LMFDB - Embedded newform 574.2.s.b.387.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(37,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 24]))

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

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

chi := DirichletCharacter("574.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.s (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			387.2
Character	$\chi$	$=$	574.387
Dual form			574.2.s.b.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 - 0.207912i) q^{2} +(-1.44848 - 2.50885i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.127997 - 1.21781i) q^{5} +(0.895212 + 2.75518i) q^{6} +(2.11882 + 1.58449i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.69620 + 4.66996i) q^{9} +O(q^{10})$	\(q+(-0.978148 - 0.207912i) q^{2} +(-1.44848 - 2.50885i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.127997 - 1.21781i) q^{5} +(0.895212 + 2.75518i) q^{6} +(2.11882 + 1.58449i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.69620 + 4.66996i) q^{9} +(-0.127997 + 1.21781i) q^{10} +(0.615794 - 5.85889i) q^{11} +(-0.302815 - 2.88110i) q^{12} +(-1.06245 - 3.26989i) q^{13} +(-1.74308 - 1.99039i) q^{14} +(-2.86989 + 2.08509i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.000302340 + 0.00287657i) q^{17} +(3.60823 - 4.00734i) q^{18} +(-2.38171 - 2.64516i) q^{19} +(0.378395 - 1.16458i) q^{20} +(0.906170 - 7.61089i) q^{21} +(-1.82047 + 5.60283i) q^{22} +(-2.83548 - 0.602700i) q^{23} +(-0.302815 + 2.88110i) q^{24} +(3.42407 - 0.727809i) q^{25} +(0.359386 + 3.41933i) q^{26} +6.93073 q^{27} +(1.29117 + 2.30930i) q^{28} +(-3.71025 + 2.69566i) q^{29} +(3.24069 - 1.44285i) q^{30} +(0.189812 - 1.80594i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-15.5910 + 6.94157i) q^{33} +(0.000893805 - 0.00275085i) q^{34} +(1.65840 - 2.78312i) q^{35} +(-4.36255 + 3.16958i) q^{36} +(0.944761 + 8.98880i) q^{37} +(1.77971 + 3.08254i) q^{38} +(-6.66471 + 7.40191i) q^{39} +(-0.612257 + 1.06046i) q^{40} +(-6.36292 - 0.716423i) q^{41} +(-2.46876 + 7.25618i) q^{42} +(2.39996 + 7.38631i) q^{43} +(2.94558 - 5.10190i) q^{44} +(6.03221 + 2.68571i) q^{45} +(2.64821 + 1.17906i) q^{46} +(5.27341 + 1.12090i) q^{47} +(0.895212 - 2.75518i) q^{48} +(1.97878 + 6.71449i) q^{49} -3.50057 q^{50} +(0.00765480 - 0.00340814i) q^{51} +(0.359386 - 3.41933i) q^{52} +(-8.83693 - 3.93445i) q^{53} +(-6.77927 - 1.44098i) q^{54} -7.21381 q^{55} +(-0.782820 - 2.52729i) q^{56} +(-3.18643 + 9.80681i) q^{57} +(4.18963 - 1.86534i) q^{58} +(5.94626 - 6.60400i) q^{59} +(-3.46985 + 0.737540i) q^{60} +(-3.35018 - 3.72075i) q^{61} +(-0.561140 + 1.72701i) q^{62} +(-13.1123 + 5.62269i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-3.84610 + 1.71240i) q^{65} +(16.6936 - 3.54832i) q^{66} +(-4.36359 - 1.94279i) q^{67} +(-0.00144621 + 0.00250490i) q^{68} +(2.59506 + 7.98679i) q^{69} +(-2.20080 + 2.37750i) q^{70} +(-6.07202 - 4.41158i) q^{71} +(4.92621 - 2.19329i) q^{72} +(-1.12173 - 1.94289i) q^{73} +(0.944761 - 8.98880i) q^{74} +(-6.78567 - 7.53625i) q^{75} +(-1.09992 - 3.38520i) q^{76} +(10.5881 - 11.4382i) q^{77} +(8.05802 - 5.85449i) q^{78} +(-1.17439 + 2.03410i) q^{79} +(0.819359 - 0.909991i) q^{80} +(-1.95042 - 3.37823i) q^{81} +(6.07492 + 2.02369i) q^{82} +14.3590 q^{83} +(3.92346 - 6.58433i) q^{84} +0.00354180 q^{85} +(-0.811812 - 7.72388i) q^{86} +(12.1372 + 5.40384i) q^{87} +(-3.94196 + 4.37799i) q^{88} +(-9.04057 - 10.0406i) q^{89} +(-5.34200 - 3.88119i) q^{90} +(2.92997 - 8.61175i) q^{91} +(-2.34520 - 1.70389i) q^{92} +(-4.80576 + 2.13966i) q^{93} +(-4.92513 - 2.19281i) q^{94} +(-2.91644 + 3.23903i) q^{95} +(-1.44848 + 2.50885i) q^{96} +(-5.87654 + 4.26956i) q^{97} +(-0.539518 - 6.97918i) q^{98} +(25.7005 + 18.6725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 14 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} + 4 q^{6} - 2 q^{7} - 28 q^{8} - 58 q^{9}+O(q^{10}) $ 112 * q + 14 * q^2 - 2 * q^3 + 14 * q^4 + 4 * q^5 + 4 * q^6 - 2 * q^7 - 28 * q^8 - 58 * q^9	\( 112 q + 14 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} + 4 q^{6} - 2 q^{7} - 28 q^{8} - 58 q^{9} + 4 q^{10} + 2 q^{11} + 3 q^{12} - 6 q^{13} + 18 q^{14} - 2 q^{15} + 14 q^{16} + 17 q^{18} - 2 q^{19} - 8 q^{20} - 25 q^{21} + 16 q^{22} - 2 q^{23} + 3 q^{24} + 26 q^{25} - 2 q^{26} - 8 q^{27} + 4 q^{28} - 42 q^{29} + q^{30} + 13 q^{31} - 56 q^{32} + 17 q^{33} - 10 q^{34} + 8 q^{35} - 24 q^{36} + q^{37} - 2 q^{38} + 14 q^{39} - 16 q^{40} - 58 q^{41} - 62 q^{42} + 18 q^{43} + 12 q^{44} + 32 q^{45} + 3 q^{46} - 25 q^{47} + 4 q^{48} + 8 q^{49} + 88 q^{50} + 23 q^{51} - 2 q^{52} + 3 q^{53} - 6 q^{54} - 12 q^{55} + 8 q^{56} - 24 q^{57} + 21 q^{58} + 18 q^{59} + q^{60} - 6 q^{61} - 16 q^{62} - 71 q^{63} - 28 q^{64} + 2 q^{65} + 2 q^{66} + 9 q^{67} - 10 q^{68} + 38 q^{69} + 55 q^{70} - 10 q^{71} + 12 q^{72} - 78 q^{73} + q^{74} - 9 q^{75} + 4 q^{76} + 43 q^{77} + 22 q^{78} + 4 q^{80} - 80 q^{81} - 6 q^{82} + 156 q^{83} - 13 q^{84} + 44 q^{85} + 11 q^{86} - 8 q^{88} + 9 q^{89} - 64 q^{90} - 52 q^{91} - 6 q^{92} - 46 q^{93} + 20 q^{94} + 49 q^{95} - 2 q^{96} + 32 q^{97} - 21 q^{98} + 12 q^{99}+O(q^{100}) \) 112 * q + 14 * q^2 - 2 * q^3 + 14 * q^4 + 4 * q^5 + 4 * q^6 - 2 * q^7 - 28 * q^8 - 58 * q^9 + 4 * q^10 + 2 * q^11 + 3 * q^12 - 6 * q^13 + 18 * q^14 - 2 * q^15 + 14 * q^16 + 17 * q^18 - 2 * q^19 - 8 * q^20 - 25 * q^21 + 16 * q^22 - 2 * q^23 + 3 * q^24 + 26 * q^25 - 2 * q^26 - 8 * q^27 + 4 * q^28 - 42 * q^29 + q^30 + 13 * q^31 - 56 * q^32 + 17 * q^33 - 10 * q^34 + 8 * q^35 - 24 * q^36 + q^37 - 2 * q^38 + 14 * q^39 - 16 * q^40 - 58 * q^41 - 62 * q^42 + 18 * q^43 + 12 * q^44 + 32 * q^45 + 3 * q^46 - 25 * q^47 + 4 * q^48 + 8 * q^49 + 88 * q^50 + 23 * q^51 - 2 * q^52 + 3 * q^53 - 6 * q^54 - 12 * q^55 + 8 * q^56 - 24 * q^57 + 21 * q^58 + 18 * q^59 + q^60 - 6 * q^61 - 16 * q^62 - 71 * q^63 - 28 * q^64 + 2 * q^65 + 2 * q^66 + 9 * q^67 - 10 * q^68 + 38 * q^69 + 55 * q^70 - 10 * q^71 + 12 * q^72 - 78 * q^73 + q^74 - 9 * q^75 + 4 * q^76 + 43 * q^77 + 22 * q^78 + 4 * q^80 - 80 * q^81 - 6 * q^82 + 156 * q^83 - 13 * q^84 + 44 * q^85 + 11 * q^86 - 8 * q^88 + 9 * q^89 - 64 * q^90 - 52 * q^91 - 6 * q^92 - 46 * q^93 + 20 * q^94 + 49 * q^95 - 2 * q^96 + 32 * q^97 - 21 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$3$	−1.44848	−	2.50885i	−0.836282	−	1.44848i	−0.892982	−	0.450092i	$-0.851391\pi$
$3$	−1.44848	−	2.50885i	−0.836282	−	1.44848i	0.0567005	−	0.998391i	$-0.481942\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−0.127997	−	1.21781i	−0.0572418	−	0.544619i	−0.985136	−	0.171776i	$-0.945050\pi$
$5$	−0.127997	−	1.21781i	−0.0572418	−	0.544619i	0.927894	−	0.372843i	$-0.121617\pi$
$6$	0.895212	+	2.75518i	0.365469	+	1.12480i
$7$	2.11882	+	1.58449i	0.800838	+	0.598881i
$7$	2.11882	+	1.58449i	0.800838	+	0.598881i
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−2.69620	+	4.66996i	−0.898735	+	1.55665i
$10$	−0.127997	+	1.21781i	−0.0404760	+	0.385104i
$11$	0.615794	−	5.85889i	0.185669	−	1.76652i	−0.364247	−	0.931302i	$-0.618674\pi$
$11$	0.615794	−	5.85889i	0.185669	−	1.76652i	0.549916	−	0.835220i	$-0.314660\pi$
$12$	−0.302815	−	2.88110i	−0.0874153	−	0.831701i
$13$	−1.06245	−	3.26989i	−0.294671	−	0.906905i	−0.983332	−	0.181821i	$-0.941801\pi$
$13$	−1.06245	−	3.26989i	−0.294671	−	0.906905i	0.688660	−	0.725084i	$-0.258199\pi$
$14$	−1.74308	−	1.99039i	−0.465858	−	0.531955i
$15$	−2.86989	+	2.08509i	−0.741001	+	0.538369i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.000302340		0.00287657i	−7.33281e−5		0.000697671i	−0.994558	−	0.104180i	$-0.966778\pi$
$17$	−0.000302340		0.00287657i	−7.33281e−5		0.000697671i	0.994485	+	0.104877i	$0.0334450\pi$
$18$	3.60823	−	4.00734i	0.850467	−	0.944539i
$19$	−2.38171	−	2.64516i	−0.546402	−	0.606841i	0.405180	−	0.914237i	$-0.367209\pi$
$19$	−2.38171	−	2.64516i	−0.546402	−	0.606841i	−0.951582	+	0.307396i	$0.900542\pi$
$20$	0.378395	−	1.16458i	0.0846118	−	0.260408i
$21$	0.906170	−	7.61089i	0.197743	−	1.66083i
$22$	−1.82047	+	5.60283i	−0.388125	+	1.19453i
$23$	−2.83548	−	0.602700i	−0.591239	−	0.125672i	−0.0974302	−	0.995242i	$-0.531062\pi$
$23$	−2.83548	−	0.602700i	−0.591239	−	0.125672i	−0.493808	+	0.869571i	$0.664396\pi$
$24$	−0.302815	+	2.88110i	−0.0618119	+	0.588101i
$25$	3.42407	−	0.727809i	0.684814	−	0.145562i
$26$	0.359386	+	3.41933i	0.0704815	+	0.670587i
$27$	6.93073			1.33382
$28$	1.29117	+	2.30930i	0.244008	+	0.436418i
$29$	−3.71025	+	2.69566i	−0.688976	+	0.500571i	−0.876323	−	0.481723i	$-0.840011\pi$
$29$	−3.71025	+	2.69566i	−0.688976	+	0.500571i	0.187347	+	0.982294i	$0.440011\pi$
$30$	3.24069	−	1.44285i	0.591666	−	0.263427i
$31$	0.189812	−	1.80594i	0.0340912	−	0.324356i	−0.964164	−	0.265307i	$-0.914527\pi$
$31$	0.189812	−	1.80594i	0.0340912	−	0.324356i	0.998255	−	0.0590489i	$-0.0188068\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−15.5910	+	6.94157i	−2.71405	+	1.20837i
$34$	0.000893805	−	0.00275085i	0.000153286	−	0.000471767i
$35$	1.65840	−	2.78312i	0.280321	−	0.470433i
$36$	−4.36255	+	3.16958i	−0.727092	+	0.528263i
$37$	0.944761	+	8.98880i	0.155318	+	1.47775i	0.743345	+	0.668908i	$0.233238\pi$
$37$	0.944761	+	8.98880i	0.155318	+	1.47775i	−0.588027	+	0.808841i	$0.700095\pi$
$38$	1.77971	+	3.08254i	0.288706	+	0.500054i
$39$	−6.66471	+	7.40191i	−1.06721	+	1.18525i
$40$	−0.612257	+	1.06046i	−0.0968063	+	0.167673i
$41$	−6.36292	−	0.716423i	−0.993721	−	0.111886i
$41$	−6.36292	−	0.716423i	−0.993721	−	0.111886i
$42$	−2.46876	+	7.25618i	−0.380938	+	1.11965i
$43$	2.39996	+	7.38631i	0.365990	+	1.12640i	0.949359	+	0.314194i	$0.101734\pi$
$43$	2.39996	+	7.38631i	0.365990	+	1.12640i	−0.583369	+	0.812207i	$0.698266\pi$
$44$	2.94558	−	5.10190i	0.444063	−	0.769140i
$45$	6.03221	+	2.68571i	0.899229	+	0.400363i
$46$	2.64821	+	1.17906i	0.390457	+	0.173843i
$47$	5.27341	+	1.12090i	0.769206	+	0.163500i	0.575769	−	0.817613i	$-0.304703\pi$
$47$	5.27341	+	1.12090i	0.769206	+	0.163500i	0.193438	+	0.981113i	$0.438036\pi$
$48$	0.895212	−	2.75518i	0.129213	−	0.397676i
$49$	1.97878	+	6.71449i	0.282683	+	0.959213i
$50$	−3.50057			−0.495055
$51$	0.00765480	−	0.00340814i	0.00107189	−	0.000477235i
$52$	0.359386	−	3.41933i	0.0498379	−	0.474176i
$53$	−8.83693	−	3.93445i	−1.21385	−	0.540439i	−0.302922	−	0.953015i	$-0.597962\pi$
$53$	−8.83693	−	3.93445i	−1.21385	−	0.540439i	−0.910923	+	0.412577i	$0.864629\pi$
$54$	−6.77927	−	1.44098i	−0.922542	−	0.196092i
$55$	−7.21381			−0.972710
$56$	−0.782820	−	2.52729i	−0.104609	−	0.337723i
$57$	−3.18643	+	9.80681i	−0.422052	+	1.29894i
$58$	4.18963	−	1.86534i	0.550126	−	0.244932i
$59$	5.94626	−	6.60400i	0.774138	−	0.859767i	−0.219120	−	0.975698i	$-0.570318\pi$
$59$	5.94626	−	6.60400i	0.774138	−	0.859767i	0.993257	+	0.115931i	$0.0369851\pi$
$60$	−3.46985	+	0.737540i	−0.447956	+	0.0952160i
$61$	−3.35018	−	3.72075i	−0.428947	−	0.476393i	0.489463	−	0.872024i	$-0.337193\pi$
$61$	−3.35018	−	3.72075i	−0.428947	−	0.476393i	−0.918410	+	0.395631i	$0.870526\pi$
$62$	−0.561140	+	1.72701i	−0.0712648	+	0.219331i
$63$	−13.1123	+	5.62269i	−1.65199	+	0.708393i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−3.84610	+	1.71240i	−0.477050	+	0.212396i
$66$	16.6936	−	3.54832i	2.05483	−	0.436768i
$67$	−4.36359	−	1.94279i	−0.533097	−	0.237350i	0.122490	−	0.992470i	$-0.460912\pi$
$67$	−4.36359	−	1.94279i	−0.533097	−	0.237350i	−0.655587	+	0.755120i	$0.727579\pi$
$68$	−0.00144621	+	0.00250490i	−0.000175378	+	0.000303764i
$69$	2.59506	+	7.98679i	0.312409	+	0.961496i
$70$	−2.20080	+	2.37750i	−0.263046	+	0.284165i
$71$	−6.07202	−	4.41158i	−0.720616	−	0.523558i	0.165965	−	0.986132i	$-0.446926\pi$
$71$	−6.07202	−	4.41158i	−0.720616	−	0.523558i	−0.886581	+	0.462573i	$0.846926\pi$
$72$	4.92621	−	2.19329i	0.580559	−	0.258482i
$73$	−1.12173	−	1.94289i	−0.131288	−	0.227398i	0.792885	−	0.609371i	$-0.208578\pi$
$73$	−1.12173	−	1.94289i	−0.131288	−	0.227398i	−0.924173	+	0.381973i	$0.875245\pi$
$74$	0.944761	−	8.98880i	0.109826	−	1.04493i
$75$	−6.78567	−	7.53625i	−0.783541	−	0.870211i
$76$	−1.09992	−	3.38520i	−0.126169	−	0.388309i
$77$	10.5881	−	11.4382i	1.20663	−	1.30350i
$78$	8.05802	−	5.85449i	0.912391	−	0.662891i
$79$	−1.17439	+	2.03410i	−0.132129	+	0.228854i	−0.924497	−	0.381189i	$-0.875515\pi$
$79$	−1.17439	+	2.03410i	−0.132129	+	0.228854i	0.792368	+	0.610043i	$0.208848\pi$
$80$	0.819359	−	0.909991i	0.0916072	−	0.101740i
$81$	−1.95042	−	3.37823i	−0.216714	−	0.375359i
$82$	6.07492	+	2.02369i	0.670863	+	0.223479i
$83$	14.3590			1.57610			0.788052	−	0.615608i	$-0.211090\pi$
$83$	14.3590			1.57610			0.788052	+	0.615608i	$0.211090\pi$
$84$	3.92346	−	6.58433i	0.428084	−	0.718409i
$85$	0.00354180			0.000384162
$86$	−0.811812	−	7.72388i	−0.0875400	−	0.832887i
$87$	12.1372	+	5.40384i	1.30125	+	0.579352i
$88$	−3.94196	+	4.37799i	−0.420214	+	0.466695i
$89$	−9.04057	−	10.0406i	−0.958298	−	1.06430i	−0.997880	−	0.0650819i	$-0.979269\pi$
$89$	−9.04057	−	10.0406i	−0.958298	−	1.06430i	0.0395815	−	0.999216i	$-0.487398\pi$
$90$	−5.34200	−	3.88119i	−0.563096	−	0.409113i
$91$	2.92997	−	8.61175i	0.307144	−	0.902757i
$92$	−2.34520	−	1.70389i	−0.244504	−	0.177643i
$93$	−4.80576	+	2.13966i	−0.498334	+	0.221873i
$94$	−4.92513	−	2.19281i	−0.507988	−	0.226171i
$95$	−2.91644	+	3.23903i	−0.299220	+	0.332318i
$96$	−1.44848	+	2.50885i	−0.147835	+	0.256058i
$97$	−5.87654	+	4.26956i	−0.596672	+	0.433508i	−0.844696	−	0.535246i	$-0.820219\pi$
$97$	−5.87654	+	4.26956i	−0.596672	+	0.433508i	0.248024	+	0.968754i	$0.420219\pi$
$98$	−0.539518	−	6.97918i	−0.0544996	−	0.705003i
$99$	25.7005	+	18.6725i	2.58300	+	1.87666i
$100$	3.42407	+	0.727809i	0.342407	+	0.0727809i
$101$	−2.60990	+	0.554751i	−0.259695	+	0.0551998i	−0.335919	−	0.941891i	$-0.609047\pi$
$101$	−2.60990	+	0.554751i	−0.259695	+	0.0551998i	0.0762243	+	0.997091i	$0.475714\pi$
$102$	−0.00819612	+	0.00174214i	−0.000811537	+	0.000172497i
$103$	1.52153	+	1.68983i	0.149921	+	0.166504i	0.813427	−	0.581667i	$-0.197599\pi$
$103$	1.52153	+	1.68983i	0.149921	+	0.166504i	−0.663507	+	0.748170i	$0.730933\pi$
$104$	−1.06245	+	3.26989i	−0.104182	+	0.320639i
$105$	−9.38458	−	0.129371i	−0.915841	−	0.0126253i
$106$	7.82580	+	5.68578i	0.760109	+	0.552251i
$107$	7.68593	+	8.53609i	0.743027	+	0.825215i	0.989591	−	0.143912i	$-0.0459682\pi$
$107$	7.68593	+	8.53609i	0.743027	+	0.825215i	−0.246564	+	0.969127i	$0.579302\pi$
$108$	6.33153	+	2.81898i	0.609252	+	0.271257i
$109$	−5.52571	−	9.57082i	−0.529267	−	0.916718i	−0.999417	−	0.0341314i	$-0.989134\pi$
$109$	−5.52571	−	9.57082i	−0.529267	−	0.916718i	0.470150	−	0.882586i	$-0.344200\pi$
$110$	7.05617	+	1.49984i	0.672779	+	0.143004i
$111$	21.1830	−	15.3904i	2.01061	−	1.46079i
$112$	0.240260	+	2.63482i	0.0227025	+	0.248967i
$113$	9.75140	+	7.08480i	0.917334	+	0.666482i	0.942859	−	0.333192i	$-0.108126\pi$
$113$	9.75140	+	7.08480i	0.917334	+	0.666482i	−0.0255249	+	0.999674i	$0.508126\pi$
$114$	5.15574	−	8.93001i	0.482880	−	0.836372i
$115$	−0.371040	+	3.53021i	−0.0345996	+	0.329194i
$116$	−4.48591	+	0.953509i	−0.416506	+	0.0885311i
$117$	18.1349	+	3.85469i	1.67657	+	0.356366i
$118$	−7.18937	+	5.22339i	−0.661835	+	0.480852i
$119$	−0.00519850	+	0.00561587i	−0.000476546	+	0.000514806i
$120$	3.54737			0.323829
$121$	−23.1878	−	4.92871i	−2.10798	−	0.448065i
$122$	2.50338	+	4.33599i	0.226646	+	0.392562i
$123$	7.41918	+	17.0013i	0.668965	+	1.53296i
$124$	0.907943	−	1.57260i	0.0815357	−	0.141224i
$125$	−3.21658	−	9.89960i	−0.287699	−	0.885447i
$126$	13.9948	−	2.77363i	1.24675	−	0.247094i
$127$	−15.5864	+	11.3242i	−1.38307	+	1.00486i	−0.386488	+	0.922295i	$0.626312\pi$
$127$	−15.5864	+	11.3242i	−1.38307	+	1.00486i	−0.996586	+	0.0825668i	$0.973688\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	15.0548	−	16.7201i	1.32550	−	1.47212i
$130$	4.11808	−	0.875326i	0.361180	−	0.0767711i
$131$	16.1340	−	7.18331i	1.40963	−	0.627609i	0.446047	−	0.895009i	$-0.352831\pi$
$131$	16.1340	−	7.18331i	1.40963	−	0.627609i	0.963586	+	0.267400i	$0.0861646\pi$
$132$	−17.0665			−1.48545
$133$	−0.855185	−	9.37840i	−0.0741539	−	0.813211i
$134$	3.86430	+	2.80758i	0.333825	+	0.242538i
$135$	−0.887109	−	8.44028i	−0.0763502	−	0.726423i
$136$	0.00193540	−	0.00214948i	0.000165959	−	0.000184317i
$137$	−3.54313	−	6.13687i	−0.302710	−	0.524308i	0.674039	−	0.738696i	$-0.264558\pi$
$137$	−3.54313	−	6.13687i	−0.302710	−	0.524308i	−0.976749	+	0.214387i	$0.931225\pi$
$138$	−0.877810	−	8.35180i	−0.0747241	−	0.710952i
$139$	4.99733	−	15.3802i	0.423868	−	1.30453i	−0.480206	−	0.877156i	$-0.659438\pi$
$139$	4.99733	−	15.3802i	0.423868	−	1.30453i	0.904074	−	0.427376i	$-0.140562\pi$
$140$	2.64702	−	1.86797i	0.223714	−	0.157872i
$141$	−4.82629	−	14.8538i	−0.406447	−	1.25091i
$142$	5.02211	+	5.57762i	0.421446	+	0.468063i
$143$	−19.8122	+	4.21121i	−1.65678	+	0.352159i
$144$	−5.27457	+	1.12114i	−0.439548	+	0.0934287i
$145$	3.75768	+	4.17333i	0.312059	+	0.346576i
$146$	0.693266	+	2.13365i	0.0573751	+	0.176582i
$147$	13.9794	−	14.6903i	1.15300	−	1.21163i
$148$	−2.79299	+	8.59595i	−0.229583	+	0.706583i
$149$	−0.421582	−	4.01109i	−0.0345374	−	0.328601i	−0.998125	−	0.0612083i	$-0.980505\pi$
$149$	−0.421582	−	4.01109i	−0.0345374	−	0.328601i	0.963588	−	0.267393i	$-0.0861621\pi$
$150$	5.07051	+	8.78238i	0.414005	+	0.717079i
$151$	9.52924	−	10.5833i	0.775478	−	0.861256i	−0.217921	−	0.975966i	$-0.569927\pi$
$151$	9.52924	−	10.5833i	0.775478	−	0.861256i	0.993399	+	0.114711i	$0.0365941\pi$
$152$	0.372060	+	3.53991i	0.0301780	+	0.287125i
$153$	−0.0126183	−	0.00916773i	−0.00102013	−	0.000741167i
$154$	−12.7349	+	8.98686i	−1.02621	+	0.724182i
$155$	−2.22358			−0.178602
$156$	−9.09915	+	4.05120i	−0.728515	+	0.324356i
$157$	−8.50247	+	1.80726i	−0.678571	+	0.144235i	−0.534289	−	0.845302i	$-0.679421\pi$
$157$	−8.50247	+	1.80726i	−0.678571	+	0.144235i	−0.144282	+	0.989537i	$0.546087\pi$
$158$	1.57164	−	1.74548i	0.125033	−	0.138863i
$159$	2.92920	+	27.8695i	0.232301	+	2.21019i
$160$	−0.990652	+	0.719751i	−0.0783179	+	0.0569013i
$161$	−5.05290	−	5.76980i	−0.398224	−	0.454724i
$162$	1.20543	+	3.70993i	0.0947074	+	0.291479i
$163$	4.99029	−	8.64344i	0.390870	−	0.677007i	−0.601695	−	0.798726i	$-0.705508\pi$
$163$	4.99029	−	8.64344i	0.390870	−	0.677007i	0.992565	+	0.121720i	$0.0388409\pi$
$164$	−5.52142	−	3.24252i	−0.431151	−	0.253198i
$165$	10.4491	+	18.0983i	0.813459	+	1.40895i
$166$	−14.0452	−	2.98540i	−1.09012	−	0.231712i
$167$	−2.31000			−0.178753			−0.0893767	−	0.995998i	$-0.528487\pi$
$167$	−2.31000			−0.178753			−0.0893767	+	0.995998i	$0.528487\pi$
$168$	−5.20668	+	5.62471i	−0.401704	+	0.433956i
$169$	0.953828	−	0.692997i	0.0733714	−	0.0533074i
$170$	−0.00346440		0.000736382i	−0.000265708		5.64779e-5i
$171$	18.7744	−	3.99061i	1.43571	−	0.305170i
$172$	−0.811812	+	7.72388i	−0.0619001	+	0.588940i
$173$	3.93471	−	6.81512i	0.299151	−	0.518144i	−0.676791	−	0.736175i	$-0.736630\pi$
$173$	3.93471	−	6.81512i	0.299151	−	0.518144i	0.975942	+	0.218031i	$0.0699633\pi$
$174$	−10.7485	−	7.80922i	−0.814840	−	0.592016i
$175$	8.40819	+	3.88331i	0.635599	+	0.293551i
$176$	4.76605	−	3.46274i	0.359255	−	0.261014i
$177$	−25.1815	−	5.35249i	−1.89276	−	0.402318i
$178$	6.75546	+	11.7008i	0.506343	+	0.877012i
$179$	21.8750	+	9.73936i	1.63501	+	0.727954i	0.999042	−	0.0437599i	$-0.0139336\pi$
$179$	21.8750	+	9.73936i	1.63501	+	0.727954i	0.635970	+	0.771714i	$0.280600\pi$
$180$	4.41832	+	4.90704i	0.329322	+	0.365749i
$181$	10.6373	+	7.72843i	0.790663	+	0.574450i	0.908160	−	0.418623i	$-0.137487\pi$
$181$	10.6373	+	7.72843i	0.790663	+	0.574450i	−0.117497	+	0.993073i	$0.537487\pi$
$182$	−4.65643	+	7.81439i	−0.345157	+	0.579241i
$183$	−4.48211	+	13.7945i	−0.331327	+	1.01972i
$184$	1.93969	+	2.15425i	0.142996	+	0.158813i
$185$	10.8257	−	2.30107i	0.795920	−	0.169178i
$186$	5.14561	−	1.09373i	0.377294	−	0.0801963i
$187$	0.0166673	+	0.00354275i	0.00121884	+	0.000259072i
$188$	4.36159	+	3.16888i	0.318102	+	0.231114i
$189$	14.6849	+	10.9817i	1.06817	+	0.798799i
$190$	3.52614	−	2.56189i	0.255813	−	0.185859i
$191$	−0.590401	+	1.02260i	−0.0427199	+	0.0739931i	−0.886595	−	0.462547i	$-0.846936\pi$
$191$	−0.590401	+	1.02260i	−0.0427199	+	0.0739931i	0.843875	+	0.536540i	$0.180269\pi$
$192$	1.93845	−	2.15286i	0.139895	−	0.155370i
$193$	20.2891	+	9.03327i	1.46044	+	0.650229i	0.974627	−	0.223835i	$-0.0718576\pi$
$193$	20.2891	+	9.03327i	1.46044	+	0.650229i	0.485811	+	0.874064i	$0.338524\pi$
$194$	6.63581	−	2.95445i	0.476424	−	0.212118i
$195$	9.86715	+	7.16890i	0.706601	+	0.513376i
$196$	−0.923324	+	6.93884i	−0.0659517	+	0.495631i
$197$	−10.7438	−	7.80585i	−0.765466	−	0.556144i	0.135116	−	0.990830i	$-0.456859\pi$
$197$	−10.7438	−	7.80585i	−0.765466	−	0.556144i	−0.900582	+	0.434686i	$0.856859\pi$
$198$	−21.2566	−	23.6079i	−1.51064	−	1.67774i
$199$	8.93524	−	9.92359i	0.633402	−	0.703464i	−0.337935	−	0.941169i	$-0.609728\pi$
$199$	8.93524	−	9.92359i	0.633402	−	0.703464i	0.971337	+	0.237705i	$0.0763952\pi$
$200$	−3.19793	−	1.42381i	−0.226128	−	0.100678i
$201$	1.44641	+	13.7617i	0.102022	+	0.970674i
$202$	2.66821			0.187734
$203$	−12.1326	−	0.167254i	−0.851541	−	0.0117389i
$204$	0.00837923			0.000586663
$205$	−0.0580319	+	7.84050i	−0.00405312	+	0.547604i
$206$	−1.13694	−	1.96924i	−0.0792146	−	0.137204i
$207$	10.4596	−	11.6166i	0.726994	−	0.807409i
$208$	1.71908	−	2.97754i	0.119197	−	0.206455i
$209$	−16.9643	+	12.3253i	−1.17345	+	0.852559i
$210$	9.15260	+	2.07771i	0.631590	+	0.143375i
$211$	−5.18066	−	15.9444i	−0.356651	−	1.09766i	−0.955046	−	0.296458i	$-0.904195\pi$
$211$	−5.18066	−	15.9444i	−0.356651	−	1.09766i	0.598395	−	0.801201i	$-0.295805\pi$
$212$	−6.47265	−	7.18860i	−0.444543	−	0.493715i
$213$	−2.27276	+	21.6239i	−0.155727	+	1.48164i
$214$	−5.74322	−	9.94755i	−0.392598	−	0.680000i
$215$	8.68790	−	3.86810i	0.592510	−	0.263802i
$216$	−5.60708	−	4.07378i	−0.381513	−	0.277186i
$217$	3.26367	−	3.52570i	0.221552	−	0.239340i
$218$	3.41508	+	10.5105i	0.231298	+	0.711863i
$219$	−3.24961	+	5.62849i	−0.219588	+	0.380338i
$220$	−6.59014	−	2.93412i	−0.444307	−	0.197818i
$221$	0.00972730	−	0.00206760i	0.000654329	−	0.000139082i
$222$	−23.9200	+	10.6499i	−1.60540	+	0.714772i
$223$	−7.33667	−	22.5799i	−0.491300	−	1.51206i	−0.822645	−	0.568555i	$-0.807503\pi$
$223$	−7.33667	−	22.5799i	−0.491300	−	1.51206i	0.331346	−	0.943509i	$-0.392497\pi$
$224$	0.312800	−	2.62720i	0.0208998	−	0.175537i
$225$	−5.83316	+	17.9526i	−0.388877	+	1.19684i
$226$	−8.06529	−	8.95741i	−0.536495	−	0.595838i
$227$	−27.9839	+	5.94817i	−1.85736	+	0.394794i	−0.993961	−	0.109732i	$-0.965001\pi$
$227$	−27.9839	+	5.94817i	−1.85736	+	0.394794i	−0.863397	+	0.504526i	$0.831667\pi$
$228$	−6.89973	+	7.66293i	−0.456946	+	0.507490i
$229$	−21.5441	+	9.59206i	−1.42368	+	0.633861i	−0.966769	−	0.255653i	$-0.917710\pi$
$229$	−21.5441	+	9.59206i	−1.42368	+	0.633861i	−0.456907	+	0.889514i	$0.651043\pi$
$230$	1.09690	−	3.37592i	0.0723277	−	0.222602i
$231$	−44.0334	−	9.99590i	−2.89718	−	0.657682i
$232$	4.58612			0.301094
$233$	12.4471	+	2.64570i	0.815434	+	0.173326i	0.596706	−	0.802460i	$-0.296476\pi$
$233$	12.4471	+	2.64570i	0.815434	+	0.173326i	0.218728	+	0.975786i	$0.429809\pi$
$234$	−16.9371	−	7.54090i	−1.10722	−	0.492964i
$235$	0.690058	−	6.56546i	0.0450144	−	0.428283i
$236$	8.11827	−	3.61449i	0.528454	−	0.235283i
$237$	6.80432			0.441988
$238$	0.00625251	−	0.00441232i	0.000405290	−	0.000286009i
$239$	6.64312	−	20.4454i	0.429707	−	1.32250i	−0.468707	−	0.883354i	$-0.655280\pi$
$239$	6.64312	−	20.4454i	0.429707	−	1.32250i	0.898414	−	0.439150i	$-0.144720\pi$
$240$	−3.46985	−	0.737540i	−0.223978	−	0.0476080i
$241$	25.2910	+	11.2603i	1.62914	+	0.725338i	0.998703	−	0.0509054i	$-0.0162107\pi$
$241$	25.2910	+	11.2603i	1.62914	+	0.725338i	0.630433	+	0.776244i	$0.282877\pi$
$242$	21.6563	+	9.64202i	1.39212	+	0.619812i
$243$	4.74578	−	8.21993i	0.304442	−	0.527309i
$244$	−1.54718	−	4.76172i	−0.0990478	−	0.304838i
$245$	7.92367	−	3.26920i	0.506225	−	0.208862i
$246$	−3.72229	−	18.1723i	−0.237324	−	1.15863i
$247$	−6.11893	+	10.5983i	−0.389338	+	0.674353i
$248$	−1.21507	+	1.34947i	−0.0771567	+	0.0856912i
$249$	−20.7988	−	36.0245i	−1.31807	−	2.28296i
$250$	1.08804	+	10.3520i	0.0688139	+	0.654720i
$251$	−6.05454	+	4.39888i	−0.382159	+	0.277655i	−0.762235	−	0.647300i	$-0.775898\pi$
$251$	−6.05454	+	4.39888i	−0.382159	+	0.277655i	0.380076	+	0.924955i	$0.375898\pi$
$252$	−14.2656	−	0.196659i	−0.898649	−	0.0123883i
$253$	−5.27723	+	16.2416i	−0.331776	+	1.02110i
$254$	17.6003	−	7.83615i	1.10434	−	0.491684i
$255$	−0.00513024	−	0.00888583i	−0.000321268	−	0.000556452i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	23.4002	−	10.4184i	1.45966	−	0.649883i	0.485193	−	0.874407i	$-0.338749\pi$
$257$	23.4002	−	10.4184i	1.45966	−	0.649883i	0.974469	+	0.224524i	$0.0720826\pi$
$258$	−18.2021	+	13.2246i	−1.13321	+	0.823329i
$259$	−12.2409	+	20.5426i	−0.760612	+	1.27646i
$260$	−4.21008			−0.261098
$261$	−2.58502	−	24.5948i	−0.160008	−	1.52238i
$262$	−17.2749	+	3.67190i	−1.06725	+	0.226851i
$263$	1.65273	−	15.7247i	0.101912	−	0.969625i	−0.817393	−	0.576080i	$-0.804582\pi$
$263$	1.65273	−	15.7247i	0.101912	−	0.969625i	0.919305	−	0.393546i	$-0.128752\pi$
$264$	16.6936	+	3.54832i	1.02742	+	0.218384i
$265$	−3.66030	+	11.2653i	−0.224851	+	0.692019i
$266$	−1.11338	+	9.35127i	−0.0682659	+	0.573363i
$267$	−12.0951	+	37.2250i	−0.740210	+	2.27813i
$268$	−3.19613	−	3.54966i	−0.195235	−	0.216830i
$269$	−15.7042	+	17.4413i	−0.957502	+	1.06341i	0.0404326	+	0.999182i	$0.487126\pi$
$269$	−15.7042	+	17.4413i	−0.957502	+	1.06341i	−0.997935	+	0.0642319i	$0.979540\pi$
$270$	−0.887109	+	8.44028i	−0.0539877	+	0.513659i
$271$	5.69668	+	6.32681i	0.346049	+	0.384326i	0.890895	−	0.454210i	$-0.150078\pi$
$271$	5.69668	+	6.32681i	0.346049	+	0.384326i	−0.544846	+	0.838536i	$0.683412\pi$
$272$	−0.00234001	+	0.00170012i	−0.000141884	+	0.000103085i
$273$	−25.8496	+	5.12314i	−1.56449	+	0.310066i
$274$	2.18977	+	6.73942i	0.132289	+	0.407144i
$275$	−2.15563	−	20.5094i	−0.129989	−	1.23677i
$276$	−0.877810	+	8.35180i	−0.0528379	+	0.502719i
$277$	2.28564	−	21.7464i	0.137331	−	1.30661i	−0.681178	−	0.732118i	$-0.738532\pi$
$277$	2.28564	−	21.7464i	0.137331	−	1.30661i	0.818508	−	0.574495i	$-0.194801\pi$
$278$	−8.08585	+	14.0051i	−0.484957	+	0.839970i
$279$	7.92190	+	5.75560i	0.474272	+	0.344579i
$280$	−2.97755	+	1.27681i	−0.177943	+	0.0763038i
$281$	−5.23524	−	16.1124i	−0.312308	−	0.961185i	−0.976848	−	0.213933i	$-0.931373\pi$
$281$	−5.23524	−	16.1124i	−0.312308	−	0.961185i	0.664540	−	0.747252i	$-0.268627\pi$
$282$	1.63255	+	15.5326i	0.0972167	+	0.924955i
$283$	−3.07680	−	1.36988i	−0.182897	−	0.0814310i	0.313245	−	0.949672i	$-0.398584\pi$
$283$	−3.07680	−	1.36988i	−0.182897	−	0.0814310i	−0.496142	+	0.868241i	$0.665251\pi$
$284$	−3.75271	−	6.49989i	−0.222683	−	0.385698i
$285$	12.3506	+	2.62521i	0.731588	+	0.155504i
$286$	20.2548			1.19769
$287$	−12.3467	−	11.6000i	−0.728803	−	0.684724i
$288$	5.39241			0.317751
$289$	16.6285	+	3.53450i	0.978147	+	0.207912i
$290$	−2.80788	−	4.86340i	−0.164885	−	0.285589i
$291$	19.2237	+	8.55895i	1.12691	+	0.501735i
$292$	−0.234505	−	2.23117i	−0.0137234	−	0.130569i
$293$	2.55922	+	7.87647i	0.149511	+	0.460148i	0.997564	−	0.0697643i	$-0.0222247\pi$
$293$	2.55922	+	7.87647i	0.149511	+	0.460148i	−0.848052	+	0.529913i	$0.822225\pi$
$294$	−16.7282	+	11.4628i	−0.975608	+	0.668523i
$295$	−8.80348	−	6.39611i	−0.512559	−	0.372396i
$296$	4.51916	−	7.82741i	0.262671	−	0.454959i
$297$	4.26790	−	40.6064i	0.247649	−	2.35622i
$298$	−0.421582	+	4.01109i	−0.0244216	+	0.232356i
$299$	1.04180	+	9.91206i	0.0602488	+	0.573229i
$300$	−3.13375	−	9.64468i	−0.180927	−	0.556836i
$301$	−6.61846	+	19.4530i	−0.381482	+	1.12125i
$302$	−11.5214	+	8.37078i	−0.662981	+	0.481684i
$303$	5.17218	+	5.74429i	0.297134	+	0.330001i
$304$	0.372060	−	3.53991i	0.0213391	−	0.203028i
$305$	−4.10234	+	4.55611i	−0.234899	+	0.260882i
$306$	0.0104365	+	0.0115909i	0.000596614	+	0.000662607i
$307$	8.99373	−	27.6799i	0.513299	−	1.57977i	−0.273056	−	0.961998i	$-0.588034\pi$
$307$	8.99373	−	27.6799i	0.513299	−	1.57977i	0.786355	−	0.617775i	$-0.211966\pi$
$308$	14.3251	−	6.14275i	0.816246	−	0.350015i
$309$	2.03561	−	6.26497i	0.115802	−	0.356401i
$310$	2.17499	+	0.462308i	0.123531	+	0.0262573i
$311$	−0.618905	+	5.88849i	−0.0350949	+	0.333905i	0.962861	+	0.269998i	$0.0870230\pi$
$311$	−0.618905	+	5.88849i	−0.0350949	+	0.333905i	−0.997956	+	0.0639076i	$0.979644\pi$
$312$	9.74260	−	2.07085i	0.551566	−	0.117239i
$313$	0.0813250	+	0.773755i	0.00459676	+	0.0437352i	0.996580	−	0.0826356i	$-0.0263337\pi$
$313$	0.0813250	+	0.773755i	0.00459676	+	0.0437352i	−0.991983	+	0.126371i	$0.959667\pi$
$314$	8.69242			0.490542
$315$	8.52567	+	15.2485i	0.480367	+	0.859157i
$316$	−1.90020	+	1.38058i	−0.106895	+	0.0776635i
$317$	−9.93796	+	4.42466i	−0.558171	+	0.248514i	−0.666377	−	0.745615i	$-0.732156\pi$
$317$	−9.93796	+	4.42466i	−0.558171	+	0.248514i	0.108206	+	0.994128i	$0.465489\pi$
$318$	2.92920	−	27.8695i	0.164261	−	1.56284i
$319$	13.5088	+	23.3979i	0.756348	+	1.31003i
$320$	1.11865	−	0.498054i	0.0625344	−	0.0278421i
$321$	10.2828	−	31.6472i	0.573929	−	1.76637i
$322$	3.74287	+	6.69428i	0.208582	+	0.373057i
$323$	0.00832906	−	0.00605142i	0.000463442	−	0.000336710i
$324$	−0.407750	−	3.87948i	−0.0226528	−	0.215527i
$325$	−6.01777	−	10.4231i	−0.333806	−	0.578169i
$326$	−6.67832	+	7.41702i	−0.369878	+	0.410791i
$327$	−16.0078	+	27.7263i	−0.885233	+	1.53327i
$328$	4.72661	+	4.31963i	0.260983	+	0.238512i
$329$	9.39735	+	10.7307i	0.518093	+	0.591600i
$330$	−6.45788	−	19.8753i	−0.355495	−	1.09410i
$331$	−3.20105	+	5.54438i	−0.175946	+	0.304747i	−0.940488	−	0.339827i	$-0.889632\pi$
$331$	−3.20105	+	5.54438i	−0.175946	+	0.304747i	0.764543	+	0.644573i	$0.222965\pi$
$332$	13.1176	+	5.84033i	0.719922	+	0.320530i
$333$	−44.5246	−	19.8236i	−2.43994	−	1.08633i
$334$	2.25952	+	0.480277i	0.123636	+	0.0262796i
$335$	−1.80742	+	5.56267i	−0.0987500	+	0.303921i
$336$	6.26234	−	4.41927i	0.341639	−	0.241091i
$337$	17.1466			0.934035			0.467018	−	0.884248i	$-0.345328\pi$
$337$	17.1466			0.934035			0.467018	+	0.884248i	$0.345328\pi$
$338$	−1.07707	+	0.479541i	−0.0585847	+	0.0260836i
$339$	3.64995	−	34.7270i	0.198238	−	1.88611i
$340$	0.00323560	+	0.00144058i	0.000175475	+	7.81264e-5i
$341$	−10.4639	−	2.22417i	−0.566653	−	0.120446i
$342$	−19.1938			−1.03788
$343$	−6.44637	+	17.3622i	−0.348071	+	0.937468i
$344$	2.39996	−	7.38631i	0.129397	−	0.398243i
$345$	9.39419	−	4.18256i	0.505766	−	0.225182i
$346$	−5.26567	+	5.84812i	−0.283084	+	0.314397i
$347$	−4.37830	+	0.930636i	−0.235039	+	0.0499591i	−0.323925	−	0.946083i	$-0.605003\pi$
$347$	−4.37830	+	0.930636i	−0.235039	+	0.0499591i	0.0888860	+	0.996042i	$0.471669\pi$
$348$	8.88996	+	9.87330i	0.476552	+	0.529265i
$349$	2.52778	−	7.77972i	0.135309	−	0.416439i	−0.860329	−	0.509740i	$-0.829742\pi$
$349$	2.52778	−	7.77972i	0.135309	−	0.416439i	0.995638	+	0.0933006i	$0.0297418\pi$
$350$	−7.41706	−	5.54661i	−0.396459	−	0.296479i
$351$	−7.36357	−	22.6627i	−0.393038	−	1.20965i
$352$	−5.38185	+	2.39615i	−0.286853	+	0.127715i
$353$	−18.3447	+	3.89928i	−0.976388	+	0.207538i	−0.668359	−	0.743839i	$-0.733003\pi$
$353$	−18.3447	+	3.89928i	−0.976388	+	0.207538i	−0.308029	+	0.951377i	$0.599670\pi$
$354$	23.5183	+	10.4710i	1.24999	+	0.556530i
$355$	−4.59525	+	7.95920i	−0.243890	+	0.422431i
$356$	−4.17510	−	12.8496i	−0.221280	−	0.681030i
$357$	0.0216193	+	0.00490774i	0.00114421	+	0.000259745i
$358$	−19.3720	−	14.0746i	−1.02384	−	0.743865i
$359$	12.4274	−	5.53301i	0.655891	−	0.292021i	−0.0516803	−	0.998664i	$-0.516458\pi$
$359$	12.4274	−	5.53301i	0.655891	−	0.292021i	0.707571	+	0.706642i	$0.249791\pi$
$360$	−3.30154	−	5.71843i	−0.174006	−	0.301388i
$361$	0.661728	−	6.29592i	0.0348278	−	0.331364i
$362$	−8.79799	−	9.77116i	−0.462412	−	0.513561i
$363$	21.2217	+	65.3137i	1.11385	+	3.42808i
$364$	6.17938	−	6.67550i	0.323887	−	0.349891i
$365$	−2.22248	+	1.61473i	−0.116330	+	0.0845188i
$366$	7.25221	−	12.5612i	0.379079	−	0.656584i
$367$	5.15016	−	5.71983i	0.268836	−	0.298573i	−0.593578	−	0.804777i	$-0.702285\pi$
$367$	5.15016	−	5.71983i	0.268836	−	0.298573i	0.862414	+	0.506204i	$0.168952\pi$
$368$	−1.44941	−	2.51046i	−0.0755559	−	0.130867i
$369$	20.5014	−	27.7830i	1.06726	−	1.44632i
$370$	−11.0675			−0.575374
$371$	−12.4897	−	22.3384i	−0.648435	−	1.15975i
$372$	−5.26056			−0.272747
$373$	2.72504	+	25.9270i	0.141097	+	1.34245i	0.804396	+	0.594093i	$0.202489\pi$
$373$	2.72504	+	25.9270i	0.141097	+	1.34245i	−0.663299	+	0.748354i	$0.730844\pi$
$374$	−0.0155665	−	0.00693066i	−0.000804926	−	0.000358376i
$375$	−20.1774	+	22.4093i	−1.04196	+	1.15721i
$376$	−3.60743	−	4.00646i	−0.186039	−	0.206617i
$377$	12.7565	+	9.26812i	0.656992	+	0.477332i
$378$	−12.0808	−	13.7949i	−0.621371	−	0.709531i
$379$	2.53620	+	1.84266i	0.130276	+	0.0946511i	0.651015	−	0.759065i	$-0.274343\pi$
$379$	2.53620	+	1.84266i	0.130276	+	0.0946511i	−0.520739	+	0.853716i	$0.674343\pi$
$380$	−3.98173	+	1.77278i	−0.204258	+	0.0909417i
$381$	50.9874	+	22.7011i	2.61216	+	1.16301i
$382$	0.790111	−	0.877507i	0.0404256	−	0.0448972i
$383$	−7.26696	+	12.5867i	−0.371324	+	0.643152i	−0.989770	−	0.142676i	$-0.954429\pi$
$383$	−7.26696	+	12.5867i	−0.371324	+	0.643152i	0.618445	+	0.785828i	$0.287763\pi$
$384$	−2.34369	+	1.70279i	−0.119601	+	0.0868953i
$385$	−15.2847	−	11.4302i	−0.778983	−	0.582537i
$386$	−17.9676	−	13.0542i	−0.914525	−	0.664441i
$387$	−40.9646	−	8.70729i	−2.08235	−	0.442616i
$388$	−7.10507	+	1.51023i	−0.360705	+	0.0766703i
$389$	19.2604	−	4.09393i	0.976542	−	0.207570i	0.308116	−	0.951349i	$-0.400302\pi$
$389$	19.2604	−	4.09393i	0.976542	−	0.207570i	0.668426	+	0.743778i	$0.266968\pi$
$390$	−8.16103	−	9.06374i	−0.413250	−	0.458960i
$391$	0.00259099	−	0.00797424i	0.000131032	−	0.000403275i
$392$	2.34581	−	6.59524i	0.118481	−	0.333110i
$393$	−41.3916	−	30.0728i	−2.08793	−	1.51697i
$394$	8.88613	+	9.86904i	0.447677	+	0.497195i
$395$	2.62746	+	1.16982i	0.132202	+	0.0588600i
$396$	15.8838	+	27.5115i	0.798190	+	1.38251i
$397$	31.9851	+	6.79864i	1.60528	+	0.341214i	0.921472	−	0.388444i	$-0.126987\pi$
$397$	31.9851	+	6.79864i	1.60528	+	0.341214i	0.683812	+	0.729658i	$0.260321\pi$
$398$	−10.8032	+	7.84899i	−0.541516	+	0.393434i
$399$	−22.2902	+	15.7300i	−1.11591	+	0.787484i
$400$	2.83202	+	2.05758i	0.141601	+	0.102879i
$401$	−7.62297	+	13.2034i	−0.380673	+	0.659345i	−0.991159	−	0.132682i	$-0.957641\pi$
$401$	−7.62297	+	13.2034i	−0.380673	+	0.659345i	0.610485	+	0.792027i	$0.290974\pi$
$402$	1.44641	−	13.7617i	0.0721404	−	0.686370i
$403$	−6.10689	+	1.29806i	−0.304206	+	0.0646610i
$404$	−2.60990	−	0.554751i	−0.129847	−	0.0275999i
$405$	−3.86438	+	2.80764i	−0.192023	+	0.139513i
$406$	11.8327	+	2.68611i	0.587247	+	0.133309i
$407$	53.2462			2.63932
$408$	−0.00819612	−	0.00174214i	−0.000405768	−	8.62487e-5i
$409$	−2.11858	−	3.66949i	−0.104757	−	0.181445i	0.808882	−	0.587971i	$-0.200073\pi$
$409$	−2.11858	−	3.66949i	−0.104757	−	0.181445i	−0.913639	+	0.406527i	$0.866740\pi$
$410$	1.68689	−	7.65710i	0.0833098	−	0.378157i
$411$	−10.2643	+	17.7783i	−0.506301	+	0.876939i
$412$	0.702670	+	2.16260i	0.0346181	+	0.106543i
$413$	23.0630	−	4.57087i	1.13486	−	0.224918i
$414$	−12.6463	+	9.18806i	−0.621531	+	0.451569i
$415$	−1.83790	−	17.4865i	−0.0902190	−	0.858377i
$416$	−2.30058	+	2.55506i	−0.112795	+	0.125272i
$417$	−45.8251	+	9.74043i	−2.24406	+	0.476991i
$418$	19.1562	−	8.52889i	0.936960	−	0.417162i
$419$	24.2259			1.18351			0.591755	−	0.806118i	$-0.298435\pi$
$419$	24.2259			1.18351			0.591755	+	0.806118i	$0.298435\pi$
$420$	−8.52062	−	3.93524i	−0.415763	−	0.192020i
$421$	9.22802	+	6.70455i	0.449746	+	0.326760i	0.789496	−	0.613756i	$-0.210342\pi$
$421$	9.22802	+	6.70455i	0.449746	+	0.326760i	−0.339749	+	0.940516i	$0.610342\pi$
$422$	1.75242	+	16.6731i	0.0853062	+	0.811635i
$423$	−19.4528	+	21.6045i	−0.945825	+	1.05045i
$424$	4.83661	+	8.37725i	0.234887	+	0.406835i
$425$	0.00105836	+	0.0100696i	5.13380e−5	+	0.000488449i
$426$	6.71895	−	20.6788i	0.325534	−	1.00189i
$427$	−1.20293	−	13.1919i	−0.0582137	−	0.638402i
$428$	3.54950	+	10.9243i	0.171572	+	0.528044i
$429$	39.2629	+	43.6059i	1.89563	+	2.10531i
$430$	−9.30227	+	1.97726i	−0.448595	+	0.0953519i
$431$	−21.4367	+	4.55650i	−1.03257	+	0.219479i	−0.692875	−	0.721058i	$-0.743656\pi$
$431$	−21.4367	+	4.55650i	−1.03257	+	0.219479i	−0.339692	+	0.940537i	$0.610323\pi$
$432$	4.63756	+	5.15053i	0.223125	+	0.247805i
$433$	−3.80669	−	11.7158i	−0.182938	−	0.563025i	0.816969	−	0.576682i	$-0.195653\pi$
$433$	−3.80669	−	11.7158i	−0.182938	−	0.563025i	−0.999907	+	0.0136569i	$0.995653\pi$
$434$	−3.92539	+	2.77010i	−0.188425	+	0.132969i
$435$	5.02730	−	15.4724i	0.241041	−	0.741847i
$436$	−1.15519	−	10.9909i	−0.0553235	−	0.526368i
$437$	5.15906	+	8.93575i	0.246791	+	0.427455i
$438$	4.34882	−	4.82986i	0.207795	−	0.230780i
$439$	2.28334	+	21.7245i	0.108978	+	1.03685i	0.903198	+	0.429224i	$0.141213\pi$
$439$	2.28334	+	21.7245i	0.108978	+	1.03685i	−0.794221	+	0.607629i	$0.792121\pi$
$440$	5.83609	+	4.24017i	0.278225	+	0.202142i
$441$	−36.6916	−	8.86281i	−1.74722	−	0.422039i
$442$	−0.00994461			−0.000473017
$443$	−16.4534	+	7.32550i	−0.781722	+	0.348045i	−0.758490	−	0.651685i	$-0.774062\pi$
$443$	−16.4534	+	7.32550i	−0.781722	+	0.348045i	−0.0232325	+	0.999730i	$0.507396\pi$
$444$	25.6115	−	5.44389i	1.21547	−	0.258356i
$445$	−11.0703	+	12.2948i	−0.524782	+	0.582830i
$446$	2.48171	+	23.6119i	0.117512	+	1.11806i
$447$	−9.45254	+	6.86767i	−0.447090	+	0.324830i
$448$	−0.852189	+	2.50475i	−0.0402621	+	0.118338i
$449$	7.18615	+	22.1167i	0.339136	+	1.04375i	0.964649	+	0.263538i	$0.0848896\pi$
$449$	7.18615	+	22.1167i	0.339136	+	1.04375i	−0.625513	+	0.780213i	$0.715110\pi$
$450$	9.43824	−	16.3475i	0.444923	−	0.770629i
$451$	−8.11569	+	36.8385i	−0.382153	+	1.73466i
$452$	6.02669	+	10.4385i	0.283472	+	0.490988i
$453$	−40.3548	−	8.57767i	−1.89603	−	0.403014i
$454$	28.6091			1.34269
$455$	−10.8625	−	2.46586i	−0.509240	−	0.115601i
$456$	8.34217	−	6.06094i	0.390658	−	0.283830i
$457$	35.7763	+	7.60449i	1.67355	+	0.355723i	0.944441	−	0.328680i	$-0.106604\pi$
$457$	35.7763	+	7.60449i	1.67355	+	0.355723i	0.729104	+	0.684403i	$0.239937\pi$
$458$	23.0676	−	4.90318i	1.07788	−	0.229110i
$459$	−0.00209543	+	0.0199367i	−9.78064e−5	+	0.000930566i
$460$	−1.77483	+	3.07409i	−0.0827517	+	0.143330i
$461$	−13.0446	−	9.47743i	−0.607546	−	0.441408i	0.241003	−	0.970524i	$-0.422524\pi$
$461$	−13.0446	−	9.47743i	−0.607546	−	0.441408i	−0.848549	+	0.529116i	$0.822524\pi$
$462$	40.9929	+	18.9325i	1.90716	+	0.880820i
$463$	24.3785	−	17.7120i	1.13296	−	0.823146i	0.146840	−	0.989160i	$-0.453090\pi$
$463$	24.3785	−	17.7120i	1.13296	−	0.823146i	0.986123	+	0.166014i	$0.0530898\pi$
$464$	−4.48591	−	0.953509i	−0.208253	−	0.0442655i
$465$	3.22081	+	5.57861i	0.149362	+	0.258702i
$466$	−11.6250	−	5.17578i	−0.538517	−	0.239763i
$467$	18.6323	+	20.6932i	0.862198	+	0.957568i	0.999456	−	0.0329675i	$-0.0104958\pi$
$467$	18.6323	+	20.6932i	0.862198	+	0.957568i	−0.137259	+	0.990535i	$0.543829\pi$
$468$	14.9992	+	10.8975i	0.693338	+	0.503739i
$469$	−6.16731	−	11.0305i	−0.284780	−	0.509341i
$470$	−2.04001	+	6.27852i	−0.0940989	+	0.289607i
$471$	16.8498	+	18.7136i	0.776398	+	0.862278i
$472$	−8.69236	+	1.84762i	−0.400098	+	0.0850435i
$473$	44.7534	−	9.51264i	2.05777	−	0.437392i
$474$	−6.65563	−	1.41470i	−0.305703	−	0.0649793i
$475$	−10.0803	−	7.32378i	−0.462517	−	0.336038i
$476$	−0.00703325	+	0.00301594i	−0.000322368	+	0.000138235i
$477$	42.1999	−	30.6600i	1.93220	−	1.40383i
$478$	−10.7488	+	18.6174i	−0.491638	+	0.851542i
$479$	6.55128	−	7.27593i	0.299336	−	0.332446i	−0.574649	−	0.818400i	$-0.694861\pi$
$479$	6.55128	−	7.27593i	0.299336	−	0.332446i	0.873984	+	0.485954i	$0.161528\pi$
$480$	3.24069	+	1.44285i	0.147916	+	0.0658566i
$481$	28.3887	−	12.6394i	1.29441	−	0.576309i
$482$	−22.3972	−	16.2725i	−1.02016	−	0.741192i
$483$	−7.15652	+	21.0344i	−0.325633	+	0.957098i
$484$	−19.1784	−	13.9339i	−0.871745	−	0.633360i
$485$	5.95167	+	6.60999i	0.270251	+	0.300144i
$486$	−6.35109	+	7.05360i	−0.288091	+	0.319958i
$487$	12.4577	+	5.54653i	0.564513	+	0.251337i	0.669093	−	0.743179i	$-0.266683\pi$
$487$	12.4577	+	5.54653i	0.564513	+	0.251337i	−0.104579	+	0.994517i	$0.533350\pi$
$488$	0.523349	+	4.97934i	0.0236909	+	0.225404i
$489$	−28.9134			−1.30751
$490$	−8.43022	+	1.55034i	−0.380839	+	0.0700371i
$491$	−8.23928			−0.371833			−0.185917	−	0.982566i	$-0.559525\pi$
$491$	−8.23928			−0.371833			−0.185917	+	0.982566i	$0.559525\pi$
$492$	−0.137292	+	18.5491i	−0.00618962	+	0.836259i
$493$	−0.00663249	−	0.0114878i	−0.000298712	−	0.000517385i
$494$	8.18872	−	9.09450i	0.368428	−	0.409181i
$495$	19.4499	−	33.6882i	0.874208	−	1.51417i
$496$	1.46908	−	1.06735i	0.0659638	−	0.0479255i
$497$	−5.87540	−	18.9684i	−0.263548	−	0.850849i
$498$	12.8543	+	39.5616i	0.576017	+	1.77280i
$499$	−14.9841	−	16.6416i	−0.670782	−	0.744979i	0.307661	−	0.951496i	$-0.400454\pi$
$499$	−14.9841	−	16.6416i	−0.670782	−	0.744979i	−0.978443	+	0.206517i	$0.933787\pi$
$500$	1.08804	−	10.3520i	0.0486588	−	0.462957i
$501$	3.34600	+	5.79544i	0.149488	+	0.258921i
$502$	6.83681	−	3.04395i	0.305142	−	0.135858i
$503$	−0.314230	−	0.228301i	−0.0140108	−	0.0101795i	0.580758	−	0.814076i	$-0.302756\pi$
$503$	−0.314230	−	0.228301i	−0.0140108	−	0.0101795i	−0.594769	+	0.803897i	$0.702756\pi$
$504$	13.9130	+	3.15835i	0.619734	+	0.140684i
$505$	1.00964	+	3.10734i	0.0449283	+	0.138275i
$506$	8.53873	−	14.7895i	0.379593	−	0.657474i
$507$	−3.12023	−	1.38921i	−0.138574	−	0.0616972i
$508$	−18.8449	+	4.00561i	−0.836107	+	0.177720i
$509$	11.3467	−	5.05189i	0.502935	−	0.223921i	−0.139556	−	0.990214i	$-0.544568\pi$
$509$	11.3467	−	5.05189i	0.502935	−	0.223921i	0.642491	+	0.766293i	$0.277901\pi$
$510$	0.00317066	+	0.00975829i	0.000140399	+	0.000432104i
$511$	0.701753	−	5.89400i	0.0310437	−	0.260735i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−16.5070	−	18.3329i	−0.728801	−	0.809416i
$514$	−25.0549	+	5.32559i	−1.10513	+	0.234902i
$515$	1.86313	−	2.06922i	0.0820994	−	0.0911806i
$516$	20.5539	−	9.15119i	0.904836	−	0.402859i
$517$	9.81456	−	30.2061i	0.431644	−	1.32846i
$518$	16.2444	−	17.5487i	0.713740	−	0.771044i
$519$	−22.7975			−1.00070
$520$	4.11808	+	0.875326i	0.180590	+	0.0383856i
$521$	−29.7307	−	13.2369i	−1.30252	−	0.579921i	−0.366030	−	0.930603i	$-0.619283\pi$
$521$	−29.7307	−	13.2369i	−1.30252	−	0.579921i	−0.936495	+	0.350682i	$0.885950\pi$
$522$	−2.58502	+	24.5948i	−0.113143	+	1.07648i
$523$	−4.72336	+	2.10298i	−0.206538	+	0.0919567i	−0.507399	−	0.861711i	$-0.669393\pi$
$523$	−4.72336	+	2.10298i	−0.206538	+	0.0919567i	0.300860	+	0.953668i	$0.402726\pi$
$524$	17.6608			0.771518
$525$	−2.43649	−	26.7198i	−0.106337	−	1.16615i
$526$	−4.88596	+	15.0374i	−0.213038	+	0.655663i
$527$	0.00513752	+	0.00109201i	0.000223794	+	4.75689e-5i
$528$	−15.5910	−	6.94157i	−0.678512	−	0.302093i
$529$	−13.3348	−	5.93705i	−0.579776	−	0.258133i
$530$	5.92249	−	10.2581i	0.257257	−	0.445582i
$531$	14.8081	+	45.5746i	0.642616	+	1.97777i
$532$	3.03329	−	8.91543i	0.131510	−	0.386533i
$533$	4.41767	+	21.5672i	0.191351	+	0.934180i
$534$	19.5703	−	33.8968i	0.846891	−	1.46686i
$535$	9.41152	−	10.4526i	0.406896	−	0.451903i
$536$	2.38827	+	4.13661i	0.103158	+	0.178674i
$537$	−7.25095	−	68.9882i	−0.312902	−	2.97706i
$538$	18.9873	−	13.7951i	0.818600	−	0.594748i
$539$	40.5580	−	7.45871i	1.74696	−	0.321270i
$540$	2.62256	−	8.07139i	0.112857	−	0.347338i
$541$	2.11974	−	0.943771i	0.0911349	−	0.0405759i	−0.360663	−	0.932696i	$-0.617450\pi$
$541$	2.11974	−	0.943771i	0.0911349	−	0.0405759i	0.451798	+	0.892120i	$0.350783\pi$
$542$	−4.25678	−	7.37296i	−0.182844	−	0.316696i
$543$	3.98154	−	37.8818i	0.170864	−	1.62566i
$544$	0.00264235	−	0.00117645i	0.000113290	−	5.04399e-5i
$545$	−10.9481	+	7.95427i	−0.468966	+	0.340724i
$546$	26.3499	+	0.363246i	1.12767	+	0.0155455i
$547$	15.5207			0.663616			0.331808	−	0.943347i	$-0.392341\pi$
$547$	15.5207			0.663616			0.331808	+	0.943347i	$0.392341\pi$
$548$	−0.740715	−	7.04743i	−0.0316418	−	0.301051i
$549$	26.4085	−	5.61331i	1.12709	−	0.239570i
$550$	−2.15563	+	20.5094i	−0.0919163	+	0.874525i
$551$	15.9672	+	3.39393i	0.680225	+	0.144586i
$552$	2.59506	−	7.98679i	0.110453	−	0.339940i
$553$	−5.71133	+	2.44908i	−0.242870	+	0.104146i
$554$	−6.75701	+	20.7959i	−0.287078	+	0.883535i
$555$	−21.4538	−	23.8269i	−0.910665	−	1.01140i
$556$	10.8210	−	12.0179i	0.458912	−	0.509673i
$557$	−1.78785	+	17.0102i	−0.0757536	+	0.720747i	0.889056	+	0.457798i	$0.151362\pi$
$557$	−1.78785	+	17.0102i	−0.0757536	+	0.720747i	−0.964810	+	0.262949i	$0.915305\pi$
$558$	−6.55213	−	7.27688i	−0.277374	−	0.308055i
$559$	21.6026	−	15.6952i	0.913692	−	0.663836i
$560$	3.17795	−	0.629838i	0.134293	−	0.0266155i
$561$	−0.0152541	−	0.0469474i	−0.000644030	−	0.00198212i
$562$	1.77088	+	16.8488i	0.0747000	+	0.710723i
$563$	1.95411	−	18.5922i	0.0823561	−	0.783566i	−0.872923	−	0.487859i	$-0.837778\pi$
$563$	1.95411	−	18.5922i	0.0823561	−	0.783566i	0.955279	−	0.295707i	$-0.0955553\pi$
$564$	1.63255	−	15.5326i	0.0687426	−	0.654042i
$565$	7.37977	−	12.7821i	0.310469	−	0.537748i
$566$	2.72475	+	1.97965i	0.114530	+	0.0832109i
$567$	1.22018	−	10.2483i	0.0512429	−	0.430388i
$568$	2.31930	+	7.13809i	0.0973159	+	0.299507i
$569$	−2.28389	−	21.7297i	−0.0957455	−	0.910957i	−0.931962	−	0.362557i	$-0.881904\pi$
$569$	−2.28389	−	21.7297i	−0.0957455	−	0.910957i	0.836216	−	0.548400i	$-0.184763\pi$
$570$	−11.5349	−	5.13568i	−0.483145	−	0.215110i
$571$	−10.1923	−	17.6537i	−0.426536	−	0.738782i	0.570026	−	0.821626i	$-0.306933\pi$
$571$	−10.1923	−	17.6537i	−0.426536	−	0.738782i	−0.996563	+	0.0828441i	$0.973600\pi$
$572$	−19.8122	−	4.21121i	−0.828390	−	0.176080i
$573$	3.42074			0.142904
$574$	9.66513	+	13.9135i	0.403415	+	0.580738i
$575$	−10.1475			−0.423182
$576$	−5.27457	−	1.12114i	−0.219774	−	0.0467144i
$577$	−12.5145	−	21.6758i	−0.520987	−	0.902376i	−0.999702	−	0.0244058i	$-0.992231\pi$
$577$	−12.5145	−	21.6758i	−0.520987	−	0.902376i	0.478715	−	0.877970i	$-0.341103\pi$
$578$	−15.5303	−	6.91452i	−0.645974	−	0.287606i
$579$	−6.72527	−	63.9866i	−0.279493	−	2.65919i
$580$	1.73537	+	5.34091i	0.0720572	+	0.221769i
$581$	30.4241	+	22.7517i	1.26220	+	0.943899i
$582$	−17.0241	−	12.3688i	−0.705673	−	0.512701i
$583$	−28.4933	+	49.3518i	−1.18007	+	2.04394i
$584$	−0.234505	+	2.23117i	−0.00970389	+	0.0923263i
$585$	2.37306	−	22.5781i	0.0981138	−	0.933491i
$586$	−0.865685	−	8.23644i	−0.0357611	−	0.340244i
$587$	−3.23553	−	9.95794i	−0.133545	−	0.411008i	0.861816	−	0.507221i	$-0.169327\pi$
$587$	−3.23553	−	9.95794i	−0.133545	−	0.411008i	−0.995361	+	0.0962127i	$0.969327\pi$
$588$	18.7459	−	7.73431i	0.773068	−	0.318958i
$589$	−5.22907	+	3.79914i	−0.215460	+	0.156541i
$590$	7.28128	+	8.08668i	0.299766	+	0.332923i
$591$	−4.02142	+	38.2613i	−0.165419	+	1.57386i
$592$	−6.04781	+	6.71678i	−0.248564	+	0.276058i
$593$	−17.1330	−	19.0281i	−0.703569	−	0.781392i	0.280371	−	0.959892i	$-0.409542\pi$
$593$	−17.1330	−	19.0281i	−0.703569	−	0.781392i	−0.983940	+	0.178500i	$0.942876\pi$
$594$	−12.6172	+	38.8317i	−0.517689	+	1.59328i
$595$	0.00750443	+	0.00561195i	0.000307652	+	0.000230067i
$596$	1.24632	−	3.83578i	0.0510513	−	0.157120i
$597$	−37.8393	−	8.04299i	−1.54866	−	0.329178i
$598$	1.04180	−	9.91206i	0.0426023	−	0.405334i
$599$	−40.1110	+	8.52585i	−1.63889	+	0.348357i	−0.932976	−	0.359940i	$-0.882797\pi$
$599$	−40.1110	+	8.52585i	−1.63889	+	0.348357i	−0.705915	+	0.708297i	$0.749464\pi$
$600$	1.06003	+	10.0855i	0.0432754	+	0.411738i
$601$	7.90849			0.322594			0.161297	−	0.986906i	$-0.448432\pi$
$601$	7.90849			0.322594			0.161297	+	0.986906i	$0.448432\pi$
$602$	10.5183	−	17.6518i	0.428695	−	0.719434i
$603$	20.8379	−	15.1396i	0.848585	−	0.616533i
$604$	13.0100	−	5.79243i	0.529369	−	0.235690i
$605$	−3.03426	+	28.8691i	−0.123360	+	1.17369i
$606$	−3.86485	−	6.69412i	−0.156999	−	0.271930i
$607$	9.75453	−	4.34300i	0.395924	−	0.176277i	−0.199110	−	0.979977i	$-0.563805\pi$
$607$	9.75453	−	4.34300i	0.395924	−	0.176277i	0.595034	+	0.803700i	$0.297138\pi$
$608$	−1.09992	+	3.38520i	−0.0446076	+	0.137288i
$609$	17.1542	+	30.6811i	0.695125	+	1.24326i
$610$	4.95996	−	3.60362i	0.200823	−	0.145906i
$611$	−1.93753	−	18.4344i	−0.0783842	−	0.745776i
$612$	−0.00779854	−	0.0135075i	−0.000315237	−	0.000546007i
$613$	−8.24761	+	9.15990i	−0.333118	+	0.369965i	−0.886313	−	0.463087i	$-0.846742\pi$
$613$	−8.24761	+	9.15990i	−0.333118	+	0.369965i	0.553195	+	0.833052i	$0.313408\pi$
$614$	−14.5522	+	25.2051i	−0.587278	+	1.01719i
$615$	19.7547	−	11.2112i	0.796585	−	0.452080i
$616$	−15.2892	+	3.03017i	−0.616018	+	0.122089i
$617$	11.4708	+	35.3034i	0.461795	+	1.42126i	0.862969	+	0.505257i	$0.168602\pi$
$617$	11.4708	+	35.3034i	0.461795	+	1.42126i	−0.401173	+	0.916002i	$0.631398\pi$
$618$	−3.29369	+	5.70483i	−0.132492	+	0.229482i
$619$	−11.3219	−	5.04082i	−0.455064	−	0.202608i	0.166387	−	0.986061i	$-0.446790\pi$
$619$	−11.3219	−	5.04082i	−0.455064	−	0.202608i	−0.621451	+	0.783453i	$0.713457\pi$
$620$	−2.03134	−	0.904411i	−0.0815806	−	0.0363220i
$621$	−19.6519	−	4.17715i	−0.788605	−	0.167623i
$622$	1.82967	−	5.63113i	0.0733629	−	0.225788i
$623$	−3.24614	−	35.5988i	−0.130054	−	1.42624i
$624$	−9.96026			−0.398729
$625$	4.34556	−	1.93477i	0.173822	−	0.0773907i
$626$	0.0813250	−	0.773755i	0.00325040	−	0.0309255i
$627$	55.4948	+	24.7079i	2.21625	+	0.986738i
$628$	−8.50247	−	1.80726i	−0.339286	−	0.0721174i
$629$	−0.0261426			−0.00104237
$630$	−5.16902	−	16.6879i	−0.205939	−	0.664861i
$631$	1.51028	−	4.64816i	0.0601232	−	0.185040i	−0.916484	−	0.400071i	$-0.868985\pi$
$631$	1.51028	−	4.64816i	0.0601232	−	0.185040i	0.976607	+	0.215031i	$0.0689853\pi$
$632$	2.14571	−	0.955333i	0.0853519	−	0.0380011i
$633$	−32.4980	+	36.0927i	−1.29168	+	1.43456i
$634$	10.6407	−	2.26176i	0.422597	−	0.0898258i
$635$	15.7857	+	17.5318i	0.626436	+	0.695728i
$636$	−8.65958	+	26.6514i	−0.343375	+	1.05680i
$637$	19.8533	−	13.6042i	0.786617	−	0.539019i
$638$	−8.34890	−	25.6953i	−0.330536	−	1.01729i
$639$	36.9733	−	16.4616i	1.46264	−	0.651210i
$640$	−1.19775	+	0.254591i	−0.0473454	+	0.0100636i
$641$	43.4653	+	19.3520i	1.71678	+	0.764358i	0.997578	+	0.0695536i	$0.0221575\pi$
$641$	43.4653	+	19.3520i	1.71678	+	0.764358i	0.719199	+	0.694805i	$0.244509\pi$
$642$	−16.6379	+	28.8177i	−0.656646	+	1.13734i
$643$	7.05805	+	21.7224i	0.278342	+	0.856649i	0.988316	+	0.152421i	$0.0487069\pi$
$643$	7.05805	+	21.7224i	0.278342	+	0.856649i	−0.709974	+	0.704228i	$0.751293\pi$
$644$	−2.26926	−	7.32618i	−0.0894214	−	0.288692i
$645$	−22.2887	−	16.1937i	−0.877618	−	0.637627i
$646$	−0.00940522	+	0.00418747i	−0.000370043	+	0.000164754i
$647$	6.03858	+	10.4591i	0.237401	+	0.411190i	0.959968	−	0.280111i	$-0.0903712\pi$
$647$	6.03858	+	10.4591i	0.237401	+	0.411190i	−0.722567	+	0.691301i	$0.757038\pi$
$648$	−0.407750	+	3.87948i	−0.0160179	+	0.152400i
$649$	−35.0304	−	38.9052i	−1.37506	−	1.52716i
$650$	3.71919	+	11.4465i	0.145878	+	0.448968i
$651$	−13.5728	−	3.08113i	−0.531960	−	0.120759i
$652$	8.07446	−	5.86644i	0.316220	−	0.229748i
$653$	−18.1616	+	31.4569i	−0.710720	+	1.23100i	0.253867	+	0.967239i	$0.418297\pi$
$653$	−18.1616	+	31.4569i	−0.710720	+	1.23100i	−0.964587	+	0.263764i	$0.915036\pi$
$654$	21.4226	−	23.7922i	0.837691	−	0.930350i
$655$	−10.8130	−	18.7286i	−0.422498	−	0.731788i
$656$	−3.72522	−	5.20795i	−0.145445	−	0.203336i
$657$	12.0976			0.471974
$658$	−6.96097	−	12.4500i	−0.271367	−	0.485351i
$659$	−29.5896			−1.15265			−0.576323	−	0.817222i	$-0.695513\pi$
$659$	−29.5896			−1.15265			−0.576323	+	0.817222i	$0.695513\pi$
$660$	2.18445	+	20.7837i	0.0850297	+	0.809003i
$661$	43.6526	+	19.4354i	1.69789	+	0.755950i	0.999178	+	0.0405477i	$0.0129103\pi$
$661$	43.6526	+	19.4354i	1.69789	+	0.755950i	0.698713	+	0.715402i	$0.253756\pi$
$662$	4.28384	−	4.75768i	0.166496	−	0.184913i
$663$	−0.0192771	−	0.0214094i	−0.000748661	−	0.000831472i
$664$	−11.6167	−	8.44001i	−0.450814	−	0.327536i
$665$	−11.3116	+	2.24185i	−0.438645	+	0.0869353i
$666$	39.4301	+	28.6476i	1.52789	+	1.11007i
$667$	12.1450	−	5.40731i	0.470257	−	0.209372i
$668$	−2.11029	−	0.939563i	−0.0816497	−	0.0363528i
$669$	−46.0225	+	51.1132i	−1.77933	+	1.97615i
$670$	2.92447	−	5.06533i	0.112982	−	0.195691i
$671$	−23.8625	+	17.3371i	−0.921201	+	0.669292i
$672$	−7.04431	+	3.02068i	−0.271740	+	0.116525i
$673$	4.61783	+	3.35505i	0.178004	+	0.129328i	0.673220	−	0.739442i	$-0.264911\pi$
$673$	4.61783	+	3.35505i	0.178004	+	0.129328i	−0.495215	+	0.868770i	$0.664911\pi$
$674$	−16.7719	−	3.56498i	−0.646030	−	0.137318i
$675$	23.7313	−	5.04424i	0.913418	−	0.194153i
$676$	1.15323	−	0.245127i	0.0443551	−	0.00942797i
$677$	−11.7932	−	13.0977i	−0.453250	−	0.503385i	0.472600	−	0.881277i	$-0.343316\pi$
$677$	−11.7932	−	13.0977i	−0.453250	−	0.503385i	−0.925850	+	0.377892i	$0.876649\pi$
$678$	−10.7903	+	33.2092i	−0.414400	+	1.27539i
$679$	−19.2164	−	0.264907i	−0.737457	−	0.0101662i
$680$	−0.00286538	−	0.00208182i	−0.000109882	−	7.98341e-5i
$681$	55.4572	+	61.5915i	2.12513	+	2.36019i
$682$	9.77282	+	4.35114i	0.374221	+	0.166614i
$683$	−5.22596	−	9.05162i	−0.199966	−	0.346351i	0.748551	−	0.663077i	$-0.230750\pi$
$683$	−5.22596	−	9.05162i	−0.199966	−	0.346351i	−0.948517	+	0.316726i	$0.897416\pi$
$684$	18.7744	+	3.99061i	0.717856	+	0.152585i
$685$	−7.02001	+	5.10034i	−0.268221	+	0.194874i
$686$	9.91530	−	15.6425i	0.378568	−	0.597232i
$687$	55.2713	+	40.1570i	2.10873	+	1.53208i
$688$	−3.88321	+	6.72592i	−0.148046	+	0.256423i
$689$	−3.47642	+	33.0760i	−0.132441	+	1.26009i
$690$	−10.0585	+	2.13800i	−0.382921	+	0.0813924i
$691$	12.3398	+	2.62290i	0.469427	+	0.0997798i	0.436551	−	0.899680i	$-0.356200\pi$
$691$	12.3398	+	2.62290i	0.469427	+	0.0997798i	0.0328762	+	0.999459i	$0.489533\pi$
$692$	6.36650	−	4.62553i	0.242018	−	0.175836i
$693$	24.8683	+	80.2858i	0.944668	+	3.04981i
$694$	4.47611			0.169911
$695$	−19.3697	−	4.11716i	−0.734736	−	0.156173i
$696$	−6.64292	−	11.5059i	−0.251799	−	0.436129i
$697$	0.00398460	−	0.0180868i	0.000150928	−	0.000685086i
$698$	−4.09004	+	7.08416i	−0.154810	+	0.268139i
$699$	−11.3917	−	35.0600i	−0.430873	−	1.32609i
$700$	6.10178	+	6.96750i	0.230626	+	0.263347i
$701$	−6.06651	+	4.40757i	−0.229129	+	0.166472i	−0.696426	−	0.717628i	$-0.745228\pi$
$701$	−6.06651	+	4.40757i	−0.229129	+	0.166472i	0.467298	+	0.884100i	$0.345228\pi$
$702$	2.49081	+	23.6985i	0.0940095	+	0.894441i
$703$	21.5266	−	23.9078i	0.811893	−	0.901698i
$704$	5.76243	−	1.22484i	0.217180	−	0.0461630i
$705$	−17.4713	+	7.77871i	−0.658006	+	0.292963i
$706$	18.7545			0.705835
$707$	−6.40890	−	2.95994i	−0.241032	−	0.111320i
$708$	−20.8274	−	15.1320i	−0.782740	−	0.568694i
$709$	−1.62344	−	15.4460i	−0.0609696	−	0.580087i	−0.981773	−	0.190059i	$-0.939132\pi$
$709$	−1.62344	−	15.4460i	−0.0609696	−	0.580087i	0.920803	−	0.390028i	$-0.127535\pi$
$710$	6.14964	−	6.82987i	0.230792	−	0.256320i
$711$	−6.33278	−	10.9687i	−0.237498	−	0.411358i
$712$	1.41228	+	13.4369i	0.0529273	+	0.503569i
$713$	−1.62665	+	5.00631i	−0.0609184	+	0.187488i
$714$	−0.0201265	−	0.00929540i	−0.000753215	−	0.000347871i
$715$	7.66433	+	23.5884i	0.286630	+	0.882155i
$716$	16.0224	+	17.7947i	0.598786	+	0.665019i
$717$	−60.9168	+	12.9483i	−2.27498	+	0.483562i
$718$	−13.3062	+	2.82831i	−0.496582	+	0.105552i
$719$	−29.2903	−	32.5302i	−1.09235	−	1.21317i	−0.975495	−	0.220023i	$-0.929387\pi$
$719$	−29.2903	−	32.5302i	−1.09235	−	1.21317i	−0.116850	−	0.993150i	$-0.537280\pi$
$720$	2.04046	+	6.27990i	0.0760436	+	0.234038i
$721$	0.546325	+	5.99128i	0.0203462	+	0.223127i
$722$	−1.95626	+	6.02076i	−0.0728046	+	0.224069i
$723$	−8.38327	−	79.7615i	−0.311777	−	2.96636i
$724$	6.57420	+	11.3868i	0.244328	+	0.423189i
$725$	−10.7422	+	11.9305i	−0.398957	+	0.443087i
$726$	−7.17848	−	68.2987i	−0.266418	−	2.53480i
$727$	−35.9697	−	26.1335i	−1.33404	−	0.969240i	−0.999641	−	0.0268096i	$-0.991465\pi$
$727$	−35.9697	−	26.1335i	−1.33404	−	0.969240i	−0.334403	−	0.942430i	$-0.608535\pi$
$728$	−7.43226	+	5.24486i	−0.275458	+	0.194388i
$729$	−39.1993			−1.45182
$730$	2.50964	−	1.11736i	0.0928859	−	0.0413555i
$731$	−0.0219728	+	0.00467047i	−0.000812694	+	0.000172744i
$732$	−9.70535	+	10.7789i	−0.358720	+	0.398399i
$733$	−2.61909	−	24.9190i	−0.0967384	−	0.920405i	−0.930008	−	0.367538i	$-0.880201\pi$
$733$	−2.61909	−	24.9190i	−0.0967384	−	0.920405i	0.833270	−	0.552866i	$-0.186466\pi$
$734$	−6.22684	+	4.52406i	−0.229837	+	0.166986i
$735$	−19.6792	−	15.1439i	−0.725879	−	0.558590i
$736$	0.895787	+	2.75695i	0.0330191	+	0.101622i
$737$	−14.0697	+	24.3694i	−0.518264	+	0.897659i
$738$	−25.8298	+	22.9134i	−0.950808	+	0.843453i
$739$	−15.2642	−	26.4384i	−0.561504	−	0.972553i	−0.997366	−	0.0725392i	$-0.976890\pi$
$739$	−15.2642	−	26.4384i	−0.561504	−	0.972553i	0.435862	−	0.900014i	$-0.356444\pi$
$740$	10.8257	+	2.30107i	0.397960	+	0.0845890i
$741$	35.4526			1.30239
$742$	7.57239	+	24.4470i	0.277991	+	0.897479i
$743$	−26.5176	+	19.2662i	−0.972836	+	0.706807i	−0.956096	−	0.293053i	$-0.905329\pi$
$743$	−26.5176	+	19.2662i	−0.972836	+	0.706807i	−0.0167400	+	0.999860i	$0.505329\pi$
$744$	5.14561	+	1.09373i	0.188647	+	0.0400982i
$745$	−4.83076	+	1.02681i	−0.176985	+	0.0376194i
$746$	2.72504	−	25.9270i	0.0997706	−	0.949254i
$747$	−38.7148	+	67.0560i	−1.41650	+	2.45345i
$748$	0.0137854	+	0.0100157i	0.000504044	+	0.000366209i
$749$	2.75974	+	30.2647i	0.100839	+	1.10585i
$750$	24.3956	−	17.7245i	0.890803	−	0.647206i
$751$	20.0310	+	4.25771i	0.730940	+	0.155366i	0.558324	−	0.829623i	$-0.311445\pi$
$751$	20.0310	+	4.25771i	0.730940	+	0.155366i	0.172616	+	0.984989i	$0.444778\pi$
$752$	2.69561	+	4.66894i	0.0982989	+	0.170259i
$753$	19.8060	+	8.81821i	0.721771	+	0.321353i
$754$	−10.5508	−	11.7178i	−0.384236	−	0.426737i
$755$	−14.1081	−	10.2501i	−0.513446	−	0.373040i
$756$	8.94872	+	16.0052i	0.325462	+	0.582102i
$757$	9.95026	−	30.6238i	0.361648	−	1.11304i	−0.590405	−	0.807107i	$-0.701032\pi$
$757$	9.95026	−	30.6238i	0.361648	−	1.11304i	0.952053	−	0.305932i	$-0.0989680\pi$
$758$	−2.09767	−	2.32970i	−0.0761909	−	0.0846185i
$759$	48.3917	−	10.2860i	1.75651	−	0.373357i
$760$	4.26330	−	0.906193i	0.154646	−	0.0328711i
$761$	−17.7034	−	3.76298i	−0.641749	−	0.136408i	−0.124468	−	0.992224i	$-0.539722\pi$
$761$	−17.7034	−	3.76298i	−0.641749	−	0.136408i	−0.517281	+	0.855816i	$0.673056\pi$
$762$	−45.1534	−	32.8059i	−1.63573	−	1.18843i
$763$	3.45688	−	29.0343i	0.125148	−	1.05111i
$764$	−0.955289	+	0.694058i	−0.0345611	+	0.0251101i
$765$	−0.00954942	+	0.0165401i	−0.000345260	+	0.000598008i
$766$	9.72508	−	10.8008i	0.351382	−	0.390249i
$767$	−27.9120	−	12.4272i	−1.00784	−	0.448721i
$768$	2.64651	−	1.17830i	0.0954977	−	0.0425183i
$769$	−23.3537	−	16.9674i	−0.842155	−	0.611861i	0.0808169	−	0.996729i	$-0.474247\pi$
$769$	−23.3537	−	16.9674i	−0.842155	−	0.611861i	−0.922972	+	0.384868i	$0.874247\pi$
$770$	12.5743	+	14.3583i	0.453145	+	0.517438i
$771$	−60.0329	−	43.6165i	−2.16203	−	1.57081i
$772$	14.8608	+	16.5046i	0.534852	+	0.594014i
$773$	−22.1802	+	24.6336i	−0.797768	+	0.886011i	−0.995550	−	0.0942354i	$-0.969959\pi$
$773$	−22.1802	+	24.6336i	−0.797768	+	0.886011i	0.197782	+	0.980246i	$0.436626\pi$
$774$	38.2590	+	17.0340i	1.37519	+	0.612275i
$775$	−0.664449	−	6.32181i	−0.0238677	−	0.227086i
$776$	7.26380			0.260755
$777$	69.2689	+	0.954906i	2.48501	+	0.0342571i
$778$	−19.6907			−0.705946
$779$	13.2596	+	18.5372i	0.475074	+	0.664165i
$780$	6.09823	+	10.5624i	0.218352	+	0.378196i
$781$	−29.5861	+	32.8587i	−1.05867	+	1.17578i
$782$	−0.00419231	+	0.00726129i	−0.000149917	+	0.000259663i
$783$	−25.7147	+	18.6829i	−0.918970	+	0.667671i
$784$	−3.66578	+	5.96339i	−0.130921	+	0.212978i
$785$	3.28917	+	10.1230i	0.117396	+	0.361307i
$786$	34.2346	+	38.0214i	1.22111	+	1.35618i
$787$	−2.86099	+	27.2205i	−0.101983	+	0.970305i	0.817168	+	0.576400i	$0.195543\pi$
$787$	−2.86099	+	27.2205i	−0.101983	+	0.970305i	−0.919151	+	0.393905i	$0.871124\pi$
$788$	−6.64005	−	11.5009i	−0.236542	−	0.409703i
$789$	−41.8448	+	18.6305i	−1.48971	+	0.663263i
$790$	−2.32682	−	1.69053i	−0.0827846	−	0.0601465i
$791$	9.43563	+	30.4624i	0.335492	+	1.08312i
$792$	−9.81672	−	30.2127i	−0.348822	−	1.07356i
$793$	−8.60705	+	14.9078i	−0.305645	+	0.529393i
$794$	−29.8726	−	13.3001i	−1.06014	−	0.472004i
$795$	33.5647	−	7.13439i	1.19042	−	0.253031i
$796$	12.1990	−	5.43136i	0.432383	−	0.192509i
$797$	−3.45883	−	10.6452i	−0.122518	−	0.377071i	0.870923	−	0.491420i	$-0.163522\pi$
$797$	−3.45883	−	10.6452i	−0.122518	−	0.377071i	−0.993441	+	0.114348i	$0.963522\pi$
$798$	25.0736	−	10.7518i	0.887596	−	0.380611i
$799$	−0.00481870	+	0.0148304i	−0.000170474	+	0.000524664i
$800$	−2.34234	−	2.60143i	−0.0828141	−	0.0919744i
$801$	71.2643	−	15.1477i	2.51800	−	0.535218i
$802$	10.2015	−	11.3299i	0.360229	−	0.400074i
$803$	−12.0739	+	5.37566i	−0.426080	+	0.189703i
$804$	−4.27601	+	13.1602i	−0.150803	+	0.464125i
$805$	−6.37975	+	6.89196i	−0.224857	+	0.242910i
$806$	6.24333			0.219912
$807$	66.5048	+	14.1360i	2.34108	+	0.497612i
$808$	2.43753	+	1.08526i	0.0857519	+	0.0381792i
$809$	−1.87287	+	17.8191i	−0.0658464	+	0.626487i	0.910980	+	0.412452i	$0.135327\pi$
$809$	−1.87287	+	17.8191i	−0.0658464	+	0.626487i	−0.976826	+	0.214035i	$0.931339\pi$
$810$	4.36368	−	1.94283i	0.153324	−	0.0682642i
$811$	−39.9893			−1.40421			−0.702107	−	0.712071i	$-0.747757\pi$
$811$	−39.9893			−1.40421			−0.702107	+	0.712071i	$0.747757\pi$
$812$	−11.0156	−	5.08756i	−0.386573	−	0.178538i
$813$	7.62144	−	23.4564i	0.267296	−	0.822651i
$814$	−52.0826	−	11.0705i	−1.82549	−	0.388021i
$815$	−11.1648	−	4.97088i	−0.391085	−	0.174122i
$816$	0.00765480	+	0.00340814i	0.000267972	+	0.000119309i
$817$	13.8219	−	23.9403i	0.483569	−	0.837565i
$818$	1.30936	+	4.02978i	0.0457805	+	0.140898i
$819$	32.3168	+	36.9019i	1.12924	+	1.28946i
$820$	−3.24203	+	7.13905i	−0.113217	+	0.249306i
$821$	20.6582	−	35.7811i	0.720977	−	1.24877i	−0.239632	−	0.970864i	$-0.577027\pi$
$821$	20.6582	−	35.7811i	0.720977	−	1.24877i	0.960609	−	0.277904i	$-0.0896398\pi$
$822$	13.7363	−	15.2557i	0.479110	−	0.532105i
$823$	22.2431	+	38.5261i	0.775345	+	1.34294i	0.934601	+	0.355699i	$0.115757\pi$
$823$	22.2431	+	38.5261i	0.775345	+	1.34294i	−0.159256	+	0.987237i	$0.550909\pi$
$824$	−0.237686	−	2.26143i	−0.00828018	−	0.0787807i
$825$	−48.3326	+	35.1157i	−1.68273	+	1.22257i
$826$	−23.5094	−	0.324088i	−0.817996	−	0.0112765i
$827$	8.61643	−	26.5187i	0.299623	−	0.922144i	−0.682007	−	0.731346i	$-0.738892\pi$
$827$	8.61643	−	26.5187i	0.299623	−	0.922144i	0.981629	−	0.190798i	$-0.0611075\pi$
$828$	14.2802	−	6.35797i	0.496273	−	0.220955i
$829$	−23.1090	−	40.0260i	−0.802610	−	1.39016i	−0.917893	−	0.396828i	$-0.870111\pi$
$829$	−23.1090	−	40.0260i	−0.802610	−	1.39016i	0.115283	−	0.993333i	$-0.463223\pi$
$830$	−1.83790	+	17.4865i	−0.0637945	+	0.606964i
$831$	−57.8690	+	25.7649i	−2.00745	+	0.893776i
$832$	2.78154	−	2.02090i	0.0964324	−	0.0700623i
$833$	−0.0199130	+	0.00366204i	−0.000689944	+	0.000126882i
$834$	46.8489			1.62224
$835$	0.295672	+	2.81313i	0.0102322	+	0.0973525i
$836$	−20.5108	+	4.35971i	−0.709382	+	0.150784i
$837$	1.31553	−	12.5165i	0.0454715	−	0.432633i
$838$	−23.6965	−	5.03684i	−0.818581	−	0.173995i
$839$	−5.03172	+	15.4861i	−0.173714	+	0.534638i	−0.999572	−	0.0292401i	$-0.990691\pi$
$839$	−5.03172	+	15.4861i	−0.173714	+	0.534638i	0.825858	+	0.563878i	$0.190691\pi$
$840$	7.51624	+	5.62078i	0.259335	+	0.193935i
$841$	−2.46208	+	7.57752i	−0.0848994	+	0.261294i
$842$	−7.63241	−	8.47665i	−0.263030	−	0.292125i
$843$	−32.8404	+	36.4729i	−1.13108	+	1.25619i
$844$	1.75242	−	16.6731i	0.0603206	−	0.573912i
$845$	−0.966022	−	1.07288i	−0.0332322	−	0.0369081i
$846$	23.5195	−	17.0879i	0.808617	−	0.587494i
$847$	−41.3212	−	47.1838i	−1.41981	−	1.62126i
$848$	−2.98919	−	9.19978i	−0.102649	−	0.315922i
$849$	1.01988	+	9.70347i	0.0350021	+	0.333022i
$850$	0.00105836	−	0.0100696i	3.63015e−5	−	0.000345385i
$851$	2.73870	−	26.0570i	0.0938814	−	0.893222i
$852$	−10.8715	+	18.8300i	−0.372451	+	0.645104i
$853$	37.9284	+	27.5566i	1.29864	+	0.943521i	0.999941	−	0.0108254i	$-0.00344590\pi$
$853$	37.9284	+	27.5566i	1.29864	+	0.943521i	0.298703	+	0.954346i	$0.403446\pi$
$854$	−1.56611	+	13.1537i	−0.0535913	+	0.450112i
$855$	−7.26284	−	22.3527i	−0.248384	−	0.764447i
$856$	−1.20066	−	11.4235i	−0.0410377	−	0.390448i
$857$	6.86858	+	3.05809i	0.234626	+	0.104462i	0.520682	−	0.853751i	$-0.325678\pi$
$857$	6.86858	+	3.05809i	0.234626	+	0.104462i	−0.286056	+	0.958213i	$0.592344\pi$
$858$	−29.3387	−	50.8162i	−1.00161	−	1.73484i
$859$	21.0882	+	4.48245i	0.719522	+	0.152939i	0.553099	−	0.833115i	$-0.313445\pi$
$859$	21.0882	+	4.48245i	0.719522	+	0.152939i	0.166423	+	0.986055i	$0.446778\pi$
$860$	9.51009			0.324291
$861$	−11.2185	+	47.7783i	−0.382326	+	1.62828i
$862$	21.9156			0.746447
$863$	27.0678	+	5.75344i	0.921399	+	0.195849i	0.644106	−	0.764936i	$-0.277229\pi$
$863$	27.0678	+	5.75344i	0.921399	+	0.195849i	0.277293	+	0.960785i	$0.410563\pi$
$864$	−3.46536	−	6.00218i	−0.117894	−	0.204198i
$865$	−8.80312	−	3.91940i	−0.299315	−	0.133264i
$866$	1.28766	+	12.2512i	0.0437563	+	0.416314i
$867$	−15.2186	−	46.8380i	−0.516850	−	1.59070i
$868$	4.41554	−	1.89343i	0.149873	−	0.0642674i
$869$	11.1944	+	8.13320i	0.379744	+	0.275900i
$870$	−8.13435	+	14.0891i	−0.275780	+	0.477665i
$871$	−1.71662	+	16.3326i	−0.0581656	+	0.553409i
$872$	−1.15519	+	10.9909i	−0.0391196	+	0.372198i
$873$	−4.09432	−	38.9548i	−0.138572	−	1.31842i
$874$	−3.18847	−	9.81311i	−0.107852	−	0.331933i
$875$	8.87048	−	26.0721i	0.299877	−	0.881398i
$876$	−5.25798	+	3.82014i	−0.177651	+	0.129071i
$877$	13.2072	+	14.6681i	0.445976	+	0.495307i	0.923654	−	0.383228i	$-0.125188\pi$
$877$	13.2072	+	14.6681i	0.445976	+	0.495307i	−0.477677	+	0.878535i	$0.658521\pi$
$878$	2.28334	−	21.7245i	0.0770588	−	0.733166i
$879$	16.0539	−	17.8296i	0.541483	−	0.601378i
$880$	−4.82698	−	5.36090i	−0.162717	−	0.180716i
$881$	−15.6973	+	48.3113i	−0.528855	+	1.62765i	0.227709	+	0.973729i	$0.426876\pi$
$881$	−15.6973	+	48.3113i	−0.528855	+	1.62765i	−0.756564	+	0.653919i	$0.773124\pi$
$882$	34.0472	+	16.2978i	1.14643	+	0.548774i
$883$	−1.57072	+	4.83417i	−0.0528588	+	0.162683i	−0.974001	−	0.226543i	$-0.927258\pi$
$883$	−1.57072	+	4.83417i	−0.0528588	+	0.162683i	0.921142	+	0.389226i	$0.127258\pi$
$884$	0.00972730	+	0.00206760i	0.000327164	+	6.95409e-5i
$885$	−3.29515	+	31.3512i	−0.110765	+	1.05386i
$886$	17.6169	−	3.74458i	0.591850	−	0.125802i
$887$	2.03234	+	19.3364i	0.0682393	+	0.649253i	0.974168	+	0.225824i	$0.0725073\pi$
$887$	2.03234	+	19.3364i	0.0682393	+	0.649253i	−0.905929	+	0.423430i	$0.860826\pi$
$888$	−26.1837			−0.878667
$889$	−50.9679	−	0.702618i	−1.70941	−	0.0235651i
$890$	13.3846	−	9.72450i	0.448653	−	0.325966i
$891$	−20.9938	+	9.34702i	−0.703317	+	0.313137i
$892$	2.48171	−	23.6119i	0.0830938	−	0.790585i
$893$	−9.59479	−	16.6187i	−0.321077	−	0.556122i
$894$	10.6738	−	4.75230i	0.356987	−	0.158941i
$895$	9.06073	−	27.8861i	0.302867	−	0.932128i
$896$	1.35433	−	2.27284i	0.0452451	−	0.0759301i
$897$	23.3588	−	16.9712i	0.779928	−	0.566651i
$898$	−2.43080	−	23.1275i	−0.0811167	−	0.771774i
$899$	4.16394	+	7.21216i	0.138875	+	0.240539i
$900$	−12.6308	+	14.0280i	−0.421028	+	0.467599i
$901$	0.0139895	−	0.0242305i	0.000466057	−	0.000807235i
$902$	15.5975	−	34.3461i	0.519340	−	1.14360i
$903$	58.3912	−	11.5726i	1.94314	−	0.385111i
$904$	−3.72470	−	11.4635i	−0.123882	−	0.381269i
$905$	8.05019	−	13.9433i	0.267598	−	0.463492i
$906$	37.6895	+	16.7805i	1.25215	+	0.557493i
$907$	6.89102	+	3.06808i	0.228813	+	0.101874i	0.517941	−	0.855416i	$-0.326699\pi$
$907$	6.89102	+	3.06808i	0.228813	+	0.101874i	−0.289128	+	0.957290i	$0.593365\pi$
$908$	−27.9839	−	5.94817i	−0.928679	−	0.197397i
$909$	4.44615	−	13.6839i	0.147470	−	0.453865i
$910$	10.1124	+	4.67041i	0.335223	+	0.154822i
$911$	25.4825			0.844273			0.422137	−	0.906532i	$-0.361280\pi$
$911$	25.4825			0.844273			0.422137	+	0.906532i	$0.361280\pi$
$912$	−9.42001	+	4.19406i	−0.311928	+	0.138879i
$913$	8.84219	−	84.1278i	0.292634	−	2.78422i
$914$	−33.4135	−	14.8766i	−1.10522	−	0.492075i
$915$	17.3727	+	3.69269i	0.574325	+	0.122077i
$916$	−23.5830			−0.779204
$917$	45.5669	+	10.3440i	1.50475	+	0.341589i
$918$	0.00619472	−	0.0190654i	0.000204456	−	0.000629251i
$919$	6.33077	−	2.81864i	0.208833	−	0.0929783i	−0.299655	−	0.954048i	$-0.596871\pi$
$919$	6.33077	−	2.81864i	0.208833	−	0.0929783i	0.508487	+	0.861069i	$0.330205\pi$
$920$	2.37518	−	2.63791i	0.0783074	−	0.0869692i
$921$	−82.4718	+	17.5299i	−2.71754	+	0.577630i
$922$	10.7890	+	11.9824i	0.355318	+	0.394621i
$923$	−7.97416	+	24.5419i	−0.262473	+	0.807808i
$924$	−36.1608	−	27.0417i	−1.18960	−	0.889607i
$925$	9.77706	+	30.0907i	0.321468	+	0.989376i
$926$	−27.5283	+	12.2564i	−0.904635	+	0.402769i
$927$	−11.9938	+	2.54936i	−0.393928	+	0.0837319i
$928$	4.18963	+	1.86534i	0.137531	+	0.0612329i
$929$	−18.3440	+	31.7728i	−0.601848	+	1.04243i	0.390694	+	0.920521i	$0.372235\pi$
$929$	−18.3440	+	31.7728i	−0.601848	+	1.04243i	−0.992541	+	0.121910i	$0.961098\pi$
$930$	−1.99057	−	6.12635i	−0.0652734	−	0.200891i
$931$	13.0480	−	21.2262i	0.427631	−	0.695659i
$932$	10.2949	+	7.47965i	0.337219	+	0.245004i
$933$	15.6698	−	6.97663i	0.513005	−	0.228405i
$934$	−13.9227	−	24.1149i	−0.455566	−	0.789063i
$935$	0.00218102	−	0.0207510i	7.13270e−5	−	0.000678631i
$936$	−12.4057	−	13.7779i	−0.405493	−	0.450345i
$937$	12.2149	+	37.5937i	0.399045	+	1.22813i	0.925766	+	0.378096i	$0.123421\pi$
$937$	12.2149	+	37.5937i	0.399045	+	1.22813i	−0.526722	+	0.850038i	$0.676579\pi$
$938$	3.73917	+	12.0717i	0.122088	+	0.394155i
$939$	1.82343	−	1.32480i	0.0595055	−	0.0432333i
$940$	3.30081	−	5.71718i	0.107661	−	0.186474i
$941$	13.8209	−	15.3497i	0.450549	−	0.500385i	−0.474488	−	0.880262i	$-0.657367\pi$
$941$	13.8209	−	15.3497i	0.450549	−	0.500385i	0.925037	+	0.379876i	$0.124034\pi$
$942$	−12.5908	−	21.8079i	−0.410231	−	0.710541i
$943$	17.6102	+	5.86634i	0.573465	+	0.191034i
$944$	8.88655			0.289233
$945$	11.4939	−	19.2890i	0.373897	−	0.627472i
$946$	−45.7533			−1.48757
$947$	−1.34274	−	12.7754i	−0.0436333	−	0.415143i	−0.994436	−	0.105345i	$-0.966405\pi$
$947$	−1.34274	−	12.7754i	−0.0436333	−	0.415143i	0.950802	−	0.309798i	$-0.100261\pi$
$948$	6.21606	+	2.76757i	0.201888	+	0.0898864i
$949$	−5.16126	+	5.73216i	−0.167542	+	0.186074i
$950$	8.33734	+	9.25955i	0.270499	+	0.300419i
$951$	25.4958	+	18.5237i	0.826756	+	0.600674i
$952$	0.00750660	−	0.00148774i	0.000243290	−	4.82178e-5i
$953$	−36.0267	−	26.1749i	−1.16702	−	0.847888i	−0.176369	−	0.984324i	$-0.556435\pi$
$953$	−36.0267	−	26.1749i	−1.16702	−	0.847888i	−0.990649	+	0.136436i	$0.956435\pi$
$954$	−47.6523	+	21.2162i	−1.54280	+	0.686899i
$955$	1.32090	+	0.588104i	0.0427434	+	0.0190306i
$956$	14.3847	−	15.9758i	0.465234	−	0.516695i
$957$	39.1345	−	67.7830i	1.26504	−	2.19111i
$958$	−7.92087	+	5.75485i	−0.255912	+	0.185931i
$959$	2.21658	−	18.6170i	0.0715770	−	0.601173i
$960$	−2.86989	−	2.08509i	−0.0926251	−	0.0672961i
$961$	27.0972	+	5.75969i	0.874103	+	0.185796i
$962$	−30.3962	+	6.46091i	−0.980012	+	0.208308i
$963$	−60.5860	+	12.8780i	−1.95236	+	0.414986i
$964$	18.5245	+	20.5736i	0.596634	+	0.662629i
$965$	8.40384	−	25.8643i	0.270529	−	0.832603i
$966$	11.3734	−	19.0868i	0.365934	−	0.614109i
$967$	−8.87306	−	6.44666i	−0.285338	−	0.207311i	0.435904	−	0.899993i	$-0.356429\pi$
$967$	−8.87306	−	6.44666i	−0.285338	−	0.207311i	−0.721243	+	0.692683i	$0.756429\pi$
$968$	15.8623	+	17.6168i	0.509833	+	0.566227i
$969$	−0.0272466	−	0.0121310i	−0.000875286	−	0.000389703i
$970$	−4.44731	−	7.70297i	−0.142795	−	0.247327i
$971$	14.2124	+	3.02093i	0.456096	+	0.0969462i	0.430230	−	0.902719i	$-0.358432\pi$
$971$	14.2124	+	3.02093i	0.456096	+	0.0969462i	0.0258659	+	0.999665i	$0.491766\pi$
$972$	7.67883	−	5.57900i	0.246299	−	0.178946i
$973$	34.9582	−	24.6696i	1.12071	−	0.790872i
$974$	−11.0323	−	8.01543i	−0.353498	−	0.256831i
$975$	−17.4333	+	30.1953i	−0.558312	+	0.967024i
$976$	0.523349	−	4.97934i	0.0167520	−	0.159385i
$977$	52.4873	−	11.1565i	1.67922	−	0.356928i	0.732942	−	0.680292i	$-0.238147\pi$
$977$	52.4873	−	11.1565i	1.67922	−	0.356928i	0.946275	+	0.323363i	$0.104814\pi$
$978$	28.2816	+	6.01144i	0.904346	+	0.192225i
$979$	−64.3937	+	46.7848i	−2.05803	+	1.49525i
$980$	8.56834	+	0.236282i	0.273705	+	0.00754776i
$981$	59.5938			1.90268
$982$	8.05923	+	1.71304i	0.257180	+	0.0546654i
$983$	−27.1318	−	46.9936i	−0.865369	−	1.49886i	−0.866680	−	0.498864i	$-0.833751\pi$
$983$	−27.1318	−	46.9936i	−0.865369	−	1.49886i	0.00131091	−	0.999999i	$-0.499583\pi$
$984$	3.99087	−	18.1152i	0.127224	−	0.577493i
$985$	−8.13083	+	14.0830i	−0.259070	+	0.448722i
$986$	0.00409910	+	0.0126157i	0.000130542	+	0.000401767i
$987$	13.3096	−	39.1197i	0.423651	−	1.24519i
$988$	−9.90063	+	7.19323i	−0.314981	+	0.228847i
$989$	−2.35330	−	22.3902i	−0.0748307	−	0.711967i
$990$	−26.0290	+	28.9082i	−0.827257	+	0.918762i
$991$	−41.0552	+	8.72655i	−1.30416	+	0.277208i	−0.807052	−	0.590480i	$-0.798939\pi$
$991$	−41.0552	+	8.72655i	−1.30416	+	0.277208i	−0.497109	+	0.867688i	$0.665605\pi$
$992$	−1.65890	+	0.738588i	−0.0526700	+	0.0234502i
$993$	18.5467			0.588560
$994$	1.80326	+	19.7755i	0.0571958	+	0.627239i
$995$	−13.2287	−	9.61120i	−0.419377	−	0.304695i
$996$	−4.34812	−	41.3696i	−0.137776	−	1.31085i
$997$	−14.3611	+	15.9496i	−0.454821	+	0.505130i	−0.926321	−	0.376736i	$-0.877046\pi$
$997$	−14.3611	+	15.9496i	−0.454821	+	0.505130i	0.471499	+	0.881866i	$0.343713\pi$
$998$	11.1967	+	19.3933i	0.354426	+	0.613884i
$999$	6.54788	+	62.2989i	0.207166	+	1.97105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.s.b.387.2	yes	112
7.4	even	3	inner	574.2.s.b.305.2	yes	112
41.16	even	5	inner	574.2.s.b.303.2	yes	112
287.221	even	15	inner	574.2.s.b.221.2	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.s.b.221.2	✓	112	287.221	even	15	inner
574.2.s.b.303.2	yes	112	41.16	even	5	inner
574.2.s.b.305.2	yes	112	7.4	even	3	inner
574.2.s.b.387.2	yes	112	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.s (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(-1.44848 - 2.50885i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.127997 - 1.21781i) q^{5} +(0.895212 + 2.75518i) q^{6} +(2.11882 + 1.58449i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.69620 + 4.66996i) q^{9} +O(q^{10})\)	\(q+(-0.978148 - 0.207912i) q^{2} +(-1.44848 - 2.50885i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.127997 - 1.21781i) q^{5} +(0.895212 + 2.75518i) q^{6} +(2.11882 + 1.58449i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-2.69620 + 4.66996i) q^{9} +(-0.127997 + 1.21781i) q^{10} +(0.615794 - 5.85889i) q^{11} +(-0.302815 - 2.88110i) q^{12} +(-1.06245 - 3.26989i) q^{13} +(-1.74308 - 1.99039i) q^{14} +(-2.86989 + 2.08509i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.000302340 + 0.00287657i) q^{17} +(3.60823 - 4.00734i) q^{18} +(-2.38171 - 2.64516i) q^{19} +(0.378395 - 1.16458i) q^{20} +(0.906170 - 7.61089i) q^{21} +(-1.82047 + 5.60283i) q^{22} +(-2.83548 - 0.602700i) q^{23} +(-0.302815 + 2.88110i) q^{24} +(3.42407 - 0.727809i) q^{25} +(0.359386 + 3.41933i) q^{26} +6.93073 q^{27} +(1.29117 + 2.30930i) q^{28} +(-3.71025 + 2.69566i) q^{29} +(3.24069 - 1.44285i) q^{30} +(0.189812 - 1.80594i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-15.5910 + 6.94157i) q^{33} +(0.000893805 - 0.00275085i) q^{34} +(1.65840 - 2.78312i) q^{35} +(-4.36255 + 3.16958i) q^{36} +(0.944761 + 8.98880i) q^{37} +(1.77971 + 3.08254i) q^{38} +(-6.66471 + 7.40191i) q^{39} +(-0.612257 + 1.06046i) q^{40} +(-6.36292 - 0.716423i) q^{41} +(-2.46876 + 7.25618i) q^{42} +(2.39996 + 7.38631i) q^{43} +(2.94558 - 5.10190i) q^{44} +(6.03221 + 2.68571i) q^{45} +(2.64821 + 1.17906i) q^{46} +(5.27341 + 1.12090i) q^{47} +(0.895212 - 2.75518i) q^{48} +(1.97878 + 6.71449i) q^{49} -3.50057 q^{50} +(0.00765480 - 0.00340814i) q^{51} +(0.359386 - 3.41933i) q^{52} +(-8.83693 - 3.93445i) q^{53} +(-6.77927 - 1.44098i) q^{54} -7.21381 q^{55} +(-0.782820 - 2.52729i) q^{56} +(-3.18643 + 9.80681i) q^{57} +(4.18963 - 1.86534i) q^{58} +(5.94626 - 6.60400i) q^{59} +(-3.46985 + 0.737540i) q^{60} +(-3.35018 - 3.72075i) q^{61} +(-0.561140 + 1.72701i) q^{62} +(-13.1123 + 5.62269i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-3.84610 + 1.71240i) q^{65} +(16.6936 - 3.54832i) q^{66} +(-4.36359 - 1.94279i) q^{67} +(-0.00144621 + 0.00250490i) q^{68} +(2.59506 + 7.98679i) q^{69} +(-2.20080 + 2.37750i) q^{70} +(-6.07202 - 4.41158i) q^{71} +(4.92621 - 2.19329i) q^{72} +(-1.12173 - 1.94289i) q^{73} +(0.944761 - 8.98880i) q^{74} +(-6.78567 - 7.53625i) q^{75} +(-1.09992 - 3.38520i) q^{76} +(10.5881 - 11.4382i) q^{77} +(8.05802 - 5.85449i) q^{78} +(-1.17439 + 2.03410i) q^{79} +(0.819359 - 0.909991i) q^{80} +(-1.95042 - 3.37823i) q^{81} +(6.07492 + 2.02369i) q^{82} +14.3590 q^{83} +(3.92346 - 6.58433i) q^{84} +0.00354180 q^{85} +(-0.811812 - 7.72388i) q^{86} +(12.1372 + 5.40384i) q^{87} +(-3.94196 + 4.37799i) q^{88} +(-9.04057 - 10.0406i) q^{89} +(-5.34200 - 3.88119i) q^{90} +(2.92997 - 8.61175i) q^{91} +(-2.34520 - 1.70389i) q^{92} +(-4.80576 + 2.13966i) q^{93} +(-4.92513 - 2.19281i) q^{94} +(-2.91644 + 3.23903i) q^{95} +(-1.44848 + 2.50885i) q^{96} +(-5.87654 + 4.26956i) q^{97} +(-0.539518 - 6.97918i) q^{98} +(25.7005 + 18.6725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 14 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} + 4 q^{6} - 2 q^{7} - 28 q^{8} - 58 q^{9}+O(q^{10}) \) 112 * q + 14 * q^2 - 2 * q^3 + 14 * q^4 + 4 * q^5 + 4 * q^6 - 2 * q^7 - 28 * q^8 - 58 * q^9	\( 112 q + 14 q^{2} - 2 q^{3} + 14 q^{4} + 4 q^{5} + 4 q^{6} - 2 q^{7} - 28 q^{8} - 58 q^{9} + 4 q^{10} + 2 q^{11} + 3 q^{12} - 6 q^{13} + 18 q^{14} - 2 q^{15} + 14 q^{16} + 17 q^{18} - 2 q^{19} - 8 q^{20} - 25 q^{21} + 16 q^{22} - 2 q^{23} + 3 q^{24} + 26 q^{25} - 2 q^{26} - 8 q^{27} + 4 q^{28} - 42 q^{29} + q^{30} + 13 q^{31} - 56 q^{32} + 17 q^{33} - 10 q^{34} + 8 q^{35} - 24 q^{36} + q^{37} - 2 q^{38} + 14 q^{39} - 16 q^{40} - 58 q^{41} - 62 q^{42} + 18 q^{43} + 12 q^{44} + 32 q^{45} + 3 q^{46} - 25 q^{47} + 4 q^{48} + 8 q^{49} + 88 q^{50} + 23 q^{51} - 2 q^{52} + 3 q^{53} - 6 q^{54} - 12 q^{55} + 8 q^{56} - 24 q^{57} + 21 q^{58} + 18 q^{59} + q^{60} - 6 q^{61} - 16 q^{62} - 71 q^{63} - 28 q^{64} + 2 q^{65} + 2 q^{66} + 9 q^{67} - 10 q^{68} + 38 q^{69} + 55 q^{70} - 10 q^{71} + 12 q^{72} - 78 q^{73} + q^{74} - 9 q^{75} + 4 q^{76} + 43 q^{77} + 22 q^{78} + 4 q^{80} - 80 q^{81} - 6 q^{82} + 156 q^{83} - 13 q^{84} + 44 q^{85} + 11 q^{86} - 8 q^{88} + 9 q^{89} - 64 q^{90} - 52 q^{91} - 6 q^{92} - 46 q^{93} + 20 q^{94} + 49 q^{95} - 2 q^{96} + 32 q^{97} - 21 q^{98} + 12 q^{99}+O(q^{100}) \) 112 * q + 14 * q^2 - 2 * q^3 + 14 * q^4 + 4 * q^5 + 4 * q^6 - 2 * q^7 - 28 * q^8 - 58 * q^9 + 4 * q^10 + 2 * q^11 + 3 * q^12 - 6 * q^13 + 18 * q^14 - 2 * q^15 + 14 * q^16 + 17 * q^18 - 2 * q^19 - 8 * q^20 - 25 * q^21 + 16 * q^22 - 2 * q^23 + 3 * q^24 + 26 * q^25 - 2 * q^26 - 8 * q^27 + 4 * q^28 - 42 * q^29 + q^30 + 13 * q^31 - 56 * q^32 + 17 * q^33 - 10 * q^34 + 8 * q^35 - 24 * q^36 + q^37 - 2 * q^38 + 14 * q^39 - 16 * q^40 - 58 * q^41 - 62 * q^42 + 18 * q^43 + 12 * q^44 + 32 * q^45 + 3 * q^46 - 25 * q^47 + 4 * q^48 + 8 * q^49 + 88 * q^50 + 23 * q^51 - 2 * q^52 + 3 * q^53 - 6 * q^54 - 12 * q^55 + 8 * q^56 - 24 * q^57 + 21 * q^58 + 18 * q^59 + q^60 - 6 * q^61 - 16 * q^62 - 71 * q^63 - 28 * q^64 + 2 * q^65 + 2 * q^66 + 9 * q^67 - 10 * q^68 + 38 * q^69 + 55 * q^70 - 10 * q^71 + 12 * q^72 - 78 * q^73 + q^74 - 9 * q^75 + 4 * q^76 + 43 * q^77 + 22 * q^78 + 4 * q^80 - 80 * q^81 - 6 * q^82 + 156 * q^83 - 13 * q^84 + 44 * q^85 + 11 * q^86 - 8 * q^88 + 9 * q^89 - 64 * q^90 - 52 * q^91 - 6 * q^92 - 46 * q^93 + 20 * q^94 + 49 * q^95 - 2 * q^96 + 32 * q^97 - 21 * q^98 + 12 * q^99

Introduction

L-functions

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