LMFDB - Embedded newform 684.2.cf.c.523.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(91,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			523.9
Character	$\chi$	$=$	684.523
Dual form			684.2.cf.c.667.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33191 - 0.475423i) q^{2} +(1.54795 - 1.26644i) q^{4} +(-3.39140 - 1.23437i) q^{5} +(-1.70277 - 0.983096i) q^{7} +(1.45963 - 2.42270i) q^{8} +(-5.10387 - 0.0317150i) q^{10} +(-4.83466 + 2.79129i) q^{11} +(0.0739637 - 0.0881465i) q^{13} +(-2.73532 - 0.499855i) q^{14} +(0.792279 - 3.92075i) q^{16} +(-0.580442 - 3.29185i) q^{17} +(-1.02155 + 4.23750i) q^{19} +(-6.81295 + 2.38425i) q^{20} +(-5.11227 + 6.01624i) q^{22} +(-2.16818 - 5.95703i) q^{23} +(6.14770 + 5.15853i) q^{25} +(0.0566059 - 0.152567i) q^{26} +(-3.88083 + 0.634672i) q^{28} +(-1.55282 - 0.273805i) q^{29} +(0.653262 - 1.13148i) q^{31} +(-0.808773 - 5.59874i) q^{32} +(-2.33811 - 4.10848i) q^{34} +(4.56128 + 5.43592i) q^{35} -7.12135i q^{37} +(0.653996 + 6.12962i) q^{38} +(-7.94069 + 6.41463i) q^{40} +(4.70052 + 5.60186i) q^{41} +(1.14640 - 3.14970i) q^{43} +(-3.94880 + 10.4436i) q^{44} +(-5.71992 - 6.90340i) q^{46} +(5.87946 + 1.03671i) q^{47} +(-1.56704 - 2.71420i) q^{49} +(10.6406 + 3.94792i) q^{50} +(0.00285995 - 0.230117i) q^{52} +(-0.762548 - 2.09508i) q^{53} +(19.8417 - 3.49863i) q^{55} +(-4.86716 + 2.69036i) q^{56} +(-2.19839 + 0.373565i) q^{58} +(-2.03426 - 11.5368i) q^{59} +(-10.4409 + 3.80016i) q^{61} +(0.332151 - 1.81761i) q^{62} +(-3.73898 - 7.07249i) q^{64} +(-0.359646 + 0.207642i) q^{65} +(0.935414 - 5.30500i) q^{67} +(-5.06741 - 4.36052i) q^{68} +(8.65955 + 5.07160i) q^{70} +(-2.08825 - 0.760061i) q^{71} +(2.21674 - 1.86006i) q^{73} +(-3.38565 - 9.48496i) q^{74} +(3.78522 + 7.85316i) q^{76} +10.9764 q^{77} +(8.78604 - 7.37237i) q^{79} +(-7.52658 + 12.3189i) q^{80} +(8.92390 + 5.22642i) q^{82} +(15.2741 + 8.81848i) q^{83} +(-2.09484 + 11.8805i) q^{85} +(0.0294547 - 4.74012i) q^{86} +(-0.294330 + 15.7872i) q^{88} +(-7.41292 + 8.83438i) q^{89} +(-0.212600 + 0.0773800i) q^{91} +(-10.9004 - 6.47530i) q^{92} +(8.32376 - 1.41443i) q^{94} +(8.69512 - 13.1101i) q^{95} +(-5.32239 + 0.938482i) q^{97} +(-3.37755 - 2.87005i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{2} - 3 q^{4} - 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} - 27 q^{16} - 18 q^{19} - 30 q^{20} + 12 q^{22} - 18 q^{28} + 12 q^{31} + 63 q^{32} - 39 q^{34} + 48 q^{38} + 33 q^{40} + 12 q^{41} + 18 q^{43}+ \cdots - 117 q^{98}+O(q^{100}) $ 60 * q + 3 * q^2 - 3 * q^4 - 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 - 27 * q^16 - 18 * q^19 - 30 * q^20 + 12 * q^22 - 18 * q^28 + 12 * q^31 + 63 * q^32 - 39 * q^34 + 48 * q^38 + 33 * q^40 + 12 * q^41 + 18 * q^43 + 9 * q^44 - 69 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 + 42 * q^56 - 36 * q^58 - 27 * q^62 + 21 * q^64 + 36 * q^65 - 42 * q^67 - 93 * q^68 + 132 * q^70 + 24 * q^71 + 18 * q^73 - 27 * q^74 + 66 * q^76 + 72 * q^77 - 12 * q^79 - 6 * q^80 - 9 * q^82 - 60 * q^85 - 123 * q^86 + 36 * q^88 + 12 * q^89 + 84 * q^91 + 99 * q^92 - 24 * q^95 + 12 * q^97 - 117 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

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 $

$2$	1.33191	−	0.475423i	0.941800	−	0.336174i
$2$	1.33191	−	0.475423i	0.941800	−	0.336174i
$3$		0			0
$3$		0			0
$4$	1.54795	−	1.26644i	0.773973	−	0.633218i
$5$	−3.39140	−	1.23437i	−1.51668	−	0.552026i	−0.556363	−	0.830939i	$-0.687804\pi$
$5$	−3.39140	−	1.23437i	−1.51668	−	0.552026i	−0.960316	+	0.278913i	$0.910026\pi$
$6$		0			0
$7$	−1.70277	−	0.983096i	−0.643587	−	0.371575i	0.142408	−	0.989808i	$-0.454516\pi$
$7$	−1.70277	−	0.983096i	−0.643587	−	0.371575i	−0.785995	+	0.618233i	$0.787849\pi$
$8$	1.45963	−	2.42270i	0.516056	−	0.856555i
$9$		0			0
$10$	−5.10387	−	0.0317150i	−1.61399	−	0.0100292i
$11$	−4.83466	+	2.79129i	−1.45770	+	0.841606i	−0.998898	−	0.0469311i	$-0.985056\pi$
$11$	−4.83466	+	2.79129i	−1.45770	+	0.841606i	−0.458806	+	0.888537i	$0.651723\pi$
$12$		0			0
$13$	0.0739637	−	0.0881465i	0.0205138	−	0.0244475i	−0.755690	−	0.654929i	$-0.772698\pi$
$13$	0.0739637	−	0.0881465i	0.0205138	−	0.0244475i	0.776204	+	0.630482i	$0.217143\pi$
$14$	−2.73532	−	0.499855i	−0.731045	−	0.133592i
$15$		0			0
$16$	0.792279	−	3.92075i	0.198070	−	0.980188i
$17$	−0.580442	−	3.29185i	−0.140778	−	0.798391i	−0.970661	−	0.240453i	$-0.922704\pi$
$17$	−0.580442	−	3.29185i	−0.140778	−	0.798391i	0.829883	−	0.557938i	$-0.188407\pi$
$18$		0			0
$19$	−1.02155	+	4.23750i	−0.234360	+	0.972150i
$19$	−1.02155	+	4.23750i	−0.234360	+	0.972150i
$20$	−6.81295	+	2.38425i	−1.52342	+	0.533135i
$21$		0			0
$22$	−5.11227	+	6.01624i	−1.08994	+	1.28267i
$23$	−2.16818	−	5.95703i	−0.452097	−	1.24213i	−0.931245	−	0.364393i	$-0.881277\pi$
$23$	−2.16818	−	5.95703i	−0.452097	−	1.24213i	0.479148	−	0.877734i	$-0.340946\pi$
$24$		0			0
$25$	6.14770	+	5.15853i	1.22954	+	1.03171i
$26$	0.0566059	−	0.152567i	0.0111013	−	0.0299208i
$27$		0			0
$28$	−3.88083	+	0.634672i	−0.733408	+	0.119942i
$29$	−1.55282	−	0.273805i	−0.288352	−	0.0508442i	0.0276012	−	0.999619i	$-0.491213\pi$
$29$	−1.55282	−	0.273805i	−0.288352	−	0.0508442i	−0.315953	+	0.948775i	$0.602324\pi$
$30$		0			0
$31$	0.653262	−	1.13148i	0.117329	−	0.203220i	−0.801379	−	0.598157i	$-0.795900\pi$
$31$	0.653262	−	1.13148i	0.117329	−	0.203220i	0.918708	+	0.394936i	$0.129233\pi$
$32$	−0.808773	−	5.59874i	−0.142972	−	0.989727i
$33$		0			0
$34$	−2.33811	−	4.10848i	−0.400983	−	0.704598i
$35$	4.56128	+	5.43592i	0.770997	+	0.918838i
$36$		0			0
$37$		−	7.12135i		−	1.17074i	−0.810766	−	0.585371i	$-0.800949\pi$
$37$		−	7.12135i		−	1.17074i	0.810766	−	0.585371i	$-0.199051\pi$
$38$	0.653996	+	6.12962i	0.106092	+	0.994356i
$39$		0			0
$40$	−7.94069	+	6.41463i	−1.25553	+	1.01424i
$41$	4.70052	+	5.60186i	0.734098	+	0.874864i	0.995919	−	0.0902527i	$-0.0287675\pi$
$41$	4.70052	+	5.60186i	0.734098	+	0.874864i	−0.261821	+	0.965116i	$0.584323\pi$
$42$		0			0
$43$	1.14640	−	3.14970i	0.174824	−	0.480324i	−0.821073	−	0.570824i	$-0.806624\pi$
$43$	1.14640	−	3.14970i	0.174824	−	0.480324i	0.995897	+	0.0904992i	$0.0288463\pi$
$44$	−3.94880	+	10.4436i	−0.595304	+	1.57442i
$45$		0			0
$46$	−5.71992	−	6.90340i	−0.843356	−	1.01785i
$47$	5.87946	+	1.03671i	0.857607	+	0.151219i	0.585127	−	0.810942i	$-0.301045\pi$
$47$	5.87946	+	1.03671i	0.857607	+	0.151219i	0.272481	+	0.962161i	$0.412156\pi$
$48$		0			0
$49$	−1.56704	−	2.71420i	−0.223864	−	0.387743i
$50$	10.6406	+	3.94792i	1.50481	+	0.558321i
$51$		0			0
$52$	0.00285995	−	0.230117i	0.000396604	−	0.0319114i
$53$	−0.762548	−	2.09508i	−0.104744	−	0.287782i	0.876239	−	0.481877i	$-0.160045\pi$
$53$	−0.762548	−	2.09508i	−0.104744	−	0.287782i	−0.980983	+	0.194096i	$0.937823\pi$
$54$		0			0
$55$	19.8417	−	3.49863i	2.67546	−	0.471755i
$56$	−4.86716	+	2.69036i	−0.650402	+	0.359514i
$57$		0			0
$58$	−2.19839	+	0.373565i	−0.288662	+	0.0490515i
$59$	−2.03426	−	11.5368i	−0.264838	−	1.50197i	−0.769497	−	0.638651i	$-0.779493\pi$
$59$	−2.03426	−	11.5368i	−0.264838	−	1.50197i	0.504659	−	0.863319i	$-0.331618\pi$
$60$		0			0
$61$	−10.4409	+	3.80016i	−1.33682	+	0.486561i	−0.908808	−	0.417214i	$-0.863007\pi$
$61$	−10.4409	+	3.80016i	−1.33682	+	0.486561i	−0.428008	+	0.903775i	$0.640784\pi$
$62$	0.332151	−	1.81761i	0.0421832	−	0.230836i
$63$		0			0
$64$	−3.73898	−	7.07249i	−0.467372	−	0.884061i
$65$	−0.359646	+	0.207642i	−0.0446086	+	0.0257548i
$66$		0			0
$67$	0.935414	−	5.30500i	0.114279	−	0.648108i	−0.872826	−	0.488032i	$-0.837715\pi$
$67$	0.935414	−	5.30500i	0.114279	−	0.648108i	0.987105	−	0.160076i	$-0.0511740\pi$
$68$	−5.06741	−	4.36052i	−0.614514	−	0.528790i
$69$		0			0
$70$	8.65955	+	5.07160i	1.03501	+	0.606172i
$71$	−2.08825	−	0.760061i	−0.247830	−	0.0902027i	0.215118	−	0.976588i	$-0.430986\pi$
$71$	−2.08825	−	0.760061i	−0.247830	−	0.0902027i	−0.462948	+	0.886385i	$0.653208\pi$
$72$		0			0
$73$	2.21674	−	1.86006i	0.259449	−	0.217704i	−0.503779	−	0.863832i	$-0.668057\pi$
$73$	2.21674	−	1.86006i	0.259449	−	0.217704i	0.763229	+	0.646129i	$0.223613\pi$
$74$	−3.38565	−	9.48496i	−0.393574	−	1.10260i
$75$		0			0
$76$	3.78522	+	7.85316i	0.434195	+	0.900819i
$77$	10.9764			1.25088
$78$		0			0
$79$	8.78604	−	7.37237i	0.988507	−	0.829456i	0.00315617	−	0.999995i	$-0.498995\pi$
$79$	8.78604	−	7.37237i	0.988507	−	0.829456i	0.985351	+	0.170539i	$0.0545509\pi$
$80$	−7.52658	+	12.3189i	−0.841498	+	1.37729i
$81$		0			0
$82$	8.92390	+	5.22642i	0.985480	+	0.577161i
$83$	15.2741	+	8.81848i	1.67655	+	0.967954i	0.963836	+	0.266495i	$0.0858656\pi$
$83$	15.2741	+	8.81848i	1.67655	+	0.967954i	0.712710	+	0.701459i	$0.247468\pi$
$84$		0			0
$85$	−2.09484	+	11.8805i	−0.227218	+	1.28862i
$86$	0.0294547	−	4.74012i	0.00317618	−	0.511141i
$87$		0			0
$88$	−0.294330	+	15.7872i	−0.0313757	+	1.68292i
$89$	−7.41292	+	8.83438i	−0.785768	+	0.936442i	−0.999179	−	0.0405206i	$-0.987098\pi$
$89$	−7.41292	+	8.83438i	−0.785768	+	0.936442i	0.213411	+	0.976963i	$0.431543\pi$
$90$		0			0
$91$	−0.212600	+	0.0773800i	−0.0222865	+	0.00811163i
$92$	−10.9004	−	6.47530i	−1.13645	−	0.675097i
$93$		0			0
$94$	8.32376	−	1.41443i	0.858530	−	0.145887i
$95$	8.69512	−	13.1101i	0.892101	−	1.34507i
$96$		0			0
$97$	−5.32239	+	0.938482i	−0.540407	+	0.0952884i	−0.437188	−	0.899370i	$-0.644025\pi$
$97$	−5.32239	+	0.938482i	−0.540407	+	0.0952884i	−0.103219	+	0.994659i	$0.532914\pi$
$98$	−3.37755	−	2.87005i	−0.341184	−	0.289919i
$99$		0			0
$100$	16.0493	+	0.199465i	1.60493	+	0.0199465i
$101$	13.7940	+	11.5745i	1.37255	+	1.15171i	0.971878	+	0.235484i	$0.0756676\pi$
$101$	13.7940	+	11.5745i	1.37255	+	1.15171i	0.400672	+	0.916222i	$0.368777\pi$
$102$		0			0
$103$	−4.46091	−	7.72652i	−0.439546	−	0.761317i	0.558108	−	0.829768i	$-0.311527\pi$
$103$	−4.46091	−	7.72652i	−0.439546	−	0.761317i	−0.997654	+	0.0684516i	$0.978194\pi$
$104$	−0.105593	−	0.307853i	−0.0103543	−	0.0301875i
$105$		0			0
$106$	−2.01169	−	2.42792i	−0.195393	−	0.235820i
$107$	−3.26682	+	5.65831i	−0.315816	+	0.547009i	−0.979611	−	0.200906i	$-0.935612\pi$
$107$	−3.26682	+	5.65831i	−0.315816	+	0.547009i	0.663795	+	0.747915i	$0.268945\pi$
$108$		0			0
$109$	−3.67153	+	10.0875i	−0.351669	+	0.966203i	0.630165	+	0.776461i	$0.282987\pi$
$109$	−3.67153	+	10.0875i	−0.351669	+	0.966203i	−0.981834	+	0.189741i	$0.939235\pi$
$110$	24.7640	−	14.0931i	2.36115	−	1.34372i
$111$		0			0
$112$	−5.20355	+	5.89726i	−0.491689	+	0.557239i
$113$		−	14.9055i		−	1.40219i	−0.713066	−	0.701097i	$-0.752694\pi$
$113$		−	14.9055i		−	1.40219i	0.713066	−	0.701097i	$-0.247306\pi$
$114$		0			0
$115$			22.8790i			2.13348i
$116$	−2.75044	+	1.54272i	−0.255372	+	0.143238i
$117$		0			0
$118$	−8.19432	−	14.3989i	−0.754348	−	1.32552i
$119$	−2.24784	+	6.17590i	−0.206060	+	0.566144i
$120$		0			0
$121$	10.0826	−	17.4636i	0.916600	−	1.58760i
$122$	−12.0996	+	10.0253i	−1.09544	+	0.907647i
$123$		0			0
$124$	−0.421736	−	2.57879i	−0.0378730	−	0.231582i
$125$	−5.45914	−	9.45551i	−0.488281	−	0.845727i
$126$		0			0
$127$	−0.891348	−	0.747930i	−0.0790943	−	0.0663680i	0.602383	−	0.798207i	$-0.294218\pi$
$127$	−0.891348	−	0.747930i	−0.0790943	−	0.0663680i	−0.681478	+	0.731839i	$0.738662\pi$
$128$	−8.34238	−	7.64229i	−0.737370	−	0.675490i
$129$		0			0
$130$	−0.380297	+	0.447543i	−0.0333542	+	0.0392521i
$131$	−13.9279	+	2.45587i	−1.21689	+	0.214570i	−0.744986	−	0.667081i	$-0.767544\pi$
$131$	−13.9279	+	2.45587i	−1.21689	+	0.214570i	−0.471902	+	0.881651i	$0.656433\pi$
$132$		0			0
$133$	5.90534	−	6.21122i	0.512058	−	0.538581i
$134$	−1.27623	−	7.51047i	−0.110250	−	0.648806i
$135$		0			0
$136$	−8.82240	−	3.39864i	−0.756515	−	0.291431i
$137$	−17.6840	+	6.43644i	−1.51084	+	0.549902i	−0.958842	−	0.283941i	$-0.908358\pi$
$137$	−17.6840	+	6.43644i	−1.51084	+	0.549902i	−0.552002	+	0.833843i	$0.686136\pi$
$138$		0			0
$139$	−4.98537	+	5.94134i	−0.422854	+	0.503938i	−0.934846	−	0.355052i	$-0.884463\pi$
$139$	−4.98537	+	5.94134i	−0.422854	+	0.503938i	0.511993	+	0.858990i	$0.328908\pi$
$140$	13.9449	+	2.63795i	1.17856	+	0.222947i
$141$		0			0
$142$	−3.14270	−	0.0195285i	−0.263730	−	0.00163879i
$143$	−0.111547	+	0.632612i	−0.00932800	+	0.0529017i
$144$		0			0
$145$	4.92827	+	2.84534i	0.409270	+	0.236292i
$146$	2.06817	−	3.53132i	0.171163	−	0.292254i
$147$		0			0
$148$	−9.01873	−	11.0235i	−0.741335	−	0.906123i
$149$	9.40224	−	7.88942i	0.770261	−	0.646326i	−0.170514	−	0.985355i	$-0.554543\pi$
$149$	9.40224	−	7.88942i	0.770261	−	0.646326i	0.940776	+	0.339029i	$0.110099\pi$
$150$		0			0
$151$	−5.39650			−0.439161			−0.219580	−	0.975594i	$-0.570469\pi$
$151$	−5.39650			−0.439161			−0.219580	+	0.975594i	$0.570469\pi$
$152$	8.77513	+	8.66009i	0.711757	+	0.702426i
$153$		0			0
$154$	14.6196	−	5.21844i	1.17808	−	0.420514i
$155$	−3.61214	+	3.03095i	−0.290134	+	0.243451i
$156$		0			0
$157$	−8.88411	−	3.23355i	−0.709029	−	0.258066i	−0.0377683	−	0.999287i	$-0.512025\pi$
$157$	−8.88411	−	3.23355i	−0.709029	−	0.258066i	−0.671261	+	0.741221i	$0.734247\pi$
$158$	8.19719	−	13.9964i	0.652134	−	1.11349i
$159$		0			0
$160$	−4.16804	+	19.9859i	−0.329512	+	1.58002i
$161$	−2.16441	+	12.2750i	−0.170580	+	0.967405i
$162$		0			0
$163$	1.61949	−	0.935013i	0.126848	−	0.0732359i	−0.435233	−	0.900318i	$-0.643334\pi$
$163$	1.61949	−	0.935013i	0.126848	−	0.0732359i	0.562081	+	0.827082i	$0.310001\pi$
$164$	14.3706	+	2.71848i	1.12215	+	0.212277i
$165$		0			0
$166$	24.5361	+	4.48376i	1.90437	+	0.348007i
$167$	14.4659	−	5.26515i	1.11940	−	0.407429i	0.284969	−	0.958537i	$-0.408017\pi$
$167$	14.4659	−	5.26515i	1.11940	−	0.407429i	0.834434	+	0.551108i	$0.185795\pi$
$168$		0			0
$169$	2.25513	+	12.7895i	0.173471	+	0.983805i
$170$	2.85810	+	16.8196i	0.219206	+	1.29000i
$171$		0			0
$172$	−2.21433	−	6.32740i	−0.168841	−	0.482460i
$173$	16.6499	−	2.93583i	1.26587	−	0.223207i	0.499899	−	0.866084i	$-0.333370\pi$
$173$	16.6499	−	2.93583i	1.26587	−	0.223207i	0.765970	+	0.642877i	$0.222259\pi$
$174$		0			0
$175$	−5.39680	−	14.8276i	−0.407960	−	1.12086i
$176$	7.11356	+	21.1670i	0.536205	+	1.59552i
$177$		0			0
$178$	−5.67325	+	15.2908i	−0.425228	+	1.14610i
$179$	4.45014	+	7.70786i	0.332619	+	0.576113i	0.983024	−	0.183474i	$-0.0587345\pi$
$179$	4.45014	+	7.70786i	0.332619	+	0.576113i	−0.650406	+	0.759587i	$0.725401\pi$
$180$		0			0
$181$	−9.01732	−	1.59000i	−0.670252	−	0.118184i	−0.171842	−	0.985125i	$-0.554972\pi$
$181$	−9.01732	−	1.59000i	−0.670252	−	0.118184i	−0.498411	+	0.866941i	$0.666083\pi$
$182$	−0.246375	+	0.204138i	−0.0182625	+	0.0151317i
$183$		0			0
$184$	−17.5968	−	3.44218i	−1.29726	−	0.253761i
$185$	−8.79036	+	24.1513i	−0.646280	+	1.77564i
$186$		0			0
$187$	11.9947	+	14.2948i	0.877143	+	1.04534i
$188$	10.4140	−	5.84119i	0.759520	−	0.426013i
$189$		0			0
$190$	5.34825	−	21.5953i	0.388003	−	1.56669i
$191$		−	15.5280i		−	1.12356i	−0.827286	−	0.561782i	$-0.810116\pi$
$191$		−	15.5280i		−	1.12356i	0.827286	−	0.561782i	$-0.189884\pi$
$192$		0			0
$193$	3.71827	+	4.43126i	0.267647	+	0.318969i	0.883082	−	0.469218i	$-0.155464\pi$
$193$	3.71827	+	4.43126i	0.267647	+	0.318969i	−0.615435	+	0.788187i	$0.711020\pi$
$194$	−6.64275	+	3.78036i	−0.476922	+	0.271414i
$195$		0			0
$196$	−5.86306	−	2.21688i	−0.418790	−	0.158348i
$197$	2.17496	−	3.76714i	0.154959	−	0.268398i	−0.778085	−	0.628159i	$-0.783809\pi$
$197$	2.17496	−	3.76714i	0.154959	−	0.268398i	0.933044	+	0.359762i	$0.117142\pi$
$198$		0			0
$199$	−3.06985	−	0.541297i	−0.217616	−	0.0383715i	0.0637771	−	0.997964i	$-0.479685\pi$
$199$	−3.06985	−	0.541297i	−0.217616	−	0.0383715i	−0.281393	+	0.959593i	$0.590796\pi$
$200$	21.4709	−	7.36451i	1.51822	−	0.520750i
$201$		0			0
$202$	23.8750	+	8.85819i	1.67984	+	0.623260i
$203$	2.37493	+	1.99280i	0.166687	+	0.139867i
$204$		0			0
$205$	−9.02658	−	24.8003i	−0.630444	−	1.73213i
$206$	−9.61487	−	8.17018i	−0.669900	−	0.569244i
$207$		0			0
$208$	−0.287001	−	0.359830i	−0.0198999	−	0.0249497i
$209$	−6.88926	−	23.3383i	−0.476540	−	1.61434i
$210$		0			0
$211$	−0.910393	−	5.16309i	−0.0626740	−	0.355442i	−0.999976	−	0.00692381i	$-0.997796\pi$
$211$	−0.910393	−	5.16309i	−0.0626740	−	0.355442i	0.937302	−	0.348518i	$-0.113315\pi$
$212$	−3.83367	−	2.27736i	−0.263298	−	0.156410i
$213$		0			0
$214$	−1.66102	+	9.08945i	−0.113545	+	0.621342i
$215$	−7.77577	+	9.26680i	−0.530303	+	0.631991i
$216$		0			0
$217$	−2.22471	+	1.28444i	−0.151023	+	0.0871934i
$218$	−0.0943337	+	15.1811i	−0.00638908	+	1.02819i
$219$		0			0
$220$	26.2831	−	30.5440i	1.77201	−	2.05927i
$221$	−0.333097	−	0.192314i	−0.0224065	−	0.0129364i
$222$		0			0
$223$	−6.80645	−	2.47734i	−0.455794	−	0.165895i	0.103913	−	0.994586i	$-0.466864\pi$
$223$	−6.80645	−	2.47734i	−0.455794	−	0.165895i	−0.559706	+	0.828691i	$0.689086\pi$
$224$	−4.12694	+	10.3285i	−0.275743	+	0.690101i
$225$		0			0
$226$	−7.08642	−	19.8527i	−0.471382	−	1.32059i
$227$	−12.9028			−0.856391			−0.428195	−	0.903686i	$-0.640851\pi$
$227$	−12.9028			−0.856391			−0.428195	+	0.903686i	$0.640851\pi$
$228$		0			0
$229$	6.50015			0.429542			0.214771	−	0.976664i	$-0.431099\pi$
$229$	6.50015			0.429542			0.214771	+	0.976664i	$0.431099\pi$
$230$	10.8772	+	30.4727i	0.717221	+	2.00931i
$231$		0			0
$232$	−2.92989	+	3.36237i	−0.192357	+	0.220751i
$233$	−9.80942	−	3.57034i	−0.642636	−	0.233901i	8.56138e−5	−	1.00000i	$-0.499973\pi$
$233$	−9.80942	−	3.57034i	−0.642636	−	0.233901i	−0.642722	+	0.766099i	$0.722195\pi$
$234$		0			0
$235$	−18.6599	−	10.7733i	−1.21724	−	0.702773i
$236$	−17.7596	−	15.2822i	−1.15605	−	0.994784i
$237$		0			0
$238$	−0.0577545	+	9.29439i	−0.00374367	+	0.602466i
$239$	24.2728	−	14.0139i	1.57008	−	0.906484i	0.573918	−	0.818913i	$-0.305423\pi$
$239$	24.2728	−	14.0139i	1.57008	−	0.906484i	0.996158	−	0.0875716i	$-0.0279107\pi$
$240$		0			0
$241$	9.48229	−	11.3006i	0.610808	−	0.727933i	−0.368653	−	0.929567i	$-0.620181\pi$
$241$	9.48229	−	11.3006i	0.610808	−	0.727933i	0.979461	+	0.201634i	$0.0646253\pi$
$242$	5.12650	−	28.0533i	0.329544	−	1.80334i
$243$		0			0
$244$	−11.3492	+	19.1051i	−0.726561	+	1.22308i
$245$	1.96415	+	11.1392i	0.125485	+	0.711661i
$246$		0			0
$247$	0.297964	+	0.403468i	0.0189590	+	0.0256720i
$248$	−1.78773	−	3.23420i	−0.113521	−	0.205372i
$249$		0			0
$250$	−11.7664	−	9.99845i	−0.744174	−	0.632358i
$251$	5.95225	+	16.3537i	0.375702	+	1.03223i	0.973119	+	0.230303i	$0.0739717\pi$
$251$	5.95225	+	16.3537i	0.375702	+	1.03223i	−0.597417	+	0.801931i	$0.703806\pi$
$252$		0			0
$253$	27.1102	+	22.7482i	1.70440	+	1.43016i
$254$	−1.54277	−	0.572405i	−0.0968023	−	0.0359159i
$255$		0			0
$256$	−14.7446	−	6.21266i	−0.921537	−	0.388291i
$257$	−2.97920	−	0.525313i	−0.185837	−	0.0327681i	0.0799549	−	0.996798i	$-0.474522\pi$
$257$	−2.97920	−	0.525313i	−0.185837	−	0.0327681i	−0.265792	+	0.964030i	$0.585633\pi$
$258$		0			0
$259$	−7.00097	+	12.1260i	−0.435019	+	0.753475i
$260$	−0.293748	+	0.776887i	−0.0182175	+	0.0481805i
$261$		0			0
$262$	−17.3831	+	9.89263i	−1.07393	+	0.611169i
$263$	0.596660	+	0.711072i	0.0367916	+	0.0438465i	0.784126	−	0.620601i	$-0.213111\pi$
$263$	0.596660	+	0.711072i	0.0367916	+	0.0438465i	−0.747335	+	0.664448i	$0.768667\pi$
$264$		0			0
$265$			8.04652i			0.494294i
$266$	4.91240	−	11.0803i	0.301199	−	0.679376i
$267$		0			0
$268$	−5.27047	−	9.39649i	−0.321945	−	0.573982i
$269$	−14.4498	−	17.2205i	−0.881017	−	1.04995i	−0.998382	−	0.0568661i	$-0.981889\pi$
$269$	−14.4498	−	17.2205i	−0.881017	−	1.04995i	0.117365	−	0.993089i	$-0.462555\pi$
$270$		0			0
$271$	2.63856	−	7.24939i	0.160281	−	0.440369i	−0.833391	−	0.552683i	$-0.813604\pi$
$271$	2.63856	−	7.24939i	0.160281	−	0.440369i	0.993673	+	0.112314i	$0.0358262\pi$
$272$	−13.3664	−	0.332294i	−0.810457	−	0.0201483i
$273$		0			0
$274$	−20.4934	+	16.9801i	−1.23805	+	1.02580i
$275$	−44.1210	−	7.77972i	−2.66059	−	0.469135i
$276$		0			0
$277$	−0.803534	−	1.39176i	−0.0482797	−	0.0836229i	0.840876	−	0.541228i	$-0.182041\pi$
$277$	−0.803534	−	1.39176i	−0.0482797	−	0.0836229i	−0.889155	+	0.457605i	$0.848707\pi$
$278$	−3.81540	+	10.2835i	−0.228833	+	0.616761i
$279$		0			0
$280$	19.8274	−	3.11620i	1.18491	−	0.186229i
$281$	−3.41959	−	9.39526i	−0.203996	−	0.560474i	0.794935	−	0.606694i	$-0.207505\pi$
$281$	−3.41959	−	9.39526i	−0.203996	−	0.560474i	−0.998931	+	0.0462199i	$0.985282\pi$
$282$		0			0
$283$	−10.9910	+	1.93801i	−0.653348	+	0.115203i	−0.490490	−	0.871447i	$-0.663182\pi$
$283$	−10.9910	+	1.93801i	−0.653348	+	0.115203i	−0.162858	+	0.986650i	$0.552071\pi$
$284$	−4.19507	+	1.46810i	−0.248932	+	0.0871159i
$285$		0			0
$286$	0.152189	+	0.895612i	0.00899910	+	0.0529587i
$287$	−2.49675	−	14.1598i	−0.147378	−	0.835824i
$288$		0			0
$289$	5.47541	−	1.99289i	0.322083	−	0.117229i
$290$	7.91672	+	1.44671i	0.464886	+	0.0849538i
$291$		0			0
$292$	1.07574	−	5.68663i	0.0629529	−	0.332785i
$293$	−1.70034	+	0.981693i	−0.0993351	+	0.0573511i	−0.548845	−	0.835924i	$-0.684932\pi$
$293$	−1.70034	+	0.981693i	−0.0993351	+	0.0573511i	0.449510	+	0.893276i	$0.351599\pi$
$294$		0			0
$295$	−7.34174	+	41.6371i	−0.427453	+	2.42420i
$296$	−17.2529	−	10.3945i	−1.00280	−	0.604169i
$297$		0			0
$298$	8.77209	−	14.9780i	0.508154	−	0.867652i
$299$	−0.685458	−	0.249486i	−0.0396411	−	0.0144282i
$300$		0			0
$301$	−5.04851	+	4.23620i	−0.290991	+	0.244170i
$302$	−7.18763	+	2.56562i	−0.413602	+	0.147635i
$303$		0			0
$304$	15.8048	+	7.36253i	0.906470	+	0.422270i
$305$	40.0999			2.29612
$306$		0			0
$307$	−9.42719	+	7.91035i	−0.538038	+	0.451468i	−0.870866	−	0.491520i	$-0.836441\pi$
$307$	−9.42719	+	7.91035i	−0.538038	+	0.451468i	0.332828	+	0.942987i	$0.391997\pi$
$308$	16.9909	−	13.9009i	0.968148	−	0.792080i
$309$		0			0
$310$	−3.37005	+	5.75423i	−0.191406	+	0.326818i
$311$	−8.74451	−	5.04865i	−0.495856	−	0.286283i	0.231145	−	0.972919i	$-0.425753\pi$
$311$	−8.74451	−	5.04865i	−0.495856	−	0.286283i	−0.727001	+	0.686637i	$0.759086\pi$
$312$		0			0
$313$	0.958695	−	5.43703i	0.0541887	−	0.307319i	−0.945652	−	0.325181i	$-0.894575\pi$
$313$	0.958695	−	5.43703i	0.0541887	−	0.307319i	0.999840	+	0.0178618i	$0.00568589\pi$
$314$	−13.3701	−	0.0830806i	−0.754519	−	0.00468851i
$315$		0			0
$316$	4.26370	−	22.5390i	0.239852	−	1.26792i
$317$	−16.9033	+	20.1446i	−0.949385	+	1.13143i	0.0418233	+	0.999125i	$0.486683\pi$
$317$	−16.9033	+	20.1446i	−0.949385	+	1.13143i	−0.991209	+	0.132308i	$0.957761\pi$
$318$		0			0
$319$	8.27163	−	3.01063i	0.463122	−	0.168563i
$320$	3.95031	+	28.6009i	0.220829	+	1.59884i
$321$		0			0
$322$	2.95301	+	17.3781i	0.164565	+	0.968446i
$323$	14.5422	+	0.903165i	0.809148	+	0.0502534i
$324$		0			0
$325$	0.909414	−	0.160354i	0.0504452	−	0.00889485i
$326$	1.71248	−	2.01529i	0.0948457	−	0.111617i
$327$		0			0
$328$	20.4327	−	3.21133i	1.12820	−	0.177316i
$329$	−8.99220	−	7.54535i	−0.495756	−	0.415989i
$330$		0			0
$331$	−17.5645	−	30.4227i	−0.965434	−	1.67218i	−0.708443	−	0.705768i	$-0.750602\pi$
$331$	−17.5645	−	30.4227i	−0.965434	−	1.67218i	−0.256991	−	0.966414i	$-0.582731\pi$
$332$	34.8115	−	5.69308i	1.91053	−	0.312448i
$333$		0			0
$334$	16.7640	−	13.8901i	0.917286	−	0.760031i
$335$	−9.72068	+	16.8367i	−0.531097	+	0.919888i
$336$		0			0
$337$	−3.15640	+	8.67213i	−0.171940	+	0.472401i	−0.995493	−	0.0948387i	$-0.969766\pi$
$337$	−3.15640	+	8.67213i	−0.171940	+	0.472401i	0.823553	+	0.567240i	$0.191989\pi$
$338$	9.08402	+	15.9622i	0.494105	+	0.868230i
$339$		0			0
$340$	11.8031	+	21.0433i	0.640115	+	1.14123i
$341$			7.29378i			0.394980i
$342$		0			0
$343$			19.9256i			1.07588i
$344$	−5.95747	−	7.37476i	−0.321205	−	0.397620i
$345$		0			0
$346$	20.7804	−	11.8260i	1.11716	−	0.635769i
$347$	−1.33452	+	3.66657i	−0.0716408	+	0.196832i	−0.970345	−	0.241723i	$-0.922287\pi$
$347$	−1.33452	+	3.66657i	−0.0716408	+	0.196832i	0.898704	+	0.438555i	$0.144510\pi$
$348$		0			0
$349$	−7.75109	+	13.4253i	−0.414906	+	0.718639i	−0.995419	−	0.0956128i	$-0.969519\pi$
$349$	−7.75109	+	13.4253i	−0.414906	+	0.718639i	0.580512	+	0.814251i	$0.302852\pi$
$350$	−14.2374	−	17.1832i	−0.761021	−	0.918480i
$351$		0			0
$352$	19.5378	+	24.8105i	1.04137	+	1.32240i
$353$	−1.90578	−	3.30091i	−0.101435	−	0.175690i	0.810841	−	0.585266i	$-0.199010\pi$
$353$	−1.90578	−	3.30091i	−0.101435	−	0.175690i	−0.912276	+	0.409576i	$0.865677\pi$
$354$		0			0
$355$	6.14390	+	5.15534i	0.326084	+	0.273617i
$356$	−0.286635	+	23.0631i	−0.0151916	+	1.22234i
$357$		0			0
$358$	9.59165	+	8.15045i	0.506935	+	0.430765i
$359$	0.124666	−	0.0219820i	0.00657961	−	0.00116016i	−0.170357	−	0.985382i	$-0.554492\pi$
$359$	0.124666	−	0.0219820i	0.00657961	−	0.00116016i	0.176937	+	0.984222i	$0.443381\pi$
$360$		0			0
$361$	−16.9129	−	8.65764i	−0.890151	−	0.455666i
$362$	−12.7661	+	2.16931i	−0.670974	+	0.114016i
$363$		0			0
$364$	−0.231096	+	0.389024i	−0.0121127	+	0.0203904i
$365$	−9.81384	+	3.57195i	−0.513680	+	0.186964i
$366$		0			0
$367$	1.56490	−	1.86497i	0.0816869	−	0.0973506i	−0.723653	−	0.690164i	$-0.757538\pi$
$367$	1.56490	−	1.86497i	0.0816869	−	0.0973506i	0.805340	+	0.592813i	$0.201983\pi$
$368$	−25.0738	+	3.78127i	−1.30706	+	0.197112i
$369$		0			0
$370$	−0.225853	+	36.3464i	−0.0117416	+	1.88956i
$371$	−0.761222	+	4.31710i	−0.0395207	+	0.224133i
$372$		0			0
$373$	−12.7636	−	7.36906i	−0.660874	−	0.381556i	0.131736	−	0.991285i	$-0.457945\pi$
$373$	−12.7636	−	7.36906i	−0.660874	−	0.381556i	−0.792610	+	0.609729i	$0.791278\pi$
$374$	22.7719	+	13.3367i	1.17751	+	0.689626i
$375$		0			0
$376$	11.0935	−	12.7310i	0.572101	−	0.656550i
$377$	−0.138987	+	0.116624i	−0.00715822	+	0.00600646i
$378$		0			0
$379$	27.3596			1.40537			0.702683	−	0.711503i	$-0.251985\pi$
$379$	27.3596			1.40537			0.702683	+	0.711503i	$0.251985\pi$
$380$	−3.14351	−	31.3055i	−0.161259	−	1.60594i
$381$		0			0
$382$	−7.38234	−	20.6818i	−0.377713	−	1.05817i
$383$	−6.78984	+	5.69735i	−0.346945	+	0.291121i	−0.799562	−	0.600584i	$-0.794935\pi$
$383$	−6.78984	+	5.69735i	−0.346945	+	0.291121i	0.452617	+	0.891705i	$0.350490\pi$
$384$		0			0
$385$	−37.2254	−	13.5489i	−1.89718	−	0.690518i
$386$	7.05910	+	4.13427i	0.359299	+	0.210429i
$387$		0			0
$388$	−7.05026	+	8.19319i	−0.357922	+	0.415946i
$389$	3.82780	−	21.7085i	0.194077	−	1.10067i	−0.719650	−	0.694337i	$-0.755698\pi$
$389$	3.82780	−	21.7085i	0.194077	−	1.10067i	0.913727	−	0.406329i	$-0.133191\pi$
$390$		0			0
$391$	−18.3511	+	10.5950i	−0.928057	+	0.535814i
$392$	−8.86300	−	0.165239i	−0.447649	−	0.00834581i
$393$		0			0
$394$	1.10586	−	6.05150i	0.0557123	−	0.304870i
$395$	−38.8972	+	14.1574i	−1.95713	+	0.712337i
$396$		0			0
$397$	−2.58993	−	14.6882i	−0.129985	−	0.737179i	−0.978222	−	0.207563i	$-0.933447\pi$
$397$	−2.58993	−	14.6882i	−0.129985	−	0.737179i	0.848237	−	0.529617i	$-0.177664\pi$
$398$	−4.34610	+	0.738518i	−0.217850	+	0.0370186i
$399$		0			0
$400$	25.0960	−	20.0166i	1.25480	−	1.00083i
$401$	0.0489938	−	0.00863892i	0.00244663	−	0.000431407i	−0.172425	−	0.985023i	$-0.555160\pi$
$401$	0.0489938	−	0.00863892i	0.00244663	−	0.000431407i	0.174871	+	0.984591i	$0.444049\pi$
$402$		0			0
$403$	−0.0514186	−	0.141272i	−0.00256134	−	0.00703724i
$404$	36.0107	+	0.447551i	1.79160	+	0.0222665i
$405$		0			0
$406$	4.11060	+	1.52513i	0.204006	+	0.0756909i
$407$	19.8777	+	34.4293i	0.985303	+	1.70659i
$408$		0			0
$409$	20.3246	+	3.58378i	1.00499	+	0.177206i	0.651836	−	0.758360i	$-0.273999\pi$
$409$	20.3246	+	3.58378i	1.00499	+	0.177206i	0.353151	+	0.935566i	$0.385110\pi$
$410$	−23.8132	−	28.7403i	−1.17605	−	1.41938i
$411$		0			0
$412$	−16.6904	−	6.31079i	−0.822277	−	0.310910i
$413$	−7.87795	+	21.6445i	−0.387649	+	1.06506i
$414$		0			0
$415$	−40.9152	−	48.7608i	−2.00845	−	2.39357i
$416$	−0.553329	−	0.342813i	−0.0271292	−	0.0168078i
$417$		0			0
$418$	−20.2714	−	27.8091i	−0.991507	−	1.36019i
$419$		−	17.1879i		−	0.839685i	−0.907597	−	0.419843i	$-0.862085\pi$
$419$		−	17.1879i		−	0.839685i	0.907597	−	0.419843i	$-0.137915\pi$
$420$		0			0
$421$	−1.30377	−	1.55377i	−0.0635417	−	0.0757260i	0.733337	−	0.679865i	$-0.237962\pi$
$421$	−1.30377	−	1.55377i	−0.0635417	−	0.0757260i	−0.796879	+	0.604139i	$0.793517\pi$
$422$	−3.66721	−	6.44393i	−0.178517	−	0.313686i
$423$		0			0
$424$	−6.18880	−	1.21061i	−0.300555	−	0.0587926i
$425$	13.4127	−	23.2315i	0.650613	−	1.12689i
$426$		0			0
$427$	21.5143	+	3.79356i	1.04115	+	0.183583i
$428$	2.10901	+	12.8960i	0.101943	+	0.623351i
$429$		0			0
$430$	−5.95095	+	16.0393i	−0.286980	+	0.773483i
$431$	−25.5727	−	21.4580i	−1.23179	−	1.03360i	−0.998120	−	0.0612822i	$-0.980481\pi$
$431$	−25.5727	−	21.4580i	−1.23179	−	1.03360i	−0.233673	−	0.972315i	$-0.575075\pi$
$432$		0			0
$433$	6.88171	+	18.9073i	0.330714	+	0.908629i	0.987926	+	0.154924i	$0.0495132\pi$
$433$	6.88171	+	18.9073i	0.330714	+	0.908629i	−0.657212	+	0.753705i	$0.728265\pi$
$434$	−2.35246	+	2.76843i	−0.112922	+	0.132889i
$435$		0			0
$436$	7.09178	+	20.2646i	0.339634	+	0.970498i
$437$	27.4578	−	3.10227i	1.31349	−	0.148402i
$438$		0			0
$439$	6.34583	+	35.9890i	0.302870	+	1.71766i	0.633365	+	0.773853i	$0.281673\pi$
$439$	6.34583	+	35.9890i	0.302870	+	1.71766i	−0.330496	+	0.943808i	$0.607216\pi$
$440$	20.4854	−	53.1773i	0.976602	−	2.53513i
$441$		0			0
$442$	−0.535084	−	0.0977818i	−0.0254513	−	0.00465101i
$443$	−12.4013	+	14.7793i	−0.589205	+	0.702187i	−0.975453	−	0.220208i	$-0.929327\pi$
$443$	−12.4013	+	14.7793i	−0.589205	+	0.702187i	0.386248	+	0.922395i	$0.373771\pi$
$444$		0			0
$445$	36.0451	−	20.8106i	1.70870	−	0.986518i
$446$	−10.2433	−	0.0636511i	−0.485036	−	0.00301397i
$447$		0			0
$448$	−0.586308	+	15.7186i	−0.0277004	+	0.742634i
$449$	10.4202	+	6.01610i	0.491759	+	0.283917i	0.725304	−	0.688429i	$-0.241699\pi$
$449$	10.4202	+	6.01610i	0.491759	+	0.283917i	−0.233545	+	0.972346i	$0.575033\pi$
$450$		0			0
$451$	−38.3618	−	13.9626i	−1.80639	−	0.657471i
$452$	−18.8769	−	23.0729i	−0.887894	−	1.08526i
$453$		0			0
$454$	−17.1854	+	6.13430i	−0.806549	+	0.287897i
$455$	0.816526			0.0382794
$456$		0			0
$457$	16.6523			0.778960			0.389480	−	0.921035i	$-0.372655\pi$
$457$	16.6523			0.778960			0.389480	+	0.921035i	$0.372655\pi$
$458$	8.65759	−	3.09032i	0.404543	−	0.144401i
$459$		0			0
$460$	28.9748	+	35.4155i	1.35096	+	1.65125i
$461$	−18.8513	−	6.86133i	−0.877995	−	0.319564i	−0.136594	−	0.990627i	$-0.543616\pi$
$461$	−18.8513	−	6.86133i	−0.877995	−	0.319564i	−0.741400	+	0.671063i	$0.765838\pi$
$462$		0			0
$463$	20.5675	+	11.8747i	0.955855	+	0.551863i	0.894895	−	0.446277i	$-0.147250\pi$
$463$	20.5675	+	11.8747i	0.955855	+	0.551863i	0.0609600	+	0.998140i	$0.480584\pi$
$464$	−2.30379	+	5.87130i	−0.106951	+	0.272568i
$465$		0			0
$466$	−14.7626	−	0.0917337i	−0.683866	−	0.00424948i
$467$	17.3535	−	10.0190i	0.803022	−	0.463625i	−0.0415046	−	0.999138i	$-0.513215\pi$
$467$	17.3535	−	10.0190i	0.803022	−	0.463625i	0.844527	+	0.535513i	$0.179882\pi$
$468$		0			0
$469$	−6.80812	+	8.11360i	−0.314370	+	0.374651i
$470$	−29.9751	−	5.47769i	−1.38265	−	0.252667i
$471$		0			0
$472$	−30.9196	−	11.9111i	−1.42319	−	0.548253i
$473$	3.24929	+	18.4276i	0.149402	+	0.847303i
$474$		0			0
$475$	−28.1395	+	20.7812i	−1.29113	+	0.953507i
$476$	4.34184	+	12.4067i	0.199008	+	0.568661i
$477$		0			0
$478$	25.6666	−	30.2050i	1.17396	−	1.38155i
$479$	5.26518	+	14.4660i	0.240572	+	0.660966i	0.999947	+	0.0103127i	$0.00328269\pi$
$479$	5.26518	+	14.4660i	0.240572	+	0.660966i	−0.759375	+	0.650653i	$0.774495\pi$
$480$		0			0
$481$	−0.627722	−	0.526721i	−0.0286217	−	0.0240164i
$482$	7.25698	−	19.5594i	0.330546	−	0.890905i
$483$		0			0
$484$	−6.50917	−	39.8017i	−0.295872	−	1.80917i
$485$	19.2088	+	3.38703i	0.872226	+	0.153797i
$486$		0			0
$487$	11.3873	−	19.7235i	0.516010	−	0.893755i	−0.483817	−	0.875169i	$-0.660750\pi$
$487$	11.3873	−	19.7235i	0.516010	−	0.893755i	0.999827	−	0.0185864i	$-0.00591657\pi$
$488$	−6.03310	+	30.8419i	−0.273106	+	1.39615i
$489$		0			0
$490$	7.91191	+	13.9026i	0.357424	+	0.628057i
$491$	−13.5104	−	16.1011i	−0.609716	−	0.726631i	0.369550	−	0.929211i	$-0.379512\pi$
$491$	−13.5104	−	16.1011i	−0.609716	−	0.726631i	−0.979266	+	0.202580i	$0.935067\pi$
$492$		0			0
$493$			5.27059i			0.237375i
$494$	0.588677	+	0.395722i	0.0264858	+	0.0178044i
$495$		0			0
$496$	−3.91870	−	3.45773i	−0.175955	−	0.155257i
$497$	2.80860	+	3.34716i	0.125983	+	0.150141i
$498$		0			0
$499$	−6.36184	+	17.4790i	−0.284795	+	0.782468i	0.711978	+	0.702201i	$0.247799\pi$
$499$	−6.36184	+	17.4790i	−0.284795	+	0.782468i	−0.996773	+	0.0802666i	$0.974423\pi$
$500$	−20.4253	−	7.72298i	−0.913446	−	0.345382i
$501$		0			0
$502$	15.7027	+	18.9517i	0.700847	+	0.845856i
$503$	6.21016	+	1.09502i	0.276897	+	0.0488245i	0.310372	−	0.950615i	$-0.399546\pi$
$503$	6.21016	+	1.09502i	0.276897	+	0.0488245i	−0.0334750	+	0.999440i	$0.510657\pi$
$504$		0			0
$505$	−32.4936	−	56.2806i	−1.44595	−	2.50445i
$506$	46.9232	+	17.4096i	2.08599	+	0.773952i
$507$		0			0
$508$	−2.32696	−	0.0289202i	−0.103242	−	0.00128313i
$509$	6.21442	+	17.0740i	0.275449	+	0.756790i	0.997864	+	0.0653302i	$0.0208101\pi$
$509$	6.21442	+	17.0740i	0.275449	+	0.756790i	−0.722414	+	0.691460i	$0.756968\pi$
$510$		0			0
$511$	−5.60322	+	0.987998i	−0.247872	+	0.0437065i
$512$	−22.5920	−	1.26477i	−0.998437	−	0.0558953i
$513$		0			0
$514$	−4.21776	+	0.716711i	−0.186037	+	0.0316127i
$515$	5.59135	+	31.7101i	0.246384	+	1.39731i
$516$		0			0
$517$	−31.3189	+	11.3992i	−1.37740	+	0.501334i
$518$	−3.55964	+	19.4791i	−0.156402	+	0.855865i
$519$		0			0
$520$	−0.0218950	+	1.17439i	−0.000960158	+	0.0515006i
$521$	25.0420	−	14.4580i	1.09711	−	0.633416i	0.161649	−	0.986848i	$-0.448319\pi$
$521$	25.0420	−	14.4580i	1.09711	−	0.633416i	0.935460	+	0.353432i	$0.114986\pi$
$522$		0			0
$523$	6.34830	−	36.0030i	0.277592	−	1.57430i	−0.453015	−	0.891503i	$-0.649652\pi$
$523$	6.34830	−	36.0030i	0.277592	−	1.57430i	0.730607	−	0.682799i	$-0.239237\pi$
$524$	−18.4495	+	21.4404i	−0.805969	+	0.936627i
$525$		0			0
$526$	1.13275	+	0.663415i	0.0493904	+	0.0289263i
$527$	−4.10385	−	1.49368i	−0.178767	−	0.0650658i
$528$		0			0
$529$	−13.1662	+	11.0477i	−0.572442	+	0.480336i
$530$	3.82550	+	10.7172i	0.166169	+	0.465526i
$531$		0			0
$532$	1.27504	−	17.0934i	0.0552799	−	0.741092i
$533$	0.841453			0.0364474
$534$		0			0
$535$	18.0635	−	15.1571i	0.780955	−	0.655299i
$536$	−11.4871	−	10.0095i	−0.496166	−	0.432347i
$537$		0			0
$538$	−27.4327	−	16.0664i	−1.18271	−	0.692672i
$539$	15.1522	+	8.74815i	0.652653	+	0.376810i
$540$		0			0
$541$	7.83058	−	44.4094i	0.336663	−	1.90931i	−0.0734954	−	0.997296i	$-0.523415\pi$
$541$	7.83058	−	44.4094i	0.336663	−	1.90931i	0.410158	−	0.912014i	$-0.365473\pi$
$542$	0.0677933	−	10.9099i	0.00291197	−	0.468622i
$543$		0			0
$544$	−17.9608	+	5.91210i	−0.770061	+	0.253479i
$545$	24.9033	−	29.6785i	1.06674	−	1.27129i
$546$		0			0
$547$	26.9570	−	9.81155i	1.15260	−	0.419512i	0.306151	−	0.951983i	$-0.400959\pi$
$547$	26.9570	−	9.81155i	1.15260	−	0.419512i	0.846448	+	0.532471i	$0.178737\pi$
$548$	−19.2225	+	32.3589i	−0.821145	+	1.38230i
$549$		0			0
$550$	−62.4636	+	10.6143i	−2.66346	+	0.452593i
$551$	2.74653	−	6.30039i	0.117006	−	0.268405i
$552$		0			0
$553$	−22.2084	+	3.91594i	−0.944396	+	0.166522i
$554$	−1.73191	−	1.47168i	−0.0735817	−	0.0625256i
$555$		0			0
$556$	−0.192769	+	15.5105i	−0.00817524	+	0.657793i
$557$	14.3725	+	12.0600i	0.608983	+	0.510998i	0.894319	−	0.447430i	$-0.147661\pi$
$557$	14.3725	+	12.0600i	0.608983	+	0.510998i	−0.285336	+	0.958428i	$0.592105\pi$
$558$		0			0
$559$	−0.192843	−	0.334014i	−0.00815640	−	0.0141273i
$560$	24.9267	−	13.5769i	1.05334	−	0.573728i
$561$		0			0
$562$	−9.02130	−	10.8878i	−0.380540	−	0.459276i
$563$	13.6287	−	23.6056i	0.574381	−	0.994857i	−0.421728	−	0.906723i	$-0.638576\pi$
$563$	13.6287	−	23.6056i	0.574381	−	0.994857i	0.996109	−	0.0881344i	$-0.0280905\pi$
$564$		0			0
$565$	−18.3989	+	50.5506i	−0.774047	+	2.12668i
$566$	−13.7176	+	7.80663i	−0.576595	+	0.328137i
$567$		0			0
$568$	−4.88947	+	3.94981i	−0.205158	+	0.165730i
$569$			13.6814i			0.573554i	0.957997	+	0.286777i	$0.0925839\pi$
$569$			13.6814i			0.573554i	−0.957997	+	0.286777i	$0.907416\pi$
$570$		0			0
$571$			4.69406i			0.196440i	0.995165	+	0.0982202i	$0.0313150\pi$
$571$			4.69406i			0.196440i	−0.995165	+	0.0982202i	$0.968685\pi$
$572$	0.628495	+	1.12052i	0.0262787	+	0.0468512i
$573$		0			0
$574$	−10.0573	−	17.6725i	−0.419784	−	0.737634i
$575$	17.4002	−	47.8067i	0.725639	−	1.99368i
$576$		0			0
$577$	3.24677	−	5.62357i	0.135165	−	0.234112i	−0.790496	−	0.612468i	$-0.790177\pi$
$577$	3.24677	−	5.62357i	0.135165	−	0.234112i	0.925660	+	0.378355i	$0.123510\pi$
$578$	6.34527	−	5.25747i	0.263928	−	0.218682i
$579$		0			0
$580$	11.2321	−	1.83691i	0.466389	−	0.0762734i
$581$	−17.3388	−	30.0317i	−0.719336	−	1.24593i
$582$		0			0
$583$	9.53464	+	8.00051i	0.394884	+	0.331347i
$584$	−1.27077	−	8.08549i	−0.0525848	−	0.334580i
$585$		0			0
$586$	−1.79798	+	2.11590i	−0.0742737	+	0.0874072i
$587$	0.243914	−	0.0430085i	0.0100674	−	0.00177515i	−0.168612	−	0.985682i	$-0.553929\pi$
$587$	0.243914	−	0.0430085i	0.0100674	−	0.00177515i	0.178680	+	0.983907i	$0.442817\pi$
$588$		0			0
$589$	4.12732	+	3.92407i	0.170063	+	0.161688i
$590$	10.0167	+	58.9471i	0.412381	+	2.42681i
$591$		0			0
$592$	−27.9210	−	5.64209i	−1.14755	−	0.231889i
$593$	−39.5353	+	14.3897i	−1.62352	+	0.590913i	−0.984048	−	0.177901i	$-0.943069\pi$
$593$	−39.5353	+	14.3897i	−1.62352	+	0.590913i	−0.639473	+	0.768814i	$0.720847\pi$
$594$		0			0
$595$	15.2467	−	18.1703i	0.625053	−	0.744909i
$596$	4.56273	−	24.1197i	0.186897	−	0.987983i
$597$		0			0
$598$	−1.03158	−	0.00641012i	−0.0421843	−	0.000262129i
$599$	3.30302	−	18.7324i	0.134958	−	0.765384i	−0.839931	−	0.542693i	$-0.817405\pi$
$599$	3.30302	−	18.7324i	0.134958	−	0.765384i	0.974889	−	0.222691i	$-0.0714840\pi$
$600$		0			0
$601$	35.6278	+	20.5697i	1.45329	+	0.839057i	0.998666	−	0.0516270i	$-0.0164407\pi$
$601$	35.6278	+	20.5697i	1.45329	+	0.839057i	0.454623	+	0.890684i	$0.349774\pi$
$602$	−4.71015	+	8.04239i	−0.191971	+	0.327783i
$603$		0			0
$604$	−8.35350	+	6.83432i	−0.339899	+	0.278085i
$605$	−55.7506	+	46.7803i	−2.26658	+	1.90189i
$606$		0			0
$607$	−5.25857			−0.213439			−0.106719	−	0.994289i	$-0.534035\pi$
$607$	−5.25857			−0.213439			−0.106719	+	0.994289i	$0.534035\pi$
$608$	24.5509	+	2.29222i	0.995670	+	0.0929616i
$609$		0			0
$610$	53.4094	−	19.0644i	2.16248	−	0.771896i
$611$	0.526249	−	0.441575i	0.0212898	−	0.0178642i
$612$		0			0
$613$	3.19955	+	1.16454i	0.129229	+	0.0470354i	0.405825	−	0.913951i	$-0.366984\pi$
$613$	3.19955	+	1.16454i	0.129229	+	0.0470354i	−0.276596	+	0.960986i	$0.589206\pi$
$614$	−8.79537	+	15.0177i	−0.354952	+	0.606067i
$615$		0			0
$616$	16.0215	−	26.5926i	0.645524	−	1.07145i
$617$	−0.527489	+	2.99154i	−0.0212359	+	0.120435i	−0.993583	−	0.113106i	$-0.963920\pi$
$617$	−0.527489	+	2.99154i	−0.0212359	+	0.120435i	0.972347	+	0.233541i	$0.0750312\pi$
$618$		0			0
$619$	22.1622	−	12.7953i	0.890773	−	0.514288i	0.0165776	−	0.999863i	$-0.494723\pi$
$619$	22.1622	−	12.7953i	0.890773	−	0.514288i	0.874195	+	0.485575i	$0.161390\pi$
$620$	−1.75290	+	9.26629i	−0.0703982	+	0.372143i
$621$		0			0
$622$	−14.0471	−	2.56698i	−0.563238	−	0.102927i
$623$	21.3076	−	7.75532i	0.853669	−	0.310710i
$624$		0			0
$625$	−0.125305	−	0.710638i	−0.00501219	−	0.0284255i
$626$	−1.30800	−	7.69740i	−0.0522780	−	0.307650i
$627$		0			0
$628$	−17.8472	+	6.24579i	−0.712182	+	0.249234i
$629$	−23.4424	+	4.13353i	−0.934710	+	0.164815i
$630$		0			0
$631$	1.29656	+	3.56226i	0.0516151	+	0.141811i	0.962821	−	0.270139i	$-0.0870698\pi$
$631$	1.29656	+	3.56226i	0.0516151	+	0.141811i	−0.911206	+	0.411951i	$0.864848\pi$
$632$	−5.03670	−	32.0469i	−0.200349	−	1.27476i
$633$		0			0
$634$	−12.9364	+	34.8669i	−0.513772	+	1.38474i
$635$	2.09970	+	3.63678i	0.0833239	+	0.144321i
$636$		0			0
$637$	−0.355152	−	0.0626229i	−0.0140716	−	0.00248121i
$638$	9.58571	−	7.94239i	0.379502	−	0.314442i
$639$		0			0
$640$	18.8589	+	36.2156i	0.745465	+	1.43155i
$641$	1.34038	−	3.68267i	0.0529419	−	0.145457i	−0.910403	−	0.413723i	$-0.864228\pi$
$641$	1.34038	−	3.68267i	0.0529419	−	0.145457i	0.963345	+	0.268266i	$0.0864506\pi$
$642$		0			0
$643$	8.07959	+	9.62888i	0.318628	+	0.379726i	0.901457	−	0.432869i	$-0.142499\pi$
$643$	8.07959	+	9.62888i	0.318628	+	0.379726i	−0.582829	+	0.812595i	$0.698054\pi$
$644$	12.1951	+	21.7421i	0.480554	+	0.856760i
$645$		0			0
$646$	19.7982	−	5.71075i	0.778950	−	0.224686i
$647$			11.1120i			0.436857i	0.975853	+	0.218429i	$0.0700931\pi$
$647$			11.1120i			0.436857i	−0.975853	+	0.218429i	$0.929907\pi$
$648$		0			0
$649$	42.0376	+	50.0985i	1.65012	+	1.96654i
$650$	1.13502	−	0.645932i	0.0445190	−	0.0253356i
$651$		0			0
$652$	1.32275	−	3.49833i	0.0518029	−	0.137005i
$653$	7.74378	−	13.4126i	0.303038	−	0.524876i	−0.673785	−	0.738928i	$-0.735333\pi$
$653$	7.74378	−	13.4126i	0.303038	−	0.524876i	0.976822	+	0.214051i	$0.0686659\pi$
$654$		0			0
$655$	50.2666	+	8.86335i	1.96408	+	0.346320i
$656$	25.6876	−	13.9913i	1.00293	−	0.546270i
$657$		0			0
$658$	−15.5640	−	5.77460i	−0.606747	−	0.225117i
$659$	36.7884	+	30.8692i	1.43307	+	1.20249i	0.943868	+	0.330324i	$0.107158\pi$
$659$	36.7884	+	30.8692i	1.43307	+	1.20249i	0.489207	+	0.872168i	$0.337286\pi$
$660$		0			0
$661$	12.7444	+	35.0149i	0.495699	+	1.36192i	0.895395	+	0.445273i	$0.146894\pi$
$661$	12.7444	+	35.0149i	0.495699	+	1.36192i	−0.399696	+	0.916648i	$0.630884\pi$
$662$	−37.8579	−	32.1696i	−1.47139	−	1.25031i
$663$		0			0
$664$	43.6590	−	24.1328i	1.69430	−	0.936535i
$665$	−27.6943	+	13.7754i	−1.07394	+	0.534186i
$666$		0			0
$667$	1.73574	+	9.84387i	0.0672081	+	0.381156i
$668$	15.7244	−	26.4703i	0.608396	−	1.02417i
$669$		0			0
$670$	−4.94248	+	27.0463i	−0.190945	+	1.04489i
$671$	39.8706	−	47.5160i	1.53919	−	1.83433i
$672$		0			0
$673$	29.1483	−	16.8288i	1.12358	−	0.648701i	0.181270	−	0.983433i	$-0.441979\pi$
$673$	29.1483	−	16.8288i	1.12358	−	0.648701i	0.942313	+	0.334732i	$0.108646\pi$
$674$	−0.0810982	+	13.0511i	−0.00312379	+	0.502709i
$675$		0			0
$676$	19.6879	+	16.9414i	0.757225	+	0.651594i
$677$	5.61581	+	3.24229i	0.215833	+	0.124611i	0.604019	−	0.796970i	$-0.293565\pi$
$677$	5.61581	+	3.24229i	0.215833	+	0.124611i	−0.388186	+	0.921581i	$0.626898\pi$
$678$		0			0
$679$	9.98544	+	3.63440i	0.383206	+	0.139476i
$680$	25.7251	+	22.4162i	0.986513	+	0.859623i
$681$		0			0
$682$	3.46763	+	9.71463i	0.132782	+	0.371992i
$683$	46.0289			1.76125			0.880624	−	0.473815i	$-0.157124\pi$
$683$	46.0289			1.76125			0.880624	+	0.473815i	$0.157124\pi$
$684$		0			0
$685$	67.9183			2.59503
$686$	9.47306	+	26.5390i	0.361683	+	1.01326i
$687$		0			0
$688$	−11.4409	−	6.99017i	−0.436181	−	0.266498i
$689$	−0.241075	−	0.0877442i	−0.00918423	−	0.00334279i
$690$		0			0
$691$	−7.27369	−	4.19947i	−0.276704	−	0.159755i	0.355226	−	0.934780i	$-0.384404\pi$
$691$	−7.27369	−	4.19947i	−0.276704	−	0.159755i	−0.631930	+	0.775025i	$0.717737\pi$
$692$	22.0551	−	25.6305i	0.838410	−	0.974327i
$693$		0			0
$694$	−0.0342882	+	5.51798i	−0.00130156	+	0.209460i
$695$	24.2412	−	13.9957i	0.919521	−	0.530886i
$696$		0			0
$697$	15.7121	−	18.7250i	0.595139	−	0.709258i
$698$	−3.94104	+	21.5662i	−0.149171	+	0.816294i
$699$		0			0
$700$	−27.1321	−	16.1176i	−1.02550	−	0.609188i
$701$	−7.46058	−	42.3111i	−0.281782	−	1.59807i	−0.716557	−	0.697528i	$-0.754283\pi$
$701$	−7.46058	−	42.3111i	−0.281782	−	1.59807i	0.434775	−	0.900539i	$-0.356828\pi$
$702$		0			0
$703$	30.1767	+	7.27481i	1.13814	+	0.274375i
$704$	37.8180	+	23.7565i	1.42532	+	0.895356i
$705$		0			0
$706$	−4.10765	−	3.49046i	−0.154594	−	0.131365i
$707$	−12.1091	−	33.2695i	−0.455410	−	1.25123i
$708$		0			0
$709$	−10.3902	−	8.71837i	−0.390210	−	0.327425i	0.426485	−	0.904495i	$-0.359752\pi$
$709$	−10.3902	−	8.71837i	−0.390210	−	0.327425i	−0.816695	+	0.577069i	$0.804196\pi$
$710$	10.6341	+	3.94548i	0.399089	+	0.148071i
$711$		0			0
$712$	10.5830	+	30.8542i	0.396613	+	1.15631i
$713$	−8.15667	−	1.43824i	−0.305470	−	0.0538626i
$714$		0			0
$715$	1.15918	−	2.00775i	0.0433507	−	0.0750857i
$716$	16.6501	+	6.29555i	0.622243	+	0.235276i
$717$		0			0
$718$	0.155593	−	0.0885469i	0.00580666	−	0.00330454i
$719$	0.441431	+	0.526077i	0.0164626	+	0.0196193i	0.774213	−	0.632925i	$-0.218146\pi$
$719$	0.441431	+	0.526077i	0.0164626	+	0.0196193i	−0.757750	+	0.652545i	$0.773702\pi$
$720$		0			0
$721$			17.5420i			0.653298i
$722$	−26.6424	−	3.49041i	−0.991527	−	0.129900i
$723$		0			0
$724$	−15.9720	+	8.95863i	−0.593593	+	0.332945i
$725$	−8.13386	−	9.69355i	−0.302084	−	0.360010i
$726$		0			0
$727$	13.2285	−	36.3450i	0.490618	−	1.34796i	−0.409498	−	0.912311i	$-0.634296\pi$
$727$	13.2285	−	36.3450i	0.490618	−	1.34796i	0.900116	−	0.435651i	$-0.143482\pi$
$728$	−0.122848	+	0.628012i	−0.00455304	+	0.0232757i
$729$		0			0
$730$	−11.3729	+	9.42322i	−0.420931	+	0.348769i
$731$	−11.0337	−	1.94555i	−0.408098	−	0.0719587i
$732$		0			0
$733$	−2.57626	−	4.46222i	−0.0951564	−	0.164816i	0.814517	−	0.580139i	$-0.197002\pi$
$733$	−2.57626	−	4.46222i	−0.0951564	−	0.164816i	−0.909674	+	0.415323i	$0.863668\pi$
$734$	1.19764	−	3.22795i	0.0442059	−	0.119146i
$735$		0			0
$736$	−31.5983	+	16.9570i	−1.16473	+	0.625042i
$737$	10.2854	+	28.2588i	0.378867	+	1.04093i
$738$		0			0
$739$	13.9534	−	2.46035i	0.513283	−	0.0905056i	0.0889933	−	0.996032i	$-0.471635\pi$
$739$	13.9534	−	2.46035i	0.513283	−	0.0905056i	0.424289	+	0.905527i	$0.360524\pi$
$740$	16.9791	+	48.5174i	0.624164	+	1.78354i
$741$		0			0
$742$	1.03857	+	6.11188i	0.0381272	+	0.224374i
$743$	3.35200	+	19.0101i	0.122973	+	0.697414i	0.982491	+	0.186309i	$0.0596525\pi$
$743$	3.35200	+	19.0101i	0.122973	+	0.697414i	−0.859518	+	0.511105i	$0.829236\pi$
$744$		0			0
$745$	−41.6252	+	15.1503i	−1.52503	+	0.555065i
$746$	−20.5033	−	3.74680i	−0.750680	−	0.137180i
$747$		0			0
$748$	36.6707	+	6.93698i	1.34081	+	0.253641i
$749$	11.1253	−	6.42320i	0.406510	−	0.234699i
$750$		0			0
$751$	4.44462	−	25.2067i	0.162186	−	0.919805i	−0.789732	−	0.613453i	$-0.789780\pi$
$751$	4.44462	−	25.2067i	0.162186	−	0.919805i	0.951918	−	0.306353i	$-0.0991087\pi$
$752$	8.72284	−	22.2305i	0.318089	−	0.810664i
$753$		0			0
$754$	−0.129672	+	0.221410i	−0.00472239	+	0.00806329i
$755$	18.3017	+	6.66127i	0.666066	+	0.242428i
$756$		0			0
$757$	−18.0416	+	15.1387i	−0.655735	+	0.550227i	−0.908805	−	0.417221i	$-0.863004\pi$
$757$	−18.0416	+	15.1387i	−0.655735	+	0.550227i	0.253070	+	0.967448i	$0.418560\pi$
$758$	36.4404	−	13.0074i	1.32357	−	0.472448i
$759$		0			0
$760$	−19.0702	−	40.2016i	−0.691750	−	1.45826i
$761$	−18.7562			−0.679910			−0.339955	−	0.940442i	$-0.610412\pi$
$761$	−18.7562			−0.679910			−0.339955	+	0.940442i	$0.610412\pi$
$762$		0			0
$763$	16.1687	−	13.5672i	0.585347	−	0.491164i
$764$	−19.6652	−	24.0364i	−0.711461	−	0.869608i
$765$		0			0
$766$	−6.33478	+	10.8164i	−0.228885	+	0.390812i
$767$	−1.16739	−	0.673995i	−0.0421522	−	0.0243366i
$768$		0			0
$769$	−0.685755	+	3.88911i	−0.0247289	+	0.140245i	−0.994673	−	0.103085i	$-0.967129\pi$
$769$	−0.685755	+	3.88911i	−0.0247289	+	0.140245i	0.969944	+	0.243330i	$0.0782397\pi$
$770$	−56.0222	−	0.348117i	−2.01890	−	0.0125453i
$771$		0			0
$772$	11.3676	+	2.15040i	0.409128	+	0.0773948i
$773$	20.5063	−	24.4384i	0.737560	−	0.878990i	−0.258650	−	0.965971i	$-0.583278\pi$
$773$	20.5063	−	24.4384i	0.737560	−	0.878990i	0.996210	+	0.0869812i	$0.0277220\pi$
$774$		0			0
$775$	9.85285	−	3.58615i	0.353925	−	0.128818i
$776$	−5.49505	+	14.2644i	−0.197261	+	0.512063i
$777$		0			0
$778$	−5.22245	−	30.7335i	−0.187234	−	1.10185i
$779$	−28.5397	+	14.1959i	−1.02254	+	0.508620i
$780$		0			0
$781$	12.2175	−	2.15428i	0.437178	−	0.0770862i
$782$	−19.4049	+	22.8361i	−0.693917	+	0.816619i
$783$		0			0
$784$	−11.8832	+	3.99359i	−0.424402	+	0.142628i
$785$	26.1382	+	21.9325i	0.932912	+	0.782806i
$786$		0			0
$787$	23.6234	+	40.9170i	0.842084	+	1.45853i	0.888129	+	0.459594i	$0.152005\pi$
$787$	23.6234	+	40.9170i	0.842084	+	1.45853i	−0.0460450	+	0.998939i	$0.514662\pi$
$788$	−1.40412	−	8.58578i	−0.0500197	−	0.305856i
$789$		0			0
$790$	−45.0766	+	37.3490i	−1.60375	+	1.32882i
$791$	−14.6536	+	25.3807i	−0.521020	+	0.902434i
$792$		0			0
$793$	−0.437274	+	1.20140i	−0.0155281	+	0.0426630i
$794$	−10.4326	−	18.3320i	−0.370240	−	0.650578i
$795$		0			0
$796$	−5.43748	+	3.04987i	−0.192726	+	0.108100i
$797$			11.7621i			0.416636i	0.978061	+	0.208318i	$0.0667988\pi$
$797$			11.7621i			0.416636i	−0.978061	+	0.208318i	$0.933201\pi$
$798$		0			0
$799$		−	19.9560i		−	0.705994i
$800$	23.9092	−	38.5914i	0.845317	−	1.36441i
$801$		0			0
$802$	0.0611479	−	0.0347990i	0.00215921	−	0.00122879i
$803$	−5.52518	+	15.1803i	−0.194980	+	0.535702i
$804$		0			0
$805$	22.4922	−	38.9577i	0.792748	−	1.37308i
$806$	−0.135648	−	0.163715i	−0.00477801	−	0.00576661i
$807$		0			0
$808$	48.1756	−	16.5242i	1.69481	−	0.581319i
$809$	2.48471	+	4.30365i	0.0873578	+	0.151308i	0.906393	−	0.422434i	$-0.138824\pi$
$809$	2.48471	+	4.30365i	0.0873578	+	0.151308i	−0.819036	+	0.573743i	$0.805491\pi$
$810$		0			0
$811$	−3.51097	−	2.94606i	−0.123287	−	0.103450i	0.579060	−	0.815285i	$-0.303420\pi$
$811$	−3.51097	−	2.94606i	−0.123287	−	0.103450i	−0.702347	+	0.711835i	$0.747864\pi$
$812$	6.20001	+	0.0770556i	0.217578	+	0.00270412i
$813$		0			0
$814$	42.8437	+	36.4062i	1.50167	+	1.27604i
$815$	−6.64649	+	1.17196i	−0.232816	+	0.0410518i
$816$		0			0
$817$	12.1758	+	8.07543i	0.425976	+	0.282524i
$818$	28.7743	−	4.88952i	1.00607	−	0.170958i
$819$		0			0
$820$	−45.3807	−	26.9580i	−1.58476	−	0.941414i
$821$	13.7267	−	4.99610i	0.479064	−	0.174365i	−0.0911900	−	0.995834i	$-0.529067\pi$
$821$	13.7267	−	4.99610i	0.479064	−	0.174365i	0.570254	+	0.821469i	$0.306845\pi$
$822$		0			0
$823$	−33.0057	+	39.3347i	−1.15051	+	1.37112i	−0.233449	+	0.972369i	$0.575001\pi$
$823$	−33.0057	+	39.3347i	−1.15051	+	1.37112i	−0.917059	+	0.398753i	$0.869443\pi$
$824$	−25.2303	−	0.470385i	−0.878940	−	0.0163866i
$825$		0			0
$826$	−0.202410	+	32.5738i	−0.00704276	+	1.13339i
$827$	−5.61047	+	31.8185i	−0.195095	+	1.10644i	0.717188	+	0.696880i	$0.245429\pi$
$827$	−5.61047	+	31.8185i	−0.195095	+	1.10644i	−0.912283	+	0.409560i	$0.865682\pi$
$828$		0			0
$829$	−3.43948	−	1.98578i	−0.119458	−	0.0689691i	0.439080	−	0.898448i	$-0.355304\pi$
$829$	−3.43948	−	1.98578i	−0.119458	−	0.0689691i	−0.558538	+	0.829479i	$0.688638\pi$
$830$	−77.6772	−	45.4928i	−2.69621	−	1.57908i
$831$		0			0
$832$	−0.899964	−	0.193530i	−0.0312006	−	0.00670943i
$833$	−8.02516	+	6.73391i	−0.278055	+	0.233316i
$834$		0			0
$835$	−55.5587			−1.92269
$836$	−40.2207	−	27.4017i	−1.39106	−	0.947706i
$837$		0			0
$838$	−8.17153	−	22.8927i	−0.282281	−	0.790815i
$839$	−25.5691	+	21.4550i	−0.882744	+	0.740710i	−0.966741	−	0.255756i	$-0.917676\pi$
$839$	−25.5691	+	21.4550i	−0.882744	+	0.740710i	0.0839976	+	0.996466i	$0.473231\pi$
$840$		0			0
$841$	−24.9148	−	9.06824i	−0.859131	−	0.312698i
$842$	−2.47519	−	1.44963i	−0.0853007	−	0.0499576i
$843$		0			0
$844$	−7.94797	−	6.83924i	−0.273580	−	0.235416i
$845$	8.13887	−	46.1578i	0.279986	−	1.58788i
$846$		0			0
$847$	−34.3367	+	19.8243i	−1.17982	+	0.681172i
$848$	−8.81845	+	1.32987i	−0.302827	+	0.0456679i
$849$		0			0
$850$	6.81970	−	37.3189i	0.233914	−	1.28003i
$851$	−42.4221	+	15.4404i	−1.45421	+	0.529289i
$852$		0			0
$853$	−2.88646	−	16.3699i	−0.0988304	−	0.560495i	−0.993506	−	0.113779i	$-0.963704\pi$
$853$	−2.88646	−	16.3699i	−0.0988304	−	0.560495i	0.894676	−	0.446716i	$-0.147407\pi$
$854$	30.4586	−	5.17574i	1.04227	−	0.177110i
$855$		0			0
$856$	8.94005	+	16.1736i	0.305565	+	0.552801i
$857$	34.9234	−	6.15794i	1.19296	−	0.210351i	0.458308	−	0.888794i	$-0.348456\pi$
$857$	34.9234	−	6.15794i	1.19296	−	0.210351i	0.734654	+	0.678442i	$0.237345\pi$
$858$		0			0
$859$	3.57775	+	9.82980i	0.122071	+	0.335388i	0.985644	−	0.168836i	$-0.0540008\pi$
$859$	3.57775	+	9.82980i	0.122071	+	0.335388i	−0.863573	+	0.504224i	$0.831779\pi$
$860$	−0.300666	+	24.1920i	−0.0102526	+	0.824942i
$861$		0			0
$862$	−44.2621	−	16.4223i	−1.50757	−	0.559344i
$863$	−6.08159	−	10.5336i	−0.207020	−	0.358569i	0.743755	−	0.668453i	$-0.233043\pi$
$863$	−6.08159	−	10.5336i	−0.207020	−	0.358569i	−0.950774	+	0.309884i	$0.899710\pi$
$864$		0			0
$865$	−60.0904	−	10.5956i	−2.04313	−	0.360260i
$866$	18.1548	+	21.9111i	0.616924	+	0.744569i
$867$		0			0
$868$	−1.81708	+	4.80570i	−0.0616757	+	0.163116i
$869$	−21.8991	+	60.1672i	−0.742876	+	2.04103i
$870$		0			0
$871$	−0.398430	−	0.474831i	−0.0135003	−	0.0160890i
$872$	19.0798	+	23.6189i	0.646124	+	0.799839i
$873$		0			0
$874$	35.0964	−	17.1860i	1.18715	−	0.581325i
$875$			21.4674i			0.725732i
$876$		0			0
$877$	−5.18825	−	6.18312i	−0.175195	−	0.208789i	0.671300	−	0.741185i	$-0.265736\pi$
$877$	−5.18825	−	6.18312i	−0.175195	−	0.208789i	−0.846495	+	0.532396i	$0.821292\pi$
$878$	25.5620	+	44.9170i	0.862676	+	1.51587i
$879$		0			0
$880$	2.00291	−	80.5664i	0.0675182	−	2.71589i
$881$	12.8256	−	22.2146i	0.432105	−	0.748427i	−0.564950	−	0.825125i	$-0.691104\pi$
$881$	12.8256	−	22.2146i	0.432105	−	0.748427i	0.997054	+	0.0766980i	$0.0244377\pi$
$882$		0			0
$883$	13.5357	+	2.38671i	0.455512	+	0.0803191i	0.396697	−	0.917950i	$-0.370157\pi$
$883$	13.5357	+	2.38671i	0.455512	+	0.0803191i	0.0588155	+	0.998269i	$0.481268\pi$
$884$	−0.759169	+	0.124155i	−0.0255336	+	0.00417578i
$885$		0			0
$886$	−9.49098	+	25.5806i	−0.318856	+	0.859396i
$887$	−16.7033	−	14.0157i	−0.560842	−	0.470603i	0.317750	−	0.948174i	$-0.397073\pi$
$887$	−16.7033	−	14.0157i	−0.560842	−	0.470603i	−0.878593	+	0.477572i	$0.841517\pi$
$888$		0			0
$889$	0.782476	+	2.14983i	0.0262434	+	0.0721031i
$890$	38.1148	−	44.8544i	1.27761	−	1.50352i
$891$		0			0
$892$	−13.6734	+	4.78513i	−0.457820	+	0.160218i
$893$	−10.3992	+	23.8552i	−0.347996	+	0.798283i
$894$		0			0
$895$	−5.57785	−	31.6335i	−0.186447	−	1.05739i
$896$	6.69207	+	21.2144i	0.223566	+	0.708725i
$897$		0			0
$898$	16.7389	+	3.05889i	0.558585	+	0.102076i
$899$	−1.32421	+	1.57813i	−0.0441647	+	0.0526335i
$900$		0			0
$901$	−6.45408	+	3.72627i	−0.215017	+	0.124140i
$902$	−57.7324	−	0.358744i	−1.92228	−	0.0119449i
$903$		0			0
$904$	−36.1116	−	21.7565i	−1.20106	−	0.723610i
$905$	28.6187	+	16.5230i	0.951318	+	0.549244i
$906$		0			0
$907$	−17.3624	−	6.31941i	−0.576510	−	0.209832i	0.0372759	−	0.999305i	$-0.488132\pi$
$907$	−17.3624	−	6.31941i	−0.576510	−	0.209832i	−0.613786	+	0.789473i	$0.710354\pi$
$908$	−19.9729	+	16.3406i	−0.662824	+	0.542282i
$909$		0			0
$910$	1.08754	−	0.388195i	0.0360515	−	0.0128685i
$911$	−7.50876			−0.248776			−0.124388	−	0.992234i	$-0.539697\pi$
$911$	−7.50876			−0.248776			−0.124388	+	0.992234i	$0.539697\pi$
$912$		0			0
$913$	−98.4598			−3.25854
$914$	22.1792	−	7.91686i	0.733624	−	0.261866i
$915$		0			0
$916$	10.0619	−	8.23203i	0.332454	−	0.271994i
$917$	26.1304	+	9.51070i	0.862903	+	0.314071i
$918$		0			0
$919$	16.6207	+	9.59598i	0.548267	+	0.316542i	0.748423	−	0.663222i	$-0.230811\pi$
$919$	16.6207	+	9.59598i	0.548267	+	0.316542i	−0.200156	+	0.979764i	$0.564145\pi$
$920$	55.4290	+	33.3948i	1.82744	+	1.10099i
$921$		0			0
$922$	−28.3702	−	0.176290i	−0.934324	−	0.00580580i
$923$	−0.221452	+	0.127855i	−0.00728917	+	0.00420840i
$924$		0			0
$925$	36.7357	−	43.7799i	1.20786	−	1.43947i
$926$	33.0395	+	6.03768i	1.08575	+	0.198410i
$927$		0			0
$928$	−0.277080	+	8.91530i	−0.00909558	+	0.292659i
$929$	−4.66977	−	26.4836i	−0.153210	−	0.868899i	−0.960404	−	0.278612i	$-0.910126\pi$
$929$	−4.66977	−	26.4836i	−0.153210	−	0.868899i	0.807194	−	0.590287i	$-0.200985\pi$
$930$		0			0
$931$	13.1023	−	3.86767i	0.429409	−	0.126758i
$932$	−19.7061	+	6.89631i	−0.645494	+	0.225896i
$933$		0			0
$934$	18.3499	−	21.5946i	0.600427	−	0.706598i
$935$	−23.0339	−	63.2852i	−0.753290	−	2.06965i
$936$		0			0
$937$	11.2301	+	9.42315i	0.366871	+	0.307841i	0.807522	−	0.589837i	$-0.200808\pi$
$937$	11.2301	+	9.42315i	0.366871	+	0.307841i	−0.440652	+	0.897678i	$0.645253\pi$
$938$	−5.21038	+	14.0433i	−0.170125	+	0.458529i
$939$		0			0
$940$	−42.5283	+	6.95508i	−1.38712	+	0.226850i
$941$	−41.2808	−	7.27891i	−1.34571	−	0.237286i	−0.546060	−	0.837746i	$-0.683873\pi$
$941$	−41.2808	−	7.27891i	−1.34571	−	0.237286i	−0.799655	+	0.600460i	$0.794984\pi$
$942$		0			0
$943$	23.1789	−	40.1470i	0.754808	−	1.30737i
$944$	−46.8448	−	1.16458i	−1.52467	−	0.0379039i
$945$		0			0
$946$	13.0887	+	22.9991i	0.425549	+	0.747765i
$947$	−33.8066	−	40.2891i	−1.09857	−	1.30922i	−0.947164	−	0.320749i	$-0.896066\pi$
$947$	−33.8066	−	40.2891i	−1.09857	−	1.30922i	−0.151402	−	0.988472i	$-0.548379\pi$
$948$		0			0
$949$		−	0.332975i		−	0.0108088i
$950$	−27.5993	+	41.0567i	−0.895439	+	1.33206i
$951$		0			0
$952$	11.6814	+	14.4604i	0.378595	+	0.468663i
$953$	−6.79493	−	8.09789i	−0.220109	−	0.262316i	0.644678	−	0.764454i	$-0.276991\pi$
$953$	−6.79493	−	8.09789i	−0.220109	−	0.262316i	−0.864788	+	0.502138i	$0.832547\pi$
$954$		0			0
$955$	−19.1672	+	52.6615i	−0.620236	+	1.70409i
$956$	19.8253	−	52.4327i	0.641195	−	1.69580i
$957$		0			0
$958$	13.8902	+	16.7641i	0.448771	+	0.541624i
$959$	36.4394	+	6.42525i	1.17669	+	0.207482i
$960$		0			0
$961$	14.6465	+	25.3685i	0.472468	+	0.818338i
$962$	−1.08648	−	0.403110i	−0.0350296	−	0.0129968i
$963$		0			0
$964$	0.366652	−	29.5014i	0.0118091	−	0.950175i
$965$	−7.14032	−	19.6179i	−0.229855	−	0.631522i
$966$		0			0
$967$	39.2804	−	6.92619i	1.26317	−	0.222731i	0.498351	−	0.866975i	$-0.333939\pi$
$967$	39.2804	−	6.92619i	1.26317	−	0.222731i	0.764820	+	0.644244i	$0.222828\pi$
$968$	−27.5922	−	49.9175i	−0.886847	−	1.60441i
$969$		0			0
$970$	27.1946	−	4.62109i	0.873165	−	0.148374i
$971$	−6.74557	−	38.2561i	−0.216476	−	1.22770i	−0.878327	−	0.478060i	$-0.841340\pi$
$971$	−6.74557	−	38.2561i	−0.216476	−	1.22770i	0.661851	−	0.749635i	$-0.269771\pi$
$972$		0			0
$973$	14.3299	−	5.21564i	0.459394	−	0.167206i
$974$	5.78990	−	31.6836i	0.185520	−	1.01521i
$975$		0			0
$976$	6.62742	+	43.9468i	0.212139	+	1.40670i
$977$	23.9306	−	13.8163i	0.765606	−	0.442023i	−0.0656987	−	0.997840i	$-0.520928\pi$
$977$	23.9306	−	13.8163i	0.765606	−	0.442023i	0.831305	+	0.555817i	$0.187594\pi$
$978$		0			0
$979$	11.1796	−	63.4028i	0.357302	−	2.02636i
$980$	17.1475	+	14.7555i	0.547758	+	0.471347i
$981$		0			0
$982$	−25.6494	−	15.0220i	−0.818505	−	0.479370i
$983$	55.3082	+	20.1305i	1.76406	+	0.642065i	0.999995	−	0.00307694i	$-0.000979421\pi$
$983$	55.3082	+	20.1305i	1.76406	+	0.642065i	0.764063	+	0.645142i	$0.223202\pi$
$984$		0			0
$985$	−12.0262	+	10.0912i	−0.383186	+	0.321531i
$986$	2.50576	+	7.01993i	0.0797995	+	0.223560i
$987$		0			0
$988$	0.972198	+	0.247195i	0.0309297	+	0.00786431i
$989$	−21.2484			−0.675661
$990$		0			0
$991$	−32.7089	+	27.4460i	−1.03903	+	0.871852i	−0.991898	−	0.127037i	$-0.959453\pi$
$991$	−32.7089	+	27.4460i	−1.03903	+	0.871852i	−0.0471344	+	0.998889i	$0.515009\pi$
$992$	−6.86322	−	2.74233i	−0.217908	−	0.0870691i
$993$		0			0
$994$	5.33211	+	3.12283i	0.169124	+	0.0990502i
$995$	9.74292	+	5.62508i	0.308871	+	0.178327i
$996$		0			0
$997$	8.78153	−	49.8025i	0.278114	−	1.57726i	−0.450781	−	0.892635i	$-0.648854\pi$
$997$	8.78153	−	49.8025i	0.278114	−	1.57726i	0.728894	−	0.684626i	$-0.240035\pi$
$998$	−0.163457	+	26.3050i	−0.00517413	+	0.832669i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.c.523.9		60
3.2	odd	2		228.2.w.a.67.2	✓	60
4.3	odd	2		684.2.cf.b.523.10		60
12.11	even	2		228.2.w.b.67.1	yes	60
19.2	odd	18		684.2.cf.b.667.10		60
57.2	even	18		228.2.w.b.211.1	yes	60
76.59	even	18	inner	684.2.cf.c.667.9		60
228.59	odd	18		228.2.w.a.211.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.2	✓	60	3.2	odd	2
228.2.w.a.211.2	yes	60	228.59	odd	18
228.2.w.b.67.1	yes	60	12.11	even	2
228.2.w.b.211.1	yes	60	57.2	even	18
684.2.cf.b.523.10		60	4.3	odd	2
684.2.cf.b.667.10		60	19.2	odd	18
684.2.cf.c.523.9		60	1.1	even	1	trivial
684.2.cf.c.667.9		60	76.59	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33191 - 0.475423i) q^{2} +(1.54795 - 1.26644i) q^{4} +(-3.39140 - 1.23437i) q^{5} +(-1.70277 - 0.983096i) q^{7} +(1.45963 - 2.42270i) q^{8} +(-5.10387 - 0.0317150i) q^{10} +(-4.83466 + 2.79129i) q^{11} +(0.0739637 - 0.0881465i) q^{13} +(-2.73532 - 0.499855i) q^{14} +(0.792279 - 3.92075i) q^{16} +(-0.580442 - 3.29185i) q^{17} +(-1.02155 + 4.23750i) q^{19} +(-6.81295 + 2.38425i) q^{20} +(-5.11227 + 6.01624i) q^{22} +(-2.16818 - 5.95703i) q^{23} +(6.14770 + 5.15853i) q^{25} +(0.0566059 - 0.152567i) q^{26} +(-3.88083 + 0.634672i) q^{28} +(-1.55282 - 0.273805i) q^{29} +(0.653262 - 1.13148i) q^{31} +(-0.808773 - 5.59874i) q^{32} +(-2.33811 - 4.10848i) q^{34} +(4.56128 + 5.43592i) q^{35} -7.12135i q^{37} +(0.653996 + 6.12962i) q^{38} +(-7.94069 + 6.41463i) q^{40} +(4.70052 + 5.60186i) q^{41} +(1.14640 - 3.14970i) q^{43} +(-3.94880 + 10.4436i) q^{44} +(-5.71992 - 6.90340i) q^{46} +(5.87946 + 1.03671i) q^{47} +(-1.56704 - 2.71420i) q^{49} +(10.6406 + 3.94792i) q^{50} +(0.00285995 - 0.230117i) q^{52} +(-0.762548 - 2.09508i) q^{53} +(19.8417 - 3.49863i) q^{55} +(-4.86716 + 2.69036i) q^{56} +(-2.19839 + 0.373565i) q^{58} +(-2.03426 - 11.5368i) q^{59} +(-10.4409 + 3.80016i) q^{61} +(0.332151 - 1.81761i) q^{62} +(-3.73898 - 7.07249i) q^{64} +(-0.359646 + 0.207642i) q^{65} +(0.935414 - 5.30500i) q^{67} +(-5.06741 - 4.36052i) q^{68} +(8.65955 + 5.07160i) q^{70} +(-2.08825 - 0.760061i) q^{71} +(2.21674 - 1.86006i) q^{73} +(-3.38565 - 9.48496i) q^{74} +(3.78522 + 7.85316i) q^{76} +10.9764 q^{77} +(8.78604 - 7.37237i) q^{79} +(-7.52658 + 12.3189i) q^{80} +(8.92390 + 5.22642i) q^{82} +(15.2741 + 8.81848i) q^{83} +(-2.09484 + 11.8805i) q^{85} +(0.0294547 - 4.74012i) q^{86} +(-0.294330 + 15.7872i) q^{88} +(-7.41292 + 8.83438i) q^{89} +(-0.212600 + 0.0773800i) q^{91} +(-10.9004 - 6.47530i) q^{92} +(8.32376 - 1.41443i) q^{94} +(8.69512 - 13.1101i) q^{95} +(-5.32239 + 0.938482i) q^{97} +(-3.37755 - 2.87005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{2} - 3 q^{4} - 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} - 27 q^{16} - 18 q^{19} - 30 q^{20} + 12 q^{22} - 18 q^{28} + 12 q^{31} + 63 q^{32} - 39 q^{34} + 48 q^{38} + 33 q^{40} + 12 q^{41} + 18 q^{43}+ \cdots - 117 q^{98}+O(q^{100}) \) 60 * q + 3 * q^2 - 3 * q^4 - 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 - 27 * q^16 - 18 * q^19 - 30 * q^20 + 12 * q^22 - 18 * q^28 + 12 * q^31 + 63 * q^32 - 39 * q^34 + 48 * q^38 + 33 * q^40 + 12 * q^41 + 18 * q^43 + 9 * q^44 - 69 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 + 42 * q^56 - 36 * q^58 - 27 * q^62 + 21 * q^64 + 36 * q^65 - 42 * q^67 - 93 * q^68 + 132 * q^70 + 24 * q^71 + 18 * q^73 - 27 * q^74 + 66 * q^76 + 72 * q^77 - 12 * q^79 - 6 * q^80 - 9 * q^82 - 60 * q^85 - 123 * q^86 + 36 * q^88 + 12 * q^89 + 84 * q^91 + 99 * q^92 - 24 * q^95 + 12 * q^97 - 117 * q^98

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