LMFDB - Embedded newform 847.2.l.k.118.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(118,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("847.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.l (of order $10$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			118.5
Character	$\chi$	$=$	847.118
Dual form			847.2.l.k.524.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.304260 + 0.418778i) q^{2} +(0.535233 - 1.64728i) q^{4} +(-1.94946 + 2.68321i) q^{5} +(0.440093 + 2.60889i) q^{7} +(1.83730 - 0.596975i) q^{8} +(-2.42705 + 1.76336i) q^{9} +O(q^{10})$	\(q+(0.304260 + 0.418778i) q^{2} +(0.535233 - 1.64728i) q^{4} +(-1.94946 + 2.68321i) q^{5} +(0.440093 + 2.60889i) q^{7} +(1.83730 - 0.596975i) q^{8} +(-2.42705 + 1.76336i) q^{9} -1.71681 q^{10} +(-1.38893 + 1.00912i) q^{13} +(-0.958644 + 0.978083i) q^{14} +(-1.99350 - 1.44836i) q^{16} +(-5.18356 - 3.76607i) q^{17} +(-1.47691 - 0.479877i) q^{18} +(-1.44942 - 4.46085i) q^{19} +(3.37657 + 4.64745i) q^{20} -1.26795 q^{23} +(-1.85410 - 5.70634i) q^{25} +(-0.845191 - 0.274619i) q^{26} +(4.53312 + 0.671411i) q^{28} +(-5.87229 - 1.90802i) q^{29} +(5.32603 + 7.33065i) q^{31} -5.13922i q^{32} -3.31662i q^{34} +(-7.85814 - 3.90508i) q^{35} +(1.60570 + 4.94183i) q^{36} +(-2.61555 + 8.04984i) q^{37} +(1.42711 - 1.96424i) q^{38} +(-1.97994 + 6.09364i) q^{40} +(-0.530524 - 1.63278i) q^{41} +5.93426i q^{43} -9.94987i q^{45} +(-0.385786 - 0.530989i) q^{46} +(-8.61770 + 2.80006i) q^{47} +(-6.61264 + 2.29631i) q^{49} +(1.82556 - 2.51267i) q^{50} +(0.918894 + 2.82807i) q^{52} +(-3.17798 + 2.30894i) q^{53} +(2.36603 + 4.53059i) q^{56} +(-0.987665 - 3.03972i) q^{58} +(6.30860 + 2.04979i) q^{59} +(6.57249 + 4.77519i) q^{61} +(-1.44942 + 4.46085i) q^{62} +(-5.66853 - 5.55587i) q^{63} +(-1.83481 + 1.33307i) q^{64} -5.69402i q^{65} +7.66025 q^{67} +(-8.97818 + 6.52303i) q^{68} +(-0.755556 - 4.47898i) q^{70} +(6.03859 + 4.38729i) q^{71} +(-3.40654 + 4.68870i) q^{72} +(1.44942 - 4.46085i) q^{73} +(-4.16690 + 1.35391i) q^{74} -8.12404 q^{76} +(5.37331 + 7.39573i) q^{79} +(7.77251 - 2.52544i) q^{80} +(2.78115 - 8.55951i) q^{81} +(0.522357 - 0.718963i) q^{82} +(-7.58925 - 5.51391i) q^{83} +(20.2103 - 6.56672i) q^{85} +(-2.48514 + 1.80556i) q^{86} +5.74456i q^{89} +(4.16679 - 3.02735i) q^{90} +(-3.24393 - 3.17946i) q^{91} +(-0.678648 + 2.08867i) q^{92} +(-3.79463 - 2.75696i) q^{94} +(14.7950 + 4.80718i) q^{95} +(-4.80368 - 6.61169i) q^{97} +(-2.97360 - 2.07055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 24 q^{9}+O(q^{10}) $ 32 * q - 24 * q^9	$ 32 q - 24 q^{9} - 12 q^{14} + 8 q^{16} - 96 q^{23} + 48 q^{25} + 40 q^{37} - 32 q^{49} + 24 q^{53} + 48 q^{56} - 16 q^{58} - 32 q^{64} - 32 q^{67} + 44 q^{70} + 32 q^{71} - 72 q^{81} - 80 q^{86} - 44 q^{91} - 24 q^{92}+O(q^{100}) $ 32 * q - 24 * q^9 - 12 * q^14 + 8 * q^16 - 96 * q^23 + 48 * q^25 + 40 * q^37 - 32 * q^49 + 24 * q^53 + 48 * q^56 - 16 * q^58 - 32 * q^64 - 32 * q^67 + 44 * q^70 + 32 * q^71 - 72 * q^81 - 80 * q^86 - 44 * q^91 - 24 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.304260	+	0.418778i	0.215144	+	0.296121i	0.902925	−	0.429797i	$-0.141415\pi$
$2$	0.304260	+	0.418778i	0.215144	+	0.296121i	−0.687781	+	0.725918i	$0.741415\pi$
$3$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$3$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$4$	0.535233	−	1.64728i	0.267617	−	0.823639i
$5$	−1.94946	+	2.68321i	−0.871826	+	1.19997i	0.106792	+	0.994281i	$0.465942\pi$
$5$	−1.94946	+	2.68321i	−0.871826	+	1.19997i	−0.978618	+	0.205685i	$0.934058\pi$
$6$		0			0
$7$	0.440093	+	2.60889i	0.166339	+	0.986069i
$7$	0.440093	+	2.60889i	0.166339	+	0.986069i
$8$	1.83730	−	0.596975i	0.649584	−	0.211063i
$9$	−2.42705	+	1.76336i	−0.809017	+	0.587785i
$10$	−1.71681			−0.542903
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−1.38893	+	1.00912i	−0.385220	+	0.279879i	−0.763494	−	0.645815i	$-0.776518\pi$
$13$	−1.38893	+	1.00912i	−0.385220	+	0.279879i	0.378274	+	0.925694i	$0.376518\pi$
$14$	−0.958644	+	0.978083i	−0.256208	+	0.261404i
$15$		0			0
$16$	−1.99350	−	1.44836i	−0.498375	−	0.362091i
$17$	−5.18356	−	3.76607i	−1.25720	−	0.913407i	−0.258580	−	0.965990i	$-0.583255\pi$
$17$	−5.18356	−	3.76607i	−1.25720	−	0.913407i	−0.998617	+	0.0525827i	$0.983255\pi$
$18$	−1.47691	−	0.479877i	−0.348111	−	0.113108i
$19$	−1.44942	−	4.46085i	−0.332519	−	1.02339i	−0.967931	−	0.251216i	$-0.919170\pi$
$19$	−1.44942	−	4.46085i	−0.332519	−	1.02339i	0.635412	−	0.772173i	$-0.280830\pi$
$20$	3.37657	+	4.64745i	0.755024	+	1.03920i
$21$		0			0
$22$		0			0
$23$	−1.26795			−0.264386			−0.132193	−	0.991224i	$-0.542202\pi$
$23$	−1.26795			−0.264386			−0.132193	+	0.991224i	$0.542202\pi$
$24$		0			0
$25$	−1.85410	−	5.70634i	−0.370820	−	1.14127i
$26$	−0.845191	−	0.274619i	−0.165756	−	0.0538573i
$27$		0			0
$28$	4.53312	+	0.671411i	0.856680	+	0.126885i
$29$	−5.87229	−	1.90802i	−1.09046	−	0.354311i	−0.292034	−	0.956408i	$-0.594332\pi$
$29$	−5.87229	−	1.90802i	−1.09046	−	0.354311i	−0.798423	+	0.602097i	$0.794332\pi$
$30$		0			0
$31$	5.32603	+	7.33065i	0.956584	+	1.31662i	0.948540	+	0.316657i	$0.102560\pi$
$31$	5.32603	+	7.33065i	0.956584	+	1.31662i	0.00804346	+	0.999968i	$0.497440\pi$
$32$		−	5.13922i		−	0.908494i
$33$		0			0
$34$		−	3.31662i		−	0.568796i
$35$	−7.85814	−	3.90508i	−1.32827	−	0.660079i
$36$	1.60570	+	4.94183i	0.267617	+	0.823639i
$37$	−2.61555	+	8.04984i	−0.429994	+	1.32339i	0.468136	+	0.883656i	$0.344926\pi$
$37$	−2.61555	+	8.04984i	−0.429994	+	1.32339i	−0.898130	+	0.439729i	$0.855074\pi$
$38$	1.42711	−	1.96424i	0.231507	−	0.318642i
$39$		0			0
$40$	−1.97994	+	6.09364i	−0.313056	+	0.963488i
$41$	−0.530524	−	1.63278i	−0.0828539	−	0.254998i	0.901045	−	0.433727i	$-0.142802\pi$
$41$	−0.530524	−	1.63278i	−0.0828539	−	0.254998i	−0.983898	+	0.178728i	$0.942802\pi$
$42$		0			0
$43$			5.93426i			0.904966i	0.891773	+	0.452483i	$0.149462\pi$
$43$			5.93426i			0.904966i	−0.891773	+	0.452483i	$0.850538\pi$
$44$		0			0
$45$		−	9.94987i		−	1.48324i
$46$	−0.385786	−	0.530989i	−0.0568811	−	0.0782901i
$47$	−8.61770	+	2.80006i	−1.25702	+	0.408431i	−0.860432	−	0.509565i	$-0.829806\pi$
$47$	−8.61770	+	2.80006i	−1.25702	+	0.408431i	−0.396589	+	0.917996i	$0.629806\pi$
$48$		0			0
$49$	−6.61264	+	2.29631i	−0.944662	+	0.328044i
$50$	1.82556	−	2.51267i	0.258173	−	0.355345i
$51$		0			0
$52$	0.918894	+	2.82807i	0.127428	+	0.392182i
$53$	−3.17798	+	2.30894i	−0.436530	+	0.317157i	−0.784254	−	0.620439i	$-0.786954\pi$
$53$	−3.17798	+	2.30894i	−0.436530	+	0.317157i	0.347725	+	0.937597i	$0.386954\pi$
$54$		0			0
$55$		0			0
$56$	2.36603	+	4.53059i	0.316173	+	0.605426i
$57$		0			0
$58$	−0.987665	−	3.03972i	−0.129687	−	0.399135i
$59$	6.30860	+	2.04979i	0.821309	+	0.266860i	0.689380	−	0.724400i	$-0.257883\pi$
$59$	6.30860	+	2.04979i	0.821309	+	0.266860i	0.131929	+	0.991259i	$0.457883\pi$
$60$		0			0
$61$	6.57249	+	4.77519i	0.841520	+	0.611400i	0.922795	−	0.385291i	$-0.125899\pi$
$61$	6.57249	+	4.77519i	0.841520	+	0.611400i	−0.0812745	+	0.996692i	$0.525899\pi$
$62$	−1.44942	+	4.46085i	−0.184076	+	0.566529i
$63$	−5.66853	−	5.55587i	−0.714168	−	0.699974i
$64$	−1.83481	+	1.33307i	−0.229351	+	0.166633i
$65$		−	5.69402i		−	0.706256i
$66$		0			0
$67$	7.66025			0.935849			0.467924	−	0.883768i	$-0.345002\pi$
$67$	7.66025			0.935849			0.467924	+	0.883768i	$0.345002\pi$
$68$	−8.97818	+	6.52303i	−1.08876	+	0.791034i
$69$		0			0
$70$	−0.755556	−	4.47898i	−0.0903062	−	0.535340i
$71$	6.03859	+	4.38729i	0.716648	+	0.520675i	0.885312	−	0.464998i	$-0.153945\pi$
$71$	6.03859	+	4.38729i	0.716648	+	0.520675i	−0.168663	+	0.985674i	$0.553945\pi$
$72$	−3.40654	+	4.68870i	−0.401465	+	0.552569i
$73$	1.44942	−	4.46085i	0.169642	−	0.522103i	−0.829707	−	0.558200i	$-0.811492\pi$
$73$	1.44942	−	4.46085i	0.169642	−	0.522103i	0.999348	+	0.0360965i	$0.0114924\pi$
$74$	−4.16690	+	1.35391i	−0.484393	+	0.157389i
$75$		0			0
$76$	−8.12404			−0.931891
$77$		0			0
$78$		0			0
$79$	5.37331	+	7.39573i	0.604545	+	0.832084i	0.996115	−	0.0880640i	$-0.0280680\pi$
$79$	5.37331	+	7.39573i	0.604545	+	0.832084i	−0.391570	+	0.920148i	$0.628068\pi$
$80$	7.77251	−	2.52544i	0.868993	−	0.282353i
$81$	2.78115	−	8.55951i	0.309017	−	0.951057i
$82$	0.522357	−	0.718963i	0.0576847	−	0.0793962i
$83$	−7.58925	−	5.51391i	−0.833029	−	0.605231i	0.0873859	−	0.996175i	$-0.472149\pi$
$83$	−7.58925	−	5.51391i	−0.833029	−	0.605231i	−0.920415	+	0.390944i	$0.872149\pi$
$84$		0			0
$85$	20.2103	−	6.56672i	2.19211	−	0.712261i
$86$	−2.48514	+	1.80556i	−0.267979	+	0.194698i
$87$		0			0
$88$		0			0
$89$			5.74456i			0.608922i	0.952525	+	0.304461i	$0.0984764\pi$
$89$			5.74456i			0.608922i	−0.952525	+	0.304461i	$0.901524\pi$
$90$	4.16679	−	3.02735i	0.439218	−	0.319111i
$91$	−3.24393	−	3.17946i	−0.340057	−	0.333298i
$92$	−0.678648	+	2.08867i	−0.0707540	+	0.217758i
$93$		0			0
$94$	−3.79463	−	2.75696i	−0.391386	−	0.284358i
$95$	14.7950	+	4.80718i	1.51793	+	0.493206i
$96$		0			0
$97$	−4.80368	−	6.61169i	−0.487739	−	0.671316i	0.492230	−	0.870465i	$-0.336182\pi$
$97$	−4.80368	−	6.61169i	−0.487739	−	0.671316i	−0.979969	+	0.199150i	$0.936182\pi$
$98$	−2.97360	−	2.07055i	−0.300379	−	0.209157i
$99$		0			0
$100$	−10.3923			−1.03923
$101$	3.79463	−	2.75696i	0.377579	−	0.274327i	−0.382767	−	0.923845i	$-0.625029\pi$
$101$	3.79463	−	2.75696i	0.377579	−	0.274327i	0.760347	+	0.649517i	$0.225029\pi$
$102$		0			0
$103$	3.99949	+	1.29951i	0.394081	+	0.128045i	0.499353	−	0.866399i	$-0.333571\pi$
$103$	3.99949	+	1.29951i	0.394081	+	0.128045i	−0.105271	+	0.994444i	$0.533571\pi$
$104$	−1.94946	+	2.68321i	−0.191161	+	0.263110i
$105$		0			0
$106$	−1.93387	−	0.628351i	−0.187834	−	0.0610309i
$107$	−0.984606	+	0.319918i	−0.0951855	+	0.0309276i	−0.356223	−	0.934401i	$-0.615936\pi$
$107$	−0.984606	+	0.319918i	−0.0951855	+	0.0309276i	0.261037	+	0.965329i	$0.415936\pi$
$108$		0			0
$109$			3.62347i			0.347065i	0.984828	+	0.173533i	$0.0555182\pi$
$109$			3.62347i			0.347065i	−0.984828	+	0.173533i	$0.944482\pi$
$110$		0			0
$111$		0			0
$112$	2.90130	−	5.83824i	0.274147	−	0.551662i
$113$	3.45980	+	10.6482i	0.325471	+	1.00170i	0.971228	+	0.238153i	$0.0765419\pi$
$113$	3.45980	+	10.6482i	0.325471	+	1.00170i	−0.645757	+	0.763543i	$0.723458\pi$
$114$		0			0
$115$	2.47182	−	3.40217i	0.230498	−	0.317254i
$116$	−6.28609	+	8.65206i	−0.583649	+	0.803324i
$117$	1.59157	−	4.89835i	0.147141	−	0.452853i
$118$	1.06105	+	3.26557i	0.0976774	+	0.300620i
$119$	7.54404	−	15.1808i	0.691561	−	1.39162i
$120$		0			0
$121$		0			0
$122$			4.20531i			0.380731i
$123$		0			0
$124$	14.9263	−	4.84985i	1.34042	−	0.435529i
$125$	3.15430	+	1.02489i	0.282129	+	0.0916693i
$126$	0.601970	−	4.06429i	0.0536278	−	0.362075i
$127$	1.82556	−	2.51267i	0.161992	−	0.222963i	−0.720303	−	0.693660i	$-0.755997\pi$
$127$	1.82556	−	2.51267i	0.161992	−	0.222963i	0.882295	+	0.470696i	$0.155997\pi$
$128$	−10.8919	−	3.53899i	−0.962716	−	0.312805i
$129$		0			0
$130$	2.38453	−	1.73246i	0.209137	−	0.151947i
$131$	−1.25679			−0.109807			−0.0549033	−	0.998492i	$-0.517485\pi$
$131$	−1.25679			−0.109807			−0.0549033	+	0.998492i	$0.517485\pi$
$132$		0			0
$133$	11.0000	−	5.74456i	0.953821	−	0.498117i
$134$	2.33071	+	3.20795i	0.201343	+	0.277124i
$135$		0			0
$136$	−11.7720	−	3.82495i	−1.00944	−	0.327987i
$137$	−13.6952	−	9.95015i	−1.17006	−	0.850099i	−0.179044	−	0.983841i	$-0.557300\pi$
$137$	−13.6952	−	9.95015i	−1.17006	−	0.850099i	−0.991016	+	0.133743i	$0.957300\pi$
$138$		0			0
$139$	4.34825	−	13.3826i	0.368814	−	1.13509i	−0.578744	−	0.815509i	$-0.696457\pi$
$139$	4.34825	−	13.3826i	0.368814	−	1.13509i	0.947558	−	0.319584i	$-0.103543\pi$
$140$	−10.6387	+	10.8544i	−0.899133	+	0.917365i
$141$		0			0
$142$			3.86370i			0.324235i
$143$		0			0
$144$	7.39230			0.616025
$145$	16.5674	−	12.0369i	1.37585	−	0.999614i
$146$	2.30911	−	0.750274i	0.191103	−	0.0620931i
$147$		0			0
$148$	11.8604	+	8.61708i	0.974918	+	0.708320i
$149$	9.61111	−	13.2286i	0.787372	−	1.08373i	−0.207058	−	0.978329i	$-0.566389\pi$
$149$	9.61111	−	13.2286i	0.787372	−	1.08373i	0.994430	−	0.105396i	$-0.0336112\pi$
$150$		0			0
$151$	−15.7796	+	5.12709i	−1.28412	+	0.417237i	−0.870031	−	0.492998i	$-0.835901\pi$
$151$	−15.7796	+	5.12709i	−1.28412	+	0.417237i	−0.414093	+	0.910235i	$0.635901\pi$
$152$	−5.32603	−	7.33065i	−0.431998	−	0.594595i
$153$	19.2217			1.55398
$154$		0			0
$155$	−30.0526			−2.41388
$156$		0			0
$157$	−10.9268	+	3.55033i	−0.872054	+	0.283348i	−0.710654	−	0.703541i	$-0.751601\pi$
$157$	−10.9268	+	3.55033i	−0.872054	+	0.283348i	−0.161400	+	0.986889i	$0.551601\pi$
$158$	−1.46228	+	4.50045i	−0.116333	+	0.358036i
$159$		0			0
$160$	13.7896	+	10.0187i	1.09016	+	0.792049i
$161$	−0.558015	−	3.30794i	−0.0439777	−	0.260702i
$162$	4.43073	−	1.43963i	0.348111	−	0.113108i
$163$	9.59203	−	6.96902i	0.751306	−	0.545856i	−0.144925	−	0.989443i	$-0.546294\pi$
$163$	9.59203	−	6.96902i	0.751306	−	0.545856i	0.896231	+	0.443587i	$0.146294\pi$
$164$	−2.97360			−0.232199
$165$		0			0
$166$		−	4.85588i		−	0.376889i
$167$	−6.57249	+	4.77519i	−0.508594	+	0.369515i	−0.812290	−	0.583254i	$-0.801779\pi$
$167$	−6.57249	+	4.77519i	−0.508594	+	0.369515i	0.303696	+	0.952769i	$0.401779\pi$
$168$		0			0
$169$	−3.10641	+	9.56055i	−0.238955	+	0.735427i
$170$	8.89919	+	6.46564i	0.682536	+	0.495892i
$171$	11.3839	+	8.27087i	0.870547	+	0.632489i
$172$	9.77537	+	3.17621i	0.745365	+	0.242184i
$173$	4.34825	+	13.3826i	0.330592	+	1.01746i	0.968853	+	0.247637i	$0.0796539\pi$
$173$	4.34825	+	13.3826i	0.330592	+	1.01746i	−0.638261	+	0.769820i	$0.720346\pi$
$174$		0			0
$175$	14.0712	−	7.34847i	1.06369	−	0.555492i
$176$		0			0
$177$		0			0
$178$	−2.40570	+	1.74784i	−0.180315	+	0.131006i
$179$	−1.95909	−	6.02946i	−0.146429	−	0.450663i	0.850763	−	0.525550i	$-0.176140\pi$
$179$	−1.95909	−	6.02946i	−0.146429	−	0.450663i	−0.997192	+	0.0748871i	$0.976140\pi$
$180$	−16.3902	−	5.32550i	−1.22165	−	0.396940i
$181$	7.27550	−	10.0139i	0.540783	−	0.744324i	−0.447942	−	0.894062i	$-0.647843\pi$
$181$	7.27550	−	10.0139i	0.540783	−	0.744324i	0.988726	+	0.149738i	$0.0478430\pi$
$182$	0.344490	−	2.32587i	0.0255353	−	0.172405i
$183$		0			0
$184$	−2.32960	+	0.756934i	−0.171741	+	0.0558019i
$185$	−16.5005	−	22.7109i	−1.21314	−	1.66974i
$186$		0			0
$187$		0			0
$188$			15.6944i			1.14463i
$189$		0			0
$190$	2.48838	+	7.65844i	0.180526	+	0.555602i
$191$	−2.24592	+	6.91223i	−0.162509	+	0.500151i	−0.998844	−	0.0480672i	$-0.984694\pi$
$191$	−2.24592	+	6.91223i	−0.162509	+	0.500151i	0.836335	+	0.548219i	$0.184694\pi$
$192$		0			0
$193$	−5.23210	+	7.20137i	−0.376615	+	0.518366i	−0.954684	−	0.297622i	$-0.903806\pi$
$193$	−5.23210	+	7.20137i	−0.376615	+	0.518366i	0.578069	+	0.815988i	$0.303806\pi$
$194$	1.30726	−	4.02335i	0.0938561	−	0.288859i
$195$		0			0
$196$	0.243355	+	12.1219i	0.0173825	+	0.865851i
$197$			19.1798i			1.36651i	0.730182	+	0.683253i	$0.239435\pi$
$197$			19.1798i			1.36651i	−0.730182	+	0.683253i	$0.760565\pi$
$198$		0			0
$199$			24.7556i			1.75488i	0.479687	+	0.877440i	$0.340750\pi$
$199$			24.7556i			1.75488i	−0.479687	+	0.877440i	$0.659250\pi$
$200$	−6.81308	−	9.37740i	−0.481758	−	0.663083i
$201$		0			0
$202$	2.30911	+	0.750274i	0.162468	+	0.0527891i
$203$	2.39348	−	16.1599i	0.167989	−	1.13420i
$204$		0			0
$205$	5.41533	+	1.75955i	0.378223	+	0.122892i
$206$	0.672677	+	2.07029i	0.0468676	+	0.144244i
$207$	3.07738	−	2.23585i	0.213893	−	0.155402i
$208$	4.23040			0.293325
$209$		0			0
$210$		0			0
$211$	12.7949	+	17.6107i	0.880838	+	1.21237i	0.976188	+	0.216926i	$0.0696030\pi$
$211$	12.7949	+	17.6107i	0.880838	+	1.21237i	−0.0953499	+	0.995444i	$0.530397\pi$
$212$	2.10250	+	6.47084i	0.144401	+	0.444419i
$213$		0			0
$214$	−0.433551	−	0.314993i	−0.0296369	−	0.0215325i
$215$	−15.9228	−	11.5686i	−1.08593	−	0.788973i
$216$		0			0
$217$	−16.7809	+	17.1212i	−1.13916	+	1.16226i
$218$	−1.51743	+	1.10248i	−0.102773	+	0.0746691i
$219$		0			0
$220$		0			0
$221$	11.0000			0.739940
$222$		0			0
$223$	−4.61821	+	1.50055i	−0.309258	+	0.100484i	−0.459534	−	0.888160i	$-0.651984\pi$
$223$	−4.61821	+	1.50055i	−0.309258	+	0.100484i	0.150276	+	0.988644i	$0.451984\pi$
$224$	13.4077	−	2.26173i	0.895837	−	0.151118i
$225$	14.5623	+	10.5801i	0.970820	+	0.705342i
$226$	−3.40654	+	4.68870i	−0.226600	+	0.311888i
$227$	−1.83779	+	5.65613i	−0.121978	+	0.375411i	−0.993338	−	0.115233i	$-0.963238\pi$
$227$	−1.83779	+	5.65613i	−0.121978	+	0.375411i	0.871360	+	0.490644i	$0.163238\pi$
$228$		0			0
$229$	3.37657	+	4.64745i	0.223130	+	0.307112i	0.905875	−	0.423544i	$-0.139214\pi$
$229$	3.37657	+	4.64745i	0.223130	+	0.307112i	−0.682745	+	0.730656i	$0.739214\pi$
$230$	2.17683			0.143536
$231$		0			0
$232$	−11.9282			−0.783125
$233$	−2.41224	−	3.32016i	−0.158031	−	0.217511i	0.722658	−	0.691205i	$-0.242920\pi$
$233$	−2.41224	−	3.32016i	−0.158031	−	0.217511i	−0.880689	+	0.473695i	$0.842920\pi$
$234$	2.53557	−	0.823858i	0.165756	−	0.0538573i
$235$	9.28675	−	28.5817i	0.605801	−	1.86446i
$236$	6.75314	−	9.29490i	0.439592	−	0.605046i
$237$		0			0
$238$	8.65272	−	1.45962i	0.560872	−	0.0946132i
$239$	23.0322	−	7.48362i	1.48983	−	0.484075i	0.552797	−	0.833316i	$-0.313561\pi$
$239$	23.0322	−	7.48362i	1.48983	−	0.484075i	0.937033	+	0.349241i	$0.113561\pi$
$240$		0			0
$241$	20.9385			1.34877			0.674383	−	0.738381i	$-0.264410\pi$
$241$	20.9385			1.34877			0.674383	+	0.738381i	$0.264410\pi$
$242$		0			0
$243$		0			0
$244$	11.3839	−	8.27087i	0.728778	−	0.529488i
$245$	6.72963	−	22.2196i	0.429940	−	1.41956i
$246$		0			0
$247$	6.51466	+	4.73318i	0.414518	+	0.301165i
$248$	14.1617	+	10.2891i	0.899271	+	0.653359i
$249$		0			0
$250$	0.530524	+	1.63278i	0.0335533	+	0.103266i
$251$	−6.37075	−	8.76858i	−0.402118	−	0.553468i	0.559156	−	0.829062i	$-0.311125\pi$
$251$	−6.37075	−	8.76858i	−0.402118	−	0.553468i	−0.961274	+	0.275595i	$0.911125\pi$
$252$	−12.1861	+	6.36396i	−0.767649	+	0.400892i
$253$		0			0
$254$	1.60770			0.100876
$255$		0			0
$256$	−0.430246	−	1.32416i	−0.0268904	−	0.0827600i
$257$	22.6988	+	7.37529i	1.41591	+	0.460058i	0.914301	−	0.405035i	$-0.132741\pi$
$257$	22.6988	+	7.37529i	1.41591	+	0.460058i	0.501612	+	0.865093i	$0.332741\pi$
$258$		0			0
$259$	−22.1522	−	3.28102i	−1.37647	−	0.203873i
$260$	−9.37963	−	3.04763i	−0.581700	−	0.189006i
$261$	17.6169	−	5.72407i	1.09046	−	0.354311i
$262$	−0.382392	−	0.526317i	−0.0236243	−	0.0325160i
$263$			5.93426i			0.365922i	0.983120	+	0.182961i	$0.0585682\pi$
$263$			5.93426i			0.365922i	−0.983120	+	0.182961i	$0.941432\pi$
$264$		0			0
$265$		−	13.0284i		−	0.800327i
$266$	5.75256	+	2.85872i	0.352712	+	0.175279i
$267$		0			0
$268$	4.10002	−	12.6186i	0.250449	−	0.770802i
$269$	−15.0733	+	20.7467i	−0.919038	+	1.26495i	0.0449463	+	0.998989i	$0.485688\pi$
$269$	−15.0733	+	20.7467i	−0.919038	+	1.26495i	−0.963985	+	0.265958i	$0.914312\pi$
$270$		0			0
$271$	5.40930	−	16.6481i	0.328592	−	1.01130i	−0.641201	−	0.767373i	$-0.721564\pi$
$271$	5.40930	−	16.6481i	0.328592	−	1.01130i	0.969793	−	0.243929i	$-0.0784363\pi$
$272$	4.87878	+	15.0153i	0.295819	+	0.910438i
$273$		0			0
$274$		−	8.76268i		−	0.529373i
$275$		0			0
$276$		0			0
$277$	0.304260	+	0.418778i	0.0182812	+	0.0251619i	0.818060	−	0.575133i	$-0.195050\pi$
$277$	0.304260	+	0.418778i	0.0182812	+	0.0251619i	−0.799779	+	0.600295i	$0.795050\pi$
$278$	6.92732	−	2.25082i	0.415473	−	0.134995i
$279$	−25.8531	−	8.40018i	−1.54778	−	0.502906i
$280$	−16.7690	−	2.48369i	−1.00214	−	0.148429i
$281$	−1.88524	+	2.59481i	−0.112464	+	0.154794i	−0.861538	−	0.507693i	$-0.830499\pi$
$281$	−1.88524	+	2.59481i	−0.112464	+	0.154794i	0.749074	+	0.662486i	$0.230499\pi$
$282$		0			0
$283$	−2.89884	−	8.92170i	−0.172318	−	0.530340i	0.827183	−	0.561933i	$-0.189942\pi$
$283$	−2.89884	−	8.92170i	−0.172318	−	0.530340i	−0.999501	+	0.0315927i	$0.989942\pi$
$284$	10.4591	−	7.59901i	0.620636	−	0.450918i
$285$		0			0
$286$		0			0
$287$	4.02628	−	2.10266i	0.237664	−	0.124116i
$288$	9.06227	+	12.4731i	0.533999	+	0.734987i
$289$	7.43265	+	22.8753i	0.437215	+	1.34561i
$290$	10.0816	+	3.27572i	0.592013	+	0.192357i
$291$		0			0
$292$	−6.57249	−	4.77519i	−0.384626	−	0.279447i
$293$	−7.77761	+	23.9370i	−0.454373	+	1.39842i	0.417496	+	0.908679i	$0.362908\pi$
$293$	−7.77761	+	23.9370i	−0.454373	+	1.39842i	−0.871870	+	0.489738i	$0.837092\pi$
$294$		0			0
$295$	−17.7984	+	12.9313i	−1.03626	+	0.752888i
$296$			16.3514i			0.950405i
$297$		0			0
$298$	8.46410			0.490312
$299$	1.76109	−	1.27951i	0.101847	−	0.0739959i
$300$		0			0
$301$	−15.4818	+	2.61162i	−0.892358	+	0.150531i
$302$	−6.94821	−	5.04817i	−0.399824	−	0.290489i
$303$		0			0
$304$	−3.57151	+	10.9920i	−0.204840	+	0.630434i
$305$	−25.6256	+	8.32627i	−1.46732	+	0.476761i
$306$	5.84839	+	8.04962i	0.334330	+	0.460166i
$307$	−24.3721			−1.39099			−0.695495	−	0.718531i	$-0.744815\pi$
$307$	−24.3721			−1.39099			−0.695495	+	0.718531i	$0.744815\pi$
$308$		0			0
$309$		0			0
$310$	−9.14379	−	12.5854i	−0.519333	−	0.714800i
$311$	−3.99949	+	1.29951i	−0.226790	+	0.0736886i	−0.420208	−	0.907428i	$-0.638043\pi$
$311$	−3.99949	+	1.29951i	−0.226790	+	0.0736886i	0.193418	+	0.981117i	$0.438043\pi$
$312$		0			0
$313$	6.23078	−	8.57593i	0.352185	−	0.484740i	−0.595766	−	0.803158i	$-0.703151\pi$
$313$	6.23078	−	8.57593i	0.352185	−	0.484740i	0.947951	+	0.318418i	$0.103151\pi$
$314$	−4.81139	−	3.49568i	−0.271523	−	0.197273i
$315$	25.9581	−	4.37887i	1.46258	−	0.246721i
$316$	15.0588	−	4.89290i	0.847123	−	0.275247i
$317$	5.72120	−	4.15670i	0.321335	−	0.233463i	−0.415410	−	0.909634i	$-0.636362\pi$
$317$	5.72120	−	4.15670i	0.321335	−	0.233463i	0.736745	+	0.676171i	$0.236362\pi$
$318$		0			0
$319$		0			0
$320$		−	7.52194i		−	0.420489i
$321$		0			0
$322$	1.21551	−	1.24016i	0.0677378	−	0.0691114i
$323$	−9.28675	+	28.5817i	−0.516729	+	1.59033i
$324$	−12.6113	−	9.16267i	−0.700629	−	0.509037i
$325$	8.33358	+	6.05470i	0.462264	+	0.335854i
$326$	5.83695	+	1.89654i	0.323279	+	0.105040i
$327$		0			0
$328$	−1.94946	−	2.68321i	−0.107641	−	0.148155i
$329$	−11.0976	−	21.2504i	−0.611833	−	1.17157i
$330$		0			0
$331$	−1.26795			−0.0696928			−0.0348464	−	0.999393i	$-0.511094\pi$
$331$	−1.26795			−0.0696928			−0.0348464	+	0.999393i	$0.511094\pi$
$332$	−13.1450	+	9.55038i	−0.721424	+	0.524145i
$333$	−7.84665	−	24.1495i	−0.429994	−	1.32339i
$334$	−3.99949	−	1.29951i	−0.218842	−	0.0711062i
$335$	−14.9334	+	20.5540i	−0.815898	+	1.12299i
$336$		0			0
$337$	−27.1025	−	8.80615i	−1.47637	−	0.479702i	−0.543344	−	0.839510i	$-0.682842\pi$
$337$	−27.1025	−	8.80615i	−1.47637	−	0.479702i	−0.933026	+	0.359809i	$0.882842\pi$
$338$	−4.94891	+	1.60800i	−0.269185	+	0.0874635i
$339$		0			0
$340$		−	36.8067i		−	1.99612i
$341$		0			0
$342$			7.28381i			0.393864i
$343$	−8.90099	−	16.2411i	−0.480608	−	0.876935i
$344$	3.54260	+	10.9030i	0.191004	+	0.587851i
$345$		0			0
$346$	−4.28132	+	5.89273i	−0.230165	+	0.316795i
$347$	16.4023	−	22.5759i	0.880524	−	1.21194i	−0.0957516	−	0.995405i	$-0.530525\pi$
$347$	16.4023	−	22.5759i	0.880524	−	1.21194i	0.976276	−	0.216532i	$-0.0694746\pi$
$348$		0			0
$349$	−11.3491	−	34.9290i	−0.607505	−	1.86971i	−0.478557	−	0.878057i	$-0.658840\pi$
$349$	−11.3491	−	34.9290i	−0.607505	−	1.86971i	−0.128948	−	0.991651i	$-0.541160\pi$
$350$	7.35870	+	3.65688i	0.393339	+	0.195469i
$351$		0			0
$352$		0			0
$353$		−	10.6004i		−	0.564204i	−0.959384	−	0.282102i	$-0.908968\pi$
$353$		−	10.6004i		−	0.564204i	0.959384	−	0.282102i	$-0.0910317\pi$
$354$		0			0
$355$	−23.5440	+	7.64991i	−1.24959	+	0.406015i
$356$	9.46289	+	3.07468i	0.501532	+	0.162958i
$357$		0			0
$358$	1.92893	−	2.65495i	0.101947	−	0.140318i
$359$	−10.8565	−	3.52750i	−0.572986	−	0.186175i	0.00816976	−	0.999967i	$-0.497399\pi$
$359$	−10.8565	−	3.52750i	−0.572986	−	0.186175i	−0.581156	+	0.813792i	$0.697399\pi$
$360$	−5.93983	−	18.2809i	−0.313056	−	0.963488i
$361$	−2.42705	+	1.76336i	−0.127740	+	0.0928082i
$362$	6.40723			0.336756
$363$		0			0
$364$	−6.97372	+	3.64191i	−0.365522	+	0.190888i
$365$	9.14379	+	12.5854i	0.478608	+	0.658747i
$366$		0			0
$367$	−12.6172	−	4.09957i	−0.658612	−	0.213996i	−0.0394044	−	0.999223i	$-0.512546\pi$
$367$	−12.6172	−	4.09957i	−0.658612	−	0.213996i	−0.619208	+	0.785227i	$0.712546\pi$
$368$	2.52766	+	1.83645i	0.131763	+	0.0957316i
$369$	4.16679	+	3.02735i	0.216914	+	0.157598i
$370$	4.49041	−	13.8201i	0.233445	−	0.718470i
$371$	−7.42238	−	7.27487i	−0.385351	−	0.377692i
$372$		0			0
$373$			12.2474i			0.634149i	0.948401	+	0.317074i	$0.102701\pi$
$373$			12.2474i			0.634149i	−0.948401	+	0.317074i	$0.897299\pi$
$374$		0			0
$375$		0			0
$376$	−14.1617	+	10.2891i	−0.730336	+	0.530620i
$377$	10.0816	−	3.27572i	0.519230	−	0.168708i
$378$		0			0
$379$	10.6178	+	7.71430i	0.545401	+	0.396257i	0.826087	−	0.563543i	$-0.190562\pi$
$379$	10.6178	+	7.71430i	0.545401	+	0.396257i	−0.280686	+	0.959800i	$0.590562\pi$
$380$	15.8375	−	21.7985i	0.812447	−	1.11824i
$381$		0			0
$382$	−3.57803	+	1.16257i	−0.183068	+	0.0594824i
$383$	8.18024	+	11.2591i	0.417991	+	0.575315i	0.965145	−	0.261717i	$-0.0842887\pi$
$383$	8.18024	+	11.2591i	0.417991	+	0.575315i	−0.547154	+	0.837032i	$0.684289\pi$
$384$		0			0
$385$		0			0
$386$	−4.60770			−0.234526
$387$	−10.4642	−	14.4027i	−0.531925	−	0.732132i
$388$	−13.4624	+	4.37419i	−0.683449	+	0.222066i
$389$	−0.127174	+	0.391400i	−0.00644796	+	0.0198448i	−0.954229	−	0.299078i	$-0.903321\pi$
$389$	−0.127174	+	0.391400i	−0.00644796	+	0.0198448i	0.947781	+	0.318923i	$0.103321\pi$
$390$		0			0
$391$	6.57249	+	4.77519i	0.332385	+	0.241492i
$392$	−10.7786	+	8.16659i	−0.544400	+	0.412475i
$393$		0			0
$394$	−8.03209	+	5.83565i	−0.404651	+	0.293996i
$395$	−30.3193			−1.52553
$396$		0			0
$397$		−	16.5831i		−	0.832283i	−0.909300	−	0.416142i	$-0.863382\pi$
$397$		−	16.5831i		−	0.832283i	0.909300	−	0.416142i	$-0.136618\pi$
$398$	−10.3671	+	7.53215i	−0.519656	+	0.377552i
$399$		0			0
$400$	−4.56870	+	14.0610i	−0.228435	+	0.703050i
$401$	1.71864	+	1.24866i	0.0858248	+	0.0623554i	0.629870	−	0.776700i	$-0.283108\pi$
$401$	1.71864	+	1.24866i	0.0858248	+	0.0623554i	−0.544045	+	0.839056i	$0.683108\pi$
$402$		0			0
$403$	−14.7950	−	4.80718i	−0.736990	−	0.239463i
$404$	−2.51047	−	7.72642i	−0.124900	−	0.384404i
$405$	17.5452	+	24.1489i	0.871826	+	1.19997i
$406$	7.49564	−	3.91447i	0.372002	−	0.194272i
$407$		0			0
$408$		0			0
$409$	4.16679	−	3.02735i	0.206034	−	0.149693i	−0.479983	−	0.877278i	$-0.659357\pi$
$409$	4.16679	−	3.02735i	0.206034	−	0.149693i	0.686018	+	0.727585i	$0.259357\pi$
$410$	0.910809	+	2.80318i	0.0449817	+	0.138439i
$411$		0			0
$412$	4.28132	−	5.89273i	0.210925	−	0.290314i
$413$	−2.57131	+	17.3605i	−0.126526	+	0.854256i
$414$	1.87265	+	0.608460i	0.0920355	+	0.0299042i
$415$	29.5899	−	9.61435i	1.45251	−	0.471950i
$416$	5.18607	+	7.13801i	0.254268	+	0.349970i
$417$		0			0
$418$		0			0
$419$			0.650564i			0.0317821i	0.999874	+	0.0158911i	$0.00505850\pi$
$419$			0.650564i			0.0317821i	−0.999874	+	0.0158911i	$0.994942\pi$
$420$		0			0
$421$	1.44010	+	4.43216i	0.0701861	+	0.216011i	0.979997	−	0.199013i	$-0.0637735\pi$
$421$	1.44010	+	4.43216i	0.0701861	+	0.216011i	−0.909811	+	0.415023i	$0.863773\pi$
$422$	−3.48199	+	10.7165i	−0.169501	+	0.521669i
$423$	15.9781	−	21.9920i	0.776882	−	1.06929i
$424$	−4.46053	+	6.13939i	−0.216622	+	0.298155i
$425$	−11.8797	+	36.5618i	−0.576248	+	1.77351i
$426$		0			0
$427$	−9.56545	+	19.2484i	−0.462905	+	0.931497i
$428$			1.79315i			0.0866752i
$429$		0			0
$430$		−	10.1880i		−	0.491309i
$431$	−21.3302	−	29.3585i	−1.02744	−	1.41415i	−0.906854	−	0.421445i	$-0.861523\pi$
$431$	−21.3302	−	29.3585i	−1.02744	−	1.41415i	−0.120585	−	0.992703i	$-0.538477\pi$
$432$		0			0
$433$	31.3165	+	10.1754i	1.50498	+	0.488996i	0.941464	−	0.337112i	$-0.109450\pi$
$433$	31.3165	+	10.1754i	1.50498	+	0.488996i	0.563511	+	0.826109i	$0.309450\pi$
$434$	−12.2758	−	1.81819i	−0.589255	−	0.0872759i
$435$		0			0
$436$	5.96886	+	1.93940i	0.285856	+	0.0928804i
$437$	1.83779	+	5.65613i	0.0879134	+	0.270569i
$438$		0			0
$439$	−25.6289			−1.22320			−0.611601	−	0.791167i	$-0.709474\pi$
$439$	−25.6289			−1.22320			−0.611601	+	0.791167i	$0.709474\pi$
$440$		0			0
$441$	12.0000	−	17.2337i	0.571429	−	0.820652i
$442$	3.34686	+	4.60656i	0.159194	+	0.219112i
$443$	0.0606144	+	0.186552i	0.00287988	+	0.00886335i	0.952486	−	0.304582i	$-0.0985168\pi$
$443$	0.0606144	+	0.186552i	0.00287988	+	0.00886335i	−0.949606	+	0.313445i	$0.898517\pi$
$444$		0			0
$445$	−15.4138	−	11.1988i	−0.730686	−	0.530875i
$446$	−2.03353	−	1.47745i	−0.0962906	−	0.0699592i
$447$		0			0
$448$	−4.28531	−	4.20015i	−0.202462	−	0.198438i
$449$	0.692847	−	0.503383i	0.0326975	−	0.0237561i	−0.571316	−	0.820730i	$-0.693567\pi$
$449$	0.692847	−	0.503383i	0.0326975	−	0.0237561i	0.604014	+	0.796974i	$0.293567\pi$
$450$			9.31749i			0.439230i
$451$		0			0
$452$	19.3923			0.912137
$453$		0			0
$454$	−2.92783	+	0.951309i	−0.137410	+	0.0446472i
$455$	14.8551	−	2.50590i	0.696417	−	0.117478i
$456$		0			0
$457$	−19.8089	+	27.2646i	−0.926621	+	1.27538i	0.0345426	+	0.999403i	$0.489003\pi$
$457$	−19.8089	+	27.2646i	−0.926621	+	1.27538i	−0.961163	+	0.275981i	$0.910997\pi$
$458$	−0.918894	+	2.82807i	−0.0429371	+	0.132147i
$459$		0			0
$460$	−4.28132	−	5.89273i	−0.199617	−	0.274750i
$461$	15.7881			0.735323			0.367662	−	0.929960i	$-0.380158\pi$
$461$	15.7881			0.735323			0.367662	+	0.929960i	$0.380158\pi$
$462$		0			0
$463$	−0.392305			−0.0182320			−0.00911598	−	0.999958i	$-0.502902\pi$
$463$	−0.392305			−0.0182320			−0.00911598	+	0.999958i	$0.502902\pi$
$464$	8.94290	+	12.3089i	0.415164	+	0.571424i
$465$		0			0
$466$	0.656462	−	2.02038i	0.0304100	−	0.0935924i
$467$	−14.9334	+	20.5540i	−0.691035	+	0.951127i	0.308965	+	0.951073i	$0.400017\pi$
$467$	−14.9334	+	20.5540i	−0.691035	+	0.951127i	−1.00000		5.41955e-5i	$0.999983\pi$
$468$	−7.21709	−	5.24352i	−0.333610	−	0.242382i
$469$	3.37122	+	19.9848i	0.155668	+	0.922811i
$470$	14.7950	−	4.80718i	0.682441	−	0.221739i
$471$		0			0
$472$	12.8145			0.589833
$473$		0			0
$474$		0			0
$475$	−22.7678	+	16.5417i	−1.04466	+	0.758987i
$476$	−20.9691	−	20.5524i	−0.961118	−	0.942016i
$477$	3.64164	−	11.2078i	0.166739	−	0.513171i
$478$	10.1418	+	7.36842i	0.463873	+	0.337024i
$479$	−31.1013	−	22.5964i	−1.42106	−	1.03246i	−0.991596	−	0.129372i	$-0.958704\pi$
$479$	−31.1013	−	22.5964i	−1.42106	−	1.03246i	−0.429460	−	0.903086i	$-0.641296\pi$
$480$		0			0
$481$	−4.49041	−	13.8201i	−0.204745	−	0.630140i
$482$	6.37075	+	8.76858i	0.290180	+	0.399398i
$483$		0			0
$484$		0			0
$485$	27.1051			1.23078
$486$		0			0
$487$	−2.42776	−	7.47189i	−0.110012	−	0.338583i	0.880862	−	0.473374i	$-0.156964\pi$
$487$	−2.42776	−	7.47189i	−0.110012	−	0.338583i	−0.990874	+	0.134790i	$0.956964\pi$
$488$	14.9263	+	4.84985i	0.675682	+	0.219542i
$489$		0			0
$490$	11.3527	−	3.94233i	0.512860	−	0.178096i
$491$	−12.4654	−	4.05024i	−0.562554	−	0.182785i	0.0139160	−	0.999903i	$-0.495570\pi$
$491$	−12.4654	−	4.05024i	−0.562554	−	0.182785i	−0.576470	+	0.817118i	$0.695570\pi$
$492$		0			0
$493$	23.2536	+	32.0058i	1.04729	+	1.44147i
$494$			4.16831i			0.187541i
$495$		0			0
$496$		−	22.3277i		−	1.00254i
$497$	−8.78843	+	17.6848i	−0.394215	+	0.793273i
$498$		0			0
$499$	4.55245	−	14.0110i	0.203796	−	0.627219i	−0.795965	−	0.605343i	$-0.793036\pi$
$499$	4.55245	−	14.0110i	0.203796	−	0.627219i	0.999761	−	0.0218762i	$-0.00696398\pi$
$500$	3.37657	−	4.64745i	0.151005	−	0.207840i
$501$		0			0
$502$	1.73373	−	5.33586i	0.0773799	−	0.238151i
$503$	11.4913	+	35.3665i	0.512371	+	1.57692i	0.788015	+	0.615656i	$0.211109\pi$
$503$	11.4913	+	35.3665i	0.512371	+	1.57692i	−0.275644	+	0.961260i	$0.588891\pi$
$504$	−13.7315	−	6.82384i	−0.611650	−	0.303958i
$505$			15.5563i			0.692248i
$506$		0			0
$507$		0			0
$508$	−3.16196	−	4.35207i	−0.140289	−	0.193092i
$509$	25.2344	−	8.19915i	1.11849	−	0.363421i	0.309301	−	0.950964i	$-0.399905\pi$
$509$	25.2344	−	8.19915i	1.11849	−	0.363421i	0.809193	+	0.587543i	$0.199905\pi$
$510$		0			0
$511$	12.2758	+	1.81819i	0.543047	+	0.0804319i
$512$	−13.0395	+	17.9473i	−0.576270	+	0.793167i
$513$		0			0
$514$	3.81773	+	11.7498i	0.168393	+	0.518260i
$515$	−11.2837	+	8.19810i	−0.497220	+	0.361251i
$516$		0			0
$517$		0			0
$518$	−5.36603	−	10.2752i	−0.235770	−	0.451464i
$519$		0			0
$520$	−3.39919	−	10.4616i	−0.149064	−	0.458772i
$521$	12.6172	+	4.09957i	0.552769	+	0.179606i	0.572065	−	0.820208i	$-0.306142\pi$
$521$	12.6172	+	4.09957i	0.552769	+	0.179606i	−0.0192959	+	0.999814i	$0.506142\pi$
$522$	7.75722	+	5.63595i	0.339525	+	0.246679i
$523$	20.7342	+	15.0643i	0.906644	+	0.658716i	0.940164	−	0.340722i	$-0.110672\pi$
$523$	20.7342	+	15.0643i	0.906644	+	0.658716i	−0.0335197	+	0.999438i	$0.510672\pi$
$524$	−0.672677	+	2.07029i	−0.0293860	+	0.0904409i
$525$		0			0
$526$	−2.48514	+	1.80556i	−0.108357	+	0.0787260i
$527$		−	58.0571i		−	2.52901i
$528$		0			0
$529$	−21.3923			−0.930100
$530$	5.45600	−	3.96401i	0.236993	−	0.172186i
$531$	−18.9258	+	6.14936i	−0.821309	+	0.266860i
$532$	−3.57533	−	21.1947i	−0.155010	−	0.918909i
$533$	2.38453	+	1.73246i	0.103285	+	0.0750413i
$534$		0			0
$535$	1.06105	−	3.26557i	0.0458731	−	0.141183i
$536$	14.0742	−	4.57298i	0.607912	−	0.197523i
$537$		0			0
$538$	−13.2745			−0.572303
$539$		0			0
$540$		0			0
$541$	6.10119	+	8.39757i	0.262311	+	0.361040i	0.919775	−	0.392446i	$-0.128371\pi$
$541$	6.10119	+	8.39757i	0.262311	+	0.361040i	−0.657464	+	0.753486i	$0.728371\pi$
$542$	8.61770	−	2.80006i	0.370162	−	0.120273i
$543$		0			0
$544$	−19.3547	+	26.6394i	−0.829824	+	1.14216i
$545$	−9.72251	−	7.06381i	−0.416466	−	0.302581i
$546$		0			0
$547$	3.84186	−	1.24830i	0.164266	−	0.0533733i	−0.225730	−	0.974190i	$-0.572477\pi$
$547$	3.84186	−	1.24830i	0.164266	−	0.0533733i	0.389996	+	0.920817i	$0.372477\pi$
$548$	−23.7208	+	17.2342i	−1.01330	+	0.736207i
$549$	−24.3721			−1.04018
$550$		0			0
$551$			28.9609i			1.23378i
$552$		0			0
$553$	−16.9299	+	17.2732i	−0.719933	+	0.734531i
$554$	−0.0828009	+	0.254835i	−0.00351787	+	0.0108269i
$555$		0			0
$556$	−19.7175	−	14.3256i	−0.836206	−	0.607539i
$557$	14.3380	+	4.65870i	0.607521	+	0.197396i	0.596592	−	0.802545i	$-0.296521\pi$
$557$	14.3380	+	4.65870i	0.607521	+	0.197396i	0.0109290	+	0.999940i	$0.496521\pi$
$558$	−4.34825	−	13.3826i	−0.184076	−	0.566529i
$559$	−5.98835	−	8.24226i	−0.253280	−	0.348611i
$560$	10.0092	+	19.1662i	0.422967	+	0.809920i
$561$		0			0
$562$	−1.66025			−0.0700336
$563$	−5.55572	+	4.03647i	−0.234146	+	0.170117i	−0.698671	−	0.715443i	$-0.746225\pi$
$563$	−5.55572	+	4.03647i	−0.234146	+	0.170117i	0.464525	+	0.885560i	$0.346225\pi$
$564$		0			0
$565$	−35.3160	−	11.4749i	−1.48576	−	0.482751i
$566$	2.85421	−	3.92849i	0.119971	−	0.165127i
$567$	23.5548	+	3.48875i	0.989209	+	0.146514i
$568$	13.7138	+	4.45588i	0.575418	+	0.186965i
$569$	−6.98881	+	2.27080i	−0.292986	+	0.0951970i	−0.451822	−	0.892108i	$-0.649226\pi$
$569$	−6.98881	+	2.27080i	−0.292986	+	0.0951970i	0.158836	+	0.987305i	$0.449226\pi$
$570$		0			0
$571$			13.4858i			0.564363i	0.959361	+	0.282182i	$0.0910580\pi$
$571$			13.4858i			0.564363i	−0.959361	+	0.282182i	$0.908942\pi$
$572$		0			0
$573$		0			0
$574$	2.10558	+	1.04636i	0.0878853	+	0.0436744i
$575$	2.35091	+	7.23535i	0.0980396	+	0.301735i
$576$	2.10250	−	6.47084i	0.0876044	−	0.269618i
$577$	−6.89310	+	9.48754i	−0.286964	+	0.394972i	−0.928025	−	0.372518i	$-0.878494\pi$
$577$	−6.89310	+	9.48754i	−0.286964	+	0.394972i	0.641061	+	0.767490i	$0.278494\pi$
$578$	−7.31823	+	10.0727i	−0.304398	+	0.418968i
$579$		0			0
$580$	−10.9608	−	33.7337i	−0.455121	−	1.40072i
$581$	11.0452	−	22.2262i	0.458234	−	0.922097i
$582$		0			0
$583$		0			0
$584$		−	9.06119i		−	0.374955i
$585$	10.0406	+	13.8197i	0.415127	+	0.571373i
$586$	−12.3907	+	4.02599i	−0.511856	+	0.166312i
$587$	−16.6167	−	5.39909i	−0.685844	−	0.222844i	−0.0546917	−	0.998503i	$-0.517418\pi$
$587$	−16.6167	−	5.39909i	−0.685844	−	0.222844i	−0.631152	+	0.775659i	$0.717418\pi$
$588$		0			0
$589$	24.9813	−	34.3838i	1.02934	−	1.41676i
$590$	−10.8307	−	3.51910i	−0.445892	−	0.144879i
$591$		0			0
$592$	16.8732	−	12.2591i	0.693484	−	0.503845i
$593$	14.5313			0.596728			0.298364	−	0.954452i	$-0.403559\pi$
$593$	14.5313			0.596728			0.298364	+	0.954452i	$0.403559\pi$
$594$		0			0
$595$	26.0263	+	49.8365i	1.06697	+	2.04310i
$596$	−16.6469	−	22.9125i	−0.681885	−	0.938534i
$597$		0			0
$598$	1.07166	+	0.348203i	0.0438234	+	0.0142391i
$599$	−38.0082	−	27.6146i	−1.55297	−	1.12830i	−0.941488	−	0.337047i	$-0.890572\pi$
$599$	−38.0082	−	27.6146i	−1.55297	−	1.12830i	−0.611487	−	0.791255i	$-0.709428\pi$
$600$		0			0
$601$	−4.87878	+	15.0153i	−0.199010	+	0.612488i	0.800897	+	0.598802i	$0.204357\pi$
$601$	−4.87878	+	15.0153i	−0.199010	+	0.612488i	−0.999906	+	0.0136860i	$0.995643\pi$
$602$	−5.80419	−	5.68884i	−0.236561	−	0.231860i
$603$	−18.5918	+	13.5078i	−0.757118	+	0.550078i
$604$			28.7375i			1.16931i
$605$		0			0
$606$		0			0
$607$	−20.7342	+	15.0643i	−0.841576	+	0.611441i	−0.922810	−	0.385254i	$-0.874114\pi$
$607$	−20.7342	+	15.0643i	−0.841576	+	0.611441i	0.0812344	+	0.996695i	$0.474114\pi$
$608$	−22.9253	+	7.44887i	−0.929743	+	0.302092i
$609$		0			0
$610$	−11.2837	−	8.19810i	−0.456864	−	0.331931i
$611$	9.14379	−	12.5854i	0.369918	−	0.509149i
$612$	10.2881	−	31.6635i	0.415871	−	1.27992i
$613$	−26.7680	+	8.69746i	−1.08115	+	0.351287i	−0.794821	−	0.606844i	$-0.792435\pi$
$613$	−26.7680	+	8.69746i	−1.08115	+	0.351287i	−0.286330	+	0.958131i	$0.592435\pi$
$614$	−7.41546	−	10.2065i	−0.299264	−	0.411901i
$615$		0			0
$616$		0			0
$617$	−19.4449			−0.782821			−0.391410	−	0.920216i	$-0.628013\pi$
$617$	−19.4449			−0.782821			−0.391410	+	0.920216i	$0.628013\pi$
$618$		0			0
$619$	40.7794	−	13.2500i	1.63906	−	0.532564i	0.662734	−	0.748855i	$-0.269396\pi$
$619$	40.7794	−	13.2500i	1.63906	−	0.532564i	0.976329	+	0.216291i	$0.0693962\pi$
$620$	−16.0851	+	49.5049i	−0.645994	+	1.98817i
$621$		0			0
$622$	−1.76109	−	1.27951i	−0.0706134	−	0.0513036i
$623$	−14.9869	+	2.52814i	−0.600439	+	0.101288i
$624$		0			0
$625$	15.3713	−	11.1679i	0.614853	−	0.446717i
$626$	5.48719			0.219312
$627$		0			0
$628$			19.8997i			0.794086i
$629$	43.8741	−	31.8764i	1.74938	−	1.27100i
$630$	9.73180	+	9.53839i	0.387724	+	0.380019i
$631$	0.783636	−	2.41178i	0.0311960	−	0.0960116i	−0.934246	−	0.356629i	$-0.883926\pi$
$631$	0.783636	−	2.41178i	0.0311960	−	0.0960116i	0.965442	+	0.260617i	$0.0839261\pi$
$632$	14.2874	+	10.3804i	0.568324	+	0.412912i
$633$		0			0
$634$	3.48147	+	1.13120i	0.138267	+	0.0449256i
$635$	3.18314	+	9.79671i	0.126319	+	0.388770i
$636$		0			0
$637$	6.86725	−	9.86233i	0.272090	−	0.390760i
$638$		0			0
$639$	−22.3923			−0.885826
$640$	30.7292	−	22.3260i	1.21468	−	0.882515i
$641$	12.7466	+	39.2299i	0.503459	+	1.54949i	0.803347	+	0.595512i	$0.203051\pi$
$641$	12.7466	+	39.2299i	0.503459	+	1.54949i	−0.299888	+	0.953974i	$0.596949\pi$
$642$		0			0
$643$	16.3605	−	22.5183i	0.645195	−	0.888034i	−0.353685	−	0.935365i	$-0.615071\pi$
$643$	16.3605	−	22.5183i	0.645195	−	0.888034i	0.998879	+	0.0473304i	$0.0150714\pi$
$644$	−5.74777	−	0.851315i	−0.226494	−	0.0335465i
$645$		0			0
$646$	−14.7950	+	4.80718i	−0.582100	+	0.189136i
$647$	8.84257	+	12.1707i	0.347637	+	0.478482i	0.946653	−	0.322256i	$-0.104441\pi$
$647$	8.84257	+	12.1707i	0.347637	+	0.478482i	−0.599015	+	0.800738i	$0.704441\pi$
$648$		−	17.3867i		−	0.683013i
$649$		0			0
$650$			5.33212i			0.209143i
$651$		0			0
$652$	−6.34594	−	19.5308i	−0.248526	−	0.764885i
$653$	0.783636	−	2.41178i	0.0306660	−	0.0943803i	−0.934552	−	0.355827i	$-0.884199\pi$
$653$	0.783636	−	2.41178i	0.0306660	−	0.0943803i	0.965218	+	0.261446i	$0.0841994\pi$
$654$		0			0
$655$	2.45007	−	3.37223i	0.0957322	−	0.131764i
$656$	−1.30726	+	4.02335i	−0.0510401	+	0.157085i
$657$	4.34825	+	13.3826i	0.169642	+	0.522103i
$658$	5.52262	−	11.1131i	0.215294	−	0.433233i
$659$		−	18.8652i		−	0.734886i	−0.930046	−	0.367443i	$-0.880233\pi$
$659$		−	18.8652i		−	0.734886i	0.930046	−	0.367443i	$-0.119767\pi$
$660$		0			0
$661$		−	32.9281i		−	1.28076i	−0.768060	−	0.640378i	$-0.778778\pi$
$661$		−	32.9281i		−	1.28076i	0.768060	−	0.640378i	$-0.221222\pi$
$662$	−0.385786	−	0.530989i	−0.0149940	−	0.0206375i
$663$		0			0
$664$	−17.2354	−	5.60012i	−0.668863	−	0.217327i
$665$	−6.03025	+	40.7141i	−0.233843	+	1.57882i
$666$	7.72586	−	10.6337i	0.299371	−	0.412049i
$667$	7.44577	+	2.41928i	0.288301	+	0.0936748i
$668$	4.34825	+	13.3826i	0.168239	+	0.517786i
$669$		0			0
$670$	−13.1512			−0.508076
$671$		0			0
$672$		0			0
$673$	−12.9143	−	17.7750i	−0.497809	−	0.685175i	0.483996	−	0.875070i	$-0.339185\pi$
$673$	−12.9143	−	17.7750i	−0.497809	−	0.685175i	−0.981804	+	0.189895i	$0.939185\pi$
$674$	−4.55840	−	14.0293i	−0.175583	−	0.540389i
$675$		0			0
$676$	14.0862	+	10.2342i	0.541778	+	0.393625i
$677$	20.3621	+	14.7939i	0.782578	+	0.568576i	0.905751	−	0.423809i	$-0.139307\pi$
$677$	20.3621	+	14.7939i	0.782578	+	0.568576i	−0.123174	+	0.992385i	$0.539307\pi$
$678$		0			0
$679$	15.1351	−	15.4420i	0.580833	−	0.592611i
$680$	33.2122	−	24.1301i	1.27363	−	0.925347i
$681$		0			0
$682$		0			0
$683$	−39.3731			−1.50657			−0.753284	−	0.657695i	$-0.771532\pi$
$683$	−39.3731			−1.50657			−0.753284	+	0.657695i	$0.771532\pi$
$684$	19.7175	−	14.3256i	0.753916	−	0.547752i
$685$	53.3966	−	17.3496i	2.04018	−	0.662894i
$686$	4.09319	−	8.66905i	0.156279	−	0.330986i
$687$		0			0
$688$	8.59495	−	11.8299i	0.327680	−	0.451012i
$689$	2.08401	−	6.41391i	0.0793943	−	0.244350i
$690$		0			0
$691$	−10.6521	−	14.6613i	−0.405224	−	0.557742i	0.556822	−	0.830632i	$-0.312021\pi$
$691$	−10.6521	−	14.6613i	−0.405224	−	0.557742i	−0.962045	+	0.272890i	$0.912021\pi$
$692$	24.3721			0.926489
$693$		0			0
$694$	14.4449			0.548320
$695$	27.4314	+	37.7561i	1.04053	+	1.43217i
$696$		0			0
$697$	−3.39919	+	10.4616i	−0.128753	+	0.396262i
$698$	11.1744	−	15.3803i	0.422958	−	0.582152i
$699$		0			0
$700$	−4.57358	−	27.1124i	−0.172865	−	1.02475i
$701$	−21.1949	+	6.88664i	−0.800521	+	0.260105i	−0.680578	−	0.732676i	$-0.738271\pi$
$701$	−21.1949	+	6.88664i	−0.800521	+	0.260105i	−0.119943	+	0.992781i	$0.538271\pi$
$702$		0			0
$703$	39.7002			1.49732
$704$		0			0
$705$		0			0
$706$	4.43923	−	3.22529i	0.167073	−	0.121385i
$707$	8.86259	+	8.68645i	0.333312	+	0.326688i
$708$		0			0
$709$	−24.7891	−	18.0103i	−0.930974	−	0.676392i	0.0152569	−	0.999884i	$-0.495143\pi$
$709$	−24.7891	−	18.0103i	−0.930974	−	0.676392i	−0.946231	+	0.323491i	$0.895143\pi$
$710$	−10.3671	−	7.53215i	−0.389071	−	0.282676i
$711$	−26.0826	−	8.47475i	−0.978174	−	0.317828i
$712$	3.42936	+	10.5545i	0.128521	+	0.395546i
$713$	−6.75314	−	9.29490i	−0.252907	−	0.348097i
$714$		0			0
$715$		0			0
$716$	−10.9808			−0.410370
$717$		0			0
$718$	−1.82597	−	5.61976i	−0.0681446	−	0.209728i
$719$	−23.5440	−	7.64991i	−0.878043	−	0.285293i	−0.164898	−	0.986311i	$-0.552730\pi$
$719$	−23.5440	−	7.64991i	−0.878043	−	0.285293i	−0.713144	+	0.701017i	$0.752730\pi$
$720$	−14.4110	+	19.8351i	−0.537067	+	0.739210i
$721$	−1.63014	+	11.0061i	−0.0607097	+	0.409890i
$722$	−1.47691	−	0.479877i	−0.0549649	−	0.0178592i
$723$		0			0
$724$	−12.6015	−	17.3445i	−0.468332	−	0.644604i
$725$			37.0470i			1.37589i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−7.85814	−	3.90508i	−0.291242	−	0.144732i
$729$	8.34346	+	25.6785i	0.309017	+	0.951057i
$730$	−2.48838	+	7.65844i	−0.0920990	+	0.283452i
$731$	22.3488	−	30.7605i	0.826602	−	1.13772i
$732$		0			0
$733$	0.918894	−	2.82807i	0.0339401	−	0.104457i	−0.932651	−	0.360779i	$-0.882511\pi$
$733$	0.918894	−	2.82807i	0.0339401	−	0.104457i	0.966591	+	0.256322i	$0.0825108\pi$
$734$	−2.12210	−	6.53114i	−0.0783280	−	0.241069i
$735$		0			0
$736$			6.51626i			0.240193i
$737$		0			0
$738$			2.66606i			0.0981391i
$739$	5.37331	+	7.39573i	0.197660	+	0.272056i	0.896329	−	0.443389i	$-0.146224\pi$
$739$	5.37331	+	7.39573i	0.197660	+	0.272056i	−0.698669	+	0.715445i	$0.746224\pi$
$740$	−46.2428	+	15.0252i	−1.69992	+	0.552337i
$741$		0			0
$742$	0.788221	−	5.32178i	0.0289365	−	0.195369i
$743$	−17.7228	+	24.3933i	−0.650185	+	0.894903i	−0.999107	−	0.0422490i	$-0.986548\pi$
$743$	−17.7228	+	24.3933i	−0.650185	+	0.894903i	0.348922	+	0.937152i	$0.386548\pi$
$744$		0			0
$745$	16.7584	+	51.5771i	0.613981	+	1.88964i
$746$	−5.12896	+	3.72641i	−0.187785	+	0.136434i
$747$	28.1425			1.02968
$748$		0			0
$749$	−1.26795	−	2.42794i	−0.0463299	−	0.0887149i
$750$		0			0
$751$	−11.2458	−	34.6111i	−0.410367	−	1.26298i	−0.916330	−	0.400424i	$-0.868863\pi$
$751$	−11.2458	−	34.6111i	−0.410367	−	1.26298i	0.505964	−	0.862555i	$-0.331137\pi$
$752$	21.2349	+	6.89963i	0.774357	+	0.251604i
$753$		0			0
$754$	4.43923	+	3.22529i	0.161667	+	0.117458i
$755$	17.0046	−	52.3349i	0.618862	−	1.90466i
$756$		0			0
$757$	21.1350	−	15.3555i	0.768166	−	0.558106i	−0.133238	−	0.991084i	$-0.542537\pi$
$757$	21.1350	−	15.3555i	0.768166	−	0.558106i	0.901404	+	0.432979i	$0.142537\pi$
$758$			6.79367i			0.246757i
$759$		0			0
$760$	30.0526			1.09012
$761$	−8.97818	+	6.52303i	−0.325459	+	0.236460i	−0.738501	−	0.674252i	$-0.764466\pi$
$761$	−8.97818	+	6.52303i	−0.325459	+	0.236460i	0.413042	+	0.910712i	$0.364466\pi$
$762$		0			0
$763$	−9.45323	+	1.59466i	−0.342230	+	0.0577306i
$764$	10.1843	+	7.39931i	0.368454	+	0.267698i
$765$	−37.4720	+	51.5757i	−1.35480	+	1.86472i
$766$	−2.22616	+	6.85141i	−0.0804344	+	0.247552i
$767$	−10.8307	+	3.51910i	−0.391073	+	0.127067i
$768$		0			0
$769$	−18.3016			−0.659974			−0.329987	−	0.943985i	$-0.607044\pi$
$769$	−18.3016			−0.659974			−0.329987	+	0.943985i	$0.607044\pi$
$770$		0			0
$771$		0			0
$772$	9.06227	+	12.4731i	0.326158	+	0.448918i
$773$	1.69038	−	0.549239i	0.0607989	−	0.0197547i	−0.278460	−	0.960448i	$-0.589824\pi$
$773$	1.69038	−	0.549239i	0.0607989	−	0.0197547i	0.339259	+	0.940693i	$0.389824\pi$
$774$	2.84771	−	8.76436i	0.102359	−	0.315028i
$775$	31.9562	−	43.9839i	1.14790	−	1.57995i
$776$	−12.7728	−	9.27999i	−0.458517	−	0.333132i
$777$		0			0
$778$	−0.202604	+	0.0658300i	−0.00726370	+	0.00236012i
$779$	−6.51466	+	4.73318i	−0.233412	+	0.169584i
$780$		0			0
$781$		0			0
$782$			4.20531i			0.150382i
$783$		0			0
$784$	16.5082	+	4.99981i	0.589578	+	0.178565i
$785$	11.7751	−	36.2401i	0.420272	−	1.29347i
$786$		0			0
$787$	2.03353	+	1.47745i	0.0724877	+	0.0526654i	0.623439	−	0.781872i	$-0.285735\pi$
$787$	2.03353	+	1.47745i	0.0724877	+	0.0526654i	−0.550951	+	0.834537i	$0.685735\pi$
$788$	31.5945	+	10.2657i	1.12551	+	0.365699i
$789$		0			0
$790$	−9.22496	−	12.6971i	−0.328209	−	0.451741i
$791$	−26.2573	+	13.7124i	−0.933602	+	0.487558i
$792$		0			0
$793$	−13.9474			−0.495288
$794$	6.94465	−	5.04558i	0.246456	−	0.179061i
$795$		0			0
$796$	40.7794	+	13.2500i	1.44539	+	0.469635i
$797$	3.89893	−	5.36641i	0.138107	−	0.190088i	−0.734361	−	0.678759i	$-0.762518\pi$
$797$	3.89893	−	5.36641i	0.138107	−	0.190088i	0.872468	+	0.488671i	$0.162518\pi$
$798$		0			0
$799$	55.2156	+	17.9406i	1.95339	+	0.634694i
$800$	−29.3261	+	9.52863i	−1.03683	+	0.336888i
$801$	−10.1297	−	13.9423i	−0.357916	−	0.492629i
$802$			1.09965i			0.0388299i
$803$		0			0
$804$		0			0
$805$	9.96372	+	4.95144i	0.351175	+	0.174515i
$806$	−2.48838	−	7.65844i	−0.0876494	−	0.269757i
$807$		0			0
$808$	5.32603	−	7.33065i	0.187369	−	0.257892i
$809$	10.9694	−	15.0980i	0.385662	−	0.530818i	−0.571412	−	0.820664i	$-0.693604\pi$
$809$	10.9694	−	15.0980i	0.385662	−	0.530818i	0.957073	+	0.289846i	$0.0936040\pi$
$810$	−4.77471	+	14.6951i	−0.167766	+	0.516332i
$811$	13.6134	+	41.8977i	0.478030	+	1.47123i	0.841827	+	0.539748i	$0.181480\pi$
$811$	13.6134	+	41.8977i	0.478030	+	1.47123i	−0.363797	+	0.931478i	$0.618520\pi$
$812$	−25.3388	−	12.5920i	−0.889216	−	0.441893i
$813$		0			0
$814$		0			0
$815$			39.3233i			1.37743i
$816$		0			0
$817$	26.4718	−	8.60122i	0.926132	−	0.300919i
$818$	2.53557	+	0.823858i	0.0886543	+	0.0288055i
$819$	13.4797	+	1.99651i	0.471019	+	0.0697637i
$820$	5.79693	−	7.97879i	0.202438	−	0.278632i
$821$	42.7502	+	13.8904i	1.49199	+	0.484778i	0.937671	−	0.347525i	$-0.112978\pi$
$821$	42.7502	+	13.8904i	1.49199	+	0.484778i	0.554322	+	0.832303i	$0.312978\pi$
$822$		0			0
$823$	−5.56251	+	4.04140i	−0.193897	+	0.140874i	−0.680498	−	0.732750i	$-0.738237\pi$
$823$	−5.56251	+	4.04140i	−0.193897	+	0.140874i	0.486601	+	0.873624i	$0.338237\pi$
$824$	8.12404			0.283014
$825$		0			0
$826$	−8.05256	+	4.20531i	−0.280184	+	0.146322i
$827$	−24.0467	−	33.0974i	−0.836185	−	1.15091i	−0.986740	−	0.162308i	$-0.948106\pi$
$827$	−24.0467	−	33.0974i	−0.836185	−	1.15091i	0.150555	−	0.988602i	$-0.451894\pi$
$828$	−2.03595	−	6.26600i	−0.0707540	−	0.217758i
$829$	−20.3897	−	6.62502i	−0.708164	−	0.230096i	−0.0672797	−	0.997734i	$-0.521432\pi$
$829$	−20.3897	−	6.62502i	−0.708164	−	0.230096i	−0.640884	+	0.767638i	$0.721432\pi$
$830$	13.0293	+	9.46635i	0.452254	+	0.328582i
$831$		0			0
$832$	1.20320	−	3.70307i	0.0417135	−	0.128381i
$833$	42.9250	+	13.0006i	1.48726	+	0.450445i
$834$		0			0
$835$		−	26.9444i		−	0.932449i
$836$		0			0
$837$		0			0
$838$	−0.272442	+	0.197941i	−0.00941135	+	0.00683775i
$839$	−2.30911	+	0.750274i	−0.0797192	+	0.0259023i	−0.348605	−	0.937270i	$-0.613345\pi$
$839$	−2.30911	+	0.750274i	−0.0797192	+	0.0259023i	0.268886	+	0.963172i	$0.413345\pi$
$840$		0			0
$841$	7.38176	+	5.36316i	0.254543	+	0.184937i
$842$	−1.41793	+	1.95161i	−0.0488651	+	0.0672570i
$843$		0			0
$844$	35.8580	−	11.6510i	1.23428	−	0.401043i
$845$	−19.5971	−	26.9731i	−0.674160	−	0.927902i
$846$	14.0712			0.483779
$847$		0			0
$848$	9.67949			0.332395
$849$		0			0
$850$	−18.9258	+	6.14936i	−0.649149	+	0.210921i
$851$	3.31639	−	10.2068i	0.113684	−	0.349884i
$852$		0			0
$853$	33.5070	+	24.3443i	1.14726	+	0.833532i	0.988114	−	0.153723i	$-0.0491263\pi$
$853$	33.5070	+	24.3443i	1.14726	+	0.833532i	0.159145	+	0.987255i	$0.449126\pi$
$854$	−10.9712	+	1.85073i	−0.375427	+	0.0633305i
$855$	−44.3849	+	14.4215i	−1.51793	+	0.493206i
$856$	−1.61803	+	1.17557i	−0.0553033	+	0.0401802i
$857$	−16.5848			−0.566527			−0.283264	−	0.959042i	$-0.591417\pi$
$857$	−16.5848			−0.566527			−0.283264	+	0.959042i	$0.591417\pi$
$858$		0			0
$859$		−	4.20531i		−	0.143483i	−0.997423	−	0.0717417i	$-0.977144\pi$
$859$		−	4.20531i		−	0.143483i	0.997423	−	0.0717417i	$-0.0228557\pi$
$860$	−27.5791	+	20.0374i	−0.940441	+	0.683271i
$861$		0			0
$862$	5.80476	−	17.8652i	0.197711	−	0.608492i
$863$	42.1539	+	30.6266i	1.43494	+	1.04254i	0.989071	+	0.147442i	$0.0471041\pi$
$863$	42.1539	+	30.6266i	1.43494	+	1.04254i	0.445866	+	0.895100i	$0.352896\pi$
$864$		0			0
$865$	−44.3849	−	14.4215i	−1.50913	−	0.490347i
$866$	5.26715	+	16.2106i	0.178985	+	0.550859i
$867$		0			0
$868$	19.2217	+	36.8067i	0.652426	+	1.24930i
$869$		0			0
$870$		0			0
$871$	−10.6396	+	7.73009i	−0.360508	+	0.261924i
$872$	2.16312	+	6.65740i	0.0732525	+	0.225448i
$873$	23.3175	+	7.57632i	0.789179	+	0.256420i
$874$	−1.80950	+	2.49056i	−0.0612072	+	0.0842445i
$875$	−1.28565	+	8.68027i	−0.0434630	+	0.293447i
$876$		0			0
$877$	17.6169	−	5.72407i	0.594880	−	0.193288i	0.00392413	−	0.999992i	$-0.498751\pi$
$877$	17.6169	−	5.72407i	0.594880	−	0.193288i	0.590955	+	0.806704i	$0.298751\pi$
$878$	−7.79785	−	10.7328i	−0.263165	−	0.362215i
$879$		0			0
$880$		0			0
$881$			42.6399i			1.43657i	0.695747	+	0.718287i	$0.255073\pi$
$881$			42.6399i			1.43657i	−0.695747	+	0.718287i	$0.744927\pi$
$882$	10.8682	−	0.218186i	0.365952	−	0.00734672i
$883$	−6.19658	−	19.0711i	−0.208532	−	0.641794i	−0.999550	−	0.0300017i	$-0.990449\pi$
$883$	−6.19658	−	19.0711i	−0.208532	−	0.641794i	0.791018	−	0.611793i	$-0.209551\pi$
$884$	5.88756	−	18.1201i	0.198020	−	0.609444i
$885$		0			0
$886$	−0.0596813	+	0.0821443i	−0.00200503	+	0.00275969i
$887$	11.2070	−	34.4915i	0.376293	−	1.15811i	−0.566309	−	0.824193i	$-0.691629\pi$
$887$	11.2070	−	34.4915i	0.376293	−	1.15811i	0.942602	−	0.333919i	$-0.108371\pi$
$888$		0			0
$889$	7.35870	+	3.65688i	0.246803	+	0.122648i
$890$		−	9.86233i		−	0.330586i
$891$		0			0
$892$			8.41062i			0.281609i
$893$	24.9813	+	34.3838i	0.835968	+	1.15061i
$894$		0			0
$895$	19.9974	+	6.49756i	0.668441	+	0.217190i
$896$	4.43940	−	29.9732i	0.148310	−	1.00134i
$897$		0			0
$898$	0.421612	+	0.136990i	0.0140694	+	0.00457141i
$899$	−17.2890	−	53.2099i	−0.576619	−	1.77465i
$900$	25.2227	−	18.3253i	0.840755	−	0.610844i
$901$	25.1689			0.838497
$902$		0			0
$903$		0			0
$904$	12.7134	+	17.4985i	0.422841	+	0.581991i
$905$	12.6859	+	39.0433i	0.421695	+	1.29784i
$906$		0			0
$907$	41.6353	+	30.2498i	1.38248	+	1.00443i	0.996644	+	0.0818616i	$0.0260865\pi$
$907$	41.6353	+	30.2498i	1.38248	+	1.00443i	0.385835	+	0.922568i	$0.373913\pi$
$908$	8.33358	+	6.05470i	0.276559	+	0.200932i
$909$	−4.34825	+	13.3826i	−0.144222	+	0.443871i
$910$	5.56922	+	5.45854i	0.184618	+	0.180949i
$911$	6.42961	−	4.67139i	0.213023	−	0.154770i	−0.476158	−	0.879360i	$-0.657971\pi$
$911$	6.42961	−	4.67139i	0.213023	−	0.154770i	0.689180	+	0.724590i	$0.257971\pi$
$912$		0			0
$913$		0			0
$914$	−17.4449			−0.577025
$915$		0			0
$916$	9.46289	−	3.07468i	0.312663	−	0.101590i
$917$	−0.553105	−	3.27884i	−0.0182651	−	0.108277i
$918$		0			0
$919$	−11.0290	+	15.1802i	−0.363814	+	0.500747i	−0.951206	−	0.308555i	$-0.900155\pi$
$919$	−11.0290	+	15.1802i	−0.363814	+	0.500747i	0.587392	+	0.809302i	$0.300155\pi$
$920$	2.51047	−	7.72642i	0.0827676	−	0.254733i
$921$		0			0
$922$	4.80368	+	6.61169i	0.158201	+	0.217744i
$923$	−12.8145			−0.421793
$924$		0			0
$925$	50.7846			1.66979
$926$	−0.119363	−	0.164289i	−0.00392250	−	0.00539886i
$927$	−11.9985	+	3.89854i	−0.394081	+	0.128045i
$928$	−9.80574	+	30.1790i	−0.321889	+	0.990673i
$929$	−23.2536	+	32.0058i	−0.762926	+	1.05008i	0.234039	+	0.972227i	$0.424806\pi$
$929$	−23.2536	+	32.0058i	−0.762926	+	1.05008i	−0.996965	+	0.0778499i	$0.975194\pi$
$930$		0			0
$931$	19.8280	+	26.1697i	0.649835	+	0.857676i
$932$	−6.76033	+	2.19656i	−0.221442	+	0.0719509i
$933$		0			0
$934$	−13.1512			−0.430321
$935$		0			0
$936$		−	9.94987i		−	0.325222i
$937$	13.7896	−	10.0187i	0.450486	−	0.327297i	−0.339302	−	0.940678i	$-0.610191\pi$
$937$	13.7896	−	10.0187i	0.450486	−	0.327297i	0.789788	+	0.613381i	$0.210191\pi$
$938$	−7.34346	+	7.49236i	−0.239772	+	0.244634i
$939$		0			0
$940$	−42.1114	−	30.5957i	−1.37352	−	0.997923i
$941$	40.0795	+	29.1195i	1.30655	+	0.949268i	0.999997	−	0.00258425i	$-0.000822593\pi$
$941$	40.0795	+	29.1195i	1.30655	+	0.949268i	0.306558	+	0.951852i	$0.400823\pi$
$942$		0			0
$943$	0.672677	+	2.07029i	0.0219054	+	0.0674179i
$944$	−9.60735	−	13.2234i	−0.312693	−	0.430384i
$945$		0			0
$946$		0			0
$947$	40.1051			1.30324			0.651621	−	0.758545i	$-0.274089\pi$
$947$	40.1051			1.30324			0.651621	+	0.758545i	$0.274089\pi$
$948$		0			0
$949$	2.48838	+	7.65844i	0.0807762	+	0.248603i
$950$	−13.8546	−	4.50164i	−0.449504	−	0.146053i
$951$		0			0
$952$	4.79813	−	32.3952i	0.155508	−	1.04993i
$953$	−16.2719	−	5.28705i	−0.527098	−	0.171264i	0.0333663	−	0.999443i	$-0.489377\pi$
$953$	−16.2719	−	5.28705i	−0.527098	−	0.171264i	−0.560464	+	0.828179i	$0.689377\pi$
$954$	5.80160	−	1.88505i	0.187834	−	0.0610309i
$955$	−14.1686	−	19.5014i	−0.458485	−	0.631051i
$956$		−	41.9459i		−	1.35663i
$957$		0			0
$958$		−	19.8997i		−	0.642932i
$959$	19.9317	−	40.1083i	0.643628	−	1.29516i
$960$		0			0
$961$	−15.7923	+	48.6039i	−0.509431	+	1.56787i
$962$	4.42128	−	6.08537i	0.142548	−	0.196200i
$963$	1.82556	−	2.51267i	0.0588279	−	0.0809696i
$964$	11.2070	−	34.4915i	0.360952	−	1.11090i
$965$	−9.12297	−	28.0776i	−0.293679	−	0.903850i
$966$		0			0
$967$			29.0421i			0.933932i	0.884275	+	0.466966i	$0.154653\pi$
$967$			29.0421i			0.933932i	−0.884275	+	0.466966i	$0.845347\pi$
$968$		0			0
$969$		0			0
$970$	8.24700	+	11.3510i	0.264795	+	0.364460i
$971$	46.0163	−	14.9516i	1.47673	−	0.479820i	0.543599	−	0.839345i	$-0.317061\pi$
$971$	46.0163	−	14.9516i	1.47673	−	0.479820i	0.933135	+	0.359525i	$0.117061\pi$
$972$		0			0
$973$	36.8273	+	5.45457i	1.18063	+	0.174865i
$974$	2.39039	−	3.29009i	0.0765931	−	0.105421i
$975$		0			0
$976$	−6.18604	−	19.0387i	−0.198010	−	0.609413i
$977$	−23.6202	+	17.1611i	−0.755677	+	0.549031i	−0.897581	−	0.440849i	$-0.854677\pi$
$977$	−23.6202	+	17.1611i	−0.755677	+	0.549031i	0.141905	+	0.989880i	$0.454677\pi$
$978$		0			0
$979$		0			0
$980$	−33.0000	−	22.9783i	−1.05415	−	0.734013i
$981$	−6.38946	−	8.79434i	−0.204000	−	0.280782i
$982$	−2.09656	−	6.45255i	−0.0669039	−	0.205909i
$983$	−11.9985	−	3.89854i	−0.382692	−	0.124344i	0.111352	−	0.993781i	$-0.464482\pi$
$983$	−11.9985	−	3.89854i	−0.382692	−	0.124344i	−0.494044	+	0.869437i	$0.664482\pi$
$984$		0			0
$985$	−51.4634	−	37.3903i	−1.63976	−	1.19136i
$986$	−6.32820	+	19.4762i	−0.201531	+	0.620248i
$987$		0			0
$988$	11.2837	−	8.19810i	0.358983	−	0.260816i
$989$		−	7.52433i		−	0.239260i
$990$		0			0
$991$	−50.0526			−1.58997			−0.794986	−	0.606628i	$-0.792522\pi$
$991$	−50.0526			−1.58997			−0.794986	+	0.606628i	$0.792522\pi$
$992$	37.6738	−	27.3716i	1.19614	−	0.869050i
$993$		0			0
$994$	−10.0800	+	1.70039i	−0.319718	+	0.0539330i
$995$	−66.4244	−	48.2602i	−2.10580	−	1.52995i
$996$		0			0
$997$	−3.42936	+	10.5545i	−0.108609	+	0.334264i	−0.990561	−	0.137076i	$-0.956230\pi$
$997$	−3.42936	+	10.5545i	−0.108609	+	0.334264i	0.881952	+	0.471340i	$0.156230\pi$
$998$	7.25263	−	2.35652i	0.229578	−	0.0745945i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.l.k.118.5		32
7.6	odd	2	inner	847.2.l.k.118.6		32
11.2	odd	10		847.2.b.d.846.5	yes	8
11.3	even	5	inner	847.2.l.k.699.5		32
11.4	even	5	inner	847.2.l.k.524.4		32
11.5	even	5	inner	847.2.l.k.475.4		32
11.6	odd	10	inner	847.2.l.k.475.6		32
11.7	odd	10	inner	847.2.l.k.524.6		32
11.8	odd	10	inner	847.2.l.k.699.3		32
11.9	even	5		847.2.b.d.846.3	✓	8
11.10	odd	2	inner	847.2.l.k.118.3		32
77.6	even	10	inner	847.2.l.k.475.5		32
77.13	even	10		847.2.b.d.846.6	yes	8
77.20	odd	10		847.2.b.d.846.4	yes	8
77.27	odd	10	inner	847.2.l.k.475.3		32
77.41	even	10	inner	847.2.l.k.699.4		32
77.48	odd	10	inner	847.2.l.k.524.3		32
77.62	even	10	inner	847.2.l.k.524.5		32
77.69	odd	10	inner	847.2.l.k.699.6		32
77.76	even	2	inner	847.2.l.k.118.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.b.d.846.3	✓	8	11.9	even	5
847.2.b.d.846.4	yes	8	77.20	odd	10
847.2.b.d.846.5	yes	8	11.2	odd	10
847.2.b.d.846.6	yes	8	77.13	even	10
847.2.l.k.118.3		32	11.10	odd	2	inner
847.2.l.k.118.4		32	77.76	even	2	inner
847.2.l.k.118.5		32	1.1	even	1	trivial
847.2.l.k.118.6		32	7.6	odd	2	inner
847.2.l.k.475.3		32	77.27	odd	10	inner
847.2.l.k.475.4		32	11.5	even	5	inner
847.2.l.k.475.5		32	77.6	even	10	inner
847.2.l.k.475.6		32	11.6	odd	10	inner
847.2.l.k.524.3		32	77.48	odd	10	inner
847.2.l.k.524.4		32	11.4	even	5	inner
847.2.l.k.524.5		32	77.62	even	10	inner
847.2.l.k.524.6		32	11.7	odd	10	inner
847.2.l.k.699.3		32	11.8	odd	10	inner
847.2.l.k.699.4		32	77.41	even	10	inner
847.2.l.k.699.5		32	11.3	even	5	inner
847.2.l.k.699.6		32	77.69	odd	10	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.l (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.304260 + 0.418778i) q^{2} +(0.535233 - 1.64728i) q^{4} +(-1.94946 + 2.68321i) q^{5} +(0.440093 + 2.60889i) q^{7} +(1.83730 - 0.596975i) q^{8} +(-2.42705 + 1.76336i) q^{9} +O(q^{10})\)	\(q+(0.304260 + 0.418778i) q^{2} +(0.535233 - 1.64728i) q^{4} +(-1.94946 + 2.68321i) q^{5} +(0.440093 + 2.60889i) q^{7} +(1.83730 - 0.596975i) q^{8} +(-2.42705 + 1.76336i) q^{9} -1.71681 q^{10} +(-1.38893 + 1.00912i) q^{13} +(-0.958644 + 0.978083i) q^{14} +(-1.99350 - 1.44836i) q^{16} +(-5.18356 - 3.76607i) q^{17} +(-1.47691 - 0.479877i) q^{18} +(-1.44942 - 4.46085i) q^{19} +(3.37657 + 4.64745i) q^{20} -1.26795 q^{23} +(-1.85410 - 5.70634i) q^{25} +(-0.845191 - 0.274619i) q^{26} +(4.53312 + 0.671411i) q^{28} +(-5.87229 - 1.90802i) q^{29} +(5.32603 + 7.33065i) q^{31} -5.13922i q^{32} -3.31662i q^{34} +(-7.85814 - 3.90508i) q^{35} +(1.60570 + 4.94183i) q^{36} +(-2.61555 + 8.04984i) q^{37} +(1.42711 - 1.96424i) q^{38} +(-1.97994 + 6.09364i) q^{40} +(-0.530524 - 1.63278i) q^{41} +5.93426i q^{43} -9.94987i q^{45} +(-0.385786 - 0.530989i) q^{46} +(-8.61770 + 2.80006i) q^{47} +(-6.61264 + 2.29631i) q^{49} +(1.82556 - 2.51267i) q^{50} +(0.918894 + 2.82807i) q^{52} +(-3.17798 + 2.30894i) q^{53} +(2.36603 + 4.53059i) q^{56} +(-0.987665 - 3.03972i) q^{58} +(6.30860 + 2.04979i) q^{59} +(6.57249 + 4.77519i) q^{61} +(-1.44942 + 4.46085i) q^{62} +(-5.66853 - 5.55587i) q^{63} +(-1.83481 + 1.33307i) q^{64} -5.69402i q^{65} +7.66025 q^{67} +(-8.97818 + 6.52303i) q^{68} +(-0.755556 - 4.47898i) q^{70} +(6.03859 + 4.38729i) q^{71} +(-3.40654 + 4.68870i) q^{72} +(1.44942 - 4.46085i) q^{73} +(-4.16690 + 1.35391i) q^{74} -8.12404 q^{76} +(5.37331 + 7.39573i) q^{79} +(7.77251 - 2.52544i) q^{80} +(2.78115 - 8.55951i) q^{81} +(0.522357 - 0.718963i) q^{82} +(-7.58925 - 5.51391i) q^{83} +(20.2103 - 6.56672i) q^{85} +(-2.48514 + 1.80556i) q^{86} +5.74456i q^{89} +(4.16679 - 3.02735i) q^{90} +(-3.24393 - 3.17946i) q^{91} +(-0.678648 + 2.08867i) q^{92} +(-3.79463 - 2.75696i) q^{94} +(14.7950 + 4.80718i) q^{95} +(-4.80368 - 6.61169i) q^{97} +(-2.97360 - 2.07055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{9}+O(q^{10}) \) 32 * q - 24 * q^9	\( 32 q - 24 q^{9} - 12 q^{14} + 8 q^{16} - 96 q^{23} + 48 q^{25} + 40 q^{37} - 32 q^{49} + 24 q^{53} + 48 q^{56} - 16 q^{58} - 32 q^{64} - 32 q^{67} + 44 q^{70} + 32 q^{71} - 72 q^{81} - 80 q^{86} - 44 q^{91} - 24 q^{92}+O(q^{100}) \) 32 * q - 24 * q^9 - 12 * q^14 + 8 * q^16 - 96 * q^23 + 48 * q^25 + 40 * q^37 - 32 * q^49 + 24 * q^53 + 48 * q^56 - 16 * q^58 - 32 * q^64 - 32 * q^67 + 44 * q^70 + 32 * q^71 - 72 * q^81 - 80 * q^86 - 44 * q^91 - 24 * q^92

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