LMFDB - Embedded newform 216.2.l.b.179.4

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			179.4
Root			$1.12063 - 0.862658i$ of defining polynomial
Character	$\chi$	$=$	216.179
Dual form			216.2.l.b.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.186766 - 1.40183i) q^{2} +(-1.93024 + 0.523628i) q^{4} +(-1.60936 + 2.78750i) q^{5} +(-1.82223 + 1.05206i) q^{7} +(1.09454 + 2.60806i) q^{8} +O(q^{10})$	\(q+(-0.186766 - 1.40183i) q^{2} +(-1.93024 + 0.523628i) q^{4} +(-1.60936 + 2.78750i) q^{5} +(-1.82223 + 1.05206i) q^{7} +(1.09454 + 2.60806i) q^{8} +(4.20817 + 1.73544i) q^{10} +(-3.47720 + 2.00756i) q^{11} +(0.341902 + 0.197397i) q^{13} +(1.81514 + 2.35795i) q^{14} +(3.45163 - 2.02145i) q^{16} +1.20474i q^{17} -1.62474 q^{19} +(1.64684 - 6.22324i) q^{20} +(3.46368 + 4.49949i) q^{22} +(2.74384 - 4.75248i) q^{23} +(-2.68011 - 4.64208i) q^{25} +(0.212861 - 0.516155i) q^{26} +(2.96644 - 2.98490i) q^{28} +(2.95670 + 5.12116i) q^{29} +(-3.34777 - 1.93284i) q^{31} +(-3.47838 - 4.46104i) q^{32} +(1.68884 - 0.225005i) q^{34} -6.77261i q^{35} +10.8195i q^{37} +(0.303447 + 2.27761i) q^{38} +(-9.03149 - 1.14629i) q^{40} +(1.23849 + 0.715041i) q^{41} +(-1.21569 - 2.10564i) q^{43} +(5.66061 - 5.69584i) q^{44} +(-7.17460 - 2.95879i) q^{46} +(0.792576 + 1.37278i) q^{47} +(-1.28633 + 2.22799i) q^{49} +(-6.00684 + 4.62403i) q^{50} +(-0.763315 - 0.201994i) q^{52} -7.07284 q^{53} -12.9236i q^{55} +(-4.73834 - 3.60095i) q^{56} +(6.62677 - 5.10125i) q^{58} +(2.29587 + 1.32552i) q^{59} +(8.18631 - 4.72637i) q^{61} +(-2.08425 + 5.05398i) q^{62} +(-5.60397 + 5.70925i) q^{64} +(-1.10049 + 0.635369i) q^{65} +(-2.60947 + 4.51973i) q^{67} +(-0.630836 - 2.32543i) q^{68} +(-9.49402 + 1.26490i) q^{70} -2.69468 q^{71} +9.49652 q^{73} +(15.1670 - 2.02072i) q^{74} +(3.13614 - 0.850761i) q^{76} +(4.22417 - 7.31647i) q^{77} +(-1.53599 + 0.886804i) q^{79} +(0.0798779 + 12.8747i) q^{80} +(0.771055 - 1.86969i) q^{82} +(1.30809 - 0.755228i) q^{83} +(-3.35821 - 1.93887i) q^{85} +(-2.72469 + 2.09745i) q^{86} +(-9.04179 - 6.87140i) q^{88} -11.2323i q^{89} -0.830698 q^{91} +(-2.80774 + 10.6102i) q^{92} +(1.77638 - 1.36744i) q^{94} +(2.61480 - 4.52897i) q^{95} +(5.84818 + 10.1294i) q^{97} +(3.36350 + 1.38710i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.186766	−	1.40183i	−0.132064	−	0.991241i
$2$	−0.186766	−	1.40183i	−0.132064	−	0.991241i
$3$		0			0
$3$		0			0
$4$	−1.93024	+	0.523628i	−0.965118	+	0.261814i
$5$	−1.60936	+	2.78750i	−0.719730	+	1.24661i	0.241377	+	0.970431i	$0.422401\pi$
$5$	−1.60936	+	2.78750i	−0.719730	+	1.24661i	−0.961107	+	0.276177i	$0.910932\pi$
$6$		0			0
$7$	−1.82223	+	1.05206i	−0.688736	+	0.397642i	−0.803139	−	0.595792i	$-0.796838\pi$
$7$	−1.82223	+	1.05206i	−0.688736	+	0.397642i	0.114402	+	0.993435i	$0.463505\pi$
$8$	1.09454	+	2.60806i	0.386978	+	0.922089i
$9$		0			0
$10$	4.20817	+	1.73544i	1.33074	+	0.548794i
$11$	−3.47720	+	2.00756i	−1.04842	+	0.605303i	−0.922206	−	0.386700i	$-0.873615\pi$
$11$	−3.47720	+	2.00756i	−1.04842	+	0.605303i	−0.126211	+	0.992003i	$0.540282\pi$
$12$		0			0
$13$	0.341902	+	0.197397i	0.0948267	+	0.0547482i	0.546663	−	0.837352i	$-0.315898\pi$
$13$	0.341902	+	0.197397i	0.0948267	+	0.0547482i	−0.451837	+	0.892101i	$0.649231\pi$
$14$	1.81514	+	2.35795i	0.485116	+	0.630190i
$15$		0			0
$16$	3.45163	−	2.02145i	0.862907	−	0.505363i
$17$			1.20474i			0.292192i	0.989270	+	0.146096i	$0.0466709\pi$
$17$			1.20474i			0.292192i	−0.989270	+	0.146096i	$0.953329\pi$
$18$		0			0
$19$	−1.62474			−0.372741			−0.186371	−	0.982480i	$-0.559673\pi$
$19$	−1.62474			−0.372741			−0.186371	+	0.982480i	$0.559673\pi$
$20$	1.64684	−	6.22324i	0.368244	−	1.39156i
$21$		0			0
$22$	3.46368	+	4.49949i	0.738460	+	0.959295i
$23$	2.74384	−	4.75248i	0.572131	−	0.990960i	−0.424216	−	0.905561i	$-0.639450\pi$
$23$	2.74384	−	4.75248i	0.572131	−	0.990960i	0.996347	−	0.0853986i	$-0.0272164\pi$
$24$		0			0
$25$	−2.68011	−	4.64208i	−0.536021	−	0.928416i
$26$	0.212861	−	0.516155i	0.0417455	−	0.101226i
$27$		0			0
$28$	2.96644	−	2.98490i	0.560604	−	0.564093i
$29$	2.95670	+	5.12116i	0.549046	+	0.950976i	0.998340	+	0.0575919i	$0.0183422\pi$
$29$	2.95670	+	5.12116i	0.549046	+	0.950976i	−0.449294	+	0.893384i	$0.648324\pi$
$30$		0			0
$31$	−3.34777	−	1.93284i	−0.601277	−	0.347148i	0.168267	−	0.985742i	$-0.446183\pi$
$31$	−3.34777	−	1.93284i	−0.601277	−	0.347148i	−0.769544	+	0.638594i	$0.779516\pi$
$32$	−3.47838	−	4.46104i	−0.614896	−	0.788608i
$33$		0			0
$34$	1.68884	−	0.225005i	0.289633	−	0.0385880i
$35$		−	6.77261i		−	1.14478i
$36$		0			0
$37$			10.8195i			1.77871i	0.457215	+	0.889356i	$0.348847\pi$
$37$			10.8195i			1.77871i	−0.457215	+	0.889356i	$0.651153\pi$
$38$	0.303447	+	2.27761i	0.0492256	+	0.369477i
$39$		0			0
$40$	−9.03149	−	1.14629i	−1.42800	−	0.181244i
$41$	1.23849	+	0.715041i	0.193419	+	0.111671i	0.593582	−	0.804773i	$-0.297713\pi$
$41$	1.23849	+	0.715041i	0.193419	+	0.111671i	−0.400163	+	0.916444i	$0.631047\pi$
$42$		0			0
$43$	−1.21569	−	2.10564i	−0.185391	−	0.321107i	0.758317	−	0.651886i	$-0.226022\pi$
$43$	−1.21569	−	2.10564i	−0.185391	−	0.321107i	−0.943708	+	0.330779i	$0.892689\pi$
$44$	5.66061	−	5.69584i	0.853369	−	0.858680i
$45$		0			0
$46$	−7.17460	−	2.95879i	−1.05784	−	0.436250i
$47$	0.792576	+	1.37278i	0.115609	+	0.200241i	0.918023	−	0.396527i	$-0.129785\pi$
$47$	0.792576	+	1.37278i	0.115609	+	0.200241i	−0.802414	+	0.596768i	$0.796451\pi$
$48$		0			0
$49$	−1.28633	+	2.22799i	−0.183761	+	0.318284i
$50$	−6.00684	+	4.62403i	−0.849495	+	0.653937i
$51$		0			0
$52$	−0.763315	−	0.201994i	−0.105853	−	0.0280115i
$53$	−7.07284			−0.971529			−0.485765	−	0.874090i	$-0.661459\pi$
$53$	−7.07284			−0.971529			−0.485765	+	0.874090i	$0.661459\pi$
$54$		0			0
$55$		−	12.9236i		−	1.74262i
$56$	−4.73834	−	3.60095i	−0.633187	−	0.481197i
$57$		0			0
$58$	6.62677	−	5.10125i	0.870137	−	0.669827i
$59$	2.29587	+	1.32552i	0.298897	+	0.172568i	0.641947	−	0.766749i	$-0.278127\pi$
$59$	2.29587	+	1.32552i	0.298897	+	0.172568i	−0.343050	+	0.939317i	$0.611460\pi$
$60$		0			0
$61$	8.18631	−	4.72637i	1.04815	−	0.605149i	0.126019	−	0.992028i	$-0.459780\pi$
$61$	8.18631	−	4.72637i	1.04815	−	0.605149i	0.922131	+	0.386879i	$0.126447\pi$
$62$	−2.08425	+	5.05398i	−0.264700	+	0.641856i
$63$		0			0
$64$	−5.60397	+	5.70925i	−0.700496	+	0.713657i
$65$	−1.10049	+	0.635369i	−0.136499	+	0.0788078i
$66$		0			0
$67$	−2.60947	+	4.51973i	−0.318797	+	0.552173i	−0.980237	−	0.197825i	$-0.936612\pi$
$67$	−2.60947	+	4.51973i	−0.318797	+	0.552173i	0.661440	+	0.749998i	$0.269946\pi$
$68$	−0.630836	−	2.32543i	−0.0765001	−	0.282000i
$69$		0			0
$70$	−9.49402	+	1.26490i	−1.13475	+	0.151184i
$71$	−2.69468			−0.319800			−0.159900	−	0.987133i	$-0.551117\pi$
$71$	−2.69468			−0.319800			−0.159900	+	0.987133i	$0.551117\pi$
$72$		0			0
$73$	9.49652			1.11148			0.555742	−	0.831355i	$-0.312434\pi$
$73$	9.49652			1.11148			0.555742	+	0.831355i	$0.312434\pi$
$74$	15.1670	−	2.02072i	1.76313	−	0.234904i
$75$		0			0
$76$	3.13614	−	0.850761i	0.359740	−	0.0975890i
$77$	4.22417	−	7.31647i	0.481388	−	0.833789i
$78$		0			0
$79$	−1.53599	+	0.886804i	−0.172812	+	0.0997732i	−0.583911	−	0.811818i	$-0.698478\pi$
$79$	−1.53599	+	0.886804i	−0.172812	+	0.0997732i	0.411099	+	0.911591i	$0.365145\pi$
$80$	0.0798779	+	12.8747i	0.00893062	+	1.43943i
$81$		0			0
$82$	0.771055	−	1.86969i	0.0851488	−	0.206473i
$83$	1.30809	−	0.755228i	0.143582	−	0.0828971i	−0.426488	−	0.904493i	$-0.640249\pi$
$83$	1.30809	−	0.755228i	0.143582	−	0.0828971i	0.570070	+	0.821596i	$0.306916\pi$
$84$		0			0
$85$	−3.35821	−	1.93887i	−0.364249	−	0.210300i
$86$	−2.72469	+	2.09745i	−0.293811	+	0.226174i
$87$		0			0
$88$	−9.04179	−	6.87140i	−0.963858	−	0.732494i
$89$		−	11.2323i		−	1.19062i	−0.803494	−	0.595312i	$-0.797028\pi$
$89$		−	11.2323i		−	1.19062i	0.803494	−	0.595312i	$-0.202972\pi$
$90$		0			0
$91$	−0.830698			−0.0870808
$92$	−2.80774	+	10.6102i	−0.292727	+	1.10619i
$93$		0			0
$94$	1.77638	−	1.36744i	0.183219	−	0.141041i
$95$	2.61480	−	4.52897i	0.268273	−	0.464662i
$96$		0			0
$97$	5.84818	+	10.1294i	0.593793	+	1.02848i	0.993716	+	0.111931i	$0.0357036\pi$
$97$	5.84818	+	10.1294i	0.593793	+	1.02848i	−0.399923	+	0.916549i	$0.630963\pi$
$98$	3.36350	+	1.38710i	0.339764	+	0.140118i
$99$		0			0
$100$	7.60397	+	7.55694i	0.760397	+	0.755694i
$101$	−2.03509	−	3.52487i	−0.202499	−	0.350738i	0.746834	−	0.665010i	$-0.231573\pi$
$101$	−2.03509	−	3.52487i	−0.202499	−	0.350738i	−0.949333	+	0.314272i	$0.898240\pi$
$102$		0			0
$103$	15.6784	+	9.05191i	1.54484	+	0.891911i	0.998523	+	0.0543294i	$0.0173021\pi$
$103$	15.6784	+	9.05191i	1.54484	+	0.891911i	0.546312	+	0.837582i	$0.316031\pi$
$104$	−0.140599	+	1.10776i	−0.0137869	+	0.108625i
$105$		0			0
$106$	1.32097	+	9.91489i	0.128304	+	0.963020i
$107$			12.3971i			1.19848i	0.800571	+	0.599238i	$0.204530\pi$
$107$			12.3971i			1.19848i	−0.800571	+	0.599238i	$0.795470\pi$
$108$		0			0
$109$		−	1.76155i		−	0.168726i	−0.996435	−	0.0843628i	$-0.973115\pi$
$109$		−	1.76155i		−	0.168726i	0.996435	−	0.0843628i	$-0.0268855\pi$
$110$	−18.1167	+	2.41370i	−1.72736	+	0.230137i
$111$		0			0
$112$	−4.16295	+	7.31487i	−0.393362	+	0.691190i
$113$	15.7938	+	9.11858i	1.48576	+	0.857804i	0.999869	−	0.0162153i	$-0.00516171\pi$
$113$	15.7938	+	9.11858i	1.48576	+	0.857804i	0.485891	+	0.874019i	$0.338495\pi$
$114$		0			0
$115$	8.83169	+	15.2969i	0.823559	+	1.42645i
$116$	−8.38872	−	8.33684i	−0.778873	−	0.774056i
$117$		0			0
$118$	1.42936	−	3.46598i	0.131583	−	0.319069i
$119$	−1.26746	−	2.19531i	−0.116188	−	0.201244i
$120$		0			0
$121$	2.56063	−	4.43514i	0.232785	−	0.403195i
$122$	−8.15447	−	10.5931i	−0.738271	−	0.959050i
$123$		0			0
$124$	7.47408	+	1.97784i	0.671192	+	0.177616i
$125$	1.15943			0.103703
$126$		0			0
$127$			2.09206i			0.185641i	0.995683	+	0.0928203i	$0.0295882\pi$
$127$			2.09206i			0.185641i	−0.995683	+	0.0928203i	$0.970412\pi$
$128$	9.05002	+	6.78949i	0.799916	+	0.600112i
$129$		0			0
$130$	1.09621	+	1.42403i	0.0961441	+	0.124896i
$131$	1.05457	+	0.608856i	0.0921382	+	0.0531960i	0.545361	−	0.838201i	$-0.316393\pi$
$131$	1.05457	+	0.608856i	0.0921382	+	0.0531960i	−0.453223	+	0.891397i	$0.649726\pi$
$132$		0			0
$133$	2.96065	−	1.70933i	0.256721	−	0.148218i
$134$	6.82324	+	2.81389i	0.589438	+	0.243083i
$135$		0			0
$136$	−3.14204	+	1.31864i	−0.269427	+	0.113072i
$137$	−6.20436	+	3.58209i	−0.530074	+	0.306038i	−0.741047	−	0.671454i	$-0.765670\pi$
$137$	−6.20436	+	3.58209i	−0.530074	+	0.306038i	0.210973	+	0.977492i	$0.432337\pi$
$138$		0			0
$139$	11.0378	−	19.1181i	0.936217	−	1.62158i	0.163767	−	0.986499i	$-0.447635\pi$
$139$	11.0378	−	19.1181i	0.936217	−	1.62158i	0.772450	−	0.635076i	$-0.219031\pi$
$140$	3.54633	+	13.0727i	0.299719	+	1.10485i
$141$		0			0
$142$	0.503276	+	3.77747i	0.0422340	+	0.316999i
$143$	−1.58515			−0.132557
$144$		0			0
$145$	−19.0337			−1.58066
$146$	−1.77363	−	13.3125i	−0.146787	−	1.10175i
$147$		0			0
$148$	−5.66539	−	20.8842i	−0.465692	−	1.71667i
$149$	−0.0838199	+	0.145180i	−0.00686679	+	0.0118936i	−0.869438	−	0.494041i	$-0.835519\pi$
$149$	−0.0838199	+	0.145180i	−0.00686679	+	0.0118936i	0.862572	+	0.505935i	$0.168852\pi$
$150$		0			0
$151$	−16.5201	+	9.53789i	−1.34439	+	0.776182i	−0.987448	−	0.157945i	$-0.949513\pi$
$151$	−16.5201	+	9.53789i	−1.34439	+	0.776182i	−0.356939	+	0.934128i	$0.616180\pi$
$152$	−1.77834	−	4.23743i	−0.144243	−	0.343701i
$153$		0			0
$154$	−11.0454	−	4.55508i	−0.890060	−	0.367059i
$155$	10.7756	−	6.22127i	0.865514	−	0.499705i
$156$		0			0
$157$	−13.3563	−	7.71126i	−1.06595	−	0.615426i	−0.138877	−	0.990310i	$-0.544349\pi$
$157$	−13.3563	−	7.71126i	−1.06595	−	0.615426i	−0.927072	+	0.374884i	$0.877683\pi$
$158$	1.53002	+	1.98757i	0.121722	+	0.158122i
$159$		0			0
$160$	18.0331	−	2.51653i	1.42564	−	0.198949i
$161$			11.5468i			0.910013i
$162$		0			0
$163$	−5.04605			−0.395237			−0.197619	−	0.980279i	$-0.563321\pi$
$163$	−5.04605			−0.395237			−0.197619	+	0.980279i	$0.563321\pi$
$164$	−2.76499	−	0.731691i	−0.215909	−	0.0571355i
$165$		0			0
$166$	−1.30301	−	1.69267i	−0.101133	−	0.131377i
$167$	−9.49899	+	16.4527i	−0.735054	+	1.27315i	0.219646	+	0.975580i	$0.429510\pi$
$167$	−9.49899	+	16.4527i	−0.735054	+	1.27315i	−0.954700	+	0.297571i	$0.903823\pi$
$168$		0			0
$169$	−6.42207	−	11.1233i	−0.494005	−	0.855642i
$170$	−2.09075	+	5.06975i	−0.160353	+	0.388832i
$171$		0			0
$172$	3.44914	+	3.42781i	0.262995	+	0.261368i
$173$	−1.26352	−	2.18848i	−0.0960636	−	0.166387i	0.813988	−	0.580881i	$-0.197292\pi$
$173$	−1.26352	−	2.18848i	−0.0960636	−	0.166387i	−0.910052	+	0.414494i	$0.863959\pi$
$174$		0			0
$175$	9.76752	+	5.63928i	0.738355	+	0.426289i
$176$	−7.94381	+	13.9584i	−0.598787	+	1.05215i
$177$		0			0
$178$	−15.7458	+	2.09782i	−1.18020	+	0.157238i
$179$		−	10.9962i		−	0.821898i	−0.911658	−	0.410949i	$-0.865197\pi$
$179$		−	10.9962i		−	0.821898i	0.911658	−	0.410949i	$-0.134803\pi$
$180$		0			0
$181$		−	14.3426i		−	1.06608i	−0.846091	−	0.533038i	$-0.821050\pi$
$181$		−	14.3426i		−	1.06608i	0.846091	−	0.533038i	$-0.178950\pi$
$182$	0.155146	+	1.16449i	0.0115002	+	0.0863181i
$183$		0			0
$184$	15.3980	+	1.95434i	1.13515	+	0.144076i
$185$	−30.1593	−	17.4125i	−2.21736	−	1.28019i
$186$		0			0
$187$	−2.41859	−	4.18913i	−0.176865	−	0.306339i
$188$	−2.24869	−	2.23478i	−0.164002	−	0.162988i
$189$		0			0
$190$	−6.83719	−	2.81964i	−0.496022	−	0.204558i
$191$	0.237073	+	0.410623i	0.0171540	+	0.0297116i	0.874475	−	0.485071i	$-0.161206\pi$
$191$	0.237073	+	0.410623i	0.0171540	+	0.0297116i	−0.857321	+	0.514782i	$0.827873\pi$
$192$		0			0
$193$	−10.6703	+	18.4815i	−0.768067	+	1.33033i	0.170543	+	0.985350i	$0.445448\pi$
$193$	−10.6703	+	18.4815i	−0.768067	+	1.33033i	−0.938610	+	0.344981i	$0.887885\pi$
$194$	13.1074	−	10.0900i	0.941053	−	0.724417i
$195$		0			0
$196$	1.31628	−	4.97410i	0.0940202	−	0.355293i
$197$	21.4346			1.52715			0.763575	−	0.645719i	$-0.223442\pi$
$197$	21.4346			1.52715			0.763575	+	0.645719i	$0.223442\pi$
$198$		0			0
$199$			6.09835i			0.432301i	0.976360	+	0.216150i	$0.0693501\pi$
$199$			6.09835i			0.432301i	−0.976360	+	0.216150i	$0.930650\pi$
$200$	9.17335	−	12.0708i	0.648654	−	0.853536i
$201$		0			0
$202$	−4.56118	+	3.51117i	−0.320923	+	0.247045i
$203$	−10.7756	−	6.22127i	−0.756296	−	0.436648i
$204$		0			0
$205$	−3.98635	+	2.30152i	−0.278419	+	0.160745i
$206$	9.76102	−	23.6689i	0.680082	−	1.64909i
$207$		0			0
$208$	1.57915	−	0.00979746i	0.109494	−	0.000679332i
$209$	5.64956	−	3.26177i	0.390788	−	0.225622i
$210$		0			0
$211$	1.36572	−	2.36549i	0.0940197	−	0.162847i	−0.815179	−	0.579209i	$-0.803362\pi$
$211$	1.36572	−	2.36549i	0.0940197	−	0.162847i	0.909199	+	0.416362i	$0.136695\pi$
$212$	13.6523	−	3.70354i	0.937640	−	0.254360i
$213$		0			0
$214$	17.3786	−	2.31537i	1.18798	−	0.158275i
$215$	7.82596			0.533726
$216$		0			0
$217$	8.13386			0.552162
$218$	−2.46938	+	0.328998i	−0.167248	+	0.0222825i
$219$		0			0
$220$	6.76717	+	24.9456i	0.456242	+	1.68183i
$221$	−0.237813	+	0.411904i	−0.0159970	+	0.0277076i
$222$		0			0
$223$	13.4015	−	7.73737i	0.897432	−	0.518133i	0.0210661	−	0.999778i	$-0.493294\pi$
$223$	13.4015	−	7.73737i	0.897432	−	0.518133i	0.876366	+	0.481645i	$0.159961\pi$
$224$	11.0317	+	4.46956i	0.737085	+	0.298635i
$225$		0			0
$226$	9.83291	−	23.8433i	0.654075	−	1.58603i
$227$	−13.9546	+	8.05671i	−0.926202	+	0.534743i	−0.885608	−	0.464433i	$-0.846258\pi$
$227$	−13.9546	+	8.05671i	−0.926202	+	0.534743i	−0.0405935	+	0.999176i	$0.512925\pi$
$228$		0			0
$229$	−9.60052	−	5.54286i	−0.634420	−	0.366283i	0.148042	−	0.988981i	$-0.452703\pi$
$229$	−9.60052	−	5.54286i	−0.634420	−	0.366283i	−0.782462	+	0.622698i	$0.786036\pi$
$230$	19.7942	−	15.2374i	1.30519	−	1.00473i
$231$		0			0
$232$	−10.1201	+	13.3166i	−0.664415	+	0.874276i
$233$		−	8.96547i		−	0.587348i	−0.955906	−	0.293674i	$-0.905122\pi$
$233$		−	8.96547i		−	0.587348i	0.955906	−	0.293674i	$-0.0948780\pi$
$234$		0			0
$235$	−5.10218			−0.332829
$236$	−5.12566	−	1.35639i	−0.333652	−	0.0882933i
$237$		0			0
$238$	−2.84072	+	2.18677i	−0.184137	+	0.141747i
$239$	−11.6179	+	20.1228i	−0.751499	+	1.30163i	0.195597	+	0.980684i	$0.437336\pi$
$239$	−11.6179	+	20.1228i	−0.751499	+	1.30163i	−0.947096	+	0.320951i	$0.895998\pi$
$240$		0			0
$241$	−4.27609	−	7.40641i	−0.275447	−	0.477089i	0.694801	−	0.719202i	$-0.255493\pi$
$241$	−4.27609	−	7.40641i	−0.275447	−	0.477089i	−0.970248	+	0.242114i	$0.922159\pi$
$242$	−6.69554	−	2.76122i	−0.430406	−	0.177498i
$243$		0			0
$244$	−13.3267	+	13.4096i	−0.853151	+	0.858461i
$245$	−4.14035	−	7.17129i	−0.264517	−	0.458157i
$246$		0			0
$247$	−0.555503	−	0.320720i	−0.0353458	−	0.0204069i
$248$	1.37669	−	10.8468i	0.0874197	−	0.688770i
$249$		0			0
$250$	−0.216543	−	1.62532i	−0.0136954	−	0.102794i
$251$			13.6971i			0.864551i	0.901742	+	0.432275i	$0.142289\pi$
$251$			13.6971i			0.864551i	−0.901742	+	0.432275i	$0.857711\pi$
$252$		0			0
$253$			22.0338i			1.38525i
$254$	2.93271	−	0.390727i	0.184015	−	0.0245164i
$255$		0			0
$256$	7.82745	−	13.9546i	0.489216	−	0.872163i
$257$	−3.88533	−	2.24320i	−0.242360	−	0.139927i	0.373901	−	0.927469i	$-0.378020\pi$
$257$	−3.88533	−	2.24320i	−0.242360	−	0.139927i	−0.616261	+	0.787542i	$0.711353\pi$
$258$		0			0
$259$	−11.3828	−	19.7155i	−0.707291	−	1.22506i
$260$	1.79151	−	1.80266i	0.111105	−	0.111796i
$261$		0			0
$262$	0.656552	−	1.59204i	0.0405619	−	0.0983564i
$263$	11.1123	+	19.2471i	0.685214	+	1.18682i	0.973370	+	0.229241i	$0.0736245\pi$
$263$	11.1123	+	19.2471i	0.685214	+	1.18682i	−0.288156	+	0.957583i	$0.593042\pi$
$264$		0			0
$265$	11.3828	−	19.7155i	0.699238	−	1.21112i
$266$	−2.94913	−	3.83107i	−0.180823	−	0.234898i
$267$		0			0
$268$	2.67023	−	10.0905i	0.163110	−	0.616378i
$269$	−12.9941			−0.792266			−0.396133	−	0.918193i	$-0.629648\pi$
$269$	−12.9941			−0.792266			−0.396133	+	0.918193i	$0.629648\pi$
$270$		0			0
$271$			11.1500i			0.677314i	0.940910	+	0.338657i	$0.109973\pi$
$271$			11.1500i			0.677314i	−0.940910	+	0.338657i	$0.890027\pi$
$272$	2.43533	+	4.15831i	0.147663	+	0.252135i
$273$		0			0
$274$	6.18023	+	8.02842i	0.373361	+	0.485015i
$275$	18.6386	+	10.7610i	1.12395	+	0.648911i
$276$		0			0
$277$	1.29497	−	0.747654i	0.0778074	−	0.0449221i	−0.460592	−	0.887612i	$-0.652363\pi$
$277$	1.29497	−	0.747654i	0.0778074	−	0.0449221i	0.538399	+	0.842690i	$0.319029\pi$
$278$	−28.8617	−	11.9025i	−1.73101	−	0.713865i
$279$		0			0
$280$	17.6634	−	7.41289i	1.05559	−	0.443005i
$281$	9.39961	−	5.42687i	0.560734	−	0.323740i	−0.192706	−	0.981256i	$-0.561726\pi$
$281$	9.39961	−	5.42687i	0.560734	−	0.323740i	0.753440	+	0.657517i	$0.228393\pi$
$282$		0			0
$283$	−12.0627	+	20.8931i	−0.717050	+	1.24197i	0.245113	+	0.969494i	$0.421175\pi$
$283$	−12.0627	+	20.8931i	−0.717050	+	1.24197i	−0.962163	+	0.272473i	$0.912159\pi$
$284$	5.20137	−	1.41101i	0.308644	−	0.0837281i
$285$		0			0
$286$	0.296053	+	2.22211i	0.0175060	+	0.131396i
$287$	−3.00907			−0.177620
$288$		0			0
$289$	15.5486			0.914624
$290$	3.55485	+	26.6819i	0.208748	+	1.56681i
$291$		0			0
$292$	−18.3305	+	4.97265i	−1.07271	+	0.291002i
$293$	3.54036	−	6.13209i	0.206830	−	0.358240i	−0.743884	−	0.668309i	$-0.767019\pi$
$293$	3.54036	−	6.13209i	0.206830	−	0.358240i	0.950714	+	0.310068i	$0.100352\pi$
$294$		0			0
$295$	−7.38979	+	4.26650i	−0.430250	+	0.248405i
$296$	−28.2179	+	11.8424i	−1.64013	+	0.688323i
$297$		0			0
$298$	0.219172	+	0.0903861i	0.0126963	+	0.00523593i
$299$	1.87625	−	1.08326i	0.108507	−	0.0626463i
$300$		0			0
$301$	4.43052	+	2.55796i	0.255371	+	0.147439i
$302$	16.4559	+	21.3770i	0.946929	+	1.23011i
$303$		0			0
$304$	−5.60800	+	3.28434i	−0.321641	+	0.188370i
$305$			30.4258i			1.74218i
$306$		0			0
$307$	12.9052			0.736541			0.368270	−	0.929719i	$-0.379950\pi$
$307$	12.9052			0.736541			0.368270	+	0.929719i	$0.379950\pi$
$308$	−4.32253	+	16.3344i	−0.246299	+	0.930739i
$309$		0			0
$310$	−10.7337	−	13.9435i	−0.609631	−	0.791940i
$311$	7.89357	−	13.6721i	0.447603	−	0.775271i	−0.550626	−	0.834752i	$-0.685611\pi$
$311$	7.89357	−	13.6721i	0.447603	−	0.775271i	0.998229	+	0.0594804i	$0.0189444\pi$
$312$		0			0
$313$	2.06365	+	3.57434i	0.116644	+	0.202034i	0.918436	−	0.395570i	$-0.129453\pi$
$313$	2.06365	+	3.57434i	0.116644	+	0.202034i	−0.801792	+	0.597604i	$0.796120\pi$
$314$	−8.31535	+	20.1634i	−0.469262	+	1.13789i
$315$		0			0
$316$	2.50047	−	2.51603i	0.140662	−	0.141538i
$317$	−7.58238	−	13.1331i	−0.425869	−	0.737627i	0.570632	−	0.821206i	$-0.306698\pi$
$317$	−7.58238	−	13.1331i	−0.425869	−	0.737627i	−0.996501	+	0.0835791i	$0.973365\pi$
$318$		0			0
$319$	−20.5621	−	11.8715i	−1.15126	−	0.664679i
$320$	−6.89572	−	24.8093i	−0.385483	−	1.38688i
$321$		0			0
$322$	16.1866	−	2.15655i	0.902043	−	0.120180i
$323$		−	1.95739i		−	0.108912i
$324$		0			0
$325$		−	2.11619i		−	0.117385i
$326$	0.942433	+	7.07369i	0.0521965	+	0.391776i
$327$		0			0
$328$	−0.509297	+	4.01269i	−0.0281212	+	0.221564i
$329$	−2.88851	−	1.66768i	−0.159248	−	0.0919421i
$330$		0			0
$331$	7.09621	+	12.2910i	0.390043	+	0.675575i	0.992455	−	0.122611i	$-0.0391267\pi$
$331$	7.09621	+	12.2910i	0.390043	+	0.675575i	−0.602412	+	0.798186i	$0.705793\pi$
$332$	−2.12947	+	2.14272i	−0.116870	+	0.117597i
$333$		0			0
$334$	24.8380	+	10.2431i	1.35907	+	0.560479i
$335$	−8.39917	−	14.5478i	−0.458896	−	0.794830i
$336$		0			0
$337$	−12.9139	+	22.3675i	−0.703464	+	1.21844i	0.263779	+	0.964583i	$0.415031\pi$
$337$	−12.9139	+	22.3675i	−0.703464	+	1.21844i	−0.967243	+	0.253853i	$0.918302\pi$
$338$	−14.3936	+	11.0801i	−0.782908	+	0.602678i
$339$		0			0
$340$	7.49739	+	1.98401i	0.406603	+	0.107598i
$341$	15.5212			0.840518
$342$		0			0
$343$		−	20.1421i		−	1.08757i
$344$	4.16101	−	5.47530i	0.224347	−	0.295208i
$345$		0			0
$346$	−2.83189	+	2.17997i	−0.152243	+	0.117196i
$347$	−11.4312	−	6.59978i	−0.613656	−	0.354295i	0.160739	−	0.986997i	$-0.448612\pi$
$347$	−11.4312	−	6.59978i	−0.613656	−	0.354295i	−0.774395	+	0.632702i	$0.781946\pi$
$348$		0			0
$349$	−12.7838	+	7.38075i	−0.684303	+	0.395082i	−0.801474	−	0.598029i	$-0.795951\pi$
$349$	−12.7838	+	7.38075i	−0.684303	+	0.395082i	0.117171	+	0.993112i	$0.462617\pi$
$350$	6.08105	−	14.7456i	0.325046	−	0.788185i
$351$		0			0
$352$	21.0509	+	8.52889i	1.12201	+	0.454591i
$353$	1.21582	−	0.701955i	0.0647116	−	0.0373613i	−0.467295	−	0.884101i	$-0.654771\pi$
$353$	1.21582	−	0.701955i	0.0647116	−	0.0373613i	0.532007	+	0.846740i	$0.321438\pi$
$354$		0			0
$355$	4.33672	−	7.51142i	0.230169	−	0.398665i
$356$	5.88157	+	21.6811i	0.311722	+	1.14909i
$357$		0			0
$358$	−15.4148	+	2.05373i	−0.814699	+	0.108543i
$359$	−11.3107			−0.596953			−0.298477	−	0.954417i	$-0.596479\pi$
$359$	−11.3107			−0.596953			−0.298477	+	0.954417i	$0.596479\pi$
$360$		0			0
$361$	−16.3602			−0.861064
$362$	−20.1058	+	2.67871i	−1.05674	+	0.140790i
$363$		0			0
$364$	1.60344	−	0.434977i	0.0840433	−	0.0227990i
$365$	−15.2834	+	26.4716i	−0.799967	+	1.38558i
$366$		0			0
$367$	9.82457	−	5.67222i	0.512838	−	0.296087i	−0.221161	−	0.975237i	$-0.570985\pi$
$367$	9.82457	−	5.67222i	0.512838	−	0.296087i	0.734000	+	0.679150i	$0.237651\pi$
$368$	−0.136186	−	21.9503i	−0.00709917	−	1.14424i
$369$		0			0
$370$	−18.7766	+	45.5302i	−0.976146	+	2.36700i
$371$	12.8883	−	7.44107i	0.669127	−	0.386321i
$372$		0			0
$373$	20.9314	+	12.0848i	1.08379	+	0.625726i	0.931916	−	0.362674i	$-0.118136\pi$
$373$	20.9314	+	12.0848i	1.08379	+	0.625726i	0.151873	+	0.988400i	$0.451470\pi$
$374$	−5.42072	+	4.17284i	−0.280299	+	0.215772i
$375$		0			0
$376$	−2.71279	+	3.56965i	−0.139902	+	0.184091i
$377$			2.33458i			0.120237i
$378$		0			0
$379$	20.7029			1.06344			0.531719	−	0.846921i	$-0.321546\pi$
$379$	20.7029			1.06344			0.531719	+	0.846921i	$0.321546\pi$
$380$	−2.67569	+	10.1112i	−0.137260	+	0.518692i
$381$		0			0
$382$	0.531344	−	0.409026i	0.0271859	−	0.0209276i
$383$	15.2027	−	26.3319i	0.776824	−	1.34550i	−0.156940	−	0.987608i	$-0.550163\pi$
$383$	15.2027	−	26.3319i	0.776824	−	1.34550i	0.933764	−	0.357890i	$-0.116504\pi$
$384$		0			0
$385$	13.5964	+	23.5497i	0.692939	+	1.20021i
$386$	27.9008	+	11.5062i	1.42011	+	0.585651i
$387$		0			0
$388$	−16.5924	−	16.4898i	−0.842351	−	0.837141i
$389$	10.1376	+	17.5588i	0.513995	+	0.890266i	0.999868	+	0.0162366i	$0.00516850\pi$
$389$	10.1376	+	17.5588i	0.513995	+	0.890266i	−0.485873	+	0.874030i	$0.661498\pi$
$390$		0			0
$391$	5.72550	+	3.30562i	0.289551	+	0.167172i
$392$	−7.21867	−	0.916205i	−0.364598	−	0.0462753i
$393$		0			0
$394$	−4.00326	−	30.0476i	−0.201681	−	1.51377i
$395$		−	5.70876i		−	0.287239i
$396$		0			0
$397$		−	12.2942i		−	0.617030i	−0.951220	−	0.308515i	$-0.900168\pi$
$397$		−	12.2942i		−	0.617030i	0.951220	−	0.308515i	$-0.0998320\pi$
$398$	8.54883	−	1.13897i	0.428514	−	0.0570913i
$399$		0			0
$400$	−18.6345	−	10.6050i	−0.931724	−	0.530251i
$401$	25.3617	+	14.6426i	1.26650	+	0.731216i	0.974325	−	0.225147i	$-0.0722863\pi$
$401$	25.3617	+	14.6426i	1.26650	+	0.731216i	0.292179	+	0.956364i	$0.405620\pi$
$402$		0			0
$403$	−0.763074	−	1.32168i	−0.0380114	−	0.0658377i
$404$	5.77392	+	5.73821i	0.287263	+	0.285487i
$405$		0			0
$406$	−6.70863	+	16.2674i	−0.332944	+	0.807337i
$407$	−21.7208	−	37.6216i	−1.07666	−	1.86483i
$408$		0			0
$409$	15.3567	−	26.5986i	0.759342	−	1.31522i	−0.183845	−	0.982955i	$-0.558855\pi$
$409$	15.3567	−	26.5986i	0.759342	−	1.31522i	0.943187	−	0.332263i	$-0.107812\pi$
$410$	3.97085	+	5.15833i	0.196106	+	0.254752i
$411$		0			0
$412$	−35.0028	−	9.26269i	−1.72446	−	0.456340i
$413$	−5.57813			−0.274482
$414$		0			0
$415$			4.86175i			0.238654i
$416$	−0.308666	−	2.21186i	−0.0151336	−	0.108446i
$417$		0			0
$418$	−5.62759	−	7.31051i	−0.275254	−	0.357569i
$419$	−11.5932	−	6.69333i	−0.566364	−	0.326991i	0.189332	−	0.981913i	$-0.439368\pi$
$419$	−11.5932	−	6.69333i	−0.566364	−	0.326991i	−0.755696	+	0.654923i	$0.772701\pi$
$420$		0			0
$421$	23.9825	−	13.8463i	1.16884	−	0.674828i	0.215431	−	0.976519i	$-0.430884\pi$
$421$	23.9825	−	13.8463i	1.16884	−	0.674828i	0.953406	+	0.301691i	$0.0975510\pi$
$422$	−3.57108	−	1.47270i	−0.173837	−	0.0716901i
$423$		0			0
$424$	−7.74150	−	18.4464i	−0.375961	−	0.895836i
$425$	5.59250	−	3.22883i	0.271276	−	0.156621i
$426$		0			0
$427$	−9.94486	+	17.2250i	−0.481266	+	0.833577i
$428$	−6.49149	−	23.9294i	−0.313778	−	1.15667i
$429$		0			0
$430$	−1.46163	−	10.9706i	−0.0704859	−	0.529051i
$431$	29.2554			1.40918			0.704592	−	0.709613i	$-0.251130\pi$
$431$	29.2554			1.40918			0.704592	+	0.709613i	$0.251130\pi$
$432$		0			0
$433$	2.57756			0.123870			0.0619348	−	0.998080i	$-0.480273\pi$
$433$	2.57756			0.123870			0.0619348	+	0.998080i	$0.480273\pi$
$434$	−1.51913	−	11.4023i	−0.0729206	−	0.547326i
$435$		0			0
$436$	0.922396	+	3.40020i	0.0441748	+	0.162840i
$437$	−4.45804	+	7.72155i	−0.213257	+	0.369372i
$438$		0			0
$439$	24.4758	−	14.1311i	1.16817	−	0.674442i	0.214920	−	0.976632i	$-0.431051\pi$
$439$	24.4758	−	14.1311i	1.16817	−	0.674442i	0.953248	+	0.302189i	$0.0977175\pi$
$440$	33.7056	−	14.1454i	1.60685	−	0.674356i
$441$		0			0
$442$	0.621833	+	0.256442i	0.0295776	+	0.0121977i
$443$	23.3499	−	13.4811i	1.10939	−	0.640506i	0.170718	−	0.985320i	$-0.445391\pi$
$443$	23.3499	−	13.4811i	1.10939	−	0.640506i	0.938671	+	0.344814i	$0.112058\pi$
$444$		0			0
$445$	31.3101	+	18.0769i	1.48424	+	0.856928i
$446$	−13.3494	−	17.3415i	−0.632113	−	0.821145i
$447$		0			0
$448$	4.20520	−	16.2993i	0.198677	−	0.770068i
$449$		−	23.4500i		−	1.10668i	−0.832957	−	0.553338i	$-0.813354\pi$
$449$		−	23.4500i		−	1.10668i	0.832957	−	0.553338i	$-0.186646\pi$
$450$		0			0
$451$	−5.74196			−0.270378
$452$	−35.2606	−	9.33091i	−1.65852	−	0.438889i
$453$		0			0
$454$	13.9004	+	18.0573i	0.652377	+	0.847469i
$455$	1.33690	−	2.31557i	0.0626746	−	0.108556i
$456$		0			0
$457$	−8.06063	−	13.9614i	−0.377060	−	0.653088i	0.613573	−	0.789638i	$-0.289732\pi$
$457$	−8.06063	−	13.9614i	−0.377060	−	0.653088i	−0.990633	+	0.136550i	$0.956398\pi$
$458$	−5.97708	+	14.4935i	−0.279291	+	0.677236i
$459$		0			0
$460$	−25.0571	−	24.9022i	−1.16830	−	1.16107i
$461$	5.14578	+	8.91276i	0.239663	+	0.415109i	0.960618	−	0.277874i	$-0.0896297\pi$
$461$	5.14578	+	8.91276i	0.239663	+	0.415109i	−0.720955	+	0.692982i	$0.756296\pi$
$462$		0			0
$463$	−22.3273	−	12.8907i	−1.03764	−	0.599080i	−0.118474	−	0.992957i	$-0.537800\pi$
$463$	−22.3273	−	12.8907i	−1.03764	−	0.599080i	−0.919163	+	0.393877i	$0.871134\pi$
$464$	20.5576	+	11.6995i	0.954364	+	0.543136i
$465$		0			0
$466$	−12.5680	+	1.67445i	−0.582203	+	0.0775674i
$467$			10.8110i			0.500271i	0.968211	+	0.250136i	$0.0804752\pi$
$467$			10.8110i			0.500271i	−0.968211	+	0.250136i	$0.919525\pi$
$468$		0			0
$469$		−	10.9813i		−	0.507069i
$470$	0.952915	+	7.15237i	0.0439547	+	0.329914i
$471$		0			0
$472$	−0.944120	+	7.43861i	−0.0434567	+	0.342390i
$473$	8.45441	+	4.88115i	0.388734	+	0.224436i
$474$		0			0
$475$	4.35448	+	7.54218i	0.199797	+	0.346059i
$476$	3.59603	+	3.57379i	0.164824	+	0.163804i
$477$		0			0
$478$	30.3785	+	12.5280i	1.38948	+	0.573018i
$479$	6.16167	+	10.6723i	0.281534	+	0.487631i	0.971763	−	0.235960i	$-0.0758236\pi$
$479$	6.16167	+	10.6723i	0.281534	+	0.487631i	−0.690229	+	0.723591i	$0.742490\pi$
$480$		0			0
$481$	−2.13574	+	3.69921i	−0.0973813	+	0.168669i
$482$	−9.58387	+	7.37761i	−0.436533	+	0.336041i
$483$		0			0
$484$	−2.62026	+	9.90169i	−0.119103	+	0.450077i
$485$	−37.6474			−1.70948
$486$		0			0
$487$			7.62691i			0.345608i	0.984956	+	0.172804i	$0.0552828\pi$
$487$			7.62691i			0.345608i	−0.984956	+	0.172804i	$0.944717\pi$
$488$	21.2869	+	16.1772i	0.963612	+	0.732307i
$489$		0			0
$490$	−9.27963	+	7.14340i	−0.419211	+	0.322706i
$491$	−22.1130	−	12.7670i	−0.997948	−	0.576165i	−0.0903072	−	0.995914i	$-0.528785\pi$
$491$	−22.1130	−	12.7670i	−0.997948	−	0.576165i	−0.907640	+	0.419749i	$0.862118\pi$
$492$		0			0
$493$	−6.16967	+	3.56206i	−0.277868	+	0.160427i
$494$	−0.345844	+	0.838619i	−0.0155603	+	0.0377312i
$495$		0			0
$496$	−15.4624	+	0.0959328i	−0.694282	+	0.00430751i
$497$	4.91031	−	2.83497i	0.220258	−	0.127166i
$498$		0			0
$499$	−5.58850	+	9.67956i	−0.250176	+	0.433317i	−0.963574	−	0.267442i	$-0.913822\pi$
$499$	−5.58850	+	9.67956i	−0.250176	+	0.433317i	0.713398	+	0.700759i	$0.247155\pi$
$500$	−2.23797	+	0.607111i	−0.100085	+	0.0271508i
$501$		0			0
$502$	19.2009	−	2.55815i	0.856979	−	0.114176i
$503$	22.3635			0.997137			0.498569	−	0.866850i	$-0.333859\pi$
$503$	22.3635			0.997137			0.498569	+	0.866850i	$0.333859\pi$
$504$		0			0
$505$	13.1008			0.582977
$506$	30.8875	−	4.11517i	1.37312	−	0.182942i
$507$		0			0
$508$	−1.09546	−	4.03818i	−0.0486034	−	0.179165i
$509$	6.12701	−	10.6123i	0.271575	−	0.470382i	−0.697690	−	0.716399i	$-0.745789\pi$
$509$	6.12701	−	10.6123i	0.271575	−	0.470382i	0.969265	+	0.246018i	$0.0791222\pi$
$510$		0			0
$511$	−17.3048	+	9.99093i	−0.765519	+	0.441973i
$512$	−21.0238	−	8.36648i	−0.929131	−	0.369750i
$513$		0			0
$514$	−2.41892	+	5.86551i	−0.106694	+	0.258717i
$515$	−50.4644	+	29.1356i	−2.22373	+	1.28387i
$516$		0			0
$517$	−5.51190	−	3.18230i	−0.242413	−	0.139957i
$518$	−25.5119	+	19.6389i	−1.12093	+	0.862883i
$519$		0			0
$520$	−2.86161	−	2.17471i	−0.125490	−	0.0953674i
$521$		−	34.9202i		−	1.52988i	−0.644101	−	0.764940i	$-0.722768\pi$
$521$		−	34.9202i		−	1.52988i	0.644101	−	0.764940i	$-0.277232\pi$
$522$		0			0
$523$	−36.8697			−1.61220			−0.806100	−	0.591779i	$-0.798426\pi$
$523$	−36.8697			−1.61220			−0.806100	+	0.591779i	$0.798426\pi$
$524$	−2.35438	−	0.623034i	−0.102852	−	0.0272173i
$525$		0			0
$526$	24.9056	−	19.1722i	1.08594	−	0.835949i
$527$	2.32857	−	4.03319i	0.101434	−	0.175689i
$528$		0			0
$529$	−3.55735	−	6.16151i	−0.154667	−	0.267892i
$530$	−29.7637	−	12.2745i	−1.29285	−	0.533169i
$531$		0			0
$532$	−4.81969	+	4.84969i	−0.208960	+	0.210261i
$533$	0.282294	+	0.488948i	0.0122275	+	0.0211787i
$534$		0			0
$535$	−34.5570	−	19.9515i	−1.49403	−	0.862579i
$536$	−14.6439	−	1.85863i	−0.632520	−	0.0802805i
$537$		0			0
$538$	2.42687	+	18.2155i	0.104630	+	0.785327i
$539$		−	10.3296i		−	0.444926i
$540$		0			0
$541$		−	11.9200i		−	0.512481i	−0.966613	−	0.256240i	$-0.917516\pi$
$541$		−	11.9200i		−	0.512481i	0.966613	−	0.256240i	$-0.0824839\pi$
$542$	15.6304	−	2.08245i	0.671382	−	0.0894487i
$543$		0			0
$544$	5.37440	−	4.19054i	0.230425	−	0.179668i
$545$	4.91031	+	2.83497i	0.210335	+	0.121437i
$546$		0			0
$547$	−10.3339	−	17.8989i	−0.441847	−	0.765302i	0.555979	−	0.831196i	$-0.312343\pi$
$547$	−10.3339	−	17.8989i	−0.441847	−	0.765302i	−0.997827	+	0.0658943i	$0.979010\pi$
$548$	10.1002	−	10.1631i	0.431459	−	0.434144i
$549$		0			0
$550$	11.6040	−	28.1378i	0.494795	−	1.19980i
$551$	−4.80388	−	8.32057i	−0.204652	−	0.354468i
$552$		0			0
$553$	1.86595	−	3.23191i	0.0793481	−	0.137435i
$554$	−1.28994	−	1.67569i	−0.0548042	−	0.0711934i
$555$		0			0
$556$	−11.2949	+	42.6822i	−0.479009	+	1.81013i
$557$	21.6506			0.917367			0.458684	−	0.888600i	$-0.348321\pi$
$557$	21.6506			0.917367			0.458684	+	0.888600i	$0.348321\pi$
$558$		0			0
$559$		−	0.959897i		−	0.0405993i
$560$	−13.6905	−	23.3765i	−0.578530	−	0.987838i
$561$		0			0
$562$	−9.36306	−	12.1631i	−0.394957	−	0.513068i
$563$	36.7299	+	21.2060i	1.54798	+	0.893726i	0.998296	+	0.0583533i	$0.0185850\pi$
$563$	36.7299	+	21.2060i	1.54798	+	0.893726i	0.549683	+	0.835373i	$0.314748\pi$
$564$		0			0
$565$	−50.8361	+	29.3502i	−2.13869	+	1.23477i
$566$	31.5414	+	13.0076i	1.32579	+	0.546751i
$567$		0			0
$568$	−2.94943	−	7.02789i	−0.123755	−	0.294884i
$569$	−19.3062	+	11.1464i	−0.809357	+	0.467282i	−0.846732	−	0.532019i	$-0.821433\pi$
$569$	−19.3062	+	11.1464i	−0.809357	+	0.467282i	0.0373758	+	0.999301i	$0.488100\pi$
$570$		0			0
$571$	1.30386	−	2.25835i	0.0545649	−	0.0945091i	−0.837453	−	0.546510i	$-0.815956\pi$
$571$	1.30386	−	2.25835i	0.0545649	−	0.0945091i	0.892018	+	0.452001i	$0.149289\pi$
$572$	3.05972	−	0.830031i	0.127933	−	0.0347053i
$573$		0			0
$574$	0.561993	+	4.21819i	0.0234571	+	0.176064i
$575$	−29.4152			−1.22670
$576$		0			0
$577$	−12.3081			−0.512394			−0.256197	−	0.966625i	$-0.582470\pi$
$577$	−12.3081			−0.512394			−0.256197	+	0.966625i	$0.582470\pi$
$578$	−2.90396	−	21.7964i	−0.120789	−	0.906613i
$579$		0			0
$580$	36.7395	−	9.96656i	1.52552	−	0.413839i
$581$	−1.58909	+	2.75239i	−0.0659267	+	0.114188i
$582$		0			0
$583$	24.5937	−	14.1992i	1.01857	−	0.588070i
$584$	10.3943	+	24.7675i	0.430120	+	1.02489i
$585$		0			0
$586$	−9.25734	−	3.81771i	−0.382417	−	0.157708i
$587$	23.8189	−	13.7518i	0.983111	−	0.567599i	0.0799032	−	0.996803i	$-0.474539\pi$
$587$	23.8189	−	13.7518i	0.983111	−	0.567599i	0.903208	+	0.429203i	$0.141206\pi$
$588$		0			0
$589$	5.43926	+	3.14036i	0.224121	+	0.129396i
$590$	7.36105	+	9.56237i	0.303050	+	0.393676i
$591$		0			0
$592$	21.8711	+	37.3448i	0.898896	+	1.53486i
$593$			33.5909i			1.37941i	0.724088	+	0.689707i	$0.242261\pi$
$593$			33.5909i			1.37941i	−0.724088	+	0.689707i	$0.757739\pi$
$594$		0			0
$595$	8.15923			0.334496
$596$	0.0857717	−	0.324123i	0.00351334	−	0.0132766i
$597$		0			0
$598$	−1.86896	−	2.42787i	−0.0764273	−	0.0992828i
$599$	−4.32570	+	7.49232i	−0.176743	+	0.306128i	−0.940763	−	0.339064i	$-0.889890\pi$
$599$	−4.32570	+	7.49232i	−0.176743	+	0.306128i	0.764020	+	0.645193i	$0.223223\pi$
$600$		0			0
$601$	11.3533	+	19.6644i	0.463109	+	0.802128i	0.999114	−	0.0420865i	$-0.0134005\pi$
$601$	11.3533	+	19.6644i	0.463109	+	0.802128i	−0.536005	+	0.844215i	$0.680067\pi$
$602$	2.75835	−	6.68857i	0.112422	−	0.272606i
$603$		0			0
$604$	26.8934	−	27.0608i	1.09428	−	1.10109i
$605$	8.24197	+	14.2755i	0.335084	+	0.580382i
$606$		0			0
$607$	18.9691	+	10.9518i	0.769932	+	0.444520i	0.832850	−	0.553498i	$-0.186708\pi$
$607$	18.9691	+	10.9518i	0.769932	+	0.444520i	−0.0629187	+	0.998019i	$0.520041\pi$
$608$	5.65146	+	7.24804i	0.229197	+	0.293947i
$609$		0			0
$610$	42.6517	−	5.68252i	1.72692	−	0.230078i
$611$			0.625810i			0.0253176i
$612$		0			0
$613$			35.2553i			1.42395i	0.702206	+	0.711973i	$0.252198\pi$
$613$			35.2553i			1.42395i	−0.702206	+	0.711973i	$0.747802\pi$
$614$	−2.41026	−	18.0909i	−0.0972704	−	0.730089i
$615$		0			0
$616$	23.7053	+	3.00872i	0.955114	+	0.121225i
$617$	−3.96793	−	2.29088i	−0.159743	−	0.0922275i	0.417998	−	0.908448i	$-0.362732\pi$
$617$	−3.96793	−	2.29088i	−0.159743	−	0.0922275i	−0.577740	+	0.816221i	$0.696065\pi$
$618$		0			0
$619$	−8.24726	−	14.2847i	−0.331486	−	0.574150i	0.651318	−	0.758805i	$-0.274216\pi$
$619$	−8.24726	−	14.2847i	−0.331486	−	0.574150i	−0.982803	+	0.184655i	$0.940883\pi$
$620$	−17.5417	+	17.6509i	−0.704494	+	0.708878i
$621$		0			0
$622$	−20.6401	−	8.51193i	−0.827593	−	0.341297i
$623$	11.8171	+	20.4678i	0.473443	+	0.820027i
$624$		0			0
$625$	11.5346	−	19.9785i	0.461384	−	0.799140i
$626$	4.62518	−	3.56044i	0.184860	−	0.142304i
$627$		0			0
$628$	29.8187	+	7.89083i	1.18989	+	0.314878i
$629$	−13.0347			−0.519726
$630$		0			0
$631$			38.0635i			1.51528i	0.652670	+	0.757642i	$0.273649\pi$
$631$			38.0635i			1.51528i	−0.652670	+	0.757642i	$0.726351\pi$
$632$	−3.99404	−	3.03531i	−0.158874	−	0.120738i
$633$		0			0
$634$	−16.9942	+	13.0820i	−0.674924	+	0.519553i
$635$	−5.83163	−	3.36689i	−0.231421	−	0.133611i
$636$		0			0
$637$	−0.879598	+	0.507836i	−0.0348510	+	0.0201212i
$638$	−12.8015	+	31.0417i	−0.506818	+	1.22895i
$639$		0			0
$640$	−33.4905	+	14.3002i	−1.32383	+	0.565263i
$641$	−30.2526	+	17.4663i	−1.19490	+	0.689878i	−0.959415	−	0.281998i	$-0.909003\pi$
$641$	−30.2526	+	17.4663i	−1.19490	+	0.689878i	−0.235490	+	0.971877i	$0.575669\pi$
$642$		0			0
$643$	18.5870	−	32.1936i	0.733000	−	1.26959i	−0.222596	−	0.974911i	$-0.571453\pi$
$643$	18.5870	−	32.1936i	0.733000	−	1.26959i	0.955595	−	0.294682i	$-0.0952137\pi$
$644$	−6.04622	−	22.2880i	−0.238254	−	0.878271i
$645$		0			0
$646$	−2.74392	+	0.365575i	−0.107958	+	0.0143834i
$647$	−9.36933			−0.368346			−0.184173	−	0.982894i	$-0.558961\pi$
$647$	−9.36933			−0.368346			−0.184173	+	0.982894i	$0.558961\pi$
$648$		0			0
$649$	−10.6443			−0.417825
$650$	−2.96652	+	0.395232i	−0.116357	+	0.0155023i
$651$		0			0
$652$	9.74007	−	2.64226i	0.381451	−	0.103479i
$653$	7.65255	−	13.2546i	0.299468	−	0.518693i	−0.676547	−	0.736400i	$-0.736524\pi$
$653$	7.65255	−	13.2546i	0.299468	−	0.518693i	0.976014	+	0.217707i	$0.0698576\pi$
$654$		0			0
$655$	−3.39437	+	1.95974i	−0.132629	+	0.0765735i
$656$	5.72022	−	0.0354897i	0.223337	−	0.00138564i
$657$		0			0
$658$	−1.79832	+	4.36065i	−0.0701059	+	0.169996i
$659$	−17.2932	+	9.98421i	−0.673646	+	0.388930i	−0.797457	−	0.603376i	$-0.793822\pi$
$659$	−17.2932	+	9.98421i	−0.673646	+	0.388930i	0.123811	+	0.992306i	$0.460488\pi$
$660$		0			0
$661$	30.6907	+	17.7193i	1.19373	+	0.689201i	0.959151	−	0.282896i	$-0.0912950\pi$
$661$	30.6907	+	17.7193i	1.19373	+	0.689201i	0.234580	+	0.972097i	$0.424628\pi$
$662$	15.9045	−	12.2432i	0.618147	−	0.475846i
$663$		0			0
$664$	3.40144	+	2.58496i	0.132002	+	0.100316i
$665$			11.0037i			0.426707i
$666$		0			0
$667$	32.4509			1.25650
$668$	9.72018	−	36.7316i	0.376085	−	1.42119i
$669$		0			0
$670$	−18.8248	+	14.4912i	−0.727265	+	0.559845i
$671$	−18.9770	+	32.8691i	−0.732598	+	1.26890i
$672$		0			0
$673$	1.95563	+	3.38725i	0.0753841	+	0.130569i	0.901253	−	0.433293i	$-0.142648\pi$
$673$	1.95563	+	3.38725i	0.0753841	+	0.130569i	−0.825869	+	0.563862i	$0.809315\pi$
$674$	33.7673	+	13.9255i	1.30067	+	0.536391i
$675$		0			0
$676$	18.2206	+	18.1079i	0.700793	+	0.696458i
$677$	1.69713	+	2.93951i	0.0652259	+	0.112974i	0.896794	−	0.442448i	$-0.145890\pi$
$677$	1.69713	+	2.93951i	0.0652259	+	0.112974i	−0.831568	+	0.555423i	$0.812557\pi$
$678$		0			0
$679$	−21.3134	−	12.3053i	−0.817934	−	0.472234i
$680$	1.38098	−	10.8806i	0.0529582	−	0.417252i
$681$		0			0
$682$	−2.89883	−	21.7580i	−0.111002	−	0.833157i
$683$			9.70867i			0.371492i	0.982598	+	0.185746i	$0.0594702\pi$
$683$			9.70867i			0.371492i	−0.982598	+	0.185746i	$0.940530\pi$
$684$		0			0
$685$		−	23.0595i		−	0.881060i
$686$	−28.2357	+	3.76186i	−1.07804	+	0.143629i
$687$		0			0
$688$	−8.45256	−	4.81041i	−0.322251	−	0.183395i
$689$	−2.41822	−	1.39616i	−0.0921269	−	0.0531895i
$690$		0			0
$691$	19.6458	+	34.0276i	0.747363	+	1.29447i	0.949083	+	0.315027i	$0.102014\pi$
$691$	19.6458	+	34.0276i	0.747363	+	1.29447i	−0.201720	+	0.979443i	$0.564653\pi$
$692$	3.58484	+	3.56267i	0.136275	+	0.135432i
$693$		0			0
$694$	−7.11679	+	17.2571i	−0.270150	+	0.655071i
$695$	35.5278	+	61.5359i	1.34765	+	2.33419i
$696$		0			0
$697$	−0.861438	+	1.49206i	−0.0326293	+	0.0565156i
$698$	12.7341	+	16.5422i	0.481994	+	0.626133i
$699$		0			0
$700$	−21.8065	−	5.77059i	−0.824208	−	0.218108i
$701$	12.0640			0.455651			0.227826	−	0.973702i	$-0.426838\pi$
$701$	12.0640			0.455651			0.227826	+	0.973702i	$0.426838\pi$
$702$		0			0
$703$		−	17.5789i		−	0.663000i
$704$	8.02444	−	31.1026i	0.302432	−	1.17222i
$705$		0			0
$706$	−1.21109	−	1.57327i	−0.0455801	−	0.0592108i
$707$	7.41677	+	4.28208i	0.278936	+	0.161044i
$708$		0			0
$709$	−11.5824	+	6.68709i	−0.434985	+	0.251139i	−0.701468	−	0.712701i	$-0.747472\pi$
$709$	−11.5824	+	6.68709i	−0.434985	+	0.251139i	0.266483	+	0.963840i	$0.414138\pi$
$710$	−11.3397	−	4.67645i	−0.425570	−	0.175504i
$711$		0			0
$712$	29.2946	−	12.2942i	1.09786	−	0.460746i
$713$	−18.3715	+	10.6068i	−0.688018	+	0.397228i
$714$		0			0
$715$	2.55109	−	4.41861i	0.0954053	−	0.165247i
$716$	5.75795	+	21.2254i	0.215185	+	0.793229i
$717$		0			0
$718$	2.11245	+	15.8556i	0.0788359	+	0.591725i
$719$	−36.4686			−1.36005			−0.680025	−	0.733189i	$-0.738031\pi$
$719$	−36.4686			−1.36005			−0.680025	+	0.733189i	$0.738031\pi$
$720$		0			0
$721$	−38.0927			−1.41865
$722$	3.05554	+	22.9342i	0.113715	+	0.853522i
$723$		0			0
$724$	7.51018	+	27.6846i	0.279114	+	1.02889i
$725$	15.8486	−	27.4505i	0.588601	−	1.01949i
$726$		0			0
$727$	−4.01460	+	2.31783i	−0.148893	+	0.0859637i	−0.572596	−	0.819838i	$-0.694064\pi$
$727$	−4.01460	+	2.31783i	−0.148893	+	0.0859637i	0.423702	+	0.905801i	$0.360730\pi$
$728$	−0.909232	−	2.16651i	−0.0336984	−	0.0802962i
$729$		0			0
$730$	39.9629	+	16.4806i	1.47910	+	0.609975i
$731$	2.53675	−	1.46459i	0.0938250	−	0.0541699i
$732$		0			0
$733$	−32.3446	−	18.6742i	−1.19467	−	0.689746i	−0.235311	−	0.971920i	$-0.575611\pi$
$733$	−32.3446	−	18.6742i	−1.19467	−	0.689746i	−0.959363	+	0.282175i	$0.908944\pi$
$734$	−9.78636	−	12.7130i	−0.361221	−	0.469244i
$735$		0			0
$736$	−30.7451	+	4.29049i	−1.13328	+	0.158150i
$737$		−	20.9547i		−	0.771876i
$738$		0			0
$739$	−21.7009			−0.798279			−0.399140	−	0.916890i	$-0.630691\pi$
$739$	−21.7009			−0.798279			−0.399140	+	0.916890i	$0.630691\pi$
$740$	67.3323	+	17.8180i	2.47518	+	0.655001i
$741$		0			0
$742$	−12.8382	−	16.6774i	−0.471305	−	0.612248i
$743$	21.4136	−	37.0894i	0.785588	−	1.36068i	−0.143060	−	0.989714i	$-0.545694\pi$
$743$	21.4136	−	37.0894i	0.785588	−	1.36068i	0.928647	−	0.370964i	$-0.120973\pi$
$744$		0			0
$745$	−0.269793	−	0.467296i	−0.00988446	−	0.0171204i
$746$	13.0315	−	31.5993i	0.477116	−	1.15693i
$747$		0			0
$748$	6.86200	+	6.81956i	0.250900	+	0.249348i
$749$	−13.0426	−	22.5904i	−0.476565	−	0.825434i
$750$		0			0
$751$	27.3860	+	15.8113i	0.999328	+	0.576962i	0.908049	−	0.418863i	$-0.137571\pi$
$751$	27.3860	+	15.8113i	0.999328	+	0.576962i	0.0912787	+	0.995825i	$0.470905\pi$
$752$	5.51069	+	3.13618i	0.200954	+	0.114365i
$753$		0			0
$754$	3.27268	−	0.436022i	0.119184	−	0.0158790i
$755$		−	61.3997i		−	2.23457i
$756$		0			0
$757$		−	32.2957i		−	1.17381i	−0.809657	−	0.586903i	$-0.800347\pi$
$757$		−	32.2957i		−	1.17381i	0.809657	−	0.586903i	$-0.199653\pi$
$758$	−3.86661	−	29.0219i	−0.140442	−	1.05412i
$759$		0			0
$760$	14.6738	+	1.86243i	0.532276	+	0.0675573i
$761$	−31.6365	−	18.2653i	−1.14682	−	0.662118i	−0.198711	−	0.980058i	$-0.563676\pi$
$761$	−31.6365	−	18.2653i	−1.14682	−	0.662118i	−0.948111	+	0.317940i	$0.897009\pi$
$762$		0			0
$763$	1.85326	+	3.20994i	0.0670924	+	0.116207i
$764$	−0.672621	−	0.668460i	−0.0243346	−	0.0241841i
$765$		0			0
$766$	−39.7521	−	16.3937i	−1.43630	−	0.592328i
$767$	0.523309	+	0.906399i	0.0188956	+	0.0327282i
$768$		0			0
$769$	−1.92161	+	3.32832i	−0.0692950	+	0.120022i	−0.898591	−	0.438787i	$-0.855408\pi$
$769$	−1.92161	+	3.32832i	−0.0692950	+	0.120022i	0.829296	+	0.558809i	$0.188742\pi$
$770$	30.4733	−	23.4582i	1.09818	−	0.845373i
$771$		0			0
$772$	10.9188	−	41.2610i	0.392976	−	1.48502i
$773$	−25.4969			−0.917059			−0.458529	−	0.888679i	$-0.651624\pi$
$773$	−25.4969			−0.917059			−0.458529	+	0.888679i	$0.651624\pi$
$774$		0			0
$775$			20.7208i			0.744314i
$776$	−20.0169	+	26.3394i	−0.718565	+	0.945529i
$777$		0			0
$778$	22.7210	−	17.4905i	0.814588	−	0.627065i
$779$	−2.01222	−	1.16176i	−0.0720953	−	0.0416243i
$780$		0			0
$781$	9.36995	−	5.40974i	0.335283	−	0.193576i
$782$	3.56457	−	8.64354i	0.127469	−	0.309092i
$783$		0			0
$784$	0.0638446	+	10.2904i	0.00228017	+	0.367516i
$785$	42.9903	−	24.8205i	1.53439	−	0.885881i
$786$		0			0
$787$	−13.2295	+	22.9142i	−0.471581	+	0.816802i	−0.999471	−	0.0325104i	$-0.989650\pi$
$787$	−13.2295	+	22.9142i	−0.471581	+	0.816802i	0.527891	+	0.849312i	$0.322983\pi$
$788$	−41.3738	+	11.2238i	−1.47388	+	0.399830i
$789$		0			0
$790$	−8.00269	+	1.06620i	−0.284723	+	0.0379339i
$791$	−38.3733			−1.36440
$792$		0			0
$793$	3.73189			0.132523
$794$	−17.2344	+	2.29615i	−0.611625	+	0.0814873i
$795$		0			0
$796$	−3.19327	−	11.7713i	−0.113182	−	0.417221i
$797$	−4.10557	+	7.11105i	−0.145427	+	0.251886i	−0.929532	−	0.368741i	$-0.879789\pi$
$797$	−4.10557	+	7.11105i	−0.145427	+	0.251886i	0.784105	+	0.620628i	$0.213122\pi$
$798$		0			0
$799$	−1.65385	+	0.954848i	−0.0585089	+	0.0337801i
$800$	−11.3861	+	28.1030i	−0.402560	+	0.993590i
$801$		0			0
$802$	15.7897	−	38.2875i	0.557553	−	1.35198i
$803$	−33.0213	+	19.0649i	−1.16530	+	0.672785i
$804$		0			0
$805$	−32.1866	−	18.5830i	−1.13443	−	0.654964i
$806$	−1.71025	+	1.31654i	−0.0602411	+	0.0463733i
$807$		0			0
$808$	6.96560	−	9.16574i	0.245049	−	0.322450i
$809$		−	4.36982i		−	0.153635i	−0.997045	−	0.0768174i	$-0.975524\pi$
$809$		−	4.36982i		−	0.153635i	0.997045	−	0.0768174i	$-0.0244759\pi$
$810$		0			0
$811$	−0.393286			−0.0138101			−0.00690507	−	0.999976i	$-0.502198\pi$
$811$	−0.393286			−0.0138101			−0.00690507	+	0.999976i	$0.502198\pi$
$812$	24.0570	+	6.36614i	0.844236	+	0.223408i
$813$		0			0
$814$	−48.6822	+	37.4753i	−1.70631	+	1.31351i
$815$	8.12094	−	14.0659i	0.284464	−	0.492706i
$816$		0			0
$817$	1.97518	+	3.42112i	0.0691029	+	0.119690i
$818$	−40.1548	−	16.5597i	−1.40398	−	0.578998i
$819$		0			0
$820$	6.48946	−	6.52985i	0.226622	−	0.228032i
$821$	8.66193	+	15.0029i	0.302304	+	0.523605i	0.976657	−	0.214803i	$-0.0689110\pi$
$821$	8.66193	+	15.0029i	0.302304	+	0.523605i	−0.674354	+	0.738408i	$0.735578\pi$
$822$		0			0
$823$	26.9923	+	15.5840i	0.940893	+	0.543225i	0.890240	−	0.455491i	$-0.150536\pi$
$823$	26.9923	+	15.5840i	0.940893	+	0.543225i	0.0506529	+	0.998716i	$0.483870\pi$
$824$	−6.44734	+	50.7978i	−0.224604	+	1.76963i
$825$		0			0
$826$	1.04181	+	7.81957i	0.0362491	+	0.272078i
$827$			36.3732i			1.26482i	0.774634	+	0.632410i	$0.217934\pi$
$827$			36.3732i			1.26482i	−0.774634	+	0.632410i	$0.782066\pi$
$828$		0			0
$829$		−	47.9890i		−	1.66673i	−0.552726	−	0.833363i	$-0.686412\pi$
$829$		−	47.9890i		−	1.66673i	0.552726	−	0.833363i	$-0.313588\pi$
$830$	6.81533	−	0.908012i	0.236564	−	0.0315175i
$831$		0			0
$832$	−3.04300	+	0.845799i	−0.105497	+	0.0293228i
$833$	−2.68415	−	1.54969i	−0.0930002	−	0.0536937i
$834$		0			0
$835$	−30.5747	−	52.9569i	−1.05808	−	1.83265i
$836$	−9.19703	+	9.25426i	−0.318086	+	0.320065i
$837$		0			0
$838$	−7.21767	+	17.5017i	−0.249330	+	0.604587i
$839$	−4.62312	−	8.00747i	−0.159608	−	0.276449i	0.775120	−	0.631815i	$-0.217690\pi$
$839$	−4.62312	−	8.00747i	−0.159608	−	0.276449i	−0.934727	+	0.355366i	$0.884356\pi$
$840$		0			0
$841$	−2.98420	+	5.16878i	−0.102903	+	0.178234i
$842$	−23.8893	−	31.0333i	−0.823279	−	1.06948i
$843$		0			0
$844$	−1.39752	+	5.28108i	−0.0481045	+	0.181782i
$845$	41.3418			1.42220
$846$		0			0
$847$			10.7758i			0.370260i
$848$	−24.4128	+	14.2974i	−0.838339	+	0.490975i
$849$		0			0
$850$	−5.57076	−	7.23668i	−0.191075	−	0.248216i
$851$	51.4193	+	29.6870i	1.76263	+	1.01766i
$852$		0			0
$853$	−13.1396	+	7.58616i	−0.449892	+	0.259745i	−0.707785	−	0.706428i	$-0.750305\pi$
$853$	−13.1396	+	7.58616i	−0.449892	+	0.259745i	0.257893	+	0.966174i	$0.416972\pi$
$854$	26.0038	+	10.7239i	0.889833	+	0.366965i
$855$		0			0
$856$	−32.3325	+	13.5692i	−1.10510	+	0.463784i
$857$	24.4191	−	14.0984i	0.834140	−	0.481591i	−0.0211282	−	0.999777i	$-0.506726\pi$
$857$	24.4191	−	14.0984i	0.834140	−	0.481591i	0.855268	+	0.518186i	$0.173392\pi$
$858$		0			0
$859$	−3.33845	+	5.78236i	−0.113906	+	0.197292i	−0.917342	−	0.398100i	$-0.869670\pi$
$859$	−3.33845	+	5.78236i	−0.113906	+	0.197292i	0.803436	+	0.595392i	$0.203003\pi$
$860$	−15.1059	+	4.09789i	−0.515109	+	0.139737i
$861$		0			0
$862$	−5.46393	−	41.0110i	−0.186102	−	1.39684i
$863$	54.3136			1.84885			0.924427	−	0.381358i	$-0.124543\pi$
$863$	54.3136			1.84885			0.924427	+	0.381358i	$0.124543\pi$
$864$		0			0
$865$	8.13386			0.276559
$866$	−0.481401	−	3.61329i	−0.0163587	−	0.122785i
$867$		0			0
$868$	−15.7003	+	4.25912i	−0.532902	+	0.144564i
$869$	3.56063	−	6.16719i	0.120786	−	0.209208i
$870$		0			0
$871$	−1.78437	+	1.03020i	−0.0604610	+	0.0349071i
$872$	4.59422	−	1.92808i	0.155580	−	0.0652931i
$873$		0			0
$874$	11.6569	+	4.80727i	0.394300	+	0.162608i
$875$	−2.11274	+	1.21979i	−0.0714238	+	0.0412365i
$876$		0			0
$877$	5.70769	+	3.29534i	0.192735	+	0.111276i	0.593262	−	0.805009i	$-0.297840\pi$
$877$	5.70769	+	3.29534i	0.192735	+	0.111276i	−0.400527	+	0.916285i	$0.631173\pi$
$878$	−24.3807	−	31.6717i	−0.822808	−	1.06887i
$879$		0			0
$880$	−26.1245	−	44.6075i	−0.880656	−	1.50372i
$881$		−	15.5607i		−	0.524252i	−0.965034	−	0.262126i	$-0.915576\pi$
$881$		−	15.5607i		−	0.524252i	0.965034	−	0.262126i	$-0.0844236\pi$
$882$		0			0
$883$	41.6548			1.40180			0.700898	−	0.713262i	$-0.252783\pi$
$883$	41.6548			1.40180			0.700898	+	0.713262i	$0.252783\pi$
$884$	0.243350	−	0.919597i	0.00818476	−	0.0309294i
$885$		0			0
$886$	−23.2591	−	30.2147i	−0.781406	−	1.01508i
$887$	−26.8247	+	46.4617i	−0.900684	+	1.56003i	−0.0740769	+	0.997253i	$0.523601\pi$
$887$	−26.8247	+	46.4617i	−0.900684	+	1.56003i	−0.826608	+	0.562779i	$0.809732\pi$
$888$		0			0
$889$	−2.20098	−	3.81221i	−0.0738186	−	0.127858i
$890$	19.4930	−	47.2675i	0.653407	−	1.58441i
$891$		0			0
$892$	−21.8166	+	21.9524i	−0.730474	+	0.735020i
$893$	−1.28773	−	2.23042i	−0.0430923	−	0.0746381i
$894$		0			0
$895$	30.6520	+	17.6970i	1.02458	+	0.591544i
$896$	−23.6341	−	2.85080i	−0.789561	−	0.0952387i
$897$		0			0
$898$	−32.8729	+	4.37968i	−1.09698	+	0.146152i
$899$		−	22.8593i		−	0.762400i
$900$		0			0
$901$		−	8.52093i		−	0.283873i
$902$	1.07241	+	8.04924i	0.0357072	+	0.268010i
$903$		0			0
$904$	−6.49483	+	51.1720i	−0.216015	+	1.70195i
$905$	39.9800	+	23.0824i	1.32898	+	0.767286i
$906$		0			0
$907$	−2.86449	−	4.96144i	−0.0951139	−	0.164742i	0.814542	−	0.580104i	$-0.196988\pi$
$907$	−2.86449	−	4.96144i	−0.0951139	−	0.164742i	−0.909656	+	0.415362i	$0.863655\pi$
$908$	22.7170	−	22.8584i	0.753891	−	0.758583i
$909$		0			0
$910$	−3.49572	−	1.44162i	−0.115882	−	0.0477894i
$911$	−21.2846	−	36.8661i	−0.705192	−	1.22143i	−0.966622	−	0.256206i	$-0.917528\pi$
$911$	−21.2846	−	36.8661i	−0.705192	−	1.22143i	0.261430	−	0.965222i	$-0.415806\pi$
$912$		0			0
$913$	−3.03234	+	5.25216i	−0.100356	+	0.173821i
$914$	−18.0660	+	13.9071i	−0.597571	+	0.460007i
$915$		0			0
$916$	21.4337	+	5.67193i	0.708189	+	0.187406i
$917$	−2.56222			−0.0846119
$918$		0			0
$919$			40.3722i			1.33175i	0.746061	+	0.665877i	$0.231943\pi$
$919$			40.3722i			1.33175i	−0.746061	+	0.665877i	$0.768057\pi$
$920$	−30.2287	+	39.7767i	−0.996611	+	1.31140i
$921$		0			0
$922$	11.5331	−	8.87810i	0.379822	−	0.292385i
$923$	−0.921317	−	0.531923i	−0.0303255	−	0.0175085i
$924$		0			0
$925$	50.2249	−	28.9974i	1.65139	−	0.953428i
$926$	−13.9005	+	33.7066i	−0.456799	+	1.10767i
$927$		0			0
$928$	12.5612	−	31.0033i	0.412341	−	1.01773i
$929$	−7.87141	+	4.54456i	−0.258253	+	0.149102i	−0.623537	−	0.781794i	$-0.714305\pi$
$929$	−7.87141	+	4.54456i	−0.258253	+	0.149102i	0.365285	+	0.930896i	$0.380972\pi$
$930$		0			0
$931$	2.08995	−	3.61991i	0.0684955	−	0.118638i
$932$	4.69458	+	17.3055i	0.153776	+	0.566860i
$933$		0			0
$934$	15.1551	−	2.01912i	0.495890	−	0.0660677i
$935$	15.5696			0.509180
$936$		0			0
$937$	5.39574			0.176271			0.0881355	−	0.996108i	$-0.471909\pi$
$937$	5.39574			0.176271			0.0881355	+	0.996108i	$0.471909\pi$
$938$	−15.3939	+	2.05094i	−0.502628	+	0.0669655i
$939$		0			0
$940$	9.84841	−	2.67164i	0.321220	−	0.0871394i
$941$	22.2304	−	38.5041i	0.724689	−	1.25520i	−0.234413	−	0.972137i	$-0.575317\pi$
$941$	22.2304	−	38.5041i	0.724689	−	1.25520i	0.959102	−	0.283061i	$-0.0913499\pi$
$942$		0			0
$943$	6.79643	−	3.92392i	0.221322	−	0.127780i
$944$	10.6040	−	0.0657899i	0.345130	−	0.00214128i
$945$		0			0
$946$	5.26353	−	12.7633i	0.171132	−	0.414969i
$947$	53.2162	−	30.7244i	1.72930	−	0.998409i	0.836454	−	0.548037i	$-0.184625\pi$
$947$	53.2162	−	30.7244i	1.72930	−	0.998409i	0.892841	−	0.450372i	$-0.148708\pi$
$948$		0			0
$949$	3.24688	+	1.87459i	0.105398	+	0.0608517i
$950$	9.75956	−	7.51286i	0.316642	−	0.243749i
$951$		0			0
$952$	4.33821	−	5.70847i	0.140602	−	0.185013i
$953$			22.6195i			0.732716i	0.930474	+	0.366358i	$0.119395\pi$
$953$			22.6195i			0.732716i	−0.930474	+	0.366358i	$0.880605\pi$
$954$		0			0
$955$	−1.52615			−0.0493850
$956$	11.8884	−	44.9252i	0.384499	−	1.45298i
$957$		0			0
$958$	13.8099	−	10.6308i	0.446179	−	0.343466i
$959$	7.53716	−	13.0547i	0.243388	−	0.421560i
$960$		0			0
$961$	−8.02829	−	13.9054i	−0.258977	−	0.448562i
$962$	5.58453	+	2.30305i	0.180053	+	0.0742532i
$963$		0			0
$964$	12.1321	+	12.0570i	0.390748	+	0.388331i
$965$	−34.3449	−	59.4871i	−1.10560	−	1.91496i
$966$		0			0
$967$	−23.8616	−	13.7765i	−0.767337	−	0.443022i	0.0645868	−	0.997912i	$-0.479427\pi$
$967$	−23.8616	−	13.7765i	−0.767337	−	0.443022i	−0.831924	+	0.554890i	$0.812760\pi$
$968$	14.3698	+	1.82384i	0.461864	+	0.0586205i
$969$		0			0
$970$	7.03128	+	52.7752i	0.225761	+	1.69451i
$971$			23.4973i			0.754064i	0.926200	+	0.377032i	$0.123055\pi$
$971$			23.4973i			0.754064i	−0.926200	+	0.377032i	$0.876945\pi$
$972$		0			0
$973$			46.4500i			1.48912i
$974$	10.6916	−	1.42445i	0.342581	−	0.0456423i
$975$		0			0
$976$	18.7019	−	32.8619i	0.598635	−	1.05188i
$977$	−26.2982	−	15.1832i	−0.841353	−	0.485755i	0.0163711	−	0.999866i	$-0.494789\pi$
$977$	−26.2982	−	15.1832i	−0.841353	−	0.485755i	−0.857724	+	0.514111i	$0.828122\pi$
$978$		0			0
$979$	22.5496	+	39.0571i	0.720689	+	1.24827i
$980$	11.7469	+	11.6743i	0.375242	+	0.372921i
$981$		0			0
$982$	−13.7671	+	33.3831i	−0.439326	+	1.06530i
$983$	−15.6881	−	27.1725i	−0.500372	−	0.866669i	−1.00000		0.000429288i	$-0.999863\pi$
$983$	−15.6881	−	27.1725i	−0.500372	−	0.866669i	0.499628	−	0.866240i	$-0.333470\pi$
$984$		0			0
$985$	−34.4960	+	59.7489i	−1.09914	+	1.90376i
$986$	6.14568	+	7.98353i	0.195718	+	0.254248i
$987$		0			0
$988$	1.24019	+	0.328188i	0.0394557	+	0.0104411i
$989$	−13.3427			−0.424272
$990$		0			0
$991$		−	19.2702i		−	0.612138i	−0.952009	−	0.306069i	$-0.900986\pi$
$991$		−	19.2702i		−	0.612138i	0.952009	−	0.306069i	$-0.0990138\pi$
$992$	3.02234	+	21.6577i	0.0959593	+	0.687632i
$993$		0			0
$994$	−4.89122	−	6.35393i	−0.155140	−	0.201534i
$995$	−16.9992	−	9.81447i	−0.538910	−	0.311140i
$996$		0			0
$997$	44.0083	−	25.4082i	1.39376	−	0.804687i	0.400029	−	0.916502i	$-0.369000\pi$
$997$	44.0083	−	25.4082i	1.39376	−	0.804687i	0.993729	+	0.111816i	$0.0356667\pi$
$998$	14.6128	+	6.02629i	0.462561	+	0.190759i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.l.b.179.4		16
3.2	odd	2		72.2.l.b.59.5	yes	16
4.3	odd	2		864.2.p.b.719.2		16
8.3	odd	2	inner	216.2.l.b.179.7		16
8.5	even	2		864.2.p.b.719.7		16
9.2	odd	6	inner	216.2.l.b.35.7		16
9.4	even	3		648.2.f.b.323.14		16
9.5	odd	6		648.2.f.b.323.3		16
9.7	even	3		72.2.l.b.11.2	✓	16
12.11	even	2		288.2.p.b.239.4		16
24.5	odd	2		288.2.p.b.239.3		16
24.11	even	2		72.2.l.b.59.2	yes	16
36.7	odd	6		288.2.p.b.47.3		16
36.11	even	6		864.2.p.b.143.7		16
36.23	even	6		2592.2.f.b.1295.4		16
36.31	odd	6		2592.2.f.b.1295.14		16
72.5	odd	6		2592.2.f.b.1295.13		16
72.11	even	6	inner	216.2.l.b.35.4		16
72.13	even	6		2592.2.f.b.1295.3		16
72.29	odd	6		864.2.p.b.143.2		16
72.43	odd	6		72.2.l.b.11.5	yes	16
72.59	even	6		648.2.f.b.323.13		16
72.61	even	6		288.2.p.b.47.4		16
72.67	odd	6		648.2.f.b.323.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.2	✓	16	9.7	even	3
72.2.l.b.11.5	yes	16	72.43	odd	6
72.2.l.b.59.2	yes	16	24.11	even	2
72.2.l.b.59.5	yes	16	3.2	odd	2
216.2.l.b.35.4		16	72.11	even	6	inner
216.2.l.b.35.7		16	9.2	odd	6	inner
216.2.l.b.179.4		16	1.1	even	1	trivial
216.2.l.b.179.7		16	8.3	odd	2	inner
288.2.p.b.47.3		16	36.7	odd	6
288.2.p.b.47.4		16	72.61	even	6
288.2.p.b.239.3		16	24.5	odd	2
288.2.p.b.239.4		16	12.11	even	2
648.2.f.b.323.3		16	9.5	odd	6
648.2.f.b.323.4		16	72.67	odd	6
648.2.f.b.323.13		16	72.59	even	6
648.2.f.b.323.14		16	9.4	even	3
864.2.p.b.143.2		16	72.29	odd	6
864.2.p.b.143.7		16	36.11	even	6
864.2.p.b.719.2		16	4.3	odd	2
864.2.p.b.719.7		16	8.5	even	2
2592.2.f.b.1295.3		16	72.13	even	6
2592.2.f.b.1295.4		16	36.23	even	6
2592.2.f.b.1295.13		16	72.5	odd	6
2592.2.f.b.1295.14		16	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.186766 - 1.40183i) q^{2} +(-1.93024 + 0.523628i) q^{4} +(-1.60936 + 2.78750i) q^{5} +(-1.82223 + 1.05206i) q^{7} +(1.09454 + 2.60806i) q^{8} +O(q^{10})\)	\(q+(-0.186766 - 1.40183i) q^{2} +(-1.93024 + 0.523628i) q^{4} +(-1.60936 + 2.78750i) q^{5} +(-1.82223 + 1.05206i) q^{7} +(1.09454 + 2.60806i) q^{8} +(4.20817 + 1.73544i) q^{10} +(-3.47720 + 2.00756i) q^{11} +(0.341902 + 0.197397i) q^{13} +(1.81514 + 2.35795i) q^{14} +(3.45163 - 2.02145i) q^{16} +1.20474i q^{17} -1.62474 q^{19} +(1.64684 - 6.22324i) q^{20} +(3.46368 + 4.49949i) q^{22} +(2.74384 - 4.75248i) q^{23} +(-2.68011 - 4.64208i) q^{25} +(0.212861 - 0.516155i) q^{26} +(2.96644 - 2.98490i) q^{28} +(2.95670 + 5.12116i) q^{29} +(-3.34777 - 1.93284i) q^{31} +(-3.47838 - 4.46104i) q^{32} +(1.68884 - 0.225005i) q^{34} -6.77261i q^{35} +10.8195i q^{37} +(0.303447 + 2.27761i) q^{38} +(-9.03149 - 1.14629i) q^{40} +(1.23849 + 0.715041i) q^{41} +(-1.21569 - 2.10564i) q^{43} +(5.66061 - 5.69584i) q^{44} +(-7.17460 - 2.95879i) q^{46} +(0.792576 + 1.37278i) q^{47} +(-1.28633 + 2.22799i) q^{49} +(-6.00684 + 4.62403i) q^{50} +(-0.763315 - 0.201994i) q^{52} -7.07284 q^{53} -12.9236i q^{55} +(-4.73834 - 3.60095i) q^{56} +(6.62677 - 5.10125i) q^{58} +(2.29587 + 1.32552i) q^{59} +(8.18631 - 4.72637i) q^{61} +(-2.08425 + 5.05398i) q^{62} +(-5.60397 + 5.70925i) q^{64} +(-1.10049 + 0.635369i) q^{65} +(-2.60947 + 4.51973i) q^{67} +(-0.630836 - 2.32543i) q^{68} +(-9.49402 + 1.26490i) q^{70} -2.69468 q^{71} +9.49652 q^{73} +(15.1670 - 2.02072i) q^{74} +(3.13614 - 0.850761i) q^{76} +(4.22417 - 7.31647i) q^{77} +(-1.53599 + 0.886804i) q^{79} +(0.0798779 + 12.8747i) q^{80} +(0.771055 - 1.86969i) q^{82} +(1.30809 - 0.755228i) q^{83} +(-3.35821 - 1.93887i) q^{85} +(-2.72469 + 2.09745i) q^{86} +(-9.04179 - 6.87140i) q^{88} -11.2323i q^{89} -0.830698 q^{91} +(-2.80774 + 10.6102i) q^{92} +(1.77638 - 1.36744i) q^{94} +(2.61480 - 4.52897i) q^{95} +(5.84818 + 10.1294i) q^{97} +(3.36350 + 1.38710i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) 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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