LMFDB - Embedded newform 841.2.e.d.63.1

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			63.1
Root			$-0.781831 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	841.63
Dual form			841.2.e.d.267.1

$q$-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 $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{14}\right)$

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	−0.978674	−	0.205419i	$-0.934144\pi$
$2$	−1.40881	+	1.12349i	−0.996180	+	0.794427i	−0.0175063	+	0.999847i	$0.505573\pi$
$3$	−0.433884	+	0.0990311i	−0.250503	+	0.0571757i	−0.345928	−	0.938261i	$-0.612436\pi$
$3$	−0.433884	+	0.0990311i	−0.250503	+	0.0571757i	0.0954255	+	0.995437i	$0.469579\pi$
$4$	0.277479	−	1.21572i	0.138740	−	0.607858i
$5$	−0.222521	−	0.279032i	−0.0995144	−	0.124787i	0.729581	−	0.683895i	$-0.239715\pi$
$5$	−0.222521	−	0.279032i	−0.0995144	−	0.124787i	−0.829095	+	0.559108i	$0.811144\pi$
$6$	0.500000	−	0.626980i	0.204124	−	0.255964i
$7$	0.900969	+	3.94740i	0.340534	+	1.49198i	0.797949	+	0.602725i	$0.205918\pi$
$7$	0.900969	+	3.94740i	0.340534	+	1.49198i	−0.457415	+	0.889253i	$0.651225\pi$
$8$	−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	0.619053	+	0.785349i	$0.287517\pi$
$11$	−1.26341	+	2.62349i	−0.380931	+	0.791012i	−0.999984	+	0.00566249i	$0.998198\pi$
$12$			0.554958i			0.160203i
$13$	4.67241	+	2.25011i	1.29589	+	0.624069i	0.949425	−	0.313993i	$-0.101667\pi$
$13$	4.67241	+	2.25011i	1.29589	+	0.624069i	0.346467	+	0.938062i	$0.387381\pi$
$14$	−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	$-0.957026\pi$
$17$		−	1.10992i		−	0.269194i	0.990900	−	0.134597i	$-0.0429740\pi$
$18$	2.19064	−	4.54892i	0.516340	−	1.07219i
$19$	1.99755	+	0.455927i	0.458269	+	0.104597i	0.445422	−	0.895321i	$-0.353054\pi$
$19$	1.99755	+	0.455927i	0.458269	+	0.104597i	0.0128465	+	0.999917i	$0.495911\pi$
$20$	−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	−0.974291	−	0.225294i	$-0.927666\pi$
$23$	−2.57942	+	3.23449i	−0.537846	+	0.674437i	0.436445	+	0.899731i	$0.356237\pi$
$24$	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	−0.958233	−	0.285988i	$-0.907678\pi$
$31$	−4.97002	+	3.96346i	−0.892642	+	0.711858i	0.0655910	+	0.997847i	$0.479107\pi$
$32$	−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	0.978631	−	0.205622i	$-0.0659219\pi$
$37$	1.26341	+	2.62349i	0.207703	+	0.431299i	−0.770929	+	0.636921i	$0.780208\pi$
$38$	−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	$0.00984757\pi$
$41$			0.396125i			0.0618643i	−0.999521	+	0.0309321i	$0.990152\pi$
$42$	2.92543	+	1.40881i	0.451403	+	0.217384i
$43$	−4.48845	−	3.57942i	−0.684482	−	0.545856i	0.218339	−	0.975873i	$-0.429936\pi$
$43$	−4.48845	−	3.57942i	−0.684482	−	0.545856i	−0.902821	+	0.430017i	$0.858508\pi$
$44$	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	0.494005	+	0.869459i	$0.335532\pi$
$47$	−3.38513	+	7.02930i	−0.493773	+	1.02533i	−0.987778	+	0.155870i	$0.950182\pi$
$48$	−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	0.559439	−	0.828871i	$-0.311016\pi$
$53$	−2.71648	−	3.40636i	−0.373137	−	0.467899i	−0.932577	+	0.360972i	$0.882445\pi$
$54$	−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	0.172374	−	0.985032i	$-0.444856\pi$
$61$	5.89726	−	1.34601i	0.755067	−	0.172339i	0.582693	+	0.812693i	$0.301999\pi$
$62$	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	−0.413168	−	0.910655i	$-0.635578\pi$
$67$	0.337282	−	0.162426i	0.0412055	−	0.0198435i	0.454373	+	0.890812i	$0.349863\pi$
$68$	−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	−0.290379	−	0.956912i	$-0.593781\pi$
$71$	−10.2763	−	4.94880i	−1.21957	−	0.587314i	−0.929192	+	0.369598i	$0.879495\pi$
$72$	2.97247	+	2.37047i	0.350309	+	0.279362i
$73$	−6.99637	−	5.57942i	−0.818863	−	0.653021i	0.121728	−	0.992563i	$-0.461156\pi$
$73$	−6.99637	−	5.57942i	−0.818863	−	0.653021i	−0.940591	+	0.339542i	$0.889728\pi$
$74$	−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	0.885963	−	0.463757i	$-0.153499\pi$
$79$	−0.257808	−	0.535344i	−0.0290057	−	0.0602309i	−0.914968	+	0.403526i	$0.867785\pi$
$80$	−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	−0.718912	−	0.695101i	$-0.755359\pi$
$83$	2.09903	−	9.19646i	0.230399	−	1.00944i	0.949310	−	0.314341i	$-0.101783\pi$
$84$	−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	−0.562737	−	0.826636i	$-0.690252\pi$
$89$	1.11276	−	0.887395i	0.117952	−	0.0940637i	0.680689	+	0.732572i	$0.261680\pi$
$90$	−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	−0.645943	−	0.763386i	$-0.723536\pi$
$97$	−15.3557	−	3.50484i	−1.55914	−	0.355863i	−0.913195	+	0.407523i	$0.866393\pi$
$98$	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	0.988293	+	0.152570i	$0.0487550\pi$
$101$	13.6372	+	10.8753i	1.35695	+	1.08213i	0.368661	+	0.929564i	$0.379816\pi$
$102$	−0.695895	−	0.554958i	−0.0689039	−	0.0549490i
$103$	2.53534	+	1.22096i	0.249815	+	0.120304i	0.554601	−	0.832116i	$-0.312871\pi$
$103$	2.53534	+	1.22096i	0.249815	+	0.120304i	−0.304786	+	0.952421i	$0.598585\pi$
$104$		−	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	−0.0798052	−	0.996810i	$-0.525430\pi$
$107$	6.72132	−	3.23682i	0.649775	−	0.312915i	0.729580	+	0.683895i	$0.239716\pi$
$108$	−1.39703	−	2.90097i	−0.134430	−	0.279146i
$109$	−0.367781	−	1.61135i	−0.0352270	−	0.154340i	0.954255	−	0.298993i	$-0.0966506\pi$
$109$	−0.367781	−	1.61135i	−0.0352270	−	0.154340i	−0.989482	+	0.144653i	$0.953793\pi$
$110$	−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	0.192921	−	0.981214i	$-0.438204\pi$
$113$	8.42407	−	1.92274i	0.792470	−	0.180876i	0.599549	+	0.800338i	$0.295347\pi$
$114$	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	0.596219	+	0.802822i	$0.296669\pi$
$127$	−4.54371	+	9.43512i	−0.403189	+	0.837231i	−0.999408	+	0.0344090i	$0.989045\pi$
$128$		−	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	0.607836	−	0.794063i	$-0.292038\pi$
$131$	−0.355523	−	0.283520i	−0.0310622	−	0.0247712i	−0.638898	+	0.769292i	$0.720609\pi$
$132$	−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	−0.988416	−	0.151769i	$-0.951503\pi$
$137$	−5.74474	−	11.9291i	−0.490806	−	1.01917i	0.497610	−	0.867401i	$-0.334211\pi$
$138$	0.738250	+	3.23449i	0.0628440	+	0.275338i
$139$	−1.74363	+	2.18644i	−0.147893	+	0.185451i	−0.850260	−	0.526364i	$-0.823555\pi$
$139$	−1.74363	+	2.18644i	−0.147893	+	0.185451i	0.702367	+	0.711815i	$0.252127\pi$
$140$	−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	−0.944223	−	0.329307i	$-0.893185\pi$
$149$	0.602679	−	2.64051i	0.0493734	−	0.216319i	0.993596	+	0.112988i	$0.0360421\pi$
$150$	−2.43631	−	3.05504i	−0.198924	−	0.249443i
$151$	1.51842	−	1.90404i	0.123567	−	0.154948i	−0.716200	−	0.697895i	$-0.754120\pi$
$151$	1.51842	−	1.90404i	0.123567	−	0.154948i	0.839767	+	0.542947i	$0.182692\pi$
$152$	−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	$0.249238\pi$
$157$			17.6775i			1.41082i	−0.708799	+	0.705411i	$0.750762\pi$
$158$	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	−0.968150	−	0.250370i	$-0.919448\pi$
$163$	−2.15473	+	4.47434i	−0.168772	+	0.350458i	0.799379	+	0.600827i	$0.205162\pi$
$164$	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	0.932487	+	0.361203i	$0.117634\pi$
$167$	3.21864	+	14.1018i	0.249066	+	1.09123i	−0.683422	+	0.730024i	$0.739509\pi$
$168$	−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	0.897394	−	0.441230i	$-0.145458\pi$
$179$	3.57942	+	4.48845i	0.267538	+	0.335482i	−0.629856	+	0.776712i	$0.716886\pi$
$180$	0.777479	−	0.974928i	0.0579499	−	0.0726668i
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	0.999688	+	0.0249747i	$0.00795053\pi$
$181$	1.47770	+	6.47421i	0.109836	+	0.481225i	−0.889852	+	0.456250i	$0.849192\pi$
$182$	−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	$0.238272\pi$
$191$			18.8116i			1.36116i	−0.732673	+	0.680581i	$0.761728\pi$
$192$	−0.244991	+	0.508729i	−0.0176807	+	0.0367144i
$193$	10.6118	+	2.42208i	0.763854	+	0.174345i	0.586662	−	0.809832i	$-0.300442\pi$
$193$	10.6118	+	2.42208i	0.763854	+	0.174345i	0.177192	+	0.984176i	$0.443299\pi$
$194$	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	−0.932584	−	0.360952i	$-0.882452\pi$
$197$	−5.23759	+	6.56773i	−0.373163	+	0.467931i	0.559422	+	0.828883i	$0.311023\pi$
$198$	9.16637	+	11.4943i	0.651425	+	0.816861i
$199$	1.47339	−	6.45532i	0.104446	−	0.457606i	−0.895476	−	0.445109i	$-0.853165\pi$
$199$	1.47339	−	6.45532i	0.104446	−	0.457606i	0.999922	−	0.0124967i	$-0.00397793\pi$
$200$	−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	0.986215	−	0.165468i	$-0.0529134\pi$
$211$	3.51456	+	7.29805i	0.241952	+	0.502419i	−0.744263	+	0.667887i	$0.767199\pi$
$212$	−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	−0.955943	−	0.293552i	$-0.905163\pi$
$223$	−19.7485	+	9.51036i	−1.32246	+	0.636861i	−0.366512	+	0.930413i	$0.619448\pi$
$224$	−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	0.243363	−	0.969935i	$-0.421749\pi$
$227$	−11.3964	−	14.2907i	−0.756407	−	0.948504i	−0.999770	+	0.0214309i	$0.993178\pi$
$228$	−0.253020	+	1.10855i	−0.0167567	+	0.0734158i
$229$	15.6230	−	3.56584i	1.03240	−	0.235638i	0.327427	−	0.944876i	$-0.393818\pi$
$229$	15.6230	−	3.56584i	1.03240	−	0.235638i	0.704968	+	0.709239i	$0.250961\pi$
$230$	−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	0.997571	+	0.0696554i	$0.0221900\pi$
$239$	1.99449	+	8.73844i	0.129013	+	0.565243i	−0.868558	+	0.495587i	$0.834953\pi$
$240$	0.340373	+	0.706791i	0.0219710	+	0.0456232i
$241$	17.9291	−	8.63419i	1.15491	−	0.556177i	0.244407	−	0.969673i	$-0.421407\pi$
$241$	17.9291	−	8.63419i	1.15491	−	0.556177i	0.910506	+	0.413496i	$0.135692\pi$
$242$	−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	0.923108	−	0.384540i	$-0.125640\pi$
$251$	25.1579	+	5.74214i	1.58795	+	0.362440i	0.664847	+	0.746980i	$0.268497\pi$
$252$	−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	0.821726	+	0.569883i	$0.193012\pi$
$257$	−2.65937	+	11.6514i	−0.165887	+	0.726797i	−0.987612	+	0.156914i	$0.949846\pi$
$258$	−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	−0.631477	−	0.775394i	$-0.717551\pi$
$263$	−0.260141	+	0.207455i	−0.0160410	+	0.0127923i	0.615437	+	0.788186i	$0.288980\pi$
$264$	−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	0.914568	−	0.404432i	$-0.132531\pi$
$269$	0.461645	+	0.958615i	0.0281470	+	0.0584478i	−0.886421	+	0.462879i	$0.846816\pi$
$270$	1.49612	−	0.720491i	0.0910507	−	0.0438477i
$271$	16.0516	+	3.66368i	0.975067	+	0.222553i	0.680233	−	0.732996i	$-0.261879\pi$
$271$	16.0516	+	3.66368i	0.975067	+	0.222553i	0.294834	+	0.955549i	$0.404736\pi$
$272$	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	0.246800	−	0.969066i	$-0.420621\pi$
$277$	−5.94116	−	2.86111i	−0.356970	−	0.171907i	−0.603769	+	0.797159i	$0.706335\pi$
$278$		−	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	0.641448	−	0.767166i	$-0.278334\pi$
$281$	27.5112	−	13.2487i	1.64118	−	0.790350i	0.999731	−	0.0231840i	$-0.00738037\pi$
$282$	2.71467	+	5.63706i	0.161656	+	0.335682i
$283$	−0.791053	−	3.46583i	−0.0470232	−	0.206022i	0.945959	−	0.324286i	$-0.105124\pi$
$283$	−0.791053	−	3.46583i	−0.0470232	−	0.206022i	−0.992982	+	0.118264i	$0.962267\pi$
$284$	−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	−0.998327	−	0.0578127i	$-0.981587\pi$
$293$	−32.0556	+	7.31647i	−1.87271	+	0.427433i	−0.874378	+	0.485246i	$0.838730\pi$
$294$	−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	$-0.862508\pi$
$307$		−	14.6703i		−	0.837275i	0.908153	−	0.418638i	$-0.137492\pi$
$308$	−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	0.994573	+	0.104045i	$0.0331786\pi$
$311$	8.03834	+	16.6918i	0.455812	+	0.946504i	−0.538760	+	0.842459i	$0.681107\pi$
$312$	0.696866	+	3.05317i	0.0394523	+	0.172852i
$313$	14.3354	−	17.9760i	0.810286	−	1.01607i	−0.189132	−	0.981952i	$-0.560567\pi$
$313$	14.3354	−	17.9760i	0.810286	−	1.01607i	0.999418	−	0.0341147i	$-0.0108612\pi$
$314$	−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	−0.881512	−	0.472162i	$-0.843474\pi$
$317$	−10.9915	+	8.76540i	−0.617342	+	0.492314i	0.264170	+	0.964476i	$0.414902\pi$
$318$	−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	$0.125301\pi$
$331$			13.9565i			0.767116i	−0.923517	+	0.383558i	$0.874699\pi$
$332$	−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	−0.998339	−	0.0576199i	$-0.981649\pi$
$337$	−6.07333	+	12.6114i	−0.330836	+	0.686987i	0.667503	+	0.744607i	$0.267363\pi$
$338$	−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	0.843976	−	0.536382i	$-0.180209\pi$
$353$	2.50335	+	3.13910i	0.133240	+	0.167078i	−0.710736	+	0.703459i	$0.751638\pi$
$354$	−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	−0.892249	−	0.451544i	$-0.850873\pi$
$359$	0.323814	−	0.672407i	0.0170903	−	0.0354883i	0.909339	+	0.416055i	$0.136588\pi$
$360$		−	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	−0.764352	−	0.644799i	$-0.776941\pi$
$367$	−33.1952	−	7.57660i	−1.73278	−	0.395495i	−0.968425	+	0.249304i	$0.919798\pi$
$368$	−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	0.510268	+	0.860015i	$0.329546\pi$
$373$	−6.23072	+	27.2986i	−0.322614	+	1.41347i	−0.832882	+	0.553450i	$0.813311\pi$
$374$	−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	−0.0450211	−	0.998986i	$-0.514336\pi$
$379$	17.8891	−	14.2661i	0.918900	−	0.732798i	0.963921	+	0.266188i	$0.0857641\pi$
$380$	−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	−0.933981	−	0.357323i	$-0.883690\pi$
$383$	−7.39344	+	9.27108i	−0.377787	+	0.473730i	0.556194	+	0.831052i	$0.312261\pi$
$384$	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	$-0.915146\pi$
$389$		−	10.3913i		−	0.526862i	0.964678	−	0.263431i	$-0.0848541\pi$
$390$	−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	−0.610348	−	0.792133i	$-0.708970\pi$
$397$	−7.40366	+	3.56541i	−0.371579	+	0.178943i	0.238769	+	0.971076i	$0.423256\pi$
$398$	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	0.999996	−	0.00286337i	$-0.000911439\pi$
$401$	15.5130	+	19.4527i	0.774684	+	0.971423i	−0.225312	+	0.974287i	$0.572340\pi$
$402$	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	−0.652194	−	0.758052i	$-0.726151\pi$
$409$	−18.4217	+	4.20464i	−0.910895	+	0.207906i	−0.258701	+	0.965958i	$0.583294\pi$
$410$	−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	0.178527	−	0.983935i	$-0.442867\pi$
$419$	−9.81378	−	4.72607i	−0.479435	−	0.230884i	−0.657962	+	0.753051i	$0.728581\pi$
$420$	0.626980	+	0.500000i	0.0305935	+	0.0243975i
$421$	−15.6060	−	12.4453i	−0.760588	−	0.606549i	0.164467	−	0.986383i	$-0.447410\pi$
$421$	−15.6060	−	12.4453i	−0.760588	−	0.606549i	−0.925055	+	0.379834i	$0.875981\pi$
$422$	−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	−0.507514	−	0.861643i	$-0.669436\pi$
$431$	6.71797	−	29.4334i	0.323593	−	1.41776i	0.831108	−	0.556112i	$-0.187707\pi$
$432$	12.4333	−	2.83781i	0.598196	−	0.136534i
$433$	15.7862	−	12.5891i	0.758638	−	0.604994i	−0.165874	−	0.986147i	$-0.553044\pi$
$433$	15.7862	−	12.5891i	0.758638	−	0.604994i	0.924512	+	0.381153i	$0.124473\pi$
$434$	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	0.886193	+	0.463316i	$0.153341\pi$
$439$	−2.37316	+	10.3975i	−0.113265	+	0.496245i	−0.999458	+	0.0329287i	$0.989517\pi$
$440$	−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	0.998445	+	0.0557448i	$0.0177533\pi$
$443$	8.82962	+	18.3349i	0.419508	+	0.871117i	−0.578937	+	0.815372i	$0.696532\pi$
$444$	−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	0.195820	−	0.980640i	$-0.437263\pi$
$449$	−15.1857	−	12.1102i	−0.716659	−	0.571516i	−0.912479	+	0.409124i	$0.865834\pi$
$450$	−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	−0.997526	−	0.0703045i	$-0.977603\pi$
$457$	−2.76391	−	12.1095i	−0.129290	−	0.566457i	0.868236	−	0.496152i	$-0.165254\pi$
$458$	−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	−0.689522	−	0.724265i	$-0.742179\pi$
$461$	−21.3961	+	4.88351i	−0.996514	+	0.227448i	−0.306991	+	0.951712i	$0.599322\pi$
$462$	−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	0.411461	−	0.911427i	$-0.365019\pi$
$467$	25.4487	−	5.80851i	1.17763	−	0.268786i	0.766167	+	0.642642i	$0.222162\pi$
$468$	−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	0.999147	−	0.0413068i	$-0.0131521\pi$
$479$	25.8520	+	20.6163i	1.18121	+	0.941981i	0.182060	+	0.983287i	$0.441724\pi$
$480$	−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	−0.904325	−	0.426845i	$-0.859625\pi$
$487$	−6.33244	+	7.94063i	−0.286950	+	0.359824i	0.617375	+	0.786669i	$0.288196\pi$
$488$	−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	−0.211405	−	0.977399i	$-0.567804\pi$
$491$	15.3879	−	12.2714i	0.694446	−	0.553802i	0.905851	+	0.423596i	$0.139232\pi$
$492$	−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	−1.00000		0.000168534i	$-0.999946\pi$
$499$	−17.3639	+	21.7736i	−0.777315	+	0.974722i	0.222685	+	0.974890i	$0.428518\pi$
$500$	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	0.227413	−	0.973798i	$-0.426973\pi$
$503$	0.219563	+	0.0501138i	0.00978982	+	0.00223446i	−0.217623	+	0.976033i	$0.569830\pi$
$504$	−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	0.864481	−	0.502665i	$-0.167647\pi$
$509$	22.7974	+	10.9786i	1.01048	+	0.486620i	0.145995	+	0.989285i	$0.453362\pi$
$510$			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	−0.328137	−	0.944630i	$-0.606421\pi$
$541$	−24.0418	−	5.48739i	−1.03364	−	0.235921i	−0.705501	+	0.708709i	$0.749278\pi$
$542$	−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	0.707913	+	0.706300i	$0.249637\pi$
$547$	−5.52768	+	24.2183i	−0.236347	+	1.03550i	−0.944259	+	0.329202i	$0.893220\pi$
$548$	−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	−0.873749	−	0.486377i	$-0.838318\pi$
$557$	−4.84146	+	6.07100i	−0.205139	+	0.257237i	0.668610	+	0.743613i	$0.266890\pi$
$558$	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	$0.144429\pi$
$563$			20.8009i			0.876652i	−0.898816	+	0.438326i	$0.855571\pi$
$564$	−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	−0.873856	−	0.486184i	$-0.838388\pi$
$569$	1.21888	−	2.53103i	0.0510981	−	0.106106i	0.924955	+	0.380078i	$0.124103\pi$
$570$	−0.571714	−	0.130490i	−0.0239465	−	0.00546563i
$571$	−2.60603	+	1.25500i	−0.109059	+	0.0525201i	−0.487618	−	0.873057i	$-0.662134\pi$
$571$	−2.60603	+	1.25500i	−0.109059	+	0.0525201i	0.378559	+	0.925577i	$0.376420\pi$
$572$	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	−0.0741270	−	0.997249i	$-0.523617\pi$
$577$	7.00872	−	1.59970i	0.291777	−	0.0665962i	0.365904	+	0.930653i	$0.380760\pi$
$578$	−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	0.891220	+	0.453570i	$0.149850\pi$
$587$	6.90635	+	30.2587i	0.285055	+	1.24891i	−0.606165	+	0.795339i	$0.707293\pi$
$588$	−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	0.962209	−	0.272312i	$-0.0877884\pi$
$593$	32.8560	+	15.8226i	1.34923	+	0.649757i	0.387025	+	0.922069i	$0.373503\pi$
$594$	−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	0.774466	−	0.632615i	$-0.218019\pi$
$599$	29.3144	+	6.69083i	1.19775	+	0.273380i	0.423288	+	0.905995i	$0.360876\pi$
$600$	2.65106	−	1.27669i	0.108229	−	0.0521205i
$601$	−14.3989	−	29.8995i	−0.587342	−	1.21963i	−0.956899	−	0.290420i	$-0.906205\pi$
$601$	−14.3989	−	29.8995i	−0.587342	−	1.21963i	0.369558	−	0.929208i	$-0.379509\pi$
$602$	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	−0.353502	−	0.935434i	$-0.615009\pi$
$607$	11.8214	−	9.42729i	0.479818	−	0.382642i	0.833319	+	0.552792i	$0.186438\pi$
$608$	−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	−0.955244	−	0.295818i	$-0.904408\pi$
$613$	0.835658	−	3.66126i	0.0337519	−	0.147877i	0.988996	+	0.147942i	$0.0472648\pi$
$614$	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	−0.980867	−	0.194681i	$-0.937633\pi$
$617$	−12.9541	−	26.8995i	−0.521514	−	1.08293i	0.459353	−	0.888254i	$-0.348081\pi$
$618$	2.03319	−	0.979132i	0.0817868	−	0.0393865i
$619$	44.9615	+	10.2622i	1.80716	+	0.412472i	0.987139	−	0.159866i	$-0.0511063\pi$
$619$	44.9615	+	10.2622i	1.80716	+	0.412472i	0.820018	+	0.572338i	$0.193963\pi$
$620$	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	0.999558	+	0.0297178i	$0.00946085\pi$
$631$	2.81043	+	12.3133i	0.111881	+	0.490185i	−0.887677	+	0.460467i	$0.847682\pi$
$632$	−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	−0.892843	−	0.450368i	$-0.851293\pi$
$641$	−38.0241	+	8.67874i	−1.50186	+	0.342790i	−0.609017	+	0.793157i	$0.708436\pi$
$642$	1.33124	−	5.83255i	0.0525399	−	0.230192i
$643$	−25.7479	−	32.2869i	−1.01540	−	1.27327i	−0.961523	−	0.274723i	$-0.911414\pi$
$643$	−25.7479	−	32.2869i	−1.01540	−	1.27327i	−0.0538762	−	0.998548i	$-0.517158\pi$
$644$	−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	−0.723306	−	0.690527i	$-0.757378\pi$
$647$	−16.1368	+	7.77109i	−0.634404	+	0.305513i	0.0889021	+	0.996040i	$0.471664\pi$
$648$	−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	0.398164	−	0.917314i	$-0.369647\pi$
$653$	−10.4145	−	8.30529i	−0.407551	−	0.325011i	−0.805715	+	0.592303i	$0.798219\pi$
$654$	−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	0.997217	−	0.0745557i	$-0.0237539\pi$
$659$	8.14213	+	16.9073i	0.317172	+	0.658615i	−0.680045	+	0.733171i	$0.738040\pi$
$660$	0.128334	+	0.562269i	0.00499540	+	0.0218863i
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	−0.985331	−	0.170655i	$-0.945412\pi$
$661$	−15.4182	+	19.3338i	−0.599698	+	0.751998i	0.385633	+	0.922652i	$0.373983\pi$
$662$	−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	−0.987118	−	0.159992i	$-0.948853\pi$
$673$	−15.8632	+	19.8919i	−0.611483	+	0.766775i	0.375636	+	0.926767i	$0.377424\pi$
$674$	−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	0.210954	−	0.977496i	$-0.432343\pi$
$677$	−0.601090	−	0.137195i	−0.0231018	−	0.00527283i	−0.234056	+	0.972223i	$0.575200\pi$
$678$	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	0.0966308	−	0.995320i	$-0.469193\pi$
$683$	−16.2371	−	7.81935i	−0.621294	−	0.299199i	−0.717924	+	0.696121i	$0.754908\pi$
$684$			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	0.906385	−	0.422453i	$-0.138831\pi$
$691$	7.69769	+	9.65260i	0.292834	+	0.367202i	−0.613551	+	0.789655i	$0.710259\pi$
$692$	−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	0.999651	+	0.0264091i	$0.00840724\pi$
$701$	21.2594	+	26.6584i	0.802955	+	1.00687i	−0.196696	+	0.980464i	$0.563021\pi$
$702$	−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	0.977941	−	0.208882i	$-0.0669825\pi$
$709$	37.9267	+	18.2645i	1.42437	+	0.685939i	0.446426	+	0.894821i	$0.352697\pi$
$710$	−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	−0.431667	+	0.902033i	$0.642074\pi$
$719$	−32.5800	+	40.8540i	−1.21503	+	1.52360i	−0.783362	+	0.621566i	$0.786497\pi$
$720$	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	−0.0834876	−	0.996509i	$-0.526606\pi$
$727$	23.4432	−	18.6953i	0.869459	−	0.693370i	0.952947	+	0.303138i	$0.0980345\pi$
$728$	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	0.875417	−	0.483369i	$-0.160587\pi$
$733$	−1.30793	−	2.71595i	−0.0483096	−	0.100316i	−0.923726	+	0.383053i	$0.874873\pi$
$734$	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	0.875525	−	0.483174i	$-0.160516\pi$
$739$	16.2914	+	12.9919i	0.599288	+	0.477916i	−0.276237	+	0.961090i	$0.589087\pi$
$740$	−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	0.498928	+	0.866643i	$0.333727\pi$
$743$	−13.3487	+	27.7189i	−0.489718	+	1.01691i	−0.988646	+	0.150266i	$0.951987\pi$
$744$	−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	−0.301277	−	0.953537i	$-0.597413\pi$
$751$	−4.35715	+	0.994492i	−0.158995	+	0.0362895i	0.142283	+	0.989826i	$0.454556\pi$
$752$	−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	−0.0700652	−	0.997542i	$-0.522321\pi$
$757$	8.24379	−	1.88159i	0.299626	−	0.0683876i	0.369691	+	0.929155i	$0.379464\pi$
$758$	−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	−0.971415	−	0.237388i	$-0.923709\pi$
$761$	−5.49516	−	24.0759i	−0.199199	−	0.872749i	0.772216	−	0.635361i	$-0.219149\pi$
$762$	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	0.948286	−	0.317418i	$-0.102816\pi$
$769$	23.5668	+	18.7939i	0.849839	+	0.677724i	−0.0984462	+	0.995142i	$0.531387\pi$
$770$	−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	0.320892	−	0.947116i	$-0.396018\pi$
$773$	5.53462	+	1.26324i	0.199067	+	0.0454356i	−0.121825	+	0.992552i	$0.538875\pi$
$774$	−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	−0.987223	−	0.159345i	$-0.949062\pi$
$787$	−0.803134	+	3.51876i	−0.0286286	+	0.125430i	0.958594	+	0.284775i	$0.0919190\pi$
$788$	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	0.948929	−	0.315490i	$-0.102169\pi$
$797$	24.0672	+	19.1930i	0.852505	+	0.679850i	−0.0964236	+	0.995340i	$0.530740\pi$
$798$	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	−0.131817	−	0.991274i	$-0.542081\pi$
$809$	5.10598	−	1.16541i	0.179517	−	0.0409735i	0.311334	+	0.950300i	$0.399224\pi$
$810$	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	−0.175701	−	0.984444i	$-0.556219\pi$
$821$	13.8802	−	6.68433i	0.484421	−	0.233285i	0.660121	+	0.751159i	$0.270505\pi$
$822$	−10.3517	−	2.36270i	−0.361056	−	0.0824086i
$823$	15.4705	−	32.1247i	0.539266	−	1.11980i	−0.436241	−	0.899830i	$-0.643690\pi$
$823$	15.4705	−	32.1247i	0.539266	−	1.11980i	0.975507	−	0.219968i	$-0.0705954\pi$
$824$		−	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	−0.972773	−	0.231760i	$-0.925552\pi$
$827$	−40.6973	−	32.4550i	−1.41518	−	1.12857i	−0.442411	−	0.896812i	$-0.645877\pi$
$828$	−13.0233	−	6.27167i	−0.452590	−	0.217956i
$829$			13.4168i			0.465986i	0.972478	+	0.232993i	$0.0748519\pi$
$829$			13.4168i			0.465986i	−0.972478	+	0.232993i	$0.925148\pi$
$830$	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	−0.107294	−	0.994227i	$-0.534218\pi$
$839$	24.2769	−	19.3602i	0.838131	−	0.668387i	0.945425	+	0.325840i	$0.105647\pi$
$840$	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	$0.119020\pi$
$853$			21.3357i			0.730521i	−0.930905	+	0.365261i	$0.880980\pi$
$854$	−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	0.579021	−	0.815313i	$-0.303435\pi$
$857$	8.85839	+	4.26597i	0.302597	+	0.145723i	−0.276424	+	0.961036i	$0.589149\pi$
$858$			12.1099i			0.413426i
$859$	−22.4681	+	46.6555i	−0.766602	+	1.59187i	0.0388778	+	0.999244i	$0.487622\pi$
$859$	−22.4681	+	46.6555i	−0.766602	+	1.59187i	−0.805480	+	0.592623i	$0.798093\pi$
$860$	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	−0.998417	−	0.0562402i	$-0.982089\pi$
$863$	−3.62147	−	15.8667i	−0.123276	−	0.540108i	0.875141	−	0.483868i	$-0.160768\pi$
$864$	−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	−0.999601	−	0.0282623i	$-0.991003\pi$
$877$	−3.29470	−	14.4350i	−0.111254	−	0.487436i	0.888346	−	0.459174i	$-0.151855\pi$
$878$	−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	−0.719190	−	0.694813i	$-0.755487\pi$
$881$	8.08661	−	16.7920i	0.272445	−	0.565737i	0.991635	+	0.129076i	$0.0412012\pi$
$882$			47.4282i			1.59699i
$883$	−29.1857	−	14.0551i	−0.982178	−	0.472992i	−0.127325	−	0.991861i	$-0.540639\pi$
$883$	−29.1857	−	14.0551i	−0.982178	−	0.472992i	−0.854854	+	0.518869i	$0.826353\pi$
$884$	−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	$0.0329929\pi$
$887$			6.16288i			0.206929i	−0.994633	+	0.103465i	$0.967007\pi$
$888$	−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	−0.932375	−	0.361492i	$-0.882267\pi$
$907$	−19.0840	−	39.6284i	−0.633675	−	1.31584i	0.298700	−	0.954347i	$-0.403447\pi$
$908$	−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	$-0.860461\pi$
$911$		−	25.6233i		−	0.848936i	0.905443	−	0.424468i	$-0.139539\pi$
$912$	−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	−0.338828	−	0.940848i	$-0.610030\pi$
$919$	5.62349	−	2.70813i	0.185502	−	0.0893330i	0.524329	+	0.851516i	$0.324316\pi$
$920$	−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	−0.493098	−	0.869974i	$-0.664136\pi$
$937$	−3.68449	+	1.77436i	−0.120367	+	0.0579657i	0.372731	+	0.927939i	$0.378421\pi$
$938$	−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	0.522197	−	0.852825i	$-0.325113\pi$
$941$	5.55280	+	2.67409i	0.181016	+	0.0871728i	−0.341181	+	0.939998i	$0.610827\pi$
$942$	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	−0.656065	−	0.754704i	$-0.727780\pi$
$947$	−48.4562	−	11.0598i	−1.57461	−	0.359395i	−0.918548	+	0.395309i	$0.870638\pi$
$948$	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	0.870335	+	0.492461i	$0.163902\pi$
$953$	−3.93541	+	17.2422i	−0.127480	+	0.558529i	−0.997815	+	0.0660678i	$0.978955\pi$
$954$	−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	0.419800	−	0.907617i	$-0.362100\pi$
$967$	12.5701	+	2.86904i	0.404226	+	0.0922620i	−0.0155736	+	0.999879i	$0.504957\pi$
$968$	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	0.560923	−	0.827868i	$-0.310447\pi$
$971$	−3.78207	−	3.01610i	−0.121372	−	0.0967912i	−0.682295	+	0.731077i	$0.739018\pi$
$972$	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	−0.655575	−	0.755130i	$-0.727574\pi$
$977$	−14.8138	+	7.13394i	−0.473935	+	0.228235i	0.181640	+	0.983365i	$0.441859\pi$
$978$	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	0.210329	−	0.977631i	$-0.432547\pi$
$983$	25.8349	−	5.89666i	0.824007	−	0.188074i	0.613678	+	0.789557i	$0.289689\pi$
$984$	−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	−0.999721	−	0.0236111i	$-0.992484\pi$
$991$	−25.1930	−	31.5910i	−0.800281	−	1.00352i	0.199440	−	0.979910i	$-0.436088\pi$
$992$	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	−0.675366	−	0.737483i	$-0.736014\pi$
$997$	10.1769	−	21.1325i	0.322305	−	0.669273i	0.997671	+	0.0682093i	$0.0217286\pi$
$998$		−	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.63.1		12
29.2	odd	28		841.2.d.a.571.1		6
29.3	odd	28		841.2.d.a.190.1		6
29.4	even	14		841.2.e.c.196.1		12
29.5	even	14		841.2.e.b.270.2		12
29.6	even	14	inner	841.2.e.d.267.1		12
29.7	even	7		841.2.e.b.651.2		12
29.8	odd	28		841.2.a.e.1.1		3
29.9	even	14		841.2.b.c.840.1		6
29.10	odd	28		841.2.d.b.645.1		6
29.11	odd	28		841.2.d.c.605.1		6
29.12	odd	4		29.2.d.a.24.1	yes	6
29.13	even	14		841.2.e.c.236.2		12
29.14	odd	28		841.2.d.d.574.1		6
29.15	odd	28		29.2.d.a.23.1	✓	6
29.16	even	7		841.2.e.c.236.1		12
29.17	odd	4		841.2.d.d.778.1		6
29.18	odd	28		841.2.d.b.605.1		6
29.19	odd	28		841.2.d.c.645.1		6
29.20	even	7		841.2.b.c.840.6		6
29.21	odd	28		841.2.a.f.1.3		3
29.22	even	14		841.2.e.b.651.1		12
29.23	even	7	inner	841.2.e.d.267.2		12
29.24	even	7		841.2.e.b.270.1		12
29.25	even	7		841.2.e.c.196.2		12
29.26	odd	28		841.2.d.e.190.1		6
29.27	odd	28		841.2.d.e.571.1		6
29.28	even	2	inner	841.2.e.d.63.2		12
87.8	even	28		7569.2.a.r.1.3		3
87.41	even	4		261.2.k.a.82.1		6
87.44	even	28		261.2.k.a.226.1		6
87.50	even	28		7569.2.a.p.1.1		3
116.15	even	28		464.2.u.f.81.1		6
116.99	even	4		464.2.u.f.401.1		6
145.12	even	4		725.2.r.b.24.2		12
145.44	odd	28		725.2.l.b.226.1		6
145.73	even	28		725.2.r.b.574.2		12
145.99	odd	4		725.2.l.b.401.1		6
145.102	even	28		725.2.r.b.574.1		12
145.128	even	4		725.2.r.b.24.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.15	odd	28
29.2.d.a.24.1	yes	6	29.12	odd	4
261.2.k.a.82.1		6	87.41	even	4
261.2.k.a.226.1		6	87.44	even	28
464.2.u.f.81.1		6	116.15	even	28
464.2.u.f.401.1		6	116.99	even	4
725.2.l.b.226.1		6	145.44	odd	28
725.2.l.b.401.1		6	145.99	odd	4
725.2.r.b.24.1		12	145.128	even	4
725.2.r.b.24.2		12	145.12	even	4
725.2.r.b.574.1		12	145.102	even	28
725.2.r.b.574.2		12	145.73	even	28
841.2.a.e.1.1		3	29.8	odd	28
841.2.a.f.1.3		3	29.21	odd	28
841.2.b.c.840.1		6	29.9	even	14
841.2.b.c.840.6		6	29.20	even	7
841.2.d.a.190.1		6	29.3	odd	28
841.2.d.a.571.1		6	29.2	odd	28
841.2.d.b.605.1		6	29.18	odd	28
841.2.d.b.645.1		6	29.10	odd	28
841.2.d.c.605.1		6	29.11	odd	28
841.2.d.c.645.1		6	29.19	odd	28
841.2.d.d.574.1		6	29.14	odd	28
841.2.d.d.778.1		6	29.17	odd	4
841.2.d.e.190.1		6	29.26	odd	28
841.2.d.e.571.1		6	29.27	odd	28
841.2.e.b.270.1		12	29.24	even	7
841.2.e.b.270.2		12	29.5	even	14
841.2.e.b.651.1		12	29.22	even	14
841.2.e.b.651.2		12	29.7	even	7
841.2.e.c.196.1		12	29.4	even	14
841.2.e.c.196.2		12	29.25	even	7
841.2.e.c.236.1		12	29.16	even	7
841.2.e.c.236.2		12	29.13	even	14
841.2.e.d.63.1		12	1.1	even	1	trivial
841.2.e.d.63.2		12	29.28	even	2	inner
841.2.e.d.267.1		12	29.6	even	14	inner
841.2.e.d.267.2		12	29.23	even	7	inner
7569.2.a.p.1.1		3	87.50	even	28
7569.2.a.r.1.3		3	87.8	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

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Representations

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Database

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