LMFDB - Embedded newform 847.2.f.w.323.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.3
Root			$0.435488 + 1.34029i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.w.729.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14012 + 0.828347i) q^{2} +(-0.668522 + 2.05750i) q^{3} +(-0.00431527 - 0.0132810i) q^{4} +(1.48162 - 1.07646i) q^{5} +(-2.46652 + 1.79203i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.877057 - 2.69930i) q^{8} +(-1.35932 - 0.987607i) q^{9} +O(q^{10})$	\(q+(1.14012 + 0.828347i) q^{2} +(-0.668522 + 2.05750i) q^{3} +(-0.00431527 - 0.0132810i) q^{4} +(1.48162 - 1.07646i) q^{5} +(-2.46652 + 1.79203i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.877057 - 2.69930i) q^{8} +(-1.35932 - 0.987607i) q^{9} +2.58091 q^{10} +0.0302106 q^{12} +(3.75955 + 2.73147i) q^{13} +(-0.435488 + 1.34029i) q^{14} +(1.22432 + 3.76807i) q^{15} +(3.21332 - 2.33461i) q^{16} +(4.42550 - 3.21531i) q^{17} +(-0.731714 - 2.25198i) q^{18} +(-1.79266 + 5.51725i) q^{19} +(-0.0206901 - 0.0150323i) q^{20} -2.16338 q^{21} -0.719682 q^{23} +(4.96748 + 3.60908i) q^{24} +(-0.508649 + 1.56546i) q^{25} +(2.02374 + 6.22842i) q^{26} +(-2.30990 + 1.67824i) q^{27} +(0.0112975 - 0.00820814i) q^{28} +(-0.362314 - 1.11509i) q^{29} +(-1.72540 + 5.31022i) q^{30} +(1.05809 + 0.768744i) q^{31} -0.0789938 q^{32} +7.70900 q^{34} +(1.48162 + 1.07646i) q^{35} +(-0.00725060 + 0.0223150i) q^{36} +(0.647310 + 1.99221i) q^{37} +(-6.61405 + 4.80539i) q^{38} +(-8.13333 + 5.90921i) q^{39} +(-1.60623 - 4.94347i) q^{40} +(-0.283259 + 0.871781i) q^{41} +(-2.46652 - 1.79203i) q^{42} +8.02379 q^{43} -3.07713 q^{45} +(-0.820525 - 0.596147i) q^{46} +(1.84663 - 5.68336i) q^{47} +(2.65528 + 8.17213i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-1.87667 + 1.36348i) q^{50} +(3.65696 + 11.2550i) q^{51} +(0.0200533 - 0.0617178i) q^{52} +(-8.20742 - 5.96304i) q^{53} -4.02373 q^{54} +2.83822 q^{56} +(-10.1533 - 7.37680i) q^{57} +(0.510598 - 1.57146i) q^{58} +(-2.37350 - 7.30488i) q^{59} +(0.0447607 - 0.0325205i) q^{60} +(5.07749 - 3.68901i) q^{61} +(0.569559 + 1.75292i) q^{62} +(0.519216 - 1.59798i) q^{63} +(-6.51669 - 4.73465i) q^{64} +8.51056 q^{65} -15.4673 q^{67} +(-0.0617999 - 0.0449003i) q^{68} +(0.481123 - 1.48075i) q^{69} +(0.797546 + 2.45459i) q^{70} +(-11.2469 + 8.17134i) q^{71} +(-3.85806 + 2.80304i) q^{72} +(1.85862 + 5.72025i) q^{73} +(-0.912233 + 2.80756i) q^{74} +(-2.88089 - 2.09309i) q^{75} +0.0810106 q^{76} -14.1679 q^{78} +(12.6538 + 9.19351i) q^{79} +(2.24780 - 6.91802i) q^{80} +(-3.46640 - 10.6685i) q^{81} +(-1.04509 + 0.759300i) q^{82} +(3.54004 - 2.57199i) q^{83} +(0.00933558 + 0.0287320i) q^{84} +(3.09576 - 9.52776i) q^{85} +(9.14810 + 6.64648i) q^{86} +2.53651 q^{87} +15.3437 q^{89} +(-3.50830 - 2.54893i) q^{90} +(-1.43602 + 4.41961i) q^{91} +(0.00310563 + 0.00955813i) q^{92} +(-2.28904 + 1.66309i) q^{93} +(6.81318 - 4.95006i) q^{94} +(3.28306 + 10.1042i) q^{95} +(0.0528090 - 0.162530i) q^{96} +(-1.95073 - 1.41729i) q^{97} -1.40927 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9 + 12 * q^10 + 18 * q^12 + 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 + 10 * q^17 - 19 * q^18 - 6 * q^19 - 24 * q^20 + 8 * q^21 + 32 * q^23 + 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 - 11 * q^28 - 12 * q^29 + 38 * q^30 - 2 * q^31 + 32 * q^32 - 24 * q^34 - 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 - 24 * q^39 + 5 * q^40 + 20 * q^41 - 2 * q^42 - 8 * q^43 + 70 * q^45 + 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 - 58 * q^50 + 16 * q^51 + 8 * q^52 - 41 * q^53 + 60 * q^54 + 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 - 12 * q^61 - 61 * q^62 - 12 * q^63 - 3 * q^64 - 8 * q^65 - 38 * q^67 - 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 + 35 * q^72 + 60 * q^73 - 4 * q^74 + 4 * q^75 + 52 * q^76 - 58 * q^78 - 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 + 20 * q^83 - 17 * q^84 - 9 * q^85 + 48 * q^86 - 72 * q^87 + 74 * q^89 + 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 + 66 * q^94 - 53 * q^95 + 48 * q^96 - 35 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.14012	+	0.828347i	0.806188	+	0.585730i	0.912723	−	0.408579i	$-0.133976\pi$
$2$	1.14012	+	0.828347i	0.806188	+	0.585730i	−0.106535	+	0.994309i	$0.533976\pi$
$3$	−0.668522	+	2.05750i	−0.385971	+	1.18790i	0.549802	+	0.835295i	$0.314703\pi$
$3$	−0.668522	+	2.05750i	−0.385971	+	1.18790i	−0.935773	+	0.352602i	$0.885297\pi$
$4$	−0.00431527	−	0.0132810i	−0.00215764	−	0.00664052i
$5$	1.48162	−	1.07646i	0.662602	−	0.481408i	−0.204939	−	0.978775i	$-0.565700\pi$
$5$	1.48162	−	1.07646i	0.662602	−	0.481408i	0.867541	+	0.497366i	$0.165700\pi$
$6$	−2.46652	+	1.79203i	−1.00695	+	0.731593i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.877057	−	2.69930i	0.310086	−	0.954348i
$9$	−1.35932	−	0.987607i	−0.453108	−	0.329202i
$10$	2.58091			0.816157
$11$		0			0
$11$		0			0
$12$	0.0302106			0.00872104
$13$	3.75955	+	2.73147i	1.04271	+	0.757574i	0.970813	−	0.239838i	$-0.0770944\pi$
$13$	3.75955	+	2.73147i	1.04271	+	0.757574i	0.0718980	+	0.997412i	$0.477094\pi$
$14$	−0.435488	+	1.34029i	−0.116389	+	0.358208i
$15$	1.22432	+	3.76807i	0.316118	+	0.972912i
$16$	3.21332	−	2.33461i	0.803329	−	0.583653i
$17$	4.42550	−	3.21531i	1.07334	−	0.779827i	0.0968307	−	0.995301i	$-0.469129\pi$
$17$	4.42550	−	3.21531i	1.07334	−	0.779827i	0.976510	+	0.215473i	$0.0691295\pi$
$18$	−0.731714	−	2.25198i	−0.172467	−	0.530798i
$19$	−1.79266	+	5.51725i	−0.411265	+	1.26574i	0.504285	+	0.863538i	$0.331756\pi$
$19$	−1.79266	+	5.51725i	−0.411265	+	1.26574i	−0.915549	+	0.402206i	$0.868244\pi$
$20$	−0.0206901	−	0.0150323i	−0.00462646	−	0.00336132i
$21$	−2.16338			−0.472088
$22$		0			0
$23$	−0.719682			−0.150064			−0.0750321	−	0.997181i	$-0.523906\pi$
$23$	−0.719682			−0.150064			−0.0750321	+	0.997181i	$0.523906\pi$
$24$	4.96748	+	3.60908i	1.01398	+	0.736701i
$25$	−0.508649	+	1.56546i	−0.101730	+	0.313092i
$26$	2.02374	+	6.22842i	0.396887	+	1.22149i
$27$	−2.30990	+	1.67824i	−0.444540	+	0.322977i
$28$	0.0112975	−	0.00820814i	0.00213503	−	0.00155119i
$29$	−0.362314	−	1.11509i	−0.0672801	−	0.207067i	0.911764	−	0.410714i	$-0.134720\pi$
$29$	−0.362314	−	1.11509i	−0.0672801	−	0.207067i	−0.979044	+	0.203647i	$0.934720\pi$
$30$	−1.72540	+	5.31022i	−0.315013	+	0.969510i
$31$	1.05809	+	0.768744i	0.190038	+	0.138070i	0.678736	−	0.734382i	$-0.262528\pi$
$31$	1.05809	+	0.768744i	0.190038	+	0.138070i	−0.488698	+	0.872453i	$0.662528\pi$
$32$	−0.0789938			−0.0139643
$33$		0			0
$34$	7.70900			1.32208
$35$	1.48162	+	1.07646i	0.250440	+	0.181955i
$36$	−0.00725060	+	0.0223150i	−0.00120843	+	0.00371917i
$37$	0.647310	+	1.99221i	0.106417	+	0.327518i	0.990060	−	0.140643i	$-0.0449168\pi$
$37$	0.647310	+	1.99221i	0.106417	+	0.327518i	−0.883643	+	0.468161i	$0.844917\pi$
$38$	−6.61405	+	4.80539i	−1.07294	+	0.779536i
$39$	−8.13333	+	5.90921i	−1.30238	+	0.946231i
$40$	−1.60623	−	4.94347i	−0.253967	−	0.781631i
$41$	−0.283259	+	0.871781i	−0.0442376	+	0.136149i	−0.970736	−	0.240150i	$-0.922803\pi$
$41$	−0.283259	+	0.871781i	−0.0442376	+	0.136149i	0.926498	+	0.376299i	$0.122803\pi$
$42$	−2.46652	−	1.79203i	−0.380592	−	0.276516i
$43$	8.02379			1.22362			0.611808	−	0.791006i	$-0.290442\pi$
$43$	8.02379			1.22362			0.611808	+	0.791006i	$0.290442\pi$
$44$		0			0
$45$	−3.07713			−0.458711
$46$	−0.820525	−	0.596147i	−0.120980	−	0.0878970i
$47$	1.84663	−	5.68336i	0.269359	−	0.829003i	−0.721298	−	0.692625i	$-0.756454\pi$
$47$	1.84663	−	5.68336i	0.269359	−	0.829003i	0.990657	−	0.136378i	$-0.0435460\pi$
$48$	2.65528	+	8.17213i	0.383257	+	1.17954i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−1.87667	+	1.36348i	−0.265401	+	0.192825i
$51$	3.65696	+	11.2550i	0.512076	+	1.57601i
$52$	0.0200533	−	0.0617178i	0.00278089	−	0.00855871i
$53$	−8.20742	−	5.96304i	−1.12738	−	0.819087i	−0.142065	−	0.989857i	$-0.545374\pi$
$53$	−8.20742	−	5.96304i	−1.12738	−	0.819087i	−0.985311	+	0.170771i	$0.945374\pi$
$54$	−4.02373			−0.547560
$55$		0			0
$56$	2.83822			0.379272
$57$	−10.1533	−	7.37680i	−1.34484	−	0.977080i
$58$	0.510598	−	1.57146i	0.0670448	−	0.206343i
$59$	−2.37350	−	7.30488i	−0.309003	−	0.951014i	−0.978153	−	0.207887i	$-0.933341\pi$
$59$	−2.37350	−	7.30488i	−0.309003	−	0.951014i	0.669150	−	0.743128i	$-0.266659\pi$
$60$	0.0447607	−	0.0325205i	0.00577858	−	0.00419838i
$61$	5.07749	−	3.68901i	0.650106	−	0.472330i	−0.213201	−	0.977008i	$-0.568389\pi$
$61$	5.07749	−	3.68901i	0.650106	−	0.472330i	0.863307	+	0.504679i	$0.168389\pi$
$62$	0.569559	+	1.75292i	0.0723341	+	0.222621i
$63$	0.519216	−	1.59798i	0.0654151	−	0.201327i
$64$	−6.51669	−	4.73465i	−0.814587	−	0.591832i
$65$	8.51056			1.05560
$66$		0			0
$67$	−15.4673			−1.88963			−0.944814	−	0.327608i	$-0.893758\pi$
$67$	−15.4673			−1.88963			−0.944814	+	0.327608i	$0.893758\pi$
$68$	−0.0617999	−	0.0449003i	−0.00749434	−	0.00544496i
$69$	0.481123	−	1.48075i	0.0579204	−	0.178261i
$70$	0.797546	+	2.45459i	0.0953250	+	0.293380i
$71$	−11.2469	+	8.17134i	−1.33476	+	0.969759i	−0.335140	+	0.942168i	$0.608784\pi$
$71$	−11.2469	+	8.17134i	−1.33476	+	0.969759i	−0.999619	+	0.0275910i	$0.991216\pi$
$72$	−3.85806	+	2.80304i	−0.454676	+	0.330342i
$73$	1.85862	+	5.72025i	0.217535	+	0.669504i	0.998964	+	0.0455099i	$0.0144912\pi$
$73$	1.85862	+	5.72025i	0.217535	+	0.669504i	−0.781429	+	0.623994i	$0.785509\pi$
$74$	−0.912233	+	2.80756i	−0.106045	+	0.326373i
$75$	−2.88089	−	2.09309i	−0.332657	−	0.241689i
$76$	0.0810106			0.00929255
$77$		0			0
$78$	−14.1679			−1.60420
$79$	12.6538	+	9.19351i	1.42366	+	1.03435i	0.991153	+	0.132722i	$0.0423716\pi$
$79$	12.6538	+	9.19351i	1.42366	+	1.03435i	0.432509	+	0.901630i	$0.357628\pi$
$80$	2.24780	−	6.91802i	0.251312	−	0.773458i
$81$	−3.46640	−	10.6685i	−0.385156	−	1.18539i
$82$	−1.04509	+	0.759300i	−0.115411	+	0.0838507i
$83$	3.54004	−	2.57199i	0.388570	−	0.282313i	−0.376299	−	0.926498i	$-0.622804\pi$
$83$	3.54004	−	2.57199i	0.388570	−	0.282313i	0.764869	+	0.644186i	$0.222804\pi$
$84$	0.00933558	+	0.0287320i	0.00101860	+	0.00313491i
$85$	3.09576	−	9.52776i	0.335782	−	1.03343i
$86$	9.14810	+	6.64648i	0.986465	+	0.716708i
$87$	2.53651			0.271942
$88$		0			0
$89$	15.3437			1.62643			0.813215	−	0.581963i	$-0.197715\pi$
$89$	15.3437			1.62643			0.813215	+	0.581963i	$0.197715\pi$
$90$	−3.50830	−	2.54893i	−0.369807	−	0.268681i
$91$	−1.43602	+	4.41961i	−0.150536	+	0.463301i
$92$	0.00310563	+	0.00955813i	0.000323784	+	0.000996504i
$93$	−2.28904	+	1.66309i	−0.237363	+	0.172454i
$94$	6.81318	−	4.95006i	0.702726	−	0.510560i
$95$	3.28306	+	10.1042i	0.336835	+	1.03667i
$96$	0.0528090	−	0.162530i	0.00538980	−	0.0165881i
$97$	−1.95073	−	1.41729i	−0.198067	−	0.143904i	0.484331	−	0.874885i	$-0.339063\pi$
$97$	−1.95073	−	1.41729i	−0.198067	−	0.143904i	−0.682398	+	0.730981i	$0.739063\pi$
$98$	−1.40927			−0.142358
$99$		0			0
$100$	0.0229859			0.00229859
$101$	−9.62396	−	6.99222i	−0.957620	−	0.695752i	−0.00502316	−	0.999987i	$-0.501599\pi$
$101$	−9.62396	−	6.99222i	−0.957620	−	0.695752i	−0.952597	+	0.304236i	$0.901599\pi$
$102$	−5.15363	+	15.8612i	−0.510285	+	1.57050i
$103$	0.122468	+	0.376917i	0.0120671	+	0.0371387i	0.956909	−	0.290389i	$-0.0937846\pi$
$103$	0.122468	+	0.376917i	0.0120671	+	0.0371387i	−0.944842	+	0.327527i	$0.893785\pi$
$104$	10.6704	−	7.75250i	1.04632	−	0.760195i
$105$	−3.20531	+	2.32880i	−0.312807	+	0.227267i
$106$	−4.41799	−	13.5972i	−0.429113	−	1.32068i
$107$	−1.01029	+	3.10934i	−0.0976680	+	0.300591i	−0.987940	−	0.154838i	$-0.950514\pi$
$107$	−1.01029	+	3.10934i	−0.0976680	+	0.300591i	0.890272	+	0.455430i	$0.150514\pi$
$108$	0.0322566	+	0.0234358i	0.00310389	+	0.00225511i
$109$	−2.84638			−0.272634			−0.136317	−	0.990665i	$-0.543527\pi$
$109$	−2.84638			−0.272634			−0.136317	+	0.990665i	$0.543527\pi$
$110$		0			0
$111$	−4.53172			−0.430132
$112$	3.21332	+	2.33461i	0.303630	+	0.220600i
$113$	4.49451	−	13.8327i	0.422807	−	1.30127i	−0.482271	−	0.876022i	$-0.660188\pi$
$113$	4.49451	−	13.8327i	0.422807	−	1.30127i	0.905078	−	0.425245i	$-0.139812\pi$
$114$	−5.46544	−	16.8209i	−0.511885	−	1.57542i
$115$	−1.06630	+	0.774711i	−0.0994328	+	0.0722421i
$116$	−0.0132461	+	0.00962382i	−0.00122987	+	0.000893550i
$117$	−2.41283	−	7.42591i	−0.223066	−	0.686526i
$118$	3.34490	−	10.2945i	0.307923	−	0.947688i
$119$	4.42550	+	3.21531i	0.405685	+	0.294747i
$120$	11.2450			1.02652
$121$		0			0
$122$	8.84474			0.800765
$123$	−1.60432	−	1.16561i	−0.144657	−	0.105099i
$124$	0.00564379	−	0.0173698i	0.000506828	−	0.00155986i
$125$	3.76118	+	11.5757i	0.336410	+	1.03536i
$126$	1.91565	−	1.39180i	0.170660	−	0.123992i
$127$	−4.07168	+	2.95825i	−0.361303	+	0.262502i	−0.753595	−	0.657339i	$-0.771682\pi$
$127$	−4.07168	+	2.95825i	−0.361303	+	0.262502i	0.392292	+	0.919841i	$0.371682\pi$
$128$	−3.45907	−	10.6459i	−0.305741	−	0.940974i
$129$	−5.36408	+	16.5089i	−0.472281	+	1.45353i
$130$	9.70307	+	7.04969i	0.851015	+	0.618299i
$131$	−0.180053			−0.0157313			−0.00786565	−	0.999969i	$-0.502504\pi$
$131$	−0.180053			−0.0157313			−0.00786565	+	0.999969i	$0.502504\pi$
$132$		0			0
$133$	−5.80118			−0.503026
$134$	−17.6346	−	12.8123i	−1.52339	−	1.10681i
$135$	−1.61584	+	4.97304i	−0.139069	+	0.428011i
$136$	−4.79769	−	14.7658i	−0.411398	−	1.26615i
$137$	−6.73422	+	4.89270i	−0.575343	+	0.418011i	−0.837042	−	0.547138i	$-0.815717\pi$
$137$	−6.73422	+	4.89270i	−0.575343	+	0.418011i	0.261699	+	0.965150i	$0.415717\pi$
$138$	1.77511	−	1.28969i	0.151107	−	0.109786i
$139$	−2.15113	−	6.62049i	−0.182456	−	0.561543i	0.817439	−	0.576015i	$-0.195393\pi$
$139$	−2.15113	−	6.62049i	−0.182456	−	0.561543i	−0.999895	+	0.0144726i	$0.995393\pi$
$140$	0.00790293	−	0.0243227i	0.000667920	−	0.00205565i
$141$	10.4590	+	7.59889i	0.880805	+	0.639942i
$142$	−19.5915			−1.64408
$143$		0			0
$144$	−6.67362			−0.556135
$145$	−1.73716	−	1.26212i	−0.144264	−	0.104814i
$146$	−2.61929	+	8.06136i	−0.216774	+	0.667163i
$147$	−0.668522	−	2.05750i	−0.0551387	−	0.169700i
$148$	0.0236654	−	0.0171939i	0.00194528	−	0.00141333i
$149$	2.60043	−	1.88933i	0.213036	−	0.154780i	−0.476150	−	0.879364i	$-0.657968\pi$
$149$	2.60043	−	1.88933i	0.213036	−	0.154780i	0.689186	+	0.724584i	$0.257968\pi$
$150$	−1.55076	−	4.77275i	−0.126619	−	0.389694i
$151$	6.88088	−	21.1772i	0.559958	−	1.72337i	−0.122517	−	0.992466i	$-0.539097\pi$
$151$	6.88088	−	21.1772i	0.559958	−	1.72337i	0.682476	−	0.730908i	$-0.260903\pi$
$152$	13.3205	+	9.67788i	1.08043	+	0.784979i
$153$	−9.19115			−0.743061
$154$		0			0
$155$	2.39521			0.192388
$156$	0.113578	+	0.0825193i	0.00909352	+	0.00660683i
$157$	4.09595	−	12.6060i	0.326892	−	1.00607i	−0.643687	−	0.765289i	$-0.722596\pi$
$157$	4.09595	−	12.6060i	0.326892	−	1.00607i	0.970579	−	0.240782i	$-0.0774040\pi$
$158$	6.81144	+	20.9634i	0.541889	+	1.66776i
$159$	17.7558	−	12.9003i	1.40813	−	1.02306i
$160$	−0.117039	+	0.0850338i	−0.00925274	+	0.00672251i
$161$	−0.222394	−	0.684459i	−0.0175271	−	0.0539429i
$162$	4.88509	−	15.0348i	0.383809	−	1.18124i
$163$	−11.0984	−	8.06344i	−0.869292	−	0.631577i	0.0611050	−	0.998131i	$-0.480538\pi$
$163$	−11.0984	−	8.06344i	−0.869292	−	0.631577i	−0.930397	+	0.366554i	$0.880538\pi$
$164$	0.0128005			0.000999552
$165$		0			0
$166$	6.16657			0.478619
$167$	−7.53081	−	5.47146i	−0.582752	−	0.423394i	0.256963	−	0.966421i	$-0.417278\pi$
$167$	−7.53081	−	5.47146i	−0.582752	−	0.423394i	−0.839715	+	0.543027i	$0.817278\pi$
$168$	−1.89741	+	5.83962i	−0.146388	+	0.450537i
$169$	2.65604	+	8.17446i	0.204311	+	0.628804i
$170$	11.4218	−	8.29844i	0.876014	−	0.636461i
$171$	7.88568	−	5.72928i	0.603033	−	0.438129i
$172$	−0.0346248	−	0.106564i	−0.00264012	−	0.00812545i
$173$	3.24643	−	9.99149i	0.246822	−	0.759639i	−0.748510	−	0.663124i	$-0.769230\pi$
$173$	3.24643	−	9.99149i	0.246822	−	0.759639i	0.995331	−	0.0965154i	$-0.0307697\pi$
$174$	2.89193	+	2.10111i	0.219236	+	0.159285i
$175$	−1.64602			−0.124428
$176$		0			0
$177$	16.6165			1.24897
$178$	17.4937	+	12.7099i	1.31121	+	0.952648i
$179$	−2.57204	+	7.91594i	−0.192244	+	0.591665i	0.807754	+	0.589520i	$0.200683\pi$
$179$	−2.57204	+	7.91594i	−0.192244	+	0.591665i	−0.999998	+	0.00214538i	$0.999317\pi$
$180$	0.0132786	+	0.0408675i	0.000989732	+	0.00304608i
$181$	11.9758	−	8.70096i	0.890158	−	0.646738i	−0.0457613	−	0.998952i	$-0.514571\pi$
$181$	11.9758	−	8.70096i	0.890158	−	0.646738i	0.935919	+	0.352215i	$0.114571\pi$
$182$	−5.29821	+	3.84937i	−0.392729	+	0.285335i
$183$	4.19572	+	12.9131i	0.310157	+	0.954565i
$184$	−0.631202	+	1.94264i	−0.0465329	+	0.143213i
$185$	3.10361	+	2.25491i	0.228182	+	0.165784i
$186$	−3.98740			−0.292370
$187$		0			0
$188$	−0.0834496			−0.00608619
$189$	−2.30990	−	1.67824i	−0.168020	−	0.122074i
$190$	−4.62671	+	14.2395i	−0.335657	+	1.03304i
$191$	−2.96865	−	9.13657i	−0.214804	−	0.661099i	−0.999167	−	0.0407974i	$-0.987010\pi$
$191$	−2.96865	−	9.13657i	−0.214804	−	0.661099i	0.784363	−	0.620302i	$-0.212990\pi$
$192$	14.0981	−	10.2429i	1.01744	−	0.739215i
$193$	1.20366	−	0.874512i	0.0866415	−	0.0629487i	−0.543621	−	0.839331i	$-0.682947\pi$
$193$	1.20366	−	0.874512i	0.0866415	−	0.0629487i	0.630263	+	0.776382i	$0.282947\pi$
$194$	−1.05007	−	3.23177i	−0.0753903	−	0.232027i
$195$	−5.68949	+	17.5104i	−0.407433	+	1.25395i
$196$	0.0112975	+	0.00820814i	0.000806966	+	0.000586295i
$197$	−14.0434			−1.00055			−0.500274	−	0.865867i	$-0.666767\pi$
$197$	−14.0434			−1.00055			−0.500274	+	0.865867i	$0.666767\pi$
$198$		0			0
$199$	−4.28729			−0.303918			−0.151959	−	0.988387i	$-0.548558\pi$
$199$	−4.28729			−0.303918			−0.151959	+	0.988387i	$0.548558\pi$
$200$	3.77954	+	2.74600i	0.267254	+	0.194171i
$201$	10.3402	−	31.8239i	0.729342	−	2.24468i
$202$	−5.18050	−	15.9440i	−0.364499	−	1.12181i
$203$	0.948551	−	0.689163i	0.0665753	−	0.0483698i
$204$	0.133697	−	0.0971364i	0.00936064	−	0.00680091i
$205$	0.518757	+	1.59657i	0.0362315	+	0.111509i
$206$	−0.172590	+	0.531177i	−0.0120249	+	0.0370088i
$207$	0.978282	+	0.710764i	0.0679953	+	0.0494015i
$208$	18.4575			1.27980
$209$		0			0
$210$	−5.58350			−0.385298
$211$	1.17734	+	0.855387i	0.0810514	+	0.0588873i	0.627573	−	0.778558i	$-0.284048\pi$
$211$	1.17734	+	0.855387i	0.0810514	+	0.0588873i	−0.546522	+	0.837445i	$0.684048\pi$
$212$	−0.0437781	+	0.134735i	−0.00300670	+	0.00925366i
$213$	−9.29373	−	28.6031i	−0.636796	−	1.95986i
$214$	−3.72746	+	2.70816i	−0.254804	+	0.185126i
$215$	11.8882	−	8.63730i	0.810771	−	0.589059i
$216$	2.50416	+	7.70703i	0.170387	+	0.524397i
$217$	−0.404153	+	1.24385i	−0.0274357	+	0.0844383i
$218$	−3.24522	−	2.35779i	−0.219794	−	0.159690i
$219$	−13.0119			−0.879264
$220$		0			0
$221$	25.4204			1.70996
$222$	−5.16671	−	3.75383i	−0.346767	−	0.251941i
$223$	−1.50072	+	4.61873i	−0.100495	+	0.309293i	−0.988647	−	0.150258i	$-0.951990\pi$
$223$	−1.50072	+	4.61873i	−0.100495	+	0.309293i	0.888151	+	0.459551i	$0.151990\pi$
$224$	−0.0244104	−	0.0751275i	−0.00163099	−	0.00501967i
$225$	2.23748	−	1.62563i	0.149165	−	0.108375i
$226$	16.5825	−	12.0479i	1.10305	−	0.801415i
$227$	0.122724	+	0.377706i	0.00814549	+	0.0250692i	0.955047	−	0.296456i	$-0.0958047\pi$
$227$	0.122724	+	0.377706i	0.00814549	+	0.0250692i	−0.946901	+	0.321525i	$0.895805\pi$
$228$	−0.0541573	+	0.166679i	−0.00358666	+	0.0110386i
$229$	−1.77145	−	1.28703i	−0.117061	−	0.0850496i	0.527715	−	0.849422i	$-0.323049\pi$
$229$	−1.77145	−	1.28703i	−0.117061	−	0.0850496i	−0.644775	+	0.764372i	$0.723049\pi$
$230$	−1.85744			−0.122476
$231$		0			0
$232$	−3.32773			−0.218476
$233$	1.01949	+	0.740701i	0.0667888	+	0.0485249i	0.620679	−	0.784065i	$-0.286857\pi$
$233$	1.01949	+	0.740701i	0.0667888	+	0.0485249i	−0.553890	+	0.832590i	$0.686857\pi$
$234$	3.40032	−	10.4651i	0.222286	−	0.684125i
$235$	−3.38190	−	10.4084i	−0.220611	−	0.678971i
$236$	−0.0867741	+	0.0630451i	−0.00564851	+	0.00410389i
$237$	−27.3750	+	19.8891i	−1.77820	+	1.29193i
$238$	2.38221	+	7.33169i	0.154416	+	0.475243i
$239$	−3.44914	+	10.6154i	−0.223106	+	0.686651i	0.775372	+	0.631505i	$0.217562\pi$
$239$	−3.44914	+	10.6154i	−0.223106	+	0.686651i	−0.998478	+	0.0551459i	$0.982438\pi$
$240$	12.7311	+	9.24969i	0.821790	+	0.597065i
$241$	−21.4843			−1.38392			−0.691962	−	0.721934i	$-0.743254\pi$
$241$	−21.4843			−1.38392			−0.691962	+	0.721934i	$0.743254\pi$
$242$		0			0
$243$	15.7022			1.00730
$244$	−0.0709047	−	0.0515153i	−0.00453921	−	0.00329793i
$245$	−0.565930	+	1.74175i	−0.0361559	+	0.111276i
$246$	−0.863595	−	2.65787i	−0.0550608	−	0.169460i
$247$	−21.8098	+	15.8457i	−1.38772	+	1.00824i
$248$	3.00307	−	2.18186i	0.190695	−	0.138548i
$249$	2.92527	+	9.00305i	0.185381	+	0.570545i
$250$	−5.30051	+	16.3133i	−0.335234	+	1.03174i
$251$	0.342877	+	0.249115i	0.0216422	+	0.0157240i	0.598554	−	0.801083i	$-0.295742\pi$
$251$	0.342877	+	0.249115i	0.0216422	+	0.0157240i	−0.576912	+	0.816807i	$0.695742\pi$
$252$	−0.0234634			−0.00147806
$253$		0			0
$254$	−7.09267			−0.445033
$255$	17.5338	+	12.7390i	1.09801	+	0.797748i
$256$	−0.103561	+	0.318729i	−0.00647259	+	0.0199206i
$257$	5.38928	+	16.5865i	0.336174	+	1.03464i	0.966141	+	0.258015i	$0.0830684\pi$
$257$	5.38928	+	16.5865i	0.336174	+	1.03464i	−0.629967	+	0.776622i	$0.716932\pi$
$258$	−19.7908	+	14.3789i	−1.23212	+	0.895189i
$259$	−1.69468	+	1.23126i	−0.105302	+	0.0765066i
$260$	−0.0367254	−	0.113029i	−0.00227761	−	0.00700976i
$261$	−0.608767	+	1.87359i	−0.0376817	+	0.115972i
$262$	−0.205282	−	0.149146i	−0.0126824	−	0.00921429i
$263$	1.51519			0.0934307			0.0467153	−	0.998908i	$-0.485125\pi$
$263$	1.51519			0.0934307			0.0467153	+	0.998908i	$0.485125\pi$
$264$		0			0
$265$	−18.5793			−1.14132
$266$	−6.61405	−	4.80539i	−0.405533	−	0.294637i
$267$	−10.2576	+	31.5697i	−0.627755	+	1.93203i
$268$	0.0667455	+	0.205421i	0.00407713	+	0.0125481i
$269$	1.64314	−	1.19381i	0.100184	−	0.0727878i	−0.536566	−	0.843859i	$-0.680279\pi$
$269$	1.64314	−	1.19381i	0.100184	−	0.0727878i	0.636749	+	0.771071i	$0.280279\pi$
$270$	−5.96165	+	4.33139i	−0.362814	+	0.263600i
$271$	2.34990	+	7.23225i	0.142746	+	0.439328i	0.996714	−	0.0809976i	$-0.0258106\pi$
$271$	2.34990	+	7.23225i	0.142746	+	0.439328i	−0.853968	+	0.520326i	$0.825811\pi$
$272$	6.71402	−	20.6636i	0.407097	−	1.25292i
$273$	−8.13333	−	5.90921i	−0.492252	−	0.357642i
$274$	−11.7307			−0.708676
$275$		0			0
$276$	−0.0217420			−0.00130872
$277$	−11.6715	−	8.47987i	−0.701274	−	0.509506i	0.179073	−	0.983836i	$-0.442690\pi$
$277$	−11.6715	−	8.47987i	−0.701274	−	0.509506i	−0.880347	+	0.474330i	$0.842690\pi$
$278$	3.03151	−	9.33004i	0.181818	−	0.559579i
$279$	−0.679064	−	2.08995i	−0.0406545	−	0.125122i
$280$	4.20516	−	3.05523i	0.251307	−	0.182585i
$281$	−14.3598	+	10.4330i	−0.856632	+	0.622379i	−0.926967	−	0.375144i	$-0.877593\pi$
$281$	−14.3598	+	10.4330i	−0.856632	+	0.622379i	0.0703347	+	0.997523i	$0.477593\pi$
$282$	5.62999	+	17.3273i	0.335261	+	1.03183i
$283$	−9.62160	+	29.6122i	−0.571945	+	1.76026i	0.0744107	+	0.997228i	$0.476292\pi$
$283$	−9.62160	+	29.6122i	−0.571945	+	1.76026i	−0.646355	+	0.763037i	$0.723708\pi$
$284$	0.157057	+	0.114109i	0.00931963	+	0.00677111i
$285$	−22.9842			−1.36147
$286$		0			0
$287$	−0.916645			−0.0541079
$288$	0.107378	+	0.0780148i	0.00632732	+	0.00459707i
$289$	3.99350	−	12.2907i	0.234912	−	0.722984i
$290$	−0.935102	−	2.87795i	−0.0549111	−	0.168999i
$291$	4.22018	−	3.06614i	0.247391	−	0.179740i
$292$	0.0679504	−	0.0493689i	0.00397650	−	0.00288909i
$293$	−7.42577	−	22.8542i	−0.433818	−	1.33515i	−0.894293	−	0.447482i	$-0.852321\pi$
$293$	−7.42577	−	22.8542i	−0.433818	−	1.33515i	0.460475	−	0.887673i	$-0.347679\pi$
$294$	0.942126	−	2.89957i	0.0549459	−	0.169106i
$295$	−11.3801	−	8.26809i	−0.662572	−	0.481387i
$296$	5.94532			0.345565
$297$		0			0
$298$	4.52983			0.262406
$299$	−2.70568	−	1.96579i	−0.156474	−	0.113685i
$300$	−0.0153666	+	0.0472935i	−0.000887190	+	0.00273049i
$301$	2.47949	+	7.63108i	0.142915	+	0.439848i
$302$	25.3871	−	18.4448i	1.46086	−	1.06138i
$303$	20.8203	−	15.1268i	1.19609	−	0.869014i
$304$	7.12023	+	21.9138i	0.408373	+	1.25684i
$305$	3.55184	−	10.9315i	0.203378	−	0.625933i
$306$	−10.4790	−	7.61346i	−0.599046	−	0.435233i
$307$	−5.46298			−0.311789			−0.155894	−	0.987774i	$-0.549826\pi$
$307$	−5.46298			−0.311789			−0.155894	+	0.987774i	$0.549826\pi$
$308$		0			0
$309$	−0.857378			−0.0487745
$310$	2.73083	+	1.98406i	0.155101	+	0.112687i
$311$	4.29176	−	13.2087i	0.243364	−	0.748996i	−0.752538	−	0.658549i	$-0.771170\pi$
$311$	4.29176	−	13.2087i	0.243364	−	0.748996i	0.995901	−	0.0904468i	$-0.0288295\pi$
$312$	8.81736	+	27.1371i	0.499185	+	1.53633i
$313$	−22.2064	+	16.1339i	−1.25518	+	0.911940i	−0.998510	−	0.0545602i	$-0.982624\pi$
$313$	−22.2064	+	16.1339i	−1.25518	+	0.911940i	−0.256667	+	0.966500i	$0.582624\pi$
$314$	15.1121	−	10.9796i	0.852823	−	0.619612i
$315$	−0.950885	−	2.92652i	−0.0535763	−	0.164891i
$316$	0.0674949	−	0.207728i	0.00379689	−	0.0116856i
$317$	−6.33113	−	4.59983i	−0.355592	−	0.258352i	0.395619	−	0.918415i	$-0.370530\pi$
$317$	−6.33113	−	4.59983i	−0.355592	−	0.258352i	−0.751211	+	0.660062i	$0.770530\pi$
$318$	30.9297			1.73445
$319$		0			0
$320$	−14.7520			−0.824659
$321$	−5.72206	−	4.15732i	−0.319374	−	0.232039i
$322$	0.313413	−	0.964586i	0.0174658	−	0.0537543i
$323$	9.80624	+	30.1805i	0.545634	+	1.67929i
$324$	−0.126730	+	0.0920749i	−0.00704057	+	0.00511527i
$325$	−6.18831	+	4.49607i	−0.343265	+	0.249397i
$326$	−5.97417	−	18.3866i	−0.330879	−	1.01834i
$327$	1.90287	−	5.85643i	0.105229	−	0.323861i
$328$	2.10477	+	1.52920i	0.116216	+	0.0844361i
$329$	5.97584			0.329458
$330$		0			0
$331$	−28.1462			−1.54705			−0.773527	−	0.633764i	$-0.781509\pi$
$331$	−28.1462			−1.54705			−0.773527	+	0.633764i	$0.781509\pi$
$332$	−0.0494349	−	0.0359166i	−0.00271309	−	0.00197118i
$333$	1.08762	−	3.34736i	0.0596013	−	0.183434i
$334$	−4.05378	−	12.4762i	−0.221813	−	0.682670i
$335$	−22.9167	+	16.6499i	−1.25207	+	0.909683i
$336$	−6.95163	+	5.05065i	−0.379242	+	0.275536i
$337$	−7.71892	−	23.7564i	−0.420476	−	1.29409i	−0.907260	−	0.420570i	$-0.861830\pi$
$337$	−7.71892	−	23.7564i	−0.420476	−	1.29409i	0.486784	−	0.873523i	$-0.338170\pi$
$338$	−3.74308	+	11.5200i	−0.203596	+	0.626605i
$339$	25.4560	+	18.4949i	1.38258	+	1.00450i
$340$	−0.139898			−0.00758701
$341$		0			0
$342$	13.7365			0.742783
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	7.03732	−	21.6586i	0.379427	−	1.16776i
$345$	−0.881123	−	2.71182i	−0.0474380	−	0.145999i
$346$	11.9778	−	8.70235i	0.643928	−	0.467841i
$347$	−16.7056	+	12.1373i	−0.896802	+	0.651565i	−0.937643	−	0.347601i	$-0.886997\pi$
$347$	−16.7056	+	12.1373i	−0.896802	+	0.651565i	0.0408403	+	0.999166i	$0.486997\pi$
$348$	−0.0109457	−	0.0336875i	−0.000586752	−	0.00180584i
$349$	−1.85324	+	5.70369i	−0.0992017	+	0.305311i	−0.988326	−	0.152355i	$-0.951314\pi$
$349$	−1.85324	+	5.70369i	−0.0992017	+	0.305311i	0.889124	+	0.457666i	$0.151314\pi$
$350$	−1.87667	−	1.36348i	−0.100312	−	0.0728810i
$351$	−13.2682			−0.708206
$352$		0			0
$353$	24.0382			1.27942			0.639712	−	0.768615i	$-0.279054\pi$
$353$	24.0382			1.27942			0.639712	+	0.768615i	$0.279054\pi$
$354$	18.9448	+	13.7642i	1.00691	+	0.731561i
$355$	−7.86750	+	24.2137i	−0.417564	+	1.28513i
$356$	−0.0662123	−	0.203780i	−0.00350924	−	0.0108003i
$357$	−9.57403	+	6.95594i	−0.506712	+	0.368148i
$358$	−9.48958	+	6.89459i	−0.501540	+	0.364390i
$359$	−3.38377	−	10.4142i	−0.178589	−	0.549640i	0.821190	−	0.570654i	$-0.193310\pi$
$359$	−3.38377	−	10.4142i	−0.178589	−	0.549640i	−0.999779	+	0.0210147i	$0.993310\pi$
$360$	−2.69882	+	8.30610i	−0.142240	+	0.437770i
$361$	−11.8550	−	8.61319i	−0.623950	−	0.453326i
$362$	20.8613			1.09645
$363$		0			0
$364$	0.0648939			0.00340136
$365$	8.91140	+	6.47451i	0.466444	+	0.338892i
$366$	−5.91290	+	18.1980i	−0.309072	+	0.951226i
$367$	3.28107	+	10.0981i	0.171270	+	0.527116i	0.999444	−	0.0333563i	$-0.0106196\pi$
$367$	3.28107	+	10.0981i	0.171270	+	0.527116i	−0.828173	+	0.560472i	$0.810620\pi$
$368$	−2.31257	+	1.68018i	−0.120551	+	0.0875853i
$369$	1.24602	−	0.905286i	0.0648651	−	0.0471273i
$370$	1.67065	+	5.14173i	0.0868530	+	0.267306i
$371$	3.13496	−	9.64840i	0.162759	−	0.500920i
$372$	0.0319654	+	0.0232242i	0.00165733	+	0.00120412i
$373$	36.6036			1.89526			0.947631	−	0.319367i	$-0.103470\pi$
$373$	36.6036			1.89526			0.947631	+	0.319367i	$0.103470\pi$
$374$		0			0
$375$	−26.3315			−1.35975
$376$	−13.7215	−	9.96925i	−0.707632	−	0.514125i
$377$	1.68370	−	5.18188i	0.0867147	−	0.266880i
$378$	−1.24340	−	3.82679i	−0.0639536	−	0.196829i
$379$	10.2404	−	7.44005i	0.526012	−	0.382170i	−0.292852	−	0.956158i	$-0.594604\pi$
$379$	10.2404	−	7.44005i	0.526012	−	0.382170i	0.818864	+	0.573988i	$0.194604\pi$
$380$	0.120027	−	0.0872048i	0.00615726	−	0.00447351i
$381$	−3.36458	−	10.3551i	−0.172373	−	0.530509i
$382$	4.18363	−	12.8759i	0.214053	−	0.658787i
$383$	12.5138	+	9.09179i	0.639424	+	0.464569i	0.859652	−	0.510879i	$-0.170680\pi$
$383$	12.5138	+	9.09179i	0.639424	+	0.464569i	−0.220228	+	0.975448i	$0.570680\pi$
$384$	24.2164			1.23579
$385$		0			0
$386$	2.09672			0.106720
$387$	−10.9069	−	7.92435i	−0.554431	−	0.402818i
$388$	−0.0104052	+	0.0320238i	−0.000528242	+	0.00162576i
$389$	−3.92852	−	12.0907i	−0.199184	−	0.613025i	−0.999902	−	0.0139838i	$-0.995549\pi$
$389$	−3.92852	−	12.0907i	−0.199184	−	0.613025i	0.800718	−	0.599041i	$-0.204451\pi$
$390$	−20.9914	+	15.2512i	−1.06294	+	0.772273i
$391$	−3.18495	+	2.31400i	−0.161070	+	0.117024i
$392$	0.877057	+	2.69930i	0.0442981	+	0.136335i
$393$	0.120369	−	0.370459i	0.00607183	−	0.0186872i
$394$	−16.0111	−	11.6328i	−0.806630	−	0.586051i
$395$	28.6446			1.44127
$396$		0			0
$397$	−18.9574			−0.951445			−0.475722	−	0.879596i	$-0.657813\pi$
$397$	−18.9574			−0.951445			−0.475722	+	0.879596i	$0.657813\pi$
$398$	−4.88803	−	3.55136i	−0.245015	−	0.178014i
$399$	3.87821	−	11.9359i	0.194153	−	0.597543i
$400$	2.02029	+	6.21782i	0.101015	+	0.310891i
$401$	7.02395	−	5.10320i	0.350759	−	0.254842i	−0.398428	−	0.917200i	$-0.630444\pi$
$401$	7.02395	−	5.10320i	0.350759	−	0.254842i	0.749188	+	0.662358i	$0.230444\pi$
$402$	38.1503	−	27.7178i	1.90276	−	1.38244i
$403$	1.87812	+	5.78026i	0.0935558	+	0.287935i
$404$	−0.0513339	+	0.157990i	−0.00255396	+	0.00786027i
$405$	−16.6201	−	12.0752i	−0.825861	−	0.600023i
$406$	1.65233			0.0820037
$407$		0			0
$408$	33.5879			1.66285
$409$	−4.62277	−	3.35864i	−0.228581	−	0.166074i	0.467600	−	0.883940i	$-0.345119\pi$
$409$	−4.62277	−	3.35864i	−0.228581	−	0.166074i	−0.696181	+	0.717866i	$0.745119\pi$
$410$	−0.731067	+	2.24999i	−0.0361048	+	0.111119i
$411$	−5.56474	−	17.1265i	−0.274489	−	0.844789i
$412$	0.00447737	−	0.00325300i	0.000220584	−	0.000160264i
$413$	6.21390	−	4.51466i	0.305766	−	0.222152i
$414$	0.526602	+	1.62071i	0.0258811	+	0.0796537i
$415$	2.47635	−	7.62144i	0.121559	−	0.374122i
$416$	−0.296981	−	0.215769i	−0.0145607	−	0.0105790i
$417$	15.0597			0.737477
$418$		0			0
$419$	−27.1909			−1.32836			−0.664181	−	0.747571i	$-0.731220\pi$
$419$	−27.1909			−1.32836			−0.664181	+	0.747571i	$0.731220\pi$
$420$	0.0447607	+	0.0325205i	0.00218410	+	0.00158684i
$421$	−7.40561	+	22.7921i	−0.360928	+	1.11082i	0.591565	+	0.806258i	$0.298510\pi$
$421$	−7.40561	+	22.7921i	−0.360928	+	1.11082i	−0.952492	+	0.304563i	$0.901490\pi$
$422$	0.633753	+	1.95049i	0.0308506	+	0.0949484i
$423$	−8.12310	+	5.90178i	−0.394959	+	0.286954i
$424$	−23.2944	+	16.9244i	−1.13128	+	0.821921i
$425$	2.78242	+	8.56341i	0.134967	+	0.415386i
$426$	13.0973	−	40.3095i	0.634569	−	1.95300i
$427$	5.07749	+	3.68901i	0.245717	+	0.178524i
$428$	0.0456549			0.00220681
$429$		0			0
$430$	20.7087			0.998663
$431$	−13.3271	−	9.68268i	−0.641942	−	0.466398i	0.218575	−	0.975820i	$-0.429859\pi$
$431$	−13.3271	−	9.68268i	−0.641942	−	0.466398i	−0.860517	+	0.509422i	$0.829859\pi$
$432$	−3.50440	+	10.7854i	−0.168605	+	0.518914i
$433$	6.20844	+	19.1076i	0.298359	+	0.918253i	0.982073	+	0.188503i	$0.0603636\pi$
$433$	6.20844	+	19.1076i	0.298359	+	0.918253i	−0.683714	+	0.729750i	$0.739636\pi$
$434$	−1.49113	+	1.08337i	−0.0715763	+	0.0520032i
$435$	3.75815	−	2.73045i	0.180189	−	0.130915i
$436$	0.0122829	+	0.0378030i	0.000588245	+	0.00181043i
$437$	1.29015	−	3.97067i	0.0617161	−	0.189943i
$438$	−14.8352	−	10.7784i	−0.708852	−	0.515011i
$439$	26.7682			1.27758			0.638788	−	0.769383i	$-0.279436\pi$
$439$	26.7682			1.27758			0.638788	+	0.769383i	$0.279436\pi$
$440$		0			0
$441$	1.68022			0.0800104
$442$	28.9823	+	21.0569i	1.37855	+	1.00157i
$443$	8.10098	−	24.9323i	0.384889	−	1.18457i	−0.551671	−	0.834062i	$-0.686010\pi$
$443$	8.10098	−	24.9323i	0.384889	−	1.18457i	0.936561	−	0.350506i	$-0.113990\pi$
$444$	0.0195556	+	0.0601859i	0.000928068	+	0.00285630i
$445$	22.7336	−	16.5169i	1.07768	−	0.782977i
$446$	−5.53691	+	4.02280i	−0.262180	+	0.190485i
$447$	2.14884	+	6.61344i	0.101637	+	0.312805i
$448$	2.48916	−	7.66083i	0.117602	−	0.361940i
$449$	−7.88582	−	5.72938i	−0.372155	−	0.270386i	0.385949	−	0.922520i	$-0.373874\pi$
$449$	−7.88582	−	5.72938i	−0.372155	−	0.270386i	−0.758104	+	0.652134i	$0.773874\pi$
$450$	3.89758			0.183734
$451$		0			0
$452$	−0.203107			−0.00955336
$453$	38.9720	+	28.3148i	1.83106	+	1.33035i
$454$	−0.172951	+	0.532289i	−0.00811700	+	0.0249816i
$455$	2.62991	+	8.09402i	0.123292	+	0.379453i
$456$	−28.8172	+	20.9369i	−1.34949	+	0.980462i
$457$	−9.61541	+	6.98601i	−0.449790	+	0.326792i	−0.789513	−	0.613734i	$-0.789667\pi$
$457$	−9.61541	+	6.98601i	−0.449790	+	0.326792i	0.339723	+	0.940526i	$0.389667\pi$
$458$	−0.953558	−	2.93475i	−0.0445568	−	0.137132i
$459$	−4.82638	+	14.8541i	−0.225276	+	0.693329i
$460$	0.0148903	+	0.0108185i	0.000694265	+	0.000504413i
$461$	9.14737			0.426035			0.213018	−	0.977048i	$-0.431671\pi$
$461$	9.14737			0.426035			0.213018	+	0.977048i	$0.431671\pi$
$462$		0			0
$463$	38.9342			1.80943			0.904713	−	0.426021i	$-0.140085\pi$
$463$	38.9342			1.80943			0.904713	+	0.426021i	$0.140085\pi$
$464$	−3.76753	−	2.73727i	−0.174903	−	0.127075i
$465$	−1.60125	+	4.92813i	−0.0742561	+	0.228537i
$466$	0.548782	+	1.68898i	0.0254218	+	0.0782404i
$467$	16.8141	−	12.2162i	0.778066	−	0.565298i	−0.126332	−	0.991988i	$-0.540320\pi$
$467$	16.8141	−	12.2162i	0.778066	−	0.565298i	0.904398	+	0.426690i	$0.140320\pi$
$468$	−0.0882119	+	0.0640897i	−0.00407760	+	0.00296255i
$469$	−4.77965	−	14.7102i	−0.220704	−	0.679256i
$470$	4.76600	−	14.6683i	0.219839	−	0.676596i
$471$	23.1987	+	16.8548i	1.06894	+	0.776629i
$472$	−21.7998			−1.00342
$473$		0			0
$474$	−47.6858			−2.19028
$475$	−7.72520	−	5.61269i	−0.354457	−	0.257528i
$476$	0.0236055	−	0.0726501i	0.00108195	−	0.00332991i
$477$	5.26741	+	16.2114i	0.241178	+	0.742270i
$478$	−12.7256	+	9.24572i	−0.582057	+	0.422889i
$479$	19.8503	−	14.4221i	0.906983	−	0.658962i	−0.0332672	−	0.999446i	$-0.510591\pi$
$479$	19.8503	−	14.4221i	0.906983	−	0.658962i	0.940250	+	0.340485i	$0.110591\pi$
$480$	−0.0967138	−	0.297654i	−0.00441436	−	0.0135860i
$481$	−3.00809	+	9.25794i	−0.137157	+	0.422126i
$482$	−24.4947	−	17.7964i	−1.11570	−	0.810606i
$483$	1.55695			0.0708436
$484$		0			0
$485$	−4.41591			−0.200516
$486$	17.9024	+	13.0069i	0.812070	+	0.590003i
$487$	−3.82295	+	11.7658i	−0.173234	+	0.533160i	−0.999548	−	0.0300493i	$-0.990434\pi$
$487$	−3.82295	+	11.7658i	−0.173234	+	0.533160i	0.826314	+	0.563209i	$0.190434\pi$
$488$	−5.50452	−	16.9412i	−0.249178	−	0.766890i
$489$	24.0100	−	17.4443i	1.08577	−	0.788858i
$490$	−2.08800	+	1.51702i	−0.0943264	+	0.0685321i
$491$	5.10653	+	15.7163i	0.230454	+	0.709266i	0.997692	+	0.0679027i	$0.0216308\pi$
$491$	5.10653	+	15.7163i	0.230454	+	0.709266i	−0.767238	+	0.641363i	$0.778369\pi$
$492$	−0.00855741	+	0.0263370i	−0.000385798	+	0.00118736i
$493$	−5.18878	−	3.76987i	−0.233691	−	0.169786i
$494$	−37.9916			−1.70932
$495$		0			0
$496$	5.19468			0.233248
$497$	−11.2469	−	8.17134i	−0.504492	−	0.366535i
$498$	−4.12249	+	12.6877i	−0.184733	+	0.568550i
$499$	−4.24619	−	13.0684i	−0.190085	−	0.585023i	0.809913	−	0.586549i	$-0.199514\pi$
$499$	−4.24619	−	13.0684i	−0.190085	−	0.585023i	−0.999999	+	0.00152665i	$0.999514\pi$
$500$	0.137507	−	0.0999048i	0.00614951	−	0.00446788i
$501$	16.2920	−	11.8368i	0.727874	−	0.528831i
$502$	0.184568	+	0.568043i	0.00823769	+	0.0253530i
$503$	−6.98278	+	21.4908i	−0.311347	+	0.958227i	0.665885	+	0.746054i	$0.268054\pi$
$503$	−6.98278	+	21.4908i	−0.311347	+	0.958227i	−0.977232	+	0.212173i	$0.931946\pi$
$504$	−3.85806	−	2.80304i	−0.171851	−	0.124857i
$505$	−21.7859			−0.969461
$506$		0			0
$507$	−18.5946			−0.825813
$508$	0.0568590	+	0.0413105i	0.00252271	+	0.00183286i
$509$	−6.63262	+	20.4131i	−0.293986	+	0.904795i	0.689575	+	0.724215i	$0.257798\pi$
$509$	−6.63262	+	20.4131i	−0.293986	+	0.904795i	−0.983560	+	0.180580i	$0.942202\pi$
$510$	9.43829	+	29.0481i	0.417934	+	1.28627i
$511$	−4.86593	+	3.53531i	−0.215256	+	0.156393i
$512$	−18.4940	+	13.4367i	−0.817327	+	0.593823i
$513$	−5.11839	−	15.7528i	−0.225983	−	0.695503i
$514$	−7.59493	+	23.3748i	−0.334998	+	1.03102i
$515$	0.587188	+	0.426617i	0.0258746	+	0.0187990i
$516$	0.242403			0.0106712
$517$		0			0
$518$	−2.95205			−0.129706
$519$	18.3872	+	13.3591i	0.807107	+	0.586398i
$520$	7.46424	−	22.9726i	0.327329	−	1.00741i
$521$	10.7265	+	33.0127i	0.469935	+	1.44631i	0.852669	+	0.522452i	$0.174983\pi$
$521$	10.7265	+	33.0127i	0.469935	+	1.44631i	−0.382734	+	0.923859i	$0.625017\pi$
$522$	−2.24605	+	1.63185i	−0.0983071	+	0.0714243i
$523$	−15.9604	+	11.5959i	−0.697900	+	0.507054i	−0.879247	−	0.476365i	$-0.841954\pi$
$523$	−15.9604	+	11.5959i	−0.697900	+	0.507054i	0.181348	+	0.983419i	$0.441954\pi$
$524$	0.000776978		0.00239129i	3.39424e−5		0.000104464i
$525$	1.10040	−	3.38669i	0.0480255	−	0.147807i
$526$	1.72750	+	1.25510i	0.0753227	+	0.0547251i
$527$	7.15430			0.311646
$528$		0			0
$529$	−22.4821			−0.977481
$530$	−21.1826	−	15.3901i	−0.920115	−	0.668503i
$531$	−3.98800	+	12.2738i	−0.173064	+	0.532637i
$532$	0.0250337	+	0.0770457i	0.00108535	+	0.00334035i
$533$	−3.44617	+	2.50379i	−0.149270	+	0.108451i
$534$	−37.8455	+	27.4964i	−1.63774	+	1.18989i
$535$	1.85022	+	5.69440i	0.0799921	+	0.246190i
$536$	−13.5657	+	41.7508i	−0.585948	+	1.80336i
$537$	−14.5676	−	10.5839i	−0.628636	−	0.456731i
$538$	2.86226			0.123401
$539$		0			0
$540$	0.0730199			0.00314227
$541$	4.48958	+	3.26187i	0.193022	+	0.140239i	0.680099	−	0.733120i	$-0.261937\pi$
$541$	4.48958	+	3.26187i	0.193022	+	0.140239i	−0.487077	+	0.873359i	$0.661937\pi$
$542$	−3.31164	+	10.1922i	−0.142247	+	0.437792i
$543$	9.89610	+	30.4571i	0.424682	+	1.30704i
$544$	−0.349587	+	0.253990i	−0.0149884	+	0.0108897i
$545$	−4.21727	+	3.06402i	−0.180648	+	0.131248i
$546$	−4.37811	−	13.4744i	−0.187366	−	0.576653i
$547$	−2.61018	+	8.03330i	−0.111603	+	0.343479i	−0.991223	−	0.132197i	$-0.957797\pi$
$547$	−2.61018	+	8.03330i	−0.111603	+	0.343479i	0.879620	+	0.475677i	$0.157797\pi$
$548$	0.0940401	+	0.0683241i	0.00401719	+	0.00291866i
$549$	−10.5453			−0.450061
$550$		0			0
$551$	6.80173			0.289763
$552$	−3.57501	−	2.59739i	−0.152162	−	0.110552i
$553$	−4.83332	+	14.8754i	−0.205534	+	0.632567i
$554$	−6.28270	−	19.3362i	−0.266926	−	0.821514i
$555$	−6.71430	+	4.87822i	−0.285006	+	0.207069i
$556$	−0.0786443	+	0.0571384i	−0.00333526	+	0.00242321i
$557$	−3.76491	−	11.5872i	−0.159524	−	0.490965i	0.839067	−	0.544028i	$-0.183102\pi$
$557$	−3.76491	−	11.5872i	−0.159524	−	0.490965i	−0.998591	+	0.0530632i	$0.983102\pi$
$558$	0.956984	−	2.94529i	0.0405123	−	0.124684i
$559$	30.1658	+	21.9168i	1.27588	+	0.926980i
$560$	7.27404			0.307384
$561$		0			0
$562$	−25.0140			−1.05515
$563$	22.1295	+	16.0780i	0.932646	+	0.677607i	0.946639	−	0.322295i	$-0.104454\pi$
$563$	22.1295	+	16.0780i	0.932646	+	0.677607i	−0.0139935	+	0.999902i	$0.504454\pi$
$564$	0.0557879	−	0.171697i	0.00234909	−	0.00722977i
$565$	−8.23118	−	25.3330i	−0.346288	−	1.06577i
$566$	−35.4990	+	25.7915i	−1.49213	+	1.08410i
$567$	9.07517	−	6.59349i	0.381121	−	0.276901i
$568$	12.1928	+	37.5255i	0.511597	+	1.57453i
$569$	2.20491	−	6.78602i	0.0924346	−	0.284485i	−0.894142	−	0.447784i	$-0.852214\pi$
$569$	2.20491	−	6.78602i	0.0924346	−	0.284485i	0.986577	+	0.163299i	$0.0522135\pi$
$570$	−26.2048	−	19.0389i	−1.09760	−	0.797451i
$571$	32.4839			1.35941			0.679705	−	0.733486i	$-0.262108\pi$
$571$	32.4839			1.35941			0.679705	+	0.733486i	$0.262108\pi$
$572$		0			0
$573$	20.7831			0.868226
$574$	−1.04509	−	0.759300i	−0.0436211	−	0.0316926i
$575$	0.366066	−	1.12664i	0.0152660	−	0.0469839i
$576$	4.18232	+	12.8719i	0.174263	+	0.536328i
$577$	−28.1391	+	20.4443i	−1.17145	+	0.851107i	−0.991182	−	0.132511i	$-0.957696\pi$
$577$	−28.1391	+	20.4443i	−1.17145	+	0.851107i	−0.180266	+	0.983618i	$0.557696\pi$
$578$	14.7341	−	10.7049i	0.612856	−	0.445266i
$579$	0.994632	+	3.06116i	0.0413355	+	0.127218i
$580$	−0.00926598	+	0.0285178i	−0.000384749	+	0.00118414i
$581$	3.54004	+	2.57199i	0.146866	+	0.106704i
$582$	7.35135			0.304723
$583$		0			0
$584$	17.0708			0.706395
$585$	−11.5686	−	8.40509i	−0.478303	−	0.347508i
$586$	10.4649	−	32.2076i	0.432301	−	1.33049i
$587$	−4.47300	−	13.7665i	−0.184621	−	0.568204i	0.815321	−	0.579009i	$-0.196560\pi$
$587$	−4.47300	−	13.7665i	−0.184621	−	0.568204i	−0.999942	+	0.0108054i	$0.996560\pi$
$588$	−0.0244409	+	0.0177573i	−0.00100792	+	0.000732300i
$589$	−6.13814	+	4.45962i	−0.252918	+	0.183755i
$590$	−6.12580	−	18.8533i	−0.252195	−	0.776177i
$591$	9.38829	−	28.8942i	0.386183	−	1.18855i
$592$	6.73106	+	4.89040i	0.276645	+	0.200994i
$593$	−15.0291			−0.617169			−0.308585	−	0.951197i	$-0.599855\pi$
$593$	−15.0291			−0.617169			−0.308585	+	0.951197i	$0.599855\pi$
$594$		0			0
$595$	10.0181			0.410701
$596$	−0.0363138	−	0.0263835i	−0.00148747	−	0.00108071i
$597$	2.86614	−	8.82108i	0.117303	−	0.361023i
$598$	−1.45645	−	4.48248i	−0.0595586	−	0.183302i
$599$	−1.42424	+	1.03477i	−0.0581927	+	0.0422795i	−0.616501	−	0.787354i	$-0.711451\pi$
$599$	−1.42424	+	1.03477i	−0.0581927	+	0.0422795i	0.558309	+	0.829633i	$0.311451\pi$
$600$	−8.17659	+	5.94064i	−0.333808	+	0.242526i
$601$	7.24227	+	22.2894i	0.295418	+	0.909204i	0.983081	+	0.183173i	$0.0586369\pi$
$601$	7.24227	+	22.2894i	0.295418	+	0.909204i	−0.687662	+	0.726031i	$0.741363\pi$
$602$	−3.49426	+	10.7542i	−0.142415	+	0.438310i
$603$	21.0250	+	15.2756i	0.856206	+	0.622070i
$604$	−0.310948			−0.0126523
$605$		0			0
$606$	36.2679			1.47328
$607$	20.4508	+	14.8583i	0.830070	+	0.603081i	0.919579	−	0.392905i	$-0.128530\pi$
$607$	20.4508	+	14.8583i	0.830070	+	0.603081i	−0.0895088	+	0.995986i	$0.528530\pi$
$608$	0.141609	−	0.435828i	0.00574301	−	0.0176752i
$609$	0.783824	+	2.41236i	0.0317622	+	0.0977539i
$610$	13.1046	−	9.52102i	0.530588	−	0.385495i
$611$	22.4664	−	16.3228i	0.908895	−	0.660351i
$612$	0.0396623	+	0.122068i	0.00160325	+	0.00493431i
$613$	0.358751	−	1.10412i	0.0144898	−	0.0445951i	−0.943550	−	0.331230i	$-0.892537\pi$
$613$	0.358751	−	1.10412i	0.0144898	−	0.0445951i	0.958040	+	0.286635i	$0.0925365\pi$
$614$	−6.22846	−	4.52524i	−0.251360	−	0.182624i
$615$	−3.63174			−0.146446
$616$		0			0
$617$	12.9711			0.522197			0.261098	−	0.965312i	$-0.415915\pi$
$617$	12.9711			0.522197			0.261098	+	0.965312i	$0.415915\pi$
$618$	−0.977515	−	0.710206i	−0.0393214	−	0.0285687i
$619$	14.1505	−	43.5507i	0.568756	−	1.75045i	−0.0877618	−	0.996141i	$-0.527971\pi$
$619$	14.1505	−	43.5507i	0.568756	−	1.75045i	0.656518	−	0.754310i	$-0.272029\pi$
$620$	−0.0103360	−	0.0318108i	−0.000415102	−	0.00127755i
$621$	1.66239	−	1.20780i	0.0667095	−	0.0484673i
$622$	15.8345	−	11.5044i	0.634906	−	0.461286i
$623$	4.74147	+	14.5927i	0.189963	+	0.584646i
$624$	−12.3393	+	37.9763i	−0.493966	+	1.52027i
$625$	11.3752	+	8.26455i	0.455007	+	0.330582i
$626$	−38.6824			−1.54606
$627$		0			0
$628$	−0.185097			−0.00738615
$629$	9.27026	+	6.73524i	0.369629	+	0.268551i
$630$	1.34005	−	4.12425i	0.0533889	−	0.164314i
$631$	−3.90000	−	12.0030i	−0.155257	−	0.477831i	0.842930	−	0.538023i	$-0.180829\pi$
$631$	−3.90000	−	12.0030i	−0.155257	−	0.477831i	−0.998187	+	0.0601922i	$0.980829\pi$
$632$	35.9142	−	26.0932i	1.42859	−	1.03793i
$633$	−2.54703	+	1.85053i	−0.101236	+	0.0735519i
$634$	−3.40800	−	10.4887i	−0.135349	−	0.416561i
$635$	−2.84825	+	8.76602i	−0.113029	+	0.347869i
$636$	−0.247951	−	0.180147i	−0.00983189	−	0.00714329i
$637$	−4.64706			−0.184123
$638$		0			0
$639$	23.3582			0.924038
$640$	−16.5849	−	12.0497i	−0.655577	−	0.476305i
$641$	8.63910	−	26.5884i	0.341224	−	1.05018i	−0.622350	−	0.782739i	$-0.713822\pi$
$641$	8.63910	−	26.5884i	0.341224	−	1.05018i	0.963574	−	0.267441i	$-0.0861780\pi$
$642$	−3.08014	−	9.47970i	−0.121564	−	0.374134i
$643$	40.2066	−	29.2118i	1.58559	−	1.15200i	0.675684	−	0.737191i	$-0.263848\pi$
$643$	40.2066	−	29.2118i	1.58559	−	1.15200i	0.909908	−	0.414809i	$-0.136152\pi$
$644$	−0.00813063	+	0.00590725i	−0.000320392	+	0.000232778i
$645$	9.82370	+	30.2342i	0.386808	+	1.19047i
$646$	−13.8196	+	42.5324i	−0.543726	+	1.67342i
$647$	8.90460	+	6.46957i	0.350076	+	0.254345i	0.748901	−	0.662682i	$-0.230582\pi$
$647$	8.90460	+	6.46957i	0.350076	+	0.254345i	−0.398825	+	0.917027i	$0.630582\pi$
$648$	−31.8377			−1.25070
$649$		0			0
$650$	−10.7797			−0.422816
$651$	−2.28904	−	1.66309i	−0.0897146	−	0.0651815i
$652$	−0.0591984	+	0.182194i	−0.00231839	+	0.00713526i
$653$	8.94184	+	27.5202i	0.349921	+	1.07695i	0.958896	+	0.283757i	$0.0915811\pi$
$653$	8.94184	+	27.5202i	0.349921	+	1.07695i	−0.608975	+	0.793190i	$0.708419\pi$
$654$	7.02066	−	5.10081i	0.274529	−	0.199457i
$655$	−0.266771	+	0.193820i	−0.0104236	+	0.00757318i
$656$	1.12507	+	3.46261i	0.0439266	+	0.135192i
$657$	3.12289	−	9.61126i	0.121835	−	0.374971i
$658$	6.81318	+	4.95006i	0.265605	+	0.192974i
$659$	10.8405			0.422288			0.211144	−	0.977455i	$-0.432281\pi$
$659$	10.8405			0.422288			0.211144	+	0.977455i	$0.432281\pi$
$660$		0			0
$661$	20.3444			0.791305			0.395652	−	0.918400i	$-0.370519\pi$
$661$	20.3444			0.791305			0.395652	+	0.918400i	$0.370519\pi$
$662$	−32.0901	−	23.3148i	−1.24722	−	0.906155i
$663$	−16.9941	+	52.3024i	−0.659995	+	2.03126i
$664$	−3.83776	−	11.8114i	−0.148934	−	0.458372i
$665$	−8.59515	+	6.24474i	−0.333306	+	0.242161i
$666$	4.01279	−	2.91546i	0.155493	−	0.112972i
$667$	0.260751	+	0.802510i	0.0100963	+	0.0310733i
$668$	−0.0401691	+	0.123628i	−0.00155419	+	0.00478331i
$669$	−8.49977	−	6.17545i	−0.328620	−	0.238757i
$670$	−39.9197			−1.54223
$671$		0			0
$672$	0.170894			0.00659237
$673$	9.77196	+	7.09974i	0.376681	+	0.273675i	0.759976	−	0.649951i	$-0.225211\pi$
$673$	9.77196	+	7.09974i	0.376681	+	0.273675i	−0.383295	+	0.923626i	$0.625211\pi$
$674$	10.8780	−	33.4791i	0.419006	−	1.28957i
$675$	−1.45229	−	4.46969i	−0.0558987	−	0.172039i
$676$	0.0971038	−	0.0705500i	0.00373476	−	0.00271346i
$677$	−2.74766	+	1.99629i	−0.105601	+	0.0767238i	−0.639333	−	0.768930i	$-0.720789\pi$
$677$	−2.74766	+	1.99629i	−0.105601	+	0.0767238i	0.533731	+	0.845654i	$0.320789\pi$
$678$	13.7028	+	42.1728i	0.526252	+	1.61964i
$679$	0.745114	−	2.29323i	0.0285949	−	0.0880059i
$680$	−23.0031	−	16.7128i	−0.882130	−	0.640905i
$681$	−0.859173			−0.0329236
$682$		0			0
$683$	−4.75643			−0.182000			−0.0909999	−	0.995851i	$-0.529006\pi$
$683$	−4.75643			−0.182000			−0.0909999	+	0.995851i	$0.529006\pi$
$684$	−0.110120	−	0.0800067i	−0.00421053	−	0.00305913i
$685$	−4.71077	+	14.4983i	−0.179989	+	0.553950i
$686$	−0.435488	−	1.34029i	−0.0166270	−	0.0511726i
$687$	3.83232	−	2.78434i	0.146212	−	0.106229i
$688$	25.7830	−	18.7324i	0.982966	−	0.714167i
$689$	−14.5683	−	44.8367i	−0.555009	−	1.70814i
$690$	1.24174	−	3.82168i	0.0472721	−	0.145489i
$691$	−5.36692	−	3.89930i	−0.204167	−	0.148336i	0.481003	−	0.876719i	$-0.340272\pi$
$691$	−5.36692	−	3.89930i	−0.204167	−	0.148336i	−0.685171	+	0.728382i	$0.740272\pi$
$692$	−0.146707			−0.00557695
$693$		0			0
$694$	−29.1003			−1.10463
$695$	−10.3139	−	7.49346i	−0.391227	−	0.284243i
$696$	2.22466	−	6.84680i	0.0843256	−	0.259527i
$697$	1.54949	+	4.76883i	0.0586910	+	0.180632i
$698$	−6.83755	+	4.96777i	−0.258805	+	0.188033i
$699$	−2.20554	+	1.60242i	−0.0834212	+	0.0606090i
$700$	0.00710304	+	0.0218609i	0.000268470	+	0.000826265i
$701$	0.936330	−	2.88173i	0.0353647	−	0.108841i	−0.931816	−	0.362931i	$-0.881776\pi$
$701$	0.936330	−	2.88173i	0.0353647	−	0.108841i	0.967181	+	0.254090i	$0.0817759\pi$
$702$	−15.1274	−	10.9907i	−0.570947	−	0.414817i
$703$	−12.1519			−0.458319
$704$		0			0
$705$	23.6762			0.891697
$706$	27.4065	+	19.9120i	1.03146	+	0.749396i
$707$	3.67603	−	11.3136i	0.138251	−	0.425493i
$708$	−0.0717048	−	0.220685i	−0.00269483	−	0.00829383i
$709$	11.0488	−	8.02741i	0.414946	−	0.301476i	−0.360655	−	0.932699i	$-0.617447\pi$
$709$	11.0488	−	8.02741i	0.414946	−	0.301476i	0.775601	+	0.631223i	$0.217447\pi$
$710$	−29.0272	+	21.0895i	−1.08937	+	0.791475i
$711$	−8.12103	−	24.9939i	−0.304562	−	0.937346i
$712$	13.4573	−	41.4173i	0.504334	−	1.55218i
$713$	−0.761485	−	0.553251i	−0.0285178	−	0.0207194i
$714$	−16.6775			−0.624140
$715$		0			0
$716$	0.116231			0.00434376
$717$	−19.5353	−	14.1932i	−0.729558	−	0.530055i
$718$	4.76864	−	14.6764i	0.177964	−	0.547717i
$719$	−0.587222	−	1.80728i	−0.0218997	−	0.0674003i	0.939509	−	0.342523i	$-0.111281\pi$
$719$	−0.587222	−	1.80728i	−0.0218997	−	0.0674003i	−0.961409	+	0.275123i	$0.911281\pi$
$720$	−9.88778	+	7.18390i	−0.368496	+	0.267728i
$721$	−0.320625	+	0.232947i	−0.0119407	+	0.00867541i
$722$	−6.38148	−	19.6402i	−0.237494	−	0.730932i
$723$	14.3627	−	44.2039i	0.534155	−	1.64396i
$724$	−0.167237	−	0.121505i	−0.00621531	−	0.00451569i
$725$	1.92992			0.0716754
$726$		0			0
$727$	−13.8211			−0.512595			−0.256298	−	0.966598i	$-0.582503\pi$
$727$	−13.8211			−0.512595			−0.256298	+	0.966598i	$0.582503\pi$
$728$	10.6704	+	7.75250i	0.395472	+	0.287327i
$729$	−0.0980447	+	0.301750i	−0.00363128	+	0.0111759i
$730$	4.79694	+	14.7635i	0.177543	+	0.546420i
$731$	35.5092	−	25.7990i	1.31336	−	0.954210i
$732$	0.153394	−	0.111447i	0.00566960	−	0.00411921i
$733$	14.9485	+	46.0068i	0.552136	+	1.69930i	0.703391	+	0.710804i	$0.251669\pi$
$733$	14.9485	+	46.0068i	0.552136	+	1.69930i	−0.151255	+	0.988495i	$0.548331\pi$
$734$	−4.62390	+	14.2309i	−0.170671	+	0.525273i
$735$	−3.20531	−	2.32880i	−0.118230	−	0.0858990i
$736$	0.0568504			0.00209553
$737$		0			0
$738$	2.17050			0.0798973
$739$	−18.7757	−	13.6414i	−0.690677	−	0.501806i	0.186206	−	0.982511i	$-0.440381\pi$
$739$	−18.7757	−	13.6414i	−0.690677	−	0.501806i	−0.876883	+	0.480705i	$0.840381\pi$
$740$	0.0165546	−	0.0509497i	0.000608558	−	0.00187295i
$741$	−18.0223	−	55.4668i	−0.662064	−	2.03762i
$742$	11.5665	−	8.40352i	0.424618	−	0.308503i
$743$	36.2691	−	26.3511i	1.33059	−	0.966727i	0.330851	−	0.943683i	$-0.392664\pi$
$743$	36.2691	−	26.3511i	1.33059	−	0.966727i	0.999734	−	0.0230437i	$-0.00733568\pi$
$744$	2.48155	+	7.63744i	0.0909782	+	0.280002i
$745$	1.81907	−	5.59854i	0.0666457	−	0.205114i
$746$	41.7325	+	30.3205i	1.52794	+	1.11011i
$747$	−7.35218			−0.269002
$748$		0			0
$749$	−3.26935			−0.119460
$750$	−30.0211	−	21.8116i	−1.09621	−	0.796446i
$751$	−12.7271	+	39.1698i	−0.464417	+	1.42933i	0.395298	+	0.918553i	$0.370641\pi$
$751$	−12.7271	+	39.1698i	−0.464417	+	1.42933i	−0.859715	+	0.510775i	$0.829359\pi$
$752$	−7.33460	−	22.5736i	−0.267465	−	0.823174i
$753$	−0.741775	+	0.538931i	−0.0270318	+	0.0196397i
$754$	6.21201	−	4.51329i	0.226228	−	0.164364i
$755$	−12.6016	−	38.7836i	−0.458618	−	1.41148i
$756$	−0.0123209	+	0.0379199i	−0.000448108	+	0.00137913i
$757$	17.7084	+	12.8659i	0.643623	+	0.467619i	0.861093	−	0.508448i	$-0.169781\pi$
$757$	17.7084	+	12.8659i	0.643623	+	0.467619i	−0.217470	+	0.976067i	$0.569781\pi$
$758$	17.8382			0.647912
$759$		0			0
$760$	30.1537			1.09379
$761$	28.8943	+	20.9930i	1.04742	+	0.760994i	0.971720	−	0.236137i	$-0.0758813\pi$
$761$	28.8943	+	20.9930i	1.04742	+	0.760994i	0.0756987	+	0.997131i	$0.475881\pi$
$762$	4.74160	−	14.5931i	0.171770	−	0.528654i
$763$	−0.879581	−	2.70707i	−0.0318430	−	0.0980026i
$764$	−0.108533	+	0.0788536i	−0.00392657	+	0.00285282i
$765$	−13.6178	+	9.89392i	−0.492353	+	0.357716i
$766$	6.73607	+	20.7315i	0.243384	+	0.749060i
$767$	11.0298	−	33.9462i	0.398263	−	1.22573i
$768$	−0.586552	−	0.426155i	−0.0211654	−	0.0153775i
$769$	5.30246			0.191212			0.0956058	−	0.995419i	$-0.469521\pi$
$769$	5.30246			0.191212			0.0956058	+	0.995419i	$0.469521\pi$
$770$		0			0
$771$	−37.7295			−1.35880
$772$	−0.0168086	−	0.0122121i	−0.000604953	−	0.000439524i
$773$	−15.4172	+	47.4494i	−0.554519	+	1.70663i	0.142690	+	0.989767i	$0.454425\pi$
$773$	−15.4172	+	47.4494i	−0.554519	+	1.70663i	−0.697209	+	0.716868i	$0.745575\pi$
$774$	−5.87112	−	18.0695i	−0.211033	−	0.649493i
$775$	−1.74163	+	1.26537i	−0.0625613	+	0.0454535i
$776$	−5.53660	+	4.02258i	−0.198752	+	0.144402i
$777$	−1.40038	−	4.30992i	−0.0502383	−	0.154618i
$778$	5.53633	−	17.0391i	0.198487	−	0.610881i
$779$	−4.30205	−	3.12562i	−0.154137	−	0.111987i
$780$	0.257109			0.00920597
$781$		0			0
$782$	−5.54803			−0.198397
$783$	2.70830	+	1.96769i	0.0967866	+	0.0703196i
$784$	−1.22738	+	3.77748i	−0.0438349	+	0.134910i
$785$	−7.50127	−	23.0865i	−0.267732	−	0.823994i
$786$	0.444104	−	0.322660i	0.0158407	−	0.0115089i
$787$	−29.0089	+	21.0762i	−1.03406	+	0.751285i	−0.969116	−	0.246604i	$-0.920685\pi$
$787$	−29.0089	+	21.0762i	−1.03406	+	0.751285i	−0.0649388	+	0.997889i	$0.520685\pi$
$788$	0.0606010	+	0.186511i	0.00215882	+	0.00664416i
$789$	−1.01294	+	3.11750i	−0.0360615	+	0.110986i
$790$	32.6583	+	23.7277i	1.16193	+	0.844193i
$791$	14.5445			0.517144
$792$		0			0
$793$	29.1655			1.03570
$794$	−21.6137	−	15.7033i	−0.767043	−	0.557289i
$795$	12.4207	−	38.2268i	0.440515	−	1.35577i
$796$	0.0185008	+	0.0569396i	0.000655744	+	0.00201817i
$797$	−11.9259	+	8.66470i	−0.422438	+	0.306919i	−0.778618	−	0.627498i	$-0.784079\pi$
$797$	−11.9259	+	8.66470i	−0.422438	+	0.306919i	0.356180	+	0.934417i	$0.384079\pi$
$798$	14.3087	−	10.3959i	0.506523	−	0.368010i
$799$	−10.1015	−	31.0892i	−0.357365	−	1.09986i
$800$	0.0401801	−	0.123662i	0.00142058	−	0.00437210i
$801$	−20.8571	−	15.1536i	−0.736949	−	0.535425i
$802$	12.2354			0.432046
$803$		0			0
$804$	−0.467275			−0.0164795
$805$	−1.06630	−	0.774711i	−0.0375821	−	0.0273050i
$806$	−2.64677	+	8.14593i	−0.0932286	+	0.286928i
$807$	1.35779	+	4.17883i	0.0477963	+	0.147102i
$808$	−27.3149	+	19.8454i	−0.960934	+	0.698159i
$809$	21.8239	−	15.8560i	0.767288	−	0.557467i	−0.133849	−	0.991002i	$-0.542734\pi$
$809$	21.8239	−	15.8560i	0.767288	−	0.557467i	0.901137	+	0.433534i	$0.142734\pi$
$810$	−8.94649	−	27.5345i	−0.314348	−	0.967463i
$811$	0.452523	−	1.39272i	0.0158902	−	0.0489051i	−0.942797	−	0.333367i	$-0.891815\pi$
$811$	0.452523	−	1.39272i	0.0158902	−	0.0489051i	0.958687	+	0.284462i	$0.0918151\pi$
$812$	−0.0132461	−	0.00962382i	−0.000464846	−	0.000337730i
$813$	−16.4513			−0.576972
$814$		0			0
$815$	−25.1236			−0.880041
$816$	38.0269	+	27.6281i	1.33121	+	0.967178i
$817$	−14.3839	+	44.2692i	−0.503230	+	1.54878i
$818$	−2.48840	−	7.65852i	−0.0870050	−	0.267774i
$819$	6.31686	−	4.58947i	0.220729	−	0.160369i
$820$	0.0189655	−	0.0137793i	0.000662305	−	0.000481193i
$821$	9.46478	+	29.1296i	0.330323	+	1.01663i	0.968980	+	0.247139i	$0.0794903\pi$
$821$	9.46478	+	29.1296i	0.330323	+	1.01663i	−0.638657	+	0.769492i	$0.720510\pi$
$822$	7.84221	−	24.1358i	0.273529	−	0.841834i
$823$	19.8483	+	14.4206i	0.691867	+	0.502671i	0.877273	−	0.479991i	$-0.159360\pi$
$823$	19.8483	+	14.4206i	0.691867	+	0.502671i	−0.185406	+	0.982662i	$0.559360\pi$
$824$	1.12482			0.0391851
$825$		0			0
$826$	10.8243			0.376626
$827$	5.31270	+	3.85990i	0.184741	+	0.134222i	0.676312	−	0.736615i	$-0.263577\pi$
$827$	5.31270	+	3.85990i	0.184741	+	0.134222i	−0.491571	+	0.870837i	$0.663577\pi$
$828$	0.00521813	−	0.0160597i	0.000181342	−	0.000558115i
$829$	−6.13221	−	18.8730i	−0.212980	−	0.655486i	−0.999291	−	0.0376547i	$-0.988011\pi$
$829$	−6.13221	−	18.8730i	−0.212980	−	0.655486i	0.786310	−	0.617832i	$-0.211989\pi$
$830$	9.13654	−	6.63808i	0.317134	−	0.230411i
$831$	25.2500	−	18.3452i	0.875912	−	0.636387i
$832$	−11.5672	−	35.6003i	−0.401022	−	1.23422i
$833$	−1.69039	+	5.20248i	−0.0585685	+	0.180255i
$834$	17.1699	+	12.4747i	0.594545	+	0.431962i
$835$	−17.0476			−0.589958
$836$		0			0
$837$	−3.73421			−0.129073
$838$	−31.0009	−	22.5235i	−1.07091	−	0.778061i
$839$	−2.45993	+	7.57090i	−0.0849263	+	0.261376i	−0.984498	−	0.175397i	$-0.943879\pi$
$839$	−2.45993	+	7.57090i	−0.0849263	+	0.261376i	0.899571	+	0.436774i	$0.143879\pi$
$840$	3.47489	+	10.6946i	0.119895	+	0.368999i
$841$	22.3493	−	16.2377i	0.770667	−	0.559922i
$842$	−27.3231	+	19.8514i	−0.941616	+	0.684124i
$843$	−11.8660	−	36.5199i	−0.408687	−	1.25781i
$844$	0.00627989	−	0.0193275i	0.000216163	−	0.000665281i
$845$	12.7347	+	9.25233i	0.438089	+	0.318290i
$846$	−14.1500			−0.486489
$847$		0			0
$848$	−40.2944			−1.38372
$849$	−54.4949	−	39.5928i	−1.87026	−	1.35882i
$850$	−3.92118	+	12.0681i	−0.134495	+	0.413934i
$851$	−0.465858	−	1.43376i	−0.0159694	−	0.0491487i
$852$	−0.339775	+	0.246861i	−0.0116405	+	0.00845731i
$853$	−27.5658	+	20.0277i	−0.943834	+	0.685736i	−0.949341	−	0.314249i	$-0.898247\pi$
$853$	−27.5658	+	20.0277i	−0.943834	+	0.685736i	0.00550627	+	0.999985i	$0.498247\pi$
$854$	2.73317	+	8.41185i	0.0935273	+	0.287847i
$855$	5.51625	−	16.9773i	0.188652	−	0.580611i
$856$	7.50697	+	5.45413i	0.256583	+	0.186418i
$857$	24.8539			0.848992			0.424496	−	0.905430i	$-0.360451\pi$
$857$	24.8539			0.848992			0.424496	+	0.905430i	$0.360451\pi$
$858$		0			0
$859$	2.05654			0.0701683			0.0350841	−	0.999384i	$-0.488830\pi$
$859$	2.05654			0.0701683			0.0350841	+	0.999384i	$0.488830\pi$
$860$	−0.166013	−	0.120616i	−0.00566101	−	0.00411296i
$861$	0.612797	−	1.88600i	0.0208841	−	0.0642746i
$862$	−7.17386	−	22.0789i	−0.244343	−	0.752009i
$863$	0.209920	−	0.152516i	0.00714576	−	0.00519170i	−0.584207	−	0.811605i	$-0.698594\pi$
$863$	0.209920	−	0.152516i	0.00714576	−	0.00519170i	0.591352	+	0.806413i	$0.298594\pi$
$864$	0.182468	−	0.132570i	0.00620767	−	0.00451014i
$865$	−5.94547	−	18.2983i	−0.202152	−	0.622160i
$866$	−8.74936	+	26.9277i	−0.297315	+	0.915042i
$867$	22.6184	+	16.4332i	0.768161	+	0.558102i
$868$	0.0182637			0.000619910
$869$		0			0
$870$	6.54651			0.221947
$871$	−58.1499	−	42.2484i	−1.97034	−	1.43153i
$872$	−2.49644	+	7.68326i	−0.0845402	+	0.260188i
$873$	1.25195	+	3.85312i	0.0423722	+	0.130408i
$874$	4.76001	−	3.45835i	0.161010	−	0.116980i
$875$	−9.84690	+	7.15419i	−0.332886	+	0.241856i
$876$	0.0561500	+	0.172812i	0.00189713	+	0.00583877i
$877$	5.74555	−	17.6830i	0.194013	−	0.597112i	−0.805973	−	0.591952i	$-0.798358\pi$
$877$	5.74555	−	17.6830i	0.194013	−	0.597112i	0.999987	−	0.00515985i	$-0.00164244\pi$
$878$	30.5190	+	22.1733i	1.02997	+	0.748314i
$879$	51.9867			1.75347
$880$		0			0
$881$	6.45292			0.217404			0.108702	−	0.994074i	$-0.465330\pi$
$881$	6.45292			0.217404			0.108702	+	0.994074i	$0.465330\pi$
$882$	1.91565	+	1.39180i	0.0645034	+	0.0468645i
$883$	−0.0860573	+	0.264857i	−0.00289606	+	0.00891316i	−0.952494	−	0.304557i	$-0.901492\pi$
$883$	−0.0860573	+	0.264857i	−0.00289606	+	0.00891316i	0.949598	+	0.313470i	$0.101492\pi$
$884$	−0.109696	−	0.337609i	−0.00368947	−	0.0113550i
$885$	24.6194	−	17.8870i	0.827572	−	0.601266i
$886$	29.8887	−	21.7154i	1.00413	−	0.729543i
$887$	9.44262	+	29.0614i	0.317052	+	0.975787i	0.974901	+	0.222637i	$0.0714664\pi$
$887$	9.44262	+	29.0614i	0.317052	+	0.975787i	−0.657849	+	0.753150i	$0.728534\pi$
$888$	−3.97457	+	12.2325i	−0.133378	+	0.410495i
$889$	−4.07168	−	2.95825i	−0.136560	−	0.0992165i
$890$	39.6008			1.32742
$891$		0			0
$892$	0.0678176			0.00227070
$893$	28.0461	+	20.3767i	0.938527	+	0.681879i
$894$	−3.02829	+	9.32011i	−0.101281	+	0.311711i
$895$	4.71041	+	14.4971i	0.157452	+	0.484586i
$896$	9.05595	−	6.57953i	0.302538	−	0.219807i
$897$	5.85342	−	4.25276i	0.195440	−	0.141995i
$898$	−4.24487	−	13.0644i	−0.141653	−	0.435964i
$899$	0.473858	−	1.45839i	0.0158041	−	0.0486399i
$900$	−0.0312453	−	0.0227011i	−0.00104151	−	0.000756702i
$901$	−55.4949			−1.84880
$902$		0			0
$903$	−17.3585			−0.577655
$904$	−33.3966	−	24.2641i	−1.11076	−	0.807011i
$905$	8.37743	−	25.7831i	0.278475	−	0.857059i
$906$	20.9783	+	64.5646i	0.696958	+	2.14502i
$907$	−25.8357	+	18.7707i	−0.857860	+	0.623272i	−0.927302	−	0.374314i	$-0.877878\pi$
$907$	−25.8357	+	18.7707i	−0.857860	+	0.623272i	0.0694417	+	0.997586i	$0.477878\pi$
$908$	0.00448674	−	0.00325981i	0.000148898	−	0.000108181i
$909$	6.17653	+	19.0094i	0.204862	+	0.630502i
$910$	−3.70624	+	11.4066i	−0.122861	+	0.378126i
$911$	−2.26559	−	1.64605i	−0.0750623	−	0.0545360i	0.549621	−	0.835414i	$-0.314772\pi$
$911$	−2.26559	−	1.64605i	−0.0750623	−	0.0545360i	−0.624684	+	0.780878i	$0.714772\pi$
$912$	−49.8477			−1.65062
$913$		0			0
$914$	−16.7496			−0.554027
$915$	20.1170	+	14.6158i	0.665046	+	0.483184i
$916$	−0.00944886	+	0.0290806i	−0.000312199	+	0.000960850i
$917$	−0.0556394	−	0.171241i	−0.00183738	−	0.00565486i
$918$	−17.8070	+	12.9375i	−0.587718	+	0.427002i
$919$	12.8099	−	9.30691i	0.422559	−	0.307007i	−0.356108	−	0.934445i	$-0.615896\pi$
$919$	12.8099	−	9.30691i	0.422559	−	0.307007i	0.778666	+	0.627438i	$0.215896\pi$
$920$	1.15598	+	3.55773i	0.0381114	+	0.117295i
$921$	3.65212	−	11.2401i	0.120341	−	0.370373i
$922$	10.4291	+	7.57719i	0.343464	+	0.249541i
$923$	−64.6030			−2.12643
$924$		0			0
$925$	−3.44799			−0.113369
$926$	44.3897	+	32.2510i	1.45874	+	1.05983i
$927$	0.205772	−	0.633302i	0.00675845	−	0.0208004i
$928$	0.0286206	+	0.0880851i	0.000939517	+	0.00289153i
$929$	22.2345	−	16.1543i	0.729490	−	0.530006i	−0.159912	−	0.987131i	$-0.551121\pi$
$929$	22.2345	−	16.1543i	0.729490	−	0.530006i	0.889402	+	0.457126i	$0.151121\pi$
$930$	−5.90782	+	4.29228i	−0.193725	+	0.140749i
$931$	−1.79266	−	5.51725i	−0.0587521	−	0.180820i
$932$	0.00543791	−	0.0167362i	0.000178125	−	0.000548212i
$933$	24.3077	+	17.6606i	0.795799	+	0.578182i
$934$	29.2894			0.958379
$935$		0			0
$936$	−22.1610			−0.724354
$937$	9.95789	+	7.23483i	0.325310	+	0.236352i	0.738438	−	0.674321i	$-0.235564\pi$
$937$	9.95789	+	7.23483i	0.325310	+	0.236352i	−0.413128	+	0.910673i	$0.635564\pi$
$938$	6.73581	−	20.7307i	0.219932	−	0.676881i
$939$	−18.3500	−	56.4754i	−0.598828	−	1.84300i
$940$	−0.123641	+	0.0898304i	−0.00403272	+	0.00292994i
$941$	−1.18128	+	0.858248i	−0.0385085	+	0.0279781i	−0.606873	−	0.794799i	$-0.707576\pi$
$941$	−1.18128	+	0.858248i	−0.0385085	+	0.0279781i	0.568365	+	0.822777i	$0.307576\pi$
$942$	12.4877	+	38.4331i	0.406870	+	1.25222i
$943$	0.203857	−	0.627406i	0.00663848	−	0.0204311i
$944$	−24.6808	−	17.9317i	−0.803293	−	0.583627i
$945$	−5.22896			−0.170098
$946$		0			0
$947$	11.0714			0.359771			0.179885	−	0.983688i	$-0.442427\pi$
$947$	11.0714			0.359771			0.179885	+	0.983688i	$0.442427\pi$
$948$	0.382278	+	0.277741i	0.0124158	+	0.00902062i
$949$	−8.63712	+	26.5823i	−0.280373	+	0.862898i
$950$	−4.15842	−	12.7983i	−0.134917	−	0.415231i
$951$	13.6966	−	9.95119i	0.444144	−	0.322690i
$952$	12.5605	−	9.12574i	0.407088	−	0.295767i
$953$	−4.58067	−	14.0979i	−0.148383	−	0.456675i	0.849048	−	0.528316i	$-0.177176\pi$
$953$	−4.58067	−	14.0979i	−0.148383	−	0.456675i	−0.997430	+	0.0716413i	$0.977176\pi$
$954$	−7.42319	+	22.8462i	−0.240335	+	0.739674i
$955$	−14.2336	−	10.3413i	−0.460588	−	0.334637i
$956$	0.155867			0.00504110
$957$		0			0
$958$	34.5782			1.11717
$959$	−6.73422	−	4.89270i	−0.217459	−	0.157993i
$960$	9.86200	−	30.3521i	0.318295	−	0.979610i
$961$	−9.05095	−	27.8560i	−0.291966	−	0.898579i
$962$	−11.0984	+	8.06343i	−0.357826	+	0.259976i
$963$	4.44411	−	3.22884i	0.143210	−	0.104048i
$964$	0.0927105	+	0.285334i	0.00298601	+	0.00918998i
$965$	0.841995	−	2.59139i	0.0271048	−	0.0834199i
$966$	1.77511	+	1.28969i	0.0571132	+	0.0414952i
$967$	16.5193			0.531224			0.265612	−	0.964080i	$-0.414426\pi$
$967$	16.5193			0.531224			0.265612	+	0.964080i	$0.414426\pi$
$968$		0			0
$969$	−68.6520			−2.20542
$970$	−5.03468	−	3.65791i	−0.161654	−	0.117448i
$971$	12.6077	−	38.8025i	0.404600	−	1.24523i	−0.516629	−	0.856209i	$-0.672813\pi$
$971$	12.6077	−	38.8025i	0.404600	−	1.24523i	0.921229	−	0.389021i	$-0.127187\pi$
$972$	−0.0677593	−	0.208542i	−0.00217338	−	0.00668897i
$973$	5.63172	−	4.09169i	0.180545	−	0.131173i
$974$	−14.1048	+	10.2477i	−0.451947	+	0.328359i
$975$	−5.11363	−	15.7381i	−0.163767	−	0.504024i
$976$	7.70317	−	23.7079i	0.246573	−	0.758872i
$977$	−39.7345	−	28.8688i	−1.27122	−	0.923594i	−0.271967	−	0.962306i	$-0.587674\pi$
$977$	−39.7345	−	28.8688i	−1.27122	−	0.923594i	−0.999250	+	0.0387127i	$0.987674\pi$
$978$	41.8243			1.33739
$979$		0			0
$980$	0.0255744			0.000816945
$981$	3.86916	+	2.81111i	0.123533	+	0.0897519i
$982$	−7.19647	+	22.1484i	−0.229648	+	0.706785i
$983$	0.342017	+	1.05262i	0.0109086	+	0.0335733i	0.956363	−	0.292182i	$-0.0943814\pi$
$983$	0.342017	+	1.05262i	0.0109086	+	0.0335733i	−0.945454	+	0.325756i	$0.894381\pi$
$984$	−4.55342	+	3.30825i	−0.145158	+	0.105463i
$985$	−20.8070	+	15.1172i	−0.662965	+	0.481672i
$986$	−2.79308	−	8.59622i	−0.0889498	−	0.273759i
$987$	−3.99497	+	12.2953i	−0.127161	+	0.391363i
$988$	0.304563	+	0.221278i	0.00968945	+	0.00703980i
$989$	−5.77458			−0.183621
$990$		0			0
$991$	41.7851			1.32735			0.663674	−	0.748022i	$-0.268996\pi$
$991$	41.7851			1.32735			0.663674	+	0.748022i	$0.268996\pi$
$992$	−0.0835821	−	0.0607260i	−0.00265374	−	0.00192805i
$993$	18.8163	−	57.9107i	0.597118	−	1.83774i
$994$	−6.05411	−	18.6326i	−0.192025	−	0.590991i
$995$	−6.35214	+	4.61510i	−0.201376	+	0.146308i
$996$	0.106947	−	0.0777013i	0.00338873	−	0.00246206i
$997$	13.6568	+	42.0314i	0.432517	+	1.33115i	0.895610	+	0.444840i	$0.146739\pi$
$997$	13.6568	+	42.0314i	0.432517	+	1.33115i	−0.463094	+	0.886309i	$0.653261\pi$
$998$	5.98401	−	18.4169i	0.189421	−	0.582977i
$999$	−4.83863	−	3.51547i	−0.153088	−	0.111225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.w.323.3		16
11.2	odd	10		847.2.f.x.148.3		16
11.3	even	5	inner	847.2.f.w.729.3		16
11.4	even	5		77.2.f.b.64.2	✓	16
11.5	even	5		847.2.a.p.1.3		8
11.6	odd	10		847.2.a.o.1.6		8
11.7	odd	10		847.2.f.x.372.3		16
11.8	odd	10		847.2.f.v.729.2		16
11.9	even	5		77.2.f.b.71.2	yes	16
11.10	odd	2		847.2.f.v.323.2		16
33.5	odd	10		7623.2.a.ct.1.6		8
33.17	even	10		7623.2.a.cw.1.3		8
33.20	odd	10		693.2.m.i.379.3		16
33.26	odd	10		693.2.m.i.64.3		16
77.4	even	15		539.2.q.g.471.2		32
77.6	even	10		5929.2.a.bs.1.6		8
77.9	even	15		539.2.q.g.214.2		32
77.20	odd	10		539.2.f.e.148.2		16
77.26	odd	30		539.2.q.f.361.3		32
77.27	odd	10		5929.2.a.bt.1.3		8
77.31	odd	30		539.2.q.f.324.3		32
77.37	even	15		539.2.q.g.361.3		32
77.48	odd	10		539.2.f.e.295.2		16
77.53	even	15		539.2.q.g.324.3		32
77.59	odd	30		539.2.q.f.471.2		32
77.75	odd	30		539.2.q.f.214.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	11.4	even	5
77.2.f.b.71.2	yes	16	11.9	even	5
539.2.f.e.148.2		16	77.20	odd	10
539.2.f.e.295.2		16	77.48	odd	10
539.2.q.f.214.2		32	77.75	odd	30
539.2.q.f.324.3		32	77.31	odd	30
539.2.q.f.361.3		32	77.26	odd	30
539.2.q.f.471.2		32	77.59	odd	30
539.2.q.g.214.2		32	77.9	even	15
539.2.q.g.324.3		32	77.53	even	15
539.2.q.g.361.3		32	77.37	even	15
539.2.q.g.471.2		32	77.4	even	15
693.2.m.i.64.3		16	33.26	odd	10
693.2.m.i.379.3		16	33.20	odd	10
847.2.a.o.1.6		8	11.6	odd	10
847.2.a.p.1.3		8	11.5	even	5
847.2.f.v.323.2		16	11.10	odd	2
847.2.f.v.729.2		16	11.8	odd	10
847.2.f.w.323.3		16	1.1	even	1	trivial
847.2.f.w.729.3		16	11.3	even	5	inner
847.2.f.x.148.3		16	11.2	odd	10
847.2.f.x.372.3		16	11.7	odd	10
5929.2.a.bs.1.6		8	77.6	even	10
5929.2.a.bt.1.3		8	77.27	odd	10
7623.2.a.ct.1.6		8	33.5	odd	10
7623.2.a.cw.1.3		8	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.14012 + 0.828347i) q^{2} +(-0.668522 + 2.05750i) q^{3} +(-0.00431527 - 0.0132810i) q^{4} +(1.48162 - 1.07646i) q^{5} +(-2.46652 + 1.79203i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.877057 - 2.69930i) q^{8} +(-1.35932 - 0.987607i) q^{9} +O(q^{10})\)	\(q+(1.14012 + 0.828347i) q^{2} +(-0.668522 + 2.05750i) q^{3} +(-0.00431527 - 0.0132810i) q^{4} +(1.48162 - 1.07646i) q^{5} +(-2.46652 + 1.79203i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.877057 - 2.69930i) q^{8} +(-1.35932 - 0.987607i) q^{9} +2.58091 q^{10} +0.0302106 q^{12} +(3.75955 + 2.73147i) q^{13} +(-0.435488 + 1.34029i) q^{14} +(1.22432 + 3.76807i) q^{15} +(3.21332 - 2.33461i) q^{16} +(4.42550 - 3.21531i) q^{17} +(-0.731714 - 2.25198i) q^{18} +(-1.79266 + 5.51725i) q^{19} +(-0.0206901 - 0.0150323i) q^{20} -2.16338 q^{21} -0.719682 q^{23} +(4.96748 + 3.60908i) q^{24} +(-0.508649 + 1.56546i) q^{25} +(2.02374 + 6.22842i) q^{26} +(-2.30990 + 1.67824i) q^{27} +(0.0112975 - 0.00820814i) q^{28} +(-0.362314 - 1.11509i) q^{29} +(-1.72540 + 5.31022i) q^{30} +(1.05809 + 0.768744i) q^{31} -0.0789938 q^{32} +7.70900 q^{34} +(1.48162 + 1.07646i) q^{35} +(-0.00725060 + 0.0223150i) q^{36} +(0.647310 + 1.99221i) q^{37} +(-6.61405 + 4.80539i) q^{38} +(-8.13333 + 5.90921i) q^{39} +(-1.60623 - 4.94347i) q^{40} +(-0.283259 + 0.871781i) q^{41} +(-2.46652 - 1.79203i) q^{42} +8.02379 q^{43} -3.07713 q^{45} +(-0.820525 - 0.596147i) q^{46} +(1.84663 - 5.68336i) q^{47} +(2.65528 + 8.17213i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-1.87667 + 1.36348i) q^{50} +(3.65696 + 11.2550i) q^{51} +(0.0200533 - 0.0617178i) q^{52} +(-8.20742 - 5.96304i) q^{53} -4.02373 q^{54} +2.83822 q^{56} +(-10.1533 - 7.37680i) q^{57} +(0.510598 - 1.57146i) q^{58} +(-2.37350 - 7.30488i) q^{59} +(0.0447607 - 0.0325205i) q^{60} +(5.07749 - 3.68901i) q^{61} +(0.569559 + 1.75292i) q^{62} +(0.519216 - 1.59798i) q^{63} +(-6.51669 - 4.73465i) q^{64} +8.51056 q^{65} -15.4673 q^{67} +(-0.0617999 - 0.0449003i) q^{68} +(0.481123 - 1.48075i) q^{69} +(0.797546 + 2.45459i) q^{70} +(-11.2469 + 8.17134i) q^{71} +(-3.85806 + 2.80304i) q^{72} +(1.85862 + 5.72025i) q^{73} +(-0.912233 + 2.80756i) q^{74} +(-2.88089 - 2.09309i) q^{75} +0.0810106 q^{76} -14.1679 q^{78} +(12.6538 + 9.19351i) q^{79} +(2.24780 - 6.91802i) q^{80} +(-3.46640 - 10.6685i) q^{81} +(-1.04509 + 0.759300i) q^{82} +(3.54004 - 2.57199i) q^{83} +(0.00933558 + 0.0287320i) q^{84} +(3.09576 - 9.52776i) q^{85} +(9.14810 + 6.64648i) q^{86} +2.53651 q^{87} +15.3437 q^{89} +(-3.50830 - 2.54893i) q^{90} +(-1.43602 + 4.41961i) q^{91} +(0.00310563 + 0.00955813i) q^{92} +(-2.28904 + 1.66309i) q^{93} +(6.81318 - 4.95006i) q^{94} +(3.28306 + 10.1042i) q^{95} +(0.0528090 - 0.162530i) q^{96} +(-1.95073 - 1.41729i) q^{97} -1.40927 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9	\( 16 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 2 q^{6} - 4 q^{7} + 5 q^{8} - 2 q^{9} + 12 q^{10} + 18 q^{12} + 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} + 10 q^{17} - 19 q^{18} - 6 q^{19} - 24 q^{20} + 8 q^{21} + 32 q^{23} + 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} - 11 q^{28} - 12 q^{29} + 38 q^{30} - 2 q^{31} + 32 q^{32} - 24 q^{34} - 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} - 24 q^{39} + 5 q^{40} + 20 q^{41} - 2 q^{42} - 8 q^{43} + 70 q^{45} + 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} - 58 q^{50} + 16 q^{51} + 8 q^{52} - 41 q^{53} + 60 q^{54} + 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} - 12 q^{61} - 61 q^{62} - 12 q^{63} - 3 q^{64} - 8 q^{65} - 38 q^{67} - 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} + 35 q^{72} + 60 q^{73} - 4 q^{74} + 4 q^{75} + 52 q^{76} - 58 q^{78} - 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} + 20 q^{83} - 17 q^{84} - 9 q^{85} + 48 q^{86} - 72 q^{87} + 74 q^{89} + 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} + 66 q^{94} - 53 q^{95} + 48 q^{96} - 35 q^{97} + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 2 * q^6 - 4 * q^7 + 5 * q^8 - 2 * q^9 + 12 * q^10 + 18 * q^12 + 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 + 10 * q^17 - 19 * q^18 - 6 * q^19 - 24 * q^20 + 8 * q^21 + 32 * q^23 + 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 - 11 * q^28 - 12 * q^29 + 38 * q^30 - 2 * q^31 + 32 * q^32 - 24 * q^34 - 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 - 24 * q^39 + 5 * q^40 + 20 * q^41 - 2 * q^42 - 8 * q^43 + 70 * q^45 + 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 - 58 * q^50 + 16 * q^51 + 8 * q^52 - 41 * q^53 + 60 * q^54 + 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 - 12 * q^61 - 61 * q^62 - 12 * q^63 - 3 * q^64 - 8 * q^65 - 38 * q^67 - 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 + 35 * q^72 + 60 * q^73 - 4 * q^74 + 4 * q^75 + 52 * q^76 - 58 * q^78 - 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 + 20 * q^83 - 17 * q^84 - 9 * q^85 + 48 * q^86 - 72 * q^87 + 74 * q^89 + 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 + 66 * q^94 - 53 * q^95 + 48 * q^96 - 35 * q^97 + 2 * q^98

Introduction

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