LMFDB - Embedded newform 1026.2.h.g.577.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1026,2,Mod(505,1026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1026, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1026.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1026 = 2 \cdot 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1026.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.19265124738$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 342)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.9
Root			$-0.672818 - 1.59603i$ of defining polynomial
Character	$\chi$	$=$	1026.577
Dual form			1026.2.h.g.505.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +4.26017 q^{5} +(-0.603898 - 1.04598i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +4.26017 q^{5} +(-0.603898 - 1.04598i) q^{7} +1.00000 q^{8} +(-2.13008 + 3.68941i) q^{10} +(0.143169 + 0.247977i) q^{11} +(1.79480 + 3.10869i) q^{13} +1.20780 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.960728 + 1.66403i) q^{17} +(-1.55888 - 4.07061i) q^{19} +(-2.13008 - 3.68941i) q^{20} -0.286339 q^{22} +(3.59889 + 6.23346i) q^{23} +13.1490 q^{25} -3.58961 q^{26} +(-0.603898 + 1.04598i) q^{28} -8.19741 q^{29} +(-0.262817 + 0.455213i) q^{31} +(-0.500000 - 0.866025i) q^{32} -1.92146 q^{34} +(-2.57270 - 4.45605i) q^{35} +2.76309 q^{37} +(4.30470 + 0.685272i) q^{38} +4.26017 q^{40} +8.96050 q^{41} +(5.56496 - 9.63879i) q^{43} +(0.143169 - 0.247977i) q^{44} -7.19778 q^{46} -5.71450 q^{47} +(2.77062 - 4.79885i) q^{49} +(-6.57451 + 11.3874i) q^{50} +(1.79480 - 3.10869i) q^{52} +(3.77851 - 6.54457i) q^{53} +(0.609926 + 1.05642i) q^{55} +(-0.603898 - 1.04598i) q^{56} +(4.09871 - 7.09917i) q^{58} -1.07655 q^{59} -2.73435 q^{61} +(-0.262817 - 0.455213i) q^{62} +1.00000 q^{64} +(7.64617 + 13.2436i) q^{65} +(0.821582 + 1.42302i) q^{67} +(0.960728 - 1.66403i) q^{68} +5.14541 q^{70} +(-0.231197 - 0.400444i) q^{71} +(3.71200 + 6.42937i) q^{73} +(-1.38155 + 2.39291i) q^{74} +(-2.74581 + 3.38534i) q^{76} +(0.172919 - 0.299505i) q^{77} +(-7.10100 + 12.2993i) q^{79} +(-2.13008 + 3.68941i) q^{80} +(-4.48025 + 7.76002i) q^{82} +(-0.609393 - 1.05550i) q^{83} +(4.09286 + 7.08904i) q^{85} +(5.56496 + 9.63879i) q^{86} +(0.143169 + 0.247977i) q^{88} +(-7.04675 + 12.2053i) q^{89} +(2.16776 - 3.75467i) q^{91} +(3.59889 - 6.23346i) q^{92} +(2.85725 - 4.94891i) q^{94} +(-6.64111 - 17.3415i) q^{95} +(-2.85458 + 4.94428i) q^{97} +(2.77062 + 4.79885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8}+O(q^{10}) $ 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8	$ 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8} - q^{11} + q^{13} - 10 q^{14} - 9 q^{16} + 5 q^{17} + 9 q^{19} + 2 q^{22} + 2 q^{23} + 18 q^{25} - 2 q^{26} + 5 q^{28} - 18 q^{29} + 4 q^{31} - 9 q^{32} - 10 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} + 2 q^{41} + 7 q^{43} - q^{44} - 4 q^{46} + 38 q^{47} + 6 q^{49} - 9 q^{50} + q^{52} + 10 q^{53} + 6 q^{55} + 5 q^{56} + 9 q^{58} - 10 q^{59} - 36 q^{61} + 4 q^{62} + 18 q^{64} + 45 q^{65} + 22 q^{67} + 5 q^{68} + 12 q^{70} - 11 q^{71} + 44 q^{73} - 10 q^{74} - 6 q^{76} + 2 q^{77} + 2 q^{79} - q^{82} + 7 q^{83} + 7 q^{86} - q^{88} - q^{89} - 25 q^{91} + 2 q^{92} - 19 q^{94} - 21 q^{95} + 6 q^{98}+O(q^{100}) $ 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8 - q^11 + q^13 - 10 * q^14 - 9 * q^16 + 5 * q^17 + 9 * q^19 + 2 * q^22 + 2 * q^23 + 18 * q^25 - 2 * q^26 + 5 * q^28 - 18 * q^29 + 4 * q^31 - 9 * q^32 - 10 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 + 2 * q^41 + 7 * q^43 - q^44 - 4 * q^46 + 38 * q^47 + 6 * q^49 - 9 * q^50 + q^52 + 10 * q^53 + 6 * q^55 + 5 * q^56 + 9 * q^58 - 10 * q^59 - 36 * q^61 + 4 * q^62 + 18 * q^64 + 45 * q^65 + 22 * q^67 + 5 * q^68 + 12 * q^70 - 11 * q^71 + 44 * q^73 - 10 * q^74 - 6 * q^76 + 2 * q^77 + 2 * q^79 - q^82 + 7 * q^83 + 7 * q^86 - q^88 - q^89 - 25 * q^91 + 2 * q^92 - 19 * q^94 - 21 * q^95 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1026\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	4.26017			1.90520			0.952602	−	0.304219i	$-0.0983954\pi$
$5$	4.26017			1.90520			0.952602	+	0.304219i	$0.0983954\pi$
$6$		0			0
$7$	−0.603898	−	1.04598i	−0.228252	−	0.395344i	0.729038	−	0.684473i	$-0.239968\pi$
$7$	−0.603898	−	1.04598i	−0.228252	−	0.395344i	−0.957290	+	0.289129i	$0.906634\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.13008	+	3.68941i	−0.673591	+	1.16669i
$11$	0.143169	+	0.247977i	0.0431672	+	0.0747678i	0.886802	−	0.462150i	$-0.152922\pi$
$11$	0.143169	+	0.247977i	0.0431672	+	0.0747678i	−0.843635	+	0.536918i	$0.819589\pi$
$12$		0			0
$13$	1.79480	+	3.10869i	0.497789	+	0.862196i	0.999997	−	0.00255079i	$-0.000811942\pi$
$13$	1.79480	+	3.10869i	0.497789	+	0.862196i	−0.502207	+	0.864747i	$0.667479\pi$
$14$	1.20780			0.322797
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.960728	+	1.66403i	0.233011	+	0.403587i	0.958693	−	0.284444i	$-0.0918089\pi$
$17$	0.960728	+	1.66403i	0.233011	+	0.403587i	−0.725682	+	0.688030i	$0.758476\pi$
$18$		0			0
$19$	−1.55888	−	4.07061i	−0.357633	−	0.933862i
$19$	−1.55888	−	4.07061i	−0.357633	−	0.933862i
$20$	−2.13008	−	3.68941i	−0.476301	−	0.824978i
$21$		0			0
$22$	−0.286339			−0.0610476
$23$	3.59889	+	6.23346i	0.750420	+	1.29977i	0.947619	+	0.319403i	$0.103482\pi$
$23$	3.59889	+	6.23346i	0.750420	+	1.29977i	−0.197199	+	0.980364i	$0.563184\pi$
$24$		0			0
$25$	13.1490			2.62980
$26$	−3.58961			−0.703980
$27$		0			0
$28$	−0.603898	+	1.04598i	−0.114126	+	0.197672i
$29$	−8.19741			−1.52222			−0.761111	−	0.648622i	$-0.775346\pi$
$29$	−8.19741			−1.52222			−0.761111	+	0.648622i	$0.775346\pi$
$30$		0			0
$31$	−0.262817	+	0.455213i	−0.0472034	+	0.0817586i	−0.888662	−	0.458563i	$-0.848364\pi$
$31$	−0.262817	+	0.455213i	−0.0472034	+	0.0817586i	0.841458	+	0.540322i	$0.181698\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−1.92146			−0.329527
$35$	−2.57270	−	4.45605i	−0.434866	−	0.753211i
$36$		0			0
$37$	2.76309			0.454250			0.227125	−	0.973866i	$-0.427067\pi$
$37$	2.76309			0.454250			0.227125	+	0.973866i	$0.427067\pi$
$38$	4.30470	+	0.685272i	0.698314	+	0.111166i
$39$		0			0
$40$	4.26017			0.673591
$41$	8.96050			1.39940			0.699698	−	0.714439i	$-0.253318\pi$
$41$	8.96050			1.39940			0.699698	+	0.714439i	$0.253318\pi$
$42$		0			0
$43$	5.56496	−	9.63879i	0.848648	−	1.46990i	−0.0337662	−	0.999430i	$-0.510750\pi$
$43$	5.56496	−	9.63879i	0.848648	−	1.46990i	0.882415	−	0.470472i	$-0.155917\pi$
$44$	0.143169	−	0.247977i	0.0215836	−	0.0373839i
$45$		0			0
$46$	−7.19778			−1.06125
$47$	−5.71450			−0.833546			−0.416773	−	0.909011i	$-0.636839\pi$
$47$	−5.71450			−0.833546			−0.416773	+	0.909011i	$0.636839\pi$
$48$		0			0
$49$	2.77062	−	4.79885i	0.395802	−	0.685550i
$50$	−6.57451	+	11.3874i	−0.929776	+	1.61042i
$51$		0			0
$52$	1.79480	−	3.10869i	0.248895	−	0.431098i
$53$	3.77851	−	6.54457i	0.519018	−	0.898966i	−0.480738	−	0.876865i	$-0.659631\pi$
$53$	3.77851	−	6.54457i	0.519018	−	0.898966i	0.999756	−	0.0221014i	$-0.00703566\pi$
$54$		0			0
$55$	0.609926	+	1.05642i	0.0822423	+	0.142448i
$56$	−0.603898	−	1.04598i	−0.0806992	−	0.139775i
$57$		0			0
$58$	4.09871	−	7.09917i	0.538186	−	0.932166i
$59$	−1.07655			−0.140155			−0.0700776	−	0.997542i	$-0.522325\pi$
$59$	−1.07655			−0.140155			−0.0700776	+	0.997542i	$0.522325\pi$
$60$		0			0
$61$	−2.73435			−0.350098			−0.175049	−	0.984560i	$-0.556008\pi$
$61$	−2.73435			−0.350098			−0.175049	+	0.984560i	$0.556008\pi$
$62$	−0.262817	−	0.455213i	−0.0333778	−	0.0578121i
$63$		0			0
$64$	1.00000			0.125000
$65$	7.64617	+	13.2436i	0.948390	+	1.64266i
$66$		0			0
$67$	0.821582	+	1.42302i	0.100372	+	0.173850i	0.911838	−	0.410550i	$-0.134663\pi$
$67$	0.821582	+	1.42302i	0.100372	+	0.173850i	−0.811466	+	0.584400i	$0.801330\pi$
$68$	0.960728	−	1.66403i	0.116505	−	0.201793i
$69$		0			0
$70$	5.14541			0.614994
$71$	−0.231197	−	0.400444i	−0.0274380	−	0.0475240i	0.851980	−	0.523574i	$-0.175402\pi$
$71$	−0.231197	−	0.400444i	−0.0274380	−	0.0475240i	−0.879418	+	0.476050i	$0.842068\pi$
$72$		0			0
$73$	3.71200	+	6.42937i	0.434457	+	0.752501i	0.997251	−	0.0740958i	$-0.0236071\pi$
$73$	3.71200	+	6.42937i	0.434457	+	0.752501i	−0.562794	+	0.826597i	$0.690274\pi$
$74$	−1.38155	+	2.39291i	−0.160601	+	0.278170i
$75$		0			0
$76$	−2.74581	+	3.38534i	−0.314966	+	0.388325i
$77$	0.172919	−	0.299505i	0.0197060	−	0.0341318i
$78$		0			0
$79$	−7.10100	+	12.2993i	−0.798925	+	1.38378i	0.121392	+	0.992605i	$0.461264\pi$
$79$	−7.10100	+	12.2993i	−0.798925	+	1.38378i	−0.920317	+	0.391174i	$0.872069\pi$
$80$	−2.13008	+	3.68941i	−0.238151	+	0.412489i
$81$		0			0
$82$	−4.48025	+	7.76002i	−0.494761	+	0.856951i
$83$	−0.609393	−	1.05550i	−0.0668896	−	0.115856i	0.830641	−	0.556808i	$-0.187974\pi$
$83$	−0.609393	−	1.05550i	−0.0668896	−	0.115856i	−0.897531	+	0.440952i	$0.854641\pi$
$84$		0			0
$85$	4.09286	+	7.08904i	0.443933	+	0.768915i
$86$	5.56496	+	9.63879i	0.600085	+	1.03938i
$87$		0			0
$88$	0.143169	+	0.247977i	0.0152619	+	0.0264344i
$89$	−7.04675	+	12.2053i	−0.746954	+	1.29376i	0.202323	+	0.979319i	$0.435151\pi$
$89$	−7.04675	+	12.2053i	−0.746954	+	1.29376i	−0.949276	+	0.314443i	$0.898182\pi$
$90$		0			0
$91$	2.16776	−	3.75467i	0.227243	−	0.393596i
$92$	3.59889	−	6.23346i	0.375210	−	0.649883i
$93$		0			0
$94$	2.85725	−	4.94891i	0.294703	−	0.510441i
$95$	−6.64111	−	17.3415i	−0.681363	−	1.77920i
$96$		0			0
$97$	−2.85458	+	4.94428i	−0.289839	+	0.502016i	−0.973771	−	0.227530i	$-0.926935\pi$
$97$	−2.85458	+	4.94428i	−0.289839	+	0.502016i	0.683932	+	0.729546i	$0.260268\pi$
$98$	2.77062	+	4.79885i	0.279874	+	0.484757i
$99$		0			0
$100$	−6.57451	−	11.3874i	−0.657451	−	1.13874i
$101$	−5.03364			−0.500866			−0.250433	−	0.968134i	$-0.580573\pi$
$101$	−5.03364			−0.500866			−0.250433	+	0.968134i	$0.580573\pi$
$102$		0			0
$103$	1.68837	−	2.92435i	0.166360	−	0.288144i	−0.770777	−	0.637105i	$-0.780132\pi$
$103$	1.68837	−	2.92435i	0.166360	−	0.288144i	0.937138	+	0.348960i	$0.113465\pi$
$104$	1.79480	+	3.10869i	0.175995	+	0.304832i
$105$		0			0
$106$	3.77851	+	6.54457i	0.367001	+	0.635665i
$107$	−7.50236			−0.725281			−0.362640	−	0.931929i	$-0.618125\pi$
$107$	−7.50236			−0.725281			−0.362640	+	0.931929i	$0.618125\pi$
$108$		0			0
$109$	5.72124	+	9.90948i	0.547995	+	0.949156i	0.998412	+	0.0563373i	$0.0179422\pi$
$109$	5.72124	+	9.90948i	0.547995	+	0.949156i	−0.450416	+	0.892819i	$0.648724\pi$
$110$	−1.21985			−0.116308
$111$		0			0
$112$	1.20780			0.114126
$113$	−0.584736	+	1.01279i	−0.0550073	+	0.0952754i	−0.892218	−	0.451605i	$-0.850852\pi$
$113$	−0.584736	+	1.01279i	−0.0550073	+	0.0952754i	0.837211	+	0.546881i	$0.184185\pi$
$114$		0			0
$115$	15.3319	+	26.5556i	1.42970	+	2.47632i
$116$	4.09871	+	7.09917i	0.380555	+	0.659141i
$117$		0			0
$118$	0.538276	−	0.932322i	0.0495524	−	0.0858272i
$119$	1.16036	−	2.00981i	0.106370	−	0.184239i
$120$		0			0
$121$	5.45901	−	9.45527i	0.496273	−	0.859570i
$122$	1.36717	−	2.36802i	0.123778	−	0.214390i
$123$		0			0
$124$	0.525634			0.0472034
$125$	34.7162			3.10511
$126$		0			0
$127$	3.36618	−	5.83039i	0.298700	−	0.517364i	−0.677139	−	0.735855i	$-0.736780\pi$
$127$	3.36618	−	5.83039i	0.298700	−	0.517364i	0.975839	+	0.218492i	$0.0701137\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−15.2923			−1.34123
$131$	−1.72729			−0.150914			−0.0754568	−	0.997149i	$-0.524041\pi$
$131$	−1.72729			−0.150914			−0.0754568	+	0.997149i	$0.524041\pi$
$132$		0			0
$133$	−3.31638	+	4.08880i	−0.287566	+	0.354544i
$134$	−1.64316			−0.141948
$135$		0			0
$136$	0.960728	+	1.66403i	0.0823818	+	0.142689i
$137$	12.7432			1.08872			0.544362	−	0.838851i	$-0.316772\pi$
$137$	12.7432			1.08872			0.544362	+	0.838851i	$0.316772\pi$
$138$		0			0
$139$	−0.347220	−	0.601402i	−0.0294508	−	0.0510103i	0.850924	−	0.525288i	$-0.176043\pi$
$139$	−0.347220	−	0.601402i	−0.0294508	−	0.0510103i	−0.880375	+	0.474278i	$0.842709\pi$
$140$	−2.57270	+	4.45605i	−0.217433	+	0.376605i
$141$		0			0
$142$	0.462393			0.0388032
$143$	−0.513922	+	0.890140i	−0.0429763	+	0.0744372i
$144$		0			0
$145$	−34.9223			−2.90014
$146$	−7.42400			−0.614415
$147$		0			0
$148$	−1.38155	−	2.39291i	−0.113562	−	0.196696i
$149$	−0.377321			−0.0309113			−0.0154557	−	0.999881i	$-0.504920\pi$
$149$	−0.377321			−0.0309113			−0.0154557	+	0.999881i	$0.504920\pi$
$150$		0			0
$151$	−9.79347	−	16.9628i	−0.796982	−	1.38041i	−0.921573	−	0.388204i	$-0.873095\pi$
$151$	−9.79347	−	16.9628i	−0.796982	−	1.38041i	0.124592	−	0.992208i	$-0.460238\pi$
$152$	−1.55888	−	4.07061i	−0.126442	−	0.330170i
$153$		0			0
$154$	0.172919	+	0.299505i	0.0139342	+	0.0241348i
$155$	−1.11964	+	1.93928i	−0.0899320	+	0.155767i
$156$		0			0
$157$	−15.1813			−1.21160			−0.605800	−	0.795617i	$-0.707147\pi$
$157$	−15.1813			−1.21160			−0.605800	+	0.795617i	$0.707147\pi$
$158$	−7.10100	−	12.2993i	−0.564925	−	0.978479i
$159$		0			0
$160$	−2.13008	−	3.68941i	−0.168398	−	0.291674i
$161$	4.34672	−	7.52874i	0.342570	−	0.593348i
$162$		0			0
$163$	0.287915			0.0225513			0.0112756	−	0.999936i	$-0.496411\pi$
$163$	0.287915			0.0225513			0.0112756	+	0.999936i	$0.496411\pi$
$164$	−4.48025	−	7.76002i	−0.349849	−	0.605956i
$165$		0			0
$166$	1.21879			0.0945962
$167$	−10.5972	−	18.3549i	−0.820035	−	1.42034i	−0.905655	−	0.424014i	$-0.860621\pi$
$167$	−10.5972	−	18.3549i	−0.820035	−	1.42034i	0.0856206	−	0.996328i	$-0.472713\pi$
$168$		0			0
$169$	0.0573505	−	0.0993339i	0.00441157	−	0.00764107i
$170$	−8.18572			−0.627816
$171$		0			0
$172$	−11.1299			−0.848648
$173$	5.44746	−	9.43527i	0.414162	−	0.717350i	−0.581178	−	0.813777i	$-0.697408\pi$
$173$	5.44746	−	9.43527i	0.414162	−	0.717350i	0.995340	+	0.0964263i	$0.0307412\pi$
$174$		0			0
$175$	−7.94066	−	13.7536i	−0.600257	−	1.03968i
$176$	−0.286339			−0.0215836
$177$		0			0
$178$	−7.04675	−	12.2053i	−0.528176	−	0.914828i
$179$	−20.6934			−1.54670			−0.773350	−	0.633979i	$-0.781421\pi$
$179$	−20.6934			−1.54670			−0.773350	+	0.633979i	$0.781421\pi$
$180$		0			0
$181$	−8.80530	+	15.2512i	−0.654493	+	1.13362i	0.327528	+	0.944842i	$0.393785\pi$
$181$	−8.80530	+	15.2512i	−0.654493	+	1.13362i	−0.982021	+	0.188774i	$0.939549\pi$
$182$	2.16776	+	3.75467i	0.160685	+	0.278314i
$183$		0			0
$184$	3.59889	+	6.23346i	0.265314	+	0.459537i
$185$	11.7712			0.865438
$186$		0			0
$187$	−0.275094	+	0.476476i	−0.0201169	+	0.0348434i
$188$	2.85725	+	4.94891i	0.208387	+	0.360936i
$189$		0			0
$190$	18.3387	+	2.91937i	1.33043	+	0.211794i
$191$	9.70640	+	16.8120i	0.702330	+	1.21647i	0.967646	+	0.252310i	$0.0811903\pi$
$191$	9.70640	+	16.8120i	0.702330	+	1.21647i	−0.265316	+	0.964161i	$0.585476\pi$
$192$		0			0
$193$	−24.6165			−1.77193			−0.885966	−	0.463751i	$-0.846503\pi$
$193$	−24.6165			−1.77193			−0.885966	+	0.463751i	$0.846503\pi$
$194$	−2.85458	−	4.94428i	−0.204947	−	0.354979i
$195$		0			0
$196$	−5.54123			−0.395802
$197$	−24.8551			−1.77085			−0.885426	−	0.464781i	$-0.846133\pi$
$197$	−24.8551			−1.77085			−0.885426	+	0.464781i	$0.846133\pi$
$198$		0			0
$199$	11.2163	−	19.4271i	0.795099	−	1.37715i	−0.127677	−	0.991816i	$-0.540752\pi$
$199$	11.2163	−	19.4271i	0.795099	−	1.37715i	0.922776	−	0.385336i	$-0.125915\pi$
$200$	13.1490			0.929776
$201$		0			0
$202$	2.51682	−	4.35926i	0.177083	−	0.306717i
$203$	4.95040	+	8.57434i	0.347450	+	0.601801i
$204$		0			0
$205$	38.1732			2.66613
$206$	1.68837	+	2.92435i	0.117634	+	0.203749i
$207$		0			0
$208$	−3.58961			−0.248895
$209$	0.786232	−	0.969354i	0.0543848	−	0.0670516i
$210$		0			0
$211$	1.53968			0.105996			0.0529980	−	0.998595i	$-0.483122\pi$
$211$	1.53968			0.105996			0.0529980	+	0.998595i	$0.483122\pi$
$212$	−7.55702			−0.519018
$213$		0			0
$214$	3.75118	−	6.49724i	0.256426	−	0.444142i
$215$	23.7077	−	41.0629i	1.61685	−	2.80046i
$216$		0			0
$217$	0.634859			0.0430970
$218$	−11.4425			−0.774983
$219$		0			0
$220$	0.609926	−	1.05642i	0.0411212	−	0.0712240i
$221$	−3.44864	+	5.97322i	−0.231981	+	0.401802i
$222$		0			0
$223$	−6.70340	+	11.6106i	−0.448893	+	0.777505i	−0.998314	−	0.0580403i	$-0.981515\pi$
$223$	−6.70340	+	11.6106i	−0.448893	+	0.777505i	0.549422	+	0.835545i	$0.314848\pi$
$224$	−0.603898	+	1.04598i	−0.0403496	+	0.0698876i
$225$		0			0
$226$	−0.584736	−	1.01279i	−0.0388960	−	0.0673699i
$227$	−8.02618	−	13.9017i	−0.532716	−	0.922691i	−0.999270	−	0.0381985i	$-0.987838\pi$
$227$	−8.02618	−	13.9017i	−0.532716	−	0.922691i	0.466554	−	0.884493i	$-0.345495\pi$
$228$		0			0
$229$	7.73445	−	13.3965i	0.511107	−	0.885263i	−0.488810	−	0.872390i	$-0.662569\pi$
$229$	7.73445	−	13.3965i	0.511107	−	0.885263i	0.999917	−	0.0128732i	$-0.00409779\pi$
$230$	−30.6637			−2.02191
$231$		0			0
$232$	−8.19741			−0.538186
$233$	−1.87821	−	3.25315i	−0.123045	−	0.213121i	0.797922	−	0.602761i	$-0.205933\pi$
$233$	−1.87821	−	3.25315i	−0.123045	−	0.213121i	−0.920967	+	0.389640i	$0.872599\pi$
$234$		0			0
$235$	−24.3447			−1.58808
$236$	0.538276	+	0.932322i	0.0350388	+	0.0606890i
$237$		0			0
$238$	1.16036	+	2.00981i	0.0752152	+	0.130276i
$239$	6.74604	−	11.6845i	0.436365	−	0.755807i	−0.561041	−	0.827788i	$-0.689599\pi$
$239$	6.74604	−	11.6845i	0.436365	−	0.755807i	0.997406	+	0.0719815i	$0.0229323\pi$
$240$		0			0
$241$	−14.1123			−0.909055			−0.454528	−	0.890733i	$-0.650192\pi$
$241$	−14.1123			−0.909055			−0.454528	+	0.890733i	$0.650192\pi$
$242$	5.45901	+	9.45527i	0.350918	+	0.607808i
$243$		0			0
$244$	1.36717	+	2.36802i	0.0875244	+	0.151597i
$245$	11.8033	−	20.4439i	0.754084	−	1.30611i
$246$		0			0
$247$	9.85639	−	12.1520i	0.627147	−	0.773216i
$248$	−0.262817	+	0.455213i	−0.0166889	+	0.0289060i
$249$		0			0
$250$	−17.3581	+	30.0651i	−1.09782	+	1.90148i
$251$	−6.77858	+	11.7408i	−0.427860	+	0.741075i	−0.996683	−	0.0813850i	$-0.974066\pi$
$251$	−6.77858	+	11.7408i	−0.427860	+	0.741075i	0.568823	+	0.822460i	$0.307399\pi$
$252$		0			0
$253$	−1.03050	+	1.78488i	−0.0647871	+	0.112215i
$254$	3.36618	+	5.83039i	0.211213	+	0.365831i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.45044	−	2.51224i	−0.0904762	−	0.156709i	0.817235	−	0.576304i	$-0.195506\pi$
$257$	−1.45044	−	2.51224i	−0.0904762	−	0.156709i	−0.907712	+	0.419595i	$0.862172\pi$
$258$		0			0
$259$	−1.66862	−	2.89014i	−0.103683	−	0.179585i
$260$	7.64617	−	13.2436i	0.474195	−	0.821330i
$261$		0			0
$262$	0.863643	−	1.49587i	0.0533560	−	0.0924153i
$263$	−14.5330	+	25.1719i	−0.896142	+	1.55216i	−0.0637568	+	0.997965i	$0.520308\pi$
$263$	−14.5330	+	25.1719i	−0.896142	+	1.55216i	−0.832385	+	0.554198i	$0.813025\pi$
$264$		0			0
$265$	16.0971	−	27.8810i	0.988836	−	1.71271i
$266$	−1.88281	−	4.91647i	−0.115443	−	0.301448i
$267$		0			0
$268$	0.821582	−	1.42302i	0.0501861	−	0.0869248i
$269$	0.390967	+	0.677175i	0.0238377	+	0.0412881i	0.877698	−	0.479214i	$-0.159078\pi$
$269$	0.390967	+	0.677175i	0.0238377	+	0.0412881i	−0.853860	+	0.520502i	$0.825745\pi$
$270$		0			0
$271$	−2.09691	−	3.63195i	−0.127378	−	0.220626i	0.795282	−	0.606240i	$-0.207323\pi$
$271$	−2.09691	−	3.63195i	−0.127378	−	0.220626i	−0.922660	+	0.385614i	$0.873990\pi$
$272$	−1.92146			−0.116505
$273$		0			0
$274$	−6.37159	+	11.0359i	−0.384922	+	0.666704i
$275$	1.88254	+	3.26065i	0.113521	+	0.196625i
$276$		0			0
$277$	0.399916	+	0.692675i	0.0240286	+	0.0416188i	0.877790	−	0.479046i	$-0.159017\pi$
$277$	0.399916	+	0.692675i	0.0240286	+	0.0416188i	−0.853761	+	0.520665i	$0.825684\pi$
$278$	0.694440			0.0416497
$279$		0			0
$280$	−2.57270	−	4.45605i	−0.153748	−	0.266300i
$281$	10.9333			0.652228			0.326114	−	0.945331i	$-0.394261\pi$
$281$	10.9333			0.652228			0.326114	+	0.945331i	$0.394261\pi$
$282$		0			0
$283$	19.8830			1.18192			0.590962	−	0.806699i	$-0.298748\pi$
$283$	19.8830			1.18192			0.590962	+	0.806699i	$0.298748\pi$
$284$	−0.231197	+	0.400444i	−0.0137190	+	0.0237620i
$285$		0			0
$286$	−0.513922	−	0.890140i	−0.0303889	−	0.0526351i
$287$	−5.41123	−	9.37252i	−0.319415	−	0.553242i
$288$		0			0
$289$	6.65400	−	11.5251i	0.391412	−	0.677945i
$290$	17.4612	−	30.2436i	1.02536	−	1.77597i
$291$		0			0
$292$	3.71200	−	6.42937i	0.217228	−	0.376251i
$293$	1.48719	−	2.57588i	0.0868823	−	0.150485i	−0.819309	−	0.573352i	$-0.805643\pi$
$293$	1.48719	−	2.57588i	0.0868823	−	0.150485i	0.906192	+	0.422867i	$0.138976\pi$
$294$		0			0
$295$	−4.58629			−0.267024
$296$	2.76309			0.160601
$297$		0			0
$298$	0.188660	−	0.326769i	0.0109288	−	0.0189292i
$299$	−12.9186	+	22.3757i	−0.747103	+	1.29402i
$300$		0			0
$301$	−13.4427			−0.774822
$302$	19.5869			1.12710
$303$		0			0
$304$	4.30470	+	0.685272i	0.246891	+	0.0393031i
$305$	−11.6488			−0.667008
$306$		0			0
$307$	−0.00786971	−	0.0136307i	−0.000449148	−	0.000777948i	0.865801	−	0.500389i	$-0.166810\pi$
$307$	−0.00786971	−	0.0136307i	−0.000449148	−	0.000777948i	−0.866250	+	0.499611i	$0.833476\pi$
$308$	−0.345839			−0.0197060
$309$		0			0
$310$	−1.11964	−	1.93928i	−0.0635916	−	0.110144i
$311$	0.925134	−	1.60238i	0.0524596	−	0.0908626i	−0.838603	−	0.544743i	$-0.816627\pi$
$311$	0.925134	−	1.60238i	0.0524596	−	0.0908626i	0.891063	+	0.453880i	$0.149961\pi$
$312$		0			0
$313$	−4.53396			−0.256275			−0.128137	−	0.991756i	$-0.540900\pi$
$313$	−4.53396			−0.256275			−0.128137	+	0.991756i	$0.540900\pi$
$314$	7.59065	−	13.1474i	0.428365	−	0.741950i
$315$		0			0
$316$	14.2020			0.798925
$317$	−11.3513			−0.637553			−0.318777	−	0.947830i	$-0.603272\pi$
$317$	−11.3513			−0.637553			−0.318777	+	0.947830i	$0.603272\pi$
$318$		0			0
$319$	−1.17362	−	2.03277i	−0.0657100	−	0.113813i
$320$	4.26017			0.238151
$321$		0			0
$322$	4.34672	+	7.52874i	0.242233	+	0.419560i
$323$	5.27596	−	6.50478i	0.293562	−	0.361936i
$324$		0			0
$325$	23.5999	+	40.8763i	1.30909	+	2.26741i
$326$	−0.143958	+	0.249342i	−0.00797308	+	0.0138098i
$327$		0			0
$328$	8.96050			0.494761
$329$	3.45098	+	5.97726i	0.190258	+	0.329537i
$330$		0			0
$331$	6.82253	+	11.8170i	0.375000	+	0.649519i	0.990327	−	0.138753i	$-0.0443094\pi$
$331$	6.82253	+	11.8170i	0.375000	+	0.649519i	−0.615327	+	0.788272i	$0.710976\pi$
$332$	−0.609393	+	1.05550i	−0.0334448	+	0.0579281i
$333$		0			0
$334$	21.1944			1.15970
$335$	3.50007	+	6.06231i	0.191229	+	0.331219i
$336$		0			0
$337$	9.67961			0.527282			0.263641	−	0.964621i	$-0.415077\pi$
$337$	9.67961			0.527282			0.263641	+	0.964621i	$0.415077\pi$
$338$	0.0573505	+	0.0993339i	0.00311945	+	0.00540305i
$339$		0			0
$340$	4.09286	−	7.08904i	0.221967	−	0.384457i
$341$	−0.150510			−0.00815055
$342$		0			0
$343$	−15.1472			−0.817874
$344$	5.56496	−	9.63879i	0.300043	−	0.519689i
$345$		0			0
$346$	5.44746	+	9.43527i	0.292857	+	0.507243i
$347$	−28.1497			−1.51115			−0.755577	−	0.655059i	$-0.772644\pi$
$347$	−28.1497			−1.51115			−0.755577	+	0.655059i	$0.772644\pi$
$348$		0			0
$349$	−2.81128	−	4.86928i	−0.150484	−	0.260647i	0.780921	−	0.624629i	$-0.214750\pi$
$349$	−2.81128	−	4.86928i	−0.150484	−	0.260647i	−0.931406	+	0.363983i	$0.881417\pi$
$350$	15.8813			0.848892
$351$		0			0
$352$	0.143169	−	0.247977i	0.00763096	−	0.0132172i
$353$	−10.3772	−	17.9738i	−0.552322	−	0.956650i	−0.998107	−	0.0615094i	$-0.980409\pi$
$353$	−10.3772	−	17.9738i	−0.552322	−	0.956650i	0.445785	−	0.895140i	$-0.352925\pi$
$354$		0			0
$355$	−0.984936	−	1.70596i	−0.0522750	−	0.0905429i
$356$	14.0935			0.746954
$357$		0			0
$358$	10.3467	−	17.9210i	0.546841	−	0.947157i
$359$	5.59882	+	9.69744i	0.295494	+	0.511811i	0.975100	−	0.221767i	$-0.0711823\pi$
$359$	5.59882	+	9.69744i	0.295494	+	0.511811i	−0.679605	+	0.733578i	$0.737849\pi$
$360$		0			0
$361$	−14.1398	+	12.6912i	−0.744198	+	0.667959i
$362$	−8.80530	−	15.2512i	−0.462796	−	0.801587i
$363$		0			0
$364$	−4.33551			−0.227243
$365$	15.8137	+	27.3902i	0.827729	+	1.43367i
$366$		0			0
$367$	−18.7488			−0.978681			−0.489340	−	0.872093i	$-0.662762\pi$
$367$	−18.7488			−0.978681			−0.489340	+	0.872093i	$0.662762\pi$
$368$	−7.19778			−0.375210
$369$		0			0
$370$	−5.88562	+	10.1942i	−0.305979	+	0.529971i
$371$	−9.12733			−0.473867
$372$		0			0
$373$	−9.69985	+	16.8006i	−0.502239	+	0.869904i	0.497758	+	0.867316i	$0.334157\pi$
$373$	−9.69985	+	16.8006i	−0.502239	+	0.869904i	−0.999997	+	0.00258747i	$0.999176\pi$
$374$	−0.275094	−	0.476476i	−0.0142248	−	0.0246380i
$375$		0			0
$376$	−5.71450			−0.294703
$377$	−14.7128	−	25.4832i	−0.757745	−	1.31245i
$378$		0			0
$379$	30.9801			1.59134			0.795670	−	0.605731i	$-0.207119\pi$
$379$	30.9801			1.59134			0.795670	+	0.605731i	$0.207119\pi$
$380$	−11.6976	+	14.4221i	−0.600075	+	0.739839i
$381$		0			0
$382$	−19.4128			−0.993245
$383$	15.8901			0.811949			0.405974	−	0.913884i	$-0.366932\pi$
$383$	15.8901			0.811949			0.405974	+	0.913884i	$0.366932\pi$
$384$		0			0
$385$	0.736665	−	1.27594i	0.0375439	−	0.0650280i
$386$	12.3082	−	21.3185i	0.626472	−	1.08508i
$387$		0			0
$388$	5.70916			0.289839
$389$	−24.3812			−1.23618			−0.618089	−	0.786108i	$-0.712093\pi$
$389$	−24.3812			−1.23618			−0.618089	+	0.786108i	$0.712093\pi$
$390$		0			0
$391$	−6.91511	+	11.9773i	−0.349712	+	0.605719i
$392$	2.77062	−	4.79885i	0.139937	−	0.242378i
$393$		0			0
$394$	12.4275	−	21.5251i	0.626091	−	1.08442i
$395$	−30.2514	+	52.3970i	−1.52212	+	2.63638i
$396$		0			0
$397$	−17.1477	−	29.7008i	−0.860620	−	1.49064i	−0.871331	−	0.490695i	$-0.836743\pi$
$397$	−17.1477	−	29.7008i	−0.860620	−	1.49064i	0.0107109	−	0.999943i	$-0.496591\pi$
$398$	11.2163	+	19.4271i	0.562220	+	0.973793i
$399$		0			0
$400$	−6.57451	+	11.3874i	−0.328725	+	0.569369i
$401$	−33.1444			−1.65515			−0.827575	−	0.561354i	$-0.810280\pi$
$401$	−33.1444			−1.65515			−0.827575	+	0.561354i	$0.810280\pi$
$402$		0			0
$403$	−1.88682			−0.0939893
$404$	2.51682	+	4.35926i	0.125217	+	0.216881i
$405$		0			0
$406$	−9.90079			−0.491368
$407$	0.395590	+	0.685183i	0.0196087	+	0.0339632i
$408$		0			0
$409$	9.12011	+	15.7965i	0.450961	+	0.781087i	0.998446	−	0.0557286i	$-0.0177482\pi$
$409$	9.12011	+	15.7965i	0.450961	+	0.781087i	−0.547485	+	0.836815i	$0.684415\pi$
$410$	−19.0866	+	33.0590i	−0.942621	+	1.63267i
$411$		0			0
$412$	−3.37674			−0.166360
$413$	0.650128	+	1.12605i	0.0319907	+	0.0554095i
$414$		0			0
$415$	−2.59612	−	4.49661i	−0.127438	−	0.220730i
$416$	1.79480	−	3.10869i	0.0879976	−	0.152416i
$417$		0			0
$418$	0.446369	+	1.16557i	0.0218326	+	0.0570101i
$419$	−3.67826	+	6.37093i	−0.179695	+	0.311240i	−0.941776	−	0.336241i	$-0.890844\pi$
$419$	−3.67826	+	6.37093i	−0.179695	+	0.311240i	0.762081	+	0.647481i	$0.224178\pi$
$420$		0			0
$421$	15.1156	−	26.1810i	0.736690	−	1.27598i	−0.217288	−	0.976108i	$-0.569721\pi$
$421$	15.1156	−	26.1810i	0.736690	−	1.27598i	0.953978	−	0.299877i	$-0.0969456\pi$
$422$	−0.769841	+	1.33340i	−0.0374753	+	0.0649091i
$423$		0			0
$424$	3.77851	−	6.54457i	0.183501	−	0.317832i
$425$	12.6326	+	21.8804i	0.612773	+	1.06135i
$426$		0			0
$427$	1.65127	+	2.86008i	0.0799104	+	0.138409i
$428$	3.75118	+	6.49724i	0.181320	+	0.314056i
$429$		0			0
$430$	23.7077	+	41.0629i	1.14328	+	1.98023i
$431$	−4.90799	+	8.50089i	−0.236410	+	0.409473i	−0.959681	−	0.281090i	$-0.909304\pi$
$431$	−4.90799	+	8.50089i	−0.236410	+	0.409473i	0.723272	+	0.690563i	$0.242637\pi$
$432$		0			0
$433$	−7.33422	+	12.7032i	−0.352460	+	0.610479i	−0.986680	−	0.162674i	$-0.947988\pi$
$433$	−7.33422	+	12.7032i	−0.352460	+	0.610479i	0.634220	+	0.773153i	$0.281321\pi$
$434$	−0.317429	+	0.549804i	−0.0152371	+	0.0263914i
$435$		0			0
$436$	5.72124	−	9.90948i	0.273998	−	0.474578i
$437$	19.7637	−	24.3669i	0.945428	−	1.16563i
$438$		0			0
$439$	1.95116	−	3.37952i	0.0931240	−	0.161296i	−0.815700	−	0.578475i	$-0.803648\pi$
$439$	1.95116	−	3.37952i	0.0931240	−	0.161296i	0.908824	+	0.417179i	$0.136981\pi$
$440$	0.609926	+	1.05642i	0.0290771	+	0.0503629i
$441$		0			0
$442$	−3.44864	−	5.97322i	−0.164035	−	0.284117i
$443$	34.7906			1.65295			0.826475	−	0.562973i	$-0.190342\pi$
$443$	34.7906			1.65295			0.826475	+	0.562973i	$0.190342\pi$
$444$		0			0
$445$	−30.0203	+	51.9967i	−1.42310	+	2.46488i
$446$	−6.70340	−	11.6106i	−0.317415	−	0.549779i
$447$		0			0
$448$	−0.603898	−	1.04598i	−0.0285315	−	0.0494180i
$449$	−17.7485			−0.837604			−0.418802	−	0.908078i	$-0.637550\pi$
$449$	−17.7485			−0.837604			−0.418802	+	0.908078i	$0.637550\pi$
$450$		0			0
$451$	1.28287	+	2.22200i	0.0604080	+	0.104630i
$452$	1.16947			0.0550073
$453$		0			0
$454$	16.0524			0.753374
$455$	9.23500	−	15.9955i	0.432944	−	0.749880i
$456$		0			0
$457$	−1.07466	−	1.86137i	−0.0502706	−	0.0870712i	0.839795	−	0.542903i	$-0.182675\pi$
$457$	−1.07466	−	1.86137i	−0.0502706	−	0.0870712i	−0.890066	+	0.455832i	$0.849342\pi$
$458$	7.73445	+	13.3965i	0.361407	+	0.625976i
$459$		0			0
$460$	15.3319	−	26.5556i	0.714852	−	1.23816i
$461$	2.22471	−	3.85331i	0.103615	−	0.179466i	−0.809557	−	0.587042i	$-0.800292\pi$
$461$	2.22471	−	3.85331i	0.103615	−	0.179466i	0.913171	+	0.407576i	$0.133626\pi$
$462$		0			0
$463$	5.23009	−	9.05878i	0.243063	−	0.420997i	−0.718522	−	0.695504i	$-0.755181\pi$
$463$	5.23009	−	9.05878i	0.243063	−	0.420997i	0.961585	+	0.274507i	$0.0885145\pi$
$464$	4.09871	−	7.09917i	0.190278	−	0.329571i
$465$		0			0
$466$	3.75641			0.174012
$467$	19.7596			0.914365			0.457183	−	0.889373i	$-0.348859\pi$
$467$	19.7596			0.914365			0.457183	+	0.889373i	$0.348859\pi$
$468$		0			0
$469$	0.992302	−	1.71872i	0.0458203	−	0.0793630i
$470$	12.1724	−	21.0832i	0.561469	−	0.972494i
$471$		0			0
$472$	−1.07655			−0.0495524
$473$	3.18693			0.146535
$474$		0			0
$475$	−20.4978	−	53.5245i	−0.940503	−	2.45587i
$476$	−2.32073			−0.106370
$477$		0			0
$478$	6.74604	+	11.6845i	0.308557	+	0.534436i
$479$	−28.0075			−1.27969			−0.639847	−	0.768502i	$-0.721002\pi$
$479$	−28.0075			−1.27969			−0.639847	+	0.768502i	$0.721002\pi$
$480$		0			0
$481$	4.95921	+	8.58961i	0.226121	+	0.391652i
$482$	7.05617	−	12.2216i	0.321400	−	0.556680i
$483$		0			0
$484$	−10.9180			−0.496273
$485$	−12.1610	+	21.0635i	−0.552202	+	0.956443i
$486$		0			0
$487$	−6.42735			−0.291251			−0.145626	−	0.989340i	$-0.546519\pi$
$487$	−6.42735			−0.291251			−0.145626	+	0.989340i	$0.546519\pi$
$488$	−2.73435			−0.123778
$489$		0			0
$490$	11.8033	+	20.4439i	0.533218	+	0.923561i
$491$	−20.5891			−0.929174			−0.464587	−	0.885527i	$-0.653797\pi$
$491$	−20.5891			−0.929174			−0.464587	+	0.885527i	$0.653797\pi$
$492$		0			0
$493$	−7.87548	−	13.6407i	−0.354694	−	0.614348i
$494$	5.59579	+	14.6119i	0.251766	+	0.657421i
$495$		0			0
$496$	−0.262817	−	0.455213i	−0.0118008	−	0.0204397i
$497$	−0.279238	+	0.483655i	−0.0125255	+	0.0216949i
$498$		0			0
$499$	−3.30652			−0.148020			−0.0740101	−	0.997257i	$-0.523580\pi$
$499$	−3.30652			−0.148020			−0.0740101	+	0.997257i	$0.523580\pi$
$500$	−17.3581	−	30.0651i	−0.776277	−	1.34455i
$501$		0			0
$502$	−6.77858	−	11.7408i	−0.302543	−	0.524019i
$503$	−9.13489	+	15.8221i	−0.407304	+	0.705472i	−0.994587	−	0.103910i	$-0.966865\pi$
$503$	−9.13489	+	15.8221i	−0.407304	+	0.705472i	0.587282	+	0.809382i	$0.300198\pi$
$504$		0			0
$505$	−21.4441			−0.954252
$506$	−1.03050	−	1.78488i	−0.0458114	−	0.0793477i
$507$		0			0
$508$	−6.73236			−0.298700
$509$	18.3723	+	31.8217i	0.814337	+	1.41047i	0.909803	+	0.415041i	$0.136233\pi$
$509$	18.3723	+	31.8217i	0.814337	+	1.41047i	−0.0954658	+	0.995433i	$0.530434\pi$
$510$		0			0
$511$	4.48334	−	7.76536i	0.198331	−	0.343520i
$512$	1.00000			0.0441942
$513$		0			0
$514$	2.90089			0.127953
$515$	7.19275	−	12.4582i	0.316950	−	0.548974i
$516$		0			0
$517$	−0.818142	−	1.41706i	−0.0359819	−	0.0623224i
$518$	3.33725			0.146630
$519$		0			0
$520$	7.64617	+	13.2436i	0.335307	+	0.580768i
$521$	16.4950			0.722658			0.361329	−	0.932438i	$-0.382323\pi$
$521$	16.4950			0.722658			0.361329	+	0.932438i	$0.382323\pi$
$522$		0			0
$523$	16.6142	−	28.7767i	0.726489	−	1.25832i	−0.231869	−	0.972747i	$-0.574484\pi$
$523$	16.6142	−	28.7767i	0.726489	−	1.25832i	0.958358	−	0.285569i	$-0.0921824\pi$
$524$	0.863643	+	1.49587i	0.0377284	+	0.0653475i
$525$		0			0
$526$	−14.5330	−	25.1719i	−0.633668	−	1.09755i
$527$	−1.00998			−0.0439956
$528$		0			0
$529$	−14.4040	+	24.9485i	−0.626262	+	1.08472i
$530$	16.0971	+	27.8810i	0.699212	+	1.21107i
$531$		0			0
$532$	5.19919	+	0.827669i	0.225413	+	0.0358840i
$533$	16.0824	+	27.8555i	0.696604	+	1.20655i
$534$		0			0
$535$	−31.9613			−1.38181
$536$	0.821582	+	1.42302i	0.0354869	+	0.0614651i
$537$		0			0
$538$	−0.781934			−0.0337116
$539$	1.58667			0.0683427
$540$		0			0
$541$	−2.24341	+	3.88571i	−0.0964519	+	0.167060i	−0.910214	−	0.414139i	$-0.864083\pi$
$541$	−2.24341	+	3.88571i	−0.0964519	+	0.167060i	0.813762	+	0.581199i	$0.197416\pi$
$542$	4.19382			0.180140
$543$		0			0
$544$	0.960728	−	1.66403i	0.0411909	−	0.0713447i
$545$	24.3734	+	42.2160i	1.04404	+	1.80834i
$546$		0			0
$547$	8.66273			0.370392			0.185196	−	0.982702i	$-0.440708\pi$
$547$	8.66273			0.370392			0.185196	+	0.982702i	$0.440708\pi$
$548$	−6.37159	−	11.0359i	−0.272181	−	0.471431i
$549$		0			0
$550$	−3.76507			−0.160543
$551$	12.7788	+	33.3685i	0.544396	+	1.42155i
$552$		0			0
$553$	17.1531			0.729424
$554$	−0.799832			−0.0339816
$555$		0			0
$556$	−0.347220	+	0.601402i	−0.0147254	+	0.0255051i
$557$	−2.38412	+	4.12942i	−0.101019	+	0.174969i	−0.912105	−	0.409958i	$-0.865543\pi$
$557$	−2.38412	+	4.12942i	−0.101019	+	0.174969i	0.811086	+	0.584927i	$0.198877\pi$
$558$		0			0
$559$	39.9521			1.68979
$560$	5.14541			0.217433
$561$		0			0
$562$	−5.46666	+	9.46854i	−0.230597	+	0.399406i
$563$	7.53129	−	13.0446i	0.317406	−	0.549763i	−0.662540	−	0.749026i	$-0.730522\pi$
$563$	7.53129	−	13.0446i	0.317406	−	0.549763i	0.979946	+	0.199263i	$0.0638549\pi$
$564$		0			0
$565$	−2.49107	+	4.31466i	−0.104800	+	0.181519i
$566$	−9.94152	+	17.2192i	−0.417873	+	0.723778i
$567$		0			0
$568$	−0.231197	−	0.400444i	−0.00970079	−	0.0168023i
$569$	2.38625	+	4.13310i	0.100037	+	0.173269i	0.911700	−	0.410857i	$-0.134771\pi$
$569$	2.38625	+	4.13310i	0.100037	+	0.173269i	−0.811663	+	0.584126i	$0.801437\pi$
$570$		0			0
$571$	−10.0266	+	17.3665i	−0.419599	+	0.726766i	−0.995899	−	0.0904717i	$-0.971163\pi$
$571$	−10.0266	+	17.3665i	−0.419599	+	0.726766i	0.576300	+	0.817238i	$0.304496\pi$
$572$	1.02784			0.0429763
$573$		0			0
$574$	10.8225			0.451720
$575$	47.3219	+	81.9639i	1.97346	+	3.41813i
$576$		0			0
$577$	35.1776			1.46446			0.732232	−	0.681056i	$-0.238479\pi$
$577$	35.1776			1.46446			0.732232	+	0.681056i	$0.238479\pi$
$578$	6.65400	+	11.5251i	0.276770	+	0.479380i
$579$		0			0
$580$	17.4612	+	30.2436i	0.725036	+	1.25580i
$581$	−0.736023	+	1.27483i	−0.0305354	+	0.0528888i
$582$		0			0
$583$	2.16387			0.0896183
$584$	3.71200	+	6.42937i	0.153604	+	0.266049i
$585$		0			0
$586$	1.48719	+	2.57588i	0.0614351	+	0.106409i
$587$	16.3700	−	28.3536i	0.675661	−	1.17028i	−0.300614	−	0.953746i	$-0.597191\pi$
$587$	16.3700	−	28.3536i	0.675661	−	1.17028i	0.976275	−	0.216534i	$-0.0694752\pi$
$588$		0			0
$589$	2.26270	+	0.360203i	0.0932327	+	0.0148419i
$590$	2.29315	−	3.97185i	0.0944074	−	0.163518i
$591$		0			0
$592$	−1.38155	+	2.39291i	−0.0567812	+	0.0983479i
$593$	24.1956	−	41.9081i	0.993595	−	1.72096i	0.398939	−	0.916977i	$-0.369379\pi$
$593$	24.1956	−	41.9081i	0.993595	−	1.72096i	0.594656	−	0.803980i	$-0.297288\pi$
$594$		0			0
$595$	4.94334	−	8.56211i	0.202657	−	0.351012i
$596$	0.188660	+	0.326769i	0.00772783	+	0.0133850i
$597$		0			0
$598$	−12.9186	−	22.3757i	−0.528281	−	0.915010i
$599$	1.30238	+	2.25579i	0.0532138	+	0.0921689i	0.891405	−	0.453207i	$-0.149720\pi$
$599$	1.30238	+	2.25579i	0.0532138	+	0.0921689i	−0.838191	+	0.545376i	$0.816387\pi$
$600$		0			0
$601$	−7.84204	−	13.5828i	−0.319883	−	0.554054i	0.660580	−	0.750756i	$-0.270310\pi$
$601$	−7.84204	−	13.5828i	−0.319883	−	0.554054i	−0.980463	+	0.196701i	$0.936977\pi$
$602$	6.72133	−	11.6417i	0.273941	−	0.474480i
$603$		0			0
$604$	−9.79347	+	16.9628i	−0.398491	+	0.690206i
$605$	23.2563	−	40.2810i	0.945502	−	1.63766i
$606$		0			0
$607$	−13.8043	+	23.9098i	−0.560300	+	0.970468i	0.437170	+	0.899379i	$0.355981\pi$
$607$	−13.8043	+	23.9098i	−0.560300	+	0.970468i	−0.997470	+	0.0710889i	$0.977353\pi$
$608$	−2.74581	+	3.38534i	−0.111357	+	0.137294i
$609$		0			0
$610$	5.82439	−	10.0881i	0.235823	−	0.408457i
$611$	−10.2564	−	17.7646i	−0.414930	−	0.718680i
$612$		0			0
$613$	9.09717	+	15.7568i	0.367431	+	0.636410i	0.989163	−	0.146821i	$-0.0469040\pi$
$613$	9.09717	+	15.7568i	0.367431	+	0.636410i	−0.621732	+	0.783230i	$0.713571\pi$
$614$	0.0157394			0.000635192
$615$		0			0
$616$	0.172919	−	0.299505i	0.00696712	−	0.0120674i
$617$	15.5951	+	27.0115i	0.627835	+	1.08744i	0.987985	+	0.154547i	$0.0493919\pi$
$617$	15.5951	+	27.0115i	0.627835	+	1.08744i	−0.360151	+	0.932894i	$0.617275\pi$
$618$		0			0
$619$	7.90370	+	13.6896i	0.317676	+	0.550232i	0.980003	−	0.198984i	$-0.0637641\pi$
$619$	7.90370	+	13.6896i	0.317676	+	0.550232i	−0.662326	+	0.749215i	$0.730431\pi$
$620$	2.23929			0.0899320
$621$		0			0
$622$	0.925134	+	1.60238i	0.0370945	+	0.0642496i
$623$	17.0221			0.681974
$624$		0			0
$625$	82.1516			3.28606
$626$	2.26698	−	3.92652i	0.0906067	−	0.156935i
$627$		0			0
$628$	7.59065	+	13.1474i	0.302900	+	0.524638i
$629$	2.65458	+	4.59787i	0.105845	+	0.183329i
$630$		0			0
$631$	−18.9848	+	32.8827i	−0.755774	+	1.30904i	0.189214	+	0.981936i	$0.439406\pi$
$631$	−18.9848	+	32.8827i	−0.755774	+	1.30904i	−0.944989	+	0.327103i	$0.893927\pi$
$632$	−7.10100	+	12.2993i	−0.282463	+	0.489240i
$633$		0			0
$634$	5.67565	−	9.83052i	0.225409	−	0.390420i
$635$	14.3405	−	24.8384i	0.569085	−	0.985683i
$636$		0			0
$637$	19.8909			0.788104
$638$	2.34724			0.0929280
$639$		0			0
$640$	−2.13008	+	3.68941i	−0.0841989	+	0.145837i
$641$	−7.12270	+	12.3369i	−0.281330	+	0.487277i	−0.971712	−	0.236167i	$-0.924109\pi$
$641$	−7.12270	+	12.3369i	−0.281330	+	0.487277i	0.690383	+	0.723444i	$0.257442\pi$
$642$		0			0
$643$	−18.5098			−0.729955			−0.364978	−	0.931016i	$-0.618923\pi$
$643$	−18.5098			−0.729955			−0.364978	+	0.931016i	$0.618923\pi$
$644$	−8.69344			−0.342570
$645$		0			0
$646$	2.99533	+	7.82150i	0.117850	+	0.307733i
$647$	−25.4450			−1.00035			−0.500173	−	0.865926i	$-0.666730\pi$
$647$	−25.4450			−1.00035			−0.500173	+	0.865926i	$0.666730\pi$
$648$		0			0
$649$	−0.154129	−	0.266960i	−0.00605011	−	0.0104791i
$650$	−47.1998			−1.85133
$651$		0			0
$652$	−0.143958	−	0.249342i	−0.00563782	−	0.00976499i
$653$	18.3350	−	31.7571i	0.717503	−	1.24275i	−0.244483	−	0.969654i	$-0.578618\pi$
$653$	18.3350	−	31.7571i	0.717503	−	1.24275i	0.961986	−	0.273098i	$-0.0880483\pi$
$654$		0			0
$655$	−7.35852			−0.287521
$656$	−4.48025	+	7.76002i	−0.174924	+	0.302978i
$657$		0			0
$658$	−6.90195			−0.269066
$659$	−17.7981			−0.693316			−0.346658	−	0.937992i	$-0.612684\pi$
$659$	−17.7981			−0.693316			−0.346658	+	0.937992i	$0.612684\pi$
$660$		0			0
$661$	10.9936	+	19.0414i	0.427600	+	0.740625i	0.996659	−	0.0816716i	$-0.0260259\pi$
$661$	10.9936	+	19.0414i	0.427600	+	0.740625i	−0.569059	+	0.822296i	$0.692693\pi$
$662$	−13.6451			−0.530330
$663$		0			0
$664$	−0.609393	−	1.05550i	−0.0236491	−	0.0409614i
$665$	−14.1283	+	17.4190i	−0.547873	+	0.675478i
$666$		0			0
$667$	−29.5016	−	51.0982i	−1.14231	−	1.97853i
$668$	−10.5972	+	18.3549i	−0.410017	+	0.710171i
$669$		0			0
$670$	−7.00015			−0.270439
$671$	−0.391475	−	0.678055i	−0.0151127	−	0.0261760i
$672$		0			0
$673$	−5.17032	−	8.95525i	−0.199301	−	0.345200i	0.749001	−	0.662569i	$-0.230534\pi$
$673$	−5.17032	−	8.95525i	−0.199301	−	0.345200i	−0.948302	+	0.317369i	$0.897201\pi$
$674$	−4.83981	+	8.38279i	−0.186422	+	0.322893i
$675$		0			0
$676$	−0.114701			−0.00441157
$677$	−19.4119	−	33.6224i	−0.746060	−	1.29221i	−0.949698	−	0.313167i	$-0.898610\pi$
$677$	−19.4119	−	33.6224i	−0.746060	−	1.29221i	0.203638	−	0.979046i	$-0.434723\pi$
$678$		0			0
$679$	6.89550			0.264625
$680$	4.09286	+	7.08904i	0.156954	+	0.271852i
$681$		0			0
$682$	0.0752548	−	0.130345i	0.00288165	−	0.00499117i
$683$	−27.2301			−1.04193			−0.520966	−	0.853578i	$-0.674428\pi$
$683$	−27.2301			−1.04193			−0.520966	+	0.853578i	$0.674428\pi$
$684$		0			0
$685$	54.2881			2.07424
$686$	7.57362	−	13.1179i	0.289162	−	0.500844i
$687$		0			0
$688$	5.56496	+	9.63879i	0.212162	+	0.367476i
$689$	27.1268			1.03345
$690$		0			0
$691$	12.4717	+	21.6017i	0.474447	+	0.821766i	0.999572	−	0.0292590i	$-0.00931477\pi$
$691$	12.4717	+	21.6017i	0.474447	+	0.821766i	−0.525125	+	0.851025i	$0.675981\pi$
$692$	−10.8949			−0.414162
$693$		0			0
$694$	14.0748	−	24.3783i	0.534274	−	0.925390i
$695$	−1.47921	−	2.56207i	−0.0561098	−	0.0971850i
$696$		0			0
$697$	8.60861	+	14.9105i	0.326074	+	0.564777i
$698$	5.62256			0.212817
$699$		0			0
$700$	−7.94066	+	13.7536i	−0.300129	+	0.519838i
$701$	−8.63762	−	14.9608i	−0.326239	−	0.565062i	0.655524	−	0.755175i	$-0.272448\pi$
$701$	−8.63762	−	14.9608i	−0.326239	−	0.565062i	−0.981762	+	0.190113i	$0.939115\pi$
$702$		0			0
$703$	−4.30734	−	11.2475i	−0.162454	−	0.424207i
$704$	0.143169	+	0.247977i	0.00539590	+	0.00934597i
$705$		0			0
$706$	20.7544			0.781101
$707$	3.03980	+	5.26510i	0.114324	+	0.198014i
$708$		0			0
$709$	−45.3938			−1.70480			−0.852400	−	0.522891i	$-0.824853\pi$
$709$	−45.3938			−1.70480			−0.852400	+	0.522891i	$0.824853\pi$
$710$	1.96987			0.0739280
$711$		0			0
$712$	−7.04675	+	12.2053i	−0.264088	+	0.457414i
$713$	−3.78340			−0.141689
$714$		0			0
$715$	−2.18939	+	3.79214i	−0.0818787	+	0.141818i
$716$	10.3467	+	17.9210i	0.386675	+	0.669741i
$717$		0			0
$718$	−11.1976			−0.417892
$719$	−10.7877	−	18.6848i	−0.402313	−	0.696827i	0.591691	−	0.806165i	$-0.298460\pi$
$719$	−10.7877	−	18.6848i	−0.402313	−	0.696827i	−0.994005	+	0.109337i	$0.965127\pi$
$720$		0			0
$721$	−4.07842			−0.151888
$722$	−3.92104	−	18.5910i	−0.145926	−	0.691886i
$723$		0			0
$724$	17.6106			0.654493
$725$	−107.788			−4.00314
$726$		0			0
$727$	−4.28045	+	7.41395i	−0.158753	+	0.274968i	−0.934419	−	0.356175i	$-0.884081\pi$
$727$	−4.28045	+	7.41395i	−0.158753	+	0.274968i	0.775666	+	0.631143i	$0.217414\pi$
$728$	2.16776	−	3.75467i	0.0803424	−	0.139157i
$729$		0			0
$730$	−31.6275			−1.17059
$731$	21.3857			0.790977
$732$		0			0
$733$	10.0403	−	17.3903i	0.370847	−	0.642325i	−0.618849	−	0.785510i	$-0.712401\pi$
$733$	10.0403	−	17.3903i	0.370847	−	0.642325i	0.989696	+	0.143185i	$0.0457342\pi$
$734$	9.37441	−	16.2370i	0.346016	−	0.599317i
$735$		0			0
$736$	3.59889	−	6.23346i	0.132657	−	0.229768i
$737$	−0.235251	+	0.407466i	−0.00866557	+	0.0150092i
$738$		0			0
$739$	5.04076	+	8.73086i	0.185427	+	0.321170i	0.943720	−	0.330744i	$-0.107300\pi$
$739$	5.04076	+	8.73086i	0.185427	+	0.321170i	−0.758293	+	0.651914i	$0.773966\pi$
$740$	−5.88562	−	10.1942i	−0.216360	−	0.374746i
$741$		0			0
$742$	4.56367	−	7.90450i	0.167537	−	0.290183i
$743$	−0.155941			−0.00572093			−0.00286047	−	0.999996i	$-0.500911\pi$
$743$	−0.155941			−0.00572093			−0.00286047	+	0.999996i	$0.500911\pi$
$744$		0			0
$745$	−1.60745			−0.0588924
$746$	−9.69985	−	16.8006i	−0.355137	−	0.615115i
$747$		0			0
$748$	0.550188			0.0201169
$749$	4.53066	+	7.84733i	0.165547	+	0.286735i
$750$		0			0
$751$	9.09592	+	15.7546i	0.331915	+	0.574893i	0.982887	−	0.184208i	$-0.0589720\pi$
$751$	9.09592	+	15.7546i	0.331915	+	0.574893i	−0.650973	+	0.759101i	$0.725639\pi$
$752$	2.85725	−	4.94891i	0.104193	−	0.180468i
$753$		0			0
$754$	29.4255			1.07161
$755$	−41.7218	−	72.2643i	−1.51841	−	2.62997i
$756$		0			0
$757$	−0.780003	−	1.35100i	−0.0283497	−	0.0491031i	0.851502	−	0.524351i	$-0.175692\pi$
$757$	−0.780003	−	1.35100i	−0.0283497	−	0.0491031i	−0.879852	+	0.475247i	$0.842359\pi$
$758$	−15.4900	+	26.8295i	−0.562623	+	0.974492i
$759$		0			0
$760$	−6.64111	−	17.3415i	−0.240898	−	0.629042i
$761$	−24.8072	+	42.9673i	−0.899260	+	1.55756i	−0.0708172	+	0.997489i	$0.522561\pi$
$761$	−24.8072	+	42.9673i	−0.899260	+	1.55756i	−0.828442	+	0.560074i	$0.810773\pi$
$762$		0			0
$763$	6.91009	−	11.9686i	0.250162	−	0.433293i
$764$	9.70640	−	16.8120i	0.351165	−	0.608236i
$765$		0			0
$766$	−7.94507	+	13.7613i	−0.287067	+	0.497215i
$767$	−1.93220	−	3.34667i	−0.0697678	−	0.120841i
$768$		0			0
$769$	−4.43385	−	7.67965i	−0.159889	−	0.276935i	0.774940	−	0.632035i	$-0.217780\pi$
$769$	−4.43385	−	7.67965i	−0.159889	−	0.276935i	−0.934828	+	0.355100i	$0.884447\pi$
$770$	0.736665	+	1.27594i	0.0265476	+	0.0459817i
$771$		0			0
$772$	12.3082	+	21.3185i	0.442983	+	0.767269i
$773$	5.10630	−	8.84436i	0.183661	−	0.318110i	−0.759464	−	0.650550i	$-0.774539\pi$
$773$	5.10630	−	8.84436i	0.183661	−	0.318110i	0.943124	+	0.332440i	$0.107872\pi$
$774$		0			0
$775$	−3.45579	+	5.98560i	−0.124136	+	0.215009i
$776$	−2.85458	+	4.94428i	−0.102474	+	0.177489i
$777$		0			0
$778$	12.1906	−	21.1148i	0.437055	−	0.757001i
$779$	−13.9684	−	36.4747i	−0.500469	−	1.30684i
$780$		0			0
$781$	0.0662006	−	0.114663i	0.00236884	−	0.00410295i
$782$	−6.91511	−	11.9773i	−0.247284	−	0.428308i
$783$		0			0
$784$	2.77062	+	4.79885i	0.0989505	+	0.171387i
$785$	−64.6749			−2.30835
$786$		0			0
$787$	0.789589	−	1.36761i	0.0281458	−	0.0487500i	−0.851609	−	0.524177i	$-0.824373\pi$
$787$	0.789589	−	1.36761i	0.0281458	−	0.0487500i	0.879755	+	0.475427i	$0.157706\pi$
$788$	12.4275	+	21.5251i	0.442713	+	0.766801i
$789$		0			0
$790$	−30.2514	−	52.3970i	−1.07630	−	1.86420i
$791$	1.41248			0.0502221
$792$		0			0
$793$	−4.90762	−	8.50026i	−0.174275	−	0.301853i
$794$	34.2955			1.21710
$795$		0			0
$796$	−22.4325			−0.795099
$797$	8.77290	−	15.1951i	0.310752	−	0.538238i	−0.667773	−	0.744365i	$-0.732752\pi$
$797$	8.77290	−	15.1951i	0.310752	−	0.538238i	0.978525	+	0.206126i	$0.0660858\pi$
$798$		0			0
$799$	−5.49008	−	9.50911i	−0.194225	−	0.336408i
$800$	−6.57451	−	11.3874i	−0.232444	−	0.402605i
$801$		0			0
$802$	16.5722	−	28.7039i	0.585184	−	1.01357i
$803$	−1.06289	+	1.84098i	−0.0375086	+	0.0649667i
$804$		0			0
$805$	18.5178	−	32.0737i	0.652665	−	1.13045i
$806$	0.943411	−	1.63404i	0.0332302	−	0.0575565i
$807$		0			0
$808$	−5.03364			−0.177083
$809$	28.1652			0.990236			0.495118	−	0.868826i	$-0.335125\pi$
$809$	28.1652			0.990236			0.495118	+	0.868826i	$0.335125\pi$
$810$		0			0
$811$	−7.68352	+	13.3082i	−0.269805	+	0.467316i	−0.968811	−	0.247800i	$-0.920293\pi$
$811$	−7.68352	+	13.3082i	−0.269805	+	0.467316i	0.699006	+	0.715115i	$0.253626\pi$
$812$	4.95040	−	8.57434i	0.173725	−	0.300900i
$813$		0			0
$814$	−0.791181			−0.0277309
$815$	1.22657			0.0429648
$816$		0			0
$817$	−47.9109	−	7.62703i	−1.67619	−	0.266836i
$818$	−18.2402			−0.637755
$819$		0			0
$820$	−19.0866	−	33.0590i	−0.666534	−	1.15447i
$821$	30.6779			1.07067			0.535334	−	0.844641i	$-0.320186\pi$
$821$	30.6779			1.07067			0.535334	+	0.844641i	$0.320186\pi$
$822$		0			0
$823$	−6.37657	−	11.0445i	−0.222273	−	0.384989i	0.733225	−	0.679987i	$-0.238014\pi$
$823$	−6.37657	−	11.0445i	−0.222273	−	0.384989i	−0.955498	+	0.294998i	$0.904681\pi$
$824$	1.68837	−	2.92435i	0.0588172	−	0.101874i
$825$		0			0
$826$	−1.30026			−0.0452417
$827$	26.6773	−	46.2064i	0.927660	−	1.60675i	0.140433	−	0.990090i	$-0.455150\pi$
$827$	26.6773	−	46.2064i	0.927660	−	1.60675i	0.787227	−	0.616664i	$-0.211516\pi$
$828$		0			0
$829$	15.8339			0.549933			0.274966	−	0.961454i	$-0.411333\pi$
$829$	15.8339			0.549933			0.274966	+	0.961454i	$0.411333\pi$
$830$	5.19223			0.180225
$831$		0			0
$832$	1.79480	+	3.10869i	0.0622237	+	0.107775i
$833$	10.6472			0.368905
$834$		0			0
$835$	−45.1458	−	78.1948i	−1.56233	−	2.70604i
$836$	−1.23260	−	0.196220i	−0.0426304	−	0.00678641i
$837$		0			0
$838$	−3.67826	−	6.37093i	−0.127063	−	0.220080i
$839$	−18.9820	+	32.8777i	−0.655331	+	1.13507i	0.326480	+	0.945204i	$0.394137\pi$
$839$	−18.9820	+	32.8777i	−0.655331	+	1.13507i	−0.981811	+	0.189862i	$0.939196\pi$
$840$		0			0
$841$	38.1976			1.31716
$842$	15.1156	+	26.1810i	0.520918	+	0.902257i
$843$		0			0
$844$	−0.769841	−	1.33340i	−0.0264990	−	0.0458976i
$845$	0.244323	−	0.423179i	0.00840495	−	0.0145578i
$846$		0			0
$847$	−13.1867			−0.453101
$848$	3.77851	+	6.54457i	0.129755	+	0.224741i
$849$		0			0
$850$	−25.2653			−0.866591
$851$	9.94406	+	17.2236i	0.340878	+	0.590418i
$852$		0			0
$853$	1.83687	−	3.18155i	0.0628931	−	0.108934i	−0.832864	−	0.553477i	$-0.813301\pi$
$853$	1.83687	−	3.18155i	0.0628931	−	0.108934i	0.895757	+	0.444543i	$0.146634\pi$
$854$	−3.30253			−0.113010
$855$		0			0
$856$	−7.50236			−0.256426
$857$	4.23582	−	7.33666i	0.144693	−	0.250615i	−0.784565	−	0.620046i	$-0.787114\pi$
$857$	4.23582	−	7.33666i	0.144693	−	0.250615i	0.929258	+	0.369431i	$0.120447\pi$
$858$		0			0
$859$	15.1361	+	26.2164i	0.516436	+	0.894493i	0.999818	+	0.0190833i	$0.00607476\pi$
$859$	15.1361	+	26.2164i	0.516436	+	0.894493i	−0.483382	+	0.875409i	$0.660592\pi$
$860$	−47.4153			−1.61685
$861$		0			0
$862$	−4.90799	−	8.50089i	−0.167167	−	0.289541i
$863$	9.96299			0.339144			0.169572	−	0.985518i	$-0.445761\pi$
$863$	9.96299			0.339144			0.169572	+	0.985518i	$0.445761\pi$
$864$		0			0
$865$	23.2071	−	40.1958i	0.789064	−	1.36670i
$866$	−7.33422	−	12.7032i	−0.249227	−	0.431674i
$867$		0			0
$868$	−0.317429	−	0.549804i	−0.0107743	−	0.0186616i
$869$	−4.06658			−0.137949
$870$		0			0
$871$	−2.94916	+	5.10809i	−0.0999284	+	0.173081i
$872$	5.72124	+	9.90948i	0.193746	+	0.335577i
$873$		0			0
$874$	11.2205	+	29.2994i	0.379539	+	0.991066i
$875$	−20.9650	−	36.3125i	−0.708747	−	1.22759i
$876$		0			0
$877$	−20.5242			−0.693053			−0.346526	−	0.938040i	$-0.612639\pi$
$877$	−20.5242			−0.693053			−0.346526	+	0.938040i	$0.612639\pi$
$878$	1.95116	+	3.37952i	0.0658486	+	0.114053i
$879$		0			0
$880$	−1.21985			−0.0411212
$881$	45.7636			1.54182			0.770908	−	0.636946i	$-0.219803\pi$
$881$	45.7636			1.54182			0.770908	+	0.636946i	$0.219803\pi$
$882$		0			0
$883$	−4.14516	+	7.17962i	−0.139496	+	0.241613i	−0.927306	−	0.374305i	$-0.877881\pi$
$883$	−4.14516	+	7.17962i	−0.139496	+	0.241613i	0.787810	+	0.615918i	$0.211215\pi$
$884$	6.89728			0.231981
$885$		0			0
$886$	−17.3953	+	30.1295i	−0.584406	+	1.01222i
$887$	11.4392	+	19.8133i	0.384091	+	0.665265i	0.991643	−	0.129015i	$-0.0411816\pi$
$887$	11.4392	+	19.8133i	0.384091	+	0.665265i	−0.607552	+	0.794280i	$0.707848\pi$
$888$		0			0
$889$	−8.13131			−0.272715
$890$	−30.0203	−	51.9967i	−1.00628	−	1.74293i
$891$		0			0
$892$	13.4068			0.448893
$893$	8.90825	+	23.2615i	0.298103	+	0.778417i
$894$		0			0
$895$	−88.1575			−2.94678
$896$	1.20780			0.0403496
$897$		0			0
$898$	8.87426	−	15.3707i	0.296138	−	0.512926i
$899$	2.15442	−	3.73157i	0.0718539	−	0.124455i
$900$		0			0
$901$	14.5205			0.483747
$902$	−2.56574			−0.0854298
$903$		0			0
$904$	−0.584736	+	1.01279i	−0.0194480	+	0.0336850i
$905$	−37.5121	+	64.9728i	−1.24694	+	2.15977i
$906$		0			0
$907$	7.66952	−	13.2840i	0.254662	−	0.441088i	−0.710142	−	0.704059i	$-0.751369\pi$
$907$	7.66952	−	13.2840i	0.254662	−	0.441088i	0.964804	+	0.262971i	$0.0847024\pi$
$908$	−8.02618	+	13.9017i	−0.266358	+	0.461346i
$909$		0			0
$910$	9.23500	+	15.9955i	0.306137	+	0.530246i
$911$	−8.38917	−	14.5305i	−0.277946	−	0.481416i	0.692928	−	0.721006i	$-0.256320\pi$
$911$	−8.38917	−	14.5305i	−0.277946	−	0.481416i	−0.970874	+	0.239591i	$0.922987\pi$
$912$		0			0
$913$	0.174493	−	0.302231i	0.00577488	−	0.0100024i
$914$	2.14933			0.0710934
$915$		0			0
$916$	−15.4689			−0.511107
$917$	1.04310	+	1.80671i	0.0344463	+	0.0596628i
$918$		0			0
$919$	16.8948			0.557308			0.278654	−	0.960391i	$-0.410112\pi$
$919$	16.8948			0.557308			0.278654	+	0.960391i	$0.410112\pi$
$920$	15.3319	+	26.5556i	0.505477	+	0.875511i
$921$		0			0
$922$	2.22471	+	3.85331i	0.0732668	+	0.126902i
$923$	0.829905	−	1.43744i	0.0273167	−	0.0473139i
$924$		0			0
$925$	36.3319			1.19459
$926$	5.23009	+	9.05878i	0.171871	+	0.297690i
$927$		0			0
$928$	4.09871	+	7.09917i	0.134547	+	0.233042i
$929$	4.42885	−	7.67099i	0.145306	−	0.251677i	−0.784181	−	0.620532i	$-0.786917\pi$
$929$	4.42885	−	7.67099i	0.145306	−	0.251677i	0.929487	+	0.368855i	$0.120250\pi$
$930$		0			0
$931$	−23.8533	−	3.79725i	−0.781761	−	0.124450i
$932$	−1.87821	+	3.25315i	−0.0615227	+	0.106560i
$933$		0			0
$934$	−9.87980	+	17.1123i	−0.323277	+	0.559932i
$935$	−1.17195	+	2.02987i	−0.0383267	+	0.0663838i
$936$		0			0
$937$	12.4430	−	21.5519i	0.406495	−	0.704070i	−0.587999	−	0.808861i	$-0.700084\pi$
$937$	12.4430	−	21.5519i	0.406495	−	0.704070i	0.994494	+	0.104792i	$0.0334176\pi$
$938$	0.992302	+	1.71872i	0.0323998	+	0.0561181i
$939$		0			0
$940$	12.1724	+	21.0832i	0.397019	+	0.687657i
$941$	−4.58982	−	7.94980i	−0.149624	−	0.259156i	0.781465	−	0.623950i	$-0.214473\pi$
$941$	−4.58982	−	7.94980i	−0.149624	−	0.259156i	−0.931088	+	0.364793i	$0.881140\pi$
$942$		0			0
$943$	32.2479	+	55.8549i	1.05014	+	1.81889i
$944$	0.538276	−	0.932322i	0.0175194	−	0.0303445i
$945$		0			0
$946$	−1.59346	+	2.75996i	−0.0518080	+	0.0897341i
$947$	0.671762	−	1.16353i	0.0218293	−	0.0378095i	−0.854904	−	0.518786i	$-0.826384\pi$
$947$	0.671762	−	1.16353i	0.0218293	−	0.0378095i	0.876734	+	0.480976i	$0.159718\pi$
$948$		0			0
$949$	−13.3246	+	23.0789i	−0.432536	+	0.749174i
$950$	56.6025	+	9.01066i	1.83643	+	0.292344i
$951$		0			0
$952$	1.16036	−	2.00981i	0.0376076	−	0.0651382i
$953$	−11.1258	−	19.2704i	−0.360400	−	0.624231i	0.627627	−	0.778514i	$-0.284026\pi$
$953$	−11.1258	−	19.2704i	−0.360400	−	0.624231i	−0.988027	+	0.154284i	$0.950693\pi$
$954$		0			0
$955$	41.3509	+	71.6218i	1.33808	+	2.31763i
$956$	−13.4921			−0.436365
$957$		0			0
$958$	14.0037	−	24.2552i	0.452440	−	0.783650i
$959$	−7.69558	−	13.3291i	−0.248503	−	0.430420i
$960$		0			0
$961$	15.3619	+	26.6075i	0.495544	+	0.858307i
$962$	−9.91842			−0.319783
$963$		0			0
$964$	7.05617	+	12.2216i	0.227264	+	0.393632i
$965$	−104.870			−3.37589
$966$		0			0
$967$	−37.2224			−1.19699			−0.598496	−	0.801126i	$-0.704235\pi$
$967$	−37.2224			−1.19699			−0.598496	+	0.801126i	$0.704235\pi$
$968$	5.45901	−	9.45527i	0.175459	−	0.303904i
$969$		0			0
$970$	−12.1610	−	21.0635i	−0.390466	−	0.676307i
$971$	−5.40935	−	9.36926i	−0.173594	−	0.300674i	0.766080	−	0.642746i	$-0.222205\pi$
$971$	−5.40935	−	9.36926i	−0.173594	−	0.300674i	−0.939674	+	0.342072i	$0.888871\pi$
$972$		0			0
$973$	−0.419371	+	0.726371i	−0.0134444	+	0.0232864i
$974$	3.21368	−	5.56625i	0.102973	−	0.178354i
$975$		0			0
$976$	1.36717	−	2.36802i	0.0437622	−	0.0757984i
$977$	21.9991	−	38.1036i	0.703815	−	1.21904i	−0.263303	−	0.964713i	$-0.584812\pi$
$977$	21.9991	−	38.1036i	0.703815	−	1.21904i	0.967118	−	0.254330i	$-0.0818549\pi$
$978$		0			0
$979$	−4.03552			−0.128976
$980$	−23.6066			−0.754084
$981$		0			0
$982$	10.2946	−	17.8307i	0.328513	−	0.569001i
$983$	−5.83674	+	10.1095i	−0.186163	+	0.322444i	−0.943968	−	0.330038i	$-0.892939\pi$
$983$	−5.83674	+	10.1095i	−0.186163	+	0.322444i	0.757805	+	0.652481i	$0.226272\pi$
$984$		0			0
$985$	−105.887			−3.37383
$986$	15.7510			0.501613
$987$		0			0
$988$	−15.4522	−	2.45986i	−0.491599	−	0.0782586i
$989$	80.1107			2.54737
$990$		0			0
$991$	−19.3542	−	33.5224i	−0.614806	−	1.06487i	−0.990419	−	0.138098i	$-0.955901\pi$
$991$	−19.3542	−	33.5224i	−0.614806	−	1.06487i	0.375613	−	0.926777i	$-0.377432\pi$
$992$	0.525634			0.0166889
$993$		0			0
$994$	−0.279238	−	0.483655i	−0.00885689	−	0.0153406i
$995$	47.7831	−	82.7628i	1.51483	−	2.62376i
$996$		0			0
$997$	−47.8051			−1.51400			−0.757002	−	0.653413i	$-0.773337\pi$
$997$	−47.8051			−1.51400			−0.757002	+	0.653413i	$0.773337\pi$
$998$	1.65326	−	2.86353i	0.0523331	−	0.0906435i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1026.2.h.g.577.9		18
3.2	odd	2		342.2.h.g.121.7	yes	18
9.2	odd	6		342.2.f.g.7.1	✓	18
9.7	even	3		1026.2.f.g.235.1		18
19.11	even	3		1026.2.f.g.847.1		18
57.11	odd	6		342.2.f.g.49.1	yes	18
171.11	odd	6		342.2.h.g.277.7	yes	18
171.106	even	3	inner	1026.2.h.g.505.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.1	✓	18	9.2	odd	6
342.2.f.g.49.1	yes	18	57.11	odd	6
342.2.h.g.121.7	yes	18	3.2	odd	2
342.2.h.g.277.7	yes	18	171.11	odd	6
1026.2.f.g.235.1		18	9.7	even	3
1026.2.f.g.847.1		18	19.11	even	3
1026.2.h.g.505.9		18	171.106	even	3	inner
1026.2.h.g.577.9		18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1026 = 2 \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1026.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +4.26017 q^{5} +(-0.603898 - 1.04598i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +4.26017 q^{5} +(-0.603898 - 1.04598i) q^{7} +1.00000 q^{8} +(-2.13008 + 3.68941i) q^{10} +(0.143169 + 0.247977i) q^{11} +(1.79480 + 3.10869i) q^{13} +1.20780 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.960728 + 1.66403i) q^{17} +(-1.55888 - 4.07061i) q^{19} +(-2.13008 - 3.68941i) q^{20} -0.286339 q^{22} +(3.59889 + 6.23346i) q^{23} +13.1490 q^{25} -3.58961 q^{26} +(-0.603898 + 1.04598i) q^{28} -8.19741 q^{29} +(-0.262817 + 0.455213i) q^{31} +(-0.500000 - 0.866025i) q^{32} -1.92146 q^{34} +(-2.57270 - 4.45605i) q^{35} +2.76309 q^{37} +(4.30470 + 0.685272i) q^{38} +4.26017 q^{40} +8.96050 q^{41} +(5.56496 - 9.63879i) q^{43} +(0.143169 - 0.247977i) q^{44} -7.19778 q^{46} -5.71450 q^{47} +(2.77062 - 4.79885i) q^{49} +(-6.57451 + 11.3874i) q^{50} +(1.79480 - 3.10869i) q^{52} +(3.77851 - 6.54457i) q^{53} +(0.609926 + 1.05642i) q^{55} +(-0.603898 - 1.04598i) q^{56} +(4.09871 - 7.09917i) q^{58} -1.07655 q^{59} -2.73435 q^{61} +(-0.262817 - 0.455213i) q^{62} +1.00000 q^{64} +(7.64617 + 13.2436i) q^{65} +(0.821582 + 1.42302i) q^{67} +(0.960728 - 1.66403i) q^{68} +5.14541 q^{70} +(-0.231197 - 0.400444i) q^{71} +(3.71200 + 6.42937i) q^{73} +(-1.38155 + 2.39291i) q^{74} +(-2.74581 + 3.38534i) q^{76} +(0.172919 - 0.299505i) q^{77} +(-7.10100 + 12.2993i) q^{79} +(-2.13008 + 3.68941i) q^{80} +(-4.48025 + 7.76002i) q^{82} +(-0.609393 - 1.05550i) q^{83} +(4.09286 + 7.08904i) q^{85} +(5.56496 + 9.63879i) q^{86} +(0.143169 + 0.247977i) q^{88} +(-7.04675 + 12.2053i) q^{89} +(2.16776 - 3.75467i) q^{91} +(3.59889 - 6.23346i) q^{92} +(2.85725 - 4.94891i) q^{94} +(-6.64111 - 17.3415i) q^{95} +(-2.85458 + 4.94428i) q^{97} +(2.77062 + 4.79885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8}+O(q^{10}) \) 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8	\( 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8} - q^{11} + q^{13} - 10 q^{14} - 9 q^{16} + 5 q^{17} + 9 q^{19} + 2 q^{22} + 2 q^{23} + 18 q^{25} - 2 q^{26} + 5 q^{28} - 18 q^{29} + 4 q^{31} - 9 q^{32} - 10 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} + 2 q^{41} + 7 q^{43} - q^{44} - 4 q^{46} + 38 q^{47} + 6 q^{49} - 9 q^{50} + q^{52} + 10 q^{53} + 6 q^{55} + 5 q^{56} + 9 q^{58} - 10 q^{59} - 36 q^{61} + 4 q^{62} + 18 q^{64} + 45 q^{65} + 22 q^{67} + 5 q^{68} + 12 q^{70} - 11 q^{71} + 44 q^{73} - 10 q^{74} - 6 q^{76} + 2 q^{77} + 2 q^{79} - q^{82} + 7 q^{83} + 7 q^{86} - q^{88} - q^{89} - 25 q^{91} + 2 q^{92} - 19 q^{94} - 21 q^{95} + 6 q^{98}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8 - q^11 + q^13 - 10 * q^14 - 9 * q^16 + 5 * q^17 + 9 * q^19 + 2 * q^22 + 2 * q^23 + 18 * q^25 - 2 * q^26 + 5 * q^28 - 18 * q^29 + 4 * q^31 - 9 * q^32 - 10 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 + 2 * q^41 + 7 * q^43 - q^44 - 4 * q^46 + 38 * q^47 + 6 * q^49 - 9 * q^50 + q^52 + 10 * q^53 + 6 * q^55 + 5 * q^56 + 9 * q^58 - 10 * q^59 - 36 * q^61 + 4 * q^62 + 18 * q^64 + 45 * q^65 + 22 * q^67 + 5 * q^68 + 12 * q^70 - 11 * q^71 + 44 * q^73 - 10 * q^74 - 6 * q^76 + 2 * q^77 + 2 * q^79 - q^82 + 7 * q^83 + 7 * q^86 - q^88 - q^89 - 25 * q^91 + 2 * q^92 - 19 * q^94 - 21 * q^95 + 6 * q^98

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