LMFDB - Embedded newform 279.2.y.b.262.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,2,Mod(10,279)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("279.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.y (of order $15$, degree $8$, 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:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7 x^{15} + 24 x^{14} - 36 x^{13} + 17 x^{12} + 18 x^{11} - 52 x^{10} + 59 x^{9} + 51 x^{8} + \cdots + 1 $ x^16 - 7x^15 + 24x^14 - 36x^13 + 17x^12 + 18x^11 - 52x^10 + 59x^9 + 51x^8 - 59x^7 - 52x^6 - 18x^5 + 17x^4 + 36x^3 + 24x^2 + 7*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 93)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			262.2
Root			$-0.515238 + 0.229399i$ of defining polynomial
Character	$\chi$	$=$	279.262
Dual form			279.2.y.b.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.483302 - 1.48745i) q^{2} +(-0.360895 - 0.262205i) q^{4} +(0.686405 - 1.18889i) q^{5} +(0.0145831 - 0.138749i) q^{7} +(1.96616 - 1.42850i) q^{8} +(-1.43667 - 1.59559i) q^{10} +(-0.454357 + 0.202293i) q^{11} +(2.00358 + 0.425875i) q^{13} +(-0.199334 - 0.0887493i) q^{14} +(-1.45027 - 4.46348i) q^{16} +(-4.82434 - 2.14793i) q^{17} +(2.80648 - 0.596536i) q^{19} +(-0.559453 + 0.249085i) q^{20} +(0.0813089 + 0.773603i) q^{22} +(-1.87974 + 1.36571i) q^{23} +(1.55770 + 2.69801i) q^{25} +(1.60180 - 2.77441i) q^{26} +(-0.0416437 + 0.0462500i) q^{28} +(-1.43974 + 4.43106i) q^{29} +(-3.54387 - 4.29429i) q^{31} -2.47951 q^{32} +(-5.52656 + 6.13787i) q^{34} +(-0.154947 - 0.112576i) q^{35} +(2.10520 + 3.64631i) q^{37} +(0.469060 - 4.46281i) q^{38} +(-0.348744 - 3.31808i) q^{40} +(7.20170 + 7.99829i) q^{41} +(-12.2899 + 2.61231i) q^{43} +(0.217018 + 0.0461285i) q^{44} +(1.12294 + 3.45606i) q^{46} +(3.28380 + 10.1065i) q^{47} +(6.82799 + 1.45134i) q^{49} +(4.76599 - 1.01304i) q^{50} +(-0.611416 - 0.679047i) q^{52} +(-1.02886 - 9.78895i) q^{53} +(-0.0713695 + 0.679036i) q^{55} +(-0.169530 - 0.293635i) q^{56} +(5.89516 + 4.28308i) q^{58} +(-2.25251 + 2.50167i) q^{59} -1.84593 q^{61} +(-8.10031 + 3.19590i) q^{62} +(1.70220 - 5.23882i) q^{64} +(1.88159 - 2.08972i) q^{65} +(-2.60973 + 4.52019i) q^{67} +(1.17788 + 2.04015i) q^{68} +(-0.242337 + 0.176068i) q^{70} +(0.592591 + 5.63812i) q^{71} +(10.1409 - 4.51501i) q^{73} +(6.44116 - 1.36911i) q^{74} +(-1.16926 - 0.520588i) q^{76} +(0.0214420 + 0.0659916i) q^{77} +(5.15533 + 2.29530i) q^{79} +(-6.30206 - 1.33954i) q^{80} +(15.3777 - 6.84658i) q^{82} +(1.42353 + 1.58099i) q^{83} +(-5.86511 + 4.26125i) q^{85} +(-2.05408 + 19.5432i) q^{86} +(-0.604365 + 1.04679i) q^{88} +(-1.96427 - 1.42713i) q^{89} +(0.0883082 - 0.271785i) q^{91} +1.03648 q^{92} +16.6200 q^{94} +(1.21717 - 3.74606i) q^{95} +(-6.84658 - 4.97433i) q^{97} +(5.45877 - 9.45487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} - 9 q^{7} - 10 q^{8} - 16 q^{10} - 10 q^{11} + 3 q^{13} + 12 q^{14} + 6 q^{16} - 3 q^{17} - 32 q^{19} + 10 q^{20} - 9 q^{22} + 22 q^{23} + 12 q^{25} - 18 q^{26} + 30 q^{28} - 38 q^{29} - 8 q^{31}+ \cdots + 32 q^{98}+O(q^{100}) $ 16 * q - 6 * q^5 - 9 * q^7 - 10 * q^8 - 16 * q^10 - 10 * q^11 + 3 * q^13 + 12 * q^14 + 6 * q^16 - 3 * q^17 - 32 * q^19 + 10 * q^20 - 9 * q^22 + 22 * q^23 + 12 * q^25 - 18 * q^26 + 30 * q^28 - 38 * q^29 - 8 * q^31 - 52 * q^34 - 3 * q^35 - 8 * q^37 - 7 * q^38 + 37 * q^40 + 40 * q^41 + q^43 - 7 * q^46 + 23 * q^47 + 25 * q^49 + 21 * q^50 - 45 * q^52 - 30 * q^53 + 46 * q^55 + 6 * q^56 + 48 * q^58 + 40 * q^59 + 26 * q^61 - 40 * q^62 + 38 * q^64 - 12 * q^65 - 32 * q^67 - 15 * q^68 + 33 * q^70 - 17 * q^71 + 27 * q^73 + 70 * q^74 - 15 * q^76 + 9 * q^77 - 21 * q^80 - 32 * q^82 + 17 * q^83 - 64 * q^85 - 26 * q^86 - 22 * q^88 + 43 * q^89 + 140 * q^92 + 88 * q^94 + 2 * q^95 + 12 * q^97 + 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{11}{15}\right)$	$1$

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 $

$2$	0.483302	−	1.48745i	0.341746	−	1.05179i	−0.621557	−	0.783369i	$-0.713499\pi$
$2$	0.483302	−	1.48745i	0.341746	−	1.05179i	0.963303	−	0.268417i	$-0.0865006\pi$
$3$		0			0
$3$		0			0
$4$	−0.360895	−	0.262205i	−0.180447	−	0.131103i
$5$	0.686405	−	1.18889i	0.306970	−	0.531687i	−0.670728	−	0.741703i	$-0.734018\pi$
$5$	0.686405	−	1.18889i	0.306970	−	0.531687i	0.977698	+	0.210016i	$0.0673516\pi$
$6$		0			0
$7$	0.0145831	−	0.138749i	0.00551189	−	0.0524422i	−0.991420	−	0.130713i	$-0.958273\pi$
$7$	0.0145831	−	0.138749i	0.00551189	−	0.0524422i	0.996932	+	0.0782711i	$0.0249400\pi$
$8$	1.96616	−	1.42850i	0.695144	−	0.505052i
$9$		0			0
$10$	−1.43667	−	1.59559i	−0.454316	−	0.504569i
$11$	−0.454357	+	0.202293i	−0.136994	+	0.0609936i	−0.474089	−	0.880477i	$-0.657222\pi$
$11$	−0.454357	+	0.202293i	−0.136994	+	0.0609936i	0.337095	+	0.941471i	$0.390556\pi$
$12$		0			0
$13$	2.00358	+	0.425875i	0.555694	+	0.118116i	0.477195	−	0.878798i	$-0.341654\pi$
$13$	2.00358	+	0.425875i	0.555694	+	0.118116i	0.0784997	+	0.996914i	$0.474987\pi$
$14$	−0.199334	−	0.0887493i	−0.0532743	−	0.0237192i
$15$		0			0
$16$	−1.45027	−	4.46348i	−0.362568	−	1.11587i
$17$	−4.82434	−	2.14793i	−1.17007	−	0.520951i	−0.272647	−	0.962114i	$-0.587899\pi$
$17$	−4.82434	−	2.14793i	−1.17007	−	0.520951i	−0.897427	+	0.441163i	$0.854566\pi$
$18$		0			0
$19$	2.80648	−	0.596536i	0.643851	−	0.136855i	0.125597	−	0.992081i	$-0.459915\pi$
$19$	2.80648	−	0.596536i	0.643851	−	0.136855i	0.518254	+	0.855227i	$0.326582\pi$
$20$	−0.559453	+	0.249085i	−0.125098	+	0.0556970i
$21$		0			0
$22$	0.0813089	+	0.773603i	0.0173351	+	0.164933i
$23$	−1.87974	+	1.36571i	−0.391952	+	0.284770i	−0.766255	−	0.642537i	$-0.777882\pi$
$23$	−1.87974	+	1.36571i	−0.391952	+	0.284770i	0.374303	+	0.927306i	$0.377882\pi$
$24$		0			0
$25$	1.55770	+	2.69801i	0.311539	+	0.539601i
$26$	1.60180	−	2.77441i	0.314140	−	0.544106i
$27$		0			0
$28$	−0.0416437	+	0.0462500i	−0.00786991	+	0.00874043i
$29$	−1.43974	+	4.43106i	−0.267353	+	0.822827i	0.723789	+	0.690021i	$0.242399\pi$
$29$	−1.43974	+	4.43106i	−0.267353	+	0.822827i	−0.991142	+	0.132806i	$0.957601\pi$
$30$		0			0
$31$	−3.54387	−	4.29429i	−0.636499	−	0.771278i
$31$	−3.54387	−	4.29429i	−0.636499	−	0.771278i
$32$	−2.47951			−0.438319
$33$		0			0
$34$	−5.52656	+	6.13787i	−0.947797	+	1.05264i
$35$	−0.154947	−	0.112576i	−0.0261908	−	0.0190288i
$36$		0			0
$37$	2.10520	+	3.64631i	0.346093	+	0.599450i	0.985552	−	0.169375i	$-0.0541750\pi$
$37$	2.10520	+	3.64631i	0.346093	+	0.599450i	−0.639459	+	0.768825i	$0.720842\pi$
$38$	0.469060	−	4.46281i	0.0760916	−	0.723963i
$39$		0			0
$40$	−0.348744	−	3.31808i	−0.0551413	−	0.524635i
$41$	7.20170	+	7.99829i	1.12472	+	1.24912i	0.965082	+	0.261948i	$0.0843647\pi$
$41$	7.20170	+	7.99829i	1.12472	+	1.24912i	0.159634	+	0.987176i	$0.448969\pi$
$42$		0			0
$43$	−12.2899	+	2.61231i	−1.87420	+	0.398373i	−0.996698	−	0.0812005i	$-0.974125\pi$
$43$	−12.2899	+	2.61231i	−1.87420	+	0.398373i	−0.877502	+	0.479574i	$0.840791\pi$
$44$	0.217018	+	0.0461285i	0.0327166	+	0.00695413i
$45$		0			0
$46$	1.12294	+	3.45606i	0.165569	+	0.509569i
$47$	3.28380	+	10.1065i	0.478992	+	1.47418i	0.840498	+	0.541815i	$0.182263\pi$
$47$	3.28380	+	10.1065i	0.478992	+	1.47418i	−0.361506	+	0.932370i	$0.617737\pi$
$48$		0			0
$49$	6.82799	+	1.45134i	0.975428	+	0.207334i
$50$	4.76599	−	1.01304i	0.674013	−	0.143266i
$51$		0			0
$52$	−0.611416	−	0.679047i	−0.0847882	−	0.0941668i
$53$	−1.02886	−	9.78895i	−0.141325	−	1.34462i	−0.803517	−	0.595282i	$-0.797040\pi$
$53$	−1.02886	−	9.78895i	−0.141325	−	1.34462i	0.662192	−	0.749334i	$-0.269626\pi$
$54$		0			0
$55$	−0.0713695	+	0.679036i	−0.00962346	+	0.0915611i
$56$	−0.169530	−	0.293635i	−0.0226544	−	0.0392386i
$57$		0			0
$58$	5.89516	+	4.28308i	0.774072	+	0.562396i
$59$	−2.25251	+	2.50167i	−0.293252	+	0.325689i	−0.871709	−	0.490023i	$-0.836988\pi$
$59$	−2.25251	+	2.50167i	−0.293252	+	0.325689i	0.578457	+	0.815713i	$0.303655\pi$
$60$		0			0
$61$	−1.84593			−0.236347			−0.118174	−	0.992993i	$-0.537704\pi$
$61$	−1.84593			−0.236347			−0.118174	+	0.992993i	$0.537704\pi$
$62$	−8.10031	+	3.19590i	−1.02874	+	0.405879i
$63$		0			0
$64$	1.70220	−	5.23882i	0.212774	−	0.654853i
$65$	1.88159	−	2.08972i	0.233382	−	0.259197i
$66$		0			0
$67$	−2.60973	+	4.52019i	−0.318830	+	0.552229i	−0.980244	−	0.197791i	$-0.936623\pi$
$67$	−2.60973	+	4.52019i	−0.318830	+	0.552229i	0.661414	+	0.750021i	$0.269956\pi$
$68$	1.17788	+	2.04015i	0.142839	+	0.247404i
$69$		0			0
$70$	−0.242337	+	0.176068i	−0.0289648	+	0.0210442i
$71$	0.592591	+	5.63812i	0.0703276	+	0.669122i	0.971723	+	0.236125i	$0.0758774\pi$
$71$	0.592591	+	5.63812i	0.0703276	+	0.669122i	−0.901395	+	0.432997i	$0.857456\pi$
$72$		0			0
$73$	10.1409	−	4.51501i	1.18690	−	0.528443i	0.284223	−	0.958758i	$-0.408264\pi$
$73$	10.1409	−	4.51501i	1.18690	−	0.528443i	0.902678	+	0.430316i	$0.141598\pi$
$74$	6.44116	−	1.36911i	0.748769	−	0.159156i
$75$		0			0
$76$	−1.16926	−	0.520588i	−0.134123	−	0.0597155i
$77$	0.0214420	+	0.0659916i	0.00244354	+	0.00752045i
$78$		0			0
$79$	5.15533	+	2.29530i	0.580020	+	0.258242i	0.675707	−	0.737170i	$-0.263838\pi$
$79$	5.15533	+	2.29530i	0.580020	+	0.258242i	−0.0956874	+	0.995411i	$0.530505\pi$
$80$	−6.30206	−	1.33954i	−0.704592	−	0.149766i
$81$		0			0
$82$	15.3777	−	6.84658i	1.69818	−	0.756078i
$83$	1.42353	+	1.58099i	0.156253	+	0.173536i	0.816188	−	0.577786i	$-0.196083\pi$
$83$	1.42353	+	1.58099i	0.156253	+	0.173536i	−0.659936	+	0.751322i	$0.729416\pi$
$84$		0			0
$85$	−5.86511	+	4.26125i	−0.636160	+	0.462198i
$86$	−2.05408	+	19.5432i	−0.221497	+	2.10740i
$87$		0			0
$88$	−0.604365	+	1.04679i	−0.0644255	+	0.111588i
$89$	−1.96427	−	1.42713i	−0.208212	−	0.151275i	0.478792	−	0.877928i	$-0.341075\pi$
$89$	−1.96427	−	1.42713i	−0.208212	−	0.151275i	−0.687004	+	0.726653i	$0.741075\pi$
$90$		0			0
$91$	0.0883082	−	0.271785i	0.00925721	−	0.0284908i
$92$	1.03648			0.108061
$93$		0			0
$94$	16.6200			1.71422
$95$	1.21717	−	3.74606i	0.124879	−	0.384338i
$96$		0			0
$97$	−6.84658	−	4.97433i	−0.695165	−	0.505067i	0.183189	−	0.983078i	$-0.441358\pi$
$97$	−6.84658	−	4.97433i	−0.695165	−	0.505067i	−0.878354	+	0.478011i	$0.841358\pi$
$98$	5.45877	−	9.45487i	0.551419	−	0.955086i
$99$		0			0
$100$	0.145268	−	1.38213i	0.0145268	−	0.138213i
$101$	−3.56816	+	2.59242i	−0.355045	+	0.257955i	−0.750982	−	0.660322i	$-0.770420\pi$
$101$	−3.56816	+	2.59242i	−0.355045	+	0.257955i	0.395937	+	0.918278i	$0.370420\pi$
$102$		0			0
$103$	−12.3191	−	13.6817i	−1.21384	−	1.34810i	−0.919839	−	0.392296i	$-0.871681\pi$
$103$	−12.3191	−	13.6817i	−1.21384	−	1.34810i	−0.293998	−	0.955806i	$-0.594986\pi$
$104$	4.54774	−	2.02478i	0.445942	−	0.198546i
$105$		0			0
$106$	−15.0578	−	3.20064i	−1.46255	−	0.310874i
$107$	−10.4481	−	4.65181i	−1.01006	−	0.449708i	−0.166098	−	0.986109i	$-0.553117\pi$
$107$	−10.4481	−	4.65181i	−1.01006	−	0.449708i	−0.843963	+	0.536401i	$0.819783\pi$
$108$		0			0
$109$	−0.0265770	−	0.0817956i	−0.00254562	−	0.00783460i	0.949776	−	0.312932i	$-0.101311\pi$
$109$	−0.0265770	−	0.0817956i	−0.00254562	−	0.00783460i	−0.952321	+	0.305097i	$0.901311\pi$
$110$	0.975539	+	0.434338i	0.0930140	+	0.0414125i
$111$		0			0
$112$	−0.640453	+	0.136132i	−0.0605171	+	0.0128633i
$113$	1.19172	−	0.530589i	0.112108	−	0.0499136i	−0.349916	−	0.936781i	$-0.613790\pi$
$113$	1.19172	−	0.530589i	0.112108	−	0.0499136i	0.462024	+	0.886867i	$0.347123\pi$
$114$		0			0
$115$	0.333414	+	3.17223i	0.0310911	+	0.295812i
$116$	1.68144	−	1.22164i	0.156118	−	0.113426i
$117$		0			0
$118$	2.63246	+	4.55956i	0.242338	+	0.419741i
$119$	−0.368377	+	0.638048i	−0.0337691	+	0.0584898i
$120$		0			0
$121$	−7.19492	+	7.99077i	−0.654083	+	0.726433i
$122$	−0.892142	+	2.74573i	−0.0807708	+	0.248587i
$123$		0			0
$124$	0.152979	+	2.47901i	0.0137379	+	0.222622i
$125$	11.1409			0.996472
$126$		0			0
$127$	−7.98540	+	8.86868i	−0.708590	+	0.786969i	−0.984719	−	0.174152i	$-0.944282\pi$
$127$	−7.98540	+	8.86868i	−0.708590	+	0.786969i	0.276129	+	0.961121i	$0.410948\pi$
$128$	−10.9817	−	7.97870i	−0.970658	−	0.705224i
$129$		0			0
$130$	−2.19897	−	3.80874i	−0.192863	−	0.334048i
$131$	1.58836	−	15.1122i	0.138775	−	1.32036i	−0.674411	−	0.738357i	$-0.735602\pi$
$131$	1.58836	−	15.1122i	0.138775	−	1.32036i	0.813186	−	0.582004i	$-0.197731\pi$
$132$		0			0
$133$	−0.0418415	−	0.398095i	−0.00362812	−	0.0345193i
$134$	5.46227	+	6.06647i	0.471868	+	0.524063i
$135$		0			0
$136$	−12.5538	+	2.66839i	−1.07648	+	0.228812i
$137$	−12.7214	−	2.70403i	−1.08687	−	0.231021i	−0.370561	−	0.928808i	$-0.620835\pi$
$137$	−12.7214	−	2.70403i	−1.08687	−	0.231021i	−0.716305	+	0.697787i	$0.754168\pi$
$138$		0			0
$139$	3.66301	+	11.2736i	0.310692	+	0.956213i	0.977491	+	0.210975i	$0.0676639\pi$
$139$	3.66301	+	11.2736i	0.310692	+	0.956213i	−0.666799	+	0.745238i	$0.732336\pi$
$140$	0.0264017	+	0.0812560i	0.00223135	+	0.00686738i
$141$		0			0
$142$	8.67283	+	1.84347i	0.727808	+	0.154700i
$143$	−0.996495	+	0.211812i	−0.0833311	+	0.0177126i
$144$		0			0
$145$	4.27980	+	4.75319i	0.355418	+	0.394731i
$146$	−1.81475	−	17.2662i	−0.150190	−	1.42896i
$147$		0			0
$148$	0.196327	−	1.86793i	0.0161380	−	0.153543i
$149$	−4.75175	−	8.23028i	−0.389279	−	0.674251i	0.603074	−	0.797685i	$-0.293942\pi$
$149$	−4.75175	−	8.23028i	−0.389279	−	0.674251i	−0.992353	+	0.123435i	$0.960609\pi$
$150$		0			0
$151$	−16.8619	−	12.2509i	−1.37220	−	0.996962i	−0.997562	−	0.0697917i	$-0.977767\pi$
$151$	−16.8619	−	12.2509i	−1.37220	−	0.996962i	−0.374639	−	0.927171i	$-0.622233\pi$
$152$	4.66585	−	5.18195i	0.378450	−	0.420312i
$153$		0			0
$154$	0.108522			0.00874497
$155$	−7.53797	+	1.26565i	−0.605465	+	0.101659i
$156$		0			0
$157$	4.36962	−	13.4483i	0.348733	−	1.07329i	−0.610821	−	0.791768i	$-0.709161\pi$
$157$	4.36962	−	13.4483i	0.348733	−	1.07329i	0.959555	−	0.281522i	$-0.0908393\pi$
$158$	5.90573	−	6.55898i	0.469835	−	0.521804i
$159$		0			0
$160$	−1.70195	+	2.94786i	−0.134551	+	0.233049i
$161$	0.162078	+	0.280727i	0.0127735	+	0.0221244i
$162$		0			0
$163$	10.9101	−	7.92663i	0.854543	−	0.620862i	−0.0718519	−	0.997415i	$-0.522891\pi$
$163$	10.9101	−	7.92663i	0.854543	−	0.620862i	0.926395	+	0.376554i	$0.122891\pi$
$164$	−0.501859	−	4.77487i	−0.0391886	−	0.372854i
$165$		0			0
$166$	3.03964	−	1.35334i	0.235922	−	0.105039i
$167$	−6.00450	+	1.27630i	−0.464642	+	0.0987628i	−0.434283	−	0.900776i	$-0.642998\pi$
$167$	−6.00450	+	1.27630i	−0.464642	+	0.0987628i	−0.0303590	+	0.999539i	$0.509665\pi$
$168$		0			0
$169$	−8.04311	−	3.58102i	−0.618701	−	0.275463i
$170$	3.50378	+	10.7835i	0.268728	+	0.827059i
$171$		0			0
$172$	5.12034	+	2.27972i	0.390422	+	0.173827i
$173$	17.7280	+	3.76821i	1.34784	+	0.286492i	0.824610	−	0.565702i	$-0.191395\pi$
$173$	17.7280	+	3.76821i	1.34784	+	0.286492i	0.523227	+	0.852193i	$0.324728\pi$
$174$		0			0
$175$	0.397061	−	0.176783i	0.0300150	−	0.0133636i
$176$	1.56187	+	1.73464i	0.117731	+	0.130753i
$177$		0			0
$178$	−3.07211	+	2.23202i	−0.230265	+	0.167297i
$179$	−0.0867375	+	0.825252i	−0.00648306	+	0.0616822i	−0.997285	−	0.0736371i	$-0.976539\pi$
$179$	−0.0867375	+	0.825252i	−0.00648306	+	0.0616822i	0.990802	+	0.135319i	$0.0432060\pi$
$180$		0			0
$181$	7.29687	−	12.6386i	0.542372	−	0.939416i	−0.456395	−	0.889777i	$-0.650860\pi$
$181$	7.29687	−	12.6386i	0.542372	−	0.939416i	0.998767	−	0.0496389i	$-0.0158071\pi$
$182$	−0.361587	−	0.262708i	−0.0268026	−	0.0194732i
$183$		0			0
$184$	−1.74495	+	5.37041i	−0.128640	+	0.395912i
$185$	5.78008			0.424960
$186$		0			0
$187$	2.62649			0.192068
$188$	1.46487	−	4.50841i	0.106837	−	0.328810i
$189$		0			0
$190$	−4.98382	−	3.62096i	−0.361564	−	0.262692i
$191$	−4.26036	+	7.37916i	−0.308269	+	0.533937i	−0.977984	−	0.208681i	$-0.933083\pi$
$191$	−4.26036	+	7.37916i	−0.308269	+	0.533937i	0.669715	+	0.742618i	$0.266416\pi$
$192$		0			0
$193$	1.71263	−	16.2946i	0.123278	−	1.17291i	−0.741569	−	0.670876i	$-0.765918\pi$
$193$	1.71263	−	16.2946i	0.123278	−	1.17291i	0.864847	−	0.502035i	$-0.167415\pi$
$194$	−10.7080	+	7.77984i	−0.768792	+	0.558560i
$195$		0			0
$196$	−2.08364	−	2.31412i	−0.148831	−	0.165294i
$197$	22.2581	−	9.90994i	1.58582	−	0.706054i	0.590905	−	0.806741i	$-0.298771\pi$
$197$	22.2581	−	9.90994i	1.58582	−	0.706054i	0.994918	+	0.100687i	$0.0321040\pi$
$198$		0			0
$199$	20.3923	+	4.33452i	1.44557	+	0.307266i	0.862873	−	0.505421i	$-0.168663\pi$
$199$	20.3923	+	4.33452i	1.44557	+	0.307266i	0.582700	+	0.812687i	$0.301996\pi$
$200$	6.91679	+	3.07955i	0.489091	+	0.217757i
$201$		0			0
$202$	2.13160	+	6.56038i	0.149979	+	0.461587i
$203$	0.593809	+	0.264381i	0.0416772	+	0.0185559i
$204$		0			0
$205$	14.4524	−	3.07195i	1.00940	−	0.214554i
$206$	−26.3048	+	11.7116i	−1.83274	+	0.815988i
$207$		0			0
$208$	−1.00486	−	9.56060i	−0.0696745	−	0.662908i
$209$	−1.15447	+	0.838772i	−0.0798564	+	0.0580191i
$210$		0			0
$211$	7.16781	+	12.4150i	0.493452	+	0.854684i	0.999972	−	0.00754431i	$-0.00240145\pi$
$211$	7.16781	+	12.4150i	0.493452	+	0.854684i	−0.506519	+	0.862229i	$0.669068\pi$
$212$	−2.19541	+	3.80256i	−0.150781	+	0.261161i
$213$		0			0
$214$	−11.9690	+	13.2929i	−0.818181	+	0.908682i
$215$	−5.33014	+	16.4045i	−0.363513	+	1.11878i
$216$		0			0
$217$	−0.647509	+	0.429085i	−0.0439558	+	0.0291282i
$218$	−0.134512			−0.00911028
$219$		0			0
$220$	0.203804	−	0.226347i	0.0137404	−	0.0152603i
$221$	−8.75122	−	6.35813i	−0.588671	−	0.427694i
$222$		0			0
$223$	−4.72798	−	8.18911i	−0.316609	−	0.548383i	0.663169	−	0.748470i	$-0.269211\pi$
$223$	−4.72798	−	8.18911i	−0.316609	−	0.548383i	−0.979778	+	0.200086i	$0.935878\pi$
$224$	−0.0361589	+	0.344029i	−0.00241597	+	0.0229864i
$225$		0			0
$226$	−0.213263	−	2.02906i	−0.0141861	−	0.134971i
$227$	0.494316	+	0.548994i	0.0328089	+	0.0364380i	0.759326	−	0.650710i	$-0.225529\pi$
$227$	0.494316	+	0.548994i	0.0328089	+	0.0364380i	−0.726517	+	0.687148i	$0.758862\pi$
$228$		0			0
$229$	11.7961	−	2.50734i	0.779509	−	0.165690i	0.199061	−	0.979987i	$-0.436211\pi$
$229$	11.7961	−	2.50734i	0.779509	−	0.165690i	0.580448	+	0.814297i	$0.302877\pi$
$230$	4.87967	+	1.03721i	0.321756	+	0.0683913i
$231$		0			0
$232$	3.49901	+	10.7689i	0.229722	+	0.707010i
$233$	4.31177	+	13.2702i	0.282473	+	0.869363i	0.987145	+	0.159829i	$0.0510944\pi$
$233$	4.31177	+	13.2702i	0.282473	+	0.869363i	−0.704672	+	0.709534i	$0.748906\pi$
$234$		0			0
$235$	14.2695	+	3.03308i	0.930841	+	0.197856i
$236$	1.46887	−	0.312218i	0.0956152	−	0.0203236i
$237$		0			0
$238$	0.771028	+	0.856313i	0.0499783	+	0.0555065i
$239$	−1.73116	−	16.4708i	−0.111979	−	1.06541i	−0.895810	−	0.444436i	$-0.853404\pi$
$239$	−1.73116	−	16.4708i	−0.111979	−	1.06541i	0.783831	−	0.620974i	$-0.213263\pi$
$240$		0			0
$241$	−2.60571	+	24.7917i	−0.167848	+	1.59697i	0.508945	+	0.860799i	$0.330036\pi$
$241$	−2.60571	+	24.7917i	−0.167848	+	1.59697i	−0.676794	+	0.736173i	$0.736631\pi$
$242$	8.40855	+	14.5640i	0.540522	+	0.936212i
$243$		0			0
$244$	0.666187	+	0.484013i	0.0426483	+	0.0309858i
$245$	6.41225	−	7.12152i	0.409664	−	0.454978i
$246$		0			0
$247$	5.87707			0.373949
$248$	−13.1022	−	3.38085i	−0.831993	−	0.214684i
$249$		0			0
$250$	5.38442	−	16.5715i	0.340540	−	1.04808i
$251$	−8.08147	+	8.97538i	−0.510098	+	0.566521i	−0.942092	−	0.335355i	$-0.891144\pi$
$251$	−8.08147	+	8.97538i	−0.510098	+	0.566521i	0.431994	+	0.901877i	$0.357810\pi$
$252$		0			0
$253$	0.577799	−	1.00078i	0.0363259	−	0.0629183i
$254$	9.33237	+	16.1641i	0.585565	+	1.01423i
$255$		0			0
$256$	−8.26261	+	6.00314i	−0.516413	+	0.375196i
$257$	−3.18111	−	30.2663i	−0.198432	−	1.88796i	−0.412229	−	0.911080i	$-0.635250\pi$
$257$	−3.18111	−	30.2663i	−0.198432	−	1.88796i	0.213797	−	0.976878i	$-0.431417\pi$
$258$		0			0
$259$	0.536622	−	0.238920i	0.0333441	−	0.0148457i
$260$	−1.22699	+	0.260805i	−0.0760947	+	0.0161744i
$261$		0			0
$262$	−21.7110	−	9.66637i	−1.34131	−	0.597190i
$263$	−0.576251	−	1.77352i	−0.0355332	−	0.109360i	0.931717	−	0.363186i	$-0.118311\pi$
$263$	−0.576251	−	1.77352i	−0.0355332	−	0.109360i	−0.967250	+	0.253826i	$0.918311\pi$
$264$		0			0
$265$	−12.3442	−	5.49599i	−0.758298	−	0.337616i
$266$	−0.612369	−	0.130163i	−0.0375468	−	0.00798081i
$267$		0			0
$268$	2.12706	−	0.947027i	0.129931	−	0.0578489i
$269$	10.4997	+	11.6610i	0.640175	+	0.710986i	0.972689	−	0.232112i	$-0.0745636\pi$
$269$	10.4997	+	11.6610i	0.640175	+	0.710986i	−0.332514	+	0.943098i	$0.607897\pi$
$270$		0			0
$271$	−11.6824	+	8.48774i	−0.709654	+	0.515594i	−0.883062	−	0.469256i	$-0.844522\pi$
$271$	−11.6824	+	8.48774i	−0.709654	+	0.515594i	0.173408	+	0.984850i	$0.444522\pi$
$272$	−2.59066	+	24.6485i	−0.157082	+	1.49453i
$273$		0			0
$274$	−10.1704	+	17.6157i	−0.614417	+	1.06420i
$275$	−1.25354	−	0.910749i	−0.0755912	−	0.0549202i
$276$		0			0
$277$	−4.39178	+	13.5165i	−0.263876	+	0.812128i	0.728074	+	0.685499i	$0.240416\pi$
$277$	−4.39178	+	13.5165i	−0.263876	+	0.812128i	−0.991950	+	0.126629i	$0.959584\pi$
$278$	18.5392			1.11191
$279$		0			0
$280$	−0.465466			−0.0278169
$281$	3.98126	−	12.2531i	0.237502	−	0.730956i	−0.759278	−	0.650767i	$-0.774448\pi$
$281$	3.98126	−	12.2531i	0.237502	−	0.730956i	0.996780	−	0.0801892i	$-0.0255524\pi$
$282$		0			0
$283$	−9.73288	−	7.07135i	−0.578560	−	0.420348i	0.259645	−	0.965704i	$-0.416395\pi$
$283$	−9.73288	−	7.07135i	−0.578560	−	0.420348i	−0.838205	+	0.545356i	$0.816395\pi$
$284$	1.26448	−	2.19015i	0.0750333	−	0.129961i
$285$		0			0
$286$	−0.166549	+	1.58461i	−0.00984824	+	0.0936997i
$287$	1.21478	−	0.882588i	0.0717061	−	0.0520975i
$288$		0			0
$289$	7.28541	+	8.09127i	0.428554	+	0.475957i
$290$	9.13858	−	4.06876i	0.536636	−	0.238926i
$291$		0			0
$292$	−4.84366	−	1.02955i	−0.283454	−	0.0602499i
$293$	25.1760	+	11.2091i	1.47080	+	0.654841i	0.976709	−	0.214571i	$-0.0688352\pi$
$293$	25.1760	+	11.2091i	1.47080	+	0.654841i	0.494089	+	0.869412i	$0.335502\pi$
$294$		0			0
$295$	1.42807	+	4.39514i	0.0831453	+	0.255895i
$296$	9.34793	+	4.16197i	0.543337	+	0.241909i
$297$		0			0
$298$	−14.5387	+	3.09029i	−0.842202	+	0.179016i
$299$	−4.34783	+	1.93578i	−0.251441	+	0.111949i
$300$		0			0
$301$	0.183229	+	1.74331i	0.0105612	+	0.100483i
$302$	−26.3720	+	19.1604i	−1.51754	+	1.10255i
$303$		0			0
$304$	−6.73279	−	11.6615i	−0.386152	−	0.668835i
$305$	−1.26706	+	2.19461i	−0.0725515	+	0.125663i
$306$		0			0
$307$	−12.6569	+	14.0569i	−0.722366	+	0.802269i	−0.986767	−	0.162144i	$-0.948159\pi$
$307$	−12.6569	+	14.0569i	−0.722366	+	0.802269i	0.264401	+	0.964413i	$0.414826\pi$
$308$	0.00956507	−	0.0294382i	0.000545020	−	0.00167740i
$309$		0			0
$310$	−1.76053	+	11.8241i	−0.0999914	+	0.671561i
$311$	−1.66050			−0.0941583			−0.0470791	−	0.998891i	$-0.514991\pi$
$311$	−1.66050			−0.0941583			−0.0470791	+	0.998891i	$0.514991\pi$
$312$		0			0
$313$	8.35955	−	9.28422i	0.472510	−	0.524775i	−0.459027	−	0.888422i	$-0.651802\pi$
$313$	8.35955	−	9.28422i	0.472510	−	0.524775i	0.931537	+	0.363647i	$0.118469\pi$
$314$	−17.8918	−	12.9992i	−1.00969	−	0.733586i
$315$		0			0
$316$	−1.25869	−	2.18012i	−0.0708069	−	0.122641i
$317$	−1.31233	+	12.4860i	−0.0737080	+	0.701285i	0.893804	+	0.448458i	$0.148027\pi$
$317$	−1.31233	+	12.4860i	−0.0737080	+	0.701285i	−0.967512	+	0.252826i	$0.918640\pi$
$318$		0			0
$319$	−0.242216	−	2.30453i	−0.0135615	−	0.129029i
$320$	−5.05998	−	5.61968i	−0.282861	−	0.314150i
$321$		0			0
$322$	0.495901	−	0.105407i	0.0276355	−	0.00587410i
$323$	−14.8207	−	3.15024i	−0.824648	−	0.175284i
$324$		0			0
$325$	1.97196	+	6.06907i	0.109385	+	0.336651i
$326$	−6.51761	−	20.0592i	−0.360977	−	1.11097i
$327$		0			0
$328$	25.5853	+	5.43832i	1.41271	+	0.300281i
$329$	1.45015	−	0.308240i	0.0799496	−	0.0169938i
$330$		0			0
$331$	7.22556	+	8.02480i	0.397153	+	0.441083i	0.908242	−	0.418445i	$-0.137425\pi$
$331$	7.22556	+	8.02480i	0.397153	+	0.441083i	−0.511089	+	0.859528i	$0.670758\pi$
$332$	−0.0992005	−	0.943830i	−0.00544433	−	0.0517994i
$333$		0			0
$334$	−1.00356	+	9.54824i	−0.0549124	+	0.522457i
$335$	3.58267	+	6.20537i	0.195742	+	0.339036i
$336$		0			0
$337$	−25.4506	−	18.4910i	−1.38638	−	1.00727i	−0.996251	−	0.0865078i	$-0.972429\pi$
$337$	−25.4506	−	18.4910i	−1.38638	−	1.00727i	−0.390132	−	0.920759i	$-0.627571\pi$
$338$	−9.21385	+	10.2330i	−0.501167	+	0.556603i
$339$		0			0
$340$	3.23401			0.175389
$341$	2.47889	+	1.23424i	0.134239	+	0.0668380i
$342$		0			0
$343$	0.602728	−	1.85501i	0.0325443	−	0.100161i
$344$	−20.4324	+	22.6924i	−1.10164	+	1.22349i
$345$		0			0
$346$	14.1730	−	24.5484i	0.761946	−	1.31973i
$347$	−9.98629	−	17.2968i	−0.536092	−	0.928538i	−0.999110	−	0.0421894i	$-0.986567\pi$
$347$	−9.98629	−	17.2968i	−0.536092	−	0.928538i	0.463018	−	0.886349i	$-0.346767\pi$
$348$		0			0
$349$	8.84728	−	6.42793i	0.473584	−	0.344079i	−0.325252	−	0.945627i	$-0.605449\pi$
$349$	8.84728	−	6.42793i	0.473584	−	0.344079i	0.798836	+	0.601548i	$0.205449\pi$
$350$	−0.0710556	−	0.676049i	−0.00379808	−	0.0361363i
$351$		0			0
$352$	1.12658	−	0.501587i	0.0600471	−	0.0267347i
$353$	−1.28378	+	0.272876i	−0.0683289	+	0.0145237i	−0.241949	−	0.970289i	$-0.577787\pi$
$353$	−1.28378	+	0.272876i	−0.0683289	+	0.0145237i	0.173620	+	0.984813i	$0.444453\pi$
$354$		0			0
$355$	7.10986	+	3.16551i	0.377352	+	0.168008i
$356$	0.334695	+	1.03008i	0.0177388	+	0.0545944i
$357$		0			0
$358$	1.18560	+	0.527864i	0.0626610	+	0.0278985i
$359$	21.3700	+	4.54234i	1.12787	+	0.239735i	0.733813	−	0.679352i	$-0.237739\pi$
$359$	21.3700	+	4.54234i	1.12787	+	0.239735i	0.394054	+	0.919087i	$0.371072\pi$
$360$		0			0
$361$	−9.83688	+	4.37966i	−0.517731	+	0.230509i
$362$	−15.2726	−	16.9620i	−0.802712	−	0.891502i
$363$		0			0
$364$	−0.103133	+	0.0749308i	−0.00540566	+	0.00392744i
$365$	1.59291	−	15.1555i	0.0833767	−	0.793276i
$366$		0			0
$367$	12.1555	−	21.0539i	0.634512	−	1.09901i	−0.352107	−	0.935960i	$-0.614535\pi$
$367$	12.1555	−	21.0539i	0.634512	−	1.09901i	0.986618	−	0.163047i	$-0.0521321\pi$
$368$	8.82194	+	6.40952i	0.459876	+	0.334119i
$369$		0			0
$370$	2.79352	−	8.59758i	0.145228	−	0.446967i
$371$	−1.37321			−0.0712935
$372$		0			0
$373$	−14.4522			−0.748307			−0.374153	−	0.927367i	$-0.622067\pi$
$373$	−14.4522			−0.748307			−0.374153	+	0.927367i	$0.622067\pi$
$374$	1.26939	−	3.90677i	0.0656384	−	0.202014i
$375$		0			0
$376$	20.8936	+	15.1801i	1.07751	+	0.782855i
$377$	−4.77172	+	8.26486i	−0.245756	+	0.425662i
$378$		0			0
$379$	0.513919	−	4.88961i	0.0263983	−	0.251163i	−0.973362	−	0.229273i	$-0.926365\pi$
$379$	0.513919	−	4.88961i	0.0263983	−	0.251163i	0.999760	−	0.0218895i	$-0.00696821\pi$
$380$	−1.42151	+	1.03279i	−0.0729218	+	0.0529808i
$381$		0			0
$382$	8.91709	+	9.90343i	0.456238	+	0.506704i
$383$	13.8812	−	6.18030i	0.709295	−	0.315798i	−0.0201893	−	0.999796i	$-0.506427\pi$
$383$	13.8812	−	6.18030i	0.709295	−	0.315798i	0.729484	+	0.683998i	$0.239760\pi$
$384$		0			0
$385$	0.0931746	+	0.0198049i	0.00474862	+	0.00100935i
$386$	−23.4097	−	10.4227i	−1.19152	−	0.530500i
$387$		0			0
$388$	1.16660	+	3.59042i	0.0592251	+	0.182276i
$389$	25.5538	+	11.3773i	1.29563	+	0.576850i	0.934598	−	0.355705i	$-0.115759\pi$
$389$	25.5538	+	11.3773i	1.29563	+	0.576850i	0.361028	+	0.932555i	$0.382426\pi$
$390$		0			0
$391$	12.0019	−	2.55109i	0.606964	−	0.129014i
$392$	15.4982	−	6.90024i	0.782777	−	0.348515i
$393$		0			0
$394$	−3.98317	−	37.8973i	−0.200669	−	1.90924i
$395$	6.26751	−	4.55361i	0.315352	−	0.229117i
$396$		0			0
$397$	−1.44269	−	2.49881i	−0.0724064	−	0.125412i	0.827549	−	0.561393i	$-0.189735\pi$
$397$	−1.44269	−	2.49881i	−0.0724064	−	0.125412i	−0.899955	+	0.435982i	$0.856401\pi$
$398$	16.3030	−	28.2377i	0.817197	−	1.41543i
$399$		0			0
$400$	9.78343	−	10.8656i	0.489171	−	0.543280i
$401$	−6.36782	+	19.5981i	−0.317994	+	0.978684i	0.656511	+	0.754316i	$0.272032\pi$
$401$	−6.36782	+	19.5981i	−0.317994	+	0.978684i	−0.974505	+	0.224367i	$0.927968\pi$
$402$		0			0
$403$	−5.27162	−	10.1132i	−0.262598	−	0.503776i
$404$	1.96748			0.0978856
$405$		0			0
$406$	0.680242	−	0.755486i	0.0337599	−	0.0374941i
$407$	−1.69414	−	1.23086i	−0.0839752	−	0.0610115i
$408$		0			0
$409$	−8.02676	−	13.9028i	−0.396898	−	0.687447i	0.596444	−	0.802655i	$-0.296580\pi$
$409$	−8.02676	−	13.9028i	−0.396898	−	0.687447i	−0.993341	+	0.115208i	$0.963247\pi$
$410$	2.41549	−	22.9819i	0.119293	−	1.13499i
$411$		0			0
$412$	0.858471	+	8.16781i	0.0422938	+	0.402399i
$413$	0.314255	+	0.349015i	0.0154635	+	0.0171739i
$414$		0			0
$415$	2.85674	−	0.607220i	0.140232	−	0.0298072i
$416$	−4.96790	−	1.05596i	−0.243572	−	0.0517727i
$417$		0			0
$418$	0.689674	+	2.12260i	0.0337331	+	0.103820i
$419$	−1.95101	−	6.00458i	−0.0953130	−	0.293343i	0.892022	−	0.451992i	$-0.149286\pi$
$419$	−1.95101	−	6.00458i	−0.0953130	−	0.293343i	−0.987335	+	0.158649i	$0.949286\pi$
$420$		0			0
$421$	−4.52846	−	0.962554i	−0.220704	−	0.0469120i	0.0962325	−	0.995359i	$-0.469321\pi$
$421$	−4.52846	−	0.962554i	−0.220704	−	0.0469120i	−0.316936	+	0.948447i	$0.602654\pi$
$422$	21.9309	−	4.66156i	1.06758	−	0.226921i
$423$		0			0
$424$	−16.0064	−	17.7770i	−0.777341	−	0.863325i
$425$	−1.71971	−	16.3619i	−0.0834181	−	0.793670i
$426$		0			0
$427$	−0.0269194	+	0.256121i	−0.00130272	+	0.0123946i
$428$	2.55095	+	4.41838i	0.123305	+	0.213570i
$429$		0			0
$430$	21.8248	+	15.8566i	1.05249	+	0.764675i
$431$	−12.7448	+	14.1545i	−0.613895	+	0.681799i	−0.967289	−	0.253675i	$-0.918361\pi$
$431$	−12.7448	+	14.1545i	−0.613895	+	0.681799i	0.353395	+	0.935474i	$0.385027\pi$
$432$		0			0
$433$	11.3696			0.546390			0.273195	−	0.961959i	$-0.411920\pi$
$433$	11.3696			0.546390			0.273195	+	0.961959i	$0.411920\pi$
$434$	0.325300	+	1.17052i	0.0156149	+	0.0561865i
$435$		0			0
$436$	−0.0118558	+	0.0364882i	−0.000567787	+	0.00174747i
$437$	−4.46075	+	4.95416i	−0.213386	+	0.236990i
$438$		0			0
$439$	−2.56265	+	4.43864i	−0.122309	+	0.211845i	−0.920678	−	0.390324i	$-0.872363\pi$
$439$	−2.56265	+	4.43864i	−0.122309	+	0.211845i	0.798369	+	0.602168i	$0.205696\pi$
$440$	0.829679	+	1.43705i	0.0395534	+	0.0685085i
$441$		0			0
$442$	−13.6869	+	9.94411i	−0.651019	+	0.472993i
$443$	−3.16748	−	30.1366i	−0.150492	−	1.43183i	−0.765563	−	0.643361i	$-0.777539\pi$
$443$	−3.16748	−	30.1366i	−0.150492	−	1.43183i	0.615071	−	0.788471i	$-0.289127\pi$
$444$		0			0
$445$	−3.04498	+	1.35571i	−0.144346	+	0.0642669i
$446$	−14.4659	+	3.07483i	−0.684982	+	0.145597i
$447$		0			0
$448$	−0.702057	−	0.312576i	−0.0331691	−	0.0147678i
$449$	−2.08780	−	6.42560i	−0.0985296	−	0.303243i	0.889628	−	0.456686i	$-0.150964\pi$
$449$	−2.08780	−	6.42560i	−0.0985296	−	0.303243i	−0.988157	+	0.153443i	$0.950964\pi$
$450$		0			0
$451$	−4.89014	−	2.17723i	−0.230268	−	0.102522i
$452$	−0.569210	−	0.120989i	−0.0267734	−	0.00569086i
$453$		0			0
$454$	1.05551	−	0.469941i	0.0495373	−	0.0220554i
$455$	−0.262506	−	0.291543i	−0.0123065	−	0.0136677i
$456$		0			0
$457$	−2.67195	+	1.94128i	−0.124988	+	0.0908094i	−0.648523	−	0.761195i	$-0.724613\pi$
$457$	−2.67195	+	1.94128i	−0.124988	+	0.0908094i	0.523535	+	0.852004i	$0.324613\pi$
$458$	1.97154	−	18.7579i	0.0921239	−	0.876501i
$459$		0			0
$460$	0.711447	−	1.23226i	0.0331714	−	0.0574546i
$461$	8.06223	+	5.85755i	0.375495	+	0.272813i	0.759486	−	0.650524i	$-0.225450\pi$
$461$	8.06223	+	5.85755i	0.375495	+	0.272813i	−0.383991	+	0.923337i	$0.625450\pi$
$462$		0			0
$463$	−8.08602	+	24.8862i	−0.375789	+	1.15656i	0.567156	+	0.823611i	$0.308044\pi$
$463$	−8.08602	+	24.8862i	−0.375789	+	1.15656i	−0.942945	+	0.332949i	$0.891956\pi$
$464$	21.8660			1.01510
$465$		0			0
$466$	21.8227			1.01092
$467$	8.41461	−	25.8975i	0.389382	−	1.19839i	−0.543869	−	0.839170i	$-0.683041\pi$
$467$	8.41461	−	25.8975i	0.389382	−	1.19839i	0.933251	−	0.359224i	$-0.116959\pi$
$468$		0			0
$469$	0.589114	+	0.428016i	0.0272027	+	0.0197639i
$470$	11.4081	−	19.7593i	0.526214	−	0.911430i
$471$		0			0
$472$	−0.855170	+	8.13640i	−0.0393624	+	0.374508i
$473$	5.05558	−	3.67309i	0.232456	−	0.168889i
$474$		0			0
$475$	5.98110	+	6.64268i	0.274432	+	0.304787i
$476$	0.300245	−	0.133678i	0.0137617	−	0.00612711i
$477$		0			0
$478$	−25.3362	−	5.38538i	−1.15885	−	0.246322i
$479$	−28.6406	−	12.7516i	−1.30862	−	0.582637i	−0.370467	−	0.928846i	$-0.620802\pi$
$479$	−28.6406	−	12.7516i	−1.30862	−	0.582637i	−0.938158	+	0.346209i	$0.887469\pi$
$480$		0			0
$481$	2.66507	+	8.20224i	0.121517	+	0.373990i
$482$	35.6170	+	15.8577i	1.62231	+	0.722300i
$483$		0			0
$484$	4.69183	−	0.997279i	0.213265	−	0.0453309i
$485$	−10.6135	+	4.72542i	−0.481932	+	0.214570i
$486$		0			0
$487$	−2.87151	−	27.3206i	−0.130121	−	1.23801i	−0.843458	−	0.537194i	$-0.819484\pi$
$487$	−2.87151	−	27.3206i	−0.130121	−	1.23801i	0.713338	−	0.700820i	$-0.247183\pi$
$488$	−3.62940	+	2.63692i	−0.164295	+	0.119368i
$489$		0			0
$490$	−7.49386	−	12.9798i	−0.338538	−	0.586365i
$491$	−17.7689	+	30.7766i	−0.801898	+	1.38893i	0.116467	+	0.993195i	$0.462843\pi$
$491$	−17.7689	+	30.7766i	−0.801898	+	1.38893i	−0.918365	+	0.395734i	$0.870490\pi$
$492$		0			0
$493$	16.4634	−	18.2845i	0.741475	−	0.823492i
$494$	2.84040	−	8.74185i	0.127796	−	0.393315i
$495$		0			0
$496$	−14.0279	+	22.0459i	−0.629872	+	0.989891i
$497$	0.790925			0.0354778
$498$		0			0
$499$	−11.7931	+	13.0975i	−0.527930	+	0.586326i	−0.946841	−	0.321701i	$-0.895745\pi$
$499$	−11.7931	+	13.0975i	−0.527930	+	0.586326i	0.418911	+	0.908027i	$0.362412\pi$
$500$	−4.02069	−	2.92120i	−0.179811	−	0.130640i
$501$		0			0
$502$	9.44465	+	16.3586i	0.421535	+	0.730120i
$503$	−0.830960	+	7.90606i	−0.0370507	+	0.352514i	0.960253	+	0.279131i	$0.0900462\pi$
$503$	−0.830960	+	7.90606i	−0.0370507	+	0.352514i	−0.997304	+	0.0733831i	$0.976620\pi$
$504$		0			0
$505$	0.632895	+	6.02160i	0.0281635	+	0.267958i
$506$	−1.20935	−	1.34312i	−0.0537624	−	0.0597092i
$507$		0			0
$508$	5.20731	−	1.10685i	0.231037	−	0.0491084i
$509$	−9.70423	−	2.06270i	−0.430132	−	0.0914274i	−0.0122423	−	0.999925i	$-0.503897\pi$
$509$	−9.70423	−	2.06270i	−0.430132	−	0.0914274i	−0.417890	+	0.908498i	$0.637230\pi$
$510$		0			0
$511$	−0.478568	−	1.47288i	−0.0211706	−	0.0651564i
$512$	−3.45327	−	10.6281i	−0.152614	−	0.469699i
$513$		0			0
$514$	−46.5570	−	9.89600i	−2.05354	−	0.436494i
$515$	−24.7220	+	5.25482i	−1.08938	+	0.231555i
$516$		0			0
$517$	−3.53649	−	3.92767i	−0.155535	−	0.172739i
$518$	−0.0960305	−	0.913669i	−0.00421934	−	0.0401443i
$519$		0			0
$520$	0.714349	−	6.79658i	0.0313263	−	0.298050i
$521$	−4.30843	−	7.46242i	−0.188756	−	0.326935i	0.756080	−	0.654479i	$-0.227112\pi$
$521$	−4.30843	−	7.46242i	−0.188756	−	0.326935i	−0.944836	+	0.327545i	$0.893779\pi$
$522$		0			0
$523$	21.3660	+	15.5233i	0.934269	+	0.678786i	0.947034	−	0.321132i	$-0.104063\pi$
$523$	21.3660	+	15.5233i	0.934269	+	0.678786i	−0.0127651	+	0.999919i	$0.504063\pi$
$524$	−4.53573	+	5.03744i	−0.198144	+	0.220062i
$525$		0			0
$526$	−2.91653			−0.127167
$527$	7.87299	+	28.3291i	0.342953	+	1.23404i
$528$		0			0
$529$	−5.43914	+	16.7400i	−0.236485	+	0.727824i
$530$	−14.1410	+	15.7052i	−0.614245	+	0.682189i
$531$		0			0
$532$	−0.0892824	+	0.154642i	−0.00387088	+	0.00670457i
$533$	11.0229	+	19.0923i	0.477456	+	0.826979i
$534$		0			0
$535$	−12.7022	+	9.22866i	−0.549162	+	0.398990i
$536$	1.32594	+	12.6154i	0.0572717	+	0.544904i
$537$		0			0
$538$	22.4197	−	9.98191i	0.966583	−	0.430351i
$539$	−3.39594	+	0.721830i	−0.146274	+	0.0310914i
$540$		0			0
$541$	13.0275	+	5.80021i	0.560095	+	0.249370i	0.667202	−	0.744877i	$-0.267492\pi$
$541$	13.0275	+	5.80021i	0.560095	+	0.249370i	−0.107106	+	0.994248i	$0.534159\pi$
$542$	6.97898	+	21.4791i	0.299773	+	0.922606i
$543$		0			0
$544$	11.9620	+	5.32582i	0.512866	+	0.228343i
$545$	−0.115489	−	0.0245478i	−0.00494698	−	0.00105151i
$546$		0			0
$547$	−15.7101	+	6.99458i	−0.671714	+	0.299067i	−0.714109	−	0.700034i	$-0.753168\pi$
$547$	−15.7101	+	6.99458i	−0.671714	+	0.299067i	0.0423947	+	0.999101i	$0.486501\pi$
$548$	3.88209	+	4.31150i	0.165835	+	0.184178i
$549$		0			0
$550$	−1.96053	+	1.42441i	−0.0835973	+	0.0607370i
$551$	−1.39731	+	13.2945i	−0.0595275	+	0.566367i
$552$		0			0
$553$	0.393651	−	0.681824i	0.0167398	−	0.0289941i
$554$	17.9826	+	13.0651i	0.764006	+	0.555083i
$555$		0			0
$556$	1.63403	−	5.02904i	0.0692984	−	0.213279i
$557$	−0.321933			−0.0136407			−0.00682037	−	0.999977i	$-0.502171\pi$
$557$	−0.321933			−0.0136407			−0.00682037	+	0.999977i	$0.502171\pi$
$558$		0			0
$559$	−25.7365			−1.08854
$560$	−0.277764	+	0.854870i	−0.0117377	+	0.0361248i
$561$		0			0
$562$	−16.3017	−	11.8439i	−0.687644	−	0.499603i
$563$	7.02126	−	12.1612i	0.295911	−	0.512533i	−0.679285	−	0.733874i	$-0.737710\pi$
$563$	7.02126	−	12.1612i	0.295911	−	0.512533i	0.975196	+	0.221341i	$0.0710435\pi$
$564$		0			0
$565$	0.187193	−	1.78103i	0.00787529	−	0.0749283i
$566$	−15.2222	+	11.0596i	−0.639837	+	0.464869i
$567$		0			0
$568$	9.21920	+	10.2390i	0.386829	+	0.429617i
$569$	−42.8138	+	19.0619i	−1.79485	+	0.799118i	−0.821350	+	0.570424i	$0.806779\pi$
$569$	−42.8138	+	19.0619i	−1.79485	+	0.799118i	−0.973498	+	0.228694i	$0.926554\pi$
$570$		0			0
$571$	−9.18699	−	1.95275i	−0.384464	−	0.0817202i	0.0116254	−	0.999932i	$-0.496299\pi$
$571$	−9.18699	−	1.95275i	−0.384464	−	0.0817202i	−0.396089	+	0.918212i	$0.629633\pi$
$572$	0.415168	+	0.184845i	0.0173590	+	0.00772874i
$573$		0			0
$574$	−0.725701	−	2.23348i	−0.0302902	−	0.0932236i
$575$	−6.61274	−	2.94418i	−0.275770	−	0.122781i
$576$		0			0
$577$	−25.0722	+	5.32925i	−1.04377	+	0.221860i	−0.697730	−	0.716361i	$-0.745806\pi$
$577$	−25.0722	+	5.32925i	−1.04377	+	0.221860i	−0.346038	+	0.938221i	$0.612473\pi$
$578$	15.5564	−	6.92616i	0.647062	−	0.288090i
$579$		0			0
$580$	−0.298243	−	2.83759i	−0.0123839	−	0.117824i
$581$	0.240120	−	0.174458i	0.00996187	−	0.00723772i
$582$		0			0
$583$	2.44771	+	4.23955i	0.101374	+	0.175584i
$584$	13.4889	−	23.3635i	0.558176	−	0.966790i
$585$		0			0
$586$	28.8406	−	32.0307i	1.19139	−	1.32318i
$587$	−3.48995	+	10.7410i	−0.144046	+	0.443327i	−0.996887	−	0.0788429i	$-0.974877\pi$
$587$	−3.48995	+	10.7410i	−0.144046	+	0.443327i	0.852841	+	0.522170i	$0.174877\pi$
$588$		0			0
$589$	−12.5075	−	9.93780i	−0.515363	−	0.409480i
$590$	7.22774			0.297561
$591$		0			0
$592$	13.2221	−	14.6847i	0.543426	−	0.603536i
$593$	−15.4547	−	11.2285i	−0.634647	−	0.461098i	0.223360	−	0.974736i	$-0.428297\pi$
$593$	−15.4547	−	11.2285i	−0.634647	−	0.461098i	−0.858007	+	0.513638i	$0.828297\pi$
$594$		0			0
$595$	0.505712	+	0.875920i	0.0207322	+	0.0359092i
$596$	−0.443141	+	4.21620i	−0.0181517	+	0.172702i
$597$		0			0
$598$	0.778060	+	7.40275i	0.0318172	+	0.302721i
$599$	12.6326	+	14.0299i	0.516155	+	0.573248i	0.943724	−	0.330735i	$-0.107297\pi$
$599$	12.6326	+	14.0299i	0.516155	+	0.573248i	−0.427569	+	0.903983i	$0.640630\pi$
$600$		0			0
$601$	42.2397	−	8.97833i	1.72299	−	0.366234i	0.763032	−	0.646361i	$-0.223710\pi$
$601$	42.2397	−	8.97833i	1.72299	−	0.366234i	0.959963	+	0.280127i	$0.0903767\pi$
$602$	2.68165	+	0.570001i	0.109296	+	0.0232315i
$603$		0			0
$604$	2.87312	+	8.84256i	0.116906	+	0.359799i
$605$	4.56150	+	14.0389i	0.185452	+	0.570761i
$606$		0			0
$607$	−11.2777	−	2.39715i	−0.457747	−	0.0972971i	−0.0267335	−	0.999643i	$-0.508511\pi$
$607$	−11.2777	−	2.39715i	−0.457747	−	0.0972971i	−0.431014	+	0.902345i	$0.641844\pi$
$608$	−6.95869	+	1.47912i	−0.282212	+	0.0599861i
$609$		0			0
$610$	2.65200	+	2.94534i	0.107376	+	0.119253i
$611$	2.27527	+	21.6477i	0.0920474	+	0.875773i
$612$		0			0
$613$	−3.10634	+	29.5548i	−0.125464	+	1.19371i	0.732780	+	0.680466i	$0.238222\pi$
$613$	−3.10634	+	29.5548i	−0.125464	+	1.19371i	−0.858244	+	0.513242i	$0.828444\pi$
$614$	14.7918	+	25.6202i	0.596950	+	1.03395i
$615$		0			0
$616$	0.136428	+	0.0991204i	0.00549682	+	0.00399368i
$617$	−23.9262	+	26.5727i	−0.963232	+	1.06978i	0.0342898	+	0.999412i	$0.489083\pi$
$617$	−23.9262	+	26.5727i	−0.963232	+	1.06978i	−0.997521	+	0.0703650i	$0.977584\pi$
$618$		0			0
$619$	6.97477			0.280340			0.140170	−	0.990127i	$-0.455235\pi$
$619$	6.97477			0.280340			0.140170	+	0.990127i	$0.455235\pi$
$620$	3.05228	+	1.51973i	0.122582	+	0.0610339i
$621$		0			0
$622$	−0.802523	+	2.46991i	−0.0321782	+	0.0990344i
$623$	−0.226657	+	0.251728i	−0.00908083	+	0.0100853i
$624$		0			0
$625$	−0.141303	+	0.244744i	−0.00565211	+	0.00978974i
$626$	−9.76963	−	16.9215i	−0.390473	−	0.676319i
$627$		0			0
$628$	−5.10319	+	3.70768i	−0.203639	+	0.147953i
$629$	−2.32416	−	22.1129i	−0.0926702	−	0.881698i
$630$		0			0
$631$	12.1657	−	5.41651i	0.484308	−	0.215628i	−0.150033	−	0.988681i	$-0.547938\pi$
$631$	12.1657	−	5.41651i	0.484308	−	0.215628i	0.634341	+	0.773053i	$0.281271\pi$
$632$	13.4151	−	2.85146i	0.533623	−	0.113425i
$633$		0			0
$634$	17.9381	+	7.98655i	0.712412	+	0.317186i
$635$	5.06266	+	15.5813i	0.200906	+	0.618324i
$636$		0			0
$637$	13.0624	+	5.81574i	0.517550	+	0.230428i
$638$	−3.54495	−	0.753501i	−0.140346	−	0.0298314i
$639$		0			0
$640$	−17.0237	+	7.57945i	−0.672922	+	0.299604i
$641$	−14.0064	−	15.5557i	−0.553219	−	0.614412i	0.400065	−	0.916487i	$-0.368988\pi$
$641$	−14.0064	−	15.5557i	−0.553219	−	0.614412i	−0.953284	+	0.302074i	$0.902321\pi$
$642$		0			0
$643$	12.1677	−	8.84032i	0.479845	−	0.348628i	−0.321420	−	0.946937i	$-0.604160\pi$
$643$	12.1677	−	8.84032i	0.479845	−	0.348628i	0.801266	+	0.598309i	$0.204160\pi$
$644$	0.0151151	−	0.143811i	0.000595619	−	0.00566694i
$645$		0			0
$646$	−11.8487	+	20.5226i	−0.466182	+	0.807451i
$647$	−14.1105	−	10.2519i	−0.554740	−	0.403043i	0.274790	−	0.961504i	$-0.411392\pi$
$647$	−14.1105	−	10.2519i	−0.554740	−	0.403043i	−0.829530	+	0.558462i	$0.811392\pi$
$648$		0			0
$649$	0.517375	−	1.59232i	0.0203087	−	0.0625039i
$650$	9.98049			0.391467
$651$		0			0
$652$	−6.01580			−0.235597
$653$	−10.6702	+	32.8395i	−0.417558	+	1.28511i	0.492386	+	0.870377i	$0.336125\pi$
$653$	−10.6702	+	32.8395i	−0.417558	+	1.28511i	−0.909943	+	0.414733i	$0.863875\pi$
$654$		0			0
$655$	−16.8765	−	12.2615i	−0.659419	−	0.479096i
$656$	25.2558	−	43.7444i	0.986074	−	1.70793i
$657$		0			0
$658$	0.242371	−	2.30600i	0.00944860	−	0.0898974i
$659$	32.4883	−	23.6041i	1.26556	−	0.919486i	0.266547	−	0.963822i	$-0.414117\pi$
$659$	32.4883	−	23.6041i	1.26556	−	0.919486i	0.999017	+	0.0443364i	$0.0141173\pi$
$660$		0			0
$661$	15.7295	+	17.4694i	0.611807	+	0.679480i	0.966843	−	0.255372i	$-0.0821981\pi$
$661$	15.7295	+	17.4694i	0.611807	+	0.679480i	−0.355036	+	0.934853i	$0.615531\pi$
$662$	15.4286	−	6.86927i	0.599651	−	0.266982i
$663$		0			0
$664$	5.05735	+	1.07497i	0.196263	+	0.0417170i
$665$	−0.502012	−	0.223510i	−0.0194672	−	0.00866734i
$666$		0			0
$667$	−3.34521	−	10.2955i	−0.129527	−	0.398643i
$668$	2.50165	+	1.11380i	0.0967916	+	0.0430944i
$669$		0			0
$670$	10.9617	−	2.32998i	0.423487	−	0.0900150i
$671$	0.838713	−	0.373419i	0.0323781	−	0.0144157i
$672$		0			0
$673$	4.21084	+	40.0634i	0.162316	+	1.54433i	0.707922	+	0.706291i	$0.249633\pi$
$673$	4.21084	+	40.0634i	0.162316	+	1.54433i	−0.545606	+	0.838042i	$0.683701\pi$
$674$	−39.8047	+	28.9198i	−1.53322	+	1.11395i
$675$		0			0
$676$	1.96375	+	3.40132i	0.0755290	+	0.130820i
$677$	4.10013	−	7.10163i	0.157581	−	0.272938i	−0.776415	−	0.630222i	$-0.782964\pi$
$677$	4.10013	−	7.10163i	0.157581	−	0.272938i	0.933996	+	0.357284i	$0.116297\pi$
$678$		0			0
$679$	−0.790027	+	0.877414i	−0.0303185	+	0.0336721i
$680$	−5.44456	+	16.7566i	−0.208789	+	0.642588i
$681$		0			0
$682$	3.03393	−	3.09072i	0.116175	−	0.118350i
$683$	37.6222			1.43957			0.719787	−	0.694195i	$-0.244239\pi$
$683$	37.6222			1.43957			0.719787	+	0.694195i	$0.244239\pi$
$684$		0			0
$685$	−11.9469	+	13.2683i	−0.456466	+	0.506957i
$686$	−2.46793	−	1.79306i	−0.0942260	−	0.0684592i
$687$		0			0
$688$	29.4838	+	51.0674i	1.12406	+	1.94693i
$689$	2.10746	−	20.0512i	0.0802879	−	0.763888i
$690$		0			0
$691$	−5.42149	−	51.5820i	−0.206243	−	1.96227i	−0.265742	−	0.964044i	$-0.585617\pi$
$691$	−5.42149	−	51.5820i	−0.206243	−	1.96227i	0.0594988	−	0.998228i	$-0.481050\pi$
$692$	−5.40991	−	6.00831i	−0.205654	−	0.228402i
$693$		0			0
$694$	−30.5545	+	6.49455i	−1.15983	+	0.246530i
$695$	15.9173	+	3.38334i	0.603779	+	0.128337i
$696$		0			0
$697$	−17.5636	−	54.0553i	−0.665270	−	2.04749i
$698$	−5.28532	−	16.2665i	−0.200052	−	0.615697i
$699$		0			0
$700$	−0.189651	−	0.0403115i	−0.00716813	−	0.00152363i
$701$	−20.3871	+	4.33342i	−0.770011	+	0.163671i	−0.576134	−	0.817355i	$-0.695440\pi$
$701$	−20.3871	+	4.33342i	−0.770011	+	0.163671i	−0.193877	+	0.981026i	$0.562106\pi$
$702$		0			0
$703$	8.08336	+	8.97748i	0.304870	+	0.338592i
$704$	0.286371	+	2.72464i	0.0107930	+	0.102689i
$705$		0			0
$706$	−0.214565	+	2.04145i	−0.00807524	+	0.0768308i
$707$	0.307660	+	0.532884i	0.0115708	+	0.0200412i
$708$		0			0
$709$	8.10799	+	5.89080i	0.304502	+	0.221234i	0.729534	−	0.683945i	$-0.239737\pi$
$709$	8.10799	+	5.89080i	0.304502	+	0.221234i	−0.425032	+	0.905178i	$0.639737\pi$
$710$	8.14476	−	9.04567i	0.305667	−	0.339478i
$711$		0			0
$712$	−5.90073			−0.221139
$713$	12.5263	+	3.23224i	0.469113	+	0.121048i
$714$		0			0
$715$	−0.432179	+	1.33011i	−0.0161626	+	0.0497433i
$716$	0.247689	−	0.275086i	0.00925656	−	0.0102805i
$717$		0			0
$718$	17.0847	−	29.5915i	0.637595	−	1.10435i
$719$	−12.2024	−	21.1352i	−0.455074	−	0.788212i	0.543618	−	0.839333i	$-0.317054\pi$
$719$	−12.2024	−	21.1352i	−0.455074	−	0.788212i	−0.998692	+	0.0511209i	$0.983721\pi$
$720$		0			0
$721$	−2.07798	+	1.50974i	−0.0773879	+	0.0562256i
$722$	1.76035	+	16.7486i	0.0655133	+	0.623318i
$723$		0			0
$724$	−5.94730	+	2.64791i	−0.221030	+	0.0984087i
$725$	−14.1977	+	3.01782i	−0.527290	+	0.112079i
$726$		0			0
$727$	27.4005	+	12.1995i	1.01623	+	0.452454i	0.846132	−	0.532973i	$-0.178925\pi$
$727$	27.4005	+	12.1995i	1.01623	+	0.452454i	0.170097	+	0.985427i	$0.445592\pi$
$728$	−0.214616	−	0.660521i	−0.00795421	−	0.0244805i
$729$		0			0
$730$	−21.7732	−	9.69407i	−0.805864	−	0.358794i
$731$	64.9019	+	13.7953i	2.40049	+	0.510239i
$732$		0			0
$733$	−38.0211	+	16.9281i	−1.40434	+	0.625254i	−0.962362	−	0.271771i	$-0.912391\pi$
$733$	−38.0211	+	16.9281i	−1.40434	+	0.625254i	−0.441981	+	0.897025i	$0.645724\pi$
$734$	−25.4419	−	28.2561i	−0.939078	−	1.04295i
$735$		0			0
$736$	4.66082	−	3.38628i	0.171800	−	0.124820i
$737$	0.271349	−	2.58171i	0.00999527	−	0.0950986i
$738$		0			0
$739$	0.309170	−	0.535498i	0.0113730	−	0.0196986i	−0.860283	−	0.509817i	$-0.829713\pi$
$739$	0.309170	−	0.535498i	0.0113730	−	0.0196986i	0.871656	+	0.490118i	$0.163046\pi$
$740$	−2.08600	−	1.51557i	−0.0766829	−	0.0557134i
$741$		0			0
$742$	−0.663675	+	2.04258i	−0.0243643	+	0.0749856i
$743$	42.4135			1.55600			0.778000	−	0.628264i	$-0.216234\pi$
$743$	42.4135			1.55600			0.778000	+	0.628264i	$0.216234\pi$
$744$		0			0
$745$	−13.0465			−0.477988
$746$	−6.98478	+	21.4969i	−0.255731	+	0.787059i
$747$		0			0
$748$	−0.947885	−	0.688679i	−0.0346581	−	0.0251806i
$749$	−0.797800	+	1.38183i	−0.0291510	+	0.0504910i
$750$		0			0
$751$	−1.66744	+	15.8646i	−0.0608458	+	0.578909i	0.921044	+	0.389458i	$0.127338\pi$
$751$	−1.66744	+	15.8646i	−0.0608458	+	0.578909i	−0.981890	+	0.189451i	$0.939329\pi$
$752$	40.3478	−	29.3144i	1.47133	−	1.06899i
$753$		0			0
$754$	9.98739	+	11.0921i	0.363719	+	0.403951i
$755$	−26.1390	+	11.6378i	−0.951297	+	0.423545i
$756$		0			0
$757$	40.0914	+	8.52169i	1.45715	+	0.309726i	0.867299	−	0.497788i	$-0.165854\pi$
$757$	40.0914	+	8.52169i	1.45715	+	0.309726i	0.589848	+	0.807514i	$0.299188\pi$
$758$	−7.02468	−	3.12759i	−0.255148	−	0.113599i
$759$		0			0
$760$	−2.95810	−	9.10409i	−0.107302	−	0.330240i
$761$	0.160376	+	0.0714040i	0.00581362	+	0.00258839i	0.409641	−	0.912247i	$-0.365654\pi$
$761$	0.160376	+	0.0714040i	0.00581362	+	0.00258839i	−0.403828	+	0.914835i	$0.632321\pi$
$762$		0			0
$763$	−0.0117366	+	0.00249470i	−0.000424894	+	9.03141e-5i
$764$	3.47240	−	1.54601i	0.125627	−	0.0559327i
$765$		0			0
$766$	−2.48409	−	23.6345i	−0.0897537	−	0.853950i
$767$	−5.57849	+	4.05301i	−0.201428	+	0.146346i
$768$		0			0
$769$	−11.5768	−	20.0516i	−0.417470	−	0.723079i	0.578215	−	0.815885i	$-0.303750\pi$
$769$	−11.5768	−	20.0516i	−0.417470	−	0.723079i	−0.995684	+	0.0928061i	$0.970416\pi$
$770$	0.0744903	−	0.129021i	0.00268444	−	0.00464959i
$771$		0			0
$772$	−4.89062	+	5.43158i	−0.176017	+	0.195487i
$773$	10.9994	−	33.8525i	0.395619	−	1.21759i	−0.532859	−	0.846204i	$-0.678882\pi$
$773$	10.9994	−	33.8525i	0.395619	−	1.21759i	0.928478	−	0.371387i	$-0.121118\pi$
$774$		0			0
$775$	6.06576	−	16.2506i	0.217888	−	0.583739i
$776$	−20.5673			−0.738324
$777$		0			0
$778$	29.2733	−	32.5113i	1.04950	−	1.16559i
$779$	24.9827	+	18.1510i	0.895098	+	0.650327i
$780$		0			0
$781$	−1.40980	−	2.44185i	−0.0504466	−	0.0873761i
$782$	2.00594	−	19.0852i	0.0717322	−	0.682486i
$783$		0			0
$784$	−3.42445	−	32.5815i	−0.122302	−	1.16362i
$785$	−12.9892	−	14.4260i	−0.463605	−	0.514885i
$786$		0			0
$787$	3.18022	−	0.675977i	0.113363	−	0.0240960i	−0.150881	−	0.988552i	$-0.548211\pi$
$787$	3.18022	−	0.675977i	0.113363	−	0.0240960i	0.264244	+	0.964456i	$0.414878\pi$
$788$	−10.6313	−	2.25975i	−0.378723	−	0.0805001i
$789$		0			0
$790$	−3.74417	−	11.5234i	−0.133212	−	0.409983i
$791$	−0.0562397	−	0.173088i	−0.00199965	−	0.00615430i
$792$		0			0
$793$	−3.69848	−	0.786136i	−0.131337	−	0.0279165i
$794$	−4.41411	+	0.938247i	−0.156651	+	0.0332972i
$795$		0			0
$796$	−6.22295	−	6.91128i	−0.220567	−	0.244964i
$797$	5.44334	+	51.7900i	0.192813	+	1.83449i	0.480765	+	0.876850i	$0.340359\pi$
$797$	5.44334	+	51.7900i	0.192813	+	1.83449i	−0.287951	+	0.957645i	$0.592974\pi$
$798$		0			0
$799$	5.86593	−	55.8106i	0.207522	−	1.97444i
$800$	−3.86232	−	6.68973i	−0.136554	−	0.236518i
$801$		0			0
$802$	26.0737	+	18.9436i	0.920693	+	0.668923i
$803$	−3.69423	+	4.10286i	−0.130367	+	0.144787i
$804$		0			0
$805$	0.445005			0.0156844
$806$	−17.5907	+	2.95353i	−0.619606	+	0.104034i
$807$		0			0
$808$	−3.31231	+	10.1942i	−0.116527	+	0.358632i
$809$	4.69606	−	5.21550i	0.165105	−	0.183367i	−0.654915	−	0.755702i	$-0.727296\pi$
$809$	4.69606	−	5.21550i	0.165105	−	0.183367i	0.820020	+	0.572335i	$0.193962\pi$
$810$		0			0
$811$	−22.6398	+	39.2134i	−0.794993	+	1.37697i	0.127851	+	0.991793i	$0.459192\pi$
$811$	−22.6398	+	39.2134i	−0.794993	+	1.37697i	−0.922844	+	0.385174i	$0.874141\pi$
$812$	−0.144980	−	0.251114i	−0.00508782	−	0.00881236i
$813$		0			0
$814$	−2.64963	+	1.92507i	−0.0928693	+	0.0674735i
$815$	−1.93515	−	18.4118i	−0.0677855	−	0.644936i
$816$		0			0
$817$	−32.9332	+	14.6628i	−1.15219	+	0.512986i
$818$	−24.5590	+	5.22018i	−0.858686	+	0.182519i
$819$		0			0
$820$	−6.02127	−	2.68084i	−0.210272	−	0.0936190i
$821$	−13.2446	−	40.7626i	−0.462239	−	1.42262i	−0.862422	−	0.506190i	$-0.831054\pi$
$821$	−13.2446	−	40.7626i	−0.462239	−	1.42262i	0.400183	−	0.916435i	$-0.368946\pi$
$822$		0			0
$823$	38.4096	+	17.1010i	1.33887	+	0.596105i	0.946203	−	0.323574i	$-0.104885\pi$
$823$	38.4096	+	17.1010i	1.33887	+	0.596105i	0.392671	+	0.919679i	$0.371551\pi$
$824$	−43.7658	−	9.30270i	−1.52465	−	0.324075i
$825$		0			0
$826$	0.671023	−	0.298759i	0.0233479	−	0.0103951i
$827$	0.279773	+	0.310719i	0.00972866	+	0.0108048i	0.747990	−	0.663711i	$-0.231019\pi$
$827$	0.279773	+	0.310719i	0.00972866	+	0.0108048i	−0.738261	+	0.674515i	$0.764353\pi$
$828$		0			0
$829$	22.5765	−	16.4028i	0.784113	−	0.569691i	−0.122098	−	0.992518i	$-0.538962\pi$
$829$	22.5765	−	16.4028i	0.784113	−	0.569691i	0.906211	+	0.422827i	$0.138962\pi$
$830$	0.477461	−	4.54274i	0.0165729	−	0.157681i
$831$		0			0
$832$	5.64158	−	9.77150i	0.195586	−	0.338766i
$833$	−29.8232	−	21.6678i	−1.03331	−	0.750745i
$834$		0			0
$835$	−2.60415	+	8.01475i	−0.0901203	+	0.277362i
$836$	0.636573			0.0220163
$837$		0			0
$838$	−9.87445			−0.341107
$839$	7.68989	−	23.6671i	0.265485	−	0.817077i	−0.726097	−	0.687592i	$-0.758668\pi$
$839$	7.68989	−	23.6671i	0.265485	−	0.817077i	0.991581	−	0.129485i	$-0.0413324\pi$
$840$		0			0
$841$	5.90004	+	4.28663i	0.203450	+	0.147815i
$842$	−3.62037	+	6.27066i	−0.124766	+	0.216101i
$843$		0			0
$844$	0.668458	−	6.35995i	0.0230093	−	0.218918i
$845$	−9.77827	+	7.10433i	−0.336383	+	0.244396i
$846$		0			0
$847$	1.00379	+	1.11482i	0.0344905	+	0.0383056i
$848$	−42.2007	+	18.7890i	−1.44918	+	0.645216i
$849$		0			0
$850$	−25.1687	−	5.34977i	−0.863279	−	0.183496i
$851$	−8.93701	−	3.97901i	−0.306357	−	0.136399i
$852$		0			0
$853$	1.11055	+	3.41792i	0.0380245	+	0.117027i	0.968267	−	0.249918i	$-0.0804036\pi$
$853$	1.11055	+	3.41792i	0.0380245	+	0.117027i	−0.930243	+	0.366945i	$0.880404\pi$
$854$	0.367957	+	0.163825i	0.0125912	+	0.00560598i
$855$		0			0
$856$	−27.1879	+	5.77896i	−0.929263	+	0.197521i
$857$	−48.7683	+	21.7130i	−1.66589	+	0.741703i	−0.999991	−	0.00433590i	$-0.998620\pi$
$857$	−48.7683	+	21.7130i	−1.66589	+	0.741703i	−0.665902	+	0.746039i	$0.731953\pi$
$858$		0			0
$859$	1.63781	+	15.5827i	0.0558813	+	0.531675i	0.986275	+	0.165112i	$0.0527987\pi$
$859$	1.63781	+	15.5827i	0.0558813	+	0.531675i	−0.930394	+	0.366562i	$0.880535\pi$
$860$	6.22497	−	4.52270i	0.212270	−	0.154223i
$861$		0			0
$862$	14.8946	+	25.7981i	0.507311	+	0.878688i
$863$	6.67716	−	11.5652i	0.227293	−	0.393683i	−0.729712	−	0.683755i	$-0.760346\pi$
$863$	6.67716	−	11.5652i	0.227293	−	0.393683i	0.957005	+	0.290072i	$0.0936792\pi$
$864$		0			0
$865$	16.6486	−	18.4901i	0.566069	−	0.628684i
$866$	5.49497	−	16.9118i	0.186727	−	0.574686i
$867$		0			0
$868$	0.346191	+	0.0149260i	0.0117505	+	0.000506622i
$869$	−2.80669			−0.0952103
$870$		0			0
$871$	−7.15386	+	7.94517i	−0.242399	+	0.269212i
$872$	−0.169100	−	0.122858i	−0.00572644	−	0.00416051i
$873$		0			0
$874$	5.21318	+	9.02950i	0.176339	+	0.305427i
$875$	0.162469	−	1.54579i	0.00549245	−	0.0522571i
$876$		0			0
$877$	−0.228375	−	2.17285i	−0.00771169	−	0.0733718i	0.989989	−	0.141143i	$-0.0450778\pi$
$877$	−0.228375	−	2.17285i	−0.00771169	−	0.0733718i	−0.997701	+	0.0677714i	$0.978411\pi$
$878$	5.36372	+	5.95702i	0.181017	+	0.201040i
$879$		0			0
$880$	3.13437	−	0.666231i	0.105660	−	0.0224586i
$881$	3.92965	+	0.835274i	0.132393	+	0.0281411i	0.273632	−	0.961835i	$-0.411775\pi$
$881$	3.92965	+	0.835274i	0.132393	+	0.0281411i	−0.141238	+	0.989976i	$0.545108\pi$
$882$		0			0
$883$	−16.2184	−	49.9152i	−0.545793	−	1.67978i	−0.719096	−	0.694911i	$-0.755444\pi$
$883$	−16.2184	−	49.9152i	−0.545793	−	1.67978i	0.173303	−	0.984869i	$-0.444556\pi$
$884$	1.49113	+	4.58923i	0.0501522	+	0.154353i
$885$		0			0
$886$	−46.3575	−	9.85360i	−1.55741	−	0.331038i
$887$	17.3037	−	3.67802i	0.581001	−	0.123496i	0.0919699	−	0.995762i	$-0.470684\pi$
$887$	17.3037	−	3.67802i	0.581001	−	0.123496i	0.489032	+	0.872266i	$0.337350\pi$
$888$		0			0
$889$	1.11407	+	1.23730i	0.0373647	+	0.0414977i
$890$	0.544910	+	5.18448i	0.0182654	+	0.173784i
$891$		0			0
$892$	−0.440924	+	4.19511i	−0.0147632	+	0.140463i
$893$	15.2448	+	26.4048i	0.510148	+	0.883603i
$894$		0			0
$895$	0.921596	+	0.669579i	0.0308056	+	0.0223816i
$896$	−1.26718	+	1.40735i	−0.0423336	+	0.0470163i
$897$		0			0
$898$	−10.5668			−0.352619
$899$	24.1305	−	9.52046i	0.804798	−	0.317525i
$900$		0			0
$901$	−16.0625	+	49.4352i	−0.535118	+	1.64692i
$902$	−5.60194	+	6.22159i	−0.186524	+	0.207156i
$903$		0			0
$904$	1.58517	−	2.74560i	0.0527221	−	0.0913174i
$905$	−10.0172	−	17.3503i	−0.332984	−	0.576745i
$906$		0			0
$907$	−5.51086	+	4.00387i	−0.182985	+	0.132946i	−0.675507	−	0.737354i	$-0.736075\pi$
$907$	−5.51086	+	4.00387i	−0.182985	+	0.132946i	0.492522	+	0.870300i	$0.336075\pi$
$908$	−0.0344470	−	0.327741i	−0.00114316	−	0.0108765i
$909$		0			0
$910$	−0.560526	+	0.249562i	−0.0185812	+	0.00827290i
$911$	56.5411	−	12.0182i	1.87329	−	0.398180i	0.876724	−	0.480994i	$-0.159724\pi$
$911$	56.5411	−	12.0182i	1.87329	−	0.398180i	0.996565	+	0.0828147i	$0.0263910\pi$
$912$		0			0
$913$	−0.966616	−	0.430365i	−0.0319903	−	0.0142430i
$914$	1.59621	+	4.91262i	0.0527978	+	0.162495i
$915$		0			0
$916$	−4.91459	−	2.18812i	−0.162383	−	0.0722974i
$917$	−2.07364	−	0.440766i	−0.0684776	−	0.0145554i
$918$		0			0
$919$	−20.4983	+	9.12644i	−0.676177	+	0.301053i	−0.715946	−	0.698155i	$-0.754004\pi$
$919$	−20.4983	+	9.12644i	−0.676177	+	0.301053i	0.0397691	+	0.999209i	$0.487338\pi$
$920$	5.18708	+	5.76083i	0.171013	+	0.189929i
$921$		0			0
$922$	12.6093	−	9.16120i	0.415266	−	0.301708i
$923$	−1.21383	+	11.5488i	−0.0399537	+	0.380134i
$924$		0			0
$925$	−6.55852	+	11.3597i	−0.215643	+	0.373504i
$926$	33.1090	+	24.0551i	1.08803	+	0.790500i
$927$		0			0
$928$	3.56985	−	10.9869i	0.117186	−	0.360661i
$929$	9.28188			0.304529			0.152264	−	0.988340i	$-0.451343\pi$
$929$	9.28188			0.304529			0.152264	+	0.988340i	$0.451343\pi$
$930$		0			0
$931$	20.0284			0.656405
$932$	1.92344	−	5.91973i	0.0630043	−	0.193907i
$933$		0			0
$934$	−34.4545	−	25.0326i	−1.12738	−	0.819093i
$935$	1.80283	−	3.12260i	0.0589590	−	0.102120i
$936$		0			0
$937$	3.23772	−	30.8048i	0.105772	−	1.00635i	−0.804954	−	0.593337i	$-0.797810\pi$
$937$	3.23772	−	30.8048i	0.105772	−	1.00635i	0.910726	−	0.413012i	$-0.135523\pi$
$938$	0.921373	−	0.669416i	0.0300839	−	0.0218572i
$939$		0			0
$940$	−4.35451	−	4.83617i	−0.142028	−	0.157738i
$941$	48.0392	−	21.3884i	1.56603	−	0.697242i	0.573498	−	0.819207i	$-0.305586\pi$
$941$	48.0392	−	21.3884i	1.56603	−	0.697242i	0.992534	+	0.121965i	$0.0389194\pi$
$942$		0			0
$943$	−24.4606	−	5.19926i	−0.796547	−	0.169311i
$944$	14.4329	+	6.42594i	0.469751	+	0.209147i
$945$		0			0
$946$	−3.02017	−	9.29513i	−0.0981943	−	0.302211i
$947$	−33.6107	−	14.9644i	−1.09220	−	0.486279i	−0.220036	−	0.975492i	$-0.570617\pi$
$947$	−33.6107	−	14.9644i	−1.09220	−	0.486279i	−0.872164	+	0.489213i	$0.837284\pi$
$948$		0			0
$949$	22.2410	−	4.72746i	0.721972	−	0.153460i
$950$	12.7713	−	5.68617i	0.414357	−	0.184484i
$951$		0			0
$952$	0.187163	+	1.78073i	0.00606598	+	0.0577139i
$953$	−2.13022	+	1.54769i	−0.0690045	+	0.0501347i	−0.621753	−	0.783214i	$-0.713579\pi$
$953$	−2.13022	+	1.54769i	−0.0690045	+	0.0501347i	0.552748	+	0.833348i	$0.313579\pi$
$954$		0			0
$955$	5.84867	+	10.1302i	0.189258	+	0.327805i
$956$	−3.69398	+	6.39816i	−0.119472	+	0.206931i
$957$		0			0
$958$	−32.8095	+	36.4387i	−1.06003	+	1.17728i
$959$	−0.560699	+	1.72565i	−0.0181059	+	0.0557242i
$960$		0			0
$961$	−5.88191	+	30.4369i	−0.189739	+	0.981835i
$962$	13.4885			0.434886
$963$		0			0
$964$	7.44090	−	8.26395i	0.239655	−	0.266164i
$965$	−18.1969	−	13.2208i	−0.585780	−	0.425594i
$966$		0			0
$967$	−0.993508	−	1.72081i	−0.0319491	−	0.0553374i	0.849609	−	0.527413i	$-0.176838\pi$
$967$	−0.993508	−	1.72081i	−0.0319491	−	0.0553374i	−0.881558	+	0.472076i	$0.843505\pi$
$968$	−2.73156	+	25.9891i	−0.0877958	+	0.835321i
$969$		0			0
$970$	1.89932	+	18.0708i	0.0609834	+	0.580218i
$971$	25.9813	+	28.8552i	0.833780	+	0.926006i	0.998175	−	0.0603884i	$-0.0192339\pi$
$971$	25.9813	+	28.8552i	0.833780	+	0.926006i	−0.164395	+	0.986395i	$0.552567\pi$
$972$		0			0
$973$	1.61761	−	0.343835i	0.0518584	−	0.0110228i
$974$	−42.0259	−	8.93287i	−1.34660	−	0.286228i
$975$		0			0
$976$	2.67711	+	8.23928i	0.0856921	+	0.263733i
$977$	−11.5348	−	35.5005i	−0.369032	−	1.13576i	−0.947418	−	0.319999i	$-0.896317\pi$
$977$	−11.5348	−	35.5005i	−0.369032	−	1.13576i	0.578386	−	0.815763i	$-0.303683\pi$
$978$		0			0
$979$	1.18118	+	0.251067i	0.0377506	+	0.00802414i
$980$	−4.18145	+	0.888795i	−0.133572	+	0.0283915i
$981$		0			0
$982$	37.1909	+	41.3047i	1.18681	+	1.31809i
$983$	−1.17356	−	11.1657i	−0.0374307	−	0.356129i	−0.997167	−	0.0752253i	$-0.976032\pi$
$983$	−1.17356	−	11.1657i	−0.0374307	−	0.356129i	0.959736	−	0.280904i	$-0.0906343\pi$
$984$		0			0
$985$	3.49625	−	33.2646i	0.111400	−	1.05990i
$986$	−19.2405	−	33.3254i	−0.612741	−	1.06130i
$987$		0			0
$988$	−2.12100	−	1.54100i	−0.0674781	−	0.0490257i
$989$	19.5342	−	21.6949i	0.621151	−	0.689858i
$990$		0			0
$991$	52.4571			1.66636			0.833178	−	0.553005i	$-0.186519\pi$
$991$	52.4571			1.66636			0.833178	+	0.553005i	$0.186519\pi$
$992$	8.78707	+	10.6477i	0.278990	+	0.338066i
$993$		0			0
$994$	0.382256	−	1.17646i	0.0121244	−	0.0373151i
$995$	19.1507	−	21.2690i	0.607117	−	0.674272i
$996$		0			0
$997$	4.82123	−	8.35061i	0.152690	−	0.264467i	−0.779526	−	0.626370i	$-0.784540\pi$
$997$	4.82123	−	8.35061i	0.152690	−	0.264467i	0.932215	+	0.361904i	$0.117873\pi$
$998$	13.7823	+	23.8717i	0.436272	+	0.755645i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.y.b.262.2		16
3.2	odd	2		93.2.m.a.76.1	✓	16
31.12	odd	30		8649.2.a.bi.1.6		8
31.19	even	15		8649.2.a.bj.1.6		8
31.20	even	15	inner	279.2.y.b.82.2		16
93.20	odd	30		93.2.m.a.82.1	yes	16
93.50	odd	30		2883.2.a.m.1.3		8
93.74	even	30		2883.2.a.n.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.a.76.1	✓	16	3.2	odd	2
93.2.m.a.82.1	yes	16	93.20	odd	30
279.2.y.b.82.2		16	31.20	even	15	inner
279.2.y.b.262.2		16	1.1	even	1	trivial
2883.2.a.m.1.3		8	93.50	odd	30
2883.2.a.n.1.3		8	93.74	even	30
8649.2.a.bi.1.6		8	31.12	odd	30
8649.2.a.bj.1.6		8	31.19	even	15

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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.483302 - 1.48745i) q^{2} +(-0.360895 - 0.262205i) q^{4} +(0.686405 - 1.18889i) q^{5} +(0.0145831 - 0.138749i) q^{7} +(1.96616 - 1.42850i) q^{8} +(-1.43667 - 1.59559i) q^{10} +(-0.454357 + 0.202293i) q^{11} +(2.00358 + 0.425875i) q^{13} +(-0.199334 - 0.0887493i) q^{14} +(-1.45027 - 4.46348i) q^{16} +(-4.82434 - 2.14793i) q^{17} +(2.80648 - 0.596536i) q^{19} +(-0.559453 + 0.249085i) q^{20} +(0.0813089 + 0.773603i) q^{22} +(-1.87974 + 1.36571i) q^{23} +(1.55770 + 2.69801i) q^{25} +(1.60180 - 2.77441i) q^{26} +(-0.0416437 + 0.0462500i) q^{28} +(-1.43974 + 4.43106i) q^{29} +(-3.54387 - 4.29429i) q^{31} -2.47951 q^{32} +(-5.52656 + 6.13787i) q^{34} +(-0.154947 - 0.112576i) q^{35} +(2.10520 + 3.64631i) q^{37} +(0.469060 - 4.46281i) q^{38} +(-0.348744 - 3.31808i) q^{40} +(7.20170 + 7.99829i) q^{41} +(-12.2899 + 2.61231i) q^{43} +(0.217018 + 0.0461285i) q^{44} +(1.12294 + 3.45606i) q^{46} +(3.28380 + 10.1065i) q^{47} +(6.82799 + 1.45134i) q^{49} +(4.76599 - 1.01304i) q^{50} +(-0.611416 - 0.679047i) q^{52} +(-1.02886 - 9.78895i) q^{53} +(-0.0713695 + 0.679036i) q^{55} +(-0.169530 - 0.293635i) q^{56} +(5.89516 + 4.28308i) q^{58} +(-2.25251 + 2.50167i) q^{59} -1.84593 q^{61} +(-8.10031 + 3.19590i) q^{62} +(1.70220 - 5.23882i) q^{64} +(1.88159 - 2.08972i) q^{65} +(-2.60973 + 4.52019i) q^{67} +(1.17788 + 2.04015i) q^{68} +(-0.242337 + 0.176068i) q^{70} +(0.592591 + 5.63812i) q^{71} +(10.1409 - 4.51501i) q^{73} +(6.44116 - 1.36911i) q^{74} +(-1.16926 - 0.520588i) q^{76} +(0.0214420 + 0.0659916i) q^{77} +(5.15533 + 2.29530i) q^{79} +(-6.30206 - 1.33954i) q^{80} +(15.3777 - 6.84658i) q^{82} +(1.42353 + 1.58099i) q^{83} +(-5.86511 + 4.26125i) q^{85} +(-2.05408 + 19.5432i) q^{86} +(-0.604365 + 1.04679i) q^{88} +(-1.96427 - 1.42713i) q^{89} +(0.0883082 - 0.271785i) q^{91} +1.03648 q^{92} +16.6200 q^{94} +(1.21717 - 3.74606i) q^{95} +(-6.84658 - 4.97433i) q^{97} +(5.45877 - 9.45487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} - 9 q^{7} - 10 q^{8} - 16 q^{10} - 10 q^{11} + 3 q^{13} + 12 q^{14} + 6 q^{16} - 3 q^{17} - 32 q^{19} + 10 q^{20} - 9 q^{22} + 22 q^{23} + 12 q^{25} - 18 q^{26} + 30 q^{28} - 38 q^{29} - 8 q^{31}+ \cdots + 32 q^{98}+O(q^{100}) \) 16 * q - 6 * q^5 - 9 * q^7 - 10 * q^8 - 16 * q^10 - 10 * q^11 + 3 * q^13 + 12 * q^14 + 6 * q^16 - 3 * q^17 - 32 * q^19 + 10 * q^20 - 9 * q^22 + 22 * q^23 + 12 * q^25 - 18 * q^26 + 30 * q^28 - 38 * q^29 - 8 * q^31 - 52 * q^34 - 3 * q^35 - 8 * q^37 - 7 * q^38 + 37 * q^40 + 40 * q^41 + q^43 - 7 * q^46 + 23 * q^47 + 25 * q^49 + 21 * q^50 - 45 * q^52 - 30 * q^53 + 46 * q^55 + 6 * q^56 + 48 * q^58 + 40 * q^59 + 26 * q^61 - 40 * q^62 + 38 * q^64 - 12 * q^65 - 32 * q^67 - 15 * q^68 + 33 * q^70 - 17 * q^71 + 27 * q^73 + 70 * q^74 - 15 * q^76 + 9 * q^77 - 21 * q^80 - 32 * q^82 + 17 * q^83 - 64 * q^85 - 26 * q^86 - 22 * q^88 + 43 * q^89 + 140 * q^92 + 88 * q^94 + 2 * q^95 + 12 * q^97 + 32 * q^98

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