$6$	−2.64575			−1.08012
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$	−1.00000			−0.353553
$9$	−2.00000	−	3.46410i	−0.666667	−	1.15470i
$10$	−0.822876	+	1.42526i	−0.260216	+	0.450708i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−1.32288	−	2.29129i	−0.381881	−	0.661438i
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	1.32288	−	2.29129i	0.353553	−	0.612372i
$15$	−4.35425			−1.12426
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$	2.00000	−	3.46410i	0.471405	−	0.816497i
$19$	2.82288	+	4.88936i	0.647612	+	1.12170i	0.983692	+	0.179863i	$0.0575656\pi$
$19$	2.82288	+	4.88936i	0.647612	+	1.12170i	−0.336080	+	0.941834i	$0.609101\pi$
$20$	−1.64575			−0.368001
$21$	7.00000			1.52753
$22$	−1.00000			−0.213201
$23$	−0.822876	−	1.42526i	−0.171581	−	0.297188i	0.767391	−	0.641179i	$-0.221554\pi$
$23$	−0.822876	−	1.42526i	−0.171581	−	0.297188i	−0.938973	+	0.343991i	$0.888221\pi$
$24$	1.32288	−	2.29129i	0.270031	−	0.467707i
$25$	1.14575	−	1.98450i	0.229150	−	0.396900i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	2.64575			0.509175
$28$	2.64575			0.500000
$29$	6.29150			1.16830			0.584151	−	0.811645i	$-0.301427\pi$
$29$	6.29150			1.16830			0.584151	+	0.811645i	$0.301427\pi$
$30$	−2.17712	−	3.77089i	−0.397487	−	0.688467i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.32288	−	2.29129i	−0.230283	−	0.398862i
$34$	−6.00000			−1.02899
$35$	2.17712	−	3.77089i	0.368001	−	0.637397i
$36$	4.00000			0.666667
$37$	−1.82288	−	3.15731i	−0.299679	−	0.519059i	0.676384	−	0.736550i	$-0.263546\pi$
$37$	−1.82288	−	3.15731i	−0.299679	−	0.519059i	−0.976062	+	0.217491i	$0.930213\pi$
$38$	−2.82288	+	4.88936i	−0.457931	+	0.793160i
$39$	−6.61438	+	11.4564i	−1.05915	+	1.83450i
$40$	−0.822876	−	1.42526i	−0.130108	−	0.225354i
$41$	10.9373			1.70811			0.854056	−	0.520181i	$-0.174136\pi$
$41$	10.9373			1.70811			0.854056	+	0.520181i	$0.174136\pi$
$42$	3.50000	+	6.06218i	0.540062	+	0.935414i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	3.29150	−	5.70105i	0.490668	−	0.849862i
$46$	0.822876	−	1.42526i	0.121326	−	0.210143i
$47$	−1.35425	−	2.34563i	−0.197537	−	0.342145i	0.750192	−	0.661220i	$-0.229961\pi$
$47$	−1.35425	−	2.34563i	−0.197537	−	0.342145i	−0.947729	+	0.319075i	$0.896628\pi$
$48$	2.64575			0.381881
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	2.29150			0.324067
$51$	−7.93725	−	13.7477i	−1.11144	−	1.92507i
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$	−0.822876	+	1.42526i	−0.113031	+	0.195775i	−0.916991	−	0.398908i	$-0.869389\pi$
$53$	−0.822876	+	1.42526i	−0.113031	+	0.195775i	0.803960	+	0.594683i	$0.202722\pi$
$54$	1.32288	+	2.29129i	0.180021	+	0.311805i
$55$	−1.64575			−0.221913
$56$	1.32288	+	2.29129i	0.176777	+	0.306186i
$57$	−14.9373			−1.97849
$58$	3.14575	+	5.44860i	0.413057	+	0.715436i
$59$	−2.32288	+	4.02334i	−0.302413	+	0.523794i	−0.976682	−	0.214692i	$-0.931125\pi$
$59$	−2.32288	+	4.02334i	−0.302413	+	0.523794i	0.674269	+	0.738486i	$0.264459\pi$
$60$	2.17712	−	3.77089i	0.281066	−	0.486820i
$61$	−7.14575	−	12.3768i	−0.914920	−	1.58469i	−0.807019	−	0.590526i	$-0.798920\pi$
$61$	−7.14575	−	12.3768i	−0.914920	−	1.58469i	−0.107901	−	0.994162i	$-0.534413\pi$
$62$	4.00000			0.508001
$63$	−5.29150	+	9.16515i	−0.666667	+	1.15470i
$64$	1.00000			0.125000
$65$	4.11438	+	7.12631i	0.510326	+	0.883910i
$66$	1.32288	−	2.29129i	0.162835	−	0.282038i
$67$	5.96863	−	10.3380i	0.729184	−	1.26298i	−0.228045	−	0.973651i	$-0.573233\pi$
$67$	5.96863	−	10.3380i	0.729184	−	1.26298i	0.957229	−	0.289333i	$-0.0934334\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	4.35425			0.524190
$70$	4.35425			0.520432
$71$	4.35425			0.516754			0.258377	−	0.966044i	$-0.416812\pi$
$71$	4.35425			0.516754			0.258377	+	0.966044i	$0.416812\pi$
$72$	2.00000	+	3.46410i	0.235702	+	0.408248i
$73$	−0.177124	+	0.306788i	−0.0207308	+	0.0359069i	−0.876205	−	0.481939i	$-0.839933\pi$
$73$	−0.177124	+	0.306788i	−0.0207308	+	0.0359069i	0.855474	+	0.517846i	$0.173266\pi$
$74$	1.82288	−	3.15731i	0.211905	−	0.367030i
$75$	3.03137	+	5.25049i	0.350033	+	0.606275i
$76$	−5.64575			−0.647612
$77$	2.64575			0.301511
$78$	−13.2288			−1.49786
$79$	1.32288	+	2.29129i	0.148835	+	0.257790i	0.930797	−	0.365536i	$-0.119114\pi$
$79$	1.32288	+	2.29129i	0.148835	+	0.257790i	−0.781962	+	0.623326i	$0.785781\pi$
$80$	0.822876	−	1.42526i	0.0920003	−	0.159349i
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	5.46863	+	9.47194i	0.603909	+	1.04600i
$83$	2.70850			0.297296			0.148648	−	0.988890i	$-0.452508\pi$
$83$	2.70850			0.297296			0.148648	+	0.988890i	$0.452508\pi$
$84$	−3.50000	+	6.06218i	−0.381881	+	0.661438i
$85$	−9.87451			−1.07104
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	−8.32288	+	14.4156i	−0.892306	+	1.54552i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−3.29150	−	5.70105i	−0.348899	−	0.604310i	0.637156	−	0.770735i	$-0.280111\pi$
$89$	−3.29150	−	5.70105i	−0.348899	−	0.604310i	−0.986054	+	0.166425i	$0.946778\pi$
$90$	6.58301			0.693910
$91$	−6.61438	−	11.4564i	−0.693375	−	1.20096i
$92$	1.64575			0.171581
$93$	5.29150	+	9.16515i	0.548703	+	0.950382i
$94$	1.35425	−	2.34563i	0.139680	−	0.241933i
$95$	−4.64575	+	8.04668i	−0.476644	+	0.825572i
$96$	1.32288	+	2.29129i	0.135015	+	0.233854i
$97$	−16.2915			−1.65415			−0.827076	−	0.562090i	$-0.809997\pi$
$97$	−16.2915			−1.65415			−0.827076	+	0.562090i	$0.809997\pi$
$98$	−7.00000			−0.707107
$99$	4.00000			0.402015
$100$	1.14575	+	1.98450i	0.114575	+	0.198450i
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$	7.93725	−	13.7477i	0.785905	−	1.36123i
$103$	1.46863	+	2.54374i	0.144708	+	0.250642i	0.929264	−	0.369416i	$-0.120442\pi$
$103$	1.46863	+	2.54374i	0.144708	+	0.250642i	−0.784556	+	0.620058i	$0.787109\pi$
$104$	−5.00000			−0.490290
$105$	5.76013	+	9.97684i	0.562131	+	0.973640i
$106$	−1.64575			−0.159849
$107$	5.46863	+	9.47194i	0.528672	+	0.915687i	0.999441	+	0.0334304i	$0.0106432\pi$
$107$	5.46863	+	9.47194i	0.528672	+	0.915687i	−0.470769	+	0.882257i	$0.656023\pi$
$108$	−1.32288	+	2.29129i	−0.127294	+	0.220479i
$109$	5.29150	−	9.16515i	0.506834	−	0.877862i	−0.493135	−	0.869953i	$-0.664149\pi$
$109$	5.29150	−	9.16515i	0.506834	−	0.877862i	0.999969	−	0.00790932i	$-0.00251764\pi$
$110$	−0.822876	−	1.42526i	−0.0784581	−	0.135893i
$111$	9.64575			0.915534
$112$	−1.32288	+	2.29129i	−0.125000	+	0.216506i
$113$	−18.2915			−1.72072			−0.860360	−	0.509687i	$-0.829761\pi$
$113$	−18.2915			−1.72072			−0.860360	+	0.509687i	$0.829761\pi$
$114$	−7.46863	−	12.9360i	−0.699501	−	1.21157i
$115$	1.35425	−	2.34563i	0.126284	−	0.218731i
$116$	−3.14575	+	5.44860i	−0.292076	+	0.505890i
$117$	−10.0000	−	17.3205i	−0.924500	−	1.60128i
$118$	−4.64575			−0.427676
$119$	15.8745			1.45521
$120$	4.35425			0.397487
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	7.14575	−	12.3768i	0.646946	−	1.12054i
$123$	−14.4686	+	25.0604i	−1.30459	+	2.25962i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	12.0000			1.07331
$126$	−10.5830			−0.942809
$127$	15.9373			1.41420			0.707101	−	0.707112i	$-0.250002\pi$
$127$	15.9373			1.41420			0.707101	+	0.707112i	$0.250002\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.29150	−	9.16515i	0.465891	−	0.806947i
$130$	−4.11438	+	7.12631i	−0.360855	+	0.625019i
$131$	−5.17712	−	8.96704i	−0.452327	−	0.783454i	0.546203	−	0.837653i	$-0.316073\pi$
$131$	−5.17712	−	8.96704i	−0.452327	−	0.783454i	−0.998530	+	0.0541989i	$0.982739\pi$
$132$	2.64575			0.230283
$133$	7.46863	−	12.9360i	0.647612	−	1.12170i
$134$	11.9373			1.03122
$135$	2.17712	+	3.77089i	0.187377	+	0.324547i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	6.43725	−	11.1497i	0.549972	−	0.952579i	−0.448304	−	0.893881i	$-0.647972\pi$
$137$	6.43725	−	11.1497i	0.549972	−	0.952579i	0.998276	−	0.0586978i	$-0.0186948\pi$
$138$	2.17712	+	3.77089i	0.185329	+	0.320999i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	2.17712	+	3.77089i	0.184001	+	0.318698i
$141$	7.16601			0.603487
$142$	2.17712	+	3.77089i	0.182700	+	0.316446i
$143$	−2.50000	+	4.33013i	−0.209061	+	0.362103i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	5.17712	+	8.96704i	0.429937	+	0.744672i
$146$	−0.354249			−0.0293178
$147$	−9.26013	−	16.0390i	−0.763763	−	1.32288i
$148$	3.64575			0.299679
$149$	7.64575	+	13.2428i	0.626364	+	1.08489i	0.988275	+	0.152682i	$0.0487911\pi$
$149$	7.64575	+	13.2428i	0.626364	+	1.08489i	−0.361911	+	0.932213i	$0.617876\pi$
$150$	−3.03137	+	5.25049i	−0.247511	+	0.428701i
$151$	4.32288	−	7.48744i	0.351791	−	0.609319i	−0.634773	−	0.772699i	$-0.718906\pi$
$151$	4.32288	−	7.48744i	0.351791	−	0.609319i	0.986563	+	0.163380i	$0.0522396\pi$
$152$	−2.82288	−	4.88936i	−0.228965	−	0.396580i
$153$	24.0000			1.94029
$154$	1.32288	+	2.29129i	0.106600	+	0.184637i
$155$	6.58301			0.528760
$156$	−6.61438	−	11.4564i	−0.529574	−	0.917249i
$157$	−10.5830	+	18.3303i	−0.844616	+	1.46292i	0.0413387	+	0.999145i	$0.486838\pi$
$157$	−10.5830	+	18.3303i	−0.844616	+	1.46292i	−0.885954	+	0.463772i	$0.846496\pi$
$158$	−1.32288	+	2.29129i	−0.105242	+	0.182285i
$159$	−2.17712	−	3.77089i	−0.172657	−	0.299051i
$160$	1.64575			0.130108
$161$	−2.17712	+	3.77089i	−0.171581	+	0.297188i
$162$	5.00000			0.392837
$163$	−0.322876	−	0.559237i	−0.0252896	−	0.0438028i	0.853104	−	0.521741i	$-0.174717\pi$
$163$	−0.322876	−	0.559237i	−0.0252896	−	0.0438028i	−0.878393	+	0.477939i	$0.841384\pi$
$164$	−5.46863	+	9.47194i	−0.427028	+	0.739634i
$165$	2.17712	−	3.77089i	0.169489	−	0.293563i
$166$	1.35425	+	2.34563i	0.105110	+	0.182056i
$167$	−11.2288			−0.868907			−0.434454	−	0.900694i	$-0.643059\pi$
$167$	−11.2288			−0.868907			−0.434454	+	0.900694i	$0.643059\pi$
$168$	−7.00000			−0.540062
$169$	12.0000			0.923077
$170$	−4.93725	−	8.55157i	−0.378670	−	0.655876i
$171$	11.2915	−	19.5575i	0.863483	−	1.49560i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	0.145751	+	0.252449i	0.0110813	+	0.0191933i	0.871513	−	0.490373i	$-0.163139\pi$
$173$	0.145751	+	0.252449i	0.0110813	+	0.0191933i	−0.860432	+	0.509566i	$0.829806\pi$
$174$	−16.6458			−1.26191
$175$	−6.06275			−0.458301
$176$	1.00000			0.0753778
$177$	−6.14575	−	10.6448i	−0.461943	−	0.800109i
$178$	3.29150	−	5.70105i	0.246709	−	0.427312i
$179$	9.96863	−	17.2662i	0.745090	−	1.29053i	−0.205062	−	0.978749i	$-0.565740\pi$
$179$	9.96863	−	17.2662i	0.745090	−	1.29053i	0.950153	−	0.311785i	$-0.100927\pi$
$180$	3.29150	+	5.70105i	0.245334	+	0.424931i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	6.61438	−	11.4564i	0.490290	−	0.849208i
$183$	37.8118			2.79513
$184$	0.822876	+	1.42526i	0.0606632	+	0.105072i
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$	−5.29150	+	9.16515i	−0.387992	+	0.672022i
$187$	−3.00000	−	5.19615i	−0.219382	−	0.379980i
$188$	2.70850			0.197537
$189$	−3.50000	−	6.06218i	−0.254588	−	0.440959i
$190$	−9.29150			−0.674076
$191$	1.35425	+	2.34563i	0.0979900	+	0.169724i	0.910853	−	0.412732i	$-0.135425\pi$
$191$	1.35425	+	2.34563i	0.0979900	+	0.169724i	−0.812863	+	0.582456i	$0.802092\pi$
$192$	−1.32288	+	2.29129i	−0.0954703	+	0.165359i
$193$	−12.7601	+	22.1012i	−0.918494	+	1.59088i	−0.116791	+	0.993157i	$0.537261\pi$
$193$	−12.7601	+	22.1012i	−0.918494	+	1.59088i	−0.801703	+	0.597722i	$0.796073\pi$
$194$	−8.14575	−	14.1089i	−0.584831	−	1.01296i
$195$	−21.7712			−1.55907
$196$	−3.50000	−	6.06218i	−0.250000	−	0.433013i
$197$	−12.8745			−0.917271			−0.458635	−	0.888625i	$-0.651662\pi$
$197$	−12.8745			−0.917271			−0.458635	+	0.888625i	$0.651662\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	−2.11438	+	3.66221i	−0.149884	+	0.259607i	−0.931185	−	0.364548i	$-0.881223\pi$
$199$	−2.11438	+	3.66221i	−0.149884	+	0.259607i	0.781300	+	0.624155i	$0.214557\pi$
$200$	−1.14575	+	1.98450i	−0.0810169	+	0.140325i
$201$	15.7915	+	27.3517i	1.11385	+	1.92924i
$202$	−3.00000			−0.211079
$203$	−8.32288	−	14.4156i	−0.584151	−	1.01178i
$204$	15.8745			1.11144
$205$	9.00000	+	15.5885i	0.628587	+	1.08875i
$206$	−1.46863	+	2.54374i	−0.102324	+	0.177231i
$207$	−3.29150	+	5.70105i	−0.228775	+	0.396250i
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$	−5.64575			−0.390525
$210$	−5.76013	+	9.97684i	−0.397487	+	0.688467i
$211$	0.937254			0.0645232			0.0322616	−	0.999479i	$-0.489729\pi$
$211$	0.937254			0.0645232			0.0322616	+	0.999479i	$0.489729\pi$
$212$	−0.822876	−	1.42526i	−0.0565153	−	0.0978874i
$213$	−5.76013	+	9.97684i	−0.394678	+	0.683602i
$214$	−5.46863	+	9.47194i	−0.373828	+	0.647488i
$215$	−3.29150	−	5.70105i	−0.224479	−	0.388808i
$216$	−2.64575			−0.180021
$217$	−10.5830			−0.718421
$218$	10.5830			0.716772
$219$	−0.468627	−	0.811686i	−0.0316669	−	0.0548486i
$220$	0.822876	−	1.42526i	0.0554783	−	0.0960912i
$221$	−15.0000	+	25.9808i	−1.00901	+	1.74766i
$222$	4.82288	+	8.35347i	0.323690	+	0.560648i
$223$	−17.6458			−1.18165			−0.590823	−	0.806801i	$-0.701197\pi$
$223$	−17.6458			−1.18165			−0.590823	+	0.806801i	$0.701197\pi$
$224$	−2.64575			−0.176777
$225$	−9.16601			−0.611067
$226$	−9.14575	−	15.8409i	−0.608366	−	1.05372i
$227$	1.35425	−	2.34563i	0.0898846	−	0.155685i	−0.817578	−	0.575818i	$-0.804683\pi$
$227$	1.35425	−	2.34563i	0.0898846	−	0.155685i	0.907462	+	0.420134i	$0.138017\pi$
$228$	7.46863	−	12.9360i	0.494622	−	0.856710i
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	0.999442	+	0.0334101i	$0.0106368\pi$
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$230$	2.70850			0.178593
$231$	−3.50000	+	6.06218i	−0.230283	+	0.398862i
$232$	−6.29150			−0.413057
$233$	−0.531373	−	0.920365i	−0.0348114	−	0.0602951i	0.848095	−	0.529845i	$-0.177750\pi$
$233$	−0.531373	−	0.920365i	−0.0348114	−	0.0602951i	−0.882906	+	0.469549i	$0.844416\pi$
$234$	10.0000	−	17.3205i	0.653720	−	1.13228i
$235$	2.22876	−	3.86032i	0.145388	−	0.251819i
$236$	−2.32288	−	4.02334i	−0.151206	−	0.261897i
$237$	−7.00000			−0.454699
$238$	7.93725	+	13.7477i	0.514496	+	0.891133i
$239$	−17.2288			−1.11444			−0.557218	−	0.830366i	$-0.688131\pi$
$239$	−17.2288			−1.11444			−0.557218	+	0.830366i	$0.688131\pi$
$240$	2.17712	+	3.77089i	0.140533	+	0.243410i
$241$	12.4059	−	21.4876i	0.799133	−	1.38414i	−0.121048	−	0.992647i	$-0.538626\pi$
$241$	12.4059	−	21.4876i	0.799133	−	1.38414i	0.920181	−	0.391492i	$-0.128041\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	10.5830	+	18.3303i	0.678900	+	1.17589i
$244$	14.2915			0.914920
$245$	−11.5203			−0.736002
$246$	−28.9373			−1.84497
$247$	14.1144	+	24.4468i	0.898076	+	1.55551i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	−3.58301	+	6.20595i	−0.227064	+	0.393286i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	−3.29150			−0.207758			−0.103879	−	0.994590i	$-0.533125\pi$
$251$	−3.29150			−0.207758			−0.103879	+	0.994590i	$0.533125\pi$
$252$	−5.29150	−	9.16515i	−0.333333	−	0.577350i
$253$	1.64575			0.103467
$254$	7.96863	+	13.8021i	0.499996	+	0.866019i
$255$	13.0627	−	22.6253i	0.818021	−	1.41685i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.7915	+	18.6914i	0.673155	+	1.16594i	0.977004	+	0.213219i	$0.0683948\pi$
$257$	10.7915	+	18.6914i	0.673155	+	1.16594i	−0.303849	+	0.952720i	$0.598272\pi$
$258$	10.5830			0.658869
$259$	−4.82288	+	8.35347i	−0.299679	+	0.519059i
$260$	−8.22876			−0.510326
$261$	−12.5830	−	21.7944i	−0.778868	−	1.34904i
$262$	5.17712	−	8.96704i	0.319844	−	0.553986i
$263$	−9.96863	+	17.2662i	−0.614692	+	1.06468i	0.375747	+	0.926722i	$0.377386\pi$
$263$	−9.96863	+	17.2662i	−0.614692	+	1.06468i	−0.990438	+	0.137955i	$0.955947\pi$
$264$	1.32288	+	2.29129i	0.0814174	+	0.141019i
$265$	−2.70850			−0.166382
$266$	14.9373			0.915862
$267$	17.4170			1.06590
$268$	5.96863	+	10.3380i	0.364592	+	0.631492i
$269$	−2.70850	+	4.69126i	−0.165140	+	0.286031i	−0.936705	−	0.350120i	$-0.886141\pi$
$269$	−2.70850	+	4.69126i	−0.165140	+	0.286031i	0.771565	+	0.636151i	$0.219474\pi$
$270$	−2.17712	+	3.77089i	−0.132496	+	0.229489i
$271$	1.03137	+	1.78639i	0.0626514	+	0.108515i	0.895650	−	0.444760i	$-0.146711\pi$
$271$	1.03137	+	1.78639i	0.0626514	+	0.108515i	−0.832998	+	0.553275i	$0.813378\pi$
$272$	6.00000			0.363803
$273$	35.0000			2.11830
$274$	12.8745			0.777777
$275$	1.14575	+	1.98450i	0.0690914	+	0.119670i
$276$	−2.17712	+	3.77089i	−0.131047	+	0.226981i
$277$	11.1458	−	19.3050i	0.669683	−	1.15993i	−0.308309	−	0.951286i	$-0.599763\pi$
$277$	11.1458	−	19.3050i	0.669683	−	1.15993i	0.977993	−	0.208639i	$-0.0669035\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$	−16.0000			−0.957895
$280$	−2.17712	+	3.77089i	−0.130108	+	0.225354i
$281$	−22.9373			−1.36832			−0.684161	−	0.729331i	$-0.739831\pi$
$281$	−22.9373			−1.36832			−0.684161	+	0.729331i	$0.739831\pi$
$282$	3.58301	+	6.20595i	0.213365	+	0.369559i
$283$	1.17712	−	2.03884i	0.0699728	−	0.121196i	−0.828916	−	0.559373i	$-0.811042\pi$
$283$	1.17712	−	2.03884i	0.0699728	−	0.121196i	0.898889	+	0.438176i	$0.144375\pi$
$284$	−2.17712	+	3.77089i	−0.129189	+	0.223761i
$285$	−12.2915	−	21.2895i	−0.728086	−	1.26108i
$286$	−5.00000			−0.295656
$287$	−14.4686	−	25.0604i	−0.854056	−	1.47927i
$288$	−4.00000			−0.235702
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−5.17712	+	8.96704i	−0.304011	+	0.526563i
$291$	21.5516	−	37.3285i	1.26338	−	2.18824i
$292$	−0.177124	−	0.306788i	−0.0103654	−	0.0179534i
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$	9.26013	−	16.0390i	0.540062	−	0.935414i
$295$	−7.64575			−0.445153
$296$	1.82288	+	3.15731i	0.105952	+	0.183515i
$297$	−1.32288	+	2.29129i	−0.0767610	+	0.132954i
$298$	−7.64575	+	13.2428i	−0.442906	+	0.767137i
$299$	−4.11438	−	7.12631i	−0.237941	−	0.412125i
$300$	−6.06275			−0.350033
$301$	5.29150	+	9.16515i	0.304997	+	0.528271i
$302$	8.64575			0.497507
$303$	−3.96863	−	6.87386i	−0.227992	−	0.394893i
$304$	2.82288	−	4.88936i	0.161903	−	0.280424i
$305$	11.7601	−	20.3691i	0.673383	−	1.16633i
$306$	12.0000	+	20.7846i	0.685994	+	1.18818i
$307$	22.2288			1.26866			0.634331	−	0.773062i	$-0.281276\pi$
$307$	22.2288			1.26866			0.634331	+	0.773062i	$0.281276\pi$
$308$	−1.32288	+	2.29129i	−0.0753778	+	0.130558i
$309$	−7.77124			−0.442091
$310$	3.29150	+	5.70105i	0.186945	+	0.323798i
$311$	−0.531373	+	0.920365i	−0.0301314	+	0.0521891i	−0.880698	−	0.473678i	$-0.842926\pi$
$311$	−0.531373	+	0.920365i	−0.0301314	+	0.0521891i	0.850566	+	0.525868i	$0.176259\pi$
$312$	6.61438	−	11.4564i	0.374465	−	0.648593i
$313$	−11.7915	−	20.4235i	−0.666495	−	1.15440i	−0.978878	−	0.204447i	$-0.934460\pi$
$313$	−11.7915	−	20.4235i	−0.666495	−	1.15440i	0.312382	−	0.949956i	$-0.398873\pi$
$314$	−21.1660			−1.19447
$315$	−17.4170			−0.981336
$316$	−2.64575			−0.148835
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	2.17712	−	3.77089i	0.122087	−	0.211461i
$319$	−3.14575	+	5.44860i	−0.176128	+	0.305063i
$320$	0.822876	+	1.42526i	0.0460001	+	0.0796746i
$321$	−28.9373			−1.61512
$322$	−4.35425			−0.242653
$323$	−33.8745			−1.88483
$324$	2.50000	+	4.33013i	0.138889	+	0.240563i
$325$	5.72876	−	9.92250i	0.317774	−	0.550401i
$326$	0.322876	−	0.559237i	0.0178824	−	0.0309733i
$327$	14.0000	+	24.2487i	0.774202	+	1.34096i
$328$	−10.9373			−0.603909
$329$	−3.58301	+	6.20595i	−0.197537	+	0.342145i
$330$	4.35425			0.239694
$331$	10.3229	+	17.8797i	0.567397	+	0.982760i	0.996822	+	0.0796575i	$0.0253827\pi$
$331$	10.3229	+	17.8797i	0.567397	+	0.982760i	−0.429426	+	0.903102i	$0.641284\pi$
$332$	−1.35425	+	2.34563i	−0.0743241	+	0.128733i
$333$	−7.29150	+	12.6293i	−0.399572	+	0.692079i
$334$	−5.61438	−	9.72439i	−0.307205	−	0.532095i
$335$	19.6458			1.07336
$336$	−3.50000	−	6.06218i	−0.190941	−	0.330719i
$337$	9.06275			0.493679			0.246840	−	0.969056i	$-0.420608\pi$
$337$	9.06275			0.493679			0.246840	+	0.969056i	$0.420608\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	24.1974	−	41.9111i	1.31422	−	2.27630i
$340$	4.93725	−	8.55157i	0.267760	−	0.463774i
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$	22.5830			1.22115
$343$	18.5203			1.00000
$344$	4.00000			0.215666
$345$	3.58301	+	6.20595i	0.192903	+	0.334117i
$346$	−0.145751	+	0.252449i	−0.00783564	+	0.0135717i
$347$	10.4059	−	18.0235i	0.558617	−	0.967553i	−0.438995	−	0.898489i	$-0.644666\pi$
$347$	10.4059	−	18.0235i	0.558617	−	0.967553i	0.997612	−	0.0690636i	$-0.0220011\pi$
$348$	−8.32288	−	14.4156i	−0.446153	−	0.772760i
$349$	−1.87451			−0.100340			−0.0501701	−	0.998741i	$-0.515976\pi$
$349$	−1.87451			−0.100340			−0.0501701	+	0.998741i	$0.515976\pi$
$350$	−3.03137	−	5.25049i	−0.162034	−	0.280651i
$351$	13.2288			0.706099
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−3.58301	+	6.20595i	−0.190704	+	0.330309i	−0.945484	−	0.325669i	$-0.894410\pi$
$353$	−3.58301	+	6.20595i	−0.190704	+	0.330309i	0.754780	+	0.655978i	$0.227744\pi$
$354$	6.14575	−	10.6448i	0.326643	−	0.565762i
$355$	3.58301	+	6.20595i	0.190166	+	0.329377i
$356$	6.58301			0.348899
$357$	−21.0000	+	36.3731i	−1.11144	+	1.92507i
$358$	19.9373			1.05372
$359$	12.9686	+	22.4623i	0.684458	+	1.18552i	0.973607	+	0.228232i	$0.0732944\pi$
$359$	12.9686	+	22.4623i	0.684458	+	1.18552i	−0.289149	+	0.957284i	$0.593372\pi$
$360$	−3.29150	+	5.70105i	−0.173477	+	0.300472i
$361$	−6.43725	+	11.1497i	−0.338803	+	0.586824i
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$	2.64575			0.138866
$364$	13.2288			0.693375
$365$	−0.583005			−0.0305159
$366$	18.9059	+	32.7459i	0.988226	+	1.71166i
$367$	18.1144	−	31.3750i	0.945563	−	1.63776i	0.190943	−	0.981601i	$-0.438846\pi$
$367$	18.1144	−	31.3750i	0.945563	−	1.63776i	0.754620	−	0.656162i	$-0.227821\pi$
$368$	−0.822876	+	1.42526i	−0.0428954	+	0.0742969i
$369$	−21.8745	−	37.8878i	−1.13874	−	1.97236i
$370$	6.00000			0.311925
$371$	4.35425			0.226061
$372$	−10.5830			−0.548703
$373$	−10.4373	−	18.0779i	−0.540421	−	0.936036i	−0.998880	−	0.0473204i	$-0.984932\pi$
$373$	−10.4373	−	18.0779i	−0.540421	−	0.936036i	0.458459	−	0.888715i	$-0.348402\pi$
$374$	3.00000	−	5.19615i	0.155126	−	0.268687i
$375$	−15.8745	+	27.4955i	−0.819756	+	1.41986i
$376$	1.35425	+	2.34563i	0.0698400	+	0.120967i
$377$	31.4575			1.62014
$378$	3.50000	−	6.06218i	0.180021	−	0.311805i
$379$	6.06275			0.311422			0.155711	−	0.987803i	$-0.450233\pi$
$379$	6.06275			0.311422			0.155711	+	0.987803i	$0.450233\pi$
$380$	−4.64575	−	8.04668i	−0.238322	−	0.412786i
$381$	−21.0830	+	36.5168i	−1.08012	+	1.87081i
$382$	−1.35425	+	2.34563i	−0.0692894	+	0.120013i
$383$	−12.0516	−	20.8740i	−0.615810	−	1.06661i	−0.990242	−	0.139359i	$-0.955496\pi$
$383$	−12.0516	−	20.8740i	−0.615810	−	1.06661i	0.374432	−	0.927254i	$-0.377838\pi$
$384$	−2.64575			−0.135015
$385$	2.17712	+	3.77089i	0.110957	+	0.192182i
$386$	−25.5203			−1.29895
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	8.14575	−	14.1089i	0.413538	−	0.716269i
$389$	−13.4059	+	23.2197i	−0.679705	+	1.17728i	0.295364	+	0.955385i	$0.404559\pi$
$389$	−13.4059	+	23.2197i	−0.679705	+	1.17728i	−0.975070	+	0.221899i	$0.928774\pi$
$390$	−10.8856	−	18.8544i	−0.551215	−	0.954732i
$391$	9.87451			0.499375
$392$	3.50000	−	6.06218i	0.176777	−	0.306186i
$393$	27.3948			1.38188
$394$	−6.43725	−	11.1497i	−0.324304	−	0.561711i
$395$	−2.17712	+	3.77089i	−0.109543	+	0.189734i
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	5.58301	+	9.67005i	0.280203	+	0.485326i	0.971435	−	0.237307i	$-0.0762649\pi$
$397$	5.58301	+	9.67005i	0.280203	+	0.485326i	−0.691232	+	0.722633i	$0.742932\pi$
$398$	−4.22876			−0.211968
$399$	19.7601	+	34.2255i	0.989244	+	1.71342i
$400$	−2.29150			−0.114575
$401$	−10.7915	−	18.6914i	−0.538902	−	0.933406i	−0.998963	−	0.0455185i	$-0.985506\pi$
$401$	−10.7915	−	18.6914i	−0.538902	−	0.933406i	0.460062	−	0.887887i	$-0.347827\pi$
$402$	−15.7915	+	27.3517i	−0.787609	+	1.36418i
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$	8.22876			0.408890
$406$	8.32288	−	14.4156i	0.413057	−	0.715436i
$407$	3.64575			0.180713
$408$	7.93725	+	13.7477i	0.392953	+	0.680614i
$409$	−1.53137	+	2.65242i	−0.0757215	+	0.131154i	−0.901400	−	0.432988i	$-0.857459\pi$
$409$	−1.53137	+	2.65242i	−0.0757215	+	0.131154i	0.825678	+	0.564141i	$0.190793\pi$
$410$	−9.00000	+	15.5885i	−0.444478	+	0.769859i
$411$	17.0314	+	29.4992i	0.840096	+	1.45509i
$412$	−2.93725			−0.144708
$413$	12.2915			0.604825
$414$	−6.58301			−0.323537
$415$	2.22876	+	3.86032i	0.109405	+	0.189496i
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$	5.29150	−	9.16515i	0.259126	−	0.448819i
$418$	−2.82288	−	4.88936i	−0.138071	−	0.239147i
$419$	−9.87451			−0.482401			−0.241201	−	0.970475i	$-0.577541\pi$
$419$	−9.87451			−0.482401			−0.241201	+	0.970475i	$0.577541\pi$
$420$	−11.5203			−0.562131
$421$	9.16601			0.446724			0.223362	−	0.974736i	$-0.428297\pi$
$421$	9.16601			0.446724			0.223362	+	0.974736i	$0.428297\pi$
$422$	0.468627	+	0.811686i	0.0228124	+	0.0395122i
$423$	−5.41699	+	9.38251i	−0.263383	+	0.456193i
$424$	0.822876	−	1.42526i	0.0399624	−	0.0692169i
$425$	6.87451	+	11.9070i	0.333463	+	0.577574i
$426$	−11.5203			−0.558158
$427$	−18.9059	+	32.7459i	−0.914920	+	1.58469i
$428$	−10.9373			−0.528672
$429$	−6.61438	−	11.4564i	−0.319345	−	0.553122i
$430$	3.29150	−	5.70105i	0.158730	−	0.274929i
$431$	−14.6144	+	25.3128i	−0.703950	+	1.21928i	0.263119	+	0.964763i	$0.415249\pi$
$431$	−14.6144	+	25.3128i	−0.703950	+	1.21928i	−0.967069	+	0.254514i	$0.918085\pi$
$432$	−1.32288	−	2.29129i	−0.0636469	−	0.110240i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	−5.29150	−	9.16515i	−0.254000	−	0.439941i
$435$	−27.3948			−1.31348
$436$	5.29150	+	9.16515i	0.253417	+	0.438931i
$437$	4.64575	−	8.04668i	0.222236	−	0.384925i
$438$	0.468627	−	0.811686i	0.0223919	−	0.0387838i
$439$	−1.96863	−	3.40976i	−0.0939574	−	0.162739i	0.815216	−	0.579158i	$-0.196618\pi$
$439$	−1.96863	−	3.40976i	−0.0939574	−	0.162739i	−0.909173	+	0.416419i	$0.863285\pi$
$440$	1.64575			0.0784581
$441$	28.0000			1.33333
$442$	−30.0000			−1.42695
$443$	−17.2288	−	29.8411i	−0.818563	−	1.41779i	−0.906741	−	0.421688i	$-0.861438\pi$
$443$	−17.2288	−	29.8411i	−0.818563	−	1.41779i	0.0881781	−	0.996105i	$-0.471896\pi$
$444$	−4.82288	+	8.35347i	−0.228884	+	0.396438i
$445$	5.41699	−	9.38251i	0.256790	−	0.444774i
$446$	−8.82288	−	15.2817i	−0.417775	−	0.723608i
$447$	−40.4575			−1.91357
$448$	−1.32288	−	2.29129i	−0.0625000	−	0.108253i
$449$	−21.8745			−1.03232			−0.516161	−	0.856492i	$-0.672639\pi$
$449$	−21.8745			−1.03232			−0.516161	+	0.856492i	$0.672639\pi$
$450$	−4.58301	−	7.93800i	−0.216045	−	0.374201i
$451$	−5.46863	+	9.47194i	−0.257508	+	0.446016i
$452$	9.14575	−	15.8409i	0.430180	−	0.745094i
$453$	11.4373	+	19.8099i	0.537369	+	0.930751i
$454$	2.70850			0.127116
$455$	10.8856	−	18.8544i	0.510326	−	0.883910i
$456$	14.9373			0.699501
$457$	−1.58301	−	2.74185i	−0.0740499	−	0.128258i	0.826623	−	0.562756i	$-0.190259\pi$
$457$	−1.58301	−	2.74185i	−0.0740499	−	0.128258i	−0.900673	+	0.434498i	$0.856926\pi$
$458$	−8.00000	+	13.8564i	−0.373815	+	0.647467i
$459$	−7.93725	+	13.7477i	−0.370479	+	0.641689i
$460$	1.35425	+	2.34563i	0.0631422	+	0.109365i
$461$	10.1660			0.473478			0.236739	−	0.971573i	$-0.423921\pi$
$461$	10.1660			0.473478			0.236739	+	0.971573i	$0.423921\pi$
$462$	−7.00000			−0.325669
$463$	30.4575			1.41548			0.707740	−	0.706473i	$-0.249715\pi$
$463$	30.4575			1.41548			0.707740	+	0.706473i	$0.249715\pi$
$464$	−3.14575	−	5.44860i	−0.146038	−	0.252945i
$465$	−8.70850	+	15.0836i	−0.403847	+	0.699483i
$466$	0.531373	−	0.920365i	0.0246154	−	0.0426351i
$467$	−10.6458	−	18.4390i	−0.492627	−	0.853254i	0.507337	−	0.861748i	$-0.330630\pi$
$467$	−10.6458	−	18.4390i	−0.492627	−	0.853254i	−0.999964	+	0.00849322i	$0.997296\pi$
$468$	20.0000			0.924500
$469$	−31.5830			−1.45837
$470$	4.45751			0.205610
$471$	−28.0000	−	48.4974i	−1.29017	−	2.23464i
$472$	2.32288	−	4.02334i	0.106919	−	0.185189i
$473$	2.00000	−	3.46410i	0.0919601	−	0.159280i
$474$	−3.50000	−	6.06218i	−0.160760	−	0.278445i
$475$	12.9373			0.593602
$476$	−7.93725	+	13.7477i	−0.363803	+	0.630126i
$477$	6.58301			0.301415
$478$	−8.61438	−	14.9205i	−0.394012	−	0.682450i
$479$	5.03137	−	8.71459i	0.229889	−	0.398180i	−0.727886	−	0.685698i	$-0.759497\pi$
$479$	5.03137	−	8.71459i	0.229889	−	0.398180i	0.957775	+	0.287518i	$0.0928303\pi$
$480$	−2.17712	+	3.77089i	−0.0993717	+	0.172117i
$481$	−9.11438	−	15.7866i	−0.415580	−	0.719805i
$482$	24.8118			1.13014
$483$	−5.76013	−	9.97684i	−0.262095	−	0.453962i
$484$	1.00000			0.0454545
$485$	−13.4059	−	23.2197i	−0.608730	−	1.05435i
$486$	−10.5830	+	18.3303i	−0.480055	+	0.831479i
$487$	4.70850	−	8.15536i	0.213362	−	0.369554i	−0.739402	−	0.673264i	$-0.764892\pi$
$487$	4.70850	−	8.15536i	0.213362	−	0.369554i	0.952765	+	0.303709i	$0.0982252\pi$
$488$	7.14575	+	12.3768i	0.323473	+	0.560272i
$489$	1.70850			0.0772609
$490$	−5.76013	−	9.97684i	−0.260216	−	0.450708i
$491$	21.2915			0.960872			0.480436	−	0.877030i	$-0.340478\pi$
$491$	21.2915			0.960872			0.480436	+	0.877030i	$0.340478\pi$
$492$	−14.4686	−	25.0604i	−0.652296	−	1.12981i
$493$	−18.8745	+	32.6916i	−0.850065	+	1.47236i
$494$	−14.1144	+	24.4468i	−0.635036	+	1.09991i
$495$	3.29150	+	5.70105i	0.147942	+	0.256243i
$496$	−4.00000			−0.179605
$497$	−5.76013	−	9.97684i	−0.258377	−	0.447522i
$498$	−7.16601			−0.321117
$499$	6.93725	+	12.0157i	0.310554	+	0.537896i	0.978482	−	0.206330i	$-0.0661521\pi$
$499$	6.93725	+	12.0157i	0.310554	+	0.537896i	−0.667928	+	0.744226i	$0.732819\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$	14.8542	−	25.7283i	0.663639	−	1.14946i
$502$	−1.64575	−	2.85052i	−0.0734535	−	0.127225i
$503$	−4.06275			−0.181149			−0.0905744	−	0.995890i	$-0.528870\pi$
$503$	−4.06275			−0.181149			−0.0905744	+	0.995890i	$0.528870\pi$
$504$	5.29150	−	9.16515i	0.235702	−	0.408248i
$505$	−4.93725			−0.219705
$506$	0.822876	+	1.42526i	0.0365813	+	0.0633606i
$507$	−15.8745	+	27.4955i	−0.705012	+	1.22112i
$508$	−7.96863	+	13.8021i	−0.353551	+	0.612368i
$509$	0.291503	+	0.504897i	0.0129206	+	0.0223792i	0.872413	−	0.488769i	$-0.162554\pi$
$509$	0.291503	+	0.504897i	0.0129206	+	0.0223792i	−0.859493	+	0.511148i	$0.829220\pi$
$510$	26.1255			1.15686
$511$	0.937254			0.0414617
$512$	−1.00000			−0.0441942
$513$	7.46863	+	12.9360i	0.329748	+	0.571140i
$514$	−10.7915	+	18.6914i	−0.475993	+	0.824444i
$515$	−2.41699	+	4.18636i	−0.106506	+	0.184473i
$516$	5.29150	+	9.16515i	0.232945	+	0.403473i
$517$	2.70850			0.119120
$518$	−9.64575			−0.423810
$519$	−0.771243			−0.0338538
$520$	−4.11438	−	7.12631i	−0.180427	−	0.312509i
$521$	16.9373	−	29.3362i	0.742035	−	1.28524i	−0.209533	−	0.977802i	$-0.567194\pi$
$521$	16.9373	−	29.3362i	0.742035	−	1.28524i	0.951567	−	0.307440i	$-0.0994723\pi$
$522$	12.5830	−	21.7944i	0.550743	−	0.953915i
$523$	10.7601	+	18.6371i	0.470508	+	0.814943i	0.999431	−	0.0337264i	$-0.0107375\pi$
$523$	10.7601	+	18.6371i	0.470508	+	0.814943i	−0.528923	+	0.848670i	$0.677404\pi$
$524$	10.3542			0.452327
$525$	8.02026	−	13.8915i	0.350033	−	0.606275i
$526$	−19.9373			−0.869306
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	−1.32288	+	2.29129i	−0.0575708	+	0.0997155i
$529$	10.1458	−	17.5730i	0.441120	−	0.764042i
$530$	−1.35425	−	2.34563i	−0.0588248	−	0.101888i
$531$	18.5830			0.806434
$532$	7.46863	+	12.9360i	0.323806	+	0.560849i
$533$	54.6863			2.36873
$534$	8.70850	+	15.0836i	0.376854	+	0.652729i
$535$	−9.00000	+	15.5885i	−0.389104	+	0.673948i
$536$	−5.96863	+	10.3380i	−0.257805	+	0.446532i
$537$	26.3745	+	45.6820i	1.13814	+	1.97132i
$538$	−5.41699			−0.233543
$539$	−3.50000	−	6.06218i	−0.150756	−	0.261116i
$540$	−4.35425			−0.187377
$541$	−1.14575	−	1.98450i	−0.0492597	−	0.0853203i	0.840344	−	0.542053i	$-0.182353\pi$
$541$	−1.14575	−	1.98450i	−0.0492597	−	0.0853203i	−0.889604	+	0.456733i	$0.849020\pi$
$542$	−1.03137	+	1.78639i	−0.0443013	+	0.0767320i
$543$	13.2288	−	22.9129i	0.567700	−	0.983286i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	17.4170			0.746062
$546$	17.5000	+	30.3109i	0.748931	+	1.29719i
$547$	−9.52026			−0.407057			−0.203528	−	0.979069i	$-0.565241\pi$
$547$	−9.52026			−0.407057			−0.203528	+	0.979069i	$0.565241\pi$
$548$	6.43725	+	11.1497i	0.274986	+	0.476289i
$549$	−28.5830	+	49.5072i	−1.21989	+	2.11292i
$550$	−1.14575	+	1.98450i	−0.0488550	+	0.0846193i
$551$	17.7601	+	30.7614i	0.756607	+	1.31048i
$552$	−4.35425			−0.185329
$553$	3.50000	−	6.06218i	0.148835	−	0.257790i
$554$	22.2915			0.947075
$555$	7.93725	+	13.7477i	0.336918	+	0.583559i
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	15.8745	−	27.4955i	0.672624	−	1.16502i	−0.304533	−	0.952502i	$-0.598500\pi$
$557$	15.8745	−	27.4955i	0.672624	−	1.16502i	0.977157	−	0.212518i	$-0.0681664\pi$
$558$	−8.00000	−	13.8564i	−0.338667	−	0.586588i
$559$	−20.0000			−0.845910
$560$	−4.35425			−0.184001
$561$	15.8745			0.670222
$562$	−11.4686	−	19.8642i	−0.483775	−	0.837923i
$563$	−14.4686	+	25.0604i	−0.609780	+	1.05617i	0.381496	+	0.924370i	$0.375409\pi$
$563$	−14.4686	+	25.0604i	−0.609780	+	1.05617i	−0.991276	+	0.131800i	$0.957924\pi$
$564$	−3.58301	+	6.20595i	−0.150872	+	0.261318i
$565$	−15.0516	−	26.0702i	−0.633227	−	1.09678i
$566$	2.35425			0.0989565
$567$	−13.2288			−0.555556
$568$	−4.35425			−0.182700
$569$	−0.583005	−	1.00979i	−0.0244409	−	0.0423328i	0.853546	−	0.521017i	$-0.174447\pi$
$569$	−0.583005	−	1.00979i	−0.0244409	−	0.0423328i	−0.877987	+	0.478684i	$0.841114\pi$
$570$	12.2915	−	21.2895i	0.514834	−	0.891719i
$571$	14.5314	−	25.1691i	0.608119	−	1.05329i	−0.383431	−	0.923569i	$-0.625258\pi$
$571$	14.5314	−	25.1691i	0.608119	−	1.05329i	0.991550	−	0.129724i	$-0.0414090\pi$
$572$	−2.50000	−	4.33013i	−0.104530	−	0.181052i
$573$	−7.16601			−0.299364
$574$	14.4686	−	25.0604i	0.603909	−	1.04600i
$575$	−3.77124			−0.157272
$576$	−2.00000	−	3.46410i	−0.0833333	−	0.144338i
$577$	−13.7288	+	23.7789i	−0.571536	+	0.989929i	0.424873	+	0.905253i	$0.360319\pi$
$577$	−13.7288	+	23.7789i	−0.571536	+	0.989929i	−0.996409	+	0.0846757i	$0.973015\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	−33.7601	−	58.4743i	−1.40302	−	2.43011i
$580$	−10.3542			−0.429937
$581$	−3.58301	−	6.20595i	−0.148648	−	0.257466i
$582$	43.1033			1.78669
$583$	−0.822876	−	1.42526i	−0.0340800	−	0.0590283i
$584$	0.177124	−	0.306788i	0.00732946	−	0.0126950i
$585$	16.4575	−	28.5052i	0.680434	−	1.17855i
$586$	6.00000	+	10.3923i	0.247858	+	0.429302i
$587$	7.93725			0.327606			0.163803	−	0.986493i	$-0.447624\pi$
$587$	7.93725			0.327606			0.163803	+	0.986493i	$0.447624\pi$
$588$	18.5203			0.763763
$589$	22.5830			0.930517
$590$	−3.82288	−	6.62141i	−0.157385	−	0.272599i
$591$	17.0314	−	29.4992i	0.700577	−	1.21344i
$592$	−1.82288	+	3.15731i	−0.0749197	+	0.129765i
$593$	−3.53137	−	6.11652i	−0.145016	−	0.251175i	0.784363	−	0.620302i	$-0.212990\pi$
$593$	−3.53137	−	6.11652i	−0.145016	−	0.251175i	−0.929379	+	0.369127i	$0.879657\pi$
$594$	−2.64575			−0.108556
$595$	13.0627	+	22.6253i	0.535520	+	0.927549i
$596$	−15.2915			−0.626364
$597$	−5.59412	−	9.68930i	−0.228952	−	0.396557i
$598$	4.11438	−	7.12631i	0.168249	−	0.291417i
$599$	−21.8745	+	37.8878i	−0.893768	+	1.54805i	−0.0584464	+	0.998291i	$0.518615\pi$
$599$	−21.8745	+	37.8878i	−0.893768	+	1.54805i	−0.835322	+	0.549761i	$0.814719\pi$
$600$	−3.03137	−	5.25049i	−0.123755	−	0.214350i
$601$	−3.41699			−0.139382			−0.0696911	−	0.997569i	$-0.522201\pi$
$601$	−3.41699			−0.139382			−0.0696911	+	0.997569i	$0.522201\pi$
$602$	−5.29150	+	9.16515i	−0.215666	+	0.373544i
$603$	−47.7490			−1.94449
$604$	4.32288	+	7.48744i	0.175895	+	0.304660i
$605$	0.822876	−	1.42526i	0.0334547	−	0.0579452i
$606$	3.96863	−	6.87386i	0.161214	−	0.279232i
$607$	−5.35425	−	9.27383i	−0.217322	−	0.376413i	0.736666	−	0.676257i	$-0.236399\pi$
$607$	−5.35425	−	9.27383i	−0.217322	−	0.376413i	−0.953988	+	0.299843i	$0.903066\pi$
$608$	5.64575			0.228965
$609$	44.0405			1.78461
$610$	23.5203			0.952307
$611$	−6.77124	−	11.7281i	−0.273935	−	0.474470i
$612$	−12.0000	+	20.7846i	−0.485071	+	0.840168i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	11.1144	+	19.2507i	0.448540	+	0.776894i
$615$	−47.6235			−1.92037
$616$	−2.64575			−0.106600
$617$	−5.70850			−0.229815			−0.114908	−	0.993376i	$-0.536657\pi$
$617$	−5.70850			−0.229815			−0.114908	+	0.993376i	$0.536657\pi$
$618$	−3.88562	−	6.73009i	−0.156303	−	0.270724i
$619$	−6.70850	+	11.6195i	−0.269637	+	0.467025i	−0.968768	−	0.247968i	$-0.920237\pi$
$619$	−6.70850	+	11.6195i	−0.269637	+	0.467025i	0.699131	+	0.714994i	$0.253570\pi$
$620$	−3.29150	+	5.70105i	−0.132190	+	0.228960i
$621$	−2.17712	−	3.77089i	−0.0873650	−	0.151321i
$622$	−1.06275			−0.0426122
$623$	−8.70850	+	15.0836i	−0.348899	+	0.604310i
$624$	13.2288			0.529574
$625$	4.14575	+	7.18065i	0.165830	+	0.287226i
$626$	11.7915	−	20.4235i	0.471283	−	0.816286i
$627$	7.46863	−	12.9360i	0.298268	−	0.516616i
$628$	−10.5830	−	18.3303i	−0.422308	−	0.731459i
$629$	21.8745			0.872194
$630$	−8.70850	−	15.0836i	−0.346955	−	0.600943i
$631$	−12.8118			−0.510028			−0.255014	−	0.966937i	$-0.582080\pi$
$631$	−12.8118			−0.510028			−0.255014	+	0.966937i	$0.582080\pi$
$632$	−1.32288	−	2.29129i	−0.0526212	−	0.0911425i
$633$	−1.23987	+	2.14752i	−0.0492804	+	0.0853562i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$	13.1144	+	22.7148i	0.520428	+	0.901408i
$636$	4.35425			0.172657
$637$	−17.5000	+	30.3109i	−0.693375	+	1.20096i
$638$	−6.29150			−0.249083
$639$	−8.70850	−	15.0836i	−0.344503	−	0.596696i
$640$	−0.822876	+	1.42526i	−0.0325270	+	0.0563384i
$641$	−6.43725	+	11.1497i	−0.254256	+	0.440385i	−0.964693	−	0.263376i	$-0.915164\pi$
$641$	−6.43725	+	11.1497i	−0.254256	+	0.440385i	0.710437	+	0.703761i	$0.248497\pi$
$642$	−14.4686	−	25.0604i	−0.571031	−	0.989055i
$643$	−30.5203			−1.20360			−0.601801	−	0.798646i	$-0.705550\pi$
$643$	−30.5203			−1.20360			−0.601801	+	0.798646i	$0.705550\pi$
$644$	−2.17712	−	3.77089i	−0.0857907	−	0.148594i
$645$	17.4170			0.685793
$646$	−16.9373	−	29.3362i	−0.666387	−	1.15422i
$647$	4.40588	−	7.63121i	0.173213	−	0.300014i	−0.766328	−	0.642449i	$-0.777918\pi$
$647$	4.40588	−	7.63121i	0.173213	−	0.300014i	0.939541	+	0.342435i	$0.111252\pi$
$648$	−2.50000	+	4.33013i	−0.0982093	+	0.170103i
$649$	−2.32288	−	4.02334i	−0.0911808	−	0.157930i
$650$	11.4575			0.449401
$651$	14.0000	−	24.2487i	0.548703	−	0.950382i
$652$	0.645751			0.0252896
$653$	−3.82288	−	6.62141i	−0.149601	−	0.259116i	0.781479	−	0.623931i	$-0.214465\pi$
$653$	−3.82288	−	6.62141i	−0.149601	−	0.259116i	−0.931080	+	0.364815i	$0.881132\pi$
$654$	−14.0000	+	24.2487i	−0.547443	+	0.948200i
$655$	8.52026	−	14.7575i	0.332914	−	0.576624i
$656$	−5.46863	−	9.47194i	−0.213514	−	0.369817i
$657$	1.41699			0.0552822
$658$	−7.16601			−0.279360
$659$	−6.58301			−0.256437			−0.128219	−	0.991746i	$-0.540926\pi$
$659$	−6.58301			−0.256437			−0.128219	+	0.991746i	$0.540926\pi$
$660$	2.17712	+	3.77089i	0.0847445	+	0.146782i
$661$	−3.70850	+	6.42331i	−0.144244	+	0.249838i	−0.929091	−	0.369852i	$-0.879408\pi$
$661$	−3.70850	+	6.42331i	−0.144244	+	0.249838i	0.784847	+	0.619690i	$0.212742\pi$
$662$	−10.3229	+	17.8797i	−0.401210	+	0.694916i
$663$	−39.6863	−	68.7386i	−1.54129	−	2.66959i
$664$	−2.70850			−0.105110
$665$	24.5830			0.953288
$666$	−14.5830			−0.565080
$667$	−5.17712	−	8.96704i	−0.200459	−	0.347205i
$668$	5.61438	−	9.72439i	0.217227	−	0.376248i
$669$	23.3431	−	40.4315i	0.902498	−	1.56317i
$670$	9.82288	+	17.0137i	0.379491	+	0.657297i
$671$	14.2915			0.551717
$672$	3.50000	−	6.06218i	0.135015	−	0.233854i
$673$	0.937254			0.0361285			0.0180642	−	0.999837i	$-0.494250\pi$
$673$	0.937254			0.0361285			0.0180642	+	0.999837i	$0.494250\pi$
$674$	4.53137	+	7.84857i	0.174542	+	0.302316i
$675$	3.03137	−	5.25049i	0.116678	−	0.202092i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	16.9373	+	29.3362i	0.650952	+	1.12748i	0.982892	+	0.184181i	$0.0589632\pi$
$677$	16.9373	+	29.3362i	0.650952	+	1.12748i	−0.331941	+	0.943300i	$0.607703\pi$
$678$	48.3948			1.85859
$679$	21.5516	+	37.3285i	0.827076	+	1.43254i
$680$	9.87451			0.378670
$681$	3.58301	+	6.20595i	0.137301	+	0.237812i
$682$	−2.00000	+	3.46410i	−0.0765840	+	0.132647i
$683$	−0.968627	+	1.67771i	−0.0370635	+	0.0641958i	−0.883962	−	0.467559i	$-0.845134\pi$
$683$	−0.968627	+	1.67771i	−0.0370635	+	0.0641958i	0.846899	+	0.531754i	$0.178467\pi$
$684$	11.2915	+	19.5575i	0.431741	+	0.747798i
$685$	21.1882			0.809561
$686$	9.26013	+	16.0390i	0.353553	+	0.612372i
$687$	−42.3320			−1.61507
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−4.11438	+	7.12631i	−0.156745	+	0.271491i
$690$	−3.58301	+	6.20595i	−0.136403	+	0.236256i
$691$	22.6144	+	39.1693i	0.860291	+	1.49007i	0.871648	+	0.490133i	$0.163052\pi$
$691$	22.6144	+	39.1693i	0.860291	+	1.49007i	−0.0113561	+	0.999936i	$0.503615\pi$
$692$	−0.291503			−0.0110813
$693$	−5.29150	−	9.16515i	−0.201008	−	0.348155i
$694$	20.8118			0.790004
$695$	−3.29150	−	5.70105i	−0.124854	−	0.216253i
$696$	8.32288	−	14.4156i	0.315478	−	0.546424i
$697$	−32.8118	+	56.8316i	−1.24283	+	2.15265i
$698$	−0.937254	−	1.62337i	−0.0354756	−	0.0614455i
$699$	2.81176			0.106351
$700$	3.03137	−	5.25049i	0.114575	−	0.198450i
$701$	24.8745			0.939497			0.469749	−	0.882800i	$-0.344345\pi$
$701$	24.8745			0.939497			0.469749	+	0.882800i	$0.344345\pi$
$702$	6.61438	+	11.4564i	0.249644	+	0.432395i
$703$	10.2915	−	17.8254i	0.388151	−	0.672298i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	5.89674	+	10.2134i	0.222084	+	0.384661i
$706$	−7.16601			−0.269696
$707$	7.93725			0.298511
$708$	12.2915			0.461943
$709$	−20.4059	−	35.3440i	−0.766359	−	1.32737i	−0.939525	−	0.342480i	$-0.888733\pi$
$709$	−20.4059	−	35.3440i	−0.766359	−	1.32737i	0.173166	−	0.984893i	$-0.444600\pi$
$710$	−3.58301	+	6.20595i	−0.134468	+	0.232905i
$711$	5.29150	−	9.16515i	0.198447	−	0.343720i
$712$	3.29150	+	5.70105i	0.123354	+	0.213656i
$713$	−6.58301			−0.246535
$714$	−42.0000			−1.57181
$715$	−8.22876			−0.307738
$716$	9.96863	+	17.2662i	0.372545	+	0.645267i
$717$	22.7915	−	39.4760i	0.851164	−	1.47426i
$718$	−12.9686	+	22.4623i	−0.483985	+	0.838286i
$719$	−13.9373	−	24.1400i	−0.519772	−	0.900271i	−0.999736	−	0.0229831i	$-0.992684\pi$
$719$	−13.9373	−	24.1400i	−0.519772	−	0.900271i	0.479964	−	0.877288i	$-0.340650\pi$
$720$	−6.58301			−0.245334
$721$	3.88562	−	6.73009i	0.144708	−	0.250642i
$722$	−12.8745			−0.479140
$723$	32.8229	+	56.8509i	1.22070	+	2.11431i
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	7.20850	−	12.4855i	0.267717	−	0.463699i
$726$	1.32288	+	2.29129i	0.0490965	+	0.0850377i
$727$	−6.70850			−0.248804			−0.124402	−	0.992232i	$-0.539701\pi$
$727$	−6.70850			−0.248804			−0.124402	+	0.992232i	$0.539701\pi$
$728$	6.61438	+	11.4564i	0.245145	+	0.424604i
$729$	−41.0000			−1.51852
$730$	−0.291503	−	0.504897i	−0.0107890	−	0.0186871i
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	−18.9059	+	32.7459i	−0.698781	+	1.21033i
$733$	5.72876	+	9.92250i	0.211596	+	0.366496i	0.952214	−	0.305431i	$-0.0988004\pi$
$733$	5.72876	+	9.92250i	0.211596	+	0.366496i	−0.740618	+	0.671926i	$0.765467\pi$
$734$	36.2288			1.33723
$735$	15.2399	−	26.3962i	0.562131	−	0.973640i
$736$	−1.64575			−0.0606632
$737$	5.96863	+	10.3380i	0.219857	+	0.380804i
$738$	21.8745	−	37.8878i	0.805212	−	1.39467i
$739$	−11.9373	+	20.6759i	−0.439119	+	0.760576i	−0.997622	−	0.0689263i	$-0.978043\pi$
$739$	−11.9373	+	20.6759i	−0.439119	+	0.760576i	0.558503	+	0.829503i	$0.311376\pi$
$740$	3.00000	+	5.19615i	0.110282	+	0.191014i
$741$	−74.6863			−2.74367
$742$	2.17712	+	3.77089i	0.0799247	+	0.138434i
$743$	−45.2915			−1.66158			−0.830792	−	0.556583i	$-0.812112\pi$
$743$	−45.2915			−1.66158			−0.830792	+	0.556583i	$0.812112\pi$
$744$	−5.29150	−	9.16515i	−0.193996	−	0.336011i
$745$	−12.5830	+	21.7944i	−0.461006	+	0.798485i
$746$	10.4373	−	18.0779i	0.382135	−	0.661877i
$747$	−5.41699	−	9.38251i	−0.198197	−	0.343288i
$748$	6.00000			0.219382
$749$	14.4686	−	25.0604i	0.528672	−	0.915687i
$750$	−31.7490			−1.15931
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	−1.35425	+	2.34563i	−0.0493844	+	0.0855362i
$753$	4.35425	−	7.54178i	0.158678	−	0.274838i
$754$	15.7288	+	27.2430i	0.572808	+	0.992132i
$755$	14.2288			0.517837
$756$	7.00000			0.254588
$757$	−23.1660			−0.841983			−0.420991	−	0.907065i	$-0.638318\pi$
$757$	−23.1660			−0.841983			−0.420991	+	0.907065i	$0.638318\pi$
$758$	3.03137	+	5.25049i	0.110104	+	0.190706i
$759$	−2.17712	+	3.77089i	−0.0790246	+	0.136875i
$760$	4.64575	−	8.04668i	0.168519	−	0.291884i
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	0.915264	−	0.402854i	$-0.131982\pi$
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	−0.806514	+	0.591215i	$0.798649\pi$
$762$	−42.1660			−1.52751
$763$	−28.0000			−1.01367
$764$	−2.70850			−0.0979900
$765$	19.7490	+	34.2063i	0.714027	+	1.23673i
$766$	12.0516	−	20.8740i	0.435443	−	0.754210i
$767$	−11.6144	+	20.1167i	−0.419371	+	0.726372i
$768$	−1.32288	−	2.29129i	−0.0477352	−	0.0826797i
$769$	27.1660			0.979631			0.489816	−	0.871826i	$-0.337064\pi$
$769$	27.1660			0.979631			0.489816	+	0.871826i	$0.337064\pi$
$770$	−2.17712	+	3.77089i	−0.0784581	+	0.135893i
$771$	−57.1033			−2.05652
$772$	−12.7601	−	22.1012i	−0.459247	−	0.795439i
$773$	9.29150	−	16.0934i	0.334192	−	0.578838i	−0.649137	−	0.760671i	$-0.724870\pi$
$773$	9.29150	−	16.0934i	0.334192	−	0.578838i	0.983329	+	0.181834i	$0.0582032\pi$
$774$	−8.00000	+	13.8564i	−0.287554	+	0.498058i
$775$	−4.58301	−	7.93800i	−0.164626	−	0.285141i
$776$	16.2915			0.584831
$777$	−12.7601	−	22.1012i	−0.457767	−	0.792876i
$778$	−26.8118			−0.961248
$779$	30.8745	+	53.4762i	1.10619	+	1.91598i
$780$	10.8856	−	18.8544i	0.389768	−	0.675098i
$781$	−2.17712	+	3.77089i	−0.0779036	+	0.134933i
$782$	4.93725	+	8.55157i	0.176556	+	0.305804i
$783$	16.6458			0.594871
$784$	7.00000			0.250000
$785$	−34.8340			−1.24328
$786$	13.6974	+	23.7246i	0.488569	+	0.846227i
$787$	−23.4059	+	40.5402i	−0.834330	+	1.44510i	0.0602456	+	0.998184i	$0.480812\pi$
$787$	−23.4059	+	40.5402i	−0.834330	+	1.44510i	−0.894575	+	0.446918i	$0.852522\pi$
$788$	6.43725	−	11.1497i	0.229318	−	0.397190i
$789$	−26.3745	−	45.6820i	−0.938957	−	1.62632i
$790$	−4.35425			−0.154917
$791$	24.1974	+	41.9111i	0.860360	+	1.49019i
$792$	−4.00000			−0.142134
$793$	−35.7288	−	61.8840i	−1.26877	−	2.19757i
$794$	−5.58301	+	9.67005i	−0.198133	+	0.343177i
$795$	3.58301	−	6.20595i	0.127076	−	0.220102i
$796$	−2.11438	−	3.66221i	−0.0749422	−	0.129804i
$797$	7.16601			0.253833			0.126917	−	0.991913i	$-0.459492\pi$
$797$	7.16601			0.253833			0.126917	+	0.991913i	$0.459492\pi$
$798$	−19.7601	+	34.2255i	−0.699501	+	1.21157i
$799$	16.2510			0.574918
$800$	−1.14575	−	1.98450i	−0.0405084	−	0.0701627i
$801$	−13.1660	+	22.8042i	−0.465198	+	0.805747i
$802$	10.7915	−	18.6914i	0.381061	−	0.660017i
$803$	−0.177124	−	0.306788i	−0.00625058	−	0.0108263i
$804$	−31.5830			−1.11385
$805$	−7.16601			−0.252569
$806$	20.0000			0.704470
$807$	−7.16601	−	12.4119i	−0.252256	−	0.436919i
$808$	1.50000	−	2.59808i	0.0527698	−	0.0914000i
$809$	−14.7085	+	25.4759i	−0.517123	+	0.895684i	0.482679	+	0.875797i	$0.339664\pi$
$809$	−14.7085	+	25.4759i	−0.517123	+	0.895684i	−0.999802	+	0.0198864i	$0.993670\pi$
$810$	4.11438	+	7.12631i	0.144565	+	0.250393i
$811$	−35.7490			−1.25532			−0.627659	−	0.778489i	$-0.715987\pi$
$811$	−35.7490			−1.25532			−0.627659	+	0.778489i	$0.715987\pi$
$812$	16.6458			0.584151
$813$	−5.45751			−0.191403
$814$	1.82288	+	3.15731i	0.0638918	+	0.110664i
$815$	0.531373	−	0.920365i	0.0186132	−	0.0322390i
$816$	−7.93725	+	13.7477i	−0.277859	+	0.481267i
$817$	−11.2915	−	19.5575i	−0.395040	−	0.684229i
$818$	−3.06275			−0.107086
$819$	−26.4575	+	45.8258i	−0.924500	+	1.60128i
$820$	−18.0000			−0.628587
$821$	9.14575	+	15.8409i	0.319189	+	0.552851i	0.980319	−	0.197420i	$-0.0632562\pi$
$821$	9.14575	+	15.8409i	0.319189	+	0.552851i	−0.661130	+	0.750271i	$0.729923\pi$
$822$	−17.0314	+	29.4992i	−0.594037	+	1.02890i
$823$	6.06275	−	10.5010i	0.211334	−	0.366041i	−0.740798	−	0.671728i	$-0.765553\pi$
$823$	6.06275	−	10.5010i	0.211334	−	0.366041i	0.952132	+	0.305686i	$0.0988859\pi$
$824$	−1.46863	−	2.54374i	−0.0511620	−	0.0886153i
$825$	−6.06275			−0.211078
$826$	6.14575	+	10.6448i	0.213838	+	0.370378i
$827$	33.3948			1.16125			0.580625	−	0.814171i	$-0.302808\pi$
$827$	33.3948			1.16125			0.580625	+	0.814171i	$0.302808\pi$
$828$	−3.29150	−	5.70105i	−0.114388	−	0.198125i
$829$	12.6974	−	21.9925i	0.440998	−	0.763832i	−0.556765	−	0.830670i	$-0.687958\pi$
$829$	12.6974	−	21.9925i	0.440998	−	0.763832i	0.997764	+	0.0668382i	$0.0212911\pi$
$830$	−2.22876	+	3.86032i	−0.0773613	+	0.133994i
$831$	29.4889	+	51.0762i	1.02296	+	1.77182i
$832$	5.00000			0.173344
$833$	−21.0000	−	36.3731i	−0.727607	−	1.26025i
$834$	10.5830			0.366460
$835$	−9.23987	−	16.0039i	−0.319759	−	0.553839i
$836$	2.82288	−	4.88936i	0.0976312	−	0.169102i
$837$	5.29150	−	9.16515i	0.182901	−	0.316794i
$838$	−4.93725	−	8.55157i	−0.170555	−	0.295409i
$839$	−3.87451			−0.133763			−0.0668814	−	0.997761i	$-0.521305\pi$
$839$	−3.87451			−0.133763			−0.0668814	+	0.997761i	$0.521305\pi$
$840$	−5.76013	−	9.97684i	−0.198743	−	0.344234i
$841$	10.5830			0.364931
$842$	4.58301	+	7.93800i	0.157941	+	0.273561i
$843$	30.3431	−	52.5559i	1.04507	−	1.81012i
$844$	−0.468627	+	0.811686i	−0.0161308	+	0.0279394i
$845$	9.87451	+	17.1031i	0.339693	+	0.588366i
$846$	−10.8340			−0.372480
$847$	−1.32288	+	2.29129i	−0.0454545	+	0.0787296i
$848$	1.64575			0.0565153
$849$	3.11438	+	5.39426i	0.106885	+	0.185131i
$850$	−6.87451	+	11.9070i	−0.235794	+	0.408407i
$851$	−3.00000	+	5.19615i	−0.102839	+	0.178122i
$852$	−5.76013	−	9.97684i	−0.197339	−	0.341801i
$853$	39.1660			1.34102			0.670509	−	0.741901i	$-0.266076\pi$
$853$	39.1660			1.34102			0.670509	+	0.741901i	$0.266076\pi$
$854$	−37.8118			−1.29389
$855$	37.1660			1.27105
$856$	−5.46863	−	9.47194i	−0.186914	−	0.323744i
$857$	−18.0000	+	31.1769i	−0.614868	+	1.06498i	0.375539	+	0.926806i	$0.377458\pi$
$857$	−18.0000	+	31.1769i	−0.614868	+	1.06498i	−0.990408	+	0.138177i	$0.955876\pi$
$858$	6.61438	−	11.4564i	0.225811	−	0.391116i
$859$	4.90588	+	8.49723i	0.167386	+	0.289922i	0.937500	−	0.347985i	$-0.113134\pi$
$859$	4.90588	+	8.49723i	0.167386	+	0.289922i	−0.770114	+	0.637907i	$0.779801\pi$
$860$	6.58301			0.224479
$861$	76.5608			2.60918
$862$	−29.2288			−0.995535
$863$	6.23987	+	10.8078i	0.212408	+	0.367901i	0.952468	−	0.304640i	$-0.0985362\pi$
$863$	6.23987	+	10.8078i	0.212408	+	0.367901i	−0.740060	+	0.672541i	$0.765203\pi$
$864$	1.32288	−	2.29129i	0.0450051	−	0.0779512i
$865$	−0.239870	+	0.415468i	−0.00815584	+	0.0141263i
$866$	−8.00000	−	13.8564i	−0.271851	−	0.470860i
$867$	50.2693			1.70723
$868$	5.29150	−	9.16515i	0.179605	−	0.311086i
$869$	−2.64575			−0.0897510
$870$	−13.6974	−	23.7246i	−0.464385	−	0.804338i
$871$	29.8431	−	51.6898i	1.01120	−	1.75144i
$872$	−5.29150	+	9.16515i	−0.179193	+	0.310371i
$873$	32.5830	+	56.4354i	1.10277	+	1.91005i
$874$	9.29150			0.314290
$875$	−15.8745	−	27.4955i	−0.536656	−	0.929516i
$876$	0.937254			0.0316669
$877$	11.4373	+	19.8099i	0.386209	+	0.668933i	0.991936	−	0.126739i	$-0.0404511\pi$
$877$	11.4373	+	19.8099i	0.386209	+	0.668933i	−0.605727	+	0.795672i	$0.707118\pi$
$878$	1.96863	−	3.40976i	0.0664379	−	0.115074i
$879$	−15.8745	+	27.4955i	−0.535434	+	0.927399i
$880$	0.822876	+	1.42526i	0.0277391	+	0.0480456i
$881$	−24.8745			−0.838043			−0.419022	−	0.907976i	$-0.637627\pi$
$881$	−24.8745			−0.838043			−0.419022	+	0.907976i	$0.637627\pi$
$882$	14.0000	+	24.2487i	0.471405	+	0.816497i
$883$	21.9373			0.738247			0.369124	−	0.929380i	$-0.379658\pi$
$883$	21.9373			0.738247			0.369124	+	0.929380i	$0.379658\pi$
$884$	−15.0000	−	25.9808i	−0.504505	−	0.873828i
$885$	10.1144	−	17.5186i	0.339991	−	0.588882i
$886$	17.2288	−	29.8411i	0.578811	−	1.00253i
$887$	−22.5516	−	39.0606i	−0.757210	−	1.31153i	−0.944268	−	0.329177i	$-0.893229\pi$
$887$	−22.5516	−	39.0606i	−0.757210	−	1.31153i	0.187059	−	0.982349i	$-0.440105\pi$
$888$	−9.64575			−0.323690
$889$	−21.0830	−	36.5168i	−0.707101	−	1.22474i
$890$	10.8340			0.363156
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	8.82288	−	15.2817i	0.295412	−	0.511668i
$893$	7.64575	−	13.2428i	0.255855	−	0.443154i
$894$	−20.2288	−	35.0372i	−0.676551	−	1.17182i
$895$	32.8118			1.09678
$896$	1.32288	−	2.29129i	0.0441942	−	0.0765466i
$897$	21.7712			0.726921
$898$	−10.9373	−	18.9439i	−0.364981	−	0.632165i
$899$	12.5830	−	21.7944i	0.419667	−	0.726884i
$900$	4.58301	−	7.93800i	0.152767	−	0.264600i
$901$	−4.93725	−	8.55157i	−0.164484	−	0.284894i
$902$	−10.9373			−0.364171
$903$	−28.0000			−0.931782
$904$	18.2915			0.608366
$905$	−8.22876	−	14.2526i	−0.273533	−	0.473773i
$906$	−11.4373	+	19.8099i	−0.379977	+	0.658140i
$907$	−21.2288	+	36.7693i	−0.704889	+	1.22090i	0.261842	+	0.965111i	$0.415670\pi$
$907$	−21.2288	+	36.7693i	−0.704889	+	1.22090i	−0.966731	+	0.255793i	$0.917663\pi$
$908$	1.35425	+	2.34563i	0.0449423	+	0.0778424i
$909$	12.0000			0.398015
$910$	21.7712			0.721710
$911$	9.29150			0.307841			0.153921	−	0.988083i	$-0.450810\pi$
$911$	9.29150			0.307841			0.153921	+	0.988083i	$0.450810\pi$
$912$	7.46863	+	12.9360i	0.247311	+	0.428355i
$913$	−1.35425	+	2.34563i	−0.0448191	+	0.0776289i
$914$	1.58301	−	2.74185i	0.0523612	−	0.0906922i
$915$	31.1144	+	53.8917i	1.02861	+	1.78160i
$916$	−16.0000			−0.528655
$917$	−13.6974	+	23.7246i	−0.452327	+	0.783454i
$918$	−15.8745			−0.523937
$919$	12.3542	+	21.3982i	0.407529	+	0.705861i	0.994612	−	0.103666i	$-0.0330572\pi$
$919$	12.3542	+	21.3982i	0.407529	+	0.705861i	−0.587083	+	0.809527i	$0.699724\pi$
$920$	−1.35425	+	2.34563i	−0.0446483	+	0.0773330i
$921$	−29.4059	+	50.9325i	−0.968957	+	1.67828i
$922$	5.08301	+	8.80402i	0.167400	+	0.289945i
$923$	21.7712			0.716609
$924$	−3.50000	−	6.06218i	−0.115142	−	0.199431i
$925$	−8.35425			−0.274686
$926$	15.2288	+	26.3770i	0.500448	+	0.866801i
$927$	5.87451	−	10.1749i	0.192944	−	0.334189i
$928$	3.14575	−	5.44860i	0.103264	−	0.178859i
$929$	−7.20850	−	12.4855i	−0.236503	−	0.409635i	0.723205	−	0.690633i	$-0.242668\pi$
$929$	−7.20850	−	12.4855i	−0.236503	−	0.409635i	−0.959708	+	0.280998i	$0.909335\pi$
$930$	−17.4170			−0.571126
$931$	−39.5203			−1.29522
$932$	1.06275			0.0348114
$933$	−1.40588	−	2.43506i	−0.0460265	−	0.0797202i
$934$	10.6458	−	18.4390i	0.348340	−	0.603342i
$935$	4.93725	−	8.55157i	0.161465	−	0.279666i
$936$	10.0000	+	17.3205i	0.326860	+	0.566139i
$937$	32.6863			1.06781			0.533907	−	0.845543i	$-0.320723\pi$
$937$	32.6863			1.06781			0.533907	+	0.845543i	$0.320723\pi$
$938$	−15.7915	−	27.3517i	−0.515611	−	0.893064i
$939$	62.3948			2.03618
$940$	2.22876	+	3.86032i	0.0726940	+	0.125910i
$941$	−25.3118	+	43.8413i	−0.825140	+	1.42918i	0.0766725	+	0.997056i	$0.475570\pi$
$941$	−25.3118	+	43.8413i	−0.825140	+	1.42918i	−0.901812	+	0.432128i	$0.857763\pi$
$942$	28.0000	−	48.4974i	0.912289	−	1.58013i
$943$	−9.00000	−	15.5885i	−0.293080	−	0.507630i
$944$	4.64575			0.151206
$945$	5.76013	−	9.97684i	0.187377	−	0.324547i
$946$	4.00000			0.130051
$947$	1.06275	+	1.84073i	0.0345346	+	0.0598157i	0.882776	−	0.469794i	$-0.155672\pi$
$947$	1.06275	+	1.84073i	0.0345346	+	0.0598157i	−0.848242	+	0.529610i	$0.822338\pi$
$948$	3.50000	−	6.06218i	0.113675	−	0.196890i
$949$	−0.885622	+	1.53394i	−0.0287485	+	0.0497939i
$950$	6.46863	+	11.2040i	0.209870	+	0.363505i
$951$	31.7490			1.02953
$952$	−15.8745			−0.514496
$953$	11.5203			0.373178			0.186589	−	0.982438i	$-0.440257\pi$
$953$	11.5203			0.373178			0.186589	+	0.982438i	$0.440257\pi$
$954$	3.29150	+	5.70105i	0.106566	+	0.184578i
$955$	−2.22876	+	3.86032i	−0.0721209	+	0.124917i
$956$	8.61438	−	14.9205i	0.278609	−	0.482565i
$957$	−8.32288	−	14.4156i	−0.269040	−	0.465992i
$958$	10.0627			0.325113
$959$	−34.0627			−1.09994
$960$	−4.35425			−0.140533
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	9.11438	−	15.7866i	0.293859	−	0.508979i
$963$	21.8745	−	37.8878i	0.704896	−	1.22092i
$964$	12.4059	+	21.4876i	0.399567	+	0.692070i
$965$	−42.0000			−1.35203
$966$	5.76013	−	9.97684i	0.185329	−	0.320999i
$967$	58.3320			1.87583			0.937916	−	0.346863i	$-0.112753\pi$
$967$	58.3320			1.87583			0.937916	+	0.346863i	$0.112753\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$	44.8118	−	77.6162i	1.43956	−	2.49339i
$970$	13.4059	−	23.2197i	0.430437	−	0.745539i
$971$	5.03137	+	8.71459i	0.161464	+	0.279665i	0.935394	−	0.353607i	$-0.115045\pi$
$971$	5.03137	+	8.71459i	0.161464	+	0.279665i	−0.773930	+	0.633272i	$0.781712\pi$
$972$	−21.1660			−0.678900
$973$	5.29150	+	9.16515i	0.169638	+	0.293821i
$974$	9.41699			0.301740
$975$	15.1569	+	26.2525i	0.485408	+	0.840752i
$976$	−7.14575	+	12.3768i	−0.228730	+	0.396172i
$977$	8.22876	−	14.2526i	0.263261	−	0.455982i	−0.703845	−	0.710353i	$-0.748535\pi$
$977$	8.22876	−	14.2526i	0.263261	−	0.455982i	0.967107	+	0.254371i	$0.0818685\pi$
$978$	0.854249	+	1.47960i	0.0273159	+	0.0473125i
$979$	6.58301			0.210394
$980$	5.76013	−	9.97684i	0.184001	−	0.318698i
$981$	−42.3320			−1.35156
$982$	10.6458	+	18.4390i	0.339720	+	0.588412i
$983$	13.3542	−	23.1302i	0.425934	−	0.737740i	−0.570573	−	0.821247i	$-0.693279\pi$
$983$	13.3542	−	23.1302i	0.425934	−	0.737740i	0.996507	+	0.0835070i	$0.0266121\pi$
$984$	14.4686	−	25.0604i	0.461243	−	0.798896i
$985$	−10.5941	−	18.3496i	−0.337557	−	0.584665i
$986$	−37.7490			−1.20217
$987$	−9.47974	−	16.4194i	−0.301743	−	0.522635i
$988$	−28.2288			−0.898076
$989$	3.29150	+	5.70105i	0.104664	+	0.181283i
$990$	−3.29150	+	5.70105i	−0.104611	+	0.181191i
$991$	11.3431	−	19.6469i	0.360327	−	0.624104i	−0.627688	−	0.778465i	$-0.715999\pi$
$991$	11.3431	−	19.6469i	0.360327	−	0.624104i	0.988014	+	0.154361i	$0.0493319\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	−54.6235			−1.73343
$994$	5.76013	−	9.97684i	0.182700	−	0.316446i
$995$	−6.95948			−0.220630
$996$	−3.58301	−	6.20595i	−0.113532	−	0.196643i
$997$	10.7085	−	18.5477i	0.339142	−	0.587410i	−0.645130	−	0.764073i	$-0.723197\pi$
$997$	10.7085	−	18.5477i	0.339142	−	0.587410i	0.984271	+	0.176663i	$0.0565301\pi$
$998$	−6.93725	+	12.0157i	−0.219595	+	0.380350i
$999$	−4.82288	−	8.35347i	−0.152589	−	0.264292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.e.f.67.1	yes	4
3.2	odd	2		1386.2.k.s.991.1		4
4.3	odd	2		1232.2.q.g.529.2		4
7.2	even	3	inner	154.2.e.f.23.1	✓	4
7.3	odd	6		1078.2.a.n.1.1		2
7.4	even	3		1078.2.a.s.1.2		2
7.5	odd	6		1078.2.e.v.177.2		4
7.6	odd	2		1078.2.e.v.67.2		4
21.2	odd	6		1386.2.k.s.793.1		4
21.11	odd	6		9702.2.a.cz.1.2		2
21.17	even	6		9702.2.a.dr.1.1		2
28.3	even	6		8624.2.a.bk.1.2		2
28.11	odd	6		8624.2.a.ca.1.1		2
28.23	odd	6		1232.2.q.g.177.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.f.23.1	✓	4	7.2	even	3	inner
154.2.e.f.67.1	yes	4	1.1	even	1	trivial
1078.2.a.n.1.1		2	7.3	odd	6
1078.2.a.s.1.2		2	7.4	even	3
1078.2.e.v.67.2		4	7.6	odd	2
1078.2.e.v.177.2		4	7.5	odd	6
1232.2.q.g.177.2		4	28.23	odd	6
1232.2.q.g.529.2		4	4.3	odd	2
1386.2.k.s.793.1		4	21.2	odd	6
1386.2.k.s.991.1		4	3.2	odd	2
8624.2.a.bk.1.2		2	28.3	even	6
8624.2.a.ca.1.1		2	28.11	odd	6
9702.2.a.cz.1.2		2	21.11	odd	6
9702.2.a.dr.1.1		2	21.17	even	6

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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} -2.64575 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} -2.64575 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(-0.822876 + 1.42526i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.32288 - 2.29129i) q^{12} +5.00000 q^{13} +(1.32288 - 2.29129i) q^{14} -4.35425 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{18} +(2.82288 + 4.88936i) q^{19} -1.64575 q^{20} +7.00000 q^{21} -1.00000 q^{22} +(-0.822876 - 1.42526i) q^{23} +(1.32288 - 2.29129i) q^{24} +(1.14575 - 1.98450i) q^{25} +(2.50000 + 4.33013i) q^{26} +2.64575 q^{27} +2.64575 q^{28} +6.29150 q^{29} +(-2.17712 - 3.77089i) q^{30} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.32288 - 2.29129i) q^{33} -6.00000 q^{34} +(2.17712 - 3.77089i) q^{35} +4.00000 q^{36} +(-1.82288 - 3.15731i) q^{37} +(-2.82288 + 4.88936i) q^{38} +(-6.61438 + 11.4564i) q^{39} +(-0.822876 - 1.42526i) q^{40} +10.9373 q^{41} +(3.50000 + 6.06218i) q^{42} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(3.29150 - 5.70105i) q^{45} +(0.822876 - 1.42526i) q^{46} +(-1.35425 - 2.34563i) q^{47} +2.64575 q^{48} +(-3.50000 + 6.06218i) q^{49} +2.29150 q^{50} +(-7.93725 - 13.7477i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(-0.822876 + 1.42526i) q^{53} +(1.32288 + 2.29129i) q^{54} -1.64575 q^{55} +(1.32288 + 2.29129i) q^{56} -14.9373 q^{57} +(3.14575 + 5.44860i) q^{58} +(-2.32288 + 4.02334i) q^{59} +(2.17712 - 3.77089i) q^{60} +(-7.14575 - 12.3768i) q^{61} +4.00000 q^{62} +(-5.29150 + 9.16515i) q^{63} +1.00000 q^{64} +(4.11438 + 7.12631i) q^{65} +(1.32288 - 2.29129i) q^{66} +(5.96863 - 10.3380i) q^{67} +(-3.00000 - 5.19615i) q^{68} +4.35425 q^{69} +4.35425 q^{70} +4.35425 q^{71} +(2.00000 + 3.46410i) q^{72} +(-0.177124 + 0.306788i) q^{73} +(1.82288 - 3.15731i) q^{74} +(3.03137 + 5.25049i) q^{75} -5.64575 q^{76} +2.64575 q^{77} -13.2288 q^{78} +(1.32288 + 2.29129i) q^{79} +(0.822876 - 1.42526i) q^{80} +(2.50000 - 4.33013i) q^{81} +(5.46863 + 9.47194i) q^{82} +2.70850 q^{83} +(-3.50000 + 6.06218i) q^{84} -9.87451 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-8.32288 + 14.4156i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-3.29150 - 5.70105i) q^{89} +6.58301 q^{90} +(-6.61438 - 11.4564i) q^{91} +1.64575 q^{92} +(5.29150 + 9.16515i) q^{93} +(1.35425 - 2.34563i) q^{94} +(-4.64575 + 8.04668i) q^{95} +(1.32288 + 2.29129i) q^{96} -16.2915 q^{97} -7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 8 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 28 q^{15} - 2 q^{16} - 12 q^{17} + 8 q^{18} + 6 q^{19} + 4 q^{20} + 28 q^{21} - 4 q^{22} + 2 q^{23} - 6 q^{25} + 10 q^{26} + 4 q^{29} - 14 q^{30} + 8 q^{31} + 2 q^{32} - 24 q^{34} + 14 q^{35} + 16 q^{36} - 2 q^{37} - 6 q^{38} + 2 q^{40} + 12 q^{41} + 14 q^{42} - 16 q^{43} - 2 q^{44} - 8 q^{45} - 2 q^{46} - 16 q^{47} - 14 q^{49} - 12 q^{50} - 10 q^{52} + 2 q^{53} + 4 q^{55} - 28 q^{57} + 2 q^{58} - 4 q^{59} + 14 q^{60} - 18 q^{61} + 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} - 12 q^{68} + 28 q^{69} + 28 q^{70} + 28 q^{71} + 8 q^{72} - 6 q^{73} + 2 q^{74} + 28 q^{75} - 12 q^{76} - 2 q^{80} + 10 q^{81} + 6 q^{82} + 32 q^{83} - 14 q^{84} + 24 q^{85} - 8 q^{86} - 28 q^{87} + 2 q^{88} + 8 q^{89} - 16 q^{90} - 4 q^{92} + 16 q^{94} - 8 q^{95} - 44 q^{97} - 28 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 8 * q^9 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 28 * q^15 - 2 * q^16 - 12 * q^17 + 8 * q^18 + 6 * q^19 + 4 * q^20 + 28 * q^21 - 4 * q^22 + 2 * q^23 - 6 * q^25 + 10 * q^26 + 4 * q^29 - 14 * q^30 + 8 * q^31 + 2 * q^32 - 24 * q^34 + 14 * q^35 + 16 * q^36 - 2 * q^37 - 6 * q^38 + 2 * q^40 + 12 * q^41 + 14 * q^42 - 16 * q^43 - 2 * q^44 - 8 * q^45 - 2 * q^46 - 16 * q^47 - 14 * q^49 - 12 * q^50 - 10 * q^52 + 2 * q^53 + 4 * q^55 - 28 * q^57 + 2 * q^58 - 4 * q^59 + 14 * q^60 - 18 * q^61 + 16 * q^62 + 4 * q^64 - 10 * q^65 + 8 * q^67 - 12 * q^68 + 28 * q^69 + 28 * q^70 + 28 * q^71 + 8 * q^72 - 6 * q^73 + 2 * q^74 + 28 * q^75 - 12 * q^76 - 2 * q^80 + 10 * q^81 + 6 * q^82 + 32 * q^83 - 14 * q^84 + 24 * q^85 - 8 * q^86 - 28 * q^87 + 2 * q^88 + 8 * q^89 - 16 * q^90 - 4 * q^92 + 16 * q^94 - 8 * q^95 - 44 * q^97 - 28 * q^98 + 16 * q^99

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