LMFDB - Embedded newform 819.2.et.d.145.1

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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.1
Character	$\chi$	$=$	819.145
Dual form			819.2.et.d.514.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85908 + 1.85908i) q^{2} -4.91234i q^{4} +(-0.502992 + 0.134776i) q^{5} +(-1.89546 + 1.84587i) q^{7} +(5.41427 + 5.41427i) q^{8} +O(q^{10})$	\(q+(-1.85908 + 1.85908i) q^{2} -4.91234i q^{4} +(-0.502992 + 0.134776i) q^{5} +(-1.89546 + 1.84587i) q^{7} +(5.41427 + 5.41427i) q^{8} +(0.684542 - 1.18566i) q^{10} +(1.93173 - 0.517606i) q^{11} +(2.40655 - 2.68487i) q^{13} +(0.0921792 - 6.95542i) q^{14} -10.3064 q^{16} -5.09260 q^{17} +(-1.86555 + 6.96234i) q^{19} +(0.662067 + 2.47087i) q^{20} +(-2.62897 + 4.55351i) q^{22} -4.78704i q^{23} +(-4.09529 + 2.36442i) q^{25} +(0.517414 + 9.46534i) q^{26} +(9.06756 + 9.31113i) q^{28} +(1.35547 + 2.34774i) q^{29} +(0.867635 - 3.23806i) q^{31} +(8.33190 - 8.33190i) q^{32} +(9.46754 - 9.46754i) q^{34} +(0.704619 - 1.18392i) q^{35} +(-5.25431 - 5.25431i) q^{37} +(-9.47532 - 16.4117i) q^{38} +(-3.45305 - 1.99362i) q^{40} +(-0.938828 + 3.50375i) q^{41} +(-3.62298 - 2.09173i) q^{43} +(-2.54266 - 9.48933i) q^{44} +(8.89947 + 8.89947i) q^{46} +(-0.0215224 - 0.0803226i) q^{47} +(0.185507 - 6.99754i) q^{49} +(3.21783 - 12.0091i) q^{50} +(-13.1890 - 11.8218i) q^{52} +(-6.85585 - 11.8747i) q^{53} +(-0.901885 + 0.520704i) q^{55} +(-20.2566 - 0.268457i) q^{56} +(-6.88456 - 1.84471i) q^{58} +(3.91130 - 3.91130i) q^{59} +(-0.652526 + 0.376736i) q^{61} +(4.40680 + 7.63280i) q^{62} +10.3665i q^{64} +(-0.848619 + 1.67481i) q^{65} +(-2.81278 - 10.4974i) q^{67} +25.0166i q^{68} +(0.891061 + 3.51095i) q^{70} +(1.34000 + 5.00093i) q^{71} +(2.05692 + 0.551150i) q^{73} +19.5363 q^{74} +(34.2014 + 9.16424i) q^{76} +(-2.70608 + 4.54683i) q^{77} +(6.17212 - 10.6904i) q^{79} +(5.18405 - 1.38906i) q^{80} +(-4.76840 - 8.25910i) q^{82} +(-7.09696 - 7.09696i) q^{83} +(2.56154 - 0.686362i) q^{85} +(10.6241 - 2.84672i) q^{86} +(13.2614 + 7.65647i) q^{88} +(9.64998 - 9.64998i) q^{89} +(0.394414 + 9.53123i) q^{91} -23.5156 q^{92} +(0.189338 + 0.109314i) q^{94} -3.75343i q^{95} +(-3.28692 + 0.880729i) q^{97} +(12.6641 + 13.3538i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{7}+O(q^{10}) $ 40 * q - 2 * q^7	$ 40 q - 2 q^{7} + 8 q^{11} + 18 q^{14} - 64 q^{16} - 8 q^{17} - 14 q^{19} + 14 q^{20} + 4 q^{22} - 24 q^{25} + 10 q^{26} - 2 q^{28} - 8 q^{29} - 8 q^{31} - 10 q^{32} + 24 q^{34} + 22 q^{35} + 12 q^{37} - 8 q^{38} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 28 q^{44} + 40 q^{46} - 10 q^{47} + 38 q^{49} + 20 q^{50} + 40 q^{52} + 8 q^{53} + 42 q^{55} - 20 q^{56} - 48 q^{58} + 26 q^{59} - 12 q^{61} + 24 q^{62} + 44 q^{65} + 46 q^{67} + 32 q^{70} + 6 q^{71} + 10 q^{73} - 40 q^{74} + 64 q^{76} + 24 q^{77} - 34 q^{80} + 24 q^{82} - 12 q^{83} + 2 q^{85} - 12 q^{86} - 84 q^{88} + 16 q^{89} + 26 q^{91} - 236 q^{92} + 30 q^{94} + 62 q^{97} + 14 q^{98}+O(q^{100}) $ 40 * q - 2 * q^7 + 8 * q^11 + 18 * q^14 - 64 * q^16 - 8 * q^17 - 14 * q^19 + 14 * q^20 + 4 * q^22 - 24 * q^25 + 10 * q^26 - 2 * q^28 - 8 * q^29 - 8 * q^31 - 10 * q^32 + 24 * q^34 + 22 * q^35 + 12 * q^37 - 8 * q^38 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 28 * q^44 + 40 * q^46 - 10 * q^47 + 38 * q^49 + 20 * q^50 + 40 * q^52 + 8 * q^53 + 42 * q^55 - 20 * q^56 - 48 * q^58 + 26 * q^59 - 12 * q^61 + 24 * q^62 + 44 * q^65 + 46 * q^67 + 32 * q^70 + 6 * q^71 + 10 * q^73 - 40 * q^74 + 64 * q^76 + 24 * q^77 - 34 * q^80 + 24 * q^82 - 12 * q^83 + 2 * q^85 - 12 * q^86 - 84 * q^88 + 16 * q^89 + 26 * q^91 - 236 * q^92 + 30 * q^94 + 62 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.85908	+	1.85908i	−1.31457	+	1.31457i	−0.396556	+	0.918010i	$0.629795\pi$
$2$	−1.85908	+	1.85908i	−1.31457	+	1.31457i	−0.918010	+	0.396556i	$0.870205\pi$
$3$		0			0
$3$		0			0
$4$		−	4.91234i		−	2.45617i
$5$	−0.502992	+	0.134776i	−0.224945	+	0.0602738i	−0.369531	−	0.929218i	$-0.620482\pi$
$5$	−0.502992	+	0.134776i	−0.224945	+	0.0602738i	0.144586	+	0.989492i	$0.453815\pi$
$6$		0			0
$7$	−1.89546	+	1.84587i	−0.716415	+	0.697674i
$7$	−1.89546	+	1.84587i	−0.716415	+	0.697674i
$8$	5.41427	+	5.41427i	1.91423	+	1.91423i
$9$		0			0
$10$	0.684542	−	1.18566i	0.216471	−	0.374939i
$11$	1.93173	−	0.517606i	0.582439	−	0.156064i	0.0444439	−	0.999012i	$-0.485848\pi$
$11$	1.93173	−	0.517606i	0.582439	−	0.156064i	0.537995	+	0.842948i	$0.319182\pi$
$12$		0			0
$13$	2.40655	−	2.68487i	0.667457	−	0.744648i
$13$	2.40655	−	2.68487i	0.667457	−	0.744648i
$14$	0.0921792	−	6.95542i	0.0246359	−	1.85891i
$15$		0			0
$16$	−10.3064			−2.57661
$17$	−5.09260			−1.23514			−0.617569	−	0.786517i	$-0.711882\pi$
$17$	−5.09260			−1.23514			−0.617569	+	0.786517i	$0.711882\pi$
$18$		0			0
$19$	−1.86555	+	6.96234i	−0.427987	+	1.59727i	0.329324	+	0.944217i	$0.393179\pi$
$19$	−1.86555	+	6.96234i	−0.427987	+	1.59727i	−0.757312	+	0.653054i	$0.773488\pi$
$20$	0.662067	+	2.47087i	0.148043	+	0.552503i
$21$		0			0
$22$	−2.62897	+	4.55351i	−0.560499	+	0.970812i
$23$		−	4.78704i		−	0.998166i	−0.866554	−	0.499083i	$-0.833670\pi$
$23$		−	4.78704i		−	0.998166i	0.866554	−	0.499083i	$-0.166330\pi$
$24$		0			0
$25$	−4.09529	+	2.36442i	−0.819058	+	0.472883i
$26$	0.517414	+	9.46534i	0.101473	+	1.85631i
$27$		0			0
$28$	9.06756	+	9.31113i	1.71361	+	1.75964i
$29$	1.35547	+	2.34774i	0.251704	+	0.435965i	0.963995	−	0.265920i	$-0.0856756\pi$
$29$	1.35547	+	2.34774i	0.251704	+	0.435965i	−0.712291	+	0.701884i	$0.752342\pi$
$30$		0			0
$31$	0.867635	−	3.23806i	0.155832	−	0.581572i	−0.843201	−	0.537599i	$-0.819332\pi$
$31$	0.867635	−	3.23806i	0.155832	−	0.581572i	0.999033	−	0.0439736i	$-0.0140018\pi$
$32$	8.33190	−	8.33190i	1.47289	−	1.47289i
$33$		0			0
$34$	9.46754	−	9.46754i	1.62367	−	1.62367i
$35$	0.704619	−	1.18392i	0.119102	−	0.200119i
$36$		0			0
$37$	−5.25431	−	5.25431i	−0.863803	−	0.863803i	0.127975	−	0.991777i	$-0.459152\pi$
$37$	−5.25431	−	5.25431i	−0.863803	−	0.863803i	−0.991777	+	0.127975i	$0.959152\pi$
$38$	−9.47532	−	16.4117i	−1.53710	−	2.66234i
$39$		0			0
$40$	−3.45305	−	1.99362i	−0.545975	−	0.315219i
$41$	−0.938828	+	3.50375i	−0.146620	+	0.547194i	0.853058	+	0.521817i	$0.174745\pi$
$41$	−0.938828	+	3.50375i	−0.146620	+	0.547194i	−0.999678	+	0.0253776i	$0.991921\pi$
$42$		0			0
$43$	−3.62298	−	2.09173i	−0.552500	−	0.318986i	0.197630	−	0.980277i	$-0.436676\pi$
$43$	−3.62298	−	2.09173i	−0.552500	−	0.318986i	−0.750130	+	0.661291i	$0.770009\pi$
$44$	−2.54266	−	9.48933i	−0.383320	−	1.43057i
$45$		0			0
$46$	8.89947	+	8.89947i	1.31216	+	1.31216i
$47$	−0.0215224	−	0.0803226i	−0.00313936	−	0.0117163i	0.964338	−	0.264672i	$-0.0852638\pi$
$47$	−0.0215224	−	0.0803226i	−0.00313936	−	0.0117163i	−0.967478	+	0.252956i	$0.918597\pi$
$48$		0			0
$49$	0.185507	−	6.99754i	0.0265010	−	0.999649i
$50$	3.21783	−	12.0091i	0.455070	−	1.69834i
$51$		0			0
$52$	−13.1890	−	11.8218i	−1.82898	−	1.63939i
$53$	−6.85585	−	11.8747i	−0.941723	−	1.63111i	−0.762183	−	0.647362i	$-0.775872\pi$
$53$	−6.85585	−	11.8747i	−0.941723	−	1.63111i	−0.179541	−	0.983751i	$-0.557461\pi$
$54$		0			0
$55$	−0.901885	+	0.520704i	−0.121610	+	0.0702117i
$56$	−20.2566	−	0.268457i	−2.70690	−	0.0358741i
$57$		0			0
$58$	−6.88456	−	1.84471i	−0.903987	−	0.242223i
$59$	3.91130	−	3.91130i	0.509208	−	0.509208i	−0.405075	−	0.914283i	$-0.632755\pi$
$59$	3.91130	−	3.91130i	0.509208	−	0.509208i	0.914283	+	0.405075i	$0.132755\pi$
$60$		0			0
$61$	−0.652526	+	0.376736i	−0.0835474	+	0.0482361i	−0.541192	−	0.840899i	$-0.682027\pi$
$61$	−0.652526	+	0.376736i	−0.0835474	+	0.0482361i	0.457644	+	0.889135i	$0.348693\pi$
$62$	4.40680	+	7.63280i	0.559664	+	0.969367i
$63$		0			0
$64$			10.3665i			1.29581i
$65$	−0.848619	+	1.67481i	−0.105258	+	0.207735i
$66$		0			0
$67$	−2.81278	−	10.4974i	−0.343636	−	1.28247i	−0.894198	−	0.447672i	$-0.852253\pi$
$67$	−2.81278	−	10.4974i	−0.343636	−	1.28247i	0.550562	−	0.834794i	$-0.314414\pi$
$68$			25.0166i			3.03371i
$69$		0			0
$70$	0.891061	+	3.51095i	0.106502	+	0.419638i
$71$	1.34000	+	5.00093i	0.159028	+	0.593502i	0.998727	+	0.0504485i	$0.0160651\pi$
$71$	1.34000	+	5.00093i	0.159028	+	0.593502i	−0.839698	+	0.543053i	$0.817268\pi$
$72$		0			0
$73$	2.05692	+	0.551150i	0.240744	+	0.0645072i	0.377174	−	0.926143i	$-0.376896\pi$
$73$	2.05692	+	0.551150i	0.240744	+	0.0645072i	−0.136429	+	0.990650i	$0.543563\pi$
$74$	19.5363			2.27105
$75$		0			0
$76$	34.2014	+	9.16424i	3.92317	+	1.05121i
$77$	−2.70608	+	4.54683i	−0.308386	+	0.518160i
$78$		0			0
$79$	6.17212	−	10.6904i	0.694418	−	1.20277i	−0.275959	−	0.961169i	$-0.588995\pi$
$79$	6.17212	−	10.6904i	0.694418	−	1.20277i	0.970377	−	0.241597i	$-0.0776713\pi$
$80$	5.18405	−	1.38906i	0.579594	−	0.155302i
$81$		0			0
$82$	−4.76840	−	8.25910i	−0.526581	−	0.912065i
$83$	−7.09696	−	7.09696i	−0.778993	−	0.778993i	0.200667	−	0.979660i	$-0.435689\pi$
$83$	−7.09696	−	7.09696i	−0.778993	−	0.778993i	−0.979660	+	0.200667i	$0.935689\pi$
$84$		0			0
$85$	2.56154	−	0.686362i	0.277838	−	0.0744464i
$86$	10.6241	−	2.84672i	1.14563	−	0.306970i
$87$		0			0
$88$	13.2614	+	7.65647i	1.41367	+	0.816182i
$89$	9.64998	−	9.64998i	1.02290	−	1.02290i	0.0231645	−	0.999732i	$-0.492626\pi$
$89$	9.64998	−	9.64998i	1.02290	−	1.02290i	0.999732	−	0.0231645i	$-0.00737415\pi$
$90$		0			0
$91$	0.394414	+	9.53123i	0.0413459	+	0.999145i
$92$	−23.5156			−2.45167
$93$		0			0
$94$	0.189338	+	0.109314i	0.0195287	+	0.0112749i
$95$		−	3.75343i		−	0.385094i
$96$		0			0
$97$	−3.28692	+	0.880729i	−0.333737	+	0.0894244i	−0.421796	−	0.906691i	$-0.638600\pi$
$97$	−3.28692	+	0.880729i	−0.333737	+	0.0894244i	0.0880594	+	0.996115i	$0.471933\pi$
$98$	12.6641	+	13.3538i	1.27927	+	1.34894i
$99$		0			0
$100$	11.6148	+	20.1175i	1.16148	+	2.01175i
$101$	−6.04762	+	10.4748i	−0.601760	+	1.04228i	0.390794	+	0.920478i	$0.372200\pi$
$101$	−6.04762	+	10.4748i	−0.601760	+	1.04228i	−0.992555	+	0.121801i	$0.961133\pi$
$102$		0			0
$103$	4.04418	−	7.00473i	0.398485	−	0.690196i	−0.595054	−	0.803686i	$-0.702869\pi$
$103$	4.04418	−	7.00473i	0.398485	−	0.690196i	0.993539	+	0.113489i	$0.0362027\pi$
$104$	27.5663	−	1.50689i	2.70310	−	0.147762i
$105$		0			0
$106$	34.8215	+	9.33040i	3.38216	+	0.906248i
$107$	5.64725			0.545940			0.272970	−	0.962023i	$-0.411994\pi$
$107$	5.64725			0.545940			0.272970	+	0.962023i	$0.411994\pi$
$108$		0			0
$109$	−9.35415	−	2.50644i	−0.895965	−	0.240073i	−0.218682	−	0.975796i	$-0.570176\pi$
$109$	−9.35415	−	2.50644i	−0.895965	−	0.240073i	−0.677282	+	0.735723i	$0.736842\pi$
$110$	0.708646	−	2.64470i	0.0675668	−	0.252163i
$111$		0			0
$112$	19.5354	−	19.0243i	1.84592	−	1.79763i
$113$	−9.60923	+	16.6437i	−0.903960	+	1.56570i	−0.0816525	+	0.996661i	$0.526020\pi$
$113$	−9.60923	+	16.6437i	−0.903960	+	1.56570i	−0.822307	+	0.569044i	$0.807314\pi$
$114$		0			0
$115$	0.645179	+	2.40784i	0.0601633	+	0.224532i
$116$	11.5329	−	6.65853i	1.07080	−	0.618229i
$117$		0			0
$118$			14.5428i			1.33878i
$119$	9.65280	−	9.40029i	0.884871	−	0.861724i
$120$		0			0
$121$	−6.06260	+	3.50025i	−0.551146	+	0.318204i
$122$	0.512715	−	1.91348i	0.0464191	−	0.173238i
$123$		0			0
$124$	−15.9064	−	4.26212i	−1.42844	−	0.382750i
$125$	3.58231	−	3.58231i	0.320411	−	0.320411i
$126$		0			0
$127$	−5.78281	+	3.33871i	−0.513141	+	0.296262i	−0.734124	−	0.679015i	$-0.762407\pi$
$127$	−5.78281	+	3.33871i	−0.513141	+	0.296262i	0.220983	+	0.975278i	$0.429074\pi$
$128$	−2.60825	−	2.60825i	−0.230539	−	0.230539i
$129$		0			0
$130$	−1.53596	−	4.69126i	−0.134713	−	0.411450i
$131$	0.269003	+	0.155309i	0.0235029	+	0.0135694i	0.511705	−	0.859161i	$-0.329014\pi$
$131$	0.269003	+	0.155309i	0.0235029	+	0.0135694i	−0.488203	+	0.872730i	$0.662347\pi$
$132$		0			0
$133$	−9.31552	−	16.6404i	−0.807758	−	1.44290i
$134$	24.7447	+	14.2864i	2.13762	+	1.23416i
$135$		0			0
$136$	−27.5727	−	27.5727i	−2.36434	−	2.36434i
$137$	3.42496	+	3.42496i	0.292614	+	0.292614i	0.838112	−	0.545498i	$-0.183660\pi$
$137$	3.42496	+	3.42496i	0.292614	+	0.292614i	−0.545498	+	0.838112i	$0.683660\pi$
$138$		0			0
$139$	−9.26980	−	5.35192i	−0.786254	−	0.453944i	0.0523882	−	0.998627i	$-0.483317\pi$
$139$	−9.26980	−	5.35192i	−0.786254	−	0.453944i	−0.838642	+	0.544683i	$0.816650\pi$
$140$	−5.81583	−	3.46133i	−0.491527	−	0.292536i
$141$		0			0
$142$	−11.7883	−	6.80597i	−0.989251	−	0.571144i
$143$	3.25911	−	6.43209i	0.272540	−	0.537879i
$144$		0			0
$145$	−0.998210	−	0.998210i	−0.0828969	−	0.0828969i
$146$	−4.84860	+	2.79934i	−0.401273	+	0.231675i
$147$		0			0
$148$	−25.8110	+	25.8110i	−2.12165	+	2.12165i
$149$	−16.4441	−	4.40620i	−1.34716	−	0.360970i	−0.488072	−	0.872803i	$-0.662300\pi$
$149$	−16.4441	−	4.40620i	−1.34716	−	0.360970i	−0.859085	+	0.511833i	$0.828966\pi$
$150$		0			0
$151$	−4.72803	+	17.6453i	−0.384762	+	1.43595i	0.453780	+	0.891114i	$0.350075\pi$
$151$	−4.72803	+	17.6453i	−0.384762	+	1.43595i	−0.838542	+	0.544837i	$0.816592\pi$
$152$	−47.7966	+	27.5954i	−3.87682	+	2.23828i
$153$		0			0
$154$	−3.42210	−	13.4837i	−0.275761	−	1.08655i
$155$			1.74565i			0.140214i
$156$		0			0
$157$	−4.25722	+	2.45791i	−0.339763	+	0.196162i	−0.660167	−	0.751119i	$-0.729515\pi$
$157$	−4.25722	+	2.45791i	−0.339763	+	0.196162i	0.320404	+	0.947281i	$0.396181\pi$
$158$	8.39988	+	31.3488i	0.668259	+	2.49398i
$159$		0			0
$160$	−3.06794	+	5.31382i	−0.242542	+	0.420094i
$161$	8.83626	+	9.07362i	0.696395	+	0.715101i
$162$		0			0
$163$	0.785395	−	2.93113i	0.0615169	−	0.229584i	−0.928322	−	0.371777i	$-0.878749\pi$
$163$	0.785395	−	2.93113i	0.0615169	−	0.229584i	0.989839	+	0.142193i	$0.0454153\pi$
$164$	17.2116	+	4.61184i	1.34400	+	0.360124i
$165$		0			0
$166$	26.3876			2.04808
$167$	−9.12053	−	2.44384i	−0.705768	−	0.189110i	−0.111955	−	0.993713i	$-0.535711\pi$
$167$	−9.12053	−	2.44384i	−0.705768	−	0.189110i	−0.593813	+	0.804603i	$0.702378\pi$
$168$		0			0
$169$	−1.41703	−	12.9225i	−0.109002	−	0.994041i
$170$	−3.48610	+	6.03810i	−0.267372	+	0.463101i
$171$		0			0
$172$	−10.2753	+	17.7973i	−0.783484	+	1.35703i
$173$	−10.9895	−	19.0343i	−0.835515	−	1.44715i	−0.893610	−	0.448843i	$-0.851836\pi$
$173$	−10.9895	−	19.0343i	−0.835515	−	1.44715i	0.0580954	−	0.998311i	$-0.481497\pi$
$174$		0			0
$175$	3.39803	−	12.0410i	0.256867	−	0.910217i
$176$	−19.9093	+	5.33467i	−1.50072	+	0.402116i
$177$		0			0
$178$			35.8801i			2.68933i
$179$	−14.7903	−	8.53916i	−1.10548	−	0.638247i	−0.167822	−	0.985817i	$-0.553673\pi$
$179$	−14.7903	−	8.53916i	−1.10548	−	0.638247i	−0.937654	+	0.347570i	$0.887007\pi$
$180$		0			0
$181$	18.0173			1.33922			0.669608	−	0.742714i	$-0.266462\pi$
$181$	18.0173			1.33922			0.669608	+	0.742714i	$0.266462\pi$
$182$	−18.4526	−	16.9861i	−1.36779	−	1.25909i
$183$		0			0
$184$	25.9183	−	25.9183i	1.91072	−	1.91072i
$185$	3.35103	+	1.93472i	0.246373	+	0.142243i
$186$		0			0
$187$	−9.83755	+	2.63596i	−0.719393	+	0.192761i
$188$	−0.394572	+	0.105725i	−0.0287771	+	0.00771081i
$189$		0			0
$190$	6.97793	+	6.97793i	0.506232	+	0.506232i
$191$	−11.0349	−	19.1130i	−0.798458	−	1.38297i	−0.920620	−	0.390460i	$-0.872316\pi$
$191$	−11.0349	−	19.1130i	−0.798458	−	1.38297i	0.122162	−	0.992510i	$-0.461017\pi$
$192$		0			0
$193$	−7.05769	+	1.89110i	−0.508024	+	0.136124i	−0.503721	−	0.863866i	$-0.668036\pi$
$193$	−7.05769	+	1.89110i	−0.508024	+	0.136124i	−0.00430227	+	0.999991i	$0.501369\pi$
$194$	4.47330	−	7.74799i	0.321165	−	0.556273i
$195$		0			0
$196$	−34.3743	−	0.911276i	−2.45531	−	0.0650911i
$197$	22.5188	+	6.03390i	1.60440	+	0.429898i	0.946368	−	0.323092i	$-0.104722\pi$
$197$	22.5188	+	6.03390i	1.60440	+	0.429898i	0.658033	+	0.752989i	$0.271389\pi$
$198$		0			0
$199$	17.7582			1.25885			0.629423	−	0.777063i	$-0.283291\pi$
$199$	17.7582			1.25885			0.629423	+	0.777063i	$0.283291\pi$
$200$	−34.9746	−	9.37142i	−2.47308	−	0.662659i
$201$		0			0
$202$	−8.23044	−	30.7164i	−0.579092	−	2.16120i
$203$	−6.90287	−	1.94802i	−0.484486	−	0.136724i
$204$		0			0
$205$		−	1.88889i		−	0.131926i
$206$	5.50389	+	20.5408i	0.383474	+	1.43114i
$207$		0			0
$208$	−24.8029	+	27.6714i	−1.71977	+	1.91867i
$209$			14.4150i			0.997107i
$210$		0			0
$211$	−2.69516	−	4.66816i	−0.185543	−	0.321370i	0.758217	−	0.652003i	$-0.226071\pi$
$211$	−2.69516	−	4.66816i	−0.185543	−	0.321370i	−0.943759	+	0.330633i	$0.892738\pi$
$212$	−58.3325	+	33.6783i	−4.00629	+	2.31303i
$213$		0			0
$214$	−10.4987	+	10.4987i	−0.717675	+	0.717675i
$215$	2.10425	+	0.563831i	0.143508	+	0.0384530i
$216$		0			0
$217$	4.33248	+	7.73914i	0.294108	+	0.525367i
$218$	22.0497	−	12.7304i	1.49340	−	0.862213i
$219$		0			0
$220$	2.55787	+	4.43037i	0.172452	+	0.298695i
$221$	−12.2556	+	13.6730i	−0.824401	+	0.919743i
$222$		0			0
$223$	3.70617	−	13.8316i	0.248183	−	0.926233i	−0.723573	−	0.690248i	$-0.757502\pi$
$223$	3.70617	−	13.8316i	0.248183	−	0.926233i	0.971757	−	0.235986i	$-0.0758318\pi$
$224$	−0.413123	+	31.1724i	−0.0276029	+	2.08279i
$225$		0			0
$226$	−13.0776	−	48.8062i	−0.869907	−	3.24654i
$227$	−4.18497	−	4.18497i	−0.277766	−	0.277766i	0.554451	−	0.832217i	$-0.312928\pi$
$227$	−4.18497	−	4.18497i	−0.277766	−	0.277766i	−0.832217	+	0.554451i	$0.812928\pi$
$228$		0			0
$229$	7.65078	+	28.5531i	0.505578	+	1.88684i	0.460081	+	0.887877i	$0.347821\pi$
$229$	7.65078	+	28.5531i	0.505578	+	1.88684i	0.0454971	+	0.998964i	$0.485513\pi$
$230$	−5.67580	−	3.27693i	−0.374251	−	0.216074i
$231$		0			0
$232$	−5.37243	+	20.0502i	−0.352718	+	1.31636i
$233$	−2.20932	−	1.27555i	−0.144737	−	0.0835641i	0.425883	−	0.904778i	$-0.359964\pi$
$233$	−2.20932	−	1.27555i	−0.144737	−	0.0835641i	−0.570620	+	0.821214i	$0.693297\pi$
$234$		0			0
$235$	0.0216512	+	0.0375009i	0.00141237	+	0.00244629i
$236$	−19.2137	−	19.2137i	−1.25070	−	1.25070i
$237$		0			0
$238$	−0.469432	+	35.4212i	−0.0304287	+	2.29601i
$239$	−7.35563	+	7.35563i	−0.475796	+	0.475796i	−0.903784	−	0.427988i	$-0.859222\pi$
$239$	−7.35563	+	7.35563i	−0.475796	+	0.475796i	0.427988	+	0.903784i	$0.359222\pi$
$240$		0			0
$241$	−2.55704	+	2.55704i	−0.164714	+	0.164714i	−0.784651	−	0.619938i	$-0.787158\pi$
$241$	−2.55704	+	2.55704i	−0.164714	+	0.164714i	0.619938	+	0.784651i	$0.287158\pi$
$242$	4.76362	−	17.7781i	0.306217	−	1.14282i
$243$		0			0
$244$	1.85066	+	3.20543i	0.118476	+	0.205207i
$245$	0.849794	+	3.54471i	0.0542913	+	0.226463i
$246$		0			0
$247$	14.2034	+	21.7640i	0.903742	+	1.38481i
$248$	22.2293	−	12.8341i	1.41156	−	0.814967i
$249$		0			0
$250$			13.3196i			0.842405i
$251$	0.0388167	−	0.0672326i	0.00245009	−	0.00424368i	−0.864798	−	0.502120i	$-0.832553\pi$
$251$	0.0388167	−	0.0672326i	0.00245009	−	0.00424368i	0.867248	+	0.497877i	$0.165887\pi$
$252$		0			0
$253$	−2.47780	−	9.24728i	−0.155778	−	0.581371i
$254$	4.54378	−	16.9576i	0.285102	−	1.06402i
$255$		0			0
$256$	−11.0350			−0.689689
$257$	−2.28983			−0.142836			−0.0714179	−	0.997446i	$-0.522752\pi$
$257$	−2.28983			−0.142836			−0.0714179	+	0.997446i	$0.522752\pi$
$258$		0			0
$259$	19.6581	+	0.260526i	1.22149	+	0.0161883i
$260$	8.22725	+	4.16871i	0.510233	+	0.258532i
$261$		0			0
$262$	−0.788830	+	0.211366i	−0.0487341	+	0.0130583i
$263$	−2.52090	+	4.36634i	−0.155446	+	0.269240i	−0.933221	−	0.359302i	$-0.883015\pi$
$263$	−2.52090	+	4.36634i	−0.155446	+	0.269240i	0.777776	+	0.628542i	$0.216348\pi$
$264$		0			0
$265$	5.04886	+	5.04886i	0.310149	+	0.310149i
$266$	48.2541	+	13.6175i	2.95865	+	0.834942i
$267$		0			0
$268$	−51.5670	+	13.8173i	−3.14996	+	0.844029i
$269$			16.3896i			0.999293i	0.866229	+	0.499646i	$0.166537\pi$
$269$			16.3896i			0.999293i	−0.866229	+	0.499646i	$0.833463\pi$
$270$		0			0
$271$	−4.64470	+	4.64470i	−0.282145	+	0.282145i	−0.833964	−	0.551819i	$-0.813934\pi$
$271$	−4.64470	+	4.64470i	−0.282145	+	0.282145i	0.551819	+	0.833964i	$0.313934\pi$
$272$	52.4865			3.18246
$273$		0			0
$274$	−12.7345			−0.769320
$275$	−6.68717	+	6.68717i	−0.403252	+	0.403252i
$276$		0			0
$277$			1.55977i			0.0937173i	0.998902	+	0.0468587i	$0.0149210\pi$
$277$			1.55977i			0.0937173i	−0.998902	+	0.0468587i	$0.985079\pi$
$278$	27.1829	−	7.28364i	1.63032	−	0.436844i
$279$		0			0
$280$	10.2251	−	2.59507i	0.611065	−	0.155085i
$281$	−0.519129	−	0.519129i	−0.0309687	−	0.0309687i	0.691453	−	0.722422i	$-0.256971\pi$
$281$	−0.519129	−	0.519129i	−0.0309687	−	0.0309687i	−0.722422	+	0.691453i	$0.756971\pi$
$282$		0			0
$283$	−13.7646	+	23.8409i	−0.818218	+	1.41720i	0.0887760	+	0.996052i	$0.471704\pi$
$283$	−13.7646	+	23.8409i	−0.818218	+	1.41720i	−0.906994	+	0.421144i	$0.861629\pi$
$284$	24.5663	−	6.58252i	1.45774	−	0.390601i
$285$		0			0
$286$	5.89883	+	18.0167i	0.348805	+	1.06535i
$287$	−4.68797	−	8.37416i	−0.276722	−	0.494311i
$288$		0			0
$289$	8.93459			0.525564
$290$	3.71150			0.217947
$291$		0			0
$292$	2.70744	−	10.1043i	0.158441	−	0.591309i
$293$	2.78349	+	10.3881i	0.162613	+	0.606881i	0.998333	+	0.0577244i	$0.0183845\pi$
$293$	2.78349	+	10.3881i	0.162613	+	0.606881i	−0.835719	+	0.549157i	$0.814949\pi$
$294$		0			0
$295$	−1.44020	+	2.49450i	−0.0838518	+	0.145236i
$296$		−	56.8965i		−	3.30704i
$297$		0			0
$298$	38.7624	−	22.3795i	2.24545	−	1.29641i
$299$	−12.8526	−	11.5202i	−0.743283	−	0.666233i
$300$		0			0
$301$	10.7283	−	2.72278i	0.618367	−	0.156939i
$302$	−24.0141	−	41.5937i	−1.38186	−	2.39345i
$303$		0			0
$304$	19.2272	−	71.7568i	1.10275	−	4.11554i
$305$	0.277440	−	0.277440i	0.0158862	−	0.0158862i
$306$		0			0
$307$	−2.62443	+	2.62443i	−0.149784	+	0.149784i	−0.778022	−	0.628237i	$-0.783777\pi$
$307$	−2.62443	+	2.62443i	−0.149784	+	0.149784i	0.628237	+	0.778022i	$0.283777\pi$
$308$	22.3356	+	13.2932i	1.27269	+	0.757450i
$309$		0			0
$310$	−3.24531	−	3.24531i	−0.184321	−	0.184321i
$311$	2.68970	+	4.65870i	0.152519	+	0.264171i	0.932153	−	0.362065i	$-0.117928\pi$
$311$	2.68970	+	4.65870i	0.152519	+	0.264171i	−0.779634	+	0.626236i	$0.784595\pi$
$312$		0			0
$313$	27.3358	+	15.7824i	1.54511	+	0.892072i	0.998504	+	0.0546842i	$0.0174152\pi$
$313$	27.3358	+	15.7824i	1.54511	+	0.892072i	0.546610	+	0.837387i	$0.315918\pi$
$314$	3.34506	−	12.4839i	0.188773	−	0.704510i
$315$		0			0
$316$	−52.5150	−	30.3196i	−2.95420	−	1.70561i
$317$	2.92857	+	10.9296i	0.164485	+	0.613866i	0.998105	+	0.0615283i	$0.0195974\pi$
$317$	2.92857	+	10.9296i	0.164485	+	0.613866i	−0.833620	+	0.552338i	$0.813736\pi$
$318$		0			0
$319$	3.83361	+	3.83361i	0.214641	+	0.214641i
$320$	−1.39715	−	5.21424i	−0.0781032	−	0.291485i
$321$		0			0
$322$	−33.2959	−	0.441265i	−1.85551	−	0.0245907i
$323$	9.50052	−	35.4564i	0.528623	−	1.97285i
$324$		0			0
$325$	−3.50737	+	16.6854i	−0.194554	+	0.925540i
$326$	3.98909	+	6.90931i	0.220935	+	0.382672i
$327$		0			0
$328$	−24.0533	+	13.8872i	−1.32812	+	0.766792i
$329$	0.189060	+	0.112520i	0.0104232	+	0.00620345i
$330$		0			0
$331$	17.5461	+	4.70146i	0.964419	+	0.258415i	0.706470	−	0.707743i	$-0.250287\pi$
$331$	17.5461	+	4.70146i	0.964419	+	0.258415i	0.257949	+	0.966158i	$0.416953\pi$
$332$	−34.8627	+	34.8627i	−1.91334	+	1.91334i
$333$		0			0
$334$	21.4991	−	12.4125i	1.17638	−	0.679181i
$335$	2.82961	+	4.90103i	0.154598	+	0.267772i
$336$		0			0
$337$		−	20.1380i		−	1.09698i	−0.836156	−	0.548492i	$-0.815202\pi$
$337$		−	20.1380i		−	1.09698i	0.836156	−	0.548492i	$-0.184798\pi$
$338$	26.6584	+	21.3896i	1.45002	+	1.16344i
$339$		0			0
$340$	−3.37164	−	12.5831i	−0.182853	−	0.682417i
$341$		−	6.70415i		−	0.363050i
$342$		0			0
$343$	12.5650	+	13.6060i	0.678444	+	0.734653i
$344$	−8.29062	−	30.9410i	−0.447000	−	1.66823i
$345$		0			0
$346$	55.8166	+	14.9560i	3.00072	+	0.804041i
$347$	9.62415			0.516651			0.258326	−	0.966058i	$-0.416829\pi$
$347$	9.62415			0.516651			0.258326	+	0.966058i	$0.416829\pi$
$348$		0			0
$349$	24.0092	+	6.43324i	1.28518	+	0.344364i	0.835829	−	0.548990i	$-0.184988\pi$
$349$	24.0092	+	6.43324i	1.28518	+	0.344364i	0.449354	+	0.893354i	$0.351654\pi$
$350$	16.0680	+	28.7024i	0.858872	+	1.53421i
$351$		0			0
$352$	11.7824	−	20.4076i	0.628002	−	1.08773i
$353$	−8.80697	+	2.35982i	−0.468748	+	0.125601i	−0.485458	−	0.874260i	$-0.661347\pi$
$353$	−8.80697	+	2.35982i	−0.468748	+	0.125601i	0.0167107	+	0.999860i	$0.494681\pi$
$354$		0			0
$355$	−1.34801	−	2.33483i	−0.0715452	−	0.123920i
$356$	−47.4040	−	47.4040i	−2.51241	−	2.51241i
$357$		0			0
$358$	43.3712	−	11.6213i	2.29224	−	0.614204i
$359$	3.40024	−	0.911092i	0.179458	−	0.0480856i	−0.167971	−	0.985792i	$-0.553722\pi$
$359$	3.40024	−	0.911092i	0.179458	−	0.0480856i	0.347429	+	0.937706i	$0.387055\pi$
$360$		0			0
$361$	−28.5394	−	16.4772i	−1.50207	−	0.867223i
$362$	−33.4956	+	33.4956i	−1.76049	+	1.76049i
$363$		0			0
$364$	46.8207	−	1.93750i	2.45407	−	0.101553i
$365$	−1.10890			−0.0580422
$366$		0			0
$367$	−1.24910	−	0.721170i	−0.0652026	−	0.0376448i	0.467044	−	0.884234i	$-0.345319\pi$
$367$	−1.24910	−	0.721170i	−0.0652026	−	0.0376448i	−0.532247	+	0.846589i	$0.678652\pi$
$368$			49.3372i			2.57188i
$369$		0			0
$370$	−9.82662	+	2.63304i	−0.510862	+	0.136885i
$371$	34.9141	+	9.85291i	1.81265	+	0.511537i
$372$		0			0
$373$	−3.69487	−	6.39971i	−0.191313	−	0.331364i	0.754372	−	0.656447i	$-0.227941\pi$
$373$	−3.69487	−	6.39971i	−0.191313	−	0.331364i	−0.945686	+	0.325082i	$0.894608\pi$
$374$	13.3883	−	23.1892i	0.692293	−	1.19909i
$375$		0			0
$376$	0.318361	−	0.551417i	0.0164182	−	0.0284371i
$377$	9.56538	+	2.01070i	0.492642	+	0.103556i
$378$		0			0
$379$	−12.7292	−	3.41078i	−0.653855	−	0.175200i	−0.0833836	−	0.996518i	$-0.526573\pi$
$379$	−12.7292	−	3.41078i	−0.653855	−	0.175200i	−0.570471	+	0.821318i	$0.693239\pi$
$380$	−18.4382			−0.945857
$381$		0			0
$382$	56.0474	+	15.0178i	2.86763	+	0.768380i
$383$	−5.33758	+	19.9201i	−0.272738	+	1.01787i	0.684604	+	0.728915i	$0.259975\pi$
$383$	−5.33758	+	19.9201i	−0.272738	+	1.01787i	−0.957342	+	0.288956i	$0.906692\pi$
$384$		0			0
$385$	0.748331	−	2.65174i	0.0381385	−	0.135145i
$386$	9.60509	−	16.6365i	0.488886	−	0.846776i
$387$		0			0
$388$	4.32644	+	16.1465i	0.219642	+	0.819714i
$389$	−31.3755	+	18.1147i	−1.59080	+	0.918449i	−0.597631	+	0.801771i	$0.703891\pi$
$389$	−31.3755	+	18.1147i	−1.59080	+	0.918449i	−0.993170	+	0.116678i	$0.962775\pi$
$390$		0			0
$391$			24.3785i			1.23287i
$392$	38.8910	−	36.8822i	1.96429	−	1.86283i
$393$		0			0
$394$	−53.0818	+	30.6468i	−2.67422	+	1.54396i
$395$	−1.66371	+	6.20905i	−0.0837104	+	0.312411i
$396$		0			0
$397$	−26.4057	−	7.07539i	−1.32526	−	0.355103i	−0.474317	−	0.880354i	$-0.657305\pi$
$397$	−26.4057	−	7.07539i	−1.32526	−	0.355103i	−0.850947	+	0.525251i	$0.823971\pi$
$398$	−33.0139	+	33.0139i	−1.65484	+	1.65484i
$399$		0			0
$400$	42.2078	−	24.3687i	2.11039	−	1.21843i
$401$	−9.72529	−	9.72529i	−0.485658	−	0.485658i	0.421275	−	0.906933i	$-0.361583\pi$
$401$	−9.72529	−	9.72529i	−0.485658	−	0.485658i	−0.906933	+	0.421275i	$0.861583\pi$
$402$		0			0
$403$	−6.60575	−	10.1220i	−0.329056	−	0.504214i
$404$	51.4557	+	29.7080i	2.56002	+	1.47803i
$405$		0			0
$406$	16.4545	−	9.21145i	0.816622	−	0.457157i
$407$	−12.8696	−	7.43026i	−0.637922	−	0.368304i
$408$		0			0
$409$	−11.0025	−	11.0025i	−0.544040	−	0.544040i	0.380671	−	0.924711i	$-0.375693\pi$
$409$	−11.0025	−	11.0025i	−0.544040	−	0.544040i	−0.924711	+	0.380671i	$0.875693\pi$
$410$	3.51160	+	3.51160i	0.173425	+	0.173425i
$411$		0			0
$412$	−34.4096	−	19.8664i	−1.69524	−	0.978748i
$413$	−0.193935	+	14.6335i	−0.00954293	+	0.720066i
$414$		0			0
$415$	4.52622	+	2.61321i	0.222183	+	0.128278i
$416$	−2.31892	−	42.4212i	−0.113694	−	2.07987i
$417$		0			0
$418$	−26.7986	−	26.7986i	−1.31076	−	1.31076i
$419$	17.5367	−	10.1248i	0.856726	−	0.494631i	−0.00618874	−	0.999981i	$-0.501970\pi$
$419$	17.5367	−	10.1248i	0.856726	−	0.494631i	0.862914	+	0.505350i	$0.168637\pi$
$420$		0			0
$421$	14.0732	−	14.0732i	0.685887	−	0.685887i	−0.275433	−	0.961320i	$-0.588821\pi$
$421$	14.0732	−	14.0732i	0.685887	−	0.685887i	0.961320	+	0.275433i	$0.0888213\pi$
$422$	13.6890	+	3.66796i	0.666370	+	0.178553i
$423$		0			0
$424$	27.1733	−	101.412i	1.31965	−	4.92501i
$425$	20.8557	−	12.0410i	1.01165	−	0.584076i
$426$		0			0
$427$	0.541428	−	1.91857i	0.0262015	−	0.0928460i
$428$		−	27.7412i		−	1.34092i
$429$		0			0
$430$	−4.96017	+	2.86375i	−0.239200	+	0.138102i
$431$	−3.34806	−	12.4951i	−0.161270	−	0.601869i	−0.998487	−	0.0549970i	$-0.982485\pi$
$431$	−3.34806	−	12.4951i	−0.161270	−	0.601869i	0.837216	−	0.546872i	$-0.184182\pi$
$432$		0			0
$433$	−10.1407	+	17.5642i	−0.487331	+	0.844082i	−0.999894	−	0.0145673i	$-0.995363\pi$
$433$	−10.1407	+	17.5642i	−0.487331	+	0.844082i	0.512563	+	0.858650i	$0.328696\pi$
$434$	−22.4421	−	6.33325i	−1.07725	−	0.304006i
$435$		0			0
$436$	−12.3125	+	45.9508i	−0.589660	+	2.20064i
$437$	33.3290	+	8.93047i	1.59434	+	0.427202i
$438$		0			0
$439$	21.5170			1.02695			0.513475	−	0.858104i	$-0.328358\pi$
$439$	21.5170			1.02695			0.513475	+	0.858104i	$0.328358\pi$
$440$	−7.70228	−	2.06382i	−0.367192	−	0.0983888i
$441$		0			0
$442$	−2.63499	−	48.2032i	−0.125333	−	2.29279i
$443$	12.3515	−	21.3934i	0.586836	−	1.01643i	−0.407808	−	0.913068i	$-0.633707\pi$
$443$	12.3515	−	21.3934i	0.586836	−	1.01643i	0.994644	−	0.103362i	$-0.0329599\pi$
$444$		0			0
$445$	−3.55328	+	6.15445i	−0.168441	+	0.291749i
$446$	18.8240	+	32.6041i	0.891342	+	1.54385i
$447$		0			0
$448$	−19.1352	−	19.6492i	−0.904051	−	0.928336i
$449$	−36.3730	+	9.74613i	−1.71655	+	0.459948i	−0.977015	−	0.213170i	$-0.931621\pi$
$449$	−36.3730	+	9.74613i	−1.71655	+	0.459948i	−0.739535	+	0.673118i	$0.764955\pi$
$450$		0			0
$451$			7.25426i			0.341590i
$452$	81.7594	+	47.2038i	3.84564	+	2.22028i
$453$		0			0
$454$	15.5604			0.730284
$455$	−1.48297	−	4.74098i	−0.0695228	−	0.222260i
$456$		0			0
$457$	−18.8834	+	18.8834i	−0.883326	+	0.883326i	−0.993871	−	0.110545i	$-0.964740\pi$
$457$	−18.8834	+	18.8834i	−0.883326	+	0.883326i	0.110545	+	0.993871i	$0.464740\pi$
$458$	−67.3058	−	38.8590i	−3.14499	−	1.81576i
$459$		0			0
$460$	11.8281	−	3.16934i	0.551490	−	0.147771i
$461$	−4.97413	+	1.33281i	−0.231668	+	0.0620754i	−0.372785	−	0.927918i	$-0.621597\pi$
$461$	−4.97413	+	1.33281i	−0.231668	+	0.0620754i	0.141117	+	0.989993i	$0.454931\pi$
$462$		0			0
$463$	13.3125	+	13.3125i	0.618683	+	0.618683i	0.945193	−	0.326511i	$-0.105873\pi$
$463$	13.3125	+	13.3125i	0.618683	+	0.618683i	−0.326511	+	0.945193i	$0.605873\pi$
$464$	−13.9700	−	24.1968i	−0.648543	−	1.12331i
$465$		0			0
$466$	6.47865	−	1.73595i	0.300118	−	0.0804162i
$467$	9.27178	−	16.0592i	0.429047	−	0.743131i	−0.567742	−	0.823207i	$-0.692183\pi$
$467$	9.27178	−	16.0592i	0.429047	−	0.743131i	0.996789	+	0.0800755i	$0.0255161\pi$
$468$		0			0
$469$	24.7084	+	14.7054i	1.14093	+	0.679032i
$470$	−0.109968	−	0.0294659i	−0.00507246	−	0.00135916i
$471$		0			0
$472$	42.3537			1.94949
$473$	−8.08133	−	2.16539i	−0.371580	−	0.0995645i
$474$		0			0
$475$	−8.82189	−	32.9238i	−0.404776	−	1.51065i
$476$	−46.1775	−	47.4179i	−2.11654	−	2.17339i
$477$		0			0
$478$		−	27.3494i		−	1.25093i
$479$	5.84154	+	21.8009i	0.266907	+	0.996109i	0.961073	+	0.276294i	$0.0891065\pi$
$479$	5.84154	+	21.8009i	0.266907	+	0.996109i	−0.694167	+	0.719814i	$0.744227\pi$
$480$		0			0
$481$	−26.7519	+	1.46237i	−1.21978	+	0.0666782i
$482$		−	9.50748i		−	0.433054i
$483$		0			0
$484$	17.1944	+	29.7816i	0.781564	+	1.35371i
$485$	1.53460	−	0.885999i	0.0696824	−	0.0402311i
$486$		0			0
$487$	−10.6047	+	10.6047i	−0.480546	+	0.480546i	−0.905306	−	0.424760i	$-0.860359\pi$
$487$	−10.6047	+	10.6047i	−0.480546	+	0.480546i	0.424760	+	0.905306i	$0.360359\pi$
$488$	−5.57271	−	1.49320i	−0.252265	−	0.0675941i
$489$		0			0
$490$	−8.16972	−	5.01006i	−0.369071	−	0.226331i
$491$	−0.576104	+	0.332614i	−0.0259992	+	0.0150106i	−0.512943	−	0.858423i	$-0.671445\pi$
$491$	−0.576104	+	0.332614i	−0.0259992	+	0.0150106i	0.486944	+	0.873433i	$0.338112\pi$
$492$		0			0
$493$	−6.90287	−	11.9561i	−0.310889	−	0.538476i
$494$	−66.8662	−	14.0557i	−3.00845	−	0.632395i
$495$		0			0
$496$	−8.94221	+	33.3728i	−0.401517	+	1.49848i
$497$	−11.7710	−	7.00559i	−0.528001	−	0.314243i
$498$		0			0
$499$	−5.08032	−	18.9600i	−0.227426	−	0.848767i	−0.981418	−	0.191883i	$-0.938541\pi$
$499$	−5.08032	−	18.9600i	−0.227426	−	0.848767i	0.753992	−	0.656884i	$-0.228126\pi$
$500$	−17.5975	−	17.5975i	−0.786985	−	0.786985i
$501$		0			0
$502$	0.0528272	+	0.197154i	0.00235779	+	0.00879941i
$503$	18.5259	+	10.6959i	0.826028	+	0.476907i	0.852491	−	0.522742i	$-0.175091\pi$
$503$	18.5259	+	10.6959i	0.826028	+	0.476907i	−0.0264628	+	0.999650i	$0.508424\pi$
$504$		0			0
$505$	1.63015	−	6.08380i	0.0725407	−	0.270726i
$506$	21.7978	+	12.5850i	0.969032	+	0.559471i
$507$		0			0
$508$	16.4009	+	28.4071i	0.727671	+	1.26036i
$509$	24.0095	+	24.0095i	1.06420	+	1.06420i	0.997792	+	0.0664113i	$0.0211549\pi$
$509$	24.0095	+	24.0095i	1.06420	+	1.06420i	0.0664113	+	0.997792i	$0.478845\pi$
$510$		0			0
$511$	−4.91615	+	2.75213i	−0.217478	+	0.121747i
$512$	25.7315	−	25.7315i	1.13718	−	1.13718i
$513$		0			0
$514$	4.25697	−	4.25697i	0.187767	−	0.187767i
$515$	−1.09012	+	4.06838i	−0.0480364	+	0.179274i
$516$		0			0
$517$	−0.0831510	−	0.144022i	−0.00365698	−	0.00633407i
$518$	−37.0303	+	36.0616i	−1.62702	+	1.58446i
$519$		0			0
$520$	−13.6625	+	4.47324i	−0.599142	+	0.196164i
$521$	−3.73842	+	2.15838i	−0.163783	+	0.0945602i	−0.579651	−	0.814865i	$-0.696811\pi$
$521$	−3.73842	+	2.15838i	−0.163783	+	0.0945602i	0.415868	+	0.909425i	$0.363478\pi$
$522$		0			0
$523$		−	35.4260i		−	1.54907i	−0.632530	−	0.774536i	$-0.717983\pi$
$523$		−	35.4260i		−	1.54907i	0.632530	−	0.774536i	$-0.282017\pi$
$524$	0.762931	−	1.32144i	0.0333288	−	0.0577272i
$525$		0			0
$526$	−3.43080	−	12.8039i	−0.149590	−	0.558277i
$527$	−4.41852	+	16.4901i	−0.192474	+	0.718322i
$528$		0			0
$529$	0.0842834			0.00366450
$530$	−18.7725			−0.815423
$531$		0			0
$532$	−81.7433	+	45.7610i	−3.54402	+	1.98399i
$533$	7.14778	+	10.9526i	0.309605	+	0.474409i
$534$		0			0
$535$	−2.84052	+	0.761115i	−0.122806	+	0.0329059i
$536$	41.6068	−	72.0652i	1.79714	−	3.11274i
$537$		0			0
$538$	−30.4696	−	30.4696i	−1.31364	−	1.31364i
$539$	−3.26362	−	13.6134i	−0.140574	−	0.586371i
$540$		0			0
$541$	2.85763	−	0.765699i	0.122859	−	0.0329200i	−0.196866	−	0.980430i	$-0.563076\pi$
$541$	2.85763	−	0.765699i	0.122859	−	0.0329200i	0.319725	+	0.947511i	$0.396410\pi$
$542$		−	17.2697i		−	0.741798i
$543$		0			0
$544$	−42.4310	+	42.4310i	−1.81922	+	1.81922i
$545$	5.04287			0.216013
$546$		0			0
$547$	14.0808			0.602052			0.301026	−	0.953616i	$-0.402671\pi$
$547$	14.0808			0.602052			0.301026	+	0.953616i	$0.402671\pi$
$548$	16.8246	−	16.8246i	0.718709	−	0.718709i
$549$		0			0
$550$		−	24.8639i		−	1.06020i
$551$	−18.8745	+	5.05740i	−0.804080	+	0.215453i
$552$		0			0
$553$	8.03418	+	31.6562i	0.341648	+	1.34616i
$554$	−2.89973	−	2.89973i	−0.123198	−	0.123198i
$555$		0			0
$556$	−26.2905	+	45.5364i	−1.11496	+	1.93117i
$557$	35.9605	−	9.63559i	1.52370	−	0.408273i	0.602739	−	0.797939i	$-0.294076\pi$
$557$	35.9605	−	9.63559i	1.52370	−	0.408273i	0.920956	+	0.389666i	$0.127409\pi$
$558$		0			0
$559$	−14.3349	+	4.69338i	−0.606302	+	0.198509i
$560$	−7.26210	+	12.2020i	−0.306880	+	0.515628i
$561$		0			0
$562$	1.93020			0.0814207
$563$	44.2524			1.86502			0.932508	−	0.361149i	$-0.117616\pi$
$563$	44.2524			1.86502			0.932508	+	0.361149i	$0.117616\pi$
$564$		0			0
$565$	2.59019	−	9.66673i	0.108970	−	0.406682i
$566$	−18.7327	−	69.9115i	−0.787395	−	2.93860i
$567$		0			0
$568$	−19.8213	+	34.3315i	−0.831684	+	1.44052i
$569$			8.31408i			0.348545i	0.984698	+	0.174272i	$0.0557573\pi$
$569$			8.31408i			0.348545i	−0.984698	+	0.174272i	$0.944243\pi$
$570$		0			0
$571$	−21.7326	+	12.5473i	−0.909481	+	0.525089i	−0.880264	−	0.474484i	$-0.842635\pi$
$571$	−21.7326	+	12.5473i	−0.909481	+	0.525089i	−0.0292166	+	0.999573i	$0.509301\pi$
$572$	−31.5966	−	16.0099i	−1.32112	−	0.669406i
$573$		0			0
$574$	24.2835	+	6.85292i	1.01358	+	0.286035i
$575$	11.3186	+	19.6043i	0.472016	+	0.817556i
$576$		0			0
$577$	−6.85235	+	25.5733i	−0.285267	+	1.06463i	0.663377	+	0.748285i	$0.269123\pi$
$577$	−6.85235	+	25.5733i	−0.285267	+	1.06463i	−0.948644	+	0.316346i	$0.897544\pi$
$578$	−16.6101	+	16.6101i	−0.690889	+	0.690889i
$579$		0			0
$580$	−4.90355	+	4.90355i	−0.203609	+	0.203609i
$581$	26.5521	+	0.351891i	1.10157	+	0.0145989i
$582$		0			0
$583$	−19.3901	−	19.3901i	−0.803055	−	0.803055i
$584$	8.15264	+	14.1208i	0.337359	+	0.584322i
$585$		0			0
$586$	−24.4871	−	14.1376i	−1.01155	−	0.584020i
$587$	0.317942	−	1.18658i	0.0131229	−	0.0489752i	−0.959054	−	0.283223i	$-0.908596\pi$
$587$	0.317942	−	1.18658i	0.0131229	−	0.0489752i	0.972177	+	0.234248i	$0.0752629\pi$
$588$		0			0
$589$	20.9258	+	12.0815i	0.862234	+	0.497811i
$590$	−1.96003	−	7.31493i	−0.0806931	−	0.301151i
$591$		0			0
$592$	54.1531	+	54.1531i	2.22568	+	2.22568i
$593$	−5.90295	−	22.0301i	−0.242405	−	0.904669i	−0.974670	−	0.223648i	$-0.928203\pi$
$593$	−5.90295	−	22.0301i	−0.242405	−	0.904669i	0.732265	−	0.681020i	$-0.238463\pi$
$594$		0			0
$595$	−3.58835	+	6.02924i	−0.147108	+	0.247175i
$596$	−21.6447	+	80.7793i	−0.886603	+	3.30885i
$597$		0			0
$598$	45.3109	−	2.47688i	1.85290	−	0.101287i
$599$	−4.86660	−	8.42920i	−0.198844	−	0.344408i	0.749310	−	0.662220i	$-0.230385\pi$
$599$	−4.86660	−	8.42920i	−0.198844	−	0.344408i	−0.948154	+	0.317812i	$0.897052\pi$
$600$		0			0
$601$	−7.28411	+	4.20549i	−0.297125	+	0.171545i	−0.641151	−	0.767415i	$-0.721543\pi$
$601$	−7.28411	+	4.20549i	−0.297125	+	0.171545i	0.344025	+	0.938960i	$0.388209\pi$
$602$	−14.8828	+	25.0066i	−0.606579	+	1.01919i
$603$		0			0
$604$	86.6795	+	23.2257i	3.52694	+	0.945041i
$605$	2.57769	−	2.57769i	0.104798	−	0.104798i
$606$		0			0
$607$	23.0886	−	13.3302i	0.937136	−	0.541056i	0.0480748	−	0.998844i	$-0.484691\pi$
$607$	23.0886	−	13.3302i	0.937136	−	0.541056i	0.889061	+	0.457788i	$0.151358\pi$
$608$	42.4659	+	73.5531i	1.72222	+	2.98297i
$609$		0			0
$610$			1.03157i			0.0417669i
$611$	−0.267450	−	0.135516i	−0.0108199	−	0.00548238i
$612$		0			0
$613$	2.45780	+	9.17262i	0.0992695	+	0.370479i	0.997632	−	0.0687757i	$-0.0219093\pi$
$613$	2.45780	+	9.17262i	0.0992695	+	0.370479i	−0.898363	+	0.439255i	$0.855243\pi$
$614$		−	9.75805i		−	0.393803i
$615$		0			0
$616$	−39.2692	+	9.96634i	−1.58220	+	0.401555i
$617$	2.76556	+	10.3212i	0.111337	+	0.415516i	0.998987	−	0.0450034i	$-0.0143299\pi$
$617$	2.76556	+	10.3212i	0.111337	+	0.415516i	−0.887650	+	0.460519i	$0.847663\pi$
$618$		0			0
$619$	−17.3520	−	4.64947i	−0.697438	−	0.186878i	−0.107355	−	0.994221i	$-0.534238\pi$
$619$	−17.3520	−	4.64947i	−0.697438	−	0.186878i	−0.590083	+	0.807343i	$0.700905\pi$
$620$	8.57525			0.344390
$621$		0			0
$622$	−13.6613	−	3.66052i	−0.547767	−	0.146774i
$623$	−0.478478	+	36.1038i	−0.0191698	+	1.44647i
$624$		0			0
$625$	10.5030	−	18.1918i	0.420121	−	0.727671i
$626$	−80.1601	+	21.4788i	−3.20384	+	0.858467i
$627$		0			0
$628$	12.0741	+	20.9129i	0.481808	+	0.834516i
$629$	26.7581	+	26.7581i	1.06692	+	1.06692i
$630$		0			0
$631$	17.3537	−	4.64990i	0.690838	−	0.185110i	0.103715	−	0.994607i	$-0.466927\pi$
$631$	17.3537	−	4.64990i	0.690838	−	0.185110i	0.587123	+	0.809497i	$0.300260\pi$
$632$	91.2984	−	24.4633i	3.63165	−	0.973099i
$633$		0			0
$634$	−25.7634	−	14.8745i	−1.02319	−	0.590741i
$635$	2.45873	−	2.45873i	0.0975717	−	0.0975717i
$636$		0			0
$637$	−18.3410	−	17.3380i	−0.726699	−	0.686956i
$638$	−14.2540			−0.564320
$639$		0			0
$640$	1.66346	+	0.960400i	0.0657541	+	0.0379631i
$641$		−	7.16758i		−	0.283103i	−0.989931	−	0.141551i	$-0.954791\pi$
$641$		−	7.16758i		−	0.283103i	0.989931	−	0.141551i	$-0.0452090\pi$
$642$		0			0
$643$	−41.0624	+	11.0026i	−1.61934	+	0.433902i	−0.950809	−	0.309779i	$-0.899745\pi$
$643$	−41.0624	+	11.0026i	−1.61934	+	0.433902i	−0.668535	+	0.743681i	$0.733078\pi$
$644$	44.5727	−	43.4067i	1.75641	−	1.71046i
$645$		0			0
$646$	48.2541	+	83.5785i	1.89853	+	3.28835i
$647$	2.36487	−	4.09607i	0.0929726	−	0.161033i	−0.815788	−	0.578351i	$-0.803696\pi$
$647$	2.36487	−	4.09607i	0.0929726	−	0.161033i	0.908761	+	0.417318i	$0.137030\pi$
$648$		0			0
$649$	5.53108	−	9.58010i	0.217114	−	0.376052i
$650$	−24.4990	−	37.5400i	−0.960929	−	1.47244i
$651$		0			0
$652$	−14.3987	−	3.85813i	−0.563898	−	0.151096i
$653$	−0.163738			−0.00640757			−0.00320379	−	0.999995i	$-0.501020\pi$
$653$	−0.163738			−0.00640757			−0.00320379	+	0.999995i	$0.501020\pi$
$654$		0			0
$655$	−0.156238	−	0.0418640i	−0.00610474	−	0.00163576i
$656$	9.67595	−	36.1111i	0.377782	−	1.40990i
$657$		0			0
$658$	−0.560662	+	0.142293i	−0.0218569	+	0.00554717i
$659$	11.4177	−	19.7761i	0.444772	−	0.770367i	−0.553265	−	0.833006i	$-0.686618\pi$
$659$	11.4177	−	19.7761i	0.444772	−	0.770367i	0.998036	+	0.0626385i	$0.0199515\pi$
$660$		0			0
$661$	8.21684	+	30.6657i	0.319598	+	1.19276i	0.919632	+	0.392782i	$0.128487\pi$
$661$	8.21684	+	30.6657i	0.319598	+	1.19276i	−0.600034	+	0.799975i	$0.704846\pi$
$662$	−41.3599	+	23.8791i	−1.60750	+	0.928089i
$663$		0			0
$664$		−	76.8497i		−	2.98235i
$665$	6.92836	+	7.11447i	0.268670	+	0.275887i
$666$		0			0
$667$	11.2387	−	6.48868i	0.435165	−	0.251243i
$668$	−12.0050	+	44.8032i	−0.464486	+	1.73349i
$669$		0			0
$670$	−14.3719	−	3.85093i	−0.555234	−	0.148774i
$671$	−1.06551	+	1.06551i	−0.0411334	+	0.0411334i
$672$		0			0
$673$	−31.2839	+	18.0618i	−1.20591	+	0.696231i	−0.961862	−	0.273534i	$-0.911808\pi$
$673$	−31.2839	+	18.0618i	−1.20591	+	0.696231i	−0.244044	+	0.969764i	$0.578474\pi$
$674$	37.4380	+	37.4380i	1.44206	+	1.44206i
$675$		0			0
$676$	−63.4799	+	6.96095i	−2.44154	+	0.267729i
$677$	34.8720	+	20.1334i	1.34024	+	0.773788i	0.986842	−	0.161685i	$-0.0516928\pi$
$677$	34.8720	+	20.1334i	1.34024	+	0.773788i	0.353398	+	0.935473i	$0.385026\pi$
$678$		0			0
$679$	4.60451	−	7.73663i	0.176705	−	0.296904i
$680$	17.5850	+	10.1527i	0.674354	+	0.389339i
$681$		0			0
$682$	12.4635	+	12.4635i	0.477254	+	0.477254i
$683$	23.3739	+	23.3739i	0.894376	+	0.894376i	0.994931	−	0.100555i	$-0.0320620\pi$
$683$	23.3739	+	23.3739i	0.894376	+	0.894376i	−0.100555	+	0.994931i	$0.532062\pi$
$684$		0			0
$685$	−2.18433	−	1.26112i	−0.0834589	−	0.0481850i
$686$	−48.6538	−	1.93531i	−1.85761	−	0.0738905i
$687$		0			0
$688$	37.3400	+	21.5583i	1.42357	+	0.821901i
$689$	−48.3809	−	10.1700i	−1.84317	−	0.387445i
$690$		0			0
$691$	−9.86544	−	9.86544i	−0.375299	−	0.375299i	0.494104	−	0.869403i	$-0.335496\pi$
$691$	−9.86544	−	9.86544i	−0.375299	−	0.375299i	−0.869403	+	0.494104i	$0.835496\pi$
$692$	−93.5032	+	53.9841i	−3.55446	+	2.05217i
$693$		0			0
$694$	−17.8920	+	17.8920i	−0.679173	+	0.679173i
$695$	5.38395	+	1.44262i	0.204225	+	0.0547218i
$696$		0			0
$697$	4.78107	−	17.8432i	0.181096	−	0.675860i
$698$	−56.5949	+	32.6751i	−2.14215	+	1.23677i
$699$		0			0
$700$	−59.1497	−	16.6923i	−2.23565	−	0.630909i
$701$		−	26.0431i		−	0.983633i	−0.870699	−	0.491817i	$-0.836333\pi$
$701$		−	26.0431i		−	0.983633i	0.870699	−	0.491817i	$-0.163667\pi$
$702$		0			0
$703$	46.3845	−	26.7801i	1.74942	−	1.01003i
$704$	5.36574	+	20.0252i	0.202229	+	0.754729i
$705$		0			0
$706$	11.9857	−	20.7599i	0.451090	−	0.781310i
$707$	−7.87212	−	31.0176i	−0.296061	−	1.16654i
$708$		0			0
$709$	−1.11304	+	4.15393i	−0.0418012	+	0.156004i	−0.983672	−	0.179972i	$-0.942399\pi$
$709$	−1.11304	+	4.15393i	−0.0418012	+	0.156004i	0.941871	+	0.335976i	$0.109066\pi$
$710$	6.84669	+	1.83457i	0.256952	+	0.0688500i
$711$		0			0
$712$	104.495			3.91613
$713$	−15.5007	−	4.15340i	−0.580506	−	0.155546i
$714$		0			0
$715$	−0.772411	+	3.67454i	−0.0288865	+	0.137420i
$716$	−41.9473	+	72.6548i	−1.56764	+	2.71524i
$717$		0			0
$718$	−4.62752	+	8.01510i	−0.172698	+	0.299121i
$719$	−2.25577	−	3.90711i	−0.0841260	−	0.145710i	0.820892	−	0.571083i	$-0.193476\pi$
$719$	−2.25577	−	3.90711i	−0.0841260	−	0.145710i	−0.905018	+	0.425372i	$0.860143\pi$
$720$		0			0
$721$	5.26427	+	20.7422i	0.196052	+	0.772480i
$722$	83.6895	−	22.4245i	3.11460	−	0.834554i
$723$		0			0
$724$		−	88.5072i		−	3.28934i
$725$	−11.1021	−	6.40979i	−0.412321	−	0.238054i
$726$		0			0
$727$	−6.85388			−0.254196			−0.127098	−	0.991890i	$-0.540566\pi$
$727$	−6.85388			−0.254196			−0.127098	+	0.991890i	$0.540566\pi$
$728$	−49.4692	+	53.7402i	−1.83345	+	1.99174i
$729$		0			0
$730$	2.06152	−	2.06152i	0.0763004	−	0.0763004i
$731$	18.4504	+	10.6524i	0.682413	+	0.393991i
$732$		0			0
$733$	−18.9182	+	5.06911i	−0.698758	+	0.187232i	−0.590674	−	0.806910i	$-0.701138\pi$
$733$	−18.9182	+	5.06911i	−0.698758	+	0.187232i	−0.108084	+	0.994142i	$0.534472\pi$
$734$	3.66289	−	0.981468i	0.135200	−	0.0362267i
$735$		0			0
$736$	−39.8851	−	39.8851i	−1.47018	−	1.47018i
$737$	−10.8671	−	18.8223i	−0.400294	−	0.693330i
$738$		0			0
$739$	9.19560	−	2.46395i	0.338266	−	0.0906380i	−0.0856877	−	0.996322i	$-0.527309\pi$
$739$	9.19560	−	2.46395i	0.338266	−	0.0906380i	0.423953	+	0.905684i	$0.360642\pi$
$740$	9.50400	−	16.4614i	0.349374	−	0.605133i
$741$		0			0
$742$	−83.2254	+	46.5907i	−3.05530	+	1.71040i
$743$	−33.4189	−	8.95458i	−1.22602	−	0.328512i	−0.412993	−	0.910734i	$-0.635516\pi$
$743$	−33.4189	−	8.95458i	−1.22602	−	0.328512i	−0.813029	+	0.582223i	$0.802183\pi$
$744$		0			0
$745$	8.86513			0.324793
$746$	18.7666	+	5.02850i	0.687095	+	0.184106i
$747$		0			0
$748$	12.9487	+	48.3254i	0.473453	+	1.76695i
$749$	−10.7041	+	10.4241i	−0.391120	+	0.380889i
$750$		0			0
$751$		−	42.7601i		−	1.56034i	−0.625568	−	0.780169i	$-0.715133\pi$
$751$		−	42.7601i		−	1.56034i	0.625568	−	0.780169i	$-0.284867\pi$
$752$	0.221819	+	0.827839i	0.00808890	+	0.0301882i
$753$		0			0
$754$	−21.5208	+	14.0447i	−0.783743	+	0.511479i
$755$		−	9.51265i		−	0.346201i
$756$		0			0
$757$	0.327683	+	0.567563i	0.0119098	+	0.0206284i	0.871919	−	0.489650i	$-0.162876\pi$
$757$	0.327683	+	0.567563i	0.0119098	+	0.0206284i	−0.860009	+	0.510279i	$0.829542\pi$
$758$	30.0055	−	17.3237i	1.08985	−	0.629224i
$759$		0			0
$760$	20.3221	−	20.3221i	0.737160	−	0.737160i
$761$	−11.7122	−	3.13826i	−0.424565	−	0.113762i	0.0402086	−	0.999191i	$-0.487198\pi$
$761$	−11.7122	−	3.13826i	−0.424565	−	0.113762i	−0.464774	+	0.885429i	$0.653864\pi$
$762$		0			0
$763$	22.3569	−	12.5157i	0.809375	−	0.453100i
$764$	−93.8897	+	54.2073i	−3.39681	+	1.96115i
$765$		0			0
$766$	−27.1101	−	46.9561i	−0.979528	−	1.69659i
$767$	−1.08858	−	19.9141i	−0.0393065	−	0.719056i
$768$		0			0
$769$	−1.93954	+	7.23846i	−0.0699416	+	0.261025i	−0.992039	−	0.125933i	$-0.959808\pi$
$769$	−1.93954	+	7.23846i	−0.0699416	+	0.261025i	0.922097	+	0.386958i	$0.126474\pi$
$770$	3.53858	+	6.32099i	0.127522	+	0.227793i
$771$		0			0
$772$	9.28974	+	34.6698i	0.334345	+	1.24779i
$773$	−21.6844	−	21.6844i	−0.779935	−	0.779935i	0.199884	−	0.979820i	$-0.435943\pi$
$773$	−21.6844	−	21.6844i	−0.779935	−	0.779935i	−0.979820	+	0.199884i	$0.935943\pi$
$774$		0			0
$775$	4.10290	+	15.3122i	0.147381	+	0.550032i
$776$	−22.5648	−	13.0278i	−0.810029	−	0.467671i
$777$		0			0
$778$	24.6529	−	92.0061i	0.883851	−	3.29858i
$779$	−22.6429	−	13.0729i	−0.811265	−	0.468384i
$780$		0			0
$781$	5.17703	+	8.96688i	0.185249	+	0.320860i
$782$	−45.3215	−	45.3215i	−1.62069	−	1.62069i
$783$		0			0
$784$	−1.91192	+	72.1196i	−0.0682827	+	2.57570i
$785$	1.81008	−	1.81008i	0.0646045	−	0.0646045i
$786$		0			0
$787$	3.22124	−	3.22124i	0.114825	−	0.114825i	−0.647360	−	0.762185i	$-0.724127\pi$
$787$	3.22124	−	3.22124i	0.114825	−	0.114825i	0.762185	+	0.647360i	$0.224127\pi$
$788$	29.6406	−	110.620i	1.05590	−	3.94068i
$789$		0			0
$790$	−8.45015	−	14.6361i	−0.300643	−	0.520728i
$791$	−12.5082	−	49.2847i	−0.444741	−	1.75236i
$792$		0			0
$793$	−0.558850	+	2.65858i	−0.0198454	+	0.0944090i
$794$	62.2440	−	35.9366i	2.20896	−	1.27534i
$795$		0			0
$796$		−	87.2344i		−	3.09194i
$797$	−16.9732	+	29.3985i	−0.601222	+	1.04135i	0.391414	+	0.920215i	$0.371986\pi$
$797$	−16.9732	+	29.3985i	−0.601222	+	1.04135i	−0.992636	+	0.121133i	$0.961347\pi$
$798$		0			0
$799$	0.109605	+	0.409051i	0.00387754	+	0.0144712i
$800$	−14.4215	+	53.8216i	−0.509876	+	1.90288i
$801$		0			0
$802$	36.1602			1.27686
$803$	4.25870			0.150286
$804$		0			0
$805$	−5.66748	−	3.37304i	−0.199752	−	0.118884i
$806$	31.0983	+	6.53704i	1.09539	+	0.230258i
$807$		0			0
$808$	−89.4567	+	23.9699i	−3.14708	+	0.843257i
$809$	14.3337	−	24.8266i	0.503945	−	0.872858i	−0.496045	−	0.868297i	$-0.665215\pi$
$809$	14.3337	−	24.8266i	0.503945	−	0.872858i	0.999990	−	0.00456129i	$-0.00145191\pi$
$810$		0			0
$811$	−3.29098	−	3.29098i	−0.115562	−	0.115562i	0.646961	−	0.762523i	$-0.276040\pi$
$811$	−3.29098	−	3.29098i	−0.115562	−	0.115562i	−0.762523	+	0.646961i	$0.776040\pi$
$812$	−9.56933	+	33.9092i	−0.335818	+	1.18998i
$813$		0			0
$814$	37.7390	−	10.1121i	1.32275	−	0.354430i
$815$			1.58019i			0.0553516i
$816$		0			0
$817$	21.3222	−	21.3222i	0.745970	−	0.745970i
$818$	40.9091			1.43035
$819$		0			0
$820$	−9.27888			−0.324032
$821$	21.0650	−	21.0650i	0.735173	−	0.735173i	−0.236467	−	0.971640i	$-0.575989\pi$
$821$	21.0650	−	21.0650i	0.735173	−	0.735173i	0.971640	+	0.236467i	$0.0759895\pi$
$822$		0			0
$823$		−	33.1629i		−	1.15599i	−0.816042	−	0.577993i	$-0.803836\pi$
$823$		−	33.1629i		−	1.15599i	0.816042	−	0.577993i	$-0.196164\pi$
$824$	59.8218	−	16.0292i	2.08399	−	0.558404i
$825$		0			0
$826$	−26.8442	−	27.5653i	−0.934030	−	0.959119i
$827$	13.0460	+	13.0460i	0.453653	+	0.453653i	0.896565	−	0.442912i	$-0.146055\pi$
$827$	13.0460	+	13.0460i	0.453653	+	0.453653i	−0.442912	+	0.896565i	$0.646055\pi$
$828$		0			0
$829$	−12.5689	+	21.7699i	−0.436535	+	0.756101i	−0.997420	−	0.0717931i	$-0.977128\pi$
$829$	−12.5689	+	21.7699i	−0.436535	+	0.756101i	0.560884	+	0.827894i	$0.310461\pi$
$830$	−13.2728	+	3.55642i	−0.460704	+	0.123445i
$831$		0			0
$832$	27.8326	+	24.9474i	0.964921	+	0.864895i
$833$	−0.944715	+	35.6357i	−0.0327324	+	1.23470i
$834$		0			0
$835$	4.91692			0.170157
$836$	70.8114			2.44906
$837$		0			0
$838$	−13.7793	+	51.4250i	−0.475998	+	1.77645i
$839$	1.98291	+	7.40032i	0.0684577	+	0.255488i	0.991670	−	0.128802i	$-0.0411131\pi$
$839$	1.98291	+	7.40032i	0.0684577	+	0.255488i	−0.923213	+	0.384289i	$0.874446\pi$
$840$		0			0
$841$	10.8254	−	18.7502i	0.373290	−	0.646557i
$842$			52.3264i			1.80329i
$843$		0			0
$844$	−22.9316	+	13.2396i	−0.789339	+	0.455725i
$845$	2.45441	+	6.30895i	0.0844342	+	0.217035i
$846$		0			0
$847$	5.03039	−	17.8254i	0.172846	−	0.612487i
$848$	70.6593	+	122.385i	2.42645	+	4.20273i
$849$		0			0
$850$	−16.3871	+	61.1576i	−0.562074	+	2.09769i
$851$	−25.1526	+	25.1526i	−0.862219	+	0.862219i
$852$		0			0
$853$	−18.8489	+	18.8489i	−0.645373	+	0.645373i	−0.951871	−	0.306498i	$-0.900843\pi$
$853$	−18.8489	+	18.8489i	−0.645373	+	0.645373i	0.306498	+	0.951871i	$0.400843\pi$
$854$	2.56021	+	4.57332i	0.0876086	+	0.156496i
$855$		0			0
$856$	30.5757	+	30.5757i	1.04506	+	1.04506i
$857$	−9.97165	−	17.2714i	−0.340625	−	0.589980i	0.643924	−	0.765090i	$-0.277305\pi$
$857$	−9.97165	−	17.2714i	−0.340625	−	0.589980i	−0.984549	+	0.175110i	$0.943972\pi$
$858$		0			0
$859$	0.354309	+	0.204560i	0.0120889	+	0.00697950i	0.506032	−	0.862515i	$-0.331112\pi$
$859$	0.354309	+	0.204560i	0.0120889	+	0.00697950i	−0.493943	+	0.869494i	$0.664445\pi$
$860$	2.76973	−	10.3368i	0.0944471	−	0.352481i
$861$		0			0
$862$	29.4537	+	17.0051i	1.00320	+	0.579196i
$863$	−2.85743	−	10.6641i	−0.0972682	−	0.363010i	0.900085	−	0.435714i	$-0.143504\pi$
$863$	−2.85743	−	10.6641i	−0.0972682	−	0.363010i	−0.997354	+	0.0727037i	$0.976837\pi$
$864$		0			0
$865$	8.09300	+	8.09300i	0.275170	+	0.275170i
$866$	−13.8009	−	51.5056i	−0.468973	−	1.75023i
$867$		0			0
$868$	38.0173	−	21.2826i	1.29039	−	0.722379i
$869$	6.38945	−	23.8458i	0.216747	−	0.808912i
$870$		0			0
$871$	−34.9533	−	17.7107i	−1.18435	−	0.600103i
$872$	−37.0754	−	64.2164i	−1.25553	−	2.17464i
$873$		0			0
$874$	−78.5636	+	45.3587i	−2.65745	+	1.53428i
$875$	−0.177623	+	13.4026i	−0.00600474	+	0.453090i
$876$		0			0
$877$	26.4696	+	7.09251i	0.893815	+	0.239497i	0.676358	−	0.736573i	$-0.263557\pi$
$877$	26.4696	+	7.09251i	0.893815	+	0.239497i	0.217457	+	0.976070i	$0.430224\pi$
$878$	−40.0018	+	40.0018i	−1.34999	+	1.34999i
$879$		0			0
$880$	9.29521	−	5.36659i	0.313341	−	0.180908i
$881$	−15.9556	−	27.6359i	−0.537557	−	0.931077i	−0.999035	−	0.0439247i	$-0.986014\pi$
$881$	−15.9556	−	27.6359i	−0.537557	−	0.931077i	0.461478	−	0.887152i	$-0.347319\pi$
$882$		0			0
$883$			32.9852i			1.11004i	0.831837	+	0.555019i	$0.187289\pi$
$883$			32.9852i			1.11004i	−0.831837	+	0.555019i	$0.812711\pi$
$884$	67.1663	+	60.2037i	2.25905	+	2.02487i
$885$		0			0
$886$	16.8096	+	62.7343i	0.564729	+	2.10760i
$887$			22.5285i			0.756433i	0.925717	+	0.378217i	$0.123463\pi$
$887$			22.5285i			0.756433i	−0.925717	+	0.378217i	$0.876537\pi$
$888$		0			0
$889$	4.79823	−	17.0027i	0.160928	−	0.570252i
$890$	−4.83579	−	18.0474i	−0.162096	−	0.604951i
$891$		0			0
$892$	−67.9456	−	18.2060i	−2.27499	−	0.609581i
$893$	0.599385			0.0200576
$894$		0			0
$895$	8.59026	+	2.30175i	0.287141	+	0.0769391i
$896$	9.75834	+	0.129326i	0.326003	+	0.00432047i
$897$		0			0
$898$	49.5015	−	85.7392i	1.65189	−	2.86115i
$899$	8.77818	−	2.35211i	0.292769	−	0.0784471i
$900$		0			0
$901$	34.9141	+	60.4730i	1.16316	+	2.01465i
$902$	−13.4862	−	13.4862i	−0.449042	−	0.449042i
$903$		0			0
$904$	−142.140	+	38.0864i	−4.72752	+	1.26673i
$905$	−9.06256	+	2.42831i	−0.301250	+	0.0807197i
$906$		0			0
$907$	−22.7405	−	13.1293i	−0.755087	−	0.435950i	0.0724419	−	0.997373i	$-0.476921\pi$
$907$	−22.7405	−	13.1293i	−0.755087	−	0.435950i	−0.827529	+	0.561423i	$0.810254\pi$
$908$	−20.5580	+	20.5580i	−0.682241	+	0.682241i
$909$		0			0
$910$	11.5708	+	6.05689i	0.383568	+	0.200784i
$911$	6.71393			0.222442			0.111221	−	0.993796i	$-0.464524\pi$
$911$	6.71393			0.222442			0.111221	+	0.993796i	$0.464524\pi$
$912$		0			0
$913$	−17.3829	−	10.0360i	−0.575289	−	0.332143i
$914$		−	70.2113i		−	2.32238i
$915$		0			0
$916$	140.263	−	37.5832i	4.63441	−	1.24179i
$917$	−0.796565	+	0.202164i	−0.0263049	+	0.00667605i
$918$		0			0
$919$	−23.9836	−	41.5408i	−0.791146	−	1.37031i	−0.925258	−	0.379339i	$-0.876151\pi$
$919$	−23.9836	−	41.5408i	−0.791146	−	1.37031i	0.134111	−	0.990966i	$-0.457182\pi$
$920$	−9.54353	+	16.5299i	−0.314641	+	0.544974i
$921$		0			0
$922$	6.76949	−	11.7251i	0.222941	−	0.386146i
$923$	16.6516	+	8.43728i	0.548094	+	0.277717i
$924$		0			0
$925$	33.9413	+	9.09454i	1.11598	+	0.299027i
$926$	−49.4978			−1.62660
$927$		0			0
$928$	30.8548	+	8.26751i	1.01286	+	0.271394i
$929$	−2.91557	+	10.8811i	−0.0956569	+	0.356996i	−0.997118	−	0.0758633i	$-0.975829\pi$
$929$	−2.91557	+	10.8811i	−0.0956569	+	0.356996i	0.901461	+	0.432860i	$0.142495\pi$
$930$		0			0
$931$	48.3732	+	14.3459i	1.58537	+	0.470166i
$932$	−6.26594	+	10.8529i	−0.205248	+	0.355500i
$933$		0			0
$934$	12.6183	+	47.0923i	0.412885	+	1.54091i
$935$	4.59294	−	2.65174i	0.150205	−	0.0867210i
$936$		0			0
$937$		−	15.4167i		−	0.503641i	−0.967774	−	0.251820i	$-0.918971\pi$
$937$		−	15.4167i		−	0.503641i	0.967774	−	0.251820i	$-0.0810292\pi$
$938$	−73.2734	+	18.5964i	−2.39246	+	0.607195i
$939$		0			0
$940$	0.184217	−	0.106358i	0.00600851	−	0.00346902i
$941$	2.10255	−	7.84684i	0.0685413	−	0.255800i	−0.923150	−	0.384440i	$-0.874395\pi$
$941$	2.10255	−	7.84684i	0.0685413	−	0.255800i	0.991691	+	0.128640i	$0.0410613\pi$
$942$		0			0
$943$	16.7726	+	4.49420i	0.546191	+	0.146351i
$944$	−40.3115	+	40.3115i	−1.31203	+	1.31203i
$945$		0			0
$946$	19.0494	−	10.9982i	0.619351	−	0.357582i
$947$	1.03018	+	1.03018i	0.0334764	+	0.0334764i	0.723647	−	0.690170i	$-0.242464\pi$
$947$	1.03018	+	1.03018i	0.0334764	+	0.0334764i	−0.690170	+	0.723647i	$0.742464\pi$
$948$		0			0
$949$	6.42984	−	4.19619i	0.208721	−	0.136214i
$950$	77.6084	+	44.8072i	2.51795	+	1.45374i
$951$		0			0
$952$	103.159	+	1.36715i	3.34339	+	0.0443095i
$953$	−21.4785	−	12.4006i	−0.695756	−	0.401695i	0.110009	−	0.993931i	$-0.464912\pi$
$953$	−21.4785	−	12.4006i	−0.695756	−	0.401695i	−0.805765	+	0.592236i	$0.798245\pi$
$954$		0			0
$955$	8.12645	+	8.12645i	0.262966	+	0.262966i
$956$	36.1334	+	36.1334i	1.16864	+	1.16864i
$957$		0			0
$958$	−51.3895	−	29.6697i	−1.66032	−	0.958585i
$959$	−12.8139	−	0.169820i	−0.413782	−	0.00548379i
$960$		0			0
$961$	17.1146	+	9.88110i	0.552083	+	0.318745i
$962$	47.0152	−	52.4525i	1.51583	−	1.69114i
$963$		0			0
$964$	12.5611	+	12.5611i	0.404565	+	0.404565i
$965$	3.29508	−	1.90242i	0.106073	−	0.0612410i
$966$		0			0
$967$	−4.62828	+	4.62828i	−0.148835	+	0.148835i	−0.777598	−	0.628762i	$-0.783562\pi$
$967$	−4.62828	+	4.62828i	−0.148835	+	0.148835i	0.628762	+	0.777598i	$0.283562\pi$
$968$	−51.7759	−	13.8733i	−1.66414	−	0.445905i
$969$		0			0
$970$	−1.20579	+	4.50007i	−0.0387156	+	0.144489i
$971$	−14.5470	+	8.39870i	−0.466835	+	0.269527i	−0.714914	−	0.699213i	$-0.753534\pi$
$971$	−14.5470	+	8.39870i	−0.466835	+	0.269527i	0.248079	+	0.968740i	$0.420201\pi$
$972$		0			0
$973$	27.4495	−	6.96654i	0.879989	−	0.223337i
$974$		−	39.4301i		−	1.26342i
$975$		0			0
$976$	6.72521	−	3.88280i	0.215269	−	0.124285i
$977$	6.36257	+	23.7454i	0.203557	+	0.759683i	0.989885	+	0.141874i	$0.0453129\pi$
$977$	6.36257	+	23.7454i	0.203557	+	0.759683i	−0.786328	+	0.617809i	$0.788020\pi$
$978$		0			0
$979$	13.6463	−	23.6361i	0.436138	−	0.755412i
$980$	17.4128	−	4.17448i	0.556232	−	0.133349i
$981$		0			0
$982$	0.452667	−	1.68938i	0.0144452	−	0.0539102i
$983$	22.4430	+	6.01359i	0.715822	+	0.191804i	0.598307	−	0.801267i	$-0.295840\pi$
$983$	22.4430	+	6.01359i	0.715822	+	0.191804i	0.117515	+	0.993071i	$0.462507\pi$
$984$		0			0
$985$	−12.1400			−0.386813
$986$	35.0603	+	9.39438i	1.11655	+	0.299178i
$987$		0			0
$988$	106.912	−	69.7720i	3.40133	−	2.21974i
$989$	−10.0132	+	17.3434i	−0.318401	+	0.551487i
$990$		0			0
$991$	24.8926	−	43.1153i	0.790741	−	1.36960i	−0.134768	−	0.990877i	$-0.543029\pi$
$991$	24.8926	−	43.1153i	0.790741	−	1.36960i	0.925509	−	0.378726i	$-0.123638\pi$
$992$	−19.7501	−	34.2082i	−0.627067	−	1.08611i
$993$		0			0
$994$	34.9071	−	8.85926i	1.10719	−	0.280999i
$995$	−8.93224	+	2.39339i	−0.283171	+	0.0758754i
$996$		0			0
$997$		−	3.16056i		−	0.100096i	−0.998747	−	0.0500480i	$-0.984063\pi$
$997$		−	3.16056i		−	0.100096i	0.998747	−	0.0500480i	$-0.0159374\pi$
$998$	44.6928	+	25.8034i	1.41473	+	0.816793i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.d.145.1		40
3.2	odd	2		273.2.bt.b.145.10	✓	40
7.3	odd	6		819.2.gh.d.262.1		40
13.7	odd	12		819.2.gh.d.397.1		40
21.17	even	6		273.2.cg.b.262.10	yes	40
39.20	even	12		273.2.cg.b.124.10	yes	40
91.59	even	12	inner	819.2.et.d.514.1		40
273.59	odd	12		273.2.bt.b.241.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.10	✓	40	3.2	odd	2
273.2.bt.b.241.10	yes	40	273.59	odd	12
273.2.cg.b.124.10	yes	40	39.20	even	12
273.2.cg.b.262.10	yes	40	21.17	even	6
819.2.et.d.145.1		40	1.1	even	1	trivial
819.2.et.d.514.1		40	91.59	even	12	inner
819.2.gh.d.262.1		40	7.3	odd	6
819.2.gh.d.397.1		40	13.7	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-1.85908 + 1.85908i) q^{2} -4.91234i q^{4} +(-0.502992 + 0.134776i) q^{5} +(-1.89546 + 1.84587i) q^{7} +(5.41427 + 5.41427i) q^{8} +O(q^{10})\)	\(q+(-1.85908 + 1.85908i) q^{2} -4.91234i q^{4} +(-0.502992 + 0.134776i) q^{5} +(-1.89546 + 1.84587i) q^{7} +(5.41427 + 5.41427i) q^{8} +(0.684542 - 1.18566i) q^{10} +(1.93173 - 0.517606i) q^{11} +(2.40655 - 2.68487i) q^{13} +(0.0921792 - 6.95542i) q^{14} -10.3064 q^{16} -5.09260 q^{17} +(-1.86555 + 6.96234i) q^{19} +(0.662067 + 2.47087i) q^{20} +(-2.62897 + 4.55351i) q^{22} -4.78704i q^{23} +(-4.09529 + 2.36442i) q^{25} +(0.517414 + 9.46534i) q^{26} +(9.06756 + 9.31113i) q^{28} +(1.35547 + 2.34774i) q^{29} +(0.867635 - 3.23806i) q^{31} +(8.33190 - 8.33190i) q^{32} +(9.46754 - 9.46754i) q^{34} +(0.704619 - 1.18392i) q^{35} +(-5.25431 - 5.25431i) q^{37} +(-9.47532 - 16.4117i) q^{38} +(-3.45305 - 1.99362i) q^{40} +(-0.938828 + 3.50375i) q^{41} +(-3.62298 - 2.09173i) q^{43} +(-2.54266 - 9.48933i) q^{44} +(8.89947 + 8.89947i) q^{46} +(-0.0215224 - 0.0803226i) q^{47} +(0.185507 - 6.99754i) q^{49} +(3.21783 - 12.0091i) q^{50} +(-13.1890 - 11.8218i) q^{52} +(-6.85585 - 11.8747i) q^{53} +(-0.901885 + 0.520704i) q^{55} +(-20.2566 - 0.268457i) q^{56} +(-6.88456 - 1.84471i) q^{58} +(3.91130 - 3.91130i) q^{59} +(-0.652526 + 0.376736i) q^{61} +(4.40680 + 7.63280i) q^{62} +10.3665i q^{64} +(-0.848619 + 1.67481i) q^{65} +(-2.81278 - 10.4974i) q^{67} +25.0166i q^{68} +(0.891061 + 3.51095i) q^{70} +(1.34000 + 5.00093i) q^{71} +(2.05692 + 0.551150i) q^{73} +19.5363 q^{74} +(34.2014 + 9.16424i) q^{76} +(-2.70608 + 4.54683i) q^{77} +(6.17212 - 10.6904i) q^{79} +(5.18405 - 1.38906i) q^{80} +(-4.76840 - 8.25910i) q^{82} +(-7.09696 - 7.09696i) q^{83} +(2.56154 - 0.686362i) q^{85} +(10.6241 - 2.84672i) q^{86} +(13.2614 + 7.65647i) q^{88} +(9.64998 - 9.64998i) q^{89} +(0.394414 + 9.53123i) q^{91} -23.5156 q^{92} +(0.189338 + 0.109314i) q^{94} -3.75343i q^{95} +(-3.28692 + 0.880729i) q^{97} +(12.6641 + 13.3538i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{7}+O(q^{10}) \) 40 * q - 2 * q^7	\( 40 q - 2 q^{7} + 8 q^{11} + 18 q^{14} - 64 q^{16} - 8 q^{17} - 14 q^{19} + 14 q^{20} + 4 q^{22} - 24 q^{25} + 10 q^{26} - 2 q^{28} - 8 q^{29} - 8 q^{31} - 10 q^{32} + 24 q^{34} + 22 q^{35} + 12 q^{37} - 8 q^{38} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 28 q^{44} + 40 q^{46} - 10 q^{47} + 38 q^{49} + 20 q^{50} + 40 q^{52} + 8 q^{53} + 42 q^{55} - 20 q^{56} - 48 q^{58} + 26 q^{59} - 12 q^{61} + 24 q^{62} + 44 q^{65} + 46 q^{67} + 32 q^{70} + 6 q^{71} + 10 q^{73} - 40 q^{74} + 64 q^{76} + 24 q^{77} - 34 q^{80} + 24 q^{82} - 12 q^{83} + 2 q^{85} - 12 q^{86} - 84 q^{88} + 16 q^{89} + 26 q^{91} - 236 q^{92} + 30 q^{94} + 62 q^{97} + 14 q^{98}+O(q^{100}) \) 40 * q - 2 * q^7 + 8 * q^11 + 18 * q^14 - 64 * q^16 - 8 * q^17 - 14 * q^19 + 14 * q^20 + 4 * q^22 - 24 * q^25 + 10 * q^26 - 2 * q^28 - 8 * q^29 - 8 * q^31 - 10 * q^32 + 24 * q^34 + 22 * q^35 + 12 * q^37 - 8 * q^38 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 28 * q^44 + 40 * q^46 - 10 * q^47 + 38 * q^49 + 20 * q^50 + 40 * q^52 + 8 * q^53 + 42 * q^55 - 20 * q^56 - 48 * q^58 + 26 * q^59 - 12 * q^61 + 24 * q^62 + 44 * q^65 + 46 * q^67 + 32 * q^70 + 6 * q^71 + 10 * q^73 - 40 * q^74 + 64 * q^76 + 24 * q^77 - 34 * q^80 + 24 * q^82 - 12 * q^83 + 2 * q^85 - 12 * q^86 - 84 * q^88 + 16 * q^89 + 26 * q^91 - 236 * q^92 + 30 * q^94 + 62 * q^97 + 14 * q^98

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