LMFDB - Embedded newform 841.2.e.d.267.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(63,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.63"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,4,-2,6,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			267.1
Root			$-0.781831 + 0.623490i$ of defining polynomial
Character	$\chi$	$=$	841.267
Dual form			841.2.e.d.63.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40881 - 1.12349i) q^{2} +(-0.433884 - 0.0990311i) q^{3} +(0.277479 + 1.21572i) q^{4} +(-0.222521 + 0.279032i) q^{5} +(0.500000 + 0.626980i) q^{6} +(0.900969 - 3.94740i) q^{7} +(-0.588735 + 1.22252i) q^{8} +(-2.52446 - 1.21572i) q^{9} +(0.626980 - 0.143104i) q^{10} +(-1.26341 - 2.62349i) q^{11} -0.554958i q^{12} +(4.67241 - 2.25011i) q^{13} +(-5.70416 + 4.54892i) q^{14} +(0.124181 - 0.0990311i) q^{15} +(4.44989 - 2.14295i) q^{16} +1.10992i q^{17} +(2.19064 + 4.54892i) q^{18} +(1.99755 - 0.455927i) q^{19} +(-0.400969 - 0.193096i) q^{20} +(-0.781831 + 1.62349i) q^{21} +(-1.16756 + 5.11543i) q^{22} +(-2.57942 - 3.23449i) q^{23} +(0.376510 - 0.472129i) q^{24} +(1.08426 + 4.75046i) q^{25} +(-9.11052 - 2.07942i) q^{26} +(2.01877 + 1.60992i) q^{27} +5.04892 q^{28} -0.286208 q^{30} +(-4.97002 - 3.96346i) q^{31} +(-6.03089 - 1.37651i) q^{32} +(0.288364 + 1.26341i) q^{33} +(1.24698 - 1.56366i) q^{34} +(0.900969 + 1.12978i) q^{35} +(0.777479 - 3.40636i) q^{36} +(1.26341 - 2.62349i) q^{37} +(-3.32640 - 1.60191i) q^{38} +(-2.25011 + 0.513574i) q^{39} +(-0.210117 - 0.436313i) q^{40} -0.396125i q^{41} +(2.92543 - 1.40881i) q^{42} +(-4.48845 + 3.57942i) q^{43} +(2.83885 - 2.26391i) q^{44} +(0.900969 - 0.433884i) q^{45} +7.45473i q^{46} +(-3.38513 - 7.02930i) q^{47} +(-2.14295 + 0.489115i) q^{48} +(-8.46346 - 4.07579i) q^{49} +(3.80957 - 7.91066i) q^{50} +(0.109916 - 0.481575i) q^{51} +(4.03199 + 5.05596i) q^{52} +(-2.71648 + 3.40636i) q^{53} +(-1.03534 - 4.53614i) q^{54} +(1.01317 + 0.231250i) q^{55} +(4.29535 + 3.42543i) q^{56} -0.911854 q^{57} -9.10992 q^{59} +(0.154851 + 0.123490i) q^{60} +(5.89726 + 1.34601i) q^{61} +(2.54892 + 11.1675i) q^{62} +(-7.07338 + 8.86973i) q^{63} +(0.791053 + 0.991949i) q^{64} +(-0.411854 + 1.80445i) q^{65} +(1.01317 - 2.10388i) q^{66} +(0.337282 + 0.162426i) q^{67} +(-1.34934 + 0.307979i) q^{68} +(0.798852 + 1.65883i) q^{69} -2.60388i q^{70} +(-10.2763 + 4.94880i) q^{71} +(2.97247 - 2.37047i) q^{72} +(-6.99637 + 5.57942i) q^{73} +(-4.72737 + 2.27658i) q^{74} -2.16852i q^{75} +(1.10855 + 2.30194i) q^{76} +(-11.4943 + 2.62349i) q^{77} +(3.74698 + 1.80445i) q^{78} +(-0.257808 + 0.535344i) q^{79} +(-0.392240 + 1.71851i) q^{80} +(4.52446 + 5.67349i) q^{81} +(-0.445042 + 0.558065i) q^{82} +(2.09903 + 9.19646i) q^{83} +(-2.19064 - 0.500000i) q^{84} +(-0.309703 - 0.246980i) q^{85} +10.3448 q^{86} +3.95108 q^{88} +(1.11276 + 0.887395i) q^{89} +(-1.75676 - 0.400969i) q^{90} +(-4.67241 - 20.4712i) q^{91} +(3.21648 - 4.03334i) q^{92} +(1.76391 + 2.21187i) q^{93} +(-3.12833 + 13.7061i) q^{94} +(-0.317278 + 0.658834i) q^{95} +(2.48039 + 1.19449i) q^{96} +(-15.3557 + 3.50484i) q^{97} +(7.34432 + 15.2506i) q^{98} +8.15883i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 2 q^{5} + 6 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{13} + 8 q^{16} + 4 q^{20} - 12 q^{22} - 14 q^{23} + 14 q^{24} - 48 q^{25} + 24 q^{28} - 36 q^{30} - 2 q^{33} - 4 q^{34} + 2 q^{35} + 10 q^{36}+ \cdots + 4 q^{96}+O(q^{100}) $ 12 * q + 4 * q^4 - 2 * q^5 + 6 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^13 + 8 * q^16 + 4 * q^20 - 12 * q^22 - 14 * q^23 + 14 * q^24 - 48 * q^25 + 24 * q^28 - 36 * q^30 - 2 * q^33 - 4 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^38 + 8 * q^42 + 2 * q^45 - 44 * q^49 + 4 * q^51 - 20 * q^52 + 6 * q^53 + 12 * q^54 + 4 * q^57 - 112 * q^59 - 6 * q^62 - 30 * q^63 - 2 * q^64 + 10 * q^65 - 38 * q^67 - 42 * q^71 - 12 * q^74 + 26 * q^78 + 36 * q^80 + 36 * q^81 - 4 * q^82 + 34 * q^83 + 32 * q^86 + 84 * q^88 - 10 * q^91 + 34 * q^93 + 16 * q^94 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

Coefficient data

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

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

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

$2$	−1.40881	−	1.12349i	−0.996180	−	0.794427i	−0.0175063	−	0.999847i	$-0.505573\pi$
$2$	−1.40881	−	1.12349i	−0.996180	−	0.794427i	−0.978674	+	0.205419i	$0.934144\pi$
$3$	−0.433884	−	0.0990311i	−0.250503	−	0.0571757i	0.0954255	−	0.995437i	$-0.469579\pi$
$3$	−0.433884	−	0.0990311i	−0.250503	−	0.0571757i	−0.345928	+	0.938261i	$0.612436\pi$
$4$	0.277479	+	1.21572i	0.138740	+	0.607858i
$5$	−0.222521	+	0.279032i	−0.0995144	+	0.124787i	−0.829095	−	0.559108i	$-0.811144\pi$
$5$	−0.222521	+	0.279032i	−0.0995144	+	0.124787i	0.729581	+	0.683895i	$0.239715\pi$
$6$	0.500000	+	0.626980i	0.204124	+	0.255964i
$7$	0.900969	−	3.94740i	0.340534	−	1.49198i	−0.457415	−	0.889253i	$-0.651225\pi$
$7$	0.900969	−	3.94740i	0.340534	−	1.49198i	0.797949	−	0.602725i	$-0.205918\pi$
$8$	−0.588735	+	1.22252i	−0.208149	+	0.432226i
$9$	−2.52446	−	1.21572i	−0.841486	−	0.405238i
$10$	0.626980	−	0.143104i	0.198269	−	0.0452535i
$11$	−1.26341	−	2.62349i	−0.380931	−	0.791012i	−0.999984	−	0.00566249i	$-0.998198\pi$
$11$	−1.26341	−	2.62349i	−0.380931	−	0.791012i	0.619053	−	0.785349i	$-0.287517\pi$
$12$		−	0.554958i		−	0.160203i
$13$	4.67241	−	2.25011i	1.29589	−	0.624069i	0.346467	−	0.938062i	$-0.387381\pi$
$13$	4.67241	−	2.25011i	1.29589	−	0.624069i	0.949425	+	0.313993i	$0.101667\pi$
$14$	−5.70416	+	4.54892i	−1.52450	+	1.21575i
$15$	0.124181	−	0.0990311i	0.0320634	−	0.0255697i
$16$	4.44989	−	2.14295i	1.11247	−	0.535738i
$17$			1.10992i			0.269194i	0.990900	+	0.134597i	$0.0429740\pi$
$17$			1.10992i			0.269194i	−0.990900	+	0.134597i	$0.957026\pi$
$18$	2.19064	+	4.54892i	0.516340	+	1.07219i
$19$	1.99755	−	0.455927i	0.458269	−	0.104597i	0.0128465	−	0.999917i	$-0.495911\pi$
$19$	1.99755	−	0.455927i	0.458269	−	0.104597i	0.445422	+	0.895321i	$0.353054\pi$
$20$	−0.400969	−	0.193096i	−0.0896594	−	0.0431777i
$21$	−0.781831	+	1.62349i	−0.170610	+	0.354275i
$22$	−1.16756	+	5.11543i	−0.248925	+	1.09061i
$23$	−2.57942	−	3.23449i	−0.537846	−	0.674437i	0.436445	−	0.899731i	$-0.356237\pi$
$23$	−2.57942	−	3.23449i	−0.537846	−	0.674437i	−0.974291	+	0.225294i	$0.927666\pi$
$24$	0.376510	−	0.472129i	0.0768548	−	0.0963729i
$25$	1.08426	+	4.75046i	0.216852	+	0.950092i
$26$	−9.11052	−	2.07942i	−1.78672	−	0.407807i
$27$	2.01877	+	1.60992i	0.388513	+	0.309829i
$28$	5.04892			0.954156
$29$		0			0
$29$		0			0
$30$	−0.286208			−0.0522542
$31$	−4.97002	−	3.96346i	−0.892642	−	0.711858i	0.0655910	−	0.997847i	$-0.479107\pi$
$31$	−4.97002	−	3.96346i	−0.892642	−	0.711858i	−0.958233	+	0.285988i	$0.907678\pi$
$32$	−6.03089	−	1.37651i	−1.06612	−	0.243335i
$33$	0.288364	+	1.26341i	0.0501978	+	0.219931i
$34$	1.24698	−	1.56366i	0.213855	−	0.268166i
$35$	0.900969	+	1.12978i	0.152292	+	0.190968i
$36$	0.777479	−	3.40636i	0.129580	−	0.567726i
$37$	1.26341	−	2.62349i	0.207703	−	0.431299i	−0.770929	−	0.636921i	$-0.780208\pi$
$37$	1.26341	−	2.62349i	0.207703	−	0.431299i	0.978631	+	0.205622i	$0.0659219\pi$
$38$	−3.32640	−	1.60191i	−0.539613	−	0.259864i
$39$	−2.25011	+	0.513574i	−0.360306	+	0.0822376i
$40$	−0.210117	−	0.436313i	−0.0332224	−	0.0689871i
$41$		−	0.396125i		−	0.0618643i	−0.999521	−	0.0309321i	$-0.990152\pi$
$41$		−	0.396125i		−	0.0618643i	0.999521	−	0.0309321i	$-0.00984757\pi$
$42$	2.92543	−	1.40881i	0.451403	−	0.217384i
$43$	−4.48845	+	3.57942i	−0.684482	+	0.545856i	−0.902821	−	0.430017i	$-0.858508\pi$
$43$	−4.48845	+	3.57942i	−0.684482	+	0.545856i	0.218339	+	0.975873i	$0.429936\pi$
$44$	2.83885	−	2.26391i	0.427972	−	0.341297i
$45$	0.900969	−	0.433884i	0.134309	−	0.0646796i
$46$			7.45473i			1.09914i
$47$	−3.38513	−	7.02930i	−0.493773	−	1.02533i	−0.987778	−	0.155870i	$-0.950182\pi$
$47$	−3.38513	−	7.02930i	−0.493773	−	1.02533i	0.494005	−	0.869459i	$-0.335532\pi$
$48$	−2.14295	+	0.489115i	−0.309309	+	0.0705977i
$49$	−8.46346	−	4.07579i	−1.20907	−	0.582255i
$50$	3.80957	−	7.91066i	0.538755	−	1.11874i
$51$	0.109916	−	0.481575i	0.0153914	−	0.0674339i
$52$	4.03199	+	5.05596i	0.559137	+	0.701135i
$53$	−2.71648	+	3.40636i	−0.373137	+	0.467899i	−0.932577	−	0.360972i	$-0.882445\pi$
$53$	−2.71648	+	3.40636i	−0.373137	+	0.467899i	0.559439	+	0.828871i	$0.311016\pi$
$54$	−1.03534	−	4.53614i	−0.140892	−	0.617290i
$55$	1.01317	+	0.231250i	0.136616	+	0.0311818i
$56$	4.29535	+	3.42543i	0.573990	+	0.457742i
$57$	−0.911854			−0.120778
$58$		0			0
$59$	−9.10992			−1.18601			−0.593005	−	0.805199i	$-0.702059\pi$
$59$	−9.10992			−1.18601			−0.593005	+	0.805199i	$0.702059\pi$
$60$	0.154851	+	0.123490i	0.0199912	+	0.0159425i
$61$	5.89726	+	1.34601i	0.755067	+	0.172339i	0.582693	−	0.812693i	$-0.301999\pi$
$61$	5.89726	+	1.34601i	0.755067	+	0.172339i	0.172374	+	0.985032i	$0.444856\pi$
$62$	2.54892	+	11.1675i	0.323713	+	1.41828i
$63$	−7.07338	+	8.86973i	−0.891162	+	1.11748i
$64$	0.791053	+	0.991949i	0.0988816	+	0.123994i
$65$	−0.411854	+	1.80445i	−0.0510842	+	0.223815i
$66$	1.01317	−	2.10388i	0.124713	−	0.258969i
$67$	0.337282	+	0.162426i	0.0412055	+	0.0198435i	0.454373	−	0.890812i	$-0.349863\pi$
$67$	0.337282	+	0.162426i	0.0412055	+	0.0198435i	−0.413168	+	0.910655i	$0.635578\pi$
$68$	−1.34934	+	0.307979i	−0.163632	+	0.0373479i
$69$	0.798852	+	1.65883i	0.0961705	+	0.199700i
$70$		−	2.60388i		−	0.311223i
$71$	−10.2763	+	4.94880i	−1.21957	+	0.587314i	−0.929192	−	0.369598i	$-0.879495\pi$
$71$	−10.2763	+	4.94880i	−1.21957	+	0.587314i	−0.290379	+	0.956912i	$0.593781\pi$
$72$	2.97247	−	2.37047i	0.350309	−	0.279362i
$73$	−6.99637	+	5.57942i	−0.818863	+	0.653021i	−0.940591	−	0.339542i	$-0.889728\pi$
$73$	−6.99637	+	5.57942i	−0.818863	+	0.653021i	0.121728	+	0.992563i	$0.461156\pi$
$74$	−4.72737	+	2.27658i	−0.549545	+	0.264647i
$75$		−	2.16852i		−	0.250399i
$76$	1.10855	+	2.30194i	0.127160	+	0.264050i
$77$	−11.4943	+	2.62349i	−1.30989	+	0.298974i
$78$	3.74698	+	1.80445i	0.424262	+	0.204314i
$79$	−0.257808	+	0.535344i	−0.0290057	+	0.0602309i	−0.914968	−	0.403526i	$-0.867785\pi$
$79$	−0.257808	+	0.535344i	−0.0290057	+	0.0602309i	0.885963	+	0.463757i	$0.153499\pi$
$80$	−0.392240	+	1.71851i	−0.0438537	+	0.192136i
$81$	4.52446	+	5.67349i	0.502718	+	0.630388i
$82$	−0.445042	+	0.558065i	−0.0491467	+	0.0616280i
$83$	2.09903	+	9.19646i	0.230399	+	1.00944i	0.949310	+	0.314341i	$0.101783\pi$
$83$	2.09903	+	9.19646i	0.230399	+	1.00944i	−0.718912	+	0.695101i	$0.755359\pi$
$84$	−2.19064	−	0.500000i	−0.239019	−	0.0545545i
$85$	−0.309703	−	0.246980i	−0.0335920	−	0.0267887i
$86$	10.3448			1.11551
$87$		0			0
$88$	3.95108			0.421187
$89$	1.11276	+	0.887395i	0.117952	+	0.0940637i	0.680689	−	0.732572i	$-0.261680\pi$
$89$	1.11276	+	0.887395i	0.117952	+	0.0940637i	−0.562737	+	0.826636i	$0.690252\pi$
$90$	−1.75676	−	0.400969i	−0.185179	−	0.0422658i
$91$	−4.67241	−	20.4712i	−0.489801	−	2.14596i
$92$	3.21648	−	4.03334i	0.335341	−	0.420505i
$93$	1.76391	+	2.21187i	0.182908	+	0.229360i
$94$	−3.12833	+	13.7061i	−0.322663	+	1.41368i
$95$	−0.317278	+	0.658834i	−0.0325520	+	0.0675949i
$96$	2.48039	+	1.19449i	0.253153	+	0.121912i
$97$	−15.3557	+	3.50484i	−1.55914	+	0.355863i	−0.913195	−	0.407523i	$-0.866393\pi$
$97$	−15.3557	+	3.50484i	−1.55914	+	0.355863i	−0.645943	+	0.763386i	$0.723536\pi$
$98$	7.34432	+	15.2506i	0.741888	+	1.54055i
$99$			8.15883i			0.819994i
$100$	−5.47434	+	2.63631i	−0.547434	+	0.263631i
$101$	13.6372	−	10.8753i	1.35695	−	1.08213i	0.368661	−	0.929564i	$-0.379816\pi$
$101$	13.6372	−	10.8753i	1.35695	−	1.08213i	0.988293	−	0.152570i	$-0.0487550\pi$
$102$	−0.695895	+	0.554958i	−0.0689039	+	0.0549490i
$103$	2.53534	−	1.22096i	0.249815	−	0.120304i	−0.304786	−	0.952421i	$-0.598585\pi$
$103$	2.53534	−	1.22096i	0.249815	−	0.120304i	0.554601	+	0.832116i	$0.312871\pi$
$104$			7.03684i			0.690019i
$105$	−0.279032	−	0.579417i	−0.0272308	−	0.0565453i
$106$	7.65402	−	1.74698i	0.743424	−	0.169682i
$107$	6.72132	+	3.23682i	0.649775	+	0.312915i	0.729580	−	0.683895i	$-0.239716\pi$
$107$	6.72132	+	3.23682i	0.649775	+	0.312915i	−0.0798052	+	0.996810i	$0.525430\pi$
$108$	−1.39703	+	2.90097i	−0.134430	+	0.279146i
$109$	−0.367781	+	1.61135i	−0.0352270	+	0.154340i	−0.989482	−	0.144653i	$-0.953793\pi$
$109$	−0.367781	+	1.61135i	−0.0352270	+	0.154340i	0.954255	+	0.298993i	$0.0966506\pi$
$110$	−1.16756	−	1.46408i	−0.111323	−	0.139594i
$111$	−0.807979	+	1.01317i	−0.0766899	+	0.0961661i
$112$	−4.44989	−	19.4962i	−0.420475	−	1.84222i
$113$	8.42407	+	1.92274i	0.792470	+	0.180876i	0.599549	−	0.800338i	$-0.295347\pi$
$113$	8.42407	+	1.92274i	0.792470	+	0.180876i	0.192921	+	0.981214i	$0.438204\pi$
$114$	1.28463	+	1.02446i	0.120317	+	0.0959493i
$115$	1.47650			0.137684
$116$		0			0
$117$	−14.5308			−1.34337
$118$	12.8342	+	10.2349i	1.18148	+	0.942199i
$119$	4.38129	+	1.00000i	0.401632	+	0.0916698i
$120$	0.0479579	+	0.210117i	0.00437793	+	0.0191810i
$121$	1.57188	−	1.97108i	0.142899	−	0.179189i
$122$	−6.79590	−	8.52179i	−0.615272	−	0.771526i
$123$	−0.0392287	+	0.171872i	−0.00353713	+	0.0154972i
$124$	3.43936	−	7.14191i	0.308864	−	0.641362i
$125$	−3.17456	−	1.52879i	−0.283942	−	0.136739i
$126$	19.9301	−	4.54892i	1.77552	−	0.405250i
$127$	−4.54371	−	9.43512i	−0.403189	−	0.837231i	−0.999408	−	0.0344090i	$-0.989045\pi$
$127$	−4.54371	−	9.43512i	−0.403189	−	0.837231i	0.596219	−	0.802822i	$-0.296669\pi$
$128$			10.0858i			0.891463i
$129$	2.30194	−	1.10855i	0.202674	−	0.0976028i
$130$	2.60751	−	2.07942i	0.228693	−	0.182377i
$131$	−0.355523	+	0.283520i	−0.0310622	+	0.0247712i	−0.638898	−	0.769292i	$-0.720609\pi$
$131$	−0.355523	+	0.283520i	−0.0310622	+	0.0247712i	0.607836	+	0.794063i	$0.292038\pi$
$132$	−1.45593	+	0.701137i	−0.126722	+	0.0610262i
$133$		−	8.29590i		−	0.719345i
$134$	−0.292682	−	0.607760i	−0.0252839	−	0.0525025i
$135$	−0.898438	+	0.205063i	−0.0773252	+	0.0176490i
$136$	−1.35690	−	0.653447i	−0.116353	−	0.0560326i
$137$	−5.74474	+	11.9291i	−0.490806	+	1.01917i	0.497610	+	0.867401i	$0.334211\pi$
$137$	−5.74474	+	11.9291i	−0.490806	+	1.01917i	−0.988416	+	0.151769i	$0.951503\pi$
$138$	0.738250	−	3.23449i	0.0628440	−	0.275338i
$139$	−1.74363	−	2.18644i	−0.147893	−	0.185451i	0.702367	−	0.711815i	$-0.252127\pi$
$139$	−1.74363	−	2.18644i	−0.147893	−	0.185451i	−0.850260	+	0.526364i	$0.823555\pi$
$140$	−1.12349	+	1.40881i	−0.0949522	+	0.119066i
$141$	0.772635	+	3.38513i	0.0650676	+	0.285080i
$142$	20.0373	+	4.57338i	1.68149	+	0.383789i
$143$	−11.8063	−	9.41521i	−0.987292	−	0.787339i
$144$	−13.8388			−1.15323
$145$		0			0
$146$	16.1250			1.33451
$147$	3.26853	+	2.60656i	0.269584	+	0.214986i
$148$	3.53999	+	0.807979i	0.290985	+	0.0664154i
$149$	0.602679	+	2.64051i	0.0493734	+	0.216319i	0.993596	−	0.112988i	$-0.0360421\pi$
$149$	0.602679	+	2.64051i	0.0493734	+	0.216319i	−0.944223	+	0.329307i	$0.893185\pi$
$150$	−2.43631	+	3.05504i	−0.198924	+	0.249443i
$151$	1.51842	+	1.90404i	0.123567	+	0.154948i	0.839767	−	0.542947i	$-0.182692\pi$
$151$	1.51842	+	1.90404i	0.123567	+	0.154948i	−0.716200	+	0.697895i	$0.754120\pi$
$152$	−0.618645	+	2.71046i	−0.0501788	+	0.219848i
$153$	1.34934	−	2.80194i	0.109088	−	0.226523i
$154$	19.1407	+	9.21768i	1.54240	+	0.742782i
$155$	2.21187	−	0.504844i	0.177661	−	0.0405501i
$156$	−1.24872	−	2.59299i	−0.0999775	−	0.207605i
$157$		−	17.6775i		−	1.41082i	−0.708799	−	0.705411i	$-0.750762\pi$
$157$		−	17.6775i		−	1.41082i	0.708799	−	0.705411i	$-0.249238\pi$
$158$	0.964656	−	0.464554i	0.0767439	−	0.0369579i
$159$	1.51597	−	1.20895i	0.120224	−	0.0958758i
$160$	1.72609	−	1.37651i	0.136459	−	0.108823i
$161$	−15.0918	+	7.26782i	−1.18940	+	0.572785i
$162$		−	13.0761i		−	1.02735i
$163$	−2.15473	−	4.47434i	−0.168772	−	0.350458i	0.799379	−	0.600827i	$-0.205162\pi$
$163$	−2.15473	−	4.47434i	−0.168772	−	0.350458i	−0.968150	+	0.250370i	$0.919448\pi$
$164$	0.481575	−	0.109916i	0.0376047	−	0.00858302i
$165$	−0.416698	−	0.200671i	−0.0324399	−	0.0156222i
$166$	7.37499	−	15.3143i	0.572410	−	1.18862i
$167$	3.21864	−	14.1018i	0.249066	−	1.09123i	−0.683422	−	0.730024i	$-0.739509\pi$
$167$	3.21864	−	14.1018i	0.249066	−	1.09123i	0.932487	−	0.361203i	$-0.117634\pi$
$168$	−1.52446	−	1.91161i	−0.117615	−	0.147484i
$169$	8.66301	−	10.8631i	0.666386	−	0.835621i
$170$	0.158834	+	0.695895i	0.0121820	+	0.0533727i
$171$	−5.59700	−	1.27748i	−0.428013	−	0.0976913i
$172$	−5.59700	−	4.46346i	−0.426767	−	0.340336i
$173$	−10.5133			−0.799314			−0.399657	−	0.916665i	$-0.630871\pi$
$173$	−10.5133			−0.799314			−0.399657	+	0.916665i	$0.630871\pi$
$174$		0			0
$175$	19.7289			1.49136
$176$	−11.2440	−	8.96681i	−0.847550	−	0.675899i
$177$	3.95264	+	0.902165i	0.297099	+	0.0678109i
$178$	−0.570688	−	2.50035i	−0.0427748	−	0.187409i
$179$	3.57942	−	4.48845i	0.267538	−	0.335482i	−0.629856	−	0.776712i	$-0.716886\pi$
$179$	3.57942	−	4.48845i	0.267538	−	0.335482i	0.897394	+	0.441230i	$0.145458\pi$
$180$	0.777479	+	0.974928i	0.0579499	+	0.0726668i
$181$	1.47770	−	6.47421i	0.109836	−	0.481225i	−0.889852	−	0.456250i	$-0.849192\pi$
$181$	1.47770	−	6.47421i	0.109836	−	0.481225i	0.999688	−	0.0249747i	$-0.00795053\pi$
$182$	−16.4166	+	34.0894i	−1.21688	+	2.52687i
$183$	−2.42543	−	1.16802i	−0.179293	−	0.0863428i
$184$	5.47282	−	1.24914i	0.403462	−	0.0920875i
$185$	0.450904	+	0.936313i	0.0331512	+	0.0688391i
$186$		−	5.09783i		−	0.373791i
$187$	2.91185	−	1.40227i	0.212936	−	0.102545i
$188$	7.60633	−	6.06584i	0.554748	−	0.442397i
$189$	8.17384	−	6.51842i	0.594559	−	0.474145i
$190$	1.18718	−	0.571714i	0.0861269	−	0.0414765i
$191$		−	18.8116i		−	1.36116i	−0.732673	−	0.680581i	$-0.761728\pi$
$191$		−	18.8116i		−	1.36116i	0.732673	−	0.680581i	$-0.238272\pi$
$192$	−0.244991	−	0.508729i	−0.0176807	−	0.0367144i
$193$	10.6118	−	2.42208i	0.763854	−	0.174345i	0.177192	−	0.984176i	$-0.443299\pi$
$193$	10.6118	−	2.42208i	0.763854	−	0.174345i	0.586662	+	0.809832i	$0.300442\pi$
$194$	25.5710	+	12.3143i	1.83589	+	0.884118i
$195$	0.357394	−	0.742135i	0.0255935	−	0.0531454i
$196$	2.60656	−	11.4201i	0.186183	−	0.815722i
$197$	−5.23759	−	6.56773i	−0.373163	−	0.467931i	0.559422	−	0.828883i	$-0.311023\pi$
$197$	−5.23759	−	6.56773i	−0.373163	−	0.467931i	−0.932584	+	0.360952i	$0.882452\pi$
$198$	9.16637	−	11.4943i	0.651425	−	0.816861i
$199$	1.47339	+	6.45532i	0.104446	+	0.457606i	0.999922	+	0.0124967i	$0.00397793\pi$
$199$	1.47339	+	6.45532i	0.104446	+	0.457606i	−0.895476	+	0.445109i	$0.853165\pi$
$200$	−6.44588	−	1.47123i	−0.455792	−	0.104032i
$201$	−0.130256	−	0.103875i	−0.00918753	−	0.00732681i
$202$	−31.4306			−2.21145
$203$		0			0
$204$	0.615957			0.0431256
$205$	0.110532	+	0.0881460i	0.00771986	+	0.00615638i
$206$	−4.94355	−	1.12833i	−0.344434	−	0.0786148i
$207$	2.57942	+	11.3012i	0.179282	+	0.785485i
$208$	15.9698	−	20.0255i	1.10731	−	1.38852i
$209$	−3.71983	−	4.66452i	−0.257306	−	0.322652i
$210$	−0.257865	+	1.12978i	−0.0177944	+	0.0779622i
$211$	3.51456	−	7.29805i	0.241952	−	0.502419i	−0.744263	−	0.667887i	$-0.767199\pi$
$211$	3.51456	−	7.29805i	0.241952	−	0.502419i	0.986215	+	0.165468i	$0.0529134\pi$
$212$	−4.89493	−	2.35727i	−0.336185	−	0.161898i
$213$	4.94880	−	1.12953i	0.339086	−	0.0773942i
$214$	−5.83255	−	12.1114i	−0.398705	−	0.827919i
$215$		−	2.04892i		−	0.139735i
$216$	−3.15668	+	1.52018i	−0.214785	+	0.103435i
$217$	−20.1232	+	16.0477i	−1.36605	+	1.08939i
$218$	2.32847	−	1.85690i	0.157704	−	0.125765i
$219$	3.58815	−	1.72796i	0.242464	−	0.116765i
$220$			1.29590i			0.0873694i
$221$	2.49744	+	5.18598i	0.167996	+	0.348847i
$222$	2.27658	−	0.519614i	0.152794	−	0.0348742i
$223$	−19.7485	−	9.51036i	−1.32246	−	0.636861i	−0.366512	−	0.930413i	$-0.619448\pi$
$223$	−19.7485	−	9.51036i	−1.32246	−	0.636861i	−0.955943	+	0.293552i	$0.905163\pi$
$224$	−10.8673	+	22.5661i	−0.726101	+	1.50776i
$225$	3.03803	−	13.3105i	0.202535	−	0.887366i
$226$	−9.70775	−	12.1731i	−0.645750	−	0.809745i
$227$	−11.3964	+	14.2907i	−0.756407	+	0.948504i	−0.999770	−	0.0214309i	$-0.993178\pi$
$227$	−11.3964	+	14.2907i	−0.756407	+	0.948504i	0.243363	+	0.969935i	$0.421749\pi$
$228$	−0.253020	−	1.10855i	−0.0167567	−	0.0734158i
$229$	15.6230	+	3.56584i	1.03240	+	0.235638i	0.704968	−	0.709239i	$-0.250961\pi$
$229$	15.6230	+	3.56584i	1.03240	+	0.235638i	0.327427	+	0.944876i	$0.393818\pi$
$230$	−2.08011	−	1.65883i	−0.137158	−	0.109380i
$231$	5.24698			0.345226
$232$		0			0
$233$	1.95646			0.128172			0.0640860	−	0.997944i	$-0.479587\pi$
$233$	1.95646			0.128172			0.0640860	+	0.997944i	$0.479587\pi$
$234$	20.4712	+	16.3252i	1.33824	+	1.06721i
$235$	2.71467	+	0.619605i	0.177085	+	0.0404186i
$236$	−2.52781	−	11.0751i	−0.164546	−	0.720925i
$237$	0.164874	−	0.206746i	0.0107097	−	0.0134296i
$238$	−5.04892	−	6.33114i	−0.327273	−	0.410387i
$239$	1.99449	−	8.73844i	0.129013	−	0.565243i	−0.868558	−	0.495587i	$-0.834953\pi$
$239$	1.99449	−	8.73844i	0.129013	−	0.565243i	0.997571	−	0.0696554i	$-0.0221900\pi$
$240$	0.340373	−	0.706791i	0.0219710	−	0.0456232i
$241$	17.9291	+	8.63419i	1.15491	+	0.556177i	0.910506	−	0.413496i	$-0.135692\pi$
$241$	17.9291	+	8.63419i	1.15491	+	0.556177i	0.244407	+	0.969673i	$0.421407\pi$
$242$	−4.42898	+	1.01089i	−0.284705	+	0.0649822i
$243$	−4.76224	−	9.88889i	−0.305498	−	0.634372i
$244$			7.54288i			0.482883i
$245$	3.02057	−	1.45463i	0.192977	−	0.0929330i
$246$	0.248362	−	0.198062i	0.0158350	−	0.0126280i
$247$	8.30746	−	6.62498i	0.528591	−	0.421537i
$248$	7.77144	−	3.74253i	0.493487	−	0.237651i
$249$		−	4.19806i		−	0.266041i
$250$	2.75478	+	5.72037i	0.174228	+	0.361788i
$251$	25.1579	−	5.74214i	1.58795	−	0.362440i	0.664847	−	0.746980i	$-0.268497\pi$
$251$	25.1579	−	5.74214i	1.58795	−	0.362440i	0.923108	+	0.384540i	$0.125640\pi$
$252$	−12.7458	−	6.13805i	−0.802909	−	0.386661i
$253$	−5.22679	+	10.8535i	−0.328606	+	0.682356i
$254$	−4.19902	+	18.3971i	−0.263470	+	1.15434i
$255$	0.109916	+	0.137831i	0.00688322	+	0.00863129i
$256$	12.9133	−	16.1928i	0.807084	−	1.01205i
$257$	−2.65937	−	11.6514i	−0.165887	−	0.726797i	−0.987612	−	0.156914i	$-0.949846\pi$
$257$	−2.65937	−	11.6514i	−0.165887	−	0.726797i	0.821726	−	0.569883i	$-0.193012\pi$
$258$	−4.48845	−	1.02446i	−0.279438	−	0.0637800i
$259$	−9.21768	−	7.35086i	−0.572759	−	0.456760i
$260$	−2.30798			−0.143135
$261$		0			0
$262$	0.819396			0.0506225
$263$	−0.260141	−	0.207455i	−0.0160410	−	0.0127923i	0.615437	−	0.788186i	$-0.288980\pi$
$263$	−0.260141	−	0.207455i	−0.0160410	−	0.0127923i	−0.631477	+	0.775394i	$0.717551\pi$
$264$	−1.71431	−	0.391280i	−0.105509	−	0.0240816i
$265$	−0.346011	−	1.51597i	−0.0212553	−	0.0931254i
$266$	−9.32036	+	11.6874i	−0.571468	+	0.716598i
$267$	−0.394928	−	0.495224i	−0.0241692	−	0.0303072i
$268$	−0.103875	+	0.455108i	−0.00634520	+	0.0278002i
$269$	0.461645	−	0.958615i	0.0281470	−	0.0584478i	−0.886421	−	0.462879i	$-0.846816\pi$
$269$	0.461645	−	0.958615i	0.0281470	−	0.0584478i	0.914568	+	0.404432i	$0.132531\pi$
$270$	1.49612	+	0.720491i	0.0910507	+	0.0438477i
$271$	16.0516	−	3.66368i	0.975067	−	0.222553i	0.294834	−	0.955549i	$-0.404736\pi$
$271$	16.0516	−	3.66368i	0.975067	−	0.222553i	0.680233	+	0.732996i	$0.261879\pi$
$272$	2.37850	+	4.93900i	0.144218	+	0.299471i
$273$			9.34481i			0.565574i
$274$	21.4955	−	10.3517i	1.29859	−	0.625367i
$275$	11.0929	−	8.84631i	0.668928	−	0.533452i
$276$	−1.79500	+	1.43147i	−0.108047	+	0.0861643i
$277$	−5.94116	+	2.86111i	−0.356970	+	0.171907i	−0.603769	−	0.797159i	$-0.706335\pi$
$277$	−5.94116	+	2.86111i	−0.356970	+	0.171907i	0.246800	+	0.969066i	$0.420621\pi$
$278$			5.03923i			0.302233i
$279$	7.72818	+	16.0477i	0.462674	+	0.960752i
$280$	−1.91161	+	0.436313i	−0.114241	+	0.0260747i
$281$	27.5112	+	13.2487i	1.64118	+	0.790350i	0.999731	+	0.0231840i	$0.00738037\pi$
$281$	27.5112	+	13.2487i	1.64118	+	0.790350i	0.641448	+	0.767166i	$0.278334\pi$
$282$	2.71467	−	5.63706i	0.161656	−	0.335682i
$283$	−0.791053	+	3.46583i	−0.0470232	+	0.206022i	−0.992982	−	0.118264i	$-0.962267\pi$
$283$	−0.791053	+	3.46583i	−0.0470232	+	0.206022i	0.945959	+	0.324286i	$0.105124\pi$
$284$	−8.86778	−	11.1198i	−0.526206	−	0.659841i
$285$	0.202907	−	0.254437i	0.0120191	−	0.0150715i
$286$	6.05496	+	26.5285i	0.358037	+	1.56866i
$287$	−1.56366	−	0.356896i	−0.0923001	−	0.0210669i
$288$	13.5513	+	10.8068i	0.798517	+	0.636796i
$289$	15.7681			0.927534
$290$		0			0
$291$	7.00969			0.410915
$292$	−8.72433	−	6.95742i	−0.510553	−	0.407152i
$293$	−32.0556	−	7.31647i	−1.87271	−	0.427433i	−0.874378	−	0.485246i	$-0.838730\pi$
$293$	−32.0556	−	7.31647i	−1.87271	−	0.427433i	−0.998327	+	0.0578127i	$0.981587\pi$
$294$	−1.67629	−	7.34432i	−0.0977633	−	0.428329i
$295$	2.02715	−	2.54196i	0.118025	−	0.147999i
$296$	2.46346	+	3.08908i	0.143186	+	0.179549i
$297$	1.67307	−	7.33020i	0.0970814	−	0.425342i
$298$	2.11752	−	4.39708i	0.122665	−	0.254716i
$299$	−19.3300	−	9.30886i	−1.11789	−	0.538345i
$300$	2.63631	−	0.601720i	0.152207	−	0.0347403i
$301$	10.0854	+	20.9426i	0.581316	+	1.20711i
$302$		−	4.38835i		−	0.252521i
$303$	−6.99396	+	3.36811i	−0.401792	+	0.193493i
$304$	7.91183	−	6.30947i	0.453774	−	0.361873i
$305$	−1.68784	+	1.34601i	−0.0966457	+	0.0770724i
$306$	−5.04892	+	2.43143i	−0.288627	+	0.138996i
$307$			14.6703i			0.837275i	0.908153	+	0.418638i	$0.137492\pi$
$307$			14.6703i			0.837275i	−0.908153	+	0.418638i	$0.862508\pi$
$308$	−6.37883	−	13.2458i	−0.363468	−	0.754749i
$309$	−1.22096	+	0.278676i	−0.0694578	+	0.0158533i
$310$	−3.68329	−	1.77378i	−0.209197	−	0.100744i
$311$	8.03834	−	16.6918i	0.455812	−	0.946504i	−0.538760	−	0.842459i	$-0.681107\pi$
$311$	8.03834	−	16.6918i	0.455812	−	0.946504i	0.994573	−	0.104045i	$-0.0331786\pi$
$312$	0.696866	−	3.05317i	0.0394523	−	0.172852i
$313$	14.3354	+	17.9760i	0.810286	+	1.01607i	0.999418	+	0.0341147i	$0.0108612\pi$
$313$	14.3354	+	17.9760i	0.810286	+	1.01607i	−0.189132	+	0.981952i	$0.560567\pi$
$314$	−19.8605	+	24.9043i	−1.12080	+	1.40543i
$315$	−0.900969	−	3.94740i	−0.0507638	−	0.222411i
$316$	−0.722362	−	0.164874i	−0.0406360	−	0.00927491i
$317$	−10.9915	−	8.76540i	−0.617342	−	0.492314i	0.264170	−	0.964476i	$-0.414902\pi$
$317$	−10.9915	−	8.76540i	−0.617342	−	0.492314i	−0.881512	+	0.472162i	$0.843474\pi$
$318$	−3.49396			−0.195932
$319$		0			0
$320$	−0.452812			−0.0253129
$321$	−2.59573	−	2.07002i	−0.144879	−	0.115537i
$322$	29.4268	+	6.71648i	1.63989	+	0.374295i
$323$	0.506041	+	2.21711i	0.0281569	+	0.123363i
$324$	−5.64191	+	7.07473i	−0.313439	+	0.393040i
$325$	15.7552	+	19.7564i	0.873940	+	1.09589i
$326$	−1.99127	+	8.72433i	−0.110286	+	0.483196i
$327$	0.319148	−	0.662718i	0.0176489	−	0.0366484i
$328$	0.484271	+	0.233212i	0.0267394	+	0.0128770i
$329$	−30.7974	+	7.02930i	−1.69792	+	0.387538i
$330$	0.361597	+	0.750864i	0.0199053	+	0.0413337i
$331$		−	13.9565i		−	0.767116i	−0.923517	−	0.383558i	$-0.874699\pi$
$331$		−	13.9565i		−	0.767116i	0.923517	−	0.383558i	$-0.125301\pi$
$332$	−10.5978	+	5.10365i	−0.581632	+	0.280099i
$333$	−6.37883	+	5.08695i	−0.349558	+	0.278763i
$334$	−20.3776	+	16.2506i	−1.11501	+	0.889195i
$335$	−0.120374	+	0.0579692i	−0.00657676	+	0.00316720i
$336$			8.89977i			0.485522i
$337$	−6.07333	−	12.6114i	−0.330836	−	0.686987i	0.667503	−	0.744607i	$-0.267363\pi$
$337$	−6.07333	−	12.6114i	−0.330836	−	0.686987i	−0.998339	+	0.0576199i	$0.981649\pi$
$338$	−24.4091	+	5.57122i	−1.32768	+	0.303034i
$339$	−3.46466	−	1.66849i	−0.188174	−	0.0906200i
$340$	0.214321	−	0.445042i	0.0116232	−	0.0241358i
$341$	−4.11894	+	18.0463i	−0.223053	+	0.977260i
$342$	6.44989	+	8.08790i	0.348770	+	0.437344i
$343$	−6.04288	+	7.57753i	−0.326285	+	0.409148i
$344$	−1.73341	−	7.59455i	−0.0934590	−	0.409471i
$345$	−0.640630	−	0.146220i	−0.0344903	−	0.00787220i
$346$	14.8113	+	11.8116i	0.796261	+	0.634997i
$347$	19.8538			1.06581			0.532905	−	0.846175i	$-0.321100\pi$
$347$	19.8538			1.06581			0.532905	+	0.846175i	$0.321100\pi$
$348$		0			0
$349$	−26.9202			−1.44101			−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202			−1.44101			−0.720503	+	0.693452i	$0.756089\pi$
$350$	−27.7942	−	22.1652i	−1.48566	−	1.18478i
$351$	13.0550	+	2.97972i	0.696825	+	0.159046i
$352$	4.00820	+	17.5611i	0.213638	+	0.936007i
$353$	2.50335	−	3.13910i	0.133240	−	0.167078i	−0.710736	−	0.703459i	$-0.751638\pi$
$353$	2.50335	−	3.13910i	0.133240	−	0.167078i	0.843976	+	0.536382i	$0.180209\pi$
$354$	−4.55496	−	5.71174i	−0.242093	−	0.303575i
$355$	0.905813	−	3.96863i	0.0480756	−	0.210633i
$356$	−0.770053	+	1.59903i	−0.0408127	+	0.0847485i
$357$	−1.80194	−	0.867767i	−0.0953687	−	0.0459271i
$358$	−10.0854	+	2.30194i	−0.533032	+	0.121661i
$359$	0.323814	+	0.672407i	0.0170903	+	0.0354883i	0.909339	−	0.416055i	$-0.136588\pi$
$359$	0.323814	+	0.672407i	0.0170903	+	0.0354883i	−0.892249	+	0.451544i	$0.850873\pi$
$360$			1.35690i			0.0715147i
$361$	−13.3361	+	6.42232i	−0.701899	+	0.338017i
$362$	−9.35551	+	7.46077i	−0.491715	+	0.392129i
$363$	−0.877213	+	0.699554i	−0.0460418	+	0.0367171i
$364$	23.5906	−	11.3606i	1.23648	−	0.595459i
$365$		−	3.19375i		−	0.167169i
$366$	2.10471	+	4.37047i	0.110015	+	0.228448i
$367$	−33.1952	+	7.57660i	−1.73278	+	0.395495i	−0.968425	−	0.249304i	$-0.919798\pi$
$367$	−33.1952	+	7.57660i	−1.73278	+	0.395495i	−0.764352	+	0.644799i	$0.776941\pi$
$368$	−18.4095	−	8.86553i	−0.959659	−	0.462148i
$369$	−0.481575	+	1.00000i	−0.0250698	+	0.0520579i
$370$	0.416698	−	1.82567i	0.0216631	−	0.0949123i
$371$	10.9988	+	13.7921i	0.571029	+	0.716048i
$372$	−2.19955	+	2.75815i	−0.114042	+	0.143004i
$373$	−6.23072	−	27.2986i	−0.322614	−	1.41347i	−0.832882	−	0.553450i	$-0.813311\pi$
$373$	−6.23072	−	27.2986i	−0.322614	−	1.41347i	0.510268	−	0.860015i	$-0.329546\pi$
$374$	−5.67770	−	1.29590i	−0.293587	−	0.0670092i
$375$	1.22599	+	0.977697i	0.0633100	+	0.0504881i
$376$	10.5864			0.545953
$377$		0			0
$378$	−18.8388			−0.968962
$379$	17.8891	+	14.2661i	0.918900	+	0.732798i	0.963921	−	0.266188i	$-0.0857641\pi$
$379$	17.8891	+	14.2661i	0.918900	+	0.732798i	−0.0450211	+	0.998986i	$0.514336\pi$
$380$	−0.888992	−	0.202907i	−0.0456043	−	0.0104089i
$381$	1.03707	+	4.54371i	0.0531308	+	0.232781i
$382$	−21.1347	+	26.5020i	−1.08134	+	1.35596i
$383$	−7.39344	−	9.27108i	−0.377787	−	0.473730i	0.556194	−	0.831052i	$-0.312261\pi$
$383$	−7.39344	−	9.27108i	−0.377787	−	0.473730i	−0.933981	+	0.357323i	$0.883690\pi$
$384$	0.998804	−	4.37604i	0.0509700	−	0.223314i
$385$	1.82567	−	3.79105i	0.0930450	−	0.193210i
$386$	−17.6712	−	8.51001i	−0.899441	−	0.433148i
$387$	15.6824	−	3.57942i	0.797184	−	0.181952i
$388$	−8.52179	−	17.6957i	−0.432628	−	0.898362i
$389$			10.3913i			0.526862i	0.964678	+	0.263431i	$0.0848541\pi$
$389$			10.3913i			0.526862i	−0.964678	+	0.263431i	$0.915146\pi$
$390$	−1.33728	+	0.644001i	−0.0677159	+	0.0326103i
$391$	3.59001	−	2.86294i	0.181555	−	0.144785i
$392$	9.96547	−	7.94720i	0.503332	−	0.401394i
$393$	0.182333	−	0.0878068i	0.00919747	−	0.00442927i
$394$			15.1371i			0.762594i
$395$	−0.0920106	−	0.191062i	−0.00462956	−	0.00961337i
$396$	−9.91882	+	2.26391i	−0.498439	+	0.113766i
$397$	−7.40366	−	3.56541i	−0.371579	−	0.178943i	0.238769	−	0.971076i	$-0.423256\pi$
$397$	−7.40366	−	3.56541i	−0.371579	−	0.178943i	−0.610348	+	0.792133i	$0.708970\pi$
$398$	5.17677	−	10.7497i	0.259488	−	0.538832i
$399$	−0.821552	+	3.59945i	−0.0411290	+	0.180198i
$400$	15.0048	+	18.8155i	0.750242	+	0.940774i
$401$	15.5130	−	19.4527i	0.774684	−	0.971423i	−0.225312	−	0.974287i	$-0.572340\pi$
$401$	15.5130	−	19.4527i	0.774684	−	0.971423i	0.999996	+	0.00286337i	$0.000911439\pi$
$402$	0.0668027	+	0.292682i	0.00333182	+	0.0145976i
$403$	−32.1402	−	7.33579i	−1.60102	−	0.365422i
$404$	17.0053	+	13.5613i	0.846047	+	0.674700i
$405$	−2.58987			−0.128692
$406$		0			0
$407$	−8.47889			−0.420283
$408$	0.524023	+	0.417895i	0.0259430	+	0.0206889i
$409$	−18.4217	−	4.20464i	−0.910895	−	0.207906i	−0.258701	−	0.965958i	$-0.583294\pi$
$409$	−18.4217	−	4.20464i	−0.910895	−	0.207906i	−0.652194	+	0.758052i	$0.726151\pi$
$410$	−0.0566871	−	0.248362i	−0.00279957	−	0.0122657i
$411$	3.67390	−	4.60692i	0.181220	−	0.227243i
$412$	2.18784	+	2.74347i	0.107787	+	0.135161i
$413$	−8.20775	+	35.9605i	−0.403877	+	1.76950i
$414$	9.06283	−	18.8192i	0.445414	−	0.924911i
$415$	−3.03319	−	1.46071i	−0.148893	−	0.0717033i
$416$	−31.2761	+	7.13856i	−1.53343	+	0.349996i
$417$	0.540006	+	1.12133i	0.0264442	+	0.0549120i
$418$			10.7506i			0.525830i
$419$	−9.81378	+	4.72607i	−0.479435	+	0.230884i	−0.657962	−	0.753051i	$-0.728581\pi$
$419$	−9.81378	+	4.72607i	−0.479435	+	0.230884i	0.178527	+	0.983935i	$0.442867\pi$
$420$	0.626980	−	0.500000i	0.0305935	−	0.0243975i
$421$	−15.6060	+	12.4453i	−0.760588	+	0.606549i	−0.925055	−	0.379834i	$-0.875981\pi$
$421$	−15.6060	+	12.4453i	−0.760588	+	0.606549i	0.164467	+	0.986383i	$0.447410\pi$
$422$	−13.1506	+	6.33301i	−0.640163	+	0.308286i
$423$			21.8605i			1.06290i
$424$	−2.56506	−	5.32640i	−0.124570	−	0.258673i
$425$	−5.27261	+	1.20344i	−0.255759	+	0.0583754i
$426$	−8.24094	−	3.96863i	−0.399275	−	0.192281i
$427$	10.6265	−	22.0661i	0.514252	−	1.06786i
$428$	−2.07002	+	9.06937i	−0.100058	+	0.438384i
$429$	4.19016	+	5.25430i	0.202303	+	0.253680i
$430$	−2.30194	+	2.88654i	−0.111009	+	0.139201i
$431$	6.71797	+	29.4334i	0.323593	+	1.41776i	0.831108	+	0.556112i	$0.187707\pi$
$431$	6.71797	+	29.4334i	0.323593	+	1.41776i	−0.507514	+	0.861643i	$0.669436\pi$
$432$	12.4333	+	2.83781i	0.598196	+	0.136534i
$433$	15.7862	+	12.5891i	0.758638	+	0.604994i	0.924512	−	0.381153i	$-0.124473\pi$
$433$	15.7862	+	12.5891i	0.758638	+	0.604994i	−0.165874	+	0.986147i	$0.553044\pi$
$434$	46.3793			2.22628
$435$		0			0
$436$	−2.06100			−0.0987039
$437$	−6.62720	−	5.28501i	−0.317022	−	0.252816i
$438$	−6.99637	−	1.59688i	−0.334299	−	0.0763016i
$439$	−2.37316	−	10.3975i	−0.113265	−	0.496245i	−0.999458	−	0.0329287i	$-0.989517\pi$
$439$	−2.37316	−	10.3975i	−0.113265	−	0.496245i	0.886193	−	0.463316i	$-0.153341\pi$
$440$	−0.879199	+	1.10248i	−0.0419141	+	0.0525587i
$441$	16.4107	+	20.5783i	0.781460	+	0.979920i
$442$	2.30798	−	10.1119i	0.109779	−	0.480975i
$443$	8.82962	−	18.3349i	0.419508	−	0.871117i	−0.578937	−	0.815372i	$-0.696532\pi$
$443$	8.82962	−	18.3349i	0.419508	−	0.871117i	0.998445	−	0.0557448i	$-0.0177533\pi$
$444$	−1.45593	−	0.701137i	−0.0690952	−	0.0332745i
$445$	−0.495224	+	0.113032i	−0.0234759	+	0.00535822i
$446$	17.1371	+	35.5855i	0.811464	+	1.68502i
$447$		−	1.20536i		−	0.0570115i
$448$	4.62833	−	2.22889i	0.218668	−	0.105305i
$449$	−15.1857	+	12.1102i	−0.716659	+	0.571516i	−0.912479	−	0.409124i	$-0.865834\pi$
$449$	−15.1857	+	12.1102i	−0.716659	+	0.571516i	0.195820	+	0.980640i	$0.437263\pi$
$450$	−19.2342	+	15.3388i	−0.906710	+	0.723077i
$451$	−1.03923	+	0.500466i	−0.0489354	+	0.0235660i
$452$			10.7748i			0.506804i
$453$	−0.470258	−	0.976501i	−0.0220946	−	0.0458800i
$454$	32.1108	−	7.32908i	1.50704	−	0.343971i
$455$	6.75182	+	3.25151i	0.316530	+	0.152433i
$456$	0.536840	−	1.11476i	0.0251399	−	0.0522034i
$457$	−2.76391	+	12.1095i	−0.129290	+	0.566457i	0.868236	+	0.496152i	$0.165254\pi$
$457$	−2.76391	+	12.1095i	−0.129290	+	0.566457i	−0.997526	+	0.0703045i	$0.977603\pi$
$458$	−18.0036	−	22.5759i	−0.841255	−	1.05490i
$459$	−1.78687	+	2.24067i	−0.0834041	+	0.104585i
$460$	0.409698	+	1.79500i	0.0191023	+	0.0836925i
$461$	−21.3961	−	4.88351i	−0.996514	−	0.227448i	−0.306991	−	0.951712i	$-0.599322\pi$
$461$	−21.3961	−	4.88351i	−0.996514	−	0.227448i	−0.689522	+	0.724265i	$0.742179\pi$
$462$	−7.39201	−	5.89493i	−0.343907	−	0.274257i
$463$	33.0073			1.53398			0.766990	−	0.641660i	$-0.221754\pi$
$463$	33.0073			1.53398			0.766990	+	0.641660i	$0.221754\pi$
$464$		0			0
$465$	−1.00969			−0.0468232
$466$	−2.75628	−	2.19806i	−0.127682	−	0.101823i
$467$	25.4487	+	5.80851i	1.17763	+	0.268786i	0.766167	−	0.642642i	$-0.222162\pi$
$467$	25.4487	+	5.80851i	1.17763	+	0.268786i	0.411461	+	0.911427i	$0.365019\pi$
$468$	−4.03199	−	17.6653i	−0.186379	−	0.816579i
$469$	0.945042	−	1.18505i	0.0436380	−	0.0547203i
$470$	−3.12833	−	3.92281i	−0.144299	−	0.180946i
$471$	−1.75063	+	7.67000i	−0.0806647	+	0.353415i
$472$	5.36333	−	11.1371i	0.246867	−	0.512625i
$473$	15.0613	+	7.25314i	0.692519	+	0.333500i
$474$	−0.464554	+	0.106031i	−0.0213377	+	0.00487018i
$475$	4.33172	+	8.99492i	0.198753	+	0.412715i
$476$			5.60388i			0.256853i
$477$	10.9988	−	5.29674i	0.503601	−	0.242521i
$478$	−12.6274	+	10.0700i	−0.577564	+	0.460592i
$479$	25.8520	−	20.6163i	1.18121	−	0.941981i	0.182060	−	0.983287i	$-0.441724\pi$
$479$	25.8520	−	20.6163i	1.18121	−	0.941981i	0.999147	+	0.0413068i	$0.0131521\pi$
$480$	−0.885239	+	0.426309i	−0.0404055	+	0.0194582i
$481$		−	15.1008i		−	0.688538i
$482$	−15.5583	−	32.3071i	−0.708660	−	1.47155i
$483$	7.26782	−	1.65883i	0.330697	−	0.0754795i
$484$	2.83244	+	1.36403i	0.128747	+	0.0620014i
$485$	2.43901	−	5.06465i	0.110750	−	0.229974i
$486$	−4.40097	+	19.2819i	−0.199632	+	0.874645i
$487$	−6.33244	−	7.94063i	−0.286950	−	0.359824i	0.617375	−	0.786669i	$-0.288196\pi$
$487$	−6.33244	−	7.94063i	−0.286950	−	0.359824i	−0.904325	+	0.426845i	$0.859625\pi$
$488$	−5.11745	+	6.41708i	−0.231656	+	0.290487i
$489$	0.491803	+	2.15473i	0.0222401	+	0.0974403i
$490$	−5.88968	−	1.34428i	−0.266069	−	0.0607285i
$491$	15.3879	+	12.2714i	0.694446	+	0.553802i	0.905851	−	0.423596i	$-0.139232\pi$
$491$	15.3879	+	12.2714i	0.694446	+	0.553802i	−0.211405	+	0.977399i	$0.567804\pi$
$492$	−0.219833			−0.00991082
$493$		0			0
$494$	−19.1468			−0.861453
$495$	−2.27658	−	1.81551i	−0.102325	−	0.0816012i
$496$	−30.6095	−	6.98643i	−1.37441	−	0.313700i
$497$	10.2763	+	45.0233i	0.460954	+	2.01957i
$498$	−4.71648	+	5.91428i	−0.211351	+	0.265025i
$499$	−17.3639	−	21.7736i	−0.777315	−	0.974722i	0.222685	−	0.974890i	$-0.428518\pi$
$499$	−17.3639	−	21.7736i	−0.777315	−	0.974722i	−1.00000		0.000168534i	$0.999946\pi$
$500$	0.977697	−	4.28357i	0.0437240	−	0.191567i
$501$	−2.79303	+	5.79978i	−0.124783	+	0.259115i
$502$	−41.8940	−	20.1751i	−1.86982	−	0.900459i
$503$	0.219563	−	0.0501138i	0.00978982	−	0.00223446i	−0.217623	−	0.976033i	$-0.569830\pi$
$503$	0.219563	−	0.0501138i	0.00978982	−	0.00223446i	0.227413	+	0.973798i	$0.426973\pi$
$504$	−6.67909	−	13.8693i	−0.297510	−	0.617787i
$505$			6.22521i			0.277018i
$506$	19.5574	−	9.41835i	0.869433	−	0.418697i
$507$	−4.83452	+	3.85540i	−0.214709	+	0.171224i
$508$	10.2096	−	8.14191i	0.452979	−	0.361239i
$509$	22.7974	−	10.9786i	1.01048	−	0.486620i	0.145995	−	0.989285i	$-0.453362\pi$
$509$	22.7974	−	10.9786i	1.01048	−	0.486620i	0.864481	+	0.502665i	$0.167647\pi$
$510$		−	0.317667i		−	0.0140665i
$511$	15.7207	+	32.6444i	0.695443	+	1.44410i
$512$	−16.7192	+	3.81604i	−0.738890	+	0.168647i
$513$	4.76659	+	2.29547i	0.210450	+	0.101348i
$514$	−9.34373	+	19.4025i	−0.412134	+	0.855806i
$515$	−0.223480	+	0.979132i	−0.00984772	+	0.0431457i
$516$	1.98643	+	2.49090i	0.0874475	+	0.109656i
$517$	−14.1645	+	17.7617i	−0.622954	+	0.781160i
$518$	4.72737	+	20.7119i	0.207709	+	0.910030i
$519$	4.56157	+	1.04115i	0.200231	+	0.0457013i
$520$	−1.96351	−	1.56584i	−0.0861054	−	0.0686668i
$521$	−23.5797			−1.03305			−0.516523	−	0.856273i	$-0.672774\pi$
$521$	−23.5797			−1.03305			−0.516523	+	0.856273i	$0.672774\pi$
$522$		0			0
$523$	3.96508			0.173381			0.0866905	−	0.996235i	$-0.472371\pi$
$523$	3.96508			0.173381			0.0866905	+	0.996235i	$0.472371\pi$
$524$	−0.443330	−	0.353543i	−0.0193669	−	0.0154446i
$525$	−8.56003	−	1.95377i	−0.373590	−	0.0852696i
$526$	0.133415	+	0.584531i	0.00581719	+	0.0254868i
$527$	4.39911	−	5.51631i	0.191628	−	0.240294i
$528$	3.99061	+	5.00406i	0.173669	+	0.217774i
$529$	1.30947	−	5.73717i	0.0569335	−	0.249442i
$530$	−1.21572	+	2.52446i	−0.0528073	+	0.109655i
$531$	22.9976	+	11.0751i	0.998011	+	0.480617i
$532$	10.0854	−	2.30194i	0.437260	−	0.0998017i
$533$	−0.891325	−	1.85086i	−0.0386076	−	0.0801694i
$534$			1.14138i			0.0493921i
$535$	−2.39881	+	1.15521i	−0.103710	+	0.0499440i
$536$	−0.397139	+	0.316708i	−0.0171538	+	0.0136797i
$537$	−1.99755	+	1.59299i	−0.0862005	+	0.0687426i
$538$	−1.72737	+	0.831855i	−0.0744720	+	0.0358638i
$539$			27.3532i			1.17818i
$540$	−0.498595	−	1.03534i	−0.0214561	−	0.0445541i
$541$	−24.0418	+	5.48739i	−1.03364	+	0.235921i	−0.705501	−	0.708709i	$-0.749278\pi$
$541$	−24.0418	+	5.48739i	−1.03364	+	0.235921i	−0.328137	+	0.944630i	$0.606421\pi$
$542$	−26.7298	−	12.8724i	−1.14814	−	0.552917i
$543$	−1.28230	+	2.66272i	−0.0550287	+	0.114268i
$544$	1.52781	−	6.69378i	0.0655044	−	0.286993i
$545$	−0.367781	−	0.461183i	−0.0157540	−	0.0197549i
$546$	10.4988	−	13.1651i	0.449307	−	0.563414i
$547$	−5.52768	−	24.2183i	−0.236347	−	1.03550i	−0.944259	−	0.329202i	$-0.893220\pi$
$547$	−5.52768	−	24.2183i	−0.236347	−	1.03550i	0.707913	−	0.706300i	$-0.249637\pi$
$548$	−16.0964	−	3.67390i	−0.687604	−	0.156941i
$549$	−13.2510	−	10.5673i	−0.565540	−	0.451003i
$550$	−25.5666			−1.09016
$551$		0			0
$552$	−2.49827			−0.106333
$553$	1.88094	+	1.50000i	0.0799857	+	0.0637865i
$554$	11.5844	+	2.64406i	0.492174	+	0.112335i
$555$	−0.102916	−	0.450904i	−0.00436854	−	0.0191398i
$556$	2.17427	−	2.72645i	0.0922095	−	0.115627i
$557$	−4.84146	−	6.07100i	−0.205139	−	0.257237i	0.668610	−	0.743613i	$-0.266890\pi$
$557$	−4.84146	−	6.07100i	−0.205139	−	0.257237i	−0.873749	+	0.486377i	$0.838318\pi$
$558$	7.14191	−	31.2907i	0.302341	−	1.32464i
$559$	−12.9178	+	26.8240i	−0.546363	+	1.13453i
$560$	6.43027	+	3.09666i	0.271729	+	0.130858i
$561$	−1.40227	+	0.320060i	−0.0592041	+	0.0135129i
$562$	−23.8733	−	49.5734i	−1.00703	−	2.09113i
$563$		−	20.8009i		−	0.876652i	−0.898816	−	0.438326i	$-0.855571\pi$
$563$		−	20.8009i		−	0.876652i	0.898816	−	0.438326i	$-0.144429\pi$
$564$	−3.90097	+	1.87861i	−0.164260	+	0.0791036i
$565$	−2.41104	+	1.92274i	−0.101433	+	0.0808902i
$566$	5.00827	−	3.99396i	0.210513	−	0.167879i
$567$	26.4720	−	12.7482i	1.11172	−	0.535375i
$568$		−	15.4765i		−	0.649380i
$569$	1.21888	+	2.53103i	0.0510981	+	0.106106i	0.924955	−	0.380078i	$-0.124103\pi$
$569$	1.21888	+	2.53103i	0.0510981	+	0.106106i	−0.873856	+	0.486184i	$0.838388\pi$
$570$	−0.571714	+	0.130490i	−0.0239465	+	0.00546563i
$571$	−2.60603	−	1.25500i	−0.109059	−	0.0525201i	0.378559	−	0.925577i	$-0.376420\pi$
$571$	−2.60603	−	1.25500i	−0.109059	−	0.0525201i	−0.487618	+	0.873057i	$0.662134\pi$
$572$	8.17021	−	16.9656i	0.341614	−	0.709368i
$573$	−1.86294	+	8.16206i	−0.0778253	+	0.340975i
$574$	1.80194	+	2.25956i	0.0752114	+	0.0943121i
$575$	12.5685	−	15.7604i	0.524144	−	0.657256i
$576$	−0.791053	−	3.46583i	−0.0329605	−	0.144409i
$577$	7.00872	+	1.59970i	0.291777	+	0.0665962i	0.365904	−	0.930653i	$-0.380760\pi$
$577$	7.00872	+	1.59970i	0.291777	+	0.0665962i	−0.0741270	+	0.997249i	$0.523617\pi$
$578$	−22.2143	−	17.7153i	−0.923992	−	0.736859i
$579$	−4.84415			−0.201316
$580$		0			0
$581$	38.1933			1.58452
$582$	−9.87533	−	7.87531i	−0.409346	−	0.326442i
$583$	12.3686	+	2.82304i	0.512254	+	0.116919i
$584$	−2.70195	−	11.8380i	−0.111807	−	0.489860i
$585$	3.23341	−	4.05456i	0.133685	−	0.167636i
$586$	36.9403	+	46.3216i	1.52599	+	1.91353i
$587$	6.90635	−	30.2587i	0.285055	−	1.24891i	−0.606165	−	0.795339i	$-0.707293\pi$
$587$	6.90635	−	30.2587i	0.285055	−	1.24891i	0.891220	−	0.453570i	$-0.149850\pi$
$588$	−2.26189	+	4.69687i	−0.0932788	+	0.193695i
$589$	−11.7349	−	5.65123i	−0.483528	−	0.232855i
$590$	−5.71174	+	1.30367i	−0.235148	+	0.0536711i
$591$	1.62209	+	3.36831i	0.0667240	+	0.138554i
$592$		−	14.3817i		−	0.591082i
$593$	32.8560	−	15.8226i	1.34923	−	0.649757i	0.387025	−	0.922069i	$-0.373503\pi$
$593$	32.8560	−	15.8226i	1.34923	−	0.649757i	0.962209	+	0.272312i	$0.0877884\pi$
$594$	−10.5925	+	8.44720i	−0.434614	+	0.346593i
$595$	−1.25396	+	1.00000i	−0.0514074	+	0.0409960i
$596$	−3.04288	+	1.46537i	−0.124641	+	0.0600240i
$597$		−	2.94677i		−	0.120603i
$598$	16.7740	+	34.8315i	0.685939	+	1.42437i
$599$	29.3144	−	6.69083i	1.19775	−	0.273380i	0.423288	−	0.905995i	$-0.360876\pi$
$599$	29.3144	−	6.69083i	1.19775	−	0.273380i	0.774466	+	0.632615i	$0.218019\pi$
$600$	2.65106	+	1.27669i	0.108229	+	0.0521205i
$601$	−14.3989	+	29.8995i	−0.587342	+	1.21963i	0.369558	+	0.929208i	$0.379509\pi$
$601$	−14.3989	+	29.8995i	−0.587342	+	1.21963i	−0.956899	+	0.290420i	$0.906205\pi$
$602$	9.32036	−	40.8351i	0.379869	−	1.66432i
$603$	−0.653989	−	0.820077i	−0.0266325	−	0.0333961i
$604$	−1.89344	+	2.37429i	−0.0770428	+	0.0966086i
$605$	0.200218	+	0.877213i	0.00814003	+	0.0356638i
$606$	13.6372	+	3.11260i	0.553974	+	0.126441i
$607$	11.8214	+	9.42729i	0.479818	+	0.382642i	0.833319	−	0.552792i	$-0.186438\pi$
$607$	11.8214	+	9.42729i	0.479818	+	0.382642i	−0.353502	+	0.935434i	$0.615009\pi$
$608$	−12.6746			−0.514021
$609$		0			0
$610$	3.89008			0.157505
$611$	−31.6334	−	25.2268i	−1.27975	−	1.02057i
$612$	3.78077	+	0.862937i	0.152829	+	0.0348821i
$613$	0.835658	+	3.66126i	0.0337519	+	0.147877i	0.988996	−	0.147942i	$-0.0472648\pi$
$613$	0.835658	+	3.66126i	0.0337519	+	0.147877i	−0.955244	+	0.295818i	$0.904408\pi$
$614$	16.4819	−	20.6676i	0.665154	−	0.834077i
$615$	−0.0392287	−	0.0491912i	−0.00158185	−	0.00198358i
$616$	3.55980	−	15.5965i	0.143429	−	0.628401i
$617$	−12.9541	+	26.8995i	−0.521514	+	1.08293i	0.459353	+	0.888254i	$0.348081\pi$
$617$	−12.9541	+	26.8995i	−0.521514	+	1.08293i	−0.980867	+	0.194681i	$0.937633\pi$
$618$	2.03319	+	0.979132i	0.0817868	+	0.0393865i
$619$	44.9615	−	10.2622i	1.80716	−	0.412472i	0.820018	−	0.572338i	$-0.193963\pi$
$619$	44.9615	−	10.2622i	1.80716	−	0.412472i	0.987139	+	0.159866i	$0.0511063\pi$
$620$	1.22749	+	2.54892i	0.0492973	+	0.102367i
$621$		−	10.6823i		−	0.428667i
$622$	−30.0776	+	14.4846i	−1.20600	+	0.580779i
$623$	4.50547	−	3.59299i	0.180508	−	0.143950i
$624$	−8.91218	+	7.10723i	−0.356773	+	0.284517i
$625$	−20.8174	+	10.0251i	−0.832697	+	0.401006i
$626$		−	41.4306i		−	1.65590i
$627$	1.15204	+	2.39224i	0.0460081	+	0.0955368i
$628$	21.4909	−	4.90515i	0.857579	−	0.195737i
$629$	2.91185	+	1.40227i	0.116103	+	0.0559124i
$630$	−3.16557	+	6.57338i	−0.126119	+	0.261890i
$631$	2.81043	−	12.3133i	0.111881	−	0.490185i	−0.887677	−	0.460467i	$-0.847682\pi$
$631$	2.81043	−	12.3133i	0.111881	−	0.490185i	0.999558	−	0.0297178i	$-0.00946085\pi$
$632$	−0.502688	−	0.630351i	−0.0199959	−	0.0250740i
$633$	−2.24764	+	2.81846i	−0.0893358	+	0.112024i
$634$	5.63706	+	24.6976i	0.223876	+	0.980867i
$635$	3.64377	+	0.831668i	0.144599	+	0.0330037i
$636$	1.89039	+	1.50753i	0.0749587	+	0.0597776i
$637$	−48.7157			−1.93019
$638$		0			0
$639$	31.9584			1.26425
$640$	−2.81425	−	2.24429i	−0.111243	−	0.0887134i
$641$	−38.0241	−	8.67874i	−1.50186	−	0.342790i	−0.609017	−	0.793157i	$-0.708436\pi$
$641$	−38.0241	−	8.67874i	−1.50186	−	0.342790i	−0.892843	+	0.450368i	$0.851293\pi$
$642$	1.33124	+	5.83255i	0.0525399	+	0.230192i
$643$	−25.7479	+	32.2869i	−1.01540	+	1.27327i	−0.0538762	+	0.998548i	$0.517158\pi$
$643$	−25.7479	+	32.2869i	−1.01540	+	1.27327i	−0.961523	+	0.274723i	$0.911414\pi$
$644$	−13.0233	−	16.3307i	−0.513188	−	0.643518i
$645$	−0.202907	+	0.888992i	−0.00798944	+	0.0350040i
$646$	1.77798	−	3.69202i	0.0699538	−	0.145261i
$647$	−16.1368	−	7.77109i	−0.634404	−	0.305513i	0.0889021	−	0.996040i	$-0.471664\pi$
$647$	−16.1368	−	7.77109i	−0.634404	−	0.305513i	−0.723306	+	0.690527i	$0.757378\pi$
$648$	−9.59967	+	2.19106i	−0.377111	+	0.0860730i
$649$	11.5095	+	23.8998i	0.451788	+	0.938148i
$650$		−	45.5338i		−	1.78598i
$651$	10.3204	−	4.97002i	0.404487	−	0.194790i
$652$	4.84164	−	3.86108i	0.189613	−	0.151211i
$653$	−10.4145	+	8.30529i	−0.407551	+	0.325011i	−0.805715	−	0.592303i	$-0.798219\pi$
$653$	−10.4145	+	8.30529i	−0.407551	+	0.325011i	0.398164	+	0.917314i	$0.369647\pi$
$654$	−1.19418	+	0.575086i	−0.0466960	+	0.0224876i
$655$		−	0.162291i		−	0.00634125i
$656$	−0.848876	−	1.76271i	−0.0331430	−	0.0688222i
$657$	24.4450	−	5.57942i	0.953691	−	0.217674i
$658$	51.2851	+	24.6976i	1.99930	+	0.962812i
$659$	8.14213	−	16.9073i	0.317172	−	0.658615i	−0.680045	−	0.733171i	$-0.738040\pi$
$659$	8.14213	−	16.9073i	0.317172	−	0.658615i	0.997217	+	0.0745557i	$0.0237539\pi$
$660$	0.128334	−	0.562269i	0.00499540	−	0.0218863i
$661$	−15.4182	−	19.3338i	−0.599698	−	0.751998i	0.385633	−	0.922652i	$-0.373983\pi$
$661$	−15.4182	−	19.3338i	−0.599698	−	0.751998i	−0.985331	+	0.170655i	$0.945412\pi$
$662$	−15.6799	+	19.6620i	−0.609418	+	0.764186i
$663$	−0.570024	−	2.49744i	−0.0221379	−	0.0969924i
$664$	−12.4786	−	2.84817i	−0.484265	−	0.110530i
$665$	2.31482	+	1.84601i	0.0897650	+	0.0715852i
$666$	14.7017			0.569680
$667$		0			0
$668$	18.0368			0.697866
$669$	7.62672	+	6.08211i	0.294866	+	0.235148i
$670$	0.234713	+	0.0535716i	0.00906774	+	0.00206965i
$671$	−3.91939	−	17.1720i	−0.151306	−	0.662916i
$672$	6.94989	−	8.71488i	0.268098	−	0.336184i
$673$	−15.8632	−	19.8919i	−0.611483	−	0.766775i	0.375636	−	0.926767i	$-0.377424\pi$
$673$	−15.8632	−	19.8919i	−0.611483	−	0.766775i	−0.987118	+	0.159992i	$0.948853\pi$
$674$	−5.61260	+	24.5904i	−0.216189	+	0.947188i
$675$	−5.45897	+	11.3357i	−0.210116	+	0.436310i
$676$	15.6102	+	7.51748i	0.600393	+	0.289134i
$677$	−0.601090	+	0.137195i	−0.0231018	+	0.00527283i	−0.234056	−	0.972223i	$-0.575200\pi$
$677$	−0.601090	+	0.137195i	−0.0231018	+	0.00527283i	0.210954	+	0.977496i	$0.432343\pi$
$678$	3.00652	+	6.24309i	0.115465	+	0.239765i
$679$			63.7730i			2.44738i
$680$	0.484271	−	0.233212i	0.0185709	−	0.00894329i
$681$	6.35994	−	5.07188i	0.243713	−	0.194355i
$682$	26.0776	−	20.7962i	0.998563	−	0.796327i
$683$	−16.2371	+	7.81935i	−0.621294	+	0.299199i	−0.717924	−	0.696121i	$-0.754908\pi$
$683$	−16.2371	+	7.81935i	−0.621294	+	0.299199i	0.0966308	+	0.995320i	$0.469193\pi$
$684$		−	7.15883i		−	0.273725i
$685$	−2.05027	−	4.25744i	−0.0783369	−	0.162668i
$686$	17.0265	−	3.88620i	0.650077	−	0.148376i
$687$	−6.42543	−	3.09432i	−0.245145	−	0.118056i
$688$	−12.3026	+	25.5465i	−0.469031	+	0.973952i
$689$	−5.02781	+	22.0283i	−0.191544	+	0.839211i
$690$	0.738250	+	0.925737i	0.0281047	+	0.0352422i
$691$	7.69769	−	9.65260i	0.292834	−	0.367202i	−0.613551	−	0.789655i	$-0.710259\pi$
$691$	7.69769	−	9.65260i	0.292834	−	0.367202i	0.906385	+	0.422453i	$0.138831\pi$
$692$	−2.91723	−	12.7812i	−0.110896	−	0.485869i
$693$	32.2062	+	7.35086i	1.22341	+	0.279236i
$694$	−27.9703	−	22.3056i	−1.06174	−	0.846708i
$695$	0.998081			0.0378594
$696$		0			0
$697$	0.439665			0.0166535
$698$	37.9255	+	30.2446i	1.43550	+	1.14477i
$699$	−0.848876	−	0.193750i	−0.0321074	−	0.00732831i
$700$	5.47434	+	23.9847i	0.206911	+	0.906535i
$701$	21.2594	−	26.6584i	0.802955	−	1.00687i	−0.196696	−	0.980464i	$-0.563021\pi$
$701$	21.2594	−	26.6584i	0.802955	−	1.00687i	0.999651	−	0.0264091i	$-0.00840724\pi$
$702$	−15.0444	−	18.8650i	−0.567813	−	0.712015i
$703$	1.32759	−	5.81656i	0.0500711	−	0.219376i
$704$	1.60295	−	3.32855i	0.0604133	−	0.125450i
$705$	−1.11649	−	0.537673i	−0.0420494	−	0.0202499i
$706$	−7.05350	+	1.60992i	−0.265462	+	0.0605900i
$707$	−30.6425	−	63.6299i	−1.15243	−	2.39305i
$708$			5.05562i			0.190002i
$709$	37.9267	−	18.2645i	1.42437	−	0.685939i	0.446426	−	0.894821i	$-0.352697\pi$
$709$	37.9267	−	18.2645i	1.42437	−	0.685939i	0.977941	+	0.208882i	$0.0669825\pi$
$710$	−5.73483	+	4.57338i	−0.215224	+	0.171636i
$711$	1.30165	−	1.03803i	0.0488157	−	0.0389292i
$712$	−1.73998	+	0.837930i	−0.0652085	+	0.0314028i
$713$			26.2989i			0.984901i
$714$	1.56366	+	3.24698i	0.0585186	+	0.121515i
$715$	5.25430	−	1.19926i	0.196500	−	0.0448497i
$716$	6.44989	+	3.10610i	0.241044	+	0.116080i
$717$	−1.73076	+	3.59395i	−0.0646362	+	0.134219i
$718$	0.299249	−	1.31110i	0.0111679	−	0.0489297i
$719$	−32.5800	−	40.8540i	−1.21503	−	1.52360i	−0.783362	−	0.621566i	$-0.786497\pi$
$719$	−32.5800	−	40.8540i	−1.21503	−	1.52360i	−0.431667	−	0.902033i	$-0.642074\pi$
$720$	3.07942	−	3.86147i	0.114763	−	0.143908i
$721$	−2.53534	−	11.1081i	−0.0944211	−	0.413686i
$722$	26.0034	+	5.93512i	0.967748	+	0.220882i
$723$	−6.92408	−	5.52177i	−0.257509	−	0.205357i
$724$	8.28083			0.307755
$725$		0			0
$726$	2.02177			0.0750349
$727$	23.4432	+	18.6953i	0.869459	+	0.693370i	0.952947	−	0.303138i	$-0.0980345\pi$
$727$	23.4432	+	18.6953i	0.869459	+	0.693370i	−0.0834876	+	0.996509i	$0.526606\pi$
$728$	27.7772	+	6.33997i	1.02949	+	0.234975i
$729$	−3.75733	−	16.4619i	−0.139160	−	0.609702i
$730$	−3.58815	+	4.49939i	−0.132803	+	0.166530i
$731$	−3.97285	−	4.98180i	−0.146941	−	0.184259i
$732$	0.746980	−	3.27273i	0.0276092	−	0.120964i
$733$	−1.30793	+	2.71595i	−0.0483096	+	0.100316i	−0.923726	−	0.383053i	$-0.874873\pi$
$733$	−1.30793	+	2.71595i	−0.0483096	+	0.100316i	0.875417	+	0.483369i	$0.160587\pi$
$734$	55.2781	+	26.6205i	2.04035	+	0.982581i
$735$	−1.45463	+	0.332010i	−0.0536549	+	0.0122464i
$736$	11.1039	+	23.0574i	0.409294	+	0.849907i
$737$		−	1.09006i		−	0.0401531i
$738$	1.80194	−	0.867767i	0.0663302	−	0.0319430i
$739$	16.2914	−	12.9919i	0.599288	−	0.477916i	−0.276237	−	0.961090i	$-0.589087\pi$
$739$	16.2914	−	12.9919i	0.599288	−	0.477916i	0.875525	+	0.483174i	$0.160516\pi$
$740$	−1.01317	+	0.807979i	−0.0372450	+	0.0297019i
$741$	−4.26055	+	2.05177i	−0.156515	+	0.0753738i
$742$		−	31.7875i		−	1.16695i
$743$	−13.3487	−	27.7189i	−0.489718	−	1.01691i	−0.988646	−	0.150266i	$-0.951987\pi$
$743$	−13.3487	−	27.7189i	−0.489718	−	1.01691i	0.498928	−	0.866643i	$-0.333727\pi$
$744$	−3.74253	+	0.854207i	−0.137208	+	0.0313168i
$745$	−0.870896	−	0.419402i	−0.0319072	−	0.0153657i
$746$	−21.8917	+	45.4587i	−0.801514	+	1.66436i
$747$	5.88135	−	25.7679i	0.215188	−	0.942798i
$748$	2.51275	+	3.15088i	0.0918751	+	0.115208i
$749$	18.8327	−	23.6155i	0.688133	−	0.862892i
$750$	−0.628761	−	2.75478i	−0.0229591	−	0.100590i
$751$	−4.35715	−	0.994492i	−0.158995	−	0.0362895i	0.142283	−	0.989826i	$-0.454556\pi$
$751$	−4.35715	−	0.994492i	−0.158995	−	0.0362895i	−0.301277	+	0.953537i	$0.597413\pi$
$752$	−30.1269	−	24.0254i	−1.09862	−	0.876117i
$753$	−11.4843			−0.418510
$754$		0			0
$755$	−0.869167			−0.0316322
$756$	10.1926	+	8.12833i	0.370702	+	0.295625i
$757$	8.24379	+	1.88159i	0.299626	+	0.0683876i	0.369691	−	0.929155i	$-0.379464\pi$
$757$	8.24379	+	1.88159i	0.299626	+	0.0683876i	−0.0700652	+	0.997542i	$0.522321\pi$
$758$	−9.17456	−	40.1964i	−0.333235	−	1.46000i
$759$	3.34266	−	4.19156i	0.121331	−	0.152144i
$760$	−0.618645	−	0.775757i	−0.0224406	−	0.0281397i
$761$	−5.49516	+	24.0759i	−0.199199	+	0.872749i	0.772216	+	0.635361i	$0.219149\pi$
$761$	−5.49516	+	24.0759i	−0.199199	+	0.872749i	−0.971415	+	0.237388i	$0.923709\pi$
$762$	3.64377	−	7.56638i	0.132000	−	0.274101i
$763$	6.02930	+	2.90356i	0.218275	+	0.105116i
$764$	22.8696	−	5.21983i	0.827392	−	0.188847i
$765$	0.481575	+	1.00000i	0.0174114	+	0.0361551i
$766$			21.3676i			0.772045i
$767$	−42.5652	+	20.4983i	−1.53694	+	0.740152i
$768$	−7.20648	+	5.74698i	−0.260042	+	0.207376i
$769$	23.5668	−	18.7939i	0.849839	−	0.677724i	−0.0984462	−	0.995142i	$-0.531387\pi$
$769$	23.5668	−	18.7939i	0.849839	−	0.677724i	0.948286	+	0.317418i	$0.102816\pi$
$770$	−6.83124	+	3.28975i	−0.246181	+	0.118554i
$771$			5.31873i			0.191549i
$772$	5.88911	+	12.2289i	0.211954	+	0.440126i
$773$	5.53462	−	1.26324i	0.199067	−	0.0454356i	−0.121825	−	0.992552i	$-0.538875\pi$
$773$	5.53462	−	1.26324i	0.199067	−	0.0454356i	0.320892	+	0.947116i	$0.396018\pi$
$774$	−26.1151	−	12.5763i	−0.938686	−	0.452048i
$775$	13.4394	−	27.9073i	0.482759	−	1.00246i
$776$	4.75571	−	20.8361i	0.170720	−	0.747973i
$777$	3.27144	+	4.10225i	0.117362	+	0.147168i
$778$	11.6746	−	14.6394i	0.418553	−	0.524849i
$779$	−0.180604	−	0.791277i	−0.00647081	−	0.0283504i
$780$	1.00139	+	0.228562i	0.0358557	+	0.00818382i
$781$	25.9662	+	20.7074i	0.929145	+	0.740968i
$782$	−8.27413			−0.295882
$783$		0			0
$784$	−46.3957			−1.65699
$785$	4.93261	+	3.93362i	0.176052	+	0.140397i
$786$	−0.355523	−	0.0811457i	−0.0126811	−	0.00289437i
$787$	−0.803134	−	3.51876i	−0.0286286	−	0.125430i	0.958594	−	0.284775i	$-0.0919190\pi$
$787$	−0.803134	−	3.51876i	−0.0286286	−	0.125430i	−0.987223	+	0.159345i	$0.949062\pi$
$788$	6.53116	−	8.18982i	0.232663	−	0.291750i
$789$	0.0923264	+	0.115774i	0.00328691	+	0.00412165i
$790$	−0.0850306	+	0.372543i	−0.00302525	+	0.0132545i
$791$	15.1797	−	31.5209i	0.539726	−	1.12075i
$792$	−9.97434	−	4.80339i	−0.354423	−	0.170681i
$793$	30.5831	−	6.98039i	1.08604	−	0.247881i
$794$	6.42465	+	13.3409i	0.228002	+	0.473452i
$795$			0.692021i			0.0245435i
$796$	−7.43900	+	3.58243i	−0.263668	+	0.126976i
$797$	24.0672	−	19.1930i	0.852505	−	0.679850i	−0.0964236	−	0.995340i	$-0.530740\pi$
$797$	24.0672	−	19.1930i	0.852505	−	0.679850i	0.948929	+	0.315490i	$0.102169\pi$
$798$	5.20136	−	4.14795i	0.184126	−	0.146836i
$799$	7.80194	−	3.75722i	0.276013	−	0.132921i
$800$		−	30.1420i		−	1.06568i
$801$	−1.73029	−	3.59299i	−0.0611369	−	0.126952i
$802$	−43.7099	+	9.97650i	−1.54345	+	0.352282i
$803$	23.4768	+	11.3058i	0.828478	+	0.398974i
$804$	0.0901398	−	0.187177i	0.00317898	−	0.00660123i
$805$	1.33028	−	5.82834i	0.0468863	−	0.205422i
$806$	37.0378	+	46.4439i	1.30460	+	1.63592i
$807$	−0.295233	+	0.370210i	−0.0103927	+	0.0130320i
$808$	5.26659	+	23.0745i	0.185278	+	0.811757i
$809$	5.10598	+	1.16541i	0.179517	+	0.0409735i	0.311334	−	0.950300i	$-0.399224\pi$
$809$	5.10598	+	1.16541i	0.179517	+	0.0409735i	−0.131817	+	0.991274i	$0.542081\pi$
$810$	3.64865	+	2.90970i	0.128200	+	0.102236i
$811$	−41.8646			−1.47006			−0.735032	−	0.678032i	$-0.762833\pi$
$811$	−41.8646			−1.47006			−0.735032	+	0.678032i	$0.762833\pi$
$812$		0			0
$813$	−7.32736			−0.256982
$814$	11.9452	+	9.52595i	0.418678	+	0.333884i
$815$	1.72796	+	0.394396i	0.0605278	+	0.0138151i
$816$	−0.542877	−	2.37850i	−0.0190045	−	0.0832641i
$817$	−7.33393	+	9.19646i	−0.256582	+	0.321743i
$818$	21.2289	+	26.6201i	0.742250	+	0.930752i
$819$	−13.0918	+	57.3589i	−0.457464	+	2.00428i
$820$	−0.0764902	+	0.158834i	−0.00267115	+	0.00554671i
$821$	13.8802	+	6.68433i	0.484421	+	0.233285i	0.660121	−	0.751159i	$-0.270505\pi$
$821$	13.8802	+	6.68433i	0.484421	+	0.233285i	−0.175701	+	0.984444i	$0.556219\pi$
$822$	−10.3517	+	2.36270i	−0.361056	+	0.0824086i
$823$	15.4705	+	32.1247i	0.539266	+	1.11980i	0.975507	+	0.219968i	$0.0705954\pi$
$823$	15.4705	+	32.1247i	0.539266	+	1.11980i	−0.436241	+	0.899830i	$0.643690\pi$
$824$			3.81833i			0.133018i
$825$	−5.68910	+	2.73972i	−0.198069	+	0.0953850i
$826$	51.9644	−	41.4403i	1.80807	−	1.44189i
$827$	−40.6973	+	32.4550i	−1.41518	+	1.12857i	−0.442411	+	0.896812i	$0.645877\pi$
$827$	−40.6973	+	32.4550i	−1.41518	+	1.12857i	−0.972773	+	0.231760i	$0.925552\pi$
$828$	−13.0233	+	6.27167i	−0.452590	+	0.217956i
$829$		−	13.4168i		−	0.465986i	−0.972478	−	0.232993i	$-0.925148\pi$
$829$		−	13.4168i		−	0.465986i	0.972478	−	0.232993i	$-0.0748519\pi$
$830$	2.63210	+	5.46562i	0.0913616	+	0.189714i
$831$	2.86111	−	0.653030i	0.0992508	−	0.0226534i
$832$	5.92812	+	2.85483i	0.205520	+	0.0989734i
$833$	4.52378	−	9.39373i	0.156740	−	0.325474i
$834$	0.499041	−	2.18644i	0.0172804	−	0.0757102i
$835$	3.21864	+	4.03604i	0.111385	+	0.139673i
$836$	4.63856	−	5.81656i	0.160428	−	0.201170i
$837$	−3.65250	−	16.0026i	−0.126249	−	0.553132i
$838$	19.1355	+	4.36754i	0.661024	+	0.150874i
$839$	24.2769	+	19.3602i	0.838131	+	0.668387i	0.945425	−	0.325840i	$-0.105647\pi$
$839$	24.2769	+	19.3602i	0.838131	+	0.668387i	−0.107294	+	0.994227i	$0.534218\pi$
$840$	0.872625			0.0301084
$841$		0			0
$842$	35.9681			1.23954
$843$	−10.6246	−	8.47285i	−0.365931	−	0.291821i
$844$	9.84757	+	2.24764i	0.338967	+	0.0773671i
$845$	1.10345	+	4.83452i	0.0379598	+	0.166313i
$846$	24.5601	−	30.7974i	0.844394	−	1.05884i
$847$	−6.36443	−	7.98074i	−0.218684	−	0.274222i
$848$	−4.78836	+	20.9792i	−0.164433	+	0.720428i
$849$	0.686450	−	1.42543i	0.0235589	−	0.0489205i
$850$	8.78017	+	4.22831i	0.301157	+	0.145030i
$851$	−11.7445	+	2.68060i	−0.402596	+	0.0918899i
$852$	2.74638	+	5.70291i	0.0940893	+	0.195378i
$853$		−	21.3357i		−	0.730521i	−0.930905	−	0.365261i	$-0.880980\pi$
$853$		−	21.3357i		−	0.730521i	0.930905	−	0.365261i	$-0.119020\pi$
$854$	−39.7618	+	19.1483i	−1.36062	+	0.655241i
$855$	1.60191	−	1.27748i	0.0547841	−	0.0436889i
$856$	−7.91416	+	6.31133i	−0.270500	+	0.215717i
$857$	8.85839	−	4.26597i	0.302597	−	0.145723i	−0.276424	−	0.961036i	$-0.589149\pi$
$857$	8.85839	−	4.26597i	0.302597	−	0.145723i	0.579021	+	0.815313i	$0.303435\pi$
$858$		−	12.1099i		−	0.413426i
$859$	−22.4681	−	46.6555i	−0.766602	−	1.59187i	−0.805480	−	0.592623i	$-0.798093\pi$
$859$	−22.4681	−	46.6555i	−0.766602	−	1.59187i	0.0388778	−	0.999244i	$-0.487622\pi$
$860$	2.49090	−	0.568532i	0.0849390	−	0.0193868i
$861$	0.643104	+	0.309703i	0.0219169	+	0.0105546i
$862$	23.6037	−	49.0136i	0.803946	−	1.66941i
$863$	−3.62147	+	15.8667i	−0.123276	+	0.540108i	0.875141	+	0.483868i	$0.160768\pi$
$863$	−3.62147	+	15.8667i	−0.123276	+	0.540108i	−0.998417	+	0.0562402i	$0.982089\pi$
$864$	−9.95891	−	12.4881i	−0.338809	−	0.424853i
$865$	2.33944	−	2.93356i	0.0795433	−	0.0997441i
$866$	−8.09611	−	35.4714i	−0.275117	−	1.20537i
$867$	−6.84152	−	1.56153i	−0.232350	−	0.0530324i
$868$	−25.0932	−	20.0112i	−0.851720	−	0.679224i
$869$	1.73019			0.0586925
$870$		0			0
$871$	1.94139			0.0657816
$872$	−1.75339	−	1.39828i	−0.0593772	−	0.0473518i
$873$	43.0258	+	9.82036i	1.45620	+	0.332369i
$874$	3.39881	+	14.8912i	0.114967	+	0.503701i
$875$	−8.89493	+	11.1539i	−0.300703	+	0.377070i
$876$	3.09634	+	3.88269i	0.104616	+	0.131184i
$877$	−3.29470	+	14.4350i	−0.111254	+	0.487436i	0.888346	+	0.459174i	$0.151855\pi$
$877$	−3.29470	+	14.4350i	−0.111254	+	0.487436i	−0.999601	+	0.0282623i	$0.991003\pi$
$878$	−8.33813	+	17.3143i	−0.281398	+	0.584330i
$879$	13.1838	+	6.34900i	0.444679	+	0.214146i
$880$	5.00406	−	1.14214i	0.168687	−	0.0385017i
$881$	8.08661	+	16.7920i	0.272445	+	0.565737i	0.991635	−	0.129076i	$-0.0412012\pi$
$881$	8.08661	+	16.7920i	0.272445	+	0.565737i	−0.719190	+	0.694813i	$0.755487\pi$
$882$		−	47.4282i		−	1.59699i
$883$	−29.1857	+	14.0551i	−0.982178	+	0.472992i	−0.854854	−	0.518869i	$-0.826353\pi$
$883$	−29.1857	+	14.0551i	−0.982178	+	0.472992i	−0.127325	+	0.991861i	$0.540639\pi$
$884$	−5.61169	+	4.47517i	−0.188742	+	0.150516i
$885$	−1.13128	+	0.902165i	−0.0380275	+	0.0303260i
$886$	−33.0383	+	15.9104i	−1.10994	+	0.534521i
$887$		−	6.16288i		−	0.206929i	−0.994633	−	0.103465i	$-0.967007\pi$
$887$		−	6.16288i		−	0.206929i	0.994633	−	0.103465i	$-0.0329929\pi$
$888$	−0.762940	−	1.58426i	−0.0256026	−	0.0531643i
$889$	−41.3379	+	9.43512i	−1.38643	+	0.316444i
$890$	0.824667	+	0.397139i	0.0276429	+	0.0133121i
$891$	9.16812	−	19.0378i	0.307144	−	0.637790i
$892$	6.08211	−	26.6474i	0.203644	−	0.892222i
$893$	−9.96681	−	12.4980i	−0.333527	−	0.418229i
$894$	−1.35421	+	1.69812i	−0.0452915	+	0.0567937i
$895$	0.455927	+	1.99755i	0.0152400	+	0.0667706i
$896$	39.8125	+	9.08695i	1.33004	+	0.303574i
$897$	7.46513	+	5.95324i	0.249253	+	0.198773i
$898$	34.9995			1.16795
$899$		0			0
$900$	17.0248			0.567492
$901$	−3.78077	−	3.01507i	−0.125956	−	0.100446i
$902$	2.02635	+	0.462500i	0.0674699	+	0.0153996i
$903$	−2.30194	−	10.0854i	−0.0766037	−	0.335623i
$904$	−7.31013	+	9.16662i	−0.243131	+	0.304877i
$905$	1.47770	+	1.85297i	0.0491203	+	0.0615949i
$906$	−0.434584	+	1.90404i	−0.0144381	+	0.0632574i
$907$	−19.0840	+	39.6284i	−0.633675	+	1.31584i	0.298700	+	0.954347i	$0.403447\pi$
$907$	−19.0840	+	39.6284i	−0.633675	+	1.31584i	−0.932375	+	0.361492i	$0.882267\pi$
$908$	−20.5356	−	9.88944i	−0.681499	−	0.328193i
$909$	−47.6479	+	10.8753i	−1.58038	+	0.360711i
$910$	−5.85901	−	12.1664i	−0.194224	−	0.403311i
$911$			25.6233i			0.848936i	0.905443	+	0.424468i	$0.139539\pi$
$911$			25.6233i			0.848936i	−0.905443	+	0.424468i	$0.860461\pi$
$912$	−4.05765	+	1.95406i	−0.134362	+	0.0647054i
$913$	21.4749	−	17.1256i	0.710715	−	0.566776i
$914$	17.4987	−	13.9547i	0.578805	−	0.461581i
$915$	0.865625	−	0.416863i	0.0286167	−	0.0137811i
$916$			19.9825i			0.660242i
$917$	0.798852	+	1.65883i	0.0263804	+	0.0547795i
$918$	5.03473	−	1.14914i	0.166171	−	0.0379274i
$919$	5.62349	+	2.70813i	0.185502	+	0.0893330i	0.524329	−	0.851516i	$-0.324316\pi$
$919$	5.62349	+	2.70813i	0.185502	+	0.0893330i	−0.338828	+	0.940848i	$0.610030\pi$
$920$	−0.869268	+	1.80505i	−0.0286589	+	0.0595108i
$921$	1.45281	−	6.36518i	0.0478718	−	0.209740i
$922$	24.6564	+	30.9182i	0.812017	+	1.01824i
$923$	−36.8796	+	46.2456i	−1.21391	+	1.52219i
$924$	1.45593	+	6.37883i	0.0478965	+	0.209848i
$925$	13.8326	+	3.15721i	0.454814	+	0.103808i
$926$	−46.5011	−	37.0834i	−1.52812	−	1.21863i
$927$	−7.88471			−0.258968
$928$		0			0
$929$	−24.5133			−0.804256			−0.402128	−	0.915583i	$-0.631729\pi$
$929$	−24.5133			−0.804256			−0.402128	+	0.915583i	$0.631729\pi$
$930$	1.42246	+	1.13437i	0.0466443	+	0.0371976i
$931$	−18.7644	−	4.28286i	−0.614979	−	0.140365i
$932$	0.542877	+	2.37850i	0.0177825	+	0.0779103i
$933$	−5.14071	+	6.44625i	−0.168299	+	0.211041i
$934$	−29.3267	−	36.7745i	−0.959599	−	1.20330i
$935$	−0.256668	+	1.12454i	−0.00839395	+	0.0367763i
$936$	8.55479	−	17.7642i	0.279622	−	0.580641i
$937$	−3.68449	−	1.77436i	−0.120367	−	0.0579657i	0.372731	−	0.927939i	$-0.378421\pi$
$937$	−3.68449	−	1.77436i	−0.120367	−	0.0579657i	−0.493098	+	0.869974i	$0.664136\pi$
$938$	−2.66277	+	0.607760i	−0.0869426	+	0.0198441i
$939$	−4.43972	−	9.21917i	−0.144885	−	0.300856i
$940$			3.47219i			0.113250i
$941$	5.55280	−	2.67409i	0.181016	−	0.0871728i	−0.341181	−	0.939998i	$-0.610827\pi$
$941$	5.55280	−	2.67409i	0.181016	−	0.0871728i	0.522197	+	0.852825i	$0.325113\pi$
$942$	11.0835	−	8.83877i	0.361119	−	0.287983i
$943$	−1.28126	+	1.02177i	−0.0417235	+	0.0332734i
$944$	−40.5381	+	19.5221i	−1.31940	+	0.635391i
$945$			3.73125i			0.121378i
$946$	−13.0697	−	27.1395i	−0.424933	−	0.882382i
$947$	−48.4562	+	11.0598i	−1.57461	+	0.359395i	−0.918548	−	0.395309i	$-0.870638\pi$
$947$	−48.4562	+	11.0598i	−1.57461	+	0.359395i	−0.656065	+	0.754704i	$0.727780\pi$
$948$	0.297093	+	0.143073i	0.00964914	+	0.00464678i
$949$	−20.1356	+	41.8119i	−0.653628	+	1.35727i
$950$	4.00312	−	17.5388i	0.129878	−	0.569034i
$951$	3.90097	+	4.89166i	0.126498	+	0.158623i
$952$	−3.80194	+	4.76748i	−0.123222	+	0.154515i
$953$	−3.93541	−	17.2422i	−0.127480	−	0.558529i	−0.997815	−	0.0660678i	$-0.978955\pi$
$953$	−3.93541	−	17.2422i	−0.127480	−	0.558529i	0.870335	−	0.492461i	$-0.163902\pi$
$954$	−21.4461	−	4.89493i	−0.694343	−	0.158479i
$955$	5.24905	+	4.18598i	0.169855	+	0.135455i
$956$	11.1769			0.361486
$957$		0			0
$958$	−59.5827			−1.92503
$959$	41.9130	+	33.4245i	1.35344	+	1.07933i
$960$	0.196468	+	0.0448424i	0.00634096	+	0.00144728i
$961$	2.09395	+	9.17419i	0.0675468	+	0.295942i
$962$	−16.9656	+	21.2742i	−0.546993	+	0.685908i
$963$	−13.0327	−	16.3424i	−0.419971	−	0.526628i
$964$	−5.52177	+	24.1925i	−0.177844	+	0.779187i
$965$	−1.68551	+	3.50000i	−0.0542585	+	0.112669i
$966$	−12.1027	−	5.82834i	−0.389397	−	0.187524i
$967$	12.5701	−	2.86904i	0.404226	−	0.0922620i	−0.0155736	−	0.999879i	$-0.504957\pi$
$967$	12.5701	−	2.86904i	0.404226	−	0.0922620i	0.419800	+	0.907617i	$0.362100\pi$
$968$	1.48426	+	3.08211i	0.0477060	+	0.0990626i
$969$		−	1.01208i		−	0.0325127i
$970$	−9.12618	+	4.39494i	−0.293024	+	0.141113i
$971$	−3.78207	+	3.01610i	−0.121372	+	0.0967912i	−0.682295	−	0.731077i	$-0.739018\pi$
$971$	−3.78207	+	3.01610i	−0.121372	+	0.0967912i	0.560923	+	0.827868i	$0.310447\pi$
$972$	10.7006	−	8.53348i	0.343223	−	0.273712i
$973$	−10.2017	+	4.91288i	−0.327052	+	0.157500i
$974$			18.3013i			0.586411i
$975$	−4.87942	−	10.1322i	−0.156266	−	0.324491i
$976$	29.1266	−	6.64795i	0.932319	−	0.212796i
$977$	−14.8138	−	7.13394i	−0.473935	−	0.228235i	0.181640	−	0.983365i	$-0.441859\pi$
$977$	−14.8138	−	7.13394i	−0.473935	−	0.228235i	−0.655575	+	0.755130i	$0.727574\pi$
$978$	1.72796	−	3.58815i	0.0552541	−	0.114736i
$979$	0.922207	−	4.04045i	0.0294739	−	0.129133i
$980$	2.60656	+	3.26853i	0.0832636	+	0.104409i
$981$	2.88740	−	3.62068i	0.0921874	−	0.115599i
$982$	−7.89181	−	34.5763i	−0.251838	−	1.10337i
$983$	25.8349	+	5.89666i	0.824007	+	0.188074i	0.613678	−	0.789557i	$-0.289689\pi$
$983$	25.8349	+	5.89666i	0.824007	+	0.188074i	0.210329	+	0.977631i	$0.432547\pi$
$984$	−0.187022	−	0.149145i	−0.00596204	−	0.00475457i
$985$	2.99808			0.0955268
$986$		0			0
$987$	14.0586			0.447490
$988$	10.3592	+	8.26122i	0.329571	+	0.262824i
$989$	23.1551	+	5.28501i	0.736291	+	0.168054i
$990$	1.16756	+	5.11543i	0.0371076	+	0.162579i
$991$	−25.1930	+	31.5910i	−0.800281	+	1.00352i	0.199440	+	0.979910i	$0.436088\pi$
$991$	−25.1930	+	31.5910i	−0.800281	+	1.00352i	−0.999721	+	0.0236111i	$0.992484\pi$
$992$	24.5179	+	30.7445i	0.778444	+	0.976137i
$993$	−1.38212	+	6.05548i	−0.0438604	+	0.192165i
$994$	36.1059	−	74.9747i	1.14521	−	2.37805i
$995$	−2.12910	−	1.02532i	−0.0674971	−	0.0325049i
$996$	5.10365	−	1.16487i	0.161715	−	0.0369105i
$997$	10.1769	+	21.1325i	0.322305	+	0.669273i	0.997671	−	0.0682093i	$-0.0217286\pi$
$997$	10.1769	+	21.1325i	0.322305	+	0.669273i	−0.675366	+	0.737483i	$0.736014\pi$
$998$			50.1831i			1.58852i
$999$	6.77413	−	3.26225i	0.214324	−	0.103213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.d.267.1		12
29.2	odd	28		29.2.d.a.24.1	yes	6
29.3	odd	28		841.2.d.b.605.1		6
29.4	even	14		841.2.e.b.270.1		12
29.5	even	14	inner	841.2.e.d.63.1		12
29.6	even	14		841.2.e.b.651.2		12
29.7	even	7		841.2.e.c.236.2		12
29.8	odd	28		841.2.d.c.645.1		6
29.9	even	14		841.2.e.c.196.2		12
29.10	odd	28		841.2.d.a.571.1		6
29.11	odd	28		841.2.a.e.1.1		3
29.12	odd	4		841.2.d.d.574.1		6
29.13	even	14		841.2.b.c.840.6		6
29.14	odd	28		841.2.d.e.190.1		6
29.15	odd	28		841.2.d.a.190.1		6
29.16	even	7		841.2.b.c.840.1		6
29.17	odd	4		29.2.d.a.23.1	✓	6
29.18	odd	28		841.2.a.f.1.3		3
29.19	odd	28		841.2.d.e.571.1		6
29.20	even	7		841.2.e.c.196.1		12
29.21	odd	28		841.2.d.b.645.1		6
29.22	even	14		841.2.e.c.236.1		12
29.23	even	7		841.2.e.b.651.1		12
29.24	even	7	inner	841.2.e.d.63.2		12
29.25	even	7		841.2.e.b.270.2		12
29.26	odd	28		841.2.d.c.605.1		6
29.27	odd	28		841.2.d.d.778.1		6
29.28	even	2	inner	841.2.e.d.267.2		12
87.2	even	28		261.2.k.a.82.1		6
87.11	even	28		7569.2.a.r.1.3		3
87.17	even	4		261.2.k.a.226.1		6
87.47	even	28		7569.2.a.p.1.1		3
116.31	even	28		464.2.u.f.401.1		6
116.75	even	4		464.2.u.f.81.1		6
145.2	even	28		725.2.r.b.24.2		12
145.17	even	4		725.2.r.b.574.1		12
145.89	odd	28		725.2.l.b.401.1		6
145.104	odd	4		725.2.l.b.226.1		6
145.118	even	28		725.2.r.b.24.1		12
145.133	even	4		725.2.r.b.574.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.17	odd	4
29.2.d.a.24.1	yes	6	29.2	odd	28
261.2.k.a.82.1		6	87.2	even	28
261.2.k.a.226.1		6	87.17	even	4
464.2.u.f.81.1		6	116.75	even	4
464.2.u.f.401.1		6	116.31	even	28
725.2.l.b.226.1		6	145.104	odd	4
725.2.l.b.401.1		6	145.89	odd	28
725.2.r.b.24.1		12	145.118	even	28
725.2.r.b.24.2		12	145.2	even	28
725.2.r.b.574.1		12	145.17	even	4
725.2.r.b.574.2		12	145.133	even	4
841.2.a.e.1.1		3	29.11	odd	28
841.2.a.f.1.3		3	29.18	odd	28
841.2.b.c.840.1		6	29.16	even	7
841.2.b.c.840.6		6	29.13	even	14
841.2.d.a.190.1		6	29.15	odd	28
841.2.d.a.571.1		6	29.10	odd	28
841.2.d.b.605.1		6	29.3	odd	28
841.2.d.b.645.1		6	29.21	odd	28
841.2.d.c.605.1		6	29.26	odd	28
841.2.d.c.645.1		6	29.8	odd	28
841.2.d.d.574.1		6	29.12	odd	4
841.2.d.d.778.1		6	29.27	odd	28
841.2.d.e.190.1		6	29.14	odd	28
841.2.d.e.571.1		6	29.19	odd	28
841.2.e.b.270.1		12	29.4	even	14
841.2.e.b.270.2		12	29.25	even	7
841.2.e.b.651.1		12	29.23	even	7
841.2.e.b.651.2		12	29.6	even	14
841.2.e.c.196.1		12	29.20	even	7
841.2.e.c.196.2		12	29.9	even	14
841.2.e.c.236.1		12	29.22	even	14
841.2.e.c.236.2		12	29.7	even	7
841.2.e.d.63.1		12	29.5	even	14	inner
841.2.e.d.63.2		12	29.24	even	7	inner
841.2.e.d.267.1		12	1.1	even	1	trivial
841.2.e.d.267.2		12	29.28	even	2	inner
7569.2.a.p.1.1		3	87.47	even	28
7569.2.a.r.1.3		3	87.11	even	28

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40881 - 1.12349i) q^{2} +(-0.433884 - 0.0990311i) q^{3} +(0.277479 + 1.21572i) q^{4} +(-0.222521 + 0.279032i) q^{5} +(0.500000 + 0.626980i) q^{6} +(0.900969 - 3.94740i) q^{7} +(-0.588735 + 1.22252i) q^{8} +(-2.52446 - 1.21572i) q^{9} +(0.626980 - 0.143104i) q^{10} +(-1.26341 - 2.62349i) q^{11} -0.554958i q^{12} +(4.67241 - 2.25011i) q^{13} +(-5.70416 + 4.54892i) q^{14} +(0.124181 - 0.0990311i) q^{15} +(4.44989 - 2.14295i) q^{16} +1.10992i q^{17} +(2.19064 + 4.54892i) q^{18} +(1.99755 - 0.455927i) q^{19} +(-0.400969 - 0.193096i) q^{20} +(-0.781831 + 1.62349i) q^{21} +(-1.16756 + 5.11543i) q^{22} +(-2.57942 - 3.23449i) q^{23} +(0.376510 - 0.472129i) q^{24} +(1.08426 + 4.75046i) q^{25} +(-9.11052 - 2.07942i) q^{26} +(2.01877 + 1.60992i) q^{27} +5.04892 q^{28} -0.286208 q^{30} +(-4.97002 - 3.96346i) q^{31} +(-6.03089 - 1.37651i) q^{32} +(0.288364 + 1.26341i) q^{33} +(1.24698 - 1.56366i) q^{34} +(0.900969 + 1.12978i) q^{35} +(0.777479 - 3.40636i) q^{36} +(1.26341 - 2.62349i) q^{37} +(-3.32640 - 1.60191i) q^{38} +(-2.25011 + 0.513574i) q^{39} +(-0.210117 - 0.436313i) q^{40} -0.396125i q^{41} +(2.92543 - 1.40881i) q^{42} +(-4.48845 + 3.57942i) q^{43} +(2.83885 - 2.26391i) q^{44} +(0.900969 - 0.433884i) q^{45} +7.45473i q^{46} +(-3.38513 - 7.02930i) q^{47} +(-2.14295 + 0.489115i) q^{48} +(-8.46346 - 4.07579i) q^{49} +(3.80957 - 7.91066i) q^{50} +(0.109916 - 0.481575i) q^{51} +(4.03199 + 5.05596i) q^{52} +(-2.71648 + 3.40636i) q^{53} +(-1.03534 - 4.53614i) q^{54} +(1.01317 + 0.231250i) q^{55} +(4.29535 + 3.42543i) q^{56} -0.911854 q^{57} -9.10992 q^{59} +(0.154851 + 0.123490i) q^{60} +(5.89726 + 1.34601i) q^{61} +(2.54892 + 11.1675i) q^{62} +(-7.07338 + 8.86973i) q^{63} +(0.791053 + 0.991949i) q^{64} +(-0.411854 + 1.80445i) q^{65} +(1.01317 - 2.10388i) q^{66} +(0.337282 + 0.162426i) q^{67} +(-1.34934 + 0.307979i) q^{68} +(0.798852 + 1.65883i) q^{69} -2.60388i q^{70} +(-10.2763 + 4.94880i) q^{71} +(2.97247 - 2.37047i) q^{72} +(-6.99637 + 5.57942i) q^{73} +(-4.72737 + 2.27658i) q^{74} -2.16852i q^{75} +(1.10855 + 2.30194i) q^{76} +(-11.4943 + 2.62349i) q^{77} +(3.74698 + 1.80445i) q^{78} +(-0.257808 + 0.535344i) q^{79} +(-0.392240 + 1.71851i) q^{80} +(4.52446 + 5.67349i) q^{81} +(-0.445042 + 0.558065i) q^{82} +(2.09903 + 9.19646i) q^{83} +(-2.19064 - 0.500000i) q^{84} +(-0.309703 - 0.246980i) q^{85} +10.3448 q^{86} +3.95108 q^{88} +(1.11276 + 0.887395i) q^{89} +(-1.75676 - 0.400969i) q^{90} +(-4.67241 - 20.4712i) q^{91} +(3.21648 - 4.03334i) q^{92} +(1.76391 + 2.21187i) q^{93} +(-3.12833 + 13.7061i) q^{94} +(-0.317278 + 0.658834i) q^{95} +(2.48039 + 1.19449i) q^{96} +(-15.3557 + 3.50484i) q^{97} +(7.34432 + 15.2506i) q^{98} +8.15883i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 2 q^{5} + 6 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{13} + 8 q^{16} + 4 q^{20} - 12 q^{22} - 14 q^{23} + 14 q^{24} - 48 q^{25} + 24 q^{28} - 36 q^{30} - 2 q^{33} - 4 q^{34} + 2 q^{35} + 10 q^{36}+ \cdots + 4 q^{96}+O(q^{100}) \) 12 * q + 4 * q^4 - 2 * q^5 + 6 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^13 + 8 * q^16 + 4 * q^20 - 12 * q^22 - 14 * q^23 + 14 * q^24 - 48 * q^25 + 24 * q^28 - 36 * q^30 - 2 * q^33 - 4 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^38 + 8 * q^42 + 2 * q^45 - 44 * q^49 + 4 * q^51 - 20 * q^52 + 6 * q^53 + 12 * q^54 + 4 * q^57 - 112 * q^59 - 6 * q^62 - 30 * q^63 - 2 * q^64 + 10 * q^65 - 38 * q^67 - 42 * q^71 - 12 * q^74 + 26 * q^78 + 36 * q^80 + 36 * q^81 - 4 * q^82 + 34 * q^83 + 32 * q^86 + 84 * q^88 - 10 * q^91 + 34 * q^93 + 16 * q^94 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more