LMFDB - Embedded newform 216.2.l.b.35.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(35,216)]

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([3, 3, 1]))

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

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

chi := DirichletCharacter("216.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.l (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} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.8
Root			$0.608741 - 1.27649i$ of defining polynomial
Character	$\chi$	$=$	216.35
Dual form			216.2.l.b.179.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40985 - 0.111062i) q^{2} +(1.97533 - 0.313160i) q^{4} +(-1.74322 - 3.01934i) q^{5} +(1.80802 + 1.04386i) q^{7} +(2.75013 - 0.660890i) q^{8} +O(q^{10})$	\(q+(1.40985 - 0.111062i) q^{2} +(1.97533 - 0.313160i) q^{4} +(-1.74322 - 3.01934i) q^{5} +(1.80802 + 1.04386i) q^{7} +(2.75013 - 0.660890i) q^{8} +(-2.79300 - 4.06320i) q^{10} +(0.116985 + 0.0675415i) q^{11} +(-2.63890 + 1.52357i) q^{13} +(2.66496 + 1.27088i) q^{14} +(3.80386 - 1.23719i) q^{16} +4.19800i q^{17} +0.919111 q^{19} +(-4.38897 - 5.41829i) q^{20} +(0.172432 + 0.0822305i) q^{22} +(-0.689877 - 1.19490i) q^{23} +(-3.57762 + 6.19662i) q^{25} +(-3.55124 + 2.44108i) q^{26} +(3.89833 + 1.49577i) q^{28} +(-4.24111 + 7.34582i) q^{29} +(-4.39877 + 2.53963i) q^{31} +(5.22546 - 2.16671i) q^{32} +(0.466236 + 5.91853i) q^{34} -7.27870i q^{35} -1.61676i q^{37} +(1.29580 - 0.102078i) q^{38} +(-6.78953 - 7.15151i) q^{40} +(-1.79408 + 1.03581i) q^{41} +(5.41106 - 9.37224i) q^{43} +(0.252236 + 0.0967817i) q^{44} +(-1.10533 - 1.60801i) q^{46} +(0.205809 - 0.356471i) q^{47} +(-1.32071 - 2.28754i) q^{49} +(-4.35568 + 9.13361i) q^{50} +(-4.73559 + 3.83596i) q^{52} +0.968137 q^{53} -0.470958i q^{55} +(5.66217 + 1.67585i) q^{56} +(-5.16348 + 10.8275i) q^{58} +(-3.88770 + 2.24457i) q^{59} +(-7.44553 - 4.29868i) q^{61} +(-5.91953 + 4.06902i) q^{62} +(7.12645 - 3.63507i) q^{64} +(9.20037 + 5.31183i) q^{65} +(3.15416 + 5.46316i) q^{67} +(1.31464 + 8.29243i) q^{68} +(-0.808385 - 10.2618i) q^{70} +11.9687 q^{71} -4.06264 q^{73} +(-0.179560 - 2.27939i) q^{74} +(1.81555 - 0.287828i) q^{76} +(0.141008 + 0.244232i) q^{77} +(10.8672 + 6.27416i) q^{79} +(-10.3665 - 9.32847i) q^{80} +(-2.41434 + 1.65959i) q^{82} +(-5.23875 - 3.02459i) q^{83} +(12.6752 - 7.31802i) q^{85} +(6.58787 - 13.8144i) q^{86} +(0.366362 + 0.108434i) q^{88} -8.35848i q^{89} -6.36158 q^{91} +(-1.73693 - 2.14428i) q^{92} +(0.250568 - 0.525426i) q^{94} +(-1.60221 - 2.77511i) q^{95} +(-0.477065 + 0.826300i) q^{97} +(-2.11606 - 3.07840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4	$ 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.40985	−	0.111062i	0.996912	−	0.0785324i
$2$	1.40985	−	0.111062i	0.996912	−	0.0785324i
$3$		0			0
$3$		0			0
$4$	1.97533	−	0.313160i	0.987665	−	0.156580i
$5$	−1.74322	−	3.01934i	−0.779591	−	1.35029i	−0.932178	−	0.362001i	$-0.882094\pi$
$5$	−1.74322	−	3.01934i	−0.779591	−	1.35029i	0.152587	−	0.988290i	$-0.451240\pi$
$6$		0			0
$7$	1.80802	+	1.04386i	0.683367	+	0.394542i	0.801122	−	0.598501i	$-0.204237\pi$
$7$	1.80802	+	1.04386i	0.683367	+	0.394542i	−0.117756	+	0.993043i	$0.537570\pi$
$8$	2.75013	−	0.660890i	0.972318	−	0.233660i
$9$		0			0
$10$	−2.79300	−	4.06320i	−0.883225	−	1.28490i
$11$	0.116985	+	0.0675415i	0.0352724	+	0.0203645i	0.517533	−	0.855664i	$-0.326851\pi$
$11$	0.116985	+	0.0675415i	0.0352724	+	0.0203645i	−0.482260	+	0.876028i	$0.660184\pi$
$12$		0			0
$13$	−2.63890	+	1.52357i	−0.731900	+	0.422563i	−0.819117	−	0.573627i	$-0.805536\pi$
$13$	−2.63890	+	1.52357i	−0.731900	+	0.422563i	0.0872168	+	0.996189i	$0.472203\pi$
$14$	2.66496	+	1.27088i	0.712241	+	0.339657i
$15$		0			0
$16$	3.80386	−	1.23719i	0.950966	−	0.309297i
$17$			4.19800i			1.01816i	0.860718	+	0.509082i	$0.170015\pi$
$17$			4.19800i			1.01816i	−0.860718	+	0.509082i	$0.829985\pi$
$18$		0			0
$19$	0.919111			0.210858			0.105429	−	0.994427i	$-0.466378\pi$
$19$	0.919111			0.210858			0.105429	+	0.994427i	$0.466378\pi$
$20$	−4.38897	−	5.41829i	−0.981403	−	1.21157i
$21$		0			0
$22$	0.172432	+	0.0822305i	0.0367627	+	0.0175316i
$23$	−0.689877	−	1.19490i	−0.143849	−	0.249154i	0.785094	−	0.619377i	$-0.212615\pi$
$23$	−0.689877	−	1.19490i	−0.143849	−	0.249154i	−0.928943	+	0.370223i	$0.879281\pi$
$24$		0			0
$25$	−3.57762	+	6.19662i	−0.715524	+	1.23932i
$26$	−3.55124	+	2.44108i	−0.696455	+	0.478736i
$27$		0			0
$28$	3.89833	+	1.49577i	0.736715	+	0.282674i
$29$	−4.24111	+	7.34582i	−0.787555	+	1.36409i	0.139906	+	0.990165i	$0.455320\pi$
$29$	−4.24111	+	7.34582i	−0.787555	+	1.36409i	−0.927461	+	0.373921i	$0.878013\pi$
$30$		0			0
$31$	−4.39877	+	2.53963i	−0.790042	+	0.456131i	−0.839977	−	0.542621i	$-0.817432\pi$
$31$	−4.39877	+	2.53963i	−0.790042	+	0.456131i	0.0499352	+	0.998752i	$0.484099\pi$
$32$	5.22546	−	2.16671i	0.923739	−	0.383023i
$33$		0			0
$34$	0.466236	+	5.91853i	0.0799589	+	1.01502i
$35$		−	7.27870i		−	1.23033i
$36$		0			0
$37$		−	1.61676i		−	0.265794i	−0.991130	−	0.132897i	$-0.957572\pi$
$37$		−	1.61676i		−	0.265794i	0.991130	−	0.132897i	$-0.0424280\pi$
$38$	1.29580	−	0.102078i	0.210207	−	0.0165592i
$39$		0			0
$40$	−6.78953	−	7.15151i	−1.07352	−	1.13075i
$41$	−1.79408	+	1.03581i	−0.280188	+	0.161767i	−0.633509	−	0.773736i	$-0.718386\pi$
$41$	−1.79408	+	1.03581i	−0.280188	+	0.161767i	0.353320	+	0.935502i	$0.385053\pi$
$42$		0			0
$43$	5.41106	−	9.37224i	0.825180	−	1.42925i	−0.0766025	−	0.997062i	$-0.524407\pi$
$43$	5.41106	−	9.37224i	0.825180	−	1.42925i	0.901782	−	0.432191i	$-0.142259\pi$
$44$	0.252236	+	0.0967817i	0.0380260	+	0.0145904i
$45$		0			0
$46$	−1.10533	−	1.60801i	−0.162972	−	0.237088i
$47$	0.205809	−	0.356471i	0.0300203	−	0.0519966i	−0.850625	−	0.525773i	$-0.823776\pi$
$47$	0.205809	−	0.356471i	0.0300203	−	0.0519966i	0.880645	+	0.473776i	$0.157109\pi$
$48$		0			0
$49$	−1.32071	−	2.28754i	−0.188673	−	0.326791i
$50$	−4.35568	+	9.13361i	−0.615987	+	1.29169i
$51$		0			0
$52$	−4.73559	+	3.83596i	−0.656708	+	0.531951i
$53$	0.968137			0.132984			0.0664919	−	0.997787i	$-0.478819\pi$
$53$	0.968137			0.132984			0.0664919	+	0.997787i	$0.478819\pi$
$54$		0			0
$55$		−	0.470958i		−	0.0635040i
$56$	5.66217	+	1.67585i	0.756639	+	0.223945i
$57$		0			0
$58$	−5.16348	+	10.8275i	−0.677998	+	1.42172i
$59$	−3.88770	+	2.24457i	−0.506136	+	0.292218i	−0.731244	−	0.682116i	$-0.761060\pi$
$59$	−3.88770	+	2.24457i	−0.506136	+	0.292218i	0.225108	+	0.974334i	$0.427726\pi$
$60$		0			0
$61$	−7.44553	−	4.29868i	−0.953303	−	0.550390i	−0.0591976	−	0.998246i	$-0.518854\pi$
$61$	−7.44553	−	4.29868i	−0.953303	−	0.550390i	−0.894105	+	0.447857i	$0.852188\pi$
$62$	−5.91953	+	4.06902i	−0.751781	+	0.516766i
$63$		0			0
$64$	7.12645	−	3.63507i	0.890806	−	0.454384i
$65$	9.20037	+	5.31183i	1.14117	+	0.658852i
$66$		0			0
$67$	3.15416	+	5.46316i	0.385342	+	0.667432i	0.991817	−	0.127671i	$-0.0407502\pi$
$67$	3.15416	+	5.46316i	0.385342	+	0.667432i	−0.606475	+	0.795103i	$0.707417\pi$
$68$	1.31464	+	8.29243i	0.159424	+	1.00561i
$69$		0			0
$70$	−0.808385	−	10.2618i	−0.0966205	−	1.22653i
$71$	11.9687			1.42042			0.710210	−	0.703990i	$-0.248600\pi$
$71$	11.9687			1.42042			0.710210	+	0.703990i	$0.248600\pi$
$72$		0			0
$73$	−4.06264			−0.475496			−0.237748	−	0.971327i	$-0.576409\pi$
$73$	−4.06264			−0.475496			−0.237748	+	0.971327i	$0.576409\pi$
$74$	−0.179560	−	2.27939i	−0.0208735	−	0.264973i
$75$		0			0
$76$	1.81555	−	0.287828i	0.208258	−	0.0330162i
$77$	0.141008	+	0.244232i	0.0160693	+	0.0278329i
$78$		0			0
$79$	10.8672	+	6.27416i	1.22265	+	0.705899i	0.965483	−	0.260468i	$-0.0838768\pi$
$79$	10.8672	+	6.27416i	1.22265	+	0.705899i	0.257170	+	0.966366i	$0.417210\pi$
$80$	−10.3665	−	9.32847i	−1.15900	−	1.04296i
$81$		0			0
$82$	−2.41434	+	1.65959i	−0.266619	+	0.183271i
$83$	−5.23875	−	3.02459i	−0.575027	−	0.331992i	0.184128	−	0.982902i	$-0.441054\pi$
$83$	−5.23875	−	3.02459i	−0.575027	−	0.331992i	−0.759155	+	0.650910i	$0.774387\pi$
$84$		0			0
$85$	12.6752	−	7.31802i	1.37482	−	0.793751i
$86$	6.58787	−	13.8144i	0.710388	−	1.48964i
$87$		0			0
$88$	0.366362	+	0.108434i	0.0390544	+	0.0115591i
$89$		−	8.35848i		−	0.885997i	−0.896522	−	0.442999i	$-0.853915\pi$
$89$		−	8.35848i		−	0.885997i	0.896522	−	0.442999i	$-0.146085\pi$
$90$		0			0
$91$	−6.36158			−0.666875
$92$	−1.73693	−	2.14428i	−0.181087	−	0.223557i
$93$		0			0
$94$	0.250568	−	0.525426i	0.0258441	−	0.0541936i
$95$	−1.60221	−	2.77511i	−0.164383	−	0.284720i
$96$		0			0
$97$	−0.477065	+	0.826300i	−0.0484386	+	0.0838981i	−0.889228	−	0.457464i	$-0.848758\pi$
$97$	−0.477065	+	0.826300i	−0.0484386	+	0.0838981i	0.840790	+	0.541362i	$0.182091\pi$
$98$	−2.11606	−	3.07840i	−0.213754	−	0.310965i
$99$		0			0
$100$	−5.12645	+	13.3607i	−0.512645	+	1.33607i
$101$	5.35926	−	9.28250i	0.533266	−	0.923644i	−0.465979	−	0.884796i	$-0.654298\pi$
$101$	5.35926	−	9.28250i	0.533266	−	0.923644i	0.999245	−	0.0388479i	$-0.0123688\pi$
$102$		0			0
$103$	7.46070	−	4.30743i	0.735124	−	0.424424i	−0.0851696	−	0.996366i	$-0.527143\pi$
$103$	7.46070	−	4.30743i	0.735124	−	0.424424i	0.820294	+	0.571942i	$0.193810\pi$
$104$	−6.25042	+	5.93405i	−0.612904	+	0.581881i
$105$		0			0
$106$	1.36492	−	0.107523i	0.132573	−	0.0104435i
$107$			4.80774i			0.464781i	0.972623	+	0.232391i	$0.0746548\pi$
$107$			4.80774i			0.464781i	−0.972623	+	0.232391i	$0.925345\pi$
$108$		0			0
$109$			7.16698i			0.686472i	0.939249	+	0.343236i	$0.111523\pi$
$109$			7.16698i			0.686472i	−0.939249	+	0.343236i	$0.888477\pi$
$110$	−0.0523054	−	0.663978i	−0.00498712	−	0.0633078i
$111$		0			0
$112$	8.16891	+	1.73384i	0.771889	+	0.163833i
$113$	0.213928	−	0.123511i	0.0201246	−	0.0116190i	−0.489904	−	0.871776i	$-0.662968\pi$
$113$	0.213928	−	0.123511i	0.0201246	−	0.0116190i	0.510029	+	0.860157i	$0.329635\pi$
$114$		0			0
$115$	−2.40521	+	4.16595i	−0.224287	+	0.388477i
$116$	−6.07719	+	15.8386i	−0.564253	+	1.47058i
$117$		0			0
$118$	−5.23178	+	3.59627i	−0.481624	+	0.331063i
$119$	−4.38212	+	7.59006i	−0.401708	+	0.695779i
$120$		0			0
$121$	−5.49088	−	9.51048i	−0.499171	−	0.864589i
$122$	−10.9745	−	5.23356i	−0.993582	−	0.473825i
$123$		0			0
$124$	−7.89371	+	6.39413i	−0.708876	+	0.574210i
$125$	7.51409			0.672081
$126$		0			0
$127$		−	17.6276i		−	1.56420i	−0.623156	−	0.782098i	$-0.714150\pi$
$127$		−	17.6276i		−	1.56420i	0.623156	−	0.782098i	$-0.285850\pi$
$128$	9.64348	−	5.91636i	0.852371	−	0.522938i
$129$		0			0
$130$	13.5610	+	6.46706i	1.18938	+	0.567199i
$131$	12.7802	−	7.37864i	1.11661	−	0.644675i	0.176076	−	0.984377i	$-0.443659\pi$
$131$	12.7802	−	7.37864i	1.11661	−	0.644675i	0.940533	+	0.339702i	$0.110326\pi$
$132$		0			0
$133$	1.66177	+	0.959423i	0.144094	+	0.0831925i
$134$	5.05362	+	7.35191i	0.436567	+	0.635108i
$135$		0			0
$136$	2.77442	+	11.5450i	0.237904	+	0.989979i
$137$	−14.8589	−	8.57878i	−1.26948	−	0.732934i	−0.294590	−	0.955624i	$-0.595183\pi$
$137$	−14.8589	−	8.57878i	−1.26948	−	0.732934i	−0.974889	+	0.222689i	$0.928516\pi$
$138$		0			0
$139$	−0.607862	−	1.05285i	−0.0515581	−	0.0893013i	0.839095	−	0.543986i	$-0.183085\pi$
$139$	−0.607862	−	1.05285i	−0.0515581	−	0.0893013i	−0.890653	+	0.454684i	$0.849752\pi$
$140$	−2.27940	−	14.3778i	−0.192644	−	1.21515i
$141$		0			0
$142$	16.8740	−	1.32926i	1.41603	−	0.111549i
$143$	−0.411617			−0.0344211
$144$		0			0
$145$	29.5727			2.45588
$146$	−5.72770	+	0.451204i	−0.474028	+	0.0373419i
$147$		0			0
$148$	−0.506305	−	3.19364i	−0.0416180	−	0.262516i
$149$	4.46357	+	7.73113i	0.365670	+	0.633359i	0.988883	−	0.148693i	$-0.0475066\pi$
$149$	4.46357	+	7.73113i	0.365670	+	0.633359i	−0.623214	+	0.782052i	$0.714173\pi$
$150$		0			0
$151$	−18.9453	−	10.9381i	−1.54175	−	0.890127i	−0.998729	−	0.0504058i	$-0.983949\pi$
$151$	−18.9453	−	10.9381i	−1.54175	−	0.890127i	−0.543017	−	0.839722i	$-0.682718\pi$
$152$	2.52768	−	0.607431i	0.205022	−	0.0492692i
$153$		0			0
$154$	0.225924	+	0.328670i	0.0182055	+	0.0264850i
$155$	15.3360	+	8.85426i	1.23182	+	0.711191i
$156$		0			0
$157$	4.85478	−	2.80291i	0.387454	−	0.223697i	−0.293602	−	0.955928i	$-0.594854\pi$
$157$	4.85478	−	2.80291i	0.387454	−	0.223697i	0.681056	+	0.732231i	$0.261521\pi$
$158$	16.0179	+	7.63868i	1.27431	+	0.607701i
$159$		0			0
$160$	−15.6511	−	12.0004i	−1.23733	−	0.948714i
$161$		−	2.88054i		−	0.227018i
$162$		0			0
$163$	−17.1763			−1.34535			−0.672676	−	0.739937i	$-0.734855\pi$
$163$	−17.1763			−1.34535			−0.672676	+	0.739937i	$0.734855\pi$
$164$	−3.21952	+	2.60790i	−0.251403	+	0.203643i
$165$		0			0
$166$	−7.72174	−	3.68238i	−0.599323	−	0.285808i
$167$	−2.31249	−	4.00535i	−0.178946	−	0.309943i	0.762574	−	0.646901i	$-0.223935\pi$
$167$	−2.31249	−	4.00535i	−0.178946	−	0.309943i	−0.941520	+	0.336958i	$0.890602\pi$
$168$		0			0
$169$	−1.85746	+	3.21721i	−0.142881	+	0.247478i
$170$	17.0573	−	11.7250i	1.30824	−	0.899267i
$171$		0			0
$172$	7.75363	−	20.2078i	0.591209	−	1.54083i
$173$	1.52076	−	2.63404i	0.115621	−	0.200262i	−0.802407	−	0.596778i	$-0.796447\pi$
$173$	1.52076	−	2.63404i	0.115621	−	0.200262i	0.918028	+	0.396516i	$0.129781\pi$
$174$		0			0
$175$	−12.9368	+	7.46907i	−0.977930	+	0.564608i
$176$	0.528557	+	0.112186i	0.0398415	+	0.00845632i
$177$		0			0
$178$	−0.928307	−	11.7842i	−0.0695795	−	0.883261i
$179$			17.9997i			1.34536i	0.739935	+	0.672679i	$0.234856\pi$
$179$			17.9997i			1.34536i	−0.739935	+	0.672679i	$0.765144\pi$
$180$		0			0
$181$			15.9507i			1.18561i	0.805347	+	0.592804i	$0.201979\pi$
$181$			15.9507i			1.18561i	−0.805347	+	0.592804i	$0.798021\pi$
$182$	−8.96885	+	0.706528i	−0.664815	+	0.0523713i
$183$		0			0
$184$	−2.68695	−	2.83020i	−0.198085	−	0.208645i
$185$	−4.88156	+	2.81837i	−0.358899	+	0.207211i
$186$		0			0
$187$	−0.283539	+	0.491104i	−0.0207344	+	0.0359131i
$188$	0.294908	−	0.768599i	0.0215084	−	0.0560558i
$189$		0			0
$190$	−2.56708	−	3.73453i	−0.186235	−	0.270931i
$191$	−2.21964	+	3.84452i	−0.160607	+	0.278180i	−0.935087	−	0.354419i	$-0.884679\pi$
$191$	−2.21964	+	3.84452i	−0.160607	+	0.278180i	0.774479	+	0.632599i	$0.218012\pi$
$192$		0			0
$193$	0.673862	+	1.16716i	0.0485057	+	0.0840143i	0.889259	−	0.457404i	$-0.151221\pi$
$193$	0.673862	+	1.16716i	0.0485057	+	0.0840143i	−0.840753	+	0.541419i	$0.817887\pi$
$194$	−0.580817	+	1.21794i	−0.0417003	+	0.0874430i
$195$		0			0
$196$	−3.32521	−	4.10505i	−0.237515	−	0.293218i
$197$	−9.16835			−0.653218			−0.326609	−	0.945160i	$-0.605906\pi$
$197$	−9.16835			−0.653218			−0.326609	+	0.945160i	$0.605906\pi$
$198$		0			0
$199$			24.0240i			1.70301i	0.524344	+	0.851507i	$0.324311\pi$
$199$			24.0240i			1.70301i	−0.524344	+	0.851507i	$0.675689\pi$
$200$	−5.74364	+	19.4059i	−0.406136	+	1.37221i
$201$		0			0
$202$	6.52479	−	13.6821i	0.459083	−	0.962670i
$203$	−15.3360	+	8.85426i	−1.07638	+	0.621447i
$204$		0			0
$205$	6.25494	+	3.61129i	0.436864	+	0.252224i
$206$	10.0400	−	6.90142i	0.699523	−	0.480844i
$207$		0			0
$208$	−8.15308	+	9.06028i	−0.565314	+	0.628217i
$209$	0.107522	+	0.0620781i	0.00743748	+	0.00429403i
$210$		0			0
$211$	10.1275	+	17.5414i	0.697208	+	1.20760i	0.969431	+	0.245365i	$0.0789078\pi$
$211$	10.1275	+	17.5414i	0.697208	+	1.20760i	−0.272223	+	0.962234i	$0.587759\pi$
$212$	1.91239	−	0.303181i	0.131344	−	0.0208226i
$213$		0			0
$214$	0.533955	+	6.77817i	0.0365004	+	0.463346i
$215$	−37.7307			−2.57321
$216$		0			0
$217$	−10.6041			−0.719852
$218$	0.795977	+	10.1043i	0.0539104	+	0.684352i
$219$		0			0
$220$	−0.147485	−	0.930298i	−0.00994344	−	0.0627207i
$221$	−6.39595	−	11.0781i	−0.430238	−	0.745194i
$222$		0			0
$223$	0.521119	+	0.300868i	0.0348967	+	0.0201476i	0.517347	−	0.855776i	$-0.326920\pi$
$223$	0.521119	+	0.300868i	0.0348967	+	0.0201476i	−0.482450	+	0.875923i	$0.660253\pi$
$224$	11.7095	+	1.53720i	0.782371	+	0.102708i
$225$		0			0
$226$	0.287888	−	0.197891i	0.0191500	−	0.0131635i
$227$	−9.23720	−	5.33310i	−0.613095	−	0.353970i	0.161081	−	0.986941i	$-0.448502\pi$
$227$	−9.23720	−	5.33310i	−0.613095	−	0.353970i	−0.774176	+	0.632971i	$0.781835\pi$
$228$		0			0
$229$	−22.1574	+	12.7926i	−1.46420	+	0.845356i	−0.999201	−	0.0399555i	$-0.987278\pi$
$229$	−22.1574	+	12.7926i	−1.46420	+	0.845356i	−0.464998	+	0.885312i	$0.653945\pi$
$230$	−2.92830	+	6.14047i	−0.193086	+	0.404891i
$231$		0			0
$232$	−6.80884	+	23.0049i	−0.447022	+	1.51035i
$233$		−	4.71086i		−	0.308619i	−0.988023	−	0.154309i	$-0.950685\pi$
$233$		−	4.71086i		−	0.308619i	0.988023	−	0.154309i	$-0.0493152\pi$
$234$		0			0
$235$	−1.43508			−0.0936141
$236$	−6.97659	+	5.65123i	−0.454137	+	0.367864i
$237$		0			0
$238$	−5.33515	+	11.1875i	−0.345827	+	0.725178i
$239$	7.51034	+	13.0083i	0.485803	+	0.841436i	0.999867	−	0.0163162i	$-0.00519384\pi$
$239$	7.51034	+	13.0083i	0.485803	+	0.841436i	−0.514064	+	0.857752i	$0.671861\pi$
$240$		0			0
$241$	12.8731	−	22.2969i	0.829230	−	1.43627i	−0.0694129	−	0.997588i	$-0.522113\pi$
$241$	12.8731	−	22.2969i	0.829230	−	1.43627i	0.898643	−	0.438681i	$-0.144554\pi$
$242$	−8.79754	−	12.7985i	−0.565527	−	0.822717i
$243$		0			0
$244$	−16.0536	−	6.15968i	−1.02772	−	0.394333i
$245$	−4.60458	+	7.97536i	−0.294176	+	0.509527i
$246$		0			0
$247$	−2.42544	+	1.40033i	−0.154327	+	0.0891009i
$248$	−10.4188	+	9.89142i	−0.661593	+	0.628106i
$249$		0			0
$250$	10.5937	−	0.834527i	0.670005	−	0.0527801i
$251$		−	5.30436i		−	0.334808i	−0.985888	−	0.167404i	$-0.946462\pi$
$251$		−	5.30436i		−	0.334808i	0.985888	−	0.167404i	$-0.0535385\pi$
$252$		0			0
$253$		−	0.186381i		−	0.0117177i
$254$	−1.95775	−	24.8522i	−0.122840	−	1.55936i
$255$		0			0
$256$	12.9387	−	9.41218i	0.808671	−	0.588261i
$257$	21.4984	−	12.4121i	1.34104	−	0.774248i	0.354077	−	0.935216i	$-0.384795\pi$
$257$	21.4984	−	12.4121i	1.34104	−	0.774248i	0.986959	+	0.160969i	$0.0514619\pi$
$258$		0			0
$259$	1.68767	−	2.92314i	0.104867	−	0.181635i
$260$	19.8372	+	7.61145i	1.23025	+	0.472042i
$261$		0			0
$262$	17.1986	−	11.8221i	1.06253	−	0.730374i
$263$	9.95859	−	17.2488i	0.614073	−	1.06361i	−0.376473	−	0.926427i	$-0.622863\pi$
$263$	9.95859	−	17.2488i	0.614073	−	1.06361i	0.990546	−	0.137178i	$-0.0438033\pi$
$264$		0			0
$265$	−1.68767	−	2.92314i	−0.103673	−	0.179567i
$266$	2.44939	+	1.16808i	0.150182	+	0.0716196i
$267$		0			0
$268$	7.94135	+	9.80380i	0.485095	+	0.598862i
$269$	−2.35540			−0.143611			−0.0718057	−	0.997419i	$-0.522876\pi$
$269$	−2.35540			−0.143611			−0.0718057	+	0.997419i	$0.522876\pi$
$270$		0			0
$271$		−	12.0774i		−	0.733648i	−0.930290	−	0.366824i	$-0.880445\pi$
$271$		−	12.0774i		−	0.733648i	0.930290	−	0.366824i	$-0.119555\pi$
$272$	5.19371	+	15.9686i	0.314915	+	0.968239i
$273$		0			0
$274$	−21.9015	−	10.4445i	−1.32312	−	0.630975i
$275$	−0.837057	+	0.483275i	−0.0504764	+	0.0291426i
$276$		0			0
$277$	−14.5504	−	8.40069i	−0.874250	−	0.504748i	−0.00549164	−	0.999985i	$-0.501748\pi$
$277$	−14.5504	−	8.40069i	−0.874250	−	0.504748i	−0.868758	+	0.495237i	$0.835081\pi$
$278$	−0.973922	−	1.41684i	−0.0584120	−	0.0849765i
$279$		0			0
$280$	−4.81042	−	20.0174i	−0.287478	−	1.19627i
$281$	−11.9853	−	6.91973i	−0.714984	−	0.412796i	0.0979194	−	0.995194i	$-0.468781\pi$
$281$	−11.9853	−	6.91973i	−0.714984	−	0.412796i	−0.812904	+	0.582398i	$0.802115\pi$
$282$		0			0
$283$	2.58123	+	4.47082i	0.153438	+	0.265763i	0.932489	−	0.361198i	$-0.117632\pi$
$283$	2.58123	+	4.47082i	0.153438	+	0.265763i	−0.779051	+	0.626960i	$0.784299\pi$
$284$	23.6421	−	3.74810i	1.40290	−	0.222409i
$285$		0			0
$286$	−0.580317	+	0.0457149i	−0.0343148	+	0.00270318i
$287$	−4.32497			−0.255295
$288$		0			0
$289$	−0.623177			−0.0366574
$290$	41.6930	−	3.28440i	2.44830	−	0.192866i
$291$		0			0
$292$	−8.02506	+	1.27226i	−0.469631	+	0.0744531i
$293$	5.41881	+	9.38566i	0.316571	+	0.548316i	0.979770	−	0.200126i	$-0.0641353\pi$
$293$	5.41881	+	9.38566i	0.316571	+	0.548316i	−0.663200	+	0.748443i	$0.730802\pi$
$294$		0			0
$295$	13.5542	+	7.82554i	0.789158	+	0.455620i
$296$	−1.06850	−	4.44631i	−0.0621054	−	0.258436i
$297$		0			0
$298$	7.15158	+	10.4040i	0.414280	+	0.602686i
$299$	3.64104	+	2.10215i	0.210567	+	0.121571i
$300$		0			0
$301$	19.5666	−	11.2968i	1.12780	−	0.651136i
$302$	−27.9247	−	13.3169i	−1.60689	−	0.766301i
$303$		0			0
$304$	3.49617	−	1.13711i	0.200519	−	0.0652179i
$305$			29.9742i			1.71632i
$306$		0			0
$307$	16.6551			0.950557			0.475279	−	0.879835i	$-0.342347\pi$
$307$	16.6551			0.950557			0.475279	+	0.879835i	$0.342347\pi$
$308$	0.355021	+	0.438282i	0.0202292	+	0.0249734i
$309$		0			0
$310$	22.6048	+	10.7799i	1.28387	+	0.612257i
$311$	6.47216	+	11.2101i	0.367002	+	0.635667i	0.989095	−	0.147277i	$-0.0470508\pi$
$311$	6.47216	+	11.2101i	0.367002	+	0.635667i	−0.622093	+	0.782943i	$0.713717\pi$
$312$		0			0
$313$	−13.3593	+	23.1390i	−0.755112	+	1.30789i	0.190206	+	0.981744i	$0.439084\pi$
$313$	−13.3593	+	23.1390i	−0.755112	+	1.30789i	−0.945318	+	0.326149i	$0.894249\pi$
$314$	6.53320	−	4.49085i	0.368690	−	0.253433i
$315$		0			0
$316$	23.4311	+	8.99039i	1.31810	+	0.505749i
$317$	12.5342	−	21.7098i	0.703990	−	1.21935i	−0.263065	−	0.964778i	$-0.584733\pi$
$317$	12.5342	−	21.7098i	0.703990	−	1.21935i	0.967055	−	0.254568i	$-0.0819332\pi$
$318$		0			0
$319$	−0.992296	+	0.572902i	−0.0555579	+	0.0320764i
$320$	−23.3985	−	15.1805i	−1.30801	−	0.848614i
$321$		0			0
$322$	−0.319918	−	4.06112i	−0.0178283	−	0.226317i
$323$			3.85842i			0.214688i
$324$		0			0
$325$		−	21.8030i		−	1.20941i
$326$	−24.2160	+	1.90763i	−1.34120	+	0.105654i
$327$		0			0
$328$	−4.24940	+	4.03431i	−0.234634	+	0.222757i
$329$	0.744211	−	0.429671i	0.0410297	−	0.0236885i
$330$		0			0
$331$	−8.47956	+	14.6870i	−0.466079	+	0.807272i	−0.999249	−	0.0387357i	$-0.987667\pi$
$331$	−8.47956	+	14.6870i	−0.466079	+	0.807272i	0.533171	+	0.846008i	$0.321000\pi$
$332$	−11.2954	−	4.33400i	−0.619917	−	0.237859i
$333$		0			0
$334$	−3.70510	−	5.39010i	−0.202734	−	0.294933i
$335$	10.9968	−	19.0470i	0.600818	−	1.04065i
$336$		0			0
$337$	4.47220	+	7.74608i	0.243616	+	0.421956i	0.961742	−	0.273958i	$-0.0883329\pi$
$337$	4.47220	+	7.74608i	0.243616	+	0.421956i	−0.718125	+	0.695914i	$0.755000\pi$
$338$	−2.26142	+	4.74207i	−0.123005	+	0.257934i
$339$		0			0
$340$	22.7460	−	18.4249i	1.23357	−	0.999229i
$341$	−0.686122			−0.0371556
$342$		0			0
$343$		−	20.1286i		−	1.08684i
$344$	8.68712	−	29.3510i	0.468378	−	1.58250i
$345$		0			0
$346$	1.85150	−	3.88248i	0.0995372	−	0.208724i
$347$	4.29330	−	2.47874i	0.230476	−	0.133066i	−0.380315	−	0.924857i	$-0.624185\pi$
$347$	4.29330	−	2.47874i	0.230476	−	0.133066i	0.610792	+	0.791791i	$0.290851\pi$
$348$		0			0
$349$	22.9731	+	13.2635i	1.22972	+	0.709980i	0.966972	−	0.254884i	$-0.0820374\pi$
$349$	22.9731	+	13.2635i	1.22972	+	0.709980i	0.262749	+	0.964864i	$0.415371\pi$
$350$	−17.4094	+	11.9670i	−0.930570	+	0.639664i
$351$		0			0
$352$	0.757644	+	0.0994621i	0.0403825	+	0.00530135i
$353$	28.7458	+	16.5964i	1.52998	+	0.883337i	0.999362	+	0.0357291i	$0.0113753\pi$
$353$	28.7458	+	16.5964i	1.52998	+	0.883337i	0.530623	+	0.847608i	$0.321958\pi$
$354$		0			0
$355$	−20.8640	−	36.1375i	−1.10735	−	1.91798i
$356$	−2.61754	−	16.5108i	−0.138729	−	0.875069i
$357$		0			0
$358$	1.99907	+	25.3767i	0.105654	+	1.34120i
$359$	20.6138			1.08795			0.543977	−	0.839100i	$-0.316918\pi$
$359$	20.6138			1.08795			0.543977	+	0.839100i	$0.316918\pi$
$360$		0			0
$361$	−18.1552			−0.955539
$362$	1.77151	+	22.4881i	0.0931087	+	1.18195i
$363$		0			0
$364$	−12.5662	+	1.99219i	−0.658649	+	0.104419i
$365$	7.08207	+	12.2665i	0.370693	+	0.642058i
$366$		0			0
$367$	10.1478	+	5.85881i	0.529708	+	0.305827i	0.740898	−	0.671618i	$-0.234400\pi$
$367$	10.1478	+	5.85881i	0.529708	+	0.305827i	−0.211189	+	0.977445i	$0.567734\pi$
$368$	−4.10251	−	3.69174i	−0.213858	−	0.192445i
$369$		0			0
$370$	−6.56923	+	4.51562i	−0.341518	+	0.234756i
$371$	1.75041	+	1.01060i	0.0908767	+	0.0524677i
$372$		0			0
$373$	−3.02771	+	1.74805i	−0.156769	+	0.0905105i	−0.576332	−	0.817216i	$-0.695517\pi$
$373$	−3.02771	+	1.74805i	−0.156769	+	0.0905105i	0.419563	+	0.907726i	$0.362183\pi$
$374$	−0.345203	+	0.723871i	−0.0178500	+	0.0374305i
$375$		0			0
$376$	0.330412	−	1.11636i	0.0170397	−	0.0575718i
$377$		−	25.8466i		−	1.33117i
$378$		0			0
$379$	20.1604			1.03557			0.517785	−	0.855511i	$-0.326757\pi$
$379$	20.1604			1.03557			0.517785	+	0.855511i	$0.326757\pi$
$380$	−4.03395	−	4.98001i	−0.206937	−	0.255469i
$381$		0			0
$382$	−2.70237	+	5.66670i	−0.138265	+	0.289934i
$383$	−5.33120	−	9.23391i	−0.272412	−	0.471831i	0.697067	−	0.717006i	$-0.254488\pi$
$383$	−5.33120	−	9.23391i	−0.272412	−	0.471831i	−0.969479	+	0.245175i	$0.921155\pi$
$384$		0			0
$385$	0.491614	−	0.851501i	0.0250550	−	0.0433965i
$386$	1.07967	+	1.57068i	0.0549537	+	0.0799455i
$387$		0			0
$388$	−0.683597	+	1.78161i	−0.0347044	+	0.0904477i
$389$	−8.34122	+	14.4474i	−0.422917	+	0.732513i	−0.996223	−	0.0868277i	$-0.972327\pi$
$389$	−8.34122	+	14.4474i	−0.422917	+	0.732513i	0.573307	+	0.819341i	$0.305660\pi$
$390$		0			0
$391$	5.01619	−	2.89610i	0.253680	−	0.146462i
$392$	−5.14394	−	5.41819i	−0.259808	−	0.273660i
$393$		0			0
$394$	−12.9260	+	1.01825i	−0.651200	+	0.0512988i
$395$		−	43.7489i		−	2.20125i
$396$		0			0
$397$		−	22.9869i		−	1.15368i	−0.816857	−	0.576840i	$-0.804285\pi$
$397$		−	22.9869i		−	1.15368i	0.816857	−	0.576840i	$-0.195715\pi$
$398$	2.66814	+	33.8701i	0.133742	+	1.69775i
$399$		0			0
$400$	−5.94239	+	27.9973i	−0.297119	+	1.39986i
$401$	−27.3094	+	15.7671i	−1.36377	+	0.787371i	−0.990123	−	0.140201i	$-0.955225\pi$
$401$	−27.3094	+	15.7671i	−1.36377	+	0.787371i	−0.373644	+	0.927572i	$0.621892\pi$
$402$		0			0
$403$	7.73862	−	13.4037i	0.385488	−	0.667685i
$404$	7.67940	−	20.0143i	0.382064	−	0.995749i
$405$		0			0
$406$	−20.6381	+	14.1864i	−1.02425	+	0.704058i
$407$	0.109199	−	0.189137i	0.00541277	−	0.00937519i
$408$		0			0
$409$	3.59259	+	6.22255i	0.177642	+	0.307686i	0.941073	−	0.338205i	$-0.109820\pi$
$409$	3.59259	+	6.22255i	0.177642	+	0.307686i	−0.763430	+	0.645890i	$0.776486\pi$
$410$	9.21958	+	4.39668i	0.455323	+	0.217137i
$411$		0			0
$412$	13.3884	−	10.8450i	0.659600	−	0.534295i
$413$	−9.37205			−0.461169
$414$		0			0
$415$			21.0901i			1.03527i
$416$	−10.4883	+	13.6791i	−0.514233	+	0.670672i
$417$		0			0
$418$	0.158485	+	0.0755789i	0.00775173	+	0.00369669i
$419$	12.5999	−	7.27453i	0.615543	−	0.355384i	−0.159589	−	0.987184i	$-0.551017\pi$
$419$	12.5999	−	7.27453i	0.615543	−	0.355384i	0.775132	+	0.631800i	$0.217683\pi$
$420$		0			0
$421$	9.38587	+	5.41893i	0.457439	+	0.264103i	0.710967	−	0.703225i	$-0.248258\pi$
$421$	9.38587	+	5.41893i	0.457439	+	0.264103i	−0.253528	+	0.967328i	$0.581591\pi$
$422$	16.2264	+	23.6059i	0.789890	+	1.14912i
$423$		0			0
$424$	2.66250	−	0.639832i	0.129303	−	0.0310730i
$425$	−26.0134	−	15.0188i	−1.26183	−	0.728520i
$426$		0			0
$427$	−8.97444	−	15.5442i	−0.434304	−	0.752236i
$428$	1.50559	+	9.49687i	0.0727754	+	0.459048i
$429$		0			0
$430$	−53.1944	+	4.19043i	−2.56526	+	0.202080i
$431$	10.8604			0.523129			0.261565	−	0.965186i	$-0.415762\pi$
$431$	10.8604			0.523129			0.261565	+	0.965186i	$0.415762\pi$
$432$		0			0
$433$	9.41382			0.452399			0.226200	−	0.974081i	$-0.427370\pi$
$433$	9.41382			0.452399			0.226200	+	0.974081i	$0.427370\pi$
$434$	−14.9501	+	1.17771i	−0.717628	+	0.0565317i
$435$		0			0
$436$	2.24441	+	14.1572i	0.107488	+	0.678005i
$437$	−0.634073	−	1.09825i	−0.0303318	−	0.0525363i
$438$		0			0
$439$	−9.25745	−	5.34479i	−0.441834	−	0.255093i	0.262541	−	0.964921i	$-0.415439\pi$
$439$	−9.25745	−	5.34479i	−0.441834	−	0.255093i	−0.704375	+	0.709828i	$0.748773\pi$
$440$	−0.311252	−	1.29520i	−0.0148383	−	0.0617461i
$441$		0			0
$442$	−10.2477	−	14.9081i	−0.487431	−	0.709105i
$443$	−18.9818	−	10.9592i	−0.901854	−	0.520686i	−0.0240526	−	0.999711i	$-0.507657\pi$
$443$	−18.9818	−	10.9592i	−0.901854	−	0.520686i	−0.877801	+	0.479025i	$0.840990\pi$
$444$		0			0
$445$	−25.2371	+	14.5707i	−1.19635	+	0.690715i
$446$	0.768113	+	0.366302i	0.0363712	+	0.0173449i
$447$		0			0
$448$	16.6793	+	0.866739i	0.788021	+	0.0409496i
$449$			18.7436i			0.884565i	0.896876	+	0.442282i	$0.145831\pi$
$449$			18.7436i			0.884565i	−0.896876	+	0.442282i	$0.854169\pi$
$450$		0			0
$451$	−0.279841			−0.0131772
$452$	0.383899	−	0.310969i	0.0180571	−	0.0146267i
$453$		0			0
$454$	−13.6153	−	6.49295i	−0.638999	−	0.304729i
$455$	11.0896	+	19.2078i	0.519890	+	0.900475i
$456$		0			0
$457$	−0.00912370	+	0.0158027i	−0.000426789	+	0.000739220i	−0.866239	−	0.499630i	$-0.833469\pi$
$457$	−0.00912370	+	0.0158027i	−0.000426789	+	0.000739220i	0.865812	+	0.500370i	$0.166803\pi$
$458$	−29.8177	+	20.4964i	−1.39329	+	0.957732i
$459$		0			0
$460$	−3.44648	+	8.98234i	−0.160693	+	0.418804i
$461$	1.25915	−	2.18091i	0.0586444	−	0.101575i	−0.835213	−	0.549927i	$-0.814656\pi$
$461$	1.25915	−	2.18091i	0.0586444	−	0.101575i	0.893857	+	0.448352i	$0.147989\pi$
$462$		0			0
$463$	23.9003	−	13.7988i	1.11074	−	0.641286i	0.171719	−	0.985146i	$-0.445068\pi$
$463$	23.9003	−	13.7988i	1.11074	−	0.641286i	0.939021	+	0.343860i	$0.111735\pi$
$464$	−7.04445	+	33.1896i	−0.327030	+	1.54079i
$465$		0			0
$466$	−0.523196	−	6.64159i	−0.0242366	−	0.307666i
$467$			28.4629i			1.31711i	0.752533	+	0.658554i	$0.228832\pi$
$467$			28.4629i			1.31711i	−0.752533	+	0.658554i	$0.771168\pi$
$468$		0			0
$469$			13.1700i			0.608134i
$470$	−2.02324	+	0.159382i	−0.0933250	+	0.00735174i
$471$		0			0
$472$	−9.20828	+	8.74220i	−0.423846	+	0.402392i
$473$	1.26603	−	0.730942i	0.0582121	−	0.0336088i
$474$		0			0
$475$	−3.28823	+	5.69538i	−0.150874	+	0.261322i
$476$	−6.27924	+	16.3652i	−0.287808	+	0.750097i
$477$		0			0
$478$	12.0331	+	17.5056i	0.550383	+	0.800686i
$479$	−19.1602	+	33.1865i	−0.875454	+	1.51633i	−0.0191747	+	0.999816i	$0.506104\pi$
$479$	−19.1602	+	33.1865i	−0.875454	+	1.51633i	−0.856279	+	0.516514i	$0.827229\pi$
$480$		0			0
$481$	2.46325	+	4.26648i	0.112315	+	0.194535i
$482$	15.6728	−	32.8649i	0.713875	−	1.49695i
$483$		0			0
$484$	−13.8246	−	17.0668i	−0.628391	−	0.775764i
$485$	3.32651			0.151049
$486$		0			0
$487$			2.25659i			0.102256i	0.998692	+	0.0511280i	$0.0162817\pi$
$487$			2.25659i			0.102256i	−0.998692	+	0.0511280i	$0.983718\pi$
$488$	−23.3172	−	6.90126i	−1.05552	−	0.312405i
$489$		0			0
$490$	−5.60599	+	11.7554i	−0.253253	+	0.531056i
$491$	17.7659	−	10.2572i	0.801765	−	0.462899i	−0.0423228	−	0.999104i	$-0.513476\pi$
$491$	17.7659	−	10.2572i	0.801765	−	0.462899i	0.844088	+	0.536205i	$0.180142\pi$
$492$		0			0
$493$	−30.8377	−	17.8042i	−1.38886	−	0.801860i
$494$	−3.26398	+	2.24362i	−0.146853	+	0.100945i
$495$		0			0
$496$	−13.5903	+	15.1025i	−0.610223	+	0.678123i
$497$	21.6396	+	12.4936i	0.970667	+	0.560415i
$498$		0			0
$499$	1.87815	+	3.25306i	0.0840777	+	0.145627i	0.904998	−	0.425416i	$-0.139872\pi$
$499$	1.87815	+	3.25306i	0.0840777	+	0.145627i	−0.820920	+	0.571043i	$0.806539\pi$
$500$	14.8428	−	2.35311i	0.663791	−	0.105234i
$501$		0			0
$502$	−0.589111	−	7.47833i	−0.0262933	−	0.333774i
$503$	33.3322			1.48621			0.743104	−	0.669175i	$-0.233353\pi$
$503$	33.3322			1.48621			0.743104	+	0.669175i	$0.233353\pi$
$504$		0			0
$505$	−37.3694			−1.66292
$506$	−0.0206998	−	0.262769i	−0.000920219	−	0.0116815i
$507$		0			0
$508$	−5.52025	−	34.8203i	−0.244921	−	1.54490i
$509$	−3.41788	−	5.91994i	−0.151495	−	0.262397i	0.780282	−	0.625427i	$-0.215075\pi$
$509$	−3.41788	−	5.91994i	−0.151495	−	0.262397i	−0.931777	+	0.363031i	$0.881742\pi$
$510$		0			0
$511$	−7.34533	−	4.24083i	−0.324938	−	0.187603i
$512$	17.1963	−	14.7067i	0.759976	−	0.649951i
$513$		0			0
$514$	28.9310	−	19.8868i	1.27609	−	0.877171i
$515$	−26.0112	−	15.0176i	−1.14619	−	0.661754i
$516$		0			0
$517$	0.0481531	−	0.0278012i	0.00211777	−	0.00122270i
$518$	2.05471	−	4.30861i	0.0902788	−	0.189309i
$519$		0			0
$520$	28.8128	+	8.52781i	1.26352	+	0.373969i
$521$			19.9468i			0.873887i	0.899489	+	0.436943i	$0.143939\pi$
$521$			19.9468i			0.873887i	−0.899489	+	0.436943i	$0.856061\pi$
$522$		0			0
$523$	−5.50358			−0.240655			−0.120327	−	0.992734i	$-0.538394\pi$
$523$	−5.50358			−0.240655			−0.120327	+	0.992734i	$0.538394\pi$
$524$	22.9344	−	18.5775i	1.00189	−	0.811561i
$525$		0			0
$526$	12.1244	−	25.4241i	0.528649	−	1.10855i
$527$	−10.6614	−	18.4660i	−0.464416	−	0.804392i
$528$		0			0
$529$	10.5481	−	18.2699i	0.458615	−	0.794344i
$530$	−2.70401	−	3.93374i	−0.117455	−	0.170871i
$531$		0			0
$532$	3.58300	+	1.37478i	0.155343	+	0.0596042i
$533$	3.15627	−	5.46682i	0.136713	−	0.236794i
$534$		0			0
$535$	14.5162	−	8.38093i	0.627590	−	0.362339i
$536$	12.2849	+	12.9399i	0.530627	+	0.558917i
$537$		0			0
$538$	−3.32075	+	0.261595i	−0.143168	+	0.0112782i
$539$		−	0.356811i		−	0.0153690i
$540$		0			0
$541$		−	12.1375i		−	0.521831i	−0.965362	−	0.260915i	$-0.915976\pi$
$541$		−	12.1375i		−	0.521831i	0.965362	−	0.260915i	$-0.0840243\pi$
$542$	−1.34133	−	17.0272i	−0.0576152	−	0.731382i
$543$		0			0
$544$	9.09583	+	21.9364i	0.389980	+	0.940517i
$545$	21.6396	−	12.4936i	0.926937	−	0.535167i
$546$		0			0
$547$	5.02439	−	8.70250i	0.214827	−	0.372092i	−0.738392	−	0.674372i	$-0.764414\pi$
$547$	5.02439	−	8.70250i	0.214827	−	0.372092i	0.953219	+	0.302280i	$0.0977477\pi$
$548$	−32.0377	−	12.2927i	−1.36858	−	0.525119i
$549$		0			0
$550$	−1.12645	+	0.774308i	−0.0480319	+	0.0330166i
$551$	−3.89805	+	6.75163i	−0.166063	+	0.287629i
$552$		0			0
$553$	13.0987	+	22.6876i	0.557013	+	0.964775i
$554$	−21.4468	−	10.2277i	−0.911189	−	0.434533i
$555$		0			0
$556$	−1.53044	−	1.88936i	−0.0649050	−	0.0801269i
$557$	−15.4323			−0.653887			−0.326944	−	0.945044i	$-0.606019\pi$
$557$	−15.4323			−0.653887			−0.326944	+	0.945044i	$0.606019\pi$
$558$		0			0
$559$			32.9766i			1.39476i
$560$	−9.00512	−	27.6872i	−0.380536	−	1.17000i
$561$		0			0
$562$	−17.6660	−	8.42464i	−0.745194	−	0.355372i
$563$	−5.08901	+	2.93814i	−0.214476	+	0.123828i	−0.603390	−	0.797446i	$-0.706184\pi$
$563$	−5.08901	+	2.93814i	−0.214476	+	0.123828i	0.388914	+	0.921274i	$0.372850\pi$
$564$		0			0
$565$	−0.745845	−	0.430614i	−0.0313779	−	0.0181161i
$566$	4.13567	+	6.01649i	0.173835	+	0.252892i
$567$		0			0
$568$	32.9154	−	7.90997i	1.38110	−	0.331895i
$569$	28.3228	+	16.3522i	1.18735	+	0.685519i	0.957704	−	0.287754i	$-0.0929087\pi$
$569$	28.3228	+	16.3522i	1.18735	+	0.685519i	0.229650	+	0.973273i	$0.426242\pi$
$570$		0			0
$571$	16.4253	+	28.4495i	0.687377	+	1.19057i	0.972683	+	0.232136i	$0.0745715\pi$
$571$	16.4253	+	28.4495i	0.687377	+	1.19057i	−0.285306	+	0.958437i	$0.592095\pi$
$572$	−0.813080	+	0.128902i	−0.0339966	+	0.00538966i
$573$		0			0
$574$	−6.09754	+	0.480338i	−0.254507	+	0.0200489i
$575$	9.87246			0.411710
$576$		0			0
$577$	−16.7158			−0.695887			−0.347943	−	0.937516i	$-0.613120\pi$
$577$	−16.7158			−0.695887			−0.347943	+	0.937516i	$0.613120\pi$
$578$	−0.878583	+	0.0692110i	−0.0365442	+	0.00287880i
$579$		0			0
$580$	58.4159	−	9.26099i	2.42559	−	0.384542i
$581$	−6.31450	−	10.9370i	−0.261970	−	0.453745i
$582$		0			0
$583$	0.113258	+	0.0653894i	0.00469066	+	0.00270815i
$584$	−11.1728	+	2.68496i	−0.462334	+	0.111104i
$585$		0			0
$586$	8.68208	+	12.6305i	0.358653	+	0.521762i
$587$	23.7005	+	13.6835i	0.978222	+	0.564777i	0.901733	−	0.432293i	$-0.142296\pi$
$587$	23.7005	+	13.6835i	0.978222	+	0.564777i	0.0764895	+	0.997070i	$0.475629\pi$
$588$		0			0
$589$	−4.04296	+	2.33420i	−0.166587	+	0.0961791i
$590$	19.9785	+	9.52744i	0.822501	+	0.392239i
$591$		0			0
$592$	−2.00024	−	6.14994i	−0.0822093	−	0.252761i
$593$		−	25.6865i		−	1.05482i	−0.849612	−	0.527408i	$-0.823164\pi$
$593$		−	25.6865i		−	1.05482i	0.849612	−	0.527408i	$-0.176836\pi$
$594$		0			0
$595$	30.5560			1.25267
$596$	11.2381	+	13.8737i	0.460331	+	0.568290i
$597$		0			0
$598$	5.36677	+	2.55933i	0.219464	+	0.104659i
$599$	−19.9859	−	34.6166i	−0.816601	−	1.41439i	−0.908173	−	0.418596i	$-0.862522\pi$
$599$	−19.9859	−	34.6166i	−0.816601	−	1.41439i	0.0915718	−	0.995798i	$-0.470811\pi$
$600$		0			0
$601$	2.01867	−	3.49645i	0.0823434	−	0.142623i	−0.821913	−	0.569613i	$-0.807093\pi$
$601$	2.01867	−	3.49645i	0.0823434	−	0.142623i	0.904256	+	0.426991i	$0.140426\pi$
$602$	26.3313	−	18.0998i	1.07318	−	0.737694i
$603$		0			0
$604$	−40.8486	−	15.6734i	−1.66210	−	0.637742i
$605$	−19.1436	+	33.1577i	−0.778298	+	1.34805i
$606$		0			0
$607$	−11.2251	+	6.48081i	−0.455612	+	0.263048i	−0.710198	−	0.704002i	$-0.751394\pi$
$607$	−11.2251	+	6.48081i	−0.455612	+	0.263048i	0.254585	+	0.967050i	$0.418061\pi$
$608$	4.80277	−	1.99144i	0.194778	−	0.0807637i
$609$		0			0
$610$	3.32898	+	42.2589i	0.134786	+	1.71101i
$611$			1.25426i			0.0507418i
$612$		0			0
$613$		−	22.0890i		−	0.892167i	−0.894991	−	0.446084i	$-0.852818\pi$
$613$		−	22.0890i		−	0.892167i	0.894991	−	0.446084i	$-0.147182\pi$
$614$	23.4811	−	1.84974i	0.947622	−	0.0746496i
$615$		0			0
$616$	0.549201	+	0.578481i	0.0221279	+	0.0233077i
$617$	−20.0171	+	11.5569i	−0.805859	+	0.465263i	−0.845516	−	0.533951i	$-0.820707\pi$
$617$	−20.0171	+	11.5569i	−0.805859	+	0.465263i	0.0396569	+	0.999213i	$0.487374\pi$
$618$		0			0
$619$	−2.24675	+	3.89149i	−0.0903046	+	0.156412i	−0.907639	−	0.419751i	$-0.862117\pi$
$619$	−2.24675	+	3.89149i	−0.0903046	+	0.156412i	0.817335	+	0.576163i	$0.195451\pi$
$620$	33.0665	+	12.6875i	1.32798	+	0.509541i
$621$		0			0
$622$	10.3698	+	15.0857i	0.415789	+	0.604882i
$623$	8.72509	−	15.1123i	0.349563	−	0.605461i
$624$		0			0
$625$	4.78939	+	8.29547i	0.191576	+	0.331819i
$626$	−16.2647	+	34.1061i	−0.650068	+	1.36315i
$627$		0			0
$628$	8.71204	−	7.05700i	0.347648	−	0.281605i
$629$	6.78716			0.270622
$630$		0			0
$631$			30.8693i			1.22889i	0.788961	+	0.614443i	$0.210619\pi$
$631$			30.8693i			1.22889i	−0.788961	+	0.614443i	$0.789381\pi$
$632$	34.0327	+	10.0728i	1.35375	+	0.400673i
$633$		0			0
$634$	15.2601	−	31.9996i	0.606057	−	1.27087i
$635$	−53.2237	+	30.7287i	−2.11212	+	1.21943i
$636$		0			0
$637$	6.97046	+	4.02440i	0.276180	+	0.159452i
$638$	−1.33536	+	0.917910i	−0.0528673	+	0.0363404i
$639$		0			0
$640$	−34.6742	−	18.8034i	−1.37062	−	0.743271i
$641$	−23.7137	−	13.6911i	−0.936633	−	0.540766i	−0.0477300	−	0.998860i	$-0.515199\pi$
$641$	−23.7137	−	13.6911i	−0.936633	−	0.540766i	−0.888903	+	0.458095i	$0.848532\pi$
$642$		0			0
$643$	−19.9857	−	34.6162i	−0.788158	−	1.36513i	−0.927094	−	0.374828i	$-0.877702\pi$
$643$	−19.9857	−	34.6162i	−0.788158	−	1.36513i	0.138937	−	0.990301i	$-0.455631\pi$
$644$	−0.902069	−	5.69002i	−0.0355465	−	0.224218i
$645$		0			0
$646$	0.428523	+	5.43978i	0.0168600	+	0.214025i
$647$	−30.9768			−1.21782			−0.608912	−	0.793238i	$-0.708394\pi$
$647$	−30.9768			−1.21782			−0.608912	+	0.793238i	$0.708394\pi$
$648$		0			0
$649$	−0.606405			−0.0238035
$650$	−2.42148	−	30.7389i	−0.0949783	−	1.20568i
$651$		0			0
$652$	−33.9289	+	5.37893i	−1.32876	+	0.210655i
$653$	2.78891	+	4.83053i	0.109138	+	0.189033i	0.915421	−	0.402497i	$-0.131857\pi$
$653$	2.78891	+	4.83053i	0.109138	+	0.189033i	−0.806283	+	0.591530i	$0.798524\pi$
$654$		0			0
$655$	−44.5573	−	25.7252i	−1.74100	−	1.00517i
$656$	−5.54294	+	6.15970i	−0.216415	+	0.240496i
$657$		0			0
$658$	1.00150	−	0.688423i	0.0390427	−	0.0268375i
$659$	5.69959	+	3.29066i	0.222025	+	0.128186i	0.606887	−	0.794788i	$-0.292418\pi$
$659$	5.69959	+	3.29066i	0.222025	+	0.128186i	−0.384863	+	0.922974i	$0.625751\pi$
$660$		0			0
$661$	26.9562	−	15.5632i	1.04847	−	0.605337i	0.126253	−	0.991998i	$-0.459705\pi$
$661$	26.9562	−	15.5632i	1.04847	−	0.605337i	0.922222	+	0.386661i	$0.126372\pi$
$662$	−10.3237	+	21.6482i	−0.401242	+	0.841381i
$663$		0			0
$664$	−16.4062	−	4.85579i	−0.636683	−	0.188441i
$665$		−	6.68993i		−	0.259425i
$666$		0			0
$667$	11.7034			0.453157
$668$	−5.82225	−	7.18771i	−0.225270	−	0.278101i
$669$		0			0
$670$	13.3884	−	28.0746i	0.517238	−	1.08462i
$671$	−0.580679	−	1.00576i	−0.0224168	−	0.0388271i
$672$		0			0
$673$	−3.54087	+	6.13297i	−0.136491	+	0.236409i	−0.926166	−	0.377116i	$-0.876916\pi$
$673$	−3.54087	+	6.13297i	−0.136491	+	0.236409i	0.789675	+	0.613525i	$0.210249\pi$
$674$	7.16541	+	10.4241i	0.276001	+	0.401521i
$675$		0			0
$676$	−2.66159	+	6.93674i	−0.102369	+	0.266798i
$677$	3.18253	−	5.51231i	0.122315	−	0.211855i	−0.798365	−	0.602173i	$-0.794302\pi$
$677$	3.18253	−	5.51231i	0.122315	−	0.211855i	0.920680	+	0.390318i	$0.127635\pi$
$678$		0			0
$679$	−1.72508	+	0.995978i	−0.0662026	+	0.0382221i
$680$	30.0220	−	28.5024i	1.15129	−	1.09302i
$681$		0			0
$682$	−0.967326	+	0.0762018i	−0.0370408	+	0.00291792i
$683$		−	51.9104i		−	1.98630i	−0.116864	−	0.993148i	$-0.537284\pi$
$683$		−	51.9104i		−	1.98630i	0.116864	−	0.993148i	$-0.462716\pi$
$684$		0			0
$685$			59.8187i			2.28556i
$686$	−2.23552	−	28.3782i	−0.0853524	−	1.08349i
$687$		0			0
$688$	8.98773	−	42.3452i	0.342654	−	1.61440i
$689$	−2.55482	+	1.47503i	−0.0973309	+	0.0561940i
$690$		0			0
$691$	−17.9150	+	31.0297i	−0.681519	+	1.18043i	0.292998	+	0.956113i	$0.405347\pi$
$691$	−17.9150	+	31.0297i	−0.681519	+	1.18043i	−0.974517	+	0.224313i	$0.927986\pi$
$692$	2.17913	−	5.67933i	0.0828382	−	0.215896i
$693$		0			0
$694$	5.77760	−	3.97146i	0.219315	−	0.150755i
$695$	−2.11927	+	3.67068i	−0.0803885	+	0.139237i
$696$		0			0
$697$	−4.34834	−	7.53154i	−0.164705	−	0.285277i
$698$	33.8616	+	16.1481i	1.28168	+	0.611214i
$699$		0			0
$700$	−23.2154	+	18.8052i	−0.877461	+	0.710768i
$701$	19.0081			0.717927			0.358964	−	0.933352i	$-0.383130\pi$
$701$	19.0081			0.717927			0.358964	+	0.933352i	$0.383130\pi$
$702$		0			0
$703$		−	1.48598i		−	0.0560449i
$704$	1.07921	+	0.0560811i	0.0406742	+	0.00211364i
$705$		0			0
$706$	42.3704	+	20.2058i	1.59463	+	0.760455i
$707$	19.3793	−	11.1886i	0.728832	−	0.420792i
$708$		0			0
$709$	38.5758	+	22.2717i	1.44874	+	0.836433i	0.998407	−	0.0564260i	$-0.0179705\pi$
$709$	38.5758	+	22.2717i	1.44874	+	0.836433i	0.450337	+	0.892859i	$0.351304\pi$
$710$	−33.4285	−	48.6311i	−1.25455	−	1.82509i
$711$		0			0
$712$	−5.52404	−	22.9869i	−0.207022	−	0.861472i
$713$	6.06922	+	3.50407i	0.227294	+	0.131228i
$714$		0			0
$715$	0.717538	+	1.24281i	0.0268344	+	0.0464786i
$716$	5.63676	+	35.5553i	0.210656	+	1.32876i
$717$		0			0
$718$	29.0623	−	2.28940i	1.08459	−	0.0854397i
$719$	−40.5385			−1.51183			−0.755915	−	0.654670i	$-0.772808\pi$
$719$	−40.5385			−1.51183			−0.755915	+	0.654670i	$0.772808\pi$
$720$		0			0
$721$	17.9854			0.669813
$722$	−25.5961	+	2.01635i	−0.952588	+	0.0750408i
$723$		0			0
$724$	4.99512	+	31.5080i	0.185642	+	1.17098i
$725$	−30.3462	−	52.5611i	−1.12703	−	1.95207i
$726$		0			0
$727$	16.5719	+	9.56779i	0.614618	+	0.354850i	0.774770	−	0.632243i	$-0.217865\pi$
$727$	16.5719	+	9.56779i	0.614618	+	0.354850i	−0.160153	+	0.987092i	$0.551199\pi$
$728$	−17.4952	+	4.20431i	−0.648415	+	0.155822i
$729$		0			0
$730$	11.3470	+	16.5073i	0.419970	+	0.610964i
$731$	39.3446	+	22.7156i	1.45521	+	0.840168i
$732$		0			0
$733$	−25.4597	+	14.6992i	−0.940377	+	0.542927i	−0.890078	−	0.455807i	$-0.849351\pi$
$733$	−25.4597	+	14.6992i	−0.940377	+	0.542927i	−0.0502985	+	0.998734i	$0.516017\pi$
$734$	14.9575	+	7.13299i	0.552090	+	0.263283i
$735$		0			0
$736$	−6.19392	−	4.74915i	−0.228311	−	0.175056i
$737$			0.852146i			0.0313892i
$738$		0			0
$739$	−0.807511			−0.0297048			−0.0148524	−	0.999890i	$-0.504728\pi$
$739$	−0.807511			−0.0297048			−0.0148524	+	0.999890i	$0.504728\pi$
$740$	−8.76009	+	7.09592i	−0.322027	+	0.260851i
$741$		0			0
$742$	2.58005	+	1.23039i	0.0947165	+	0.0451689i
$743$	−13.2127	−	22.8850i	−0.484725	−	0.839569i	0.515121	−	0.857118i	$-0.327747\pi$
$743$	−13.2127	−	22.8850i	−0.484725	−	0.839569i	−0.999846	+	0.0175489i	$0.994414\pi$
$744$		0			0
$745$	15.5620	−	26.9541i	0.570146	−	0.987521i
$746$	−4.07446	+	2.80074i	−0.149177	+	0.102542i
$747$		0			0
$748$	−0.406289	+	1.05889i	−0.0148554	+	0.0387167i
$749$	−5.01860	+	8.69248i	−0.183376	+	0.317616i
$750$		0			0
$751$	2.08658	−	1.20469i	0.0761405	−	0.0439597i	−0.461446	−	0.887168i	$-0.652669\pi$
$751$	2.08658	−	1.20469i	0.0761405	−	0.0439597i	0.537587	+	0.843208i	$0.319336\pi$
$752$	0.341846	−	1.61059i	0.0124658	−	0.0587322i
$753$		0			0
$754$	−2.87056	−	36.4397i	−0.104540	−	1.32705i
$755$			76.2698i			2.77574i
$756$		0			0
$757$			3.61528i			0.131400i	0.997839	+	0.0656998i	$0.0209280\pi$
$757$			3.61528i			0.131400i	−0.997839	+	0.0656998i	$0.979072\pi$
$758$	28.4231	−	2.23905i	1.03237	−	0.0813258i
$759$		0			0
$760$	−6.24033	−	6.57303i	−0.226361	−	0.238429i
$761$	−7.79878	+	4.50263i	−0.282706	+	0.163220i	−0.634648	−	0.772802i	$-0.718855\pi$
$761$	−7.79878	+	4.50263i	−0.282706	+	0.163220i	0.351942	+	0.936022i	$0.385521\pi$
$762$		0			0
$763$	−7.48133	+	12.9580i	−0.270842	+	0.469112i
$764$	−3.18057	+	8.28930i	−0.115069	+	0.299896i
$765$		0			0
$766$	−8.54171	−	12.4263i	−0.308624	−	0.448981i
$767$	6.83951	−	11.8464i	0.246961	−	0.427748i
$768$		0			0
$769$	7.58489	+	13.1374i	0.273518	+	0.473747i	0.969760	−	0.244060i	$-0.0784794\pi$
$769$	7.58489	+	13.1374i	0.273518	+	0.473747i	−0.696242	+	0.717807i	$0.745146\pi$
$770$	0.598531	−	1.25508i	0.0215696	−	0.0452301i
$771$		0			0
$772$	1.69661	+	2.09451i	0.0610623	+	0.0753830i
$773$	31.6926			1.13990			0.569952	−	0.821678i	$-0.306962\pi$
$773$	31.6926			1.13990			0.569952	+	0.821678i	$0.306962\pi$
$774$		0			0
$775$		−	36.3433i		−	1.30549i
$776$	−0.765897	+	2.58772i	−0.0274941	+	0.0928938i
$777$		0			0
$778$	−10.1553	+	21.2950i	−0.364084	+	0.763463i
$779$	−1.64896	+	0.952026i	−0.0590800	+	0.0341099i
$780$		0			0
$781$	1.40016	+	0.808381i	0.0501016	+	0.0289262i
$782$	6.75042	−	4.64016i	0.241394	−	0.165932i
$783$		0			0
$784$	−7.85392	−	7.06752i	−0.280497	−	0.252411i
$785$	−16.9259	−	9.77217i	−0.604111	−	0.348784i
$786$		0			0
$787$	10.3290	+	17.8904i	0.368189	+	0.637723i	0.989283	−	0.146014i	$-0.0466444\pi$
$787$	10.3290	+	17.8904i	0.368189	+	0.637723i	−0.621093	+	0.783737i	$0.713311\pi$
$788$	−18.1105	+	2.87116i	−0.645161	+	0.102281i
$789$		0			0
$790$	−4.85883	−	61.6793i	−0.172869	−	2.19445i
$791$	0.515713			0.0183367
$792$		0			0
$793$	26.1974			0.930297
$794$	−2.55297	−	32.4080i	−0.0906014	−	1.15012i
$795$		0			0
$796$	7.52333	+	47.4553i	0.266657	+	1.68201i
$797$	17.8453	+	30.9089i	0.632112	+	1.09485i	0.987119	+	0.159987i	$0.0511452\pi$
$797$	17.8453	+	30.9089i	0.632112	+	1.09485i	−0.355007	+	0.934864i	$0.615521\pi$
$798$		0			0
$799$	1.49646	+	0.863984i	0.0529411	+	0.0305655i
$800$	−5.26843	+	40.1318i	−0.186267	+	1.41887i
$801$		0			0
$802$	−36.7510	+	25.2622i	−1.29772	+	0.892040i
$803$	−0.475269	−	0.274397i	−0.0167719	−	0.00968325i
$804$		0			0
$805$	−8.69734	+	5.02141i	−0.306541	+	0.176981i
$806$	9.42162	−	19.7566i	0.331863	−	0.695896i
$807$		0			0
$808$	8.60394	−	29.0700i	0.302686	−	1.02268i
$809$		−	18.7528i		−	0.659314i	−0.944101	−	0.329657i	$-0.893067\pi$
$809$		−	18.7528i		−	0.659314i	0.944101	−	0.329657i	$-0.106933\pi$
$810$		0			0
$811$	−33.9206			−1.19111			−0.595556	−	0.803314i	$-0.703068\pi$
$811$	−33.9206			−1.19111			−0.595556	+	0.803314i	$0.703068\pi$
$812$	−27.5209	+	22.2927i	−0.965795	+	0.782321i
$813$		0			0
$814$	0.132947	−	0.278782i	0.00465980	−	0.00977131i
$815$	29.9421	+	51.8612i	1.04882	+	1.81662i
$816$		0			0
$817$	4.97337	−	8.61412i	0.173996	−	0.301370i
$818$	5.75609	+	8.37384i	0.201257	+	0.292785i
$819$		0			0
$820$	13.4865	+	5.17470i	0.470969	+	0.180708i
$821$	5.34636	−	9.26017i	0.186589	−	0.323182i	−0.757522	−	0.652810i	$-0.773590\pi$
$821$	5.34636	−	9.26017i	0.186589	−	0.323182i	0.944111	+	0.329628i	$0.106923\pi$
$822$		0			0
$823$	−33.4172	+	19.2934i	−1.16485	+	0.672527i	−0.952462	−	0.304658i	$-0.901458\pi$
$823$	−33.4172	+	19.2934i	−1.16485	+	0.672527i	−0.212390	+	0.977185i	$0.568125\pi$
$824$	17.6712	−	16.7767i	0.615604	−	0.584445i
$825$		0			0
$826$	−13.2131	+	1.04088i	−0.459744	+	0.0362167i
$827$			0.214418i			0.00745604i	0.999993	+	0.00372802i	$0.00118667\pi$
$827$			0.214418i			0.00745604i	−0.999993	+	0.00372802i	$0.998813\pi$
$828$		0			0
$829$		−	35.5733i		−	1.23551i	−0.786369	−	0.617757i	$-0.788042\pi$
$829$		−	35.5733i		−	1.23551i	0.786369	−	0.617757i	$-0.211958\pi$
$830$	2.34230	+	29.7338i	0.0813024	+	1.03207i
$831$		0			0
$832$	−13.2677	+	20.4503i	−0.459975	+	0.708985i
$833$	9.60309	−	5.54434i	0.332727	−	0.192100i
$834$		0			0
$835$	−8.06235	+	13.9644i	−0.279009	+	0.483258i
$836$	0.231833	+	0.0889531i	0.00801810	+	0.00307651i
$837$		0			0
$838$	16.9559	−	11.6553i	0.585733	−	0.402627i
$839$	−20.5867	+	35.6571i	−0.710730	+	1.23102i	0.253853	+	0.967243i	$0.418302\pi$
$839$	−20.5867	+	35.6571i	−0.710730	+	1.23102i	−0.964583	+	0.263778i	$0.915031\pi$
$840$		0			0
$841$	−21.4741	−	37.1942i	−0.740486	−	1.28256i
$842$	13.8345	+	6.59745i	0.476767	+	0.227363i
$843$		0			0
$844$	25.4985	+	31.4785i	0.877693	+	1.08353i
$845$	12.9518			0.445556
$846$		0			0
$847$		−	22.9268i		−	0.787775i
$848$	3.68266	−	1.19777i	0.126463	−	0.0411315i
$849$		0			0
$850$	−38.3429	−	18.2851i	−1.31515	−	0.627175i
$851$	−1.93187	+	1.11537i	−0.0662237	+	0.0382343i
$852$		0			0
$853$	−30.9858	−	17.8897i	−1.06093	−	0.612530i	−0.135243	−	0.990812i	$-0.543181\pi$
$853$	−30.9858	−	17.8897i	−1.06093	−	0.612530i	−0.925690	+	0.378282i	$0.876515\pi$
$854$	−14.3789	−	20.9182i	−0.492037	−	0.715806i
$855$		0			0
$856$	3.17739	+	13.2219i	0.108601	+	0.451915i
$857$	−26.3688	−	15.2241i	−0.900742	−	0.520044i	−0.0233014	−	0.999728i	$-0.507418\pi$
$857$	−26.3688	−	15.2241i	−0.900742	−	0.520044i	−0.877441	+	0.479685i	$0.840751\pi$
$858$		0			0
$859$	−11.7147	−	20.2904i	−0.399700	−	0.692301i	0.593989	−	0.804473i	$-0.297552\pi$
$859$	−11.7147	−	20.2904i	−0.399700	−	0.692301i	−0.993689	+	0.112172i	$0.964219\pi$
$860$	−74.5305	+	11.8157i	−2.54147	+	0.402913i
$861$		0			0
$862$	15.3115	−	1.20618i	0.521513	−	0.0410826i
$863$	32.2240			1.09692			0.548458	−	0.836178i	$-0.315215\pi$
$863$	32.2240			1.09692			0.548458	+	0.836178i	$0.315215\pi$
$864$		0			0
$865$	−10.6041			−0.360549
$866$	13.2720	−	1.04551i	0.451002	−	0.0355280i
$867$		0			0
$868$	−20.9466	+	3.32077i	−0.710972	+	0.112714i
$869$	0.847532	+	1.46797i	0.0287506	+	0.0497974i
$870$		0			0
$871$	−16.6470	−	9.61117i	−0.564063	−	0.325662i
$872$	4.73659	+	19.7101i	0.160401	+	0.667470i
$873$		0			0
$874$	−1.01592	−	1.47794i	−0.0343640	−	0.0499920i
$875$	13.5856	+	7.84366i	0.459278	+	0.265164i
$876$		0			0
$877$	−1.74081	+	1.00506i	−0.0587829	+	0.0339384i	−0.529103	−	0.848557i	$-0.677472\pi$
$877$	−1.74081	+	1.00506i	−0.0587829	+	0.0339384i	0.470320	+	0.882496i	$0.344138\pi$
$878$	−13.6452	−	6.50718i	−0.460502	−	0.219607i
$879$		0			0
$880$	−0.582663	−	1.79146i	−0.0196416	−	0.0603901i
$881$		−	21.6545i		−	0.729558i	−0.931094	−	0.364779i	$-0.881145\pi$
$881$		−	21.6545i		−	0.729558i	0.931094	−	0.364779i	$-0.118855\pi$
$882$		0			0
$883$	−23.3462			−0.785664			−0.392832	−	0.919610i	$-0.628505\pi$
$883$	−23.3462			−0.785664			−0.392832	+	0.919610i	$0.628505\pi$
$884$	−16.1033	−	19.8800i	−0.541614	−	0.668636i
$885$		0			0
$886$	−27.9786	−	13.3426i	−0.939959	−	0.448253i
$887$	24.4901	+	42.4181i	0.822297	+	1.42426i	0.903968	+	0.427600i	$0.140641\pi$
$887$	24.4901	+	42.4181i	0.822297	+	1.42426i	−0.0816710	+	0.996659i	$0.526026\pi$
$888$		0			0
$889$	18.4007	−	31.8710i	0.617141	−	1.06892i
$890$	−33.9622	+	23.3453i	−1.13842	+	0.782535i
$891$		0			0
$892$	1.12360	+	0.431121i	0.0376210	+	0.0144350i
$893$	0.189161	−	0.327636i	0.00633003	−	0.0109639i
$894$		0			0
$895$	54.3471	−	31.3773i	1.81662	−	1.04883i
$896$	23.6114	−	0.630457i	0.788803	−	0.0210621i
$897$		0			0
$898$	2.08169	+	26.4256i	0.0694670	+	0.881833i
$899$		−	43.0834i		−	1.43691i
$900$		0			0
$901$			4.06424i			0.135399i
$902$	−0.394533	+	0.0310796i	−0.0131365	+	0.00103484i
$903$		0			0
$904$	0.506702	−	0.481055i	0.0168526	−	0.0159996i
$905$	48.1607	−	27.8056i	1.60092	−	0.924289i
$906$		0			0
$907$	−9.93443	+	17.2069i	−0.329867	+	0.571347i	−0.982485	−	0.186340i	$-0.940337\pi$
$907$	−9.93443	+	17.2069i	−0.329867	+	0.571347i	0.652618	+	0.757687i	$0.273671\pi$
$908$	−19.9166	−	7.64192i	−0.660957	−	0.253606i
$909$		0			0
$910$	17.7679	+	25.8484i	0.589001	+	0.856866i
$911$	−24.0672	+	41.6857i	−0.797383	+	1.38111i	0.123932	+	0.992291i	$0.460450\pi$
$911$	−24.0672	+	41.6857i	−0.797383	+	1.38111i	−0.921315	+	0.388817i	$0.872884\pi$
$912$		0			0
$913$	−0.408571	−	0.707665i	−0.0135217	−	0.0234203i
$914$	−0.0111079	+	0.0232927i	−0.000367418	+	0.000770453i
$915$		0			0
$916$	−39.7620	+	32.2083i	−1.31377	+	1.06419i
$917$	30.8091			1.01741
$918$		0			0
$919$		−	34.3644i		−	1.13358i	−0.823864	−	0.566788i	$-0.808186\pi$
$919$		−	34.3644i		−	1.13358i	0.823864	−	0.566788i	$-0.191814\pi$
$920$	−3.86141	+	13.0465i	−0.127307	+	0.430130i
$921$		0			0
$922$	1.53299	−	3.21459i	0.0504864	−	0.105867i
$923$	−31.5841	+	18.2351i	−1.03960	+	0.600216i
$924$		0			0
$925$	10.0185	+	5.78416i	0.329405	+	0.190182i
$926$	32.1632	−	22.1086i	1.05695	−	0.726535i
$927$		0			0
$928$	−6.24550	+	47.5745i	−0.205019	+	1.56171i
$929$	−15.1165	−	8.72750i	−0.495955	−	0.286340i	0.231086	−	0.972933i	$-0.425772\pi$
$929$	−15.1165	−	8.72750i	−0.495955	−	0.286340i	−0.727042	+	0.686593i	$0.759105\pi$
$930$		0			0
$931$	−1.21388	−	2.10250i	−0.0397833	−	0.0689067i
$932$	−1.47525	−	9.30551i	−0.0483235	−	0.304812i
$933$		0			0
$934$	3.16114	+	40.1284i	0.103436	+	1.31304i
$935$	1.97708			0.0646574
$936$		0			0
$937$	42.3068			1.38210			0.691051	−	0.722806i	$-0.257148\pi$
$937$	42.3068			1.38210			0.691051	+	0.722806i	$0.257148\pi$
$938$	1.46268	+	18.5677i	0.0477583	+	0.606256i
$939$		0			0
$940$	−2.83475	+	0.449408i	−0.0924594	+	0.0146581i
$941$	−11.6752	−	20.2221i	−0.380602	−	0.659222i	0.610546	−	0.791980i	$-0.290950\pi$
$941$	−11.6752	−	20.2221i	−0.380602	−	0.659222i	−0.991148	+	0.132758i	$0.957617\pi$
$942$		0			0
$943$	2.47539	+	1.42917i	0.0806097	+	0.0465400i
$944$	−12.0113	+	13.3478i	−0.390936	+	0.434435i
$945$		0			0
$946$	1.70373	−	1.17112i	0.0553929	−	0.0380765i
$947$	−28.1206	−	16.2354i	−0.913796	−	0.527580i	−0.0321454	−	0.999483i	$-0.510234\pi$
$947$	−28.1206	−	16.2354i	−0.913796	−	0.527580i	−0.881651	+	0.471903i	$0.843567\pi$
$948$		0			0
$949$	10.7209	−	6.18973i	0.348016	−	0.200927i
$950$	−4.00335	+	8.39480i	−0.129886	+	0.272363i
$951$		0			0
$952$	−7.03522	+	23.7698i	−0.228013	+	0.770382i
$953$			11.0705i			0.358607i	0.983794	+	0.179304i	$0.0573844\pi$
$953$			11.0705i			0.358607i	−0.983794	+	0.179304i	$0.942616\pi$
$954$		0			0
$955$	15.4772			0.500832
$956$	18.9091	+	23.3437i	0.611563	+	0.754990i
$957$		0			0
$958$	−23.3272	+	48.9158i	−0.753669	+	1.58040i
$959$	−17.9101	−	31.0212i	−0.578347	−	1.00173i
$960$		0			0
$961$	−2.60055	+	4.50429i	−0.0838888	+	0.145300i
$962$	3.94665	+	5.74151i	0.127245	+	0.185114i
$963$		0			0
$964$	18.4462	−	48.0751i	0.594111	−	1.54839i
$965$	2.34938	−	4.06924i	0.0756291	−	0.130993i
$966$		0			0
$967$	−40.9201	+	23.6252i	−1.31590	+	0.759736i	−0.983066	−	0.183249i	$-0.941338\pi$
$967$	−40.9201	+	23.6252i	−1.31590	+	0.759736i	−0.332835	+	0.942985i	$0.608005\pi$
$968$	−21.3860	−	22.5262i	−0.687373	−	0.724019i
$969$		0			0
$970$	4.68987	−	0.369448i	0.150583	−	0.0118623i
$971$			33.9428i			1.08928i	0.838671	+	0.544638i	$0.183333\pi$
$971$			33.9428i			1.08928i	−0.838671	+	0.544638i	$0.816667\pi$
$972$		0			0
$973$		−	2.53809i		−	0.0813674i
$974$	0.250621	+	3.18145i	0.00803042	+	0.101940i
$975$		0			0
$976$	−33.6401	−	7.14007i	−1.07679	−	0.228548i
$977$	−26.9476	+	15.5582i	−0.862131	+	0.497752i	−0.864725	−	0.502245i	$-0.832508\pi$
$977$	−26.9476	+	15.5582i	−0.862131	+	0.497752i	0.00259421	+	0.999997i	$0.499174\pi$
$978$		0			0
$979$	0.564544	−	0.977819i	0.0180429	−	0.0312512i
$980$	−6.59800	+	17.1959i	−0.210765	+	0.549304i
$981$		0			0
$982$	23.9080	−	16.4341i	0.762936	−	0.524434i
$983$	18.2288	−	31.5733i	0.581410	−	1.00703i	−0.413903	−	0.910321i	$-0.635835\pi$
$983$	18.2288	−	31.5733i	0.581410	−	1.00703i	0.995313	−	0.0967103i	$-0.0308320\pi$
$984$		0			0
$985$	15.9824	+	27.6824i	0.509243	+	0.882034i
$986$	−45.4538	−	21.6763i	−1.44754	−	0.690313i
$987$		0			0
$988$	−4.35253	+	3.52567i	−0.138472	+	0.112166i
$989$	−14.9319			−0.474806
$990$		0			0
$991$			21.5164i			0.683490i	0.939793	+	0.341745i	$0.111018\pi$
$991$			21.5164i			0.683490i	−0.939793	+	0.341745i	$0.888982\pi$
$992$	−17.4829	+	22.8016i	−0.555084	+	0.723951i
$993$		0			0
$994$	31.8960	+	15.2107i	1.01168	+	0.482455i
$995$	72.5365	−	41.8790i	2.29956	−	1.32765i
$996$		0			0
$997$	49.4923	+	28.5744i	1.56744	+	0.904961i	0.996467	+	0.0839906i	$0.0267666\pi$
$997$	49.4923	+	28.5744i	1.56744	+	0.904961i	0.570971	+	0.820970i	$0.306567\pi$
$998$	3.00920	+	4.37772i	0.0952544	+	0.138574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.l.b.35.8		16
3.2	odd	2		72.2.l.b.11.1	✓	16
4.3	odd	2		864.2.p.b.143.1		16
8.3	odd	2	inner	216.2.l.b.35.5		16
8.5	even	2		864.2.p.b.143.8		16
9.2	odd	6		648.2.f.b.323.10		16
9.4	even	3		72.2.l.b.59.4	yes	16
9.5	odd	6	inner	216.2.l.b.179.5		16
9.7	even	3		648.2.f.b.323.7		16
12.11	even	2		288.2.p.b.47.8		16
24.5	odd	2		288.2.p.b.47.7		16
24.11	even	2		72.2.l.b.11.4	yes	16
36.7	odd	6		2592.2.f.b.1295.16		16
36.11	even	6		2592.2.f.b.1295.2		16
36.23	even	6		864.2.p.b.719.8		16
36.31	odd	6		288.2.p.b.239.7		16
72.5	odd	6		864.2.p.b.719.1		16
72.11	even	6		648.2.f.b.323.8		16
72.13	even	6		288.2.p.b.239.8		16
72.29	odd	6		2592.2.f.b.1295.15		16
72.43	odd	6		648.2.f.b.323.9		16
72.59	even	6	inner	216.2.l.b.179.8		16
72.61	even	6		2592.2.f.b.1295.1		16
72.67	odd	6		72.2.l.b.59.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.1	✓	16	3.2	odd	2
72.2.l.b.11.4	yes	16	24.11	even	2
72.2.l.b.59.1	yes	16	72.67	odd	6
72.2.l.b.59.4	yes	16	9.4	even	3
216.2.l.b.35.5		16	8.3	odd	2	inner
216.2.l.b.35.8		16	1.1	even	1	trivial
216.2.l.b.179.5		16	9.5	odd	6	inner
216.2.l.b.179.8		16	72.59	even	6	inner
288.2.p.b.47.7		16	24.5	odd	2
288.2.p.b.47.8		16	12.11	even	2
288.2.p.b.239.7		16	36.31	odd	6
288.2.p.b.239.8		16	72.13	even	6
648.2.f.b.323.7		16	9.7	even	3
648.2.f.b.323.8		16	72.11	even	6
648.2.f.b.323.9		16	72.43	odd	6
648.2.f.b.323.10		16	9.2	odd	6
864.2.p.b.143.1		16	4.3	odd	2
864.2.p.b.143.8		16	8.5	even	2
864.2.p.b.719.1		16	72.5	odd	6
864.2.p.b.719.8		16	36.23	even	6
2592.2.f.b.1295.1		16	72.61	even	6
2592.2.f.b.1295.2		16	36.11	even	6
2592.2.f.b.1295.15		16	72.29	odd	6
2592.2.f.b.1295.16		16	36.7	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40985 - 0.111062i) q^{2} +(1.97533 - 0.313160i) q^{4} +(-1.74322 - 3.01934i) q^{5} +(1.80802 + 1.04386i) q^{7} +(2.75013 - 0.660890i) q^{8} +O(q^{10})\)	\(q+(1.40985 - 0.111062i) q^{2} +(1.97533 - 0.313160i) q^{4} +(-1.74322 - 3.01934i) q^{5} +(1.80802 + 1.04386i) q^{7} +(2.75013 - 0.660890i) q^{8} +(-2.79300 - 4.06320i) q^{10} +(0.116985 + 0.0675415i) q^{11} +(-2.63890 + 1.52357i) q^{13} +(2.66496 + 1.27088i) q^{14} +(3.80386 - 1.23719i) q^{16} +4.19800i q^{17} +0.919111 q^{19} +(-4.38897 - 5.41829i) q^{20} +(0.172432 + 0.0822305i) q^{22} +(-0.689877 - 1.19490i) q^{23} +(-3.57762 + 6.19662i) q^{25} +(-3.55124 + 2.44108i) q^{26} +(3.89833 + 1.49577i) q^{28} +(-4.24111 + 7.34582i) q^{29} +(-4.39877 + 2.53963i) q^{31} +(5.22546 - 2.16671i) q^{32} +(0.466236 + 5.91853i) q^{34} -7.27870i q^{35} -1.61676i q^{37} +(1.29580 - 0.102078i) q^{38} +(-6.78953 - 7.15151i) q^{40} +(-1.79408 + 1.03581i) q^{41} +(5.41106 - 9.37224i) q^{43} +(0.252236 + 0.0967817i) q^{44} +(-1.10533 - 1.60801i) q^{46} +(0.205809 - 0.356471i) q^{47} +(-1.32071 - 2.28754i) q^{49} +(-4.35568 + 9.13361i) q^{50} +(-4.73559 + 3.83596i) q^{52} +0.968137 q^{53} -0.470958i q^{55} +(5.66217 + 1.67585i) q^{56} +(-5.16348 + 10.8275i) q^{58} +(-3.88770 + 2.24457i) q^{59} +(-7.44553 - 4.29868i) q^{61} +(-5.91953 + 4.06902i) q^{62} +(7.12645 - 3.63507i) q^{64} +(9.20037 + 5.31183i) q^{65} +(3.15416 + 5.46316i) q^{67} +(1.31464 + 8.29243i) q^{68} +(-0.808385 - 10.2618i) q^{70} +11.9687 q^{71} -4.06264 q^{73} +(-0.179560 - 2.27939i) q^{74} +(1.81555 - 0.287828i) q^{76} +(0.141008 + 0.244232i) q^{77} +(10.8672 + 6.27416i) q^{79} +(-10.3665 - 9.32847i) q^{80} +(-2.41434 + 1.65959i) q^{82} +(-5.23875 - 3.02459i) q^{83} +(12.6752 - 7.31802i) q^{85} +(6.58787 - 13.8144i) q^{86} +(0.366362 + 0.108434i) q^{88} -8.35848i q^{89} -6.36158 q^{91} +(-1.73693 - 2.14428i) q^{92} +(0.250568 - 0.525426i) q^{94} +(-1.60221 - 2.77511i) q^{95} +(-0.477065 + 0.826300i) q^{97} +(-2.11606 - 3.07840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4	\( 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

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