LMFDB - Embedded newform 1218.2.i.b.1045.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(697,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.697"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,3,-3,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1045.1
Root			$0.356769 + 0.617942i$ of defining polynomial
Character	$\chi$	$=$	1218.1045
Dual form			1218.2.i.b.697.1

$q$-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} +(-1.60220 + 2.77509i) q^{5} -1.00000 q^{6} +(2.63409 + 0.248083i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.60220 - 2.77509i) q^{10} +(1.64323 + 2.84616i) q^{11} +(0.500000 - 0.866025i) q^{12} +3.77733 q^{13} +(-1.53189 + 2.15715i) q^{14} -3.20440 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.73630 + 4.73940i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(2.10220 - 3.64112i) q^{19} +3.20440 q^{20} +(1.10220 + 2.40523i) q^{21} -3.28646 q^{22} +(0.897799 - 1.55503i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.63409 - 4.56239i) q^{25} +(-1.88866 + 3.27126i) q^{26} -1.00000 q^{27} +(-1.10220 - 2.40523i) q^{28} +1.00000 q^{29} +(1.60220 - 2.77509i) q^{30} +(3.44983 + 5.97529i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.64323 + 2.84616i) q^{33} -5.47259 q^{34} +(-4.90880 + 6.91238i) q^{35} +1.00000 q^{36} +(2.31574 - 4.01098i) q^{37} +(2.10220 + 3.64112i) q^{38} +(1.88866 + 3.27126i) q^{39} +(-1.60220 + 2.77509i) q^{40} -5.49086 q^{41} +(-2.63409 - 0.248083i) q^{42} -10.8359 q^{43} +(1.64323 - 2.84616i) q^{44} +(-1.60220 - 2.77509i) q^{45} +(0.897799 + 1.55503i) q^{46} +(4.17251 - 7.22700i) q^{47} -1.00000 q^{48} +(6.87691 + 1.30695i) q^{49} +5.26819 q^{50} +(-2.73630 + 4.73940i) q^{51} +(-1.88866 - 3.27126i) q^{52} +(4.06379 + 7.03869i) q^{53} +(0.500000 - 0.866025i) q^{54} -10.5311 q^{55} +(2.63409 + 0.248083i) q^{56} +4.20440 q^{57} +(-0.500000 + 0.866025i) q^{58} +(-2.14061 - 3.70765i) q^{59} +(1.60220 + 2.77509i) q^{60} +(-3.45245 + 5.97982i) q^{61} -6.89967 q^{62} +(-1.53189 + 2.15715i) q^{63} +1.00000 q^{64} +(-6.05203 + 10.4824i) q^{65} +(-1.64323 - 2.84616i) q^{66} +(-1.37953 - 2.38941i) q^{67} +(2.73630 - 4.73940i) q^{68} +1.79560 q^{69} +(-3.53189 - 7.70734i) q^{70} -15.7355 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-6.10220 - 10.5693i) q^{73} +(2.31574 + 4.01098i) q^{74} +(2.63409 - 4.56239i) q^{75} -4.20440 q^{76} +(3.62234 + 7.90471i) q^{77} -3.77733 q^{78} +(1.54103 - 2.66914i) q^{79} +(-1.60220 - 2.77509i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.74543 - 4.75523i) q^{82} -5.28646 q^{83} +(1.53189 - 2.15715i) q^{84} -17.5364 q^{85} +(5.41794 - 9.38415i) q^{86} +(0.500000 + 0.866025i) q^{87} +(1.64323 + 2.84616i) q^{88} +(1.70702 - 2.95664i) q^{89} +3.20440 q^{90} +(9.94983 + 0.937092i) q^{91} -1.79560 q^{92} +(-3.44983 + 5.97529i) q^{93} +(4.17251 + 7.22700i) q^{94} +(6.73630 + 11.6676i) q^{95} +(0.500000 - 0.866025i) q^{96} +8.99477 q^{97} +(-4.57031 + 5.30210i) q^{98} -3.28646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - q^{5} - 6 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - q^{10} + 11 q^{11} + 3 q^{12} + 10 q^{13} - 4 q^{14} - 2 q^{15} - 3 q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots - 22 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - q^5 - 6 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - q^10 + 11 * q^11 + 3 * q^12 + 10 * q^13 - 4 * q^14 - 2 * q^15 - 3 * q^16 - 6 * q^17 - 3 * q^18 + 4 * q^19 + 2 * q^20 - 2 * q^21 - 22 * q^22 + 14 * q^23 + 3 * q^24 - 2 * q^25 - 5 * q^26 - 6 * q^27 + 2 * q^28 + 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 - 11 * q^33 + 12 * q^34 + 5 * q^35 + 6 * q^36 + 3 * q^37 + 4 * q^38 + 5 * q^39 - q^40 - 18 * q^41 - 2 * q^42 - 26 * q^43 + 11 * q^44 - q^45 + 14 * q^46 + 13 * q^47 - 6 * q^48 + 12 * q^49 + 4 * q^50 + 6 * q^51 - 5 * q^52 + 14 * q^53 + 3 * q^54 + 8 * q^55 + 2 * q^56 + 8 * q^57 - 3 * q^58 - 6 * q^59 + q^60 - 4 * q^61 + 8 * q^62 - 4 * q^63 + 6 * q^64 - 3 * q^65 - 11 * q^66 + 13 * q^67 - 6 * q^68 + 28 * q^69 - 16 * q^70 - 6 * q^71 - 3 * q^72 - 28 * q^73 + 3 * q^74 + 2 * q^75 - 8 * q^76 - 15 * q^77 - 10 * q^78 + 19 * q^79 - q^80 - 3 * q^81 + 9 * q^82 - 34 * q^83 + 4 * q^84 - 50 * q^85 + 13 * q^86 + 3 * q^87 + 11 * q^88 + q^89 + 2 * q^90 + 35 * q^91 - 28 * q^92 + 4 * q^93 + 13 * q^94 + 18 * q^95 + 3 * q^96 + 38 * q^97 - 24 * q^98 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.60220	+	2.77509i	−0.716526	+	1.24106i	0.245842	+	0.969310i	$0.420936\pi$
$5$	−1.60220	+	2.77509i	−0.716526	+	1.24106i	−0.962368	+	0.271749i	$0.912398\pi$
$6$	−1.00000			−0.408248
$7$	2.63409	+	0.248083i	0.995594	+	0.0937667i
$7$	2.63409	+	0.248083i	0.995594	+	0.0937667i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.60220	−	2.77509i	−0.506660	−	0.877562i
$11$	1.64323	+	2.84616i	0.495453	+	0.858149i	0.999986	−	0.00524272i	$-0.00166882\pi$
$11$	1.64323	+	2.84616i	0.495453	+	0.858149i	−0.504533	+	0.863392i	$0.668335\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.77733			1.04764			0.523821	−	0.851828i	$-0.324506\pi$
$13$	3.77733			1.04764			0.523821	+	0.851828i	$0.324506\pi$
$14$	−1.53189	+	2.15715i	−0.409416	+	0.576523i
$15$	−3.20440			−0.827373
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.73630	+	4.73940i	0.663649	+	1.14947i	0.979650	+	0.200715i	$0.0643265\pi$
$17$	2.73630	+	4.73940i	0.663649	+	1.14947i	−0.316001	+	0.948759i	$0.602340\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	2.10220	−	3.64112i	0.482278	−	0.835330i	−0.517515	−	0.855674i	$-0.673143\pi$
$19$	2.10220	−	3.64112i	0.482278	−	0.835330i	0.999793	+	0.0203442i	$0.00647620\pi$
$20$	3.20440			0.716526
$21$	1.10220	+	2.40523i	0.240520	+	0.524865i
$22$	−3.28646			−0.700676
$23$	0.897799	−	1.55503i	0.187204	−	0.324247i	−0.757113	−	0.653284i	$-0.773391\pi$
$23$	0.897799	−	1.55503i	0.187204	−	0.324247i	0.944317	+	0.329037i	$0.106724\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−2.63409	−	4.56239i	−0.526819	−	0.912477i
$26$	−1.88866	+	3.27126i	−0.370397	+	0.641547i
$27$	−1.00000			−0.192450
$28$	−1.10220	−	2.40523i	−0.208296	−	0.454547i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$	1.60220	−	2.77509i	0.292521	−	0.506660i
$31$	3.44983	+	5.97529i	0.619608	+	1.07319i	0.989557	+	0.144141i	$0.0460419\pi$
$31$	3.44983	+	5.97529i	0.619608	+	1.07319i	−0.369949	+	0.929052i	$0.620625\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.64323	+	2.84616i	−0.286050	+	0.495453i
$34$	−5.47259			−0.938542
$35$	−4.90880	+	6.91238i	−0.829739	+	1.16841i
$36$	1.00000			0.166667
$37$	2.31574	−	4.01098i	0.380705	−	0.659401i	−0.610458	−	0.792049i	$-0.709015\pi$
$37$	2.31574	−	4.01098i	0.380705	−	0.659401i	0.991163	+	0.132648i	$0.0423480\pi$
$38$	2.10220	+	3.64112i	0.341022	+	0.590667i
$39$	1.88866	+	3.27126i	0.302428	+	0.523821i
$40$	−1.60220	+	2.77509i	−0.253330	+	0.438781i
$41$	−5.49086			−0.857529			−0.428764	−	0.903416i	$-0.641051\pi$
$41$	−5.49086			−0.857529			−0.428764	+	0.903416i	$0.641051\pi$
$42$	−2.63409	−	0.248083i	−0.406450	−	0.0382801i
$43$	−10.8359			−1.65246			−0.826228	−	0.563336i	$-0.809518\pi$
$43$	−10.8359			−1.65246			−0.826228	+	0.563336i	$0.809518\pi$
$44$	1.64323	−	2.84616i	0.247726	−	0.429075i
$45$	−1.60220	−	2.77509i	−0.238842	−	0.413686i
$46$	0.897799	+	1.55503i	0.132373	+	0.229277i
$47$	4.17251	−	7.22700i	0.608623	−	1.05417i	−0.382845	−	0.923813i	$-0.625056\pi$
$47$	4.17251	−	7.22700i	0.608623	−	1.05417i	0.991468	−	0.130353i	$-0.0416110\pi$
$48$	−1.00000			−0.144338
$49$	6.87691	+	1.30695i	0.982416	+	0.186707i
$50$	5.26819			0.745034
$51$	−2.73630	+	4.73940i	−0.383158	+	0.663649i
$52$	−1.88866	−	3.27126i	−0.261910	−	0.453642i
$53$	4.06379	+	7.03869i	0.558204	+	0.966838i	0.997647	+	0.0685672i	$0.0218428\pi$
$53$	4.06379	+	7.03869i	0.558204	+	0.966838i	−0.439442	+	0.898271i	$0.644824\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−10.5311			−1.42002
$56$	2.63409	+	0.248083i	0.351996	+	0.0331515i
$57$	4.20440			0.556887
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$	−2.14061	−	3.70765i	−0.278684	−	0.482695i	0.692374	−	0.721539i	$-0.256565\pi$
$59$	−2.14061	−	3.70765i	−0.278684	−	0.482695i	−0.971058	+	0.238844i	$0.923232\pi$
$60$	1.60220	+	2.77509i	0.206843	+	0.358263i
$61$	−3.45245	+	5.97982i	−0.442041	+	0.765637i	−0.997841	−	0.0656787i	$-0.979079\pi$
$61$	−3.45245	+	5.97982i	−0.442041	+	0.765637i	0.555800	+	0.831316i	$0.312412\pi$
$62$	−6.89967			−0.876259
$63$	−1.53189	+	2.15715i	−0.193000	+	0.271776i
$64$	1.00000			0.125000
$65$	−6.05203	+	10.4824i	−0.750662	+	1.30019i
$66$	−1.64323	−	2.84616i	−0.202268	−	0.350338i
$67$	−1.37953	−	2.38941i	−0.168536	−	0.291913i	0.769369	−	0.638804i	$-0.220571\pi$
$67$	−1.37953	−	2.38941i	−0.168536	−	0.291913i	−0.937905	+	0.346891i	$0.887237\pi$
$68$	2.73630	−	4.73940i	0.331825	−	0.574737i
$69$	1.79560			0.216165
$70$	−3.53189	−	7.70734i	−0.422142	−	0.921203i
$71$	−15.7355			−1.86747			−0.933733	−	0.357971i	$-0.883469\pi$
$71$	−15.7355			−1.86747			−0.933733	+	0.357971i	$0.883469\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−6.10220	−	10.5693i	−0.714209	−	1.23705i	−0.963264	−	0.268556i	$-0.913453\pi$
$73$	−6.10220	−	10.5693i	−0.714209	−	1.23705i	0.249055	−	0.968489i	$-0.419880\pi$
$74$	2.31574	+	4.01098i	0.269199	+	0.466267i
$75$	2.63409	−	4.56239i	0.304159	−	0.526819i
$76$	−4.20440			−0.482278
$77$	3.62234	+	7.90471i	0.412804	+	0.900826i
$78$	−3.77733			−0.427698
$79$	1.54103	−	2.66914i	0.173379	−	0.300302i	−0.766220	−	0.642579i	$-0.777865\pi$
$79$	1.54103	−	2.66914i	0.173379	−	0.300302i	0.939599	+	0.342277i	$0.111198\pi$
$80$	−1.60220	−	2.77509i	−0.179131	−	0.310265i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.74543	−	4.75523i	0.303182	−	0.525127i
$83$	−5.28646			−0.580265			−0.290132	−	0.956987i	$-0.593699\pi$
$83$	−5.28646			−0.580265			−0.290132	+	0.956987i	$0.593699\pi$
$84$	1.53189	−	2.15715i	0.167143	−	0.235364i
$85$	−17.5364			−1.90209
$86$	5.41794	−	9.38415i	0.584231	−	1.01192i
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	1.64323	+	2.84616i	0.175169	+	0.303402i
$89$	1.70702	−	2.95664i	0.180944	−	0.313404i	−0.761259	−	0.648449i	$-0.775418\pi$
$89$	1.70702	−	2.95664i	0.180944	−	0.313404i	0.942202	+	0.335045i	$0.108752\pi$
$90$	3.20440			0.337774
$91$	9.94983	+	0.937092i	1.04303	+	0.0982339i
$92$	−1.79560			−0.187204
$93$	−3.44983	+	5.97529i	−0.357731	+	0.619608i
$94$	4.17251	+	7.22700i	0.430361	+	0.745408i
$95$	6.73630	+	11.6676i	0.691129	+	1.19707i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	8.99477			0.913280			0.456640	−	0.889652i	$-0.349053\pi$
$97$	8.99477			0.913280			0.456640	+	0.889652i	$0.349053\pi$
$98$	−4.57031	+	5.30210i	−0.461671	+	0.535593i
$99$	−3.28646			−0.330302
$100$	−2.63409	+	4.56239i	−0.263409	+	0.456239i
$101$	−3.41142	−	5.90875i	−0.339449	−	0.587943i	0.644880	−	0.764284i	$-0.276907\pi$
$101$	−3.41142	−	5.90875i	−0.339449	−	0.587943i	−0.984329	+	0.176341i	$0.943574\pi$
$102$	−2.73630	−	4.73940i	−0.270934	−	0.469271i
$103$	−0.222674	+	0.385683i	−0.0219408	+	0.0380025i	−0.876787	−	0.480878i	$-0.840318\pi$
$103$	−0.222674	+	0.385683i	−0.0219408	+	0.0380025i	0.854847	+	0.518881i	$0.173651\pi$
$104$	3.77733			0.370397
$105$	−8.44070	−	0.794959i	−0.823728	−	0.0775800i
$106$	−8.12758			−0.789420
$107$	−0.172508	+	0.298792i	−0.0166769	+	0.0288853i	−0.874243	−	0.485488i	$-0.838642\pi$
$107$	−0.172508	+	0.298792i	−0.0166769	+	0.0288853i	0.857566	+	0.514373i	$0.171975\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	6.91142	+	11.9709i	0.661994	+	1.14661i	0.980091	+	0.198549i	$0.0636229\pi$
$109$	6.91142	+	11.9709i	0.661994	+	1.14661i	−0.318097	+	0.948058i	$0.603044\pi$
$110$	5.26557	−	9.12024i	0.502053	−	0.869581i
$111$	4.63148			0.439600
$112$	−1.53189	+	2.15715i	−0.144750	+	0.203832i
$113$	7.82284			0.735911			0.367955	−	0.929843i	$-0.380058\pi$
$113$	7.82284			0.735911			0.367955	+	0.929843i	$0.380058\pi$
$114$	−2.10220	+	3.64112i	−0.196889	+	0.341022i
$115$	2.87691	+	4.98295i	0.268273	+	0.464663i
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$	−1.88866	+	3.27126i	−0.174607	+	0.302428i
$118$	4.28123			0.394119
$119$	6.03189	+	13.1629i	0.552943	+	1.20664i
$120$	−3.20440			−0.292521
$121$	0.0995835	−	0.172484i	0.00905305	−	0.0156803i
$122$	−3.45245	−	5.97982i	−0.312570	−	0.541387i
$123$	−2.74543	−	4.75523i	−0.247547	−	0.428764i
$124$	3.44983	−	5.97529i	0.309804	−	0.536597i
$125$	0.859386			0.0768658
$126$	−1.10220	−	2.40523i	−0.0981918	−	0.214275i
$127$	−20.2682			−1.79851			−0.899255	−	0.437424i	$-0.855891\pi$
$127$	−20.2682			−1.79851			−0.899255	+	0.437424i	$0.855891\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.41794	−	9.38415i	−0.477023	−	0.826228i
$130$	−6.05203	−	10.4824i	−0.530799	−	0.919370i
$131$	0.792981	−	1.37348i	0.0692831	−	0.120002i	−0.829303	−	0.558799i	$-0.811262\pi$
$131$	0.792981	−	1.37348i	0.0692831	−	0.120002i	0.898586	+	0.438798i	$0.144595\pi$
$132$	3.28646			0.286050
$133$	6.44070	−	9.06953i	0.558479	−	0.786428i
$134$	2.75905			0.238346
$135$	1.60220	−	2.77509i	0.137895	−	0.238842i
$136$	2.73630	+	4.73940i	0.234635	+	0.406400i
$137$	−2.47724	−	4.29071i	−0.211645	−	0.366580i	0.740584	−	0.671963i	$-0.234549\pi$
$137$	−2.47724	−	4.29071i	−0.211645	−	0.366580i	−0.952230	+	0.305383i	$0.901215\pi$
$138$	−0.897799	+	1.55503i	−0.0764257	+	0.132373i
$139$	21.2902			1.80581			0.902905	−	0.429839i	$-0.141430\pi$
$139$	21.2902			1.80581			0.902905	+	0.429839i	$0.141430\pi$
$140$	8.44070	+	0.794959i	0.713369	+	0.0671863i
$141$	8.34502			0.702777
$142$	7.86777	−	13.6274i	0.660249	−	1.14358i
$143$	6.20702	+	10.7509i	0.519057	+	0.899033i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.60220	+	2.77509i	−0.133056	+	0.230459i
$146$	12.2044			1.01004
$147$	2.30660	+	6.60905i	0.190245	+	0.545106i
$148$	−4.63148			−0.380705
$149$	0.518273	−	0.897675i	0.0424586	−	0.0735404i	−0.844015	−	0.536319i	$-0.819814\pi$
$149$	0.518273	−	0.897675i	0.0424586	−	0.0735404i	0.886474	+	0.462779i	$0.153148\pi$
$150$	2.63409	+	4.56239i	0.215073	+	0.372517i
$151$	−4.50448	−	7.80200i	−0.366570	−	0.634917i	0.622457	−	0.782654i	$-0.286135\pi$
$151$	−4.50448	−	7.80200i	−0.366570	−	0.634917i	−0.989027	+	0.147737i	$0.952801\pi$
$152$	2.10220	−	3.64112i	0.170511	−	0.295334i
$153$	−5.47259			−0.442433
$154$	−8.65685	−	0.815317i	−0.697589	−	0.0657001i
$155$	−22.1093			−1.77586
$156$	1.88866	−	3.27126i	0.151214	−	0.261910i
$157$	−6.65685	−	11.5300i	−0.531275	−	0.920195i	−0.999334	−	0.0364975i	$-0.988380\pi$
$157$	−6.65685	−	11.5300i	−0.531275	−	0.920195i	0.468059	−	0.883697i	$-0.344953\pi$
$158$	1.54103	+	2.66914i	0.122598	+	0.212346i
$159$	−4.06379	+	7.03869i	−0.322279	+	0.558204i
$160$	3.20440			0.253330
$161$	2.75067	−	3.87338i	0.216783	−	0.305265i
$162$	1.00000			0.0785674
$163$	−6.13148	+	10.6200i	−0.480254	+	0.831825i	−0.999743	−	0.0226521i	$-0.992789\pi$
$163$	−6.13148	+	10.6200i	−0.480254	+	0.831825i	0.519489	+	0.854477i	$0.326122\pi$
$164$	2.74543	+	4.75523i	0.214382	+	0.371321i
$165$	−5.26557	−	9.12024i	−0.409924	−	0.710010i
$166$	2.64323	−	4.57821i	0.205155	−	0.355338i
$167$	20.3775			1.57686			0.788429	−	0.615126i	$-0.210895\pi$
$167$	20.3775			1.57686			0.788429	+	0.615126i	$0.210895\pi$
$168$	1.10220	+	2.40523i	0.0850366	+	0.185568i
$169$	1.26819			0.0975530
$170$	8.76819	−	15.1869i	0.672489	−	1.16479i
$171$	2.10220	+	3.64112i	0.160759	+	0.278443i
$172$	5.41794	+	9.38415i	0.413114	+	0.715534i
$173$	5.53841	−	9.59281i	0.421078	−	0.729328i	−0.574967	−	0.818176i	$-0.694985\pi$
$173$	5.53841	−	9.59281i	0.421078	−	0.729328i	0.996045	+	0.0888483i	$0.0283186\pi$
$174$	−1.00000			−0.0758098
$175$	−5.80660	−	12.6712i	−0.438938	−	0.957855i
$176$	−3.28646			−0.247726
$177$	2.14061	−	3.70765i	0.160898	−	0.278684i
$178$	1.70702	+	2.95664i	0.127946	+	0.221610i
$179$	3.58393	+	6.20755i	0.267875	+	0.463974i	0.968313	−	0.249740i	$-0.0803451\pi$
$179$	3.58393	+	6.20755i	0.267875	+	0.463974i	−0.700438	+	0.713714i	$0.747012\pi$
$180$	−1.60220	+	2.77509i	−0.119421	+	0.206843i
$181$	−13.0455			−0.969665			−0.484833	−	0.874607i	$-0.661120\pi$
$181$	−13.0455			−0.969665			−0.484833	+	0.874607i	$0.661120\pi$
$182$	−5.78646	+	8.14826i	−0.428921	+	0.603989i
$183$	−6.90490			−0.510425
$184$	0.897799	−	1.55503i	0.0661866	−	0.114639i
$185$	7.42056	+	12.8528i	0.545570	+	0.944955i
$186$	−3.44983	−	5.97529i	−0.252954	−	0.438129i
$187$	−8.99273	+	15.5759i	−0.657614	+	1.13902i
$188$	−8.34502			−0.608623
$189$	−2.63409	−	0.248083i	−0.191602	−	0.0180454i
$190$	−13.4726			−0.977404
$191$	6.51624	−	11.2865i	0.471498	−	0.816659i	−0.527970	−	0.849263i	$-0.677047\pi$
$191$	6.51624	−	11.2865i	0.471498	−	0.816659i	0.999468	+	0.0326038i	$0.0103800\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	7.66075	+	13.2688i	0.551433	+	0.955110i	0.998171	+	0.0604456i	$0.0192522\pi$
$193$	7.66075	+	13.2688i	0.551433	+	0.955110i	−0.446738	+	0.894665i	$0.647415\pi$
$194$	−4.49738	+	7.78970i	−0.322893	+	0.559268i
$195$	−12.1041			−0.866790
$196$	−2.30660	−	6.60905i	−0.164757	−	0.472075i
$197$	−16.0858			−1.14607			−0.573033	−	0.819532i	$-0.694233\pi$
$197$	−16.0858			−1.14607			−0.573033	+	0.819532i	$0.694233\pi$
$198$	1.64323	−	2.84616i	0.116779	−	0.202268i
$199$	−7.51362	−	13.0140i	−0.532626	−	0.922536i	−0.999274	−	0.0380929i	$-0.987872\pi$
$199$	−7.51362	−	13.0140i	−0.532626	−	0.922536i	0.466648	−	0.884443i	$-0.345462\pi$
$200$	−2.63409	−	4.56239i	−0.186259	−	0.322609i
$201$	1.37953	−	2.38941i	0.0973043	−	0.168536i
$202$	6.82284			0.480053
$203$	2.63409	+	0.248083i	0.184877	+	0.0174120i
$204$	5.47259			0.383158
$205$	8.79747	−	15.2377i	0.614442	−	1.06424i
$206$	−0.222674	−	0.385683i	−0.0155145	−	0.0268718i
$207$	0.897799	+	1.55503i	0.0624014	+	0.108082i
$208$	−1.88866	+	3.27126i	−0.130955	+	0.226821i
$209$	13.8176			0.955784
$210$	4.90880	−	6.91238i	0.338740	−	0.476999i
$211$	23.1313			1.59243			0.796213	−	0.605017i	$-0.206834\pi$
$211$	23.1313			1.59243			0.796213	+	0.605017i	$0.206834\pi$
$212$	4.06379	−	7.03869i	0.279102	−	0.483419i
$213$	−7.86777	−	13.6274i	−0.539091	−	0.933733i
$214$	−0.172508	−	0.298792i	−0.0117924	−	0.0204250i
$215$	17.3613	−	30.0706i	1.18403	−	2.05080i
$216$	−1.00000			−0.0680414
$217$	7.60482	+	16.5953i	0.516249	+	1.12656i
$218$	−13.8228			−0.936201
$219$	6.10220	−	10.5693i	0.412349	−	0.714209i
$220$	5.26557	+	9.12024i	0.355005	+	0.614886i
$221$	10.3359	+	17.9023i	0.695266	+	1.20424i
$222$	−2.31574	+	4.01098i	−0.155422	+	0.269199i
$223$	−0.386795			−0.0259017			−0.0129509	−	0.999916i	$-0.504123\pi$
$223$	−0.386795			−0.0259017			−0.0129509	+	0.999916i	$0.504123\pi$
$224$	−1.10220	−	2.40523i	−0.0736439	−	0.160706i
$225$	5.26819			0.351213
$226$	−3.91142	+	6.77478i	−0.260184	+	0.450652i
$227$	−7.86777	−	13.6274i	−0.522202	−	0.904481i	−0.999666	−	0.0258298i	$-0.991777\pi$
$227$	−7.86777	−	13.6274i	−0.522202	−	0.904481i	0.477464	−	0.878651i	$-0.341556\pi$
$228$	−2.10220	−	3.64112i	−0.139222	−	0.241139i
$229$	−8.20178	+	14.2059i	−0.541989	+	0.938753i	0.456801	+	0.889569i	$0.348995\pi$
$229$	−8.20178	+	14.2059i	−0.541989	+	0.938753i	−0.998790	+	0.0491836i	$0.984338\pi$
$230$	−5.75382			−0.379396
$231$	−5.03451	+	7.08940i	−0.331247	+	0.466448i
$232$	1.00000			0.0656532
$233$	−4.32749	+	7.49544i	−0.283503	+	0.491042i	−0.972245	−	0.233964i	$-0.924830\pi$
$233$	−4.32749	+	7.49544i	−0.283503	+	0.491042i	0.688742	+	0.725007i	$0.258163\pi$
$234$	−1.88866	−	3.27126i	−0.123466	−	0.213849i
$235$	13.3704	+	23.1582i	0.872188	+	1.51067i
$236$	−2.14061	+	3.70765i	−0.139342	+	0.241348i
$237$	3.08206			0.200201
$238$	−14.4153	−	1.35766i	−0.934407	−	0.0880040i
$239$	8.74078			0.565394			0.282697	−	0.959209i	$-0.408771\pi$
$239$	8.74078			0.565394			0.282697	+	0.959209i	$0.408771\pi$
$240$	1.60220	−	2.77509i	0.103422	−	0.179131i
$241$	−1.29298	−	2.23951i	−0.0832882	−	0.144259i	0.821372	−	0.570392i	$-0.193209\pi$
$241$	−1.29298	−	2.23951i	−0.0832882	−	0.144259i	−0.904661	+	0.426133i	$0.859876\pi$
$242$	0.0995835	+	0.172484i	0.00640147	+	0.0110877i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	6.90490			0.442041
$245$	−14.6451	+	16.9901i	−0.935641	+	1.08546i
$246$	5.49086			0.350085
$247$	7.94070	−	13.7537i	0.505254	−	0.875126i
$248$	3.44983	+	5.97529i	0.219065	+	0.379431i
$249$	−2.64323	−	4.57821i	−0.167508	−	0.290132i
$250$	−0.429693	+	0.744250i	−0.0271762	+	0.0470705i
$251$	15.4491			0.975138			0.487569	−	0.873085i	$-0.337884\pi$
$251$	15.4491			0.975138			0.487569	+	0.873085i	$0.337884\pi$
$252$	2.63409	+	0.248083i	0.165932	+	0.0156278i
$253$	5.90117			0.371003
$254$	10.1341	−	17.5528i	0.635870	−	1.10136i
$255$	−8.76819	−	15.1869i	−0.549085	−	0.951044i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.35864	+	11.0135i	−0.396641	+	0.687002i	−0.993309	−	0.115486i	$-0.963157\pi$
$257$	−6.35864	+	11.0135i	−0.396641	+	0.687002i	0.596668	+	0.802488i	$0.296491\pi$
$258$	10.8359			0.674612
$259$	7.09493	−	9.99080i	0.440858	−	0.620798i
$260$	12.1041			0.750662
$261$	−0.500000	+	0.866025i	−0.0309492	+	0.0536056i
$262$	0.792981	+	1.37348i	0.0489905	+	0.0848541i
$263$	−6.41794	−	11.1162i	−0.395747	−	0.685454i	0.597449	−	0.801907i	$-0.296181\pi$
$263$	−6.41794	−	11.1162i	−0.395747	−	0.685454i	−0.993196	+	0.116453i	$0.962848\pi$
$264$	−1.64323	+	2.84616i	−0.101134	+	0.175169i
$265$	−26.0440			−1.59987
$266$	4.63409	+	10.1126i	0.284135	+	0.620042i
$267$	3.41404			0.208936
$268$	−1.37953	+	2.38941i	−0.0842680	+	0.145956i
$269$	5.69265	+	9.85996i	0.347087	+	0.601172i	0.985731	−	0.168330i	$-0.0538376\pi$
$269$	5.69265	+	9.85996i	0.347087	+	0.601172i	−0.638644	+	0.769503i	$0.720504\pi$
$270$	1.60220	+	2.77509i	0.0975068	+	0.168887i
$271$	10.6861	−	18.5089i	0.649136	−	1.12434i	−0.334193	−	0.942504i	$-0.608464\pi$
$271$	10.6861	−	18.5089i	0.649136	−	1.12434i	0.983330	−	0.181832i	$-0.0582028\pi$
$272$	−5.47259			−0.331825
$273$	4.16337	+	9.08535i	0.251979	+	0.549871i
$274$	4.95449			0.299311
$275$	8.65685	−	14.9941i	0.522028	−	0.904179i
$276$	−0.897799	−	1.55503i	−0.0540412	−	0.0936020i
$277$	−0.251951	−	0.436392i	−0.0151383	−	0.0262202i	0.858357	−	0.513053i	$-0.171486\pi$
$277$	−0.251951	−	0.436392i	−0.0151383	−	0.0262202i	−0.873495	+	0.486833i	$0.838152\pi$
$278$	−10.6451	+	18.4379i	−0.638451	+	1.10583i
$279$	−6.89967			−0.413072
$280$	−4.90880	+	6.91238i	−0.293357	+	0.413094i
$281$	26.9489			1.60764			0.803819	−	0.594874i	$-0.202798\pi$
$281$	26.9489			1.60764			0.803819	+	0.594874i	$0.202798\pi$
$282$	−4.17251	+	7.22700i	−0.248469	+	0.430361i
$283$	2.80008	+	4.84989i	0.166448	+	0.288296i	0.937168	−	0.348877i	$-0.113437\pi$
$283$	2.80008	+	4.84989i	0.166448	+	0.288296i	−0.770721	+	0.637173i	$0.780104\pi$
$284$	7.86777	+	13.6274i	0.466866	+	0.808636i
$285$	−6.73630	+	11.6676i	−0.399024	+	0.691129i
$286$	−12.4140			−0.734057
$287$	−14.4635	−	1.36219i	−0.853751	−	0.0804077i
$288$	1.00000			0.0589256
$289$	−6.47463	+	11.2144i	−0.380860	+	0.659669i
$290$	−1.60220	−	2.77509i	−0.0940845	−	0.162959i
$291$	4.49738	+	7.78970i	0.263641	+	0.456640i
$292$	−6.10220	+	10.5693i	−0.357104	+	0.618523i
$293$	11.4946			0.671522			0.335761	−	0.941947i	$-0.391007\pi$
$293$	11.4946			0.671522			0.335761	+	0.941947i	$0.391007\pi$
$294$	−6.87691	−	1.30695i	−0.401069	−	0.0762229i
$295$	13.7188			0.798738
$296$	2.31574	−	4.01098i	0.134600	−	0.233133i
$297$	−1.64323	−	2.84616i	−0.0953499	−	0.165151i
$298$	0.518273	+	0.897675i	0.0300227	+	0.0520009i
$299$	3.39128	−	5.87387i	0.196123	−	0.339695i
$300$	−5.26819			−0.304159
$301$	−28.5427	−	2.68820i	−1.64518	−	0.154945i
$302$	9.00897			0.518408
$303$	3.41142	−	5.90875i	0.195981	−	0.339449i
$304$	2.10220	+	3.64112i	0.120569	+	0.208832i
$305$	−11.0630	−	19.1617i	−0.633468	−	1.09720i
$306$	2.73630	−	4.73940i	0.156424	−	0.270934i
$307$	24.6912			1.40920			0.704601	−	0.709604i	$-0.251126\pi$
$307$	24.6912			1.40920			0.704601	+	0.709604i	$0.251126\pi$
$308$	5.03451	−	7.08940i	0.286868	−	0.403956i
$309$	−0.445349			−0.0253350
$310$	11.0547	−	19.1472i	0.627862	−	1.08749i
$311$	1.70178	+	2.94758i	0.0964993	+	0.167142i	0.910233	−	0.414096i	$-0.135902\pi$
$311$	1.70178	+	2.94758i	0.0964993	+	0.167142i	−0.813734	+	0.581237i	$0.802569\pi$
$312$	1.88866	+	3.27126i	0.106924	+	0.185199i
$313$	13.8385	−	23.9690i	0.782198	−	1.35481i	−0.148461	−	0.988918i	$-0.547432\pi$
$313$	13.8385	−	23.9690i	0.782198	−	1.35481i	0.930659	−	0.365888i	$-0.119235\pi$
$314$	13.3137			0.751336
$315$	−3.53189	−	7.70734i	−0.199000	−	0.434259i
$316$	−3.08206			−0.173379
$317$	−15.7727	+	27.3191i	−0.885882	+	1.53439i	−0.0411818	+	0.999152i	$0.513112\pi$
$317$	−15.7727	+	27.3191i	−0.885882	+	1.53439i	−0.844700	+	0.535240i	$0.820221\pi$
$318$	−4.06379	−	7.03869i	−0.227886	−	0.394710i
$319$	1.64323	+	2.84616i	0.0920033	+	0.159354i
$320$	−1.60220	+	2.77509i	−0.0895657	+	0.155132i
$321$	−0.345015			−0.0192569
$322$	1.97911	+	4.31884i	0.110291	+	0.240679i
$323$	23.0090			1.28025
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−9.94983	−	17.2336i	−0.551917	−	0.955949i
$326$	−6.13148	−	10.6200i	−0.339591	−	0.588189i
$327$	−6.91142	+	11.9709i	−0.382202	+	0.661994i
$328$	−5.49086			−0.303182
$329$	12.7837	−	18.0015i	0.704787	−	0.992453i
$330$	10.5311			0.579720
$331$	−6.08131	+	10.5331i	−0.334259	+	0.578954i	−0.983342	−	0.181764i	$-0.941819\pi$
$331$	−6.08131	+	10.5331i	−0.334259	+	0.578954i	0.649083	+	0.760717i	$0.275153\pi$
$332$	2.64323	+	4.57821i	0.145066	+	0.251262i
$333$	2.31574	+	4.01098i	0.126902	+	0.219800i
$334$	−10.1887	+	17.6474i	−0.557503	+	0.965624i
$335$	8.84111			0.483042
$336$	−2.63409	−	0.248083i	−0.143702	−	0.0135341i
$337$	−0.578159			−0.0314943			−0.0157472	−	0.999876i	$-0.505013\pi$
$337$	−0.578159			−0.0314943			−0.0157472	+	0.999876i	$0.505013\pi$
$338$	−0.634095	+	1.09828i	−0.0344902	+	0.0597388i
$339$	3.91142	+	6.77478i	0.212439	+	0.367955i
$340$	8.76819	+	15.1869i	0.475522	+	0.823628i
$341$	−11.3377	+	19.6376i	−0.613973	+	1.06343i
$342$	−4.20440			−0.227348
$343$	17.7902	+	5.14868i	0.960580	+	0.278003i
$344$	−10.8359			−0.584231
$345$	−2.87691	+	4.98295i	−0.154888	+	0.268273i
$346$	5.53841	+	9.59281i	0.297747	+	0.515713i
$347$	5.44797	+	9.43615i	0.292462	+	0.506559i	0.974391	−	0.224859i	$-0.0721921\pi$
$347$	5.44797	+	9.43615i	0.292462	+	0.506559i	−0.681929	+	0.731418i	$0.738859\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	14.8579			0.795324			0.397662	−	0.917532i	$-0.369822\pi$
$349$	14.8579			0.795324			0.397662	+	0.917532i	$0.369822\pi$
$350$	13.8769	+	1.30695i	0.741752	+	0.0698594i
$351$	−3.77733			−0.201619
$352$	1.64323	−	2.84616i	0.0875845	−	0.151701i
$353$	2.02276	+	3.50352i	0.107661	+	0.186473i	0.914822	−	0.403857i	$-0.132331\pi$
$353$	2.02276	+	3.50352i	0.107661	+	0.186473i	−0.807162	+	0.590331i	$0.798997\pi$
$354$	2.14061	+	3.70765i	0.113772	+	0.197059i
$355$	25.2115	−	43.6676i	1.33809	−	2.31764i
$356$	−3.41404			−0.180944
$357$	−8.38343	+	11.8052i	−0.443698	+	0.624798i
$358$	−7.16786			−0.378833
$359$	13.3769	−	23.1695i	0.706006	−	1.22284i	−0.260321	−	0.965522i	$-0.583828\pi$
$359$	13.3769	−	23.1695i	0.706006	−	1.22284i	0.966327	−	0.257317i	$-0.0828383\pi$
$360$	−1.60220	−	2.77509i	−0.0844434	−	0.146260i
$361$	0.661504	+	1.14576i	0.0348160	+	0.0603031i
$362$	6.52276	−	11.2977i	0.342829	−	0.593796i
$363$	0.199167			0.0104536
$364$	−4.16337	−	9.08535i	−0.218220	−	0.476202i
$365$	39.1078			2.04700
$366$	3.45245	−	5.97982i	0.180462	−	0.312570i
$367$	1.16861	+	2.02408i	0.0610007	+	0.105656i	0.894913	−	0.446241i	$-0.147237\pi$
$367$	1.16861	+	2.02408i	0.0610007	+	0.105656i	−0.833912	+	0.551897i	$0.813904\pi$
$368$	0.897799	+	1.55503i	0.0468010	+	0.0810617i
$369$	2.74543	−	4.75523i	0.142921	−	0.247547i
$370$	−14.8411			−0.771553
$371$	8.95822	+	19.5487i	0.465088	+	1.01492i
$372$	6.89967			0.357731
$373$	6.19527	−	10.7305i	0.320779	−	0.555605i	−0.659870	−	0.751380i	$-0.729389\pi$
$373$	6.19527	−	10.7305i	0.320779	−	0.555605i	0.980649	+	0.195775i	$0.0627221\pi$
$374$	−8.99273	−	15.5759i	−0.465003	−	0.805409i
$375$	0.429693	+	0.744250i	0.0221893	+	0.0384329i
$376$	4.17251	−	7.22700i	0.215181	−	0.372704i
$377$	3.77733			0.194542
$378$	1.53189	−	2.15715i	0.0787921	−	0.110952i
$379$	34.8266			1.78892			0.894461	−	0.447147i	$-0.147560\pi$
$379$	34.8266			1.78892			0.894461	+	0.447147i	$0.147560\pi$
$380$	6.73630	−	11.6676i	0.345565	−	0.598536i
$381$	−10.1341	−	17.5528i	−0.519185	−	0.899255i
$382$	6.51624	+	11.2865i	0.333400	+	0.577465i
$383$	16.9543	−	29.3657i	0.866325	−	1.50052i	0.000599873	−	1.00000i	$-0.499809\pi$
$383$	16.9543	−	29.3657i	0.866325	−	1.50052i	0.865725	−	0.500519i	$-0.166858\pi$
$384$	−1.00000			−0.0510310
$385$	−27.7400	−	2.61260i	−1.41376	−	0.133151i
$386$	−15.3215			−0.779844
$387$	5.41794	−	9.38415i	0.275409	−	0.477023i
$388$	−4.49738	−	7.78970i	−0.228320	−	0.395462i
$389$	7.01752	+	12.1547i	0.355803	+	0.616268i	0.987255	−	0.159147i	$-0.0508742\pi$
$389$	7.01752	+	12.1547i	0.355803	+	0.616268i	−0.631452	+	0.775415i	$0.717541\pi$
$390$	6.05203	−	10.4824i	0.306457	−	0.530799i
$391$	9.82658			0.496951
$392$	6.87691	+	1.30695i	0.347336	+	0.0660110i
$393$	1.58596			0.0800012
$394$	8.04290	−	13.9307i	0.405195	−	0.701819i
$395$	4.93808	+	8.55301i	0.248462	+	0.430348i
$396$	1.64323	+	2.84616i	0.0825755	+	0.143025i
$397$	11.8092	−	20.4542i	0.592688	−	1.02657i	−0.401181	−	0.915999i	$-0.631400\pi$
$397$	11.8092	−	20.4542i	0.592688	−	1.02657i	0.993869	−	0.110566i	$-0.0352665\pi$
$398$	15.0272			0.753248
$399$	11.0748	+	1.04304i	0.554433	+	0.0522174i
$400$	5.26819			0.263409
$401$	−5.28646	+	9.15642i	−0.263993	+	0.457250i	−0.967299	−	0.253637i	$-0.918373\pi$
$401$	−5.28646	+	9.15642i	−0.263993	+	0.457250i	0.703306	+	0.710887i	$0.251706\pi$
$402$	1.37953	+	2.38941i	0.0688045	+	0.119173i
$403$	13.0311	+	22.5706i	0.649128	+	1.12432i
$404$	−3.41142	+	5.90875i	−0.169725	+	0.293971i
$405$	3.20440			0.159228
$406$	−1.53189	+	2.15715i	−0.0760266	+	0.107058i
$407$	15.2212			0.754486
$408$	−2.73630	+	4.73940i	−0.135467	+	0.234635i
$409$	−18.5910	−	32.2006i	−0.919267	−	1.59222i	−0.800531	−	0.599292i	$-0.795449\pi$
$409$	−18.5910	−	32.2006i	−0.919267	−	1.59222i	−0.118737	−	0.992926i	$-0.537884\pi$
$410$	8.79747	+	15.2377i	0.434476	+	0.752534i
$411$	2.47724	−	4.29071i	0.122193	−	0.211645i
$412$	0.445349			0.0219408
$413$	−4.71877	−	10.2974i	−0.232196	−	0.506700i
$414$	−1.79560			−0.0882488
$415$	8.46997	−	14.6704i	0.415775	−	0.720143i
$416$	−1.88866	−	3.27126i	−0.0925993	−	0.160387i
$417$	10.6451	+	18.4379i	0.521293	+	0.902905i
$418$	−6.90880	+	11.9664i	−0.337921	+	0.585296i
$419$	−19.8594			−0.970195			−0.485097	−	0.874460i	$-0.661216\pi$
$419$	−19.8594			−0.970195			−0.485097	+	0.874460i	$0.661216\pi$
$420$	3.53189	+	7.70734i	0.172339	+	0.376080i
$421$	−40.2992			−1.96406			−0.982031	−	0.188722i	$-0.939566\pi$
$421$	−40.2992			−1.96406			−0.982031	+	0.188722i	$0.939566\pi$
$422$	−11.5657	+	20.0323i	−0.563007	+	0.975157i
$423$	4.17251	+	7.22700i	0.202874	+	0.351389i
$424$	4.06379	+	7.03869i	0.197355	+	0.341829i
$425$	14.4153	−	24.9681i	0.699246	−	1.21113i
$426$	15.7355			0.762390
$427$	−10.5776	+	14.8949i	−0.511885	+	0.720815i
$428$	0.345015			0.0166769
$429$	−6.20702	+	10.7509i	−0.299678	+	0.519057i
$430$	17.3613	+	30.0706i	0.837234	+	1.45013i
$431$	−8.83459	−	15.3020i	−0.425547	−	0.737070i	0.570924	−	0.821003i	$-0.306585\pi$
$431$	−8.83459	−	15.3020i	−0.425547	−	0.737070i	−0.996471	+	0.0839332i	$0.973252\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−25.9489			−1.24703			−0.623513	−	0.781813i	$-0.714295\pi$
$433$	−25.9489			−1.24703			−0.623513	+	0.781813i	$0.714295\pi$
$434$	−18.1744	−	1.71169i	−0.872398	−	0.0821639i
$435$	−3.20440			−0.153639
$436$	6.91142	−	11.9709i	0.330997	−	0.573304i
$437$	−3.77471	−	6.53799i	−0.180569	−	0.312754i
$438$	6.10220	+	10.5693i	0.291574	+	0.505022i
$439$	−7.94070	+	13.7537i	−0.378989	+	0.656428i	−0.990915	−	0.134487i	$-0.957061\pi$
$439$	−7.94070	+	13.7537i	−0.378989	+	0.656428i	0.611927	+	0.790915i	$0.290395\pi$
$440$	−10.5311			−0.502053
$441$	−4.57031	+	5.30210i	−0.217634	+	0.252481i
$442$	−20.6718			−0.983255
$443$	−14.0657	+	24.3624i	−0.668279	+	1.15749i	0.310106	+	0.950702i	$0.399636\pi$
$443$	−14.0657	+	24.3624i	−0.668279	+	1.15749i	−0.978385	+	0.206792i	$0.933698\pi$
$444$	−2.31574	−	4.01098i	−0.109900	−	0.190353i
$445$	5.46997	+	9.47427i	0.259302	+	0.449124i
$446$	0.193398	−	0.334975i	0.00915765	−	0.0158615i
$447$	1.03655			0.0490269
$448$	2.63409	+	0.248083i	0.124449	+	0.0117208i
$449$	−29.6807			−1.40072			−0.700360	−	0.713790i	$-0.746977\pi$
$449$	−29.6807			−1.40072			−0.700360	+	0.713790i	$0.746977\pi$
$450$	−2.63409	+	4.56239i	−0.124172	+	0.215073i
$451$	−9.02276	−	15.6279i	−0.424865	−	0.735888i
$452$	−3.91142	−	6.77478i	−0.183978	−	0.318659i
$453$	4.50448	−	7.80200i	0.211639	−	0.366570i
$454$	15.7355			0.738506
$455$	−18.5421	+	26.1103i	−0.869269	+	1.22407i
$456$	4.20440			0.196889
$457$	−8.46084	+	14.6546i	−0.395781	+	0.685513i	−0.993201	−	0.116416i	$-0.962859\pi$
$457$	−8.46084	+	14.6546i	−0.395781	+	0.685513i	0.597419	+	0.801929i	$0.296193\pi$
$458$	−8.20178	−	14.2059i	−0.383244	−	0.663798i
$459$	−2.73630	−	4.73940i	−0.127719	−	0.221216i
$460$	2.87691	−	4.98295i	0.134137	−	0.232331i
$461$	−29.5088			−1.37436			−0.687181	−	0.726486i	$-0.741152\pi$
$461$	−29.5088			−1.37436			−0.687181	+	0.726486i	$0.741152\pi$
$462$	−3.62234	−	7.90471i	−0.168527	−	0.367760i
$463$	−5.51287			−0.256205			−0.128102	−	0.991761i	$-0.540889\pi$
$463$	−5.51287			−0.256205			−0.128102	+	0.991761i	$0.540889\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	−11.0547	−	19.1472i	−0.512647	−	0.887931i
$466$	−4.32749	−	7.49544i	−0.200467	−	0.347219i
$467$	14.2180	−	24.6263i	0.657932	−	1.13957i	−0.323219	−	0.946324i	$-0.604765\pi$
$467$	14.2180	−	24.6263i	0.657932	−	1.13957i	0.981150	−	0.193247i	$-0.0619018\pi$
$468$	3.77733			0.174607
$469$	−3.04103	−	6.63617i	−0.140422	−	0.306430i
$470$	−26.7408			−1.23346
$471$	6.65685	−	11.5300i	0.306732	−	0.531275i
$472$	−2.14061	−	3.70765i	−0.0985297	−	0.170659i
$473$	−17.8059	−	30.8406i	−0.818714	−	1.41805i
$474$	−1.54103	+	2.66914i	−0.0707819	+	0.122598i
$475$	−22.1496			−1.01629
$476$	8.38343	−	11.8052i	0.384254	−	0.541091i
$477$	−8.12758			−0.372136
$478$	−4.37039	+	7.56974i	−0.199897	+	0.346232i
$479$	4.65237	+	8.05814i	0.212572	+	0.368186i	0.952519	−	0.304480i	$-0.0984826\pi$
$479$	4.65237	+	8.05814i	0.212572	+	0.368186i	−0.739947	+	0.672666i	$0.765149\pi$
$480$	1.60220	+	2.77509i	0.0731301	+	0.126665i
$481$	8.74730	−	15.1508i	0.398843	−	0.690816i
$482$	2.58596			0.117787
$483$	4.72978	+	0.445458i	0.215212	+	0.0202691i
$484$	−0.199167			−0.00905305
$485$	−14.4114	+	24.9613i	−0.654389	+	1.13343i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	13.3568	+	23.1346i	0.605253	+	1.04833i	0.992011	+	0.126148i	$0.0402614\pi$
$487$	13.3568	+	23.1346i	0.605253	+	1.04833i	−0.386758	+	0.922181i	$0.626405\pi$
$488$	−3.45245	+	5.97982i	−0.156285	+	0.270694i
$489$	−12.2630			−0.554550
$490$	−7.39128	−	21.1781i	−0.333904	−	0.956727i
$491$	−16.9817			−0.766375			−0.383187	−	0.923671i	$-0.625174\pi$
$491$	−16.9817			−0.766375			−0.383187	+	0.923671i	$0.625174\pi$
$492$	−2.74543	+	4.75523i	−0.123774	+	0.214382i
$493$	2.73630	+	4.73940i	0.123237	+	0.213452i
$494$	7.94070	+	13.7537i	0.357269	+	0.618808i
$495$	5.26557	−	9.12024i	0.236670	−	0.409924i
$496$	−6.89967			−0.309804
$497$	−41.4489	−	3.90373i	−1.85924	−	0.175106i
$498$	5.28646			0.236892
$499$	8.29095	−	14.3603i	0.371154	−	0.642857i	−0.618590	−	0.785714i	$-0.712296\pi$
$499$	8.29095	−	14.3603i	0.371154	−	0.642857i	0.989743	+	0.142857i	$0.0456289\pi$
$500$	−0.429693	−	0.744250i	−0.0192165	−	0.0332839i
$501$	10.1887	+	17.6474i	0.455200	+	0.788429i
$502$	−7.72454	+	13.3793i	−0.344763	+	0.597147i
$503$	−41.5621			−1.85316			−0.926582	−	0.376094i	$-0.877267\pi$
$503$	−41.5621			−1.85316			−0.926582	+	0.376094i	$0.877267\pi$
$504$	−1.53189	+	2.15715i	−0.0682360	+	0.0960872i
$505$	21.8631			0.972896
$506$	−2.95058	+	5.11056i	−0.131169	+	0.227192i
$507$	0.634095	+	1.09828i	0.0281611	+	0.0487765i
$508$	10.1341	+	17.5528i	0.449628	+	0.778778i
$509$	−13.9569	+	24.1741i	−0.618630	+	1.07150i	0.371106	+	0.928591i	$0.378979\pi$
$509$	−13.9569	+	24.1741i	−0.618630	+	1.07150i	−0.989736	+	0.142908i	$0.954355\pi$
$510$	17.5364			0.776524
$511$	−13.4517	−	29.3544i	−0.595068	−	1.29856i
$512$	1.00000			0.0441942
$513$	−2.10220	+	3.64112i	−0.0928144	+	0.160759i
$514$	−6.35864	−	11.0135i	−0.280467	−	0.485784i
$515$	−0.713538	−	1.23588i	−0.0314422	−	0.0544596i
$516$	−5.41794	+	9.38415i	−0.238511	+	0.413114i
$517$	27.4256			1.20618
$518$	5.10482	+	11.1398i	0.224293	+	0.489454i
$519$	11.0768			0.486219
$520$	−6.05203	+	10.4824i	−0.265399	+	0.459685i
$521$	−12.6087	−	21.8389i	−0.552398	−	0.956781i	−0.998101	−	0.0616005i	$-0.980380\pi$
$521$	−12.6087	−	21.8389i	−0.552398	−	0.956781i	0.445703	−	0.895181i	$-0.352954\pi$
$522$	−0.500000	−	0.866025i	−0.0218844	−	0.0379049i
$523$	−13.7447	+	23.8065i	−0.601013	+	1.04099i	0.391655	+	0.920112i	$0.371903\pi$
$523$	−13.7447	+	23.8065i	−0.601013	+	1.04099i	−0.992668	+	0.120873i	$0.961431\pi$
$524$	−1.58596			−0.0692831
$525$	8.07031	−	11.3643i	0.352217	−	0.495978i
$526$	12.8359			0.559671
$527$	−18.8795	+	32.7003i	−0.822405	+	1.42445i
$528$	−1.64323	−	2.84616i	−0.0715125	−	0.123863i
$529$	9.88791	+	17.1264i	0.429909	+	0.744625i
$530$	13.0220	−	22.5548i	0.565640	−	0.979717i
$531$	4.28123			0.185789
$532$	−11.0748	−	1.04304i	−0.480153	−	0.0452216i
$533$	−20.7408			−0.898383
$534$	−1.70702	+	2.95664i	−0.0738699	+	0.127946i
$535$	−0.552784	−	0.957450i	−0.0238989	−	0.0413942i
$536$	−1.37953	−	2.38941i	−0.0595865	−	0.103207i
$537$	−3.58393	+	6.20755i	−0.154658	+	0.267875i
$538$	−11.3853			−0.490855
$539$	7.58056	+	21.7204i	0.326518	+	0.935564i
$540$	−3.20440			−0.137895
$541$	8.25382	−	14.2960i	0.354859	−	0.614634i	−0.632235	−	0.774777i	$-0.717862\pi$
$541$	8.25382	−	14.2960i	0.354859	−	0.614634i	0.987094	+	0.160143i	$0.0511954\pi$
$542$	10.6861	+	18.5089i	0.459009	+	0.795026i
$543$	−6.52276	−	11.2977i	−0.279918	−	0.484833i
$544$	2.73630	−	4.73940i	0.117318	−	0.203200i
$545$	−44.2939			−1.89734
$546$	−9.94983	−	0.937092i	−0.425814	−	0.0401038i
$547$	13.0000			0.555840			0.277920	−	0.960604i	$-0.410355\pi$
$547$	13.0000			0.555840			0.277920	+	0.960604i	$0.410355\pi$
$548$	−2.47724	+	4.29071i	−0.105823	+	0.183290i
$549$	−3.45245	−	5.97982i	−0.147347	−	0.255212i
$550$	8.65685	+	14.9941i	0.369129	+	0.639351i
$551$	2.10220	−	3.64112i	0.0895568	−	0.155117i
$552$	1.79560			0.0764257
$553$	4.72139	−	6.64847i	0.200774	−	0.282722i
$554$	0.503902			0.0214087
$555$	−7.42056	+	12.8528i	−0.314985	+	0.545570i
$556$	−10.6451	−	18.4379i	−0.451453	−	0.781939i
$557$	−6.33588	−	10.9741i	−0.268460	−	0.464986i	0.700004	−	0.714138i	$-0.253181\pi$
$557$	−6.33588	−	10.9741i	−0.268460	−	0.464986i	−0.968464	+	0.249152i	$0.919848\pi$
$558$	3.44983	−	5.97529i	0.146043	−	0.252954i
$559$	−40.9306			−1.73118
$560$	−3.53189	−	7.70734i	−0.149250	−	0.325694i
$561$	−17.9855			−0.759347
$562$	−13.4745	+	23.3384i	−0.568386	+	0.984473i
$563$	5.24281	+	9.08082i	0.220958	+	0.382711i	0.955099	−	0.296286i	$-0.0957482\pi$
$563$	5.24281	+	9.08082i	0.220958	+	0.382711i	−0.734141	+	0.678997i	$0.762415\pi$
$564$	−4.17251	−	7.22700i	−0.175694	−	0.304311i
$565$	−12.5338	+	21.7091i	−0.527299	+	0.913309i
$566$	−5.60017			−0.235393
$567$	−1.10220	−	2.40523i	−0.0462881	−	0.101010i
$568$	−15.7355			−0.660249
$569$	14.6477	−	25.3706i	0.614064	−	1.06359i	−0.376484	−	0.926423i	$-0.622867\pi$
$569$	14.6477	−	25.3706i	0.614064	−	1.06359i	0.990548	−	0.137167i	$-0.0437997\pi$
$570$	−6.73630	−	11.6676i	−0.282152	−	0.488702i
$571$	23.3970	+	40.5249i	0.979136	+	1.69591i	0.665549	+	0.746354i	$0.268197\pi$
$571$	23.3970	+	40.5249i	0.979136	+	1.69591i	0.313587	+	0.949560i	$0.398469\pi$
$572$	6.20702	−	10.7509i	0.259528	−	0.449517i
$573$	13.0325			0.544440
$574$	8.41142	−	11.8446i	0.351086	−	0.494385i
$575$	−9.45955			−0.394491
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	20.5910	+	35.6647i	0.857216	+	1.48474i	0.874574	+	0.484892i	$0.161141\pi$
$577$	20.5910	+	35.6647i	0.857216	+	1.48474i	−0.0173583	+	0.999849i	$0.505526\pi$
$578$	−6.47463	−	11.2144i	−0.269309	−	0.466457i
$579$	−7.66075	+	13.2688i	−0.318370	+	0.551433i
$580$	3.20440			0.133056
$581$	−13.9250	−	1.31148i	−0.577708	−	0.0544095i
$582$	−8.99477			−0.372845
$583$	−13.3555	+	23.1324i	−0.553128	+	0.958045i
$584$	−6.10220	−	10.5693i	−0.252511	−	0.437362i
$585$	−6.05203	−	10.4824i	−0.250221	−	0.433395i
$586$	−5.74730	+	9.95461i	−0.237419	+	0.411221i
$587$	9.25922			0.382169			0.191084	−	0.981574i	$-0.438800\pi$
$587$	9.25922			0.382169			0.191084	+	0.981574i	$0.438800\pi$
$588$	4.57031	−	5.30210i	0.188476	−	0.218655i
$589$	29.0090			1.19529
$590$	−6.85939	+	11.8808i	−0.282396	+	0.489125i
$591$	−8.04290	−	13.9307i	−0.330841	−	0.573033i
$592$	2.31574	+	4.01098i	0.0951763	+	0.164850i
$593$	−8.46532	+	14.6624i	−0.347629	+	0.602111i	−0.985828	−	0.167760i	$-0.946346\pi$
$593$	−8.46532	+	14.6624i	−0.347629	+	0.602111i	0.638199	+	0.769872i	$0.279680\pi$
$594$	3.28646			0.134845
$595$	−46.1925	−	4.35048i	−1.89371	−	0.178352i
$596$	−1.03655			−0.0424586
$597$	7.51362	−	13.0140i	0.307512	−	0.532626i
$598$	3.39128	+	5.87387i	0.138680	+	0.240200i
$599$	−21.8989	−	37.9300i	−0.894765	−	1.54978i	−0.834095	−	0.551621i	$-0.814009\pi$
$599$	−21.8989	−	37.9300i	−0.894765	−	1.54978i	−0.0606709	−	0.998158i	$-0.519324\pi$
$600$	2.63409	−	4.56239i	0.107536	−	0.186259i
$601$	−37.3540			−1.52370			−0.761850	−	0.647753i	$-0.775709\pi$
$601$	−37.3540			−1.52370			−0.761850	+	0.647753i	$0.775709\pi$
$602$	16.5994	−	23.3746i	0.676542	−	0.952679i
$603$	2.75905			0.112357
$604$	−4.50448	+	7.80200i	−0.183285	+	0.317459i
$605$	0.319106	+	0.552707i	0.0129735	+	0.0224707i
$606$	3.41142	+	5.90875i	0.138579	+	0.240027i
$607$	23.3652	−	40.4696i	0.948362	−	1.64261i	0.199488	−	0.979900i	$-0.436072\pi$
$607$	23.3652	−	40.4696i	0.948362	−	1.64261i	0.748875	−	0.662712i	$-0.230594\pi$
$608$	−4.20440			−0.170511
$609$	1.10220	+	2.40523i	0.0446634	+	0.0974650i
$610$	22.1261			0.895859
$611$	15.7609	−	27.2987i	0.637619	−	1.10439i
$612$	2.73630	+	4.73940i	0.110608	+	0.191579i
$613$	13.6731	+	23.6825i	0.552251	+	0.956527i	0.998112	+	0.0614244i	$0.0195643\pi$
$613$	13.6731	+	23.6825i	0.552251	+	0.956527i	−0.445861	+	0.895102i	$0.647102\pi$
$614$	−12.3456	+	21.3832i	−0.498228	+	0.862956i
$615$	17.5949			0.709496
$616$	3.62234	+	7.90471i	0.145948	+	0.318490i
$617$	−18.8501			−0.758876			−0.379438	−	0.925217i	$-0.623883\pi$
$617$	−18.8501			−0.758876			−0.379438	+	0.925217i	$0.623883\pi$
$618$	0.222674	−	0.385683i	0.00895727	−	0.0155145i
$619$	14.8495	+	25.7201i	0.596852	+	1.03378i	0.993283	+	0.115713i	$0.0369153\pi$
$619$	14.8495	+	25.7201i	0.596852	+	1.03378i	−0.396431	+	0.918065i	$0.629751\pi$
$620$	11.0547	+	19.1472i	0.443965	+	0.768971i
$621$	−0.897799	+	1.55503i	−0.0360274	+	0.0624014i
$622$	−3.40357			−0.136471
$623$	5.22994	−	7.36460i	0.209533	−	0.295056i
$624$	−3.77733			−0.151214
$625$	11.7936	−	20.4271i	0.471743	−	0.817082i
$626$	13.8385	+	23.9690i	0.553098	+	0.957993i
$627$	6.90880	+	11.9664i	0.275911	+	0.477892i
$628$	−6.65685	+	11.5300i	−0.265637	+	0.460097i
$629$	25.3462			1.01062
$630$	8.44070	+	0.794959i	0.336285	+	0.0316719i
$631$	−19.5599			−0.778667			−0.389333	−	0.921097i	$-0.627295\pi$
$631$	−19.5599			−0.778667			−0.389333	+	0.921097i	$0.627295\pi$
$632$	1.54103	−	2.66914i	0.0612989	−	0.106173i
$633$	11.5657	+	20.0323i	0.459694	+	0.796213i
$634$	−15.7727	−	27.3191i	−0.626413	−	1.08498i
$635$	32.4737	−	56.2461i	1.28868	−	2.23206i
$636$	8.12758			0.322279
$637$	25.9763	+	4.93678i	1.02922	+	0.195602i
$638$	−3.28646			−0.130112
$639$	7.86777	−	13.6274i	0.311244	−	0.539091i
$640$	−1.60220	−	2.77509i	−0.0633325	−	0.109695i
$641$	−20.5090	−	35.5226i	−0.810056	−	1.40306i	−0.912824	−	0.408352i	$-0.866104\pi$
$641$	−20.5090	−	35.5226i	−0.810056	−	1.40306i	0.102769	−	0.994705i	$-0.467230\pi$
$642$	0.172508	−	0.298792i	0.00680833	−	0.0117924i
$643$	43.2458			1.70545			0.852725	−	0.522360i	$-0.174948\pi$
$643$	43.2458			1.70545			0.852725	+	0.522360i	$0.174948\pi$
$644$	−4.72978	−	0.445458i	−0.186379	−	0.0175535i
$645$	34.7225			1.36720
$646$	−11.5045	+	19.9264i	−0.452638	+	0.783992i
$647$	−17.1914	−	29.7763i	−0.675862	−	1.17063i	−0.976216	−	0.216800i	$-0.930438\pi$
$647$	−17.1914	−	29.7763i	−0.675862	−	1.17063i	0.300354	−	0.953828i	$-0.402895\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	7.03505	−	12.1851i	0.276150	−	0.478305i
$650$	19.8997			0.780529
$651$	−10.5696	+	14.8836i	−0.414254	+	0.583335i
$652$	12.2630			0.480254
$653$	−10.7544	+	18.6272i	−0.420852	+	0.728937i	−0.996023	−	0.0890959i	$-0.971602\pi$
$653$	−10.7544	+	18.6272i	−0.420852	+	0.728937i	0.575171	+	0.818033i	$0.304936\pi$
$654$	−6.91142	−	11.9709i	−0.270258	−	0.468100i
$655$	2.54103	+	4.40119i	0.0992863	+	0.171969i
$656$	2.74543	−	4.75523i	0.107191	−	0.185660i
$657$	12.2044			0.476139
$658$	9.19788	+	20.0717i	0.358571	+	0.782477i
$659$	−36.1026			−1.40636			−0.703178	−	0.711014i	$-0.748236\pi$
$659$	−36.1026			−1.40636			−0.703178	+	0.711014i	$0.748236\pi$
$660$	−5.26557	+	9.12024i	−0.204962	+	0.355005i
$661$	−2.65498	−	4.59857i	−0.103267	−	0.178864i	0.809762	−	0.586759i	$-0.199596\pi$
$661$	−2.65498	−	4.59857i	−0.103267	−	0.178864i	−0.913029	+	0.407895i	$0.866263\pi$
$662$	−6.08131	−	10.5331i	−0.236357	−	0.409382i
$663$	−10.3359	+	17.9023i	−0.401412	+	0.695266i
$664$	−5.28646			−0.205155
$665$	14.8495	+	32.4047i	0.575839	+	1.25660i
$666$	−4.63148			−0.179466
$667$	0.897799	−	1.55503i	0.0347629	−	0.0602112i
$668$	−10.1887	−	17.6474i	−0.394214	−	0.682799i
$669$	−0.193398	−	0.334975i	−0.00747719	−	0.0129509i
$670$	−4.42056	+	7.65663i	−0.170781	+	0.295801i
$671$	−22.6927			−0.876042
$672$	1.53189	−	2.15715i	0.0590941	−	0.0832139i
$673$	−0.0104689			−0.000403547			−0.000201773	−	1.00000i	$-0.500064\pi$
$673$	−0.0104689			−0.000403547			−0.000201773		1.00000i	$0.500064\pi$
$674$	0.289079	−	0.500700i	0.0111349	−	0.0192862i
$675$	2.63409	+	4.56239i	0.101386	+	0.175606i
$676$	−0.634095	−	1.09828i	−0.0243883	−	0.0422417i
$677$	−3.00710	+	5.20845i	−0.115572	+	0.200177i	−0.918008	−	0.396561i	$-0.870204\pi$
$677$	−3.00710	+	5.20845i	−0.115572	+	0.200177i	0.802436	+	0.596738i	$0.203537\pi$
$678$	−7.82284			−0.300434
$679$	23.6931	+	2.23145i	0.909256	+	0.0856353i
$680$	−17.5364			−0.672489
$681$	7.86777	−	13.6274i	0.301494	−	0.522202i
$682$	−11.3377	−	19.6376i	−0.434145	−	0.751961i
$683$	21.3833	+	37.0369i	0.818208	+	1.41718i	0.907002	+	0.421127i	$0.138365\pi$
$683$	21.3833	+	37.0369i	0.818208	+	1.41718i	−0.0887937	+	0.996050i	$0.528301\pi$
$684$	2.10220	−	3.64112i	0.0803797	−	0.139222i
$685$	15.8762			0.606597
$686$	−13.3540	+	12.8324i	−0.509858	+	0.489944i
$687$	−16.4036			−0.625835
$688$	5.41794	−	9.38415i	0.206557	−	0.357767i
$689$	15.3502	+	26.5874i	0.584798	+	1.01290i
$690$	−2.87691	−	4.98295i	−0.109522	−	0.189698i
$691$	−6.37953	+	11.0497i	−0.242689	+	0.420349i	−0.961479	−	0.274878i	$-0.911363\pi$
$691$	−6.37953	+	11.0497i	−0.242689	+	0.420349i	0.718791	+	0.695227i	$0.244696\pi$
$692$	−11.0768			−0.421078
$693$	−8.65685	−	0.815317i	−0.328847	−	0.0309713i
$694$	−10.8959			−0.413604
$695$	−34.1112	+	59.0823i	−1.29391	+	2.24112i
$696$	0.500000	+	0.866025i	0.0189525	+	0.0328266i
$697$	−15.0246	−	26.0234i	−0.569098	−	0.985707i
$698$	−7.42894	+	12.8673i	−0.281190	+	0.487035i
$699$	−8.65498			−0.327362
$700$	−8.07031	+	11.3643i	−0.305029	+	0.429529i
$701$	−19.7277			−0.745107			−0.372553	−	0.928011i	$-0.621518\pi$
$701$	−19.7277			−0.745107			−0.372553	+	0.928011i	$0.621518\pi$
$702$	1.88866	−	3.27126i	0.0712830	−	0.123466i
$703$	−9.73630	−	16.8638i	−0.367211	−	0.636029i
$704$	1.64323	+	2.84616i	0.0619316	+	0.107269i
$705$	−13.3704	+	23.1582i	−0.503558	+	0.872188i
$706$	−4.04551			−0.152255
$707$	−7.52014	−	16.4105i	−0.282824	−	0.617182i
$708$	−4.28123			−0.160898
$709$	−7.46607	+	12.9316i	−0.280394	+	0.485657i	−0.971482	−	0.237114i	$-0.923799\pi$
$709$	−7.46607	+	12.9316i	−0.280394	+	0.485657i	0.691088	+	0.722771i	$0.257132\pi$
$710$	25.2115	+	43.6676i	0.946171	+	1.63882i
$711$	1.54103	+	2.66914i	0.0577931	+	0.100101i
$712$	1.70702	−	2.95664i	0.0639732	−	0.110805i
$713$	12.3890			0.463973
$714$	−6.03189	−	13.1629i	−0.225738	−	0.492608i
$715$	−39.7796			−1.48767
$716$	3.58393	−	6.20755i	0.133938	−	0.231987i
$717$	4.37039	+	7.56974i	0.163215	+	0.282697i
$718$	13.3769	+	23.1695i	0.499222	+	0.864678i
$719$	7.13334	−	12.3553i	0.266029	−	0.460776i	−0.701804	−	0.712370i	$-0.747622\pi$
$719$	7.13334	−	12.3553i	0.266029	−	0.460776i	0.967833	+	0.251595i	$0.0809550\pi$
$720$	3.20440			0.119421
$721$	−0.682227	+	0.960684i	−0.0254075	+	0.0357778i
$722$	−1.32301			−0.0492372
$723$	1.29298	−	2.23951i	0.0480865	−	0.0832882i
$724$	6.52276	+	11.2977i	0.242416	+	0.419877i
$725$	−2.63409	−	4.56239i	−0.0978278	−	0.169443i
$726$	−0.0995835	+	0.172484i	−0.00369589	+	0.00640147i
$727$	8.50390			0.315392			0.157696	−	0.987488i	$-0.449593\pi$
$727$	8.50390			0.315392			0.157696	+	0.987488i	$0.449593\pi$
$728$	9.94983	+	0.937092i	0.368765	+	0.0347309i
$729$	1.00000			0.0370370
$730$	−19.5539	+	33.8684i	−0.723722	+	1.25352i
$731$	−29.6502	−	51.3556i	−1.09665	−	1.89946i
$732$	3.45245	+	5.97982i	0.127606	+	0.221021i
$733$	−17.4250	+	30.1811i	−0.643609	+	1.11476i	0.341012	+	0.940059i	$0.389230\pi$
$733$	−17.4250	+	30.1811i	−0.643609	+	1.11476i	−0.984621	+	0.174704i	$0.944103\pi$
$734$	−2.33721			−0.0862681
$735$	−22.0364	−	4.18799i	−0.812824	−	0.154476i
$736$	−1.79560			−0.0661866
$737$	4.53376	−	7.85271i	0.167003	−	0.289258i
$738$	2.74543	+	4.75523i	0.101061	+	0.175042i
$739$	−3.27658	−	5.67520i	−0.120531	−	0.208765i	0.799446	−	0.600738i	$-0.205126\pi$
$739$	−3.27658	−	5.67520i	−0.120531	−	0.208765i	−0.919977	+	0.391972i	$0.871793\pi$
$740$	7.42056	−	12.8528i	0.272785	−	0.472478i
$741$	15.8814			0.583418
$742$	−21.4088	−	2.01632i	−0.785942	−	0.0740213i
$743$	6.13131			0.224936			0.112468	−	0.993655i	$-0.464124\pi$
$743$	6.13131			0.224936			0.112468	+	0.993655i	$0.464124\pi$
$744$	−3.44983	+	5.97529i	−0.126477	+	0.219065i
$745$	1.66075	+	2.87651i	0.0608453	+	0.105387i
$746$	6.19527	+	10.7305i	0.226825	+	0.392872i
$747$	2.64323	−	4.57821i	0.0967108	−	0.167508i
$748$	17.9855			0.657614
$749$	−0.528527	+	0.744250i	−0.0193120	+	0.0271943i
$750$	−0.859386			−0.0313803
$751$	8.85212	−	15.3323i	0.323018	−	0.559484i	−0.658091	−	0.752938i	$-0.728636\pi$
$751$	8.85212	−	15.3323i	0.323018	−	0.559484i	0.981109	+	0.193454i	$0.0619691\pi$
$752$	4.17251	+	7.22700i	0.152156	+	0.263541i
$753$	7.72454	+	13.3793i	0.281498	+	0.487569i
$754$	−1.88866	+	3.27126i	−0.0687810	+	0.119132i
$755$	28.8684			1.05063
$756$	1.10220	+	2.40523i	0.0400867	+	0.0874775i
$757$	−10.7915			−0.392225			−0.196112	−	0.980581i	$-0.562832\pi$
$757$	−10.7915			−0.392225			−0.196112	+	0.980581i	$0.562832\pi$
$758$	−17.4133	+	30.1607i	−0.632479	+	1.09549i
$759$	2.95058	+	5.11056i	0.107099	+	0.185502i
$760$	6.73630	+	11.6676i	0.244351	+	0.423229i
$761$	3.71541	−	6.43527i	0.134683	−	0.233278i	−0.790793	−	0.612084i	$-0.790332\pi$
$761$	3.71541	−	6.43527i	0.134683	−	0.233278i	0.925476	+	0.378805i	$0.123665\pi$
$762$	20.2682			0.734239
$763$	15.2355	+	33.2472i	0.551564	+	1.20363i
$764$	−13.0325			−0.471498
$765$	8.76819	−	15.1869i	0.317015	−	0.549085i
$766$	16.9543	+	29.3657i	0.612584	+	1.06103i
$767$	−8.08580	−	14.0050i	−0.291961	−	0.505692i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	25.3995			0.915929			0.457965	−	0.888970i	$-0.348579\pi$
$769$	25.3995			0.915929			0.457965	+	0.888970i	$0.348579\pi$
$770$	16.1326	−	22.7173i	0.581378	−	0.818674i
$771$	−12.7173			−0.458001
$772$	7.66075	−	13.2688i	0.275717	−	0.477555i
$773$	5.29560	+	9.17225i	0.190469	+	0.329903i	0.945406	−	0.325895i	$-0.105666\pi$
$773$	5.29560	+	9.17225i	0.190469	+	0.329903i	−0.754936	+	0.655798i	$0.772332\pi$
$774$	5.41794	+	9.38415i	0.194744	+	0.337306i
$775$	18.1744	−	31.4789i	0.652843	−	1.13076i
$776$	8.99477			0.322893
$777$	12.1997	+	1.14899i	0.437664	+	0.0412199i
$778$	−14.0350			−0.503181
$779$	−11.5429	+	19.9929i	−0.413567	+	0.716319i
$780$	6.05203	+	10.4824i	0.216698	+	0.375331i
$781$	−25.8571	−	44.7859i	−0.925241	−	1.60256i
$782$	−4.91329	+	8.51006i	−0.175699	+	0.304319i
$783$	−1.00000			−0.0357371
$784$	−4.57031	+	5.30210i	−0.163225	+	0.189361i
$785$	42.6625			1.52269
$786$	−0.792981	+	1.37348i	−0.0282847	+	0.0489905i
$787$	−6.43621	−	11.1478i	−0.229426	−	0.397378i	0.728212	−	0.685352i	$-0.240352\pi$
$787$	−6.43621	−	11.1478i	−0.229426	−	0.397378i	−0.957638	+	0.287974i	$0.907018\pi$
$788$	8.04290	+	13.9307i	0.286516	+	0.496261i
$789$	6.41794	−	11.1162i	0.228485	−	0.395747i
$790$	−9.87616			−0.351378
$791$	20.6061	+	1.94072i	0.732669	+	0.0690040i
$792$	−3.28646			−0.116779
$793$	−13.0410	+	22.5877i	−0.463101	+	0.802114i
$794$	11.8092	+	20.4542i	0.419094	+	0.725891i
$795$	−13.0220	−	22.5548i	−0.461843	−	0.799936i
$796$	−7.51362	+	13.0140i	−0.266313	+	0.461268i
$797$	12.4125			0.439675			0.219837	−	0.975537i	$-0.429447\pi$
$797$	12.4125			0.439675			0.219837	+	0.975537i	$0.429447\pi$
$798$	−6.44070	+	9.06953i	−0.227998	+	0.321058i
$799$	45.6689			1.61565
$800$	−2.63409	+	4.56239i	−0.0931293	+	0.161305i
$801$	1.70702	+	2.95664i	0.0603145	+	0.104468i
$802$	−5.28646	−	9.15642i	−0.186671	−	0.323324i
$803$	20.0547	−	34.7357i	0.707713	−	1.22580i
$804$	−2.75905			−0.0973043
$805$	6.34186	+	13.8393i	0.223521	+	0.487771i
$806$	−26.0623			−0.918005
$807$	−5.69265	+	9.85996i	−0.200391	+	0.347087i
$808$	−3.41142	−	5.90875i	−0.120013	−	0.207869i
$809$	1.50839	+	2.61260i	0.0530321	+	0.0918542i	0.891323	−	0.453369i	$-0.149778\pi$
$809$	1.50839	+	2.61260i	0.0530321	+	0.0918542i	−0.838291	+	0.545224i	$0.816445\pi$
$810$	−1.60220	+	2.77509i	−0.0562956	+	0.0975068i
$811$	2.78256			0.0977089			0.0488545	−	0.998806i	$-0.484443\pi$
$811$	2.78256			0.0977089			0.0488545	+	0.998806i	$0.484443\pi$
$812$	−1.10220	−	2.40523i	−0.0386797	−	0.0844072i
$813$	21.3723			0.749558
$814$	−7.61059	+	13.1819i	−0.266751	+	0.462026i
$815$	−19.6477	−	34.0308i	−0.688229	−	1.19205i
$816$	−2.73630	−	4.73940i	−0.0957895	−	0.165912i
$817$	−22.7792	+	39.4547i	−0.796943	+	1.38035i
$818$	37.1821			1.30004
$819$	−5.78646	+	8.14826i	−0.202195	+	0.284723i
$820$	−17.5949			−0.614442
$821$	26.3020	−	45.5563i	0.917944	−	1.58993i	0.115412	−	0.993318i	$-0.463181\pi$
$821$	26.3020	−	45.5563i	0.917944	−	1.58993i	0.802532	−	0.596609i	$-0.203486\pi$
$822$	2.47724	+	4.29071i	0.0864038	+	0.149656i
$823$	0.0156555	+	0.0271162i	0.000545718	+	0.000945211i	0.866298	−	0.499527i	$-0.166493\pi$
$823$	0.0156555	+	0.0271162i	0.000545718	+	0.000945211i	−0.865752	+	0.500473i	$0.833160\pi$
$824$	−0.222674	+	0.385683i	−0.00775723	+	0.0134359i
$825$	17.3137			0.602786
$826$	11.2772	+	1.06210i	0.392383	+	0.0369552i
$827$	−45.3775			−1.57793			−0.788965	−	0.614438i	$-0.789383\pi$
$827$	−45.3775			−1.57793			−0.788965	+	0.614438i	$0.789383\pi$
$828$	0.897799	−	1.55503i	0.0312007	−	0.0540412i
$829$	−25.0923	−	43.4612i	−0.871492	−	1.50947i	−0.860453	−	0.509530i	$-0.829819\pi$
$829$	−25.0923	−	43.4612i	−0.871492	−	1.50947i	−0.0110389	−	0.999939i	$-0.503514\pi$
$830$	8.46997	+	14.6704i	0.293997	+	0.509218i
$831$	0.251951	−	0.436392i	0.00874008	−	0.0151383i
$832$	3.77733			0.130955
$833$	12.6231	+	36.1686i	0.437364	+	1.25317i
$834$	−21.2902			−0.737219
$835$	−32.6488	+	56.5494i	−1.12986	+	1.95697i
$836$	−6.90880	−	11.9664i	−0.238946	−	0.413867i
$837$	−3.44983	−	5.97529i	−0.119244	−	0.206536i
$838$	9.92969	−	17.1987i	0.343016	−	0.594120i
$839$	27.0000			0.932144			0.466072	−	0.884747i	$-0.345669\pi$
$839$	27.0000			0.932144			0.466072	+	0.884747i	$0.345669\pi$
$840$	−8.44070	−	0.794959i	−0.291232	−	0.0274287i
$841$	1.00000			0.0344828
$842$	20.1496	−	34.9001i	0.694400	−	1.20274i
$843$	13.4745	+	23.3384i	0.464085	+	0.803819i
$844$	−11.5657	−	20.0323i	−0.398106	−	0.689540i
$845$	−2.03189	+	3.51934i	−0.0698993	+	0.121069i
$846$	−8.34502			−0.286908
$847$	0.305103	−	0.429634i	0.0104835	−	0.0147624i
$848$	−8.12758			−0.279102
$849$	−2.80008	+	4.84989i	−0.0960986	+	0.166448i
$850$	14.4153	+	24.9681i	0.494441	+	0.856398i
$851$	−4.15814	−	7.20210i	−0.142539	−	0.246885i
$852$	−7.86777	+	13.6274i	−0.269545	+	0.466866i
$853$	−46.3394			−1.58663			−0.793316	−	0.608810i	$-0.791647\pi$
$853$	−46.3394			−1.58663			−0.793316	+	0.608810i	$0.791647\pi$
$854$	−7.61059	−	16.6079i	−0.260429	−	0.568311i
$855$	−13.4726			−0.460753
$856$	−0.172508	+	0.298792i	−0.00589619	+	0.0102125i
$857$	24.4765	+	42.3945i	0.836101	+	1.44817i	0.893131	+	0.449797i	$0.148504\pi$
$857$	24.4765	+	42.3945i	0.836101	+	1.44817i	−0.0570297	+	0.998372i	$0.518163\pi$
$858$	−6.20702	−	10.7509i	−0.211904	−	0.367029i
$859$	21.4277	−	37.1138i	0.731102	−	1.26631i	−0.225310	−	0.974287i	$-0.572340\pi$
$859$	21.4277	−	37.1138i	0.731102	−	1.26631i	0.956412	−	0.292019i	$-0.0943271\pi$
$860$	−34.7225			−1.18403
$861$	−6.05203	−	13.2068i	−0.206253	−	0.450087i
$862$	17.6692			0.601815
$863$	16.5774	−	28.7129i	0.564302	−	0.977399i	−0.432813	−	0.901484i	$-0.642479\pi$
$863$	16.5774	−	28.7129i	0.564302	−	0.977399i	0.997114	−	0.0759151i	$-0.0241878\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	17.7473	+	30.7392i	0.603426	+	1.04516i
$866$	12.9745	−	22.4724i	0.440890	−	0.763644i
$867$	−12.9493			−0.439780
$868$	10.5696	−	14.8836i	0.358754	−	0.505183i
$869$	10.1291			0.343605
$870$	1.60220	−	2.77509i	0.0543197	−	0.0940845i
$871$	−5.21092	−	9.02558i	−0.176565	−	0.305820i
$872$	6.91142	+	11.9709i	0.234050	+	0.405387i
$873$	−4.49738	+	7.78970i	−0.152213	+	0.263641i
$874$	7.54942			0.255363
$875$	2.26370	+	0.213199i	0.0765272	+	0.00720746i
$876$	−12.2044			−0.412349
$877$	−10.1680	+	17.6115i	−0.343350	+	0.594699i	−0.985053	−	0.172254i	$-0.944895\pi$
$877$	−10.1680	+	17.6115i	−0.343350	+	0.594699i	0.641703	+	0.766953i	$0.278228\pi$
$878$	−7.94070	−	13.7537i	−0.267986	−	0.464165i
$879$	5.74730	+	9.95461i	0.193852	+	0.335761i
$880$	5.26557	−	9.12024i	0.177502	−	0.307443i
$881$	2.29053			0.0771699			0.0385850	−	0.999255i	$-0.487715\pi$
$881$	2.29053			0.0771699			0.0385850	+	0.999255i	$0.487715\pi$
$882$	−2.30660	−	6.60905i	−0.0776673	−	0.222538i
$883$	49.9112			1.67965			0.839823	−	0.542860i	$-0.182659\pi$
$883$	49.9112			1.67965			0.839823	+	0.542860i	$0.182659\pi$
$884$	10.3359	−	17.9023i	0.347633	−	0.602118i
$885$	6.85939	+	11.8808i	0.230576	+	0.399369i
$886$	−14.0657	−	24.3624i	−0.472545	−	0.818472i
$887$	4.21429	−	7.29936i	0.141502	−	0.245089i	−0.786560	−	0.617513i	$-0.788140\pi$
$887$	4.21429	−	7.29936i	0.141502	−	0.245089i	0.928062	+	0.372425i	$0.121474\pi$
$888$	4.63148			0.155422
$889$	−53.3883	−	5.02820i	−1.79059	−	0.168640i
$890$	−10.9399			−0.366708
$891$	1.64323	−	2.84616i	0.0550503	−	0.0953499i
$892$	0.193398	+	0.334975i	0.00647543	+	0.0112158i
$893$	−17.5429	−	30.3852i	−0.587051	−	1.01680i
$894$	−0.518273	+	0.897675i	−0.0173336	+	0.0300227i
$895$	−22.9687			−0.767759
$896$	−1.53189	+	2.15715i	−0.0511770	+	0.0720654i
$897$	6.78256			0.226463
$898$	14.8404	−	25.7043i	0.495229	−	0.857762i
$899$	3.44983	+	5.97529i	0.115058	+	0.199287i
$900$	−2.63409	−	4.56239i	−0.0878032	−	0.152080i
$901$	−22.2394	+	38.5199i	−0.740903	+	1.28328i
$902$	18.0455			0.600850
$903$	−11.9433	−	26.0628i	−0.397449	−	0.867317i
$904$	7.82284			0.260184
$905$	20.9015	−	36.2025i	0.694791	−	1.20341i
$906$	4.50448	+	7.80200i	0.149651	+	0.259204i
$907$	−16.4263	−	28.4512i	−0.545427	−	0.944708i	−0.998580	−	0.0532747i	$-0.983034\pi$
$907$	−16.4263	−	28.4512i	−0.545427	−	0.944708i	0.453153	−	0.891433i	$-0.350299\pi$
$908$	−7.86777	+	13.6274i	−0.261101	+	0.452241i
$909$	6.82284			0.226299
$910$	−13.3411	−	29.1131i	−0.442254	−	0.965091i
$911$	−44.5558			−1.47620			−0.738100	−	0.674691i	$-0.764277\pi$
$911$	−44.5558			−1.47620			−0.738100	+	0.674691i	$0.764277\pi$
$912$	−2.10220	+	3.64112i	−0.0696108	+	0.120569i
$913$	−8.68688	−	15.0461i	−0.287494	−	0.497954i
$914$	−8.46084	−	14.6546i	−0.279860	−	0.484731i
$915$	11.0630	−	19.1617i	0.365733	−	0.633468i
$916$	16.4036			0.541989
$917$	2.42953	−	3.42116i	0.0802300	−	0.112977i
$918$	5.47259			0.180622
$919$	12.6321	−	21.8794i	0.416693	−	0.721734i	−0.578911	−	0.815390i	$-0.696522\pi$
$919$	12.6321	−	21.8794i	0.416693	−	0.721734i	0.995605	+	0.0936567i	$0.0298556\pi$
$920$	2.87691	+	4.98295i	0.0948489	+	0.164283i
$921$	12.3456	+	21.3832i	0.406801	+	0.704601i
$922$	14.7544	−	25.5554i	0.485910	−	0.841621i
$923$	−59.4383			−1.95643
$924$	8.65685	+	0.815317i	0.284790	+	0.0268220i
$925$	−24.3995			−0.802251
$926$	2.75644	−	4.77429i	0.0905821	−	0.156893i
$927$	−0.222674	−	0.385683i	−0.00731358	−	0.0126675i
$928$	−0.500000	−	0.866025i	−0.0164133	−	0.0284287i
$929$	−13.1080	+	22.7037i	−0.430059	+	0.744883i	−0.996878	−	0.0789589i	$-0.974840\pi$
$929$	−13.1080	+	22.7037i	−0.430059	+	0.744883i	0.566819	+	0.823842i	$0.308174\pi$
$930$	22.1093			0.724993
$931$	19.2154	−	22.2922i	0.629759	−	0.730596i
$932$	8.65498			0.283503
$933$	−1.70178	+	2.94758i	−0.0557139	+	0.0964993i
$934$	14.2180	+	24.6263i	0.465228	+	0.805798i
$935$	−28.8163	−	49.9113i	−0.942394	−	1.63228i
$936$	−1.88866	+	3.27126i	−0.0617329	+	0.106924i
$937$	7.77326			0.253941			0.126971	−	0.991906i	$-0.459475\pi$
$937$	7.77326			0.253941			0.126971	+	0.991906i	$0.459475\pi$
$938$	7.26761	+	0.684475i	0.237296	+	0.0223489i
$939$	27.6770			0.903205
$940$	13.3704	−	23.1582i	0.436094	−	0.755337i
$941$	−4.09958	−	7.10069i	−0.133643	−	0.231476i	0.791436	−	0.611253i	$-0.209334\pi$
$941$	−4.09958	−	7.10069i	−0.133643	−	0.231476i	−0.925078	+	0.379777i	$0.876001\pi$
$942$	6.65685	+	11.5300i	0.216892	+	0.375668i
$943$	−4.92969	+	8.53848i	−0.160533	+	0.278051i
$944$	4.28123			0.139342
$945$	4.90880	−	6.91238i	0.159683	−	0.224860i
$946$	35.6117			1.15784
$947$	−28.7245	+	49.7524i	−0.933422	+	1.61673i	−0.155999	+	0.987757i	$0.549860\pi$
$947$	−28.7245	+	49.7524i	−0.933422	+	1.61673i	−0.777424	+	0.628977i	$0.783474\pi$
$948$	−1.54103	−	2.66914i	−0.0500503	−	0.0866897i
$949$	−23.0500	−	39.9238i	−0.748235	−	1.29598i
$950$	11.0748	−	19.1821i	0.359314	−	0.622350i
$951$	−31.5453			−1.02293
$952$	6.03189	+	13.1629i	0.195495	+	0.426611i
$953$	−14.0220			−0.454217			−0.227109	−	0.973869i	$-0.572927\pi$
$953$	−14.0220			−0.454217			−0.227109	+	0.973869i	$0.572927\pi$
$954$	4.06379	−	7.03869i	0.131570	−	0.227886i
$955$	20.8806	+	36.1663i	0.675682	+	1.17032i
$956$	−4.37039	−	7.56974i	−0.141349	−	0.244823i
$957$	−1.64323	+	2.84616i	−0.0531181	+	0.0920033i
$958$	−9.30473			−0.300622
$959$	−5.46084	−	11.9167i	−0.176340	−	0.384810i
$960$	−3.20440			−0.103422
$961$	−8.30270	+	14.3807i	−0.267829	+	0.463894i
$962$	8.74730	+	15.1508i	0.282024	+	0.488480i
$963$	−0.172508	−	0.298792i	−0.00555898	−	0.00962844i
$964$	−1.29298	+	2.23951i	−0.0416441	+	0.0721297i
$965$	−49.0963			−1.58046
$966$	−2.75067	+	3.87338i	−0.0885012	+	0.124624i
$967$	35.4413			1.13971			0.569857	−	0.821744i	$-0.306998\pi$
$967$	35.4413			1.13971			0.569857	+	0.821744i	$0.306998\pi$
$968$	0.0995835	−	0.172484i	0.00320074	−	0.00554384i
$969$	11.5045	+	19.9264i	0.369577	+	0.640127i
$970$	−14.4114	−	24.9613i	−0.462723	−	0.801459i
$971$	17.6809	−	30.6242i	0.567407	−	0.982778i	−0.429414	−	0.903108i	$-0.641280\pi$
$971$	17.6809	−	30.6242i	0.567407	−	0.982778i	0.996821	−	0.0796700i	$-0.0253867\pi$
$972$	−1.00000			−0.0320750
$973$	56.0804	+	5.28175i	1.79785	+	0.169325i
$974$	−26.7135			−0.855957
$975$	9.94983	−	17.2336i	0.318650	−	0.551917i
$976$	−3.45245	−	5.97982i	−0.110510	−	0.191409i
$977$	23.5310	+	40.7568i	0.752823	+	1.30393i	0.946450	+	0.322852i	$0.104642\pi$
$977$	23.5310	+	40.7568i	0.752823	+	1.30393i	−0.193627	+	0.981075i	$0.562025\pi$
$978$	6.13148	−	10.6200i	0.196063	−	0.339591i
$979$	11.2201			0.358596
$980$	22.0364	+	4.18799i	0.703926	+	0.133781i
$981$	−13.8228			−0.441329
$982$	8.49086	−	14.7066i	0.270954	−	0.469307i
$983$	21.8631	+	37.8680i	0.697325	+	1.20780i	0.969391	+	0.245524i	$0.0789600\pi$
$983$	21.8631	+	37.8680i	0.697325	+	1.20780i	−0.272065	+	0.962279i	$0.587707\pi$
$984$	−2.74543	−	4.75523i	−0.0875212	−	0.151591i
$985$	25.7727	−	44.6396i	0.821186	−	1.42234i
$986$	−5.47259			−0.174283
$987$	21.9816	+	2.07026i	0.699681	+	0.0658971i
$988$	−15.8814			−0.505254
$989$	−9.72844	+	16.8502i	−0.309347	+	0.535804i
$990$	5.26557	+	9.12024i	0.167351	+	0.289860i
$991$	−19.6613	−	34.0544i	−0.624563	−	1.08177i	−0.988625	−	0.150400i	$-0.951944\pi$
$991$	−19.6613	−	34.0544i	−0.624563	−	1.08177i	0.364062	−	0.931375i	$-0.381390\pi$
$992$	3.44983	−	5.97529i	0.109532	−	0.189716i
$993$	−12.1626			−0.385969
$994$	24.1052	−	33.9440i	0.764570	−	1.07664i
$995$	48.1533			1.52656
$996$	−2.64323	+	4.57821i	−0.0837540	+	0.145066i
$997$	1.93696	+	3.35492i	0.0613442	+	0.106251i	0.895066	−	0.445933i	$-0.147128\pi$
$997$	1.93696	+	3.35492i	0.0613442	+	0.106251i	−0.833722	+	0.552184i	$0.813795\pi$
$998$	8.29095	+	14.3603i	0.262445	+	0.454569i
$999$	−2.31574	+	4.01098i	−0.0732667	+	0.126902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.i.b.1045.1	yes	6
7.2	even	3		8526.2.a.by.1.3		3
7.4	even	3	inner	1218.2.i.b.697.1	✓	6
7.5	odd	6		8526.2.a.ca.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.i.b.697.1	✓	6	7.4	even	3	inner
1218.2.i.b.1045.1	yes	6	1.1	even	1	trivial
8526.2.a.by.1.3		3	7.2	even	3
8526.2.a.ca.1.1		3	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.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} +(-1.60220 + 2.77509i) q^{5} -1.00000 q^{6} +(2.63409 + 0.248083i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.60220 - 2.77509i) q^{10} +(1.64323 + 2.84616i) q^{11} +(0.500000 - 0.866025i) q^{12} +3.77733 q^{13} +(-1.53189 + 2.15715i) q^{14} -3.20440 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.73630 + 4.73940i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(2.10220 - 3.64112i) q^{19} +3.20440 q^{20} +(1.10220 + 2.40523i) q^{21} -3.28646 q^{22} +(0.897799 - 1.55503i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.63409 - 4.56239i) q^{25} +(-1.88866 + 3.27126i) q^{26} -1.00000 q^{27} +(-1.10220 - 2.40523i) q^{28} +1.00000 q^{29} +(1.60220 - 2.77509i) q^{30} +(3.44983 + 5.97529i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.64323 + 2.84616i) q^{33} -5.47259 q^{34} +(-4.90880 + 6.91238i) q^{35} +1.00000 q^{36} +(2.31574 - 4.01098i) q^{37} +(2.10220 + 3.64112i) q^{38} +(1.88866 + 3.27126i) q^{39} +(-1.60220 + 2.77509i) q^{40} -5.49086 q^{41} +(-2.63409 - 0.248083i) q^{42} -10.8359 q^{43} +(1.64323 - 2.84616i) q^{44} +(-1.60220 - 2.77509i) q^{45} +(0.897799 + 1.55503i) q^{46} +(4.17251 - 7.22700i) q^{47} -1.00000 q^{48} +(6.87691 + 1.30695i) q^{49} +5.26819 q^{50} +(-2.73630 + 4.73940i) q^{51} +(-1.88866 - 3.27126i) q^{52} +(4.06379 + 7.03869i) q^{53} +(0.500000 - 0.866025i) q^{54} -10.5311 q^{55} +(2.63409 + 0.248083i) q^{56} +4.20440 q^{57} +(-0.500000 + 0.866025i) q^{58} +(-2.14061 - 3.70765i) q^{59} +(1.60220 + 2.77509i) q^{60} +(-3.45245 + 5.97982i) q^{61} -6.89967 q^{62} +(-1.53189 + 2.15715i) q^{63} +1.00000 q^{64} +(-6.05203 + 10.4824i) q^{65} +(-1.64323 - 2.84616i) q^{66} +(-1.37953 - 2.38941i) q^{67} +(2.73630 - 4.73940i) q^{68} +1.79560 q^{69} +(-3.53189 - 7.70734i) q^{70} -15.7355 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-6.10220 - 10.5693i) q^{73} +(2.31574 + 4.01098i) q^{74} +(2.63409 - 4.56239i) q^{75} -4.20440 q^{76} +(3.62234 + 7.90471i) q^{77} -3.77733 q^{78} +(1.54103 - 2.66914i) q^{79} +(-1.60220 - 2.77509i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.74543 - 4.75523i) q^{82} -5.28646 q^{83} +(1.53189 - 2.15715i) q^{84} -17.5364 q^{85} +(5.41794 - 9.38415i) q^{86} +(0.500000 + 0.866025i) q^{87} +(1.64323 + 2.84616i) q^{88} +(1.70702 - 2.95664i) q^{89} +3.20440 q^{90} +(9.94983 + 0.937092i) q^{91} -1.79560 q^{92} +(-3.44983 + 5.97529i) q^{93} +(4.17251 + 7.22700i) q^{94} +(6.73630 + 11.6676i) q^{95} +(0.500000 - 0.866025i) q^{96} +8.99477 q^{97} +(-4.57031 + 5.30210i) q^{98} -3.28646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - q^{5} - 6 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - q^{10} + 11 q^{11} + 3 q^{12} + 10 q^{13} - 4 q^{14} - 2 q^{15} - 3 q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots - 22 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - q^5 - 6 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - q^10 + 11 * q^11 + 3 * q^12 + 10 * q^13 - 4 * q^14 - 2 * q^15 - 3 * q^16 - 6 * q^17 - 3 * q^18 + 4 * q^19 + 2 * q^20 - 2 * q^21 - 22 * q^22 + 14 * q^23 + 3 * q^24 - 2 * q^25 - 5 * q^26 - 6 * q^27 + 2 * q^28 + 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 - 11 * q^33 + 12 * q^34 + 5 * q^35 + 6 * q^36 + 3 * q^37 + 4 * q^38 + 5 * q^39 - q^40 - 18 * q^41 - 2 * q^42 - 26 * q^43 + 11 * q^44 - q^45 + 14 * q^46 + 13 * q^47 - 6 * q^48 + 12 * q^49 + 4 * q^50 + 6 * q^51 - 5 * q^52 + 14 * q^53 + 3 * q^54 + 8 * q^55 + 2 * q^56 + 8 * q^57 - 3 * q^58 - 6 * q^59 + q^60 - 4 * q^61 + 8 * q^62 - 4 * q^63 + 6 * q^64 - 3 * q^65 - 11 * q^66 + 13 * q^67 - 6 * q^68 + 28 * q^69 - 16 * q^70 - 6 * q^71 - 3 * q^72 - 28 * q^73 + 3 * q^74 + 2 * q^75 - 8 * q^76 - 15 * q^77 - 10 * q^78 + 19 * q^79 - q^80 - 3 * q^81 + 9 * q^82 - 34 * q^83 + 4 * q^84 - 50 * q^85 + 13 * q^86 + 3 * q^87 + 11 * q^88 + q^89 + 2 * q^90 + 35 * q^91 - 28 * q^92 + 4 * q^93 + 13 * q^94 + 18 * q^95 + 3 * q^96 + 38 * q^97 - 24 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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