LMFDB - Embedded newform 567.2.w.a.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(37,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 6]))

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

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

chi := DirichletCharacter("567.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.w (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	567.37
Dual form			567.2.w.a.46.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.337831 - 1.91594i) q^{2} +(-1.67729 + 0.610485i) q^{4} +(-0.582582 + 3.30399i) q^{5} +(0.666452 - 2.56044i) q^{7} +(-0.209199 - 0.362343i) q^{8} +O(q^{10})$	\(q+(-0.337831 - 1.91594i) q^{2} +(-1.67729 + 0.610485i) q^{4} +(-0.582582 + 3.30399i) q^{5} +(0.666452 - 2.56044i) q^{7} +(-0.209199 - 0.362343i) q^{8} +6.52704 q^{10} +(0.778751 + 4.41652i) q^{11} +(2.58000 + 2.16488i) q^{13} +(-5.13078 - 0.411883i) q^{14} +(-3.35824 + 2.81790i) q^{16} +3.96521 q^{17} +4.97740 q^{19} +(-1.03987 - 5.89742i) q^{20} +(8.19868 - 2.98408i) q^{22} +(-1.70156 - 1.42778i) q^{23} +(-5.87847 - 2.13959i) q^{25} +(3.27617 - 5.67449i) q^{26} +(0.445273 + 4.70147i) q^{28} +(3.26643 - 2.74086i) q^{29} +(2.19236 - 0.797953i) q^{31} +(5.89240 + 4.94431i) q^{32} +(-1.33957 - 7.59708i) q^{34} +(8.07139 + 3.69362i) q^{35} +(1.49965 + 2.59748i) q^{37} +(-1.68152 - 9.53637i) q^{38} +(1.31905 - 0.480096i) q^{40} +(-0.219856 - 0.184481i) q^{41} +(9.46658 + 3.44555i) q^{43} +(-4.00242 - 6.93239i) q^{44} +(-2.16069 + 3.74243i) q^{46} +(5.08474 + 1.85069i) q^{47} +(-6.11168 - 3.41282i) q^{49} +(-2.11338 + 11.9856i) q^{50} +(-5.64906 - 2.05609i) q^{52} +(-5.11933 - 8.86693i) q^{53} -15.0458 q^{55} +(-1.06718 + 0.294156i) q^{56} +(-6.35481 - 5.33232i) q^{58} +(-2.56062 - 2.14861i) q^{59} +(-9.73706 - 3.54400i) q^{61} +(-2.26947 - 3.93084i) q^{62} +(3.09848 - 5.36673i) q^{64} +(-8.65580 + 7.26308i) q^{65} +(-2.20525 + 12.5066i) q^{67} +(-6.65082 + 2.42070i) q^{68} +(4.34996 - 16.7121i) q^{70} +(-2.77738 + 4.81056i) q^{71} +(-2.30040 + 3.98440i) q^{73} +(4.46997 - 3.75075i) q^{74} +(-8.34856 + 3.03863i) q^{76} +(11.8272 + 0.949453i) q^{77} +(0.215339 + 1.22125i) q^{79} +(-7.35385 - 12.7372i) q^{80} +(-0.279180 + 0.483554i) q^{82} +(8.72055 - 7.31741i) q^{83} +(-2.31006 + 13.1010i) q^{85} +(3.40335 - 19.3014i) q^{86} +(1.43738 - 1.20611i) q^{88} -12.2622 q^{89} +(7.26249 - 5.16315i) q^{91} +(3.72566 + 1.35603i) q^{92} +(1.82803 - 10.3673i) q^{94} +(-2.89974 + 16.4453i) q^{95} +(10.3763 + 3.77665i) q^{97} +(-4.47402 + 12.8625i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−0.337831	−	1.91594i	−0.238883	−	1.35477i	−0.834281	−	0.551340i	$-0.814117\pi$
$2$	−0.337831	−	1.91594i	−0.238883	−	1.35477i	0.595398	−	0.803431i	$-0.296994\pi$
$3$		0			0
$3$		0			0
$4$	−1.67729	+	0.610485i	−0.838647	+	0.305243i
$5$	−0.582582	+	3.30399i	−0.260539	+	1.47759i	0.520906	+	0.853614i	$0.325594\pi$
$5$	−0.582582	+	3.30399i	−0.260539	+	1.47759i	−0.781445	+	0.623974i	$0.785517\pi$
$6$		0			0
$7$	0.666452	−	2.56044i	0.251895	−	0.967755i
$7$	0.666452	−	2.56044i	0.251895	−	0.967755i
$8$	−0.209199	−	0.362343i	−0.0739629	−	0.128108i
$9$		0			0
$10$	6.52704			2.06403
$11$	0.778751	+	4.41652i	0.234802	+	1.33163i	0.843029	+	0.537867i	$0.180770\pi$
$11$	0.778751	+	4.41652i	0.234802	+	1.33163i	−0.608227	+	0.793763i	$0.708119\pi$
$12$		0			0
$13$	2.58000	+	2.16488i	0.715564	+	0.600430i	0.926154	−	0.377145i	$-0.123094\pi$
$13$	2.58000	+	2.16488i	0.715564	+	0.600430i	−0.210590	+	0.977574i	$0.567538\pi$
$14$	−5.13078	−	0.411883i	−1.37126	−	0.110080i
$15$		0			0
$16$	−3.35824	+	2.81790i	−0.839560	+	0.704474i
$17$	3.96521			0.961704			0.480852	−	0.876802i	$-0.340327\pi$
$17$	3.96521			0.961704			0.480852	+	0.876802i	$0.340327\pi$
$18$		0			0
$19$	4.97740			1.14189			0.570946	−	0.820987i	$-0.306576\pi$
$19$	4.97740			1.14189			0.570946	+	0.820987i	$0.306576\pi$
$20$	−1.03987	−	5.89742i	−0.232523	−	1.31870i
$21$		0			0
$22$	8.19868	−	2.98408i	1.74796	−	0.636207i
$23$	−1.70156	−	1.42778i	−0.354800	−	0.297713i	0.447914	−	0.894077i	$-0.352167\pi$
$23$	−1.70156	−	1.42778i	−0.354800	−	0.297713i	−0.802714	+	0.596364i	$0.796611\pi$
$24$		0			0
$25$	−5.87847	−	2.13959i	−1.17569	−	0.427918i
$26$	3.27617	−	5.67449i	0.642509	−	1.11286i
$27$		0			0
$28$	0.445273	+	4.70147i	0.0841488	+	0.888494i
$29$	3.26643	−	2.74086i	0.606561	−	0.508965i	−0.286986	−	0.957935i	$-0.592653\pi$
$29$	3.26643	−	2.74086i	0.606561	−	0.508965i	0.893547	+	0.448970i	$0.148209\pi$
$30$		0			0
$31$	2.19236	−	0.797953i	0.393759	−	0.143317i	−0.137550	−	0.990495i	$-0.543923\pi$
$31$	2.19236	−	0.797953i	0.393759	−	0.143317i	0.531309	+	0.847178i	$0.321700\pi$
$32$	5.89240	+	4.94431i	1.04164	+	0.874040i
$33$		0			0
$34$	−1.33957	−	7.59708i	−0.229734	−	1.30289i
$35$	8.07139	+	3.69362i	1.36431	+	0.624335i
$36$		0			0
$37$	1.49965	+	2.59748i	0.246541	+	0.427022i	0.962564	−	0.271055i	$-0.0873725\pi$
$37$	1.49965	+	2.59748i	0.246541	+	0.427022i	−0.716022	+	0.698077i	$0.754039\pi$
$38$	−1.68152	−	9.53637i	−0.272778	−	1.54700i
$39$		0			0
$40$	1.31905	−	0.480096i	0.208560	−	0.0759098i
$41$	−0.219856	−	0.184481i	−0.0343358	−	0.0288112i	0.625458	−	0.780258i	$-0.284912\pi$
$41$	−0.219856	−	0.184481i	−0.0343358	−	0.0288112i	−0.659794	+	0.751446i	$0.729356\pi$
$42$		0			0
$43$	9.46658	+	3.44555i	1.44364	+	0.525442i	0.940807	−	0.338942i	$-0.110069\pi$
$43$	9.46658	+	3.44555i	1.44364	+	0.525442i	0.502833	+	0.864384i	$0.332291\pi$
$44$	−4.00242	−	6.93239i	−0.603387	−	1.04510i
$45$		0			0
$46$	−2.16069	+	3.74243i	−0.318577	+	0.551791i
$47$	5.08474	+	1.85069i	0.741686	+	0.269952i	0.685103	−	0.728446i	$-0.259757\pi$
$47$	5.08474	+	1.85069i	0.741686	+	0.269952i	0.0565829	+	0.998398i	$0.481979\pi$
$48$		0			0
$49$	−6.11168	−	3.41282i	−0.873098	−	0.487545i
$50$	−2.11338	+	11.9856i	−0.298878	+	1.69502i
$51$		0			0
$52$	−5.64906	−	2.05609i	−0.783383	−	0.285128i
$53$	−5.11933	−	8.86693i	−0.703194	−	1.21797i	−0.967340	−	0.253484i	$-0.918423\pi$
$53$	−5.11933	−	8.86693i	−0.703194	−	1.21797i	0.264146	−	0.964483i	$-0.414910\pi$
$54$		0			0
$55$	−15.0458			−2.02878
$56$	−1.06718	+	0.294156i	−0.142608	+	0.0393083i
$57$		0			0
$58$	−6.35481	−	5.33232i	−0.834428	−	0.700168i
$59$	−2.56062	−	2.14861i	−0.333364	−	0.279726i	0.460705	−	0.887553i	$-0.347597\pi$
$59$	−2.56062	−	2.14861i	−0.333364	−	0.279726i	−0.794069	+	0.607828i	$0.792041\pi$
$60$		0			0
$61$	−9.73706	−	3.54400i	−1.24670	−	0.453763i	−0.367417	−	0.930057i	$-0.619758\pi$
$61$	−9.73706	−	3.54400i	−1.24670	−	0.453763i	−0.879286	+	0.476294i	$0.841980\pi$
$62$	−2.26947	−	3.93084i	−0.288223	−	0.499218i
$63$		0			0
$64$	3.09848	−	5.36673i	0.387310	−	0.670841i
$65$	−8.65580	+	7.26308i	−1.07362	+	0.900875i
$66$		0			0
$67$	−2.20525	+	12.5066i	−0.269414	+	1.52792i	0.486749	+	0.873542i	$0.338183\pi$
$67$	−2.20525	+	12.5066i	−0.269414	+	1.52792i	−0.756163	+	0.654383i	$0.772928\pi$
$68$	−6.65082	+	2.42070i	−0.806531	+	0.293553i
$69$		0			0
$70$	4.34996	−	16.7121i	0.519920	−	1.99748i
$71$	−2.77738	+	4.81056i	−0.329614	+	0.570908i	−0.982435	−	0.186604i	$-0.940252\pi$
$71$	−2.77738	+	4.81056i	−0.329614	+	0.570908i	0.652821	+	0.757512i	$0.273585\pi$
$72$		0			0
$73$	−2.30040	+	3.98440i	−0.269241	+	0.466339i	−0.968666	−	0.248367i	$-0.920106\pi$
$73$	−2.30040	+	3.98440i	−0.269241	+	0.466339i	0.699425	+	0.714706i	$0.253440\pi$
$74$	4.46997	−	3.75075i	0.519623	−	0.436016i
$75$		0			0
$76$	−8.34856	+	3.03863i	−0.957646	+	0.348554i
$77$	11.8272	+	0.949453i	1.34784	+	0.108200i
$78$		0			0
$79$	0.215339	+	1.22125i	0.0242276	+	0.137401i	0.994522	−	0.104524i	$-0.0333320\pi$
$79$	0.215339	+	1.22125i	0.0242276	+	0.137401i	−0.970295	+	0.241926i	$0.922221\pi$
$80$	−7.35385	−	12.7372i	−0.822185	−	1.42407i
$81$		0			0
$82$	−0.279180	+	0.483554i	−0.0308303	+	0.0533996i
$83$	8.72055	−	7.31741i	0.957205	−	0.803190i	−0.0232914	−	0.999729i	$-0.507415\pi$
$83$	8.72055	−	7.31741i	0.957205	−	0.803190i	0.980496	+	0.196539i	$0.0629701\pi$
$84$		0			0
$85$	−2.31006	+	13.1010i	−0.250561	+	1.42100i
$86$	3.40335	−	19.3014i	0.366993	−	2.08132i
$87$		0			0
$88$	1.43738	−	1.20611i	0.153225	−	0.128571i
$89$	−12.2622			−1.29979			−0.649896	−	0.760023i	$-0.725188\pi$
$89$	−12.2622			−1.29979			−0.649896	+	0.760023i	$0.725188\pi$
$90$		0			0
$91$	7.26249	−	5.16315i	0.761316	−	0.541245i
$92$	3.72566	+	1.35603i	0.388427	+	0.141376i
$93$		0			0
$94$	1.82803	−	10.3673i	0.188547	−	1.06930i
$95$	−2.89974	+	16.4453i	−0.297507	+	1.68725i
$96$		0			0
$97$	10.3763	+	3.77665i	1.05355	+	0.383461i	0.810001	−	0.586428i	$-0.199466\pi$
$97$	10.3763	+	3.77665i	1.05355	+	0.383461i	0.243548	+	0.969889i	$0.421689\pi$
$98$	−4.47402	+	12.8625i	−0.451944	+	1.29931i
$99$		0			0
$100$	11.1661			1.11661
$101$	−0.654384	+	0.549094i	−0.0651137	+	0.0546369i	−0.674764	−	0.738034i	$-0.735754\pi$
$101$	−0.654384	+	0.549094i	−0.0651137	+	0.0546369i	0.609650	+	0.792671i	$0.291310\pi$
$102$		0			0
$103$	−0.125872	+	0.713854i	−0.0124025	+	0.0703381i	−0.990381	−	0.138368i	$-0.955814\pi$
$103$	−0.125872	+	0.713854i	−0.0124025	+	0.0703381i	0.977978	+	0.208706i	$0.0669253\pi$
$104$	0.244695	−	1.38774i	0.0239944	−	0.136079i
$105$		0			0
$106$	−15.2590	+	12.8038i	−1.48209	+	1.24362i
$107$	−6.26413	+	10.8498i	−0.605577	+	1.04889i	0.386384	+	0.922338i	$0.373724\pi$
$107$	−6.26413	+	10.8498i	−0.605577	+	1.04889i	−0.991960	+	0.126551i	$0.959609\pi$
$108$		0			0
$109$	2.45242	+	4.24772i	0.234899	+	0.406857i	0.959243	−	0.282581i	$-0.0911906\pi$
$109$	2.45242	+	4.24772i	0.234899	+	0.406857i	−0.724344	+	0.689439i	$0.757857\pi$
$110$	5.08295	+	28.8268i	0.484640	+	2.74853i
$111$		0			0
$112$	4.97694	+	10.4766i	0.470277	+	0.989941i
$113$	4.66204	−	1.69685i	0.438568	−	0.159626i	−0.113293	−	0.993562i	$-0.536140\pi$
$113$	4.66204	−	1.69685i	0.438568	−	0.159626i	0.551861	+	0.833936i	$0.313918\pi$
$114$		0			0
$115$	5.70867	−	4.79014i	0.532336	−	0.446683i
$116$	−3.80551	+	6.59134i	−0.353333	+	0.611990i
$117$		0			0
$118$	−3.25155	+	5.63185i	−0.299329	+	0.518454i
$119$	2.64262	−	10.1527i	0.242249	−	0.930694i
$120$		0			0
$121$	−8.56257	+	3.11652i	−0.778415	+	0.283320i
$122$	−3.50059	+	19.8529i	−0.316929	+	1.79739i
$123$		0			0
$124$	−3.19009	+	2.67681i	−0.286479	+	0.240384i
$125$	2.10648	−	3.64853i	0.188409	−	0.326334i
$126$		0			0
$127$	−0.898740	−	1.55666i	−0.0797503	−	0.138132i	0.823392	−	0.567473i	$-0.192079\pi$
$127$	−0.898740	−	1.55666i	−0.0797503	−	0.138132i	−0.903142	+	0.429342i	$0.858746\pi$
$128$	3.12714	+	1.13818i	0.276402	+	0.100602i
$129$		0			0
$130$	16.8398	+	14.1303i	1.47695	+	1.23931i
$131$	6.83829	+	5.73801i	0.597464	+	0.501332i	0.890629	−	0.454730i	$-0.150264\pi$
$131$	6.83829	+	5.73801i	0.597464	+	0.501332i	−0.293165	+	0.956062i	$0.594709\pi$
$132$		0			0
$133$	3.31719	−	12.7443i	0.287637	−	1.10507i
$134$	24.7069			2.13435
$135$		0			0
$136$	−0.829517	−	1.43676i	−0.0711305	−	0.123202i
$137$	−17.6751	−	6.43321i	−1.51009	−	0.549627i	−0.551437	−	0.834216i	$-0.685920\pi$
$137$	−17.6751	−	6.43321i	−1.51009	−	0.549627i	−0.958649	+	0.284590i	$0.908143\pi$
$138$		0			0
$139$	2.88707	−	16.3734i	0.244878	−	1.38877i	−0.575899	−	0.817521i	$-0.695348\pi$
$139$	2.88707	−	16.3734i	0.244878	−	1.38877i	0.820777	−	0.571249i	$-0.193541\pi$
$140$	−15.7930	−	1.26781i	−1.33475	−	0.107150i
$141$		0			0
$142$	10.1550	+	3.69612i	0.852189	+	0.310172i
$143$	−7.55205	+	13.0805i	−0.631535	+	1.09385i
$144$		0			0
$145$	7.15280	+	12.3890i	0.594008	+	1.02885i
$146$	8.41101	+	3.06136i	0.696100	+	0.253360i
$147$		0			0
$148$	−4.10108	−	3.44122i	−0.337107	−	0.282866i
$149$	0.861789	−	0.313665i	0.0706005	−	0.0256965i	−0.306478	−	0.951878i	$-0.599151\pi$
$149$	0.861789	−	0.313665i	0.0706005	−	0.0256965i	0.377079	+	0.926181i	$0.376929\pi$
$150$		0			0
$151$	−1.77206	−	10.0499i	−0.144208	−	0.817847i	−0.967999	−	0.250953i	$-0.919256\pi$
$151$	−1.77206	−	10.0499i	−0.144208	−	0.817847i	0.823791	−	0.566894i	$-0.191855\pi$
$152$	−1.04127	−	1.80352i	−0.0844578	−	0.146285i
$153$		0			0
$154$	−2.17651	−	22.9810i	−0.175388	−	1.85186i
$155$	1.35920	+	7.70840i	0.109173	+	0.619153i
$156$		0			0
$157$	−3.20692	−	2.69093i	−0.255940	−	0.214759i	0.505785	−	0.862660i	$-0.331203\pi$
$157$	−3.20692	−	2.69093i	−0.255940	−	0.214759i	−0.761725	+	0.647900i	$0.775647\pi$
$158$	2.26709	−	0.825153i	0.180360	−	0.0656456i
$159$		0			0
$160$	−19.7688	+	16.5880i	−1.56286	+	1.31139i
$161$	−4.78975	+	3.40520i	−0.377485	+	0.268367i
$162$		0			0
$163$	5.01262	−	8.68211i	0.392619	−	0.680036i	−0.600175	−	0.799868i	$-0.704903\pi$
$163$	5.01262	−	8.68211i	0.392619	−	0.680036i	0.992794	+	0.119833i	$0.0382359\pi$
$164$	0.481387	+	0.175211i	0.0375900	+	0.0136816i
$165$		0			0
$166$	−16.9658	−	14.2360i	−1.31680	−	1.10493i
$167$	14.3390	−	5.21896i	1.10958	−	0.403855i	0.278743	−	0.960366i	$-0.410082\pi$
$167$	14.3390	−	5.21896i	1.10958	−	0.403855i	0.830841	+	0.556510i	$0.187860\pi$
$168$		0			0
$169$	−0.287712	−	1.63170i	−0.0221317	−	0.125515i
$170$	25.8811			1.98499
$171$		0			0
$172$	−17.9817			−1.37109
$173$	7.20431	−	6.04513i	0.547733	−	0.459603i	−0.326439	−	0.945218i	$-0.605849\pi$
$173$	7.20431	−	6.04513i	0.547733	−	0.459603i	0.874173	+	0.485615i	$0.161404\pi$
$174$		0			0
$175$	−9.39600	+	13.6255i	−0.710271	+	1.02999i
$176$	−15.0605	−	12.6373i	−1.13523	−	0.952571i
$177$		0			0
$178$	4.14256	+	23.4936i	0.310498	+	1.76092i
$179$	−2.87366			−0.214787			−0.107394	−	0.994217i	$-0.534250\pi$
$179$	−2.87366			−0.214787			−0.107394	+	0.994217i	$0.534250\pi$
$180$		0			0
$181$	−2.27490	−	3.94025i	−0.169092	−	0.292876i	0.769009	−	0.639238i	$-0.220750\pi$
$181$	−2.27490	−	3.94025i	−0.169092	−	0.292876i	−0.938101	+	0.346362i	$0.887417\pi$
$182$	−12.3458	−	12.1702i	−0.915129	−	0.902115i
$183$		0			0
$184$	−0.161381	+	0.915238i	−0.0118972	+	0.0674723i
$185$	−9.45570	+	3.44159i	−0.695197	+	0.253031i
$186$		0			0
$187$	3.08791	+	17.5124i	0.225810	+	1.28063i
$188$	−9.65843			−0.704414
$189$		0			0
$190$	32.4877			2.35690
$191$	3.07816	+	17.4571i	0.222728	+	1.26315i	0.866982	+	0.498340i	$0.166057\pi$
$191$	3.07816	+	17.4571i	0.222728	+	1.26315i	−0.644254	+	0.764812i	$0.722832\pi$
$192$		0			0
$193$	−18.5038	+	6.73485i	−1.33194	+	0.484785i	−0.907264	−	0.420563i	$-0.861833\pi$
$193$	−18.5038	+	6.73485i	−1.33194	+	0.484785i	−0.424672	+	0.905347i	$0.639611\pi$
$194$	3.73040	−	21.1561i	0.267827	−	1.51892i
$195$		0			0
$196$	12.3346	+	1.99321i	0.881041	+	0.142372i
$197$	−9.63644	−	16.6908i	−0.686568	−	1.18917i	−0.972941	−	0.231052i	$-0.925783\pi$
$197$	−9.63644	−	16.6908i	−0.686568	−	1.18917i	0.286373	−	0.958118i	$-0.407550\pi$
$198$		0			0
$199$	−11.5653			−0.819841			−0.409921	−	0.912121i	$-0.634444\pi$
$199$	−11.5653			−0.819841			−0.409921	+	0.912121i	$0.634444\pi$
$200$	0.454504	+	2.57762i	0.0321383	+	0.182265i
$201$		0			0
$202$	1.27310	+	1.06826i	0.0895750	+	0.0751623i
$203$	−4.84088	−	10.1901i	−0.339763	−	0.715207i
$204$		0			0
$205$	0.737609	−	0.618927i	0.0515168	−	0.0432277i
$206$	1.41022			0.0982548
$207$		0			0
$208$	−14.7647			−1.02375
$209$	3.87615	+	21.9828i	0.268119	+	1.52058i
$210$		0			0
$211$	−20.8302	+	7.58159i	−1.43401	+	0.521938i	−0.938079	−	0.346422i	$-0.887397\pi$
$211$	−20.8302	+	7.58159i	−1.43401	+	0.521938i	−0.495934	+	0.868360i	$0.665174\pi$
$212$	13.9998	+	11.7472i	0.961507	+	0.806800i
$213$		0			0
$214$	22.9037	+	8.33628i	1.56567	+	0.569856i
$215$	−16.8991	+	29.2701i	−1.15251	+	1.99621i
$216$		0			0
$217$	−0.582008	−	6.14519i	−0.0395093	−	0.417163i
$218$	7.30985	−	6.13369i	0.495085	−	0.415426i
$219$		0			0
$220$	25.2363	−	9.18525i	1.70143	−	0.619269i
$221$	10.2303	+	8.58420i	0.688161	+	0.577436i
$222$		0			0
$223$	−3.09264	−	17.5392i	−0.207098	−	1.17451i	−0.894104	−	0.447860i	$-0.852186\pi$
$223$	−3.09264	−	17.5392i	−0.207098	−	1.17451i	0.687005	−	0.726652i	$-0.258925\pi$
$224$	16.5866	−	11.7920i	1.10824	−	0.787885i
$225$		0			0
$226$	−4.82603	−	8.35893i	−0.321023	−	0.556028i
$227$	−0.557083	−	3.15938i	−0.0369749	−	0.209695i	0.960723	−	0.277509i	$-0.0895088\pi$
$227$	−0.557083	−	3.15938i	−0.0369749	−	0.209695i	−0.997698	+	0.0678137i	$0.978398\pi$
$228$		0			0
$229$	3.80028	−	1.38319i	0.251129	−	0.0914036i	−0.213388	−	0.976967i	$-0.568450\pi$
$229$	3.80028	−	1.38319i	0.251129	−	0.0914036i	0.464518	+	0.885564i	$0.346228\pi$
$230$	−11.1062	−	9.31918i	−0.732319	−	0.614489i
$231$		0			0
$232$	−1.67646	−	0.610183i	−0.110065	−	0.0400605i
$233$	−7.67364	−	13.2911i	−0.502717	−	0.870732i	−0.999995	−	0.00314038i	$-0.999000\pi$
$233$	−7.67364	−	13.2911i	−0.502717	−	0.870732i	0.497278	−	0.867591i	$-0.334333\pi$
$234$		0			0
$235$	−9.07695	+	15.7217i	−0.592115	+	1.02557i
$236$	5.60661	+	2.04064i	0.364959	+	0.132834i
$237$		0			0
$238$	−20.3446	−	1.63320i	−1.31875	−	0.105865i
$239$	0.262379	−	1.48803i	0.0169719	−	0.0962524i	−0.975145	−	0.221567i	$-0.928883\pi$
$239$	0.262379	−	1.48803i	0.0169719	−	0.0962524i	0.992117	+	0.125315i	$0.0399940\pi$
$240$		0			0
$241$	−18.0343	−	6.56396i	−1.16169	−	0.422822i	−0.311991	−	0.950085i	$-0.600996\pi$
$241$	−18.0343	−	6.56396i	−1.16169	−	0.422822i	−0.849702	+	0.527263i	$0.823218\pi$
$242$	8.86376	+	15.3525i	0.569784	+	0.986894i
$243$		0			0
$244$	18.4955			1.18405
$245$	14.8365	−	18.2047i	0.947867	−	1.16305i
$246$		0			0
$247$	12.8417	+	10.7755i	0.817098	+	0.685627i
$248$	−0.747771	−	0.627455i	−0.0474835	−	0.0398434i
$249$		0			0
$250$	−7.70198	−	2.80329i	−0.487116	−	0.177296i
$251$	−4.44988	−	7.70741i	−0.280874	−	0.486488i	0.690726	−	0.723116i	$-0.257291\pi$
$251$	−4.44988	−	7.70741i	−0.280874	−	0.486488i	−0.971600	+	0.236629i	$0.923958\pi$
$252$		0			0
$253$	4.98072	−	8.62686i	0.313135	−	0.542366i
$254$	−2.67884	+	2.24782i	−0.168086	+	0.141041i
$255$		0			0
$256$	3.27643	−	18.5815i	0.204777	−	1.16135i
$257$	9.22466	−	3.35750i	0.575418	−	0.209435i	−0.0378856	−	0.999282i	$-0.512062\pi$
$257$	9.22466	−	3.35750i	0.575418	−	0.209435i	0.613304	+	0.789847i	$0.289840\pi$
$258$		0			0
$259$	7.65012	−	2.10868i	0.475355	−	0.131027i
$260$	10.0843	−	17.4666i	0.625404	−	1.08323i
$261$		0			0
$262$	8.68346	−	15.0402i	0.536466	−	0.929187i
$263$	−5.70996	+	4.79123i	−0.352091	+	0.295440i	−0.801629	−	0.597822i	$-0.796033\pi$
$263$	−5.70996	+	4.79123i	−0.352091	+	0.295440i	0.449538	+	0.893261i	$0.351589\pi$
$264$		0			0
$265$	32.2787	−	11.7485i	1.98286	−	0.721703i
$266$	−25.5379	−	2.05011i	−1.56583	−	0.125700i
$267$		0			0
$268$	−3.93624	−	22.3235i	−0.240444	−	1.36363i
$269$	−8.61215	−	14.9167i	−0.525092	−	0.909486i	−0.999573	−	0.0292204i	$-0.990698\pi$
$269$	−8.61215	−	14.9167i	−0.525092	−	0.909486i	0.474481	−	0.880266i	$-0.342636\pi$
$270$		0			0
$271$	0.412552	−	0.714562i	0.0250608	−	0.0434065i	−0.853223	−	0.521546i	$-0.825355\pi$
$271$	0.412552	−	0.714562i	0.0250608	−	0.0434065i	0.878284	+	0.478140i	$0.158689\pi$
$272$	−13.3161	+	11.1735i	−0.807408	+	0.677496i
$273$		0			0
$274$	−6.35442	+	36.0377i	−0.383885	+	2.17712i
$275$	4.87167	−	27.6286i	0.293773	−	1.66607i
$276$		0			0
$277$	8.81649	−	7.39791i	0.529731	−	0.444497i	−0.338277	−	0.941046i	$-0.609844\pi$
$277$	8.81649	−	7.39791i	0.529731	−	0.444497i	0.868009	+	0.496549i	$0.165400\pi$
$278$	−32.3456			−1.93996
$279$		0			0
$280$	−0.350170	−	3.69731i	−0.0209267	−	0.220957i
$281$	22.9354	+	8.34780i	1.36821	+	0.497988i	0.918583	−	0.395228i	$-0.129334\pi$
$281$	22.9354	+	8.34780i	1.36821	+	0.497988i	0.449628	+	0.893216i	$0.351557\pi$
$282$		0			0
$283$	0.104052	−	0.590109i	0.00618526	−	0.0350784i	−0.981559	−	0.191160i	$-0.938775\pi$
$283$	0.104052	−	0.590109i	0.00618526	−	0.0350784i	0.987744	+	0.156081i	$0.0498862\pi$
$284$	1.72171	−	9.76428i	0.102164	−	0.579403i
$285$		0			0
$286$	27.6128	+	10.0502i	1.63278	+	0.594283i
$287$	−0.618877	+	0.439981i	−0.0365311	+	0.0259712i
$288$		0			0
$289$	−1.27713			−0.0751252
$290$	21.3201	−	17.8897i	1.25196	−	1.05052i
$291$		0			0
$292$	1.42602	−	8.08738i	0.0834517	−	0.473278i
$293$	−1.42904	+	8.10449i	−0.0834854	+	0.473469i	0.914188	+	0.405291i	$0.132830\pi$
$293$	−1.42904	+	8.10449i	−0.0834854	+	0.473469i	−0.997673	+	0.0681782i	$0.978281\pi$
$294$		0			0
$295$	8.59076	−	7.20851i	0.500174	−	0.419695i
$296$	0.627451	−	1.08678i	0.0364699	−	0.0631677i
$297$		0			0
$298$	−0.892102	−	1.54517i	−0.0516781	−	0.0895091i
$299$	−1.29906	−	7.36735i	−0.0751268	−	0.426065i
$300$		0			0
$301$	15.1311	−	21.9423i	0.872145	−	1.26473i
$302$	−18.6562	+	6.79032i	−1.07355	+	0.390739i
$303$		0			0
$304$	−16.7153	+	14.0258i	−0.958687	+	0.804434i
$305$	17.3820	−	30.1065i	0.995289	−	1.72389i
$306$		0			0
$307$	−11.6784	+	20.2276i	−0.666521	+	1.15445i	0.312349	+	0.949967i	$0.398884\pi$
$307$	−11.6784	+	20.2276i	−0.666521	+	1.15445i	−0.978870	+	0.204482i	$0.934449\pi$
$308$	−20.4174	+	5.62783i	−1.16339	+	0.320676i
$309$		0			0
$310$	14.3096	−	5.20827i	0.812732	−	0.295810i
$311$	4.32728	−	24.5412i	0.245378	−	1.39161i	−0.574236	−	0.818690i	$-0.694701\pi$
$311$	4.32728	−	24.5412i	0.245378	−	1.39161i	0.819614	−	0.572917i	$-0.194188\pi$
$312$		0			0
$313$	−18.0599	+	15.1540i	−1.02080	+	0.856557i	−0.989728	−	0.142960i	$-0.954338\pi$
$313$	−18.0599	+	15.1540i	−1.02080	+	0.856557i	−0.0310764	+	0.999517i	$0.509894\pi$
$314$	−4.07224	+	7.05333i	−0.229810	+	0.398042i
$315$		0			0
$316$	−1.10674	−	1.91694i	−0.0622592	−	0.107836i
$317$	−14.2494	−	5.18635i	−0.800326	−	0.291295i	−0.0907041	−	0.995878i	$-0.528912\pi$
$317$	−14.2494	−	5.18635i	−0.800326	−	0.291295i	−0.709621	+	0.704583i	$0.751134\pi$
$318$		0			0
$319$	14.6488	+	12.2918i	0.820175	+	0.688208i
$320$	15.9265	+	13.3639i	0.890318	+	0.747065i
$321$		0			0
$322$	8.14226	+	8.02647i	0.453751	+	0.447298i
$323$	19.7364			1.09816
$324$		0			0
$325$	−10.5345	−	18.2463i	−0.584351	−	1.01212i
$326$	−18.3278	−	6.67077i	−1.01508	−	0.369460i
$327$		0			0
$328$	−0.0208518	+	0.118257i	−0.00115135	+	0.00652963i
$329$	8.12732	−	11.7858i	0.448074	−	0.649770i
$330$		0			0
$331$	15.3332	+	5.58083i	0.842789	+	0.306750i	0.727097	−	0.686535i	$-0.240869\pi$
$331$	15.3332	+	5.58083i	0.842789	+	0.306750i	0.115692	+	0.993285i	$0.463091\pi$
$332$	−10.1598	+	17.5972i	−0.557589	+	0.965773i
$333$		0			0
$334$	−14.8434	−	25.7094i	−0.812192	−	1.40676i
$335$	−40.0369	−	14.5723i	−2.18745	−	0.796167i
$336$		0			0
$337$	0.0798940	+	0.0670390i	0.00435210	+	0.00365185i	0.644961	−	0.764215i	$-0.276874\pi$
$337$	0.0798940	+	0.0670390i	0.00435210	+	0.00365185i	−0.640609	+	0.767867i	$0.721318\pi$
$338$	−3.02903	+	1.10248i	−0.164758	+	0.0599669i
$339$		0			0
$340$	−4.12332	−	23.3845i	−0.223618	−	1.26820i
$341$	5.23148	+	9.06118i	0.283300	+	0.490691i
$342$		0			0
$343$	−12.8115	+	13.3741i	−0.691753	+	0.722134i
$344$	−0.731925	−	4.15095i	−0.0394628	−	0.223804i
$345$		0			0
$346$	−14.0159	−	11.7608i	−0.753501	−	0.632262i
$347$	23.4434	−	8.53269i	1.25851	−	0.458059i	0.375239	−	0.926928i	$-0.377561\pi$
$347$	23.4434	−	8.53269i	1.25851	−	0.458059i	0.883268	+	0.468869i	$0.155339\pi$
$348$		0			0
$349$	22.2592	−	18.6777i	1.19151	−	0.999793i	0.191675	−	0.981458i	$-0.438608\pi$
$349$	22.2592	−	18.6777i	1.19151	−	0.999793i	0.999832	−	0.0183346i	$-0.00583640\pi$
$350$	29.2799	+	13.3990i	1.56508	+	0.716207i
$351$		0			0
$352$	−17.2479	+	29.8743i	−0.919318	+	1.59231i
$353$	−4.12531	−	1.50149i	−0.219568	−	0.0799162i	0.229894	−	0.973216i	$-0.426162\pi$
$353$	−4.12531	−	1.50149i	−0.219568	−	0.0799162i	−0.449462	+	0.893299i	$0.648384\pi$
$354$		0			0
$355$	−14.2760	−	11.9790i	−0.757690	−	0.635778i
$356$	20.5673	−	7.48590i	1.09007	−	0.396752i
$357$		0			0
$358$	0.970810	+	5.50574i	0.0513089	+	0.290987i
$359$	−6.73487			−0.355453			−0.177727	−	0.984080i	$-0.556874\pi$
$359$	−6.73487			−0.355453			−0.177727	+	0.984080i	$0.556874\pi$
$360$		0			0
$361$	5.77447			0.303919
$362$	−6.78073	+	5.68971i	−0.356387	+	0.299044i
$363$		0			0
$364$	−9.02931	+	13.0938i	−0.473264	+	0.686300i
$365$	−11.8243	−	9.92173i	−0.618910	−	0.519327i
$366$		0			0
$367$	1.44020	+	8.16779i	0.0751779	+	0.426355i	0.999047	+	0.0436465i	$0.0138975\pi$
$367$	1.44020	+	8.16779i	0.0751779	+	0.426355i	−0.923869	+	0.382709i	$0.874991\pi$
$368$	9.73758			0.507607
$369$		0			0
$370$	9.78830	+	16.9538i	0.508870	+	0.881388i
$371$	−26.1150	+	7.19833i	−1.35582	+	0.373719i
$372$		0			0
$373$	2.03256	−	11.5272i	0.105242	−	0.596858i	−0.885881	−	0.463912i	$-0.846445\pi$
$373$	2.03256	−	11.5272i	0.105242	−	0.596858i	0.991123	−	0.132946i	$-0.0424436\pi$
$374$	32.5095	−	11.8325i	1.68102	−	0.611843i
$375$		0			0
$376$	−0.393136	−	2.22958i	−0.0202744	−	0.114982i
$377$	14.3610			0.739631
$378$		0			0
$379$	−26.9202			−1.38280			−0.691398	−	0.722474i	$-0.743005\pi$
$379$	−26.9202			−1.38280			−0.691398	+	0.722474i	$0.743005\pi$
$380$	−5.17587	−	29.3538i	−0.265516	−	1.50582i
$381$		0			0
$382$	32.4068	−	11.7951i	1.65808	−	0.603490i
$383$	−2.90547	+	16.4777i	−0.148463	+	0.841973i	0.816059	+	0.577969i	$0.196154\pi$
$383$	−2.90547	+	16.4777i	−0.148463	+	0.841973i	−0.964522	+	0.264004i	$0.914957\pi$
$384$		0			0
$385$	−10.0273	+	38.5239i	−0.511039	+	1.96336i
$386$	19.1547	+	33.1769i	0.974949	+	1.68866i
$387$		0			0
$388$	−19.7096			−1.00061
$389$	−0.278066	−	1.57699i	−0.0140985	−	0.0799567i	0.976947	−	0.213483i	$-0.0684809\pi$
$389$	−0.278066	−	1.57699i	−0.0140985	−	0.0799567i	−0.991045	+	0.133527i	$0.957370\pi$
$390$		0			0
$391$	−6.74704	−	5.66144i	−0.341213	−	0.286311i
$392$	0.0419465	+	2.92848i	0.00211862	+	0.147911i
$393$		0			0
$394$	−28.7230	+	24.1015i	−1.44704	+	1.21421i
$395$	−4.16045			−0.209335
$396$		0			0
$397$	11.8414			0.594301			0.297150	−	0.954831i	$-0.403964\pi$
$397$	11.8414			0.594301			0.297150	+	0.954831i	$0.403964\pi$
$398$	3.90711	+	22.1583i	0.195846	+	1.11070i
$399$		0			0
$400$	25.7705	−	9.37968i	1.28852	−	0.468984i
$401$	−0.120005	−	0.100696i	−0.00599275	−	0.00502852i	0.639786	−	0.768553i	$-0.279023\pi$
$401$	−0.120005	−	0.100696i	−0.00599275	−	0.00502852i	−0.645779	+	0.763524i	$0.723467\pi$
$402$		0			0
$403$	7.38377	+	2.68747i	0.367812	+	0.133872i
$404$	0.762382	−	1.32048i	0.0379299	−	0.0656965i
$405$		0			0
$406$	−17.8882	+	12.7174i	−0.887779	+	0.631152i
$407$	−10.3039	+	8.64603i	−0.510748	+	0.428568i
$408$		0			0
$409$	25.2545	−	9.19188i	1.24875	−	0.454509i	0.368774	−	0.929519i	$-0.379778\pi$
$409$	25.2545	−	9.19188i	1.24875	−	0.454509i	0.879981	+	0.475010i	$0.157555\pi$
$410$	−1.43501	−	1.20412i	−0.0708702	−	0.0594672i
$411$		0			0
$412$	−0.224673	−	1.27419i	−0.0110689	−	0.0627747i
$413$	−7.20792	+	5.12435i	−0.354678	+	0.252153i
$414$		0			0
$415$	19.0962	+	33.0756i	0.937396	+	1.62362i
$416$	4.49858	+	25.5127i	0.220561	+	1.25086i
$417$		0			0
$418$	40.8081	−	14.8529i	1.99599	−	0.726480i
$419$	18.4551	+	15.4857i	0.901593	+	0.756526i	0.970501	−	0.241097i	$-0.0775072\pi$
$419$	18.4551	+	15.4857i	0.901593	+	0.756526i	−0.0689084	+	0.997623i	$0.521952\pi$
$420$		0			0
$421$	−3.47375	−	1.26434i	−0.169300	−	0.0616202i	0.255980	−	0.966682i	$-0.417602\pi$
$421$	−3.47375	−	1.26434i	−0.169300	−	0.0616202i	−0.425280	+	0.905062i	$0.639824\pi$
$422$	21.5629	+	37.3481i	1.04967	+	1.81808i
$423$		0			0
$424$	−2.14191	+	3.70990i	−0.104021	+	0.180169i
$425$	−23.3094	−	8.48392i	−1.13067	−	0.411530i
$426$		0			0
$427$	−15.5635	+	22.5692i	−0.753169	+	1.09220i
$428$	3.88316	−	22.0225i	0.187699	−	1.06450i
$429$		0			0
$430$	61.7888	+	22.4893i	2.97972	+	1.08453i
$431$	−1.18001	−	2.04383i	−0.0568390	−	0.0984480i	0.836206	−	0.548416i	$-0.184769\pi$
$431$	−1.18001	−	2.04383i	−0.0568390	−	0.0984480i	−0.893045	+	0.449968i	$0.851436\pi$
$432$		0			0
$433$	15.5635			0.747935			0.373968	−	0.927442i	$-0.377997\pi$
$433$	15.5635			0.747935			0.373968	+	0.927442i	$0.377997\pi$
$434$	−11.5772	+	3.19113i	−0.555722	+	0.153179i
$435$		0			0
$436$	−6.70660	−	5.62751i	−0.321188	−	0.269509i
$437$	−8.46934	−	7.10662i	−0.405144	−	0.339956i
$438$		0			0
$439$	−37.0202	−	13.4742i	−1.76688	−	0.643090i	−0.999999	−	0.00129654i	$-0.999587\pi$
$439$	−37.0202	−	13.4742i	−1.76688	−	0.643090i	−0.766877	−	0.641794i	$-0.778190\pi$
$440$	3.14757	+	5.45174i	0.150054	+	0.259902i
$441$		0			0
$442$	12.9907	−	22.5005i	0.617904	−	1.07024i
$443$	2.38457	−	2.00089i	0.113295	−	0.0950654i	−0.584380	−	0.811480i	$-0.698662\pi$
$443$	2.38457	−	2.00089i	0.113295	−	0.0950654i	0.697675	+	0.716414i	$0.254218\pi$
$444$		0			0
$445$	7.14375	−	40.5142i	0.338646	−	1.92056i
$446$	−32.5592	+	11.8506i	−1.54172	+	0.561142i
$447$		0			0
$448$	−11.6762	−	11.5101i	−0.551648	−	0.543803i
$449$	7.45557	−	12.9134i	0.351850	−	0.609422i	−0.634724	−	0.772739i	$-0.718886\pi$
$449$	7.45557	−	12.9134i	0.351850	−	0.609422i	0.986574	+	0.163317i	$0.0522194\pi$
$450$		0			0
$451$	0.643552	−	1.11466i	0.0303037	−	0.0524875i
$452$	−6.78372	+	5.69222i	−0.319080	+	0.267740i
$453$		0			0
$454$	−5.86496	+	2.13467i	−0.275256	+	0.100185i
$455$	12.8280	+	27.0031i	0.601386	+	1.26593i
$456$		0			0
$457$	−4.80493	−	27.2501i	−0.224765	−	1.27471i	−0.863133	−	0.504976i	$-0.831501\pi$
$457$	−4.80493	−	27.2501i	−0.224765	−	1.27471i	0.638368	−	0.769731i	$-0.279610\pi$
$458$	−3.93395	−	6.81380i	−0.183821	−	0.318388i
$459$		0			0
$460$	−6.65081	+	11.5195i	−0.310095	+	0.537101i
$461$	26.9668	−	22.6278i	1.25597	−	1.05388i	0.259868	−	0.965644i	$-0.416321\pi$
$461$	26.9668	−	22.6278i	1.25597	−	1.05388i	0.996099	−	0.0882379i	$-0.0281236\pi$
$462$		0			0
$463$	−3.64646	+	20.6801i	−0.169465	+	0.961086i	0.774874	+	0.632115i	$0.217813\pi$
$463$	−3.64646	+	20.6801i	−0.169465	+	0.961086i	−0.944340	+	0.328971i	$0.893298\pi$
$464$	−3.24599	+	18.4089i	−0.150691	+	0.854612i
$465$		0			0
$466$	−22.8726	+	19.1924i	−1.05955	+	0.889070i
$467$	36.2367			1.67684			0.838418	−	0.545028i	$-0.183481\pi$
$467$	36.2367			1.67684			0.838418	+	0.545028i	$0.183481\pi$
$468$		0			0
$469$	30.5527	+	13.9815i	1.41079	+	0.645604i
$470$	33.1883	+	12.0796i	1.53086	+	0.557189i
$471$		0			0
$472$	−0.242857	+	1.37731i	−0.0111784	+	0.0633958i
$473$	−7.84524	+	44.4926i	−0.360724	+	2.04577i
$474$		0			0
$475$	−29.2595	−	10.6496i	−1.34252	−	0.488636i
$476$	1.76560	+	18.6423i	0.0809262	+	0.854468i
$477$		0			0
$478$	−2.93960			−0.134454
$479$	24.9795	−	20.9603i	1.14134	−	0.957701i	0.141861	−	0.989887i	$-0.454691\pi$
$479$	24.9795	−	20.9603i	1.14134	−	0.957701i	0.999482	+	0.0321859i	$0.0102469\pi$
$480$		0			0
$481$	−1.75411	+	9.94807i	−0.0799807	+	0.453593i
$482$	−6.48356	+	36.7701i	−0.295318	+	1.67483i
$483$		0			0
$484$	12.4594	−	10.4546i	0.566335	−	0.475211i
$485$	−18.5230	+	32.0828i	−0.841088	+	1.45681i
$486$		0			0
$487$	−15.5004	−	26.8476i	−0.702392	−	1.21658i	−0.967624	−	0.252394i	$-0.918782\pi$
$487$	−15.5004	−	26.8476i	−0.702392	−	1.21658i	0.265232	−	0.964185i	$-0.414551\pi$
$488$	0.752838	+	4.26956i	0.0340794	+	0.193274i
$489$		0			0
$490$	−39.8912	−	22.2756i	−1.80210	−	1.00631i
$491$	−39.1653	+	14.2550i	−1.76751	+	0.643320i	−0.767509	+	0.641038i	$0.778504\pi$
$491$	−39.1653	+	14.2550i	−1.76751	+	0.643320i	−0.999997	+	0.00228119i	$0.999274\pi$
$492$		0			0
$493$	12.9521	−	10.8681i	0.583332	−	0.489473i
$494$	16.3068	−	28.2442i	0.733677	−	1.27077i
$495$		0			0
$496$	−5.11391	+	8.85756i	−0.229621	+	0.397716i
$497$	10.4662	+	10.3173i	0.469471	+	0.462795i
$498$		0			0
$499$	−16.7437	+	6.09421i	−0.749552	+	0.272814i	−0.688417	−	0.725315i	$-0.741694\pi$
$499$	−16.7437	+	6.09421i	−0.749552	+	0.272814i	−0.0611345	+	0.998130i	$0.519472\pi$
$500$	−1.30581	+	7.40563i	−0.0583977	+	0.331190i
$501$		0			0
$502$	−13.2636	+	11.1295i	−0.591984	+	0.496733i
$503$	−13.0372	+	22.5811i	−0.581300	+	1.00684i	0.414025	+	0.910265i	$0.364122\pi$
$503$	−13.0372	+	22.5811i	−0.581300	+	1.00684i	−0.995326	+	0.0965762i	$0.969211\pi$
$504$		0			0
$505$	−1.43297	−	2.48197i	−0.0637662	−	0.110446i
$506$	−18.2112	−	6.62832i	−0.809585	−	0.294665i
$507$		0			0
$508$	2.45777	+	2.06232i	0.109046	+	0.0915005i
$509$	−4.02263	−	3.37539i	−0.178300	−	0.149611i	0.549270	−	0.835645i	$-0.314906\pi$
$509$	−4.02263	−	3.37539i	−0.178300	−	0.149611i	−0.727570	+	0.686034i	$0.759350\pi$
$510$		0			0
$511$	8.66871	+	8.54544i	0.383481	+	0.378028i
$512$	−30.0523			−1.32814
$513$		0			0
$514$	−9.54914	−	16.5396i	−0.421194	−	0.729530i
$515$	−2.28523	−	0.831757i	−0.100699	−	0.0366516i
$516$		0			0
$517$	−4.21388	+	23.8981i	−0.185326	+	1.05104i
$518$	−6.62454	−	13.9448i	−0.291065	−	0.612698i
$519$		0			0
$520$	4.44251	+	1.61694i	0.194817	+	0.0709076i
$521$	−13.7210	+	23.7655i	−0.601130	+	1.04119i	0.391520	+	0.920169i	$0.371949\pi$
$521$	−13.7210	+	23.7655i	−0.601130	+	1.04119i	−0.992650	+	0.121018i	$0.961384\pi$
$522$		0			0
$523$	7.93861	+	13.7501i	0.347131	+	0.601249i	0.985739	−	0.168284i	$-0.0538225\pi$
$523$	7.93861	+	13.7501i	0.347131	+	0.601249i	−0.638607	+	0.769533i	$0.720489\pi$
$524$	−14.9728	−	5.44965i	−0.654090	−	0.238069i
$525$		0			0
$526$	11.1087	+	9.32129i	0.484362	+	0.406428i
$527$	8.69316	−	3.16405i	0.378680	−	0.137828i
$528$		0			0
$529$	−3.13715	−	17.7917i	−0.136398	−	0.773551i
$530$	−33.4141	−	57.8749i	−1.45141	−	2.51392i
$531$		0			0
$532$	2.21630	+	23.4011i	0.0960889	+	1.01456i
$533$	−0.167850	−	0.951925i	−0.00727040	−	0.0412325i
$534$		0			0
$535$	−32.1982	−	27.0175i	−1.39205	−	1.16807i
$536$	4.99302	−	1.81731i	0.215665	−	0.0784958i
$537$		0			0
$538$	−25.6700	+	21.5396i	−1.10671	+	0.928640i
$539$	10.3133	−	29.6501i	0.444225	−	1.27712i
$540$		0			0
$541$	7.33572	−	12.7058i	0.315387	−	0.546267i	−0.664133	−	0.747615i	$-0.731199\pi$
$541$	7.33572	−	12.7058i	0.315387	−	0.546267i	0.979520	+	0.201348i	$0.0645323\pi$
$542$	−1.50843	−	0.549023i	−0.0647925	−	0.0235825i
$543$		0			0
$544$	23.3646	+	19.6052i	1.00175	+	0.840568i
$545$	−15.4631	+	5.62812i	−0.662368	+	0.241082i
$546$		0			0
$547$	−0.350819	−	1.98960i	−0.0150000	−	0.0850690i	0.976389	−	0.216021i	$-0.0693078\pi$
$547$	−0.350819	−	1.98960i	−0.0150000	−	0.0850690i	−0.991389	+	0.130952i	$0.958197\pi$
$548$	33.5738			1.43420
$549$		0			0
$550$	−54.5804			−2.32732
$551$	16.2583	−	13.6423i	0.692627	−	0.581183i
$552$		0			0
$553$	3.27045	+	0.262542i	0.139074	+	0.0111644i
$554$	−17.1524	−	14.3926i	−0.728736	−	0.611482i
$555$		0			0
$556$	5.15324	+	29.2255i	0.218546	+	1.23944i
$557$	12.8589			0.544848			0.272424	−	0.962177i	$-0.412175\pi$
$557$	12.8589			0.544848			0.272424	+	0.962177i	$0.412175\pi$
$558$		0			0
$559$	16.9646	+	29.3836i	0.717526	+	1.24279i
$560$	−37.5139	+	10.3403i	−1.58525	+	0.436958i
$561$		0			0
$562$	8.24556	−	46.7629i	0.347818	−	1.97257i
$563$	2.36642	−	0.861307i	0.0997327	−	0.0362998i	−0.291672	−	0.956518i	$-0.594212\pi$
$563$	2.36642	−	0.861307i	0.0997327	−	0.0362998i	0.391405	+	0.920219i	$0.371989\pi$
$564$		0			0
$565$	2.89033	+	16.3919i	0.121597	+	0.689612i
$566$	−1.16576			−0.0490007
$567$		0			0
$568$	2.32410			0.0975169
$569$	−6.15504	−	34.9070i	−0.258033	−	1.46338i	−0.788166	−	0.615463i	$-0.788969\pi$
$569$	−6.15504	−	34.9070i	−0.258033	−	1.46338i	0.530133	−	0.847914i	$-0.322142\pi$
$570$		0			0
$571$	1.23492	−	0.449474i	0.0516797	−	0.0188099i	−0.316051	−	0.948742i	$-0.602357\pi$
$571$	1.23492	−	0.449474i	0.0516797	−	0.0188099i	0.367731	+	0.929932i	$0.380135\pi$
$572$	4.68154	−	26.5503i	0.195745	−	1.11013i
$573$		0			0
$574$	1.05205	+	1.03709i	0.0439117	+	0.0432873i
$575$	6.94772	+	12.0338i	0.289740	+	0.501844i
$576$		0			0
$577$	−6.32197			−0.263187			−0.131594	−	0.991304i	$-0.542009\pi$
$577$	−6.32197			−0.263187			−0.131594	+	0.991304i	$0.542009\pi$
$578$	0.431454	+	2.44689i	0.0179461	+	0.101777i
$579$		0			0
$580$	−19.5607	−	16.4134i	−0.812213	−	0.681527i
$581$	−12.9239	−	27.2051i	−0.536176	−	1.12866i
$582$		0			0
$583$	35.1743	−	29.5147i	1.45677	−	1.22238i
$584$	1.92496			0.0796554
$585$		0			0
$586$	16.0104			0.661386
$587$	−1.97608	−	11.2069i	−0.0815614	−	0.462558i	−0.998046	−	0.0624873i	$-0.980097\pi$
$587$	−1.97608	−	11.2069i	−0.0815614	−	0.462558i	0.916484	−	0.400071i	$-0.131014\pi$
$588$		0			0
$589$	10.9122	−	3.97173i	0.449631	−	0.163652i
$590$	−16.7133	−	14.0241i	−0.688074	−	0.577363i
$591$		0			0
$592$	−12.3556	−	4.49707i	−0.507812	−	0.184829i
$593$	22.5967	−	39.1386i	0.927935	−	1.60723i	0.141162	−	0.989986i	$-0.454916\pi$
$593$	22.5967	−	39.1386i	0.927935	−	1.60723i	0.786772	−	0.617243i	$-0.211751\pi$
$594$		0			0
$595$	32.0048	+	14.6460i	1.31207	+	0.600425i
$596$	−1.25399	+	1.05222i	−0.0513653	+	0.0431006i
$597$		0			0
$598$	−13.6765	+	4.97784i	−0.559274	+	0.203559i
$599$	−11.4990	−	9.64879i	−0.469836	−	0.394239i	0.376899	−	0.926254i	$-0.376990\pi$
$599$	−11.4990	−	9.64879i	−0.469836	−	0.394239i	−0.846735	+	0.532016i	$0.821435\pi$
$600$		0			0
$601$	8.02293	+	45.5003i	0.327262	+	1.85600i	0.493276	+	0.869873i	$0.335799\pi$
$601$	8.02293	+	45.5003i	0.327262	+	1.85600i	−0.166014	+	0.986123i	$0.553090\pi$
$602$	−47.1518	−	21.5775i	−1.92176	−	0.879434i
$603$		0			0
$604$	9.10757	+	15.7748i	0.370582	+	0.641866i
$605$	−5.30855	−	30.1063i	−0.215823	−	1.22399i
$606$		0			0
$607$	34.1836	−	12.4418i	1.38747	−	0.504998i	0.463037	−	0.886339i	$-0.346760\pi$
$607$	34.1836	−	12.4418i	1.38747	−	0.504998i	0.924434	+	0.381341i	$0.124538\pi$
$608$	29.3288	+	24.6098i	1.18944	+	0.998060i
$609$		0			0
$610$	−63.5542	−	23.1318i	−2.57323	−	0.936581i
$611$	9.11212	+	15.7827i	0.368637	+	0.638498i
$612$		0			0
$613$	8.08643	−	14.0061i	0.326608	−	0.565701i	−0.655229	−	0.755431i	$-0.727428\pi$
$613$	8.08643	−	14.0061i	0.326608	−	0.565701i	0.981836	+	0.189729i	$0.0607611\pi$
$614$	42.7001	+	15.5416i	1.72323	+	0.627206i
$615$		0			0
$616$	−2.13021	−	4.48414i	−0.0858287	−	0.180671i
$617$	−8.46705	+	48.0190i	−0.340871	+	1.93317i	0.0181293	+	0.999836i	$0.494229\pi$
$617$	−8.46705	+	48.0190i	−0.340871	+	1.93317i	−0.359000	+	0.933338i	$0.616882\pi$
$618$		0			0
$619$	−7.95236	−	2.89442i	−0.319633	−	0.116337i	0.177221	−	0.984171i	$-0.443289\pi$
$619$	−7.95236	−	2.89442i	−0.319633	−	0.116337i	−0.496854	+	0.867834i	$0.665511\pi$
$620$	−6.98564	−	12.0995i	−0.280550	−	0.485927i
$621$		0			0
$622$	−48.4813			−1.94392
$623$	−8.17218	+	31.3966i	−0.327411	+	1.25788i
$624$		0			0
$625$	−13.1334	−	11.0202i	−0.525335	−	0.440809i
$626$	35.1354	+	29.4821i	1.40429	+	1.17834i
$627$		0			0
$628$	7.02172	+	2.55570i	0.280197	+	0.101983i
$629$	5.94644	+	10.2995i	0.237100	+	0.410669i
$630$		0			0
$631$	17.6216	−	30.5215i	0.701505	−	1.21504i	−0.266433	−	0.963853i	$-0.585845\pi$
$631$	17.6216	−	30.5215i	0.701505	−	1.21504i	0.967938	−	0.251189i	$-0.0808216\pi$
$632$	0.397463	−	0.333511i	0.0158102	−	0.0132663i
$633$		0			0
$634$	−5.12283	+	29.0530i	−0.203454	+	1.15384i
$635$	5.66679	−	2.06254i	0.224880	−	0.0818495i
$636$		0			0
$637$	−8.37983	−	22.0361i	−0.332021	−	0.873104i
$638$	18.6015	−	32.2187i	0.736439	−	1.27555i
$639$		0			0
$640$	−5.58236	+	9.66894i	−0.220662	+	0.382198i
$641$	−4.44072	+	3.72621i	−0.175398	+	0.147176i	−0.726260	−	0.687420i	$-0.758743\pi$
$641$	−4.44072	+	3.72621i	−0.175398	+	0.147176i	0.550863	+	0.834596i	$0.314299\pi$
$642$		0			0
$643$	4.93946	−	1.79782i	0.194793	−	0.0708990i	−0.242781	−	0.970081i	$-0.578060\pi$
$643$	4.93946	−	1.79782i	0.194793	−	0.0708990i	0.437575	+	0.899182i	$0.355838\pi$
$644$	5.95500	−	8.63559i	0.234660	−	0.340290i
$645$		0			0
$646$	−6.66757	−	37.8137i	−0.262332	−	1.48776i
$647$	9.29941	+	16.1071i	0.365598	+	0.633234i	0.988872	−	0.148770i	$-0.0475313\pi$
$647$	9.29941	+	16.1071i	0.365598	+	0.633234i	−0.623274	+	0.782003i	$0.714198\pi$
$648$		0			0
$649$	7.49531	−	12.9823i	0.294217	−	0.509598i
$650$	−31.3999	+	26.3477i	−1.23161	+	1.03344i
$651$		0			0
$652$	−3.10734	+	17.6226i	−0.121693	+	0.690154i
$653$	−3.41885	+	19.3892i	−0.133790	+	0.758760i	0.841905	+	0.539626i	$0.181434\pi$
$653$	−3.41885	+	19.3892i	−0.133790	+	0.758760i	−0.975695	+	0.219134i	$0.929677\pi$
$654$		0			0
$655$	−22.9422	+	19.2508i	−0.896425	+	0.752190i
$656$	1.25818			0.0491237
$657$		0			0
$658$	−25.3264	−	11.5898i	−0.987327	−	0.451819i
$659$	−39.3495	−	14.3220i	−1.53284	−	0.557907i	−0.568523	−	0.822667i	$-0.692485\pi$
$659$	−39.3495	−	14.3220i	−1.53284	−	0.557907i	−0.964314	+	0.264760i	$0.914707\pi$
$660$		0			0
$661$	−6.38080	+	36.1873i	−0.248184	+	1.40752i	0.564795	+	0.825231i	$0.308955\pi$
$661$	−6.38080	+	36.1873i	−0.248184	+	1.40752i	−0.812980	+	0.582292i	$0.802156\pi$
$662$	5.51247	−	31.2628i	0.214248	−	1.21506i
$663$		0			0
$664$	−4.47574	−	1.62904i	−0.173692	−	0.0632189i
$665$	40.1745	+	18.3846i	1.55790	+	0.712924i
$666$		0			0
$667$	−9.47137			−0.366733
$668$	−20.8646	+	17.5075i	−0.807276	+	0.677385i
$669$		0			0
$670$	−14.3938	+	81.6311i	−0.556080	+	3.15369i
$671$	8.06939	−	45.7638i	0.311515	−	1.76669i
$672$		0			0
$673$	−17.1674	+	14.4052i	−0.661756	+	0.555280i	−0.910613	−	0.413261i	$-0.864390\pi$
$673$	−17.1674	+	14.4052i	−0.661756	+	0.555280i	0.248856	+	0.968540i	$0.419945\pi$
$674$	0.101452	−	0.175720i	0.00390778	−	0.00676847i
$675$		0			0
$676$	1.47871	+	2.56120i	0.0568733	+	0.0985075i
$677$	2.90202	+	16.4582i	0.111534	+	0.632540i	0.988408	+	0.151820i	$0.0485134\pi$
$677$	2.90202	+	16.4582i	0.111534	+	0.632540i	−0.876874	+	0.480720i	$0.840375\pi$
$678$		0			0
$679$	16.5852	−	24.0508i	0.636480	−	0.922986i
$680$	5.23032	−	1.90368i	0.200573	−	0.0730028i
$681$		0			0
$682$	15.5933	−	13.0843i	0.597098	−	0.501025i
$683$	−11.7796	+	20.4029i	−0.450734	+	0.780693i	−0.998432	−	0.0559825i	$-0.982171\pi$
$683$	−11.7796	+	20.4029i	−0.450734	+	0.780693i	0.547698	+	0.836676i	$0.315504\pi$
$684$		0			0
$685$	31.5525	−	54.6505i	1.20556	−	2.08809i
$686$	29.9520	+	20.0277i	1.14357	+	0.764662i
$687$		0			0
$688$	−41.5002	+	15.1049i	−1.58218	+	0.575867i
$689$	5.98797	−	33.9595i	0.228123	−	1.29375i
$690$		0			0
$691$	−0.829616	+	0.696131i	−0.0315601	+	0.0264821i	−0.658431	−	0.752641i	$-0.728780\pi$
$691$	−0.829616	+	0.696131i	−0.0315601	+	0.0264821i	0.626871	+	0.779123i	$0.284335\pi$
$692$	−8.39328	+	14.5376i	−0.319065	+	0.552636i
$693$		0			0
$694$	−24.2680	−	42.0334i	−0.921200	−	1.59557i
$695$	52.4154	+	19.0777i	1.98823	+	0.723657i
$696$		0			0
$697$	−0.871776	−	0.731507i	−0.0330209	−	0.0277078i
$698$	−43.3051	−	36.3373i	−1.63912	−	1.37539i
$699$		0			0
$700$	7.44168	−	28.5902i	0.281269	−	1.08061i
$701$	−39.4989			−1.49185			−0.745927	−	0.666028i	$-0.767993\pi$
$701$	−39.4989			−1.49185			−0.745927	+	0.666028i	$0.767993\pi$
$702$		0			0
$703$	7.46437	+	12.9287i	0.281524	+	0.487614i
$704$	26.1152	+	9.50516i	0.984254	+	0.358239i
$705$		0			0
$706$	−1.48310	+	8.41107i	−0.0558172	+	0.316555i
$707$	0.969804	+	2.04145i	0.0364732	+	0.0767768i
$708$		0			0
$709$	44.8746	+	16.3330i	1.68530	+	0.613400i	0.994021	−	0.109187i	$-0.0348247\pi$
$709$	44.8746	+	16.3330i	1.68530	+	0.613400i	0.691280	+	0.722587i	$0.257047\pi$
$710$	−18.1281	+	31.3987i	−0.680334	+	1.17837i
$711$		0			0
$712$	2.56524	+	4.44313i	0.0961364	+	0.166513i
$713$	−4.86973	−	1.77244i	−0.182373	−	0.0663783i
$714$		0			0
$715$	−38.8183	−	32.5724i	−1.45172	−	1.21814i
$716$	4.81997	−	1.75432i	0.180131	−	0.0655622i
$717$		0			0
$718$	2.27525	+	12.9036i	0.0849116	+	0.481558i
$719$	0.374888	+	0.649326i	0.0139810	+	0.0242158i	0.872931	−	0.487843i	$-0.162216\pi$
$719$	0.374888	+	0.649326i	0.0139810	+	0.0242158i	−0.858950	+	0.512059i	$0.828883\pi$
$720$		0			0
$721$	1.74389	+	0.798036i	0.0649459	+	0.0297204i
$722$	−1.95079	−	11.0635i	−0.0726011	−	0.411741i
$723$		0			0
$724$	6.22115	+	5.22016i	0.231207	+	0.194006i
$725$	−25.0659	+	9.12325i	−0.930925	+	0.338829i
$726$		0			0
$727$	33.4171	−	28.0403i	1.23937	−	1.03996i	0.241798	−	0.970327i	$-0.422263\pi$
$727$	33.4171	−	28.0403i	1.23937	−	1.03996i	0.997573	−	0.0696290i	$-0.0221815\pi$
$728$	−3.39014	−	1.55139i	−0.125647	−	0.0574982i
$729$		0			0
$730$	−15.0148	+	26.0064i	−0.555722	+	0.962539i
$731$	37.5370	+	13.6623i	1.38835	+	0.505320i
$732$		0			0
$733$	−16.8320	−	14.1238i	−0.621705	−	0.521673i	0.276634	−	0.960975i	$-0.410781\pi$
$733$	−16.8320	−	14.1238i	−0.621705	−	0.521673i	−0.898339	+	0.439303i	$0.855226\pi$
$734$	15.1624	−	5.51867i	0.559655	−	0.203698i
$735$		0			0
$736$	−2.96690	−	16.8261i	−0.109361	−	0.620219i
$737$	−56.9530			−2.09789
$738$		0			0
$739$	40.1114			1.47552			0.737761	−	0.675062i	$-0.235883\pi$
$739$	40.1114			1.47552			0.737761	+	0.675062i	$0.235883\pi$
$740$	13.7590	−	11.5451i	0.505789	−	0.424408i
$741$		0			0
$742$	22.6140	+	47.6029i	0.830186	+	1.74756i
$743$	6.31887	+	5.30216i	0.231817	+	0.194518i	0.751295	−	0.659966i	$-0.229429\pi$
$743$	6.31887	+	5.30216i	0.231817	+	0.194518i	−0.519479	+	0.854484i	$0.673874\pi$
$744$		0			0
$745$	0.534284	+	3.03008i	0.0195747	+	0.111013i
$746$	−22.7721			−0.833747
$747$		0			0
$748$	−15.8704	−	27.4884i	−0.580280	−	1.00507i
$749$	23.6055	+	23.2698i	0.862526	+	0.850260i
$750$		0			0
$751$	−4.27142	+	24.2244i	−0.155866	+	0.883962i	0.802123	+	0.597159i	$0.203704\pi$
$751$	−4.27142	+	24.2244i	−0.155866	+	0.883962i	−0.957989	+	0.286803i	$0.907407\pi$
$752$	−22.2908	+	8.11320i	−0.812863	+	0.295858i
$753$		0			0
$754$	−4.85160	−	27.5148i	−0.176685	−	1.00203i
$755$	34.2370			1.24601
$756$		0			0
$757$	−20.6308			−0.749839			−0.374920	−	0.927057i	$-0.622330\pi$
$757$	−20.6308			−0.749839			−0.374920	+	0.927057i	$0.622330\pi$
$758$	9.09447	+	51.5773i	0.330326	+	1.87337i
$759$		0			0
$760$	6.56544	−	2.38963i	0.238154	−	0.0866809i
$761$	2.38678	−	13.5361i	0.0865206	−	0.490682i	−0.910498	−	0.413514i	$-0.864301\pi$
$761$	2.38678	−	13.5361i	0.0865206	−	0.490682i	0.997018	−	0.0771680i	$-0.0245878\pi$
$762$		0			0
$763$	12.5104	−	3.44837i	0.452908	−	0.124839i
$764$	−15.8203	−	27.4015i	−0.572358	−	0.991353i
$765$		0			0
$766$	32.5518			1.17615
$767$	−1.95491	−	11.0869i	−0.0705878	−	0.400323i
$768$		0			0
$769$	11.6423	+	9.76902i	0.419831	+	0.352280i	0.828099	−	0.560582i	$-0.189423\pi$
$769$	11.6423	+	9.76902i	0.419831	+	0.352280i	−0.408268	+	0.912862i	$0.633867\pi$
$770$	77.1968	+	6.19712i	2.78198	+	0.223329i
$771$		0			0
$772$	26.9249	−	22.5926i	0.969047	−	0.813127i
$773$	−38.0394			−1.36818			−0.684091	−	0.729397i	$-0.739801\pi$
$773$	−38.0394			−1.36818			−0.684091	+	0.729397i	$0.739801\pi$
$774$		0			0
$775$	−14.5950			−0.524268
$776$	−0.802259	−	4.54984i	−0.0287994	−	0.163330i
$777$		0			0
$778$	−2.92748	+	1.06551i	−0.104955	+	0.0382005i
$779$	−1.09431	−	0.918237i	−0.0392078	−	0.0328992i
$780$		0			0
$781$	−23.4088	−	8.52011i	−0.837633	−	0.304874i
$782$	−8.56760	+	14.8395i	−0.306377	+	0.530660i
$783$		0			0
$784$	30.1415	−	5.76104i	1.07648	−	0.205751i
$785$	10.7591	−	9.02794i	0.384008	−	0.322221i
$786$		0			0
$787$	−14.2005	+	5.16858i	−0.506195	+	0.184240i	−0.582478	−	0.812846i	$-0.697917\pi$
$787$	−14.2005	+	5.16858i	−0.506195	+	0.184240i	0.0762834	+	0.997086i	$0.475695\pi$
$788$	26.3526	+	22.1125i	0.938774	+	0.787725i
$789$		0			0
$790$	1.40553	+	7.97115i	0.0500065	+	0.283601i
$791$	−1.23764	−	13.0677i	−0.0440054	−	0.464635i
$792$		0			0
$793$	−17.4493	−	30.2231i	−0.619643	−	1.07325i
$794$	−4.00038	−	22.6873i	−0.141968	−	0.805141i
$795$		0			0
$796$	19.3984	−	7.06044i	0.687558	−	0.250251i
$797$	0.774338	+	0.649747i	0.0274285	+	0.0230152i	0.656399	−	0.754414i	$-0.272079\pi$
$797$	0.774338	+	0.649747i	0.0274285	+	0.0230152i	−0.628970	+	0.777429i	$0.716523\pi$
$798$		0			0
$799$	20.1621	+	7.33839i	0.713282	+	0.259613i
$800$	−24.0595	−	41.6723i	−0.850633	−	1.47334i
$801$		0			0
$802$	−0.152386	+	0.263940i	−0.00538093	+	0.00932004i
$803$	−19.3886	−	7.05689i	−0.684210	−	0.249032i
$804$		0			0
$805$	−8.46030	−	17.8091i	−0.298187	−	0.627688i
$806$	2.65456	−	15.0547i	0.0935027	−	0.530280i
$807$		0			0
$808$	0.335857	+	0.122242i	0.0118154	+	0.00430045i
$809$	−1.37661	−	2.38435i	−0.0483989	−	0.0838293i	0.840811	−	0.541329i	$-0.182079\pi$
$809$	−1.37661	−	2.38435i	−0.0483989	−	0.0838293i	−0.889210	+	0.457499i	$0.848745\pi$
$810$		0			0
$811$	33.2392			1.16718			0.583592	−	0.812047i	$-0.301647\pi$
$811$	33.2392			1.16718			0.583592	+	0.812047i	$0.301647\pi$
$812$	14.3405	+	14.1366i	0.503253	+	0.496097i
$813$		0			0
$814$	20.0462	+	16.8208i	0.702620	+	0.589569i
$815$	25.7653	+	21.6197i	0.902520	+	0.757305i
$816$		0			0
$817$	47.1189	+	17.1499i	1.64848	+	0.599998i
$818$	−26.1428	−	45.2807i	−0.914062	−	1.58320i
$819$		0			0
$820$	−0.859341	+	1.48842i	−0.0300095	+	0.0519780i
$821$	−14.3062	+	12.0043i	−0.499289	+	0.418953i	−0.857341	−	0.514749i	$-0.827885\pi$
$821$	−14.3062	+	12.0043i	−0.499289	+	0.418953i	0.358053	+	0.933701i	$0.383441\pi$
$822$		0			0
$823$	3.20620	−	18.1833i	0.111761	−	0.633829i	−0.876542	−	0.481326i	$-0.840155\pi$
$823$	3.20620	−	18.1833i	0.111761	−	0.633829i	0.988303	−	0.152503i	$-0.0487334\pi$
$824$	0.284992	−	0.103729i	0.00992817	−	0.00361356i
$825$		0			0
$826$	12.2530	+	12.0787i	0.426336	+	0.420273i
$827$	9.06140	−	15.6948i	0.315096	−	0.545762i	−0.664362	−	0.747411i	$-0.731297\pi$
$827$	9.06140	−	15.6948i	0.315096	−	0.545762i	0.979458	+	0.201649i	$0.0646300\pi$
$828$		0			0
$829$	−4.26434	+	7.38606i	−0.148107	+	0.256529i	−0.930528	−	0.366221i	$-0.880651\pi$
$829$	−4.26434	+	7.38606i	−0.148107	+	0.256529i	0.782421	+	0.622750i	$0.213985\pi$
$830$	56.9194	−	47.7611i	1.97570	−	1.65781i
$831$		0			0
$832$	19.6124	−	7.13834i	0.679939	−	0.247477i
$833$	−24.2341	−	13.5325i	−0.839662	−	0.468874i
$834$		0			0
$835$	8.88975	+	50.4163i	0.307643	+	1.74473i
$836$	−19.9216	−	34.5052i	−0.689003	−	1.19339i
$837$		0			0
$838$	23.4349	−	40.5904i	0.809545	−	1.40217i
$839$	24.2173	−	20.3207i	0.836073	−	0.701548i	−0.120604	−	0.992701i	$-0.538483\pi$
$839$	24.2173	−	20.3207i	0.836073	−	0.701548i	0.956677	+	0.291153i	$0.0940387\pi$
$840$		0			0
$841$	−1.87855	+	10.6538i	−0.0647776	+	0.367372i
$842$	−1.24886	+	7.08261i	−0.0430384	+	0.244083i
$843$		0			0
$844$	30.3100	−	25.4331i	1.04331	−	0.875444i
$845$	5.55873			0.191226
$846$		0			0
$847$	2.27312	+	24.0009i	0.0781052	+	0.824682i
$848$	42.1780	+	15.3515i	1.44840	+	0.527174i
$849$		0			0
$850$	−8.38001	+	47.5254i	−0.287432	+	1.63011i
$851$	1.15687	−	6.56094i	0.0396570	−	0.224906i
$852$		0			0
$853$	−18.4639	−	6.72031i	−0.632192	−	0.230099i	0.00599331	−	0.999982i	$-0.498092\pi$
$853$	−18.4639	−	6.72031i	−0.632192	−	0.230099i	−0.638185	+	0.769883i	$0.720314\pi$
$854$	48.4990	+	22.1940i	1.65960	+	0.759464i
$855$		0			0
$856$	5.24180			0.179161
$857$	−1.19408	+	1.00195i	−0.0407889	+	0.0342260i	−0.662954	−	0.748660i	$-0.730698\pi$
$857$	−1.19408	+	1.00195i	−0.0407889	+	0.0342260i	0.622165	+	0.782886i	$0.286253\pi$
$858$		0			0
$859$	−8.53280	+	48.3919i	−0.291135	+	1.65111i	0.391372	+	0.920233i	$0.372001\pi$
$859$	−8.53280	+	48.3919i	−0.291135	+	1.65111i	−0.682507	+	0.730879i	$0.739110\pi$
$860$	10.4758	−	59.4113i	0.357223	−	2.02591i
$861$		0			0
$862$	−3.51721	+	2.95129i	−0.119797	+	0.100521i
$863$	−4.07047	+	7.05026i	−0.138560	+	0.239994i	−0.926952	−	0.375180i	$-0.877581\pi$
$863$	−4.07047	+	7.05026i	−0.138560	+	0.239994i	0.788391	+	0.615174i	$0.210914\pi$
$864$		0			0
$865$	15.7759	+	27.3247i	0.536398	+	0.929069i
$866$	−5.25784	−	29.8187i	−0.178669	−	1.01328i
$867$		0			0
$868$	4.72775	+	9.95200i	0.160470	+	0.337793i
$869$	−5.22598	+	1.90210i	−0.177279	+	0.0645243i
$870$		0			0
$871$	−32.7649	+	27.4930i	−1.11019	+	0.931564i
$872$	1.02609	−	1.77723i	0.0347477	−	0.0601847i
$873$		0			0
$874$	−10.7546	+	18.6276i	−0.363781	+	0.630087i
$875$	−7.93796	−	7.82507i	−0.268352	−	0.264536i
$876$		0			0
$877$	−42.5608	+	15.4908i	−1.43717	+	0.523089i	−0.938979	−	0.343976i	$-0.888226\pi$
$877$	−42.5608	+	15.4908i	−1.43717	+	0.523089i	−0.498196	+	0.867064i	$0.666004\pi$
$878$	−13.3092	+	75.4803i	−0.449164	+	2.54734i
$879$		0			0
$880$	50.5274	−	42.3976i	1.70328	−	1.42922i
$881$	−0.111855	+	0.193739i	−0.00376850	+	0.00652724i	−0.867904	−	0.496733i	$-0.834533\pi$
$881$	−0.111855	+	0.193739i	−0.00376850	+	0.00652724i	0.864135	+	0.503260i	$0.167866\pi$
$882$		0			0
$883$	28.2842	+	48.9896i	0.951838	+	1.64863i	0.741443	+	0.671016i	$0.234142\pi$
$883$	28.2842	+	48.9896i	0.951838	+	1.64863i	0.210396	+	0.977616i	$0.432525\pi$
$884$	−22.3997	−	8.15282i	−0.753383	−	0.274209i
$885$		0			0
$886$	−4.63917	−	3.89273i	−0.155856	−	0.130779i
$887$	0.835656	+	0.701199i	0.0280586	+	0.0235440i	0.656709	−	0.754144i	$-0.271948\pi$
$887$	0.835656	+	0.701199i	0.0280586	+	0.0235440i	−0.628651	+	0.777688i	$0.716392\pi$
$888$		0			0
$889$	−4.58471	+	1.26373i	−0.153766	+	0.0423840i
$890$	−80.0360			−2.68281
$891$		0			0
$892$	15.8947	+	27.5304i	0.532194	+	0.921787i
$893$	25.3088	+	9.21164i	0.846926	+	0.308256i
$894$		0			0
$895$	1.67414	−	9.49452i	0.0559603	−	0.317367i
$896$	4.99834	−	7.24829i	0.166983	−	0.242148i
$897$		0			0
$898$	−27.2600	−	9.92183i	−0.909678	−	0.331096i
$899$	4.97410	−	8.61540i	0.165896	−	0.287340i
$900$		0			0
$901$	−20.2992	−	35.1592i	−0.676264	−	1.17132i
$902$	−2.35304	−	0.856436i	−0.0783476	−	0.0285162i
$903$		0			0
$904$	−1.59013	−	1.33428i	−0.0528871	−	0.0443775i
$905$	14.3439	−	5.22074i	0.476806	−	0.173543i
$906$		0			0
$907$	7.18272	+	40.7352i	0.238498	+	1.35259i	0.835120	+	0.550068i	$0.185398\pi$
$907$	7.18272	+	40.7352i	0.238498	+	1.35259i	−0.596621	+	0.802523i	$0.703490\pi$
$908$	2.86315	+	4.95911i	0.0950168	+	0.164574i
$909$		0			0
$910$	47.4026	−	33.7001i	1.57138	−	1.11715i
$911$	6.65639	+	37.7502i	0.220536	+	1.25072i	0.871037	+	0.491217i	$0.163448\pi$
$911$	6.65639	+	37.7502i	0.220536	+	1.25072i	−0.650502	+	0.759505i	$0.725441\pi$
$912$		0			0
$913$	39.1086	+	32.8160i	1.29431	+	1.08605i
$914$	−50.5863	+	18.4119i	−1.67324	+	0.609011i
$915$		0			0
$916$	−5.52977	+	4.64003i	−0.182709	+	0.153311i
$917$	19.2492	−	13.6849i	0.635665	−	0.451916i
$918$		0			0
$919$	−2.47835	+	4.29263i	−0.0817533	+	0.141601i	−0.904003	−	0.427526i	$-0.859385\pi$
$919$	−2.47835	+	4.29263i	−0.0817533	+	0.141601i	0.822250	+	0.569127i	$0.192719\pi$
$920$	−2.92992	−	1.06640i	−0.0965966	−	0.0351583i
$921$		0			0
$922$	−52.4636	−	44.0222i	−1.72780	−	1.44979i
$923$	−17.5799	+	6.39857i	−0.578651	+	0.210612i
$924$		0			0
$925$	−3.25814	−	18.4778i	−0.107127	−	0.607547i
$926$	40.8537			1.34253
$927$		0			0
$928$	32.7988			1.07667
$929$	−18.8911	+	15.8515i	−0.619796	+	0.520071i	−0.897739	−	0.440527i	$-0.854792\pi$
$929$	−18.8911	+	15.8515i	−0.619796	+	0.520071i	0.277943	+	0.960597i	$0.410347\pi$
$930$		0			0
$931$	−30.4203	−	16.9869i	−0.996984	−	0.556725i
$932$	20.9850	+	17.6085i	0.687387	+	0.576786i
$933$		0			0
$934$	−12.2419	−	69.4273i	−0.400567	−	2.27173i
$935$	−59.6598			−1.95108
$936$		0			0
$937$	−20.2545	−	35.0818i	−0.661684	−	1.14607i	−0.980173	−	0.198144i	$-0.936509\pi$
$937$	−20.2545	−	35.0818i	−0.661684	−	1.14607i	0.318488	−	0.947927i	$-0.396825\pi$
$938$	16.4659	−	63.2604i	0.537632	−	2.06552i
$939$		0			0
$940$	5.62683	−	31.9113i	0.183527	−	1.04083i
$941$	−22.1138	+	8.04877i	−0.720890	+	0.262382i	−0.676303	−	0.736623i	$-0.736419\pi$
$941$	−22.1138	+	8.04877i	−0.720890	+	0.262382i	−0.0445863	+	0.999006i	$0.514197\pi$
$942$		0			0
$943$	0.110700	+	0.627813i	0.00360490	+	0.0204444i
$944$	14.6537			0.476938
$945$		0			0
$946$	87.8953			2.85772
$947$	−4.82267	−	27.3507i	−0.156716	−	0.888779i	−0.957200	−	0.289426i	$-0.906536\pi$
$947$	−4.82267	−	27.3507i	−0.156716	−	0.888779i	0.800485	−	0.599353i	$-0.204575\pi$
$948$		0			0
$949$	−14.5608	+	5.29970i	−0.472663	+	0.172035i
$950$	−10.5191	+	59.6571i	−0.341286	+	1.93553i
$951$		0			0
$952$	−4.23158	+	1.16639i	−0.137146	+	0.0378029i
$953$	21.0460	+	36.4528i	0.681748	+	1.18082i	0.974447	+	0.224617i	$0.0721131\pi$
$953$	21.0460	+	36.4528i	0.681748	+	1.18082i	−0.292699	+	0.956204i	$0.594554\pi$
$954$		0			0
$955$	−59.4713			−1.92445
$956$	0.468331	+	2.65604i	0.0151469	+	0.0859024i
$957$		0			0
$958$	−48.5975	−	40.7781i	−1.57011	−	1.31748i
$959$	−28.2515	+	40.9686i	−0.912287	+	1.32294i
$960$		0			0
$961$	−19.5777	+	16.4276i	−0.631538	+	0.529923i
$962$	19.6525			0.633621
$963$		0			0
$964$	34.2561			1.10331
$965$	−11.4718	−	65.0601i	−0.369292	−	2.09436i
$966$		0			0
$967$	45.8194	−	16.6769i	1.47345	−	0.536293i	0.524417	−	0.851461i	$-0.324283\pi$
$967$	45.8194	−	16.6769i	1.47345	−	0.536293i	0.949036	+	0.315168i	$0.102061\pi$
$968$	2.92053	+	2.45061i	0.0938693	+	0.0787657i
$969$		0			0
$970$	67.7263	+	24.6504i	2.17456	+	0.791475i
$971$	1.76073	−	3.04968i	0.0565045	−	0.0978687i	−0.836390	−	0.548136i	$-0.815338\pi$
$971$	1.76073	−	3.04968i	0.0565045	−	0.0978687i	0.892894	+	0.450267i	$0.148671\pi$
$972$		0			0
$973$	−39.9989	−	18.3042i	−1.28231	−	0.586806i
$974$	−46.2017	+	38.7678i	−1.48040	+	1.24220i
$975$		0			0
$976$	42.6860	−	15.5364i	1.36635	−	0.497309i
$977$	−2.69837	−	2.26420i	−0.0863286	−	0.0724383i	0.598602	−	0.801047i	$-0.295723\pi$
$977$	−2.69837	−	2.26420i	−0.0863286	−	0.0724383i	−0.684931	+	0.728608i	$0.740168\pi$
$978$		0			0
$979$	−9.54922	−	54.1563i	−0.305194	−	1.73084i
$980$	−13.7714	+	39.5921i	−0.439912	+	1.26472i
$981$		0			0
$982$	40.5430	+	70.2225i	1.29378	+	2.24089i
$983$	4.48086	+	25.4122i	0.142917	+	0.810524i	0.969016	+	0.246999i	$0.0794443\pi$
$983$	4.48086	+	25.4122i	0.142917	+	0.810524i	−0.826098	+	0.563526i	$0.809445\pi$
$984$		0			0
$985$	60.7602	−	22.1149i	1.93598	−	0.704640i
$986$	−25.1981	−	21.1438i	−0.802472	−	0.673354i
$987$		0			0
$988$	−28.1176	−	10.2340i	−0.894540	−	0.325586i
$989$	−11.1885	−	19.3790i	−0.355773	−	0.616217i
$990$		0			0
$991$	23.5548	−	40.7982i	0.748244	−	1.29600i	−0.200420	−	0.979710i	$-0.564231\pi$
$991$	23.5548	−	40.7982i	0.748244	−	1.29600i	0.948664	−	0.316287i	$-0.102436\pi$
$992$	16.8636	+	6.13785i	0.535420	+	0.194877i
$993$		0			0
$994$	16.2315	−	23.5380i	0.514832	−	0.746579i
$995$	6.73773	−	38.2116i	0.213600	−	1.21139i
$996$		0			0
$997$	0.455226	+	0.165689i	0.0144172	+	0.00524742i	0.349219	−	0.937041i	$-0.386447\pi$
$997$	0.455226	+	0.165689i	0.0144172	+	0.00524742i	−0.334801	+	0.942289i	$0.608669\pi$
$998$	17.3327	+	30.0211i	0.548656	+	0.950300i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.w.a.37.5		132
3.2	odd	2		189.2.w.a.184.18	yes	132
7.4	even	3		567.2.u.a.361.18		132
21.11	odd	6		189.2.u.a.130.5	yes	132
27.11	odd	18		189.2.u.a.16.5	✓	132
27.16	even	9		567.2.u.a.289.18		132
189.11	odd	18		189.2.w.a.151.18	yes	132
189.151	even	9	inner	567.2.w.a.46.5		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.5	✓	132	27.11	odd	18
189.2.u.a.130.5	yes	132	21.11	odd	6
189.2.w.a.151.18	yes	132	189.11	odd	18
189.2.w.a.184.18	yes	132	3.2	odd	2
567.2.u.a.289.18		132	27.16	even	9
567.2.u.a.361.18		132	7.4	even	3
567.2.w.a.37.5		132	1.1	even	1	trivial
567.2.w.a.46.5		132	189.151	even	9	inner

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.w (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.337831 - 1.91594i) q^{2} +(-1.67729 + 0.610485i) q^{4} +(-0.582582 + 3.30399i) q^{5} +(0.666452 - 2.56044i) q^{7} +(-0.209199 - 0.362343i) q^{8} +O(q^{10})\)	\(q+(-0.337831 - 1.91594i) q^{2} +(-1.67729 + 0.610485i) q^{4} +(-0.582582 + 3.30399i) q^{5} +(0.666452 - 2.56044i) q^{7} +(-0.209199 - 0.362343i) q^{8} +6.52704 q^{10} +(0.778751 + 4.41652i) q^{11} +(2.58000 + 2.16488i) q^{13} +(-5.13078 - 0.411883i) q^{14} +(-3.35824 + 2.81790i) q^{16} +3.96521 q^{17} +4.97740 q^{19} +(-1.03987 - 5.89742i) q^{20} +(8.19868 - 2.98408i) q^{22} +(-1.70156 - 1.42778i) q^{23} +(-5.87847 - 2.13959i) q^{25} +(3.27617 - 5.67449i) q^{26} +(0.445273 + 4.70147i) q^{28} +(3.26643 - 2.74086i) q^{29} +(2.19236 - 0.797953i) q^{31} +(5.89240 + 4.94431i) q^{32} +(-1.33957 - 7.59708i) q^{34} +(8.07139 + 3.69362i) q^{35} +(1.49965 + 2.59748i) q^{37} +(-1.68152 - 9.53637i) q^{38} +(1.31905 - 0.480096i) q^{40} +(-0.219856 - 0.184481i) q^{41} +(9.46658 + 3.44555i) q^{43} +(-4.00242 - 6.93239i) q^{44} +(-2.16069 + 3.74243i) q^{46} +(5.08474 + 1.85069i) q^{47} +(-6.11168 - 3.41282i) q^{49} +(-2.11338 + 11.9856i) q^{50} +(-5.64906 - 2.05609i) q^{52} +(-5.11933 - 8.86693i) q^{53} -15.0458 q^{55} +(-1.06718 + 0.294156i) q^{56} +(-6.35481 - 5.33232i) q^{58} +(-2.56062 - 2.14861i) q^{59} +(-9.73706 - 3.54400i) q^{61} +(-2.26947 - 3.93084i) q^{62} +(3.09848 - 5.36673i) q^{64} +(-8.65580 + 7.26308i) q^{65} +(-2.20525 + 12.5066i) q^{67} +(-6.65082 + 2.42070i) q^{68} +(4.34996 - 16.7121i) q^{70} +(-2.77738 + 4.81056i) q^{71} +(-2.30040 + 3.98440i) q^{73} +(4.46997 - 3.75075i) q^{74} +(-8.34856 + 3.03863i) q^{76} +(11.8272 + 0.949453i) q^{77} +(0.215339 + 1.22125i) q^{79} +(-7.35385 - 12.7372i) q^{80} +(-0.279180 + 0.483554i) q^{82} +(8.72055 - 7.31741i) q^{83} +(-2.31006 + 13.1010i) q^{85} +(3.40335 - 19.3014i) q^{86} +(1.43738 - 1.20611i) q^{88} -12.2622 q^{89} +(7.26249 - 5.16315i) q^{91} +(3.72566 + 1.35603i) q^{92} +(1.82803 - 10.3673i) q^{94} +(-2.89974 + 16.4453i) q^{95} +(10.3763 + 3.77665i) q^{97} +(-4.47402 + 12.8625i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

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