LMFDB - Embedded newform 546.2.i.k.235.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.21870000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 24x^{4} - 43x^{3} + 138x^{2} - 117x + 73 $ x^6 - 3x^5 + 24x^4 - 43x^3 + 138x^2 - 117*x + 73
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			235.3
Root			$0.500000 - 3.23735i$ of defining polynomial
Character	$\chi$	$=$	546.235
Dual form			546.2.i.k.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.70942 + 2.96080i) q^{5} +1.00000 q^{6} +(2.36521 - 1.18566i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.70942 + 2.96080i) q^{5} +1.00000 q^{6} +(2.36521 - 1.18566i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.70942 + 2.96080i) q^{10} +(2.36521 - 4.09666i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(2.20942 + 1.45550i) q^{14} +3.41883 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.89783 + 6.75125i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.34421 - 2.32824i) q^{19} -3.41883 q^{20} +(0.155792 - 2.64116i) q^{21} +4.73042 q^{22} +(1.86521 + 3.23063i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.34421 + 5.79234i) q^{25} +(0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(-0.155792 + 2.64116i) q^{28} -3.00000 q^{29} +(1.70942 + 2.96080i) q^{30} +(2.84421 - 4.92631i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.36521 - 4.09666i) q^{33} -7.79567 q^{34} +(7.55362 + 4.97611i) q^{35} +1.00000 q^{36} +(1.55362 + 2.69096i) q^{37} +(1.34421 - 2.32824i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-1.70942 - 2.96080i) q^{40} +0.892750 q^{41} +(2.36521 - 1.18566i) q^{42} -12.8377 q^{43} +(2.36521 + 4.09666i) q^{44} +(1.70942 - 2.96080i) q^{45} +(-1.86521 + 3.23063i) q^{46} +(5.07462 + 8.78951i) q^{47} -1.00000 q^{48} +(4.18842 - 5.60867i) q^{49} -6.68842 q^{50} +(3.89783 + 6.75125i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(4.60725 - 7.97999i) q^{53} +(-0.500000 - 0.866025i) q^{54} +16.1725 q^{55} +(-2.36521 + 1.18566i) q^{56} -2.68842 q^{57} +(-1.50000 - 2.59808i) q^{58} +(3.05362 - 5.28903i) q^{59} +(-1.70942 + 2.96080i) q^{60} +(-1.52100 - 2.63445i) q^{61} +5.68842 q^{62} +(-2.20942 - 1.45550i) q^{63} +1.00000 q^{64} +(1.70942 + 2.96080i) q^{65} +(2.36521 - 4.09666i) q^{66} +(0.0326253 - 0.0565087i) q^{67} +(-3.89783 - 6.75125i) q^{68} +3.73042 q^{69} +(-0.532625 + 9.02969i) q^{70} -12.6884 q^{71} +(0.500000 + 0.866025i) q^{72} +(-5.86521 + 10.1588i) q^{73} +(-1.55362 + 2.69096i) q^{74} +(3.34421 + 5.79234i) q^{75} +2.68842 q^{76} +(0.736959 - 12.4938i) q^{77} +1.00000 q^{78} +(-7.26304 - 12.5800i) q^{79} +(1.70942 - 2.96080i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.446375 + 0.773145i) q^{82} +0.934749 q^{83} +(2.20942 + 1.45550i) q^{84} -26.6521 q^{85} +(-6.41883 - 11.1177i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(-2.36521 + 4.09666i) q^{88} +(-7.55362 - 13.0833i) q^{89} +3.41883 q^{90} +(2.36521 - 1.18566i) q^{91} -3.73042 q^{92} +(-2.84421 - 4.92631i) q^{93} +(-5.07462 + 8.78951i) q^{94} +(4.59562 - 7.95985i) q^{95} +(-0.500000 - 0.866025i) q^{96} -4.79567 q^{97} +(6.95146 + 0.822941i) q^{98} -4.73042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} - 6 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{21} + 6 q^{22} - 3 q^{24} - 18 q^{25} + 3 q^{26} - 6 q^{27} - 3 q^{28} - 18 q^{29} - 3 q^{30} + 15 q^{31} + 3 q^{32} - 3 q^{33} - 12 q^{34} + 30 q^{35} + 6 q^{36} - 6 q^{37} + 6 q^{38} + 3 q^{39} + 3 q^{40} + 36 q^{41} + 3 q^{42} - 24 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{47} - 6 q^{48} + 21 q^{49} - 36 q^{50} + 6 q^{51} - 3 q^{52} - 3 q^{53} - 3 q^{54} + 54 q^{55} - 3 q^{56} - 12 q^{57} - 9 q^{58} + 3 q^{59} + 3 q^{60} + 30 q^{62} + 6 q^{64} - 3 q^{65} + 3 q^{66} - 6 q^{67} - 6 q^{68} + 3 q^{70} - 72 q^{71} + 3 q^{72} - 24 q^{73} + 6 q^{74} + 18 q^{75} + 12 q^{76} + 33 q^{77} + 6 q^{78} - 15 q^{79} - 3 q^{80} - 3 q^{81} + 18 q^{82} + 18 q^{83} - 48 q^{85} - 12 q^{86} - 9 q^{87} - 3 q^{88} - 30 q^{89} - 6 q^{90} + 3 q^{91} - 15 q^{93} - 6 q^{94} - 6 q^{95} - 3 q^{96} + 6 q^{97} + 9 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 - 6 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^21 + 6 * q^22 - 3 * q^24 - 18 * q^25 + 3 * q^26 - 6 * q^27 - 3 * q^28 - 18 * q^29 - 3 * q^30 + 15 * q^31 + 3 * q^32 - 3 * q^33 - 12 * q^34 + 30 * q^35 + 6 * q^36 - 6 * q^37 + 6 * q^38 + 3 * q^39 + 3 * q^40 + 36 * q^41 + 3 * q^42 - 24 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^47 - 6 * q^48 + 21 * q^49 - 36 * q^50 + 6 * q^51 - 3 * q^52 - 3 * q^53 - 3 * q^54 + 54 * q^55 - 3 * q^56 - 12 * q^57 - 9 * q^58 + 3 * q^59 + 3 * q^60 + 30 * q^62 + 6 * q^64 - 3 * q^65 + 3 * q^66 - 6 * q^67 - 6 * q^68 + 3 * q^70 - 72 * q^71 + 3 * q^72 - 24 * q^73 + 6 * q^74 + 18 * q^75 + 12 * q^76 + 33 * q^77 + 6 * q^78 - 15 * q^79 - 3 * q^80 - 3 * q^81 + 18 * q^82 + 18 * q^83 - 48 * q^85 - 12 * q^86 - 9 * q^87 - 3 * q^88 - 30 * q^89 - 6 * q^90 + 3 * q^91 - 15 * q^93 - 6 * q^94 - 6 * q^95 - 3 * q^96 + 6 * q^97 + 9 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.70942	+	2.96080i	0.764474	+	1.32411i	0.940524	+	0.339727i	$0.110335\pi$
$5$	1.70942	+	2.96080i	0.764474	+	1.32411i	−0.176050	+	0.984381i	$0.556332\pi$
$6$	1.00000			0.408248
$7$	2.36521	−	1.18566i	0.893965	−	0.448138i
$7$	2.36521	−	1.18566i	0.893965	−	0.448138i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.70942	+	2.96080i	−0.540565	+	0.936286i
$11$	2.36521	−	4.09666i	0.713137	−	1.23519i	−0.250537	−	0.968107i	$-0.580607\pi$
$11$	2.36521	−	4.09666i	0.713137	−	1.23519i	0.963674	−	0.267082i	$-0.0860596\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	2.20942	+	1.45550i	0.590491	+	0.388999i
$15$	3.41883			0.882739
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.89783	+	6.75125i	−0.945363	+	1.63742i	−0.190341	+	0.981718i	$0.560960\pi$
$17$	−3.89783	+	6.75125i	−0.945363	+	1.63742i	−0.755022	+	0.655700i	$0.772374\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.34421	−	2.32824i	−0.308383	−	0.534134i	0.669626	−	0.742698i	$-0.266454\pi$
$19$	−1.34421	−	2.32824i	−0.308383	−	0.534134i	−0.978009	+	0.208564i	$0.933121\pi$
$20$	−3.41883			−0.764474
$21$	0.155792	−	2.64116i	0.0339965	−	0.576348i
$22$	4.73042			1.00853
$23$	1.86521	+	3.23063i	0.388923	+	0.673634i	0.992305	−	0.123818i	$-0.0395140\pi$
$23$	1.86521	+	3.23063i	0.388923	+	0.673634i	−0.603382	+	0.797452i	$0.706181\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−3.34421	+	5.79234i	−0.668842	+	1.15847i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$	−1.00000			−0.192450
$28$	−0.155792	+	2.64116i	−0.0294418	+	0.499132i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	1.70942	+	2.96080i	0.312095	+	0.540565i
$31$	2.84421	−	4.92631i	0.510835	−	0.884792i	−0.489086	−	0.872235i	$-0.662670\pi$
$31$	2.84421	−	4.92631i	0.510835	−	0.884792i	0.999921	−	0.0125566i	$-0.00399699\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.36521	−	4.09666i	−0.411730	−	0.713137i
$34$	−7.79567			−1.33695
$35$	7.55362	+	4.97611i	1.27680	+	0.841116i
$36$	1.00000			0.166667
$37$	1.55362	+	2.69096i	0.255414	+	0.442391i	0.965008	−	0.262221i	$-0.0844548\pi$
$37$	1.55362	+	2.69096i	0.255414	+	0.442391i	−0.709594	+	0.704611i	$0.751121\pi$
$38$	1.34421	−	2.32824i	0.218059	−	0.377690i
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	−1.70942	−	2.96080i	−0.270282	−	0.468143i
$41$	0.892750			0.139424			0.0697121	−	0.997567i	$-0.477792\pi$
$41$	0.892750			0.139424			0.0697121	+	0.997567i	$0.477792\pi$
$42$	2.36521	−	1.18566i	0.364960	−	0.182951i
$43$	−12.8377			−1.95773			−0.978863	−	0.204518i	$-0.934437\pi$
$43$	−12.8377			−1.95773			−0.978863	+	0.204518i	$0.934437\pi$
$44$	2.36521	+	4.09666i	0.356569	+	0.617595i
$45$	1.70942	−	2.96080i	0.254825	−	0.441369i
$46$	−1.86521	+	3.23063i	−0.275010	+	0.476331i
$47$	5.07462	+	8.78951i	0.740210	+	1.28208i	0.952399	+	0.304853i	$0.0986073\pi$
$47$	5.07462	+	8.78951i	0.740210	+	1.28208i	−0.212189	+	0.977229i	$0.568059\pi$
$48$	−1.00000			−0.144338
$49$	4.18842	−	5.60867i	0.598345	−	0.801238i
$50$	−6.68842			−0.945885
$51$	3.89783	+	6.75125i	0.545806	+	0.945363i
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	4.60725	−	7.97999i	0.632854	−	1.09614i	−0.354111	−	0.935203i	$-0.615216\pi$
$53$	4.60725	−	7.97999i	0.632854	−	1.09614i	0.986965	−	0.160933i	$-0.0514502\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	16.1725			2.18070
$56$	−2.36521	+	1.18566i	−0.316064	+	0.158441i
$57$	−2.68842			−0.356090
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	3.05362	−	5.28903i	0.397548	−	0.688573i	−0.595875	−	0.803077i	$-0.703195\pi$
$59$	3.05362	−	5.28903i	0.397548	−	0.688573i	0.993423	+	0.114504i	$0.0365279\pi$
$60$	−1.70942	+	2.96080i	−0.220685	+	0.382237i
$61$	−1.52100	−	2.63445i	−0.194744	−	0.337307i	0.752073	−	0.659080i	$-0.229054\pi$
$61$	−1.52100	−	2.63445i	−0.194744	−	0.337307i	−0.946817	+	0.321774i	$0.895721\pi$
$62$	5.68842			0.722430
$63$	−2.20942	−	1.45550i	−0.278360	−	0.183376i
$64$	1.00000			0.125000
$65$	1.70942	+	2.96080i	0.212027	+	0.367242i
$66$	2.36521	−	4.09666i	0.291137	−	0.504264i
$67$	0.0326253	−	0.0565087i	0.00398581	−	0.00690363i	−0.864026	−	0.503448i	$-0.832065\pi$
$67$	0.0326253	−	0.0565087i	0.00398581	−	0.00690363i	0.868011	+	0.496544i	$0.165398\pi$
$68$	−3.89783	−	6.75125i	−0.472682	−	0.818709i
$69$	3.73042			0.449089
$70$	−0.532625	+	9.02969i	−0.0636609	+	1.07925i
$71$	−12.6884			−1.50584			−0.752919	−	0.658113i	$-0.771355\pi$
$71$	−12.6884			−1.50584			−0.752919	+	0.658113i	$0.771355\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−5.86521	+	10.1588i	−0.686471	+	1.18900i	0.286502	+	0.958080i	$0.407508\pi$
$73$	−5.86521	+	10.1588i	−0.686471	+	1.18900i	−0.972972	+	0.230922i	$0.925826\pi$
$74$	−1.55362	+	2.69096i	−0.180605	+	0.312817i
$75$	3.34421	+	5.79234i	0.386156	+	0.668842i
$76$	2.68842			0.308383
$77$	0.736959	−	12.4938i	0.0839843	−	1.42380i
$78$	1.00000			0.113228
$79$	−7.26304	−	12.5800i	−0.817156	−	1.41536i	−0.907769	−	0.419470i	$-0.862216\pi$
$79$	−7.26304	−	12.5800i	−0.817156	−	1.41536i	0.0906135	−	0.995886i	$-0.471117\pi$
$80$	1.70942	−	2.96080i	0.191119	−	0.331027i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.446375	+	0.773145i	0.0492939	+	0.0853795i
$83$	0.934749			0.102602			0.0513010	−	0.998683i	$-0.483663\pi$
$83$	0.934749			0.102602			0.0513010	+	0.998683i	$0.483663\pi$
$84$	2.20942	+	1.45550i	0.241067	+	0.158808i
$85$	−26.6521			−2.89082
$86$	−6.41883	−	11.1177i	−0.692161	−	1.19886i
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	−2.36521	+	4.09666i	−0.252132	+	0.436705i
$89$	−7.55362	−	13.0833i	−0.800683	−	1.38682i	−0.919167	−	0.393867i	$-0.871137\pi$
$89$	−7.55362	−	13.0833i	−0.800683	−	1.38682i	0.118485	−	0.992956i	$-0.462196\pi$
$90$	3.41883			0.360377
$91$	2.36521	−	1.18566i	0.247941	−	0.124291i
$92$	−3.73042			−0.388923
$93$	−2.84421	−	4.92631i	−0.294931	−	0.510835i
$94$	−5.07462	+	8.78951i	−0.523408	+	0.906568i
$95$	4.59562	−	7.95985i	0.471501	−	0.816664i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−4.79567			−0.486926			−0.243463	−	0.969910i	$-0.578283\pi$
$97$	−4.79567			−0.486926			−0.243463	+	0.969910i	$0.578283\pi$
$98$	6.95146	+	0.822941i	0.702203	+	0.0831296i
$99$	−4.73042			−0.475425
$100$	−3.34421	−	5.79234i	−0.334421	−	0.579234i
$101$	−0.311583	+	0.539678i	−0.0310037	+	0.0537000i	−0.881111	−	0.472910i	$-0.843204\pi$
$101$	−0.311583	+	0.539678i	−0.0310037	+	0.0537000i	0.850107	+	0.526610i	$0.176537\pi$
$102$	−3.89783	+	6.75125i	−0.385943	+	0.668473i
$103$	−4.41883	−	7.65364i	−0.435401	−	0.754136i	0.561928	−	0.827186i	$-0.310060\pi$
$103$	−4.41883	−	7.65364i	−0.435401	−	0.754136i	−0.997328	+	0.0730505i	$0.976727\pi$
$104$	−1.00000			−0.0980581
$105$	8.08625	−	4.05358i	0.789137	−	0.395589i
$106$	9.21450			0.894991
$107$	−2.88621	−	4.99906i	−0.279020	−	0.483277i	0.692121	−	0.721781i	$-0.256676\pi$
$107$	−2.88621	−	4.99906i	−0.279020	−	0.483277i	−0.971142	+	0.238504i	$0.923343\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	−0.945769	−	0.324840i	$-0.894690\pi$
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	0.754204	+	0.656640i	$0.228023\pi$
$110$	8.08625	+	14.0058i	0.770994	+	1.33540i
$111$	3.10725			0.294927
$112$	−2.20942	−	1.45550i	−0.208770	−	0.137532i
$113$	10.6333			1.00030			0.500150	−	0.865939i	$-0.333278\pi$
$113$	10.6333			1.00030			0.500150	+	0.865939i	$0.333278\pi$
$114$	−1.34421	−	2.32824i	−0.125897	−	0.218059i
$115$	−6.37683	+	11.0450i	−0.594643	+	1.02995i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	6.10725			0.562218
$119$	−1.21450	+	20.5896i	−0.111333	+	1.88745i
$120$	−3.41883			−0.312095
$121$	−5.68842	−	9.85263i	−0.517129	−	0.895693i
$122$	1.52100	−	2.63445i	0.137705	−	0.238512i
$123$	0.446375	−	0.773145i	0.0402483	−	0.0697121i
$124$	2.84421	+	4.92631i	0.255417	+	0.442396i
$125$	−5.77241			−0.516300
$126$	0.155792	−	2.64116i	0.0138790	−	0.235293i
$127$	−6.17250			−0.547721			−0.273860	−	0.961769i	$-0.588301\pi$
$127$	−6.17250			−0.547721			−0.273860	+	0.961769i	$0.588301\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.41883	+	11.1177i	−0.565147	+	0.978863i
$130$	−1.70942	+	2.96080i	−0.149926	+	0.259679i
$131$	10.2355	+	17.7284i	0.894280	+	1.54894i	0.834694	+	0.550715i	$0.185645\pi$
$131$	10.2355	+	17.7284i	0.894280	+	1.54894i	0.0595861	+	0.998223i	$0.481022\pi$
$132$	4.73042			0.411730
$133$	−5.93983	−	3.91299i	−0.515049	−	0.339299i
$134$	0.0652506			0.00563679
$135$	−1.70942	−	2.96080i	−0.147123	−	0.254825i
$136$	3.89783	−	6.75125i	0.334236	−	0.578914i
$137$	5.55362	−	9.61916i	0.474478	−	0.821820i	−0.525095	−	0.851044i	$-0.675970\pi$
$137$	5.55362	−	9.61916i	0.474478	−	0.821820i	0.999573	+	0.0292235i	$0.00930344\pi$
$138$	1.86521	+	3.23063i	0.158777	+	0.275010i
$139$	−2.26958			−0.192504			−0.0962518	−	0.995357i	$-0.530685\pi$
$139$	−2.26958			−0.192504			−0.0962518	+	0.995357i	$0.530685\pi$
$140$	−8.08625	+	4.05358i	−0.683413	+	0.342590i
$141$	10.1492			0.854721
$142$	−6.34421	−	10.9885i	−0.532394	−	0.922134i
$143$	2.36521	−	4.09666i	0.197789	−	0.342580i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−5.12825	−	8.88239i	−0.425878	−	0.737642i
$146$	−11.7304			−0.970816
$147$	−2.76304	−	6.43161i	−0.227892	−	0.530470i
$148$	−3.10725			−0.255414
$149$	4.13479	+	7.16167i	0.338735	+	0.586707i	0.984195	−	0.177087i	$-0.0566675\pi$
$149$	4.13479	+	7.16167i	0.338735	+	0.586707i	−0.645460	+	0.763794i	$0.723334\pi$
$150$	−3.34421	+	5.79234i	−0.273053	+	0.472942i
$151$	2.63479	−	4.56359i	0.214416	−	0.371380i	−0.738676	−	0.674061i	$-0.764548\pi$
$151$	2.63479	−	4.56359i	0.214416	−	0.371380i	0.953092	+	0.302681i	$0.0978817\pi$
$152$	1.34421	+	2.32824i	0.109030	+	0.188845i
$153$	7.79567			0.630242
$154$	11.1884	−	5.60867i	0.901588	−	0.451959i
$155$	19.4477			1.56208
$156$	0.500000	+	0.866025i	0.0400320	+	0.0693375i
$157$	5.62825	−	9.74841i	0.449183	−	0.778008i	−0.549150	−	0.835724i	$-0.685048\pi$
$157$	5.62825	−	9.74841i	0.449183	−	0.778008i	0.998333	+	0.0577158i	$0.0183817\pi$
$158$	7.26304	−	12.5800i	0.577817	−	1.00081i
$159$	−4.60725	−	7.97999i	−0.365379	−	0.632854i
$160$	3.41883			0.270282
$161$	8.24204	+	5.42962i	0.649564	+	0.427914i
$162$	−1.00000			−0.0785674
$163$	−8.18187	−	14.1714i	−0.640854	−	1.10999i	−0.985243	−	0.171164i	$-0.945247\pi$
$163$	−8.18187	−	14.1714i	−0.640854	−	1.10999i	0.344389	−	0.938827i	$-0.388086\pi$
$164$	−0.446375	+	0.773145i	−0.0348560	+	0.0603724i
$165$	8.08625	−	14.0058i	0.629514	−	1.09035i
$166$	0.467375	+	0.809517i	0.0362753	+	0.0628307i
$167$	22.9869			1.77878			0.889390	−	0.457148i	$-0.151129\pi$
$167$	22.9869			1.77878			0.889390	+	0.457148i	$0.151129\pi$
$168$	−0.155792	+	2.64116i	−0.0120196	+	0.203770i
$169$	1.00000			0.0769231
$170$	−13.3260	−	23.0814i	−1.02206	−	1.77026i
$171$	−1.34421	+	2.32824i	−0.102794	+	0.178045i
$172$	6.41883	−	11.1177i	0.489431	−	0.847720i
$173$	−5.38621	−	9.32918i	−0.409506	−	0.709285i	0.585329	−	0.810796i	$-0.300966\pi$
$173$	−5.38621	−	9.32918i	−0.409506	−	0.709285i	−0.994834	+	0.101511i	$0.967632\pi$
$174$	−3.00000			−0.227429
$175$	−1.04200	+	17.6652i	−0.0787677	+	1.33536i
$176$	−4.73042			−0.356569
$177$	−3.05362	−	5.28903i	−0.229524	−	0.397548i
$178$	7.55362	−	13.0833i	0.566168	−	0.980632i
$179$	−9.52608	+	16.4997i	−0.712013	+	1.23324i	0.252088	+	0.967704i	$0.418883\pi$
$179$	−9.52608	+	16.4997i	−0.712013	+	1.23324i	−0.964100	+	0.265538i	$0.914450\pi$
$180$	1.70942	+	2.96080i	0.127412	+	0.220685i
$181$	13.7957			1.02542			0.512712	−	0.858561i	$-0.328641\pi$
$181$	13.7957			1.02542			0.512712	+	0.858561i	$0.328641\pi$
$182$	2.20942	+	1.45550i	0.163773	+	0.107889i
$183$	−3.04200			−0.224871
$184$	−1.86521	−	3.23063i	−0.137505	−	0.238166i
$185$	−5.31158	+	9.19993i	−0.390515	+	0.676392i
$186$	2.84421	−	4.92631i	0.208547	−	0.361215i
$187$	18.4384	+	31.9362i	1.34835	+	2.33541i
$188$	−10.1492			−0.740210
$189$	−2.36521	+	1.18566i	−0.172044	+	0.0862441i
$190$	9.19125			0.666803
$191$	−5.14925	−	8.91876i	−0.372587	−	0.645339i	0.617376	−	0.786668i	$-0.288196\pi$
$191$	−5.14925	−	8.91876i	−0.372587	−	0.645339i	−0.989963	+	0.141329i	$0.954862\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−8.81667	+	15.2709i	−0.634637	+	1.09922i	0.351954	+	0.936017i	$0.385517\pi$
$193$	−8.81667	+	15.2709i	−0.634637	+	1.09922i	−0.986592	+	0.163207i	$0.947816\pi$
$194$	−2.39783	−	4.15317i	−0.172154	−	0.298180i
$195$	3.41883			0.244828
$196$	2.76304	+	6.43161i	0.197360	+	0.459401i
$197$	−8.26958			−0.589183			−0.294592	−	0.955623i	$-0.595184\pi$
$197$	−8.26958			−0.589183			−0.294592	+	0.955623i	$0.595184\pi$
$198$	−2.36521	−	4.09666i	−0.168088	−	0.291137i
$199$	2.51163	−	4.35026i	0.178044	−	0.308382i	−0.763166	−	0.646202i	$-0.776356\pi$
$199$	2.51163	−	4.35026i	0.178044	−	0.308382i	0.941211	+	0.337820i	$0.109690\pi$
$200$	3.34421	−	5.79234i	0.236471	−	0.409580i
$201$	−0.0326253	−	0.0565087i	−0.00230121	−	0.00398581i
$202$	−0.623166			−0.0438458
$203$	−7.09562	+	3.55698i	−0.498015	+	0.249651i
$204$	−7.79567			−0.545806
$205$	1.52608	+	2.64325i	0.106586	+	0.184613i
$206$	4.41883	−	7.65364i	0.307875	−	0.533255i
$207$	1.86521	−	3.23063i	0.129641	−	0.224545i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	−12.7173			−0.879676
$210$	7.55362	+	4.97611i	0.521250	+	0.343384i
$211$	14.5681			1.00291			0.501454	−	0.865184i	$-0.332799\pi$
$211$	14.5681			1.00291			0.501454	+	0.865184i	$0.332799\pi$
$212$	4.60725	+	7.97999i	0.316427	+	0.548068i
$213$	−6.34421	+	10.9885i	−0.434698	+	0.752919i
$214$	2.88621	−	4.99906i	0.197297	−	0.341729i
$215$	−21.9449	−	38.0097i	−1.49663	−	2.59224i
$216$	1.00000			0.0680414
$217$	0.886207	−	15.0240i	0.0601597	−	1.01990i
$218$	−4.00000			−0.270914
$219$	5.86521	+	10.1588i	0.396334	+	0.686471i
$220$	−8.08625	+	14.0058i	−0.545175	+	0.944271i
$221$	−3.89783	+	6.75125i	−0.262197	+	0.454138i
$222$	1.55362	+	2.69096i	0.104272	+	0.180605i
$223$	−10.3217			−0.691195			−0.345598	−	0.938383i	$-0.612324\pi$
$223$	−10.3217			−0.691195			−0.345598	+	0.938383i	$0.612324\pi$
$224$	0.155792	−	2.64116i	0.0104093	−	0.176470i
$225$	6.68842			0.445894
$226$	5.31667	+	9.20874i	0.353659	+	0.612556i
$227$	−2.22104	+	3.84696i	−0.147416	+	0.255332i	−0.930272	−	0.366872i	$-0.880429\pi$
$227$	−2.22104	+	3.84696i	−0.147416	+	0.255332i	0.782856	+	0.622203i	$0.213762\pi$
$228$	1.34421	−	2.32824i	0.0890224	−	0.154191i
$229$	10.7304	+	18.5856i	0.709086	+	1.22817i	0.965197	+	0.261525i	$0.0842255\pi$
$229$	10.7304	+	18.5856i	0.709086	+	1.22817i	−0.256111	+	0.966647i	$0.582441\pi$
$230$	−12.7537			−0.840952
$231$	−10.4515	−	6.88512i	−0.687655	−	0.453008i
$232$	3.00000			0.196960
$233$	3.83258	+	6.63823i	0.251081	+	0.434885i	0.963824	−	0.266541i	$-0.0858807\pi$
$233$	3.83258	+	6.63823i	0.251081	+	0.434885i	−0.712743	+	0.701425i	$0.752547\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$	−17.3493	+	30.0499i	−1.13174	+	1.96024i
$236$	3.05362	+	5.28903i	0.198774	+	0.344287i
$237$	−14.5261			−0.943570
$238$	−18.4384	+	9.24302i	−1.19518	+	0.599136i
$239$	−9.52608			−0.616191			−0.308096	−	0.951355i	$-0.599692\pi$
$239$	−9.52608			−0.616191			−0.308096	+	0.951355i	$0.599692\pi$
$240$	−1.70942	−	2.96080i	−0.110342	−	0.191119i
$241$	3.68187	−	6.37719i	0.237170	−	0.410791i	−0.722731	−	0.691130i	$-0.757113\pi$
$241$	3.68187	−	6.37719i	0.237170	−	0.410791i	0.959901	+	0.280339i	$0.0904467\pi$
$242$	5.68842	−	9.85263i	0.365665	−	0.633351i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.04200			0.194744
$245$	23.7659	+	2.81350i	1.51835	+	0.179748i
$246$	0.892750			0.0569197
$247$	−1.34421	−	2.32824i	−0.0855299	−	0.148142i
$248$	−2.84421	+	4.92631i	−0.180607	+	0.312821i
$249$	0.467375	−	0.809517i	0.0296187	−	0.0513010i
$250$	−2.88621	−	4.99906i	−0.182540	−	0.316168i
$251$	12.7406			0.804178			0.402089	−	0.915601i	$-0.368284\pi$
$251$	12.7406			0.804178			0.402089	+	0.915601i	$0.368284\pi$
$252$	2.36521	−	1.18566i	0.148994	−	0.0746896i
$253$	17.6464			1.10942
$254$	−3.08625	−	5.34554i	−0.193649	−	0.335409i
$255$	−13.3260	+	23.0814i	−0.834509	+	1.44541i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.73042	+	11.6574i	0.419832	+	0.727170i	0.995922	−	0.0902160i	$-0.0287557\pi$
$257$	6.73042	+	11.6574i	0.419832	+	0.727170i	−0.576090	+	0.817386i	$0.695422\pi$
$258$	−12.8377			−0.799238
$259$	6.86521	+	4.52260i	0.426583	+	0.281021i
$260$	−3.41883			−0.212027
$261$	1.50000	+	2.59808i	0.0928477	+	0.160817i
$262$	−10.2355	+	17.7284i	−0.632351	+	1.09526i
$263$	−12.0145	+	20.8096i	−0.740843	+	1.28318i	0.211269	+	0.977428i	$0.432240\pi$
$263$	−12.0145	+	20.8096i	−0.740843	+	1.28318i	−0.952112	+	0.305750i	$0.901093\pi$
$264$	2.36521	+	4.09666i	0.145568	+	0.252132i
$265$	31.5028			1.93520
$266$	0.418833	−	7.10054i	0.0256803	−	0.435362i
$267$	−15.1072			−0.924549
$268$	0.0326253	+	0.0565087i	0.00199291	+	0.00345182i
$269$	−7.96083	+	13.7886i	−0.485380	+	0.840704i	−0.999859	−	0.0167997i	$-0.994652\pi$
$269$	−7.96083	+	13.7886i	−0.485380	+	0.840704i	0.514478	+	0.857503i	$0.327986\pi$
$270$	1.70942	−	2.96080i	0.104032	−	0.180188i
$271$	9.82604	+	17.0192i	0.596889	+	1.03384i	0.993277	+	0.115760i	$0.0369302\pi$
$271$	9.82604	+	17.0192i	0.596889	+	1.03384i	−0.396388	+	0.918083i	$0.629736\pi$
$272$	7.79567			0.472682
$273$	0.155792	−	2.64116i	0.00942893	−	0.159850i
$274$	11.1072			0.671013
$275$	15.8195	+	27.4002i	0.953952	+	1.65229i
$276$	−1.86521	+	3.23063i	−0.112272	+	0.194461i
$277$	2.58625	−	4.47952i	0.155393	−	0.269148i	−0.777809	−	0.628500i	$-0.783669\pi$
$277$	2.58625	−	4.47952i	0.155393	−	0.269148i	0.933202	+	0.359352i	$0.117002\pi$
$278$	−1.13479	−	1.96552i	−0.0680603	−	0.117884i
$279$	−5.68842			−0.340557
$280$	−7.55362	−	4.97611i	−0.451415	−	0.297379i
$281$	−24.4290			−1.45731			−0.728656	−	0.684880i	$-0.759855\pi$
$281$	−24.4290			−1.45731			−0.728656	+	0.684880i	$0.759855\pi$
$282$	5.07462	+	8.78951i	0.302189	+	0.523408i
$283$	1.59562	−	2.76370i	0.0948500	−	0.164285i	−0.814696	−	0.579888i	$-0.803096\pi$
$283$	1.59562	−	2.76370i	0.0948500	−	0.164285i	0.909546	+	0.415603i	$0.136430\pi$
$284$	6.34421	−	10.9885i	0.376460	−	0.652047i
$285$	−4.59562	−	7.95985i	−0.272221	−	0.471501i
$286$	4.73042			0.279715
$287$	2.11154	−	1.05850i	0.124640	−	0.0624812i
$288$	−1.00000			−0.0589256
$289$	−21.8862	−	37.9080i	−1.28742	−	2.22988i
$290$	5.12825	−	8.88239i	0.301141	−	0.521592i
$291$	−2.39783	+	4.15317i	−0.140563	+	0.243463i
$292$	−5.86521	−	10.1588i	−0.343235	−	0.594501i
$293$	2.58117			0.150793			0.0753967	−	0.997154i	$-0.475978\pi$
$293$	2.58117			0.150793			0.0753967	+	0.997154i	$0.475978\pi$
$294$	4.18842	−	5.60867i	0.244273	−	0.327104i
$295$	20.8797			1.21566
$296$	−1.55362	−	2.69096i	−0.0903026	−	0.156409i
$297$	−2.36521	+	4.09666i	−0.137243	+	0.237712i
$298$	−4.13479	+	7.16167i	−0.239522	+	0.414864i
$299$	1.86521	+	3.23063i	0.107868	+	0.186832i
$300$	−6.68842			−0.386156
$301$	−30.3637	+	15.2211i	−1.75014	+	0.877331i
$302$	5.26958			0.303230
$303$	0.311583	+	0.539678i	0.0179000	+	0.0310037i
$304$	−1.34421	+	2.32824i	−0.0770956	+	0.133534i
$305$	5.20004	−	9.00674i	0.297754	−	0.515724i
$306$	3.89783	+	6.75125i	0.222824	+	0.385943i
$307$	23.3116			1.33046			0.665231	−	0.746637i	$-0.268333\pi$
$307$	23.3116			1.33046			0.665231	+	0.746637i	$0.268333\pi$
$308$	10.4515	+	6.88512i	0.595527	+	0.392316i
$309$	−8.83767			−0.502757
$310$	9.72387	+	16.8422i	0.552279	+	0.956575i
$311$	−5.39129	+	9.33799i	−0.305712	+	0.529509i	−0.977420	−	0.211308i	$-0.932228\pi$
$311$	−5.39129	+	9.33799i	−0.305712	+	0.529509i	0.671708	+	0.740816i	$0.265561\pi$
$312$	−0.500000	+	0.866025i	−0.0283069	+	0.0490290i
$313$	−7.42538	−	12.8611i	−0.419707	−	0.726954i	0.576203	−	0.817307i	$-0.304534\pi$
$313$	−7.42538	−	12.8611i	−0.419707	−	0.726954i	−0.995910	+	0.0903528i	$0.971201\pi$
$314$	11.2565			0.635241
$315$	0.532625	−	9.02969i	0.0300100	−	0.508765i
$316$	14.5261			0.817156
$317$	−11.5326	−	19.9751i	−0.647737	−	1.12191i	−0.983662	−	0.180024i	$-0.942382\pi$
$317$	−11.5326	−	19.9751i	−0.647737	−	1.12191i	0.335925	−	0.941889i	$-0.390951\pi$
$318$	4.60725	−	7.97999i	0.258362	−	0.447496i
$319$	−7.09562	+	12.2900i	−0.397279	+	0.688107i
$320$	1.70942	+	2.96080i	0.0955593	+	0.165514i
$321$	−5.77241			−0.322185
$322$	−0.581167	+	9.85263i	−0.0323872	+	0.549065i
$323$	20.9580			1.16613
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−3.34421	+	5.79234i	−0.185503	+	0.321301i
$326$	8.18187	−	14.1714i	0.453152	−	0.784882i
$327$	2.00000	+	3.46410i	0.110600	+	0.191565i
$328$	−0.892750			−0.0492939
$329$	22.4239	+	14.7722i	1.23627	+	0.814419i
$330$	16.1725			0.890267
$331$	−0.0652506	−	0.113017i	−0.00358650	−	0.00621200i	0.864227	−	0.503103i	$-0.167808\pi$
$331$	−0.0652506	−	0.113017i	−0.00358650	−	0.00621200i	−0.867813	+	0.496891i	$0.834475\pi$
$332$	−0.467375	+	0.809517i	−0.0256505	+	0.0444280i
$333$	1.55362	−	2.69096i	0.0851381	−	0.147464i
$334$	11.4935	+	19.9073i	0.628894	+	1.08928i
$335$	0.223081			0.0121882
$336$	−2.36521	+	1.18566i	−0.129033	+	0.0646831i
$337$	16.0522			0.874417			0.437209	−	0.899360i	$-0.355967\pi$
$337$	16.0522			0.874417			0.437209	+	0.899360i	$0.355967\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$	5.31667	−	9.20874i	0.288762	−	0.500150i
$340$	13.3260	−	23.0814i	0.722706	−	1.25176i
$341$	−13.4543	−	23.3035i	−0.728591	−	1.26196i
$342$	−2.68842			−0.145373
$343$	3.25650	−	18.2317i	0.175834	−	0.984420i
$344$	12.8377			0.692161
$345$	6.37683	+	11.0450i	0.343317	+	0.594643i
$346$	5.38621	−	9.32918i	0.289564	−	0.501540i
$347$	−10.6609	+	18.4652i	−0.572306	+	0.991263i	0.424023	+	0.905651i	$0.360618\pi$
$347$	−10.6609	+	18.4652i	−0.572306	+	0.991263i	−0.996329	+	0.0856111i	$0.972716\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	6.35358			0.340099			0.170050	−	0.985435i	$-0.445607\pi$
$349$	6.35358			0.340099			0.170050	+	0.985435i	$0.445607\pi$
$350$	−15.8195	+	7.93019i	−0.845588	+	0.423887i
$351$	−1.00000			−0.0533761
$352$	−2.36521	−	4.09666i	−0.126066	−	0.218353i
$353$	−15.2145	+	26.3523i	−0.809786	+	1.40259i	0.103226	+	0.994658i	$0.467084\pi$
$353$	−15.2145	+	26.3523i	−0.809786	+	1.40259i	−0.913012	+	0.407933i	$0.866250\pi$
$354$	3.05362	−	5.28903i	0.162298	−	0.281109i
$355$	−21.6898	−	37.5678i	−1.15117	−	1.99389i
$356$	15.1072			0.800683
$357$	17.2239	+	11.3466i	0.911584	+	0.600525i
$358$	−19.0522			−1.00694
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	0.999590	−	0.0286287i	$-0.00911406\pi$
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	−0.524588	+	0.851356i	$0.675781\pi$
$360$	−1.70942	+	2.96080i	−0.0900942	+	0.156048i
$361$	5.88621	−	10.1952i	0.309800	−	0.536590i
$362$	6.89783	+	11.9474i	0.362542	+	0.627941i
$363$	−11.3768			−0.597129
$364$	−0.155792	+	2.64116i	−0.00816570	+	0.138434i
$365$	−40.1043			−2.09916
$366$	−1.52100	−	2.63445i	−0.0795039	−	0.137705i
$367$	−2.11379	+	3.66120i	−0.110339	+	0.191113i	−0.915907	−	0.401391i	$-0.868527\pi$
$367$	−2.11379	+	3.66120i	−0.110339	+	0.191113i	0.805568	+	0.592503i	$0.201860\pi$
$368$	1.86521	−	3.23063i	0.0972307	−	0.168408i
$369$	−0.446375	−	0.773145i	−0.0232374	−	0.0402483i
$370$	−10.6232			−0.552272
$371$	1.43554	−	24.3370i	0.0745296	−	1.26351i
$372$	5.68842			0.294931
$373$	17.8427	+	30.9045i	0.923862	+	1.60018i	0.793380	+	0.608726i	$0.208319\pi$
$373$	17.8427	+	30.9045i	0.923862	+	1.60018i	0.130482	+	0.991451i	$0.458348\pi$
$374$	−18.4384	+	31.9362i	−0.953426	+	1.65138i
$375$	−2.88621	+	4.99906i	−0.149043	+	0.258150i
$376$	−5.07462	−	8.78951i	−0.261704	−	0.453284i
$377$	−3.00000			−0.154508
$378$	−2.20942	−	1.45550i	−0.113640	−	0.0748628i
$379$	9.67533			0.496988			0.248494	−	0.968633i	$-0.420064\pi$
$379$	9.67533			0.496988			0.248494	+	0.968633i	$0.420064\pi$
$380$	4.59562	+	7.95985i	0.235751	+	0.408332i
$381$	−3.08625	+	5.34554i	−0.158113	+	0.273860i
$382$	5.14925	−	8.91876i	0.263458	−	0.456323i
$383$	1.83767	+	3.18293i	0.0939003	+	0.162640i	0.909149	−	0.416471i	$-0.136733\pi$
$383$	1.83767	+	3.18293i	0.0939003	+	0.162640i	−0.815249	+	0.579111i	$0.803400\pi$
$384$	1.00000			0.0510310
$385$	38.2513	−	19.1751i	1.94947	−	0.977254i
$386$	−17.6333			−0.897513
$387$	6.41883	+	11.1177i	0.326288	+	0.565147i
$388$	2.39783	−	4.15317i	0.121732	−	0.210845i
$389$	−3.23696	+	5.60658i	−0.164120	+	0.284265i	−0.936343	−	0.351088i	$-0.885812\pi$
$389$	−3.23696	+	5.60658i	−0.164120	+	0.284265i	0.772222	+	0.635353i	$0.219145\pi$
$390$	1.70942	+	2.96080i	0.0865597	+	0.149926i
$391$	−29.0811			−1.47069
$392$	−4.18842	+	5.60867i	−0.211547	+	0.283281i
$393$	20.4710			1.03263
$394$	−4.13479	−	7.16167i	−0.208308	−	0.360800i
$395$	24.8311	−	43.0088i	1.24939	−	2.16401i
$396$	2.36521	−	4.09666i	0.118856	−	0.205865i
$397$	3.93046	+	6.80775i	0.197264	+	0.341671i	0.947640	−	0.319340i	$-0.103461\pi$
$397$	3.93046	+	6.80775i	0.197264	+	0.341671i	−0.750376	+	0.661011i	$0.770128\pi$
$398$	5.02325			0.251793
$399$	−6.35866	+	3.18755i	−0.318331	+	0.159577i
$400$	6.68842			0.334421
$401$	2.82321	+	4.88994i	0.140984	+	0.244192i	0.927868	−	0.372910i	$-0.121640\pi$
$401$	2.82321	+	4.88994i	0.140984	+	0.244192i	−0.786883	+	0.617102i	$0.788307\pi$
$402$	0.0326253	−	0.0565087i	0.00162720	−	0.00281840i
$403$	2.84421	−	4.92631i	0.141680	−	0.245397i
$404$	−0.311583	−	0.539678i	−0.0155018	−	0.0268500i
$405$	−3.41883			−0.169883
$406$	−6.62825	−	4.36650i	−0.328954	−	0.216706i
$407$	14.6986			0.728582
$408$	−3.89783	−	6.75125i	−0.192971	−	0.334236i
$409$	−12.8587	+	22.2719i	−0.635820	+	1.10127i	0.350521	+	0.936555i	$0.386005\pi$
$409$	−12.8587	+	22.2719i	−0.635820	+	1.10127i	−0.986341	+	0.164718i	$0.947329\pi$
$410$	−1.52608	+	2.64325i	−0.0753678	+	0.130541i
$411$	−5.55362	−	9.61916i	−0.273940	−	0.474478i
$412$	8.83767			0.435401
$413$	0.951458	−	16.1302i	0.0468182	−	0.793717i
$414$	3.73042			0.183340
$415$	1.59788	+	2.76760i	0.0784366	+	0.135856i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	−1.13479	+	1.96552i	−0.0555710	+	0.0962518i
$418$	−6.35866	−	11.0135i	−0.311012	−	0.538689i
$419$	8.83767			0.431748			0.215874	−	0.976421i	$-0.430740\pi$
$419$	8.83767			0.431748			0.215874	+	0.976421i	$0.430740\pi$
$420$	−0.532625	+	9.02969i	−0.0259895	+	0.440604i
$421$	−10.1594			−0.495140			−0.247570	−	0.968870i	$-0.579632\pi$
$421$	−10.1594			−0.495140			−0.247570	+	0.968870i	$0.579632\pi$
$422$	7.28404	+	12.6163i	0.354582	+	0.614153i
$423$	5.07462	−	8.78951i	0.246737	−	0.427360i
$424$	−4.60725	+	7.97999i	−0.223748	+	0.387543i
$425$	−26.0703	−	45.1551i	−1.26460	−	2.19035i
$426$	−12.6884			−0.614756
$427$	−6.72104	−	4.42763i	−0.325254	−	0.214268i
$428$	5.77241			0.279020
$429$	−2.36521	−	4.09666i	−0.114193	−	0.197789i
$430$	21.9449	−	38.0097i	1.05828	−	1.83299i
$431$	5.83767	−	10.1111i	0.281190	−	0.487036i	−0.690488	−	0.723344i	$-0.742604\pi$
$431$	5.83767	−	10.1111i	0.281190	−	0.487036i	0.971678	+	0.236308i	$0.0759374\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	6.60442			0.317388			0.158694	−	0.987328i	$-0.449272\pi$
$433$	6.60442			0.317388			0.158694	+	0.987328i	$0.449272\pi$
$434$	13.4543	−	6.74453i	0.645827	−	0.323748i
$435$	−10.2565			−0.491761
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	5.01446	−	8.68529i	0.239874	−	0.415474i
$438$	−5.86521	+	10.1588i	−0.280250	+	0.485408i
$439$	12.5051	+	21.6594i	0.596835	+	1.03375i	0.993285	+	0.115692i	$0.0369087\pi$
$439$	12.5051	+	21.6594i	0.596835	+	1.03375i	−0.396450	+	0.918056i	$0.629758\pi$
$440$	−16.1725			−0.770994
$441$	−6.95146	−	0.822941i	−0.331022	−	0.0391877i
$442$	−7.79567			−0.370802
$443$	8.43983	+	14.6182i	0.400989	+	0.694533i	0.993845	−	0.110775i	$-0.0353334\pi$
$443$	8.43983	+	14.6182i	0.400989	+	0.694533i	−0.592857	+	0.805308i	$0.702000\pi$
$444$	−1.55362	+	2.69096i	−0.0737318	+	0.127707i
$445$	25.8246	−	44.7295i	1.22420	−	2.12038i
$446$	−5.16087	−	8.93890i	−0.244374	−	0.423269i
$447$	8.26958			0.391138
$448$	2.36521	−	1.18566i	0.111746	−	0.0560172i
$449$	−20.1680			−0.951787			−0.475893	−	0.879503i	$-0.657875\pi$
$449$	−20.1680			−0.951787			−0.475893	+	0.879503i	$0.657875\pi$
$450$	3.34421	+	5.79234i	0.157647	+	0.273053i
$451$	2.11154	−	3.65730i	0.0994286	−	0.172215i
$452$	−5.31667	+	9.20874i	−0.250075	+	0.433142i
$453$	−2.63479	−	4.56359i	−0.123793	−	0.214416i
$454$	−4.44208			−0.208477
$455$	7.55362	+	4.97611i	0.354119	+	0.233284i
$456$	2.68842			0.125897
$457$	8.12825	+	14.0785i	0.380223	+	0.658566i	0.991094	−	0.133164i	$-0.0425138\pi$
$457$	8.12825	+	14.0785i	0.380223	+	0.658566i	−0.610871	+	0.791730i	$0.709180\pi$
$458$	−10.7304	+	18.5856i	−0.501399	+	0.868449i
$459$	3.89783	−	6.75125i	0.181935	−	0.315121i
$460$	−6.37683	−	11.0450i	−0.297321	−	0.514976i
$461$	−16.0840			−0.749106			−0.374553	−	0.927205i	$-0.622204\pi$
$461$	−16.0840			−0.749106			−0.374553	+	0.927205i	$0.622204\pi$
$462$	0.736959	−	12.4938i	0.0342864	−	0.581264i
$463$	1.67533			0.0778592			0.0389296	−	0.999242i	$-0.487605\pi$
$463$	1.67533			0.0778592			0.0389296	+	0.999242i	$0.487605\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$	9.72387	−	16.8422i	0.450934	−	0.781040i
$466$	−3.83258	+	6.63823i	−0.177541	+	0.307510i
$467$	−15.9725	−	27.6651i	−0.739117	−	1.28019i	−0.952893	−	0.303306i	$-0.901910\pi$
$467$	−15.9725	−	27.6651i	−0.739117	−	1.28019i	0.213776	−	0.976883i	$-0.431424\pi$
$468$	1.00000			0.0462250
$469$	0.0101655	−	0.172337i	0.000469399	−	0.00795780i
$470$	−34.6986			−1.60053
$471$	−5.62825	−	9.74841i	−0.259336	−	0.449183i
$472$	−3.05362	+	5.28903i	−0.140554	+	0.243447i
$473$	−30.3637	+	52.5916i	−1.39613	+	2.41816i
$474$	−7.26304	−	12.5800i	−0.333603	−	0.577817i
$475$	17.9813			0.825036
$476$	−17.2239	−	11.3466i	−0.789455	−	0.520070i
$477$	−9.21450			−0.421903
$478$	−4.76304	−	8.24983i	−0.217856	−	0.377338i
$479$	−18.8470	+	32.6440i	−0.861143	+	1.49154i	0.00968322	+	0.999953i	$0.496918\pi$
$479$	−18.8470	+	32.6440i	−0.861143	+	1.49154i	−0.870826	+	0.491591i	$0.836416\pi$
$480$	1.70942	−	2.96080i	0.0780238	−	0.135141i
$481$	1.55362	+	2.69096i	0.0708392	+	0.122697i
$482$	7.36375			0.335410
$483$	8.82321	−	4.42301i	0.401470	−	0.201254i
$484$	11.3768			0.517129
$485$	−8.19779	−	14.1990i	−0.372242	−	0.644743i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	2.47246	−	4.28242i	0.112038	−	0.194055i	−0.804554	−	0.593880i	$-0.797596\pi$
$487$	2.47246	−	4.28242i	0.112038	−	0.194055i	0.916592	+	0.399824i	$0.130929\pi$
$488$	1.52100	+	2.63445i	0.0688524	+	0.119256i
$489$	−16.3637			−0.739994
$490$	9.44638	+	21.9886i	0.426744	+	0.993344i
$491$	28.2014			1.27271			0.636356	−	0.771396i	$-0.280441\pi$
$491$	28.2014			1.27271			0.636356	+	0.771396i	$0.280441\pi$
$492$	0.446375	+	0.773145i	0.0201241	+	0.0348560i
$493$	11.6935	−	20.2537i	0.526649	−	0.912182i
$494$	1.34421	−	2.32824i	0.0604788	−	0.104752i
$495$	−8.08625	−	14.0058i	−0.363450	−	0.629514i
$496$	−5.68842			−0.255417
$497$	−30.0107	+	15.0442i	−1.34617	+	0.674823i
$498$	0.934749			0.0418871
$499$	−9.87966	−	17.1121i	−0.442275	−	0.766042i	0.555583	−	0.831461i	$-0.312495\pi$
$499$	−9.87966	−	17.1121i	−0.442275	−	0.766042i	−0.997858	+	0.0654189i	$0.979162\pi$
$500$	2.88621	−	4.99906i	0.129075	−	0.223565i
$501$	11.4935	−	19.9073i	0.513490	−	0.889390i
$502$	6.37029	+	11.0337i	0.284320	+	0.492457i
$503$	−2.40867			−0.107397			−0.0536986	−	0.998557i	$-0.517101\pi$
$503$	−2.40867			−0.107397			−0.0536986	+	0.998557i	$0.517101\pi$
$504$	2.20942	+	1.45550i	0.0984152	+	0.0648331i
$505$	−2.13050			−0.0948061
$506$	8.82321	+	15.2822i	0.392239	+	0.679379i
$507$	0.500000	−	0.866025i	0.0222058	−	0.0384615i
$508$	3.08625	−	5.34554i	0.136930	−	0.237170i
$509$	−12.7891	−	22.1514i	−0.566868	−	0.981844i	−0.996873	−	0.0790177i	$-0.974822\pi$
$509$	−12.7891	−	22.1514i	−0.566868	−	0.981844i	0.430005	−	0.902826i	$-0.358512\pi$
$510$	−26.6521			−1.18017
$511$	−1.82750	+	30.9819i	−0.0808438	+	1.37056i
$512$	−1.00000			−0.0441942
$513$	1.34421	+	2.32824i	0.0593483	+	0.102794i
$514$	−6.73042	+	11.6574i	−0.296866	+	0.514187i
$515$	15.1072	−	26.1665i	0.665705	−	1.15303i
$516$	−6.41883	−	11.1177i	−0.282573	−	0.489431i
$517$	48.0102			2.11148
$518$	−0.484083	+	8.20674i	−0.0212694	+	0.360584i
$519$	−10.7724			−0.472857
$520$	−1.70942	−	2.96080i	−0.0749629	−	0.129839i
$521$	−7.39558	+	12.8095i	−0.324006	+	0.561195i	−0.981311	−	0.192430i	$-0.938363\pi$
$521$	−7.39558	+	12.8095i	−0.324006	+	0.561195i	0.657304	+	0.753625i	$0.271697\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	11.2565	+	19.4968i	0.492212	+	0.852537i	0.999960	−	0.00896925i	$-0.00285504\pi$
$523$	11.2565	+	19.4968i	0.492212	+	0.852537i	−0.507747	+	0.861506i	$0.669522\pi$
$524$	−20.4710			−0.894280
$525$	14.7775	+	9.73499i	0.644943	+	0.424870i
$526$	−24.0289			−1.04771
$527$	22.1725	+	38.4039i	0.965849	+	1.67290i
$528$	−2.36521	+	4.09666i	−0.102932	+	0.178284i
$529$	4.54200	−	7.86697i	0.197478	−	0.342042i
$530$	15.7514	+	27.2823i	0.684198	+	1.18507i
$531$	−6.10725			−0.265032
$532$	6.35866	−	3.18755i	0.275683	−	0.138198i
$533$	0.892750			0.0386693
$534$	−7.55362	−	13.0833i	−0.326877	−	0.566168i
$535$	9.86746	−	17.0909i	0.426608	−	0.738906i
$536$	−0.0326253	+	0.0565087i	−0.00140920	+	0.00244080i
$537$	9.52608	+	16.4997i	0.411081	+	0.712013i
$538$	−15.9217			−0.686432
$539$	−13.0703	−	30.4242i	−0.562979	−	1.31046i
$540$	3.41883			0.147123
$541$	−14.6609	−	25.3934i	−0.630320	−	1.09175i	−0.987486	−	0.157706i	$-0.949590\pi$
$541$	−14.6609	−	25.3934i	−0.630320	−	1.09175i	0.357166	−	0.934041i	$-0.383743\pi$
$542$	−9.82604	+	17.0192i	−0.422065	+	0.731037i
$543$	6.89783	−	11.9474i	0.296014	−	0.512712i
$544$	3.89783	+	6.75125i	0.167118	+	0.289457i
$545$	−13.6753			−0.585787
$546$	2.36521	−	1.18566i	0.101222	−	0.0507416i
$547$	7.64642			0.326937			0.163469	−	0.986549i	$-0.447732\pi$
$547$	7.64642			0.326937			0.163469	+	0.986549i	$0.447732\pi$
$548$	5.55362	+	9.61916i	0.237239	+	0.410910i
$549$	−1.52100	+	2.63445i	−0.0649147	+	0.112436i
$550$	−15.8195	+	27.4002i	−0.674546	+	1.16835i
$551$	4.03263	+	6.98471i	0.171796	+	0.297559i
$552$	−3.73042			−0.158777
$553$	−32.0942	−	21.1427i	−1.36478	−	0.899079i
$554$	5.17250			0.219758
$555$	5.31158	+	9.19993i	0.225464	+	0.390515i
$556$	1.13479	−	1.96552i	0.0481259	−	0.0833565i
$557$	−6.11379	+	10.5894i	−0.259050	+	0.448687i	−0.965988	−	0.258588i	$-0.916743\pi$
$557$	−6.11379	+	10.5894i	−0.259050	+	0.448687i	0.706938	+	0.707276i	$0.250076\pi$
$558$	−2.84421	−	4.92631i	−0.120405	−	0.208547i
$559$	−12.8377			−0.542975
$560$	0.532625	−	9.02969i	0.0225075	−	0.381574i
$561$	36.8767			1.55694
$562$	−12.2145	−	21.1561i	−0.515238	−	0.892418i
$563$	15.1558	−	26.2506i	0.638740	−	1.10633i	−0.346969	−	0.937877i	$-0.612789\pi$
$563$	15.1558	−	26.2506i	0.638740	−	1.10633i	0.985709	−	0.168454i	$-0.0538776\pi$
$564$	−5.07462	+	8.78951i	−0.213680	+	0.370105i
$565$	18.1768	+	31.4831i	0.764703	+	1.32451i
$566$	3.19125			0.134138
$567$	−0.155792	+	2.64116i	−0.00654263	+	0.110918i
$568$	12.6884			0.532394
$569$	−9.04708	−	15.6700i	−0.379273	−	0.656921i	0.611683	−	0.791103i	$-0.290493\pi$
$569$	−9.04708	−	15.6700i	−0.379273	−	0.656921i	−0.990957	+	0.134182i	$0.957159\pi$
$570$	4.59562	−	7.95985i	0.192489	−	0.333402i
$571$	6.21450	−	10.7638i	0.260069	−	0.450452i	−0.706191	−	0.708021i	$-0.749588\pi$
$571$	6.21450	−	10.7638i	0.260069	−	0.450452i	0.966260	+	0.257569i	$0.0829215\pi$
$572$	2.36521	+	4.09666i	0.0988943	+	0.171290i
$573$	−10.2985			−0.430226
$574$	1.97246	+	1.29940i	0.0823288	+	0.0542358i
$575$	−24.9506			−1.04051
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	1.04854	−	1.81613i	0.0436514	−	0.0756064i	−0.843374	−	0.537327i	$-0.819434\pi$
$577$	1.04854	−	1.81613i	0.0436514	−	0.0756064i	0.887026	+	0.461720i	$0.152768\pi$
$578$	21.8862	−	37.9080i	0.910346	−	1.57677i
$579$	8.81667	+	15.2709i	0.366408	+	0.634637i
$580$	10.2565			0.425878
$581$	2.21088	−	1.10830i	0.0917226	−	0.0459799i
$582$	−4.79567			−0.198787
$583$	−21.7942	−	37.7487i	−0.902624	−	1.56339i
$584$	5.86521	−	10.1588i	0.242704	−	0.420376i
$585$	1.70942	−	2.96080i	0.0706757	−	0.122414i
$586$	1.29058	+	2.23536i	0.0533135	+	0.0923417i
$587$	47.7826			1.97220			0.986099	−	0.166158i	$-0.0531363\pi$
$587$	47.7826			1.97220			0.986099	+	0.166158i	$0.0531363\pi$
$588$	6.95146	+	0.822941i	0.286673	+	0.0339375i
$589$	−15.2928			−0.630130
$590$	10.4398	+	18.0823i	0.429801	+	0.744437i
$591$	−4.13479	+	7.16167i	−0.170083	+	0.294592i
$592$	1.55362	−	2.69096i	0.0638536	−	0.110598i
$593$	4.66087	+	8.07287i	0.191399	+	0.331513i	0.945714	−	0.325000i	$-0.105364\pi$
$593$	4.66087	+	8.07287i	0.191399	+	0.331513i	−0.754315	+	0.656513i	$0.772031\pi$
$594$	−4.73042			−0.194091
$595$	−63.0377	+	31.6003i	−2.58429	+	1.29549i
$596$	−8.26958			−0.338735
$597$	−2.51163	−	4.35026i	−0.102794	−	0.178044i
$598$	−1.86521	+	3.23063i	−0.0762740	+	0.132110i
$599$	2.82321	−	4.88994i	0.115353	−	0.199798i	−0.802568	−	0.596561i	$-0.796533\pi$
$599$	2.82321	−	4.88994i	0.115353	−	0.199798i	0.917921	+	0.396763i	$0.129867\pi$
$600$	−3.34421	−	5.79234i	−0.136527	−	0.236471i
$601$	−19.3450			−0.789099			−0.394550	−	0.918875i	$-0.629099\pi$
$601$	−19.3450			−0.789099			−0.394550	+	0.918875i	$0.629099\pi$
$602$	−28.3637	−	18.6852i	−1.15602	−	0.761553i
$603$	−0.0652506			−0.00265721
$604$	2.63479	+	4.56359i	0.107208	+	0.185690i
$605$	19.4477	−	33.6845i	0.790663	−	1.36947i
$606$	−0.311583	+	0.539678i	−0.0126572	+	0.0219229i
$607$	−21.4818	−	37.2076i	−0.871921	−	1.51021i	−0.860007	−	0.510282i	$-0.829541\pi$
$607$	−21.4818	−	37.2076i	−0.871921	−	1.51021i	−0.0119134	−	0.999929i	$-0.503792\pi$
$608$	−2.68842			−0.109030
$609$	−0.467375	+	7.92348i	−0.0189390	+	0.321076i
$610$	10.4001			0.421087
$611$	5.07462	+	8.78951i	0.205297	+	0.355585i
$612$	−3.89783	+	6.75125i	−0.157561	+	0.272903i
$613$	−13.9449	+	24.1533i	−0.563230	+	0.975543i	0.433982	+	0.900921i	$0.357108\pi$
$613$	−13.9449	+	24.1533i	−0.563230	+	0.975543i	−0.997212	+	0.0746212i	$0.976225\pi$
$614$	11.6558	+	20.1884i	0.470389	+	0.814738i
$615$	3.05216			0.123075
$616$	−0.736959	+	12.4938i	−0.0296929	+	0.503389i
$617$	41.4347			1.66810			0.834048	−	0.551691i	$-0.186017\pi$
$617$	41.4347			1.66810			0.834048	+	0.551691i	$0.186017\pi$
$618$	−4.41883	−	7.65364i	−0.177752	−	0.307875i
$619$	15.3116	−	26.5204i	0.615424	−	1.06595i	−0.374885	−	0.927071i	$-0.622318\pi$
$619$	15.3116	−	26.5204i	0.615424	−	1.06595i	0.990310	−	0.138875i	$-0.0443487\pi$
$620$	−9.72387	+	16.8422i	−0.390520	+	0.676401i
$621$	−1.86521	−	3.23063i	−0.0748482	−	0.129641i
$622$	−10.7826			−0.432342
$623$	−33.3782	−	21.9886i	−1.33727	−	0.880955i
$624$	−1.00000			−0.0400320
$625$	6.85358	+	11.8708i	0.274143	+	0.474830i
$626$	7.42538	−	12.8611i	0.296778	−	0.514034i
$627$	−6.35866	+	11.0135i	−0.253941	+	0.439838i
$628$	5.62825	+	9.74841i	0.224592	+	0.389004i
$629$	−24.2231			−0.965837
$630$	8.08625	−	4.05358i	0.322164	−	0.161498i
$631$	−12.9347			−0.514924			−0.257462	−	0.966288i	$-0.582886\pi$
$631$	−12.9347			−0.514924			−0.257462	+	0.966288i	$0.582886\pi$
$632$	7.26304	+	12.5800i	0.288908	+	0.500404i
$633$	7.28404	−	12.6163i	0.289515	−	0.501454i
$634$	11.5326	−	19.9751i	0.458019	−	0.793312i
$635$	−10.5514	−	18.2755i	−0.418718	−	0.725242i
$636$	9.21450			0.365379
$637$	4.18842	−	5.60867i	0.165951	−	0.222224i
$638$	−14.1912			−0.561837
$639$	6.34421	+	10.9885i	0.250973	+	0.434698i
$640$	−1.70942	+	2.96080i	−0.0675706	+	0.117036i
$641$	3.46083	−	5.99434i	0.136695	−	0.236762i	−0.789549	−	0.613688i	$-0.789685\pi$
$641$	3.46083	−	5.99434i	0.136695	−	0.236762i	0.926244	+	0.376926i	$0.123019\pi$
$642$	−2.88621	−	4.99906i	−0.113910	−	0.197297i
$643$	−19.2276			−0.758262			−0.379131	−	0.925343i	$-0.623777\pi$
$643$	−19.2276			−0.758262			−0.379131	+	0.925343i	$0.623777\pi$
$644$	−8.82321	+	4.42301i	−0.347683	+	0.174291i
$645$	−43.8898			−1.72816
$646$	10.4790	+	18.1502i	0.412291	+	0.714109i
$647$	−3.52608	+	6.10735i	−0.138625	+	0.240105i	−0.926976	−	0.375120i	$-0.877601\pi$
$647$	−3.52608	+	6.10735i	−0.138625	+	0.240105i	0.788352	+	0.615225i	$0.210935\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−14.4449	−	25.0193i	−0.567013	−	0.982094i
$650$	−6.68842			−0.262341
$651$	−12.5681	−	8.27949i	−0.492582	−	0.324499i
$652$	16.3637			0.640854
$653$	1.50937	+	2.61431i	0.0590664	+	0.102306i	0.894047	−	0.447974i	$-0.147854\pi$
$653$	1.50937	+	2.61431i	0.0590664	+	0.102306i	−0.834980	+	0.550280i	$0.814521\pi$
$654$	−2.00000	+	3.46410i	−0.0782062	+	0.135457i
$655$	−34.9935	+	60.6104i	−1.36731	+	2.36825i
$656$	−0.446375	−	0.773145i	−0.0174280	−	0.0301862i
$657$	11.7304			0.457647
$658$	−1.58117	+	26.8058i	−0.0616403	+	1.04500i
$659$	−12.3536			−0.481227			−0.240614	−	0.970621i	$-0.577349\pi$
$659$	−12.3536			−0.481227			−0.240614	+	0.970621i	$0.577349\pi$
$660$	8.08625	+	14.0058i	0.314757	+	0.545175i
$661$	−20.2942	+	35.1506i	−0.789353	+	1.36720i	0.137011	+	0.990570i	$0.456251\pi$
$661$	−20.2942	+	35.1506i	−0.789353	+	1.36720i	−0.926364	+	0.376630i	$0.877083\pi$
$662$	0.0652506	−	0.113017i	0.00253604	−	0.00439254i
$663$	3.89783	+	6.75125i	0.151379	+	0.262197i
$664$	−0.934749			−0.0362753
$665$	1.43192	−	24.2756i	0.0555274	−	0.941366i
$666$	3.10725			0.120403
$667$	−5.59562	−	9.69190i	−0.216663	−	0.375272i
$668$	−11.4935	+	19.9073i	−0.444695	+	0.770235i
$669$	−5.16087	+	8.93890i	−0.199531	+	0.345598i
$670$	0.111540	+	0.193194i	0.00430918	+	0.00746372i
$671$	−14.3899			−0.555517
$672$	−2.20942	−	1.45550i	−0.0852301	−	0.0561471i
$673$	28.5261			1.09960			0.549800	−	0.835296i	$-0.314704\pi$
$673$	28.5261			1.09960			0.549800	+	0.835296i	$0.314704\pi$
$674$	8.02608	+	13.9016i	0.309153	+	0.535469i
$675$	3.34421	−	5.79234i	0.128719	−	0.222947i
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	9.06808	+	15.7064i	0.348515	+	0.603645i	0.985986	−	0.166829i	$-0.0533528\pi$
$677$	9.06808	+	15.7064i	0.348515	+	0.603645i	−0.637471	+	0.770474i	$0.720019\pi$
$678$	10.6333			0.408371
$679$	−11.3427	+	5.68603i	−0.435295	+	0.218210i
$680$	26.6521			1.02206
$681$	2.22104	+	3.84696i	0.0851105	+	0.147416i
$682$	13.4543	−	23.3035i	0.515191	−	0.892338i
$683$	−5.59788	+	9.69581i	−0.214197	+	0.371000i	−0.953024	−	0.302895i	$-0.902047\pi$
$683$	−5.59788	+	9.69581i	−0.214197	+	0.371000i	0.738827	+	0.673895i	$0.235380\pi$
$684$	−1.34421	−	2.32824i	−0.0513971	−	0.0890224i
$685$	37.9738			1.45091
$686$	17.4174	−	6.29564i	0.664998	−	0.240369i
$687$	21.4608			0.818782
$688$	6.41883	+	11.1177i	0.244716	+	0.423860i
$689$	4.60725	−	7.97999i	0.175522	−	0.304013i
$690$	−6.37683	+	11.0450i	−0.242762	+	0.420476i
$691$	0.320957	+	0.555913i	0.0122098	+	0.0211479i	0.872066	−	0.489389i	$-0.162780\pi$
$691$	0.320957	+	0.555913i	0.0122098	+	0.0211479i	−0.859856	+	0.510537i	$0.829447\pi$
$692$	10.7724			0.409506
$693$	−11.1884	+	5.60867i	−0.425013	+	0.213056i
$694$	−21.3217			−0.809363
$695$	−3.87966	−	6.71978i	−0.147164	−	0.254896i
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	−3.47979	+	6.02718i	−0.131807	+	0.228296i
$698$	3.17679	+	5.50236i	0.120243	+	0.208268i
$699$	7.66517			0.289923
$700$	−14.7775	−	9.73499i	−0.558537	−	0.367948i
$701$	30.0334			1.13435			0.567173	−	0.823599i	$-0.308037\pi$
$701$	30.0334			1.13435			0.567173	+	0.823599i	$0.308037\pi$
$702$	−0.500000	−	0.866025i	−0.0188713	−	0.0326860i
$703$	4.17679	−	7.23441i	0.157531	−	0.272851i
$704$	2.36521	−	4.09666i	0.0891421	−	0.154399i
$705$	17.3493	+	30.0499i	0.653412	+	1.13174i
$706$	−30.4290			−1.14521
$707$	−0.0970840	+	1.64588i	−0.00365122	+	0.0618998i
$708$	6.10725			0.229524
$709$	−15.1217	−	26.1916i	−0.567908	−	0.983645i	−0.996773	−	0.0802762i	$-0.974420\pi$
$709$	−15.1217	−	26.1916i	−0.567908	−	0.983645i	0.428865	−	0.903369i	$-0.358914\pi$
$710$	21.6898	−	37.5678i	0.814003	−	1.40989i
$711$	−7.26304	+	12.5800i	−0.272385	+	0.471785i
$712$	7.55362	+	13.0833i	0.283084	+	0.490316i
$713$	21.2202			0.794701
$714$	−1.21450	+	20.5896i	−0.0454515	+	0.770547i
$715$	16.1725			0.604817
$716$	−9.52608	−	16.4997i	−0.356006	−	0.616621i
$717$	−4.76304	+	8.24983i	−0.177879	+	0.308096i
$718$	−9.00000	+	15.5885i	−0.335877	+	0.581756i
$719$	−21.2985	−	36.8901i	−0.794300	−	1.37577i	−0.923283	−	0.384121i	$-0.874505\pi$
$719$	−21.2985	−	36.8901i	−0.794300	−	1.37577i	0.128983	−	0.991647i	$-0.458829\pi$
$720$	−3.41883			−0.127412
$721$	−19.5261	−	12.8632i	−0.727189	−	0.479051i
$722$	11.7724			0.438124
$723$	−3.68187	−	6.37719i	−0.136930	−	0.237170i
$724$	−6.89783	+	11.9474i	−0.256356	+	0.444022i
$725$	10.0326	−	17.3770i	0.372602	−	0.645366i
$726$	−5.68842	−	9.85263i	−0.211117	−	0.365665i
$727$	19.3637			0.718162			0.359081	−	0.933306i	$-0.383090\pi$
$727$	19.3637			0.718162			0.359081	+	0.933306i	$0.383090\pi$
$728$	−2.36521	+	1.18566i	−0.0876604	+	0.0439435i
$729$	1.00000			0.0370370
$730$	−20.0522	−	34.7314i	−0.742164	−	1.28547i
$731$	50.0391	−	86.6702i	1.85076	−	3.20561i
$732$	1.52100	−	2.63445i	0.0562178	−	0.0973720i
$733$	−13.0377	−	22.5820i	−0.481559	−	0.834084i	0.518217	−	0.855249i	$-0.326596\pi$
$733$	−13.0377	−	22.5820i	−0.481559	−	0.834084i	−0.999776	+	0.0211648i	$0.993263\pi$
$734$	−4.22759			−0.156043
$735$	14.3195	−	19.1751i	0.528183	−	0.707284i
$736$	3.73042			0.137505
$737$	−0.154331	−	0.267310i	−0.00568486	−	0.00984647i
$738$	0.446375	−	0.773145i	0.0164313	−	0.0284598i
$739$	10.3217	−	17.8778i	0.379692	−	0.657645i	−0.611326	−	0.791379i	$-0.709363\pi$
$739$	10.3217	−	17.8778i	0.379692	−	0.657645i	0.991017	+	0.133734i	$0.0426968\pi$
$740$	−5.31158	−	9.19993i	−0.195258	−	0.338196i
$741$	−2.68842			−0.0987615
$742$	21.7942	−	10.9253i	0.800090	−	0.401079i
$743$	−2.81892			−0.103416			−0.0517080	−	0.998662i	$-0.516467\pi$
$743$	−2.81892			−0.103416			−0.0517080	+	0.998662i	$0.516467\pi$
$744$	2.84421	+	4.92631i	0.104274	+	0.180607i
$745$	−14.1362	+	24.4846i	−0.517909	+	0.897045i
$746$	−17.8427	+	30.9045i	−0.653269	+	1.13150i
$747$	−0.467375	−	0.809517i	−0.0171003	−	0.0296187i
$748$	−36.8767			−1.34835
$749$	−12.7537	−	8.40175i	−0.466009	−	0.306993i
$750$	−5.77241			−0.210779
$751$	8.03546	+	13.9178i	0.293218	+	0.507868i	0.974569	−	0.224089i	$-0.0719405\pi$
$751$	8.03546	+	13.9178i	0.293218	+	0.507868i	−0.681351	+	0.731957i	$0.738607\pi$
$752$	5.07462	−	8.78951i	0.185053	−	0.320520i
$753$	6.37029	−	11.0337i	0.232146	−	0.402089i
$754$	−1.50000	−	2.59808i	−0.0546268	−	0.0946164i
$755$	18.0158			0.655663
$756$	0.155792	−	2.64116i	0.00566608	−	0.0960581i
$757$	5.34050			0.194104			0.0970518	−	0.995279i	$-0.469059\pi$
$757$	5.34050			0.194104			0.0970518	+	0.995279i	$0.469059\pi$
$758$	4.83767	+	8.37908i	0.175712	+	0.304342i
$759$	8.82321	−	15.2822i	0.320262	−	0.554710i
$760$	−4.59562	+	7.95985i	−0.166701	+	0.288734i
$761$	18.1594	+	31.4530i	0.658278	+	1.14017i	0.981061	+	0.193698i	$0.0620483\pi$
$761$	18.1594	+	31.4530i	0.658278	+	1.14017i	−0.322783	+	0.946473i	$0.604618\pi$
$762$	−6.17250			−0.223606
$763$	−0.623166	+	10.5646i	−0.0225601	+	0.382466i
$764$	10.2985			0.372587
$765$	13.3260	+	23.0814i	0.481804	+	0.834509i
$766$	−1.83767	+	3.18293i	−0.0663975	+	0.115004i
$767$	3.05362	−	5.28903i	0.110260	−	0.190976i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	39.9783			1.44166			0.720828	−	0.693114i	$-0.243762\pi$
$769$	39.9783			1.44166			0.720828	+	0.693114i	$0.243762\pi$
$770$	35.7318	+	23.5391i	1.28768	+	0.848289i
$771$	13.4608			0.484780
$772$	−8.81667	−	15.2709i	−0.317319	−	0.549612i
$773$	−9.29850	+	16.1055i	−0.334444	+	0.579273i	−0.983378	−	0.181571i	$-0.941882\pi$
$773$	−9.29850	+	16.1055i	−0.334444	+	0.579273i	0.648934	+	0.760845i	$0.275215\pi$
$774$	−6.41883	+	11.1177i	−0.230720	+	0.399619i
$775$	19.0233	+	32.9492i	0.683335	+	1.18357i
$776$	4.79567			0.172154
$777$	7.34929	−	3.68414i	0.263654	−	0.132168i
$778$	−6.47392			−0.232101
$779$	−1.20004	−	2.07853i	−0.0429960	−	0.0744712i
$780$	−1.70942	+	2.96080i	−0.0612069	+	0.106014i
$781$	−30.0107	+	51.9801i	−1.07387	+	1.86000i
$782$	−14.5405	−	25.1850i	−0.519969	−	0.900612i
$783$	3.00000			0.107211
$784$	−6.95146	−	0.822941i	−0.248266	−	0.0293908i
$785$	38.4841			1.37356
$786$	10.2355	+	17.7284i	0.365088	+	0.632351i
$787$	−0.386207	+	0.668931i	−0.0137668	+	0.0238448i	−0.872827	−	0.488030i	$-0.837716\pi$
$787$	−0.386207	+	0.668931i	−0.0137668	+	0.0238448i	0.859060	+	0.511875i	$0.171049\pi$
$788$	4.13479	−	7.16167i	0.147296	−	0.255124i
$789$	12.0145	+	20.8096i	0.427726	+	0.740843i
$790$	49.6622			1.76690
$791$	25.1500	−	12.6075i	0.894232	−	0.448272i
$792$	4.73042			0.168088
$793$	−1.52100	−	2.63445i	−0.0540123	−	0.0935520i
$794$	−3.93046	+	6.80775i	−0.139487	+	0.241598i
$795$	15.7514	−	27.2823i	0.558645	−	0.967602i
$796$	2.51163	+	4.35026i	0.0890222	+	0.154191i
$797$	7.10275			0.251592			0.125796	−	0.992056i	$-0.459851\pi$
$797$	7.10275			0.251592			0.125796	+	0.992056i	$0.459851\pi$
$798$	−5.93983	−	3.91299i	−0.210268	−	0.138518i
$799$	−79.1202			−2.79907
$800$	3.34421	+	5.79234i	0.118236	+	0.204790i
$801$	−7.55362	+	13.0833i	−0.266894	+	0.462274i
$802$	−2.82321	+	4.88994i	−0.0996910	+	0.172670i
$803$	27.7449	+	48.0555i	0.979095	+	1.69584i
$804$	0.0652506			0.00230121
$805$	−1.98691	+	33.6845i	−0.0700295	+	1.18722i
$806$	5.68842			0.200366
$807$	7.96083	+	13.7886i	0.280235	+	0.485380i
$808$	0.311583	−	0.539678i	0.0109615	−	0.0189858i
$809$	10.3399	−	17.9093i	0.363532	−	0.629656i	−0.625007	−	0.780619i	$-0.714904\pi$
$809$	10.3399	−	17.9093i	0.363532	−	0.629656i	0.988539	+	0.150963i	$0.0482374\pi$
$810$	−1.70942	−	2.96080i	−0.0600628	−	0.104032i
$811$	36.2985			1.27461			0.637306	−	0.770611i	$-0.280049\pi$
$811$	36.2985			1.27461			0.637306	+	0.770611i	$0.280049\pi$
$812$	0.467375	−	7.92348i	0.0164016	−	0.278060i
$813$	19.6521			0.689229
$814$	7.34929	+	12.7293i	0.257593	+	0.446163i
$815$	27.9725	−	48.4497i	0.979832	−	1.69712i
$816$	3.89783	−	6.75125i	0.136451	−	0.236341i
$817$	17.2565	+	29.8891i	0.603728	+	1.04569i
$818$	−25.7173			−0.899185
$819$	−2.20942	−	1.45550i	−0.0772033	−	0.0508593i
$820$	−3.05216			−0.106586
$821$	26.0964	+	45.2003i	0.910771	+	1.57750i	0.812977	+	0.582295i	$0.197845\pi$
$821$	26.0964	+	45.2003i	0.910771	+	1.57750i	0.0977938	+	0.995207i	$0.468821\pi$
$822$	5.55362	−	9.61916i	0.193705	−	0.335507i
$823$	−19.5536	+	33.8679i	−0.681597	+	1.18056i	0.292897	+	0.956144i	$0.405381\pi$
$823$	−19.5536	+	33.8679i	−0.681597	+	1.18056i	−0.974493	+	0.224416i	$0.927953\pi$
$824$	4.41883	+	7.65364i	0.153937	+	0.266627i
$825$	31.6390			1.10153
$826$	14.4449	−	7.24113i	0.502603	−	0.251951i
$827$	−51.6724			−1.79683			−0.898413	−	0.439152i	$-0.855279\pi$
$827$	−51.6724			−1.79683			−0.898413	+	0.439152i	$0.855279\pi$
$828$	1.86521	+	3.23063i	0.0648205	+	0.112272i
$829$	15.9920	−	27.6990i	0.555425	−	0.962024i	−0.442445	−	0.896795i	$-0.645889\pi$
$829$	15.9920	−	27.6990i	0.555425	−	0.962024i	0.997870	−	0.0652288i	$-0.0207777\pi$
$830$	−1.59788	+	2.76760i	−0.0554631	+	0.0960649i
$831$	−2.58625	−	4.47952i	−0.0897160	−	0.155393i
$832$	1.00000			0.0346688
$833$	21.5397	+	50.1387i	0.746308	+	1.73720i
$834$	−2.26958			−0.0785893
$835$	39.2942	+	68.0596i	1.35983	+	2.35530i
$836$	6.35866	−	11.0135i	0.219919	−	0.380911i
$837$	−2.84421	+	4.92631i	−0.0983102	+	0.170278i
$838$	4.41883	+	7.65364i	0.152646	+	0.264391i
$839$	−18.0187			−0.622076			−0.311038	−	0.950397i	$-0.600677\pi$
$839$	−18.0187			−0.622076			−0.311038	+	0.950397i	$0.600677\pi$
$840$	−8.08625	+	4.05358i	−0.279002	+	0.139862i
$841$	−20.0000			−0.689655
$842$	−5.07971	−	8.79831i	−0.175058	−	0.303210i
$843$	−12.2145	+	21.1561i	−0.420690	+	0.728656i
$844$	−7.28404	+	12.6163i	−0.250727	+	0.434272i
$845$	1.70942	+	2.96080i	0.0588057	+	0.101854i
$846$	10.1492			0.348938
$847$	−25.1362	−	16.5590i	−0.863689	−	0.568973i
$848$	−9.21450			−0.316427
$849$	−1.59562	−	2.76370i	−0.0547617	−	0.0948500i
$850$	26.0703	−	45.1551i	0.894205	−	1.54881i
$851$	−5.79567	+	10.0384i	−0.198673	+	0.344112i
$852$	−6.34421	−	10.9885i	−0.217349	−	0.376460i
$853$	49.1651			1.68338			0.841690	−	0.539961i	$-0.181561\pi$
$853$	49.1651			1.68338			0.841690	+	0.539961i	$0.181561\pi$
$854$	0.473918	−	8.03441i	0.0162171	−	0.274932i
$855$	−9.19125			−0.314334
$856$	2.88621	+	4.99906i	0.0986485	+	0.170864i
$857$	−18.8007	+	32.5639i	−0.642221	+	1.11236i	0.342714	+	0.939440i	$0.388654\pi$
$857$	−18.8007	+	32.5639i	−0.642221	+	1.11236i	−0.984936	+	0.172920i	$0.944680\pi$
$858$	2.36521	−	4.09666i	0.0807469	−	0.139858i
$859$	2.89275	+	5.01039i	0.0986994	+	0.170952i	0.911147	−	0.412082i	$-0.135198\pi$
$859$	2.89275	+	5.01039i	0.0986994	+	0.170952i	−0.812447	+	0.583035i	$0.801865\pi$
$860$	43.8898			1.49663
$861$	0.139083	−	2.35790i	0.00473994	−	0.0803569i
$862$	11.6753			0.397663
$863$	−9.46083	−	16.3866i	−0.322050	−	0.557808i	0.658861	−	0.752265i	$-0.271039\pi$
$863$	−9.46083	−	16.3866i	−0.322050	−	0.557808i	−0.980911	+	0.194457i	$0.937705\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	18.4145	−	31.8949i	0.626113	−	1.08446i
$866$	3.30221	+	5.71959i	0.112214	+	0.194360i
$867$	−43.7724			−1.48659
$868$	12.5681	+	8.27949i	0.426588	+	0.281024i
$869$	−68.7144			−2.33098
$870$	−5.12825	−	8.88239i	−0.173864	−	0.301141i
$871$	0.0326253	−	0.0565087i	0.00110547	−	0.00191472i
$872$	2.00000	−	3.46410i	0.0677285	−	0.117309i
$873$	2.39783	+	4.15317i	0.0811544	+	0.140563i
$874$	10.0289			0.339233
$875$	−13.6530	+	6.84413i	−0.461554	+	0.231374i
$876$	−11.7304			−0.396334
$877$	15.1870	+	26.3046i	0.512827	+	0.888243i	0.999889	+	0.0148753i	$0.00473514\pi$
$877$	15.1870	+	26.3046i	0.512827	+	0.888243i	−0.487062	+	0.873367i	$0.661932\pi$
$878$	−12.5051	+	21.6594i	−0.422026	+	0.730971i
$879$	1.29058	−	2.23536i	0.0435303	−	0.0753967i
$880$	−8.08625	−	14.0058i	−0.272587	−	0.472135i
$881$	−42.0578			−1.41696			−0.708482	−	0.705729i	$-0.750620\pi$
$881$	−42.0578			−1.41696			−0.708482	+	0.705729i	$0.750620\pi$
$882$	−2.76304	−	6.43161i	−0.0930364	−	0.216564i
$883$	8.84625			0.297700			0.148850	−	0.988860i	$-0.452443\pi$
$883$	8.84625			0.297700			0.148850	+	0.988860i	$0.452443\pi$
$884$	−3.89783	−	6.75125i	−0.131098	−	0.227069i
$885$	10.4398	−	18.0823i	0.350931	−	0.607831i
$886$	−8.43983	+	14.6182i	−0.283542	+	0.491109i
$887$	−22.2797	−	38.5897i	−0.748081	−	1.29571i	−0.948741	−	0.316053i	$-0.897642\pi$
$887$	−22.2797	−	38.5897i	−0.748081	−	1.29571i	0.200661	−	0.979661i	$-0.435691\pi$
$888$	−3.10725			−0.104272
$889$	−14.5992	+	7.31849i	−0.489643	+	0.245454i
$890$	51.6492			1.73128
$891$	2.36521	+	4.09666i	0.0792374	+	0.137243i
$892$	5.16087	−	8.93890i	0.172799	−	0.299296i
$893$	13.6427	−	23.6299i	0.456536	−	0.790743i
$894$	4.13479	+	7.16167i	0.138288	+	0.239522i
$895$	−65.1362			−2.17726
$896$	2.20942	+	1.45550i	0.0738114	+	0.0486248i
$897$	3.73042			0.124555
$898$	−10.0840	−	17.4660i	−0.336507	−	0.582848i
$899$	−8.53263	+	14.7789i	−0.284579	+	0.492905i
$900$	−3.34421	+	5.79234i	−0.111474	+	0.193078i
$901$	35.9166	+	62.2093i	1.19655	+	2.07249i
$902$	4.22308			0.140613
$903$	−2.00000	+	33.9063i	−0.0665558	+	1.12833i
$904$	−10.6333			−0.353659
$905$	23.5825	+	40.8462i	0.783910	+	1.35777i
$906$	2.63479	−	4.56359i	0.0875351	−	0.151615i
$907$	21.0145	−	36.3981i	0.697774	−	1.20858i	−0.271463	−	0.962449i	$-0.587508\pi$
$907$	21.0145	−	36.3981i	0.697774	−	1.20858i	0.969237	−	0.246130i	$-0.0791592\pi$
$908$	−2.22104	−	3.84696i	−0.0737079	−	0.127666i
$909$	0.623166			0.0206691
$910$	−0.532625	+	9.02969i	−0.0176564	+	0.299331i
$911$	46.0000			1.52405			0.762024	−	0.647549i	$-0.224206\pi$
$911$	46.0000			1.52405			0.762024	+	0.647549i	$0.224206\pi$
$912$	1.34421	+	2.32824i	0.0445112	+	0.0770956i
$913$	2.21088	−	3.82935i	0.0731693	−	0.126733i
$914$	−8.12825	+	14.0785i	−0.268859	+	0.465677i
$915$	−5.20004	−	9.00674i	−0.171908	−	0.297754i
$916$	−21.4608			−0.709086
$917$	45.2290	+	29.7955i	1.49359	+	0.983935i
$918$	7.79567			0.257295
$919$	−4.95800	−	8.58751i	−0.163549	−	0.283276i	0.772590	−	0.634905i	$-0.218961\pi$
$919$	−4.95800	−	8.58751i	−0.163549	−	0.283276i	−0.936139	+	0.351630i	$0.885628\pi$
$920$	6.37683	−	11.0450i	0.210238	−	0.364143i
$921$	11.6558	−	20.1884i	0.384071	−	0.665231i
$922$	−8.04200	−	13.9292i	−0.264849	−	0.458732i
$923$	−12.6884			−0.417644
$924$	11.1884	−	5.60867i	0.368072	−	0.184512i
$925$	−20.7826			−0.683327
$926$	0.837665	+	1.45088i	0.0275274	+	0.0476788i
$927$	−4.41883	+	7.65364i	−0.145134	+	0.251379i
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$	10.1492	+	17.5790i	0.332986	+	0.576749i	0.983096	−	0.183092i	$-0.0586105\pi$
$929$	10.1492	+	17.5790i	0.332986	+	0.576749i	−0.650110	+	0.759840i	$0.725277\pi$
$930$	19.4477			0.637717
$931$	−18.6884	−	2.21241i	−0.612488	−	0.0725088i
$932$	−7.66517			−0.251081
$933$	5.39129	+	9.33799i	0.176503	+	0.305712i
$934$	15.9725	−	27.6651i	0.522635	−	0.905230i
$935$	−63.0377	+	109.185i	−2.06155	+	3.57072i
$936$	0.500000	+	0.866025i	0.0163430	+	0.0283069i
$937$	−34.2667			−1.11944			−0.559722	−	0.828681i	$-0.689092\pi$
$937$	−34.2667			−1.11944			−0.559722	+	0.828681i	$0.689092\pi$
$938$	0.154331	−	0.0773651i	0.00503909	−	0.00252606i
$939$	−14.8508			−0.484636
$940$	−17.3493	−	30.0499i	−0.565871	−	0.980118i
$941$	12.5746	−	21.7799i	0.409921	−	0.710004i	−0.584959	−	0.811063i	$-0.698890\pi$
$941$	12.5746	−	21.7799i	0.409921	−	0.710004i	0.994880	+	0.101058i	$0.0322229\pi$
$942$	5.62825	−	9.74841i	0.183378	−	0.317620i
$943$	1.66517	+	2.88415i	0.0542252	+	0.0939209i
$944$	−6.10725			−0.198774
$945$	−7.55362	−	4.97611i	−0.245719	−	0.161873i
$946$	−60.7275			−1.97442
$947$	−13.6050	−	23.5645i	−0.442103	−	0.765745i	0.555742	−	0.831355i	$-0.312434\pi$
$947$	−13.6050	−	23.5645i	−0.442103	−	0.765745i	−0.997845	+	0.0656097i	$0.979101\pi$
$948$	7.26304	−	12.5800i	0.235893	−	0.408578i
$949$	−5.86521	+	10.1588i	−0.190393	+	0.329770i
$950$	8.99063	+	15.5722i	0.291694	+	0.505230i
$951$	−23.0653			−0.747942
$952$	1.21450	−	20.5896i	0.0393621	−	0.667313i
$953$	54.5028			1.76552			0.882760	−	0.469824i	$-0.155683\pi$
$953$	54.5028			1.76552			0.882760	+	0.469824i	$0.155683\pi$
$954$	−4.60725	−	7.97999i	−0.149165	−	0.258362i
$955$	17.6044	−	30.4917i	0.569666	−	0.986690i
$956$	4.76304	−	8.24983i	0.154048	−	0.266819i
$957$	7.09562	+	12.2900i	0.229369	+	0.397279i
$958$	−37.6941			−1.21784
$959$	1.73042	−	29.3360i	0.0558780	−	0.947310i
$960$	3.41883			0.110342
$961$	−0.679043	−	1.17614i	−0.0219046	−	0.0379399i
$962$	−1.55362	+	2.69096i	−0.0500909	+	0.0867599i
$963$	−2.88621	+	4.99906i	−0.0930067	+	0.161092i
$964$	3.68187	+	6.37719i	0.118585	+	0.205396i
$965$	−60.2854			−1.94066
$966$	8.24204	+	5.42962i	0.265183	+	0.174695i
$967$	−13.9767			−0.449462			−0.224731	−	0.974421i	$-0.572150\pi$
$967$	−13.9767			−0.449462			−0.224731	+	0.974421i	$0.572150\pi$
$968$	5.68842	+	9.85263i	0.182833	+	0.316675i
$969$	10.4790	−	18.1502i	0.336634	−	0.583067i
$970$	8.19779	−	14.1990i	0.263215	−	0.455902i
$971$	17.9892	+	31.1581i	0.577300	+	0.999913i	0.995788	+	0.0916902i	$0.0292269\pi$
$971$	17.9892	+	31.1581i	0.577300	+	0.999913i	−0.418488	+	0.908222i	$0.637440\pi$
$972$	−1.00000			−0.0320750
$973$	−5.36804	+	2.69096i	−0.172091	+	0.0862681i
$974$	4.94491			0.158445
$975$	3.34421	+	5.79234i	0.107100	+	0.185503i
$976$	−1.52100	+	2.63445i	−0.0486860	+	0.0843266i
$977$	−6.73042	+	11.6574i	−0.215325	+	0.372954i	−0.953373	−	0.301794i	$-0.902414\pi$
$977$	−6.73042	+	11.6574i	−0.215325	+	0.372954i	0.738048	+	0.674748i	$0.235748\pi$
$978$	−8.18187	−	14.1714i	−0.261627	−	0.453152i
$979$	−71.4636			−2.28399
$980$	−14.3195	+	19.1751i	−0.457420	+	0.612526i
$981$	4.00000			0.127710
$982$	14.1007	+	24.4231i	0.449972	+	0.779374i
$983$	−1.03263	+	1.78856i	−0.0329356	+	0.0570462i	−0.882023	−	0.471206i	$-0.843819\pi$
$983$	−1.03263	+	1.78856i	−0.0329356	+	0.0570462i	0.849088	+	0.528252i	$0.177152\pi$
$984$	−0.446375	+	0.773145i	−0.0142299	+	0.0246469i
$985$	−14.1362	−	24.4846i	−0.450416	−	0.780143i
$986$	23.3870			0.744794
$987$	24.0051	−	12.0336i	0.764090	−	0.383033i
$988$	2.68842			0.0855299
$989$	−23.9449	−	41.4738i	−0.761404	−	1.31879i
$990$	8.08625	−	14.0058i	0.256998	−	0.445133i
$991$	11.5094	−	19.9348i	0.365607	−	0.633250i	−0.623266	−	0.782010i	$-0.714195\pi$
$991$	11.5094	−	19.9348i	0.365607	−	0.633250i	0.988873	+	0.148759i	$0.0475280\pi$
$992$	−2.84421	−	4.92631i	−0.0903037	−	0.156411i
$993$	−0.130501			−0.00414133
$994$	−28.0340	−	18.4680i	−0.889184	−	0.585769i
$995$	17.1737			0.544442
$996$	0.467375	+	0.809517i	0.0148093	+	0.0256505i
$997$	13.1963	−	22.8567i	0.417932	−	0.723879i	−0.577799	−	0.816179i	$-0.696088\pi$
$997$	13.1963	−	22.8567i	0.417932	−	0.723879i	0.995731	+	0.0922995i	$0.0294217\pi$
$998$	9.87966	−	17.1121i	0.312735	−	0.541673i
$999$	−1.55362	−	2.69096i	−0.0491545	−	0.0851381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.k.235.3	yes	6
3.2	odd	2		1638.2.j.q.235.1		6
7.2	even	3	inner	546.2.i.k.79.3	✓	6
7.3	odd	6		3822.2.a.bw.1.3		3
7.4	even	3		3822.2.a.bv.1.1		3
21.2	odd	6		1638.2.j.q.1171.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.k.79.3	✓	6	7.2	even	3	inner
546.2.i.k.235.3	yes	6	1.1	even	1	trivial
1638.2.j.q.235.1		6	3.2	odd	2
1638.2.j.q.1171.1		6	21.2	odd	6
3822.2.a.bv.1.1		3	7.4	even	3
3822.2.a.bw.1.3		3	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.70942 + 2.96080i) q^{5} +1.00000 q^{6} +(2.36521 - 1.18566i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.70942 + 2.96080i) q^{5} +1.00000 q^{6} +(2.36521 - 1.18566i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.70942 + 2.96080i) q^{10} +(2.36521 - 4.09666i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(2.20942 + 1.45550i) q^{14} +3.41883 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.89783 + 6.75125i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.34421 - 2.32824i) q^{19} -3.41883 q^{20} +(0.155792 - 2.64116i) q^{21} +4.73042 q^{22} +(1.86521 + 3.23063i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.34421 + 5.79234i) q^{25} +(0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(-0.155792 + 2.64116i) q^{28} -3.00000 q^{29} +(1.70942 + 2.96080i) q^{30} +(2.84421 - 4.92631i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.36521 - 4.09666i) q^{33} -7.79567 q^{34} +(7.55362 + 4.97611i) q^{35} +1.00000 q^{36} +(1.55362 + 2.69096i) q^{37} +(1.34421 - 2.32824i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-1.70942 - 2.96080i) q^{40} +0.892750 q^{41} +(2.36521 - 1.18566i) q^{42} -12.8377 q^{43} +(2.36521 + 4.09666i) q^{44} +(1.70942 - 2.96080i) q^{45} +(-1.86521 + 3.23063i) q^{46} +(5.07462 + 8.78951i) q^{47} -1.00000 q^{48} +(4.18842 - 5.60867i) q^{49} -6.68842 q^{50} +(3.89783 + 6.75125i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(4.60725 - 7.97999i) q^{53} +(-0.500000 - 0.866025i) q^{54} +16.1725 q^{55} +(-2.36521 + 1.18566i) q^{56} -2.68842 q^{57} +(-1.50000 - 2.59808i) q^{58} +(3.05362 - 5.28903i) q^{59} +(-1.70942 + 2.96080i) q^{60} +(-1.52100 - 2.63445i) q^{61} +5.68842 q^{62} +(-2.20942 - 1.45550i) q^{63} +1.00000 q^{64} +(1.70942 + 2.96080i) q^{65} +(2.36521 - 4.09666i) q^{66} +(0.0326253 - 0.0565087i) q^{67} +(-3.89783 - 6.75125i) q^{68} +3.73042 q^{69} +(-0.532625 + 9.02969i) q^{70} -12.6884 q^{71} +(0.500000 + 0.866025i) q^{72} +(-5.86521 + 10.1588i) q^{73} +(-1.55362 + 2.69096i) q^{74} +(3.34421 + 5.79234i) q^{75} +2.68842 q^{76} +(0.736959 - 12.4938i) q^{77} +1.00000 q^{78} +(-7.26304 - 12.5800i) q^{79} +(1.70942 - 2.96080i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.446375 + 0.773145i) q^{82} +0.934749 q^{83} +(2.20942 + 1.45550i) q^{84} -26.6521 q^{85} +(-6.41883 - 11.1177i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(-2.36521 + 4.09666i) q^{88} +(-7.55362 - 13.0833i) q^{89} +3.41883 q^{90} +(2.36521 - 1.18566i) q^{91} -3.73042 q^{92} +(-2.84421 - 4.92631i) q^{93} +(-5.07462 + 8.78951i) q^{94} +(4.59562 - 7.95985i) q^{95} +(-0.500000 - 0.866025i) q^{96} -4.79567 q^{97} +(6.95146 + 0.822941i) q^{98} -4.73042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} - 6 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{21} + 6 q^{22} - 3 q^{24} - 18 q^{25} + 3 q^{26} - 6 q^{27} - 3 q^{28} - 18 q^{29} - 3 q^{30} + 15 q^{31} + 3 q^{32} - 3 q^{33} - 12 q^{34} + 30 q^{35} + 6 q^{36} - 6 q^{37} + 6 q^{38} + 3 q^{39} + 3 q^{40} + 36 q^{41} + 3 q^{42} - 24 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{47} - 6 q^{48} + 21 q^{49} - 36 q^{50} + 6 q^{51} - 3 q^{52} - 3 q^{53} - 3 q^{54} + 54 q^{55} - 3 q^{56} - 12 q^{57} - 9 q^{58} + 3 q^{59} + 3 q^{60} + 30 q^{62} + 6 q^{64} - 3 q^{65} + 3 q^{66} - 6 q^{67} - 6 q^{68} + 3 q^{70} - 72 q^{71} + 3 q^{72} - 24 q^{73} + 6 q^{74} + 18 q^{75} + 12 q^{76} + 33 q^{77} + 6 q^{78} - 15 q^{79} - 3 q^{80} - 3 q^{81} + 18 q^{82} + 18 q^{83} - 48 q^{85} - 12 q^{86} - 9 q^{87} - 3 q^{88} - 30 q^{89} - 6 q^{90} + 3 q^{91} - 15 q^{93} - 6 q^{94} - 6 q^{95} - 3 q^{96} + 6 q^{97} + 9 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 - 6 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^21 + 6 * q^22 - 3 * q^24 - 18 * q^25 + 3 * q^26 - 6 * q^27 - 3 * q^28 - 18 * q^29 - 3 * q^30 + 15 * q^31 + 3 * q^32 - 3 * q^33 - 12 * q^34 + 30 * q^35 + 6 * q^36 - 6 * q^37 + 6 * q^38 + 3 * q^39 + 3 * q^40 + 36 * q^41 + 3 * q^42 - 24 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^47 - 6 * q^48 + 21 * q^49 - 36 * q^50 + 6 * q^51 - 3 * q^52 - 3 * q^53 - 3 * q^54 + 54 * q^55 - 3 * q^56 - 12 * q^57 - 9 * q^58 + 3 * q^59 + 3 * q^60 + 30 * q^62 + 6 * q^64 - 3 * q^65 + 3 * q^66 - 6 * q^67 - 6 * q^68 + 3 * q^70 - 72 * q^71 + 3 * q^72 - 24 * q^73 + 6 * q^74 + 18 * q^75 + 12 * q^76 + 33 * q^77 + 6 * q^78 - 15 * q^79 - 3 * q^80 - 3 * q^81 + 18 * q^82 + 18 * q^83 - 48 * q^85 - 12 * q^86 - 9 * q^87 - 3 * q^88 - 30 * q^89 - 6 * q^90 + 3 * q^91 - 15 * q^93 - 6 * q^94 - 6 * q^95 - 3 * q^96 + 6 * q^97 + 9 * q^98 - 6 * q^99

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