LMFDB - Embedded newform 111.2.o.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [111,2,Mod(4,111)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(111, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("111.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 111 = 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	111.o (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:	$0.886339462436$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.15342238784889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 12x^{10} + 48x^{8} + 77x^{6} + 48x^{4} + 12x^{2} + 1 $ x^12 + 12x^10 + 48x^8 + 77x^6 + 48x^4 + 12*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			25.2
Root			$-0.714852i$ of defining polynomial
Character	$\chi$	$=$	111.25
Dual form			111.2.o.a.40.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.459498 + 0.547608i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.258560 - 1.46637i) q^{4} +(0.899190 + 2.47051i) q^{5} -0.714852i q^{6} +(2.71652 - 0.988733i) q^{7} +(2.15996 - 1.24705i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(0.459498 + 0.547608i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.258560 - 1.46637i) q^{4} +(0.899190 + 2.47051i) q^{5} -0.714852i q^{6} +(2.71652 - 0.988733i) q^{7} +(2.15996 - 1.24705i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.939693 + 1.62760i) q^{10} +(-0.249768 - 0.432610i) q^{11} +(-1.14063 + 0.957103i) q^{12} +(-4.16195 - 0.733865i) q^{13} +(1.78967 + 1.03327i) q^{14} +(0.899190 - 2.47051i) q^{15} +(-1.12299 - 0.408734i) q^{16} +(-5.47729 + 0.965795i) q^{17} +(-0.459498 + 0.547608i) q^{18} +(-3.72226 + 4.43602i) q^{19} +(3.85516 - 0.679769i) q^{20} +(-2.71652 - 0.988733i) q^{21} +(0.122133 - 0.335558i) q^{22} +(5.73629 + 3.31185i) q^{23} +(-2.45622 - 0.433097i) q^{24} +(-1.46463 + 1.22897i) q^{25} +(-1.51054 - 2.61633i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.747461 - 4.23906i) q^{28} +(-5.19695 + 3.00046i) q^{29} +(1.76604 - 0.642788i) q^{30} -7.80381i q^{31} +(-1.99825 - 5.49016i) q^{32} +(-0.0867434 + 0.491946i) q^{33} +(-3.04568 - 2.55563i) q^{34} +(4.88534 + 5.82212i) q^{35} +1.48899 q^{36} +(5.98588 - 1.08132i) q^{37} -4.13957 q^{38} +(2.71652 + 3.23743i) q^{39} +(5.02307 + 4.21486i) q^{40} +(0.632243 - 3.58563i) q^{41} +(-0.706798 - 1.94191i) q^{42} +5.07845i q^{43} +(-0.698945 + 0.254395i) q^{44} +(-2.27683 + 1.31453i) q^{45} +(0.822217 + 4.66303i) q^{46} +(-1.28873 + 2.23215i) q^{47} +(0.597529 + 1.03495i) q^{48} +(1.03959 - 0.872319i) q^{49} +(-1.34599 - 0.237334i) q^{50} +(4.81665 + 2.78089i) q^{51} +(-2.15223 + 5.91320i) q^{52} +(-0.577438 - 0.210170i) q^{53} +(0.703991 - 0.124133i) q^{54} +(0.844177 - 1.00605i) q^{55} +(4.63458 - 5.52328i) q^{56} +(5.70284 - 1.00556i) q^{57} +(-4.03107 - 1.46719i) q^{58} +(-1.02042 + 2.80357i) q^{59} +(-3.39017 - 1.95732i) q^{60} +(-5.37766 - 0.948226i) q^{61} +(4.27343 - 3.58583i) q^{62} +(1.44543 + 2.50356i) q^{63} +(0.893204 - 1.54708i) q^{64} +(-1.92937 - 10.9420i) q^{65} +(-0.309252 + 0.178547i) q^{66} +(10.9065 - 3.96963i) q^{67} +8.28143i q^{68} +(-2.26544 - 6.22424i) q^{69} +(-0.943438 + 5.35050i) q^{70} +(-5.64781 - 4.73908i) q^{71} +(1.60318 + 1.91060i) q^{72} +11.2204 q^{73} +(3.34264 + 2.78105i) q^{74} +1.91194 q^{75} +(5.54240 + 6.60517i) q^{76} +(-1.10624 - 0.928242i) q^{77} +(-0.524604 + 2.97518i) q^{78} +(2.67379 + 7.34618i) q^{79} -3.14187i q^{80} +(-0.939693 + 0.342020i) q^{81} +(2.25403 - 1.30137i) q^{82} +(-2.04149 - 11.5779i) q^{83} +(-2.15223 + 3.72777i) q^{84} +(-7.31113 - 12.6632i) q^{85} +(-2.78100 + 2.33354i) q^{86} +(5.90976 + 1.04205i) q^{87} +(-1.07898 - 0.622947i) q^{88} +(-5.23986 + 14.3964i) q^{89} +(-1.76604 - 0.642788i) q^{90} +(-12.0316 + 2.12150i) q^{91} +(6.33956 - 7.55519i) q^{92} +(-5.01619 + 5.97806i) q^{93} +(-1.81452 + 0.319948i) q^{94} +(-14.3062 - 5.20704i) q^{95} +(-1.99825 + 5.49016i) q^{96} +(-0.249498 - 0.144048i) q^{97} +(0.955378 + 0.168459i) q^{98} +(0.382666 - 0.321095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{7} - 9 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^7 - 9 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{7} - 9 q^{8} - 6 q^{11} - 6 q^{12} - 6 q^{13} + 27 q^{14} - 3 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 12 q^{19} + 9 q^{20} + 6 q^{21} - 21 q^{22} - 6 q^{24} - 15 q^{25} + 6 q^{27} + 39 q^{28} + 27 q^{29} + 12 q^{30} - 33 q^{32} - 12 q^{33} + 15 q^{34} + 36 q^{35} + 15 q^{37} - 48 q^{38} - 6 q^{39} + 15 q^{40} + 12 q^{41} + 18 q^{42} - 21 q^{44} - 15 q^{46} + 9 q^{47} - 18 q^{49} - 18 q^{50} + 9 q^{51} + 6 q^{52} - 12 q^{53} - 3 q^{54} - 39 q^{55} - 18 q^{56} - 3 q^{57} - 15 q^{58} - 15 q^{61} + 39 q^{62} + 12 q^{63} - 9 q^{64} - 24 q^{65} + 18 q^{66} + 6 q^{67} - 12 q^{69} - 15 q^{70} - 3 q^{71} - 6 q^{72} + 90 q^{73} + 72 q^{74} - 24 q^{75} - 6 q^{76} + 27 q^{77} + 9 q^{78} + 6 q^{79} + 27 q^{82} - 3 q^{83} + 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{87} + 63 q^{88} + 39 q^{89} - 12 q^{90} - 27 q^{91} + 6 q^{92} - 24 q^{93} + 30 q^{94} - 36 q^{95} - 33 q^{96} - 18 q^{97} - 42 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^7 - 9 * q^8 - 6 * q^11 - 6 * q^12 - 6 * q^13 + 27 * q^14 - 3 * q^15 + 3 * q^16 - 6 * q^17 - 3 * q^18 - 12 * q^19 + 9 * q^20 + 6 * q^21 - 21 * q^22 - 6 * q^24 - 15 * q^25 + 6 * q^27 + 39 * q^28 + 27 * q^29 + 12 * q^30 - 33 * q^32 - 12 * q^33 + 15 * q^34 + 36 * q^35 + 15 * q^37 - 48 * q^38 - 6 * q^39 + 15 * q^40 + 12 * q^41 + 18 * q^42 - 21 * q^44 - 15 * q^46 + 9 * q^47 - 18 * q^49 - 18 * q^50 + 9 * q^51 + 6 * q^52 - 12 * q^53 - 3 * q^54 - 39 * q^55 - 18 * q^56 - 3 * q^57 - 15 * q^58 - 15 * q^61 + 39 * q^62 + 12 * q^63 - 9 * q^64 - 24 * q^65 + 18 * q^66 + 6 * q^67 - 12 * q^69 - 15 * q^70 - 3 * q^71 - 6 * q^72 + 90 * q^73 + 72 * q^74 - 24 * q^75 - 6 * q^76 + 27 * q^77 + 9 * q^78 + 6 * q^79 + 27 * q^82 - 3 * q^83 + 6 * q^84 - 27 * q^85 - 12 * q^86 + 9 * q^87 + 63 * q^88 + 39 * q^89 - 12 * q^90 - 27 * q^91 + 6 * q^92 - 24 * q^93 + 30 * q^94 - 36 * q^95 - 33 * q^96 - 18 * q^97 - 42 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	0.459498	+	0.547608i	0.324914	+	0.387217i	0.903632	−	0.428311i	$-0.140891\pi$
$2$	0.459498	+	0.547608i	0.324914	+	0.387217i	−0.578718	+	0.815528i	$0.696447\pi$
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$4$	0.258560	−	1.46637i	0.129280	−	0.733183i
$5$	0.899190	+	2.47051i	0.402130	+	1.10484i	0.961231	+	0.275744i	$0.0889242\pi$
$5$	0.899190	+	2.47051i	0.402130	+	1.10484i	−0.559101	+	0.829100i	$0.688854\pi$
$6$		−	0.714852i		−	0.291837i
$7$	2.71652	−	0.988733i	1.02675	−	0.373706i	0.226907	−	0.973916i	$-0.427139\pi$
$7$	2.71652	−	0.988733i	1.02675	−	0.373706i	0.799842	+	0.600210i	$0.204916\pi$
$8$	2.15996	−	1.24705i	0.763661	−	0.440900i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−0.939693	+	1.62760i	−0.297157	+	0.514691i
$11$	−0.249768	−	0.432610i	−0.0753078	−	0.130437i	0.825912	−	0.563799i	$-0.190661\pi$
$11$	−0.249768	−	0.432610i	−0.0753078	−	0.130437i	−0.901220	+	0.433362i	$0.857327\pi$
$12$	−1.14063	+	0.957103i	−0.329272	+	0.276292i
$13$	−4.16195	−	0.733865i	−1.15432	−	0.203537i	−0.436458	−	0.899725i	$-0.643767\pi$
$13$	−4.16195	−	0.733865i	−1.15432	−	0.203537i	−0.717860	+	0.696187i	$0.754878\pi$
$14$	1.78967	+	1.03327i	0.478311	+	0.276153i
$15$	0.899190	−	2.47051i	0.232170	−	0.637882i
$16$	−1.12299	−	0.408734i	−0.280747	−	0.102183i
$17$	−5.47729	+	0.965795i	−1.32844	+	0.234240i	−0.792425	−	0.609970i	$-0.791182\pi$
$17$	−5.47729	+	0.965795i	−1.32844	+	0.234240i	−0.536014	+	0.844209i	$0.680071\pi$
$18$	−0.459498	+	0.547608i	−0.108305	+	0.129072i
$19$	−3.72226	+	4.43602i	−0.853945	+	1.01769i	0.145653	+	0.989336i	$0.453472\pi$
$19$	−3.72226	+	4.43602i	−0.853945	+	1.01769i	−0.999598	+	0.0283566i	$0.990973\pi$
$20$	3.85516	−	0.679769i	0.862040	−	0.152001i
$21$	−2.71652	−	0.988733i	−0.592794	−	0.215759i
$22$	0.122133	−	0.335558i	0.0260389	−	0.0715412i
$23$	5.73629	+	3.31185i	1.19610	+	0.690568i	0.959683	−	0.281084i	$-0.0906938\pi$
$23$	5.73629	+	3.31185i	1.19610	+	0.690568i	0.236416	+	0.971652i	$0.424027\pi$
$24$	−2.45622	−	0.433097i	−0.501373	−	0.0884056i
$25$	−1.46463	+	1.22897i	−0.292926	+	0.245794i
$26$	−1.51054	−	2.61633i	−0.296241	−	0.513104i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−0.747461	−	4.23906i	−0.141257	−	0.801108i
$29$	−5.19695	+	3.00046i	−0.965050	+	0.557172i	−0.897724	−	0.440559i	$-0.854780\pi$
$29$	−5.19695	+	3.00046i	−0.965050	+	0.557172i	−0.0673266	+	0.997731i	$0.521447\pi$
$30$	1.76604	−	0.642788i	0.322434	−	0.117356i
$31$		−	7.80381i		−	1.40161i	−0.713355	−	0.700803i	$-0.752825\pi$
$31$		−	7.80381i		−	1.40161i	0.713355	−	0.700803i	$-0.247175\pi$
$32$	−1.99825	−	5.49016i	−0.353245	−	0.970532i
$33$	−0.0867434	+	0.491946i	−0.0151001	+	0.0856368i
$34$	−3.04568	−	2.55563i	−0.522330	−	0.438287i
$35$	4.88534	+	5.82212i	0.825773	+	0.984118i
$36$	1.48899			0.248165
$37$	5.98588	−	1.08132i	0.984072	−	0.177768i
$37$	5.98588	−	1.08132i	0.984072	−	0.177768i
$38$	−4.13957			−0.671527
$39$	2.71652	+	3.23743i	0.434992	+	0.518403i
$40$	5.02307	+	4.21486i	0.794217	+	0.666427i
$41$	0.632243	−	3.58563i	0.0987398	−	0.559981i	−0.894797	−	0.446473i	$-0.852680\pi$
$41$	0.632243	−	3.58563i	0.0987398	−	0.559981i	0.993537	−	0.113508i	$-0.0362089\pi$
$42$	−0.706798	−	1.94191i	−0.109061	−	0.299643i
$43$			5.07845i			0.774457i	0.921984	+	0.387229i	$0.126568\pi$
$43$			5.07845i			0.774457i	−0.921984	+	0.387229i	$0.873432\pi$
$44$	−0.698945	+	0.254395i	−0.105370	+	0.0383515i
$45$	−2.27683	+	1.31453i	−0.339410	+	0.195958i
$46$	0.822217	+	4.66303i	0.121229	+	0.687526i
$47$	−1.28873	+	2.23215i	−0.187981	+	0.325593i	−0.944577	−	0.328290i	$-0.893528\pi$
$47$	−1.28873	+	2.23215i	−0.187981	+	0.325593i	0.756596	+	0.653883i	$0.226861\pi$
$48$	0.597529	+	1.03495i	0.0862459	+	0.149382i
$49$	1.03959	−	0.872319i	0.148513	−	0.124617i
$50$	−1.34599	−	0.237334i	−0.190352	−	0.0335641i
$51$	4.81665	+	2.78089i	0.674466	+	0.389403i
$52$	−2.15223	+	5.91320i	−0.298460	+	0.820013i
$53$	−0.577438	−	0.210170i	−0.0793172	−	0.0288691i	0.302057	−	0.953290i	$-0.402327\pi$
$53$	−0.577438	−	0.210170i	−0.0793172	−	0.0288691i	−0.381374	+	0.924421i	$0.624549\pi$
$54$	0.703991	−	0.124133i	0.0958011	−	0.0168923i
$55$	0.844177	−	1.00605i	0.113829	−	0.135656i
$56$	4.63458	−	5.52328i	0.619322	−	0.738079i
$57$	5.70284	−	1.00556i	0.755359	−	0.133190i
$58$	−4.03107	−	1.46719i	−0.529305	−	0.192651i
$59$	−1.02042	+	2.80357i	−0.132847	+	0.364993i	−0.988224	−	0.153011i	$-0.951103\pi$
$59$	−1.02042	+	2.80357i	−0.132847	+	0.364993i	0.855378	+	0.518005i	$0.173325\pi$
$60$	−3.39017	−	1.95732i	−0.437669	−	0.252688i
$61$	−5.37766	−	0.948226i	−0.688539	−	0.121408i	−0.181577	−	0.983377i	$-0.558120\pi$
$61$	−5.37766	−	0.948226i	−0.688539	−	0.121408i	−0.506961	+	0.861969i	$0.669231\pi$
$62$	4.27343	−	3.58583i	0.542726	−	0.455401i
$63$	1.44543	+	2.50356i	0.182107	+	0.315419i
$64$	0.893204	−	1.54708i	0.111651	−	0.193384i
$65$	−1.92937	−	10.9420i	−0.239309	−	1.35719i
$66$	−0.309252	+	0.178547i	−0.0380663	+	0.0219776i
$67$	10.9065	−	3.96963i	1.33244	−	0.484967i	0.425015	−	0.905187i	$-0.360269\pi$
$67$	10.9065	−	3.96963i	1.33244	−	0.484967i	0.907423	+	0.420219i	$0.138047\pi$
$68$			8.28143i			1.00427i
$69$	−2.26544	−	6.22424i	−0.272727	−	0.749310i
$70$	−0.943438	+	5.35050i	−0.112762	+	0.639508i
$71$	−5.64781	−	4.73908i	−0.670272	−	0.562425i	0.242874	−	0.970058i	$-0.421910\pi$
$71$	−5.64781	−	4.73908i	−0.670272	−	0.562425i	−0.913146	+	0.407633i	$0.866354\pi$
$72$	1.60318	+	1.91060i	0.188937	+	0.225166i
$73$	11.2204			1.31325			0.656624	−	0.754218i	$-0.271984\pi$
$73$	11.2204			1.31325			0.656624	+	0.754218i	$0.271984\pi$
$74$	3.34264	+	2.78105i	0.388574	+	0.323290i
$75$	1.91194			0.220772
$76$	5.54240	+	6.60517i	0.635757	+	0.757665i
$77$	−1.10624	−	0.928242i	−0.126067	−	0.105783i
$78$	−0.524604	+	2.97518i	−0.0593997	+	0.336873i
$79$	2.67379	+	7.34618i	0.300825	+	0.826510i	0.994357	+	0.106084i	$0.0338313\pi$
$79$	2.67379	+	7.34618i	0.300825	+	0.826510i	−0.693532	+	0.720426i	$0.743947\pi$
$80$		−	3.14187i		−	0.351272i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	2.25403	−	1.30137i	0.248916	−	0.143712i
$83$	−2.04149	−	11.5779i	−0.224082	−	1.27083i	−0.864432	−	0.502750i	$-0.832321\pi$
$83$	−2.04149	−	11.5779i	−0.224082	−	1.27083i	0.640349	−	0.768084i	$-0.278790\pi$
$84$	−2.15223	+	3.72777i	−0.234827	+	0.406733i
$85$	−7.31113	−	12.6632i	−0.793003	−	1.37352i
$86$	−2.78100	+	2.33354i	−0.299883	+	0.251632i
$87$	5.90976	+	1.04205i	0.633593	+	0.111719i
$88$	−1.07898	−	0.622947i	−0.115019	−	0.0664064i
$89$	−5.23986	+	14.3964i	−0.555425	+	1.52602i	0.270777	+	0.962642i	$0.412719\pi$
$89$	−5.23986	+	14.3964i	−0.555425	+	1.52602i	−0.826202	+	0.563374i	$0.809503\pi$
$90$	−1.76604	−	0.642788i	−0.186157	−	0.0677558i
$91$	−12.0316	+	2.12150i	−1.26126	+	0.222394i
$92$	6.33956	−	7.55519i	0.660945	−	0.787683i
$93$	−5.01619	+	5.97806i	−0.520155	+	0.619896i
$94$	−1.81452	+	0.319948i	−0.187153	+	0.0330001i
$95$	−14.3062	−	5.20704i	−1.46779	−	0.534231i
$96$	−1.99825	+	5.49016i	−0.203946	+	0.560337i
$97$	−0.249498	−	0.144048i	−0.0253327	−	0.0146258i	0.487280	−	0.873246i	$-0.337989\pi$
$97$	−0.249498	−	0.144048i	−0.0253327	−	0.0146258i	−0.512613	+	0.858620i	$0.671322\pi$
$98$	0.955378	+	0.168459i	0.0965078	+	0.0170169i
$99$	0.382666	−	0.321095i	0.0384594	−	0.0322713i
$100$	1.42343	+	2.46545i	0.142343	+	0.246545i
$101$	−0.214177	+	0.370966i	−0.0213115	+	0.0369125i	−0.876484	−	0.481430i	$-0.840117\pi$
$101$	−0.214177	+	0.370966i	−0.0213115	+	0.0369125i	0.855173	+	0.518343i	$0.173451\pi$
$102$	0.690400	+	3.91545i	0.0683598	+	0.387687i
$103$	15.7883	−	9.11537i	1.55567	−	0.898164i	0.558003	−	0.829839i	$-0.311568\pi$
$103$	15.7883	−	9.11537i	1.55567	−	0.898164i	0.997663	−	0.0683259i	$-0.0217658\pi$
$104$	−9.90483	+	3.60506i	−0.971248	+	0.353505i
$105$		−	7.60024i		−	0.741708i
$106$	−0.150240	−	0.412782i	−0.0145926	−	0.0400930i
$107$	0.915888	−	5.19426i	0.0885423	−	0.502148i	−0.907994	−	0.418984i	$-0.862386\pi$
$107$	0.915888	−	5.19426i	0.0885423	−	0.502148i	0.996536	−	0.0831641i	$-0.0265026\pi$
$108$	−1.14063	−	0.957103i	−0.109757	−	0.0920972i
$109$	−4.38570	−	5.22668i	−0.420074	−	0.500625i	0.513957	−	0.857816i	$-0.328179\pi$
$109$	−4.38570	−	5.22668i	−0.420074	−	0.500625i	−0.934031	+	0.357191i	$0.883735\pi$
$110$	0.938819			0.0895129
$111$	−5.28051	−	3.01931i	−0.501204	−	0.286580i
$112$	−3.45475			−0.326443
$113$	−5.91128	−	7.04479i	−0.556086	−	0.662718i	0.412627	−	0.910900i	$-0.364611\pi$
$113$	−5.91128	−	7.04479i	−0.556086	−	0.662718i	−0.968713	+	0.248182i	$0.920167\pi$
$114$	3.17109	+	2.66086i	0.297000	+	0.249213i
$115$	−3.02392	+	17.1495i	−0.281982	+	1.59920i
$116$	3.05605	+	8.39644i	0.283747	+	0.779590i
$117$		−	4.22616i		−	0.390709i
$118$	−2.00413	+	0.729445i	−0.184496	+	0.0671509i
$119$	−13.9243	+	8.03918i	−1.27644	+	0.736951i
$120$	−1.13864	−	6.45753i	−0.103943	−	0.589489i
$121$	5.37523	−	9.31018i	0.488657	−	0.846380i
$122$	−1.95177	−	3.38056i	−0.176705	−	0.306061i
$123$	−2.78912	+	2.34035i	−0.251487	+	0.211023i
$124$	−11.4432	−	2.01775i	−1.02763	−	0.181199i
$125$	7.03099	+	4.05934i	0.628871	+	0.363079i
$126$	−0.706798	+	1.94191i	−0.0629665	+	0.172999i
$127$	6.12154	+	2.22806i	0.543199	+	0.197708i	0.599022	−	0.800732i	$-0.295556\pi$
$127$	6.12154	+	2.22806i	0.543199	+	0.197708i	−0.0558233	+	0.998441i	$0.517778\pi$
$128$	−10.2499	+	1.80733i	−0.905969	+	0.159747i
$129$	3.26437	−	3.89032i	0.287412	−	0.342524i
$130$	5.10539	−	6.08437i	0.447773	−	0.533635i
$131$	10.4755	−	1.84712i	0.915250	−	0.161383i	0.303864	−	0.952715i	$-0.401723\pi$
$131$	10.4755	−	1.84712i	0.915250	−	0.161383i	0.611387	+	0.791332i	$0.290612\pi$
$132$	0.698945	+	0.254395i	0.0608353	+	0.0221422i
$133$	−5.72557	+	15.7309i	−0.496470	+	1.36404i
$134$	7.18530	+	4.14843i	0.620715	+	0.358370i
$135$	2.58912	+	0.456531i	0.222836	+	0.0392919i
$136$	−10.6263	+	8.91656i	−0.911201	+	0.764589i
$137$	7.97439	+	13.8121i	0.681298	+	1.18004i	0.974585	+	0.224019i	$0.0719176\pi$
$137$	7.97439	+	13.8121i	0.681298	+	1.18004i	−0.293287	+	0.956025i	$0.594749\pi$
$138$	2.36748	−	4.10060i	0.201533	−	0.349066i
$139$	1.50024	+	8.50827i	0.127248	+	0.721662i	0.979947	+	0.199258i	$0.0638533\pi$
$139$	1.50024	+	8.50827i	0.127248	+	0.721662i	−0.852699	+	0.522403i	$0.825036\pi$
$140$	9.80052	−	5.65833i	0.828295	−	0.478216i
$141$	2.42203	−	0.881546i	0.203972	−	0.0742396i
$142$		−	5.27038i		−	0.442281i
$143$	0.722044	+	1.98380i	0.0603803	+	0.165894i
$144$	0.207520	−	1.17690i	0.0172933	−	0.0980752i
$145$	−12.0857	−	10.1411i	−1.00366	−	0.842174i
$146$	5.15575	+	6.14438i	0.426693	+	0.508513i
$147$	−1.35709			−0.111931
$148$	−0.0379066	−	9.05708i	−0.00311591	−	0.744487i
$149$	9.73659			0.797653			0.398826	−	0.917026i	$-0.369418\pi$
$149$	9.73659			0.797653			0.398826	+	0.917026i	$0.369418\pi$
$150$	0.878532	+	1.04699i	0.0717318	+	0.0854866i
$151$	−6.65386	−	5.58325i	−0.541484	−	0.454359i	0.330561	−	0.943785i	$-0.392762\pi$
$151$	−6.65386	−	5.58325i	−0.541484	−	0.454359i	−0.872045	+	0.489426i	$0.837206\pi$
$152$	−2.50798	+	14.2235i	−0.203424	+	1.15368i
$153$	−1.90224	−	5.22637i	−0.153787	−	0.422527i
$154$		−	1.03231i		−	0.0831858i
$155$	19.2793	−	7.01711i	1.54855	−	0.563628i
$156$	5.44964	−	3.14635i	0.436320	−	0.251909i
$157$	−1.28062	−	7.26274i	−0.102204	−	0.579630i	−0.992300	−	0.123856i	$-0.960474\pi$
$157$	−1.28062	−	7.26274i	−0.102204	−	0.579630i	0.890096	−	0.455774i	$-0.150637\pi$
$158$	−2.79423	+	4.83974i	−0.222297	+	0.385029i
$159$	0.307248	+	0.532170i	0.0243664	+	0.0422038i
$160$	11.7667	−	9.87340i	0.930236	−	0.780560i
$161$	18.8573	+	3.32505i	1.48616	+	0.262051i
$162$	−0.619080	−	0.357426i	−0.0486395	−	0.0280820i
$163$	−0.0826195	+	0.226995i	−0.00647126	+	0.0177796i	−0.942886	−	0.333115i	$-0.891900\pi$
$163$	−0.0826195	+	0.226995i	−0.00647126	+	0.0177796i	0.936415	+	0.350895i	$0.114122\pi$
$164$	−5.09437	−	1.85420i	−0.397804	−	0.144789i
$165$	−1.29335	+	0.228053i	−0.100687	+	0.0177539i
$166$	5.40207	−	6.43793i	0.419282	−	0.499680i
$167$	16.4113	−	19.5582i	1.26994	−	1.51346i	0.515878	−	0.856662i	$-0.327466\pi$
$167$	16.4113	−	19.5582i	1.26994	−	1.51346i	0.754066	−	0.656799i	$-0.228090\pi$
$168$	−7.10059	+	1.25202i	−0.547822	+	0.0965958i
$169$	4.56730	+	1.66236i	0.351331	+	0.127874i
$170$	3.57505	−	9.82237i	0.274194	−	0.753341i
$171$	−5.01499	−	2.89541i	−0.383506	−	0.221417i
$172$	7.44687	+	1.31308i	0.567819	+	0.100122i
$173$	−9.06467	+	7.60616i	−0.689174	+	0.578286i	−0.918671	−	0.395024i	$-0.870736\pi$
$173$	−9.06467	+	7.60616i	−0.689174	+	0.578286i	0.229497	+	0.973309i	$0.426292\pi$
$174$	2.14489	+	3.71505i	0.162603	+	0.281637i
$175$	−2.76358	+	4.78666i	−0.208907	+	0.361837i
$176$	0.103663	+	0.587904i	0.00781392	+	0.0443149i
$177$	2.58378	−	1.49175i	0.194209	−	0.112127i
$178$	−10.2913	+	3.74573i	−0.771365	+	0.280754i
$179$		−	21.1611i		−	1.58166i	−0.612038	−	0.790828i	$-0.709650\pi$
$179$		−	21.1611i		−	1.58166i	0.612038	−	0.790828i	$-0.290350\pi$
$180$	1.33888	+	3.67855i	0.0997944	+	0.274183i
$181$	−3.81369	+	21.6285i	−0.283469	+	1.60763i	0.427234	+	0.904141i	$0.359488\pi$
$181$	−3.81369	+	21.6285i	−0.283469	+	1.60763i	−0.710703	+	0.703492i	$0.751623\pi$
$182$	−6.69026	−	5.61380i	−0.495915	−	0.416122i
$183$	3.51002	+	4.18308i	0.259468	+	0.309222i
$184$	16.5202			1.21789
$185$	8.05386	+	13.8158i	0.592131	+	1.01576i
$186$	−5.57856			−0.409040
$187$	1.78586	+	2.12831i	0.130595	+	0.155637i
$188$	2.93994	+	2.46690i	0.214417	+	0.179917i
$189$	0.501993	−	2.84694i	0.0365146	−	0.207085i
$190$	−3.72226	−	10.2268i	−0.270041	−	0.741932i
$191$			1.19745i			0.0866446i	0.999061	+	0.0433223i	$0.0137942\pi$
$191$			1.19745i			0.0866446i	−0.999061	+	0.0433223i	$0.986206\pi$
$192$	−1.67867	+	0.610988i	−0.121148	+	0.0440942i
$193$	−7.55904	+	4.36421i	−0.544111	+	0.314143i	−0.746744	−	0.665112i	$-0.768384\pi$
$193$	−7.55904	+	4.36421i	−0.544111	+	0.314143i	0.202632	+	0.979255i	$0.435050\pi$
$194$	−0.0357621	−	0.202817i	−0.00256757	−	0.0145614i
$195$	−5.55541	+	9.62224i	−0.397831	+	0.689063i
$196$	−1.01034	−	1.74997i	−0.0721674	−	0.124998i
$197$	−19.2587	+	16.1599i	−1.37212	+	1.15135i	−0.400098	+	0.916472i	$0.631024\pi$
$197$	−19.2587	+	16.1599i	−1.37212	+	1.15135i	−0.972025	+	0.234876i	$0.924531\pi$
$198$	0.351668	+	0.0620086i	0.0249920	+	0.00440676i
$199$	−8.49253	−	4.90317i	−0.602020	−	0.347576i	0.167816	−	0.985818i	$-0.446329\pi$
$199$	−8.49253	−	4.90317i	−0.602020	−	0.347576i	−0.769836	+	0.638242i	$0.779662\pi$
$200$	−1.63095	+	4.48100i	−0.115326	+	0.316855i
$201$	−10.9065	−	3.96963i	−0.769283	−	0.279996i
$202$	−0.301558	+	0.0531728i	−0.0212176	+	0.00374123i
$203$	−11.1510	+	13.2892i	−0.782646	+	0.932721i
$204$	5.32320	−	6.34395i	0.372699	−	0.444165i
$205$	9.42682	−	1.66220i	0.658398	−	0.116093i
$206$	12.2463	+	4.45730i	0.853243	+	0.310555i
$207$	−2.26544	+	6.22424i	−0.157459	+	0.432615i
$208$	4.37386	+	2.52525i	0.303273	+	0.175095i
$209$	2.84877	+	0.502314i	0.197053	+	0.0347458i
$210$	4.16195	−	3.49229i	0.287202	−	0.240991i
$211$	5.84492	+	10.1237i	0.402381	+	0.696944i	0.994013	−	0.109264i	$-0.0348495\pi$
$211$	5.84492	+	10.1237i	0.402381	+	0.696944i	−0.591632	+	0.806208i	$0.701516\pi$
$212$	−0.457489	+	0.792394i	−0.0314205	+	0.0544218i
$213$	1.28026	+	7.26069i	0.0877216	+	0.497494i
$214$	3.26527	−	1.88520i	0.223209	−	0.128870i
$215$	−12.5463	+	4.56650i	−0.855654	+	0.311433i
$216$		−	2.49411i		−	0.169703i
$217$	−7.71588	−	21.1992i	−0.523788	−	1.43910i
$218$	0.846950	−	4.80329i	0.0573627	−	0.325320i
$219$	−8.59533	−	7.21234i	−0.580818	−	0.487364i
$220$	−1.25697	−	1.49800i	−0.0847448	−	0.100995i
$221$	23.5050			1.58112
$222$	−0.772985	−	4.27901i	−0.0518794	−	0.287189i
$223$	8.86848			0.593877			0.296939	−	0.954897i	$-0.404034\pi$
$223$	8.86848			0.593877			0.296939	+	0.954897i	$0.404034\pi$
$224$	−10.8566	−	12.9384i	−0.725387	−	0.864483i
$225$	−1.46463	−	1.22897i	−0.0976420	−	0.0819314i
$226$	1.14156	−	6.47413i	0.0759356	−	0.430652i
$227$	2.02291	+	5.55789i	0.134265	+	0.368890i	0.988546	−	0.150922i	$-0.0482242\pi$
$227$	2.02291	+	5.55789i	0.134265	+	0.368890i	−0.854281	+	0.519812i	$0.826002\pi$
$228$		−	8.62244i		−	0.571035i
$229$	−16.6407	+	6.05671i	−1.09965	+	0.400239i	−0.827186	−	0.561928i	$-0.810060\pi$
$229$	−16.6407	+	6.05671i	−1.09965	+	0.400239i	−0.272461	+	0.962167i	$0.587838\pi$
$230$	−10.7807	+	6.22424i	−0.710858	+	0.410414i
$231$	0.250763	+	1.42215i	0.0164990	+	0.0935705i
$232$	−7.48348	+	12.9618i	−0.491314	+	0.850982i
$233$	−5.76176	−	9.97966i	−0.377465	−	0.653789i	0.613227	−	0.789906i	$-0.289871\pi$
$233$	−5.76176	−	9.97966i	−0.377465	−	0.653789i	−0.990693	+	0.136117i	$0.956538\pi$
$234$	2.31428	−	1.94191i	0.151289	−	0.126947i
$235$	−6.67337	−	1.17669i	−0.435322	−	0.0767591i
$236$	3.84722	+	2.22119i	0.250433	+	0.144587i
$237$	2.67379	−	7.34618i	0.173681	−	0.477186i
$238$	−10.8005	−	3.93106i	−0.700092	−	0.254813i
$239$	−6.07166	+	1.07060i	−0.392743	+	0.0692512i	−0.366533	−	0.930405i	$-0.619455\pi$
$239$	−6.07166	+	1.07060i	−0.392743	+	0.0692512i	−0.0262107	+	0.999656i	$0.508344\pi$
$240$	−2.01956	+	2.40682i	−0.130362	+	0.155359i
$241$	0.195861	−	0.233418i	0.0126165	−	0.0150358i	−0.759699	−	0.650275i	$-0.774654\pi$
$241$	0.195861	−	0.233418i	0.0126165	−	0.0150358i	0.772316	+	0.635239i	$0.219098\pi$
$242$	7.56823	−	1.33448i	0.486505	−	0.0857839i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	−2.78089	+	7.64044i	−0.178029	+	0.489129i
$245$	3.08986	+	1.78393i	0.197404	+	0.113971i
$246$	−2.56319	−	0.451960i	−0.163423	−	0.0288159i
$247$	18.7473	−	15.7309i	1.19286	−	1.00093i
$248$	−9.73177	−	16.8559i	−0.617968	−	1.07035i
$249$	−5.87823	+	10.1814i	−0.372518	+	0.645219i
$250$	1.00779	+	5.71549i	0.0637385	+	0.361479i
$251$	−7.90271	+	4.56263i	−0.498815	+	0.287991i	−0.728224	−	0.685339i	$-0.759654\pi$
$251$	−7.90271	+	4.56263i	−0.498815	+	0.287991i	0.229409	+	0.973330i	$0.426321\pi$
$252$	4.04487	−	1.47221i	0.254803	−	0.0927406i
$253$		−	3.30877i		−	0.208021i
$254$	1.59273	+	4.37599i	0.0999368	+	0.274574i
$255$	−2.53913	+	14.4001i	−0.159006	+	0.901770i
$256$	−8.43644	−	7.07901i	−0.527277	−	0.442438i
$257$	−12.4486	−	14.8356i	−0.776520	−	0.925420i	0.222251	−	0.974990i	$-0.428660\pi$
$257$	−12.4486	−	14.8356i	−0.776520	−	0.925420i	−0.998771	+	0.0495691i	$0.984215\pi$
$258$	3.63034			0.226015
$259$	15.1916	−	8.85587i	0.943962	−	0.550277i
$260$	−16.5439			−1.02601
$261$	−3.85732	−	4.59698i	−0.238762	−	0.284546i
$262$	5.82497	+	4.88773i	0.359868	+	0.301965i
$263$	−2.79635	+	15.8589i	−0.172430	+	0.977901i	0.768638	+	0.639684i	$0.220935\pi$
$263$	−2.79635	+	15.8589i	−0.172430	+	0.977901i	−0.941068	+	0.338217i	$0.890176\pi$
$264$	0.426121	+	1.17076i	0.0262259	+	0.0720552i
$265$		−	1.61555i		−	0.0992422i
$266$	−11.2452	+	4.09293i	−0.689490	+	0.250954i
$267$	13.2678	−	7.66017i	0.811976	−	0.468795i
$268$	−3.00096	−	17.0193i	−0.183313	−	1.03962i
$269$	1.39279	−	2.41238i	0.0849198	−	0.147085i	−0.820437	−	0.571737i	$-0.806270\pi$
$269$	1.39279	−	2.41238i	0.0849198	−	0.147085i	0.905357	+	0.424651i	$0.139603\pi$
$270$	0.939693	+	1.62760i	0.0571879	+	0.0990523i
$271$	−23.1099	+	19.3915i	−1.40383	+	1.17795i	−0.444460	+	0.895799i	$0.646605\pi$
$271$	−23.1099	+	19.3915i	−1.40383	+	1.17795i	−0.959369	+	0.282154i	$0.908951\pi$
$272$	6.54568	+	1.15418i	0.396890	+	0.0699824i
$273$	10.5804	+	6.10862i	0.640358	+	0.369711i
$274$	−3.89938	+	10.7134i	−0.235570	+	0.647223i
$275$	0.897482	+	0.326657i	0.0541202	+	0.0196981i
$276$	−9.71277	+	1.71262i	−0.584640	+	0.103088i
$277$	−17.5070	+	20.8640i	−1.05189	+	1.25360i	−0.0855493	+	0.996334i	$0.527265\pi$
$277$	−17.5070	+	20.8640i	−1.05189	+	1.25360i	−0.966342	+	0.257261i	$0.917180\pi$
$278$	−3.96984	+	4.73107i	−0.238095	+	0.283751i
$279$	7.68525	−	1.35512i	0.460104	−	0.0811287i
$280$	17.8126	+	6.48327i	1.06451	+	0.387450i
$281$	4.81806	−	13.2375i	0.287421	−	0.789684i	−0.709004	−	0.705205i	$-0.750855\pi$
$281$	4.81806	−	13.2375i	0.287421	−	0.789684i	0.996425	−	0.0844791i	$-0.0269226\pi$
$282$	1.59566	+	0.921254i	0.0950201	+	0.0548599i
$283$	10.7327	+	1.89246i	0.637991	+	0.112495i	0.483282	−	0.875465i	$-0.339445\pi$
$283$	10.7327	+	1.89246i	0.637991	+	0.112495i	0.154710	+	0.987960i	$0.450556\pi$
$284$	−8.40952	+	7.05643i	−0.499013	+	0.418722i
$285$	7.61218	+	13.1847i	0.450907	+	0.780994i
$286$	−0.754567	+	1.30695i	−0.0446185	+	0.0772815i
$287$	−1.82773	−	10.3656i	−0.107887	−	0.611860i
$288$	5.05976	−	2.92125i	0.298149	−	0.172136i
$289$	13.0932	−	4.76554i	0.770189	−	0.280326i
$290$		−	11.2781i		−	0.662270i
$291$	0.0985345	+	0.270721i	0.00577619	+	0.0158700i
$292$	2.90115	−	16.4532i	0.169777	−	0.962852i
$293$	23.0934	+	19.3777i	1.34913	+	1.13206i	0.979178	+	0.203006i	$0.0650710\pi$
$293$	23.0934	+	19.3777i	1.34913	+	1.13206i	0.369954	+	0.929050i	$0.379373\pi$
$294$	−0.623579	−	0.743152i	−0.0363679	−	0.0433415i
$295$	−7.84378			−0.456682
$296$	11.5808	−	9.80033i	0.673120	−	0.569633i
$297$	−0.499535			−0.0289860
$298$	4.47394	+	5.33184i	0.259169	+	0.308865i
$299$	−21.4437	−	17.9934i	−1.24012	−	1.04059i
$300$	0.494351	−	2.80360i	0.0285414	−	0.161866i
$301$	5.02124	+	13.7957i	0.289419	+	0.795173i
$302$		−	6.20920i		−	0.357299i
$303$	0.402522	−	0.146506i	0.0231243	−	0.00841655i
$304$	5.99320	−	3.46018i	0.343734	−	0.198455i
$305$	−2.49294	−	14.1382i	−0.142745	−	0.809549i
$306$	1.98793	−	3.44319i	0.113642	−	0.196834i
$307$	3.09379	+	5.35860i	0.176572	+	0.305832i	0.940704	−	0.339228i	$-0.110166\pi$
$307$	3.09379	+	5.35860i	0.176572	+	0.305832i	−0.764132	+	0.645060i	$0.776833\pi$
$308$	−1.64717	+	1.38214i	−0.0938562	+	0.0787547i
$309$	−17.9538	−	3.16574i	−1.02135	−	0.180092i
$310$	12.7014	+	7.33318i	0.721393	+	0.416497i
$311$	2.25118	−	6.18507i	0.127653	−	0.350723i	−0.859359	−	0.511373i	$-0.829137\pi$
$311$	2.25118	−	6.18507i	0.127653	−	0.350723i	0.987011	+	0.160650i	$0.0513592\pi$
$312$	9.90483	+	3.60506i	0.560750	+	0.204096i
$313$	17.5015	−	3.08599i	0.989244	−	0.174430i	0.344464	−	0.938799i	$-0.388061\pi$
$313$	17.5015	−	3.08599i	0.989244	−	0.174430i	0.644779	+	0.764369i	$0.276949\pi$
$314$	3.38870	−	4.03849i	0.191235	−	0.227905i
$315$	−4.88534	+	5.82212i	−0.275258	+	0.328039i
$316$	11.4635	−	2.02133i	0.644874	−	0.113709i
$317$	−11.8279	−	4.30500i	−0.664320	−	0.241793i	−0.0122195	−	0.999925i	$-0.503890\pi$
$317$	−11.8279	−	4.30500i	−0.664320	−	0.241793i	−0.652100	+	0.758133i	$0.726112\pi$
$318$	−0.150240	+	0.412782i	−0.00842507	+	0.0231477i
$319$	2.59606	+	1.49884i	0.145352	+	0.0839188i
$320$	4.62522	+	0.815551i	0.258558	+	0.0455907i
$321$	−4.04042	+	3.39031i	−0.225514	+	0.189229i
$322$	6.84406	+	11.8543i	0.381405	+	0.660612i
$323$	16.1036	−	27.8923i	0.896030	−	1.55197i
$324$	0.258560	+	1.46637i	0.0143644	+	0.0814648i
$325$	6.99762	−	4.04008i	0.388158	−	0.224103i
$326$	−0.162268	+	0.0590607i	−0.00898719	+	0.00327107i
$327$			6.82294i			0.377309i
$328$	−3.10585	−	8.53326i	−0.171492	−	0.471170i
$329$	−1.29387	+	7.33791i	−0.0713335	+	0.404552i
$330$	−0.719177	−	0.603461i	−0.0395894	−	0.0332194i
$331$	−9.96211	−	11.8724i	−0.547567	−	0.652565i	0.419299	−	0.907848i	$-0.362276\pi$
$331$	−9.96211	−	11.8724i	−0.547567	−	0.652565i	−0.966866	+	0.255283i	$0.917831\pi$
$332$	−17.5052			−0.960724
$333$	2.10433	+	5.70717i	0.115317	+	0.312751i
$334$	18.2512			0.998661
$335$	19.6140	+	23.3750i	1.07163	+	1.27711i
$336$	2.64649	+	2.22067i	0.144378	+	0.121147i
$337$	−0.159844	+	0.906520i	−0.00870725	+	0.0493813i	−0.988852	−	0.148903i	$-0.952426\pi$
$337$	−0.159844	+	0.906520i	−0.00870725	+	0.0493813i	0.980145	+	0.198284i	$0.0635369\pi$
$338$	1.18834	+	3.26494i	0.0646372	+	0.177589i
$339$			9.19631i			0.499475i
$340$	−20.4593	+	7.44658i	−1.10956	+	0.403848i
$341$	−3.37601	+	1.94914i	−0.182821	+	0.105552i
$342$	−0.718829	−	4.07668i	−0.0388698	−	0.220442i
$343$	−8.15644	+	14.1274i	−0.440406	+	0.762806i
$344$	6.33311	+	10.9693i	0.341458	+	0.591423i
$345$	13.3400	−	11.1936i	0.718199	−	0.602641i
$346$	−8.33039	−	1.46887i	−0.447844	−	0.0789670i
$347$	−18.6390	−	10.7613i	−1.00060	−	0.577694i	−0.0921715	−	0.995743i	$-0.529381\pi$
$347$	−18.6390	−	10.7613i	−1.00060	−	0.577694i	−0.908425	+	0.418049i	$0.862714\pi$
$348$	3.05605	−	8.39644i	0.163822	−	0.450096i
$349$	−7.86359	−	2.86211i	−0.420928	−	0.153205i	0.122867	−	0.992423i	$-0.460791\pi$
$349$	−7.86359	−	2.86211i	−0.420928	−	0.153205i	−0.543796	+	0.839218i	$0.683013\pi$
$350$	−3.89107	+	0.686100i	−0.207986	+	0.0366736i
$351$	−2.71652	+	3.23743i	−0.144997	+	0.172801i
$352$	−1.87600	+	2.23573i	−0.0999911	+	0.119165i
$353$	22.4340	−	3.95572i	1.19404	−	0.210542i	0.458920	−	0.888478i	$-0.348237\pi$
$353$	22.4340	−	3.95572i	1.19404	−	0.210542i	0.735121	+	0.677936i	$0.237125\pi$
$354$	2.00413	+	0.729445i	0.106519	+	0.0387696i
$355$	6.62946	−	18.2143i	0.351855	−	0.966714i
$356$	19.7556	+	11.4059i	1.04704	+	0.604511i
$357$	15.8341	+	2.79198i	0.838030	+	0.147767i
$358$	11.5880	−	9.72349i	0.612445	−	0.513902i
$359$	−14.5953	−	25.2798i	−0.770311	−	1.33422i	−0.937393	−	0.348274i	$-0.886768\pi$
$359$	−14.5953	−	25.2798i	−0.770311	−	1.33422i	0.167082	−	0.985943i	$-0.446565\pi$
$360$	−3.27858	+	5.67866i	−0.172796	+	0.299292i
$361$	−2.52371	−	14.3127i	−0.132827	−	0.753300i
$362$	−13.5963	+	7.84984i	−0.714606	+	0.412578i
$363$	−10.1021	+	3.67688i	−0.530224	+	0.192986i
$364$			18.1913i			0.953484i
$365$	10.0893	+	27.7201i	0.528097	+	1.45093i
$366$	−0.677841	+	3.84423i	−0.0354313	+	0.200941i
$367$	−5.72866	−	4.80692i	−0.299034	−	0.250919i	0.480908	−	0.876771i	$-0.340307\pi$
$367$	−5.72866	−	4.80692i	−0.299034	−	0.250919i	−0.779942	+	0.625852i	$0.784751\pi$
$368$	−5.08811	−	6.06378i	−0.265236	−	0.316096i
$369$	3.64094			0.189540
$370$	−3.86493	+	10.7587i	−0.200928	+	0.559318i
$371$	−1.77643			−0.0922274
$372$	7.46904	+	8.90126i	0.387252	+	0.461509i
$373$	19.6813	+	16.5146i	1.01906	+	0.855094i	0.989509	−	0.144470i	$-0.0461476\pi$
$373$	19.6813	+	16.5146i	1.01906	+	0.855094i	0.0295516	+	0.999563i	$0.490592\pi$
$374$	−0.344879	+	1.95591i	−0.0178333	+	0.101137i
$375$	−2.77675	−	7.62907i	−0.143391	−	0.393964i
$376$			6.42849i			0.331524i
$377$	23.8314	−	8.67393i	1.22738	−	0.446730i
$378$	1.78967	−	1.03327i	0.0920509	−	0.0531456i
$379$	−0.861299	−	4.88467i	−0.0442420	−	0.250909i	0.954663	−	0.297688i	$-0.0962154\pi$
$379$	−0.861299	−	4.88467i	−0.0442420	−	0.250909i	−0.998905	+	0.0467791i	$0.985104\pi$
$380$	−11.3344	+	19.6318i	−0.581445	+	1.00709i
$381$	−3.25720	−	5.64164i	−0.166872	−	0.289030i
$382$	−0.655734	+	0.550226i	−0.0335503	+	0.0281520i
$383$	−17.2652	−	3.04432i	−0.882210	−	0.155557i	−0.285850	−	0.958274i	$-0.592276\pi$
$383$	−17.2652	−	3.04432i	−0.882210	−	0.155557i	−0.596360	+	0.802717i	$0.703387\pi$
$384$	9.01359	+	5.20400i	0.459973	+	0.265565i
$385$	1.29851	−	3.56763i	0.0661782	−	0.181823i
$386$	−5.86324	−	2.13404i	−0.298431	−	0.108620i
$387$	−5.00130	+	0.881864i	−0.254230	+	0.0448277i
$388$	−0.275737	+	0.328611i	−0.0139984	+	0.0166827i
$389$	8.56811	−	10.2111i	0.434420	−	0.517722i	−0.503772	−	0.863837i	$-0.668055\pi$
$389$	8.56811	−	10.2111i	0.434420	−	0.517722i	0.938192	+	0.346115i	$0.112499\pi$
$390$	−7.82191	+	1.37921i	−0.396078	+	0.0698392i
$391$	−34.6179	−	12.5999i	−1.75070	−	0.637204i
$392$	1.15764	−	3.18060i	0.0584698	−	0.160645i
$393$	−9.21202	−	5.31856i	−0.464685	−	0.268286i
$394$	−17.6986	−	3.12075i	−0.891644	−	0.157221i
$395$	−15.7445	+	13.2112i	−0.792193	+	0.664729i
$396$	−0.371901	−	0.644151i	−0.0186887	−	0.0323698i
$397$	−2.49901	+	4.32840i	−0.125421	+	0.217236i	−0.921898	−	0.387434i	$-0.873362\pi$
$397$	−2.49901	+	4.32840i	−0.125421	+	0.217236i	0.796476	+	0.604670i	$0.206695\pi$
$398$	−1.21729	−	6.90357i	−0.0610171	−	0.346045i
$399$	14.4976	−	8.37022i	0.725790	−	0.419035i
$400$	2.14708	−	0.781474i	0.107354	−	0.0390737i
$401$		−	18.2354i		−	0.910632i	−0.890330	−	0.455316i	$-0.849526\pi$
$401$		−	18.2354i		−	0.910632i	0.890330	−	0.455316i	$-0.150474\pi$
$402$	−2.83770	−	7.79651i	−0.141531	−	0.388854i
$403$	−5.72694	+	32.4791i	−0.285279	+	1.61790i
$404$	0.488595	+	0.409980i	0.0243085	+	0.0203972i
$405$	−1.68993	−	2.01397i	−0.0839731	−	0.100075i
$406$	−12.4011			−0.615458
$407$	−1.96287	−	2.31947i	−0.0972958	−	0.114972i
$408$	13.8717			0.686752
$409$	−5.70706	−	6.80142i	−0.282196	−	0.336308i	0.606263	−	0.795264i	$-0.292668\pi$
$409$	−5.70706	−	6.80142i	−0.282196	−	0.336308i	−0.888459	+	0.458956i	$0.848224\pi$
$410$	5.24184	+	4.39843i	0.258876	+	0.217223i
$411$	2.76948	−	15.7065i	0.136608	−	0.774744i
$412$	−9.28426	−	25.5083i	−0.457403	−	1.25670i
$413$			8.62487i			0.424402i
$414$	−4.44941	+	1.61945i	−0.218676	+	0.0795917i
$415$	26.7675	−	15.4542i	1.31396	−	0.758617i
$416$	4.28761	+	24.3162i	0.210217	+	1.19220i
$417$	4.31976	−	7.48204i	0.211540	−	0.366397i
$418$	1.03393	+	1.79082i	0.0505712	+	0.0875919i
$419$	21.1559	−	17.7519i	1.03353	−	0.867237i	0.0422652	−	0.999106i	$-0.486543\pi$
$419$	21.1559	−	17.7519i	1.03353	−	0.867237i	0.991267	+	0.131870i	$0.0420981\pi$
$420$	−11.1447	−	1.96512i	−0.543808	−	0.0958879i
$421$	23.8782	+	13.7861i	1.16375	+	0.671892i	0.952200	−	0.305474i	$-0.0988150\pi$
$421$	23.8782	+	13.7861i	1.16375	+	0.671892i	0.211552	+	0.977367i	$0.432148\pi$
$422$	−2.85809	+	7.85254i	−0.139130	+	0.382256i
$423$	−2.42203	−	0.881546i	−0.117763	−	0.0428623i
$424$	−1.50934	+	0.266137i	−0.0732999	+	0.0129247i
$425$	6.83528	−	8.14596i	0.331560	−	0.395137i
$426$	−3.38774	+	4.03735i	−0.164136	+	0.195610i
$427$	−15.5461	+	2.74119i	−0.752327	+	0.132656i
$428$	−7.37988	−	2.68606i	−0.356720	−	0.129835i
$429$	0.722044	−	1.98380i	0.0348606	−	0.0957787i
$430$	−8.26567	−	4.77219i	−0.398606	−	0.230135i
$431$	−6.31613	−	1.11370i	−0.304237	−	0.0536452i	0.0194454	−	0.999811i	$-0.493810\pi$
$431$	−6.31613	−	1.11370i	−0.304237	−	0.0536452i	−0.323683	+	0.946166i	$0.604921\pi$
$432$	−0.915467	+	0.768168i	−0.0440454	+	0.0369585i
$433$	−12.2312	−	21.1851i	−0.587795	−	1.01809i	−0.994521	−	0.104541i	$-0.966663\pi$
$433$	−12.2312	−	21.1851i	−0.587795	−	1.01809i	0.406725	−	0.913551i	$-0.366671\pi$
$434$	8.06343	−	13.9663i	0.387057	−	0.670403i
$435$	2.73961	+	15.5371i	0.131354	+	0.744947i
$436$	−8.79819	+	5.07964i	−0.421357	+	0.243270i
$437$	−36.0434	+	13.1187i	−1.72419	+	0.627554i
$438$		−	8.02092i		−	0.383254i
$439$	−0.0536597	−	0.147429i	−0.00256104	−	0.00703640i	0.938406	−	0.345536i	$-0.112303\pi$
$439$	−0.0536597	−	0.147429i	−0.00256104	−	0.00703640i	−0.940967	+	0.338500i	$0.890081\pi$
$440$	0.568789	−	3.22576i	0.0271160	−	0.153782i
$441$	1.03959	+	0.872319i	0.0495043	+	0.0415390i
$442$	10.8005	+	12.8715i	0.513727	+	0.612236i
$443$	2.48937			0.118274			0.0591368	−	0.998250i	$-0.481165\pi$
$443$	2.48937			0.118274			0.0591368	+	0.998250i	$0.481165\pi$
$444$	−5.79274	+	6.96249i	−0.274911	+	0.330425i
$445$	−40.2780			−1.90936
$446$	4.07504	+	4.85645i	0.192959	+	0.229959i
$447$	−7.45866	−	6.25856i	−0.352783	−	0.296020i
$448$	0.896765	−	5.08580i	0.0423681	−	0.240282i
$449$	11.7792	+	32.3630i	0.555894	+	1.52731i	0.825538	+	0.564347i	$0.190872\pi$
$449$	11.7792	+	32.3630i	0.555894	+	1.52731i	−0.269644	+	0.962960i	$0.586906\pi$
$450$		−	1.36675i		−	0.0644293i
$451$	−1.70909	+	0.622059i	−0.0804781	+	0.0292916i
$452$	−11.8587	+	6.84660i	−0.557784	+	0.322037i
$453$	1.50831	+	8.55404i	0.0708665	+	0.401904i
$454$	−2.11403	+	3.66160i	−0.0992161	+	0.171847i
$455$	−16.0599	−	27.8166i	−0.752900	−	1.30406i
$456$	11.0639	−	9.28372i	0.518115	−	0.434750i
$457$	30.1668	+	5.31923i	1.41115	+	0.248823i	0.826715	−	0.562621i	$-0.190207\pi$
$457$	30.1668	+	5.31923i	1.41115	+	0.248823i	0.584430	+	0.811444i	$0.301318\pi$
$458$	−10.9631	−	6.32952i	−0.512270	−	0.295759i
$459$	−1.90224	+	5.22637i	−0.0887891	+	0.243946i
$460$	24.3656	+	8.86836i	1.13605	+	0.413489i
$461$	12.9566	−	2.28459i	0.603448	−	0.106404i	0.136426	−	0.990650i	$-0.456438\pi$
$461$	12.9566	−	2.28459i	0.603448	−	0.106404i	0.467021	+	0.884246i	$0.345327\pi$
$462$	−0.663555	+	0.790794i	−0.0308714	+	0.0367911i
$463$	−9.49510	+	11.3158i	−0.441275	+	0.525891i	−0.940140	−	0.340789i	$-0.889306\pi$
$463$	−9.49510	+	11.3158i	−0.441275	+	0.525891i	0.498865	+	0.866680i	$0.333750\pi$
$464$	7.06250	−	1.24531i	0.327868	−	0.0578121i
$465$	−19.2793	−	7.01711i	−0.894058	−	0.325411i
$466$	2.81743	−	7.74082i	0.130515	−	0.358586i
$467$	9.17380	+	5.29649i	0.424513	+	0.245093i	0.697006	−	0.717065i	$-0.254515\pi$
$467$	9.17380	+	5.29649i	0.424513	+	0.245093i	−0.272494	+	0.962158i	$0.587848\pi$
$468$	−6.19710	−	1.09272i	−0.286461	−	0.0505108i
$469$	25.7028	−	21.5672i	1.18684	−	0.995880i
$470$	−2.42203	−	4.19508i	−0.111720	−	0.193504i
$471$	−3.68739	+	6.38675i	−0.169906	+	0.294286i
$472$	1.29214	+	7.32811i	0.0594757	+	0.337304i
$473$	2.19699	−	1.26843i	0.101018	−	0.0583226i
$474$	5.25143	−	1.91136i	0.241206	−	0.0877918i
$475$		−	11.0717i		−	0.508003i
$476$	8.18813	+	22.4967i	0.375302	+	1.03113i
$477$	0.106706	−	0.605161i	0.00488574	−	0.0277084i
$478$	−3.37618	−	2.83295i	−0.154423	−	0.129576i
$479$	7.99757	+	9.53113i	0.365418	+	0.435489i	0.917156	−	0.398529i	$-0.130479\pi$
$479$	7.99757	+	9.53113i	0.365418	+	0.435489i	−0.551737	+	0.834018i	$0.686035\pi$
$480$	−15.3603			−0.701097
$481$	−25.7065	+	0.107590i	−1.17212	+	0.00490566i
$482$	0.217820			0.00992141
$483$	−12.3082	−	14.6684i	−0.560044	−	0.667434i
$484$	−12.2623	−	10.2893i	−0.557378	−	0.467695i
$485$	0.131525	−	0.745913i	0.00597222	−	0.0338702i
$486$	0.244494	+	0.671741i	0.0110905	+	0.0304708i
$487$			3.39573i			0.153875i	0.997036	+	0.0769376i	$0.0245142\pi$
$487$			3.39573i			0.153875i	−0.997036	+	0.0769376i	$0.975486\pi$
$488$	−12.7980	+	4.65810i	−0.579339	+	0.210862i
$489$	0.209200	−	0.120782i	0.00946035	−	0.00546194i
$490$	0.442888	+	2.51174i	0.0200076	+	0.113469i
$491$	0.178442	−	0.309070i	0.00805296	−	0.0139481i	−0.861971	−	0.506958i	$-0.830770\pi$
$491$	0.178442	−	0.309070i	0.00805296	−	0.0139481i	0.870024	+	0.493010i	$0.164103\pi$
$492$	2.71066	+	4.69500i	0.122206	+	0.211667i
$493$	25.5674	−	21.4536i	1.15150	−	0.966222i
$494$	17.2287	+	3.03788i	0.775156	+	0.136681i
$495$	1.13736	+	0.656653i	0.0511204	+	0.0295144i
$496$	−3.18968	+	8.76357i	−0.143221	+	0.393496i
$497$	−20.0281	−	7.28963i	−0.898383	−	0.326985i
$498$	−8.27644	+	1.45936i	−0.370876	+	0.0653955i
$499$	−18.2070	+	21.6982i	−0.815056	+	0.971345i	−0.999935	−	0.0114159i	$-0.996366\pi$
$499$	−18.2070	+	21.6982i	−0.815056	+	0.971345i	0.184879	+	0.982761i	$0.440811\pi$
$500$	7.77042	−	9.26042i	0.347504	−	0.414139i
$501$	−25.1436	+	4.43349i	−1.12333	+	0.198074i
$502$	−6.12981	−	2.23107i	−0.273587	−	0.0995775i
$503$	−3.20686	+	8.81078i	−0.142987	+	0.392853i	−0.990427	−	0.138038i	$-0.955920\pi$
$503$	−3.20686	+	8.81078i	−0.142987	+	0.392853i	0.847440	+	0.530891i	$0.178143\pi$
$504$	6.24415	+	3.60506i	0.278137	+	0.160582i
$505$	−1.10906	−	0.195557i	−0.0493525	−	0.00870218i
$506$	1.81191	−	1.52037i	0.0805492	−	0.0675888i
$507$	−2.43021	−	4.20925i	−0.107929	−	0.186939i
$508$	4.84994	−	8.40033i	0.215181	−	0.372705i
$509$	2.36211	+	13.3962i	0.104699	+	0.593776i	0.991340	+	0.131318i	$0.0419210\pi$
$509$	2.36211	+	13.3962i	0.104699	+	0.593776i	−0.886642	+	0.462457i	$0.846968\pi$
$510$	−9.05234	+	5.22637i	−0.400844	+	0.231428i
$511$	30.4805	−	11.0940i	1.34838	−	0.490769i
$512$			12.9433i			0.572020i
$513$	1.98057	+	5.44158i	0.0874445	+	0.240252i
$514$	2.40402	−	13.6339i	0.106037	−	0.601364i
$515$	36.7163	+	30.8086i	1.61791	+	1.35759i
$516$	−4.86060	−	5.79264i	−0.213976	−	0.255007i
$517$	1.28754			0.0566258
$518$	11.8301	+	4.24981i	0.519783	+	0.186726i
$519$	11.8331			0.519415
$520$	−17.8126	−	21.2283i	−0.781136	−	0.930922i
$521$	32.7532	+	27.4832i	1.43494	+	1.20406i	0.942718	+	0.333591i	$0.108261\pi$
$521$	32.7532	+	27.4832i	1.43494	+	1.20406i	0.492225	+	0.870468i	$0.336184\pi$
$522$	0.744911	−	4.22460i	0.0326039	−	0.184906i
$523$	−9.08449	−	24.9594i	−0.397237	−	1.09140i	−0.963624	−	0.267260i	$-0.913882\pi$
$523$	−9.08449	−	24.9594i	−0.397237	−	1.09140i	0.566388	−	0.824139i	$-0.308341\pi$
$524$		−	15.8385i		−	0.691910i
$525$	5.19383	−	1.89040i	0.226677	−	0.0825037i
$526$	−9.96937	+	5.75582i	−0.434685	+	0.250966i
$527$	7.53687	+	42.7437i	0.328311	+	1.86195i
$528$	0.298487	−	0.516994i	0.0129900	−	0.0224993i
$529$	10.4367	+	18.0769i	0.453769	+	0.785951i
$530$	0.884686	−	0.742340i	0.0384283	−	0.0322452i
$531$	−2.93817	−	0.518078i	−0.127506	−	0.0224827i
$532$	21.5868	+	12.4632i	0.935907	+	0.540346i
$533$	−5.26273	+	14.4592i	−0.227954	+	0.626299i
$534$	10.2913	+	3.74573i	0.445348	+	0.162093i
$535$	13.6560	−	2.40792i	0.590401	−	0.104104i
$536$	18.6072	−	22.1752i	0.803709	−	0.957823i
$537$	−13.6021	+	16.2104i	−0.586974	+	0.699529i
$538$	1.96102	−	0.345781i	0.0845457	−	0.0149077i
$539$	−0.637030	−	0.231860i	−0.0274388	−	0.00998692i
$540$	1.33888	−	3.67855i	0.0576163	−	0.158300i
$541$	−15.0335	−	8.67959i	−0.646340	−	0.373165i	0.140712	−	0.990051i	$-0.455061\pi$
$541$	−15.0335	−	8.67959i	−0.646340	−	0.373165i	−0.787053	+	0.616886i	$0.788394\pi$
$542$	−21.2379	−	3.74482i	−0.912248	−	0.160854i
$543$	16.8240	−	14.1170i	0.721986	−	0.605818i
$544$	16.2474	+	28.1413i	0.696601	+	1.20655i
$545$	8.96895	−	15.5347i	0.384188	−	0.665432i
$546$	1.51656	+	8.60084i	0.0649027	+	0.368082i
$547$	−22.9775	+	13.2661i	−0.982446	+	0.567216i	−0.903008	−	0.429624i	$-0.858646\pi$
$547$	−22.9775	+	13.2661i	−0.982446	+	0.567216i	−0.0794384	+	0.996840i	$0.525313\pi$
$548$	22.3154	−	8.12213i	0.953266	−	0.346960i
$549$		−	5.46062i		−	0.233054i
$550$	0.233511	+	0.641567i	0.00995695	+	0.0273565i
$551$	6.03431	−	34.2223i	0.257070	−	1.45792i
$552$	−12.6552	−	10.6190i	−0.538642	−	0.451974i
$553$	14.5268	+	17.3124i	0.617743	+	0.736198i
$554$	−19.4697			−0.827188
$555$	2.71103	−	15.7605i	0.115077	−	0.668994i
$556$	12.8641			0.545561
$557$	−8.42459	−	10.0400i	−0.356961	−	0.425410i	0.557441	−	0.830217i	$-0.311783\pi$
$557$	−8.42459	−	10.0400i	−0.356961	−	0.425410i	−0.914402	+	0.404807i	$0.867339\pi$
$558$	4.27343	+	3.58583i	0.180909	+	0.151800i
$559$	3.72690	−	21.1363i	0.157631	−	0.893970i
$560$	−3.10648	−	8.53497i	−0.131273	−	0.360668i
$561$		−	2.77831i		−	0.117300i
$562$	9.46285	−	3.44420i	0.399166	−	0.145285i
$563$	0.411062	−	0.237327i	0.0173242	−	0.0100021i	−0.491313	−	0.870983i	$-0.663483\pi$
$563$	0.411062	−	0.237327i	0.0173242	−	0.0100021i	0.508637	+	0.860981i	$0.330150\pi$
$564$	−0.666430	−	3.77951i	−0.0280618	−	0.159146i
$565$	12.0888	−	20.9384i	0.508580	−	0.880887i
$566$	3.89531	+	6.74688i	0.163732	+	0.283593i
$567$	−2.21453	+	1.85821i	−0.0930015	+	0.0780375i
$568$	−18.1089	−	3.19309i	−0.759834	−	0.133979i
$569$	−22.1280	−	12.7756i	−0.927652	−	0.535580i	−0.0415841	−	0.999135i	$-0.513240\pi$
$569$	−22.1280	−	12.7756i	−0.927652	−	0.535580i	−0.886068	+	0.463555i	$0.846574\pi$
$570$	−3.72226	+	10.2268i	−0.155908	+	0.428355i
$571$	17.0714	+	6.21347i	0.714415	+	0.260026i	0.673553	−	0.739139i	$-0.264767\pi$
$571$	17.0714	+	6.21347i	0.714415	+	0.260026i	0.0408621	+	0.999165i	$0.486990\pi$
$572$	3.09567	−	0.545850i	0.129436	−	0.0228231i
$573$	0.769707	−	0.917301i	0.0321550	−	0.0383208i
$574$	4.83643	−	5.76383i	0.201869	−	0.240578i
$575$	−12.4717	+	2.19910i	−0.520106	+	0.0917088i
$576$	1.67867	+	0.610988i	0.0699448	+	0.0254578i
$577$	−9.35837	+	25.7119i	−0.389594	+	1.07040i	0.577591	+	0.816326i	$0.303993\pi$
$577$	−9.35837	+	25.7119i	−0.389594	+	1.07040i	−0.967185	+	0.254074i	$0.918229\pi$
$578$	8.62594	+	4.98019i	0.358792	+	0.207149i
$579$	8.59582	+	1.51567i	0.357230	+	0.0629893i
$580$	−17.9955	+	15.1000i	−0.747221	+	0.626993i
$581$	−16.9932	−	29.4330i	−0.704995	−	1.22109i
$582$	−0.102973	+	0.178354i	−0.00426836	+	0.00739302i
$583$	0.0533035	+	0.302299i	0.00220761	+	0.0125200i
$584$	24.2356	−	13.9924i	1.00288	−	0.579012i
$585$	10.4407	−	3.80012i	0.431672	−	0.157116i
$586$			21.5501i			0.890228i
$587$	−5.66080	−	15.5529i	−0.233646	−	0.641938i	0.766353	−	0.642419i	$-0.222069\pi$
$587$	−5.66080	−	15.5529i	−0.233646	−	0.641938i	−1.00000		0.000480919i	$0.999847\pi$
$588$	−0.350889	+	1.98999i	−0.0144704	+	0.0820657i
$589$	34.6178	+	29.0478i	1.42640	+	1.19689i
$590$	−3.60420	−	4.29531i	−0.148382	−	0.176835i
$591$	25.1404			1.03414
$592$	−7.16404	−	1.23232i	−0.294440	−	0.0506480i
$593$	20.9159			0.858914			0.429457	−	0.903087i	$-0.358705\pi$
$593$	20.9159			0.858914			0.429457	+	0.903087i	$0.358705\pi$
$594$	−0.229535	−	0.273549i	−0.00941795	−	0.0112239i
$595$	−32.3814	−	27.1712i	−1.32751	−	1.11391i
$596$	2.51749	−	14.2774i	0.103121	−	0.584826i
$597$	3.35396	+	9.21494i	0.137269	+	0.377142i
$598$		−	20.0107i		−	0.818298i
$599$	2.65557	−	0.966548i	0.108504	−	0.0394921i	−0.287198	−	0.957871i	$-0.592724\pi$
$599$	2.65557	−	0.966548i	0.108504	−	0.0394921i	0.395701	+	0.918379i	$0.370502\pi$
$600$	4.12971	−	2.38429i	0.168595	−	0.0973383i
$601$	−4.22321	−	23.9510i	−0.172268	−	0.976981i	−0.941250	−	0.337711i	$-0.890347\pi$
$601$	−4.22321	−	23.9510i	−0.172268	−	0.976981i	0.768982	−	0.639271i	$-0.220764\pi$
$602$	−5.24741	+	9.08878i	−0.213868	+	0.370431i
$603$	5.80321	+	10.0515i	0.236325	+	0.409327i
$604$	−9.90752	+	8.31339i	−0.403131	+	0.338267i
$605$	27.8342	+	4.90792i	1.13162	+	0.199535i
$606$	0.265186	+	0.153105i	0.0107724	+	0.00621947i
$607$	1.64248	−	4.51267i	0.0666662	−	0.183164i	−0.901886	−	0.431974i	$-0.857817\pi$
$607$	1.64248	−	4.51267i	0.0666662	−	0.183164i	0.968552	+	0.248810i	$0.0800395\pi$
$608$	31.7925	+	11.5715i	1.28935	+	0.469287i
$609$	17.0843	−	3.01242i	0.692291	−	0.122070i
$610$	6.59668	−	7.86161i	0.267092	−	0.318307i
$611$	7.00175	−	8.34436i	0.283261	−	0.337577i
$612$	−8.15562	+	1.43806i	−0.329671	+	0.0581300i
$613$	−2.53326	−	0.922032i	−0.102318	−	0.0372405i	0.290354	−	0.956919i	$-0.406227\pi$
$613$	−2.53326	−	0.922032i	−0.102318	−	0.0372405i	−0.392672	+	0.919679i	$0.628449\pi$
$614$	−1.51282	+	4.15645i	−0.0610526	+	0.167741i
$615$	−8.28981	−	4.78612i	−0.334277	−	0.192995i
$616$	−3.54699	−	0.625430i	−0.142912	−	0.0251993i
$617$	−23.6332	+	19.8306i	−0.951437	+	0.798350i	−0.979539	−	0.201255i	$-0.935498\pi$
$617$	−23.6332	+	19.8306i	−0.951437	+	0.798350i	0.0281020	+	0.999605i	$0.491054\pi$
$618$	−6.51614	−	11.2863i	−0.262118	−	0.454001i
$619$	−3.55412	+	6.15591i	−0.142852	+	0.247427i	−0.928569	−	0.371159i	$-0.878961\pi$
$619$	−3.55412	+	6.15591i	−0.142852	+	0.247427i	0.785718	+	0.618585i	$0.212294\pi$
$620$	−5.30478	−	30.0849i	−0.213045	−	1.20824i
$621$	5.73629	−	3.31185i	0.230189	−	0.132900i
$622$	4.42140	−	1.60926i	0.177282	−	0.0645254i
$623$			44.2890i			1.77440i
$624$	−1.72737	−	4.74592i	−0.0691503	−	0.189989i
$625$	−5.36646	+	30.4347i	−0.214658	+	1.21739i
$626$	9.73181	+	8.16596i	0.388961	+	0.326377i
$627$	−1.85940	−	2.21595i	−0.0742573	−	0.0884964i
$628$	−10.9810			−0.438188
$629$	−31.7421	+	11.7038i	−1.26564	+	0.466663i
$630$	−5.43304			−0.216458
$631$	22.9890	+	27.3972i	0.915178	+	1.09067i	0.995581	+	0.0939039i	$0.0299346\pi$
$631$	22.9890	+	27.3972i	0.915178	+	1.09067i	−0.0804036	+	0.996762i	$0.525621\pi$
$632$	14.9364	+	12.5331i	0.594137	+	0.498540i
$633$	2.02992	−	11.5122i	0.0806820	−	0.457571i
$634$	−3.07743	−	8.45518i	−0.122220	−	0.335798i
$635$			17.1267i			0.679654i
$636$	0.859798	−	0.312941i	0.0340932	−	0.0124089i
$637$	−4.96689	+	2.86763i	−0.196795	+	0.113620i
$638$	0.372109	+	2.11034i	0.0147319	+	0.0835490i
$639$	3.68635	−	6.38494i	0.145830	−	0.252584i
$640$	−13.6816	−	23.6972i	−0.540813	−	0.936715i
$641$	−28.5475	+	23.9542i	−1.12756	+	0.946134i	−0.998961	−	0.0455629i	$-0.985492\pi$
$641$	−28.5475	+	23.9542i	−1.12756	+	0.946134i	−0.128597	+	0.991697i	$0.541047\pi$
$642$	−3.71313	−	0.654724i	−0.146545	−	0.0258399i
$643$	−28.7836	−	16.6182i	−1.13511	−	0.655358i	−0.189897	−	0.981804i	$-0.560815\pi$
$643$	−28.7836	−	16.6182i	−1.13511	−	0.655358i	−0.945216	+	0.326446i	$0.894149\pi$
$644$	9.75148	−	26.7920i	0.384262	−	1.05575i
$645$	12.5463	+	4.56650i	0.494012	+	0.179806i
$646$	22.6736	−	3.99797i	0.892082	−	0.157298i
$647$	−17.6705	+	21.0589i	−0.694700	+	0.827912i	−0.991916	−	0.126899i	$-0.959498\pi$
$647$	−17.6705	+	21.0589i	−0.694700	+	0.827912i	0.297215	+	0.954810i	$0.403942\pi$
$648$	−1.60318	+	1.91060i	−0.0629789	+	0.0750554i
$649$	1.46772	−	0.258798i	0.0576130	−	0.0101587i
$650$	5.42777	+	1.97555i	0.212895	+	0.0774873i
$651$	−7.71588	+	21.1992i	−0.302409	+	0.830863i
$652$	0.311496	+	0.179842i	0.0121991	+	0.00704317i
$653$	−16.9377	−	2.98657i	−0.662823	−	0.116874i	−0.167891	−	0.985806i	$-0.553696\pi$
$653$	−16.9377	−	2.98657i	−0.662823	−	0.116874i	−0.494931	+	0.868932i	$0.664807\pi$
$654$	−3.73630	+	3.13513i	−0.146101	+	0.122593i
$655$	13.9828	+	24.2189i	0.546353	+	0.946311i
$656$	−2.17557	+	3.76819i	−0.0849417	+	0.147123i
$657$	1.94840	+	11.0499i	0.0760144	+	0.431099i
$658$	−4.61283	+	2.66322i	−0.179827	+	0.103823i
$659$	−29.4449	+	10.7171i	−1.14701	+	0.417477i	−0.844440	−	0.535650i	$-0.820067\pi$
$659$	−29.4449	+	10.7171i	−1.14701	+	0.417477i	−0.302569	+	0.953127i	$0.597844\pi$
$660$			1.95550i			0.0761176i
$661$	−11.4856	−	31.5564i	−0.446737	−	1.22740i	−0.934982	−	0.354694i	$-0.884585\pi$
$661$	−11.4856	−	31.5564i	−0.446737	−	1.22740i	0.488245	−	0.872706i	$-0.337637\pi$
$662$	1.92384	−	10.9107i	0.0747723	−	0.424055i
$663$	−18.0059	−	15.1087i	−0.699290	−	0.586774i
$664$	−18.8477	−	22.4619i	−0.731434	−	0.871689i
$665$	−44.0116			−1.70670
$666$	−2.15836	+	3.77478i	−0.0836346	+	0.146270i
$667$	−39.7483			−1.53906
$668$	−24.4362	−	29.1219i	−0.945465	−	1.12676i
$669$	−6.79365	−	5.70055i	−0.262658	−	0.220396i
$670$	−3.78778	+	21.4815i	−0.146335	+	0.829905i
$671$	0.932953	+	2.56327i	0.0360162	+	0.0989538i
$672$			16.8899i			0.651541i
$673$	9.61271	−	3.49874i	0.370543	−	0.134866i	−0.150035	−	0.988681i	$-0.547939\pi$
$673$	9.61271	−	3.49874i	0.370543	−	0.134866i	0.520578	+	0.853814i	$0.325717\pi$
$674$	−0.569865	+	0.329012i	−0.0219504	+	0.0126731i
$675$	0.332005	+	1.88289i	0.0127789	+	0.0724726i
$676$	3.61855	−	6.26751i	0.139175	−	0.241058i
$677$	−13.8509	−	23.9905i	−0.532334	−	0.922030i	−0.999287	−	0.0377480i	$-0.987982\pi$
$677$	−13.8509	−	23.9905i	−0.532334	−	0.922030i	0.466953	−	0.884282i	$-0.345352\pi$
$678$	−5.03598	+	4.22569i	−0.193405	+	0.162286i
$679$	−0.820192	−	0.144622i	−0.0314761	−	0.00555008i
$680$	−31.5835	−	18.2347i	−1.21117	−	0.699271i
$681$	2.02291	−	5.55789i	0.0775180	−	0.212979i
$682$	−2.61863	−	0.953104i	−0.100273	−	0.0364962i
$683$	43.0286	−	7.58710i	1.64644	−	0.290312i	0.727915	−	0.685667i	$-0.240490\pi$
$683$	43.0286	−	7.58710i	1.64644	−	0.290312i	0.918528	+	0.395355i	$0.129378\pi$
$684$	−5.54240	+	6.60517i	−0.211919	+	0.252555i
$685$	−26.9522	+	32.1204i	−1.02979	+	1.22726i
$686$	−11.4841	+	2.02496i	−0.438466	+	0.0773134i
$687$	16.6407	+	6.05671i	0.634881	+	0.231078i
$688$	2.07574	−	5.70304i	0.0791367	−	0.217426i
$689$	2.24903	+	1.29848i	0.0856813	+	0.0494681i
$690$	12.2594	+	2.16166i	0.466706	+	0.0822928i
$691$	16.1978	−	13.5915i	0.616192	−	0.517047i	−0.280412	−	0.959880i	$-0.590471\pi$
$691$	16.1978	−	13.5915i	0.616192	−	0.517047i	0.896604	+	0.442833i	$0.146027\pi$
$692$	8.80965	+	15.2588i	0.334893	+	0.580051i
$693$	0.722044	−	1.25062i	0.0274282	−	0.0475070i
$694$	−2.67165	−	15.1517i	−0.101414	−	0.575149i
$695$	−19.6707	+	11.3569i	−0.746153	+	0.430791i
$696$	14.0643	−	5.11900i	0.533107	−	0.194035i
$697$			20.2502i			0.767029i
$698$	−2.04599	−	5.62130i	−0.0774417	−	0.212769i
$699$	−2.00104	+	11.3484i	−0.0756862	+	0.429238i
$700$	6.30444	+	5.29005i	0.238285	+	0.199945i
$701$	6.60042	+	7.86608i	0.249295	+	0.297098i	0.876151	−	0.482037i	$-0.160103\pi$
$701$	6.60042	+	7.86608i	0.249295	+	0.297098i	−0.626856	+	0.779135i	$0.715659\pi$
$702$	−3.02108			−0.114023
$703$	−17.4842	+	30.5784i	−0.659430	+	1.15329i
$704$	−0.892374			−0.0336326
$705$	4.35573	+	5.19096i	0.164046	+	0.195503i
$706$	12.4745	+	10.4674i	0.469486	+	0.393945i
$707$	−0.215031	+	1.21950i	−0.00808708	+	0.0458641i
$708$	−1.51939	−	4.17448i	−0.0571020	−	0.156886i
$709$		−	25.6122i		−	0.961886i	−0.876752	−	0.480943i	$-0.840294\pi$
$709$		−	25.6122i		−	0.961886i	0.876752	−	0.480943i	$-0.159706\pi$
$710$	13.0205	−	4.73908i	0.488651	−	0.177854i
$711$	−6.77028	+	3.90882i	−0.253905	+	0.146592i
$712$	6.63520	+	37.6301i	0.248665	+	1.41025i
$713$	25.8450	−	44.7649i	0.967904	−	1.67646i
$714$	5.74682	+	9.95379i	0.215069	+	0.372511i
$715$	−4.25173	+	3.56763i	−0.159006	+	0.133422i
$716$	−31.0300	−	5.47142i	−1.15964	−	0.204476i
$717$	5.33933	+	3.08266i	0.199401	+	0.115124i
$718$	7.13692	−	19.6085i	0.266347	−	0.731783i
$719$	−24.3214	−	8.85225i	−0.907033	−	0.330133i	−0.153966	−	0.988076i	$-0.549205\pi$
$719$	−24.3214	−	8.85225i	−0.907033	−	0.330133i	−0.753068	+	0.657943i	$0.771427\pi$
$720$	3.09414	−	0.545581i	0.115312	−	0.0203326i
$721$	33.8766	−	40.3725i	1.26163	−	1.50355i
$722$	6.67810	−	7.95865i	0.248533	−	0.296190i
$723$	−0.300077	+	0.0529117i	−0.0111600	+	0.00196781i
$724$	30.7292	+	11.1845i	1.14204	+	0.415669i
$725$	3.92414	−	10.7815i	0.145739	−	0.400414i
$726$	−6.65539	−	3.84249i	−0.247005	−	0.142608i
$727$	35.4642	+	6.25330i	1.31530	+	0.231922i	0.786902	−	0.617078i	$-0.211684\pi$
$727$	35.4642	+	6.25330i	1.31530	+	0.231922i	0.528393	+	0.849000i	$0.322795\pi$
$728$	−23.3422	+	19.5865i	−0.865121	+	0.725923i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−10.5437	+	18.2623i	−0.390241	+	0.675917i
$731$	−4.90474	−	27.8162i	−0.181409	−	1.02882i
$732$	7.04147	−	4.06540i	0.260260	−	0.150261i
$733$	−22.1242	+	8.05256i	−0.817177	+	0.297428i	−0.716585	−	0.697500i	$-0.754296\pi$
$733$	−22.1242	+	8.05256i	−0.817177	+	0.297428i	−0.100592	+	0.994928i	$0.532074\pi$
$734$		−	5.34583i		−	0.197318i
$735$	−1.22028	−	3.35269i	−0.0450107	−	0.123666i
$736$	6.72001	−	38.1111i	0.247703	−	1.40479i
$737$	−4.44138	−	3.72676i	−0.163600	−	0.137277i
$738$	1.67301	+	1.99381i	0.0615842	+	0.0733932i
$739$	12.5729			0.462502			0.231251	−	0.972894i	$-0.425718\pi$
$739$	12.5729			0.462502			0.231251	+	0.972894i	$0.425718\pi$
$740$	22.3415	−	8.23768i	0.821289	−	0.302823i
$741$	−24.4729			−0.899034
$742$	−0.816263	−	0.972785i	−0.0299660	−	0.0357121i
$743$	−23.6335	−	19.8309i	−0.867031	−	0.727525i	0.0964399	−	0.995339i	$-0.469254\pi$
$743$	−23.6335	−	19.8309i	−0.867031	−	0.727525i	−0.963471	+	0.267814i	$0.913699\pi$
$744$	−3.37981	+	19.1678i	−0.123910	+	0.702727i
$745$	8.75505	+	24.0543i	0.320760	+	0.881282i
$746$			18.3661i			0.672430i
$747$	11.0475	−	4.02095i	0.404205	−	0.147119i
$748$	3.58263	−	2.06843i	0.130994	−	0.0756294i
$749$	−2.64771	−	15.0159i	−0.0967451	−	0.548669i
$750$	2.90183	−	5.02611i	0.105960	−	0.183528i
$751$	12.9382	+	22.4096i	0.472121	+	0.817738i	0.999491	−	0.0318978i	$-0.0101551\pi$
$751$	12.9382	+	22.4096i	0.472121	+	0.817738i	−0.527370	+	0.849636i	$0.676822\pi$
$752$	2.35959	−	1.97993i	0.0860453	−	0.0722006i
$753$	8.98663	+	1.58459i	0.327491	+	0.0577455i
$754$	15.7004	+	9.06463i	0.571775	+	0.330114i
$755$	7.81037	−	21.4588i	0.284248	−	0.780966i
$756$	−4.04487	−	1.47221i	−0.147110	−	0.0535438i
$757$	0.397951	−	0.0701695i	0.0144638	−	0.00255035i	−0.166412	−	0.986056i	$-0.553218\pi$
$757$	0.397951	−	0.0701695i	0.0144638	−	0.00255035i	0.180875	+	0.983506i	$0.442107\pi$
$758$	2.27912	−	2.71615i	0.0827813	−	0.0986550i
$759$	−2.12684	+	2.53466i	−0.0771993	+	0.0920025i
$760$	−37.3944	+	6.59363i	−1.35644	+	0.239176i
$761$	39.9615	+	14.5448i	1.44860	+	0.527248i	0.942201	−	0.335049i	$-0.108753\pi$
$761$	39.9615	+	14.5448i	1.44860	+	0.527248i	0.506402	+	0.862298i	$0.330975\pi$
$762$	1.59273	−	4.37599i	0.0576986	−	0.158525i
$763$	−17.0816	−	9.86209i	−0.618397	−	0.357032i
$764$	1.75590	+	0.309613i	0.0635263	+	0.0112014i
$765$	11.2013	−	9.39901i	0.404984	−	0.339822i
$766$	−6.26622	−	10.8534i	−0.226408	−	0.392150i
$767$	6.30436	−	10.9195i	0.227637	−	0.394279i
$768$	1.91239	+	10.8457i	0.0690073	+	0.391360i
$769$	−3.38558	+	1.95466i	−0.122087	+	0.0704870i	−0.559800	−	0.828628i	$-0.689122\pi$
$769$	−3.38558	+	1.95466i	−0.122087	+	0.0704870i	0.437713	+	0.899115i	$0.355789\pi$
$770$	2.55032	−	0.928242i	0.0919073	−	0.0334515i
$771$			19.3665i			0.697468i
$772$	4.44507	+	12.2127i	0.159982	+	0.439546i
$773$	3.61396	−	20.4958i	0.129985	−	0.737182i	−0.848236	−	0.529618i	$-0.822335\pi$
$773$	3.61396	−	20.4958i	0.129985	−	0.737182i	0.978221	−	0.207564i	$-0.0665535\pi$
$774$	−2.78100	−	2.33354i	−0.0999611	−	0.0838773i
$775$	9.59065	+	11.4297i	0.344506	+	0.410567i
$776$	−0.718541			−0.0257941
$777$	−17.3299	−	2.98100i	−0.621707	−	0.106943i
$778$	9.52869			0.341620
$779$	13.5525	+	16.1513i	0.485570	+	0.578680i
$780$	12.6733	+	10.6342i	0.453778	+	0.380765i
$781$	−0.639532	+	3.62697i	−0.0228843	+	0.129783i
$782$	−9.00705	−	24.7467i	−0.322091	−	0.884939i
$783$			6.00093i			0.214456i
$784$	−1.52399	+	0.554688i	−0.0544283	+	0.0198103i
$785$	16.7911	−	9.69436i	0.599301	−	0.346007i
$786$	−1.32041	−	7.48844i	−0.0470976	−	0.267104i
$787$	6.98978	−	12.1066i	0.249159	−	0.431555i	−0.714134	−	0.700009i	$-0.753179\pi$
$787$	6.98978	−	12.1066i	0.249159	−	0.431555i	0.963293	+	0.268454i	$0.0865126\pi$
$788$	18.7169	+	32.4186i	0.666761	+	1.15486i
$789$	12.3360	−	10.3512i	0.439174	−	0.368511i
$790$	−14.4691	−	2.55130i	−0.514789	−	0.0907712i
$791$	−23.0235	−	13.2926i	−0.818622	−	0.472632i
$792$	0.426121	−	1.17076i	0.0151416	−	0.0416011i
$793$	21.6857	+	7.89295i	0.770082	+	0.280287i
$794$	−3.51856	+	0.620416i	−0.124869	+	0.0220178i
$795$	−1.03845	+	1.23758i	−0.0368301	+	0.0438924i
$796$	−9.38567	+	11.1854i	−0.332666	+	0.396456i
$797$	−42.5811	+	7.50820i	−1.50830	+	0.265954i	−0.865823	−	0.500350i	$-0.833205\pi$
$797$	−42.5811	+	7.50820i	−1.50830	+	0.265954i	−0.642478	+	0.766304i	$0.722094\pi$
$798$	11.2452	+	4.09293i	0.398077	+	0.144888i
$799$	4.90298	−	13.4708i	0.173455	−	0.476563i
$800$	9.67395	+	5.58526i	0.342026	+	0.197469i
$801$	−15.0876	−	2.66035i	−0.533094	−	0.0939988i
$802$	9.98585	−	8.37913i	0.352613	−	0.295877i
$803$	−2.80249	−	4.85406i	−0.0988978	−	0.171296i
$804$	−8.64091	+	14.9665i	−0.304741	+	0.527827i
$805$	8.74175	+	49.5769i	0.308106	+	1.74736i
$806$	−20.4173	+	11.7879i	−0.719170	+	0.415213i
$807$	−2.61759	+	0.952723i	−0.0921434	+	0.0335375i
$808$			1.06836i			0.0375849i
$809$	7.53764	+	20.7095i	0.265009	+	0.728107i	0.998811	+	0.0487436i	$0.0155217\pi$
$809$	7.53764	+	20.7095i	0.265009	+	0.728107i	−0.733802	+	0.679363i	$0.762256\pi$
$810$	0.326352	−	1.85083i	0.0114668	−	0.0650316i
$811$	−9.52227	−	7.99014i	−0.334372	−	0.280572i	0.460106	−	0.887864i	$-0.347811\pi$
$811$	−9.52227	−	7.99014i	−0.334372	−	0.280572i	−0.794479	+	0.607292i	$0.792256\pi$
$812$	16.6037	+	19.7875i	0.582675	+	0.694405i
$813$	30.1679			1.05803
$814$	0.368228	−	2.14068i	0.0129064	−	0.0750306i
$815$	−0.635084			−0.0222460
$816$	−4.27239	−	5.09164i	−0.149564	−	0.178243i
$817$	−22.5281	−	18.9033i	−0.788159	−	0.661344i
$818$	1.10213	−	6.25047i	0.0385349	−	0.218543i
$819$	−4.17854	−	11.4805i	−0.146010	−	0.401160i
$820$		−	14.2530i		−	0.497735i
$821$	−35.9532	+	13.0859i	−1.25478	+	0.456701i	−0.882013	−	0.471226i	$-0.843812\pi$
$821$	−35.9532	+	13.0859i	−1.25478	+	0.456701i	−0.372763	+	0.927927i	$0.621589\pi$
$822$	9.87357	−	5.70051i	0.344380	−	0.198828i
$823$	2.49568	+	14.1537i	0.0869940	+	0.493367i	0.996908	+	0.0785714i	$0.0250359\pi$
$823$	2.49568	+	14.1537i	0.0869940	+	0.493367i	−0.909915	+	0.414796i	$0.863853\pi$
$824$	22.7347	−	39.3777i	0.792002	−	1.37179i
$825$	−0.477540	−	0.827124i	−0.0166258	−	0.0287968i
$826$	−4.72305	+	3.96311i	−0.164336	+	0.137894i
$827$	32.2924	+	5.69403i	1.12292	+	0.198001i	0.704121	−	0.710080i	$-0.251341\pi$
$827$	32.2924	+	5.69403i	1.12292	+	0.198001i	0.418796	+	0.908080i	$0.362452\pi$
$828$	8.54126	+	4.93130i	0.296829	+	0.171375i
$829$	12.6078	−	34.6397i	0.437887	−	1.20309i	−0.502976	−	0.864300i	$-0.667762\pi$
$829$	12.6078	−	34.6397i	0.437887	−	1.20309i	0.940864	−	0.338785i	$-0.110016\pi$
$830$	20.7624	+	7.55691i	0.720674	+	0.262304i
$831$	26.8222	−	4.72948i	0.930452	−	0.164064i
$832$	−4.85282	+	5.78336i	−0.168241	+	0.200502i
$833$	−4.85166	+	5.78198i	−0.168100	+	0.200334i
$834$	6.08215	−	1.07245i	0.210608	−	0.0371358i
$835$	63.0756	+	22.9576i	2.18282	+	0.794481i
$836$	1.47315	−	4.04746i	0.0509501	−	0.139984i
$837$	−6.75830	−	3.90190i	−0.233601	−	0.134870i
$838$	19.4422	+	3.42818i	0.671618	+	0.118424i
$839$	−1.46263	+	1.22729i	−0.0504954	+	0.0423707i	−0.667686	−	0.744443i	$-0.732715\pi$
$839$	−1.46263	+	1.22729i	−0.0504954	+	0.0423707i	0.617191	+	0.786814i	$0.288271\pi$
$840$	−9.47791	−	16.4162i	−0.327019	−	0.566414i
$841$	3.50556	−	6.07181i	0.120881	−	0.209373i
$842$	3.42261	+	19.4106i	0.117951	+	0.668932i
$843$	−12.1998	+	7.04353i	−0.420182	+	0.242592i
$844$	16.3563	−	5.95321i	0.563007	−	0.204918i
$845$			12.7783i			0.439587i
$846$	−0.630175	−	1.73139i	−0.0216659	−	0.0595265i
$847$	5.39666	−	30.6060i	0.185431	−	1.05163i
$848$	0.562551	+	0.472037i	0.0193181	+	0.0162098i
$849$	−7.00526	−	8.34854i	−0.240420	−	0.286521i
$850$	7.60159			0.260732
$851$	37.9179	+	13.6215i	1.29981	+	0.466941i
$852$	10.9778			0.376095
$853$	−2.18937	−	2.60919i	−0.0749627	−	0.0893371i	0.727260	−	0.686362i	$-0.240794\pi$
$853$	−2.18937	−	2.60919i	−0.0749627	−	0.0893371i	−0.802222	+	0.597025i	$0.796349\pi$
$854$	−8.64449	−	7.25358i	−0.295808	−	0.248213i
$855$	2.64368	−	14.9931i	0.0904121	−	0.512752i
$856$	−4.49924	−	12.3616i	−0.153781	−	0.422510i
$857$			34.3970i			1.17498i	0.809232	+	0.587489i	$0.199883\pi$
$857$			34.3970i			1.17498i	−0.809232	+	0.587489i	$0.800117\pi$
$858$	1.41812	−	0.516154i	0.0484139	−	0.0176212i
$859$	21.0740	−	12.1671i	0.719037	−	0.415136i	−0.0953610	−	0.995443i	$-0.530401\pi$
$859$	21.0740	−	12.1671i	0.719037	−	0.415136i	0.814398	+	0.580306i	$0.197067\pi$
$860$	3.45217	+	19.5783i	0.117718	+	0.667613i
$861$	−5.26273	+	9.11532i	−0.179353	+	0.310649i
$862$	−2.29237	−	3.97051i	−0.0780786	−	0.135236i
$863$	−35.0202	+	29.3854i	−1.19210	+	1.00029i	−0.192281	+	0.981340i	$0.561588\pi$
$863$	−35.0202	+	29.3854i	−1.19210	+	1.00029i	−0.999820	+	0.0189515i	$0.993967\pi$
$864$	−5.75374	−	1.01454i	−0.195746	−	0.0345154i
$865$	−26.9419	−	15.5549i	−0.916053	−	0.528883i
$866$	5.98092	−	16.4324i	0.203240	−	0.558397i
$867$	−13.0932	−	4.76554i	−0.444669	−	0.161846i
$868$	−33.0808	+	5.83304i	−1.12284	+	0.197986i
$869$	2.51021	−	2.99155i	0.0851529	−	0.101481i
$870$	−7.24939	+	8.63949i	−0.245777	+	0.292906i
$871$	−48.3054	+	8.51754i	−1.63677	+	0.288606i
$872$	−15.9909	−	5.82021i	−0.541520	−	0.197097i
$873$	0.0985345	−	0.270721i	0.00333489	−	0.00916253i
$874$	−23.7458	−	13.7096i	−0.803213	−	0.463735i
$875$	23.1134	+	4.07552i	0.781377	+	0.137778i
$876$	−12.7983	+	10.7391i	−0.432416	+	0.362840i
$877$	−12.3351	−	21.3650i	−0.416525	−	0.721443i	0.579062	−	0.815284i	$-0.303419\pi$
$877$	−12.3351	−	21.3650i	−0.416525	−	0.721443i	−0.995587	+	0.0938405i	$0.970086\pi$
$878$	0.0560767	−	0.0971278i	0.00189250	−	0.00327790i
$879$	−5.23485	−	29.6883i	−0.176567	−	1.00136i
$880$	−1.35921	+	0.784738i	−0.0458188	+	0.0264535i
$881$	8.13781	−	2.96192i	0.274170	−	0.0997897i	−0.201276	−	0.979535i	$-0.564509\pi$
$881$	8.13781	−	2.96192i	0.274170	−	0.0997897i	0.475446	+	0.879745i	$0.342287\pi$
$882$			0.970116i			0.0326655i
$883$	15.7227	+	43.1977i	0.529110	+	1.45372i	0.860120	+	0.510091i	$0.170388\pi$
$883$	15.7227	+	43.1977i	0.529110	+	1.45372i	−0.331010	+	0.943627i	$0.607389\pi$
$884$	6.07745	−	34.4669i	0.204407	−	1.15925i
$885$	6.00868	+	5.04188i	0.201980	+	0.169481i
$886$	1.14386	+	1.36320i	0.0384287	+	0.0457976i
$887$	13.4380			0.451204			0.225602	−	0.974220i	$-0.427565\pi$
$887$	13.4380			0.451204			0.225602	+	0.974220i	$0.427565\pi$
$888$	−15.1709	+	0.0634950i	−0.509103	+	0.00213075i
$889$	18.8323			0.631614
$890$	−18.5077	−	22.0566i	−0.620378	−	0.739338i
$891$	0.382666	+	0.321095i	0.0128198	+	0.0107571i
$892$	2.29303	−	13.0044i	0.0767764	−	0.435421i
$893$	−5.10487	−	14.0255i	−0.170828	−	0.469346i
$894$		−	6.96022i		−	0.232785i
$895$	52.2787	−	19.0279i	1.74748	−	0.636032i
$896$	−26.0570	+	15.0440i	−0.870505	+	0.502586i
$897$	4.86090	+	27.5675i	0.162301	+	0.920453i
$898$	−12.3098	+	21.3211i	−0.410782	+	0.711495i
$899$	23.4150	+	40.5560i	0.780935	+	1.35262i
$900$	−2.18082	+	1.82992i	−0.0726939	+	0.0609974i
$901$	3.36578	+	0.593477i	0.112130	+	0.0197716i
$902$	−1.12597	−	0.650079i	−0.0374907	−	0.0216452i
$903$	5.02124	−	13.7957i	0.167096	−	0.459093i
$904$	−21.5534	−	7.84478i	−0.716854	−	0.260913i
$905$	−56.8625	+	10.0264i	−1.89017	+	0.333289i
$906$	−3.99120	+	4.75652i	−0.132599	+	0.158025i
$907$	−0.821225	+	0.978698i	−0.0272683	+	0.0324971i	−0.779506	−	0.626394i	$-0.784530\pi$
$907$	−0.821225	+	0.978698i	−0.0272683	+	0.0324971i	0.752238	+	0.658892i	$0.228974\pi$
$908$	8.67295	−	1.52927i	0.287822	−	0.0507508i
$909$	−0.402522	−	0.146506i	−0.0133508	−	0.00485930i
$910$	7.85309	−	21.5762i	0.260328	−	0.715244i
$911$	−11.5011	−	6.64016i	−0.381048	−	0.219998i	0.297226	−	0.954807i	$-0.403939\pi$
$911$	−11.5011	−	6.64016i	−0.381048	−	0.219998i	−0.678274	+	0.734809i	$0.737272\pi$
$912$	−6.81522	−	1.20171i	−0.225674	−	0.0397925i
$913$	−4.49880	+	3.77494i	−0.148888	+	0.124932i
$914$	10.9487	+	18.9638i	0.362152	+	0.627266i
$915$	−7.17814	+	12.4329i	−0.237302	+	0.411019i
$916$	4.57874	+	25.9674i	0.151286	+	0.857985i
$917$	26.6307	−	15.3752i	0.879423	−	0.507735i
$918$	−3.73608	+	1.35982i	−0.123309	+	0.0448808i
$919$		−	17.4950i		−	0.577108i	−0.957464	−	0.288554i	$-0.906826\pi$
$919$		−	17.4950i		−	0.577108i	0.957464	−	0.288554i	$-0.0931745\pi$
$920$	14.8548	+	40.8133i	0.489749	+	1.34557i
$921$	1.07446	−	6.09358i	0.0354047	−	0.200790i
$922$	7.20458	+	6.04536i	0.237270	+	0.199093i
$923$	20.0281	+	23.8686i	0.659233	+	0.785643i
$924$	2.15023			0.0707373
$925$	−7.43818	+	8.94021i	−0.244566	+	0.293952i
$926$	−10.5596			−0.347010
$927$	11.7185	+	13.9656i	0.384886	+	0.458689i
$928$	26.8579	+	22.5364i	0.881652	+	0.739794i
$929$	3.13836	−	17.7985i	0.102966	−	0.583950i	−0.889047	−	0.457816i	$-0.848632\pi$
$929$	3.13836	−	17.7985i	0.102966	−	0.583950i	0.992013	−	0.126134i	$-0.0402570\pi$
$930$	−5.01619	−	13.7819i	−0.164487	−	0.451925i
$931$			7.85864i			0.257557i
$932$	−16.1236	+	5.86851i	−0.528146	+	0.192229i
$933$	−5.70019	+	3.29101i	−0.186616	+	0.107743i
$934$	1.31494	+	7.45737i	0.0430260	+	0.244013i
$935$	−3.65217	+	6.32574i	−0.119439	+	0.206874i
$936$	−5.27025	−	9.12834i	−0.172263	−	0.298369i
$937$	17.1848	−	14.4198i	0.561403	−	0.471073i	−0.317377	−	0.948299i	$-0.602802\pi$
$937$	17.1848	−	14.4198i	0.561403	−	0.471073i	0.878780	+	0.477226i	$0.158358\pi$
$938$	23.6207	+	4.16497i	0.771244	+	0.135991i
$939$	−15.3906	−	8.88575i	−0.502252	−	0.289975i
$940$	−3.45093	+	9.48135i	−0.112557	+	0.309248i
$941$	−7.01216	−	2.55222i	−0.228590	−	0.0831999i	0.225186	−	0.974316i	$-0.427701\pi$
$941$	−7.01216	−	2.55222i	−0.228590	−	0.0831999i	−0.453776	+	0.891116i	$0.649923\pi$
$942$	−5.19178	+	0.915452i	−0.169157	+	0.0298270i
$943$	15.5018	−	18.4743i	0.504808	−	0.601607i
$944$	2.29183	−	2.73129i	0.0745926	−	0.0888960i
$945$	7.48478	−	1.31977i	0.243480	−	0.0429321i
$946$	1.70412	+	0.620248i	0.0554056	+	0.0201660i
$947$	1.27598	−	3.50572i	0.0414637	−	0.113921i	−0.917233	−	0.398352i	$-0.869582\pi$
$947$	1.27598	−	3.50572i	0.0414637	−	0.113921i	0.958697	+	0.284431i	$0.0918046\pi$
$948$	−10.0809	−	5.82018i	−0.327411	−	0.189031i
$949$	−46.6988	−	8.23426i	−1.51591	−	0.267295i
$950$	6.06294	−	5.08741i	0.196708	−	0.165057i
$951$	6.29348	+	10.9006i	0.204080	+	0.353477i
$952$	−20.0506	+	34.7286i	−0.649844	+	1.12556i
$953$	−9.44210	−	53.5488i	−0.305860	−	1.73462i	−0.619430	−	0.785052i	$-0.712636\pi$
$953$	−9.44210	−	53.5488i	−0.305860	−	1.73462i	0.313571	−	0.949565i	$-0.398475\pi$
$954$	0.380422	−	0.219637i	0.0123166	−	0.00711101i
$955$	−2.95831	+	1.07674i	−0.0957287	+	0.0348424i
$956$			9.18010i			0.296906i
$957$	−1.02526	−	2.81689i	−0.0331421	−	0.0910572i
$958$	−1.54446	+	8.75907i	−0.0498992	+	0.282993i
$959$	35.3190	+	29.6362i	1.14051	+	0.957003i
$960$	−3.01890	−	3.59778i	−0.0974345	−	0.116118i
$961$	−29.8994			−0.964497
$962$	−11.8710	−	14.0276i	−0.382736	−	0.452269i
$963$	5.27439			0.169965
$964$	−0.291635	−	0.347557i	−0.00939293	−	0.0111941i
$965$	−17.5788	−	14.7504i	−0.565882	−	0.474832i
$966$	2.37692	−	13.4802i	0.0764761	−	0.433717i
$967$	−4.02486	−	11.0582i	−0.129431	−	0.355608i	0.858002	−	0.513646i	$-0.171705\pi$
$967$	−4.02486	−	11.0582i	−0.129431	−	0.355608i	−0.987433	+	0.158038i	$0.949483\pi$
$968$		−	26.8128i		−	0.861797i
$969$	−30.2649	+	11.0155i	−0.972250	+	0.353870i
$970$	0.468903	−	0.270721i	0.0150556	−	0.00869234i
$971$	−2.14063	−	12.1401i	−0.0686961	−	0.389595i	−0.999698	−	0.0245802i	$-0.992175\pi$
$971$	−2.14063	−	12.1401i	−0.0686961	−	0.389595i	0.931002	−	0.365015i	$-0.118936\pi$
$972$	0.744494	−	1.28950i	0.0238796	−	0.0413608i
$973$	12.4878	+	21.6296i	0.400342	+	0.693412i
$974$	−1.85953	+	1.56033i	−0.0595831	+	0.0499962i
$975$	−7.95740	−	1.40310i	−0.254841	−	0.0449353i
$976$	5.65147	+	3.26288i	0.180899	+	0.104442i
$977$	−1.85473	+	5.09583i	−0.0593380	+	0.163030i	−0.965819	−	0.259216i	$-0.916536\pi$
$977$	−1.85473	+	5.09583i	−0.0593380	+	0.163030i	0.906481	+	0.422246i	$0.138758\pi$
$978$	0.162268	+	0.0590607i	0.00518876	+	0.00188855i
$979$	7.53678	−	1.32894i	0.240877	−	0.0424730i
$980$	3.41481	−	4.06961i	0.109082	−	0.129999i
$981$	4.38570	−	5.22668i	0.140025	−	0.166875i
$982$	0.251243	−	0.0443009i	0.00801748	−	0.00141370i
$983$	12.4194	+	4.52029i	0.396117	+	0.144175i	0.532396	−	0.846496i	$-0.321292\pi$
$983$	12.4194	+	4.52029i	0.396117	+	0.144175i	−0.136278	+	0.990671i	$0.543514\pi$
$984$	−3.10585	+	8.53326i	−0.0990110	+	0.272030i
$985$	−57.2404	−	33.0478i	−1.82383	−	1.05299i
$986$	23.4963	+	4.14304i	0.748276	+	0.131941i
$987$	5.70788	−	4.78948i	0.181684	−	0.152451i
$988$	−18.2199	−	31.5578i	−0.579652	−	1.00399i
$989$	−16.8191	+	29.1315i	−0.534815	+	0.926328i
$990$	0.163024	+	0.924556i	0.00518125	+	0.0293843i
$991$	2.64944	−	1.52966i	0.0841623	−	0.0485911i	−0.457328	−	0.889298i	$-0.651194\pi$
$991$	2.64944	−	1.52966i	0.0841623	−	0.0485911i	0.541491	+	0.840707i	$0.317860\pi$
$992$	−42.8441	+	15.5940i	−1.36030	+	0.495110i
$993$			15.4983i			0.491823i
$994$	−5.21100	−	14.3171i	−0.165283	−	0.454111i
$995$	4.47689	−	25.3897i	0.141927	−	0.804909i
$996$	13.4098	+	11.2521i	0.424905	+	0.356538i
$997$	−23.0186	−	27.4325i	−0.729007	−	0.868797i	0.266466	−	0.963844i	$-0.414144\pi$
$997$	−23.0186	−	27.4325i	−0.729007	−	0.868797i	−0.995473	+	0.0950477i	$0.969700\pi$
$998$	−20.2482			−0.640945
$999$	2.05649	−	5.72458i	0.0650644	−	0.181118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.o.a.25.2	✓	12
3.2	odd	2		333.2.bl.b.136.1		12
37.3	even	18	inner	111.2.o.a.40.2	yes	12
37.15	odd	36		4107.2.a.p.1.4		12
37.22	odd	36		4107.2.a.p.1.9		12
111.77	odd	18		333.2.bl.b.262.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.o.a.25.2	✓	12	1.1	even	1	trivial
111.2.o.a.40.2	yes	12	37.3	even	18	inner
333.2.bl.b.136.1		12	3.2	odd	2
333.2.bl.b.262.1		12	111.77	odd	18
4107.2.a.p.1.4		12	37.15	odd	36
4107.2.a.p.1.9		12	37.22	odd	36

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:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.o (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.459498 + 0.547608i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.258560 - 1.46637i) q^{4} +(0.899190 + 2.47051i) q^{5} -0.714852i q^{6} +(2.71652 - 0.988733i) q^{7} +(2.15996 - 1.24705i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.459498 + 0.547608i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(0.258560 - 1.46637i) q^{4} +(0.899190 + 2.47051i) q^{5} -0.714852i q^{6} +(2.71652 - 0.988733i) q^{7} +(2.15996 - 1.24705i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.939693 + 1.62760i) q^{10} +(-0.249768 - 0.432610i) q^{11} +(-1.14063 + 0.957103i) q^{12} +(-4.16195 - 0.733865i) q^{13} +(1.78967 + 1.03327i) q^{14} +(0.899190 - 2.47051i) q^{15} +(-1.12299 - 0.408734i) q^{16} +(-5.47729 + 0.965795i) q^{17} +(-0.459498 + 0.547608i) q^{18} +(-3.72226 + 4.43602i) q^{19} +(3.85516 - 0.679769i) q^{20} +(-2.71652 - 0.988733i) q^{21} +(0.122133 - 0.335558i) q^{22} +(5.73629 + 3.31185i) q^{23} +(-2.45622 - 0.433097i) q^{24} +(-1.46463 + 1.22897i) q^{25} +(-1.51054 - 2.61633i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.747461 - 4.23906i) q^{28} +(-5.19695 + 3.00046i) q^{29} +(1.76604 - 0.642788i) q^{30} -7.80381i q^{31} +(-1.99825 - 5.49016i) q^{32} +(-0.0867434 + 0.491946i) q^{33} +(-3.04568 - 2.55563i) q^{34} +(4.88534 + 5.82212i) q^{35} +1.48899 q^{36} +(5.98588 - 1.08132i) q^{37} -4.13957 q^{38} +(2.71652 + 3.23743i) q^{39} +(5.02307 + 4.21486i) q^{40} +(0.632243 - 3.58563i) q^{41} +(-0.706798 - 1.94191i) q^{42} +5.07845i q^{43} +(-0.698945 + 0.254395i) q^{44} +(-2.27683 + 1.31453i) q^{45} +(0.822217 + 4.66303i) q^{46} +(-1.28873 + 2.23215i) q^{47} +(0.597529 + 1.03495i) q^{48} +(1.03959 - 0.872319i) q^{49} +(-1.34599 - 0.237334i) q^{50} +(4.81665 + 2.78089i) q^{51} +(-2.15223 + 5.91320i) q^{52} +(-0.577438 - 0.210170i) q^{53} +(0.703991 - 0.124133i) q^{54} +(0.844177 - 1.00605i) q^{55} +(4.63458 - 5.52328i) q^{56} +(5.70284 - 1.00556i) q^{57} +(-4.03107 - 1.46719i) q^{58} +(-1.02042 + 2.80357i) q^{59} +(-3.39017 - 1.95732i) q^{60} +(-5.37766 - 0.948226i) q^{61} +(4.27343 - 3.58583i) q^{62} +(1.44543 + 2.50356i) q^{63} +(0.893204 - 1.54708i) q^{64} +(-1.92937 - 10.9420i) q^{65} +(-0.309252 + 0.178547i) q^{66} +(10.9065 - 3.96963i) q^{67} +8.28143i q^{68} +(-2.26544 - 6.22424i) q^{69} +(-0.943438 + 5.35050i) q^{70} +(-5.64781 - 4.73908i) q^{71} +(1.60318 + 1.91060i) q^{72} +11.2204 q^{73} +(3.34264 + 2.78105i) q^{74} +1.91194 q^{75} +(5.54240 + 6.60517i) q^{76} +(-1.10624 - 0.928242i) q^{77} +(-0.524604 + 2.97518i) q^{78} +(2.67379 + 7.34618i) q^{79} -3.14187i q^{80} +(-0.939693 + 0.342020i) q^{81} +(2.25403 - 1.30137i) q^{82} +(-2.04149 - 11.5779i) q^{83} +(-2.15223 + 3.72777i) q^{84} +(-7.31113 - 12.6632i) q^{85} +(-2.78100 + 2.33354i) q^{86} +(5.90976 + 1.04205i) q^{87} +(-1.07898 - 0.622947i) q^{88} +(-5.23986 + 14.3964i) q^{89} +(-1.76604 - 0.642788i) q^{90} +(-12.0316 + 2.12150i) q^{91} +(6.33956 - 7.55519i) q^{92} +(-5.01619 + 5.97806i) q^{93} +(-1.81452 + 0.319948i) q^{94} +(-14.3062 - 5.20704i) q^{95} +(-1.99825 + 5.49016i) q^{96} +(-0.249498 - 0.144048i) q^{97} +(0.955378 + 0.168459i) q^{98} +(0.382666 - 0.321095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{7} - 9 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^7 - 9 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{7} - 9 q^{8} - 6 q^{11} - 6 q^{12} - 6 q^{13} + 27 q^{14} - 3 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 12 q^{19} + 9 q^{20} + 6 q^{21} - 21 q^{22} - 6 q^{24} - 15 q^{25} + 6 q^{27} + 39 q^{28} + 27 q^{29} + 12 q^{30} - 33 q^{32} - 12 q^{33} + 15 q^{34} + 36 q^{35} + 15 q^{37} - 48 q^{38} - 6 q^{39} + 15 q^{40} + 12 q^{41} + 18 q^{42} - 21 q^{44} - 15 q^{46} + 9 q^{47} - 18 q^{49} - 18 q^{50} + 9 q^{51} + 6 q^{52} - 12 q^{53} - 3 q^{54} - 39 q^{55} - 18 q^{56} - 3 q^{57} - 15 q^{58} - 15 q^{61} + 39 q^{62} + 12 q^{63} - 9 q^{64} - 24 q^{65} + 18 q^{66} + 6 q^{67} - 12 q^{69} - 15 q^{70} - 3 q^{71} - 6 q^{72} + 90 q^{73} + 72 q^{74} - 24 q^{75} - 6 q^{76} + 27 q^{77} + 9 q^{78} + 6 q^{79} + 27 q^{82} - 3 q^{83} + 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{87} + 63 q^{88} + 39 q^{89} - 12 q^{90} - 27 q^{91} + 6 q^{92} - 24 q^{93} + 30 q^{94} - 36 q^{95} - 33 q^{96} - 18 q^{97} - 42 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^7 - 9 * q^8 - 6 * q^11 - 6 * q^12 - 6 * q^13 + 27 * q^14 - 3 * q^15 + 3 * q^16 - 6 * q^17 - 3 * q^18 - 12 * q^19 + 9 * q^20 + 6 * q^21 - 21 * q^22 - 6 * q^24 - 15 * q^25 + 6 * q^27 + 39 * q^28 + 27 * q^29 + 12 * q^30 - 33 * q^32 - 12 * q^33 + 15 * q^34 + 36 * q^35 + 15 * q^37 - 48 * q^38 - 6 * q^39 + 15 * q^40 + 12 * q^41 + 18 * q^42 - 21 * q^44 - 15 * q^46 + 9 * q^47 - 18 * q^49 - 18 * q^50 + 9 * q^51 + 6 * q^52 - 12 * q^53 - 3 * q^54 - 39 * q^55 - 18 * q^56 - 3 * q^57 - 15 * q^58 - 15 * q^61 + 39 * q^62 + 12 * q^63 - 9 * q^64 - 24 * q^65 + 18 * q^66 + 6 * q^67 - 12 * q^69 - 15 * q^70 - 3 * q^71 - 6 * q^72 + 90 * q^73 + 72 * q^74 - 24 * q^75 - 6 * q^76 + 27 * q^77 + 9 * q^78 + 6 * q^79 + 27 * q^82 - 3 * q^83 + 6 * q^84 - 27 * q^85 - 12 * q^86 + 9 * q^87 + 63 * q^88 + 39 * q^89 - 12 * q^90 - 27 * q^91 + 6 * q^92 - 24 * q^93 + 30 * q^94 - 36 * q^95 - 33 * q^96 - 18 * q^97 - 42 * q^98 + 3 * q^99

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