LMFDB - Embedded newform 216.2.n.b.37.3

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			37.3
Root			$0.587625 + 1.28635i$ of defining polynomial
Character	$\chi$	$=$	216.37
Dual form			216.2.n.b.181.3

$q$-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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

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

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	−0.0116467	−	0.999932i	$-0.503707\pi$
$5$	−1.97542	−	1.14051i	−0.883437	−	0.510052i	−0.871790	+	0.489880i	$0.837041\pi$
$6$		0			0
$7$	−0.907824	−	1.57240i	−0.343125	−	0.594311i	0.641886	−	0.766800i	$-0.278152\pi$
$7$	−0.907824	−	1.57240i	−0.343125	−	0.594311i	−0.985011	+	0.172490i	$0.944819\pi$
$8$	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	−0.976640	−	0.214880i	$-0.931064\pi$
$11$	−4.24153	+	2.44885i	−1.27887	+	0.738355i	−0.302228	+	0.953236i	$0.597730\pi$
$12$		0			0
$13$	−4.00895	−	2.31457i	−1.11188	−	0.641946i	−0.172567	−	0.984998i	$-0.555206\pi$
$13$	−4.00895	−	2.31457i	−1.11188	−	0.641946i	−0.939317	+	0.343052i	$0.888539\pi$
$14$	−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	$0.0785322\pi$
$19$			2.12907i			0.488442i	−0.969720	+	0.244221i	$0.921468\pi$
$20$	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	−0.719723	−	0.694261i	$-0.755731\pi$
$23$	1.15765	−	2.00511i	0.241387	−	0.418094i	0.961109	+	0.276168i	$0.0890645\pi$
$24$		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	−0.176539	−	0.984294i	$-0.556490\pi$
$29$	3.16440	−	1.82697i	0.587615	−	0.339260i	0.764154	+	0.645034i	$0.223157\pi$
$30$		0			0
$31$	−2.65800	+	4.60379i	−0.477391	+	0.826865i	−0.999664	−	0.0259130i	$-0.991751\pi$
$31$	−2.65800	+	4.60379i	−0.477391	+	0.826865i	0.522273	+	0.852778i	$0.325084\pi$
$32$	−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	$-0.772115\pi$
$37$		−	7.98438i		−	1.31262i	0.754489	−	0.656312i	$-0.227885\pi$
$38$	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	−0.620455	−	0.784242i	$-0.713052\pi$
$41$	2.36240	−	4.09180i	0.368946	−	0.639033i	0.989401	+	0.145209i	$0.0463855\pi$
$42$		0			0
$43$	2.20800	−	1.27479i	0.336717	−	0.194404i	−0.322102	−	0.946705i	$-0.604390\pi$
$43$	2.20800	−	1.27479i	0.336717	−	0.194404i	0.658819	+	0.752301i	$0.271056\pi$
$44$	−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	0.974905	−	0.222623i	$-0.0714619\pi$
$47$	2.02005	+	3.49884i	0.294655	+	0.510358i	−0.680249	+	0.732981i	$0.738129\pi$
$48$		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	$-0.789016\pi$
$53$		−	8.95958i		−	1.23069i	0.788257	−	0.615347i	$-0.210984\pi$
$54$		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	0.685365	−	0.728200i	$-0.259643\pi$
$59$	3.05255	+	1.76239i	0.397408	+	0.229444i	−0.287957	+	0.957643i	$0.592976\pi$
$60$		0			0
$61$	−1.71675	+	0.991165i	−0.219807	+	0.126906i	−0.605861	−	0.795571i	$-0.707171\pi$
$61$	−1.71675	+	0.991165i	−0.219807	+	0.126906i	0.386054	+	0.922476i	$0.373838\pi$
$62$	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	0.891222	−	0.453568i	$-0.149849\pi$
$67$	7.72723	+	4.46132i	0.944031	+	0.545036i	0.0528093	+	0.998605i	$0.483182\pi$
$68$	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	−0.997535	−	0.0701739i	$-0.977645\pi$
$79$	−4.97330	−	8.61401i	−0.559540	−	0.969151i	0.437995	−	0.898977i	$-0.355689\pi$
$80$	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	−0.318803	−	0.947821i	$-0.603281\pi$
$83$	3.12153	−	1.80221i	0.342632	−	0.197819i	0.661435	+	0.750002i	$0.269948\pi$
$84$		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	0.964818	+	0.262918i	$0.0846849\pi$
$97$	6.99370	+	12.1134i	0.710103	+	1.22993i	−0.254715	+	0.967016i	$0.581982\pi$
$98$	−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	−0.555207	−	0.831712i	$-0.687361\pi$
$101$	−1.13087	+	0.652911i	−0.112526	+	0.0649671i	0.442681	+	0.896679i	$0.354028\pi$
$102$		0			0
$103$	−3.22312	+	5.58261i	−0.317584	+	0.550071i	−0.979983	−	0.199080i	$-0.936205\pi$
$103$	−3.22312	+	5.58261i	−0.317584	+	0.550071i	0.662400	+	0.749151i	$0.269538\pi$
$104$	−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	$-0.952056\pi$
$107$		−	3.10427i		−	0.300101i	0.988678	−	0.150051i	$-0.0479437\pi$
$108$		0			0
$109$			18.0837i			1.73210i	0.499955	+	0.866051i	$0.333350\pi$
$109$			18.0837i			1.73210i	−0.499955	+	0.866051i	$0.666650\pi$
$110$	−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	−0.791636	−	0.610993i	$-0.790770\pi$
$113$	1.41718	−	2.45463i	0.133317	−	0.230913i	0.924953	+	0.380080i	$0.124104\pi$
$114$		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	0.357398	−	0.933952i	$-0.383664\pi$
$131$	−3.12153	−	1.80221i	−0.272729	−	0.157460i	−0.630127	+	0.776492i	$0.716997\pi$
$132$		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	−0.999996	−	0.00287543i	$-0.999085\pi$
$137$	−5.88147	−	10.1870i	−0.502488	−	0.870335i	0.497508	−	0.867460i	$-0.334249\pi$
$138$		0			0
$139$	−11.0400	−	6.37395i	−0.936400	−	0.540631i	−0.0475703	−	0.998868i	$-0.515148\pi$
$139$	−11.0400	−	6.37395i	−0.936400	−	0.540631i	−0.888830	+	0.458237i	$0.848481\pi$
$140$	−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	0.204769	−	0.978810i	$-0.434356\pi$
$149$	−6.59790	−	3.80930i	−0.540521	−	0.312070i	−0.745290	+	0.666740i	$0.767689\pi$
$150$		0			0
$151$	2.26988	+	3.93155i	0.184720	+	0.319945i	0.943482	−	0.331423i	$-0.107529\pi$
$151$	2.26988	+	3.93155i	0.184720	+	0.319945i	−0.758762	+	0.651368i	$0.774195\pi$
$152$	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	0.880643	−	0.473780i	$-0.157111\pi$
$157$	11.4105	+	6.58787i	0.910659	+	0.525769i	0.0300161	+	0.999549i	$0.490444\pi$
$158$	−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	$-0.701408\pi$
$163$		−	20.5911i		−	1.61282i	0.591358	−	0.806409i	$-0.298592\pi$
$164$	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	−0.947386	−	0.320094i	$-0.896285\pi$
$167$	−2.53912	+	4.39789i	−0.196483	+	0.340319i	0.750903	+	0.660413i	$0.229619\pi$
$168$		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	−0.857041	−	0.515248i	$-0.827700\pi$
$173$	−11.0398	+	6.37385i	−0.839343	+	0.484595i	0.0176977	+	0.999843i	$0.494366\pi$
$174$		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	$-0.893077\pi$
$179$		−	8.82019i		−	0.659252i	0.944112	−	0.329626i	$-0.106923\pi$
$180$		0			0
$181$		−	15.4369i		−	1.14741i	−0.819061	−	0.573707i	$-0.805505\pi$
$181$		−	15.4369i		−	1.14741i	0.819061	−	0.573707i	$-0.194495\pi$
$182$	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	0.637446	−	0.770495i	$-0.279991\pi$
$191$	−4.81698	−	8.34326i	−0.348545	−	0.603697i	−0.985991	+	0.166797i	$0.946657\pi$
$192$		0			0
$193$	3.49335	−	6.05066i	0.251457	−	0.435536i	−0.712470	−	0.701702i	$-0.752424\pi$
$193$	3.49335	−	6.05066i	0.251457	−	0.435536i	0.963927	+	0.266166i	$0.0857570\pi$
$194$	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	$0.0491632\pi$
$197$			4.31842i			0.307675i	−0.988096	+	0.153837i	$0.950837\pi$
$198$		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	−0.158696	−	0.987328i	$-0.550729\pi$
$211$	−15.8781	−	9.16723i	−1.09309	−	0.631098i	−0.934399	+	0.356229i	$0.884062\pi$
$212$	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	0.764314	−	0.644844i	$-0.223078\pi$
$223$	−2.63263	−	4.55986i	−0.176294	−	0.305350i	−0.940608	+	0.339494i	$0.889744\pi$
$224$	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	−0.550119	−	0.835086i	$-0.685418\pi$
$227$	−1.53638	+	0.887027i	−0.101973	+	0.0588741i	0.448146	+	0.893960i	$0.352084\pi$
$228$		0			0
$229$	−3.30687	−	1.90922i	−0.218524	−	0.126165i	0.386742	−	0.922188i	$-0.373600\pi$
$229$	−3.30687	−	1.90922i	−0.218524	−	0.126165i	−0.605267	+	0.796023i	$0.706934\pi$
$230$	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	0.434632	+	0.900608i	$0.356879\pi$
$239$	−8.69811	+	15.0656i	−0.562634	+	0.974510i	−0.997266	+	0.0739020i	$0.976455\pi$
$240$		0			0
$241$	−6.85611	−	11.8751i	−0.441641	−	0.764944i	0.556171	−	0.831068i	$-0.312270\pi$
$241$	−6.85611	−	11.8751i	−0.441641	−	0.764944i	−0.997811	+	0.0661240i	$0.978937\pi$
$242$	−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	$-0.954564\pi$
$251$		−	4.50751i		−	0.284512i	0.989830	−	0.142256i	$-0.0454356\pi$
$252$		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	−0.708776	−	0.705434i	$-0.750752\pi$
$257$	4.11258	−	7.12320i	0.256536	−	0.444333i	0.965311	+	0.261101i	$0.0840856\pi$
$258$		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	0.778056	−	0.628195i	$-0.216206\pi$
$263$	−2.51376	−	4.35395i	−0.155005	−	0.268476i	−0.933061	+	0.359719i	$0.882873\pi$
$264$		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	$0.249491\pi$
$269$			23.1577i			1.41195i	−0.708236	+	0.705976i	$0.750509\pi$
$270$		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	0.206983	−	0.978345i	$-0.433636\pi$
$277$	19.2687	−	11.1248i	1.15775	−	0.668425i	0.950763	+	0.309920i	$0.100302\pi$
$278$	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	0.998010	+	0.0630590i	$0.0200856\pi$
$281$	9.28029	+	16.0739i	0.553616	+	0.958890i	−0.444394	+	0.895831i	$0.646581\pi$
$282$		0			0
$283$	1.75962	+	1.01592i	0.104599	+	0.0603901i	0.551387	−	0.834250i	$-0.314099\pi$
$283$	1.75962	+	1.01592i	0.104599	+	0.0603901i	−0.446788	+	0.894640i	$0.647432\pi$
$284$	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	−0.904057	−	0.427411i	$-0.859426\pi$
$293$	−29.5484	−	17.0598i	−1.72623	−	0.996642i	−0.822178	−	0.569231i	$-0.807241\pi$
$294$		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	$0.0435169\pi$
$307$			4.77588i			0.272574i	−0.990669	+	0.136287i	$0.956483\pi$
$308$	−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	−0.352976	−	0.935632i	$-0.614830\pi$
$311$	11.1771	−	19.3592i	0.633793	−	1.09776i	0.986769	−	0.162130i	$-0.0518364\pi$
$312$		0			0
$313$	1.22411	+	2.12022i	0.0691907	+	0.119842i	0.898545	−	0.438881i	$-0.144625\pi$
$313$	1.22411	+	2.12022i	0.0691907	+	0.119842i	−0.829355	+	0.558723i	$0.811292\pi$
$314$	−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	−0.0418263	−	0.999125i	$-0.513318\pi$
$317$	14.2886	−	8.24953i	0.802528	−	0.463340i	0.844354	+	0.535785i	$0.179984\pi$
$318$		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	−0.509020	−	0.860755i	$-0.669992\pi$
$331$	−0.329200	+	0.190064i	−0.0180945	+	0.0104469i	0.490925	+	0.871202i	$0.336659\pi$
$332$	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	−0.926437	−	0.376450i	$-0.877145\pi$
$337$	−2.51872	+	4.36255i	−0.137203	+	0.237643i	0.789234	+	0.614093i	$0.210478\pi$
$338$	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	0.708302	−	0.705910i	$-0.249462\pi$
$347$	8.40337	+	4.85169i	0.451116	+	0.260452i	−0.257185	+	0.966362i	$0.582795\pi$
$348$		0			0
$349$	−26.1239	+	15.0827i	−1.39838	+	0.807356i	−0.994223	−	0.107333i	$-0.965769\pi$
$349$	−26.1239	+	15.0827i	−1.39838	+	0.807356i	−0.404158	+	0.914689i	$0.632436\pi$
$350$	−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	−0.966848	−	0.255352i	$-0.917809\pi$
$353$	−13.2376	−	22.9282i	−0.704565	−	1.22034i	0.262283	−	0.964991i	$-0.415525\pi$
$354$		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	0.999996	+	0.00285720i	$0.000909476\pi$
$367$	9.62599	+	16.6727i	0.502472	+	0.870308i	−0.497524	+	0.867450i	$0.665757\pi$
$368$	−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	0.245793	−	0.969322i	$-0.420952\pi$
$373$	−9.09206	−	5.24930i	−0.470769	−	0.271799i	−0.716562	+	0.697524i	$0.754285\pi$
$374$	−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	$0.365677\pi$
$379$			35.5203i			1.82455i	−0.409574	+	0.912277i	$0.634323\pi$
$380$	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	−0.125105	+	0.992144i	$0.539927\pi$
$383$	−18.0395	+	31.2453i	−0.921774	+	1.59656i	−0.796669	+	0.604416i	$0.793407\pi$
$384$		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	0.0150612	−	0.999887i	$-0.495206\pi$
$389$	17.5243	−	10.1177i	0.888519	−	0.512987i	0.873458	+	0.486900i	$0.161872\pi$
$390$		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	$0.0319647\pi$
$397$			3.99499i			0.200503i	−0.994962	+	0.100251i	$0.968035\pi$
$398$	−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	0.268807	+	0.963194i	$0.413371\pi$
$401$	−14.0124	+	24.2702i	−0.699747	+	1.21200i	−0.968554	+	0.248803i	$0.919963\pi$
$402$		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	−0.587826	−	0.808987i	$-0.700016\pi$
$409$	8.22481	−	14.2458i	0.406691	−	0.704409i	0.994517	+	0.104579i	$0.0333494\pi$
$410$	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	0.909515	−	0.415672i	$-0.136453\pi$
$419$	20.5573	+	11.8688i	1.00429	+	0.579827i	0.0947752	+	0.995499i	$0.469787\pi$
$420$		0			0
$421$	25.9420	−	14.9776i	1.26433	−	0.729963i	0.290424	−	0.956898i	$-0.406204\pi$
$421$	25.9420	−	14.9776i	1.26433	−	0.729963i	0.973910	+	0.226935i	$0.0728704\pi$
$422$	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	0.664994	−	0.746849i	$-0.268434\pi$
$439$	−6.58518	−	11.4059i	−0.314293	−	0.544372i	−0.979287	+	0.202477i	$0.935101\pi$
$440$	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	0.182554	−	0.983196i	$-0.441564\pi$
$443$	23.6849	−	13.6745i	1.12530	−	0.649694i	0.942749	+	0.333502i	$0.108230\pi$
$444$		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	0.791288	−	0.611443i	$-0.209411\pi$
$457$	−2.86205	−	4.95722i	−0.133881	−	0.231889i	−0.925170	+	0.379554i	$0.876077\pi$
$458$	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	0.0243074	−	0.999705i	$-0.492262\pi$
$461$	19.3717	−	11.1843i	0.902231	−	0.520903i	0.877923	+	0.478801i	$0.158929\pi$
$462$		0			0
$463$	18.5733	−	32.1699i	0.863174	−	1.49506i	−0.00567564	−	0.999984i	$-0.501807\pi$
$463$	18.5733	−	32.1699i	0.863174	−	1.49506i	0.868849	−	0.495077i	$-0.164860\pi$
$464$	−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	$0.175885\pi$
$467$			22.6850i			1.04974i	−0.851184	+	0.524868i	$0.824115\pi$
$468$		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	−0.992641	−	0.121091i	$-0.961361\pi$
$479$	−13.1576	−	22.7897i	−0.601188	−	1.04129i	0.391453	−	0.920198i	$-0.371973\pi$
$480$		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	−0.261920	−	0.965090i	$-0.584356\pi$
$491$	−27.2256	−	15.7187i	−1.22867	−	0.709374i	−0.966752	+	0.255715i	$0.917689\pi$
$492$		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	0.609410	−	0.792855i	$-0.291406\pi$
$499$	5.08156	+	2.93384i	0.227482	+	0.131337i	−0.381928	+	0.924192i	$0.624740\pi$
$500$	−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	0.771633	−	0.636068i	$-0.219440\pi$
$509$	13.6855	+	7.90133i	0.606599	+	0.350220i	−0.165034	+	0.986288i	$0.552773\pi$
$510$		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	$-0.680374\pi$
$523$		−	38.5894i		−	1.68740i	0.536818	−	0.843698i	$-0.319626\pi$
$524$	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	$-0.838781\pi$
$541$		−	22.5666i		−	0.970214i	0.874455	−	0.485107i	$-0.161219\pi$
$542$	−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	−0.721158	−	0.692770i	$-0.756390\pi$
$547$	−11.2679	+	6.50552i	−0.481780	+	0.278156i	0.239378	+	0.970927i	$0.423057\pi$
$548$	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	$-0.961217\pi$
$557$		−	5.73693i		−	0.243081i	0.992586	−	0.121541i	$-0.0387835\pi$
$558$		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	0.194066	−	0.980988i	$-0.437832\pi$
$563$	−13.2510	−	7.65045i	−0.558462	−	0.322428i	−0.752528	+	0.658560i	$0.771166\pi$
$564$		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	0.692900	−	0.721034i	$-0.256333\pi$
$569$	−6.63095	−	11.4851i	−0.277984	−	0.481482i	−0.970884	+	0.239552i	$0.922999\pi$
$570$		0			0
$571$	23.4262	+	13.5251i	0.980357	+	0.566009i	0.902378	−	0.430946i	$-0.141820\pi$
$571$	23.4262	+	13.5251i	0.980357	+	0.566009i	0.0779788	+	0.996955i	$0.475153\pi$
$572$	−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	−0.531095	+	0.847312i	$0.678219\pi$
$587$	−37.0796	+	21.4079i	−1.53044	+	0.883598i	−0.999341	+	0.0362861i	$0.988447\pi$
$588$		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	−0.845720	−	0.533627i	$-0.820829\pi$
$599$	0.961228	−	1.66490i	0.0392747	−	0.0680258i	0.884995	+	0.465601i	$0.154162\pi$
$600$		0			0
$601$	−21.5937	−	37.4014i	−0.880825	−	1.52563i	−0.850425	−	0.526096i	$-0.823655\pi$
$601$	−21.5937	−	37.4014i	−0.880825	−	1.52563i	−0.0303994	−	0.999538i	$-0.509678\pi$
$602$	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	−0.0637546	−	0.997966i	$-0.520307\pi$
$607$	20.5078	−	35.5206i	0.832386	−	1.44174i	0.896141	−	0.443770i	$-0.146359\pi$
$608$	−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	$0.0325757\pi$
$613$			5.05878i			0.204322i	−0.994768	+	0.102161i	$0.967424\pi$
$614$	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	−0.336698	−	0.941613i	$-0.609310\pi$
$617$	16.0739	−	27.8408i	0.647112	−	1.12083i	0.983809	−	0.179217i	$-0.0573566\pi$
$618$		0			0
$619$	−27.3562	+	15.7941i	−1.09954	+	0.634820i	−0.936100	−	0.351734i	$-0.885592\pi$
$619$	−27.3562	+	15.7941i	−1.09954	+	0.634820i	−0.163440	+	0.986553i	$0.552259\pi$
$620$	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	0.992618	+	0.121284i	$0.0387011\pi$
$641$	15.2248	+	26.3701i	0.601344	+	1.04156i	−0.391274	+	0.920274i	$0.627966\pi$
$642$		0			0
$643$	−14.5911	−	8.42419i	−0.575418	−	0.332218i	0.183893	−	0.982946i	$-0.441130\pi$
$643$	−14.5911	−	8.42419i	−0.575418	−	0.332218i	−0.759310	+	0.650729i	$0.774463\pi$
$644$	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	−0.262858	−	0.964834i	$-0.584665\pi$
$653$	−31.4276	−	18.1448i	−1.22986	−	0.710059i	−0.967000	+	0.254775i	$0.917999\pi$
$654$		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	−0.826476	−	0.562972i	$-0.809658\pi$
$659$	−19.3088	+	11.1480i	−0.752166	+	0.434263i	0.0743103	+	0.997235i	$0.476324\pi$
$660$		0			0
$661$	5.19793	+	3.00103i	0.202176	+	0.116726i	0.597670	−	0.801742i	$-0.296093\pi$
$661$	5.19793	+	3.00103i	0.202176	+	0.116726i	−0.395494	+	0.918469i	$0.629427\pi$
$662$	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	0.785753	−	0.618541i	$-0.212276\pi$
$673$	−3.70444	−	6.41629i	−0.142796	−	0.247330i	−0.928548	+	0.371211i	$0.878943\pi$
$674$	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	−0.655667	−	0.755050i	$-0.727612\pi$
$677$	−8.57613	+	4.95143i	−0.329607	+	0.190299i	0.326059	+	0.945349i	$0.394279\pi$
$678$		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	$-0.731228\pi$
$683$		−	39.0736i		−	1.49511i	0.664200	−	0.747555i	$-0.268772\pi$
$684$		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	−0.460012	−	0.887913i	$-0.652155\pi$
$691$	2.07502	−	1.19801i	0.0789375	−	0.0455746i	0.538949	+	0.842338i	$0.318821\pi$
$692$	−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	$0.198468\pi$
$701$			30.9184i			1.16777i	−0.811836	+	0.583885i	$0.801532\pi$
$702$		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	−0.581576	−	0.813492i	$-0.697564\pi$
$709$	−4.46959	+	2.58052i	−0.167859	+	0.0969133i	0.413717	+	0.910406i	$0.364230\pi$
$710$	−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	0.845564	−	0.533873i	$-0.179264\pi$
$727$	−1.06681	−	1.84777i	−0.0395658	−	0.0685299i	−0.885130	+	0.465344i	$0.845931\pi$
$728$	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	0.850787	−	0.525510i	$-0.176125\pi$
$733$	22.2298	+	12.8344i	0.821076	+	0.474048i	−0.0297113	+	0.999559i	$0.509459\pi$
$734$	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	$0.0320367\pi$
$739$			5.46282i			0.200953i	−0.994939	+	0.100476i	$0.967963\pi$
$740$	−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	−0.373083	−	0.927798i	$-0.621699\pi$
$743$	16.8170	−	29.1279i	0.616955	−	1.06860i	0.990038	−	0.140800i	$-0.0449674\pi$
$744$		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	−0.999082	−	0.0428462i	$-0.986357\pi$
$751$	−12.6727	+	21.9498i	−0.462435	+	0.800961i	0.536647	+	0.843807i	$0.319691\pi$
$752$	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	$-0.977125\pi$
$757$		−	3.95103i		−	0.143603i	0.997419	−	0.0718014i	$-0.0228748\pi$
$758$	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	−0.0346607	−	0.999399i	$-0.511035\pi$
$761$	23.3979	−	40.5264i	0.848175	−	1.46908i	0.882835	−	0.469682i	$-0.155632\pi$
$762$		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	−0.815314	−	0.579019i	$-0.803436\pi$
$769$	2.60083	−	4.50478i	0.0937885	−	0.162446i	0.909102	+	0.416573i	$0.136769\pi$
$770$	−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	$0.246205\pi$
$773$			38.8477i			1.39725i	−0.715486	+	0.698627i	$0.753795\pi$
$774$		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	−0.457595	−	0.889161i	$-0.651289\pi$
$787$	−40.8579	−	23.5893i	−1.45643	−	0.840869i	−0.998833	+	0.0482918i	$0.984622\pi$
$788$	−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	0.383179	−	0.923674i	$-0.374829\pi$
$797$	−6.35645	−	3.66990i	−0.225157	−	0.129995i	−0.608336	+	0.793680i	$0.708163\pi$
$798$		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	$-0.909369\pi$
$811$		−	15.9986i		−	0.561785i	0.959739	−	0.280893i	$-0.0906305\pi$
$812$	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	0.00996351	−	0.999950i	$-0.496828\pi$
$821$	25.2413	−	14.5731i	0.880928	−	0.508604i	0.870964	+	0.491347i	$0.163495\pi$
$822$		0			0
$823$	−4.15695	+	7.20005i	−0.144902	+	0.250978i	−0.929336	−	0.369234i	$-0.879620\pi$
$823$	−4.15695	+	7.20005i	−0.144902	+	0.250978i	0.784434	+	0.620212i	$0.212953\pi$
$824$	−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	$-0.726965\pi$
$827$		−	43.5035i		−	1.51277i	0.654129	−	0.756383i	$-0.273035\pi$
$828$		0			0
$829$			15.9248i			0.553092i	0.961001	+	0.276546i	$0.0891897\pi$
$829$			15.9248i			0.553092i	−0.961001	+	0.276546i	$0.910810\pi$
$830$	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	0.958142	+	0.286295i	$0.0924237\pi$
$839$	21.0582	+	36.4739i	0.727009	+	1.25922i	−0.231132	+	0.972922i	$0.574243\pi$
$840$		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	−0.953923	−	0.300053i	$-0.902996\pi$
$853$	−34.2013	+	19.7461i	−1.17103	+	0.676095i	−0.217108	+	0.976148i	$0.569662\pi$
$854$	−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	0.996959	−	0.0779326i	$-0.0248319\pi$
$857$	12.6170	+	21.8532i	0.430988	+	0.746493i	−0.565971	+	0.824425i	$0.691499\pi$
$858$		0			0
$859$	47.5539	+	27.4552i	1.62252	+	0.936761i	0.986244	+	0.165297i	$0.0528584\pi$
$859$	47.5539	+	27.4552i	1.62252	+	0.936761i	0.636274	+	0.771463i	$0.280475\pi$
$860$	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	0.596296	−	0.802765i	$-0.296639\pi$
$877$	5.90001	+	3.40637i	0.199229	+	0.115025i	−0.397067	+	0.917790i	$0.629972\pi$
$878$	−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	$-0.824380\pi$
$883$		−	31.1510i		−	1.04832i	0.851621	−	0.524158i	$-0.175620\pi$
$884$	−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	−0.0578015	−	0.998328i	$-0.518409\pi$
$887$	24.8886	−	43.1083i	0.835677	−	1.44743i	0.893478	−	0.449107i	$-0.148258\pi$
$888$		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	−0.750556	−	0.660806i	$-0.770214\pi$
$907$	−16.6712	+	9.62515i	−0.553559	+	0.319598i	0.196997	+	0.980404i	$0.436881\pi$
$908$	−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	0.620348	−	0.784326i	$-0.286991\pi$
$911$	−11.1396	−	19.2944i	−0.369072	−	0.639252i	−0.989421	+	0.145074i	$0.953658\pi$
$912$		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	0.923421	−	0.383789i	$-0.125381\pi$
$929$	3.94220	+	6.82809i	0.129339	+	0.224022i	−0.794081	+	0.607811i	$0.792048\pi$
$930$		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	0.801857	−	0.597516i	$-0.203845\pi$
$941$	21.0227	+	12.1375i	0.685322	+	0.395671i	−0.116535	+	0.993187i	$0.537179\pi$
$942$		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	−0.471896	−	0.881654i	$-0.656430\pi$
$947$	1.71382	−	0.989473i	0.0556916	−	0.0321536i	0.527587	+	0.849501i	$0.323097\pi$
$948$		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	−0.865940	−	0.500148i	$-0.833279\pi$
$967$	0.00531192	−	0.00920052i	0.000170820	−	0.000295869i	0.866111	+	0.499852i	$0.166612\pi$
$968$	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	$0.0884651\pi$
$971$			17.0984i			0.548715i	−0.961628	+	0.274357i	$0.911535\pi$
$972$		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	−0.764404	−	0.644737i	$-0.776967\pi$
$977$	5.50612	−	9.53688i	0.176156	−	0.305112i	0.940561	+	0.339625i	$0.110300\pi$
$978$		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	−0.958796	−	0.284095i	$-0.908307\pi$
$983$	−22.7443	−	39.3943i	−0.725432	−	1.25648i	0.233364	−	0.972389i	$-0.425027\pi$
$984$		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	−0.465316	−	0.885145i	$-0.654059\pi$
$997$	2.16558	−	1.25030i	0.0685847	−	0.0395974i	0.533900	+	0.845547i	$0.320726\pi$
$998$	−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.37.3		16
3.2	odd	2		72.2.n.b.13.6	yes	16
4.3	odd	2		864.2.r.b.145.2		16
8.3	odd	2		864.2.r.b.145.7		16
8.5	even	2	inner	216.2.n.b.37.4		16
9.2	odd	6		72.2.n.b.61.5	yes	16
9.4	even	3		648.2.d.k.325.7		8
9.5	odd	6		648.2.d.j.325.2		8
9.7	even	3	inner	216.2.n.b.181.4		16
12.11	even	2		288.2.r.b.49.8		16
24.5	odd	2		72.2.n.b.13.5	✓	16
24.11	even	2		288.2.r.b.49.1		16
36.7	odd	6		864.2.r.b.721.7		16
36.11	even	6		288.2.r.b.241.1		16
36.23	even	6		2592.2.d.j.1297.2		8
36.31	odd	6		2592.2.d.k.1297.7		8
72.5	odd	6		648.2.d.j.325.1		8
72.11	even	6		288.2.r.b.241.8		16
72.13	even	6		648.2.d.k.325.8		8
72.29	odd	6		72.2.n.b.61.6	yes	16
72.43	odd	6		864.2.r.b.721.2		16
72.59	even	6		2592.2.d.j.1297.7		8
72.61	even	6	inner	216.2.n.b.181.3		16
72.67	odd	6		2592.2.d.k.1297.2		8

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