LMFDB - Embedded newform 483.2.i.h.415.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, degree $2$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 245x^16 - 416x^15 + 1707x^14 - 2021x^13 + 7135x^12 - 6640x^11 + 20315x^10 - 10565x^9 + 29358x^8 - 9009x^7 + 30661x^6 - 4026x^5 + 15786x^4 - 84x^3 + 5800x^2 + 152*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.8
Root			$-0.526755 - 0.912367i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.h.277.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.526755 - 0.912367i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.445058 + 0.770863i) q^{4} +(-1.08806 + 1.88457i) q^{5} +1.05351 q^{6} +(1.36439 - 2.26681i) q^{7} +3.04477 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.526755 - 0.912367i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.445058 + 0.770863i) q^{4} +(-1.08806 + 1.88457i) q^{5} +1.05351 q^{6} +(1.36439 - 2.26681i) q^{7} +3.04477 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.14628 + 1.98542i) q^{10} +(1.31121 + 2.27109i) q^{11} +(-0.445058 + 0.770863i) q^{12} -3.30704 q^{13} +(-1.34946 - 2.43888i) q^{14} -2.17612 q^{15} +(0.713731 - 1.23622i) q^{16} +(1.48456 + 2.57133i) q^{17} +(0.526755 + 0.912367i) q^{18} +(-0.348884 + 0.604285i) q^{19} -1.93700 q^{20} +(2.64531 + 0.0481928i) q^{21} +2.76276 q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.52238 + 2.63685i) q^{24} +(0.132258 + 0.229078i) q^{25} +(-1.74200 + 3.01723i) q^{26} -1.00000 q^{27} +(2.35463 + 0.0428972i) q^{28} +7.31827 q^{29} +(-1.14628 + 1.98542i) q^{30} +(-2.80105 - 4.85155i) q^{31} +(2.29284 + 3.97132i) q^{32} +(-1.31121 + 2.27109i) q^{33} +3.12800 q^{34} +(2.78743 + 5.03772i) q^{35} -0.890116 q^{36} +(2.26348 - 3.92045i) q^{37} +(0.367553 + 0.636621i) q^{38} +(-1.65352 - 2.86398i) q^{39} +(-3.31288 + 5.73808i) q^{40} +2.28774 q^{41} +(1.43740 - 2.38811i) q^{42} -7.79527 q^{43} +(-1.16713 + 2.02153i) q^{44} +(-1.08806 - 1.88457i) q^{45} +(0.526755 + 0.912367i) q^{46} +(1.90697 - 3.30297i) q^{47} +1.42746 q^{48} +(-3.27687 - 6.18564i) q^{49} +0.278671 q^{50} +(-1.48456 + 2.57133i) q^{51} +(-1.47182 - 2.54927i) q^{52} +(-1.56530 - 2.71117i) q^{53} +(-0.526755 + 0.912367i) q^{54} -5.70671 q^{55} +(4.15426 - 6.90191i) q^{56} -0.697769 q^{57} +(3.85494 - 6.67695i) q^{58} +(-6.08141 - 10.5333i) q^{59} +(-0.968498 - 1.67749i) q^{60} +(-0.742296 + 1.28569i) q^{61} -5.90186 q^{62} +(1.28092 + 2.31500i) q^{63} +7.68599 q^{64} +(3.59825 - 6.23236i) q^{65} +(1.38138 + 2.39262i) q^{66} +(-5.63777 - 9.76490i) q^{67} +(-1.32143 + 2.28879i) q^{68} -1.00000 q^{69} +(6.06454 + 0.110485i) q^{70} +13.8643 q^{71} +(-1.52238 + 2.63685i) q^{72} +(-0.352915 - 0.611266i) q^{73} +(-2.38459 - 4.13024i) q^{74} +(-0.132258 + 0.229078i) q^{75} -0.621095 q^{76} +(6.93715 + 0.126382i) q^{77} -3.48400 q^{78} +(4.30203 - 7.45134i) q^{79} +(1.55316 + 2.69015i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.20508 - 2.08726i) q^{82} -11.5918 q^{83} +(1.14017 + 2.06062i) q^{84} -6.46115 q^{85} +(-4.10620 + 7.11214i) q^{86} +(3.65914 + 6.33781i) q^{87} +(3.99234 + 6.91494i) q^{88} +(0.166888 - 0.289058i) q^{89} -2.29256 q^{90} +(-4.51210 + 7.49644i) q^{91} -0.890116 q^{92} +(2.80105 - 4.85155i) q^{93} +(-2.00901 - 3.47971i) q^{94} +(-0.759213 - 1.31500i) q^{95} +(-2.29284 + 3.97132i) q^{96} +0.124876 q^{97} +(-7.36968 - 0.268614i) q^{98} -2.62243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.526755	−	0.912367i	0.372472	−	0.645141i	−0.617473	−	0.786592i	$-0.711844\pi$
$2$	0.526755	−	0.912367i	0.372472	−	0.645141i	0.989945	+	0.141451i	$0.0451769\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.445058	+	0.770863i	0.222529	+	0.385432i
$5$	−1.08806	+	1.88457i	−0.486594	+	0.842806i	−0.999881	−	0.0154108i	$-0.995094\pi$
$5$	−1.08806	+	1.88457i	−0.486594	+	0.842806i	0.513287	+	0.858217i	$0.328428\pi$
$6$	1.05351			0.430094
$7$	1.36439	−	2.26681i	0.515692	−	0.856774i
$7$	1.36439	−	2.26681i	0.515692	−	0.856774i
$8$	3.04477			1.07649
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.14628	+	1.98542i	0.362486	+	0.627844i
$11$	1.31121	+	2.27109i	0.395346	+	0.684760i	0.993145	−	0.116886i	$-0.0372913\pi$
$11$	1.31121	+	2.27109i	0.395346	+	0.684760i	−0.597799	+	0.801646i	$0.703958\pi$
$12$	−0.445058	+	0.770863i	−0.128477	+	0.222529i
$13$	−3.30704			−0.917208			−0.458604	−	0.888641i	$-0.651650\pi$
$13$	−3.30704			−0.917208			−0.458604	+	0.888641i	$0.651650\pi$
$14$	−1.34946	−	2.43888i	−0.360659	−	0.651818i
$15$	−2.17612			−0.561871
$16$	0.713731	−	1.23622i	0.178433	−	0.309054i
$17$	1.48456	+	2.57133i	0.360059	+	0.623640i	0.987970	−	0.154645i	$-0.0494233\pi$
$17$	1.48456	+	2.57133i	0.360059	+	0.623640i	−0.627911	+	0.778285i	$0.716090\pi$
$18$	0.526755	+	0.912367i	0.124157	+	0.215047i
$19$	−0.348884	+	0.604285i	−0.0800396	+	0.138633i	−0.903267	−	0.429080i	$-0.858838\pi$
$19$	−0.348884	+	0.604285i	−0.0800396	+	0.138633i	0.823227	+	0.567712i	$0.192171\pi$
$20$	−1.93700			−0.433126
$21$	2.64531	+	0.0481928i	0.577254	+	0.0105165i
$22$	2.76276			0.589022
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	1.52238	+	2.63685i	0.310755	+	0.538244i
$25$	0.132258	+	0.229078i	0.0264516	+	0.0458156i
$26$	−1.74200	+	3.01723i	−0.341634	+	0.591728i
$27$	−1.00000			−0.192450
$28$	2.35463	+	0.0428972i	0.444984	+	0.00810681i
$29$	7.31827			1.35897			0.679485	−	0.733690i	$-0.262203\pi$
$29$	7.31827			1.35897			0.679485	+	0.733690i	$0.262203\pi$
$30$	−1.14628	+	1.98542i	−0.209281	+	0.362486i
$31$	−2.80105	−	4.85155i	−0.503083	−	0.871365i	−0.999994	−	0.00356314i	$-0.998866\pi$
$31$	−2.80105	−	4.85155i	−0.503083	−	0.871365i	0.496911	−	0.867801i	$-0.334468\pi$
$32$	2.29284	+	3.97132i	0.405321	+	0.702037i
$33$	−1.31121	+	2.27109i	−0.228253	+	0.395346i
$34$	3.12800			0.536448
$35$	2.78743	+	5.03772i	0.471162	+	0.851530i
$36$	−0.890116			−0.148353
$37$	2.26348	−	3.92045i	0.372113	−	0.644519i	−0.617777	−	0.786353i	$-0.711967\pi$
$37$	2.26348	−	3.92045i	0.372113	−	0.644519i	0.989890	+	0.141834i	$0.0453000\pi$
$38$	0.367553	+	0.636621i	0.0596250	+	0.103274i
$39$	−1.65352	−	2.86398i	−0.264775	−	0.458604i
$40$	−3.31288	+	5.73808i	−0.523813	+	0.907271i
$41$	2.28774			0.357285			0.178643	−	0.983914i	$-0.442829\pi$
$41$	2.28774			0.357285			0.178643	+	0.983914i	$0.442829\pi$
$42$	1.43740	−	2.38811i	0.221796	−	0.368493i
$43$	−7.79527			−1.18877			−0.594384	−	0.804182i	$-0.702604\pi$
$43$	−7.79527			−1.18877			−0.594384	+	0.804182i	$0.702604\pi$
$44$	−1.16713	+	2.02153i	−0.175952	+	0.304758i
$45$	−1.08806	−	1.88457i	−0.162198	−	0.280935i
$46$	0.526755	+	0.912367i	0.0776658	+	0.134521i
$47$	1.90697	−	3.30297i	0.278160	−	0.481788i	−0.692767	−	0.721161i	$-0.743609\pi$
$47$	1.90697	−	3.30297i	0.278160	−	0.481788i	0.970928	+	0.239373i	$0.0769420\pi$
$48$	1.42746			0.206036
$49$	−3.27687	−	6.18564i	−0.468124	−	0.883663i
$50$	0.278671			0.0394100
$51$	−1.48456	+	2.57133i	−0.207880	+	0.360059i
$52$	−1.47182	−	2.54927i	−0.204105	−	0.353521i
$53$	−1.56530	−	2.71117i	−0.215010	−	0.372408i	0.738266	−	0.674510i	$-0.235645\pi$
$53$	−1.56530	−	2.71117i	−0.215010	−	0.372408i	−0.953276	+	0.302102i	$0.902312\pi$
$54$	−0.526755	+	0.912367i	−0.0716823	+	0.124157i
$55$	−5.70671			−0.769493
$56$	4.15426	−	6.90191i	0.555136	−	0.922307i
$57$	−0.697769			−0.0924217
$58$	3.85494	−	6.67695i	0.506178	−	0.876727i
$59$	−6.08141	−	10.5333i	−0.791733	−	1.37132i	−0.924893	−	0.380227i	$-0.875846\pi$
$59$	−6.08141	−	10.5333i	−0.791733	−	1.37132i	0.133161	−	0.991094i	$-0.457487\pi$
$60$	−0.968498	−	1.67749i	−0.125033	−	0.216563i
$61$	−0.742296	+	1.28569i	−0.0950412	+	0.164616i	−0.909626	−	0.415429i	$-0.863632\pi$
$61$	−0.742296	+	1.28569i	−0.0950412	+	0.164616i	0.814585	+	0.580045i	$0.196965\pi$
$62$	−5.90186			−0.749537
$63$	1.28092	+	2.31500i	0.161381	+	0.291663i
$64$	7.68599			0.960749
$65$	3.59825	−	6.23236i	0.446308	−	0.773029i
$66$	1.38138	+	2.39262i	0.170036	+	0.294511i
$67$	−5.63777	−	9.76490i	−0.688763	−	1.19297i	−0.972238	−	0.233993i	$-0.924821\pi$
$67$	−5.63777	−	9.76490i	−0.688763	−	1.19297i	0.283475	−	0.958980i	$-0.408513\pi$
$68$	−1.32143	+	2.28879i	−0.160247	+	0.277556i
$69$	−1.00000			−0.120386
$70$	6.06454	+	0.110485i	0.724851	+	0.0132055i
$71$	13.8643			1.64539			0.822693	−	0.568486i	$-0.192471\pi$
$71$	13.8643			1.64539			0.822693	+	0.568486i	$0.192471\pi$
$72$	−1.52238	+	2.63685i	−0.179415	+	0.310755i
$73$	−0.352915	−	0.611266i	−0.0413055	−	0.0715433i	0.844634	−	0.535345i	$-0.179818\pi$
$73$	−0.352915	−	0.611266i	−0.0413055	−	0.0715433i	−0.885939	+	0.463802i	$0.846485\pi$
$74$	−2.38459	−	4.13024i	−0.277203	−	0.480131i
$75$	−0.132258	+	0.229078i	−0.0152719	+	0.0264516i
$76$	−0.621095			−0.0712445
$77$	6.93715	+	0.126382i	0.790561	+	0.0144026i
$78$	−3.48400			−0.394485
$79$	4.30203	−	7.45134i	0.484016	−	0.838341i	−0.515815	−	0.856700i	$-0.672511\pi$
$79$	4.30203	−	7.45134i	0.484016	−	0.838341i	0.999831	+	0.0183590i	$0.00584417\pi$
$80$	1.55316	+	2.69015i	0.173649	+	0.300768i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.20508	−	2.08726i	0.133079	−	0.230499i
$83$	−11.5918			−1.27237			−0.636185	−	0.771537i	$-0.719489\pi$
$83$	−11.5918			−1.27237			−0.636185	+	0.771537i	$0.719489\pi$
$84$	1.14017	+	2.06062i	0.124402	+	0.224832i
$85$	−6.46115			−0.700811
$86$	−4.10620	+	7.11214i	−0.442783	+	0.766922i
$87$	3.65914	+	6.33781i	0.392301	+	0.679485i
$88$	3.99234	+	6.91494i	0.425585	+	0.737135i
$89$	0.166888	−	0.289058i	0.0176901	−	0.0306401i	−0.857045	−	0.515242i	$-0.827702\pi$
$89$	0.166888	−	0.289058i	0.0176901	−	0.0306401i	0.874735	+	0.484602i	$0.161035\pi$
$90$	−2.29256			−0.241657
$91$	−4.51210	+	7.49644i	−0.472997	+	0.785840i
$92$	−0.890116			−0.0928010
$93$	2.80105	−	4.85155i	0.290455	−	0.503083i
$94$	−2.00901	−	3.47971i	−0.207214	−	0.358905i
$95$	−0.759213	−	1.31500i	−0.0778936	−	0.134916i
$96$	−2.29284	+	3.97132i	−0.234012	+	0.405321i
$97$	0.124876			0.0126793			0.00633963	−	0.999980i	$-0.497982\pi$
$97$	0.124876			0.0126793			0.00633963	+	0.999980i	$0.497982\pi$
$98$	−7.36968	−	0.268614i	−0.744450	−	0.0271341i
$99$	−2.62243			−0.263564
$100$	−0.117725	+	0.203906i	−0.0117725	+	0.0203906i
$101$	4.38986	+	7.60346i	0.436807	+	0.756572i	0.997441	−	0.0714914i	$-0.0227758\pi$
$101$	4.38986	+	7.60346i	0.436807	+	0.756572i	−0.560634	+	0.828064i	$0.689443\pi$
$102$	1.56400	+	2.70893i	0.154859	+	0.268224i
$103$	2.73241	−	4.73267i	0.269232	−	0.466324i	−0.699432	−	0.714700i	$-0.746563\pi$
$103$	2.73241	−	4.73267i	0.269232	−	0.466324i	0.968664	+	0.248376i	$0.0798967\pi$
$104$	−10.0692			−0.987363
$105$	−2.96908	+	4.93285i	−0.289752	+	0.481396i
$106$	−3.29811			−0.320341
$107$	−5.42133	+	9.39002i	−0.524100	+	0.907767i	0.475507	+	0.879712i	$0.342265\pi$
$107$	−5.42133	+	9.39002i	−0.524100	+	0.907767i	−0.999606	+	0.0280551i	$0.991069\pi$
$108$	−0.445058	−	0.770863i	−0.0428257	−	0.0741763i
$109$	0.528680	+	0.915701i	0.0506384	+	0.0877083i	0.890234	−	0.455504i	$-0.150541\pi$
$109$	0.528680	+	0.915701i	0.0506384	+	0.0877083i	−0.839595	+	0.543213i	$0.817208\pi$
$110$	−3.00604	+	5.20661i	−0.286615	+	0.496431i
$111$	4.52695			0.429679
$112$	−1.82846	−	3.30458i	−0.172774	−	0.312253i
$113$	−14.0938			−1.32584			−0.662918	−	0.748692i	$-0.730682\pi$
$113$	−14.0938			−1.32584			−0.662918	+	0.748692i	$0.730682\pi$
$114$	−0.367553	+	0.636621i	−0.0344245	+	0.0596250i
$115$	−1.08806	−	1.88457i	−0.101462	−	0.175737i
$116$	3.25706	+	5.64139i	0.302410	+	0.523790i
$117$	1.65352	−	2.86398i	0.152868	−	0.264775i
$118$	−12.8137			−1.17959
$119$	7.85425	+	0.143090i	0.719998	+	0.0131171i
$120$	−6.62577			−0.604847
$121$	2.06143	−	3.57050i	0.187403	−	0.324591i
$122$	0.782016	+	1.35449i	0.0708004	+	0.122630i
$123$	1.14387	+	1.98124i	0.103139	+	0.178643i
$124$	2.49326	−	4.31844i	0.223901	−	0.387808i
$125$	−11.4562			−1.02467
$126$	2.78686	+	0.0507716i	0.248274	+	0.00452310i
$127$	15.7177			1.39472			0.697360	−	0.716721i	$-0.254358\pi$
$127$	15.7177			1.39472			0.697360	+	0.716721i	$0.254358\pi$
$128$	−0.537052	+	0.930201i	−0.0474691	+	0.0822190i
$129$	−3.89763	−	6.75090i	−0.343168	−	0.594384i
$130$	−3.79080	−	6.56585i	−0.332475	−	0.575863i
$131$	5.00147	−	8.66280i	0.436980	−	0.756872i	−0.560475	−	0.828172i	$-0.689381\pi$
$131$	5.00147	−	8.66280i	0.436980	−	0.756872i	0.997455	+	0.0712996i	$0.0227146\pi$
$132$	−2.33427			−0.203172
$133$	0.893786	+	1.61534i	0.0775011	+	0.140068i
$134$	−11.8789			−1.02618
$135$	1.08806	−	1.88457i	0.0936452	−	0.162198i
$136$	4.52014	+	7.82911i	0.387599	+	0.671341i
$137$	−3.03387	−	5.25481i	−0.259201	−	0.448949i	0.706827	−	0.707386i	$-0.250126\pi$
$137$	−3.03387	−	5.25481i	−0.259201	−	0.448949i	−0.966028	+	0.258437i	$0.916792\pi$
$138$	−0.526755	+	0.912367i	−0.0448404	+	0.0776658i
$139$	14.1199			1.19763			0.598815	−	0.800887i	$-0.295638\pi$
$139$	14.1199			1.19763			0.598815	+	0.800887i	$0.295638\pi$
$140$	−2.64282	+	4.39080i	−0.223359	+	0.371091i
$141$	3.81394			0.321192
$142$	7.30307	−	12.6493i	0.612860	−	1.06150i
$143$	−4.33624	−	7.51059i	−0.362615	−	0.628067i
$144$	0.713731	+	1.23622i	0.0594776	+	0.103018i
$145$	−7.96271	+	13.7918i	−0.661267	+	1.14535i
$146$	−0.743598			−0.0615406
$147$	3.71849	−	5.93067i	0.306696	−	0.489153i
$148$	4.02951			0.331224
$149$	−0.507952	+	0.879799i	−0.0416131	+	0.0720759i	−0.886082	−	0.463529i	$-0.846583\pi$
$149$	−0.507952	+	0.879799i	−0.0416131	+	0.0720759i	0.844469	+	0.535605i	$0.179916\pi$
$150$	0.139335	+	0.241336i	0.0113767	+	0.0197050i
$151$	−11.2693	−	19.5190i	−0.917080	−	1.58843i	−0.803827	−	0.594864i	$-0.797206\pi$
$151$	−11.2693	−	19.5190i	−0.917080	−	1.58843i	−0.113254	−	0.993566i	$-0.536127\pi$
$152$	−1.06227	+	1.83991i	−0.0861616	+	0.149236i
$153$	−2.96912			−0.240039
$154$	3.76948	−	6.26265i	0.303754	−	0.504659i
$155$	12.1908			0.979189
$156$	1.47182	−	2.54927i	0.117840	−	0.204105i
$157$	5.68305	+	9.84334i	0.453557	+	0.785584i	0.998604	−	0.0528218i	$-0.0168215\pi$
$157$	5.68305	+	9.84334i	0.453557	+	0.785584i	−0.545047	+	0.838406i	$0.683488\pi$
$158$	−4.53223	−	7.85006i	−0.360565	−	0.624517i
$159$	1.56530	−	2.71117i	0.124136	−	0.215010i
$160$	−9.97899			−0.788909
$161$	1.28092	+	2.31500i	0.100951	+	0.182448i
$162$	−1.05351			−0.0827716
$163$	−7.38352	+	12.7886i	−0.578322	+	1.00168i	0.417350	+	0.908746i	$0.362959\pi$
$163$	−7.38352	+	12.7886i	−0.578322	+	1.00168i	−0.995672	+	0.0929373i	$0.970374\pi$
$164$	1.01818	+	1.76353i	0.0795063	+	0.137709i
$165$	−2.85336	−	4.94216i	−0.222133	−	0.384746i
$166$	−6.10606	+	10.5760i	−0.473922	+	0.820858i
$167$	−8.85336			−0.685093			−0.342547	−	0.939501i	$-0.611290\pi$
$167$	−8.85336			−0.685093			−0.342547	+	0.939501i	$0.611290\pi$
$168$	8.05436	+	0.146736i	0.621407	+	0.0113209i
$169$	−2.06349			−0.158730
$170$	−3.40345	+	5.89494i	−0.261032	+	0.452121i
$171$	−0.348884	−	0.604285i	−0.0266799	−	0.0462109i
$172$	−3.46935	−	6.00909i	−0.264535	−	0.458188i
$173$	−7.85202	+	13.6001i	−0.596978	+	1.03400i	0.396287	+	0.918127i	$0.370299\pi$
$173$	−7.85202	+	13.6001i	−0.596978	+	1.03400i	−0.993265	+	0.115869i	$0.963035\pi$
$174$	7.70988			0.584484
$175$	0.699728	+	0.0127478i	0.0528945	+	0.000963642i
$176$	3.74342			0.282171
$177$	6.08141	−	10.5333i	0.457107	−	0.791733i
$178$	−0.175818	−	0.304526i	−0.0131781	−	0.0228252i
$179$	2.65376	+	4.59645i	0.198351	+	0.343555i	0.947994	−	0.318288i	$-0.103108\pi$
$179$	2.65376	+	4.59645i	0.198351	+	0.343555i	−0.749643	+	0.661843i	$0.769775\pi$
$180$	0.968498	−	1.67749i	0.0721876	−	0.125033i
$181$	1.93050			0.143493			0.0717463	−	0.997423i	$-0.477143\pi$
$181$	1.93050			0.143493			0.0717463	+	0.997423i	$0.477143\pi$
$182$	4.46273	+	8.06548i	0.330799	+	0.597853i
$183$	−1.48459			−0.109744
$184$	−1.52238	+	2.63685i	−0.112232	+	0.194391i
$185$	4.92559	+	8.53137i	0.362136	+	0.627238i
$186$	−2.95093	−	5.11116i	−0.216373	−	0.374769i
$187$	−3.89316	+	6.74314i	−0.284696	+	0.493107i
$188$	3.39485			0.247595
$189$	−1.36439	+	2.26681i	−0.0992449	+	0.164886i
$190$	−1.59968			−0.116053
$191$	−5.22089	+	9.04284i	−0.377770	+	0.654317i	−0.990737	−	0.135791i	$-0.956642\pi$
$191$	−5.22089	+	9.04284i	−0.377770	+	0.654317i	0.612967	+	0.790108i	$0.289976\pi$
$192$	3.84300	+	6.65627i	0.277344	+	0.480375i
$193$	−12.3081	−	21.3183i	−0.885959	−	1.53453i	−0.844610	−	0.535382i	$-0.820168\pi$
$193$	−12.3081	−	21.3183i	−0.885959	−	1.53453i	−0.0413492	−	0.999145i	$-0.513166\pi$
$194$	0.0657792	−	0.113933i	0.00472267	−	0.00817991i
$195$	7.19650			0.515352
$196$	3.30989	−	5.27898i	0.236420	−	0.377070i
$197$	5.17797			0.368915			0.184458	−	0.982840i	$-0.440947\pi$
$197$	5.17797			0.368915			0.184458	+	0.982840i	$0.440947\pi$
$198$	−1.38138	+	2.39262i	−0.0981703	+	0.170036i
$199$	8.31855	+	14.4082i	0.589687	+	1.02137i	0.994273	+	0.106867i	$0.0340821\pi$
$199$	8.31855	+	14.4082i	0.589687	+	1.02137i	−0.404587	+	0.914500i	$0.632585\pi$
$200$	0.402695	+	0.697489i	0.0284749	+	0.0493199i
$201$	5.63777	−	9.76490i	0.397658	−	0.688763i
$202$	9.24952			0.650794
$203$	9.98500	−	16.5891i	0.700809	−	1.16433i
$204$	−2.64286			−0.185037
$205$	−2.48919	+	4.31141i	−0.173853	+	0.301122i
$206$	−2.87862	−	4.98592i	−0.200563	−	0.347385i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	−2.36034	+	4.08822i	−0.163660	+	0.283467i
$209$	−1.82985			−0.126573
$210$	2.93659	+	5.30729i	0.202644	+	0.366238i
$211$	28.5995			1.96887			0.984435	−	0.175751i	$-0.0562354\pi$
$211$	28.5995			1.96887			0.984435	+	0.175751i	$0.0562354\pi$
$212$	1.39330	−	2.41326i	0.0956919	−	0.165743i
$213$	6.93213	+	12.0068i	0.474982	+	0.822693i
$214$	5.71143	+	9.89248i	0.390425	+	0.676236i
$215$	8.48171	−	14.6907i	0.578448	−	1.00190i
$216$	−3.04477			−0.207170
$217$	−14.8193	−	0.269981i	−1.00600	−	0.0183275i
$218$	1.11394			0.0754456
$219$	0.352915	−	0.611266i	0.0238478	−	0.0413055i
$220$	−2.53982	−	4.39909i	−0.171234	−	0.296587i
$221$	−4.90950	−	8.50350i	−0.330249	−	0.572008i
$222$	2.38459	−	4.13024i	0.160044	−	0.277203i
$223$	16.5464			1.10803			0.554016	−	0.832506i	$-0.313095\pi$
$223$	16.5464			1.10803			0.554016	+	0.832506i	$0.313095\pi$
$224$	12.1306	+	0.220997i	0.810508	+	0.0147660i
$225$	−0.264516			−0.0176344
$226$	−7.42400	+	12.8587i	−0.493837	+	0.855351i
$227$	8.98250	+	15.5581i	0.596189	+	1.03263i	0.993378	+	0.114893i	$0.0366526\pi$
$227$	8.98250	+	15.5581i	0.596189	+	1.03263i	−0.397189	+	0.917737i	$0.630014\pi$
$228$	−0.310548	−	0.537884i	−0.0205665	−	0.0356222i
$229$	−14.0030	+	24.2540i	−0.925348	+	1.60275i	−0.134346	+	0.990934i	$0.542893\pi$
$229$	−14.0030	+	24.2540i	−0.925348	+	1.60275i	−0.791001	+	0.611815i	$0.790440\pi$
$230$	−2.29256			−0.151167
$231$	3.35912	+	6.07094i	0.221014	+	0.399438i
$232$	22.2824			1.46291
$233$	−11.6231	+	20.1318i	−0.761454	+	1.31888i	0.180648	+	0.983548i	$0.442181\pi$
$233$	−11.6231	+	20.1318i	−0.761454	+	1.31888i	−0.942101	+	0.335329i	$0.891153\pi$
$234$	−1.74200	−	3.01723i	−0.113878	−	0.197243i
$235$	4.14979	+	7.18765i	0.270703	+	0.468871i
$236$	5.41316	−	9.37587i	0.352367	−	0.610317i
$237$	8.60406			0.558894
$238$	4.26782	−	7.09058i	0.276642	−	0.459614i
$239$	6.43482			0.416234			0.208117	−	0.978104i	$-0.433267\pi$
$239$	6.43482			0.416234			0.208117	+	0.978104i	$0.433267\pi$
$240$	−1.55316	+	2.69015i	−0.100256	+	0.173649i
$241$	−11.7589	−	20.3669i	−0.757455	−	1.31195i	−0.944145	−	0.329531i	$-0.893109\pi$
$241$	−11.7589	−	20.3669i	−0.757455	−	1.31195i	0.186690	−	0.982419i	$-0.440224\pi$
$242$	−2.17174	−	3.76156i	−0.139605	−	0.241802i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.32146			−0.0845977
$245$	15.2227	+	0.554845i	0.972543	+	0.0354477i
$246$	2.41016			0.153666
$247$	1.15377	−	1.99840i	0.0734129	−	0.127155i
$248$	−8.52853	−	14.7718i	−0.541562	−	0.938013i
$249$	−5.79592	−	10.0388i	−0.367302	−	0.636185i
$250$	−6.03461	+	10.4523i	−0.381662	+	0.661059i
$251$	−3.12594			−0.197307			−0.0986537	−	0.995122i	$-0.531454\pi$
$251$	−3.12594			−0.197307			−0.0986537	+	0.995122i	$0.531454\pi$
$252$	−1.21447	+	2.01773i	−0.0765043	+	0.127105i
$253$	−2.62243			−0.164871
$254$	8.27937	−	14.3403i	0.519494	−	0.899790i
$255$	−3.23058	−	5.59552i	−0.202307	−	0.350405i
$256$	8.25178	+	14.2925i	0.515736	+	0.893282i
$257$	10.2668	−	17.7826i	0.640426	−	1.10925i	−0.344912	−	0.938635i	$-0.612091\pi$
$257$	10.2668	−	17.7826i	0.640426	−	1.10925i	0.985338	−	0.170615i	$-0.0545756\pi$
$258$	−8.21240			−0.511282
$259$	−5.79866	−	10.4799i	−0.360311	−	0.651190i
$260$	6.40572			0.397266
$261$	−3.65914	+	6.33781i	−0.226495	+	0.392301i
$262$	−5.26910	−	9.12634i	−0.325526	−	0.563827i
$263$	−9.72378	−	16.8421i	−0.599594	−	1.03853i	−0.992881	−	0.119112i	$-0.961995\pi$
$263$	−9.72378	−	16.8421i	−0.599594	−	1.03853i	0.393287	−	0.919416i	$-0.371338\pi$
$264$	−3.99234	+	6.91494i	−0.245712	+	0.425585i
$265$	6.81254			0.418491
$266$	1.94459	+	0.0354269i	0.119230	+	0.00217216i
$267$	0.333776			0.0204267
$268$	5.01827	−	8.69190i	0.306540	−	0.530942i
$269$	−3.85970	−	6.68520i	−0.235330	−	0.407604i	0.724038	−	0.689760i	$-0.242284\pi$
$269$	−3.85970	−	6.68520i	−0.235330	−	0.407604i	−0.959369	+	0.282156i	$0.908950\pi$
$270$	−1.14628	−	1.98542i	−0.0697604	−	0.120829i
$271$	−15.4319	+	26.7288i	−0.937418	+	1.62366i	−0.167155	+	0.985931i	$0.553458\pi$
$271$	−15.4319	+	26.7288i	−0.937418	+	1.62366i	−0.770263	+	0.637726i	$0.779875\pi$
$272$	4.23831			0.256985
$273$	−8.74815	−	0.159376i	−0.529462	−	0.00964585i
$274$	−6.39242			−0.386180
$275$	−0.346838	+	0.600741i	−0.0209151	+	0.0362260i
$276$	−0.445058	−	0.770863i	−0.0267893	−	0.0464005i
$277$	−3.20072	−	5.54381i	−0.192313	−	0.333095i	0.753704	−	0.657214i	$-0.228265\pi$
$277$	−3.20072	−	5.54381i	−0.192313	−	0.333095i	−0.946016	+	0.324119i	$0.894932\pi$
$278$	7.43771	−	12.8825i	0.446084	−	0.772640i
$279$	5.60209			0.335388
$280$	8.48708	+	15.3387i	0.507200	+	0.916661i
$281$	−4.79227			−0.285883			−0.142941	−	0.989731i	$-0.545656\pi$
$281$	−4.79227			−0.285883			−0.142941	+	0.989731i	$0.545656\pi$
$282$	2.00901	−	3.47971i	0.119635	−	0.207214i
$283$	5.85073	+	10.1338i	0.347790	+	0.602389i	0.985857	−	0.167592i	$-0.0535990\pi$
$283$	5.85073	+	10.1338i	0.347790	+	0.602389i	−0.638067	+	0.769981i	$0.720266\pi$
$284$	6.17040	+	10.6874i	0.366146	+	0.634183i
$285$	0.759213	−	1.31500i	0.0449719	−	0.0778936i
$286$	−9.13655			−0.540255
$287$	3.12138	−	5.18588i	0.184249	−	0.306113i
$288$	−4.58569			−0.270214
$289$	4.09216	−	7.08783i	0.240715	−	0.416931i
$290$	8.38880	+	14.5298i	0.492607	+	0.853221i
$291$	0.0624381	+	0.108146i	0.00366019	+	0.00633963i
$292$	0.314135	−	0.544098i	0.0183834	−	0.0318409i
$293$	19.9031			1.16275			0.581376	−	0.813635i	$-0.302515\pi$
$293$	19.9031			1.16275			0.581376	+	0.813635i	$0.302515\pi$
$294$	−3.45221	−	6.51664i	−0.201337	−	0.380058i
$295$	26.4677			1.54101
$296$	6.89175	−	11.9369i	0.400575	−	0.693816i
$297$	−1.31121	−	2.27109i	−0.0760844	−	0.131782i
$298$	0.535133	+	0.926877i	0.0309994	+	0.0536925i
$299$	1.65352	−	2.86398i	0.0956255	−	0.165628i
$300$	−0.235450			−0.0135937
$301$	−10.6358	+	17.6704i	−0.613038	+	1.01851i
$302$	−23.7446			−1.36635
$303$	−4.38986	+	7.60346i	−0.252191	+	0.436807i
$304$	0.498019	+	0.862594i	0.0285633	+	0.0494732i
$305$	−1.61532	−	2.79782i	−0.0924931	−	0.160203i
$306$	−1.56400	+	2.70893i	−0.0894079	+	0.154859i
$307$	21.7588			1.24184			0.620920	−	0.783874i	$-0.286759\pi$
$307$	21.7588			1.24184			0.620920	+	0.783874i	$0.286759\pi$
$308$	2.99001	+	5.40384i	0.170372	+	0.307912i
$309$	5.46482			0.310883
$310$	6.42157	−	11.1225i	0.364721	−	0.631715i
$311$	4.07173	+	7.05244i	0.230886	+	0.399907i	0.958069	−	0.286537i	$-0.0925041\pi$
$311$	4.07173	+	7.05244i	0.230886	+	0.399907i	−0.727183	+	0.686444i	$0.759171\pi$
$312$	−5.03458	−	8.72015i	−0.285027	−	0.493681i
$313$	−0.525219	+	0.909706i	−0.0296871	+	0.0514196i	−0.880487	−	0.474070i	$-0.842784\pi$
$313$	−0.525219	+	0.909706i	−0.0296871	+	0.0514196i	0.850800	+	0.525489i	$0.176118\pi$
$314$	11.9743			0.675749
$315$	−5.75651	−	0.104873i	−0.324342	−	0.00590894i
$316$	7.65861			0.430831
$317$	−8.18399	+	14.1751i	−0.459658	+	0.796152i	−0.998943	−	0.0459720i	$-0.985361\pi$
$317$	−8.18399	+	14.1751i	−0.459658	+	0.796152i	0.539284	+	0.842124i	$0.318695\pi$
$318$	−1.64906	−	2.85625i	−0.0924745	−	0.160171i
$319$	9.59583	+	16.6205i	0.537263	+	0.930567i
$320$	−8.36281	+	14.4848i	−0.467495	+	0.809725i
$321$	−10.8427			−0.605178
$322$	2.78686	+	0.0507716i	0.155306	+	0.00282939i
$323$	−2.07176			−0.115276
$324$	0.445058	−	0.770863i	0.0247254	−	0.0428257i
$325$	−0.437383	−	0.757570i	−0.0242616	−	0.0420224i
$326$	7.77862	+	13.4730i	0.430818	+	0.746198i
$327$	−0.528680	+	0.915701i	−0.0292361	+	0.0506384i
$328$	6.96564			0.384613
$329$	−4.88535	−	8.82929i	−0.269338	−	0.486775i
$330$	−6.01208			−0.330954
$331$	−14.6464	+	25.3684i	−0.805042	+	1.39437i	0.111221	+	0.993796i	$0.464524\pi$
$331$	−14.6464	+	25.3684i	−0.805042	+	1.39437i	−0.916263	+	0.400577i	$0.868810\pi$
$332$	−5.15904	−	8.93572i	−0.283139	−	0.490412i
$333$	2.26348	+	3.92045i	0.124038	+	0.214840i
$334$	−4.66355	+	8.07751i	−0.255178	+	0.441982i
$335$	24.5369			1.34059
$336$	1.94762	−	3.23579i	0.106251	−	0.176527i
$337$	−4.27417			−0.232829			−0.116414	−	0.993201i	$-0.537140\pi$
$337$	−4.27417			−0.232829			−0.116414	+	0.993201i	$0.537140\pi$
$338$	−1.08695	+	1.88266i	−0.0591224	+	0.102403i
$339$	−7.04691	−	12.2056i	−0.382736	−	0.662918i
$340$	−2.87559	−	4.98066i	−0.155951	−	0.270114i
$341$	7.34554	−	12.7229i	0.397784	−	0.688981i
$342$	−0.735106			−0.0397500
$343$	−18.4926	−	1.01160i	−0.998507	−	0.0546214i
$344$	−23.7348			−1.27969
$345$	1.08806	−	1.88457i	0.0585791	−	0.101462i
$346$	8.27218	+	14.3278i	0.444715	+	0.770269i
$347$	−9.22195	−	15.9729i	−0.495060	−	0.857469i	0.504924	−	0.863164i	$-0.331521\pi$
$347$	−9.22195	−	15.9729i	−0.495060	−	0.857469i	−0.999984	+	0.00569469i	$0.998187\pi$
$348$	−3.25706	+	5.64139i	−0.174597	+	0.302410i
$349$	−19.9398			−1.06736			−0.533678	−	0.845688i	$-0.679190\pi$
$349$	−19.9398			−1.06736			−0.533678	+	0.845688i	$0.679190\pi$
$350$	0.380216	−	0.631694i	0.0203234	−	0.0337655i
$351$	3.30704			0.176517
$352$	−6.01282	+	10.4145i	−0.320485	+	0.555095i
$353$	11.0427	+	19.1266i	0.587746	+	1.01801i	0.994527	+	0.104480i	$0.0333179\pi$
$353$	11.0427	+	19.1266i	0.587746	+	1.01801i	−0.406781	+	0.913526i	$0.633349\pi$
$354$	−6.40683	−	11.0970i	−0.340519	−	0.589797i
$355$	−15.0851	+	26.1282i	−0.800635	+	1.38674i
$356$	0.297099			0.0157462
$357$	3.80321	+	6.87353i	0.201287	+	0.363786i
$358$	5.59153			0.295521
$359$	6.01948	−	10.4261i	0.317696	−	0.550266i	−0.662311	−	0.749229i	$-0.730424\pi$
$359$	6.01948	−	10.4261i	0.317696	−	0.550266i	0.980007	+	0.198963i	$0.0637575\pi$
$360$	−3.31288	−	5.73808i	−0.174604	−	0.302424i
$361$	9.25656	+	16.0328i	0.487187	+	0.843833i
$362$	1.01690	−	1.76132i	0.0534470	−	0.0925730i
$363$	4.12286			0.216394
$364$	−7.78687	−	0.141863i	−0.408143	−	0.00743563i
$365$	1.53597			0.0803962
$366$	−0.782016	+	1.35449i	−0.0408766	+	0.0708004i
$367$	−10.8238	−	18.7474i	−0.565000	−	0.978608i	−0.997050	−	0.0767584i	$-0.975543\pi$
$367$	−10.8238	−	18.7474i	−0.565000	−	0.978608i	0.432050	−	0.901850i	$-0.357790\pi$
$368$	0.713731	+	1.23622i	0.0372058	+	0.0644423i
$369$	−1.14387	+	1.98124i	−0.0595475	+	0.103139i
$370$	10.3783			0.539543
$371$	−8.28140	−	0.150872i	−0.429949	−	0.00783289i
$372$	4.98651			0.258539
$373$	−10.9713	+	19.0029i	−0.568074	+	0.983933i	0.428682	+	0.903455i	$0.358978\pi$
$373$	−10.9713	+	19.0029i	−0.568074	+	0.983933i	−0.996756	+	0.0804778i	$0.974355\pi$
$374$	4.10148	+	7.10397i	0.212082	+	0.367338i
$375$	−5.72810	−	9.92136i	−0.295798	−	0.512337i
$376$	5.80628	−	10.0568i	0.299436	−	0.518639i
$377$	−24.2018			−1.24646
$378$	1.34946	+	2.43888i	0.0694089	+	0.125442i
$379$	11.8759			0.610026			0.305013	−	0.952348i	$-0.401339\pi$
$379$	11.8759			0.610026			0.305013	+	0.952348i	$0.401339\pi$
$380$	0.675788	−	1.17050i	0.0346672	−	0.0600453i
$381$	7.85884	+	13.6119i	0.402621	+	0.697360i
$382$	5.50026	+	9.52673i	0.281418	+	0.487430i
$383$	2.23345	−	3.86846i	0.114124	−	0.197669i	−0.803305	−	0.595568i	$-0.796927\pi$
$383$	2.23345	−	3.86846i	0.114124	−	0.197669i	0.917429	+	0.397899i	$0.130260\pi$
$384$	−1.07410			−0.0548126
$385$	−7.78620	+	12.9360i	−0.396821	+	0.659282i
$386$	−25.9335			−1.31998
$387$	3.89763	−	6.75090i	0.198128	−	0.343168i
$388$	0.0555772	+	0.0962625i	0.00282150	+	0.00488699i
$389$	1.35712	+	2.35061i	0.0688089	+	0.119181i	0.898377	−	0.439225i	$-0.144747\pi$
$389$	1.35712	+	2.35061i	0.0688089	+	0.119181i	−0.829568	+	0.558405i	$0.811413\pi$
$390$	3.79080	−	6.56585i	0.191954	−	0.332475i
$391$	−2.96912			−0.150155
$392$	−9.97730	−	18.8338i	−0.503930	−	0.951252i
$393$	10.0029			0.504581
$394$	2.72752	−	4.72421i	0.137411	−	0.238002i
$395$	9.36172	+	16.2150i	0.471039	+	0.815864i
$396$	−1.16713	−	2.02153i	−0.0586507	−	0.101586i
$397$	3.69088	−	6.39280i	0.185240	−	0.320845i	−0.758417	−	0.651769i	$-0.774027\pi$
$397$	3.69088	−	6.39280i	0.185240	−	0.320845i	0.943657	+	0.330924i	$0.107360\pi$
$398$	17.5274			0.878567
$399$	−0.952030	+	1.58171i	−0.0476611	+	0.0791845i
$400$	0.377587			0.0188793
$401$	−1.35095	+	2.33992i	−0.0674634	+	0.116850i	−0.897784	−	0.440436i	$-0.854824\pi$
$401$	−1.35095	+	2.33992i	−0.0674634	+	0.116850i	0.830321	+	0.557286i	$0.188157\pi$
$402$	−5.93945	−	10.2874i	−0.296233	−	0.513090i
$403$	9.26317	+	16.0443i	0.461431	+	0.799222i
$404$	−3.90748	+	6.76796i	−0.194405	+	0.336719i
$405$	2.17612			0.108132
$406$	−9.87574	−	17.8484i	−0.490125	−	0.885801i
$407$	11.8716			0.588454
$408$	−4.52014	+	7.82911i	−0.223780	+	0.387599i
$409$	−12.4048	−	21.4857i	−0.613376	−	1.06240i	−0.990667	−	0.136303i	$-0.956478\pi$
$409$	−12.4048	−	21.4857i	−0.613376	−	1.06240i	0.377292	−	0.926094i	$-0.376855\pi$
$410$	2.62239	+	4.54212i	0.129511	+	0.224319i
$411$	3.03387	−	5.25481i	0.149650	−	0.259201i
$412$	4.86432			0.239648
$413$	−32.1745	−	0.586161i	−1.58320	−	0.0288431i
$414$	−1.05351			−0.0517772
$415$	12.6126	−	21.8457i	0.619128	−	1.07236i
$416$	−7.58253	−	13.1333i	−0.371764	−	0.643914i
$417$	7.05993	+	12.2282i	0.345726	+	0.598815i
$418$	−0.963882	+	1.66949i	−0.0471450	+	0.0816576i
$419$	−20.0785			−0.980899			−0.490450	−	0.871470i	$-0.663167\pi$
$419$	−20.0785			−0.980899			−0.490450	+	0.871470i	$0.663167\pi$
$420$	−5.12396	−	0.0933493i	−0.250024	−	0.00455498i
$421$	−26.5979			−1.29630			−0.648151	−	0.761512i	$-0.724458\pi$
$421$	−26.5979			−1.29630			−0.648151	+	0.761512i	$0.724458\pi$
$422$	15.0649	−	26.0932i	0.733349	−	1.27020i
$423$	1.90697	+	3.30297i	0.0927201	+	0.160596i
$424$	−4.76596	−	8.25489i	−0.231456	−	0.400893i
$425$	−0.392691	+	0.680160i	−0.0190483	+	0.0329926i
$426$	14.6061			0.707670
$427$	1.90164	+	3.43683i	0.0920269	+	0.166320i
$428$	−9.65122			−0.466509
$429$	4.33624	−	7.51059i	0.209356	−	0.362615i
$430$	−8.93557	−	15.4769i	−0.430911	−	0.746360i
$431$	12.0110	+	20.8036i	0.578548	+	1.00207i	0.995646	+	0.0932128i	$0.0297137\pi$
$431$	12.0110	+	20.8036i	0.578548	+	1.00207i	−0.417098	+	0.908861i	$0.636953\pi$
$432$	−0.713731	+	1.23622i	−0.0343394	+	0.0594776i
$433$	−14.0909			−0.677165			−0.338582	−	0.940937i	$-0.609947\pi$
$433$	−14.0909			−0.677165			−0.338582	+	0.940937i	$0.609947\pi$
$434$	−8.05245	+	13.3784i	−0.386530	+	0.642184i
$435$	−15.9254			−0.763565
$436$	−0.470587	+	0.815080i	−0.0225370	+	0.0390353i
$437$	−0.348884	−	0.604285i	−0.0166894	−	0.0289069i
$438$	−0.371799	−	0.643975i	−0.0177653	−	0.0307703i
$439$	−1.44976	+	2.51106i	−0.0691933	+	0.119846i	−0.898546	−	0.438878i	$-0.855376\pi$
$439$	−1.44976	+	2.51106i	−0.0691933	+	0.119846i	0.829353	+	0.558725i	$0.188709\pi$
$440$	−17.3756			−0.828350
$441$	6.99535	+	0.254970i	0.333112	+	0.0121414i
$442$	−10.3444			−0.492034
$443$	−6.99794	+	12.1208i	−0.332482	+	0.575876i	−0.982998	−	0.183617i	$-0.941220\pi$
$443$	−6.99794	+	12.1208i	−0.332482	+	0.575876i	0.650516	+	0.759493i	$0.274553\pi$
$444$	2.01476	+	3.48966i	0.0956161	+	0.165612i
$445$	0.363167	+	0.629024i	0.0172158	+	0.0298186i
$446$	8.71593	−	15.0964i	0.412711	−	0.714837i
$447$	−1.01590			−0.0480506
$448$	10.4867	−	17.4227i	0.495451	−	0.823145i
$449$	12.6648			0.597690			0.298845	−	0.954302i	$-0.403399\pi$
$449$	12.6648			0.597690			0.298845	+	0.954302i	$0.403399\pi$
$450$	−0.139335	+	0.241336i	−0.00656833	+	0.0113767i
$451$	2.99972	+	5.19567i	0.141251	+	0.244654i
$452$	−6.27257	−	10.8644i	−0.295037	−	0.511019i
$453$	11.2693	−	19.5190i	0.529477	−	0.917080i
$454$	18.9263			0.888256
$455$	−9.21815	−	16.6599i	−0.432153	−	0.781030i
$456$	−2.12454			−0.0994908
$457$	1.77836	−	3.08021i	0.0831881	−	0.144086i	−0.821430	−	0.570310i	$-0.806823\pi$
$457$	1.77836	−	3.08021i	0.0831881	−	0.144086i	0.904618	+	0.426224i	$0.140156\pi$
$458$	14.7524	+	25.5518i	0.689332	+	1.19396i
$459$	−1.48456	−	2.57133i	−0.0692934	−	0.120020i
$460$	0.968498	−	1.67749i	0.0451565	−	0.0782133i
$461$	16.1441			0.751904			0.375952	−	0.926639i	$-0.377316\pi$
$461$	16.1441			0.751904			0.375952	+	0.926639i	$0.377316\pi$
$462$	7.30835	+	0.133145i	0.340015	+	0.00619447i
$463$	9.78687			0.454834			0.227417	−	0.973797i	$-0.426972\pi$
$463$	9.78687			0.454834			0.227417	+	0.973797i	$0.426972\pi$
$464$	5.22328	−	9.04698i	0.242485	−	0.419996i
$465$	6.09540	+	10.5575i	0.282667	+	0.489594i
$466$	12.2450	+	21.2090i	0.567241	+	0.982490i
$467$	15.0788	−	26.1172i	0.697763	−	1.20856i	−0.271478	−	0.962445i	$-0.587512\pi$
$467$	15.0788	−	26.1172i	0.697763	−	1.20856i	0.969240	−	0.246116i	$-0.0791544\pi$
$468$	2.94365			0.136070
$469$	−29.8273	−	0.543400i	−1.37730	−	0.0250919i
$470$	8.74370			0.403317
$471$	−5.68305	+	9.84334i	−0.261861	+	0.453557i
$472$	−18.5165	−	32.0715i	−0.852290	−	1.47621i
$473$	−10.2213	−	17.7038i	−0.469975	−	0.814020i
$474$	4.53223	−	7.85006i	0.208172	−	0.360565i
$475$	−0.184571			−0.00846871
$476$	3.38529	+	6.11824i	0.155165	+	0.280429i
$477$	3.13059			0.143340
$478$	3.38957	−	5.87091i	0.155035	−	0.268529i
$479$	−1.46083	−	2.53024i	−0.0667471	−	0.115609i	0.830721	−	0.556690i	$-0.187929\pi$
$479$	−1.46083	−	2.53024i	−0.0667471	−	0.115609i	−0.897468	+	0.441080i	$0.854595\pi$
$480$	−4.98950	−	8.64206i	−0.227738	−	0.394454i
$481$	−7.48540	+	12.9651i	−0.341305	+	0.591158i
$482$	−24.7762			−1.12852
$483$	−1.36439	+	2.26681i	−0.0620820	+	0.103143i
$484$	3.66983			0.166810
$485$	−0.135873	+	0.235338i	−0.00616966	+	0.0106862i
$486$	−0.526755	−	0.912367i	−0.0238941	−	0.0413858i
$487$	−16.1191	−	27.9191i	−0.730427	−	1.26514i	−0.956701	−	0.291073i	$-0.905988\pi$
$487$	−16.1191	−	27.9191i	−0.730427	−	1.26514i	0.226274	−	0.974064i	$-0.427346\pi$
$488$	−2.26012	+	3.91464i	−0.102311	+	0.177207i
$489$	−14.7670			−0.667789
$490$	8.52486	−	13.5964i	0.385114	−	0.614224i
$491$	−12.1670			−0.549091			−0.274546	−	0.961574i	$-0.588527\pi$
$491$	−12.1670			−0.549091			−0.274546	+	0.961574i	$0.588527\pi$
$492$	−1.01818	+	1.76353i	−0.0459030	+	0.0795063i
$493$	10.8644	+	18.8177i	0.489309	+	0.847508i
$494$	−1.21551	−	2.10533i	−0.0546885	−	0.0947233i
$495$	2.85336	−	4.94216i	0.128249	−	0.222133i
$496$	−7.99677			−0.359066
$497$	18.9163	−	31.4277i	0.848512	−	1.40972i
$498$	−12.2121			−0.547238
$499$	−15.9148	+	27.5652i	−0.712444	+	1.23399i	0.251492	+	0.967859i	$0.419079\pi$
$499$	−15.9148	+	27.5652i	−0.712444	+	1.23399i	−0.963937	+	0.266131i	$0.914255\pi$
$500$	−5.09867	−	8.83116i	−0.228020	−	0.394942i
$501$	−4.42668	−	7.66723i	−0.197769	−	0.342547i
$502$	−1.64660	+	2.85200i	−0.0734915	+	0.127291i
$503$	0.217299			0.00968890			0.00484445	−	0.999988i	$-0.498458\pi$
$503$	0.217299			0.00968890			0.00484445	+	0.999988i	$0.498458\pi$
$504$	3.90010	+	7.04865i	0.173724	+	0.313972i
$505$	−19.1057			−0.850192
$506$	−1.38138	+	2.39262i	−0.0614098	+	0.106365i
$507$	−1.03174	−	1.78703i	−0.0458213	−	0.0793649i
$508$	6.99528	+	12.1162i	0.310366	+	0.537569i
$509$	−7.57985	+	13.1287i	−0.335971	+	0.581919i	−0.983671	−	0.179977i	$-0.942398\pi$
$509$	−7.57985	+	13.1287i	−0.335971	+	0.581919i	0.647700	+	0.761896i	$0.275731\pi$
$510$	−6.80689			−0.301414
$511$	−1.86714	−	0.0340159i	−0.0825973	−	0.00150477i
$512$	15.2385			0.673452
$513$	0.348884	−	0.604285i	0.0154036	−	0.0266799i
$514$	−10.8162	−	18.7342i	−0.477082	−	0.826330i
$515$	5.94604	+	10.2988i	0.262014	+	0.453821i
$516$	3.46935	−	6.00909i	0.152729	−	0.264535i
$517$	10.0018			0.439878
$518$	−12.6160	−	0.229841i	−0.554315	−	0.0100986i
$519$	−15.7040			−0.689330
$520$	10.9558	−	18.9761i	0.480445	−	0.832156i
$521$	13.2885	+	23.0163i	0.582179	+	1.00836i	0.995221	+	0.0976518i	$0.0311331\pi$
$521$	13.2885	+	23.0163i	0.582179	+	1.00836i	−0.413041	+	0.910712i	$0.635534\pi$
$522$	3.85494	+	6.67695i	0.168726	+	0.292242i
$523$	18.2681	−	31.6412i	0.798807	−	1.38357i	−0.121587	−	0.992581i	$-0.538798\pi$
$523$	18.2681	−	31.6412i	0.798807	−	1.38357i	0.920394	−	0.390993i	$-0.127868\pi$
$524$	8.90377			0.388963
$525$	0.338824	+	0.612356i	0.0147875	+	0.0267254i
$526$	−20.4882			−0.893328
$527$	8.31664	−	14.4048i	0.362279	−	0.627485i
$528$	1.87171	+	3.24189i	0.0814557	+	0.141085i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	3.58854	−	6.21553i	0.155876	−	0.269985i
$531$	12.1628			0.527822
$532$	−0.847417	+	1.40791i	−0.0367402	+	0.0610404i
$533$	−7.56565			−0.327705
$534$	0.175818	−	0.304526i	0.00760839	−	0.0131781i
$535$	−11.7974	−	20.4338i	−0.510048	−	0.883429i
$536$	−17.1657	−	29.7319i	−0.741445	−	1.28422i
$537$	−2.65376	+	4.59645i	−0.114518	+	0.198351i
$538$	−8.13247			−0.350616
$539$	9.75147	−	15.5528i	0.420026	−	0.669905i
$540$	1.93700			0.0833550
$541$	−4.97320	+	8.61383i	−0.213814	+	0.370337i	−0.952905	−	0.303268i	$-0.901922\pi$
$541$	−4.97320	+	8.61383i	−0.213814	+	0.370337i	0.739091	+	0.673606i	$0.235255\pi$
$542$	16.2576	+	28.1590i	0.698325	+	1.20953i
$543$	0.965248	+	1.67186i	0.0414228	+	0.0717463i
$544$	−6.80773	+	11.7913i	−0.291879	+	0.505549i
$545$	−2.30094			−0.0985614
$546$	−4.75354	+	7.89757i	−0.203433	+	0.337985i
$547$	−35.8124			−1.53123			−0.765614	−	0.643300i	$-0.777565\pi$
$547$	−35.8124			−1.53123			−0.765614	+	0.643300i	$0.777565\pi$
$548$	2.70049	−	4.67739i	0.115359	−	0.199808i
$549$	−0.742296	−	1.28569i	−0.0316804	−	0.0548721i
$550$	0.365397	+	0.632886i	0.0155806	+	0.0269864i
$551$	−2.55323	+	4.42233i	−0.108771	+	0.188397i
$552$	−3.04477			−0.129594
$553$	−11.0211	−	19.9184i	−0.468666	−	0.847018i
$554$	−6.74398			−0.286524
$555$	−4.92559	+	8.53137i	−0.209079	+	0.362136i
$556$	6.28415	+	10.8845i	0.266507	+	0.461604i
$557$	6.75130	+	11.6936i	0.286062	+	0.495474i	0.972866	−	0.231369i	$-0.0743204\pi$
$557$	6.75130	+	11.6936i	0.286062	+	0.495474i	−0.686804	+	0.726842i	$0.740987\pi$
$558$	2.95093	−	5.11116i	0.124923	−	0.216373i
$559$	25.7793			1.09035
$560$	8.21719	+	0.149702i	0.347240	+	0.00632608i
$561$	−7.78631			−0.328738
$562$	−2.52435	+	4.37231i	−0.106483	+	0.184435i
$563$	−18.7091	−	32.4051i	−0.788495	−	1.36571i	−0.926889	−	0.375336i	$-0.877527\pi$
$563$	−18.7091	−	32.4051i	−0.788495	−	1.36571i	0.138394	−	0.990377i	$-0.455806\pi$
$564$	1.69743	+	2.94003i	0.0714745	+	0.123797i
$565$	15.3349	−	26.5608i	0.645144	−	1.11742i
$566$	12.3276			0.518168
$567$	−2.64531	−	0.0481928i	−0.111093	−	0.00202391i
$568$	42.2135			1.77124
$569$	−21.4927	+	37.2264i	−0.901019	+	1.56061i	−0.0748455	+	0.997195i	$0.523846\pi$
$569$	−21.4927	+	37.2264i	−0.901019	+	1.56061i	−0.826174	+	0.563416i	$0.809487\pi$
$570$	−0.799839	−	1.38536i	−0.0335016	−	0.0580264i
$571$	10.3749	+	17.9698i	0.434175	+	0.752012i	0.997228	−	0.0744082i	$-0.0237068\pi$
$571$	10.3749	+	17.9698i	0.434175	+	0.752012i	−0.563053	+	0.826421i	$0.690373\pi$
$572$	3.85976	−	6.68529i	0.161385	−	0.279526i
$573$	−10.4418			−0.436211
$574$	−3.08722	−	5.57953i	−0.128858	−	0.232885i
$575$	−0.264516			−0.0110311
$576$	−3.84300	+	6.65627i	−0.160125	+	0.277344i
$577$	19.1817	+	33.2237i	0.798544	+	1.38312i	0.920564	+	0.390592i	$0.127730\pi$
$577$	19.1817	+	33.2237i	0.798544	+	1.38312i	−0.122020	+	0.992528i	$0.538937\pi$
$578$	−4.31113	−	7.46710i	−0.179319	−	0.310590i
$579$	12.3081	−	21.3183i	0.511509	−	0.885959i
$580$	−14.1755			−0.588604
$581$	−15.8158	+	26.2765i	−0.656151	+	1.09013i
$582$	0.131558			0.00545327
$583$	4.10488	−	7.10986i	0.170007	−	0.294460i
$584$	−1.07454	−	1.86116i	−0.0444649	−	0.0770155i
$585$	3.59825	+	6.23236i	0.148769	+	0.257676i
$586$	10.4841	−	18.1589i	0.433093	−	0.750139i
$587$	−21.7316			−0.896958			−0.448479	−	0.893793i	$-0.648034\pi$
$587$	−21.7316			−0.896958			−0.448479	+	0.893793i	$0.648034\pi$
$588$	6.22668	+	0.226953i	0.256784	+	0.00935938i
$589$	3.90896			0.161066
$590$	13.9420	−	24.1483i	0.573984	−	0.994169i
$591$	2.58899	+	4.48426i	0.106497	+	0.184458i
$592$	−3.23102	−	5.59630i	−0.132794	−	0.230006i
$593$	0.434004	−	0.751716i	0.0178224	−	0.0308693i	−0.856977	−	0.515355i	$-0.827660\pi$
$593$	0.434004	−	0.751716i	0.0178224	−	0.0308693i	0.874799	+	0.484486i	$0.160993\pi$
$594$	−2.76276			−0.113357
$595$	−8.81555	+	14.6462i	−0.361402	+	0.600436i
$596$	−0.904273			−0.0370404
$597$	−8.31855	+	14.4082i	−0.340456	+	0.589687i
$598$	−1.74200	−	3.01723i	−0.0712357	−	0.123384i
$599$	6.53259	+	11.3148i	0.266914	+	0.462309i	0.968063	−	0.250706i	$-0.0806626\pi$
$599$	6.53259	+	11.3148i	0.266914	+	0.462309i	−0.701149	+	0.713015i	$0.747329\pi$
$600$	−0.402695	+	0.697489i	−0.0164400	+	0.0284749i
$601$	−14.4244			−0.588385			−0.294192	−	0.955746i	$-0.595051\pi$
$601$	−14.4244			−0.588385			−0.294192	+	0.955746i	$0.595051\pi$
$602$	10.5194	+	19.0117i	0.428740	+	0.774860i
$603$	11.2755			0.459176
$604$	10.0310	−	17.3741i	0.408154	−	0.706943i
$605$	4.48592	+	7.76983i	0.182378	+	0.315889i
$606$	4.62476	+	8.01032i	0.187868	+	0.325397i
$607$	−14.4916	+	25.1002i	−0.588195	+	1.01878i	0.406274	+	0.913751i	$0.366828\pi$
$607$	−14.4916	+	25.1002i	−0.588195	+	1.01878i	−0.994469	+	0.105032i	$0.966505\pi$
$608$	−3.19975			−0.129767
$609$	19.3591	+	0.352688i	0.784471	+	0.0142917i
$610$	−3.40352			−0.137804
$611$	−6.30643	+	10.9231i	−0.255131	+	0.441900i
$612$	−1.32143	−	2.28879i	−0.0534157	−	0.0925187i
$613$	2.97847	+	5.15886i	0.120299	+	0.208364i	0.919886	−	0.392187i	$-0.128281\pi$
$613$	2.97847	+	5.15886i	0.120299	+	0.208364i	−0.799586	+	0.600551i	$0.794948\pi$
$614$	11.4616	−	19.8520i	0.462551	−	0.801161i
$615$	−4.97839			−0.200748
$616$	21.1220	+	0.384805i	0.851029	+	0.0155042i
$617$	−40.0363			−1.61180			−0.805901	−	0.592050i	$-0.798319\pi$
$617$	−40.0363			−1.61180			−0.805901	+	0.592050i	$0.798319\pi$
$618$	2.87862	−	4.98592i	0.115795	−	0.200563i
$619$	−5.25875	−	9.10842i	−0.211367	−	0.366098i	0.740776	−	0.671752i	$-0.234458\pi$
$619$	−5.25875	−	9.10842i	−0.211367	−	0.366098i	−0.952143	+	0.305654i	$0.901125\pi$
$620$	5.42561	+	9.39744i	0.217898	+	0.377410i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	8.57921			0.343995
$623$	−0.427540	−	0.772692i	−0.0171290	−	0.0309573i
$624$	−4.72067			−0.188978
$625$	11.8037	−	20.4447i	0.472149	−	0.817786i
$626$	0.553324	+	0.958385i	0.0221153	+	0.0383048i
$627$	−0.914925	−	1.58470i	−0.0365386	−	0.0632867i
$628$	−5.05858	+	8.76171i	−0.201859	+	0.349630i
$629$	13.4411			0.535930
$630$	−3.12795	+	5.19680i	−0.124621	+	0.207046i
$631$	44.9392			1.78900			0.894501	−	0.447065i	$-0.147531\pi$
$631$	44.9392			1.78900			0.894501	+	0.447065i	$0.147531\pi$
$632$	13.0987	−	22.6876i	0.521038	−	0.902464i
$633$	14.2997	+	24.7679i	0.568364	+	0.984435i
$634$	8.62191	+	14.9336i	0.342420	+	0.593089i
$635$	−17.1018	+	29.6211i	−0.678663	+	1.17548i
$636$	2.78659			0.110496
$637$	10.8367	+	20.4562i	0.429367	+	0.810503i
$638$	20.2186			0.800462
$639$	−6.93213	+	12.0068i	−0.274231	+	0.474982i
$640$	−1.16869	−	2.02423i	−0.0461964	−	0.0800146i
$641$	16.0204	+	27.7482i	0.632769	+	1.09599i	0.986983	+	0.160824i	$0.0514151\pi$
$641$	16.0204	+	27.7482i	0.632769	+	1.09599i	−0.354214	+	0.935164i	$0.615252\pi$
$642$	−5.71143	+	9.89248i	−0.225412	+	0.390425i
$643$	38.5772			1.52134			0.760669	−	0.649140i	$-0.224871\pi$
$643$	38.5772			1.52134			0.760669	+	0.649140i	$0.224871\pi$
$644$	−1.21447	+	2.01773i	−0.0478567	+	0.0795095i
$645$	16.9634			0.667934
$646$	−1.09131	+	1.89020i	−0.0429370	+	0.0743691i
$647$	−15.4667	−	26.7891i	−0.608058	−	1.05319i	−0.991560	−	0.129648i	$-0.958615\pi$
$647$	−15.4667	−	26.7891i	−0.608058	−	1.05319i	0.383502	−	0.923540i	$-0.374718\pi$
$648$	−1.52238	−	2.63685i	−0.0598049	−	0.103585i
$649$	15.9481	−	27.6229i	0.626017	−	1.08429i
$650$	−0.921575			−0.0361472
$651$	−7.17583	−	12.9689i	−0.281243	−	0.508290i
$652$	−13.1444			−0.514774
$653$	−21.2788	+	36.8560i	−0.832704	+	1.44229i	0.0631822	+	0.998002i	$0.479875\pi$
$653$	−21.2788	+	36.8560i	−0.832704	+	1.44229i	−0.895886	+	0.444284i	$0.853458\pi$
$654$	0.556970	+	0.964701i	0.0217793	+	0.0377228i
$655$	10.8838	+	18.8513i	0.425264	+	0.736579i
$656$	1.63283	−	2.82815i	0.0637513	−	0.110421i
$657$	0.705829			0.0275370
$658$	−10.6289	−	0.193640i	−0.414359	−	0.00754888i
$659$	32.5053			1.26623			0.633113	−	0.774059i	$-0.281777\pi$
$659$	32.5053			1.26623			0.633113	+	0.774059i	$0.281777\pi$
$660$	2.53982	−	4.39909i	0.0988623	−	0.171234i
$661$	−16.7914	−	29.0835i	−0.653109	−	1.13122i	−0.982364	−	0.186977i	$-0.940131\pi$
$661$	−16.7914	−	29.0835i	−0.653109	−	1.13122i	0.329255	−	0.944241i	$-0.393202\pi$
$662$	15.4302	+	26.7259i	0.599711	+	1.03873i
$663$	4.90950	−	8.50350i	0.190669	−	0.330249i
$664$	−35.2945			−1.36969
$665$	−4.01671	−	0.0731772i	−0.155761	−	0.00283769i
$666$	4.76919			0.184802
$667$	−3.65914	+	6.33781i	−0.141682	+	0.245401i
$668$	−3.94026	−	6.82473i	−0.152453	−	0.264057i
$669$	8.27322	+	14.3296i	0.319861	+	0.554016i
$670$	12.9249	−	22.3866i	0.499334	−	0.864871i
$671$	−3.89324			−0.150297
$672$	5.87390	+	10.6159i	0.226591	+	0.409517i
$673$	−1.23960			−0.0477832			−0.0238916	−	0.999715i	$-0.507606\pi$
$673$	−1.23960			−0.0477832			−0.0238916	+	0.999715i	$0.507606\pi$
$674$	−2.25144	+	3.89961i	−0.0867222	+	0.150207i
$675$	−0.132258	−	0.229078i	−0.00509062	−	0.00881721i
$676$	−0.918371	−	1.59067i	−0.0353220	−	0.0611795i
$677$	−2.84916	+	4.93490i	−0.109502	+	0.189663i	−0.915569	−	0.402162i	$-0.868259\pi$
$677$	−2.84916	+	4.93490i	−0.109502	+	0.189663i	0.806066	+	0.591825i	$0.201592\pi$
$678$	−14.8480			−0.570234
$679$	0.170380	−	0.283071i	0.00653859	−	0.0108633i
$680$	−19.6727			−0.754414
$681$	−8.98250	+	15.5581i	−0.344210	+	0.596189i
$682$	−7.73861	−	13.4037i	−0.296327	−	0.513253i
$683$	−13.6259	−	23.6007i	−0.521380	−	0.903056i	−0.999691	−	0.0248657i	$-0.992084\pi$
$683$	−13.6259	−	23.6007i	−0.521380	−	0.903056i	0.478311	−	0.878190i	$-0.341249\pi$
$684$	0.310548	−	0.537884i	0.0118741	−	0.0205665i
$685$	13.2041			0.504503
$686$	−10.6640	+	16.3392i	−0.407155	+	0.623833i
$687$	−28.0061			−1.06850
$688$	−5.56372	+	9.63665i	−0.212115	+	0.367394i
$689$	5.17650	+	8.96596i	0.197209	+	0.341576i
$690$	−1.14628	−	1.98542i	−0.0436382	−	0.0755835i
$691$	22.5757	−	39.1023i	0.858820	−	1.48752i	−0.0142345	−	0.999899i	$-0.504531\pi$
$691$	22.5757	−	39.1023i	0.858820	−	1.48752i	0.873055	−	0.487622i	$-0.162136\pi$
$692$	−13.9784			−0.531379
$693$	−3.57802	+	5.94455i	−0.135918	+	0.225815i
$694$	−19.4308			−0.737584
$695$	−15.3632	+	26.6099i	−0.582760	+	1.00937i
$696$	11.1412	+	19.2972i	0.422307	+	0.731457i
$697$	3.39629	+	5.88255i	0.128644	+	0.222817i
$698$	−10.5034	+	18.1925i	−0.397560	+	0.688594i
$699$	−23.2462			−0.879251
$700$	0.301593	+	0.545068i	0.0113991	+	0.0206016i
$701$	−0.456514			−0.0172423			−0.00862116	−	0.999963i	$-0.502744\pi$
$701$	−0.456514			−0.0172423			−0.00862116	+	0.999963i	$0.502744\pi$
$702$	1.74200	−	3.01723i	0.0657476	−	0.113878i
$703$	1.57938	+	2.73557i	0.0595675	+	0.103174i
$704$	10.0780	+	17.4556i	0.379828	+	0.657882i
$705$	−4.14979	+	7.18765i	−0.156290	+	0.270703i
$706$	23.2673			0.875676
$707$	23.2251	+	0.423119i	0.873470	+	0.0159130i
$708$	10.8263			0.406878
$709$	4.95123	−	8.57579i	0.185948	−	0.322071i	−0.757948	−	0.652315i	$-0.773798\pi$
$709$	4.95123	−	8.57579i	0.185948	−	0.322071i	0.943895	+	0.330245i	$0.107131\pi$
$710$	15.8923	+	27.5263i	0.596429	+	1.03304i
$711$	4.30203	+	7.45134i	0.161339	+	0.279447i
$712$	0.508135	−	0.880115i	0.0190431	−	0.0329837i
$713$	5.60209			0.209800
$714$	8.27454	+	0.150747i	0.309667	+	0.00564157i
$715$	18.8723			0.705785
$716$	−2.36215	+	4.09137i	−0.0882779	+	0.152902i
$717$	3.21741	+	5.57271i	0.120156	+	0.208117i
$718$	−6.34159	−	10.9840i	−0.236666	−	0.409918i
$719$	13.6043	−	23.5633i	0.507355	−	0.878764i	−0.492609	−	0.870251i	$-0.663957\pi$
$719$	13.6043	−	23.5633i	0.507355	−	0.878764i	0.999964	−	0.00851331i	$-0.00270990\pi$
$720$	−3.10632			−0.115766
$721$	−6.99999	−	12.6511i	−0.260693	−	0.471151i
$722$	19.5038			0.725855
$723$	11.7589	−	20.3669i	0.437317	−	0.757455i
$724$	0.859183	+	1.48815i	0.0319313	+	0.0553066i
$725$	0.967902	+	1.67645i	0.0359470	+	0.0622620i
$726$	2.17174	−	3.76156i	0.0806008	−	0.139605i
$727$	−29.0386			−1.07698			−0.538491	−	0.842631i	$-0.681006\pi$
$727$	−29.0386			−1.07698			−0.538491	+	0.842631i	$0.681006\pi$
$728$	−13.7383	+	22.8249i	−0.509175	+	0.845947i
$729$	1.00000			0.0370370
$730$	0.809078	−	1.40136i	0.0299453	−	0.0518668i
$731$	−11.5725	−	20.0442i	−0.428026	−	0.741363i
$732$	−0.660729	−	1.14442i	−0.0244213	−	0.0422989i
$733$	10.3993	−	18.0121i	0.384108	−	0.665294i	−0.607537	−	0.794291i	$-0.707843\pi$
$733$	10.3993	−	18.0121i	0.384108	−	0.665294i	0.991645	+	0.128997i	$0.0411758\pi$
$734$	−22.8060			−0.841786
$735$	7.13084	+	13.4607i	0.263025	+	0.496504i
$736$	−4.58569			−0.169031
$737$	14.7847	−	25.6078i	0.544600	−	0.943275i
$738$	1.20508	+	2.08726i	0.0443596	+	0.0768330i
$739$	−8.42350	−	14.5899i	−0.309864	−	0.536699i	0.668469	−	0.743740i	$-0.266950\pi$
$739$	−8.42350	−	14.5899i	−0.309864	−	0.536699i	−0.978332	+	0.207041i	$0.933617\pi$
$740$	−4.38434	+	7.59391i	−0.161172	+	0.279158i
$741$	2.30755			0.0847699
$742$	−4.49992	+	7.47620i	−0.165197	+	0.274460i
$743$	−38.5982			−1.41603			−0.708016	−	0.706197i	$-0.750409\pi$
$743$	−38.5982			−1.41603			−0.708016	+	0.706197i	$0.750409\pi$
$744$	8.52853	−	14.7718i	0.312671	−	0.541562i
$745$	−1.10536	−	1.91454i	−0.0404974	−	0.0701435i
$746$	11.5584	+	20.0198i	0.423183	+	0.732975i
$747$	5.79592	−	10.0388i	0.212062	−	0.367302i
$748$	−6.93072			−0.253412
$749$	13.8886	+	25.1008i	0.507477	+	0.917163i
$750$	−12.0692			−0.440706
$751$	−12.0016	+	20.7874i	−0.437945	+	0.758542i	−0.997531	−	0.0702297i	$-0.977627\pi$
$751$	−12.0016	+	20.7874i	−0.437945	+	0.758542i	0.559586	+	0.828772i	$0.310960\pi$
$752$	−2.72213	−	4.71486i	−0.0992658	−	0.171933i
$753$	−1.56297	−	2.70714i	−0.0569577	−	0.0986537i
$754$	−12.7484	+	22.0809i	−0.464271	+	0.804140i
$755$	49.0465			1.78498
$756$	−2.35463	−	0.0428972i	−0.0856372	−	0.00156016i
$757$	−6.54398			−0.237845			−0.118923	−	0.992904i	$-0.537944\pi$
$757$	−6.54398			−0.237845			−0.118923	+	0.992904i	$0.537944\pi$
$758$	6.25571	−	10.8352i	0.227218	−	0.393553i
$759$	−1.31121	−	2.27109i	−0.0475941	−	0.0824354i
$760$	−2.31163	−	4.00385i	−0.0838515	−	0.145235i
$761$	−8.00453	+	13.8642i	−0.290164	+	0.502579i	−0.973848	−	0.227199i	$-0.927043\pi$
$761$	−8.00453	+	13.8642i	−0.290164	+	0.502579i	0.683684	+	0.729778i	$0.260376\pi$
$762$	16.5587			0.599860
$763$	2.79705	+	0.0509572i	0.101260	+	0.00184477i
$764$	−9.29439			−0.336259
$765$	3.23058	−	5.59552i	0.116802	−	0.202307i
$766$	−2.35297	−	4.07546i	−0.0850162	−	0.147252i
$767$	20.1115	+	34.8341i	0.726183	+	1.25779i
$768$	−8.25178	+	14.2925i	−0.297761	+	0.515736i
$769$	35.3103			1.27332			0.636661	−	0.771144i	$-0.280315\pi$
$769$	35.3103			1.27332			0.636661	+	0.771144i	$0.280315\pi$
$770$	7.70099	+	13.9180i	0.277525	+	0.501570i
$771$	20.5336			0.739500
$772$	10.9557	−	18.9758i	0.394303	−	0.682953i
$773$	27.1450	+	47.0166i	0.976339	+	1.69107i	0.675444	+	0.737412i	$0.263952\pi$
$773$	27.1450	+	47.0166i	0.976339	+	1.69107i	0.300895	+	0.953657i	$0.402714\pi$
$774$	−4.10620	−	7.11214i	−0.147594	−	0.255641i
$775$	0.740922	−	1.28332i	0.0266147	−	0.0460980i
$776$	0.380219			0.0136491
$777$	6.17654	−	10.2617i	0.221582	−	0.368138i
$778$	2.85949			0.102518
$779$	−0.798157	+	1.38245i	−0.0285969	+	0.0495313i
$780$	3.20286	+	5.54752i	0.114681	+	0.198633i
$781$	18.1790	+	31.4870i	0.650497	+	1.12669i
$782$	−1.56400	+	2.70893i	−0.0559285	+	0.0968710i
$783$	−7.31827			−0.261534
$784$	−9.98560	−	0.363960i	−0.356629	−	0.0129986i
$785$	−24.7340			−0.882793
$786$	5.26910	−	9.12634i	0.187942	−	0.325526i
$787$	−25.9797	−	44.9982i	−0.926077	−	1.60401i	−0.789820	−	0.613339i	$-0.789826\pi$
$787$	−25.9797	−	44.9982i	−0.926077	−	1.60401i	−0.136257	−	0.990674i	$-0.543507\pi$
$788$	2.30450	+	3.99151i	0.0820944	+	0.142192i
$789$	9.72378	−	16.8421i	0.346176	−	0.599594i
$790$	19.7253			0.701796
$791$	−19.2295	+	31.9480i	−0.683723	+	1.13594i
$792$	−7.98469			−0.283723
$793$	2.45480	−	4.25184i	0.0871725	−	0.150987i
$794$	−3.88838	−	6.73488i	−0.137994	−	0.239012i
$795$	3.40627	+	5.89983i	0.120808	+	0.209245i
$796$	−7.40448	+	12.8249i	−0.262445	+	0.454568i
$797$	24.3737			0.863361			0.431680	−	0.902027i	$-0.357921\pi$
$797$	24.3737			0.863361			0.431680	+	0.902027i	$0.357921\pi$
$798$	0.941613	+	1.70177i	0.0333327	+	0.0602422i
$799$	11.3241			0.400616
$800$	−0.606495	+	1.05048i	−0.0214428	+	0.0371401i
$801$	0.166888	+	0.289058i	0.00589669	+	0.0102134i
$802$	1.42324	+	2.46513i	0.0502565	+	0.0870468i
$803$	0.925494	−	1.60300i	0.0326600	−	0.0565687i
$804$	10.0365			0.353961
$805$	−5.75651	−	0.104873i	−0.202890	−	0.00369629i
$806$	19.5177			0.687481
$807$	3.85970	−	6.68520i	0.135868	−	0.235330i
$808$	13.3661	+	23.1508i	0.470218	+	0.814441i
$809$	−4.71611	−	8.16855i	−0.165810	−	0.287191i	0.771133	−	0.636674i	$-0.219690\pi$
$809$	−4.71611	−	8.16855i	−0.165810	−	0.287191i	−0.936943	+	0.349483i	$0.886357\pi$
$810$	1.14628	−	1.98542i	0.0402762	−	0.0697604i
$811$	26.7248			0.938436			0.469218	−	0.883082i	$-0.344536\pi$
$811$	26.7248			0.938436			0.469218	+	0.883082i	$0.344536\pi$
$812$	17.2319	+	0.313934i	0.604720	+	0.0110169i
$813$	−30.8637			−1.08244
$814$	6.25343	−	10.8313i	0.219183	−	0.379635i
$815$	−16.0674	−	27.8296i	−0.562817	−	0.974827i
$816$	2.11915	+	3.67048i	0.0741852	+	0.128493i
$817$	2.71965	−	4.71057i	0.0951484	−	0.164802i
$818$	−26.1371			−0.913861
$819$	−4.23605	−	7.65581i	−0.148020	−	0.267516i
$820$	−4.43134			−0.154749
$821$	22.0582	−	38.2060i	0.769837	−	1.33340i	−0.167814	−	0.985819i	$-0.553671\pi$
$821$	22.0582	−	38.2060i	0.769837	−	1.33340i	0.937651	−	0.347578i	$-0.112996\pi$
$822$	−3.19621	−	5.53600i	−0.111481	−	0.193090i
$823$	−0.738602	−	1.27930i	−0.0257461	−	0.0445935i	0.852865	−	0.522131i	$-0.174863\pi$
$823$	−0.738602	−	1.27930i	−0.0257461	−	0.0445935i	−0.878611	+	0.477538i	$0.841529\pi$
$824$	8.31955	−	14.4099i	0.289825	−	0.501992i
$825$	−0.693675			−0.0241507
$826$	−17.4829	+	29.0462i	−0.608307	+	1.01064i
$827$	−39.6798			−1.37980			−0.689900	−	0.723904i	$-0.742346\pi$
$827$	−39.6798			−1.37980			−0.689900	+	0.723904i	$0.742346\pi$
$828$	0.445058	−	0.770863i	0.0154668	−	0.0267893i
$829$	1.55399	+	2.69159i	0.0539724	+	0.0934829i	0.891749	−	0.452530i	$-0.149478\pi$
$829$	1.55399	+	2.69159i	0.0539724	+	0.0934829i	−0.837777	+	0.546013i	$0.816145\pi$
$830$	−13.2875	−	23.0146i	−0.461216	−	0.798850i
$831$	3.20072	−	5.54381i	0.111032	−	0.192313i
$832$	−25.4179			−0.881207
$833$	11.0406	−	17.6089i	0.382536	−	0.610111i
$834$	14.8754			0.515093
$835$	9.63297	−	16.6848i	0.333363	−	0.577401i
$836$	−0.814389	−	1.41056i	−0.0281662	−	0.0487853i
$837$	2.80105	+	4.85155i	0.0968183	+	0.167694i
$838$	−10.5765	+	18.3190i	−0.365358	+	0.632818i
$839$	52.8937			1.82609			0.913046	−	0.407856i	$-0.133724\pi$
$839$	52.8937			1.82609			0.913046	+	0.407856i	$0.133724\pi$
$840$	−9.04015	+	15.0194i	−0.311915	+	0.518217i
$841$	24.5571			0.846798
$842$	−14.0106	+	24.2670i	−0.482837	+	0.836297i
$843$	−2.39614	−	4.15023i	−0.0825273	−	0.142941i
$844$	12.7284	+	22.0463i	0.438131	+	0.758864i
$845$	2.24519	−	3.88879i	0.0772370	−	0.133778i
$846$	4.01803			0.138143
$847$	−5.28106	−	9.54445i	−0.181459	−	0.327951i
$848$	−4.46880			−0.153459
$849$	−5.85073	+	10.1338i	−0.200796	+	0.347790i
$850$	0.413704	+	0.716556i	0.0141899	+	0.0245777i
$851$	2.26348	+	3.92045i	0.0775909	+	0.134391i
$852$	−6.17040	+	10.6874i	−0.211394	+	0.366146i
$853$	14.0250			0.480205			0.240103	−	0.970748i	$-0.422819\pi$
$853$	14.0250			0.480205			0.240103	+	0.970748i	$0.422819\pi$
$854$	4.13735	+	0.0753751i	0.141577	+	0.00257928i
$855$	1.51843			0.0519291
$856$	−16.5067	+	28.5904i	−0.564187	+	0.977200i
$857$	−11.0928	−	19.2133i	−0.378923	−	0.656313i	0.611983	−	0.790871i	$-0.290372\pi$
$857$	−11.0928	−	19.2133i	−0.378923	−	0.656313i	−0.990906	+	0.134558i	$0.957039\pi$
$858$	−4.56827	−	7.91248i	−0.155958	−	0.270128i
$859$	−3.25991	+	5.64634i	−0.111227	+	0.192651i	−0.916265	−	0.400572i	$-0.868811\pi$
$859$	−3.25991	+	5.64634i	−0.111227	+	0.192651i	0.805038	+	0.593223i	$0.202145\pi$
$860$	15.0994			0.514886
$861$	6.05179	+	0.110253i	0.206244	+	0.00375740i
$862$	25.3073			0.861972
$863$	7.92773	−	13.7312i	0.269863	−	0.467417i	−0.698963	−	0.715158i	$-0.746355\pi$
$863$	7.92773	−	13.7312i	0.269863	−	0.467417i	0.968826	+	0.247741i	$0.0796882\pi$
$864$	−2.29284	−	3.97132i	−0.0780041	−	0.135107i
$865$	−17.0869	−	29.5954i	−0.580972	−	1.00627i
$866$	−7.42245	+	12.8561i	−0.252225	+	0.436867i
$867$	8.18432			0.277954
$868$	−6.38732	−	11.5438i	−0.216800	−	0.391822i
$869$	22.5636			0.765416
$870$	−8.38880	+	14.5298i	−0.284407	+	0.492607i
$871$	18.6443	+	32.2929i	0.631739	+	1.09420i
$872$	1.60971	+	2.78810i	0.0545116	+	0.0944169i
$873$	−0.0624381	+	0.108146i	−0.00211321	+	0.00366019i
$874$	−0.735106			−0.0248653
$875$	−15.6308	+	25.9690i	−0.528416	+	0.877914i
$876$	0.628270			0.0212273
$877$	17.1200	−	29.6527i	0.578102	−	1.00130i	−0.417595	−	0.908633i	$-0.637127\pi$
$877$	17.1200	−	29.6527i	0.578102	−	1.00130i	0.995697	−	0.0926686i	$-0.0295397\pi$
$878$	1.52734	+	2.64543i	0.0515451	+	0.0892788i
$879$	9.95155	+	17.2366i	0.335658	+	0.581376i
$880$	−4.07306	+	7.05474i	−0.137303	+	0.237815i
$881$	−41.1806			−1.38741			−0.693704	−	0.720260i	$-0.744023\pi$
$881$	−41.1806			−1.38741			−0.693704	+	0.720260i	$0.744023\pi$
$882$	3.91747	−	6.24802i	0.131908	−	0.210382i
$883$	43.6733			1.46972			0.734862	−	0.678216i	$-0.237247\pi$
$883$	43.6733			1.46972			0.734862	+	0.678216i	$0.237247\pi$
$884$	4.37003	−	7.56911i	0.146980	−	0.254577i
$885$	13.2339	+	22.9217i	0.444851	+	0.770505i
$886$	7.37241	+	12.7694i	0.247681	+	0.428996i
$887$	6.16986	−	10.6865i	0.207164	−	0.358818i	−0.743656	−	0.668562i	$-0.766910\pi$
$887$	6.16986	−	10.6865i	0.207164	−	0.358818i	0.950820	+	0.309744i	$0.100243\pi$
$888$	13.7835			0.462544
$889$	21.4451	−	35.6290i	0.719245	−	1.19496i
$890$	0.765201			0.0256496
$891$	1.31121	−	2.27109i	0.0439273	−	0.0760844i
$892$	7.36413	+	12.7550i	0.246569	+	0.427071i
$893$	1.33062	+	2.30471i	0.0445277	+	0.0771242i
$894$	−0.535133	+	0.926877i	−0.0178975	+	0.0309994i
$895$	−11.5498			−0.386067
$896$	1.37584	+	2.48656i	0.0459636	+	0.0830700i
$897$	3.30704			0.110419
$898$	6.67126	−	11.5550i	0.222623	−	0.385594i
$899$	−20.4988	−	35.5050i	−0.683674	−	1.18416i
$900$	−0.117725	−	0.203906i	−0.00392417	−	0.00679686i
$901$	4.64756	−	8.04980i	0.154833	−	0.268178i
$902$	6.32047			0.210449
$903$	−20.6209	−	0.375676i	−0.686221	−	0.0125017i
$904$	−42.9124			−1.42725
$905$	−2.10049	+	3.63816i	−0.0698227	+	0.120937i
$906$	−11.8723	−	20.5634i	−0.394431	−	0.683174i
$907$	11.7736	+	20.3925i	0.390936	+	0.677122i	0.992573	−	0.121648i	$-0.0388179\pi$
$907$	11.7736	+	20.3925i	0.390936	+	0.677122i	−0.601637	+	0.798770i	$0.705485\pi$
$908$	−7.99547	+	13.8486i	−0.265339	+	0.459580i
$909$	−8.77972			−0.291205
$910$	−20.0557	−	0.365378i	−0.664839	−	0.0121122i
$911$	19.5967			0.649268			0.324634	−	0.945840i	$-0.394759\pi$
$911$	19.5967			0.649268			0.324634	+	0.945840i	$0.394759\pi$
$912$	−0.498019	+	0.862594i	−0.0164911	+	0.0285633i
$913$	−15.1994	−	26.3261i	−0.503027	−	0.871268i
$914$	−1.87352	−	3.24503i	−0.0619705	−	0.107336i
$915$	1.61532	−	2.79782i	0.0534009	−	0.0924931i
$916$	−24.9287			−0.823667
$917$	−12.8130	−	23.1568i	−0.423121	−	0.764706i
$918$	−3.12800			−0.103239
$919$	19.1264	−	33.1278i	0.630920	−	1.09279i	−0.356444	−	0.934317i	$-0.616011\pi$
$919$	19.1264	−	33.1278i	0.630920	−	1.09279i	0.987364	−	0.158469i	$-0.0506559\pi$
$920$	−3.31288	−	5.73808i	−0.109223	−	0.189179i
$921$	10.8794	+	18.8437i	0.358488	+	0.620920i
$922$	8.50397	−	14.7293i	0.280063	−	0.485084i
$923$	−45.8497			−1.50916
$924$	−3.18486	+	5.29134i	−0.104774	+	0.174072i
$925$	1.19745			0.0393720
$926$	5.15528	−	8.92921i	0.169413	−	0.293432i
$927$	2.73241	+	4.73267i	0.0897441	+	0.155441i
$928$	16.7797	+	29.0632i	0.550819	+	0.954047i
$929$	16.3841	−	28.3781i	0.537546	−	0.931057i	−0.461490	−	0.887146i	$-0.652685\pi$
$929$	16.3841	−	28.3781i	0.537546	−	0.931057i	0.999035	−	0.0439110i	$-0.0139818\pi$
$930$	12.8431			0.421143
$931$	4.88114	+	0.177910i	0.159973	+	0.00583077i
$932$	−20.6918			−0.677782
$933$	−4.07173	+	7.05244i	−0.133302	+	0.230886i
$934$	−15.8857	−	27.5148i	−0.519794	−	0.900310i
$935$	−8.47196	−	14.6739i	−0.277063	−	0.479887i
$936$	5.03458	−	8.72015i	0.164560	−	0.285027i
$937$	−49.1394			−1.60531			−0.802657	−	0.596441i	$-0.796581\pi$
$937$	−49.1394			−1.60531			−0.802657	+	0.596441i	$0.796581\pi$
$938$	−16.2075	+	26.9272i	−0.529193	+	0.879205i
$939$	−1.05044			−0.0342797
$940$	−3.69380	+	6.39784i	−0.120478	+	0.208675i
$941$	−29.8420	−	51.6879i	−0.972821	−	1.68498i	−0.686945	−	0.726710i	$-0.741049\pi$
$941$	−29.8420	−	51.6879i	−0.972821	−	1.68498i	−0.285876	−	0.958266i	$-0.592285\pi$
$942$	5.98715	+	10.3701i	0.195072	+	0.337875i
$943$	−1.14387	+	1.98124i	−0.0372495	+	0.0645181i
$944$	−17.3620			−0.565084
$945$	−2.78743	−	5.03772i	−0.0906751	−	0.163877i
$946$	−21.5364			−0.700210
$947$	1.33035	−	2.30423i	0.0432304	−	0.0748773i	−0.843601	−	0.536971i	$-0.819568\pi$
$947$	1.33035	−	2.30423i	0.0432304	−	0.0748773i	0.886831	+	0.462094i	$0.152902\pi$
$948$	3.82931	+	6.63255i	0.124370	+	0.215415i
$949$	1.16710	+	2.02148i	0.0378858	+	0.0656200i
$950$	−0.0972238	+	0.168397i	−0.00315436	+	0.00546351i
$951$	−16.3680			−0.530768
$952$	23.9144	+	0.435677i	0.775069	+	0.0141204i
$953$	−23.2051			−0.751686			−0.375843	−	0.926683i	$-0.622647\pi$
$953$	−23.2051			−0.751686			−0.375843	+	0.926683i	$0.622647\pi$
$954$	1.64906	−	2.85625i	0.0533902	−	0.0924745i
$955$	−11.3613	−	19.6783i	−0.367642	−	0.636774i
$956$	2.86387	+	4.96036i	0.0926240	+	0.160430i
$957$	−9.59583	+	16.6205i	−0.310189	+	0.537263i
$958$	−3.07800			−0.0994458
$959$	−16.0510	−	0.292421i	−0.518315	−	0.00944277i
$960$	−16.7256			−0.539817
$961$	−0.191710	+	0.332051i	−0.00618419	+	0.0107113i
$962$	7.88595	+	13.6589i	0.254253	+	0.440379i
$963$	−5.42133	−	9.39002i	−0.174700	−	0.302589i
$964$	10.4667	−	18.1289i	0.337111	−	0.583894i
$965$	53.5679			1.72441
$966$	1.34946	+	2.43888i	0.0434182	+	0.0784697i
$967$	−6.58436			−0.211739			−0.105869	−	0.994380i	$-0.533763\pi$
$967$	−6.58436			−0.211739			−0.105869	+	0.994380i	$0.533763\pi$
$968$	6.27658	−	10.8714i	0.201737	−	0.349419i
$969$	−1.03588	−	1.79420i	−0.0332773	−	0.0576379i
$970$	0.143143	+	0.247931i	0.00459605	+	0.00796060i
$971$	−20.9110	+	36.2190i	−0.671067	+	1.16232i	0.306535	+	0.951859i	$0.400830\pi$
$971$	−20.9110	+	36.2190i	−0.671067	+	1.16232i	−0.977602	+	0.210463i	$0.932503\pi$
$972$	0.890116			0.0285505
$973$	19.2650	−	32.0070i	0.617608	−	1.02610i
$974$	−33.9633			−1.08825
$975$	0.437383	−	0.757570i	0.0140075	−	0.0242616i
$976$	1.05960	+	1.83528i	0.0339169	+	0.0587458i
$977$	8.62798	+	14.9441i	0.276033	+	0.478104i	0.970395	−	0.241522i	$-0.0776466\pi$
$977$	8.62798	+	14.9441i	0.276033	+	0.478104i	−0.694362	+	0.719626i	$0.744313\pi$
$978$	−7.77862	+	13.4730i	−0.248733	+	0.430818i
$979$	0.875303			0.0279748
$980$	6.34728	+	11.9816i	0.202756	+	0.382737i
$981$	−1.05736			−0.0337589
$982$	−6.40905	+	11.1008i	−0.204521	+	0.354241i
$983$	−30.5595	−	52.9306i	−0.974697	−	1.68822i	−0.680932	−	0.732346i	$-0.738425\pi$
$983$	−30.5595	−	52.9306i	−0.974697	−	1.68822i	−0.293764	−	0.955878i	$-0.594908\pi$
$984$	3.48282	+	6.03242i	0.111028	+	0.192306i
$985$	−5.63394	+	9.75827i	−0.179512	+	0.310924i
$986$	22.8916			0.729016
$987$	5.20371	−	8.64549i	0.165636	−	0.275189i
$988$	2.05399			0.0653460
$989$	3.89763	−	6.75090i	0.123938	−	0.214666i
$990$	−3.00604	−	5.20661i	−0.0955382	−	0.165477i
$991$	−13.8482	−	23.9857i	−0.439901	−	0.761931i	0.557780	−	0.829989i	$-0.311653\pi$
$991$	−13.8482	−	23.9857i	−0.439901	−	0.761931i	−0.997681	+	0.0680574i	$0.978320\pi$
$992$	12.8447	−	22.2477i	0.407820	−	0.706366i
$993$	−29.2929			−0.929582
$994$	−18.7093	−	33.8133i	−0.593423	−	1.07249i
$995$	−36.2043			−1.14775
$996$	5.15904	−	8.93572i	0.163471	−	0.283139i
$997$	−7.82041	−	13.5453i	−0.247675	−	0.428985i	0.715205	−	0.698914i	$-0.246333\pi$
$997$	−7.82041	−	13.5453i	−0.247675	−	0.428985i	−0.962880	+	0.269929i	$0.913000\pi$
$998$	16.7664	+	29.0403i	0.530731	+	0.919254i
$999$	−2.26348	+	3.92045i	−0.0716132	+	0.124038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.415.8	yes	20
7.2	even	3		3381.2.a.bi.1.3		10
7.4	even	3	inner	483.2.i.h.277.8	✓	20
7.5	odd	6		3381.2.a.bj.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.8	✓	20	7.4	even	3	inner
483.2.i.h.415.8	yes	20	1.1	even	1	trivial
3381.2.a.bi.1.3		10	7.2	even	3
3381.2.a.bj.1.3		10	7.5	odd	6

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.526755 - 0.912367i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.445058 + 0.770863i) q^{4} +(-1.08806 + 1.88457i) q^{5} +1.05351 q^{6} +(1.36439 - 2.26681i) q^{7} +3.04477 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.526755 - 0.912367i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.445058 + 0.770863i) q^{4} +(-1.08806 + 1.88457i) q^{5} +1.05351 q^{6} +(1.36439 - 2.26681i) q^{7} +3.04477 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.14628 + 1.98542i) q^{10} +(1.31121 + 2.27109i) q^{11} +(-0.445058 + 0.770863i) q^{12} -3.30704 q^{13} +(-1.34946 - 2.43888i) q^{14} -2.17612 q^{15} +(0.713731 - 1.23622i) q^{16} +(1.48456 + 2.57133i) q^{17} +(0.526755 + 0.912367i) q^{18} +(-0.348884 + 0.604285i) q^{19} -1.93700 q^{20} +(2.64531 + 0.0481928i) q^{21} +2.76276 q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.52238 + 2.63685i) q^{24} +(0.132258 + 0.229078i) q^{25} +(-1.74200 + 3.01723i) q^{26} -1.00000 q^{27} +(2.35463 + 0.0428972i) q^{28} +7.31827 q^{29} +(-1.14628 + 1.98542i) q^{30} +(-2.80105 - 4.85155i) q^{31} +(2.29284 + 3.97132i) q^{32} +(-1.31121 + 2.27109i) q^{33} +3.12800 q^{34} +(2.78743 + 5.03772i) q^{35} -0.890116 q^{36} +(2.26348 - 3.92045i) q^{37} +(0.367553 + 0.636621i) q^{38} +(-1.65352 - 2.86398i) q^{39} +(-3.31288 + 5.73808i) q^{40} +2.28774 q^{41} +(1.43740 - 2.38811i) q^{42} -7.79527 q^{43} +(-1.16713 + 2.02153i) q^{44} +(-1.08806 - 1.88457i) q^{45} +(0.526755 + 0.912367i) q^{46} +(1.90697 - 3.30297i) q^{47} +1.42746 q^{48} +(-3.27687 - 6.18564i) q^{49} +0.278671 q^{50} +(-1.48456 + 2.57133i) q^{51} +(-1.47182 - 2.54927i) q^{52} +(-1.56530 - 2.71117i) q^{53} +(-0.526755 + 0.912367i) q^{54} -5.70671 q^{55} +(4.15426 - 6.90191i) q^{56} -0.697769 q^{57} +(3.85494 - 6.67695i) q^{58} +(-6.08141 - 10.5333i) q^{59} +(-0.968498 - 1.67749i) q^{60} +(-0.742296 + 1.28569i) q^{61} -5.90186 q^{62} +(1.28092 + 2.31500i) q^{63} +7.68599 q^{64} +(3.59825 - 6.23236i) q^{65} +(1.38138 + 2.39262i) q^{66} +(-5.63777 - 9.76490i) q^{67} +(-1.32143 + 2.28879i) q^{68} -1.00000 q^{69} +(6.06454 + 0.110485i) q^{70} +13.8643 q^{71} +(-1.52238 + 2.63685i) q^{72} +(-0.352915 - 0.611266i) q^{73} +(-2.38459 - 4.13024i) q^{74} +(-0.132258 + 0.229078i) q^{75} -0.621095 q^{76} +(6.93715 + 0.126382i) q^{77} -3.48400 q^{78} +(4.30203 - 7.45134i) q^{79} +(1.55316 + 2.69015i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.20508 - 2.08726i) q^{82} -11.5918 q^{83} +(1.14017 + 2.06062i) q^{84} -6.46115 q^{85} +(-4.10620 + 7.11214i) q^{86} +(3.65914 + 6.33781i) q^{87} +(3.99234 + 6.91494i) q^{88} +(0.166888 - 0.289058i) q^{89} -2.29256 q^{90} +(-4.51210 + 7.49644i) q^{91} -0.890116 q^{92} +(2.80105 - 4.85155i) q^{93} +(-2.00901 - 3.47971i) q^{94} +(-0.759213 - 1.31500i) q^{95} +(-2.29284 + 3.97132i) q^{96} +0.124876 q^{97} +(-7.36968 - 0.268614i) q^{98} -2.62243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

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