LMFDB - Embedded newform 279.2.y.d.82.3

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 93)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			82.3
Character	$\chi$	$=$	279.82
Dual form			279.2.y.d.262.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.418031 + 1.28657i) q^{2} +(0.137526 - 0.0999185i) q^{4} +(-1.63328 - 2.82893i) q^{5} +(-0.149090 - 1.41850i) q^{7} +(2.37488 + 1.72545i) q^{8} +O(q^{10})$	\(q+(0.418031 + 1.28657i) q^{2} +(0.137526 - 0.0999185i) q^{4} +(-1.63328 - 2.82893i) q^{5} +(-0.149090 - 1.41850i) q^{7} +(2.37488 + 1.72545i) q^{8} +(2.95685 - 3.28391i) q^{10} +(4.38826 + 1.95378i) q^{11} +(3.02956 - 0.643952i) q^{13} +(1.76267 - 0.784793i) q^{14} +(-1.12208 + 3.45340i) q^{16} +(3.32456 - 1.48019i) q^{17} +(-3.39558 - 0.721752i) q^{19} +(-0.507281 - 0.225856i) q^{20} +(-0.679240 + 6.46254i) q^{22} +(-6.09693 - 4.42968i) q^{23} +(-2.83523 + 4.91076i) q^{25} +(2.09494 + 3.62854i) q^{26} +(-0.162238 - 0.180184i) q^{28} +(0.609968 + 1.87729i) q^{29} +(-4.70038 - 2.98436i) q^{31} +0.958934 q^{32} +(3.29413 + 3.65850i) q^{34} +(-3.76933 + 2.73858i) q^{35} +(-4.53564 + 7.85596i) q^{37} +(-0.490874 - 4.67035i) q^{38} +(1.00233 - 9.53653i) q^{40} +(-3.43795 + 3.81823i) q^{41} +(4.10301 + 0.872121i) q^{43} +(0.798719 - 0.169773i) q^{44} +(3.15038 - 9.69586i) q^{46} +(-3.27633 + 10.0835i) q^{47} +(4.85712 - 1.03241i) q^{49} +(-7.50325 - 1.59486i) q^{50} +(0.352300 - 0.391269i) q^{52} +(0.0300848 - 0.286238i) q^{53} +(-1.64017 - 15.6052i) q^{55} +(2.09349 - 3.62602i) q^{56} +(-2.16027 + 1.56953i) q^{58} +(-2.55052 - 2.83264i) q^{59} -6.98631 q^{61} +(1.87468 - 7.29492i) q^{62} +(2.64502 + 8.14054i) q^{64} +(-6.76982 - 7.51865i) q^{65} +(4.01427 + 6.95292i) q^{67} +(0.309315 - 0.535749i) q^{68} +(-5.09907 - 3.70469i) q^{70} +(-1.00247 + 9.53784i) q^{71} +(10.4141 + 4.63666i) q^{73} +(-12.0033 - 2.55137i) q^{74} +(-0.539096 + 0.240021i) q^{76} +(2.11719 - 6.51605i) q^{77} +(-8.15681 + 3.63165i) q^{79} +(11.6021 - 2.46610i) q^{80} +(-6.34959 - 2.82702i) q^{82} +(4.38393 - 4.86884i) q^{83} +(-9.61729 - 6.98737i) q^{85} +(0.593142 + 5.64337i) q^{86} +(7.05045 + 12.2117i) q^{88} +(1.18956 - 0.864265i) q^{89} +(-1.36513 - 4.20142i) q^{91} -1.28109 q^{92} -14.3427 q^{94} +(3.50415 + 10.7847i) q^{95} +(7.55896 - 5.49190i) q^{97} +(3.35870 + 5.81743i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} + 6 q^{5} - q^{7} + 22 q^{8}+O(q^{10}) $ 24 * q - 4 * q^4 + 6 * q^5 - q^7 + 22 * q^8	$ 24 q - 4 q^{4} + 6 q^{5} - q^{7} + 22 q^{8} + 24 q^{10} + 22 q^{11} - 8 q^{13} - 10 q^{14} - 2 q^{16} + 17 q^{17} + 5 q^{19} + 22 q^{20} - 37 q^{22} - 26 q^{23} - 8 q^{25} - 4 q^{26} - 36 q^{28} - 2 q^{29} - 36 q^{32} + 40 q^{34} - 9 q^{35} - 13 q^{37} + q^{38} - 27 q^{40} - 36 q^{41} - 11 q^{43} + 38 q^{44} - 23 q^{46} + 13 q^{47} - 22 q^{49} - 71 q^{50} + 9 q^{52} + 20 q^{53} + 26 q^{55} - 28 q^{56} + 40 q^{58} + 16 q^{59} + 70 q^{61} + 2 q^{62} + 34 q^{64} - 94 q^{65} + 4 q^{67} - 51 q^{68} - 43 q^{70} + 5 q^{71} - 12 q^{73} - 74 q^{74} + 71 q^{76} - 25 q^{77} - 29 q^{79} + 113 q^{80} - 60 q^{82} + 11 q^{83} + 16 q^{85} + 144 q^{86} + 26 q^{88} + 27 q^{89} - 81 q^{91} - 28 q^{92} - 80 q^{94} + 56 q^{95} - 21 q^{97} + 14 q^{98}+O(q^{100}) $ 24 * q - 4 * q^4 + 6 * q^5 - q^7 + 22 * q^8 + 24 * q^10 + 22 * q^11 - 8 * q^13 - 10 * q^14 - 2 * q^16 + 17 * q^17 + 5 * q^19 + 22 * q^20 - 37 * q^22 - 26 * q^23 - 8 * q^25 - 4 * q^26 - 36 * q^28 - 2 * q^29 - 36 * q^32 + 40 * q^34 - 9 * q^35 - 13 * q^37 + q^38 - 27 * q^40 - 36 * q^41 - 11 * q^43 + 38 * q^44 - 23 * q^46 + 13 * q^47 - 22 * q^49 - 71 * q^50 + 9 * q^52 + 20 * q^53 + 26 * q^55 - 28 * q^56 + 40 * q^58 + 16 * q^59 + 70 * q^61 + 2 * q^62 + 34 * q^64 - 94 * q^65 + 4 * q^67 - 51 * q^68 - 43 * q^70 + 5 * q^71 - 12 * q^73 - 74 * q^74 + 71 * q^76 - 25 * q^77 - 29 * q^79 + 113 * q^80 - 60 * q^82 + 11 * q^83 + 16 * q^85 + 144 * q^86 + 26 * q^88 + 27 * q^89 - 81 * q^91 - 28 * q^92 - 80 * q^94 + 56 * q^95 - 21 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{4}{15}\right)$	$1$

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 $

$2$	0.418031	+	1.28657i	0.295593	+	0.909741i	0.983022	+	0.183489i	$0.0587393\pi$
$2$	0.418031	+	1.28657i	0.295593	+	0.909741i	−0.687429	+	0.726252i	$0.741261\pi$
$3$		0			0
$3$		0			0
$4$	0.137526	−	0.0999185i	0.0687630	−	0.0499592i
$5$	−1.63328	−	2.82893i	−0.730427	−	1.26514i	−0.956701	−	0.291072i	$-0.905988\pi$
$5$	−1.63328	−	2.82893i	−0.730427	−	1.26514i	0.226274	−	0.974064i	$-0.427345\pi$
$6$		0			0
$7$	−0.149090	−	1.41850i	−0.0563509	−	0.536143i	−0.985887	−	0.167412i	$-0.946459\pi$
$7$	−0.149090	−	1.41850i	−0.0563509	−	0.536143i	0.929536	−	0.368731i	$-0.120208\pi$
$8$	2.37488	+	1.72545i	0.839648	+	0.610040i
$9$		0			0
$10$	2.95685	−	3.28391i	0.935038	−	1.03846i
$11$	4.38826	+	1.95378i	1.32311	+	0.589087i	0.942053	−	0.335464i	$-0.108893\pi$
$11$	4.38826	+	1.95378i	1.32311	+	0.589087i	0.381058	+	0.924551i	$0.375560\pi$
$12$		0			0
$13$	3.02956	−	0.643952i	0.840248	−	0.178600i	0.232367	−	0.972628i	$-0.425353\pi$
$13$	3.02956	−	0.643952i	0.840248	−	0.178600i	0.607881	+	0.794028i	$0.292020\pi$
$14$	1.76267	−	0.784793i	0.471094	−	0.209745i
$15$		0			0
$16$	−1.12208	+	3.45340i	−0.280519	+	0.863350i
$17$	3.32456	−	1.48019i	0.806323	−	0.358998i	0.0381758	−	0.999271i	$-0.487845\pi$
$17$	3.32456	−	1.48019i	0.806323	−	0.358998i	0.768148	+	0.640273i	$0.221179\pi$
$18$		0			0
$19$	−3.39558	−	0.721752i	−0.778998	−	0.165581i	−0.198782	−	0.980044i	$-0.563699\pi$
$19$	−3.39558	−	0.721752i	−0.778998	−	0.165581i	−0.580216	+	0.814462i	$0.697032\pi$
$20$	−0.507281	−	0.225856i	−0.113432	−	0.0505030i
$21$		0			0
$22$	−0.679240	+	6.46254i	−0.144815	+	1.37782i
$23$	−6.09693	−	4.42968i	−1.27130	−	0.923652i	−0.272045	−	0.962285i	$-0.587700\pi$
$23$	−6.09693	−	4.42968i	−1.27130	−	0.923652i	−0.999253	+	0.0386325i	$0.987700\pi$
$24$		0			0
$25$	−2.83523	+	4.91076i	−0.567046	+	0.982153i
$26$	2.09494	+	3.62854i	0.410851	+	0.711615i
$27$		0			0
$28$	−0.162238	−	0.180184i	−0.0306602	−	0.0340515i
$29$	0.609968	+	1.87729i	0.113268	+	0.348604i	0.991582	−	0.129481i	$-0.0413312\pi$
$29$	0.609968	+	1.87729i	0.113268	+	0.348604i	−0.878314	+	0.478085i	$0.841331\pi$
$30$		0			0
$31$	−4.70038	−	2.98436i	−0.844213	−	0.536008i
$31$	−4.70038	−	2.98436i	−0.844213	−	0.536008i
$32$	0.958934			0.169517
$33$		0			0
$34$	3.29413	+	3.65850i	0.564939	+	0.627428i
$35$	−3.76933	+	2.73858i	−0.637134	+	0.462905i
$36$		0			0
$37$	−4.53564	+	7.85596i	−0.745654	+	1.29151i	0.204234	+	0.978922i	$0.434530\pi$
$37$	−4.53564	+	7.85596i	−0.745654	+	1.29151i	−0.949888	+	0.312589i	$0.898804\pi$
$38$	−0.490874	−	4.67035i	−0.0796303	−	0.757632i
$39$		0			0
$40$	1.00233	−	9.53653i	0.158482	−	1.50786i
$41$	−3.43795	+	3.81823i	−0.536918	+	0.596308i	−0.949171	−	0.314762i	$-0.898075\pi$
$41$	−3.43795	+	3.81823i	−0.536918	+	0.596308i	0.412253	+	0.911070i	$0.364742\pi$
$42$		0			0
$43$	4.10301	+	0.872121i	0.625703	+	0.132997i	0.509842	−	0.860268i	$-0.329704\pi$
$43$	4.10301	+	0.872121i	0.625703	+	0.132997i	0.115861	+	0.993265i	$0.463037\pi$
$44$	0.798719	−	0.169773i	0.120411	−	0.0255942i
$45$		0			0
$46$	3.15038	−	9.69586i	0.464498	−	1.42958i
$47$	−3.27633	+	10.0835i	−0.477901	+	1.47083i	0.364104	+	0.931358i	$0.381375\pi$
$47$	−3.27633	+	10.0835i	−0.477901	+	1.47083i	−0.842005	+	0.539470i	$0.818625\pi$
$48$		0			0
$49$	4.85712	−	1.03241i	0.693874	−	0.147487i
$50$	−7.50325	−	1.59486i	−1.06112	−	0.225548i
$51$		0			0
$52$	0.352300	−	0.391269i	0.0488552	−	0.0542592i
$53$	0.0300848	−	0.286238i	0.00413247	−	0.0393178i	−0.992261	−	0.124167i	$-0.960374\pi$
$53$	0.0300848	−	0.286238i	0.00413247	−	0.0393178i	0.996394	+	0.0848491i	$0.0270408\pi$
$54$		0			0
$55$	−1.64017	−	15.6052i	−0.221160	−	2.10420i
$56$	2.09349	−	3.62602i	0.279754	−	0.484548i
$57$		0			0
$58$	−2.16027	+	1.56953i	−0.283658	+	0.206089i
$59$	−2.55052	−	2.83264i	−0.332050	−	0.368779i	0.553881	−	0.832596i	$-0.313146\pi$
$59$	−2.55052	−	2.83264i	−0.332050	−	0.368779i	−0.885931	+	0.463817i	$0.846480\pi$
$60$		0			0
$61$	−6.98631			−0.894505			−0.447252	−	0.894408i	$-0.647597\pi$
$61$	−6.98631			−0.894505			−0.447252	+	0.894408i	$0.647597\pi$
$62$	1.87468	−	7.29492i	0.238085	−	0.926456i
$63$		0			0
$64$	2.64502	+	8.14054i	0.330628	+	1.01757i
$65$	−6.76982	−	7.51865i	−0.839693	−	0.932574i
$66$		0			0
$67$	4.01427	+	6.95292i	0.490421	+	0.849435i	0.999939	−	0.0110253i	$-0.00350955\pi$
$67$	4.01427	+	6.95292i	0.490421	+	0.849435i	−0.509518	+	0.860460i	$0.670176\pi$
$68$	0.309315	−	0.535749i	0.0375099	−	0.0649691i
$69$		0			0
$70$	−5.09907	−	3.70469i	−0.609456	−	0.442795i
$71$	−1.00247	+	9.53784i	−0.118971	+	1.13193i	0.758289	+	0.651918i	$0.226036\pi$
$71$	−1.00247	+	9.53784i	−0.118971	+	1.13193i	−0.877260	+	0.480015i	$0.840631\pi$
$72$		0			0
$73$	10.4141	+	4.63666i	1.21888	+	0.542680i	0.912440	−	0.409210i	$-0.134196\pi$
$73$	10.4141	+	4.63666i	1.21888	+	0.542680i	0.306439	+	0.951890i	$0.400862\pi$
$74$	−12.0033	−	2.55137i	−1.39535	−	0.296591i
$75$		0			0
$76$	−0.539096	+	0.240021i	−0.0618386	+	0.0275323i
$77$	2.11719	−	6.51605i	0.241276	−	0.742572i
$78$		0			0
$79$	−8.15681	+	3.63165i	−0.917713	+	0.408592i	−0.810563	−	0.585651i	$-0.800839\pi$
$79$	−8.15681	+	3.63165i	−0.917713	+	0.408592i	−0.107149	+	0.994243i	$0.534172\pi$
$80$	11.6021	−	2.46610i	1.29715	−	0.275719i
$81$		0			0
$82$	−6.34959	−	2.82702i	−0.701195	−	0.312192i
$83$	4.38393	−	4.86884i	0.481198	−	0.534425i	−0.452843	−	0.891590i	$-0.649590\pi$
$83$	4.38393	−	4.86884i	0.481198	−	0.534425i	0.934041	+	0.357165i	$0.116257\pi$
$84$		0			0
$85$	−9.61729	−	6.98737i	−1.04314	−	0.757887i
$86$	0.593142	+	5.64337i	0.0639602	+	0.608541i
$87$		0			0
$88$	7.05045	+	12.2117i	0.751581	+	1.30178i
$89$	1.18956	−	0.864265i	0.126093	−	0.0916119i	−0.522951	−	0.852363i	$-0.675169\pi$
$89$	1.18956	−	0.864265i	0.126093	−	0.0916119i	0.649044	+	0.760751i	$0.275169\pi$
$90$		0			0
$91$	−1.36513	−	4.20142i	−0.143104	−	0.440429i
$92$	−1.28109			−0.133563
$93$		0			0
$94$	−14.3427			−1.47934
$95$	3.50415	+	10.7847i	0.359518	+	1.10648i
$96$		0			0
$97$	7.55896	−	5.49190i	0.767496	−	0.557618i	−0.133704	−	0.991021i	$-0.542687\pi$
$97$	7.55896	−	5.49190i	0.767496	−	0.557618i	0.901200	+	0.433403i	$0.142687\pi$
$98$	3.35870	+	5.81743i	0.339279	+	0.587649i
$99$		0			0
$100$	0.100758	+	0.958649i	0.0100758	+	0.0958649i
$101$	−10.2342	−	7.43558i	−1.01834	−	0.739867i	−0.0523982	−	0.998626i	$-0.516687\pi$
$101$	−10.2342	−	7.43558i	−1.01834	−	0.739867i	−0.965942	+	0.258759i	$0.916687\pi$
$102$		0			0
$103$	2.06380	−	2.29208i	0.203352	−	0.225845i	−0.632839	−	0.774283i	$-0.718111\pi$
$103$	2.06380	−	2.29208i	0.203352	−	0.225845i	0.836191	+	0.548438i	$0.184777\pi$
$104$	8.30595	+	3.69805i	0.814466	+	0.362624i
$105$		0			0
$106$	0.380841	−	0.0809502i	0.0369905	−	0.00786258i
$107$	−9.90377	+	4.40944i	−0.957434	+	0.426277i	−0.825137	−	0.564933i	$-0.808902\pi$
$107$	−9.90377	+	4.40944i	−0.957434	+	0.426277i	−0.132297	+	0.991210i	$0.542235\pi$
$108$		0			0
$109$	5.12929	−	15.7863i	0.491297	−	1.51206i	−0.331353	−	0.943507i	$-0.607505\pi$
$109$	5.12929	−	15.7863i	0.491297	−	1.51206i	0.822649	−	0.568549i	$-0.192495\pi$
$110$	19.3915	−	8.63364i	1.84890	−	0.823185i
$111$		0			0
$112$	5.06594	+	1.07680i	0.478687	+	0.101748i
$113$	4.73374	+	2.10760i	0.445313	+	0.198266i	0.617127	−	0.786863i	$-0.288296\pi$
$113$	4.73374	+	2.10760i	0.445313	+	0.198266i	−0.171814	+	0.985129i	$0.554963\pi$
$114$		0			0
$115$	−2.57324	+	24.4827i	−0.239956	+	2.28303i
$116$	0.271462	+	0.197229i	0.0252046	+	0.0183122i
$117$		0			0
$118$	2.57819	−	4.46556i	0.237342	−	0.411088i
$119$	−2.59531	−	4.49521i	−0.237912	−	0.412075i
$120$		0			0
$121$	8.07915	+	8.97281i	0.734469	+	0.815710i
$122$	−2.92050	−	8.98836i	−0.264409	−	0.813768i
$123$		0			0
$124$	−0.944617	+	0.0592271i	−0.0848292	+	0.00531875i
$125$	2.19010			0.195889
$126$		0			0
$127$	1.84302	+	2.04688i	0.163542	+	0.181631i	0.819346	−	0.573300i	$-0.194337\pi$
$127$	1.84302	+	2.04688i	0.163542	+	0.181631i	−0.655804	+	0.754931i	$0.727670\pi$
$128$	−7.81607	+	5.67870i	−0.690849	+	0.501931i
$129$		0			0
$130$	6.84326	−	11.8529i	0.600193	−	1.03957i
$131$	1.20921	+	11.5049i	0.105650	+	1.00519i	0.911005	+	0.412396i	$0.135308\pi$
$131$	1.20921	+	11.5049i	0.105650	+	1.00519i	−0.805355	+	0.592792i	$0.798025\pi$
$132$		0			0
$133$	−0.517558	+	4.92423i	−0.0448780	+	0.426985i
$134$	−7.26732	+	8.07118i	−0.627801	+	0.697243i
$135$		0			0
$136$	10.4494	+	2.22109i	0.896031	+	0.190457i
$137$	6.63206	−	1.40969i	0.566615	−	0.120438i	0.0843076	−	0.996440i	$-0.473132\pi$
$137$	6.63206	−	1.40969i	0.566615	−	0.120438i	0.482307	+	0.876002i	$0.339799\pi$
$138$		0			0
$139$	2.16472	−	6.66232i	0.183609	−	0.565091i	−0.816313	−	0.577611i	$-0.803985\pi$
$139$	2.16472	−	6.66232i	0.183609	−	0.565091i	0.999922	+	0.0125197i	$0.00398526\pi$
$140$	−0.244746	+	0.753252i	−0.0206848	+	0.0636614i
$141$		0			0
$142$	−12.6902	+	2.69737i	−1.06493	+	0.226359i
$143$	14.5526	+	3.09326i	1.21695	+	0.258671i
$144$		0			0
$145$	4.31446	−	4.79170i	0.358297	−	0.397929i
$146$	−1.61196	+	15.3367i	−0.133406	+	1.26928i
$147$		0			0
$148$	0.161187	+	1.53359i	0.0132495	+	0.126061i
$149$	7.31915	−	12.6771i	0.599608	−	1.03855i	−0.393271	−	0.919423i	$-0.628657\pi$
$149$	7.31915	−	12.6771i	0.599608	−	1.03855i	0.992879	−	0.119129i	$-0.0380102\pi$
$150$		0			0
$151$	−13.6986	+	9.95262i	−1.11478	+	0.809933i	−0.983409	−	0.181401i	$-0.941937\pi$
$151$	−13.6986	+	9.95262i	−1.11478	+	0.809933i	−0.131367	+	0.991334i	$0.541937\pi$
$152$	−6.81874	−	7.57298i	−0.553073	−	0.614250i
$153$		0			0
$154$	9.26839			0.746868
$155$	−0.765505	+	18.1714i	−0.0614869	+	1.45956i
$156$		0			0
$157$	5.09238	+	15.6727i	0.406416	+	1.25082i	0.919707	+	0.392605i	$0.128426\pi$
$157$	5.09238	+	15.6727i	0.406416	+	1.25082i	−0.513291	+	0.858215i	$0.671574\pi$
$158$	−8.08216	−	8.97615i	−0.642982	−	0.714104i
$159$		0			0
$160$	−1.56621	−	2.71276i	−0.123820	−	0.214462i
$161$	−5.37451	+	9.30893i	−0.423571	+	0.733646i
$162$		0			0
$163$	−8.56703	−	6.22431i	−0.671022	−	0.487526i	0.199345	−	0.979929i	$-0.436118\pi$
$163$	−8.56703	−	6.22431i	−0.671022	−	0.487526i	−0.870367	+	0.492403i	$0.836118\pi$
$164$	−0.0912958	+	0.868622i	−0.00712900	+	0.0678279i
$165$		0			0
$166$	8.09672	+	3.60489i	0.628427	+	0.279794i
$167$	0.486959	+	0.103506i	0.0376820	+	0.00800956i	0.226714	−	0.973961i	$-0.427202\pi$
$167$	0.486959	+	0.103506i	0.0376820	+	0.00800956i	−0.189032	+	0.981971i	$0.560535\pi$
$168$		0			0
$169$	−3.11255	+	1.38580i	−0.239427	+	0.106600i
$170$	4.96940	−	15.2942i	0.381136	−	1.17302i
$171$		0			0
$172$	0.651411	−	0.290027i	0.0496696	−	0.0221143i
$173$	16.4460	−	3.49571i	1.25037	−	0.265774i	0.465283	−	0.885162i	$-0.345953\pi$
$173$	16.4460	−	3.49571i	1.25037	−	0.265774i	0.785085	+	0.619388i	$0.212619\pi$
$174$		0			0
$175$	7.38863	+	3.28963i	0.558528	+	0.248673i
$176$	−11.6712	+	12.9621i	−0.879747	+	0.977058i
$177$		0			0
$178$	1.60921	+	1.16916i	0.120615	+	0.0876322i
$179$	−2.15541	−	20.5074i	−0.161103	−	1.53279i	−0.714358	−	0.699780i	$-0.753281\pi$
$179$	−2.15541	−	20.5074i	−0.161103	−	1.53279i	0.553255	−	0.833012i	$-0.313385\pi$
$180$		0			0
$181$	−11.7207	−	20.3009i	−0.871194	−	1.50895i	−0.860763	−	0.509006i	$-0.830013\pi$
$181$	−11.7207	−	20.3009i	−0.871194	−	1.50895i	−0.0104307	−	0.999946i	$-0.503320\pi$
$182$	4.83475	−	3.51265i	0.358376	−	0.260375i
$183$		0			0
$184$	−6.83629	−	21.0399i	−0.503978	−	1.55109i
$185$	29.6319			2.17858
$186$		0			0
$187$	17.4810			1.27834
$188$	0.556947	+	1.71411i	0.0406196	+	0.125014i
$189$		0			0
$190$	−12.4104	+	9.01666i	−0.900343	+	0.654137i
$191$	5.91834	+	10.2509i	0.428236	+	0.741727i	0.996717	−	0.0809700i	$-0.0258018\pi$
$191$	5.91834	+	10.2509i	0.428236	+	0.741727i	−0.568480	+	0.822697i	$0.692468\pi$
$192$		0			0
$193$	0.605204	+	5.75813i	0.0435635	+	0.414479i	0.994472	+	0.105006i	$0.0334861\pi$
$193$	0.605204	+	5.75813i	0.0435635	+	0.414479i	−0.950908	+	0.309473i	$0.899847\pi$
$194$	10.2256	+	7.42933i	0.734155	+	0.533395i
$195$		0			0
$196$	0.564823	−	0.627299i	0.0403445	−	0.0448071i
$197$	−14.7208	−	6.55412i	−1.04881	−	0.466962i	−0.191358	−	0.981520i	$-0.561289\pi$
$197$	−14.7208	−	6.55412i	−1.04881	−	0.466962i	−0.857455	+	0.514558i	$0.827956\pi$
$198$		0			0
$199$	−9.00185	+	1.91340i	−0.638124	+	0.135638i	−0.515602	−	0.856828i	$-0.672432\pi$
$199$	−9.00185	+	1.91340i	−0.638124	+	0.135638i	−0.122522	+	0.992466i	$0.539098\pi$
$200$	−15.2066	+	6.77043i	−1.07527	+	0.478742i
$201$		0			0
$202$	5.28816	−	16.2753i	0.372074	−	1.14513i
$203$	2.57199	−	1.14513i	0.180519	−	0.0803721i
$204$		0			0
$205$	16.4167	+	3.48947i	1.14659	+	0.243715i
$206$	3.81165	+	1.69706i	0.265570	+	0.118240i
$207$		0			0
$208$	−1.17557	+	11.1848i	−0.0815114	+	0.775529i
$209$	−13.4905	−	9.80144i	−0.933160	−	0.677980i
$210$		0			0
$211$	−6.75600	+	11.7017i	−0.465102	+	0.805581i	−0.999206	−	0.0398381i	$-0.987316\pi$
$211$	−6.75600	+	11.7017i	−0.465102	+	0.805581i	0.534104	+	0.845419i	$0.320649\pi$
$212$	−0.0244630	−	0.0423712i	−0.00168013	−	0.00291006i
$213$		0			0
$214$	−9.81314	−	10.8986i	−0.670812	−	0.745013i
$215$	−4.23420	−	13.0315i	−0.288770	−	0.888744i
$216$		0			0
$217$	−3.53254	+	7.11243i	−0.239805	+	0.482823i
$218$	22.4544			1.52080
$219$		0			0
$220$	−1.78481	−	1.98223i	−0.120332	−	0.133642i
$221$	9.11876	−	6.62517i	0.613394	−	0.445657i
$222$		0			0
$223$	2.14570	−	3.71646i	0.143687	−	0.248872i	−0.785196	−	0.619248i	$-0.787438\pi$
$223$	2.14570	−	3.71646i	0.143687	−	0.248872i	0.928882	+	0.370375i	$0.120771\pi$
$224$	−0.142968	−	1.36025i	−0.00955245	−	0.0908855i
$225$		0			0
$226$	−0.732716	+	6.97132i	−0.0487395	+	0.463726i
$227$	5.10824	−	5.67327i	0.339046	−	0.376548i	−0.549377	−	0.835575i	$-0.685135\pi$
$227$	5.10824	−	5.67327i	0.339046	−	0.376548i	0.888423	+	0.459026i	$0.151802\pi$
$228$		0			0
$229$	−13.1494	−	2.79498i	−0.868935	−	0.184698i	−0.248191	−	0.968711i	$-0.579836\pi$
$229$	−13.1494	−	2.79498i	−0.868935	−	0.184698i	−0.620744	+	0.784013i	$0.713169\pi$
$230$	−32.5744	+	6.92390i	−2.14789	+	0.456548i
$231$		0			0
$232$	−1.79057	+	5.51081i	−0.117557	+	0.361802i
$233$	4.54128	−	13.9766i	0.297509	−	0.915640i	−0.684858	−	0.728677i	$-0.740136\pi$
$233$	4.54128	−	13.9766i	0.297509	−	0.915640i	0.982367	−	0.186963i	$-0.0598644\pi$
$234$		0			0
$235$	33.8767	−	7.20071i	2.20987	−	0.469722i
$236$	−0.633797	−	0.134718i	−0.0412566	−	0.00876937i
$237$		0			0
$238$	4.69847	−	5.21818i	0.304557	−	0.338244i
$239$	0.487058	−	4.63405i	0.0315052	−	0.299752i	−0.967411	−	0.253211i	$-0.918513\pi$
$239$	0.487058	−	4.63405i	0.0315052	−	0.299752i	0.998916	−	0.0465412i	$-0.0148199\pi$
$240$		0			0
$241$	−1.42086	−	13.5186i	−0.0915259	−	0.870811i	−0.939908	−	0.341427i	$-0.889090\pi$
$241$	−1.42086	−	13.5186i	−0.0915259	−	0.870811i	0.848382	−	0.529384i	$-0.177577\pi$
$242$	−8.16679	+	14.1453i	−0.524981	+	0.909294i
$243$		0			0
$244$	−0.960799	+	0.698061i	−0.0615088	+	0.0446888i
$245$	−10.8537	−	12.0542i	−0.693415	−	0.770116i
$246$		0			0
$247$	−10.7519			−0.684125
$248$	−6.01347	−	15.1978i	−0.381856	−	0.965061i
$249$		0			0
$250$	0.915532	+	2.81772i	0.0579033	+	0.178208i
$251$	−14.2768	−	15.8560i	−0.901147	−	1.00082i	−0.999984	−	0.00572108i	$-0.998179\pi$
$251$	−14.2768	−	15.8560i	−0.901147	−	1.00082i	0.0988370	−	0.995104i	$-0.468488\pi$
$252$		0			0
$253$	−18.1003	−	31.3507i	−1.13796	−	1.97100i
$254$	−1.86301	+	3.22683i	−0.116896	+	0.202470i
$255$		0			0
$256$	3.27610	+	2.38023i	0.204756	+	0.148764i
$257$	−2.21124	+	21.0386i	−0.137934	+	1.31235i	0.678367	+	0.734723i	$0.262688\pi$
$257$	−2.21124	+	21.0386i	−0.137934	+	1.31235i	−0.816301	+	0.577627i	$0.803979\pi$
$258$		0			0
$259$	11.8199	+	5.26256i	0.734453	+	0.327000i
$260$	−1.68228	−	0.357579i	−0.104330	−	0.0221761i
$261$		0			0
$262$	−14.2964	+	6.36515i	−0.883232	+	0.393240i
$263$	−2.70179	+	8.31526i	−0.166600	+	0.512741i	−0.999151	−	0.0412075i	$-0.986880\pi$
$263$	−2.70179	+	8.31526i	−0.166600	+	0.512741i	0.832551	+	0.553948i	$0.186880\pi$
$264$		0			0
$265$	−0.858884	+	0.382400i	−0.0527608	+	0.0234906i
$266$	−6.55172	+	1.39261i	−0.401712	+	0.0853864i
$267$		0			0
$268$	1.24679	+	0.555108i	0.0761600	+	0.0339086i
$269$	−8.97841	+	9.97154i	−0.547423	+	0.607975i	−0.951838	−	0.306600i	$-0.900809\pi$
$269$	−8.97841	+	9.97154i	−0.547423	+	0.607975i	0.404415	+	0.914576i	$0.367475\pi$
$270$		0			0
$271$	18.1022	+	13.1520i	1.09963	+	0.798929i	0.981000	−	0.194009i	$-0.0621490\pi$
$271$	18.1022	+	13.1520i	1.09963	+	0.798929i	0.118632	+	0.992938i	$0.462149\pi$
$272$	1.38127	+	13.1419i	0.0837518	+	0.796845i
$273$		0			0
$274$	4.58607	+	7.94330i	0.277055	+	0.479872i
$275$	−22.0363	+	16.0103i	−1.32884	+	0.965457i
$276$		0			0
$277$	−5.61898	−	17.2935i	−0.337612	−	1.03906i	−0.965421	−	0.260696i	$-0.916048\pi$
$277$	−5.61898	−	17.2935i	−0.337612	−	1.03906i	0.627809	−	0.778367i	$-0.283952\pi$
$278$	9.47645			0.568360
$279$		0			0
$280$	−13.6770			−0.817358
$281$	1.95900	+	6.02919i	0.116864	+	0.359671i	0.992331	−	0.123607i	$-0.0394461\pi$
$281$	1.95900	+	6.02919i	0.116864	+	0.359671i	−0.875467	+	0.483278i	$0.839446\pi$
$282$		0			0
$283$	−17.5987	+	12.7862i	−1.04613	+	0.760059i	−0.971473	−	0.237150i	$-0.923787\pi$
$283$	−17.5987	+	12.7862i	−1.04613	+	0.760059i	−0.0746584	+	0.997209i	$0.523787\pi$
$284$	0.815141	+	1.41187i	0.0483697	+	0.0837788i
$285$		0			0
$286$	2.10377	+	20.0160i	0.124399	+	1.18357i
$287$	5.92874	+	4.30748i	0.349962	+	0.254262i
$288$		0			0
$289$	−2.51350	+	2.79152i	−0.147853	+	0.164207i
$290$	7.96843	+	3.54777i	0.467922	+	0.208332i
$291$		0			0
$292$	1.89550	−	0.402901i	0.110926	−	0.0235780i
$293$	16.1026	−	7.16932i	0.940721	−	0.418836i	0.121679	−	0.992569i	$-0.461172\pi$
$293$	16.1026	−	7.16932i	0.940721	−	0.418836i	0.819042	+	0.573733i	$0.194505\pi$
$294$		0			0
$295$	−3.84762	+	11.8418i	−0.224017	+	0.689454i
$296$	−24.3267	+	10.8309i	−1.41396	+	0.629536i
$297$		0			0
$298$	19.3696	+	4.11714i	1.12205	+	0.238500i
$299$	−21.3235	−	9.49384i	−1.23317	−	0.549043i
$300$		0			0
$301$	0.625385	−	5.95014i	0.0360466	−	0.342961i
$302$	−18.5312	−	13.4637i	−1.06635	−	0.774748i
$303$		0			0
$304$	6.30260	−	10.9164i	0.361479	−	0.626100i
$305$	11.4106	+	19.7638i	0.653370	+	1.13167i
$306$		0			0
$307$	−2.52181	−	2.80076i	−0.143927	−	0.159848i	0.666871	−	0.745173i	$-0.267633\pi$
$307$	−2.52181	−	2.80076i	−0.143927	−	0.159848i	−0.810798	+	0.585326i	$0.800967\pi$
$308$	−0.359904	−	1.10767i	−0.0205075	−	0.0631155i
$309$		0			0
$310$	−23.6987	+	6.61132i	−1.34600	+	0.375498i
$311$	3.50161			0.198558			0.0992792	−	0.995060i	$-0.468346\pi$
$311$	3.50161			0.198558			0.0992792	+	0.995060i	$0.468346\pi$
$312$		0			0
$313$	−11.7841	−	13.0876i	−0.666076	−	0.739752i	0.311521	−	0.950239i	$-0.399162\pi$
$313$	−11.7841	−	13.0876i	−0.666076	−	0.739752i	−0.977597	+	0.210487i	$0.932495\pi$
$314$	−18.0353	+	13.1034i	−1.01779	+	0.739467i
$315$		0			0
$316$	−0.758905	+	1.31446i	−0.0426917	+	0.0739442i
$317$	2.05768	+	19.5776i	0.115571	+	1.09959i	0.886521	+	0.462689i	$0.153115\pi$
$317$	2.05768	+	19.5776i	0.115571	+	1.09959i	−0.770950	+	0.636896i	$0.780218\pi$
$318$		0			0
$319$	−0.991109	+	9.42977i	−0.0554915	+	0.527966i
$320$	18.7089	−	20.7784i	1.04586	−	1.16155i
$321$		0			0
$322$	−14.2233	−	3.02325i	−0.792633	−	0.168479i
$323$	−12.3571	+	2.62658i	−0.687568	+	0.146147i
$324$		0			0
$325$	−5.42719	+	16.7032i	−0.301047	+	0.926526i
$326$	4.42672	−	13.6240i	0.245173	−	0.754565i
$327$		0			0
$328$	−14.7529	+	3.13583i	−0.814594	+	0.173147i
$329$	14.7919	+	3.14412i	0.815505	+	0.173341i
$330$		0			0
$331$	9.75171	−	10.8304i	0.536003	−	0.595291i	−0.412933	−	0.910761i	$-0.635496\pi$
$331$	9.75171	−	10.8304i	0.536003	−	0.595291i	0.948935	+	0.315470i	$0.102162\pi$
$332$	0.116416	−	1.10763i	0.00638918	−	0.0607890i
$333$		0			0
$334$	0.0703961	+	0.669775i	0.00385191	+	0.0366484i
$335$	13.1129	−	22.7122i	0.716434	−	1.24090i
$336$		0			0
$337$	21.3763	−	15.5308i	1.16444	−	0.846018i	0.174110	−	0.984726i	$-0.444295\pi$
$337$	21.3763	−	15.5308i	1.16444	−	0.846018i	0.990333	+	0.138708i	$0.0442950\pi$
$338$	−3.08407	−	3.42520i	−0.167751	−	0.186306i
$339$		0			0
$340$	−2.02080			−0.109593
$341$	−14.7957	−	22.2797i	−0.801232	−	1.20651i
$342$		0			0
$343$	−5.27392	−	16.2314i	−0.284765	−	0.876415i
$344$	8.23936	+	9.15073i	0.444236	+	0.493374i
$345$		0			0
$346$	11.3724	+	19.6976i	0.611385	+	1.05895i
$347$	−0.862463	+	1.49383i	−0.0462994	+	0.0801930i	−0.888246	−	0.459367i	$-0.848076\pi$
$347$	−0.862463	+	1.49383i	−0.0462994	+	0.0801930i	0.841947	+	0.539560i	$0.181410\pi$
$348$		0			0
$349$	−0.201963	−	0.146735i	−0.0108108	−	0.00785452i	0.582367	−	0.812926i	$-0.302127\pi$
$349$	−0.201963	−	0.146735i	−0.0108108	−	0.00785452i	−0.593178	+	0.805072i	$0.702127\pi$
$350$	−1.14365	+	10.8811i	−0.0611309	+	0.581622i
$351$		0			0
$352$	4.20806	+	1.87355i	0.224290	+	0.0998604i
$353$	3.38702	+	0.719933i	0.180273	+	0.0383182i	0.297163	−	0.954827i	$-0.403959\pi$
$353$	3.38702	+	0.719933i	0.180273	+	0.0383182i	−0.116891	+	0.993145i	$0.537293\pi$
$354$		0			0
$355$	28.6192	−	12.7421i	1.51895	−	0.676280i
$356$	0.0772392	−	0.237718i	0.00409367	−	0.0125990i
$357$		0			0
$358$	25.4831	−	11.3458i	1.34682	−	0.599644i
$359$	27.7672	−	5.90211i	1.46550	−	0.311501i	0.595021	−	0.803710i	$-0.297144\pi$
$359$	27.7672	−	5.90211i	1.46550	−	0.311501i	0.870477	+	0.492209i	$0.163810\pi$
$360$		0			0
$361$	−6.34836	−	2.82647i	−0.334124	−	0.148762i
$362$	21.2188	−	23.5659i	1.11524	−	1.23860i
$363$		0			0
$364$	−0.607540	−	0.441404i	−0.0318437	−	0.0231358i
$365$	−3.89240	−	37.0338i	−0.203738	−	1.93844i
$366$		0			0
$367$	0.174051	+	0.301464i	0.00908537	+	0.0157363i	0.870532	−	0.492111i	$-0.163775\pi$
$367$	0.174051	+	0.301464i	0.00908537	+	0.0157363i	−0.861447	+	0.507848i	$0.830441\pi$
$368$	22.1387	−	16.0847i	1.15406	−	0.838473i
$369$		0			0
$370$	12.3871	+	38.1235i	0.643974	+	1.98195i
$371$	−0.410514			−0.0213128
$372$		0			0
$373$	34.9539			1.80984			0.904922	−	0.425577i	$-0.139929\pi$
$373$	34.9539			1.80984			0.904922	+	0.425577i	$0.139929\pi$
$374$	7.30760	+	22.4905i	0.377867	+	1.16296i
$375$		0			0
$376$	−25.1795	+	18.2940i	−1.29853	+	0.943439i
$377$	3.05682	+	5.29456i	0.157434	+	0.272684i
$378$		0			0
$379$	1.69389	+	16.1163i	0.0870095	+	0.827840i	0.947797	+	0.318875i	$0.103305\pi$
$379$	1.69389	+	16.1163i	0.0870095	+	0.827840i	−0.860787	+	0.508965i	$0.830028\pi$
$380$	1.55950	+	1.13304i	0.0800006	+	0.0581239i
$381$		0			0
$382$	−10.7144	+	11.8995i	−0.548196	+	0.608833i
$383$	22.5923	+	10.0587i	1.15441	+	0.513978i	0.892470	−	0.451106i	$-0.148970\pi$
$383$	22.5923	+	10.0587i	1.15441	+	0.513978i	0.261942	+	0.965084i	$0.415637\pi$
$384$		0			0
$385$	−21.8914	+	4.65316i	−1.11569	+	0.237147i
$386$	−7.15523	+	3.18571i	−0.364192	+	0.162149i
$387$		0			0
$388$	0.490810	−	1.51056i	0.0249171	−	0.0766870i
$389$	−0.912340	+	0.406200i	−0.0462575	+	0.0205952i	−0.429735	−	0.902955i	$-0.641393\pi$
$389$	−0.912340	+	0.406200i	−0.0462575	+	0.0205952i	0.383478	+	0.923550i	$0.374726\pi$
$390$		0			0
$391$	−26.8264	−	5.70212i	−1.35667	−	0.288368i
$392$	13.3165	+	5.92887i	0.672583	+	0.299453i
$393$		0			0
$394$	2.27857	−	21.6791i	0.114793	−	1.09218i
$395$	23.5961	+	17.1435i	1.18725	+	0.862585i
$396$		0			0
$397$	6.79946	−	11.7770i	0.341255	−	0.591071i	−0.643411	−	0.765521i	$-0.722481\pi$
$397$	6.79946	−	11.7770i	0.341255	−	0.591071i	0.984666	+	0.174450i	$0.0558147\pi$
$398$	−6.22478	−	10.7816i	−0.312020	−	0.540434i
$399$		0			0
$400$	−13.7775	−	15.3014i	−0.688874	−	0.765072i
$401$	−0.712040	−	2.19143i	−0.0355576	−	0.109435i	0.931702	−	0.363223i	$-0.118324\pi$
$401$	−0.712040	−	2.19143i	−0.0355576	−	0.109435i	−0.967260	+	0.253788i	$0.918324\pi$
$402$		0			0
$403$	−16.1619	−	6.01448i	−0.805079	−	0.299603i
$404$	−2.15042			−0.106987
$405$		0			0
$406$	2.54846	+	2.83035i	0.126478	+	0.140468i
$407$	−35.2524	+	25.6124i	−1.74740	+	1.26956i
$408$		0			0
$409$	3.07389	−	5.32413i	0.151994	−	0.263261i	−0.779966	−	0.625821i	$-0.784764\pi$
$409$	3.07389	−	5.32413i	0.151994	−	0.263261i	0.931960	+	0.362560i	$0.118097\pi$
$410$	2.37324	+	22.5799i	0.117206	+	1.11514i
$411$		0			0
$412$	0.0548047	−	0.521432i	0.00270004	−	0.0256891i
$413$	−3.63785	+	4.04024i	−0.179007	+	0.198807i
$414$		0			0
$415$	−20.9338	−	4.44962i	−1.02760	−	0.218423i
$416$	2.90515	−	0.617508i	0.142437	−	0.0302758i
$417$		0			0
$418$	6.97076	−	21.4538i	0.340951	−	1.04934i
$419$	−1.41520	+	4.35554i	−0.0691370	+	0.212782i	−0.979656	−	0.200686i	$-0.935683\pi$
$419$	−1.41520	+	4.35554i	−0.0691370	+	0.212782i	0.910519	+	0.413468i	$0.135683\pi$
$420$		0			0
$421$	25.5370	−	5.42805i	1.24460	−	0.264547i	0.461890	−	0.886937i	$-0.347172\pi$
$421$	25.5370	−	5.42805i	1.24460	−	0.264547i	0.782707	+	0.622390i	$0.213838\pi$
$422$	−17.8793	−	3.80036i	−0.870351	−	0.184999i
$423$		0			0
$424$	0.565338	−	0.627871i	0.0274552	−	0.0304921i
$425$	−2.15703	+	20.5228i	−0.104631	+	0.995501i
$426$		0			0
$427$	1.04159	+	9.91008i	0.0504062	+	0.479582i
$428$	−0.921441	+	1.59598i	−0.0445395	+	0.0771447i
$429$		0			0
$430$	14.9959	−	10.8952i	0.723168	−	0.525413i
$431$	7.96657	+	8.84778i	0.383736	+	0.426182i	0.903807	−	0.427941i	$-0.140761\pi$
$431$	7.96657	+	8.84778i	0.383736	+	0.426182i	−0.520070	+	0.854123i	$0.674094\pi$
$432$		0			0
$433$	33.6810			1.61861			0.809304	−	0.587391i	$-0.199845\pi$
$433$	33.6810			1.61861			0.809304	+	0.587391i	$0.199845\pi$
$434$	−10.6273	−	1.57164i	−0.510129	−	0.0754410i
$435$		0			0
$436$	−0.871935	−	2.68354i	−0.0417581	−	0.128518i
$437$	17.5055	+	19.4418i	0.837400	+	0.930027i
$438$		0			0
$439$	0.385671	+	0.668002i	0.0184071	+	0.0318820i	0.875082	−	0.483974i	$-0.160807\pi$
$439$	0.385671	+	0.668002i	0.0184071	+	0.0318820i	−0.856675	+	0.515856i	$0.827474\pi$
$440$	23.0308	−	39.8905i	1.09795	−	1.90170i
$441$		0			0
$442$	12.3357	+	8.96238i	0.586748	+	0.426297i
$443$	3.74931	−	35.6723i	0.178135	−	1.69484i	−0.431462	−	0.902131i	$-0.642002\pi$
$443$	3.74931	−	35.6723i	0.178135	−	1.69484i	0.609597	−	0.792711i	$-0.291331\pi$
$444$		0			0
$445$	−4.38783	−	1.95359i	−0.208003	−	0.0926090i
$446$	5.67845	+	1.20699i	0.268882	+	0.0571527i
$447$		0			0
$448$	11.1530	−	4.96564i	0.526930	−	0.234604i
$449$	2.17372	−	6.69002i	0.102584	−	0.315722i	−0.886572	−	0.462591i	$-0.846920\pi$
$449$	2.17372	−	6.69002i	0.102584	−	0.315722i	0.989156	+	0.146870i	$0.0469198\pi$
$450$		0			0
$451$	−22.5466	+	10.0384i	−1.06168	+	0.472690i
$452$	0.861600	−	0.183139i	0.0405263	−	0.00861413i
$453$		0			0
$454$	9.43446	+	4.20049i	0.442781	+	0.197139i
$455$	−9.65590	+	10.7240i	−0.452675	+	0.502747i
$456$		0			0
$457$	−2.60474	−	1.89245i	−0.121844	−	0.0885251i	0.525194	−	0.850982i	$-0.323993\pi$
$457$	−2.60474	−	1.89245i	−0.121844	−	0.0885251i	−0.647039	+	0.762457i	$0.723993\pi$
$458$	−1.90091	−	18.0860i	−0.0888237	−	0.845101i
$459$		0			0
$460$	2.09239	+	3.62412i	0.0975581	+	0.168976i
$461$	−10.0142	+	7.27572i	−0.466406	+	0.338864i	−0.796039	−	0.605245i	$-0.793075\pi$
$461$	−10.0142	+	7.27572i	−0.466406	+	0.338864i	0.329633	+	0.944109i	$0.393075\pi$
$462$		0			0
$463$	2.08682	+	6.42257i	0.0969828	+	0.298482i	0.987765	−	0.155947i	$-0.0498431\pi$
$463$	2.08682	+	6.42257i	0.0969828	+	0.298482i	−0.890783	+	0.454430i	$0.849843\pi$
$464$	−7.16746			−0.332741
$465$		0			0
$466$	19.8803			0.920937
$467$	−4.34942	−	13.3861i	−0.201267	−	0.619436i	−0.999846	−	0.0175461i	$-0.994415\pi$
$467$	−4.34942	−	13.3861i	−0.201267	−	0.619436i	0.798579	−	0.601890i	$-0.205585\pi$
$468$		0			0
$469$	9.26424	−	6.73086i	0.427783	−	0.310802i
$470$	23.4257	+	40.5745i	1.08055	+	1.87156i
$471$		0			0
$472$	−1.16960	−	11.1280i	−0.0538352	−	0.512208i
$473$	16.3011	+	11.8435i	0.749527	+	0.544563i
$474$		0			0
$475$	13.1716	−	14.6285i	0.604354	−	0.671203i
$476$	−0.806076	−	0.358888i	−0.0369464	−	0.0164496i
$477$		0			0
$478$	6.16563	−	1.31054i	0.282009	−	0.0599429i
$479$	−12.7647	+	5.68321i	−0.583234	+	0.259672i	−0.677074	−	0.735915i	$-0.736752\pi$
$479$	−12.7647	+	5.68321i	−0.583234	+	0.259672i	0.0938404	+	0.995587i	$0.470086\pi$
$480$		0			0
$481$	−8.68212	+	26.7208i	−0.395870	+	1.21836i
$482$	16.7987	−	7.47924i	0.765158	−	0.340670i
$483$		0			0
$484$	2.00764	+	0.426738i	0.0912565	+	0.0193972i
$485$	−27.8821	−	12.4139i	−1.26606	−	0.563687i
$486$		0			0
$487$	0.945188	−	8.99286i	0.0428305	−	0.407505i	−0.952011	−	0.306064i	$-0.900988\pi$
$487$	0.945188	−	8.99286i	0.0428305	−	0.407505i	0.994842	−	0.101441i	$-0.0323455\pi$
$488$	−16.5917	−	12.0545i	−0.751069	−	0.545684i
$489$		0			0
$490$	10.9714	−	19.0030i	0.495638	−	0.858469i
$491$	−8.41149	−	14.5691i	−0.379605	−	0.657496i	0.611399	−	0.791322i	$-0.290607\pi$
$491$	−8.41149	−	14.5691i	−0.379605	−	0.657496i	−0.991005	+	0.133826i	$0.957274\pi$
$492$		0			0
$493$	4.80661	+	5.33828i	0.216479	+	0.240424i
$494$	−4.49462	−	13.8330i	−0.202222	−	0.622376i
$495$		0			0
$496$	15.5804	−	12.8836i	0.699580	−	0.578491i
$497$	13.6789			0.613582
$498$		0			0
$499$	−2.73113	−	3.03322i	−0.122262	−	0.135786i	0.678906	−	0.734225i	$-0.262454\pi$
$499$	−2.73113	−	3.03322i	−0.122262	−	0.135786i	−0.801168	+	0.598439i	$0.795788\pi$
$500$	0.301196	−	0.218832i	0.0134699	−	0.00978645i
$501$		0			0
$502$	14.4317	−	24.9965i	0.644119	−	1.11565i
$503$	0.779835	+	7.41963i	0.0347711	+	0.330825i	0.998055	+	0.0623400i	$0.0198563\pi$
$503$	0.779835	+	7.41963i	0.0347711	+	0.330825i	−0.963284	+	0.268485i	$0.913477\pi$
$504$		0			0
$505$	−4.31939	+	41.0962i	−0.192210	+	1.82876i
$506$	32.7683	−	36.3929i	1.45673	−	1.61786i
$507$		0			0
$508$	0.457985	+	0.0973476i	0.0203198	+	0.00431910i
$509$	13.3996	−	2.84817i	0.593926	−	0.126243i	0.0988649	−	0.995101i	$-0.468479\pi$
$509$	13.3996	−	2.84817i	0.593926	−	0.126243i	0.495062	+	0.868858i	$0.335146\pi$
$510$		0			0
$511$	5.02446	−	15.4637i	0.222269	−	0.684074i
$512$	−7.66376	+	23.5866i	−0.338693	+	1.04239i
$513$		0			0
$514$	−27.9919	+	5.94987i	−1.23467	+	0.262437i
$515$	−9.85490	−	2.09472i	−0.434259	−	0.0923046i
$516$		0			0
$517$	−34.0783	+	37.8478i	−1.49876	+	1.66454i
$518$	−1.82955	+	17.4070i	−0.0803859	+	0.764821i
$519$		0			0
$520$	−3.10446	−	29.5369i	−0.136139	−	1.29528i
$521$	−9.22884	+	15.9848i	−0.404323	+	0.700307i	−0.994242	−	0.107155i	$-0.965826\pi$
$521$	−9.22884	+	15.9848i	−0.404323	+	0.700307i	0.589920	+	0.807462i	$0.299159\pi$
$522$		0			0
$523$	−25.9172	+	18.8299i	−1.13328	+	0.823376i	−0.986169	−	0.165744i	$-0.946997\pi$
$523$	−25.9172	+	18.8299i	−1.13328	+	0.823376i	−0.147111	+	0.989120i	$0.546997\pi$
$524$	1.31585	+	1.46140i	0.0574832	+	0.0638416i
$525$		0			0
$526$	−11.8276			−0.515707
$527$	−20.0441	−	2.96424i	−0.873135	−	0.129124i
$528$		0			0
$529$	10.4431	+	32.1406i	0.454049	+	1.39742i
$530$	−0.851024	−	0.945158i	−0.0369661	−	0.0410550i
$531$		0			0
$532$	0.420844	+	0.728924i	0.0182459	+	0.0316028i
$533$	−7.95672	+	13.7814i	−0.344644	+	0.596940i
$534$		0			0
$535$	28.6497	+	20.8152i	1.23863	+	0.899920i
$536$	−2.46352	+	23.4388i	−0.106408	+	1.01240i
$537$		0			0
$538$	−16.5823	−	7.38293i	−0.714915	−	0.318301i
$539$	23.3314	+	4.95924i	1.00495	+	0.213610i
$540$		0			0
$541$	−26.7744	+	11.9207i	−1.15112	+	0.512513i	−0.891421	−	0.453176i	$-0.850291\pi$
$541$	−26.7744	+	11.9207i	−1.15112	+	0.512513i	−0.259702	+	0.965689i	$0.583624\pi$
$542$	−9.35370	+	28.7877i	−0.401776	+	1.23654i
$543$		0			0
$544$	3.18803	−	1.41940i	0.136686	−	0.0608564i
$545$	−53.0360	+	11.2732i	−2.27181	+	0.482889i
$546$		0			0
$547$	−9.53909	−	4.24708i	−0.407862	−	0.181592i	0.192542	−	0.981289i	$-0.438327\pi$
$547$	−9.53909	−	4.24708i	−0.407862	−	0.181592i	−0.600404	+	0.799697i	$0.704994\pi$
$548$	0.771227	−	0.856534i	0.0329452	−	0.0365893i
$549$		0			0
$550$	−29.8102	−	21.6584i	−1.27111	−	0.923516i
$551$	−0.716256	−	6.81472i	−0.0305135	−	0.290317i
$552$		0			0
$553$	6.36760	+	11.0290i	0.270778	+	0.469001i
$554$	19.9003	−	14.4584i	0.845483	−	0.614279i
$555$		0			0
$556$	−0.367984	−	1.13254i	−0.0156060	−	0.0480303i
$557$	32.9017			1.39409			0.697044	−	0.717028i	$-0.254498\pi$
$557$	32.9017			1.39409			0.697044	+	0.717028i	$0.254498\pi$
$558$		0			0
$559$	12.9919			0.549499
$560$	−5.22793	−	16.0899i	−0.220920	−	0.679923i
$561$		0			0
$562$	−6.93804	+	5.04078i	−0.292663	+	0.212632i
$563$	−16.3035	−	28.2386i	−0.687113	−	1.19011i	−0.972768	−	0.231781i	$-0.925545\pi$
$563$	−16.3035	−	28.2386i	−0.687113	−	1.19011i	0.285655	−	0.958332i	$-0.407789\pi$
$564$		0			0
$565$	−1.76930	−	16.8337i	−0.0744348	−	0.708200i
$566$	−23.8071	−	17.2969i	−1.00069	−	0.727041i
$567$		0			0
$568$	−18.8378	+	20.9216i	−0.790419	+	0.877849i
$569$	−18.4304	−	8.20573i	−0.772642	−	0.344002i	−0.0177420	−	0.999843i	$-0.505648\pi$
$569$	−18.4304	−	8.20573i	−0.772642	−	0.344002i	−0.754900	+	0.655840i	$0.772314\pi$
$570$		0			0
$571$	−23.4135	+	4.97670i	−0.979826	+	0.208268i	−0.669867	−	0.742481i	$-0.733649\pi$
$571$	−23.4135	+	4.97670i	−0.979826	+	0.208268i	−0.309959	+	0.950750i	$0.600315\pi$
$572$	2.31044	−	1.02867i	0.0966043	−	0.0430110i
$573$		0			0
$574$	−3.06347	+	9.42839i	−0.127867	+	0.393533i
$575$	39.0393	−	17.3814i	1.62805	−	0.724855i
$576$		0			0
$577$	−34.4064	−	7.31330i	−1.43236	−	0.304457i	−0.574566	−	0.818458i	$-0.694829\pi$
$577$	−34.4064	−	7.31330i	−1.43236	−	0.304457i	−0.857789	+	0.514001i	$0.828163\pi$
$578$	−4.64221	−	2.06684i	−0.193090	−	0.0859694i
$579$		0			0
$580$	0.114572	−	1.09008i	0.00475733	−	0.0452630i
$581$	−7.56006	−	5.49271i	−0.313644	−	0.227876i
$582$		0			0
$583$	0.691266	−	1.19731i	0.0286293	−	0.0495874i
$584$	16.7319	+	28.9806i	0.692373	+	1.19922i
$585$		0			0
$586$	15.9552	+	17.7200i	0.659103	+	0.732008i
$587$	3.53695	+	10.8856i	0.145986	+	0.449297i	0.997136	−	0.0756239i	$-0.0240948\pi$
$587$	3.53695	+	10.8856i	0.145986	+	0.449297i	−0.851151	+	0.524921i	$0.824095\pi$
$588$		0			0
$589$	13.8065	+	13.5261i	0.568888	+	0.557335i
$590$	−16.8437			−0.693443
$591$		0			0
$592$	−22.0404	−	24.4784i	−0.905856	−	1.00605i
$593$	−31.4634	+	22.8595i	−1.29205	+	0.938727i	−0.999845	−	0.0176300i	$-0.994388\pi$
$593$	−31.4634	+	22.8595i	−1.29205	+	0.938727i	−0.292202	+	0.956357i	$0.594388\pi$
$594$		0			0
$595$	−8.47775	+	14.6839i	−0.347554	+	0.601981i
$596$	−0.260107	−	2.47475i	−0.0106544	−	0.101370i
$597$		0			0
$598$	3.30057	−	31.4029i	0.134971	−	1.28416i
$599$	−11.3133	+	12.5647i	−0.462248	+	0.513379i	−0.928530	−	0.371257i	$-0.878927\pi$
$599$	−11.3133	+	12.5647i	−0.462248	+	0.513379i	0.466281	+	0.884636i	$0.345593\pi$
$600$		0			0
$601$	−12.0115	−	2.55312i	−0.489959	−	0.104144i	−0.0436944	−	0.999045i	$-0.513913\pi$
$601$	−12.0115	−	2.55312i	−0.489959	−	0.104144i	−0.446265	+	0.894901i	$0.647246\pi$
$602$	7.91670	−	1.68275i	0.322661	−	0.0685836i
$603$		0			0
$604$	−0.889463	+	2.73749i	−0.0361918	+	0.111387i
$605$	12.1879	−	37.5105i	0.495509	−	1.52502i
$606$		0			0
$607$	15.0377	−	3.19636i	0.610360	−	0.129736i	0.107647	−	0.994189i	$-0.465668\pi$
$607$	15.0377	−	3.19636i	0.610360	−	0.129736i	0.502713	+	0.864453i	$0.332335\pi$
$608$	−3.25613	−	0.692113i	−0.132054	−	0.0280689i
$609$		0			0
$610$	−20.6574	+	22.9424i	−0.836396	+	0.928911i
$611$	−3.43253	+	32.6583i	−0.138865	+	1.32121i
$612$		0			0
$613$	2.00947	+	19.1189i	0.0811619	+	0.772204i	0.957096	+	0.289772i	$0.0935796\pi$
$613$	2.00947	+	19.1189i	0.0811619	+	0.772204i	−0.875934	+	0.482432i	$0.839754\pi$
$614$	2.54917	−	4.41529i	0.102876	−	0.178187i
$615$		0			0
$616$	16.2712	−	11.8217i	0.655586	−	0.476311i
$617$	−7.11429	−	7.90122i	−0.286411	−	0.318091i	0.582721	−	0.812672i	$-0.301988\pi$
$617$	−7.11429	−	7.90122i	−0.286411	−	0.318091i	−0.869131	+	0.494581i	$0.835321\pi$
$618$		0			0
$619$	22.7175			0.913093			0.456546	−	0.889700i	$-0.349086\pi$
$619$	22.7175			0.913093			0.456546	+	0.889700i	$0.349086\pi$
$620$	1.71038	+	2.57552i	0.0686904	+	0.103435i
$621$		0			0
$622$	1.46379	+	4.50507i	0.0586924	+	0.180637i
$623$	−1.40331	−	1.55854i	−0.0562226	−	0.0624415i
$624$		0			0
$625$	10.5991	+	18.3582i	0.423964	+	0.734327i
$626$	11.9119	−	20.6320i	0.476096	−	0.824622i
$627$		0			0
$628$	2.26633	+	1.64658i	0.0904364	+	0.0657059i
$629$	−3.45070	+	32.8312i	−0.137588	+	1.30906i
$630$		0			0
$631$	−13.8808	−	6.18014i	−0.552587	−	0.246027i	0.111395	−	0.993776i	$-0.464468\pi$
$631$	−13.8808	−	6.18014i	−0.552587	−	0.246027i	−0.663982	+	0.747749i	$0.731135\pi$
$632$	−25.6377	−	5.44946i	−1.01981	−	0.216768i
$633$		0			0
$634$	−24.3277	+	10.8314i	−0.966176	+	0.430169i
$635$	2.78031	−	8.55692i	0.110333	−	0.339571i
$636$		0			0
$637$	14.0501	−	6.25550i	0.556685	−	0.247852i
$638$	−12.5464	+	2.66681i	−0.496715	+	0.105580i
$639$		0			0
$640$	28.8305	+	12.8362i	1.13963	+	0.507394i
$641$	14.5229	−	16.1294i	0.573622	−	0.637072i	−0.384605	−	0.923081i	$-0.625662\pi$
$641$	14.5229	−	16.1294i	0.573622	−	0.637072i	0.958227	+	0.286010i	$0.0923290\pi$
$642$		0			0
$643$	−27.3906	−	19.9004i	−1.08018	−	0.784796i	−0.102465	−	0.994737i	$-0.532673\pi$
$643$	−27.3906	−	19.9004i	−1.08018	−	0.784796i	−0.977714	+	0.209940i	$0.932673\pi$
$644$	0.190999	+	1.81723i	0.00752641	+	0.0716090i
$645$		0			0
$646$	−8.54494	−	14.8003i	−0.336196	−	0.582309i
$647$	8.83959	−	6.42234i	0.347520	−	0.252488i	−0.400308	−	0.916381i	$-0.631097\pi$
$647$	8.83959	−	6.42234i	0.347520	−	0.252488i	0.747828	+	0.663893i	$0.231097\pi$
$648$		0			0
$649$	−5.65800	−	17.4135i	−0.222096	−	0.683541i
$650$	−23.7585			−0.931886
$651$		0			0
$652$	−1.80011			−0.0704979
$653$	−11.3941	−	35.0673i	−0.445884	−	1.37229i	−0.881511	−	0.472163i	$-0.843473\pi$
$653$	−11.3941	−	35.0673i	−0.445884	−	1.37229i	0.435627	−	0.900127i	$-0.356527\pi$
$654$		0			0
$655$	30.5716	−	22.2115i	1.19453	−	0.867877i
$656$	−9.32824	−	16.1570i	−0.364207	−	0.630824i
$657$		0			0
$658$	2.13836	+	20.3451i	0.0833620	+	0.793136i
$659$	−17.0295	−	12.3726i	−0.663374	−	0.481970i	0.204426	−	0.978882i	$-0.434467\pi$
$659$	−17.0295	−	12.3726i	−0.663374	−	0.481970i	−0.867801	+	0.496912i	$0.834467\pi$
$660$		0			0
$661$	17.9476	−	19.9328i	0.698080	−	0.775297i	−0.284989	−	0.958531i	$-0.591990\pi$
$661$	17.9476	−	19.9328i	0.698080	−	0.775297i	0.983069	+	0.183234i	$0.0586566\pi$
$662$	18.0105	+	8.01881i	0.700000	+	0.311660i
$663$		0			0
$664$	18.8123	−	3.99867i	0.730058	−	0.155179i
$665$	14.7756	−	6.57853i	0.572974	−	0.255105i
$666$		0			0
$667$	4.59685	−	14.1477i	0.177991	−	0.547799i
$668$	0.0773117	−	0.0344214i	0.00299128	−	0.00133180i
$669$		0			0
$670$	34.7024	+	7.37622i	1.34067	+	0.284968i
$671$	−30.6577	−	13.6497i	−1.18353	−	0.526941i
$672$		0			0
$673$	2.63640	−	25.0837i	0.101626	−	0.966905i	−0.818294	−	0.574799i	$-0.805080\pi$
$673$	2.63640	−	25.0837i	0.101626	−	0.966905i	0.919920	−	0.392105i	$-0.128253\pi$
$674$	28.9175	+	21.0098i	1.11386	+	0.809266i
$675$		0			0
$676$	−0.289590	+	0.501584i	−0.0111381	+	0.0192917i
$677$	5.01179	+	8.68068i	0.192619	+	0.333626i	0.946117	−	0.323824i	$-0.104969\pi$
$677$	5.01179	+	8.68068i	0.192619	+	0.333626i	−0.753499	+	0.657450i	$0.771635\pi$
$678$		0			0
$679$	−8.91724	−	9.90360i	−0.342212	−	0.380065i
$680$	−10.7836	−	33.1884i	−0.413531	−	1.27272i
$681$		0			0
$682$	22.4793	−	28.3493i	0.860776	−	1.08555i
$683$	−37.1303			−1.42075			−0.710375	−	0.703823i	$-0.751475\pi$
$683$	−37.1303			−1.42075			−0.710375	+	0.703823i	$0.751475\pi$
$684$		0			0
$685$	−14.8199	−	16.4592i	−0.566241	−	0.628874i
$686$	18.6782	−	13.5705i	0.713137	−	0.518124i
$687$		0			0
$688$	−7.61568	+	13.1907i	−0.290345	+	0.502892i
$689$	−0.0931799	−	0.886547i	−0.00354987	−	0.0337748i
$690$		0			0
$691$	0.647258	−	6.15824i	0.0246228	−	0.234271i	−0.975288	−	0.220936i	$-0.929089\pi$
$691$	0.647258	−	6.15824i	0.0246228	−	0.234271i	0.999911	−	0.0133344i	$-0.00424460\pi$
$692$	1.91247	−	2.12401i	0.0727012	−	0.0807428i
$693$		0			0
$694$	−2.28245	−	0.485150i	−0.0866406	−	0.0184160i
$695$	−22.3828	+	4.75762i	−0.849030	+	0.180467i
$696$		0			0
$697$	−5.77797	+	17.7828i	−0.218856	+	0.673570i
$698$	0.104357	−	0.321179i	0.00394998	−	0.0121568i
$699$		0			0
$700$	1.34482	−	0.285851i	0.0508295	−	0.0108042i
$701$	0.809388	+	0.172041i	0.0305702	+	0.00649789i	0.223171	−	0.974779i	$-0.428359\pi$
$701$	0.809388	+	0.172041i	0.0305702	+	0.00649789i	−0.192601	+	0.981277i	$0.561692\pi$
$702$		0			0
$703$	21.0712	−	23.4019i	0.794714	−	0.882619i
$704$	−4.29777	+	40.8906i	−0.161978	+	1.54112i
$705$		0			0
$706$	0.489637	+	4.65858i	0.0184277	+	0.175328i
$707$	−9.02155	+	15.6258i	−0.339290	+	0.587668i
$708$		0			0
$709$	19.8174	−	14.3982i	0.744260	−	0.540736i	−0.149783	−	0.988719i	$-0.547857\pi$
$709$	19.8174	−	14.3982i	0.744260	−	0.540736i	0.894042	+	0.447983i	$0.147857\pi$
$710$	28.3573	+	31.4940i	1.06423	+	1.18195i
$711$		0			0
$712$	4.31631			0.161761
$713$	15.4381	+	39.0166i	0.578162	+	1.46118i
$714$		0			0
$715$	−15.0180	−	46.2205i	−0.561640	−	1.72855i
$716$	−2.34549	−	2.60493i	−0.0876550	−	0.0973508i
$717$		0			0
$718$	19.2010	+	33.2572i	0.716577	+	1.24115i
$719$	7.08615	−	12.2736i	0.264269	−	0.457727i	−0.703103	−	0.711088i	$-0.748203\pi$
$719$	7.08615	−	12.2736i	0.264269	−	0.457727i	0.967372	+	0.253361i	$0.0815361\pi$
$720$		0			0
$721$	−3.55901	−	2.58577i	−0.132544	−	0.0962992i
$722$	0.982635	−	9.34915i	0.0365699	−	0.347939i
$723$		0			0
$724$	−3.64033	−	1.62078i	−0.135292	−	0.0602359i
$725$	−10.9483	−	2.32714i	−0.406610	−	0.0864276i
$726$		0			0
$727$	−31.2480	+	13.9125i	−1.15893	+	0.515987i	−0.893905	−	0.448256i	$-0.852045\pi$
$727$	−31.2480	+	13.9125i	−1.15893	+	0.515987i	−0.265020	+	0.964243i	$0.585379\pi$
$728$	4.00735	−	12.3333i	0.148522	−	0.457104i
$729$		0			0
$730$	46.0193	−	20.4891i	1.70325	−	0.758336i
$731$	14.9316	−	3.17381i	0.552265	−	0.117387i
$732$		0			0
$733$	−13.6813	−	6.09132i	−0.505332	−	0.224988i	0.138205	−	0.990404i	$-0.455867\pi$
$733$	−13.6813	−	6.09132i	−0.505332	−	0.224988i	−0.643536	+	0.765415i	$0.722534\pi$
$734$	−0.315096	+	0.349950i	−0.0116304	+	0.0129169i
$735$		0			0
$736$	−5.84656	−	4.24777i	−0.215507	−	0.156575i
$737$	4.03119	+	38.3543i	0.148491	+	1.41280i
$738$		0			0
$739$	10.0421	+	17.3934i	0.369404	+	0.639827i	0.989473	−	0.144721i	$-0.0462284\pi$
$739$	10.0421	+	17.3934i	0.369404	+	0.639827i	−0.620068	+	0.784548i	$0.712895\pi$
$740$	4.07516	−	2.96078i	0.149806	−	0.108840i
$741$		0			0
$742$	−0.171608	−	0.528154i	−0.00629992	−	0.0193892i
$743$	16.3801			0.600928			0.300464	−	0.953793i	$-0.402859\pi$
$743$	16.3801			0.600928			0.300464	+	0.953793i	$0.402859\pi$
$744$		0			0
$745$	−47.8170			−1.75188
$746$	14.6118	+	44.9706i	0.534977	+	1.64649i
$747$		0			0
$748$	2.40409	−	1.74667i	0.0879022	−	0.0638647i
$749$	7.73136	+	13.3911i	0.282498	+	0.489300i
$750$		0			0
$751$	−2.67660	−	25.4661i	−0.0976705	−	0.929272i	−0.928146	−	0.372217i	$-0.878598\pi$
$751$	−2.67660	−	25.4661i	−0.0976705	−	0.929272i	0.830475	−	0.557055i	$-0.188069\pi$
$752$	−31.1460	−	22.6289i	−1.13578	−	0.825192i
$753$		0			0
$754$	−5.53397	+	6.14609i	−0.201535	+	0.223828i
$755$	50.5290	+	22.4969i	1.83894	+	0.818748i
$756$		0			0
$757$	30.1887	−	6.41681i	1.09723	−	0.233223i	0.376482	−	0.926424i	$-0.377134\pi$
$757$	30.1887	−	6.41681i	1.09723	−	0.233223i	0.720744	+	0.693201i	$0.243800\pi$
$758$	−20.0267	+	8.91644i	−0.727401	+	0.323860i
$759$		0			0
$760$	−10.2865	+	31.6586i	−0.373130	+	1.14838i
$761$	−18.9916	+	8.45560i	−0.688445	+	0.306515i	−0.720981	−	0.692955i	$-0.756308\pi$
$761$	−18.9916	+	8.45560i	−0.688445	+	0.306515i	0.0325360	+	0.999471i	$0.489642\pi$
$762$		0			0
$763$	−23.1577	−	4.92231i	−0.838363	−	0.178200i
$764$	1.83818	+	0.818409i	0.0665029	+	0.0296090i
$765$		0			0
$766$	−3.49697	+	33.2714i	−0.126351	+	1.20214i
$767$	−9.55104	−	6.93924i	−0.344868	−	0.250561i
$768$		0			0
$769$	−8.70269	+	15.0735i	−0.313827	+	0.543565i	−0.979187	−	0.202958i	$-0.934945\pi$
$769$	−8.70269	+	15.0735i	−0.313827	+	0.543565i	0.665360	+	0.746522i	$0.268278\pi$
$770$	−15.1379	−	26.2196i	−0.545532	−	0.944890i
$771$		0			0
$772$	0.658575	+	0.731421i	0.0237026	+	0.0263244i
$773$	−9.26303	−	28.5087i	−0.333168	−	1.02539i	−0.967617	−	0.252421i	$-0.918773\pi$
$773$	−9.26303	−	28.5087i	−0.333168	−	1.02539i	0.634450	−	0.772964i	$-0.281227\pi$
$774$		0			0
$775$	27.9822	−	14.6211i	1.00515	−	0.525205i
$776$	27.4277			0.984596
$777$		0			0
$778$	−0.903991	−	1.00398i	−0.0324097	−	0.0359946i
$779$	14.4296	−	10.4838i	0.516996	−	0.375619i
$780$		0			0
$781$	−23.0339	+	39.8960i	−0.824219	+	1.42759i
$782$	−3.87809	−	36.8976i	−0.138680	−	1.31946i
$783$		0			0
$784$	−1.88473	+	17.9320i	−0.0673118	+	0.640429i
$785$	36.0198	−	40.0040i	1.28560	−	1.42780i
$786$		0			0
$787$	39.4672	+	8.38902i	1.40686	+	0.299036i	0.847898	−	0.530160i	$-0.177868\pi$
$787$	39.4672	+	8.38902i	1.40686	+	0.299036i	0.558958	+	0.829196i	$0.311201\pi$
$788$	−2.67937	+	0.569518i	−0.0954486	+	0.0202882i
$789$		0			0
$790$	−12.1924	+	37.5245i	−0.433788	+	1.33506i
$791$	2.28387	−	7.02904i	0.0812052	−	0.249924i
$792$		0			0
$793$	−21.1654	+	4.49885i	−0.751606	+	0.159759i
$794$	17.9943	+	3.82481i	0.638594	+	0.135737i
$795$		0			0
$796$	−1.04680	+	1.16259i	−0.0371030	+	0.0412070i
$797$	1.07763	−	10.2530i	0.0381716	−	0.363179i	−0.958717	−	0.284361i	$-0.908219\pi$
$797$	1.07763	−	10.2530i	0.0381716	−	0.363179i	0.996889	−	0.0788180i	$-0.0251146\pi$
$798$		0			0
$799$	4.03314	+	38.3727i	0.142682	+	1.35753i
$800$	−2.71880	+	4.70910i	−0.0961241	+	0.166492i
$801$		0			0
$802$	2.52177	−	1.83218i	0.0890469	−	0.0646964i
$803$	36.6408	+	40.6938i	1.29303	+	1.43605i
$804$		0			0
$805$	35.1124			1.23755
$806$	0.981879	−	23.3076i	0.0345852	−	0.820974i
$807$		0			0
$808$	−11.4753	−	35.3172i	−0.403699	−	1.24246i
$809$	−14.9350	−	16.5870i	−0.525086	−	0.583167i	0.421009	−	0.907056i	$-0.361676\pi$
$809$	−14.9350	−	16.5870i	−0.525086	−	0.583167i	−0.946095	+	0.323889i	$0.895009\pi$
$810$		0			0
$811$	19.3338	+	33.4871i	0.678901	+	1.17589i	0.975312	+	0.220830i	$0.0708766\pi$
$811$	19.3338	+	33.4871i	0.678901	+	1.17589i	−0.296412	+	0.955060i	$0.595790\pi$
$812$	0.239297	−	0.414474i	0.00839767	−	0.0145452i
$813$		0			0
$814$	−47.6887	−	34.6478i	−1.67149	−	1.21441i
$815$	−3.61575	+	34.4016i	−0.126654	+	1.20504i
$816$		0			0
$817$	−13.3026	−	5.92271i	−0.465400	−	0.207209i
$818$	8.13484	+	1.72911i	0.284428	+	0.0604570i
$819$		0			0
$820$	2.60638	−	1.16044i	0.0910188	−	0.0405242i
$821$	−11.1023	+	34.1693i	−0.387472	+	1.19252i	0.547199	+	0.837002i	$0.315694\pi$
$821$	−11.1023	+	34.1693i	−0.387472	+	1.19252i	−0.934671	+	0.355513i	$0.884306\pi$
$822$		0			0
$823$	−2.48601	+	1.10684i	−0.0866568	+	0.0385821i	−0.449607	−	0.893226i	$-0.648436\pi$
$823$	−2.48601	+	1.10684i	−0.0866568	+	0.0385821i	0.362951	+	0.931808i	$0.381769\pi$
$824$	8.85616	−	1.88243i	0.308519	−	0.0655777i
$825$		0			0
$826$	−6.71878	−	2.99139i	−0.233776	−	0.104084i
$827$	9.01033	−	10.0070i	0.313320	−	0.347977i	−0.565830	−	0.824522i	$-0.691444\pi$
$827$	9.01033	−	10.0070i	0.313320	−	0.347977i	0.879150	+	0.476545i	$0.158111\pi$
$828$		0			0
$829$	27.0794	+	19.6744i	0.940507	+	0.683319i	0.948543	−	0.316649i	$-0.102558\pi$
$829$	27.0794	+	19.6744i	0.940507	+	0.683319i	−0.00803530	+	0.999968i	$0.502558\pi$
$830$	−3.02625	−	28.7929i	−0.105043	−	0.999415i
$831$		0			0
$832$	13.2554	+	22.9589i	0.459547	+	0.795958i
$833$	14.6196	−	10.6218i	0.506539	−	0.368022i
$834$		0			0
$835$	−0.502530	−	1.54663i	−0.0173908	−	0.0535232i
$836$	−2.83464			−0.0980382
$837$		0			0
$838$	−6.19529			−0.214013
$839$	3.92752	+	12.0876i	0.135593	+	0.417312i	0.995682	−	0.0928322i	$-0.0295920\pi$
$839$	3.92752	+	12.0876i	0.135593	+	0.417312i	−0.860089	+	0.510144i	$0.829592\pi$
$840$		0			0
$841$	20.3093	−	14.7556i	0.700322	−	0.508814i
$842$	17.6588	+	30.5860i	0.608563	+	1.05406i
$843$		0			0
$844$	0.240094	+	2.28434i	0.00826438	+	0.0786303i
$845$	9.00400	+	6.54179i	0.309747	+	0.225044i
$846$		0			0
$847$	11.5234	−	12.7980i	0.395949	−	0.439746i
$848$	0.954736	+	0.425076i	0.0327858	+	0.0145972i
$849$		0			0
$850$	−27.3057	+	5.80400i	−0.936577	+	0.199076i
$851$	62.4529	−	27.8058i	2.14086	−	0.953171i
$852$		0			0
$853$	5.65126	−	17.3928i	0.193496	−	0.595518i	−0.806495	−	0.591241i	$-0.798638\pi$
$853$	5.65126	−	17.3928i	0.193496	−	0.595518i	0.999991	−	0.00427758i	$-0.00136160\pi$
$854$	−12.3146	+	5.48280i	−0.421396	+	0.187618i
$855$		0			0
$856$	−31.1286	−	6.61659i	−1.06395	−	0.226150i
$857$	−28.3569	−	12.6253i	−0.968652	−	0.431272i	−0.139455	−	0.990228i	$-0.544535\pi$
$857$	−28.3569	−	12.6253i	−0.968652	−	0.431272i	−0.829197	+	0.558957i	$0.811202\pi$
$858$		0			0
$859$	1.49681	−	14.2412i	0.0510704	−	0.485902i	−0.938855	−	0.344313i	$-0.888112\pi$
$859$	1.49681	−	14.2412i	0.0510704	−	0.485902i	0.989925	−	0.141590i	$-0.0452214\pi$
$860$	−1.88440	−	1.36910i	−0.0642577	−	0.0466859i
$861$		0			0
$862$	−8.05299	+	13.9482i	−0.274286	+	0.475077i
$863$	−0.752888	−	1.30404i	−0.0256286	−	0.0443900i	0.852927	−	0.522031i	$-0.174825\pi$
$863$	−0.752888	−	1.30404i	−0.0256286	−	0.0443900i	−0.878555	+	0.477641i	$0.841492\pi$
$864$		0			0
$865$	−36.7501	−	40.8152i	−1.24954	−	1.38776i
$866$	14.0797	+	43.3330i	0.478449	+	1.47251i
$867$		0			0
$868$	0.224847	+	1.33111i	0.00763181	+	0.0451808i
$869$	−42.8897			−1.45493
$870$		0			0
$871$	16.6388	+	18.4793i	0.563785	+	0.626146i
$872$	39.4200	−	28.6403i	1.33493	−	0.969884i
$873$		0			0
$874$	−17.6954	+	30.6492i	−0.598554	+	1.03673i
$875$	−0.326524	−	3.10666i	−0.0110385	−	0.105024i
$876$		0			0
$877$	−3.62842	+	34.5221i	−0.122523	+	1.16573i	0.744556	+	0.667560i	$0.232661\pi$
$877$	−3.62842	+	34.5221i	−0.122523	+	1.16573i	−0.867079	+	0.498170i	$0.834005\pi$
$878$	−0.698208	+	0.775438i	−0.0235634	+	0.0261698i
$879$		0			0
$880$	55.7313	+	11.8460i	1.87870	+	0.399330i
$881$	−35.8985	+	7.63046i	−1.20945	+	0.257077i	−0.768143	−	0.640279i	$-0.778819\pi$
$881$	−35.8985	+	7.63046i	−1.20945	+	0.257077i	−0.441308	+	0.897356i	$0.645485\pi$
$882$		0			0
$883$	2.49000	−	7.66344i	0.0837953	−	0.257895i	−0.900377	−	0.435111i	$-0.856709\pi$
$883$	2.49000	−	7.66344i	0.0837953	−	0.257895i	0.984172	+	0.177216i	$0.0567091\pi$
$884$	0.592090	−	1.82227i	0.0199141	−	0.0612894i
$885$		0			0
$886$	47.4622	−	10.0884i	1.59452	−	0.338926i
$887$	12.7888	+	2.71834i	0.429406	+	0.0912730i	0.417544	−	0.908657i	$-0.362891\pi$
$887$	12.7888	+	2.71834i	0.429406	+	0.0912730i	0.0118617	+	0.999930i	$0.496224\pi$
$888$		0			0
$889$	2.62873	−	2.91950i	0.0881647	−	0.0979168i
$890$	0.679174	−	6.46191i	0.0227660	−	0.216604i
$891$		0			0
$892$	−0.0762536	−	0.725504i	−0.00255316	−	0.0242917i
$893$	18.4028	−	31.8746i	0.615826	−	1.06664i
$894$		0			0
$895$	−54.4935	+	39.5918i	−1.82152	+	1.32341i
$896$	9.22055	+	10.2405i	0.308037	+	0.342110i
$897$		0			0
$898$	9.51585			0.317548
$899$	2.73543	−	10.6443i	0.0912317	−	0.355008i
$900$		0			0
$901$	−0.323667	−	0.996145i	−0.0107829	−	0.0331864i
$902$	−22.3403	−	24.8114i	−0.743851	−	0.826130i
$903$		0			0
$904$	7.60552	+	13.1731i	0.252956	+	0.438132i
$905$	−38.2865	+	66.3141i	−1.27269	+	2.20436i
$906$		0			0
$907$	29.3669	+	21.3363i	0.975112	+	0.708461i	0.956611	−	0.291368i	$-0.0941105\pi$
$907$	29.3669	+	21.3363i	0.975112	+	0.708461i	0.0185014	+	0.999829i	$0.494110\pi$
$908$	0.135651	−	1.29063i	0.00450173	−	0.0428311i
$909$		0			0
$910$	−17.8336	−	7.94002i	−0.591177	−	0.263209i
$911$	40.9081	+	8.69528i	1.35535	+	0.288088i	0.827602	−	0.561316i	$-0.189705\pi$
$911$	40.9081	+	8.69528i	1.35535	+	0.288088i	0.527744	+	0.849403i	$0.323038\pi$
$912$		0			0
$913$	28.7505	−	12.8005i	0.951502	−	0.423636i
$914$	1.34591	−	4.14227i	0.0445186	−	0.137014i
$915$		0			0
$916$	−2.08765	+	0.929482i	−0.0689779	+	0.0307109i
$917$	16.1394	−	3.43054i	0.532971	−	0.113286i
$918$		0			0
$919$	−32.0815	−	14.2836i	−1.05827	−	0.471172i	−0.197572	−	0.980288i	$-0.563306\pi$
$919$	−32.0815	−	14.2836i	−1.05827	−	0.471172i	−0.860698	+	0.509116i	$0.829972\pi$
$920$	−48.3549	+	53.7036i	−1.59421	+	1.77055i
$921$		0			0
$922$	−13.5469	−	9.84243i	−0.446145	−	0.324143i
$923$	3.10488	+	29.5410i	0.102198	+	0.972353i
$924$		0			0
$925$	−25.7192	−	44.5469i	−0.845641	−	1.46469i
$926$	−7.39072	+	5.36967i	−0.242874	+	0.176458i
$927$		0			0
$928$	0.584919	+	1.80020i	0.0192009	+	0.0590943i
$929$	16.5352			0.542501			0.271251	−	0.962509i	$-0.412563\pi$
$929$	16.5352			0.542501			0.271251	+	0.962509i	$0.412563\pi$
$930$		0			0
$931$	−17.2378			−0.564948
$932$	−0.771979	−	2.37591i	−0.0252870	−	0.0778255i
$933$		0			0
$934$	15.4040	−	11.1916i	0.504033	−	0.366202i
$935$	−28.5514	−	49.4525i	−0.933731	−	1.61727i
$936$		0			0
$937$	−1.85306	−	17.6307i	−0.0605368	−	0.575969i	−0.982182	−	0.187934i	$-0.939821\pi$
$937$	−1.85306	−	17.6307i	−0.0605368	−	0.575969i	0.921645	−	0.388034i	$-0.126846\pi$
$938$	12.5325	+	9.10537i	0.409199	+	0.297301i
$939$		0			0
$940$	3.93944	−	4.37519i	0.128490	−	0.142703i
$941$	−3.05750	−	1.36129i	−0.0996718	−	0.0443767i	0.356295	−	0.934373i	$-0.384040\pi$
$941$	−3.05750	−	1.36129i	−0.0996718	−	0.0443767i	−0.455967	+	0.889997i	$0.650706\pi$
$942$		0			0
$943$	37.8745	−	8.05048i	1.23336	−	0.262160i
$944$	12.6441	−	5.62953i	0.411532	−	0.183226i
$945$		0			0
$946$	−8.42305	+	25.9235i	−0.273857	+	0.842845i
$947$	−6.18026	+	2.75163i	−0.200832	+	0.0894160i	−0.504688	−	0.863302i	$-0.668392\pi$
$947$	−6.18026	+	2.75163i	−0.200832	+	0.0894160i	0.303856	+	0.952718i	$0.401726\pi$
$948$		0			0
$949$	34.5359	+	7.34084i	1.12108	+	0.238294i
$950$	24.3267	+	10.8310i	0.789264	+	0.351403i
$951$		0			0
$952$	1.59271	−	15.1537i	0.0516202	−	0.491133i
$953$	5.64439	+	4.10089i	0.182840	+	0.132841i	0.675440	−	0.737415i	$-0.263954\pi$
$953$	5.64439	+	4.10089i	0.182840	+	0.132841i	−0.492601	+	0.870256i	$0.663954\pi$
$954$		0			0
$955$	19.3327	−	33.4852i	0.625590	−	1.08355i
$956$	−0.396044	−	0.685968i	−0.0128090	−	0.0221858i
$957$		0			0
$958$	−12.6479	−	14.0469i	−0.408634	−	0.453834i
$959$	−2.98842	−	9.19741i	−0.0965011	−	0.297000i
$960$		0			0
$961$	13.1871	+	28.0553i	0.425392	+	0.905009i
$962$	−38.0075			−1.22541
$963$		0			0
$964$	−1.54617	−	1.71719i	−0.0497986	−	0.0553070i
$965$	15.3009	−	11.1167i	0.492553	−	0.357860i
$966$		0			0
$967$	6.36487	−	11.0243i	0.204680	−	0.354517i	−0.745351	−	0.666673i	$-0.767718\pi$
$967$	6.36487	−	11.0243i	0.204680	−	0.354517i	0.950031	+	0.312156i	$0.101051\pi$
$968$	3.70488	+	35.2496i	0.119079	+	1.13296i
$969$		0			0
$970$	4.31576	−	41.0617i	0.138571	−	1.31841i
$971$	−27.9118	+	30.9992i	−0.895734	+	0.994813i	0.104266	+	0.994549i	$0.466751\pi$
$971$	−27.9118	+	30.9992i	−0.895734	+	0.994813i	−1.00000		0.000263577i	$0.999916\pi$
$972$		0			0
$973$	−9.77325	−	2.07737i	−0.313316	−	0.0665974i
$974$	11.9650	−	2.54325i	0.383385	−	0.0814910i
$975$		0			0
$976$	7.83918	−	24.1265i	0.250926	−	0.772271i
$977$	−4.56051	+	14.0358i	−0.145904	+	0.449045i	−0.997126	−	0.0757598i	$-0.975862\pi$
$977$	−4.56051	+	14.0358i	−0.145904	+	0.449045i	0.851222	+	0.524805i	$0.175862\pi$
$978$		0			0
$979$	6.90868	−	1.46849i	0.220802	−	0.0469330i
$980$	−2.69710	−	0.573286i	−0.0861557	−	0.0183130i
$981$		0			0
$982$	15.2279	−	16.9123i	0.485942	−	0.539694i
$983$	4.81179	−	45.7812i	0.153472	−	1.46019i	−0.598566	−	0.801073i	$-0.704263\pi$
$983$	4.81179	−	45.7812i	0.153472	−	1.46019i	0.752039	−	0.659119i	$-0.229071\pi$
$984$		0			0
$985$	5.50209	+	52.3488i	0.175311	+	1.66797i
$986$	−4.85875	+	8.41560i	−0.154734	+	0.268007i
$987$		0			0
$988$	−1.47866	+	1.07431i	−0.0470425	+	0.0341783i
$989$	−21.1525	−	23.4923i	−0.672611	−	0.747011i
$990$		0			0
$991$	−6.23101			−0.197934			−0.0989672	−	0.995091i	$-0.531554\pi$
$991$	−6.23101			−0.197934			−0.0989672	+	0.995091i	$0.531554\pi$
$992$	−4.50736	−	2.86181i	−0.143109	−	0.0908625i
$993$		0			0
$994$	5.71821	+	17.5988i	0.181371	+	0.558201i
$995$	20.1155	+	22.3405i	0.637703	+	0.708241i
$996$		0			0
$997$	−6.97285	−	12.0773i	−0.220832	−	0.382493i	0.734229	−	0.678902i	$-0.237544\pi$
$997$	−6.97285	−	12.0773i	−0.220832	−	0.382493i	−0.955061	+	0.296410i	$0.904211\pi$
$998$	2.76075	−	4.78176i	0.0873901	−	0.151364i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.y.d.82.3		24
3.2	odd	2		93.2.m.b.82.1	yes	24
31.13	odd	30		8649.2.a.bl.1.11		12
31.14	even	15	inner	279.2.y.d.262.3		24
31.18	even	15		8649.2.a.bk.1.11		12
93.14	odd	30		93.2.m.b.76.1	✓	24
93.44	even	30		2883.2.a.s.1.2		12
93.80	odd	30		2883.2.a.t.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.76.1	✓	24	93.14	odd	30
93.2.m.b.82.1	yes	24	3.2	odd	2
279.2.y.d.82.3		24	1.1	even	1	trivial
279.2.y.d.262.3		24	31.14	even	15	inner
2883.2.a.s.1.2		12	93.44	even	30
2883.2.a.t.1.2		12	93.80	odd	30
8649.2.a.bk.1.11		12	31.18	even	15
8649.2.a.bl.1.11		12	31.13	odd	30

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)

\(f(q)\)	\(=\)	\(q+(0.418031 + 1.28657i) q^{2} +(0.137526 - 0.0999185i) q^{4} +(-1.63328 - 2.82893i) q^{5} +(-0.149090 - 1.41850i) q^{7} +(2.37488 + 1.72545i) q^{8} +O(q^{10})\)	\(q+(0.418031 + 1.28657i) q^{2} +(0.137526 - 0.0999185i) q^{4} +(-1.63328 - 2.82893i) q^{5} +(-0.149090 - 1.41850i) q^{7} +(2.37488 + 1.72545i) q^{8} +(2.95685 - 3.28391i) q^{10} +(4.38826 + 1.95378i) q^{11} +(3.02956 - 0.643952i) q^{13} +(1.76267 - 0.784793i) q^{14} +(-1.12208 + 3.45340i) q^{16} +(3.32456 - 1.48019i) q^{17} +(-3.39558 - 0.721752i) q^{19} +(-0.507281 - 0.225856i) q^{20} +(-0.679240 + 6.46254i) q^{22} +(-6.09693 - 4.42968i) q^{23} +(-2.83523 + 4.91076i) q^{25} +(2.09494 + 3.62854i) q^{26} +(-0.162238 - 0.180184i) q^{28} +(0.609968 + 1.87729i) q^{29} +(-4.70038 - 2.98436i) q^{31} +0.958934 q^{32} +(3.29413 + 3.65850i) q^{34} +(-3.76933 + 2.73858i) q^{35} +(-4.53564 + 7.85596i) q^{37} +(-0.490874 - 4.67035i) q^{38} +(1.00233 - 9.53653i) q^{40} +(-3.43795 + 3.81823i) q^{41} +(4.10301 + 0.872121i) q^{43} +(0.798719 - 0.169773i) q^{44} +(3.15038 - 9.69586i) q^{46} +(-3.27633 + 10.0835i) q^{47} +(4.85712 - 1.03241i) q^{49} +(-7.50325 - 1.59486i) q^{50} +(0.352300 - 0.391269i) q^{52} +(0.0300848 - 0.286238i) q^{53} +(-1.64017 - 15.6052i) q^{55} +(2.09349 - 3.62602i) q^{56} +(-2.16027 + 1.56953i) q^{58} +(-2.55052 - 2.83264i) q^{59} -6.98631 q^{61} +(1.87468 - 7.29492i) q^{62} +(2.64502 + 8.14054i) q^{64} +(-6.76982 - 7.51865i) q^{65} +(4.01427 + 6.95292i) q^{67} +(0.309315 - 0.535749i) q^{68} +(-5.09907 - 3.70469i) q^{70} +(-1.00247 + 9.53784i) q^{71} +(10.4141 + 4.63666i) q^{73} +(-12.0033 - 2.55137i) q^{74} +(-0.539096 + 0.240021i) q^{76} +(2.11719 - 6.51605i) q^{77} +(-8.15681 + 3.63165i) q^{79} +(11.6021 - 2.46610i) q^{80} +(-6.34959 - 2.82702i) q^{82} +(4.38393 - 4.86884i) q^{83} +(-9.61729 - 6.98737i) q^{85} +(0.593142 + 5.64337i) q^{86} +(7.05045 + 12.2117i) q^{88} +(1.18956 - 0.864265i) q^{89} +(-1.36513 - 4.20142i) q^{91} -1.28109 q^{92} -14.3427 q^{94} +(3.50415 + 10.7847i) q^{95} +(7.55896 - 5.49190i) q^{97} +(3.35870 + 5.81743i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} + 6 q^{5} - q^{7} + 22 q^{8}+O(q^{10}) \) 24 * q - 4 * q^4 + 6 * q^5 - q^7 + 22 * q^8	\( 24 q - 4 q^{4} + 6 q^{5} - q^{7} + 22 q^{8} + 24 q^{10} + 22 q^{11} - 8 q^{13} - 10 q^{14} - 2 q^{16} + 17 q^{17} + 5 q^{19} + 22 q^{20} - 37 q^{22} - 26 q^{23} - 8 q^{25} - 4 q^{26} - 36 q^{28} - 2 q^{29} - 36 q^{32} + 40 q^{34} - 9 q^{35} - 13 q^{37} + q^{38} - 27 q^{40} - 36 q^{41} - 11 q^{43} + 38 q^{44} - 23 q^{46} + 13 q^{47} - 22 q^{49} - 71 q^{50} + 9 q^{52} + 20 q^{53} + 26 q^{55} - 28 q^{56} + 40 q^{58} + 16 q^{59} + 70 q^{61} + 2 q^{62} + 34 q^{64} - 94 q^{65} + 4 q^{67} - 51 q^{68} - 43 q^{70} + 5 q^{71} - 12 q^{73} - 74 q^{74} + 71 q^{76} - 25 q^{77} - 29 q^{79} + 113 q^{80} - 60 q^{82} + 11 q^{83} + 16 q^{85} + 144 q^{86} + 26 q^{88} + 27 q^{89} - 81 q^{91} - 28 q^{92} - 80 q^{94} + 56 q^{95} - 21 q^{97} + 14 q^{98}+O(q^{100}) \) 24 * q - 4 * q^4 + 6 * q^5 - q^7 + 22 * q^8 + 24 * q^10 + 22 * q^11 - 8 * q^13 - 10 * q^14 - 2 * q^16 + 17 * q^17 + 5 * q^19 + 22 * q^20 - 37 * q^22 - 26 * q^23 - 8 * q^25 - 4 * q^26 - 36 * q^28 - 2 * q^29 - 36 * q^32 + 40 * q^34 - 9 * q^35 - 13 * q^37 + q^38 - 27 * q^40 - 36 * q^41 - 11 * q^43 + 38 * q^44 - 23 * q^46 + 13 * q^47 - 22 * q^49 - 71 * q^50 + 9 * q^52 + 20 * q^53 + 26 * q^55 - 28 * q^56 + 40 * q^58 + 16 * q^59 + 70 * q^61 + 2 * q^62 + 34 * q^64 - 94 * q^65 + 4 * q^67 - 51 * q^68 - 43 * q^70 + 5 * q^71 - 12 * q^73 - 74 * q^74 + 71 * q^76 - 25 * q^77 - 29 * q^79 + 113 * q^80 - 60 * q^82 + 11 * q^83 + 16 * q^85 + 144 * q^86 + 26 * q^88 + 27 * q^89 - 81 * q^91 - 28 * q^92 - 80 * q^94 + 56 * q^95 - 21 * q^97 + 14 * q^98

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