LMFDB - Embedded newform 1197.2.j.k.856.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1197,2,Mod(172,1197)] 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("1197.172"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1197, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.2
Root			$-0.198169 + 0.343239i$ of defining polynomial
Character	$\chi$	$=$	1197.856
Dual form			1197.2.j.k.172.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.198169 + 0.343239i) q^{2} +(0.921458 + 1.59601i) q^{4} +(-0.421458 + 0.729986i) q^{5} +(1.79981 - 1.93925i) q^{7} -1.52310 q^{8} +(-0.167040 - 0.289322i) q^{10} +(-0.0179894 - 0.0311586i) q^{11} +1.96402 q^{13} +(0.308961 + 1.00206i) q^{14} +(-1.54109 + 2.66924i) q^{16} +(1.62676 + 2.81763i) q^{17} +(-0.500000 + 0.866025i) q^{19} -1.55342 q^{20} +0.0142598 q^{22} +(0.641921 - 1.11184i) q^{23} +(2.14475 + 3.71481i) q^{25} +(-0.389209 + 0.674129i) q^{26} +(4.75351 + 1.08558i) q^{28} +7.06045 q^{29} +(1.80976 + 3.13460i) q^{31} +(-2.13389 - 3.69600i) q^{32} -1.28949 q^{34} +(0.657084 + 2.13115i) q^{35} +(1.08137 - 1.87298i) q^{37} +(-0.198169 - 0.343239i) q^{38} +(0.641921 - 1.11184i) q^{40} -0.130805 q^{41} -4.50884 q^{43} +(0.0331530 - 0.0574227i) q^{44} +(0.254418 + 0.440665i) q^{46} +(-3.99277 + 6.91568i) q^{47} +(-0.521390 - 6.98056i) q^{49} -1.70009 q^{50} +(1.80976 + 3.13460i) q^{52} +(1.49085 + 2.58222i) q^{53} +0.0303272 q^{55} +(-2.74128 + 2.95366i) q^{56} +(-1.39916 + 2.42342i) q^{58} +(6.48994 + 11.2409i) q^{59} +(-1.29380 + 2.24092i) q^{61} -1.43456 q^{62} -4.47286 q^{64} +(-0.827752 + 1.43371i) q^{65} +(-2.25952 - 3.91361i) q^{67} +(-2.99798 + 5.19265i) q^{68} +(-0.861707 - 0.196791i) q^{70} +2.64985 q^{71} +(-3.10649 - 5.38059i) q^{73} +(0.428588 + 0.742336i) q^{74} -1.84292 q^{76} +(-0.0928019 - 0.0211935i) q^{77} +(-5.18641 + 8.98312i) q^{79} +(-1.29900 - 2.24994i) q^{80} +(0.0259214 - 0.0448973i) q^{82} -10.2752 q^{83} -2.74244 q^{85} +(0.893513 - 1.54761i) q^{86} +(0.0273996 + 0.0474576i) q^{88} +(4.18641 - 7.25107i) q^{89} +(3.53486 - 3.80873i) q^{91} +2.36601 q^{92} +(-1.58249 - 2.74095i) q^{94} +(-0.421458 - 0.729986i) q^{95} -2.55162 q^{97} +(2.49932 + 1.20437i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} + 2 q^{7} + 6 q^{8} + 3 q^{10} - 2 q^{11} + 12 q^{13} - 2 q^{14} + 4 q^{16} - 2 q^{17} - 4 q^{19} - 24 q^{20} - 12 q^{22} + 5 q^{23} + 4 q^{25} - 6 q^{26} + 8 q^{28} + 8 q^{29} - 17 q^{31}+ \cdots - 27 q^{98}+O(q^{100}) $ 8 * q + 4 * q^5 + 2 * q^7 + 6 * q^8 + 3 * q^10 - 2 * q^11 + 12 * q^13 - 2 * q^14 + 4 * q^16 - 2 * q^17 - 4 * q^19 - 24 * q^20 - 12 * q^22 + 5 * q^23 + 4 * q^25 - 6 * q^26 + 8 * q^28 + 8 * q^29 - 17 * q^31 + 4 * q^32 + 16 * q^34 + 20 * q^35 + 3 * q^37 + 5 * q^40 - 14 * q^41 - 30 * q^43 + 17 * q^44 - q^46 + 16 * q^47 + 14 * q^49 + 28 * q^50 - 17 * q^52 + 4 * q^53 + 30 * q^55 - 18 * q^56 + 5 * q^58 + 17 * q^59 + 9 * q^61 + 14 * q^62 - 26 * q^64 + 23 * q^65 + 5 * q^67 - 10 * q^68 + 33 * q^70 - 12 * q^71 - 15 * q^73 - 10 * q^74 + 4 * q^77 - 5 * q^79 - 25 * q^80 - 31 * q^82 - 68 * q^83 - 24 * q^85 + 17 * q^86 - 11 * q^88 - 3 * q^89 + 45 * q^91 - 14 * q^92 + 6 * q^94 + 4 * q^95 + 22 * q^97 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−0.198169	+	0.343239i	−0.140127	+	0.242707i	−0.927544	−	0.373713i	$-0.878084\pi$
$2$	−0.198169	+	0.343239i	−0.140127	+	0.242707i	0.787417	+	0.616420i	$0.211418\pi$
$3$		0			0
$3$		0			0
$4$	0.921458	+	1.59601i	0.460729	+	0.798006i
$5$	−0.421458	+	0.729986i	−0.188482	+	0.326460i	−0.944744	−	0.327808i	$-0.893690\pi$
$5$	−0.421458	+	0.729986i	−0.188482	+	0.326460i	0.756263	+	0.654268i	$0.227023\pi$
$6$		0			0
$7$	1.79981	−	1.93925i	0.680263	−	0.732968i
$7$	1.79981	−	1.93925i	0.680263	−	0.732968i
$8$	−1.52310			−0.538496
$9$		0			0
$10$	−0.167040	−	0.289322i	−0.0528227	−	0.0914916i
$11$	−0.0179894	−	0.0311586i	−0.00542402	−	0.00939468i	0.863301	−	0.504690i	$-0.168393\pi$
$11$	−0.0179894	−	0.0311586i	−0.00542402	−	0.00939468i	−0.868725	+	0.495295i	$0.835060\pi$
$12$		0			0
$13$	1.96402			0.544721			0.272361	−	0.962195i	$-0.412196\pi$
$13$	1.96402			0.544721			0.272361	+	0.962195i	$0.412196\pi$
$14$	0.308961	+	1.00206i	0.0825732	+	0.267813i
$15$		0			0
$16$	−1.54109	+	2.66924i	−0.385271	+	0.667309i
$17$	1.62676	+	2.81763i	0.394547	+	0.683375i	0.993043	−	0.117751i	$-0.0375684\pi$
$17$	1.62676	+	2.81763i	0.394547	+	0.683375i	−0.598497	+	0.801125i	$0.704235\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	−1.55342			−0.347356
$21$		0			0
$22$	0.0142598			0.00304020
$23$	0.641921	−	1.11184i	0.133850	−	0.231834i	−0.791308	−	0.611418i	$-0.790599\pi$
$23$	0.641921	−	1.11184i	0.133850	−	0.231834i	0.925157	+	0.379584i	$0.123933\pi$
$24$		0			0
$25$	2.14475	+	3.71481i	0.428949	+	0.742962i
$26$	−0.389209	+	0.674129i	−0.0763301	+	0.132208i
$27$		0			0
$28$	4.75351	+	1.08558i	0.898330	+	0.205154i
$29$	7.06045			1.31109			0.655546	−	0.755155i	$-0.272438\pi$
$29$	7.06045			1.31109			0.655546	+	0.755155i	$0.272438\pi$
$30$		0			0
$31$	1.80976	+	3.13460i	0.325043	+	0.562991i	0.981521	−	0.191354i	$-0.0612879\pi$
$31$	1.80976	+	3.13460i	0.325043	+	0.562991i	−0.656478	+	0.754345i	$0.727955\pi$
$32$	−2.13389	−	3.69600i	−0.377221	−	0.653367i
$33$		0			0
$34$	−1.28949			−0.221146
$35$	0.657084	+	2.13115i	0.111068	+	0.360230i
$36$		0			0
$37$	1.08137	−	1.87298i	0.177776	−	0.307917i	−0.763343	−	0.645994i	$-0.776443\pi$
$37$	1.08137	−	1.87298i	0.177776	−	0.307917i	0.941118	+	0.338077i	$0.109776\pi$
$38$	−0.198169	−	0.343239i	−0.0321473	−	0.0556808i
$39$		0			0
$40$	0.641921	−	1.11184i	0.101497	−	0.175797i
$41$	−0.130805			−0.0204282			−0.0102141	−	0.999948i	$-0.503251\pi$
$41$	−0.130805			−0.0204282			−0.0102141	+	0.999948i	$0.503251\pi$
$42$		0			0
$43$	−4.50884			−0.687591			−0.343796	−	0.939045i	$-0.611713\pi$
$43$	−4.50884			−0.687591			−0.343796	+	0.939045i	$0.611713\pi$
$44$	0.0331530	−	0.0574227i	0.00499801	−	0.00865680i
$45$		0			0
$46$	0.254418	+	0.440665i	0.0375119	+	0.0649725i
$47$	−3.99277	+	6.91568i	−0.582405	+	1.00876i	0.412788	+	0.910827i	$0.364555\pi$
$47$	−3.99277	+	6.91568i	−0.582405	+	1.00876i	−0.995193	+	0.0979283i	$0.968778\pi$
$48$		0			0
$49$	−0.521390	−	6.98056i	−0.0744842	−	0.997222i
$50$	−1.70009			−0.240429
$51$		0			0
$52$	1.80976	+	3.13460i	0.250969	+	0.434691i
$53$	1.49085	+	2.58222i	0.204783	+	0.354695i	0.950064	−	0.312056i	$-0.101018\pi$
$53$	1.49085	+	2.58222i	0.204783	+	0.354695i	−0.745280	+	0.666751i	$0.767684\pi$
$54$		0			0
$55$	0.0303272			0.00408931
$56$	−2.74128	+	2.95366i	−0.366319	+	0.394700i
$57$		0			0
$58$	−1.39916	+	2.42342i	−0.183719	+	0.318211i
$59$	6.48994	+	11.2409i	0.844919	+	1.46344i	0.885692	+	0.464273i	$0.153685\pi$
$59$	6.48994	+	11.2409i	0.844919	+	1.46344i	−0.0407734	+	0.999168i	$0.512982\pi$
$60$		0			0
$61$	−1.29380	+	2.24092i	−0.165654	+	0.286921i	−0.936887	−	0.349632i	$-0.886307\pi$
$61$	−1.29380	+	2.24092i	−0.165654	+	0.286921i	0.771234	+	0.636552i	$0.219640\pi$
$62$	−1.43456			−0.182189
$63$		0			0
$64$	−4.47286			−0.559107
$65$	−0.827752	+	1.43371i	−0.102670	+	0.177830i
$66$		0			0
$67$	−2.25952	−	3.91361i	−0.276045	−	0.478124i	0.694353	−	0.719634i	$-0.255690\pi$
$67$	−2.25952	−	3.91361i	−0.276045	−	0.478124i	−0.970398	+	0.241511i	$0.922357\pi$
$68$	−2.99798	+	5.19265i	−0.363558	+	0.629701i
$69$		0			0
$70$	−0.861707	−	0.196791i	−0.102994	−	0.0235210i
$71$	2.64985			0.314480			0.157240	−	0.987560i	$-0.449740\pi$
$71$	2.64985			0.314480			0.157240	+	0.987560i	$0.449740\pi$
$72$		0			0
$73$	−3.10649	−	5.38059i	−0.363587	−	0.629751i	0.624961	−	0.780656i	$-0.285115\pi$
$73$	−3.10649	−	5.38059i	−0.363587	−	0.629751i	−0.988548	+	0.150905i	$0.951781\pi$
$74$	0.428588	+	0.742336i	0.0498223	+	0.0862948i
$75$		0			0
$76$	−1.84292			−0.211397
$77$	−0.0928019	−	0.0211935i	−0.0105758	−	0.00241522i
$78$		0			0
$79$	−5.18641	+	8.98312i	−0.583516	+	1.01068i	0.411542	+	0.911391i	$0.364990\pi$
$79$	−5.18641	+	8.98312i	−0.583516	+	1.01068i	−0.995059	+	0.0992892i	$0.968343\pi$
$80$	−1.29900	−	2.24994i	−0.145233	−	0.251551i
$81$		0			0
$82$	0.0259214	−	0.0448973i	0.00286255	−	0.00495807i
$83$	−10.2752			−1.12785			−0.563927	−	0.825825i	$-0.690710\pi$
$83$	−10.2752			−1.12785			−0.563927	+	0.825825i	$0.690710\pi$
$84$		0			0
$85$	−2.74244			−0.297459
$86$	0.893513	−	1.54761i	0.0963499	−	0.166883i
$87$		0			0
$88$	0.0273996	+	0.0474576i	0.00292081	+	0.00505899i
$89$	4.18641	−	7.25107i	0.443758	−	0.768612i	−0.554207	−	0.832379i	$-0.686978\pi$
$89$	4.18641	−	7.25107i	0.443758	−	0.768612i	0.997965	+	0.0637675i	$0.0203116\pi$
$90$		0			0
$91$	3.53486	−	3.80873i	0.370554	−	0.399263i
$92$	2.36601			0.246674
$93$		0			0
$94$	−1.58249	−	2.74095i	−0.163221	−	0.282707i
$95$	−0.421458	−	0.729986i	−0.0432407	−	0.0748950i
$96$		0			0
$97$	−2.55162			−0.259077			−0.129539	−	0.991574i	$-0.541350\pi$
$97$	−2.55162			−0.259077			−0.129539	+	0.991574i	$0.541350\pi$
$98$	2.49932	+	1.20437i	0.252470	+	0.121660i
$99$		0			0
$100$	−3.95259	+	6.84608i	−0.395259	+	0.684608i
$101$	3.56508	+	6.17491i	0.354739	+	0.614426i	0.987073	−	0.160270i	$-0.0512363\pi$
$101$	3.56508	+	6.17491i	0.354739	+	0.614426i	−0.632334	+	0.774696i	$0.717903\pi$
$102$		0			0
$103$	−1.45461	+	2.51946i	−0.143327	+	0.248250i	−0.928748	−	0.370713i	$-0.879113\pi$
$103$	−1.45461	+	2.51946i	−0.143327	+	0.248250i	0.785420	+	0.618963i	$0.212447\pi$
$104$	−2.99139			−0.293330
$105$		0			0
$106$	−1.18176			−0.114783
$107$	4.30466	−	7.45588i	0.416147	−	0.720788i	−0.579401	−	0.815042i	$-0.696714\pi$
$107$	4.30466	−	7.45588i	0.416147	−	0.720788i	0.995548	+	0.0942550i	$0.0300469\pi$
$108$		0			0
$109$	−0.287469	−	0.497911i	−0.0275346	−	0.0476913i	0.851930	−	0.523656i	$-0.175432\pi$
$109$	−0.287469	−	0.497911i	−0.0275346	−	0.0476913i	−0.879464	+	0.475965i	$0.842099\pi$
$110$	−0.00600991	+	0.0104095i	−0.000573023	+	0.000992505i
$111$		0			0
$112$	2.40267	+	7.79266i	0.227031	+	0.736337i
$113$	15.2784			1.43727			0.718637	−	0.695385i	$-0.244766\pi$
$113$	15.2784			1.43727			0.718637	+	0.695385i	$0.244766\pi$
$114$		0			0
$115$	0.541085	+	0.937187i	0.0504564	+	0.0873931i
$116$	6.50591	+	11.2686i	0.604058	+	1.04626i
$117$		0			0
$118$	−5.14443			−0.473583
$119$	8.39193	+	1.91649i	0.769287	+	0.175685i
$120$		0			0
$121$	5.49935	−	9.52516i	0.499941	−	0.865923i
$122$	−0.512782	−	0.888164i	−0.0464251	−	0.0804106i
$123$		0			0
$124$	−3.33524	+	5.77681i	−0.299513	+	0.518772i
$125$	−7.83026			−0.700360
$126$		0			0
$127$	1.02235			0.0907193			0.0453597	−	0.998971i	$-0.485557\pi$
$127$	1.02235			0.0907193			0.0453597	+	0.998971i	$0.485557\pi$
$128$	5.15416	−	8.92726i	0.455567	−	0.789066i
$129$		0			0
$130$	−0.328070	−	0.568234i	−0.0287736	−	0.0498374i
$131$	−8.49106	+	14.7070i	−0.741868	+	1.28495i	0.209776	+	0.977749i	$0.432726\pi$
$131$	−8.49106	+	14.7070i	−0.741868	+	1.28495i	−0.951644	+	0.307203i	$0.900607\pi$
$132$		0			0
$133$	0.779537	+	2.52830i	0.0675945	+	0.219232i
$134$	1.79107			0.154725
$135$		0			0
$136$	−2.47771	−	4.29151i	−0.212462	−	0.367994i
$137$	−1.12111	−	1.94181i	−0.0957825	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$137$	−1.12111	−	1.94181i	−0.0957825	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$138$		0			0
$139$	16.8301			1.42751			0.713753	−	0.700397i	$-0.246994\pi$
$139$	16.8301			1.42751			0.713753	+	0.700397i	$0.246994\pi$
$140$	−2.79586	+	3.01248i	−0.236293	+	0.254601i
$141$		0			0
$142$	−0.525119	+	0.909533i	−0.0440670	+	0.0763263i
$143$	−0.0353316	−	0.0611962i	−0.00295458	−	0.00511748i
$144$		0			0
$145$	−2.97568	+	5.15403i	−0.247117	+	0.428019i
$146$	2.46244			0.203793
$147$		0			0
$148$	3.98574			0.327626
$149$	6.36601	−	11.0263i	0.521524	−	0.903306i	−0.478163	−	0.878271i	$-0.658697\pi$
$149$	6.36601	−	11.0263i	0.521524	−	0.903306i	0.999687	−	0.0250347i	$-0.00796962\pi$
$150$		0			0
$151$	5.91342	+	10.2424i	0.481228	+	0.833511i	0.999768	−	0.0215425i	$-0.00685771\pi$
$151$	5.91342	+	10.2424i	0.481228	+	0.833511i	−0.518540	+	0.855053i	$0.673524\pi$
$152$	0.761548	−	1.31904i	0.0617697	−	0.106988i
$153$		0			0
$154$	0.0256649	−	0.0276534i	0.00206814	−	0.00222837i
$155$	−3.05096			−0.245059
$156$		0			0
$157$	−3.68843	−	6.38855i	−0.294369	−	0.509862i	0.680469	−	0.732777i	$-0.261776\pi$
$157$	−3.68843	−	6.38855i	−0.294369	−	0.509862i	−0.974838	+	0.222915i	$0.928443\pi$
$158$	−2.05557	−	3.56036i	−0.163533	−	0.283247i
$159$		0			0
$160$	3.59737			0.284397
$161$	−1.00080	−	3.24594i	−0.0788743	−	0.255816i
$162$		0			0
$163$	9.02470	−	15.6312i	0.706869	−	1.22433i	−0.259144	−	0.965839i	$-0.583440\pi$
$163$	9.02470	−	15.6312i	0.706869	−	1.22433i	0.966013	−	0.258494i	$-0.0832263\pi$
$164$	−0.120531	−	0.208766i	−0.00941188	−	0.0163019i
$165$		0			0
$166$	2.03624	−	3.52686i	0.158043	−	0.273738i
$167$	−22.6354			−1.75158			−0.875790	−	0.482693i	$-0.839659\pi$
$167$	−22.6354			−1.75158			−0.875790	+	0.482693i	$0.839659\pi$
$168$		0			0
$169$	−9.14262			−0.703279
$170$	0.543467	−	0.941312i	0.0416820	−	0.0721954i
$171$		0			0
$172$	−4.15470	−	7.19616i	−0.316793	−	0.548702i
$173$	3.44141	−	5.96070i	0.261646	−	0.453183i	−0.705034	−	0.709174i	$-0.749068\pi$
$173$	3.44141	−	5.96070i	0.261646	−	0.453183i	0.966679	+	0.255990i	$0.0824015\pi$
$174$		0			0
$175$	11.0641	+	2.52674i	0.836366	+	0.191003i
$176$	0.110893			0.00835888
$177$		0			0
$178$	1.65923	+	2.87388i	0.124365	+	0.215406i
$179$	0.310439	+	0.537696i	0.0232033	+	0.0401893i	0.877394	−	0.479771i	$-0.159280\pi$
$179$	0.310439	+	0.537696i	0.0232033	+	0.0401893i	−0.854191	+	0.519960i	$0.825947\pi$
$180$		0			0
$181$	−9.31058			−0.692050			−0.346025	−	0.938225i	$-0.612469\pi$
$181$	−9.31058			−0.692050			−0.346025	+	0.938225i	$0.612469\pi$
$182$	0.606805	+	1.96808i	0.0449794	+	0.145883i
$183$		0			0
$184$	−0.977707	+	1.69344i	−0.0720775	+	0.124842i
$185$	0.911502	+	1.57877i	0.0670150	+	0.116073i
$186$		0			0
$187$	0.0585289	−	0.101375i	0.00428006	−	0.00741328i
$188$	−14.7167			−1.07332
$189$		0			0
$190$	0.334080			0.0242367
$191$	9.16919	−	15.8815i	0.663459	−	1.14915i	−0.316241	−	0.948679i	$-0.602421\pi$
$191$	9.16919	−	15.8815i	0.663459	−	1.14915i	0.979701	−	0.200466i	$-0.0642457\pi$
$192$		0			0
$193$	7.60019	+	13.1639i	0.547074	+	0.947559i	0.998473	+	0.0552373i	$0.0175915\pi$
$193$	7.60019	+	13.1639i	0.547074	+	0.947559i	−0.451400	+	0.892322i	$0.649075\pi$
$194$	0.505652	−	0.875814i	0.0363037	−	0.0628798i
$195$		0			0
$196$	10.6606	−	7.26443i	0.761472	−	0.518888i
$197$	−7.77205			−0.553736			−0.276868	−	0.960908i	$-0.589296\pi$
$197$	−7.77205			−0.553736			−0.276868	+	0.960908i	$0.589296\pi$
$198$		0			0
$199$	−12.8631	−	22.2795i	−0.911840	−	1.57935i	−0.811463	−	0.584403i	$-0.801329\pi$
$199$	−12.8631	−	22.2795i	−0.911840	−	1.57935i	−0.100377	−	0.994950i	$-0.532005\pi$
$200$	−3.26665	−	5.65801i	−0.230987	−	0.400082i
$201$		0			0
$202$	−2.82596			−0.198834
$203$	12.7074	−	13.6920i	0.891888	−	0.960989i
$204$		0			0
$205$	0.0551286	−	0.0954856i	0.00385035	−	0.00666900i
$206$	−0.576518	−	0.998559i	−0.0401679	−	0.0695729i
$207$		0			0
$208$	−3.02672	+	5.24244i	−0.209866	+	0.363498i
$209$	0.0359789			0.00248871
$210$		0			0
$211$	17.2470			1.18733			0.593667	−	0.804711i	$-0.297680\pi$
$211$	17.2470			1.18733			0.593667	+	0.804711i	$0.297680\pi$
$212$	−2.74750	+	4.75882i	−0.188699	+	0.326837i
$213$		0			0
$214$	1.70610	+	2.95505i	0.116627	+	0.202003i
$215$	1.90028	−	3.29139i	0.129598	−	0.224471i
$216$		0			0
$217$	9.33600	+	2.13209i	0.633769	+	0.144736i
$218$	0.227870			0.0154333
$219$		0			0
$220$	0.0279452	+	0.0484025i	0.00188407	+	0.00326330i
$221$	3.19499	+	5.53388i	0.214918	+	0.372249i
$222$		0			0
$223$	15.7257			1.05307			0.526537	−	0.850152i	$-0.323490\pi$
$223$	15.7257			1.05307			0.526537	+	0.850152i	$0.323490\pi$
$224$	−11.0081	−	2.51395i	−0.735507	−	0.167970i
$225$		0			0
$226$	−3.02772	+	5.24416i	−0.201401	+	0.348836i
$227$	−3.25181	−	5.63230i	−0.215830	−	0.373829i	0.737699	−	0.675130i	$-0.235912\pi$
$227$	−3.25181	−	5.63230i	−0.215830	−	0.373829i	−0.953529	+	0.301301i	$0.902579\pi$
$228$		0			0
$229$	−3.93630	+	6.81788i	−0.260118	+	0.450538i	−0.966273	−	0.257519i	$-0.917095\pi$
$229$	−3.93630	+	6.81788i	−0.260118	+	0.450538i	0.706155	+	0.708057i	$0.250428\pi$
$230$	−0.428906			−0.0282812
$231$		0			0
$232$	−10.7537			−0.706018
$233$	11.1395	−	19.2941i	0.729771	−	1.26400i	−0.227208	−	0.973846i	$-0.572960\pi$
$233$	11.1395	−	19.2941i	0.729771	−	1.26400i	0.956980	−	0.290155i	$-0.0937069\pi$
$234$		0			0
$235$	−3.36557	−	5.82933i	−0.219545	−	0.380264i
$236$	−11.9604	+	20.7161i	−0.778557	+	1.34850i
$237$		0			0
$238$	−2.32084	+	2.50065i	−0.150438	+	0.162093i
$239$	−26.5221			−1.71557			−0.857784	−	0.514009i	$-0.828160\pi$
$239$	−26.5221			−1.71557			−0.857784	+	0.514009i	$0.828160\pi$
$240$		0			0
$241$	−5.54028	−	9.59605i	−0.356881	−	0.618136i	0.630557	−	0.776143i	$-0.282827\pi$
$241$	−5.54028	−	9.59605i	−0.356881	−	0.618136i	−0.987438	+	0.158007i	$0.949493\pi$
$242$	2.17961	+	3.77519i	0.140110	+	0.242678i
$243$		0			0
$244$	−4.76872			−0.305286
$245$	5.31545	+	2.56140i	0.339592	+	0.163642i
$246$		0			0
$247$	−0.982011	+	1.70089i	−0.0624838	+	0.108225i
$248$	−2.75644	−	4.77430i	−0.175034	−	0.303168i
$249$		0			0
$250$	1.55172	−	2.68765i	0.0981392	−	0.169982i
$251$	−3.32163			−0.209659			−0.104830	−	0.994490i	$-0.533430\pi$
$251$	−3.32163			−0.209659			−0.104830	+	0.994490i	$0.533430\pi$
$252$		0			0
$253$	−0.0461912			−0.00290401
$254$	−0.202599	+	0.350912i	−0.0127122	+	0.0220182i
$255$		0			0
$256$	−2.43007	−	4.20900i	−0.151879	−	0.263062i
$257$	15.0595	−	26.0837i	0.939383	−	1.62706i	0.172758	−	0.984964i	$-0.444732\pi$
$257$	15.0595	−	26.0837i	0.939383	−	1.62706i	0.766625	−	0.642095i	$-0.221935\pi$
$258$		0			0
$259$	−1.68593	−	5.46805i	−0.104759	−	0.339768i
$260$	−3.05096			−0.189212
$261$		0			0
$262$	−3.36534	−	5.82893i	−0.207911	−	0.360113i
$263$	−12.7833	−	22.1414i	−0.788253	−	1.36529i	−0.927036	−	0.374972i	$-0.877652\pi$
$263$	−12.7833	−	22.1414i	−0.788253	−	1.36529i	0.138783	−	0.990323i	$-0.455681\pi$
$264$		0			0
$265$	−2.51332			−0.154392
$266$	−1.02229	−	0.233464i	−0.0626808	−	0.0143146i
$267$		0			0
$268$	4.16411	−	7.21245i	0.254364	−	0.440571i
$269$	−3.17565	−	5.50038i	−0.193623	−	0.335364i	0.752825	−	0.658220i	$-0.228690\pi$
$269$	−3.17565	−	5.50038i	−0.193623	−	0.335364i	−0.946448	+	0.322856i	$0.895357\pi$
$270$		0			0
$271$	−3.93087	+	6.80846i	−0.238783	+	0.413585i	−0.960365	−	0.278744i	$-0.910082\pi$
$271$	−3.93087	+	6.80846i	−0.238783	+	0.413585i	0.721582	+	0.692329i	$0.243415\pi$
$272$	−10.0279			−0.608030
$273$		0			0
$274$	0.888674			0.0536868
$275$	0.0771656	−	0.133655i	0.00465326	−	0.00805968i
$276$		0			0
$277$	2.93784	+	5.08849i	0.176518	+	0.305738i	0.940686	−	0.339280i	$-0.110183\pi$
$277$	2.93784	+	5.08849i	0.176518	+	0.305738i	−0.764168	+	0.645018i	$0.776850\pi$
$278$	−3.33520	+	5.77674i	−0.200032	+	0.346466i
$279$		0			0
$280$	−1.00080	−	3.24594i	−0.0598094	−	0.193982i
$281$	−16.7309			−0.998084			−0.499042	−	0.866578i	$-0.666315\pi$
$281$	−16.7309			−0.998084			−0.499042	+	0.866578i	$0.666315\pi$
$282$		0			0
$283$	10.4479	+	18.0962i	0.621060	+	1.07571i	0.989289	+	0.145973i	$0.0466312\pi$
$283$	10.4479	+	18.0962i	0.621060	+	1.07571i	−0.368228	+	0.929735i	$0.620036\pi$
$284$	2.44173	+	4.22920i	0.144890	+	0.250957i
$285$		0			0
$286$	0.0280066			0.00165606
$287$	−0.235423	+	0.253663i	−0.0138966	+	0.0149732i
$288$		0			0
$289$	3.20732	−	5.55525i	0.188666	−	0.326779i
$290$	−1.17938	−	2.04274i	−0.0692554	−	0.119954i
$291$		0			0
$292$	5.72499	−	9.91598i	0.335030	−	0.580289i
$293$	12.1831			0.711744			0.355872	−	0.934535i	$-0.384184\pi$
$293$	12.1831			0.711744			0.355872	+	0.934535i	$0.384184\pi$
$294$		0			0
$295$	−10.9409			−0.637007
$296$	−1.64703	+	2.85273i	−0.0957315	+	0.165812i
$297$		0			0
$298$	2.52310	+	4.37013i	0.146159	+	0.253155i
$299$	1.26075	−	2.18368i	0.0729108	−	0.126285i
$300$		0			0
$301$	−8.11503	+	8.74376i	−0.467743	+	0.503982i
$302$	−4.68744			−0.269732
$303$		0			0
$304$	−1.54109	−	2.66924i	−0.0883873	−	0.153091i
$305$	−1.09056	−	1.88891i	−0.0624454	−	0.108159i
$306$		0			0
$307$	−25.2971			−1.44378			−0.721890	−	0.692008i	$-0.756726\pi$
$307$	−25.2971			−1.44378			−0.721890	+	0.692008i	$0.756726\pi$
$308$	−0.0516880	−	0.167642i	−0.00294520	−	0.00955228i
$309$		0			0
$310$	0.604606	−	1.04721i	0.0343393	−	0.0594774i
$311$	4.94365	+	8.56265i	0.280329	+	0.485543i	0.971466	−	0.237180i	$-0.0762232\pi$
$311$	4.94365	+	8.56265i	0.280329	+	0.485543i	−0.691137	+	0.722724i	$0.742890\pi$
$312$		0			0
$313$	0.687371	−	1.19056i	0.0388525	−	0.0672945i	−0.845945	−	0.533270i	$-0.820963\pi$
$313$	0.687371	−	1.19056i	0.0388525	−	0.0672945i	0.884798	+	0.465975i	$0.154296\pi$
$314$	2.92373			0.164996
$315$		0			0
$316$	−19.1162			−1.07537
$317$	13.3451	−	23.1144i	0.749535	−	1.29823i	−0.198511	−	0.980099i	$-0.563610\pi$
$317$	13.3451	−	23.1144i	0.749535	−	1.29823i	0.948046	−	0.318134i	$-0.103056\pi$
$318$		0			0
$319$	−0.127014	−	0.219994i	−0.00711140	−	0.0123173i
$320$	1.88512	−	3.26513i	0.105381	−	0.182526i
$321$		0			0
$322$	1.31246	+	0.299731i	0.0731407	+	0.0167034i
$323$	−3.25351			−0.181030
$324$		0			0
$325$	4.21233	+	7.29597i	0.233658	+	0.404707i
$326$	3.57684	+	6.19526i	0.198103	+	0.343124i
$327$		0			0
$328$	0.199228			0.0110005
$329$	6.22502	+	20.1899i	0.343197	+	1.11310i
$330$		0			0
$331$	18.1868	−	31.5004i	0.999635	−	1.73142i	0.476412	−	0.879222i	$-0.341937\pi$
$331$	18.1868	−	31.5004i	0.999635	−	1.73142i	0.523223	−	0.852196i	$-0.324729\pi$
$332$	−9.46819	−	16.3994i	−0.519635	−	0.900034i
$333$		0			0
$334$	4.48564	−	7.76935i	0.245443	−	0.425120i
$335$	3.80918			0.208118
$336$		0			0
$337$	30.0191			1.63524			0.817622	−	0.575756i	$-0.195292\pi$
$337$	30.0191			1.63524			0.817622	+	0.575756i	$0.195292\pi$
$338$	1.81179	−	3.13811i	0.0985482	−	0.170690i
$339$		0			0
$340$	−2.52704	−	4.37696i	−0.137048	−	0.237374i
$341$	0.0651132	−	0.112779i	0.00352608	−	0.00610735i
$342$		0			0
$343$	−14.4755	−	11.5525i	−0.781601	−	0.623779i
$344$	6.86739			0.370265
$345$		0			0
$346$	1.36396	+	2.36245i	0.0733271	+	0.127006i
$347$	14.1044	+	24.4295i	0.757162	+	1.31144i	0.944292	+	0.329108i	$0.106748\pi$
$347$	14.1044	+	24.4295i	0.757162	+	1.31144i	−0.187131	+	0.982335i	$0.559919\pi$
$348$		0			0
$349$	−4.32568			−0.231548			−0.115774	−	0.993276i	$-0.536935\pi$
$349$	−4.32568			−0.231548			−0.115774	+	0.993276i	$0.536935\pi$
$350$	−3.05984	+	3.29690i	−0.163555	+	0.176227i
$351$		0			0
$352$	−0.0767749	+	0.132978i	−0.00409211	+	0.00708775i
$353$	−10.1227	−	17.5330i	−0.538776	−	0.933187i	−0.998970	−	0.0453691i	$-0.985554\pi$
$353$	−10.1227	−	17.5330i	−0.538776	−	0.933187i	0.460194	−	0.887818i	$-0.347780\pi$
$354$		0			0
$355$	−1.11680	+	1.93436i	−0.0592737	+	0.102665i
$356$	15.4304			0.817809
$357$		0			0
$358$	−0.246078			−0.0130056
$359$	6.57989	−	11.3967i	0.347273	−	0.601495i	−0.638491	−	0.769629i	$-0.720441\pi$
$359$	6.57989	−	11.3967i	0.347273	−	0.601495i	0.985764	+	0.168134i	$0.0537743\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	1.84507	−	3.19576i	0.0969747	−	0.167965i
$363$		0			0
$364$	9.33600	+	2.13209i	0.489339	+	0.111752i
$365$	5.23701			0.274118
$366$		0			0
$367$	−12.2002	−	21.1314i	−0.636848	−	1.10305i	−0.986120	−	0.166031i	$-0.946905\pi$
$367$	−12.2002	−	21.1314i	−0.636848	−	1.10305i	0.349273	−	0.937021i	$-0.386429\pi$
$368$	1.97851	+	3.42688i	0.103137	+	0.178638i
$369$		0			0
$370$	−0.722527			−0.0375624
$371$	7.69081	+	1.75638i	0.399287	+	0.0911864i
$372$		0			0
$373$	−1.23438	+	2.13800i	−0.0639136	+	0.110702i	−0.896212	−	0.443627i	$-0.853692\pi$
$373$	−1.23438	+	2.13800i	−0.0639136	+	0.110702i	0.832298	+	0.554328i	$0.187025\pi$
$374$	0.0231973	+	0.0401788i	0.00119950	+	0.00207760i
$375$		0			0
$376$	6.08137	−	10.5332i	0.313623	−	0.543210i
$377$	13.8669			0.714180
$378$		0			0
$379$	−18.7800			−0.964665			−0.482332	−	0.875988i	$-0.660210\pi$
$379$	−18.7800			−0.964665			−0.482332	+	0.875988i	$0.660210\pi$
$380$	0.776711	−	1.34530i	0.0398445	−	0.0690126i
$381$		0			0
$382$	3.63410	+	6.29445i	0.185937	+	0.322052i
$383$	15.8144	−	27.3914i	0.808081	−	1.39964i	−0.106111	−	0.994354i	$-0.533840\pi$
$383$	15.8144	−	27.3914i	0.808081	−	1.39964i	0.914192	−	0.405282i	$-0.132827\pi$
$384$		0			0
$385$	0.0545831	−	0.0588120i	0.00278181	−	0.00299734i
$386$	−6.02449			−0.306639
$387$		0			0
$388$	−2.35121	−	4.07241i	−0.119364	−	0.206745i
$389$	−2.16873	−	3.75636i	−0.109959	−	0.190455i	0.805794	−	0.592196i	$-0.201739\pi$
$389$	−2.16873	−	3.75636i	−0.109959	−	0.190455i	−0.915754	+	0.401741i	$0.868405\pi$
$390$		0			0
$391$	4.17700			0.211240
$392$	0.794126	+	10.6321i	0.0401094	+	0.537000i
$393$		0			0
$394$	1.54018	−	2.66767i	0.0775932	−	0.134395i
$395$	−4.37170	−	7.57201i	−0.219964	−	0.380989i
$396$		0			0
$397$	−0.682778	+	1.18261i	−0.0342676	+	0.0593533i	−0.882651	−	0.470030i	$-0.844243\pi$
$397$	−0.682778	+	1.18261i	−0.0342676	+	0.0593533i	0.848383	+	0.529383i	$0.177577\pi$
$398$	10.1963			0.511093
$399$		0			0
$400$	−13.2209			−0.661047
$401$	11.3302	−	19.6246i	0.565806	−	0.980004i	−0.431169	−	0.902271i	$-0.641899\pi$
$401$	11.3302	−	19.6246i	0.565806	−	0.980004i	0.996974	−	0.0777327i	$-0.0247681\pi$
$402$		0			0
$403$	3.55441	+	6.15642i	0.177058	+	0.306673i
$404$	−6.57015	+	11.3798i	−0.326877	+	0.566168i
$405$		0			0
$406$	2.18140	+	7.07503i	0.108261	+	0.351128i
$407$	−0.0778128			−0.00385704
$408$		0			0
$409$	13.3916	+	23.1950i	0.662174	+	1.14692i	0.980043	+	0.198785i	$0.0636994\pi$
$409$	13.3916	+	23.1950i	0.662174	+	1.14692i	−0.317869	+	0.948135i	$0.602967\pi$
$410$	0.0218496	+	0.0378446i	0.00107907	+	0.00186901i
$411$		0			0
$412$	−5.36145			−0.264140
$413$	33.4796	+	7.64584i	1.64742	+	0.376227i
$414$		0			0
$415$	4.33058	−	7.50078i	0.212580	−	0.368199i
$416$	−4.19100	−	7.25902i	−0.205481	−	0.355903i
$417$		0			0
$418$	−0.00712991	+	0.0123494i	−0.000348735	+	0.000604027i
$419$	−29.9706			−1.46416			−0.732081	−	0.681218i	$-0.761451\pi$
$419$	−29.9706			−1.46416			−0.732081	+	0.681218i	$0.761451\pi$
$420$		0			0
$421$	−28.9616			−1.41150			−0.705750	−	0.708460i	$-0.749390\pi$
$421$	−28.9616			−1.41150			−0.705750	+	0.708460i	$0.749390\pi$
$422$	−3.41783	+	5.91986i	−0.166377	+	0.288174i
$423$		0			0
$424$	−2.27070	−	3.93297i	−0.110275	−	0.191002i
$425$	−6.97796	+	12.0862i	−0.338481	+	0.586266i
$426$		0			0
$427$	2.01713	+	6.54222i	0.0976156	+	0.316600i
$428$	15.8662			0.766924
$429$		0			0
$430$	0.753156	+	1.30450i	0.0363204	+	0.0629088i
$431$	10.4379	+	18.0789i	0.502774	+	0.870831i	0.999995	+	0.00320655i	$0.00102068\pi$
$431$	10.4379	+	18.0789i	0.502774	+	0.870831i	−0.497220	+	0.867624i	$0.665646\pi$
$432$		0			0
$433$	−7.01266			−0.337007			−0.168503	−	0.985701i	$-0.553893\pi$
$433$	−7.01266			−0.337007			−0.168503	+	0.985701i	$0.553893\pi$
$434$	−2.58193	+	2.78197i	−0.123936	+	0.133539i
$435$		0			0
$436$	0.529782	−	0.917609i	0.0253719	−	0.0439455i
$437$	0.641921	+	1.11184i	0.0307072	+	0.0531865i
$438$		0			0
$439$	0.874034	−	1.51387i	0.0417153	−	0.0722531i	−0.844414	−	0.535691i	$-0.820051\pi$
$439$	0.874034	−	1.51387i	0.0417153	−	0.0722531i	0.886129	+	0.463438i	$0.153384\pi$
$440$	−0.0461912			−0.00220208
$441$		0			0
$442$	−2.53259			−0.120463
$443$	−9.44051	+	16.3514i	−0.448532	+	0.776880i	−0.998291	−	0.0584433i	$-0.981386\pi$
$443$	−9.44051	+	16.3514i	−0.448532	+	0.776880i	0.549759	+	0.835323i	$0.314720\pi$
$444$		0			0
$445$	3.52879	+	6.11204i	0.167281	+	0.289738i
$446$	−3.11636	+	5.39769i	−0.147564	+	0.255588i
$447$		0			0
$448$	−8.05028	+	8.67399i	−0.380340	+	0.409808i
$449$	−19.9572			−0.941839			−0.470920	−	0.882176i	$-0.656078\pi$
$449$	−19.9572			−0.941839			−0.470920	+	0.882176i	$0.656078\pi$
$450$		0			0
$451$	0.00235310	+	0.00407569i	0.000110803	+	0.000191917i
$452$	14.0784	+	24.3846i	0.662194	+	1.14695i
$453$		0			0
$454$	2.57763			0.120974
$455$	1.29053	+	4.18562i	0.0605009	+	0.196225i
$456$		0			0
$457$	10.7787	−	18.6693i	0.504208	−	0.873314i	−0.495780	−	0.868448i	$-0.665118\pi$
$457$	10.7787	−	18.6693i	0.504208	−	0.873314i	0.999988	−	0.00486577i	$-0.00154883\pi$
$458$	−1.56011	−	2.70219i	−0.0728991	−	0.126265i
$459$		0			0
$460$	−0.997174	+	1.72716i	−0.0464935	+	0.0805291i
$461$	27.9766			1.30300			0.651500	−	0.758649i	$-0.274140\pi$
$461$	27.9766			1.30300			0.651500	+	0.758649i	$0.274140\pi$
$462$		0			0
$463$	38.8491			1.80547			0.902736	−	0.430195i	$-0.141555\pi$
$463$	38.8491			1.80547			0.902736	+	0.430195i	$0.141555\pi$
$464$	−10.8808	+	18.8460i	−0.505126	+	0.874905i
$465$		0			0
$466$	4.41500	+	7.64701i	0.204521	+	0.354241i
$467$	−4.31966	+	7.48187i	−0.199890	+	0.346219i	−0.948493	−	0.316799i	$-0.897392\pi$
$467$	−4.31966	+	7.48187i	−0.199890	+	0.346219i	0.748603	+	0.663019i	$0.230725\pi$
$468$		0			0
$469$	−11.6562	−	2.66196i	−0.538232	−	0.122918i
$470$	2.66781			0.123057
$471$		0			0
$472$	−9.88480	−	17.1210i	−0.454985	−	0.788057i
$473$	0.0811114	+	0.140489i	0.00372951	+	0.00645970i
$474$		0			0
$475$	−4.28949			−0.196815
$476$	4.67407	+	15.1596i	0.214236	+	0.694839i
$477$		0			0
$478$	5.25586	−	9.10341i	0.240397	−	0.416380i
$479$	7.42013	+	12.8521i	0.339035	+	0.587225i	0.984251	−	0.176774i	$-0.0565663\pi$
$479$	7.42013	+	12.8521i	0.339035	+	0.587225i	−0.645217	+	0.764000i	$0.723233\pi$
$480$		0			0
$481$	2.12383	−	3.67858i	0.0968383	−	0.167729i
$482$	4.39166			0.200034
$483$		0			0
$484$	20.2697			0.921349
$485$	1.07540	−	1.86264i	0.0488313	−	0.0845783i
$486$		0			0
$487$	−8.95213	−	15.5055i	−0.405660	−	0.702623i	0.588738	−	0.808324i	$-0.299625\pi$
$487$	−8.95213	−	15.5055i	−0.405660	−	0.702623i	−0.994398	+	0.105701i	$0.966291\pi$
$488$	1.97058	−	3.41314i	0.0892038	−	0.154506i
$489$		0			0
$490$	−1.93253	+	1.31688i	−0.0873030	+	0.0594906i
$491$	−19.1867			−0.865883			−0.432942	−	0.901422i	$-0.642524\pi$
$491$	−19.1867			−0.865883			−0.432942	+	0.901422i	$0.642524\pi$
$492$		0			0
$493$	11.4856	+	19.8937i	0.517287	+	0.895968i
$494$	−0.389209	−	0.674129i	−0.0175113	−	0.0303305i
$495$		0			0
$496$	−11.1560			−0.500919
$497$	4.76922	−	5.13873i	0.213929	−	0.230504i
$498$		0			0
$499$	−12.2922	+	21.2906i	−0.550272	+	0.953100i	0.447982	+	0.894043i	$0.352143\pi$
$499$	−12.2922	+	21.2906i	−0.550272	+	0.953100i	−0.998255	+	0.0590574i	$0.981191\pi$
$500$	−7.21525	−	12.4972i	−0.322676	−	0.558891i
$501$		0			0
$502$	0.658245	−	1.14011i	0.0293789	−	0.0508857i
$503$	−16.7355			−0.746199			−0.373099	−	0.927791i	$-0.621705\pi$
$503$	−16.7355			−0.746199			−0.373099	+	0.927791i	$0.621705\pi$
$504$		0			0
$505$	−6.01013			−0.267447
$506$	0.00915367	−	0.0158546i	0.000406930	−	0.000704824i
$507$		0			0
$508$	0.942057	+	1.63169i	0.0417970	+	0.0723946i
$509$	−11.7592	+	20.3675i	−0.521217	+	0.902775i	0.478478	+	0.878099i	$0.341189\pi$
$509$	−11.7592	+	20.3675i	−0.521217	+	0.902775i	−0.999696	+	0.0246752i	$0.992145\pi$
$510$		0			0
$511$	−16.0254	−	3.65977i	−0.708922	−	0.161899i
$512$	22.5429			0.996264
$513$		0			0
$514$	5.96864	+	10.3380i	0.263266	+	0.455989i
$515$	−1.22611	−	2.12369i	−0.0540291	−	0.0935811i
$516$		0			0
$517$	0.287311			0.0126359
$518$	2.21095	+	0.504922i	0.0971436	+	0.0221850i
$519$		0			0
$520$	1.26075	−	2.18368i	0.0552874	−	0.0957605i
$521$	3.02740	+	5.24361i	0.132633	+	0.229727i	0.924691	−	0.380719i	$-0.124324\pi$
$521$	3.02740	+	5.24361i	0.132633	+	0.229727i	−0.792058	+	0.610446i	$0.790990\pi$
$522$		0			0
$523$	−18.6378	+	32.2816i	−0.814973	+	1.41157i	0.0943746	+	0.995537i	$0.469915\pi$
$523$	−18.6378	+	32.2816i	−0.814973	+	1.41157i	−0.909347	+	0.416038i	$0.863418\pi$
$524$	−31.2966			−1.36720
$525$		0			0
$526$	10.1330			0.441822
$527$	−5.88809	+	10.1985i	−0.256489	+	0.444252i
$528$		0			0
$529$	10.6759	+	18.4912i	0.464169	+	0.803963i
$530$	0.498062	−	0.862669i	0.0216344	−	0.0374719i
$531$		0			0
$532$	−3.31689	+	3.57388i	−0.143806	+	0.154947i
$533$	−0.256903			−0.0111277
$534$		0			0
$535$	3.62846	+	6.28468i	0.156872	+	0.271711i
$536$	3.44147	+	5.96080i	0.148649	+	0.257467i
$537$		0			0
$538$	2.51726			0.108527
$539$	−0.208125	+	0.141822i	−0.00896458	+	0.00610871i
$540$		0			0
$541$	2.26300	−	3.91963i	0.0972938	−	0.168518i	−0.813270	−	0.581887i	$-0.802315\pi$
$541$	2.26300	−	3.91963i	0.0972938	−	0.168518i	0.910564	+	0.413369i	$0.135648\pi$
$542$	−1.55795	−	2.69846i	−0.0669199	−	0.115909i
$543$		0			0
$544$	6.94263	−	12.0250i	0.297663	−	0.515567i
$545$	0.484625			0.0207590
$546$		0			0
$547$	11.7047			0.500456			0.250228	−	0.968187i	$-0.419494\pi$
$547$	11.7047			0.500456			0.250228	+	0.968187i	$0.419494\pi$
$548$	2.06610	−	3.57859i	0.0882595	−	0.152870i
$549$		0			0
$550$	0.0305837	+	0.0529725i	0.00130409	+	0.00225876i
$551$	−3.53023	+	6.11453i	−0.150393	+	0.260488i
$552$		0			0
$553$	8.08599	+	26.2256i	0.343851	+	1.11523i
$554$	−2.32876			−0.0989396
$555$		0			0
$556$	15.5082	+	26.8610i	0.657694	+	1.13916i
$557$	7.63463	+	13.2236i	0.323490	+	0.560300i	0.981206	−	0.192966i	$-0.0618106\pi$
$557$	7.63463	+	13.2236i	0.323490	+	0.560300i	−0.657716	+	0.753266i	$0.728477\pi$
$558$		0			0
$559$	−8.85545			−0.374546
$560$	−6.70116	−	1.53037i	−0.283176	−	0.0646697i
$561$		0			0
$562$	3.31556	−	5.74271i	0.139858	−	0.242242i
$563$	−15.2869	−	26.4777i	−0.644267	−	1.11590i	−0.984470	−	0.175551i	$-0.943829\pi$
$563$	−15.2869	−	26.4777i	−0.644267	−	1.11590i	0.340203	−	0.940352i	$-0.389504\pi$
$564$		0			0
$565$	−6.43922	+	11.1531i	−0.270900	+	0.469213i
$566$	−8.28177			−0.348109
$567$		0			0
$568$	−4.03598			−0.169346
$569$	−4.32265	+	7.48704i	−0.181215	+	0.313873i	−0.942294	−	0.334785i	$-0.891336\pi$
$569$	−4.32265	+	7.48704i	−0.181215	+	0.313873i	0.761080	+	0.648658i	$0.224670\pi$
$570$		0			0
$571$	−0.587899	−	1.01827i	−0.0246028	−	0.0426133i	0.853462	−	0.521155i	$-0.174499\pi$
$571$	−0.587899	−	1.01827i	−0.0246028	−	0.0426133i	−0.878065	+	0.478542i	$0.841165\pi$
$572$	0.0651132	−	0.112779i	0.00272252	−	0.00471555i
$573$		0			0
$574$	−0.0404135	−	0.131075i	−0.00168683	−	0.00547095i
$575$	5.50703			0.229659
$576$		0			0
$577$	6.17057	+	10.6877i	0.256884	+	0.444936i	0.965406	−	0.260753i	$-0.0839708\pi$
$577$	6.17057	+	10.6877i	0.256884	+	0.444936i	−0.708522	+	0.705689i	$0.750637\pi$
$578$	1.27119	+	2.20176i	0.0528744	+	0.0915811i
$579$		0			0
$580$	−10.9679			−0.455416
$581$	−18.4934	+	19.9263i	−0.767237	+	0.826680i
$582$		0			0
$583$	0.0536390	−	0.0929055i	0.00222150	−	0.00384775i
$584$	4.73148	+	8.19516i	0.195790	+	0.339118i
$585$		0			0
$586$	−2.41432	+	4.18172i	−0.0997345	+	0.172745i
$587$	−19.9966			−0.825350			−0.412675	−	0.910878i	$-0.635405\pi$
$587$	−19.9966			−0.825350			−0.412675	+	0.910878i	$0.635405\pi$
$588$		0			0
$589$	−3.61953			−0.149140
$590$	2.16816	−	3.75536i	0.0892617	−	0.154606i
$591$		0			0
$592$	3.33296	+	5.77286i	0.136984	+	0.237263i
$593$	5.58702	−	9.67700i	0.229431	−	0.397387i	−0.728208	−	0.685356i	$-0.759647\pi$
$593$	5.58702	−	9.67700i	0.229431	−	0.397387i	0.957640	+	0.287969i	$0.0929800\pi$
$594$		0			0
$595$	−4.93586	+	5.31828i	−0.202351	+	0.218028i
$596$	23.4640			0.961125
$597$		0			0
$598$	0.499682	+	0.865475i	0.0204335	+	0.0353919i
$599$	−12.0269	−	20.8313i	−0.491407	−	0.851143i	0.508544	−	0.861036i	$-0.330184\pi$
$599$	−12.0269	−	20.8313i	−0.491407	−	0.851143i	−0.999951	+	0.00989358i	$0.996851\pi$
$600$		0			0
$601$	32.2158			1.31411			0.657054	−	0.753843i	$-0.271802\pi$
$601$	32.2158			1.31411			0.657054	+	0.753843i	$0.271802\pi$
$602$	−1.39305	−	4.51814i	−0.0567766	−	0.184146i
$603$		0			0
$604$	−10.8979	+	18.8758i	−0.443431	+	0.768045i
$605$	4.63549	+	8.02891i	0.188460	+	0.326421i
$606$		0			0
$607$	1.12862	−	1.95482i	0.0458092	−	0.0793438i	−0.842212	−	0.539147i	$-0.818747\pi$
$607$	1.12862	−	1.95482i	0.0458092	−	0.0793438i	0.888021	+	0.459803i	$0.152080\pi$
$608$	4.26777			0.173081
$609$		0			0
$610$	0.864463			0.0350011
$611$	−7.84188	+	13.5825i	−0.317249	+	0.549491i
$612$		0			0
$613$	−6.44356	−	11.1606i	−0.260253	−	0.450771i	0.706056	−	0.708156i	$-0.250473\pi$
$613$	−6.44356	−	11.1606i	−0.260253	−	0.450771i	−0.966309	+	0.257385i	$0.917139\pi$
$614$	5.01310	−	8.68294i	0.202312	−	0.350415i
$615$		0			0
$616$	0.141346	+	0.0322797i	0.00569500	+	0.00130059i
$617$	−25.0627			−1.00899			−0.504493	−	0.863416i	$-0.668321\pi$
$617$	−25.0627			−1.00899			−0.504493	+	0.863416i	$0.668321\pi$
$618$		0			0
$619$	8.41827	+	14.5809i	0.338359	+	0.586055i	0.984124	−	0.177481i	$-0.0567949\pi$
$619$	8.41827	+	14.5809i	0.338359	+	0.586055i	−0.645765	+	0.763536i	$0.723462\pi$
$620$	−2.81133	−	4.86936i	−0.112906	−	0.195558i
$621$		0			0
$622$	−3.91872			−0.157126
$623$	−6.52692	−	21.1690i	−0.261495	−	0.848119i
$624$		0			0
$625$	−7.42361	+	12.8581i	−0.296944	+	0.514323i
$626$	0.272432	+	0.471865i	0.0108886	+	0.0188595i
$627$		0			0
$628$	6.79747	−	11.7736i	0.271248	−	0.469816i
$629$	7.03649			0.280563
$630$		0			0
$631$	−25.8497			−1.02906			−0.514530	−	0.857472i	$-0.672034\pi$
$631$	−25.8497			−1.02906			−0.514530	+	0.857472i	$0.672034\pi$
$632$	7.89939	−	13.6821i	0.314221	−	0.544247i
$633$		0			0
$634$	5.28918	+	9.16112i	0.210060	+	0.363835i
$635$	−0.430880	+	0.746305i	−0.0170989	+	0.0296162i
$636$		0			0
$637$	−1.02402	−	13.7100i	−0.0405732	−	0.543208i
$638$	0.100681			0.00398599
$639$		0			0
$640$	4.34452	+	7.52493i	0.171732	+	0.297449i
$641$	24.6670	+	42.7244i	0.974286	+	1.68751i	0.682270	+	0.731100i	$0.260993\pi$
$641$	24.6670	+	42.7244i	0.974286	+	1.68751i	0.292016	+	0.956413i	$0.405674\pi$
$642$		0			0
$643$	−2.55951			−0.100937			−0.0504686	−	0.998726i	$-0.516071\pi$
$643$	−2.55951			−0.100937			−0.0504686	+	0.998726i	$0.516071\pi$
$644$	4.25836	−	4.58829i	0.167803	−	0.180804i
$645$		0			0
$646$	0.644747	−	1.11673i	0.0253672	−	0.0439373i
$647$	−17.5916	−	30.4696i	−0.691597	−	1.19788i	−0.971314	−	0.237799i	$-0.923574\pi$
$647$	−17.5916	−	30.4696i	−0.691597	−	1.19788i	0.279717	−	0.960082i	$-0.409759\pi$
$648$		0			0
$649$	0.233501	−	0.404435i	0.00916571	−	0.0158755i
$650$	−3.33902			−0.130967
$651$		0			0
$652$	33.2635			1.30270
$653$	−14.0120	+	24.2695i	−0.548332	+	0.949739i	0.450057	+	0.893000i	$0.351404\pi$
$653$	−14.0120	+	24.2695i	−0.548332	+	0.949739i	−0.998389	+	0.0567392i	$0.981930\pi$
$654$		0			0
$655$	−7.15725	−	12.3967i	−0.279657	−	0.484380i
$656$	0.201581	−	0.349149i	0.00787042	−	0.0136320i
$657$		0			0
$658$	−8.16356	−	1.86434i	−0.318249	−	0.0726795i
$659$	−30.0543			−1.17075			−0.585374	−	0.810763i	$-0.699052\pi$
$659$	−30.0543			−1.17075			−0.585374	+	0.810763i	$0.699052\pi$
$660$		0			0
$661$	−4.19955	−	7.27383i	−0.163343	−	0.282919i	0.772722	−	0.634744i	$-0.218895\pi$
$661$	−4.19955	−	7.27383i	−0.163343	−	0.282919i	−0.936066	+	0.351825i	$0.885561\pi$
$662$	7.20811	+	12.4848i	0.280151	+	0.485236i
$663$		0			0
$664$	15.6502			0.607344
$665$	−2.17417	−	0.496522i	−0.0843107	−	0.0192543i
$666$		0			0
$667$	4.53225	−	7.85009i	0.175489	−	0.303957i
$668$	−20.8576	−	36.1264i	−0.807003	−	1.39777i
$669$		0			0
$670$	−0.754862	+	1.30746i	−0.0291629	+	0.0505115i
$671$	0.0930988			0.00359404
$672$		0			0
$673$	12.5476			0.483673			0.241837	−	0.970317i	$-0.422250\pi$
$673$	12.5476			0.483673			0.241837	+	0.970317i	$0.422250\pi$
$674$	−5.94886	+	10.3037i	−0.229141	+	0.396885i
$675$		0			0
$676$	−8.42454	−	14.5917i	−0.324021	−	0.561220i
$677$	−7.58276	+	13.1337i	−0.291429	+	0.504770i	−0.974148	−	0.225911i	$-0.927464\pi$
$677$	−7.58276	+	13.1337i	−0.291429	+	0.504770i	0.682719	+	0.730681i	$0.260797\pi$
$678$		0			0
$679$	−4.59241	+	4.94822i	−0.176241	+	0.189895i
$680$	4.17700			0.160180
$681$		0			0
$682$	0.0258069	+	0.0446988i	0.000988197	+	0.00171161i
$683$	14.8908	+	25.7916i	0.569781	+	0.986890i	0.996587	+	0.0825467i	$0.0263054\pi$
$683$	14.8908	+	25.7916i	0.569781	+	0.986890i	−0.426806	+	0.904343i	$0.640361\pi$
$684$		0			0
$685$	1.88999			0.0722130
$686$	6.83388	−	2.67918i	0.260919	−	0.102292i
$687$		0			0
$688$	6.94850	−	12.0352i	0.264909	−	0.458836i
$689$	2.92805	+	5.07154i	0.111550	+	0.193210i
$690$		0			0
$691$	13.9759	−	24.2070i	0.531668	−	0.920876i	−0.467648	−	0.883915i	$-0.654899\pi$
$691$	13.9759	−	24.2070i	0.531668	−	0.920876i	0.999317	−	0.0369619i	$-0.0117680\pi$
$692$	12.6845			0.482191
$693$		0			0
$694$	−11.1802			−0.424395
$695$	−7.09316	+	12.2857i	−0.269059	+	0.466024i
$696$		0			0
$697$	−0.212787	−	0.368558i	−0.00805989	−	0.0139601i
$698$	0.857216	−	1.48474i	0.0324461	−	0.0561983i
$699$		0			0
$700$	6.16238	+	19.9867i	0.232916	+	0.755426i
$701$	3.66534			0.138438			0.0692190	−	0.997601i	$-0.477949\pi$
$701$	3.66534			0.138438			0.0692190	+	0.997601i	$0.477949\pi$
$702$		0			0
$703$	1.08137	+	1.87298i	0.0407846	+	0.0706409i
$704$	0.0804642	+	0.139368i	0.00303261	+	0.00525263i
$705$		0			0
$706$	8.02402			0.301988
$707$	18.3912	+	4.20005i	0.691671	+	0.157959i
$708$		0			0
$709$	8.48085	−	14.6893i	0.318505	−	0.551667i	−0.661671	−	0.749794i	$-0.730153\pi$
$709$	8.48085	−	14.6893i	0.318505	−	0.551667i	0.980176	+	0.198127i	$0.0634859\pi$
$710$	−0.442631	−	0.766660i	−0.0166117	−	0.0287722i
$711$		0			0
$712$	−6.37630	+	11.0441i	−0.238962	+	0.413894i
$713$	4.64690			0.174028
$714$		0			0
$715$	0.0595632			0.00222754
$716$	−0.572113	+	0.990928i	−0.0213809	+	0.0370327i
$717$		0			0
$718$	2.60786	+	4.51695i	0.0973246	+	0.168571i
$719$	−18.9783	+	32.8715i	−0.707773	+	1.22590i	0.257909	+	0.966169i	$0.416967\pi$
$719$	−18.9783	+	32.8715i	−0.707773	+	1.22590i	−0.965681	+	0.259729i	$0.916367\pi$
$720$		0			0
$721$	2.26785	+	7.35540i	0.0844590	+	0.273929i
$722$	0.396339			0.0147502
$723$		0			0
$724$	−8.57930	−	14.8598i	−0.318847	−	0.552260i
$725$	15.1429	+	26.2282i	0.562392	+	0.974092i
$726$		0			0
$727$	32.1265			1.19150			0.595752	−	0.803168i	$-0.296854\pi$
$727$	32.1265			1.19150			0.595752	+	0.803168i	$0.296854\pi$
$728$	−5.38393	+	5.80106i	−0.199542	+	0.215002i
$729$		0			0
$730$	−1.03782	+	1.79755i	−0.0384113	+	0.0665303i
$731$	−7.33478	−	12.7042i	−0.271287	−	0.469882i
$732$		0			0
$733$	−7.31092	+	12.6629i	−0.270035	+	0.467715i	−0.968871	−	0.247568i	$-0.920369\pi$
$733$	−7.31092	+	12.6629i	−0.270035	+	0.467715i	0.698835	+	0.715282i	$0.253702\pi$
$734$	9.67086			0.356958
$735$		0			0
$736$	−5.47914			−0.201964
$737$	−0.0812952	+	0.140807i	−0.00299455	+	0.00518671i
$738$		0			0
$739$	−14.4596	−	25.0447i	−0.531904	−	0.921286i	−0.999306	−	0.0372406i	$-0.988143\pi$
$739$	−14.4596	−	25.0447i	−0.531904	−	0.921286i	0.467402	−	0.884045i	$-0.345190\pi$
$740$	−1.67982	+	2.90954i	−0.0617515	+	0.106957i
$741$		0			0
$742$	−2.12694	+	2.29173i	−0.0780824	+	0.0841320i
$743$	−20.8522			−0.764992			−0.382496	−	0.923957i	$-0.624935\pi$
$743$	−20.8522			−0.764992			−0.382496	+	0.923957i	$0.624935\pi$
$744$		0			0
$745$	5.36601	+	9.29420i	0.196595	+	0.340513i
$746$	−0.489231	−	0.847372i	−0.0179120	−	0.0310245i
$747$		0			0
$748$	0.215728			0.00788779
$749$	−6.71128	−	21.7670i	−0.245225	−	0.795347i
$750$		0			0
$751$	16.4962	−	28.5722i	0.601954	−	1.04261i	−0.390571	−	0.920573i	$-0.627722\pi$
$751$	16.4962	−	28.5722i	0.601954	−	1.04261i	0.992525	−	0.122042i	$-0.0389442\pi$
$752$	−12.3064	−	21.3153i	−0.448768	−	0.777289i
$753$		0			0
$754$	−2.74799	+	4.75966i	−0.100076	+	0.173336i
$755$	−9.96904			−0.362810
$756$		0			0
$757$	14.8974			0.541455			0.270728	−	0.962656i	$-0.412736\pi$
$757$	14.8974			0.541455			0.270728	+	0.962656i	$0.412736\pi$
$758$	3.72162	−	6.44604i	0.135175	−	0.234131i
$759$		0			0
$760$	0.641921	+	1.11184i	0.0232849	+	0.0403306i
$761$	−5.78718	+	10.0237i	−0.209785	+	0.363358i	−0.951647	−	0.307195i	$-0.900610\pi$
$761$	−5.78718	+	10.0237i	−0.209785	+	0.363358i	0.741862	+	0.670553i	$0.233943\pi$
$762$		0			0
$763$	−1.48296	−	0.338669i	−0.0536869	−	0.0122606i
$764$	33.7961			1.22270
$765$		0			0
$766$	6.26788	+	10.8563i	0.226468	+	0.392253i
$767$	12.7464	+	22.0774i	0.460245	+	0.797168i
$768$		0			0
$769$	−52.4315			−1.89073			−0.945365	−	0.326015i	$-0.894294\pi$
$769$	−52.4315			−1.89073			−0.945365	+	0.326015i	$0.894294\pi$
$770$	0.00936990	+	0.0303898i	0.000337668	+	0.00109517i
$771$		0			0
$772$	−14.0065	+	24.2600i	−0.504105	+	0.873136i
$773$	21.6869	+	37.5628i	0.780023	+	1.35104i	0.931927	+	0.362645i	$0.118126\pi$
$773$	21.6869	+	37.5628i	0.780023	+	1.35104i	−0.151904	+	0.988395i	$0.548541\pi$
$774$		0			0
$775$	−7.76296	+	13.4458i	−0.278854	+	0.482989i
$776$	3.88635			0.139512
$777$		0			0
$778$	1.71911			0.0616329
$779$	0.0654023	−	0.113280i	0.00234328	−	0.00405868i
$780$		0			0
$781$	−0.0476694	−	0.0825658i	−0.00170574	−	0.00295444i
$782$	−0.827752	+	1.43371i	−0.0296004	+	0.0512693i
$783$		0			0
$784$	19.4363	+	9.36592i	0.694152	+	0.334497i
$785$	6.21807			0.221932
$786$		0			0
$787$	−10.6928	−	18.5204i	−0.381156	−	0.660182i	0.610072	−	0.792346i	$-0.291141\pi$
$787$	−10.6928	−	18.5204i	−0.381156	−	0.660182i	−0.991228	+	0.132165i	$0.957807\pi$
$788$	−7.16162	−	12.4043i	−0.255122	−	0.441884i
$789$		0			0
$790$	3.46535			0.123292
$791$	27.4982	−	29.6287i	0.977725	−	1.05348i
$792$		0			0
$793$	−2.54104	+	4.40122i	−0.0902351	+	0.156292i
$794$	−0.270611	−	0.468712i	−0.00960363	−	0.0166340i
$795$		0			0
$796$	23.7056	−	41.0593i	0.840222	−	1.45531i
$797$	44.1477			1.56379			0.781897	−	0.623408i	$-0.214252\pi$
$797$	44.1477			1.56379			0.781897	+	0.623408i	$0.214252\pi$
$798$		0			0
$799$	−25.9811			−0.919144
$800$	9.15329	−	15.8540i	0.323618	−	0.560522i
$801$		0			0
$802$	4.49061	+	7.77797i	0.158569	+	0.274650i
$803$	−0.111768	+	0.193588i	−0.00394421	+	0.00683156i
$804$		0			0
$805$	2.79129	+	0.637456i	0.0983800	+	0.0224674i
$806$	−2.81750			−0.0992422
$807$		0			0
$808$	−5.42996	−	9.40497i	−0.191025	−	0.330866i
$809$	−11.9496	−	20.6974i	−0.420127	−	0.727681i	0.575825	−	0.817573i	$-0.304681\pi$
$809$	−11.9496	−	20.6974i	−0.420127	−	0.727681i	−0.995951	+	0.0898924i	$0.971348\pi$
$810$		0			0
$811$	−45.1710			−1.58617			−0.793083	−	0.609113i	$-0.791526\pi$
$811$	−45.1710			−1.58617			−0.793083	+	0.609113i	$0.791526\pi$
$812$	33.5620	+	7.66465i	1.17779	+	0.268976i
$813$		0			0
$814$	0.0154201	−	0.0267084i	0.000540475	−	0.000936130i
$815$	7.60706	+	13.1758i	0.266464	+	0.461529i
$816$		0			0
$817$	2.25442	−	3.90477i	0.0788721	−	0.136610i
$818$	−10.6152			−0.371153
$819$		0			0
$820$	0.203195			0.00709587
$821$	−10.8031	+	18.7115i	−0.377030	+	0.653035i	−0.990629	−	0.136583i	$-0.956388\pi$
$821$	−10.8031	+	18.7115i	−0.377030	+	0.653035i	0.613599	+	0.789618i	$0.289721\pi$
$822$		0			0
$823$	3.65882	+	6.33726i	0.127538	+	0.220903i	0.922722	−	0.385465i	$-0.125959\pi$
$823$	3.65882	+	6.33726i	0.127538	+	0.220903i	−0.795184	+	0.606368i	$0.792626\pi$
$824$	2.21551	−	3.83738i	0.0771810	−	0.133681i
$825$		0			0
$826$	−9.25898	+	9.97634i	−0.322161	+	0.347121i
$827$	−46.0507			−1.60134			−0.800669	−	0.599106i	$-0.795523\pi$
$827$	−46.0507			−1.60134			−0.800669	+	0.599106i	$0.795523\pi$
$828$		0			0
$829$	−16.0223	−	27.7515i	−0.556478	−	0.963848i	−0.997787	−	0.0664930i	$-0.978819\pi$
$829$	−16.0223	−	27.7515i	−0.556478	−	0.963848i	0.441309	−	0.897355i	$-0.354514\pi$
$830$	1.71637	+	2.97285i	0.0595762	+	0.103189i
$831$		0			0
$832$	−8.78479			−0.304558
$833$	18.8204	−	12.8247i	0.652089	−	0.444351i
$834$		0			0
$835$	9.53986	−	16.5235i	0.330141	−	0.571820i
$836$	0.0331530	+	0.0574227i	0.00114662	+	0.00198601i
$837$		0			0
$838$	5.93926	−	10.2871i	0.205168	−	0.355362i
$839$	−12.5994			−0.434980			−0.217490	−	0.976063i	$-0.569787\pi$
$839$	−12.5994			−0.434980			−0.217490	+	0.976063i	$0.569787\pi$
$840$		0			0
$841$	20.8500			0.718964
$842$	5.73929	−	9.94075i	0.197789	−	0.342581i
$843$		0			0
$844$	15.8924	+	27.5265i	0.547039	+	0.947500i
$845$	3.85323	−	6.67399i	0.132555	−	0.229592i
$846$		0			0
$847$	−8.57390	−	27.8081i	−0.294603	−	0.955497i
$848$	−9.19008			−0.315589
$849$		0			0
$850$	−2.76564	−	4.79022i	−0.0948605	−	0.164303i
$851$	−1.38830	−	2.40461i	−0.0475905	−	0.0824291i
$852$		0			0
$853$	−37.1154			−1.27081			−0.635403	−	0.772181i	$-0.719166\pi$
$853$	−37.1154			−1.27081			−0.635403	+	0.772181i	$0.719166\pi$
$854$	−2.64528	−	0.604111i	−0.0905196	−	0.0206723i
$855$		0			0
$856$	−6.55640	+	11.3560i	−0.224093	+	0.388141i
$857$	25.2112	+	43.6670i	0.861197	+	1.49164i	0.870774	+	0.491683i	$0.163618\pi$
$857$	25.2112	+	43.6670i	0.861197	+	1.49164i	−0.00957724	+	0.999954i	$0.503049\pi$
$858$		0			0
$859$	−4.92248	+	8.52598i	−0.167953	+	0.290903i	−0.937700	−	0.347446i	$-0.887049\pi$
$859$	−4.92248	+	8.52598i	−0.167953	+	0.290903i	0.769747	+	0.638349i	$0.220382\pi$
$860$	7.00413			0.238839
$861$		0			0
$862$	−8.27386			−0.281809
$863$	16.3611	−	28.3382i	0.556937	−	0.964643i	−0.440813	−	0.897599i	$-0.645310\pi$
$863$	16.3611	−	28.3382i	0.556937	−	0.964643i	0.997750	−	0.0670442i	$-0.0213568\pi$
$864$		0			0
$865$	2.90082	+	5.02437i	0.0986308	+	0.170834i
$866$	1.38969	−	2.40702i	0.0472237	−	0.0817938i
$867$		0			0
$868$	5.19989	+	16.8650i	0.176496	+	0.572436i
$869$	0.373202			0.0126600
$870$		0			0
$871$	−4.43775	−	7.68641i	−0.150368	−	0.260444i
$872$	0.437843	+	0.758367i	0.0148272	+	0.0256815i
$873$		0			0
$874$	−0.508836			−0.0172116
$875$	−14.0930	+	15.1848i	−0.476429	+	0.513341i
$876$		0			0
$877$	−3.43836	+	5.95541i	−0.116105	+	0.201100i	−0.918221	−	0.396069i	$-0.870374\pi$
$877$	−3.43836	+	5.95541i	−0.116105	+	0.201100i	0.802116	+	0.597168i	$0.203708\pi$
$878$	0.346413	+	0.600005i	0.0116909	+	0.0202492i
$879$		0			0
$880$	−0.0467368	+	0.0809504i	−0.00157550	+	0.00272884i
$881$	40.9688			1.38027			0.690137	−	0.723679i	$-0.257550\pi$
$881$	40.9688			1.38027			0.690137	+	0.723679i	$0.257550\pi$
$882$		0			0
$883$	3.64432			0.122641			0.0613206	−	0.998118i	$-0.480469\pi$
$883$	3.64432			0.122641			0.0613206	+	0.998118i	$0.480469\pi$
$884$	−5.88809	+	10.1985i	−0.198038	+	0.343012i
$885$		0			0
$886$	−3.74164	−	6.48070i	−0.125703	−	0.217724i
$887$	3.14427	−	5.44604i	0.105574	−	0.182860i	−0.808398	−	0.588636i	$-0.799665\pi$
$887$	3.14427	−	5.44604i	0.105574	−	0.182860i	0.913973	+	0.405776i	$0.132999\pi$
$888$		0			0
$889$	1.84004	−	1.98260i	0.0617130	−	0.0664944i
$890$	−2.79719			−0.0937620
$891$		0			0
$892$	14.4906	+	25.0985i	0.485181	+	0.840359i
$893$	−3.99277	−	6.91568i	−0.133613	−	0.231424i
$894$		0			0
$895$	−0.523348			−0.0174936
$896$	−8.03571	−	26.0626i	−0.268454	−	0.870689i
$897$		0			0
$898$	3.95491	−	6.85010i	0.131977	−	0.228591i
$899$	12.7777	+	22.1317i	0.426162	+	0.738133i
$900$		0			0
$901$	−4.85049	+	8.40129i	−0.161593	+	0.279888i
$902$	−0.00186525			−6.21060e−5
$903$		0			0
$904$	−23.2705			−0.773966
$905$	3.92402	−	6.79659i	0.130439	−	0.225926i
$906$		0			0
$907$	25.8334	+	44.7447i	0.857782	+	1.48572i	0.874039	+	0.485855i	$0.161492\pi$
$907$	25.8334	+	44.7447i	0.857782	+	1.48572i	−0.0162569	+	0.999868i	$0.505175\pi$
$908$	5.99281	−	10.3798i	0.198878	−	0.344467i
$909$		0			0
$910$	−1.69241	−	0.386501i	−0.0561029	−	0.0128124i
$911$	48.0342			1.59144			0.795722	−	0.605662i	$-0.207091\pi$
$911$	48.0342			1.59144			0.795722	+	0.605662i	$0.207091\pi$
$912$		0			0
$913$	0.184846	+	0.320162i	0.00611750	+	0.0105958i
$914$	4.27203	+	7.39937i	0.141306	+	0.244749i
$915$		0			0
$916$	−14.5086			−0.479376
$917$	13.2382	+	42.9360i	0.437164	+	1.41787i
$918$		0			0
$919$	−11.8773	+	20.5720i	−0.391794	+	0.678608i	−0.992686	−	0.120722i	$-0.961479\pi$
$919$	−11.8773	+	20.5720i	−0.391794	+	0.678608i	0.600892	+	0.799330i	$0.294812\pi$
$920$	−0.824124	−	1.42743i	−0.0271706	−	0.0470608i
$921$		0			0
$922$	−5.54410	+	9.60267i	−0.182585	+	0.316247i
$923$	5.20437			0.171304
$924$		0			0
$925$	9.27704			0.305027
$926$	−7.69870	+	13.3345i	−0.252995	+	0.438200i
$927$		0			0
$928$	−15.0662	−	26.0954i	−0.494572	−	0.856625i
$929$	−2.86320	+	4.95920i	−0.0939384	+	0.162706i	−0.909165	−	0.416436i	$-0.863279\pi$
$929$	−2.86320	+	4.95920i	−0.0939384	+	0.162706i	0.815227	+	0.579142i	$0.196612\pi$
$930$		0			0
$931$	6.30603	+	3.03874i	0.206672	+	0.0995907i
$932$	41.0582			1.34491
$933$		0			0
$934$	−1.71205	−	2.96535i	−0.0560199	−	0.0970293i
$935$	0.0493349	+	0.0854506i	0.00161343	+	0.00279453i
$936$		0			0
$937$	−24.1920			−0.790319			−0.395159	−	0.918613i	$-0.629311\pi$
$937$	−24.1920			−0.790319			−0.395159	+	0.918613i	$0.629311\pi$
$938$	3.22359	−	3.47334i	0.105254	−	0.113409i
$939$		0			0
$940$	6.20246	−	10.7430i	0.202302	−	0.350397i
$941$	3.07866	+	5.33239i	0.100361	+	0.173831i	0.911834	−	0.410560i	$-0.134667\pi$
$941$	3.07866	+	5.33239i	0.100361	+	0.173831i	−0.811472	+	0.584391i	$0.801333\pi$
$942$		0			0
$943$	−0.0839662	+	0.145434i	−0.00273431	+	0.00473597i
$944$	−40.0062			−1.30209
$945$		0			0
$946$	−0.0642952			−0.00209042
$947$	−12.7265	+	22.0430i	−0.413557	+	0.716301i	−0.995276	−	0.0970888i	$-0.969047\pi$
$947$	−12.7265	+	22.0430i	−0.413557	+	0.716301i	0.581719	+	0.813390i	$0.302380\pi$
$948$		0			0
$949$	−6.10121	−	10.5676i	−0.198054	−	0.343039i
$950$	0.850046	−	1.47232i	0.0275791	−	0.0477684i
$951$		0			0
$952$	−12.7817	−	2.91900i	−0.414258	−	0.0946054i
$953$	−11.3961			−0.369157			−0.184579	−	0.982818i	$-0.559092\pi$
$953$	−11.3961			−0.369157			−0.184579	+	0.982818i	$0.559092\pi$
$954$		0			0
$955$	7.72885	+	13.3868i	0.250100	+	0.433186i
$956$	−24.4390	−	42.3295i	−0.790412	−	1.36903i
$957$		0			0
$958$	−5.88177			−0.190031
$959$	−5.78343	−	1.32078i	−0.186757	−	0.0426502i
$960$		0			0
$961$	8.94952	−	15.5010i	0.288694	−	0.500033i
$962$	0.841755	+	1.45796i	0.0271393	+	0.0470066i
$963$		0			0
$964$	10.2103	−	17.6847i	0.328851	−	0.569586i
$965$	−12.8126			−0.412453
$966$		0			0
$967$	45.9401			1.47733			0.738667	−	0.674071i	$-0.235456\pi$
$967$	45.9401			1.47733			0.738667	+	0.674071i	$0.235456\pi$
$968$	−8.37604	+	14.5077i	−0.269216	+	0.466296i
$969$		0			0
$970$	0.426222	+	0.738238i	0.0136852	+	0.0237034i
$971$	−0.347191	+	0.601352i	−0.0111419	+	0.0192983i	−0.871543	−	0.490320i	$-0.836880\pi$
$971$	−0.347191	+	0.601352i	−0.0111419	+	0.0192983i	0.860401	+	0.509618i	$0.170213\pi$
$972$		0			0
$973$	30.2909	−	32.6377i	0.971080	−	1.04632i
$974$	7.09615			0.227375
$975$		0			0
$976$	−3.98770	−	6.90690i	−0.127643	−	0.221085i
$977$	−18.3718	−	31.8208i	−0.587765	−	1.01804i	−0.994525	−	0.104503i	$-0.966675\pi$
$977$	−18.3718	−	31.8208i	−0.587765	−	1.01804i	0.406760	−	0.913535i	$-0.366659\pi$
$978$		0			0
$979$	−0.301244			−0.00962781
$980$	0.809939	+	10.8438i	0.0258725	+	0.346391i
$981$		0			0
$982$	3.80221	−	6.58563i	0.121334	−	0.210156i
$983$	−6.67886	−	11.5681i	−0.213022	−	0.368966i	0.739637	−	0.673006i	$-0.234997\pi$
$983$	−6.67886	−	11.5681i	−0.213022	−	0.368966i	−0.952659	+	0.304041i	$0.901664\pi$
$984$		0			0
$985$	3.27559	−	5.67349i	0.104369	−	0.180772i
$986$	−9.10440			−0.289943
$987$		0			0
$988$	−3.61953			−0.115152
$989$	−2.89431	+	5.01310i	−0.0920339	+	0.159407i
$990$		0			0
$991$	−20.1635	−	34.9241i	−0.640514	−	1.10940i	−0.985318	−	0.170728i	$-0.945388\pi$
$991$	−20.1635	−	34.9241i	−0.640514	−	1.10940i	0.344805	−	0.938674i	$-0.387945\pi$
$992$	7.72366	−	13.3778i	0.245226	−	0.424745i
$993$		0			0
$994$	0.818700	+	2.65532i	0.0259676	+	0.0842217i
$995$	21.6850			0.687460
$996$		0			0
$997$	3.94737	+	6.83704i	0.125014	+	0.216531i	0.921739	−	0.387812i	$-0.126769\pi$
$997$	3.94737	+	6.83704i	0.125014	+	0.216531i	−0.796724	+	0.604343i	$0.793436\pi$
$998$	−4.87185	−	8.43830i	−0.154216	−	0.267110i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.k.856.2		8
3.2	odd	2		399.2.j.d.58.3	✓	8
7.2	even	3		8379.2.a.br.1.3		4
7.4	even	3	inner	1197.2.j.k.172.2		8
7.5	odd	6		8379.2.a.bt.1.3		4
21.2	odd	6		2793.2.a.bc.1.2		4
21.5	even	6		2793.2.a.bd.1.2		4
21.11	odd	6		399.2.j.d.172.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.d.58.3	✓	8	3.2	odd	2
399.2.j.d.172.3	yes	8	21.11	odd	6
1197.2.j.k.172.2		8	7.4	even	3	inner
1197.2.j.k.856.2		8	1.1	even	1	trivial
2793.2.a.bc.1.2		4	21.2	odd	6
2793.2.a.bd.1.2		4	21.5	even	6
8379.2.a.br.1.3		4	7.2	even	3
8379.2.a.bt.1.3		4	7.5	odd	6

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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.198169 + 0.343239i) q^{2} +(0.921458 + 1.59601i) q^{4} +(-0.421458 + 0.729986i) q^{5} +(1.79981 - 1.93925i) q^{7} -1.52310 q^{8} +(-0.167040 - 0.289322i) q^{10} +(-0.0179894 - 0.0311586i) q^{11} +1.96402 q^{13} +(0.308961 + 1.00206i) q^{14} +(-1.54109 + 2.66924i) q^{16} +(1.62676 + 2.81763i) q^{17} +(-0.500000 + 0.866025i) q^{19} -1.55342 q^{20} +0.0142598 q^{22} +(0.641921 - 1.11184i) q^{23} +(2.14475 + 3.71481i) q^{25} +(-0.389209 + 0.674129i) q^{26} +(4.75351 + 1.08558i) q^{28} +7.06045 q^{29} +(1.80976 + 3.13460i) q^{31} +(-2.13389 - 3.69600i) q^{32} -1.28949 q^{34} +(0.657084 + 2.13115i) q^{35} +(1.08137 - 1.87298i) q^{37} +(-0.198169 - 0.343239i) q^{38} +(0.641921 - 1.11184i) q^{40} -0.130805 q^{41} -4.50884 q^{43} +(0.0331530 - 0.0574227i) q^{44} +(0.254418 + 0.440665i) q^{46} +(-3.99277 + 6.91568i) q^{47} +(-0.521390 - 6.98056i) q^{49} -1.70009 q^{50} +(1.80976 + 3.13460i) q^{52} +(1.49085 + 2.58222i) q^{53} +0.0303272 q^{55} +(-2.74128 + 2.95366i) q^{56} +(-1.39916 + 2.42342i) q^{58} +(6.48994 + 11.2409i) q^{59} +(-1.29380 + 2.24092i) q^{61} -1.43456 q^{62} -4.47286 q^{64} +(-0.827752 + 1.43371i) q^{65} +(-2.25952 - 3.91361i) q^{67} +(-2.99798 + 5.19265i) q^{68} +(-0.861707 - 0.196791i) q^{70} +2.64985 q^{71} +(-3.10649 - 5.38059i) q^{73} +(0.428588 + 0.742336i) q^{74} -1.84292 q^{76} +(-0.0928019 - 0.0211935i) q^{77} +(-5.18641 + 8.98312i) q^{79} +(-1.29900 - 2.24994i) q^{80} +(0.0259214 - 0.0448973i) q^{82} -10.2752 q^{83} -2.74244 q^{85} +(0.893513 - 1.54761i) q^{86} +(0.0273996 + 0.0474576i) q^{88} +(4.18641 - 7.25107i) q^{89} +(3.53486 - 3.80873i) q^{91} +2.36601 q^{92} +(-1.58249 - 2.74095i) q^{94} +(-0.421458 - 0.729986i) q^{95} -2.55162 q^{97} +(2.49932 + 1.20437i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} + 2 q^{7} + 6 q^{8} + 3 q^{10} - 2 q^{11} + 12 q^{13} - 2 q^{14} + 4 q^{16} - 2 q^{17} - 4 q^{19} - 24 q^{20} - 12 q^{22} + 5 q^{23} + 4 q^{25} - 6 q^{26} + 8 q^{28} + 8 q^{29} - 17 q^{31}+ \cdots - 27 q^{98}+O(q^{100}) \) 8 * q + 4 * q^5 + 2 * q^7 + 6 * q^8 + 3 * q^10 - 2 * q^11 + 12 * q^13 - 2 * q^14 + 4 * q^16 - 2 * q^17 - 4 * q^19 - 24 * q^20 - 12 * q^22 + 5 * q^23 + 4 * q^25 - 6 * q^26 + 8 * q^28 + 8 * q^29 - 17 * q^31 + 4 * q^32 + 16 * q^34 + 20 * q^35 + 3 * q^37 + 5 * q^40 - 14 * q^41 - 30 * q^43 + 17 * q^44 - q^46 + 16 * q^47 + 14 * q^49 + 28 * q^50 - 17 * q^52 + 4 * q^53 + 30 * q^55 - 18 * q^56 + 5 * q^58 + 17 * q^59 + 9 * q^61 + 14 * q^62 - 26 * q^64 + 23 * q^65 + 5 * q^67 - 10 * q^68 + 33 * q^70 - 12 * q^71 - 15 * q^73 - 10 * q^74 + 4 * q^77 - 5 * q^79 - 25 * q^80 - 31 * q^82 - 68 * q^83 - 24 * q^85 + 17 * q^86 - 11 * q^88 - 3 * q^89 + 45 * q^91 - 14 * q^92 + 6 * q^94 + 4 * q^95 + 22 * q^97 - 27 * q^98

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