LMFDB - Embedded newform 429.2.n.d.196.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.8
Character	$\chi$	$=$	429.196
Dual form			429.2.n.d.313.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.693505 - 2.13439i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.45663 - 1.78484i) q^{4} +(0.185200 + 0.569986i) q^{5} +(0.693505 + 2.13439i) q^{6} +(-3.43059 - 2.49247i) q^{7} +(-1.88200 + 1.36735i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.693505 - 2.13439i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.45663 - 1.78484i) q^{4} +(0.185200 + 0.569986i) q^{5} +(0.693505 + 2.13439i) q^{6} +(-3.43059 - 2.49247i) q^{7} +(-1.88200 + 1.36735i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.34501 q^{10} +(-1.78679 - 2.79417i) q^{11} +3.03656 q^{12} +(-0.309017 + 0.951057i) q^{13} +(-7.69902 + 5.59367i) q^{14} +(-0.484859 - 0.352271i) q^{15} +(-0.263415 - 0.810707i) q^{16} +(1.18179 + 3.63717i) q^{17} +(-1.81562 - 1.31912i) q^{18} +(-4.11080 + 2.98667i) q^{19} +(0.562370 - 1.73080i) q^{20} +4.24044 q^{21} +(-7.20299 + 1.87592i) q^{22} -8.18018 q^{23} +(0.718858 - 2.21242i) q^{24} +(3.75450 - 2.72780i) q^{25} +(1.81562 + 1.31912i) q^{26} +(0.309017 + 0.951057i) q^{27} +(3.97901 + 12.2461i) q^{28} +(-4.04614 - 2.93969i) q^{29} +(-1.08813 + 0.790576i) q^{30} +(1.48050 - 4.55652i) q^{31} -6.56559 q^{32} +(3.08791 + 1.21029i) q^{33} +8.58270 q^{34} +(0.785329 - 2.41699i) q^{35} +(-2.45663 + 1.78484i) q^{36} +(0.993647 + 0.721927i) q^{37} +(3.52386 + 10.8453i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-1.12792 - 0.819479i) q^{40} +(6.36818 - 4.62675i) q^{41} +(2.94077 - 9.05075i) q^{42} +7.54807 q^{43} +(-0.597692 + 10.0534i) q^{44} +0.599319 q^{45} +(-5.67299 + 17.4597i) q^{46} +(3.97002 - 2.88439i) q^{47} +(0.689628 + 0.501044i) q^{48} +(3.39342 + 10.4439i) q^{49} +(-3.21843 - 9.90530i) q^{50} +(-3.09396 - 2.24789i) q^{51} +(2.45663 - 1.78484i) q^{52} +(3.84632 - 11.8378i) q^{53} +2.24423 q^{54} +(1.26173 - 1.53592i) q^{55} +9.86443 q^{56} +(1.57019 - 4.83254i) q^{57} +(-9.08046 + 6.59734i) q^{58} +(-2.35967 - 1.71440i) q^{59} +(0.562370 + 1.73080i) q^{60} +(-1.70005 - 5.23222i) q^{61} +(-8.69865 - 6.31994i) q^{62} +(-3.43059 + 2.49247i) q^{63} +(-4.02644 + 12.3921i) q^{64} -0.599319 q^{65} +(4.72470 - 5.75147i) q^{66} +11.8248 q^{67} +(3.58856 - 11.0445i) q^{68} +(6.61790 - 4.80819i) q^{69} +(-4.61417 - 3.35239i) q^{70} +(-3.32418 - 10.2308i) q^{71} +(0.718858 + 2.21242i) q^{72} +(6.58726 + 4.78592i) q^{73} +(2.22997 - 1.62017i) q^{74} +(-1.43409 + 4.41368i) q^{75} +15.4295 q^{76} +(-0.834655 + 14.0392i) q^{77} -2.24423 q^{78} +(-2.85498 + 8.78672i) q^{79} +(0.413307 - 0.300285i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-5.45892 - 16.8008i) q^{82} +(-0.0533641 - 0.164238i) q^{83} +(-10.4172 - 7.56853i) q^{84} +(-1.85427 + 1.34720i) q^{85} +(5.23462 - 16.1105i) q^{86} +5.00130 q^{87} +(7.18333 + 2.81546i) q^{88} -7.65543 q^{89} +(0.415631 - 1.27918i) q^{90} +(3.43059 - 2.49247i) q^{91} +(20.0957 + 14.6003i) q^{92} +(1.48050 + 4.55652i) q^{93} +(-3.40318 - 10.4739i) q^{94} +(-2.46368 - 1.78997i) q^{95} +(5.31167 - 3.85916i) q^{96} +(4.76540 - 14.6664i) q^{97} +24.6446 q^{98} +(-3.20956 + 0.835888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.693505	−	2.13439i	0.490382	−	1.50924i	−0.333650	−	0.942697i	$-0.608280\pi$
$2$	0.693505	−	2.13439i	0.490382	−	1.50924i	0.824032	−	0.566543i	$-0.191720\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−2.45663	−	1.78484i	−1.22831	−	0.892422i
$5$	0.185200	+	0.569986i	0.0828239	+	0.254906i	0.983890	−	0.178777i	$-0.0572140\pi$
$5$	0.185200	+	0.569986i	0.0828239	+	0.254906i	−0.901066	+	0.433682i	$0.857214\pi$
$6$	0.693505	+	2.13439i	0.283122	+	0.871360i
$7$	−3.43059	−	2.49247i	−1.29664	−	0.942065i	−0.296724	−	0.954963i	$-0.595894\pi$
$7$	−3.43059	−	2.49247i	−1.29664	−	0.942065i	−0.999917	+	0.0128985i	$0.995894\pi$
$8$	−1.88200	+	1.36735i	−0.665386	+	0.483431i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	1.34501			0.425329
$11$	−1.78679	−	2.79417i	−0.538736	−	0.842474i
$11$	−1.78679	−	2.79417i	−0.538736	−	0.842474i
$12$	3.03656			0.876579
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−7.69902	+	5.59367i	−2.05765	+	1.49497i
$15$	−0.484859	−	0.352271i	−0.125190	−	0.0909560i
$16$	−0.263415	−	0.810707i	−0.0658537	−	0.202677i
$17$	1.18179	+	3.63717i	0.286625	+	0.882142i	0.985907	+	0.167296i	$0.0535034\pi$
$17$	1.18179	+	3.63717i	0.286625	+	0.882142i	−0.699281	+	0.714847i	$0.746497\pi$
$18$	−1.81562	−	1.31912i	−0.427945	−	0.310921i
$19$	−4.11080	+	2.98667i	−0.943082	+	0.685189i	−0.949161	−	0.314792i	$-0.898065\pi$
$19$	−4.11080	+	2.98667i	−0.943082	+	0.685189i	0.00607836	+	0.999982i	$0.498065\pi$
$20$	0.562370	−	1.73080i	0.125750	−	0.387018i
$21$	4.24044			0.925340
$22$	−7.20299	+	1.87592i	−1.53568	+	0.399948i
$23$	−8.18018			−1.70569			−0.852843	−	0.522168i	$-0.825123\pi$
$23$	−8.18018			−1.70569			−0.852843	+	0.522168i	$0.825123\pi$
$24$	0.718858	−	2.21242i	0.146736	−	0.451608i
$25$	3.75450	−	2.72780i	0.750900	−	0.545561i
$26$	1.81562	+	1.31912i	0.356072	+	0.258702i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	3.97901	+	12.2461i	0.751962	+	2.31430i
$29$	−4.04614	−	2.93969i	−0.751349	−	0.545887i	0.144896	−	0.989447i	$-0.453715\pi$
$29$	−4.04614	−	2.93969i	−0.751349	−	0.545887i	−0.896245	+	0.443560i	$0.853715\pi$
$30$	−1.08813	+	0.790576i	−0.198665	+	0.144339i
$31$	1.48050	−	4.55652i	0.265906	−	0.818375i	−0.725577	−	0.688141i	$-0.758427\pi$
$31$	1.48050	−	4.55652i	0.265906	−	0.818375i	0.991483	−	0.130234i	$-0.0415729\pi$
$32$	−6.56559			−1.16064
$33$	3.08791	+	1.21029i	0.537537	+	0.210684i
$34$	8.58270			1.47192
$35$	0.785329	−	2.41699i	0.132745	−	0.408547i
$36$	−2.45663	+	1.78484i	−0.409438	+	0.297474i
$37$	0.993647	+	0.721927i	0.163355	+	0.118684i	0.666459	−	0.745541i	$-0.267809\pi$
$37$	0.993647	+	0.721927i	0.163355	+	0.118684i	−0.503105	+	0.864225i	$0.667809\pi$
$38$	3.52386	+	10.8453i	0.571645	+	1.75934i
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$	−1.12792	−	0.819479i	−0.178339	−	0.129571i
$41$	6.36818	−	4.62675i	0.994543	−	0.722578i	0.0336316	−	0.999434i	$-0.489293\pi$
$41$	6.36818	−	4.62675i	0.994543	−	0.722578i	0.960911	+	0.276857i	$0.0892927\pi$
$42$	2.94077	−	9.05075i	0.453770	−	1.39656i
$43$	7.54807			1.15107			0.575535	−	0.817777i	$-0.304794\pi$
$43$	7.54807			1.15107			0.575535	+	0.817777i	$0.304794\pi$
$44$	−0.597692	+	10.0534i	−0.0901055	+	1.51560i
$45$	0.599319			0.0893412
$46$	−5.67299	+	17.4597i	−0.836437	+	2.57429i
$47$	3.97002	−	2.88439i	0.579087	−	0.420731i	−0.259308	−	0.965795i	$-0.583494\pi$
$47$	3.97002	−	2.88439i	0.579087	−	0.420731i	0.838395	+	0.545063i	$0.183494\pi$
$48$	0.689628	+	0.501044i	0.0995393	+	0.0723195i
$49$	3.39342	+	10.4439i	0.484775	+	1.49198i
$50$	−3.21843	−	9.90530i	−0.455154	−	1.40082i
$51$	−3.09396	−	2.24789i	−0.433241	−	0.314768i
$52$	2.45663	−	1.78484i	0.340673	−	0.247513i
$53$	3.84632	−	11.8378i	0.528333	−	1.62604i	−0.229297	−	0.973356i	$-0.573643\pi$
$53$	3.84632	−	11.8378i	0.528333	−	1.62604i	0.757630	−	0.652684i	$-0.226357\pi$
$54$	2.24423			0.305401
$55$	1.26173	−	1.53592i	0.170131	−	0.207104i
$56$	9.86443			1.31819
$57$	1.57019	−	4.83254i	0.207976	−	0.640085i
$58$	−9.08046	+	6.59734i	−1.19232	+	0.866273i
$59$	−2.35967	−	1.71440i	−0.307202	−	0.223196i	0.423493	−	0.905899i	$-0.360804\pi$
$59$	−2.35967	−	1.71440i	−0.307202	−	0.223196i	−0.730695	+	0.682704i	$0.760804\pi$
$60$	0.562370	+	1.73080i	0.0726017	+	0.223445i
$61$	−1.70005	−	5.23222i	−0.217669	−	0.669918i	−0.998953	−	0.0457418i	$-0.985435\pi$
$61$	−1.70005	−	5.23222i	−0.217669	−	0.669918i	0.781284	−	0.624176i	$-0.214565\pi$
$62$	−8.69865	−	6.31994i	−1.10473	−	0.802633i
$63$	−3.43059	+	2.49247i	−0.432214	+	0.314022i
$64$	−4.02644	+	12.3921i	−0.503305	+	1.54901i
$65$	−0.599319			−0.0743364
$66$	4.72470	−	5.75147i	0.581570	−	0.707956i
$67$	11.8248			1.44463			0.722314	−	0.691565i	$-0.243078\pi$
$67$	11.8248			1.44463			0.722314	+	0.691565i	$0.243078\pi$
$68$	3.58856	−	11.0445i	0.435177	−	1.33934i
$69$	6.61790	−	4.80819i	0.796702	−	0.578838i
$70$	−4.61417	−	3.35239i	−0.551499	−	0.400688i
$71$	−3.32418	−	10.2308i	−0.394508	−	1.21417i	−0.929344	−	0.369214i	$-0.879627\pi$
$71$	−3.32418	−	10.2308i	−0.394508	−	1.21417i	0.534837	−	0.844955i	$-0.320373\pi$
$72$	0.718858	+	2.21242i	0.0847183	+	0.260736i
$73$	6.58726	+	4.78592i	0.770980	+	0.560150i	0.902258	−	0.431196i	$-0.141908\pi$
$73$	6.58726	+	4.78592i	0.770980	+	0.560150i	−0.131278	+	0.991346i	$0.541908\pi$
$74$	2.22997	−	1.62017i	0.259229	−	0.188341i
$75$	−1.43409	+	4.41368i	−0.165595	+	0.509648i
$76$	15.4295			1.76988
$77$	−0.834655	+	14.0392i	−0.0951178	+	1.59991i
$78$	−2.24423			−0.254109
$79$	−2.85498	+	8.78672i	−0.321210	+	0.988583i	0.651912	+	0.758294i	$0.273967\pi$
$79$	−2.85498	+	8.78672i	−0.321210	+	0.988583i	−0.973122	+	0.230289i	$0.926033\pi$
$80$	0.413307	−	0.300285i	0.0462092	−	0.0335729i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−5.45892	−	16.8008i	−0.602837	−	1.85534i
$83$	−0.0533641	−	0.164238i	−0.00585747	−	0.0180274i	0.948085	−	0.318017i	$-0.103017\pi$
$83$	−0.0533641	−	0.164238i	−0.00585747	−	0.0180274i	−0.953943	+	0.299989i	$0.903017\pi$
$84$	−10.4172	−	7.56853i	−1.13661	−	0.825794i
$85$	−1.85427	+	1.34720i	−0.201124	+	0.146125i
$86$	5.23462	−	16.1105i	0.564464	−	1.73724i
$87$	5.00130			0.536196
$88$	7.18333	+	2.81546i	0.765746	+	0.300129i
$89$	−7.65543			−0.811474			−0.405737	−	0.913990i	$-0.632985\pi$
$89$	−7.65543			−0.811474			−0.405737	+	0.913990i	$0.632985\pi$
$90$	0.415631	−	1.27918i	0.0438113	−	0.134837i
$91$	3.43059	−	2.49247i	0.359623	−	0.261282i
$92$	20.0957	+	14.6003i	2.09512	+	1.52219i
$93$	1.48050	+	4.55652i	0.153521	+	0.472489i
$94$	−3.40318	−	10.4739i	−0.351011	−	1.08030i
$95$	−2.46368	−	1.78997i	−0.252768	−	0.183647i
$96$	5.31167	−	3.85916i	0.542121	−	0.393874i
$97$	4.76540	−	14.6664i	0.483853	−	1.48915i	−0.349782	−	0.936831i	$-0.613744\pi$
$97$	4.76540	−	14.6664i	0.483853	−	1.48915i	0.833635	−	0.552316i	$-0.186256\pi$
$98$	24.6446			2.48949
$99$	−3.20956	+	0.835888i	−0.322573	+	0.0840100i
$100$	−14.0921			−1.40921
$101$	−4.13807	+	12.7357i	−0.411753	+	1.26725i	0.503370	+	0.864071i	$0.332093\pi$
$101$	−4.13807	+	12.7357i	−0.411753	+	1.26725i	−0.915123	+	0.403174i	$0.867907\pi$
$102$	−6.94355	+	5.04478i	−0.687514	+	0.499508i
$103$	10.6265	+	7.72060i	1.04706	+	0.760734i	0.971651	−	0.236419i	$-0.0759738\pi$
$103$	10.6265	+	7.72060i	1.04706	+	0.760734i	0.0754089	+	0.997153i	$0.475974\pi$
$104$	−0.718858	−	2.21242i	−0.0704899	−	0.216945i
$105$	0.785329	+	2.41699i	0.0766403	+	0.235874i
$106$	−22.5989	−	16.4191i	−2.19500	−	1.59476i
$107$	−11.1714	+	8.11649i	−1.07998	+	0.784651i	−0.977679	−	0.210103i	$-0.932620\pi$
$107$	−11.1714	+	8.11649i	−1.07998	+	0.784651i	−0.102300	+	0.994754i	$0.532620\pi$
$108$	0.938348	−	2.88794i	0.0902926	−	0.277892i
$109$	−14.7998			−1.41757			−0.708784	−	0.705426i	$-0.750756\pi$
$109$	−14.7998			−1.41757			−0.708784	+	0.705426i	$0.750756\pi$
$110$	−2.40324	−	3.75818i	−0.229140	−	0.358329i
$111$	−1.22822			−0.116577
$112$	−1.11699	+	3.43776i	−0.105546	+	0.324837i
$113$	1.53880	−	1.11800i	0.144758	−	0.105173i	−0.513049	−	0.858359i	$-0.671484\pi$
$113$	1.53880	−	1.11800i	0.144758	−	0.105173i	0.657807	+	0.753186i	$0.271484\pi$
$114$	−9.22557	−	6.70277i	−0.864054	−	0.627772i
$115$	−1.51497	−	4.66259i	−0.141271	−	0.434789i
$116$	4.69296	+	14.4435i	0.435731	+	1.34104i
$117$	0.809017	+	0.587785i	0.0747936	+	0.0543408i
$118$	−5.29563	+	3.84750i	−0.487502	+	0.354191i
$119$	5.01130	−	15.4232i	0.459385	−	1.41384i
$120$	1.39418			0.127271
$121$	−4.61479	+	9.98518i	−0.419526	+	0.907743i
$122$	−12.3466			−1.11781
$123$	−2.43243	+	7.48625i	−0.219325	+	0.675012i
$124$	−11.7697	+	8.55121i	−1.05695	+	0.767921i
$125$	4.67444	+	3.39618i	0.418095	+	0.303764i
$126$	2.94077	+	9.05075i	0.261984	+	0.806305i
$127$	−0.820167	−	2.52421i	−0.0727780	−	0.223988i	0.908050	−	0.418861i	$-0.137570\pi$
$127$	−0.820167	−	2.52421i	−0.0727780	−	0.223988i	−0.980828	+	0.194873i	$0.937570\pi$
$128$	13.0338	+	9.46964i	1.15204	+	0.837006i
$129$	−6.10652	+	4.43664i	−0.537649	+	0.390625i
$130$	−0.415631	+	1.27918i	−0.0364532	+	0.112191i
$131$	−12.2963			−1.07433			−0.537166	−	0.843477i	$-0.680505\pi$
$131$	−12.2963			−1.07433			−0.537166	+	0.843477i	$0.680505\pi$
$132$	−5.42568	−	8.48467i	−0.472245	−	0.738495i
$133$	21.5467			1.86833
$134$	8.20055	−	25.2387i	0.708419	−	2.18029i
$135$	−0.484859	+	0.352271i	−0.0417300	+	0.0303187i
$136$	−7.19739	−	5.22921i	−0.617172	−	0.448401i
$137$	−0.885018	−	2.72380i	−0.0756122	−	0.232710i	0.906106	−	0.423051i	$-0.139041\pi$
$137$	−0.885018	−	2.72380i	−0.0756122	−	0.232710i	−0.981718	+	0.190340i	$0.939041\pi$
$138$	−5.67299	−	17.4597i	−0.482917	−	1.48627i
$139$	−3.45251	−	2.50839i	−0.292838	−	0.212759i	0.431660	−	0.902037i	$-0.357928\pi$
$139$	−3.45251	−	2.50839i	−0.292838	−	0.212759i	−0.724498	+	0.689277i	$0.757928\pi$
$140$	−6.24322	+	4.53596i	−0.527648	+	0.383359i
$141$	−1.51641	+	4.66704i	−0.127705	+	0.393036i
$142$	−24.1418			−2.02593
$143$	3.20956	−	0.835888i	0.268397	−	0.0699005i
$144$	−0.852428			−0.0710356
$145$	0.926240	−	2.85067i	0.0769200	−	0.236736i
$146$	14.7833	−	10.7407i	1.22347	−	0.888907i
$147$	−8.88410	−	6.45467i	−0.732748	−	0.532372i
$148$	−1.15249	−	3.54701i	−0.0947344	−	0.291563i
$149$	0.333193	+	1.02546i	0.0272962	+	0.0840091i	0.963777	−	0.266711i	$-0.0859369\pi$
$149$	0.333193	+	1.02546i	0.0272962	+	0.0840091i	−0.936480	+	0.350720i	$0.885937\pi$
$150$	8.42595	+	6.12181i	0.687976	+	0.499844i
$151$	14.8520	−	10.7906i	1.20864	−	0.878127i	0.213531	−	0.976936i	$-0.431504\pi$
$151$	14.8520	−	10.7906i	1.20864	−	0.878127i	0.995106	+	0.0988097i	$0.0315035\pi$
$152$	3.65268	−	11.2418i	0.296272	−	0.911831i
$153$	3.82434			0.309180
$154$	29.3862	+	11.5177i	2.36801	+	0.928123i
$155$	2.87134			0.230632
$156$	−0.938348	+	2.88794i	−0.0751280	+	0.231220i
$157$	−6.55823	+	4.76483i	−0.523404	+	0.380275i	−0.817885	−	0.575382i	$-0.804853\pi$
$157$	−6.55823	+	4.76483i	−0.523404	+	0.380275i	0.294481	+	0.955657i	$0.404853\pi$
$158$	16.7743	+	12.1873i	1.33449	+	0.969566i
$159$	3.84632	+	11.8378i	0.305033	+	0.938795i
$160$	−1.21595	−	3.74230i	−0.0961290	−	0.295855i
$161$	28.0628	+	20.3888i	2.21166	+	1.60687i
$162$	−1.81562	+	1.31912i	−0.142648	+	0.103640i
$163$	6.85341	−	21.0926i	0.536800	−	1.65210i	−0.202927	−	0.979194i	$-0.565045\pi$
$163$	6.85341	−	21.0926i	0.536800	−	1.65210i	0.739727	−	0.672907i	$-0.234955\pi$
$164$	−23.9023			−1.86646
$165$	−0.117965	+	1.98421i	−0.00918358	+	0.154471i
$166$	−0.387555			−0.0300801
$167$	3.31769	−	10.2108i	0.256730	−	0.790135i	−0.736753	−	0.676161i	$-0.763642\pi$
$167$	3.31769	−	10.2108i	0.256730	−	0.790135i	0.993484	−	0.113973i	$-0.0363578\pi$
$168$	−7.98049	+	5.79817i	−0.615708	+	0.447338i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	1.58951	+	4.89202i	0.121910	+	0.375201i
$171$	1.57019	+	4.83254i	0.120075	+	0.369553i
$172$	−18.5428	−	13.4721i	−1.41387	−	1.02724i
$173$	−5.37786	+	3.90724i	−0.408871	+	0.297062i	−0.773145	−	0.634230i	$-0.781317\pi$
$173$	−5.37786	+	3.90724i	−0.408871	+	0.297062i	0.364274	+	0.931292i	$0.381317\pi$
$174$	3.46843	−	10.6747i	0.262941	−	0.809248i
$175$	−19.6791			−1.48760
$176$	−1.79459	+	2.18459i	−0.135272	+	0.164669i
$177$	2.91671			0.219233
$178$	−5.30908	+	16.3397i	−0.397932	+	1.22471i
$179$	−4.77214	+	3.46716i	−0.356687	+	0.259148i	−0.751669	−	0.659541i	$-0.770751\pi$
$179$	−4.77214	+	3.46716i	−0.356687	+	0.259148i	0.394982	+	0.918689i	$0.370751\pi$
$180$	−1.47230	−	1.06969i	−0.109739	−	0.0797301i
$181$	1.20445	+	3.70692i	0.0895261	+	0.275533i	0.985789	−	0.167991i	$-0.0537280\pi$
$181$	1.20445	+	3.70692i	0.0895261	+	0.275533i	−0.896262	+	0.443524i	$0.853728\pi$
$182$	−2.94077	−	9.05075i	−0.217984	−	0.670886i
$183$	4.45080	+	3.23369i	0.329012	+	0.239041i
$184$	15.3951	−	11.1852i	1.13494	−	0.824581i
$185$	−0.227465	+	0.700066i	−0.0167236	+	0.0514699i
$186$	10.7521			0.788383
$187$	8.05126	−	9.80095i	0.588767	−	0.716717i
$188$	−14.9011			−1.08677
$189$	1.31037	−	4.03290i	0.0953153	−	0.293350i
$190$	−5.52906	+	4.01710i	−0.401120	+	0.291431i
$191$	3.85530	+	2.80104i	0.278960	+	0.202676i	0.718464	−	0.695565i	$-0.244846\pi$
$191$	3.85530	+	2.80104i	0.278960	+	0.202676i	−0.439504	+	0.898241i	$0.644846\pi$
$192$	−4.02644	−	12.3921i	−0.290583	−	0.894323i
$193$	5.87292	+	18.0750i	0.422742	+	1.30107i	0.905140	+	0.425113i	$0.139766\pi$
$193$	5.87292	+	18.0750i	0.422742	+	1.30107i	−0.482398	+	0.875952i	$0.660234\pi$
$194$	−27.9989	−	20.3424i	−2.01021	−	1.46050i
$195$	0.484859	−	0.352271i	0.0347215	−	0.0252266i
$196$	10.3043	−	31.7135i	0.736023	−	2.26525i
$197$	0.171645			0.0122292			0.00611459	−	0.999981i	$-0.498054\pi$
$197$	0.171645			0.0122292			0.00611459	+	0.999981i	$0.498054\pi$
$198$	−0.441736	+	7.43014i	−0.0313928	+	0.528037i
$199$	5.98377			0.424179			0.212089	−	0.977250i	$-0.431973\pi$
$199$	5.98377			0.424179			0.212089	+	0.977250i	$0.431973\pi$
$200$	−3.33609	+	10.2674i	−0.235897	+	0.726017i
$201$	−9.56646	+	6.95044i	−0.674766	+	0.490246i
$202$	24.3131	+	17.6645i	1.71066	+	1.24287i
$203$	6.55355	+	20.1697i	0.459969	+	1.41564i
$204$	3.58856	+	11.0445i	0.251250	+	0.773267i
$205$	3.81657	+	2.77290i	0.266561	+	0.193668i
$206$	23.8483	−	17.3268i	1.66159	−	1.20721i
$207$	−2.52781	+	7.77981i	−0.175695	+	0.540734i
$208$	0.852428			0.0591052
$209$	15.6904	+	6.14974i	1.08533	+	0.425386i
$210$	5.70343			0.393574
$211$	0.516510	−	1.58965i	0.0355580	−	0.109436i	−0.931702	−	0.363223i	$-0.881676\pi$
$211$	0.516510	−	1.58965i	0.0355580	−	0.109436i	0.967260	+	0.253787i	$0.0816762\pi$
$212$	−30.5775	+	22.2159i	−2.10007	+	1.52579i
$213$	8.70282	+	6.32297i	0.596307	+	0.433242i
$214$	9.57633	+	29.4729i	0.654624	+	2.01473i
$215$	1.39790	+	4.30230i	0.0953360	+	0.293414i
$216$	−1.88200	−	1.36735i	−0.128054	−	0.0930364i
$217$	−16.4360	+	11.9414i	−1.11575	+	0.810638i
$218$	−10.2638	+	31.5886i	−0.695149	+	2.13945i
$219$	−8.14230			−0.550205
$220$	−5.84098	+	1.52121i	−0.393799	+	0.102560i
$221$	−3.82434			−0.257253
$222$	−0.851773	+	2.62149i	−0.0571673	+	0.175943i
$223$	−6.80272	+	4.94247i	−0.455544	+	0.330972i	−0.791781	−	0.610805i	$-0.790846\pi$
$223$	−6.80272	+	4.94247i	−0.455544	+	0.330972i	0.336237	+	0.941778i	$0.390846\pi$
$224$	22.5238	+	16.3645i	1.50494	+	1.09340i
$225$	−1.43409	−	4.41368i	−0.0956061	−	0.294245i
$226$	−1.31909	−	4.05974i	−0.0877444	−	0.270050i
$227$	8.28511	+	6.01948i	0.549902	+	0.399527i	0.827749	−	0.561098i	$-0.189621\pi$
$227$	8.28511	+	6.01948i	0.549902	+	0.399527i	−0.277847	+	0.960625i	$0.589621\pi$
$228$	−12.4827	+	9.06920i	−0.826686	+	0.600623i
$229$	2.85560	−	8.78864i	0.188704	−	0.580770i	−0.811289	−	0.584645i	$-0.801234\pi$
$229$	2.85560	−	8.78864i	0.188704	−	0.580770i	0.999992	+	0.00387561i	$0.00123365\pi$
$230$	−11.0024			−0.725478
$231$	−7.57676	−	11.8485i	−0.498514	−	0.779575i
$232$	11.6344			0.763836
$233$	4.36333	−	13.4289i	0.285851	−	0.879759i	−0.700291	−	0.713857i	$-0.746946\pi$
$233$	4.36333	−	13.4289i	0.285851	−	0.879759i	0.986142	−	0.165902i	$-0.0530536\pi$
$234$	1.81562	−	1.31912i	0.118691	−	0.0862338i
$235$	2.37931	+	1.72867i	0.155209	+	0.112766i
$236$	2.73689	+	8.42327i	0.178156	+	0.548308i
$237$	−2.85498	−	8.78672i	−0.185451	−	0.570759i
$238$	−29.4437	−	21.3921i	−1.90855	−	1.38664i
$239$	−5.94882	+	4.32207i	−0.384797	+	0.279571i	−0.763320	−	0.646020i	$-0.776432\pi$
$239$	−5.94882	+	4.32207i	−0.384797	+	0.279571i	0.378523	+	0.925592i	$0.376432\pi$
$240$	−0.157869	+	0.485872i	−0.0101904	+	0.0313629i
$241$	−13.4027			−0.863344			−0.431672	−	0.902031i	$-0.642076\pi$
$241$	−13.4027			−0.863344			−0.431672	+	0.902031i	$0.642076\pi$
$242$	18.1119	+	16.7745i	1.16427	+	1.07831i
$243$	1.00000			0.0641500
$244$	−5.16231	+	15.8880i	−0.330483	+	1.01712i
$245$	−5.32441	+	3.86841i	−0.340164	+	0.247144i
$246$	14.2917	+	10.3835i	0.911202	+	0.662027i
$247$	−1.57019	−	4.83254i	−0.0999085	−	0.307487i
$248$	3.44406	+	10.5997i	0.218698	+	0.673083i
$249$	0.139709	+	0.101505i	0.00885370	+	0.00643259i
$250$	10.4905	−	7.62180i	0.663478	−	0.482045i
$251$	−7.32019	+	22.5292i	−0.462046	+	1.42203i	0.400613	+	0.916247i	$0.368797\pi$
$251$	−7.32019	+	22.5292i	−0.462046	+	1.42203i	−0.862659	+	0.505785i	$0.831203\pi$
$252$	12.8764			0.811134
$253$	14.6162	+	22.8568i	0.918915	+	1.43700i
$254$	−5.95644			−0.373740
$255$	0.708267	−	2.17982i	0.0443534	−	0.136506i
$256$	8.16822	−	5.93456i	0.510514	−	0.370910i
$257$	−1.05810	−	0.768752i	−0.0660023	−	0.0479535i	0.554295	−	0.832320i	$-0.312988\pi$
$257$	−1.05810	−	0.768752i	−0.0660023	−	0.0479535i	−0.620297	+	0.784367i	$0.712988\pi$
$258$	5.23462	+	16.1105i	0.325893	+	1.00300i
$259$	−1.60941	−	4.95327i	−0.100004	−	0.307781i
$260$	1.47230	+	1.06969i	0.0913084	+	0.0663394i
$261$	−4.04614	+	2.93969i	−0.250450	+	0.181962i
$262$	−8.52753	+	26.2451i	−0.526833	+	1.62142i
$263$	−3.31828			−0.204614			−0.102307	−	0.994753i	$-0.532622\pi$
$263$	−3.31828			−0.204614			−0.102307	+	0.994753i	$0.532622\pi$
$264$	−7.46632	+	1.94451i	−0.459520	+	0.119676i
$265$	7.45970			0.458246
$266$	14.9427	−	45.9889i	0.916196	−	2.81976i
$267$	6.19337	−	4.49975i	0.379028	−	0.275380i
$268$	−29.0491	−	21.1054i	−1.77446	−	1.28922i
$269$	−9.57735	−	29.4760i	−0.583941	−	1.79719i	−0.603482	−	0.797377i	$-0.706220\pi$
$269$	−9.57735	−	29.4760i	−0.583941	−	1.79719i	0.0195404	−	0.999809i	$-0.493780\pi$
$270$	0.415631	+	1.27918i	0.0252945	+	0.0778484i
$271$	−3.03358	−	2.20403i	−0.184277	−	0.133885i	0.491822	−	0.870696i	$-0.336331\pi$
$271$	−3.03358	−	2.20403i	−0.184277	−	0.133885i	−0.676099	+	0.736810i	$0.736331\pi$
$272$	2.63737	−	1.91617i	0.159914	−	0.116185i
$273$	−1.31037	+	4.03290i	−0.0793071	+	0.244082i
$274$	−6.42742			−0.388295
$275$	−14.3304	−	5.61671i	−0.864158	−	0.338701i
$276$	−24.8396			−1.49517
$277$	5.58394	−	17.1856i	0.335506	−	1.03258i	−0.630966	−	0.775810i	$-0.717341\pi$
$277$	5.58394	−	17.1856i	0.335506	−	1.03258i	0.966472	−	0.256771i	$-0.0826587\pi$
$278$	−7.74822	+	5.62941i	−0.464707	+	0.337630i
$279$	−3.87601	−	2.81608i	−0.232051	−	0.168595i
$280$	1.82689	+	5.62259i	0.109178	+	0.336014i
$281$	−8.80485	−	27.0985i	−0.525253	−	1.61656i	−0.763815	−	0.645436i	$-0.776676\pi$
$281$	−8.80485	−	27.0985i	−0.525253	−	1.61656i	0.238562	−	0.971127i	$-0.423324\pi$
$282$	8.90963	+	6.47323i	0.530561	+	0.385475i
$283$	10.4601	−	7.59971i	0.621789	−	0.451756i	−0.231757	−	0.972774i	$-0.574447\pi$
$283$	10.4601	−	7.59971i	0.621789	−	0.451756i	0.853546	+	0.521018i	$0.174447\pi$
$284$	−10.0941	+	31.0663i	−0.598973	+	1.84345i
$285$	3.04528			0.180387
$286$	0.441736	−	7.43014i	0.0261204	−	0.439354i
$287$	−33.3787			−1.97028
$288$	−2.02888	+	6.24425i	−0.119553	+	0.367946i
$289$	1.92094	−	1.39564i	0.112996	−	0.0820966i
$290$	−5.44209	−	3.95391i	−0.319571	−	0.232182i
$291$	4.76540	+	14.6664i	0.279353	+	0.859759i
$292$	−7.64031	−	23.5145i	−0.447115	−	1.37608i
$293$	6.63756	+	4.82247i	0.387770	+	0.281732i	0.764541	−	0.644575i	$-0.222966\pi$
$293$	6.63756	+	4.82247i	0.387770	+	0.281732i	−0.376771	+	0.926307i	$0.622966\pi$
$294$	−19.9379	+	14.4858i	−1.16280	+	0.844827i
$295$	0.540174	−	1.66248i	0.0314501	−	0.0967935i
$296$	−2.85717			−0.166069
$297$	2.10527	−	2.56278i	0.122160	−	0.148708i
$298$	2.41980			0.140175
$299$	2.52781	−	7.77981i	0.146187	−	0.449918i
$300$	11.4008	−	8.28314i	0.658223	−	0.478227i
$301$	−25.8943	−	18.8133i	−1.49252	−	1.08438i
$302$	−12.7314	−	39.1832i	−0.732610	−	2.25474i
$303$	−4.13807	−	12.7357i	−0.237726	−	0.731644i
$304$	3.50416	+	2.54592i	0.200977	+	0.146019i
$305$	2.66745	−	1.93801i	0.152738	−	0.110970i
$306$	2.65220	−	8.16263i	0.151616	−	0.466626i
$307$	17.3076			0.987799			0.493900	−	0.869519i	$-0.335571\pi$
$307$	17.3076			0.987799			0.493900	+	0.869519i	$0.335571\pi$
$308$	27.1082	−	32.9993i	1.54463	−	1.88031i
$309$	−13.1351			−0.747228
$310$	1.99129	−	6.12856i	0.113098	−	0.348079i
$311$	−1.65064	+	1.19926i	−0.0935991	+	0.0680038i	−0.633601	−	0.773660i	$-0.718424\pi$
$311$	−1.65064	+	1.19926i	−0.0935991	+	0.0680038i	0.540001	+	0.841664i	$0.318424\pi$
$312$	1.88200	+	1.36735i	0.106547	+	0.0774109i
$313$	−6.07614	−	18.7004i	−0.343444	−	1.05701i	−0.962412	−	0.271595i	$-0.912449\pi$
$313$	−6.07614	−	18.7004i	−0.343444	−	1.05701i	0.618968	−	0.785416i	$-0.287551\pi$
$314$	5.62184	+	17.3022i	0.317259	+	0.976422i
$315$	−2.05602	−	1.49378i	−0.115843	−	0.0841652i
$316$	22.6965	−	16.4900i	1.27678	−	0.927635i
$317$	−7.16310	+	22.0457i	−0.402320	+	1.23821i	0.520793	+	0.853683i	$0.325636\pi$
$317$	−7.16310	+	22.0457i	−0.402320	+	1.23821i	−0.923113	+	0.384530i	$0.874364\pi$
$318$	27.9338			1.56645
$319$	−0.984417	+	16.5582i	−0.0551168	+	0.927081i
$320$	−7.80902			−0.436538
$321$	4.26709	−	13.1328i	0.238166	−	0.732999i
$322$	62.9794	−	45.7572i	3.50970	−	2.54995i
$323$	−15.7211	−	11.4221i	−0.874746	−	0.635540i
$324$	0.938348	+	2.88794i	0.0521305	+	0.160441i
$325$	1.43409	+	4.41368i	0.0795491	+	0.244827i
$326$	−40.2669	−	29.2556i	−2.23018	−	1.62032i
$327$	11.9733	−	8.69913i	0.662126	−	0.481063i
$328$	−5.65850	+	17.4151i	−0.312438	+	0.961586i
$329$	−20.8088			−1.14722
$330$	4.15327	+	1.62784i	0.228630	+	0.0896099i
$331$	−10.9532			−0.602041			−0.301020	−	0.953618i	$-0.597327\pi$
$331$	−10.9532			−0.602041			−0.301020	+	0.953618i	$0.597327\pi$
$332$	−0.162043	+	0.498718i	−0.00889328	+	0.0273707i
$333$	0.993647	−	0.721927i	0.0544515	−	0.0395613i
$334$	−19.4930	−	14.1625i	−1.06661	−	0.774935i
$335$	2.18995	+	6.73997i	0.119650	+	0.368244i
$336$	−1.11699	−	3.43776i	−0.0609370	−	0.187545i
$337$	21.7756	+	15.8209i	1.18619	+	0.861818i	0.992856	−	0.119315i	$-0.0380698\pi$
$337$	21.7756	+	15.8209i	1.18619	+	0.861818i	0.193334	+	0.981133i	$0.438070\pi$
$338$	−1.81562	+	1.31912i	−0.0987566	+	0.0717509i
$339$	−0.587769	+	1.80897i	−0.0319232	+	0.0982496i
$340$	6.95980			0.377448
$341$	−15.3770	+	4.00475i	−0.832714	+	0.216869i
$342$	11.4034			0.616627
$343$	5.21703	−	16.0564i	0.281693	−	0.866963i
$344$	−14.2054	+	10.3209i	−0.765906	+	0.556463i
$345$	3.96624	+	2.88164i	0.213535	+	0.155142i
$346$	4.61000	+	14.1881i	0.247835	+	0.762758i
$347$	−2.55062	−	7.85000i	−0.136924	−	0.421410i	0.858960	−	0.512043i	$-0.171111\pi$
$347$	−2.55062	−	7.85000i	−0.136924	−	0.421410i	−0.995884	+	0.0906327i	$0.971111\pi$
$348$	−12.2863	−	8.92655i	−0.658617	−	0.478513i
$349$	−0.283914	+	0.206276i	−0.0151976	+	0.0110417i	−0.595358	−	0.803460i	$-0.702990\pi$
$349$	−0.283914	+	0.206276i	−0.0151976	+	0.0110417i	0.580161	+	0.814502i	$0.302990\pi$
$350$	−13.6476	+	42.0029i	−0.729492	+	2.24515i
$351$	−1.00000			−0.0533761
$352$	11.7313	+	18.3454i	0.625281	+	0.977812i
$353$	−11.1982			−0.596018			−0.298009	−	0.954563i	$-0.596323\pi$
$353$	−11.1982			−0.596018			−0.298009	+	0.954563i	$0.596323\pi$
$354$	2.02275	−	6.22538i	0.107508	−	0.330875i
$355$	5.21576	−	3.78947i	0.276824	−	0.201124i
$356$	18.8065	+	13.6638i	0.996745	+	0.724178i
$357$	5.01130	+	15.4232i	0.265226	+	0.816282i
$358$	4.09077	+	12.5901i	0.216204	+	0.665407i
$359$	−7.94346	−	5.77126i	−0.419240	−	0.304596i	0.358092	−	0.933686i	$-0.383427\pi$
$359$	−7.94346	−	5.77126i	−0.419240	−	0.304596i	−0.777332	+	0.629091i	$0.783427\pi$
$360$	−1.12792	+	0.819479i	−0.0594464	+	0.0431903i
$361$	2.10715	−	6.48514i	0.110903	−	0.341323i
$362$	8.74730			0.459748
$363$	−2.13570	−	10.7907i	−0.112095	−	0.566364i
$364$	−12.8764			−0.674904
$365$	−1.50795	+	4.64100i	−0.0789298	+	0.242921i
$366$	9.98860	−	7.25714i	0.522113	−	0.379337i
$367$	18.1224	+	13.1667i	0.945980	+	0.687295i	0.949853	−	0.312698i	$-0.101233\pi$
$367$	18.1224	+	13.1667i	0.945980	+	0.687295i	−0.00387251	+	0.999993i	$0.501233\pi$
$368$	2.15478	+	6.63173i	0.112326	+	0.345703i
$369$	−2.43243	−	7.48625i	−0.126627	−	0.389718i
$370$	1.33646	+	0.970998i	0.0694794	+	0.0504798i
$371$	−42.7004	+	31.0236i	−2.21689	+	1.61067i
$372$	4.49564	−	13.8361i	0.233088	−	0.717371i
$373$	−24.0981			−1.24775			−0.623877	−	0.781523i	$-0.714443\pi$
$373$	−24.0981			−1.24775			−0.623877	+	0.781523i	$0.714443\pi$
$374$	−15.3354	−	23.9815i	−0.792977	−	1.24005i
$375$	−5.77793			−0.298371
$376$	−3.52759	+	10.8568i	−0.181922	+	0.559898i
$377$	4.04614	−	2.93969i	0.208387	−	0.151402i
$378$	−7.69902	−	5.59367i	−0.395995	−	0.287707i
$379$	7.72151	+	23.7644i	0.396627	+	1.22069i	0.927687	+	0.373359i	$0.121794\pi$
$379$	7.72151	+	23.7644i	0.396627	+	1.22069i	−0.531060	+	0.847334i	$0.678206\pi$
$380$	2.85753	+	8.79458i	0.146588	+	0.451152i
$381$	2.14722	+	1.56005i	0.110006	+	0.0799238i
$382$	8.65217	−	6.28617i	0.442684	−	0.321629i
$383$	7.76853	−	23.9091i	0.396953	−	1.22170i	−0.530477	−	0.847700i	$-0.677987\pi$
$383$	7.76853	−	23.9091i	0.396953	−	1.22170i	0.927430	−	0.373997i	$-0.122013\pi$
$384$	−16.1107			−0.822147
$385$	−8.15671	+	2.12431i	−0.415704	+	0.108265i
$386$	42.6519			2.17092
$387$	2.33248	−	7.17864i	0.118567	−	0.364911i
$388$	−37.8840	+	27.5244i	−1.92327	+	1.39734i
$389$	10.8842	+	7.90784i	0.551851	+	0.400943i	0.828467	−	0.560037i	$-0.189213\pi$
$389$	10.8842	+	7.90784i	0.551851	+	0.400943i	−0.276617	+	0.960980i	$0.589213\pi$
$390$	−0.415631	−	1.27918i	−0.0210463	−	0.0647738i
$391$	−9.66723	−	29.7527i	−0.488893	−	1.50466i
$392$	−20.6668	−	15.0153i	−1.04383	−	0.758389i
$393$	9.94791	−	7.22758i	0.501806	−	0.364583i
$394$	0.119036	−	0.366356i	0.00599697	−	0.0184568i
$395$	−5.53705			−0.278599
$396$	9.37663	+	3.67510i	0.471193	+	0.184681i
$397$	26.7538			1.34274			0.671368	−	0.741124i	$-0.265707\pi$
$397$	26.7538			1.34274			0.671368	+	0.741124i	$0.265707\pi$
$398$	4.14978	−	12.7717i	0.208009	−	0.640187i
$399$	−17.4316	+	12.6648i	−0.872672	+	0.634033i
$400$	−3.20044	−	2.32526i	−0.160022	−	0.116263i
$401$	8.16787	+	25.1381i	0.407884	+	1.25534i	0.918463	+	0.395507i	$0.129431\pi$
$401$	8.16787	+	25.1381i	0.407884	+	1.25534i	−0.510579	+	0.859831i	$0.670569\pi$
$402$	8.20055	+	25.2387i	0.409006	+	1.25879i
$403$	3.87601	+	2.81608i	0.193078	+	0.140279i
$404$	32.8969	−	23.9010i	1.63668	−	1.18912i
$405$	0.185200	−	0.569986i	0.00920265	−	0.0283228i
$406$	47.5950			2.36210
$407$	0.241752	−	4.06635i	0.0119832	−	0.201561i
$408$	8.89647			0.440441
$409$	−0.585205	+	1.80108i	−0.0289365	+	0.0890575i	−0.964482	−	0.264149i	$-0.914909\pi$
$409$	−0.585205	+	1.80108i	−0.0289365	+	0.0890575i	0.935545	+	0.353207i	$0.114909\pi$
$410$	8.56526	−	6.22303i	0.423008	−	0.307333i
$411$	2.31701	+	1.68340i	0.114290	+	0.0830362i
$412$	−12.3253	−	37.9333i	−0.607223	−	1.86884i
$413$	3.82196	+	11.7628i	0.188066	+	0.578809i
$414$	14.8521	+	10.7907i	0.729940	+	0.530333i
$415$	0.0837303	−	0.0608336i	0.00411016	−	0.00298620i
$416$	2.02888	−	6.24425i	0.0994740	−	0.306149i
$417$	4.26754			0.208982
$418$	24.0073	−	29.2245i	1.17423	−	1.42942i
$419$	20.5326			1.00308			0.501541	−	0.865134i	$-0.332767\pi$
$419$	20.5326			1.00308			0.501541	+	0.865134i	$0.332767\pi$
$420$	2.38470	−	7.33934i	0.116361	−	0.358123i
$421$	−14.5992	+	10.6069i	−0.711521	+	0.516950i	−0.883664	−	0.468122i	$-0.844931\pi$
$421$	−14.5992	+	10.6069i	−0.711521	+	0.516950i	0.172143	+	0.985072i	$0.444931\pi$
$422$	−3.03474	−	2.20487i	−0.147729	−	0.107331i
$423$	−1.51641	−	4.66704i	−0.0737305	−	0.226919i
$424$	8.94760	+	27.5379i	0.434534	+	1.33736i
$425$	14.3585	+	10.4321i	0.696489	+	0.506029i
$426$	19.5311	−	14.1902i	0.946285	−	0.687516i
$427$	−7.20897	+	22.1869i	−0.348867	+	1.07370i
$428$	41.9306			2.02679
$429$	−2.10527	+	2.56278i	−0.101643	+	0.123732i
$430$	10.1522			0.489583
$431$	7.93182	−	24.4116i	0.382063	−	1.17587i	−0.556526	−	0.830830i	$-0.687866\pi$
$431$	7.93182	−	24.4116i	0.382063	−	1.17587i	0.938589	−	0.345038i	$-0.112134\pi$
$432$	0.689628	−	0.501044i	0.0331798	−	0.0241065i
$433$	−9.55928	−	6.94522i	−0.459389	−	0.333766i	0.333902	−	0.942608i	$-0.391634\pi$
$433$	−9.55928	−	6.94522i	−0.459389	−	0.333766i	−0.793292	+	0.608842i	$0.791634\pi$
$434$	14.0892	+	43.3622i	0.676305	+	2.08145i
$435$	0.926240	+	2.85067i	0.0444098	+	0.136679i
$436$	36.3577	+	26.4154i	1.74122	+	1.26507i
$437$	33.6271	−	24.4315i	1.60860	−	1.16872i
$438$	−5.64672	+	17.3788i	−0.269811	+	0.830392i
$439$	−30.0764			−1.43547			−0.717735	−	0.696316i	$-0.754821\pi$
$439$	−30.0764			−1.43547			−0.717735	+	0.696316i	$0.754821\pi$
$440$	−0.274420	+	4.61582i	−0.0130824	+	0.220051i
$441$	10.9813			0.522921
$442$	−2.65220	+	8.16263i	−0.126152	+	0.388257i
$443$	−13.0315	+	9.46794i	−0.619145	+	0.449835i	−0.852623	−	0.522527i	$-0.824989\pi$
$443$	−13.0315	+	9.46794i	−0.619145	+	0.449835i	0.233478	+	0.972362i	$0.424989\pi$
$444$	3.01727	+	2.19217i	0.143193	+	0.104036i
$445$	−1.41778	−	4.36349i	−0.0672094	−	0.206849i
$446$	5.83142	+	17.9473i	0.276126	+	0.849828i
$447$	−0.872310	−	0.633770i	−0.0412589	−	0.0299763i
$448$	44.7000	−	32.4764i	2.11188	−	1.53437i
$449$	7.83164	−	24.1033i	0.369598	−	1.13751i	−0.577454	−	0.816423i	$-0.695954\pi$
$449$	7.83164	−	24.1033i	0.369598	−	1.13751i	0.947051	−	0.321082i	$-0.104046\pi$
$450$	−10.4151			−0.490970
$451$	−24.3065	−	9.52677i	−1.14455	−	0.448598i
$452$	−5.77572			−0.271667
$453$	−5.67295	+	17.4596i	−0.266539	+	0.820322i
$454$	18.5937	−	13.5091i	0.872644	−	0.634013i
$455$	2.05602	+	1.49378i	0.0963876	+	0.0700297i
$456$	3.65268	+	11.2418i	0.171053	+	0.526446i
$457$	6.69102	+	20.5928i	0.312993	+	0.963292i	0.976573	+	0.215187i	$0.0690362\pi$
$457$	6.69102	+	20.5928i	0.312993	+	0.963292i	−0.663580	+	0.748105i	$0.730964\pi$
$458$	−16.7780	−	12.1899i	−0.783984	−	0.569598i
$459$	−3.09396	+	2.24789i	−0.144414	+	0.104923i
$460$	−4.60029	+	14.1582i	−0.214490	+	0.660131i
$461$	26.9843			1.25679			0.628393	−	0.777896i	$-0.283713\pi$
$461$	26.9843			1.25679			0.628393	+	0.777896i	$0.283713\pi$
$462$	−30.5439	+	7.95475i	−1.42103	+	0.370088i
$463$	−15.9770			−0.742514			−0.371257	−	0.928530i	$-0.621073\pi$
$463$	−15.9770			−0.742514			−0.371257	+	0.928530i	$0.621073\pi$
$464$	−1.31742	+	4.05459i	−0.0611595	+	0.188230i
$465$	−2.32297	+	1.68773i	−0.107725	+	0.0782668i
$466$	−25.6366	−	18.6261i	−1.18759	−	0.862836i
$467$	−5.24462	−	16.1413i	−0.242692	−	0.746930i	−0.996007	−	0.0892701i	$-0.971547\pi$
$467$	−5.24462	−	16.1413i	−0.242692	−	0.746930i	0.753315	−	0.657659i	$-0.228453\pi$
$468$	−0.938348	−	2.88794i	−0.0433752	−	0.133495i
$469$	−40.5660	−	29.4729i	−1.87316	−	1.36093i
$470$	5.33971	−	3.87953i	0.246303	−	0.178949i
$471$	2.50502	−	7.70966i	0.115425	−	0.355242i
$472$	6.78506			0.312308
$473$	−13.4868	−	21.0906i	−0.620123	−	0.969747i
$474$	−20.7342			−0.952354
$475$	−7.28695	+	22.4269i	−0.334348	+	1.02902i
$476$	−39.8389	+	28.9446i	−1.82601	+	1.32668i
$477$	−10.0698	−	7.31614i	−0.461064	−	0.334983i
$478$	5.09944	+	15.6945i	0.233243	+	0.717848i
$479$	−8.15113	−	25.0866i	−0.372435	−	1.14624i	−0.945193	−	0.326512i	$-0.894127\pi$
$479$	−8.15113	−	25.0866i	−0.372435	−	1.14624i	0.572759	−	0.819724i	$-0.305873\pi$
$480$	3.18339	+	2.31287i	0.145301	+	0.105567i
$481$	−0.993647	+	0.721927i	−0.0453064	+	0.0329170i
$482$	−9.29484	+	28.6066i	−0.423368	+	1.30299i
$483$	−34.6876			−1.57834
$484$	29.1588	−	16.2932i	1.32540	−	0.740599i
$485$	9.24219			0.419666
$486$	0.693505	−	2.13439i	0.0314580	−	0.0968178i
$487$	27.4325	−	19.9309i	1.24309	−	0.903155i	0.245286	−	0.969451i	$-0.421118\pi$
$487$	27.4325	−	19.9309i	1.24309	−	0.903155i	0.997800	+	0.0662957i	$0.0211181\pi$
$488$	10.3538	+	7.52246i	0.468693	+	0.340526i
$489$	6.85341	+	21.0926i	0.309922	+	0.953841i
$490$	4.56418	+	14.0471i	0.206189	+	0.634584i
$491$	14.6931	+	10.6752i	0.663090	+	0.481763i	0.867705	−	0.497079i	$-0.165594\pi$
$491$	14.6931	+	10.6752i	0.663090	+	0.481763i	−0.204615	+	0.978843i	$0.565594\pi$
$492$	19.3374	−	14.0494i	0.871795	−	0.633396i
$493$	5.91047	−	18.1906i	0.266194	−	0.819262i
$494$	−11.4034			−0.513065
$495$	−1.07086	−	1.67460i	−0.0481314	−	0.0752677i
$496$	−4.08399			−0.183377
$497$	−14.0960	+	43.3830i	−0.632292	+	1.94599i
$498$	0.313539	−	0.227799i	0.0140500	−	0.0102079i
$499$	−11.7170	−	8.51290i	−0.524525	−	0.381090i	0.293781	−	0.955873i	$-0.405086\pi$
$499$	−11.7170	−	8.51290i	−0.524525	−	0.381090i	−0.818306	+	0.574783i	$0.805086\pi$
$500$	−5.42171	−	16.6863i	−0.242466	−	0.746234i
$501$	3.31769	+	10.2108i	0.148223	+	0.456184i
$502$	43.0095	+	31.2482i	1.91961	+	1.39468i
$503$	0.0105908	−	0.00769470i	0.000472223	−	0.000343090i	−0.587549	−	0.809189i	$-0.699907\pi$
$503$	0.0105908	−	0.00769470i	0.000472223	−	0.000343090i	0.588021	+	0.808845i	$0.299907\pi$
$504$	3.04828	−	9.38163i	0.135781	−	0.417891i
$505$	−8.02552			−0.357131
$506$	58.9217	−	15.3454i	2.61939	−	0.682186i
$507$	1.00000			0.0444116
$508$	−2.49048	+	7.66492i	−0.110497	+	0.340076i
$509$	9.23683	−	6.71095i	0.409415	−	0.297458i	−0.363950	−	0.931419i	$-0.618572\pi$
$509$	9.23683	−	6.71095i	0.409415	−	0.297458i	0.773365	+	0.633961i	$0.218572\pi$
$510$	−4.16140	−	3.02343i	−0.184270	−	0.133880i
$511$	−10.6694	−	32.8371i	−0.471987	−	1.45263i
$512$	2.95502	+	9.09462i	0.130595	+	0.401929i
$513$	−4.11080	−	2.98667i	−0.181496	−	0.131865i
$514$	−2.37461	+	1.72526i	−0.104740	+	0.0760978i
$515$	−2.43261	+	7.48681i	−0.107194	+	0.329908i
$516$	22.9202			1.00900
$517$	−15.1531	−	5.93913i	−0.666431	−	0.261203i
$518$	−11.6883			−0.513556
$519$	2.05416	−	6.32205i	0.0901676	−	0.277507i
$520$	1.12792	−	0.819479i	0.0494624	−	0.0359365i
$521$	18.2472	+	13.2573i	0.799423	+	0.580815i	0.910745	−	0.412970i	$-0.135509\pi$
$521$	18.2472	+	13.2573i	0.799423	+	0.580815i	−0.111322	+	0.993784i	$0.535509\pi$
$522$	3.46843	+	10.6747i	0.151809	+	0.467220i
$523$	2.26996	+	6.98622i	0.0992584	+	0.305486i	0.988340	−	0.152263i	$-0.0486559\pi$
$523$	2.26996	+	6.98622i	0.0992584	+	0.305486i	−0.889082	+	0.457749i	$0.848656\pi$
$524$	30.2074	+	21.9470i	1.31962	+	0.958758i
$525$	15.9207	−	11.5671i	0.694838	−	0.504829i
$526$	−2.30124	+	7.08250i	−0.100339	+	0.308812i
$527$	18.3225			0.798139
$528$	0.167785	−	2.82220i	0.00730191	−	0.122820i
$529$	43.9153			1.90936
$530$	5.17333	−	15.9219i	0.224715	−	0.691602i
$531$	−2.35967	+	1.71440i	−0.102401	+	0.0743985i
$532$	−52.9321	−	38.4574i	−2.29490	−	1.66734i
$533$	2.43243	+	7.48625i	0.105360	+	0.324265i
$534$	−5.30908	−	16.3397i	−0.229746	−	0.707086i
$535$	−6.69523	−	4.86437i	−0.289460	−	0.210305i
$536$	−22.2542	+	16.1686i	−0.961235	+	0.698378i
$537$	1.82280	−	5.60999i	0.0786595	−	0.242089i
$538$	−69.5552			−2.99874
$539$	23.1187	−	28.1428i	0.995792	−	1.21220i
$540$	1.81987			0.0783146
$541$	−6.62424	+	20.3873i	−0.284798	+	0.876520i	0.701661	+	0.712511i	$0.252442\pi$
$541$	−6.62424	+	20.3873i	−0.284798	+	0.876520i	−0.986459	+	0.164008i	$0.947558\pi$
$542$	−6.80805	+	4.94634i	−0.292431	+	0.212463i
$543$	−3.15329	−	2.29100i	−0.135321	−	0.0983163i
$544$	−7.75913	−	23.8801i	−0.332670	−	1.02385i
$545$	−2.74093	−	8.43571i	−0.117408	−	0.361346i
$546$	7.69902	+	5.59367i	0.329488	+	0.239387i
$547$	7.45122	−	5.41363i	0.318591	−	0.231470i	−0.416983	−	0.908914i	$-0.636913\pi$
$547$	7.45122	−	5.41363i	0.318591	−	0.231470i	0.735574	+	0.677444i	$0.236913\pi$
$548$	−2.68741	+	8.27099i	−0.114800	+	0.353319i
$549$	−5.50149			−0.234798
$550$	−21.9265	+	26.6915i	−0.934948	+	1.13813i
$551$	25.4128			1.08262
$552$	−5.88039	+	18.0980i	−0.250286	+	0.770301i
$553$	31.6949	−	23.0277i	1.34780	−	0.979237i
$554$	−32.8082	−	23.8366i	−1.39389	−	1.01272i
$555$	−0.227465	−	0.700066i	−0.00965536	−	0.0297161i
$556$	4.00444	+	12.3244i	0.169826	+	0.522670i
$557$	12.9805	+	9.43086i	0.550000	+	0.399598i	0.827785	−	0.561045i	$-0.189600\pi$
$557$	12.9805	+	9.43086i	0.550000	+	0.399598i	−0.277785	+	0.960643i	$0.589600\pi$
$558$	−8.69865	+	6.31994i	−0.368243	+	0.267544i
$559$	−2.33248	+	7.17864i	−0.0986534	+	0.303624i
$560$	−2.16634			−0.0915446
$561$	−0.752753	+	12.6616i	−0.0317813	+	0.534571i
$562$	−63.9450			−2.69736
$563$	−0.0154855	+	0.0476594i	−0.000652634	+	0.00200860i	−0.951382	−	0.308013i	$-0.900336\pi$
$563$	−0.0154855	+	0.0476594i	−0.000652634	+	0.00200860i	0.950730	+	0.310021i	$0.100336\pi$
$564$	12.0552	−	8.75862i	0.507616	−	0.368804i
$565$	0.922232	+	0.670041i	0.0387986	+	0.0281888i
$566$	−8.96660	−	27.5964i	−0.376894	−	1.15996i
$567$	1.31037	+	4.03290i	0.0550303	+	0.169366i
$568$	20.2451	+	14.7090i	0.849467	+	0.617174i
$569$	30.8769	−	22.4334i	1.29443	−	0.940455i	0.294541	−	0.955639i	$-0.404833\pi$
$569$	30.8769	−	22.4334i	1.29443	−	0.940455i	0.999885	+	0.0151835i	$0.00483324\pi$
$570$	2.11191	−	6.49980i	0.0884583	−	0.272247i
$571$	29.6803			1.24208			0.621041	−	0.783778i	$-0.286710\pi$
$571$	29.6803			1.24208			0.621041	+	0.783778i	$0.286710\pi$
$572$	−9.37663	−	3.67510i	−0.392057	−	0.153664i
$573$	−4.76541			−0.199078
$574$	−23.1483	+	71.2430i	−0.966189	+	2.97363i
$575$	−30.7125	+	22.3139i	−1.28080	+	0.930555i
$576$	10.5414	+	7.65874i	0.439223	+	0.319114i
$577$	−2.42142	−	7.45235i	−0.100805	−	0.310245i	0.887918	−	0.460002i	$-0.152151\pi$
$577$	−2.42142	−	7.45235i	−0.100805	−	0.310245i	−0.988723	+	0.149756i	$0.952151\pi$
$578$	−1.64666	−	5.06791i	−0.0684922	−	0.210797i
$579$	−15.3755	−	11.1709i	−0.638984	−	0.464249i
$580$	−7.36344	+	5.34985i	−0.305750	+	0.222140i
$581$	−0.226287	+	0.696441i	−0.00938798	+	0.0288932i
$582$	34.6086			1.43457
$583$	−39.9493	+	10.4043i	−1.65453	+	0.430901i
$584$	−18.9412			−0.783793
$585$	−0.185200	+	0.569986i	−0.00765707	+	0.0235660i
$586$	14.8962	−	10.8227i	0.615356	−	0.447083i
$587$	0.519697	+	0.377582i	0.0214502	+	0.0155845i	0.598459	−	0.801154i	$-0.295780\pi$
$587$	0.519697	+	0.377582i	0.0214502	+	0.0155845i	−0.577008	+	0.816738i	$0.695780\pi$
$588$	10.3043	+	31.7135i	0.424943	+	1.30784i
$589$	7.52278	+	23.1527i	0.309971	+	0.953991i
$590$	−3.17377	−	2.30588i	−0.130662	−	0.0949316i
$591$	−0.138863	+	0.100890i	−0.00571208	+	0.00415007i
$592$	0.323530	−	0.995723i	0.0132970	−	0.0409239i
$593$	−21.7316			−0.892410			−0.446205	−	0.894931i	$-0.647225\pi$
$593$	−21.7316			−0.892410			−0.446205	+	0.894931i	$0.647225\pi$
$594$	−4.00996	−	6.27076i	−0.164530	−	0.257292i
$595$	9.71910			0.398444
$596$	1.01176	−	3.11388i	0.0414433	−	0.127549i
$597$	−4.84098	+	3.51717i	−0.198128	+	0.143948i
$598$	−14.8521	−	10.7907i	−0.607347	−	0.441263i
$599$	12.4590	+	38.3449i	0.509062	+	1.56673i	0.793833	+	0.608136i	$0.208083\pi$
$599$	12.4590	+	38.3449i	0.509062	+	1.56673i	−0.284770	+	0.958596i	$0.591917\pi$
$600$	−3.33609	−	10.2674i	−0.136195	−	0.419166i
$601$	−30.4446	−	22.1193i	−1.24186	−	0.902264i	−0.244138	−	0.969740i	$-0.578505\pi$
$601$	−30.4446	−	22.1193i	−1.24186	−	0.902264i	−0.997721	+	0.0674768i	$0.978505\pi$
$602$	−58.1128	+	42.2214i	−2.36850	+	1.72082i
$603$	3.65406	−	11.2460i	0.148805	−	0.457974i
$604$	−55.7453			−2.26825
$605$	−6.54607	−	0.781114i	−0.266136	−	0.0317568i
$606$	−30.0526			−1.22080
$607$	5.80041	−	17.8518i	0.235431	−	0.724584i	−0.761632	−	0.648009i	$-0.775602\pi$
$607$	5.80041	−	17.8518i	0.235431	−	0.724584i	0.997064	−	0.0765742i	$-0.0243982\pi$
$608$	26.9898	−	19.6093i	1.09458	−	0.795261i
$609$	−17.1574	−	12.4656i	−0.695253	−	0.505131i
$610$	−2.28659	−	7.03739i	−0.0925811	−	0.284935i
$611$	1.51641	+	4.66704i	0.0613475	+	0.188808i
$612$	−9.39498	−	6.82586i	−0.379770	−	0.275919i
$613$	26.2215	−	19.0510i	1.05907	−	0.769463i	0.0851577	−	0.996367i	$-0.472861\pi$
$613$	26.2215	−	19.0510i	1.05907	−	0.769463i	0.973917	+	0.226905i	$0.0728606\pi$
$614$	12.0029	−	36.9412i	0.484399	−	1.49083i
$615$	−4.71754			−0.190230
$616$	−17.6256	−	27.5629i	−0.710157	−	1.11054i
$617$	5.26903			0.212123			0.106062	−	0.994360i	$-0.466176\pi$
$617$	5.26903			0.212123			0.106062	+	0.994360i	$0.466176\pi$
$618$	−9.10923	+	28.0353i	−0.366427	+	1.12775i
$619$	−6.18228	+	4.49169i	−0.248487	+	0.180536i	−0.705056	−	0.709152i	$-0.749078\pi$
$619$	−6.18228	+	4.49169i	−0.248487	+	0.180536i	0.456569	+	0.889688i	$0.349078\pi$
$620$	−7.05382	−	5.12490i	−0.283288	−	0.205821i
$621$	−2.52781	−	7.77981i	−0.101438	−	0.312193i
$622$	1.41496	+	4.35480i	0.0567347	+	0.174611i
$623$	26.2626	+	19.0809i	1.05219	+	0.764461i
$624$	−0.689628	+	0.501044i	−0.0276072	+	0.0200578i
$625$	6.10039	−	18.7751i	0.244015	−	0.751002i
$626$	−44.1278			−1.76370
$627$	−16.3085	+	4.24734i	−0.651300	+	0.169622i
$628$	24.6156			0.982270
$629$	−1.45149	+	4.46722i	−0.0578746	+	0.178120i
$630$	−4.61417	+	3.35239i	−0.183833	+	0.133563i
$631$	9.08933	+	6.60378i	0.361840	+	0.262892i	0.753819	−	0.657082i	$-0.228209\pi$
$631$	9.08933	+	6.60378i	0.361840	+	0.262892i	−0.391979	+	0.919974i	$0.628209\pi$
$632$	−6.64146	−	20.4403i	−0.264183	−	0.813072i
$633$	0.516510	+	1.58965i	0.0205294	+	0.0631831i
$634$	42.0865	+	30.5777i	1.67147	+	1.21439i
$635$	1.28687	−	0.934968i	0.0510680	−	0.0371031i
$636$	11.6796	−	35.9460i	0.463125	−	1.42535i
$637$	−10.9813			−0.435097
$638$	34.6589	+	13.5843i	1.37216	+	0.537808i
$639$	−10.7573			−0.425551
$640$	−2.98370	+	9.18289i	−0.117941	+	0.362986i
$641$	8.53926	−	6.20414i	0.337281	−	0.245049i	−0.406233	−	0.913770i	$-0.633158\pi$
$641$	8.53926	−	6.20414i	0.337281	−	0.245049i	0.743514	+	0.668721i	$0.233158\pi$
$642$	−25.0712	−	18.2153i	−0.989479	−	0.718899i
$643$	14.1562	+	43.5682i	0.558265	+	1.71816i	0.687162	+	0.726504i	$0.258856\pi$
$643$	14.1562	+	43.5682i	0.558265	+	1.71816i	−0.128897	+	0.991658i	$0.541144\pi$
$644$	−32.5490	−	100.176i	−1.28261	−	3.94747i
$645$	−3.65975	−	2.65896i	−0.144103	−	0.104697i
$646$	−35.2817	+	25.6337i	−1.38814	+	1.00854i
$647$	1.89127	−	5.82072i	0.0743534	−	0.228836i	−0.906972	−	0.421191i	$-0.861612\pi$
$647$	1.89127	−	5.82072i	0.0743534	−	0.228836i	0.981326	+	0.192354i	$0.0616123\pi$
$648$	2.32627			0.0913847
$649$	−0.574102	+	9.65657i	−0.0225355	+	0.379054i
$650$	10.4151			0.408512
$651$	6.27799	−	19.3217i	0.246054	−	0.757276i
$652$	−54.4833	+	39.5844i	−2.13373	+	1.55025i
$653$	−21.9373	−	15.9384i	−0.858472	−	0.623716i	0.0689968	−	0.997617i	$-0.478020\pi$
$653$	−21.9373	−	15.9384i	−0.858472	−	0.623716i	−0.927469	+	0.373900i	$0.878020\pi$
$654$	−10.2638	−	31.5886i	−0.401345	−	1.23521i
$655$	−2.27727	−	7.00872i	−0.0889803	−	0.273853i
$656$	−5.42841	−	3.94397i	−0.211944	−	0.153986i
$657$	6.58726	−	4.78592i	0.256993	−	0.186717i
$658$	−14.4310	+	44.4140i	−0.562578	+	1.73144i
$659$	−18.8115			−0.732794			−0.366397	−	0.930459i	$-0.619409\pi$
$659$	−18.8115			−0.732794			−0.366397	+	0.930459i	$0.619409\pi$
$660$	3.83131	−	4.66392i	0.149133	−	0.181543i
$661$	−41.9725			−1.63254			−0.816271	−	0.577669i	$-0.803962\pi$
$661$	−41.9725			−1.63254			−0.816271	+	0.577669i	$0.803962\pi$
$662$	−7.59607	+	23.3783i	−0.295230	+	0.908624i
$663$	3.09396	−	2.24789i	0.120159	−	0.0873009i
$664$	0.325001	+	0.236127i	0.0126125	+	0.00916352i
$665$	3.99044	+	12.2813i	0.154742	+	0.476248i
$666$	−0.851773	−	2.62149i	−0.0330055	−	0.101581i
$667$	33.0981	+	24.0472i	1.28156	+	0.931111i
$668$	−26.3750	+	19.1626i	−1.02048	+	0.741422i
$669$	2.59841	−	7.99708i	0.100460	−	0.309185i
$670$	15.9044			0.614442
$671$	−11.5821	+	14.0991i	−0.447122	+	0.544290i
$672$	−27.8410			−1.07399
$673$	−3.81478	+	11.7407i	−0.147049	+	0.452571i	−0.997269	−	0.0738574i	$-0.976469\pi$
$673$	−3.81478	+	11.7407i	−0.147049	+	0.452571i	0.850220	+	0.526428i	$0.176469\pi$
$674$	48.8693	−	35.5056i	1.88238	−	1.36763i
$675$	3.75450	+	2.72780i	0.144511	+	0.104993i
$676$	0.938348	+	2.88794i	0.0360903	+	0.111075i
$677$	11.1643	+	34.3603i	0.429080	+	1.32057i	0.899033	+	0.437881i	$0.144271\pi$
$677$	11.1643	+	34.3603i	0.429080	+	1.32057i	−0.469953	+	0.882691i	$0.655729\pi$
$678$	3.45342	+	2.50905i	0.132628	+	0.0963597i
$679$	−52.9037	+	38.4368i	−2.03026	+	1.47507i
$680$	1.64762	−	5.07087i	0.0631835	−	0.194459i
$681$	−10.2410			−0.392434
$682$	−2.11636	+	35.5979i	−0.0810397	+	1.36311i
$683$	−28.9368			−1.10724			−0.553618	−	0.832771i	$-0.686753\pi$
$683$	−28.9368			−1.10724			−0.553618	+	0.832771i	$0.686753\pi$
$684$	4.76796	−	14.6743i	0.182308	−	0.561085i
$685$	1.38863	−	1.00890i	0.0530567	−	0.0385479i
$686$	−30.6525	−	22.2703i	−1.17032	−	0.850285i
$687$	2.85560	+	8.78864i	0.108948	+	0.335308i
$688$	−1.98827	−	6.11927i	−0.0758021	−	0.233295i
$689$	10.0698	+	7.31614i	0.383629	+	0.278723i
$690$	8.90114	−	6.46706i	0.338861	−	0.246197i
$691$	10.4766	−	32.2436i	0.398548	−	1.22660i	−0.527616	−	0.849483i	$-0.676914\pi$
$691$	10.4766	−	32.2436i	0.398548	−	1.22660i	0.926164	−	0.377121i	$-0.123086\pi$
$692$	20.1852			0.767327
$693$	13.0941	+	5.13214i	0.497404	+	0.194954i
$694$	−18.5238			−0.703154
$695$	0.790347	−	2.43244i	0.0299796	−	0.0922676i
$696$	−9.41243	+	6.83853i	−0.356777	+	0.259214i
$697$	24.3541	+	17.6943i	0.922477	+	0.670219i
$698$	0.243377	+	0.749037i	0.00921194	+	0.0283515i
$699$	4.36333	+	13.4289i	0.165036	+	0.507929i
$700$	48.3443	+	35.1242i	1.82724	+	1.32757i
$701$	19.2252	−	13.9679i	0.726126	−	0.527561i	−0.162210	−	0.986756i	$-0.551862\pi$
$701$	19.2252	−	13.9679i	0.726126	−	0.527561i	0.888335	+	0.459195i	$0.151862\pi$
$702$	−0.693505	+	2.13439i	−0.0261746	+	0.0805573i
$703$	−6.24084			−0.235378
$704$	41.8200	−	10.8915i	1.57615	−	0.410488i
$705$	−2.94099			−0.110764
$706$	−7.76598	+	23.9012i	−0.292277	+	0.899535i
$707$	45.9392	−	33.3768i	1.72772	−	1.25526i
$708$	−7.16526	−	5.20587i	−0.269287	−	0.195649i
$709$	−6.80532	−	20.9446i	−0.255579	−	0.786592i	−0.993715	−	0.111940i	$-0.964294\pi$
$709$	−6.80532	−	20.9446i	−0.255579	−	0.786592i	0.738136	−	0.674652i	$-0.235706\pi$
$710$	−4.47105	−	13.7605i	−0.167796	−	0.516422i
$711$	7.47443	+	5.43049i	0.280313	+	0.203659i
$712$	14.4075	−	10.4677i	0.539943	−	0.392292i
$713$	−12.1108	+	37.2732i	−0.453552	+	1.39589i
$714$	36.3944			1.36203
$715$	1.07086	+	1.67460i	0.0400477	+	0.0626265i
$716$	17.9117			0.669393
$717$	2.27225	−	6.99326i	0.0848586	−	0.261168i
$718$	−17.8269	+	12.9520i	−0.665296	+	0.483365i
$719$	0.321522	+	0.233599i	0.0119907	+	0.00871179i	0.593764	−	0.804639i	$-0.297641\pi$
$719$	0.321522	+	0.233599i	0.0119907	+	0.00871179i	−0.581774	+	0.813351i	$0.697641\pi$
$720$	−0.157869	−	0.485872i	−0.00588345	−	0.0181074i
$721$	−17.2118	−	52.9724i	−0.641001	−	1.97280i
$722$	−12.3805	−	8.99495i	−0.460754	−	0.334758i
$723$	10.8430	−	7.87792i	0.403256	−	0.292983i
$724$	3.65739	−	11.2563i	0.135926	−	0.418336i
$725$	−23.2101			−0.862002
$726$	−24.5126	−	2.92498i	−0.909748	−	0.108556i
$727$	−29.7153			−1.10208			−0.551040	−	0.834479i	$-0.685769\pi$
$727$	−29.7153			−1.10208			−0.551040	+	0.834479i	$0.685769\pi$
$728$	−3.04828	+	9.38163i	−0.112977	+	0.347706i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	8.85992	+	6.43711i	0.327920	+	0.238248i
$731$	8.92021	+	27.4536i	0.329926	+	1.01541i
$732$	−5.16231	−	15.8880i	−0.190804	−	0.587236i
$733$	−8.33865	−	6.05839i	−0.307995	−	0.223772i	0.423041	−	0.906111i	$-0.360963\pi$
$733$	−8.33865	−	6.05839i	−0.307995	−	0.223772i	−0.731036	+	0.682339i	$0.760963\pi$
$734$	40.6707	−	29.5490i	1.50118	−	1.09067i
$735$	2.03374	−	6.25922i	0.0750157	−	0.230875i
$736$	53.7077			1.97969
$737$	−21.1284	−	33.0405i	−0.778274	−	1.21706i
$738$	−17.6655			−0.650274
$739$	−4.36216	+	13.4253i	−0.160465	+	0.493859i	−0.998674	−	0.0514901i	$-0.983603\pi$
$739$	−4.36216	+	13.4253i	−0.160465	+	0.493859i	0.838209	+	0.545349i	$0.183603\pi$
$740$	1.80831	−	1.31381i	0.0664747	−	0.0482967i
$741$	4.11080	+	2.98667i	0.151014	+	0.109718i
$742$	36.6036	+	112.654i	1.34376	+	4.13567i
$743$	4.56810	+	14.0592i	0.167587	+	0.515781i	0.999218	−	0.0395486i	$-0.0125920\pi$
$743$	4.56810	+	14.0592i	0.167587	+	0.515781i	−0.831630	+	0.555330i	$0.812592\pi$
$744$	−9.01666	−	6.55099i	−0.330567	−	0.240171i
$745$	−0.522792	+	0.379831i	−0.0191536	+	0.0139159i
$746$	−16.7122	+	51.4348i	−0.611876	+	1.88316i
$747$	−0.172690			−0.00631839
$748$	−37.2721	+	9.70704i	−1.36280	+	0.354925i
$749$	58.5546			2.13954
$750$	−4.00702	+	12.3323i	−0.146316	+	0.450313i
$751$	5.04309	−	3.66402i	0.184025	−	0.133702i	−0.491959	−	0.870619i	$-0.663719\pi$
$751$	5.04309	−	3.66402i	0.184025	−	0.133702i	0.675984	+	0.736916i	$0.263719\pi$
$752$	−3.38416	−	2.45873i	−0.123407	−	0.0896608i
$753$	−7.32019	−	22.5292i	−0.266763	−	0.821011i
$754$	−3.46843	−	10.6747i	−0.126313	−	0.388750i
$755$	8.90108	+	6.46701i	0.323943	+	0.235359i
$756$	−10.4172	+	7.56853i	−0.378869	+	0.275265i
$757$	−7.34316	+	22.5999i	−0.266892	+	0.821408i	0.724360	+	0.689422i	$0.242135\pi$
$757$	−7.34316	+	22.5999i	−0.266892	+	0.821408i	−0.991252	+	0.131986i	$0.957865\pi$
$758$	56.0772			2.03682
$759$	−25.2597	−	9.90035i	−0.916868	−	0.359360i
$760$	7.08415			0.256969
$761$	10.3164	−	31.7506i	0.373969	−	1.15096i	−0.570202	−	0.821504i	$-0.693135\pi$
$761$	10.3164	−	31.7506i	0.373969	−	1.15096i	0.944171	−	0.329455i	$-0.106865\pi$
$762$	4.81886	−	3.50111i	0.174569	−	0.126832i
$763$	50.7722	+	36.8882i	1.83808	+	1.33544i
$764$	−4.47162	−	13.7622i	−0.161777	−	0.497900i
$765$	0.708267	+	2.17982i	0.0256075	+	0.0788117i
$766$	−45.6437	−	33.1621i	−1.64917	−	1.19820i
$767$	2.35967	−	1.71440i	0.0852026	−	0.0619033i
$768$	−3.11998	+	9.60232i	−0.112583	+	0.346494i
$769$	2.35864			0.0850549			0.0425274	−	0.999095i	$-0.486459\pi$
$769$	2.35864			0.0850549			0.0425274	+	0.999095i	$0.486459\pi$
$770$	−1.12262	+	18.8828i	−0.0404564	+	0.680489i
$771$	1.30788			0.0471021
$772$	17.8335	−	54.8857i	0.641840	−	1.97538i
$773$	−31.1481	+	22.6304i	−1.12032	+	0.813959i	−0.984257	−	0.176741i	$-0.943444\pi$
$773$	−31.1481	+	22.6304i	−1.12032	+	0.813959i	−0.136061	+	0.990700i	$0.543444\pi$
$774$	−13.7044	−	9.95684i	−0.492595	−	0.357891i
$775$	−6.87074	−	21.1460i	−0.246804	−	0.759586i
$776$	11.0856	+	34.1181i	0.397951	+	1.22477i
$777$	4.21350	+	3.06129i	0.151159	+	0.109823i
$778$	24.4266	−	17.7470i	0.875737	−	0.636260i
$779$	−12.3597	+	38.0393i	−0.442833	+	1.36290i
$780$	−1.81987			−0.0651617
$781$	−22.6469	+	27.5685i	−0.810371	+	0.986480i
$782$	−70.2080			−2.51063
$783$	1.54549	−	4.75652i	0.0552312	−	0.169984i
$784$	7.57305	−	5.50214i	0.270466	−	0.196505i
$785$	−3.93047	−	2.85566i	−0.140285	−	0.101923i
$786$	−8.52753	−	26.2451i	−0.304167	−	0.936130i
$787$	11.2307	+	34.5647i	0.400333	+	1.23210i	0.924730	+	0.380623i	$0.124291\pi$
$787$	11.2307	+	34.5647i	0.400333	+	1.23210i	−0.524398	+	0.851474i	$0.675709\pi$
$788$	−0.421667	−	0.306359i	−0.0150213	−	0.0109136i
$789$	2.68455	−	1.95044i	0.0955724	−	0.0694374i
$790$	−3.83997	+	11.8182i	−0.136620	+	0.420473i
$791$	−8.06558			−0.286779
$792$	4.89743	−	5.96173i	0.174023	−	0.211841i
$793$	5.50149			0.195364
$794$	18.5539	−	57.1030i	0.658453	−	2.02651i
$795$	−6.03502	+	4.38470i	−0.214040	+	0.155509i
$796$	−14.6999	−	10.6801i	−0.521024	−	0.378546i
$797$	1.31660	+	4.05207i	0.0466362	+	0.143532i	0.971663	−	0.236370i	$-0.0759578\pi$
$797$	1.31660	+	4.05207i	0.0466362	+	0.143532i	−0.925027	+	0.379902i	$0.875958\pi$
$798$	14.9427	+	45.9889i	0.528966	+	1.62799i
$799$	15.1827	+	11.0309i	0.537126	+	0.390245i
$800$	−24.6505	+	17.9096i	−0.871527	+	0.633201i
$801$	−2.36566	+	7.28075i	−0.0835864	+	0.257253i
$802$	59.3189			2.09462
$803$	1.60267	−	26.9573i	0.0565568	−	0.951304i
$804$	35.9067			1.26633
$805$	−6.42413	+	19.7714i	−0.226421	+	0.696852i
$806$	8.69865	−	6.31994i	0.306397	−	0.222610i
$807$	25.0738	+	18.2172i	0.882640	+	0.641276i
$808$	−9.62628	−	29.6266i	−0.338651	−	1.04226i
$809$	−7.74546	−	23.8381i	−0.272316	−	0.838102i	−0.989917	−	0.141648i	$-0.954760\pi$
$809$	−7.74546	−	23.8381i	−0.272316	−	0.838102i	0.717601	−	0.696454i	$-0.245240\pi$
$810$	−1.08813	−	0.790576i	−0.0382332	−	0.0277780i
$811$	18.3854	−	13.3578i	0.645599	−	0.469055i	−0.216170	−	0.976356i	$-0.569357\pi$
$811$	18.3854	−	13.3578i	0.645599	−	0.469055i	0.861769	+	0.507300i	$0.169357\pi$
$812$	19.9002	−	61.2466i	0.698361	−	2.14934i
$813$	3.74972			0.131508
$814$	−8.51151	−	3.33602i	−0.298328	−	0.116928i
$815$	13.2917			0.465590
$816$	−1.00739	+	3.10042i	−0.0352656	+	0.108536i
$817$	−31.0286	+	22.5436i	−1.08555	+	0.788701i
$818$	3.43835	+	2.49811i	0.120219	+	0.0873443i
$819$	−1.31037	−	4.03290i	−0.0457880	−	0.140921i
$820$	−4.42670	−	13.6240i	−0.154587	−	0.475770i
$821$	28.3305	+	20.5833i	0.988740	+	0.718362i	0.959645	−	0.281215i	$-0.0907373\pi$
$821$	28.3305	+	20.5833i	0.988740	+	0.718362i	0.0290955	+	0.999577i	$0.490737\pi$
$822$	5.19989	−	3.77794i	0.181367	−	0.131771i
$823$	1.01098	−	3.11147i	0.0352405	−	0.108459i	−0.931889	−	0.362744i	$-0.881840\pi$
$823$	1.01098	−	3.11147i	0.0352405	−	0.108459i	0.967129	+	0.254285i	$0.0818400\pi$
$824$	−30.5558			−1.06446
$825$	14.8950	−	3.87921i	0.518577	−	0.135057i
$826$	27.7569			0.965786
$827$	−5.93074	+	18.2530i	−0.206232	+	0.634717i	0.793428	+	0.608664i	$0.208294\pi$
$827$	−5.93074	+	18.2530i	−0.206232	+	0.634717i	−0.999661	+	0.0260538i	$0.991706\pi$
$828$	20.0957	−	14.6003i	0.698372	−	0.507397i
$829$	6.15147	+	4.46931i	0.213649	+	0.155225i	0.689463	−	0.724321i	$-0.257846\pi$
$829$	6.15147	+	4.46931i	0.213649	+	0.155225i	−0.475814	+	0.879546i	$0.657846\pi$
$830$	−0.0717752	−	0.220901i	−0.00249135	−	0.00766759i
$831$	5.58394	+	17.1856i	0.193705	+	0.596161i
$832$	−10.5414	−	7.65874i	−0.365456	−	0.265519i
$833$	−33.9758	+	24.6849i	−1.17719	+	0.855280i
$834$	2.95956	−	9.10858i	0.102481	−	0.315404i
$835$	6.43445			0.222673
$836$	−27.5691	−	43.1125i	−0.953498	−	1.49108i
$837$	4.79101			0.165602
$838$	14.2394	−	43.8245i	0.491893	−	1.51389i
$839$	34.5144	−	25.0762i	1.19157	−	0.865725i	0.198139	−	0.980174i	$-0.436510\pi$
$839$	34.5144	−	25.0762i	1.19157	−	0.865725i	0.993429	+	0.114449i	$0.0365101\pi$
$840$	−4.78286	−	3.47495i	−0.165024	−	0.119897i
$841$	−1.23205	−	3.79185i	−0.0424843	−	0.130753i
$842$	12.5147	+	38.5163i	0.431285	+	1.32736i
$843$	23.0514	+	16.7478i	0.793932	+	0.576825i
$844$	−4.10616	+	2.98330i	−0.141340	+	0.102689i
$845$	0.185200	−	0.569986i	0.00637107	−	0.0196081i
$846$	−11.0129			−0.378632
$847$	40.7192	−	22.7528i	1.39913	−	0.781796i
$848$	−10.6101			−0.364353
$849$	−3.99540	+	12.2966i	−0.137122	+	0.422018i
$850$	32.2237	−	23.4119i	1.10526	−	0.803022i
$851$	−8.12821	−	5.90549i	−0.278631	−	0.202438i
$852$	−10.0941	−	31.0663i	−0.345817	−	1.06432i
$853$	10.3137	+	31.7422i	0.353133	+	1.08683i	0.957084	+	0.289811i	$0.0935925\pi$
$853$	10.3137	+	31.7422i	0.353133	+	1.08683i	−0.603950	+	0.797022i	$0.706408\pi$
$854$	42.3561	+	30.7735i	1.44940	+	1.05305i
$855$	−2.46368	+	1.78997i	−0.0842561	+	0.0612157i
$856$	9.92643	−	30.5504i	0.339278	−	1.04419i
$857$	−29.0218			−0.991364			−0.495682	−	0.868504i	$-0.665082\pi$
$857$	−29.0218			−0.991364			−0.495682	+	0.868504i	$0.665082\pi$
$858$	4.00996	+	6.27076i	0.136898	+	0.214080i
$859$	44.8776			1.53120			0.765601	−	0.643315i	$-0.222441\pi$
$859$	44.8776			1.53120			0.765601	+	0.643315i	$0.222441\pi$
$860$	4.24481	−	13.0642i	0.144747	−	0.445485i
$861$	27.0039	−	19.6195i	0.920291	−	0.668630i
$862$	−46.6032	−	33.8592i	−1.58731	−	1.15325i
$863$	−6.81152	−	20.9637i	−0.231867	−	0.713613i	−0.997522	−	0.0703611i	$-0.977585\pi$
$863$	−6.81152	−	20.9637i	−0.231867	−	0.713613i	0.765655	−	0.643252i	$-0.222415\pi$
$864$	−2.02888	−	6.24425i	−0.0690239	−	0.212434i
$865$	−3.22305	−	2.34168i	−0.109587	−	0.0796197i
$866$	−21.4532	+	15.5867i	−0.729009	+	0.529656i
$867$	−0.733733	+	2.25820i	−0.0249189	+	0.0766924i
$868$	61.6907			2.09392
$869$	29.6528	−	7.72269i	1.00590	−	0.261974i
$870$	6.72679			0.228060
$871$	−3.65406	+	11.2460i	−0.123813	+	0.381058i
$872$	27.8532	−	20.2366i	0.943230	−	0.685297i
$873$	−12.4760	−	9.06433i	−0.422248	−	0.306781i
$874$	−28.8258	−	88.7166i	−0.975046	−	3.00088i
$875$	−7.57121	−	23.3018i	−0.255954	−	0.787744i
$876$	20.0026	+	14.5327i	0.675825	+	0.491016i
$877$	−5.49048	+	3.98906i	−0.185400	+	0.134701i	−0.676614	−	0.736338i	$-0.736553\pi$
$877$	−5.49048	+	3.98906i	−0.185400	+	0.134701i	0.491214	+	0.871039i	$0.336553\pi$
$878$	−20.8582	+	64.1948i	−0.703929	+	2.16647i
$879$	−8.20448			−0.276730
$880$	−1.57754	−	0.618306i	−0.0531789	−	0.0208431i
$881$	7.88187			0.265547			0.132773	−	0.991146i	$-0.457612\pi$
$881$	7.88187			0.265547			0.132773	+	0.991146i	$0.457612\pi$
$882$	7.61561	−	23.4384i	0.256431	−	0.789214i
$883$	−19.5818	+	14.2270i	−0.658981	+	0.478778i	−0.866319	−	0.499492i	$-0.833520\pi$
$883$	−19.5818	+	14.2270i	−0.658981	+	0.478778i	0.207337	+	0.978269i	$0.433520\pi$
$884$	9.39498	+	6.82586i	0.315988	+	0.229578i
$885$	0.540174	+	1.66248i	0.0181577	+	0.0558838i
$886$	11.1708	+	34.3803i	0.375292	+	1.15503i
$887$	−18.2306	−	13.2453i	−0.612123	−	0.444734i	0.238038	−	0.971256i	$-0.423496\pi$
$887$	−18.2306	−	13.2453i	−0.612123	−	0.444734i	−0.850161	+	0.526522i	$0.823496\pi$
$888$	2.31150	−	1.67940i	0.0775687	−	0.0563570i
$889$	−3.47787	+	10.7038i	−0.116644	+	0.358993i
$890$	−10.2966			−0.345144
$891$	−0.196832	+	3.31078i	−0.00659412	+	0.110915i
$892$	25.5333			0.854918
$893$	−7.70524	+	23.7143i	−0.257846	+	0.793569i
$894$	−1.95766	+	1.42233i	−0.0654740	+	0.0475697i
$895$	−2.86004	−	2.07794i	−0.0956005	−	0.0694578i
$896$	−21.1110	−	64.9729i	−0.705268	−	2.17059i
$897$	2.52781	+	7.77981i	0.0844013	+	0.259760i
$898$	−46.0145	−	33.4315i	−1.53552	−	1.11562i
$899$	−19.3851	+	14.0841i	−0.646529	+	0.469731i
$900$	−4.35470	+	13.4024i	−0.145157	+	0.446747i
$901$	47.6014			1.58583
$902$	−37.1905	+	45.2727i	−1.23831	+	1.50742i
$903$	32.0071			1.06513
$904$	−1.36731	+	4.20816i	−0.0454761	+	0.139961i
$905$	−1.88983	+	1.37304i	−0.0628201	+	0.0456414i
$906$	33.3312	+	24.2166i	1.10736	+	0.804542i
$907$	4.42947	+	13.6325i	0.147078	+	0.452660i	0.997272	−	0.0738093i	$-0.0235156\pi$
$907$	4.42947	+	13.6325i	0.147078	+	0.452660i	−0.850194	+	0.526469i	$0.823516\pi$
$908$	−9.60958	−	29.5753i	−0.318905	−	0.981489i
$909$	10.8336	+	7.87107i	0.359328	+	0.261067i
$910$	4.61417	−	3.35239i	0.152958	−	0.111131i
$911$	15.3408	−	47.2141i	0.508263	−	1.56427i	−0.286952	−	0.957945i	$-0.592642\pi$
$911$	15.3408	−	47.2141i	0.508263	−	1.56427i	0.795215	−	0.606327i	$-0.207358\pi$
$912$	−4.33138			−0.143426
$913$	−0.363558	+	0.442566i	−0.0120320	+	0.0146468i
$914$	48.5934			1.60733
$915$	−1.01887	+	3.13577i	−0.0336829	+	0.103665i
$916$	−22.7015	+	16.4936i	−0.750079	+	0.544964i
$917$	42.1835	+	30.6481i	1.39302	+	1.01209i
$918$	2.65220	+	8.16263i	0.0875356	+	0.269407i
$919$	−15.1864	−	46.7389i	−0.500953	−	1.54177i	−0.807470	−	0.589908i	$-0.799164\pi$
$919$	−15.1864	−	46.7389i	−0.500953	−	1.54177i	0.306518	−	0.951865i	$-0.400836\pi$
$920$	9.22655	+	6.70348i	0.304190	+	0.221007i
$921$	−14.0022	+	10.1732i	−0.461387	+	0.335218i
$922$	18.7138	−	57.5951i	0.616305	−	1.89679i
$923$	10.7573			0.354080
$924$	−2.53448	+	42.6308i	−0.0833783	+	1.40245i
$925$	5.69992			0.187412
$926$	−11.0801	+	34.1011i	−0.364115	+	1.12063i
$927$	10.6265	−	7.72060i	0.349020	−	0.253578i
$928$	26.5653	+	19.3008i	0.872048	+	0.633580i
$929$	17.2604	+	53.1222i	0.566297	+	1.74288i	0.664066	+	0.747674i	$0.268829\pi$
$929$	17.2604	+	53.1222i	0.566297	+	1.74288i	−0.0977693	+	0.995209i	$0.531171\pi$
$930$	1.99129	+	6.12856i	0.0652970	+	0.200963i
$931$	−45.1421	−	32.7977i	−1.47947	−	1.07490i
$932$	−34.6877	+	25.2021i	−1.13623	+	0.825521i
$933$	0.630488	−	1.94044i	0.0206412	−	0.0635272i
$934$	−38.0889			−1.24631
$935$	7.07750	+	2.77398i	0.231459	+	0.0907187i
$936$	−2.32627			−0.0760367
$937$	13.8996	−	42.7787i	0.454081	−	1.39752i	−0.418129	−	0.908388i	$-0.637314\pi$
$937$	13.8996	−	42.7787i	0.454081	−	1.39752i	0.872210	−	0.489131i	$-0.162686\pi$
$938$	−91.0394	+	66.1440i	−2.97254	+	2.15968i
$939$	15.9075	+	11.5575i	0.519123	+	0.377165i
$940$	−2.75967	−	8.49340i	−0.0900106	−	0.277024i
$941$	−7.76613	−	23.9017i	−0.253168	−	0.779172i	−0.994185	−	0.107686i	$-0.965656\pi$
$941$	−7.76613	−	23.9017i	−0.253168	−	0.779172i	0.741017	−	0.671487i	$-0.234344\pi$
$942$	−14.7182	−	10.6934i	−0.479544	−	0.348409i
$943$	−52.0929	+	37.8477i	−1.69638	+	1.23249i
$944$	−0.768303	+	2.36459i	−0.0250061	+	0.0769610i
$945$	2.54138			0.0826710
$946$	−54.3687	+	14.1596i	−1.76768	+	0.460368i
$947$	−7.31392			−0.237670			−0.118835	−	0.992914i	$-0.537916\pi$
$947$	−7.31392			−0.237670			−0.118835	+	0.992914i	$0.537916\pi$
$948$	−8.66931	+	26.6814i	−0.281566	+	0.866571i
$949$	−6.58726	+	4.78592i	−0.213831	+	0.155358i
$950$	42.8142	+	31.1063i	1.38908	+	1.00922i
$951$	−7.16310	−	22.0457i	−0.232279	−	0.714882i
$952$	11.6577	+	35.8786i	0.377827	+	1.16283i
$953$	6.54135	+	4.75257i	0.211895	+	0.153951i	0.688671	−	0.725074i	$-0.258195\pi$
$953$	6.54135	+	4.75257i	0.211895	+	0.153951i	−0.476776	+	0.879025i	$0.658195\pi$
$954$	−22.5989	+	16.4191i	−0.731667	+	0.531587i
$955$	−0.882554	+	2.71622i	−0.0285588	+	0.0878948i
$956$	22.3283			0.722147
$957$	−8.93626	−	13.9745i	−0.288868	−	0.451731i
$958$	−59.1974			−1.91258
$959$	−3.75287	+	11.5501i	−0.121186	+	0.372973i
$960$	6.31763	−	4.59003i	0.203901	−	0.148143i
$961$	6.50954	+	4.72946i	0.209985	+	0.152563i
$962$	0.851773	+	2.62149i	0.0274623	+	0.0845201i
$963$	4.26709	+	13.1328i	0.137505	+	0.423197i
$964$	32.9255	+	23.9218i	1.06046	+	0.770468i
$965$	−9.21483	+	6.69496i	−0.296636	+	0.215518i
$966$	−24.0560	+	74.0367i	−0.773989	+	2.38209i
$967$	3.65884			0.117660			0.0588302	−	0.998268i	$-0.481263\pi$
$967$	3.65884			0.117660			0.0588302	+	0.998268i	$0.481263\pi$
$968$	−4.96822	−	25.1021i	−0.159685	−	0.806812i
$969$	19.4324			0.624257
$970$	6.40950	−	19.7264i	0.205797	−	0.633377i
$971$	43.7907	−	31.8158i	1.40531	−	1.02102i	0.411327	−	0.911488i	$-0.365065\pi$
$971$	43.7907	−	31.8158i	1.40531	−	1.02102i	0.993983	−	0.109530i	$-0.0349346\pi$
$972$	−2.45663	−	1.78484i	−0.0787964	−	0.0572489i
$973$	5.59205	+	17.2105i	0.179273	+	0.551745i
$974$	−23.5157	−	72.3738i	−0.753491	−	2.31901i
$975$	−3.75450	−	2.72780i	−0.120240	−	0.0873596i
$976$	−3.79398	+	2.75649i	−0.121442	+	0.0882331i
$977$	6.17255	−	18.9972i	0.197477	−	0.607773i	−0.802461	−	0.596704i	$-0.796477\pi$
$977$	6.17255	−	18.9972i	0.197477	−	0.607773i	0.999939	−	0.0110689i	$-0.00352341\pi$
$978$	49.7727			1.59155
$979$	13.6786	+	21.3906i	0.437171	+	0.683646i
$980$	19.9846			0.638385
$981$	−4.57340	+	14.0755i	−0.146018	+	0.449396i
$982$	32.9746	−	23.9575i	1.05226	−	0.764514i
$983$	25.3402	+	18.4107i	0.808227	+	0.587211i	0.913316	−	0.407252i	$-0.133513\pi$
$983$	25.3402	+	18.4107i	0.808227	+	0.587211i	−0.105089	+	0.994463i	$0.533513\pi$
$984$	−5.65850	−	17.4151i	−0.180386	−	0.555172i
$985$	0.0317886	+	0.0978351i	0.00101287	+	0.00311729i
$986$	−34.7268	−	25.2305i	−1.10593	−	0.803502i
$987$	16.8346	−	12.2311i	0.535853	−	0.389320i
$988$	−4.76796	+	14.6743i	−0.151689	+	0.466851i
$989$	−61.7445			−1.96336
$990$	−4.31689	+	1.12428i	−0.137200	+	0.0357319i
$991$	23.9408			0.760504			0.380252	−	0.924883i	$-0.375837\pi$
$991$	23.9408			0.760504			0.380252	+	0.924883i	$0.375837\pi$
$992$	−9.72038	+	29.9163i	−0.308622	+	0.949842i
$993$	8.86130	−	6.43811i	0.281205	−	0.204307i
$994$	82.8205	+	60.1726i	2.62691	+	1.90856i
$995$	1.10819	+	3.41067i	0.0351321	+	0.108126i
$996$	−0.162043	−	0.498718i	−0.00513454	−	0.0158025i
$997$	27.6393	+	20.0812i	0.875347	+	0.635976i	0.932016	−	0.362417i	$-0.118048\pi$
$997$	27.6393	+	20.0812i	0.875347	+	0.635976i	−0.0566697	+	0.998393i	$0.518048\pi$
$998$	−26.2956	+	19.1049i	−0.832373	+	0.604754i
$999$	−0.379539	+	1.16810i	−0.0120081	+	0.0369571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.d.196.8	✓	36
11.4	even	5		4719.2.a.bq.1.16		18
11.5	even	5	inner	429.2.n.d.313.8	yes	36
11.7	odd	10		4719.2.a.br.1.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.196.8	✓	36	1.1	even	1	trivial
429.2.n.d.313.8	yes	36	11.5	even	5	inner
4719.2.a.bq.1.16		18	11.4	even	5
4719.2.a.br.1.3		18	11.7	odd	10

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.693505 - 2.13439i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.45663 - 1.78484i) q^{4} +(0.185200 + 0.569986i) q^{5} +(0.693505 + 2.13439i) q^{6} +(-3.43059 - 2.49247i) q^{7} +(-1.88200 + 1.36735i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.693505 - 2.13439i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.45663 - 1.78484i) q^{4} +(0.185200 + 0.569986i) q^{5} +(0.693505 + 2.13439i) q^{6} +(-3.43059 - 2.49247i) q^{7} +(-1.88200 + 1.36735i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.34501 q^{10} +(-1.78679 - 2.79417i) q^{11} +3.03656 q^{12} +(-0.309017 + 0.951057i) q^{13} +(-7.69902 + 5.59367i) q^{14} +(-0.484859 - 0.352271i) q^{15} +(-0.263415 - 0.810707i) q^{16} +(1.18179 + 3.63717i) q^{17} +(-1.81562 - 1.31912i) q^{18} +(-4.11080 + 2.98667i) q^{19} +(0.562370 - 1.73080i) q^{20} +4.24044 q^{21} +(-7.20299 + 1.87592i) q^{22} -8.18018 q^{23} +(0.718858 - 2.21242i) q^{24} +(3.75450 - 2.72780i) q^{25} +(1.81562 + 1.31912i) q^{26} +(0.309017 + 0.951057i) q^{27} +(3.97901 + 12.2461i) q^{28} +(-4.04614 - 2.93969i) q^{29} +(-1.08813 + 0.790576i) q^{30} +(1.48050 - 4.55652i) q^{31} -6.56559 q^{32} +(3.08791 + 1.21029i) q^{33} +8.58270 q^{34} +(0.785329 - 2.41699i) q^{35} +(-2.45663 + 1.78484i) q^{36} +(0.993647 + 0.721927i) q^{37} +(3.52386 + 10.8453i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-1.12792 - 0.819479i) q^{40} +(6.36818 - 4.62675i) q^{41} +(2.94077 - 9.05075i) q^{42} +7.54807 q^{43} +(-0.597692 + 10.0534i) q^{44} +0.599319 q^{45} +(-5.67299 + 17.4597i) q^{46} +(3.97002 - 2.88439i) q^{47} +(0.689628 + 0.501044i) q^{48} +(3.39342 + 10.4439i) q^{49} +(-3.21843 - 9.90530i) q^{50} +(-3.09396 - 2.24789i) q^{51} +(2.45663 - 1.78484i) q^{52} +(3.84632 - 11.8378i) q^{53} +2.24423 q^{54} +(1.26173 - 1.53592i) q^{55} +9.86443 q^{56} +(1.57019 - 4.83254i) q^{57} +(-9.08046 + 6.59734i) q^{58} +(-2.35967 - 1.71440i) q^{59} +(0.562370 + 1.73080i) q^{60} +(-1.70005 - 5.23222i) q^{61} +(-8.69865 - 6.31994i) q^{62} +(-3.43059 + 2.49247i) q^{63} +(-4.02644 + 12.3921i) q^{64} -0.599319 q^{65} +(4.72470 - 5.75147i) q^{66} +11.8248 q^{67} +(3.58856 - 11.0445i) q^{68} +(6.61790 - 4.80819i) q^{69} +(-4.61417 - 3.35239i) q^{70} +(-3.32418 - 10.2308i) q^{71} +(0.718858 + 2.21242i) q^{72} +(6.58726 + 4.78592i) q^{73} +(2.22997 - 1.62017i) q^{74} +(-1.43409 + 4.41368i) q^{75} +15.4295 q^{76} +(-0.834655 + 14.0392i) q^{77} -2.24423 q^{78} +(-2.85498 + 8.78672i) q^{79} +(0.413307 - 0.300285i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-5.45892 - 16.8008i) q^{82} +(-0.0533641 - 0.164238i) q^{83} +(-10.4172 - 7.56853i) q^{84} +(-1.85427 + 1.34720i) q^{85} +(5.23462 - 16.1105i) q^{86} +5.00130 q^{87} +(7.18333 + 2.81546i) q^{88} -7.65543 q^{89} +(0.415631 - 1.27918i) q^{90} +(3.43059 - 2.49247i) q^{91} +(20.0957 + 14.6003i) q^{92} +(1.48050 + 4.55652i) q^{93} +(-3.40318 - 10.4739i) q^{94} +(-2.46368 - 1.78997i) q^{95} +(5.31167 - 3.85916i) q^{96} +(4.76540 - 14.6664i) q^{97} +24.6446 q^{98} +(-3.20956 + 0.835888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Introduction

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