LMFDB - Embedded newform 950.2.l.j.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	950.101
Dual form			950.2.l.j.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.799943 + 0.291155i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.799943 + 0.291155i) q^{6} +(-2.52492 + 4.37330i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.74300 - 1.46255i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.799943 + 0.291155i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.799943 + 0.291155i) q^{6} +(-2.52492 + 4.37330i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.74300 - 1.46255i) q^{9} +(1.10985 + 1.92232i) q^{11} +(0.425641 - 0.737231i) q^{12} +(-4.57862 + 1.66648i) q^{13} +(-0.876897 - 4.97313i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(3.35193 - 2.81261i) q^{17} +2.27532 q^{18} +(-3.62288 - 2.42379i) q^{19} +(-3.29310 + 2.76324i) q^{21} +(-2.08584 - 0.759185i) q^{22} +(0.792004 - 4.49168i) q^{23} +(0.147823 + 0.838348i) q^{24} +(2.43623 - 4.21968i) q^{26} +(-2.24539 - 3.88913i) q^{27} +(3.86841 + 3.24598i) q^{28} +(-1.48750 - 1.24816i) q^{29} +(3.76171 - 6.51548i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.328125 + 1.86089i) q^{33} +(-0.759821 + 4.30916i) q^{34} +(-1.74300 + 1.46255i) q^{36} -2.47962 q^{37} +(4.33327 - 0.472007i) q^{38} -4.14784 q^{39} +(-9.83650 - 3.58019i) q^{41} +(0.746486 - 4.23353i) q^{42} +(1.46256 + 8.29461i) q^{43} +(2.08584 - 0.759185i) q^{44} +(2.28048 + 3.94991i) q^{46} +(-3.69450 - 3.10005i) q^{47} +(-0.652119 - 0.547193i) q^{48} +(-9.25048 - 16.0223i) q^{49} +(3.50026 - 1.27399i) q^{51} +(0.846095 + 4.79844i) q^{52} +(-1.77156 + 10.0470i) q^{53} +(4.21995 + 1.53594i) q^{54} -5.04985 q^{56} +(-2.19239 - 2.99371i) q^{57} +1.94179 q^{58} +(-3.98298 + 3.34212i) q^{59} +(-0.909174 + 5.15618i) q^{61} +(1.30643 + 7.40913i) q^{62} +(10.7971 - 3.92982i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.44751 - 1.21461i) q^{66} +(1.13105 + 0.949064i) q^{67} +(-2.18782 - 3.78941i) q^{68} +(1.94133 - 3.36249i) q^{69} +(2.23230 + 12.6600i) q^{71} +(0.395105 - 2.24075i) q^{72} +(-12.4977 - 4.54881i) q^{73} +(1.89950 - 1.59387i) q^{74} +(-3.01608 + 3.14695i) q^{76} -11.2092 q^{77} +(3.17743 - 2.66618i) q^{78} +(5.71688 + 2.08077i) q^{79} +(0.521473 + 2.95742i) q^{81} +(9.83650 - 3.58019i) q^{82} +(-6.23822 + 10.8049i) q^{83} +(2.14942 + 3.72290i) q^{84} +(-6.45206 - 5.41392i) q^{86} +(-0.826507 - 1.43155i) q^{87} +(-1.10985 + 1.92232i) q^{88} +(-5.85651 + 2.13160i) q^{89} +(4.27265 - 24.2314i) q^{91} +(-4.28591 - 1.55994i) q^{92} +(4.90617 - 4.11677i) q^{93} +4.82282 q^{94} +0.851281 q^{96} +(-1.50605 + 1.26373i) q^{97} +(17.3852 + 6.32770i) q^{98} +(0.877018 - 4.97382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) $ 24 * q - 3 * q^7 + 12 * q^8	$ 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 12 * q^8 - 6 * q^11 + 3 * q^12 - 24 * q^13 - 15 * q^14 + 9 * q^17 - 30 * q^18 - 15 * q^19 - 18 * q^21 - 12 * q^23 - 9 * q^26 + 21 * q^27 - 12 * q^28 - 12 * q^29 + 9 * q^31 + 42 * q^33 - 9 * q^34 - 66 * q^37 - 6 * q^38 + 66 * q^39 + 18 * q^41 - 9 * q^42 + 3 * q^43 - 3 * q^46 + 12 * q^47 - 27 * q^49 - 3 * q^51 + 12 * q^52 + 45 * q^53 + 27 * q^54 - 6 * q^56 + 27 * q^57 + 18 * q^58 + 36 * q^59 + 12 * q^61 + 24 * q^62 + 63 * q^63 - 12 * q^64 + 48 * q^66 + 54 * q^67 - 3 * q^68 + 21 * q^69 - 39 * q^71 - 48 * q^73 + 18 * q^74 + 6 * q^76 - 48 * q^77 + 12 * q^78 - 42 * q^79 - 36 * q^81 - 18 * q^82 + 3 * q^83 + 9 * q^84 - 39 * q^86 + 24 * q^87 + 6 * q^88 - 36 * q^89 + 12 * q^91 + 15 * q^92 + 6 * q^93 + 12 * q^94 + 6 * q^96 + 54 * q^97 - 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	0.799943	+	0.291155i	0.461847	+	0.168099i	0.562456	−	0.826827i	$-0.309857\pi$
$3$	0.799943	+	0.291155i	0.461847	+	0.168099i	−0.100608	+	0.994926i	$0.532079\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−0.799943	+	0.291155i	−0.326575	+	0.118864i
$7$	−2.52492	+	4.37330i	−0.954331	+	1.65295i	−0.218441	+	0.975850i	$0.570097\pi$
$7$	−2.52492	+	4.37330i	−0.954331	+	1.65295i	−0.735891	+	0.677100i	$0.763236\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.74300	−	1.46255i	−0.580999	−	0.487516i
$10$		0			0
$11$	1.10985	+	1.92232i	0.334634	+	0.579602i	0.983414	−	0.181373i	$-0.0580541\pi$
$11$	1.10985	+	1.92232i	0.334634	+	0.579602i	−0.648781	+	0.760975i	$0.724721\pi$
$12$	0.425641	−	0.737231i	0.122872	−	0.212820i
$13$	−4.57862	+	1.66648i	−1.26988	+	0.462199i	−0.887073	−	0.461629i	$-0.847265\pi$
$13$	−4.57862	+	1.66648i	−1.26988	+	0.462199i	−0.382808	+	0.923828i	$0.625043\pi$
$14$	−0.876897	−	4.97313i	−0.234361	−	1.32912i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.35193	−	2.81261i	0.812963	−	0.682157i	−0.138350	−	0.990383i	$-0.544180\pi$
$17$	3.35193	−	2.81261i	0.812963	−	0.682157i	0.951313	+	0.308226i	$0.0997354\pi$
$18$	2.27532			0.536298
$19$	−3.62288	−	2.42379i	−0.831145	−	0.556056i
$19$	−3.62288	−	2.42379i	−0.831145	−	0.556056i
$20$		0			0
$21$	−3.29310	+	2.76324i	−0.718614	+	0.602989i
$22$	−2.08584	−	0.759185i	−0.444703	−	0.161859i
$23$	0.792004	−	4.49168i	0.165144	−	0.936579i	−0.783771	−	0.621049i	$-0.786707\pi$
$23$	0.792004	−	4.49168i	0.165144	−	0.936579i	0.948916	−	0.315530i	$-0.102182\pi$
$24$	0.147823	+	0.838348i	0.0301743	+	0.171127i
$25$		0			0
$26$	2.43623	−	4.21968i	0.477785	−	0.827548i
$27$	−2.24539	−	3.88913i	−0.432126	−	0.748463i
$28$	3.86841	+	3.24598i	0.731060	+	0.613432i
$29$	−1.48750	−	1.24816i	−0.276222	−	0.231778i	0.494143	−	0.869380i	$-0.335482\pi$
$29$	−1.48750	−	1.24816i	−0.276222	−	0.231778i	−0.770365	+	0.637603i	$0.779926\pi$
$30$		0			0
$31$	3.76171	−	6.51548i	0.675624	−	1.17021i	−0.300662	−	0.953731i	$-0.597208\pi$
$31$	3.76171	−	6.51548i	0.675624	−	1.17021i	0.976286	−	0.216484i	$-0.0694590\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.328125	+	1.86089i	0.0571192	+	0.323939i
$34$	−0.759821	+	4.30916i	−0.130308	+	0.739015i
$35$		0			0
$36$	−1.74300	+	1.46255i	−0.290499	+	0.243758i
$37$	−2.47962			−0.407648			−0.203824	−	0.979008i	$-0.565337\pi$
$37$	−2.47962			−0.407648			−0.203824	+	0.979008i	$0.565337\pi$
$38$	4.33327	−	0.472007i	0.702949	−	0.0765697i
$39$	−4.14784			−0.664186
$40$		0			0
$41$	−9.83650	−	3.58019i	−1.53620	−	0.559132i	−0.571072	−	0.820900i	$-0.693472\pi$
$41$	−9.83650	−	3.58019i	−1.53620	−	0.559132i	−0.965131	+	0.261768i	$0.915695\pi$
$42$	0.746486	−	4.23353i	0.115185	−	0.653248i
$43$	1.46256	+	8.29461i	0.223039	+	1.26492i	0.866399	+	0.499353i	$0.166429\pi$
$43$	1.46256	+	8.29461i	0.223039	+	1.26492i	−0.643360	+	0.765564i	$0.722460\pi$
$44$	2.08584	−	0.759185i	0.314453	−	0.114451i
$45$		0			0
$46$	2.28048	+	3.94991i	0.336239	+	0.582383i
$47$	−3.69450	−	3.10005i	−0.538898	−	0.452189i	0.332263	−	0.943187i	$-0.392188\pi$
$47$	−3.69450	−	3.10005i	−0.538898	−	0.452189i	−0.871161	+	0.490998i	$0.836632\pi$
$48$	−0.652119	−	0.547193i	−0.0941253	−	0.0789805i
$49$	−9.25048	−	16.0223i	−1.32150	−	2.28890i
$50$		0			0
$51$	3.50026	−	1.27399i	0.490134	−	0.178394i
$52$	0.846095	+	4.79844i	0.117332	+	0.665425i
$53$	−1.77156	+	10.0470i	−0.243342	+	1.38006i	0.580971	+	0.813925i	$0.302673\pi$
$53$	−1.77156	+	10.0470i	−0.243342	+	1.38006i	−0.824312	+	0.566135i	$0.808438\pi$
$54$	4.21995	+	1.53594i	0.574263	+	0.209015i
$55$		0			0
$56$	−5.04985			−0.674814
$57$	−2.19239	−	2.99371i	−0.290390	−	0.396527i
$58$	1.94179			0.254970
$59$	−3.98298	+	3.34212i	−0.518540	+	0.435107i	−0.864122	−	0.503282i	$-0.832126\pi$
$59$	−3.98298	+	3.34212i	−0.518540	+	0.435107i	0.345582	+	0.938388i	$0.387681\pi$
$60$		0			0
$61$	−0.909174	+	5.15618i	−0.116408	+	0.660181i	0.869636	+	0.493694i	$0.164354\pi$
$61$	−0.909174	+	5.15618i	−0.116408	+	0.660181i	−0.986044	+	0.166488i	$0.946757\pi$
$62$	1.30643	+	7.40913i	0.165917	+	0.940961i
$63$	10.7971	−	3.92982i	1.36031	−	0.495111i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−1.44751	−	1.21461i	−0.178177	−	0.149508i
$67$	1.13105	+	0.949064i	0.138180	+	0.115947i	0.709258	−	0.704949i	$-0.249030\pi$
$67$	1.13105	+	0.949064i	0.138180	+	0.115947i	−0.571078	+	0.820896i	$0.693475\pi$
$68$	−2.18782	−	3.78941i	−0.265312	−	0.459534i
$69$	1.94133	−	3.36249i	0.233709	−	0.404796i
$70$		0			0
$71$	2.23230	+	12.6600i	0.264926	+	1.50247i	0.769247	+	0.638952i	$0.220632\pi$
$71$	2.23230	+	12.6600i	0.264926	+	1.50247i	−0.504321	+	0.863516i	$0.668257\pi$
$72$	0.395105	−	2.24075i	0.0465636	−	0.264075i
$73$	−12.4977	−	4.54881i	−1.46275	−	0.532398i	−0.516629	−	0.856210i	$-0.672813\pi$
$73$	−12.4977	−	4.54881i	−1.46275	−	0.532398i	−0.946121	+	0.323812i	$0.895035\pi$
$74$	1.89950	−	1.59387i	0.220813	−	0.185284i
$75$		0			0
$76$	−3.01608	+	3.14695i	−0.345968	+	0.360980i
$77$	−11.2092			−1.27741
$78$	3.17743	−	2.66618i	0.359773	−	0.301885i
$79$	5.71688	+	2.08077i	0.643199	+	0.234105i	0.642966	−	0.765895i	$-0.277704\pi$
$79$	5.71688	+	2.08077i	0.643199	+	0.234105i	0.000232843		1.00000i	$0.499926\pi$
$80$		0			0
$81$	0.521473	+	2.95742i	0.0579415	+	0.328602i
$82$	9.83650	−	3.58019i	1.08626	−	0.395366i
$83$	−6.23822	+	10.8049i	−0.684733	+	1.18599i	0.288787	+	0.957393i	$0.406748\pi$
$83$	−6.23822	+	10.8049i	−0.684733	+	1.18599i	−0.973521	+	0.228599i	$0.926585\pi$
$84$	2.14942	+	3.72290i	0.234521	+	0.406202i
$85$		0			0
$86$	−6.45206	−	5.41392i	−0.695744	−	0.583798i
$87$	−0.826507	−	1.43155i	−0.0886108	−	0.153478i
$88$	−1.10985	+	1.92232i	−0.118311	+	0.204920i
$89$	−5.85651	+	2.13160i	−0.620789	+	0.225949i	−0.633217	−	0.773974i	$-0.718266\pi$
$89$	−5.85651	+	2.13160i	−0.620789	+	0.225949i	0.0124282	+	0.999923i	$0.496044\pi$
$90$		0			0
$91$	4.27265	−	24.2314i	0.447896	−	2.54014i
$92$	−4.28591	−	1.55994i	−0.446837	−	0.162635i
$93$	4.90617	−	4.11677i	0.508746	−	0.426889i
$94$	4.82282			0.497436
$95$		0			0
$96$	0.851281			0.0868835
$97$	−1.50605	+	1.26373i	−0.152917	+	0.128312i	−0.716036	−	0.698063i	$-0.754045\pi$
$97$	−1.50605	+	1.26373i	−0.152917	+	0.128312i	0.563120	+	0.826375i	$0.309601\pi$
$98$	17.3852	+	6.32770i	1.75617	+	0.639194i
$99$	0.877018	−	4.97382i	0.0881437	−	0.499888i
$100$		0			0
$101$	9.23147	−	3.35998i	0.918565	−	0.334330i	0.160898	−	0.986971i	$-0.448561\pi$
$101$	9.23147	−	3.35998i	0.918565	−	0.334330i	0.757668	+	0.652641i	$0.226339\pi$
$102$	−1.86245	+	3.22586i	−0.184410	+	0.319407i
$103$	−6.63954	−	11.5000i	−0.654213	−	1.13313i	−0.982090	−	0.188410i	$-0.939666\pi$
$103$	−6.63954	−	11.5000i	−0.654213	−	1.13313i	0.327877	−	0.944720i	$-0.393667\pi$
$104$	−3.73253	−	3.13196i	−0.366004	−	0.307114i
$105$		0			0
$106$	−5.10099	−	8.83517i	−0.495452	−	0.858148i
$107$	7.39351	−	12.8059i	0.714757	−	1.23800i	−0.248296	−	0.968684i	$-0.579870\pi$
$107$	7.39351	−	12.8059i	0.714757	−	1.23800i	0.963053	−	0.269312i	$-0.0867963\pi$
$108$	−4.21995	+	1.53594i	−0.406065	+	0.147796i
$109$	1.52425	+	8.64446i	0.145997	+	0.827989i	0.966561	+	0.256435i	$0.0825481\pi$
$109$	1.52425	+	8.64446i	0.145997	+	0.827989i	−0.820565	+	0.571554i	$0.806341\pi$
$110$		0			0
$111$	−1.98356	−	0.721956i	−0.188271	−	0.0685250i
$112$	3.86841	−	3.24598i	0.365530	−	0.306716i
$113$	0.0389940			0.00366825			0.00183412	−	0.999998i	$-0.499416\pi$
$113$	0.0389940			0.00366825			0.00183412	+	0.999998i	$0.499416\pi$
$114$	3.60379	+	0.884075i	0.337526	+	0.0828012i
$115$		0			0
$116$	−1.48750	+	1.24816i	−0.138111	+	0.115889i
$117$	10.4178	+	3.79178i	0.963129	+	0.350550i
$118$	0.902869	−	5.12042i	0.0831158	−	0.471373i
$119$	3.83698	+	21.7606i	0.351736	+	1.99479i
$120$		0			0
$121$	3.03645	−	5.25928i	0.276041	−	0.478116i
$122$	−2.61786	−	4.53427i	−0.237010	−	0.410514i
$123$	−6.82624	−	5.72790i	−0.615502	−	0.516467i
$124$	−5.76328	−	4.83597i	−0.517558	−	0.434283i
$125$		0			0
$126$	−5.74501	+	9.95065i	−0.511806	+	0.886474i
$127$	0.0801932	−	0.0291879i	0.00711599	−	0.00259001i	−0.338460	−	0.940981i	$-0.609906\pi$
$127$	0.0801932	−	0.0291879i	0.00711599	−	0.00259001i	0.345576	+	0.938391i	$0.387684\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−1.24505	+	7.06105i	−0.109621	+	0.621691i
$130$		0			0
$131$	−0.668494	+	0.560933i	−0.0584066	+	0.0490090i	−0.671524	−	0.740983i	$-0.734360\pi$
$131$	−0.668494	+	0.560933i	−0.0584066	+	0.0490090i	0.613117	+	0.789992i	$0.289915\pi$
$132$	1.88960			0.164468
$133$	19.7474	−	9.72402i	1.71232	−	0.843179i
$134$	−1.47648			−0.127549
$135$		0			0
$136$	4.11175	+	1.49656i	0.352580	+	0.128329i
$137$	−1.96498	+	11.1440i	−0.167880	+	0.952092i	0.778166	+	0.628059i	$0.216150\pi$
$137$	−1.96498	+	11.1440i	−0.167880	+	0.952092i	−0.946046	+	0.324034i	$0.894961\pi$
$138$	0.674218	+	3.82368i	0.0573932	+	0.325493i
$139$	0.183382	−	0.0667458i	0.0155543	−	0.00566130i	−0.334231	−	0.942491i	$-0.608477\pi$
$139$	0.183382	−	0.0667458i	0.0155543	−	0.00566130i	0.349786	+	0.936830i	$0.386254\pi$
$140$		0			0
$141$	−2.05279	−	3.55553i	−0.172876	−	0.299430i
$142$	−9.84775	−	8.26324i	−0.826404	−	0.693436i
$143$	−8.28512	−	6.95204i	−0.692837	−	0.581359i
$144$	1.13766	+	1.97049i	0.0948050	+	0.164207i
$145$		0			0
$146$	12.4977	−	4.54881i	1.03432	−	0.376462i
$147$	−2.73487	−	15.5102i	−0.225569	−	1.27926i
$148$	−0.430582	+	2.44195i	−0.0353936	+	0.200727i
$149$	0.121973	+	0.0443946i	0.00999244	+	0.00363695i	0.347012	−	0.937861i	$-0.387196\pi$
$149$	0.121973	+	0.0443946i	0.00999244	+	0.00363695i	−0.337019	+	0.941498i	$0.609419\pi$
$150$		0			0
$151$	3.54764			0.288703			0.144352	−	0.989526i	$-0.453890\pi$
$151$	3.54764			0.288703			0.144352	+	0.989526i	$0.453890\pi$
$152$	0.287627	−	4.34940i	0.0233297	−	0.352783i
$153$	−9.95598			−0.804893
$154$	8.58674	−	7.20513i	0.691939	−	0.580606i
$155$		0			0
$156$	−0.720265	+	4.08483i	−0.0576673	+	0.327048i
$157$	0.731513	+	4.14861i	0.0583811	+	0.331095i	0.999984	−	0.00562936i	$-0.00179189\pi$
$157$	0.731513	+	4.14861i	0.0583811	+	0.331095i	−0.941603	+	0.336725i	$0.890681\pi$
$158$	−5.71688	+	2.08077i	−0.454810	+	0.165537i
$159$	−4.34238	+	7.52122i	−0.344373	+	0.596471i
$160$		0			0
$161$	17.6437	+	14.8048i	1.39052	+	1.16678i
$162$	−2.30046	−	1.93032i	−0.180742	−	0.151660i
$163$	−11.2080	−	19.4128i	−0.877877	−	1.52053i	−0.853666	−	0.520820i	$-0.825626\pi$
$163$	−11.2080	−	19.4128i	−0.877877	−	1.52053i	−0.0242101	−	0.999707i	$-0.507707\pi$
$164$	−5.23389	+	9.06537i	−0.408698	+	0.707886i
$165$		0			0
$166$	−2.16651	−	12.2869i	−0.168154	−	0.953647i
$167$	−0.658237	+	3.73305i	−0.0509359	+	0.288872i	−0.999626	−	0.0273344i	$-0.991298\pi$
$167$	−0.658237	+	3.73305i	−0.0509359	+	0.288872i	0.948690	+	0.316206i	$0.102409\pi$
$168$	−4.03959	−	1.47029i	−0.311661	−	0.113435i
$169$	8.22804	−	6.90415i	0.632926	−	0.531088i
$170$		0			0
$171$	2.76975	+	9.52329i	0.211808	+	0.728264i
$172$	8.42257			0.642215
$173$	−14.9324	+	12.5298i	−1.13529	+	0.952624i	−0.999275	−	0.0380827i	$-0.987875\pi$
$173$	−14.9324	+	12.5298i	−1.13529	+	0.952624i	−0.136018	+	0.990706i	$0.543431\pi$
$174$	1.55332	+	0.565364i	0.117757	+	0.0428601i
$175$		0			0
$176$	−0.385448	−	2.18599i	−0.0290543	−	0.164775i
$177$	−4.15923	+	1.51384i	−0.312627	+	0.113787i
$178$	3.11619	−	5.39739i	0.233568	−	0.404552i
$179$	−4.39396	−	7.61057i	−0.328420	−	0.568840i	0.653778	−	0.756686i	$-0.273183\pi$
$179$	−4.39396	−	7.61057i	−0.328420	−	0.568840i	−0.982199	+	0.187846i	$0.939850\pi$
$180$		0			0
$181$	7.42429	+	6.22972i	0.551843	+	0.463051i	0.875565	−	0.483101i	$-0.160490\pi$
$181$	7.42429	+	6.22972i	0.551843	+	0.463051i	−0.323721	+	0.946152i	$0.604934\pi$
$182$	12.3026	+	21.3087i	0.911930	+	1.57951i
$183$	−2.22854	+	3.85994i	−0.164738	+	0.285335i
$184$	4.28591	−	1.55994i	0.315961	−	0.115000i
$185$		0			0
$186$	−1.11214	+	6.30725i	−0.0815460	+	0.462470i
$187$	9.12689	+	3.32192i	0.667425	+	0.242923i
$188$	−3.69450	+	3.10005i	−0.269449	+	0.226094i
$189$	22.6778			1.64956
$190$		0			0
$191$	1.85152			0.133971			0.0669857	−	0.997754i	$-0.478662\pi$
$191$	1.85152			0.133971			0.0669857	+	0.997754i	$0.478662\pi$
$192$	−0.652119	+	0.547193i	−0.0470627	+	0.0394903i
$193$	−0.455254	−	0.165699i	−0.0327699	−	0.0119273i	0.325583	−	0.945513i	$-0.394439\pi$
$193$	−0.455254	−	0.165699i	−0.0327699	−	0.0119273i	−0.358353	+	0.933586i	$0.616662\pi$
$194$	0.341395	−	1.93615i	0.0245107	−	0.139007i
$195$		0			0
$196$	−17.3852	+	6.32770i	−1.24180	+	0.451979i
$197$	−9.79734	+	16.9695i	−0.698031	+	1.20903i	0.271117	+	0.962547i	$0.412607\pi$
$197$	−9.79734	+	16.9695i	−0.698031	+	1.20903i	−0.969148	+	0.246479i	$0.920726\pi$
$198$	2.52527	+	4.37390i	0.179463	+	0.310840i
$199$	7.58202	+	6.36207i	0.537475	+	0.450995i	0.870673	−	0.491861i	$-0.163683\pi$
$199$	7.58202	+	6.36207i	0.537475	+	0.450995i	−0.333198	+	0.942857i	$0.608128\pi$
$200$		0			0
$201$	0.628451	+	1.08851i	0.0443275	+	0.0767775i
$202$	−4.91196	+	8.50776i	−0.345604	+	0.598604i
$203$	9.21441	−	3.35377i	0.646725	−	0.235389i
$204$	−0.646822	−	3.66831i	−0.0452866	−	0.256833i
$205$		0			0
$206$	12.4783	+	4.54171i	0.869401	+	0.316436i
$207$	−7.94975	+	6.67063i	−0.552546	+	0.463641i
$208$	4.87247			0.337845
$209$	0.638449	−	9.65440i	0.0441624	−	0.667809i
$210$		0			0
$211$	−14.3277	+	12.0224i	−0.986361	+	0.827655i	−0.985037	−	0.172344i	$-0.944866\pi$
$211$	−14.3277	+	12.0224i	−0.986361	+	0.827655i	−0.00132403	+	0.999999i	$0.500421\pi$
$212$	9.58672	+	3.48928i	0.658419	+	0.239645i
$213$	−1.90032	+	10.7772i	−0.130208	+	0.738444i
$214$	2.56774	+	14.5624i	0.175527	+	0.995463i
$215$		0			0
$216$	2.24539	−	3.88913i	0.152779	−	0.264622i
$217$	18.9961	+	32.9022i	1.28954	+	2.23355i
$218$	−6.72420	−	5.64227i	−0.455420	−	0.382143i
$219$	−8.67307	−	7.27757i	−0.586072	−	0.491773i
$220$		0			0
$221$	−10.6601	+	18.4638i	−0.717074	+	1.24201i
$222$	1.98356	−	0.721956i	0.133128	−	0.0484545i
$223$	−0.540502	−	3.06534i	−0.0361947	−	0.205270i	0.961348	−	0.275338i	$-0.0887897\pi$
$223$	−0.540502	−	3.06534i	−0.0361947	−	0.205270i	−0.997542	+	0.0700673i	$0.977679\pi$
$224$	−0.876897	+	4.97313i	−0.0585901	+	0.332281i
$225$		0			0
$226$	−0.0298712	+	0.0250649i	−0.00198700	+	0.00166729i
$227$	−1.34903			−0.0895381			−0.0447690	−	0.998997i	$-0.514255\pi$
$227$	−1.34903			−0.0895381			−0.0447690	+	0.998997i	$0.514255\pi$
$228$	−3.32894	+	1.63923i	−0.220464	+	0.108561i
$229$	16.0289			1.05922			0.529611	−	0.848240i	$-0.322338\pi$
$229$	16.0289			1.05922			0.529611	+	0.848240i	$0.322338\pi$
$230$		0			0
$231$	−8.96671	−	3.26361i	−0.589966	−	0.214730i
$232$	0.337189	−	1.91229i	0.0221376	−	0.125548i
$233$	2.98216	+	16.9127i	0.195368	+	1.10799i	0.911894	+	0.410426i	$0.134620\pi$
$233$	2.98216	+	16.9127i	0.195368	+	1.10799i	−0.716526	+	0.697560i	$0.754269\pi$
$234$	−10.4178	+	3.79178i	−0.681035	+	0.247876i
$235$		0			0
$236$	2.59971	+	4.50282i	0.169227	+	0.293109i
$237$	3.96734	+	3.32900i	0.257707	+	0.216242i
$238$	−16.9267	−	14.2032i	−1.09720	−	0.920659i
$239$	13.9049	+	24.0841i	0.899436	+	1.55787i	0.828217	+	0.560408i	$0.189356\pi$
$239$	13.9049	+	24.0841i	0.899436	+	1.55787i	0.0712188	+	0.997461i	$0.477311\pi$
$240$		0			0
$241$	6.09195	−	2.21729i	0.392417	−	0.142828i	−0.138273	−	0.990394i	$-0.544155\pi$
$241$	6.09195	−	2.21729i	0.392417	−	0.142828i	0.530690	+	0.847566i	$0.321933\pi$
$242$	1.05455	+	5.98063i	0.0677889	+	0.384450i
$243$	−2.78337	+	15.7853i	−0.178553	+	1.01263i
$244$	4.91997	+	1.79072i	0.314969	+	0.114639i
$245$		0			0
$246$	8.91103			0.568146
$247$	20.6270	+	5.06017i	1.31246	+	0.321971i
$248$	7.52343			0.477738
$249$	−8.13612	+	6.82702i	−0.515606	+	0.432645i
$250$		0			0
$251$	2.10127	−	11.9169i	0.132631	−	0.752189i	−0.843849	−	0.536581i	$-0.819716\pi$
$251$	2.10127	−	11.9169i	0.132631	−	0.752189i	0.976480	−	0.215608i	$-0.0691732\pi$
$252$	−1.99522	−	11.3155i	−0.125687	−	0.712807i
$253$	9.51346	−	3.46262i	0.598106	−	0.217693i
$254$	−0.0426699	+	0.0739064i	−0.00267735	+	0.00463730i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−18.2072	−	15.2776i	−1.13573	−	0.952992i	−0.136440	−	0.990648i	$-0.543566\pi$
$257$	−18.2072	−	15.2776i	−1.13573	−	0.952992i	−0.999291	+	0.0376568i	$0.988011\pi$
$258$	−3.58499	−	6.20938i	−0.223192	−	0.386579i
$259$	6.26086	−	10.8441i	0.389031	−	0.673821i
$260$		0			0
$261$	0.767213	+	4.35108i	0.0474893	+	0.269325i
$262$	0.151535	−	0.859400i	0.00936189	−	0.0530939i
$263$	−16.2362	−	5.90950i	−1.00117	−	0.364395i	−0.211133	−	0.977457i	$-0.567715\pi$
$263$	−16.2362	−	5.90950i	−1.00117	−	0.364395i	−0.790035	+	0.613062i	$0.789938\pi$
$264$	−1.44751	+	1.21461i	−0.0890884	+	0.0747540i
$265$		0			0
$266$	−8.87694	+	20.1424i	−0.544280	+	1.23501i
$267$	−5.30550			−0.324691
$268$	1.13105	−	0.949064i	0.0690899	−	0.0579733i
$269$	−9.95234	−	3.62236i	−0.606805	−	0.220859i	0.0202997	−	0.999794i	$-0.493538\pi$
$269$	−9.95234	−	3.62236i	−0.606805	−	0.220859i	−0.627105	+	0.778935i	$0.715760\pi$
$270$		0			0
$271$	1.78816	+	10.1411i	0.108623	+	0.616030i	0.989711	+	0.143079i	$0.0457002\pi$
$271$	1.78816	+	10.1411i	0.108623	+	0.616030i	−0.881089	+	0.472951i	$0.843189\pi$
$272$	−4.11175	+	1.49656i	−0.249312	+	0.0907420i
$273$	10.4730	−	18.1397i	0.633854	−	1.09787i
$274$	−5.65793	−	9.79983i	−0.341808	−	0.592029i
$275$		0			0
$276$	−2.97429	−	2.49573i	−0.179031	−	0.150225i
$277$	−3.75024	−	6.49560i	−0.225330	−	0.390283i	0.731088	−	0.682283i	$-0.239013\pi$
$277$	−3.75024	−	6.49560i	−0.225330	−	0.390283i	−0.956418	+	0.292000i	$0.905679\pi$
$278$	−0.0975758	+	0.169006i	−0.00585221	+	0.0101363i
$279$	−16.0859	+	5.85477i	−0.963035	+	0.350516i
$280$		0			0
$281$	2.03848	−	11.5608i	0.121605	−	0.689659i	−0.861661	−	0.507485i	$-0.830575\pi$
$281$	2.03848	−	11.5608i	0.121605	−	0.689659i	0.983266	−	0.182174i	$-0.0583135\pi$
$282$	3.85798	+	1.40419i	0.229739	+	0.0836183i
$283$	14.3608	−	12.0502i	0.853663	−	0.716309i	−0.106930	−	0.994267i	$-0.534102\pi$
$283$	14.3608	−	12.0502i	0.853663	−	0.716309i	0.960593	+	0.277958i	$0.0896576\pi$
$284$	12.8553			0.762823
$285$		0			0
$286$	10.8155			0.639531
$287$	40.4937	−	33.9782i	2.39026	−	2.00567i
$288$	−2.13810	−	0.778205i	−0.125989	−	0.0458562i
$289$	0.372684	−	2.11360i	0.0219226	−	0.124329i
$290$		0			0
$291$	−1.57270	+	0.572415i	−0.0921932	+	0.0335556i
$292$	−6.64991	+	11.5180i	−0.389157	+	0.674039i
$293$	8.76356	+	15.1789i	0.511973	+	0.886763i	0.999904	+	0.0138805i	$0.00441843\pi$
$293$	8.76356	+	15.1789i	0.511973	+	0.886763i	−0.487931	+	0.872882i	$0.662248\pi$
$294$	12.0648	+	10.1236i	0.703635	+	0.590420i
$295$		0			0
$296$	−1.23981	−	2.14742i	−0.0720626	−	0.124816i
$297$	4.98411	−	8.63274i	0.289208	−	0.500922i
$298$	−0.121973	+	0.0443946i	−0.00706572	+	0.00257171i
$299$	3.85901	+	21.8855i	0.223172	+	1.26567i
$300$		0			0
$301$	−39.9677	−	14.5470i	−2.30370	−	0.838477i
$302$	−2.71765	+	2.28038i	−0.156383	+	0.131221i
$303$	8.36292			0.480437
$304$	2.57540	+	3.51672i	0.147710	+	0.201698i
$305$		0			0
$306$	7.62672	−	6.39958i	0.435991	−	0.365840i
$307$	10.6520	+	3.87700i	0.607940	+	0.221272i	0.627602	−	0.778535i	$-0.284037\pi$
$307$	10.6520	+	3.87700i	0.607940	+	0.221272i	−0.0196617	+	0.999807i	$0.506259\pi$
$308$	−1.94646	+	11.0389i	−0.110910	+	0.628999i
$309$	−1.96296	−	11.1325i	−0.111669	−	0.633306i
$310$		0			0
$311$	3.53458	−	6.12208i	0.200428	−	0.347151i	−0.748238	−	0.663430i	$-0.769100\pi$
$311$	3.53458	−	6.12208i	0.200428	−	0.347151i	0.948666	+	0.316279i	$0.102433\pi$
$312$	−2.07392	−	3.59214i	−0.117413	−	0.203365i
$313$	−9.27773	−	7.78494i	−0.524408	−	0.440031i	0.341757	−	0.939788i	$-0.388978\pi$
$313$	−9.27773	−	7.78494i	−0.524408	−	0.440031i	−0.866165	+	0.499758i	$0.833422\pi$
$314$	−3.22705	−	2.70782i	−0.182113	−	0.152811i
$315$		0			0
$316$	3.04189	−	5.26870i	0.171119	−	0.296388i
$317$	−10.2800	+	3.74161i	−0.577382	+	0.210150i	−0.614171	−	0.789173i	$-0.710509\pi$
$317$	−10.2800	+	3.74161i	−0.577382	+	0.210150i	0.0367885	+	0.999323i	$0.488287\pi$
$318$	−1.50809	−	8.55281i	−0.0845696	−	0.479618i
$319$	0.748462	−	4.24474i	0.0419058	−	0.237660i
$320$		0			0
$321$	9.64290	−	8.09135i	0.538214	−	0.451615i
$322$	−23.0322			−1.28353
$323$	−18.9608	+	2.06533i	−1.05501	+	0.114918i
$324$	3.00304			0.166836
$325$		0			0
$326$	21.0641	+	7.66671i	1.16663	+	0.424620i
$327$	−1.29757	+	7.35887i	−0.0717556	+	0.406946i
$328$	−1.81771	−	10.3088i	−0.100366	−	0.569206i
$329$	22.8858	−	8.32973i	1.26173	−	0.459233i
$330$		0			0
$331$	−2.70804	−	4.69047i	−0.148847	−	0.257811i	0.781954	−	0.623336i	$-0.214223\pi$
$331$	−2.70804	−	4.69047i	−0.148847	−	0.257811i	−0.930802	+	0.365524i	$0.880890\pi$
$332$	9.55750	+	8.01970i	0.524536	+	0.440138i
$333$	4.32198	+	3.62657i	0.236843	+	0.198735i
$334$	−1.89532	−	3.28279i	−0.103707	−	0.179626i
$335$		0			0
$336$	4.03959	−	1.47029i	0.220378	−	0.0802109i
$337$	2.25340	+	12.7797i	0.122750	+	0.696152i	0.982619	+	0.185636i	$0.0594345\pi$
$337$	2.25340	+	12.7797i	0.122750	+	0.696152i	−0.859868	+	0.510516i	$0.829454\pi$
$338$	−1.86515	+	10.5778i	−0.101451	+	0.575355i
$339$	0.0311930	+	0.0113533i	0.00169417	+	0.000616627i
$340$		0			0
$341$	16.6998			0.904346
$342$	−8.24320	−	5.51490i	−0.445741	−	0.298212i
$343$	58.0781			3.13592
$344$	−6.45206	+	5.41392i	−0.347872	+	0.291899i
$345$		0			0
$346$	3.38491	−	19.1968i	0.181974	−	1.03203i
$347$	−1.91731	−	10.8736i	−0.102927	−	0.583727i	−0.992028	−	0.126017i	$-0.959781\pi$
$347$	−1.91731	−	10.8736i	−0.102927	−	0.583727i	0.889101	−	0.457710i	$-0.151330\pi$
$348$	−1.55332	+	0.565364i	−0.0832669	+	0.0303067i
$349$	14.3239	−	24.8097i	0.766740	−	1.32803i	−0.172582	−	0.984995i	$-0.555211\pi$
$349$	14.3239	−	24.8097i	0.766740	−	1.32803i	0.939322	−	0.343038i	$-0.111456\pi$
$350$		0			0
$351$	16.7620	+	14.0650i	0.894687	+	0.750732i
$352$	1.70040	+	1.42680i	0.0906314	+	0.0760487i
$353$	8.60962	+	14.9123i	0.458244	+	0.793701i	0.998868	−	0.0475627i	$-0.0151454\pi$
$353$	8.60962	+	14.9123i	0.458244	+	0.793701i	−0.540625	+	0.841264i	$0.681812\pi$
$354$	2.21308	−	3.83317i	0.117624	−	0.203731i
$355$		0			0
$356$	1.08224	+	6.13769i	0.0573586	+	0.325297i
$357$	−3.26635	+	18.5244i	−0.172874	+	0.980415i
$358$	8.25795	+	3.00565i	0.436446	+	0.158853i
$359$	−9.78292	+	8.20884i	−0.516323	+	0.433246i	−0.863348	−	0.504610i	$-0.831636\pi$
$359$	−9.78292	+	8.20884i	−0.516323	+	0.433246i	0.347025	+	0.937856i	$0.387192\pi$
$360$		0			0
$361$	7.25046	+	17.5622i	0.381603	+	0.924326i
$362$	−9.69172			−0.509386
$363$	3.96025	−	3.32305i	0.207859	−	0.174415i
$364$	−23.1213	−	8.41548i	−1.21189	−	0.441091i
$365$		0			0
$366$	−0.773963	−	4.38936i	−0.0404557	−	0.229436i
$367$	−24.6214	+	8.96147i	−1.28523	+	0.467785i	−0.892158	−	0.451724i	$-0.850809\pi$
$367$	−24.6214	+	8.96147i	−1.28523	+	0.467785i	−0.393070	+	0.919509i	$0.628587\pi$
$368$	−2.28048	+	3.94991i	−0.118878	+	0.205903i
$369$	11.9088	+	20.6266i	0.619946	+	1.07378i
$370$		0			0
$371$	−39.4654	−	33.1154i	−2.04894	−	1.71927i
$372$	−3.20228	−	5.54651i	−0.166030	−	0.287573i
$373$	−2.22363	+	3.85144i	−0.115135	+	0.199420i	−0.917834	−	0.396965i	$-0.870063\pi$
$373$	−2.22363	+	3.85144i	−0.115135	+	0.199420i	0.802699	+	0.596385i	$0.203397\pi$
$374$	−9.12689	+	3.32192i	−0.471940	+	0.171772i
$375$		0			0
$376$	0.837474	−	4.74955i	0.0431894	−	0.244939i
$377$	8.89075	+	3.23597i	0.457897	+	0.166661i
$378$	−17.3722	+	14.5770i	−0.893528	+	0.749759i
$379$	−34.9948			−1.79756			−0.898782	−	0.438395i	$-0.855547\pi$
$379$	−34.9948			−1.79756			−0.898782	+	0.438395i	$0.855547\pi$
$380$		0			0
$381$	0.0726482			0.00372188
$382$	−1.41835	+	1.19013i	−0.0725690	+	0.0608926i
$383$	−23.0237	−	8.37992i	−1.17645	−	0.428194i	−0.321506	−	0.946908i	$-0.604189\pi$
$383$	−23.0237	−	8.37992i	−1.17645	−	0.428194i	−0.854948	+	0.518714i	$0.826411\pi$
$384$	0.147823	−	0.838348i	0.00754358	−	0.0427818i
$385$		0			0
$386$	0.455254	−	0.165699i	0.0231718	−	0.00843386i
$387$	9.58202	−	16.5965i	0.487082	−	0.843650i
$388$	0.983007	+	1.70262i	0.0499046	+	0.0864373i
$389$	−5.75726	−	4.83092i	−0.291905	−	0.244937i	0.485061	−	0.874481i	$-0.338798\pi$
$389$	−5.75726	−	4.83092i	−0.291905	−	0.244937i	−0.776965	+	0.629543i	$0.783242\pi$
$390$		0			0
$391$	−9.97857	−	17.2834i	−0.504638	−	0.874058i
$392$	9.25048	−	16.0223i	0.467220	−	0.809248i
$393$	−0.698076	+	0.254079i	−0.0352133	+	0.0128166i
$394$	−3.40258	−	19.2970i	−0.171419	−	0.972168i
$395$		0			0
$396$	−4.74596	−	1.72739i	−0.238494	−	0.0868046i
$397$	2.18542	−	1.83378i	0.109683	−	0.0920350i	−0.586297	−	0.810096i	$-0.699415\pi$
$397$	2.18542	−	1.83378i	0.109683	−	0.0920350i	0.695980	+	0.718061i	$0.254970\pi$
$398$	−9.89763			−0.496123
$399$	18.6280	−	2.02908i	0.932568	−	0.101581i
$400$		0			0
$401$	−19.3861	+	16.2669i	−0.968097	+	0.812330i	−0.982251	−	0.187570i	$-0.939939\pi$
$401$	−19.3861	+	16.2669i	−0.968097	+	0.812330i	0.0141541	+	0.999900i	$0.495494\pi$
$402$	−1.18110	−	0.429886i	−0.0589080	−	0.0214407i
$403$	−6.36554	+	36.1008i	−0.317090	+	1.79831i
$404$	−1.70591	−	9.67467i	−0.0848720	−	0.481333i
$405$		0			0
$406$	−4.90288	+	8.49204i	−0.243326	+	0.421453i
$407$	−2.75202	−	4.76664i	−0.136413	−	0.236274i
$408$	2.85344	+	2.39432i	0.141266	+	0.118536i
$409$	−12.6896	−	10.6479i	−0.627462	−	0.526503i	0.272677	−	0.962106i	$-0.412091\pi$
$409$	−12.6896	−	10.6479i	−0.627462	−	0.526503i	−0.900139	+	0.435602i	$0.856535\pi$
$410$		0			0
$411$	−4.81649	+	8.34241i	−0.237580	+	0.411501i
$412$	−12.4783	+	4.54171i	−0.614760	+	0.223754i
$413$	−4.55935	−	25.8574i	−0.224351	−	1.27236i
$414$	1.80206	−	10.2200i	0.0885665	−	0.502286i
$415$		0			0
$416$	−3.73253	+	3.13196i	−0.183002	+	0.153557i
$417$	0.166129			0.00813536
$418$	5.71665	+	7.80608i	0.279610	+	0.381808i
$419$	38.3266			1.87237			0.936187	−	0.351501i	$-0.114329\pi$
$419$	38.3266			1.87237			0.936187	+	0.351501i	$0.114329\pi$
$420$		0			0
$421$	−9.76019	−	3.55242i	−0.475682	−	0.173134i	0.0930423	−	0.995662i	$-0.470341\pi$
$421$	−9.76019	−	3.55242i	−0.475682	−	0.173134i	−0.568725	+	0.822528i	$0.692563\pi$
$422$	3.24783	−	18.4194i	0.158102	−	0.896640i
$423$	1.90552	+	10.8068i	0.0926496	+	0.525442i
$424$	−9.58672	+	3.48928i	−0.465572	+	0.169455i
$425$		0			0
$426$	−5.47175	−	9.47734i	−0.265107	−	0.459179i
$427$	−20.2539	−	16.9951i	−0.980156	−	0.822448i
$428$	−11.3275	−	9.50491i	−0.547536	−	0.459437i
$429$	−4.60350	−	7.97349i	−0.222259	−	0.384964i
$430$		0			0
$431$	2.78263	−	1.01279i	0.134034	−	0.0487846i	−0.274132	−	0.961692i	$-0.588391\pi$
$431$	2.78263	−	1.01279i	0.134034	−	0.0487846i	0.408166	+	0.912908i	$0.366168\pi$
$432$	0.779816	+	4.42256i	0.0375189	+	0.212780i
$433$	6.28540	−	35.6463i	0.302057	−	1.71305i	−0.334986	−	0.942223i	$-0.608732\pi$
$433$	6.28540	−	35.6463i	0.302057	−	1.71305i	0.637043	−	0.770828i	$-0.280157\pi$
$434$	−35.7010	−	12.9941i	−1.71370	−	0.623736i
$435$		0			0
$436$	8.77781			0.420381
$437$	−13.7562	+	14.3531i	−0.658049	+	0.686603i
$438$	11.3219			0.540981
$439$	−4.90663	+	4.11715i	−0.234181	+	0.196501i	−0.752325	−	0.658792i	$-0.771068\pi$
$439$	−4.90663	+	4.11715i	−0.234181	+	0.196501i	0.518144	+	0.855293i	$0.326623\pi$
$440$		0			0
$441$	−7.30983	+	41.4561i	−0.348087	+	1.97410i
$442$	−3.70221	−	20.9963i	−0.176096	−	0.998690i
$443$	28.6547	−	10.4295i	1.36143	−	0.495518i	0.444931	−	0.895565i	$-0.353228\pi$
$443$	28.6547	−	10.4295i	1.36143	−	0.495518i	0.916495	+	0.400046i	$0.131006\pi$
$444$	−1.05543	+	1.82806i	−0.0500884	+	0.0867557i
$445$		0			0
$446$	2.38441	+	2.00076i	0.112905	+	0.0947387i
$447$	0.0846459	+	0.0710263i	0.00400361	+	0.00335943i
$448$	−2.52492	−	4.37330i	−0.119291	−	0.206619i
$449$	−10.9555	+	18.9754i	−0.517020	+	0.895504i	0.482785	+	0.875739i	$0.339625\pi$
$449$	−10.9555	+	18.9754i	−0.517020	+	0.895504i	−0.999805	+	0.0197655i	$0.993708\pi$
$450$		0			0
$451$	−4.03479	−	22.8824i	−0.189991	−	1.07749i
$452$	0.00677124	−	0.0384016i	0.000318492	−	0.00180626i
$453$	2.83791	+	1.03292i	0.133337	+	0.0485306i
$454$	1.03341	−	0.867138i	0.0485006	−	0.0406968i
$455$		0			0
$456$	1.49644	−	3.39553i	0.0700770	−	0.159010i
$457$	8.35607			0.390881			0.195440	−	0.980716i	$-0.437386\pi$
$457$	8.35607			0.390881			0.195440	+	0.980716i	$0.437386\pi$
$458$	−12.2789	+	10.3032i	−0.573755	+	0.481437i
$459$	−18.4650	−	6.72071i	−0.861872	−	0.313696i
$460$		0			0
$461$	2.15399	+	12.2159i	0.100321	+	0.568951i	0.992986	+	0.118230i	$0.0377219\pi$
$461$	2.15399	+	12.2159i	0.100321	+	0.568951i	−0.892665	+	0.450721i	$0.851167\pi$
$462$	8.96671	−	3.26361i	0.417169	−	0.151837i
$463$	7.89495	−	13.6745i	0.366909	−	0.635506i	−0.622171	−	0.782881i	$-0.713749\pi$
$463$	7.89495	−	13.6745i	0.366909	−	0.635506i	0.989081	+	0.147376i	$0.0470826\pi$
$464$	0.970897	+	1.68164i	0.0450728	+	0.0780683i
$465$		0			0
$466$	−13.1557	−	11.0390i	−0.609427	−	0.511370i
$467$	5.75594	+	9.96957i	0.266353	+	0.461337i	0.967917	−	0.251269i	$-0.0808480\pi$
$467$	5.75594	+	9.96957i	0.266353	+	0.461337i	−0.701564	+	0.712606i	$0.747515\pi$
$468$	5.54321	−	9.60113i	0.256235	−	0.443812i
$469$	−7.00636	+	2.55010i	−0.323523	+	0.117753i
$470$		0			0
$471$	−0.622723	+	3.53164i	−0.0286936	+	0.162729i
$472$	−4.88585	−	1.77830i	−0.224890	−	0.0818531i
$473$	−14.3217	+	12.0173i	−0.658512	+	0.552557i
$474$	−5.17900			−0.237879
$475$		0			0
$476$	22.0963			1.01278
$477$	17.7820	−	14.9209i	0.814182	−	0.683180i
$478$	−26.1327	−	9.51154i	−1.19528	−	0.435048i
$479$	2.23499	−	12.6753i	0.102119	−	0.579148i	−0.890212	−	0.455546i	$-0.849444\pi$
$479$	2.23499	−	12.6753i	0.102119	−	0.579148i	0.992332	−	0.123603i	$-0.0394448\pi$
$480$		0			0
$481$	11.3533	−	4.13225i	0.517664	−	0.188414i
$482$	−3.24146	+	5.61437i	−0.147644	+	0.255728i
$483$	9.80343	+	16.9800i	0.446072	+	0.772619i
$484$	−4.65211	−	3.90358i	−0.211459	−	0.177436i
$485$		0			0
$486$	−8.01439	−	13.8813i	−0.363540	−	0.629670i
$487$	7.69825	−	13.3338i	0.348841	−	0.604210i	−0.637203	−	0.770696i	$-0.719909\pi$
$487$	7.69825	−	13.3338i	0.348841	−	0.604210i	0.986044	+	0.166486i	$0.0532420\pi$
$488$	−4.91997	+	1.79072i	−0.222717	+	0.0810622i
$489$	−3.31360	−	18.7924i	−0.149846	−	0.849821i
$490$		0			0
$491$	−3.11273	−	1.13294i	−0.140475	−	0.0511289i	0.270826	−	0.962628i	$-0.412703\pi$
$491$	−3.11273	−	1.13294i	−0.140475	−	0.0511289i	−0.411301	+	0.911500i	$0.634926\pi$
$492$	−6.82624	+	5.72790i	−0.307751	+	0.258234i
$493$	−8.49659			−0.382667
$494$	−19.0538	+	9.38246i	−0.857271	+	0.422137i
$495$		0			0
$496$	−5.76328	+	4.83597i	−0.258779	+	0.217141i
$497$	−61.0024	−	22.2031i	−2.73633	−	0.995943i
$498$	1.84431	−	10.4596i	0.0826455	−	0.468706i
$499$	4.48776	+	25.4513i	0.200900	+	1.13936i	0.903763	+	0.428034i	$0.140794\pi$
$499$	4.48776	+	25.4513i	0.200900	+	1.13936i	−0.702863	+	0.711325i	$0.748095\pi$
$500$		0			0
$501$	−1.61345	+	2.79458i	−0.0720836	+	0.124852i
$502$	6.05037	+	10.4796i	0.270041	+	0.467725i
$503$	31.3745	+	26.3263i	1.39892	+	1.17383i	0.961576	+	0.274539i	$0.0885251\pi$
$503$	31.3745	+	26.3263i	1.39892	+	1.17383i	0.437344	+	0.899294i	$0.355919\pi$
$504$	8.80187	+	7.38564i	0.392066	+	0.328983i
$505$		0			0
$506$	−5.06201	+	8.76766i	−0.225034	+	0.389770i
$507$	8.59214	−	3.12728i	0.381590	−	0.138888i
$508$	−0.0148191	−	0.0840433i	−0.000657491	−	0.00372882i
$509$	−2.52764	+	14.3350i	−0.112036	+	0.635387i	0.876139	+	0.482058i	$0.160111\pi$
$509$	−2.52764	+	14.3350i	−0.112036	+	0.635387i	−0.988175	+	0.153329i	$0.951001\pi$
$510$		0			0
$511$	51.4491	−	43.1709i	2.27598	−	1.90977i
$512$	−1.00000			−0.0441942
$513$	−1.29167	+	19.5322i	−0.0570287	+	0.862368i
$514$	23.7678			1.04835
$515$		0			0
$516$	6.73757	+	2.45228i	0.296605	+	0.107955i
$517$	1.85895	−	10.5426i	0.0817564	−	0.463664i
$518$	2.17437	+	12.3315i	0.0955365	+	0.541814i
$519$	−15.5932	+	5.67547i	−0.684466	+	0.249125i
$520$		0			0
$521$	−17.9537	−	31.0968i	−0.786568	−	1.36238i	−0.928058	−	0.372436i	$-0.878523\pi$
$521$	−17.9537	−	31.0968i	−0.786568	−	1.36238i	0.141490	−	0.989940i	$-0.454811\pi$
$522$	−3.38454	−	2.83997i	−0.148137	−	0.124302i
$523$	−17.1224	−	14.3674i	−0.748712	−	0.628244i	0.186450	−	0.982464i	$-0.440302\pi$
$523$	−17.1224	−	14.3674i	−0.748712	−	0.628244i	−0.935162	+	0.354221i	$0.884746\pi$
$524$	0.436329	+	0.755744i	0.0190611	+	0.0330148i
$525$		0			0
$526$	16.2362	−	5.90950i	0.707932	−	0.257666i
$527$	−5.71646	−	32.4197i	−0.249013	−	1.41222i
$528$	0.328125	−	1.86089i	0.0142798	−	0.0809848i
$529$	2.06505	+	0.751616i	0.0897847	+	0.0326790i
$530$		0			0
$531$	11.8303			0.513393
$532$	−6.14718	−	21.1360i	−0.266514	−	0.916362i
$533$	51.0039			2.20923
$534$	4.06425	−	3.41031i	0.175877	−	0.147579i
$535$		0			0
$536$	−0.256388	+	1.45405i	−0.0110743	+	0.0628054i
$537$	−1.29906	−	7.36734i	−0.0560586	−	0.317924i
$538$	9.95234	−	3.62236i	0.429076	−	0.156171i
$539$	20.5334	−	35.5648i	0.884435	−	1.53189i
$540$		0			0
$541$	−23.7227	−	19.9057i	−1.01992	−	0.855812i	−0.0302998	−	0.999541i	$-0.509646\pi$
$541$	−23.7227	−	19.9057i	−1.01992	−	0.855812i	−0.989617	+	0.143729i	$0.954091\pi$
$542$	−7.88840	−	6.61916i	−0.338836	−	0.284317i
$543$	4.12519	+	7.14504i	0.177029	+	0.306623i
$544$	2.18782	−	3.78941i	0.0938019	−	0.162470i
$545$		0			0
$546$	3.63723	+	20.6277i	0.155659	+	0.882786i
$547$	5.21283	−	29.5635i	0.222885	−	1.26404i	−0.643803	−	0.765191i	$-0.722644\pi$
$547$	5.21283	−	29.5635i	0.222885	−	1.26404i	0.866688	−	0.498851i	$-0.166244\pi$
$548$	10.6334	+	3.87025i	0.454238	+	0.165329i
$549$	9.12585	−	7.65750i	0.389482	−	0.326814i
$550$		0			0
$551$	2.36375	+	8.12733i	0.100699	+	0.346236i
$552$	3.88267			0.165257
$553$	−23.5345	+	19.7478i	−1.00079	+	0.839762i
$554$	7.04814	+	2.56531i	0.299447	+	0.108990i
$555$		0			0
$556$	−0.0338877	−	0.192187i	−0.00143716	−	0.00815053i
$557$	41.2003	−	14.9957i	1.74571	−	0.635388i	0.746176	−	0.665749i	$-0.231888\pi$
$557$	41.2003	−	14.9957i	1.74571	−	0.635388i	0.999539	+	0.0303609i	$0.00966566\pi$
$558$	8.55911	−	14.8248i	0.362336	−	0.627584i
$559$	−20.5194	−	35.5406i	−0.867876	−	1.50321i
$560$		0			0
$561$	6.33380	+	5.31469i	0.267413	+	0.224386i
$562$	5.86957	+	10.1664i	0.247593	+	0.428843i
$563$	9.15044	−	15.8490i	0.385645	−	0.667957i	−0.606213	−	0.795302i	$-0.707312\pi$
$563$	9.15044	−	15.8490i	0.385645	−	0.667957i	0.991858	+	0.127345i	$0.0406455\pi$
$564$	−3.85798	+	1.40419i	−0.162450	+	0.0591271i
$565$		0			0
$566$	−3.25534	+	18.4619i	−0.136832	+	0.776013i
$567$	−14.2504	−	5.18671i	−0.598459	−	0.217821i
$568$	−9.84775	+	8.26324i	−0.413202	+	0.346718i
$569$	−31.3182			−1.31293			−0.656464	−	0.754357i	$-0.727949\pi$
$569$	−31.3182			−1.31293			−0.656464	+	0.754357i	$0.727949\pi$
$570$		0			0
$571$	−3.99941			−0.167370			−0.0836850	−	0.996492i	$-0.526669\pi$
$571$	−3.99941			−0.167370			−0.0836850	+	0.996492i	$0.526669\pi$
$572$	−8.28512	+	6.95204i	−0.346418	+	0.290679i
$573$	1.48111	+	0.539080i	0.0618743	+	0.0225204i
$574$	−9.17917	+	52.0576i	−0.383131	+	2.17284i
$575$		0			0
$576$	2.13810	−	0.778205i	0.0890876	−	0.0324252i
$577$	−16.5274	+	28.6263i	−0.688045	+	1.19173i	0.284425	+	0.958698i	$0.408197\pi$
$577$	−16.5274	+	28.6263i	−0.688045	+	1.19173i	−0.972469	+	0.233030i	$0.925136\pi$
$578$	1.07310	+	1.85866i	0.0446351	+	0.0773103i
$579$	−0.315933	−	0.265100i	−0.0131297	−	0.0110172i
$580$		0			0
$581$	−31.5020	−	54.5631i	−1.30692	−	2.26366i
$582$	0.836815	−	1.44941i	0.0346871	−	0.0600798i
$583$	−21.2797	+	7.74519i	−0.881316	+	0.320773i
$584$	−2.30949	−	13.0978i	−0.0955674	−	0.541989i
$585$		0			0
$586$	−16.4701	−	5.99463i	−0.680374	−	0.247636i
$587$	−3.93270	+	3.29993i	−0.162320	+	0.136202i	−0.720330	−	0.693632i	$-0.756010\pi$
$587$	−3.93270	+	3.29993i	−0.162320	+	0.136202i	0.558010	+	0.829834i	$0.311565\pi$
$588$	−15.7495			−0.649499
$589$	−29.4204	+	14.4872i	−1.21225	+	0.596933i
$590$		0			0
$591$	−12.7781	+	10.7221i	−0.525619	+	0.441047i
$592$	2.33008	+	0.848081i	0.0957659	+	0.0348559i
$593$	−0.858582	+	4.86926i	−0.0352577	+	0.199957i	−0.997349	−	0.0727727i	$-0.976815\pi$
$593$	−0.858582	+	4.86926i	−0.0352577	+	0.199957i	0.962091	+	0.272729i	$0.0879263\pi$
$594$	1.73096	+	9.81678i	0.0710223	+	0.402788i
$595$		0			0
$596$	0.0649006	−	0.112411i	0.00265843	−	0.00460454i
$597$	4.21283	+	7.29684i	0.172420	+	0.298640i
$598$	−17.0239	−	14.2848i	−0.696160	−	0.584148i
$599$	−10.2340	−	8.58736i	−0.418151	−	0.350870i	0.409308	−	0.912396i	$-0.365770\pi$
$599$	−10.2340	−	8.58736i	−0.418151	−	0.350870i	−0.827459	+	0.561526i	$0.810214\pi$
$600$		0			0
$601$	−24.2452	+	41.9939i	−0.988983	+	1.71297i	−0.366292	+	0.930500i	$0.619373\pi$
$601$	−24.2452	+	41.9939i	−0.988983	+	1.71297i	−0.622691	+	0.782468i	$0.713961\pi$
$602$	39.9677	−	14.5470i	1.62896	−	0.592893i
$603$	−0.583366	−	3.30843i	−0.0237565	−	0.134730i
$604$	0.616042	−	3.49375i	0.0250664	−	0.142159i
$605$		0			0
$606$	−6.40637	+	5.37558i	−0.260241	+	0.218368i
$607$	−31.8211			−1.29158			−0.645788	−	0.763517i	$-0.723471\pi$
$607$	−31.8211			−1.29158			−0.645788	+	0.763517i	$0.723471\pi$
$608$	−4.23338	−	1.03852i	−0.171686	−	0.0421177i
$609$	8.34747			0.338256
$610$		0			0
$611$	22.0819	+	8.03715i	0.893337	+	0.325148i
$612$	−1.72884	+	9.80472i	−0.0698841	+	0.396332i
$613$	6.02775	+	34.1851i	0.243458	+	1.38072i	0.824046	+	0.566524i	$0.191712\pi$
$613$	6.02775	+	34.1851i	0.243458	+	1.38072i	−0.580587	+	0.814198i	$0.697177\pi$
$614$	−10.6520	+	3.87700i	−0.429878	+	0.156463i
$615$		0			0
$616$	−5.60459	−	9.70744i	−0.225816	−	0.391124i
$617$	−11.6167	−	9.74759i	−0.467672	−	0.392423i	0.378273	−	0.925694i	$-0.376518\pi$
$617$	−11.6167	−	9.74759i	−0.467672	−	0.392423i	−0.845944	+	0.533271i	$0.820963\pi$
$618$	8.65954	+	7.26622i	0.348338	+	0.292290i
$619$	−2.32371	−	4.02478i	−0.0933977	−	0.161770i	0.815541	−	0.578699i	$-0.196439\pi$
$619$	−2.32371	−	4.02478i	−0.0933977	−	0.161770i	−0.908939	+	0.416930i	$0.863106\pi$
$620$		0			0
$621$	−19.2471	+	7.00536i	−0.772358	+	0.281115i
$622$	1.22755	+	6.96177i	0.0492202	+	0.279142i
$623$	5.46515	−	30.9944i	0.218956	−	1.24176i
$624$	3.89770	+	1.41864i	0.156033	+	0.0567912i
$625$		0			0
$626$	12.1112			0.484061
$627$	3.32165	−	7.53708i	0.132654	−	0.301002i
$628$	4.21261			0.168102
$629$	−8.31153	+	6.97420i	−0.331402	+	0.278080i
$630$		0			0
$631$	5.37475	−	30.4817i	0.213965	−	1.21346i	−0.668728	−	0.743507i	$-0.733161\pi$
$631$	5.37475	−	30.4817i	0.213965	−	1.21346i	0.882693	−	0.469950i	$-0.155728\pi$
$632$	1.05644	+	5.99135i	0.0420228	+	0.238323i
$633$	−14.9617	+	5.44563i	−0.594676	+	0.216444i
$634$	5.46987	−	9.47410i	0.217236	−	0.376265i
$635$		0			0
$636$	6.65291	+	5.58245i	0.263805	+	0.221359i
$637$	69.0553	+	57.9443i	2.73607	+	2.29584i
$638$	2.15511	+	3.73276i	0.0853216	+	0.147781i
$639$	14.6250	−	25.3312i	0.578555	−	1.00209i
$640$		0			0
$641$	8.35103	+	47.3611i	0.329846	+	1.87065i	0.473167	+	0.880973i	$0.343111\pi$
$641$	8.35103	+	47.3611i	0.329846	+	1.87065i	−0.143321	+	0.989676i	$0.545778\pi$
$642$	−2.18587	+	12.3967i	−0.0862693	+	0.489258i
$643$	27.2856	+	9.93113i	1.07604	+	0.391646i	0.818431	−	0.574605i	$-0.194844\pi$
$643$	27.2856	+	9.93113i	1.07604	+	0.391646i	0.257606	+	0.966250i	$0.417066\pi$
$644$	17.6437	−	14.8048i	0.695258	−	0.583391i
$645$		0			0
$646$	13.1973	−	13.7699i	0.519239	−	0.541770i
$647$	−40.5552			−1.59439			−0.797194	−	0.603723i	$-0.793683\pi$
$647$	−40.5552			−1.59439			−0.797194	+	0.603723i	$0.793683\pi$
$648$	−2.30046	+	1.93032i	−0.0903708	+	0.0758301i
$649$	−10.8452	−	3.94732i	−0.425710	−	0.154946i
$650$		0			0
$651$	5.61613	+	31.8507i	0.220114	+	1.24833i
$652$	−21.0641	+	7.66671i	−0.824934	+	0.300251i
$653$	11.9266	−	20.6575i	0.466725	−	0.808391i	−0.532553	−	0.846397i	$-0.678767\pi$
$653$	11.9266	−	20.6575i	0.466725	−	0.808391i	0.999278	+	0.0380061i	$0.0121006\pi$
$654$	−3.73619	−	6.47128i	−0.146097	−	0.253047i
$655$		0			0
$656$	8.01879	+	6.72856i	0.313081	+	0.262706i
$657$	15.1307	+	26.2071i	0.590304	+	1.02244i
$658$	−12.1773	+	21.0916i	−0.474719	+	0.822237i
$659$	39.5190	−	14.3837i	1.53944	−	0.560310i	0.573529	−	0.819185i	$-0.305574\pi$
$659$	39.5190	−	14.3837i	1.53944	−	0.560310i	0.965911	+	0.258875i	$0.0833517\pi$
$660$		0			0
$661$	1.33225	−	7.55554i	0.0518184	−	0.293877i	−0.947875	−	0.318643i	$-0.896773\pi$
$661$	1.33225	−	7.55554i	0.0518184	−	0.293877i	0.999693	+	0.0247661i	$0.00788411\pi$
$662$	5.08945	+	1.85241i	0.197807	+	0.0719959i
$663$	−13.9033	+	11.6662i	−0.539959	+	0.453079i
$664$	−12.4764			−0.484179
$665$		0			0
$666$	−5.64194			−0.218621
$667$	−6.78444	+	5.69282i	−0.262695	+	0.220427i
$668$	3.56203	+	1.29647i	0.137819	+	0.0501621i
$669$	0.460119	−	2.60947i	0.0177892	−	0.100888i
$670$		0			0
$671$	−10.9209	+	3.97488i	−0.421597	+	0.153449i
$672$	−2.14942	+	3.72290i	−0.0829157	+	0.143614i
$673$	−6.11296	−	10.5879i	−0.235637	−	0.408135i	0.723821	−	0.689988i	$-0.242384\pi$
$673$	−6.11296	−	10.5879i	−0.235637	−	0.408135i	−0.959458	+	0.281853i	$0.909051\pi$
$674$	−9.94081	−	8.34133i	−0.382906	−	0.321296i
$675$		0			0
$676$	−5.37047	−	9.30193i	−0.206557	−	0.357767i
$677$	5.17201	−	8.95818i	0.198776	−	0.344291i	−0.749356	−	0.662168i	$-0.769637\pi$
$677$	5.17201	−	8.95818i	0.198776	−	0.344291i	0.948132	+	0.317877i	$0.102970\pi$
$678$	−0.0311930	+	0.0113533i	−0.00119796	+	0.000436021i
$679$	−1.72399	−	9.77724i	−0.0661607	−	0.375216i
$680$		0			0
$681$	−1.07914	−	0.392776i	−0.0413529	−	0.0150512i
$682$	−12.7928	+	10.7344i	−0.489862	+	0.411043i
$683$	20.3440			0.778443			0.389221	−	0.921144i	$-0.372744\pi$
$683$	20.3440			0.778443			0.389221	+	0.921144i	$0.372744\pi$
$684$	9.85957	−	1.07397i	0.376990	−	0.0410642i
$685$		0			0
$686$	−44.4904	+	37.3319i	−1.69865	+	1.42534i
$687$	12.8222	+	4.66691i	0.489199	+	0.178054i
$688$	1.46256	−	8.29461i	0.0557597	−	0.316229i
$689$	−8.63185	−	48.9536i	−0.328847	−	1.86498i
$690$		0			0
$691$	14.7919	−	25.6203i	0.562709	−	0.974641i	−0.434550	−	0.900648i	$-0.643092\pi$
$691$	14.7919	−	25.6203i	0.562709	−	0.974641i	0.997259	−	0.0739930i	$-0.0235742\pi$
$692$	9.74646	+	16.8814i	0.370505	+	0.641733i
$693$	19.5376	+	16.3940i	0.742171	+	0.622756i
$694$	8.45818	+	7.09726i	0.321068	+	0.269408i
$695$		0			0
$696$	0.826507	−	1.43155i	0.0313287	−	0.0542628i
$697$	−43.0410	+	15.6656i	−1.63029	+	0.593378i
$698$	4.97463	+	28.2126i	0.188293	+	1.06786i
$699$	−2.53866	+	14.3974i	−0.0960209	+	0.544561i
$700$		0			0
$701$	−2.79045	+	2.34146i	−0.105394	+	0.0884359i	−0.693962	−	0.720012i	$-0.744136\pi$
$701$	−2.79045	+	2.34146i	−0.105394	+	0.0884359i	0.588568	+	0.808448i	$0.299692\pi$
$702$	−21.8812			−0.825852
$703$	8.98337	+	6.01009i	0.338814	+	0.226675i
$704$	−2.21971			−0.0836584
$705$		0			0
$706$	−16.1808	−	5.88932i	−0.608972	−	0.221648i
$707$	−8.61456	+	48.8556i	−0.323984	+	1.83740i
$708$	0.768595	+	4.35892i	0.0288856	+	0.163818i
$709$	38.1690	−	13.8924i	1.43347	−	0.521739i	0.495544	−	0.868583i	$-0.334969\pi$
$709$	38.1690	−	13.8924i	1.43347	−	0.521739i	0.937923	+	0.346843i	$0.112746\pi$
$710$		0			0
$711$	−6.92127	−	11.9880i	−0.259568	−	0.449585i
$712$	−4.77427	−	4.00609i	−0.178923	−	0.150135i
$713$	−26.2861	−	22.0567i	−0.984424	−	0.826029i
$714$	−9.40508	−	16.2901i	−0.351976	−	0.609641i
$715$		0			0
$716$	−8.25795	+	3.00565i	−0.308614	+	0.112326i
$717$	4.11095	+	23.3144i	0.153526	+	0.870691i
$718$	2.21761	−	12.5767i	0.0827604	−	0.469357i
$719$	29.1532	+	10.6109i	1.08723	+	0.395720i	0.822595	−	0.568628i	$-0.192525\pi$
$719$	29.1532	+	10.6109i	1.08723	+	0.395720i	0.264638	+	0.964348i	$0.414748\pi$
$720$		0			0
$721$	67.0573			2.49735
$722$	−16.8429	−	8.79292i	−0.626829	−	0.327238i
$723$	5.51878			0.205246
$724$	7.42429	−	6.22972i	0.275922	−	0.231526i
$725$		0			0
$726$	−0.897716	+	5.09120i	−0.0333174	+	0.188952i
$727$	1.09022	+	6.18292i	0.0404339	+	0.229312i	0.998328	−	0.0578114i	$-0.0184122\pi$
$727$	1.09022	+	6.18292i	0.0404339	+	0.229312i	−0.957894	+	0.287123i	$0.907301\pi$
$728$	23.1213	−	8.41548i	0.856934	−	0.311898i
$729$	−2.31793	+	4.01478i	−0.0858494	+	0.148695i
$730$		0			0
$731$	28.2319	+	23.6894i	1.04419	+	0.876183i
$732$	3.41432	+	2.86495i	0.126197	+	0.105892i
$733$	13.4260	+	23.2546i	0.495902	+	0.858927i	0.999989	−	0.00472555i	$-0.00150419\pi$
$733$	13.4260	+	23.2546i	0.495902	+	0.858927i	−0.504087	+	0.863653i	$0.668171\pi$
$734$	13.1008	−	22.6912i	0.483559	−	0.837548i
$735$		0			0
$736$	−0.792004	−	4.49168i	−0.0291936	−	0.165565i
$737$	−0.569107	+	3.22757i	−0.0209633	+	0.118889i
$738$	−22.3812	−	8.14609i	−0.823863	−	0.299862i
$739$	−29.5975	+	24.8353i	−1.08876	+	0.913581i	−0.996619	−	0.0821650i	$-0.973817\pi$
$739$	−29.5975	+	24.8353i	−1.08876	+	0.913581i	−0.0921443	+	0.995746i	$0.529372\pi$
$740$		0			0
$741$	15.0271	+	10.0535i	0.552035	+	0.369325i
$742$	51.5184			1.89130
$743$	1.32354	−	1.11058i	0.0485559	−	0.0407432i	−0.618187	−	0.786031i	$-0.712132\pi$
$743$	1.32354	−	1.11058i	0.0485559	−	0.0407432i	0.666743	+	0.745288i	$0.267688\pi$
$744$	6.01831	+	2.19049i	0.220642	+	0.0803071i
$745$		0			0
$746$	−0.772258	−	4.37969i	−0.0282744	−	0.160352i
$747$	26.6759	−	9.70923i	0.976020	−	0.355242i
$748$	4.85632	−	8.41139i	0.177565	−	0.307551i
$749$	37.3361	+	64.6680i	1.36423	+	2.36292i
$750$		0			0
$751$	13.6370	+	11.4428i	0.497622	+	0.417555i	0.856749	−	0.515734i	$-0.172481\pi$
$751$	13.6370	+	11.4428i	0.497622	+	0.417555i	−0.359126	+	0.933289i	$0.616925\pi$
$752$	2.41141	+	4.17669i	0.0879351	+	0.152308i
$753$	5.15057	−	8.92105i	0.187697	−	0.325101i
$754$	−8.89075	+	3.23597i	−0.323782	+	0.117847i
$755$		0			0
$756$	3.93795	−	22.3332i	0.143222	−	0.812252i
$757$	−0.0353520	−	0.0128671i	−0.00128489	−	0.000467662i	0.341378	−	0.939926i	$-0.389107\pi$
$757$	−0.0353520	−	0.0128671i	−0.00128489	−	0.000467662i	−0.342663	+	0.939459i	$0.611329\pi$
$758$	26.8076	−	22.4943i	0.973696	−	0.817028i
$759$	8.61838			0.312828
$760$		0			0
$761$	−11.8171			−0.428370			−0.214185	−	0.976793i	$-0.568709\pi$
$761$	−11.8171			−0.428370			−0.214185	+	0.976793i	$0.568709\pi$
$762$	−0.0556517	+	0.0466973i	−0.00201605	+	0.00169167i
$763$	−41.6534	−	15.1606i	−1.50795	−	0.548851i
$764$	0.321513	−	1.82339i	0.0116319	−	0.0659680i
$765$		0			0
$766$	23.0237	−	8.37992i	0.831878	−	0.302779i
$767$	12.6670	−	21.9399i	0.457379	−	0.792203i
$768$	0.425641	+	0.737231i	0.0153590	+	0.0266025i
$769$	33.4794	+	28.0926i	1.20730	+	1.01304i	0.999391	+	0.0348957i	$0.0111099\pi$
$769$	33.4794	+	28.0926i	1.20730	+	1.01304i	0.207908	+	0.978148i	$0.433335\pi$
$770$		0			0
$771$	−10.1165	−	17.5223i	−0.364338	−	0.631051i
$772$	−0.242236	+	0.419565i	−0.00871826	+	0.0151005i
$773$	−16.3855	+	5.96385i	−0.589347	+	0.214505i	−0.619442	−	0.785042i	$-0.712641\pi$
$773$	−16.3855	+	5.96385i	−0.589347	+	0.214505i	0.0300952	+	0.999547i	$0.490419\pi$
$774$	3.32780	+	18.8729i	0.119615	+	0.678372i
$775$		0			0
$776$	−1.84745	−	0.672416i	−0.0663195	−	0.0241383i
$777$	8.16565	−	6.85180i	0.292941	−	0.245807i
$778$	7.51557			0.269446
$779$	26.9588	+	36.8122i	0.965898	+	1.31893i
$780$		0			0
$781$	−21.8591	+	18.3420i	−0.782181	+	0.656328i
$782$	18.7536	+	6.82574i	0.670626	+	0.244088i
$783$	−1.51424	+	8.58770i	−0.0541146	+	0.306899i
$784$	3.21266	+	18.2199i	0.114738	+	0.650710i
$785$		0			0
$786$	0.371438	−	0.643350i	0.0132488	−	0.0229475i
$787$	14.9205	+	25.8430i	0.531857	+	0.921203i	0.999308	+	0.0371843i	$0.0118388\pi$
$787$	14.9205	+	25.8430i	0.531857	+	0.921203i	−0.467452	+	0.884019i	$0.654828\pi$
$788$	15.0104	+	12.5952i	0.534723	+	0.448686i
$789$	−11.2675	−	9.45452i	−0.401132	−	0.336590i
$790$		0			0
$791$	−0.0984569	+	0.170532i	−0.00350072	+	0.00606343i
$792$	4.74596	−	1.72739i	0.168640	−	0.0613801i
$793$	−4.42992	−	25.1233i	−0.157311	−	0.892156i
$794$	−0.495394	+	2.80952i	−0.0175809	+	0.0997062i
$795$		0			0
$796$	7.58202	−	6.36207i	0.268738	−	0.225498i
$797$	−8.25156			−0.292285			−0.146143	−	0.989264i	$-0.546686\pi$
$797$	−8.25156			−0.292285			−0.146143	+	0.989264i	$0.546686\pi$
$798$	−12.9656	+	13.5282i	−0.458978	+	0.478894i
$799$	−21.1029			−0.746567
$800$		0			0
$801$	13.3254	+	4.85007i	0.470831	+	0.171369i
$802$	4.39448	−	24.9223i	0.155174	−	0.880038i
$803$	−5.12639	−	29.0732i	−0.180906	−	1.02597i
$804$	1.18110	−	0.429886i	0.0416542	−	0.0151609i
$805$		0			0
$806$	−18.3288	−	31.7465i	−0.645606	−	1.11822i
$807$	−6.90663	−	5.79535i	−0.243125	−	0.204006i
$808$	7.52556	+	6.31469i	0.264748	+	0.222150i
$809$	−17.2942	−	29.9544i	−0.608030	−	1.05314i	−0.991565	−	0.129613i	$-0.958627\pi$
$809$	−17.2942	−	29.9544i	−0.608030	−	1.05314i	0.383534	−	0.923527i	$-0.374707\pi$
$810$		0			0
$811$	−15.0518	+	5.47841i	−0.528541	+	0.192373i	−0.592487	−	0.805580i	$-0.701854\pi$
$811$	−15.0518	+	5.47841i	−0.528541	+	0.192373i	0.0639460	+	0.997953i	$0.479631\pi$
$812$	−1.70275	−	9.65680i	−0.0597549	−	0.338887i
$813$	−1.52222	+	8.63296i	−0.0533867	+	0.302771i
$814$	5.17211	+	1.88249i	0.181282	+	0.0659813i
$815$		0			0
$816$	−3.72490			−0.130397
$817$	14.8057	−	33.5953i	0.517987	−	1.17535i
$818$	16.5651			0.579187
$819$	−42.8868	+	35.9863i	−1.49859	+	1.25746i
$820$		0			0
$821$	−5.38408	+	30.5347i	−0.187906	+	1.06567i	0.734259	+	0.678870i	$0.237530\pi$
$821$	−5.38408	+	30.5347i	−0.187906	+	1.06567i	−0.922165	+	0.386797i	$0.873581\pi$
$822$	−1.67275	−	9.48664i	−0.0583439	−	0.330885i
$823$	−34.2461	+	12.4645i	−1.19374	+	0.434487i	−0.861036	−	0.508544i	$-0.830184\pi$
$823$	−34.2461	+	12.4645i	−1.19374	+	0.434487i	−0.332706	+	0.943031i	$0.607962\pi$
$824$	6.63954	−	11.5000i	0.231299	−	0.400622i
$825$		0			0
$826$	20.1135	+	16.8772i	0.699837	+	0.587233i
$827$	16.8476	+	14.1368i	0.585849	+	0.491585i	0.886862	−	0.462035i	$-0.152880\pi$
$827$	16.8476	+	14.1368i	0.585849	+	0.491585i	−0.301013	+	0.953620i	$0.597325\pi$
$828$	5.18883	+	8.98732i	0.180324	+	0.312331i
$829$	−14.1054	+	24.4313i	−0.489902	+	0.848536i	−0.999932	−	0.0116207i	$-0.996301\pi$
$829$	−14.1054	+	24.4313i	−0.489902	+	0.848536i	0.510030	+	0.860157i	$0.329634\pi$
$830$		0			0
$831$	−1.10875	−	6.28801i	−0.0384620	−	0.218129i
$832$	0.846095	−	4.79844i	0.0293331	−	0.166356i
$833$	−76.0714	−	27.6877i	−2.63572	−	0.959323i
$834$	−0.127262	+	0.106786i	−0.00440672	+	0.00369768i
$835$		0			0
$836$	−9.39686	−	2.30522i	−0.324997	−	0.0797276i
$837$	−33.7861			−1.16782
$838$	−29.3598	+	24.6358i	−1.01422	+	0.851031i
$839$	31.7659	+	11.5618i	1.09668	+	0.399159i	0.826091	−	0.563537i	$-0.190560\pi$
$839$	31.7659	+	11.5618i	1.09668	+	0.399159i	0.270588	+	0.962695i	$0.412782\pi$
$840$		0			0
$841$	−4.38105	−	24.8461i	−0.151071	−	0.856763i
$842$	9.76019	−	3.55242i	0.336358	−	0.122424i
$843$	4.99665	−	8.65445i	0.172094	−	0.298075i
$844$	9.35175	+	16.1977i	0.321901	+	0.557548i
$845$		0			0
$846$	−8.40616	−	7.05361i	−0.289010	−	0.242508i
$847$	15.3336	+	26.5586i	0.526869	+	0.912563i
$848$	5.10099	−	8.83517i	0.175169	−	0.303401i
$849$	14.9963	−	5.45821i	0.514672	−	0.187325i
$850$		0			0
$851$	−1.96387	+	11.1377i	−0.0673206	+	0.381794i
$852$	10.2835	+	3.74289i	0.352308	+	0.128229i
$853$	19.0144	−	15.9550i	0.651040	−	0.546287i	−0.256346	−	0.966585i	$-0.582519\pi$
$853$	19.0144	−	15.9550i	0.651040	−	0.546287i	0.907386	+	0.420298i	$0.138074\pi$
$854$	26.4396			0.904745
$855$		0			0
$856$	14.7870			0.505410
$857$	27.5731	−	23.1366i	0.941881	−	0.790332i	−0.0360308	−	0.999351i	$-0.511471\pi$
$857$	27.5731	−	23.1366i	0.941881	−	0.790332i	0.977912	+	0.209019i	$0.0670270\pi$
$858$	8.65175	+	3.14898i	0.295366	+	0.107504i
$859$	−1.04772	+	5.94193i	−0.0357479	+	0.202736i	−0.997451	−	0.0713578i	$-0.977267\pi$
$859$	−1.04772	+	5.94193i	−0.0357479	+	0.202736i	0.961703	+	0.274094i	$0.0883779\pi$
$860$		0			0
$861$	42.2855	−	15.3907i	1.44109	−	0.524513i
$862$	−1.48061	+	2.56448i	−0.0504296	+	0.0873467i
$863$	−2.70201	−	4.68002i	−0.0919775	−	0.159310i	0.816366	−	0.577535i	$-0.195985\pi$
$863$	−2.70201	−	4.68002i	−0.0919775	−	0.159310i	−0.908343	+	0.418226i	$0.862652\pi$
$864$	−3.44014	−	2.88662i	−0.117036	−	0.0982048i
$865$		0			0
$866$	18.0981	+	31.3468i	0.614998	+	1.06521i
$867$	0.913510	−	1.58225i	0.0310244	−	0.0537359i
$868$	35.7010	−	12.9941i	1.21177	−	0.441048i
$869$	2.34498	+	13.2990i	0.0795480	+	0.451139i
$870$		0			0
$871$	−6.76025	−	2.46053i	−0.229062	−	0.0833719i
$872$	−6.72420	+	5.64227i	−0.227710	+	0.191071i
$873$	4.47331			0.151399
$874$	1.31186	−	19.8375i	0.0443743	−	0.671012i
$875$		0			0
$876$	−8.67307	+	7.27757i	−0.293036	+	0.245886i
$877$	−26.2139	−	9.54107i	−0.885180	−	0.322179i	−0.140881	−	0.990026i	$-0.544994\pi$
$877$	−26.2139	−	9.54107i	−0.885180	−	0.322179i	−0.744298	+	0.667847i	$0.767216\pi$
$878$	1.11224	−	6.30785i	0.0375364	−	0.212879i
$879$	2.59092	+	14.6938i	0.0873895	+	0.495611i
$880$		0			0
$881$	24.2475	−	41.9980i	0.816920	−	1.41495i	−0.0910206	−	0.995849i	$-0.529013\pi$
$881$	24.2475	−	41.9980i	0.816920	−	1.41495i	0.907941	−	0.419098i	$-0.137654\pi$
$882$	−21.0478	−	36.4559i	−0.708716	−	1.22753i
$883$	−29.6743	−	24.8997i	−0.998618	−	0.837940i	−0.0118259	−	0.999930i	$-0.503764\pi$
$883$	−29.6743	−	24.8997i	−0.998618	−	0.837940i	−0.986792	+	0.161990i	$0.948209\pi$
$884$	16.3322	+	13.7043i	0.549311	+	0.460926i
$885$		0			0
$886$	−15.2468	+	26.4083i	−0.512228	+	0.887205i
$887$	2.16410	−	0.787669i	0.0726635	−	0.0264473i	−0.305433	−	0.952214i	$-0.598801\pi$
$887$	2.16410	−	0.787669i	0.0726635	−	0.0264473i	0.378096	+	0.925766i	$0.376579\pi$
$888$	−0.366546	−	2.07879i	−0.0123005	−	0.0697596i
$889$	−0.0748342	+	0.424406i	−0.00250986	+	0.0142341i
$890$		0			0
$891$	−5.10636	+	4.28475i	−0.171070	+	0.143544i
$892$	−3.11263			−0.104219
$893$	5.87082	+	20.1858i	0.196460	+	0.675492i
$894$	−0.110497			−0.00369558
$895$		0			0
$896$	4.74530	+	1.72715i	0.158529	+	0.0577000i
$897$	−3.28510	+	18.6308i	−0.109686	+	0.622063i
$898$	−3.80479	−	21.5780i	−0.126967	−	0.720068i
$899$	−13.7279	+	4.99656i	−0.457852	+	0.166645i
$900$		0			0
$901$	22.3201	+	38.6595i	0.743590	+	1.28794i
$902$	17.7994	+	14.9354i	0.592654	+	0.497296i
$903$	−27.7364	−	23.2736i	−0.923009	−	0.774497i
$904$	0.0194970	+	0.0337698i	0.000648461	+	0.00112317i
$905$		0			0
$906$	−2.83791	+	1.03292i	−0.0942833	+	0.0343163i
$907$	−0.597590	−	3.38910i	−0.0198427	−	0.112533i	0.973278	−	0.229631i	$-0.0737520\pi$
$907$	−0.597590	−	3.38910i	−0.0198427	−	0.112533i	−0.993120	+	0.117098i	$0.962641\pi$
$908$	−0.234256	+	1.32853i	−0.00777406	+	0.0440889i
$909$	−21.0045	−	7.64503i	−0.696677	−	0.253570i
$910$		0			0
$911$	−13.5169			−0.447834			−0.223917	−	0.974608i	$-0.571885\pi$
$911$	−13.5169			−0.447834			−0.223917	+	0.974608i	$0.571885\pi$
$912$	1.03627	+	3.56301i	0.0343142	+	0.117983i
$913$	−27.6940			−0.916539
$914$	−6.40112	+	5.37118i	−0.211730	+	0.177663i
$915$		0			0
$916$	2.78340	−	15.7854i	0.0919660	−	0.521565i
$917$	−0.765231	−	4.33984i	−0.0252701	−	0.143314i
$918$	18.4650	−	6.72071i	0.609435	−	0.221816i
$919$	1.47338	−	2.55196i	0.0486022	−	0.0841815i	−0.840701	−	0.541500i	$-0.817857\pi$
$919$	1.47338	−	2.55196i	0.0486022	−	0.0841815i	0.889303	+	0.457318i	$0.151190\pi$
$920$		0			0
$921$	7.39215	+	6.20275i	0.243580	+	0.204388i
$922$	−9.50227	−	7.97336i	−0.312941	−	0.262588i
$923$	−31.3186	−	54.2453i	−1.03086	−	1.78551i
$924$	−4.77109	+	8.26376i	−0.156957	+	0.271858i
$925$		0			0
$926$	2.74189	+	15.5500i	0.0901040	+	0.511005i
$927$	−5.24663	+	29.7551i	−0.172322	+	0.977287i
$928$	−1.82469	−	0.664133i	−0.0598984	−	0.0218012i
$929$	−24.4020	+	20.4757i	−0.800603	+	0.671786i	−0.948345	−	0.317240i	$-0.897244\pi$
$929$	−24.4020	+	20.4757i	−0.800603	+	0.671786i	0.147742	+	0.989026i	$0.452800\pi$
$930$		0			0
$931$	−5.32138	+	80.4680i	−0.174401	+	2.63723i
$932$	17.1736			0.562539
$933$	4.60994	−	3.86820i	0.150923	−	0.126639i
$934$	−10.8176	−	3.93729i	−0.353963	−	0.128832i
$935$		0			0
$936$	1.92514	+	10.9180i	0.0629251	+	0.356866i
$937$	−2.82907	+	1.02970i	−0.0924216	+	0.0336387i	−0.387817	−	0.921736i	$-0.626771\pi$
$937$	−2.82907	+	1.02970i	−0.0924216	+	0.0336387i	0.295396	+	0.955375i	$0.404549\pi$
$938$	3.72800	−	6.45709i	0.121724	−	0.210832i
$939$	−5.15502	−	8.92876i	−0.168228	−	0.291379i
$940$		0			0
$941$	−26.3537	−	22.1134i	−0.859106	−	0.720875i	0.102670	−	0.994716i	$-0.467262\pi$
$941$	−26.3537	−	22.1134i	−0.859106	−	0.720875i	−0.961775	+	0.273840i	$0.911706\pi$
$942$	−1.79306	−	3.10567i	−0.0584210	−	0.101188i
$943$	−23.8716	+	41.3468i	−0.777366	+	1.34644i
$944$	4.88585	−	1.77830i	0.159021	−	0.0578789i
$945$		0			0
$946$	3.24647	−	18.4116i	0.105552	−	0.598613i
$947$	11.0825	+	4.03368i	0.360131	+	0.131077i	0.515748	−	0.856740i	$-0.327514\pi$
$947$	11.0825	+	4.03368i	0.360131	+	0.131077i	−0.155616	+	0.987818i	$0.549736\pi$
$948$	3.96734	−	3.32900i	0.128853	−	0.108121i
$949$	64.8030			2.10359
$950$		0			0
$951$	−9.31280			−0.301988
$952$	−16.9267	+	14.2032i	−0.548599	+	0.460329i
$953$	8.54236	+	3.10917i	0.276714	+	0.100716i	0.476650	−	0.879093i	$-0.341851\pi$
$953$	8.54236	+	3.10917i	0.276714	+	0.100716i	−0.199935	+	0.979809i	$0.564073\pi$
$954$	−4.03086	+	22.8601i	−0.130504	+	0.740124i
$955$		0			0
$956$	26.1327	−	9.51154i	0.845193	−	0.307625i
$957$	1.83460	−	3.17763i	0.0593043	−	0.102718i
$958$	6.43541	+	11.1465i	0.207919	+	0.360126i
$959$	−43.7744	−	36.7311i	−1.41355	−	1.18611i
$960$		0			0
$961$	−12.8010	−	22.1720i	−0.412935	−	0.715225i
$962$	−6.04094	+	10.4632i	−0.194768	+	0.337348i
$963$	−31.6161	+	11.5073i	−1.01882	+	0.370819i
$964$	−1.12575	−	6.38443i	−0.0362579	−	0.205629i
$965$		0			0
$966$	−18.4244	−	6.70594i	−0.592796	−	0.215760i
$967$	−3.90883	+	3.27990i	−0.125700	+	0.105474i	−0.703470	−	0.710725i	$-0.748367\pi$
$967$	−3.90883	+	3.27990i	−0.125700	+	0.105474i	0.577771	+	0.816199i	$0.303923\pi$
$968$	6.07290			0.195190
$969$	−15.7689	−	3.86839i	−0.506570	−	0.124271i
$970$		0			0
$971$	−2.03318	+	1.70604i	−0.0652479	+	0.0547495i	−0.674828	−	0.737975i	$-0.735782\pi$
$971$	−2.03318	+	1.70604i	−0.0652479	+	0.0547495i	0.609580	+	0.792724i	$0.291338\pi$
$972$	15.0621	+	5.48216i	0.483118	+	0.175841i
$973$	−0.171128	+	0.970514i	−0.00548610	+	0.0311132i
$974$	2.67357	+	15.1626i	0.0856668	+	0.485841i
$975$		0			0
$976$	2.61786	−	4.53427i	0.0837957	−	0.145138i
$977$	−16.3936	−	28.3946i	−0.524478	−	0.908422i	−0.999594	−	0.0284992i	$-0.990927\pi$
$977$	−16.3936	−	28.3946i	−0.524478	−	0.908422i	0.475116	−	0.879923i	$-0.342406\pi$
$978$	14.6179	+	12.2659i	0.467428	+	0.392219i
$979$	−10.5975	−	8.89235i	−0.338697	−	0.284201i
$980$		0			0
$981$	9.98617	−	17.2966i	0.318834	−	0.552236i
$982$	3.11273	−	1.13294i	0.0993311	−	0.0361536i
$983$	5.99682	+	34.0096i	0.191269	+	1.08474i	0.917633	+	0.397429i	$0.130098\pi$
$983$	5.99682	+	34.0096i	0.191269	+	1.08474i	−0.726364	+	0.687310i	$0.758791\pi$
$984$	1.54738	−	8.77565i	0.0493288	−	0.279757i
$985$		0			0
$986$	6.50877	−	5.46150i	0.207281	−	0.173930i
$987$	20.7325			0.659924
$988$	8.56513	−	19.4349i	0.272493	−	0.618307i
$989$	38.4151			1.22153
$990$		0			0
$991$	−9.49996	−	3.45770i	−0.301776	−	0.109838i	0.186694	−	0.982418i	$-0.440223\pi$
$991$	−9.49996	−	3.45770i	−0.301776	−	0.109838i	−0.488470	+	0.872581i	$0.662445\pi$
$992$	1.30643	−	7.40913i	0.0414792	−	0.235240i
$993$	−0.800624	−	4.54056i	−0.0254070	−	0.144090i
$994$	61.0024	−	22.2031i	1.93488	−	0.704238i
$995$		0			0
$996$	5.31048	+	9.19801i	0.168269	+	0.291450i
$997$	7.18916	+	6.03242i	0.227683	+	0.191049i	0.749492	−	0.662014i	$-0.230298\pi$
$997$	7.18916	+	6.03242i	0.227683	+	0.191049i	−0.521809	+	0.853063i	$0.674742\pi$
$998$	−19.7976	−	16.6122i	−0.626683	−	0.525850i
$999$	5.56772	+	9.64358i	0.176155	+	0.305109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.j.101.3	✓	24
5.2	odd	4		950.2.u.h.899.3		48
5.3	odd	4		950.2.u.h.899.6		48
5.4	even	2		950.2.l.k.101.2	yes	24
19.16	even	9	inner	950.2.l.j.301.3	yes	24
95.54	even	18		950.2.l.k.301.2	yes	24
95.73	odd	36		950.2.u.h.149.3		48
95.92	odd	36		950.2.u.h.149.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.101.3	✓	24	1.1	even	1	trivial
950.2.l.j.301.3	yes	24	19.16	even	9	inner
950.2.l.k.101.2	yes	24	5.4	even	2
950.2.l.k.301.2	yes	24	95.54	even	18
950.2.u.h.149.3		48	95.73	odd	36
950.2.u.h.149.6		48	95.92	odd	36
950.2.u.h.899.3		48	5.2	odd	4
950.2.u.h.899.6		48	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.799943 + 0.291155i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.799943 + 0.291155i) q^{6} +(-2.52492 + 4.37330i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.74300 - 1.46255i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.799943 + 0.291155i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.799943 + 0.291155i) q^{6} +(-2.52492 + 4.37330i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.74300 - 1.46255i) q^{9} +(1.10985 + 1.92232i) q^{11} +(0.425641 - 0.737231i) q^{12} +(-4.57862 + 1.66648i) q^{13} +(-0.876897 - 4.97313i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(3.35193 - 2.81261i) q^{17} +2.27532 q^{18} +(-3.62288 - 2.42379i) q^{19} +(-3.29310 + 2.76324i) q^{21} +(-2.08584 - 0.759185i) q^{22} +(0.792004 - 4.49168i) q^{23} +(0.147823 + 0.838348i) q^{24} +(2.43623 - 4.21968i) q^{26} +(-2.24539 - 3.88913i) q^{27} +(3.86841 + 3.24598i) q^{28} +(-1.48750 - 1.24816i) q^{29} +(3.76171 - 6.51548i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.328125 + 1.86089i) q^{33} +(-0.759821 + 4.30916i) q^{34} +(-1.74300 + 1.46255i) q^{36} -2.47962 q^{37} +(4.33327 - 0.472007i) q^{38} -4.14784 q^{39} +(-9.83650 - 3.58019i) q^{41} +(0.746486 - 4.23353i) q^{42} +(1.46256 + 8.29461i) q^{43} +(2.08584 - 0.759185i) q^{44} +(2.28048 + 3.94991i) q^{46} +(-3.69450 - 3.10005i) q^{47} +(-0.652119 - 0.547193i) q^{48} +(-9.25048 - 16.0223i) q^{49} +(3.50026 - 1.27399i) q^{51} +(0.846095 + 4.79844i) q^{52} +(-1.77156 + 10.0470i) q^{53} +(4.21995 + 1.53594i) q^{54} -5.04985 q^{56} +(-2.19239 - 2.99371i) q^{57} +1.94179 q^{58} +(-3.98298 + 3.34212i) q^{59} +(-0.909174 + 5.15618i) q^{61} +(1.30643 + 7.40913i) q^{62} +(10.7971 - 3.92982i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.44751 - 1.21461i) q^{66} +(1.13105 + 0.949064i) q^{67} +(-2.18782 - 3.78941i) q^{68} +(1.94133 - 3.36249i) q^{69} +(2.23230 + 12.6600i) q^{71} +(0.395105 - 2.24075i) q^{72} +(-12.4977 - 4.54881i) q^{73} +(1.89950 - 1.59387i) q^{74} +(-3.01608 + 3.14695i) q^{76} -11.2092 q^{77} +(3.17743 - 2.66618i) q^{78} +(5.71688 + 2.08077i) q^{79} +(0.521473 + 2.95742i) q^{81} +(9.83650 - 3.58019i) q^{82} +(-6.23822 + 10.8049i) q^{83} +(2.14942 + 3.72290i) q^{84} +(-6.45206 - 5.41392i) q^{86} +(-0.826507 - 1.43155i) q^{87} +(-1.10985 + 1.92232i) q^{88} +(-5.85651 + 2.13160i) q^{89} +(4.27265 - 24.2314i) q^{91} +(-4.28591 - 1.55994i) q^{92} +(4.90617 - 4.11677i) q^{93} +4.82282 q^{94} +0.851281 q^{96} +(-1.50605 + 1.26373i) q^{97} +(17.3852 + 6.32770i) q^{98} +(0.877018 - 4.97382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) \) 24 * q - 3 * q^7 + 12 * q^8	\( 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 12 * q^8 - 6 * q^11 + 3 * q^12 - 24 * q^13 - 15 * q^14 + 9 * q^17 - 30 * q^18 - 15 * q^19 - 18 * q^21 - 12 * q^23 - 9 * q^26 + 21 * q^27 - 12 * q^28 - 12 * q^29 + 9 * q^31 + 42 * q^33 - 9 * q^34 - 66 * q^37 - 6 * q^38 + 66 * q^39 + 18 * q^41 - 9 * q^42 + 3 * q^43 - 3 * q^46 + 12 * q^47 - 27 * q^49 - 3 * q^51 + 12 * q^52 + 45 * q^53 + 27 * q^54 - 6 * q^56 + 27 * q^57 + 18 * q^58 + 36 * q^59 + 12 * q^61 + 24 * q^62 + 63 * q^63 - 12 * q^64 + 48 * q^66 + 54 * q^67 - 3 * q^68 + 21 * q^69 - 39 * q^71 - 48 * q^73 + 18 * q^74 + 6 * q^76 - 48 * q^77 + 12 * q^78 - 42 * q^79 - 36 * q^81 - 18 * q^82 + 3 * q^83 + 9 * q^84 - 39 * q^86 + 24 * q^87 + 6 * q^88 - 36 * q^89 + 12 * q^91 + 15 * q^92 + 6 * q^93 + 12 * q^94 + 6 * q^96 + 54 * q^97 - 3 * q^98 + 51 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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