LMFDB - Embedded newform 483.2.i.h.277.4

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			277.4
Root			$0.599601 - 1.03854i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.h.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599601 - 1.03854i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.280958 - 0.486633i) q^{4} +(0.286327 + 0.495932i) q^{5} -1.19920 q^{6} +(-1.87398 - 1.86767i) q^{7} -3.07225 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.599601 - 1.03854i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.280958 - 0.486633i) q^{4} +(0.286327 + 0.495932i) q^{5} -1.19920 q^{6} +(-1.87398 - 1.86767i) q^{7} -3.07225 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.343363 - 0.594723i) q^{10} +(-1.26255 + 2.18680i) q^{11} +(-0.280958 - 0.486633i) q^{12} -5.05314 q^{13} +(-0.816015 + 3.06606i) q^{14} +0.572653 q^{15} +(1.28021 + 2.21739i) q^{16} +(1.12612 - 1.95049i) q^{17} +(-0.599601 + 1.03854i) q^{18} +(-1.19967 - 2.07789i) q^{19} +0.321783 q^{20} +(-2.55444 + 0.689075i) q^{21} +3.02811 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-1.53613 + 2.66065i) q^{24} +(2.33603 - 4.04613i) q^{25} +(3.02987 + 5.24788i) q^{26} -1.00000 q^{27} +(-1.43538 + 0.387202i) q^{28} +0.796522 q^{29} +(-0.343363 - 0.594723i) q^{30} +(1.72866 - 2.99412i) q^{31} +(-1.53702 + 2.66220i) q^{32} +(1.26255 + 2.18680i) q^{33} -2.70088 q^{34} +(0.389671 - 1.46413i) q^{35} -0.561916 q^{36} +(-4.40243 - 7.62523i) q^{37} +(-1.43865 + 2.49181i) q^{38} +(-2.52657 + 4.37615i) q^{39} +(-0.879668 - 1.52363i) q^{40} +10.9790 q^{41} +(2.24728 + 2.23972i) q^{42} -1.90984 q^{43} +(0.709448 + 1.22880i) q^{44} +(0.286327 - 0.495932i) q^{45} +(-0.599601 + 1.03854i) q^{46} +(0.968258 + 1.67707i) q^{47} +2.56042 q^{48} +(0.0235820 + 6.99996i) q^{49} -5.60275 q^{50} +(-1.12612 - 1.95049i) q^{51} +(-1.41972 + 2.45903i) q^{52} +(-4.78530 + 8.28839i) q^{53} +(0.599601 + 1.03854i) q^{54} -1.44601 q^{55} +(5.75733 + 5.73797i) q^{56} -2.39935 q^{57} +(-0.477595 - 0.827219i) q^{58} +(2.20464 - 3.81854i) q^{59} +(0.160891 - 0.278672i) q^{60} +(-1.06335 - 1.84178i) q^{61} -4.14602 q^{62} +(-0.680465 + 2.55675i) q^{63} +8.80724 q^{64} +(-1.44685 - 2.50602i) q^{65} +(1.51405 - 2.62242i) q^{66} +(-2.00778 + 3.47758i) q^{67} +(-0.632783 - 1.09601i) q^{68} -1.00000 q^{69} +(-1.75420 + 0.473206i) q^{70} +0.424132 q^{71} +(1.53613 + 2.66065i) q^{72} +(7.00045 - 12.1251i) q^{73} +(-5.27940 + 9.14418i) q^{74} +(-2.33603 - 4.04613i) q^{75} -1.34823 q^{76} +(6.45023 - 1.73998i) q^{77} +6.05973 q^{78} +(-2.48666 - 4.30702i) q^{79} +(-0.733116 + 1.26979i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.58304 - 11.4022i) q^{82} -10.1555 q^{83} +(-0.382364 + 1.43668i) q^{84} +1.28975 q^{85} +(1.14514 + 1.98344i) q^{86} +(0.398261 - 0.689808i) q^{87} +(3.87888 - 6.71841i) q^{88} +(-1.91357 - 3.31439i) q^{89} -0.686727 q^{90} +(9.46947 + 9.43762i) q^{91} -0.561916 q^{92} +(-1.72866 - 2.99412i) q^{93} +(1.16114 - 2.01115i) q^{94} +(0.686997 - 1.18991i) q^{95} +(1.53702 + 2.66220i) q^{96} +15.4364 q^{97} +(7.25559 - 4.22167i) q^{98} +2.52510 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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.599601	−	1.03854i	−0.423982	−	0.734358i	0.572343	−	0.820014i	$-0.306035\pi$
$2$	−0.599601	−	1.03854i	−0.423982	−	0.734358i	−0.996325	+	0.0856564i	$0.972701\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.280958	−	0.486633i	0.140479	−	0.243317i
$5$	0.286327	+	0.495932i	0.128049	+	0.221788i	0.922921	−	0.384990i	$-0.125795\pi$
$5$	0.286327	+	0.495932i	0.128049	+	0.221788i	−0.794872	+	0.606778i	$0.792462\pi$
$6$	−1.19920			−0.489572
$7$	−1.87398	−	1.86767i	−0.708297	−	0.705915i
$7$	−1.87398	−	1.86767i	−0.708297	−	0.705915i
$8$	−3.07225			−1.08621
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.343363	−	0.594723i	0.108581	−	0.188068i
$11$	−1.26255	+	2.18680i	−0.380674	+	0.659346i	−0.991159	−	0.132682i	$-0.957641\pi$
$11$	−1.26255	+	2.18680i	−0.380674	+	0.659346i	0.610485	+	0.792028i	$0.290975\pi$
$12$	−0.280958	−	0.486633i	−0.0811055	−	0.140479i
$13$	−5.05314			−1.40149			−0.700744	−	0.713413i	$-0.747149\pi$
$13$	−5.05314			−1.40149			−0.700744	+	0.713413i	$0.747149\pi$
$14$	−0.816015	+	3.06606i	−0.218089	+	0.819438i
$15$	0.572653			0.147858
$16$	1.28021	+	2.21739i	0.320052	+	0.554347i
$17$	1.12612	−	1.95049i	0.273123	−	0.473064i	−0.696537	−	0.717521i	$-0.745277\pi$
$17$	1.12612	−	1.95049i	0.273123	−	0.473064i	0.969660	+	0.244458i	$0.0786099\pi$
$18$	−0.599601	+	1.03854i	−0.141327	+	0.244786i
$19$	−1.19967	−	2.07789i	−0.275224	−	0.476702i	0.694968	−	0.719041i	$-0.255419\pi$
$19$	−1.19967	−	2.07789i	−0.275224	−	0.476702i	−0.970192	+	0.242339i	$0.922085\pi$
$20$	0.321783			0.0719528
$21$	−2.55444	+	0.689075i	−0.557425	+	0.150368i
$22$	3.02811			0.645595
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−1.53613	+	2.66065i	−0.313561	+	0.543103i
$25$	2.33603	−	4.04613i	0.467207	−	0.809226i
$26$	3.02987	+	5.24788i	0.594206	+	1.02919i
$27$	−1.00000			−0.192450
$28$	−1.43538	+	0.387202i	−0.271262	+	0.0731743i
$29$	0.796522			0.147910			0.0739552	−	0.997262i	$-0.476438\pi$
$29$	0.796522			0.147910			0.0739552	+	0.997262i	$0.476438\pi$
$30$	−0.343363	−	0.594723i	−0.0626893	−	0.108581i
$31$	1.72866	−	2.99412i	0.310476	−	0.537760i	−0.667989	−	0.744171i	$-0.732845\pi$
$31$	1.72866	−	2.99412i	0.310476	−	0.537760i	0.978465	+	0.206411i	$0.0661782\pi$
$32$	−1.53702	+	2.66220i	−0.271710	+	0.470615i
$33$	1.26255	+	2.18680i	0.219782	+	0.380674i
$34$	−2.70088			−0.463197
$35$	0.389671	−	1.46413i	0.0658664	−	0.247483i
$36$	−0.561916			−0.0936526
$37$	−4.40243	−	7.62523i	−0.723754	−	1.25358i	−0.959485	−	0.281761i	$-0.909081\pi$
$37$	−4.40243	−	7.62523i	−0.723754	−	1.25358i	0.235730	−	0.971819i	$-0.424252\pi$
$38$	−1.43865	+	2.49181i	−0.233380	+	0.404226i
$39$	−2.52657	+	4.37615i	−0.404575	+	0.700744i
$40$	−0.879668	−	1.52363i	−0.139088	−	0.240907i
$41$	10.9790			1.71464			0.857319	−	0.514785i	$-0.172128\pi$
$41$	10.9790			1.71464			0.857319	+	0.514785i	$0.172128\pi$
$42$	2.24728	+	2.23972i	0.346762	+	0.345596i
$43$	−1.90984			−0.291248			−0.145624	−	0.989340i	$-0.546519\pi$
$43$	−1.90984			−0.291248			−0.145624	+	0.989340i	$0.546519\pi$
$44$	0.709448	+	1.22880i	0.106953	+	0.185248i
$45$	0.286327	−	0.495932i	0.0426831	−	0.0739292i
$46$	−0.599601	+	1.03854i	−0.0884063	+	0.153124i
$47$	0.968258	+	1.67707i	0.141235	+	0.244626i	0.927962	−	0.372675i	$-0.121559\pi$
$47$	0.968258	+	1.67707i	0.141235	+	0.244626i	−0.786727	+	0.617301i	$0.788226\pi$
$48$	2.56042			0.369565
$49$	0.0235820	+	6.99996i	0.00336886	+	0.999994i
$50$	−5.60275			−0.792349
$51$	−1.12612	−	1.95049i	−0.157688	−	0.273123i
$52$	−1.41972	+	2.45903i	−0.196880	+	0.341005i
$53$	−4.78530	+	8.28839i	−0.657312	+	1.13850i	0.323997	+	0.946058i	$0.394973\pi$
$53$	−4.78530	+	8.28839i	−0.657312	+	1.13850i	−0.981309	+	0.192439i	$0.938360\pi$
$54$	0.599601	+	1.03854i	0.0815953	+	0.141327i
$55$	−1.44601			−0.194980
$56$	5.75733	+	5.73797i	0.769356	+	0.766768i
$57$	−2.39935			−0.317801
$58$	−0.477595	−	0.827219i	−0.0627113	−	0.108619i
$59$	2.20464	−	3.81854i	0.287019	−	0.497132i	−0.686078	−	0.727528i	$-0.740669\pi$
$59$	2.20464	−	3.81854i	0.287019	−	0.497132i	0.973097	+	0.230397i	$0.0740023\pi$
$60$	0.160891	−	0.278672i	0.0207710	−	0.0359764i
$61$	−1.06335	−	1.84178i	−0.136148	−	0.235815i	0.789887	−	0.613252i	$-0.210139\pi$
$61$	−1.06335	−	1.84178i	−0.136148	−	0.235815i	−0.926035	+	0.377437i	$0.876806\pi$
$62$	−4.14602			−0.526545
$63$	−0.680465	+	2.55675i	−0.0857305	+	0.322120i
$64$	8.80724			1.10091
$65$	−1.44685	−	2.50602i	−0.179459	−	0.310833i
$66$	1.51405	−	2.62242i	0.186367	−	0.322797i
$67$	−2.00778	+	3.47758i	−0.245289	+	0.424854i	−0.962213	−	0.272298i	$-0.912216\pi$
$67$	−2.00778	+	3.47758i	−0.245289	+	0.424854i	0.716924	+	0.697152i	$0.245550\pi$
$68$	−0.632783	−	1.09601i	−0.0767362	−	0.132911i
$69$	−1.00000			−0.120386
$70$	−1.75420	+	0.473206i	−0.209668	+	0.0565589i
$71$	0.424132			0.0503353			0.0251676	−	0.999683i	$-0.491988\pi$
$71$	0.424132			0.0503353			0.0251676	+	0.999683i	$0.491988\pi$
$72$	1.53613	+	2.66065i	0.181034	+	0.313561i
$73$	7.00045	−	12.1251i	0.819341	−	1.41914i	−0.0868270	−	0.996223i	$-0.527673\pi$
$73$	7.00045	−	12.1251i	0.819341	−	1.41914i	0.906168	−	0.422917i	$-0.138994\pi$
$74$	−5.27940	+	9.14418i	−0.613717	+	1.06299i
$75$	−2.33603	−	4.04613i	−0.269742	−	0.467207i
$76$	−1.34823			−0.154653
$77$	6.45023	−	1.73998i	0.735072	−	0.198290i
$78$	6.05973			0.686129
$79$	−2.48666	−	4.30702i	−0.279771	−	0.484577i	0.691557	−	0.722322i	$-0.256925\pi$
$79$	−2.48666	−	4.30702i	−0.279771	−	0.484577i	−0.971328	+	0.237745i	$0.923592\pi$
$80$	−0.733116	+	1.26979i	−0.0819649	+	0.141967i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.58304	−	11.4022i	−0.726975	−	1.25916i
$83$	−10.1555			−1.11471			−0.557355	−	0.830275i	$-0.688184\pi$
$83$	−10.1555			−1.11471			−0.557355	+	0.830275i	$0.688184\pi$
$84$	−0.382364	+	1.43668i	−0.0417193	+	0.156754i
$85$	1.28975			0.139893
$86$	1.14514	+	1.98344i	0.123484	+	0.213880i
$87$	0.398261	−	0.689808i	0.0426981	−	0.0739552i
$88$	3.87888	−	6.71841i	0.413490	−	0.716185i
$89$	−1.91357	−	3.31439i	−0.202838	−	0.351325i	0.746604	−	0.665269i	$-0.231683\pi$
$89$	−1.91357	−	3.31439i	−0.202838	−	0.351325i	−0.949442	+	0.313944i	$0.898350\pi$
$90$	−0.686727			−0.0723874
$91$	9.46947	+	9.43762i	0.992670	+	0.989331i
$92$	−0.561916			−0.0585838
$93$	−1.72866	−	2.99412i	−0.179253	−	0.310476i
$94$	1.16114	−	2.01115i	0.119762	−	0.207434i
$95$	0.686997	−	1.18991i	0.0704844	−	0.122083i
$96$	1.53702	+	2.66220i	0.156872	+	0.271710i
$97$	15.4364			1.56733			0.783665	−	0.621184i	$-0.213348\pi$
$97$	15.4364			1.56733			0.783665	+	0.621184i	$0.213348\pi$
$98$	7.25559	−	4.22167i	0.732925	−	0.426453i
$99$	2.52510			0.253782
$100$	−1.31265	−	2.27358i	−0.131265	−	0.227358i
$101$	3.44592	−	5.96851i	0.342882	−	0.593888i	−0.642085	−	0.766634i	$-0.721930\pi$
$101$	3.44592	−	5.96851i	0.342882	−	0.593888i	0.984967	+	0.172745i	$0.0552637\pi$
$102$	−1.35044	+	2.33903i	−0.133714	+	0.231599i
$103$	−5.37963	−	9.31779i	−0.530071	−	0.918109i	−0.999385	−	0.0350779i	$-0.988832\pi$
$103$	−5.37963	−	9.31779i	−0.530071	−	0.918109i	0.469314	−	0.883031i	$-0.344501\pi$
$104$	15.5245			1.52230
$105$	−1.07314	−	1.06953i	−0.104728	−	0.104375i
$106$	11.4771			1.11475
$107$	−4.36734	−	7.56446i	−0.422207	−	0.731284i	0.573948	−	0.818892i	$-0.305411\pi$
$107$	−4.36734	−	7.56446i	−0.422207	−	0.731284i	−0.996155	+	0.0876080i	$0.972078\pi$
$108$	−0.280958	+	0.486633i	−0.0270352	+	0.0468263i
$109$	1.49673	−	2.59242i	0.143361	−	0.248309i	−0.785399	−	0.618990i	$-0.787542\pi$
$109$	1.49673	−	2.59242i	0.143361	−	0.248309i	0.928760	+	0.370681i	$0.120876\pi$
$110$	0.867028	+	1.50174i	0.0826679	+	0.143185i
$111$	−8.80485			−0.835720
$112$	1.74228	−	6.54635i	0.164630	−	0.618572i
$113$	16.3312			1.53631			0.768156	−	0.640263i	$-0.221175\pi$
$113$	16.3312			1.53631			0.768156	+	0.640263i	$0.221175\pi$
$114$	1.43865	+	2.49181i	0.134742	+	0.233380i
$115$	0.286327	−	0.495932i	0.0267001	−	0.0462459i
$116$	0.223789	−	0.387614i	0.0207783	−	0.0359891i
$117$	2.52657	+	4.37615i	0.233581	+	0.404575i
$118$	−5.28761			−0.486764
$119$	−5.75320	+	1.55196i	−0.527395	+	0.142268i
$120$	−1.75934			−0.160605
$121$	2.31193	+	4.00437i	0.210175	+	0.364034i
$122$	−1.27517	+	2.20866i	−0.115449	+	0.199963i
$123$	5.48952	−	9.50813i	0.494973	−	0.857319i
$124$	−0.971360	−	1.68244i	−0.0872307	−	0.151088i
$125$	5.53874			0.495400
$126$	3.06329	−	0.826339i	0.272900	−	0.0736162i
$127$	18.5959			1.65012			0.825061	−	0.565044i	$-0.191141\pi$
$127$	18.5959			1.65012			0.825061	+	0.565044i	$0.191141\pi$
$128$	−2.20678	−	3.82226i	−0.195054	−	0.337843i
$129$	−0.954920	+	1.65397i	−0.0840760	+	0.145624i
$130$	−1.73506	+	3.00522i	−0.152175	+	0.263575i
$131$	−8.95601	−	15.5123i	−0.782490	−	1.35531i	−0.930487	−	0.366325i	$-0.880616\pi$
$131$	−8.95601	−	15.5123i	−0.782490	−	1.35531i	0.147997	−	0.988988i	$-0.452718\pi$
$132$	1.41890			0.123499
$133$	−1.63267	+	6.13453i	−0.141571	+	0.531931i
$134$	4.81547			0.415993
$135$	−0.286327	−	0.495932i	−0.0246431	−	0.0426831i
$136$	−3.45972	+	5.99240i	−0.296668	+	0.513844i
$137$	−8.07612	+	13.9882i	−0.689989	+	1.19510i	0.281852	+	0.959458i	$0.409051\pi$
$137$	−8.07612	+	13.9882i	−0.689989	+	1.19510i	−0.971841	+	0.235638i	$0.924282\pi$
$138$	0.599601	+	1.03854i	0.0510414	+	0.0884063i
$139$	−1.14087			−0.0967677			−0.0483839	−	0.998829i	$-0.515407\pi$
$139$	−1.14087			−0.0967677			−0.0483839	+	0.998829i	$0.515407\pi$
$140$	−0.603014	−	0.600986i	−0.0509640	−	0.0507926i
$141$	1.93652			0.163084
$142$	−0.254310	−	0.440478i	−0.0213412	−	0.0369641i
$143$	6.37985	−	11.0502i	0.533510	−	0.924066i
$144$	1.28021	−	2.21739i	0.106684	−	0.184782i
$145$	0.228066	+	0.395021i	0.0189398	+	0.0328047i
$146$	−16.7899			−1.38954
$147$	6.07393	+	3.47956i	0.500970	+	0.286989i
$148$	−4.94758			−0.406689
$149$	−4.01171	−	6.94849i	−0.328652	−	0.569242i	0.653592	−	0.756847i	$-0.273261\pi$
$149$	−4.01171	−	6.94849i	−0.328652	−	0.569242i	−0.982245	+	0.187604i	$0.939928\pi$
$150$	−2.80138	+	4.85212i	−0.228731	+	0.396174i
$151$	−10.1347	+	17.5539i	−0.824753	+	1.42851i	0.0773557	+	0.997004i	$0.475352\pi$
$151$	−10.1347	+	17.5539i	−0.824753	+	1.42851i	−0.902108	+	0.431510i	$0.857981\pi$
$152$	3.68570	+	6.38382i	0.298950	+	0.517796i
$153$	−2.25223			−0.182082
$154$	−5.67461	−	5.65552i	−0.457273	−	0.455735i
$155$	1.97984			0.159025
$156$	1.41972	+	2.45903i	0.113668	+	0.196880i
$157$	3.32459	−	5.75836i	0.265331	−	0.459567i	−0.702319	−	0.711862i	$-0.747852\pi$
$157$	3.32459	−	5.75836i	0.265331	−	0.459567i	0.967650	+	0.252295i	$0.0811853\pi$
$158$	−2.98200	+	5.16498i	−0.237236	+	0.410904i
$159$	4.78530	+	8.28839i	0.379499	+	0.657312i
$160$	−1.76036			−0.139169
$161$	−0.680465	+	2.55675i	−0.0536282	+	0.201500i
$162$	1.19920			0.0942182
$163$	−1.87355	−	3.24509i	−0.146748	−	0.254175i	0.783276	−	0.621674i	$-0.213547\pi$
$163$	−1.87355	−	3.24509i	−0.146748	−	0.254175i	−0.930024	+	0.367500i	$0.880214\pi$
$164$	3.08465	−	5.34277i	0.240871	−	0.417200i
$165$	−0.723005	+	1.25228i	−0.0562858	+	0.0974899i
$166$	6.08924	+	10.5469i	0.472616	+	0.818596i
$167$	−2.97131			−0.229927			−0.114964	−	0.993370i	$-0.536675\pi$
$167$	−2.97131			−0.229927			−0.114964	+	0.993370i	$0.536675\pi$
$168$	7.84789	−	2.11701i	0.605478	−	0.163331i
$169$	12.5342			0.964170
$170$	−0.773334	−	1.33945i	−0.0593120	−	0.102731i
$171$	−1.19967	+	2.07789i	−0.0917413	+	0.158901i
$172$	−0.536584	+	0.929391i	−0.0409142	+	0.0708654i
$173$	−5.75903	−	9.97493i	−0.437851	−	0.758380i	0.559673	−	0.828714i	$-0.310927\pi$
$173$	−5.75903	−	9.97493i	−0.437851	−	0.758380i	−0.997523	+	0.0703340i	$0.977593\pi$
$174$	−0.955190			−0.0724128
$175$	−11.9345	+	3.21940i	−0.902166	+	0.243364i
$176$	−6.46532			−0.487342
$177$	−2.20464	−	3.81854i	−0.165711	−	0.287019i
$178$	−2.29475	+	3.97462i	−0.171999	+	0.297911i
$179$	5.95674	−	10.3174i	0.445228	−	0.771157i	−0.552840	−	0.833287i	$-0.686456\pi$
$179$	5.95674	−	10.3174i	0.445228	−	0.771157i	0.998068	+	0.0621303i	$0.0197894\pi$
$180$	−0.160891	−	0.278672i	−0.0119921	−	0.0207710i
$181$	25.9847			1.93143			0.965713	−	0.259612i	$-0.0835947\pi$
$181$	25.9847			1.93143			0.965713	+	0.259612i	$0.0835947\pi$
$182$	4.12344	−	15.4932i	0.305649	−	1.14843i
$183$	−2.12670			−0.157210
$184$	1.53613	+	2.66065i	0.113245	+	0.196146i
$185$	2.52106	−	4.36661i	0.185352	−	0.321040i
$186$	−2.07301	+	3.59056i	−0.152000	+	0.263272i
$187$	2.84356	+	4.92519i	0.207942	+	0.360166i
$188$	1.08816			0.0793621
$189$	1.87398	+	1.86767i	0.136312	+	0.135853i
$190$	−1.64770			−0.119536
$191$	9.01168	+	15.6087i	0.652062	+	1.12941i	0.982622	+	0.185620i	$0.0594294\pi$
$191$	9.01168	+	15.6087i	0.652062	+	1.12941i	−0.330559	+	0.943785i	$0.607237\pi$
$192$	4.40362	−	7.62729i	0.317804	−	0.550453i
$193$	2.34144	−	4.05550i	0.168541	−	0.291921i	−0.769366	−	0.638808i	$-0.779428\pi$
$193$	2.34144	−	4.05550i	0.168541	−	0.291921i	0.937907	+	0.346887i	$0.112761\pi$
$194$	−9.25568	−	16.0313i	−0.664519	−	1.15098i
$195$	−2.89370			−0.207222
$196$	3.41304	+	1.95522i	0.243788	+	0.139658i
$197$	−22.4797			−1.60161			−0.800804	−	0.598926i	$-0.795594\pi$
$197$	−22.4797			−1.60161			−0.800804	+	0.598926i	$0.795594\pi$
$198$	−1.51405	−	2.62242i	−0.107599	−	0.186367i
$199$	−1.36686	+	2.36747i	−0.0968941	+	0.167826i	−0.910398	−	0.413735i	$-0.864224\pi$
$199$	−1.36686	+	2.36747i	−0.0968941	+	0.167826i	0.813503	+	0.581560i	$0.197557\pi$
$200$	−7.17689	+	12.4307i	−0.507483	+	0.878986i
$201$	2.00778	+	3.47758i	0.141618	+	0.245289i
$202$	−8.26470			−0.581502
$203$	−1.49266	−	1.48764i	−0.104764	−	0.104412i
$204$	−1.26557			−0.0886073
$205$	3.14359	+	5.44486i	0.219558	+	0.380286i
$206$	−6.45126	+	11.1739i	−0.449481	+	0.778523i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	−6.46908	−	11.2048i	−0.448550	−	0.776911i
$209$	6.05860			0.419082
$210$	−0.467294	+	1.75579i	−0.0322463	+	0.121161i
$211$	−3.94428			−0.271536			−0.135768	−	0.990741i	$-0.543350\pi$
$211$	−3.94428			−0.271536			−0.135768	+	0.990741i	$0.543350\pi$
$212$	2.68894	+	4.65737i	0.184677	+	0.319870i
$213$	0.212066	−	0.367309i	0.0145305	−	0.0251676i
$214$	−5.23732	+	9.07131i	−0.358016	+	0.620102i
$215$	−0.546838	−	0.947151i	−0.0372940	−	0.0645952i
$216$	3.07225			0.209040
$217$	−8.83151	+	2.38235i	−0.599522	+	0.161724i
$218$	−3.58977			−0.243130
$219$	−7.00045	−	12.1251i	−0.473047	−	0.819341i
$220$	−0.406268	+	0.703676i	−0.0273906	+	0.0474418i
$221$	−5.69042	+	9.85610i	−0.382779	+	0.662993i
$222$	5.27940	+	9.14418i	0.354330	+	0.613717i
$223$	−17.8955			−1.19837			−0.599187	−	0.800609i	$-0.704509\pi$
$223$	−17.8955			−1.19837			−0.599187	+	0.800609i	$0.704509\pi$
$224$	7.85248	−	2.11825i	0.524666	−	0.141531i
$225$	−4.67207			−0.311471
$226$	−9.79221	−	16.9606i	−0.651368	−	1.12820i
$227$	−9.08883	+	15.7423i	−0.603247	+	1.04485i	0.389079	+	0.921204i	$0.372793\pi$
$227$	−9.08883	+	15.7423i	−0.603247	+	1.04485i	−0.992326	+	0.123650i	$0.960540\pi$
$228$	−0.674115	+	1.16760i	−0.0446444	+	0.0773263i
$229$	−3.58735	−	6.21347i	−0.237059	−	0.410597i	0.722810	−	0.691046i	$-0.242850\pi$
$229$	−3.58735	−	6.21347i	−0.237059	−	0.410597i	−0.959869	+	0.280449i	$0.909517\pi$
$230$	−0.686727			−0.0452814
$231$	1.71824	−	6.45606i	0.113052	−	0.424777i
$232$	−2.44712			−0.160661
$233$	7.19351	+	12.4595i	0.471262	+	0.816250i	0.999460	−	0.0328714i	$-0.0104652\pi$
$233$	7.19351	+	12.4595i	0.471262	+	0.816250i	−0.528197	+	0.849122i	$0.677132\pi$
$234$	3.02987	−	5.24788i	0.198069	−	0.343065i
$235$	−0.554476	+	0.960381i	−0.0361700	+	0.0626483i
$236$	−1.23882	−	2.14570i	−0.0806403	−	0.139673i
$237$	−4.97332			−0.323052
$238$	5.06139	+	5.04437i	0.328081	+	0.326978i
$239$	−1.51078			−0.0977241			−0.0488620	−	0.998806i	$-0.515559\pi$
$239$	−1.51078			−0.0977241			−0.0488620	+	0.998806i	$0.515559\pi$
$240$	0.733116	+	1.26979i	0.0473225	+	0.0819649i
$241$	−15.3915	+	26.6588i	−0.991453	+	1.71725i	−0.382741	+	0.923856i	$0.625020\pi$
$241$	−15.3915	+	26.6588i	−0.991453	+	1.71725i	−0.608712	+	0.793392i	$0.708313\pi$
$242$	2.77247	−	4.80205i	0.178221	−	0.308688i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.19503			−0.0765037
$245$	−3.46475	+	2.01597i	−0.221355	+	0.128796i
$246$	−13.1661			−0.839439
$247$	6.06211	+	10.4999i	0.385723	+	0.668092i
$248$	−5.31087	+	9.19870i	−0.337241	+	0.584118i
$249$	−5.07774	+	8.79491i	−0.321789	+	0.557355i
$250$	−3.32103	−	5.75220i	−0.210041	−	0.363801i
$251$	12.8572			0.811540			0.405770	−	0.913975i	$-0.367003\pi$
$251$	12.8572			0.811540			0.405770	+	0.913975i	$0.367003\pi$
$252$	1.05302	+	1.04948i	0.0663338	+	0.0661108i
$253$	2.52510			0.158752
$254$	−11.1501	−	19.3126i	−0.699621	−	1.21178i
$255$	0.644874	−	1.11696i	0.0403836	−	0.0699465i
$256$	6.16087	−	10.6709i	0.385054	−	0.666933i
$257$	−2.08407	−	3.60971i	−0.130000	−	0.225167i	0.793676	−	0.608341i	$-0.208165\pi$
$257$	−2.08407	−	3.60971i	−0.130000	−	0.225167i	−0.923676	+	0.383173i	$0.874831\pi$
$258$	2.29028			0.142587
$259$	−5.99140	+	22.5118i	−0.372287	+	1.39882i
$260$	−1.62601			−0.100841
$261$	−0.398261	−	0.689808i	−0.0246517	−	0.0426981i
$262$	−10.7401	+	18.6023i	−0.663523	+	1.14926i
$263$	−4.56752	+	7.91118i	−0.281645	+	0.487824i	−0.971790	−	0.235847i	$-0.924213\pi$
$263$	−4.56752	+	7.91118i	−0.281645	+	0.487824i	0.690145	+	0.723671i	$0.257547\pi$
$264$	−3.87888	−	6.71841i	−0.238728	−	0.413490i
$265$	−5.48064			−0.336673
$266$	7.34990	−	1.98267i	0.450651	−	0.121566i
$267$	−3.82713			−0.234217
$268$	1.12820	+	1.95411i	0.0689160	+	0.119366i
$269$	4.51600	−	7.82195i	0.275346	−	0.476913i	−0.694877	−	0.719129i	$-0.744541\pi$
$269$	4.51600	−	7.82195i	0.275346	−	0.476913i	0.970222	+	0.242216i	$0.0778744\pi$
$270$	−0.343363	+	0.594723i	−0.0208964	+	0.0361937i
$271$	−3.52651	−	6.10809i	−0.214220	−	0.371040i	0.738811	−	0.673913i	$-0.235388\pi$
$271$	−3.52651	−	6.10809i	−0.214220	−	0.371040i	−0.953031	+	0.302873i	$0.902054\pi$
$272$	5.76666			0.349655
$273$	12.9080	−	3.48199i	0.781225	−	0.210740i
$274$	19.3698			1.17017
$275$	5.89873	+	10.2169i	0.355707	+	0.616102i
$276$	−0.280958	+	0.486633i	−0.0169117	+	0.0292919i
$277$	−5.65599	+	9.79646i	−0.339835	+	0.588612i	−0.984402	−	0.175936i	$-0.943705\pi$
$277$	−5.65599	+	9.79646i	−0.339835	+	0.588612i	0.644566	+	0.764549i	$0.277038\pi$
$278$	0.684069	+	1.18484i	0.0410277	+	0.0710621i
$279$	−3.45731			−0.206984
$280$	−1.19717	+	4.49818i	−0.0715444	+	0.268818i
$281$	−22.3499			−1.33329			−0.666643	−	0.745377i	$-0.732269\pi$
$281$	−22.3499			−1.33329			−0.666643	+	0.745377i	$0.732269\pi$
$282$	−1.16114	−	2.01115i	−0.0691447	−	0.119762i
$283$	9.23844	−	16.0015i	0.549168	−	0.951188i	−0.449163	−	0.893450i	$-0.648278\pi$
$283$	9.23844	−	16.0015i	0.549168	−	0.951188i	0.998332	−	0.0577380i	$-0.0183888\pi$
$284$	0.119163	−	0.206397i	0.00707104	−	0.0122474i
$285$	−0.686997	−	1.18991i	−0.0406942	−	0.0704844i
$286$	−15.3014			−0.904794
$287$	−20.5745	−	20.5053i	−1.21447	−	1.21039i
$288$	3.07405			0.181140
$289$	5.96372	+	10.3295i	0.350807	+	0.607616i
$290$	0.273497	−	0.473710i	0.0160603	−	0.0278172i
$291$	7.71820	−	13.3683i	0.452449	−	0.783665i
$292$	−3.93367	−	6.81331i	−0.230200	−	0.398719i
$293$	0.717401			0.0419110			0.0209555	−	0.999780i	$-0.493329\pi$
$293$	0.717401			0.0419110			0.0209555	+	0.999780i	$0.493329\pi$
$294$	−0.0282796	−	8.39436i	−0.00164930	−	0.489569i
$295$	2.52498			0.147010
$296$	13.5254	+	23.4266i	0.786146	+	1.36165i
$297$	1.26255	−	2.18680i	0.0732607	−	0.126891i
$298$	−4.81085	+	8.33264i	−0.278685	+	0.482697i
$299$	2.52657	+	4.37615i	0.146115	+	0.253079i
$300$	−2.62531			−0.151572
$301$	3.57900	+	3.56696i	0.206290	+	0.205596i
$302$	24.3072			1.39872
$303$	−3.44592	−	5.96851i	−0.197963	−	0.342882i
$304$	3.07167	−	5.32028i	0.176172	−	0.305139i
$305$	0.608931	−	1.05470i	0.0348673	−	0.0603919i
$306$	1.35044	+	2.33903i	0.0771996	+	0.133714i
$307$	−8.27982			−0.472555			−0.236277	−	0.971686i	$-0.575927\pi$
$307$	−8.27982			−0.472555			−0.236277	+	0.971686i	$0.575927\pi$
$308$	0.965509	−	3.62776i	0.0550150	−	0.206711i
$309$	−10.7593			−0.612073
$310$	−1.18712	−	2.05614i	−0.0674236	−	0.116781i
$311$	4.47306	−	7.74757i	0.253644	−	0.439325i	−0.710882	−	0.703311i	$-0.751704\pi$
$311$	4.47306	−	7.74757i	0.253644	−	0.439325i	0.964526	+	0.263987i	$0.0850374\pi$
$312$	7.76226	−	13.4446i	0.439451	−	0.761152i
$313$	2.46922	+	4.27681i	0.139569	+	0.241740i	0.927333	−	0.374236i	$-0.122095\pi$
$313$	2.46922	+	4.27681i	0.139569	+	0.241740i	−0.787765	+	0.615976i	$0.788762\pi$
$314$	−7.97371			−0.449983
$315$	−1.46281	+	0.394601i	−0.0824200	+	0.0222332i
$316$	−2.79458			−0.157208
$317$	7.87069	+	13.6324i	0.442062	+	0.765674i	0.997842	−	0.0656555i	$-0.0209138\pi$
$317$	7.87069	+	13.6324i	0.442062	+	0.765674i	−0.555781	+	0.831329i	$0.687581\pi$
$318$	5.73854	−	9.93945i	0.321801	−	0.557376i
$319$	−1.00565	+	1.74184i	−0.0563056	+	0.0975242i
$320$	2.52175	+	4.36780i	0.140970	+	0.244167i
$321$	−8.73468			−0.487522
$322$	3.06329	−	0.826339i	0.170711	−	0.0460501i
$323$	−5.40389			−0.300680
$324$	0.280958	+	0.486633i	0.0156088	+	0.0270352i
$325$	−11.8043	+	20.4457i	−0.654785	+	1.13412i
$326$	−2.24677	+	3.89151i	−0.124437	+	0.215531i
$327$	−1.49673	−	2.59242i	−0.0827696	−	0.143361i
$328$	−33.7304			−1.86245
$329$	1.31773	−	4.95119i	0.0726489	−	0.272968i
$330$	1.73406			0.0954567
$331$	13.6672	+	23.6723i	0.751218	+	1.30115i	0.947233	+	0.320547i	$0.103867\pi$
$331$	13.6672	+	23.6723i	0.751218	+	1.30115i	−0.196015	+	0.980601i	$0.562800\pi$
$332$	−2.85326	+	4.94200i	−0.156593	+	0.271227i
$333$	−4.40243	+	7.62523i	−0.241251	+	0.417860i
$334$	1.78160	+	3.08583i	0.0974849	+	0.168849i
$335$	−2.29952			−0.125636
$336$	−4.79817	−	4.78203i	−0.261762	−	0.260881i
$337$	9.73803			0.530465			0.265232	−	0.964185i	$-0.414551\pi$
$337$	9.73803			0.530465			0.265232	+	0.964185i	$0.414551\pi$
$338$	−7.51552	−	13.0173i	−0.408790	−	0.708046i
$339$	8.16561	−	14.1433i	0.443495	−	0.768156i
$340$	0.362365	−	0.627635i	0.0196520	−	0.0340383i
$341$	4.36504	+	7.56047i	0.236380	+	0.409422i
$342$	2.87730			0.155587
$343$	13.0295	−	13.1618i	0.703525	−	0.710671i
$344$	5.86751			0.316355
$345$	−0.286327	−	0.495932i	−0.0154153	−	0.0267001i
$346$	−6.90623	+	11.9619i	−0.371281	+	0.643078i
$347$	14.4646	−	25.0535i	0.776502	−	1.34494i	−0.157445	−	0.987528i	$-0.550326\pi$
$347$	14.4646	−	25.0535i	0.776502	−	1.34494i	0.933947	−	0.357412i	$-0.116341\pi$
$348$	−0.223789	−	0.387614i	−0.0119964	−	0.0207783i
$349$	19.9972			1.07042			0.535212	−	0.844718i	$-0.320232\pi$
$349$	19.9972			1.07042			0.535212	+	0.844718i	$0.320232\pi$
$350$	10.4994	+	10.4641i	0.561218	+	0.559331i
$351$	5.05314			0.269717
$352$	−3.88114	−	6.72234i	−0.206866	−	0.358302i
$353$	12.2984	−	21.3014i	0.654577	−	1.13376i	−0.327423	−	0.944878i	$-0.606180\pi$
$353$	12.2984	−	21.3014i	0.654577	−	1.13376i	0.982000	−	0.188883i	$-0.0604866\pi$
$354$	−2.64380	+	4.57920i	−0.140517	+	0.243382i
$355$	0.121440	+	0.210341i	0.00644539	+	0.0111637i
$356$	−2.15052			−0.113978
$357$	−1.53257	+	5.75840i	−0.0811120	+	0.304767i
$358$	−14.2867			−0.755074
$359$	−10.1575	−	17.5933i	−0.536091	−	0.928537i	−0.999110	−	0.0421885i	$-0.986567\pi$
$359$	−10.1575	−	17.5933i	−0.536091	−	0.928537i	0.463018	−	0.886349i	$-0.346766\pi$
$360$	−0.879668	+	1.52363i	−0.0463626	+	0.0803023i
$361$	6.62157	−	11.4689i	0.348504	−	0.603626i
$362$	−15.5804	−	26.9861i	−0.818889	−	1.41836i
$363$	4.62385			0.242689
$364$	7.25318	−	1.95658i	0.380170	−	0.102553i
$365$	8.01767			0.419664
$366$	1.27517	+	2.20866i	0.0666543	+	0.115449i
$367$	1.74011	−	3.01396i	0.0908330	−	0.157327i	−0.817029	−	0.576597i	$-0.804380\pi$
$367$	1.74011	−	3.01396i	0.0908330	−	0.157327i	0.907862	+	0.419269i	$0.137714\pi$
$368$	1.28021	−	2.21739i	0.0667355	−	0.115589i
$369$	−5.48952	−	9.50813i	−0.285773	−	0.494973i
$370$	−6.04653			−0.314344
$371$	24.4476	−	6.59486i	1.26925	−	0.342388i
$372$	−1.94272			−0.100725
$373$	15.0544	+	26.0751i	0.779490	+	1.35012i	0.932236	+	0.361850i	$0.117855\pi$
$373$	15.0544	+	26.0751i	0.779490	+	1.35012i	−0.152747	+	0.988265i	$0.548812\pi$
$374$	3.41000	−	5.90630i	0.176327	−	0.305407i
$375$	2.76937	−	4.79669i	0.143010	−	0.247700i
$376$	−2.97473	−	5.15239i	−0.153410	−	0.265714i
$377$	−4.02494			−0.207295
$378$	0.816015	−	3.06606i	0.0419713	−	0.157701i
$379$	−26.6106			−1.36689			−0.683446	−	0.730001i	$-0.739520\pi$
$379$	−26.6106			−1.36689			−0.683446	+	0.730001i	$0.739520\pi$
$380$	−0.386034	−	0.668631i	−0.0198031	−	0.0343000i
$381$	9.29796	−	16.1045i	0.476349	−	0.825061i
$382$	10.8068	−	18.7180i	0.552925	−	0.957695i
$383$	11.0088	+	19.0678i	0.562524	+	0.974320i	0.997275	+	0.0737692i	$0.0235028\pi$
$383$	11.0088	+	19.0678i	0.562524	+	0.974320i	−0.434752	+	0.900550i	$0.643164\pi$
$384$	−4.41356			−0.225229
$385$	2.70979	+	2.70067i	0.138104	+	0.137639i
$386$	−5.61573			−0.285833
$387$	0.954920	+	1.65397i	0.0485413	+	0.0840760i
$388$	4.33698	−	7.51187i	0.220177	−	0.381357i
$389$	−9.19319	+	15.9231i	−0.466113	+	0.807332i	−0.999251	−	0.0386966i	$-0.987679\pi$
$389$	−9.19319	+	15.9231i	−0.466113	+	0.807332i	0.533138	+	0.846028i	$0.321013\pi$
$390$	1.73506	+	3.00522i	0.0878583	+	0.152175i
$391$	−2.25223			−0.113900
$392$	−0.0724500	−	21.5057i	−0.00365928	−	1.08620i
$393$	−17.9120			−0.903542
$394$	13.4788	+	23.3460i	0.679053	+	1.17615i
$395$	1.42399	−	2.46643i	0.0716489	−	0.124099i
$396$	0.709448	−	1.22880i	0.0356511	−	0.0617495i
$397$	−5.03657	−	8.72360i	−0.252778	−	0.437825i	0.711511	−	0.702675i	$-0.248011\pi$
$397$	−5.03657	−	8.72360i	−0.252778	−	0.437825i	−0.964290	+	0.264850i	$0.914678\pi$
$398$	3.27828			0.164325
$399$	4.49632	+	4.48120i	0.225098	+	0.224340i
$400$	11.9625			0.598123
$401$	5.44575	+	9.43232i	0.271948	+	0.471028i	0.969361	−	0.245642i	$-0.0789988\pi$
$401$	5.44575	+	9.43232i	0.271948	+	0.471028i	−0.697413	+	0.716670i	$0.745665\pi$
$402$	2.40773	−	4.17032i	0.120087	−	0.207996i
$403$	−8.73514	+	15.1297i	−0.435129	+	0.753665i
$404$	−1.93632	−	3.35380i	−0.0963353	−	0.166858i
$405$	−0.572653			−0.0284554
$406$	−0.649974	+	2.44218i	−0.0322577	+	0.121203i
$407$	22.2332			1.10206
$408$	3.45972	+	5.99240i	0.171281	+	0.296668i
$409$	6.25528	−	10.8345i	0.309304	−	0.535730i	−0.668906	−	0.743347i	$-0.733237\pi$
$409$	6.25528	−	10.8345i	0.309304	−	0.535730i	0.978210	+	0.207617i	$0.0665707\pi$
$410$	3.76980	−	6.52949i	0.186177	−	0.322468i
$411$	8.07612	+	13.9882i	0.398365	+	0.689989i
$412$	−6.04580			−0.297855
$413$	−11.2632	+	3.03832i	−0.554227	+	0.149506i
$414$	1.19920			0.0589375
$415$	−2.90779	−	5.03643i	−0.142738	−	0.247229i
$416$	7.76679	−	13.4525i	0.380798	−	0.659562i
$417$	−0.570437	+	0.988026i	−0.0279344	+	0.0483839i
$418$	−3.63274	−	6.29209i	−0.177683	−	0.307756i
$419$	32.3891			1.58231			0.791157	−	0.611613i	$-0.209479\pi$
$419$	32.3891			1.58231			0.791157	+	0.611613i	$0.209479\pi$
$420$	−0.821976	+	0.221732i	−0.0401083	+	0.0108194i
$421$	−2.76745			−0.134877			−0.0674387	−	0.997723i	$-0.521483\pi$
$421$	−2.76745			−0.134877			−0.0674387	+	0.997723i	$0.521483\pi$
$422$	2.36500	+	4.09629i	0.115126	+	0.199404i
$423$	0.968258	−	1.67707i	0.0470783	−	0.0815420i
$424$	14.7017	−	25.4640i	0.713976	−	1.23664i
$425$	−5.26129	−	9.11283i	−0.255210	−	0.442037i
$426$	−0.508620			−0.0246427
$427$	−1.44715	+	5.43744i	−0.0700323	+	0.263136i
$428$	−4.90815			−0.237245
$429$	−6.37985	−	11.0502i	−0.308022	−	0.533510i
$430$	−0.655769	+	1.13583i	−0.0316240	+	0.0547744i
$431$	−18.9624	+	32.8439i	−0.913389	+	1.58204i	−0.104146	+	0.994562i	$0.533211\pi$
$431$	−18.9624	+	32.8439i	−0.913389	+	1.58204i	−0.809243	+	0.587474i	$0.800122\pi$
$432$	−1.28021	−	2.21739i	−0.0615941	−	0.106684i
$433$	17.8080			0.855798			0.427899	−	0.903827i	$-0.359254\pi$
$433$	17.8080			0.855798			0.427899	+	0.903827i	$0.359254\pi$
$434$	7.76954	+	7.74341i	0.372950	+	0.371696i
$435$	0.456131			0.0218698
$436$	−0.841038	−	1.45672i	−0.0402784	−	0.0697643i
$437$	−1.19967	+	2.07789i	−0.0573881	+	0.0993992i
$438$	−8.39496	+	14.5405i	−0.401127	+	0.694772i
$439$	−19.5160	−	33.8027i	−0.931448	−	1.61332i	−0.780848	−	0.624721i	$-0.785213\pi$
$439$	−19.5160	−	33.8027i	−0.931448	−	1.61332i	−0.150600	−	0.988595i	$-0.548120\pi$
$440$	4.44251			0.211788
$441$	6.05035	−	3.52040i	0.288112	−	0.167638i
$442$	13.6479			0.649166
$443$	−9.95038	−	17.2346i	−0.472757	−	0.818839i	0.526757	−	0.850016i	$-0.323408\pi$
$443$	−9.95038	−	17.2346i	−0.472757	−	0.818839i	−0.999514	+	0.0311772i	$0.990074\pi$
$444$	−2.47379	+	4.28473i	−0.117401	+	0.203344i
$445$	1.09581	−	1.89800i	0.0519464	−	0.0899737i
$446$	10.7302	+	18.5852i	0.508088	+	0.880035i
$447$	−8.02342			−0.379495
$448$	−16.5046	−	16.4491i	−0.779768	−	0.777145i
$449$	31.7323			1.49754			0.748769	−	0.662831i	$-0.230645\pi$
$449$	31.7323			1.49754			0.748769	+	0.662831i	$0.230645\pi$
$450$	2.80138	+	4.85212i	0.132058	+	0.228731i
$451$	−13.8616	+	24.0090i	−0.652718	+	1.13054i
$452$	4.58838	−	7.94731i	0.215819	−	0.373810i
$453$	10.1347	+	17.5539i	0.476171	+	0.824753i
$454$	21.7987			1.02306
$455$	−1.96906	+	7.39846i	−0.0923110	+	0.346845i
$456$	7.37140			0.345197
$457$	3.13923	+	5.43730i	0.146847	+	0.254346i	0.930060	−	0.367407i	$-0.119754\pi$
$457$	3.13923	+	5.43730i	0.146847	+	0.254346i	−0.783214	+	0.621753i	$0.786421\pi$
$458$	−4.30195	+	7.45120i	−0.201017	+	0.348172i
$459$	−1.12612	+	1.95049i	−0.0525626	+	0.0910411i
$460$	−0.160891	−	0.278672i	−0.00750160	−	0.0129932i
$461$	−20.4402			−0.951996			−0.475998	−	0.879446i	$-0.657913\pi$
$461$	−20.4402			−0.951996			−0.475998	+	0.879446i	$0.657913\pi$
$462$	−7.73513	+	2.08659i	−0.359871	+	0.0970771i
$463$	−8.31436			−0.386401			−0.193201	−	0.981159i	$-0.561887\pi$
$463$	−8.31436			−0.386401			−0.193201	+	0.981159i	$0.561887\pi$
$464$	1.01972	+	1.76620i	0.0473391	+	0.0819937i
$465$	0.989921	−	1.71459i	0.0459065	−	0.0795124i
$466$	8.62646	−	14.9415i	0.399613	−	0.692150i
$467$	−1.73920	−	3.01239i	−0.0804807	−	0.139397i	0.822976	−	0.568076i	$-0.192312\pi$
$467$	−1.73920	−	3.01239i	−0.0804807	−	0.139397i	−0.903457	+	0.428680i	$0.858979\pi$
$468$	2.83944			0.131253
$469$	10.2575	−	2.76702i	0.473648	−	0.127769i
$470$	1.32986			0.0613417
$471$	−3.32459	−	5.75836i	−0.153189	−	0.265331i
$472$	−6.77320	+	11.7315i	−0.311762	+	0.539987i
$473$	2.41127	−	4.17644i	0.110870	−	0.192033i
$474$	2.98200	+	5.16498i	0.136968	+	0.237236i
$475$	−11.2099			−0.514346
$476$	−0.861173	+	3.23573i	−0.0394718	+	0.148310i
$477$	9.57060			0.438208
$478$	0.905863	+	1.56900i	0.0414332	+	0.0717645i
$479$	−10.3767	+	17.9730i	−0.474124	+	0.821208i	−0.999561	−	0.0296251i	$-0.990569\pi$
$479$	−10.3767	+	17.9730i	−0.474124	+	0.821208i	0.525437	+	0.850833i	$0.323902\pi$
$480$	−0.880182	+	1.52452i	−0.0401746	+	0.0695845i
$481$	22.2461	+	38.5313i	1.01433	+	1.75688i
$482$	36.9150			1.68143
$483$	1.87398	+	1.86767i	0.0852689	+	0.0849821i
$484$	2.59822			0.118101
$485$	4.41986	+	7.65541i	0.200695	+	0.347614i
$486$	0.599601	−	1.03854i	0.0271984	−	0.0471091i
$487$	13.1481	−	22.7731i	0.595796	−	1.03195i	−0.397638	−	0.917543i	$-0.630170\pi$
$487$	13.1481	−	22.7731i	0.595796	−	1.03195i	0.993434	−	0.114407i	$-0.0364968\pi$
$488$	3.26688	+	5.65840i	0.147885	+	0.256144i
$489$	−3.74710			−0.169450
$490$	4.17113	+	2.38951i	0.188433	+	0.107947i
$491$	−5.35237			−0.241549			−0.120775	−	0.992680i	$-0.538538\pi$
$491$	−5.35237			−0.241549			−0.120775	+	0.992680i	$0.538538\pi$
$492$	−3.08465	−	5.34277i	−0.139067	−	0.240871i
$493$	0.896977	−	1.55361i	0.0403978	−	0.0699710i
$494$	7.26970	−	12.5915i	0.327079	−	0.566518i
$495$	0.723005	+	1.25228i	0.0324966	+	0.0562858i
$496$	8.85217			0.397474
$497$	−0.794814	−	0.792141i	−0.0356523	−	0.0355324i
$498$	12.1785			0.545730
$499$	−19.4297	−	33.6533i	−0.869794	−	1.50653i	−0.862207	−	0.506555i	$-0.830919\pi$
$499$	−19.4297	−	33.6533i	−0.869794	−	1.50653i	−0.00758604	−	0.999971i	$-0.502415\pi$
$500$	1.55615	−	2.69534i	0.0695933	−	0.120539i
$501$	−1.48566	+	2.57323i	−0.0663743	+	0.114964i
$502$	−7.70919	−	13.3527i	−0.344078	−	0.595961i
$503$	−22.5980			−1.00760			−0.503798	−	0.863822i	$-0.668064\pi$
$503$	−22.5980			−1.00760			−0.503798	+	0.863822i	$0.668064\pi$
$504$	2.09056	−	7.85498i	0.0931210	−	0.349889i
$505$	3.94663			0.175623
$506$	−1.51405	−	2.62242i	−0.0673079	−	0.116581i
$507$	6.26710	−	10.8549i	0.278332	−	0.482085i
$508$	5.22467	−	9.04939i	0.231807	−	0.401502i
$509$	20.8219	+	36.0645i	0.922913	+	1.59853i	0.794884	+	0.606761i	$0.207531\pi$
$509$	20.8219	+	36.0645i	0.922913	+	1.59853i	0.128028	+	0.991771i	$0.459135\pi$
$510$	−1.54667			−0.0684877
$511$	−35.7645	+	9.64767i	−1.58213	+	0.426788i
$512$	−23.6034			−1.04313
$513$	1.19967	+	2.07789i	0.0529669	+	0.0917413i
$514$	−2.49922	+	4.32877i	−0.110236	+	0.190934i
$515$	3.08066	−	5.33586i	0.135750	−	0.235126i
$516$	0.536584	+	0.929391i	0.0236218	+	0.0409142i
$517$	−4.88990			−0.215058
$518$	26.9718	−	7.27580i	1.18507	−	0.319680i
$519$	−11.5181			−0.505586
$520$	4.44509	+	7.69911i	0.194930	+	0.337628i
$521$	−8.70386	+	15.0755i	−0.381323	+	0.660471i	−0.991252	−	0.131986i	$-0.957865\pi$
$521$	−8.70386	+	15.0755i	−0.381323	+	0.660471i	0.609929	+	0.792456i	$0.291198\pi$
$522$	−0.477595	+	0.827219i	−0.0209038	+	0.0362064i
$523$	−9.21577	−	15.9622i	−0.402977	−	0.697977i	0.591106	−	0.806594i	$-0.298691\pi$
$523$	−9.21577	−	15.9622i	−0.402977	−	0.697977i	−0.994084	+	0.108616i	$0.965358\pi$
$524$	−10.0650			−0.439694
$525$	−3.17918	+	11.9453i	−0.138751	+	0.521336i
$526$	10.9548			0.477650
$527$	−3.89334	−	6.74346i	−0.169597	−	0.293750i
$528$	−3.23266	+	5.59913i	−0.140684	+	0.243671i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	3.28620	+	5.69186i	0.142743	+	0.247239i
$531$	−4.40927			−0.191346
$532$	2.52655	+	2.51806i	0.109540	+	0.109172i
$533$	−55.4786			−2.40305
$534$	2.29475	+	3.97462i	0.0993036	+	0.171999i
$535$	2.50097	−	4.33181i	0.108126	−	0.187281i
$536$	6.16841	−	10.6840i	0.266435	−	0.461478i
$537$	−5.95674	−	10.3174i	−0.257052	−	0.445228i
$538$	−10.8312			−0.466966
$539$	−15.3373	−	8.78624i	−0.660625	−	0.378450i
$540$	−0.321783			−0.0138473
$541$	8.42701	+	14.5960i	0.362305	+	0.627531i	0.988340	−	0.152264i	$-0.0486564\pi$
$541$	8.42701	+	14.5960i	0.362305	+	0.627531i	−0.626034	+	0.779795i	$0.715323\pi$
$542$	−4.22899	+	7.32483i	−0.181651	+	0.314628i
$543$	12.9923	−	22.5034i	0.557555	−	0.965713i
$544$	3.46174	+	5.99590i	0.148421	+	0.257072i
$545$	1.71422			0.0734291
$546$	−11.3558	−	11.3176i	−0.485983	−	0.484349i
$547$	34.9994			1.49647			0.748233	−	0.663436i	$-0.230903\pi$
$547$	34.9994			1.49647			0.748233	+	0.663436i	$0.230903\pi$
$548$	4.53810	+	7.86021i	0.193858	+	0.335772i
$549$	−1.06335	+	1.84178i	−0.0453827	+	0.0786051i
$550$	7.07376	−	12.2521i	0.301626	−	0.522432i
$551$	−0.955566	−	1.65509i	−0.0407085	−	0.0705092i
$552$	3.07225			0.130764
$553$	−3.38417	+	12.7155i	−0.143909	+	0.540719i
$554$	13.5653			0.576336
$555$	−2.52106	−	4.36661i	−0.107013	−	0.185352i
$556$	−0.320538	+	0.555187i	−0.0135938	+	0.0235452i
$557$	12.7006	−	21.9981i	0.538143	−	0.932091i	−0.460861	−	0.887472i	$-0.652459\pi$
$557$	12.7006	−	21.9981i	0.538143	−	0.932091i	0.999004	−	0.0446189i	$-0.0142074\pi$
$558$	2.07301	+	3.59056i	0.0877574	+	0.152000i
$559$	9.65068			0.408180
$560$	3.74541	−	1.01034i	0.158272	−	0.0426948i
$561$	5.68712			0.240110
$562$	13.4010	+	23.2113i	0.565289	+	0.979109i
$563$	5.23673	−	9.07029i	0.220702	−	0.382267i	−0.734319	−	0.678804i	$-0.762499\pi$
$563$	5.23673	−	9.07029i	0.220702	−	0.382267i	0.955021	+	0.296537i	$0.0958318\pi$
$564$	0.544079	−	0.942373i	0.0229099	−	0.0396811i
$565$	4.67606	+	8.09918i	0.196723	+	0.340735i
$566$	−22.1575			−0.931350
$567$	2.55444	−	0.689075i	0.107276	−	0.0289384i
$568$	−1.30304			−0.0546744
$569$	−12.0421	−	20.8575i	−0.504830	−	0.874392i	−0.999984	−	0.00558658i	$-0.998222\pi$
$569$	−12.0421	−	20.8575i	−0.504830	−	0.874392i	0.495154	−	0.868805i	$-0.335112\pi$
$570$	−0.823848	+	1.42695i	−0.0345072	+	0.0597682i
$571$	−12.8985	+	22.3408i	−0.539783	+	0.934932i	0.459132	+	0.888368i	$0.348161\pi$
$571$	−12.8985	+	22.3408i	−0.539783	+	0.934932i	−0.998915	+	0.0465641i	$0.985173\pi$
$572$	−3.58494	−	6.20929i	−0.149894	−	0.259624i
$573$	18.0234			0.752937
$574$	−8.95906	+	33.6624i	−0.373944	+	1.40504i
$575$	−4.67207			−0.194839
$576$	−4.40362	−	7.62729i	−0.183484	−	0.317804i
$577$	−5.79294	+	10.0337i	−0.241163	+	0.417707i	−0.961046	−	0.276389i	$-0.910862\pi$
$577$	−5.79294	+	10.0337i	−0.241163	+	0.417707i	0.719883	+	0.694096i	$0.244196\pi$
$578$	7.15171	−	12.3871i	0.297472	−	0.515236i
$579$	−2.34144	−	4.05550i	−0.0973071	−	0.168541i
$580$	0.256307			0.0106426
$581$	19.0311	+	18.9671i	0.789545	+	0.786890i
$582$	−18.5114			−0.767321
$583$	−12.0834	−	20.9290i	−0.500443	−	0.866792i
$584$	−21.5072	+	37.2515i	−0.889973	+	1.54148i
$585$	−1.44685	+	2.50602i	−0.0598198	+	0.103611i
$586$	−0.430154	−	0.745049i	−0.0177695	−	0.0307777i
$587$	−8.06567			−0.332906			−0.166453	−	0.986049i	$-0.553231\pi$
$587$	−8.06567			−0.332906			−0.166453	+	0.986049i	$0.553231\pi$
$588$	3.39979	−	1.97817i	0.140205	−	0.0815783i
$589$	−8.29529			−0.341802
$590$	−1.51398	−	2.62230i	−0.0623297	−	0.107958i
$591$	−11.2398	+	19.4680i	−0.462345	+	0.800804i
$592$	11.2721	−	19.5238i	0.463279	−	0.802422i
$593$	12.2969	+	21.2988i	0.504973	+	0.874639i	0.999983	+	0.00575190i	$0.00183090\pi$
$593$	12.2969	+	21.2988i	0.504973	+	0.874639i	−0.495010	+	0.868887i	$0.664836\pi$
$594$	−3.02811			−0.124245
$595$	−2.41696	−	2.40883i	−0.0990857	−	0.0987525i
$596$	−4.50849			−0.184675
$597$	1.36686	+	2.36747i	0.0559418	+	0.0968941i
$598$	3.02987	−	5.24788i	0.123900	−	0.214602i
$599$	8.71370	−	15.0926i	0.356032	−	0.616666i	−0.631262	−	0.775570i	$-0.717463\pi$
$599$	8.71370	−	15.0926i	0.356032	−	0.616666i	0.987294	+	0.158904i	$0.0507960\pi$
$600$	7.17689	+	12.4307i	0.292995	+	0.507483i
$601$	46.7989			1.90897			0.954484	−	0.298263i	$-0.0964071\pi$
$601$	46.7989			1.90897			0.954484	+	0.298263i	$0.0964071\pi$
$602$	1.55846	−	5.85568i	0.0635180	−	0.238660i
$603$	4.01556			0.163526
$604$	5.69486	+	9.86379i	0.231721	+	0.401352i
$605$	−1.32393	+	2.29312i	−0.0538255	+	0.0932285i
$606$	−4.13235	+	7.15744i	−0.167865	+	0.290751i
$607$	8.95156	+	15.5046i	0.363333	+	0.629311i	0.988507	−	0.151174i	$-0.0483055\pi$
$607$	8.95156	+	15.5046i	0.363333	+	0.629311i	−0.625174	+	0.780485i	$0.714972\pi$
$608$	7.37570			0.299124
$609$	−2.03467	+	0.548863i	−0.0824490	+	0.0222411i
$610$	−1.46046			−0.0591324
$611$	−4.89274	−	8.47448i	−0.197939	−	0.342841i
$612$	−0.632783	+	1.09601i	−0.0255787	+	0.0443036i
$613$	17.4493	−	30.2230i	0.704770	−	1.22070i	−0.262005	−	0.965067i	$-0.584384\pi$
$613$	17.4493	−	30.2230i	0.704770	−	1.22070i	0.966775	−	0.255631i	$-0.0822831\pi$
$614$	4.96459	+	8.59892i	0.200354	+	0.347024i
$615$	6.28719			0.253524
$616$	−19.8167	+	5.34567i	−0.798439	+	0.215383i
$617$	−47.6661			−1.91896			−0.959482	−	0.281771i	$-0.909078\pi$
$617$	−47.6661			−1.91896			−0.959482	+	0.281771i	$0.909078\pi$
$618$	6.45126	+	11.1739i	0.259508	+	0.449481i
$619$	−19.7161	+	34.1492i	−0.792455	+	1.37257i	0.131988	+	0.991251i	$0.457864\pi$
$619$	−19.7161	+	34.1492i	−0.792455	+	1.37257i	−0.924443	+	0.381321i	$0.875469\pi$
$620$	0.556252	−	0.963457i	0.0223396	−	0.0386934i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−10.7282			−0.430162
$623$	−2.60423	+	9.78501i	−0.104336	+	0.392028i
$624$	−12.9382			−0.517941
$625$	−10.0943	−	17.4838i	−0.403771	−	0.699352i
$626$	2.96109	−	5.12876i	0.118349	−	0.204987i
$627$	3.02930	−	5.24690i	0.120979	−	0.209541i
$628$	−1.86814	−	3.23571i	−0.0745469	−	0.129119i
$629$	−19.8306			−0.790697
$630$	1.28691	+	1.28258i	0.0512717	+	0.0510993i
$631$	−6.93619			−0.276125			−0.138063	−	0.990423i	$-0.544088\pi$
$631$	−6.93619			−0.276125			−0.138063	+	0.990423i	$0.544088\pi$
$632$	7.63964	+	13.2323i	0.303889	+	0.526351i
$633$	−1.97214	+	3.41585i	−0.0783856	+	0.135768i
$634$	9.43854	−	16.3480i	0.374852	−	0.649263i
$635$	5.32451	+	9.22232i	0.211297	+	0.365977i
$636$	5.37787			0.213247
$637$	−0.119163	−	35.3718i	−0.00472142	−	1.40148i
$638$	2.41195			0.0954902
$639$	−0.212066	−	0.367309i	−0.00838921	−	0.0145305i
$640$	1.26372	−	2.18883i	0.0499530	−	0.0865210i
$641$	−12.8180	+	22.2015i	−0.506281	+	0.876905i	0.493692	+	0.869637i	$0.335647\pi$
$641$	−12.8180	+	22.2015i	−0.506281	+	0.876905i	−0.999974	+	0.00726846i	$0.997686\pi$
$642$	5.23732	+	9.07131i	0.206701	+	0.358016i
$643$	14.2975			0.563840			0.281920	−	0.959438i	$-0.409029\pi$
$643$	14.2975			0.563840			0.281920	+	0.959438i	$0.409029\pi$
$644$	1.05302	+	1.04948i	0.0414947	+	0.0413551i
$645$	−1.09368			−0.0430635
$646$	3.24017	+	5.61215i	0.127483	+	0.220807i
$647$	16.6635	−	28.8621i	0.655111	−	1.13469i	−0.326755	−	0.945109i	$-0.605955\pi$
$647$	16.6635	−	28.8621i	0.655111	−	1.13469i	0.981866	−	0.189577i	$-0.0607116\pi$
$648$	1.53613	−	2.66065i	0.0603448	−	0.104520i
$649$	5.56693	+	9.64221i	0.218521	+	0.378490i
$650$	28.3115			1.11047
$651$	−2.35258	+	8.83949i	−0.0922049	+	0.346447i
$652$	−2.10556			−0.0824599
$653$	−0.358495	−	0.620931i	−0.0140290	−	0.0242989i	0.858926	−	0.512100i	$-0.171132\pi$
$653$	−0.358495	−	0.620931i	−0.0140290	−	0.0242989i	−0.872955	+	0.487801i	$0.837799\pi$
$654$	−1.79489	+	3.10883i	−0.0701856	+	0.121565i
$655$	5.12869	−	8.88315i	0.200394	−	0.347093i
$656$	14.0555	+	24.3448i	0.548774	+	0.950505i
$657$	−14.0009			−0.546228
$658$	−5.93211	+	1.60022i	−0.231258	+	0.0623830i
$659$	−22.0825			−0.860214			−0.430107	−	0.902778i	$-0.641524\pi$
$659$	−22.0825			−0.860214			−0.430107	+	0.902778i	$0.641524\pi$
$660$	0.406268	+	0.703676i	0.0158139	+	0.0273906i
$661$	10.3855	−	17.9882i	0.403949	−	0.699660i	−0.590250	−	0.807221i	$-0.700971\pi$
$661$	10.3855	−	17.9882i	0.403949	−	0.699660i	0.994199	+	0.107561i	$0.0343040\pi$
$662$	16.3897	−	28.3879i	0.637006	−	1.10333i
$663$	5.69042	+	9.85610i	0.220998	+	0.382779i
$664$	31.2002			1.21080
$665$	−3.50979	+	0.946784i	−0.136104	+	0.0367147i
$666$	10.5588			0.409145
$667$	−0.398261	−	0.689808i	−0.0154207	−	0.0267095i
$668$	−0.834814	+	1.44594i	−0.0322999	+	0.0559451i
$669$	−8.94776	+	15.4980i	−0.345941	+	0.599187i
$670$	1.37880	+	2.38815i	0.0532676	+	0.0922621i
$671$	5.37014			0.207312
$672$	2.09178	−	7.85957i	0.0806922	−	0.303189i
$673$	10.5462			0.406525			0.203262	−	0.979124i	$-0.434846\pi$
$673$	10.5462			0.406525			0.203262	+	0.979124i	$0.434846\pi$
$674$	−5.83893	−	10.1133i	−0.224907	−	0.389551i
$675$	−2.33603	+	4.04613i	−0.0899140	+	0.155736i
$676$	3.52158	−	6.09956i	0.135446	−	0.234599i
$677$	7.01729	+	12.1543i	0.269696	+	0.467128i	0.968783	−	0.247909i	$-0.0797434\pi$
$677$	7.01729	+	12.1543i	0.269696	+	0.467128i	−0.699087	+	0.715037i	$0.746410\pi$
$678$	−19.5844			−0.752135
$679$	−28.9275	−	28.8302i	−1.11013	−	1.10640i
$680$	−3.96244			−0.151952
$681$	9.08883	+	15.7423i	0.348285	+	0.603247i
$682$	5.23456	−	9.06652i	0.200442	−	0.347175i
$683$	−21.6615	+	37.5189i	−0.828856	+	1.43562i	0.0700803	+	0.997541i	$0.477674\pi$
$683$	−21.6615	+	37.5189i	−0.828856	+	1.43562i	−0.898936	+	0.438079i	$0.855659\pi$
$684$	0.674115	+	1.16760i	0.0257754	+	0.0446444i
$685$	−9.24963			−0.353410
$686$	−21.4815	−	5.63977i	−0.820168	−	0.215327i
$687$	−7.17469			−0.273732
$688$	−2.44499	−	4.23486i	−0.0932146	−	0.161452i
$689$	24.1808	−	41.8824i	0.921215	−	1.59559i
$690$	−0.343363	+	0.594723i	−0.0130716	+	0.0226407i
$691$	−18.9514	−	32.8247i	−0.720944	−	1.24871i	−0.960622	−	0.277859i	$-0.910375\pi$
$691$	−18.9514	−	32.8247i	−0.720944	−	1.24871i	0.239678	−	0.970852i	$-0.422958\pi$
$692$	−6.47217			−0.246035
$693$	−4.73199	−	4.71607i	−0.179753	−	0.179149i
$694$	−34.6920			−1.31689
$695$	−0.326663	−	0.565797i	−0.0123910	−	0.0214619i
$696$	−1.22356	+	2.11927i	−0.0463789	+	0.0803306i
$697$	12.3637	−	21.4145i	0.468308	−	0.811133i
$698$	−11.9903	−	20.7678i	−0.453840	−	0.786075i
$699$	14.3870			0.544167
$700$	−1.78643	+	6.71226i	−0.0675207	+	0.253699i
$701$	−17.9525			−0.678058			−0.339029	−	0.940776i	$-0.610099\pi$
$701$	−17.9525			−0.678058			−0.339029	+	0.940776i	$0.610099\pi$
$702$	−3.02987	−	5.24788i	−0.114355	−	0.198069i
$703$	−10.5629	+	18.2956i	−0.398389	+	0.690030i
$704$	−11.1196	+	19.2597i	−0.419086	+	0.725878i
$705$	0.554476	+	0.960381i	0.0208828	+	0.0361700i
$706$	−29.4965			−1.11011
$707$	−17.6048	+	4.74899i	−0.662097	+	0.178604i
$708$	−2.47764			−0.0931154
$709$	−15.9553	−	27.6353i	−0.599213	−	1.03787i	−0.992938	−	0.118638i	$-0.962147\pi$
$709$	−15.9553	−	27.6353i	−0.599213	−	1.03787i	0.393725	−	0.919228i	$-0.371186\pi$
$710$	0.145632	−	0.252241i	0.00546545	−	0.00946644i
$711$	−2.48666	+	4.30702i	−0.0932570	+	0.161526i
$712$	5.87896	+	10.1827i	0.220323	+	0.381611i
$713$	−3.45731			−0.129477
$714$	6.89925	−	1.86111i	0.258198	−	0.0696502i
$715$	7.30688			0.273262
$716$	−3.34719	−	5.79749i	−0.125090	−	0.216663i
$717$	−0.755389	+	1.30837i	−0.0282105	+	0.0488620i
$718$	−12.1809	+	21.0979i	−0.454586	+	0.787366i
$719$	−5.16417	−	8.94461i	−0.192591	−	0.333578i	0.753517	−	0.657428i	$-0.228356\pi$
$719$	−5.16417	−	8.94461i	−0.192591	−	0.333578i	−0.946108	+	0.323851i	$0.895022\pi$
$720$	1.46623			0.0546433
$721$	−7.32130	+	27.5087i	−0.272659	+	1.02448i
$722$	−15.8812			−0.591037
$723$	15.3915	+	26.6588i	0.572416	+	0.991453i
$724$	7.30060	−	12.6450i	0.271325	−	0.469948i
$725$	1.86070	−	3.22283i	0.0691048	−	0.119693i
$726$	−2.77247	−	4.80205i	−0.102896	−	0.178221i
$727$	32.5415			1.20690			0.603448	−	0.797402i	$-0.293793\pi$
$727$	32.5415			1.20690			0.603448	+	0.797402i	$0.293793\pi$
$728$	−29.0926	−	28.9948i	−1.07824	−	1.07462i
$729$	1.00000			0.0370370
$730$	−4.80740	−	8.32666i	−0.177930	−	0.308184i
$731$	−2.15070	+	3.72512i	−0.0795466	+	0.137779i
$732$	−0.597513	+	1.03492i	−0.0220847	+	0.0382519i
$733$	−15.4663	−	26.7885i	−0.571262	−	0.989454i	−0.996437	−	0.0843430i	$-0.973121\pi$
$733$	−15.4663	−	26.7885i	−0.571262	−	0.989454i	0.425175	−	0.905111i	$-0.360212\pi$
$734$	−4.17349			−0.154046
$735$	0.0135043	+	4.00855i	0.000498115	+	0.147858i
$736$	3.07405			0.113311
$737$	−5.06985	−	8.78124i	−0.186750	−	0.323461i
$738$	−6.58304	+	11.4022i	−0.242325	+	0.419719i
$739$	−15.8009	+	27.3679i	−0.581244	+	1.00674i	0.414089	+	0.910237i	$0.364100\pi$
$739$	−15.8009	+	27.3679i	−0.581244	+	1.00674i	−0.995332	+	0.0965070i	$0.969233\pi$
$740$	−1.41663	−	2.45367i	−0.0520762	−	0.0901986i
$741$	12.1242			0.445395
$742$	−21.5078	−	21.4355i	−0.789576	−	0.786921i
$743$	−10.6217			−0.389674			−0.194837	−	0.980836i	$-0.562418\pi$
$743$	−10.6217			−0.389674			−0.194837	+	0.980836i	$0.562418\pi$
$744$	5.31087	+	9.19870i	0.194706	+	0.337241i
$745$	2.29732	−	3.97908i	0.0841673	−	0.145782i
$746$	18.0533	−	31.2693i	0.660979	−	1.14485i
$747$	5.07774	+	8.79491i	0.185785	+	0.321789i
$748$	3.19568			0.116846
$749$	−5.94365	+	22.3324i	−0.217176	+	0.816008i
$750$	−6.64207			−0.242534
$751$	0.0130557	+	0.0226132i	0.000476410	+	0.000825167i	0.866264	−	0.499587i	$-0.166515\pi$
$751$	0.0130557	+	0.0226132i	0.000476410	+	0.000825167i	−0.865787	+	0.500413i	$0.833182\pi$
$752$	−2.47915	+	4.29401i	−0.0904052	+	0.156586i
$753$	6.42860	−	11.1347i	0.234271	−	0.405770i
$754$	2.41335	+	4.18005i	0.0878892	+	0.152229i
$755$	−11.6074			−0.422436
$756$	1.43538	−	0.387202i	0.0522043	−	0.0140824i
$757$	1.50079			0.0545471			0.0272735	−	0.999628i	$-0.491317\pi$
$757$	1.50079			0.0545471			0.0272735	+	0.999628i	$0.491317\pi$
$758$	15.9557	+	27.6361i	0.579537	+	1.00379i
$759$	1.26255	−	2.18680i	0.0458277	−	0.0793759i
$760$	−2.11063	+	3.65572i	−0.0765605	+	0.132607i
$761$	18.7466	+	32.4700i	0.679562	+	1.17704i	0.975113	+	0.221709i	$0.0711635\pi$
$761$	18.7466	+	32.4700i	0.679562	+	1.17704i	−0.295551	+	0.955327i	$0.595503\pi$
$762$	−22.3003			−0.807853
$763$	−7.64664	+	2.06272i	−0.276827	+	0.0746756i
$764$	10.1276			0.366404
$765$	−0.644874	−	1.11696i	−0.0233155	−	0.0403836i
$766$	13.2018	−	22.8661i	0.477000	−	0.826187i
$767$	−11.1403	+	19.2956i	−0.402254	+	0.696725i
$768$	−6.16087	−	10.6709i	−0.222311	−	0.385054i
$769$	32.9794			1.18927			0.594633	−	0.803997i	$-0.297297\pi$
$769$	32.9794			1.18927			0.594633	+	0.803997i	$0.297297\pi$
$770$	1.17996	−	4.43355i	0.0425230	−	0.159774i
$771$	−4.16813			−0.150112
$772$	−1.31569	−	2.27885i	−0.0473529	−	0.0820176i
$773$	21.3621	−	37.0002i	0.768340	−	1.33080i	−0.170123	−	0.985423i	$-0.554416\pi$
$773$	21.3621	−	37.0002i	0.768340	−	1.33080i	0.938463	−	0.345381i	$-0.112250\pi$
$774$	1.14514	−	1.98344i	0.0411612	−	0.0712934i
$775$	−8.07640	−	13.9887i	−0.290113	−	0.502490i
$776$	−47.4245			−1.70244
$777$	16.5001	+	16.4446i	0.591938	+	0.589947i
$778$	22.0490			0.790494
$779$	−13.1713	−	22.8133i	−0.471909	−	0.817371i
$780$	−0.813007	+	1.40817i	−0.0291103	+	0.0504205i
$781$	−0.535489	+	0.927494i	−0.0191613	+	0.0331884i
$782$	1.35044	+	2.33903i	0.0482917	+	0.0836436i
$783$	−0.796522			−0.0284654
$784$	−15.4914	+	9.01371i	−0.553266	+	0.321918i
$785$	3.80768			0.135902
$786$	10.7401	+	18.6023i	0.383085	+	0.663523i
$787$	−5.89676	+	10.2135i	−0.210197	+	0.364072i	−0.951776	−	0.306794i	$-0.900744\pi$
$787$	−5.89676	+	10.2135i	−0.210197	+	0.364072i	0.741579	+	0.670865i	$0.234077\pi$
$788$	−6.31583	+	10.9393i	−0.224992	+	0.389698i
$789$	4.56752	+	7.91118i	0.162608	+	0.281645i
$790$	−3.41531			−0.121511
$791$	−30.6043	−	30.5014i	−1.08816	−	1.08451i
$792$	−7.75776			−0.275660
$793$	5.37326	+	9.30675i	0.190810	+	0.330492i
$794$	−6.03987	+	10.4614i	−0.214347	+	0.371260i
$795$	−2.74032	+	4.74637i	−0.0971891	+	0.168337i
$796$	0.768060	+	1.33032i	0.0272232	+	0.0471519i
$797$	−30.7118			−1.08787			−0.543934	−	0.839128i	$-0.683066\pi$
$797$	−30.7118			−1.08787			−0.543934	+	0.839128i	$0.683066\pi$
$798$	1.95790	−	7.35653i	0.0693090	−	0.260418i
$799$	4.36148			0.154298
$800$	7.18108	+	12.4380i	0.253890	+	0.439750i
$801$	−1.91357	+	3.31439i	−0.0676125	+	0.117108i
$802$	6.53056	−	11.3113i	0.230602	−	0.399414i
$803$	17.6769	+	30.6172i	0.623803	+	1.08046i
$804$	2.25641			0.0795773
$805$	−1.46281	+	0.394601i	−0.0515573	+	0.0139079i
$806$	20.9504			0.737946
$807$	−4.51600	−	7.82195i	−0.158971	−	0.275346i
$808$	−10.5867	+	18.3368i	−0.372440	+	0.645085i
$809$	20.6065	−	35.6914i	0.724484	−	1.25484i	−0.234701	−	0.972068i	$-0.575411\pi$
$809$	20.6065	−	35.6914i	0.724484	−	1.25484i	0.959186	−	0.282776i	$-0.0912554\pi$
$810$	0.343363	+	0.594723i	0.0120646	+	0.0208964i
$811$	37.4927			1.31655			0.658273	−	0.752779i	$-0.271287\pi$
$811$	37.4927			1.31655			0.658273	+	0.752779i	$0.271287\pi$
$812$	−1.14331	+	0.308415i	−0.0401224	+	0.0108232i
$813$	−7.05301			−0.247360
$814$	−13.3310	−	23.0900i	−0.467252	−	0.809304i
$815$	1.07290	−	1.85831i	0.0375819	−	0.0650937i
$816$	2.88333	−	4.99408i	0.100937	−	0.174828i
$817$	2.29118	+	3.96844i	0.0801583	+	0.138838i
$818$	−15.0027			−0.524557
$819$	3.43848	−	12.9196i	0.120150	−	0.451448i
$820$	3.53287			0.123373
$821$	−15.4289	−	26.7237i	−0.538473	−	0.932663i	−0.998987	−	0.0450103i	$-0.985668\pi$
$821$	−15.4289	−	26.7237i	−0.538473	−	0.932663i	0.460513	−	0.887653i	$-0.347665\pi$
$822$	9.68489	−	16.7747i	0.337799	−	0.585086i
$823$	3.60448	−	6.24315i	0.125644	−	0.217622i	−0.796340	−	0.604849i	$-0.793234\pi$
$823$	3.60448	−	6.24315i	0.125644	−	0.217622i	0.921985	+	0.387226i	$0.126567\pi$
$824$	16.5276	+	28.6266i	0.575766	+	0.997255i
$825$	11.7975			0.410735
$826$	9.90885	+	9.87553i	0.344773	+	0.343614i
$827$	49.7245			1.72909			0.864546	−	0.502554i	$-0.167606\pi$
$827$	49.7245			1.72909			0.864546	+	0.502554i	$0.167606\pi$
$828$	0.280958	+	0.486633i	0.00976396	+	0.0169117i
$829$	−11.1829	+	19.3693i	−0.388398	+	0.672725i	−0.992234	−	0.124384i	$-0.960305\pi$
$829$	−11.1829	+	19.3693i	−0.388398	+	0.672725i	0.603836	+	0.797108i	$0.293638\pi$
$830$	−3.48702	+	6.03970i	−0.121036	+	0.209641i
$831$	5.65599	+	9.79646i	0.196204	+	0.339835i
$832$	−44.5042			−1.54291
$833$	13.6799	+	7.83677i	0.473981	+	0.271528i
$834$	1.36814			0.0473748
$835$	−0.850767	−	1.47357i	−0.0294420	−	0.0509950i
$836$	1.70221	−	2.94831i	0.0588722	−	0.101970i
$837$	−1.72866	+	2.99412i	−0.0597511	+	0.103492i
$838$	−19.4206	−	33.6374i	−0.670872	−	1.16198i
$839$	25.3478			0.875102			0.437551	−	0.899194i	$-0.355846\pi$
$839$	25.3478			0.875102			0.437551	+	0.899194i	$0.355846\pi$
$840$	3.29696	+	3.28587i	0.113756	+	0.113373i
$841$	−28.3656			−0.978123
$842$	1.65937	+	2.87411i	0.0571855	+	0.0990483i
$843$	−11.1750	+	19.3556i	−0.384886	+	0.666643i
$844$	−1.10818	+	1.91942i	−0.0381450	+	0.0660691i
$845$	3.58888	+	6.21612i	0.123461	+	0.213841i
$846$	−2.32227			−0.0798414
$847$	3.14637	−	11.8220i	0.108111	−	0.406210i
$848$	−24.5048			−0.841497
$849$	−9.23844	−	16.0015i	−0.317063	−	0.549168i
$850$	−6.30935	+	10.9281i	−0.216409	+	0.374831i
$851$	−4.40243	+	7.62523i	−0.150913	+	0.261389i
$852$	−0.119163	−	0.206397i	−0.00408247	−	0.00707104i
$853$	7.98030			0.273240			0.136620	−	0.990624i	$-0.456376\pi$
$853$	7.98030			0.273240			0.136620	+	0.990624i	$0.456376\pi$
$854$	6.51470	−	1.75738i	0.222929	−	0.0601362i
$855$	−1.37399			−0.0469896
$856$	13.4176	+	23.2399i	0.458603	+	0.794324i
$857$	−9.33159	+	16.1628i	−0.318761	+	0.552110i	−0.980230	−	0.197862i	$-0.936600\pi$
$857$	−9.33159	+	16.1628i	−0.318761	+	0.552110i	0.661469	+	0.749973i	$0.269933\pi$
$858$	−7.65072	+	13.2514i	−0.261191	+	0.452397i
$859$	−3.29686	−	5.71032i	−0.112487	−	0.194834i	0.804285	−	0.594243i	$-0.202548\pi$
$859$	−3.29686	−	5.71032i	−0.112487	−	0.194834i	−0.916773	+	0.399410i	$0.869215\pi$
$860$	−0.614554			−0.0209561
$861$	−28.0453	+	7.56538i	−0.955782	+	0.257827i
$862$	45.4796			1.54904
$863$	3.25342	+	5.63508i	0.110748	+	0.191820i	0.916072	−	0.401014i	$-0.131342\pi$
$863$	3.25342	+	5.63508i	0.110748	+	0.191820i	−0.805324	+	0.592834i	$0.798009\pi$
$864$	1.53702	−	2.66220i	0.0522906	−	0.0905700i
$865$	3.29793	−	5.71218i	0.112133	−	0.194220i
$866$	−10.6777	−	18.4943i	−0.362843	−	0.628462i
$867$	11.9274			0.405077
$868$	−1.32195	+	4.96705i	−0.0448700	+	0.168593i
$869$	12.5581			0.426006
$870$	−0.273497	−	0.473710i	−0.00927240	−	0.0160603i
$871$	10.1456	−	17.5727i	0.343770	−	0.595428i
$872$	−4.59834	+	7.96457i	−0.155720	+	0.269714i
$873$	−7.71820	−	13.3683i	−0.261222	−	0.452449i
$874$	2.87730			0.0973261
$875$	−10.3795	−	10.3446i	−0.350890	−	0.349710i
$876$	−7.86733			−0.265812
$877$	−14.4989	−	25.1128i	−0.489593	−	0.848000i	0.510335	−	0.859976i	$-0.329521\pi$
$877$	−14.4989	−	25.1128i	−0.489593	−	0.848000i	−0.999928	+	0.0119755i	$0.996188\pi$
$878$	−23.4036	+	40.5363i	−0.789834	+	1.36803i
$879$	0.358701	−	0.621288i	0.0120987	−	0.0209555i
$880$	−1.85119	−	3.20636i	−0.0624038	−	0.108086i
$881$	−0.393718			−0.0132647			−0.00663235	−	0.999978i	$-0.502111\pi$
$881$	−0.393718			−0.0132647			−0.00663235	+	0.999978i	$0.502111\pi$
$882$	−7.28387	−	4.17269i	−0.245261	−	0.140502i
$883$	56.9604			1.91687			0.958435	−	0.285310i	$-0.0920964\pi$
$883$	56.9604			1.91687			0.958435	+	0.285310i	$0.0920964\pi$
$884$	3.19754	+	5.53830i	0.107545	+	0.186273i
$885$	1.26249	−	2.18670i	0.0424382	−	0.0735052i
$886$	−11.9325	+	20.6677i	−0.400880	+	0.694345i
$887$	−4.92220	−	8.52551i	−0.165271	−	0.286259i	0.771480	−	0.636253i	$-0.219517\pi$
$887$	−4.92220	−	8.52551i	−0.165271	−	0.286259i	−0.936752	+	0.349995i	$0.886183\pi$
$888$	27.0507			0.907763
$889$	−34.8483	−	34.7311i	−1.16878	−	1.16484i
$890$	−2.62819			−0.0880972
$891$	−1.26255	−	2.18680i	−0.0422971	−	0.0732607i
$892$	−5.02789	+	8.70856i	−0.168346	+	0.291584i
$893$	2.32319	−	4.02387i	0.0777424	−	0.134654i
$894$	4.81085	+	8.33264i	0.160899	+	0.278685i
$895$	6.82229			0.228044
$896$	−3.00328	+	11.2844i	−0.100332	+	0.376984i
$897$	5.05314			0.168719
$898$	−19.0267	−	32.9552i	−0.634929	−	1.09973i
$899$	1.37691	−	2.38488i	0.0459226	−	0.0795403i
$900$	−1.31265	+	2.27358i	−0.0437551	+	0.0757861i
$901$	10.7776	+	18.6674i	0.359054	+	0.621901i
$902$	33.2457			1.10696
$903$	4.87857	−	1.31602i	0.162349	−	0.0437945i
$904$	−50.1736			−1.66875
$905$	7.44011	+	12.8866i	0.247318	+	0.428367i
$906$	12.1536	−	21.0506i	0.403776	−	0.699360i
$907$	11.1397	−	19.2945i	0.369887	−	0.640663i	−0.619660	−	0.784870i	$-0.712730\pi$
$907$	11.1397	−	19.2945i	0.369887	−	0.640663i	0.989548	+	0.144207i	$0.0460630\pi$
$908$	5.10716	+	8.84586i	0.169487	+	0.293560i
$909$	−6.89184			−0.228588
$910$	8.86424	−	2.39118i	0.293847	−	0.0792667i
$911$	5.74501			0.190341			0.0951703	−	0.995461i	$-0.469660\pi$
$911$	5.74501			0.190341			0.0951703	+	0.995461i	$0.469660\pi$
$912$	−3.07167	−	5.32028i	−0.101713	−	0.176172i
$913$	12.8218	−	22.2080i	0.424340	−	0.734979i
$914$	3.76456	−	6.52042i	0.124521	−	0.215676i
$915$	−0.608931	−	1.05470i	−0.0201306	−	0.0348673i
$916$	−4.03157			−0.133207
$917$	−12.1885	+	45.7965i	−0.402500	+	1.51234i
$918$	2.70088			0.0891424
$919$	−10.0372	−	17.3849i	−0.331096	−	0.573475i	0.651631	−	0.758536i	$-0.274085\pi$
$919$	−10.0372	−	17.3849i	−0.331096	−	0.573475i	−0.982727	+	0.185061i	$0.940752\pi$
$920$	−0.879668	+	1.52363i	−0.0290018	+	0.0502326i
$921$	−4.13991	+	7.17054i	−0.136415	+	0.236277i
$922$	12.2560	+	21.2280i	0.403629	+	0.699106i
$923$	−2.14320			−0.0705443
$924$	−2.65898	−	2.65003i	−0.0874739	−	0.0871797i
$925$	−41.1369			−1.35257
$926$	4.98530	+	8.63479i	0.163827	+	0.283757i
$927$	−5.37963	+	9.31779i	−0.176690	+	0.306036i
$928$	−1.22427	+	2.12050i	−0.0401887	+	0.0696089i
$929$	18.5681	+	32.1609i	0.609199	+	1.05516i	0.991373	+	0.131074i	$0.0418424\pi$
$929$	18.5681	+	32.1609i	0.609199	+	1.05516i	−0.382173	+	0.924091i	$0.624824\pi$
$930$	−2.37423			−0.0778541
$931$	14.5169	−	8.44666i	0.475772	−	0.276828i
$932$	8.08429			0.264810
$933$	−4.47306	−	7.74757i	−0.146442	−	0.253644i
$934$	−2.08565	+	3.61246i	−0.0682447	+	0.118203i
$935$	−1.62837	+	2.82043i	−0.0532535	+	0.0922379i
$936$	−7.76226	−	13.4446i	−0.253717	−	0.439451i
$937$	−7.45112			−0.243418			−0.121709	−	0.992566i	$-0.538837\pi$
$937$	−7.45112			−0.243418			−0.121709	+	0.992566i	$0.538837\pi$
$938$	−9.02407	−	8.99373i	−0.294646	−	0.293656i
$939$	4.93844			0.161160
$940$	0.311569	+	0.539653i	0.0101623	+	0.0176015i
$941$	−10.6880	+	18.5121i	−0.348417	+	0.603477i	−0.985969	−	0.166931i	$-0.946614\pi$
$941$	−10.6880	+	18.5121i	−0.348417	+	0.603477i	0.637551	+	0.770408i	$0.279947\pi$
$942$	−3.98686	+	6.90544i	−0.129899	+	0.224991i
$943$	−5.48952	−	9.50813i	−0.178763	−	0.309627i
$944$	11.2896			0.367445
$945$	−0.389671	+	1.46413i	−0.0126760	+	0.0476282i
$946$	−5.78320			−0.188028
$947$	4.40192	+	7.62436i	0.143043	+	0.247758i	0.928641	−	0.370979i	$-0.120978\pi$
$947$	4.40192	+	7.62436i	0.143043	+	0.247758i	−0.785598	+	0.618737i	$0.787645\pi$
$948$	−1.39729	+	2.42018i	−0.0453819	+	0.0786038i
$949$	−35.3743	+	61.2700i	−1.14830	+	1.98891i
$950$	6.72147	+	11.6419i	0.218073	+	0.377714i
$951$	15.7414			0.510449
$952$	17.6753	−	4.76800i	0.572859	−	0.154532i
$953$	45.2400			1.46547			0.732734	−	0.680515i	$-0.238244\pi$
$953$	45.2400			1.46547			0.732734	+	0.680515i	$0.238244\pi$
$954$	−5.73854	−	9.93945i	−0.185792	−	0.321801i
$955$	−5.16057	+	8.93837i	−0.166992	+	0.289239i
$956$	−0.424465	+	0.735195i	−0.0137282	+	0.0237779i
$957$	1.00565	+	1.74184i	0.0325081	+	0.0563056i
$958$	24.8876			0.804081
$959$	41.2600	−	11.1301i	1.33235	−	0.359409i
$960$	5.04350			0.162778
$961$	9.52349	+	16.4952i	0.307209	+	0.532102i
$962$	26.6775	−	46.2068i	0.860118	−	1.48977i
$963$	−4.36734	+	7.56446i	−0.140736	+	0.243761i
$964$	8.64872	+	14.9800i	0.278556	+	0.482474i
$965$	2.68167			0.0863261
$966$	0.816015	−	3.06606i	0.0262548	−	0.0986488i
$967$	−5.60142			−0.180130			−0.0900648	−	0.995936i	$-0.528707\pi$
$967$	−5.60142			−0.180130			−0.0900648	+	0.995936i	$0.528707\pi$
$968$	−7.10282	−	12.3025i	−0.228293	−	0.395416i
$969$	−2.70194	+	4.67990i	−0.0867989	+	0.150340i
$970$	5.30030	−	9.18038i	0.170182	−	0.294764i
$971$	−6.22638	−	10.7844i	−0.199814	−	0.346088i	0.748654	−	0.662961i	$-0.230700\pi$
$971$	−6.22638	−	10.7844i	−0.199814	−	0.346088i	−0.948468	+	0.316873i	$0.897367\pi$
$972$	0.561916			0.0180235
$973$	2.13797	+	2.13078i	0.0685403	+	0.0683097i
$974$	−31.5344			−1.01043
$975$	11.8043	+	20.4457i	0.378040	+	0.654785i
$976$	2.72262	−	4.71572i	0.0871490	−	0.150947i
$977$	20.0954	−	34.8063i	0.642909	−	1.11355i	−0.341871	−	0.939747i	$-0.611061\pi$
$977$	20.0954	−	34.8063i	0.642909	−	1.11355i	0.984780	−	0.173805i	$-0.0556061\pi$
$978$	2.24677	+	3.89151i	0.0718436	+	0.124437i
$979$	9.66390			0.308860
$980$	0.00758829	+	2.25247i	0.000242399	+	0.0719524i
$981$	−2.99347			−0.0955740
$982$	3.20929	+	5.55864i	0.102412	+	0.177383i
$983$	−23.2599	+	40.2873i	−0.741875	+	1.28497i	0.209765	+	0.977752i	$0.432730\pi$
$983$	−23.2599	+	40.2873i	−0.741875	+	1.28497i	−0.951641	+	0.307214i	$0.900603\pi$
$984$	−16.8652	+	29.2114i	−0.537643	+	0.931225i
$985$	−6.43653	−	11.1484i	−0.205085	−	0.355217i
$986$	−2.15131			−0.0685117
$987$	−3.62899	−	3.61678i	−0.115512	−	0.115123i
$988$	6.81279			0.216744
$989$	0.954920	+	1.65397i	0.0303647	+	0.0525932i
$990$	0.867028	−	1.50174i	0.0275560	−	0.0477283i
$991$	7.26506	−	12.5835i	0.230782	−	0.399727i	−0.727256	−	0.686366i	$-0.759205\pi$
$991$	7.26506	−	12.5835i	0.230782	−	0.399727i	0.958039	+	0.286639i	$0.0925382\pi$
$992$	5.31397	+	9.20407i	0.168719	+	0.292230i
$993$	27.3344			0.867432
$994$	−0.346098	+	1.30041i	−0.0109776	+	0.0412466i
$995$	−1.56547			−0.0496288
$996$	2.85326	+	4.94200i	0.0904091	+	0.156593i
$997$	2.04137	−	3.53576i	0.0646510	−	0.111979i	−0.831888	−	0.554943i	$-0.812740\pi$
$997$	2.04137	−	3.53576i	0.0646510	−	0.111979i	0.896539	+	0.442965i	$0.146073\pi$
$998$	−23.3001	+	40.3570i	−0.737553	+	1.27748i
$999$	4.40243	+	7.62523i	0.139287	+	0.241251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.277.4	✓	20
7.2	even	3	inner	483.2.i.h.415.4	yes	20
7.3	odd	6		3381.2.a.bj.1.7		10
7.4	even	3		3381.2.a.bi.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.4	✓	20	1.1	even	1	trivial
483.2.i.h.415.4	yes	20	7.2	even	3	inner
3381.2.a.bi.1.7		10	7.4	even	3
3381.2.a.bj.1.7		10	7.3	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)

\(f(q)\)	\(=\)	\(q+(-0.599601 - 1.03854i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.280958 - 0.486633i) q^{4} +(0.286327 + 0.495932i) q^{5} -1.19920 q^{6} +(-1.87398 - 1.86767i) q^{7} -3.07225 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.599601 - 1.03854i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.280958 - 0.486633i) q^{4} +(0.286327 + 0.495932i) q^{5} -1.19920 q^{6} +(-1.87398 - 1.86767i) q^{7} -3.07225 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.343363 - 0.594723i) q^{10} +(-1.26255 + 2.18680i) q^{11} +(-0.280958 - 0.486633i) q^{12} -5.05314 q^{13} +(-0.816015 + 3.06606i) q^{14} +0.572653 q^{15} +(1.28021 + 2.21739i) q^{16} +(1.12612 - 1.95049i) q^{17} +(-0.599601 + 1.03854i) q^{18} +(-1.19967 - 2.07789i) q^{19} +0.321783 q^{20} +(-2.55444 + 0.689075i) q^{21} +3.02811 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-1.53613 + 2.66065i) q^{24} +(2.33603 - 4.04613i) q^{25} +(3.02987 + 5.24788i) q^{26} -1.00000 q^{27} +(-1.43538 + 0.387202i) q^{28} +0.796522 q^{29} +(-0.343363 - 0.594723i) q^{30} +(1.72866 - 2.99412i) q^{31} +(-1.53702 + 2.66220i) q^{32} +(1.26255 + 2.18680i) q^{33} -2.70088 q^{34} +(0.389671 - 1.46413i) q^{35} -0.561916 q^{36} +(-4.40243 - 7.62523i) q^{37} +(-1.43865 + 2.49181i) q^{38} +(-2.52657 + 4.37615i) q^{39} +(-0.879668 - 1.52363i) q^{40} +10.9790 q^{41} +(2.24728 + 2.23972i) q^{42} -1.90984 q^{43} +(0.709448 + 1.22880i) q^{44} +(0.286327 - 0.495932i) q^{45} +(-0.599601 + 1.03854i) q^{46} +(0.968258 + 1.67707i) q^{47} +2.56042 q^{48} +(0.0235820 + 6.99996i) q^{49} -5.60275 q^{50} +(-1.12612 - 1.95049i) q^{51} +(-1.41972 + 2.45903i) q^{52} +(-4.78530 + 8.28839i) q^{53} +(0.599601 + 1.03854i) q^{54} -1.44601 q^{55} +(5.75733 + 5.73797i) q^{56} -2.39935 q^{57} +(-0.477595 - 0.827219i) q^{58} +(2.20464 - 3.81854i) q^{59} +(0.160891 - 0.278672i) q^{60} +(-1.06335 - 1.84178i) q^{61} -4.14602 q^{62} +(-0.680465 + 2.55675i) q^{63} +8.80724 q^{64} +(-1.44685 - 2.50602i) q^{65} +(1.51405 - 2.62242i) q^{66} +(-2.00778 + 3.47758i) q^{67} +(-0.632783 - 1.09601i) q^{68} -1.00000 q^{69} +(-1.75420 + 0.473206i) q^{70} +0.424132 q^{71} +(1.53613 + 2.66065i) q^{72} +(7.00045 - 12.1251i) q^{73} +(-5.27940 + 9.14418i) q^{74} +(-2.33603 - 4.04613i) q^{75} -1.34823 q^{76} +(6.45023 - 1.73998i) q^{77} +6.05973 q^{78} +(-2.48666 - 4.30702i) q^{79} +(-0.733116 + 1.26979i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.58304 - 11.4022i) q^{82} -10.1555 q^{83} +(-0.382364 + 1.43668i) q^{84} +1.28975 q^{85} +(1.14514 + 1.98344i) q^{86} +(0.398261 - 0.689808i) q^{87} +(3.87888 - 6.71841i) q^{88} +(-1.91357 - 3.31439i) q^{89} -0.686727 q^{90} +(9.46947 + 9.43762i) q^{91} -0.561916 q^{92} +(-1.72866 - 2.99412i) q^{93} +(1.16114 - 2.01115i) q^{94} +(0.686997 - 1.18991i) q^{95} +(1.53702 + 2.66220i) q^{96} +15.4364 q^{97} +(7.25559 - 4.22167i) q^{98} +2.52510 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

Introduction

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