LMFDB - Embedded newform 756.2.bt.a.103.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.18
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28497 - 0.590645i) q^{2} +(-0.974544 - 1.43187i) q^{3} +(1.30228 + 1.51792i) q^{4} +(2.54084 + 0.448019i) q^{5} +(0.406527 + 2.41552i) q^{6} +(-0.471692 - 2.60336i) q^{7} +(-0.776834 - 2.71966i) q^{8} +(-1.10053 + 2.79085i) q^{9} +O(q^{10})$	\(q+(-1.28497 - 0.590645i) q^{2} +(-0.974544 - 1.43187i) q^{3} +(1.30228 + 1.51792i) q^{4} +(2.54084 + 0.448019i) q^{5} +(0.406527 + 2.41552i) q^{6} +(-0.471692 - 2.60336i) q^{7} +(-0.776834 - 2.71966i) q^{8} +(-1.10053 + 2.79085i) q^{9} +(-3.00028 - 2.07643i) q^{10} +(-0.0215904 + 0.00380697i) q^{11} +(0.904340 - 3.34398i) q^{12} +(0.574333 - 0.684463i) q^{13} +(-0.931554 + 3.62384i) q^{14} +(-1.83466 - 4.07478i) q^{15} +(-0.608144 + 3.95350i) q^{16} -2.27533i q^{17} +(3.06254 - 2.93612i) q^{18} -4.27797 q^{19} +(2.62883 + 4.44024i) q^{20} +(-3.26801 + 3.21250i) q^{21} +(0.0299915 + 0.00786043i) q^{22} +(3.79334 - 4.52073i) q^{23} +(-3.13715 + 3.76275i) q^{24} +(1.55670 + 0.566594i) q^{25} +(-1.14227 + 0.540286i) q^{26} +(5.06866 - 1.14398i) q^{27} +(3.33742 - 4.10629i) q^{28} +(4.69164 - 3.93675i) q^{29} +(-0.0492782 + 6.31959i) q^{30} +(-0.392870 + 0.142993i) q^{31} +(3.11656 - 4.72092i) q^{32} +(0.0264919 + 0.0272047i) q^{33} +(-1.34391 + 2.92372i) q^{34} +(-0.0321391 - 6.82607i) q^{35} +(-5.66947 + 1.96395i) q^{36} +(-1.57053 - 2.72024i) q^{37} +(5.49705 + 2.52676i) q^{38} +(-1.53978 - 0.155333i) q^{39} +(-0.755357 - 7.25826i) q^{40} +(1.11533 - 1.32920i) q^{41} +(6.09672 - 2.19772i) q^{42} +(-0.465033 + 1.27767i) q^{43} +(-0.0338954 - 0.0278147i) q^{44} +(-4.04663 + 6.59805i) q^{45} +(-7.54447 + 3.56847i) q^{46} +(6.45098 + 2.34796i) q^{47} +(6.25358 - 2.98207i) q^{48} +(-6.55501 + 2.45597i) q^{49} +(-1.66566 - 1.64751i) q^{50} +(-3.25799 + 2.21741i) q^{51} +(1.78690 - 0.0195719i) q^{52} +(-4.92230 - 8.52568i) q^{53} +(-7.18874 - 1.52380i) q^{54} -0.0565635 q^{55} +(-6.71383 + 3.30522i) q^{56} +(4.16907 + 6.12552i) q^{57} +(-8.35382 + 2.28750i) q^{58} +(2.18601 + 1.83428i) q^{59} +(3.79595 - 8.09136i) q^{60} +(1.71157 - 4.70249i) q^{61} +(0.589282 + 0.0483052i) q^{62} +(7.78471 + 1.54866i) q^{63} +(-6.79306 + 4.22545i) q^{64} +(1.76594 - 1.48180i) q^{65} +(-0.0179729 - 0.0506044i) q^{66} +(-12.9096 - 2.27632i) q^{67} +(3.45376 - 2.96311i) q^{68} +(-10.1699 - 1.02594i) q^{69} +(-3.99048 + 8.79026i) q^{70} +(-10.1386 - 5.85351i) q^{71} +(8.44508 + 0.825035i) q^{72} +(-8.88117 - 5.12755i) q^{73} +(0.411386 + 4.42305i) q^{74} +(-0.705785 - 2.78118i) q^{75} +(-5.57111 - 6.49360i) q^{76} +(0.0200950 + 0.0544120i) q^{77} +(1.88682 + 1.10906i) q^{78} +(2.23004 - 0.393216i) q^{79} +(-3.31644 + 9.77277i) q^{80} +(-6.57767 - 6.14282i) q^{81} +(-2.21826 + 1.04922i) q^{82} +(-7.12087 + 5.97512i) q^{83} +(-9.13216 - 0.776999i) q^{84} +(1.01939 - 5.78126i) q^{85} +(1.35220 - 1.36709i) q^{86} +(-10.2091 - 2.88130i) q^{87} +(0.0271258 + 0.0557611i) q^{88} -0.800851i q^{89} +(9.09689 - 6.08816i) q^{90} +(-2.05282 - 1.17234i) q^{91} +(11.8021 - 0.129268i) q^{92} +(0.587616 + 0.423187i) q^{93} +(-6.90248 - 6.82729i) q^{94} +(-10.8697 - 1.91661i) q^{95} +(-9.79698 + 0.138221i) q^{96} +(-3.86882 + 10.6295i) q^{97} +(9.87358 + 0.715837i) q^{98} +(0.0131362 - 0.0644452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.28497	−	0.590645i	−0.908609	−	0.417649i
$2$	−1.28497	−	0.590645i	−0.908609	−	0.417649i
$3$	−0.974544	−	1.43187i	−0.562653	−	0.826693i
$3$	−0.974544	−	1.43187i	−0.562653	−	0.826693i
$4$	1.30228	+	1.51792i	0.651139	+	0.758958i
$5$	2.54084	+	0.448019i	1.13630	+	0.200360i	0.709987	−	0.704215i	$-0.248701\pi$
$5$	2.54084	+	0.448019i	1.13630	+	0.200360i	0.426313	+	0.904576i	$0.359812\pi$
$6$	0.406527	+	2.41552i	0.165964	+	0.986132i
$7$	−0.471692	−	2.60336i	−0.178283	−	0.983979i
$7$	−0.471692	−	2.60336i	−0.178283	−	0.983979i
$8$	−0.776834	−	2.71966i	−0.274652	−	0.961544i
$9$	−1.10053	+	2.79085i	−0.366843	+	0.930283i
$10$	−3.00028	−	2.07643i	−0.948772	−	0.656623i
$11$	−0.0215904	+	0.00380697i	−0.00650975	+	0.00114785i	−0.176902	−	0.984228i	$-0.556608\pi$
$11$	−0.0215904	+	0.00380697i	−0.00650975	+	0.00114785i	0.170392	+	0.985376i	$0.445496\pi$
$12$	0.904340	−	3.34398i	0.261060	−	0.965322i
$13$	0.574333	−	0.684463i	0.159291	−	0.189836i	−0.680496	−	0.732752i	$-0.738235\pi$
$13$	0.574333	−	0.684463i	0.159291	−	0.189836i	0.839787	+	0.542916i	$0.182680\pi$
$14$	−0.931554	+	3.62384i	−0.248968	+	0.968512i
$15$	−1.83466	−	4.07478i	−0.473706	−	1.05210i
$16$	−0.608144	+	3.95350i	−0.152036	+	0.988375i
$17$		−	2.27533i		−	0.551848i	−0.961179	−	0.275924i	$-0.911016\pi$
$17$		−	2.27533i		−	0.551848i	0.961179	−	0.275924i	$-0.0889838\pi$
$18$	3.06254	−	2.93612i	0.721848	−	0.692051i
$19$	−4.27797			−0.981434			−0.490717	−	0.871319i	$-0.663265\pi$
$19$	−4.27797			−0.981434			−0.490717	+	0.871319i	$0.663265\pi$
$20$	2.62883	+	4.44024i	0.587824	+	0.992867i
$21$	−3.26801	+	3.21250i	−0.713138	+	0.701024i
$22$	0.0299915	+	0.00786043i	0.00639421	+	0.00167585i
$23$	3.79334	−	4.52073i	0.790967	−	0.942638i	−0.208406	−	0.978042i	$-0.566828\pi$
$23$	3.79334	−	4.52073i	0.790967	−	0.942638i	0.999373	+	0.0354046i	$0.0112720\pi$
$24$	−3.13715	+	3.76275i	−0.640368	+	0.768069i
$25$	1.55670	+	0.566594i	0.311341	+	0.113319i
$26$	−1.14227	+	0.540286i	−0.224018	+	0.105959i
$27$	5.06866	−	1.14398i	0.975464	−	0.220159i
$28$	3.33742	−	4.10629i	0.630712	−	0.776017i
$29$	4.69164	−	3.93675i	0.871215	−	0.731036i	−0.0931384	−	0.995653i	$-0.529690\pi$
$29$	4.69164	−	3.93675i	0.871215	−	0.731036i	0.964354	+	0.264617i	$0.0852455\pi$
$30$	−0.0492782	+	6.31959i	−0.00899692	+	1.15379i
$31$	−0.392870	+	0.142993i	−0.0705614	+	0.0256823i	−0.377060	−	0.926189i	$-0.623065\pi$
$31$	−0.392870	+	0.142993i	−0.0705614	+	0.0256823i	0.306498	+	0.951871i	$0.400843\pi$
$32$	3.11656	−	4.72092i	0.550935	−	0.834548i
$33$	0.0264919	+	0.0272047i	0.00461165	+	0.00473573i
$34$	−1.34391	+	2.92372i	−0.230479	+	0.501414i
$35$	−0.0321391	−	6.82607i	−0.00543251	−	1.15382i
$36$	−5.66947	+	1.96395i	−0.944912	+	0.327325i
$37$	−1.57053	−	2.72024i	−0.258194	−	0.447205i	0.707564	−	0.706649i	$-0.249794\pi$
$37$	−1.57053	−	2.72024i	−0.258194	−	0.447205i	−0.965758	+	0.259444i	$0.916461\pi$
$38$	5.49705	+	2.52676i	0.891739	+	0.409895i
$39$	−1.53978	−	0.155333i	−0.246562	−	0.0248733i
$40$	−0.755357	−	7.25826i	−0.119432	−	1.14763i
$41$	1.11533	−	1.32920i	0.174186	−	0.207587i	−0.671887	−	0.740653i	$-0.734516\pi$
$41$	1.11533	−	1.32920i	0.174186	−	0.207587i	0.846073	+	0.533067i	$0.178960\pi$
$42$	6.09672	−	2.19772i	0.940745	−	0.339116i
$43$	−0.465033	+	1.27767i	−0.0709169	+	0.194843i	−0.970087	−	0.242756i	$-0.921949\pi$
$43$	−0.465033	+	1.27767i	−0.0709169	+	0.194843i	0.899171	+	0.437598i	$0.144171\pi$
$44$	−0.0338954	−	0.0278147i	−0.00510992	−	0.00419323i
$45$	−4.04663	+	6.59805i	−0.603236	+	0.983579i
$46$	−7.54447	+	3.56847i	−1.11237	+	0.526142i
$47$	6.45098	+	2.34796i	0.940972	+	0.342486i	0.766549	−	0.642185i	$-0.221972\pi$
$47$	6.45098	+	2.34796i	0.940972	+	0.342486i	0.174422	+	0.984671i	$0.444194\pi$
$48$	6.25358	−	2.98207i	0.902626	−	0.430425i
$49$	−6.55501	+	2.45597i	−0.936430	+	0.350853i
$50$	−1.66566	−	1.64751i	−0.235560	−	0.232994i
$51$	−3.25799	+	2.21741i	−0.456209	+	0.310499i
$52$	1.78690	−	0.0195719i	0.247798	−	0.00271414i
$53$	−4.92230	−	8.52568i	−0.676130	−	1.17109i	−0.976137	−	0.217155i	$-0.930322\pi$
$53$	−4.92230	−	8.52568i	−0.676130	−	1.17109i	0.300007	−	0.953937i	$-0.403011\pi$
$54$	−7.18874	−	1.52380i	−0.978264	−	0.207362i
$55$	−0.0565635			−0.00762702
$56$	−6.71383	+	3.30522i	−0.897173	+	0.441679i
$57$	4.16907	+	6.12552i	0.552207	+	0.811345i
$58$	−8.35382	+	2.28750i	−1.09691	+	0.300364i
$59$	2.18601	+	1.83428i	0.284594	+	0.238803i	0.773898	−	0.633311i	$-0.218304\pi$
$59$	2.18601	+	1.83428i	0.284594	+	0.238803i	−0.489303	+	0.872114i	$0.662749\pi$
$60$	3.79595	−	8.09136i	0.490055	−	1.04459i
$61$	1.71157	−	4.70249i	0.219144	−	0.602093i	−0.780593	−	0.625040i	$-0.785083\pi$
$61$	1.71157	−	4.70249i	0.219144	−	0.602093i	0.999737	+	0.0229471i	$0.00730495\pi$
$62$	0.589282	+	0.0483052i	0.0748389	+	0.00613477i
$63$	7.78471	+	1.54866i	0.980781	+	0.195113i
$64$	−6.79306	+	4.22545i	−0.849132	+	0.528181i
$65$	1.76594	−	1.48180i	0.219038	−	0.183795i
$66$	−0.0179729	−	0.0506044i	−0.00221231	−	0.00622897i
$67$	−12.9096	−	2.27632i	−1.57716	−	0.278096i	−0.684565	−	0.728952i	$-0.740008\pi$
$67$	−12.9096	−	2.27632i	−1.57716	−	0.278096i	−0.892597	+	0.450855i	$0.851119\pi$
$68$	3.45376	−	2.96311i	0.418830	−	0.359330i
$69$	−10.1699	−	1.02594i	−1.22431	−	0.123509i
$70$	−3.99048	+	8.79026i	−0.476954	+	1.05064i
$71$	−10.1386	−	5.85351i	−1.20323	−	0.694683i	−0.241956	−	0.970287i	$-0.577789\pi$
$71$	−10.1386	−	5.85351i	−1.20323	−	0.694683i	−0.961271	+	0.275604i	$0.911122\pi$
$72$	8.44508	+	0.825035i	0.995262	+	0.0972314i
$73$	−8.88117	−	5.12755i	−1.03946	−	0.600134i	−0.119781	−	0.992800i	$-0.538219\pi$
$73$	−8.88117	−	5.12755i	−1.03946	−	0.600134i	−0.919681	+	0.392666i	$0.871553\pi$
$74$	0.411386	+	4.42305i	0.0478226	+	0.514169i
$75$	−0.705785	−	2.78118i	−0.0814970	−	0.321143i
$76$	−5.57111	−	6.49360i	−0.639050	−	0.744868i
$77$	0.0200950	+	0.0544120i	0.00229003	+	0.00620082i
$78$	1.88682	+	1.10906i	0.213640	+	0.125576i
$79$	2.23004	−	0.393216i	0.250899	−	0.0442403i	−0.0467841	−	0.998905i	$-0.514897\pi$
$79$	2.23004	−	0.393216i	0.250899	−	0.0442403i	0.297683	+	0.954665i	$0.403786\pi$
$80$	−3.31644	+	9.77277i	−0.370790	+	1.09263i
$81$	−6.57767	−	6.14282i	−0.730852	−	0.682536i
$82$	−2.21826	+	1.04922i	−0.244965	+	0.115867i
$83$	−7.12087	+	5.97512i	−0.781617	+	0.655854i	−0.943655	−	0.330930i	$-0.892638\pi$
$83$	−7.12087	+	5.97512i	−0.781617	+	0.655854i	0.162039	+	0.986784i	$0.448193\pi$
$84$	−9.13216	−	0.776999i	−0.996400	−	0.0847776i
$85$	1.01939	−	5.78126i	0.110569	−	0.627065i
$86$	1.35220	−	1.36709i	0.145811	−	0.147417i
$87$	−10.2091	−	2.88130i	−1.09453	−	0.308908i
$88$	0.0271258	+	0.0557611i	0.00289162	+	0.00594415i
$89$		−	0.800851i		−	0.0848900i	−0.999099	−	0.0424450i	$-0.986485\pi$
$89$		−	0.800851i		−	0.0848900i	0.999099	−	0.0424450i	$-0.0135147\pi$
$90$	9.09689	−	6.08816i	0.958896	−	0.641748i
$91$	−2.05282	−	1.17234i	−0.215194	−	0.122895i
$92$	11.8021	−	0.129268i	1.23045	−	0.0134772i
$93$	0.587616	+	0.423187i	0.0609330	+	0.0438825i
$94$	−6.90248	−	6.82729i	−0.711936	−	0.704181i
$95$	−10.8697	−	1.91661i	−1.11520	−	0.196640i
$96$	−9.79698	+	0.138221i	−0.999900	+	0.0141072i
$97$	−3.86882	+	10.6295i	−0.392820	+	1.07926i	0.572889	+	0.819633i	$0.305823\pi$
$97$	−3.86882	+	10.6295i	−0.392820	+	1.07926i	−0.965708	+	0.259630i	$0.916399\pi$
$98$	9.87358	+	0.715837i	0.997382	+	0.0723105i
$99$	0.0131362	−	0.0644452i	0.00132024	−	0.00647699i
$100$	1.16722	+	3.10081i	0.116722	+	0.310081i
$101$	0.563992	+	0.672140i	0.0561193	+	0.0668804i	0.793374	−	0.608735i	$-0.208323\pi$
$101$	0.563992	+	0.672140i	0.0561193	+	0.0668804i	−0.737255	+	0.675615i	$0.763878\pi$
$102$	5.49610	−	0.924982i	0.544195	−	0.0915869i
$103$	0.701791	−	3.98005i	0.0691495	−	0.392166i	−0.930515	−	0.366254i	$-0.880640\pi$
$103$	0.701791	−	3.98005i	0.0691495	−	0.392166i	0.999664	−	0.0259119i	$-0.00824892\pi$
$104$	−2.30767	−	1.03027i	−0.226285	−	0.101027i
$105$	−9.74276	+	6.69832i	−0.950796	+	0.653689i
$106$	1.28935	+	13.8625i	0.125233	+	1.34645i
$107$	15.6581	+	9.04021i	1.51373	+	0.873950i	0.999871	+	0.0160728i	$0.00511634\pi$
$107$	15.6581	+	9.04021i	1.51373	+	0.873950i	0.513855	+	0.857877i	$0.328217\pi$
$108$	8.33727	+	6.20402i	0.802255	+	0.596982i
$109$	2.78883	+	4.83039i	0.267121	+	0.462668i	0.968117	−	0.250498i	$-0.0805943\pi$
$109$	2.78883	+	4.83039i	0.267121	+	0.462668i	−0.700996	+	0.713165i	$0.747261\pi$
$110$	0.0726822	+	0.0334089i	0.00692997	+	0.00318541i
$111$	−2.36449	+	4.89980i	−0.224428	+	0.465069i
$112$	10.5793	−	0.281617i	0.999646	−	0.0266103i
$113$	17.0992	−	6.22362i	1.60856	−	0.585468i	0.627407	−	0.778692i	$-0.284116\pi$
$113$	17.0992	−	6.22362i	1.60856	−	0.585468i	0.981155	+	0.193223i	$0.0618942\pi$
$114$	−1.73911	−	10.3335i	−0.162883	−	0.967823i
$115$	11.6637	−	9.78698i	1.08764	−	0.912641i
$116$	12.0855	+	1.99477i	1.12211	+	0.185210i
$117$	1.27816	+	2.35615i	0.118166	+	0.217826i
$118$	−1.72554	−	3.64814i	−0.158849	−	0.335839i
$119$	−5.92351	+	1.07326i	−0.543007	+	0.0983851i
$120$	−9.65679	+	8.15507i	−0.881540	+	0.744452i
$121$	−10.3362	+	3.76206i	−0.939652	+	0.342005i
$122$	−4.97681	+	5.03162i	−0.450579	+	0.455541i
$123$	−2.99020	−	0.301652i	−0.269617	−	0.0271991i
$124$	−0.728677	−	0.410127i	−0.0654371	−	0.0368305i
$125$	−7.47041	−	4.31304i	−0.668173	−	0.385770i
$126$	−9.08838	−	6.58797i	−0.809657	−	0.586903i
$127$	14.3332	−	8.27529i	1.27187	−	0.734313i	0.296528	−	0.955024i	$-0.404171\pi$
$127$	14.3332	−	8.27529i	1.27187	−	0.734313i	0.975339	+	0.220711i	$0.0708378\pi$
$128$	11.2246	−	1.41727i	0.992123	−	0.125271i
$129$	2.28266	−	0.579274i	0.200977	−	0.0510022i
$130$	−3.14440	+	0.861022i	−0.275782	+	0.0755166i
$131$	13.9899	+	11.7390i	1.22231	+	1.02564i	0.998701	+	0.0509579i	$0.0162274\pi$
$131$	13.9899	+	11.7390i	1.22231	+	1.02564i	0.223606	+	0.974680i	$0.428217\pi$
$132$	−0.00679465	+	0.0756406i	−0.000591399	+	0.00658367i
$133$	2.01789	+	11.1371i	0.174973	+	0.965711i
$134$	15.2439	+	10.5500i	1.31688	+	0.911380i
$135$	13.3912	−	0.635823i	1.15253	−	0.0547229i
$136$	−6.18811	+	1.76755i	−0.530626	+	0.151566i
$137$	−15.5087	−	5.64470i	−1.32500	−	0.482259i	−0.419940	−	0.907552i	$-0.637949\pi$
$137$	−15.5087	−	5.64470i	−1.32500	−	0.482259i	−0.905056	+	0.425293i	$0.860171\pi$
$138$	12.4620	+	7.32510i	1.06084	+	0.623554i
$139$	3.60966	−	20.4714i	0.306167	−	1.73636i	−0.311792	−	0.950150i	$-0.600929\pi$
$139$	3.60966	−	20.4714i	0.306167	−	1.73636i	0.617959	−	0.786210i	$-0.287960\pi$
$140$	10.3196	−	8.93823i	0.872162	−	0.755418i
$141$	−2.92477	−	11.5252i	−0.246310	−	0.970595i
$142$	9.57038	+	13.5098i	0.803129	+	1.13372i
$143$	−0.00979435	+	0.0169643i	−0.000819045	+	0.00141863i
$144$	−10.3643	−	6.04818i	−0.863695	−	0.504015i
$145$	13.6845	−	7.90073i	1.13643	−	0.656120i
$146$	8.38345	+	11.8343i	0.693819	+	0.979417i
$147$	9.90479	+	6.99250i	0.816934	+	0.576732i
$148$	2.08383	−	5.92645i	0.171290	−	0.487151i
$149$	16.2402	−	5.91094i	1.33045	−	0.484243i	0.423655	−	0.905823i	$-0.360747\pi$
$149$	16.2402	−	5.91094i	1.33045	−	0.484243i	0.906791	+	0.421581i	$0.138525\pi$
$150$	−0.735777	+	3.99059i	−0.0600760	+	0.325830i
$151$	15.5008	−	2.73320i	1.26144	−	0.222425i	0.497355	−	0.867547i	$-0.334305\pi$
$151$	15.5008	−	2.73320i	1.26144	−	0.222425i	0.764080	+	0.645122i	$0.223193\pi$
$152$	3.32328	+	11.6346i	0.269553	+	0.943691i
$153$	6.35010	+	2.50407i	0.513375	+	0.202442i
$154$	0.00631678	−	0.0817866i	0.000509021	−	0.00659055i
$155$	−1.06228	+	0.187309i	−0.0853247	+	0.0150450i
$156$	−1.76944	−	2.53954i	−0.141668	−	0.203326i
$157$	−6.84827	+	8.16145i	−0.546551	+	0.651355i	−0.966643	−	0.256127i	$-0.917553\pi$
$157$	−6.84827	+	8.16145i	−0.546551	+	0.651355i	0.420092	+	0.907482i	$0.361998\pi$
$158$	−3.09778	−	0.811891i	−0.246446	−	0.0645906i
$159$	−7.41070	+	15.3568i	−0.587707	+	1.21787i
$160$	10.0337	−	10.5988i	0.793238	−	0.837912i
$161$	−13.5584	−	7.74306i	−1.06855	−	0.610239i
$162$	4.82386	+	11.7784i	0.378998	+	0.925397i
$163$	18.1681	+	10.4894i	1.42304	+	0.821591i	0.996557	−	0.0829054i	$-0.0264199\pi$
$163$	18.1681	+	10.4894i	1.42304	+	0.821591i	0.426481	+	0.904497i	$0.359753\pi$
$164$	3.47010	−	0.0380080i	0.270969	−	0.00296793i
$165$	0.0551236	+	0.0809918i	0.00429136	+	0.00630520i
$166$	12.6792	−	3.47192i	0.984100	−	0.269474i
$167$	−13.3048	+	4.84256i	−1.02956	+	0.374728i	−0.800912	−	0.598782i	$-0.795652\pi$
$167$	−13.3048	+	4.84256i	−1.02956	+	0.374728i	−0.228645	+	0.973510i	$0.573430\pi$
$168$	11.2756	+	6.39228i	0.869930	+	0.493175i
$169$	2.11879	+	12.0163i	0.162984	+	0.924329i
$170$	−4.72455	+	6.82662i	−0.362356	+	0.523578i
$171$	4.70804	−	11.9392i	0.360032	−	0.913011i
$172$	−2.54500	+	0.957997i	−0.194054	+	0.0730466i
$173$	−2.84922	−	3.39557i	−0.216622	−	0.258160i	0.646780	−	0.762677i	$-0.276115\pi$
$173$	−2.84922	−	3.39557i	−0.216622	−	0.258160i	−0.863402	+	0.504516i	$0.831671\pi$
$174$	11.4166	+	9.73235i	0.865489	+	0.737807i
$175$	0.740765	−	4.31993i	0.0559966	−	0.326556i
$176$	−0.00192079	−	0.0876729i	−0.000144785	−	0.00660859i
$177$	0.496097	−	4.91768i	0.0372890	−	0.369635i
$178$	−0.473018	+	1.02907i	−0.0354542	+	0.0771318i
$179$		−	12.7516i		−	0.953097i	−0.879148	−	0.476548i	$-0.841888\pi$
$179$		−	12.7516i		−	0.953097i	0.879148	−	0.476548i	$-0.158112\pi$
$180$	−15.2851	+	2.45005i	−1.13929	+	0.182616i
$181$	3.21880	−	1.85838i	0.239252	−	0.138132i	−0.375581	−	0.926790i	$-0.622557\pi$
$181$	3.21880	−	1.85838i	0.239252	−	0.138132i	0.614833	+	0.788657i	$0.289223\pi$
$182$	1.94536	+	2.71890i	0.144200	+	0.201539i
$183$	−8.40138	+	2.13203i	−0.621048	+	0.157605i
$184$	−15.2416	−	6.80473i	−1.12363	−	0.501651i
$185$	−2.77176	−	7.61534i	−0.203784	−	0.559891i
$186$	−0.505114	−	0.890854i	−0.0370368	−	0.0653206i
$187$	0.00866211	+	0.0491253i	0.000633436	+	0.00359240i
$188$	4.83695	+	12.8497i	0.352771	+	0.937164i
$189$	−5.36905	−	12.6560i	−0.390541	−	0.920586i
$190$	12.8351	+	8.88289i	0.931157	+	0.644433i
$191$	−5.79612	+	1.02201i	−0.419392	+	0.0739502i	−0.379362	−	0.925248i	$-0.623857\pi$
$191$	−5.79612	+	1.02201i	−0.419392	+	0.0739502i	−0.0400303	+	0.999198i	$0.512745\pi$
$192$	12.6704	+	5.60893i	0.914410	+	0.404789i
$193$	16.2691	−	5.92148i	1.17108	−	0.426238i	0.318036	−	0.948079i	$-0.396977\pi$
$193$	16.2691	−	5.92148i	1.17108	−	0.426238i	0.853043	+	0.521841i	$0.174755\pi$
$194$	11.2496	−	11.3735i	0.807672	−	0.816567i
$195$	−3.84274	−	1.08453i	−0.275185	−	0.0776647i
$196$	−12.2644	−	6.75160i	−0.876030	−	0.482257i
$197$	9.57817	+	16.5899i	0.682416	+	1.18198i	0.974241	+	0.225508i	$0.0724040\pi$
$197$	9.57817	+	16.5899i	0.682416	+	1.18198i	−0.291825	+	0.956472i	$0.594263\pi$
$198$	−0.0549438	+	0.0750511i	−0.00390469	+	0.00533365i
$199$	−12.7070			−0.900776			−0.450388	−	0.892833i	$-0.648714\pi$
$199$	−12.7070			−0.900776			−0.450388	+	0.892833i	$0.648714\pi$
$200$	0.331639	−	4.67385i	0.0234504	−	0.330491i
$201$	9.32160	+	20.7033i	0.657495	+	1.46030i
$202$	−0.327715	−	1.19680i	−0.0230580	−	0.0842063i
$203$	−12.4618	−	10.3571i	−0.874647	−	0.726926i
$204$	−7.60864	−	2.05767i	−0.532711	−	0.144066i
$205$	3.42940	−	2.87761i	0.239520	−	0.200981i
$206$	−3.25257	+	4.69973i	−0.226618	+	0.327445i
$207$	8.44199	+	15.5619i	0.586759	+	1.08162i
$208$	2.35675	+	2.68688i	0.163411	+	0.186301i
$209$	0.0923631	−	0.0162861i	0.00638889	−	0.00112653i
$210$	16.4754	−	2.85261i	1.13691	−	0.196849i
$211$	−1.05034	−	2.88579i	−0.0723084	−	0.198666i	0.898274	−	0.439437i	$-0.144822\pi$
$211$	−1.05034	−	2.88579i	−0.0723084	−	0.198666i	−0.970582	+	0.240771i	$0.922600\pi$
$212$	6.53106	−	18.5745i	0.448555	−	1.27570i
$213$	1.49899	+	20.2217i	0.102709	+	1.38557i
$214$	−14.7806	−	20.8647i	−1.01038	−	1.42628i
$215$	−1.75400	+	3.03801i	−0.119622	+	0.207191i
$216$	−7.04875	−	12.8963i	−0.479606	−	0.877484i
$217$	0.557576	+	0.955334i	0.0378507	+	0.0648523i
$218$	−0.730506	−	7.85410i	−0.0494761	−	0.531947i
$219$	1.31308	+	17.7137i	0.0887300	+	1.19698i
$220$	−0.0736614	−	0.0858586i	−0.00496625	−	0.00578859i
$221$	−1.55738	−	1.30680i	−0.104761	−	0.0879046i
$222$	5.93234	−	4.89951i	0.398152	−	0.328833i
$223$	0.994965	+	5.64273i	0.0666278	+	0.377865i	0.999829	+	0.0185098i	$0.00589219\pi$
$223$	0.994965	+	5.64273i	0.0666278	+	0.377865i	−0.933201	+	0.359355i	$0.882997\pi$
$224$	−13.7603	−	5.88671i	−0.919401	−	0.393323i
$225$	−3.29448	+	3.72097i	−0.219632	+	0.248065i
$226$	−25.6479	−	2.10244i	−1.70607	−	0.139852i
$227$	0.0692734	+	0.392869i	0.00459784	+	0.0260756i	0.987020	−	0.160595i	$-0.0513413\pi$
$227$	0.0692734	+	0.392869i	0.00459784	+	0.0260756i	−0.982423	+	0.186671i	$0.940230\pi$
$228$	−3.86874	+	14.3054i	−0.256214	+	0.947400i
$229$	9.32617	+	25.6234i	0.616291	+	1.69324i	0.715887	+	0.698217i	$0.246023\pi$
$229$	9.32617	+	25.6234i	0.616291	+	1.69324i	−0.0995959	+	0.995028i	$0.531755\pi$
$230$	−20.7681	+	5.68686i	−1.36941	+	0.374981i
$231$	0.0583277	−	0.0818003i	0.00383768	−	0.00538207i
$232$	−14.3512	−	9.70144i	−0.942205	−	0.636930i
$233$	−0.979508	−	1.69656i	−0.0641697	−	0.111145i	0.832156	−	0.554542i	$-0.187107\pi$
$233$	−0.979508	−	1.69656i	−0.0641697	−	0.111145i	−0.896325	+	0.443397i	$0.853773\pi$
$234$	−0.250750	−	3.78251i	−0.0163921	−	0.247270i
$235$	15.3390	+	8.85597i	1.00061	+	0.577700i
$236$	0.0625080	+	5.70692i	0.00406892	+	0.371489i
$237$	−2.73631	−	2.80993i	−0.177742	−	0.182525i
$238$	8.24542	+	2.11959i	0.534471	+	0.137393i
$239$	−2.32503	−	0.409966i	−0.150394	−	0.0265185i	0.0979444	−	0.995192i	$-0.468773\pi$
$239$	−2.32503	−	0.409966i	−0.150394	−	0.0265185i	−0.248338	+	0.968673i	$0.579884\pi$
$240$	17.2254	−	4.77526i	1.11189	−	0.308242i
$241$	−3.18719	+	8.75674i	−0.205305	+	0.564071i	−0.999022	−	0.0442162i	$-0.985921\pi$
$241$	−3.18719	+	8.75674i	−0.205305	+	0.564071i	0.793717	+	0.608287i	$0.208143\pi$
$242$	15.5037	+	1.27088i	0.996613	+	0.0816954i
$243$	−2.38553	+	15.4048i	−0.153032	+	0.988221i
$244$	9.36693	−	3.52594i	0.599656	−	0.225725i
$245$	−17.7556	+	3.30348i	−1.13436	+	0.211051i
$246$	3.66413	+	2.15376i	0.233617	+	0.137318i
$247$	−2.45698	+	2.92811i	−0.156334	+	0.186311i
$248$	0.694086	+	0.957388i	0.0440745	+	0.0607942i
$249$	15.4952	+	4.37318i	0.981969	+	0.277139i
$250$	7.05175	+	9.95447i	0.445992	+	0.629576i
$251$	7.53512	+	13.0512i	0.475613	+	0.823785i	0.999610	−	0.0279349i	$-0.00889311\pi$
$251$	7.53512	+	13.0512i	0.475613	+	0.823785i	−0.523997	+	0.851720i	$0.675560\pi$
$252$	7.78712	+	13.8333i	0.490542	+	0.871417i
$253$	−0.0646896	+	0.112046i	−0.00406700	+	0.00704425i
$254$	−23.3055	+	2.16763i	−1.46231	+	0.136009i
$255$	−9.27147	+	4.17444i	−0.580602	+	0.261414i
$256$	−15.2603	−	4.80859i	−0.953770	−	0.300537i
$257$	−5.39290	−	14.8169i	−0.336400	−	0.924251i	−0.986407	−	0.164323i	$-0.947456\pi$
$257$	−5.39290	−	14.8169i	−0.336400	−	0.924251i	0.650007	−	0.759928i	$-0.274766\pi$
$258$	−3.27528	−	0.603890i	−0.203910	−	0.0375966i
$259$	−6.34097	+	5.37179i	−0.394009	+	0.333787i
$260$	4.54900	+	0.750836i	0.282117	+	0.0465649i
$261$	5.82359	+	17.4262i	0.360471	+	1.07865i
$262$	−11.0431	−	23.3473i	−0.682243	−	1.44240i
$263$	−13.4581	−	16.0388i	−0.829865	−	0.988994i	−0.999994	−	0.00357253i	$-0.998863\pi$
$263$	−13.4581	−	16.0388i	−0.829865	−	0.988994i	0.170129	−	0.985422i	$-0.445582\pi$
$264$	0.0534076	−	0.0931824i	0.00328701	−	0.00573498i
$265$	−8.68714	−	23.8677i	−0.533646	−	1.46618i
$266$	3.98516	−	15.5027i	0.244346	−	0.950530i
$267$	−1.14672	+	0.780464i	−0.0701780	+	0.0477636i
$268$	−13.3567	−	22.5601i	−0.815888	−	1.37808i
$269$	−19.3596	+	11.1773i	−1.18038	+	0.681492i	−0.956102	−	0.293034i	$-0.905335\pi$
$269$	−19.3596	+	11.1773i	−1.18038	+	0.681492i	−0.224276	+	0.974526i	$0.572002\pi$
$270$	−17.5828	−	7.09243i	−1.07005	−	0.431631i
$271$	9.67507	−	16.7577i	0.587719	−	1.01796i	−0.406812	−	0.913512i	$-0.633360\pi$
$271$	9.67507	−	16.7577i	0.587719	−	1.01796i	0.994531	−	0.104446i	$-0.0333071\pi$
$272$	8.99551	+	1.38373i	0.545433	+	0.0839007i
$273$	0.321912	+	4.08187i	0.0194830	+	0.247046i
$274$	16.5941	+	16.4134i	1.00249	+	0.991568i
$275$	−0.0357669	−	0.00630667i	−0.00215683	−	0.000380306i
$276$	−11.6867	−	16.7731i	−0.703459	−	1.00962i
$277$	12.8476	−	10.7804i	0.771939	−	0.647733i	−0.169266	−	0.985570i	$-0.554140\pi$
$277$	12.8476	−	10.7804i	0.771939	−	0.647733i	0.941205	+	0.337837i	$0.109695\pi$
$278$	−16.7296	+	24.1730i	−1.00338	+	1.44980i
$279$	0.0332934	−	1.25381i	0.00199322	−	0.0750635i
$280$	−18.5396	+	5.39013i	−1.10795	+	0.322122i
$281$	18.5116	+	6.73766i	1.10431	+	0.401935i	0.828903	−	0.559393i	$-0.188966\pi$
$281$	18.5116	+	6.73766i	1.10431	+	0.401935i	0.275406	+	0.961328i	$0.411188\pi$
$282$	−3.04906	+	16.5370i	−0.181569	+	0.984762i
$283$	0.410267	−	2.32674i	0.0243879	−	0.138310i	−0.970183	−	0.242375i	$-0.922074\pi$
$283$	0.410267	−	2.32674i	0.0243879	−	0.138310i	0.994571	+	0.104064i	$0.0331848\pi$
$284$	−4.31810	−	23.0124i	−0.256232	−	1.36553i
$285$	7.84860	+	17.4318i	0.464911	+	1.03257i
$286$	0.0226053	−	0.0160136i	0.00133668	−	0.000946904i
$287$	−3.98650	−	2.27665i	−0.235316	−	0.134386i
$288$	9.74550	+	13.8934i	0.574259	+	0.818674i
$289$	11.8229			0.695464
$290$	−22.2506	+	2.06952i	−1.30660	+	0.121526i
$291$	18.9905	−	4.81925i	1.11324	−	0.282509i
$292$	−3.78256	−	20.1584i	−0.221358	−	1.17968i
$293$	24.1949	+	4.26622i	1.41348	+	0.249235i	0.827671	−	0.561213i	$-0.189665\pi$
$293$	24.1949	+	4.26622i	1.41348	+	0.249235i	0.585811	+	0.810448i	$0.300776\pi$
$294$	−8.59724	−	14.8353i	−0.501401	−	0.865215i
$295$	4.73252	+	5.63999i	0.275538	+	0.328373i
$296$	−6.17808	+	6.38449i	−0.359094	+	0.371091i
$297$	−0.105079	+	0.0439953i	−0.00609732	+	0.00255287i
$298$	−24.3593	−	1.99681i	−1.41110	−	0.115672i
$299$	−0.915633	−	5.19281i	−0.0529524	−	0.300308i
$300$	3.30247	−	4.69319i	0.190668	−	0.270961i
$301$	3.54559	+	0.607984i	0.204364	+	0.0350436i
$302$	−21.5323	−	5.64337i	−1.23905	−	0.324739i
$303$	0.412785	−	1.46260i	0.0237139	−	0.0840239i
$304$	2.60162	−	16.9130i	0.149213	−	0.970025i
$305$	6.45564	−	11.1815i	0.369649	−	0.640250i
$306$	−6.68065	−	6.96829i	−0.381907	−	0.398351i
$307$	−11.3212	+	19.6089i	−0.646136	+	1.11914i	0.337901	+	0.941182i	$0.390283\pi$
$307$	−11.3212	+	19.6089i	−0.646136	+	1.11914i	−0.984038	+	0.177960i	$0.943050\pi$
$308$	−0.0564236	+	0.101362i	−0.00321503	+	0.00577564i
$309$	−6.38286	+	2.87386i	−0.363108	+	0.163488i
$310$	1.47563	+	0.386746i	0.0838103	+	0.0219657i
$311$	0.475491	−	2.69664i	0.0269626	−	0.152913i	−0.968354	−	0.249580i	$-0.919707\pi$
$311$	0.475491	−	2.69664i	0.0269626	−	0.152913i	0.995317	+	0.0966677i	$0.0308184\pi$
$312$	0.773699	+	4.30833i	0.0438021	+	0.243911i
$313$	−4.98001	−	5.93495i	−0.281487	−	0.335463i	0.606712	−	0.794922i	$-0.292488\pi$
$313$	−4.98001	−	5.93495i	−0.281487	−	0.335463i	−0.888199	+	0.459458i	$0.848044\pi$
$314$	13.6203	−	6.44230i	0.768639	−	0.363560i
$315$	19.0859	+	7.42260i	1.07537	+	0.418216i
$316$	3.50100	+	2.87294i	0.196947	+	0.161615i
$317$	25.2189	+	9.17895i	1.41644	+	0.515541i	0.933012	−	0.359845i	$-0.117170\pi$
$317$	25.2189	+	9.17895i	1.41644	+	0.515541i	0.483425	+	0.875386i	$0.339393\pi$
$318$	18.5929	−	15.3558i	1.04264	−	0.861113i
$319$	−0.0863073	+	0.102857i	−0.00483228	+	0.00575889i
$320$	−19.1532	+	7.69278i	−1.07070	+	0.430039i
$321$	−2.31505	−	31.2305i	−0.129214	−	1.74312i
$322$	12.8487	+	17.9578i	0.716030	+	1.00075i
$323$			9.73379i			0.541603i
$324$	0.758343	−	17.9840i	0.0421302	−	0.999112i
$325$	1.28188	−	0.740094i	0.0711059	−	0.0410530i
$326$	−17.1500	−	24.2094i	−0.949848	−	1.34083i
$327$	4.19868	−	8.70068i	0.232188	−	0.481149i
$328$	−4.48141	−	2.00076i	−0.247444	−	0.110473i
$329$	3.06973	−	17.9018i	0.169240	−	0.986956i
$330$	−0.0229946	−	0.136630i	−0.00126581	−	0.00752124i
$331$	4.43563	−	12.1868i	0.243804	−	0.669847i	−0.756078	−	0.654482i	$-0.772887\pi$
$331$	4.43563	−	12.1868i	0.243804	−	0.669847i	0.999882	−	0.0153650i	$-0.00489101\pi$
$332$	−18.3431	−	3.02762i	−1.00671	−	0.166162i
$333$	9.32020	−	1.38941i	0.510744	−	0.0761392i
$334$	19.9565	+	1.63589i	1.09197	+	0.0895121i
$335$	−31.7815	−	11.5675i	−1.73641	−	0.632002i
$336$	−10.7132	−	14.8737i	−0.584452	−	0.811428i
$337$	13.6585	+	11.4608i	0.744025	+	0.624311i	0.933915	−	0.357494i	$-0.116369\pi$
$337$	13.6585	+	11.4608i	0.744025	+	0.624311i	−0.189891	+	0.981805i	$0.560813\pi$
$338$	4.37477	−	16.6920i	0.237956	−	0.907924i
$339$	−25.5754	−	18.4188i	−1.38906	−	1.00037i
$340$	10.1030	−	5.98145i	0.547912	−	0.324390i
$341$	0.00793784	−	0.00458292i	0.000429858	−	0.000248179i
$342$	−13.1015	+	12.5607i	−0.708446	+	0.679203i
$343$	9.48575	+	15.9066i	0.512182	+	0.858877i
$344$	3.83607	+	0.272193i	0.206827	+	0.0146757i
$345$	−25.3805	−	7.16308i	−1.36644	−	0.385647i
$346$	1.65558	+	6.04607i	0.0890045	+	0.325039i
$347$	5.83555	+	16.0331i	0.313269	+	0.860699i	0.991992	+	0.126305i	$0.0403116\pi$
$347$	5.83555	+	16.0331i	0.313269	+	0.860699i	−0.678723	+	0.734395i	$0.737466\pi$
$348$	−8.92156	−	19.2489i	−0.478246	−	1.03185i
$349$	17.5872	+	20.9596i	0.941420	+	1.12194i	0.992377	+	0.123240i	$0.0393284\pi$
$349$	17.5872	+	20.9596i	0.941420	+	1.12194i	−0.0509570	+	0.998701i	$0.516227\pi$
$350$	−3.50340	+	5.11343i	−0.187265	+	0.273325i
$351$	2.12808	−	4.12634i	0.113589	−	0.220248i
$352$	−0.0493153	+	0.113791i	−0.00262852	+	0.00606509i
$353$	7.14629	−	19.6343i	0.380359	−	1.04503i	−0.590847	−	0.806784i	$-0.701206\pi$
$353$	7.14629	−	19.6343i	0.380359	−	1.04503i	0.971206	−	0.238243i	$-0.0765715\pi$
$354$	−3.54207	+	6.02603i	−0.188259	+	0.320280i
$355$	−23.1380	−	19.4151i	−1.22804	−	1.03045i
$356$	1.21563	−	1.04293i	0.0644280	−	0.0552752i
$357$	7.30948	+	7.43579i	0.386859	+	0.393544i
$358$	−7.53164	+	16.3853i	−0.398060	+	0.865992i
$359$			13.8954i			0.733374i	0.930344	+	0.366687i	$0.119508\pi$
$359$			13.8954i			0.733374i	−0.930344	+	0.366687i	$0.880492\pi$
$360$	21.0880	+	5.87984i	1.11143	+	0.309895i
$361$	−0.698962			−0.0367875
$362$	−5.23370	+	0.486784i	−0.275077	+	0.0255848i
$363$	15.4598	+	11.1338i	0.811431	+	0.584373i
$364$	−0.893820	−	4.64272i	−0.0468489	−	0.243345i
$365$	−20.2684	−	17.0072i	−1.06090	−	0.890199i
$366$	12.0548	+	2.22264i	0.630113	+	0.116179i
$367$	5.39809	+	30.6141i	0.281778	+	1.59804i	0.716573	+	0.697512i	$0.245710\pi$
$367$	5.39809	+	30.6141i	0.281778	+	1.59804i	−0.434796	+	0.900529i	$0.643179\pi$
$368$	15.5658	+	17.7462i	0.811424	+	0.925087i
$369$	2.48215	+	4.57556i	0.129215	+	0.238194i
$370$	−0.936344	+	11.4226i	−0.0486782	+	0.593832i
$371$	−19.8736	+	16.8360i	−1.03179	+	0.874084i
$372$	0.122877	+	1.44306i	0.00637086	+	0.0748192i
$373$	−0.757692	+	4.29709i	−0.0392318	+	0.222495i	−0.998120	−	0.0612893i	$-0.980479\pi$
$373$	−0.757692	+	4.29709i	−0.0392318	+	0.222495i	0.958888	+	0.283784i	$0.0915899\pi$
$374$	0.0178851	−	0.0682406i	0.000924814	−	0.00352864i
$375$	1.10450	+	14.8999i	0.0570362	+	0.769429i
$376$	1.37431	−	19.3684i	0.0708747	−	0.998850i
$377$		−	5.47226i		−	0.281836i
$378$	−0.576123	+	19.4337i	−0.0296325	+	0.999561i
$379$			21.4856i			1.10364i	0.833963	+	0.551821i	$0.186067\pi$
$379$			21.4856i			1.10364i	−0.833963	+	0.551821i	$0.813933\pi$
$380$	−11.2461	−	18.9952i	−0.576911	−	0.974433i
$381$	−25.8175	−	12.4587i	−1.32267	−	0.638281i
$382$	8.05147	+	2.11019i	0.411949	+	0.107967i
$383$	0.220752	−	1.25195i	0.0112799	−	0.0639715i	−0.978648	−	0.205542i	$-0.934104\pi$
$383$	0.220752	−	1.25195i	0.0112799	−	0.0639715i	0.989928	+	0.141571i	$0.0452153\pi$
$384$	−12.9682	−	14.6910i	−0.661781	−	0.749697i
$385$	0.0266806	+	0.147255i	0.00135977	+	0.00750483i
$386$	−24.4028	−	2.00037i	−1.24207	−	0.101816i
$387$	−3.05399	−	2.70395i	−0.155243	−	0.137449i
$388$	−21.1730	+	7.97002i	−1.07490	+	0.404617i
$389$	5.46584	+	30.9983i	0.277129	+	1.57168i	0.732117	+	0.681179i	$0.238532\pi$
$389$	5.46584	+	30.9983i	0.277129	+	1.57168i	−0.454988	+	0.890497i	$0.650357\pi$
$390$	4.29723	+	3.66328i	0.217598	+	0.185497i
$391$	−10.2862	−	8.63111i	−0.520193	−	0.436494i
$392$	11.7716	+	15.9195i	0.594554	+	0.804056i
$393$	3.17491	−	31.4720i	0.160153	−	1.58755i
$394$	−2.50891	−	26.9747i	−0.126397	−	1.35897i
$395$	5.84235			0.293960
$396$	0.114930	−	0.0639859i	0.00577543	−	0.00321541i
$397$		−	10.9691i		−	0.550521i	−0.961370	−	0.275261i	$-0.911236\pi$
$397$		−	10.9691i		−	0.550521i	0.961370	−	0.275261i	$-0.0887641\pi$
$398$	16.3281	+	7.50533i	0.818453	+	0.376208i
$399$	13.9804	−	13.7430i	0.699897	−	0.688009i
$400$	−3.18673	+	5.80986i	−0.159337	+	0.290493i
$401$	5.03576	+	4.22550i	0.251474	+	0.211011i	0.759807	−	0.650149i	$-0.225294\pi$
$401$	5.03576	+	4.22550i	0.251474	+	0.211011i	−0.508333	+	0.861161i	$0.669738\pi$
$402$	0.250375	−	32.1088i	0.0124875	−	1.60144i
$403$	−0.127765	+	0.351030i	−0.00636441	+	0.0174861i
$404$	−0.285778	+	1.73141i	−0.0142180	+	0.0861407i
$405$	−13.9607	−	18.5549i	−0.693714	−	0.921999i
$406$	9.89564	+	20.6690i	0.491112	+	1.02579i
$407$	0.0442643	+	0.0527522i	0.00219410	+	0.00261483i
$408$	8.56150	+	7.13804i	0.423857	+	0.353386i
$409$	1.17761	+	3.23545i	0.0582289	+	0.159983i	0.965396	−	0.260787i	$-0.0839822\pi$
$409$	1.17761	+	3.23545i	0.0582289	+	0.159983i	−0.907167	+	0.420770i	$0.861760\pi$
$410$	−6.10631	+	1.67207i	−0.301569	+	0.0825779i
$411$	7.03138	+	27.7075i	0.346833	+	1.36671i
$412$	6.95532	−	4.11788i	0.342664	−	0.202873i
$413$	3.74417	−	6.55619i	0.184239	−	0.322609i
$414$	−1.65615	−	24.9827i	−0.0813954	−	1.22783i
$415$	−20.7700	+	11.9916i	−1.01956	+	0.588642i
$416$	−1.44135	−	4.84455i	−0.0706682	−	0.237523i
$417$	−32.8302	+	14.7817i	−1.60770	+	0.723862i
$418$	−0.128303	−	0.0336267i	−0.00627550	−	0.00164473i
$419$	12.6585	+	10.6218i	0.618410	+	0.518908i	0.897303	−	0.441414i	$-0.145523\pi$
$419$	12.6585	+	10.6218i	0.618410	+	0.518908i	−0.278893	+	0.960322i	$0.589968\pi$
$420$	−22.8553	−	6.06562i	−1.11522	−	0.295972i
$421$	17.1433	+	6.23965i	0.835513	+	0.304102i	0.724120	−	0.689674i	$-0.242246\pi$
$421$	17.1433	+	6.23965i	0.835513	+	0.304102i	0.111394	+	0.993776i	$0.464469\pi$
$422$	−0.354822	+	4.32852i	−0.0172725	+	0.210709i
$423$	−13.6523	+	15.4197i	−0.663798	+	0.749731i
$424$	−19.3631	+	20.0100i	−0.940355	+	0.971772i
$425$	1.28919	−	3.54201i	0.0625348	−	0.171813i
$426$	10.0177	−	26.8695i	0.485357	−	1.30183i
$427$	−13.0496	−	2.23770i	−0.631516	−	0.108290i
$428$	6.66892	+	35.5406i	0.322354	+	1.71792i
$429$	0.0338358	−	0.00250818i	0.00163361	−	0.000121096i
$430$	4.04821	−	2.86775i	0.195222	−	0.138295i
$431$	26.8790	−	15.5186i	1.29472	−	0.747504i	0.315229	−	0.949016i	$-0.397919\pi$
$431$	26.8790	−	15.5186i	1.29472	−	0.747504i	0.979486	+	0.201511i	$0.0645853\pi$
$432$	1.44026	+	20.7346i	0.0692946	+	0.997596i
$433$		−	36.0913i		−	1.73444i	−0.497928	−	0.867219i	$-0.665905\pi$
$433$		−	36.0913i		−	1.73444i	0.497928	−	0.867219i	$-0.334095\pi$
$434$	−0.152204	−	1.55690i	−0.00730601	−	0.0747337i
$435$	−24.6490	−	11.8948i	−1.18183	−	0.570313i
$436$	−3.70030	+	10.5237i	−0.177212	+	0.503995i
$437$	−16.2278	+	19.3396i	−0.776282	+	0.925137i
$438$	8.77525	−	23.5371i	0.419298	−	1.12465i
$439$	−24.4368	−	8.89427i	−1.16631	−	0.424501i	−0.314960	−	0.949105i	$-0.601991\pi$
$439$	−24.4368	−	8.89427i	−1.16631	−	0.424501i	−0.851346	+	0.524604i	$0.824213\pi$
$440$	0.0439404	+	0.153833i	0.00209478	+	0.00733371i
$441$	0.359736	−	20.9969i	0.0171303	−	0.999853i
$442$	1.22933	+	2.59905i	0.0584732	+	0.123624i
$443$	−16.6008	−	19.7841i	−0.788729	−	0.939971i	0.210563	−	0.977580i	$-0.432470\pi$
$443$	−16.6008	−	19.7841i	−0.788729	−	0.939971i	−0.999293	+	0.0376095i	$0.988026\pi$
$444$	−10.5167	+	2.79180i	−0.499101	+	0.132493i
$445$	0.358797	−	2.03484i	0.0170086	−	0.0964606i
$446$	2.05435	−	7.83838i	0.0972762	−	0.371158i
$447$	−24.2905	−	17.4934i	−1.14890	−	0.827410i
$448$	14.2046	+	15.6917i	0.671105	+	0.741363i
$449$	7.66885	−	13.2828i	0.361915	−	0.626856i	−0.626361	−	0.779533i	$-0.715456\pi$
$449$	7.66885	−	13.2828i	0.361915	−	0.626856i	0.988276	+	0.152678i	$0.0487896\pi$
$450$	6.43107	−	2.83546i	0.303163	−	0.133665i
$451$	−0.0190203	+	0.0329441i	−0.000895631	+	0.00155128i
$452$	31.7149	+	17.8504i	1.49174	+	0.839610i
$453$	−19.0198	−	19.5315i	−0.893627	−	0.917672i
$454$	0.143032	−	0.545740i	0.00671282	−	0.0256128i
$455$	−4.69065	−	3.89844i	−0.219901	−	0.182762i
$456$	13.4206	−	16.0969i	0.628478	−	0.753809i
$457$	0.0189025	+	0.107201i	0.000884220	+	0.00501466i	0.985247	−	0.171140i	$-0.0547451\pi$
$457$	0.0189025	+	0.107201i	0.000884220	+	0.00501466i	−0.984362	+	0.176155i	$0.943634\pi$
$458$	3.15053	−	38.4337i	0.147215	−	1.79589i
$459$	−2.60294	−	11.5329i	−0.121495	−	0.538308i
$460$	30.0452	+	4.95911i	1.40086	+	0.231220i
$461$	−8.74412	−	10.4208i	−0.407254	−	0.485346i	0.522963	−	0.852355i	$-0.324826\pi$
$461$	−8.74412	−	10.4208i	−0.407254	−	0.485346i	−0.930218	+	0.367009i	$0.880382\pi$
$462$	−0.123264	+	0.0706597i	−0.00573476	+	0.00328739i
$463$	−27.3163	−	4.81660i	−1.26950	−	0.223846i	−0.501982	−	0.864878i	$-0.667396\pi$
$463$	−27.3163	−	4.81660i	−1.26950	−	0.223846i	−0.767515	+	0.641032i	$0.778507\pi$
$464$	12.7108	+	20.9425i	0.590082	+	0.972231i
$465$	1.30345	+	1.33852i	0.0604458	+	0.0620722i
$466$	0.256573	+	2.75856i	0.0118855	+	0.127788i
$467$	33.7914			1.56368			0.781839	−	0.623480i	$-0.214282\pi$
$467$	33.7914			1.56368			0.781839	+	0.623480i	$0.214282\pi$
$468$	−1.91191	+	5.00850i	−0.0883783	+	0.231518i
$469$	0.163294	+	34.6822i	0.00754021	+	1.60147i
$470$	−14.4794	−	20.4395i	−0.667883	−	0.942805i
$471$	18.3601	+	1.85218i	0.845989	+	0.0853438i
$472$	3.29044	−	7.37012i	0.151455	−	0.339237i
$473$	0.00517621	−	0.0293557i	0.000238002	−	0.00134978i
$474$	1.85639	+	5.22685i	0.0852669	+	0.240077i
$475$	−6.65954	−	2.42387i	−0.305561	−	0.111215i
$476$	−9.34317	−	7.59372i	−0.428243	−	0.348058i
$477$	29.2110	−	4.35464i	1.33748	−	0.199385i
$478$	2.74544	+	1.90006i	0.125574	+	0.0869067i
$479$	−15.3933	+	12.9165i	−0.703336	+	0.590169i	−0.922721	−	0.385469i	$-0.874040\pi$
$479$	−15.3933	+	12.9165i	−0.703336	+	0.590169i	0.219384	+	0.975638i	$0.429595\pi$
$480$	−24.9545	−	4.03804i	−1.13901	−	0.184310i
$481$	−2.76391	−	0.487353i	−0.126024	−	0.0222214i
$482$	9.26756	−	9.36962i	0.422126	−	0.426775i
$483$	2.12616	+	26.9599i	0.0967436	+	1.22672i
$484$	−19.1711	−	10.7902i	−0.871412	−	0.490464i
$485$	−14.5923	+	25.2746i	−0.662603	+	1.14766i
$486$	12.1641	−	18.3857i	0.551775	−	0.833993i
$487$	30.5849	−	17.6582i	1.38593	−	0.800169i	0.393080	−	0.919504i	$-0.371410\pi$
$487$	30.5849	−	17.6582i	1.38593	−	0.800169i	0.992854	+	0.119335i	$0.0380763\pi$
$488$	−14.1188	−	1.00182i	−0.639127	−	0.0453501i
$489$	−2.68616	−	36.2368i	−0.121473	−	1.63869i
$490$	24.7665	+	6.24239i	1.11884	+	0.282002i
$491$	−8.13405	−	22.3481i	−0.367085	−	1.00856i	−0.976465	−	0.215678i	$-0.930804\pi$
$491$	−8.13405	−	22.3481i	−0.367085	−	1.00856i	0.609380	−	0.792878i	$-0.291418\pi$
$492$	−3.43618	−	4.93170i	−0.154915	−	0.222338i
$493$	−8.95740	−	10.6750i	−0.403421	−	0.480779i
$494$	4.88661	−	2.31133i	0.219859	−	0.103992i
$495$	0.0622498	−	0.157860i	0.00279792	−	0.00709528i
$496$	−0.326401	−	1.64017i	−0.0146558	−	0.0736458i
$497$	−10.4565	+	29.1554i	−0.469039	+	1.30780i
$498$	−17.3278	−	14.7715i	−0.776479	−	0.661929i
$499$	−7.46287	−	20.5041i	−0.334084	−	0.917888i	−0.987037	−	0.160490i	$-0.948693\pi$
$499$	−7.46287	−	20.5041i	−0.334084	−	0.917888i	0.652954	−	0.757398i	$-0.273530\pi$
$500$	−3.18171	−	16.9562i	−0.142290	−	0.758306i
$501$	19.9001	+	14.3315i	0.889069	+	0.640286i
$502$	−1.97375	−	21.2209i	−0.0880928	−	0.947137i
$503$	4.72425	−	8.18264i	0.210644	−	0.364846i	−0.741272	−	0.671204i	$-0.765777\pi$
$503$	4.72425	−	8.18264i	0.210644	−	0.364846i	0.951916	+	0.306358i	$0.0991106\pi$
$504$	−1.83561	−	22.3748i	−0.0817646	−	0.996652i
$505$	1.13188	+	1.96048i	0.0503682	+	0.0872403i
$506$	0.149303	−	0.105766i	0.00663733	−	0.00470189i
$507$	15.1410	−	14.7442i	0.672433	−	0.654815i
$508$	31.2270	+	10.9799i	1.38548	+	0.487155i
$509$	−7.30862	+	8.71007i	−0.323949	+	0.386067i	−0.903299	−	0.429012i	$-0.858862\pi$
$509$	−7.30862	+	8.71007i	−0.323949	+	0.386067i	0.579350	+	0.815079i	$0.303306\pi$
$510$	14.3791	+	0.112124i	0.636719	+	0.00496493i
$511$	−9.15969	+	25.5395i	−0.405201	+	1.12980i
$512$	16.7688	+	15.1923i	0.741085	+	0.671411i
$513$	−21.6836	+	4.89392i	−0.957353	+	0.216072i
$514$	−1.82181	+	22.2245i	−0.0803565	+	0.980280i
$515$	3.56628	−	9.79828i	0.157149	−	0.431764i
$516$	3.85194	+	2.71051i	0.169572	+	0.119323i
$517$	−0.148218	−	0.0261348i	−0.00651861	−	0.00114941i
$518$	11.3208	−	3.15730i	0.497406	−	0.138724i
$519$	−2.08534	+	7.38886i	−0.0915363	+	0.324335i
$520$	−5.40184	−	3.65164i	−0.236886	−	0.160135i
$521$	1.26798	+	0.732068i	0.0555511	+	0.0320725i	0.527518	−	0.849544i	$-0.323123\pi$
$521$	1.26798	+	0.732068i	0.0555511	+	0.0320725i	−0.471967	+	0.881616i	$0.656456\pi$
$522$	2.80955	−	25.8317i	0.122971	−	1.13062i
$523$	−14.7657	−	25.5750i	−0.645660	−	1.11832i	−0.984149	−	0.177345i	$-0.943249\pi$
$523$	−14.7657	−	25.5750i	−0.645660	−	1.11832i	0.338489	−	0.940970i	$-0.390084\pi$
$524$	0.400037	+	36.5230i	0.0174757	+	1.59551i
$525$	−6.90750	+	3.14927i	−0.301468	+	0.137446i
$526$	7.82004	+	28.5583i	0.340970	+	1.24520i
$527$	0.325356	+	0.893907i	0.0141727	+	0.0389392i
$528$	−0.123665	+	0.0881914i	−0.00538181	+	0.00383804i
$529$	−2.05365	−	11.6468i	−0.0892890	−	0.506383i
$530$	−2.93465	+	35.8002i	−0.127473	+	1.55506i
$531$	−7.52496	+	4.08214i	−0.326556	+	0.177150i
$532$	−14.2774	+	17.5666i	−0.619003	+	0.761609i
$533$	−0.269218	−	1.52681i	−0.0116611	−	0.0661335i
$534$	1.93447	−	0.325568i	0.0837128	−	0.0140887i
$535$	35.7346	+	29.9849i	1.54494	+	1.29636i
$536$	3.83785	+	36.8781i	0.165770	+	1.59289i
$537$	−18.2586	+	12.4270i	−0.787919	+	0.536263i
$538$	31.4783	−	2.92778i	1.35713	−	0.126226i
$539$	0.132176	−	0.0779802i	0.00569321	−	0.00335885i
$540$	18.4042	+	19.4987i	0.791990	+	0.839091i
$541$	−1.56875	+	2.71716i	−0.0674460	+	0.116820i	−0.897776	−	0.440452i	$-0.854818\pi$
$541$	−1.56875	+	2.71716i	−0.0674460	+	0.116820i	0.830330	+	0.557271i	$0.188152\pi$
$542$	−22.3300	+	15.8186i	−0.959155	+	0.679466i
$543$	−5.79783	−	2.79785i	−0.248809	−	0.120067i
$544$	−10.7416	−	7.09119i	−0.460544	−	0.304032i
$545$	4.92187	+	13.5227i	0.210830	+	0.579250i
$546$	1.99729	−	5.43521i	0.0854761	−	0.232605i
$547$	−4.25006	+	0.749400i	−0.181719	+	0.0320420i	−0.263767	−	0.964586i	$-0.584965\pi$
$547$	−4.25006	+	0.749400i	−0.181719	+	0.0320420i	0.0820478	+	0.996628i	$0.473854\pi$
$548$	−11.6284	−	30.8919i	−0.496742	−	1.31963i
$549$	11.2403	+	9.95196i	0.479725	+	0.424739i
$550$	0.0422343	+	0.0292294i	0.00180088	+	0.00124635i
$551$	−20.0707	+	16.8413i	−0.855040	+	0.717464i
$552$	5.11012	+	28.4556i	0.217501	+	1.21115i
$553$	−2.07558	−	5.62013i	−0.0882625	−	0.238992i
$554$	−22.8762	+	6.26412i	−0.971915	+	0.266137i
$555$	−8.20302	+	11.3903i	−0.348199	+	0.483491i
$556$	35.7747	−	21.1803i	1.51718	−	0.898244i
$557$	12.7110			0.538581			0.269291	−	0.963059i	$-0.413211\pi$
$557$	12.7110			0.538581			0.269291	+	0.963059i	$0.413211\pi$
$558$	−0.783335	+	1.59144i	−0.0331612	+	0.0673708i
$559$	0.607433	+	1.05210i	0.0256917	+	0.0444993i
$560$	27.0064	+	4.02417i	1.14123	+	0.170052i
$561$	0.0618996	−	0.0602778i	0.00261340	−	0.00254493i
$562$	−19.8072	−	19.5914i	−0.835516	−	0.826415i
$563$	19.0624	−	6.93815i	0.803385	−	0.292408i	0.0924965	−	0.995713i	$-0.470515\pi$
$563$	19.0624	−	6.93815i	0.803385	−	0.292408i	0.710888	+	0.703305i	$0.248293\pi$
$564$	13.6854	−	19.4485i	0.576260	−	0.818931i
$565$	46.2348	−	8.15244i	1.94511	−	0.342976i
$566$	−1.90146	+	2.74746i	−0.0799242	+	0.115484i
$567$	−12.8894	+	20.0216i	−0.541303	+	0.840828i
$568$	−8.04353	+	32.1206i	−0.337499	+	1.34775i
$569$	−1.10620	−	6.27359i	−0.0463745	−	0.263003i	0.952801	−	0.303594i	$-0.0981868\pi$
$569$	−1.10620	−	6.27359i	−0.0463745	−	0.263003i	−0.999176	+	0.0405918i	$0.987076\pi$
$570$	0.210811	−	27.0350i	0.00882988	−	1.13237i
$571$	−4.28632	−	11.7766i	−0.179377	−	0.492834i	0.817120	−	0.576468i	$-0.195570\pi$
$571$	−4.28632	−	11.7766i	−0.179377	−	0.492834i	−0.996497	+	0.0836340i	$0.973347\pi$
$572$	−0.0385054	+	0.00722524i	−0.00160999	+	0.000302103i
$573$	7.11196	+	7.30332i	0.297107	+	0.305101i
$574$	3.77783	+	5.28002i	0.157683	+	0.220384i
$575$	8.46654	−	4.88816i	0.353079	−	0.203850i
$576$	−4.31661	−	23.6086i	−0.179859	−	0.983692i
$577$			20.5486i			0.855448i	0.903909	+	0.427724i	$0.140684\pi$
$577$			20.5486i			0.855448i	−0.903909	+	0.427724i	$0.859316\pi$
$578$	−15.1920	−	6.98312i	−0.631904	−	0.290459i
$579$	−24.3338	−	17.5246i	−1.01128	−	0.728299i
$580$	29.8136	+	10.4829i	1.23794	+	0.435280i
$581$	18.9143	+	15.7198i	0.784696	+	0.652167i
$582$	−27.2486	−	5.02404i	−1.12949	−	0.208253i
$583$	0.138732	+	0.165334i	0.00574567	+	0.00684743i
$584$	−7.04596	+	28.1370i	−0.291564	+	1.16432i
$585$	2.19201	+	6.55925i	0.0906285	+	0.271191i
$586$	−28.5698	−	19.7725i	−1.18021	−	0.816796i
$587$	6.26647	+	35.5389i	0.258645	+	1.46685i	0.786540	+	0.617539i	$0.211870\pi$
$587$	6.26647	+	35.5389i	0.258645	+	1.46685i	−0.527896	+	0.849309i	$0.677019\pi$
$588$	2.28476	+	24.1408i	0.0942218	+	0.995551i
$589$	1.68068	−	0.611719i	0.0692514	−	0.0252054i
$590$	−2.74989	−	10.0424i	−0.113211	−	0.413441i
$591$	14.4203	−	29.8823i	0.593171	−	1.22919i
$592$	11.7096	−	4.55480i	0.481261	−	0.187201i
$593$	−21.1858	−	12.2316i	−0.869997	−	0.502293i	−0.00264981	−	0.999996i	$-0.500843\pi$
$593$	−21.1858	−	12.2316i	−0.869997	−	0.502293i	−0.867347	+	0.497703i	$0.834177\pi$
$594$	0.161009	+	0.00553205i	0.00660628	+	0.000226983i
$595$	−15.5316	+	0.0731271i	−0.636732	+	0.00299792i
$596$	30.1215	+	16.9535i	1.23383	+	0.694444i
$597$	12.3835	+	18.1948i	0.506824	+	0.744665i
$598$	−1.89055	+	7.21340i	−0.0773102	+	0.294978i
$599$	−14.9246	+	17.7865i	−0.609803	+	0.726735i	−0.979281	−	0.202504i	$-0.935092\pi$
$599$	−14.9246	+	17.7865i	−0.609803	+	0.726735i	0.369478	+	0.929239i	$0.379536\pi$
$600$	−7.01557	+	4.08001i	−0.286409	+	0.166566i
$601$	−33.2376	+	5.86068i	−1.35579	+	0.239062i	−0.803855	−	0.594826i	$-0.797221\pi$
$601$	−33.2376	+	5.86068i	−1.35579	+	0.239062i	−0.551934	+	0.833888i	$0.686110\pi$
$602$	−4.19686	−	2.87542i	−0.171051	−	0.117193i
$603$	20.5603	−	33.5237i	0.837280	−	1.36519i
$604$	24.3351	+	19.9695i	0.990181	+	0.812547i
$605$	−27.9481	+	4.92800i	−1.13625	+	0.200352i
$606$	−1.39429	+	1.63558i	−0.0566391	+	0.0664408i
$607$	26.4238	−	9.61748i	1.07251	−	0.390362i	0.255395	−	0.966837i	$-0.417794\pi$
$607$	26.4238	−	9.61748i	1.07251	−	0.390362i	0.817115	+	0.576475i	$0.195572\pi$
$608$	−13.3325	+	20.1960i	−0.540706	+	0.819054i
$609$	−2.68550	+	27.9372i	−0.108822	+	1.13207i
$610$	−14.8996	+	10.5549i	−0.603266	+	0.427354i
$611$	5.31210	−	3.06694i	0.214905	−	0.124075i
$612$	4.46863	+	12.8999i	0.180633	+	0.521448i
$613$	7.53179	−	13.0454i	0.304206	−	0.526901i	−0.672878	−	0.739753i	$-0.734942\pi$
$613$	7.53179	−	13.0454i	0.304206	−	0.526901i	0.977084	+	0.212853i	$0.0682755\pi$
$614$	26.1293	−	18.5100i	1.05449	−	0.747003i
$615$	−7.46248	−	2.10612i	−0.300916	−	0.0849268i
$616$	0.132371	−	0.0969205i	0.00533340	−	0.00390504i
$617$	2.39307	−	13.5717i	0.0963412	−	0.546378i	−0.897987	−	0.440022i	$-0.854971\pi$
$617$	2.39307	−	13.5717i	0.0963412	−	0.546378i	0.994328	−	0.106356i	$-0.0339183\pi$
$618$	9.89920	+	0.0771908i	0.398204	+	0.00310507i
$619$	40.2422	+	14.6470i	1.61747	+	0.588712i	0.982898	−	0.184151i	$-0.0589534\pi$
$619$	40.2422	+	14.6470i	1.61747	+	0.588712i	0.634574	+	0.772862i	$0.281176\pi$
$620$	−1.66771	−	1.36853i	−0.0669768	−	0.0549615i
$621$	14.0555	−	27.2536i	0.564029	−	1.09365i
$622$	−2.20375	+	3.18425i	−0.0883622	+	0.127677i
$623$	−2.08491	+	0.377755i	−0.0835300	+	0.0151344i
$624$	1.55052	−	5.99305i	0.0620703	−	0.239914i
$625$	−23.3940	−	19.6299i	−0.935760	−	0.785196i
$626$	2.89371	+	10.5676i	0.115656	+	0.422367i
$627$	−0.113332	−	0.116381i	−0.00452603	−	0.00464781i
$628$	−21.3068	+	0.233373i	−0.850232	+	0.00931261i
$629$	−6.18945	+	3.57348i	−0.246789	+	0.142484i
$630$	−20.1406	−	20.8108i	−0.802422	−	0.829121i
$631$	10.3293	+	5.96365i	0.411205	+	0.237409i	0.691307	−	0.722561i	$-0.257035\pi$
$631$	10.3293	+	5.96365i	0.411205	+	0.237409i	−0.280103	+	0.959970i	$0.590368\pi$
$632$	−2.80178	−	5.75947i	−0.111449	−	0.229100i
$633$	−3.10848	+	4.31628i	−0.123551	+	0.171557i
$634$	−26.9840	−	26.6901i	−1.07167	−	1.06000i
$635$	40.1260	−	14.6047i	1.59235	−	0.579568i
$636$	−32.9611	+	8.74994i	−1.30699	+	0.346958i
$637$	−2.08373	+	5.89721i	−0.0825606	+	0.233656i
$638$	0.171654	−	0.0811909i	0.00679584	−	0.00321438i
$639$	27.4940	−	21.8532i	1.08765	−	0.864501i
$640$	29.1549	+	1.42776i	1.15245	+	0.0564372i
$641$	−36.0404	+	30.2415i	−1.42351	+	1.19447i	−0.474082	+	0.880481i	$0.657220\pi$
$641$	−36.0404	+	30.2415i	−1.42351	+	1.19447i	−0.949428	+	0.313985i	$0.898336\pi$
$642$	−15.4714	+	41.4975i	−0.610606	+	1.63778i
$643$	−28.4872	+	10.3685i	−1.12343	+	0.408894i	−0.835901	−	0.548879i	$-0.815055\pi$
$643$	−28.4872	+	10.3685i	−1.12343	+	0.408894i	−0.287525	+	0.957773i	$0.592832\pi$
$644$	−5.90349	−	30.6642i	−0.232630	−	1.20834i
$645$	6.05940	−	0.449171i	0.238589	−	0.0176861i
$646$	5.74921	−	12.5076i	0.226200	−	0.492105i
$647$	−3.51536	−	6.08878i	−0.138203	−	0.239375i	0.788613	−	0.614889i	$-0.210799\pi$
$647$	−3.51536	−	6.08878i	−0.138203	−	0.239375i	−0.926816	+	0.375515i	$0.877466\pi$
$648$	−11.5966	+	22.6610i	−0.455558	+	0.890206i
$649$	−0.0541799	−	0.0312808i	−0.00212675	−	0.00122788i
$650$	−2.08430	+	0.193860i	−0.0817532	+	0.00760383i
$651$	0.824536	−	1.72939i	0.0323161	−	0.0677803i
$652$	7.73796	+	41.2378i	0.303042	+	1.61500i
$653$	−4.43004	+	25.1240i	−0.173361	+	0.983177i	0.766658	+	0.642055i	$0.221918\pi$
$653$	−4.43004	+	25.1240i	−0.173361	+	0.983177i	−0.940019	+	0.341122i	$0.889193\pi$
$654$	−10.5342	+	8.70015i	−0.411919	+	0.340203i
$655$	30.2870	+	36.0946i	1.18341	+	1.41033i
$656$	4.57673	+	5.21782i	0.178691	+	0.203722i
$657$	24.0842	−	19.1430i	0.939614	−	0.746839i
$658$	−14.5181	+	21.1900i	−0.565973	+	0.826074i
$659$	−10.5725	+	29.0478i	−0.411848	+	1.13154i	0.544360	+	0.838852i	$0.316773\pi$
$659$	−10.5725	+	29.0478i	−0.411848	+	1.13154i	−0.956207	+	0.292690i	$0.905449\pi$
$660$	−0.0511526	+	0.189147i	−0.00199111	+	0.00736253i
$661$	37.6062	+	6.63100i	1.46271	+	0.257916i	0.847647	−	0.530560i	$-0.178018\pi$
$661$	37.6062	+	6.63100i	1.46271	+	0.257916i	0.615066	+	0.788476i	$0.289129\pi$
$662$	−12.8977	+	13.0397i	−0.501283	+	0.506804i
$663$	−0.353435	+	3.50350i	−0.0137263	+	0.136065i
$664$	21.7820	+	14.7246i	0.845305	+	0.571426i
$665$	0.137490	+	29.2017i	0.00533165	+	1.13239i
$666$	−12.7968	−	3.71958i	−0.495866	−	0.144131i
$667$		−	36.1431i		−	1.39947i
$668$	−24.6772	−	13.8892i	−0.954788	−	0.537391i
$669$	7.11004	−	6.92375i	0.274890	−	0.267688i
$670$	34.0059	+	33.6355i	1.31376	+	1.29945i
$671$	−0.0190512	+	0.108045i	−0.000735463	+	0.00417102i
$672$	4.98100	+	25.4399i	0.192146	+	0.981366i
$673$	5.33611	−	4.47753i	0.205692	−	0.172596i	−0.534122	−	0.845407i	$-0.679358\pi$
$673$	5.33611	−	4.47753i	0.205692	−	0.172596i	0.739814	+	0.672811i	$0.234913\pi$
$674$	−10.7814	−	22.7941i	−0.415285	−	0.877995i
$675$	8.53858	+	1.09103i	0.328650	+	0.0419938i
$676$	−15.4805	+	18.8647i	−0.595402	+	0.725565i
$677$	16.5095	−	2.91107i	0.634511	−	0.111881i	0.152865	−	0.988247i	$-0.451150\pi$
$677$	16.5095	−	2.91107i	0.634511	−	0.111881i	0.481646	+	0.876366i	$0.340039\pi$
$678$	21.9846	+	38.7735i	0.844312	+	1.48909i
$679$	29.4974	+	5.05810i	1.13201	+	0.194112i
$680$	−16.5149	+	1.71868i	−0.633318	+	0.0659086i
$681$	0.495029	−	0.482059i	0.0189696	−	0.0184725i
$682$	−0.0129067	+	0.00120045i	−0.000494225	+	4.59676e-5i
$683$	−10.9148	−	6.30165i	−0.417643	−	0.241126i	0.276426	−	0.961035i	$-0.410850\pi$
$683$	−10.9148	−	6.30165i	−0.417643	−	0.241126i	−0.694068	+	0.719909i	$0.744183\pi$
$684$	24.2538	−	8.40171i	0.927369	−	0.321247i
$685$	−36.8762	−	21.2905i	−1.40897	−	0.813468i
$686$	−2.79371	−	26.0422i	−0.106664	−	0.994295i
$687$	27.6008	−	38.3251i	1.05304	−	1.46219i
$688$	−4.76845	−	2.61551i	−0.181796	−	0.0997155i
$689$	−8.66255	−	1.52744i	−0.330017	−	0.0581909i
$690$	28.3823	+	24.1952i	1.08049	+	0.921094i
$691$	−36.0103	+	30.2162i	−1.36990	+	1.14948i	−0.397112	+	0.917770i	$0.629988\pi$
$691$	−36.0103	+	30.2162i	−1.36990	+	1.14948i	−0.972785	+	0.231710i	$0.925568\pi$
$692$	1.44371	−	8.74686i	0.0548818	−	0.332506i
$693$	−0.173971	−	0.00380001i	−0.00660860	−	0.000144351i
$694$	1.97134	−	24.0487i	0.0748312	−	0.912875i
$695$	18.3432	−	50.3974i	0.695796	−	1.91168i
$696$	0.0946634	+	30.0036i	0.00358821	+	1.13729i
$697$	−3.02438	−	2.53775i	−0.114556	−	0.0961243i
$698$	−10.2193	−	37.3201i	−0.386805	−	1.41259i
$699$	−1.47469	+	3.05590i	−0.0557777	+	0.115585i
$700$	7.52197	−	4.50133i	0.284304	−	0.170134i
$701$	45.6745			1.72510			0.862552	−	0.505969i	$-0.168865\pi$
$701$	45.6745			1.72510			0.862552	+	0.505969i	$0.168865\pi$
$702$	−5.17171	+	4.04526i	−0.195194	+	0.152679i
$703$	6.71869	+	11.6371i	0.253400	+	0.438902i
$704$	0.130579	−	0.117090i	0.00492137	−	0.00441300i
$705$	−2.26787	−	30.5940i	−0.0854131	−	1.15224i
$706$	−20.7796	+	21.0085i	−0.782051	+	0.790664i
$707$	1.48379	−	1.78532i	0.0558038	−	0.0671439i
$708$	8.11068	−	5.65115i	0.304818	−	0.212383i
$709$	18.9319	+	6.89065i	0.711003	+	0.258784i	0.672101	−	0.740459i	$-0.265392\pi$
$709$	18.9319	+	6.89065i	0.711003	+	0.258784i	0.0389014	+	0.999243i	$0.487614\pi$
$710$	18.2642	+	38.6141i	0.685442	+	1.44916i
$711$	−1.35682	+	6.65645i	−0.0508847	+	0.249636i
$712$	−2.17804	+	0.622129i	−0.0816255	+	0.0233153i
$713$	−0.843857	+	2.31848i	−0.0316027	+	0.0868277i
$714$	−5.00053	−	13.8720i	−0.187140	−	0.519148i
$715$	−0.0324863	+	0.0387156i	−0.00121492	+	0.00144788i
$716$	19.3558	−	16.6061i	0.723361	−	0.620599i
$717$	1.67882	+	3.72868i	0.0626968	+	0.139250i
$718$	8.20727	−	17.8552i	0.306293	−	0.666350i
$719$	0.478086	+	0.828069i	0.0178296	+	0.0308818i	0.874803	−	0.484480i	$-0.160991\pi$
$719$	0.478086	+	0.828069i	0.0178296	+	0.0308818i	−0.856973	+	0.515361i	$0.827658\pi$
$720$	−23.6245	−	20.0109i	−0.880432	−	0.745763i
$721$	−10.6926	+	0.0503437i	−0.398212	+	0.00187490i
$722$	0.898143	+	0.412838i	0.0334254	+	0.0153643i
$723$	15.6446	−	3.97016i	0.581829	−	0.147652i
$724$	7.01264	+	2.46575i	0.260623	+	0.0916390i
$725$	9.53404	−	3.47011i	0.354085	−	0.128876i
$726$	−13.2893	−	23.4378i	−0.493210	−	0.869860i
$727$	−21.8677	+	18.3492i	−0.811029	+	0.680534i	−0.950853	−	0.309642i	$-0.899791\pi$
$727$	−21.8677	+	18.3492i	−0.811029	+	0.680534i	0.139824	+	0.990176i	$0.455346\pi$
$728$	−1.59367	+	6.49367i	−0.0590653	+	0.240671i
$729$	24.3826	−	11.5969i	0.903060	−	0.429515i
$730$	15.9990	+	33.8252i	0.592151	+	1.25193i
$731$	2.90711	+	1.05810i	0.107524	+	0.0391354i
$732$	−14.1772	−	9.97609i	−0.524004	−	0.368727i
$733$	−25.3960	+	30.2658i	−0.938024	+	1.11789i	0.0548226	+	0.998496i	$0.482541\pi$
$733$	−25.3960	+	30.2658i	−0.938024	+	1.11789i	−0.992847	+	0.119397i	$0.961904\pi$
$734$	11.1457	−	42.5264i	0.411394	−	1.56968i
$735$	22.0338	+	22.2044i	0.812727	+	0.819022i
$736$	−9.51983	−	31.9972i	−0.350906	−	1.17943i
$737$	0.287390			0.0105861
$738$	−0.486948	−	7.34551i	−0.0179248	−	0.270392i
$739$		−	39.7605i		−	1.46261i	−0.682049	−	0.731307i	$-0.738911\pi$
$739$		−	39.7605i		−	1.46261i	0.682049	−	0.731307i	$-0.261089\pi$
$740$	7.94986	−	14.1246i	0.292243	−	0.519230i
$741$	6.58713	+	0.664512i	0.241984	+	0.0244115i
$742$	35.4811	−	9.89550i	1.30255	−	0.363275i
$743$	19.2453	−	22.9357i	0.706042	−	0.841428i	−0.287154	−	0.957884i	$-0.592709\pi$
$743$	19.2453	−	22.9357i	0.706042	−	0.841428i	0.993196	+	0.116457i	$0.0371537\pi$
$744$	0.694443	−	1.92686i	0.0254595	−	0.0706421i
$745$	43.9119	−	7.74286i	1.60881	−	0.283676i
$746$	3.51166	−	5.07409i	0.128571	−	0.185775i
$747$	−8.83892	−	26.4491i	−0.323399	−	0.967720i
$748$	−0.0632876	+	0.0771231i	−0.00231402	+	0.00281990i
$749$	16.1491	−	45.0279i	0.590077	−	1.64529i
$750$	7.38131	−	19.7983i	0.269527	−	0.722931i
$751$	−21.2186	−	3.74142i	−0.774279	−	0.136526i	−0.227472	−	0.973785i	$-0.573046\pi$
$751$	−21.2186	−	3.74142i	−0.774279	−	0.136526i	−0.546807	+	0.837258i	$0.684157\pi$
$752$	−13.2058	+	24.0760i	−0.481566	+	0.877963i
$753$	11.3444	−	23.5083i	0.413413	−	0.856691i
$754$	−3.23216	+	7.03167i	−0.117708	+	0.256078i
$755$	40.6096			1.47793
$756$	12.2187	−	24.6314i	0.444390	−	0.895834i
$757$	−31.0042			−1.12687			−0.563433	−	0.826162i	$-0.690520\pi$
$757$	−31.0042			−1.12687			−0.563433	+	0.826162i	$0.690520\pi$
$758$	12.6904	−	27.6083i	0.460934	−	1.00278i
$759$	0.223478	−	0.0165660i	0.00811174	−	0.000601307i
$760$	3.23139	+	31.0506i	0.117215	+	1.12632i
$761$	−30.2669	−	5.33687i	−1.09717	−	0.193461i	−0.404376	−	0.914593i	$-0.632511\pi$
$761$	−30.2669	−	5.33687i	−1.09717	−	0.193461i	−0.692798	+	0.721131i	$0.743622\pi$
$762$	25.8160	+	31.2580i	0.935214	+	1.13236i
$763$	11.2598	−	9.53879i	0.407632	−	0.345327i
$764$	−9.09949	−	7.46708i	−0.329208	−	0.270150i
$765$	15.0127	+	9.20741i	0.542787	+	0.332895i
$766$	−1.02311	+	1.47832i	−0.0369666	+	0.0534140i
$767$	2.51099	−	0.442756i	0.0906667	−	0.0159870i
$768$	7.98655	+	26.5371i	0.288190	+	0.957573i
$769$	7.74769	−	9.23334i	0.279389	−	0.332963i	−0.608041	−	0.793906i	$-0.708044\pi$
$769$	7.74769	−	9.23334i	0.279389	−	0.332963i	0.887430	+	0.460943i	$0.152489\pi$
$770$	0.0526919	−	0.204977i	0.00189888	−	0.00738685i
$771$	−15.9603	+	22.1616i	−0.574796	+	0.798132i
$772$	30.1753	+	16.9838i	1.08603	+	0.611260i
$773$		−	15.6185i		−	0.561757i	−0.959743	−	0.280879i	$-0.909374\pi$
$773$		−	15.6185i		−	0.561757i	0.959743	−	0.280879i	$-0.0906258\pi$
$774$	2.32721	+	5.27831i	0.0836498	+	0.189725i
$775$	−0.692601			−0.0248790
$776$	31.9140	+	2.26450i	1.14565	+	0.0812909i
$777$	13.8713	+	3.84444i	0.497629	+	0.137919i
$778$	11.2856	−	43.0601i	0.404607	−	1.54378i
$779$	−4.77137	+	5.68630i	−0.170952	+	0.203733i
$780$	−3.35810	−	7.24532i	−0.120239	−	0.259424i
$781$	0.241180	+	0.0877823i	0.00863010	+	0.00314110i
$782$	8.11944	+	17.1661i	0.290351	+	0.613860i
$783$	19.2767	−	25.3212i	0.688894	−	0.904906i
$784$	−5.72331	−	27.4088i	−0.204404	−	0.978887i
$785$	−21.0569	+	17.6688i	−0.751552	+	0.630627i
$786$	−22.6684	+	38.5652i	−0.808555	+	1.37557i
$787$	−16.4872	+	6.00084i	−0.587704	+	0.213907i	−0.618719	−	0.785612i	$-0.712348\pi$
$787$	−16.4872	+	6.00084i	−0.587704	+	0.213907i	0.0310153	+	0.999519i	$0.490126\pi$
$788$	−12.7086	+	36.1435i	−0.452725	+	1.28756i
$789$	−9.84999	+	34.9009i	−0.350669	+	1.24250i
$790$	−7.50722	−	3.45075i	−0.267095	−	0.122772i
$791$	−24.2679	−	41.5799i	−0.862868	−	1.47841i
$792$	−0.185474	+	0.0143373i	−0.00659052	+	0.000509454i
$793$	−2.23567	−	3.87230i	−0.0793911	−	0.137509i
$794$	−6.47881	+	14.0949i	−0.229924	+	0.500208i
$795$	−25.7096	+	35.6990i	−0.911825	+	1.26611i
$796$	−16.5481	−	19.2882i	−0.586530	−	0.683652i
$797$	−18.5509	+	22.1081i	−0.657106	+	0.783109i	−0.986967	−	0.160921i	$-0.948554\pi$
$797$	−18.5509	+	22.1081i	−0.657106	+	0.783109i	0.329861	+	0.944030i	$0.392998\pi$
$798$	−26.0816	+	9.40178i	−0.923279	+	0.332820i
$799$	5.34239	−	14.6781i	0.189000	−	0.519273i
$800$	7.52640	−	5.58325i	0.266099	−	0.197398i
$801$	2.23505	+	0.881361i	0.0789717	+	0.0311413i
$802$	−3.97501	−	8.40397i	−0.140362	−	0.296754i
$803$	0.211269	+	0.0768955i	0.00745550	+	0.00271358i
$804$	−19.2866	+	41.1109i	−0.680187	+	1.44987i
$805$	−30.9808	−	25.7483i	−1.09193	−	0.907510i
$806$	0.371507	−	0.375599i	0.0130858	−	0.0132299i
$807$	34.8713	+	16.8278i	1.22753	+	0.592367i
$808$	1.38986	−	2.05601i	0.0488951	−	0.0723300i
$809$	−6.26265	−	10.8472i	−0.220183	−	0.381368i	0.734680	−	0.678413i	$-0.237332\pi$
$809$	−6.26265	−	10.8472i	−0.220183	−	0.381368i	−0.954863	+	0.297045i	$0.903999\pi$
$810$	6.97973	+	32.0882i	0.245243	+	1.12747i
$811$	25.1633			0.883603			0.441801	−	0.897113i	$-0.354340\pi$
$811$	25.1633			0.883603			0.441801	+	0.897113i	$0.354340\pi$
$812$	−0.507512	−	32.4038i	−0.0178102	−	1.13715i
$813$	−33.4237	+	2.47763i	−1.17222	+	0.0868944i
$814$	−0.0257204	−	0.0939293i	−0.000901500	−	0.00329222i
$815$	41.4630	+	34.7915i	1.45238	+	1.21869i
$816$	−6.78519	−	14.2289i	−0.237529	−	0.498113i
$817$	1.98940	−	5.46583i	0.0696002	−	0.191225i
$818$	0.397814	−	4.85299i	0.0139093	−	0.169681i
$819$	5.53101	−	4.43890i	0.193269	−	0.155108i
$820$	8.83401	+	1.45810i	0.308497	+	0.0509190i
$821$	−21.0254	+	17.6424i	−0.733793	+	0.615725i	−0.931163	−	0.364604i	$-0.881204\pi$
$821$	−21.0254	+	17.6424i	−0.733793	+	0.615725i	0.197370	+	0.980329i	$0.436760\pi$
$822$	7.33019	−	39.7563i	0.255670	−	1.38666i
$823$	1.67159	+	0.294747i	0.0582680	+	0.0102742i	0.202706	−	0.979240i	$-0.435026\pi$
$823$	1.67159	+	0.294747i	0.0582680	+	0.0102742i	−0.144438	+	0.989514i	$0.546137\pi$
$824$	−11.3696	+	1.18321i	−0.396077	+	0.0412192i
$825$	0.0258260	+	0.0573598i	0.000899147	+	0.00199701i
$826$	−8.68352	+	6.21301i	−0.302138	+	0.216178i
$827$	10.7645	+	6.21490i	0.374319	+	0.216113i	0.675344	−	0.737503i	$-0.263995\pi$
$827$	10.7645	+	6.21490i	0.374319	+	0.216113i	−0.301024	+	0.953616i	$0.597329\pi$
$828$	−12.6278	+	33.0801i	−0.438846	+	1.14961i
$829$	2.12544	+	1.22712i	0.0738195	+	0.0426197i	0.536455	−	0.843929i	$-0.319763\pi$
$829$	2.12544	+	1.22712i	0.0738195	+	0.0426197i	−0.462636	+	0.886548i	$0.653096\pi$
$830$	33.7715	−	3.14107i	1.17223	−	0.109028i
$831$	−27.9568	−	7.89018i	−0.969810	−	0.273707i
$832$	−1.00931	+	7.07641i	−0.0349917	+	0.245330i
$833$	5.58815	+	14.9148i	0.193618	+	0.516767i
$834$	50.9165	+	0.397030i	1.76309	+	0.0137480i
$835$	−35.9750	+	6.34337i	−1.24497	+	0.219521i
$836$	0.145003	+	0.118991i	0.00501505	+	0.00411537i
$837$	−1.82774	+	1.17422i	−0.0631760	+	0.0405869i
$838$	−9.99211	−	21.1253i	−0.345172	−	0.729762i
$839$	−3.22655	+	2.70740i	−0.111393	+	0.0934697i	−0.696783	−	0.717282i	$-0.745386\pi$
$839$	−3.22655	+	2.70740i	−0.111393	+	0.0934697i	0.585390	+	0.810752i	$0.300941\pi$
$840$	25.7856	+	21.2935i	0.889689	+	0.734694i
$841$	1.47765	−	8.38020i	0.0509536	−	0.288972i
$842$	−18.3431	−	18.1433i	−0.632147	−	0.625261i
$843$	−8.39285	−	33.0724i	−0.289065	−	1.13907i
$844$	3.01255	−	5.35243i	0.103696	−	0.184238i
$845$			31.4808i			1.08297i
$846$	26.6503	−	11.7501i	0.916256	−	0.403978i
$847$	14.6695	+	25.1343i	0.504050	+	0.863624i
$848$	36.6997	−	14.2755i	1.26027	−	0.490222i
$849$	−3.73143	+	1.68006i	−0.128062	+	0.0576595i
$850$	−3.74864	+	3.78992i	−0.128577	+	0.129993i
$851$	−18.2551	−	3.21886i	−0.625775	−	0.110341i
$852$	−28.7427	+	28.6096i	−0.984708	+	0.980147i
$853$	−17.4901	+	48.0537i	−0.598850	+	1.64533i	0.154719	+	0.987958i	$0.450553\pi$
$853$	−17.4901	+	48.0537i	−0.598850	+	1.64533i	−0.753569	+	0.657368i	$0.771670\pi$
$854$	15.4467	+	10.5831i	0.528574	+	0.362145i
$855$	17.3114	−	28.2263i	0.592036	−	0.965318i
$856$	12.4225	−	49.6074i	0.424592	−	1.69555i
$857$	5.05055	+	6.01901i	0.172523	+	0.205605i	0.845377	−	0.534171i	$-0.179376\pi$
$857$	5.05055	+	6.01901i	0.172523	+	0.205605i	−0.672853	+	0.739776i	$0.734932\pi$
$858$	−0.0449593	−	0.0167620i	−0.00153488	−	0.000572245i
$859$	−1.70879	+	9.69101i	−0.0583030	+	0.330653i	−0.999983	−	0.00585725i	$-0.998136\pi$
$859$	−1.70879	+	9.69101i	−0.0583030	+	0.330653i	0.941680	+	0.336510i	$0.109247\pi$
$860$	−6.89564	+	1.29391i	−0.235139	+	0.0441221i
$861$	0.625142	+	7.92686i	0.0213048	+	0.270147i
$862$	−43.7046	+	4.06494i	−1.48858	+	0.138453i
$863$	−28.0058	−	16.1692i	−0.953329	−	0.550405i	−0.0592156	−	0.998245i	$-0.518860\pi$
$863$	−28.0058	−	16.1692i	−0.953329	−	0.550405i	−0.894114	+	0.447840i	$0.852193\pi$
$864$	10.3961	−	27.4940i	0.353683	−	0.935365i
$865$	−5.71815	−	9.90412i	−0.194423	−	0.336750i
$866$	−21.3171	+	46.3761i	−0.724386	+	1.57592i
$867$	−11.5219	−	16.9289i	−0.391305	−	0.574935i
$868$	−0.723999	+	2.09046i	−0.0245741	+	0.0709550i
$869$	−0.0466505	+	0.0169794i	−0.00158251	+	0.000575986i
$870$	24.6475	+	29.8432i	0.835627	+	1.01178i
$871$	−8.97248	+	7.52880i	−0.304021	+	0.255104i
$872$	10.9705	−	11.3371i	0.371509	−	0.383921i
$873$	−25.4076	−	22.4954i	−0.859917	−	0.761354i
$874$	32.2750	−	15.2658i	1.09172	−	0.516374i
$875$	−7.70468	+	21.4826i	−0.260466	+	0.726245i
$876$	−25.1780	+	25.0614i	−0.850685	+	0.846745i
$877$	−27.7033	+	10.0832i	−0.935476	+	0.340485i	−0.764378	−	0.644769i	$-0.776954\pi$
$877$	−27.7033	+	10.0832i	−0.935476	+	0.340485i	−0.171098	+	0.985254i	$0.554731\pi$
$878$	26.1471	+	25.8623i	0.882423	+	0.872811i
$879$	−17.4703	−	38.8017i	−0.589259	−	1.30875i
$880$	0.0343987	−	0.223624i	0.00115958	−	0.00753835i
$881$	−50.1300	−	28.9426i	−1.68892	−	0.975100i	−0.955344	−	0.295496i	$-0.904515\pi$
$881$	−50.1300	−	28.9426i	−1.68892	−	0.975100i	−0.733579	−	0.679604i	$-0.762151\pi$
$882$	−12.8640	+	26.7679i	−0.433152	+	0.901321i
$883$	11.2503	−	6.49536i	0.378602	−	0.218586i	−0.298608	−	0.954376i	$-0.596522\pi$
$883$	11.2503	−	6.49536i	0.378602	−	0.218586i	0.677210	+	0.735790i	$0.263189\pi$
$884$	−0.0445326	−	4.06578i	−0.00149779	−	0.136747i
$885$	3.46372	−	12.2728i	0.116432	−	0.412545i
$886$	9.64614	+	35.2271i	0.324068	+	1.18348i
$887$	20.0056	+	16.7867i	0.671721	+	0.563641i	0.913574	−	0.406672i	$-0.133311\pi$
$887$	20.0056	+	16.7867i	0.671721	+	0.563641i	−0.241853	+	0.970313i	$0.577755\pi$
$888$	15.1626	+	2.62428i	0.508823	+	0.0880649i
$889$	−28.3045	−	33.4112i	−0.949301	−	1.12058i
$890$	−1.66291	+	2.40278i	−0.0557408	+	0.0805413i
$891$	0.165400	+	0.107585i	0.00554111	+	0.00360424i
$892$	−7.26947	+	8.85867i	−0.243400	+	0.296610i
$893$	−27.5971	−	10.0445i	−0.923501	−	0.336127i
$894$	20.8800	+	36.8255i	0.698333	+	1.23163i
$895$	5.71295	−	32.3997i	0.190963	−	1.08300i
$896$	−8.98423	−	28.5532i	−0.300142	−	0.953894i
$897$	−6.54313	+	6.37169i	−0.218469	+	0.212745i
$898$	−17.6996	+	12.5384i	−0.590645	+	0.418413i
$899$	−1.28027	+	2.21750i	−0.0426995	+	0.0739578i
$900$	−9.93846	−	0.155003i	−0.331282	−	0.00516677i
$901$	−19.3987	+	11.1999i	−0.646265	+	0.373121i
$902$	0.0438987	−	0.0310978i	0.00146167	−	0.00103545i
$903$	−2.58477	−	5.66934i	−0.0860158	−	0.188664i
$904$	−30.2094	−	41.6693i	−1.00475	−	1.38590i
$905$	9.01107	−	3.27976i	0.299538	−	0.109023i
$906$	12.9036	+	36.3313i	0.428693	+	1.20703i
$907$	2.13066	−	0.375693i	0.0707474	−	0.0124747i	−0.138162	−	0.990410i	$-0.544120\pi$
$907$	2.13066	−	0.375693i	0.0707474	−	0.0124747i	0.208910	+	0.977935i	$0.433008\pi$
$908$	−0.506129	+	0.616776i	−0.0167965	+	0.0204684i
$909$	−2.49653	+	0.834307i	−0.0828047	+	0.0276722i
$910$	3.72474	+	7.77987i	0.123474	+	0.257900i
$911$	14.5264	−	2.56139i	0.481280	−	0.0848627i	0.0722559	−	0.997386i	$-0.476980\pi$
$911$	14.5264	−	2.56139i	0.481280	−	0.0848627i	0.409024	+	0.912523i	$0.365869\pi$
$912$	−26.7526	+	12.7572i	−0.885868	+	0.422434i
$913$	0.130995	−	0.156114i	0.00433531	−	0.00516662i
$914$	0.0390288	−	0.148915i	0.00129096	−	0.00492566i
$915$	−22.3018	+	1.65319i	−0.737274	+	0.0546527i
$916$	−26.7490	+	47.5252i	−0.883811	+	1.57028i
$917$	23.9618	−	41.9581i	0.791289	−	1.38558i
$918$	−3.46714	+	16.3568i	−0.114433	+	0.539853i
$919$	−10.2822	−	5.93643i	−0.339178	−	0.195825i	0.320730	−	0.947171i	$-0.396072\pi$
$919$	−10.2822	−	5.93643i	−0.339178	−	0.195825i	−0.659909	+	0.751346i	$0.729405\pi$
$920$	−35.6780	−	24.1183i	−1.17627	−	0.795157i
$921$	39.1106	−	2.89919i	1.28874	−	0.0955315i
$922$	5.08089	+	18.5551i	0.167330	+	0.611079i
$923$	−9.82942	+	3.57762i	−0.323539	+	0.117759i
$924$	0.200125	−	0.0179901i	0.00658363	−	0.000591832i
$925$	−0.903582	−	5.12447i	−0.0297096	−	0.168492i
$926$	32.2556	+	22.3234i	1.05999	+	0.733592i
$927$	10.3354	+	6.33876i	0.339459	+	0.208192i
$928$	−3.96333	−	34.4179i	−0.130103	−	1.12982i
$929$	20.7736	+	24.7570i	0.681559	+	0.812250i	0.990307	−	0.138893i	$-0.0443545\pi$
$929$	20.7736	+	24.7570i	0.681559	+	0.812250i	−0.308748	+	0.951144i	$0.599910\pi$
$930$	−0.884296	−	2.48982i	−0.0289972	−	0.0816445i
$931$	28.0422	−	10.5066i	0.919045	−	0.344340i
$932$	1.29964	−	3.69620i	0.0425712	−	0.121073i
$933$	−4.32464	+	1.94715i	−0.141582	+	0.0637469i
$934$	−43.4208	−	19.9587i	−1.42077	−	0.653068i
$935$			0.128700i			0.00420896i
$936$	5.41499	−	5.30650i	0.176995	−	0.173448i
$937$	−43.0517	+	24.8559i	−1.40644	+	0.812007i	−0.995042	−	0.0994509i	$-0.968291\pi$
$937$	−43.0517	+	24.8559i	−1.40644	+	0.812007i	−0.411394	+	0.911458i	$0.634958\pi$
$938$	20.2750	−	44.6619i	0.662003	−	1.45826i
$939$	−3.64486	+	12.9146i	−0.118946	+	0.421453i
$940$	6.53300	+	34.8163i	0.213083	+	1.13558i
$941$	−5.08315	−	13.9658i	−0.165706	−	0.455274i	0.828851	−	0.559470i	$-0.188995\pi$
$941$	−5.08315	−	13.9658i	−0.165706	−	0.455274i	−0.994557	+	0.104196i	$0.966773\pi$
$942$	−22.4982	−	13.2243i	−0.733029	−	0.430870i
$943$	−1.77813	−	10.0843i	−0.0579038	−	0.328389i
$944$	−8.58123	+	7.52688i	−0.279295	+	0.244979i
$945$	−7.97181	−	34.5623i	−0.259323	−	1.12431i
$946$	−0.0239901	+	0.0346638i	−0.000779984	+	0.00112702i
$947$	36.8097	−	6.49055i	1.19616	−	0.210914i	0.460119	−	0.887857i	$-0.347807\pi$
$947$	36.8097	−	6.49055i	1.19616	−	0.210914i	0.736036	+	0.676943i	$0.236695\pi$
$948$	0.701809	−	7.81279i	0.0227937	−	0.253748i
$949$	−8.61037	+	3.13392i	−0.279504	+	0.101731i
$950$	7.12564	+	7.04802i	0.231186	+	0.228668i
$951$	−11.4339	−	45.0557i	−0.370768	−	1.46103i
$952$	7.52047	+	15.2762i	0.243740	+	0.495103i
$953$	−19.9486	−	34.5520i	−0.646199	−	1.11925i	−0.984023	−	0.178040i	$-0.943024\pi$
$953$	−19.9486	−	34.5520i	−0.646199	−	1.11925i	0.337824	−	0.941209i	$-0.390309\pi$
$954$	−40.1072	−	11.6578i	−1.29852	−	0.377434i
$955$	−15.1849			−0.491372
$956$	−2.40554	−	4.06309i	−0.0778008	−	0.131410i
$957$	0.231389	+	0.0233426i	0.00747973	+	0.000754558i
$958$	27.4089	−	7.50530i	0.885541	−	0.242485i
$959$	−7.37988	+	43.0373i	−0.238309	+	1.38975i
$960$	29.6807	+	19.9280i	0.957940	+	0.643174i
$961$	−23.6135	+	19.8141i	−0.761725	+	0.639163i
$962$	3.26369	+	2.25872i	0.105225	+	0.0728242i
$963$	−42.4621	+	33.7504i	−1.36832	+	1.08759i
$964$	−17.4426	+	6.56582i	−0.561789	+	0.211471i
$965$	43.9903	−	7.75668i	1.41610	−	0.249696i
$966$	13.1917	−	35.8984i	0.424435	−	1.15501i
$967$	0.00313372	+	0.00860982i	0.000100774	+	0.000276873i	0.939743	−	0.341882i	$-0.111064\pi$
$967$	0.00313372	+	0.00860982i	0.000100774	+	0.000276873i	−0.939642	+	0.342159i	$0.888842\pi$
$968$	18.2610	+	25.1883i	0.586931	+	0.809583i
$969$	13.9376	−	9.48600i	0.447739	−	0.304734i
$970$	33.6789	−	23.8582i	1.08137	−	0.766040i
$971$	23.7475	−	41.1319i	0.762094	−	1.31999i	−0.179675	−	0.983726i	$-0.557505\pi$
$971$	23.7475	−	41.1319i	0.762094	−	1.31999i	0.941769	−	0.336260i	$-0.109162\pi$
$972$	−26.4899	+	16.4404i	−0.849664	+	0.527325i
$973$	−54.9971	+	0.258943i	−1.76313	+	0.00830132i
$974$	−49.7303	+	4.62539i	−1.59346	+	0.148207i
$975$	−2.30897	−	1.11424i	−0.0739462	−	0.0356842i
$976$	17.5504	+	9.62647i	0.561776	+	0.308136i
$977$	27.8144	+	23.3390i	0.889861	+	0.746682i	0.968182	−	0.250246i	$-0.0805116\pi$
$977$	27.8144	+	23.3390i	0.889861	+	0.746682i	−0.0783213	+	0.996928i	$0.524956\pi$
$978$	−17.9515	+	48.1497i	−0.574024	+	1.53966i
$979$	0.00304882	+	0.0172907i	9.74406e−5	+	0.000552613i
$980$	−28.1371	−	22.6495i	−0.898807	−	0.723511i
$981$	−16.5501	+	2.46720i	−0.528403	+	0.0787718i
$982$	−2.74781	+	33.5209i	−0.0876862	+	1.06970i
$983$	−3.77689	−	21.4198i	−0.120464	−	0.683186i	−0.983899	−	0.178726i	$-0.942803\pi$
$983$	−3.77689	−	21.4198i	−0.120464	−	0.683186i	0.863435	−	0.504460i	$-0.168309\pi$
$984$	1.50250	+	8.36664i	0.0478979	+	0.266719i
$985$	16.9040	+	46.4435i	0.538608	+	1.47981i
$986$	5.20482	+	19.0077i	0.165755	+	0.605328i
$987$	−28.6247	+	13.0506i	−0.911133	+	0.415404i
$988$	−7.64430	+	0.0837282i	−0.243198	+	0.00266375i
$989$	4.01196	+	6.94893i	0.127573	+	0.220963i
$990$	−0.173228	+	0.166077i	−0.00550555	+	0.00527829i
$991$	22.7097	+	13.1114i	0.721397	+	0.416499i	0.815267	−	0.579086i	$-0.196590\pi$
$991$	22.7097	+	13.1114i	0.721397	+	0.416499i	−0.0938698	+	0.995584i	$0.529924\pi$
$992$	−0.549343	+	2.30035i	−0.0174417	+	0.0730362i
$993$	−21.7727	+	5.52530i	−0.690935	+	0.175340i
$994$	30.6568	−	31.2877i	0.972374	−	0.992385i
$995$	−32.2865	−	5.69299i	−1.02355	−	0.180480i
$996$	13.5410	+	29.2155i	0.429062	+	0.925730i
$997$	8.31766	−	22.8526i	0.263423	−	0.723749i	−0.735508	−	0.677516i	$-0.763056\pi$
$997$	8.31766	−	22.8526i	0.263423	−	0.723749i	0.998931	−	0.0462325i	$-0.0147215\pi$
$998$	−2.52107	+	30.7549i	−0.0798032	+	0.973530i
$999$	−11.0724	−	11.9913i	−0.350315	−	0.379389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.103.18	✓	840
4.3	odd	2	inner	756.2.bt.a.103.104	yes	840
7.3	odd	6		756.2.cd.a.535.113	yes	840
27.16	even	9		756.2.cd.a.691.82	yes	840
28.3	even	6		756.2.cd.a.535.82	yes	840
108.43	odd	18		756.2.cd.a.691.113	yes	840
189.178	odd	18	inner	756.2.bt.a.367.104	yes	840
756.367	even	18	inner	756.2.bt.a.367.18	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.18	✓	840	1.1	even	1	trivial
756.2.bt.a.103.104	yes	840	4.3	odd	2	inner
756.2.bt.a.367.18	yes	840	756.367	even	18	inner
756.2.bt.a.367.104	yes	840	189.178	odd	18	inner
756.2.cd.a.535.82	yes	840	28.3	even	6
756.2.cd.a.535.113	yes	840	7.3	odd	6
756.2.cd.a.691.82	yes	840	27.16	even	9
756.2.cd.a.691.113	yes	840	108.43	odd	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28497 - 0.590645i) q^{2} +(-0.974544 - 1.43187i) q^{3} +(1.30228 + 1.51792i) q^{4} +(2.54084 + 0.448019i) q^{5} +(0.406527 + 2.41552i) q^{6} +(-0.471692 - 2.60336i) q^{7} +(-0.776834 - 2.71966i) q^{8} +(-1.10053 + 2.79085i) q^{9} +O(q^{10})\)	\(q+(-1.28497 - 0.590645i) q^{2} +(-0.974544 - 1.43187i) q^{3} +(1.30228 + 1.51792i) q^{4} +(2.54084 + 0.448019i) q^{5} +(0.406527 + 2.41552i) q^{6} +(-0.471692 - 2.60336i) q^{7} +(-0.776834 - 2.71966i) q^{8} +(-1.10053 + 2.79085i) q^{9} +(-3.00028 - 2.07643i) q^{10} +(-0.0215904 + 0.00380697i) q^{11} +(0.904340 - 3.34398i) q^{12} +(0.574333 - 0.684463i) q^{13} +(-0.931554 + 3.62384i) q^{14} +(-1.83466 - 4.07478i) q^{15} +(-0.608144 + 3.95350i) q^{16} -2.27533i q^{17} +(3.06254 - 2.93612i) q^{18} -4.27797 q^{19} +(2.62883 + 4.44024i) q^{20} +(-3.26801 + 3.21250i) q^{21} +(0.0299915 + 0.00786043i) q^{22} +(3.79334 - 4.52073i) q^{23} +(-3.13715 + 3.76275i) q^{24} +(1.55670 + 0.566594i) q^{25} +(-1.14227 + 0.540286i) q^{26} +(5.06866 - 1.14398i) q^{27} +(3.33742 - 4.10629i) q^{28} +(4.69164 - 3.93675i) q^{29} +(-0.0492782 + 6.31959i) q^{30} +(-0.392870 + 0.142993i) q^{31} +(3.11656 - 4.72092i) q^{32} +(0.0264919 + 0.0272047i) q^{33} +(-1.34391 + 2.92372i) q^{34} +(-0.0321391 - 6.82607i) q^{35} +(-5.66947 + 1.96395i) q^{36} +(-1.57053 - 2.72024i) q^{37} +(5.49705 + 2.52676i) q^{38} +(-1.53978 - 0.155333i) q^{39} +(-0.755357 - 7.25826i) q^{40} +(1.11533 - 1.32920i) q^{41} +(6.09672 - 2.19772i) q^{42} +(-0.465033 + 1.27767i) q^{43} +(-0.0338954 - 0.0278147i) q^{44} +(-4.04663 + 6.59805i) q^{45} +(-7.54447 + 3.56847i) q^{46} +(6.45098 + 2.34796i) q^{47} +(6.25358 - 2.98207i) q^{48} +(-6.55501 + 2.45597i) q^{49} +(-1.66566 - 1.64751i) q^{50} +(-3.25799 + 2.21741i) q^{51} +(1.78690 - 0.0195719i) q^{52} +(-4.92230 - 8.52568i) q^{53} +(-7.18874 - 1.52380i) q^{54} -0.0565635 q^{55} +(-6.71383 + 3.30522i) q^{56} +(4.16907 + 6.12552i) q^{57} +(-8.35382 + 2.28750i) q^{58} +(2.18601 + 1.83428i) q^{59} +(3.79595 - 8.09136i) q^{60} +(1.71157 - 4.70249i) q^{61} +(0.589282 + 0.0483052i) q^{62} +(7.78471 + 1.54866i) q^{63} +(-6.79306 + 4.22545i) q^{64} +(1.76594 - 1.48180i) q^{65} +(-0.0179729 - 0.0506044i) q^{66} +(-12.9096 - 2.27632i) q^{67} +(3.45376 - 2.96311i) q^{68} +(-10.1699 - 1.02594i) q^{69} +(-3.99048 + 8.79026i) q^{70} +(-10.1386 - 5.85351i) q^{71} +(8.44508 + 0.825035i) q^{72} +(-8.88117 - 5.12755i) q^{73} +(0.411386 + 4.42305i) q^{74} +(-0.705785 - 2.78118i) q^{75} +(-5.57111 - 6.49360i) q^{76} +(0.0200950 + 0.0544120i) q^{77} +(1.88682 + 1.10906i) q^{78} +(2.23004 - 0.393216i) q^{79} +(-3.31644 + 9.77277i) q^{80} +(-6.57767 - 6.14282i) q^{81} +(-2.21826 + 1.04922i) q^{82} +(-7.12087 + 5.97512i) q^{83} +(-9.13216 - 0.776999i) q^{84} +(1.01939 - 5.78126i) q^{85} +(1.35220 - 1.36709i) q^{86} +(-10.2091 - 2.88130i) q^{87} +(0.0271258 + 0.0557611i) q^{88} -0.800851i q^{89} +(9.09689 - 6.08816i) q^{90} +(-2.05282 - 1.17234i) q^{91} +(11.8021 - 0.129268i) q^{92} +(0.587616 + 0.423187i) q^{93} +(-6.90248 - 6.82729i) q^{94} +(-10.8697 - 1.91661i) q^{95} +(-9.79698 + 0.138221i) q^{96} +(-3.86882 + 10.6295i) q^{97} +(9.87358 + 0.715837i) q^{98} +(0.0131362 - 0.0644452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

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