LMFDB - Embedded newform 110.2.k.a.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, 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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			83.1
Character	$\chi$	$=$	110.83
Dual form			110.2.k.a.57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-0.348671 - 2.20142i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.49719 - 1.66085i) q^{5} +(2.11978 + 0.688757i) q^{6} +(-3.91761 - 0.620489i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-1.87153 + 0.608097i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.348671 - 2.20142i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.49719 - 1.66085i) q^{5} +(2.11978 + 0.688757i) q^{6} +(-3.91761 - 0.620489i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-1.87153 + 0.608097i) q^{9} +(2.15954 - 0.579997i) q^{10} +(2.83922 - 1.71431i) q^{11} +(-1.57605 + 1.57605i) q^{12} +(2.65534 + 1.35296i) q^{13} +(2.33142 - 3.20892i) q^{14} +(-3.13421 + 3.87504i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(4.15761 - 2.11841i) q^{17} +(0.307838 - 1.94362i) q^{18} +(2.59693 + 1.88678i) q^{19} +(-0.463629 + 2.18748i) q^{20} +8.84068i q^{21} +(0.238480 + 3.30804i) q^{22} +(-5.14200 - 5.14200i) q^{23} +(-0.688757 - 2.11978i) q^{24} +(-0.516841 + 4.97322i) q^{25} +(-2.41100 + 1.75169i) q^{26} +(-1.04442 - 2.04980i) q^{27} +(1.80073 + 3.53413i) q^{28} +(0.0660203 - 0.0479665i) q^{29} +(-2.02979 - 4.55183i) q^{30} +(-0.600717 - 1.84882i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.76387 - 5.65259i) q^{33} +4.66620i q^{34} +(4.83487 + 7.43555i) q^{35} +(1.59202 + 1.15667i) q^{36} +(-0.916611 + 5.78725i) q^{37} +(-2.86011 + 1.45730i) q^{38} +(2.05261 - 6.31728i) q^{39} +(-1.73857 - 1.40619i) q^{40} +(1.64181 - 2.25975i) q^{41} +(-7.87710 - 4.01358i) q^{42} +(-2.07213 + 2.07213i) q^{43} +(-3.05575 - 1.28933i) q^{44} +(3.81199 + 2.19789i) q^{45} +(6.91597 - 2.24713i) q^{46} +(12.1843 - 1.92981i) q^{47} +(2.20142 + 0.348671i) q^{48} +(8.30529 + 2.69855i) q^{49} +(-4.19653 - 2.71830i) q^{50} +(-6.11316 - 8.41404i) q^{51} +(-0.466200 - 2.94347i) q^{52} +(1.67555 - 3.28846i) q^{53} +2.30054 q^{54} +(-7.09805 - 2.14887i) q^{55} -3.96645 q^{56} +(3.24812 - 6.37480i) q^{57} +(0.0127659 + 0.0806009i) q^{58} +(-1.48475 - 2.04358i) q^{59} +(4.97722 + 0.257934i) q^{60} +(1.70602 + 0.554319i) q^{61} +(1.92003 + 0.304102i) q^{62} +(7.70925 - 1.22102i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-1.72848 - 6.43577i) q^{65} +(7.19925 - 1.67841i) q^{66} +(2.34748 - 2.34748i) q^{67} +(-4.15761 - 2.11841i) q^{68} +(-9.52685 + 13.1126i) q^{69} +(-8.82012 + 0.932234i) q^{70} +(-1.98584 + 6.11179i) q^{71} +(-1.75336 + 0.893382i) q^{72} +(-1.22279 + 7.72040i) q^{73} +(-4.74035 - 3.44406i) q^{74} +(11.1284 - 0.596233i) q^{75} -3.20998i q^{76} +(-12.1867 + 4.95428i) q^{77} +(4.69687 + 4.69687i) q^{78} +(-3.80642 - 11.7150i) q^{79} +(2.04222 - 0.910682i) q^{80} +(-8.92437 + 6.48393i) q^{81} +(1.26809 + 2.48877i) q^{82} +(6.86376 + 13.4709i) q^{83} +(7.15226 - 5.19642i) q^{84} +(-9.74309 - 3.73350i) q^{85} +(-0.905554 - 2.78701i) q^{86} +(-0.128614 - 0.128614i) q^{87} +(2.53609 - 2.13735i) q^{88} -5.99094i q^{89} +(-3.68895 + 2.39869i) q^{90} +(-9.56310 - 6.94800i) q^{91} +(-1.13757 + 7.18235i) q^{92} +(-3.86058 + 1.96706i) q^{93} +(-3.81210 + 11.7324i) q^{94} +(-0.754441 - 7.13797i) q^{95} +(-1.31009 + 1.80319i) q^{96} +(9.78069 + 4.98351i) q^{97} +(-6.17495 + 6.17495i) q^{98} +(-4.27122 + 4.93489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−0.348671	−	2.20142i	−0.201306	−	1.27099i	−0.856743	−	0.515744i	$-0.827516\pi$
$3$	−0.348671	−	2.20142i	−0.201306	−	1.27099i	0.655437	−	0.755250i	$-0.272484\pi$
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−1.49719	−	1.66085i	−0.669564	−	0.742754i
$5$	−1.49719	−	1.66085i	−0.669564	−	0.742754i
$6$	2.11978	+	0.688757i	0.865396	+	0.281184i
$7$	−3.91761	−	0.620489i	−1.48072	−	0.234523i	−0.636815	−	0.771017i	$-0.719748\pi$
$7$	−3.91761	−	0.620489i	−1.48072	−	0.234523i	−0.843904	+	0.536494i	$0.819748\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−1.87153	+	0.608097i	−0.623843	+	0.202699i
$10$	2.15954	−	0.579997i	0.682906	−	0.183411i
$11$	2.83922	−	1.71431i	0.856056	−	0.516883i
$11$	2.83922	−	1.71431i	0.856056	−	0.516883i
$12$	−1.57605	+	1.57605i	−0.454965	+	0.454965i
$13$	2.65534	+	1.35296i	0.736460	+	0.375245i	0.781637	−	0.623734i	$-0.214385\pi$
$13$	2.65534	+	1.35296i	0.736460	+	0.375245i	−0.0451771	+	0.998979i	$0.514385\pi$
$14$	2.33142	−	3.20892i	0.623098	−	0.857621i
$15$	−3.13421	+	3.87504i	−0.809249	+	1.00053i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	4.15761	−	2.11841i	1.00837	−	0.513790i	0.129869	−	0.991531i	$-0.458544\pi$
$17$	4.15761	−	2.11841i	1.00837	−	0.513790i	0.878500	+	0.477742i	$0.158544\pi$
$18$	0.307838	−	1.94362i	0.0725582	−	0.458115i
$19$	2.59693	+	1.88678i	0.595776	+	0.432856i	0.844377	−	0.535750i	$-0.179971\pi$
$19$	2.59693	+	1.88678i	0.595776	+	0.432856i	−0.248601	+	0.968606i	$0.579971\pi$
$20$	−0.463629	+	2.18748i	−0.103671	+	0.489134i
$21$			8.84068i			1.92919i
$22$	0.238480	+	3.30804i	0.0508440	+	0.705276i
$23$	−5.14200	−	5.14200i	−1.07218	−	1.07218i	−0.997184	−	0.0749964i	$-0.976105\pi$
$23$	−5.14200	−	5.14200i	−1.07218	−	1.07218i	−0.0749964	−	0.997184i	$-0.523895\pi$
$24$	−0.688757	−	2.11978i	−0.140592	−	0.432698i
$25$	−0.516841	+	4.97322i	−0.103368	+	0.994643i
$26$	−2.41100	+	1.75169i	−0.472836	+	0.343536i
$27$	−1.04442	−	2.04980i	−0.200999	−	0.394483i
$28$	1.80073	+	3.53413i	0.340306	+	0.667888i
$29$	0.0660203	−	0.0479665i	0.0122597	−	0.00890716i	−0.581639	−	0.813447i	$-0.697588\pi$
$29$	0.0660203	−	0.0479665i	0.0122597	−	0.00890716i	0.593898	+	0.804540i	$0.297588\pi$
$30$	−2.02979	−	4.55183i	−0.370587	−	0.831047i
$31$	−0.600717	−	1.84882i	−0.107892	−	0.332057i	0.882506	−	0.470300i	$-0.155854\pi$
$31$	−0.600717	−	1.84882i	−0.107892	−	0.332057i	−0.990398	+	0.138243i	$0.955854\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−4.76387	−	5.65259i	−0.829283	−	0.983990i
$34$			4.66620i			0.800246i
$35$	4.83487	+	7.43555i	0.817243	+	1.25684i
$36$	1.59202	+	1.15667i	0.265336	+	0.192778i
$37$	−0.916611	+	5.78725i	−0.150690	+	0.951419i	0.790235	+	0.612804i	$0.209958\pi$
$37$	−0.916611	+	5.78725i	−0.150690	+	0.951419i	−0.940925	+	0.338615i	$0.890042\pi$
$38$	−2.86011	+	1.45730i	−0.463971	+	0.236405i
$39$	2.05261	−	6.31728i	0.328680	−	1.01157i
$40$	−1.73857	−	1.40619i	−0.274892	−	0.222338i
$41$	1.64181	−	2.25975i	0.256407	−	0.352914i	−0.661335	−	0.750090i	$-0.730010\pi$
$41$	1.64181	−	2.25975i	0.256407	−	0.352914i	0.917742	+	0.397177i	$0.130010\pi$
$42$	−7.87710	−	4.01358i	−1.21546	−	0.619309i
$43$	−2.07213	+	2.07213i	−0.315997	+	0.315997i	−0.847227	−	0.531231i	$-0.821730\pi$
$43$	−2.07213	+	2.07213i	−0.315997	+	0.315997i	0.531231	+	0.847227i	$0.321730\pi$
$44$	−3.05575	−	1.28933i	−0.460672	−	0.194374i
$45$	3.81199	+	2.19789i	0.568259	+	0.327642i
$46$	6.91597	−	2.24713i	1.01970	−	0.331322i
$47$	12.1843	−	1.92981i	1.77727	−	0.281492i	0.820352	−	0.571858i	$-0.193777\pi$
$47$	12.1843	−	1.92981i	1.77727	−	0.281492i	0.956915	+	0.290367i	$0.0937772\pi$
$48$	2.20142	+	0.348671i	0.317748	+	0.0503264i
$49$	8.30529	+	2.69855i	1.18647	+	0.385507i
$50$	−4.19653	−	2.71830i	−0.593479	−	0.384426i
$51$	−6.11316	−	8.41404i	−0.856013	−	1.17820i
$52$	−0.466200	−	2.94347i	−0.0646503	−	0.408186i
$53$	1.67555	−	3.28846i	0.230155	−	0.451704i	−0.746830	−	0.665016i	$-0.768425\pi$
$53$	1.67555	−	3.28846i	0.230155	−	0.451704i	0.976984	+	0.213311i	$0.0684249\pi$
$54$	2.30054			0.313064
$55$	−7.09805	−	2.14887i	−0.957101	−	0.289754i
$56$	−3.96645			−0.530039
$57$	3.24812	−	6.37480i	0.430225	−	0.844363i
$58$	0.0127659	+	0.0806009i	0.00167625	+	0.0105834i
$59$	−1.48475	−	2.04358i	−0.193298	−	0.266052i	0.701356	−	0.712811i	$-0.252578\pi$
$59$	−1.48475	−	2.04358i	−0.193298	−	0.266052i	−0.894654	+	0.446759i	$0.852578\pi$
$60$	4.97722	+	0.257934i	0.642556	+	0.0332991i
$61$	1.70602	+	0.554319i	0.218433	+	0.0709733i	0.416189	−	0.909278i	$-0.363365\pi$
$61$	1.70602	+	0.554319i	0.218433	+	0.0709733i	−0.197756	+	0.980251i	$0.563365\pi$
$62$	1.92003	+	0.304102i	0.243844	+	0.0386210i
$63$	7.70925	−	1.22102i	0.971274	−	0.153835i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	−1.72848	−	6.43577i	−0.214392	−	0.798259i
$66$	7.19925	−	1.67841i	0.886166	−	0.206599i
$67$	2.34748	−	2.34748i	0.286790	−	0.286790i	−0.549020	−	0.835809i	$-0.684999\pi$
$67$	2.34748	−	2.34748i	0.286790	−	0.286790i	0.835809	+	0.549020i	$0.184999\pi$
$68$	−4.15761	−	2.11841i	−0.504184	−	0.256895i
$69$	−9.52685	+	13.1126i	−1.14690	+	1.57857i
$70$	−8.82012	+	0.932234i	−1.05421	+	0.111423i
$71$	−1.98584	+	6.11179i	−0.235676	+	0.725336i	0.761355	+	0.648335i	$0.224534\pi$
$71$	−1.98584	+	6.11179i	−0.235676	+	0.725336i	−0.997031	+	0.0770011i	$0.975466\pi$
$72$	−1.75336	+	0.893382i	−0.206636	+	0.105286i
$73$	−1.22279	+	7.72040i	−0.143117	+	0.903604i	0.806737	+	0.590911i	$0.201231\pi$
$73$	−1.22279	+	7.72040i	−0.143117	+	0.903604i	−0.949854	+	0.312694i	$0.898769\pi$
$74$	−4.74035	−	3.44406i	−0.551054	−	0.400364i
$75$	11.1284	−	0.596233i	1.28499	−	0.0688470i
$76$		−	3.20998i		−	0.368210i
$77$	−12.1867	+	4.95428i	−1.38880	+	0.564593i
$78$	4.69687	+	4.69687i	0.531816	+	0.531816i
$79$	−3.80642	−	11.7150i	−0.428256	−	1.31803i	−0.899842	−	0.436215i	$-0.856319\pi$
$79$	−3.80642	−	11.7150i	−0.428256	−	1.31803i	0.471587	−	0.881820i	$-0.343681\pi$
$80$	2.04222	−	0.910682i	0.228327	−	0.101817i
$81$	−8.92437	+	6.48393i	−0.991596	+	0.720437i
$82$	1.26809	+	2.48877i	0.140037	+	0.274838i
$83$	6.86376	+	13.4709i	0.753396	+	1.47862i	0.874002	+	0.485922i	$0.161516\pi$
$83$	6.86376	+	13.4709i	0.753396	+	1.47862i	−0.120606	+	0.992700i	$0.538484\pi$
$84$	7.15226	−	5.19642i	0.780375	−	0.566976i
$85$	−9.74309	−	3.73350i	−1.05679	−	0.404955i
$86$	−0.905554	−	2.78701i	−0.0976484	−	0.300531i
$87$	−0.128614	−	0.128614i	−0.0137889	−	0.0137889i
$88$	2.53609	−	2.13735i	0.270348	−	0.227842i
$89$		−	5.99094i		−	0.635038i	−0.948252	−	0.317519i	$-0.897150\pi$
$89$		−	5.99094i		−	0.635038i	0.948252	−	0.317519i	$-0.102850\pi$
$90$	−3.68895	+	2.39869i	−0.388849	+	0.252844i
$91$	−9.56310	−	6.94800i	−1.00249	−	0.728349i
$92$	−1.13757	+	7.18235i	−0.118600	+	0.748812i
$93$	−3.86058	+	1.96706i	−0.400323	+	0.203975i
$94$	−3.81210	+	11.7324i	−0.393188	+	1.21011i
$95$	−0.754441	−	7.13797i	−0.0774040	−	0.732340i
$96$	−1.31009	+	1.80319i	−0.133711	+	0.184037i
$97$	9.78069	+	4.98351i	0.993078	+	0.505999i	0.873499	−	0.486826i	$-0.161845\pi$
$97$	9.78069	+	4.98351i	0.993078	+	0.505999i	0.119579	+	0.992825i	$0.461845\pi$
$98$	−6.17495	+	6.17495i	−0.623764	+	0.623764i
$99$	−4.27122	+	4.93489i	−0.429273	+	0.495976i
$100$	4.32721	−	2.50505i	0.432721	−	0.250505i
$101$	−7.31649	+	2.37727i	−0.728018	+	0.236547i	−0.649496	−	0.760365i	$-0.725020\pi$
$101$	−7.31649	+	2.37727i	−0.728018	+	0.236547i	−0.0785218	+	0.996912i	$0.525020\pi$
$102$	10.2723	−	1.62697i	1.01711	−	0.161094i
$103$	5.63036	+	0.891762i	0.554776	+	0.0878679i	0.427526	−	0.904003i	$-0.359385\pi$
$103$	5.63036	+	0.891762i	0.554776	+	0.0878679i	0.127250	+	0.991871i	$0.459385\pi$
$104$	2.83430	+	0.920920i	0.277926	+	0.0903037i
$105$	14.6830	−	13.2362i	1.43292	−	1.29172i
$106$	2.16935	+	2.98586i	0.210706	+	0.290012i
$107$	1.97017	+	12.4391i	0.190463	+	1.20254i	0.878816	+	0.477161i	$0.158334\pi$
$107$	1.97017	+	12.4391i	0.190463	+	1.20254i	−0.688353	+	0.725376i	$0.741666\pi$
$108$	−1.04442	+	2.04980i	−0.100500	+	0.197242i
$109$	13.0770			1.25255			0.626273	−	0.779604i	$-0.284580\pi$
$109$	13.0770			1.25255			0.626273	+	0.779604i	$0.284580\pi$
$110$	5.13711	−	5.34885i	0.489804	−	0.509992i
$111$	13.0598			1.23958
$112$	1.80073	−	3.53413i	0.170153	−	0.333944i
$113$	−0.0655098	−	0.413613i	−0.00616264	−	0.0389094i	0.984415	−	0.175859i	$-0.0562702\pi$
$113$	−0.0655098	−	0.413613i	−0.00616264	−	0.0389094i	−0.990578	+	0.136949i	$0.956270\pi$
$114$	4.20537	+	5.78820i	0.393869	+	0.542115i
$115$	−0.841532	+	16.2386i	−0.0784733	+	1.51426i
$116$	−0.0776115	−	0.0252175i	−0.00720605	−	0.00234139i
$117$	−5.79229	−	0.917408i	−0.535497	−	0.0848144i
$118$	2.49491	−	0.395154i	0.229675	−	0.0363769i
$119$	−17.6024	+	5.71935i	−1.61361	+	0.524292i
$120$	−2.48943	+	4.31763i	−0.227253	+	0.394144i
$121$	5.12231	−	9.73457i	0.465665	−	0.884961i
$122$	−1.26842	+	1.26842i	−0.114837	+	0.114837i
$123$	−5.54712	−	2.82640i	−0.500167	−	0.254848i
$124$	−1.14263	+	1.57270i	−0.102611	+	0.141232i
$125$	9.03357	−	6.58746i	0.807987	−	0.589200i
$126$	−2.41198	+	7.42332i	−0.214877	+	0.661322i
$127$	−7.73399	+	3.94067i	−0.686281	+	0.349678i	−0.762114	−	0.647443i	$-0.775838\pi$
$127$	−7.73399	+	3.94067i	−0.686281	+	0.349678i	0.0758331	+	0.997121i	$0.475838\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	5.28413	+	3.83915i	0.465242	+	0.338018i
$130$	6.51903	+	1.38169i	0.571757	+	0.121182i
$131$		−	1.31996i		−	0.115326i	−0.998336	−	0.0576628i	$-0.981635\pi$
$131$		−	1.31996i		−	0.115326i	0.998336	−	0.0576628i	$-0.0183648\pi$
$132$	−1.77291	+	7.17656i	−0.154312	+	0.624640i
$133$	−9.00303	−	9.00303i	−0.780661	−	0.780661i
$134$	1.02588	+	3.15735i	0.0886229	+	0.272753i
$135$	−1.84070	+	4.80356i	−0.158422	+	0.413425i
$136$	3.77503	−	2.74272i	0.323706	−	0.235186i
$137$	−8.13766	−	15.9711i	−0.695248	−	1.36450i	−0.920710	−	0.390248i	$-0.872389\pi$
$137$	−8.13766	−	15.9711i	−0.695248	−	1.36450i	0.225462	−	0.974252i	$-0.427611\pi$
$138$	−7.35830	−	14.4415i	−0.626380	−	1.22934i
$139$	−2.00508	+	1.45677i	−0.170068	+	0.123562i	−0.669564	−	0.742755i	$-0.733519\pi$
$139$	−2.00508	+	1.45677i	−0.170068	+	0.123562i	0.499495	+	0.866317i	$0.333519\pi$
$140$	3.17362	−	8.28201i	0.268220	−	0.699957i
$141$	−8.49666	−	26.1500i	−0.715548	−	2.20223i
$142$	−4.54409	−	4.54409i	−0.381332	−	0.381332i
$143$	9.85849	−	0.710708i	0.824408	−	0.0594324i
$144$		−	1.96784i		−	0.163987i
$145$	−0.178510	−	0.0378347i	−0.0148245	−	0.00314200i
$146$	−6.32379	−	4.59450i	−0.523361	−	0.380244i
$147$	3.04484	−	19.2244i	0.251134	−	1.58560i
$148$	5.22076	−	2.66011i	0.429144	−	0.218660i
$149$	−3.39237	+	10.4406i	−0.277914	+	0.855331i	0.710520	+	0.703677i	$0.248460\pi$
$149$	−3.39237	+	10.4406i	−0.277914	+	0.855331i	−0.988434	+	0.151654i	$0.951540\pi$
$150$	−4.52093	+	10.1861i	−0.369132	+	0.831694i
$151$	−7.30350	+	10.0524i	−0.594350	+	0.818053i	−0.995176	−	0.0981010i	$-0.968723\pi$
$151$	−7.30350	+	10.0524i	−0.594350	+	0.818053i	0.400826	+	0.916154i	$0.368723\pi$
$152$	2.86011	+	1.45730i	0.231986	+	0.118203i
$153$	−6.49290	+	6.49290i	−0.524920	+	0.524920i
$154$	1.11833	−	13.1076i	0.0901177	−	1.05624i
$155$	−2.17122	+	3.76573i	−0.174396	+	0.302471i
$156$	−6.31728	+	2.05261i	−0.505787	+	0.164340i
$157$	5.61637	−	0.889545i	0.448235	−	0.0709934i	0.0717635	−	0.997422i	$-0.477137\pi$
$157$	5.61637	−	0.889545i	0.448235	−	0.0709934i	0.376471	+	0.926428i	$0.377137\pi$
$158$	12.1662	+	1.92693i	0.967889	+	0.153299i
$159$	−7.82350	−	2.54201i	−0.620444	−	0.201595i
$160$	−0.115724	+	2.23307i	−0.00914880	+	0.176540i
$161$	16.9538	+	23.3349i	1.33615	+	1.83905i
$162$	−1.72565	−	10.8953i	−0.135580	−	0.856017i
$163$	−5.50237	+	10.7990i	−0.430979	+	0.845843i	0.568749	+	0.822511i	$0.307427\pi$
$163$	−5.50237	+	10.7990i	−0.430979	+	0.845843i	−0.999728	+	0.0233320i	$0.992573\pi$
$164$	−2.79321			−0.218113
$165$	−2.25569	+	16.3751i	−0.175605	+	1.27480i
$166$	−15.1187			−1.17344
$167$	−1.86387	+	3.65804i	−0.144230	+	0.283068i	−0.951809	−	0.306692i	$-0.900778\pi$
$167$	−1.86387	+	3.65804i	−0.144230	+	0.283068i	0.807578	+	0.589760i	$0.200778\pi$
$168$	1.38299	+	8.73183i	0.106700	+	0.673676i
$169$	−2.42088	−	3.33205i	−0.186221	−	0.256312i
$170$	7.74985	−	6.98619i	0.594386	−	0.535816i
$171$	−6.00757	−	1.95198i	−0.459410	−	0.149271i
$172$	2.89436	+	0.458421i	0.220693	+	0.0349543i
$173$	12.8231	−	2.03097i	0.974919	−	0.154412i	0.351405	−	0.936224i	$-0.385704\pi$
$173$	12.8231	−	2.03097i	0.974919	−	0.154412i	0.623515	+	0.781812i	$0.285704\pi$
$174$	0.172986	−	0.0562064i	0.0131140	−	0.00426100i
$175$	5.11061	−	19.1624i	0.386326	−	1.44854i
$176$	0.753035	+	3.23001i	0.0567622	+	0.243471i
$177$	−3.98110	+	3.98110i	−0.299238	+	0.299238i
$178$	5.33796	+	2.71983i	0.400097	+	0.203860i
$179$	4.78324	−	6.58357i	0.357516	−	0.492079i	−0.591938	−	0.805983i	$-0.701637\pi$
$179$	4.78324	−	6.58357i	0.357516	−	0.492079i	0.949455	+	0.313904i	$0.101637\pi$
$180$	−0.462502	−	4.37586i	−0.0344729	−	0.326157i
$181$	5.23127	−	16.1002i	0.388837	−	1.19672i	−0.544821	−	0.838552i	$-0.683402\pi$
$181$	5.23127	−	16.1002i	0.388837	−	1.19672i	0.933658	−	0.358165i	$-0.116598\pi$
$182$	10.5323	−	5.36646i	0.780704	−	0.397789i
$183$	0.625452	−	3.94895i	0.0462348	−	0.291915i
$184$	−5.88307	−	4.27430i	−0.433706	−	0.315106i
$185$	10.9841	−	7.14227i	0.807567	−	0.525110i
$186$		−	4.33283i		−	0.317698i
$187$	8.17276	−	13.1420i	0.597652	−	0.961041i
$188$	−8.72302	−	8.72302i	−0.636192	−	0.636192i
$189$	2.81977	+	8.67836i	0.205108	+	0.631258i
$190$	6.70248	+	2.56836i	0.486249	+	0.186328i
$191$	−8.26779	+	6.00690i	−0.598236	+	0.434644i	−0.845252	−	0.534367i	$-0.820550\pi$
$191$	−8.26779	+	6.00690i	−0.598236	+	0.434644i	0.247016	+	0.969011i	$0.420550\pi$
$192$	−1.01188	−	1.98593i	−0.0730264	−	0.143322i
$193$	−10.0127	−	19.6510i	−0.720728	−	1.41451i	−0.902290	−	0.431129i	$-0.858115\pi$
$193$	−10.0127	−	19.6510i	−0.720728	−	1.41451i	0.181563	−	0.983379i	$-0.441885\pi$
$194$	−8.88068	+	6.45219i	−0.637596	+	0.463240i
$195$	−13.5652	+	6.04910i	−0.971423	+	0.433185i
$196$	−2.69855	−	8.30529i	−0.192754	−	0.593235i
$197$	10.9542	+	10.9542i	0.780453	+	0.780453i	0.979907	−	0.199454i	$-0.0639168\pi$
$197$	10.9542	+	10.9542i	0.780453	+	0.780453i	−0.199454	+	0.979907i	$0.563917\pi$
$198$	−2.45793	−	6.04608i	−0.174678	−	0.429676i
$199$			7.77743i			0.551327i	0.961254	+	0.275664i	$0.0888976\pi$
$199$			7.77743i			0.551327i	−0.961254	+	0.275664i	$0.911102\pi$
$200$	0.267505	+	4.99284i	0.0189155	+	0.353047i
$201$	−5.98629	−	4.34929i	−0.422240	−	0.306776i
$202$	1.20345	−	7.59830i	0.0846746	−	0.534614i
$203$	−0.288405	+	0.146949i	−0.0202420	+	0.0103138i
$204$	−3.21388	+	9.89130i	−0.225016	+	0.692529i
$205$	−6.21120	+	0.656487i	−0.433809	+	0.0458511i
$206$	−3.35070	+	4.61184i	−0.233454	+	0.321322i
$207$	12.7502	+	6.49657i	0.886202	+	0.451543i
$208$	−2.10729	+	2.10729i	−0.146114	+	0.146114i
$209$	10.6078	+	0.905046i	0.733753	+	0.0626033i
$210$	5.12756	+	19.0918i	0.353836	+	1.31746i
$211$	9.07668	−	2.94919i	0.624864	−	0.203031i	0.0205655	−	0.999789i	$-0.493453\pi$
$211$	9.07668	−	2.94919i	0.624864	−	0.203031i	0.604299	+	0.796758i	$0.293453\pi$
$212$	−3.64528	+	0.577356i	−0.250359	+	0.0396530i
$213$	14.1471	+	2.24067i	0.969340	+	0.153528i
$214$	−11.9778	−	3.89182i	−0.818785	−	0.266039i
$215$	6.54387	+	0.339122i	0.446288	+	0.0231279i
$216$	−1.35222	−	1.86118i	−0.0920071	−	0.126637i
$217$	1.20621	+	7.61569i	0.0818826	+	0.516986i
$218$	−5.93682	+	11.6517i	−0.402092	+	0.789150i
$219$	17.4222			1.17729
$220$	2.43366	+	7.00552i	0.164077	+	0.472312i
$221$	13.9060			0.935420
$222$	−5.92903	+	11.6364i	−0.397930	+	0.780982i
$223$	2.90351	+	18.3320i	0.194433	+	1.22760i	0.871023	+	0.491243i	$0.163457\pi$
$223$	2.90351	+	18.3320i	0.194433	+	1.22760i	−0.676589	+	0.736361i	$0.736543\pi$
$224$	2.33142	+	3.20892i	0.155774	+	0.214405i
$225$	−2.05691	−	9.62181i	−0.137128	−	0.641454i
$226$	0.398272	+	0.129407i	0.0264927	+	0.00860799i
$227$	−11.1178	−	1.76089i	−0.737915	−	0.116874i	−0.223848	−	0.974624i	$-0.571862\pi$
$227$	−11.1178	−	1.76089i	−0.737915	−	0.116874i	−0.514067	+	0.857750i	$0.671862\pi$
$228$	−7.06652	+	1.11923i	−0.467992	+	0.0741226i
$229$	−4.10397	+	1.33346i	−0.271198	+	0.0881177i	−0.441459	−	0.897281i	$-0.645539\pi$
$229$	−4.10397	+	1.33346i	−0.271198	+	0.0881177i	0.170261	+	0.985399i	$0.445539\pi$
$230$	−14.0867	−	8.12199i	−0.928848	−	0.535548i
$231$	15.1556	+	25.1006i	0.997167	+	1.65150i
$232$	0.0577038	−	0.0577038i	0.00378844	−	0.00378844i
$233$	−13.0340	−	6.64117i	−0.853887	−	0.435077i	−0.0284660	−	0.999595i	$-0.509062\pi$
$233$	−13.0340	−	6.64117i	−0.853887	−	0.435077i	−0.825421	+	0.564518i	$0.809062\pi$
$234$	3.44706	−	4.74447i	0.225341	−	0.310156i
$235$	−21.4474	−	17.3471i	−1.39907	−	1.13160i
$236$	−0.780579	+	2.40237i	−0.0508113	+	0.156381i
$237$	−24.4624	+	12.4642i	−1.58900	+	0.809638i
$238$	2.89532	−	18.2804i	0.187676	−	1.18494i
$239$	6.12048	+	4.44679i	0.395901	+	0.287639i	0.767869	−	0.640606i	$-0.221317\pi$
$239$	6.12048	+	4.44679i	0.395901	+	0.287639i	−0.371968	+	0.928245i	$0.621317\pi$
$240$	−2.71686	−	4.17826i	−0.175373	−	0.269706i
$241$			6.31704i			0.406917i	0.979084	+	0.203458i	$0.0652181\pi$
$241$			6.31704i			0.406917i	−0.979084	+	0.203458i	$0.934782\pi$
$242$	6.34809	+	8.98342i	0.408070	+	0.577476i
$243$	12.5054	+	12.5054i	0.802220	+	0.802220i
$244$	−0.554319	−	1.70602i	−0.0354867	−	0.109217i
$245$	−7.95271	−	17.8341i	−0.508080	−	1.13938i
$246$	5.03668	−	3.65936i	0.321127	−	0.233313i
$247$	4.34299	+	8.52359i	0.276338	+	0.542343i
$248$	−0.882540	−	1.73208i	−0.0560413	−	0.109987i
$249$	27.2620	−	19.8070i	1.72766	−	1.25522i
$250$	1.76831	+	11.0396i	0.111838	+	0.698206i
$251$	6.45616	+	19.8700i	0.407509	+	1.25418i	0.918782	+	0.394765i	$0.129174\pi$
$251$	6.45616	+	19.8700i	0.407509	+	1.25418i	−0.511273	+	0.859418i	$0.670826\pi$
$252$	−5.51921	−	5.51921i	−0.347678	−	0.347678i
$253$	−23.4142	−	5.78429i	−1.47204	−	0.363655i
$254$		−	8.68006i		−	0.544636i
$255$	−4.82189	+	22.7505i	−0.301958	+	1.42469i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	0.961438	−	6.07028i	0.0599729	−	0.378654i	−0.939386	−	0.342860i	$-0.888604\pi$
$257$	0.961438	−	6.07028i	0.0599729	−	0.378654i	0.999359	−	0.0357933i	$-0.0113958\pi$
$258$	−5.81965	+	2.96526i	−0.362315	+	0.184609i
$259$	7.18185	−	22.1035i	0.446259	−	1.37344i
$260$	−4.19067	+	5.18122i	−0.259894	+	0.321326i
$261$	−0.0943906	+	0.129918i	−0.00584263	+	0.00804169i
$262$	1.17609	+	0.599250i	0.0726594	+	0.0370218i
$263$	17.2139	−	17.2139i	1.06145	−	1.06145i	0.0634691	−	0.997984i	$-0.479784\pi$
$263$	17.2139	−	17.2139i	1.06145	−	1.06145i	0.997984	−	0.0634691i	$-0.0202164\pi$
$264$	−5.58948	−	4.83777i	−0.344009	−	0.297744i
$265$	−7.97025	+	2.14061i	−0.489609	+	0.131496i
$266$	12.1090	−	3.93447i	0.742453	−	0.241238i
$267$	−13.1886	+	2.08887i	−0.807129	+	0.127837i
$268$	−3.27896	−	0.519336i	−0.200294	−	0.0317235i
$269$	−25.5811	−	8.31179i	−1.55971	−	0.506779i	−0.602976	−	0.797759i	$-0.706019\pi$
$269$	−25.5811	−	8.31179i	−1.55971	−	0.506779i	−0.956729	+	0.290980i	$0.906019\pi$
$270$	−3.44435	−	3.82085i	−0.209616	−	0.232529i
$271$	13.3592	+	18.3874i	0.811515	+	1.11695i	0.991088	+	0.133210i	$0.0425284\pi$
$271$	13.3592	+	18.3874i	0.811515	+	1.11695i	−0.179573	+	0.983745i	$0.557472\pi$
$272$	0.729954	+	4.60875i	0.0442600	+	0.279446i
$273$	−11.9611	+	23.4750i	−0.723920	+	1.42077i
$274$	17.9247			1.08287
$275$	7.05819	+	15.0061i	0.425625	+	0.904900i
$276$	16.2080			0.975610
$277$	−9.44205	+	18.5311i	−0.567318	+	1.11342i	0.412017	+	0.911176i	$0.364825\pi$
$277$	−9.44205	+	18.5311i	−0.567318	+	1.11342i	−0.979334	+	0.202247i	$0.935175\pi$
$278$	−0.387709	−	2.44790i	−0.0232532	−	0.146815i
$279$	2.24852	+	3.09482i	0.134615	+	0.185282i
$280$	5.93853	+	6.58767i	0.354895	+	0.393689i
$281$	−6.11005	−	1.98528i	−0.364495	−	0.118432i	0.121043	−	0.992647i	$-0.461376\pi$
$281$	−6.11005	−	1.98528i	−0.364495	−	0.118432i	−0.485538	+	0.874216i	$0.661376\pi$
$282$	27.1572	+	4.30129i	1.61719	+	0.256138i
$283$	0.957628	−	0.151673i	0.0569251	−	0.00901605i	−0.127907	−	0.991786i	$-0.540826\pi$
$283$	0.957628	−	0.151673i	0.0569251	−	0.00901605i	0.184832	+	0.982770i	$0.440826\pi$
$284$	6.11179	−	1.98584i	0.362668	−	0.117838i
$285$	−15.4506	+	4.14965i	−0.915217	+	0.245804i
$286$	−3.84242	+	9.10663i	−0.227207	+	0.538487i
$287$	−7.83411	+	7.83411i	−0.462433	+	0.462433i
$288$	1.75336	+	0.893382i	0.103318	+	0.0526430i
$289$	2.80573	−	3.86175i	0.165043	−	0.227162i
$290$	0.114753	−	0.141877i	0.00673852	−	0.00833131i
$291$	7.56058	−	23.2691i	0.443209	−	1.36406i
$292$	6.96467	−	3.54868i	0.407577	−	0.207671i
$293$	−0.677974	+	4.28056i	−0.0396077	+	0.250073i	−0.999546	−	0.0301394i	$-0.990405\pi$
$293$	−0.677974	+	4.28056i	−0.0396077	+	0.250073i	0.959938	+	0.280212i	$0.0904049\pi$
$294$	15.7467	+	11.4407i	0.918367	+	0.667233i
$295$	−1.17113	+	5.52558i	−0.0681858	+	0.321711i
$296$			5.85939i			0.340570i
$297$	−6.47932	−	4.02936i	−0.375968	−	0.233807i
$298$	−7.76258	−	7.76258i	−0.449674	−	0.449674i
$299$	−6.69682	−	20.6107i	−0.387287	−	1.19195i
$300$	−7.02345	−	8.65258i	−0.405499	−	0.499557i
$301$	9.40354	−	6.83207i	0.542011	−	0.393794i
$302$	−5.64104	−	11.0712i	−0.324605	−	0.637074i
$303$	7.78443	+	15.2778i	0.447204	+	0.877687i
$304$	−2.59693	+	1.88678i	−0.148944	+	0.108214i
$305$	−1.63360	−	3.66336i	−0.0935394	−	0.209764i
$306$	−2.83750	−	8.73293i	−0.162209	−	0.499228i
$307$	−13.5031	−	13.5031i	−0.770662	−	0.770662i	0.207560	−	0.978222i	$-0.433448\pi$
$307$	−13.5031	−	13.5031i	−0.770662	−	0.770662i	−0.978222	+	0.207560i	$0.933448\pi$
$308$	11.1712	+	6.94716i	0.636540	+	0.395851i
$309$		−	12.7058i		−	0.722805i
$310$	−2.36958	−	3.64418i	−0.134583	−	0.206975i
$311$	−18.7825	−	13.6463i	−1.06506	−	0.773812i	−0.0900427	−	0.995938i	$-0.528700\pi$
$311$	−18.7825	−	13.6463i	−1.06506	−	0.773812i	−0.975018	+	0.222126i	$0.928700\pi$
$312$	1.03910	−	6.56060i	0.0588273	−	0.371421i
$313$	30.1218	−	15.3478i	1.70258	−	0.867510i	0.717263	−	0.696803i	$-0.245395\pi$
$313$	30.1218	−	15.3478i	1.70258	−	0.867510i	0.985322	−	0.170707i	$-0.0546052\pi$
$314$	−1.75719	+	5.40807i	−0.0991638	+	0.305195i
$315$	−13.5702	−	10.9758i	−0.764591	−	0.618416i
$316$	−7.24024	+	9.96533i	−0.407295	+	0.560594i
$317$	10.5767	+	5.38910i	0.594047	+	0.302682i	0.725046	−	0.688700i	$-0.241818\pi$
$317$	10.5767	+	5.38910i	0.594047	+	0.302682i	−0.130999	+	0.991382i	$0.541818\pi$
$318$	5.81674	−	5.81674i	0.326187	−	0.326187i
$319$	0.105217	−	0.249366i	0.00589100	−	0.0139618i
$320$	−1.93714	−	1.11690i	−0.108290	−	0.0624368i
$321$	26.6969	−	8.67435i	1.49008	−	0.484155i
$322$	−28.4884	+	4.51212i	−1.58760	+	0.251451i
$323$	14.7940	+	2.34314i	0.823159	+	0.130376i
$324$	10.4912	+	3.40880i	0.582846	+	0.189378i
$325$	−8.10097	+	12.5063i	−0.449361	+	0.693726i
$326$	−7.12396	−	9.80529i	−0.394560	−	0.543065i
$327$	−4.55956	−	28.7879i	−0.252144	−	1.59198i
$328$	1.26809	−	2.48877i	0.0700185	−	0.137419i
$329$	−48.9309			−2.69765
$330$	−13.5662	−	9.44396i	−0.746797	−	0.519873i
$331$	11.2700			0.619456			0.309728	−	0.950825i	$-0.399762\pi$
$331$	11.2700			0.619456			0.309728	+	0.950825i	$0.399762\pi$
$332$	6.86376	−	13.4709i	0.376698	−	0.739311i
$333$	−1.80375	−	11.3884i	−0.0988447	−	0.624081i
$334$	−2.41316	−	3.32144i	−0.132042	−	0.181741i
$335$	−7.41342	−	0.384185i	−0.405039	−	0.0209903i
$336$	−8.40798	−	2.73192i	−0.458693	−	0.149038i
$337$	−16.5766	−	2.62548i	−0.902987	−	0.143019i	−0.312360	−	0.949964i	$-0.601119\pi$
$337$	−16.5766	−	2.62548i	−0.902987	−	0.143019i	−0.590627	+	0.806945i	$0.701119\pi$
$338$	4.06794	−	0.644298i	0.221267	−	0.0350452i
$339$	−0.887696	+	0.288430i	−0.0482130	+	0.0156654i
$340$	2.70638	+	10.0768i	0.146774	+	0.546493i
$341$	−4.87500	−	4.21938i	−0.263996	−	0.228492i
$342$	4.46660	−	4.46660i	0.241526	−	0.241526i
$343$	−6.12358	−	3.12012i	−0.330642	−	0.168471i
$344$	−1.72247	+	2.37077i	−0.0928691	+	0.127823i
$345$	36.0415	−	3.80938i	1.94041	−	0.205090i
$346$	−4.01194	+	12.3475i	−0.215683	+	0.663804i
$347$	−6.10579	+	3.11106i	−0.327776	+	0.167010i	−0.610133	−	0.792299i	$-0.708884\pi$
$347$	−6.10579	+	3.11106i	−0.327776	+	0.167010i	0.282357	+	0.959309i	$0.408884\pi$
$348$	−0.0284535	+	0.179649i	−0.00152527	+	0.00963017i
$349$	9.07565	+	6.59384i	0.485808	+	0.352960i	0.803570	−	0.595210i	$-0.202931\pi$
$349$	9.07565	+	6.59384i	0.485808	+	0.352960i	−0.317762	+	0.948171i	$0.602931\pi$
$350$	14.7537	+	13.2532i	0.788618	+	0.708411i
$351$		−	6.85598i		−	0.365945i
$352$	−3.21983	−	0.795433i	−0.171617	−	0.0423967i
$353$	−15.7594	−	15.7594i	−0.838790	−	0.838790i	0.149910	−	0.988700i	$-0.452102\pi$
$353$	−15.7594	−	15.7594i	−0.838790	−	0.838790i	−0.988700	+	0.149910i	$0.952102\pi$
$354$	−1.73981	−	5.35457i	−0.0924696	−	0.284592i
$355$	13.1240	−	5.85233i	0.696547	−	0.310610i
$356$	−4.84677	+	3.52138i	−0.256878	+	0.186633i
$357$	18.7282	+	36.7561i	0.991200	+	1.94534i
$358$	3.69445	+	7.25077i	0.195258	+	0.383215i
$359$	12.7399	−	9.25607i	0.672386	−	0.488517i	−0.198437	−	0.980114i	$-0.563587\pi$
$359$	12.7399	−	9.25607i	0.672386	−	0.488517i	0.870823	+	0.491597i	$0.163587\pi$
$360$	4.10889	+	1.57451i	0.216557	+	0.0829837i
$361$	−2.68723	−	8.27043i	−0.141433	−	0.435286i
$362$	11.9704	+	11.9704i	0.629152	+	0.629152i
$363$	−23.2159	−	7.88222i	−1.21852	−	0.413709i
$364$			11.8206i			0.619570i
$365$	14.6532	−	9.52804i	0.766982	−	0.498720i
$366$	3.23459	+	2.35007i	0.169075	+	0.122840i
$367$	4.35420	−	27.4914i	0.227288	−	1.43504i	−0.565102	−	0.825021i	$-0.691163\pi$
$367$	4.35420	−	27.4914i	0.227288	−	1.43504i	0.792389	−	0.610016i	$-0.208837\pi$
$368$	6.47929	−	3.30136i	0.337756	−	0.172096i
$369$	−1.69854	+	5.22757i	−0.0884225	+	0.272136i
$370$	1.37713	+	13.0294i	0.0715937	+	0.677368i
$371$	−8.60461	+	11.8432i	−0.446729	+	0.614870i
$372$	3.86058	+	1.96706i	0.200162	+	0.101987i
$373$	−19.2605	+	19.2605i	−0.997270	+	0.997270i	−0.999996	−	0.00272613i	$-0.999132\pi$
$373$	−19.2605	+	19.2605i	−0.997270	+	0.997270i	0.00272613	+	0.999996i	$0.499132\pi$
$374$	7.99929	+	13.2483i	0.413633	+	0.685056i
$375$	−17.6515	−	17.5899i	−0.911522	−	0.908337i
$376$	11.7324	−	3.81210i	0.605054	−	0.196594i
$377$	0.240203	−	0.0380445i	0.0123711	−	0.00195939i
$378$	−9.01262	−	1.42746i	−0.463559	−	0.0734206i
$379$	20.6465	+	6.70844i	1.06054	+	0.344590i	0.786796	−	0.617214i	$-0.211739\pi$
$379$	20.6465	+	6.70844i	1.06054	+	0.344590i	0.273742	+	0.961803i	$0.411739\pi$
$380$	−5.33129	+	4.80595i	−0.273489	+	0.246540i
$381$	11.3717	+	15.6518i	0.582590	+	0.801866i
$382$	−1.59869	−	10.0937i	−0.0817960	−	0.516440i
$383$	14.7184	−	28.8865i	0.752075	−	1.47603i	−0.123188	−	0.992383i	$-0.539312\pi$
$383$	14.7184	−	28.8865i	0.752075	−	1.47603i	0.875263	−	0.483647i	$-0.160688\pi$
$384$	2.22887			0.113741
$385$	26.4741	+	12.8227i	1.34924	+	0.653506i
$386$	22.0548			1.12256
$387$	2.61800	−	5.13811i	0.133080	−	0.261185i
$388$	−1.71720	−	10.8420i	−0.0871776	−	0.550418i
$389$	6.37358	+	8.77248i	0.323153	+	0.444782i	0.939427	−	0.342750i	$-0.111358\pi$
$389$	6.37358	+	8.77248i	0.323153	+	0.444782i	−0.616273	+	0.787532i	$0.711358\pi$
$390$	0.768684	−	14.8329i	0.0389238	−	0.751093i
$391$	−32.2713	−	10.4856i	−1.63203	−	0.530278i
$392$	8.62518	+	1.36610i	0.435638	+	0.0689982i
$393$	−2.90580	+	0.460233i	−0.146578	+	0.0232157i
$394$	−14.7333	+	4.78715i	−0.742255	+	0.241173i
$395$	−13.7578	+	23.8614i	−0.692232	+	1.20060i
$396$	6.50297	+	0.554829i	0.326787	+	0.0278812i
$397$	−1.10287	+	1.10287i	−0.0553516	+	0.0553516i	−0.734241	−	0.678889i	$-0.762462\pi$
$397$	−1.10287	+	1.10287i	−0.0553516	+	0.0553516i	0.678889	+	0.734241i	$0.262462\pi$
$398$	−6.92974	−	3.53088i	−0.347356	−	0.176987i
$399$	−16.6804	+	22.9586i	−0.835064	+	1.14937i
$400$	−4.57010	−	2.02835i	−0.228505	−	0.101418i
$401$	−6.24701	+	19.2263i	−0.311961	+	0.960116i	0.665027	+	0.746820i	$0.268420\pi$
$401$	−6.24701	+	19.2263i	−0.311961	+	0.960116i	−0.976987	+	0.213297i	$0.931580\pi$
$402$	6.59297	−	3.35928i	0.328827	−	0.167546i
$403$	0.906274	−	5.72199i	0.0451447	−	0.285033i
$404$	6.22378	+	4.52184i	0.309644	+	0.224970i
$405$	24.1303	+	5.11435i	1.19904	+	0.254134i
$406$		−	0.323684i		−	0.0160642i
$407$	7.31866	+	18.0026i	0.362773	+	0.892357i
$408$	−7.35414	−	7.35414i	−0.364084	−	0.364084i
$409$	6.20451	+	19.0955i	0.306793	+	0.944212i	0.979002	+	0.203851i	$0.0653457\pi$
$409$	6.20451	+	19.0955i	0.306793	+	0.944212i	−0.672209	+	0.740362i	$0.734654\pi$
$410$	2.23489	−	5.83226i	0.110373	−	0.288035i
$411$	−32.3217	+	23.4831i	−1.59431	+	1.15834i
$412$	−2.58799	−	5.07922i	−0.127501	−	0.250235i
$413$	4.54865	+	8.92723i	0.223825	+	0.439280i
$414$	−11.5770	+	8.41116i	−0.568977	+	0.413386i
$415$	12.0968	−	31.5682i	0.593807	−	1.54962i
$416$	−0.920920	−	2.83430i	−0.0451518	−	0.138963i
$417$	3.90609	+	3.90609i	0.191282	+	0.191282i
$418$	−5.62222	+	9.04069i	−0.274992	+	0.442195i
$419$			0.0907865i			0.00443521i	0.999998	+	0.00221761i	$0.000705886\pi$
$419$			0.0907865i			0.00443521i	−0.999998	+	0.00221761i	$0.999294\pi$
$420$	−19.3388	−	4.09879i	−0.943635	−	0.200001i
$421$	25.5580	+	18.5690i	1.24562	+	0.904997i	0.997960	−	0.0638492i	$-0.0203377\pi$
$421$	25.5580	+	18.5690i	1.24562	+	0.904997i	0.247662	+	0.968846i	$0.420338\pi$
$422$	−1.49298	+	9.42628i	−0.0726770	+	0.458864i
$423$	−21.6298	+	11.0210i	−1.05168	+	0.535857i
$424$	1.14050	−	3.51008i	0.0553873	−	0.170465i
$425$	8.38648	+	21.7716i	0.406804	+	1.05608i
$426$	−8.41909	+	11.5879i	−0.407906	+	0.561434i
$427$	−6.33958	−	3.23018i	−0.306794	−	0.156319i
$428$	8.90544	−	8.90544i	0.430461	−	0.430461i
$429$	−5.00194	−	21.4549i	−0.241496	−	1.03585i
$430$	−3.27301	+	5.67667i	−0.157839	+	0.273753i
$431$	−6.52048	+	2.11863i	−0.314081	+	0.102051i	−0.461815	−	0.886976i	$-0.652802\pi$
$431$	−6.52048	+	2.11863i	−0.314081	+	0.102051i	0.147735	+	0.989027i	$0.452802\pi$
$432$	2.27222	−	0.359884i	0.109322	−	0.0173149i
$433$	−16.4334	−	2.60280i	−0.789740	−	0.125083i	−0.251481	−	0.967862i	$-0.580918\pi$
$433$	−16.4334	−	2.60280i	−0.789740	−	0.125083i	−0.538259	+	0.842780i	$0.680918\pi$
$434$	−7.33323	−	2.38271i	−0.352006	−	0.114374i
$435$	−0.0210488	+	0.406169i	−0.00100921	+	0.0194743i
$436$	−7.68644	−	10.5795i	−0.368114	−	0.506665i
$437$	−3.65158	−	23.0552i	−0.174679	−	1.10288i
$438$	−7.90953	+	15.5233i	−0.377932	+	0.741733i
$439$	−0.201886			−0.00963548			−0.00481774	−	0.999988i	$-0.501534\pi$
$439$	−0.201886			−0.00963548			−0.00481774	+	0.999988i	$0.501534\pi$
$440$	−7.34682	−	1.01203i	−0.350246	−	0.0482468i
$441$	−17.1846			−0.818313
$442$	−6.31320	+	12.3904i	−0.300288	+	0.589349i
$443$	−1.46049	−	9.22116i	−0.0693899	−	0.438111i	−0.997785	−	0.0665168i	$-0.978811\pi$
$443$	−1.46049	−	9.22116i	−0.0693899	−	0.438111i	0.928395	−	0.371594i	$-0.121189\pi$
$444$	−7.67636	−	10.5656i	−0.364304	−	0.501421i
$445$	−9.95004	+	8.96957i	−0.471677	+	0.425198i
$446$	−17.6521	−	5.73552i	−0.835852	−	0.271585i
$447$	24.1671	+	3.82769i	1.14307	+	0.181044i
$448$	−3.91761	+	0.620489i	−0.185090	+	0.0293153i
$449$	−28.7015	+	9.32569i	−1.35451	+	0.440107i	−0.894206	−	0.447655i	$-0.852259\pi$
$449$	−28.7015	+	9.32569i	−1.35451	+	0.440107i	−0.460303	+	0.887762i	$0.652259\pi$
$450$	9.50692	+	2.53549i	0.448160	+	0.119524i
$451$	0.787538	−	9.23048i	0.0370837	−	0.434647i
$452$	−0.296114	+	0.296114i	−0.0139280	+	0.0139280i
$453$	24.6761	+	12.5731i	1.15939	+	0.590737i
$454$	6.61634	−	9.10662i	0.310520	−	0.427395i
$455$	2.77821	+	26.2854i	0.130244	+	1.23228i
$456$	2.21090	−	6.80444i	0.103535	−	0.318647i
$457$	24.4688	−	12.4675i	1.14460	−	0.583203i	0.224340	−	0.974511i	$-0.427977\pi$
$457$	24.4688	−	12.4675i	1.14460	−	0.583203i	0.920260	+	0.391308i	$0.127977\pi$
$458$	0.675042	−	4.26205i	0.0315426	−	0.199152i
$459$	−8.68461	−	6.30974i	−0.405363	−	0.294513i
$460$	13.6320	−	8.86401i	0.635594	−	0.413287i
$461$		−	14.8765i		−	0.692866i	−0.938075	−	0.346433i	$-0.887393\pi$
$461$		−	14.8765i		−	0.692866i	0.938075	−	0.346433i	$-0.112607\pi$
$462$	−29.2453	+	2.10832i	−1.36062	+	0.0980880i
$463$	19.4801	+	19.4801i	0.905318	+	0.905318i	0.995890	−	0.0905720i	$-0.0288695\pi$
$463$	19.4801	+	19.4801i	0.905318	+	0.905318i	−0.0905720	+	0.995890i	$0.528870\pi$
$464$	0.0252175	+	0.0776115i	0.00117069	+	0.00360302i
$465$	9.04701	+	3.46677i	0.419545	+	0.160768i
$466$	11.8346	−	8.59837i	0.548229	−	0.398312i
$467$	13.8779	+	27.2368i	0.642191	+	1.26037i	0.950984	+	0.309241i	$0.100075\pi$
$467$	13.8779	+	27.2368i	0.642191	+	1.26037i	−0.308793	+	0.951129i	$0.599925\pi$
$468$	2.66242	+	5.22530i	0.123071	+	0.241539i
$469$	−10.6531	+	7.73992i	−0.491914	+	0.357396i
$470$	25.1933	−	11.2344i	1.16208	−	0.518203i
$471$	−3.91653	−	12.0539i	−0.180464	−	0.555412i
$472$	−1.78616	−	1.78616i	−0.0822145	−	0.0822145i
$473$	−2.33096	+	9.43549i	−0.107178	+	0.433844i
$474$		−	27.4548i		−	1.26104i
$475$	−10.7255	+	11.9399i	−0.492122	+	0.547841i
$476$	14.9735	+	10.8789i	0.686308	+	0.498632i
$477$	−1.13615	+	7.17334i	−0.0520205	+	0.328445i
$478$	−6.74076	+	3.43459i	−0.308315	+	0.157094i
$479$	−3.79842	+	11.6903i	−0.173554	+	0.534145i	−0.999564	−	0.0295100i	$-0.990605\pi$
$479$	−3.79842	+	11.6903i	−0.173554	+	0.534145i	0.826010	+	0.563655i	$0.190605\pi$
$480$	4.95629	−	0.523850i	0.226223	−	0.0239104i
$481$	−10.2639	+	14.1270i	−0.467992	+	0.644136i
$482$	−5.62853	−	2.86788i	−0.256372	−	0.130628i
$483$	45.4587	−	45.4587i	2.06844	−	2.06844i
$484$	−10.8863	+	1.57780i	−0.494830	+	0.0717182i
$485$	−6.36670	−	23.7055i	−0.289097	−	1.07641i
$486$	−16.8197	+	5.46505i	−0.762957	+	0.247900i
$487$	−6.26281	+	0.991932i	−0.283795	+	0.0449487i	−0.296709	−	0.954968i	$-0.595889\pi$
$487$	−6.26281	+	0.991932i	−0.283795	+	0.0449487i	0.0129141	+	0.999917i	$0.495889\pi$
$488$	1.77173	+	0.280615i	0.0802025	+	0.0127028i
$489$	25.6917	+	8.34774i	1.16182	+	0.377498i
$490$	19.5007	+	1.01058i	0.880954	+	0.0456535i
$491$	−13.6000	−	18.7188i	−0.613761	−	0.844770i	0.383119	−	0.923699i	$-0.374850\pi$
$491$	−13.6000	−	18.7188i	−0.613761	−	0.844770i	−0.996880	+	0.0789292i	$0.974850\pi$
$492$	0.973911	+	6.14903i	0.0439073	+	0.277220i
$493$	0.172874	−	0.339284i	0.00778585	−	0.0152806i
$494$	−9.56625			−0.430406
$495$	14.5909	−	0.294630i	0.655814	−	0.0132426i
$496$	1.94396			0.0872864
$497$	11.5721	−	22.7114i	0.519078	−	1.01875i
$498$	5.27147	+	33.2828i	0.236220	+	1.49144i
$499$	24.4517	+	33.6549i	1.09461	+	1.50660i	0.842345	+	0.538939i	$0.181175\pi$
$499$	24.4517	+	33.6549i	1.09461	+	1.50660i	0.252263	+	0.967659i	$0.418825\pi$
$500$	−10.6392	−	3.43630i	−0.475798	−	0.153676i
$501$	8.70279	+	2.82771i	0.388812	+	0.126333i
$502$	−20.6353	−	3.26832i	−0.921000	−	0.145872i
$503$	−14.7659	+	2.33868i	−0.658377	+	0.104277i	−0.476678	−	0.879078i	$-0.658159\pi$
$503$	−14.7659	+	2.33868i	−0.658377	+	0.104277i	−0.181698	+	0.983354i	$0.558159\pi$
$504$	7.42332	−	2.41198i	0.330661	−	0.107438i
$505$	14.9025	+	8.59236i	0.663151	+	0.382355i
$506$	15.7837	−	18.2362i	0.701669	−	0.810697i
$507$	−6.49117	+	6.49117i	−0.288283	+	0.288283i
$508$	7.73399	+	3.94067i	0.343140	+	0.174839i
$509$	14.5639	−	20.0455i	0.645534	−	0.888501i	−0.353362	−	0.935487i	$-0.614962\pi$
$509$	14.5639	−	20.0455i	0.645534	−	0.888501i	0.998896	+	0.0469857i	$0.0149615\pi$
$510$	−18.0817	−	14.6248i	−0.800672	−	0.647598i
$511$	9.58085	−	29.4868i	0.423832	−	1.30442i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	1.15522	−	7.29376i	0.0510041	−	0.322027i
$514$	4.97218	+	3.61250i	0.219313	+	0.159340i
$515$	−6.94864	−	10.6863i	−0.306194	−	0.470896i
$516$		−	6.53154i		−	0.287535i
$517$	31.2857	−	26.3668i	1.37594	−	1.15961i
$518$	16.4338	+	16.4338i	0.722062	+	0.722062i
$519$	−8.94207	−	27.5209i	−0.392513	−	1.20803i
$520$	−2.71398	−	6.08614i	−0.119016	−	0.266895i
$521$	−2.66594	+	1.93692i	−0.116797	+	0.0848580i	−0.644650	−	0.764477i	$-0.722997\pi$
$521$	−2.66594	+	1.93692i	−0.116797	+	0.0848580i	0.527853	+	0.849336i	$0.322997\pi$
$522$	−0.0729049	−	0.143084i	−0.00319096	−	0.00626262i
$523$	15.1878	+	29.8077i	0.664116	+	1.30340i	0.939659	+	0.342112i	$0.111142\pi$
$523$	15.1878	+	29.8077i	0.664116	+	1.30340i	−0.275543	+	0.961289i	$0.588858\pi$
$524$	−1.06787	+	0.775854i	−0.0466502	+	0.0338933i
$525$	−43.9666	−	4.56922i	−1.91886	−	0.199417i
$526$	7.52274	+	23.1526i	0.328007	+	1.00950i
$527$	−6.41410	−	6.41410i	−0.279402	−	0.279402i
$528$	6.84805	−	2.78396i	0.298023	−	0.121156i
$529$			29.8802i			1.29914i
$530$	1.71112	−	8.07336i	0.0743265	−	0.350684i
$531$	4.02145	+	2.92175i	0.174516	+	0.126793i
$532$	−1.99176	+	12.5754i	−0.0863535	+	0.545215i
$533$	7.41692	−	3.77911i	0.321262	−	0.163691i
$534$	4.12630	−	12.6994i	0.178563	−	0.549559i
$535$	17.7098	−	21.8959i	0.765663	−	0.946643i
$536$	1.95135	−	2.68580i	0.0842854	−	0.116009i
$537$	−16.1610	−	8.23444i	−0.697399	−	0.355342i
$538$	19.0194	−	19.0194i	0.819986	−	0.819986i
$539$	28.2067	−	6.57603i	1.21495	−	0.283250i
$540$	4.96810	−	1.33431i	0.213793	−	0.0574194i
$541$	−1.96815	+	0.639490i	−0.0846173	+	0.0274938i	−0.351020	−	0.936368i	$-0.614165\pi$
$541$	−1.96815	+	0.639490i	−0.0846173	+	0.0274938i	0.266402	+	0.963862i	$0.414165\pi$
$542$	−22.4482	+	3.55545i	−0.964235	+	0.152720i
$543$	−37.2674	−	5.90257i	−1.59930	−	0.253303i
$544$	−4.43782	−	1.44193i	−0.190270	−	0.0618224i
$545$	−19.5787	−	21.7189i	−0.838659	−	0.930334i
$546$	−15.4862	−	21.3149i	−0.662747	−	0.912193i
$547$	2.25132	+	14.2143i	0.0962595	+	0.607758i	0.987909	+	0.155033i	$0.0495483\pi$
$547$	2.25132	+	14.2143i	0.0962595	+	0.607758i	−0.891650	+	0.452726i	$0.850452\pi$
$548$	−8.13766	+	15.9711i	−0.347624	+	0.682250i
$549$	−3.52995			−0.150654
$550$	−16.5749	−	0.523718i	−0.706754	−	0.0223314i
$551$	0.261952			0.0111595
$552$	−7.35830	+	14.4415i	−0.313190	+	0.614670i
$553$	7.64308	+	48.2565i	0.325017	+	2.05207i
$554$	−12.2247	−	16.8259i	−0.519378	−	0.714862i
$555$	−19.5530	−	21.6904i	−0.829979	−	0.920705i
$556$	2.35711	+	0.765872i	0.0999637	+	0.0324802i
$557$	−17.8430	−	2.82606i	−0.756033	−	0.119744i	−0.233493	−	0.972359i	$-0.575016\pi$
$557$	−17.8430	−	2.82606i	−0.756033	−	0.119744i	−0.522540	+	0.852615i	$0.675016\pi$
$558$	−3.77831	+	0.598426i	−0.159949	+	0.0253334i
$559$	−8.30573	+	2.69870i	−0.351295	+	0.114143i
$560$	−8.56569	+	2.30053i	−0.361967	+	0.0972150i
$561$	−31.7808	−	13.4095i	−1.34179	−	0.566148i
$562$	4.54280	−	4.54280i	0.191626	−	0.191626i
$563$	−36.8694	−	18.7859i	−1.55386	−	0.791731i	−0.554674	−	0.832068i	$-0.687157\pi$
$563$	−36.8694	−	18.7859i	−1.55386	−	0.791731i	−0.999186	+	0.0403368i	$0.987157\pi$
$564$	−16.1616	+	22.2445i	−0.680526	+	0.936664i
$565$	−0.588868	+	0.728059i	−0.0247738	+	0.0306297i
$566$	−0.299612	+	0.922111i	−0.0125936	+	0.0387592i
$567$	38.9854	−	19.8641i	1.63723	−	0.834212i
$568$	−1.00530	+	6.34720i	−0.0421814	+	0.266323i
$569$	16.9040	+	12.2815i	0.708653	+	0.514867i	0.882739	−	0.469864i	$-0.155697\pi$
$569$	16.9040	+	12.2815i	0.708653	+	0.514867i	−0.174086	+	0.984731i	$0.555697\pi$
$570$	3.31708	−	15.6505i	0.138937	−	0.655529i
$571$			0.865366i			0.0362145i	0.999836	+	0.0181072i	$0.00576403\pi$
$571$			0.865366i			0.0362145i	−0.999836	+	0.0181072i	$0.994236\pi$
$572$	−6.36965	−	7.55794i	−0.266328	−	0.316013i
$573$	16.1065	+	16.1065i	0.672858	+	0.672858i
$574$	−3.42363	−	10.5369i	−0.142900	−	0.439800i
$575$	28.2298	−	22.9147i	1.17727	−	0.955607i
$576$	−1.59202	+	1.15667i	−0.0663341	+	0.0481945i
$577$	−5.60142	−	10.9934i	−0.233190	−	0.457661i	0.744526	−	0.667594i	$-0.232676\pi$
$577$	−5.60142	−	10.9934i	−0.233190	−	0.457661i	−0.977716	+	0.209932i	$0.932676\pi$
$578$	2.16707	+	4.25312i	0.0901384	+	0.176907i
$579$	−39.7690	+	28.8939i	−1.65274	+	1.20079i
$580$	0.0743167	+	0.166656i	0.00308583	+	0.00692003i
$581$	−18.5310	−	57.0326i	−0.768797	−	2.36611i
$582$	17.3005	+	17.3005i	0.717127	+	0.717127i
$583$	−0.880162	−	12.2090i	−0.0364526	−	0.505647i
$584$			7.81664i			0.323455i
$585$	7.14848	+	10.9937i	0.295553	+	0.454531i
$586$	−3.50621	−	2.54741i	−0.144840	−	0.105233i
$587$	−1.30289	+	8.22614i	−0.0537761	+	0.339529i	0.946101	+	0.323871i	$0.104984\pi$
$587$	−1.30289	+	8.22614i	−0.0537761	+	0.339529i	−0.999877	+	0.0156582i	$0.995016\pi$
$588$	−17.3426	+	8.83648i	−0.715195	+	0.364410i
$589$	1.92829	−	5.93466i	0.0794537	−	0.244533i
$590$	−4.39164	−	3.55204i	−0.180801	−	0.146235i
$591$	20.2954	−	27.9342i	0.834841	−	1.14906i
$592$	−5.22076	−	2.66011i	−0.214572	−	0.109330i
$593$	−21.2622	+	21.2622i	−0.873133	+	0.873133i	−0.992813	−	0.119680i	$-0.961813\pi$
$593$	−21.2622	+	21.2622i	−0.873133	+	0.873133i	0.119680	+	0.992813i	$0.461813\pi$
$594$	6.53173	−	3.94383i	0.268000	−	0.161817i
$595$	35.8531	+	20.6719i	1.46983	+	0.847466i
$596$	10.4406	−	3.39237i	0.427665	−	0.138957i
$597$	17.1214	−	2.71177i	0.700733	−	0.110985i
$598$	21.4046	+	3.39015i	0.875297	+	0.138634i
$599$	−31.8537	−	10.3499i	−1.30151	−	0.422885i	−0.425401	−	0.905005i	$-0.639867\pi$
$599$	−31.8537	−	10.3499i	−1.30151	−	0.422885i	−0.876105	+	0.482120i	$0.839867\pi$
$600$	10.8981	−	2.32975i	0.444913	−	0.0951117i
$601$	−12.4882	−	17.1885i	−0.509403	−	0.701133i	0.474415	−	0.880301i	$-0.342659\pi$
$601$	−12.4882	−	17.1885i	−0.509403	−	0.701133i	−0.983819	+	0.179168i	$0.942659\pi$
$602$	1.81830	+	11.4803i	0.0741084	+	0.467902i
$603$	−2.96588	+	5.82086i	−0.120780	+	0.237044i
$604$	12.4255			0.505585
$605$	−23.8367	+	6.06712i	−0.969101	+	0.246664i
$606$	−17.1467			−0.696537
$607$	−15.2661	+	29.9613i	−0.619630	+	1.21609i	0.341470	+	0.939893i	$0.389075\pi$
$607$	−15.2661	+	29.9613i	−0.619630	+	1.21609i	−0.961100	+	0.276200i	$0.910925\pi$
$608$	−0.502151	−	3.17046i	−0.0203649	−	0.128579i
$609$	0.424057	+	0.583664i	0.0171836	+	0.0236513i
$610$	4.00572	+	0.207588i	0.162187	+	0.00840498i
$611$	34.9645	+	11.3607i	1.41451	+	0.459604i
$612$	9.06929	+	1.43643i	0.366604	+	0.0580644i
$613$	17.0295	−	2.69721i	0.687816	−	0.108939i	0.197263	−	0.980351i	$-0.436795\pi$
$613$	17.0295	−	2.69721i	0.687816	−	0.108939i	0.490553	+	0.871411i	$0.336795\pi$
$614$	18.1616	−	5.90107i	0.732943	−	0.238148i
$615$	3.61088	+	13.4446i	0.145605	+	0.542139i
$616$	−11.2616	+	6.79970i	−0.453743	+	0.273968i
$617$	−15.8379	+	15.8379i	−0.637611	+	0.637611i	−0.949965	−	0.312355i	$-0.898882\pi$
$617$	−15.8379	+	15.8379i	−0.637611	+	0.637611i	0.312355	+	0.949965i	$0.398882\pi$
$618$	11.3209	+	5.76829i	0.455394	+	0.232035i
$619$	7.27397	−	10.0118i	0.292366	−	0.402407i	−0.637415	−	0.770521i	$-0.719996\pi$
$619$	7.27397	−	10.0118i	0.292366	−	0.402407i	0.929781	+	0.368114i	$0.119996\pi$
$620$	4.32275	−	0.456889i	0.173606	−	0.0183491i
$621$	−5.16962	+	15.9105i	−0.207450	+	0.638465i
$622$	20.6861	−	10.5401i	0.829435	−	0.422618i
$623$	−3.71731	+	23.4702i	−0.148931	+	0.940312i
$624$	5.37380	+	3.90429i	0.215124	+	0.156297i
$625$	−24.4658	−	5.14072i	−0.978630	−	0.205629i
$626$			33.8065i			1.35118i
$627$	−1.70623	−	23.6677i	−0.0681402	−	0.945198i
$628$	−4.02088	−	4.02088i	−0.160450	−	0.160450i
$629$	8.44886	+	26.0029i	0.336878	+	1.03680i
$630$	15.9402	−	7.10819i	0.635074	−	0.283197i
$631$	−32.0471	+	23.2836i	−1.27577	+	0.926905i	−0.999417	−	0.0341502i	$-0.989128\pi$
$631$	−32.0471	+	23.2836i	−1.27577	+	0.926905i	−0.276358	+	0.961055i	$0.589128\pi$
$632$	−5.59218	−	10.9753i	−0.222445	−	0.436573i
$633$	−9.65720	−	18.9533i	−0.383839	−	0.753327i
$634$	−9.60345	+	6.97731i	−0.381402	+	0.277104i
$635$	18.1241	+	6.94507i	0.719233	+	0.275607i
$636$	2.54201	+	7.82350i	0.100797	+	0.310222i
$637$	18.4023	+	18.4023i	0.729127	+	0.729127i
$638$	0.174420	+	0.206959i	0.00690534	+	0.00819357i
$639$		−	12.6460i		−	0.500268i
$640$	1.87461	−	1.21894i	0.0741006	−	0.0481830i
$641$	26.3762	+	19.1634i	1.04180	+	0.756910i	0.970636	−	0.240555i	$-0.0773294\pi$
$641$	26.3762	+	19.1634i	1.04180	+	0.756910i	0.0711615	+	0.997465i	$0.477329\pi$
$642$	−4.39124	+	27.7252i	−0.173308	+	1.09423i
$643$	−11.4937	+	5.85631i	−0.453266	+	0.230950i	−0.665692	−	0.746227i	$-0.731863\pi$
$643$	−11.4937	+	5.85631i	−0.453266	+	0.230950i	0.212426	+	0.977177i	$0.431863\pi$
$644$	8.91314	−	27.4318i	0.351227	−	1.08097i
$645$	−1.53511	−	14.5241i	−0.0604448	−	0.571885i
$646$	−8.80407	+	12.1178i	−0.346392	+	0.476767i
$647$	0.708311	+	0.360903i	0.0278466	+	0.0141885i	0.467858	−	0.883803i	$-0.345026\pi$
$647$	0.708311	+	0.360903i	0.0278466	+	0.0141885i	−0.440012	+	0.897992i	$0.645026\pi$
$648$	−7.80018	+	7.80018i	−0.306420	+	0.306420i
$649$	−7.71885	−	3.25686i	−0.302991	−	0.127843i
$650$	−7.46545	−	12.8958i	−0.292819	−	0.505814i
$651$	16.3448	−	5.31074i	0.640603	−	0.208144i
$652$	11.9708	−	1.89599i	0.468812	−	0.0742525i
$653$	3.86249	+	0.611758i	0.151151	+	0.0239400i	0.231551	−	0.972823i	$-0.425620\pi$
$653$	3.86249	+	0.611758i	0.151151	+	0.0239400i	−0.0804004	+	0.996763i	$0.525620\pi$
$654$	27.7202	+	9.00685i	1.08395	+	0.352196i
$655$	−2.19226	+	1.97623i	−0.0856586	+	0.0772179i
$656$	1.64181	+	2.25975i	0.0641017	+	0.0882285i
$657$	−2.40626	−	15.1925i	−0.0938772	−	0.592717i
$658$	22.2142	−	43.5978i	0.865999	−	1.69962i
$659$	2.33997			0.0911522			0.0455761	−	0.998961i	$-0.485488\pi$
$659$	2.33997			0.0911522			0.0455761	+	0.998961i	$0.485488\pi$
$660$	14.5736	−	7.80014i	0.567276	−	0.303620i
$661$	−28.1337			−1.09428			−0.547138	−	0.837043i	$-0.684283\pi$
$661$	−28.1337			−1.09428			−0.547138	+	0.837043i	$0.684283\pi$
$662$	−5.11648	+	10.0417i	−0.198858	+	0.390280i
$663$	−4.84863	−	30.6130i	−0.188305	−	1.18891i
$664$	8.88657	+	12.2313i	0.344866	+	0.474667i
$665$	−1.47342	+	28.4319i	−0.0571369	+	1.10254i
$666$	10.9660	+	3.56308i	0.424925	+	0.138067i
$667$	−0.586120	−	0.0928322i	−0.0226946	−	0.00359448i
$668$	4.05497	−	0.642245i	0.156892	−	0.0248492i
$669$	39.3442	−	12.7837i	1.52114	−	0.494247i
$670$	3.70793	−	6.43099i	0.143250	−	0.248451i
$671$	5.79403	−	1.35081i	0.223676	−	0.0521473i
$672$	6.25130	−	6.25130i	0.241149	−	0.241149i
$673$	−18.4073	−	9.37899i	−0.709550	−	0.361534i	0.0616753	−	0.998096i	$-0.480356\pi$
$673$	−18.4073	−	9.37899i	−0.709550	−	0.361534i	−0.771225	+	0.636563i	$0.780356\pi$
$674$	9.86495	−	13.5779i	0.379984	−	0.523003i
$675$	10.7339	−	4.13472i	0.413147	−	0.159146i
$676$	−1.27273	+	3.91706i	−0.0489512	+	0.150656i
$677$	2.56283	−	1.30583i	0.0984976	−	0.0501870i	−0.404048	−	0.914738i	$-0.632397\pi$
$677$	2.56283	−	1.30583i	0.0984976	−	0.0501870i	0.502545	+	0.864551i	$0.332397\pi$
$678$	0.146013	−	0.921887i	0.00560758	−	0.0354049i
$679$	−35.2247	−	25.5923i	−1.35180	−	0.982141i
$680$	−10.2072	−	2.16338i	−0.391428	−	0.0829619i
$681$			25.0890i			0.961413i
$682$	5.97270	−	2.42810i	0.228706	−	0.0929768i
$683$	4.54465	+	4.54465i	0.173896	+	0.173896i	0.788689	−	0.614793i	$-0.210760\pi$
$683$	4.54465	+	4.54465i	0.173896	+	0.173896i	−0.614793	+	0.788689i	$0.710760\pi$
$684$	1.95198	+	6.00757i	0.0746357	+	0.229705i
$685$	−14.3419	+	37.4272i	−0.547976	+	1.43002i
$686$	5.56010	−	4.03965i	0.212285	−	0.154234i
$687$	4.36646	+	8.56965i	0.166591	+	0.326953i
$688$	−1.33039	−	2.61104i	−0.0507206	−	0.0995448i
$689$	8.89833	−	6.46501i	0.338999	−	0.246297i
$690$	−12.9683	+	33.8427i	−0.493696	+	1.28837i
$691$	6.11570	+	18.8222i	0.232652	+	0.716030i	0.997424	+	0.0717289i	$0.0228516\pi$
$691$	6.11570	+	18.8222i	0.232652	+	0.716030i	−0.764772	+	0.644301i	$0.777148\pi$
$692$	−9.18030	−	9.18030i	−0.348983	−	0.348983i
$693$	19.7950	−	16.6828i	0.751951	−	0.633726i
$694$		−	6.85269i		−	0.260124i
$695$	5.42147	+	1.14906i	0.205648	+	0.0435865i
$696$	−0.147150	−	0.106911i	−0.00557772	−	0.00405245i
$697$	2.03891	−	12.8732i	0.0772293	−	0.487607i
$698$	−9.99542	+	5.09292i	−0.378332	+	0.192770i
$699$	−10.0754	+	31.0090i	−0.381088	+	1.17287i
$700$	−18.5067	+	7.12883i	−0.699487	+	0.269445i
$701$	−3.26547	+	4.49454i	−0.123335	+	0.169756i	−0.866220	−	0.499663i	$-0.833457\pi$
$701$	−3.26547	+	4.49454i	−0.123335	+	0.169756i	0.742885	+	0.669420i	$0.233457\pi$
$702$	6.10872	+	3.11255i	0.230559	+	0.117476i
$703$	−13.2996	+	13.2996i	−0.501605	+	0.501605i
$704$	2.17051	−	2.50777i	0.0818041	−	0.0945151i
$705$	−30.7101	+	53.2632i	−1.15661	+	2.00601i
$706$	21.1964	−	6.88712i	0.797737	−	0.259200i
$707$	30.1382	−	4.77343i	1.13347	−	0.179523i
$708$	5.56081	+	0.880746i	0.208988	+	0.0331005i
$709$	−31.7561	−	10.3182i	−1.19262	−	0.387507i	−0.355582	−	0.934645i	$-0.615717\pi$
$709$	−31.7561	−	10.3182i	−1.19262	−	0.387507i	−0.837042	+	0.547138i	$0.815717\pi$
$710$	−0.743680	+	14.3504i	−0.0279098	+	0.538562i
$711$	14.2477	+	19.6102i	0.534329	+	0.735440i
$712$	−0.937189	−	5.91718i	−0.0351226	−	0.221756i
$713$	−6.41772	+	12.5955i	−0.240346	+	0.471705i
$714$	−41.2523			−1.54383
$715$	−15.9404	−	15.3094i	−0.596138	−	0.572539i
$716$	−8.13773			−0.304121
$717$	7.65524	−	15.0242i	0.285890	−	0.561091i
$718$	2.46343	+	15.5535i	0.0919344	+	0.580451i
$719$	11.8552	+	16.3173i	0.442125	+	0.608532i	0.970683	−	0.240365i	$-0.0772671\pi$
$719$	11.8552	+	16.3173i	0.442125	+	0.608532i	−0.528558	+	0.848897i	$0.677267\pi$
$720$	−3.26829	+	2.94624i	−0.121802	+	0.109800i
$721$	−21.5043	−	6.98716i	−0.800860	−	0.260215i
$722$	8.58898	+	1.36036i	0.319649	+	0.0506274i
$723$	13.9065	−	2.20257i	0.517188	−	0.0819146i
$724$	−16.1002	+	5.23127i	−0.598359	+	0.194419i
$725$	0.204426	+	0.353124i	0.00759219	+	0.0131147i
$726$	17.5629	−	17.1071i	0.651821	−	0.634904i
$727$	3.28024	−	3.28024i	0.121657	−	0.121657i	−0.643657	−	0.765314i	$-0.722584\pi$
$727$	3.28024	−	3.28024i	0.121657	−	0.121657i	0.765314	+	0.643657i	$0.222584\pi$
$728$	−10.5323	−	5.36646i	−0.390352	−	0.198894i
$729$	3.71759	−	5.11682i	0.137688	−	0.189512i
$730$	1.83714	+	17.3817i	0.0679957	+	0.643326i
$731$	−4.22549	+	13.0047i	−0.156285	+	0.480997i
$732$	−3.56240	+	1.81513i	−0.131670	+	0.0670892i
$733$	5.38308	−	33.9874i	0.198828	−	1.25535i	−0.663180	−	0.748460i	$-0.730794\pi$
$733$	5.38308	−	33.9874i	0.198828	−	1.25535i	0.862009	−	0.506894i	$-0.169206\pi$
$734$	22.5182	+	16.3604i	0.831162	+	0.603875i
$735$	−36.4875	+	23.7255i	−1.34586	+	0.875130i
$736$			7.27188i			0.268045i
$737$	2.64070	−	10.6893i	0.0972716	−	0.393745i
$738$	−3.88668	−	3.88668i	−0.143071	−	0.143071i
$739$	0.0954132	+	0.293652i	0.00350983	+	0.0108022i	0.952796	−	0.303611i	$-0.0981923\pi$
$739$	0.0954132	+	0.293652i	0.00350983	+	0.0108022i	−0.949286	+	0.314413i	$0.898192\pi$
$740$	−12.2345	−	4.68820i	−0.449749	−	0.172342i
$741$	17.2498	−	12.5327i	0.633686	−	0.460400i
$742$	−6.64599	−	13.0435i	−0.243982	−	0.478841i
$743$	−0.565075	−	1.10902i	−0.0207306	−	0.0406860i	0.880409	−	0.474215i	$-0.157268\pi$
$743$	−0.565075	−	1.10902i	−0.0207306	−	0.0406860i	−0.901140	+	0.433529i	$0.857268\pi$
$744$	−3.50533	+	2.54677i	−0.128512	+	0.0933692i
$745$	22.4194	−	9.99742i	0.821382	−	0.366277i
$746$	−8.41714	−	25.9053i	−0.308173	−	0.948460i
$747$	−21.0374	−	21.0374i	−0.769716	−	0.769716i
$748$	−15.4360	+	1.11279i	−0.564395	+	0.0406878i
$749$		−	49.9542i		−	1.82529i
$750$	23.6863	−	7.74200i	0.864902	−	0.282698i
$751$	−19.6696	−	14.2908i	−0.717754	−	0.521479i	0.167912	−	0.985802i	$-0.446298\pi$
$751$	−19.6696	−	14.2908i	−0.717754	−	0.521479i	−0.885666	+	0.464323i	$0.846298\pi$
$752$	−1.92981	+	12.1843i	−0.0703729	+	0.444317i
$753$	41.4912	−	21.1408i	1.51202	−	0.770415i
$754$	−0.0751522	+	0.231295i	−0.00273688	+	0.00842326i
$755$	27.6303	−	2.92035i	1.00557	−	0.106283i
$756$	5.36352	−	7.38225i	0.195069	−	0.268490i
$757$	25.1939	+	12.8369i	0.915688	+	0.466566i	0.847313	−	0.531093i	$-0.178219\pi$
$757$	25.1939	+	12.8369i	0.915688	+	0.466566i	0.0683747	+	0.997660i	$0.478219\pi$
$758$	−15.3506	+	15.3506i	−0.557558	+	0.557558i
$759$	−4.56982	+	53.5614i	−0.165874	+	1.94416i
$760$	−1.86178	−	6.93207i	−0.0675337	−	0.251453i
$761$	−32.7506	+	10.6413i	−1.18721	+	0.385747i	−0.835040	−	0.550190i	$-0.814555\pi$
$761$	−32.7506	+	10.6413i	−1.18721	+	0.385747i	−0.352168	+	0.935937i	$0.614555\pi$
$762$	−19.1085	+	3.02649i	−0.692228	+	0.109638i
$763$	−51.2305	−	8.11411i	−1.85467	−	0.293750i
$764$	9.71936	+	3.15801i	0.351634	+	0.114253i
$765$	20.5048	+	1.06262i	0.741354	+	0.0384191i
$766$	19.0560	+	26.2284i	0.688522	+	0.947670i
$767$	−1.17762	−	7.43522i	−0.0425215	−	0.268470i
$768$	−1.01188	+	1.98593i	−0.0365132	+	0.0716612i
$769$	22.6026			0.815072			0.407536	−	0.913189i	$-0.366388\pi$
$769$	22.6026			0.815072			0.407536	+	0.913189i	$0.366388\pi$
$770$	−23.4441	+	17.7672i	−0.844866	+	0.640285i
$771$	−13.6985			−0.493339
$772$	−10.0127	+	19.6510i	−0.360364	+	0.707254i
$773$	−6.87959	−	43.4361i	−0.247442	−	1.56229i	−0.728158	−	0.685410i	$-0.759623\pi$
$773$	−6.87959	−	43.4361i	−0.247442	−	1.56229i	0.480716	−	0.876876i	$-0.340377\pi$
$774$	3.38954	+	4.66530i	0.121835	+	0.167691i
$775$	9.50504	−	2.03195i	0.341431	−	0.0729898i
$776$	10.4399	+	3.39212i	0.374769	+	0.121770i
$777$	−51.1632	−	8.10346i	−1.83547	−	0.290710i
$778$	−10.7099	+	1.69628i	−0.383968	+	0.0608145i
$779$	8.52730	−	2.77069i	0.305522	−	0.0992701i
$780$	12.8672	+	7.41890i	0.460721	+	0.265639i
$781$	4.83924	+	20.7570i	0.173162	+	0.742746i
$782$	23.9936	−	23.9936i	0.858008	−	0.858008i
$783$	−0.167275	−	0.0852307i	−0.00597791	−	0.00304590i
$784$	−5.13295	+	7.06490i	−0.183320	+	0.252318i
$785$	−9.88617	−	7.99612i	−0.352853	−	0.285394i
$786$	0.909134	−	2.79803i	0.0324277	−	0.0998023i
$787$	−17.0929	+	8.70928i	−0.609297	+	0.310452i	−0.731277	−	0.682080i	$-0.761075\pi$
$787$	−17.0929	+	8.70928i	−0.609297	+	0.310452i	0.121980	+	0.992533i	$0.461075\pi$
$788$	2.42341	−	15.3008i	0.0863305	−	0.545069i
$789$	−43.8970	−	31.8931i	−1.56278	−	1.13542i
$790$	−15.0147	−	23.0912i	−0.534200	−	0.821547i
$791$			1.66102i			0.0590592i
$792$	−3.44664	+	5.54230i	−0.122471	+	0.196937i
$793$	3.78009	+	3.78009i	0.134235	+	0.134235i
$794$	−0.481974	−	1.48336i	−0.0171046	−	0.0526425i
$795$	7.49138	+	16.7995i	0.265692	+	0.595818i
$796$	6.29207	−	4.57146i	0.223017	−	0.162031i
$797$	−1.75108	−	3.43669i	−0.0620265	−	0.121734i	0.857912	−	0.513797i	$-0.171762\pi$
$797$	−1.75108	−	3.43669i	−0.0620265	−	0.121734i	−0.919938	+	0.392063i	$0.871762\pi$
$798$	−12.8835	−	25.2853i	−0.456071	−	0.895090i
$799$	46.5696	−	33.8348i	1.64751	−	1.19699i
$800$	3.88206	−	3.15113i	0.137251	−	0.111409i
$801$	3.64307	+	11.2122i	0.128722	+	0.396164i
$802$	−14.2947	−	14.2947i	−0.504763	−	0.504763i
$803$	9.76335	+	24.0161i	0.344541	+	0.847511i
$804$			7.39946i			0.260959i
$805$	13.3727	−	63.0945i	0.471325	−	2.22379i
$806$	4.68689	+	3.40522i	0.165089	+	0.119944i
$807$	−9.37840	+	59.2129i	−0.330135	+	2.08439i
$808$	−6.85452	+	3.49255i	−0.241141	+	0.122868i
$809$	−9.68199	+	29.7981i	−0.340400	+	1.04764i	0.623600	+	0.781744i	$0.285670\pi$
$809$	−9.68199	+	29.7981i	−0.340400	+	1.04764i	−0.964000	+	0.265901i	$0.914330\pi$
$810$	−15.5118	+	19.1784i	−0.545031	+	0.673860i
$811$	29.8031	−	41.0204i	1.04653	−	1.44042i	0.154746	−	0.987954i	$-0.450544\pi$
$811$	29.8031	−	41.0204i	1.04653	−	1.44042i	0.891781	−	0.452467i	$-0.149456\pi$
$812$	0.288405	+	0.146949i	0.0101210	+	0.00515692i
$813$	35.8205	−	35.8205i	1.25628	−	1.25628i
$814$	−19.3631	−	1.65204i	−0.678675	−	0.0579041i
$815$	26.1736	−	7.02956i	0.916821	−	0.246235i
$816$	9.89130	−	3.21388i	0.346265	−	0.112508i
$817$	−9.29081	+	1.47152i	−0.325044	+	0.0514820i
$818$	−19.8310	−	3.14092i	−0.693375	−	0.109820i
$819$	22.1227	+	7.18810i	0.773030	+	0.251173i
$820$	4.18196	+	4.63910i	0.146040	+	0.162004i
$821$	−3.78341	−	5.20742i	−0.132042	−	0.181740i	0.737877	−	0.674936i	$-0.235829\pi$
$821$	−3.78341	−	5.20742i	−0.132042	−	0.181740i	−0.869918	+	0.493196i	$0.835829\pi$
$822$	−6.24985	−	39.4600i	−0.217988	−	1.37632i
$823$	−5.20789	+	10.2211i	−0.181536	+	0.356284i	−0.963784	−	0.266682i	$-0.914073\pi$
$823$	−5.20789	+	10.2211i	−0.181536	+	0.356284i	0.782249	+	0.622966i	$0.214073\pi$
$824$	5.70055			0.198588
$825$	30.5737	−	20.7703i	1.06444	−	0.723128i
$826$	−10.0193			−0.348615
$827$	8.69429	−	17.0635i	0.302330	−	0.593356i	−0.688999	−	0.724763i	$-0.741949\pi$
$827$	8.69429	−	17.0635i	0.302330	−	0.593356i	0.991329	+	0.131407i	$0.0419494\pi$
$828$	−2.23856	−	14.1337i	−0.0777955	−	0.491181i
$829$	−1.12936	−	1.55443i	−0.0392242	−	0.0539875i	0.788954	−	0.614452i	$-0.210623\pi$
$829$	−1.12936	−	1.55443i	−0.0392242	−	0.0539875i	−0.828179	+	0.560464i	$0.810623\pi$
$830$	22.6356	+	25.1099i	0.785694	+	0.871579i
$831$	44.0869	+	14.3247i	1.52936	+	0.496919i
$832$	2.94347	+	0.466200i	0.102046	+	0.0161626i
$833$	40.2468	−	6.37447i	1.39447	−	0.220862i
$834$	−5.25368	+	1.70703i	−0.181920	+	0.0591094i
$835$	8.86603	−	2.38119i	0.306821	−	0.0824044i
$836$	−5.50288	−	9.11382i	−0.190321	−	0.315208i
$837$	−3.16229	+	3.16229i	−0.109305	+	0.109305i
$838$	−0.0808914	−	0.0412162i	−0.00279435	−	0.00142379i
$839$	1.68441	−	2.31839i	0.0581522	−	0.0800396i	−0.778950	−	0.627085i	$-0.784248\pi$
$839$	1.68441	−	2.31839i	0.0581522	−	0.0800396i	0.837103	+	0.547046i	$0.184248\pi$
$840$	12.4317	−	15.3702i	0.428933	−	0.530321i
$841$	−8.95943	+	27.5743i	−0.308946	+	0.950838i
$842$	−28.1482	+	14.3422i	−0.970051	+	0.494266i
$843$	−2.24004	+	14.1430i	−0.0771509	+	0.487112i
$844$	−7.72108	−	5.60970i	−0.265771	−	0.193094i
$845$	−1.90952	+	9.00943i	−0.0656895	+	0.309934i
$846$		−	24.2757i		−	0.834617i
$847$	−26.1074	+	34.9580i	−0.897062	+	1.20117i
$848$	2.60973	+	2.60973i	0.0896186	+	0.0896186i
$849$	−0.667795	−	2.05526i	−0.0229187	−	0.0705364i
$850$	−23.2060	−	2.41168i	−0.795959	−	0.0827199i
$851$	34.4712	−	25.0448i	1.18166	−	0.858526i
$852$	−6.50269	−	12.7622i	−0.222778	−	0.437227i
$853$	−8.62287	−	16.9233i	−0.295241	−	0.579444i	0.694967	−	0.719042i	$-0.255419\pi$
$853$	−8.62287	−	16.9233i	−0.295241	−	0.579444i	−0.990208	+	0.139598i	$0.955419\pi$
$854$	5.75621	−	4.18213i	0.196974	−	0.143110i
$855$	5.75253	+	12.9001i	0.196733	+	0.441176i
$856$	3.89182	+	11.9778i	0.133020	+	0.409393i
$857$	−9.24508	−	9.24508i	−0.315806	−	0.315806i	0.531348	−	0.847154i	$-0.321686\pi$
$857$	−9.24508	−	9.24508i	−0.315806	−	0.315806i	−0.847154	+	0.531348i	$0.821686\pi$
$858$	21.3873	+	5.28357i	0.730151	+	0.180378i
$859$		−	0.806684i		−	0.0275237i	−0.999905	−	0.0137619i	$-0.995619\pi$
$859$		−	0.806684i		−	0.0275237i	0.999905	−	0.0137619i	$-0.00438067\pi$
$860$	−3.57203	−	5.49343i	−0.121805	−	0.187324i
$861$	19.9777	+	14.5147i	0.680839	+	0.494659i
$862$	1.07252	−	6.77163i	0.0365302	−	0.230643i
$863$	−9.72398	+	4.95462i	−0.331008	+	0.168657i	−0.611594	−	0.791172i	$-0.709471\pi$
$863$	−9.72398	+	4.95462i	−0.331008	+	0.168657i	0.280586	+	0.959829i	$0.409471\pi$
$864$	−0.710906	+	2.18794i	−0.0241855	+	0.0744353i
$865$	−22.5717	−	18.2564i	−0.767461	−	0.620737i
$866$	9.77973	−	13.4607i	0.332329	−	0.457412i
$867$	−9.47964	−	4.83012i	−0.321945	−	0.164039i
$868$	5.45223	−	5.45223i	0.185061	−	0.185061i
$869$	−30.8903	−	26.7359i	−1.04788	−	0.906954i
$870$	−0.352343	−	0.203151i	−0.0119455	−	0.00688747i
$871$	9.40940	−	3.05730i	0.318825	−	0.103593i
$872$	12.9160	−	2.04569i	0.437390	−	0.0692757i
$873$	−21.3353	−	3.37918i	−0.722091	−	0.114368i
$874$	22.2001	+	7.21325i	0.750930	+	0.243992i
$875$	−39.4775	+	20.2019i	−1.33458	+	0.682948i
$876$	−10.2405	−	14.0949i	−0.345995	−	0.476222i
$877$	5.12456	+	32.3552i	0.173044	+	1.09256i	0.909388	+	0.415949i	$0.136551\pi$
$877$	5.12456	+	32.3552i	0.173044	+	1.09256i	−0.736344	+	0.676608i	$0.763449\pi$
$878$	0.0916542	−	0.179882i	0.00309318	−	0.00607071i
$879$	9.65972			0.325814
$880$	4.23712	−	6.08661i	0.142833	−	0.205180i
$881$	54.9218			1.85036			0.925181	−	0.379526i	$-0.123913\pi$
$881$	54.9218			1.85036			0.925181	+	0.379526i	$0.123913\pi$
$882$	7.80164	−	15.3116i	0.262695	−	0.515567i
$883$	−2.20791	−	13.9402i	−0.0743021	−	0.469125i	−0.996582	−	0.0826036i	$-0.973676\pi$
$883$	−2.20791	−	13.9402i	−0.0743021	−	0.469125i	0.922280	−	0.386522i	$-0.126324\pi$
$884$	−8.17375	−	11.2502i	−0.274913	−	0.378385i
$885$	12.5725	+	0.651542i	0.422619	+	0.0219013i
$886$	8.87916	+	2.88501i	0.298301	+	0.0969240i
$887$	−32.2431	−	5.10680i	−1.08262	−	0.171470i	−0.410460	−	0.911878i	$-0.634632\pi$
$887$	−32.2431	−	5.10680i	−1.08262	−	0.171470i	−0.672157	+	0.740409i	$0.734632\pi$
$888$	12.8990	−	2.04300i	0.432863	−	0.0685587i
$889$	32.7439	−	10.6391i	1.09820	−	0.356826i
$890$	−3.47472	−	12.9377i	−0.116473	−	0.433671i
$891$	−14.2228	+	33.7084i	−0.476481	+	1.12927i
$892$	13.1243	−	13.1243i	0.439434	−	0.439434i
$893$	35.2829	+	17.9776i	1.18070	+	0.601596i
$894$	−14.3821	+	19.7953i	−0.481011	+	0.662054i
$895$	−18.0957	+	1.91261i	−0.604874	+	0.0639315i
$896$	1.22570	−	3.77231i	0.0409477	−	0.126024i
$897$	−43.0379	+	21.9289i	−1.43699	+	0.732185i
$898$	4.72097	−	29.8070i	0.157541	−	0.994673i
$899$	−0.128341	−	0.0932451i	−0.00428041	−	0.00310990i
$900$	−6.57519	+	7.31964i	−0.219173	+	0.243988i
$901$		−	17.2216i		−	0.573735i
$902$	7.86689	+	4.89225i	0.261939	+	0.162894i
$903$	−18.3190	−	18.3190i	−0.609619	−	0.609619i
$904$	−0.129407	−	0.398272i	−0.00430400	−	0.0132463i
$905$	−34.5722	+	15.4167i	−1.14922	+	0.512469i
$906$	−22.4055	+	16.2785i	−0.744372	+	0.540818i
$907$	4.83372	+	9.48671i	0.160501	+	0.315001i	0.957226	−	0.289341i	$-0.0934361\pi$
$907$	4.83372	+	9.48671i	0.160501	+	0.315001i	−0.796725	+	0.604342i	$0.793436\pi$
$908$	5.11030	+	10.0295i	0.169591	+	0.332841i
$909$	12.2474	−	8.89827i	0.406221	−	0.295137i
$910$	−24.6817	−	9.45790i	−0.818191	−	0.313526i
$911$	0.763148	+	2.34873i	0.0252842	+	0.0778168i	0.962902	−	0.269850i	$-0.0869741\pi$
$911$	0.763148	+	2.34873i	0.0252842	+	0.0778168i	−0.937618	+	0.347667i	$0.886974\pi$
$912$	5.05907	+	5.05907i	0.167523	+	0.167523i
$913$	42.5810	+	26.4802i	1.40922	+	0.876367i
$914$			27.4619i			0.908360i
$915$	−7.49503	+	4.87355i	−0.247778	+	0.161115i
$916$	3.49105	+	2.53640i	0.115348	+	0.0838049i
$917$	−0.819022	+	5.17110i	−0.0270465	+	0.170765i
$918$	9.56475	−	4.87348i	0.315684	−	0.160849i
$919$	12.9101	−	39.7333i	0.425866	−	1.31068i	−0.476297	−	0.879285i	$-0.658021\pi$
$919$	12.9101	−	39.7333i	0.425866	−	1.31068i	0.902163	−	0.431396i	$-0.141979\pi$
$920$	1.70911	+	16.1703i	0.0563477	+	0.533121i
$921$	−25.0179	+	34.4342i	−0.824368	+	1.13465i
$922$	13.2550	+	6.75377i	0.436531	+	0.222424i
$923$	−13.5421	+	13.5421i	−0.445745	+	0.445745i
$924$	11.3986	−	27.0149i	0.374985	−	0.888726i
$925$	−28.3075	−	7.54959i	−0.930746	−	0.248229i
$926$	−26.2007	+	8.51312i	−0.861008	+	0.279759i
$927$	−11.0797	+	1.75485i	−0.363904	+	0.0576367i
$928$	−0.0806009	−	0.0127659i	−0.00264585	−	0.000419062i
$929$	28.4482	+	9.24339i	0.933356	+	0.303266i	0.735934	−	0.677053i	$-0.236743\pi$
$929$	28.4482	+	9.24339i	0.933356	+	0.303266i	0.197422	+	0.980319i	$0.436743\pi$
$930$	−7.19617	+	6.48707i	−0.235972	+	0.212719i
$931$	16.4767	+	22.6782i	0.540001	+	0.743247i
$932$	2.28839	+	14.4483i	0.0749587	+	0.473271i
$933$	−23.4924	+	46.1065i	−0.769107	+	1.50946i
$934$	−30.5686			−1.00024
$935$	−34.0631	+	6.10241i	−1.11398	+	0.199570i
$936$	−5.86449			−0.191687
$937$	13.7881	−	27.0607i	0.450439	−	0.884036i	−0.548417	−	0.836205i	$-0.684769\pi$
$937$	13.7881	−	27.0607i	0.450439	−	0.884036i	0.998855	−	0.0478305i	$-0.0152307\pi$
$938$	−2.05992	−	13.0058i	−0.0672587	−	0.424655i
$939$	−44.2897	−	60.9595i	−1.44534	−	1.98934i
$940$	−1.42760	+	27.5476i	−0.0465631	+	0.898505i
$941$	37.8725	+	12.3055i	1.23461	+	0.401149i	0.852382	−	0.522920i	$-0.175157\pi$
$941$	37.8725	+	12.3055i	1.23461	+	0.401149i	0.382227	+	0.924068i	$0.375157\pi$
$942$	12.5181	+	1.98268i	0.407863	+	0.0645991i
$943$	−20.0618	+	3.17748i	−0.653302	+	0.103473i
$944$	2.40237	−	0.780579i	0.0781906	−	0.0254057i
$945$	10.1917	−	17.6764i	0.331536	−	0.575012i
$946$	−7.34885	−	6.36053i	−0.238932	−	0.206799i
$947$	−4.82949	+	4.82949i	−0.156937	+	0.156937i	−0.781208	−	0.624271i	$-0.785396\pi$
$947$	−4.82949	+	4.82949i	−0.156937	+	0.156937i	0.624271	+	0.781208i	$0.285396\pi$
$948$	24.4624	+	12.4642i	0.794502	+	0.404819i
$949$	−13.6924	+	18.8459i	−0.444473	+	0.611764i
$950$	−5.76924	−	14.9771i	−0.187179	−	0.485923i
$951$	8.17590	−	25.1628i	0.265122	−	0.815961i
$952$	−16.4909	+	8.40256i	−0.534475	+	0.272328i
$953$	−3.09310	+	19.5290i	−0.100195	+	0.632608i	0.885573	+	0.464499i	$0.153766\pi$
$953$	−3.09310	+	19.5290i	−0.100195	+	0.632608i	−0.985769	+	0.168108i	$0.946234\pi$
$954$	−5.87569	−	4.26894i	−0.190233	−	0.138212i
$955$	22.3550	+	4.73807i	0.723391	+	0.153320i
$956$		−	7.56533i		−	0.244680i
$957$	−0.585647	−	0.144680i	−0.0189313	−	0.00467683i
$958$	−8.69172	−	8.69172i	−0.280817	−	0.280817i
$959$	21.9704	+	67.6178i	0.709460	+	2.18349i
$960$	−1.78335	+	4.65391i	−0.0575575	+	0.150204i
$961$	22.0223	−	16.0001i	0.710396	−	0.516133i
$962$	−7.92755	−	15.5587i	−0.255595	−	0.501632i
$963$	−11.2514	−	22.0822i	−0.362572	−	0.711588i
$964$	5.11060	−	3.71307i	0.164601	−	0.119590i
$965$	−17.6464	+	46.0508i	−0.568059	+	1.48243i
$966$	19.8662	+	61.1418i	0.639184	+	1.96721i
$967$	1.05132	+	1.05132i	0.0338081	+	0.0338081i	0.723809	−	0.690001i	$-0.242390\pi$
$967$	1.05132	+	1.05132i	0.0338081	+	0.0338081i	−0.690001	+	0.723809i	$0.742390\pi$
$968$	3.53643	−	10.4160i	0.113665	−	0.334784i
$969$		−	33.3848i		−	1.07247i
$970$	24.0122	+	5.08931i	0.770985	+	0.163408i
$971$	−36.1581	−	26.2704i	−1.16037	−	0.843057i	−0.170544	−	0.985350i	$-0.554553\pi$
$971$	−36.1581	−	26.2704i	−1.16037	−	0.843057i	−0.989825	+	0.142293i	$0.954553\pi$
$972$	2.76659	−	17.4675i	0.0887383	−	0.560272i
$973$	8.75903	−	4.46295i	0.280802	−	0.143076i
$974$	1.95944	−	6.03053i	0.0627845	−	0.193231i
$975$	30.3563	+	13.4731i	0.972180	+	0.431484i
$976$	−1.05438	+	1.45123i	−0.0337498	+	0.0464526i
$977$	−12.0814	−	6.15577i	−0.386517	−	0.196940i	0.249924	−	0.968265i	$-0.419594\pi$
$977$	−12.0814	−	6.15577i	−0.386517	−	0.196940i	−0.636441	+	0.771325i	$0.719594\pi$
$978$	−19.1017	+	19.1017i	−0.610804	+	0.610804i
$979$	−10.2703	−	17.0096i	−0.328240	−	0.543628i
$980$	−9.75359	+	16.9165i	−0.311567	+	0.540377i
$981$	−24.4739	+	7.95206i	−0.781392	+	0.253890i
$982$	22.8529	−	3.61954i	0.729265	−	0.115504i
$983$	25.7257	+	4.07455i	0.820523	+	0.129958i	0.552562	−	0.833472i	$-0.313650\pi$
$983$	25.7257	+	4.07455i	0.820523	+	0.129958i	0.267961	+	0.963430i	$0.413650\pi$
$984$	−5.92098	−	1.92384i	−0.188754	−	0.0613298i
$985$	1.79275	−	34.5938i	0.0571217	−	1.10225i
$986$	0.223821	+	0.308064i	0.00712792	+	0.00981074i
$987$	17.0608	+	107.718i	0.543052	+	3.42869i
$988$	4.34299	−	8.52359i	0.138169	−	0.271171i
$989$	21.3098			0.677611
$990$	−6.36163	+	13.1344i	−0.202186	+	0.417438i
$991$	34.9392			1.10988			0.554940	−	0.831890i	$-0.312741\pi$
$991$	34.9392			1.10988			0.554940	+	0.831890i	$0.312741\pi$
$992$	−0.882540	+	1.73208i	−0.0280207	+	0.0549936i
$993$	−3.92953	−	24.8101i	−0.124700	−	0.787324i
$994$	14.9824	+	20.6216i	0.475214	+	0.654076i
$995$	12.9171	−	11.6443i	0.409501	−	0.369149i
$996$	−32.0484	−	10.4131i	−1.01549	−	0.329953i
$997$	54.0159	+	8.55527i	1.71070	+	0.270948i	0.933571	−	0.358393i	$-0.116675\pi$
$997$	54.0159	+	8.55527i	1.71070	+	0.270948i	0.777129	+	0.629341i	$0.216675\pi$
$998$	−41.0875	+	6.50762i	−1.30060	+	0.205995i
$999$	12.8200	−	4.16548i	0.405607	−	0.131790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.83.1	yes	48
3.2	odd	2		990.2.bh.c.523.5		48
4.3	odd	2		880.2.cm.c.193.5		48
5.2	odd	4	inner	110.2.k.a.17.1	yes	48
5.3	odd	4		550.2.bh.b.457.6		48
5.4	even	2		550.2.bh.b.193.6		48
11.2	odd	10	inner	110.2.k.a.13.1	✓	48
15.2	even	4		990.2.bh.c.127.4		48
20.7	even	4		880.2.cm.c.17.5		48
33.2	even	10		990.2.bh.c.343.4		48
44.35	even	10		880.2.cm.c.673.5		48
55.2	even	20	inner	110.2.k.a.57.1	yes	48
55.13	even	20		550.2.bh.b.57.6		48
55.24	odd	10		550.2.bh.b.343.6		48
165.2	odd	20		990.2.bh.c.937.5		48
220.167	odd	20		880.2.cm.c.497.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.13.1	✓	48	11.2	odd	10	inner
110.2.k.a.17.1	yes	48	5.2	odd	4	inner
110.2.k.a.57.1	yes	48	55.2	even	20	inner
110.2.k.a.83.1	yes	48	1.1	even	1	trivial
550.2.bh.b.57.6		48	55.13	even	20
550.2.bh.b.193.6		48	5.4	even	2
550.2.bh.b.343.6		48	55.24	odd	10
550.2.bh.b.457.6		48	5.3	odd	4
880.2.cm.c.17.5		48	20.7	even	4
880.2.cm.c.193.5		48	4.3	odd	2
880.2.cm.c.497.5		48	220.167	odd	20
880.2.cm.c.673.5		48	44.35	even	10
990.2.bh.c.127.4		48	15.2	even	4
990.2.bh.c.343.4		48	33.2	even	10
990.2.bh.c.523.5		48	3.2	odd	2
990.2.bh.c.937.5		48	165.2	odd	20

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.348671 - 2.20142i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.49719 - 1.66085i) q^{5} +(2.11978 + 0.688757i) q^{6} +(-3.91761 - 0.620489i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-1.87153 + 0.608097i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.348671 - 2.20142i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.49719 - 1.66085i) q^{5} +(2.11978 + 0.688757i) q^{6} +(-3.91761 - 0.620489i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-1.87153 + 0.608097i) q^{9} +(2.15954 - 0.579997i) q^{10} +(2.83922 - 1.71431i) q^{11} +(-1.57605 + 1.57605i) q^{12} +(2.65534 + 1.35296i) q^{13} +(2.33142 - 3.20892i) q^{14} +(-3.13421 + 3.87504i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(4.15761 - 2.11841i) q^{17} +(0.307838 - 1.94362i) q^{18} +(2.59693 + 1.88678i) q^{19} +(-0.463629 + 2.18748i) q^{20} +8.84068i q^{21} +(0.238480 + 3.30804i) q^{22} +(-5.14200 - 5.14200i) q^{23} +(-0.688757 - 2.11978i) q^{24} +(-0.516841 + 4.97322i) q^{25} +(-2.41100 + 1.75169i) q^{26} +(-1.04442 - 2.04980i) q^{27} +(1.80073 + 3.53413i) q^{28} +(0.0660203 - 0.0479665i) q^{29} +(-2.02979 - 4.55183i) q^{30} +(-0.600717 - 1.84882i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.76387 - 5.65259i) q^{33} +4.66620i q^{34} +(4.83487 + 7.43555i) q^{35} +(1.59202 + 1.15667i) q^{36} +(-0.916611 + 5.78725i) q^{37} +(-2.86011 + 1.45730i) q^{38} +(2.05261 - 6.31728i) q^{39} +(-1.73857 - 1.40619i) q^{40} +(1.64181 - 2.25975i) q^{41} +(-7.87710 - 4.01358i) q^{42} +(-2.07213 + 2.07213i) q^{43} +(-3.05575 - 1.28933i) q^{44} +(3.81199 + 2.19789i) q^{45} +(6.91597 - 2.24713i) q^{46} +(12.1843 - 1.92981i) q^{47} +(2.20142 + 0.348671i) q^{48} +(8.30529 + 2.69855i) q^{49} +(-4.19653 - 2.71830i) q^{50} +(-6.11316 - 8.41404i) q^{51} +(-0.466200 - 2.94347i) q^{52} +(1.67555 - 3.28846i) q^{53} +2.30054 q^{54} +(-7.09805 - 2.14887i) q^{55} -3.96645 q^{56} +(3.24812 - 6.37480i) q^{57} +(0.0127659 + 0.0806009i) q^{58} +(-1.48475 - 2.04358i) q^{59} +(4.97722 + 0.257934i) q^{60} +(1.70602 + 0.554319i) q^{61} +(1.92003 + 0.304102i) q^{62} +(7.70925 - 1.22102i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-1.72848 - 6.43577i) q^{65} +(7.19925 - 1.67841i) q^{66} +(2.34748 - 2.34748i) q^{67} +(-4.15761 - 2.11841i) q^{68} +(-9.52685 + 13.1126i) q^{69} +(-8.82012 + 0.932234i) q^{70} +(-1.98584 + 6.11179i) q^{71} +(-1.75336 + 0.893382i) q^{72} +(-1.22279 + 7.72040i) q^{73} +(-4.74035 - 3.44406i) q^{74} +(11.1284 - 0.596233i) q^{75} -3.20998i q^{76} +(-12.1867 + 4.95428i) q^{77} +(4.69687 + 4.69687i) q^{78} +(-3.80642 - 11.7150i) q^{79} +(2.04222 - 0.910682i) q^{80} +(-8.92437 + 6.48393i) q^{81} +(1.26809 + 2.48877i) q^{82} +(6.86376 + 13.4709i) q^{83} +(7.15226 - 5.19642i) q^{84} +(-9.74309 - 3.73350i) q^{85} +(-0.905554 - 2.78701i) q^{86} +(-0.128614 - 0.128614i) q^{87} +(2.53609 - 2.13735i) q^{88} -5.99094i q^{89} +(-3.68895 + 2.39869i) q^{90} +(-9.56310 - 6.94800i) q^{91} +(-1.13757 + 7.18235i) q^{92} +(-3.86058 + 1.96706i) q^{93} +(-3.81210 + 11.7324i) q^{94} +(-0.754441 - 7.13797i) q^{95} +(-1.31009 + 1.80319i) q^{96} +(9.78069 + 4.98351i) q^{97} +(-6.17495 + 6.17495i) q^{98} +(-4.27122 + 4.93489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

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