LMFDB - Embedded newform 928.2.k.e.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [928,2,Mod(191,928)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(928, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("928.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 928 = 2^{5} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	928.k (of order $4$, degree $2$, 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:	$7.41011730757$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 23x^{8} + 153x^{6} + 273x^{4} + 103x^{2} + 9 $ x^10 + 23x^8 + 153x^6 + 273x^4 + 103x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.3
Root			$-2.85539i$ of defining polynomial
Character	$\chi$	$=$	928.191
Dual form			928.2.k.e.447.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.775651 - 0.775651i) q^{3} +2.46535i q^{5} +2.99199i q^{7} -1.79673i q^{9} +O(q^{10})$	\(q+(-0.775651 - 0.775651i) q^{3} +2.46535i q^{5} +2.99199i q^{7} -1.79673i q^{9} +(-2.16569 - 2.16569i) q^{11} +5.18414i q^{13} +(1.91225 - 1.91225i) q^{15} +(-0.777448 + 0.777448i) q^{17} +(-3.60195 - 3.60195i) q^{19} +(2.32074 - 2.32074i) q^{21} +0.543289i q^{23} -1.07794 q^{25} +(-3.72059 + 3.72059i) q^{27} +(-5.32875 - 0.777448i) q^{29} +(-6.95178 - 6.95178i) q^{31} +3.35964i q^{33} -7.37629 q^{35} +(1.25344 + 1.25344i) q^{37} +(4.02108 - 4.02108i) q^{39} +(0.312100 + 0.312100i) q^{41} +(1.54509 + 1.54509i) q^{43} +4.42957 q^{45} +(0.0877510 - 0.0877510i) q^{47} -1.95199 q^{49} +1.20606 q^{51} -12.2707 q^{53} +(5.33918 - 5.33918i) q^{55} +5.58770i q^{57} +0.387407i q^{59} +(-10.3127 + 10.3127i) q^{61} +5.37580 q^{63} -12.7807 q^{65} -5.72680 q^{67} +(0.421402 - 0.421402i) q^{69} -7.37939 q^{71} +(8.16811 + 8.16811i) q^{73} +(0.836106 + 0.836106i) q^{75} +(6.47972 - 6.47972i) q^{77} +(5.34983 + 5.34983i) q^{79} +0.381559 q^{81} +10.4260i q^{83} +(-1.91668 - 1.91668i) q^{85} +(3.53022 + 4.73628i) q^{87} +(1.86651 - 1.86651i) q^{89} -15.5109 q^{91} +10.7843i q^{93} +(8.88005 - 8.88005i) q^{95} +(5.12859 + 5.12859i) q^{97} +(-3.89117 + 3.89117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3}+O(q^{10}) $ 10 * q - 2 * q^3	$ 10 q - 2 q^{3} - 14 q^{11} + 14 q^{15} + 6 q^{17} - 12 q^{19} - 28 q^{21} + 2 q^{25} - 2 q^{27} - 28 q^{29} + 14 q^{31} + 4 q^{35} + 10 q^{37} + 6 q^{39} + 14 q^{41} - 30 q^{43} - 36 q^{45} + 6 q^{47} - 42 q^{49} - 56 q^{51} + 4 q^{53} - 42 q^{55} - 26 q^{61} + 32 q^{63} - 36 q^{65} - 56 q^{67} + 16 q^{69} - 36 q^{71} - 22 q^{73} + 8 q^{75} + 28 q^{77} - 6 q^{79} - 54 q^{81} - 16 q^{85} + 58 q^{87} + 58 q^{89} + 20 q^{91} + 52 q^{95} + 26 q^{97} - 68 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 - 14 * q^11 + 14 * q^15 + 6 * q^17 - 12 * q^19 - 28 * q^21 + 2 * q^25 - 2 * q^27 - 28 * q^29 + 14 * q^31 + 4 * q^35 + 10 * q^37 + 6 * q^39 + 14 * q^41 - 30 * q^43 - 36 * q^45 + 6 * q^47 - 42 * q^49 - 56 * q^51 + 4 * q^53 - 42 * q^55 - 26 * q^61 + 32 * q^63 - 36 * q^65 - 56 * q^67 + 16 * q^69 - 36 * q^71 - 22 * q^73 + 8 * q^75 + 28 * q^77 - 6 * q^79 - 54 * q^81 - 16 * q^85 + 58 * q^87 + 58 * q^89 + 20 * q^91 + 52 * q^95 + 26 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/928\mathbb{Z}\right)^\times$.

$n$	$321$	$581$	$639$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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
$3$	−0.775651	−	0.775651i	−0.447822	−	0.447822i	0.446808	−	0.894630i	$-0.352561\pi$
$3$	−0.775651	−	0.775651i	−0.447822	−	0.447822i	−0.894630	+	0.446808i	$0.852561\pi$
$4$		0			0
$5$			2.46535i			1.10254i	0.834328	+	0.551269i	$0.185856\pi$
$5$			2.46535i			1.10254i	−0.834328	+	0.551269i	$0.814144\pi$
$6$		0			0
$7$			2.99199i			1.13086i	0.824795	+	0.565432i	$0.191291\pi$
$7$			2.99199i			1.13086i	−0.824795	+	0.565432i	$0.808709\pi$
$8$		0			0
$9$		−	1.79673i		−	0.598911i
$10$		0			0
$11$	−2.16569	−	2.16569i	−0.652981	−	0.652981i	0.300729	−	0.953710i	$-0.402770\pi$
$11$	−2.16569	−	2.16569i	−0.652981	−	0.652981i	−0.953710	+	0.300729i	$0.902770\pi$
$12$		0			0
$13$			5.18414i			1.43782i	0.695102	+	0.718911i	$0.255359\pi$
$13$			5.18414i			1.43782i	−0.695102	+	0.718911i	$0.744641\pi$
$14$		0			0
$15$	1.91225	−	1.91225i	0.493741	−	0.493741i
$16$		0			0
$17$	−0.777448	+	0.777448i	−0.188559	+	0.188559i	−0.795073	−	0.606514i	$-0.792567\pi$
$17$	−0.777448	+	0.777448i	−0.188559	+	0.188559i	0.606514	+	0.795073i	$0.292567\pi$
$18$		0			0
$19$	−3.60195	−	3.60195i	−0.826343	−	0.826343i	0.160666	−	0.987009i	$-0.448636\pi$
$19$	−3.60195	−	3.60195i	−0.826343	−	0.826343i	−0.987009	+	0.160666i	$0.948636\pi$
$20$		0			0
$21$	2.32074	−	2.32074i	0.506426	−	0.506426i
$22$		0			0
$23$			0.543289i			0.113284i	0.998395	+	0.0566418i	$0.0180393\pi$
$23$			0.543289i			0.113284i	−0.998395	+	0.0566418i	$0.981961\pi$
$24$		0			0
$25$	−1.07794			−0.215588
$26$		0			0
$27$	−3.72059	+	3.72059i	−0.716028	+	0.716028i
$28$		0			0
$29$	−5.32875	−	0.777448i	−0.989524	−	0.144369i
$29$	−5.32875	−	0.777448i	−0.989524	−	0.144369i
$30$		0			0
$31$	−6.95178	−	6.95178i	−1.24858	−	1.24858i	−0.956349	−	0.292227i	$-0.905604\pi$
$31$	−6.95178	−	6.95178i	−1.24858	−	1.24858i	−0.292227	−	0.956349i	$-0.594396\pi$
$32$		0			0
$33$			3.35964i			0.584838i
$34$		0			0
$35$	−7.37629			−1.24682
$36$		0			0
$37$	1.25344	+	1.25344i	0.206065	+	0.206065i	0.802592	−	0.596528i	$-0.203453\pi$
$37$	1.25344	+	1.25344i	0.206065	+	0.206065i	−0.596528	+	0.802592i	$0.703453\pi$
$38$		0			0
$39$	4.02108	−	4.02108i	0.643888	−	0.643888i
$40$		0			0
$41$	0.312100	+	0.312100i	0.0487419	+	0.0487419i	0.731058	−	0.682316i	$-0.239027\pi$
$41$	0.312100	+	0.312100i	0.0487419	+	0.0487419i	−0.682316	+	0.731058i	$0.739027\pi$
$42$		0			0
$43$	1.54509	+	1.54509i	0.235623	+	0.235623i	0.815035	−	0.579412i	$-0.196718\pi$
$43$	1.54509	+	1.54509i	0.235623	+	0.235623i	−0.579412	+	0.815035i	$0.696718\pi$
$44$		0			0
$45$	4.42957			0.660321
$46$		0			0
$47$	0.0877510	−	0.0877510i	0.0127998	−	0.0127998i	−0.700678	−	0.713478i	$-0.747119\pi$
$47$	0.0877510	−	0.0877510i	0.0127998	−	0.0127998i	0.713478	+	0.700678i	$0.247119\pi$
$48$		0			0
$49$	−1.95199			−0.278856
$50$		0			0
$51$	1.20606			0.168882
$52$		0			0
$53$	−12.2707			−1.68551			−0.842756	−	0.538295i	$-0.819069\pi$
$53$	−12.2707			−1.68551			−0.842756	+	0.538295i	$0.819069\pi$
$54$		0			0
$55$	5.33918	−	5.33918i	0.719935	−	0.719935i
$56$		0			0
$57$			5.58770i			0.740110i
$58$		0			0
$59$			0.387407i			0.0504361i	0.999682	+	0.0252181i	$0.00802801\pi$
$59$			0.387407i			0.0504361i	−0.999682	+	0.0252181i	$0.991972\pi$
$60$		0			0
$61$	−10.3127	+	10.3127i	−1.32041	+	1.32041i	−0.406966	+	0.913443i	$0.633413\pi$
$61$	−10.3127	+	10.3127i	−1.32041	+	1.32041i	−0.913443	+	0.406966i	$0.866587\pi$
$62$		0			0
$63$	5.37580			0.677287
$64$		0			0
$65$	−12.7807			−1.58525
$66$		0			0
$67$	−5.72680			−0.699640			−0.349820	−	0.936817i	$-0.613757\pi$
$67$	−5.72680			−0.699640			−0.349820	+	0.936817i	$0.613757\pi$
$68$		0			0
$69$	0.421402	−	0.421402i	0.0507309	−	0.0507309i
$70$		0			0
$71$	−7.37939			−0.875773			−0.437887	−	0.899030i	$-0.644273\pi$
$71$	−7.37939			−0.875773			−0.437887	+	0.899030i	$0.644273\pi$
$72$		0			0
$73$	8.16811	+	8.16811i	0.956005	+	0.956005i	0.999072	−	0.0430668i	$-0.0137128\pi$
$73$	8.16811	+	8.16811i	0.956005	+	0.956005i	−0.0430668	+	0.999072i	$0.513713\pi$
$74$		0			0
$75$	0.836106	+	0.836106i	0.0965452	+	0.0965452i
$76$		0			0
$77$	6.47972	−	6.47972i	0.738433	−	0.738433i
$78$		0			0
$79$	5.34983	+	5.34983i	0.601903	+	0.601903i	0.940817	−	0.338914i	$-0.110060\pi$
$79$	5.34983	+	5.34983i	0.601903	+	0.601903i	−0.338914	+	0.940817i	$0.610060\pi$
$80$		0			0
$81$	0.381559			0.0423954
$82$		0			0
$83$			10.4260i			1.14440i	0.820114	+	0.572200i	$0.193910\pi$
$83$			10.4260i			1.14440i	−0.820114	+	0.572200i	$0.806090\pi$
$84$		0			0
$85$	−1.91668	−	1.91668i	−0.207893	−	0.207893i
$86$		0			0
$87$	3.53022	+	4.73628i	0.378479	+	0.507782i
$88$		0			0
$89$	1.86651	−	1.86651i	0.197849	−	0.197849i	−0.601228	−	0.799077i	$-0.705322\pi$
$89$	1.86651	−	1.86651i	0.197849	−	0.197849i	0.799077	+	0.601228i	$0.205322\pi$
$90$		0			0
$91$	−15.5109			−1.62598
$92$		0			0
$93$			10.7843i			1.11828i
$94$		0			0
$95$	8.88005	−	8.88005i	0.911074	−	0.911074i
$96$		0			0
$97$	5.12859	+	5.12859i	0.520729	+	0.520729i	0.917792	−	0.397063i	$-0.129970\pi$
$97$	5.12859	+	5.12859i	0.520729	+	0.520729i	−0.397063	+	0.917792i	$0.629970\pi$
$98$		0			0
$99$	−3.89117	+	3.89117i	−0.391077	+	0.391077i
$100$		0			0
$101$	11.8300	−	11.8300i	1.17713	−	1.17713i	0.196660	−	0.980472i	$-0.436990\pi$
$101$	11.8300	−	11.8300i	1.17713	−	1.17713i	0.980472	−	0.196660i	$-0.0630096\pi$
$102$		0			0
$103$			13.5130i			1.33148i	0.746184	+	0.665740i	$0.231884\pi$
$103$			13.5130i			1.33148i	−0.746184	+	0.665740i	$0.768116\pi$
$104$		0			0
$105$	5.72143	+	5.72143i	0.558354	+	0.558354i
$106$		0			0
$107$			11.6335i			1.12465i	0.826917	+	0.562325i	$0.190093\pi$
$107$			11.6335i			1.12465i	−0.826917	+	0.562325i	$0.809907\pi$
$108$		0			0
$109$			1.02777i			0.0984421i	0.998788	+	0.0492211i	$0.0156739\pi$
$109$			1.02777i			0.0984421i	−0.998788	+	0.0492211i	$0.984326\pi$
$110$		0			0
$111$		−	1.94447i		−	0.184561i
$112$		0			0
$113$	−12.9227	−	12.9227i	−1.21566	−	1.21566i	−0.969136	−	0.246528i	$-0.920710\pi$
$113$	−12.9227	−	12.9227i	−1.21566	−	1.21566i	−0.246528	−	0.969136i	$-0.579290\pi$
$114$		0			0
$115$	−1.33940			−0.124899
$116$		0			0
$117$	9.31451			0.861127
$118$		0			0
$119$	−2.32612	−	2.32612i	−0.213235	−	0.213235i
$120$		0			0
$121$		−	1.61956i		−	0.147232i
$122$		0			0
$123$		−	0.484162i		−	0.0436554i
$124$		0			0
$125$			9.66924i			0.864843i
$126$		0			0
$127$	−7.46861	−	7.46861i	−0.662732	−	0.662732i	0.293291	−	0.956023i	$-0.405249\pi$
$127$	−7.46861	−	7.46861i	−0.662732	−	0.662732i	−0.956023	+	0.293291i	$0.905249\pi$
$128$		0			0
$129$		−	2.39690i		−	0.211035i
$130$		0			0
$131$	5.33185	−	5.33185i	0.465846	−	0.465846i	−0.434720	−	0.900566i	$-0.643153\pi$
$131$	5.33185	−	5.33185i	0.465846	−	0.465846i	0.900566	+	0.434720i	$0.143153\pi$
$132$		0			0
$133$	10.7770	−	10.7770i	0.934483	−	0.934483i
$134$		0			0
$135$	−9.17255	−	9.17255i	−0.789447	−	0.789447i
$136$		0			0
$137$	10.0055	−	10.0055i	0.854830	−	0.854830i	−0.135893	−	0.990724i	$-0.543390\pi$
$137$	10.0055	−	10.0055i	0.854830	−	0.854830i	0.990724	+	0.135893i	$0.0433904\pi$
$138$		0			0
$139$		−	14.4047i		−	1.22179i	−0.791712	−	0.610895i	$-0.790810\pi$
$139$		−	14.4047i		−	1.22179i	0.791712	−	0.610895i	$-0.209190\pi$
$140$		0			0
$141$	−0.136128			−0.0114641
$142$		0			0
$143$	11.2272	−	11.2272i	0.938870	−	0.938870i
$144$		0			0
$145$	1.91668	−	13.1372i	0.159172	−	1.09099i
$146$		0			0
$147$	1.51406	+	1.51406i	0.124878	+	0.124878i
$148$		0			0
$149$		−	4.42008i		−	0.362107i	−0.983473	−	0.181054i	$-0.942049\pi$
$149$		−	4.42008i		−	0.362107i	0.983473	−	0.181054i	$-0.0579507\pi$
$150$		0			0
$151$	12.0858			0.983525			0.491762	−	0.870729i	$-0.336353\pi$
$151$	12.0858			0.983525			0.491762	+	0.870729i	$0.336353\pi$
$152$		0			0
$153$	1.39687	+	1.39687i	0.112930	+	0.112930i
$154$		0			0
$155$	17.1386	−	17.1386i	1.37660	−	1.37660i
$156$		0			0
$157$	−8.66076	−	8.66076i	−0.691204	−	0.691204i	0.271293	−	0.962497i	$-0.412549\pi$
$157$	−8.66076	−	8.66076i	−0.691204	−	0.691204i	−0.962497	+	0.271293i	$0.912549\pi$
$158$		0			0
$159$	9.51779	+	9.51779i	0.754810	+	0.754810i
$160$		0			0
$161$	−1.62551			−0.128108
$162$		0			0
$163$	−12.8511	+	12.8511i	−1.00658	+	1.00658i	−0.00659855	+	0.999978i	$0.502100\pi$
$163$	−12.8511	+	12.8511i	−1.00658	+	1.00658i	−0.999978	+	0.00659855i	$0.997900\pi$
$164$		0			0
$165$	−8.28268			−0.644806
$166$		0			0
$167$	2.79970			0.216647			0.108324	−	0.994116i	$-0.465452\pi$
$167$	2.79970			0.216647			0.108324	+	0.994116i	$0.465452\pi$
$168$		0			0
$169$	−13.8753			−1.06733
$170$		0			0
$171$	−6.47173	+	6.47173i	−0.494906	+	0.494906i
$172$		0			0
$173$		−	13.9213i		−	1.05841i	−0.848493	−	0.529207i	$-0.822490\pi$
$173$		−	13.9213i		−	1.05841i	0.848493	−	0.529207i	$-0.177510\pi$
$174$		0			0
$175$		−	3.22519i		−	0.243801i
$176$		0			0
$177$	0.300493	−	0.300493i	0.0225864	−	0.0225864i
$178$		0			0
$179$	12.8503			0.960475			0.480237	−	0.877139i	$-0.340551\pi$
$179$	12.8503			0.960475			0.480237	+	0.877139i	$0.340551\pi$
$180$		0			0
$181$	18.4493			1.37133			0.685664	−	0.727918i	$-0.259512\pi$
$181$	18.4493			1.37133			0.685664	+	0.727918i	$0.259512\pi$
$182$		0			0
$183$	15.9981			1.18262
$184$		0			0
$185$	−3.09017	+	3.09017i	−0.227194	+	0.227194i
$186$		0			0
$187$	3.36743			0.246251
$188$		0			0
$189$	−11.1320	−	11.1320i	−0.809731	−	0.809731i
$190$		0			0
$191$	5.30913	+	5.30913i	0.384155	+	0.384155i	0.872597	−	0.488442i	$-0.162434\pi$
$191$	5.30913	+	5.30913i	0.384155	+	0.384155i	−0.488442	+	0.872597i	$0.662434\pi$
$192$		0			0
$193$	−7.22318	+	7.22318i	−0.519936	+	0.519936i	−0.917552	−	0.397616i	$-0.869838\pi$
$193$	−7.22318	+	7.22318i	−0.519936	+	0.519936i	0.397616	+	0.917552i	$0.369838\pi$
$194$		0			0
$195$	9.91336	+	9.91336i	0.709911	+	0.709911i
$196$		0			0
$197$	−0.179097			−0.0127601			−0.00638007	−	0.999980i	$-0.502031\pi$
$197$	−0.179097			−0.0127601			−0.00638007	+	0.999980i	$0.502031\pi$
$198$		0			0
$199$			23.9560i			1.69819i	0.528236	+	0.849097i	$0.322853\pi$
$199$			23.9560i			1.69819i	−0.528236	+	0.849097i	$0.677147\pi$
$200$		0			0
$201$	4.44200	+	4.44200i	0.313314	+	0.313314i
$202$		0			0
$203$	2.32612	−	15.9436i	0.163261	−	1.11902i
$204$		0			0
$205$	−0.769436	+	0.769436i	−0.0537397	+	0.0537397i
$206$		0			0
$207$	0.976145			0.0678467
$208$		0			0
$209$			15.6014i			1.07917i
$210$		0			0
$211$	−8.76322	+	8.76322i	−0.603285	+	0.603285i	−0.941183	−	0.337898i	$-0.890284\pi$
$211$	−8.76322	+	8.76322i	−0.603285	+	0.603285i	0.337898	+	0.941183i	$0.390284\pi$
$212$		0			0
$213$	5.72383	+	5.72383i	0.392191	+	0.392191i
$214$		0			0
$215$	−3.80918	+	3.80918i	−0.259784	+	0.259784i
$216$		0			0
$217$	20.7996	−	20.7996i	1.41197	−	1.41197i
$218$		0			0
$219$		−	12.6712i		−	0.856241i
$220$		0			0
$221$	−4.03040	−	4.03040i	−0.271114	−	0.271114i
$222$		0			0
$223$			21.8418i			1.46263i	0.682038	+	0.731317i	$0.261094\pi$
$223$			21.8418i			1.46263i	−0.682038	+	0.731317i	$0.738906\pi$
$224$		0			0
$225$			1.93677i			0.129118i
$226$		0			0
$227$		−	20.3719i		−	1.35213i	−0.736843	−	0.676064i	$-0.763684\pi$
$227$		−	20.3719i		−	1.35213i	0.736843	−	0.676064i	$-0.236316\pi$
$228$		0			0
$229$	5.84378	+	5.84378i	0.386168	+	0.386168i	0.873318	−	0.487150i	$-0.161964\pi$
$229$	5.84378	+	5.84378i	0.386168	+	0.386168i	−0.487150	+	0.873318i	$0.661964\pi$
$230$		0			0
$231$	−10.0520			−0.661373
$232$		0			0
$233$	18.2916			1.19832			0.599161	−	0.800629i	$-0.295501\pi$
$233$	18.2916			1.19832			0.599161	+	0.800629i	$0.295501\pi$
$234$		0			0
$235$	0.216337	+	0.216337i	0.0141123	+	0.0141123i
$236$		0			0
$237$		−	8.29920i		−	0.539091i
$238$		0			0
$239$			6.00216i			0.388248i	0.980977	+	0.194124i	$0.0621864\pi$
$239$			6.00216i			0.388248i	−0.980977	+	0.194124i	$0.937814\pi$
$240$		0			0
$241$		−	2.52304i		−	0.162524i	−0.996693	−	0.0812618i	$-0.974105\pi$
$241$		−	2.52304i		−	0.162524i	0.996693	−	0.0812618i	$-0.0258950\pi$
$242$		0			0
$243$	10.8658	+	10.8658i	0.697042	+	0.697042i
$244$		0			0
$245$		−	4.81233i		−	0.307449i
$246$		0			0
$247$	18.6730	−	18.6730i	1.18813	−	1.18813i
$248$		0			0
$249$	8.08691	−	8.08691i	0.512487	−	0.512487i
$250$		0			0
$251$	18.0150	+	18.0150i	1.13710	+	1.13710i	0.988968	+	0.148129i	$0.0473251\pi$
$251$	18.0150	+	18.0150i	1.13710	+	1.13710i	0.148129	+	0.988968i	$0.452675\pi$
$252$		0			0
$253$	1.17660	−	1.17660i	0.0739720	−	0.0739720i
$254$		0			0
$255$			2.97335i			0.186198i
$256$		0			0
$257$	−12.0499			−0.751655			−0.375828	−	0.926690i	$-0.622642\pi$
$257$	−12.0499			−0.751655			−0.375828	+	0.926690i	$0.622642\pi$
$258$		0			0
$259$	−3.75029	+	3.75029i	−0.233031	+	0.233031i
$260$		0			0
$261$	−1.39687	+	9.57433i	−0.0864638	+	0.592636i
$262$		0			0
$263$	−12.3894	−	12.3894i	−0.763961	−	0.763961i	0.213075	−	0.977036i	$-0.431652\pi$
$263$	−12.3894	−	12.3894i	−0.763961	−	0.763961i	−0.977036	+	0.213075i	$0.931652\pi$
$264$		0			0
$265$		−	30.2516i		−	1.85834i
$266$		0			0
$267$	−2.89551			−0.177203
$268$		0			0
$269$	6.79999	+	6.79999i	0.414603	+	0.414603i	0.883338	−	0.468736i	$-0.155290\pi$
$269$	6.79999	+	6.79999i	0.414603	+	0.414603i	−0.468736	+	0.883338i	$0.655290\pi$
$270$		0			0
$271$	−6.97140	+	6.97140i	−0.423482	+	0.423482i	−0.886401	−	0.462919i	$-0.846802\pi$
$271$	−6.97140	+	6.97140i	−0.423482	+	0.423482i	0.462919	+	0.886401i	$0.346802\pi$
$272$		0			0
$273$	12.0310	+	12.0310i	0.728151	+	0.728151i
$274$		0			0
$275$	2.33449	+	2.33449i	0.140775	+	0.140775i
$276$		0			0
$277$	6.61701			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$277$	6.61701			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$278$		0			0
$279$	−12.4905	+	12.4905i	−0.747785	+	0.747785i
$280$		0			0
$281$	−7.56485			−0.451281			−0.225640	−	0.974211i	$-0.572447\pi$
$281$	−7.56485			−0.451281			−0.225640	+	0.974211i	$0.572447\pi$
$282$		0			0
$283$	10.2593			0.609854			0.304927	−	0.952376i	$-0.401368\pi$
$283$	10.2593			0.609854			0.304927	+	0.952376i	$0.401368\pi$
$284$		0			0
$285$	−13.7756			−0.815998
$286$		0			0
$287$	−0.933800	+	0.933800i	−0.0551205	+	0.0551205i
$288$		0			0
$289$			15.7911i			0.928891i
$290$		0			0
$291$		−	7.95598i		−	0.466388i
$292$		0			0
$293$	−4.88579	+	4.88579i	−0.285431	+	0.285431i	−0.835270	−	0.549839i	$-0.814689\pi$
$293$	−4.88579	+	4.88579i	−0.285431	+	0.285431i	0.549839	+	0.835270i	$0.314689\pi$
$294$		0			0
$295$	−0.955093			−0.0556077
$296$		0			0
$297$	16.1153			0.935104
$298$		0			0
$299$	−2.81649			−0.162882
$300$		0			0
$301$	−4.62288	+	4.62288i	−0.266458	+	0.266458i
$302$		0			0
$303$	−18.3519			−1.05429
$304$		0			0
$305$	−25.4245	−	25.4245i	−1.45580	−	1.45580i
$306$		0			0
$307$	9.44690	+	9.44690i	0.539163	+	0.539163i	0.923283	−	0.384120i	$-0.125495\pi$
$307$	9.44690	+	9.44690i	0.539163	+	0.539163i	−0.384120	+	0.923283i	$0.625495\pi$
$308$		0			0
$309$	10.4814	−	10.4814i	0.596266	−	0.596266i
$310$		0			0
$311$	−16.0284	−	16.0284i	−0.908888	−	0.908888i	0.0872947	−	0.996183i	$-0.472178\pi$
$311$	−16.0284	−	16.0284i	−0.908888	−	0.908888i	−0.996183	+	0.0872947i	$0.972178\pi$
$312$		0			0
$313$	−26.4075			−1.49264			−0.746319	−	0.665588i	$-0.768181\pi$
$313$	−26.4075			−1.49264			−0.746319	+	0.665588i	$0.768181\pi$
$314$		0			0
$315$			13.2532i			0.746734i
$316$		0			0
$317$	−13.6921	−	13.6921i	−0.769026	−	0.769026i	0.208909	−	0.977935i	$-0.433009\pi$
$317$	−13.6921	−	13.6921i	−0.769026	−	0.769026i	−0.977935	+	0.208909i	$0.933009\pi$
$318$		0			0
$319$	9.85672	+	13.2241i	0.551870	+	0.740410i
$320$		0			0
$321$	9.02350	−	9.02350i	0.503643	−	0.503643i
$322$		0			0
$323$	5.60065			0.311629
$324$		0			0
$325$		−	5.58820i		−	0.309977i
$326$		0			0
$327$	0.797187	−	0.797187i	0.0440846	−	0.0440846i
$328$		0			0
$329$	0.262550	+	0.262550i	0.0144748	+	0.0144748i
$330$		0			0
$331$	−3.51047	+	3.51047i	−0.192953	+	0.192953i	−0.796971	−	0.604018i	$-0.793566\pi$
$331$	−3.51047	+	3.51047i	−0.192953	+	0.192953i	0.604018	+	0.796971i	$0.293566\pi$
$332$		0			0
$333$	2.25210	−	2.25210i	0.123414	−	0.123414i
$334$		0			0
$335$		−	14.1186i		−	0.771380i
$336$		0			0
$337$	13.8707	+	13.8707i	0.755587	+	0.755587i	0.975516	−	0.219929i	$-0.0705827\pi$
$337$	13.8707	+	13.8707i	0.755587	+	0.755587i	−0.219929	+	0.975516i	$0.570583\pi$
$338$		0			0
$339$			20.0470i			1.08880i
$340$		0			0
$341$			30.1108i			1.63059i
$342$		0			0
$343$			15.1036i			0.815517i
$344$		0			0
$345$	1.03890	+	1.03890i	0.0559327	+	0.0559327i
$346$		0			0
$347$	6.66993			0.358061			0.179030	−	0.983844i	$-0.442704\pi$
$347$	6.66993			0.358061			0.179030	+	0.983844i	$0.442704\pi$
$348$		0			0
$349$	−16.0198			−0.857518			−0.428759	−	0.903419i	$-0.641049\pi$
$349$	−16.0198			−0.857518			−0.428759	+	0.903419i	$0.641049\pi$
$350$		0			0
$351$	−19.2880	−	19.2880i	−1.02952	−	1.02952i
$352$		0			0
$353$			31.8849i			1.69706i	0.529145	+	0.848531i	$0.322513\pi$
$353$			31.8849i			1.69706i	−0.529145	+	0.848531i	$0.677487\pi$
$354$		0			0
$355$		−	18.1928i		−	0.965572i
$356$		0			0
$357$			3.60851i			0.190982i
$358$		0			0
$359$	−8.41746	−	8.41746i	−0.444257	−	0.444257i	0.449183	−	0.893440i	$-0.351715\pi$
$359$	−8.41746	−	8.41746i	−0.444257	−	0.444257i	−0.893440	+	0.449183i	$0.851715\pi$
$360$		0			0
$361$			6.94803i			0.365686i
$362$		0			0
$363$	−1.25621	+	1.25621i	−0.0659339	+	0.0659339i
$364$		0			0
$365$	−20.1372	+	20.1372i	−1.05403	+	1.05403i
$366$		0			0
$367$	22.2834	+	22.2834i	1.16319	+	1.16319i	0.983774	+	0.179411i	$0.0574191\pi$
$367$	22.2834	+	22.2834i	1.16319	+	1.16319i	0.179411	+	0.983774i	$0.442581\pi$
$368$		0			0
$369$	0.560761	−	0.560761i	0.0291920	−	0.0291920i
$370$		0			0
$371$		−	36.7138i		−	1.90609i
$372$		0			0
$373$	24.9127			1.28993			0.644965	−	0.764212i	$-0.276872\pi$
$373$	24.9127			1.28993			0.644965	+	0.764212i	$0.276872\pi$
$374$		0			0
$375$	7.49995	−	7.49995i	0.387296	−	0.387296i
$376$		0			0
$377$	4.03040	−	27.6250i	0.207576	−	1.42276i
$378$		0			0
$379$	24.3797	+	24.3797i	1.25230	+	1.25230i	0.954686	+	0.297614i	$0.0961908\pi$
$379$	24.3797	+	24.3797i	1.25230	+	1.25230i	0.297614	+	0.954686i	$0.403809\pi$
$380$		0			0
$381$			11.5861i			0.593572i
$382$		0			0
$383$	−28.3688			−1.44958			−0.724788	−	0.688972i	$-0.758062\pi$
$383$	−28.3688			−1.44958			−0.724788	+	0.688972i	$0.758062\pi$
$384$		0			0
$385$	15.9748	+	15.9748i	0.814150	+	0.814150i
$386$		0			0
$387$	2.77611	−	2.77611i	0.141117	−	0.141117i
$388$		0			0
$389$	−0.0610650	−	0.0610650i	−0.00309612	−	0.00309612i	0.705557	−	0.708653i	$-0.250697\pi$
$389$	−0.0610650	−	0.0610650i	−0.00309612	−	0.00309612i	−0.708653	+	0.705557i	$0.750697\pi$
$390$		0			0
$391$	−0.422379	−	0.422379i	−0.0213606	−	0.0213606i
$392$		0			0
$393$	−8.27131			−0.417233
$394$		0			0
$395$	−13.1892	+	13.1892i	−0.663620	+	0.663620i
$396$		0			0
$397$	4.90424			0.246137			0.123068	−	0.992398i	$-0.460727\pi$
$397$	4.90424			0.246137			0.123068	+	0.992398i	$0.460727\pi$
$398$		0			0
$399$	−16.7183			−0.836964
$400$		0			0
$401$	−34.3236			−1.71404			−0.857020	−	0.515283i	$-0.827687\pi$
$401$	−34.3236			−1.71404			−0.857020	+	0.515283i	$0.827687\pi$
$402$		0			0
$403$	36.0390	−	36.0390i	1.79523	−	1.79523i
$404$		0			0
$405$			0.940675i			0.0467425i
$406$		0			0
$407$		−	5.42914i		−	0.269113i
$408$		0			0
$409$	14.3536	−	14.3536i	0.709738	−	0.709738i	−0.256742	−	0.966480i	$-0.582649\pi$
$409$	14.3536	−	14.3536i	0.709738	−	0.709738i	0.966480	+	0.256742i	$0.0826490\pi$
$410$		0			0
$411$	−15.5216			−0.765624
$412$		0			0
$413$	−1.15912			−0.0570364
$414$		0			0
$415$	−25.7037			−1.26174
$416$		0			0
$417$	−11.1730	+	11.1730i	−0.547144	+	0.547144i
$418$		0			0
$419$	33.4300			1.63316			0.816580	−	0.577232i	$-0.195867\pi$
$419$	33.4300			1.63316			0.816580	+	0.577232i	$0.195867\pi$
$420$		0			0
$421$	8.73343	+	8.73343i	0.425641	+	0.425641i	0.887141	−	0.461499i	$-0.152688\pi$
$421$	8.73343	+	8.73343i	0.425641	+	0.425641i	−0.461499	+	0.887141i	$0.652688\pi$
$422$		0			0
$423$	−0.157665	−	0.157665i	−0.00766594	−	0.00766594i
$424$		0			0
$425$	0.838043	−	0.838043i	0.0406511	−	0.0406511i
$426$		0			0
$427$	−30.8555	−	30.8555i	−1.49320	−	1.49320i
$428$		0			0
$429$	−17.4168			−0.840893
$430$		0			0
$431$		−	5.15146i		−	0.248137i	−0.992274	−	0.124069i	$-0.960406\pi$
$431$		−	5.15146i		−	0.248137i	0.992274	−	0.124069i	$-0.0395943\pi$
$432$		0			0
$433$	−16.6537	−	16.6537i	−0.800326	−	0.800326i	0.182820	−	0.983146i	$-0.441477\pi$
$433$	−16.6537	−	16.6537i	−0.800326	−	0.800326i	−0.983146	+	0.182820i	$0.941477\pi$
$434$		0			0
$435$	−11.6766	+	8.70322i	−0.559849	+	0.417288i
$436$		0			0
$437$	1.95690	−	1.95690i	0.0936111	−	0.0936111i
$438$		0			0
$439$	−8.73247			−0.416778			−0.208389	−	0.978046i	$-0.566822\pi$
$439$	−8.73247			−0.416778			−0.208389	+	0.978046i	$0.566822\pi$
$440$		0			0
$441$			3.50720i			0.167010i
$442$		0			0
$443$	4.98351	−	4.98351i	0.236773	−	0.236773i	−0.578739	−	0.815513i	$-0.696455\pi$
$443$	4.98351	−	4.98351i	0.236773	−	0.236773i	0.815513	+	0.578739i	$0.196455\pi$
$444$		0			0
$445$	4.60159	+	4.60159i	0.218136	+	0.218136i
$446$		0			0
$447$	−3.42844	+	3.42844i	−0.162160	+	0.162160i
$448$		0			0
$449$	−3.55048	+	3.55048i	−0.167557	+	0.167557i	−0.785905	−	0.618347i	$-0.787802\pi$
$449$	−3.55048	+	3.55048i	−0.167557	+	0.167557i	0.618347	+	0.785905i	$0.287802\pi$
$450$		0			0
$451$		−	1.35183i		−	0.0636550i
$452$		0			0
$453$	−9.37433	−	9.37433i	−0.440444	−	0.440444i
$454$		0			0
$455$		−	38.2397i		−	1.79271i
$456$		0			0
$457$			21.8617i			1.02265i	0.859388	+	0.511324i	$0.170845\pi$
$457$			21.8617i			1.02265i	−0.859388	+	0.511324i	$0.829155\pi$
$458$		0			0
$459$		−	5.78513i		−	0.270027i
$460$		0			0
$461$	9.69607	+	9.69607i	0.451591	+	0.451591i	0.895882	−	0.444291i	$-0.146545\pi$
$461$	9.69607	+	9.69607i	0.451591	+	0.451591i	−0.444291	+	0.895882i	$0.646545\pi$
$462$		0			0
$463$	−2.53802			−0.117952			−0.0589759	−	0.998259i	$-0.518784\pi$
$463$	−2.53802			−0.117952			−0.0589759	+	0.998259i	$0.518784\pi$
$464$		0			0
$465$	−26.5871			−1.23295
$466$		0			0
$467$	−19.6170	−	19.6170i	−0.907764	−	0.907764i	0.0883272	−	0.996092i	$-0.471848\pi$
$467$	−19.6170	−	19.6170i	−0.907764	−	0.907764i	−0.996092	+	0.0883272i	$0.971848\pi$
$468$		0			0
$469$		−	17.1345i		−	0.791199i
$470$		0			0
$471$			13.4354i			0.619073i
$472$		0			0
$473$		−	6.69236i		−	0.307715i
$474$		0			0
$475$	3.88269	+	3.88269i	0.178150	+	0.178150i
$476$		0			0
$477$			22.0472i			1.00947i
$478$		0			0
$479$	7.39378	−	7.39378i	0.337830	−	0.337830i	−0.517720	−	0.855550i	$-0.673219\pi$
$479$	7.39378	−	7.39378i	0.337830	−	0.337830i	0.855550	+	0.517720i	$0.173219\pi$
$480$		0			0
$481$	−6.49802	+	6.49802i	−0.296284	+	0.296284i
$482$		0			0
$483$	1.26083	+	1.26083i	0.0573698	+	0.0573698i
$484$		0			0
$485$	−12.6437	+	12.6437i	−0.574123	+	0.574123i
$486$		0			0
$487$		−	6.93119i		−	0.314082i	−0.987592	−	0.157041i	$-0.949805\pi$
$487$		−	6.93119i		−	0.314082i	0.987592	−	0.157041i	$-0.0501955\pi$
$488$		0			0
$489$	19.9359			0.901535
$490$		0			0
$491$	−2.67258	+	2.67258i	−0.120612	+	0.120612i	−0.764836	−	0.644225i	$-0.777180\pi$
$491$	−2.67258	+	2.67258i	−0.120612	+	0.120612i	0.644225	+	0.764836i	$0.277180\pi$
$492$		0			0
$493$	4.74725	−	3.53840i	0.213806	−	0.159362i
$494$		0			0
$495$	−9.59308	−	9.59308i	−0.431177	−	0.431177i
$496$		0			0
$497$		−	22.0791i		−	0.990381i
$498$		0			0
$499$	−10.8237			−0.484534			−0.242267	−	0.970210i	$-0.577891\pi$
$499$	−10.8237			−0.484534			−0.242267	+	0.970210i	$0.577891\pi$
$500$		0			0
$501$	−2.17159	−	2.17159i	−0.0970195	−	0.0970195i
$502$		0			0
$503$	−17.0672	+	17.0672i	−0.760990	+	0.760990i	−0.976501	−	0.215511i	$-0.930858\pi$
$503$	−17.0672	+	17.0672i	−0.760990	+	0.760990i	0.215511	+	0.976501i	$0.430858\pi$
$504$		0			0
$505$	29.1651	+	29.1651i	1.29783	+	1.29783i
$506$		0			0
$507$	10.7624	+	10.7624i	0.477974	+	0.477974i
$508$		0			0
$509$	12.2422			0.542627			0.271314	−	0.962491i	$-0.412542\pi$
$509$	12.2422			0.542627			0.271314	+	0.962491i	$0.412542\pi$
$510$		0			0
$511$	−24.4389	+	24.4389i	−1.08111	+	1.08111i
$512$		0			0
$513$	26.8027			1.18337
$514$		0			0
$515$	−33.3144			−1.46801
$516$		0			0
$517$	−0.380083			−0.0167160
$518$		0			0
$519$	−10.7980	+	10.7980i	−0.473981	+	0.473981i
$520$		0			0
$521$			2.37122i			0.103885i	0.998650	+	0.0519425i	$0.0165413\pi$
$521$			2.37122i			0.103885i	−0.998650	+	0.0519425i	$0.983459\pi$
$522$		0			0
$523$		−	39.9342i		−	1.74620i	−0.487539	−	0.873101i	$-0.662105\pi$
$523$		−	39.9342i		−	1.74620i	0.487539	−	0.873101i	$-0.337895\pi$
$524$		0			0
$525$	−2.50162	+	2.50162i	−0.109180	+	0.109180i
$526$		0			0
$527$	10.8093			0.470860
$528$		0			0
$529$	22.7048			0.987167
$530$		0			0
$531$	0.696067			0.0302067
$532$		0			0
$533$	−1.61797	+	1.61797i	−0.0700821	+	0.0700821i
$534$		0			0
$535$	−28.6805			−1.23997
$536$		0			0
$537$	−9.96733	−	9.96733i	−0.430122	−	0.430122i
$538$		0			0
$539$	4.22741	+	4.22741i	0.182087	+	0.182087i
$540$		0			0
$541$	−24.5852	+	24.5852i	−1.05700	+	1.05700i	−0.0587273	+	0.998274i	$0.518704\pi$
$541$	−24.5852	+	24.5852i	−1.05700	+	1.05700i	−0.998274	+	0.0587273i	$0.981296\pi$
$542$		0			0
$543$	−14.3102	−	14.3102i	−0.614111	−	0.614111i
$544$		0			0
$545$	−2.53380			−0.108536
$546$		0			0
$547$		−	1.14260i		−	0.0488541i	−0.999702	−	0.0244270i	$-0.992224\pi$
$547$		−	1.14260i		−	0.0488541i	0.999702	−	0.0244270i	$-0.00777614\pi$
$548$		0			0
$549$	18.5292	+	18.5292i	0.790807	+	0.790807i
$550$		0			0
$551$	16.3935	+	21.9942i	0.698388	+	0.936984i
$552$		0			0
$553$	−16.0066	+	16.0066i	−0.680671	+	0.680671i
$554$		0			0
$555$	4.79379			0.203485
$556$		0			0
$557$		−	46.6643i		−	1.97723i	−0.150464	−	0.988615i	$-0.548077\pi$
$557$		−	46.6643i		−	1.97723i	0.150464	−	0.988615i	$-0.451923\pi$
$558$		0			0
$559$	−8.00994	+	8.00994i	−0.338785	+	0.338785i
$560$		0			0
$561$	−2.61195	−	2.61195i	−0.110277	−	0.110277i
$562$		0			0
$563$	−14.3509	+	14.3509i	−0.604819	+	0.604819i	−0.941588	−	0.336768i	$-0.890666\pi$
$563$	−14.3509	+	14.3509i	−0.604819	+	0.604819i	0.336768	+	0.941588i	$0.390666\pi$
$564$		0			0
$565$	31.8589	−	31.8589i	1.34031	−	1.34031i
$566$		0			0
$567$			1.14162i			0.0479435i
$568$		0			0
$569$	0.151465	+	0.151465i	0.00634972	+	0.00634972i	0.710275	−	0.703925i	$-0.248571\pi$
$569$	0.151465	+	0.151465i	0.00634972	+	0.00634972i	−0.703925	+	0.710275i	$0.748571\pi$
$570$		0			0
$571$			3.21465i			0.134529i	0.997735	+	0.0672644i	$0.0214271\pi$
$571$			3.21465i			0.134529i	−0.997735	+	0.0672644i	$0.978573\pi$
$572$		0			0
$573$		−	8.23606i		−	0.344066i
$574$		0			0
$575$		−	0.585633i		−	0.0244226i
$576$		0			0
$577$	11.5393	+	11.5393i	0.480389	+	0.480389i	0.905256	−	0.424867i	$-0.139679\pi$
$577$	11.5393	+	11.5393i	0.480389	+	0.480389i	−0.424867	+	0.905256i	$0.639679\pi$
$578$		0			0
$579$	11.2053			0.465677
$580$		0			0
$581$	−31.1944			−1.29416
$582$		0			0
$583$	26.5746	+	26.5746i	1.10061	+	1.10061i
$584$		0			0
$585$			22.9635i			0.949424i
$586$		0			0
$587$			23.6876i			0.977693i	0.872370	+	0.488847i	$0.162582\pi$
$587$			23.6876i			0.977693i	−0.872370	+	0.488847i	$0.837418\pi$
$588$		0			0
$589$			50.0799i			2.06350i
$590$		0			0
$591$	0.138917	+	0.138917i	0.00571428	+	0.00571428i
$592$		0			0
$593$			46.8698i			1.92471i	0.271789	+	0.962357i	$0.412385\pi$
$593$			46.8698i			1.92471i	−0.271789	+	0.962357i	$0.587615\pi$
$594$		0			0
$595$	5.73468	−	5.73468i	0.235099	−	0.235099i
$596$		0			0
$597$	18.5815	−	18.5815i	0.760489	−	0.760489i
$598$		0			0
$599$	−12.9531	−	12.9531i	−0.529249	−	0.529249i	0.391099	−	0.920349i	$-0.372095\pi$
$599$	−12.9531	−	12.9531i	−0.529249	−	0.529249i	−0.920349	+	0.391099i	$0.872095\pi$
$600$		0			0
$601$	−17.8122	+	17.8122i	−0.726576	+	0.726576i	−0.969936	−	0.243360i	$-0.921750\pi$
$601$	−17.8122	+	17.8122i	−0.726576	+	0.726576i	0.243360	+	0.969936i	$0.421750\pi$
$602$		0			0
$603$			10.2895i			0.419022i
$604$		0			0
$605$	3.99277			0.162329
$606$		0			0
$607$	25.4323	−	25.4323i	1.03227	−	1.03227i	0.0328052	−	0.999462i	$-0.489556\pi$
$607$	25.4323	−	25.4323i	1.03227	−	1.03227i	0.999462	−	0.0328052i	$-0.0104441\pi$
$608$		0			0
$609$	−14.1709	+	10.5624i	−0.574233	+	0.428009i
$610$		0			0
$611$	0.454913	+	0.454913i	0.0184038	+	0.0184038i
$612$		0			0
$613$		−	32.0241i		−	1.29344i	−0.762727	−	0.646721i	$-0.776140\pi$
$613$		−	32.0241i		−	1.29344i	0.762727	−	0.646721i	$-0.223860\pi$
$614$		0			0
$615$	1.19363			0.0481317
$616$		0			0
$617$	−8.66041	−	8.66041i	−0.348655	−	0.348655i	0.510954	−	0.859608i	$-0.329292\pi$
$617$	−8.66041	−	8.66041i	−0.348655	−	0.348655i	−0.859608	+	0.510954i	$0.829292\pi$
$618$		0			0
$619$	13.8606	−	13.8606i	0.557103	−	0.557103i	−0.371379	−	0.928481i	$-0.621115\pi$
$619$	13.8606	−	13.8606i	0.557103	−	0.557103i	0.928481	+	0.371379i	$0.121115\pi$
$620$		0			0
$621$	−2.02135	−	2.02135i	−0.0811142	−	0.0811142i
$622$		0			0
$623$	5.58456	+	5.58456i	0.223741	+	0.223741i
$624$		0			0
$625$	−29.2277			−1.16911
$626$		0			0
$627$	12.1012	−	12.1012i	0.483277	−	0.483277i
$628$		0			0
$629$	−1.94897			−0.0777107
$630$		0			0
$631$	−33.3931			−1.32936			−0.664679	−	0.747129i	$-0.731432\pi$
$631$	−33.3931			−1.32936			−0.664679	+	0.747129i	$0.731432\pi$
$632$		0			0
$633$	13.5944			0.540329
$634$		0			0
$635$	18.4127	−	18.4127i	0.730686	−	0.730686i
$636$		0			0
$637$		−	10.1194i		−	0.400945i
$638$		0			0
$639$			13.2588i			0.524510i
$640$		0			0
$641$	−23.0284	+	23.0284i	−0.909568	+	0.909568i	−0.996237	−	0.0866695i	$-0.972378\pi$
$641$	−23.0284	+	23.0284i	−0.909568	+	0.909568i	0.0866695	+	0.996237i	$0.472378\pi$
$642$		0			0
$643$	−44.4095			−1.75134			−0.875670	−	0.482909i	$-0.839580\pi$
$643$	−44.4095			−1.75134			−0.875670	+	0.482909i	$0.839580\pi$
$644$		0			0
$645$	5.90918			0.232674
$646$		0			0
$647$	14.4439			0.567849			0.283925	−	0.958847i	$-0.408363\pi$
$647$	14.4439			0.567849			0.283925	+	0.958847i	$0.408363\pi$
$648$		0			0
$649$	0.839004	−	0.839004i	0.0329338	−	0.0329338i
$650$		0			0
$651$	−32.2665			−1.26462
$652$		0			0
$653$	−26.3897	−	26.3897i	−1.03271	−	1.03271i	−0.999447	−	0.0332631i	$-0.989410\pi$
$653$	−26.3897	−	26.3897i	−1.03271	−	1.03271i	−0.0332631	−	0.999447i	$-0.510590\pi$
$654$		0			0
$655$	13.1449	+	13.1449i	0.513613	+	0.513613i
$656$		0			0
$657$	14.6759	−	14.6759i	0.572562	−	0.572562i
$658$		0			0
$659$	−0.834329	−	0.834329i	−0.0325009	−	0.0325009i	0.690670	−	0.723170i	$-0.257316\pi$
$659$	−0.834329	−	0.834329i	−0.0325009	−	0.0325009i	−0.723170	+	0.690670i	$0.757316\pi$
$660$		0			0
$661$	−26.1470			−1.01700			−0.508501	−	0.861061i	$-0.669800\pi$
$661$	−26.1470			−1.01700			−0.508501	+	0.861061i	$0.669800\pi$
$662$		0			0
$663$			6.25237i			0.242822i
$664$		0			0
$665$	26.5690	+	26.5690i	1.03030	+	1.03030i
$666$		0			0
$667$	0.422379	−	2.89505i	0.0163546	−	0.112097i
$668$		0			0
$669$	16.9416	−	16.9416i	0.655000	−	0.655000i
$670$		0			0
$671$	44.6684			1.72440
$672$		0			0
$673$		−	26.0543i		−	1.00432i	−0.864775	−	0.502160i	$-0.832539\pi$
$673$		−	26.0543i		−	1.00432i	0.864775	−	0.502160i	$-0.167461\pi$
$674$		0			0
$675$	4.01057	−	4.01057i	0.154367	−	0.154367i
$676$		0			0
$677$	−3.12042	−	3.12042i	−0.119927	−	0.119927i	0.644596	−	0.764523i	$-0.277026\pi$
$677$	−3.12042	−	3.12042i	−0.119927	−	0.119927i	−0.764523	+	0.644596i	$0.777026\pi$
$678$		0			0
$679$	−15.3447	+	15.3447i	−0.588874	+	0.588874i
$680$		0			0
$681$	−15.8015	+	15.8015i	−0.605513	+	0.605513i
$682$		0			0
$683$			34.2257i			1.30961i	0.755799	+	0.654804i	$0.227249\pi$
$683$			34.2257i			1.30961i	−0.755799	+	0.654804i	$0.772751\pi$
$684$		0			0
$685$	24.6671	+	24.6671i	0.942482	+	0.942482i
$686$		0			0
$687$		−	9.06547i		−	0.345869i
$688$		0			0
$689$		−	63.6131i		−	2.42347i
$690$		0			0
$691$		−	45.6948i		−	1.73831i	−0.494539	−	0.869155i	$-0.664663\pi$
$691$		−	45.6948i		−	1.73831i	0.494539	−	0.869155i	$-0.335337\pi$
$692$		0			0
$693$	−11.6423	−	11.6423i	−0.442255	−	0.442255i
$694$		0			0
$695$	35.5126			1.34707
$696$		0			0
$697$	−0.485284			−0.0183814
$698$		0			0
$699$	−14.1879	−	14.1879i	−0.536635	−	0.536635i
$700$		0			0
$701$			30.7350i			1.16085i	0.814315	+	0.580423i	$0.197113\pi$
$701$			30.7350i			1.16085i	−0.814315	+	0.580423i	$0.802887\pi$
$702$		0			0
$703$		−	9.02967i		−	0.340560i
$704$		0			0
$705$		−	0.335604i		−	0.0126396i
$706$		0			0
$707$	35.3953	+	35.3953i	1.33118	+	1.33118i
$708$		0			0
$709$			23.9978i			0.901256i	0.892712	+	0.450628i	$0.148800\pi$
$709$			23.9978i			0.901256i	−0.892712	+	0.450628i	$0.851200\pi$
$710$		0			0
$711$	9.61221	−	9.61221i	0.360486	−	0.360486i
$712$		0			0
$713$	3.77682	−	3.77682i	0.141443	−	0.141443i
$714$		0			0
$715$	27.6791	+	27.6791i	1.03514	+	1.03514i
$716$		0			0
$717$	4.65558	−	4.65558i	0.173866	−	0.173866i
$718$		0			0
$719$		−	32.1811i		−	1.20015i	−0.799943	−	0.600076i	$-0.795137\pi$
$719$		−	32.1811i		−	1.20015i	0.799943	−	0.600076i	$-0.204863\pi$
$720$		0			0
$721$	−40.4309			−1.50572
$722$		0			0
$723$	−1.95700	+	1.95700i	−0.0727817	+	0.0727817i
$724$		0			0
$725$	5.74408	+	0.838043i	0.213330	+	0.0311241i
$726$		0			0
$727$	29.4327	+	29.4327i	1.09160	+	1.09160i	0.995358	+	0.0962401i	$0.0306817\pi$
$727$	29.4327	+	29.4327i	1.09160	+	1.09160i	0.0962401	+	0.995358i	$0.469318\pi$
$728$		0			0
$729$		−	18.0008i		−	0.666697i
$730$		0			0
$731$	−2.40245			−0.0888578
$732$		0			0
$733$	3.46894	+	3.46894i	0.128128	+	0.128128i	0.768263	−	0.640135i	$-0.221121\pi$
$733$	3.46894	+	3.46894i	0.128128	+	0.128128i	−0.640135	+	0.768263i	$0.721121\pi$
$734$		0			0
$735$	−3.73269	+	3.73269i	−0.137682	+	0.137682i
$736$		0			0
$737$	12.4025	+	12.4025i	0.456852	+	0.456852i
$738$		0			0
$739$	1.63354	+	1.63354i	0.0600908	+	0.0600908i	0.736514	−	0.676423i	$-0.236471\pi$
$739$	1.63354	+	1.63354i	0.0600908	+	0.0600908i	−0.676423	+	0.736514i	$0.736471\pi$
$740$		0			0
$741$	−28.9674			−1.06415
$742$		0			0
$743$	3.88931	−	3.88931i	0.142685	−	0.142685i	−0.632156	−	0.774841i	$-0.717830\pi$
$743$	3.88931	−	3.88931i	0.142685	−	0.142685i	0.774841	+	0.632156i	$0.217830\pi$
$744$		0			0
$745$	10.8970			0.399237
$746$		0			0
$747$	18.7327			0.685393
$748$		0			0
$749$	−34.8072			−1.27183
$750$		0			0
$751$	−28.8942	+	28.8942i	−1.05437	+	1.05437i	−0.0559304	+	0.998435i	$0.517813\pi$
$751$	−28.8942	+	28.8942i	−1.05437	+	1.05437i	−0.998435	+	0.0559304i	$0.982187\pi$
$752$		0			0
$753$		−	27.9467i		−	1.01843i
$754$		0			0
$755$			29.7956i			1.08437i
$756$		0			0
$757$	1.62958	−	1.62958i	0.0592281	−	0.0592281i	−0.676872	−	0.736100i	$-0.736665\pi$
$757$	1.62958	−	1.62958i	0.0592281	−	0.0592281i	0.736100	+	0.676872i	$0.236665\pi$
$758$		0			0
$759$	−1.82526			−0.0662526
$760$		0			0
$761$	23.9830			0.869384			0.434692	−	0.900579i	$-0.356857\pi$
$761$	23.9830			0.869384			0.434692	+	0.900579i	$0.356857\pi$
$762$		0			0
$763$	−3.07506			−0.111325
$764$		0			0
$765$	−3.44376	+	3.44376i	−0.124509	+	0.124509i
$766$		0			0
$767$	−2.00837			−0.0725181
$768$		0			0
$769$	−0.128359	−	0.128359i	−0.00462876	−	0.00462876i	0.704789	−	0.709417i	$-0.251042\pi$
$769$	−0.128359	−	0.128359i	−0.00462876	−	0.00462876i	−0.709417	+	0.704789i	$0.751042\pi$
$770$		0			0
$771$	9.34655	+	9.34655i	0.336608	+	0.336608i
$772$		0			0
$773$	5.78703	−	5.78703i	0.208145	−	0.208145i	−0.595334	−	0.803479i	$-0.702980\pi$
$773$	5.78703	−	5.78703i	0.208145	−	0.208145i	0.803479	+	0.595334i	$0.202980\pi$
$774$		0			0
$775$	7.49361	+	7.49361i	0.269178	+	0.269178i
$776$		0			0
$777$	5.81782			0.208713
$778$		0			0
$779$		−	2.24834i		−	0.0805550i
$780$		0			0
$781$	15.9815	+	15.9815i	0.571863	+	0.571863i
$782$		0			0
$783$	22.7187	−	16.9335i	0.811898	−	0.605155i
$784$		0			0
$785$	21.3518	−	21.3518i	0.762078	−	0.762078i
$786$		0			0
$787$	−21.2238			−0.756548			−0.378274	−	0.925694i	$-0.623482\pi$
$787$	−21.2238			−0.756548			−0.378274	+	0.925694i	$0.623482\pi$
$788$		0			0
$789$			19.2196i			0.684237i
$790$		0			0
$791$	38.6645	−	38.6645i	1.37475	−	1.37475i
$792$		0			0
$793$	−53.4626	−	53.4626i	−1.89851	−	1.89851i
$794$		0			0
$795$	−23.4647	+	23.4647i	−0.832206	+	0.832206i
$796$		0			0
$797$	8.34477	−	8.34477i	0.295587	−	0.295587i	−0.543695	−	0.839283i	$-0.682975\pi$
$797$	8.34477	−	8.34477i	0.295587	−	0.295587i	0.839283	+	0.543695i	$0.182975\pi$
$798$		0			0
$799$			0.136444i			0.00482703i
$800$		0			0
$801$	−3.35361	−	3.35361i	−0.118494	−	0.118494i
$802$		0			0
$803$		−	35.3792i		−	1.24851i
$804$		0			0
$805$		−	4.00746i		−	0.141244i
$806$		0			0
$807$		−	10.5488i		−	0.371337i
$808$		0			0
$809$	−16.0913	−	16.0913i	−0.565740	−	0.565740i	0.365192	−	0.930932i	$-0.381003\pi$
$809$	−16.0913	−	16.0913i	−0.565740	−	0.565740i	−0.930932	+	0.365192i	$0.881003\pi$
$810$		0			0
$811$	16.1949			0.568681			0.284341	−	0.958723i	$-0.408225\pi$
$811$	16.1949			0.568681			0.284341	+	0.958723i	$0.408225\pi$
$812$		0			0
$813$	10.8147			0.379289
$814$		0			0
$815$	−31.6825	−	31.6825i	−1.10979	−	1.10979i
$816$		0			0
$817$		−	11.1306i		−	0.389412i
$818$		0			0
$819$			27.8689i			0.973818i
$820$		0			0
$821$		−	5.11879i		−	0.178647i	−0.996003	−	0.0893235i	$-0.971530\pi$
$821$		−	5.11879i		−	0.178647i	0.996003	−	0.0893235i	$-0.0284705\pi$
$822$		0			0
$823$	−7.59476	−	7.59476i	−0.264737	−	0.264737i	0.562239	−	0.826975i	$-0.309940\pi$
$823$	−7.59476	−	7.59476i	−0.264737	−	0.264737i	−0.826975	+	0.562239i	$0.809940\pi$
$824$		0			0
$825$		−	3.62149i		−	0.126084i
$826$		0			0
$827$	−36.5313	+	36.5313i	−1.27032	+	1.27032i	−0.324395	+	0.945922i	$0.605161\pi$
$827$	−36.5313	+	36.5313i	−1.27032	+	1.27032i	−0.945922	+	0.324395i	$0.894839\pi$
$828$		0			0
$829$	26.8041	−	26.8041i	0.930944	−	0.930944i	−0.0668209	−	0.997765i	$-0.521286\pi$
$829$	26.8041	−	26.8041i	0.930944	−	0.930944i	0.997765	+	0.0668209i	$0.0212856\pi$
$830$		0			0
$831$	−5.13249	−	5.13249i	−0.178044	−	0.178044i
$832$		0			0
$833$	1.51757	−	1.51757i	0.0525807	−	0.0525807i
$834$		0			0
$835$			6.90224i			0.238862i
$836$		0			0
$837$	51.7294			1.78803
$838$		0			0
$839$	29.2179	−	29.2179i	1.00871	−	1.00871i	0.00875301	−	0.999962i	$-0.497214\pi$
$839$	29.2179	−	29.2179i	1.00871	−	1.00871i	0.999962	−	0.00875301i	$-0.00278621\pi$
$840$		0			0
$841$	27.7911	+	8.28566i	0.958315	+	0.285712i
$842$		0			0
$843$	5.86768	+	5.86768i	0.202094	+	0.202094i
$844$		0			0
$845$		−	34.2074i		−	1.17677i
$846$		0			0
$847$	4.84569			0.166500
$848$		0			0
$849$	−7.95766	−	7.95766i	−0.273106	−	0.273106i
$850$		0			0
$851$	−0.680982	+	0.680982i	−0.0233438	+	0.0233438i
$852$		0			0
$853$	4.30375	+	4.30375i	0.147358	+	0.147358i	0.776937	−	0.629579i	$-0.216773\pi$
$853$	4.30375	+	4.30375i	0.147358	+	0.147358i	−0.629579	+	0.776937i	$0.716773\pi$
$854$		0			0
$855$	−15.9551	−	15.9551i	−0.545652	−	0.545652i
$856$		0			0
$857$	−8.09665			−0.276576			−0.138288	−	0.990392i	$-0.544160\pi$
$857$	−8.09665			−0.276576			−0.138288	+	0.990392i	$0.544160\pi$
$858$		0			0
$859$	18.6302	−	18.6302i	0.635655	−	0.635655i	−0.313825	−	0.949481i	$-0.601611\pi$
$859$	18.6302	−	18.6302i	0.635655	−	0.635655i	0.949481	+	0.313825i	$0.101611\pi$
$860$		0			0
$861$	1.44861			0.0493683
$862$		0			0
$863$	32.1705			1.09510			0.547549	−	0.836774i	$-0.315561\pi$
$863$	32.1705			1.09510			0.547549	+	0.836774i	$0.315561\pi$
$864$		0			0
$865$	34.3207			1.16694
$866$		0			0
$867$	12.2484	−	12.2484i	0.415978	−	0.415978i
$868$		0			0
$869$		−	23.1722i		−	0.786062i
$870$		0			0
$871$		−	29.6885i		−	1.00596i
$872$		0			0
$873$	9.21469	−	9.21469i	0.311870	−	0.311870i
$874$		0			0
$875$	−28.9302			−0.978021
$876$		0			0
$877$	−5.38215			−0.181742			−0.0908712	−	0.995863i	$-0.528965\pi$
$877$	−5.38215			−0.181742			−0.0908712	+	0.995863i	$0.528965\pi$
$878$		0			0
$879$	7.57933			0.255645
$880$		0			0
$881$	21.2225	−	21.2225i	0.715004	−	0.715004i	−0.252574	−	0.967578i	$-0.581277\pi$
$881$	21.2225	−	21.2225i	0.715004	−	0.715004i	0.967578	+	0.252574i	$0.0812771\pi$
$882$		0			0
$883$	−21.9622			−0.739088			−0.369544	−	0.929213i	$-0.620486\pi$
$883$	−21.9622			−0.739088			−0.369544	+	0.929213i	$0.620486\pi$
$884$		0			0
$885$	0.740819	+	0.740819i	0.0249024	+	0.0249024i
$886$		0			0
$887$	21.0521	+	21.0521i	0.706861	+	0.706861i	0.965874	−	0.259013i	$-0.0833971\pi$
$887$	21.0521	+	21.0521i	0.706861	+	0.706861i	−0.259013	+	0.965874i	$0.583397\pi$
$888$		0			0
$889$	22.3460	−	22.3460i	0.749460	−	0.749460i
$890$		0			0
$891$	−0.826339	−	0.826339i	−0.0276834	−	0.0276834i
$892$		0			0
$893$	−0.632149			−0.0211541
$894$		0			0
$895$			31.6804i			1.05896i
$896$		0			0
$897$	2.18461	+	2.18461i	0.0729420	+	0.0729420i
$898$		0			0
$899$	31.6396	+	42.4489i	1.05524	+	1.41575i
$900$		0			0
$901$	9.53985	−	9.53985i	0.317818	−	0.317818i
$902$		0			0
$903$	7.17148			0.238652
$904$		0			0
$905$			45.4840i			1.51194i
$906$		0			0
$907$	−20.5384	+	20.5384i	−0.681966	+	0.681966i	−0.960443	−	0.278477i	$-0.910171\pi$
$907$	−20.5384	+	20.5384i	−0.681966	+	0.681966i	0.278477	+	0.960443i	$0.410171\pi$
$908$		0			0
$909$	−21.2554	−	21.2554i	−0.704997	−	0.704997i
$910$		0			0
$911$	−30.5805	+	30.5805i	−1.01318	+	1.01318i	−0.0132639	+	0.999912i	$0.504222\pi$
$911$	−30.5805	+	30.5805i	−1.01318	+	1.01318i	−0.999912	+	0.0132639i	$0.995778\pi$
$912$		0			0
$913$	22.5794	−	22.5794i	0.747271	−	0.747271i
$914$		0			0
$915$			39.4410i			1.30388i
$916$		0			0
$917$	15.9528	+	15.9528i	0.526809	+	0.526809i
$918$		0			0
$919$		−	57.9443i		−	1.91141i	−0.294332	−	0.955703i	$-0.595097\pi$
$919$		−	57.9443i		−	1.91141i	0.294332	−	0.955703i	$-0.404903\pi$
$920$		0			0
$921$		−	14.6550i		−	0.482898i
$922$		0			0
$923$		−	38.2558i		−	1.25921i
$924$		0			0
$925$	−1.35114	−	1.35114i	−0.0444251	−	0.0444251i
$926$		0			0
$927$	24.2793			0.797437
$928$		0			0
$929$	30.2244			0.991630			0.495815	−	0.868428i	$-0.334869\pi$
$929$	30.2244			0.991630			0.495815	+	0.868428i	$0.334869\pi$
$930$		0			0
$931$	7.03096	+	7.03096i	0.230430	+	0.230430i
$932$		0			0
$933$			24.8649i			0.814040i
$934$		0			0
$935$			8.30188i			0.271501i
$936$		0			0
$937$			2.86535i			0.0936068i	0.998904	+	0.0468034i	$0.0149034\pi$
$937$			2.86535i			0.0936068i	−0.998904	+	0.0468034i	$0.985097\pi$
$938$		0			0
$939$	20.4830	+	20.4830i	0.668437	+	0.668437i
$940$		0			0
$941$			48.1764i			1.57051i	0.619174	+	0.785253i	$0.287467\pi$
$941$			48.1764i			1.57051i	−0.619174	+	0.785253i	$0.712533\pi$
$942$		0			0
$943$	−0.169561	+	0.169561i	−0.00552165	+	0.00552165i
$944$		0			0
$945$	27.4441	−	27.4441i	0.892758	−	0.892758i
$946$		0			0
$947$	6.86194	+	6.86194i	0.222983	+	0.222983i	0.809753	−	0.586770i	$-0.199601\pi$
$947$	6.86194	+	6.86194i	0.222983	+	0.222983i	−0.586770	+	0.809753i	$0.699601\pi$
$948$		0			0
$949$	−42.3446	+	42.3446i	−1.37457	+	1.37457i
$950$		0			0
$951$			21.2406i			0.688774i
$952$		0			0
$953$	32.9340			1.06684			0.533418	−	0.845851i	$-0.320907\pi$
$953$	32.9340			1.06684			0.533418	+	0.845851i	$0.320907\pi$
$954$		0			0
$955$	−13.0889	+	13.0889i	−0.423545	+	0.423545i
$956$		0			0
$957$	2.61195	−	17.9027i	0.0844323	−	0.578712i
$958$		0			0
$959$	29.9364	+	29.9364i	0.966698	+	0.966698i
$960$		0			0
$961$			65.6544i			2.11788i
$962$		0			0
$963$	20.9022			0.673564
$964$		0			0
$965$	−17.8076	−	17.8076i	−0.573248	−	0.573248i
$966$		0			0
$967$	17.9896	−	17.9896i	0.578508	−	0.578508i	−0.355984	−	0.934492i	$-0.615854\pi$
$967$	17.9896	−	17.9896i	0.578508	−	0.578508i	0.934492	+	0.355984i	$0.115854\pi$
$968$		0			0
$969$	−4.34415	−	4.34415i	−0.139554	−	0.139554i
$970$		0			0
$971$	−32.1824	−	32.1824i	−1.03278	−	1.03278i	−0.999444	−	0.0333395i	$-0.989386\pi$
$971$	−32.1824	−	32.1824i	−1.03278	−	1.03278i	−0.0333395	−	0.999444i	$-0.510614\pi$
$972$		0			0
$973$	43.0986			1.38168
$974$		0			0
$975$	−4.33449	+	4.33449i	−0.138815	+	0.138815i
$976$		0			0
$977$	−39.4361			−1.26167			−0.630836	−	0.775916i	$-0.717288\pi$
$977$	−39.4361			−1.26167			−0.630836	+	0.775916i	$0.717288\pi$
$978$		0			0
$979$	−8.08455			−0.258383
$980$		0			0
$981$	1.84662			0.0589580
$982$		0			0
$983$	−28.9725	+	28.9725i	−0.924080	+	0.924080i	−0.997315	−	0.0732344i	$-0.976668\pi$
$983$	−28.9725	+	28.9725i	−0.924080	+	0.924080i	0.0732344	+	0.997315i	$0.476668\pi$
$984$		0			0
$985$		−	0.441537i		−	0.0140685i
$986$		0			0
$987$		−	0.407294i		−	0.0129643i
$988$		0			0
$989$	−0.839428	+	0.839428i	−0.0266923	+	0.0266923i
$990$		0			0
$991$	53.2976			1.69305			0.846527	−	0.532345i	$-0.178689\pi$
$991$	53.2976			1.69305			0.846527	+	0.532345i	$0.178689\pi$
$992$		0			0
$993$	5.44579			0.172817
$994$		0			0
$995$	−59.0598			−1.87232
$996$		0			0
$997$	10.5923	−	10.5923i	0.335463	−	0.335463i	−0.519194	−	0.854657i	$-0.673768\pi$
$997$	10.5923	−	10.5923i	0.335463	−	0.335463i	0.854657	+	0.519194i	$0.173768\pi$
$998$		0			0
$999$	−9.32709			−0.295096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	928.2.k.e.191.3	✓	10
4.3	odd	2		928.2.k.f.191.3	yes	10
29.12	odd	4		928.2.k.f.447.3	yes	10
116.99	even	4	inner	928.2.k.e.447.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
928.2.k.e.191.3	✓	10	1.1	even	1	trivial
928.2.k.e.447.3	yes	10	116.99	even	4	inner
928.2.k.f.191.3	yes	10	4.3	odd	2
928.2.k.f.447.3	yes	10	29.12	odd	4

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:	\( N \)	\(=\)	\( 928 = 2^{5} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	928.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.775651 - 0.775651i) q^{3} +2.46535i q^{5} +2.99199i q^{7} -1.79673i q^{9} +O(q^{10})\)	\(q+(-0.775651 - 0.775651i) q^{3} +2.46535i q^{5} +2.99199i q^{7} -1.79673i q^{9} +(-2.16569 - 2.16569i) q^{11} +5.18414i q^{13} +(1.91225 - 1.91225i) q^{15} +(-0.777448 + 0.777448i) q^{17} +(-3.60195 - 3.60195i) q^{19} +(2.32074 - 2.32074i) q^{21} +0.543289i q^{23} -1.07794 q^{25} +(-3.72059 + 3.72059i) q^{27} +(-5.32875 - 0.777448i) q^{29} +(-6.95178 - 6.95178i) q^{31} +3.35964i q^{33} -7.37629 q^{35} +(1.25344 + 1.25344i) q^{37} +(4.02108 - 4.02108i) q^{39} +(0.312100 + 0.312100i) q^{41} +(1.54509 + 1.54509i) q^{43} +4.42957 q^{45} +(0.0877510 - 0.0877510i) q^{47} -1.95199 q^{49} +1.20606 q^{51} -12.2707 q^{53} +(5.33918 - 5.33918i) q^{55} +5.58770i q^{57} +0.387407i q^{59} +(-10.3127 + 10.3127i) q^{61} +5.37580 q^{63} -12.7807 q^{65} -5.72680 q^{67} +(0.421402 - 0.421402i) q^{69} -7.37939 q^{71} +(8.16811 + 8.16811i) q^{73} +(0.836106 + 0.836106i) q^{75} +(6.47972 - 6.47972i) q^{77} +(5.34983 + 5.34983i) q^{79} +0.381559 q^{81} +10.4260i q^{83} +(-1.91668 - 1.91668i) q^{85} +(3.53022 + 4.73628i) q^{87} +(1.86651 - 1.86651i) q^{89} -15.5109 q^{91} +10.7843i q^{93} +(8.88005 - 8.88005i) q^{95} +(5.12859 + 5.12859i) q^{97} +(-3.89117 + 3.89117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3}+O(q^{10}) \) 10 * q - 2 * q^3	\( 10 q - 2 q^{3} - 14 q^{11} + 14 q^{15} + 6 q^{17} - 12 q^{19} - 28 q^{21} + 2 q^{25} - 2 q^{27} - 28 q^{29} + 14 q^{31} + 4 q^{35} + 10 q^{37} + 6 q^{39} + 14 q^{41} - 30 q^{43} - 36 q^{45} + 6 q^{47} - 42 q^{49} - 56 q^{51} + 4 q^{53} - 42 q^{55} - 26 q^{61} + 32 q^{63} - 36 q^{65} - 56 q^{67} + 16 q^{69} - 36 q^{71} - 22 q^{73} + 8 q^{75} + 28 q^{77} - 6 q^{79} - 54 q^{81} - 16 q^{85} + 58 q^{87} + 58 q^{89} + 20 q^{91} + 52 q^{95} + 26 q^{97} - 68 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 - 14 * q^11 + 14 * q^15 + 6 * q^17 - 12 * q^19 - 28 * q^21 + 2 * q^25 - 2 * q^27 - 28 * q^29 + 14 * q^31 + 4 * q^35 + 10 * q^37 + 6 * q^39 + 14 * q^41 - 30 * q^43 - 36 * q^45 + 6 * q^47 - 42 * q^49 - 56 * q^51 + 4 * q^53 - 42 * q^55 - 26 * q^61 + 32 * q^63 - 36 * q^65 - 56 * q^67 + 16 * q^69 - 36 * q^71 - 22 * q^73 + 8 * q^75 + 28 * q^77 - 6 * q^79 - 54 * q^81 - 16 * q^85 + 58 * q^87 + 58 * q^89 + 20 * q^91 + 52 * q^95 + 26 * q^97 - 68 * q^99

Introduction

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