LMFDB - Embedded newform 135.2.p.a.124.6

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			124.6
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.795984 + 0.948617i) q^{2} +(-0.595931 + 1.62630i) q^{3} +(0.0810128 + 0.459446i) q^{4} +(2.17384 + 0.523837i) q^{5} +(-1.06839 - 1.85982i) q^{6} +(2.24130 + 0.395202i) q^{7} +(-2.64518 - 1.52719i) q^{8} +(-2.28973 - 1.93833i) q^{9} +O(q^{10})$	\(q+(-0.795984 + 0.948617i) q^{2} +(-0.595931 + 1.62630i) q^{3} +(0.0810128 + 0.459446i) q^{4} +(2.17384 + 0.523837i) 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} +(-2.22727 + 1.64518i) 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} +(-2.14738 + 3.22316i) 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} +(-0.0645661 + 1.04120i) 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} +(4.45119 + 2.27748i) q^{25} -1.91463 q^{26} +(4.51684 - 2.56869i) q^{27} +1.06177i q^{28} +(4.94693 + 4.15097i) q^{29} +(-1.34826 - 4.60263i) 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} +(4.66522 + 2.03319i) 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} +(-4.95020 - 4.70552i) 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} +(-3.96215 - 5.41307i) 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} +(-5.70353 + 2.40964i) 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} +(-1.65483 - 0.725488i) 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} +(1.54001 + 3.09533i) 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} +(-5.64216 + 2.80712i) 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} +(-6.35648 + 5.88177i) 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} +(11.4317 - 3.37572i) 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} +(8.28875 + 0.550159i) 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} +(7.04866 - 7.41518i) 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	−0.970146	−	0.242521i	$-0.922026\pi$
$2$	−0.795984	+	0.948617i	−0.562846	+	0.670774i	0.407300	+	0.913294i	$0.366470\pi$
$3$	−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
$5$	2.17384	+	0.523837i	0.972172	+	0.234267i
$5$	2.17384	+	0.523837i	0.972172	+	0.234267i
$6$	−1.06839	−	1.85982i	−0.436168	−	0.759270i
$7$	2.24130	+	0.395202i	0.847133	+	0.149372i	0.580333	−	0.814379i	$-0.302923\pi$
$7$	2.24130	+	0.395202i	0.847133	+	0.149372i	0.266800	+	0.963752i	$0.414034\pi$
$8$	−2.64518	−	1.52719i	−0.935211	−	0.539945i
$9$	−2.28973	−	1.93833i	−0.763244	−	0.646110i
$10$	−2.22727	+	1.64518i	−0.704324	+	0.520251i
$11$	−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	0.886049	−	0.463591i	$-0.153439\pi$
$13$	0.993836	+	1.18441i	0.275641	+	0.328496i	−0.610409	+	0.792087i	$0.708995\pi$
$14$	−2.15894	+	1.81156i	−0.577000	+	0.484161i
$15$	−2.14738	+	3.22316i	−0.554451	+	0.832216i
$16$	2.67745	−	0.974511i	0.669361	−	0.243628i
$17$	4.61649	−	2.66533i	1.11966	−	0.646438i	0.178348	−	0.983967i	$-0.442925\pi$
$17$	4.61649	−	2.66533i	1.11966	−	0.646438i	0.941315	+	0.337530i	$0.109591\pi$
$18$	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	$-0.00920339\pi$
$20$	−0.0645661	+	1.04120i	−0.0144374	+	0.232820i
$21$	−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	−0.674468	−	0.738304i	$-0.735627\pi$
$23$	−5.06318	+	0.892775i	−1.05575	+	0.186156i	−0.381278	+	0.924461i	$0.624516\pi$
$24$	4.06003	−	3.39176i	0.828749	−	0.692340i
$25$	4.45119	+	2.27748i	0.890238	+	0.455496i
$26$	−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	$0.517553\pi$
$30$	−1.34826	−	4.60263i	−0.246158	−	0.840321i
$31$	−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
$35$	4.66522	+	2.03319i	0.788566	+	0.343671i
$36$	0.705061	−	1.20904i	0.117510	−	0.201506i
$37$	−3.18754	+	1.84032i	−0.524028	+	0.302548i	−0.738581	−	0.674165i	$-0.764504\pi$
$37$	−3.18754	+	1.84032i	−0.524028	+	0.302548i	0.214553	+	0.976712i	$0.431170\pi$
$38$	1.93781	+	5.32410i	0.314355	+	0.863683i
$39$	−2.51847	+	0.910455i	−0.403277	+	0.145790i
$40$	−4.95020	−	4.70552i	−0.782695	−	0.744009i
$41$	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	$0.111377\pi$
$43$	2.88612	+	7.92956i	0.440130	+	1.20925i	−0.499277	+	0.866442i	$0.666401\pi$
$44$	−1.20949	−	2.09490i	−0.182337	−	0.315817i
$45$	−3.96215	−	5.41307i	−0.590642	−	0.806933i
$46$	3.18331	−	5.51365i	0.469353	−	0.812944i
$47$	6.68721	+	1.17913i	0.975429	+	0.171995i	0.638573	−	0.769561i	$-0.279525\pi$
$47$	6.68721	+	1.17913i	0.975429	+	0.171995i	0.336857	+	0.941556i	$0.390636\pi$
$48$	−0.0107219	+	4.93508i	−0.00154758	+	0.712318i
$49$	−1.71059	−	0.622605i	−0.244371	−	0.0889436i
$50$	−5.70353	+	2.40964i	−0.806602	+	0.340774i
$51$	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	$-0.849144\pi$
$53$		−	6.64507i		−	0.912771i	0.889782	−	0.456385i	$-0.150856\pi$
$54$	−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	$0.548206\pi$
$60$	−1.65483	−	0.725488i	−0.213638	−	0.0936601i
$61$	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
$65$	1.54001	+	3.09533i	0.191014	+	0.383928i
$66$	8.50367	+	7.16697i	1.04673	+	0.882193i
$67$	−2.22595	−	2.65278i	−0.271943	−	0.324089i	0.612738	−	0.790286i	$-0.290068\pi$
$67$	−2.22595	−	2.65278i	−0.271943	−	0.324089i	−0.884681	+	0.466197i	$0.845624\pi$
$68$	1.59857	+	1.90510i	0.193855	+	0.231028i
$69$	1.56538	−	8.76630i	0.188450	−	1.05534i
$70$	−5.64216	+	2.80712i	−0.674367	+	0.335515i
$71$	−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	0.177497	−	0.984121i	$-0.443200\pi$
$73$	−5.00704	−	2.89081i	−0.586029	−	0.338344i	−0.763526	+	0.645777i	$0.776533\pi$
$74$	0.791465	−	4.48862i	0.0920059	−	0.521792i
$75$	−6.35648	+	5.88177i	−0.733983	+	0.679168i
$76$	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	−0.998110	−	0.0614583i	$-0.980425\pi$
$83$	−6.96279	+	8.29793i	−0.764265	+	0.910816i	0.233844	+	0.972274i	$0.424869\pi$
$84$	−1.72677	−	0.632744i	−0.188406	−	0.0690381i
$85$	11.4317	−	3.37572i	1.23994	−	0.366149i
$86$	−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	$0.0874696\pi$
$90$	8.28875	+	0.550159i	0.873710	+	0.0579918i
$91$	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
$95$	7.04866	−	7.41518i	0.723178	−	0.760781i
$96$	3.41753	+	2.88032i	0.348800	+	0.293972i
$97$	−2.48117	−	6.81695i	−0.251924	−	0.692157i	−0.999605	−	0.0280982i	$-0.991055\pi$
$97$	−2.48117	−	6.81695i	−0.251924	−	0.692157i	0.747681	−	0.664058i	$-0.231167\pi$
$98$	1.95222	−	1.12712i	0.197204	−	0.113856i
$99$	14.5937	+	5.38358i	1.46672	+	0.541070i
$100$	−0.685777	+	2.22959i	−0.0685777	+	0.222959i
$101$	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	−0.895595	−	0.444870i	$-0.853250\pi$
$103$	0.775652	−	2.13109i	0.0764273	−	0.209982i	0.972023	+	0.234888i	$0.0754722\pi$
$104$	−0.820053	−	4.65075i	−0.0804128	−	0.456044i
$105$	−6.08673	+	6.37543i	−0.594004	+	0.622178i
$106$	6.30363	+	5.28937i	0.612263	+	0.513749i
$107$		−	4.36720i		−	0.422193i	−0.977465	−	0.211097i	$-0.932297\pi$
$107$		−	4.36720i		−	0.422193i	0.977465	−	0.211097i	$-0.0677034\pi$
$108$	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	$0.624366\pi$
$110$	7.93440	−	11.9656i	0.756515	−	1.14087i
$111$	−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	$-0.623619\pi$
$113$	5.38234	−	14.7879i	0.506328	−	1.39112i	0.884999	−	0.465593i	$-0.154159\pi$
$114$	−9.81341	−	0.0213206i	−0.919110	−	0.00199686i
$115$	−11.4742	−	0.711529i	−1.06998	−	0.0663504i
$116$	−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
$120$	10.6026	−	5.24637i	0.967880	−	0.478925i
$121$	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
$125$	8.48316	+	7.28258i	0.758757	+	0.651374i
$126$	8.45480	+	0.0367379i	0.753213	+	0.00327287i
$127$	2.90443	+	1.67688i	0.257727	+	0.148799i	0.623297	−	0.781985i	$-0.285793\pi$
$127$	2.90443	+	1.67688i	0.257727	+	0.148799i	−0.365570	+	0.930784i	$0.619126\pi$
$128$	−5.76393	−	1.01634i	−0.509464	−	0.0898323i
$129$	−14.6158	−	0.0317543i	−1.28685	−	0.00279581i
$130$	−4.16210	−	1.00295i	−0.365040	−	0.0879649i
$131$	−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
$135$	11.1645	−	3.21784i	0.960885	−	0.276948i
$136$	−16.2819			−1.39616
$137$	−3.81854	+	4.55076i	−0.326240	+	0.388798i	−0.904088	−	0.427347i	$-0.859448\pi$
$137$	−3.81854	+	4.55076i	−0.326240	+	0.388798i	0.577848	+	0.816145i	$0.303893\pi$
$138$	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	$0.708325\pi$
$140$	−0.556197	+	2.30813i	−0.0470072	+	0.195073i
$141$	−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
$145$	8.57942	+	11.6149i	0.712482	+	0.964569i
$146$	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	$0.963751\pi$
$150$	−0.519888	−	10.7117i	−0.0424487	−	0.874603i
$151$	−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
$155$	0.181768	−	2.93121i	0.0145999	−	0.235441i
$156$	−0.622333	−	1.08334i	−0.0498265	−	0.0867367i
$157$	−4.36413	+	11.9904i	−0.348296	+	0.956935i	0.634611	+	0.772832i	$0.281160\pi$
$157$	−4.36413	+	11.9904i	−0.348296	+	0.956935i	−0.982907	+	0.184103i	$0.941062\pi$
$158$	20.1933	−	3.56063i	1.60649	−	0.283268i
$159$	10.8069	+	3.96000i	0.857044	+	0.314049i
$160$	3.18874	−	4.80883i	0.252092	−	0.380171i
$161$	−11.7009			−0.922163
$162$	−9.60305	−	5.65616i	−0.754487	−	0.444390i
$163$		−	24.6659i		−	1.93198i	−0.258578	−	0.965990i	$-0.583254\pi$
$163$		−	24.6659i		−	1.93198i	0.258578	−	0.965990i	$-0.416746\pi$
$164$	1.52391	+	1.27871i	0.118997	+	0.0998503i
$165$	4.74682	−	19.5123i	0.369539	−	1.51903i
$166$	−2.32929	−	13.2100i	−0.180788	−	1.02530i
$167$	−1.83304	+	5.03625i	−0.141845	+	0.389716i	−0.990190	−	0.139728i	$-0.955377\pi$
$167$	−1.83304	+	5.03625i	−0.141845	+	0.389716i	0.848345	+	0.529444i	$0.177599\pi$
$168$	10.4402	−	5.99743i	0.805477	−	0.462712i
$169$	1.84231	−	10.4483i	0.141717	−	0.803714i
$170$	−5.89720	+	13.5314i	−0.452295	+	1.03781i
$171$	−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	$0.0721437\pi$
$173$	4.89834	+	13.4581i	0.372414	+	1.02320i	−0.602012	+	0.798487i	$0.705634\pi$
$174$	2.43482	−	13.6353i	0.184583	−	1.03369i
$175$	9.07640	+	6.86364i	0.686111	+	0.518843i
$176$	−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	$0.901546\pi$
$180$	2.16603	−	2.25892i	0.161446	−	0.168370i
$181$	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
$185$	−7.89323	+	2.33083i	−0.580322	+	0.171366i
$186$	−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	−0.814957	−	0.579521i	$-0.803240\pi$
$193$	−19.2071	+	3.38673i	−1.38256	+	0.243782i	−0.567601	+	0.823304i	$0.692128\pi$
$194$	8.44165	+	3.07251i	0.606075	+	0.220593i
$195$	−5.95168	+	0.659920i	−0.426209	+	0.0472579i
$196$	0.147474	−	0.836365i	0.0105338	−	0.0597404i
$197$	7.83426	+	4.52311i	0.558168	+	0.322259i	0.752410	−	0.658695i	$-0.228891\pi$
$197$	7.83426	+	4.52311i	0.558168	+	0.322259i	−0.194242	+	0.980954i	$0.562225\pi$
$198$	−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	$0.716866\pi$
$200$	−8.29603	−	12.8222i	−0.586618	−	0.906664i
$201$	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
$205$	8.53650	−	4.24713i	0.596215	−	0.296633i
$206$	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
$210$	−1.20290	−	10.8487i	−0.0830081	−	0.748633i
$211$	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
$220$	−1.53185	−	5.18755i	−0.103278	−	0.349745i
$221$	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	−0.476010	−	0.879440i	$-0.657917\pi$
$223$	−18.2797	−	3.22320i	−1.22410	−	0.215842i	−0.748089	+	0.663598i	$0.769029\pi$
$224$	2.93637	−	5.08593i	0.196194	−	0.339818i
$225$	−5.77752	−	13.8427i	−0.385168	−	0.922846i
$226$	9.74376	+	16.8767i	0.648145	+	1.12262i
$227$	−8.41561	−	23.1217i	−0.558564	−	1.53464i	−0.821722	−	0.569888i	$-0.806986\pi$
$227$	−8.41561	−	23.1217i	−0.558564	−	1.53464i	0.263158	−	0.964753i	$-0.415236\pi$
$228$	−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	$0.299254\pi$
$230$	9.80827	−	10.3183i	0.646738	−	0.680367i
$231$	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	−0.725551	−	0.688169i	$-0.758415\pi$
$233$	−7.51547	+	4.33906i	−0.492355	+	0.284261i	0.233196	+	0.972430i	$0.425082\pi$
$234$	4.38399	+	3.71118i	0.286590	+	0.242608i
$235$	13.9193	+	6.06626i	0.907993	+	0.395719i
$236$	−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	$0.905516\pi$
$240$	−2.60849	+	10.7225i	−0.168377	+	0.692133i
$241$	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
$245$	−3.39242	−	2.24952i	−0.216734	−	0.143717i
$246$	−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
$250$	−13.6608	+	2.25045i	−0.863988	+	0.142331i
$251$	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
$255$	−1.32256	+	20.6032i	−0.0828222	+	1.29022i
$256$	−8.07425	+	6.77510i	−0.504641	+	0.423444i
$257$	−11.8239	−	14.0912i	−0.737553	−	0.878982i	0.258656	−	0.965970i	$-0.416720\pi$
$257$	−11.8239	−	14.0912i	−0.737553	−	0.878982i	−0.996209	+	0.0869875i	$0.972276\pi$
$258$	11.6641	−	13.8395i	0.726174	−	0.861612i
$259$	−7.87153	+	2.86500i	−0.489113	+	0.178023i
$260$	−1.29738	+	0.958312i	−0.0804598	+	0.0594320i
$261$	−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	0.381516	−	0.924362i	$-0.375402\pi$
$263$	6.87408	+	1.21209i	0.423874	+	0.0747404i	0.0423576	+	0.999103i	$0.486513\pi$
$264$	−13.7668	+	23.7256i	−0.847289	+	1.46021i
$265$	3.48094	−	14.4453i	0.213832	−	0.887370i
$266$	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	$0.589019\pi$
$270$	−5.83425	+	13.1522i	−0.355061	+	0.800415i
$271$	−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
$275$	−25.7264	−	3.20296i	−1.55136	−	0.193146i
$276$	4.15446	+	0.00902597i	0.250069	+	0.000543299i
$277$	9.53431	+	1.68116i	0.572861	+	0.101011i	0.452572	−	0.891728i	$-0.350507\pi$
$277$	9.53431	+	1.68116i	0.572861	+	0.101011i	0.120289	+	0.992739i	$0.461618\pi$
$278$	−17.0845	−	9.86372i	−1.02466	−	0.591587i
$279$	−1.98490	+	3.40371i	−0.118833	+	0.203775i
$280$	−9.23526	−	12.5028i	−0.551913	−	0.747187i
$281$	−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	0.997033	−	0.0769758i	$-0.0245264\pi$
$283$	12.5849	+	14.9981i	0.748094	+	0.891543i	−0.248939	+	0.968519i	$0.580082\pi$
$284$	0.00932686	−	0.00782616i	0.000553447	−	0.000464397i
$285$	7.85882	+	15.8822i	0.465516	+	0.940781i
$286$	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
$290$	−17.8472	−	1.10673i	−1.04803	−	0.0649892i
$291$	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	0.788819	−	0.614625i	$-0.210693\pi$
$293$	29.7888	−	5.25257i	1.74028	−	0.306858i	0.951462	+	0.307767i	$0.0995817\pi$
$294$	0.669644	+	3.84659i	0.0390544	+	0.224338i
$295$	5.62094	+	3.72726i	0.327264	+	0.217009i
$296$	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
$300$	−3.21731	−	2.44396i	−0.185752	−	0.141102i
$301$	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
$305$	5.14363	−	11.8022i	0.294523	−	0.675794i
$306$	15.2254	−	12.6633i	0.870381	−	0.723915i
$307$	15.8229	−	9.13533i	0.903058	−	0.521381i	0.0248672	−	0.999691i	$-0.492084\pi$
$307$	15.8229	−	9.13533i	0.903058	−	0.521381i	0.878191	+	0.478310i	$0.158750\pi$
$308$	−1.88292	−	5.17329i	−0.107289	−	0.294775i
$309$	3.00356	+	2.53143i	0.170867	+	0.144008i
$310$	2.63591	+	2.50563i	0.149710	+	0.142310i
$311$	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	0.963723	−	0.266906i	$-0.0860014\pi$
$313$	0.953665	+	2.62017i	0.0539043	+	0.148101i	−0.909818	+	0.415007i	$0.863779\pi$
$314$	−7.90048	−	13.6840i	−0.445850	−	0.772235i
$315$	−6.74112	−	13.6982i	−0.379819	−	0.771805i
$316$	3.86253	−	6.69010i	0.217284	−	0.376348i
$317$	−2.71702	−	0.479083i	−0.152603	−	0.0269080i	0.0968248	−	0.995301i	$-0.469131\pi$
$317$	−2.71702	−	0.479083i	−0.152603	−	0.0269080i	−0.249428	+	0.968393i	$0.580242\pi$
$318$	−12.3587	+	7.09952i	−0.693039	+	0.398121i
$319$	−31.4642	−	11.4520i	−1.76166	−	0.641190i
$320$	5.63225	+	19.0733i	0.314852	+	1.06623i
$321$	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
$330$	14.7313	+	20.0344i	0.810933	+	1.10286i
$331$	−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
$335$	−3.44923	−	6.93276i	−0.188452	−	0.378777i
$336$	−1.97439	+	11.0568i	−0.107712	+	0.603197i
$337$	9.17286	+	10.9318i	0.499677	+	0.595492i	0.955651	−	0.294501i	$-0.0951534\pi$
$337$	9.17286	+	10.9318i	0.499677	+	0.595492i	−0.455974	+	0.889993i	$0.650709\pi$
$338$	8.44497	+	10.0643i	0.459346	+	0.547427i
$339$	20.8421	+	17.5659i	1.13199	+	0.954047i
$340$	2.47708	+	4.97879i	0.134338	+	0.270013i
$341$	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
$345$	7.99501	−	18.2366i	0.430437	−	0.981823i
$346$	−16.6656	−	6.06577i	−0.895946	−	0.326098i
$347$	17.3984	−	3.06781i	0.933994	−	0.164688i	0.314114	−	0.949385i	$-0.398292\pi$
$347$	17.3984	−	3.06781i	0.933994	−	0.164688i	0.619880	+	0.784697i	$0.287181\pi$
$348$	−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	$0.544892\pi$
$353$	−20.5015	+	24.4328i	−1.09119	+	1.30043i	−0.950621	+	0.310355i	$0.899552\pi$
$354$	−1.10954	−	6.37346i	−0.0589714	−	0.338745i
$355$	−0.0165266	−	0.0559666i	−0.000877141	−	0.00297040i
$356$	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	$0.236625\pi$
$360$	2.21378	+	20.3695i	0.116676	+	1.07357i
$361$	−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
$365$	−9.37019	−	8.90705i	−0.490458	−	0.466216i
$366$	−11.6136	+	4.19846i	−0.607053	+	0.219457i
$367$	−7.40606	−	20.3480i	−0.386593	−	1.06216i	−0.968525	−	0.248918i	$-0.919925\pi$
$367$	−7.40606	−	20.3480i	−0.386593	−	1.06216i	0.581931	−	0.813238i	$-0.302297\pi$
$368$	−12.6864	+	7.32448i	−0.661323	+	0.381815i
$369$	−12.7920	−	0.0555839i	−0.665924	−	0.00289358i
$370$	4.07183	−	9.34296i	0.211684	−	0.485717i
$371$	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	$0.401589\pi$
$373$	−10.4509	+	28.7136i	−0.541126	+	1.48673i	−0.845393	+	0.534145i	$0.820634\pi$
$374$	−5.94343	−	33.7068i	−0.307327	−	1.74294i
$375$	−16.8991	+	9.45628i	−0.872665	+	0.488320i
$376$	−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	$0.553310\pi$
$380$	3.97791	+	2.63776i	0.204062	+	0.135314i
$381$	−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	−0.987957	−	0.154727i	$-0.950550\pi$
$383$	−2.57705	+	7.08040i	−0.131681	+	0.361791i	0.856276	+	0.516519i	$0.172772\pi$
$384$	5.08778	−	8.76824i	0.259635	−	0.447452i
$385$	−26.3360	−	1.63312i	−1.34220	−	0.0832316i
$386$	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	$0.453073\pi$
$390$	4.11143	−	6.17115i	0.208191	−	0.312489i
$391$	−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
$395$	−21.9986	−	29.7820i	−1.10687	−	1.49850i
$396$	−1.29119	+	7.14114i	−0.0648850	+	0.358856i
$397$	1.40079	+	0.808746i	0.0703036	+	0.0405898i	0.534740	−	0.845017i	$-0.320410\pi$
$397$	1.40079	+	0.808746i	0.0703036	+	0.0405898i	−0.464436	+	0.885607i	$0.653743\pi$
$398$	−12.3102	−	2.17062i	−0.617054	−	0.108803i
$399$	8.98389	+	15.6389i	0.449757	+	0.782925i
$400$	14.1372	+	1.76010i	0.706862	+	0.0880050i
$401$	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
$405$	−1.42006	+	20.0744i	−0.0705635	+	0.997507i
$406$	−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	$-0.146597\pi$
$410$	−2.76601	+	11.4785i	−0.136604	+	0.566884i
$411$	−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
$415$	−19.4828	+	14.3910i	−0.956372	+	0.706428i
$416$	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	$0.988438\pi$
$420$	−3.42227	−	2.28003i	−0.166990	−	0.111254i
$421$	−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
$425$	26.6191	−	1.34993i	1.29122	−	0.0654811i
$426$	−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
$430$	−19.4737	−	12.9131i	−0.939106	−	0.622723i
$431$	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	$0.242267\pi$
$433$			28.7044i			1.37944i	−0.724074	+	0.689722i	$0.757733\pi$
$434$	2.83554	+	2.37930i	0.136110	+	0.114210i
$435$	−24.0022	+	7.03105i	−1.15082	+	0.337113i
$436$	−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	$0.0758996\pi$
$440$	32.4635	+	14.1482i	1.54764	+	0.674488i
$441$	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	0.960303	−	0.278960i	$-0.0899896\pi$
$443$	0.954638	+	2.62285i	0.0453562	+	0.124615i	−0.914947	+	0.403575i	$0.867767\pi$
$444$	2.79703	−	1.01116i	0.132741	−	0.0479874i
$445$	7.15777	−	7.52996i	0.339311	−	0.356954i
$446$	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	$0.641411\pi$
$450$	17.7302	+	5.53791i	0.835811	+	0.261060i
$451$	−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
$455$	2.22834	+	7.54618i	0.104466	+	0.353770i
$456$	−4.15138	−	23.8465i	−0.194406	−	1.11671i
$457$	−19.7351	+	23.5193i	−0.923167	+	1.10019i	0.0715399	+	0.997438i	$0.477209\pi$
$457$	−19.7351	+	23.5193i	−0.923167	+	1.10019i	−0.994707	+	0.102750i	$0.967236\pi$
$458$		−	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	0.631968	−	0.774995i	$-0.282247\pi$
$463$	32.0801	−	5.65658i	1.49089	−	0.262884i	0.858919	+	0.512111i	$0.171136\pi$
$464$	17.2903	+	6.29316i	0.802682	+	0.292153i
$465$	4.65872	+	2.04241i	0.216043	+	0.0947145i
$466$	1.86609	−	10.5831i	0.0864450	−	0.490254i
$467$	11.8736	+	6.85522i	0.549445	+	0.317222i	0.748898	−	0.662685i	$-0.230583\pi$
$467$	11.8736	+	6.85522i	0.549445	+	0.317222i	−0.199453	+	0.979907i	$0.563917\pi$
$468$	2.13271	−	0.366507i	0.0985846	−	0.0169418i
$469$	−3.94064	−	6.82538i	−0.181962	−	0.315167i
$470$	−16.8341	+	8.37540i	−0.776498	+	0.386329i
$471$	−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
$475$	19.2070	−	12.4271i	0.881279	−	0.570194i
$476$	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	$-0.0314269\pi$
$480$	5.92035	+	8.05160i	0.270226	+	0.367504i
$481$	−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	$-0.745897\pi$
$487$		−	31.6087i		−	1.43233i	0.697933	−	0.716163i	$-0.254103\pi$
$488$	−11.3040	+	13.4716i	−0.511709	+	0.609831i
$489$	40.1142	+	14.6992i	1.81403	+	0.664719i
$490$	4.83425	−	1.42753i	0.218389	−	0.0644890i
$491$	−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
$495$	28.9042	+	19.3478i	1.29915	+	0.869617i
$496$	−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	$-0.0715791\pi$
$500$	−2.65871	+	4.48754i	−0.118901	+	0.200689i
$501$	−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	−0.610087	−	0.792334i	$-0.708866\pi$
$503$	−5.13479	+	2.96457i	−0.228949	+	0.132184i	0.381138	+	0.924518i	$0.375532\pi$
$504$	3.53203	+	20.5530i	0.157329	+	0.915502i
$505$	0.389768	−	0.894337i	0.0173444	−	0.0397975i
$506$	−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	$-0.466420\pi$
$510$	−18.4918	−	17.6544i	−0.818829	−	0.781750i
$511$	−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
$515$	2.80249	−	4.22633i	0.123492	−	0.186235i
$516$	−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
$520$	0.653571	−	10.5396i	0.0286610	−	0.462191i
$521$	−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	−0.794957	−	0.606666i	$-0.792507\pi$
$523$	−15.2548	+	8.80738i	−0.667047	+	0.385120i	0.127910	+	0.991786i	$0.459173\pi$
$524$	2.41925	−	0.880534i	0.105685	−	0.0384663i
$525$	−16.5713	+	10.6707i	−0.723230	+	0.465709i
$526$	−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
$530$	10.9323	+	14.8003i	0.474870	+	0.642886i
$531$	−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
$535$	2.28770	−	9.49361i	0.0989060	−	0.410444i
$536$	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
$540$	2.38289	+	4.86879i	0.102543	+	0.209519i
$541$	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
$545$	−17.2869	−	4.16568i	−0.740490	−	0.178438i
$546$	3.78786	−	6.52798i	0.162106	−	0.279372i
$547$	29.8441	+	5.26232i	1.27604	+	0.225000i	0.770298	−	0.637684i	$-0.220107\pi$
$547$	29.8441	+	5.26232i	1.27604	+	0.225000i	0.505743	+	0.862684i	$0.331219\pi$
$548$	−2.40018	−	1.38575i	−0.102531	−	0.0591961i
$549$	−13.2798	+	11.0451i	−0.566770	+	0.471395i
$550$	23.5162	−	21.8550i	1.00273	−	0.931899i
$551$	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
$555$	0.913188	−	14.2258i	0.0387627	−	0.603852i
$556$	−6.98398	+	2.54196i	−0.296187	+	0.107803i
$557$	24.6008	−	14.2033i	1.04237	−	0.601812i	0.121865	−	0.992547i	$-0.461112\pi$
$557$	24.6008	−	14.2033i	1.04237	−	0.601812i	0.920503	+	0.390735i	$0.127779\pi$
$558$	−1.64887	−	4.59221i	−0.0698021	−	0.194404i
$559$	−6.52350	+	11.2990i	−0.275915	+	0.477898i
$560$	14.4722	+	0.897439i	0.611563	+	0.0379237i
$561$	−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	−0.303146	−	0.952944i	$-0.598037\pi$
$563$	−6.21863	+	1.09651i	−0.262084	+	0.0462124i	0.0410621	+	0.999157i	$0.486926\pi$
$564$	−5.15203	−	1.88787i	−0.216940	−	0.0794937i
$565$	19.4468	−	29.3270i	0.818133	−	1.23380i
$566$	−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	$0.698098\pi$
$570$	−21.3216	−	5.18698i	−0.893065	−	0.217259i
$571$	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
$575$	−24.5704	−	7.55738i	−1.02466	−	0.315165i
$576$	4.74740	−	26.2562i	0.197808	−	1.09401i
$577$	−19.6374	+	11.3377i	−0.817517	+	0.471994i	−0.849559	−	0.527493i	$-0.823132\pi$
$577$	−19.6374	+	11.3377i	−0.817517	+	0.471994i	0.0320424	+	0.999487i	$0.489799\pi$
$578$	4.83505	+	13.2842i	0.201112	+	0.552550i
$579$	5.93826	−	33.2549i	0.246785	−	1.38203i
$580$	−4.64140	+	4.88274i	−0.192724	+	0.202745i
$581$	−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
$585$	2.47356	−	10.0725i	0.102269	−	0.416447i
$586$	−18.7288	+	32.4391i	−0.773678	+	1.34005i
$587$	−18.6058	−	3.28071i	−0.767946	−	0.135410i	−0.224067	−	0.974574i	$-0.571934\pi$
$587$	−18.6058	−	3.28071i	−0.767946	−	0.135410i	−0.543878	+	0.839164i	$0.683045\pi$
$588$	1.27230	+	0.738253i	0.0524688	+	0.0304450i
$589$	−5.64683	−	2.05528i	−0.232673	−	0.0846862i
$590$	−8.00992	+	2.36528i	−0.329763	+	0.0973772i
$591$	−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	$0.0573974\pi$
$593$			8.73461i			0.358688i	−0.983786	+	0.179344i	$0.942603\pi$
$594$	−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	$0.569415\pi$
$600$	25.7966	−	5.85074i	1.05314	−	0.238856i
$601$	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
$605$	31.7998	−	15.8212i	1.29284	−	0.643225i
$606$	−0.880043	+	0.318146i	−0.0357493	+	0.0129238i
$607$	2.88515	+	3.43839i	0.117105	+	0.139560i	0.821412	−	0.570335i	$-0.193187\pi$
$607$	2.88515	+	3.43839i	0.117105	+	0.139560i	−0.704307	+	0.709895i	$0.748742\pi$
$608$	−7.58895	−	9.04416i	−0.307773	−	0.366789i
$609$	−23.9398	+	8.65451i	−0.970088	+	0.350698i
$610$	7.10156	+	14.2737i	0.287534	+	0.577926i
$611$	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	0.847685	−	0.530501i	$-0.177996\pi$
$613$	20.1066	+	11.6086i	0.812100	+	0.468866i	−0.0355848	+	0.999367i	$0.511329\pi$
$614$	−3.92882	+	22.2814i	−0.158554	+	0.899205i
$615$	1.81997	+	16.4139i	0.0733883	+	0.661874i
$616$	33.8694	+	12.3275i	1.36464	+	0.496687i
$617$	−43.5312	+	7.67572i	−1.75250	+	0.309013i	−0.955505	−	0.294975i	$-0.904689\pi$
$617$	−43.5312	+	7.67572i	−1.75250	+	0.309013i	−0.796993	+	0.603988i	$0.793577\pi$
$618$	−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
$625$	14.6262	+	20.2750i	0.585047	+	0.811000i
$626$	−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
$630$	18.3602	+	4.50880i	0.731486	+	0.179635i
$631$	−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
$635$	5.43538	+	5.16672i	0.215696	+	0.205035i
$636$	−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
$640$	−11.9975	−	5.22872i	−0.474242	−	0.206683i
$641$	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	−0.910981	−	0.412449i	$-0.864674\pi$
$643$	1.31828	−	3.62196i	0.0519881	−	0.142836i	0.962969	+	0.269613i	$0.0868957\pi$
$644$	−0.947926	−	5.37595i	−0.0373535	−	0.211842i
$645$	−31.7558	−	7.72533i	−1.25038	−	0.304185i
$646$	23.1364	+	19.4137i	0.910288	+	0.763823i
$647$			16.5713i			0.651486i	0.945458	+	0.325743i	$0.105614\pi$
$647$			16.5713i			0.651486i	−0.945458	+	0.325743i	$0.894386\pi$
$648$	9.62609	−	25.7490i	0.378148	−	1.01152i
$649$	−15.6390			−0.613884
$650$	−8.52237	−	4.36053i	−0.334275	−	0.171034i
$651$	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	−0.969445	−	0.245309i	$-0.921111\pi$
$653$	−1.76642	+	4.85320i	−0.0691254	+	0.189920i	0.900320	+	0.435230i	$0.143333\pi$
$654$	8.49608	+	14.7898i	0.332223	+	0.578325i
$655$	0.763716	−	12.3158i	0.0298409	−	0.481218i
$656$	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	$0.637026\pi$
$660$	9.34941	+	0.600161i	0.363925	+	0.0233612i
$661$	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
$665$	18.7287	−	13.8340i	0.726267	−	0.536460i
$666$	−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
$670$	9.32207	+	2.24637i	0.360143	+	0.0867847i
$671$	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	−0.633265	−	0.773935i	$-0.718286\pi$
$673$	6.19702	−	7.38532i	0.238878	−	0.284683i	0.872143	+	0.489252i	$0.162730\pi$
$674$	−17.6715			−0.680682
$675$	25.9554	−	1.14672i	0.999025	−	0.0441372i
$676$	4.94968			0.190372
$677$	−15.8761	+	18.9204i	−0.610167	+	0.727169i	−0.979346	−	0.202189i	$-0.935194\pi$
$677$	−15.8761	+	18.9204i	−0.610167	+	0.727169i	0.369179	+	0.929358i	$0.379639\pi$
$678$	−33.2532	+	5.78898i	−1.27708	+	0.222324i
$679$	−2.86697	−	16.2594i	−0.110024	−	0.623979i
$680$	−35.3943	−	8.52907i	−1.35731	−	0.327075i
$681$	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	0.114438	−	0.993430i	$-0.463493\pi$
$683$	−17.9981	−	10.3912i	−0.688678	−	0.397609i	−0.803117	+	0.595822i	$0.796826\pi$
$684$	−3.17770	−	5.55958i	−0.121502	−	0.212576i
$685$	−10.6848	+	7.89235i	−0.408244	+	0.301551i
$686$	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
$690$	10.9356	+	22.1002i	0.416312	+	0.841341i
$691$	−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
$695$	−2.20473	+	35.5537i	−0.0836300	+	1.34863i
$696$	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
$700$	−2.41817	+	4.72616i	−0.0913983	+	0.178632i
$701$	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
$705$	−18.1605	+	19.0219i	−0.683964	+	0.716406i
$706$	−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	$0.983848\pi$
$710$	0.0662458	+	0.0288711i	0.00248616	+	0.00108351i
$711$	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
$715$	−12.9926	−	12.3504i	−0.485894	−	0.461877i
$716$	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	$0.793932\pi$
$720$	−15.8835	−	10.6321i	−0.591945	−	0.396233i
$721$	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
$725$	12.5660	+	29.7433i	0.466689	+	1.10464i
$726$	−31.9892	−	11.7219i	−1.18723	−	0.435040i
$727$	7.62291	−	9.08463i	0.282718	−	0.336930i	−0.605932	−	0.795517i	$-0.707200\pi$
$727$	7.62291	−	9.08463i	0.282718	−	0.336930i	0.888650	+	0.458586i	$0.151644\pi$
$728$		−	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	−0.402968	−	0.915214i	$-0.632021\pi$
$733$	−12.6872	+	2.23709i	−0.468612	+	0.0826289i	−0.0656441	+	0.997843i	$0.520910\pi$
$734$	25.1976	+	9.17116i	0.930059	+	0.338514i
$735$	5.68005	−	4.17655i	0.209512	−	0.154054i
$736$	−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	$0.982480\pi$
$740$	−1.71034	−	3.43769i	−0.0628734	−	0.126372i
$741$	−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	$0.0507766\pi$
$743$	26.5027	+	31.5847i	0.972291	+	1.15873i	−0.0150131	+	0.999887i	$0.504779\pi$
$744$	−5.31301	−	4.47785i	−0.194784	−	0.164166i
$745$	−40.7674	+	20.2829i	−1.49360	+	0.743107i
$746$	−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
$750$	4.48101	−	23.5578i	0.163623	−	0.860210i
$751$	−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	$0.0659152\pi$
$757$			11.3137i			0.411203i	−0.978636	+	0.205602i	$0.934085\pi$
$758$	5.16630	−	6.15696i	0.187648	−	0.223631i
$759$	7.91891	+	45.4881i	0.287438	+	1.65111i
$760$	−29.9694	+	8.84979i	−1.08710	+	0.321016i
$761$	−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
$765$	−32.7189	−	14.4290i	−1.18295	−	0.521680i
$766$	−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	$0.365952\pi$
$770$	22.5122	−	23.6828i	0.811284	−	0.853469i
$771$	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	−0.422407	−	0.906406i	$-0.638815\pi$
$773$	4.20823	−	2.42962i	0.151359	−	0.0873874i	0.573767	+	0.819019i	$0.305482\pi$
$774$	15.5563	+	27.2167i	0.559160	+	0.978286i
$775$	1.93061	−	6.27678i	0.0693496	−	0.225468i
$776$	−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
$780$	−0.785360	−	2.68102i	−0.0281204	−	0.0959958i
$781$	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
$785$	−15.7679	+	23.7791i	−0.562782	+	0.848711i
$786$	−9.08349	+	7.58838i	−0.323997	+	0.270669i
$787$	−4.82676	+	0.851088i	−0.172055	+	0.0303380i	−0.259012	−	0.965874i	$-0.583397\pi$
$787$	−4.82676	+	0.851088i	−0.172055	+	0.0303380i	0.0869567	+	0.996212i	$0.472286\pi$
$788$	−1.44345	+	3.96585i	−0.0514209	+	0.141278i
$789$	−6.06770	+	10.4570i	−0.216016	+	0.372280i
$790$	45.7623	+	2.83777i	1.62815	+	0.100963i
$791$	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
$795$	21.4181	+	14.2695i	0.759623	+	0.506087i
$796$	−3.60756	+	3.02710i	−0.127866	+	0.107293i
$797$	35.8673	+	42.7450i	1.27049	+	1.51411i	0.752270	+	0.658855i	$0.228959\pi$
$797$	35.8673	+	42.7450i	1.27049	+	1.51411i	0.518215	+	0.855250i	$0.326597\pi$
$798$	−21.9864	−	3.92607i	−0.778310	−	0.138981i
$799$	34.0142	−	12.3802i	1.20334	−	0.437978i
$800$	9.45087	−	8.78326i	0.334139	−	0.310535i
$801$	−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
$805$	−25.4360	−	6.12939i	−0.896502	−	0.216033i
$806$	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	$0.355036\pi$
$810$	−17.9126	−	17.3260i	−0.629385	−	0.608775i
$811$	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
$815$	12.9209	−	53.6198i	0.452600	−	1.87822i
$816$	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
$820$	2.64290	+	3.57799i	0.0922939	+	0.124949i
$821$	−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	0.899267	−	0.437400i	$-0.144101\pi$
$823$	8.96086	+	10.6791i	0.312356	+	0.372251i	−0.586911	+	0.809651i	$0.699656\pi$
$824$	−5.30632	+	4.45253i	−0.184854	+	0.155111i
$825$	20.5401	−	39.9302i	0.715115	−	1.39019i
$826$	−7.98790	+	2.90736i	−0.277935	+	0.101160i
$827$	−30.3778	+	17.5386i	−1.05634	+	0.609878i	−0.924418	−	0.381382i	$-0.875448\pi$
$827$	−30.3778	+	17.5386i	−1.05634	+	0.609878i	−0.131922	+	0.991260i	$0.542115\pi$
$828$	−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	$0.974031\pi$
$830$	1.85641	−	29.9367i	0.0644369	−	1.03912i
$831$	−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
$835$	−6.62292	+	9.98779i	−0.229196	+	0.345642i
$836$	−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	$0.818200\pi$
$840$	25.8370	−	7.56853i	0.891461	−	0.261139i
$841$	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
$845$	9.47810	−	21.7479i	0.326057	−	0.748149i
$846$	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
$850$	−19.9078	+	26.3259i	−0.682833	+	0.902970i
$851$	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	$-0.797704\pi$
$853$	−16.6428	−	45.7258i	−0.569840	−	1.56562i	0.234916	−	0.972016i	$-0.424518\pi$
$854$	8.11330	+	14.0526i	0.277631	+	0.480872i
$855$	−30.5126	+	3.31614i	−1.04351	+	0.113410i
$856$	−6.66956	+	11.5520i	−0.227961	+	0.394840i
$857$	−9.48011	−	1.67160i	−0.323835	−	0.0571008i	0.00936777	−	0.999956i	$-0.497018\pi$
$857$	−9.48011	−	1.67160i	−0.323835	−	0.0571008i	−0.333202	+	0.942855i	$0.608129\pi$
$858$	−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	$0.795243\pi$
$860$	−8.44262	+	2.49306i	−0.287891	+	0.0850125i
$861$	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	$0.0606279\pi$
$863$			11.1232i			0.378637i	−0.981916	+	0.189319i	$0.939372\pi$
$864$	−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
$870$	12.4356	−	28.3655i	0.421606	−	0.961680i
$871$	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
$875$	16.1352	+	19.6750i	0.545470	+	0.665138i
$876$	3.57235	+	3.01081i	0.120699	+	0.101726i
$877$	−34.3783	−	40.9704i	−1.16087	−	1.38347i	−0.909563	−	0.415567i	$-0.863583\pi$
$877$	−34.3783	−	40.9704i	−1.16087	−	1.38347i	−0.251309	−	0.967907i	$-0.580861\pi$
$878$	−2.13039	−	2.53890i	−0.0718971	−	0.0856836i
$879$	−9.20980	+	51.5758i	−0.310639	+	1.73961i
$880$	−29.5762	+	14.7149i	−0.997013	+	0.496041i
$881$	−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	0.218537	−	0.975829i	$-0.429871\pi$
$883$	−15.3713	−	8.87464i	−0.517286	−	0.298655i	−0.735824	+	0.677173i	$0.763205\pi$
$884$	−0.667701	+	3.78672i	−0.0224572	+	0.127361i
$885$	−9.41134	+	6.92017i	−0.316359	+	0.232619i
$886$	−3.24795	−	1.18216i	−0.109117	−	0.0397154i
$887$	−2.06559	+	0.364220i	−0.0693559	+	0.0122293i	−0.208218	−	0.978082i	$-0.566766\pi$
$887$	−2.06559	+	0.364220i	−0.0693559	+	0.0122293i	0.138863	+	0.990312i	$0.455655\pi$
$888$	−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
$895$	−3.60355	−	12.2032i	−0.120453	−	0.407909i
$896$	−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
$900$	5.89192	−	3.77590i	0.196397	−	0.125863i
$901$	−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
$905$	15.6410	−	16.4543i	0.519925	−	0.546960i
$906$	3.14921	+	2.65418i	0.104626	+	0.0881793i
$907$	14.6217	+	40.1727i	0.485504	+	1.33391i	0.904713	+	0.426022i	$0.140085\pi$
$907$	14.6217	+	40.1727i	0.485504	+	1.33391i	−0.419208	+	0.907890i	$0.637692\pi$
$908$	9.94141	−	5.73967i	0.329917	−	0.190478i
$909$	−1.00631	+	0.836966i	−0.0333770	+	0.0277604i
$910$	−8.93216	−	3.89280i	−0.296098	−	0.129045i
$911$	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
$915$	16.1288	+	15.3984i	0.533201	+	0.509056i
$916$	−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	$0.420648\pi$
$920$	29.2647	+	19.4055i	0.964829	+	0.639780i
$921$	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
$925$	−18.3796	+	0.932081i	−0.604318	+	0.0306467i
$926$	−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	$0.241152\pi$
$930$	−5.64573	+	2.79362i	−0.185131	+	0.0916063i
$931$	−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
$935$	−49.7124	+	36.7203i	−1.62577	+	1.20088i
$936$	−7.13699	+	12.2385i	−0.233280	+	0.400028i
$937$	47.0967	+	27.1913i	1.53858	+	0.888300i	0.998922	+	0.0464165i	$0.0147801\pi$
$937$	47.0967	+	27.1913i	1.53858	+	0.888300i	0.539659	+	0.841884i	$0.318553\pi$
$938$	9.61136	+	1.69474i	0.313822	+	0.0553353i
$939$	−4.82952	−	0.0104926i	−0.157605	−	0.000342413i
$940$	−1.65948	+	6.88660i	−0.0541264	+	0.224616i
$941$	−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
$945$	26.2947	−	2.79994i	0.855366	−	0.0910820i
$946$	54.1812			1.76158
$947$	26.0639	−	31.0617i	0.846962	−	1.00937i	−0.152815	−	0.988255i	$-0.548834\pi$
$947$	26.0639	−	31.0617i	0.846962	−	1.00937i	0.999777	−	0.0211155i	$-0.00672177\pi$
$948$	8.57834	+	10.2685i	0.278612	+	0.333505i
$949$	−1.55227	−	8.80337i	−0.0503889	−	0.285769i
$950$	−3.49996	+	28.1119i	−0.113554	+	0.912070i
$951$	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	0.827251	−	0.561833i	$-0.189904\pi$
$953$	23.2862	+	13.4443i	0.754315	+	0.435504i	−0.0729359	+	0.997337i	$0.523237\pi$
$954$	−4.18107	−	24.3298i	−0.135367	−	0.787705i
$955$	−8.44638	−	11.4348i	−0.273319	−	0.370023i
$956$	−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
$960$	−34.3755	−	2.20664i	−1.10946	−	0.0712191i
$961$	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
$965$	−43.5273	−	2.69918i	−1.40119	−	0.0868896i
$966$	12.5012	+	21.7617i	0.402218	+	0.700171i
$967$	−13.0453	+	35.8418i	−0.419510	+	1.15259i	0.532474	+	0.846446i	$0.321262\pi$
$967$	−13.0453	+	35.8418i	−0.419510	+	1.15259i	−0.951984	+	0.306147i	$0.900960\pi$
$968$	−47.7794	+	8.42480i	−1.53569	+	0.270783i
$969$	39.6649	+	14.5345i	1.27422	+	0.466916i
$970$	16.7413	+	11.1012i	0.537532	+	0.356438i
$971$	−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
$975$	−13.2837	−	1.68315i	−0.425419	−	0.0539039i
$976$	−2.84870	−	16.1558i	−0.0911846	−	0.517134i
$977$	7.16089	−	19.6744i	0.229097	−	0.629439i	−0.770874	−	0.636987i	$-0.780180\pi$
$977$	7.16089	−	19.6744i	0.229097	−	0.629439i	0.999972	+	0.00754795i	$0.00240261\pi$
$978$	−45.8742	+	26.3527i	−1.46689	+	0.842668i
$979$	−4.18324	+	23.7243i	−0.133697	+	0.758233i
$980$	0.758704	−	1.74087i	0.0242359	−	0.0556102i
$981$	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	$-0.908104\pi$
$983$	−12.7694	−	35.0835i	−0.407279	−	1.11899i	0.551335	−	0.834284i	$-0.314119\pi$
$984$	3.96546	−	22.2070i	0.126414	−	0.707933i
$985$	14.6611	+	13.9364i	0.467141	+	0.444051i
$986$	−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
$990$	−41.3609	+	12.0185i	−1.31454	+	0.381973i
$991$	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
$995$	6.39236	+	21.6474i	0.202652	+	0.686270i
$996$	6.71743	−	5.61177i	0.212850	−	0.177816i
$997$	30.6391	−	36.5143i	0.970351	−	1.15642i	−0.0173159	−	0.999850i	$-0.505512\pi$
$997$	30.6391	−	36.5143i	0.970351	−	1.15642i	0.987667	−	0.156569i	$-0.0500435\pi$
$998$			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.124.6	yes	96
3.2	odd	2		405.2.p.a.289.11		96
5.2	odd	4		675.2.l.h.151.6		96
5.3	odd	4		675.2.l.h.151.11		96
5.4	even	2	inner	135.2.p.a.124.11	yes	96
15.14	odd	2		405.2.p.a.289.6		96
27.5	odd	18		405.2.p.a.199.6		96
27.22	even	9	inner	135.2.p.a.49.11	yes	96
135.22	odd	36		675.2.l.h.76.6		96
135.49	even	18	inner	135.2.p.a.49.6	✓	96
135.59	odd	18		405.2.p.a.199.11		96
135.103	odd	36		675.2.l.h.76.11		96

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

\(f(q)\)	\(=\)	\(q+(-0.795984 + 0.948617i) q^{2} +(-0.595931 + 1.62630i) q^{3} +(0.0810128 + 0.459446i) q^{4} +(2.17384 + 0.523837i) q^{5} +(-1.06839 - 1.85982i) q^{6} +(2.24130 + 0.395202i) q^{7} +(-2.64518 - 1.52719i) q^{8} +(-2.28973 - 1.93833i) q^{9} +O(q^{10})\)	\(q+(-0.795984 + 0.948617i) q^{2} +(-0.595931 + 1.62630i) q^{3} +(0.0810128 + 0.459446i) q^{4} +(2.17384 + 0.523837i) 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} +(-2.22727 + 1.64518i) 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} +(-2.14738 + 3.22316i) 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} +(-0.0645661 + 1.04120i) 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} +(4.45119 + 2.27748i) q^{25} -1.91463 q^{26} +(4.51684 - 2.56869i) q^{27} +1.06177i q^{28} +(4.94693 + 4.15097i) q^{29} +(-1.34826 - 4.60263i) 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} +(4.66522 + 2.03319i) 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} +(-4.95020 - 4.70552i) 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} +(-3.96215 - 5.41307i) 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} +(-5.70353 + 2.40964i) 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} +(-1.65483 - 0.725488i) 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} +(1.54001 + 3.09533i) 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} +(-5.64216 + 2.80712i) 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} +(-6.35648 + 5.88177i) 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} +(11.4317 - 3.37572i) 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} +(8.28875 + 0.550159i) 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} +(7.04866 - 7.41518i) 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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