LMFDB - Embedded newform 966.2.l.c.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.11
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.633338 - 1.61211i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.42388 + 2.46624i) q^{5} +(-1.35454 + 1.07946i) q^{6} +(0.837175 + 2.50981i) q^{7} -1.00000i q^{8} +(-2.19777 - 2.04201i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.633338 - 1.61211i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.42388 + 2.46624i) q^{5} +(-1.35454 + 1.07946i) q^{6} +(0.837175 + 2.50981i) q^{7} -1.00000i q^{8} +(-2.19777 - 2.04201i) q^{9} +(2.46624 - 1.42388i) q^{10} +(0.238022 - 0.137422i) q^{11} +(1.71279 - 0.257566i) q^{12} +0.481291i q^{13} +(0.529889 - 2.59215i) q^{14} +(3.07404 + 3.85741i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.32798 - 2.30012i) q^{17} +(0.882314 + 2.86732i) q^{18} +(-5.64383 - 3.25847i) q^{19} -2.84777 q^{20} +(4.57629 + 0.239943i) q^{21} -0.274844 q^{22} +(0.866025 + 0.500000i) q^{23} +(-1.61211 - 0.633338i) q^{24} +(-1.55489 - 2.69314i) q^{25} +(0.240646 - 0.416811i) q^{26} +(-4.68387 + 2.24974i) q^{27} +(-1.75497 + 1.97992i) q^{28} +9.99256i q^{29} +(-0.733487 - 4.87763i) q^{30} +(-4.31139 + 2.48918i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.0707904 - 0.470751i) q^{33} +2.65595i q^{34} +(-7.38182 - 1.50900i) q^{35} +(0.669554 - 2.92433i) q^{36} +(-1.41244 + 2.44642i) q^{37} +(3.25847 + 5.64383i) q^{38} +(0.775892 + 0.304820i) q^{39} +(2.46624 + 1.42388i) q^{40} -8.28910 q^{41} +(-3.84321 - 2.49594i) q^{42} -5.43884 q^{43} +(0.238022 + 0.137422i) q^{44} +(8.16546 - 2.51262i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.68975 + 2.92673i) q^{47} +(1.07946 + 1.35454i) q^{48} +(-5.59828 + 4.20230i) q^{49} +3.10977i q^{50} +(-4.54910 + 0.684083i) q^{51} +(-0.416811 + 0.240646i) q^{52} +(0.408700 - 0.235963i) q^{53} +(5.18122 + 0.393600i) q^{54} +0.782691i q^{55} +(2.50981 - 0.837175i) q^{56} +(-8.82744 + 7.03474i) q^{57} +(4.99628 - 8.65381i) q^{58} +(-0.676766 - 1.17219i) q^{59} +(-1.80360 + 4.59090i) q^{60} +(8.28474 + 4.78320i) q^{61} +4.97836 q^{62} +(3.28515 - 7.22550i) q^{63} -1.00000 q^{64} +(-1.18698 - 0.685303i) q^{65} +(-0.174069 + 0.443077i) q^{66} +(-6.38691 - 11.0625i) q^{67} +(1.32798 - 2.30012i) q^{68} +(1.35454 - 1.07946i) q^{69} +(5.63835 + 4.99774i) q^{70} +8.10946i q^{71} +(-2.04201 + 2.19777i) q^{72} +(2.35684 - 1.36072i) q^{73} +(2.44642 - 1.41244i) q^{74} +(-5.32640 + 0.800971i) q^{75} -6.51693i q^{76} +(0.544168 + 0.482343i) q^{77} +(-0.519532 - 0.651928i) q^{78} +(-1.12295 + 1.94500i) q^{79} +(-1.42388 - 2.46624i) q^{80} +(0.660351 + 8.97574i) q^{81} +(7.17857 + 4.14455i) q^{82} +10.0232 q^{83} +(2.08035 + 4.08315i) q^{84} +7.56353 q^{85} +(4.71018 + 2.71942i) q^{86} +(16.1091 + 6.32867i) q^{87} +(-0.137422 - 0.238022i) q^{88} +(4.40438 - 7.62861i) q^{89} +(-8.32780 - 1.90673i) q^{90} +(-1.20795 + 0.402925i) q^{91} +1.00000i q^{92} +(1.28226 + 8.52691i) q^{93} +(2.92673 - 1.68975i) q^{94} +(16.0723 - 9.27935i) q^{95} +(-0.257566 - 1.71279i) q^{96} +9.15367i q^{97} +(6.94940 - 0.840159i) q^{98} +(-0.803734 - 0.184023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.633338	−	1.61211i	0.365658	−	0.930749i
$3$	0.633338	−	1.61211i	0.365658	−	0.930749i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.42388	+	2.46624i	−0.636780	+	1.10294i	0.349355	+	0.936990i	$0.386401\pi$
$5$	−1.42388	+	2.46624i	−0.636780	+	1.10294i	−0.986135	+	0.165945i	$0.946933\pi$
$6$	−1.35454	+	1.07946i	−0.552988	+	0.440686i
$7$	0.837175	+	2.50981i	0.316422	+	0.948618i
$7$	0.837175	+	2.50981i	0.316422	+	0.948618i
$8$		−	1.00000i		−	0.353553i
$9$	−2.19777	−	2.04201i	−0.732589	−	0.680672i
$10$	2.46624	−	1.42388i	0.779893	−	0.450271i
$11$	0.238022	−	0.137422i	0.0717662	−	0.0414343i	−0.463687	−	0.885999i	$-0.653474\pi$
$11$	0.238022	−	0.137422i	0.0717662	−	0.0414343i	0.535454	+	0.844565i	$0.320141\pi$
$12$	1.71279	−	0.257566i	0.494441	−	0.0743528i
$13$			0.481291i			0.133486i	0.997770	+	0.0667431i	$0.0212608\pi$
$13$			0.481291i			0.133486i	−0.997770	+	0.0667431i	$0.978739\pi$
$14$	0.529889	−	2.59215i	0.141619	−	0.692780i
$15$	3.07404	+	3.85741i	0.793713	+	0.995979i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.32798	−	2.30012i	−0.322082	−	0.557862i	0.658836	−	0.752287i	$-0.271049\pi$
$17$	−1.32798	−	2.30012i	−0.322082	−	0.557862i	−0.980917	+	0.194425i	$0.937716\pi$
$18$	0.882314	+	2.86732i	0.207963	+	0.675834i
$19$	−5.64383	−	3.25847i	−1.29478	−	0.747544i	−0.315285	−	0.948997i	$-0.602100\pi$
$19$	−5.64383	−	3.25847i	−1.29478	−	0.747544i	−0.979498	+	0.201453i	$0.935434\pi$
$20$	−2.84777			−0.636780
$21$	4.57629	+	0.239943i	0.998628	+	0.0523598i
$22$	−0.274844			−0.0585969
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$	−1.61211	−	0.633338i	−0.329070	−	0.129280i
$25$	−1.55489	−	2.69314i	−0.310977	−	0.538628i
$26$	0.240646	−	0.416811i	0.0471945	−	0.0817433i
$27$	−4.68387	+	2.24974i	−0.901411	+	0.432964i
$28$	−1.75497	+	1.97992i	−0.331658	+	0.374170i
$29$			9.99256i			1.85557i	0.373113	+	0.927786i	$0.378290\pi$
$29$			9.99256i			1.85557i	−0.373113	+	0.927786i	$0.621710\pi$
$30$	−0.733487	−	4.87763i	−0.133916	−	0.890530i
$31$	−4.31139	+	2.48918i	−0.774349	+	0.447070i	−0.834424	−	0.551124i	$-0.814199\pi$
$31$	−4.31139	+	2.48918i	−0.774349	+	0.447070i	0.0600751	+	0.998194i	$0.480866\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.0707904	−	0.470751i	−0.0123230	−	0.0819472i
$34$			2.65595i			0.455492i
$35$	−7.38182	−	1.50900i	−1.24776	−	0.255068i
$36$	0.669554	−	2.92433i	0.111592	−	0.487388i
$37$	−1.41244	+	2.44642i	−0.232204	+	0.402189i	−0.958456	−	0.285239i	$-0.907927\pi$
$37$	−1.41244	+	2.44642i	−0.232204	+	0.402189i	0.726252	+	0.687428i	$0.241260\pi$
$38$	3.25847	+	5.64383i	0.528593	+	0.915550i
$39$	0.775892	+	0.304820i	0.124242	+	0.0488103i
$40$	2.46624	+	1.42388i	0.389946	+	0.225136i
$41$	−8.28910			−1.29454			−0.647270	−	0.762261i	$-0.724089\pi$
$41$	−8.28910			−1.29454			−0.647270	+	0.762261i	$0.724089\pi$
$42$	−3.84321	−	2.49594i	−0.593020	−	0.385132i
$43$	−5.43884			−0.829416			−0.414708	−	0.909955i	$-0.636116\pi$
$43$	−5.43884			−0.829416			−0.414708	+	0.909955i	$0.636116\pi$
$44$	0.238022	+	0.137422i	0.0358831	+	0.0207171i
$45$	8.16546	−	2.51262i	1.21723	−	0.374560i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−1.68975	+	2.92673i	−0.246475	+	0.426907i	−0.962545	−	0.271121i	$-0.912606\pi$
$47$	−1.68975	+	2.92673i	−0.246475	+	0.426907i	0.716070	+	0.698028i	$0.245939\pi$
$48$	1.07946	+	1.35454i	0.155806	+	0.195511i
$49$	−5.59828	+	4.20230i	−0.799754	+	0.600328i
$50$			3.10977i			0.439788i
$51$	−4.54910	+	0.684083i	−0.637001	+	0.0957907i
$52$	−0.416811	+	0.240646i	−0.0578012	+	0.0333716i
$53$	0.408700	−	0.235963i	0.0561393	−	0.0324120i	−0.471668	−	0.881776i	$-0.656348\pi$
$53$	0.408700	−	0.235963i	0.0561393	−	0.0324120i	0.527807	+	0.849364i	$0.323014\pi$
$54$	5.18122	+	0.393600i	0.705075	+	0.0535621i
$55$			0.782691i			0.105538i
$56$	2.50981	−	0.837175i	0.335387	−	0.111872i
$57$	−8.82744	+	7.03474i	−1.16922	+	0.931774i
$58$	4.99628	−	8.65381i	0.656044	−	1.13630i
$59$	−0.676766	−	1.17219i	−0.0881074	−	0.152606i	0.818604	−	0.574359i	$-0.194749\pi$
$59$	−0.676766	−	1.17219i	−0.0881074	−	0.152606i	−0.906711	+	0.421752i	$0.861415\pi$
$60$	−1.80360	+	4.59090i	−0.232844	+	0.592682i
$61$	8.28474	+	4.78320i	1.06075	+	0.612425i	0.925640	−	0.378405i	$-0.123527\pi$
$61$	8.28474	+	4.78320i	1.06075	+	0.612425i	0.135112	+	0.990830i	$0.456861\pi$
$62$	4.97836			0.632253
$63$	3.28515	−	7.22550i	0.413890	−	0.910327i
$64$	−1.00000			−0.125000
$65$	−1.18698	−	0.685303i	−0.147227	−	0.0850013i
$66$	−0.174069	+	0.443077i	−0.0214264	+	0.0545390i
$67$	−6.38691	−	11.0625i	−0.780285	−	1.35149i	−0.931776	−	0.363035i	$-0.881741\pi$
$67$	−6.38691	−	11.0625i	−0.780285	−	1.35149i	0.151490	−	0.988459i	$-0.451593\pi$
$68$	1.32798	−	2.30012i	0.161041	−	0.278931i
$69$	1.35454	−	1.07946i	0.163067	−	0.129951i
$70$	5.63835	+	4.99774i	0.673911	+	0.597345i
$71$			8.10946i			0.962415i	0.876607	+	0.481208i	$0.159802\pi$
$71$			8.10946i			0.962415i	−0.876607	+	0.481208i	$0.840198\pi$
$72$	−2.04201	+	2.19777i	−0.240654	+	0.259009i
$73$	2.35684	−	1.36072i	0.275848	−	0.159261i	−0.355694	−	0.934602i	$-0.615756\pi$
$73$	2.35684	−	1.36072i	0.275848	−	0.159261i	0.631542	+	0.775342i	$0.282422\pi$
$74$	2.44642	−	1.41244i	0.284391	−	0.164193i
$75$	−5.32640	+	0.800971i	−0.615039	+	0.0924882i
$76$		−	6.51693i		−	0.747544i
$77$	0.544168	+	0.482343i	0.0620138	+	0.0549681i
$78$	−0.519532	−	0.651928i	−0.0588255	−	0.0738163i
$79$	−1.12295	+	1.94500i	−0.126342	+	0.218830i	−0.922257	−	0.386578i	$-0.873657\pi$
$79$	−1.12295	+	1.94500i	−0.126342	+	0.218830i	0.795915	+	0.605408i	$0.206990\pi$
$80$	−1.42388	−	2.46624i	−0.159195	−	0.275734i
$81$	0.660351	+	8.97574i	0.0733723	+	0.997305i
$82$	7.17857	+	4.14455i	0.792741	+	0.457689i
$83$	10.0232			1.10019			0.550095	−	0.835102i	$-0.314591\pi$
$83$	10.0232			1.10019			0.550095	+	0.835102i	$0.314591\pi$
$84$	2.08035	+	4.08315i	0.226985	+	0.445509i
$85$	7.56353			0.820380
$86$	4.71018	+	2.71942i	0.507911	+	0.293243i
$87$	16.1091	+	6.32867i	1.72707	+	0.678504i
$88$	−0.137422	−	0.238022i	−0.0146492	−	0.0253732i
$89$	4.40438	−	7.62861i	0.466863	−	0.808631i	−0.532420	−	0.846480i	$-0.678717\pi$
$89$	4.40438	−	7.62861i	0.466863	−	0.808631i	0.999283	+	0.0378494i	$0.0120507\pi$
$90$	−8.32780	−	1.90673i	−0.877828	−	0.200987i
$91$	−1.20795	+	0.402925i	−0.126627	+	0.0422380i
$92$			1.00000i			0.104257i
$93$	1.28226	+	8.52691i	0.132964	+	0.884199i
$94$	2.92673	−	1.68975i	0.301869	−	0.174284i
$95$	16.0723	−	9.27935i	1.64898	−	0.952041i
$96$	−0.257566	−	1.71279i	−0.0262877	−	0.174811i
$97$			9.15367i			0.929414i	0.885464	+	0.464707i	$0.153840\pi$
$97$			9.15367i			0.929414i	−0.885464	+	0.464707i	$0.846160\pi$
$98$	6.94940	−	0.840159i	0.701995	−	0.0848689i
$99$	−0.803734	−	0.184023i	−0.0807783	−	0.0184950i
$100$	1.55489	−	2.69314i	0.155489	−	0.269314i
$101$	−1.39121	−	2.40965i	−0.138431	−	0.239769i	0.788472	−	0.615070i	$-0.210872\pi$
$101$	−1.39121	−	2.40965i	−0.138431	−	0.239769i	−0.926903	+	0.375302i	$0.877539\pi$
$102$	4.28167	+	1.68212i	0.423949	+	0.166554i
$103$	−7.05990	−	4.07604i	−0.695633	−	0.401624i	0.110086	−	0.993922i	$-0.464887\pi$
$103$	−7.05990	−	4.07604i	−0.695633	−	0.401624i	−0.805719	+	0.592298i	$0.798221\pi$
$104$	0.481291			0.0471945
$105$	−7.10786	+	10.9446i	−0.693656	+	1.06808i
$106$	−0.471926			−0.0458375
$107$	8.94992	+	5.16724i	0.865221	+	0.499536i	0.865757	−	0.500464i	$-0.166837\pi$
$107$	8.94992	+	5.16724i	0.865221	+	0.499536i	−0.000535988		1.00000i	$0.500171\pi$
$108$	−4.29027	−	2.93148i	−0.412832	−	0.282082i
$109$	−0.372276	−	0.644801i	−0.0356576	−	0.0617608i	0.847646	−	0.530562i	$-0.178019\pi$
$109$	−0.372276	−	0.644801i	−0.0356576	−	0.0617608i	−0.883303	+	0.468802i	$0.844686\pi$
$110$	0.391345	−	0.677830i	0.0373133	−	0.0646286i
$111$	3.04934	+	3.82642i	0.289430	+	0.363188i
$112$	−2.59215	−	0.529889i	−0.244935	−	0.0500698i
$113$			7.89825i			0.743004i	0.928432	+	0.371502i	$0.121157\pi$
$113$			7.89825i			0.743004i	−0.928432	+	0.371502i	$0.878843\pi$
$114$	11.1622	−	1.67854i	1.04543	−	0.157210i
$115$	−2.46624	+	1.42388i	−0.229978	+	0.132778i
$116$	−8.65381	+	4.99628i	−0.803486	+	0.463893i
$117$	0.982804	−	1.05777i	0.0908603	−	0.0977905i
$118$			1.35353i			0.124603i
$119$	4.66112	−	5.25857i	0.427284	−	0.482052i
$120$	3.85741	−	3.07404i	0.352132	−	0.280620i
$121$	−5.46223	+	9.46086i	−0.496566	+	0.860078i
$122$	−4.78320	−	8.28474i	−0.433050	−	0.750065i
$123$	−5.24980	+	13.3629i	−0.473359	+	1.20489i
$124$	−4.31139	−	2.48918i	−0.387174	−	0.223535i
$125$	−5.38293			−0.481464
$126$	−6.45777	+	4.61489i	−0.575304	+	0.411127i
$127$	−11.2003			−0.993870			−0.496935	−	0.867788i	$-0.665541\pi$
$127$	−11.2003			−0.993870			−0.496935	+	0.867788i	$0.665541\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.44463	+	8.76799i	−0.303282	+	0.771978i
$130$	0.685303	+	1.18698i	0.0601050	+	0.104105i
$131$	3.67616	−	6.36730i	0.321188	−	0.556313i	−0.659546	−	0.751664i	$-0.729251\pi$
$131$	3.67616	−	6.36730i	0.321188	−	0.556313i	0.980733	+	0.195351i	$0.0625846\pi$
$132$	0.372287	−	0.296682i	0.0324034	−	0.0258228i
$133$	3.45325	−	16.8928i	0.299435	−	1.46479i
$134$			12.7738i			1.10349i
$135$	1.12088	−	14.7549i	0.0964700	−	1.26990i
$136$	−2.30012	+	1.32798i	−0.197234	+	0.113873i
$137$	2.45441	−	1.41705i	0.209694	−	0.121067i	−0.391475	−	0.920189i	$-0.628035\pi$
$137$	2.45441	−	1.41705i	0.209694	−	0.121067i	0.601169	+	0.799122i	$0.294702\pi$
$138$	−1.71279	+	0.257566i	−0.145803	+	0.0219255i
$139$		−	5.62888i		−	0.477435i	−0.971089	−	0.238717i	$-0.923273\pi$
$139$		−	5.62888i		−	0.477435i	0.971089	−	0.238717i	$-0.0767270\pi$
$140$	−2.38408	−	7.14735i	−0.201491	−	0.604061i
$141$	3.64801	+	4.57765i	0.307218	+	0.385508i
$142$	4.05473	−	7.02300i	0.340265	−	0.589357i
$143$	0.0661400	+	0.114558i	0.00553090	+	0.00957980i
$144$	2.86732	−	0.882314i	0.238943	−	0.0735262i
$145$	−24.6440	−	14.2282i	−2.04658	−	1.18159i
$146$	−2.72145			−0.225229
$147$	3.22895	+	11.6865i	0.266319	+	0.963885i
$148$	−2.82489			−0.232204
$149$	−19.7897	−	11.4256i	−1.62124	−	0.936022i	−0.986590	−	0.163220i	$-0.947812\pi$
$149$	−19.7897	−	11.4256i	−1.62124	−	0.936022i	−0.634648	−	0.772802i	$-0.718855\pi$
$150$	5.01328	+	1.96954i	0.409333	+	0.160812i
$151$	3.57199	+	6.18687i	0.290684	+	0.503480i	0.973972	−	0.226669i	$-0.0727837\pi$
$151$	3.57199	+	6.18687i	0.290684	+	0.503480i	−0.683287	+	0.730150i	$0.739450\pi$
$152$	−3.25847	+	5.64383i	−0.264297	+	0.457775i
$153$	−1.77830	+	7.76688i	−0.143767	+	0.627915i
$154$	−0.230092	−	0.689805i	−0.0185414	−	0.0555861i
$155$		−	14.1772i		−	1.13874i
$156$	0.123964	+	0.824353i	0.00992508	+	0.0660010i
$157$	−16.1749	+	9.33860i	−1.29090	+	0.745301i	−0.978814	−	0.204753i	$-0.934361\pi$
$157$	−16.1749	+	9.33860i	−1.29090	+	0.745301i	−0.312086	+	0.950054i	$0.601028\pi$
$158$	1.94500	−	1.12295i	0.154736	−	0.0893370i
$159$	−0.121552	−	0.808312i	−0.00963971	−	0.0641033i
$160$			2.84777i			0.225136i
$161$	−0.529889	+	2.59215i	−0.0417611	+	0.204290i
$162$	3.91599	−	8.10340i	0.307669	−	0.636663i
$163$	9.93053	−	17.2002i	0.777819	−	1.34722i	−0.155377	−	0.987855i	$-0.549659\pi$
$163$	9.93053	−	17.2002i	0.777819	−	1.34722i	0.933196	−	0.359367i	$-0.117007\pi$
$164$	−4.14455	−	7.17857i	−0.323635	−	0.560552i
$165$	1.26178	+	0.495708i	0.0982294	+	0.0385908i
$166$	−8.68036	−	5.01161i	−0.673726	−	0.388976i
$167$	−0.181734			−0.0140630			−0.00703149	−	0.999975i	$-0.502238\pi$
$167$	−0.181734			−0.0140630			−0.00703149	+	0.999975i	$0.502238\pi$
$168$	0.239943	−	4.57629i	0.0185120	−	0.353068i
$169$	12.7684			0.982181
$170$	−6.55021	−	3.78177i	−0.502378	−	0.290048i
$171$	5.74998	+	18.6861i	0.439712	+	1.42896i
$172$	−2.71942	−	4.71018i	−0.207354	−	0.359148i
$173$	−1.03672	+	1.79565i	−0.0788201	+	0.136520i	−0.902741	−	0.430184i	$-0.858449\pi$
$173$	−1.03672	+	1.79565i	−0.0788201	+	0.136520i	0.823921	+	0.566705i	$0.191782\pi$
$174$	−10.7865	−	13.5353i	−0.817724	−	1.02611i
$175$	5.45756	−	6.15710i	0.412553	−	0.465433i
$176$			0.274844i			0.0207171i
$177$	−2.31832	+	0.348623i	−0.174255	+	0.0262041i
$178$	−7.62861	+	4.40438i	−0.571788	+	0.330122i
$179$	−4.14708	+	2.39432i	−0.309967	+	0.178960i	−0.646912	−	0.762565i	$-0.723940\pi$
$179$	−4.14708	+	2.39432i	−0.309967	+	0.178960i	0.336945	+	0.941525i	$0.390607\pi$
$180$	6.25872	+	5.81518i	0.466498	+	0.433438i
$181$		−	11.0499i		−	0.821334i	−0.911785	−	0.410667i	$-0.865296\pi$
$181$		−	11.0499i		−	0.821334i	0.911785	−	0.410667i	$-0.134704\pi$
$182$	1.24758	+	0.255031i	0.0924766	+	0.0189042i
$183$	12.9581	−	10.3265i	0.957887	−	0.763356i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−4.02231	−	6.96684i	−0.295726	−	0.512212i
$186$	3.15299	−	8.02565i	0.231188	−	0.588469i
$187$	−0.632174	−	0.364986i	−0.0462292	−	0.0266904i
$188$	−3.37949			−0.246475
$189$	−9.56765	−	9.87219i	−0.695944	−	0.718096i
$190$	−18.5587			−1.34639
$191$	22.0177	+	12.7119i	1.59314	+	0.919803i	0.992763	+	0.120089i	$0.0383180\pi$
$191$	22.0177	+	12.7119i	1.59314	+	0.919803i	0.600382	+	0.799714i	$0.295015\pi$
$192$	−0.633338	+	1.61211i	−0.0457072	+	0.116344i
$193$	5.75992	+	9.97647i	0.414608	+	0.718122i	0.995387	−	0.0959392i	$-0.0305854\pi$
$193$	5.75992	+	9.97647i	0.414608	+	0.718122i	−0.580779	+	0.814061i	$0.697252\pi$
$194$	4.57684	−	7.92731i	0.328598	−	0.569148i
$195$	−1.85654	+	1.47951i	−0.132950	+	0.105950i
$196$	−6.43843	−	2.74710i	−0.459888	−	0.196221i
$197$			25.6839i			1.82990i	0.403569	+	0.914949i	$0.367770\pi$
$197$			25.6839i			1.82990i	−0.403569	+	0.914949i	$0.632230\pi$
$198$	0.604042	+	0.561235i	0.0429274	+	0.0398852i
$199$	15.8095	−	9.12764i	1.12071	−	0.647041i	0.179127	−	0.983826i	$-0.442673\pi$
$199$	15.8095	−	9.12764i	1.12071	−	0.647041i	0.941582	+	0.336785i	$0.109339\pi$
$200$	−2.69314	+	1.55489i	−0.190434	+	0.109947i
$201$	−21.8789	+	3.29010i	−1.54322	+	0.232066i
$202$			2.78242i			0.195770i
$203$	−25.0794	+	8.36552i	−1.76023	+	0.587145i
$204$	−2.86698	−	3.59759i	−0.200729	−	0.251882i
$205$	11.8027	−	20.4429i	0.824337	−	1.42779i
$206$	4.07604	+	7.05990i	0.283991	+	0.491887i
$207$	−0.882314	−	2.86732i	−0.0613250	−	0.199292i
$208$	−0.416811	−	0.240646i	−0.0289006	−	0.0166858i
$209$	−1.79114			−0.123896
$210$	11.6279	−	5.92435i	0.802399	−	0.408819i
$211$	11.7868			0.811438			0.405719	−	0.913998i	$-0.367021\pi$
$211$	11.7868			0.811438			0.405719	+	0.913998i	$0.367021\pi$
$212$	0.408700	+	0.235963i	0.0280696	+	0.0162060i
$213$	13.0733	+	5.13603i	0.895767	+	0.351915i
$214$	−5.16724	−	8.94992i	−0.353225	−	0.611804i
$215$	7.74428	−	13.4135i	0.528155	−	0.914792i
$216$	2.24974	+	4.68387i	0.153076	+	0.318697i
$217$	−9.85676	−	8.73688i	−0.669120	−	0.593098i
$218$			0.744552i			0.0504274i
$219$	−0.700952	−	4.66128i	−0.0473659	−	0.314980i
$220$	−0.677830	+	0.391345i	−0.0456993	+	0.0263845i
$221$	1.10703	−	0.639144i	0.0744668	−	0.0429934i
$222$	−0.727594	−	4.83844i	−0.0488329	−	0.324735i
$223$			24.3125i			1.62809i	0.580805	+	0.814043i	$0.302738\pi$
$223$			24.3125i			1.62809i	−0.580805	+	0.814043i	$0.697262\pi$
$224$	1.97992	+	1.75497i	0.132289	+	0.117259i
$225$	−2.08216	+	9.09400i	−0.138811	+	0.606266i
$226$	3.94912	−	6.84008i	0.262692	−	0.454995i
$227$	−6.98878	−	12.1049i	−0.463862	−	0.803432i	0.535288	−	0.844670i	$-0.320203\pi$
$227$	−6.98878	−	12.1049i	−0.463862	−	0.803432i	−0.999149	+	0.0412377i	$0.986870\pi$
$228$	−10.5060	−	4.12742i	−0.695776	−	0.273345i
$229$	−23.3045	−	13.4549i	−1.54001	−	0.889124i	−0.998837	−	0.0482106i	$-0.984648\pi$
$229$	−23.3045	−	13.4549i	−1.54001	−	0.889124i	−0.541170	−	0.840913i	$-0.682019\pi$
$230$	2.84777			0.187776
$231$	1.12223	−	0.571771i	0.0738373	−	0.0376198i
$232$	9.99256			0.656044
$233$	19.6849	+	11.3651i	1.28960	+	0.744550i	0.978583	−	0.205855i	$-0.0659974\pi$
$233$	19.6849	+	11.3651i	1.28960	+	0.744550i	0.311016	+	0.950405i	$0.399331\pi$
$234$	−1.38002	+	0.424650i	−0.0902145	+	0.0277602i
$235$	−4.81200	−	8.33463i	−0.313900	−	0.543691i
$236$	0.676766	−	1.17219i	0.0440537	−	0.0763032i
$237$	2.42435	+	3.04216i	0.157478	+	0.197609i
$238$	−6.66593	+	2.22350i	−0.432088	+	0.144128i
$239$		−	8.12322i		−	0.525448i	−0.964871	−	0.262724i	$-0.915379\pi$
$239$		−	8.12322i		−	0.525448i	0.964871	−	0.262724i	$-0.0846208\pi$
$240$	−4.87763	+	0.733487i	−0.314850	+	0.0473464i
$241$	9.06262	−	5.23230i	0.583775	−	0.337042i	−0.178857	−	0.983875i	$-0.557240\pi$
$241$	9.06262	−	5.23230i	0.583775	−	0.337042i	0.762632	+	0.646833i	$0.223907\pi$
$242$	9.46086	−	5.46223i	0.608167	−	0.351125i
$243$	14.8881	+	4.62012i	0.955070	+	0.296381i
$244$			9.56639i			0.612425i
$245$	−2.39258	−	19.7903i	−0.152856	−	1.26435i
$246$	11.2279	−	8.94771i	0.715866	−	0.570485i
$247$	1.56827	−	2.71633i	0.0997868	−	0.172836i
$248$	2.48918	+	4.31139i	0.158063	+	0.273774i
$249$	6.34808	−	16.1585i	0.402293	−	1.02400i
$250$	4.66175	+	2.69146i	0.294835	+	0.170223i
$251$	13.8151			0.872000			0.436000	−	0.899947i	$-0.356395\pi$
$251$	13.8151			0.872000			0.436000	+	0.899947i	$0.356395\pi$
$252$	7.90004	−	0.767724i	0.497656	−	0.0483620i
$253$	0.274844			0.0172793
$254$	9.69979	+	5.60017i	0.608619	+	0.351386i
$255$	4.79027	−	12.1932i	0.299978	−	0.763568i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.05671	−	7.02643i	0.253051	−	0.438297i	−0.711313	−	0.702875i	$-0.751899\pi$
$257$	4.05671	−	7.02643i	0.253051	−	0.438297i	0.964364	+	0.264578i	$0.0852327\pi$
$258$	7.36713	−	5.87099i	0.458657	−	0.365512i
$259$	−7.32251	−	1.49688i	−0.454999	−	0.0930114i
$260$		−	1.37061i		−	0.0850013i
$261$	20.4050	−	21.9613i	1.26303	−	1.35937i
$262$	−6.36730	+	3.67616i	−0.393373	+	0.227114i
$263$	−6.46323	+	3.73155i	−0.398540	+	0.230097i	−0.685854	−	0.727739i	$-0.740571\pi$
$263$	−6.46323	+	3.73155i	−0.398540	+	0.230097i	0.287314	+	0.957837i	$0.407238\pi$
$264$	−0.470751	+	0.0707904i	−0.0289727	+	0.00435685i
$265$			1.34394i			0.0825573i
$266$	−11.4370	+	12.9030i	−0.701249	+	0.791134i
$267$	−9.50866	−	11.9318i	−0.581920	−	0.730215i
$268$	6.38691	−	11.0625i	0.390143	−	0.675747i
$269$	−0.567685	−	0.983260i	−0.0346124	−	0.0599504i	0.848200	−	0.529676i	$-0.177686\pi$
$269$	−0.567685	−	0.983260i	−0.0346124	−	0.0599504i	−0.882813	+	0.469725i	$0.844353\pi$
$270$	−8.34817	+	12.2177i	−0.508053	+	0.743545i
$271$	9.90150	+	5.71663i	0.601473	+	0.347261i	0.769621	−	0.638501i	$-0.220445\pi$
$271$	9.90150	+	5.71663i	0.601473	+	0.347261i	−0.168148	+	0.985762i	$0.553779\pi$
$272$	2.65595			0.161041
$273$	−0.115482	+	2.20253i	−0.00698931	+	0.133303i
$274$	−2.83411			−0.171215
$275$	−0.740193	−	0.427351i	−0.0446353	−	0.0257702i
$276$	1.61211	+	0.633338i	0.0970373	+	0.0381225i
$277$	6.14447	+	10.6425i	0.369185	+	0.639448i	0.989438	−	0.144954i	$-0.0463035\pi$
$277$	6.14447	+	10.6425i	0.369185	+	0.639448i	−0.620253	+	0.784402i	$0.712970\pi$
$278$	−2.81444	+	4.87475i	−0.168799	+	0.292368i
$279$	14.5584	+	3.33328i	0.871587	+	0.199558i
$280$	−1.50900	+	7.38182i	−0.0901800	+	0.441148i
$281$		−	32.0542i		−	1.91220i	−0.293048	−	0.956098i	$-0.594669\pi$
$281$		−	32.0542i		−	1.91220i	0.293048	−	0.956098i	$-0.405331\pi$
$282$	−0.870442	−	5.78837i	−0.0518340	−	0.344692i
$283$	−7.19506	+	4.15407i	−0.427702	+	0.246934i	−0.698367	−	0.715740i	$-0.746090\pi$
$283$	−7.19506	+	4.15407i	−0.427702	+	0.246934i	0.270665	+	0.962674i	$0.412756\pi$
$284$	−7.02300	+	4.05473i	−0.416738	+	0.240604i
$285$	−4.78009	−	31.7872i	−0.283148	−	1.88291i
$286$		−	0.132280i		−	0.00782188i
$287$	−6.93943	−	20.8041i	−0.409622	−	1.22802i
$288$	−2.92433	−	0.669554i	−0.172318	−	0.0394538i
$289$	4.97296	−	8.61342i	0.292527	−	0.506672i
$290$	14.2282	+	24.6440i	0.835511	+	1.44715i
$291$	14.7567	+	5.79737i	0.865052	+	0.339848i
$292$	2.35684	+	1.36072i	0.137924	+	0.0796304i
$293$	0.870596			0.0508607			0.0254304	−	0.999677i	$-0.491904\pi$
$293$	0.870596			0.0508607			0.0254304	+	0.999677i	$0.491904\pi$
$294$	3.04689	−	11.7353i	0.177698	−	0.684415i
$295$	3.85454			0.224420
$296$	2.44642	+	1.41244i	0.142195	+	0.0820966i
$297$	−0.805699	+	1.17915i	−0.0467514	+	0.0684215i
$298$	11.4256	+	19.7897i	0.661867	+	1.14639i
$299$	−0.240646	+	0.416811i	−0.0139169	+	0.0241048i
$300$	−3.35686	−	4.21231i	−0.193808	−	0.243198i
$301$	−4.55326	−	13.6505i	−0.262446	−	0.786799i
$302$		−	7.14398i		−	0.411090i
$303$	−4.76571	+	0.716656i	−0.273783	+	0.0411708i
$304$	5.64383	−	3.25847i	0.323696	−	0.186886i
$305$	−23.5930	+	13.6214i	−1.35093	+	0.779960i
$306$	5.42349	−	5.83716i	0.310041	−	0.333688i
$307$			17.8590i			1.01927i	0.860391	+	0.509634i	$0.170219\pi$
$307$			17.8590i			1.01927i	−0.860391	+	0.509634i	$0.829781\pi$
$308$	−0.145637	+	0.712435i	−0.00829843	+	0.0405948i
$309$	−11.0423	+	8.79980i	−0.628175	+	0.500603i
$310$	−7.08861	+	12.2778i	−0.402606	+	0.697334i
$311$	−13.5283	−	23.4316i	−0.767117	−	1.32869i	−0.939120	−	0.343589i	$-0.888357\pi$
$311$	−13.5283	−	23.4316i	−0.767117	−	1.32869i	0.172003	−	0.985096i	$-0.444976\pi$
$312$	0.304820	−	0.775892i	0.0172570	−	0.0439263i
$313$	−24.1388	−	13.9365i	−1.36441	−	0.787740i	−0.374199	−	0.927348i	$-0.622082\pi$
$313$	−24.1388	−	13.9365i	−1.36441	−	0.787740i	−0.990207	+	0.139609i	$0.955416\pi$
$314$	18.6772			1.05402
$315$	13.1421	+	18.3902i	0.740475	+	1.03617i
$316$	−2.24590			−0.126342
$317$	−6.71665	−	3.87786i	−0.377245	−	0.217802i	0.299374	−	0.954136i	$-0.403222\pi$
$317$	−6.71665	−	3.87786i	−0.377245	−	0.217802i	−0.676619	+	0.736334i	$0.736555\pi$
$318$	−0.298889	+	0.760795i	−0.0167609	+	0.0426633i
$319$	1.37320	+	2.37845i	0.0768842	+	0.133167i
$320$	1.42388	−	2.46624i	0.0795975	−	0.137867i
$321$	13.9985	−	11.1556i	0.781318	−	0.622645i
$322$	1.75497	−	1.97992i	0.0978007	−	0.110337i
$323$			17.3087i			0.963080i
$324$	−7.44304	+	5.05975i	−0.413502	+	0.281097i
$325$	1.29619	−	0.748353i	0.0718995	−	0.0415112i
$326$	−17.2002	+	9.93053i	−0.952630	+	0.550001i
$327$	−1.27526	+	0.191771i	−0.0705223	+	0.0106050i
$328$			8.28910i			0.457689i
$329$	−8.76013	−	1.79076i	−0.482962	−	0.0987276i
$330$	−0.844880	−	1.06019i	−0.0465091	−	0.0583613i
$331$	1.40887	−	2.44023i	0.0774384	−	0.134127i	−0.824706	−	0.565562i	$-0.808659\pi$
$331$	1.40887	−	2.44023i	0.0774384	−	0.134127i	0.902144	+	0.431435i	$0.141993\pi$
$332$	5.01161	+	8.68036i	0.275048	+	0.476396i
$333$	8.09985	−	2.49244i	0.443869	−	0.136585i
$334$	0.157386	+	0.0908669i	0.00861178	+	0.00497202i
$335$	36.3769			1.98748
$336$	−2.49594	+	3.84321i	−0.136165	+	0.209664i
$337$	20.6664			1.12577			0.562886	−	0.826534i	$-0.309691\pi$
$337$	20.6664			1.12577			0.562886	+	0.826534i	$0.309691\pi$
$338$	−11.0577	−	6.38418i	−0.601461	−	0.347254i
$339$	12.7328	+	5.00226i	0.691551	+	0.271685i
$340$	3.78177	+	6.55021i	0.205095	+	0.355235i
$341$	−0.684136	+	1.18496i	−0.0370481	+	0.0641691i
$342$	4.36344	−	19.0577i	0.235948	−	1.03052i
$343$	−15.2337	−	10.5325i	−0.822542	−	0.568704i
$344$			5.43884i			0.293243i
$345$	0.733487	+	4.87763i	0.0394896	+	0.262603i
$346$	1.79565	−	1.03672i	0.0965345	−	0.0557342i
$347$	0.274115	−	0.158261i	0.0147153	−	0.00849587i	−0.492624	−	0.870242i	$-0.663962\pi$
$347$	0.274115	−	0.158261i	0.0147153	−	0.00849587i	0.507340	+	0.861746i	$0.330629\pi$
$348$	2.57374	+	17.1152i	0.137967	+	0.917470i
$349$			6.25090i			0.334603i	0.985906	+	0.167301i	$0.0535053\pi$
$349$			6.25090i			0.334603i	−0.985906	+	0.167301i	$0.946495\pi$
$350$	−7.80493	+	2.60342i	−0.417191	+	0.139159i
$351$	−1.08278	−	2.25431i	−0.0577947	−	0.120326i
$352$	0.137422	−	0.238022i	0.00732461	−	0.0126866i
$353$	−1.74530	−	3.02295i	−0.0928929	−	0.160895i	0.815834	−	0.578286i	$-0.196278\pi$
$353$	−1.74530	−	3.02295i	−0.0928929	−	0.160895i	−0.908727	+	0.417390i	$0.862945\pi$
$354$	2.18203	+	0.857243i	0.115974	+	0.0455619i
$355$	−19.9998	−	11.5469i	−1.06148	−	0.612847i
$356$	8.80876			0.466863
$357$	−5.52531	−	10.8447i	−0.292430	−	0.573960i
$358$	4.78864			0.253087
$359$	−2.27301	−	1.31232i	−0.119965	−	0.0692618i	0.438817	−	0.898577i	$-0.355398\pi$
$359$	−2.27301	−	1.31232i	−0.119965	−	0.0692618i	−0.558782	+	0.829315i	$0.688731\pi$
$360$	−2.51262	−	8.16546i	−0.132427	−	0.430357i
$361$	11.7352	+	20.3260i	0.617643	+	1.06979i
$362$	−5.52496	+	9.56951i	−0.290385	+	0.502962i
$363$	11.7925	+	14.7976i	0.618944	+	0.776673i
$364$	−0.952918	−	0.844652i	−0.0499465	−	0.0442718i
$365$			7.75005i			0.405656i
$366$	−16.3852	+	2.46397i	−0.856471	+	0.128794i
$367$	21.6844	−	12.5195i	1.13192	−	0.653512i	0.187500	−	0.982265i	$-0.439962\pi$
$367$	21.6844	−	12.5195i	1.13192	−	0.653512i	0.944416	+	0.328753i	$0.106628\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	18.2175	+	16.9265i	0.948366	+	0.881157i
$370$			8.04461i			0.418219i
$371$	0.934376	+	0.828217i	0.0485104	+	0.0429989i
$372$	−6.74339	+	5.37392i	−0.349629	+	0.278625i
$373$	7.25090	−	12.5589i	0.375437	−	0.650276i	−0.614955	−	0.788562i	$-0.710826\pi$
$373$	7.25090	−	12.5589i	0.375437	−	0.650276i	0.990392	+	0.138286i	$0.0441592\pi$
$374$	0.364986	+	0.632174i	0.0188730	+	0.0326890i
$375$	−3.40921	+	8.67784i	−0.176051	+	0.448122i
$376$	2.92673	+	1.68975i	0.150934	+	0.0871420i
$377$	−4.80933			−0.247693
$378$	3.34973	+	13.3334i	0.172292	+	0.685796i
$379$	−17.2157			−0.884310			−0.442155	−	0.896939i	$-0.645786\pi$
$379$	−17.2157			−0.884310			−0.442155	+	0.896939i	$0.645786\pi$
$380$	16.0723	+	9.27935i	0.824492	+	0.476021i
$381$	−7.09361	+	18.0561i	−0.363416	+	0.925044i
$382$	−12.7119	−	22.0177i	−0.650399	−	1.12652i
$383$	−11.6789	+	20.2284i	−0.596762	+	1.03362i	0.396534	+	0.918020i	$0.370213\pi$
$383$	−11.6789	+	20.2284i	−0.596762	+	1.03362i	−0.993296	+	0.115602i	$0.963120\pi$
$384$	1.35454	−	1.07946i	0.0691235	−	0.0550857i
$385$	−1.96440	+	0.655249i	−0.100115	+	0.0333946i
$386$		−	11.5198i		−	0.586344i
$387$	11.9533	+	11.1062i	0.607621	+	0.564560i
$388$	−7.92731	+	4.57684i	−0.402448	+	0.232354i
$389$	−24.8918	+	14.3713i	−1.26206	+	0.728653i	−0.973473	−	0.228800i	$-0.926520\pi$
$389$	−24.8918	+	14.3713i	−1.26206	+	0.728653i	−0.288590	+	0.957453i	$0.593187\pi$
$390$	2.34756	−	0.353021i	0.118873	−	0.0178759i
$391$		−	2.65595i		−	0.134317i
$392$	4.20230	+	5.59828i	0.212248	+	0.282756i
$393$	−7.93650	−	9.95901i	−0.400344	−	0.502366i
$394$	12.8419	−	22.2429i	0.646967	−	1.12058i
$395$	−3.19790	−	5.53892i	−0.160904	−	0.278693i
$396$	−0.242498	−	0.788065i	−0.0121860	−	0.0396018i
$397$	−26.8872	−	15.5233i	−1.34943	−	0.779093i	−0.361260	−	0.932465i	$-0.617653\pi$
$397$	−26.8872	−	15.5233i	−1.34943	−	0.779093i	−0.988169	+	0.153372i	$0.950987\pi$
$398$	−18.2553			−0.915055
$399$	−25.0460	−	16.2659i	−1.25387	−	0.814313i
$400$	3.10977			0.155489
$401$	4.63453	+	2.67575i	0.231437	+	0.133620i	0.611235	−	0.791449i	$-0.290673\pi$
$401$	4.63453	+	2.67575i	0.231437	+	0.133620i	−0.379798	+	0.925070i	$0.624006\pi$
$402$	20.5927	+	8.09014i	1.02707	+	0.403500i
$403$	−1.19802	−	2.07503i	−0.0596777	−	0.103365i
$404$	1.39121	−	2.40965i	0.0692153	−	0.119884i
$405$	−23.0766	−	11.1518i	−1.14668	−	0.554139i
$406$	25.9022	+	5.29495i	1.28550	+	0.262784i
$407$			0.776402i			0.0384848i
$408$	0.684083	+	4.54910i	0.0338671	+	0.225214i
$409$	1.46016	−	0.843026i	0.0722005	−	0.0416850i	−0.463465	−	0.886115i	$-0.653394\pi$
$409$	1.46016	−	0.843026i	0.0722005	−	0.0416850i	0.535666	+	0.844430i	$0.320061\pi$
$410$	−20.4429	+	11.8027i	−1.00960	+	0.582895i
$411$	−0.729969	−	4.85424i	−0.0360067	−	0.239442i
$412$		−	8.15207i		−	0.401624i
$413$	2.37541	−	2.67988i	0.116886	−	0.131868i
$414$	−0.669554	+	2.92433i	−0.0329068	+	0.143723i
$415$	−14.2719	+	24.7196i	−0.700579	+	1.21344i
$416$	0.240646	+	0.416811i	0.0117986	+	0.0204358i
$417$	−9.07434	−	3.56498i	−0.444372	−	0.174578i
$418$	1.55117	+	0.895569i	0.0758703	+	0.0438037i
$419$	24.6544			1.20445			0.602224	−	0.798327i	$-0.294281\pi$
$419$	24.6544			1.20445			0.602224	+	0.798327i	$0.294281\pi$
$420$	−13.0322	−	0.683301i	−0.635906	−	0.0333417i
$421$	40.6301			1.98019			0.990096	−	0.140392i	$-0.0448363\pi$
$421$	40.6301			1.98019			0.990096	+	0.140392i	$0.0448363\pi$
$422$	−10.2077	−	5.89341i	−0.496902	−	0.286887i
$423$	9.69008	−	2.98177i	0.471148	−	0.144979i
$424$	−0.235963	−	0.408700i	−0.0114594	−	0.0198482i
$425$	−4.12970	+	7.15286i	−0.200320	+	0.346965i
$426$	−8.75379	−	10.9846i	−0.424123	−	0.532205i
$427$	−5.06913	+	24.7975i	−0.245312	+	1.20003i
$428$			10.3345i			0.499536i
$429$	0.226568	−	0.0340708i	0.0109388	−	0.00164495i
$430$	−13.4135	+	7.74428i	−0.646855	+	0.373462i
$431$	−24.7766	+	14.3048i	−1.19345	+	0.689036i	−0.959086	−	0.283114i	$-0.908633\pi$
$431$	−24.7766	+	14.3048i	−1.19345	+	0.689036i	−0.234359	+	0.972150i	$0.575299\pi$
$432$	0.393600	−	5.18122i	0.0189371	−	0.249282i
$433$			33.9113i			1.62967i	0.579692	+	0.814836i	$0.303173\pi$
$433$			33.9113i			1.62967i	−0.579692	+	0.814836i	$0.696827\pi$
$434$	4.16776	+	12.4947i	0.200059	+	0.599767i
$435$	−38.5454	+	30.7175i	−1.84811	+	1.47279i
$436$	0.372276	−	0.644801i	0.0178288	−	0.0308804i
$437$	−3.25847	−	5.64383i	−0.155874	−	0.269981i
$438$	−1.72360	+	4.38726i	−0.0823566	+	0.209631i
$439$	31.9875	+	18.4680i	1.52668	+	0.881430i	0.999498	+	0.0316790i	$0.0100854\pi$
$439$	31.9875	+	18.4680i	1.52668	+	0.881430i	0.527184	+	0.849751i	$0.323248\pi$
$440$	0.782691			0.0373133
$441$	20.8849	+	2.19609i	0.994517	+	0.104576i
$442$	−1.27829			−0.0608019
$443$	28.4235	+	16.4103i	1.35044	+	0.779679i	0.988311	−	0.152449i	$-0.0487158\pi$
$443$	28.4235	+	16.4103i	1.35044	+	0.779679i	0.362131	+	0.932127i	$0.382049\pi$
$444$	−1.78911	+	4.55401i	−0.0849073	+	0.216124i
$445$	12.5426	+	21.7245i	0.594578	+	1.02984i
$446$	12.1563	−	21.0552i	0.575615	−	0.996995i
$447$	−30.9529	+	24.6668i	−1.46402	+	1.16670i
$448$	−0.837175	−	2.50981i	−0.0395528	−	0.118577i
$449$			0.435472i			0.0205512i	0.999947	+	0.0102756i	$0.00327088\pi$
$449$			0.435472i			0.0205512i	−0.999947	+	0.0102756i	$0.996729\pi$
$450$	6.35020	−	6.83455i	0.299351	−	0.322184i
$451$	−1.97299	+	1.13910i	−0.0929043	+	0.0536383i
$452$	−6.84008	+	3.94912i	−0.321730	+	0.185751i
$453$	12.2362	−	1.84004i	0.574905	−	0.0864528i
$454$			13.9776i			0.656000i
$455$	0.726269	−	3.55281i	0.0340480	−	0.166558i
$456$	7.03474	+	8.82744i	0.329432	+	0.413383i
$457$	−19.0984	+	33.0794i	−0.893385	+	1.54739i	−0.0575953	+	0.998340i	$0.518343\pi$
$457$	−19.0984	+	33.0794i	−0.893385	+	1.54739i	−0.835790	+	0.549049i	$0.814990\pi$
$458$	13.4549	+	23.3045i	0.628705	+	1.08895i
$459$	11.3948	+	7.78587i	0.531862	+	0.363413i
$460$	−2.46624	−	1.42388i	−0.114989	−	0.0663889i
$461$	−27.7211			−1.29110			−0.645551	−	0.763717i	$-0.723372\pi$
$461$	−27.7211			−1.29110			−0.645551	+	0.763717i	$0.723372\pi$
$462$	−1.25776	−	0.0659468i	−0.0585165	−	0.00306812i
$463$	26.0865			1.21234			0.606171	−	0.795334i	$-0.292705\pi$
$463$	26.0865			1.21234			0.606171	+	0.795334i	$0.292705\pi$
$464$	−8.65381	−	4.99628i	−0.401743	−	0.231946i
$465$	−22.8552	−	8.97897i	−1.05988	−	0.416390i
$466$	−11.3651	−	19.6849i	−0.526476	−	0.911884i
$467$	−1.98716	+	3.44186i	−0.0919548	+	0.159270i	−0.908334	−	0.418246i	$-0.862645\pi$
$467$	−1.98716	+	3.44186i	−0.0919548	+	0.159270i	0.816379	+	0.577517i	$0.195978\pi$
$468$	1.40745	+	0.322250i	0.0650596	+	0.0148960i
$469$	22.4177	−	25.2911i	1.03515	−	1.16784i
$470$			9.62400i			0.443922i
$471$	4.81061	+	31.9902i	0.221661	+	1.47403i
$472$	−1.17219	+	0.676766i	−0.0539545	+	0.0311507i
$473$	−1.29456	+	0.747416i	−0.0595241	+	0.0343662i
$474$	−0.578466	−	3.84676i	−0.0265698	−	0.176687i
$475$			20.2662i			0.929876i
$476$	6.88461	+	1.40736i	0.315556	+	0.0645063i
$477$	−1.38007	−	0.315980i	−0.0631890	−	0.0144677i
$478$	−4.06161	+	7.03492i	−0.185774	+	0.321770i
$479$	−12.0001	−	20.7847i	−0.548297	−	0.949679i	−0.998391	−	0.0566978i	$-0.981943\pi$
$479$	−12.0001	−	20.7847i	−0.548297	−	0.949679i	0.450094	−	0.892981i	$-0.351390\pi$
$480$	4.59090	+	1.80360i	0.209545	+	0.0823226i
$481$	−1.17744	−	0.679796i	−0.0536867	−	0.0309961i
$482$	−10.4646			−0.476650
$483$	3.84321	+	2.49594i	0.174872	+	0.113569i
$484$	−10.9245			−0.496566
$485$	−22.5751	−	13.0338i	−1.02508	−	0.591832i
$486$	−10.5834	−	11.4452i	−0.480072	−	0.519164i
$487$	19.2400	+	33.3247i	0.871847	+	1.51008i	0.860083	+	0.510153i	$0.170411\pi$
$487$	19.2400	+	33.3247i	0.871847	+	1.51008i	0.0117640	+	0.999931i	$0.496255\pi$
$488$	4.78320	−	8.28474i	0.216525	−	0.375032i
$489$	−21.4391	−	26.9026i	−0.969511	−	1.21658i
$490$	−7.82310	+	18.3352i	−0.353412	+	0.828298i
$491$		−	37.4903i		−	1.69191i	−0.533252	−	0.845956i	$-0.679030\pi$
$491$		−	37.4903i		−	1.69191i	0.533252	−	0.845956i	$-0.320970\pi$
$492$	−14.1975	+	2.13499i	−0.640074	+	0.0962528i
$493$	22.9841	−	13.2699i	1.03515	−	0.597645i
$494$	−2.71633	+	1.56827i	−0.122213	+	0.0705599i
$495$	1.59827	−	1.72017i	0.0718367	−	0.0773160i
$496$		−	4.97836i		−	0.223535i
$497$	−20.3532	+	6.78903i	−0.912965	+	0.304530i
$498$	−13.5768	+	10.8196i	−0.608392	+	0.484838i
$499$	−10.4417	+	18.0856i	−0.467437	+	0.809624i	−0.999308	−	0.0372012i	$-0.988156\pi$
$499$	−10.4417	+	18.0856i	−0.467437	+	0.809624i	0.531871	+	0.846825i	$0.321489\pi$
$500$	−2.69146	−	4.66175i	−0.120366	−	0.208480i
$501$	−0.115099	+	0.292974i	−0.00514224	+	0.0130891i
$502$	−11.9642	−	6.90754i	−0.533988	−	0.308298i
$503$	−19.2012			−0.856138			−0.428069	−	0.903746i	$-0.640806\pi$
$503$	−19.2012			−0.856138			−0.428069	+	0.903746i	$0.640806\pi$
$504$	−7.22550	−	3.28515i	−0.321849	−	0.146332i
$505$	7.92368			0.352599
$506$	−0.238022	−	0.137422i	−0.0105814	−	0.00610915i
$507$	8.08669	−	20.5839i	0.359142	−	0.914165i
$508$	−5.60017	−	9.69979i	−0.248468	−	0.430358i
$509$	6.17194	−	10.6901i	0.273566	−	0.473831i	−0.696206	−	0.717842i	$-0.745130\pi$
$509$	6.17194	−	10.6901i	0.273566	−	0.473831i	0.969772	+	0.244011i	$0.0784633\pi$
$510$	−10.2451	+	8.16449i	−0.453661	+	0.361530i
$511$	5.38825	+	4.77606i	0.238362	+	0.211280i
$512$			1.00000i			0.0441942i
$513$	33.7657	+	2.56506i	1.49079	+	0.113250i
$514$	−7.02643	+	4.05671i	−0.309923	+	0.178934i
$515$	20.1050	−	11.6076i	0.885930	−	0.511492i
$516$	−9.31561	+	1.40086i	−0.410097	+	0.0616694i
$517$			0.928832i			0.0408500i
$518$	5.59304	+	4.95759i	0.245744	+	0.217824i
$519$	2.23818	+	2.80855i	0.0982451	+	0.123281i
$520$	−0.685303	+	1.18698i	−0.0300525	+	0.0520525i
$521$	−13.4003	−	23.2099i	−0.587076	−	1.01685i	−0.994613	−	0.103657i	$-0.966946\pi$
$521$	−13.4003	−	23.2099i	−0.587076	−	1.01685i	0.407537	−	0.913189i	$-0.366388\pi$
$522$	−28.6519	+	8.81657i	−1.25406	+	0.385891i
$523$	10.2121	+	5.89593i	0.446542	+	0.257811i	0.706369	−	0.707844i	$-0.250332\pi$
$523$	10.2121	+	5.89593i	0.446542	+	0.257811i	−0.259827	+	0.965655i	$0.583665\pi$
$524$	7.35232			0.321188
$525$	−6.46941	−	12.6977i	−0.282348	−	0.554172i
$526$	7.46310			0.325407
$527$	11.4508	+	6.61115i	0.498807	+	0.287986i
$528$	0.443077	+	0.174069i	0.0192825	+	0.00757538i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	0.671968	−	1.16388i	0.0291884	−	0.0505558i
$531$	−0.906262	+	3.95817i	−0.0393284	+	0.171770i
$532$	16.3563	−	5.45581i	0.709134	−	0.236540i
$533$		−	3.98947i		−	0.172803i
$534$	2.26883	+	15.0876i	0.0981821	+	0.652903i
$535$	−25.4873	+	14.7151i	−1.10191	+	0.636189i
$536$	−11.0625	+	6.38691i	−0.477825	+	0.275872i
$537$	1.23339	+	8.20194i	0.0532247	+	0.353940i
$538$			1.13537i			0.0489493i
$539$	−0.755023	+	1.76956i	−0.0325212	+	0.0762205i
$540$	13.3386	−	6.40675i	0.574001	−	0.275702i
$541$	17.8605	−	30.9353i	0.767884	−	1.33001i	−0.170825	−	0.985301i	$-0.554643\pi$
$541$	17.8605	−	30.9353i	0.767884	−	1.33001i	0.938708	−	0.344712i	$-0.112023\pi$
$542$	−5.71663	−	9.90150i	−0.245550	−	0.425306i
$543$	−17.8136	−	6.99833i	−0.764456	−	0.300327i
$544$	−2.30012	−	1.32798i	−0.0986169	−	0.0569365i
$545$	2.12031			0.0908241
$546$	1.20128	−	1.84970i	0.0514098	−	0.0791601i
$547$	−13.2602			−0.566964			−0.283482	−	0.958978i	$-0.591490\pi$
$547$	−13.2602			−0.566964			−0.283482	+	0.958978i	$0.591490\pi$
$548$	2.45441	+	1.41705i	0.104847	+	0.0605335i
$549$	−8.44056	−	27.4299i	−0.360234	−	1.17068i
$550$	0.427351	+	0.740193i	0.0182223	+	0.0315620i
$551$	32.5604	−	56.3963i	1.38712	−	2.40256i
$552$	−1.07946	−	1.35454i	−0.0459447	−	0.0576530i
$553$	−5.82169	−	1.19008i	−0.247564	−	0.0506072i
$554$		−	12.2889i		−	0.522107i
$555$	−13.7788	+	2.07202i	−0.584876	+	0.0879522i
$556$	4.87475	−	2.81444i	0.206735	−	0.119359i
$557$	−4.88494	+	2.82032i	−0.206981	+	0.119501i	−0.599908	−	0.800069i	$-0.704796\pi$
$557$	−4.88494	+	2.82032i	−0.206981	+	0.119501i	0.392926	+	0.919570i	$0.371463\pi$
$558$	−10.9413	−	10.1659i	−0.463181	−	0.430357i
$559$		−	2.61767i		−	0.110716i
$560$	4.99774	−	5.63835i	0.211193	−	0.238264i
$561$	−0.988776	+	0.787972i	−0.0417462	+	0.0332682i
$562$	−16.0271	+	27.7598i	−0.676063	+	1.17098i
$563$	−3.44566	−	5.96806i	−0.145217	−	0.251524i	0.784237	−	0.620462i	$-0.213055\pi$
$563$	−3.44566	−	5.96806i	−0.145217	−	0.251524i	−0.929454	+	0.368938i	$0.879721\pi$
$564$	−2.14036	+	5.44810i	−0.0901254	+	0.229406i
$565$	−19.4790	−	11.2462i	−0.819486	−	0.473130i
$566$	8.30814			0.349217
$567$	−21.9746	+	9.17162i	−0.922845	+	0.385172i
$568$	8.10946			0.340265
$569$	17.1760	+	9.91654i	0.720053	+	0.415723i	0.814772	−	0.579781i	$-0.196862\pi$
$569$	17.1760	+	9.91654i	0.720053	+	0.415723i	−0.0947189	+	0.995504i	$0.530195\pi$
$570$	−11.7539	+	29.9186i	−0.492318	+	1.25315i
$571$	7.98850	+	13.8365i	0.334308	+	0.579039i	0.983352	−	0.181712i	$-0.0581640\pi$
$571$	7.98850	+	13.8365i	0.334308	+	0.579039i	−0.649043	+	0.760751i	$0.724831\pi$
$572$	−0.0661400	+	0.114558i	−0.00276545	+	0.00478990i
$573$	34.4376	−	27.4439i	1.43865	−	1.14649i
$574$	−4.39231	+	21.4866i	−0.183331	+	0.896832i
$575$		−	3.10977i		−	0.129686i
$576$	2.19777	+	2.04201i	0.0915736	+	0.0850840i
$577$	−40.7205	+	23.5100i	−1.69522	+	0.978733i	−0.745039	+	0.667021i	$0.767569\pi$
$577$	−40.7205	+	23.5100i	−1.69522	+	0.978733i	−0.950176	+	0.311712i	$0.899097\pi$
$578$	−8.61342	+	4.97296i	−0.358271	+	0.206848i
$579$	19.7311	−	2.96711i	0.819996	−	0.123309i
$580$		−	28.4565i		−	1.18159i
$581$	8.39118	+	25.1563i	0.348125	+	1.04366i
$582$	−9.88098	−	12.3990i	−0.409580	−	0.513955i
$583$	0.0648530	−	0.112329i	0.00268594	−	0.00465218i
$584$	−1.36072	−	2.35684i	−0.0563072	−	0.0975269i
$585$	1.20930	+	3.92996i	0.0499986	+	0.162484i
$586$	−0.753958	−	0.435298i	−0.0311457	−	0.0179820i
$587$	−22.9187			−0.945955			−0.472978	−	0.881074i	$-0.656821\pi$
$587$	−22.9187			−0.945955			−0.472978	+	0.881074i	$0.656821\pi$
$588$	−8.50632	+	8.63959i	−0.350795	+	0.356291i
$589$	32.4437			1.33682
$590$	−3.33813	−	1.92727i	−0.137429	−	0.0793445i
$591$	41.4051	+	16.2666i	1.70318	+	0.669117i
$592$	−1.41244	−	2.44642i	−0.0580510	−	0.100547i
$593$	−15.7510	+	27.2815i	−0.646816	+	1.12032i	0.337063	+	0.941482i	$0.390567\pi$
$593$	−15.7510	+	27.2815i	−0.646816	+	1.12032i	−0.983879	+	0.178836i	$0.942767\pi$
$594$	1.28733	−	0.618328i	0.0528199	−	0.0253703i
$595$	6.33200	+	18.9830i	0.259587	+	0.778228i
$596$		−	22.8512i		−	0.936022i
$597$	−4.70194	−	31.2675i	−0.192437	−	1.27969i
$598$	0.416811	−	0.240646i	0.0170447	−	0.00984073i
$599$	23.3487	−	13.4804i	0.954003	−	0.550794i	0.0596810	−	0.998218i	$-0.480992\pi$
$599$	23.3487	−	13.4804i	0.954003	−	0.550794i	0.894322	+	0.447423i	$0.147658\pi$
$600$	0.800971	+	5.32640i	0.0326995	+	0.217449i
$601$			4.71673i			0.192400i	0.995362	+	0.0961998i	$0.0306688\pi$
$601$			4.71673i			0.192400i	−0.995362	+	0.0961998i	$0.969331\pi$
$602$	−2.88198	+	14.0983i	−0.117461	+	0.574603i
$603$	−8.55276	+	37.3548i	−0.348295	+	1.52121i
$604$	−3.57199	+	6.18687i	−0.145342	+	0.251740i
$605$	−15.5552	−	26.9423i	−0.632407	−	1.09536i
$606$	4.48555	+	1.76221i	0.182213	+	0.0715849i
$607$	37.6451	+	21.7344i	1.52797	+	0.882172i	0.999447	+	0.0332518i	$0.0105863\pi$
$607$	37.6451	+	21.7344i	1.52797	+	0.882172i	0.528520	+	0.848921i	$0.322747\pi$
$608$	−6.51693			−0.264297
$609$	−2.39764	+	45.7288i	−0.0971573	+	1.85303i
$610$	27.2428			1.10303
$611$	−1.40861	−	0.813260i	−0.0569862	−	0.0329010i
$612$	−7.61546	+	2.34338i	−0.307837	+	0.0947257i
$613$	7.11518	+	12.3238i	0.287379	+	0.497756i	0.973183	−	0.230031i	$-0.0738826\pi$
$613$	7.11518	+	12.3238i	0.287379	+	0.497756i	−0.685804	+	0.727786i	$0.740549\pi$
$614$	8.92951	−	15.4664i	0.360366	−	0.624172i
$615$	−25.4810	−	31.9745i	−1.02749	−	1.28934i
$616$	0.482343	−	0.544168i	0.0194341	−	0.0219252i
$617$			41.9520i			1.68892i	0.535616	+	0.844462i	$0.320080\pi$
$617$			41.9520i			1.68892i	−0.535616	+	0.844462i	$0.679920\pi$
$618$	13.9628	−	2.09970i	0.561667	−	0.0844621i
$619$	−11.2959	+	6.52167i	−0.454019	+	0.262128i	−0.709526	−	0.704679i	$-0.751091\pi$
$619$	−11.2959	+	6.52167i	−0.454019	+	0.262128i	0.255507	+	0.966807i	$0.417758\pi$
$620$	12.2778	−	7.08861i	0.493090	−	0.284685i
$621$	−5.18122	−	0.393600i	−0.207915	−	0.0157946i
$622$			27.0565i			1.08487i
$623$	22.8336	+	4.66767i	0.914808	+	0.187006i
$624$	−0.651928	+	0.519532i	−0.0260980	+	0.0207979i
$625$	15.4391	−	26.7413i	0.617564	−	1.06965i
$626$	13.9365	+	24.1388i	0.557016	+	0.964780i
$627$	−1.13440	+	2.88750i	−0.0453034	+	0.115316i
$628$	−16.1749	−	9.33860i	−0.645450	−	0.372651i
$629$	7.50276			0.299155
$630$	−2.18630	−	22.4975i	−0.0871042	−	0.896320i
$631$	26.8169			1.06757			0.533783	−	0.845622i	$-0.320770\pi$
$631$	26.8169			1.06757			0.533783	+	0.845622i	$0.320770\pi$
$632$	1.94500	+	1.12295i	0.0773681	+	0.0446685i
$633$	7.46504	−	19.0016i	0.296709	−	0.755245i
$634$	3.87786	+	6.71665i	0.154009	+	0.266752i
$635$	15.9480	−	27.6227i	0.632876	−	1.09617i
$636$	0.639243	−	0.509423i	0.0253476	−	0.0201999i
$637$	−2.02253	−	2.69440i	−0.0801355	−	0.106756i
$638$		−	2.74639i		−	0.108731i
$639$	16.5596	−	17.8227i	0.655089	−	0.705055i
$640$	−2.46624	+	1.42388i	−0.0974866	+	0.0562839i
$641$	12.5061	−	7.22042i	0.493963	−	0.285189i	−0.232254	−	0.972655i	$-0.574610\pi$
$641$	12.5061	−	7.22042i	0.493963	−	0.285189i	0.726217	+	0.687466i	$0.241277\pi$
$642$	−17.7008	+	2.66181i	−0.698596	+	0.105053i
$643$		−	12.6652i		−	0.499467i	−0.968315	−	0.249733i	$-0.919657\pi$
$643$		−	12.6652i		−	0.499467i	0.968315	−	0.249733i	$-0.0803430\pi$
$644$	−2.50981	+	0.837175i	−0.0989003	+	0.0329893i
$645$	−16.7192	−	20.9799i	−0.658318	−	0.826081i
$646$	8.65433	−	14.9897i	0.340500	−	0.589764i
$647$	−11.7643	−	20.3764i	−0.462503	−	0.801079i	0.536582	−	0.843848i	$-0.319715\pi$
$647$	−11.7643	−	20.3764i	−0.462503	−	0.801079i	−0.999085	+	0.0427693i	$0.986382\pi$
$648$	8.97574	−	0.660351i	0.352600	−	0.0259410i
$649$	−0.322170	−	0.186005i	−0.0126463	−	0.00730133i
$650$	−1.49671			−0.0587057
$651$	−20.3274	+	10.3567i	−0.796695	+	0.405912i
$652$	19.8611			0.777819
$653$	14.0113	+	8.08942i	0.548304	+	0.316563i	0.748438	−	0.663205i	$-0.230804\pi$
$653$	14.0113	+	8.08942i	0.548304	+	0.316563i	−0.200134	+	0.979769i	$0.564138\pi$
$654$	1.20030	+	0.471553i	0.0469353	+	0.0184392i
$655$	10.4688	+	18.1326i	0.409052	+	0.708498i
$656$	4.14455	−	7.17857i	0.161818	−	0.280276i
$657$	−7.95841	−	1.82216i	−0.310487	−	0.0710891i
$658$	6.69112	+	5.93091i	0.260847	+	0.231211i
$659$			9.42487i			0.367141i	0.983007	+	0.183570i	$0.0587655\pi$
$659$			9.42487i			0.367141i	−0.983007	+	0.183570i	$0.941234\pi$
$660$	0.201594	+	1.34059i	0.00784705	+	0.0521823i
$661$	−33.8994	+	19.5718i	−1.31853	+	0.761255i	−0.983493	−	0.180948i	$-0.942083\pi$
$661$	−33.8994	+	19.5718i	−1.31853	+	0.761255i	−0.335040	+	0.942204i	$0.608750\pi$
$662$	−2.44023	+	1.40887i	−0.0948423	+	0.0547572i
$663$	−0.329243	−	2.18944i	−0.0127867	−	0.0850308i
$664$		−	10.0232i		−	0.388976i
$665$	36.7447	+	32.5700i	1.42490	+	1.26301i
$666$	−8.26089	−	1.89141i	−0.320103	−	0.0732907i
$667$	−4.99628	+	8.65381i	−0.193457	+	0.335077i
$668$	−0.0908669	−	0.157386i	−0.00351575	−	0.00608945i
$669$	39.1943	+	15.3980i	1.51534	+	0.595322i
$670$	−31.5033	−	18.1884i	−1.21708	−	0.702680i
$671$	2.62926			0.101502
$672$	4.08315	−	2.08035i	0.157511	−	0.0802512i
$673$	7.13000			0.274841			0.137421	−	0.990513i	$-0.456119\pi$
$673$	7.13000			0.274841			0.137421	+	0.990513i	$0.456119\pi$
$674$	−17.8977	−	10.3332i	−0.689392	−	0.398021i
$675$	13.3418	+	9.11623i	0.513525	+	0.350884i
$676$	6.38418	+	11.0577i	0.245545	+	0.425297i
$677$	−7.28280	+	12.6142i	−0.279901	+	0.484802i	−0.971360	−	0.237613i	$-0.923635\pi$
$677$	−7.28280	+	12.6142i	−0.279901	+	0.484802i	0.691459	+	0.722416i	$0.256968\pi$
$678$	−8.52580	−	10.6985i	−0.327431	−	0.410873i
$679$	−22.9740	+	7.66322i	−0.881660	+	0.294088i
$680$		−	7.56353i		−	0.290048i
$681$	−23.9407	+	3.60014i	−0.917409	+	0.137958i
$682$	1.18496	−	0.684136i	0.0453744	−	0.0261969i
$683$	−13.8963	+	8.02305i	−0.531728	+	0.306993i	−0.741720	−	0.670710i	$-0.765990\pi$
$683$	−13.8963	+	8.02305i	−0.531728	+	0.306993i	0.209992	+	0.977703i	$0.432656\pi$
$684$	−13.3077	+	14.3227i	−0.508832	+	0.547642i
$685$			8.07087i			0.308372i
$686$	7.92650	+	16.7383i	0.302635	+	0.639071i
$687$	−36.4503	+	29.0479i	−1.39067	+	1.10825i
$688$	2.71942	−	4.71018i	0.103677	−	0.179574i
$689$	0.113567	+	0.196704i	0.00432656	+	0.00749382i
$690$	1.80360	−	4.59090i	0.0686618	−	0.174773i
$691$	10.2606	+	5.92395i	0.390331	+	0.225358i	0.682304	−	0.731069i	$-0.260978\pi$
$691$	10.2606	+	5.92395i	0.390331	+	0.225358i	−0.291973	+	0.956427i	$0.594312\pi$
$692$	−2.07343			−0.0788201
$693$	−0.211004	−	2.17128i	−0.00801538	−	0.0824800i
$694$	−0.316521			−0.0120150
$695$	13.8821	+	8.01486i	0.526580	+	0.304021i
$696$	6.32867	−	16.1091i	0.239888	−	0.610612i
$697$	11.0077	+	19.0660i	0.416948	+	0.722174i
$698$	3.12545	−	5.41344i	0.118300	−	0.204902i
$699$	30.7888	−	24.5361i	1.16454	−	0.928042i
$700$	8.06098	+	1.64784i	0.304676	+	0.0622823i
$701$			14.1866i			0.535820i	0.963444	+	0.267910i	$0.0863331\pi$
$701$			14.1866i			0.535820i	−0.963444	+	0.267910i	$0.913667\pi$
$702$	−0.189436	+	2.49368i	−0.00714981	+	0.0941178i
$703$	15.9432	−	9.20479i	0.601308	−	0.347165i
$704$	−0.238022	+	0.137422i	−0.00897078	+	0.00517928i
$705$	−16.4839	+	2.47881i	−0.620821	+	0.0933575i
$706$			3.49060i			0.131370i
$707$	4.88306	−	5.50896i	0.183646	−	0.207186i
$708$	−1.46108	−	1.83341i	−0.0549106	−	0.0689038i
$709$	2.89759	−	5.01878i	0.108821	−	0.188484i	−0.806472	−	0.591273i	$-0.798626\pi$
$709$	2.89759	−	5.01878i	0.108821	−	0.188484i	0.915293	+	0.402789i	$0.131959\pi$
$710$	11.5469	+	19.9998i	0.433348	+	0.750581i
$711$	6.43971	−	1.98159i	0.241508	−	0.0743153i
$712$	−7.62861	−	4.40438i	−0.285894	−	0.165061i
$713$	−4.97836			−0.186441
$714$	−0.637276	+	12.1544i	−0.0238495	+	0.454867i
$715$	−0.376702			−0.0140879
$716$	−4.14708	−	2.39432i	−0.154984	−	0.0894799i
$717$	−13.0955	−	5.14475i	−0.489060	−	0.192134i
$718$	1.31232	+	2.27301i	0.0489755	+	0.0848280i
$719$	−16.5127	+	28.6009i	−0.615821	+	1.06663i	0.374419	+	0.927260i	$0.377842\pi$
$719$	−16.5127	+	28.6009i	−0.615821	+	1.06663i	−0.990240	+	0.139374i	$0.955491\pi$
$720$	−1.90673	+	8.32780i	−0.0710597	+	0.310359i
$721$	4.31970	−	21.1314i	0.160874	−	0.786973i
$722$		−	23.4704i		−	0.873479i
$723$	−2.69533	−	17.9237i	−0.100240	−	0.666590i
$724$	9.56951	−	5.52496i	0.355648	−	0.205334i
$725$	26.9114	−	15.5373i	0.999464	−	0.577041i
$726$	−2.81377	−	18.7113i	−0.104429	−	0.694443i
$727$		−	13.9670i		−	0.518006i	−0.965876	−	0.259003i	$-0.916606\pi$
$727$		−	13.9670i		−	0.518006i	0.965876	−	0.259003i	$-0.0833940\pi$
$728$	0.402925	+	1.20795i	0.0149334	+	0.0447696i
$729$	16.8773	−	21.0750i	0.625085	−	0.780557i
$730$	3.87502	−	6.71174i	0.143421	−	0.248413i
$731$	7.22265	+	12.5100i	0.267140	+	0.462699i
$732$	15.4220	+	6.05876i	0.570015	+	0.223938i
$733$	16.9332	+	9.77637i	0.625441	+	0.361098i	0.778984	−	0.627043i	$-0.215735\pi$
$733$	16.9332	+	9.77637i	0.625441	+	0.361098i	−0.153543	+	0.988142i	$0.549069\pi$
$734$	−25.0390			−0.924205
$735$	−33.4193	−	8.67684i	−1.23269	−	0.320050i
$736$	1.00000			0.0368605
$737$	−3.04045	−	1.75540i	−0.111996	−	0.0646611i
$738$	−7.31359	−	23.7675i	−0.269217	−	0.874894i
$739$	−10.4943	−	18.1766i	−0.386037	−	0.668636i	0.605875	−	0.795560i	$-0.292823\pi$
$739$	−10.4943	−	18.1766i	−0.386037	−	0.668636i	−0.991913	+	0.126923i	$0.959490\pi$
$740$	4.02231	−	6.96684i	0.147863	−	0.256106i
$741$	−3.38576	−	4.24857i	−0.124379	−	0.156075i
$742$	−0.395085	−	1.18444i	−0.0145040	−	0.0434823i
$743$		−	20.6083i		−	0.756046i	−0.925796	−	0.378023i	$-0.876604\pi$
$743$		−	20.6083i		−	0.756046i	0.925796	−	0.378023i	$-0.123396\pi$
$744$	8.52691	−	1.28226i	0.312612	−	0.0470098i
$745$	56.3565	−	32.5374i	2.06474	−	1.19208i
$746$	−12.5589	+	7.25090i	−0.459815	+	0.265474i
$747$	−22.0287	−	20.4675i	−0.805987	−	0.748868i
$748$		−	0.729972i		−	0.0266904i
$749$	−5.47613	+	26.7885i	−0.200093	+	0.978829i
$750$	7.29139	−	5.81063i	0.266244	−	0.212174i
$751$	−5.21971	+	9.04080i	−0.190470	+	0.329904i	−0.945406	−	0.325895i	$-0.894334\pi$
$751$	−5.21971	+	9.04080i	−0.190470	+	0.329904i	0.754936	+	0.655798i	$0.227668\pi$
$752$	−1.68975	−	2.92673i	−0.0616187	−	0.106727i
$753$	8.74961	−	22.2713i	0.318853	−	0.811613i
$754$	4.16500	+	2.40467i	0.151681	+	0.0875728i
$755$	−20.3444			−0.740408
$756$	3.76574	−	13.2219i	0.136959	−	0.480877i
$757$	−48.3266			−1.75646			−0.878230	−	0.478239i	$-0.841275\pi$
$757$	−48.3266			−1.75646			−0.878230	+	0.478239i	$0.841275\pi$
$758$	14.9092	+	8.60784i	0.541527	+	0.312651i
$759$	0.174069	−	0.443077i	0.00631831	−	0.0160827i
$760$	−9.27935	−	16.0723i	−0.336597	−	0.583004i
$761$	0.00131245	−	0.00227322i	4.75761e−5	−	8.24043e-5i	−0.866002	−	0.500041i	$-0.833318\pi$
$761$	0.00131245	−	0.00227322i	4.75761e−5	−	8.24043e-5i	0.866049	+	0.499959i	$0.166652\pi$
$762$	15.1713	−	12.0903i	0.549599	−	0.437984i
$763$	1.30667	−	1.47415i	0.0473045	−	0.0533679i
$764$			25.4238i			0.919803i
$765$	−16.6229	−	15.4448i	−0.601001	−	0.558409i
$766$	20.2284	−	11.6789i	0.730881	−	0.421974i
$767$	0.564166	−	0.325721i	0.0203709	−	0.0117611i
$768$	−1.71279	+	0.257566i	−0.0618051	+	0.00929411i
$769$		−	30.4790i		−	1.09910i	−0.835460	−	0.549551i	$-0.814799\pi$
$769$		−	30.4790i		−	1.09910i	0.835460	−	0.549551i	$-0.185201\pi$
$770$	2.02885	+	0.414740i	0.0731146	+	0.0149462i
$771$	−8.75808	−	10.9900i	−0.315415	−	0.395794i
$772$	−5.75992	+	9.97647i	−0.207304	+	0.359061i
$773$	−3.47904	−	6.02588i	−0.125132	−	0.216736i	0.796652	−	0.604438i	$-0.206602\pi$
$773$	−3.47904	−	6.02588i	−0.125132	−	0.216736i	−0.921785	+	0.387702i	$0.873269\pi$
$774$	−4.79877	−	15.5949i	−0.172488	−	0.560547i
$775$	13.4074	+	7.74079i	0.481610	+	0.278057i
$776$	9.15367			0.328598
$777$	−7.05075	+	10.8566i	−0.252944	+	0.389480i
$778$	28.7426			1.03047
$779$	46.7823	+	27.0098i	1.67615	+	0.967725i
$780$	−2.20956	−	0.868056i	−0.0791149	−	0.0310814i
$781$	1.11442	+	1.93023i	0.0398770	+	0.0690689i
$782$	−1.32798	+	2.30012i	−0.0474883	+	0.0822522i
$783$	−22.4807	−	46.8039i	−0.803395	−	1.67263i
$784$	−0.840159	−	6.94940i	−0.0300057	−	0.248193i
$785$		−	53.1883i		−	1.89837i
$786$	1.89371	+	12.5930i	0.0675463	+	0.449178i
$787$	33.9097	−	19.5778i	1.20875	−	0.697873i	0.246265	−	0.969203i	$-0.420797\pi$
$787$	33.9097	−	19.5778i	1.20875	−	0.697873i	0.962487	+	0.271330i	$0.0874633\pi$
$788$	−22.2429	+	12.8419i	−0.792369	+	0.457475i
$789$	1.92224	+	12.7827i	0.0684335	+	0.455078i
$790$			6.39579i			0.227552i
$791$	−19.8231	+	6.61221i	−0.704828	+	0.235103i
$792$	−0.184023	+	0.803734i	−0.00653896	+	0.0285594i
$793$	−2.30211	+	3.98737i	−0.0817503	+	0.141596i
$794$	15.5233	+	26.8872i	0.550902	+	0.954190i
$795$	2.16657	+	0.851166i	0.0768402	+	0.0301877i
$796$	15.8095	+	9.12764i	0.560354	+	0.323521i
$797$	−16.5847			−0.587461			−0.293731	−	0.955888i	$-0.594897\pi$
$797$	−16.5847			−0.587461			−0.293731	+	0.955888i	$0.594897\pi$
$798$	13.5575	+	26.6096i	0.479930	+	0.941971i
$799$	8.97577			0.317540
$800$	−2.69314	−	1.55489i	−0.0952169	−	0.0549735i
$801$	−25.2575	+	7.77209i	−0.892431	+	0.274613i
$802$	−2.67575	−	4.63453i	−0.0944839	−	0.163651i
$803$	0.373987	−	0.647764i	0.0131977	−	0.0228591i
$804$	−13.7888	−	17.3026i	−0.486292	−	0.610217i
$805$	−5.63835	−	4.99774i	−0.198726	−	0.176147i
$806$			2.39604i			0.0843970i
$807$	−1.94465	+	0.292433i	−0.0684551	+	0.0102941i
$808$	−2.40965	+	1.39121i	−0.0847710	+	0.0489426i
$809$	−29.3754	+	16.9599i	−1.03278	+	0.596278i	−0.917781	−	0.397087i	$-0.870021\pi$
$809$	−29.3754	+	16.9599i	−1.03278	+	0.596278i	−0.115003	+	0.993365i	$0.536688\pi$
$810$	14.4090	+	21.1961i	0.506280	+	0.744753i
$811$		−	7.62542i		−	0.267765i	−0.990997	−	0.133882i	$-0.957256\pi$
$811$		−	7.62542i		−	0.267765i	0.990997	−	0.133882i	$-0.0427444\pi$
$812$	−19.7845	−	17.5366i	−0.694298	−	0.615416i
$813$	15.4868	−	12.3417i	0.543146	−	0.432842i
$814$	0.388201	−	0.672384i	0.0136064	−	0.0235670i
$815$	28.2798	+	48.9821i	0.990599	+	1.71577i
$816$	1.68212	−	4.28167i	0.0588858	−	0.149889i
$817$	30.6959	+	17.7223i	1.07391	+	0.620024i
$818$	−1.68605			−0.0589514
$819$	3.47757	+	1.58111i	0.121516	+	0.0552486i
$820$	23.6054			0.824337
$821$	−35.1188	−	20.2758i	−1.22565	−	0.707632i	−0.259536	−	0.965733i	$-0.583570\pi$
$821$	−35.1188	−	20.2758i	−1.22565	−	0.707632i	−0.966118	+	0.258101i	$0.916903\pi$
$822$	−1.79495	+	4.56888i	−0.0626059	+	0.159358i
$823$	−25.4338	−	44.0526i	−0.886567	−	1.53558i	−0.843907	−	0.536489i	$-0.819750\pi$
$823$	−25.4338	−	44.0526i	−0.886567	−	1.53558i	−0.0426594	−	0.999090i	$-0.513583\pi$
$824$	−4.07604	+	7.05990i	−0.141995	+	0.245943i
$825$	−1.15773	+	0.922612i	−0.0403069	+	0.0321212i
$826$	−3.39710	+	1.13314i	−0.118200	+	0.0394271i
$827$		−	26.7283i		−	0.929433i	−0.885460	−	0.464716i	$-0.846156\pi$
$827$		−	26.7283i		−	0.929433i	0.885460	−	0.464716i	$-0.153844\pi$
$828$	2.04201	−	2.19777i	0.0709649	−	0.0763776i
$829$	−2.90483	+	1.67711i	−0.100889	+	0.0582483i	−0.549596	−	0.835431i	$-0.685218\pi$
$829$	−2.90483	+	1.67711i	−0.100889	+	0.0582483i	0.448707	+	0.893679i	$0.351885\pi$
$830$	24.7196	−	14.2719i	0.858031	−	0.495384i
$831$	21.0484	−	3.16521i	0.730161	−	0.109800i
$832$		−	0.481291i		−	0.0166858i
$833$	17.1002	+	7.29617i	0.592486	+	0.252797i
$834$	6.07612	+	7.62453i	0.210399	+	0.264016i
$835$	0.258768	−	0.448199i	0.00895502	−	0.0155106i
$836$	−0.895569	−	1.55117i	−0.0309739	−	0.0536484i
$837$	14.5940	−	21.3585i	0.504441	−	0.738259i
$838$	−21.3514	−	12.3272i	−0.737570	−	0.425837i
$839$	16.2890			0.562357			0.281179	−	0.959655i	$-0.409275\pi$
$839$	16.2890			0.562357			0.281179	+	0.959655i	$0.409275\pi$
$840$	10.9446	+	7.10786i	0.377624	+	0.245244i
$841$	−70.8512			−2.44315
$842$	−35.1867	−	20.3151i	−1.21262	−	0.700104i
$843$	−51.6748	−	20.3012i	−1.77977	−	0.699209i
$844$	5.89341	+	10.2077i	0.202859	+	0.351363i
$845$	−18.1807	+	31.4898i	−0.625433	+	1.08328i
$846$	−9.88275	−	2.26275i	−0.339776	−	0.0777950i
$847$	−28.3178	−	5.78875i	−0.973011	−	0.198904i
$848$			0.471926i			0.0162060i
$849$	2.13989	+	14.2301i	0.0734410	+	0.488377i
$850$	7.15286	−	4.12970i	0.245341	−	0.141648i
$851$	−2.44642	+	1.41244i	−0.0838623	+	0.0484179i
$852$	2.08872	+	13.8898i	0.0715583	+	0.475857i
$853$		−	21.1736i		−	0.724971i	−0.931989	−	0.362485i	$-0.881928\pi$
$853$		−	21.1736i		−	0.724971i	0.931989	−	0.362485i	$-0.118072\pi$
$854$	16.7887	−	18.9407i	0.574499	−	0.648137i
$855$	−54.2717	−	12.4260i	−1.85605	−	0.424962i
$856$	5.16724	−	8.94992i	0.176613	−	0.305902i
$857$	19.9662	+	34.5826i	0.682034	+	1.18132i	0.974359	+	0.224999i	$0.0722377\pi$
$857$	19.9662	+	34.5826i	0.682034	+	1.18132i	−0.292325	+	0.956319i	$0.594429\pi$
$858$	−0.213249	−	0.0837779i	−0.00728021	−	0.00286013i
$859$	−14.9604	−	8.63737i	−0.510441	−	0.294703i	0.222574	−	0.974916i	$-0.428554\pi$
$859$	−14.9604	−	8.63737i	−0.510441	−	0.294703i	−0.733015	+	0.680213i	$0.761887\pi$
$860$	15.4886			0.528155
$861$	−37.9333	−	1.98891i	−1.29276	−	0.0677819i
$862$	28.6095			0.974444
$863$	26.6502	+	15.3865i	0.907183	+	0.523762i	0.879524	−	0.475855i	$-0.157861\pi$
$863$	26.6502	+	15.3865i	0.907183	+	0.523762i	0.0276590	+	0.999617i	$0.491195\pi$
$864$	−2.93148	+	4.29027i	−0.0997310	+	0.145958i
$865$	−2.95233	−	5.11358i	−0.100382	−	0.173867i
$866$	16.9556	−	29.3680i	0.576176	−	0.997966i
$867$	−10.7362	−	13.4721i	−0.364619	−	0.457538i
$868$	2.63798	−	12.9046i	0.0895389	−	0.438012i
$869$			0.617271i			0.0209395i
$870$	48.7400	−	7.32941i	1.65244	−	0.248490i
$871$	5.32426	−	3.07396i	0.180406	−	0.104157i
$872$	−0.644801	+	0.372276i	−0.0218357	+	0.0126069i
$873$	18.6919	−	20.1176i	0.632626	−	0.680878i
$874$			6.51693i			0.220439i
$875$	−4.50645	−	13.5101i	−0.152346	−	0.456725i
$876$	3.68631	−	2.93768i	0.124549	−	0.0992550i
$877$	−22.7283	+	39.3665i	−0.767479	+	1.32931i	0.171448	+	0.985193i	$0.445156\pi$
$877$	−22.7283	+	39.3665i	−0.767479	+	1.32931i	−0.938926	+	0.344119i	$0.888178\pi$
$878$	−18.4680	−	31.9875i	−0.623265	−	1.07953i
$879$	0.551381	−	1.40349i	0.0185976	−	0.0473386i
$880$	−0.677830	−	0.391345i	−0.0228497	−	0.0131923i
$881$	48.2293			1.62489			0.812444	−	0.583040i	$-0.198137\pi$
$881$	48.2293			1.62489			0.812444	+	0.583040i	$0.198137\pi$
$882$	−16.9888	−	12.3443i	−0.572042	−	0.415654i
$883$	21.5877			0.726484			0.363242	−	0.931695i	$-0.381670\pi$
$883$	21.5877			0.726484			0.363242	+	0.931695i	$0.381670\pi$
$884$	1.10703	+	0.639144i	0.0372334	+	0.0214967i
$885$	2.44123	−	6.21392i	0.0820609	−	0.208879i
$886$	−16.4103	−	28.4235i	−0.551316	−	0.954907i
$887$	16.6487	−	28.8364i	0.559009	−	0.968232i	−0.438570	−	0.898697i	$-0.644515\pi$
$887$	16.6487	−	28.8364i	0.559009	−	0.968232i	0.997579	−	0.0695354i	$-0.0221517\pi$
$888$	3.82642	−	3.04934i	0.128406	−	0.102329i
$889$	−9.37665	−	28.1107i	−0.314483	−	0.942803i
$890$		−	25.0853i		−	0.840860i
$891$	1.39064	+	2.04567i	0.0465882	+	0.0685327i
$892$	−21.0552	+	12.1563i	−0.704982	+	0.407021i
$893$	19.0733	−	11.0120i	0.638263	−	0.368501i
$894$	39.1394	−	5.88569i	1.30902	−	0.196847i
$895$		−	13.6369i		−	0.455832i
$896$	−0.529889	+	2.59215i	−0.0177024	+	0.0865975i
$897$	0.519532	+	0.651928i	0.0173467	+	0.0217672i
$898$	0.217736	−	0.377130i	0.00726594	−	0.0125850i
$899$	−24.8733	−	43.0818i	−0.829571	−	1.43686i
$900$	−8.91671	+	2.74380i	−0.297224	+	0.0914598i
$901$	−1.08549	−	0.626707i	−0.0361629	−	0.0208786i
$902$	2.27821			0.0758561
$903$	−24.8897	−	1.30501i	−0.828278	−	0.0434280i
$904$	7.89825			0.262692
$905$	27.2517	+	15.7338i	0.905878	+	0.523009i
$906$	−11.5168	−	4.52455i	−0.382622	−	0.150318i
$907$	−21.5083	−	37.2535i	−0.714171	−	1.23698i	−0.963278	−	0.268505i	$-0.913470\pi$
$907$	−21.5083	−	37.2535i	−0.714171	−	1.23698i	0.249107	−	0.968476i	$-0.419863\pi$
$908$	6.98878	−	12.1049i	0.231931	−	0.401716i
$909$	−1.86298	+	8.13671i	−0.0617911	+	0.269878i
$910$	−2.40537	+	2.71369i	−0.0797373	+	0.0899579i
$911$			3.43102i			0.113675i	0.998383	+	0.0568374i	$0.0181017\pi$
$911$			3.43102i			0.113675i	−0.998383	+	0.0568374i	$0.981898\pi$
$912$	−1.67854	−	11.1622i	−0.0555820	−	0.369616i
$913$	2.38574	−	1.37741i	0.0789565	−	0.0455856i
$914$	33.0794	−	19.0984i	1.09417	−	0.631719i
$915$	7.01682	+	46.6614i	0.231969	+	1.54258i
$916$		−	26.9098i		−	0.889124i
$917$	19.0583	+	3.89592i	0.629360	+	0.128655i
$918$	−5.97521	−	12.4401i	−0.197211	−	0.410586i
$919$	−19.5966	+	33.9424i	−0.646434	+	1.11966i	0.337535	+	0.941313i	$0.390407\pi$
$919$	−19.5966	+	33.9424i	−0.646434	+	1.11966i	−0.983968	+	0.178343i	$0.942926\pi$
$920$	1.42388	+	2.46624i	0.0469440	+	0.0813095i
$921$	28.7906	+	11.3108i	0.948684	+	0.372704i
$922$	24.0072	+	13.8606i	0.790635	+	0.456473i
$923$	−3.90301			−0.128469
$924$	1.05628	+	0.685994i	0.0347492	+	0.0225675i
$925$	8.78475			0.288841
$926$	−22.5916	−	13.0432i	−0.742405	−	0.428628i
$927$	7.19269	+	23.3746i	0.236239	+	0.767723i
$928$	4.99628	+	8.65381i	0.164011	+	0.284075i
$929$	−21.4788	+	37.2023i	−0.704695	+	1.22057i	0.262106	+	0.965039i	$0.415583\pi$
$929$	−21.4788	+	37.2023i	−0.704695	+	1.22057i	−0.966801	+	0.255529i	$0.917750\pi$
$930$	15.3037	+	19.2036i	0.501827	+	0.629711i
$931$	45.2888	−	5.47526i	1.48428	−	0.179444i
$932$			22.7301i			0.744550i
$933$	−46.3422	+	6.96883i	−1.51718	+	0.228149i
$934$	3.44186	−	1.98716i	0.112621	−	0.0650218i
$935$	1.80028	−	1.03939i	0.0588756	−	0.0339918i
$936$	−1.05777	−	0.982804i	−0.0345742	−	0.0321240i
$937$			25.6308i			0.837320i	0.908143	+	0.418660i	$0.137500\pi$
$937$			25.6308i			0.837320i	−0.908143	+	0.418660i	$0.862500\pi$
$938$	−32.0598	+	10.6939i	−1.04679	+	0.349169i
$939$	−37.7552	+	30.0877i	−1.23209	+	0.981876i
$940$	4.81200	−	8.33463i	0.156950	−	0.271846i
$941$	14.4409	+	25.0124i	0.470760	+	0.815380i	0.999441	−	0.0334407i	$-0.0106465\pi$
$941$	14.4409	+	25.0124i	0.470760	+	0.815380i	−0.528681	+	0.848821i	$0.677313\pi$
$942$	11.8290	−	30.1096i	0.385409	−	0.981024i
$943$	−7.17857	−	4.14455i	−0.233767	−	0.134965i
$944$	1.35353			0.0440537
$945$	37.9704	−	9.53925i	1.23518	−	0.310312i
$946$	1.49483			0.0486012
$947$	15.9147	+	9.18836i	0.517158	+	0.298581i	0.735771	−	0.677230i	$-0.236820\pi$
$947$	15.9147	+	9.18836i	0.517158	+	0.298581i	−0.218613	+	0.975812i	$0.570153\pi$
$948$	−1.42241	+	3.62062i	−0.0461978	+	0.117592i
$949$	0.654905	+	1.13433i	0.0212591	+	0.0368219i
$950$	10.1331	−	17.5510i	0.328761	−	0.569430i
$951$	−10.5054	+	8.37195i	−0.340662	+	0.271479i
$952$	−5.25857	−	4.66112i	−0.170431	−	0.151068i
$953$			35.0470i			1.13529i	0.823275	+	0.567643i	$0.192144\pi$
$953$			35.0470i			1.13529i	−0.823275	+	0.567643i	$0.807856\pi$
$954$	1.03718	+	0.963681i	0.0335801	+	0.0312003i
$955$	−62.7013	+	36.2006i	−2.02897	+	1.17142i
$956$	7.03492	−	4.06161i	0.227525	−	0.131362i
$957$	4.70400	−	0.707377i	0.152059	−	0.0228663i
$958$			24.0001i			0.775410i
$959$	5.61130	+	4.97377i	0.181198	+	0.160611i
$960$	−3.07404	−	3.85741i	−0.0992141	−	0.124497i
$961$	−3.10794	+	5.38312i	−0.100256	+	0.173649i
$962$	0.679796	+	1.17744i	0.0219175	+	0.0379623i
$963$	−9.11825	−	29.6322i	−0.293832	−	0.954886i
$964$	9.06262	+	5.23230i	0.291887	+	0.168521i
$965$	−32.8058			−1.05606
$966$	−2.08035	−	4.08315i	−0.0669341	−	0.131373i
$967$	−21.6692			−0.696835			−0.348417	−	0.937339i	$-0.613281\pi$
$967$	−21.6692			−0.696835			−0.348417	+	0.937339i	$0.613281\pi$
$968$	9.46086	+	5.46223i	0.304084	+	0.175563i
$969$	27.9034	+	10.9622i	0.896386	+	0.352158i
$970$	13.0338	+	22.5751i	0.418489	+	0.724844i
$971$	22.7918	−	39.4766i	0.731424	−	1.26686i	−0.224851	−	0.974393i	$-0.572190\pi$
$971$	22.7918	−	39.4766i	0.731424	−	1.26686i	0.956275	−	0.292470i	$-0.0944771\pi$
$972$	3.44289	+	15.2035i	0.110431	+	0.487653i
$973$	14.1274	−	4.71235i	0.452904	−	0.151071i
$974$		−	38.4800i		−	1.23298i
$975$	−0.385500	−	2.56355i	−0.0123459	−	0.0820993i
$976$	−8.28474	+	4.78320i	−0.265188	+	0.153106i
$977$	3.06467	−	1.76939i	0.0980476	−	0.0566078i	−0.450174	−	0.892941i	$-0.648638\pi$
$977$	3.06467	−	1.76939i	0.0980476	−	0.0566078i	0.548222	+	0.836333i	$0.315305\pi$
$978$	5.11553	+	34.0179i	0.163577	+	1.08777i
$979$		−	2.42103i		−	0.0773765i
$980$	15.9426	−	11.9672i	0.509267	−	0.382277i
$981$	−0.498518	+	2.17732i	−0.0159164	+	0.0695163i
$982$	−18.7451	+	32.4675i	−0.598182	+	1.03608i
$983$	4.00421	+	6.93550i	0.127715	+	0.221208i	0.922791	−	0.385301i	$-0.125903\pi$
$983$	4.00421	+	6.93550i	0.127715	+	0.221208i	−0.795076	+	0.606510i	$0.792569\pi$
$984$	13.3629	+	5.24980i	0.425994	+	0.167358i
$985$	−63.3425	−	36.5708i	−2.01826	−	1.16524i
$986$	−26.5398			−0.845198
$987$	−8.43501	+	12.9881i	−0.268489	+	0.413416i
$988$	3.13654			0.0997868
$989$	−4.71018	−	2.71942i	−0.149775	−	0.0864726i
$990$	−2.24423	+	0.690579i	−0.0713262	+	0.0219480i
$991$	−18.8374	−	32.6274i	−0.598390	−	1.03644i	−0.993059	−	0.117619i	$-0.962474\pi$
$991$	−18.8374	−	32.6274i	−0.598390	−	1.03644i	0.394668	−	0.918824i	$-0.370859\pi$
$992$	−2.48918	+	4.31139i	−0.0790316	+	0.136887i
$993$	−3.04162	−	3.81674i	−0.0965229	−	0.121120i
$994$	21.0209	+	4.29711i	0.666742	+	0.136296i
$995$			51.9868i			1.64809i
$996$	17.1677	−	2.58164i	0.543979	−	0.0818023i
$997$	−19.5837	+	11.3067i	−0.620223	+	0.358086i	−0.776956	−	0.629555i	$-0.783237\pi$
$997$	−19.5837	+	11.3067i	−0.620223	+	0.358086i	0.156733	+	0.987641i	$0.449904\pi$
$998$	18.0856	−	10.4417i	0.572491	−	0.330528i
$999$	1.11187	−	14.6364i	0.0351781	−	0.463074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.47.11	✓	56
3.2	odd	2	inner	966.2.l.c.47.28	yes	56
7.3	odd	6	inner	966.2.l.c.185.28	yes	56
21.17	even	6	inner	966.2.l.c.185.11	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.11	✓	56	1.1	even	1	trivial
966.2.l.c.47.28	yes	56	3.2	odd	2	inner
966.2.l.c.185.11	yes	56	21.17	even	6	inner
966.2.l.c.185.28	yes	56	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.633338 - 1.61211i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.42388 + 2.46624i) q^{5} +(-1.35454 + 1.07946i) q^{6} +(0.837175 + 2.50981i) q^{7} -1.00000i q^{8} +(-2.19777 - 2.04201i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.633338 - 1.61211i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.42388 + 2.46624i) q^{5} +(-1.35454 + 1.07946i) q^{6} +(0.837175 + 2.50981i) q^{7} -1.00000i q^{8} +(-2.19777 - 2.04201i) q^{9} +(2.46624 - 1.42388i) q^{10} +(0.238022 - 0.137422i) q^{11} +(1.71279 - 0.257566i) q^{12} +0.481291i q^{13} +(0.529889 - 2.59215i) q^{14} +(3.07404 + 3.85741i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.32798 - 2.30012i) q^{17} +(0.882314 + 2.86732i) q^{18} +(-5.64383 - 3.25847i) q^{19} -2.84777 q^{20} +(4.57629 + 0.239943i) q^{21} -0.274844 q^{22} +(0.866025 + 0.500000i) q^{23} +(-1.61211 - 0.633338i) q^{24} +(-1.55489 - 2.69314i) q^{25} +(0.240646 - 0.416811i) q^{26} +(-4.68387 + 2.24974i) q^{27} +(-1.75497 + 1.97992i) q^{28} +9.99256i q^{29} +(-0.733487 - 4.87763i) q^{30} +(-4.31139 + 2.48918i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.0707904 - 0.470751i) q^{33} +2.65595i q^{34} +(-7.38182 - 1.50900i) q^{35} +(0.669554 - 2.92433i) q^{36} +(-1.41244 + 2.44642i) q^{37} +(3.25847 + 5.64383i) q^{38} +(0.775892 + 0.304820i) q^{39} +(2.46624 + 1.42388i) q^{40} -8.28910 q^{41} +(-3.84321 - 2.49594i) q^{42} -5.43884 q^{43} +(0.238022 + 0.137422i) q^{44} +(8.16546 - 2.51262i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.68975 + 2.92673i) q^{47} +(1.07946 + 1.35454i) q^{48} +(-5.59828 + 4.20230i) q^{49} +3.10977i q^{50} +(-4.54910 + 0.684083i) q^{51} +(-0.416811 + 0.240646i) q^{52} +(0.408700 - 0.235963i) q^{53} +(5.18122 + 0.393600i) q^{54} +0.782691i q^{55} +(2.50981 - 0.837175i) q^{56} +(-8.82744 + 7.03474i) q^{57} +(4.99628 - 8.65381i) q^{58} +(-0.676766 - 1.17219i) q^{59} +(-1.80360 + 4.59090i) q^{60} +(8.28474 + 4.78320i) q^{61} +4.97836 q^{62} +(3.28515 - 7.22550i) q^{63} -1.00000 q^{64} +(-1.18698 - 0.685303i) q^{65} +(-0.174069 + 0.443077i) q^{66} +(-6.38691 - 11.0625i) q^{67} +(1.32798 - 2.30012i) q^{68} +(1.35454 - 1.07946i) q^{69} +(5.63835 + 4.99774i) q^{70} +8.10946i q^{71} +(-2.04201 + 2.19777i) q^{72} +(2.35684 - 1.36072i) q^{73} +(2.44642 - 1.41244i) q^{74} +(-5.32640 + 0.800971i) q^{75} -6.51693i q^{76} +(0.544168 + 0.482343i) q^{77} +(-0.519532 - 0.651928i) q^{78} +(-1.12295 + 1.94500i) q^{79} +(-1.42388 - 2.46624i) q^{80} +(0.660351 + 8.97574i) q^{81} +(7.17857 + 4.14455i) q^{82} +10.0232 q^{83} +(2.08035 + 4.08315i) q^{84} +7.56353 q^{85} +(4.71018 + 2.71942i) q^{86} +(16.1091 + 6.32867i) q^{87} +(-0.137422 - 0.238022i) q^{88} +(4.40438 - 7.62861i) q^{89} +(-8.32780 - 1.90673i) q^{90} +(-1.20795 + 0.402925i) q^{91} +1.00000i q^{92} +(1.28226 + 8.52691i) q^{93} +(2.92673 - 1.68975i) q^{94} +(16.0723 - 9.27935i) q^{95} +(-0.257566 - 1.71279i) q^{96} +9.15367i q^{97} +(6.94940 - 0.840159i) q^{98} +(-0.803734 - 0.184023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

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