LMFDB - Embedded newform 592.2.be.f.415.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 885 x^{16} + 9292 x^{14} + 58264 x^{12} + 224256 x^{10} + 523884 x^{8} + 706272 x^{6} + \cdots + 144 $ x^20 + 46x^18 + 885x^16 + 9292x^14 + 58264x^12 + 224256x^10 + 523884x^8 + 706272x^6 + 490896x^4 + 133632*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			415.3
Root			$1.04018i$ of defining polynomial
Character	$\chi$	$=$	592.415
Dual form			592.2.be.f.495.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.520091 + 0.900825i) q^{3} +(-3.71558 + 0.995586i) q^{5} +(0.391848 + 0.226234i) q^{7} +(0.959010 + 1.66105i) q^{9} +O(q^{10})$	\(q+(-0.520091 + 0.900825i) q^{3} +(-3.71558 + 0.995586i) q^{5} +(0.391848 + 0.226234i) q^{7} +(0.959010 + 1.66105i) q^{9} -3.70591 q^{11} +(2.76896 - 0.741941i) q^{13} +(1.03559 - 3.86488i) q^{15} +(1.35886 - 5.07133i) q^{17} +(-2.05859 - 7.68276i) q^{19} +(-0.407594 + 0.235324i) q^{21} +(-3.08303 + 3.08303i) q^{23} +(8.48420 - 4.89836i) q^{25} -5.11564 q^{27} +(-1.61065 + 1.61065i) q^{29} +(-7.18477 - 7.18477i) q^{31} +(1.92741 - 3.33837i) q^{33} +(-1.68118 - 0.450470i) q^{35} +(-6.05947 - 0.531801i) q^{37} +(-0.771754 + 2.88022i) q^{39} +(6.45703 + 3.72797i) q^{41} +(5.69590 - 5.69590i) q^{43} +(-5.21700 - 5.21700i) q^{45} +7.98636i q^{47} +(-3.39764 - 5.88488i) q^{49} +(3.86165 + 3.86165i) q^{51} +(-2.69388 - 4.66593i) q^{53} +(13.7696 - 3.68955i) q^{55} +(7.99148 + 2.14131i) q^{57} +(1.98576 + 0.532082i) q^{59} +(2.32349 + 8.67138i) q^{61} +0.867841i q^{63} +(-9.54962 + 5.51348i) q^{65} +(-2.55365 + 4.42306i) q^{67} +(-1.17381 - 4.38072i) q^{69} +(-8.28367 - 4.78258i) q^{71} +4.35299i q^{73} +10.1904i q^{75} +(-1.45215 - 0.838401i) q^{77} +(0.277275 + 1.03481i) q^{79} +(-0.216430 + 0.374867i) q^{81} +(2.79430 - 1.61329i) q^{83} +20.1958i q^{85} +(-0.613230 - 2.28860i) q^{87} +(-0.454613 - 0.121813i) q^{89} +(1.25286 + 0.335704i) q^{91} +(10.2090 - 2.73548i) q^{93} +(15.2977 + 26.4964i) q^{95} +(-1.98578 - 1.98578i) q^{97} +(-3.55400 - 6.15571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 4 q^{5} + 6 q^{7} - 16 q^{9}+O(q^{10}) $ 20 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 - 16 * q^9	$ 20 q + 4 q^{3} - 4 q^{5} + 6 q^{7} - 16 q^{9} - 4 q^{11} + 4 q^{13} - 8 q^{15} - 4 q^{17} - 10 q^{19} - 18 q^{21} - 8 q^{23} + 42 q^{25} - 68 q^{27} - 8 q^{29} - 28 q^{31} - 20 q^{33} + 10 q^{35} - 24 q^{37} + 14 q^{39} - 6 q^{41} - 32 q^{43} + 8 q^{45} - 12 q^{49} + 58 q^{51} + 6 q^{53} - 26 q^{55} - 2 q^{57} + 56 q^{59} - 8 q^{61} + 6 q^{65} - 20 q^{67} + 26 q^{69} + 30 q^{71} + 60 q^{77} - 50 q^{79} - 22 q^{81} - 36 q^{83} + 32 q^{87} - 20 q^{89} + 50 q^{91} - 50 q^{93} + 72 q^{95} + 32 q^{97} + 14 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 - 16 * q^9 - 4 * q^11 + 4 * q^13 - 8 * q^15 - 4 * q^17 - 10 * q^19 - 18 * q^21 - 8 * q^23 + 42 * q^25 - 68 * q^27 - 8 * q^29 - 28 * q^31 - 20 * q^33 + 10 * q^35 - 24 * q^37 + 14 * q^39 - 6 * q^41 - 32 * q^43 + 8 * q^45 - 12 * q^49 + 58 * q^51 + 6 * q^53 - 26 * q^55 - 2 * q^57 + 56 * q^59 - 8 * q^61 + 6 * q^65 - 20 * q^67 + 26 * q^69 + 30 * q^71 + 60 * q^77 - 50 * q^79 - 22 * q^81 - 36 * q^83 + 32 * q^87 - 20 * q^89 + 50 * q^91 - 50 * q^93 + 72 * q^95 + 32 * q^97 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.520091	+	0.900825i	−0.300275	+	0.520091i	−0.976198	−	0.216881i	$-0.930412\pi$
$3$	−0.520091	+	0.900825i	−0.300275	+	0.520091i	0.675923	+	0.736972i	$0.263745\pi$
$4$		0			0
$5$	−3.71558	+	0.995586i	−1.66166	+	0.445240i	−0.962843	−	0.270063i	$-0.912955\pi$
$5$	−3.71558	+	0.995586i	−1.66166	+	0.445240i	−0.698814	+	0.715303i	$0.746289\pi$
$6$		0			0
$7$	0.391848	+	0.226234i	0.148105	+	0.0855083i	0.572221	−	0.820099i	$-0.306082\pi$
$7$	0.391848	+	0.226234i	0.148105	+	0.0855083i	−0.424116	+	0.905608i	$0.639415\pi$
$8$		0			0
$9$	0.959010	+	1.66105i	0.319670	+	0.553685i
$10$		0			0
$11$	−3.70591			−1.11737			−0.558687	−	0.829379i	$-0.688695\pi$
$11$	−3.70591			−1.11737			−0.558687	+	0.829379i	$0.688695\pi$
$12$		0			0
$13$	2.76896	−	0.741941i	0.767971	−	0.205777i	0.146496	−	0.989211i	$-0.453200\pi$
$13$	2.76896	−	0.741941i	0.767971	−	0.205777i	0.621475	+	0.783434i	$0.286534\pi$
$14$		0			0
$15$	1.03559	−	3.86488i	0.267389	−	0.997908i
$16$		0			0
$17$	1.35886	−	5.07133i	0.329572	−	1.22998i	−0.580064	−	0.814571i	$-0.696973\pi$
$17$	1.35886	−	5.07133i	0.329572	−	1.22998i	0.909636	−	0.415407i	$-0.136361\pi$
$18$		0			0
$19$	−2.05859	−	7.68276i	−0.472273	−	1.76255i	−0.631574	−	0.775316i	$-0.717591\pi$
$19$	−2.05859	−	7.68276i	−0.472273	−	1.76255i	0.159301	−	0.987230i	$-0.449076\pi$
$20$		0			0
$21$	−0.407594	+	0.235324i	−0.0889443	+	0.0513520i
$22$		0			0
$23$	−3.08303	+	3.08303i	−0.642856	+	0.642856i	−0.951256	−	0.308401i	$-0.900206\pi$
$23$	−3.08303	+	3.08303i	−0.642856	+	0.642856i	0.308401	+	0.951256i	$0.400206\pi$
$24$		0			0
$25$	8.48420	−	4.89836i	1.69684	−	0.979671i
$26$		0			0
$27$	−5.11564			−0.984505
$28$		0			0
$29$	−1.61065	+	1.61065i	−0.299091	+	0.299091i	−0.840658	−	0.541567i	$-0.817831\pi$
$29$	−1.61065	+	1.61065i	−0.299091	+	0.299091i	0.541567	+	0.840658i	$0.317831\pi$
$30$		0			0
$31$	−7.18477	−	7.18477i	−1.29042	−	1.29042i	−0.934525	−	0.355898i	$-0.884175\pi$
$31$	−7.18477	−	7.18477i	−1.29042	−	1.29042i	−0.355898	−	0.934525i	$-0.615825\pi$
$32$		0			0
$33$	1.92741	−	3.33837i	0.335519	−	0.581136i
$34$		0			0
$35$	−1.68118	−	0.450470i	−0.284171	−	0.0761434i
$36$		0			0
$37$	−6.05947	−	0.531801i	−0.996171	−	0.0874275i
$37$	−6.05947	−	0.531801i	−0.996171	−	0.0874275i
$38$		0			0
$39$	−0.771754	+	2.88022i	−0.123580	+	0.461205i
$40$		0			0
$41$	6.45703	+	3.72797i	1.00842	+	0.582211i	0.910728	−	0.413006i	$-0.135521\pi$
$41$	6.45703	+	3.72797i	1.00842	+	0.582211i	0.0976907	+	0.995217i	$0.468854\pi$
$42$		0			0
$43$	5.69590	−	5.69590i	0.868617	−	0.868617i	−0.123702	−	0.992319i	$-0.539477\pi$
$43$	5.69590	−	5.69590i	0.868617	−	0.868617i	0.992319	+	0.123702i	$0.0394767\pi$
$44$		0			0
$45$	−5.21700	−	5.21700i	−0.777704	−	0.777704i
$46$		0			0
$47$			7.98636i			1.16493i	0.812856	+	0.582465i	$0.197912\pi$
$47$			7.98636i			1.16493i	−0.812856	+	0.582465i	$0.802088\pi$
$48$		0			0
$49$	−3.39764	−	5.88488i	−0.485377	−	0.840697i
$50$		0			0
$51$	3.86165	+	3.86165i	0.540739	+	0.540739i
$52$		0			0
$53$	−2.69388	−	4.66593i	−0.370033	−	0.640915i	0.619537	−	0.784967i	$-0.287320\pi$
$53$	−2.69388	−	4.66593i	−0.370033	−	0.640915i	−0.989570	+	0.144052i	$0.953987\pi$
$54$		0			0
$55$	13.7696	−	3.68955i	1.85669	−	0.497499i
$56$		0			0
$57$	7.99148	+	2.14131i	1.05850	+	0.283623i
$58$		0			0
$59$	1.98576	+	0.532082i	0.258524	+	0.0692712i	0.385753	−	0.922602i	$-0.373942\pi$
$59$	1.98576	+	0.532082i	0.258524	+	0.0692712i	−0.127229	+	0.991873i	$0.540608\pi$
$60$		0			0
$61$	2.32349	+	8.67138i	0.297492	+	1.11026i	0.939218	+	0.343322i	$0.111552\pi$
$61$	2.32349	+	8.67138i	0.297492	+	1.11026i	−0.641726	+	0.766934i	$0.721781\pi$
$62$		0			0
$63$			0.867841i			0.109338i
$64$		0			0
$65$	−9.54962	+	5.51348i	−1.18448	+	0.683863i
$66$		0			0
$67$	−2.55365	+	4.42306i	−0.311979	+	0.540363i	−0.978791	−	0.204863i	$-0.934325\pi$
$67$	−2.55365	+	4.42306i	−0.311979	+	0.540363i	0.666812	+	0.745226i	$0.267658\pi$
$68$		0			0
$69$	−1.17381	−	4.38072i	−0.141310	−	0.527377i
$70$		0			0
$71$	−8.28367	−	4.78258i	−0.983091	−	0.567588i	−0.0798889	−	0.996804i	$-0.525457\pi$
$71$	−8.28367	−	4.78258i	−0.983091	−	0.567588i	−0.903202	+	0.429216i	$0.858790\pi$
$72$		0			0
$73$			4.35299i			0.509479i	0.967010	+	0.254739i	$0.0819897\pi$
$73$			4.35299i			0.509479i	−0.967010	+	0.254739i	$0.918010\pi$
$74$		0			0
$75$			10.1904i			1.17668i
$76$		0			0
$77$	−1.45215	−	0.838401i	−0.165488	−	0.0955447i
$78$		0			0
$79$	0.277275	+	1.03481i	0.0311959	+	0.116425i	0.979768	−	0.200136i	$-0.0641385\pi$
$79$	0.277275	+	1.03481i	0.0311959	+	0.116425i	−0.948572	+	0.316561i	$0.897472\pi$
$80$		0			0
$81$	−0.216430	+	0.374867i	−0.0240477	+	0.0416519i
$82$		0			0
$83$	2.79430	−	1.61329i	0.306714	−	0.177082i	−0.338741	−	0.940880i	$-0.610001\pi$
$83$	2.79430	−	1.61329i	0.306714	−	0.177082i	0.645455	+	0.763798i	$0.276668\pi$
$84$		0			0
$85$			20.1958i			2.19054i
$86$		0			0
$87$	−0.613230	−	2.28860i	−0.0657451	−	0.245364i
$88$		0			0
$89$	−0.454613	−	0.121813i	−0.0481889	−	0.0129122i	0.234644	−	0.972081i	$-0.424608\pi$
$89$	−0.454613	−	0.121813i	−0.0481889	−	0.0129122i	−0.282833	+	0.959169i	$0.591274\pi$
$90$		0			0
$91$	1.25286	+	0.335704i	0.131336	+	0.0351913i
$92$		0			0
$93$	10.2090	−	2.73548i	1.05862	−	0.283656i
$94$		0			0
$95$	15.2977	+	26.4964i	1.56951	+	2.71847i
$96$		0			0
$97$	−1.98578	−	1.98578i	−0.201626	−	0.201626i	0.599071	−	0.800696i	$-0.295537\pi$
$97$	−1.98578	−	1.98578i	−0.201626	−	0.201626i	−0.800696	+	0.599071i	$0.795537\pi$
$98$		0			0
$99$	−3.55400	−	6.15571i	−0.357191	−	0.618673i
$100$		0			0
$101$		−	7.79226i		−	0.775359i	−0.921794	−	0.387680i	$-0.873277\pi$
$101$		−	7.79226i		−	0.775359i	0.921794	−	0.387680i	$-0.126723\pi$
$102$		0			0
$103$	−9.40036	−	9.40036i	−0.926245	−	0.926245i	0.0712160	−	0.997461i	$-0.477312\pi$
$103$	−9.40036	−	9.40036i	−0.926245	−	0.926245i	−0.997461	+	0.0712160i	$0.977312\pi$
$104$		0			0
$105$	1.28016	−	1.28016i	0.124931	−	0.124931i
$106$		0			0
$107$	−7.29367	−	4.21100i	−0.705106	−	0.407093i	0.104140	−	0.994563i	$-0.466791\pi$
$107$	−7.29367	−	4.21100i	−0.705106	−	0.407093i	−0.809246	+	0.587469i	$0.800124\pi$
$108$		0			0
$109$	−0.733778	+	2.73850i	−0.0702832	+	0.262301i	−0.992122	−	0.125272i	$-0.960020\pi$
$109$	−0.733778	+	2.73850i	−0.0702832	+	0.262301i	0.921839	+	0.387573i	$0.126686\pi$
$110$		0			0
$111$	3.63054	−	5.18194i	0.344595	−	0.491848i
$112$		0			0
$113$	−13.7247	−	3.67752i	−1.29111	−	0.345952i	−0.453029	−	0.891496i	$-0.649657\pi$
$113$	−13.7247	−	3.67752i	−1.29111	−	0.345952i	−0.838083	+	0.545543i	$0.816323\pi$
$114$		0			0
$115$	8.38581	−	14.5246i	0.781981	−	1.35443i
$116$		0			0
$117$	3.88786	+	3.88786i	0.359433	+	0.359433i
$118$		0			0
$119$	1.67977	−	1.67977i	0.153984	−	0.153984i
$120$		0			0
$121$	2.73376			0.248524
$122$		0			0
$123$	−6.71649	+	3.87777i	−0.605606	+	0.349647i
$124$		0			0
$125$	−13.0470	+	13.0470i	−1.16696	+	1.16696i
$126$		0			0
$127$	1.65099	−	0.953198i	0.146501	−	0.0845826i	−0.424958	−	0.905213i	$-0.639711\pi$
$127$	1.65099	−	0.953198i	0.146501	−	0.0845826i	0.571459	+	0.820631i	$0.306378\pi$
$128$		0			0
$129$	2.16862	+	8.09340i	0.190936	+	0.712584i
$130$		0			0
$131$	−3.06496	+	11.4386i	−0.267787	+	0.999394i	0.692736	+	0.721191i	$0.256405\pi$
$131$	−3.06496	+	11.4386i	−0.267787	+	0.999394i	−0.960523	+	0.278202i	$0.910261\pi$
$132$		0			0
$133$	0.931445	−	3.47620i	0.0807665	−	0.301425i
$134$		0			0
$135$	19.0076	−	5.09306i	1.63591	−	0.438341i
$136$		0			0
$137$	3.16165			0.270118			0.135059	−	0.990838i	$-0.456878\pi$
$137$	3.16165			0.270118			0.135059	+	0.990838i	$0.456878\pi$
$138$		0			0
$139$	3.22864	+	5.59218i	0.273850	+	0.474322i	0.969844	−	0.243725i	$-0.0783695\pi$
$139$	3.22864	+	5.59218i	0.273850	+	0.474322i	−0.695994	+	0.718047i	$0.745036\pi$
$140$		0			0
$141$	−7.19431	−	4.15363i	−0.605870	−	0.349799i
$142$		0			0
$143$	−10.2615	+	2.74956i	−0.858111	+	0.229930i
$144$		0			0
$145$	4.38097	−	7.58805i	0.363819	−	0.630154i
$146$		0			0
$147$	7.06833			0.582986
$148$		0			0
$149$	−6.02517			−0.493601			−0.246800	−	0.969066i	$-0.579379\pi$
$149$	−6.02517			−0.493601			−0.246800	+	0.969066i	$0.579379\pi$
$150$		0			0
$151$	−9.56543	+	16.5678i	−0.778423	+	1.34827i	0.154427	+	0.988004i	$0.450647\pi$
$151$	−9.56543	+	16.5678i	−0.778423	+	1.34827i	−0.932850	+	0.360264i	$0.882686\pi$
$152$		0			0
$153$	9.72691	−	2.60632i	0.786374	−	0.210708i
$154$		0			0
$155$	33.8486	+	19.5425i	2.71879	+	1.56969i
$156$		0			0
$157$	7.48687	+	12.9676i	0.597517	+	1.03493i	0.993186	+	0.116537i	$0.0371793\pi$
$157$	7.48687	+	12.9676i	0.597517	+	1.03493i	−0.395669	+	0.918393i	$0.629487\pi$
$158$		0			0
$159$	5.60425			0.444446
$160$		0			0
$161$	−1.90556	+	0.510594i	−0.150179	+	0.0402405i
$162$		0			0
$163$	−4.18747	+	15.6279i	−0.327988	+	1.22407i	0.583285	+	0.812267i	$0.301767\pi$
$163$	−4.18747	+	15.6279i	−0.327988	+	1.22407i	−0.911274	+	0.411801i	$0.864900\pi$
$164$		0			0
$165$	−3.83781	+	14.3229i	−0.298773	+	1.11504i
$166$		0			0
$167$	−4.78816	−	17.8697i	−0.370519	−	1.38280i	−0.859783	−	0.510660i	$-0.829401\pi$
$167$	−4.78816	−	17.8697i	−0.370519	−	1.38280i	0.489264	−	0.872136i	$-0.337266\pi$
$168$		0			0
$169$	−4.14167	+	2.39119i	−0.318590	+	0.183938i
$170$		0			0
$171$	10.7873	−	10.7873i	0.824923	−	0.824923i
$172$		0			0
$173$	−16.8754	+	9.74301i	−1.28301	+	0.740747i	−0.977398	−	0.211409i	$-0.932195\pi$
$173$	−16.8754	+	9.74301i	−1.28301	+	0.740747i	−0.305614	+	0.952156i	$0.598862\pi$
$174$		0			0
$175$	4.43269			0.335080
$176$		0			0
$177$	−1.51209	+	1.51209i	−0.113656	+	0.113656i
$178$		0			0
$179$	8.96518	+	8.96518i	0.670089	+	0.670089i	0.957736	−	0.287647i	$-0.0928731\pi$
$179$	8.96518	+	8.96518i	0.670089	+	0.670089i	−0.287647	+	0.957736i	$0.592873\pi$
$180$		0			0
$181$	6.14616	−	10.6455i	0.456840	−	0.791270i	−0.541952	−	0.840410i	$-0.682314\pi$
$181$	6.14616	−	10.6455i	0.456840	−	0.791270i	0.998792	+	0.0491392i	$0.0156478\pi$
$182$		0			0
$183$	−9.01982	−	2.41685i	−0.666764	−	0.178659i
$184$		0			0
$185$	23.0439	−	4.05678i	1.69422	−	0.298260i
$186$		0			0
$187$	−5.03580	+	18.7939i	−0.368255	+	1.37434i
$188$		0			0
$189$	−2.00455	−	1.15733i	−0.145810	−	0.0841834i
$190$		0			0
$191$	7.55836	−	7.55836i	0.546904	−	0.546904i	−0.378640	−	0.925544i	$-0.623608\pi$
$191$	7.55836	−	7.55836i	0.546904	−	0.546904i	0.925544	+	0.378640i	$0.123608\pi$
$192$		0			0
$193$	−13.1110	−	13.1110i	−0.943752	−	0.943752i	0.0547484	−	0.998500i	$-0.482564\pi$
$193$	−13.1110	−	13.1110i	−0.943752	−	0.943752i	−0.998500	+	0.0547484i	$0.982564\pi$
$194$		0			0
$195$		−	11.4700i		−	0.821387i
$196$		0			0
$197$	−8.38806	−	14.5285i	−0.597624	−	1.03512i	−0.993171	−	0.116670i	$-0.962778\pi$
$197$	−8.38806	−	14.5285i	−0.597624	−	1.03512i	0.395547	−	0.918446i	$-0.370555\pi$
$198$		0			0
$199$	13.6708	+	13.6708i	0.969094	+	0.969094i	0.999537	−	0.0304421i	$-0.00969151\pi$
$199$	13.6708	+	13.6708i	0.969094	+	0.969094i	−0.0304421	+	0.999537i	$0.509692\pi$
$200$		0			0
$201$	−2.65627	−	4.60079i	−0.187359	−	0.324515i
$202$		0			0
$203$	−0.995516	+	0.266748i	−0.0698715	+	0.0187220i
$204$		0			0
$205$	−27.7031	−	7.42303i	−1.93487	−	0.518447i
$206$		0			0
$207$	−8.07773	−	2.16442i	−0.561441	−	0.150438i
$208$		0			0
$209$	7.62894	+	28.4716i	0.527705	+	1.96942i
$210$		0			0
$211$			0.960048i			0.0660925i	0.999454	+	0.0330462i	$0.0105209\pi$
$211$			0.960048i			0.0660925i	−0.999454	+	0.0330462i	$0.989479\pi$
$212$		0			0
$213$	8.61653	−	4.97476i	0.590395	−	0.340865i
$214$		0			0
$215$	−15.4928	+	26.8343i	−1.05660	+	1.83009i
$216$		0			0
$217$	−1.18990	−	4.44078i	−0.0807759	−	0.301460i
$218$		0			0
$219$	−3.92128	−	2.26395i	−0.264975	−	0.152984i
$220$		0			0
$221$		−	15.0505i		−	1.01241i
$222$		0			0
$223$		−	10.3189i		−	0.691002i	−0.938418	−	0.345501i	$-0.887709\pi$
$223$		−	10.3189i		−	0.691002i	0.938418	−	0.345501i	$-0.112291\pi$
$224$		0			0
$225$	16.2729	+	9.39514i	1.08486	+	0.626343i
$226$		0			0
$227$	−3.31790	−	12.3826i	−0.220217	−	0.821861i	−0.984265	−	0.176701i	$-0.943457\pi$
$227$	−3.31790	−	12.3826i	−0.220217	−	0.821861i	0.764048	−	0.645160i	$-0.223209\pi$
$228$		0			0
$229$	−0.344429	+	0.596568i	−0.0227605	+	0.0394223i	−0.877181	−	0.480159i	$-0.840579\pi$
$229$	−0.344429	+	0.596568i	−0.0227605	+	0.0394223i	0.854421	+	0.519582i	$0.173912\pi$
$230$		0			0
$231$	1.51051	−	0.872091i	0.0993840	−	0.0573794i
$232$		0			0
$233$		−	27.6876i		−	1.81388i	−0.421264	−	0.906938i	$-0.638413\pi$
$233$		−	27.6876i		−	1.81388i	0.421264	−	0.906938i	$-0.361587\pi$
$234$		0			0
$235$	−7.95110	−	29.6739i	−0.518673	−	1.93571i
$236$		0			0
$237$	−1.07639	−	0.288417i	−0.0699189	−	0.0187347i
$238$		0			0
$239$	10.6942	+	2.86551i	0.691752	+	0.185354i	0.587533	−	0.809200i	$-0.300099\pi$
$239$	10.6942	+	2.86551i	0.691752	+	0.185354i	0.104219	+	0.994554i	$0.466766\pi$
$240$		0			0
$241$	11.7158	−	3.13923i	0.754679	−	0.202216i	0.139087	−	0.990280i	$-0.455583\pi$
$241$	11.7158	−	3.13923i	0.754679	−	0.202216i	0.615593	+	0.788064i	$0.288917\pi$
$242$		0			0
$243$	−7.89859	−	13.6808i	−0.506695	−	0.877621i
$244$		0			0
$245$	18.4831	+	18.4831i	1.18084	+	1.18084i
$246$		0			0
$247$	−11.4003	−	19.7459i	−0.725384	−	1.25640i
$248$		0			0
$249$			3.35623i			0.212693i
$250$		0			0
$251$	−13.4595	−	13.4595i	−0.849558	−	0.849558i	0.140520	−	0.990078i	$-0.455123\pi$
$251$	−13.4595	−	13.4595i	−0.849558	−	0.849558i	−0.990078	+	0.140520i	$0.955123\pi$
$252$		0			0
$253$	11.4254	−	11.4254i	0.718310	−	0.718310i
$254$		0			0
$255$	−18.1929	−	10.5036i	−1.13928	−	0.657764i
$256$		0			0
$257$	1.18533	−	4.42371i	0.0739388	−	0.275943i	−0.919052	−	0.394137i	$-0.871044\pi$
$257$	1.18533	−	4.42371i	0.0739388	−	0.275943i	0.992991	+	0.118193i	$0.0377103\pi$
$258$		0			0
$259$	−2.25408	−	1.57924i	−0.140062	−	0.0981293i
$260$		0			0
$261$	−4.22002	−	1.13075i	−0.261212	−	0.0699917i
$262$		0			0
$263$	3.24764	−	5.62507i	0.200258	−	0.346857i	−0.748354	−	0.663300i	$-0.769155\pi$
$263$	3.24764	−	5.62507i	0.200258	−	0.346857i	0.948611	+	0.316443i	$0.102489\pi$
$264$		0			0
$265$	14.6547	+	14.6547i	0.900228	+	0.900228i
$266$		0			0
$267$	0.346173	−	0.346173i	0.0211854	−	0.0211854i
$268$		0			0
$269$	8.42875			0.513910			0.256955	−	0.966423i	$-0.417281\pi$
$269$	8.42875			0.513910			0.256955	+	0.966423i	$0.417281\pi$
$270$		0			0
$271$	−20.3420	+	11.7444i	−1.23569	+	0.713424i	−0.968210	−	0.250140i	$-0.919523\pi$
$271$	−20.3420	+	11.7444i	−1.23569	+	0.713424i	−0.267477	+	0.963564i	$0.586190\pi$
$272$		0			0
$273$	−0.954014	+	0.954014i	−0.0577396	+	0.0577396i
$274$		0			0
$275$	−31.4417	+	18.1529i	−1.89600	+	1.09466i
$276$		0			0
$277$	2.98376	+	11.1356i	0.179277	+	0.669071i	0.995783	+	0.0917345i	$0.0292411\pi$
$277$	2.98376	+	11.1356i	0.179277	+	0.669071i	−0.816507	+	0.577336i	$0.804092\pi$
$278$		0			0
$279$	5.04402	−	18.8246i	0.301978	−	1.12700i
$280$		0			0
$281$	−4.93608	+	18.4217i	−0.294462	+	1.09895i	0.647182	+	0.762335i	$0.275947\pi$
$281$	−4.93608	+	18.4217i	−0.294462	+	1.09895i	−0.941644	+	0.336611i	$0.890719\pi$
$282$		0			0
$283$	23.8025	−	6.37787i	1.41491	−	0.379125i	0.531237	−	0.847223i	$-0.321727\pi$
$283$	23.8025	−	6.37787i	1.41491	−	0.379125i	0.883677	+	0.468098i	$0.155061\pi$
$284$		0			0
$285$	−31.8248			−1.88514
$286$		0			0
$287$	1.68678	+	2.92160i	0.0995678	+	0.172456i
$288$		0			0
$289$	−9.14944	−	5.28243i	−0.538202	−	0.310731i
$290$		0			0
$291$	2.82163	−	0.756053i	0.165407	−	0.0443206i
$292$		0			0
$293$	4.44794	−	7.70407i	0.259852	−	0.450076i	−0.706350	−	0.707862i	$-0.749660\pi$
$293$	4.44794	−	7.70407i	0.259852	−	0.450076i	0.966202	+	0.257786i	$0.0829930\pi$
$294$		0			0
$295$	−7.90797			−0.460420
$296$		0			0
$297$	18.9581			1.10006
$298$		0			0
$299$	−6.24936	+	10.8242i	−0.361410	+	0.625980i
$300$		0			0
$301$	3.52054	−	0.943325i	0.202920	−	0.0543723i
$302$		0			0
$303$	7.01946	+	4.05269i	0.403258	+	0.232821i
$304$		0			0
$305$	−17.2662	−	29.9060i	−0.988660	−	1.71241i
$306$		0			0
$307$	−3.30968			−0.188893			−0.0944467	−	0.995530i	$-0.530108\pi$
$307$	−3.30968			−0.188893			−0.0944467	+	0.995530i	$0.530108\pi$
$308$		0			0
$309$	13.3571	−	3.57903i	0.759860	−	0.203604i
$310$		0			0
$311$	−2.19948	+	8.20857i	−0.124721	+	0.465465i	−0.999830	−	0.0184613i	$-0.994123\pi$
$311$	−2.19948	+	8.20857i	−0.124721	+	0.465465i	0.875108	+	0.483927i	$0.160790\pi$
$312$		0			0
$313$	3.42703	−	12.7898i	0.193707	−	0.722924i	−0.798891	−	0.601476i	$-0.794579\pi$
$313$	3.42703	−	12.7898i	0.193707	−	0.722924i	0.992598	−	0.121448i	$-0.0387539\pi$
$314$		0			0
$315$	−0.864011	−	3.22453i	−0.0486815	−	0.181682i
$316$		0			0
$317$	−18.0830	+	10.4402i	−1.01564	+	0.586383i	−0.912839	−	0.408319i	$-0.866115\pi$
$317$	−18.0830	+	10.4402i	−1.01564	+	0.586383i	−0.102805	+	0.994702i	$0.532782\pi$
$318$		0			0
$319$	5.96894	−	5.96894i	0.334196	−	0.334196i
$320$		0			0
$321$	7.58675	−	4.38021i	0.423451	−	0.244480i
$322$		0			0
$323$	−41.7591			−2.32354
$324$		0			0
$325$	19.8581	−	19.8581i	1.10153	−	1.10153i
$326$		0			0
$327$	−2.08527	−	2.08527i	−0.115316	−	0.115316i
$328$		0			0
$329$	−1.80678	+	3.12944i	−0.0996112	+	0.172532i
$330$		0			0
$331$	−20.0842	−	5.38155i	−1.10393	−	0.295797i	−0.339566	−	0.940582i	$-0.610280\pi$
$331$	−20.0842	−	5.38155i	−1.10393	−	0.295797i	−0.764364	+	0.644786i	$0.776947\pi$
$332$		0			0
$333$	−4.92774	−	10.5751i	−0.270039	−	0.579512i
$334$		0			0
$335$	5.08477	−	18.9766i	0.277810	−	1.03680i
$336$		0			0
$337$	−5.51153	−	3.18208i	−0.300232	−	0.173339i	0.342315	−	0.939585i	$-0.388789\pi$
$337$	−5.51153	−	3.18208i	−0.300232	−	0.173339i	−0.642547	+	0.766246i	$0.722122\pi$
$338$		0			0
$339$	10.4509	−	10.4509i	0.567615	−	0.567615i
$340$		0			0
$341$	26.6261	+	26.6261i	1.44188	+	1.44188i
$342$		0			0
$343$		−	6.24191i		−	0.337032i
$344$		0			0
$345$	8.72277	+	15.1083i	0.469618	+	0.813403i
$346$		0			0
$347$	13.7495	+	13.7495i	0.738114	+	0.738114i	0.972213	−	0.234099i	$-0.0752140\pi$
$347$	13.7495	+	13.7495i	0.738114	+	0.738114i	−0.234099	+	0.972213i	$0.575214\pi$
$348$		0			0
$349$	2.20346	+	3.81650i	0.117948	+	0.204293i	0.918955	−	0.394363i	$-0.129035\pi$
$349$	2.20346	+	3.81650i	0.117948	+	0.204293i	−0.801006	+	0.598656i	$0.795702\pi$
$350$		0			0
$351$	−14.1650	+	3.79550i	−0.756072	+	0.202589i
$352$		0			0
$353$	−34.8273	−	9.33194i	−1.85367	−	0.496689i	−0.853948	−	0.520358i	$-0.825798\pi$
$353$	−34.8273	−	9.33194i	−1.85367	−	0.496689i	−0.999720	+	0.0236692i	$0.992465\pi$
$354$		0			0
$355$	35.5401	+	9.52294i	1.88627	+	0.505425i
$356$		0			0
$357$	0.639545	+	2.38681i	0.0338483	+	0.126324i
$358$		0			0
$359$			24.4787i			1.29194i	0.763363	+	0.645969i	$0.223547\pi$
$359$			24.4787i			1.29194i	−0.763363	+	0.645969i	$0.776453\pi$
$360$		0			0
$361$	−38.3325	+	22.1313i	−2.01750	+	1.16481i
$362$		0			0
$363$	−1.42181	+	2.46264i	−0.0746254	+	0.129255i
$364$		0			0
$365$	−4.33377	−	16.1739i	−0.226840	−	0.846579i
$366$		0			0
$367$	7.74855	+	4.47363i	0.404471	+	0.233522i	0.688411	−	0.725320i	$-0.258308\pi$
$367$	7.74855	+	4.47363i	0.404471	+	0.233522i	−0.283940	+	0.958842i	$0.591642\pi$
$368$		0			0
$369$			14.3006i			0.744462i
$370$		0			0
$371$		−	2.43778i		−	0.126563i
$372$		0			0
$373$	7.67391	+	4.43054i	0.397340	+	0.229404i	0.685336	−	0.728227i	$-0.259655\pi$
$373$	7.67391	+	4.43054i	0.397340	+	0.229404i	−0.287995	+	0.957632i	$0.592989\pi$
$374$		0			0
$375$	−4.96743	−	18.5387i	−0.256517	−	0.957335i
$376$		0			0
$377$	−3.26483	+	5.65485i	−0.168147	+	0.291239i
$378$		0			0
$379$	−11.7663	+	6.79327i	−0.604394	+	0.348947i	−0.770768	−	0.637116i	$-0.780127\pi$
$379$	−11.7663	+	6.79327i	−0.604394	+	0.348947i	0.166374	+	0.986063i	$0.446794\pi$
$380$		0			0
$381$			1.98300i			0.101592i
$382$		0			0
$383$	−3.19638	−	11.9290i	−0.163327	−	0.609545i	−0.998248	−	0.0591747i	$-0.981153\pi$
$383$	−3.19638	−	11.9290i	−0.163327	−	0.609545i	0.834920	−	0.550371i	$-0.185514\pi$
$384$		0			0
$385$	6.23029	+	1.66940i	0.317525	+	0.0850806i
$386$		0			0
$387$	14.9236	+	3.99878i	0.758611	+	0.203269i
$388$		0			0
$389$	30.7393	−	8.23657i	1.55854	−	0.417611i	0.626342	−	0.779549i	$-0.284551\pi$
$389$	30.7393	−	8.23657i	1.55854	−	0.417611i	0.932202	+	0.361938i	$0.117885\pi$
$390$		0			0
$391$	11.4456	+	19.8244i	0.578831	+	1.00256i
$392$		0			0
$393$	−8.71010	−	8.71010i	−0.439366	−	0.439366i
$394$		0			0
$395$	−2.06048	−	3.56885i	−0.103674	−	0.179568i
$396$		0			0
$397$		−	22.1296i		−	1.11065i	−0.831632	−	0.555327i	$-0.812593\pi$
$397$		−	22.1296i		−	1.11065i	0.831632	−	0.555327i	$-0.187407\pi$
$398$		0			0
$399$	2.64701	+	2.64701i	0.132516	+	0.132516i
$400$		0			0
$401$	−12.5316	+	12.5316i	−0.625799	+	0.625799i	−0.947008	−	0.321209i	$-0.895911\pi$
$401$	−12.5316	+	12.5316i	−0.625799	+	0.625799i	0.321209	+	0.947008i	$0.395911\pi$
$402$		0			0
$403$	−25.2250	−	14.5637i	−1.25655	−	0.725468i
$404$		0			0
$405$	0.430949	−	1.60832i	0.0214140	−	0.0799182i
$406$		0			0
$407$	22.4558	+	1.97080i	1.11310	+	0.0976891i
$408$		0			0
$409$	29.7882	+	7.98171i	1.47293	+	0.394670i	0.903935	−	0.427671i	$-0.140666\pi$
$409$	29.7882	+	7.98171i	1.47293	+	0.394670i	0.568995	+	0.822341i	$0.307332\pi$
$410$		0			0
$411$	−1.64434	+	2.84809i	−0.0811096	+	0.140486i
$412$		0			0
$413$	0.657741	+	0.657741i	0.0323653	+	0.0323653i
$414$		0			0
$415$	−8.77627	+	8.77627i	−0.430810	+	0.430810i
$416$		0			0
$417$	−6.71676			−0.328921
$418$		0			0
$419$	20.8825	−	12.0565i	1.02018	−	0.588998i	0.106021	−	0.994364i	$-0.466189\pi$
$419$	20.8825	−	12.0565i	1.02018	−	0.588998i	0.914155	+	0.405365i	$0.132856\pi$
$420$		0			0
$421$	0.0872911	−	0.0872911i	0.00425431	−	0.00425431i	−0.704976	−	0.709231i	$-0.749042\pi$
$421$	0.0872911	−	0.0872911i	0.00425431	−	0.00425431i	0.709231	+	0.704976i	$0.249042\pi$
$422$		0			0
$423$	−13.2658	+	7.65899i	−0.645004	+	0.372393i
$424$		0			0
$425$	−13.3123	−	49.6823i	−0.645743	−	2.40995i
$426$		0			0
$427$	−1.05130	+	3.92352i	−0.0508761	+	0.189872i
$428$		0			0
$429$	2.86005	−	10.6738i	0.138084	−	0.515338i
$430$		0			0
$431$	−4.51843	+	1.21071i	−0.217645	+	0.0583179i	−0.365994	−	0.930617i	$-0.619271\pi$
$431$	−4.51843	+	1.21071i	−0.217645	+	0.0583179i	0.148349	+	0.988935i	$0.452604\pi$
$432$		0			0
$433$	17.1228			0.822870			0.411435	−	0.911439i	$-0.365028\pi$
$433$	17.1228			0.822870			0.411435	+	0.911439i	$0.365028\pi$
$434$		0			0
$435$	4.55700	+	7.89296i	0.218492	+	0.378439i
$436$		0			0
$437$	30.0328	+	17.3395i	1.43667	+	0.829459i
$438$		0			0
$439$	40.3959	−	10.8240i	1.92799	−	0.516604i	0.947641	−	0.319337i	$-0.103460\pi$
$439$	40.3959	−	10.8240i	1.92799	−	0.516604i	0.980350	−	0.197266i	$-0.0632064\pi$
$440$		0			0
$441$	6.51673	−	11.2873i	0.310321	−	0.537491i
$442$		0			0
$443$	12.5587			0.596684			0.298342	−	0.954459i	$-0.403566\pi$
$443$	12.5587			0.596684			0.298342	+	0.954459i	$0.403566\pi$
$444$		0			0
$445$	1.81043			0.0858224
$446$		0			0
$447$	3.13364	−	5.42762i	0.148216	−	0.256718i
$448$		0			0
$449$	−3.53343	+	0.946780i	−0.166753	+	0.0446813i	−0.341230	−	0.939980i	$-0.610843\pi$
$449$	−3.53343	+	0.946780i	−0.166753	+	0.0446813i	0.174477	+	0.984661i	$0.444177\pi$
$450$		0			0
$451$	−23.9292	−	13.8155i	−1.12678	−	0.650547i
$452$		0			0
$453$	−9.94979	−	17.2335i	−0.467482	−	0.809703i
$454$		0			0
$455$	−4.98934			−0.233904
$456$		0			0
$457$	−0.522702	+	0.140057i	−0.0244510	+	0.00655161i	−0.271024	−	0.962573i	$-0.587362\pi$
$457$	−0.522702	+	0.140057i	−0.0244510	+	0.00655161i	0.246573	+	0.969124i	$0.420696\pi$
$458$		0			0
$459$	−6.95143	+	25.9431i	−0.324465	+	1.21092i
$460$		0			0
$461$	1.88726	−	7.04334i	0.0878984	−	0.328041i	−0.907949	−	0.419081i	$-0.862352\pi$
$461$	1.88726	−	7.04334i	0.0878984	−	0.328041i	0.995847	+	0.0910397i	$0.0290190\pi$
$462$		0			0
$463$	−2.05312	−	7.66234i	−0.0954165	−	0.356099i	0.901666	−	0.432434i	$-0.142345\pi$
$463$	−2.05312	−	7.66234i	−0.0954165	−	0.356099i	−0.997082	+	0.0763344i	$0.975678\pi$
$464$		0			0
$465$	−35.2088	+	20.3278i	−1.63277	+	0.942679i
$466$		0			0
$467$	11.7383	−	11.7383i	0.543186	−	0.543186i	−0.381275	−	0.924461i	$-0.624515\pi$
$467$	11.7383	−	11.7383i	0.543186	−	0.543186i	0.924461	+	0.381275i	$0.124515\pi$
$468$		0			0
$469$	−2.00129	+	1.15545i	−0.0924110	+	0.0533535i
$470$		0			0
$471$	−15.5754			−0.717677
$472$		0			0
$473$	−21.1085	+	21.1085i	−0.970570	+	0.970570i
$474$		0			0
$475$	−55.0984	−	55.0984i	−2.52809	−	2.52809i
$476$		0			0
$477$	5.16691	−	8.94935i	0.236577	−	0.409763i
$478$		0			0
$479$	15.1379	+	4.05620i	0.691670	+	0.185332i	0.587496	−	0.809227i	$-0.300114\pi$
$479$	15.1379	+	4.05620i	0.691670	+	0.185332i	0.104173	+	0.994559i	$0.466780\pi$
$480$		0			0
$481$	−17.1730	+	3.02323i	−0.783021	+	0.137848i
$482$		0			0
$483$	0.531111	−	1.98213i	0.0241664	−	0.0901902i
$484$		0			0
$485$	9.35534	+	5.40131i	0.424804	+	0.245261i
$486$		0			0
$487$	−14.5580	+	14.5580i	−0.659687	+	0.659687i	−0.955306	−	0.295619i	$-0.904474\pi$
$487$	−14.5580	+	14.5580i	−0.659687	+	0.659687i	0.295619	+	0.955306i	$0.404474\pi$
$488$		0			0
$489$	−11.9001	−	11.9001i	−0.538141	−	0.538141i
$490$		0			0
$491$		−	11.3260i		−	0.511137i	−0.966791	−	0.255569i	$-0.917737\pi$
$491$		−	11.3260i		−	0.511137i	0.966791	−	0.255569i	$-0.0822626\pi$
$492$		0			0
$493$	5.97950	+	10.3568i	0.269303	+	0.466447i
$494$		0			0
$495$	19.3337	+	19.3337i	0.868986	+	0.868986i
$496$		0			0
$497$	−2.16396	−	3.74809i	−0.0970669	−	0.168125i
$498$		0			0
$499$	31.3689	−	8.40526i	1.40426	−	0.376271i	0.524390	−	0.851478i	$-0.324294\pi$
$499$	31.3689	−	8.40526i	1.40426	−	0.376271i	0.879874	+	0.475207i	$0.157627\pi$
$500$		0			0
$501$	18.5877	+	4.98056i	0.830438	+	0.222515i
$502$		0			0
$503$	0.788935	+	0.211394i	0.0351769	+	0.00942561i	0.276365	−	0.961053i	$-0.410870\pi$
$503$	0.788935	+	0.211394i	0.0351769	+	0.00942561i	−0.241188	+	0.970478i	$0.577537\pi$
$504$		0			0
$505$	7.75787	+	28.9528i	0.345221	+	1.28838i
$506$		0			0
$507$		−	4.97456i		−	0.220928i
$508$		0			0
$509$	8.12440	−	4.69063i	0.360108	−	0.207908i	−0.309020	−	0.951055i	$-0.600001\pi$
$509$	8.12440	−	4.69063i	0.360108	−	0.207908i	0.669128	+	0.743147i	$0.266668\pi$
$510$		0			0
$511$	−0.984793	+	1.70571i	−0.0435647	+	0.0754562i
$512$		0			0
$513$	10.5310	+	39.3022i	0.464955	+	1.73524i
$514$		0			0
$515$	44.2866	+	25.5689i	1.95150	+	1.12670i
$516$		0			0
$517$		−	29.5967i		−	1.30166i
$518$		0			0
$519$		−	20.2690i		−	0.889711i
$520$		0			0
$521$	−34.6706	−	20.0171i	−1.51894	−	0.876963i	−0.999751	−	0.0223067i	$-0.992899\pi$
$521$	−34.6706	−	20.0171i	−1.51894	−	0.876963i	−0.519194	−	0.854657i	$-0.673768\pi$
$522$		0			0
$523$	2.32944	+	8.69360i	0.101859	+	0.380144i	0.997970	−	0.0636865i	$-0.0202858\pi$
$523$	2.32944	+	8.69360i	0.101859	+	0.380144i	−0.896111	+	0.443831i	$0.853619\pi$
$524$		0			0
$525$	−2.30540	+	3.99308i	−0.100616	+	0.174272i
$526$		0			0
$527$	−46.1994	+	26.6732i	−2.01248	+	1.16190i
$528$		0			0
$529$			3.98989i			0.173473i
$530$		0			0
$531$	1.02054	+	3.80872i	0.0442879	+	0.165285i
$532$		0			0
$533$	20.6452	+	5.53186i	0.894243	+	0.239612i
$534$		0			0
$535$	31.2926	+	8.38483i	1.35290	+	0.362508i
$536$		0			0
$537$	−12.7388	+	3.41334i	−0.549718	+	0.147297i
$538$		0			0
$539$	12.5913	+	21.8088i	0.542347	+	0.939373i
$540$		0			0
$541$	−2.16264	−	2.16264i	−0.0929791	−	0.0929791i	0.659087	−	0.752066i	$-0.270943\pi$
$541$	−2.16264	−	2.16264i	−0.0929791	−	0.0929791i	−0.752066	+	0.659087i	$0.770943\pi$
$542$		0			0
$543$	6.39313	+	11.0732i	0.274355	+	0.475197i
$544$		0			0
$545$		−	10.9056i		−	0.467146i
$546$		0			0
$547$	31.7690	+	31.7690i	1.35834	+	1.35834i	0.875959	+	0.482386i	$0.160230\pi$
$547$	31.7690	+	31.7690i	1.35834	+	1.35834i	0.482386	+	0.875959i	$0.339770\pi$
$548$		0			0
$549$	−12.1754	+	12.1754i	−0.519632	+	0.519632i
$550$		0			0
$551$	15.6899	+	9.05859i	0.668414	+	0.385909i
$552$		0			0
$553$	−0.125458	+	0.468216i	−0.00533502	+	0.0199106i
$554$		0			0
$555$	−8.33048	+	22.8684i	−0.353609	+	0.970710i
$556$		0			0
$557$	3.43327	+	0.919942i	0.145472	+	0.0389792i	0.330820	−	0.943694i	$-0.392675\pi$
$557$	3.43327	+	0.919942i	0.145472	+	0.0389792i	−0.185348	+	0.982673i	$0.559341\pi$
$558$		0			0
$559$	11.5457	−	19.9978i	0.488331	−	0.845815i
$560$		0			0
$561$	−14.3109	−	14.3109i	−0.604207	−	0.604207i
$562$		0			0
$563$	−18.0428	+	18.0428i	−0.760413	+	0.760413i	−0.976397	−	0.215984i	$-0.930704\pi$
$563$	−18.0428	+	18.0428i	−0.760413	+	0.760413i	0.215984	+	0.976397i	$0.430704\pi$
$564$		0			0
$565$	54.6565			2.29942
$566$		0			0
$567$	−0.169615	+	0.0979273i	−0.00712316	+	0.00411256i
$568$		0			0
$569$	−33.2506	+	33.2506i	−1.39394	+	1.39394i	−0.577661	+	0.816277i	$0.696034\pi$
$569$	−33.2506	+	33.2506i	−1.39394	+	1.39394i	−0.816277	+	0.577661i	$0.803966\pi$
$570$		0			0
$571$	14.0098	−	8.08858i	0.586293	−	0.338496i	−0.177337	−	0.984150i	$-0.556748\pi$
$571$	14.0098	−	8.08858i	0.586293	−	0.338496i	0.763630	+	0.645654i	$0.223415\pi$
$572$		0			0
$573$	2.87772	+	10.7398i	0.120218	+	0.448661i
$574$		0			0
$575$	−11.0553	+	41.2588i	−0.461036	+	1.72061i
$576$		0			0
$577$	−11.2210	+	41.8773i	−0.467136	+	1.74337i	0.182574	+	0.983192i	$0.441557\pi$
$577$	−11.2210	+	41.8773i	−0.467136	+	1.74337i	−0.649710	+	0.760182i	$0.725110\pi$
$578$		0			0
$579$	18.6297	−	4.99180i	0.774222	−	0.207452i
$580$		0			0
$581$	1.45992			0.0605678
$582$		0			0
$583$	9.98327	+	17.2915i	0.413465	+	0.716142i
$584$		0			0
$585$	−18.3164	−	10.5750i	−0.757288	−	0.437221i
$586$		0			0
$587$	2.76719	−	0.741467i	0.114214	−	0.0306036i	−0.201259	−	0.979538i	$-0.564503\pi$
$587$	2.76719	−	0.741467i	0.114214	−	0.0306036i	0.315473	+	0.948934i	$0.397837\pi$
$588$		0			0
$589$	−40.4084	+	69.9894i	−1.66500	+	2.88386i
$590$		0			0
$591$	17.4502			0.717806
$592$		0			0
$593$	12.3133			0.505647			0.252824	−	0.967512i	$-0.418641\pi$
$593$	12.3133			0.505647			0.252824	+	0.967512i	$0.418641\pi$
$594$		0			0
$595$	−4.56896	+	7.91368i	−0.187309	+	0.324429i
$596$		0			0
$597$	−19.4250	+	5.20491i	−0.795012	+	0.213023i
$598$		0			0
$599$	0.534801	+	0.308768i	0.0218514	+	0.0126159i	0.510886	−	0.859649i	$-0.329317\pi$
$599$	0.534801	+	0.308768i	0.0218514	+	0.0126159i	−0.489035	+	0.872264i	$0.662651\pi$
$600$		0			0
$601$	13.7013	+	23.7314i	0.558888	+	0.968022i	0.997590	+	0.0693894i	$0.0221051\pi$
$601$	13.7013	+	23.7314i	0.558888	+	0.968022i	−0.438702	+	0.898633i	$0.644562\pi$
$602$		0			0
$603$	−9.79592			−0.398921
$604$		0			0
$605$	−10.1575	+	2.72169i	−0.412961	+	0.110653i
$606$		0			0
$607$	6.69188	−	24.9744i	0.271615	−	1.01368i	−0.686461	−	0.727167i	$-0.740837\pi$
$607$	6.69188	−	24.9744i	0.271615	−	1.01368i	0.958076	−	0.286515i	$-0.0924967\pi$
$608$		0			0
$609$	0.277466	−	1.03552i	0.0112435	−	0.0419613i
$610$		0			0
$611$	5.92540	+	22.1139i	0.239716	+	0.894633i
$612$		0			0
$613$	3.45931	−	1.99723i	0.139720	−	0.0806674i	−0.428510	−	0.903537i	$-0.640961\pi$
$613$	3.45931	−	1.99723i	0.139720	−	0.0806674i	0.568231	+	0.822869i	$0.307628\pi$
$614$		0			0
$615$	21.0950	−	21.0950i	0.850633	−	0.850633i
$616$		0			0
$617$	2.33062	−	1.34558i	0.0938271	−	0.0541711i	−0.452352	−	0.891839i	$-0.649415\pi$
$617$	2.33062	−	1.34558i	0.0938271	−	0.0541711i	0.546179	+	0.837668i	$0.316082\pi$
$618$		0			0
$619$	44.0910			1.77217			0.886083	−	0.463527i	$-0.153416\pi$
$619$	44.0910			1.77217			0.886083	+	0.463527i	$0.153416\pi$
$620$		0			0
$621$	15.7717	−	15.7717i	0.632895	−	0.632895i
$622$		0			0
$623$	−0.150581	−	0.150581i	−0.00603290	−	0.00603290i
$624$		0			0
$625$	10.9960	−	19.0456i	0.439840	−	0.761825i
$626$		0			0
$627$	−29.6157	−	7.93550i	−1.18274	−	0.316913i
$628$		0			0
$629$	−10.9309	+	30.0069i	−0.435843	+	1.19645i
$630$		0			0
$631$	−0.956298	+	3.56895i	−0.0380696	+	0.142078i	−0.982345	−	0.187079i	$-0.940098\pi$
$631$	−0.956298	+	3.56895i	−0.0380696	+	0.142078i	0.944275	+	0.329157i	$0.106765\pi$
$632$		0			0
$633$	−0.864835	−	0.499313i	−0.0343741	−	0.0198459i
$634$		0			0
$635$	−5.18538	+	5.18538i	−0.205776	+	0.205776i
$636$		0			0
$637$	−13.7742	−	13.7742i	−0.545752	−	0.545752i
$638$		0			0
$639$		−	18.3462i		−	0.725763i
$640$		0			0
$641$	9.36328	+	16.2177i	0.369827	+	0.640560i	0.989538	−	0.144270i	$-0.0460835\pi$
$641$	9.36328	+	16.2177i	0.369827	+	0.640560i	−0.619711	+	0.784830i	$0.712750\pi$
$642$		0			0
$643$	−15.9179	−	15.9179i	−0.627739	−	0.627739i	0.319760	−	0.947499i	$-0.396398\pi$
$643$	−15.9179	−	15.9179i	−0.627739	−	0.627739i	−0.947499	+	0.319760i	$0.896398\pi$
$644$		0			0
$645$	−16.1154	−	27.9126i	−0.634542	−	1.09906i
$646$		0			0
$647$	−14.2770	+	3.82552i	−0.561288	+	0.150397i	−0.528298	−	0.849059i	$-0.677170\pi$
$647$	−14.2770	+	3.82552i	−0.561288	+	0.150397i	−0.0329899	+	0.999456i	$0.510503\pi$
$648$		0			0
$649$	−7.35904	−	1.97185i	−0.288868	−	0.0774018i
$650$		0			0
$651$	4.61922	+	1.23772i	0.181041	+	0.0485099i
$652$		0			0
$653$	−8.27314	−	30.8758i	−0.323753	−	1.20826i	−0.915559	−	0.402183i	$-0.868252\pi$
$653$	−8.27314	−	30.8758i	−0.323753	−	1.20826i	0.591806	−	0.806080i	$-0.298415\pi$
$654$		0			0
$655$		−	45.5524i		−	1.77988i
$656$		0			0
$657$	−7.23055	+	4.17456i	−0.282091	+	0.162865i
$658$		0			0
$659$	−11.2230	+	19.4388i	−0.437185	+	0.757226i	−0.997471	−	0.0710727i	$-0.977358\pi$
$659$	−11.2230	+	19.4388i	−0.437185	+	0.757226i	0.560286	+	0.828299i	$0.310691\pi$
$660$		0			0
$661$	−11.6763	−	43.5765i	−0.454155	−	1.69493i	−0.690560	−	0.723275i	$-0.742636\pi$
$661$	−11.6763	−	43.5765i	−0.454155	−	1.69493i	0.236405	−	0.971655i	$-0.424031\pi$
$662$		0			0
$663$	13.5579	+	7.82763i	0.526544	+	0.304000i
$664$		0			0
$665$			13.8434i			0.536825i
$666$		0			0
$667$		−	9.93138i		−	0.384545i
$668$		0			0
$669$	9.29548	+	5.36675i	0.359384	+	0.207490i
$670$		0			0
$671$	−8.61064	−	32.1353i	−0.332410	−	1.24057i
$672$		0			0
$673$	4.76466	−	8.25264i	0.183664	−	0.318116i	−0.759461	−	0.650552i	$-0.774537\pi$
$673$	4.76466	−	8.25264i	0.183664	−	0.318116i	0.943126	+	0.332437i	$0.107871\pi$
$674$		0			0
$675$	−43.4021	+	25.0582i	−1.67055	+	0.964491i
$676$		0			0
$677$			49.8314i			1.91518i	0.288142	+	0.957588i	$0.406963\pi$
$677$			49.8314i			1.91518i	−0.288142	+	0.957588i	$0.593037\pi$
$678$		0			0
$679$	−0.328874	−	1.22738i	−0.0126210	−	0.0471024i
$680$		0			0
$681$	12.8801	+	3.45122i	0.493568	+	0.132251i
$682$		0			0
$683$	−4.99887	−	1.33944i	−0.191277	−	0.0512524i	0.161909	−	0.986806i	$-0.448235\pi$
$683$	−4.99887	−	1.33944i	−0.191277	−	0.0512524i	−0.353186	+	0.935553i	$0.614902\pi$
$684$		0			0
$685$	−11.7473	+	3.14769i	−0.448843	+	0.120267i
$686$		0			0
$687$	−0.358269	−	0.620540i	−0.0136688	−	0.0236751i
$688$		0			0
$689$	−10.9211	−	10.9211i	−0.416060	−	0.416060i
$690$		0			0
$691$	15.1551	+	26.2494i	0.576527	+	0.998575i	0.995874	+	0.0907483i	$0.0289259\pi$
$691$	15.1551	+	26.2494i	0.576527	+	0.998575i	−0.419347	+	0.907826i	$0.637741\pi$
$692$		0			0
$693$		−	3.21614i		−	0.122171i
$694$		0			0
$695$	−17.5638	−	17.5638i	−0.666232	−	0.666232i
$696$		0			0
$697$	27.6799	−	27.6799i	1.04845	−	1.04845i
$698$		0			0
$699$	24.9417	+	14.4001i	0.943381	+	0.544661i
$700$		0			0
$701$	12.0651	−	45.0276i	0.455693	−	1.70067i	−0.230350	−	0.973108i	$-0.573987\pi$
$701$	12.0651	−	45.0276i	0.455693	−	1.70067i	0.686043	−	0.727561i	$-0.259346\pi$
$702$		0			0
$703$	8.38827	+	47.6482i	0.316369	+	1.79709i
$704$		0			0
$705$	30.8663	+	8.27060i	1.16249	+	0.311489i
$706$		0			0
$707$	1.76287	−	3.05339i	0.0662997	−	0.114834i
$708$		0			0
$709$	−33.7608	−	33.7608i	−1.26791	−	1.26791i	−0.947164	−	0.320750i	$-0.896065\pi$
$709$	−33.7608	−	33.7608i	−1.26791	−	1.26791i	−0.320750	−	0.947164i	$-0.603935\pi$
$710$		0			0
$711$	−1.45296	+	1.45296i	−0.0544902	+	0.0544902i
$712$		0			0
$713$	44.3017			1.65911
$714$		0			0
$715$	35.3900	−	20.4324i	1.32351	−	0.764130i
$716$		0			0
$717$	−8.14330	+	8.14330i	−0.304117	+	0.304117i
$718$		0			0
$719$	−7.31236	+	4.22179i	−0.272705	+	0.157446i	−0.630116	−	0.776501i	$-0.716993\pi$
$719$	−7.31236	+	4.22179i	−0.272705	+	0.157446i	0.357411	+	0.933947i	$0.383659\pi$
$720$		0			0
$721$	−1.55684	−	5.81019i	−0.0579796	−	0.216383i
$722$		0			0
$723$	−3.26538	+	12.1865i	−0.121441	+	0.453223i
$724$		0			0
$725$	−5.77555	+	21.5547i	−0.214499	+	0.800520i
$726$		0			0
$727$	0.217855	−	0.0583740i	0.00807978	−	0.00216497i	−0.254777	−	0.967000i	$-0.582002\pi$
$727$	0.217855	−	0.0583740i	0.00807978	−	0.00216497i	0.262857	+	0.964835i	$0.415335\pi$
$728$		0			0
$729$	15.1334			0.560495
$730$		0			0
$731$	−21.1459	−	36.6257i	−0.782108	−	1.35465i
$732$		0			0
$733$	−6.16846	−	3.56136i	−0.227837	−	0.131542i	0.381737	−	0.924271i	$-0.375326\pi$
$733$	−6.16846	−	3.56136i	−0.227837	−	0.131542i	−0.609574	+	0.792729i	$0.708659\pi$
$734$		0			0
$735$	−26.2629	+	7.03713i	−0.968722	+	0.259568i
$736$		0			0
$737$	9.46361	−	16.3915i	0.348597	−	0.603787i
$738$		0			0
$739$	−48.4627			−1.78273			−0.891365	−	0.453286i	$-0.850252\pi$
$739$	−48.4627			−1.78273			−0.891365	+	0.453286i	$0.850252\pi$
$740$		0			0
$741$	23.7168			0.871258
$742$		0			0
$743$	−5.38554	+	9.32803i	−0.197576	+	0.342212i	−0.947742	−	0.319038i	$-0.896640\pi$
$743$	−5.38554	+	9.32803i	−0.197576	+	0.342212i	0.750166	+	0.661250i	$0.229974\pi$
$744$		0			0
$745$	22.3870	−	5.99857i	0.820195	−	0.219771i
$746$		0			0
$747$	5.35952	+	3.09432i	0.196095	+	0.113215i
$748$		0			0
$749$	−1.90534	−	3.30015i	−0.0696197	−	0.120585i
$750$		0			0
$751$	2.16059			0.0788411			0.0394206	−	0.999223i	$-0.487449\pi$
$751$	2.16059			0.0788411			0.0394206	+	0.999223i	$0.487449\pi$
$752$		0			0
$753$	19.1249	−	5.12449i	0.696949	−	0.186747i
$754$		0			0
$755$	19.0464	−	71.0822i	0.693170	−	2.58694i
$756$		0			0
$757$	1.45051	−	5.41337i	0.0527196	−	0.196752i	−0.934543	−	0.355849i	$-0.884192\pi$
$757$	1.45051	−	5.41337i	0.0527196	−	0.196752i	0.987263	+	0.159097i	$0.0508583\pi$
$758$		0			0
$759$	4.35004	+	16.2346i	0.157896	+	0.589277i
$760$		0			0
$761$	24.4896	−	14.1391i	0.887746	−	0.512540i	0.0145413	−	0.999894i	$-0.495371\pi$
$761$	24.4896	−	14.1391i	0.887746	−	0.512540i	0.873204	+	0.487354i	$0.162038\pi$
$762$		0			0
$763$	−0.907070	+	0.907070i	−0.0328381	+	0.0328381i
$764$		0			0
$765$	−33.5463	+	19.3679i	−1.21287	+	0.700250i
$766$		0			0
$767$	5.89326			0.212793
$768$		0			0
$769$	−8.40543	+	8.40543i	−0.303108	+	0.303108i	−0.842228	−	0.539121i	$-0.818757\pi$
$769$	−8.40543	+	8.40543i	−0.303108	+	0.303108i	0.539121	+	0.842228i	$0.318757\pi$
$770$		0			0
$771$	3.36851	+	3.36851i	0.121314	+	0.121314i
$772$		0			0
$773$	−10.9274	+	18.9269i	−0.393033	+	0.680753i	−0.992848	−	0.119386i	$-0.961907\pi$
$773$	−10.9274	+	18.9269i	−0.393033	+	0.680753i	0.599815	+	0.800139i	$0.295241\pi$
$774$		0			0
$775$	−96.1506	−	25.7635i	−3.45383	−	0.925451i
$776$		0			0
$777$	2.59495	−	1.20918i	0.0930933	−	0.0433792i
$778$		0			0
$779$	15.3487	−	57.2822i	0.549925	−	2.05235i
$780$		0			0
$781$	30.6985	+	17.7238i	1.09848	+	0.634207i
$782$		0			0
$783$	8.23952	−	8.23952i	0.294457	−	0.294457i
$784$		0			0
$785$	−40.7284	−	40.7284i	−1.45366	−	1.45366i
$786$		0			0
$787$		−	29.8820i		−	1.06518i	−0.846374	−	0.532589i	$-0.821219\pi$
$787$		−	29.8820i		−	1.06518i	0.846374	−	0.532589i	$-0.178781\pi$
$788$		0			0
$789$	3.37813	+	5.85110i	0.120265	+	0.208305i
$790$		0			0
$791$	−4.54602	−	4.54602i	−0.161638	−	0.161638i
$792$		0			0
$793$	12.8673	+	22.2868i	0.456931	+	0.791428i
$794$		0			0
$795$	−20.8230	+	5.57952i	−0.738517	+	0.197885i
$796$		0			0
$797$	13.0203	+	3.48877i	0.461201	+	0.123579i	0.481936	−	0.876206i	$-0.339934\pi$
$797$	13.0203	+	3.48877i	0.461201	+	0.123579i	−0.0207345	+	0.999785i	$0.506600\pi$
$798$		0			0
$799$	40.5014	+	10.8523i	1.43284	+	0.383928i
$800$		0			0
$801$	−0.233640	−	0.871957i	−0.00825527	−	0.0308091i
$802$		0			0
$803$		−	16.1318i		−	0.569278i
$804$		0			0
$805$	6.57193	−	3.79430i	0.231630	−	0.133732i
$806$		0			0
$807$	−4.38372	+	7.59283i	−0.154314	+	0.267280i
$808$		0			0
$809$	−0.0549753	−	0.205171i	−0.00193283	−	0.00721341i	0.964953	−	0.262424i	$-0.0845219\pi$
$809$	−0.0549753	−	0.205171i	−0.00193283	−	0.00721341i	−0.966886	+	0.255211i	$0.917855\pi$
$810$		0			0
$811$	26.0320	+	15.0296i	0.914108	+	0.527760i	0.881751	−	0.471716i	$-0.156365\pi$
$811$	26.0320	+	15.0296i	0.914108	+	0.527760i	0.0323572	+	0.999476i	$0.489699\pi$
$812$		0			0
$813$		−	24.4327i		−	0.856893i
$814$		0			0
$815$		−	62.2355i		−	2.18002i
$816$		0			0
$817$	−55.4858	−	32.0347i	−1.94120	−	1.12075i
$818$		0			0
$819$	0.643887	+	2.40302i	0.0224992	+	0.0839682i
$820$		0			0
$821$	14.6882	−	25.4407i	0.512622	−	0.887887i	−0.487271	−	0.873251i	$-0.662008\pi$
$821$	14.6882	−	25.4407i	0.512622	−	0.887887i	0.999893	−	0.0146360i	$-0.00465896\pi$
$822$		0			0
$823$	−17.3997	+	10.0457i	−0.606516	+	0.350172i	−0.771601	−	0.636107i	$-0.780544\pi$
$823$	−17.3997	+	10.0457i	−0.606516	+	0.350172i	0.165085	+	0.986279i	$0.447210\pi$
$824$		0			0
$825$		−	37.7646i		−	1.31479i
$826$		0			0
$827$	−0.791958	−	2.95563i	−0.0275391	−	0.102777i	0.950788	−	0.309841i	$-0.100276\pi$
$827$	−0.791958	−	2.95563i	−0.0275391	−	0.102777i	−0.978327	+	0.207064i	$0.933609\pi$
$828$		0			0
$829$	4.34708	+	1.16480i	0.150980	+	0.0404550i	0.333518	−	0.942744i	$-0.391764\pi$
$829$	4.34708	+	1.16480i	0.150980	+	0.0404550i	−0.182537	+	0.983199i	$0.558431\pi$
$830$		0			0
$831$	−11.5830	−	3.10366i	−0.401810	−	0.107665i
$832$		0			0
$833$	−34.4611	+	9.23381i	−1.19400	+	0.319933i
$834$		0			0
$835$	35.5816	+	61.6291i	1.23135	+	2.13276i
$836$		0			0
$837$	36.7547	+	36.7547i	1.27043	+	1.27043i
$838$		0			0
$839$	21.1960	+	36.7125i	0.731767	+	1.26746i	0.956127	+	0.292952i	$0.0946375\pi$
$839$	21.1960	+	36.7125i	0.731767	+	1.26746i	−0.224360	+	0.974506i	$0.572029\pi$
$840$		0			0
$841$			23.8116i			0.821089i
$842$		0			0
$843$	−14.0275	−	14.0275i	−0.483133	−	0.483133i
$844$		0			0
$845$	13.0080	−	13.0080i	0.447491	−	0.447491i
$846$		0			0
$847$	1.07122	+	0.618469i	0.0368075	+	0.0212508i
$848$		0			0
$849$	−6.63415	+	24.7590i	−0.227684	+	0.849726i
$850$		0			0
$851$	20.3211	−	17.0420i	0.696597	−	0.584191i
$852$		0			0
$853$	−38.3714	−	10.2816i	−1.31381	−	0.352034i	−0.467155	−	0.884176i	$-0.654721\pi$
$853$	−38.3714	−	10.2816i	−1.31381	−	0.352034i	−0.846656	+	0.532141i	$0.821387\pi$
$854$		0			0
$855$	−29.3413	+	50.8206i	−1.00345	+	1.73803i
$856$		0			0
$857$	21.8423	+	21.8423i	0.746120	+	0.746120i	0.973748	−	0.227628i	$-0.0730970\pi$
$857$	21.8423	+	21.8423i	0.746120	+	0.746120i	−0.227628	+	0.973748i	$0.573097\pi$
$858$		0			0
$859$	−37.2710	+	37.2710i	−1.27167	+	1.27167i	−0.326458	+	0.945212i	$0.605855\pi$
$859$	−37.2710	+	37.2710i	−1.27167	+	1.27167i	−0.945212	+	0.326458i	$0.894145\pi$
$860$		0			0
$861$	−3.50913			−0.119591
$862$		0			0
$863$	7.19301	−	4.15289i	0.244853	−	0.141366i	−0.372552	−	0.928011i	$-0.621517\pi$
$863$	7.19301	−	4.15289i	0.244853	−	0.141366i	0.617405	+	0.786645i	$0.288184\pi$
$864$		0			0
$865$	53.0018	−	53.0018i	1.80211	−	1.80211i
$866$		0			0
$867$	9.51709	−	5.49469i	0.323217	−	0.186610i
$868$		0			0
$869$	−1.02756	−	3.83490i	−0.0348575	−	0.130090i
$870$		0			0
$871$	−3.78932	+	14.1419i	−0.128396	+	0.479181i
$872$		0			0
$873$	1.39411	−	5.20287i	0.0471833	−	0.176091i
$874$		0			0
$875$	−8.06412	+	2.16078i	−0.272617	+	0.0730475i
$876$		0			0
$877$	−23.6131			−0.797358			−0.398679	−	0.917091i	$-0.630531\pi$
$877$	−23.6131			−0.797358			−0.398679	+	0.917091i	$0.630531\pi$
$878$		0			0
$879$	4.62667	+	8.01364i	0.156054	+	0.270293i
$880$		0			0
$881$	−43.6978	−	25.2289i	−1.47222	−	0.849984i	−0.472703	−	0.881222i	$-0.656722\pi$
$881$	−43.6978	−	25.2289i	−1.47222	−	0.849984i	−0.999512	+	0.0312378i	$0.990055\pi$
$882$		0			0
$883$	−36.8470	+	9.87312i	−1.24000	+	0.332257i	−0.818465	−	0.574556i	$-0.805175\pi$
$883$	−36.8470	+	9.87312i	−1.24000	+	0.332257i	−0.421534	+	0.906813i	$0.638508\pi$
$884$		0			0
$885$	4.11287	−	7.12370i	0.138253	−	0.239460i
$886$		0			0
$887$	19.0310			0.638998			0.319499	−	0.947587i	$-0.396485\pi$
$887$	19.0310			0.638998			0.319499	+	0.947587i	$0.396485\pi$
$888$		0			0
$889$	0.862582			0.0289301
$890$		0			0
$891$	0.802068	−	1.38922i	0.0268703	−	0.0465407i
$892$		0			0
$893$	61.3573	−	16.4406i	2.05324	−	0.550165i
$894$		0			0
$895$	−42.2364	−	24.3852i	−1.41181	−	0.815108i
$896$		0			0
$897$	−6.50047	−	11.2591i	−0.217044	−	0.375932i
$898$		0			0
$899$	23.1444			0.771908
$900$		0			0
$901$	−27.3231	+	7.32120i	−0.910264	+	0.243904i
$902$		0			0
$903$	−0.981230	+	3.66200i	−0.0326533	+	0.121864i
$904$		0			0
$905$	−12.2381	+	45.6730i	−0.406807	+	1.51822i
$906$		0			0
$907$	−1.01752	−	3.79743i	−0.0337862	−	0.126092i	0.946973	−	0.321313i	$-0.104124\pi$
$907$	−1.01752	−	3.79743i	−0.0337862	−	0.126092i	−0.980759	+	0.195221i	$0.937457\pi$
$908$		0			0
$909$	12.9434	−	7.47286i	0.429305	−	0.247859i
$910$		0			0
$911$	38.3196	−	38.3196i	1.26959	−	1.26959i	0.323284	−	0.946302i	$-0.395213\pi$
$911$	38.3196	−	38.3196i	1.26959	−	1.26959i	0.946302	−	0.323284i	$-0.104787\pi$
$912$		0			0
$913$	−10.3554	+	5.97870i	−0.342714	+	0.197866i
$914$		0			0
$915$	35.9200			1.18748
$916$		0			0
$917$	−3.78879	+	3.78879i	−0.125117	+	0.125117i
$918$		0			0
$919$	−14.6942	−	14.6942i	−0.484718	−	0.484718i	0.421916	−	0.906635i	$-0.361358\pi$
$919$	−14.6942	−	14.6942i	−0.484718	−	0.484718i	−0.906635	+	0.421916i	$0.861358\pi$
$920$		0			0
$921$	1.72134	−	2.98144i	0.0567199	−	0.0982418i
$922$		0			0
$923$	−26.4855	−	7.09678i	−0.871782	−	0.233593i
$924$		0			0
$925$	−54.0147	+	25.1695i	−1.77599	+	0.827569i
$926$		0			0
$927$	6.59947	−	24.6295i	0.216755	−	0.808940i
$928$		0			0
$929$	−11.6416	−	6.72125i	−0.381947	−	0.220517i	0.296718	−	0.954965i	$-0.404108\pi$
$929$	−11.6416	−	6.72125i	−0.381947	−	0.220517i	−0.678665	+	0.734448i	$0.737441\pi$
$930$		0			0
$931$	−38.2178	+	38.2178i	−1.25254	+	1.25254i
$932$		0			0
$933$	−6.25055	−	6.25055i	−0.204634	−	0.204634i
$934$		0			0
$935$		−	74.8437i		−	2.44765i
$936$		0			0
$937$	−6.12014	−	10.6004i	−0.199936	−	0.346300i	0.748571	−	0.663054i	$-0.230740\pi$
$937$	−6.12014	−	10.6004i	−0.199936	−	0.346300i	−0.948508	+	0.316754i	$0.897407\pi$
$938$		0			0
$939$	9.73904	+	9.73904i	0.317821	+	0.317821i
$940$		0			0
$941$	−5.56631	−	9.64113i	−0.181457	−	0.314292i	0.760920	−	0.648845i	$-0.224748\pi$
$941$	−5.56631	−	9.64113i	−0.181457	−	0.314292i	−0.942377	+	0.334554i	$0.891415\pi$
$942$		0			0
$943$	−31.4006	+	8.41378i	−1.02255	+	0.273990i
$944$		0			0
$945$	8.60030	+	2.30444i	0.279768	+	0.0749635i
$946$		0			0
$947$	−3.26943	−	0.876042i	−0.106242	−	0.0284675i	0.205306	−	0.978698i	$-0.434181\pi$
$947$	−3.26943	−	0.876042i	−0.106242	−	0.0284675i	−0.311549	+	0.950230i	$0.600848\pi$
$948$		0			0
$949$	3.22966	+	12.0532i	0.104839	+	0.391265i
$950$		0			0
$951$		−	21.7195i		−	0.704304i
$952$		0			0
$953$	15.9098	−	9.18554i	0.515370	−	0.297549i	−0.219668	−	0.975575i	$-0.570498\pi$
$953$	15.9098	−	9.18554i	0.515370	−	0.297549i	0.735038	+	0.678026i	$0.237164\pi$
$954$		0			0
$955$	−20.5587	+	35.6087i	−0.665263	+	1.15227i
$956$		0			0
$957$	2.27257	+	8.48136i	0.0734619	+	0.274163i
$958$		0			0
$959$	1.23889	+	0.715271i	0.0400057	+	0.0230973i
$960$		0			0
$961$			72.2419i			2.33038i
$962$		0			0
$963$		−	16.1536i		−	0.520542i
$964$		0			0
$965$	61.7682	+	35.6619i	1.98839	+	1.14800i
$966$		0			0
$967$	1.38269	+	5.16029i	0.0444645	+	0.165944i	0.984588	−	0.174891i	$-0.0559572\pi$
$967$	1.38269	+	5.16029i	0.0444645	+	0.165944i	−0.940123	+	0.340834i	$0.889291\pi$
$968$		0			0
$969$	21.7186	−	37.6177i	0.697701	−	1.20845i
$970$		0			0
$971$	−46.3073	+	26.7355i	−1.48607	+	0.857984i	−0.999874	−	0.0158651i	$-0.994950\pi$
$971$	−46.3073	+	26.7355i	−1.48607	+	0.857984i	−0.486197	+	0.873849i	$0.661616\pi$
$972$		0			0
$973$			2.92171i			0.0936658i
$974$		0			0
$975$	7.56065	+	28.2167i	0.242135	+	0.903658i
$976$		0			0
$977$	−8.95033	−	2.39823i	−0.286346	−	0.0767263i	0.112787	−	0.993619i	$-0.464022\pi$
$977$	−8.95033	−	2.39823i	−0.286346	−	0.0767263i	−0.399133	+	0.916893i	$0.630689\pi$
$978$		0			0
$979$	1.68475	+	0.451429i	0.0538450	+	0.0144277i
$980$		0			0
$981$	−5.25249	+	1.40740i	−0.167699	+	0.0449349i
$982$		0			0
$983$	−23.0979	−	40.0068i	−0.736710	−	1.27602i	−0.953969	−	0.299905i	$-0.903045\pi$
$983$	−23.0979	−	40.0068i	−0.736710	−	1.27602i	0.217259	−	0.976114i	$-0.430288\pi$
$984$		0			0
$985$	45.6309	+	45.6309i	1.45392	+	1.45392i
$986$		0			0
$987$	−1.87938	−	3.25519i	−0.0598215	−	0.103614i
$988$		0			0
$989$			35.1213i			1.11679i
$990$		0			0
$991$	2.77202	+	2.77202i	0.0880563	+	0.0880563i	0.749763	−	0.661707i	$-0.230168\pi$
$991$	2.77202	+	2.77202i	0.0880563	+	0.0880563i	−0.661707	+	0.749763i	$0.730168\pi$
$992$		0			0
$993$	15.2935	−	15.2935i	0.485324	−	0.485324i
$994$		0			0
$995$	−64.4052	−	37.1844i	−2.04178	−	1.17882i
$996$		0			0
$997$	15.3602	−	57.3252i	0.486464	−	1.81551i	−0.0869147	−	0.996216i	$-0.527701\pi$
$997$	15.3602	−	57.3252i	0.486464	−	1.81551i	0.573378	−	0.819291i	$-0.305633\pi$
$998$		0			0
$999$	30.9981	+	2.72050i	0.980736	+	0.0860728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.f.415.3	yes	20
4.3	odd	2		592.2.be.e.415.3	✓	20
37.14	odd	12		592.2.be.e.495.3	yes	20
148.51	even	12	inner	592.2.be.f.495.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.e.415.3	✓	20	4.3	odd	2
592.2.be.e.495.3	yes	20	37.14	odd	12
592.2.be.f.415.3	yes	20	1.1	even	1	trivial
592.2.be.f.495.3	yes	20	148.51	even	12	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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.520091 + 0.900825i) q^{3} +(-3.71558 + 0.995586i) q^{5} +(0.391848 + 0.226234i) q^{7} +(0.959010 + 1.66105i) q^{9} +O(q^{10})\)	\(q+(-0.520091 + 0.900825i) q^{3} +(-3.71558 + 0.995586i) q^{5} +(0.391848 + 0.226234i) q^{7} +(0.959010 + 1.66105i) q^{9} -3.70591 q^{11} +(2.76896 - 0.741941i) q^{13} +(1.03559 - 3.86488i) q^{15} +(1.35886 - 5.07133i) q^{17} +(-2.05859 - 7.68276i) q^{19} +(-0.407594 + 0.235324i) q^{21} +(-3.08303 + 3.08303i) q^{23} +(8.48420 - 4.89836i) q^{25} -5.11564 q^{27} +(-1.61065 + 1.61065i) q^{29} +(-7.18477 - 7.18477i) q^{31} +(1.92741 - 3.33837i) q^{33} +(-1.68118 - 0.450470i) q^{35} +(-6.05947 - 0.531801i) q^{37} +(-0.771754 + 2.88022i) q^{39} +(6.45703 + 3.72797i) q^{41} +(5.69590 - 5.69590i) q^{43} +(-5.21700 - 5.21700i) q^{45} +7.98636i q^{47} +(-3.39764 - 5.88488i) q^{49} +(3.86165 + 3.86165i) q^{51} +(-2.69388 - 4.66593i) q^{53} +(13.7696 - 3.68955i) q^{55} +(7.99148 + 2.14131i) q^{57} +(1.98576 + 0.532082i) q^{59} +(2.32349 + 8.67138i) q^{61} +0.867841i q^{63} +(-9.54962 + 5.51348i) q^{65} +(-2.55365 + 4.42306i) q^{67} +(-1.17381 - 4.38072i) q^{69} +(-8.28367 - 4.78258i) q^{71} +4.35299i q^{73} +10.1904i q^{75} +(-1.45215 - 0.838401i) q^{77} +(0.277275 + 1.03481i) q^{79} +(-0.216430 + 0.374867i) q^{81} +(2.79430 - 1.61329i) q^{83} +20.1958i q^{85} +(-0.613230 - 2.28860i) q^{87} +(-0.454613 - 0.121813i) q^{89} +(1.25286 + 0.335704i) q^{91} +(10.2090 - 2.73548i) q^{93} +(15.2977 + 26.4964i) q^{95} +(-1.98578 - 1.98578i) q^{97} +(-3.55400 - 6.15571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 4 q^{5} + 6 q^{7} - 16 q^{9}+O(q^{10}) \) 20 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 - 16 * q^9	\( 20 q + 4 q^{3} - 4 q^{5} + 6 q^{7} - 16 q^{9} - 4 q^{11} + 4 q^{13} - 8 q^{15} - 4 q^{17} - 10 q^{19} - 18 q^{21} - 8 q^{23} + 42 q^{25} - 68 q^{27} - 8 q^{29} - 28 q^{31} - 20 q^{33} + 10 q^{35} - 24 q^{37} + 14 q^{39} - 6 q^{41} - 32 q^{43} + 8 q^{45} - 12 q^{49} + 58 q^{51} + 6 q^{53} - 26 q^{55} - 2 q^{57} + 56 q^{59} - 8 q^{61} + 6 q^{65} - 20 q^{67} + 26 q^{69} + 30 q^{71} + 60 q^{77} - 50 q^{79} - 22 q^{81} - 36 q^{83} + 32 q^{87} - 20 q^{89} + 50 q^{91} - 50 q^{93} + 72 q^{95} + 32 q^{97} + 14 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 - 16 * q^9 - 4 * q^11 + 4 * q^13 - 8 * q^15 - 4 * q^17 - 10 * q^19 - 18 * q^21 - 8 * q^23 + 42 * q^25 - 68 * q^27 - 8 * q^29 - 28 * q^31 - 20 * q^33 + 10 * q^35 - 24 * q^37 + 14 * q^39 - 6 * q^41 - 32 * q^43 + 8 * q^45 - 12 * q^49 + 58 * q^51 + 6 * q^53 - 26 * q^55 - 2 * q^57 + 56 * q^59 - 8 * q^61 + 6 * q^65 - 20 * q^67 + 26 * q^69 + 30 * q^71 + 60 * q^77 - 50 * q^79 - 22 * q^81 - 36 * q^83 + 32 * q^87 - 20 * q^89 + 50 * q^91 - 50 * q^93 + 72 * q^95 + 32 * q^97 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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