LMFDB - Embedded newform 819.2.et.c.271.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.7
Character	$\chi$	$=$	819.271
Dual form			819.2.et.c.136.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20543 + 1.20543i) q^{2} +0.906108i q^{4} +(-0.363968 - 1.35835i) q^{5} +(0.864271 + 2.50061i) q^{7} +(1.31861 - 1.31861i) q^{8} +O(q^{10})$	\(q+(1.20543 + 1.20543i) q^{2} +0.906108i q^{4} +(-0.363968 - 1.35835i) q^{5} +(0.864271 + 2.50061i) q^{7} +(1.31861 - 1.31861i) q^{8} +(1.19865 - 2.07613i) q^{10} +(-0.392515 - 1.46489i) q^{11} +(-1.37191 + 3.33435i) q^{13} +(-1.97248 + 4.05611i) q^{14} +4.99118 q^{16} +5.17026 q^{17} +(4.68519 + 1.25539i) q^{19} +(1.23081 - 0.329795i) q^{20} +(1.29267 - 2.23896i) q^{22} +2.14980i q^{23} +(2.61749 - 1.51121i) q^{25} +(-5.67305 + 2.36557i) q^{26} +(-2.26582 + 0.783122i) q^{28} +(0.744307 + 1.28918i) q^{29} +(1.89045 + 0.506544i) q^{31} +(3.37929 + 3.37929i) q^{32} +(6.23237 + 6.23237i) q^{34} +(3.08213 - 2.08412i) q^{35} +(6.70890 - 6.70890i) q^{37} +(4.13437 + 7.16094i) q^{38} +(-2.27106 - 1.31120i) q^{40} +(-6.34762 - 1.70084i) q^{41} +(-7.27334 - 4.19927i) q^{43} +(1.32735 - 0.355661i) q^{44} +(-2.59143 + 2.59143i) q^{46} +(-6.20311 + 1.66212i) q^{47} +(-5.50607 + 4.32240i) q^{49} +(4.97684 + 1.33354i) q^{50} +(-3.02128 - 1.24310i) q^{52} +(-1.87579 - 3.24897i) q^{53} +(-1.84696 + 1.06635i) q^{55} +(4.43695 + 2.15769i) q^{56} +(-0.656802 + 2.45122i) q^{58} +(5.98603 + 5.98603i) q^{59} +(-2.79969 + 1.61640i) q^{61} +(1.66819 + 2.88940i) q^{62} -1.83539i q^{64} +(5.02854 + 0.649937i) q^{65} +(-12.5811 + 3.37110i) q^{67} +4.68481i q^{68} +(6.22754 + 1.20302i) q^{70} +(2.71213 - 0.726713i) q^{71} +(-3.82844 + 14.2879i) q^{73} +16.1742 q^{74} +(-1.13752 + 4.24529i) q^{76} +(3.32387 - 2.24759i) q^{77} +(3.67744 - 6.36951i) q^{79} +(-1.81663 - 6.77977i) q^{80} +(-5.60135 - 9.70182i) q^{82} +(-0.0684765 + 0.0684765i) q^{83} +(-1.88181 - 7.02301i) q^{85} +(-3.70557 - 13.8294i) q^{86} +(-2.44918 - 1.41404i) q^{88} +(-7.89157 - 7.89157i) q^{89} +(-9.52359 - 0.548833i) q^{91} -1.94795 q^{92} +(-9.48096 - 5.47383i) q^{94} -6.82105i q^{95} +(-3.39415 - 12.6671i) q^{97} +(-11.8475 - 1.42683i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.20543	+	1.20543i	0.852365	+	0.852365i	0.990424	−	0.138059i	$-0.0440862\pi$
$2$	1.20543	+	1.20543i	0.852365	+	0.852365i	−0.138059	+	0.990424i	$0.544086\pi$
$3$		0			0
$3$		0			0
$4$			0.906108i			0.453054i
$5$	−0.363968	−	1.35835i	−0.162772	−	0.607472i	−0.998314	−	0.0580459i	$-0.981513\pi$
$5$	−0.363968	−	1.35835i	−0.162772	−	0.607472i	0.835542	−	0.549426i	$-0.185154\pi$
$6$		0			0
$7$	0.864271	+	2.50061i	0.326664	+	0.945141i
$7$	0.864271	+	2.50061i	0.326664	+	0.945141i
$8$	1.31861	−	1.31861i	0.466198	−	0.466198i
$9$		0			0
$10$	1.19865	−	2.07613i	0.379047	−	0.656529i
$11$	−0.392515	−	1.46489i	−0.118348	−	0.441680i	0.881168	−	0.472804i	$-0.156758\pi$
$11$	−0.392515	−	1.46489i	−0.118348	−	0.441680i	−0.999516	+	0.0311237i	$0.990091\pi$
$12$		0			0
$13$	−1.37191	+	3.33435i	−0.380500	+	0.924781i
$13$	−1.37191	+	3.33435i	−0.380500	+	0.924781i
$14$	−1.97248	+	4.05611i	−0.527169	+	1.08404i
$15$		0			0
$16$	4.99118			1.24780
$17$	5.17026			1.25397			0.626986	−	0.779031i	$-0.284288\pi$
$17$	5.17026			1.25397			0.626986	+	0.779031i	$0.284288\pi$
$18$		0			0
$19$	4.68519	+	1.25539i	1.07486	+	0.288007i	0.752487	−	0.658607i	$-0.228854\pi$
$19$	4.68519	+	1.25539i	1.07486	+	0.288007i	0.322370	+	0.946614i	$0.395521\pi$
$20$	1.23081	−	0.329795i	0.275218	−	0.0737443i
$21$		0			0
$22$	1.29267	−	2.23896i	0.275597	−	0.477348i
$23$			2.14980i			0.448264i	0.974559	+	0.224132i	$0.0719547\pi$
$23$			2.14980i			0.448264i	−0.974559	+	0.224132i	$0.928045\pi$
$24$		0			0
$25$	2.61749	−	1.51121i	0.523498	−	0.302242i
$26$	−5.67305	+	2.36557i	−1.11258	+	0.463927i
$27$		0			0
$28$	−2.26582	+	0.783122i	−0.428200	+	0.147996i
$29$	0.744307	+	1.28918i	0.138214	+	0.239394i	0.926821	−	0.375504i	$-0.122530\pi$
$29$	0.744307	+	1.28918i	0.138214	+	0.239394i	−0.788606	+	0.614898i	$0.789197\pi$
$30$		0			0
$31$	1.89045	+	0.506544i	0.339534	+	0.0909779i	0.424557	−	0.905401i	$-0.360430\pi$
$31$	1.89045	+	0.506544i	0.339534	+	0.0909779i	−0.0850231	+	0.996379i	$0.527096\pi$
$32$	3.37929	+	3.37929i	0.597380	+	0.597380i
$33$		0			0
$34$	6.23237	+	6.23237i	1.06884	+	1.06884i
$35$	3.08213	−	2.08412i	0.520975	−	0.352281i
$36$		0			0
$37$	6.70890	−	6.70890i	1.10294	−	1.10294i	0.108882	−	0.994055i	$-0.465273\pi$
$37$	6.70890	−	6.70890i	1.10294	−	1.10294i	0.994055	−	0.108882i	$-0.0347270\pi$
$38$	4.13437	+	7.16094i	0.670684	+	1.16166i
$39$		0			0
$40$	−2.27106	−	1.31120i	−0.359086	−	0.207318i
$41$	−6.34762	−	1.70084i	−0.991331	−	0.265626i	−0.273522	−	0.961866i	$-0.588188\pi$
$41$	−6.34762	−	1.70084i	−0.991331	−	0.265626i	−0.717810	+	0.696239i	$0.754855\pi$
$42$		0			0
$43$	−7.27334	−	4.19927i	−1.10917	−	0.640382i	−0.170559	−	0.985347i	$-0.554557\pi$
$43$	−7.27334	−	4.19927i	−1.10917	−	0.640382i	−0.938615	+	0.344965i	$0.887891\pi$
$44$	1.32735	−	0.355661i	0.200105	−	0.0536179i
$45$		0			0
$46$	−2.59143	+	2.59143i	−0.382085	+	0.382085i
$47$	−6.20311	+	1.66212i	−0.904817	+	0.242445i	−0.681084	−	0.732206i	$-0.738491\pi$
$47$	−6.20311	+	1.66212i	−0.904817	+	0.242445i	−0.223733	+	0.974650i	$0.571824\pi$
$48$		0			0
$49$	−5.50607	+	4.32240i	−0.786582	+	0.617486i
$50$	4.97684	+	1.33354i	0.703832	+	0.188591i
$51$		0			0
$52$	−3.02128	−	1.24310i	−0.418976	−	0.172387i
$53$	−1.87579	−	3.24897i	−0.257660	−	0.446280i	0.707955	−	0.706258i	$-0.249618\pi$
$53$	−1.87579	−	3.24897i	−0.257660	−	0.446280i	−0.965615	+	0.259978i	$0.916285\pi$
$54$		0			0
$55$	−1.84696	+	1.06635i	−0.249045	+	0.143786i
$56$	4.43695	+	2.15769i	0.592913	+	0.288333i
$57$		0			0
$58$	−0.656802	+	2.45122i	−0.0862423	+	0.321861i
$59$	5.98603	+	5.98603i	0.779315	+	0.779315i	0.979714	−	0.200399i	$-0.0642239\pi$
$59$	5.98603	+	5.98603i	0.779315	+	0.779315i	−0.200399	+	0.979714i	$0.564224\pi$
$60$		0			0
$61$	−2.79969	+	1.61640i	−0.358463	+	0.206959i	−0.668407	−	0.743796i	$-0.733023\pi$
$61$	−2.79969	+	1.61640i	−0.358463	+	0.206959i	0.309943	+	0.950755i	$0.399690\pi$
$62$	1.66819	+	2.88940i	0.211861	+	0.366954i
$63$		0			0
$64$		−	1.83539i		−	0.229423i
$65$	5.02854	+	0.649937i	0.623713	+	0.0806147i
$66$		0			0
$67$	−12.5811	+	3.37110i	−1.53703	+	0.411845i	−0.925304	−	0.379227i	$-0.876190\pi$
$67$	−12.5811	+	3.37110i	−1.53703	+	0.411845i	−0.611723	+	0.791072i	$0.709523\pi$
$68$			4.68481i			0.568117i
$69$		0			0
$70$	6.22754	+	1.20302i	0.744333	+	0.143789i
$71$	2.71213	−	0.726713i	0.321870	−	0.0862449i	−0.0942662	−	0.995547i	$-0.530050\pi$
$71$	2.71213	−	0.726713i	0.321870	−	0.0862449i	0.416137	+	0.909302i	$0.363384\pi$
$72$		0			0
$73$	−3.82844	+	14.2879i	−0.448085	+	1.67228i	0.259574	+	0.965723i	$0.416418\pi$
$73$	−3.82844	+	14.2879i	−0.448085	+	1.67228i	−0.707660	+	0.706554i	$0.750249\pi$
$74$	16.1742			1.88021
$75$		0			0
$76$	−1.13752	+	4.24529i	−0.130483	+	0.486968i
$77$	3.32387	−	2.24759i	0.378790	−	0.256136i
$78$		0			0
$79$	3.67744	−	6.36951i	0.413744	−	0.716626i	−0.581551	−	0.813510i	$-0.697554\pi$
$79$	3.67744	−	6.36951i	0.413744	−	0.716626i	0.995296	+	0.0968836i	$0.0308874\pi$
$80$	−1.81663	−	6.77977i	−0.203106	−	0.758001i
$81$		0			0
$82$	−5.60135	−	9.70182i	−0.618566	−	1.07139i
$83$	−0.0684765	+	0.0684765i	−0.00751627	+	0.00751627i	−0.710855	−	0.703339i	$-0.751692\pi$
$83$	−0.0684765	+	0.0684765i	−0.00751627	+	0.00751627i	0.703339	+	0.710855i	$0.251692\pi$
$84$		0			0
$85$	−1.88181	−	7.02301i	−0.204111	−	0.761753i
$86$	−3.70557	−	13.8294i	−0.399582	−	1.49126i
$87$		0			0
$88$	−2.44918	−	1.41404i	−0.261084	−	0.150737i
$89$	−7.89157	−	7.89157i	−0.836505	−	0.836505i	0.151892	−	0.988397i	$-0.451463\pi$
$89$	−7.89157	−	7.89157i	−0.836505	−	0.836505i	−0.988397	+	0.151892i	$0.951463\pi$
$90$		0			0
$91$	−9.52359	−	0.548833i	−0.998344	−	0.0575333i
$92$	−1.94795			−0.203088
$93$		0			0
$94$	−9.48096	−	5.47383i	−0.977886	−	0.564583i
$95$		−	6.82105i		−	0.699825i
$96$		0			0
$97$	−3.39415	−	12.6671i	−0.344624	−	1.28615i	−0.893051	−	0.449955i	$-0.851440\pi$
$97$	−3.39415	−	12.6671i	−0.344624	−	1.28615i	0.548428	−	0.836198i	$-0.315227\pi$
$98$	−11.8475	−	1.42683i	−1.19678	−	0.144131i
$99$		0			0
$100$	1.36932	+	2.37173i	0.136932	+	0.237173i
$101$	−8.59776	+	14.8918i	−0.855509	+	1.48179i	0.0206627	+	0.999787i	$0.493422\pi$
$101$	−8.59776	+	14.8918i	−0.855509	+	1.48179i	−0.876172	+	0.481999i	$0.839911\pi$
$102$		0			0
$103$	0.176474	−	0.305661i	0.0173885	−	0.0301177i	−0.857200	−	0.514983i	$-0.827798\pi$
$103$	0.176474	−	0.305661i	0.0173885	−	0.0301177i	0.874589	+	0.484866i	$0.161131\pi$
$104$	2.58768	+	6.20570i	0.253743	+	0.608519i
$105$		0			0
$106$	1.65526	−	6.17753i	0.160773	−	0.600014i
$107$	−13.4093			−1.29633			−0.648164	−	0.761500i	$-0.724463\pi$
$107$	−13.4093			−1.29633			−0.648164	+	0.761500i	$0.724463\pi$
$108$		0			0
$109$	2.54648	−	9.50358i	0.243908	−	0.910277i	−0.730021	−	0.683425i	$-0.760490\pi$
$109$	2.54648	−	9.50358i	0.243908	−	0.910277i	0.973929	−	0.226853i	$-0.0728436\pi$
$110$	−3.51178	−	0.940979i	−0.334835	−	0.0897188i
$111$		0			0
$112$	4.31373	+	12.4810i	0.407610	+	1.17934i
$113$	−0.325800	+	0.564301i	−0.0306486	+	0.0530850i	−0.880943	−	0.473223i	$-0.843091\pi$
$113$	−0.325800	+	0.564301i	−0.0306486	+	0.0530850i	0.850294	+	0.526308i	$0.176424\pi$
$114$		0			0
$115$	2.92018	−	0.782460i	0.272308	−	0.0729647i
$116$	−1.16813	+	0.674422i	−0.108458	+	0.0626185i
$117$		0			0
$118$			14.4315i			1.32852i
$119$	4.46850	+	12.9288i	0.409627	+	1.18518i
$120$		0			0
$121$	7.53445	−	4.35002i	0.684950	−	0.395456i
$122$	−5.32327	−	1.42637i	−0.481947	−	0.129137i
$123$		0			0
$124$	−0.458983	+	1.71295i	−0.0412179	+	0.153827i
$125$	−7.97733	−	7.97733i	−0.713514	−	0.713514i
$126$		0			0
$127$	−1.63609	+	0.944595i	−0.145179	+	0.0838192i	−0.570830	−	0.821068i	$-0.693378\pi$
$127$	−1.63609	+	0.944595i	−0.145179	+	0.0838192i	0.425651	+	0.904887i	$0.360045\pi$
$128$	8.97101	−	8.97101i	0.792933	−	0.792933i
$129$		0			0
$130$	5.27808	+	6.84498i	0.462918	+	0.600345i
$131$	−8.89476	−	5.13539i	−0.777139	−	0.448681i	0.0582763	−	0.998300i	$-0.481440\pi$
$131$	−8.89476	−	5.13539i	−0.777139	−	0.448681i	−0.835415	+	0.549619i	$0.814773\pi$
$132$		0			0
$133$	0.910028	+	12.8008i	0.0789095	+	1.10997i
$134$	−19.2292	−	11.1020i	−1.66115	−	0.959066i
$135$		0			0
$136$	6.81754	−	6.81754i	0.584599	−	0.584599i
$137$	−6.59189	+	6.59189i	−0.563183	+	0.563183i	−0.930210	−	0.367027i	$-0.880376\pi$
$137$	−6.59189	+	6.59189i	−0.563183	+	0.563183i	0.367027	+	0.930210i	$0.380376\pi$
$138$		0			0
$139$	0.141825	+	0.0818824i	0.0120294	+	0.00694518i	0.506003	−	0.862532i	$-0.331123\pi$
$139$	0.141825	+	0.0818824i	0.0120294	+	0.00694518i	−0.493973	+	0.869477i	$0.664456\pi$
$140$	1.88844	+	2.79274i	0.159602	+	0.236030i
$141$		0			0
$142$	4.14527	+	2.39327i	0.347863	+	0.200839i
$143$	5.42294	+	0.700913i	0.453489	+	0.0586133i
$144$		0			0
$145$	1.48025	−	1.48025i	0.122928	−	0.122928i
$146$	−21.8380	+	12.6082i	−1.80732	+	1.04346i
$147$		0			0
$148$	6.07899	+	6.07899i	0.499690	+	0.499690i
$149$	5.39257	−	20.1254i	0.441777	−	1.64873i	−0.282532	−	0.959258i	$-0.591174\pi$
$149$	5.39257	−	20.1254i	0.441777	−	1.64873i	0.724309	−	0.689476i	$-0.242159\pi$
$150$		0			0
$151$	3.50140	+	0.938197i	0.284940	+	0.0763494i	0.398458	−	0.917187i	$-0.369545\pi$
$151$	3.50140	+	0.938197i	0.284940	+	0.0763494i	−0.113518	+	0.993536i	$0.536212\pi$
$152$	7.83330	−	4.52256i	0.635365	−	0.366828i
$153$		0			0
$154$	6.71598	+	1.29738i	0.541189	+	0.104546i
$155$		−	2.75225i		−	0.221066i
$156$		0			0
$157$	12.8664	−	7.42842i	1.02685	−	0.592852i	0.110770	−	0.993846i	$-0.464668\pi$
$157$	12.8664	−	7.42842i	1.02685	−	0.592852i	0.916081	+	0.400994i	$0.131335\pi$
$158$	12.1109	−	3.24510i	0.963489	−	0.258166i
$159$		0			0
$160$	3.36030	−	5.82021i	0.265655	−	0.460128i
$161$	−5.37581	+	1.85801i	−0.423673	+	0.146432i
$162$		0			0
$163$	−15.5228	−	4.15931i	−1.21584	−	0.325782i	−0.406787	−	0.913523i	$-0.633351\pi$
$163$	−15.5228	−	4.15931i	−1.21584	−	0.325782i	−0.809050	+	0.587740i	$0.800018\pi$
$164$	1.54114	−	5.75162i	0.120343	−	0.449126i
$165$		0			0
$166$	−0.165087			−0.0128132
$167$	−3.41310	+	12.7379i	−0.264114	+	0.985686i	0.698677	+	0.715438i	$0.253773\pi$
$167$	−3.41310	+	12.7379i	−0.264114	+	0.985686i	−0.962791	+	0.270249i	$0.912894\pi$
$168$		0			0
$169$	−9.23572	−	9.14885i	−0.710440	−	0.703758i
$170$	6.19734	−	10.7341i	0.475315	−	0.823269i
$171$		0			0
$172$	3.80499	−	6.59043i	0.290128	−	0.502516i
$173$	7.01638	+	12.1527i	0.533445	+	0.923954i	0.999237	+	0.0390600i	$0.0124363\pi$
$173$	7.01638	+	12.1527i	0.533445	+	0.923954i	−0.465791	+	0.884895i	$0.654230\pi$
$174$		0			0
$175$	6.04116	+	5.23922i	0.456668	+	0.396048i
$176$	−1.95912	−	7.31152i	−0.147674	−	0.551127i
$177$		0			0
$178$		−	19.0254i		−	1.42602i
$179$	15.5849	+	8.99797i	1.16487	+	0.672540i	0.952467	−	0.304642i	$-0.0985368\pi$
$179$	15.5849	+	8.99797i	1.16487	+	0.672540i	0.212406	+	0.977182i	$0.431870\pi$
$180$		0			0
$181$	14.8428			1.10325			0.551627	−	0.834091i	$-0.314007\pi$
$181$	14.8428			1.10325			0.551627	+	0.834091i	$0.314007\pi$
$182$	−10.8184	−	12.1416i	−0.801914	−	0.899993i
$183$		0			0
$184$	2.83474	+	2.83474i	0.208980	+	0.208980i
$185$	−11.5549	−	6.67120i	−0.849530	−	0.490476i
$186$		0			0
$187$	−2.02941	−	7.57385i	−0.148405	−	0.553854i
$188$	−1.50606	−	5.62069i	−0.109841	−	0.409931i
$189$		0			0
$190$	8.22228	−	8.22228i	0.596507	−	0.596507i
$191$	7.23283	+	12.5276i	0.523349	+	0.906468i	0.999631	+	0.0271748i	$0.00865108\pi$
$191$	7.23283	+	12.5276i	0.523349	+	0.906468i	−0.476281	+	0.879293i	$0.658016\pi$
$192$		0			0
$193$	4.69718	+	17.5301i	0.338111	+	1.26185i	0.900457	+	0.434945i	$0.143232\pi$
$193$	4.69718	+	17.5301i	0.338111	+	1.26185i	−0.562346	+	0.826902i	$0.690101\pi$
$194$	11.1779	−	19.3607i	0.802527	−	1.39002i
$195$		0			0
$196$	−3.91656	−	4.98909i	−0.279754	−	0.356364i
$197$	6.18216	−	23.0721i	0.440460	−	1.64382i	−0.287191	−	0.957873i	$-0.592721\pi$
$197$	6.18216	−	23.0721i	0.440460	−	1.64382i	0.727651	−	0.685947i	$-0.240612\pi$
$198$		0			0
$199$	2.98353			0.211497			0.105749	−	0.994393i	$-0.466276\pi$
$199$	2.98353			0.211497			0.105749	+	0.994393i	$0.466276\pi$
$200$	1.45875	−	5.44413i	0.103149	−	0.384958i
$201$		0			0
$202$	−28.3149	+	7.58695i	−1.99223	+	0.533816i
$203$	−2.58044	+	2.97542i	−0.181112	+	0.208833i
$204$		0			0
$205$			9.24133i			0.645442i
$206$	0.581178	−	0.155726i	0.0404926	−	0.0108500i
$207$		0			0
$208$	−6.84746	+	16.6423i	−0.474786	+	1.15394i
$209$		−	7.35604i		−	0.508828i
$210$		0			0
$211$	−2.05578	−	3.56072i	−0.141526	−	0.245130i	0.786546	−	0.617532i	$-0.211867\pi$
$211$	−2.05578	−	3.56072i	−0.141526	−	0.245130i	−0.928071	+	0.372402i	$0.878534\pi$
$212$	2.94392	−	1.69967i	0.202189	−	0.116734i
$213$		0			0
$214$	−16.1640	−	16.1640i	−1.10495	−	1.10495i
$215$	−3.05680	+	11.4081i	−0.208472	+	0.778028i
$216$		0			0
$217$	0.367191	+	5.16506i	0.0249265	+	0.350627i
$218$	14.5255	−	8.38628i	0.983788	−	0.567990i
$219$		0			0
$220$	−0.966224	−	1.67355i	−0.0651428	−	0.112831i
$221$	−7.09313	+	17.2394i	−0.477136	+	1.15965i
$222$		0			0
$223$	−16.9482	−	4.54125i	−1.13493	−	0.304105i	−0.358022	−	0.933713i	$-0.616549\pi$
$223$	−16.9482	−	4.54125i	−1.13493	−	0.304105i	−0.776912	+	0.629609i	$0.783215\pi$
$224$	−5.52966	+	11.3709i	−0.369466	+	0.759751i
$225$		0			0
$226$	−1.07295	+	0.287496i	−0.0713717	+	0.0191240i
$227$	4.90655	−	4.90655i	0.325659	−	0.325659i	−0.525274	−	0.850933i	$-0.676037\pi$
$227$	4.90655	−	4.90655i	0.325659	−	0.325659i	0.850933	+	0.525274i	$0.176037\pi$
$228$		0			0
$229$	8.65510	−	2.31913i	0.571945	−	0.153252i	0.0387566	−	0.999249i	$-0.487660\pi$
$229$	8.65510	−	2.31913i	0.571945	−	0.153252i	0.533189	+	0.845996i	$0.320994\pi$
$230$	4.46326	+	2.57686i	0.294299	+	0.169913i
$231$		0			0
$232$	2.68137	+	0.718470i	0.176040	+	0.0471699i
$233$	−5.51653	−	3.18497i	−0.361400	−	0.208654i	0.308295	−	0.951291i	$-0.400242\pi$
$233$	−5.51653	−	3.18497i	−0.361400	−	0.208654i	−0.669695	+	0.742636i	$0.733575\pi$
$234$		0			0
$235$	4.51547	+	7.82103i	0.294557	+	0.510188i
$236$	−5.42399	+	5.42399i	−0.353072	+	0.353072i
$237$		0			0
$238$	−10.1983	+	20.9712i	−0.661055	+	1.35936i
$239$	11.4926	+	11.4926i	0.743396	+	0.743396i	0.973230	−	0.229834i	$-0.0738183\pi$
$239$	11.4926	+	11.4926i	0.743396	+	0.743396i	−0.229834	+	0.973230i	$0.573818\pi$
$240$		0			0
$241$	−0.164298	−	0.164298i	−0.0105834	−	0.0105834i	0.701795	−	0.712379i	$-0.252382\pi$
$241$	−0.164298	−	0.164298i	−0.0105834	−	0.0105834i	−0.712379	+	0.701795i	$0.752382\pi$
$242$	14.3259	+	3.83860i	0.920901	+	0.246755i
$243$		0			0
$244$	−1.46463	−	2.53682i	−0.0937636	−	0.162403i
$245$	7.87537	+	5.90595i	0.503139	+	0.377317i
$246$		0			0
$247$	−10.6136	+	13.8998i	−0.675326	+	0.884421i
$248$	3.16069	−	1.82482i	0.200704	−	0.115876i
$249$		0			0
$250$		−	19.2322i		−	1.21635i
$251$	−4.39247	+	7.60798i	−0.277250	+	0.480211i	−0.970700	−	0.240293i	$-0.922756\pi$
$251$	−4.39247	+	7.60798i	−0.277250	+	0.480211i	0.693450	+	0.720504i	$0.256090\pi$
$252$		0			0
$253$	3.14922	−	0.843830i	0.197989	−	0.0530511i
$254$	−3.11082	−	0.833542i	−0.195190	−	0.0523011i
$255$		0			0
$256$	17.9570			1.12231
$257$	−22.7247			−1.41753			−0.708763	−	0.705447i	$-0.750746\pi$
$257$	−22.7247			−1.41753			−0.708763	+	0.705447i	$0.750746\pi$
$258$		0			0
$259$	22.5746	+	10.9780i	1.40272	+	0.682141i
$260$	−0.588913	+	4.55640i	−0.0365228	+	0.282576i
$261$		0			0
$262$	−4.53164	−	16.9123i	−0.279966	−	1.04485i
$263$	−4.09771	+	7.09745i	−0.252676	+	0.437647i	−0.964262	−	0.264952i	$-0.914644\pi$
$263$	−4.09771	+	7.09745i	−0.252676	+	0.437647i	0.711586	+	0.702599i	$0.247977\pi$
$264$		0			0
$265$	−3.73050	+	3.73050i	−0.229163	+	0.229163i
$266$	−14.3335	+	16.5274i	−0.878843	+	1.01336i
$267$		0			0
$268$	−3.05458	−	11.3998i	−0.186588	−	0.696356i
$269$		−	24.5019i		−	1.49391i	−0.664875	−	0.746954i	$-0.731515\pi$
$269$		−	24.5019i		−	1.49391i	0.664875	−	0.746954i	$-0.268485\pi$
$270$		0			0
$271$	−5.87162	−	5.87162i	−0.356675	−	0.356675i	0.505910	−	0.862586i	$-0.331157\pi$
$271$	−5.87162	−	5.87162i	−0.356675	−	0.356675i	−0.862586	+	0.505910i	$0.831157\pi$
$272$	25.8057			1.56470
$273$		0			0
$274$	−15.8921			−0.960076
$275$	−3.24115	−	3.24115i	−0.195449	−	0.195449i
$276$		0			0
$277$		−	1.49932i		−	0.0900852i	−0.998985	−	0.0450426i	$-0.985658\pi$
$277$		−	1.49932i		−	0.0900852i	0.998985	−	0.0450426i	$-0.0143424\pi$
$278$	0.0722558	+	0.269662i	0.00433362	+	0.0161733i
$279$		0			0
$280$	1.31598	−	6.81226i	0.0786447	−	0.407110i
$281$	−19.5020	+	19.5020i	−1.16339	+	1.16339i	−0.179665	+	0.983728i	$0.557501\pi$
$281$	−19.5020	+	19.5020i	−1.16339	+	1.16339i	−0.983728	+	0.179665i	$0.942499\pi$
$282$		0			0
$283$	−7.83136	+	13.5643i	−0.465526	+	0.806315i	−0.999225	−	0.0393597i	$-0.987468\pi$
$283$	−7.83136	+	13.5643i	−0.465526	+	0.806315i	0.533699	+	0.845674i	$0.320802\pi$
$284$	0.658480	+	2.45748i	0.0390736	+	0.145825i
$285$		0			0
$286$	5.69205	+	7.38185i	0.336578	+	0.436498i
$287$	−1.23293	−	17.3429i	−0.0727775	−	1.02372i
$288$		0			0
$289$	9.73158			0.572446
$290$	3.56866			0.209559
$291$		0			0
$292$	−12.9464	−	3.46898i	−0.757631	−	0.203007i
$293$	−13.6614	+	3.66056i	−0.798107	+	0.213852i	−0.634753	−	0.772715i	$-0.718898\pi$
$293$	−13.6614	+	3.66056i	−0.798107	+	0.213852i	−0.163354	+	0.986567i	$0.552231\pi$
$294$		0			0
$295$	5.95239	−	10.3098i	0.346562	−	0.600263i
$296$		−	17.6928i		−	1.02837i
$297$		0			0
$298$	30.7600	−	17.7593i	1.78188	−	1.02877i
$299$	−7.16818	−	2.94933i	−0.414546	−	0.170564i
$300$		0			0
$301$	4.21458	−	21.8171i	0.242924	−	1.25752i
$302$	3.08975	+	5.35161i	0.177795	+	0.307950i
$303$		0			0
$304$	23.3847	+	6.26590i	1.34120	+	0.359374i
$305$	3.21464	+	3.21464i	0.184069	+	0.184069i
$306$		0			0
$307$	0.977336	+	0.977336i	0.0557795	+	0.0557795i	0.734446	−	0.678667i	$-0.237442\pi$
$307$	0.977336	+	0.977336i	0.0557795	+	0.0557795i	−0.678667	+	0.734446i	$0.737442\pi$
$308$	2.03655	+	3.01178i	0.116043	+	0.171612i
$309$		0			0
$310$	3.31764	−	3.31764i	0.188429	−	0.188429i
$311$	4.20663	+	7.28609i	0.238536	+	0.413156i	0.960294	−	0.278989i	$-0.0899992\pi$
$311$	4.20663	+	7.28609i	0.238536	+	0.413156i	−0.721759	+	0.692145i	$0.756666\pi$
$312$		0			0
$313$	−14.4104	−	8.31988i	−0.814527	−	0.470267i	0.0339987	−	0.999422i	$-0.489176\pi$
$313$	−14.4104	−	8.31988i	−0.814527	−	0.470267i	−0.848525	+	0.529155i	$0.822509\pi$
$314$	24.4639	+	6.55509i	1.38058	+	0.369925i
$315$		0			0
$316$	5.77146	+	3.33216i	0.324670	+	0.187448i
$317$	8.06223	−	2.16027i	0.452820	−	0.121333i	−0.0251986	−	0.999682i	$-0.508022\pi$
$317$	8.06223	−	2.16027i	0.452820	−	0.121333i	0.478019	+	0.878350i	$0.341355\pi$
$318$		0			0
$319$	1.59635	−	1.59635i	0.0893783	−	0.0893783i
$320$	−2.49310	+	0.668023i	−0.139368	+	0.0373436i
$321$		0			0
$322$	−8.71984	−	4.24045i	−0.485937	−	0.236311i
$323$	24.2237	+	6.49071i	1.34784	+	0.361153i
$324$		0			0
$325$	1.44793	+	10.8009i	0.0803166	+	0.599124i
$326$	−13.6978	−	23.7253i	−0.758652	−	1.31402i
$327$		0			0
$328$	−10.6128	+	6.12727i	−0.585991	+	0.338322i
$329$	−9.51747	−	14.0750i	−0.524715	−	0.775981i
$330$		0			0
$331$	1.91640	−	7.15210i	0.105335	−	0.393115i	−0.893048	−	0.449961i	$-0.851438\pi$
$331$	1.91640	−	7.15210i	0.105335	−	0.393115i	0.998383	+	0.0568462i	$0.0181045\pi$
$332$	−0.0620471	−	0.0620471i	−0.00340528	−	0.00340528i
$333$		0			0
$334$	−19.4688	+	11.2403i	−1.06529	+	0.615043i
$335$	9.15825	+	15.8626i	0.500369	+	0.866664i
$336$		0			0
$337$			27.7667i			1.51255i	0.654256	+	0.756273i	$0.272982\pi$
$337$			27.7667i			1.51255i	−0.654256	+	0.756273i	$0.727018\pi$
$338$	−0.104718	−	22.1613i	−0.00569593	−	1.20541i
$339$		0			0
$340$	6.36361	−	1.70512i	0.345115	−	0.0924733i
$341$		−	2.96812i		−	0.160733i
$342$		0			0
$343$	−15.5674	−	10.0328i	−0.840559	−	0.541720i
$344$	−15.1279	+	4.05350i	−0.815640	+	0.218550i
$345$		0			0
$346$	−6.19149	+	23.1070i	−0.332856	+	1.24224i
$347$	10.8321			0.581499			0.290750	−	0.956799i	$-0.406095\pi$
$347$	10.8321			0.581499			0.290750	+	0.956799i	$0.406095\pi$
$348$		0			0
$349$	0.622157	−	2.32192i	0.0333033	−	0.124290i	−0.947273	−	0.320428i	$-0.896173\pi$
$349$	0.622157	−	2.32192i	0.0333033	−	0.124290i	0.980576	+	0.196138i	$0.0628401\pi$
$350$	0.966677	+	13.5977i	0.0516710	+	0.726826i
$351$		0			0
$352$	3.62386	−	6.27671i	0.193152	−	0.334550i
$353$	−3.11894	−	11.6401i	−0.166005	−	0.619538i	−0.997910	−	0.0646202i	$-0.979416\pi$
$353$	−3.11894	−	11.6401i	−0.166005	−	0.619538i	0.831905	−	0.554918i	$-0.187250\pi$
$354$		0			0
$355$	−1.97426	−	3.41952i	−0.104783	−	0.181489i
$356$	7.15062	−	7.15062i	0.378982	−	0.378982i
$357$		0			0
$358$	7.94011	+	29.6329i	0.419648	+	1.56615i
$359$	7.12307	+	26.5837i	0.375941	+	1.40303i	0.851965	+	0.523599i	$0.175411\pi$
$359$	7.12307	+	26.5837i	0.375941	+	1.40303i	−0.476023	+	0.879433i	$0.657922\pi$
$360$		0			0
$361$	3.92054	+	2.26352i	0.206344	+	0.119133i
$362$	17.8919	+	17.8919i	0.940376	+	0.940376i
$363$		0			0
$364$	0.497302	−	8.62940i	0.0260657	−	0.452303i
$365$	20.8014			1.08880
$366$		0			0
$367$	12.2228	+	7.05683i	0.638024	+	0.368363i	0.783853	−	0.620946i	$-0.213252\pi$
$367$	12.2228	+	7.05683i	0.638024	+	0.368363i	−0.145829	+	0.989310i	$0.546585\pi$
$368$			10.7301i			0.559343i
$369$		0			0
$370$	−5.88689	−	21.9702i	−0.306045	−	1.14218i
$371$	6.50320	−	7.49861i	0.337629	−	0.389308i
$372$		0			0
$373$	−14.9945	−	25.9713i	−0.776387	−	1.34474i	−0.934012	−	0.357243i	$-0.883717\pi$
$373$	−14.9945	−	25.9713i	−0.776387	−	1.34474i	0.157624	−	0.987499i	$-0.449616\pi$
$374$	6.68342	−	11.5760i	0.345591	−	0.598582i
$375$		0			0
$376$	−5.98778	+	10.3711i	−0.308796	+	0.534851i
$377$	−5.31969	+	0.713140i	−0.273978	+	0.0367286i
$378$		0			0
$379$	−6.76234	+	25.2374i	−0.347358	+	1.29636i	0.542475	+	0.840072i	$0.317487\pi$
$379$	−6.76234	+	25.2374i	−0.347358	+	1.29636i	−0.889833	+	0.456286i	$0.849179\pi$
$380$	6.18061			0.317058
$381$		0			0
$382$	−6.38250	+	23.8198i	−0.326557	+	1.21873i
$383$	−30.7142	−	8.22985i	−1.56942	−	0.420526i	−0.633792	−	0.773504i	$-0.718502\pi$
$383$	−30.7142	−	8.22985i	−1.56942	−	0.420526i	−0.935632	+	0.352978i	$0.885169\pi$
$384$		0			0
$385$	−4.26279	−	3.69692i	−0.217252	−	0.188413i
$386$	−15.4692	+	26.7934i	−0.787360	+	1.36375i
$387$		0			0
$388$	11.4778	−	3.07546i	0.582697	−	0.156133i
$389$	−12.1261	+	7.00102i	−0.614818	+	0.354966i	−0.774849	−	0.632147i	$-0.782174\pi$
$389$	−12.1261	+	7.00102i	−0.614818	+	0.354966i	0.160030	+	0.987112i	$0.448841\pi$
$390$		0			0
$391$			11.1150i			0.562111i
$392$	−1.56080	+	12.9599i	−0.0788321	+	0.654574i
$393$		0			0
$394$	35.2639	−	20.3596i	1.77657	−	1.02570i
$395$	−9.99049	−	2.67694i	−0.502676	−	0.134692i
$396$		0			0
$397$	−4.60637	+	17.1912i	−0.231187	+	0.862802i	0.748644	+	0.662973i	$0.230705\pi$
$397$	−4.60637	+	17.1912i	−0.231187	+	0.862802i	−0.979831	+	0.199829i	$0.935961\pi$
$398$	3.59643	+	3.59643i	0.180273	+	0.180273i
$399$		0			0
$400$	13.0644	−	7.54272i	0.653218	−	0.377136i
$401$	−1.38205	+	1.38205i	−0.0690162	+	0.0690162i	−0.740772	−	0.671756i	$-0.765540\pi$
$401$	−1.38205	+	1.38205i	−0.0690162	+	0.0690162i	0.671756	+	0.740772i	$0.265540\pi$
$402$		0			0
$403$	−4.28252	+	5.60847i	−0.213327	+	0.279378i
$404$	−13.4935	−	7.79050i	−0.671329	−	0.387592i
$405$		0			0
$406$	−6.69718	+	0.476112i	−0.332376	+	0.0236290i
$407$	−12.4611	−	7.19444i	−0.617675	−	0.356615i
$408$		0			0
$409$	−11.0600	+	11.0600i	−0.546882	+	0.546882i	−0.925538	−	0.378656i	$-0.876387\pi$
$409$	−11.0600	+	11.0600i	−0.546882	+	0.546882i	0.378656	+	0.925538i	$0.376387\pi$
$410$	−11.1397	+	11.1397i	−0.550153	+	0.550153i
$411$		0			0
$412$	0.276962	+	0.159904i	0.0136449	+	0.00787791i
$413$	−9.79517	+	20.1423i	−0.481989	+	0.991136i
$414$		0			0
$415$	0.117938	+	0.0680917i	0.00578936	+	0.00334249i
$416$	−15.9038	+	6.63164i	−0.779749	+	0.325143i
$417$		0			0
$418$	8.86717	−	8.86717i	0.433707	−	0.433707i
$419$	32.1543	−	18.5643i	1.57084	−	0.906924i	0.574772	−	0.818314i	$-0.305091\pi$
$419$	32.1543	−	18.5643i	1.57084	−	0.906924i	0.996066	−	0.0886099i	$-0.0282425\pi$
$420$		0			0
$421$	−23.1846	−	23.1846i	−1.12995	−	1.12995i	−0.990185	−	0.139764i	$-0.955366\pi$
$421$	−23.1846	−	23.1846i	−1.12995	−	1.12995i	−0.139764	−	0.990185i	$-0.544634\pi$
$422$	1.81409	−	6.77028i	0.0883085	−	0.329572i
$423$		0			0
$424$	−6.75755	−	1.81068i	−0.328176	−	0.0879344i
$425$	13.5331	−	7.81334i	0.656451	−	0.379002i
$426$		0			0
$427$	−6.46167	−	5.60391i	−0.312702	−	0.271192i
$428$		−	12.1503i		−	0.587307i
$429$		0			0
$430$	−17.4364	+	10.0669i	−0.840859	+	0.485470i
$431$	15.9999	−	4.28716i	0.770688	−	0.206505i	0.148012	−	0.988986i	$-0.452712\pi$
$431$	15.9999	−	4.28716i	0.770688	−	0.206505i	0.622675	+	0.782480i	$0.286046\pi$
$432$		0			0
$433$	0.814551	−	1.41084i	0.0391448	−	0.0678008i	−0.845789	−	0.533517i	$-0.820870\pi$
$433$	0.814551	−	1.41084i	0.0391448	−	0.0678008i	0.884934	+	0.465716i	$0.154203\pi$
$434$	−5.78347	+	6.66872i	−0.277616	+	0.320109i
$435$		0			0
$436$	8.61126	+	2.30738i	0.412405	+	0.110504i
$437$	−2.69885	+	10.0722i	−0.129103	+	0.481820i
$438$		0			0
$439$	27.9803			1.33543			0.667713	−	0.744419i	$-0.267273\pi$
$439$	27.9803			1.33543			0.667713	+	0.744419i	$0.267273\pi$
$440$	−1.02933	+	3.84151i	−0.0490714	+	0.183137i
$441$		0			0
$442$	−29.3311	+	12.2306i	−1.39514	+	0.581751i
$443$	−12.7182	+	22.0285i	−0.604258	+	1.04661i	0.387910	+	0.921697i	$0.373197\pi$
$443$	−12.7182	+	22.0285i	−0.604258	+	1.04661i	−0.992168	+	0.124908i	$0.960136\pi$
$444$		0			0
$445$	−7.84723	+	13.5918i	−0.371994	+	0.644313i
$446$	−14.9556	−	25.9039i	−0.708170	−	1.22659i
$447$		0			0
$448$	4.58958	−	1.58627i	0.216837	−	0.0749443i
$449$	0.665392	+	2.48328i	0.0314018	+	0.117193i	0.979848	−	0.199746i	$-0.0640116\pi$
$449$	0.665392	+	2.48328i	0.0314018	+	0.117193i	−0.948446	+	0.316939i	$0.897345\pi$
$450$		0			0
$451$			9.96615i			0.469288i
$452$	−0.511318	−	0.295209i	−0.0240504	−	0.0138855i
$453$		0			0
$454$	11.8290			0.555162
$455$	2.72078	+	13.1361i	0.127552	+	0.615831i
$456$		0			0
$457$	−10.0248	−	10.0248i	−0.468940	−	0.468940i	0.432631	−	0.901571i	$-0.357585\pi$
$457$	−10.0248	−	10.0248i	−0.468940	−	0.468940i	−0.901571	+	0.432631i	$0.857585\pi$
$458$	13.2286	+	7.63755i	0.618133	+	0.356879i
$459$		0			0
$460$	0.708993	+	2.64600i	0.0330570	+	0.123370i
$461$	−10.8132	−	40.3552i	−0.503619	−	1.87953i	−0.475089	−	0.879938i	$-0.657584\pi$
$461$	−10.8132	−	40.3552i	−0.503619	−	1.87953i	−0.0285297	−	0.999593i	$-0.509083\pi$
$462$		0			0
$463$	19.6177	−	19.6177i	0.911713	−	0.911713i	−0.0846939	−	0.996407i	$-0.526991\pi$
$463$	19.6177	−	19.6177i	0.911713	−	0.911713i	0.996407	+	0.0846939i	$0.0269912\pi$
$464$	3.71497	+	6.43452i	0.172463	+	0.298715i
$465$		0			0
$466$	−2.81053	−	10.4890i	−0.130195	−	0.485895i
$467$	14.6509	−	25.3761i	0.677962	−	1.17426i	−0.297632	−	0.954681i	$-0.596197\pi$
$467$	14.6509	−	25.3761i	0.677962	−	1.17426i	0.975594	−	0.219584i	$-0.0704700\pi$
$468$		0			0
$469$	−19.3033	−	28.5469i	−0.891342	−	1.31817i
$470$	−3.98461	+	14.8707i	−0.183796	+	0.685937i
$471$		0			0
$472$	15.7865			0.726630
$473$	−3.29655	+	12.3029i	−0.151576	+	0.565688i
$474$		0			0
$475$	14.1606	−	3.79432i	0.649733	−	0.174095i
$476$	−11.7149	+	4.04894i	−0.536950	+	0.185583i
$477$		0			0
$478$			27.7070i			1.26729i
$479$	8.64079	−	2.31529i	0.394808	−	0.105788i	−0.0559526	−	0.998433i	$-0.517820\pi$
$479$	8.64079	−	2.31529i	0.394808	−	0.105788i	0.450760	+	0.892645i	$0.351153\pi$
$480$		0			0
$481$	13.1658	+	31.5738i	0.600308	+	1.43964i
$482$		−	0.396098i		−	0.0180418i
$483$		0			0
$484$	3.94159	+	6.82703i	0.179163	+	0.310319i
$485$	−15.9710	+	9.22088i	−0.725207	+	0.418698i
$486$		0			0
$487$	14.5064	+	14.5064i	0.657346	+	0.657346i	0.954751	−	0.297406i	$-0.0961214\pi$
$487$	14.5064	+	14.5064i	0.657346	+	0.657346i	−0.297406	+	0.954751i	$0.596121\pi$
$488$	−1.56029	+	5.82309i	−0.0706311	+	0.263599i
$489$		0			0
$490$	2.37399	+	16.6124i	0.107246	+	0.750470i
$491$	27.6274	−	15.9507i	1.24681	−	0.719845i	0.276337	−	0.961061i	$-0.410879\pi$
$491$	27.6274	−	15.9507i	1.24681	−	0.719845i	0.970472	+	0.241216i	$0.0775461\pi$
$492$		0			0
$493$	3.84826	+	6.66538i	0.173317	+	0.300194i
$494$	−29.5490	+	3.96125i	−1.32947	+	0.178225i
$495$		0			0
$496$	9.43557	+	2.52825i	0.423669	+	0.113522i
$497$	4.16124	+	6.15389i	0.186657	+	0.276040i
$498$		0			0
$499$	−22.1352	+	5.93111i	−0.990907	+	0.265513i	−0.717632	−	0.696423i	$-0.754774\pi$
$499$	−22.1352	+	5.93111i	−0.990907	+	0.265513i	−0.273276	+	0.961936i	$0.588107\pi$
$500$	7.22832	−	7.22832i	0.323260	−	0.323260i
$501$		0			0
$502$	−14.4657	+	3.87606i	−0.645634	+	0.172997i
$503$	23.9880	+	13.8495i	1.06957	+	0.617518i	0.928065	−	0.372419i	$-0.121472\pi$
$503$	23.9880	+	13.8495i	1.06957	+	0.617518i	0.141508	+	0.989937i	$0.454805\pi$
$504$		0			0
$505$	23.3575	+	6.25863i	1.03940	+	0.278505i
$506$	4.81332	+	2.77897i	0.213978	+	0.123540i
$507$		0			0
$508$	−0.855905	−	1.48247i	−0.0379746	−	0.0657740i
$509$	−30.4769	+	30.4769i	−1.35087	+	1.35087i	−0.466174	+	0.884693i	$0.654368\pi$
$509$	−30.4769	+	30.4769i	−1.35087	+	1.35087i	−0.884693	+	0.466174i	$0.845632\pi$
$510$		0			0
$511$	−39.0373	+	2.77522i	−1.72691	+	0.122768i
$512$	3.70385	+	3.70385i	0.163689	+	0.163689i
$513$		0			0
$514$	−27.3929	−	27.3929i	−1.20825	−	1.20825i
$515$	−0.479425	−	0.128462i	−0.0211260	−	0.00566070i
$516$		0			0
$517$	4.86963	+	8.43445i	0.214166	+	0.370947i
$518$	13.9789	+	40.4453i	0.614196	+	1.77706i
$519$		0			0
$520$	7.48768	−	5.77365i	0.328356	−	0.253191i
$521$	−1.66737	+	0.962655i	−0.0730487	+	0.0421747i	−0.536079	−	0.844168i	$-0.680095\pi$
$521$	−1.66737	+	0.962655i	−0.0730487	+	0.0421747i	0.463031	+	0.886342i	$0.346762\pi$
$522$		0			0
$523$		−	1.27342i		−	0.0556829i	−0.999612	−	0.0278414i	$-0.991137\pi$
$523$		−	1.27342i		−	0.0556829i	0.999612	−	0.0278414i	$-0.00886335\pi$
$524$	4.65322	−	8.05961i	0.203277	−	0.352086i
$525$		0			0
$526$	−13.4949	+	3.61596i	−0.588408	+	0.157663i
$527$	9.77410	+	2.61896i	0.425766	+	0.114084i
$528$		0			0
$529$	18.3784			0.799059
$530$	−8.99370			−0.390661
$531$		0			0
$532$	−11.5989	+	0.824584i	−0.502877	+	0.0357502i
$533$	14.3795	−	18.8317i	0.622847	−	0.815694i
$534$		0			0
$535$	4.88057	+	18.2145i	0.211006	+	0.787483i
$536$	−12.1444	+	21.0347i	−0.524557	+	0.908560i
$537$		0			0
$538$	29.5353	−	29.5353i	1.27336	−	1.27336i
$539$	8.49305	+	6.36917i	0.365822	+	0.274339i
$540$		0			0
$541$	−6.06372	−	22.6301i	−0.260700	−	0.972944i	−0.964830	−	0.262874i	$-0.915330\pi$
$541$	−6.06372	−	22.6301i	−0.260700	−	0.972944i	0.704131	−	0.710070i	$-0.251337\pi$
$542$		−	14.1556i		−	0.608036i
$543$		0			0
$544$	17.4718	+	17.4718i	0.749098	+	0.749098i
$545$	−13.8360			−0.592669
$546$		0			0
$547$	39.4093			1.68502			0.842510	−	0.538680i	$-0.181077\pi$
$547$	39.4093			1.68502			0.842510	+	0.538680i	$0.181077\pi$
$548$	−5.97296	−	5.97296i	−0.255152	−	0.255152i
$549$		0			0
$550$		−	7.81395i		−	0.333188i
$551$	1.86880	+	6.97444i	0.0796134	+	0.297121i
$552$		0			0
$553$	19.1059	+	3.69085i	0.812468	+	0.156951i
$554$	1.80732	−	1.80732i	0.0767855	−	0.0767855i
$555$		0			0
$556$	−0.0741943	+	0.128508i	−0.00314654	+	0.00544997i
$557$	−3.89152	−	14.5233i	−0.164889	−	0.615374i	−0.998054	−	0.0623501i	$-0.980140\pi$
$557$	−3.89152	−	14.5233i	−0.164889	−	0.615374i	0.833165	−	0.553024i	$-0.186526\pi$
$558$		0			0
$559$	23.9802	−	18.4908i	1.01425	−	0.782078i
$560$	15.3835	−	10.4022i	0.650070	−	0.439575i
$561$		0			0
$562$	−47.0165			−1.98327
$563$	17.2519			0.727081			0.363541	−	0.931578i	$-0.381568\pi$
$563$	17.2519			0.727081			0.363541	+	0.931578i	$0.381568\pi$
$564$		0			0
$565$	0.885099	+	0.237161i	0.0372364	+	0.00997746i
$566$	−25.7909	+	6.91066i	−1.08407	+	0.290477i
$567$		0			0
$568$	2.61798	−	4.53448i	0.109848	−	0.190263i
$569$			10.5691i			0.443081i	0.975151	+	0.221540i	$0.0711085\pi$
$569$			10.5691i			0.443081i	−0.975151	+	0.221540i	$0.928892\pi$
$570$		0			0
$571$	−4.73797	+	2.73547i	−0.198278	+	0.114476i	−0.595852	−	0.803094i	$-0.703185\pi$
$571$	−4.73797	+	2.73547i	−0.198278	+	0.114476i	0.397574	+	0.917570i	$0.369852\pi$
$572$	−0.635102	+	4.91376i	−0.0265550	+	0.205455i
$573$		0			0
$574$	19.4194	−	22.3918i	0.810549	−	0.934615i
$575$	3.24880	+	5.62708i	0.135484	+	0.234665i
$576$		0			0
$577$	−19.3289	−	5.17915i	−0.804671	−	0.215611i	−0.167037	−	0.985951i	$-0.553420\pi$
$577$	−19.3289	−	5.17915i	−0.804671	−	0.215611i	−0.637634	+	0.770340i	$0.720087\pi$
$578$	11.7307	+	11.7307i	0.487933	+	0.487933i
$579$		0			0
$580$	1.34126	+	1.34126i	0.0556930	+	0.0556930i
$581$	−0.230415	−	0.112051i	−0.00955923	−	0.00464864i
$582$		0			0
$583$	−4.02310	+	4.02310i	−0.166620	+	0.166620i
$584$	13.7920	+	23.8884i	0.570716	+	0.988508i
$585$		0			0
$586$	−20.8803	−	12.0553i	−0.862559	−	0.497999i
$587$	1.59431	+	0.427193i	0.0658041	+	0.0176321i	0.291571	−	0.956549i	$-0.405822\pi$
$587$	1.59431	+	0.427193i	0.0658041	+	0.0176321i	−0.225767	+	0.974181i	$0.572489\pi$
$588$		0			0
$589$	8.22120	+	4.74651i	0.338748	+	0.195577i
$590$	19.6029	−	5.25259i	0.807040	−	0.216246i
$591$		0			0
$592$	33.4854	−	33.4854i	1.37624	−	1.37624i
$593$	34.8670	−	9.34258i	1.43182	−	0.383654i	0.542156	−	0.840278i	$-0.317608\pi$
$593$	34.8670	−	9.34258i	1.43182	−	0.383654i	0.889660	+	0.456624i	$0.150941\pi$
$594$		0			0
$595$	15.9354	−	10.7755i	0.653288	−	0.441751i
$596$	18.2357	+	4.88625i	0.746965	+	0.200149i
$597$		0			0
$598$	−5.08551	−	12.1959i	−0.207962	−	0.498728i
$599$	5.29544	+	9.17197i	0.216366	+	0.374757i	0.953694	−	0.300778i	$-0.0972463\pi$
$599$	5.29544	+	9.17197i	0.216366	+	0.374757i	−0.737328	+	0.675534i	$0.763913\pi$
$600$		0			0
$601$	−24.1270	+	13.9297i	−0.984160	+	0.568205i	−0.903523	−	0.428539i	$-0.859029\pi$
$601$	−24.1270	+	13.9297i	−0.984160	+	0.568205i	−0.0806362	+	0.996744i	$0.525695\pi$
$602$	31.3793	−	21.2185i	1.27892	−	0.864802i
$603$		0			0
$604$	−0.850107	+	3.17264i	−0.0345904	+	0.129093i
$605$	−8.65115	−	8.65115i	−0.351719	−	0.351719i
$606$		0			0
$607$	19.2975	−	11.1414i	0.783262	−	0.452216i	−0.0543233	−	0.998523i	$-0.517300\pi$
$607$	19.2975	−	11.1414i	0.783262	−	0.452216i	0.837585	+	0.546307i	$0.183967\pi$
$608$	11.5903	+	20.0750i	0.470049	+	0.814148i
$609$		0			0
$610$			7.75001i			0.313789i
$611$	2.96804	−	22.9636i	0.120074	−	0.929007i
$612$		0			0
$613$	−37.2994	+	9.99436i	−1.50651	+	0.403668i	−0.915275	−	0.402831i	$-0.868026\pi$
$613$	−37.2994	+	9.99436i	−1.50651	+	0.403668i	−0.591236	+	0.806499i	$0.701360\pi$
$614$			2.35621i			0.0950890i
$615$		0			0
$616$	1.41919	−	7.34656i	0.0571809	−	0.296001i
$617$	−19.0276	+	5.09843i	−0.766022	+	0.205255i	−0.620613	−	0.784117i	$-0.713116\pi$
$617$	−19.0276	+	5.09843i	−0.766022	+	0.205255i	−0.145409	+	0.989372i	$0.546450\pi$
$618$		0			0
$619$	−9.15720	+	34.1751i	−0.368059	+	1.37361i	0.495167	+	0.868798i	$0.335107\pi$
$619$	−9.15720	+	34.1751i	−0.368059	+	1.37361i	−0.863226	+	0.504817i	$0.831560\pi$
$620$	2.49384			0.100155
$621$		0			0
$622$	−3.71207	+	13.8536i	−0.148840	+	0.555480i
$623$	12.9133	−	26.5542i	0.517359	−	1.06387i
$624$		0			0
$625$	−0.376462	+	0.652052i	−0.0150585	+	0.0260821i
$626$	−7.34174	−	27.3997i	−0.293435	−	1.09511i
$627$		0			0
$628$	6.73095	+	11.6583i	0.268594	+	0.465219i
$629$	34.6868	−	34.6868i	1.38305	−	1.38305i
$630$		0			0
$631$	1.11023	+	4.14343i	0.0441976	+	0.164948i	0.984497	−	0.175400i	$-0.0561219\pi$
$631$	1.11023	+	4.14343i	0.0441976	+	0.164948i	−0.940300	+	0.340348i	$0.889455\pi$
$632$	−3.54979	−	13.2480i	−0.141203	−	0.526976i
$633$		0			0
$634$	12.3225	+	7.11439i	0.489388	+	0.282548i
$635$	1.87857	+	1.87857i	0.0745489	+	0.0745489i
$636$		0			0
$637$	−6.85854	−	24.2891i	−0.271745	−	0.962369i
$638$	3.84856			0.152366
$639$		0			0
$640$	−15.4509	−	8.92060i	−0.610752	−	0.352618i
$641$		−	35.3132i		−	1.39479i	−0.716689	−	0.697393i	$-0.754343\pi$
$641$		−	35.3132i		−	1.39479i	0.716689	−	0.697393i	$-0.245657\pi$
$642$		0			0
$643$	−2.90713	−	10.8495i	−0.114646	−	0.427864i	0.884614	−	0.466323i	$-0.154422\pi$
$643$	−2.90713	−	10.8495i	−0.114646	−	0.427864i	−0.999260	+	0.0384591i	$0.987755\pi$
$644$	−1.68356	−	4.87106i	−0.0663414	−	0.191947i
$645$		0			0
$646$	21.3758	+	37.0239i	0.841019	+	1.45669i
$647$	−6.78354	+	11.7494i	−0.266689	+	0.461918i	−0.968005	−	0.250932i	$-0.919263\pi$
$647$	−6.78354	+	11.7494i	−0.266689	+	0.461918i	0.701316	+	0.712851i	$0.252596\pi$
$648$		0			0
$649$	6.41925	−	11.1185i	0.251978	−	0.436438i
$650$	−11.2743	+	14.7650i	−0.442213	+	0.579131i
$651$		0			0
$652$	3.76878	−	14.0653i	0.147597	−	0.550839i
$653$	14.6552			0.573501			0.286751	−	0.958005i	$-0.407425\pi$
$653$	14.6552			0.573501			0.286751	+	0.958005i	$0.407425\pi$
$654$		0			0
$655$	−3.73824	+	13.9513i	−0.146065	+	0.545123i
$656$	−31.6821	−	8.48920i	−1.23698	−	0.331448i
$657$		0			0
$658$	5.49379	−	28.4390i	0.214170	−	1.10867i
$659$	25.1178	−	43.5054i	0.978452	−	1.69473i	0.310415	−	0.950601i	$-0.399532\pi$
$659$	25.1178	−	43.5054i	0.978452	−	1.69473i	0.668037	−	0.744128i	$-0.267135\pi$
$660$		0			0
$661$	−1.25098	+	0.335198i	−0.0486574	+	0.0130377i	−0.283066	−	0.959101i	$-0.591351\pi$
$661$	−1.25098	+	0.335198i	−0.0486574	+	0.0130377i	0.234408	+	0.972138i	$0.424685\pi$
$662$	10.9314	−	6.31125i	0.424861	−	0.245294i
$663$		0			0
$664$			0.180587i			0.00700814i
$665$	17.0568	−	5.89523i	0.661433	−	0.228607i
$666$		0			0
$667$	−2.77147	+	1.60011i	−0.107312	+	0.0619566i
$668$	−11.5419	−	3.09264i	−0.446569	−	0.119658i
$669$		0			0
$670$	−8.08155	+	30.1607i	−0.312217	+	1.16521i
$671$	3.46677	+	3.46677i	0.133833	+	0.133833i
$672$		0			0
$673$	19.6264	−	11.3313i	0.756543	−	0.436790i	−0.0715103	−	0.997440i	$-0.522782\pi$
$673$	19.6264	−	11.3313i	0.756543	−	0.436790i	0.828053	+	0.560650i	$0.189449\pi$
$674$	−33.4707	+	33.4707i	−1.28924	+	1.28924i
$675$		0			0
$676$	8.28984	−	8.36856i	0.318840	−	0.321868i
$677$	23.6738	+	13.6681i	0.909859	+	0.525307i	0.880386	−	0.474258i	$-0.157284\pi$
$677$	23.6738	+	13.6681i	0.909859	+	0.525307i	0.0294729	+	0.999566i	$0.490617\pi$
$678$		0			0
$679$	28.7421	−	19.4353i	1.10302	−	0.745857i
$680$	−11.7420	−	6.77923i	−0.450284	−	0.259972i
$681$		0			0
$682$	3.57785	−	3.57785i	0.137003	−	0.137003i
$683$	−20.0961	+	20.0961i	−0.768954	+	0.768954i	−0.977922	−	0.208968i	$-0.932989\pi$
$683$	−20.0961	+	20.0961i	−0.768954	+	0.768954i	0.208968	+	0.977922i	$0.432989\pi$
$684$		0			0
$685$	11.3533	+	6.55485i	0.433788	+	0.250448i
$686$	−6.67152	−	30.8591i	−0.254720	−	1.17821i
$687$		0			0
$688$	−36.3026	−	20.9593i	−1.38402	−	0.799066i
$689$	13.4066	−	1.79725i	0.510751	−	0.0684697i
$690$		0			0
$691$	7.07012	−	7.07012i	0.268960	−	0.268960i	−0.559721	−	0.828681i	$-0.689092\pi$
$691$	7.07012	−	7.07012i	0.268960	−	0.268960i	0.828681	+	0.559721i	$0.189092\pi$
$692$	−11.0117	+	6.35759i	−0.418601	+	0.241679i
$693$		0			0
$694$	13.0573	+	13.0573i	0.495650	+	0.495650i
$695$	0.0596052	−	0.222450i	0.00226096	−	0.00843800i
$696$		0			0
$697$	−32.8188	−	8.79378i	−1.24310	−	0.333088i
$698$	3.54887	−	2.04894i	0.134327	−	0.0775536i
$699$		0			0
$700$	−4.74730	+	5.47394i	−0.179431	+	0.206895i
$701$			36.1836i			1.36664i	0.730121	+	0.683318i	$0.239464\pi$
$701$			36.1836i			1.36664i	−0.730121	+	0.683318i	$0.760536\pi$
$702$		0			0
$703$	39.8548	−	23.0102i	1.50315	−	0.867846i
$704$	−2.68864	+	0.720418i	−0.101332	+	0.0271518i
$705$		0			0
$706$	10.2716	−	17.7909i	0.386576	−	0.669569i
$707$	−44.6692	−	8.62911i	−1.67996	−	0.324531i
$708$		0			0
$709$	−30.8750	−	8.27293i	−1.15954	−	0.310697i	−0.372755	−	0.927930i	$-0.621587\pi$
$709$	−30.8750	−	8.27293i	−1.15954	−	0.310697i	−0.786780	+	0.617233i	$0.788253\pi$
$710$	1.74215	−	6.50180i	0.0653818	−	0.244008i
$711$		0			0
$712$	−20.8118			−0.779954
$713$	−1.08897	+	4.06408i	−0.0407822	+	0.152201i
$714$		0			0
$715$	−1.02169	−	7.62135i	−0.0382092	−	0.285022i
$716$	−8.15313	+	14.1216i	−0.304697	+	0.527750i
$717$		0			0
$718$	−23.4583	+	40.6310i	−0.875457	+	1.51634i
$719$	10.5168	+	18.2157i	0.392212	+	0.679330i	0.992741	−	0.120272i	$-0.0383768\pi$
$719$	10.5168	+	18.2157i	0.392212	+	0.679330i	−0.600529	+	0.799603i	$0.705043\pi$
$720$		0			0
$721$	0.916860	+	0.177117i	0.0341456	+	0.00659619i
$722$	1.99741	+	7.45444i	0.0743359	+	0.277425i
$723$		0			0
$724$			13.4491i			0.499833i
$725$	3.89643	+	2.24961i	0.144710	+	0.0835482i
$726$		0			0
$727$	−31.1689			−1.15599			−0.577995	−	0.816040i	$-0.696165\pi$
$727$	−31.1689			−1.15599			−0.577995	+	0.816040i	$0.696165\pi$
$728$	−13.2816	+	11.8342i	−0.492248	+	0.438604i
$729$		0			0
$730$	25.0746	+	25.0746i	0.928053	+	0.928053i
$731$	−37.6051	−	21.7113i	−1.39087	−	0.803021i
$732$		0			0
$733$	1.40351	+	5.23797i	0.0518398	+	0.193469i	0.986990	−	0.160783i	$-0.0514021\pi$
$733$	1.40351	+	5.23797i	0.0518398	+	0.193469i	−0.935150	+	0.354252i	$0.884735\pi$
$734$	6.22718	+	23.2402i	0.229849	+	0.857810i
$735$		0			0
$736$	−7.26481	+	7.26481i	−0.267784	+	0.267784i
$737$	9.87655	+	17.1067i	0.363807	+	0.630133i
$738$		0			0
$739$	7.93352	+	29.6083i	0.291839	+	1.08916i	0.943695	+	0.330816i	$0.107324\pi$
$739$	7.93352	+	29.6083i	0.291839	+	1.08916i	−0.651856	+	0.758343i	$0.726009\pi$
$740$	6.04482	−	10.4699i	0.222212	−	0.384883i
$741$		0			0
$742$	16.8782	−	1.19989i	0.619617	−	0.0440494i
$743$	1.70775	−	6.37341i	0.0626512	−	0.233818i	−0.927499	−	0.373825i	$-0.878046\pi$
$743$	1.70775	−	6.37341i	0.0626512	−	0.233818i	0.990150	+	0.140008i	$0.0447127\pi$
$744$		0			0
$745$	−29.3000			−1.07347
$746$	13.2317	−	49.3813i	0.484446	−	1.80798i
$747$		0			0
$748$	6.86272	−	1.83886i	0.250926	−	0.0672354i
$749$	−11.5893	−	33.5315i	−0.423463	−	1.22521i
$750$		0			0
$751$			8.46455i			0.308876i	0.988002	+	0.154438i	$0.0493567\pi$
$751$			8.46455i			0.308876i	−0.988002	+	0.154438i	$0.950643\pi$
$752$	−30.9609	+	8.29594i	−1.12903	+	0.302522i
$753$		0			0
$754$	−7.27213	−	5.55285i	−0.264835	−	0.202223i
$755$		−	5.09759i		−	0.185520i
$756$		0			0
$757$	13.5330	+	23.4399i	0.491866	+	0.851937i	0.999956	−	0.00936661i	$-0.00298153\pi$
$757$	13.5330	+	23.4399i	0.491866	+	0.851937i	−0.508090	+	0.861304i	$0.669648\pi$
$758$	−38.5734	+	22.2703i	−1.40105	+	0.808895i
$759$		0			0
$760$	−8.99429	−	8.99429i	−0.326257	−	0.326257i
$761$	4.69735	−	17.5308i	0.170279	−	0.635489i	−0.827029	−	0.562159i	$-0.809971\pi$
$761$	4.69735	−	17.5308i	0.170279	−	0.635489i	0.997308	−	0.0733299i	$-0.0233626\pi$
$762$		0			0
$763$	25.9656	−	1.84593i	0.940016	−	0.0668270i
$764$	−11.3514	+	6.55373i	−0.410679	+	0.237105i
$765$		0			0
$766$	−27.1033	−	46.9442i	−0.979281	−	1.69616i
$767$	−28.1718	+	11.7472i	−1.01723	+	0.424167i
$768$		0			0
$769$	39.4162	+	10.5616i	1.42139	+	0.380859i	0.885975	−	0.463732i	$-0.153490\pi$
$769$	39.4162	+	10.5616i	1.42139	+	0.380859i	0.535411	+	0.844592i	$0.320157\pi$
$770$	−0.682111	−	9.59485i	−0.0245816	−	0.345774i
$771$		0			0
$772$	−15.8842	+	4.25616i	−0.571684	+	0.153182i
$773$	7.87836	−	7.87836i	0.283365	−	0.283365i	−0.551085	−	0.834449i	$-0.685786\pi$
$773$	7.87836	−	7.87836i	0.283365	−	0.283365i	0.834449	+	0.551085i	$0.185786\pi$
$774$		0			0
$775$	5.71372	−	1.53099i	0.205243	−	0.0549946i
$776$	−21.1785	−	12.2274i	−0.760265	−	0.438939i
$777$		0			0
$778$	−23.0564	−	6.17793i	−0.826610	−	0.221490i
$779$	−27.6046	−	15.9375i	−0.989037	−	0.571021i
$780$		0			0
$781$	−2.12910	−	3.68772i	−0.0761853	−	0.131957i
$782$	−13.3983	+	13.3983i	−0.479124	+	0.479124i
$783$		0			0
$784$	−27.4818	+	21.5739i	−0.981494	+	0.770497i
$785$	−14.7733	−	14.7733i	−0.527283	−	0.527283i
$786$		0			0
$787$	−0.429238	−	0.429238i	−0.0153007	−	0.0153007i	0.699415	−	0.714716i	$-0.253444\pi$
$787$	−0.429238	−	0.429238i	−0.0153007	−	0.0153007i	−0.714716	+	0.699415i	$0.753444\pi$
$788$	20.9058	+	5.60170i	0.744739	+	0.199552i
$789$		0			0
$790$	−8.81594	−	15.2697i	−0.313657	−	0.543270i
$791$	−1.69267	−	0.326988i	−0.0601846	−	0.0116263i
$792$		0			0
$793$	−1.54872	−	11.5527i	−0.0549966	−	0.410248i
$794$	−26.2754	+	15.1701i	−0.932478	+	0.538367i
$795$		0			0
$796$			2.70340i			0.0958196i
$797$	25.9638	−	44.9707i	0.919687	−	1.59294i	0.119796	−	0.992799i	$-0.461776\pi$
$797$	25.9638	−	44.9707i	0.919687	−	1.59294i	0.799891	−	0.600145i	$-0.204891\pi$
$798$		0			0
$799$	−32.0717	+	8.59358i	−1.13461	+	0.304019i
$800$	13.9521	+	3.73845i	0.493280	+	0.132174i
$801$		0			0
$802$	−3.33192			−0.117654
$803$	22.4329			0.791641
$804$		0			0
$805$	4.48045	+	6.62596i	0.157915	+	0.233535i
$806$	−11.9229	+	1.59834i	−0.419965	+	0.0562992i
$807$		0			0
$808$	8.29931	+	30.9734i	0.291969	+	1.08964i
$809$	3.61649	−	6.26395i	0.127149	−	0.220229i	−0.795422	−	0.606056i	$-0.792751\pi$
$809$	3.61649	−	6.26395i	0.127149	−	0.220229i	0.922571	+	0.385827i	$0.126084\pi$
$810$		0			0
$811$	25.2728	−	25.2728i	0.887448	−	0.887448i	−0.106830	−	0.994277i	$-0.534070\pi$
$811$	25.2728	−	25.2728i	0.887448	−	0.887448i	0.994277	+	0.106830i	$0.0340700\pi$
$812$	−2.69605	−	2.33816i	−0.0946128	−	0.0820533i
$813$		0			0
$814$	−6.34861	−	23.6933i	−0.222519	−	0.830451i
$815$			22.5992i			0.791615i
$816$		0			0
$817$	−28.8053	−	28.8053i	−1.00777	−	1.00777i
$818$	−26.6641			−0.932287
$819$		0			0
$820$	−8.37364			−0.292420
$821$	−26.1285	−	26.1285i	−0.911890	−	0.911890i	0.0845305	−	0.996421i	$-0.473061\pi$
$821$	−26.1285	−	26.1285i	−0.911890	−	0.911890i	−0.996421	+	0.0845305i	$0.973061\pi$
$822$		0			0
$823$		−	22.9126i		−	0.798683i	−0.916802	−	0.399341i	$-0.869239\pi$
$823$		−	22.9126i		−	0.798683i	0.916802	−	0.399341i	$-0.130761\pi$
$824$	−0.170348	−	0.635746i	−0.00593434	−	0.0221473i
$825$		0			0
$826$	−36.0874	+	12.4727i	−1.25564	+	0.433980i
$827$	1.34175	−	1.34175i	0.0466571	−	0.0466571i	−0.683393	−	0.730050i	$-0.739497\pi$
$827$	1.34175	−	1.34175i	0.0466571	−	0.0466571i	0.730050	+	0.683393i	$0.239497\pi$
$828$		0			0
$829$	3.94656	−	6.83564i	0.137070	−	0.237412i	−0.789317	−	0.613987i	$-0.789565\pi$
$829$	3.94656	−	6.83564i	0.137070	−	0.237412i	0.926386	+	0.376575i	$0.122898\pi$
$830$	0.0600864	+	0.224246i	0.00208563	+	0.00778368i
$831$		0			0
$832$	6.11982	+	2.51799i	0.212166	+	0.0872955i
$833$	−28.4678	+	22.3479i	−0.986351	+	0.774310i
$834$		0			0
$835$	18.5447			0.641767
$836$	6.66536			0.230526
$837$		0			0
$838$	61.1375	+	16.3817i	2.11196	+	0.565898i
$839$	−20.2818	+	5.43449i	−0.700205	+	0.187619i	−0.591322	−	0.806435i	$-0.701394\pi$
$839$	−20.2818	+	5.43449i	−0.700205	+	0.187619i	−0.108883	+	0.994055i	$0.534727\pi$
$840$		0			0
$841$	13.3920	−	23.1956i	0.461794	−	0.799850i
$842$		−	55.8947i		−	1.92626i
$843$		0			0
$844$	3.22639	−	1.86276i	0.111057	−	0.0641188i
$845$	−9.06582	+	15.8752i	−0.311874	+	0.546124i
$846$		0			0
$847$	17.3895	+	15.0811i	0.597510	+	0.518193i
$848$	−9.36243	−	16.2162i	−0.321507	−	0.556867i
$849$		0			0
$850$	25.7316	+	6.89475i	0.882585	+	0.236488i
$851$	14.4228	+	14.4228i	0.494407	+	0.494407i
$852$		0			0
$853$	−5.56250	−	5.56250i	−0.190456	−	0.190456i	0.605437	−	0.795893i	$-0.292998\pi$
$853$	−5.56250	−	5.56250i	−0.190456	−	0.190456i	−0.795893	+	0.605437i	$0.792998\pi$
$854$	−1.03397	−	14.5442i	−0.0353816	−	0.497692i
$855$		0			0
$856$	−17.6816	+	17.6816i	−0.604346	+	0.604346i
$857$	7.92167	+	13.7207i	0.270599	+	0.468691i	0.969015	−	0.247000i	$-0.0794449\pi$
$857$	7.92167	+	13.7207i	0.270599	+	0.468691i	−0.698416	+	0.715692i	$0.746112\pi$
$858$		0			0
$859$	−22.0070	−	12.7057i	−0.750867	−	0.433514i	0.0751398	−	0.997173i	$-0.476060\pi$
$859$	−22.0070	−	12.7057i	−0.750867	−	0.433514i	−0.826007	+	0.563659i	$0.809393\pi$
$860$	−10.3370	−	2.76979i	−0.352489	−	0.0944491i
$861$		0			0
$862$	24.4546	+	14.1188i	0.832925	+	0.480890i
$863$	−31.5462	+	8.45278i	−1.07385	+	0.287736i	−0.752072	−	0.659081i	$-0.770946\pi$
$863$	−31.5462	+	8.45278i	−1.07385	+	0.287736i	−0.321773	+	0.946817i	$0.604279\pi$
$864$		0			0
$865$	13.9539	−	13.9539i	0.474447	−	0.474447i
$866$	2.68255	−	0.718787i	0.0911568	−	0.0244254i
$867$		0			0
$868$	−4.68010	+	0.332714i	−0.158853	+	0.0112931i
$869$	−10.7741	−	2.88690i	−0.365485	−	0.0979315i
$870$		0			0
$871$	6.01975	−	46.5746i	0.203971	−	1.57812i
$872$	−9.17368	−	15.8893i	−0.310660	−	0.538079i
$873$		0			0
$874$	−15.3946	+	8.88808i	−0.520730	+	0.300644i
$875$	13.0536	−	26.8427i	0.441292	−	0.907450i
$876$		0			0
$877$	−11.8921	+	44.3819i	−0.401568	+	1.49867i	0.408732	+	0.912654i	$0.365971\pi$
$877$	−11.8921	+	44.3819i	−0.401568	+	1.49867i	−0.810299	+	0.586016i	$0.800696\pi$
$878$	33.7282	+	33.7282i	1.13827	+	1.13827i
$879$		0			0
$880$	−9.21854	+	5.32233i	−0.310757	+	0.179416i
$881$	−16.3535	−	28.3251i	−0.550963	−	0.954296i	−0.998205	−	0.0598832i	$-0.980927\pi$
$881$	−16.3535	−	28.3251i	−0.550963	−	0.954296i	0.447242	−	0.894413i	$-0.352406\pi$
$882$		0			0
$883$			57.1171i			1.92214i	0.276302	+	0.961071i	$0.410891\pi$
$883$			57.1171i			1.92214i	−0.276302	+	0.961071i	$0.589109\pi$
$884$	−15.6208	−	6.42714i	−0.525384	−	0.216168i
$885$		0			0
$886$	−41.8846	+	11.2229i	−1.40714	+	0.377042i
$887$			26.1341i			0.877498i	0.898610	+	0.438749i	$0.144578\pi$
$887$			26.1341i			0.877498i	−0.898610	+	0.438749i	$0.855422\pi$
$888$		0			0
$889$	−3.77608	−	3.27482i	−0.126646	−	0.109834i
$890$	−25.8432	+	6.92466i	−0.866265	+	0.232115i
$891$		0			0
$892$	4.11486	−	15.3569i	0.137776	−	0.514186i
$893$	−31.1494			−1.04237
$894$		0			0
$895$	6.54995	−	24.4448i	0.218941	−	0.817098i
$896$	30.1864	+	14.6796i	1.00846	+	0.490411i
$897$		0			0
$898$	−2.19133	+	3.79549i	−0.0731256	+	0.126657i
$899$	0.754048	+	2.81415i	0.0251489	+	0.0938570i
$900$		0			0
$901$	−9.69834	−	16.7980i	−0.323098	−	0.559623i
$902$	−12.0135	+	12.0135i	−0.400004	+	0.400004i
$903$		0			0
$904$	0.314490	+	1.17369i	0.0104598	+	0.0390365i
$905$	−5.40230	−	20.1616i	−0.179578	−	0.670196i
$906$		0			0
$907$	−9.38851	−	5.42046i	−0.311740	−	0.179983i	0.335965	−	0.941875i	$-0.390938\pi$
$907$	−9.38851	−	5.42046i	−0.311740	−	0.179983i	−0.647705	+	0.761891i	$0.724271\pi$
$908$	4.44587	+	4.44587i	0.147541	+	0.147541i
$909$		0			0
$910$	−12.5549	+	19.1143i	−0.416192	+	0.633634i
$911$	−35.4311			−1.17389			−0.586943	−	0.809628i	$-0.699669\pi$
$911$	−35.4311			−1.17389			−0.586943	+	0.809628i	$0.699669\pi$
$912$		0			0
$913$	0.127188	+	0.0734323i	0.00420932	+	0.00243025i
$914$		−	24.1683i		−	0.799417i
$915$		0			0
$916$	2.10138	+	7.84245i	0.0694315	+	0.259122i
$917$	5.15412	−	26.6807i	0.170204	−	0.881074i
$918$		0			0
$919$	7.75577	+	13.4334i	0.255839	+	0.443126i	0.965123	−	0.261797i	$-0.0843149\pi$
$919$	7.75577	+	13.4334i	0.255839	+	0.443126i	−0.709284	+	0.704923i	$0.750982\pi$
$920$	2.81881	−	4.88233i	0.0929335	−	0.160966i
$921$		0			0
$922$	35.6108	−	61.6797i	1.17278	−	2.03131i
$923$	−1.29769	+	10.0402i	−0.0427139	+	0.330476i
$924$		0			0
$925$	7.42193	−	27.6990i	0.244032	−	0.910738i
$926$	47.2955			1.55423
$927$		0			0
$928$	−1.84128	+	6.87174i	−0.0604429	+	0.225576i
$929$	53.2944	+	14.2802i	1.74853	+	0.468518i	0.984312	−	0.176436i	$-0.0564567\pi$
$929$	53.2944	+	14.2802i	1.74853	+	0.468518i	0.764222	+	0.644954i	$0.223123\pi$
$930$		0			0
$931$	−31.2233	+	13.3390i	−1.02330	+	0.437168i
$932$	2.88593	−	4.99857i	0.0945317	−	0.163734i
$933$		0			0
$934$	48.2496	−	12.9284i	1.57877	−	0.423031i
$935$	−9.54928	+	5.51328i	−0.312295	+	0.180304i
$936$		0			0
$937$		−	4.36357i		−	0.142552i	−0.997457	−	0.0712758i	$-0.977293\pi$
$937$		−	4.36357i		−	0.142552i	0.997457	−	0.0712758i	$-0.0227070\pi$
$938$	11.1425	−	57.6798i	0.363815	−	1.88331i
$939$		0			0
$940$	−7.08669	+	4.09150i	−0.231142	+	0.133450i
$941$	8.90484	+	2.38605i	0.290290	+	0.0777829i	0.401025	−	0.916067i	$-0.368654\pi$
$941$	8.90484	+	2.38605i	0.290290	+	0.0777829i	−0.110736	+	0.993850i	$0.535321\pi$
$942$		0			0
$943$	3.65646	−	13.6461i	0.119071	−	0.444378i
$944$	29.8774	+	29.8774i	0.972426	+	0.972426i
$945$		0			0
$946$	−18.8040	+	10.8565i	−0.611371	+	0.352975i
$947$	−39.0303	+	39.0303i	−1.26832	+	1.26832i	−0.321357	+	0.946958i	$0.604139\pi$
$947$	−39.0303	+	39.0303i	−1.26832	+	1.26832i	−0.946958	+	0.321357i	$0.895861\pi$
$948$		0			0
$949$	−42.3886	−	32.3671i	−1.37599	−	1.05068i
$950$	21.6433	+	12.4958i	0.702203	+	0.405417i
$951$		0			0
$952$	22.9402	+	11.1558i	0.743496	+	0.361561i
$953$	30.1513	+	17.4079i	0.976697	+	0.563896i	0.901271	−	0.433255i	$-0.142635\pi$
$953$	30.1513	+	17.4079i	0.976697	+	0.563896i	0.0754255	+	0.997151i	$0.475969\pi$
$954$		0			0
$955$	14.3844	−	14.3844i	0.465467	−	0.465467i
$956$	−10.4136	+	10.4136i	−0.336798	+	0.336798i
$957$		0			0
$958$	13.2068	+	7.62492i	0.426691	+	0.246350i
$959$	−22.1809	−	10.7866i	−0.716259	−	0.348316i
$960$		0			0
$961$	−23.5296	−	13.5848i	−0.759019	−	0.438220i
$962$	−22.1895	+	53.9303i	−0.715419	+	1.73878i
$963$		0			0
$964$	0.148872	−	0.148872i	0.00479483	−	0.00479483i
$965$	22.1024	−	12.7608i	0.711502	−	0.410786i
$966$		0			0
$967$	−24.1180	−	24.1180i	−0.775583	−	0.775583i	0.203494	−	0.979076i	$-0.434770\pi$
$967$	−24.1180	−	24.1180i	−0.775583	−	0.775583i	−0.979076	+	0.203494i	$0.934770\pi$
$968$	4.19902	−	15.6710i	0.134962	−	0.503683i
$969$		0			0
$970$	−30.3670	−	8.13681i	−0.975026	−	0.261257i
$971$	40.0392	−	23.1166i	1.28492	−	0.741848i	0.307175	−	0.951653i	$-0.400616\pi$
$971$	40.0392	−	23.1166i	1.28492	−	0.741848i	0.977743	+	0.209805i	$0.0672829\pi$
$972$		0			0
$973$	−0.0821810	+	0.425416i	−0.00263460	+	0.0136382i
$974$			34.9727i			1.12060i
$975$		0			0
$976$	−13.9738	+	8.06776i	−0.447289	+	0.258243i
$977$	7.76823	−	2.08149i	0.248528	−	0.0665928i	−0.132404	−	0.991196i	$-0.542270\pi$
$977$	7.76823	−	2.08149i	0.248528	−	0.0665928i	0.380932	+	0.924603i	$0.375603\pi$
$978$		0			0
$979$	−8.46270	+	14.6578i	−0.270469	+	0.468466i
$980$	−5.35143	+	7.13593i	−0.170945	+	0.227949i
$981$		0			0
$982$	52.5303	+	14.0754i	1.67631	+	0.449165i
$983$	−2.20054	+	8.21252i	−0.0701863	+	0.261939i	−0.992099	−	0.125459i	$-0.959959\pi$
$983$	−2.20054	+	8.21252i	−0.0701863	+	0.261939i	0.921912	+	0.387398i	$0.126626\pi$
$984$		0			0
$985$	−33.5901			−1.07027
$986$	−3.39583	+	12.6734i	−0.108145	+	0.403604i
$987$		0			0
$988$	−12.5947	−	9.61705i	−0.400690	−	0.305959i
$989$	9.02758	−	15.6362i	0.287060	−	0.497203i
$990$		0			0
$991$	5.44662	−	9.43383i	0.173018	−	0.299675i	−0.766456	−	0.642297i	$-0.777982\pi$
$991$	5.44662	−	9.43383i	0.173018	−	0.299675i	0.939473	+	0.342622i	$0.111315\pi$
$992$	4.67661	+	8.10013i	0.148483	+	0.257179i
$993$		0			0
$994$	−2.40200	+	12.4341i	−0.0761868	+	0.394387i
$995$	−1.08591	−	4.05268i	−0.0344257	−	0.128479i
$996$		0			0
$997$			0.973665i			0.0308363i	0.999881	+	0.0154181i	$0.00490794\pi$
$997$			0.973665i			0.0308363i	−0.999881	+	0.0154181i	$0.995092\pi$
$998$	−33.8319	−	19.5328i	−1.07093	−	0.618301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.271.7		36
3.2	odd	2		273.2.bt.a.271.3	yes	36
7.3	odd	6		819.2.gh.c.388.3		36
13.6	odd	12		819.2.gh.c.19.3		36
21.17	even	6		273.2.cg.a.115.7	yes	36
39.32	even	12		273.2.cg.a.19.7	yes	36
91.45	even	12	inner	819.2.et.c.136.7		36
273.227	odd	12		273.2.bt.a.136.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.3	✓	36	273.227	odd	12
273.2.bt.a.271.3	yes	36	3.2	odd	2
273.2.cg.a.19.7	yes	36	39.32	even	12
273.2.cg.a.115.7	yes	36	21.17	even	6
819.2.et.c.136.7		36	91.45	even	12	inner
819.2.et.c.271.7		36	1.1	even	1	trivial
819.2.gh.c.19.3		36	13.6	odd	12
819.2.gh.c.388.3		36	7.3	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20543 + 1.20543i) q^{2} +0.906108i q^{4} +(-0.363968 - 1.35835i) q^{5} +(0.864271 + 2.50061i) q^{7} +(1.31861 - 1.31861i) q^{8} +O(q^{10})\)	\(q+(1.20543 + 1.20543i) q^{2} +0.906108i q^{4} +(-0.363968 - 1.35835i) q^{5} +(0.864271 + 2.50061i) q^{7} +(1.31861 - 1.31861i) q^{8} +(1.19865 - 2.07613i) q^{10} +(-0.392515 - 1.46489i) q^{11} +(-1.37191 + 3.33435i) q^{13} +(-1.97248 + 4.05611i) q^{14} +4.99118 q^{16} +5.17026 q^{17} +(4.68519 + 1.25539i) q^{19} +(1.23081 - 0.329795i) q^{20} +(1.29267 - 2.23896i) q^{22} +2.14980i q^{23} +(2.61749 - 1.51121i) q^{25} +(-5.67305 + 2.36557i) q^{26} +(-2.26582 + 0.783122i) q^{28} +(0.744307 + 1.28918i) q^{29} +(1.89045 + 0.506544i) q^{31} +(3.37929 + 3.37929i) q^{32} +(6.23237 + 6.23237i) q^{34} +(3.08213 - 2.08412i) q^{35} +(6.70890 - 6.70890i) q^{37} +(4.13437 + 7.16094i) q^{38} +(-2.27106 - 1.31120i) q^{40} +(-6.34762 - 1.70084i) q^{41} +(-7.27334 - 4.19927i) q^{43} +(1.32735 - 0.355661i) q^{44} +(-2.59143 + 2.59143i) q^{46} +(-6.20311 + 1.66212i) q^{47} +(-5.50607 + 4.32240i) q^{49} +(4.97684 + 1.33354i) q^{50} +(-3.02128 - 1.24310i) q^{52} +(-1.87579 - 3.24897i) q^{53} +(-1.84696 + 1.06635i) q^{55} +(4.43695 + 2.15769i) q^{56} +(-0.656802 + 2.45122i) q^{58} +(5.98603 + 5.98603i) q^{59} +(-2.79969 + 1.61640i) q^{61} +(1.66819 + 2.88940i) q^{62} -1.83539i q^{64} +(5.02854 + 0.649937i) q^{65} +(-12.5811 + 3.37110i) q^{67} +4.68481i q^{68} +(6.22754 + 1.20302i) q^{70} +(2.71213 - 0.726713i) q^{71} +(-3.82844 + 14.2879i) q^{73} +16.1742 q^{74} +(-1.13752 + 4.24529i) q^{76} +(3.32387 - 2.24759i) q^{77} +(3.67744 - 6.36951i) q^{79} +(-1.81663 - 6.77977i) q^{80} +(-5.60135 - 9.70182i) q^{82} +(-0.0684765 + 0.0684765i) q^{83} +(-1.88181 - 7.02301i) q^{85} +(-3.70557 - 13.8294i) q^{86} +(-2.44918 - 1.41404i) q^{88} +(-7.89157 - 7.89157i) q^{89} +(-9.52359 - 0.548833i) q^{91} -1.94795 q^{92} +(-9.48096 - 5.47383i) q^{94} -6.82105i q^{95} +(-3.39415 - 12.6671i) q^{97} +(-11.8475 - 1.42683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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