LMFDB - Embedded newform 819.2.et.c.136.8

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			136.8
Character	$\chi$	$=$	819.136
Dual form			819.2.et.c.271.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48267 - 1.48267i) q^{2} -2.39661i q^{4} +(-0.507149 + 1.89270i) q^{5} +(-0.313052 + 2.62717i) q^{7} +(-0.588043 - 0.588043i) q^{8} +O(q^{10})$	\(q+(1.48267 - 1.48267i) q^{2} -2.39661i q^{4} +(-0.507149 + 1.89270i) q^{5} +(-0.313052 + 2.62717i) q^{7} +(-0.588043 - 0.588043i) q^{8} +(2.05432 + 3.55819i) q^{10} +(-0.648767 + 2.42123i) q^{11} +(3.33753 + 1.36415i) q^{13} +(3.43106 + 4.35937i) q^{14} +3.04948 q^{16} -7.32088 q^{17} +(0.930935 - 0.249443i) q^{19} +(4.53608 + 1.21544i) q^{20} +(2.62798 + 4.55179i) q^{22} +6.63818i q^{23} +(1.00500 + 0.580235i) q^{25} +(6.97103 - 2.92587i) q^{26} +(6.29629 + 0.750265i) q^{28} +(5.21743 - 9.03685i) q^{29} +(-2.92062 + 0.782577i) q^{31} +(5.69745 - 5.69745i) q^{32} +(-10.8544 + 10.8544i) q^{34} +(-4.81368 - 1.92488i) q^{35} +(-0.974084 - 0.974084i) q^{37} +(1.01043 - 1.75011i) q^{38} +(1.41122 - 0.814767i) q^{40} +(-0.710011 + 0.190247i) q^{41} +(10.1261 - 5.84633i) q^{43} +(5.80275 + 1.55484i) q^{44} +(9.84223 + 9.84223i) q^{46} +(3.62699 + 0.971849i) q^{47} +(-6.80400 - 1.64488i) q^{49} +(2.35037 - 0.629781i) q^{50} +(3.26933 - 7.99876i) q^{52} +(1.15862 - 2.00679i) q^{53} +(-4.25365 - 2.45585i) q^{55} +(1.72898 - 1.36080i) q^{56} +(-5.66294 - 21.1344i) q^{58} +(3.35900 - 3.35900i) q^{59} +(-8.18748 - 4.72704i) q^{61} +(-3.17000 + 5.49061i) q^{62} -10.7959i q^{64} +(-4.27455 + 5.62513i) q^{65} +(-6.06032 - 1.62386i) q^{67} +17.5453i q^{68} +(-9.99105 + 4.28314i) q^{70} +(-8.32895 - 2.23174i) q^{71} +(2.01139 + 7.50661i) q^{73} -2.88849 q^{74} +(-0.597819 - 2.23109i) q^{76} +(-6.15788 - 2.46239i) q^{77} +(-2.31642 - 4.01217i) q^{79} +(-1.54654 + 5.77176i) q^{80} +(-0.770638 + 1.33478i) q^{82} +(10.1090 + 10.1090i) q^{83} +(3.71277 - 13.8563i) q^{85} +(6.34554 - 23.6819i) q^{86} +(1.80529 - 1.04229i) q^{88} +(2.89859 - 2.89859i) q^{89} +(-4.62866 + 8.34119i) q^{91} +15.9091 q^{92} +(6.81855 - 3.93669i) q^{94} +1.88849i q^{95} +(-2.63968 + 9.85141i) q^{97} +(-12.5269 + 7.64926i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.48267	−	1.48267i	1.04840	−	1.04840i	0.0496376	−	0.998767i	$-0.484193\pi$
$2$	1.48267	−	1.48267i	1.04840	−	1.04840i	0.998767	−	0.0496376i	$-0.0158066\pi$
$3$		0			0
$3$		0			0
$4$		−	2.39661i		−	1.19831i
$5$	−0.507149	+	1.89270i	−0.226804	+	0.846443i	0.754870	+	0.655874i	$0.227700\pi$
$5$	−0.507149	+	1.89270i	−0.226804	+	0.846443i	−0.981674	+	0.190569i	$0.938967\pi$
$6$		0			0
$7$	−0.313052	+	2.62717i	−0.118323	+	0.992975i
$7$	−0.313052	+	2.62717i	−0.118323	+	0.992975i
$8$	−0.588043	−	0.588043i	−0.207905	−	0.207905i
$9$		0			0
$10$	2.05432	+	3.55819i	0.649633	+	1.12520i
$11$	−0.648767	+	2.42123i	−0.195611	+	0.730029i	0.796497	+	0.604642i	$0.206684\pi$
$11$	−0.648767	+	2.42123i	−0.195611	+	0.730029i	−0.992108	+	0.125387i	$0.959983\pi$
$12$		0			0
$13$	3.33753	+	1.36415i	0.925664	+	0.378347i
$13$	3.33753	+	1.36415i	0.925664	+	0.378347i
$14$	3.43106	+	4.35937i	0.916990	+	1.16509i
$15$		0			0
$16$	3.04948			0.762369
$17$	−7.32088			−1.77557			−0.887787	−	0.460254i	$-0.847758\pi$
$17$	−7.32088			−1.77557			−0.887787	+	0.460254i	$0.847758\pi$
$18$		0			0
$19$	0.930935	−	0.249443i	0.213571	−	0.0572262i	−0.150447	−	0.988618i	$-0.548071\pi$
$19$	0.930935	−	0.249443i	0.213571	−	0.0572262i	0.364018	+	0.931392i	$0.381405\pi$
$20$	4.53608	+	1.21544i	1.01430	+	0.271780i
$21$		0			0
$22$	2.62798	+	4.55179i	0.560287	+	0.970445i
$23$			6.63818i			1.38416i	0.721822	+	0.692079i	$0.243305\pi$
$23$			6.63818i			1.38416i	−0.721822	+	0.692079i	$0.756695\pi$
$24$		0			0
$25$	1.00500	+	0.580235i	0.200999	+	0.116047i
$26$	6.97103	−	2.92587i	1.36713	−	0.573810i
$27$		0			0
$28$	6.29629	+	0.750265i	1.18989	+	0.141787i
$29$	5.21743	−	9.03685i	0.968852	−	1.67810i	0.269965	−	0.962870i	$-0.412988\pi$
$29$	5.21743	−	9.03685i	0.968852	−	1.67810i	0.698888	−	0.715232i	$-0.253679\pi$
$30$		0			0
$31$	−2.92062	+	0.782577i	−0.524558	+	0.140555i	−0.511374	−	0.859358i	$-0.670863\pi$
$31$	−2.92062	+	0.782577i	−0.524558	+	0.140555i	−0.0131839	+	0.999913i	$0.504197\pi$
$32$	5.69745	−	5.69745i	1.00718	−	1.00718i
$33$		0			0
$34$	−10.8544	+	10.8544i	−1.86152	+	1.86152i
$35$	−4.81368	−	1.92488i	−0.813661	−	0.325364i
$36$		0			0
$37$	−0.974084	−	0.974084i	−0.160138	−	0.160138i	0.622490	−	0.782628i	$-0.286121\pi$
$37$	−0.974084	−	0.974084i	−0.160138	−	0.160138i	−0.782628	+	0.622490i	$0.786121\pi$
$38$	1.01043	−	1.75011i	0.163913	−	0.283905i
$39$		0			0
$40$	1.41122	−	0.814767i	0.223133	−	0.128826i
$41$	−0.710011	+	0.190247i	−0.110885	+	0.0297116i	−0.313835	−	0.949478i	$-0.601614\pi$
$41$	−0.710011	+	0.190247i	−0.110885	+	0.0297116i	0.202950	+	0.979189i	$0.434947\pi$
$42$		0			0
$43$	10.1261	−	5.84633i	1.54422	−	0.891556i	0.545656	−	0.838009i	$-0.316281\pi$
$43$	10.1261	−	5.84633i	1.54422	−	0.891556i	0.998565	−	0.0535470i	$-0.0170527\pi$
$44$	5.80275	+	1.55484i	0.874798	+	0.234401i
$45$		0			0
$46$	9.84223	+	9.84223i	1.45116	+	1.45116i
$47$	3.62699	+	0.971849i	0.529051	+	0.141759i	0.513450	−	0.858120i	$-0.328367\pi$
$47$	3.62699	+	0.971849i	0.529051	+	0.141759i	0.0156008	+	0.999878i	$0.495034\pi$
$48$		0			0
$49$	−6.80400	−	1.64488i	−0.972000	−	0.234983i
$50$	2.35037	−	0.629781i	0.332393	−	0.0890645i
$51$		0			0
$52$	3.26933	−	7.99876i	0.453375	−	1.10923i
$53$	1.15862	−	2.00679i	0.159149	−	0.275654i	−0.775413	−	0.631454i	$-0.782458\pi$
$53$	1.15862	−	2.00679i	0.159149	−	0.275654i	0.934562	+	0.355800i	$0.115792\pi$
$54$		0			0
$55$	−4.25365	−	2.45585i	−0.573563	−	0.331147i
$56$	1.72898	−	1.36080i	0.231044	−	0.181844i
$57$		0			0
$58$	−5.66294	−	21.1344i	−0.743580	−	2.77508i
$59$	3.35900	−	3.35900i	0.437305	−	0.437305i	−0.453799	−	0.891104i	$-0.649932\pi$
$59$	3.35900	−	3.35900i	0.437305	−	0.437305i	0.891104	+	0.453799i	$0.149932\pi$
$60$		0			0
$61$	−8.18748	−	4.72704i	−1.04830	−	0.605236i	−0.126126	−	0.992014i	$-0.540254\pi$
$61$	−8.18748	−	4.72704i	−1.04830	−	0.605236i	−0.922173	+	0.386778i	$0.873588\pi$
$62$	−3.17000	+	5.49061i	−0.402591	+	0.697308i
$63$		0			0
$64$		−	10.7959i		−	1.34949i
$65$	−4.27455	+	5.62513i	−0.530193	+	0.697711i
$66$		0			0
$67$	−6.06032	−	1.62386i	−0.740386	−	0.198386i	−0.131136	−	0.991364i	$-0.541863\pi$
$67$	−6.06032	−	1.62386i	−0.740386	−	0.198386i	−0.609249	+	0.792979i	$0.708529\pi$
$68$			17.5453i			2.12768i
$69$		0			0
$70$	−9.99105	+	4.28314i	−1.19416	+	0.511933i
$71$	−8.32895	−	2.23174i	−0.988465	−	0.264858i	−0.271859	−	0.962337i	$-0.587639\pi$
$71$	−8.32895	−	2.23174i	−0.988465	−	0.264858i	−0.716606	+	0.697479i	$0.754305\pi$
$72$		0			0
$73$	2.01139	+	7.50661i	0.235415	+	0.878583i	0.977961	+	0.208787i	$0.0669516\pi$
$73$	2.01139	+	7.50661i	0.235415	+	0.878583i	−0.742546	+	0.669795i	$0.766382\pi$
$74$	−2.88849			−0.335780
$75$		0			0
$76$	−0.597819	−	2.23109i	−0.0685745	−	0.255923i
$77$	−6.15788	−	2.46239i	−0.701755	−	0.280615i
$78$		0			0
$79$	−2.31642	−	4.01217i	−0.260618	−	0.451404i	0.705788	−	0.708423i	$-0.250593\pi$
$79$	−2.31642	−	4.01217i	−0.260618	−	0.451404i	−0.966406	+	0.257019i	$0.917260\pi$
$80$	−1.54654	+	5.77176i	−0.172908	+	0.645302i
$81$		0			0
$82$	−0.770638	+	1.33478i	−0.0851028	+	0.147402i
$83$	10.1090	+	10.1090i	1.10961	+	1.10961i	0.993202	+	0.116405i	$0.0371372\pi$
$83$	10.1090	+	10.1090i	1.10961	+	1.10961i	0.116405	+	0.993202i	$0.462863\pi$
$84$		0			0
$85$	3.71277	−	13.8563i	0.402707	−	1.50292i
$86$	6.34554	−	23.6819i	0.684257	−	2.55368i
$87$		0			0
$88$	1.80529	−	1.04229i	0.192445	−	0.111108i
$89$	2.89859	−	2.89859i	0.307250	−	0.307250i	−0.536592	−	0.843842i	$-0.680289\pi$
$89$	2.89859	−	2.89859i	0.307250	−	0.307250i	0.843842	+	0.536592i	$0.180289\pi$
$90$		0			0
$91$	−4.62866	+	8.34119i	−0.485216	+	0.874394i
$92$	15.9091			1.65864
$93$		0			0
$94$	6.81855	−	3.93669i	0.703280	−	0.406039i
$95$			1.88849i			0.193755i
$96$		0			0
$97$	−2.63968	+	9.85141i	−0.268019	+	1.00026i	0.692358	+	0.721554i	$0.256572\pi$
$97$	−2.63968	+	9.85141i	−0.268019	+	1.00026i	−0.960377	+	0.278705i	$0.910095\pi$
$98$	−12.5269	+	7.64926i	−1.26541	+	0.772692i
$99$		0			0
$100$	1.39060	−	2.40859i	0.139060	−	0.240859i
$101$	1.90282	+	3.29578i	0.189337	+	0.327942i	0.945030	−	0.326985i	$-0.106033\pi$
$101$	1.90282	+	3.29578i	0.189337	+	0.327942i	−0.755692	+	0.654927i	$0.772699\pi$
$102$		0			0
$103$	−4.75097	−	8.22892i	−0.468127	−	0.810819i	0.531210	−	0.847240i	$-0.321738\pi$
$103$	−4.75097	−	8.22892i	−0.468127	−	0.810819i	−0.999337	+	0.0364211i	$0.988404\pi$
$104$	−1.16043	−	2.76479i	−0.113790	−	0.271110i
$105$		0			0
$106$	−1.25755	−	4.69325i	−0.122144	−	0.455849i
$107$	9.75503			0.943055			0.471527	−	0.881851i	$-0.343703\pi$
$107$	9.75503			0.943055			0.471527	+	0.881851i	$0.343703\pi$
$108$		0			0
$109$	1.54206	+	5.75506i	0.147703	+	0.551235i	0.999620	+	0.0275585i	$0.00877324\pi$
$109$	1.54206	+	5.75506i	0.147703	+	0.551235i	−0.851917	+	0.523676i	$0.824560\pi$
$110$	−9.94797	+	2.66555i	−0.948501	+	0.254150i
$111$		0			0
$112$	−0.954645	+	8.01148i	−0.0902055	+	0.757014i
$113$	−5.65861	−	9.80099i	−0.532317	−	0.922000i	−0.999288	−	0.0377273i	$-0.987988\pi$
$113$	−5.65861	−	9.80099i	−0.532317	−	0.922000i	0.466971	−	0.884273i	$-0.345345\pi$
$114$		0			0
$115$	−12.5641	−	3.36655i	−1.17161	−	0.313932i
$116$	−21.6578	−	12.5042i	−2.01088	−	1.16098i
$117$		0			0
$118$		−	9.96057i		−	0.916945i
$119$	2.29182	−	19.2332i	0.210091	−	1.76310i
$120$		0			0
$121$	4.08482	+	2.35837i	0.371347	+	0.214397i
$122$	−19.1479	+	5.13068i	−1.73357	+	0.464510i
$123$		0			0
$124$	1.87553	+	6.99958i	0.168428	+	0.628581i
$125$	−8.53568	+	8.53568i	−0.763454	+	0.763454i
$126$		0			0
$127$	9.81199	+	5.66496i	0.870673	+	0.502684i	0.867572	−	0.497312i	$-0.165679\pi$
$127$	9.81199	+	5.66496i	0.870673	+	0.502684i	0.00310144	+	0.999995i	$0.499013\pi$
$128$	−4.61185	−	4.61185i	−0.407634	−	0.407634i
$129$		0			0
$130$	2.00246	+	14.6779i	0.175627	+	1.28734i
$131$	12.3925	−	7.15480i	1.08274	−	0.625118i	0.151102	−	0.988518i	$-0.451718\pi$
$131$	12.3925	−	7.15480i	1.08274	−	0.625118i	0.931633	+	0.363401i	$0.118384\pi$
$132$		0			0
$133$	0.363897	+	2.52381i	0.0315539	+	0.218842i
$134$	−11.3931	+	6.57780i	−0.984213	+	0.568235i
$135$		0			0
$136$	4.30500	+	4.30500i	0.369150	+	0.369150i
$137$	4.02745	+	4.02745i	0.344089	+	0.344089i	0.857902	−	0.513813i	$-0.171768\pi$
$137$	4.02745	+	4.02745i	0.344089	+	0.344089i	−0.513813	+	0.857902i	$0.671768\pi$
$138$		0			0
$139$	9.38055	−	5.41586i	0.795648	−	0.459368i	−0.0462992	−	0.998928i	$-0.514743\pi$
$139$	9.38055	−	5.41586i	0.795648	−	0.459368i	0.841947	+	0.539560i	$0.181409\pi$
$140$	−4.61319	+	11.5365i	−0.389885	+	0.975015i
$141$		0			0
$142$	−15.6580	+	9.04015i	−1.31399	+	0.758633i
$143$	−5.46820	+	7.19592i	−0.457274	+	0.601753i
$144$		0			0
$145$	14.4581	+	14.4581i	1.20068	+	1.20068i
$146$	14.1120	+	8.14759i	1.16792	+	0.674300i
$147$		0			0
$148$	−2.33450	+	2.33450i	−0.191895	+	0.191895i
$149$	−2.30894	−	8.61708i	−0.189156	−	0.705939i	−0.993703	−	0.112050i	$-0.964258\pi$
$149$	−2.30894	−	8.61708i	−0.189156	−	0.705939i	0.804547	−	0.593889i	$-0.202408\pi$
$150$		0			0
$151$	−12.4233	+	3.32882i	−1.01100	+	0.270896i	−0.726046	−	0.687647i	$-0.758644\pi$
$151$	−12.4233	+	3.32882i	−1.01100	+	0.270896i	−0.284951	+	0.958542i	$0.591977\pi$
$152$	−0.694113	−	0.400747i	−0.0563000	−	0.0325048i
$153$		0			0
$154$	−12.7810	+	5.47918i	−1.02992	+	0.441525i
$155$		−	5.92474i		−	0.475887i
$156$		0			0
$157$	−3.95550	−	2.28371i	−0.315683	−	0.182260i	0.333784	−	0.942650i	$-0.391675\pi$
$157$	−3.95550	−	2.28371i	−0.315683	−	0.182260i	−0.649467	+	0.760390i	$0.725008\pi$
$158$	−9.38320	−	2.51422i	−0.746487	−	0.200021i
$159$		0			0
$160$	7.89413	+	13.6730i	0.624086	+	1.08095i
$161$	−17.4396	−	2.07810i	−1.37443	−	0.163777i
$162$		0			0
$163$	2.47798	−	0.663973i	0.194091	−	0.0520064i	−0.160464	−	0.987042i	$-0.551299\pi$
$163$	2.47798	−	0.663973i	0.194091	−	0.0520064i	0.354555	+	0.935035i	$0.384632\pi$
$164$	0.455948	+	1.70162i	0.0356036	+	0.132874i
$165$		0			0
$166$	29.9766			2.32664
$167$	−1.90396	−	7.10569i	−0.147333	−	0.549855i	−0.999640	−	0.0268134i	$-0.991464\pi$
$167$	−1.90396	−	7.10569i	−0.147333	−	0.549855i	0.852307	−	0.523041i	$-0.175203\pi$
$168$		0			0
$169$	9.27820	+	9.10577i	0.713708	+	0.700444i
$170$	−15.0394	−	26.0491i	−1.15347	−	1.99787i
$171$		0			0
$172$	−14.0114	−	24.2684i	−1.06836	−	1.85045i
$173$	9.17077	−	15.8842i	0.697241	−	1.20766i	−0.272178	−	0.962247i	$-0.587744\pi$
$173$	9.17077	−	15.8842i	0.697241	−	1.20766i	0.969419	−	0.245410i	$-0.0789225\pi$
$174$		0			0
$175$	−1.83899	+	2.45865i	−0.139015	+	0.185856i
$176$	−1.97840	+	7.38349i	−0.149127	+	0.556551i
$177$		0			0
$178$		−	8.59529i		−	0.644244i
$179$	1.65369	−	0.954758i	0.123603	−	0.0713620i	−0.436924	−	0.899498i	$-0.643932\pi$
$179$	1.65369	−	0.954758i	0.123603	−	0.0713620i	0.560527	+	0.828136i	$0.310599\pi$
$180$		0			0
$181$	−18.9344			−1.40738			−0.703691	−	0.710506i	$-0.748466\pi$
$181$	−18.9344			−1.40738			−0.703691	+	0.710506i	$0.748466\pi$
$182$	5.50445	+	19.2300i	0.408017	+	1.42542i
$183$		0			0
$184$	3.90354	−	3.90354i	0.287773	−	0.287773i
$185$	2.33766	−	1.34965i	0.171868	−	0.0992281i
$186$		0			0
$187$	4.74955	−	17.7255i	0.347321	−	1.29622i
$188$	2.32914	−	8.69248i	0.169870	−	0.633965i
$189$		0			0
$190$	2.80000	+	2.80000i	0.203134	+	0.203134i
$191$	5.39449	−	9.34352i	0.390331	−	0.676074i	−0.602162	−	0.798374i	$-0.705694\pi$
$191$	5.39449	−	9.34352i	0.390331	−	0.676074i	0.992493	+	0.122300i	$0.0390271\pi$
$192$		0			0
$193$	5.08690	−	18.9846i	0.366163	−	1.36654i	−0.499674	−	0.866213i	$-0.666547\pi$
$193$	5.08690	−	18.9846i	0.366163	−	1.36654i	0.865837	−	0.500326i	$-0.166786\pi$
$194$	10.6926	+	18.5201i	0.767685	+	1.32967i
$195$		0			0
$196$	−3.94214	+	16.3065i	−0.281581	+	1.16475i
$197$	2.96842	+	11.0783i	0.211491	+	0.789295i	0.987372	+	0.158417i	$0.0506389\pi$
$197$	2.96842	+	11.0783i	0.211491	+	0.789295i	−0.775881	+	0.630879i	$0.782694\pi$
$198$		0			0
$199$	−5.55472			−0.393764			−0.196882	−	0.980427i	$-0.563082\pi$
$199$	−5.55472			−0.393764			−0.196882	+	0.980427i	$0.563082\pi$
$200$	−0.249778	−	0.932185i	−0.0176620	−	0.0659155i
$201$		0			0
$202$	7.70779	+	2.06530i	0.542318	+	0.145314i
$203$	22.1080	+	16.5361i	1.55168	+	1.16060i
$204$		0			0
$205$		−	1.44032i		−	0.100597i
$206$	−19.2449	−	5.15665i	−1.34085	−	0.359281i
$207$		0			0
$208$	10.1777	+	4.15994i	0.705698	+	0.288440i
$209$			2.41584i			0.167107i
$210$		0			0
$211$	−8.06339	+	13.9662i	−0.555106	+	0.961473i	0.442789	+	0.896626i	$0.353989\pi$
$211$	−8.06339	+	13.9662i	−0.555106	+	0.961473i	−0.997895	+	0.0648467i	$0.979344\pi$
$212$	−4.80949	−	2.77676i	−0.330317	−	0.190709i
$213$		0			0
$214$	14.4635	−	14.4635i	0.988703	−	0.988703i
$215$	5.92991	+	22.1307i	0.404417	+	1.50930i
$216$		0			0
$217$	−1.14165	−	7.91793i	−0.0775004	−	0.537504i
$218$	10.8192	+	6.24648i	0.732770	+	0.423065i
$219$		0			0
$220$	−5.88571	+	10.1944i	−0.396815	+	0.687303i
$221$	−24.4337	−	9.98677i	−1.64359	−	0.671783i
$222$		0			0
$223$	25.6580	−	6.87505i	1.71819	−	0.460387i	0.740781	−	0.671747i	$-0.234456\pi$
$223$	25.6580	−	6.87505i	1.71819	−	0.460387i	0.977408	+	0.211359i	$0.0677890\pi$
$224$	13.1845	+	16.7517i	0.880929	+	1.11927i
$225$		0			0
$226$	−22.9215	−	6.14179i	−1.52471	−	0.408546i
$227$	−1.25693	−	1.25693i	−0.0834252	−	0.0834252i	0.664163	−	0.747588i	$-0.268788\pi$
$227$	−1.25693	−	1.25693i	−0.0834252	−	0.0834252i	−0.747588	+	0.664163i	$0.768788\pi$
$228$		0			0
$229$	−8.68390	−	2.32685i	−0.573849	−	0.153762i	−0.0397875	−	0.999208i	$-0.512668\pi$
$229$	−8.68390	−	2.32685i	−0.573849	−	0.153762i	−0.534061	+	0.845446i	$0.679335\pi$
$230$	−23.6199	+	13.6370i	−1.55745	+	0.899194i
$231$		0			0
$232$	−8.38214	+	2.24599i	−0.550314	+	0.147456i
$233$	−0.891738	+	0.514845i	−0.0584197	+	0.0337286i	−0.528925	−	0.848668i	$-0.677405\pi$
$233$	−0.891738	+	0.514845i	−0.0584197	+	0.0337286i	0.470506	+	0.882397i	$0.344072\pi$
$234$		0			0
$235$	−3.67884	+	6.37195i	−0.239981	+	0.415660i
$236$	−8.05022	−	8.05022i	−0.524025	−	0.524025i
$237$		0			0
$238$	−25.1184	−	31.9144i	−1.62818	−	2.06870i
$239$	13.2347	−	13.2347i	0.856079	−	0.856079i	−0.134795	−	0.990874i	$-0.543038\pi$
$239$	13.2347	−	13.2347i	0.856079	−	0.856079i	0.990874	+	0.134795i	$0.0430376\pi$
$240$		0			0
$241$	2.07666	−	2.07666i	0.133769	−	0.133769i	−0.637052	−	0.770821i	$-0.719846\pi$
$241$	2.07666	−	2.07666i	0.133769	−	0.133769i	0.770821	+	0.637052i	$0.219846\pi$
$242$	9.55311	−	2.55975i	0.614097	−	0.164547i
$243$		0			0
$244$	−11.3289	+	19.6222i	−0.725257	+	1.25618i
$245$	6.56391	−	12.0438i	0.419353	−	0.769447i
$246$		0			0
$247$	3.44730	+	0.437409i	0.219346	+	0.0278317i
$248$	2.17764	+	1.25726i	0.138280	+	0.0798361i
$249$		0			0
$250$			25.3112i			1.60082i
$251$	−0.244838	−	0.424072i	−0.0154540	−	0.0267672i	0.858195	−	0.513324i	$-0.171586\pi$
$251$	−0.244838	−	0.424072i	−0.0154540	−	0.0267672i	−0.873649	+	0.486557i	$0.838253\pi$
$252$		0			0
$253$	−16.0726	−	4.30664i	−1.01047	−	0.270756i
$254$	22.9472	−	6.14868i	1.43983	−	0.385802i
$255$		0			0
$256$	7.91613			0.494758
$257$	−18.7117			−1.16720			−0.583602	−	0.812040i	$-0.698357\pi$
$257$	−18.7117			−1.16720			−0.583602	+	0.812040i	$0.698357\pi$
$258$		0			0
$259$	2.86402	−	2.25414i	0.177961	−	0.140065i
$260$	13.4812	+	10.2444i	0.836072	+	0.635333i
$261$		0			0
$262$	7.76574	−	28.9821i	0.479769	−	1.79052i
$263$	−1.72119	−	2.98119i	−0.106133	−	0.183828i	0.808067	−	0.589090i	$-0.200514\pi$
$263$	−1.72119	−	2.98119i	−0.106133	−	0.183828i	−0.914201	+	0.405262i	$0.867180\pi$
$264$		0			0
$265$	3.21067	+	3.21067i	0.197230	+	0.197230i
$266$	4.28151	+	3.20243i	0.262516	+	0.196354i
$267$		0			0
$268$	−3.89176	+	14.5242i	−0.237727	+	0.887208i
$269$			9.04672i			0.551588i	0.961217	+	0.275794i	$0.0889408\pi$
$269$			9.04672i			0.551588i	−0.961217	+	0.275794i	$0.911059\pi$
$270$		0			0
$271$	−5.53295	+	5.53295i	−0.336103	+	0.336103i	−0.854898	−	0.518796i	$-0.826381\pi$
$271$	−5.53295	+	5.53295i	−0.336103	+	0.336103i	0.518796	+	0.854898i	$0.326381\pi$
$272$	−22.3249			−1.35364
$273$		0			0
$274$	11.9428			0.721488
$275$	−2.05689	+	2.05689i	−0.124035	+	0.124035i
$276$		0			0
$277$		−	1.54911i		−	0.0930772i	−0.998916	−	0.0465386i	$-0.985181\pi$
$277$		−	1.54911i		−	0.0930772i	0.998916	−	0.0465386i	$-0.0148190\pi$
$278$	5.87832	−	21.9382i	0.352558	−	1.31576i
$279$		0			0
$280$	1.69874	+	3.96257i	0.101519	+	0.236809i
$281$	−4.20181	−	4.20181i	−0.250659	−	0.250659i	0.570582	−	0.821241i	$-0.306718\pi$
$281$	−4.20181	−	4.20181i	−0.250659	−	0.250659i	−0.821241	+	0.570582i	$0.806718\pi$
$282$		0			0
$283$	−2.32807	−	4.03233i	−0.138389	−	0.239697i	0.788498	−	0.615038i	$-0.210859\pi$
$283$	−2.32807	−	4.03233i	−0.138389	−	0.239697i	−0.926887	+	0.375340i	$0.877526\pi$
$284$	−5.34860	+	19.9613i	−0.317381	+	1.18448i
$285$		0			0
$286$	2.56163	+	18.7767i	0.151473	+	1.11029i
$287$	−0.277540	−	1.92487i	−0.0163826	−	0.113622i
$288$		0			0
$289$	36.5953			2.15266
$290$	42.8731			2.51759
$291$		0			0
$292$	17.9904	−	4.82052i	1.05281	−	0.282100i
$293$	−10.8009	−	2.89410i	−0.630997	−	0.169075i	−0.0708751	−	0.997485i	$-0.522579\pi$
$293$	−10.8009	−	2.89410i	−0.630997	−	0.169075i	−0.560122	+	0.828410i	$0.689246\pi$
$294$		0			0
$295$	4.65408	+	8.06111i	0.270971	+	0.469336i
$296$			1.14561i			0.0665871i
$297$		0			0
$298$	−16.1997	−	9.35289i	−0.938422	−	0.541798i
$299$	−9.05547	+	22.1551i	−0.523691	+	1.28126i
$300$		0			0
$301$	12.1893	+	28.4332i	0.702577	+	1.63886i
$302$	−13.4841	+	23.3552i	−0.775925	+	1.34394i
$303$		0			0
$304$	2.83886	−	0.760671i	0.162820	−	0.0436275i
$305$	13.0992	−	13.0992i	0.750056	−	0.750056i
$306$		0			0
$307$	2.63969	−	2.63969i	0.150655	−	0.150655i	−0.627756	−	0.778411i	$-0.716026\pi$
$307$	2.63969	−	2.63969i	0.150655	−	0.150655i	0.778411	+	0.627756i	$0.216026\pi$
$308$	−5.90139	+	14.7580i	−0.336263	+	0.840917i
$309$		0			0
$310$	−8.78443	−	8.78443i	−0.498922	−	0.498922i
$311$	16.2833	−	28.2035i	0.923341	−	1.59927i	0.129133	−	0.991627i	$-0.458780\pi$
$311$	16.2833	−	28.2035i	0.923341	−	1.59927i	0.794208	−	0.607646i	$-0.207886\pi$
$312$		0			0
$313$	−12.7123	+	7.33945i	−0.718541	+	0.414850i	−0.814216	−	0.580563i	$-0.802833\pi$
$313$	−12.7123	+	7.33945i	−0.718541	+	0.414850i	0.0956743	+	0.995413i	$0.469499\pi$
$314$	−9.25067	+	2.47871i	−0.522046	+	0.139882i
$315$		0			0
$316$	−9.61560	+	5.55157i	−0.540920	+	0.312300i
$317$	−9.92063	−	2.65822i	−0.557198	−	0.149301i	−0.0307793	−	0.999526i	$-0.509799\pi$
$317$	−9.92063	−	2.65822i	−0.557198	−	0.149301i	−0.526419	+	0.850225i	$0.676466\pi$
$318$		0			0
$319$	18.4954	+	18.4954i	1.03554	+	1.03554i
$320$	20.4335	+	5.47513i	1.14226	+	0.306069i
$321$		0			0
$322$	−28.9383	+	22.7760i	−1.61267	+	1.26926i
$323$	−6.81526	+	1.82614i	−0.379211	+	0.101609i
$324$		0			0
$325$	2.56268	+	3.30752i	0.142152	+	0.183468i
$326$	2.68957	−	4.65848i	0.148962	−	0.258009i
$327$		0			0
$328$	0.529391	+	0.305644i	0.0292307	+	0.0168764i
$329$	−3.68864	+	9.22446i	−0.203362	+	0.508561i
$330$		0			0
$331$	−6.55085	−	24.4481i	−0.360068	−	1.34379i	−0.873986	−	0.485951i	$-0.838473\pi$
$331$	−6.55085	−	24.4481i	−0.360068	−	1.34379i	0.513918	−	0.857839i	$-0.328193\pi$
$332$	24.2274	−	24.2274i	1.32965	−	1.32965i
$333$		0			0
$334$	−13.3583	−	7.71243i	−0.730935	−	0.422006i
$335$	6.14696	−	10.6469i	0.335845	−	0.581700i
$336$		0			0
$337$		−	0.741618i		−	0.0403985i	−0.999796	−	0.0201993i	$-0.993570\pi$
$337$		−	0.741618i		−	0.0403985i	0.999796	−	0.0201993i	$-0.00643006\pi$
$338$	27.2573	−	0.255654i	1.48260	−	0.0139058i
$339$		0			0
$340$	−33.2081	−	8.89808i	−1.80096	−	0.482566i
$341$		−	7.57920i		−	0.410436i
$342$		0			0
$343$	6.45138	−	17.3603i	0.348342	−	0.937368i
$344$	−9.39250	−	2.51671i	−0.506410	−	0.135692i
$345$		0			0
$346$	−9.95385	−	37.1483i	−0.535122	−	1.99710i
$347$	−34.1772			−1.83473			−0.917364	−	0.398048i	$-0.869688\pi$
$347$	−34.1772			−1.83473			−0.917364	+	0.398048i	$0.869688\pi$
$348$		0			0
$349$	7.26033	+	27.0959i	0.388636	+	1.45041i	0.832354	+	0.554244i	$0.186993\pi$
$349$	7.26033	+	27.0959i	0.388636	+	1.45041i	−0.443718	+	0.896167i	$0.646341\pi$
$350$	0.918749	+	6.37198i	0.0491092	+	0.340596i
$351$		0			0
$352$	10.0985	+	17.4912i	0.538253	+	0.932282i
$353$	2.49904	−	9.32655i	0.133011	−	0.496402i	−0.866988	−	0.498330i	$-0.833947\pi$
$353$	2.49904	−	9.32655i	0.133011	−	0.496402i	0.999998	+	0.00192769i	$0.000613602\pi$
$354$		0			0
$355$	8.44803	−	14.6324i	0.448375	−	0.776608i
$356$	−6.94679	−	6.94679i	−0.368179	−	0.368179i
$357$		0			0
$358$	1.03628	−	3.86746i	0.0547693	−	0.204402i
$359$	−8.84959	+	33.0271i	−0.467064	+	1.74311i	0.182891	+	0.983133i	$0.441454\pi$
$359$	−8.84959	+	33.0271i	−0.467064	+	1.74311i	−0.649955	+	0.759973i	$0.725212\pi$
$360$		0			0
$361$	−15.6501	+	9.03557i	−0.823688	+	0.475556i
$362$	−28.0734	+	28.0734i	−1.47551	+	1.47551i
$363$		0			0
$364$	19.9906	+	11.0931i	1.04779	+	0.581437i
$365$	−15.2279			−0.797063
$366$		0			0
$367$	−23.1967	+	13.3926i	−1.21086	+	0.699090i	−0.962947	−	0.269692i	$-0.913078\pi$
$367$	−23.1967	+	13.3926i	−1.21086	+	0.699090i	−0.247913	+	0.968782i	$0.579745\pi$
$368$			20.2430i			1.05524i
$369$		0			0
$370$	1.46489	−	5.46705i	0.0761561	−	0.284218i
$371$	4.90946	+	3.67212i	0.254886	+	0.190647i
$372$		0			0
$373$	−1.83233	+	3.17370i	−0.0948747	+	0.164328i	−0.909556	−	0.415581i	$-0.863578\pi$
$373$	−1.83233	+	3.17370i	−0.0948747	+	0.164328i	0.814682	+	0.579908i	$0.196912\pi$
$374$	−19.2391	−	33.3231i	−0.994831	−	1.72310i
$375$		0			0
$376$	−1.56134	−	2.70432i	−0.0805198	−	0.139464i
$377$	29.7409	−	23.0434i	1.53174	−	1.18680i
$378$		0			0
$379$	−6.16351	−	23.0025i	−0.316598	−	1.18156i	−0.922492	−	0.386016i	$-0.873851\pi$
$379$	−6.16351	−	23.0025i	−0.316598	−	1.18156i	0.605894	−	0.795545i	$-0.292816\pi$
$380$	4.52597			0.232178
$381$		0			0
$382$	−5.85511	−	21.8516i	−0.299574	−	1.11802i
$383$	29.5578	−	7.91998i	1.51033	−	0.404692i	0.593786	−	0.804623i	$-0.297632\pi$
$383$	29.5578	−	7.91998i	1.51033	−	0.404692i	0.916545	+	0.399931i	$0.130966\pi$
$384$		0			0
$385$	7.78354	−	10.4062i	0.396686	−	0.530351i
$386$	−20.6056	−	35.6900i	−1.04880	−	1.81657i
$387$		0			0
$388$	23.6100	+	6.32628i	1.19862	+	0.321168i
$389$	1.02102	+	0.589484i	0.0517676	+	0.0298880i	0.525660	−	0.850694i	$-0.323818\pi$
$389$	1.02102	+	0.589484i	0.0517676	+	0.0298880i	−0.473893	+	0.880583i	$0.657152\pi$
$390$		0			0
$391$		−	48.5974i		−	2.45767i
$392$	3.03378	+	4.96831i	0.153229	+	0.250937i
$393$		0			0
$394$	20.8266	+	12.0242i	1.04923	+	0.605773i
$395$	8.76861	−	2.34954i	0.441197	−	0.118218i
$396$		0			0
$397$	−3.14500	−	11.7373i	−0.157843	−	0.589078i	−0.998845	−	0.0480464i	$-0.984700\pi$
$397$	−3.14500	−	11.7373i	−0.157843	−	0.589078i	0.841002	−	0.541032i	$-0.181966\pi$
$398$	−8.23581	+	8.23581i	−0.412824	+	0.412824i
$399$		0			0
$400$	3.06471	+	1.76941i	0.153236	+	0.0884707i
$401$	1.52505	+	1.52505i	0.0761573	+	0.0761573i	0.744159	−	0.668002i	$-0.232850\pi$
$401$	1.52505	+	1.52505i	0.0761573	+	0.0761573i	−0.668002	+	0.744159i	$0.732850\pi$
$402$		0			0
$403$	−10.8152	−	1.37228i	−0.538743	−	0.0683582i
$404$	7.89869	−	4.56031i	0.392975	−	0.226884i
$405$		0			0
$406$	57.2963	−	8.26131i	2.84357	−	0.410002i
$407$	2.99044	−	1.72653i	0.148230	−	0.0855809i
$408$		0			0
$409$	−3.39607	−	3.39607i	−0.167925	−	0.167925i	0.618142	−	0.786067i	$-0.287886\pi$
$409$	−3.39607	−	3.39607i	−0.167925	−	0.167925i	−0.786067	+	0.618142i	$0.787886\pi$
$410$	−2.13552	−	2.13552i	−0.105466	−	0.105466i
$411$		0			0
$412$	−19.7215	+	11.3862i	−0.971609	+	0.560959i
$413$	7.77311	+	9.87620i	0.382490	+	0.485976i
$414$		0			0
$415$	−24.2601	+	14.0066i	−1.19088	+	0.687556i
$416$	26.7876	−	11.2432i	1.31337	−	0.551245i
$417$		0			0
$418$	3.58189	+	3.58189i	0.175196	+	0.175196i
$419$	18.2738	+	10.5504i	0.892733	+	0.515420i	0.874836	−	0.484420i	$-0.160969\pi$
$419$	18.2738	+	10.5504i	0.892733	+	0.515420i	0.0178978	+	0.999840i	$0.494303\pi$
$420$		0			0
$421$	24.4128	−	24.4128i	1.18981	−	1.18981i	0.212688	−	0.977120i	$-0.431778\pi$
$421$	24.4128	−	24.4128i	1.18981	−	1.18981i	0.977120	−	0.212688i	$-0.0682218\pi$
$422$	8.75191	+	32.6626i	0.426036	+	1.58999i
$423$		0			0
$424$	−1.86140	+	0.498760i	−0.0903975	+	0.0242219i
$425$	−7.35746	−	4.24783i	−0.356889	−	0.206050i
$426$		0			0
$427$	14.9818	−	20.0300i	0.725022	−	0.969322i
$428$		−	23.3790i		−	1.13007i
$429$		0			0
$430$	41.6046	+	24.0204i	2.00635	+	1.15837i
$431$	7.96117	+	2.13319i	0.383476	+	0.102752i	0.445407	−	0.895328i	$-0.353059\pi$
$431$	7.96117	+	2.13319i	0.383476	+	0.102752i	−0.0619308	+	0.998080i	$0.519726\pi$
$432$		0			0
$433$	−13.2942	−	23.0262i	−0.638878	−	1.10657i	−0.985679	−	0.168631i	$-0.946065\pi$
$433$	−13.2942	−	23.0262i	−0.638878	−	1.10657i	0.346801	−	0.937939i	$-0.387268\pi$
$434$	−13.4324	−	10.0470i	−0.644774	−	0.482270i
$435$		0			0
$436$	13.7926	−	3.69573i	0.660548	−	0.176993i
$437$	1.65585	+	6.17972i	0.0792101	+	0.295616i
$438$		0			0
$439$	−17.8799			−0.853362			−0.426681	−	0.904402i	$-0.640317\pi$
$439$	−17.8799			−0.853362			−0.426681	+	0.904402i	$0.640317\pi$
$440$	1.05719	+	3.94548i	0.0503994	+	0.188093i
$441$		0			0
$442$	−51.0341	+	21.4199i	−2.42744	+	1.01884i
$443$	−10.8928	−	18.8669i	−0.517532	−	0.896392i	−0.999793	−	0.0203640i	$-0.993517\pi$
$443$	−10.8928	−	18.8669i	−0.517532	−	0.896392i	0.482261	−	0.876028i	$-0.339816\pi$
$444$		0			0
$445$	4.01615	+	6.95618i	0.190384	+	0.329755i
$446$	27.8489	−	48.2358i	1.31869	−	2.28403i
$447$		0			0
$448$	28.3626	+	3.37968i	1.34001	+	0.159675i
$449$	0.850694	−	3.17483i	0.0401467	−	0.149830i	−0.942943	−	0.332954i	$-0.891955\pi$
$449$	0.850694	−	3.17483i	0.0401467	−	0.149830i	0.983090	+	0.183125i	$0.0586212\pi$
$450$		0			0
$451$		−	1.84253i		−	0.0867612i
$452$	−23.4892	+	13.5615i	−1.10484	+	0.637878i
$453$		0			0
$454$	−3.72721			−0.174927
$455$	−13.4400	−	12.9909i	−0.630076	−	0.609024i
$456$		0			0
$457$	25.5511	−	25.5511i	1.19523	−	1.19523i	0.219653	−	0.975578i	$-0.429507\pi$
$457$	25.5511	−	25.5511i	1.19523	−	1.19523i	0.975578	−	0.219653i	$-0.0704925\pi$
$458$	−16.3253	+	9.42541i	−0.762831	+	0.440421i
$459$		0			0
$460$	−8.06830	+	30.1113i	−0.376187	+	1.40395i
$461$	−3.32485	+	12.4085i	−0.154854	+	0.577922i	0.844264	+	0.535927i	$0.180038\pi$
$461$	−3.32485	+	12.4085i	−0.154854	+	0.577922i	−0.999118	+	0.0419948i	$0.986629\pi$
$462$		0			0
$463$	22.2200	+	22.2200i	1.03265	+	1.03265i	0.999449	+	0.0332014i	$0.0105703\pi$
$463$	22.2200	+	22.2200i	1.03265	+	1.03265i	0.0332014	+	0.999449i	$0.489430\pi$
$464$	15.9104	−	27.5577i	0.738623	−	1.27933i
$465$		0			0
$466$	−0.558807	+	2.08550i	−0.0258862	+	0.0966087i
$467$	17.1486	+	29.7023i	0.793543	+	1.37446i	0.923760	+	0.382972i	$0.125099\pi$
$467$	17.1486	+	29.7023i	0.793543	+	1.37446i	−0.130217	+	0.991486i	$0.541567\pi$
$468$		0			0
$469$	6.16334	−	15.4131i	0.284597	−	0.711711i
$470$	3.99298	+	14.9020i	0.184182	+	0.687378i
$471$		0			0
$472$	−3.95048			−0.181835
$473$	7.58581	+	28.3106i	0.348796	+	1.30172i
$474$		0			0
$475$	1.08032	+	0.289472i	0.0495686	+	0.0132819i
$476$	−46.0944	−	5.49260i	−2.11273	−	0.251753i
$477$		0			0
$478$		−	39.2452i		−	1.79503i
$479$	−2.30910	−	0.618722i	−0.105505	−	0.0282701i	0.205680	−	0.978619i	$-0.434059\pi$
$479$	−2.30910	−	0.618722i	−0.105505	−	0.0282701i	−0.311186	+	0.950349i	$0.600726\pi$
$480$		0			0
$481$	−1.92224	−	4.57983i	−0.0876465	−	0.208822i
$482$		−	6.15798i		−	0.280489i
$483$		0			0
$484$	5.65210	−	9.78972i	0.256913	−	0.444987i
$485$	−17.3071	−	9.99226i	−0.785875	−	0.453725i
$486$		0			0
$487$	−5.93438	+	5.93438i	−0.268912	+	0.268912i	−0.828662	−	0.559749i	$-0.810897\pi$
$487$	−5.93438	+	5.93438i	−0.268912	+	0.268912i	0.559749	+	0.828662i	$0.310897\pi$
$488$	2.03489	+	7.59430i	0.0921149	+	0.343778i
$489$		0			0
$490$	−8.12479	−	27.5890i	−0.367041	−	1.24634i
$491$	5.46870	+	3.15735i	0.246799	+	0.142489i	0.618298	−	0.785944i	$-0.287823\pi$
$491$	5.46870	+	3.15735i	0.246799	+	0.142489i	−0.371499	+	0.928433i	$0.621156\pi$
$492$		0			0
$493$	−38.1962	+	66.1577i	−1.72027	+	2.97959i
$494$	5.75974	−	4.46267i	0.259143	−	0.200785i
$495$		0			0
$496$	−8.90635	+	2.38645i	−0.399907	+	0.107155i
$497$	8.47054	−	21.1829i	0.379956	−	0.950182i
$498$		0			0
$499$	33.9532	+	9.09774i	1.51996	+	0.407271i	0.919727	−	0.392558i	$-0.128410\pi$
$499$	33.9532	+	9.09774i	1.51996	+	0.407271i	0.600228	+	0.799829i	$0.295077\pi$
$500$	20.4567	+	20.4567i	0.914851	+	0.914851i
$501$		0			0
$502$	−0.991772	−	0.265744i	−0.0442649	−	0.0118608i
$503$	8.32980	−	4.80921i	0.371408	−	0.214432i	−0.302666	−	0.953097i	$-0.597877\pi$
$503$	8.32980	−	4.80921i	0.371408	−	0.214432i	0.674073	+	0.738665i	$0.264543\pi$
$504$		0			0
$505$	−7.20294	+	1.93002i	−0.320527	+	0.0858849i
$506$	−30.2156	+	17.4450i	−1.34325	+	0.775525i
$507$		0			0
$508$	13.5767	−	23.5155i	0.602369	−	1.04333i
$509$	9.11455	+	9.11455i	0.403995	+	0.403995i	0.879638	−	0.475643i	$-0.157785\pi$
$509$	9.11455	+	9.11455i	0.403995	+	0.403995i	−0.475643	+	0.879638i	$0.657785\pi$
$510$		0			0
$511$	−20.3508	+	2.93429i	−0.900266	+	0.129806i
$512$	20.9607	−	20.9607i	0.926340	−	0.926340i
$513$		0			0
$514$	−27.7432	+	27.7432i	−1.22370	+	1.22370i
$515$	17.9844	−	4.81889i	0.792485	−	0.212346i
$516$		0			0
$517$	−4.70614	+	8.15128i	−0.206976	+	0.358493i
$518$	0.904247	−	7.58853i	0.0397303	−	0.333421i
$519$		0			0
$520$	5.82144	−	0.794198i	0.255287	−	0.0348279i
$521$	9.09809	+	5.25278i	0.398594	+	0.230129i	0.685877	−	0.727717i	$-0.259419\pi$
$521$	9.09809	+	5.25278i	0.398594	+	0.230129i	−0.287283	+	0.957846i	$0.592752\pi$
$522$		0			0
$523$			0.571212i			0.0249773i	0.999922	+	0.0124887i	$0.00397537\pi$
$523$			0.571212i			0.0249773i	−0.999922	+	0.0124887i	$0.996025\pi$
$524$	−17.1473	−	29.6999i	−0.749082	−	1.29745i
$525$		0			0
$526$	−6.97208	−	1.86816i	−0.303997	−	0.0814558i
$527$	21.3815	−	5.72915i	0.931392	−	0.249566i
$528$		0			0
$529$	−21.0655			−0.915891
$530$	9.52071			0.413553
$531$		0			0
$532$	6.04859	−	0.872121i	0.262240	−	0.0378112i
$533$	−2.62921	−	0.333606i	−0.113884	−	0.0144501i
$534$		0			0
$535$	−4.94725	+	18.4634i	−0.213888	+	0.798242i
$536$	2.60883	+	4.51863i	0.112684	+	0.195175i
$537$		0			0
$538$	13.4133	+	13.4133i	0.578288	+	0.578288i
$539$	8.39684	−	15.4069i	0.361678	−	0.663622i
$540$		0			0
$541$	−3.18970	+	11.9041i	−0.137136	+	0.511798i	0.862844	+	0.505470i	$0.168681\pi$
$541$	−3.18970	+	11.9041i	−0.137136	+	0.511798i	−0.999980	+	0.00632795i	$0.997986\pi$
$542$			16.4070i			0.704743i
$543$		0			0
$544$	−41.7103	+	41.7103i	−1.78832	+	1.78832i
$545$	−11.6747			−0.500089
$546$		0			0
$547$	−16.2110			−0.693132			−0.346566	−	0.938026i	$-0.612652\pi$
$547$	−16.2110			−0.693132			−0.346566	+	0.938026i	$0.612652\pi$
$548$	9.65224	−	9.65224i	0.412323	−	0.412323i
$549$		0			0
$550$			6.09938i			0.260078i
$551$	2.60291	−	9.71418i	0.110887	−	0.413838i
$552$		0			0
$553$	11.2658	−	4.82961i	0.479070	−	0.205376i
$554$	−2.29682	−	2.29682i	−0.0975826	−	0.0975826i
$555$		0			0
$556$	−12.9797	−	22.4815i	−0.550463	−	0.953429i
$557$	−8.66766	+	32.3481i	−0.367260	+	1.37063i	0.497070	+	0.867710i	$0.334409\pi$
$557$	−8.66766	+	32.3481i	−0.367260	+	1.37063i	−0.864330	+	0.502924i	$0.832257\pi$
$558$		0			0
$559$	41.7715	−	5.69873i	1.76675	−	0.241031i
$560$	−14.6792	−	5.86987i	−0.620310	−	0.248047i
$561$		0			0
$562$	−12.4598			−0.525584
$563$	0.157014			0.00661736			0.00330868	−	0.999995i	$-0.498947\pi$
$563$	0.157014			0.00661736			0.00330868	+	0.999995i	$0.498947\pi$
$564$		0			0
$565$	21.4201	−	5.73951i	0.901152	−	0.241463i
$566$	−9.43036	−	2.52686i	−0.396388	−	0.106212i
$567$		0			0
$568$	3.58543	+	6.21014i	0.150441	+	0.260572i
$569$			42.2556i			1.77145i	0.464213	+	0.885724i	$0.346337\pi$
$569$			42.2556i			1.77145i	−0.464213	+	0.885724i	$0.653663\pi$
$570$		0			0
$571$	28.4747	+	16.4399i	1.19163	+	0.687987i	0.958676	−	0.284502i	$-0.0918281\pi$
$571$	28.4747	+	16.4399i	1.19163	+	0.687987i	0.232952	+	0.972488i	$0.425161\pi$
$572$	17.2458	+	13.1051i	0.721084	+	0.547954i
$573$		0			0
$574$	−3.26545	−	2.44245i	−0.136297	−	0.101946i
$575$	−3.85171	+	6.67136i	−0.160627	+	0.278215i
$576$		0			0
$577$	41.6112	−	11.1497i	1.73230	−	0.464167i	0.751586	−	0.659635i	$-0.229289\pi$
$577$	41.6112	−	11.1497i	1.73230	−	0.464167i	0.980710	+	0.195467i	$0.0626223\pi$
$578$	54.2587	−	54.2587i	2.25686	−	2.25686i
$579$		0			0
$580$	34.6504	−	34.6504i	1.43878	−	1.43878i
$581$	−29.7227	+	23.3934i	−1.23310	+	0.970521i
$582$		0			0
$583$	4.10723	+	4.10723i	0.170104	+	0.170104i
$584$	3.23143	−	5.59700i	0.133717	−	0.231605i
$585$		0			0
$586$	−20.3052	+	11.7232i	−0.838800	+	0.484281i
$587$	15.3441	−	4.11144i	0.633318	−	0.169697i	0.0721432	−	0.997394i	$-0.477016\pi$
$587$	15.3441	−	4.11144i	0.633318	−	0.169697i	0.561175	+	0.827697i	$0.310349\pi$
$588$		0			0
$589$	−2.52369	+	1.45706i	−0.103987	+	0.0600369i
$590$	18.8524	+	5.05149i	0.776142	+	0.207967i
$591$		0			0
$592$	−2.97045	−	2.97045i	−0.122085	−	0.122085i
$593$	−18.7597	−	5.02665i	−0.770369	−	0.206420i	−0.147834	−	0.989012i	$-0.547230\pi$
$593$	−18.7597	−	5.02665i	−0.770369	−	0.206420i	−0.622534	+	0.782592i	$0.713897\pi$
$594$		0			0
$595$	35.2404	+	14.0918i	1.44472	+	0.577708i
$596$	−20.6518	+	5.53363i	−0.845931	+	0.226666i
$597$		0			0
$598$	19.4225	+	46.2750i	0.794243	+	1.89232i
$599$	−22.3885	+	38.7780i	−0.914770	+	1.58443i	−0.107531	+	0.994202i	$0.534295\pi$
$599$	−22.3885	+	38.7780i	−0.914770	+	1.58443i	−0.807238	+	0.590226i	$0.799039\pi$
$600$		0			0
$601$	−33.7722	−	19.4984i	−1.37760	−	0.795355i	−0.385726	−	0.922613i	$-0.626049\pi$
$601$	−33.7722	−	19.4984i	−1.37760	−	0.795355i	−0.991870	+	0.127258i	$0.959382\pi$
$602$	60.2297	+	24.0844i	2.45478	+	0.981608i
$603$		0			0
$604$	7.97789	+	29.7739i	0.324616	+	1.21148i
$605$	−6.53531	+	6.53531i	−0.265698	+	0.265698i
$606$		0			0
$607$	27.6946	+	15.9895i	1.12409	+	0.648992i	0.942441	−	0.334372i	$-0.108524\pi$
$607$	27.6946	+	15.9895i	1.12409	+	0.648992i	0.181646	+	0.983364i	$0.441857\pi$
$608$	3.88276	−	6.72514i	0.157467	−	0.272741i
$609$		0			0
$610$		−	38.8434i		−	1.57272i
$611$	10.7794	+	8.19132i	0.436089	+	0.331386i
$612$		0			0
$613$	−21.4241	−	5.74057i	−0.865311	−	0.231859i	−0.201252	−	0.979540i	$-0.564501\pi$
$613$	−21.4241	−	5.74057i	−0.865311	−	0.231859i	−0.664059	+	0.747680i	$0.731168\pi$
$614$		−	7.82757i		−	0.315895i
$615$		0			0
$616$	2.17311	+	5.06909i	0.0875570	+	0.204239i
$617$	−19.7363	−	5.28833i	−0.794554	−	0.212900i	−0.161363	−	0.986895i	$-0.551589\pi$
$617$	−19.7363	−	5.28833i	−0.794554	−	0.212900i	−0.633192	+	0.773995i	$0.718256\pi$
$618$		0			0
$619$	−7.46806	−	27.8712i	−0.300167	−	1.12024i	−0.937027	−	0.349258i	$-0.886434\pi$
$619$	−7.46806	−	27.8712i	−0.300167	−	1.12024i	0.636860	−	0.770980i	$-0.280233\pi$
$620$	−14.1993			−0.570258
$621$		0			0
$622$	−17.6737	−	65.9592i	−0.708651	−	2.64472i
$623$	6.70766	+	8.52248i	0.268737	+	0.341446i
$624$		0			0
$625$	−8.92548	−	15.4594i	−0.357019	−	0.618375i
$626$	−7.96615	+	29.7301i	−0.318391	+	1.18825i
$627$		0			0
$628$	−5.47316	+	9.47979i	−0.218403	+	0.378285i
$629$	7.13115	+	7.13115i	0.284338	+	0.284338i
$630$		0			0
$631$	−0.897330	+	3.34888i	−0.0357221	+	0.133317i	−0.981484	−	0.191544i	$-0.938651\pi$
$631$	−0.897330	+	3.34888i	−0.0357221	+	0.133317i	0.945762	+	0.324860i	$0.105317\pi$
$632$	−0.997169	+	3.72148i	−0.0396652	+	0.148033i
$633$		0			0
$634$	−18.6503	+	10.7677i	−0.740697	+	0.427641i
$635$	−15.6982	+	15.6982i	−0.622965	+	0.622965i
$636$		0			0
$637$	−20.4647	−	14.7715i	−0.810840	−	0.585268i
$638$	54.8451			2.17134
$639$		0			0
$640$	11.0678	−	6.38997i	0.437491	−	0.252586i
$641$			6.69397i			0.264396i	0.991223	+	0.132198i	$0.0422035\pi$
$641$			6.69397i			0.264396i	−0.991223	+	0.132198i	$0.957797\pi$
$642$		0			0
$643$	−11.3176	+	42.2380i	−0.446324	+	1.66570i	0.266092	+	0.963948i	$0.414268\pi$
$643$	−11.3176	+	42.2380i	−0.446324	+	1.66570i	−0.712416	+	0.701757i	$0.752399\pi$
$644$	−4.98040	+	41.7960i	−0.196255	+	1.64699i
$645$		0			0
$646$	−7.39721	+	12.8123i	−0.291039	+	0.504095i
$647$	−1.21242	−	2.09997i	−0.0476652	−	0.0825585i	0.841208	−	0.540711i	$-0.181845\pi$
$647$	−1.21242	−	2.09997i	−0.0476652	−	0.0825585i	−0.888874	+	0.458152i	$0.848511\pi$
$648$		0			0
$649$	5.95371	+	10.3121i	0.233704	+	0.404787i
$650$	8.70356	+	1.10435i	0.341382	+	0.0433161i
$651$		0			0
$652$	−1.59129	−	5.93876i	−0.0623196	−	0.232580i
$653$	−18.9747			−0.742539			−0.371269	−	0.928525i	$-0.621077\pi$
$653$	−18.9747			−0.742539			−0.371269	+	0.928525i	$0.621077\pi$
$654$		0			0
$655$	7.25709	+	27.0838i	0.283558	+	1.05825i
$656$	−2.16516	+	0.580154i	−0.0845354	+	0.0226512i
$657$		0			0
$658$	8.20778	+	19.1459i	0.319973	+	0.746383i
$659$	1.16446	+	2.01691i	0.0453610	+	0.0785676i	0.887814	−	0.460202i	$-0.152223\pi$
$659$	1.16446	+	2.01691i	0.0453610	+	0.0785676i	−0.842453	+	0.538769i	$0.818890\pi$
$660$		0			0
$661$	−24.8482	−	6.65805i	−0.966482	−	0.258968i	−0.259140	−	0.965840i	$-0.583439\pi$
$661$	−24.8482	−	6.65805i	−0.966482	−	0.258968i	−0.707342	+	0.706872i	$0.750106\pi$
$662$	−45.9612	−	26.5357i	−1.78633	−	1.03134i
$663$		0			0
$664$		−	11.8891i		−	0.461385i
$665$	−4.96137	−	0.591196i	−0.192394	−	0.0229256i
$666$		0			0
$667$	59.9883	+	34.6343i	2.32276	+	1.34104i
$668$	−17.0296	+	4.56306i	−0.658894	+	0.176550i
$669$		0			0
$670$	−6.67184	−	24.8997i	−0.257756	−	0.961958i
$671$	16.7570	−	16.7570i	0.646898	−	0.646898i
$672$		0			0
$673$	−24.9952	−	14.4310i	−0.963493	−	0.556273i	−0.0662467	−	0.997803i	$-0.521102\pi$
$673$	−24.9952	−	14.4310i	−0.963493	−	0.556273i	−0.897246	+	0.441530i	$0.854436\pi$
$674$	−1.09957	−	1.09957i	−0.0423540	−	0.0423540i
$675$		0			0
$676$	21.8230	−	22.2362i	0.839346	−	0.855240i
$677$	−13.4814	+	7.78352i	−0.518134	+	0.299145i	−0.736171	−	0.676796i	$-0.763368\pi$
$677$	−13.4814	+	7.78352i	−0.518134	+	0.299145i	0.218037	+	0.975941i	$0.430035\pi$
$678$		0			0
$679$	−25.0549	−	10.0189i	−0.961520	−	0.384489i
$680$	−10.3314	+	5.96481i	−0.396189	+	0.228740i
$681$		0			0
$682$	−11.2374	−	11.2374i	−0.430304	−	0.430304i
$683$	29.7469	+	29.7469i	1.13823	+	1.13823i	0.988767	+	0.149467i	$0.0477557\pi$
$683$	29.7469	+	29.7469i	1.13823	+	1.13823i	0.149467	+	0.988767i	$0.452244\pi$
$684$		0			0
$685$	−9.66529	+	5.58026i	−0.369292	+	0.213211i
$686$	−16.1743	−	35.3048i	−0.617538	−	1.34794i
$687$		0			0
$688$	30.8794	−	17.8282i	1.17727	−	0.679695i
$689$	6.60449	−	5.11719i	0.251611	−	0.194949i
$690$		0			0
$691$	15.4899	+	15.4899i	0.589263	+	0.589263i	0.937432	−	0.348169i	$-0.113197\pi$
$691$	15.4899	+	15.4899i	0.589263	+	0.589263i	−0.348169	+	0.937432i	$0.613197\pi$
$692$	−38.0684	−	21.9788i	−1.44714	−	0.835508i
$693$		0			0
$694$	−50.6735	+	50.6735i	−1.92354	+	1.92354i
$695$	5.49329	+	20.5013i	0.208373	+	0.777657i
$696$		0			0
$697$	5.19791	−	1.39278i	0.196885	−	0.0527551i
$698$	50.9389	+	29.4096i	1.92807	+	1.11317i
$699$		0			0
$700$	5.89243	+	4.40735i	0.222713	+	0.166582i
$701$			15.8478i			0.598564i	0.954165	+	0.299282i	$0.0967471\pi$
$701$			15.8478i			0.598564i	−0.954165	+	0.299282i	$0.903253\pi$
$702$		0			0
$703$	−1.14979	−	0.663830i	−0.0433650	−	0.0250368i
$704$	26.1394	+	7.00403i	0.985165	+	0.263974i
$705$		0			0
$706$	−10.1229	−	17.5334i	−0.380981	−	0.659879i
$707$	−9.25423	+	3.96727i	−0.348041	+	0.149204i
$708$		0			0
$709$	−46.6694	+	12.5050i	−1.75271	+	0.469637i	−0.985201	−	0.171404i	$-0.945170\pi$
$709$	−46.6694	+	12.5050i	−1.75271	+	0.469637i	−0.767507	+	0.641041i	$0.778503\pi$
$710$	−9.16940	−	34.2207i	−0.344121	−	1.28428i
$711$		0			0
$712$	−3.40899			−0.127757
$713$	−5.19489	−	19.3876i	−0.194550	−	0.726071i
$714$		0			0
$715$	−10.8466	−	13.9991i	−0.405638	−	0.523536i
$716$	−2.28818	−	3.96325i	−0.0855134	−	0.148114i
$717$		0			0
$718$	35.8473	+	62.0893i	1.33781	+	2.31715i
$719$	−5.32163	+	9.21734i	−0.198463	+	0.343749i	−0.948030	−	0.318180i	$-0.896928\pi$
$719$	−5.32163	+	9.21734i	−0.198463	+	0.343749i	0.749567	+	0.661928i	$0.230262\pi$
$720$		0			0
$721$	23.1060	−	9.90549i	0.860513	−	0.368900i
$722$	−9.80710	+	36.6006i	−0.364983	+	1.36213i
$723$		0			0
$724$			45.3784i			1.68647i
$725$	10.4870	−	6.05467i	0.389478	−	0.224865i
$726$		0			0
$727$	5.89296			0.218558			0.109279	−	0.994011i	$-0.465146\pi$
$727$	5.89296			0.218558			0.109279	+	0.994011i	$0.465146\pi$
$728$	7.62684	−	2.18313i	0.282669	−	0.0809120i
$729$		0			0
$730$	−22.5779	+	22.5779i	−0.835645	+	0.835645i
$731$	−74.1322	+	42.8003i	−2.74188	+	1.58302i
$732$		0			0
$733$	9.93532	−	37.0791i	0.366970	−	1.36955i	−0.497762	−	0.867314i	$-0.665845\pi$
$733$	9.93532	−	37.0791i	0.366970	−	1.36955i	0.864731	−	0.502235i	$-0.167489\pi$
$734$	−14.5362	+	54.2499i	−0.536542	+	2.00240i
$735$		0			0
$736$	37.8207	+	37.8207i	1.39409	+	1.39409i
$737$	7.86347	−	13.6199i	0.289655	−	0.501696i
$738$		0			0
$739$	−5.34503	+	19.9479i	−0.196620	+	0.733796i	0.795221	+	0.606319i	$0.207355\pi$
$739$	−5.34503	+	19.9479i	−0.196620	+	0.733796i	−0.991842	+	0.127477i	$0.959312\pi$
$740$	−3.23458	−	5.60246i	−0.118906	−	0.205950i
$741$		0			0
$742$	12.7236	−	1.83457i	0.467099	−	0.0673491i
$743$	−8.72671	−	32.5685i	−0.320152	−	1.19482i	−0.919097	−	0.394033i	$-0.871080\pi$
$743$	−8.72671	−	32.5685i	−0.320152	−	1.19482i	0.598945	−	0.800790i	$-0.295587\pi$
$744$		0			0
$745$	17.4806			0.640439
$746$	1.98879	+	7.42228i	0.0728150	+	0.271749i
$747$		0			0
$748$	−42.4812	−	11.3828i	−1.55327	−	0.416197i
$749$	−3.05384	+	25.6281i	−0.111585	+	0.936430i
$750$		0			0
$751$			31.7749i			1.15948i	0.814801	+	0.579741i	$0.196846\pi$
$751$			31.7749i			1.15948i	−0.814801	+	0.579741i	$0.803154\pi$
$752$	11.0604	+	2.96363i	0.403332	+	0.108072i
$753$		0			0
$754$	9.93020	−	78.2617i	0.361637	−	2.85012i
$755$		−	25.2019i		−	0.917191i
$756$		0			0
$757$	−13.6215	+	23.5930i	−0.495080	+	0.857504i	−0.999984	−	0.00567171i	$-0.998195\pi$
$757$	−13.6215	+	23.5930i	−0.495080	+	0.857504i	0.504904	+	0.863176i	$0.331528\pi$
$758$	−43.2436	−	24.9667i	−1.57068	−	0.906831i
$759$		0			0
$760$	1.11051	−	1.11051i	0.0402826	−	0.0402826i
$761$	−7.38152	−	27.5482i	−0.267580	−	0.998622i	−0.960652	−	0.277754i	$-0.910410\pi$
$761$	−7.38152	−	27.5482i	−0.267580	−	0.998622i	0.693072	−	0.720868i	$-0.256257\pi$
$762$		0			0
$763$	−15.6022	+	2.24962i	−0.564839	+	0.0814418i
$764$	−22.3928	−	12.9285i	−0.810143	−	0.467736i
$765$		0			0
$766$	32.0817	−	55.5671i	1.15916	−	2.00772i
$767$	15.7929	−	6.62859i	0.570250	−	0.239344i
$768$		0			0
$769$	−27.2629	+	7.30506i	−0.983124	+	0.263427i	−0.714360	−	0.699779i	$-0.753282\pi$
$769$	−27.2629	+	7.30506i	−0.983124	+	0.263427i	−0.268764	+	0.963206i	$0.586615\pi$
$770$	−3.88861	−	26.9694i	−0.140136	−	0.971910i
$771$		0			0
$772$	−45.4986	−	12.1913i	−1.63753	−	0.438775i
$773$	−8.57861	−	8.57861i	−0.308551	−	0.308551i	0.535796	−	0.844347i	$-0.320011\pi$
$773$	−8.57861	−	8.57861i	−0.308551	−	0.308551i	−0.844347	+	0.535796i	$0.820011\pi$
$774$		0			0
$775$	−3.38929	−	0.908157i	−0.121747	−	0.0326220i
$776$	7.34530	−	4.24081i	0.263681	−	0.152236i
$777$		0			0
$778$	2.38784	−	0.639819i	0.0856082	−	0.0229386i
$779$	−0.613518	+	0.354215i	−0.0219816	+	0.0126911i
$780$		0			0
$781$	10.8071	−	18.7184i	0.386708	−	0.669799i
$782$	−72.0538	−	72.0538i	−2.57664	−	2.57664i
$783$		0			0
$784$	−20.7486	−	5.01602i	−0.741022	−	0.179144i
$785$	6.32841	−	6.32841i	0.225871	−	0.225871i
$786$		0			0
$787$	13.1589	−	13.1589i	0.469063	−	0.469063i	−0.432548	−	0.901611i	$-0.642385\pi$
$787$	13.1589	−	13.1589i	0.469063	−	0.469063i	0.901611	+	0.432548i	$0.142385\pi$
$788$	26.5504	−	7.11415i	0.945817	−	0.253431i
$789$		0			0
$790$	9.51735	−	16.4845i	0.338612	−	0.586494i
$791$	27.5203	−	11.7979i	0.978508	−	0.419484i
$792$		0			0
$793$	−20.8776	−	26.9456i	−0.741384	−	0.956865i
$794$	−22.0655	−	12.7395i	−0.783076	−	0.452109i
$795$		0			0
$796$			13.3125i			0.471849i
$797$	−16.8639	−	29.2091i	−0.597350	−	1.03464i	−0.993211	−	0.116330i	$-0.962887\pi$
$797$	−16.8639	−	29.2091i	−0.597350	−	1.03464i	0.395861	−	0.918311i	$-0.370446\pi$
$798$		0			0
$799$	−26.5528	−	7.11479i	−0.939369	−	0.251703i
$800$	9.03178	−	2.42006i	0.319322	−	0.0855620i
$801$		0			0
$802$	4.52228			0.159687
$803$	−19.4802			−0.687440
$804$		0			0
$805$	12.7777	−	31.9541i	0.450355	−	1.12623i
$806$	−18.0700	+	14.0007i	−0.636488	+	0.493154i
$807$		0			0
$808$	0.819120	−	3.05700i	0.0288165	−	0.107545i
$809$	−22.6796	−	39.2823i	−0.797373	−	1.38109i	−0.921321	−	0.388802i	$-0.872889\pi$
$809$	−22.6796	−	39.2823i	−0.797373	−	1.38109i	0.123948	−	0.992289i	$-0.460444\pi$
$810$		0			0
$811$	11.6911	+	11.6911i	0.410531	+	0.410531i	0.881924	−	0.471392i	$-0.156248\pi$
$811$	11.6911	+	11.6911i	0.410531	+	0.410531i	−0.471392	+	0.881924i	$0.656248\pi$
$812$	39.6305	−	52.9842i	1.39076	−	1.85938i
$813$		0			0
$814$	1.87395	−	6.99369i	0.0656821	−	0.245129i
$815$			5.02682i			0.176082i
$816$		0			0
$817$	7.96844	−	7.96844i	0.278781	−	0.278781i
$818$	−10.0705			−0.352106
$819$		0			0
$820$	−3.45190			−0.120546
$821$	−12.7335	+	12.7335i	−0.444402	+	0.444402i	−0.893488	−	0.449086i	$-0.851750\pi$
$821$	−12.7335	+	12.7335i	−0.444402	+	0.444402i	0.449086	+	0.893488i	$0.351750\pi$
$822$		0			0
$823$			22.4156i			0.781358i	0.920527	+	0.390679i	$0.127760\pi$
$823$			22.4156i			0.781358i	−0.920527	+	0.390679i	$0.872240\pi$
$824$	−2.04518	+	7.63273i	−0.0712474	+	0.265899i
$825$		0			0
$826$	26.1681	+	3.11818i	0.910504	+	0.108495i
$827$	−21.3413	−	21.3413i	−0.742110	−	0.742110i	0.230873	−	0.972984i	$-0.425842\pi$
$827$	−21.3413	−	21.3413i	−0.742110	−	0.742110i	−0.972984	+	0.230873i	$0.925842\pi$
$828$		0			0
$829$	−1.16634	−	2.02016i	−0.0405086	−	0.0701629i	0.845060	−	0.534671i	$-0.179564\pi$
$829$	−1.16634	−	2.02016i	−0.0405086	−	0.0701629i	−0.885569	+	0.464508i	$0.846231\pi$
$830$	−15.2026	+	56.7368i	−0.527690	+	1.96936i
$831$		0			0
$832$	14.7272	−	36.0316i	0.510574	−	1.24917i
$833$	49.8112	+	12.0420i	1.72586	+	0.417230i
$834$		0			0
$835$	14.4146			0.498836
$836$	5.78983			0.200245
$837$		0			0
$838$	42.7367	−	11.4513i	1.47631	−	0.395577i
$839$	−32.4718	−	8.70079i	−1.12105	−	0.300385i	−0.349742	−	0.936846i	$-0.613731\pi$
$839$	−32.4718	−	8.70079i	−1.12105	−	0.300385i	−0.771308	+	0.636462i	$0.780397\pi$
$840$		0			0
$841$	−39.9432	−	69.1836i	−1.37735	−	2.38564i
$842$		−	72.3923i		−	2.49480i
$843$		0			0
$844$	33.4715	+	19.3248i	1.15214	+	0.665187i
$845$	−21.9400	+	12.9429i	−0.754757	+	0.445250i
$846$		0			0
$847$	−7.47459	+	9.99320i	−0.256830	+	0.343370i
$848$	3.53319	−	6.11966i	0.121330	−	0.210150i
$849$		0			0
$850$	−17.2068	+	4.61055i	−0.590189	+	0.158141i
$851$	6.46615	−	6.46615i	0.221657	−	0.221657i
$852$		0			0
$853$	4.02453	−	4.02453i	0.137797	−	0.137797i	−0.634844	−	0.772641i	$-0.718935\pi$
$853$	4.02453	−	4.02453i	0.137797	−	0.137797i	0.772641	+	0.634844i	$0.218935\pi$
$854$	−7.48483	−	51.9110i	−0.256126	−	1.77636i
$855$		0			0
$856$	−5.73638	−	5.73638i	−0.196066	−	0.196066i
$857$	−7.66605	+	13.2780i	−0.261867	+	0.453567i	−0.966738	−	0.255768i	$-0.917672\pi$
$857$	−7.66605	+	13.2780i	−0.261867	+	0.453567i	0.704871	+	0.709336i	$0.251005\pi$
$858$		0			0
$859$	−27.5049	+	15.8800i	−0.938455	+	0.541817i	−0.889476	−	0.456983i	$-0.848930\pi$
$859$	−27.5049	+	15.8800i	−0.938455	+	0.541817i	−0.0489791	+	0.998800i	$0.515597\pi$
$860$	53.0388	−	14.2117i	1.80861	−	0.484615i
$861$		0			0
$862$	14.9666	−	8.64096i	0.509764	−	0.294312i
$863$	1.30949	+	0.350876i	0.0445754	+	0.0119439i	0.281038	−	0.959697i	$-0.409321\pi$
$863$	1.30949	+	0.350876i	0.0445754	+	0.0119439i	−0.236462	+	0.971641i	$0.575988\pi$
$864$		0			0
$865$	25.4132	+	25.4132i	0.864076	+	0.864076i
$866$	−53.8511	−	14.4294i	−1.82994	−	0.490330i
$867$		0			0
$868$	−18.9762	+	2.73610i	−0.644094	+	0.0928692i
$869$	11.2172	−	3.00564i	0.380517	−	0.101959i
$870$		0			0
$871$	−18.0113	−	13.6868i	−0.610290	−	0.463761i
$872$	2.47742	−	4.29103i	0.0838962	−	0.145312i
$873$		0			0
$874$	11.6175	+	6.70740i	0.392969	+	0.226881i
$875$	−19.7525	−	25.0967i	−0.667757	−	0.848425i
$876$		0			0
$877$	12.1476	+	45.3356i	0.410197	+	1.53088i	0.794265	+	0.607571i	$0.207856\pi$
$877$	12.1476	+	45.3356i	0.410197	+	1.53088i	−0.384069	+	0.923305i	$0.625477\pi$
$878$	−26.5100	+	26.5100i	−0.894669	+	0.894669i
$879$		0			0
$880$	−12.9714	−	7.48905i	−0.437266	−	0.252456i
$881$	−3.74445	+	6.48558i	−0.126154	+	0.218505i	−0.922183	−	0.386753i	$-0.873597\pi$
$881$	−3.74445	+	6.48558i	−0.126154	+	0.218505i	0.796030	+	0.605258i	$0.206930\pi$
$882$		0			0
$883$		−	21.6436i		−	0.728364i	−0.931328	−	0.364182i	$-0.881349\pi$
$883$		−	21.6436i		−	0.728364i	0.931328	−	0.364182i	$-0.118651\pi$
$884$	−23.9344	+	58.5580i	−0.805001	+	1.96952i
$885$		0			0
$886$	−44.1237	−	11.8229i	−1.48236	−	0.397198i
$887$			9.93222i			0.333491i	0.986000	+	0.166746i	$0.0533259\pi$
$887$			9.93222i			0.333491i	−0.986000	+	0.166746i	$0.946674\pi$
$888$		0			0
$889$	−17.9544	+	24.0043i	−0.602173	+	0.805078i
$890$	16.2683	+	4.35909i	0.545316	+	0.146117i
$891$		0			0
$892$	−16.4768	−	61.4923i	−0.551685	−	2.05892i
$893$	3.61891			0.121102
$894$		0			0
$895$	0.968408	+	3.61415i	0.0323703	+	0.120808i
$896$	13.5598	−	10.6723i	0.453002	−	0.356538i
$897$		0			0
$898$	−3.44593	−	5.96852i	−0.114992	−	0.199172i
$899$	−8.16608	+	30.4762i	−0.272354	+	1.01644i
$900$		0			0
$901$	−8.48212	+	14.6915i	−0.282580	+	0.489444i
$902$	−2.73186	−	2.73186i	−0.0909609	−	0.0909609i
$903$		0			0
$904$	−2.43590	+	9.09091i	−0.0810169	+	0.302359i
$905$	9.60255	−	35.8372i	0.319199	−	1.19127i
$906$		0			0
$907$	34.7910	−	20.0866i	1.15522	−	0.666965i	0.205064	−	0.978749i	$-0.434260\pi$
$907$	34.7910	−	20.0866i	1.15522	−	0.666965i	0.950153	+	0.311784i	$0.100926\pi$
$908$	−3.01237	+	3.01237i	−0.0999689	+	0.0999689i
$909$		0			0
$910$	−39.1883	+	0.665823i	−1.29908	+	0.0220718i
$911$	−15.0163			−0.497513			−0.248757	−	0.968566i	$-0.580022\pi$
$911$	−15.0163			−0.497513			−0.248757	+	0.968566i	$0.580022\pi$
$912$		0			0
$913$	−31.0346	+	17.9178i	−1.02710	+	0.592994i
$914$		−	75.7677i		−	2.50617i
$915$		0			0
$916$	−5.57654	+	20.8119i	−0.184254	+	0.687646i
$917$	14.9173	+	34.7969i	0.492614	+	1.14910i
$918$		0			0
$919$	−9.43771	+	16.3466i	−0.311321	+	0.539224i	−0.978649	−	0.205540i	$-0.934105\pi$
$919$	−9.43771	+	16.3466i	−0.311321	+	0.539224i	0.667327	+	0.744765i	$0.267438\pi$
$920$	5.40857	+	9.36792i	0.178315	+	0.308851i
$921$		0			0
$922$	13.4681	+	23.3274i	0.443547	+	0.768246i
$923$	−24.7537	−	18.8104i	−0.814778	−	0.619152i
$924$		0			0
$925$	−0.413754	−	1.54415i	−0.0136041	−	0.0507713i
$926$	65.8897			2.16527
$927$		0			0
$928$	−21.7610	−	81.2131i	−0.714339	−	2.66595i
$929$	−45.2763	+	12.1317i	−1.48547	+	0.398029i	−0.908203	−	0.418529i	$-0.862546\pi$
$929$	−45.2763	+	12.1317i	−1.48547	+	0.398029i	−0.577262	+	0.816559i	$0.695879\pi$
$930$		0			0
$931$	−6.74438	+	0.165935i	−0.221038	+	0.00543829i
$932$	1.23388	+	2.13715i	0.0404172	+	0.0700046i
$933$		0			0
$934$	69.4643	+	18.6129i	2.27294	+	0.609033i
$935$	31.1405	+	17.9790i	1.01840	+	0.587975i
$936$		0			0
$937$			17.9722i			0.587126i	0.955940	+	0.293563i	$0.0948411\pi$
$937$			17.9722i			0.587126i	−0.955940	+	0.293563i	$0.905159\pi$
$938$	−13.7143	−	31.9907i	−0.447789	−	1.04453i
$939$		0			0
$940$	15.2711	+	8.81676i	0.498088	+	0.287571i
$941$	34.1628	−	9.15389i	1.11367	−	0.298408i	0.345353	−	0.938473i	$-0.387759\pi$
$941$	34.1628	−	9.15389i	1.11367	−	0.298408i	0.768321	+	0.640065i	$0.221092\pi$
$942$		0			0
$943$	−1.26289	−	4.71319i	−0.0411255	−	0.153482i
$944$	10.2432	−	10.2432i	0.333388	−	0.333388i
$945$		0			0
$946$	53.2225	+	30.7280i	1.73041	+	0.999054i
$947$	0.0932783	+	0.0932783i	0.00303114	+	0.00303114i	0.708621	−	0.705590i	$-0.249318\pi$
$947$	0.0932783	+	0.0932783i	0.00303114	+	0.00303114i	−0.705590	+	0.708621i	$0.749318\pi$
$948$		0			0
$949$	−3.52706	+	27.7974i	−0.114493	+	0.902341i
$950$	2.03095	−	1.17257i	0.0658927	−	0.0380432i
$951$		0			0
$952$	−12.6576	+	9.96225i	−0.410236	+	0.322878i
$953$	−30.3290	+	17.5105i	−0.982454	+	0.567220i	−0.903010	−	0.429619i	$-0.858648\pi$
$953$	−30.3290	+	17.5105i	−0.982454	+	0.567220i	−0.0794437	+	0.996839i	$0.525314\pi$
$954$		0			0
$955$	14.9487	+	14.9487i	0.483729	+	0.483729i
$956$	−31.7183	−	31.7183i	−1.02584	−	1.02584i
$957$		0			0
$958$	−4.34099	+	2.50627i	−0.140251	+	0.0809740i
$959$	−11.8416	+	9.31998i	−0.382385	+	0.300958i
$960$		0			0
$961$	−18.9292	+	10.9288i	−0.610620	+	0.352542i
$962$	−9.64041	−	3.94032i	−0.310819	−	0.127041i
$963$		0			0
$964$	−4.97694	−	4.97694i	−0.160296	−	0.160296i
$965$	33.3524	+	19.2560i	1.07365	+	0.619872i
$966$		0			0
$967$	−13.6207	+	13.6207i	−0.438014	+	0.438014i	−0.891343	−	0.453329i	$-0.850236\pi$
$967$	−13.6207	+	13.6207i	−0.438014	+	0.438014i	0.453329	+	0.891343i	$0.350236\pi$
$968$	−1.01523	−	3.78887i	−0.0326306	−	0.121779i
$969$		0			0
$970$	−40.4759	+	10.8455i	−1.29960	+	0.348228i
$971$	−2.95070	−	1.70359i	−0.0946923	−	0.0546707i	0.451906	−	0.892066i	$-0.350744\pi$
$971$	−2.95070	−	1.70359i	−0.0946923	−	0.0546707i	−0.546598	+	0.837395i	$0.684078\pi$
$972$		0			0
$973$	11.2918	+	26.3397i	0.361997	+	0.844412i
$974$			17.5974i			0.563858i
$975$		0			0
$976$	−24.9675	−	14.4150i	−0.799191	−	0.461413i
$977$	11.5654	+	3.09893i	0.370009	+	0.0991436i	0.439032	−	0.898471i	$-0.355321\pi$
$977$	11.5654	+	3.09893i	0.370009	+	0.0991436i	−0.0690229	+	0.997615i	$0.521988\pi$
$978$		0			0
$979$	5.13764	+	8.89866i	0.164200	+	0.284402i
$980$	−28.8642	−	15.7311i	−0.922033	−	0.502513i
$981$		0			0
$982$	12.7896	−	3.42696i	0.408132	−	0.109359i
$983$	2.94720	+	10.9991i	0.0940010	+	0.350817i	0.996866	−	0.0791074i	$-0.0252070\pi$
$983$	2.94720	+	10.9991i	0.0940010	+	0.350817i	−0.902865	+	0.429924i	$0.858540\pi$
$984$		0			0
$985$	−22.4734			−0.716061
$986$	41.4577	+	154.722i	1.32028	+	4.92736i
$987$		0			0
$988$	1.04830	−	8.26184i	0.0333509	−	0.262844i
$989$	38.8090	+	67.2192i	1.23405	+	2.13744i
$990$		0			0
$991$	−16.9431	−	29.3463i	−0.538216	−	0.932217i	−0.999000	−	0.0447048i	$-0.985765\pi$
$991$	−16.9431	−	29.3463i	−0.538216	−	0.932217i	0.460785	−	0.887512i	$-0.347568\pi$
$992$	−12.1814	+	21.0987i	−0.386759	+	0.669886i
$993$		0			0
$994$	−18.8482	−	43.9662i	−0.597829	−	1.39452i
$995$	2.81707	−	10.5134i	0.0893071	−	0.333299i
$996$		0			0
$997$		−	36.5027i		−	1.15605i	−0.816018	−	0.578026i	$-0.803823\pi$
$997$		−	36.5027i		−	1.15605i	0.816018	−	0.578026i	$-0.196177\pi$
$998$	63.8303	−	36.8524i	2.02051	−	1.16654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.136.8		36
3.2	odd	2		273.2.bt.a.136.2	✓	36
7.5	odd	6		819.2.gh.c.19.2		36
13.11	odd	12		819.2.gh.c.388.2		36
21.5	even	6		273.2.cg.a.19.8	yes	36
39.11	even	12		273.2.cg.a.115.8	yes	36
91.89	even	12	inner	819.2.et.c.271.8		36
273.89	odd	12		273.2.bt.a.271.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.2	✓	36	3.2	odd	2
273.2.bt.a.271.2	yes	36	273.89	odd	12
273.2.cg.a.19.8	yes	36	21.5	even	6
273.2.cg.a.115.8	yes	36	39.11	even	12
819.2.et.c.136.8		36	1.1	even	1	trivial
819.2.et.c.271.8		36	91.89	even	12	inner
819.2.gh.c.19.2		36	7.5	odd	6
819.2.gh.c.388.2		36	13.11	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)

\(f(q)\)	\(=\)	\(q+(1.48267 - 1.48267i) q^{2} -2.39661i q^{4} +(-0.507149 + 1.89270i) q^{5} +(-0.313052 + 2.62717i) q^{7} +(-0.588043 - 0.588043i) q^{8} +O(q^{10})\)	\(q+(1.48267 - 1.48267i) q^{2} -2.39661i q^{4} +(-0.507149 + 1.89270i) q^{5} +(-0.313052 + 2.62717i) q^{7} +(-0.588043 - 0.588043i) q^{8} +(2.05432 + 3.55819i) q^{10} +(-0.648767 + 2.42123i) q^{11} +(3.33753 + 1.36415i) q^{13} +(3.43106 + 4.35937i) q^{14} +3.04948 q^{16} -7.32088 q^{17} +(0.930935 - 0.249443i) q^{19} +(4.53608 + 1.21544i) q^{20} +(2.62798 + 4.55179i) q^{22} +6.63818i q^{23} +(1.00500 + 0.580235i) q^{25} +(6.97103 - 2.92587i) q^{26} +(6.29629 + 0.750265i) q^{28} +(5.21743 - 9.03685i) q^{29} +(-2.92062 + 0.782577i) q^{31} +(5.69745 - 5.69745i) q^{32} +(-10.8544 + 10.8544i) q^{34} +(-4.81368 - 1.92488i) q^{35} +(-0.974084 - 0.974084i) q^{37} +(1.01043 - 1.75011i) q^{38} +(1.41122 - 0.814767i) q^{40} +(-0.710011 + 0.190247i) q^{41} +(10.1261 - 5.84633i) q^{43} +(5.80275 + 1.55484i) q^{44} +(9.84223 + 9.84223i) q^{46} +(3.62699 + 0.971849i) q^{47} +(-6.80400 - 1.64488i) q^{49} +(2.35037 - 0.629781i) q^{50} +(3.26933 - 7.99876i) q^{52} +(1.15862 - 2.00679i) q^{53} +(-4.25365 - 2.45585i) q^{55} +(1.72898 - 1.36080i) q^{56} +(-5.66294 - 21.1344i) q^{58} +(3.35900 - 3.35900i) q^{59} +(-8.18748 - 4.72704i) q^{61} +(-3.17000 + 5.49061i) q^{62} -10.7959i q^{64} +(-4.27455 + 5.62513i) q^{65} +(-6.06032 - 1.62386i) q^{67} +17.5453i q^{68} +(-9.99105 + 4.28314i) q^{70} +(-8.32895 - 2.23174i) q^{71} +(2.01139 + 7.50661i) q^{73} -2.88849 q^{74} +(-0.597819 - 2.23109i) q^{76} +(-6.15788 - 2.46239i) q^{77} +(-2.31642 - 4.01217i) q^{79} +(-1.54654 + 5.77176i) q^{80} +(-0.770638 + 1.33478i) q^{82} +(10.1090 + 10.1090i) q^{83} +(3.71277 - 13.8563i) q^{85} +(6.34554 - 23.6819i) q^{86} +(1.80529 - 1.04229i) q^{88} +(2.89859 - 2.89859i) q^{89} +(-4.62866 + 8.34119i) q^{91} +15.9091 q^{92} +(6.81855 - 3.93669i) q^{94} +1.88849i q^{95} +(-2.63968 + 9.85141i) q^{97} +(-12.5269 + 7.64926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 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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