LMFDB - Embedded newform 684.2.ce.a.503.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(35,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 4]))

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

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

chi := DirichletCharacter("684.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.ce (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			503.8
Character	$\chi$	$=$	684.503
Dual form			684.2.ce.a.359.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22358 + 0.709127i) q^{2} +(0.994278 - 1.73534i) q^{4} +(0.294744 - 0.809802i) q^{5} +(2.07545 + 1.19826i) q^{7} +(0.0140029 + 2.82839i) q^{8} +O(q^{10})$	\(q+(-1.22358 + 0.709127i) q^{2} +(0.994278 - 1.73534i) q^{4} +(0.294744 - 0.809802i) q^{5} +(2.07545 + 1.19826i) q^{7} +(0.0140029 + 2.82839i) q^{8} +(0.213611 + 1.19987i) q^{10} +(1.68767 + 2.92312i) q^{11} +(1.65614 + 1.38967i) q^{13} +(-3.38919 + 0.00559306i) q^{14} +(-2.02282 - 3.45082i) q^{16} +(-7.72199 + 1.36160i) q^{17} +(0.789602 - 4.28679i) q^{19} +(-1.11223 - 1.31665i) q^{20} +(-4.13785 - 2.37989i) q^{22} +(2.80559 - 1.02115i) q^{23} +(3.26132 + 2.73657i) q^{25} +(-3.01187 - 0.525950i) q^{26} +(4.14296 - 2.41021i) q^{28} +(4.45240 + 0.785078i) q^{29} +(7.62096 + 4.39996i) q^{31} +(4.92215 + 2.78791i) q^{32} +(8.48290 - 7.14189i) q^{34} +(1.58208 - 1.32752i) q^{35} -7.33783 q^{37} +(2.07374 + 5.80514i) q^{38} +(2.29456 + 0.822312i) q^{40} +(4.47507 + 5.33318i) q^{41} +(-1.61673 + 4.44193i) q^{43} +(6.75063 - 0.0222807i) q^{44} +(-2.70873 + 3.23898i) q^{46} +(1.49426 - 8.47439i) q^{47} +(-0.628347 - 1.08833i) q^{49} +(-5.93105 - 1.03571i) q^{50} +(4.05822 - 1.49226i) q^{52} +(0.0611610 + 0.168038i) q^{53} +(2.86458 - 0.505103i) q^{55} +(-3.36009 + 5.88696i) q^{56} +(-6.00457 + 2.19671i) q^{58} +(0.802194 + 4.54947i) q^{59} +(-2.65253 + 0.965440i) q^{61} +(-12.4450 + 0.0205375i) q^{62} +(-7.99961 + 0.0792114i) q^{64} +(1.61349 - 0.931551i) q^{65} +(11.8747 + 2.09382i) q^{67} +(-5.31497 + 14.7541i) q^{68} +(-0.994412 + 2.74622i) q^{70} +(9.81994 + 3.57417i) q^{71} +(-5.28753 + 4.43677i) q^{73} +(8.97840 - 5.20346i) q^{74} +(-6.65395 - 5.63249i) q^{76} +8.08905i q^{77} +(3.94292 + 4.69899i) q^{79} +(-3.39070 + 0.620977i) q^{80} +(-9.25749 - 3.35216i) q^{82} +(7.58820 - 13.1432i) q^{83} +(-1.17339 + 6.65461i) q^{85} +(-1.17170 - 6.58151i) q^{86} +(-8.24411 + 4.81431i) q^{88} +(-2.98845 + 3.56150i) q^{89} +(1.77205 + 4.86867i) q^{91} +(1.01749 - 5.88398i) q^{92} +(4.18107 + 11.4287i) q^{94} +(-3.23872 - 1.90292i) q^{95} +(0.117541 + 0.666610i) q^{97} +(1.54059 + 0.886075i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{4}+O(q^{10}) $ 240 * q + 12 * q^4	$ 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) $ 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$-1$	$-1$

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 $

$2$	−1.22358	+	0.709127i	−0.865199	+	0.501428i
$2$	−1.22358	+	0.709127i	−0.865199	+	0.501428i
$3$		0			0
$3$		0			0
$4$	0.994278	−	1.73534i	0.497139	−	0.867671i
$5$	0.294744	−	0.809802i	0.131813	−	0.362154i	−0.856174	−	0.516687i	$-0.827165\pi$
$5$	0.294744	−	0.809802i	0.131813	−	0.362154i	0.987988	+	0.154533i	$0.0493872\pi$
$6$		0			0
$7$	2.07545	+	1.19826i	0.784445	+	0.452900i	0.838003	−	0.545665i	$-0.183723\pi$
$7$	2.07545	+	1.19826i	0.784445	+	0.452900i	−0.0535581	+	0.998565i	$0.517056\pi$
$8$	0.0140029	+	2.82839i	0.00495077	+	0.999988i
$9$		0			0
$10$	0.213611	+	1.19987i	0.0675497	+	0.379431i
$11$	1.68767	+	2.92312i	0.508850	+	0.881355i	0.999947	+	0.0102500i	$0.00326272\pi$
$11$	1.68767	+	2.92312i	0.508850	+	0.881355i	−0.491097	+	0.871105i	$0.663404\pi$
$12$		0			0
$13$	1.65614	+	1.38967i	0.459331	+	0.385425i	0.842885	−	0.538094i	$-0.180855\pi$
$13$	1.65614	+	1.38967i	0.459331	+	0.385425i	−0.383554	+	0.923519i	$0.625300\pi$
$14$	−3.38919	+	0.00559306i	−0.905798	+	0.00149481i
$15$		0			0
$16$	−2.02282	−	3.45082i	−0.505706	−	0.862706i
$17$	−7.72199	+	1.36160i	−1.87286	+	0.330235i	−0.990186	−	0.139754i	$-0.955369\pi$
$17$	−7.72199	+	1.36160i	−1.87286	+	0.330235i	−0.882672	+	0.469989i	$0.844258\pi$
$18$		0			0
$19$	0.789602	−	4.28679i	0.181147	−	0.983456i
$19$	0.789602	−	4.28679i	0.181147	−	0.983456i
$20$	−1.11223	−	1.31665i	−0.248701	−	0.294412i
$21$		0			0
$22$	−4.13785	−	2.37989i	−0.882193	−	0.507395i
$23$	2.80559	−	1.02115i	0.585007	−	0.212925i	−0.0325250	−	0.999471i	$-0.510355\pi$
$23$	2.80559	−	1.02115i	0.585007	−	0.212925i	0.617532	+	0.786546i	$0.288133\pi$
$24$		0			0
$25$	3.26132	+	2.73657i	0.652263	+	0.547314i
$26$	−3.01187	−	0.525950i	−0.590676	−	0.103147i
$27$		0			0
$28$	4.14296	−	2.41021i	0.782946	−	0.455486i
$29$	4.45240	+	0.785078i	0.826789	+	0.145785i	0.571003	−	0.820948i	$-0.306555\pi$
$29$	4.45240	+	0.785078i	0.826789	+	0.145785i	0.255786	+	0.966733i	$0.417666\pi$
$30$		0			0
$31$	7.62096	+	4.39996i	1.36876	+	0.790257i	0.990770	−	0.135551i	$-0.0432805\pi$
$31$	7.62096	+	4.39996i	1.36876	+	0.790257i	0.377994	+	0.925808i	$0.376614\pi$
$32$	4.92215	+	2.78791i	0.870122	+	0.492837i
$33$		0			0
$34$	8.48290	−	7.14189i	1.45481	−	1.22482i
$35$	1.58208	−	1.32752i	0.267420	−	0.224392i
$36$		0			0
$37$	−7.33783			−1.20633			−0.603166	−	0.797615i	$-0.706094\pi$
$37$	−7.33783			−1.20633			−0.603166	+	0.797615i	$0.706094\pi$
$38$	2.07374	+	5.80514i	0.336405	+	0.941718i
$39$		0			0
$40$	2.29456	+	0.822312i	0.362803	+	0.130019i
$41$	4.47507	+	5.33318i	0.698888	+	0.832903i	0.992400	−	0.123053i	$-0.0392685\pi$
$41$	4.47507	+	5.33318i	0.698888	+	0.832903i	−0.293512	+	0.955955i	$0.594824\pi$
$42$		0			0
$43$	−1.61673	+	4.44193i	−0.246549	+	0.677388i	0.753258	+	0.657726i	$0.228481\pi$
$43$	−1.61673	+	4.44193i	−0.246549	+	0.677388i	−0.999807	+	0.0196624i	$0.993741\pi$
$44$	6.75063	−	0.0222807i	1.01770	−	0.00335894i
$45$		0			0
$46$	−2.70873	+	3.23898i	−0.399381	+	0.477562i
$47$	1.49426	−	8.47439i	0.217961	−	1.23612i	−0.657734	−	0.753251i	$-0.728485\pi$
$47$	1.49426	−	8.47439i	0.217961	−	1.23612i	0.875694	−	0.482866i	$-0.160404\pi$
$48$		0			0
$49$	−0.628347	−	1.08833i	−0.0897638	−	0.155475i
$50$	−5.93105	−	1.03571i	−0.838777	−	0.146472i
$51$		0			0
$52$	4.05822	−	1.49226i	0.562773	−	0.206939i
$53$	0.0611610	+	0.168038i	0.00840111	+	0.0230819i	0.943822	−	0.330453i	$-0.107202\pi$
$53$	0.0611610	+	0.168038i	0.00840111	+	0.0230819i	−0.935421	+	0.353535i	$0.884979\pi$
$54$		0			0
$55$	2.86458	−	0.505103i	0.386260	−	0.0681080i
$56$	−3.36009	+	5.88696i	−0.449011	+	0.786678i
$57$		0			0
$58$	−6.00457	+	2.19671i	−0.788438	+	0.288442i
$59$	0.802194	+	4.54947i	0.104437	+	0.592291i	0.991444	+	0.130534i	$0.0416693\pi$
$59$	0.802194	+	4.54947i	0.104437	+	0.592291i	−0.887007	+	0.461756i	$0.847220\pi$
$60$		0			0
$61$	−2.65253	+	0.965440i	−0.339621	+	0.123612i	−0.506200	−	0.862416i	$-0.668950\pi$
$61$	−2.65253	+	0.965440i	−0.339621	+	0.123612i	0.166579	+	0.986028i	$0.446728\pi$
$62$	−12.4450	+	0.0205375i	−1.58051	+	0.00260826i
$63$		0			0
$64$	−7.99961	+	0.0792114i	−0.999951	+	0.00990142i
$65$	1.61349	−	0.931551i	0.200129	−	0.115545i
$66$		0			0
$67$	11.8747	+	2.09382i	1.45072	+	0.255801i	0.842813	−	0.538207i	$-0.180898\pi$
$67$	11.8747	+	2.09382i	1.45072	+	0.255801i	0.607907	+	0.794008i	$0.292009\pi$
$68$	−5.31497	+	14.7541i	−0.644535	+	1.78920i
$69$		0			0
$70$	−0.994412	+	2.74622i	−0.118855	+	0.328236i
$71$	9.81994	+	3.57417i	1.16541	+	0.424176i	0.851028	−	0.525120i	$-0.175980\pi$
$71$	9.81994	+	3.57417i	1.16541	+	0.424176i	0.314385	+	0.949296i	$0.398202\pi$
$72$		0			0
$73$	−5.28753	+	4.43677i	−0.618859	+	0.519284i	−0.897445	−	0.441127i	$-0.854579\pi$
$73$	−5.28753	+	4.43677i	−0.618859	+	0.519284i	0.278586	+	0.960411i	$0.410134\pi$
$74$	8.97840	−	5.20346i	1.04372	−	0.604890i
$75$		0			0
$76$	−6.65395	−	5.63249i	−0.763261	−	0.646090i
$77$			8.08905i			0.921833i
$78$		0			0
$79$	3.94292	+	4.69899i	0.443613	+	0.528677i	0.940798	−	0.338967i	$-0.110078\pi$
$79$	3.94292	+	4.69899i	0.443613	+	0.528677i	−0.497185	+	0.867644i	$0.665633\pi$
$80$	−3.39070	+	0.620977i	−0.379092	+	0.0694273i
$81$		0			0
$82$	−9.25749	−	3.35216i	−1.02232	−	0.370184i
$83$	7.58820	−	13.1432i	0.832914	−	1.44265i	−0.0628044	−	0.998026i	$-0.520004\pi$
$83$	7.58820	−	13.1432i	0.832914	−	1.44265i	0.895718	−	0.444623i	$-0.146662\pi$
$84$		0			0
$85$	−1.17339	+	6.65461i	−0.127272	+	0.721793i
$86$	−1.17170	−	6.58151i	−0.126348	−	0.709702i
$87$		0			0
$88$	−8.24411	+	4.81431i	−0.878825	+	0.513208i
$89$	−2.98845	+	3.56150i	−0.316775	+	0.377518i	−0.900812	−	0.434209i	$-0.857028\pi$
$89$	−2.98845	+	3.56150i	−0.316775	+	0.377518i	0.584037	+	0.811727i	$0.301472\pi$
$90$		0			0
$91$	1.77205	+	4.86867i	0.185762	+	0.510376i
$92$	1.01749	−	5.88398i	0.106081	−	0.613447i
$93$		0			0
$94$	4.18107	+	11.4287i	0.431245	+	1.17878i
$95$	−3.23872	−	1.90292i	−0.332285	−	0.195236i
$96$		0			0
$97$	0.117541	+	0.666610i	0.0119345	+	0.0676840i	0.990193	−	0.139704i	$-0.0446150\pi$
$97$	0.117541	+	0.666610i	0.0119345	+	0.0676840i	−0.978259	+	0.207388i	$0.933504\pi$
$98$	1.54059	+	0.886075i	0.155623	+	0.0895071i
$99$		0			0
$100$	7.99154	−	2.93859i	0.799154	−	0.293859i
$101$	1.47271	−	1.75510i	0.146540	−	0.174639i	−0.687782	−	0.725918i	$-0.741415\pi$
$101$	1.47271	−	1.75510i	0.146540	−	0.174639i	0.834321	+	0.551278i	$0.185860\pi$
$102$		0			0
$103$	−15.5341	+	8.96861i	−1.53062	+	0.883704i	−0.531287	+	0.847192i	$0.678291\pi$
$103$	−15.5341	+	8.96861i	−1.53062	+	0.883704i	−0.999333	+	0.0365116i	$0.988375\pi$
$104$	−3.90734	+	4.70368i	−0.383146	+	0.461234i
$105$		0			0
$106$	−0.193996	−	0.162237i	−0.0188425	−	0.0157578i
$107$	−1.32317	+	2.29180i	−0.127916	+	0.221557i	−0.922869	−	0.385114i	$-0.874162\pi$
$107$	−1.32317	+	2.29180i	−0.127916	+	0.221557i	0.794953	+	0.606671i	$0.207495\pi$
$108$		0			0
$109$	4.06044	+	1.47788i	0.388920	+	0.141555i	0.529077	−	0.848574i	$-0.322538\pi$
$109$	4.06044	+	1.47788i	0.388920	+	0.141555i	−0.140157	+	0.990129i	$0.544761\pi$
$110$	−3.14685	+	2.64938i	−0.300040	+	0.252609i
$111$		0			0
$112$	−0.0632778	−	9.58587i	−0.00597919	−	0.905780i
$113$		−	13.1332i		−	1.23546i	−0.786389	−	0.617732i	$-0.788052\pi$
$113$		−	13.1332i		−	1.23546i	0.786389	−	0.617732i	$-0.211948\pi$
$114$		0			0
$115$		−	2.57295i		−	0.239929i
$116$	5.78930	−	6.94584i	0.537523	−	0.644905i
$117$		0			0
$118$	−4.20770	−	4.99777i	−0.387350	−	0.460082i
$119$	−17.6581	−	6.42703i	−1.61872	−	0.589165i
$120$		0			0
$121$	−0.196433	+	0.340233i	−0.0178576	+	0.0309302i
$122$	2.56095	−	3.06227i	0.231857	−	0.277245i
$123$		0			0
$124$	15.2128	−	8.85018i	1.36615	−	0.794770i
$125$	6.90892	−	3.98887i	0.617953	−	0.356775i
$126$		0			0
$127$	−4.91926	+	5.86255i	−0.436514	+	0.520217i	−0.938790	−	0.344490i	$-0.888052\pi$
$127$	−4.91926	+	5.86255i	−0.436514	+	0.520217i	0.502276	+	0.864707i	$0.332496\pi$
$128$	9.73196	−	5.76966i	0.860192	−	0.509971i
$129$		0			0
$130$	−1.31365	+	2.28400i	−0.115214	+	0.200320i
$131$	−1.44419	−	8.19039i	−0.126179	−	0.715598i	−0.980600	−	0.196017i	$-0.937199\pi$
$131$	−1.44419	−	8.19039i	−0.126179	−	0.715598i	0.854421	−	0.519581i	$-0.173912\pi$
$132$		0			0
$133$	6.77546	−	7.95085i	0.587507	−	0.689426i
$134$	−16.0143	+	5.85869i	−1.38343	+	0.506114i
$135$		0			0
$136$	−3.95926	−	21.8218i	−0.339504	−	1.87120i
$137$	−2.75030	−	7.55638i	−0.234974	−	0.645585i	−0.999999	−	0.00158449i	$-0.999496\pi$
$137$	−2.75030	−	7.55638i	−0.234974	−	0.645585i	0.765025	−	0.644001i	$-0.222727\pi$
$138$		0			0
$139$	5.11738	−	6.09866i	0.434051	−	0.517282i	−0.504036	−	0.863683i	$-0.668152\pi$
$139$	5.11738	−	6.09866i	0.434051	−	0.517282i	0.938086	+	0.346401i	$0.112596\pi$
$140$	−0.730678	−	4.06537i	−0.0617536	−	0.343587i
$141$		0			0
$142$	−14.5500	+	2.59032i	−1.22101	+	0.217375i
$143$	−1.26716	+	7.18641i	−0.105965	+	0.600958i
$144$		0			0
$145$	1.94807	−	3.37416i	0.161779	−	0.280209i
$146$	3.32347	−	9.17826i	0.275052	−	0.759598i
$147$		0			0
$148$	−7.29585	+	12.7337i	−0.599715	+	1.04670i
$149$	1.57760	+	1.88011i	0.129242	+	0.154025i	0.826785	−	0.562519i	$-0.190168\pi$
$149$	1.57760	+	1.88011i	0.129242	+	0.154025i	−0.697542	+	0.716543i	$0.745723\pi$
$150$		0			0
$151$		−	1.55905i		−	0.126874i	−0.997986	−	0.0634370i	$-0.979794\pi$
$151$		−	1.55905i		−	0.126874i	0.997986	−	0.0634370i	$-0.0202062\pi$
$152$	12.1358	+	2.17328i	0.984341	+	0.176276i
$153$		0			0
$154$	−5.73616	−	9.89757i	−0.462233	−	0.797569i
$155$	5.80933	−	4.87461i	0.466617	−	0.391538i
$156$		0			0
$157$	−11.7845	−	4.28921i	−0.940506	−	0.342316i	−0.174140	−	0.984721i	$-0.555715\pi$
$157$	−11.7845	−	4.28921i	−0.940506	−	0.342316i	−0.766366	+	0.642405i	$0.777937\pi$
$158$	−8.15664	−	2.95354i	−0.648907	−	0.234971i
$159$		0			0
$160$	3.70843	−	3.16425i	0.293177	−	0.250156i
$161$	7.04647	+	1.24248i	0.555340	+	0.0979214i
$162$		0			0
$163$	10.5297	−	6.07933i	0.824750	−	0.476170i	−0.0273018	−	0.999627i	$-0.508692\pi$
$163$	10.5297	−	6.07933i	0.824750	−	0.476170i	0.852052	+	0.523458i	$0.175358\pi$
$164$	13.7044	−	2.46311i	1.07013	−	0.192337i
$165$		0			0
$166$	0.0354191	+	21.4627i	0.00274905	+	1.66582i
$167$	−9.20385	+	3.34993i	−0.712215	+	0.259225i	−0.672617	−	0.739991i	$-0.734830\pi$
$167$	−9.20385	+	3.34993i	−0.712215	+	0.259225i	−0.0395978	+	0.999216i	$0.512608\pi$
$168$		0			0
$169$	−1.44580	−	8.19952i	−0.111215	−	0.630732i
$170$	−3.28323	−	8.97450i	−0.251812	−	0.688313i
$171$		0			0
$172$	6.10079	+	7.22209i	0.465181	+	0.550679i
$173$	14.7175	−	2.59509i	1.11895	−	0.197301i	0.416571	−	0.909103i	$-0.363232\pi$
$173$	14.7175	−	2.59509i	1.11895	−	0.197301i	0.702380	+	0.711802i	$0.252121\pi$
$174$		0			0
$175$	3.48957	+	9.58751i	0.263787	+	0.724748i
$176$	6.67333	−	11.7368i	0.503022	−	0.884695i
$177$		0			0
$178$	1.13104	−	6.47695i	0.0847753	−	0.485468i
$179$	4.64063	+	8.03781i	0.346857	+	0.600774i	0.985689	−	0.168572i	$-0.0539155\pi$
$179$	4.64063	+	8.03781i	0.346857	+	0.600774i	−0.638832	+	0.769346i	$0.720582\pi$
$180$		0			0
$181$	4.37903	−	24.8347i	0.325491	−	1.84595i	−0.180712	−	0.983536i	$-0.557840\pi$
$181$	4.37903	−	24.8347i	0.325491	−	1.84595i	0.506203	−	0.862414i	$-0.331049\pi$
$182$	−5.62075	−	4.70058i	−0.416638	−	0.348430i
$183$		0			0
$184$	2.92751	+	7.92102i	0.215819	+	0.583946i
$185$	−2.16278	+	5.94219i	−0.159011	+	0.436879i
$186$		0			0
$187$	−17.0123	−	20.2744i	−1.24406	−	1.48261i
$188$	−13.2202	−	11.0190i	−0.964186	−	0.803640i
$189$		0			0
$190$	5.31223	+	0.0317121i	0.385390	+	0.00230064i
$191$	−24.9747			−1.80710			−0.903551	−	0.428480i	$-0.859049\pi$
$191$	−24.9747			−1.80710			−0.903551	+	0.428480i	$0.859049\pi$
$192$		0			0
$193$	−9.61468	+	8.06768i	−0.692080	+	0.580724i	−0.919508	−	0.393071i	$-0.871413\pi$
$193$	−9.61468	+	8.06768i	−0.692080	+	0.580724i	0.227428	+	0.973795i	$0.426968\pi$
$194$	−0.616532	−	0.732296i	−0.0442644	−	0.0525758i
$195$		0			0
$196$	−2.51337	+	0.00829549i	−0.179527	+	0.000592535i
$197$	−17.3740	−	10.0309i	−1.23785	−	0.714672i	−0.269195	−	0.963086i	$-0.586757\pi$
$197$	−17.3740	−	10.0309i	−1.23785	−	0.714672i	−0.968654	+	0.248414i	$0.920091\pi$
$198$		0			0
$199$	−18.6219	−	3.28354i	−1.32007	−	0.232764i	−0.531161	−	0.847271i	$-0.678244\pi$
$199$	−18.6219	−	3.28354i	−1.32007	−	0.232764i	−0.788911	+	0.614507i	$0.789355\pi$
$200$	−7.69443	+	9.26260i	−0.544078	+	0.654965i
$201$		0			0
$202$	−0.557378	+	3.19184i	−0.0392170	+	0.224577i
$203$	8.29999	+	6.96451i	0.582545	+	0.488813i
$204$		0			0
$205$	5.63782	−	2.05200i	0.393762	−	0.143318i
$206$	12.6473	−	21.9894i	0.881177	−	1.53208i
$207$		0			0
$208$	1.44542	−	8.52611i	0.100222	−	0.591179i
$209$	13.8634	−	4.92656i	0.958951	−	0.340777i
$210$		0			0
$211$	−15.5643	+	2.74440i	−1.07149	+	0.188933i	−0.681450	−	0.731865i	$-0.738650\pi$
$211$	−15.5643	+	2.74440i	−1.07149	+	0.188933i	−0.390041	+	0.920798i	$0.627539\pi$
$212$	0.352415	+	0.0609417i	0.0242040	+	0.00418549i
$213$		0			0
$214$	−0.00617611	−	3.74250i	−0.000422190	−	0.255832i
$215$	3.12056	+	2.61846i	0.212821	+	0.178578i
$216$		0			0
$217$	10.5446	+	18.2638i	0.715814	+	1.23983i
$218$	−6.01627	+	1.07107i	−0.407473	+	0.0725420i
$219$		0			0
$220$	1.97166	−	5.47324i	0.132929	−	0.369006i
$221$	−14.6809	−	8.47602i	−0.987544	−	0.570159i
$222$		0			0
$223$	0.278472	−	0.765095i	0.0186479	−	0.0512346i	−0.930019	−	0.367510i	$-0.880210\pi$
$223$	0.278472	−	0.765095i	0.0186479	−	0.0512346i	0.948667	+	0.316276i	$0.102432\pi$
$224$	6.87502	+	11.6842i	0.459357	+	0.780682i
$225$		0			0
$226$	9.31308	+	16.0694i	0.619497	+	1.06892i
$227$	−4.39878			−0.291958			−0.145979	−	0.989288i	$-0.546633\pi$
$227$	−4.39878			−0.291958			−0.145979	+	0.989288i	$0.546633\pi$
$228$		0			0
$229$	4.48158			0.296151			0.148076	−	0.988976i	$-0.452692\pi$
$229$	4.48158			0.296151			0.148076	+	0.988976i	$0.452692\pi$
$230$	1.82455	+	3.14821i	0.120307	+	0.207587i
$231$		0			0
$232$	−2.15816	+	12.6041i	−0.141690	+	0.827501i
$233$	−5.42325	+	14.9003i	−0.355289	+	0.976148i	0.625354	+	0.780341i	$0.284955\pi$
$233$	−5.42325	+	14.9003i	−0.355289	+	0.976148i	−0.980643	+	0.195807i	$0.937268\pi$
$234$		0			0
$235$	−6.42215	−	3.70783i	−0.418935	−	0.241872i
$236$	8.69249	+	3.13136i	0.565833	+	0.203834i
$237$		0			0
$238$	26.1637	−	4.65789i	1.69594	−	0.301926i
$239$	−8.37012	−	14.4975i	−0.541418	−	0.937764i	−0.998823	−	0.0485054i	$-0.984554\pi$
$239$	−8.37012	−	14.4975i	−0.541418	−	0.937764i	0.457405	−	0.889259i	$-0.348779\pi$
$240$		0			0
$241$	−18.8812	−	15.8432i	−1.21624	−	1.02055i	−0.999013	−	0.0444297i	$-0.985853\pi$
$241$	−18.8812	−	15.8432i	−1.21624	−	1.02055i	−0.217231	−	0.976120i	$-0.569703\pi$
$242$	−0.000916882	−	0.555597i	−5.89394e−5	−	0.0357151i
$243$		0			0
$244$	−0.961978	+	5.56295i	−0.0615844	+	0.356132i
$245$	−1.06653	+	0.188058i	−0.0681382	+	0.0120146i
$246$		0			0
$247$	7.26491	−	6.00224i	0.462255	−	0.381914i
$248$	−12.3381	+	21.6167i	−0.783471	+	1.37266i
$249$		0			0
$250$	−5.62498	+	9.77998i	−0.355755	+	0.618541i
$251$	15.4669	−	5.62948i	0.976261	−	0.355330i	0.195875	−	0.980629i	$-0.437245\pi$
$251$	15.4669	−	5.62948i	0.976261	−	0.355330i	0.780385	+	0.625299i	$0.215023\pi$
$252$		0			0
$253$	7.71986	+	6.47773i	0.485344	+	0.407252i
$254$	1.86180	−	10.6617i	0.116820	−	0.668972i
$255$		0			0
$256$	−7.81637	+	13.9608i	−0.488523	+	0.872551i
$257$	−8.62199	−	1.52029i	−0.537825	−	0.0948331i	−0.101864	−	0.994798i	$-0.532481\pi$
$257$	−8.62199	−	1.52029i	−0.537825	−	0.0948331i	−0.435962	+	0.899965i	$0.643592\pi$
$258$		0			0
$259$	−15.2293	−	8.79263i	−0.946302	−	0.546348i
$260$	−0.0122984	−	3.72619i	−0.000762716	−	0.231088i
$261$		0			0
$262$	7.57510	+	8.99746i	0.467991	+	0.555865i
$263$	−15.4391	+	12.9549i	−0.952016	+	0.798836i	−0.979636	−	0.200782i	$-0.935652\pi$
$263$	−15.4391	+	12.9549i	−0.952016	+	0.798836i	0.0276198	+	0.999618i	$0.491207\pi$
$264$		0			0
$265$	0.154105			0.00946657
$266$	−2.65213	+	14.5331i	−0.162613	+	0.891083i
$267$		0			0
$268$	15.4402	−	18.5247i	0.943161	−	1.13158i
$269$	−4.82085	−	5.74526i	−0.293932	−	0.350295i	0.598787	−	0.800908i	$-0.295650\pi$
$269$	−4.82085	−	5.74526i	−0.293932	−	0.350295i	−0.892719	+	0.450614i	$0.851205\pi$
$270$		0			0
$271$	−0.169153	+	0.464745i	−0.0102753	+	0.0282313i	−0.944724	−	0.327866i	$-0.893671\pi$
$271$	−0.169153	+	0.464745i	−0.0102753	+	0.0282313i	0.934449	+	0.356097i	$0.115893\pi$
$272$	20.3189	+	23.8930i	1.23201	+	1.44872i
$273$		0			0
$274$	8.72363	+	7.29550i	0.527014	+	0.440737i
$275$	−2.49532	+	14.1516i	−0.150473	+	0.853376i
$276$		0			0
$277$	12.0558	+	20.8812i	0.724361	+	1.25463i	0.959236	+	0.282605i	$0.0911986\pi$
$277$	12.0558	+	20.8812i	0.724361	+	1.25463i	−0.234875	+	0.972026i	$0.575468\pi$
$278$	−1.93678	+	11.0911i	−0.116161	+	0.665197i
$279$		0			0
$280$	3.77690	+	4.45615i	0.225713	+	0.266306i
$281$	3.69312	+	10.1468i	0.220313	+	0.605305i	0.999776	−	0.0211428i	$-0.00673047\pi$
$281$	3.69312	+	10.1468i	0.220313	+	0.605305i	−0.779464	+	0.626448i	$0.784508\pi$
$282$		0			0
$283$	13.1383	−	2.31664i	0.780990	−	0.137710i	0.231082	−	0.972934i	$-0.425774\pi$
$283$	13.1383	−	2.31664i	0.780990	−	0.137710i	0.549909	+	0.835225i	$0.314662\pi$
$284$	15.9662	−	13.4872i	0.947417	−	0.800321i
$285$		0			0
$286$	−3.54561	−	9.69169i	−0.209656	−	0.573082i
$287$	2.89723	+	16.4310i	0.171018	+	0.969893i
$288$		0			0
$289$	41.8005	−	15.2141i	2.45885	−	0.894948i
$290$	0.00909293	+	5.50998i	0.000533955	+	0.323557i
$291$		0			0
$292$	2.44203	+	13.5871i	0.142909	+	0.795122i
$293$	−22.8738	+	13.2062i	−1.33630	+	0.771513i	−0.986257	−	0.165220i	$-0.947167\pi$
$293$	−22.8738	+	13.2062i	−1.33630	+	0.771513i	−0.350043	+	0.936733i	$0.613833\pi$
$294$		0			0
$295$	3.92061	+	0.691310i	0.228267	+	0.0402496i
$296$	−0.102751	−	20.7543i	−0.00597228	−	1.20632i
$297$		0			0
$298$	−3.26355	−	1.18174i	−0.189053	−	0.0684564i
$299$	6.06553	+	2.20767i	0.350779	+	0.127673i
$300$		0			0
$301$	−8.67803	+	7.28173i	−0.500193	+	0.419712i
$302$	1.10557	+	1.90762i	0.0636182	+	0.109771i
$303$		0			0
$304$	−16.3902	+	5.94663i	−0.940041	+	0.341063i
$305$			2.43258i			0.139289i
$306$		0			0
$307$	−11.2323	−	13.3861i	−0.641059	−	0.763985i	0.343478	−	0.939161i	$-0.388395\pi$
$307$	−11.2323	−	13.3861i	−0.641059	−	0.763985i	−0.984537	+	0.175176i	$0.943950\pi$
$308$	14.0373	+	8.04276i	0.799848	+	0.458279i
$309$		0			0
$310$	−3.65144	+	10.0840i	−0.207388	+	0.572733i
$311$	8.24491	−	14.2806i	0.467526	−	0.809779i	−0.531786	−	0.846879i	$-0.678479\pi$
$311$	8.24491	−	14.2806i	0.467526	−	0.809779i	0.999312	+	0.0371003i	$0.0118121\pi$
$312$		0			0
$313$	−0.926830	+	5.25632i	−0.0523875	+	0.297105i	−0.999733	−	0.0231090i	$-0.992644\pi$
$313$	−0.926830	+	5.25632i	−0.0523875	+	0.297105i	0.947345	+	0.320213i	$0.103755\pi$
$314$	17.4608	−	3.10854i	0.985372	−	0.175425i
$315$		0			0
$316$	12.0747	−	2.17021i	0.679255	−	0.122084i
$317$	14.4777	−	17.2539i	0.813149	−	0.969073i	−0.186762	−	0.982405i	$-0.559799\pi$
$317$	14.4777	−	17.2539i	0.813149	−	0.969073i	0.999911	+	0.0133319i	$0.00424380\pi$
$318$		0			0
$319$	5.21928	+	14.3399i	0.292224	+	0.802878i
$320$	−2.29369	+	6.50144i	−0.128221	+	0.363442i
$321$		0			0
$322$	−9.50297	+	3.47657i	−0.529580	+	0.193742i
$323$	−0.260433	+	34.1776i	−0.0144909	+	1.90170i
$324$		0			0
$325$	1.59828	+	9.06430i	0.0886567	+	0.502797i
$326$	−8.57288	+	14.9054i	−0.474808	+	0.825535i
$327$		0			0
$328$	−15.0217	+	12.7319i	−0.829432	+	0.703003i
$329$	13.2558	−	15.7976i	0.730815	−	0.870951i
$330$		0			0
$331$	4.85664	−	2.80398i	0.266945	−	0.154121i	−0.360553	−	0.932739i	$-0.617412\pi$
$331$	4.85664	−	2.80398i	0.266945	−	0.154121i	0.627499	+	0.778618i	$0.284079\pi$
$332$	−15.2631	−	26.2361i	−0.837671	−	1.43989i
$333$		0			0
$334$	8.88608	−	10.6256i	0.486225	−	0.581406i
$335$	5.19556	−	8.99898i	0.283864	−	0.491667i
$336$		0			0
$337$	−23.1701	−	8.43324i	−1.26216	−	0.459388i	−0.377665	−	0.925942i	$-0.623273\pi$
$337$	−23.1701	−	8.43324i	−1.26216	−	0.459388i	−0.884493	+	0.466554i	$0.845495\pi$
$338$	7.58354	+	9.00749i	0.412490	+	0.489943i
$339$		0			0
$340$	10.3813	+	8.65276i	0.563007	+	0.469262i
$341$			29.7027i			1.60849i
$342$		0			0
$343$		−	19.7873i		−	1.06842i
$344$	−12.5862	−	4.51055i	−0.678600	−	0.243192i
$345$		0			0
$346$	−16.1677	+	13.6119i	−0.869183	+	0.731778i
$347$	15.8250	+	5.75983i	0.849531	+	0.309204i	0.729849	−	0.683608i	$-0.239590\pi$
$347$	15.8250	+	5.75983i	0.849531	+	0.309204i	0.119682	+	0.992812i	$0.461813\pi$
$348$		0			0
$349$	−1.63536	+	2.83252i	−0.0875387	+	0.151621i	−0.906470	−	0.422270i	$-0.861233\pi$
$349$	−1.63536	+	2.83252i	−0.0875387	+	0.151621i	0.818932	+	0.573891i	$0.194567\pi$
$350$	−11.0685	−	9.25650i	−0.591637	−	0.494781i
$351$		0			0
$352$	0.157547	+	19.0931i	0.00839728	+	1.01767i
$353$	−9.30139	+	5.37016i	−0.495063	+	0.285825i	−0.726673	−	0.686984i	$-0.758934\pi$
$353$	−9.30139	+	5.37016i	−0.495063	+	0.285825i	0.231609	+	0.972809i	$0.425601\pi$
$354$		0			0
$355$	5.78873	−	6.89874i	0.307234	−	0.366147i
$356$	3.20906	+	8.72710i	0.170080	+	0.462535i
$357$		0			0
$358$	−11.3780	−	6.54408i	−0.601346	−	0.345865i
$359$	1.27735	+	7.24418i	0.0674157	+	0.382333i	0.999783	+	0.0208216i	$0.00662819\pi$
$359$	1.27735	+	7.24418i	0.0674157	+	0.382333i	−0.932368	+	0.361512i	$0.882261\pi$
$360$		0			0
$361$	−17.7531	−	6.76971i	−0.934371	−	0.356300i
$362$	12.2529	+	33.4925i	0.643998	+	1.76032i
$363$		0			0
$364$	10.2107	+	1.76570i	0.535187	+	0.0925477i
$365$	2.03443	+	5.58956i	0.106487	+	0.292571i
$366$		0			0
$367$	−7.86751	+	9.37613i	−0.410680	+	0.489430i	−0.931246	−	0.364392i	$-0.881277\pi$
$367$	−7.86751	+	9.37613i	−0.410680	+	0.489430i	0.520565	+	0.853822i	$0.325721\pi$
$368$	−9.19904	−	7.61600i	−0.479533	−	0.397012i
$369$		0			0
$370$	−1.56744	−	8.80441i	−0.0814874	−	0.457720i
$371$	−0.0744173	+	0.422042i	−0.00386356	+	0.0219113i
$372$		0			0
$373$	−7.64556	+	13.2425i	−0.395872	+	0.685671i	−0.993212	−	0.116317i	$-0.962891\pi$
$373$	−7.64556	+	13.2425i	−0.395872	+	0.685671i	0.597340	+	0.801988i	$0.296224\pi$
$374$	35.1929	+	12.7434i	1.81978	+	0.658948i
$375$		0			0
$376$	23.9898	+	4.10770i	1.23718	+	0.211838i
$377$	6.28281	+	7.48756i	0.323581	+	0.385629i
$378$		0			0
$379$		−	35.8226i		−	1.84008i	−0.391820	−	0.920042i	$-0.628155\pi$
$379$		−	35.8226i		−	1.84008i	0.391820	−	0.920042i	$-0.371845\pi$
$380$	−6.52241	+	3.72824i	−0.334593	+	0.191255i
$381$		0			0
$382$	30.5584	−	17.7102i	1.56350	−	0.906133i
$383$	−25.6781	+	21.5465i	−1.31209	+	1.10097i	−0.324171	+	0.945998i	$0.605085\pi$
$383$	−25.6781	+	21.5465i	−1.31209	+	1.10097i	−0.987918	+	0.154976i	$0.950470\pi$
$384$		0			0
$385$	6.55053	+	2.38420i	0.333846	+	0.121510i
$386$	6.04329	−	16.6894i	0.307595	−	0.849471i
$387$		0			0
$388$	1.27366	+	0.458821i	0.0646605	+	0.0232931i
$389$	−16.6303	−	2.93236i	−0.843187	−	0.148677i	−0.264662	−	0.964341i	$-0.585260\pi$
$389$	−16.6303	−	2.93236i	−0.843187	−	0.148677i	−0.578525	+	0.815665i	$0.696372\pi$
$390$		0			0
$391$	−20.2744	+	11.7054i	−1.02532	+	0.591969i
$392$	3.06942	−	1.79245i	0.155029	−	0.0905324i
$393$		0			0
$394$	28.3716	−	0.0468207i	1.42934	−	0.00235880i
$395$	4.96740	−	1.80799i	0.249937	−	0.0909696i
$396$		0			0
$397$	−6.52241	−	36.9904i	−0.327350	−	1.85650i	−0.492616	−	0.870247i	$-0.663959\pi$
$397$	−6.52241	−	36.9904i	−0.327350	−	1.85650i	0.165266	−	0.986249i	$-0.447152\pi$
$398$	25.1138	−	9.18763i	1.25884	−	0.460534i
$399$		0			0
$400$	2.84635	−	16.7898i	0.142318	−	0.839491i
$401$	30.9269	−	5.45325i	1.54442	−	0.272322i	0.664441	−	0.747341i	$-0.268670\pi$
$401$	30.9269	−	5.45325i	1.54442	−	0.272322i	0.879976	+	0.475018i	$0.157559\pi$
$402$		0			0
$403$	6.50691	+	17.8776i	0.324132	+	0.890546i
$404$	−1.58143	−	4.30071i	−0.0786788	−	0.213968i
$405$		0			0
$406$	−15.0944	−	2.63587i	−0.749122	−	0.130816i
$407$	−12.3838	−	21.4494i	−0.613843	−	1.06321i
$408$		0			0
$409$	−1.46956	+	8.33427i	−0.0726649	+	0.412103i	0.926678	+	0.375856i	$0.122651\pi$
$409$	−1.46956	+	8.33427i	−0.0726649	+	0.412103i	−0.999343	+	0.0362469i	$0.988460\pi$
$410$	−5.44317	+	6.50870i	−0.268819	+	0.321442i
$411$		0			0
$412$	0.118404	+	35.8743i	0.00583337	+	1.76740i
$413$	−3.78654	+	10.4034i	−0.186323	+	0.511919i
$414$		0			0
$415$	−8.40678	−	10.0188i	−0.412672	−	0.491804i
$416$	4.27752	+	11.4573i	0.209722	+	0.561742i
$417$		0			0
$418$	−13.4694	+	15.8589i	−0.658808	+	0.775685i
$419$	−16.7413			−0.817867			−0.408933	−	0.912564i	$-0.634099\pi$
$419$	−16.7413			−0.817867			−0.408933	+	0.912564i	$0.634099\pi$
$420$		0			0
$421$	1.74700	−	1.46590i	0.0851434	−	0.0714438i	−0.599223	−	0.800583i	$-0.704524\pi$
$421$	1.74700	−	1.46590i	0.0851434	−	0.0714438i	0.684366	+	0.729139i	$0.260079\pi$
$422$	17.0980	−	14.3950i	0.832316	−	0.700740i
$423$		0			0
$424$	−0.474422	+	0.175340i	−0.0230400	+	0.00851528i
$425$	−28.9100	−	16.6912i	−1.40234	−	0.809641i
$426$		0			0
$427$	−6.66202	−	1.17469i	−0.322398	−	0.0568475i
$428$	2.66146	+	4.57485i	0.128647	+	0.221134i
$429$		0			0
$430$	−5.67507	−	0.991014i	−0.273676	−	0.0477909i
$431$	6.09376	+	5.11327i	0.293526	+	0.246298i	0.777644	−	0.628705i	$-0.216415\pi$
$431$	6.09376	+	5.11327i	0.293526	+	0.246298i	−0.484118	+	0.875003i	$0.660859\pi$
$432$		0			0
$433$	9.28136	−	3.37814i	0.446034	−	0.162343i	−0.109231	−	0.994016i	$-0.534839\pi$
$433$	9.28136	−	3.37814i	0.446034	−	0.162343i	0.555265	+	0.831673i	$0.312617\pi$
$434$	−25.8535	−	14.8697i	−1.24101	−	0.713767i
$435$		0			0
$436$	6.60184	−	5.57683i	0.316171	−	0.267082i
$437$	−2.16216	−	12.8333i	−0.103430	−	0.613899i
$438$		0			0
$439$	21.4928	−	3.78976i	1.02579	−	0.180875i	0.364658	−	0.931141i	$-0.381186\pi$
$439$	21.4928	−	3.78976i	1.02579	−	0.180875i	0.661136	+	0.750266i	$0.270075\pi$
$440$	1.46874	+	8.09508i	0.0700195	+	0.385918i
$441$		0			0
$442$	23.9738	−	0.0395631i	1.14032	−	0.00188182i
$443$	14.9033	+	12.5054i	0.708078	+	0.594148i	0.924059	−	0.382250i	$-0.124851\pi$
$443$	14.9033	+	12.5054i	0.708078	+	0.594148i	−0.215981	+	0.976397i	$0.569295\pi$
$444$		0			0
$445$	2.00328	+	3.46978i	0.0949645	+	0.164483i
$446$	0.201818	+	1.13362i	0.00955636	+	0.0536787i
$447$		0			0
$448$	−16.6977	−	9.42121i	−0.788891	−	0.445110i
$449$	−15.9971	−	9.23594i	−0.754951	−	0.435871i	0.0725292	−	0.997366i	$-0.476893\pi$
$449$	−15.9971	−	9.23594i	−0.754951	−	0.435871i	−0.827480	+	0.561495i	$0.810226\pi$
$450$		0			0
$451$	−8.03712	+	22.0818i	−0.378453	+	1.03979i
$452$	−22.7905	−	13.0580i	−1.07198	−	0.614197i
$453$		0			0
$454$	5.38225	−	3.11930i	0.252601	−	0.146396i
$455$	4.46496			0.209321
$456$		0			0
$457$	39.9109			1.86695			0.933477	−	0.358637i	$-0.116758\pi$
$457$	39.9109			1.86695			0.933477	+	0.358637i	$0.116758\pi$
$458$	−5.48355	+	3.17801i	−0.256230	+	0.148499i
$459$		0			0
$460$	−4.46496	−	2.55823i	−0.208180	−	0.119278i
$461$	−5.09196	+	13.9900i	−0.237156	+	0.651581i	0.762831	+	0.646598i	$0.223809\pi$
$461$	−5.09196	+	13.9900i	−0.237156	+	0.651581i	−0.999988	+	0.00498392i	$0.998414\pi$
$462$		0			0
$463$	11.1531	+	6.43926i	0.518329	+	0.299258i	0.736251	−	0.676709i	$-0.236594\pi$
$463$	11.1531	+	6.43926i	0.518329	+	0.299258i	−0.217922	+	0.975966i	$0.569928\pi$
$464$	−6.29724	−	16.9525i	−0.292342	−	0.787000i
$465$		0			0
$466$	−3.93041	−	22.0774i	−0.182073	−	1.02271i
$467$	7.54976	+	13.0766i	0.349361	+	0.605111i	0.986136	−	0.165938i	$-0.0530653\pi$
$467$	7.54976	+	13.0766i	0.349361	+	0.605111i	−0.636775	+	0.771050i	$0.719732\pi$
$468$		0			0
$469$	22.1363	+	18.5745i	1.02216	+	0.857693i
$470$	10.4873	−	0.0173069i	0.483744	−	0.000798306i
$471$		0			0
$472$	−12.8565	+	2.33263i	−0.591766	+	0.107368i
$473$	−15.7128	+	2.77059i	−0.722476	+	0.127392i
$474$		0			0
$475$	14.3062	−	11.8198i	0.656415	−	0.542328i
$476$	−28.7102	+	24.2526i	−1.31593	+	1.11162i
$477$		0			0
$478$	20.5220	+	11.8033i	0.938656	+	0.539870i
$479$	−6.31766	+	2.29944i	−0.288661	+	0.105064i	−0.482292	−	0.876010i	$-0.660196\pi$
$479$	−6.31766	+	2.29944i	−0.288661	+	0.105064i	0.193631	+	0.981074i	$0.437974\pi$
$480$		0			0
$481$	−12.1525	−	10.1972i	−0.554106	−	0.464950i
$482$	34.3374	+	5.99620i	1.56403	+	0.273119i
$483$		0			0
$484$	0.395111	+	0.679165i	0.0179596	+	0.0308711i
$485$	0.574466	+	0.101294i	0.0260852	+	0.00459952i
$486$		0			0
$487$	−7.89672	−	4.55917i	−0.357834	−	0.206596i	0.310296	−	0.950640i	$-0.399572\pi$
$487$	−7.89672	−	4.55917i	−0.357834	−	0.206596i	−0.668130	+	0.744044i	$0.732905\pi$
$488$	−2.76779	−	7.48886i	−0.125292	−	0.339005i
$489$		0			0
$490$	1.17163	−	0.986410i	0.0529286	−	0.0445615i
$491$	28.3728	−	23.8076i	1.28045	−	1.07442i	0.287264	−	0.957851i	$-0.407254\pi$
$491$	28.3728	−	23.8076i	1.28045	−	1.07442i	0.993182	−	0.116571i	$-0.0371903\pi$
$492$		0			0
$493$	−35.4503			−1.59660
$494$	−4.63281	+	12.4959i	−0.208440	+	0.562219i
$495$		0			0
$496$	−0.232354	−	35.1989i	−0.0104330	−	1.58048i
$497$	16.0980	+	19.1848i	0.722093	+	0.860558i
$498$		0			0
$499$	7.82010	−	21.4856i	0.350076	−	0.961825i	−0.632269	−	0.774749i	$-0.717876\pi$
$499$	7.82010	−	21.4856i	0.350076	−	0.961825i	0.982345	−	0.187077i	$-0.0599013\pi$
$500$	−0.0526614	−	15.9554i	−0.00235509	−	0.713546i
$501$		0			0
$502$	−14.9329	+	17.8561i	−0.666487	+	0.796956i
$503$	−3.18840	+	18.0823i	−0.142164	+	0.806250i	0.827437	+	0.561558i	$0.189798\pi$
$503$	−3.18840	+	18.0823i	−0.142164	+	0.806250i	−0.969601	+	0.244692i	$0.921313\pi$
$504$		0			0
$505$	−0.987215	−	1.70991i	−0.0439305	−	0.0760899i
$506$	−14.0394	−	2.45164i	−0.624126	−	0.108989i
$507$		0			0
$508$	5.28241	+	14.3656i	0.234369	+	0.637371i
$509$	−1.37680	−	3.78273i	−0.0610256	−	0.167666i	0.905433	−	0.424490i	$-0.139546\pi$
$509$	−1.37680	−	3.78273i	−0.0610256	−	0.167666i	−0.966458	+	0.256823i	$0.917324\pi$
$510$		0			0
$511$	−16.2904	+	2.87244i	−0.720645	+	0.127069i
$512$	−0.336059	−	22.6249i	−0.0148518	−	0.999890i
$513$		0			0
$514$	11.6277	−	4.25390i	0.512878	−	0.187631i
$515$	2.68422	+	15.2230i	0.118281	+	0.670805i
$516$		0			0
$517$	27.2935	−	9.93402i	1.20037	−	0.436898i
$518$	24.8693	−	0.0410409i	1.09269	−	0.00180324i
$519$		0			0
$520$	2.65739	+	4.55055i	0.116534	+	0.199555i
$521$	−0.605646	+	0.349670i	−0.0265338	+	0.0153193i	−0.513208	−	0.858264i	$-0.671543\pi$
$521$	−0.605646	+	0.349670i	−0.0265338	+	0.0153193i	0.486674	+	0.873583i	$0.338210\pi$
$522$		0			0
$523$	26.9707	+	4.75567i	1.17935	+	0.207951i	0.728753	−	0.684777i	$-0.240100\pi$
$523$	26.9707	+	4.75567i	1.17935	+	0.207951i	0.450596	+	0.892728i	$0.351212\pi$
$524$	−15.6491	−	5.63737i	−0.683632	−	0.246270i
$525$		0			0
$526$	9.70422	−	26.7997i	0.423124	−	1.16852i
$527$	−64.8400	−	23.5998i	−2.82447	−	1.02802i
$528$		0			0
$529$	−10.7904	+	9.05423i	−0.469148	+	0.393662i
$530$	−0.188559	+	0.109280i	−0.00819047	+	0.00474681i
$531$		0			0
$532$	−7.06075	−	19.6631i	−0.306122	−	0.852503i
$533$			15.0514i			0.651947i
$534$		0			0
$535$	1.46591	+	1.74700i	0.0633768	+	0.0755296i
$536$	−5.75587	+	33.6155i	−0.248616	+	1.45197i
$537$		0			0
$538$	9.97280	+	3.61117i	0.429958	+	0.155689i
$539$	2.12088	−	3.67347i	0.0913527	−	0.158227i
$540$		0			0
$541$	−6.20240	+	35.1756i	−0.266662	+	1.51232i	0.497598	+	0.867408i	$0.334215\pi$
$541$	−6.20240	+	35.1756i	−0.266662	+	1.51232i	−0.764260	+	0.644908i	$0.776896\pi$
$542$	−0.122591	−	0.688602i	−0.00526574	−	0.0295780i
$543$		0			0
$544$	−41.8048	−	14.8262i	−1.79237	−	0.635669i
$545$	2.39358	−	2.85256i	0.102530	−	0.122190i
$546$		0			0
$547$	−7.02410	−	19.2985i	−0.300329	−	0.825146i	−0.994443	−	0.105281i	$-0.966426\pi$
$547$	−7.02410	−	19.2985i	−0.300329	−	0.825146i	0.694114	−	0.719865i	$-0.255796\pi$
$548$	−15.8475	−	2.74044i	−0.676970	−	0.117066i
$549$		0			0
$550$	−6.98210	−	19.0851i	−0.297718	−	0.813792i
$551$	6.88108	−	18.4666i	0.293144	−	0.786702i
$552$		0			0
$553$	2.55271	+	14.4771i	0.108552	+	0.615630i
$554$	−29.5586	−	17.0007i	−1.25582	−	0.722290i
$555$		0			0
$556$	−5.49516	−	14.9442i	−0.233047	−	0.633774i
$557$	6.07847	−	7.24404i	0.257553	−	0.306940i	−0.621737	−	0.783226i	$-0.713573\pi$
$557$	6.07847	−	7.24404i	0.257553	−	0.306940i	0.879290	+	0.476286i	$0.158017\pi$
$558$		0			0
$559$	−8.85035	+	5.10975i	−0.374330	+	0.216119i
$560$	−7.78131	−	2.77413i	−0.328820	−	0.117229i
$561$		0			0
$562$	−11.7141	−	9.79644i	−0.494132	−	0.413238i
$563$	13.3746	−	23.1654i	0.563671	−	0.976306i	−0.433501	−	0.901153i	$-0.642722\pi$
$563$	13.3746	−	23.1654i	0.563671	−	0.976306i	0.997172	−	0.0751534i	$-0.0239446\pi$
$564$		0			0
$565$	−10.6353	−	3.87092i	−0.447429	−	0.162851i
$566$	−14.4329	+	12.1513i	−0.606661	+	0.510757i
$567$		0			0
$568$	−9.97164	+	27.8247i	−0.418401	+	1.16750i
$569$		−	30.3341i		−	1.27167i	−0.771825	−	0.635835i	$-0.780656\pi$
$569$		−	30.3341i		−	1.27167i	0.771825	−	0.635835i	$-0.219344\pi$
$570$		0			0
$571$			36.5696i			1.53039i	0.643799	+	0.765195i	$0.277357\pi$
$571$			36.5696i			1.53039i	−0.643799	+	0.765195i	$0.722643\pi$
$572$	11.2110	+	9.34424i	0.468754	+	0.390702i
$573$		0			0
$574$	−15.1967	−	18.0501i	−0.634297	−	0.753397i
$575$	11.9444	+	4.34740i	0.498115	+	0.181299i
$576$		0			0
$577$	5.56387	−	9.63690i	0.231627	−	0.401189i	−0.726660	−	0.686997i	$-0.758929\pi$
$577$	5.56387	−	9.63690i	0.231627	−	0.401189i	0.958287	+	0.285808i	$0.0922618\pi$
$578$	−40.3573	+	48.2575i	−1.67864	+	2.00725i
$579$		0			0
$580$	−3.91840	−	6.73543i	−0.162703	−	0.279673i
$581$	31.4978	−	18.1853i	1.30675	−	0.754453i
$582$		0			0
$583$	−0.387978	+	0.462374i	−0.0160684	+	0.0191496i
$584$	−12.6230	−	14.8931i	−0.522342	−	0.616281i
$585$		0			0
$586$	18.6229	−	32.3792i	0.769307	−	1.33757i
$587$	−5.71714	−	32.4235i	−0.235971	−	1.33826i	−0.840558	−	0.541721i	$-0.817773\pi$
$587$	−5.71714	−	32.4235i	−0.235971	−	1.33826i	0.604587	−	0.796539i	$-0.293338\pi$
$588$		0			0
$589$	24.8792	−	29.1952i	1.02513	−	1.20297i
$590$	−5.28739	+	1.93434i	−0.217679	+	0.0796356i
$591$		0			0
$592$	14.8431	+	25.3216i	0.610049	+	1.04071i
$593$	−12.0571	−	33.1267i	−0.495126	−	1.36035i	−0.895934	−	0.444187i	$-0.853493\pi$
$593$	−12.0571	−	33.1267i	−0.495126	−	1.36035i	0.400808	−	0.916162i	$-0.368729\pi$
$594$		0			0
$595$	−10.4092	+	12.4053i	−0.426738	+	0.508566i
$596$	4.83121	−	0.868324i	0.197894	−	0.0355679i
$597$		0			0
$598$	−8.98716	+	1.59998i	−0.367512	+	0.0654279i
$599$	5.37209	−	30.4666i	0.219498	−	1.24483i	−0.653432	−	0.756985i	$-0.726671\pi$
$599$	5.37209	−	30.4666i	0.219498	−	1.24483i	0.872929	−	0.487847i	$-0.162218\pi$
$600$		0			0
$601$	15.3151	−	26.5266i	0.624717	−	1.08204i	−0.363879	−	0.931446i	$-0.618548\pi$
$601$	15.3151	−	26.5266i	0.624717	−	1.08204i	0.988596	−	0.150595i	$-0.0481189\pi$
$602$	5.45456	−	15.0636i	0.222311	−	0.613945i
$603$		0			0
$604$	−2.70549	−	1.55013i	−0.110085	−	0.0630740i
$605$	0.217623	+	0.259354i	0.00884765	+	0.0105442i
$606$		0			0
$607$			19.0703i			0.774038i	0.922072	+	0.387019i	$0.126495\pi$
$607$			19.0703i			0.774038i	−0.922072	+	0.387019i	$0.873505\pi$
$608$	15.8377	−	18.8989i	0.642304	−	0.766450i
$609$		0			0
$610$	−1.72501	−	2.97644i	−0.0698435	−	0.120513i
$611$	14.2513	−	11.9583i	0.576546	−	0.483780i
$612$		0			0
$613$	−36.7090	−	13.3610i	−1.48266	−	0.539645i	−0.531156	−	0.847274i	$-0.678242\pi$
$613$	−36.7090	−	13.3610i	−1.48266	−	0.539645i	−0.951506	+	0.307629i	$0.900464\pi$
$614$	23.2360	+	8.41380i	0.937727	+	0.339553i
$615$		0			0
$616$	−22.8790	+	0.113270i	−0.921822	+	0.00456378i
$617$	13.9514	+	2.46001i	0.561662	+	0.0990362i	0.447269	−	0.894399i	$-0.352397\pi$
$617$	13.9514	+	2.46001i	0.561662	+	0.0990362i	0.114393	+	0.993436i	$0.463508\pi$
$618$		0			0
$619$	−9.86407	+	5.69503i	−0.396471	+	0.228902i	−0.684960	−	0.728581i	$-0.740180\pi$
$619$	−9.86407	+	5.69503i	−0.396471	+	0.228902i	0.288489	+	0.957483i	$0.406847\pi$
$620$	−2.68302	−	14.9279i	−0.107753	−	0.599518i
$621$		0			0
$622$	0.0384844	+	23.3201i	0.00154308	+	0.935051i
$623$	−10.4700	+	3.81076i	−0.419470	+	0.152675i
$624$		0			0
$625$	2.50257	+	14.1928i	0.100103	+	0.567712i
$626$	−2.59335	−	7.08874i	−0.103651	−	0.283323i
$627$		0			0
$628$	−19.1603	+	16.1855i	−0.764580	+	0.645871i
$629$	56.6627	−	9.99116i	2.25929	−	0.398374i
$630$		0			0
$631$	14.5251	+	39.9073i	0.578234	+	1.58869i	0.791155	+	0.611616i	$0.209480\pi$
$631$	14.5251	+	39.9073i	0.578234	+	1.58869i	−0.212920	+	0.977070i	$0.568297\pi$
$632$	−13.2354	+	11.2179i	−0.526475	+	0.446225i
$633$		0			0
$634$	−5.47940	+	31.3779i	−0.217615	+	1.24618i
$635$	3.29758	+	5.71158i	0.130861	+	0.226657i
$636$		0			0
$637$	0.471784	−	2.67562i	0.0186928	−	0.106012i
$638$	−16.5550	−	13.8448i	−0.655417	−	0.548120i
$639$		0			0
$640$	−1.80385	−	9.58153i	−0.0713033	−	0.378743i
$641$	−8.79213	+	24.1562i	−0.347268	+	0.954111i	0.635959	+	0.771723i	$0.280605\pi$
$641$	−8.79213	+	24.1562i	−0.347268	+	0.954111i	−0.983227	+	0.182388i	$0.941617\pi$
$642$		0			0
$643$	11.1027	+	13.2317i	0.437847	+	0.521806i	0.939169	−	0.343455i	$-0.111597\pi$
$643$	11.1027	+	13.2317i	0.437847	+	0.521806i	−0.501322	+	0.865261i	$0.667153\pi$
$644$	9.16228	−	10.9927i	0.361044	−	0.433172i
$645$		0			0
$646$	−23.9176	−	42.0036i	−0.941027	−	1.65261i
$647$	−2.56660			−0.100904			−0.0504518	−	0.998726i	$-0.516066\pi$
$647$	−2.56660			−0.100904			−0.0504518	+	0.998726i	$0.516066\pi$
$648$		0			0
$649$	−11.9448	+	10.0229i	−0.468875	+	0.393433i
$650$	−8.38336	−	9.95748i	−0.328822	−	0.390564i
$651$		0			0
$652$	−0.0802598	−	24.3172i	−0.00314322	−	0.952334i
$653$	−1.23323	−	0.712004i	−0.0482599	−	0.0278629i	0.475676	−	0.879621i	$-0.342204\pi$
$653$	−1.23323	−	0.712004i	−0.0482599	−	0.0278629i	−0.523936	+	0.851758i	$0.675537\pi$
$654$		0			0
$655$	−7.05826	−	1.24456i	−0.275789	−	0.0486290i
$656$	9.35159	−	26.2308i	0.365118	−	1.02414i
$657$		0			0
$658$	−5.01694	+	28.7296i	−0.195581	+	1.12000i
$659$	−5.23948	−	4.39644i	−0.204101	−	0.171261i	0.535008	−	0.844847i	$-0.320309\pi$
$659$	−5.23948	−	4.39644i	−0.204101	−	0.171261i	−0.739109	+	0.673586i	$0.764753\pi$
$660$		0			0
$661$	6.12000	−	2.22750i	0.238040	−	0.0866396i	−0.220246	−	0.975444i	$-0.570686\pi$
$661$	6.12000	−	2.22750i	0.238040	−	0.0866396i	0.458286	+	0.888805i	$0.348464\pi$
$662$	−3.95409	+	6.87486i	−0.153680	+	0.267199i
$663$		0			0
$664$	37.2803	+	21.2784i	1.44675	+	0.825761i
$665$	−4.44159	−	7.83024i	−0.172237	−	0.303644i
$666$		0			0
$667$	13.2933	−	2.34397i	0.514719	−	0.0907588i
$668$	−3.33791	+	19.3026i	−0.129148	+	0.746839i
$669$		0			0
$670$	0.0242511	+	14.6953i	0.000936901	+	0.567727i
$671$	−7.29868	−	6.12432i	−0.281762	−	0.236427i
$672$		0			0
$673$	6.77884	+	11.7413i	0.261305	+	0.452594i	0.966589	−	0.256331i	$-0.0825138\pi$
$673$	6.77884	+	11.7413i	0.261305	+	0.452594i	−0.705284	+	0.708925i	$0.749180\pi$
$674$	34.3307	−	6.11186i	1.32237	−	0.235420i
$675$		0			0
$676$	−15.6665	−	5.64365i	−0.602558	−	0.217063i
$677$	12.1931	+	7.03971i	0.468620	+	0.270558i	0.715662	−	0.698447i	$-0.246125\pi$
$677$	12.1931	+	7.03971i	0.468620	+	0.270558i	−0.247042	+	0.969005i	$0.579458\pi$
$678$		0			0
$679$	−0.554821	+	1.52436i	−0.0212921	+	0.0584995i
$680$	−18.8383	−	3.22561i	−0.722415	−	0.123697i
$681$		0			0
$682$	−21.0630	−	36.3435i	−0.806543	−	1.39166i
$683$	43.9380			1.68124			0.840621	−	0.541624i	$-0.182190\pi$
$683$	43.9380			1.68124			0.840621	+	0.541624i	$0.182190\pi$
$684$		0			0
$685$	−6.92980			−0.264774
$686$	14.0317	+	24.2113i	0.535734	+	0.924392i
$687$		0			0
$688$	18.5987	−	3.40619i	0.709068	−	0.129860i
$689$	−0.132226	+	0.363289i	−0.00503743	+	0.0138402i
$690$		0			0
$691$	6.64458	+	3.83625i	0.252772	+	0.145938i	0.621033	−	0.783785i	$-0.286713\pi$
$691$	6.64458	+	3.83625i	0.252772	+	0.145938i	−0.368261	+	0.929722i	$0.620047\pi$
$692$	10.1299	−	28.1201i	0.385081	−	1.06897i
$693$		0			0
$694$	−23.4475	+	4.17434i	−0.890057	+	0.158456i
$695$	−3.43039	−	5.94161i	−0.130122	−	0.225378i
$696$		0			0
$697$	−41.8181	−	35.0895i	−1.58397	−	1.32911i
$698$	−0.00763327	−	4.62548i	−0.000288924	−	0.175077i
$699$		0			0
$700$	20.1072	+	3.47706i	0.759981	+	0.131420i
$701$	−9.62261	+	1.69673i	−0.363441	+	0.0640845i	−0.352387	−	0.935854i	$-0.614630\pi$
$701$	−9.62261	+	1.69673i	−0.363441	+	0.0640845i	−0.0110543	+	0.999939i	$0.503519\pi$
$702$		0			0
$703$	−5.79397	+	31.4557i	−0.218524	+	1.18638i
$704$	−13.7322	−	23.2502i	−0.517552	−	0.876273i
$705$		0			0
$706$	7.57284	−	13.1667i	0.285008	−	0.495534i
$707$	5.15960	−	1.87794i	0.194047	−	0.0706272i
$708$		0			0
$709$	−15.8648	−	13.3121i	−0.595814	−	0.499947i	0.294283	−	0.955718i	$-0.404919\pi$
$709$	−15.8648	−	13.3121i	−0.595814	−	0.499947i	−0.890097	+	0.455771i	$0.849364\pi$
$710$	−2.19087	+	12.5461i	−0.0822220	+	0.470846i
$711$		0			0
$712$	−10.1152	−	8.40264i	−0.379081	−	0.314902i
$713$	25.8744	+	4.56235i	0.969002	+	0.170861i
$714$		0			0
$715$	5.44608	+	3.14430i	0.203672	+	0.117590i
$716$	18.5624	−	0.0612660i	0.693710	−	0.00228962i
$717$		0			0
$718$	−6.69998	−	7.95801i	−0.250041	−	0.296990i
$719$	−15.4370	+	12.9532i	−0.575704	+	0.483073i	−0.883533	−	0.468368i	$-0.844842\pi$
$719$	−15.4370	+	12.9532i	−0.575704	+	0.483073i	0.307829	+	0.951442i	$0.400398\pi$
$720$		0			0
$721$	−42.9869			−1.60092
$722$	26.5228	−	4.30592i	0.987077	−	0.160250i
$723$		0			0
$724$	−38.7428	−	32.2917i	−1.43986	−	1.20011i
$725$	12.3723	+	14.7447i	0.459494	+	0.547604i
$726$		0			0
$727$	18.3825	−	50.5056i	0.681771	−	1.87315i	0.264398	−	0.964414i	$-0.414827\pi$
$727$	18.3825	−	50.5056i	0.681771	−	1.87315i	0.417372	−	0.908735i	$-0.362951\pi$
$728$	−13.7457	+	5.08023i	−0.509450	+	0.188286i
$729$		0			0
$730$	−6.45300	−	5.39659i	−0.238836	−	0.199737i
$731$	6.43627	−	36.5019i	0.238054	−	1.35007i
$732$		0			0
$733$	11.0451	+	19.1307i	0.407961	+	0.706609i	0.994661	−	0.103195i	$-0.0329067\pi$
$733$	11.0451	+	19.1307i	0.407961	+	0.706609i	−0.586700	+	0.809804i	$0.699573\pi$
$734$	2.97763	−	17.0515i	0.109906	−	0.629381i
$735$		0			0
$736$	16.6564	+	2.79547i	0.613965	+	0.103042i
$737$	13.9200	+	38.2448i	0.512748	+	1.40876i
$738$		0			0
$739$	44.9753	−	7.93037i	1.65444	−	0.291723i	0.732999	−	0.680230i	$-0.238120\pi$
$739$	44.9753	−	7.93037i	1.65444	−	0.291723i	0.921446	+	0.388506i	$0.127009\pi$
$740$	8.16133	+	9.66136i	0.300016	+	0.355158i
$741$		0			0
$742$	−0.208226	−	0.569171i	−0.00764421	−	0.0208949i
$743$	1.88482	+	10.6893i	0.0691474	+	0.392154i	0.999664	+	0.0259055i	$0.00824691\pi$
$743$	1.88482	+	10.6893i	0.0691474	+	0.392154i	−0.930517	+	0.366249i	$0.880642\pi$
$744$		0			0
$745$	1.98751	−	0.723393i	0.0728166	−	0.0265031i
$746$	−0.0356868	−	21.6249i	−0.00130659	−	0.791743i
$747$		0			0
$748$	−52.0980	+	9.36368i	−1.90489	+	0.342370i
$749$	−5.49236	+	3.17101i	−0.200686	+	0.115866i
$750$		0			0
$751$	−1.46846	−	0.258930i	−0.0535849	−	0.00944847i	0.146791	−	0.989167i	$-0.453105\pi$
$751$	−1.46846	−	0.258930i	−0.0535849	−	0.00944847i	−0.200376	+	0.979719i	$0.564216\pi$
$752$	−32.2663	+	11.9857i	−1.17663	+	0.437075i
$753$		0			0
$754$	−12.9971	−	4.70629i	−0.473327	−	0.171393i
$755$	−1.26252	−	0.459521i	−0.0459480	−	0.0167237i
$756$		0			0
$757$	−39.1287	+	32.8329i	−1.42216	+	1.19333i	−0.471984	+	0.881607i	$0.656462\pi$
$757$	−39.1287	+	32.8329i	−1.42216	+	1.19333i	−0.950173	+	0.311724i	$0.899094\pi$
$758$	25.4028	+	43.8317i	0.922670	+	1.59204i
$759$		0			0
$760$	5.33687	−	9.18701i	0.193588	−	0.333248i
$761$			21.3388i			0.773530i	0.922178	+	0.386765i	$0.126408\pi$
$761$			21.3388i			0.773530i	−0.922178	+	0.386765i	$0.873592\pi$
$762$		0			0
$763$	6.65635	+	7.93273i	0.240976	+	0.287184i
$764$	−24.8318	+	43.3396i	−0.898381	+	1.56797i
$765$		0			0
$766$	16.1399	−	44.5728i	0.583159	−	1.61048i
$767$	−4.99371	+	8.64936i	−0.180312	+	0.312310i
$768$		0			0
$769$	−8.44886	+	47.9159i	−0.304674	+	1.72789i	0.320362	+	0.947295i	$0.396195\pi$
$769$	−8.44886	+	47.9159i	−0.304674	+	1.72789i	−0.625036	+	0.780596i	$0.714916\pi$
$770$	−9.70577	+	1.72791i	−0.349772	+	0.0622695i
$771$		0			0
$772$	4.44051	+	24.7063i	0.159817	+	0.889198i
$773$	−15.0239	+	17.9048i	−0.540373	+	0.643992i	−0.965271	−	0.261249i	$-0.915866\pi$
$773$	−15.0239	+	17.9048i	−0.540373	+	0.643992i	0.424898	+	0.905241i	$0.360310\pi$
$774$		0			0
$775$	12.8136	+	35.2050i	0.460277	+	1.26460i
$776$	−1.88379	+	0.341787i	−0.0676240	+	0.0122694i
$777$		0			0
$778$	22.4278	−	8.20499i	0.804076	−	0.294163i
$779$	26.3957	−	14.9726i	0.945725	−	0.536448i
$780$		0			0
$781$	6.12505	+	34.7369i	0.219172	+	1.24298i
$782$	16.5066	−	28.6996i	0.590276	−	1.02630i
$783$		0			0
$784$	−2.48460	+	4.36981i	−0.0887355	+	0.156065i
$785$	−6.94682	+	8.27890i	−0.247943	+	0.295487i
$786$		0			0
$787$	−11.9135	+	6.87826i	−0.424670	+	0.245184i	−0.697074	−	0.717000i	$-0.745515\pi$
$787$	−11.9135	+	6.87826i	−0.424670	+	0.245184i	0.272403	+	0.962183i	$0.412182\pi$
$788$	−34.6817	+	20.1764i	−1.23548	+	0.718754i
$789$		0			0
$790$	−4.79590	+	5.73472i	−0.170630	+	0.204032i
$791$	15.7369	−	27.2572i	0.559541	−	0.969154i
$792$		0			0
$793$	−5.73460	−	2.08722i	−0.203642	−	0.0741195i
$794$	34.2116	+	40.6354i	1.21412	+	1.44210i
$795$		0			0
$796$	−24.2134	+	29.0506i	−0.858222	+	1.02967i
$797$		−	10.8460i		−	0.384185i	−0.981377	−	0.192093i	$-0.938473\pi$
$797$		−	10.8460i		−	0.384185i	0.981377	−	0.192093i	$-0.0615274\pi$
$798$		0			0
$799$			67.4737i			2.38705i
$800$	8.42339	+	22.5621i	0.297812	+	0.797689i
$801$		0			0
$802$	−33.9744	+	28.6036i	−1.19968	+	1.01003i
$803$	−21.8928	−	7.96833i	−0.772580	−	0.281196i
$804$		0			0
$805$	3.08307	−	5.34003i	0.108664	−	0.188211i
$806$	−20.6392	−	17.2604i	−0.726984	−	0.607970i
$807$		0			0
$808$	4.98474	+	4.14082i	0.175363	+	0.145673i
$809$	−17.9152	+	10.3433i	−0.629864	+	0.363652i	−0.780700	−	0.624907i	$-0.785137\pi$
$809$	−17.9152	+	10.3433i	−0.629864	+	0.363652i	0.150835	+	0.988559i	$0.451804\pi$
$810$		0			0
$811$	6.57226	−	7.83251i	0.230783	−	0.275037i	−0.638208	−	0.769864i	$-0.720324\pi$
$811$	6.57226	−	7.83251i	0.230783	−	0.275037i	0.868991	+	0.494827i	$0.164769\pi$
$812$	20.3383	−	7.47865i	0.713735	−	0.262449i
$813$		0			0
$814$	30.3629	+	17.4633i	1.06422	+	0.612087i
$815$	−1.81949	−	10.3188i	−0.0637338	−	0.361452i
$816$		0			0
$817$	17.7650	+	10.4379i	0.621520	+	0.365177i
$818$	−4.11194	−	11.2397i	−0.143771	−	0.392988i
$819$		0			0
$820$	2.04464	−	11.8238i	0.0714019	−	0.412905i
$821$	−17.0854	−	46.9419i	−0.596286	−	1.63828i	−0.758610	−	0.651545i	$-0.774121\pi$
$821$	−17.0854	−	46.9419i	−0.596286	−	1.63828i	0.162324	−	0.986737i	$-0.448101\pi$
$822$		0			0
$823$	10.3566	−	12.3425i	0.361008	−	0.430232i	−0.554717	−	0.832039i	$-0.687173\pi$
$823$	10.3566	−	12.3425i	0.361008	−	0.430232i	0.915724	+	0.401807i	$0.131618\pi$
$824$	−25.5843	−	43.8109i	−0.891271	−	1.52623i
$825$		0			0
$826$	−2.74423	−	15.4145i	−0.0954840	−	0.536340i
$827$	−1.54355	+	8.75389i	−0.0536744	+	0.304403i	−0.999813	−	0.0193604i	$-0.993837\pi$
$827$	−1.54355	+	8.75389i	−0.0536744	+	0.304403i	0.946138	+	0.323763i	$0.104948\pi$
$828$		0			0
$829$	7.48543	−	12.9651i	0.259980	−	0.450298i	−0.706256	−	0.707956i	$-0.749617\pi$
$829$	7.48543	−	12.9651i	0.259980	−	0.450298i	0.966236	+	0.257658i	$0.0829508\pi$
$830$	17.3909	+	6.29730i	0.603648	+	0.218583i
$831$		0			0
$832$	−13.3586	−	10.9856i	−0.463125	−	0.380858i
$833$	6.33395	+	7.54851i	0.219458	+	0.261540i
$834$		0			0
$835$			8.44066i			0.292101i
$836$	5.23480	−	28.9561i	0.181049	−	1.00147i
$837$		0			0
$838$	20.4843	−	11.8717i	0.707618	−	0.410102i
$839$	−19.4852	+	16.3500i	−0.672704	+	0.564465i	−0.913864	−	0.406020i	$-0.866916\pi$
$839$	−19.4852	+	16.3500i	−0.672704	+	0.564465i	0.241161	+	0.970485i	$0.422472\pi$
$840$		0			0
$841$	−8.04360	−	2.92763i	−0.277366	−	0.100953i
$842$	−1.09807	+	3.03249i	−0.0378420	+	0.104506i
$843$		0			0
$844$	−10.7128	+	29.7381i	−0.368748	+	1.02363i
$845$	−7.06613	−	1.24595i	−0.243082	−	0.0428619i
$846$		0			0
$847$	−0.815374	+	0.470756i	−0.0280166	+	0.0161754i
$848$	0.456153	−	0.550968i	0.0156644	−	0.0189203i
$849$		0			0
$850$	47.2097	−	0.0779086i	1.61928	−	0.00267224i
$851$	−20.5870	+	7.49305i	−0.705713	+	0.256859i
$852$		0			0
$853$	0.208823	+	1.18429i	0.00714995	+	0.0405494i	0.988174	−	0.153337i	$-0.0490019\pi$
$853$	0.208823	+	1.18429i	0.00714995	+	0.0405494i	−0.981024	+	0.193886i	$0.937891\pi$
$854$	8.98450	−	3.28689i	0.307443	−	0.112475i
$855$		0			0
$856$	−6.50065	−	3.71036i	−0.222188	−	0.126818i
$857$	24.2624	−	4.27811i	0.828786	−	0.146137i	0.256867	−	0.966447i	$-0.417310\pi$
$857$	24.2624	−	4.27811i	0.828786	−	0.146137i	0.571920	+	0.820309i	$0.306199\pi$
$858$		0			0
$859$	−18.3498	−	50.4156i	−0.626086	−	1.72016i	−0.691576	−	0.722303i	$-0.743083\pi$
$859$	−18.3498	−	50.4156i	−0.626086	−	1.72016i	0.0654906	−	0.997853i	$-0.479139\pi$
$860$	7.64663	−	2.81176i	0.260748	−	0.0958803i
$861$		0			0
$862$	−11.0821	−	1.93523i	−0.377459	−	0.0659141i
$863$	−15.4850	−	26.8209i	−0.527117	−	0.912993i	−0.999501	−	0.0316000i	$-0.989940\pi$
$863$	−15.4850	−	26.8209i	−0.527117	−	0.912993i	0.472384	−	0.881393i	$-0.343394\pi$
$864$		0			0
$865$	2.23638	−	12.6831i	0.0760392	−	0.431240i
$866$	−8.96093	+	10.7151i	−0.304505	+	0.364113i
$867$		0			0
$868$	42.1782	−	0.139211i	1.43162	−	0.00472512i
$869$	−7.08139	+	19.4560i	−0.240220	+	0.659998i
$870$		0			0
$871$	16.7564	+	19.9695i	0.567769	+	0.676641i
$872$	−4.12317	+	11.5052i	−0.139628	+	0.389616i
$873$		0			0
$874$	11.7460	+	14.1693i	0.397314	+	0.479282i
$875$	19.1188			0.646333
$876$		0			0
$877$	41.1372	−	34.5182i	1.38910	−	1.16560i	0.423403	−	0.905941i	$-0.360835\pi$
$877$	41.1372	−	34.5182i	1.38910	−	1.16560i	0.965701	−	0.259655i	$-0.0836090\pi$
$878$	−23.6106	+	19.8782i	−0.796820	+	0.670855i
$879$		0			0
$880$	−7.53756	−	8.86343i	−0.254091	−	0.298786i
$881$	−10.8128	−	6.24276i	−0.364292	−	0.210324i	0.306670	−	0.951816i	$-0.400785\pi$
$881$	−10.8128	−	6.24276i	−0.364292	−	0.210324i	−0.670962	+	0.741492i	$0.734119\pi$
$882$		0			0
$883$	0.870075	+	0.153418i	0.0292803	+	0.00516291i	0.188269	−	0.982117i	$-0.439712\pi$
$883$	0.870075	+	0.153418i	0.0292803	+	0.00516291i	−0.158989	+	0.987280i	$0.550823\pi$
$884$	−29.3057	+	17.0488i	−0.985656	+	0.573415i
$885$		0			0
$886$	−27.1032	−	4.73293i	−0.910551	−	0.159006i
$887$	20.0221	+	16.8005i	0.672276	+	0.564106i	0.913738	−	0.406304i	$-0.133183\pi$
$887$	20.0221	+	16.8005i	0.672276	+	0.564106i	−0.241462	+	0.970410i	$0.577627\pi$
$888$		0			0
$889$	−17.2345	+	6.27285i	−0.578027	+	0.210385i
$890$	−4.91168	−	2.82496i	−0.164640	−	0.0946930i
$891$		0			0
$892$	−1.05082	−	1.24396i	−0.0351842	−	0.0416509i
$893$	−35.1480	−	13.0970i	−1.17618	−	0.438274i
$894$		0			0
$895$	7.87683	−	1.38890i	0.263293	−	0.0464257i
$896$	27.1117	−	0.313204i	0.905739	−	0.0104634i
$897$		0			0
$898$	26.1232	−	0.0431101i	0.871741	−	0.00143860i
$899$	30.4772	+	25.5734i	1.01647	+	0.852921i
$900$		0			0
$901$	−0.701085	−	1.21432i	−0.0233565	−	0.0404547i
$902$	−5.82477	−	32.7181i	−0.193944	−	1.08939i
$903$		0			0
$904$	37.1457	−	0.183902i	1.23545	−	0.00611650i
$905$	−18.8205	−	10.8660i	−0.625615	−	0.361199i
$906$		0			0
$907$	16.9326	−	46.5219i	0.562238	−	1.54473i	−0.254111	−	0.967175i	$-0.581783\pi$
$907$	16.9326	−	46.5219i	0.562238	−	1.54473i	0.816348	−	0.577560i	$-0.195995\pi$
$908$	−4.37361	+	7.63339i	−0.145143	+	0.253323i
$909$		0			0
$910$	−5.46322	+	3.16623i	−0.181104	+	0.104959i
$911$	40.7601			1.35044			0.675221	−	0.737615i	$-0.264048\pi$
$911$	40.7601			1.35044			0.675221	+	0.737615i	$0.264048\pi$
$912$		0			0
$913$	51.2254			1.69531
$914$	−48.8341	+	28.3019i	−1.61529	+	0.936144i
$915$		0			0
$916$	4.45593	−	7.77707i	0.147228	−	0.256962i
$917$	6.81688	−	18.7292i	0.225113	−	0.618494i
$918$		0			0
$919$	−12.4780	−	7.20419i	−0.411612	−	0.237644i	0.279870	−	0.960038i	$-0.409709\pi$
$919$	−12.4780	−	7.20419i	−0.411612	−	0.237644i	−0.691482	+	0.722394i	$0.743042\pi$
$920$	7.27732	−	0.0360288i	0.239926	−	0.00118784i
$921$		0			0
$922$	−3.69032	−	20.7287i	−0.121534	−	0.682665i
$923$	11.2963	+	19.5658i	0.371823	+	0.644016i
$924$		0			0
$925$	−23.9310	−	20.0805i	−0.786847	−	0.660243i
$926$	−18.2129	+	0.0300562i	−0.598514	+	0.000987708i
$927$		0			0
$928$	19.7266	+	16.2771i	0.647559	+	0.534323i
$929$	−23.3111	+	4.11037i	−0.764812	+	0.134857i	−0.542428	−	0.840102i	$-0.682495\pi$
$929$	−23.3111	+	4.11037i	−0.764812	+	0.134857i	−0.222384	+	0.974959i	$0.571384\pi$
$930$		0			0
$931$	−5.16157	+	1.83424i	−0.169164	+	0.0601148i
$932$	20.4648	+	24.2262i	0.670347	+	0.793555i
$933$		0			0
$934$	−18.5107	−	10.6464i	−0.605687	−	0.348362i
$935$	−21.4325	+	7.80080i	−0.700918	+	0.255113i
$936$		0			0
$937$	41.2829	+	34.6405i	1.34865	+	1.13166i	0.979311	+	0.202362i	$0.0648619\pi$
$937$	41.2829	+	34.6405i	1.34865	+	1.13166i	0.369344	+	0.929293i	$0.379583\pi$
$938$	−40.2571	−	7.02994i	−1.31444	−	0.229536i
$939$		0			0
$940$	−12.8198	+	7.45801i	−0.418134	+	0.243254i
$941$	35.2664	+	6.21841i	1.14965	+	0.202714i	0.715823	−	0.698281i	$-0.246052\pi$
$941$	35.2664	+	6.21841i	1.14965	+	0.202714i	0.433828	+	0.900996i	$0.357163\pi$
$942$		0			0
$943$	18.0012	+	10.3930i	0.586200	+	0.338443i
$944$	14.0767	−	11.9710i	0.458158	−	0.389623i
$945$		0			0
$946$	17.2611	−	14.5324i	0.561207	−	0.472489i
$947$	−7.68149	+	6.44553i	−0.249615	+	0.209452i	−0.759006	−	0.651083i	$-0.774315\pi$
$947$	−7.68149	+	6.44553i	−0.249615	+	0.209452i	0.509392	+	0.860535i	$0.329870\pi$
$948$		0			0
$949$	−14.9225			−0.484406
$950$	−9.12305	+	24.6073i	−0.295991	+	0.798367i
$951$		0			0
$952$	17.9309	−	50.0341i	0.581144	−	1.62162i
$953$	−7.01559	−	8.36085i	−0.227257	−	0.270835i	0.640352	−	0.768082i	$-0.278789\pi$
$953$	−7.01559	−	8.36085i	−0.227257	−	0.270835i	−0.867609	+	0.497247i	$0.834344\pi$
$954$		0			0
$955$	−7.36113	+	20.2245i	−0.238200	+	0.654450i
$956$	−33.4803	+	0.110503i	−1.08283	+	0.00357393i
$957$		0			0
$958$	6.09955	−	7.29357i	0.197067	−	0.235644i
$959$	3.34641	−	18.9784i	0.108061	−	0.612846i
$960$		0			0
$961$	23.2194	+	40.2171i	0.749011	+	1.29733i
$962$	22.1006	+	3.85934i	0.712552	+	0.124430i
$963$		0			0
$964$	−46.2665	+	17.0128i	−1.49014	+	0.547944i
$965$	3.69935	+	10.1639i	0.119086	+	0.327187i
$966$		0			0
$967$	4.74891	−	0.837361i	0.152715	−	0.0269277i	−0.0967681	−	0.995307i	$-0.530851\pi$
$967$	4.74891	−	0.837361i	0.152715	−	0.0269277i	0.249483	+	0.968379i	$0.419739\pi$
$968$	−0.965062	−	0.550826i	−0.0310183	−	0.0177042i
$969$		0			0
$970$	−0.774734	+	0.283429i	−0.0248752	+	0.00910035i
$971$	8.78529	+	49.8239i	0.281933	+	1.59892i	0.716038	+	0.698061i	$0.245954\pi$
$971$	8.78529	+	49.8239i	0.281933	+	1.59892i	−0.434105	+	0.900862i	$0.642935\pi$
$972$		0			0
$973$	17.9286	−	6.52549i	0.574766	−	0.209198i
$974$	12.8953	−	0.0212806i	0.413191	−	0.000681875i
$975$		0			0
$976$	8.69715	+	7.20048i	0.278389	+	0.230482i
$977$	27.0288	−	15.6051i	0.864728	−	0.499251i	−0.000864660	−	1.00000i	$-0.500275\pi$
$977$	27.0288	−	15.6051i	0.864728	−	0.499251i	0.865593	+	0.500749i	$0.166942\pi$
$978$		0			0
$979$	−15.4542	−	2.72499i	−0.493918	−	0.0870911i
$980$	−0.734083	+	2.03778i	−0.0234494	+	0.0650945i
$981$		0			0
$982$	−17.8337	+	49.2503i	−0.569095	+	1.57164i
$983$	1.24629	+	0.453613i	0.0397505	+	0.0144680i	0.361819	−	0.932248i	$-0.382156\pi$
$983$	1.24629	+	0.453613i	0.0397505	+	0.0144680i	−0.322068	+	0.946716i	$0.604378\pi$
$984$		0			0
$985$	−13.2439	+	11.1130i	−0.421987	+	0.354089i
$986$	43.3762	−	25.1388i	1.38138	−	0.800582i
$987$		0			0
$988$	−3.19261	−	18.5750i	−0.101570	−	0.590949i
$989$			14.1132i			0.448773i
$990$		0			0
$991$	−14.0462	−	16.7396i	−0.446192	−	0.531751i	0.495329	−	0.868705i	$-0.335047\pi$
$991$	−14.0462	−	16.7396i	−0.446192	−	0.531751i	−0.941521	+	0.336955i	$0.890603\pi$
$992$	25.2448	+	42.9038i	0.801524	+	1.36220i
$993$		0			0
$994$	−33.3016	−	12.0586i	−1.05626	−	0.382475i
$995$	−8.14771	+	14.1123i	−0.258300	+	0.447388i
$996$		0			0
$997$	8.63415	−	48.9667i	0.273446	−	1.55079i	−0.470408	−	0.882449i	$-0.655893\pi$
$997$	8.63415	−	48.9667i	0.273446	−	1.55079i	0.743855	−	0.668341i	$-0.232995\pi$
$998$	5.66749	+	31.8347i	0.179401	+	1.00771i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.ce.a.503.8	yes	240
3.2	odd	2	inner	684.2.ce.a.503.33	yes	240
4.3	odd	2	inner	684.2.ce.a.503.3	yes	240
12.11	even	2	inner	684.2.ce.a.503.38	yes	240
19.17	even	9	inner	684.2.ce.a.359.38	yes	240
57.17	odd	18	inner	684.2.ce.a.359.3	✓	240
76.55	odd	18	inner	684.2.ce.a.359.33	yes	240
228.131	even	18	inner	684.2.ce.a.359.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.ce.a.359.3	✓	240	57.17	odd	18	inner
684.2.ce.a.359.8	yes	240	228.131	even	18	inner
684.2.ce.a.359.33	yes	240	76.55	odd	18	inner
684.2.ce.a.359.38	yes	240	19.17	even	9	inner
684.2.ce.a.503.3	yes	240	4.3	odd	2	inner
684.2.ce.a.503.8	yes	240	1.1	even	1	trivial
684.2.ce.a.503.33	yes	240	3.2	odd	2	inner
684.2.ce.a.503.38	yes	240	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.22358 + 0.709127i) q^{2} +(0.994278 - 1.73534i) q^{4} +(0.294744 - 0.809802i) q^{5} +(2.07545 + 1.19826i) q^{7} +(0.0140029 + 2.82839i) q^{8} +O(q^{10})\)	\(q+(-1.22358 + 0.709127i) q^{2} +(0.994278 - 1.73534i) q^{4} +(0.294744 - 0.809802i) q^{5} +(2.07545 + 1.19826i) q^{7} +(0.0140029 + 2.82839i) q^{8} +(0.213611 + 1.19987i) q^{10} +(1.68767 + 2.92312i) q^{11} +(1.65614 + 1.38967i) q^{13} +(-3.38919 + 0.00559306i) q^{14} +(-2.02282 - 3.45082i) q^{16} +(-7.72199 + 1.36160i) q^{17} +(0.789602 - 4.28679i) q^{19} +(-1.11223 - 1.31665i) q^{20} +(-4.13785 - 2.37989i) q^{22} +(2.80559 - 1.02115i) q^{23} +(3.26132 + 2.73657i) q^{25} +(-3.01187 - 0.525950i) q^{26} +(4.14296 - 2.41021i) q^{28} +(4.45240 + 0.785078i) q^{29} +(7.62096 + 4.39996i) q^{31} +(4.92215 + 2.78791i) q^{32} +(8.48290 - 7.14189i) q^{34} +(1.58208 - 1.32752i) q^{35} -7.33783 q^{37} +(2.07374 + 5.80514i) q^{38} +(2.29456 + 0.822312i) q^{40} +(4.47507 + 5.33318i) q^{41} +(-1.61673 + 4.44193i) q^{43} +(6.75063 - 0.0222807i) q^{44} +(-2.70873 + 3.23898i) q^{46} +(1.49426 - 8.47439i) q^{47} +(-0.628347 - 1.08833i) q^{49} +(-5.93105 - 1.03571i) q^{50} +(4.05822 - 1.49226i) q^{52} +(0.0611610 + 0.168038i) q^{53} +(2.86458 - 0.505103i) q^{55} +(-3.36009 + 5.88696i) q^{56} +(-6.00457 + 2.19671i) q^{58} +(0.802194 + 4.54947i) q^{59} +(-2.65253 + 0.965440i) q^{61} +(-12.4450 + 0.0205375i) q^{62} +(-7.99961 + 0.0792114i) q^{64} +(1.61349 - 0.931551i) q^{65} +(11.8747 + 2.09382i) q^{67} +(-5.31497 + 14.7541i) q^{68} +(-0.994412 + 2.74622i) q^{70} +(9.81994 + 3.57417i) q^{71} +(-5.28753 + 4.43677i) q^{73} +(8.97840 - 5.20346i) q^{74} +(-6.65395 - 5.63249i) q^{76} +8.08905i q^{77} +(3.94292 + 4.69899i) q^{79} +(-3.39070 + 0.620977i) q^{80} +(-9.25749 - 3.35216i) q^{82} +(7.58820 - 13.1432i) q^{83} +(-1.17339 + 6.65461i) q^{85} +(-1.17170 - 6.58151i) q^{86} +(-8.24411 + 4.81431i) q^{88} +(-2.98845 + 3.56150i) q^{89} +(1.77205 + 4.86867i) q^{91} +(1.01749 - 5.88398i) q^{92} +(4.18107 + 11.4287i) q^{94} +(-3.23872 - 1.90292i) q^{95} +(0.117541 + 0.666610i) q^{97} +(1.54059 + 0.886075i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{4}+O(q^{10}) \) 240 * q + 12 * q^4	\( 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) \) 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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