LMFDB - Embedded newform 135.2.p.a.124.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(4,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.p (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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.11
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.795984 - 0.948617i) q^{2} +(0.595931 - 1.62630i) q^{3} +(0.0810128 + 0.459446i) q^{4} +(2.00198 + 0.996037i) q^{5} +(-1.06839 - 1.85982i) q^{6} +(-2.24130 - 0.395202i) q^{7} +(2.64518 + 1.52719i) q^{8} +(-2.28973 - 1.93833i) q^{9} +O(q^{10})$	\(q+(0.795984 - 0.948617i) q^{2} +(0.595931 - 1.62630i) q^{3} +(0.0810128 + 0.459446i) q^{4} +(2.00198 + 0.996037i) q^{5} +(-1.06839 - 1.85982i) q^{6} +(-2.24130 - 0.395202i) q^{7} +(2.64518 + 1.52719i) q^{8} +(-2.28973 - 1.93833i) q^{9} +(2.53840 - 1.10628i) q^{10} +(-4.87230 + 1.77337i) q^{11} +(0.795478 + 0.142047i) q^{12} +(-0.993836 - 1.18441i) q^{13} +(-2.15894 + 1.81156i) q^{14} +(2.81290 - 2.66225i) q^{15} +(2.67745 - 0.974511i) q^{16} +(-4.61649 + 2.66533i) q^{17} +(-3.66133 + 0.629199i) q^{18} +(2.28767 - 3.96236i) q^{19} +(-0.295440 + 1.00049i) q^{20} +(-1.97838 + 3.40953i) q^{21} +(-2.19602 + 6.03353i) q^{22} +(5.06318 - 0.892775i) q^{23} +(4.06003 - 3.39176i) q^{24} +(3.01582 + 3.98808i) q^{25} -1.91463 q^{26} +(-4.51684 + 2.56869i) q^{27} -1.06177i q^{28} +(4.94693 + 4.15097i) q^{29} +(-0.286437 - 4.78748i) q^{30} +(-0.228069 - 1.29344i) q^{31} +(-0.882557 + 2.42480i) q^{32} +(-0.0195113 + 8.98066i) q^{33} +(-1.14627 + 6.50084i) q^{34} +(-4.09340 - 3.02361i) q^{35} +(0.705061 - 1.20904i) q^{36} +(3.18754 - 1.84032i) q^{37} +(-1.93781 - 5.32410i) q^{38} +(-2.51847 + 0.910455i) q^{39} +(3.77444 + 5.69210i) q^{40} +(3.26644 - 2.74087i) q^{41} +(1.65958 + 4.59066i) q^{42} +(-2.88612 - 7.92956i) q^{43} +(-1.20949 - 2.09490i) q^{44} +(-2.65334 - 6.16115i) q^{45} +(3.18331 - 5.51365i) q^{46} +(-6.68721 - 1.17913i) q^{47} +(0.0107219 - 4.93508i) q^{48} +(-1.71059 - 0.622605i) q^{49} +(6.18371 + 0.313593i) q^{50} +(1.58353 + 9.09617i) q^{51} +(0.463658 - 0.552567i) q^{52} +6.64507i q^{53} +(-1.15863 + 6.32939i) q^{54} +(-11.5206 - 1.30274i) q^{55} +(-5.32509 - 4.46828i) q^{56} +(-5.08071 - 6.08174i) q^{57} +(7.87536 - 1.38864i) q^{58} +(2.83430 + 1.03160i) q^{59} +(1.45104 + 1.07670i) q^{60} +(0.999796 - 5.67013i) q^{61} +(-1.40852 - 0.813210i) q^{62} +(4.36595 + 5.24929i) q^{63} +(4.44699 + 7.70241i) q^{64} +(-0.809923 - 3.36106i) q^{65} +(8.50367 + 7.16697i) q^{66} +(2.22595 + 2.65278i) q^{67} +(-1.59857 - 1.90510i) q^{68} +(1.56538 - 8.76630i) q^{69} +(-6.12653 + 1.47633i) q^{70} +(-0.0130487 - 0.0226011i) q^{71} +(-3.09654 - 8.62409i) q^{72} +(5.00704 + 2.89081i) q^{73} +(0.791465 - 4.48862i) q^{74} +(8.28306 - 2.52802i) q^{75} +(2.00582 + 0.730059i) q^{76} +(11.6211 - 2.04912i) q^{77} +(-1.14099 + 3.11377i) q^{78} +(-12.6845 - 10.6435i) q^{79} +(6.33083 + 0.715887i) q^{80} +(1.48575 + 8.87652i) q^{81} -5.28029i q^{82} +(6.96279 - 8.29793i) q^{83} +(-1.72677 - 0.632744i) q^{84} +(-11.8969 + 0.737738i) q^{85} +(-9.81943 - 3.57398i) q^{86} +(9.69877 - 5.57153i) q^{87} +(-15.5964 - 2.75006i) q^{88} +(2.32308 - 4.02369i) q^{89} +(-7.95659 - 2.38717i) q^{90} +(1.75941 + 3.04738i) q^{91} +(0.820364 + 2.25393i) q^{92} +(-2.23944 - 0.399893i) q^{93} +(-6.44146 + 5.40503i) q^{94} +(8.52651 - 5.65395i) q^{95} +(3.41753 + 2.88032i) q^{96} +(2.48117 + 6.81695i) q^{97} +(-1.95222 + 1.12712i) q^{98} +(14.5937 + 5.38358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.795984	−	0.948617i	0.562846	−	0.670774i	−0.407300	−	0.913294i	$-0.633530\pi$
$2$	0.795984	−	0.948617i	0.562846	−	0.670774i	0.970146	+	0.242521i	$0.0779742\pi$
$3$	0.595931	−	1.62630i	0.344061	−	0.938947i
$3$	0.595931	−	1.62630i	0.344061	−	0.938947i
$4$	0.0810128	+	0.459446i	0.0405064	+	0.229723i
$5$	2.00198	+	0.996037i	0.895311	+	0.445441i
$5$	2.00198	+	0.996037i	0.895311	+	0.445441i
$6$	−1.06839	−	1.85982i	−0.436168	−	0.759270i
$7$	−2.24130	−	0.395202i	−0.847133	−	0.149372i	−0.266800	−	0.963752i	$-0.585966\pi$
$7$	−2.24130	−	0.395202i	−0.847133	−	0.149372i	−0.580333	+	0.814379i	$0.697077\pi$
$8$	2.64518	+	1.52719i	0.935211	+	0.539945i
$9$	−2.28973	−	1.93833i	−0.763244	−	0.646110i
$10$	2.53840	−	1.10628i	0.802713	−	0.349836i
$11$	−4.87230	+	1.77337i	−1.46905	+	0.534692i	−0.947844	−	0.318736i	$-0.896742\pi$
$11$	−4.87230	+	1.77337i	−1.46905	+	0.534692i	−0.521211	+	0.853428i	$0.674520\pi$
$12$	0.795478	+	0.142047i	0.229635	+	0.0410054i
$13$	−0.993836	−	1.18441i	−0.275641	−	0.328496i	0.610409	−	0.792087i	$-0.291005\pi$
$13$	−0.993836	−	1.18441i	−0.275641	−	0.328496i	−0.886049	+	0.463591i	$0.846561\pi$
$14$	−2.15894	+	1.81156i	−0.577000	+	0.484161i
$15$	2.81290	−	2.66225i	0.726287	−	0.687391i
$16$	2.67745	−	0.974511i	0.669361	−	0.243628i
$17$	−4.61649	+	2.66533i	−1.11966	+	0.646438i	−0.941315	−	0.337530i	$-0.890409\pi$
$17$	−4.61649	+	2.66533i	−1.11966	+	0.646438i	−0.178348	+	0.983967i	$0.557075\pi$
$18$	−3.66133	+	0.629199i	−0.862983	+	0.148304i
$19$	2.28767	−	3.96236i	0.524827	−	0.909027i	−0.474755	−	0.880118i	$-0.657463\pi$
$19$	2.28767	−	3.96236i	0.524827	−	0.909027i	0.999582	−	0.0289093i	$-0.00920339\pi$
$20$	−0.295440	+	1.00049i	−0.0660623	+	0.223717i
$21$	−1.97838	+	3.40953i	−0.431718	+	0.744020i
$22$	−2.19602	+	6.03353i	−0.468194	+	1.28635i
$23$	5.06318	−	0.892775i	1.05575	−	0.186156i	0.381278	−	0.924461i	$-0.375484\pi$
$23$	5.06318	−	0.892775i	1.05575	−	0.186156i	0.674468	+	0.738304i	$0.264373\pi$
$24$	4.06003	−	3.39176i	0.828749	−	0.692340i
$25$	3.01582	+	3.98808i	0.603164	+	0.797617i
$26$	−1.91463			−0.375490
$27$	−4.51684	+	2.56869i	−0.869266	+	0.494345i
$28$		−	1.06177i		−	0.200657i
$29$	4.94693	+	4.15097i	0.918622	+	0.770816i	0.973740	−	0.227664i	$-0.0731088\pi$
$29$	4.94693	+	4.15097i	0.918622	+	0.770816i	−0.0551173	+	0.998480i	$0.517553\pi$
$30$	−0.286437	−	4.78748i	−0.0522960	−	0.874070i
$31$	−0.228069	−	1.29344i	−0.0409624	−	0.232309i	0.957453	−	0.288591i	$-0.0931867\pi$
$31$	−0.228069	−	1.29344i	−0.0409624	−	0.232309i	−0.998415	+	0.0562816i	$0.982076\pi$
$32$	−0.882557	+	2.42480i	−0.156015	+	0.428649i
$33$	−0.0195113	+	8.98066i	−0.00339649	+	1.56333i
$34$	−1.14627	+	6.50084i	−0.196584	+	1.11489i
$35$	−4.09340	−	3.02361i	−0.691911	−	0.511083i
$36$	0.705061	−	1.20904i	0.117510	−	0.201506i
$37$	3.18754	−	1.84032i	0.524028	−	0.302548i	−0.214553	−	0.976712i	$-0.568830\pi$
$37$	3.18754	−	1.84032i	0.524028	−	0.302548i	0.738581	+	0.674165i	$0.235496\pi$
$38$	−1.93781	−	5.32410i	−0.314355	−	0.863683i
$39$	−2.51847	+	0.910455i	−0.403277	+	0.145790i
$40$	3.77444	+	5.69210i	0.596792	+	0.900000i
$41$	3.26644	−	2.74087i	0.510132	−	0.428052i	−0.351044	−	0.936359i	$-0.614173\pi$
$41$	3.26644	−	2.74087i	0.510132	−	0.428052i	0.861176	+	0.508307i	$0.169729\pi$
$42$	1.65958	+	4.59066i	0.256078	+	0.708354i
$43$	−2.88612	−	7.92956i	−0.440130	−	1.20925i	−0.939407	−	0.342804i	$-0.888623\pi$
$43$	−2.88612	−	7.92956i	−0.440130	−	1.20925i	0.499277	−	0.866442i	$-0.333599\pi$
$44$	−1.20949	−	2.09490i	−0.182337	−	0.315817i
$45$	−2.65334	−	6.16115i	−0.395537	−	0.918450i
$46$	3.18331	−	5.51365i	0.469353	−	0.812944i
$47$	−6.68721	−	1.17913i	−0.975429	−	0.171995i	−0.336857	−	0.941556i	$-0.609364\pi$
$47$	−6.68721	−	1.17913i	−0.975429	−	0.171995i	−0.638573	+	0.769561i	$0.720475\pi$
$48$	0.0107219	−	4.93508i	0.00154758	−	0.712318i
$49$	−1.71059	−	0.622605i	−0.244371	−	0.0889436i
$50$	6.18371	+	0.313593i	0.874509	+	0.0443488i
$51$	1.58353	+	9.09617i	0.221739	+	1.27372i
$52$	0.463658	−	0.552567i	0.0642979	−	0.0766272i
$53$			6.64507i			0.912771i	0.889782	+	0.456385i	$0.150856\pi$
$53$			6.64507i			0.912771i	−0.889782	+	0.456385i	$0.849144\pi$
$54$	−1.15863	+	6.32939i	−0.157669	+	0.861321i
$55$	−11.5206	−	1.30274i	−1.55343	−	0.175662i
$56$	−5.32509	−	4.46828i	−0.711596	−	0.597100i
$57$	−5.08071	−	6.08174i	−0.672956	−	0.805546i
$58$	7.87536	−	1.38864i	1.03409	−	0.182337i
$59$	2.83430	+	1.03160i	0.368995	+	0.134303i	0.519861	−	0.854251i	$-0.325984\pi$
$59$	2.83430	+	1.03160i	0.368995	+	0.134303i	−0.150866	+	0.988554i	$0.548206\pi$
$60$	1.45104	+	1.07670i	0.187329	+	0.139001i
$61$	0.999796	−	5.67013i	0.128011	−	0.725985i	−0.851463	−	0.524414i	$-0.824284\pi$
$61$	0.999796	−	5.67013i	0.128011	−	0.725985i	0.979474	−	0.201571i	$-0.0646046\pi$
$62$	−1.40852	−	0.813210i	−0.178882	−	0.103278i
$63$	4.36595	+	5.24929i	0.550058	+	0.661349i
$64$	4.44699	+	7.70241i	0.555874	+	0.962801i
$65$	−0.809923	−	3.36106i	−0.100459	−	0.416888i
$66$	8.50367	+	7.16697i	1.04673	+	0.882193i
$67$	2.22595	+	2.65278i	0.271943	+	0.324089i	0.884681	−	0.466197i	$-0.154376\pi$
$67$	2.22595	+	2.65278i	0.271943	+	0.324089i	−0.612738	+	0.790286i	$0.709932\pi$
$68$	−1.59857	−	1.90510i	−0.193855	−	0.231028i
$69$	1.56538	−	8.76630i	0.188450	−	1.05534i
$70$	−6.12653	+	1.47633i	−0.732260	+	0.176455i
$71$	−0.0130487	−	0.0226011i	−0.00154860	−	0.00268225i	0.865250	−	0.501341i	$-0.167160\pi$
$71$	−0.0130487	−	0.0226011i	−0.00154860	−	0.00268225i	−0.866799	+	0.498658i	$0.833826\pi$
$72$	−3.09654	−	8.62409i	−0.364931	−	1.01636i
$73$	5.00704	+	2.89081i	0.586029	+	0.338344i	0.763526	−	0.645777i	$-0.223467\pi$
$73$	5.00704	+	2.89081i	0.586029	+	0.338344i	−0.177497	+	0.984121i	$0.556800\pi$
$74$	0.791465	−	4.48862i	0.0920059	−	0.521792i
$75$	8.28306	−	2.52802i	0.956446	−	0.291911i
$76$	2.00582	+	0.730059i	0.230083	+	0.0837435i
$77$	11.6211	−	2.04912i	1.32435	−	0.233519i
$78$	−1.14099	+	3.11377i	−0.129191	+	0.352565i
$79$	−12.6845	−	10.6435i	−1.42712	−	1.19749i	−0.947393	−	0.320073i	$-0.896292\pi$
$79$	−12.6845	−	10.6435i	−1.42712	−	1.19749i	−0.479724	−	0.877420i	$-0.659263\pi$
$80$	6.33083	+	0.715887i	0.707809	+	0.0800386i
$81$	1.48575	+	8.87652i	0.165083	+	0.986280i
$82$		−	5.28029i		−	0.583110i
$83$	6.96279	−	8.29793i	0.764265	−	0.910816i	−0.233844	−	0.972274i	$-0.575131\pi$
$83$	6.96279	−	8.29793i	0.764265	−	0.910816i	0.998110	+	0.0614583i	$0.0195751\pi$
$84$	−1.72677	−	0.632744i	−0.188406	−	0.0690381i
$85$	−11.8969	+	0.737738i	−1.29040	+	0.0800189i
$86$	−9.81943	−	3.57398i	−1.05886	−	0.385392i
$87$	9.69877	−	5.57153i	1.03982	−	0.597331i
$88$	−15.5964	−	2.75006i	−1.66258	−	0.293158i
$89$	2.32308	−	4.02369i	0.246246	−	0.426510i	−0.716235	−	0.697859i	$-0.754136\pi$
$89$	2.32308	−	4.02369i	0.246246	−	0.426510i	0.962481	+	0.271349i	$0.0874696\pi$
$90$	−7.95659	−	2.38717i	−0.838699	−	0.251630i
$91$	1.75941	+	3.04738i	0.184436	+	0.319453i
$92$	0.820364	+	2.25393i	0.0855289	+	0.234989i
$93$	−2.23944	−	0.399893i	−0.232220	−	0.0414670i
$94$	−6.44146	+	5.40503i	−0.664386	+	0.557486i
$95$	8.52651	−	5.65395i	0.874802	−	0.580083i
$96$	3.41753	+	2.88032i	0.348800	+	0.293972i
$97$	2.48117	+	6.81695i	0.251924	+	0.692157i	0.999605	+	0.0280982i	$0.00894512\pi$
$97$	2.48117	+	6.81695i	0.251924	+	0.692157i	−0.747681	+	0.664058i	$0.768833\pi$
$98$	−1.95222	+	1.12712i	−0.197204	+	0.113856i
$99$	14.5937	+	5.38358i	1.46672	+	0.541070i
$100$	−1.58799	+	1.70869i	−0.158799	+	0.170869i
$101$	0.0757615	−	0.429665i	0.00753855	−	0.0427532i	−0.980806	−	0.194984i	$-0.937535\pi$
$101$	0.0757615	−	0.429665i	0.00753855	−	0.0427532i	0.988345	+	0.152231i	$0.0486457\pi$
$102$	9.88925	+	5.73824i	0.979182	+	0.568171i
$103$	−0.775652	+	2.13109i	−0.0764273	+	0.209982i	−0.972023	−	0.234888i	$-0.924528\pi$
$103$	−0.775652	+	2.13109i	−0.0764273	+	0.209982i	0.895595	+	0.444870i	$0.146750\pi$
$104$	−0.820053	−	4.65075i	−0.0804128	−	0.456044i
$105$	−7.35669	+	4.85525i	−0.717939	+	0.473824i
$106$	6.30363	+	5.28937i	0.612263	+	0.513749i
$107$			4.36720i			0.422193i	0.977465	+	0.211097i	$0.0677034\pi$
$107$			4.36720i			0.422193i	−0.977465	+	0.211097i	$0.932297\pi$
$108$	−1.54610	−	1.86715i	−0.148773	−	0.179666i
$109$	−7.95224			−0.761686			−0.380843	−	0.924640i	$-0.624366\pi$
$109$	−7.95224			−0.761686			−0.380843	+	0.924640i	$0.624366\pi$
$110$	−10.4060	+	9.89166i	−0.992174	+	0.943133i
$111$	−1.09338	−	6.28061i	−0.103779	−	0.596129i
$112$	−6.38610	+	1.12604i	−0.603429	+	0.106401i
$113$	−5.38234	+	14.7879i	−0.506328	+	1.39112i	0.378671	+	0.925531i	$0.376381\pi$
$113$	−5.38234	+	14.7879i	−0.506328	+	1.39112i	−0.884999	+	0.465593i	$0.845841\pi$
$114$	−9.81341	−	0.0213206i	−0.919110	−	0.00199686i
$115$	11.0256	+	3.25580i	1.02814	+	0.303605i
$116$	−1.50638	+	2.60913i	−0.139864	+	0.242252i
$117$	−0.0201547	+	4.63836i	−0.00186330	+	0.428817i
$118$	3.23466	−	1.86753i	0.297774	−	0.171920i
$119$	11.4003	−	4.14937i	1.04506	−	0.380372i
$120$	11.5064	−	2.74629i	1.05039	−	0.250701i
$121$	12.1680	−	10.2102i	1.10618	−	0.928196i
$122$	−4.58296	−	5.46176i	−0.414922	−	0.494484i
$123$	−2.51091	−	6.94559i	−0.226401	−	0.626263i
$124$	0.575791	−	0.209571i	0.0517075	−	0.0188200i
$125$	2.06532	+	10.9879i	0.184728	+	0.982790i
$126$	8.45480	+	0.0367379i	0.753213	+	0.00327287i
$127$	−2.90443	−	1.67688i	−0.257727	−	0.148799i	0.365570	−	0.930784i	$-0.380874\pi$
$127$	−2.90443	−	1.67688i	−0.257727	−	0.148799i	−0.623297	+	0.781985i	$0.714207\pi$
$128$	5.76393	+	1.01634i	0.509464	+	0.0898323i
$129$	−14.6158	−	0.0317543i	−1.28685	−	0.00279581i
$130$	−3.83304	−	1.90704i	−0.336180	−	0.167259i
$131$	−0.958255	−	5.43454i	−0.0837231	−	0.474818i	−0.997625	−	0.0688819i	$-0.978057\pi$
$131$	−0.958255	−	5.43454i	−0.0837231	−	0.474818i	0.913902	−	0.405936i	$-0.133054\pi$
$132$	−4.12771	+	0.718583i	−0.359271	+	0.0625447i
$133$	−6.69329	+	7.97675i	−0.580382	+	0.691672i
$134$	4.28829			0.370452
$135$	−11.6011	+	0.643523i	−0.998465	+	0.0553857i
$136$	−16.2819			−1.39616
$137$	3.81854	−	4.55076i	0.326240	−	0.388798i	−0.577848	−	0.816145i	$-0.696107\pi$
$137$	3.81854	−	4.55076i	0.326240	−	0.388798i	0.904088	+	0.427347i	$0.140552\pi$
$138$	−7.06985	−	8.46279i	−0.601825	−	0.720400i
$139$	2.76633	+	15.6886i	0.234637	+	1.33069i	0.843377	+	0.537323i	$0.180564\pi$
$139$	2.76633	+	15.6886i	0.234637	+	1.33069i	−0.608740	+	0.793370i	$0.708325\pi$
$140$	1.05757	−	2.12565i	0.0893807	−	0.179650i
$141$	−5.90275	+	10.1728i	−0.497101	+	0.856700i
$142$	−0.0318263	−	0.00561184i	−0.00267081	−	0.000470935i
$143$	6.94267	+	4.00835i	0.580575	+	0.335195i
$144$	−8.01956	−	2.95841i	−0.668296	−	0.246534i
$145$	5.76913	+	13.2375i	0.479100	+	1.09931i
$146$	6.72780	−	2.44872i	0.556796	−	0.202657i
$147$	−2.03194	+	2.41092i	−0.167592	+	0.198849i
$148$	1.10376	+	1.31541i	0.0907286	+	0.108126i
$149$	−15.5994	+	13.0894i	−1.27795	+	1.07233i	−0.284430	+	0.958697i	$0.591804\pi$
$149$	−15.5994	+	13.0894i	−1.27795	+	1.07233i	−0.993523	+	0.113632i	$0.963751\pi$
$150$	4.19506	−	9.86972i	0.342526	−	0.805859i
$151$	−1.80439	+	0.656743i	−0.146839	+	0.0534450i	−0.414394	−	0.910098i	$-0.636006\pi$
$151$	−1.80439	+	0.656743i	−0.146839	+	0.0534450i	0.267555	+	0.963543i	$0.413784\pi$
$152$	12.1026	−	6.98743i	0.981649	−	0.566755i
$153$	15.7368	+	2.84539i	1.27225	+	0.230036i
$154$	7.30642	−	12.6551i	0.588768	−	1.01978i
$155$	0.831728	−	2.81661i	0.0668060	−	0.226235i
$156$	−0.622333	−	1.08334i	−0.0498265	−	0.0867367i
$157$	4.36413	−	11.9904i	0.348296	−	0.956935i	−0.634611	−	0.772832i	$-0.718840\pi$
$157$	4.36413	−	11.9904i	0.348296	−	0.956935i	0.982907	−	0.184103i	$-0.0589380\pi$
$158$	−20.1933	+	3.56063i	−1.60649	+	0.283268i
$159$	10.8069	+	3.96000i	0.857044	+	0.314049i
$160$	−4.18205	+	3.97534i	−0.330620	+	0.314279i
$161$	−11.7009			−0.922163
$162$	9.60305	+	5.65616i	0.754487	+	0.444390i
$163$			24.6659i			1.93198i	0.258578	+	0.965990i	$0.416746\pi$
$163$			24.6659i			1.93198i	−0.258578	+	0.965990i	$0.583254\pi$
$164$	1.52391	+	1.27871i	0.118997	+	0.0998503i
$165$	−8.98412	+	17.9596i	−0.699413	+	1.39816i
$166$	−2.32929	−	13.2100i	−0.180788	−	1.02530i
$167$	1.83304	−	5.03625i	0.141845	−	0.389716i	−0.848345	−	0.529444i	$-0.822401\pi$
$167$	1.83304	−	5.03625i	0.141845	−	0.389716i	0.990190	+	0.139728i	$0.0446227\pi$
$168$	−10.4402	+	5.99743i	−0.805477	+	0.462712i
$169$	1.84231	−	10.4483i	0.141717	−	0.803714i
$170$	−8.76989	+	11.8728i	−0.672620	+	0.910603i
$171$	−12.9185	+	4.63848i	−0.987903	+	0.354714i
$172$	3.40939	−	1.96841i	0.259964	−	0.150090i
$173$	−4.89834	−	13.4581i	−0.372414	−	1.02320i	−0.974426	−	0.224711i	$-0.927856\pi$
$173$	−4.89834	−	13.4581i	−0.372414	−	1.02320i	0.602012	−	0.798487i	$-0.294366\pi$
$174$	2.43482	−	13.6353i	0.184583	−	1.03369i
$175$	−5.18327	−	10.1304i	−0.391818	−	0.765784i
$176$	−11.3172	+	9.49622i	−0.853063	+	0.715805i
$177$	3.36675	−	3.99468i	0.253060	−	0.300258i
$178$	−1.96781	−	5.40651i	−0.147493	−	0.405235i
$179$	−2.84521	−	4.92805i	−0.212661	−	0.368340i	0.739885	−	0.672733i	$-0.234880\pi$
$179$	−2.84521	−	4.92805i	−0.212661	−	0.368340i	−0.952547	+	0.304393i	$0.901546\pi$
$180$	2.61576	−	1.71820i	0.194967	−	0.128067i
$181$	5.07635	−	8.79249i	0.377322	−	0.653541i	−0.613350	−	0.789811i	$-0.710178\pi$
$181$	5.07635	−	8.79249i	0.377322	−	0.653541i	0.990672	+	0.136271i	$0.0435117\pi$
$182$	4.29126	+	0.756665i	0.318090	+	0.0560878i
$183$	−8.62554	−	5.00498i	−0.637619	−	0.369979i
$184$	14.7564	+	5.37091i	1.08786	+	0.395948i
$185$	8.21440	−	0.509384i	0.603935	−	0.0374507i
$186$	−2.16191	+	1.80607i	−0.158519	+	0.132427i
$187$	17.7663	−	21.1731i	1.29920	−	1.54833i
$188$		−	3.16794i		−	0.231046i
$189$	11.1388	−	3.97215i	0.810225	−	0.288931i
$190$	1.42354	−	12.5889i	0.103274	−	0.913291i
$191$	−4.87022	−	4.08660i	−0.352397	−	0.295696i	0.449355	−	0.893353i	$-0.351654\pi$
$191$	−4.87022	−	4.08660i	−0.352397	−	0.295696i	−0.801752	+	0.597657i	$0.796098\pi$
$192$	15.1766	−	2.64205i	1.09527	−	0.190674i
$193$	19.2071	−	3.38673i	1.38256	−	0.243782i	0.567601	−	0.823304i	$-0.307872\pi$
$193$	19.2071	−	3.38673i	1.38256	−	0.243782i	0.814957	+	0.579521i	$0.196760\pi$
$194$	8.44165	+	3.07251i	0.606075	+	0.220593i
$195$	−5.94876	−	0.685775i	−0.425999	−	0.0491094i
$196$	0.147474	−	0.836365i	0.0105338	−	0.0597404i
$197$	−7.83426	−	4.52311i	−0.558168	−	0.322259i	0.194242	−	0.980954i	$-0.437775\pi$
$197$	−7.83426	−	4.52311i	−0.558168	−	0.322259i	−0.752410	+	0.658695i	$0.771109\pi$
$198$	16.7233	−	9.55854i	1.18847	−	0.679296i
$199$	5.04715	+	8.74191i	0.357783	+	0.619698i	0.987590	−	0.157054i	$-0.0501995\pi$
$199$	5.04715	+	8.74191i	0.357783	+	0.619698i	−0.629807	+	0.776751i	$0.716866\pi$
$200$	1.88680	+	15.1549i	0.133417	+	1.07162i
$201$	5.64074	−	2.03919i	0.397867	−	0.143834i
$202$	−0.347282	−	0.413875i	−0.0244347	−	0.0291201i
$203$	−9.44710	−	11.2586i	−0.663057	−	0.790200i
$204$	−4.05091	+	1.46445i	−0.283621	+	0.102532i
$205$	9.26934	−	2.23366i	0.647399	−	0.156006i
$206$	1.40418	+	2.43211i	0.0978338	+	0.169453i
$207$	−13.3238	−	7.76990i	−0.926069	−	0.540045i
$208$	−3.81516	−	2.20268i	−0.264534	−	0.152729i
$209$	−4.11947	+	23.3627i	−0.284950	+	1.61603i
$210$	−1.25003	+	10.8434i	−0.0862603	+	0.748265i
$211$	3.35281	+	1.22032i	0.230817	+	0.0840106i	0.454839	−	0.890573i	$-0.349697\pi$
$211$	3.35281	+	1.22032i	0.230817	+	0.0840106i	−0.224022	+	0.974584i	$0.571919\pi$
$212$	−3.05305	+	0.538336i	−0.209685	+	0.0369730i
$213$	−0.0445323	+	0.00775253i	−0.00305131	+	0.000531195i
$214$	4.14280	+	3.47622i	0.283196	+	0.237630i
$215$	2.12018	−	18.7495i	0.144595	−	1.27870i
$216$	−15.8707	−	0.103443i	−1.07987	−	0.00703843i
$217$			2.98913i			0.202915i
$218$	−6.32986	+	7.54363i	−0.428712	+	0.510919i
$219$	7.68519	−	6.42024i	0.519317	−	0.433840i
$220$	−0.334775	−	5.39863i	−0.0225705	−	0.363975i
$221$	7.74487	+	2.81890i	0.520977	+	0.189620i
$222$	−6.82821	−	3.96207i	−0.458279	−	0.265917i
$223$	18.2797	+	3.22320i	1.22410	+	0.215842i	0.748089	−	0.663598i	$-0.230971\pi$
$223$	18.2797	+	3.22320i	1.22410	+	0.215842i	0.476010	+	0.879440i	$0.342083\pi$
$224$	2.93637	−	5.08593i	0.196194	−	0.339818i
$225$	0.824802	−	14.9773i	0.0549868	−	0.998487i
$226$	9.74376	+	16.8767i	0.648145	+	1.12262i
$227$	8.41561	+	23.1217i	0.558564	+	1.53464i	0.821722	+	0.569888i	$0.193014\pi$
$227$	8.41561	+	23.1217i	0.558564	+	1.53464i	−0.263158	+	0.964753i	$0.584764\pi$
$228$	2.38263	−	2.82701i	0.157793	−	0.187223i
$229$	−1.56307	+	1.31157i	−0.103291	+	0.0866713i	−0.692971	−	0.720966i	$-0.743698\pi$
$229$	−1.56307	+	1.31157i	−0.103291	+	0.0866713i	0.589680	+	0.807637i	$0.299254\pi$
$230$	11.8647	−	7.86751i	0.782336	−	0.518768i
$231$	3.59291	−	20.1207i	0.236396	−	1.32384i
$232$	6.74618	+	18.5350i	0.442908	+	1.21688i
$233$	7.51547	−	4.33906i	0.492355	−	0.284261i	−0.233196	−	0.972430i	$-0.574918\pi$
$233$	7.51547	−	4.33906i	0.492355	−	0.284261i	0.725551	+	0.688169i	$0.241585\pi$
$234$	4.38399	+	3.71118i	0.286590	+	0.242608i
$235$	−12.2132	−	9.02130i	−0.796699	−	0.588485i
$236$	−0.244351	+	1.38578i	−0.0159059	+	0.0902068i
$237$	−24.8687	+	14.2860i	−1.61540	+	0.927977i
$238$	5.13829	−	14.1173i	0.333066	−	0.915092i
$239$	0.654990	+	3.71463i	0.0423678	+	0.240280i	0.998636	−	0.0522114i	$-0.0166270\pi$
$239$	0.654990	+	3.71463i	0.0423678	+	0.240280i	−0.956268	+	0.292491i	$0.905516\pi$
$240$	4.93699	−	9.86924i	0.318681	−	0.637057i
$241$	0.433776	+	0.363981i	0.0279420	+	0.0234461i	0.656652	−	0.754194i	$-0.271972\pi$
$241$	0.433776	+	0.363981i	0.0279420	+	0.0234461i	−0.628710	+	0.777640i	$0.716417\pi$
$242$		−	19.6699i		−	1.26443i
$243$	15.3213	+	2.87351i	0.982863	+	0.184336i
$244$	2.68612			0.171961
$245$	−2.80443	−	2.95026i	−0.179169	−	0.188485i
$246$	−8.58736	−	3.14669i	−0.547510	−	0.200626i
$247$	−6.96662	+	1.22840i	−0.443275	+	0.0781614i
$248$	1.37205	−	3.76969i	0.0871256	−	0.239375i
$249$	−9.34561	−	16.2686i	−0.592254	−	1.03098i
$250$	12.0673	+	6.78701i	0.763203	+	0.429248i
$251$	0.425928	−	0.737730i	0.0268844	−	0.0465651i	−0.852270	−	0.523102i	$-0.824775\pi$
$251$	0.425928	−	0.737730i	0.0268844	−	0.0465651i	0.879155	+	0.476537i	$0.158108\pi$
$252$	−2.05807	+	2.43118i	−0.129646	+	0.153150i
$253$	−23.0861	+	13.3288i	−1.45141	+	0.837973i
$254$	−3.90260	+	1.42043i	−0.244871	+	0.0891257i
$255$	−5.88993	+	19.7876i	−0.368842	+	1.23915i
$256$	−8.07425	+	6.77510i	−0.504641	+	0.423444i
$257$	11.8239	+	14.0912i	0.737553	+	0.878982i	0.996209	−	0.0869875i	$-0.0277240\pi$
$257$	11.8239	+	14.0912i	0.737553	+	0.878982i	−0.258656	+	0.965970i	$0.583280\pi$
$258$	−11.6641	+	13.8395i	−0.726174	+	0.861612i
$259$	−7.87153	+	2.86500i	−0.489113	+	0.178023i
$260$	1.47861	−	0.644405i	0.0916995	−	0.0399643i
$261$	−3.28120	−	19.0934i	−0.203101	−	1.18185i
$262$	−5.91805	−	3.41679i	−0.365618	−	0.211090i
$263$	−6.87408	−	1.21209i	−0.423874	−	0.0747404i	−0.0423576	−	0.999103i	$-0.513487\pi$
$263$	−6.87408	−	1.21209i	−0.423874	−	0.0747404i	−0.381516	+	0.924362i	$0.624598\pi$
$264$	−13.7668	+	23.7256i	−0.847289	+	1.46021i
$265$	−6.61873	+	13.3033i	−0.406586	+	0.817214i
$266$	2.23913	+	12.6987i	0.137290	+	0.778610i
$267$	−5.15935	−	6.17587i	−0.315747	−	0.377957i
$268$	−1.03848	+	1.23761i	−0.0634352	+	0.0755992i
$269$	−9.05450			−0.552062			−0.276031	−	0.961149i	$-0.589019\pi$
$269$	−9.05450			−0.552062			−0.276031	+	0.961149i	$0.589019\pi$
$270$	−8.62385	+	11.5173i	−0.524831	+	0.700918i
$271$	−2.68123			−0.162873			−0.0814364	−	0.996679i	$-0.525951\pi$
$271$	−2.68123			−0.162873			−0.0814364	+	0.996679i	$0.525951\pi$
$272$	−9.76300	+	11.6351i	−0.591969	+	0.705481i
$273$	6.00446	−	1.04530i	0.363406	−	0.0632646i
$274$	−1.27743	−	7.24467i	−0.0771724	−	0.437667i
$275$	−21.7664	−	14.0830i	−1.31256	−	0.849236i
$276$	4.15446	+	0.00902597i	0.250069	+	0.000543299i
$277$	−9.53431	−	1.68116i	−0.572861	−	0.101011i	−0.120289	−	0.992739i	$-0.538382\pi$
$277$	−9.53431	−	1.68116i	−0.572861	−	0.101011i	−0.452572	+	0.891728i	$0.649493\pi$
$278$	17.0845	+	9.86372i	1.02466	+	0.591587i
$279$	−1.98490	+	3.40371i	−0.118833	+	0.203775i
$280$	−6.21014	−	14.2494i	−0.371127	−	0.851564i
$281$	−12.4600	+	4.53506i	−0.743300	+	0.270539i	−0.685784	−	0.727806i	$-0.740540\pi$
$281$	−12.4600	+	4.53506i	−0.743300	+	0.270539i	−0.0575163	+	0.998345i	$0.518318\pi$
$282$	4.95155	+	13.6968i	0.294861	+	0.815633i
$283$	−12.5849	−	14.9981i	−0.748094	−	0.891543i	0.248939	−	0.968519i	$-0.419918\pi$
$283$	−12.5849	−	14.9981i	−0.748094	−	0.891543i	−0.997033	+	0.0769758i	$0.975474\pi$
$284$	0.00932686	−	0.00782616i	0.000553447	−	0.000464397i
$285$	−4.11383	−	17.2361i	−0.243682	−	1.02098i
$286$	9.32865	−	3.39535i	0.551615	−	0.200771i
$287$	−8.40428	+	4.85221i	−0.496089	+	0.286417i
$288$	6.72089	−	3.84147i	0.396032	−	0.226361i
$289$	5.70798	−	9.88651i	0.335763	−	0.581559i
$290$	17.1494	+	5.06413i	1.00705	+	0.297376i
$291$	12.5650	+	0.0272988i	0.736576	+	0.00160028i
$292$	−0.922540	+	2.53466i	−0.0539875	+	0.148330i
$293$	−29.7888	+	5.25257i	−1.74028	+	0.306858i	−0.951462	−	0.307767i	$-0.900418\pi$
$293$	−29.7888	+	5.25257i	−1.74028	+	0.306858i	−0.788819	+	0.614625i	$0.789307\pi$
$294$	0.669644	+	3.84659i	0.0390544	+	0.224338i
$295$	4.64670	+	4.88831i	0.270541	+	0.284609i
$296$	11.2421			0.653436
$297$	17.4522	−	20.5255i	1.01268	−	1.19101i
$298$			25.2169i			1.46077i
$299$	−6.08938	−	5.10960i	−0.352158	−	0.295496i
$300$	1.83252	+	3.60082i	0.105801	+	0.207893i
$301$	3.33490	+	18.9131i	0.192220	+	1.09014i
$302$	−0.813265	+	2.23443i	−0.0467982	+	0.128577i
$303$	−0.653617	−	0.379262i	−0.0375493	−	0.0217880i
$304$	2.26375	−	12.8384i	0.129835	−	0.736330i
$305$	7.64922	−	10.3556i	0.437993	−	0.592962i
$306$	15.2254	−	12.6633i	0.870381	−	0.723915i
$307$	−15.8229	+	9.13533i	−0.903058	+	0.521381i	−0.878191	−	0.478310i	$-0.841250\pi$
$307$	−15.8229	+	9.13533i	−0.903058	+	0.521381i	−0.0248672	+	0.999691i	$0.507916\pi$
$308$	1.88292	+	5.17329i	0.107289	+	0.294775i
$309$	3.00356	+	2.53143i	0.170867	+	0.144008i
$310$	−2.00984	−	3.03097i	−0.114151	−	0.172147i
$311$	25.8479	−	21.6890i	1.46570	−	1.22987i	0.545681	−	0.837993i	$-0.316271\pi$
$311$	25.8479	−	21.6890i	1.46570	−	1.22987i	0.920018	−	0.391875i	$-0.128174\pi$
$312$	−8.05223	−	1.43787i	−0.455868	−	0.0814034i
$313$	−0.953665	−	2.62017i	−0.0539043	−	0.148101i	0.909818	−	0.415007i	$-0.136221\pi$
$313$	−0.953665	−	2.62017i	−0.0539043	−	0.148101i	−0.963723	+	0.266906i	$0.913999\pi$
$314$	−7.90048	−	13.6840i	−0.445850	−	0.772235i
$315$	3.51204	+	14.8576i	0.197881	+	0.837132i
$316$	3.86253	−	6.69010i	0.217284	−	0.376348i
$317$	2.71702	+	0.479083i	0.152603	+	0.0269080i	0.249428	−	0.968393i	$-0.419758\pi$
$317$	2.71702	+	0.479083i	0.152603	+	0.0269080i	−0.0968248	+	0.995301i	$0.530869\pi$
$318$	12.3587	−	7.09952i	0.693039	−	0.398121i
$319$	−31.4642	−	11.4520i	−1.76166	−	0.641190i
$320$	1.23088	+	19.8494i	0.0688085	+	1.10962i
$321$	7.10240	+	2.60255i	0.396417	+	0.145260i
$322$	−9.31377	+	11.0997i	−0.519036	+	0.618563i
$323$			24.3896i			1.35707i
$324$	−3.95792	+	1.40173i	−0.219884	+	0.0778741i
$325$	1.72629	−	7.53547i	0.0957572	−	0.417993i
$326$	23.3985	+	19.6337i	1.29592	+	1.08741i
$327$	−4.73899	+	12.9328i	−0.262067	+	0.715183i
$328$	12.8261	−	2.26160i	0.708206	−	0.124876i
$329$	14.5221	+	5.28560i	0.800627	+	0.291404i
$330$	9.88559	+	22.8181i	0.544184	+	1.25609i
$331$	−4.85007	+	27.5061i	−0.266584	+	1.51187i	0.497902	+	0.867233i	$0.334104\pi$
$331$	−4.85007	+	27.5061i	−0.266584	+	1.51187i	−0.764486	+	0.644640i	$0.777007\pi$
$332$	4.37653	+	2.52679i	0.240193	+	0.138676i
$333$	−10.8658	−	1.96465i	−0.595440	−	0.107662i
$334$	−3.31840	−	5.74763i	−0.181575	−	0.314496i
$335$	1.81403	+	7.52793i	0.0991109	+	0.411295i
$336$	−1.97439	+	11.0568i	−0.107712	+	0.603197i
$337$	−9.17286	−	10.9318i	−0.499677	−	0.595492i	0.455974	−	0.889993i	$-0.349291\pi$
$337$	−9.17286	−	10.9318i	−0.499677	−	0.595492i	−0.955651	+	0.294501i	$0.904847\pi$
$338$	−8.44497	−	10.0643i	−0.459346	−	0.547427i
$339$	20.8421	+	17.5659i	1.13199	+	0.954047i
$340$	−1.30275	−	5.40621i	−0.0706515	−	0.293193i
$341$	3.40498	+	5.89759i	0.184390	+	0.319372i
$342$	−5.88279	+	15.9469i	−0.318105	+	0.862309i
$343$	17.3847	+	10.0371i	0.938685	+	0.541950i
$344$	4.47567	−	25.3828i	0.241312	−	1.36855i
$345$	11.8654	−	15.9908i	0.638812	−	0.860913i
$346$	−16.6656	−	6.06577i	−0.895946	−	0.326098i
$347$	−17.3984	+	3.06781i	−0.933994	+	0.164688i	−0.619880	−	0.784697i	$-0.712819\pi$
$347$	−17.3984	+	3.06781i	−0.933994	+	0.164688i	−0.314114	+	0.949385i	$0.601708\pi$
$348$	3.34554	+	4.00470i	0.179340	+	0.214674i
$349$	18.7439	+	15.7280i	1.00334	+	0.841899i	0.987443	−	0.157975i	$-0.0504965\pi$
$349$	18.7439	+	15.7280i	1.00334	+	0.841899i	0.0158927	+	0.999874i	$0.494941\pi$
$350$	−13.7356	−	3.14667i	−0.734201	−	0.168197i
$351$	7.53138	+	2.79692i	0.401995	+	0.149289i
$352$		−	13.3795i		−	0.713129i
$353$	20.5015	−	24.4328i	1.09119	−	1.30043i	0.140567	−	0.990071i	$-0.455108\pi$
$353$	20.5015	−	24.4328i	1.09119	−	1.30043i	0.950621	−	0.310355i	$-0.100448\pi$
$354$	−1.10954	−	6.37346i	−0.0589714	−	0.338745i
$355$	−0.00361176	−	0.0582438i	−0.000191692	−	0.00309126i
$356$	2.03687	+	0.741359i	0.107954	+	0.0392920i
$357$	0.0456530	−	21.0131i	0.00241621	−	1.11213i
$358$	−6.93958	−	1.22364i	−0.366768	−	0.0646711i
$359$	−4.13080	+	7.15476i	−0.218015	+	0.377614i	−0.954201	−	0.299166i	$-0.903292\pi$
$359$	−4.13080	+	7.15476i	−0.218015	+	0.377614i	0.736186	+	0.676780i	$0.236625\pi$
$360$	2.39071	−	20.3495i	0.126001	−	1.07251i
$361$	−0.966856	−	1.67464i	−0.0508871	−	0.0881391i
$362$	−4.30002	−	11.8142i	−0.226004	−	0.620941i
$363$	−9.35354	−	25.8734i	−0.490934	−	1.35800i
$364$	−1.25757	+	1.05523i	−0.0659148	+	0.0553091i
$365$	7.14461	+	10.7745i	0.373966	+	0.563965i
$366$	−11.6136	+	4.19846i	−0.607053	+	0.219457i
$367$	7.40606	+	20.3480i	0.386593	+	1.06216i	0.968525	+	0.248918i	$0.0800750\pi$
$367$	7.40606	+	20.3480i	0.386593	+	1.06216i	−0.581931	+	0.813238i	$0.697703\pi$
$368$	12.6864	−	7.32448i	0.661323	−	0.381815i
$369$	−12.7920	−	0.0555839i	−0.665924	−	0.00289358i
$370$	6.05533	−	8.19779i	0.314801	−	0.426183i
$371$	2.62615	−	14.8936i	0.136343	−	0.773238i
$372$	0.00230578	−	1.06130i	0.000119549	−	0.0550259i
$373$	10.4509	−	28.7136i	0.541126	−	1.48673i	−0.304267	−	0.952587i	$-0.598411\pi$
$373$	10.4509	−	28.7136i	0.541126	−	1.48673i	0.845393	−	0.534145i	$-0.179366\pi$
$374$	−5.94343	−	33.7068i	−0.307327	−	1.74294i
$375$	19.1005	+	3.18920i	0.986345	+	0.164689i
$376$	−15.8881	−	13.3317i	−0.819365	−	0.687529i
$377$		−	9.98457i		−	0.514232i
$378$	5.09822	−	13.7282i	0.262224	−	0.706102i
$379$	−6.49045			−0.333392			−0.166696	−	0.986008i	$-0.553310\pi$
$379$	−6.49045			−0.333392			−0.166696	+	0.986008i	$0.553310\pi$
$380$	3.28844	+	3.45943i	0.168693	+	0.177465i
$381$	−4.45795	+	3.72419i	−0.228388	+	0.190796i
$382$	−7.75324	+	1.36711i	−0.396690	+	0.0699472i
$383$	2.57705	−	7.08040i	0.131681	−	0.361791i	−0.856276	−	0.516519i	$-0.827228\pi$
$383$	2.57705	−	7.08040i	0.131681	−	0.361791i	0.987957	+	0.154727i	$0.0494499\pi$
$384$	5.08778	−	8.76824i	0.259635	−	0.447452i
$385$	25.3063	+	7.47280i	1.28973	+	0.380849i
$386$	12.0758	−	20.9160i	0.614645	−	1.06460i
$387$	−8.76165	+	23.7508i	−0.445380	+	1.20732i
$388$	−2.93102	+	1.69222i	−0.148800	+	0.0859096i
$389$	−7.42372	+	2.70201i	−0.376398	+	0.136997i	−0.523289	−	0.852155i	$-0.675295\pi$
$389$	−7.42372	+	2.70201i	−0.376398	+	0.136997i	0.146892	+	0.989153i	$0.453073\pi$
$390$	−5.38566	+	5.09723i	−0.272713	+	0.258108i
$391$	−20.9946	+	17.6165i	−1.06174	+	0.890906i
$392$	−3.57399	−	4.25931i	−0.180514	−	0.215128i
$393$	−9.40926	−	1.68019i	−0.474635	−	0.0847545i
$394$	−10.5267	+	3.83139i	−0.530325	+	0.193023i
$395$	−14.7927	−	33.9424i	−0.744301	−	1.70783i
$396$	−1.29119	+	7.14114i	−0.0648850	+	0.358856i
$397$	−1.40079	−	0.808746i	−0.0703036	−	0.0405898i	0.464436	−	0.885607i	$-0.346257\pi$
$397$	−1.40079	−	0.808746i	−0.0703036	−	0.0405898i	−0.534740	+	0.845017i	$0.679590\pi$
$398$	12.3102	+	2.17062i	0.617054	+	0.108803i
$399$	8.98389	+	15.6389i	0.449757	+	0.782925i
$400$	11.9611	+	7.73893i	0.598056	+	0.386947i
$401$	2.06958	+	11.7372i	0.103350	+	0.586127i	0.991867	+	0.127282i	$0.0406254\pi$
$401$	2.06958	+	11.7372i	0.103350	+	0.586127i	−0.888517	+	0.458844i	$0.848264\pi$
$402$	2.55553	−	6.97407i	0.127458	−	0.347835i
$403$	−1.30530	+	1.55560i	−0.0650216	+	0.0774898i
$404$	0.203545			0.0101268
$405$	−5.86690	+	19.2504i	−0.291529	+	0.956562i
$406$	−18.1999			−0.903244
$407$	−12.2671	+	14.6193i	−0.608055	+	0.724652i
$408$	−9.70289	+	26.4793i	−0.480365	+	1.31092i
$409$	−1.98160	−	11.2382i	−0.0979836	−	0.555693i	−0.993792	−	0.111253i	$-0.964514\pi$
$409$	−1.98160	−	11.2382i	−0.0979836	−	0.555693i	0.895809	−	0.444440i	$-0.146597\pi$
$410$	5.25936	−	10.5710i	0.259741	−	0.522065i
$411$	−5.12534	−	8.92205i	−0.252814	−	0.440092i
$412$	−1.04196	−	0.183725i	−0.0513336	−	0.00905149i
$413$	−5.94484	−	3.43226i	−0.292527	−	0.168890i
$414$	−17.9762	+	6.45449i	−0.883482	+	0.317221i
$415$	22.2044	−	9.67706i	1.08997	−	0.475028i
$416$	3.74908	−	1.36455i	0.183814	−	0.0669027i
$417$	27.1630	+	4.85045i	1.33018	+	0.237528i
$418$	18.8832	+	22.5041i	0.923609	+	1.10071i
$419$	−24.7402	+	20.7595i	−1.20864	+	1.01417i	−0.209296	+	0.977852i	$0.567117\pi$
$419$	−24.7402	+	20.7595i	−1.20864	+	1.01417i	−0.999340	+	0.0363142i	$0.988438\pi$
$420$	−2.82671	−	2.98666i	−0.137930	−	0.145734i
$421$	−12.6800	+	4.61514i	−0.617986	+	0.224928i	−0.631994	−	0.774974i	$-0.717763\pi$
$421$	−12.6800	+	4.61514i	−0.617986	+	0.224928i	0.0140082	+	0.999902i	$0.495541\pi$
$422$	3.82641	−	2.20918i	0.186267	−	0.107541i
$423$	13.0264	+	15.6619i	0.633363	+	0.761509i
$424$	−10.1483	+	17.5774i	−0.492846	+	0.853634i
$425$	−24.5521	−	10.3728i	−1.19095	−	0.503154i
$426$	−0.0280929	+	0.0484150i	−0.00136110	+	0.00234572i
$427$	−4.48169	+	12.3134i	−0.216884	+	0.595885i
$428$	−2.00649	+	0.353799i	−0.0969875	+	0.0171015i
$429$	10.6562	−	8.90219i	0.514484	−	0.429802i
$430$	−16.0984	−	16.9355i	−0.776336	−	0.816704i
$431$	23.0480			1.11018			0.555092	−	0.831789i	$-0.312683\pi$
$431$	23.0480			1.11018			0.555092	+	0.831789i	$0.312683\pi$
$432$	−9.59037	+	11.2792i	−0.461417	+	0.542673i
$433$		−	28.7044i		−	1.37944i	−0.724074	−	0.689722i	$-0.757733\pi$
$433$		−	28.7044i		−	1.37944i	0.724074	−	0.689722i	$-0.242267\pi$
$434$	2.83554	+	2.37930i	0.136110	+	0.114210i
$435$	24.9662	−	1.49374i	1.19704	−	0.0716192i
$436$	−0.644233	−	3.65363i	−0.0308532	−	0.174977i
$437$	8.04538	−	22.1045i	0.384863	−	1.05740i
$438$	0.0269418	−	12.4007i	0.00128733	−	0.592529i
$439$	−0.464755	+	2.63576i	−0.0221816	+	0.125798i	−0.993888	−	0.110395i	$-0.964789\pi$
$439$	−0.464755	+	2.63576i	−0.0221816	+	0.125798i	0.971706	+	0.236193i	$0.0758996\pi$
$440$	−28.4844	−	21.0401i	−1.35794	−	1.00305i
$441$	2.70999	+	4.74130i	0.129047	+	0.225776i
$442$	8.83886	−	5.10312i	0.420422	−	0.242731i
$443$	−0.954638	−	2.62285i	−0.0453562	−	0.124615i	0.914947	−	0.403575i	$-0.132233\pi$
$443$	−0.954638	−	2.62285i	−0.0453562	−	0.124615i	−0.960303	+	0.278960i	$0.910010\pi$
$444$	2.79703	−	1.01116i	0.132741	−	0.0479874i
$445$	8.65849	−	5.74146i	0.410452	−	0.272171i
$446$	17.6079	−	14.7748i	0.833760	−	0.699608i
$447$	11.9913	+	33.1698i	0.567167	+	1.56888i
$448$	−6.92304	−	19.0209i	−0.327083	−	0.898653i
$449$	12.0160	+	20.8123i	0.567069	+	0.982192i	0.996854	+	0.0792608i	$0.0252560\pi$
$449$	12.0160	+	20.8123i	0.567069	+	0.982192i	−0.429785	+	0.902931i	$0.641411\pi$
$450$	−13.5512	−	12.7041i	−0.638810	−	0.598878i
$451$	−11.0545	+	19.1470i	−0.520536	+	0.901595i
$452$	−7.23026	−	1.27489i	−0.340083	−	0.0599658i
$453$	−0.00722574	+	3.32585i	−0.000339495	+	0.156262i
$454$	28.6323	+	10.4213i	1.34378	+	0.489097i
$455$	0.486987	+	7.85323i	0.0228303	+	0.368165i
$456$	−4.15138	−	23.8465i	−0.194406	−	1.11671i
$457$	19.7351	−	23.5193i	0.923167	−	1.10019i	−0.0715399	−	0.997438i	$-0.522791\pi$
$457$	19.7351	−	23.5193i	0.923167	−	1.10019i	0.994707	−	0.102750i	$-0.0327642\pi$
$458$			2.52675i			0.118067i
$459$	14.0055	−	23.8972i	0.653722	−	1.11543i
$460$	−0.602649	+	5.32943i	−0.0280987	+	0.248486i
$461$	−8.31123	−	6.97395i	−0.387093	−	0.324809i	0.428387	−	0.903595i	$-0.359082\pi$
$461$	−8.31123	−	6.97395i	−0.387093	−	0.324809i	−0.815479	+	0.578786i	$0.803527\pi$
$462$	−16.2269	−	19.4240i	−0.754944	−	0.903687i
$463$	−32.0801	+	5.65658i	−1.49089	+	0.262884i	−0.858919	−	0.512111i	$-0.828864\pi$
$463$	−32.0801	+	5.65658i	−1.49089	+	0.262884i	−0.631968	+	0.774995i	$0.717753\pi$
$464$	17.2903	+	6.29316i	0.802682	+	0.292153i
$465$	−4.08501	−	3.03114i	−0.189438	−	0.140566i
$466$	1.86609	−	10.5831i	0.0864450	−	0.490254i
$467$	−11.8736	−	6.85522i	−0.549445	−	0.317222i	0.199453	−	0.979907i	$-0.436083\pi$
$467$	−11.8736	−	6.85522i	−0.549445	−	0.317222i	−0.748898	+	0.662685i	$0.769417\pi$
$468$	−2.13271	+	0.366507i	−0.0985846	+	0.0169418i
$469$	−3.94064	−	6.82538i	−0.181962	−	0.315167i
$470$	−18.2793	+	4.40481i	−0.843159	+	0.203179i
$471$	−16.8993	−	14.2428i	−0.778676	−	0.656275i
$472$	5.92178	+	7.05730i	0.272572	+	0.324839i
$473$	28.1241	+	33.5170i	1.29315	+	1.54111i
$474$	−6.24316	+	34.9624i	−0.286758	+	1.60587i
$475$	22.7014	−	2.82635i	1.04161	−	0.129682i
$476$	2.82998	+	4.90167i	0.129712	+	0.224668i
$477$	12.8803	−	15.2154i	0.589750	−	0.696667i
$478$	4.04513	+	2.33545i	0.185020	+	0.106821i
$479$	2.05131	−	11.6335i	0.0937266	−	0.531550i	−0.901403	−	0.432980i	$-0.857462\pi$
$479$	2.05131	−	11.6335i	0.0937266	−	0.531550i	0.995130	−	0.0985701i	$-0.0314269\pi$
$480$	3.97290	+	9.17032i	0.181337	+	0.418566i
$481$	−5.34758	−	1.94636i	−0.243829	−	0.0887465i
$482$	0.690558	−	0.121764i	0.0314541	−	0.00554620i
$483$	−6.97295	+	19.0293i	−0.317280	+	0.865863i
$484$	5.67678	+	4.76339i	0.258036	+	0.216518i
$485$	−1.82270	+	16.1187i	−0.0827643	+	0.731913i
$486$	14.9214	−	12.2468i	0.676848	−	0.555526i
$487$			31.6087i			1.43233i	0.697933	+	0.716163i	$0.254103\pi$
$487$			31.6087i			1.43233i	−0.697933	+	0.716163i	$0.745897\pi$
$488$	11.3040	−	13.4716i	0.511709	−	0.609831i
$489$	40.1142	+	14.6992i	1.81403	+	0.664719i
$490$	−5.03095	+	0.311975i	−0.227275	+	0.0140936i
$491$	−15.3997	−	5.60502i	−0.694977	−	0.252951i	−0.0297121	−	0.999558i	$-0.509459\pi$
$491$	−15.3997	−	5.60502i	−0.694977	−	0.252951i	−0.665265	+	0.746608i	$0.731681\pi$
$492$	2.98771	−	1.71631i	0.134696	−	0.0773773i
$493$	−33.9012	−	5.97769i	−1.52683	−	0.269222i
$494$	−4.38004	+	7.58644i	−0.197067	+	0.341330i
$495$	23.8539	+	25.3136i	1.07215	+	1.13776i
$496$	−1.87111	−	3.24087i	−0.0840155	−	0.145519i
$497$	0.0203142	+	0.0558127i	0.000911215	+	0.00250354i
$498$	−22.8716	−	4.08414i	−1.02490	−	0.183015i
$499$	30.4626	−	25.5612i	1.36369	−	1.14427i	0.388871	−	0.921292i	$-0.372865\pi$
$499$	30.4626	−	25.5612i	1.36369	−	1.14427i	0.974823	−	0.222982i	$-0.0715791\pi$
$500$	−4.88104	+	1.83907i	−0.218287	+	0.0822456i
$501$	−7.09810	−	5.98234i	−0.317120	−	0.267271i
$502$	−0.360791	−	0.991264i	−0.0161029	−	0.0442423i
$503$	5.13479	−	2.96457i	0.228949	−	0.132184i	−0.381138	−	0.924518i	$-0.624468\pi$
$503$	5.13479	−	2.96457i	0.228949	−	0.132184i	0.610087	+	0.792334i	$0.291134\pi$
$504$	3.53203	+	20.5530i	0.157329	+	0.915502i
$505$	0.579634	−	0.784717i	0.0257934	−	0.0349195i
$506$	−5.73228	+	32.5094i	−0.254831	+	1.44522i
$507$	−15.8942	−	9.22262i	−0.705886	−	0.409591i
$508$	0.535138	−	1.47028i	0.0237429	−	0.0652331i
$509$	−7.53016	−	42.7057i	−0.333768	−	1.89290i	−0.439067	−	0.898454i	$-0.644691\pi$
$509$	−7.53016	−	42.7057i	−0.333768	−	1.89290i	0.105298	−	0.994441i	$-0.466420\pi$
$510$	14.0825	+	21.3379i	0.623586	+	0.944858i
$511$	−10.0798	−	8.45798i	−0.445905	−	0.374159i
$512$			24.7579i			1.09416i
$513$	−0.154954	+	23.7736i	−0.00684137	+	1.04963i
$514$	22.7787			1.00473
$515$	−3.67548	+	3.49381i	−0.161961	+	0.153956i
$516$	−1.16948	−	6.71775i	−0.0514834	−	0.295732i
$517$	34.6731	−	6.11381i	1.52492	−	0.268885i
$518$	−3.54783	+	9.74757i	−0.155883	+	0.428284i
$519$	−24.8060	−	0.0538934i	−1.08886	−	0.00236566i
$520$	2.99059	−	10.1275i	0.131146	−	0.444120i
$521$	−16.3247	+	28.2751i	−0.715196	+	1.23876i	0.247688	+	0.968840i	$0.420329\pi$
$521$	−16.3247	+	28.2751i	−0.715196	+	1.23876i	−0.962884	+	0.269916i	$0.913004\pi$
$522$	−20.7241	−	12.0854i	−0.907070	−	0.528966i
$523$	15.2548	−	8.80738i	0.667047	−	0.385120i	−0.127910	−	0.991786i	$-0.540827\pi$
$523$	15.2548	−	8.80738i	0.667047	−	0.385120i	0.794957	+	0.606666i	$0.207493\pi$
$524$	2.41925	−	0.880534i	0.105685	−	0.0384663i
$525$	−19.5639	+	2.39258i	−0.853840	+	0.104421i
$526$	−6.62147	+	5.55607i	−0.288710	+	0.242256i
$527$	4.50033	+	5.36328i	0.196037	+	0.233628i
$528$	8.69950	+	24.0642i	0.378597	+	1.04726i
$529$	3.22579	−	1.17409i	0.140252	−	0.0510475i
$530$	7.35131	+	16.8678i	0.319320	+	0.732692i
$531$	−4.49021	−	7.85591i	−0.194859	−	0.340917i
$532$	−4.20713	−	2.42899i	−0.182402	−	0.105310i
$533$	−6.49261	−	1.14482i	−0.281226	−	0.0495878i
$534$	−9.96530	−	0.0216506i	−0.431241	−	0.000936913i
$535$	−4.34989	+	8.74303i	−0.188062	+	0.377994i
$536$	1.83671	+	10.4165i	0.0793340	+	0.449925i
$537$	−9.71006	+	1.69040i	−0.419020	+	0.0729463i
$538$	−7.20724	+	8.58925i	−0.310726	+	0.370309i
$539$	9.43865			0.406551
$540$	−1.23550	−	5.27796i	−0.0531676	−	0.227127i
$541$	40.8023			1.75423			0.877113	−	0.480284i	$-0.159466\pi$
$541$	40.8023			1.75423			0.877113	+	0.480284i	$0.159466\pi$
$542$	−2.13421	+	2.54346i	−0.0916723	+	0.109251i
$543$	−11.2741	−	13.4954i	−0.483819	−	0.579143i
$544$	−2.38859	−	13.5464i	−0.102410	−	0.580797i
$545$	−15.9202	−	7.92072i	−0.681946	−	0.339287i
$546$	3.78786	−	6.52798i	0.162106	−	0.279372i
$547$	−29.8441	−	5.26232i	−1.27604	−	0.225000i	−0.505743	−	0.862684i	$-0.668781\pi$
$547$	−29.8441	−	5.26232i	−1.27604	−	0.225000i	−0.770298	+	0.637684i	$0.779893\pi$
$548$	2.40018	+	1.38575i	0.102531	+	0.0591961i
$549$	−13.2798	+	11.0451i	−0.566770	+	0.471395i
$550$	−30.6850	+	9.43811i	−1.30841	+	0.402442i
$551$	27.7646	−	10.1055i	1.18281	−	0.430508i
$552$	17.5286	−	20.7978i	0.746065	−	0.885212i
$553$	24.2234	+	28.8684i	1.03008	+	1.22761i
$554$	−9.18393	+	7.70623i	−0.390188	+	0.327407i
$555$	4.06680	−	13.6627i	0.172626	−	0.579948i
$556$	−6.98398	+	2.54196i	−0.296187	+	0.107803i
$557$	−24.6008	+	14.2033i	−1.04237	+	0.601812i	−0.920503	−	0.390735i	$-0.872221\pi$
$557$	−24.6008	+	14.2033i	−1.04237	+	0.601812i	−0.121865	+	0.992547i	$0.538888\pi$
$558$	1.64887	+	4.59221i	0.0698021	+	0.194404i
$559$	−6.52350	+	11.2990i	−0.275915	+	0.477898i
$560$	−13.9064	−	4.10648i	−0.587652	−	0.173530i
$561$	−23.8463	−	41.5111i	−1.00679	−	1.75260i
$562$	−5.61591	+	15.4296i	−0.236893	+	0.650858i
$563$	6.21863	−	1.09651i	0.262084	−	0.0462124i	−0.0410621	−	0.999157i	$-0.513074\pi$
$563$	6.21863	−	1.09651i	0.262084	−	0.0462124i	0.303146	+	0.952944i	$0.401963\pi$
$564$	−5.15203	−	1.88787i	−0.216940	−	0.0794937i
$565$	−25.5046	+	24.2439i	−1.07299	+	1.01995i
$566$	−24.2448			−1.01909
$567$	0.178002	−	20.4821i	0.00747538	−	0.860169i
$568$		−	0.0797117i		−	0.00334463i
$569$	2.76710	+	2.32188i	0.116003	+	0.0973381i	0.698944	−	0.715176i	$-0.253654\pi$
$569$	2.76710	+	2.32188i	0.116003	+	0.0973381i	−0.582941	+	0.812515i	$0.698098\pi$
$570$	−19.6250	−	9.81720i	−0.822000	−	0.411197i
$571$	6.03614	+	34.2327i	0.252605	+	1.43259i	0.802147	+	0.597127i	$0.203691\pi$
$571$	6.03614	+	34.2327i	0.252605	+	1.43259i	−0.549542	+	0.835466i	$0.685198\pi$
$572$	−1.27918	+	3.51451i	−0.0534851	+	0.146949i
$573$	−9.54837	+	5.48513i	−0.398889	+	0.229145i
$574$	−2.08678	+	11.8347i	−0.0871006	+	0.493972i
$575$	18.8301	+	17.4999i	0.785270	+	0.729798i
$576$	4.74740	−	26.2562i	0.197808	−	1.09401i
$577$	19.6374	−	11.3377i	0.817517	−	0.471994i	−0.0320424	−	0.999487i	$-0.510201\pi$
$577$	19.6374	−	11.3377i	0.817517	−	0.471994i	0.849559	+	0.527493i	$0.176868\pi$
$578$	−4.83505	−	13.2842i	−0.201112	−	0.552550i
$579$	5.93826	−	33.2549i	0.246785	−	1.38203i
$580$	−5.61453	+	3.72301i	−0.233131	+	0.154589i
$581$	−18.8851	+	15.8465i	−0.783485	+	0.657422i
$582$	10.0275	−	11.8977i	0.415652	−	0.493175i
$583$	−11.7842	−	32.3768i	−0.488051	−	1.34091i
$584$	8.82966	+	15.2934i	0.365374	+	0.632847i
$585$	−4.66033	+	9.26582i	−0.192681	+	0.383094i
$586$	−18.7288	+	32.4391i	−0.773678	+	1.34005i
$587$	18.6058	+	3.28071i	0.767946	+	0.135410i	0.543878	−	0.839164i	$-0.316955\pi$
$587$	18.6058	+	3.28071i	0.767946	+	0.135410i	0.224067	+	0.974574i	$0.428066\pi$
$588$	−1.27230	−	0.738253i	−0.0524688	−	0.0304450i
$589$	−5.64683	−	2.05528i	−0.232673	−	0.0846862i
$590$	8.33584	−	0.516914i	0.343181	−	0.0212810i
$591$	−12.0246	+	10.0454i	−0.494628	+	0.413214i
$592$	6.74104	−	8.03366i	0.277055	−	0.330181i
$593$		−	8.73461i		−	0.358688i	−0.983786	−	0.179344i	$-0.942603\pi$
$593$		−	8.73461i		−	0.358688i	0.983786	−	0.179344i	$-0.0573974\pi$
$594$	−5.57918	−	32.8934i	−0.228917	−	1.34963i
$595$	26.9560	+	3.04817i	1.10509	+	0.124963i
$596$	−7.27765	−	6.10667i	−0.298104	−	0.250139i
$597$	17.2248	−	2.99862i	0.704963	−	0.122725i
$598$	−9.69410	+	1.70933i	−0.396421	+	0.0698998i
$599$	6.00796	+	2.18672i	0.245479	+	0.0893469i	0.461829	−	0.886969i	$-0.347193\pi$
$599$	6.00796	+	2.18672i	0.245479	+	0.0893469i	−0.216351	+	0.976316i	$0.569415\pi$
$600$	25.7709	+	5.96278i	1.05209	+	0.243429i
$601$	2.30763	−	13.0872i	0.0941304	−	0.533840i	−0.900880	−	0.434068i	$-0.857078\pi$
$601$	2.30763	−	13.0872i	0.0941304	−	0.533840i	0.995010	−	0.0997716i	$-0.0318112\pi$
$602$	20.5959	+	11.8910i	0.839425	+	0.484642i
$603$	0.0451415	−	10.3888i	0.00183830	−	0.423064i
$604$	−0.447916	−	0.775814i	−0.0182255	−	0.0315674i
$605$	34.5297	−	8.32073i	1.40383	−	0.338286i
$606$	−0.880043	+	0.318146i	−0.0357493	+	0.0129238i
$607$	−2.88515	−	3.43839i	−0.117105	−	0.139560i	0.704307	−	0.709895i	$-0.251258\pi$
$607$	−2.88515	−	3.43839i	−0.117105	−	0.139560i	−0.821412	+	0.570335i	$0.806813\pi$
$608$	7.58895	+	9.04416i	0.307773	+	0.366789i
$609$	−23.9398	+	8.65451i	−0.970088	+	0.350698i
$610$	−3.73486	−	15.4991i	−0.151220	−	0.627540i
$611$	5.24941	+	9.09225i	0.212369	+	0.367833i
$612$	−0.0324185	+	7.46073i	−0.00131044	+	0.301582i
$613$	−20.1066	−	11.6086i	−0.812100	−	0.468866i	0.0355848	−	0.999367i	$-0.488671\pi$
$613$	−20.1066	−	11.6086i	−0.812100	−	0.468866i	−0.847685	+	0.530501i	$0.822004\pi$
$614$	−3.92882	+	22.2814i	−0.158554	+	0.899205i
$615$	1.89128	−	16.4059i	0.0762636	−	0.661549i
$616$	33.8694	+	12.3275i	1.36464	+	0.496687i
$617$	43.5312	−	7.67572i	1.75250	−	0.309013i	0.796993	−	0.603988i	$-0.206423\pi$
$617$	43.5312	−	7.67572i	1.75250	−	0.309013i	0.955505	+	0.294975i	$0.0953114\pi$
$618$	4.79214	−	0.834253i	0.192768	−	0.0335586i
$619$	−3.65944	−	3.07064i	−0.147085	−	0.123419i	0.566276	−	0.824216i	$-0.308384\pi$
$619$	−3.65944	−	3.07064i	−0.147085	−	0.123419i	−0.713361	+	0.700796i	$0.752828\pi$
$620$	1.36146	+	0.153953i	0.0546775	+	0.00618291i
$621$	−20.5763	+	17.0383i	−0.825698	+	0.683722i
$622$		−	41.7838i		−	1.67538i
$623$	−6.79689	+	8.10022i	−0.272312	+	0.324529i
$624$	−5.85581	+	4.89197i	−0.234420	+	0.195835i
$625$	−6.80964	+	24.0547i	−0.272386	+	0.962188i
$626$	−3.24464	−	1.18095i	−0.129682	−	0.0472004i
$627$	35.5399	+	20.6221i	1.41933	+	0.823566i
$628$	5.86248	+	1.03371i	0.233938	+	0.0412496i
$629$	−9.81015	+	16.9917i	−0.391156	+	0.677502i
$630$	16.8897	+	8.49484i	0.672903	+	0.338443i
$631$	−18.1400	−	31.4193i	−0.722140	−	1.25078i	−0.960140	−	0.279518i	$-0.909825\pi$
$631$	−18.1400	−	31.4193i	−0.722140	−	1.25078i	0.238000	−	0.971265i	$-0.423508\pi$
$632$	−17.2980	−	47.5258i	−0.688076	−	1.89047i
$633$	3.98266	−	4.72546i	0.158297	−	0.187820i
$634$	2.61717	−	2.19607i	0.103941	−	0.0872169i
$635$	−4.14438	−	6.24999i	−0.164465	−	0.248023i
$636$	−0.943911	+	5.28600i	−0.0374285	+	0.209604i
$637$	0.962632	+	2.64481i	0.0381409	+	0.104791i
$638$	−35.9086	+	20.7318i	−1.42163	+	0.820781i
$639$	−0.0139302	+	0.0770431i	−0.000551071	+	0.00304778i
$640$	10.5269	+	7.77577i	0.416114	+	0.307364i
$641$	3.91713	−	22.2151i	0.154717	−	0.877445i	−0.804327	−	0.594187i	$-0.797474\pi$
$641$	3.91713	−	22.2151i	0.154717	−	0.877445i	0.959044	−	0.283258i	$-0.0914151\pi$
$642$	8.12222	−	4.66587i	0.320558	−	0.184147i
$643$	−1.31828	+	3.62196i	−0.0519881	+	0.142836i	−0.962969	−	0.269613i	$-0.913104\pi$
$643$	−1.31828	+	3.62196i	−0.0519881	+	0.142836i	0.910981	+	0.412449i	$0.135326\pi$
$644$	−0.947926	−	5.37595i	−0.0373535	−	0.211842i
$645$	−29.2289	−	14.6215i	−1.15089	−	0.575719i
$646$	23.1364	+	19.4137i	0.910288	+	0.763823i
$647$		−	16.5713i		−	0.651486i	−0.945458	−	0.325743i	$-0.894386\pi$
$647$		−	16.5713i		−	0.651486i	0.945458	−	0.325743i	$-0.105614\pi$
$648$	−9.62609	+	25.7490i	−0.378148	+	1.01152i
$649$	−15.6390			−0.613884
$650$	−5.77418	−	7.63570i	−0.226482	−	0.299497i
$651$	4.86123	+	1.78131i	0.190527	+	0.0698152i
$652$	−11.3326	+	1.99825i	−0.443821	+	0.0782576i
$653$	1.76642	−	4.85320i	0.0691254	−	0.189920i	−0.900320	−	0.435230i	$-0.856667\pi$
$653$	1.76642	−	4.85320i	0.0691254	−	0.189920i	0.969445	+	0.245309i	$0.0788894\pi$
$654$	8.49608	+	14.7898i	0.332223	+	0.578325i
$655$	3.49459	−	11.8343i	0.136545	−	0.462403i
$656$	6.07471	−	10.5217i	0.237178	−	0.410804i
$657$	−5.86142	−	16.3245i	−0.228676	−	0.636879i
$658$	16.5733	−	9.56862i	0.646096	−	0.373024i
$659$	−33.9146	+	12.3439i	−1.32113	+	0.480850i	−0.903819	−	0.427915i	$-0.859248\pi$
$659$	−33.9146	+	12.3439i	−1.32113	+	0.480850i	−0.417307	+	0.908766i	$0.637026\pi$
$660$	−8.97931	−	2.67276i	−0.349519	−	0.104037i
$661$	29.5546	−	24.7993i	1.14954	−	0.964580i	0.149833	−	0.988711i	$-0.452127\pi$
$661$	29.5546	−	24.7993i	1.14954	−	0.964580i	0.999709	+	0.0241316i	$0.00768206\pi$
$662$	22.2322	+	26.4953i	0.864079	+	1.02977i
$663$	9.19981	−	10.9157i	0.357291	−	0.423929i
$664$	31.0903	−	11.3160i	1.20654	−	0.439144i
$665$	−21.3450	+	9.30251i	−0.827722	+	0.360736i
$666$	−10.5127	+	8.74362i	−0.407358	+	0.338808i
$667$	28.7531	+	16.6006i	1.11332	+	0.642778i
$668$	2.46238	+	0.434185i	0.0952725	+	0.0167991i
$669$	16.1354	−	27.8076i	0.623829	−	1.07510i
$670$	8.58506	+	4.27130i	0.331670	+	0.165015i
$671$	5.18394	+	29.3996i	0.200124	+	1.13496i
$672$	−6.52141	−	7.80629i	−0.251569	−	0.301134i
$673$	−6.19702	+	7.38532i	−0.238878	+	0.284683i	−0.872143	−	0.489252i	$-0.837270\pi$
$673$	−6.19702	+	7.38532i	−0.238878	+	0.284683i	0.633265	+	0.773935i	$0.281714\pi$
$674$	−17.6715			−0.680682
$675$	−23.8661	−	10.2668i	−0.918608	−	0.395170i
$676$	4.94968			0.190372
$677$	15.8761	−	18.9204i	0.610167	−	0.727169i	−0.369179	−	0.929358i	$-0.620361\pi$
$677$	15.8761	−	18.9204i	0.610167	−	0.727169i	0.979346	+	0.202189i	$0.0648056\pi$
$678$	33.2532	−	5.78898i	1.27708	−	0.222324i
$679$	−2.86697	−	16.2594i	−0.110024	−	0.623979i
$680$	−32.5960	−	16.2174i	−1.25000	−	0.621908i
$681$	42.6180	+	0.0925918i	1.63313	+	0.00354813i
$682$	8.30486	+	1.46437i	0.318010	+	0.0560737i
$683$	17.9981	+	10.3912i	0.688678	+	0.397609i	0.803117	−	0.595822i	$-0.203174\pi$
$683$	17.9981	+	10.3912i	0.688678	+	0.397609i	−0.114438	+	0.993430i	$0.536507\pi$
$684$	−3.17770	−	5.55958i	−0.121502	−	0.212576i
$685$	12.1774	−	5.30711i	0.465273	−	0.202774i
$686$	23.3593	−	8.50208i	0.891861	−	0.324611i
$687$	1.20154	+	3.32364i	0.0458414	+	0.126805i
$688$	−15.4549	−	18.4184i	−0.589212	−	0.702195i
$689$	7.87048	−	6.60411i	0.299841	−	0.251597i
$690$	−5.72442	−	23.9841i	−0.217925	−	0.913060i
$691$	−12.2565	+	4.46098i	−0.466257	+	0.169704i	−0.564456	−	0.825463i	$-0.690914\pi$
$691$	−12.2565	+	4.46098i	−0.466257	+	0.169704i	0.0981988	+	0.995167i	$0.468692\pi$
$692$	5.78643	−	3.34080i	0.219967	−	0.126998i
$693$	−30.5812	−	17.8337i	−1.16168	−	0.677446i
$694$	−10.9387	+	18.9463i	−0.415226	+	0.719193i
$695$	−10.0883	+	34.1637i	−0.382672	+	1.29590i
$696$	34.1638	+	0.0742241i	1.29497	+	0.00281346i
$697$	−7.77416	+	21.3593i	−0.294467	+	0.809042i
$698$	29.8396	−	5.26153i	1.12945	−	0.199152i
$699$	−2.57793	−	14.8082i	−0.0975062	−	0.560098i
$700$	4.23445	−	3.20212i	0.160047	−	0.121029i
$701$	25.6062			0.967135			0.483567	−	0.875307i	$-0.339341\pi$
$701$	25.6062			0.967135			0.483567	+	0.875307i	$0.339341\pi$
$702$	8.64807	−	4.91809i	0.326400	−	0.185621i
$703$		−	16.8402i		−	0.635141i
$704$	−35.3263	−	29.6423i	−1.33141	−	1.11719i
$705$	−21.9496	+	14.4863i	−0.826670	+	0.545584i
$706$	−6.85846	−	38.8962i	−0.258121	−	1.46388i
$707$	−0.339609	+	0.933067i	−0.0127723	+	0.0350916i
$708$	2.10809	+	1.22322i	0.0792268	+	0.0459714i
$709$	−2.06567	+	11.7150i	−0.0775777	+	0.439965i	0.921135	+	0.389243i	$0.127263\pi$
$709$	−2.06567	+	11.7150i	−0.0775777	+	0.439965i	−0.998713	+	0.0507221i	$0.983848\pi$
$710$	−0.0581260	−	0.0429350i	−0.00218143	−	0.00161132i
$711$	8.41337	+	48.9576i	0.315526	+	1.83605i
$712$	12.2899	−	7.09558i	0.460584	−	0.265918i
$713$	−2.30951	−	6.34531i	−0.0864917	−	0.237634i
$714$	−19.8970	−	16.7694i	−0.744628	−	0.627579i
$715$	9.90660	+	14.9398i	0.370486	+	0.558716i
$716$	2.03368	−	1.70646i	0.0760021	−	0.0637733i
$717$	6.43145	+	1.14845i	0.240187	+	0.0428897i
$718$	3.49908	+	9.61363i	0.130584	+	0.358777i
$719$	3.31070	+	5.73431i	0.123468	+	0.213854i	0.921133	−	0.389247i	$-0.127265\pi$
$719$	3.31070	+	5.73431i	0.123468	+	0.213854i	−0.797665	+	0.603101i	$0.793932\pi$
$720$	−13.1083	−	13.9104i	−0.488517	−	0.518411i
$721$	2.58068	−	4.46987i	0.0961096	−	0.166467i
$722$	−2.35820	−	0.415814i	−0.0877630	−	0.0154750i
$723$	0.850445	−	0.488544i	0.0316284	−	0.0181692i
$724$	4.45093	+	1.62000i	0.165417	+	0.0602070i
$725$	−1.63535	+	32.2474i	−0.0607355	+	1.19764i
$726$	−31.9892	−	11.7219i	−1.18723	−	0.435040i
$727$	−7.62291	+	9.08463i	−0.282718	+	0.336930i	−0.888650	−	0.458586i	$-0.848356\pi$
$727$	−7.62291	+	9.08463i	−0.282718	+	0.336930i	0.605932	+	0.795517i	$0.292800\pi$
$728$			10.7478i			0.398341i
$729$	13.8037	−	23.2047i	0.511246	−	0.859434i
$730$	15.9079	+	1.79886i	0.588778	+	0.0665787i
$731$	34.4587	+	28.9142i	1.27450	+	1.06943i
$732$	1.60074	−	4.36844i	0.0591650	−	0.161462i
$733$	12.6872	−	2.23709i	0.468612	−	0.0826289i	0.0656441	−	0.997843i	$-0.479090\pi$
$733$	12.6872	−	2.23709i	0.468612	−	0.0826289i	0.402968	+	0.915214i	$0.367979\pi$
$734$	25.1976	+	9.17116i	0.930059	+	0.338514i
$735$	−6.46926	+	2.80271i	−0.238622	+	0.103380i
$736$	−2.30374	+	13.0651i	−0.0849169	+	0.481588i
$737$	−15.5499	−	8.97771i	−0.572786	−	0.330698i
$738$	−10.2349	+	12.0905i	−0.376754	+	0.445056i
$739$	−12.2765	−	21.2636i	−0.451600	−	0.782194i	0.546886	−	0.837207i	$-0.315813\pi$
$739$	−12.2765	−	21.2636i	−0.451600	−	0.782194i	−0.998486	+	0.0550133i	$0.982480\pi$
$740$	0.899506	+	3.73281i	0.0330665	+	0.137221i
$741$	−2.15387	+	12.0619i	−0.0791243	+	0.443104i
$742$	−12.0380	−	14.3463i	−0.441928	−	0.526669i
$743$	−26.5027	−	31.5847i	−0.972291	−	1.15873i	−0.987304	−	0.158844i	$-0.949223\pi$
$743$	−26.5027	−	31.5847i	−0.972291	−	1.15873i	0.0150131	−	0.999887i	$-0.495221\pi$
$744$	−5.31301	−	4.47785i	−0.194784	−	0.164166i
$745$	−44.2672	+	10.6672i	−1.62182	+	0.390816i
$746$	−18.9194	−	32.7694i	−0.692690	−	1.19977i
$747$	−32.0270	+	5.50385i	−1.17181	+	0.201375i
$748$	11.1672	+	6.44737i	0.408313	+	0.235739i
$749$	1.72593	−	9.78822i	0.0630640	−	0.357654i
$750$	18.2290	−	15.5805i	0.665630	−	0.568920i
$751$	−11.6980	−	4.25772i	−0.426866	−	0.155366i	0.119648	−	0.992816i	$-0.461823\pi$
$751$	−11.6980	−	4.25772i	−0.426866	−	0.155366i	−0.546514	+	0.837450i	$0.684045\pi$
$752$	−19.0537	+	3.35968i	−0.694817	+	0.122515i
$753$	−0.945949	−	1.13233i	−0.0344723	−	0.0412642i
$754$	−9.47154	−	7.94756i	−0.344933	−	0.289433i
$755$	−4.26648	−	0.482451i	−0.155273	−	0.0175582i
$756$	2.72737	+	4.79586i	0.0991935	+	0.174424i
$757$		−	11.3137i		−	0.411203i	−0.978636	−	0.205602i	$-0.934085\pi$
$757$		−	11.3137i		−	0.411203i	0.978636	−	0.205602i	$-0.0659152\pi$
$758$	−5.16630	+	6.15696i	−0.187648	+	0.223631i
$759$	7.91891	+	45.4881i	0.287438	+	1.65111i
$760$	31.1888	−	1.93405i	1.13134	−	0.0701555i
$761$	−21.2994	−	7.75233i	−0.772101	−	0.281022i	−0.0742262	−	0.997241i	$-0.523649\pi$
$761$	−21.2994	−	7.75233i	−0.772101	−	0.281022i	−0.697875	+	0.716220i	$0.745871\pi$
$762$	−0.0156281	+	7.19329i	−0.000566147	+	0.260585i
$763$	17.8234	+	3.14274i	0.645250	+	0.113775i
$764$	1.48302	−	2.56867i	0.0536539	−	0.0929313i
$765$	28.6706	+	21.3708i	1.03659	+	0.772664i
$766$	−4.66529	−	8.08053i	−0.168564	−	0.291961i
$767$	−1.59500	−	4.38222i	−0.0575920	−	0.158233i
$768$	6.20668	+	17.1687i	0.223964	+	0.619521i
$769$	−11.6191	+	9.74955i	−0.418994	+	0.351578i	−0.827780	−	0.561052i	$-0.810397\pi$
$769$	−11.6191	+	9.74955i	−0.418994	+	0.351578i	0.408786	+	0.912630i	$0.365952\pi$
$770$	27.2322	−	18.0577i	0.981381	−	0.650756i
$771$	29.9627	−	10.8319i	1.07908	−	0.390101i
$772$	3.11204	+	8.55027i	0.112005	+	0.307731i
$773$	−4.20823	+	2.42962i	−0.151359	+	0.0873874i	−0.573767	−	0.819019i	$-0.694518\pi$
$773$	−4.20823	+	2.42962i	−0.151359	+	0.0873874i	0.422407	+	0.906406i	$0.361185\pi$
$774$	15.5563	+	27.2167i	0.559160	+	0.978286i
$775$	4.47054	−	4.81035i	0.160587	−	0.172793i
$776$	−3.84768	+	21.8213i	−0.138124	+	0.783338i
$777$	−0.0315219	+	14.5089i	−0.00113084	+	0.520502i
$778$	−3.34599	+	9.19303i	−0.119960	+	0.329586i
$779$	−3.38777	−	19.2130i	−0.121379	−	0.688377i
$780$	−0.166849	−	2.78869i	−0.00597414	−	0.0998512i
$781$	0.103657	+	0.0869789i	0.00370916	+	0.00311235i
$782$			33.9383i			1.21363i
$783$	−33.0071	−	6.04211i	−1.17958	−	0.215928i
$784$	−5.18676			−0.185241
$785$	20.6797	−	19.6576i	0.738091	−	0.701609i
$786$	−9.08349	+	7.58838i	−0.323997	+	0.270669i
$787$	4.82676	−	0.851088i	0.172055	−	0.0303380i	−0.0869567	−	0.996212i	$-0.527714\pi$
$787$	4.82676	−	0.851088i	0.172055	−	0.0303380i	0.259012	+	0.965874i	$0.416603\pi$
$788$	1.44345	−	3.96585i	0.0514209	−	0.141278i
$789$	−6.06770	+	10.4570i	−0.216016	+	0.372280i
$790$	−43.9731	−	12.9850i	−1.56449	−	0.461985i
$791$	17.9076	−	31.0170i	0.636723	−	1.10284i
$792$	30.3810	+	36.5279i	1.07954	+	1.29796i
$793$	−7.70938	+	4.45101i	−0.273768	+	0.158060i
$794$	−1.88220	+	0.685063i	−0.0667966	+	0.0243120i
$795$	17.6909	+	18.6919i	0.627430	+	0.662934i
$796$	−3.60756	+	3.02710i	−0.127866	+	0.107293i
$797$	−35.8673	−	42.7450i	−1.27049	−	1.51411i	−0.752270	−	0.658855i	$-0.771041\pi$
$797$	−35.8673	−	42.7450i	−1.27049	−	1.51411i	−0.518215	−	0.855250i	$-0.673403\pi$
$798$	21.9864	+	3.92607i	0.778310	+	0.138981i
$799$	34.0142	−	12.3802i	1.20334	−	0.437978i
$800$	−12.3320	+	3.79307i	−0.436001	+	0.134105i
$801$	−13.1185	+	4.71028i	−0.463518	+	0.166430i
$802$	12.7814	+	7.37937i	0.451328	+	0.260575i
$803$	−29.5223	−	5.20557i	−1.04182	−	0.183701i
$804$	1.39387	+	2.42641i	0.0491581	+	0.0855731i
$805$	−23.4250	−	11.6546i	−0.825623	−	0.410770i
$806$	0.436667	+	2.47646i	0.0153809	+	0.0872296i
$807$	−5.39585	+	14.7254i	−0.189943	+	0.518358i
$808$	0.856584	−	1.02084i	0.0301345	−	0.0359129i
$809$	25.0205			0.879673			0.439837	−	0.898078i	$-0.355036\pi$
$809$	25.0205			0.879673			0.439837	+	0.898078i	$0.355036\pi$
$810$	13.5913	+	20.8885i	0.477551	+	0.733947i
$811$	22.4129			0.787024			0.393512	−	0.919320i	$-0.371260\pi$
$811$	22.4129			0.787024			0.393512	+	0.919320i	$0.371260\pi$
$812$	4.40739	−	5.25253i	0.154669	−	0.184328i
$813$	−1.59783	+	4.36049i	−0.0560382	+	0.152929i
$814$	4.10374	+	23.2735i	0.143836	+	0.815735i
$815$	−24.5681	+	49.3805i	−0.860584	+	1.72972i
$816$	13.1041	+	22.8113i	0.458736	+	0.798556i
$817$	−38.0222	−	6.70435i	−1.33023	−	0.234555i
$818$	−12.2381	−	7.06565i	−0.427894	−	0.247045i
$819$	1.87826	−	10.3880i	0.0656318	−	0.362986i
$820$	1.77718	+	4.07781i	0.0620619	+	0.142403i
$821$	−37.8576	+	13.7790i	−1.32124	+	0.480892i	−0.903855	−	0.427838i	$-0.859275\pi$
$821$	−37.8576	+	13.7790i	−1.32124	+	0.480892i	−0.417384	+	0.908730i	$0.637053\pi$
$822$	−12.5433	−	2.23983i	−0.437498	−	0.0781231i
$823$	−8.96086	−	10.6791i	−0.312356	−	0.372251i	0.586911	−	0.809651i	$-0.300344\pi$
$823$	−8.96086	−	10.6791i	−0.312356	−	0.372251i	−0.899267	+	0.437400i	$0.855899\pi$
$824$	−5.30632	+	4.45253i	−0.184854	+	0.155111i
$825$	−35.8745	+	27.0062i	−1.24899	+	0.940237i
$826$	−7.98790	+	2.90736i	−0.277935	+	0.101160i
$827$	30.3778	−	17.5386i	1.05634	−	0.609878i	0.131922	−	0.991260i	$-0.457885\pi$
$827$	30.3778	−	17.5386i	1.05634	−	0.609878i	0.924418	+	0.381382i	$0.124552\pi$
$828$	2.49045	−	6.75104i	0.0865491	−	0.234615i
$829$	−16.3803	+	28.3716i	−0.568912	+	0.985385i	0.427762	+	0.903892i	$0.359302\pi$
$829$	−16.3803	+	28.3716i	−0.568912	+	0.985385i	−0.996674	+	0.0814933i	$0.974031\pi$
$830$	8.49451	−	28.7662i	0.294849	−	0.998491i
$831$	−8.41586	+	14.5038i	−0.291943	+	0.503132i
$832$	4.70322	−	12.9220i	0.163055	−	0.447989i
$833$	9.55639	−	1.68505i	0.331109	−	0.0583835i
$834$	26.2226	−	21.9064i	0.908014	−	0.758558i
$835$	8.68600	−	8.25667i	0.300591	−	0.285734i
$836$	−11.0676			−0.382782
$837$	4.35260	+	5.25643i	0.150448	+	0.181689i
$838$			39.9932i			1.38154i
$839$	−13.1790	−	11.0585i	−0.454991	−	0.381783i	0.386293	−	0.922376i	$-0.373755\pi$
$839$	−13.1790	−	11.0585i	−0.454991	−	0.381783i	−0.841284	+	0.540593i	$0.818200\pi$
$840$	−26.8747	+	1.60792i	−0.927264	+	0.0554786i
$841$	2.20580	+	12.5097i	0.0760621	+	0.431370i
$842$	−5.71508	+	15.7021i	−0.196955	+	0.541128i
$843$	−0.0498965	+	22.9663i	−0.00171853	+	0.791001i
$844$	−0.289053	+	1.63930i	−0.00994960	+	0.0564270i
$845$	14.0951	−	19.0822i	0.484888	−	0.656448i
$846$	25.2259	+	0.109612i	0.867286	+	0.00376854i
$847$	−31.3072	+	18.0752i	−1.07573	+	0.621073i
$848$	6.47569	+	17.7918i	0.222376	+	0.610973i
$849$	−31.8912	+	11.5290i	−1.09450	+	0.395675i
$850$	−29.3829	+	15.0339i	−1.00782	+	0.515660i
$851$	14.4961	−	12.1636i	0.496919	−	0.416964i
$852$	−0.00716956	−	0.0198322i	−0.000245625	−	0.000679439i
$853$	16.6428	+	45.7258i	0.569840	+	1.56562i	0.804756	+	0.593606i	$0.202296\pi$
$853$	16.6428	+	45.7258i	0.569840	+	1.56562i	−0.234916	+	0.972016i	$0.575482\pi$
$854$	8.11330	+	14.0526i	0.277631	+	0.480872i
$855$	−30.4827	−	3.58118i	−1.04248	−	0.122474i
$856$	−6.66956	+	11.5520i	−0.227961	+	0.394840i
$857$	9.48011	+	1.67160i	0.323835	+	0.0571008i	0.333202	−	0.942855i	$-0.391871\pi$
$857$	9.48011	+	1.67160i	0.323835	+	0.0571008i	−0.00936777	+	0.999956i	$0.502982\pi$
$858$	0.0373570	−	17.1946i	0.00127535	−	0.587015i
$859$	−30.1158	−	10.9613i	−1.02754	−	0.373993i	−0.227395	−	0.973803i	$-0.573021\pi$
$859$	−30.1158	−	10.9613i	−1.02754	−	0.373993i	−0.800143	+	0.599809i	$0.795243\pi$
$860$	8.78614	−	0.544838i	0.299605	−	0.0185788i
$861$	2.88280	+	16.5595i	0.0982457	+	0.564346i
$862$	18.3459	−	21.8638i	0.624863	−	0.744682i
$863$		−	11.1232i		−	0.378637i	−0.981916	−	0.189319i	$-0.939372\pi$
$863$		−	11.1232i		−	0.378637i	0.981916	−	0.189319i	$-0.0606279\pi$
$864$	−2.24221	−	13.2195i	−0.0762815	−	0.449735i
$865$	3.59838	−	31.8217i	0.122348	−	1.08197i
$866$	−27.2295	−	22.8482i	−0.925295	−	0.776415i
$867$	−12.6769	−	15.1746i	−0.430531	−	0.515356i
$868$	−1.37334	+	0.242158i	−0.0466143	+	0.00821936i
$869$	80.6777	+	29.3643i	2.73680	+	0.996114i
$870$	18.4557	−	24.8723i	0.625707	−	0.843251i
$871$	0.929747	−	5.27286i	0.0315033	−	0.178664i
$872$	−21.0351	−	12.1446i	−0.712338	−	0.411268i
$873$	7.53229	−	20.4183i	0.254930	−	0.691055i
$874$	−14.5647	−	25.2268i	−0.492659	−	0.853310i
$875$	−0.286568	−	25.4435i	−0.00968776	−	0.860147i
$876$	3.57235	+	3.01081i	0.120699	+	0.101726i
$877$	34.3783	+	40.9704i	1.16087	+	1.38347i	0.909563	+	0.415567i	$0.136417\pi$
$877$	34.3783	+	40.9704i	1.16087	+	1.38347i	0.251309	+	0.967907i	$0.419139\pi$
$878$	2.13039	+	2.53890i	0.0718971	+	0.0856836i
$879$	−9.20980	+	51.5758i	−0.310639	+	1.73961i
$880$	−32.1153	+	7.73891i	−1.08261	+	0.260879i
$881$	−12.0656	−	20.8982i	−0.406500	−	0.704078i	0.587995	−	0.808864i	$-0.299917\pi$
$881$	−12.0656	−	20.8982i	−0.406500	−	0.704078i	−0.994495	+	0.104787i	$0.966584\pi$
$882$	6.65479	+	1.20326i	0.224078	+	0.0405158i
$883$	15.3713	+	8.87464i	0.517286	+	0.298655i	0.735824	−	0.677173i	$-0.236795\pi$
$883$	15.3713	+	8.87464i	0.517286	+	0.298655i	−0.218537	+	0.975829i	$0.570129\pi$
$884$	−0.667701	+	3.78672i	−0.0224572	+	0.127361i
$885$	10.7190	−	4.64384i	0.360315	−	0.156101i
$886$	−3.24795	−	1.18216i	−0.109117	−	0.0397154i
$887$	2.06559	−	0.364220i	0.0693559	−	0.0122293i	−0.138863	−	0.990312i	$-0.544345\pi$
$887$	2.06559	−	0.364220i	0.0693559	−	0.0122293i	0.208218	+	0.978082i	$0.433234\pi$
$888$	6.69953	−	18.2831i	0.224822	−	0.613542i
$889$	5.84701	+	4.90623i	0.196103	+	0.164550i
$890$	1.44557	−	12.7837i	0.0484558	−	0.428511i
$891$	−22.9804	−	40.6143i	−0.769872	−	1.36063i
$892$			8.65966i			0.289947i
$893$	−19.9703	+	23.7996i	−0.668280	+	0.796425i
$894$	41.0103	+	15.0275i	1.37159	+	0.502595i
$895$	−0.787527	−	12.6998i	−0.0263241	−	0.424507i
$896$	−12.5171	−	4.55584i	−0.418166	−	0.152200i
$897$	−11.9386	+	6.85822i	−0.398619	+	0.228989i
$898$	29.3074	+	5.16769i	0.978001	+	0.172448i
$899$	4.24080	−	7.34528i	0.141439	−	0.244979i
$900$	6.94809	−	0.834401i	0.231603	−	0.0278134i
$901$	−17.7113	−	30.6769i	−0.590049	−	1.02200i
$902$	9.36392	+	25.7272i	0.311785	+	0.856621i
$903$	32.7459	+	5.84737i	1.08972	+	0.194588i
$904$	−36.8212	+	30.8966i	−1.22465	+	1.02761i
$905$	18.9204	−	12.5461i	0.628935	−	0.417048i
$906$	3.14921	+	2.65418i	0.104626	+	0.0881793i
$907$	−14.6217	−	40.1727i	−0.485504	−	1.33391i	−0.904713	−	0.426022i	$-0.859915\pi$
$907$	−14.6217	−	40.1727i	−0.485504	−	1.33391i	0.419208	−	0.907890i	$-0.362308\pi$
$908$	−9.94141	+	5.73967i	−0.329917	+	0.190478i
$909$	−1.00631	+	0.836966i	−0.0333770	+	0.0277604i
$910$	7.83734	+	5.78908i	0.259805	+	0.191906i
$911$	3.61639	−	20.5096i	0.119816	−	0.679513i	−0.864436	−	0.502743i	$-0.832324\pi$
$911$	3.61639	−	20.5096i	0.119816	−	0.679513i	0.984252	−	0.176770i	$-0.0565647\pi$
$912$	−19.5300	−	11.3323i	−0.646704	−	0.375251i
$913$	−19.2095	+	52.7776i	−0.635741	+	1.74668i
$914$	−6.60204	−	37.4420i	−0.218376	−	1.23847i
$915$	−12.2830	−	18.6112i	−0.406063	−	0.615268i
$916$	−0.729227	−	0.611894i	−0.0240943	−	0.0202175i
$917$			12.5591i			0.414739i
$918$	−11.5211	−	32.3077i	−0.380254	−	1.06631i
$919$	14.9586			0.493438			0.246719	−	0.969087i	$-0.420648\pi$
$919$	14.9586			0.493438			0.246719	+	0.969087i	$0.420648\pi$
$920$	24.1924	+	25.4504i	0.797601	+	0.839075i
$921$	5.42750	+	31.1768i	0.178842	+	1.02731i
$922$	−13.2312	+	2.33302i	−0.435747	+	0.0768340i
$923$	−0.0138006	+	0.0379168i	−0.000454252	+	0.00124805i
$924$	9.53543	+	0.0207167i	0.313693	+	0.000681528i
$925$	16.9524	+	7.16207i	0.557392	+	0.235488i
$926$	−20.1693	+	34.9343i	−0.662804	+	1.14801i
$927$	5.90679	−	3.37615i	0.194004	−	0.110887i
$928$	−14.4312	+	8.33188i	−0.473729	+	0.273507i
$929$	25.6422	−	9.33300i	0.841294	−	0.306206i	0.114808	−	0.993388i	$-0.463375\pi$
$929$	25.6422	−	9.33300i	0.841294	−	0.306206i	0.726486	+	0.687182i	$0.241152\pi$
$930$	−6.12700	+	1.46236i	−0.200912	+	0.0479528i
$931$	−6.38026	+	5.35367i	−0.209105	+	0.175460i
$932$	2.60241	+	3.10144i	0.0852449	+	0.101591i
$933$	−19.8693	−	54.9617i	−0.650491	−	1.79936i
$934$	−15.9542	+	5.80685i	−0.522037	+	0.190006i
$935$	56.6569	−	24.6921i	1.85288	−	0.807517i
$936$	−7.13699	+	12.2385i	−0.233280	+	0.400028i
$937$	−47.0967	−	27.1913i	−1.53858	−	0.888300i	−0.998922	−	0.0464165i	$-0.985220\pi$
$937$	−47.0967	−	27.1913i	−1.53858	−	0.888300i	−0.539659	−	0.841884i	$-0.681447\pi$
$938$	−9.61136	−	1.69474i	−0.313822	−	0.0553353i
$939$	−4.82952	−	0.0104926i	−0.157605	−	0.000342413i
$940$	3.15538	−	6.34214i	0.102917	−	0.206858i
$941$	−8.21935	−	46.6142i	−0.267943	−	1.51958i	−0.760522	−	0.649313i	$-0.775057\pi$
$941$	−8.21935	−	46.6142i	−0.267943	−	1.51958i	0.492579	−	0.870268i	$-0.336054\pi$
$942$	−26.9625	+	4.69385i	−0.878487	+	0.152934i
$943$	14.0916	−	16.7937i	0.458885	−	0.546878i
$944$	8.59400			0.279711
$945$	26.2559	+	3.14246i	0.854106	+	0.102224i
$946$	54.1812			1.76158
$947$	−26.0639	+	31.0617i	−0.846962	+	1.00937i	0.152815	+	0.988255i	$0.451166\pi$
$947$	−26.0639	+	31.0617i	−0.846962	+	1.00937i	−0.999777	+	0.0211155i	$0.993278\pi$
$948$	−8.57834	−	10.2685i	−0.278612	−	0.333505i
$949$	−1.55227	−	8.80337i	−0.0503889	−	0.285769i
$950$	15.3889	−	23.7847i	0.499280	−	0.771677i
$951$	2.39829	−	4.13319i	0.0777699	−	0.134028i
$952$	36.4927	+	6.43465i	1.18273	+	0.208548i
$953$	−23.2862	−	13.4443i	−0.754315	−	0.435504i	0.0729359	−	0.997337i	$-0.476763\pi$
$953$	−23.2862	−	13.4443i	−0.754315	−	0.435504i	−0.827251	+	0.561833i	$0.810096\pi$
$954$	−4.18107	−	24.3298i	−0.135367	−	0.787705i
$955$	−5.67967	−	13.0322i	−0.183790	−	0.421712i
$956$	−1.65361	+	0.601865i	−0.0534816	+	0.0194657i
$957$	−37.3750	+	44.3457i	−1.20816	+	1.43349i
$958$	−9.40297	−	11.2060i	−0.303796	−	0.362050i
$959$	−10.3570	+	8.69054i	−0.334444	+	0.280632i
$960$	33.0147	+	9.82709i	1.06555	+	0.317168i
$961$	27.5095	−	10.0126i	0.887403	−	0.322988i
$962$	−6.10295	+	3.52354i	−0.196767	+	0.113603i
$963$	8.46508	−	9.99972i	0.272783	−	0.322236i
$964$	−0.132088	+	0.228784i	−0.00425428	+	0.00736864i
$965$	41.8255	+	12.3508i	1.34641	+	0.397587i
$966$	12.5012	+	21.7617i	0.402218	+	0.700171i
$967$	13.0453	−	35.8418i	0.419510	−	1.15259i	−0.532474	−	0.846446i	$-0.678738\pi$
$967$	13.0453	−	35.8418i	0.419510	−	1.15259i	0.951984	−	0.306147i	$-0.0990401\pi$
$968$	47.7794	−	8.42480i	1.53569	−	0.270783i
$969$	39.6649	+	14.5345i	1.27422	+	0.466916i
$970$	13.8397	+	14.5593i	0.444364	+	0.467470i
$971$	−52.8853			−1.69717			−0.848585	−	0.529059i	$-0.822545\pi$
$971$	−52.8853			−1.69717			−0.848585	+	0.529059i	$0.822545\pi$
$972$	−0.0789999	+	7.27212i	−0.00253392	+	0.233253i
$973$		−	36.2562i		−	1.16232i
$974$	29.9846	+	25.1600i	0.960767	+	0.806179i
$975$	−11.2262	−	7.29809i	−0.359527	−	0.233726i
$976$	−2.84870	−	16.1558i	−0.0911846	−	0.517134i
$977$	−7.16089	+	19.6744i	−0.229097	+	0.629439i	−0.999972	−	0.00754795i	$-0.997597\pi$
$977$	−7.16089	+	19.6744i	−0.229097	+	0.629439i	0.770874	+	0.636987i	$0.219820\pi$
$978$	45.8742	−	26.3527i	1.46689	−	0.842668i
$979$	−4.18324	+	23.7243i	−0.133697	+	0.758233i
$980$	1.12829	−	1.52749i	0.0360419	−	0.0487940i
$981$	18.2085	+	15.4141i	0.581353	+	0.492133i
$982$	−17.5749	+	10.1469i	−0.560838	+	0.323800i
$983$	12.7694	+	35.0835i	0.407279	+	1.11899i	0.958615	+	0.284707i	$0.0918963\pi$
$983$	12.7694	+	35.0835i	0.407279	+	1.11899i	−0.551335	+	0.834284i	$0.685881\pi$
$984$	3.96546	−	22.2070i	0.126414	−	0.707933i
$985$	−11.1788	−	16.8584i	−0.356187	−	0.537153i
$986$	−32.6553	+	27.4011i	−1.03996	+	0.872628i
$987$	17.2501	−	20.4674i	0.549078	−	0.651486i
$988$	−1.12877	−	3.10127i	−0.0359110	−	0.0986646i
$989$	−21.6923	−	37.5721i	−0.689774	−	1.19472i
$990$	43.0003	−	2.47898i	1.36664	−	0.0787872i
$991$	17.5105	−	30.3291i	0.556240	−	0.963436i	−0.441566	−	0.897229i	$-0.645577\pi$
$991$	17.5105	−	30.3291i	0.556240	−	0.963436i	0.997806	−	0.0662071i	$-0.0210898\pi$
$992$	3.33763	+	0.588514i	0.105970	+	0.0186853i
$993$	41.8430	+	24.2794i	1.32785	+	0.770485i
$994$	0.0691147	+	0.0251557i	0.00219218	+	0.000797890i
$995$	1.39700	+	22.5282i	0.0442879	+	0.714193i
$996$	6.71743	−	5.61177i	0.212850	−	0.177816i
$997$	−30.6391	+	36.5143i	−0.970351	+	1.15642i	0.0173159	+	0.999850i	$0.494488\pi$
$997$	−30.6391	+	36.5143i	−0.970351	+	1.15642i	−0.987667	+	0.156569i	$0.949957\pi$
$998$		−	49.2436i		−	1.55878i
$999$	−9.67036	+	16.5002i	−0.305957	+	0.522045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.124.11	yes	96
3.2	odd	2		405.2.p.a.289.6		96
5.2	odd	4		675.2.l.h.151.11		96
5.3	odd	4		675.2.l.h.151.6		96
5.4	even	2	inner	135.2.p.a.124.6	yes	96
15.14	odd	2		405.2.p.a.289.11		96
27.5	odd	18		405.2.p.a.199.11		96
27.22	even	9	inner	135.2.p.a.49.6	✓	96
135.22	odd	36		675.2.l.h.76.11		96
135.49	even	18	inner	135.2.p.a.49.11	yes	96
135.59	odd	18		405.2.p.a.199.6		96
135.103	odd	36		675.2.l.h.76.6		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.6	✓	96	27.22	even	9	inner
135.2.p.a.49.11	yes	96	135.49	even	18	inner
135.2.p.a.124.6	yes	96	5.4	even	2	inner
135.2.p.a.124.11	yes	96	1.1	even	1	trivial
405.2.p.a.199.6		96	135.59	odd	18
405.2.p.a.199.11		96	27.5	odd	18
405.2.p.a.289.6		96	3.2	odd	2
405.2.p.a.289.11		96	15.14	odd	2
675.2.l.h.76.6		96	135.103	odd	36
675.2.l.h.76.11		96	135.22	odd	36
675.2.l.h.151.6		96	5.3	odd	4
675.2.l.h.151.11		96	5.2	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.795984 - 0.948617i) q^{2} +(0.595931 - 1.62630i) q^{3} +(0.0810128 + 0.459446i) q^{4} +(2.00198 + 0.996037i) q^{5} +(-1.06839 - 1.85982i) q^{6} +(-2.24130 - 0.395202i) q^{7} +(2.64518 + 1.52719i) q^{8} +(-2.28973 - 1.93833i) q^{9} +O(q^{10})\)	\(q+(0.795984 - 0.948617i) q^{2} +(0.595931 - 1.62630i) q^{3} +(0.0810128 + 0.459446i) q^{4} +(2.00198 + 0.996037i) q^{5} +(-1.06839 - 1.85982i) q^{6} +(-2.24130 - 0.395202i) q^{7} +(2.64518 + 1.52719i) q^{8} +(-2.28973 - 1.93833i) q^{9} +(2.53840 - 1.10628i) q^{10} +(-4.87230 + 1.77337i) q^{11} +(0.795478 + 0.142047i) q^{12} +(-0.993836 - 1.18441i) q^{13} +(-2.15894 + 1.81156i) q^{14} +(2.81290 - 2.66225i) q^{15} +(2.67745 - 0.974511i) q^{16} +(-4.61649 + 2.66533i) q^{17} +(-3.66133 + 0.629199i) q^{18} +(2.28767 - 3.96236i) q^{19} +(-0.295440 + 1.00049i) q^{20} +(-1.97838 + 3.40953i) q^{21} +(-2.19602 + 6.03353i) q^{22} +(5.06318 - 0.892775i) q^{23} +(4.06003 - 3.39176i) q^{24} +(3.01582 + 3.98808i) q^{25} -1.91463 q^{26} +(-4.51684 + 2.56869i) q^{27} -1.06177i q^{28} +(4.94693 + 4.15097i) q^{29} +(-0.286437 - 4.78748i) q^{30} +(-0.228069 - 1.29344i) q^{31} +(-0.882557 + 2.42480i) q^{32} +(-0.0195113 + 8.98066i) q^{33} +(-1.14627 + 6.50084i) q^{34} +(-4.09340 - 3.02361i) q^{35} +(0.705061 - 1.20904i) q^{36} +(3.18754 - 1.84032i) q^{37} +(-1.93781 - 5.32410i) q^{38} +(-2.51847 + 0.910455i) q^{39} +(3.77444 + 5.69210i) q^{40} +(3.26644 - 2.74087i) q^{41} +(1.65958 + 4.59066i) q^{42} +(-2.88612 - 7.92956i) q^{43} +(-1.20949 - 2.09490i) q^{44} +(-2.65334 - 6.16115i) q^{45} +(3.18331 - 5.51365i) q^{46} +(-6.68721 - 1.17913i) q^{47} +(0.0107219 - 4.93508i) q^{48} +(-1.71059 - 0.622605i) q^{49} +(6.18371 + 0.313593i) q^{50} +(1.58353 + 9.09617i) q^{51} +(0.463658 - 0.552567i) q^{52} +6.64507i q^{53} +(-1.15863 + 6.32939i) q^{54} +(-11.5206 - 1.30274i) q^{55} +(-5.32509 - 4.46828i) q^{56} +(-5.08071 - 6.08174i) q^{57} +(7.87536 - 1.38864i) q^{58} +(2.83430 + 1.03160i) q^{59} +(1.45104 + 1.07670i) q^{60} +(0.999796 - 5.67013i) q^{61} +(-1.40852 - 0.813210i) q^{62} +(4.36595 + 5.24929i) q^{63} +(4.44699 + 7.70241i) q^{64} +(-0.809923 - 3.36106i) q^{65} +(8.50367 + 7.16697i) q^{66} +(2.22595 + 2.65278i) q^{67} +(-1.59857 - 1.90510i) q^{68} +(1.56538 - 8.76630i) q^{69} +(-6.12653 + 1.47633i) q^{70} +(-0.0130487 - 0.0226011i) q^{71} +(-3.09654 - 8.62409i) q^{72} +(5.00704 + 2.89081i) q^{73} +(0.791465 - 4.48862i) q^{74} +(8.28306 - 2.52802i) q^{75} +(2.00582 + 0.730059i) q^{76} +(11.6211 - 2.04912i) q^{77} +(-1.14099 + 3.11377i) q^{78} +(-12.6845 - 10.6435i) q^{79} +(6.33083 + 0.715887i) q^{80} +(1.48575 + 8.87652i) q^{81} -5.28029i q^{82} +(6.96279 - 8.29793i) q^{83} +(-1.72677 - 0.632744i) q^{84} +(-11.8969 + 0.737738i) q^{85} +(-9.81943 - 3.57398i) q^{86} +(9.69877 - 5.57153i) q^{87} +(-15.5964 - 2.75006i) q^{88} +(2.32308 - 4.02369i) q^{89} +(-7.95659 - 2.38717i) q^{90} +(1.75941 + 3.04738i) q^{91} +(0.820364 + 2.25393i) q^{92} +(-2.23944 - 0.399893i) q^{93} +(-6.44146 + 5.40503i) q^{94} +(8.52651 - 5.65395i) q^{95} +(3.41753 + 2.88032i) q^{96} +(2.48117 + 6.81695i) q^{97} +(-1.95222 + 1.12712i) q^{98} +(14.5937 + 5.38358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

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