LMFDB - Embedded newform 216.2.n.b.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(37,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("216.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			181.3
Root			$0.587625 - 1.28635i$ of defining polynomial
Character	$\chi$	$=$	216.181
Dual form			216.2.n.b.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.820200 + 1.15207i) q^{2} +(-0.654545 - 1.88986i) q^{4} +(-1.97542 + 1.14051i) q^{5} +(-0.907824 + 1.57240i) q^{7} +(2.71411 + 0.795980i) q^{8} +O(q^{10})$	\(q+(-0.820200 + 1.15207i) q^{2} +(-0.654545 - 1.88986i) q^{4} +(-1.97542 + 1.14051i) q^{5} +(-0.907824 + 1.57240i) q^{7} +(2.71411 + 0.795980i) q^{8} +(0.306290 - 3.21128i) q^{10} +(-4.24153 - 2.44885i) q^{11} +(-4.00895 + 2.31457i) q^{13} +(-1.06692 - 2.33556i) q^{14} +(-3.14314 + 2.47400i) q^{16} -1.92788 q^{17} -2.12907i q^{19} +(3.44841 + 2.98676i) q^{20} +(6.30015 - 2.87801i) q^{22} +(1.15765 + 2.00511i) q^{23} +(0.101535 - 0.175863i) q^{25} +(0.621589 - 6.51702i) q^{26} +(3.56582 + 0.686457i) q^{28} +(3.16440 + 1.82697i) q^{29} +(-2.65800 - 4.60379i) q^{31} +(-0.272218 - 5.65030i) q^{32} +(1.58125 - 2.22106i) q^{34} -4.14154i q^{35} +7.98438i q^{37} +(2.45284 + 1.74626i) q^{38} +(-6.26935 + 1.52308i) q^{40} +(2.36240 + 4.09180i) q^{41} +(2.20800 + 1.27479i) q^{43} +(-1.85171 + 9.61877i) q^{44} +(-3.25953 - 0.310892i) q^{46} +(2.02005 - 3.49884i) q^{47} +(1.85171 + 3.20726i) q^{49} +(0.119328 + 0.261218i) q^{50} +(6.99825 + 6.06137i) q^{52} +8.95958i q^{53} +11.1718 q^{55} +(-3.71554 + 3.54506i) q^{56} +(-4.70024 + 2.14714i) q^{58} +(3.05255 - 1.76239i) q^{59} +(-1.71675 - 0.991165i) q^{61} +(7.48399 + 0.713818i) q^{62} +(6.73283 + 4.32076i) q^{64} +(5.27959 - 9.14451i) q^{65} +(7.72723 - 4.46132i) q^{67} +(1.26188 + 3.64342i) q^{68} +(4.77135 + 3.39689i) q^{70} -13.3561 q^{71} -11.5592 q^{73} +(-9.19859 - 6.54879i) q^{74} +(-4.02364 + 1.39357i) q^{76} +(7.70112 - 4.44625i) q^{77} +(-4.97330 + 8.61401i) q^{79} +(3.38742 - 8.47198i) q^{80} +(-6.65170 - 0.634435i) q^{82} +(3.12153 + 1.80221i) q^{83} +(3.80838 - 2.19877i) q^{85} +(-3.27965 + 1.49820i) q^{86} +(-9.56276 - 10.0226i) q^{88} -2.49965 q^{89} -8.40489i q^{91} +(3.03164 - 3.50023i) q^{92} +(2.37407 + 5.19699i) q^{94} +(2.42823 + 4.20582i) q^{95} +(6.99370 - 12.1134i) q^{97} +(-5.21376 - 0.497285i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) $ 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8	$ 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8} - 16 q^{10} - 16 q^{14} - 9 q^{16} + 28 q^{17} + 8 q^{20} + q^{22} + 10 q^{23} + 2 q^{25} - 28 q^{26} + 4 q^{28} - 10 q^{31} - 11 q^{32} + q^{34} - 23 q^{38} + 6 q^{40} + 8 q^{41} - 18 q^{44} - 20 q^{46} - 6 q^{47} + 18 q^{49} + 23 q^{50} - 8 q^{52} - 4 q^{55} - 10 q^{56} - 14 q^{58} + 52 q^{62} + 26 q^{64} + 14 q^{65} + 39 q^{68} - 72 q^{71} - 44 q^{73} + 38 q^{74} + 5 q^{76} - 30 q^{79} + 96 q^{80} + 38 q^{82} - 7 q^{86} + 31 q^{88} - 64 q^{89} + 30 q^{92} - 12 q^{94} - 44 q^{95} - 66 q^{98}+O(q^{100}) $ 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8 - 16 * q^10 - 16 * q^14 - 9 * q^16 + 28 * q^17 + 8 * q^20 + q^22 + 10 * q^23 + 2 * q^25 - 28 * q^26 + 4 * q^28 - 10 * q^31 - 11 * q^32 + q^34 - 23 * q^38 + 6 * q^40 + 8 * q^41 - 18 * q^44 - 20 * q^46 - 6 * q^47 + 18 * q^49 + 23 * q^50 - 8 * q^52 - 4 * q^55 - 10 * q^56 - 14 * q^58 + 52 * q^62 + 26 * q^64 + 14 * q^65 + 39 * q^68 - 72 * q^71 - 44 * q^73 + 38 * q^74 + 5 * q^76 - 30 * q^79 + 96 * q^80 + 38 * q^82 - 7 * q^86 + 31 * q^88 - 64 * q^89 + 30 * q^92 - 12 * q^94 - 44 * q^95 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.820200	+	1.15207i	−0.579969	+	0.814639i
$2$	−0.820200	+	1.15207i	−0.579969	+	0.814639i
$3$		0			0
$3$		0			0
$4$	−0.654545	−	1.88986i	−0.327272	−	0.944930i
$5$	−1.97542	+	1.14051i	−0.883437	+	0.510052i	−0.871790	−	0.489880i	$-0.837041\pi$
$5$	−1.97542	+	1.14051i	−0.883437	+	0.510052i	−0.0116467	+	0.999932i	$0.503707\pi$
$6$		0			0
$7$	−0.907824	+	1.57240i	−0.343125	+	0.594311i	−0.985011	−	0.172490i	$-0.944819\pi$
$7$	−0.907824	+	1.57240i	−0.343125	+	0.594311i	0.641886	+	0.766800i	$0.278152\pi$
$8$	2.71411	+	0.795980i	0.959584	+	0.281421i
$9$		0			0
$10$	0.306290	−	3.21128i	0.0968573	−	1.01550i
$11$	−4.24153	−	2.44885i	−1.27887	−	0.738355i	−0.302228	−	0.953236i	$-0.597730\pi$
$11$	−4.24153	−	2.44885i	−1.27887	−	0.738355i	−0.976640	+	0.214880i	$0.931064\pi$
$12$		0			0
$13$	−4.00895	+	2.31457i	−1.11188	+	0.641946i	−0.939317	−	0.343052i	$-0.888539\pi$
$13$	−4.00895	+	2.31457i	−1.11188	+	0.641946i	−0.172567	+	0.984998i	$0.555206\pi$
$14$	−1.06692	−	2.33556i	−0.285146	−	0.624205i
$15$		0			0
$16$	−3.14314	+	2.47400i	−0.785786	+	0.618499i
$17$	−1.92788			−0.467579			−0.233790	−	0.972287i	$-0.575113\pi$
$17$	−1.92788			−0.467579			−0.233790	+	0.972287i	$0.575113\pi$
$18$		0			0
$19$		−	2.12907i		−	0.488442i	−0.969720	−	0.244221i	$-0.921468\pi$
$19$		−	2.12907i		−	0.488442i	0.969720	−	0.244221i	$-0.0785322\pi$
$20$	3.44841	+	2.98676i	0.771088	+	0.667860i
$21$		0			0
$22$	6.30015	−	2.87801i	1.34320	−	0.613593i
$23$	1.15765	+	2.00511i	0.241387	+	0.418094i	0.961109	−	0.276168i	$-0.0890645\pi$
$23$	1.15765	+	2.00511i	0.241387	+	0.418094i	−0.719723	+	0.694261i	$0.755731\pi$
$24$		0			0
$25$	0.101535	−	0.175863i	0.0203069	−	0.0351726i
$26$	0.621589	−	6.51702i	0.121904	−	1.27809i
$27$		0			0
$28$	3.56582	+	0.686457i	0.673877	+	0.129728i
$29$	3.16440	+	1.82697i	0.587615	+	0.339260i	0.764154	−	0.645034i	$-0.223157\pi$
$29$	3.16440	+	1.82697i	0.587615	+	0.339260i	−0.176539	+	0.984294i	$0.556490\pi$
$30$		0			0
$31$	−2.65800	−	4.60379i	−0.477391	−	0.826865i	0.522273	−	0.852778i	$-0.325084\pi$
$31$	−2.65800	−	4.60379i	−0.477391	−	0.826865i	−0.999664	+	0.0259130i	$0.991751\pi$
$32$	−0.272218	−	5.65030i	−0.0481218	−	0.998841i
$33$		0			0
$34$	1.58125	−	2.22106i	0.271181	−	0.380908i
$35$		−	4.14154i		−	0.700048i
$36$		0			0
$37$			7.98438i			1.31262i	0.754489	+	0.656312i	$0.227885\pi$
$37$			7.98438i			1.31262i	−0.754489	+	0.656312i	$0.772115\pi$
$38$	2.45284	+	1.74626i	0.397904	+	0.283281i
$39$		0			0
$40$	−6.26935	+	1.52308i	−0.991272	+	0.240820i
$41$	2.36240	+	4.09180i	0.368946	+	0.639033i	0.989401	−	0.145209i	$-0.0463855\pi$
$41$	2.36240	+	4.09180i	0.368946	+	0.639033i	−0.620455	+	0.784242i	$0.713052\pi$
$42$		0			0
$43$	2.20800	+	1.27479i	0.336717	+	0.194404i	0.658819	−	0.752301i	$-0.271056\pi$
$43$	2.20800	+	1.27479i	0.336717	+	0.194404i	−0.322102	+	0.946705i	$0.604390\pi$
$44$	−1.85171	+	9.61877i	−0.279156	+	1.45008i
$45$		0			0
$46$	−3.25953	−	0.310892i	−0.480592	−	0.0458386i
$47$	2.02005	−	3.49884i	0.294655	−	0.510358i	−0.680249	−	0.732981i	$-0.738129\pi$
$47$	2.02005	−	3.49884i	0.294655	−	0.510358i	0.974905	+	0.222623i	$0.0714619\pi$
$48$		0			0
$49$	1.85171	+	3.20726i	0.264530	+	0.458179i
$50$	0.119328	+	0.261218i	0.0168756	+	0.0369418i
$51$		0			0
$52$	6.99825	+	6.06137i	0.970483	+	0.840561i
$53$			8.95958i			1.23069i	0.788257	+	0.615347i	$0.210984\pi$
$53$			8.95958i			1.23069i	−0.788257	+	0.615347i	$0.789016\pi$
$54$		0			0
$55$	11.1718			1.50640
$56$	−3.71554	+	3.54506i	−0.496509	+	0.473728i
$57$		0			0
$58$	−4.70024	+	2.14714i	−0.617172	+	0.281934i
$59$	3.05255	−	1.76239i	0.397408	−	0.229444i	−0.287957	−	0.957643i	$-0.592976\pi$
$59$	3.05255	−	1.76239i	0.397408	−	0.229444i	0.685365	+	0.728200i	$0.259643\pi$
$60$		0			0
$61$	−1.71675	−	0.991165i	−0.219807	−	0.126906i	0.386054	−	0.922476i	$-0.373838\pi$
$61$	−1.71675	−	0.991165i	−0.219807	−	0.126906i	−0.605861	+	0.795571i	$0.707171\pi$
$62$	7.48399	+	0.713818i	0.950468	+	0.0906550i
$63$		0			0
$64$	6.73283	+	4.32076i	0.841604	+	0.540095i
$65$	5.27959	−	9.14451i	0.654852	−	1.13424i
$66$		0			0
$67$	7.72723	−	4.46132i	0.944031	−	0.545036i	0.0528093	−	0.998605i	$-0.483182\pi$
$67$	7.72723	−	4.46132i	0.944031	−	0.545036i	0.891222	+	0.453568i	$0.149849\pi$
$68$	1.26188	+	3.64342i	0.153026	+	0.441830i
$69$		0			0
$70$	4.77135	+	3.39689i	0.570286	+	0.406006i
$71$	−13.3561			−1.58508			−0.792539	−	0.609821i	$-0.791241\pi$
$71$	−13.3561			−1.58508			−0.792539	+	0.609821i	$0.791241\pi$
$72$		0			0
$73$	−11.5592			−1.35290			−0.676450	−	0.736489i	$-0.736482\pi$
$73$	−11.5592			−1.35290			−0.676450	+	0.736489i	$0.736482\pi$
$74$	−9.19859	−	6.54879i	−1.06931	−	0.761281i
$75$		0			0
$76$	−4.02364	+	1.39357i	−0.461543	+	0.159854i
$77$	7.70112	−	4.44625i	0.877625	−	0.506697i
$78$		0			0
$79$	−4.97330	+	8.61401i	−0.559540	+	0.969151i	0.437995	+	0.898977i	$0.355689\pi$
$79$	−4.97330	+	8.61401i	−0.559540	+	0.969151i	−0.997535	+	0.0701739i	$0.977645\pi$
$80$	3.38742	−	8.47198i	0.378725	−	0.947196i
$81$		0			0
$82$	−6.65170	−	0.634435i	−0.734558	−	0.0700616i
$83$	3.12153	+	1.80221i	0.342632	+	0.197819i	0.661435	−	0.750002i	$-0.269948\pi$
$83$	3.12153	+	1.80221i	0.342632	+	0.197819i	−0.318803	+	0.947821i	$0.603281\pi$
$84$		0			0
$85$	3.80838	−	2.19877i	0.413077	−	0.238490i
$86$	−3.27965	+	1.49820i	−0.353654	+	0.161555i
$87$		0			0
$88$	−9.56276	−	10.0226i	−1.01939	−	1.06841i
$89$	−2.49965			−0.264962			−0.132481	−	0.991186i	$-0.542294\pi$
$89$	−2.49965			−0.264962			−0.132481	+	0.991186i	$0.542294\pi$
$90$		0			0
$91$		−	8.40489i		−	0.881072i
$92$	3.03164	−	3.50023i	0.316070	−	0.364924i
$93$		0			0
$94$	2.37407	+	5.19699i	0.244866	+	0.536029i
$95$	2.42823	+	4.20582i	0.249131	+	0.431508i
$96$		0			0
$97$	6.99370	−	12.1134i	0.710103	−	1.22993i	−0.254715	−	0.967016i	$-0.581982\pi$
$97$	6.99370	−	12.1134i	0.710103	−	1.22993i	0.964818	−	0.262918i	$-0.0846849\pi$
$98$	−5.21376	−	0.497285i	−0.526670	−	0.0502334i
$99$		0			0
$100$	−0.398816	−	0.0767760i	−0.0398816	−	0.00767760i
$101$	−1.13087	−	0.652911i	−0.112526	−	0.0649671i	0.442681	−	0.896679i	$-0.354028\pi$
$101$	−1.13087	−	0.652911i	−0.112526	−	0.0649671i	−0.555207	+	0.831712i	$0.687361\pi$
$102$		0			0
$103$	−3.22312	−	5.58261i	−0.317584	−	0.550071i	0.662400	−	0.749151i	$-0.269538\pi$
$103$	−3.22312	−	5.58261i	−0.317584	−	0.550071i	−0.979983	+	0.199080i	$0.936205\pi$
$104$	−12.7231	+	3.09096i	−1.24760	+	0.303094i
$105$		0			0
$106$	−10.3221	−	7.34865i	−1.00257	−	0.713764i
$107$			3.10427i			0.300101i	0.988678	+	0.150051i	$0.0479437\pi$
$107$			3.10427i			0.300101i	−0.988678	+	0.150051i	$0.952056\pi$
$108$		0			0
$109$		−	18.0837i		−	1.73210i	−0.499955	−	0.866051i	$-0.666650\pi$
$109$		−	18.0837i		−	1.73210i	0.499955	−	0.866051i	$-0.333350\pi$
$110$	−9.16307	+	12.8707i	−0.873665	+	1.22717i
$111$		0			0
$112$	−1.03668	−	7.18822i	−0.0979574	−	0.679223i
$113$	1.41718	+	2.45463i	0.133317	+	0.230913i	0.924953	−	0.380080i	$-0.124104\pi$
$113$	1.41718	+	2.45463i	0.133317	+	0.230913i	−0.791636	+	0.610993i	$0.790770\pi$
$114$		0			0
$115$	−4.57370	−	2.64063i	−0.426500	−	0.246240i
$116$	1.38147	−	7.17611i	0.128267	−	0.666285i
$117$		0			0
$118$	−0.473298	+	4.96227i	−0.0435706	+	0.456814i
$119$	1.75018	−	3.03139i	0.160438	−	0.277887i
$120$		0			0
$121$	6.49370	+	11.2474i	0.590337	+	1.02249i
$122$	2.54997	−	1.16487i	0.230863	−	0.105462i
$123$		0			0
$124$	−6.96074	+	8.03663i	−0.625093	+	0.721711i
$125$		−	10.9419i		−	0.978674i
$126$		0			0
$127$	−7.44962			−0.661047			−0.330523	−	0.943798i	$-0.607225\pi$
$127$	−7.44962			−0.661047			−0.330523	+	0.943798i	$0.607225\pi$
$128$	−10.5001	+	4.21283i	−0.928086	+	0.372365i
$129$		0			0
$130$	6.20483	+	13.5828i	0.544200	+	1.19129i
$131$	−3.12153	+	1.80221i	−0.272729	+	0.157460i	−0.630127	−	0.776492i	$-0.716997\pi$
$131$	−3.12153	+	1.80221i	−0.272729	+	0.157460i	0.357398	+	0.933952i	$0.383664\pi$
$132$		0			0
$133$	3.34774	+	1.93282i	0.290286	+	0.167597i
$134$	−1.19811	+	12.5615i	−0.103501	+	1.08515i
$135$		0			0
$136$	−5.23248	−	1.53455i	−0.448682	−	0.131587i
$137$	−5.88147	+	10.1870i	−0.502488	+	0.870335i	0.497508	+	0.867460i	$0.334249\pi$
$137$	−5.88147	+	10.1870i	−0.502488	+	0.870335i	−0.999996	+	0.00287543i	$0.999085\pi$
$138$		0			0
$139$	−11.0400	+	6.37395i	−0.936400	+	0.540631i	−0.888830	−	0.458237i	$-0.848481\pi$
$139$	−11.0400	+	6.37395i	−0.936400	+	0.540631i	−0.0475703	+	0.998868i	$0.515148\pi$
$140$	−7.82693	+	2.71082i	−0.661496	+	0.229106i
$141$		0			0
$142$	10.9547	−	15.3872i	0.919296	−	1.29127i
$143$	22.6721			1.89594
$144$		0			0
$145$	−8.33472			−0.692161
$146$	9.48083	−	13.3170i	0.784639	−	1.10212i
$147$		0			0
$148$	15.0894	−	5.22613i	1.24034	−	0.429586i
$149$	−6.59790	+	3.80930i	−0.540521	+	0.312070i	−0.745290	−	0.666740i	$-0.767689\pi$
$149$	−6.59790	+	3.80930i	−0.540521	+	0.312070i	0.204769	+	0.978810i	$0.434356\pi$
$150$		0			0
$151$	2.26988	−	3.93155i	0.184720	−	0.319945i	−0.758762	−	0.651368i	$-0.774195\pi$
$151$	2.26988	−	3.93155i	0.184720	−	0.319945i	0.943482	+	0.331423i	$0.107529\pi$
$152$	1.69470	−	5.77854i	0.137458	−	0.468701i
$153$		0			0
$154$	−1.19406	+	12.5191i	−0.0962201	+	1.00882i
$155$	10.5014	+	6.06296i	0.843489	+	0.486989i
$156$		0			0
$157$	11.4105	−	6.58787i	0.910659	−	0.525769i	0.0300161	−	0.999549i	$-0.490444\pi$
$157$	11.4105	−	6.58787i	0.910659	−	0.525769i	0.880643	+	0.473780i	$0.157111\pi$
$158$	−5.84486	−	12.7948i	−0.464992	−	1.01790i
$159$		0			0
$160$	6.98198	+	10.8513i	0.551974	+	0.857869i
$161$	−4.20377			−0.331303
$162$		0			0
$163$			20.5911i			1.61282i	0.591358	+	0.806409i	$0.298592\pi$
$163$			20.5911i			1.61282i	−0.591358	+	0.806409i	$0.701408\pi$
$164$	6.18664	−	7.14288i	0.483095	−	0.557765i
$165$		0			0
$166$	−4.63656	+	2.11805i	−0.359867	+	0.164393i
$167$	−2.53912	−	4.39789i	−0.196483	−	0.340319i	0.750903	−	0.660413i	$-0.229619\pi$
$167$	−2.53912	−	4.39789i	−0.196483	−	0.340319i	−0.947386	+	0.320094i	$0.896285\pi$
$168$		0			0
$169$	4.21446	−	7.29967i	0.324190	−	0.561513i
$170$	−0.590490	+	6.19096i	−0.0452885	+	0.474825i
$171$		0			0
$172$	0.963939	−	5.00722i	0.0734997	−	0.381797i
$173$	−11.0398	−	6.37385i	−0.839343	−	0.484595i	0.0176977	−	0.999843i	$-0.494366\pi$
$173$	−11.0398	−	6.37385i	−0.839343	−	0.484595i	−0.857041	+	0.515248i	$0.827700\pi$
$174$		0			0
$175$	0.184351	+	0.319306i	0.0139356	+	0.0241372i
$176$	19.3902	−	2.79644i	1.46159	−	0.210790i
$177$		0			0
$178$	2.05021	−	2.87978i	0.153670	−	0.215849i
$179$			8.82019i			0.659252i	0.944112	+	0.329626i	$0.106923\pi$
$179$			8.82019i			0.659252i	−0.944112	+	0.329626i	$0.893077\pi$
$180$		0			0
$181$			15.4369i			1.14741i	0.819061	+	0.573707i	$0.194495\pi$
$181$			15.4369i			1.14741i	−0.819061	+	0.573707i	$0.805505\pi$
$182$	9.68305	+	6.89369i	0.717755	+	0.510994i
$183$		0			0
$184$	1.54597	+	6.36356i	0.113970	+	0.469128i
$185$	−9.10628	−	15.7725i	−0.669507	−	1.15962i
$186$		0			0
$187$	8.17715	+	4.72108i	0.597972	+	0.345239i
$188$	−7.93453	−	1.52748i	−0.578685	−	0.111403i
$189$		0			0
$190$	−6.83704	−	0.652112i	−0.496011	−	0.0473092i
$191$	−4.81698	+	8.34326i	−0.348545	+	0.603697i	−0.985991	−	0.166797i	$-0.946657\pi$
$191$	−4.81698	+	8.34326i	−0.348545	+	0.603697i	0.637446	+	0.770495i	$0.279991\pi$
$192$		0			0
$193$	3.49335	+	6.05066i	0.251457	+	0.435536i	0.963927	−	0.266166i	$-0.0857570\pi$
$193$	3.49335	+	6.05066i	0.251457	+	0.435536i	−0.712470	+	0.701702i	$0.752424\pi$
$194$	8.21934	+	17.9927i	0.590114	+	1.29180i
$195$		0			0
$196$	4.84924	−	5.59876i	0.346374	−	0.399912i
$197$		−	4.31842i		−	0.307675i	−0.988096	−	0.153837i	$-0.950837\pi$
$197$		−	4.31842i		−	0.307675i	0.988096	−	0.153837i	$-0.0491632\pi$
$198$		0			0
$199$	5.90649			0.418700			0.209350	−	0.977841i	$-0.432865\pi$
$199$	5.90649			0.418700			0.209350	+	0.977841i	$0.432865\pi$
$200$	0.415560	−	0.396493i	0.0293845	−	0.0280363i
$201$		0			0
$202$	1.67974	−	0.767333i	0.118186	−	0.0539894i
$203$	−5.74544	+	3.31713i	−0.403251	+	0.232817i
$204$		0			0
$205$	−9.33350	−	5.38870i	−0.651880	−	0.376363i
$206$	9.07518	+	0.865585i	0.632298	+	0.0603082i
$207$		0			0
$208$	6.87447	−	17.1932i	0.476659	−	1.19213i
$209$	−5.21376	+	9.03050i	−0.360644	+	0.624653i
$210$		0			0
$211$	−15.8781	+	9.16723i	−1.09309	+	0.631098i	−0.934399	−	0.356229i	$-0.884062\pi$
$211$	−15.8781	+	9.16723i	−1.09309	+	0.631098i	−0.158696	+	0.987328i	$0.550729\pi$
$212$	16.9324	−	5.86445i	1.16292	−	0.402772i
$213$		0			0
$214$	−3.57635	−	2.54612i	−0.244474	−	0.174049i
$215$	−5.81565			−0.396624
$216$		0			0
$217$	9.65199			0.655220
$218$	20.8337	+	14.8322i	1.41104	+	1.00457i
$219$		0			0
$220$	−7.31241	−	21.1131i	−0.493003	−	1.42344i
$221$	7.72877	−	4.46221i	0.519893	−	0.300161i
$222$		0			0
$223$	−2.63263	+	4.55986i	−0.176294	+	0.305350i	−0.940608	−	0.339494i	$-0.889744\pi$
$223$	−2.63263	+	4.55986i	−0.176294	+	0.305350i	0.764314	+	0.644844i	$0.223078\pi$
$224$	9.13165	+	4.70145i	0.610134	+	0.314129i
$225$		0			0
$226$	−3.99029	−	0.380591i	−0.265430	−	0.0253166i
$227$	−1.53638	−	0.887027i	−0.101973	−	0.0588741i	0.448146	−	0.893960i	$-0.352084\pi$
$227$	−1.53638	−	0.887027i	−0.101973	−	0.0588741i	−0.550119	+	0.835086i	$0.685418\pi$
$228$		0			0
$229$	−3.30687	+	1.90922i	−0.218524	+	0.126165i	−0.605267	−	0.796023i	$-0.706934\pi$
$229$	−3.30687	+	1.90922i	−0.218524	+	0.126165i	0.386742	+	0.922188i	$0.373600\pi$
$230$	6.79354	−	3.10339i	0.447953	−	0.204632i
$231$		0			0
$232$	7.13432	+	7.47740i	0.468391	+	0.490915i
$233$	20.3207			1.33125			0.665627	−	0.746284i	$-0.268164\pi$
$233$	20.3207			1.33125			0.665627	+	0.746284i	$0.268164\pi$
$234$		0			0
$235$			9.21558i			0.601158i
$236$	−5.32870	−	4.61533i	−0.346869	−	0.300432i
$237$		0			0
$238$	2.05689	+	4.50268i	0.133328	+	0.291865i
$239$	−8.69811	−	15.0656i	−0.562634	−	0.974510i	−0.997266	−	0.0739020i	$-0.976455\pi$
$239$	−8.69811	−	15.0656i	−0.562634	−	0.974510i	0.434632	−	0.900608i	$-0.356879\pi$
$240$		0			0
$241$	−6.85611	+	11.8751i	−0.441641	+	0.764944i	−0.997811	−	0.0661240i	$-0.978937\pi$
$241$	−6.85611	+	11.8751i	−0.441641	+	0.764944i	0.556171	+	0.831068i	$0.312270\pi$
$242$	−18.2840	−	1.74391i	−1.17534	−	0.112103i
$243$		0			0
$244$	−0.749475	+	3.89317i	−0.0479802	+	0.249235i
$245$	−7.31583	−	4.22379i	−0.467391	−	0.269848i
$246$		0			0
$247$	4.92788	+	8.53534i	0.313553	+	0.543090i
$248$	−3.54959	−	14.6109i	−0.225399	−	0.927795i
$249$		0			0
$250$	12.6059	+	8.97455i	0.797266	+	0.567601i
$251$			4.50751i			0.284512i	0.989830	+	0.142256i	$0.0454356\pi$
$251$			4.50751i			0.284512i	−0.989830	+	0.142256i	$0.954564\pi$
$252$		0			0
$253$		−	11.3396i		−	0.712916i
$254$	6.11018	−	8.58250i	0.383387	−	0.538514i
$255$		0			0
$256$	3.75869	−	15.5522i	0.234918	−	0.972015i
$257$	4.11258	+	7.12320i	0.256536	+	0.444333i	0.965311	−	0.261101i	$-0.0840856\pi$
$257$	4.11258	+	7.12320i	0.256536	+	0.444333i	−0.708776	+	0.705434i	$0.750752\pi$
$258$		0			0
$259$	−12.5546	−	7.24842i	−0.780106	−	0.450395i
$260$	−20.7376	−	3.99219i	−1.28609	−	0.247585i
$261$		0			0
$262$	0.483993	−	5.07440i	0.0299012	−	0.313498i
$263$	−2.51376	+	4.35395i	−0.155005	+	0.268476i	−0.933061	−	0.359719i	$-0.882873\pi$
$263$	−2.51376	+	4.35395i	−0.155005	+	0.268476i	0.778056	+	0.628195i	$0.216206\pi$
$264$		0			0
$265$	−10.2185	−	17.6990i	−0.627718	−	1.08724i
$266$	−4.97257	+	2.27155i	−0.304888	+	0.139277i
$267$		0			0
$268$	−13.4891	−	11.6832i	−0.823977	−	0.713668i
$269$		−	23.1577i		−	1.41195i	−0.708236	−	0.705976i	$-0.750509\pi$
$269$		−	23.1577i		−	1.41195i	0.708236	−	0.705976i	$-0.249491\pi$
$270$		0			0
$271$	20.9367			1.27181			0.635906	−	0.771766i	$-0.280627\pi$
$271$	20.9367			1.27181			0.635906	+	0.771766i	$0.280627\pi$
$272$	6.05960	−	4.76956i	0.367417	−	0.289197i
$273$		0			0
$274$	−6.91220	−	15.1313i	−0.417581	−	0.914113i
$275$	−0.861323	+	0.497285i	−0.0519398	+	0.0299874i
$276$		0			0
$277$	19.2687	+	11.1248i	1.15775	+	0.668425i	0.950763	−	0.309920i	$-0.100302\pi$
$277$	19.2687	+	11.1248i	1.15775	+	0.668425i	0.206983	+	0.978345i	$0.433636\pi$
$278$	1.71175	−	17.9468i	0.102664	−	1.07638i
$279$		0			0
$280$	3.29658	−	11.2406i	0.197008	−	0.671755i
$281$	9.28029	−	16.0739i	0.553616	−	0.958890i	−0.444394	−	0.895831i	$-0.646581\pi$
$281$	9.28029	−	16.0739i	0.553616	−	0.958890i	0.998010	−	0.0630590i	$-0.0200856\pi$
$282$		0			0
$283$	1.75962	−	1.01592i	0.104599	−	0.0603901i	−0.446788	−	0.894640i	$-0.647432\pi$
$283$	1.75962	−	1.01592i	0.104599	−	0.0603901i	0.551387	+	0.834250i	$0.314099\pi$
$284$	8.74217	+	25.2412i	0.518752	+	1.49779i
$285$		0			0
$286$	−18.5957	+	26.1199i	−1.09958	+	1.54450i
$287$	−8.57859			−0.506378
$288$		0			0
$289$	−13.2833			−0.781370
$290$	6.83613	−	9.60220i	0.401432	−	0.563861i
$291$		0			0
$292$	7.56600	+	21.8452i	0.442766	+	1.27840i
$293$	−29.5484	+	17.0598i	−1.72623	+	0.996642i	−0.822178	+	0.569231i	$0.807241\pi$
$293$	−29.5484	+	17.0598i	−1.72623	+	0.996642i	−0.904057	+	0.427411i	$0.859426\pi$
$294$		0			0
$295$	−4.02005	+	6.96294i	−0.234057	+	0.405398i
$296$	−6.35541	+	21.6705i	−0.369401	+	1.25957i
$297$		0			0
$298$	1.02300	−	10.7256i	0.0592611	−	0.621320i
$299$	−9.28192	−	5.35892i	−0.536787	−	0.309914i
$300$		0			0
$301$	−4.00895	+	2.31457i	−0.231072	+	0.133410i
$302$	2.66767	+	5.83972i	0.153507	+	0.336038i
$303$		0			0
$304$	5.26731	+	6.69197i	0.302101	+	0.383811i
$305$	4.52174			0.258914
$306$		0			0
$307$		−	4.77588i		−	0.272574i	−0.990669	−	0.136287i	$-0.956483\pi$
$307$		−	4.77588i		−	0.272574i	0.990669	−	0.136287i	$-0.0435169\pi$
$308$	−13.4435	−	11.6438i	−0.766015	−	0.663466i
$309$		0			0
$310$	−15.5982	+	7.12549i	−0.885917	+	0.404701i
$311$	11.1771	+	19.3592i	0.633793	+	1.09776i	0.986769	+	0.162130i	$0.0518364\pi$
$311$	11.1771	+	19.3592i	0.633793	+	1.09776i	−0.352976	+	0.935632i	$0.614830\pi$
$312$		0			0
$313$	1.22411	−	2.12022i	0.0691907	−	0.119842i	−0.829355	−	0.558723i	$-0.811292\pi$
$313$	1.22411	−	2.12022i	0.0691907	−	0.119842i	0.898545	+	0.438881i	$0.144625\pi$
$314$	−1.76920	+	18.5491i	−0.0998420	+	1.04679i
$315$		0			0
$316$	19.5345	+	3.76059i	1.09890	+	0.211550i
$317$	14.2886	+	8.24953i	0.802528	+	0.463340i	0.844354	−	0.535785i	$-0.179984\pi$
$317$	14.2886	+	8.24953i	0.802528	+	0.463340i	−0.0418263	+	0.999125i	$0.513318\pi$
$318$		0			0
$319$	−8.94793	−	15.4983i	−0.500988	−	0.867737i
$320$	−18.2281	−	0.856461i	−1.01898	−	0.0478776i
$321$		0			0
$322$	3.44793	−	4.84305i	0.192146	−	0.269893i
$323$			4.10459i			0.228385i
$324$		0			0
$325$			0.940035i			0.0521438i
$326$	−23.7224	−	16.8888i	−1.31386	−	0.935385i
$327$		0			0
$328$	3.15484	+	12.9861i	0.174197	+	0.717035i
$329$	3.66771	+	6.35266i	0.202207	+	0.350233i
$330$		0			0
$331$	−0.329200	−	0.190064i	−0.0180945	−	0.0104469i	0.490925	−	0.871202i	$-0.336659\pi$
$331$	−0.329200	−	0.190064i	−0.0180945	−	0.0104469i	−0.509020	+	0.860755i	$0.669992\pi$
$332$	1.36275	−	7.07888i	0.0747909	−	0.388504i
$333$		0			0
$334$	7.14928	+	0.681893i	0.391191	+	0.0373115i
$335$	−10.1764	+	17.6260i	−0.555994	+	0.963010i
$336$		0			0
$337$	−2.51872	−	4.36255i	−0.137203	−	0.237643i	0.789234	−	0.614093i	$-0.210478\pi$
$337$	−2.51872	−	4.36255i	−0.137203	−	0.237643i	−0.926437	+	0.376450i	$0.877145\pi$
$338$	4.95305	+	10.8426i	0.269410	+	0.589757i
$339$		0			0
$340$	−6.64812	−	5.75811i	−0.360545	−	0.312277i
$341$			26.0361i			1.40994i
$342$		0			0
$343$	−19.4337			−1.04932
$344$	4.97806	+	5.21745i	0.268399	+	0.281306i
$345$		0			0
$346$	16.3980	−	7.49086i	0.881563	−	0.402711i
$347$	8.40337	−	4.85169i	0.451116	−	0.260452i	−0.257185	−	0.966362i	$-0.582795\pi$
$347$	8.40337	−	4.85169i	0.451116	−	0.260452i	0.708302	+	0.705910i	$0.249462\pi$
$348$		0			0
$349$	−26.1239	−	15.0827i	−1.39838	−	0.807356i	−0.404158	−	0.914689i	$-0.632436\pi$
$349$	−26.1239	−	15.0827i	−1.39838	−	0.807356i	−0.994223	+	0.107333i	$0.965769\pi$
$350$	−0.519068	−	0.0495084i	−0.0277454	−	0.00264633i
$351$		0			0
$352$	−12.6821	+	24.6325i	−0.675958	+	1.31292i
$353$	−13.2376	+	22.9282i	−0.704565	+	1.22034i	0.262283	+	0.964991i	$0.415525\pi$
$353$	−13.2376	+	22.9282i	−0.704565	+	1.22034i	−0.966848	+	0.255352i	$0.917809\pi$
$354$		0			0
$355$	26.3840	−	15.2328i	1.40032	−	0.808473i
$356$	1.63613	+	4.72399i	0.0867148	+	0.250371i
$357$		0			0
$358$	−10.1615	−	7.23431i	−0.537052	−	0.382345i
$359$	23.4619			1.23827			0.619135	−	0.785285i	$-0.287483\pi$
$359$	23.4619			1.23827			0.619135	+	0.785285i	$0.287483\pi$
$360$		0			0
$361$	14.4671			0.761424
$362$	−17.7844	−	12.6613i	−0.934727	−	0.665464i
$363$		0			0
$364$	−15.8841	+	5.50138i	−0.832551	+	0.288350i
$365$	22.8343	−	13.1834i	1.19520	−	0.690050i
$366$		0			0
$367$	9.62599	−	16.6727i	0.502472	−	0.870308i	−0.497524	−	0.867450i	$-0.665757\pi$
$367$	9.62599	−	16.6727i	0.502472	−	0.870308i	0.999996	−	0.00285720i	$-0.000909476\pi$
$368$	−8.59928	−	3.43832i	−0.448269	−	0.179235i
$369$		0			0
$370$	25.6401	+	2.44553i	1.33296	+	0.127137i
$371$	−14.0880	−	8.13373i	−0.731414	−	0.422282i
$372$		0			0
$373$	−9.09206	+	5.24930i	−0.470769	+	0.271799i	−0.716562	−	0.697524i	$-0.754285\pi$
$373$	−9.09206	+	5.24930i	−0.470769	+	0.271799i	0.245793	+	0.969322i	$0.420952\pi$
$374$	−12.1459	+	5.54844i	−0.628051	+	0.286903i
$375$		0			0
$376$	8.26766	−	7.88832i	0.426372	−	0.406809i
$377$	−16.9146			−0.871145
$378$		0			0
$379$		−	35.5203i		−	1.82455i	−0.409574	−	0.912277i	$-0.634323\pi$
$379$		−	35.5203i		−	1.82455i	0.409574	−	0.912277i	$-0.365677\pi$
$380$	6.35902	−	7.34191i	0.326211	−	0.376632i
$381$		0			0
$382$	−5.66116	−	12.3927i	−0.289650	−	0.634064i
$383$	−18.0395	−	31.2453i	−0.921774	−	1.59656i	−0.796669	−	0.604416i	$-0.793407\pi$
$383$	−18.0395	−	31.2453i	−0.921774	−	1.59656i	−0.125105	−	0.992144i	$-0.539927\pi$
$384$		0			0
$385$	−10.1420	+	17.5664i	−0.516884	+	0.895269i
$386$	−9.83605	−	0.938156i	−0.500642	−	0.0477509i
$387$		0			0
$388$	−27.4704	−	5.28833i	−1.39460	−	0.268474i
$389$	17.5243	+	10.1177i	0.888519	+	0.512987i	0.873458	−	0.486900i	$-0.161872\pi$
$389$	17.5243	+	10.1177i	0.888519	+	0.512987i	0.0150612	+	0.999887i	$0.495206\pi$
$390$		0			0
$391$	−2.23181	−	3.86560i	−0.112867	−	0.195492i
$392$	2.47284	+	10.1788i	0.124897	+	0.514106i
$393$		0			0
$394$	4.97513	+	3.54197i	0.250644	+	0.178442i
$395$		−	22.6884i		−	1.14158i
$396$		0			0
$397$		−	3.99499i		−	0.200503i	−0.994962	−	0.100251i	$-0.968035\pi$
$397$		−	3.99499i		−	0.200503i	0.994962	−	0.100251i	$-0.0319647\pi$
$398$	−4.84450	+	6.80471i	−0.242833	+	0.341089i
$399$		0			0
$400$	0.115947	+	0.803959i	0.00579733	+	0.0401979i
$401$	−14.0124	−	24.2702i	−0.699747	−	1.21200i	−0.968554	−	0.248803i	$-0.919963\pi$
$401$	−14.0124	−	24.2702i	−0.699747	−	1.21200i	0.268807	−	0.963194i	$-0.413371\pi$
$402$		0			0
$403$	21.3116	+	12.3042i	1.06161	+	0.612918i
$404$	−0.493702	+	2.56455i	−0.0245626	+	0.127591i
$405$		0			0
$406$	0.890832	−	9.33988i	0.0442112	−	0.463531i
$407$	19.5525	−	33.8660i	0.969183	−	1.67867i
$408$		0			0
$409$	8.22481	+	14.2458i	0.406691	+	0.704409i	0.994517	−	0.104579i	$-0.0333494\pi$
$409$	8.22481	+	14.2458i	0.406691	+	0.704409i	−0.587826	+	0.808987i	$0.700016\pi$
$410$	13.8635	−	6.33307i	0.684670	−	0.312768i
$411$		0			0
$412$	−8.44068	+	9.74532i	−0.415842	+	0.480118i
$413$			6.39976i			0.314912i
$414$		0			0
$415$	−8.22179			−0.403592
$416$	14.1693	+	22.0217i	0.694708	+	1.07970i
$417$		0			0
$418$	−6.12747	−	13.4135i	−0.299704	−	0.656074i
$419$	20.5573	−	11.8688i	1.00429	−	0.579827i	0.0947752	−	0.995499i	$-0.469787\pi$
$419$	20.5573	−	11.8688i	1.00429	−	0.579827i	0.909515	+	0.415672i	$0.136453\pi$
$420$		0			0
$421$	25.9420	+	14.9776i	1.26433	+	0.729963i	0.973910	−	0.226935i	$-0.0728704\pi$
$421$	25.9420	+	14.9776i	1.26433	+	0.729963i	0.290424	+	0.956898i	$0.406204\pi$
$422$	2.46190	−	25.8117i	0.119844	−	1.25649i
$423$		0			0
$424$	−7.13165	+	24.3173i	−0.346343	+	1.18095i
$425$	−0.195746	+	0.339043i	−0.00949509	+	0.0164460i
$426$		0			0
$427$	3.11701	−	1.79961i	0.150843	−	0.0870891i
$428$	5.86664	−	2.03188i	0.283575	−	0.0982148i
$429$		0			0
$430$	4.76999	−	6.70005i	0.230030	−	0.323105i
$431$	11.0367			0.531621			0.265810	−	0.964025i	$-0.414360\pi$
$431$	11.0367			0.531621			0.265810	+	0.964025i	$0.414360\pi$
$432$		0			0
$433$	34.9394			1.67908			0.839541	−	0.543297i	$-0.182824\pi$
$433$	34.9394			1.67908			0.839541	+	0.543297i	$0.182824\pi$
$434$	−7.91656	+	11.1198i	−0.380007	+	0.533767i
$435$		0			0
$436$	−34.1756	+	11.8366i	−1.63672	+	0.566869i
$437$	4.26901	−	2.46472i	0.204215	−	0.117903i
$438$		0			0
$439$	−6.58518	+	11.4059i	−0.314293	+	0.544372i	−0.979287	−	0.202477i	$-0.935101\pi$
$439$	−6.58518	+	11.4059i	−0.314293	+	0.544372i	0.664994	+	0.746849i	$0.268434\pi$
$440$	30.3214	+	8.89249i	1.44552	+	0.423933i
$441$		0			0
$442$	−1.19835	+	12.5640i	−0.0569996	+	0.597609i
$443$	23.6849	+	13.6745i	1.12530	+	0.649694i	0.942749	−	0.333502i	$-0.108230\pi$
$443$	23.6849	+	13.6745i	1.12530	+	0.649694i	0.182554	+	0.983196i	$0.441564\pi$
$444$		0			0
$445$	4.93787	−	2.85088i	0.234077	−	0.135145i
$446$	−3.09400	−	6.77298i	−0.146505	−	0.320710i
$447$		0			0
$448$	−12.9062	+	6.66420i	−0.609760	+	0.314854i
$449$	13.8225			0.652323			0.326161	−	0.945314i	$-0.394245\pi$
$449$	13.8225			0.652323			0.326161	+	0.945314i	$0.394245\pi$
$450$		0			0
$451$		−	23.1407i		−	1.08965i
$452$	3.71130	−	4.28495i	0.174565	−	0.201547i
$453$		0			0
$454$	2.28206	−	1.04248i	0.107102	−	0.0489259i
$455$	9.58588	+	16.6032i	0.449393	+	0.778371i
$456$		0			0
$457$	−2.86205	+	4.95722i	−0.133881	+	0.231889i	−0.925170	−	0.379554i	$-0.876077\pi$
$457$	−2.86205	+	4.95722i	−0.133881	+	0.231889i	0.791288	+	0.611443i	$0.209411\pi$
$458$	0.512731	−	5.37570i	0.0239584	−	0.251190i
$459$		0			0
$460$	−1.99672	+	10.3721i	−0.0930977	+	0.483600i
$461$	19.3717	+	11.1843i	0.902231	+	0.520903i	0.877923	−	0.478801i	$-0.158929\pi$
$461$	19.3717	+	11.1843i	0.902231	+	0.520903i	0.0243074	+	0.999705i	$0.492262\pi$
$462$		0			0
$463$	18.5733	+	32.1699i	0.863174	+	1.49506i	0.868849	+	0.495077i	$0.164860\pi$
$463$	18.5733	+	32.1699i	0.863174	+	1.49506i	−0.00567564	+	0.999984i	$0.501807\pi$
$464$	−14.4661	+	2.08629i	−0.671571	+	0.0968537i
$465$		0			0
$466$	−16.6671	+	23.4110i	−0.772086	+	1.08449i
$467$		−	22.6850i		−	1.04974i	−0.851184	−	0.524868i	$-0.824115\pi$
$467$		−	22.6850i		−	1.04974i	0.851184	−	0.524868i	$-0.175885\pi$
$468$		0			0
$469$			16.2004i			0.748063i
$470$	−10.6170	−	7.55862i	−0.489727	−	0.348653i
$471$		0			0
$472$	9.68780	−	2.35356i	0.445917	−	0.108331i
$473$	−6.24353	−	10.8141i	−0.287078	−	0.497233i
$474$		0			0
$475$	−0.374425	−	0.216174i	−0.0171798	−	0.00991875i
$476$	−6.87447	−	1.32340i	−0.315091	−	0.0606582i
$477$		0			0
$478$	24.4908	+	2.33592i	1.12018	+	0.106842i
$479$	−13.1576	+	22.7897i	−0.601188	+	1.04129i	0.391453	+	0.920198i	$0.371973\pi$
$479$	−13.1576	+	22.7897i	−0.601188	+	1.04129i	−0.992641	+	0.121091i	$0.961361\pi$
$480$		0			0
$481$	−18.4804	−	32.0090i	−0.842634	−	1.45948i
$482$	−8.05763	−	17.6387i	−0.367015	−	0.803421i
$483$		0			0
$484$	17.0056	−	19.6341i	0.772984	−	0.892460i
$485$			31.9056i			1.44876i
$486$		0			0
$487$	−24.0388			−1.08930			−0.544652	−	0.838662i	$-0.683338\pi$
$487$	−24.0388			−1.08930			−0.544652	+	0.838662i	$0.683338\pi$
$488$	−3.87050	−	4.05663i	−0.175209	−	0.183635i
$489$		0			0
$490$	10.8666	−	4.96401i	0.490901	−	0.224251i
$491$	−27.2256	+	15.7187i	−1.22867	+	0.709374i	−0.966752	−	0.255715i	$-0.917689\pi$
$491$	−27.2256	+	15.7187i	−1.22867	+	0.709374i	−0.261920	+	0.965090i	$0.584356\pi$
$492$		0			0
$493$	−6.10058	−	3.52217i	−0.274756	−	0.158631i
$494$	−13.8752	−	1.32340i	−0.624274	−	0.0595428i
$495$		0			0
$496$	19.7442	+	7.89449i	0.886542	+	0.354473i
$497$	12.1250	−	21.0011i	0.543881	−	0.942029i
$498$		0			0
$499$	5.08156	−	2.93384i	0.227482	−	0.131337i	−0.381928	−	0.924192i	$-0.624740\pi$
$499$	5.08156	−	2.93384i	0.227482	−	0.131337i	0.609410	+	0.792855i	$0.291406\pi$
$500$	−20.6787	+	7.16197i	−0.924779	+	0.320293i
$501$		0			0
$502$	−5.19298	−	3.69706i	−0.231774	−	0.165008i
$503$	−32.4317			−1.44606			−0.723029	−	0.690818i	$-0.757251\pi$
$503$	−32.4317			−1.44606			−0.723029	+	0.690818i	$0.757251\pi$
$504$		0			0
$505$	2.97861			0.132546
$506$	13.0641	+	9.30076i	0.580769	+	0.413469i
$507$		0			0
$508$	4.87611	+	14.0787i	0.216342	+	0.624643i
$509$	13.6855	−	7.90133i	0.606599	−	0.350220i	−0.165034	−	0.986288i	$-0.552773\pi$
$509$	13.6855	−	7.90133i	0.606599	−	0.350220i	0.771633	+	0.636068i	$0.219440\pi$
$510$		0			0
$511$	10.4937	−	18.1756i	0.464214	−	0.804042i
$512$	14.8344	+	17.0862i	0.655596	+	0.755112i
$513$		0			0
$514$	−11.5796	−	1.10445i	−0.510753	−	0.0487153i
$515$	12.7341	+	7.35202i	0.561130	+	0.323969i
$516$		0			0
$517$	−17.1362	+	9.89361i	−0.753650	+	0.435120i
$518$	18.6480	−	8.51870i	0.819346	−	0.374290i
$519$		0			0
$520$	21.6083	−	20.6168i	0.947585	−	0.904107i
$521$	−5.50310			−0.241095			−0.120548	−	0.992708i	$-0.538465\pi$
$521$	−5.50310			−0.241095			−0.120548	+	0.992708i	$0.538465\pi$
$522$		0			0
$523$			38.5894i			1.68740i	0.536818	+	0.843698i	$0.319626\pi$
$523$			38.5894i			1.68740i	−0.536818	+	0.843698i	$0.680374\pi$
$524$	5.44911	+	4.71962i	0.238046	+	0.206178i
$525$		0			0
$526$	−2.95429	−	6.46714i	−0.128813	−	0.281981i
$527$	5.12430	+	8.87555i	0.223218	+	0.386625i
$528$		0			0
$529$	8.81970	−	15.2762i	0.383465	−	0.664181i
$530$	28.7717	+	2.74423i	1.24976	+	0.119202i
$531$		0			0
$532$	1.46151	−	7.59189i	0.0633647	−	0.329150i
$533$	−18.9415	−	10.9359i	−0.820449	−	0.473686i
$534$		0			0
$535$	−3.54046	−	6.13225i	−0.153067	−	0.265120i
$536$	24.5237	−	5.95781i	1.05926	−	0.257338i
$537$		0			0
$538$	26.6794	+	18.9940i	1.15023	+	0.818888i
$539$		−	18.1382i		−	0.781268i
$540$		0			0
$541$			22.5666i			0.970214i	0.874455	+	0.485107i	$0.161219\pi$
$541$			22.5666i			0.970214i	−0.874455	+	0.485107i	$0.838781\pi$
$542$	−17.1723	+	24.1206i	−0.737612	+	1.03607i
$543$		0			0
$544$	0.524803	+	10.8931i	0.0225008	+	0.467037i
$545$	20.6246	+	35.7229i	0.883463	+	1.53020i
$546$		0			0
$547$	−11.2679	−	6.50552i	−0.481780	−	0.278156i	0.239378	−	0.970927i	$-0.423057\pi$
$547$	−11.2679	−	6.50552i	−0.481780	−	0.278156i	−0.721158	+	0.692770i	$0.756390\pi$
$548$	23.1017	+	4.44731i	0.986856	+	0.189980i
$549$		0			0
$550$	0.133548	−	1.40018i	0.00569452	−	0.0597039i
$551$	3.88974	−	6.73723i	0.165709	−	0.287016i
$552$		0			0
$553$	−9.02976	−	15.6400i	−0.383985	−	0.665081i
$554$	−28.6208	+	13.0744i	−1.21598	+	0.555479i
$555$		0			0
$556$	19.2720	+	16.6920i	0.817316	+	0.707899i
$557$			5.73693i			0.243081i	0.992586	+	0.121541i	$0.0387835\pi$
$557$			5.73693i			0.243081i	−0.992586	+	0.121541i	$0.961217\pi$
$558$		0			0
$559$	−11.8024			−0.499186
$560$	10.2461	+	13.0174i	0.432979	+	0.550087i
$561$		0			0
$562$	10.9067	+	23.8754i	0.460069	+	1.00712i
$563$	−13.2510	+	7.65045i	−0.558462	+	0.322428i	−0.752528	−	0.658560i	$-0.771166\pi$
$563$	−13.2510	+	7.65045i	−0.558462	+	0.322428i	0.194066	+	0.980988i	$0.437832\pi$
$564$		0			0
$565$	−5.59908	−	3.23263i	−0.235555	−	0.135998i
$566$	−0.272830	+	2.86047i	−0.0114679	+	0.120235i
$567$		0			0
$568$	−36.2500	−	10.6312i	−1.52102	−	0.446075i
$569$	−6.63095	+	11.4851i	−0.277984	+	0.481482i	−0.970884	−	0.239552i	$-0.922999\pi$
$569$	−6.63095	+	11.4851i	−0.277984	+	0.481482i	0.692900	+	0.721034i	$0.256333\pi$
$570$		0			0
$571$	23.4262	−	13.5251i	0.980357	−	0.566009i	0.0779788	−	0.996955i	$-0.475153\pi$
$571$	23.4262	−	13.5251i	0.980357	−	0.566009i	0.902378	+	0.430946i	$0.141820\pi$
$572$	−14.8399	−	42.8471i	−0.620488	−	1.79153i
$573$		0			0
$574$	7.03616	−	9.88317i	0.293684	−	0.412515i
$575$	0.470166			0.0196073
$576$		0			0
$577$	−4.78434			−0.199174			−0.0995872	−	0.995029i	$-0.531752\pi$
$577$	−4.78434			−0.199174			−0.0995872	+	0.995029i	$0.531752\pi$
$578$	10.8949	−	15.3033i	0.453170	−	0.636534i
$579$		0			0
$580$	5.45544	+	15.7514i	0.226525	+	0.654043i
$581$	−5.66760	+	3.27219i	−0.235132	+	0.135753i
$582$		0			0
$583$	21.9406	−	38.0023i	0.908689	−	1.57390i
$584$	−31.3729	−	9.20087i	−1.29822	−	0.380735i
$585$		0			0
$586$	4.58148	−	48.0343i	0.189259	−	1.98428i
$587$	−37.0796	−	21.4079i	−1.53044	−	0.883598i	−0.999341	−	0.0362861i	$-0.988447\pi$
$587$	−37.0796	−	21.4079i	−1.53044	−	0.883598i	−0.531095	−	0.847312i	$-0.678219\pi$
$588$		0			0
$589$	−9.80179	+	5.65906i	−0.403876	+	0.233178i
$590$	−4.72457	−	10.3424i	−0.194507	−	0.425790i
$591$		0			0
$592$	−19.7533	−	25.0961i	−0.811857	−	1.03144i
$593$	0.825572			0.0339022			0.0169511	−	0.999856i	$-0.494604\pi$
$593$	0.825572			0.0339022			0.0169511	+	0.999856i	$0.494604\pi$
$594$		0			0
$595$			7.98438i			0.327328i
$596$	11.5177	+	9.97575i	0.471782	+	0.408623i
$597$		0			0
$598$	13.7869	−	6.29807i	0.563788	−	0.257547i
$599$	0.961228	+	1.66490i	0.0392747	+	0.0680258i	0.884995	−	0.465601i	$-0.154162\pi$
$599$	0.961228	+	1.66490i	0.0392747	+	0.0680258i	−0.845720	+	0.533627i	$0.820829\pi$
$600$		0			0
$601$	−21.5937	+	37.4014i	−0.880825	+	1.52563i	−0.0303994	+	0.999538i	$0.509678\pi$
$601$	−21.5937	+	37.4014i	−0.880825	+	1.52563i	−0.850425	+	0.526096i	$0.823655\pi$
$602$	0.621589	−	6.51702i	0.0253341	−	0.265614i
$603$		0			0
$604$	−8.91581	−	1.71638i	−0.362779	−	0.0698386i
$605$	−25.6556	−	14.8123i	−1.04305	−	0.602205i
$606$		0			0
$607$	20.5078	+	35.5206i	0.832386	+	1.44174i	0.896141	+	0.443770i	$0.146359\pi$
$607$	20.5078	+	35.5206i	0.832386	+	1.44174i	−0.0637546	+	0.997966i	$0.520307\pi$
$608$	−12.0299	+	0.579571i	−0.487876	+	0.0235047i
$609$		0			0
$610$	−3.70873	+	5.20937i	−0.150162	+	0.210921i
$611$			18.7022i			0.756611i
$612$		0			0
$613$		−	5.05878i		−	0.204322i	−0.994768	−	0.102161i	$-0.967424\pi$
$613$		−	5.05878i		−	0.204322i	0.994768	−	0.102161i	$-0.0325757\pi$
$614$	5.50216	+	3.91717i	0.222049	+	0.158084i
$615$		0			0
$616$	24.4409	−	5.93768i	0.984750	−	0.239236i
$617$	16.0739	+	27.8408i	0.647112	+	1.12083i	0.983809	+	0.179217i	$0.0573566\pi$
$617$	16.0739	+	27.8408i	0.647112	+	1.12083i	−0.336698	+	0.941613i	$0.609310\pi$
$618$		0			0
$619$	−27.3562	−	15.7941i	−1.09954	−	0.634820i	−0.163440	−	0.986553i	$-0.552259\pi$
$619$	−27.3562	−	15.7941i	−1.09954	−	0.634820i	−0.936100	+	0.351734i	$0.885592\pi$
$620$	4.58454	−	23.8146i	0.184120	−	0.956416i
$621$		0			0
$622$	−31.4707	−	3.00165i	−1.26186	−	0.120355i
$623$	2.26924	−	3.93044i	0.0909153	−	0.157470i
$624$		0			0
$625$	12.9871	+	22.4942i	0.519482	+	0.899770i
$626$	1.43863	+	3.14927i	0.0574993	+	0.125870i
$627$		0			0
$628$	−19.9189	−	17.2522i	−0.794849	−	0.688440i
$629$		−	15.3929i		−	0.613756i
$630$		0			0
$631$	−15.4885			−0.616586			−0.308293	−	0.951292i	$-0.599758\pi$
$631$	−15.4885			−0.616586			−0.308293	+	0.951292i	$0.599758\pi$
$632$	−20.3547	+	19.4207i	−0.809665	+	0.772516i
$633$		0			0
$634$	−21.2236	+	9.69525i	−0.842896	+	0.385048i
$635$	14.7162	−	8.49638i	0.583993	−	0.337168i
$636$		0			0
$637$	−14.8468	−	8.57182i	−0.588253	−	0.339628i
$638$	25.1942	+	2.40301i	0.997449	+	0.0951361i
$639$		0			0
$640$	15.9374	−	20.2976i	0.629980	−	0.802334i
$641$	15.2248	−	26.3701i	0.601344	−	1.04156i	−0.391274	−	0.920274i	$-0.627966\pi$
$641$	15.2248	−	26.3701i	0.601344	−	1.04156i	0.992618	−	0.121284i	$-0.0387011\pi$
$642$		0			0
$643$	−14.5911	+	8.42419i	−0.575418	+	0.332218i	−0.759310	−	0.650729i	$-0.774463\pi$
$643$	−14.5911	+	8.42419i	−0.575418	+	0.332218i	0.183893	+	0.982946i	$0.441130\pi$
$644$	2.75155	+	7.94454i	0.108426	+	0.313059i
$645$		0			0
$646$	−4.72878	−	3.36658i	−0.186051	−	0.132456i
$647$	−18.6734			−0.734126			−0.367063	−	0.930196i	$-0.619637\pi$
$647$	−18.6734			−0.734126			−0.367063	+	0.930196i	$0.619637\pi$
$648$		0			0
$649$	−17.2633			−0.677644
$650$	−1.08299	−	0.771017i	−0.0424783	−	0.0302418i
$651$		0			0
$652$	38.9143	−	13.4778i	1.52400	−	0.527831i
$653$	−31.4276	+	18.1448i	−1.22986	+	0.710059i	−0.967000	−	0.254775i	$-0.917999\pi$
$653$	−31.4276	+	18.1448i	−1.22986	+	0.710059i	−0.262858	+	0.964834i	$0.584665\pi$
$654$		0			0
$655$	4.11089	−	7.12028i	0.160626	−	0.278212i
$656$	−17.5485	−	7.01655i	−0.685153	−	0.273950i
$657$		0			0
$658$	−10.3270	−	0.984980i	−0.402588	−	0.0383985i
$659$	−19.3088	−	11.1480i	−0.752166	−	0.434263i	0.0743103	−	0.997235i	$-0.476324\pi$
$659$	−19.3088	−	11.1480i	−0.752166	−	0.434263i	−0.826476	+	0.562972i	$0.809658\pi$
$660$		0			0
$661$	5.19793	−	3.00103i	0.202176	−	0.116726i	−0.395494	−	0.918469i	$-0.629427\pi$
$661$	5.19793	−	3.00103i	0.202176	−	0.116726i	0.597670	+	0.801742i	$0.296093\pi$
$662$	0.488978	−	0.223373i	0.0190047	−	0.00868162i
$663$		0			0
$664$	7.03765	+	7.37609i	0.273114	+	0.286248i
$665$	−8.81762			−0.341933
$666$		0			0
$667$			8.45996i			0.327571i
$668$	−6.64943	+	7.67720i	−0.257274	+	0.297040i
$669$		0			0
$670$	−11.9598	−	26.1807i	−0.462046	−	1.01145i
$671$	4.85442	+	8.40810i	0.187403	+	0.324591i
$672$		0			0
$673$	−3.70444	+	6.41629i	−0.142796	+	0.247330i	−0.928548	−	0.371211i	$-0.878943\pi$
$673$	−3.70444	+	6.41629i	−0.142796	+	0.247330i	0.785753	+	0.618541i	$0.212276\pi$
$674$	7.09183	+	0.676414i	0.273167	+	0.0260545i
$675$		0			0
$676$	−16.5539	−	3.18679i	−0.636689	−	0.122569i
$677$	−8.57613	−	4.95143i	−0.329607	−	0.190299i	0.326059	−	0.945349i	$-0.394279\pi$
$677$	−8.57613	−	4.95143i	−0.329607	−	0.190299i	−0.655667	+	0.755050i	$0.727612\pi$
$678$		0			0
$679$	12.6981	+	21.9938i	0.487309	+	0.844043i
$680$	12.0865	−	2.93632i	0.463498	−	0.112603i
$681$		0			0
$682$	−29.9955	−	21.3548i	−1.14859	−	0.817719i
$683$			39.0736i			1.49511i	0.664200	+	0.747555i	$0.268772\pi$
$683$			39.0736i			1.49511i	−0.664200	+	0.747555i	$0.731228\pi$
$684$		0			0
$685$		−	26.8316i		−	1.02518i
$686$	15.9395	−	22.3890i	0.608572	−	0.854815i
$687$		0			0
$688$	−10.0939	+	1.45574i	−0.384826	+	0.0554994i
$689$	−20.7376	−	35.9185i	−0.790039	−	1.36839i
$690$		0			0
$691$	2.07502	+	1.19801i	0.0789375	+	0.0455746i	0.538949	−	0.842338i	$-0.318821\pi$
$691$	2.07502	+	1.19801i	0.0789375	+	0.0455746i	−0.460012	+	0.887913i	$0.652155\pi$
$692$	−4.81962	+	25.0357i	−0.183215	+	0.951715i
$693$		0			0
$694$	−1.30294	+	13.6606i	−0.0494590	+	0.518551i
$695$	14.5391	−	25.1825i	0.551500	−	0.955227i
$696$		0			0
$697$	−4.55443	−	7.88850i	−0.172511	−	0.298798i
$698$	38.8032	−	17.7259i	1.46872	−	0.670934i
$699$		0			0
$700$	0.482777	−	0.557398i	0.0182472	−	0.0210677i
$701$		−	30.9184i		−	1.16777i	−0.811836	−	0.583885i	$-0.801532\pi$
$701$		−	30.9184i		−	1.16777i	0.811836	−	0.583885i	$-0.198468\pi$
$702$		0			0
$703$	16.9993			0.641141
$704$	−17.9766	−	34.8143i	−0.677519	−	1.31211i
$705$		0			0
$706$	−15.5575	−	34.0563i	−0.585513	−	1.28173i
$707$	2.05327	−	1.18546i	0.0772212	−	0.0445837i
$708$		0			0
$709$	−4.46959	−	2.58052i	−0.167859	−	0.0969133i	0.413717	−	0.910406i	$-0.364230\pi$
$709$	−4.46959	−	2.58052i	−0.167859	−	0.0969133i	−0.581576	+	0.813492i	$0.697564\pi$
$710$	−4.09084	+	42.8902i	−0.153526	+	1.60964i
$711$		0			0
$712$	−6.78434	−	1.98967i	−0.254254	−	0.0745661i
$713$	6.15406	−	10.6591i	0.230471	−	0.399188i
$714$		0			0
$715$	−44.7870	+	25.8578i	−1.67494	+	0.967027i
$716$	16.6689	−	5.77320i	0.622947	−	0.215755i
$717$		0			0
$718$	−19.2434	+	27.0298i	−0.718158	+	1.00874i
$719$	−14.7871			−0.551465			−0.275733	−	0.961234i	$-0.588920\pi$
$719$	−14.7871			−0.551465			−0.275733	+	0.961234i	$0.588920\pi$
$720$		0			0
$721$	11.7041			0.435884
$722$	−11.8659	+	16.6671i	−0.441602	+	0.620286i
$723$		0			0
$724$	29.1735	−	10.1041i	1.08423	−	0.375517i
$725$	0.642593	−	0.371001i	0.0238653	−	0.0137786i
$726$		0			0
$727$	−1.06681	+	1.84777i	−0.0395658	+	0.0685299i	−0.885130	−	0.465344i	$-0.845931\pi$
$727$	−1.06681	+	1.84777i	−0.0395658	+	0.0685299i	0.845564	+	0.533873i	$0.179264\pi$
$728$	6.69012	−	22.8118i	0.247952	−	0.845463i
$729$		0			0
$730$	−3.54046	+	37.1198i	−0.131038	+	1.37386i
$731$	−4.25675	−	2.45764i	−0.157442	−	0.0908990i
$732$		0			0
$733$	22.2298	−	12.8344i	0.821076	−	0.474048i	−0.0297113	−	0.999559i	$-0.509459\pi$
$733$	22.2298	−	12.8344i	0.821076	−	0.474048i	0.850787	+	0.525510i	$0.176125\pi$
$734$	11.3129	+	24.7648i	0.417568	+	0.914085i
$735$		0			0
$736$	11.0143	−	7.08689i	0.405993	−	0.261226i
$737$	−43.7003			−1.60972
$738$		0			0
$739$		−	5.46282i		−	0.200953i	−0.994939	−	0.100476i	$-0.967963\pi$
$739$		−	5.46282i		−	0.200953i	0.994939	−	0.100476i	$-0.0320367\pi$
$740$	−23.8474	+	27.5334i	−0.876649	+	1.01215i
$741$		0			0
$742$	20.9257	−	9.55916i	0.768205	−	0.350928i
$743$	16.8170	+	29.1279i	0.616955	+	1.06860i	0.990038	+	0.140800i	$0.0449674\pi$
$743$	16.8170	+	29.1279i	0.616955	+	1.06860i	−0.373083	+	0.927798i	$0.621699\pi$
$744$		0			0
$745$	8.68910	−	15.0500i	0.318344	−	0.551388i
$746$	1.40972	−	14.7802i	0.0516137	−	0.541141i
$747$		0			0
$748$	3.56987	−	18.5438i	0.130527	−	0.678029i
$749$	−4.88115	−	2.81813i	−0.178353	−	0.102972i
$750$		0			0
$751$	−12.6727	−	21.9498i	−0.462435	−	0.800961i	0.536647	−	0.843807i	$-0.319691\pi$
$751$	−12.6727	−	21.9498i	−0.462435	−	0.800961i	−0.999082	+	0.0428462i	$0.986357\pi$
$752$	2.30679	+	15.9949i	0.0841198	+	0.583276i
$753$		0			0
$754$	13.8733	−	19.4868i	0.505237	−	0.709669i
$755$			10.3553i			0.376868i
$756$		0			0
$757$			3.95103i			0.143603i	0.997419	+	0.0718014i	$0.0228748\pi$
$757$			3.95103i			0.143603i	−0.997419	+	0.0718014i	$0.977125\pi$
$758$	40.9219	+	29.1337i	1.48635	+	1.05818i
$759$		0			0
$760$	3.24275	+	13.3479i	0.117627	+	0.484179i
$761$	23.3979	+	40.5264i	0.848175	+	1.46908i	0.882835	+	0.469682i	$0.155632\pi$
$761$	23.3979	+	40.5264i	0.848175	+	1.46908i	−0.0346607	+	0.999399i	$0.511035\pi$
$762$		0			0
$763$	28.4347	+	16.4168i	1.02941	+	0.594328i
$764$	18.9205	+	3.64239i	0.684521	+	0.131777i
$765$		0			0
$766$	50.7928	+	4.84459i	1.83522	+	0.175042i
$767$	−8.15835	+	14.1307i	−0.294581	+	0.510229i
$768$		0			0
$769$	2.60083	+	4.50478i	0.0937885	+	0.162446i	0.909102	−	0.416573i	$-0.136769\pi$
$769$	2.60083	+	4.50478i	0.0937885	+	0.162446i	−0.815314	+	0.579019i	$0.803436\pi$
$770$	−11.9194	−	26.0923i	−0.429544	−	0.940302i
$771$		0			0
$772$	9.14835	−	10.5624i	0.329256	−	0.380148i
$773$		−	38.8477i		−	1.39725i	−0.715486	−	0.698627i	$-0.753795\pi$
$773$		−	38.8477i		−	1.39725i	0.715486	−	0.698627i	$-0.246205\pi$
$774$		0			0
$775$	−1.07952			−0.0387773
$776$	28.6238	−	27.3104i	1.02753	−	0.980387i
$777$		0			0
$778$	−26.0298	+	11.8908i	−0.933212	+	0.426306i
$779$	8.71173	−	5.02972i	0.312130	−	0.180209i
$780$		0			0
$781$	56.6503	+	32.7071i	2.02711	+	1.17035i
$782$	6.28399	+	0.599362i	0.224715	+	0.0214332i
$783$		0			0
$784$	−13.7549	−	5.49974i	−0.491247	−	0.196419i
$785$	−15.0271	+	26.0277i	−0.536340	+	0.928968i
$786$		0			0
$787$	−40.8579	+	23.5893i	−1.45643	+	0.840869i	−0.998833	−	0.0482918i	$-0.984622\pi$
$787$	−40.8579	+	23.5893i	−1.45643	+	0.840869i	−0.457595	+	0.889161i	$0.651289\pi$
$788$	−8.16121	+	2.82660i	−0.290731	+	0.100693i
$789$		0			0
$790$	26.1387	+	18.6090i	0.929974	+	0.662080i
$791$	−5.14621			−0.182978
$792$		0			0
$793$	9.17648			0.325866
$794$	4.60252	+	3.27669i	0.163337	+	0.116285i
$795$		0			0
$796$	−3.86606	−	11.1624i	−0.137029	−	0.395642i
$797$	−6.35645	+	3.66990i	−0.225157	+	0.129995i	−0.608336	−	0.793680i	$-0.708163\pi$
$797$	−6.35645	+	3.66990i	−0.225157	+	0.129995i	0.383179	+	0.923674i	$0.374829\pi$
$798$		0			0
$799$	−3.89442	+	6.74533i	−0.137775	+	0.238633i
$800$	−1.02132	−	0.525828i	−0.0361091	−	0.0185908i
$801$		0			0
$802$	39.4541	+	3.76310i	1.39317	+	0.132880i
$803$	49.0286	+	28.3067i	1.73018	+	0.998920i
$804$		0			0
$805$	8.30423	−	4.79445i	0.292686	−	0.168982i
$806$	−31.6552	+	14.4606i	−1.11501	+	0.509351i
$807$		0			0
$808$	−2.54962	−	2.67223i	−0.0896953	−	0.0940087i
$809$	−2.25520			−0.0792887			−0.0396443	−	0.999214i	$-0.512622\pi$
$809$	−2.25520			−0.0792887			−0.0396443	+	0.999214i	$0.512622\pi$
$810$		0			0
$811$			15.9986i			0.561785i	0.959739	+	0.280893i	$0.0906305\pi$
$811$			15.9986i			0.561785i	−0.959739	+	0.280893i	$0.909369\pi$
$812$	10.0296	+	8.68687i	0.351969	+	0.304849i
$813$		0			0
$814$	22.9791	+	50.3028i	0.805417	+	1.76311i
$815$	−23.4844	−	40.6761i	−0.822622	−	1.42482i
$816$		0			0
$817$	2.71411	−	4.70098i	0.0949548	−	0.164467i
$818$	−23.1582	−	2.20881i	−0.809707	−	0.0772293i
$819$		0			0
$820$	−4.07470	+	21.1662i	−0.142295	+	0.739154i
$821$	25.2413	+	14.5731i	0.880928	+	0.508604i	0.870964	−	0.491347i	$-0.163495\pi$
$821$	25.2413	+	14.5731i	0.880928	+	0.508604i	0.00996351	+	0.999950i	$0.496828\pi$
$822$		0			0
$823$	−4.15695	−	7.20005i	−0.144902	−	0.250978i	0.784434	−	0.620212i	$-0.212953\pi$
$823$	−4.15695	−	7.20005i	−0.144902	−	0.250978i	−0.929336	+	0.369234i	$0.879620\pi$
$824$	−4.30428	−	17.7174i	−0.149947	−	0.617215i
$825$		0			0
$826$	−7.37300	−	5.24908i	−0.256539	−	0.182639i
$827$			43.5035i			1.51277i	0.654129	+	0.756383i	$0.273035\pi$
$827$			43.5035i			1.51277i	−0.654129	+	0.756383i	$0.726965\pi$
$828$		0			0
$829$		−	15.9248i		−	0.553092i	−0.961001	−	0.276546i	$-0.910810\pi$
$829$		−	15.9248i		−	0.553092i	0.961001	−	0.276546i	$-0.0891897\pi$
$830$	6.74351	−	9.47210i	0.234071	−	0.328781i
$831$		0			0
$832$	−36.9923	−	1.73811i	−1.28248	−	0.0602582i
$833$	−3.56987	−	6.18320i	−0.123689	−	0.214235i
$834$		0			0
$835$	10.0317	+	5.79180i	0.347161	+	0.200433i
$836$	20.4790	+	3.94242i	0.708282	+	0.136351i
$837$		0			0
$838$	−3.18741	+	33.4183i	−0.110107	+	1.15442i
$839$	21.0582	−	36.4739i	0.727009	−	1.25922i	−0.231132	−	0.972922i	$-0.574243\pi$
$839$	21.0582	−	36.4739i	0.727009	−	1.25922i	0.958142	−	0.286295i	$-0.0924237\pi$
$840$		0			0
$841$	−7.82437	−	13.5522i	−0.269806	−	0.467318i
$842$	−38.5329	+	17.6024i	−1.32793	+	0.606619i
$843$		0			0
$844$	27.7177	+	24.0070i	0.954083	+	0.826357i
$845$			19.2266i			0.661415i
$846$		0			0
$847$	−23.5806			−0.810238
$848$	−22.1660	−	28.1613i	−0.761182	−	0.967061i
$849$		0			0
$850$	−0.230051	−	0.503597i	−0.00789068	−	0.0172732i
$851$	−16.0095	+	9.24311i	−0.548800	+	0.316850i
$852$		0			0
$853$	−34.2013	−	19.7461i	−1.17103	−	0.676095i	−0.217108	−	0.976148i	$-0.569662\pi$
$853$	−34.2013	−	19.7461i	−1.17103	−	0.676095i	−0.953923	+	0.300053i	$0.902996\pi$
$854$	−0.483293	+	5.06706i	−0.0165379	+	0.173391i
$855$		0			0
$856$	−2.47094	+	8.42535i	−0.0844549	+	0.287972i
$857$	12.6170	−	21.8532i	0.430988	−	0.746493i	−0.565971	−	0.824425i	$-0.691499\pi$
$857$	12.6170	−	21.8532i	0.430988	−	0.746493i	0.996959	+	0.0779326i	$0.0248319\pi$
$858$		0			0
$859$	47.5539	−	27.4552i	1.62252	−	0.936761i	0.636274	−	0.771463i	$-0.280475\pi$
$859$	47.5539	−	27.4552i	1.62252	−	0.936761i	0.986244	−	0.165297i	$-0.0528584\pi$
$860$	3.80660	+	10.9908i	0.129804	+	0.374782i
$861$		0			0
$862$	−9.05233	+	12.7151i	−0.308324	+	0.433079i
$863$	54.3877			1.85138			0.925689	−	0.378285i	$-0.123486\pi$
$863$	54.3877			1.85138			0.925689	+	0.378285i	$0.123486\pi$
$864$		0			0
$865$	29.0778			0.988675
$866$	−28.6573	+	40.2528i	−0.973815	+	1.36784i
$867$		0			0
$868$	−6.31766	−	18.2409i	−0.214435	−	0.619137i
$869$	42.1888	−	24.3577i	1.43116	−	0.826278i
$870$		0			0
$871$	−20.6521	+	35.7704i	−0.699768	+	1.21203i
$872$	14.3942	−	49.0812i	0.487451	−	1.66210i
$873$		0			0
$874$	−0.661911	+	6.93977i	−0.0223895	+	0.234741i
$875$	17.2050	+	9.93334i	0.581637	+	0.335808i
$876$		0			0
$877$	5.90001	−	3.40637i	0.199229	−	0.115025i	−0.397067	−	0.917790i	$-0.629972\pi$
$877$	5.90001	−	3.40637i	0.199229	−	0.115025i	0.596296	+	0.802765i	$0.296639\pi$
$878$	−7.73922	−	16.9417i	−0.261186	−	0.571754i
$879$		0			0
$880$	−35.1144	+	27.6389i	−1.18371	+	0.931706i
$881$	43.2881			1.45841			0.729207	−	0.684293i	$-0.239889\pi$
$881$	43.2881			1.45841			0.729207	+	0.684293i	$0.239889\pi$
$882$		0			0
$883$			31.1510i			1.04832i	0.851621	+	0.524158i	$0.175620\pi$
$883$			31.1510i			1.04832i	−0.851621	+	0.524158i	$0.824380\pi$
$884$	−13.4918	−	11.6856i	−0.453778	−	0.393029i
$885$		0			0
$886$	−35.1803	+	16.0709i	−1.18191	+	0.539913i
$887$	24.8886	+	43.1083i	0.835677	+	1.44743i	0.893478	+	0.449107i	$0.148258\pi$
$887$	24.8886	+	43.1083i	0.835677	+	1.44743i	−0.0578015	+	0.998328i	$0.518409\pi$
$888$		0			0
$889$	6.76295	−	11.7138i	0.226822	−	0.392867i
$890$	−0.765617	+	8.02708i	−0.0256636	+	0.269068i
$891$		0			0
$892$	10.3407	+	1.99068i	0.346231	+	0.0666529i
$893$	−7.44926	−	4.30083i	−0.249280	−	0.143922i
$894$		0			0
$895$	−10.0595	−	17.4236i	−0.336253	−	0.582407i
$896$	2.90800	−	20.3348i	0.0971496	−	0.679339i
$897$		0			0
$898$	−11.3372	+	15.9245i	−0.378327	+	0.531407i
$899$		−	19.4243i		−	0.647838i
$900$		0			0
$901$		−	17.2730i		−	0.575447i
$902$	26.6597	+	18.9800i	0.887672	+	0.631964i
$903$		0			0
$904$	1.89256	+	7.79021i	0.0629456	+	0.259098i
$905$	−17.6059	−	30.4944i	−0.585241	−	1.01367i
$906$		0			0
$907$	−16.6712	−	9.62515i	−0.553559	−	0.319598i	0.196997	−	0.980404i	$-0.436881\pi$
$907$	−16.6712	−	9.62515i	−0.553559	−	0.319598i	−0.750556	+	0.660806i	$0.770214\pi$
$908$	−0.670731	+	3.48413i	−0.0222590	+	0.115625i
$909$		0			0
$910$	−26.9905	−	2.57433i	−0.894725	−	0.0853383i
$911$	−11.1396	+	19.2944i	−0.369072	+	0.639252i	−0.989421	−	0.145074i	$-0.953658\pi$
$911$	−11.1396	+	19.2944i	−0.369072	+	0.639252i	0.620348	+	0.784326i	$0.286991\pi$
$912$		0			0
$913$	−8.82669	−	15.2883i	−0.292121	−	0.505968i
$914$	−3.36363	−	7.36321i	−0.111259	−	0.243553i
$915$		0			0
$916$	5.77266	+	4.99986i	0.190734	+	0.165200i
$917$		−	6.54438i		−	0.216114i
$918$		0			0
$919$	28.0122			0.924039			0.462019	−	0.886870i	$-0.347125\pi$
$919$	28.0122			0.924039			0.462019	+	0.886870i	$0.347125\pi$
$920$	−10.3117	−	10.8075i	−0.339965	−	0.356314i
$921$		0			0
$922$	−28.7738	+	13.1443i	−0.947613	+	0.432884i
$923$	53.5440	−	30.9136i	1.76242	−	1.01753i
$924$		0			0
$925$	1.40416	+	0.810691i	0.0461684	+	0.0266554i
$926$	−52.2958	−	4.98794i	−1.71855	−	0.163914i
$927$		0			0
$928$	9.46151	−	18.3772i	0.310589	−	0.603260i
$929$	3.94220	−	6.82809i	0.129339	−	0.224022i	−0.794081	−	0.607811i	$-0.792048\pi$
$929$	3.94220	−	6.82809i	0.129339	−	0.224022i	0.923421	+	0.383789i	$0.125381\pi$
$930$		0			0
$931$	6.82847	−	3.94242i	0.223794	−	0.129208i
$932$	−13.3008	−	38.4033i	−0.435683	−	1.25794i
$933$		0			0
$934$	26.1348	+	18.6062i	0.855156	+	0.608814i
$935$	−21.5378			−0.704361
$936$		0			0
$937$	−8.98600			−0.293560			−0.146780	−	0.989169i	$-0.546891\pi$
$937$	−8.98600			−0.293560			−0.146780	+	0.989169i	$0.546891\pi$
$938$	−18.6640	−	13.2875i	−0.609401	−	0.433853i
$939$		0			0
$940$	17.4162	−	6.03201i	0.568053	−	0.196742i
$941$	21.0227	−	12.1375i	0.685322	−	0.395671i	−0.116535	−	0.993187i	$-0.537179\pi$
$941$	21.0227	−	12.1375i	0.685322	−	0.395671i	0.801857	+	0.597516i	$0.203845\pi$
$942$		0			0
$943$	−5.46967	+	9.47375i	−0.178117	+	0.308508i
$944$	−5.23445	+	13.0914i	−0.170367	+	0.426090i
$945$		0			0
$946$	17.5796	+	1.67673i	0.571561	+	0.0545151i
$947$	1.71382	+	0.989473i	0.0556916	+	0.0321536i	0.527587	−	0.849501i	$-0.323097\pi$
$947$	1.71382	+	0.989473i	0.0556916	+	0.0321536i	−0.471896	+	0.881654i	$0.656430\pi$
$948$		0			0
$949$	46.3402	−	26.7545i	1.50427	−	0.868488i
$950$	0.556151	−	0.254059i	0.0180439	−	0.00824275i
$951$		0			0
$952$	7.16310	−	6.83444i	0.232157	−	0.221505i
$953$	−28.9674			−0.938347			−0.469173	−	0.883106i	$-0.655448\pi$
$953$	−28.9674			−0.938347			−0.469173	+	0.883106i	$0.655448\pi$
$954$		0			0
$955$		−	21.9753i		−	0.711104i
$956$	−22.7785	+	26.2993i	−0.736710	+	0.850580i
$957$		0			0
$958$	−15.4635	−	33.8507i	−0.499604	−	1.09367i
$959$	−10.6787	−	18.4960i	−0.344833	−	0.597268i
$960$		0			0
$961$	1.37008	−	2.37304i	0.0441961	−	0.0765498i
$962$	52.0343	+	4.96300i	1.67765	+	0.160014i
$963$		0			0
$964$	26.9300	+	5.18428i	0.867355	+	0.166975i
$965$	−13.8017	−	7.96842i	−0.444293	−	0.256512i
$966$		0			0
$967$	0.00531192	+	0.00920052i	0.000170820	+	0.000295869i	0.866111	−	0.499852i	$-0.166612\pi$
$967$	0.00531192	+	0.00920052i	0.000170820	+	0.000295869i	−0.865940	+	0.500148i	$0.833279\pi$
$968$	8.67193	+	35.6956i	0.278726	+	1.14730i
$969$		0			0
$970$	−36.7576	−	26.1690i	−1.18021	−	0.840235i
$971$		−	17.0984i		−	0.548715i	−0.961628	−	0.274357i	$-0.911535\pi$
$971$		−	17.0984i		−	0.548715i	0.961628	−	0.274357i	$-0.0884651\pi$
$972$		0			0
$973$		−	23.1457i		−	0.742017i
$974$	19.7166	−	27.6945i	0.631762	−	0.887389i
$975$		0			0
$976$	7.84812	−	1.13185i	0.251212	−	0.0362297i
$977$	5.50612	+	9.53688i	0.176156	+	0.305112i	0.940561	−	0.339625i	$-0.110300\pi$
$977$	5.50612	+	9.53688i	0.176156	+	0.305112i	−0.764404	+	0.644737i	$0.776967\pi$
$978$		0			0
$979$	10.6023	+	6.12126i	0.338852	+	0.195636i
$980$	−3.19385	+	16.5905i	−0.102024	+	0.529966i
$981$		0			0
$982$	4.22133	−	44.2583i	0.134708	−	1.41234i
$983$	−22.7443	+	39.3943i	−0.725432	+	1.25648i	0.233364	+	0.972389i	$0.425027\pi$
$983$	−22.7443	+	39.3943i	−0.725432	+	1.25648i	−0.958796	+	0.284095i	$0.908307\pi$
$984$		0			0
$985$	4.92521	+	8.53071i	0.156930	+	0.271811i
$986$	9.06150	−	4.13943i	0.288577	−	0.131826i
$987$		0			0
$988$	12.9051	−	14.8998i	0.410565	−	0.474024i
$989$			5.90304i			0.187706i
$990$		0			0
$991$	3.93737			0.125075			0.0625374	−	0.998043i	$-0.480081\pi$
$991$	3.93737			0.125075			0.0625374	+	0.998043i	$0.480081\pi$
$992$	−25.2892	+	16.2717i	−0.802934	+	0.516628i
$993$		0			0
$994$	14.2499	+	31.1940i	0.451979	+	0.989413i
$995$	−11.6678	+	6.73642i	−0.369895	+	0.213559i
$996$		0			0
$997$	2.16558	+	1.25030i	0.0685847	+	0.0395974i	0.533900	−	0.845547i	$-0.320726\pi$
$997$	2.16558	+	1.25030i	0.0685847	+	0.0395974i	−0.465316	+	0.885145i	$0.654059\pi$
$998$	−0.787897	+	8.26066i	−0.0249404	+	0.261487i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.n.b.181.3		16
3.2	odd	2		72.2.n.b.61.6	yes	16
4.3	odd	2		864.2.r.b.721.2		16
8.3	odd	2		864.2.r.b.721.7		16
8.5	even	2	inner	216.2.n.b.181.4		16
9.2	odd	6		648.2.d.j.325.1		8
9.4	even	3	inner	216.2.n.b.37.4		16
9.5	odd	6		72.2.n.b.13.5	✓	16
9.7	even	3		648.2.d.k.325.8		8
12.11	even	2		288.2.r.b.241.8		16
24.5	odd	2		72.2.n.b.61.5	yes	16
24.11	even	2		288.2.r.b.241.1		16
36.7	odd	6		2592.2.d.k.1297.2		8
36.11	even	6		2592.2.d.j.1297.7		8
36.23	even	6		288.2.r.b.49.1		16
36.31	odd	6		864.2.r.b.145.7		16
72.5	odd	6		72.2.n.b.13.6	yes	16
72.11	even	6		2592.2.d.j.1297.2		8
72.13	even	6	inner	216.2.n.b.37.3		16
72.29	odd	6		648.2.d.j.325.2		8
72.43	odd	6		2592.2.d.k.1297.7		8
72.59	even	6		288.2.r.b.49.8		16
72.61	even	6		648.2.d.k.325.7		8
72.67	odd	6		864.2.r.b.145.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.5	✓	16	9.5	odd	6
72.2.n.b.13.6	yes	16	72.5	odd	6
72.2.n.b.61.5	yes	16	24.5	odd	2
72.2.n.b.61.6	yes	16	3.2	odd	2
216.2.n.b.37.3		16	72.13	even	6	inner
216.2.n.b.37.4		16	9.4	even	3	inner
216.2.n.b.181.3		16	1.1	even	1	trivial
216.2.n.b.181.4		16	8.5	even	2	inner
288.2.r.b.49.1		16	36.23	even	6
288.2.r.b.49.8		16	72.59	even	6
288.2.r.b.241.1		16	24.11	even	2
288.2.r.b.241.8		16	12.11	even	2
648.2.d.j.325.1		8	9.2	odd	6
648.2.d.j.325.2		8	72.29	odd	6
648.2.d.k.325.7		8	72.61	even	6
648.2.d.k.325.8		8	9.7	even	3
864.2.r.b.145.2		16	72.67	odd	6
864.2.r.b.145.7		16	36.31	odd	6
864.2.r.b.721.2		16	4.3	odd	2
864.2.r.b.721.7		16	8.3	odd	2
2592.2.d.j.1297.2		8	72.11	even	6
2592.2.d.j.1297.7		8	36.11	even	6
2592.2.d.k.1297.2		8	36.7	odd	6
2592.2.d.k.1297.7		8	72.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.820200 + 1.15207i) q^{2} +(-0.654545 - 1.88986i) q^{4} +(-1.97542 + 1.14051i) q^{5} +(-0.907824 + 1.57240i) q^{7} +(2.71411 + 0.795980i) q^{8} +O(q^{10})\)	\(q+(-0.820200 + 1.15207i) q^{2} +(-0.654545 - 1.88986i) q^{4} +(-1.97542 + 1.14051i) q^{5} +(-0.907824 + 1.57240i) q^{7} +(2.71411 + 0.795980i) q^{8} +(0.306290 - 3.21128i) q^{10} +(-4.24153 - 2.44885i) q^{11} +(-4.00895 + 2.31457i) q^{13} +(-1.06692 - 2.33556i) q^{14} +(-3.14314 + 2.47400i) q^{16} -1.92788 q^{17} -2.12907i q^{19} +(3.44841 + 2.98676i) q^{20} +(6.30015 - 2.87801i) q^{22} +(1.15765 + 2.00511i) q^{23} +(0.101535 - 0.175863i) q^{25} +(0.621589 - 6.51702i) q^{26} +(3.56582 + 0.686457i) q^{28} +(3.16440 + 1.82697i) q^{29} +(-2.65800 - 4.60379i) q^{31} +(-0.272218 - 5.65030i) q^{32} +(1.58125 - 2.22106i) q^{34} -4.14154i q^{35} +7.98438i q^{37} +(2.45284 + 1.74626i) q^{38} +(-6.26935 + 1.52308i) q^{40} +(2.36240 + 4.09180i) q^{41} +(2.20800 + 1.27479i) q^{43} +(-1.85171 + 9.61877i) q^{44} +(-3.25953 - 0.310892i) q^{46} +(2.02005 - 3.49884i) q^{47} +(1.85171 + 3.20726i) q^{49} +(0.119328 + 0.261218i) q^{50} +(6.99825 + 6.06137i) q^{52} +8.95958i q^{53} +11.1718 q^{55} +(-3.71554 + 3.54506i) q^{56} +(-4.70024 + 2.14714i) q^{58} +(3.05255 - 1.76239i) q^{59} +(-1.71675 - 0.991165i) q^{61} +(7.48399 + 0.713818i) q^{62} +(6.73283 + 4.32076i) q^{64} +(5.27959 - 9.14451i) q^{65} +(7.72723 - 4.46132i) q^{67} +(1.26188 + 3.64342i) q^{68} +(4.77135 + 3.39689i) q^{70} -13.3561 q^{71} -11.5592 q^{73} +(-9.19859 - 6.54879i) q^{74} +(-4.02364 + 1.39357i) q^{76} +(7.70112 - 4.44625i) q^{77} +(-4.97330 + 8.61401i) q^{79} +(3.38742 - 8.47198i) q^{80} +(-6.65170 - 0.634435i) q^{82} +(3.12153 + 1.80221i) q^{83} +(3.80838 - 2.19877i) q^{85} +(-3.27965 + 1.49820i) q^{86} +(-9.56276 - 10.0226i) q^{88} -2.49965 q^{89} -8.40489i q^{91} +(3.03164 - 3.50023i) q^{92} +(2.37407 + 5.19699i) q^{94} +(2.42823 + 4.20582i) q^{95} +(6.99370 - 12.1134i) q^{97} +(-5.21376 - 0.497285i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) \) 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8} - 16 q^{10} - 16 q^{14} - 9 q^{16} + 28 q^{17} + 8 q^{20} + q^{22} + 10 q^{23} + 2 q^{25} - 28 q^{26} + 4 q^{28} - 10 q^{31} - 11 q^{32} + q^{34} - 23 q^{38} + 6 q^{40} + 8 q^{41} - 18 q^{44} - 20 q^{46} - 6 q^{47} + 18 q^{49} + 23 q^{50} - 8 q^{52} - 4 q^{55} - 10 q^{56} - 14 q^{58} + 52 q^{62} + 26 q^{64} + 14 q^{65} + 39 q^{68} - 72 q^{71} - 44 q^{73} + 38 q^{74} + 5 q^{76} - 30 q^{79} + 96 q^{80} + 38 q^{82} - 7 q^{86} + 31 q^{88} - 64 q^{89} + 30 q^{92} - 12 q^{94} - 44 q^{95} - 66 q^{98}+O(q^{100}) \) 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8 - 16 * q^10 - 16 * q^14 - 9 * q^16 + 28 * q^17 + 8 * q^20 + q^22 + 10 * q^23 + 2 * q^25 - 28 * q^26 + 4 * q^28 - 10 * q^31 - 11 * q^32 + q^34 - 23 * q^38 + 6 * q^40 + 8 * q^41 - 18 * q^44 - 20 * q^46 - 6 * q^47 + 18 * q^49 + 23 * q^50 - 8 * q^52 - 4 * q^55 - 10 * q^56 - 14 * q^58 + 52 * q^62 + 26 * q^64 + 14 * q^65 + 39 * q^68 - 72 * q^71 - 44 * q^73 + 38 * q^74 + 5 * q^76 - 30 * q^79 + 96 * q^80 + 38 * q^82 - 7 * q^86 + 31 * q^88 - 64 * q^89 + 30 * q^92 - 12 * q^94 - 44 * q^95 - 66 * q^98

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