LMFDB - Embedded newform 189.2.ba.a.38.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			38.14
Character	$\chi$	$=$	189.38
Dual form			189.2.ba.a.5.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.491776 + 0.0867134i) q^{2} +(-1.45806 - 0.934910i) q^{3} +(-1.64506 - 0.598753i) q^{4} +(9.76251e-5 + 0.000553660i) q^{5} +(-0.635971 - 0.586200i) q^{6} +(-2.32328 + 1.26584i) q^{7} +(-1.62200 - 0.936464i) q^{8} +(1.25189 + 2.72631i) q^{9} +0.000280742i q^{10} +(-4.66356 - 0.822312i) q^{11} +(1.83882 + 2.41100i) q^{12} +(-1.77003 - 2.10944i) q^{13} +(-1.25230 + 0.421052i) q^{14} +(0.000375278 - 0.000898541i) q^{15} +(1.96567 + 1.64940i) q^{16} -0.800172 q^{17} +(0.379240 + 1.44929i) q^{18} -5.20473i q^{19} +(0.000170906 - 0.000969257i) q^{20} +(4.57094 + 0.326381i) q^{21} +(-2.22212 - 0.808787i) q^{22} +(1.01988 + 1.21545i) q^{23} +(1.48947 + 2.88185i) q^{24} +(4.69846 - 1.71010i) q^{25} +(-0.687542 - 1.19086i) q^{26} +(0.723528 - 5.14553i) q^{27} +(4.57987 - 0.691318i) q^{28} +(-5.40692 + 6.44372i) q^{29} +(0.000262469 - 0.000409339i) q^{30} +(2.76219 - 7.58906i) q^{31} +(3.23144 + 3.85108i) q^{32} +(6.03097 + 5.55899i) q^{33} +(-0.393506 - 0.0693856i) q^{34} +(-0.000927658 - 0.00116273i) q^{35} +(-0.427042 - 5.23452i) q^{36} +(-1.02790 + 1.78038i) q^{37} +(0.451320 - 2.55956i) q^{38} +(0.608677 + 4.73051i) q^{39} +(0.000360134 - 0.000989460i) q^{40} +(5.20305 - 4.36588i) q^{41} +(2.21958 + 0.556868i) q^{42} +(-6.39715 + 2.32837i) q^{43} +(7.17948 + 4.14508i) q^{44} +(-0.00138723 + 0.000959276i) q^{45} +(0.396159 + 0.686167i) q^{46} +(-6.96860 + 2.53636i) q^{47} +(-1.32404 - 4.24265i) q^{48} +(3.79528 - 5.88182i) q^{49} +(2.45888 - 0.433567i) q^{50} +(1.16670 + 0.748089i) q^{51} +(1.64877 + 4.52997i) q^{52} +(-9.11266 - 5.26120i) q^{53} +(0.802000 - 2.46771i) q^{54} -0.00266231i q^{55} +(4.95379 + 0.122467i) q^{56} +(-4.86596 + 7.58882i) q^{57} +(-3.21775 + 2.70001i) q^{58} +(-10.1204 + 8.49198i) q^{59} +(-0.00115536 + 0.00125345i) q^{60} +(1.24316 + 3.41555i) q^{61} +(2.01645 - 3.49260i) q^{62} +(-6.35957 - 4.74930i) q^{63} +(-1.31080 - 2.27037i) q^{64} +(0.000995113 - 0.00118593i) q^{65} +(2.48385 + 3.25675i) q^{66} +(0.369304 + 2.09442i) q^{67} +(1.31633 + 0.479105i) q^{68} +(-0.350717 - 2.72570i) q^{69} +(-0.000355376 - 0.000652243i) q^{70} +(7.56979 - 4.37042i) q^{71} +(0.522528 - 5.59443i) q^{72} +(6.22020 - 3.59123i) q^{73} +(-0.659882 + 0.786416i) q^{74} +(-8.44944 - 1.89921i) q^{75} +(-3.11635 + 8.56210i) q^{76} +(11.8757 - 3.99288i) q^{77} +(-0.110866 + 2.37913i) q^{78} +(0.447434 - 2.53753i) q^{79} +(-0.000721305 + 0.00124934i) q^{80} +(-5.86556 + 6.82607i) q^{81} +(2.93732 - 1.69586i) q^{82} +(-1.47761 - 1.23986i) q^{83} +(-7.32405 - 3.27378i) q^{84} +(-7.81169e-5 - 0.000443023i) q^{85} +(-3.34787 + 0.590319i) q^{86} +(13.9079 - 4.34035i) q^{87} +(6.79425 + 5.70105i) q^{88} -3.23581 q^{89} +(-0.000765391 + 0.000351457i) q^{90} +(6.78250 + 2.66024i) q^{91} +(-0.950016 - 2.61015i) q^{92} +(-11.1225 + 8.48291i) q^{93} +(-3.64693 + 0.643052i) q^{94} +(0.00288165 - 0.000508113i) q^{95} +(-1.11122 - 8.63621i) q^{96} +(-0.614218 - 1.68755i) q^{97} +(2.37646 - 2.56344i) q^{98} +(-3.59637 - 13.7438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.491776	+	0.0867134i	0.347738	+	0.0613156i	0.344790	−	0.938680i	$-0.387950\pi$
$2$	0.491776	+	0.0867134i	0.347738	+	0.0613156i	0.00294872	+	0.999996i	$0.499061\pi$
$3$	−1.45806	−	0.934910i	−0.841812	−	0.539770i
$3$	−1.45806	−	0.934910i	−0.841812	−	0.539770i
$4$	−1.64506	−	0.598753i	−0.822530	−	0.299377i
$5$	9.76251e−5	0	0.000553660i	4.36593e−5	0	0.000247604i	0.984830	−	0.173524i	$-0.0555155\pi$
$5$	9.76251e−5	0	0.000553660i	4.36593e−5	0	0.000247604i	−0.984786	+	0.173772i	$0.944404\pi$
$6$	−0.635971	−	0.586200i	−0.259634	−	0.239315i
$7$	−2.32328	+	1.26584i	−0.878118	+	0.478444i
$7$	−2.32328	+	1.26584i	−0.878118	+	0.478444i
$8$	−1.62200	−	0.936464i	−0.573465	−	0.331090i
$9$	1.25189	+	2.72631i	0.417296	+	0.908771i
$10$		0	0.000280742i		0	8.87784e-5i
$11$	−4.66356	−	0.822312i	−1.40612	−	0.247936i	−0.581463	−	0.813573i	$-0.697519\pi$
$11$	−4.66356	−	0.822312i	−1.40612	−	0.247936i	−0.824654	+	0.565637i	$0.808630\pi$
$12$	1.83882	+	2.41100i	0.530821	+	0.695996i
$13$	−1.77003	−	2.10944i	−0.490918	−	0.585053i	0.462533	−	0.886602i	$-0.346941\pi$
$13$	−1.77003	−	2.10944i	−0.490918	−	0.585053i	−0.953451	+	0.301549i	$0.902496\pi$
$14$	−1.25230	+	0.421052i	−0.334691	+	0.112531i
$15$	0.000375278	0	0.000898541i	9.68965e−5	0	0.000232002i
$16$	1.96567	+	1.64940i	0.491418	+	0.412349i
$17$	−0.800172			−0.194070			−0.0970351	−	0.995281i	$-0.530936\pi$
$17$	−0.800172			−0.194070			−0.0970351	+	0.995281i	$0.530936\pi$
$18$	0.379240	+	1.44929i	0.0893878	+	0.341601i
$19$		−	5.20473i		−	1.19405i	−0.802224	−	0.597024i	$-0.796350\pi$
$19$		−	5.20473i		−	1.19405i	0.802224	−	0.597024i	$-0.203650\pi$
$20$	0.000170906	0	0.000969257i	3.82158e−5	0	0.000216732i
$21$	4.57094	+	0.326381i	0.997460	+	0.0712221i
$22$	−2.22212	−	0.808787i	−0.473758	−	0.172434i
$23$	1.01988	+	1.21545i	0.212661	+	0.253439i	0.861821	−	0.507213i	$-0.169324\pi$
$23$	1.01988	+	1.21545i	0.212661	+	0.253439i	−0.649160	+	0.760651i	$0.724880\pi$
$24$	1.48947	+	2.88185i	0.304037	+	0.588255i
$25$	4.69846	−	1.71010i	0.939693	−	0.342020i
$26$	−0.687542	−	1.19086i	−0.134838	−	0.233546i
$27$	0.723528	−	5.14553i	0.139243	−	0.990258i
$28$	4.57987	−	0.691318i	0.865514	−	0.130647i
$29$	−5.40692	+	6.44372i	−1.00404	+	1.19657i	−0.0236057	+	0.999721i	$0.507515\pi$
$29$	−5.40692	+	6.44372i	−1.00404	+	1.19657i	−0.980434	+	0.196847i	$0.936930\pi$
$30$	0.000262469	0	0.000409339i	4.79200e−5	0	7.47348e-5i
$31$	2.76219	−	7.58906i	0.496104	−	1.36304i	−0.398907	−	0.916991i	$-0.630610\pi$
$31$	2.76219	−	7.58906i	0.496104	−	1.36304i	0.895011	−	0.446044i	$-0.147167\pi$
$32$	3.23144	+	3.85108i	0.571243	+	0.680780i
$33$	6.03097	+	5.55899i	1.04986	+	0.967696i
$34$	−0.393506	−	0.0693856i	−0.0674856	−	0.0118995i
$35$	−0.000927658	−	0.00116273i	−0.000156803	−	0.000196537i
$36$	−0.427042	−	5.23452i	−0.0711737	−	0.872420i
$37$	−1.02790	+	1.78038i	−0.168986	+	0.292693i	−0.938064	−	0.346463i	$-0.887383\pi$
$37$	−1.02790	+	1.78038i	−0.168986	+	0.292693i	0.769077	+	0.639156i	$0.220716\pi$
$38$	0.451320	−	2.55956i	0.0732138	−	0.415216i
$39$	0.608677	+	4.73051i	0.0974663	+	0.757488i
$40$	0.000360134	0	0.000989460i	5.69422e−5	0	0.000156447i
$41$	5.20305	−	4.36588i	0.812580	−	0.681836i	−0.138642	−	0.990343i	$-0.544274\pi$
$41$	5.20305	−	4.36588i	0.812580	−	0.681836i	0.951222	+	0.308507i	$0.0998292\pi$
$42$	2.21958	+	0.556868i	0.342488	+	0.0859266i
$43$	−6.39715	+	2.32837i	−0.975556	+	0.355073i	−0.780111	−	0.625641i	$-0.784837\pi$
$43$	−6.39715	+	2.32837i	−0.975556	+	0.355073i	−0.195445	+	0.980715i	$0.562615\pi$
$44$	7.17948	+	4.14508i	1.08235	+	0.624894i
$45$	−0.00138723		0.000959276i	−0.000206797		0.000143000i
$46$	0.396159	+	0.686167i	0.0584104	+	0.101170i
$47$	−6.96860	+	2.53636i	−1.01647	+	0.369967i	−0.795916	−	0.605407i	$-0.793010\pi$
$47$	−6.96860	+	2.53636i	−1.01647	+	0.369967i	−0.220559	+	0.975374i	$0.570788\pi$
$48$	−1.32404	−	4.24265i	−0.191108	−	0.612373i
$49$	3.79528	−	5.88182i	0.542183	−	0.840261i
$50$	2.45888	−	0.433567i	0.347738	−	0.0613156i
$51$	1.16670	+	0.748089i	0.163371	+	0.104753i
$52$	1.64877	+	4.52997i	0.228644	+	0.628194i
$53$	−9.11266	−	5.26120i	−1.25172	−	0.722681i	−0.280269	−	0.959921i	$-0.590424\pi$
$53$	−9.11266	−	5.26120i	−1.25172	−	0.722681i	−0.971451	+	0.237241i	$0.923757\pi$
$54$	0.802000	−	2.46771i	0.109138	−	0.335813i
$55$		−	0.00266231i		−	0.000358985i
$56$	4.95379	+	0.122467i	0.661978	+	0.0163653i
$57$	−4.86596	+	7.58882i	−0.644512	+	1.00516i
$58$	−3.21775	+	2.70001i	−0.422511	+	0.354529i
$59$	−10.1204	+	8.49198i	−1.31756	+	1.10556i	−0.330740	+	0.943722i	$0.607298\pi$
$59$	−10.1204	+	8.49198i	−1.31756	+	1.10556i	−0.986817	+	0.161840i	$0.948257\pi$
$60$	−0.00115536	+	0.00125345i	−0.000149156	+	0.000161820i
$61$	1.24316	+	3.41555i	0.159170	+	0.437317i	0.993484	−	0.113974i	$-0.0363579\pi$
$61$	1.24316	+	3.41555i	0.159170	+	0.437317i	−0.834314	+	0.551290i	$0.814136\pi$
$62$	2.01645	−	3.49260i	0.256090	−	0.443560i
$63$	−6.35957	−	4.74930i	−0.801231	−	0.598355i
$64$	−1.31080	−	2.27037i	−0.163850	−	0.283797i
$65$	0.000995113	−	0.00118593i	0.000123429	−	0.000147096i
$66$	2.48385	+	3.25675i	0.305741	+	0.400878i
$67$	0.369304	+	2.09442i	0.0451176	+	0.255875i	0.999021	−	0.0442393i	$-0.0140864\pi$
$67$	0.369304	+	2.09442i	0.0451176	+	0.255875i	−0.953903	+	0.300114i	$0.902975\pi$
$68$	1.31633	+	0.479105i	0.159629	+	0.0581001i
$69$	−0.350717	−	2.72570i	−0.0422214	−	0.328136i
$70$	−0.000355376	0	0.000652243i	−4.24755e−5	0	7.79579e-5i
$71$	7.56979	−	4.37042i	0.898369	−	0.518673i	0.0216981	−	0.999765i	$-0.493093\pi$
$71$	7.56979	−	4.37042i	0.898369	−	0.518673i	0.876671	+	0.481091i	$0.159759\pi$
$72$	0.522528	−	5.59443i	0.0615806	−	0.659310i
$73$	6.22020	−	3.59123i	0.728019	−	0.420322i	−0.0896781	−	0.995971i	$-0.528584\pi$
$73$	6.22020	−	3.59123i	0.728019	−	0.420322i	0.817697	+	0.575649i	$0.195250\pi$
$74$	−0.659882	+	0.786416i	−0.0767097	+	0.0914191i
$75$	−8.44944	−	1.89921i	−0.975657	−	0.219302i
$76$	−3.11635	+	8.56210i	−0.357470	+	0.982140i
$77$	11.8757	−	3.99288i	1.35336	−	0.455031i
$78$	−0.110866	+	2.37913i	−0.0125531	+	0.269384i
$79$	0.447434	−	2.53753i	0.0503403	−	0.285494i	−0.949237	−	0.314561i	$-0.898143\pi$
$79$	0.447434	−	2.53753i	0.0503403	−	0.285494i	0.999577	+	0.0290673i	$0.00925372\pi$
$80$	−0.000721305		0.00124934i	−8.06443e−5		0.000139680i
$81$	−5.86556	+	6.82607i	−0.651729	+	0.758452i
$82$	2.93732	−	1.69586i	0.324373	−	0.187277i
$83$	−1.47761	−	1.23986i	−0.162188	−	0.136092i	0.558082	−	0.829786i	$-0.311538\pi$
$83$	−1.47761	−	1.23986i	−0.162188	−	0.136092i	−0.720270	+	0.693694i	$0.755982\pi$
$84$	−7.32405	−	3.27378i	−0.799119	−	0.357199i
$85$	−7.81169e−5	0	0.000443023i	−8.47297e−6	0	4.80526e-5i
$86$	−3.34787	+	0.590319i	−0.361010	+	0.0636558i
$87$	13.9079	−	4.34035i	1.49109	−	0.465335i
$88$	6.79425	+	5.70105i	0.724269	+	0.607734i
$89$	−3.23581			−0.342995			−0.171498	−	0.985185i	$-0.554861\pi$
$89$	−3.23581			−0.342995			−0.171498	+	0.985185i	$0.554861\pi$
$90$	−0.000765391	0	0.000351457i	−8.06792e−5	0	3.70469e-5i
$91$	6.78250	+	2.66024i	0.710999	+	0.278869i
$92$	−0.950016	−	2.61015i	−0.0990461	−	0.272127i
$93$	−11.1225	+	8.48291i	−1.15335	+	0.879637i
$94$	−3.64693	+	0.643052i	−0.376152	+	0.0663257i
$95$	0.00288165		0.000508113i	0.000295651		5.21313e-5i
$96$	−1.11122	−	8.63621i	−0.113414	−	0.881429i
$97$	−0.614218	−	1.68755i	−0.0623644	−	0.171345i	0.904597	−	0.426268i	$-0.140172\pi$
$97$	−0.614218	−	1.68755i	−0.0623644	−	0.171345i	−0.966961	+	0.254923i	$0.917950\pi$
$98$	2.37646	−	2.56344i	0.240059	−	0.258947i
$99$	−3.59637	−	13.7438i	−0.361449	−	1.38130i
$100$	−8.75318			−0.875318
$101$	−3.26288	−	2.73788i	−0.324668	−	0.272429i	0.465855	−	0.884861i	$-0.345747\pi$
$101$	−3.26288	−	2.73788i	−0.324668	−	0.272429i	−0.790523	+	0.612432i	$0.790191\pi$
$102$	0.508886	+	0.469061i	0.0503872	+	0.0464439i
$103$	−15.8365	+	2.79240i	−1.56041	+	0.275143i	−0.886168	−	0.463365i	$-0.846642\pi$
$103$	−15.8365	+	2.79240i	−1.56041	+	0.275143i	−0.674245	+	0.738508i	$0.735531\pi$
$104$	0.895580	+	5.07909i	0.0878189	+	0.498046i
$105$	0.000265535		0.00256261i	2.59135e−5		0.000250085i
$106$	−4.02517	−	3.37752i	−0.390959	−	0.328054i
$107$	3.48765	−	2.01360i	0.337164	−	0.194662i	−0.321853	−	0.946790i	$-0.604306\pi$
$107$	3.48765	−	2.01360i	0.337164	−	0.194662i	0.659017	+	0.752128i	$0.270972\pi$
$108$	−4.27115	+	8.03150i	−0.410992	+	0.772831i
$109$	0.587845	−	1.01818i	0.0563054	−	0.0975238i	−0.836499	−	0.547969i	$-0.815401\pi$
$109$	0.587845	−	1.01818i	0.0563054	−	0.0975238i	0.892804	+	0.450445i	$0.148735\pi$
$110$	0.000230858	−	0.00130926i	2.20114e−5	−	0.000124833i
$111$	3.16324	−	1.63491i	0.300242	−	0.155179i
$112$	−6.65469	−	1.34378i	−0.628809	−	0.126975i
$113$	−5.04317	+	13.8560i	−0.474422	+	1.30346i	0.439745	+	0.898123i	$0.355069\pi$
$113$	−5.04317	+	13.8560i	−0.474422	+	1.30346i	−0.914166	+	0.405340i	$0.867153\pi$
$114$	−3.05101	+	3.31006i	−0.285754	+	0.310015i
$115$	−0.000573380	0	0.000683327i	−5.34679e−5	0	6.37206e-5i
$116$	12.7529	−	7.36290i	1.18408	−	0.683628i
$117$	3.53511	−	7.46644i	0.326821	−	0.690272i
$118$	−5.71332	+	3.29858i	−0.525953	+	0.303659i
$119$	1.85903	−	1.01289i	0.170417	−	0.0928517i
$120$	−0.00145015	+	0.00110600i	−0.000132380	+	0.000100964i
$121$	10.7360	+	3.90758i	0.976000	+	0.355235i
$122$	0.315182	+	1.78749i	0.0285352	+	0.161831i
$123$	−11.6681	+	1.50134i	−1.05208	+	0.135371i
$124$	−9.08794	+	10.8306i	−0.816121	+	0.972616i
$125$	0.00281100	+	0.00486880i	0.000251424	+	0.000435479i
$126$	−2.71566	−	2.88705i	−0.241930	−	0.257199i
$127$	−3.46785	+	6.00649i	−0.307722	+	0.532990i	−0.977864	−	0.209243i	$-0.932900\pi$
$127$	−3.46785	+	6.00649i	−0.307722	+	0.532990i	0.670142	+	0.742233i	$0.266233\pi$
$128$	−3.88657	−	10.6783i	−0.343528	−	0.943834i
$129$	11.5043	+	2.58585i	1.01289	+	0.227671i
$130$	0.000592209	0	0.000496922i	5.19401e−5	0	4.35829e-5i
$131$	8.46265	−	7.10101i	0.739385	−	0.620418i	−0.193287	−	0.981142i	$-0.561915\pi$
$131$	8.46265	−	7.10101i	0.739385	−	0.620418i	0.932672	+	0.360724i	$0.117470\pi$
$132$	−6.59285	−	12.7559i	−0.573834	−	1.11026i
$133$	6.58838	+	12.0921i	0.571285	+	1.04851i
$134$			1.06201i			0.0917438i
$135$	0.00291951		0.000101745i	0.000251271		8.75683e-6i
$136$	1.29788	+	0.749332i	0.111292	+	0.0642547i
$137$	−3.43808	−	9.44606i	−0.293735	−	0.807031i	−0.995512	−	0.0946343i	$-0.969832\pi$
$137$	−3.43808	−	9.44606i	−0.293735	−	0.807031i	0.701777	−	0.712397i	$-0.252390\pi$
$138$	0.0638805	−	1.37085i	0.00543787	−	0.116694i
$139$	0.409252	−	0.0721623i	0.0347123	−	0.00612072i	−0.156265	−	0.987715i	$-0.549945\pi$
$139$	0.409252	−	0.0721623i	0.0347123	−	0.00612072i	0.190977	+	0.981594i	$0.438834\pi$
$140$	0.000829865		0.00246820i	7.01364e−5		0.000208601i
$141$	12.5319	+	2.81684i	1.05538	+	0.237221i
$142$	4.10162	−	1.49287i	0.344200	−	0.125279i
$143$	6.52003	+	11.2930i	0.545232	+	0.944370i
$144$	−2.03597	+	7.42390i	−0.169664	+	0.618658i
$145$	−0.00409548	−	0.00236453i	−0.000340111	−	0.000196363i
$146$	3.37035	−	1.22671i	0.278932	−	0.101523i
$147$	−11.0327	+	5.02782i	−0.909964	+	0.414688i
$148$	2.75697	−	2.31338i	0.226622	−	0.190158i
$149$	0.315032	−	0.865543i	0.0258084	−	0.0709081i	−0.926119	−	0.377231i	$-0.876876\pi$
$149$	0.315032	−	0.865543i	0.0258084	−	0.0709081i	0.951928	+	0.306323i	$0.0990986\pi$
$150$	−3.99055	−	1.66666i	−0.325827	−	0.136083i
$151$	−0.209027	+	1.18545i	−0.0170104	+	0.0964707i	−0.992131	−	0.125204i	$-0.960041\pi$
$151$	−0.209027	+	1.18545i	−0.0170104	+	0.0964707i	0.975121	+	0.221675i	$0.0711524\pi$
$152$	−4.87404	+	8.44209i	−0.395337	+	0.684744i
$153$	−1.00172	−	2.18152i	−0.0809847	−	0.176365i
$154$	6.18642	−	0.933822i	0.498516	−	0.0752495i
$155$	0.00447142		0.000788431i	0.000359153		6.33283e-5i
$156$	1.83110	−	8.14643i	0.146605	−	0.652236i
$157$	−7.40718	−	8.82753i	−0.591157	−	0.704514i	0.384671	−	0.923054i	$-0.374315\pi$
$157$	−7.40718	−	8.82753i	−0.591157	−	0.704514i	−0.975828	+	0.218540i	$0.929871\pi$
$158$	0.440075	−	1.20910i	0.0350105	−	0.0961905i
$159$	8.36807	+	16.1907i	0.663631	+	1.28400i
$160$	−0.00181672	+	0.00216508i	−0.000143624	+	0.000171164i
$161$	−3.90805	−	1.53282i	−0.307997	−	0.120803i
$162$	−3.47645	+	2.84828i	−0.273136	+	0.223782i
$163$	−3.42292	−	5.92867i	−0.268104	−	0.464369i	0.700268	−	0.713880i	$-0.253064\pi$
$163$	−3.42292	−	5.92867i	−0.268104	−	0.464369i	−0.968372	+	0.249510i	$0.919730\pi$
$164$	−11.1734	+	4.06679i	−0.872498	+	0.317563i
$165$	−0.00248902	+	0.00388180i	−0.000193770	+	0.000302198i
$166$	−0.619139	−	0.737861i	−0.0480545	−	0.0572691i
$167$	4.35768	+	1.58606i	0.337207	+	0.122733i	0.505073	−	0.863076i	$-0.331465\pi$
$167$	4.35768	+	1.58606i	0.337207	+	0.122733i	−0.167866	+	0.985810i	$0.553688\pi$
$168$	−7.10843	−	4.80991i	−0.548427	−	0.371093i
$169$	0.940696	−	5.33495i	0.0723613	−	0.410381i
$170$		0	0.000224642i		0	1.72292e-5i
$171$	14.1897	−	6.51574i	1.08512	−	0.498271i
$172$	11.9178			0.908725
$173$	18.4317	+	15.4661i	1.40134	+	1.17586i	0.960501	+	0.278276i	$0.0897630\pi$
$173$	18.4317	+	15.4661i	1.40134	+	1.17586i	0.440838	+	0.897587i	$0.354681\pi$
$174$	7.21595	−	0.928479i	0.547040	−	0.0703878i
$175$	−8.75113	+	9.92057i	−0.661524	+	0.749924i
$176$	−7.81072	−	9.30846i	−0.588755	−	0.701651i
$177$	22.6953	−	2.92022i	1.70589	−	0.219497i
$178$	−1.59129	−	0.280588i	−0.119273	−	0.0210310i
$179$		−	24.6678i		−	1.84376i	−0.387475	−	0.921880i	$-0.626653\pi$
$179$		−	24.6678i		−	1.84376i	0.387475	−	0.921880i	$-0.373347\pi$
$180$	0.00285645		0.000747457i	0.000212907		5.57121e-5i
$181$	7.78429	+	4.49426i	0.578601	+	0.334056i	0.760577	−	0.649247i	$-0.224916\pi$
$181$	7.78429	+	4.49426i	0.578601	+	0.334056i	−0.181976	+	0.983303i	$0.558249\pi$
$182$	3.10479	+	1.89638i	0.230143	+	0.140569i
$183$	1.38063	−	6.14233i	0.102059	−	0.454054i
$184$	−0.516030	−	2.92655i	−0.0380422	−	0.215748i
$185$	−0.00108608		0.000395299i	−7.98498e−5		2.90630e-5i
$186$	−6.20538	+	3.20722i	−0.455000	+	0.235165i
$187$	3.73165	+	0.657991i	0.272885	+	0.0481171i
$188$	12.9824			0.946841
$189$	4.83248	+	12.8704i	0.351511	+	0.936184i
$190$	0.00146119			0.000106006
$191$	20.5434	+	3.62235i	1.48647	+	0.262104i	0.857159	−	0.515051i	$-0.172227\pi$
$191$	20.5434	+	3.62235i	1.48647	+	0.262104i	0.629308	+	0.777156i	$0.283338\pi$
$192$	−0.211366	+	4.53582i	−0.0152541	+	0.327345i
$193$	17.1757	+	6.25143i	1.23633	+	0.449988i	0.875762	−	0.482744i	$-0.160360\pi$
$193$	17.1757	+	6.25143i	1.23633	+	0.449988i	0.360571	+	0.932732i	$0.382582\pi$
$194$	−0.155725	−	0.883158i	−0.0111804	−	0.0634070i
$195$	−0.00255967		0.000798817i	−0.000183302		5.72045e-5i
$196$	−9.76522	+	7.40352i	−0.697516	+	0.528823i
$197$	−8.92564	−	5.15322i	−0.635925	−	0.367152i	0.147118	−	0.989119i	$-0.453000\pi$
$197$	−8.92564	−	5.15322i	−0.635925	−	0.367152i	−0.783043	+	0.621967i	$0.786334\pi$
$198$	−0.576842	−	7.07071i	−0.0409944	−	0.502494i
$199$		−	11.1728i		−	0.792020i	−0.918246	−	0.396010i	$-0.870395\pi$
$199$		−	11.1728i		−	0.792020i	0.918246	−	0.396010i	$-0.129605\pi$
$200$	−9.22237	−	1.62615i	−0.652120	−	0.114986i
$201$	1.41963	−	3.39907i	0.100133	−	0.239752i
$202$	−1.36719	−	1.62936i	−0.0961955	−	0.114641i
$203$	4.40506	−	21.8149i	0.309175	−	1.53111i
$204$	−1.47137	−	1.92922i	−0.103017	−	0.135072i
$205$	0.00292516	+	0.00245450i	0.000204302	+	0.000171430i
$206$	−8.03013			−0.559486
$207$	−2.03692	+	4.30213i	−0.141576	+	0.299019i
$208$		−	7.06595i		−	0.489935i
$209$	−4.27991	+	24.2726i	−0.296048	+	1.67897i
$210$	−9.16288e−5		0.00128325i	−6.32299e−6		8.85530e-5i
$211$	22.3190	+	8.12346i	1.53651	+	0.559242i	0.965204	−	0.261498i	$-0.0842165\pi$
$211$	22.3190	+	8.12346i	1.53651	+	0.559242i	0.571302	+	0.820740i	$0.306439\pi$
$212$	11.8407	+	14.1112i	0.813224	+	0.969163i
$213$	−15.1232	−	0.704729i	−1.03622	−	0.0482873i
$214$	1.88975	−	0.687813i	0.129181	−	0.0470179i
$215$	−0.00191365	−	0.00331454i	−0.000130510	−	0.000226050i
$216$	−5.99217	+	7.66851i	−0.407716	+	0.521776i
$217$	3.18921	+	21.1280i	0.216498	+	1.43426i
$218$	0.377378	−	0.449742i	0.0255593	−	0.0304603i
$219$	−12.4269	−	0.579086i	−0.839733	−	0.0391310i
$220$	−0.00159406	+	0.00437965i	−0.000107472	+	0.000295276i
$221$	1.41633	+	1.68791i	0.0952726	+	0.113541i
$222$	1.69738	−	0.529714i	0.113920	−	0.0355521i
$223$	−23.8004	−	4.19666i	−1.59380	−	0.281029i	−0.694871	−	0.719134i	$-0.744539\pi$
$223$	−23.8004	−	4.19666i	−1.59380	−	0.281029i	−0.898924	+	0.438105i	$0.855650\pi$
$224$	−12.3824	−	4.85664i	−0.827334	−	0.324498i
$225$	10.5442	+	10.6686i	0.702948	+	0.711242i
$226$	−3.68161	+	6.37674i	−0.244897	+	0.424174i
$227$	0.742956	−	4.21351i	0.0493117	−	0.279661i	−0.950174	−	0.311719i	$-0.899095\pi$
$227$	0.742956	−	4.21351i	0.0493117	−	0.279661i	0.999486	+	0.0320585i	$0.0102063\pi$
$228$	12.5486	−	9.57056i	0.831053	−	0.633826i
$229$	4.43062	−	12.1730i	0.292784	−	0.804417i	−0.702873	−	0.711315i	$-0.748100\pi$
$229$	4.43062	−	12.1730i	0.292784	−	0.804417i	0.995657	−	0.0931013i	$-0.0296780\pi$
$230$	−0.000341228	0	0.000286324i	−2.24999e−5	0	1.88797e-5i
$231$	−21.0485	−	5.28083i	−1.38489	−	0.347453i
$232$	14.8044	−	5.38834i	0.971953	−	0.353762i
$233$	−9.70366	−	5.60241i	−0.635708	−	0.367026i	0.147251	−	0.989099i	$-0.452957\pi$
$233$	−9.70366	−	5.60241i	−0.635708	−	0.367026i	−0.782959	+	0.622073i	$0.786291\pi$
$234$	2.38593	−	3.36527i	0.155973	−	0.219995i
$235$	−0.00208459	−	0.00361062i	−0.000135984	−	0.000235531i
$236$	21.7332	−	7.91023i	1.41471	−	0.514912i
$237$	−3.02474	+	3.28156i	−0.196478	+	0.213160i
$238$	1.00206	−	0.336914i	0.0649536	−	0.0218389i
$239$	12.3508	−	2.17779i	0.798909	−	0.140869i	0.240733	−	0.970591i	$-0.422612\pi$
$239$	12.3508	−	2.17779i	0.798909	−	0.140869i	0.558177	+	0.829722i	$0.311501\pi$
$240$	0.00221972	−	0.00114725i	0.000143283	−	7.40550e-5i
$241$	−6.86595	−	18.8641i	−0.442275	−	1.21514i	−0.937992	−	0.346656i	$-0.887317\pi$
$241$	−6.86595	−	18.8641i	−0.442275	−	1.21514i	0.495717	−	0.868484i	$-0.334905\pi$
$242$	4.94087	+	2.85261i	0.317611	+	0.183373i
$243$	14.9341	−	4.46906i	0.958023	−	0.286691i
$244$		−	6.36314i		−	0.407358i
$245$	0.00362704	+	0.00152708i	0.000231723	+	9.75615e-5i
$246$	−5.86827	−	0.273457i	−0.374147	−	0.0174350i
$247$	−10.9791	+	9.21254i	−0.698582	+	0.586180i
$248$	−11.5872	+	9.72278i	−0.735786	+	0.617397i
$249$	0.995284	+	3.18922i	0.0630736	+	0.202108i
$250$	0.000960194		0.00263811i	6.07280e−5		0.000166849i
$251$	−11.2730	+	19.5255i	−0.711547	+	1.23244i	0.252729	+	0.967537i	$0.418672\pi$
$251$	−11.2730	+	19.5255i	−0.711547	+	1.23244i	−0.964276	+	0.264899i	$0.914661\pi$
$252$	7.61823	+	11.6207i	0.479903	+	0.732035i
$253$	−3.75681	−	6.50699i	−0.236189	−	0.409091i
$254$	−2.22625	+	2.65314i	−0.139687	+	0.166473i
$255$	−0.000300287	0	0.000718987i	−1.88047e−5	0	4.50247e-5i
$256$	−0.0749017	−	0.424789i	−0.00468135	−	0.0265493i
$257$	−27.6153	−	10.0512i	−1.72260	−	0.626974i	−0.724537	−	0.689236i	$-0.757946\pi$
$257$	−27.6153	−	10.0512i	−1.72260	−	0.626974i	−0.998060	+	0.0622616i	$0.980169\pi$
$258$	5.43329	+	2.26923i	0.338262	+	0.141276i
$259$	0.134425	−	5.43750i	0.00835277	−	0.337870i
$260$	−0.00234710	+	0.00135510i	−0.000145561	+	8.40396e-5i
$261$	−24.3364	−	6.67415i	−1.50639	−	0.413119i
$262$	4.77748	−	2.75828i	0.295154	−	0.170407i
$263$	−10.7751	+	12.8412i	−0.664420	+	0.791825i	−0.988013	−	0.154371i	$-0.950665\pi$
$263$	−10.7751	+	12.8412i	−0.664420	+	0.791825i	0.323593	+	0.946197i	$0.395109\pi$
$264$	−4.57646	−	14.6645i	−0.281662	−	0.902537i
$265$	0.00202329	−	0.00555894i	0.000124290	−	0.000341483i
$266$	2.19146	+	6.51789i	0.134367	+	0.399637i
$267$	4.71801	+	3.02519i	0.288738	+	0.185139i
$268$	0.646517	−	3.66658i	0.0394923	−	0.223972i
$269$	−4.71711	+	8.17027i	−0.287607	+	0.498150i	−0.973238	−	0.229799i	$-0.926193\pi$
$269$	−4.71711	+	8.17027i	−0.287607	+	0.498150i	0.685631	+	0.727949i	$0.259526\pi$
$270$	0.00144457		0.000203125i	8.79136e−5		1.23618e-5i
$271$	−3.40065	+	1.96337i	−0.206575	+	0.119266i	−0.599719	−	0.800211i	$-0.704721\pi$
$271$	−3.40065	+	1.96337i	−0.206575	+	0.119266i	0.393144	+	0.919477i	$0.371388\pi$
$272$	−1.57288	−	1.31980i	−0.0953696	−	0.0800246i
$273$	−7.40222	−	10.2198i	−0.448003	−	0.618532i
$274$	−0.871668	−	4.94347i	−0.0526594	−	0.298646i
$275$	−23.3178	+	4.11156i	−1.40612	+	0.247936i
$276$	−1.05507	+	4.69394i	−0.0635078	+	0.282542i
$277$	−17.5744	−	14.7467i	−1.05595	−	0.886043i	−0.0622389	−	0.998061i	$-0.519824\pi$
$277$	−17.5744	−	14.7467i	−1.05595	−	0.886043i	−0.993706	+	0.112018i	$0.964269\pi$
$278$	0.207518			0.0124461
$279$	24.1481	−	1.97005i	1.44571	−	0.117944i
$280$	0.000415809		0.00275467i	2.48494e−5		0.000164623i
$281$	0.608889	+	1.67291i	0.0363233	+	0.0997974i	0.956528	−	0.291639i	$-0.0942006\pi$
$281$	0.608889	+	1.67291i	0.0363233	+	0.0997974i	−0.920205	+	0.391436i	$0.871978\pi$
$282$	5.91864	+	2.47194i	0.352450	+	0.147202i
$283$	−4.38907	+	0.773911i	−0.260903	+	0.0460042i	−0.302569	−	0.953127i	$-0.597844\pi$
$283$	−4.38907	+	0.773911i	−0.260903	+	0.0460042i	0.0416665	+	0.999132i	$0.486733\pi$
$284$	−15.0696	+	2.65717i	−0.894214	+	0.157674i
$285$	−0.00467666	−	0.00195322i	−0.000277022	−	0.000115699i
$286$	2.22714	+	6.11901i	0.131693	+	0.361825i
$287$	−6.56164	+	16.7294i	−0.387321	+	0.987507i
$288$	−6.45384	+	13.6310i	−0.380296	+	0.803215i
$289$	−16.3597			−0.962337
$290$	−0.00180902	−	0.00151795i	−0.000106229	−	8.91371e-5i
$291$	−0.682140	+	3.03479i	−0.0399877	+	0.177903i
$292$	−12.3829	+	2.18343i	−0.724652	+	0.127776i
$293$	1.23196	+	6.98681i	0.0719721	+	0.408174i	0.999415	+	0.0342085i	$0.0108910\pi$
$293$	1.23196	+	6.98681i	0.0719721	+	0.408174i	−0.927443	+	0.373965i	$0.877998\pi$
$294$	−5.86161	+	1.51588i	−0.341856	+	0.0884077i
$295$	−0.00568967	−	0.00477420i	−0.000331265	−	0.000277965i
$296$	3.33453	−	1.92519i	0.193815	−	0.111899i
$297$	−7.60545	+	23.4015i	−0.441313	+	1.35790i
$298$	0.229979	−	0.398336i	0.0133223	−	0.0230750i
$299$	0.758694	−	4.30277i	0.0438764	−	0.248836i
$300$	12.7627	+	8.18344i	0.736854	+	0.472471i
$301$	11.9150	−	13.5073i	0.686771	−	0.778546i
$302$	−0.205589	+	0.564852i	−0.0118303	+	0.0325036i
$303$	2.19781	+	7.04249i	0.126261	+	0.404581i
$304$	8.58466	−	10.2308i	0.492364	−	0.586777i
$305$	−0.00176969	+	0.00102173i	−0.000101332	+	5.85042e-5i
$306$	−0.303458	−	1.15968i	−0.0173475	−	0.0662946i
$307$	−6.20672	+	3.58345i	−0.354236	+	0.204518i	−0.666549	−	0.745461i	$-0.732229\pi$
$307$	−6.20672	+	3.58345i	−0.354236	+	0.204518i	0.312313	+	0.949979i	$0.398896\pi$
$308$	−21.9270	−	0.542076i	−1.24941	−	0.0308877i
$309$	25.7012	+	10.7342i	1.46209	+	0.610646i
$310$	0.00213057		0.000775463i	0.000121008		4.40434e-5i
$311$	−4.03708	−	22.8954i	−0.228922	−	1.29828i	−0.855044	−	0.518556i	$-0.826470\pi$
$311$	−4.03708	−	22.8954i	−0.228922	−	1.29828i	0.626122	−	0.779725i	$-0.284641\pi$
$312$	3.44268	−	8.24291i	0.194903	−	0.466663i
$313$	15.3541	−	18.2983i	0.867863	−	1.03428i	−0.131216	−	0.991354i	$-0.541888\pi$
$313$	15.3541	−	18.2983i	0.867863	−	1.03428i	0.999078	−	0.0429247i	$-0.0136676\pi$
$314$	−2.87721	−	4.98347i	−0.162370	−	0.281234i
$315$	0.00200864	−	0.00398469i	0.000113174	−	0.000224512i
$316$	−2.25541	+	3.90648i	−0.126877	+	0.219757i
$317$	−9.82360	−	26.9901i	−0.551748	−	1.51592i	−0.831322	−	0.555791i	$-0.812415\pi$
$317$	−9.82360	−	26.9901i	−0.551748	−	1.51592i	0.279574	−	0.960124i	$-0.409807\pi$
$318$	2.71127	+	8.68781i	0.152041	+	0.487188i
$319$	30.5143	−	25.6045i	1.70847	−	1.43358i
$320$	0.00112905		0.000947383i	6.31156e−5		5.29603e-5i
$321$	−6.96774	−	0.324692i	−0.388901	−	0.0181225i
$322$	−1.78897	−	1.09268i	−0.0996954	−	0.0608929i
$323$			4.16468i			0.231729i
$324$	13.7363	−	7.71728i	0.763129	−	0.428738i
$325$	−11.9238	−	6.88420i	−0.661412	−	0.381866i
$326$	−1.16922	−	3.21239i	−0.0647569	−	0.177918i
$327$	−1.80902	+	0.934984i	−0.100039	+	0.0517047i
$328$	−12.5279	+	2.20900i	−0.691735	+	0.121972i
$329$	12.9794	−	14.7138i	0.715577	−	0.811201i
$330$	−0.00156064	+	0.00169315i	−8.59106e−5	+	9.32047e-5i
$331$	24.4353	−	8.89374i	1.34309	−	0.488844i	0.432304	−	0.901728i	$-0.357701\pi$
$331$	24.4353	−	8.89374i	1.34309	−	0.488844i	0.910784	+	0.412884i	$0.135478\pi$
$332$	1.68838	+	2.92436i	0.0926620	+	0.160495i
$333$	−6.14070	−	0.573550i	−0.336508	−	0.0314304i
$334$	2.00547	+	1.15786i	0.109734	+	0.0633551i
$335$	−0.00112355		0.000408937i	−6.13858e−5		2.23426e-5i
$336$	8.44664	+	8.18084i	0.460802	+	0.446302i
$337$	5.30836	−	4.45424i	0.289165	−	0.242638i	−0.486653	−	0.873596i	$-0.661782\pi$
$337$	5.30836	−	4.45424i	0.289165	−	0.242638i	0.775817	+	0.630958i	$0.217338\pi$
$338$	0.925224	−	2.54203i	0.0503256	−	0.138268i
$339$	20.3074	−	15.4880i	1.10294	−	0.841192i
$340$	−0.000136754	0	0.000775572i	−7.41655e−6	0	4.20613e-5i
$341$	−19.1222	+	33.1207i	−1.03553	+	1.79358i
$342$	7.54317	−	1.97384i	0.407888	−	0.106733i
$343$	−1.37203	+	18.4694i	−0.0740826	+	0.997252i
$344$	12.5566	+	2.21407i	0.677008	+	0.119375i
$345$	0.00147487		0.000460275i	7.94045e−5		2.47804e-5i
$346$	7.72317	+	9.20412i	0.415200	+	0.494817i
$347$	−0.540900	+	1.48611i	−0.0290370	+	0.0797786i	−0.953364	−	0.301823i	$-0.902405\pi$
$347$	−0.540900	+	1.48611i	−0.0290370	+	0.0797786i	0.924327	+	0.381601i	$0.124627\pi$
$348$	−25.4782	−	1.18727i	−1.36577	−	0.0636441i
$349$	−11.3433	+	13.5184i	−0.607194	+	0.723626i	−0.978812	−	0.204760i	$-0.934359\pi$
$349$	−11.3433	+	13.5184i	−0.607194	+	0.723626i	0.371618	+	0.928386i	$0.378803\pi$
$350$	−5.16384	+	4.11986i	−0.276019	+	0.220216i
$351$	−12.1349	+	7.58151i	−0.647711	+	0.404671i
$352$	−11.9032	−	20.6170i	−0.634444	−	1.09889i
$353$	−2.55746	+	0.930839i	−0.136120	+	0.0495435i	−0.409182	−	0.912453i	$-0.634186\pi$
$353$	−2.55746	+	0.930839i	−0.136120	+	0.0495435i	0.273062	+	0.961996i	$0.411964\pi$
$354$	11.4142	+	0.531896i	0.606660	+	0.0282700i
$355$	0.00315873	+	0.00376442i	0.000167648	+	0.000199795i
$356$	5.32310	+	1.93745i	0.282124	+	0.102685i
$357$	−3.65754	−	0.261161i	−0.193577	−	0.0138221i
$358$	2.13903	−	12.1311i	0.113051	−	0.641146i
$359$			22.8763i			1.20737i	0.797224	+	0.603683i	$0.206301\pi$
$359$			22.8763i			1.20737i	−0.797224	+	0.603683i	$0.793699\pi$
$360$	0.00314842		0.000256855i	0.000165937		1.35374e-5i
$361$	−8.08924			−0.425750
$362$	3.43841	+	2.88517i	0.180719	+	0.151641i
$363$	−12.0005	−	15.7347i	−0.629863	−	0.825857i
$364$	−9.56480	−	8.43730i	−0.501332	−	0.442235i
$365$	0.00259557	+	0.00309328i	0.000135858	+	0.000161910i
$366$	1.21158	−	2.90093i	0.0633305	−	0.151634i
$367$	7.27732	+	1.28319i	0.379873	+	0.0669819i	0.360325	−	0.932827i	$-0.382666\pi$
$367$	7.27732	+	1.28319i	0.379873	+	0.0669819i	0.0195487	+	0.999809i	$0.493777\pi$
$368$			4.07137i			0.212235i
$369$	18.4164	+	8.71956i	0.958719	+	0.453922i
$370$	−0.000499828	0	0.000288576i	−2.59848e−5	0	1.50023e-5i
$371$	27.8311	+	0.688038i	1.44492	+	0.0357211i
$372$	23.3764	−	7.29526i	1.21201	−	0.378242i
$373$	5.62504	+	31.9012i	0.291254	+	1.65178i	0.682051	+	0.731304i	$0.261088\pi$
$373$	5.62504	+	31.9012i	0.291254	+	1.65178i	−0.390798	+	0.920477i	$0.627801\pi$
$374$	1.77808	+	0.647169i	0.0919424	+	0.0334643i
$375$	0.000453274	−	0.00972705i	2.34070e−5	−	0.000502303i
$376$	13.6783	+	2.41185i	0.705405	+	0.124382i
$377$	23.1631			1.19296
$378$	1.26046	+	6.74840i	0.0648313	+	0.347100i
$379$	−6.72815			−0.345602			−0.172801	−	0.984957i	$-0.555282\pi$
$379$	−6.72815			−0.345602			−0.172801	+	0.984957i	$0.555282\pi$
$380$	−0.00504472		0.000889521i	−0.000258789		4.56315e-5i
$381$	10.6719	−	5.51571i	0.546736	−	0.282578i
$382$	9.78864	+	3.56278i	0.500831	+	0.182287i
$383$	0.0493036	+	0.279615i	0.00251930	+	0.0142876i	0.986041	−	0.166500i	$-0.0532465\pi$
$383$	0.0493036	+	0.279615i	0.00251930	+	0.0142876i	−0.983522	+	0.180787i	$0.942135\pi$
$384$	−4.31636	+	19.2032i	−0.220268	+	0.979957i
$385$	0.00337006	+	0.00618529i	0.000171754	+	0.000315231i
$386$	7.90450	+	4.56367i	0.402329	+	0.232285i
$387$	−14.3564	−	14.5258i	−0.729776	−	0.738387i
$388$			3.14389i			0.159607i
$389$	−0.733433	−	0.129324i	−0.0371865	−	0.00655699i	0.155024	−	0.987911i	$-0.450455\pi$
$389$	−0.733433	−	0.129324i	−0.0371865	−	0.00655699i	−0.192211	+	0.981354i	$0.561566\pi$
$390$	−0.00132805		0.000170881i	−6.72486e−5		8.65291e-6i
$391$	−0.816083	−	0.972570i	−0.0412711	−	0.0491850i
$392$	−11.6641	+	5.98620i	−0.589124	+	0.302349i
$393$	−18.9779	+	2.44189i	−0.957307	+	0.123177i
$394$	−3.94256	−	3.30820i	−0.198623	−	0.166665i
$395$	0.00144861			7.28873e−5
$396$	−2.31287	+	24.7627i	−0.116226	+	1.24437i
$397$		−	16.7288i		−	0.839593i	−0.907618	−	0.419797i	$-0.862101\pi$
$397$		−	16.7288i		−	0.839593i	0.907618	−	0.419797i	$-0.137899\pi$
$398$	0.968833	−	5.49452i	0.0485632	−	0.275416i
$399$	1.69872	−	23.7905i	0.0850426	−	1.19102i
$400$	12.0563	+	4.38812i	0.602814	+	0.219406i
$401$	−11.8787	−	14.1565i	−0.593194	−	0.706941i	0.383023	−	0.923739i	$-0.374883\pi$
$401$	−11.8787	−	14.1565i	−0.593194	−	0.706941i	−0.976216	+	0.216798i	$0.930439\pi$
$402$	0.992885	−	1.54848i	0.0495206	−	0.0772311i
$403$	−20.8978	+	7.60619i	−1.04099	+	0.378891i
$404$	3.72832	+	6.45763i	0.185491	+	0.321279i
$405$	−0.00435195	−	0.00258113i	−0.000216250	−	0.000128257i
$406$	4.05795	−	10.3461i	0.201393	−	0.513467i
$407$	6.25772	−	7.45767i	0.310184	−	0.369663i
$408$	−1.19183	−	2.30597i	−0.0590045	−	0.114163i
$409$	−6.09589	+	16.7483i	−0.301423	+	0.828152i	0.692831	+	0.721100i	$0.256363\pi$
$409$	−6.09589	+	16.7483i	−0.301423	+	0.828152i	−0.994253	+	0.107052i	$0.965859\pi$
$410$	0.00122569	+	0.00146072i	6.05323e−5	+	7.21396e-5i
$411$	−3.81828	+	16.9872i	−0.188342	+	0.837918i
$412$	27.7239	+	4.88847i	1.36586	+	0.240838i
$413$	12.7629	−	32.5401i	0.628021	−	1.60119i
$414$	−1.37476	+	1.93906i	−0.0675658	+	0.0952994i
$415$	0.000542208	0	0.000939132i	2.66159e−5	0	4.61002e-5i
$416$	2.40387	−	13.6330i	0.117860	−	0.668415i
$417$	−0.664181	−	0.277397i	−0.0325251	−	0.0135842i
$418$	−4.20952	+	11.5656i	−0.205894	+	0.565690i
$419$	0.812929	−	0.682129i	0.0397142	−	0.0333242i	−0.622715	−	0.782449i	$-0.713970\pi$
$419$	0.812929	−	0.682129i	0.0397142	−	0.0333242i	0.662429	+	0.749125i	$0.269526\pi$
$420$	0.00109755	−	0.00437463i	5.35549e−5	−	0.000213460i
$421$	−14.4175	+	5.24755i	−0.702667	+	0.255750i	−0.668549	−	0.743668i	$-0.733084\pi$
$421$	−14.4175	+	5.24755i	−0.702667	+	0.255750i	−0.0341181	+	0.999418i	$0.510862\pi$
$422$	10.2716	+	5.93029i	0.500011	+	0.288682i
$423$	−15.6388	−	15.8233i	−0.760385	−	0.769357i
$424$	9.85384	+	17.0674i	0.478545	+	0.828864i
$425$	−3.75958	+	1.36837i	−0.182366	+	0.0663759i
$426$	−7.37610	−	1.65795i	−0.357373	−	0.0803280i
$427$	−7.21177	−	6.36165i	−0.349002	−	0.307862i
$428$	−6.94305	+	1.22425i	−0.335605	+	0.0591762i
$429$	1.05135	−	22.5616i	0.0507598	−	1.08928i
$430$	−0.000653672	−	0.00179595i	−3.15229e−5	−	8.66084e-5i
$431$	−3.29736	−	1.90373i	−0.158828	−	0.0916996i	0.418479	−	0.908226i	$-0.362563\pi$
$431$	−3.29736	−	1.90373i	−0.158828	−	0.0916996i	−0.577308	+	0.816527i	$0.695897\pi$
$432$	9.90924	−	8.92105i	0.476758	−	0.429214i
$433$			29.5261i			1.41893i	0.704739	+	0.709467i	$0.251064\pi$
$433$			29.5261i			1.41893i	−0.704739	+	0.709467i	$0.748936\pi$
$434$	−0.263703	+	10.6668i	−0.0126582	+	0.512023i
$435$	0.00376084	+	0.00727653i	0.000180319	+	0.000348883i
$436$	−1.57668	+	1.32299i	−0.0755092	+	0.0633598i
$437$	6.32610	−	5.30822i	0.302618	−	0.253927i
$438$	−6.06104	−	1.36236i	−0.289608	−	0.0650961i
$439$	5.64596	+	15.5122i	0.269467	+	0.740355i	0.998441	+	0.0558134i	$0.0177752\pi$
$439$	5.64596	+	15.5122i	0.269467	+	0.740355i	−0.728974	+	0.684541i	$0.760003\pi$
$440$	−0.00249315	+	0.00431827i	−0.000118856	+	0.000205865i
$441$	20.7870	+	2.98373i	0.989855	+	0.142083i
$442$	0.550152	+	0.952891i	0.0261681	+	0.0453244i
$443$	17.9563	−	21.3994i	0.853127	−	1.01672i	−0.146494	−	0.989212i	$-0.546799\pi$
$443$	17.9563	−	21.3994i	0.853127	−	1.01672i	0.999622	−	0.0275061i	$-0.00875656\pi$
$444$	−6.18264	+	0.795522i	−0.293415	+	0.0377538i
$445$	−0.000315896	−	0.00179154i	−1.49749e−5	−	8.49270e-5i
$446$	−11.3406	−	4.12763i	−0.536992	−	0.195449i
$447$	−1.26854	+	0.967489i	−0.0599999	+	0.0457606i
$448$	5.91930	+	3.61545i	0.279661	+	0.170814i
$449$	20.1252	−	11.6193i	0.949765	−	0.548347i	0.0567572	−	0.998388i	$-0.481924\pi$
$449$	20.1252	−	11.6193i	0.949765	−	0.548347i	0.893008	+	0.450041i	$0.148591\pi$
$450$	4.26028	+	6.16090i	0.200832	+	0.290428i
$451$	−27.8549	+	16.0820i	−1.31164	+	0.757273i
$452$	16.5926	−	19.7743i	0.780452	−	0.930107i
$453$	1.41307	−	1.53304i	0.0663916	−	0.0720285i
$454$	0.730736	−	2.00768i	0.0342952	−	0.0942252i
$455$	−0.000810726		0.00401490i	−3.80074e−5		0.000188222i
$456$	14.9993	−	7.75230i	0.702404	−	0.363035i
$457$	3.14739	−	17.8497i	0.147229	−	0.834976i	−0.818322	−	0.574760i	$-0.805095\pi$
$457$	3.14739	−	17.8497i	0.147229	−	0.834976i	0.965551	−	0.260215i	$-0.0837936\pi$
$458$	3.23444	−	5.60221i	0.151135	−	0.261774i
$459$	−0.578947	+	4.11731i	−0.0270229	+	0.192180i
$460$	0.00135239		0.000780802i	6.30555e−5		3.64051e-5i
$461$	−0.780576	−	0.654981i	−0.0363550	−	0.0305055i	0.624429	−	0.781081i	$-0.285332\pi$
$461$	−0.780576	−	0.654981i	−0.0363550	−	0.0305055i	−0.660784	+	0.750576i	$0.729776\pi$
$462$	−9.89322	−	4.42217i	−0.460274	−	0.205738i
$463$	5.96496	+	33.8290i	0.277215	+	1.57216i	0.731837	+	0.681480i	$0.238663\pi$
$463$	5.96496	+	33.8290i	0.277215	+	1.57216i	−0.454621	+	0.890685i	$0.650225\pi$
$464$	−21.2565	+	3.74809i	−0.986807	+	0.174001i
$465$	−0.00578249	−	0.00532995i	−0.000268156	−	0.000247171i
$466$	−4.28622	−	3.59657i	−0.198556	−	0.166608i
$467$	−1.42508			−0.0659449			−0.0329724	−	0.999456i	$-0.510497\pi$
$467$	−1.42508			−0.0659449			−0.0329724	+	0.999456i	$0.510497\pi$
$468$	−10.2860	+	10.1661i	−0.475472	+	0.469927i
$469$	−3.50921	−	4.39846i	−0.162040	−	0.203102i
$470$	−0.000712064	−	0.00195638i	−3.28451e−5	−	9.02410e-5i
$471$	2.54718	+	19.7961i	0.117368	+	0.912158i
$472$	24.3677	−	4.29668i	1.12161	−	0.197771i
$473$	31.7482	−	5.59806i	1.45978	−	0.257399i
$474$	−1.77205	+	1.35151i	−0.0813931	+	0.0620767i
$475$	−8.90062	−	24.4542i	−0.408388	−	1.12204i
$476$	−3.66468	+	0.553173i	−0.167970	+	0.0253546i
$477$	2.93564	−	31.4304i	0.134414	−	1.43910i
$478$	6.26269			0.286449
$479$	27.4187	+	23.0070i	1.25279	+	1.05122i	0.996411	+	0.0846415i	$0.0269745\pi$
$479$	27.4187	+	23.0070i	1.25279	+	1.05122i	0.256381	+	0.966576i	$0.417470\pi$
$480$	0.00467304	−	0.00145835i	0.000213294	−	6.65643e-5i
$481$	5.57503	−	0.983028i	0.254200	−	0.0448222i
$482$	−1.74075	−	9.87226i	−0.0792888	−	0.449669i
$483$	4.26513	+	5.88862i	0.194070	+	0.267941i
$484$	−15.3217	−	12.8564i	−0.696441	−	0.584383i
$485$	0.000874365	0	0.000504815i	3.97029e−5	0	2.29225e-5i
$486$	7.73176	−	0.902792i	0.350720	−	0.0409515i
$487$	−17.4657	+	30.2515i	−0.791446	+	1.37082i	0.133625	+	0.991032i	$0.457338\pi$
$487$	−17.4657	+	30.2515i	−0.791446	+	1.37082i	−0.925071	+	0.379793i	$0.875995\pi$
$488$	1.18213	−	6.70421i	0.0535127	−	0.303485i
$489$	−0.551945	+	11.8445i	−0.0249598	+	0.535626i
$490$	0.00165128	+	0.00106549i	7.45970e−5	+	4.81341e-5i
$491$	−3.72269	+	10.2280i	−0.168003	+	0.461584i	−0.994912	−	0.100752i	$-0.967875\pi$
$491$	−3.72269	+	10.2280i	−0.168003	+	0.461584i	0.826909	+	0.562336i	$0.190097\pi$
$492$	20.0936	+	4.51651i	0.905891	+	0.203620i
$493$	4.32647	−	5.15608i	0.194854	−	0.232218i
$494$	−6.19810	+	3.57847i	−0.278866	+	0.161003i
$495$	0.00725828	−	0.00333291i	0.000326235	−	0.000149803i
$496$	17.9469	−	10.3617i	0.805841	−	0.465252i
$497$	−12.0545	+	19.7359i	−0.540718	+	0.885276i
$498$	0.212909	+	1.65469i	0.00954068	+	0.0741482i
$499$	−5.96349	−	2.17053i	−0.266962	−	0.0971663i	0.205071	−	0.978747i	$-0.434258\pi$
$499$	−5.96349	−	2.17053i	−0.266962	−	0.0971663i	−0.472033	+	0.881581i	$0.656480\pi$
$500$	−0.00170906	−	0.00969257i	−7.64316e−5	−	0.000433465i
$501$	−4.87093	−	6.38661i	−0.217617	−	0.285333i
$502$	−7.23693	+	8.62463i	−0.323000	+	0.384936i
$503$	−6.72425	−	11.6468i	−0.299820	−	0.519303i	0.676275	−	0.736649i	$-0.263593\pi$
$503$	−6.72425	−	11.6468i	−0.299820	−	0.519303i	−0.976095	+	0.217346i	$0.930260\pi$
$504$	5.86770	+	13.6589i	0.261368	+	0.608415i
$505$	0.00119731	−	0.00207381i	5.32798e−5	−	9.22833e-5i
$506$	−1.28327	−	3.52575i	−0.0570482	−	0.156739i
$507$	−6.35929	+	6.89923i	−0.282426	+	0.306405i
$508$	9.30123	−	7.80466i	0.412675	−	0.346276i
$509$	13.2396	−	11.1093i	0.586833	−	0.492411i	−0.300350	−	0.953829i	$-0.597104\pi$
$509$	13.2396	−	11.1093i	0.586833	−	0.492411i	0.887183	+	0.461418i	$0.152659\pi$
$510$	−0.000210020	0	0.000327542i	−9.29984e−6	0	1.45038e-5i
$511$	−9.90533	+	16.2172i	−0.438186	+	0.717409i
$512$			22.5118i			0.994888i
$513$	−26.7811	−	3.76577i	−1.18242	−	0.166263i
$514$	−12.7090	−	7.33754i	−0.560570	−	0.323645i
$515$	−0.00309207	−	0.00849540i	−0.000136253	−	0.000374352i
$516$	−17.3769	−	11.1421i	−0.764976	−	0.490503i
$517$	34.5842	−	6.09812i	1.52101	−	0.268195i
$518$	0.537611	−	2.66237i	0.0236213	−	0.116978i
$519$	−12.4152	−	39.7825i	−0.544968	−	1.74626i
$520$	−0.00272466		0.000991693i	−0.000119484		4.34886e-5i
$521$	−14.2785	−	24.7311i	−0.625553	−	1.08349i	−0.988434	−	0.151653i	$-0.951540\pi$
$521$	−14.2785	−	24.7311i	−0.625553	−	1.08349i	0.362881	−	0.931835i	$-0.381793\pi$
$522$	−11.3893	−	5.39248i	−0.498498	−	0.236023i
$523$	−13.1449	−	7.58924i	−0.574788	−	0.331854i	0.184271	−	0.982875i	$-0.441008\pi$
$523$	−13.1449	−	7.58924i	−0.574788	−	0.331854i	−0.759059	+	0.651021i	$0.774341\pi$
$524$	−18.1733	+	6.61455i	−0.793905	+	0.288958i
$525$	22.0345	−	6.28328i	0.961666	−	0.274225i
$526$	−6.41244	+	5.38068i	−0.279596	+	0.234609i
$527$	−2.21023	+	6.07255i	−0.0962790	+	0.264525i
$528$	2.68595	+	20.8746i	0.116891	+	0.908451i
$529$	3.55675	−	20.1713i	0.154641	−	0.877015i
$530$	0.00147704	−	0.00255831i	6.41585e−5	−	0.000111126i
$531$	−35.8213	−	16.9602i	−1.55451	−	0.736011i
$532$	−3.59812	−	23.8370i	−0.155998	−	1.03346i
$533$	−18.4191	−	3.24779i	−0.797821	−	0.140677i
$534$	2.05788	+	1.89683i	0.0890532	+	0.0820839i
$535$	0.00145533	+	0.00173439i	6.29194e−5	+	7.49844e-5i
$536$	1.36234	−	3.74300i	0.0588442	−	0.161673i
$537$	−23.0622	+	35.9672i	−0.995207	+	1.55210i
$538$	−3.02823	+	3.60891i	−0.130556	+	0.155591i
$539$	−22.5362	+	24.3094i	−0.970703	+	1.04708i
$540$	−0.00486369	−	0.00158069i	−0.000209300	−	6.80220e-5i
$541$	8.84080	+	15.3127i	0.380096	+	0.658345i	0.991076	−	0.133301i	$-0.0425577\pi$
$541$	8.84080	+	15.3127i	0.380096	+	0.658345i	−0.610980	+	0.791646i	$0.709224\pi$
$542$	−1.84261	+	0.670655i	−0.0791469	+	0.0288071i
$543$	−7.14824	−	13.8305i	−0.306760	−	0.593524i
$544$	−2.58570	−	3.08152i	−0.110861	−	0.132119i
$545$	0.000621113	0	0.000226067i	2.66055e−5	0	9.68363e-6i
$546$	−2.75404	−	5.66774i	−0.117862	−	0.242557i
$547$	−1.23750	+	7.01822i	−0.0529117	+	0.300077i	−0.999767	−	0.0215823i	$-0.993130\pi$
$547$	−1.23750	+	7.01822i	−0.0529117	+	0.300077i	0.946855	+	0.321660i	$0.104241\pi$
$548$			17.5979i			0.751745i
$549$	−7.75557	+	7.66513i	−0.331000	+	0.327140i
$550$	−11.8237			−0.504163
$551$	33.5378	+	28.1416i	1.42876	+	1.19887i
$552$	−1.98366	+	4.74953i	−0.0844300	+	0.202153i
$553$	2.17260	+	6.46177i	0.0923882	+	0.274782i
$554$	−7.36395	−	8.77601i	−0.312864	−	0.372857i
$555$	0.00121400	+	0.00159175i	5.15312e−5	+	6.75661e-5i
$556$	−0.716453	−	0.126330i	−0.0303844	−	0.00535758i
$557$			7.64857i			0.324080i	0.986784	+	0.162040i	$0.0518074\pi$
$557$			7.64857i			0.324080i	−0.986784	+	0.162040i	$0.948193\pi$
$558$	12.0463	+	1.12514i	0.509960	+	0.0476310i
$559$	16.2347	+	9.37312i	0.686655	+	0.396441i
$560$	9.43293e−5	−	0.00381562i	3.98614e−6	−	0.000161239i
$561$	−4.82582	−	4.44815i	−0.203746	−	0.187801i
$562$	0.154374	+	0.875496i	0.00651185	+	0.0369306i
$563$	33.9970	+	12.3739i	1.43280	+	0.521498i	0.937733	−	0.347356i	$-0.112920\pi$
$563$	33.9970	+	12.3739i	1.43280	+	0.521498i	0.495070	+	0.868853i	$0.335143\pi$
$564$	−18.9292	−	12.1374i	−0.797062	−	0.511077i
$565$	−0.00816385	−	0.00143951i	−0.000343456	−	6.05605e-5i
$566$	−2.22555			−0.0935467
$567$	4.98660	−	23.2838i	0.209418	−	0.977826i
$568$	−16.3710			−0.686910
$569$	−5.25761	−	0.927059i	−0.220411	−	0.0388643i	0.0623521	−	0.998054i	$-0.480140\pi$
$569$	−5.25761	−	0.927059i	−0.220411	−	0.0388643i	−0.282763	+	0.959190i	$0.591251\pi$
$570$	−0.00213050	−	0.00136608i	−8.92369e−5	−	5.72187e-5i
$571$	−34.9232	−	12.7110i	−1.46149	−	0.531939i	−0.515715	−	0.856760i	$-0.672473\pi$
$571$	−34.9232	−	12.7110i	−1.46149	−	0.531939i	−0.945775	+	0.324822i	$0.894696\pi$
$572$	−3.96411	−	22.4816i	−0.165748	−	0.940003i
$573$	−26.5670	−	24.4878i	−1.10985	−	1.02299i
$574$	−4.67752	+	7.65815i	−0.195236	+	0.319645i
$575$	6.87043	+	3.96664i	0.286517	+	0.165421i
$576$	4.54877	−	6.41590i	0.189532	−	0.267329i
$577$			25.3559i			1.05558i	0.849374	+	0.527791i	$0.176980\pi$
$577$			25.3559i			1.05558i	−0.849374	+	0.527791i	$0.823020\pi$
$578$	−8.04532	−	1.41861i	−0.334641	−	0.0590063i
$579$	−19.1987	−	25.1727i	−0.797869	−	1.04614i
$580$	0.00532154	+	0.00634197i	0.000220965	+	0.000263336i
$581$	5.00236	+	1.01012i	0.207533	+	0.0419069i
$582$	−0.598617	+	1.43329i	−0.0248135	+	0.0594117i
$583$	38.1711	+	32.0294i	1.58089	+	1.32652i
$584$	−13.4522			−0.556658
$585$	0.00447898	+	0.00122834i	0.000185183	+	5.07855e-5i
$586$			3.54278i			0.146351i
$587$	2.85469	−	16.1897i	0.117826	−	0.668222i	−0.867487	−	0.497460i	$-0.834266\pi$
$587$	2.85469	−	16.1897i	0.117826	−	0.668222i	0.985312	−	0.170762i	$-0.0546229\pi$
$588$	21.1599	−	1.66519i	0.872621	−	0.0686713i
$589$	−39.4990	−	14.3765i	−1.62753	−	0.592372i
$590$	−0.00238406	−	0.00284121i	−9.81501e−5	−	0.000116971i
$591$	8.19633	+	15.8584i	0.337152	+	0.652326i
$592$	−4.95708	+	1.80423i	−0.203735	+	0.0741533i
$593$	−15.3209	−	26.5365i	−0.629153	−	1.08973i	−0.987722	−	0.156222i	$-0.950068\pi$
$593$	−15.3209	−	26.5365i	−0.629153	−	1.08973i	0.358569	−	0.933503i	$-0.383265\pi$
$594$	−5.76941	+	10.8488i	−0.236722	+	0.445133i
$595$	0.000742286	0	0.000930384i	3.04307e−5	0	3.81420e-5i
$596$	−1.03649	+	1.23524i	−0.0424564	+	0.0505976i
$597$	−10.4456	+	16.2907i	−0.427509	+	0.666732i
$598$	0.746216	−	2.05021i	0.0305150	−	0.0838393i
$599$	12.5598	+	14.9682i	0.513181	+	0.611585i	0.958954	−	0.283561i	$-0.0915158\pi$
$599$	12.5598	+	14.9682i	0.513181	+	0.611585i	−0.445773	+	0.895146i	$0.647071\pi$
$600$	11.9265	+	10.9931i	0.486896	+	0.448792i
$601$	−20.6262	−	3.63695i	−0.841360	−	0.148354i	−0.263672	−	0.964612i	$-0.584934\pi$
$601$	−20.6262	−	3.63695i	−0.841360	−	0.148354i	−0.577688	+	0.816258i	$0.696045\pi$
$602$	7.03079	−	5.60936i	0.286554	−	0.228620i
$603$	−5.24773	+	3.62882i	−0.213704	+	0.147777i
$604$	1.05366	−	1.82498i	0.0428726	−	0.0742576i
$605$	−0.00111537	+	0.00632557i	−4.53462e−5	+	0.000257171i
$606$	0.470150	+	3.65391i	0.0190985	+	0.148430i
$607$	−9.22736	+	25.3520i	−0.374527	+	1.02900i	0.599063	+	0.800702i	$0.295540\pi$
$607$	−9.22736	+	25.3520i	−0.374527	+	1.02900i	−0.973590	+	0.228302i	$0.926683\pi$
$608$	20.0438	−	16.8188i	0.812884	−	0.682091i
$609$	−26.8178	+	27.6891i	−1.08671	+	1.12202i
$610$	−0.000958889	0	0.000349007i	−3.88243e−5	0	1.41309e-5i
$611$	17.6849	+	10.2104i	0.715456	+	0.413069i
$612$	0.341707	+	4.18852i	0.0138127	+	0.169311i
$613$	13.4525	+	23.3005i	0.543343	+	0.941097i	0.998709	+	0.0507931i	$0.0161749\pi$
$613$	13.4525	+	23.3005i	0.543343	+	0.941097i	−0.455366	+	0.890304i	$0.650492\pi$
$614$	−3.36305	+	1.22405i	−0.135722	+	0.0493986i
$615$	−0.00197033	−	0.00631358i	−7.94513e−5	−	0.000254588i
$616$	−23.0016	−	4.64469i	−0.926761	−	0.187140i
$617$	−22.1664	+	3.90853i	−0.892386	+	0.157352i	−0.600995	−	0.799253i	$-0.705229\pi$
$617$	−22.1664	+	3.90853i	−0.892386	+	0.157352i	−0.291390	+	0.956604i	$0.594118\pi$
$618$	11.7084	+	7.50745i	0.470982	+	0.301994i
$619$	3.67268	+	10.0906i	0.147617	+	0.405575i	0.991359	−	0.131173i	$-0.0418745\pi$
$619$	3.67268	+	10.0906i	0.147617	+	0.405575i	−0.843742	+	0.536749i	$0.819652\pi$
$620$	−0.00688367	−	0.00397429i	−0.000276455	−	0.000159611i
$621$	6.99206	−	4.36844i	0.280582	−	0.175299i
$622$		−	11.6095i		−	0.465499i
$623$	7.51770	−	4.09603i	0.301190	−	0.164104i
$624$	−6.60603	+	10.3026i	−0.264453	+	0.412434i
$625$	19.1511	−	16.0697i	0.766044	−	0.642787i
$626$	9.13746	−	7.66724i	0.365207	−	0.306445i
$627$	28.9331	−	31.3896i	1.15548	−	1.25358i
$628$	6.89975	+	18.9569i	0.275330	+	0.756463i
$629$	0.822500	−	1.42461i	0.0327952	−	0.0568030i
$630$	0.00133333	−	0.00178540i	5.31211e−5	−	7.11320e-5i
$631$	−0.130873	−	0.226679i	−0.00520998	−	0.00902394i	0.863409	−	0.504505i	$-0.168325\pi$
$631$	−0.130873	−	0.226679i	−0.00520998	−	0.00902394i	−0.868619	+	0.495481i	$0.834992\pi$
$632$	−3.10204	+	3.69687i	−0.123393	+	0.147054i
$633$	−24.9478	−	32.7108i	−0.991587	−	1.30014i
$634$	−2.49061	−	14.1249i	−0.0989146	−	0.560973i
$635$	−0.00366410	−	0.00133362i	−0.000145405	−	5.29233e-5i
$636$	−4.07178	−	31.6450i	−0.161457	−	1.25481i
$637$	−19.1251	+	2.40510i	−0.757765	+	0.0952934i
$638$	17.2264	−	9.94569i	0.682001	−	0.393754i
$639$	21.3917	+	15.1663i	0.846241	+	0.599971i
$640$	0.00553270	−	0.00319431i	0.000218699	−	0.000126266i
$641$	−32.1360	+	38.2982i	−1.26930	+	1.51269i	−0.513131	+	0.858310i	$0.671515\pi$
$641$	−32.1360	+	38.2982i	−1.26930	+	1.51269i	−0.756166	+	0.654380i	$0.772930\pi$
$642$	−3.39841	−	0.763872i	−0.134125	−	0.0301476i
$643$	5.42130	−	14.8949i	0.213795	−	0.587397i	−0.785718	−	0.618584i	$-0.787706\pi$
$643$	5.42130	−	14.8949i	0.213795	−	0.587397i	0.999514	+	0.0311869i	$0.00992871\pi$
$644$	5.51120	+	4.86154i	0.217172	+	0.191571i
$645$	−0.000308576		0.00662189i	−1.21502e−5		0.000260737i
$646$	−0.361134	+	2.04809i	−0.0142086	+	0.0805811i
$647$	7.51759	−	13.0208i	0.295547	−	0.511902i	−0.679565	−	0.733615i	$-0.737831\pi$
$647$	7.51759	−	13.0208i	0.295547	−	0.511902i	0.975112	+	0.221713i	$0.0711648\pi$
$648$	15.9063	−	5.57902i	0.624859	−	0.219165i
$649$	54.1799	−	31.2808i	2.12675	−	1.22788i
$650$	−5.26688	−	4.41943i	−0.206584	−	0.173344i
$651$	15.1027	−	33.7876i	0.591923	−	1.32424i
$652$	2.08110	+	11.8025i	0.0815022	+	0.462222i
$653$	15.1536	−	2.67199i	0.593007	−	0.104563i	0.130912	−	0.991394i	$-0.458209\pi$
$653$	15.1536	−	2.67199i	0.593007	−	0.104563i	0.462094	+	0.886831i	$0.347098\pi$
$654$	−0.970708	+	0.302937i	−0.0379577	+	0.0118458i
$655$	0.00475771	+	0.00399219i	0.000185899	+	0.000155988i
$656$	17.4286			0.680471
$657$	17.5778	+	12.4624i	0.685775	+	0.486204i
$658$	7.65884	−	6.11043i	0.298573	−	0.238209i
$659$	−5.58157	−	15.3352i	−0.217427	−	0.597376i	0.782245	−	0.622971i	$-0.214074\pi$
$659$	−5.58157	−	15.3352i	−0.217427	−	0.597376i	−0.999672	+	0.0255942i	$0.991852\pi$
$660$	0.00641882	−	0.00489550i	0.000249852	−	0.000190557i
$661$	29.6565	−	5.22925i	1.15351	−	0.203394i	0.436000	−	0.899947i	$-0.356395\pi$
$661$	29.6565	−	5.22925i	1.15351	−	0.203394i	0.717506	+	0.696553i	$0.245284\pi$
$662$	12.7879	−	2.25486i	0.497017	−	0.0876375i
$663$	−0.487046	−	3.78522i	−0.0189153	−	0.147006i
$664$	1.23560	+	3.39478i	0.0479505	+	0.131743i
$665$	−0.00605170	+	0.00482821i	−0.000234675	+	0.000187230i
$666$	−2.97011	−	0.814539i	−0.115090	−	0.0315628i
$667$	−13.3465			−0.516777
$668$	−6.21898	−	5.21834i	−0.240620	−	0.201904i
$669$	30.7790	+	28.3703i	1.18999	+	1.09686i
$670$	−0.000587993	0	0.000103679i	−2.27162e−5	0	4.00547e-6i
$671$	−2.98890	−	16.9509i	−0.115385	−	0.654383i
$672$	13.5138	+	18.6577i	0.521305	+	0.719737i
$673$	8.51271	+	7.14301i	0.328141	+	0.275343i	0.791942	−	0.610597i	$-0.209070\pi$
$673$	8.51271	+	7.14301i	0.328141	+	0.275343i	−0.463801	+	0.885939i	$0.653515\pi$
$674$	2.99677	−	1.73018i	0.115431	−	0.0666442i
$675$	−5.39991	−	25.4134i	−0.207843	−	0.978162i
$676$	−4.74182	+	8.21308i	−0.182378	+	0.315888i
$677$	5.39839	−	30.6158i	0.207477	−	1.17666i	−0.686017	−	0.727585i	$-0.740643\pi$
$677$	5.39839	−	30.6158i	0.207477	−	1.17666i	0.893494	−	0.449075i	$-0.148246\pi$
$678$	11.3297	−	5.85570i	0.435114	−	0.224887i
$679$	3.56318	+	3.14315i	0.136742	+	0.120623i
$680$	−0.000288169	0	0.000791738i	−1.10508e−5	0	3.03618e-5i
$681$	−5.02253	+	5.44897i	−0.192464	+	0.208805i
$682$	−12.2759	+	14.6298i	−0.470067	+	0.560204i
$683$	17.3662	−	10.0264i	0.664500	−	0.383649i	−0.129490	−	0.991581i	$-0.541334\pi$
$683$	17.3662	−	10.0264i	0.664500	−	0.383649i	0.793989	+	0.607932i	$0.208001\pi$
$684$	−27.2443	+	2.22264i	−1.04171	+	0.0849848i
$685$	0.00489426	−	0.00282570i	0.000187000	−	0.000107965i
$686$	−2.27627	+	8.96382i	−0.0869085	+	0.342240i
$687$	−17.8408	+	13.6068i	−0.680669	+	0.519132i
$688$	−16.4151	−	5.97461i	−0.625820	−	0.227780i
$689$	5.03151	+	28.5351i	0.191685	+	1.08710i
$690$	0.000765219	0	9.84610e-5i	2.91314e−5	0	3.74835e-6i
$691$	−3.41783	+	4.07321i	−0.130020	+	0.154952i	−0.827127	−	0.562016i	$-0.810026\pi$
$691$	−3.41783	+	4.07321i	−0.130020	+	0.154952i	0.697106	+	0.716968i	$0.254471\pi$
$692$	−21.0610	−	36.4787i	−0.800618	−	1.38671i
$693$	25.7529	+	27.3782i	0.978270	+	1.04001i
$694$	−0.394867	+	0.683930i	−0.0149890	+	0.0259616i
$695$	7.99067e−5	0	0.000219542i	3.03103e−6	0	8.32769e-6i
$696$	−26.6233	−	5.98420i	−1.00915	−	0.226830i
$697$	−4.16334	+	3.49346i	−0.157698	+	0.132324i
$698$	−6.75060	+	5.66443i	−0.255514	+	0.214402i
$699$	8.91078	+	17.2407i	0.337037	+	0.652103i
$700$	20.3361	−	11.0802i	0.768633	−	0.418791i
$701$			16.0144i			0.604857i	0.953172	+	0.302428i	$0.0977973\pi$
$701$			16.0144i			0.604857i	−0.953172	+	0.302428i	$0.902203\pi$
$702$	−6.62505	+	2.67615i	−0.250047	+	0.101005i
$703$	9.26641	+	5.34997i	0.349489	+	0.201778i
$704$	4.24605	+	11.6659i	0.160029	+	0.439676i
$705$	−0.000336140		0.00721341i	−1.26598e−5		0.000271673i
$706$	−1.33841	+	0.235998i	−0.0503718	+	0.00888192i
$707$	11.0463	+	2.23057i	0.415439	+	0.0838893i
$708$	−39.0837	−	8.78497i	−1.46885	−	0.330159i
$709$	−0.229579	+	0.0835600i	−0.00862202	+	0.00313816i	−0.346328	−	0.938114i	$-0.612571\pi$
$709$	−0.229579	+	0.0835600i	−0.00862202	+	0.00313816i	0.337706	+	0.941252i	$0.390349\pi$
$710$	0.00122696	+	0.00212516i	4.60470e−5	+	7.97558e-5i
$711$	7.47822	−	1.95685i	0.280455	−	0.0733876i
$712$	5.24849	+	3.03022i	0.196696	+	0.113562i
$713$	12.0412	−	4.38265i	0.450948	−	0.164132i
$714$	−1.77604	−	0.445590i	−0.0664667	−	0.0166758i
$715$	−0.00561597	+	0.00471236i	−0.000210025	+	0.000176232i
$716$	−14.7699	+	40.5801i	−0.551979	+	1.51655i
$717$	−20.0443	−	8.37157i	−0.748569	−	0.312642i
$718$	−1.98368	+	11.2500i	−0.0740305	+	0.419848i
$719$	−17.6366	+	30.5475i	−0.657734	+	1.13923i	0.323467	+	0.946239i	$0.395152\pi$
$719$	−17.6366	+	30.5475i	−0.657734	+	1.13923i	−0.981201	+	0.192989i	$0.938182\pi$
$720$	−0.00430907		0.000402474i	−0.000160590		1.49993e-5i
$721$	33.2578	−	26.5340i	1.23859	−	0.988178i
$722$	−3.97810	−	0.701446i	−0.148049	−	0.0261051i
$723$	−7.62521	+	33.9240i	−0.283584	+	1.26165i
$724$	−10.1147	−	12.0542i	−0.375909	−	0.447991i
$725$	−14.3848	+	39.5219i	−0.534238	+	1.46781i
$726$	−4.53716	−	8.77855i	−0.168390	−	0.325803i
$727$	28.8861	−	34.4251i	1.07133	−	1.27676i	0.112229	−	0.993682i	$-0.464201\pi$
$727$	28.8861	−	34.4251i	1.07133	−	1.27676i	0.959098	−	0.283075i	$-0.0913546\pi$
$728$	−8.51002	−	10.6665i	−0.315402	−	0.395326i
$729$	−25.9530	−	7.44587i	−0.961223	−	0.275773i
$730$	0.00100821	+	0.00174627i	3.73155e−5	+	6.46324e-5i
$731$	5.11882	−	1.86310i	0.189326	−	0.0689092i
$732$	−5.94896	+	9.27785i	−0.219880	+	0.342919i
$733$	−28.0884	−	33.4744i	−1.03747	−	1.23641i	−0.971115	−	0.238610i	$-0.923308\pi$
$733$	−28.0884	−	33.4744i	−1.03747	−	1.23641i	−0.0663525	−	0.997796i	$-0.521136\pi$
$734$	3.46755	+	1.26208i	0.127989	+	0.0465843i
$735$	−0.00386077	−	0.00561753i	−0.000142407	−	0.000207206i
$736$	−1.38510	+	7.85530i	−0.0510555	+	0.289550i
$737$		−	10.0712i		−	0.370976i
$738$	8.30064	+	5.88502i	0.305551	+	0.216631i
$739$	35.4098			1.30257			0.651286	−	0.758833i	$-0.274230\pi$
$739$	35.4098			1.30257			0.651286	+	0.758833i	$0.274230\pi$
$740$	0.00154997	+	0.00130058i	5.69781e−5	+	4.78103e-5i
$741$	24.6211	−	3.16800i	0.904477	−	0.116379i
$742$	13.6270	+	2.75169i	0.500264	+	0.101018i
$743$	14.2073	+	16.9316i	0.521216	+	0.621161i	0.960868	−	0.277007i	$-0.0893426\pi$
$743$	14.2073	+	16.9316i	0.521216	+	0.621161i	−0.439652	+	0.898168i	$0.644898\pi$
$744$	25.9847	−	3.34346i	0.952646	−	0.122577i
$745$	0.000509971	0	8.99217e-5i	1.86839e−5	0	3.29448e-6i
$746$			16.1760i			0.592246i
$747$	1.53045	−	5.58058i	0.0559961	−	0.204183i
$748$	−5.74482	−	3.31677i	−0.210051	−	0.121273i
$749$	−5.55390	+	9.09297i	−0.202935	+	0.332250i
$750$	0.00106637	−	0.00474423i	3.89385e−5	−	0.000173235i
$751$	7.28917	+	41.3389i	0.265985	+	1.50848i	0.766214	+	0.642585i	$0.222138\pi$
$751$	7.28917	+	41.3389i	0.265985	+	1.50848i	−0.500229	+	0.865893i	$0.666751\pi$
$752$	−17.8815	−	6.50832i	−0.652070	−	0.237334i
$753$	34.6913	−	17.9301i	1.26422	−	0.653408i
$754$	11.3910	+	2.00855i	0.414837	+	0.0731470i
$755$	−0.000676743	0		−2.46292e−5	0
$756$	−0.243536	−	24.0660i	−0.00885734	−	0.875274i
$757$	7.91633			0.287724			0.143862	−	0.989598i	$-0.454048\pi$
$757$	7.91633			0.287724			0.143862	+	0.989598i	$0.454048\pi$
$758$	−3.30875	−	0.583421i	−0.120179	−	0.0211908i
$759$	−0.605786	+	12.9999i	−0.0219886	+	0.471866i
$760$	−0.00514988	−	0.00187440i	−0.000186806	−	6.79917e-5i
$761$	−5.73553	−	32.5278i	−0.207913	−	1.17913i	−0.892790	−	0.450474i	$-0.851255\pi$
$761$	−5.73553	−	32.5278i	−0.207913	−	1.17913i	0.684877	−	0.728659i	$-0.259856\pi$
$762$	5.72646	−	1.78710i	0.207448	−	0.0647398i
$763$	−0.0768760	+	3.10964i	−0.00278310	+	0.112576i
$764$	−31.6262	−	18.2594i	−1.14420	−	0.660602i
$765$	0.00111003		0.000767586i	4.01331e−5		2.77521e-5i
$766$			0.141783i			0.00512283i
$767$	35.8267	+	6.31721i	1.29363	+	0.228101i
$768$	−0.287928	+	0.689394i	−0.0103897	+	0.0248764i
$769$	−19.7511	−	23.5384i	−0.712241	−	0.848816i	0.281611	−	0.959529i	$-0.409131\pi$
$769$	−19.7511	−	23.5384i	−0.712241	−	0.848816i	−0.993852	+	0.110713i	$0.964687\pi$
$770$	0.00112097	+	0.00333401i	4.03969e−5	+	0.000120149i
$771$	30.8679	+	40.4731i	1.11168	+	1.45760i
$772$	−24.5120	−	20.5680i	−0.882205	−	0.740258i
$773$	31.5260			1.13391			0.566956	−	0.823748i	$-0.308121\pi$
$773$	31.5260			1.13391			0.566956	+	0.823748i	$0.308121\pi$
$774$	−5.80055	−	8.38832i	−0.208496	−	0.301512i
$775$		−	40.3805i		−	1.45051i
$776$	−0.584066	+	3.31240i	−0.0209668	+	0.118908i
$777$	−5.27957	+	7.80253i	−0.189403	+	0.279914i
$778$	−0.349471	−	0.127197i	−0.0125291	−	0.00456023i
$779$	−22.7232	−	27.0805i	−0.814145	−	0.970260i
$780$	0.00468911		0.000218509i	0.000167897		7.82389e-6i
$781$	−38.8960	+	14.1570i	−1.39181	+	0.506577i
$782$	−0.316995	−	0.549052i	−0.0113357	−	0.0196341i
$783$	29.2443	+	32.4837i	1.04511	+	1.16087i
$784$	17.1617	−	5.30183i	0.612919	−	0.189351i
$785$	0.00416432	−	0.00496285i	0.000148631	−	0.000177132i
$786$	−9.54461	−	0.444772i	−0.340445	−	0.0158645i
$787$	−16.3204	+	44.8400i	−0.581760	+	1.59837i	0.203411	+	0.979093i	$0.434797\pi$
$787$	−16.3204	+	44.8400i	−0.581760	+	1.59837i	−0.785171	+	0.619279i	$0.787425\pi$
$788$	11.5977	+	13.8216i	0.413151	+	0.492374i
$789$	27.7162	−	8.64960i	0.986721	−	0.307934i
$790$	0.000712390	0	0.000125614i	2.53457e−5	0	4.46913e-6i
$791$	−5.82282	−	38.5753i	−0.207036	−	1.37158i
$792$	−7.03721	+	25.6603i	−0.250056	+	0.911799i
$793$	5.00447	−	8.66800i	0.177714	−	0.307810i
$794$	1.45061	−	8.22681i	0.0514802	−	0.291959i
$795$	−0.00814718	+	0.00621368i	−0.000288951	+	0.000220377i
$796$	−6.68976	+	18.3800i	−0.237112	+	0.651460i
$797$	−29.5128	+	24.7642i	−1.04540	+	0.877192i	−0.992602	−	0.121413i	$-0.961257\pi$
$797$	−29.5128	+	24.7642i	−1.04540	+	0.877192i	−0.0527949	+	0.998605i	$0.516813\pi$
$798$	2.89835	−	11.5523i	0.102600	−	0.408947i
$799$	5.57608	−	2.02953i	0.197267	−	0.0717995i
$800$	21.7685	+	12.5681i	0.769633	+	0.444348i
$801$	−4.05087	−	8.82183i	−0.143130	−	0.311704i
$802$	−4.61410	−	7.99186i	−0.162930	−	0.282202i
$803$	−31.9614	+	11.6330i	−1.12789	+	0.410519i
$804$	−4.37058	+	4.74166i	−0.154138	+	0.167225i
$805$	0.000467137	−	0.00231337i	1.64644e−5	−	8.15356e-5i
$806$	−10.9366	+	1.92842i	−0.385226	+	0.0679257i
$807$	14.5163	−	7.50269i	0.510998	−	0.264107i
$808$	2.72847	+	7.49641i	0.0959873	+	0.263723i
$809$	−36.7753	−	21.2322i	−1.29295	−	0.746486i	−0.313775	−	0.949497i	$-0.601594\pi$
$809$	−36.7753	−	21.2322i	−1.29295	−	0.746486i	−0.979176	+	0.203011i	$0.934927\pi$
$810$	−0.00191637	−	0.00164671i	−6.73342e−5	−	5.78594e-5i
$811$		−	22.9043i		−	0.804277i	−0.915579	−	0.402139i	$-0.868267\pi$
$811$		−	22.9043i		−	0.804277i	0.915579	−	0.402139i	$-0.131733\pi$
$812$	−20.3083	+	33.2493i	−0.712683	+	1.16682i
$813$	6.79393	+	0.316593i	0.238274	+	0.0111034i
$814$	3.72408	−	3.12487i	0.130529	−	0.109527i
$815$	0.00294830	−	0.00247392i	0.000103275	−	8.66577e-5i
$816$	1.05946	+	3.39485i	0.0370884	+	0.118843i
$817$	12.1186	+	33.2955i	0.423975	+	1.16486i
$818$	−4.45012	+	7.70784i	−0.155595	+	0.269498i
$819$	1.23828	+	21.8215i	0.0432689	+	0.762506i
$820$	−0.00334243	−	0.00578925i	−0.000116723	−	0.000202169i
$821$	1.32257	−	1.57617i	0.0461579	−	0.0550089i	−0.742472	−	0.669878i	$-0.766347\pi$
$821$	1.32257	−	1.57617i	0.0461579	−	0.0550089i	0.788629	+	0.614869i	$0.210791\pi$
$822$	−3.35076	+	8.02282i	−0.116871	+	0.279828i
$823$	0.562875	+	3.19222i	0.0196206	+	0.111274i	0.993045	−	0.117734i	$-0.0375630\pi$
$823$	0.562875	+	3.19222i	0.0196206	+	0.111274i	−0.973425	+	0.229008i	$0.926452\pi$
$824$	28.3018	+	10.3010i	0.985939	+	0.358852i
$825$	37.8427	+	15.8051i	1.31752	+	0.550265i
$826$	9.09815	−	14.8957i	0.316565	−	0.518288i
$827$	47.0423	−	27.1599i	1.63582	−	0.944441i	0.653569	−	0.756867i	$-0.273271\pi$
$827$	47.0423	−	27.1599i	1.63582	−	0.944441i	0.982251	−	0.187574i	$-0.0600624\pi$
$828$	5.92677	−	5.85765i	0.205969	−	0.203568i
$829$	−7.34388	+	4.23999i	−0.255063	+	0.147261i	−0.622081	−	0.782953i	$-0.713712\pi$
$829$	−7.34388	+	4.23999i	−0.255063	+	0.147261i	0.367017	+	0.930214i	$0.380379\pi$
$830$	0.000348080	0	0.000414826i	1.20820e−5	0	1.43988e-5i
$831$	11.8378	+	37.9321i	0.410648	+	1.31585i
$832$	−2.46906	+	6.78368i	−0.0855992	+	0.235182i
$833$	−3.03688	+	4.70647i	−0.105221	+	0.163070i
$834$	−0.302574	−	0.194011i	−0.0104773	−	0.00671804i
$835$	−0.000452721		0.00256751i	−1.56671e−5		8.88523e-5i
$836$	21.5740	−	37.3673i	0.746153	−	1.29237i
$837$	−37.0512	−	19.7038i	−1.28068	−	0.681064i
$838$	0.458929	−	0.264963i	0.0158534	−	0.00915299i
$839$	−11.5622	−	9.70185i	−0.399172	−	0.334945i	0.421002	−	0.907060i	$-0.361679\pi$
$839$	−11.5622	−	9.70185i	−0.399172	−	0.334945i	−0.820173	+	0.572115i	$0.806123\pi$
$840$	0.00196909	−	0.00440522i	6.79401e−5	−	0.000151995i
$841$	−7.25090	−	41.1219i	−0.250031	−	1.41800i
$842$	−7.54523	+	1.33043i	−0.260026	+	0.0458496i
$843$	0.676221	−	3.00846i	0.0232903	−	0.103617i
$844$	−31.8522	−	26.7272i	−1.09640	−	0.919987i
$845$	0.00304558			0.000104771
$846$	−6.31870	−	9.13764i	−0.217241	−	0.314158i
$847$	−29.8891	+	4.51168i	−1.02700	+	0.155023i
$848$	−9.23471	−	25.3722i	−0.317121	−	0.871284i
$849$	7.12307	+	2.97497i	0.244463	+	0.102101i
$850$	−1.96753	+	0.346928i	−0.0674856	+	0.0118995i
$851$	−3.21231	+	0.566417i	−0.110117	+	0.0194165i
$852$	24.4566	+	10.2144i	0.837868	+	0.349938i
$853$	5.23344	+	14.3788i	0.179190	+	0.492319i	0.996473	−	0.0839170i	$-0.0267430\pi$
$853$	5.23344	+	14.3788i	0.179190	+	0.492319i	−0.817283	+	0.576236i	$0.804521\pi$
$854$	−2.99494	−	3.75386i	−0.102485	−	0.128455i
$855$	0.00499278	+	0.00722018i	0.000170749	+	0.000246925i
$856$	−7.54264			−0.257802
$857$	−13.4455	−	11.2821i	−0.459289	−	0.385389i	0.383580	−	0.923507i	$-0.374691\pi$
$857$	−13.4455	−	11.2821i	−0.459289	−	0.385389i	−0.842869	+	0.538118i	$0.819135\pi$
$858$	2.47342	−	11.0041i	0.0844412	−	0.375673i
$859$	−15.6157	+	2.75347i	−0.532801	+	0.0939472i	−0.433575	−	0.901118i	$-0.642748\pi$
$859$	−15.6157	+	2.75347i	−0.532801	+	0.0939472i	−0.0992264	+	0.995065i	$0.531637\pi$
$860$	0.00116348	+	0.00659842i	3.96743e−5	+	0.000225004i
$861$	25.2078	−	18.2580i	0.859079	−	0.622231i
$862$	−1.45649	−	1.22214i	−0.0496081	−	0.0416261i
$863$	−1.76440	+	1.01868i	−0.0600610	+	0.0346762i	−0.529730	−	0.848166i	$-0.677707\pi$
$863$	−1.76440	+	1.01868i	−0.0600610	+	0.0346762i	0.469669	+	0.882843i	$0.344373\pi$
$864$	22.1539	−	13.8411i	0.753690	−	0.470884i
$865$	−0.00676353	+	0.0117148i	−0.000229967	+	0.000398315i
$866$	−2.56031	+	14.5202i	−0.0870028	+	0.493417i
$867$	23.8535	+	15.2949i	0.810107	+	0.519441i
$868$	7.40402	−	36.6664i	0.251309	−	1.24454i
$869$	−4.17328	+	11.4660i	−0.141569	+	0.388957i
$870$	0.00121852	+	0.00390454i	4.13117e−5	+	0.000132376i
$871$	3.76439	−	4.48622i	0.127551	−	0.152010i
$872$	−1.90697	+	1.10099i	−0.0645783	+	0.0372843i
$873$	3.83186	−	3.78717i	0.129689	−	0.128176i
$874$	3.57132	−	2.06190i	0.120802	−	0.0697448i
$875$	−0.0126939	−	0.00775331i	−0.000429132	−	0.000262110i
$876$	20.0963	+	8.39328i	0.678991	+	0.283583i
$877$	17.0905	+	6.22045i	0.577106	+	0.210050i	0.614049	−	0.789268i	$-0.289540\pi$
$877$	17.0905	+	6.22045i	0.577106	+	0.210050i	−0.0369427	+	0.999317i	$0.511762\pi$
$878$	1.43144	+	8.11809i	0.0483087	+	0.273972i
$879$	4.73576	−	11.3390i	0.159733	−	0.382454i
$880$	0.00439119	−	0.00523322i	0.000148027	−	0.000176412i
$881$	−13.3725	−	23.1618i	−0.450530	−	0.780341i	0.547889	−	0.836551i	$-0.315432\pi$
$881$	−13.3725	−	23.1618i	−0.450530	−	0.780341i	−0.998419	+	0.0562101i	$0.982098\pi$
$882$	9.96380	+	3.26984i	0.335499	+	0.110101i
$883$	10.5208	−	18.2226i	0.354054	−	0.613240i	−0.632901	−	0.774232i	$-0.718136\pi$
$883$	10.5208	−	18.2226i	0.354054	−	0.613240i	0.986956	+	0.160992i	$0.0514694\pi$
$884$	−1.31930	−	3.62475i	−0.0443729	−	0.121914i
$885$	0.00383244	+	0.0122804i	0.000128826	+	0.000412801i
$886$	10.6861	−	8.96668i	0.359006	−	0.301242i
$887$	−17.0586	+	14.3138i	−0.572771	+	0.480612i	−0.882564	−	0.470192i	$-0.844185\pi$
$887$	−17.0586	+	14.3138i	−0.572771	+	0.480612i	0.309793	+	0.950804i	$0.399740\pi$
$888$	−6.66183	−	0.310437i	−0.223556	−	0.0104176i
$889$	0.453511	−	18.3445i	0.0152103	−	0.615256i
$890$		0	0.000908428i		0	3.04506e-5i
$891$	32.9676	−	27.0105i	1.10445	−	0.904885i
$892$	36.6404	+	21.1543i	1.22681	+	0.708300i
$893$	13.2011	+	36.2697i	0.441758	+	1.21372i
$894$	−0.707732	+	0.365788i	−0.0236701	+	0.0122338i
$895$	0.0136576	−	0.00240820i	0.000456523	−	8.04973e-5i
$896$	22.5466	+	19.8888i	0.753230	+	0.664439i
$897$	−5.12892	+	5.56439i	−0.171250	+	0.185790i
$898$	10.9046	−	3.96896i	0.363892	−	0.132446i
$899$	33.9668	+	58.8322i	1.13286	+	1.96216i
$900$	−10.9580	−	23.8639i	−0.365267	−	0.795464i
$901$	7.29169	+	4.20986i	0.242922	+	0.140251i
$902$	−15.0929	+	5.49336i	−0.502538	+	0.182909i
$903$	−30.0009	+	8.55494i	−0.998368	+	0.284691i
$904$	21.1557	−	17.7517i	0.703627	−	0.590414i
$905$	−0.00172835	+	0.00474860i	−5.74522e−5	+	0.000157849i
$906$	0.827847	−	0.631381i	0.0275034	−	0.0209762i
$907$	0.624448	−	3.54142i	0.0207345	−	0.117591i	−0.972684	−	0.232134i	$-0.925429\pi$
$907$	0.624448	−	3.54142i	0.0207345	−	0.117591i	0.993418	+	0.114543i	$0.0365404\pi$
$908$	−3.74506	+	6.48664i	−0.124284	+	0.215267i
$909$	3.37956	−	12.3231i	0.112093	−	0.408733i
$910$	−0.000746842		0.00190413i	−2.47576e−5		6.31214e-5i
$911$	−51.8774	−	9.14738i	−1.71877	−	0.303066i	−0.774585	−	0.632470i	$-0.782041\pi$
$911$	−51.8774	−	9.14738i	−1.71877	−	0.303066i	−0.944189	+	0.329403i	$0.893152\pi$
$912$	−22.0818	+	6.89125i	−0.731203	+	0.228192i
$913$	5.87135	+	6.99721i	0.194313	+	0.231574i
$914$	3.09562	−	8.50515i	0.102394	−	0.281326i
$915$	0.00353554		0.000164754i	0.000116881		5.44660e-6i
$916$	−14.5773	+	17.3725i	−0.481647	+	0.574005i
$917$	−10.6724	+	27.2100i	−0.352432	+	0.898555i
$918$	−0.641738	+	1.97459i	−0.0211805	+	0.0651713i
$919$	−27.2723	−	47.2370i	−0.899629	−	1.55820i	−0.827969	−	0.560774i	$-0.810504\pi$
$919$	−27.2723	−	47.2370i	−0.899629	−	1.55820i	−0.0716603	−	0.997429i	$-0.522830\pi$
$920$	0.00156994		0.000571410i	5.17592e−5		1.88388e-5i
$921$	12.4000	+	0.577831i	0.408593	+	0.0190402i
$922$	−0.327073	−	0.389790i	−0.0107716	−	0.0128371i
$923$	−22.6179	−	8.23224i	−0.744477	−	0.270968i
$924$	31.4641	+	21.2901i	1.03509	+	0.700394i
$925$	−1.78494	+	10.1229i	−0.0586884	+	0.332838i
$926$			17.1535i			0.563700i
$927$	−27.4384	−	39.6794i	−0.901195	−	1.30324i
$928$	−42.2874			−1.38815
$929$	−32.1029	−	26.9376i	−1.05326	−	0.883793i	−0.0598303	−	0.998209i	$-0.519056\pi$
$929$	−32.1029	−	26.9376i	−1.05326	−	0.883793i	−0.993433	+	0.114416i	$0.963500\pi$
$930$	−0.00238151	−	0.00312256i	−7.80928e−5	−	0.000102393i
$931$	−30.6133	−	19.7534i	−1.00331	−	0.647392i
$932$	12.6086	+	15.0264i	0.413010	+	0.492206i
$933$	−15.5189	+	37.1573i	−0.508065	+	1.21647i
$934$	−0.700821	−	0.123574i	−0.0229316	−	0.00404345i
$935$			0.00213030i			6.96683e-5i
$936$	−12.7260	+	8.80008i	−0.415963	+	0.287639i
$937$	−24.5420	−	14.1693i	−0.801751	−	0.462891i	0.0423320	−	0.999104i	$-0.486521\pi$
$937$	−24.5420	−	14.1693i	−0.801751	−	0.462891i	−0.844083	+	0.536212i	$0.819855\pi$
$938$	−1.34434	−	2.46735i	−0.0438943	−	0.0805619i
$939$	−39.4944	+	12.3253i	−1.28885	+	0.402222i
$940$	0.00126741	+	0.00718785i	4.13384e−5	+	0.000234442i
$941$	−15.2577	−	5.55334i	−0.497386	−	0.181034i	0.0811321	−	0.996703i	$-0.474146\pi$
$941$	−15.2577	−	5.55334i	−0.497386	−	0.181034i	−0.578518	+	0.815670i	$0.696369\pi$
$942$	−0.463949	+	9.95614i	−0.0151163	+	0.324389i
$943$	10.6130	+	1.87136i	0.345608	+	0.0609399i
$944$	−33.8999			−1.10335
$945$	−0.00665405	+	0.00393203i	−0.000216456	+	0.000127909i
$946$	16.0984			0.523405
$947$	9.66361	+	1.70396i	0.314025	+	0.0553711i	0.328440	−	0.944525i	$-0.393477\pi$
$947$	9.66361	+	1.70396i	0.314025	+	0.0553711i	−0.0144143	+	0.999896i	$0.504588\pi$
$948$	6.94073	−	3.58729i	0.225424	−	0.116510i
$949$	−18.5854	−	6.76454i	−0.603308	−	0.219586i
$950$	−2.25660	−	12.7978i	−0.0732138	−	0.415216i
$951$	−10.9099	+	48.5374i	−0.353778	+	1.57393i
$952$	−3.96388	−	0.0979946i	−0.128470	−	0.00317602i
$953$	−34.8176	−	20.1019i	−1.12785	−	0.651166i	−0.184458	−	0.982840i	$-0.559053\pi$
$953$	−34.8176	−	20.1019i	−1.12785	−	0.651166i	−0.943394	+	0.331675i	$0.892386\pi$
$954$	4.16911	−	15.2022i	0.134980	−	0.492188i
$955$			0.0117277i			0.000379499i
$956$	−21.6218	−	3.81251i	−0.699300	−	0.123305i
$957$	−68.4296	+	8.80486i	−2.21201	+	0.284621i
$958$	11.4888	+	13.6919i	0.371188	+	0.442364i
$959$	19.9449	+	17.5938i	0.644054	+	0.568133i
$960$	−0.00253194		0.000325785i	−8.17179e−5		1.05147e-5i
$961$	−26.2167	−	21.9984i	−0.845701	−	0.709627i
$962$	2.82691			0.0911432
$963$	9.85584	+	6.98763i	0.317600	+	0.225173i
$964$			35.1435i			1.13190i
$965$	−0.00178439	+	0.0101198i	−5.74415e−5	+	0.000325767i
$966$	1.58687	+	3.26573i	0.0510566	+	0.105073i
$967$	−6.39685	−	2.32826i	−0.205709	−	0.0748719i	0.237111	−	0.971483i	$-0.423800\pi$
$967$	−6.39685	−	2.32826i	−0.205709	−	0.0748719i	−0.442820	+	0.896611i	$0.646022\pi$
$968$	−13.7545	−	16.3920i	−0.442087	−	0.526859i
$969$	3.89360	−	6.07236i	0.125081	−	0.195072i
$970$	0.000473766	0	0.000172437i	1.52117e−5	0	5.53661e-6i
$971$	−14.6415	−	25.3599i	−0.469869	−	0.813836i	0.529538	−	0.848286i	$-0.322365\pi$
$971$	−14.6415	−	25.3599i	−0.469869	−	0.813836i	−0.999406	+	0.0344500i	$0.989032\pi$
$972$	−27.2434	−	1.58996i	−0.873832	−	0.0509980i
$973$	−0.859463	+	0.685703i	−0.0275531	+	0.0219826i
$974$	−11.2124	+	13.3624i	−0.359269	+	0.428160i
$975$	10.9495	+	21.1852i	0.350665	+	0.678471i
$976$	−3.18995	+	8.76432i	−0.102108	+	0.280539i
$977$	−5.03211	−	5.99703i	−0.160991	−	0.191862i	0.679518	−	0.733659i	$-0.262189\pi$
$977$	−5.03211	−	5.99703i	−0.160991	−	0.191862i	−0.840510	+	0.541796i	$0.817744\pi$
$978$	−1.29851	+	5.77698i	−0.0415218	+	0.184727i
$979$	15.0904	+	2.66085i	0.482291	+	0.0850410i
$980$	−0.00505236	−	0.00468384i	−0.000161392	−	0.000149620i
$981$	3.51179	+	0.328006i	0.112123	+	0.0104724i
$982$	−2.71764	+	4.70709i	−0.0867233	+	0.150209i
$983$	−1.04697	+	5.93768i	−0.0333932	+	0.189382i	−0.996941	−	0.0781524i	$-0.975098\pi$
$983$	−1.04697	+	5.93768i	−0.0333932	+	0.189382i	0.963548	+	0.267535i	$0.0862090\pi$
$984$	20.3316	+	8.49156i	0.648148	+	0.270701i
$985$	0.00198176	−	0.00544485i	6.31442e−5	−	0.000173487i
$986$	2.57475	−	2.16048i	0.0819969	−	0.0688036i
$987$	−32.6809	+	9.31914i	−1.04024	+	0.296632i
$988$	23.5773	−	8.58143i	0.750093	−	0.273012i
$989$	−9.35438	−	5.40075i	−0.297452	−	0.171734i
$990$	0.00385845	−	0.00100965i	0.000122630	−	3.20889e-5i
$991$	−11.3468	−	19.6532i	−0.360442	−	0.624304i	0.627592	−	0.778543i	$-0.284041\pi$
$991$	−11.3468	−	19.6532i	−0.360442	−	0.624304i	−0.988034	+	0.154239i	$0.950707\pi$
$992$	38.1519	−	13.8861i	1.21132	−	0.440886i
$993$	−43.9431	−	9.87723i	−1.39449	−	0.313444i
$994$	−7.63947	+	8.66035i	−0.242309	+	0.274690i
$995$	0.00618594	−	0.00109075i	0.000196107	−	3.45790e-5i
$996$	0.272251	−	5.84238i	0.00862661	−	0.185123i
$997$	3.33531	+	9.16369i	0.105630	+	0.290217i	0.981236	−	0.192809i	$-0.0617598\pi$
$997$	3.33531	+	9.16369i	0.105630	+	0.290217i	−0.875606	+	0.483026i	$0.839538\pi$
$998$	−2.74449	−	1.58453i	−0.0868752	−	0.0501574i
$999$	8.41730	+	6.57727i	0.266312	+	0.208096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.38.14	yes	132
3.2	odd	2		567.2.ba.a.521.9		132
7.5	odd	6		189.2.bd.a.173.9	yes	132
21.5	even	6		567.2.bd.a.278.14		132
27.5	odd	18		189.2.bd.a.59.9	yes	132
27.22	even	9		567.2.bd.a.206.14		132
189.5	even	18	inner	189.2.ba.a.5.14	✓	132
189.103	odd	18		567.2.ba.a.530.9		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.14	✓	132	189.5	even	18	inner
189.2.ba.a.38.14	yes	132	1.1	even	1	trivial
189.2.bd.a.59.9	yes	132	27.5	odd	18
189.2.bd.a.173.9	yes	132	7.5	odd	6
567.2.ba.a.521.9		132	3.2	odd	2
567.2.ba.a.530.9		132	189.103	odd	18
567.2.bd.a.206.14		132	27.22	even	9
567.2.bd.a.278.14		132	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.491776 + 0.0867134i) q^{2} +(-1.45806 - 0.934910i) q^{3} +(-1.64506 - 0.598753i) q^{4} +(9.76251e-5 + 0.000553660i) q^{5} +(-0.635971 - 0.586200i) q^{6} +(-2.32328 + 1.26584i) q^{7} +(-1.62200 - 0.936464i) q^{8} +(1.25189 + 2.72631i) q^{9} +0.000280742i q^{10} +(-4.66356 - 0.822312i) q^{11} +(1.83882 + 2.41100i) q^{12} +(-1.77003 - 2.10944i) q^{13} +(-1.25230 + 0.421052i) q^{14} +(0.000375278 - 0.000898541i) q^{15} +(1.96567 + 1.64940i) q^{16} -0.800172 q^{17} +(0.379240 + 1.44929i) q^{18} -5.20473i q^{19} +(0.000170906 - 0.000969257i) q^{20} +(4.57094 + 0.326381i) q^{21} +(-2.22212 - 0.808787i) q^{22} +(1.01988 + 1.21545i) q^{23} +(1.48947 + 2.88185i) q^{24} +(4.69846 - 1.71010i) q^{25} +(-0.687542 - 1.19086i) q^{26} +(0.723528 - 5.14553i) q^{27} +(4.57987 - 0.691318i) q^{28} +(-5.40692 + 6.44372i) q^{29} +(0.000262469 - 0.000409339i) q^{30} +(2.76219 - 7.58906i) q^{31} +(3.23144 + 3.85108i) q^{32} +(6.03097 + 5.55899i) q^{33} +(-0.393506 - 0.0693856i) q^{34} +(-0.000927658 - 0.00116273i) q^{35} +(-0.427042 - 5.23452i) q^{36} +(-1.02790 + 1.78038i) q^{37} +(0.451320 - 2.55956i) q^{38} +(0.608677 + 4.73051i) q^{39} +(0.000360134 - 0.000989460i) q^{40} +(5.20305 - 4.36588i) q^{41} +(2.21958 + 0.556868i) q^{42} +(-6.39715 + 2.32837i) q^{43} +(7.17948 + 4.14508i) q^{44} +(-0.00138723 + 0.000959276i) q^{45} +(0.396159 + 0.686167i) q^{46} +(-6.96860 + 2.53636i) q^{47} +(-1.32404 - 4.24265i) q^{48} +(3.79528 - 5.88182i) q^{49} +(2.45888 - 0.433567i) q^{50} +(1.16670 + 0.748089i) q^{51} +(1.64877 + 4.52997i) q^{52} +(-9.11266 - 5.26120i) q^{53} +(0.802000 - 2.46771i) q^{54} -0.00266231i q^{55} +(4.95379 + 0.122467i) q^{56} +(-4.86596 + 7.58882i) q^{57} +(-3.21775 + 2.70001i) q^{58} +(-10.1204 + 8.49198i) q^{59} +(-0.00115536 + 0.00125345i) q^{60} +(1.24316 + 3.41555i) q^{61} +(2.01645 - 3.49260i) q^{62} +(-6.35957 - 4.74930i) q^{63} +(-1.31080 - 2.27037i) q^{64} +(0.000995113 - 0.00118593i) q^{65} +(2.48385 + 3.25675i) q^{66} +(0.369304 + 2.09442i) q^{67} +(1.31633 + 0.479105i) q^{68} +(-0.350717 - 2.72570i) q^{69} +(-0.000355376 - 0.000652243i) q^{70} +(7.56979 - 4.37042i) q^{71} +(0.522528 - 5.59443i) q^{72} +(6.22020 - 3.59123i) q^{73} +(-0.659882 + 0.786416i) q^{74} +(-8.44944 - 1.89921i) q^{75} +(-3.11635 + 8.56210i) q^{76} +(11.8757 - 3.99288i) q^{77} +(-0.110866 + 2.37913i) q^{78} +(0.447434 - 2.53753i) q^{79} +(-0.000721305 + 0.00124934i) q^{80} +(-5.86556 + 6.82607i) q^{81} +(2.93732 - 1.69586i) q^{82} +(-1.47761 - 1.23986i) q^{83} +(-7.32405 - 3.27378i) q^{84} +(-7.81169e-5 - 0.000443023i) q^{85} +(-3.34787 + 0.590319i) q^{86} +(13.9079 - 4.34035i) q^{87} +(6.79425 + 5.70105i) q^{88} -3.23581 q^{89} +(-0.000765391 + 0.000351457i) q^{90} +(6.78250 + 2.66024i) q^{91} +(-0.950016 - 2.61015i) q^{92} +(-11.1225 + 8.48291i) q^{93} +(-3.64693 + 0.643052i) q^{94} +(0.00288165 - 0.000508113i) q^{95} +(-1.11122 - 8.63621i) q^{96} +(-0.614218 - 1.68755i) q^{97} +(2.37646 - 2.56344i) q^{98} +(-3.59637 - 13.7438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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