LMFDB - Embedded newform 828.2.c.e.323.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [828,2,Mod(323,828)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("828.323"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-4,0,4,0,0,0,-4,0,-8,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 7 x^{10} + 20 x^{9} + 49 x^{8} - 382 x^{7} - 235 x^{6} + 2192 x^{5} + 668 x^{4} + \cdots + 1516 $ x^12 - 6x^11 + 7x^10 + 20x^9 + 49x^8 - 382x^7 - 235x^6 + 2192x^5 + 668x^4 - 5508x^3 - 94x^2 + 3288*x + 1516
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.11
Root			$-1.66767 - 0.569132i$ of defining polynomial
Character	$\chi$	$=$	828.323
Dual form			828.2.c.e.323.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06244 + 0.933389i) q^{2} +(0.257569 + 1.98335i) q^{4} +1.22862i q^{5} +3.40840i q^{7} +(-1.57758 + 2.34760i) q^{8} +(-1.14678 + 1.30533i) q^{10} +2.21869 q^{11} -4.82020 q^{13} +(-3.18136 + 3.62123i) q^{14} +(-3.86732 + 1.02170i) q^{16} +1.01086i q^{17} -8.63604i q^{19} +(-2.43677 + 0.316453i) q^{20} +(2.35723 + 2.07090i) q^{22} -1.00000 q^{23} +3.49050 q^{25} +(-5.12119 - 4.49913i) q^{26} +(-6.76003 + 0.877898i) q^{28} +9.68395i q^{29} -3.37624i q^{31} +(-5.06244 - 2.52422i) q^{32} +(-0.943523 + 1.07398i) q^{34} -4.18761 q^{35} +4.73094 q^{37} +(8.06079 - 9.17530i) q^{38} +(-2.88430 - 1.93824i) q^{40} +3.51413i q^{41} +3.87111i q^{43} +(0.571466 + 4.40043i) q^{44} +(-1.06244 - 0.933389i) q^{46} +2.64002 q^{47} -4.61718 q^{49} +(3.70846 + 3.25800i) q^{50} +(-1.24154 - 9.56013i) q^{52} +13.5760i q^{53} +2.72592i q^{55} +(-8.00157 - 5.37702i) q^{56} +(-9.03890 + 10.2886i) q^{58} -0.774720 q^{59} -9.56384 q^{61} +(3.15134 - 3.58706i) q^{62} +(-3.02248 - 7.40707i) q^{64} -5.92218i q^{65} -8.78558i q^{67} +(-2.00488 + 0.260365i) q^{68} +(-4.44910 - 3.90867i) q^{70} +15.6645 q^{71} +10.0471 q^{73} +(5.02635 + 4.41581i) q^{74} +(17.1282 - 2.22438i) q^{76} +7.56219i q^{77} +8.25854i q^{79} +(-1.25527 - 4.75145i) q^{80} +(-3.28005 + 3.73356i) q^{82} +2.16629 q^{83} -1.24195 q^{85} +(-3.61325 + 4.11283i) q^{86} +(-3.50017 + 5.20861i) q^{88} -4.80574i q^{89} -16.4292i q^{91} +(-0.257569 - 1.98335i) q^{92} +(2.80487 + 2.46417i) q^{94} +10.6104 q^{95} +12.8144 q^{97} +(-4.90549 - 4.30963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 8 q^{10} - 12 q^{11} - 4 q^{13} + 12 q^{14} - 12 q^{16} - 20 q^{20} + 4 q^{22} - 12 q^{23} - 40 q^{25} - 8 q^{26} - 24 q^{28} - 44 q^{32} - 28 q^{34} - 40 q^{35} - 32 q^{37}+ \cdots + 20 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 8 * q^10 - 12 * q^11 - 4 * q^13 + 12 * q^14 - 12 * q^16 - 20 * q^20 + 4 * q^22 - 12 * q^23 - 40 * q^25 - 8 * q^26 - 24 * q^28 - 44 * q^32 - 28 * q^34 - 40 * q^35 - 32 * q^37 + 32 * q^38 - 12 * q^40 - 4 * q^44 + 4 * q^46 - 32 * q^49 + 20 * q^50 + 32 * q^52 + 8 * q^56 - 16 * q^58 + 24 * q^59 - 56 * q^61 + 28 * q^64 - 16 * q^68 + 64 * q^70 + 56 * q^71 + 8 * q^73 + 36 * q^74 - 28 * q^76 - 28 * q^80 + 24 * q^82 + 28 * q^83 - 12 * q^85 + 8 * q^86 + 4 * q^88 - 4 * q^92 + 16 * q^94 - 8 * q^95 - 4 * q^97 + 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.06244	+	0.933389i	0.751260	+	0.660006i
$2$	1.06244	+	0.933389i	0.751260	+	0.660006i
$3$		0			0
$3$		0			0
$4$	0.257569	+	1.98335i	0.128785	+	0.991673i
$5$			1.22862i			0.549454i	0.961522	+	0.274727i	$0.0885874\pi$
$5$			1.22862i			0.549454i	−0.961522	+	0.274727i	$0.911413\pi$
$6$		0			0
$7$			3.40840i			1.28825i	0.764919	+	0.644127i	$0.222779\pi$
$7$			3.40840i			1.28825i	−0.764919	+	0.644127i	$0.777221\pi$
$8$	−1.57758	+	2.34760i	−0.557759	+	0.830003i
$9$		0			0
$10$	−1.14678	+	1.30533i	−0.362643	+	0.412783i
$11$	2.21869			0.668961			0.334480	−	0.942403i	$-0.391439\pi$
$11$	2.21869			0.668961			0.334480	+	0.942403i	$0.391439\pi$
$12$		0			0
$13$	−4.82020			−1.33688			−0.668442	−	0.743764i	$-0.733038\pi$
$13$	−4.82020			−1.33688			−0.668442	+	0.743764i	$0.733038\pi$
$14$	−3.18136	+	3.62123i	−0.850255	+	0.967814i
$15$		0			0
$16$	−3.86732	+	1.02170i	−0.966829	+	0.255424i
$17$			1.01086i			0.245169i	0.992458	+	0.122584i	$0.0391182\pi$
$17$			1.01086i			0.245169i	−0.992458	+	0.122584i	$0.960882\pi$
$18$		0			0
$19$		−	8.63604i		−	1.98124i	−0.136633	−	0.990622i	$-0.543628\pi$
$19$		−	8.63604i		−	1.98124i	0.136633	−	0.990622i	$-0.456372\pi$
$20$	−2.43677	+	0.316453i	−0.544878	+	0.0707611i
$21$		0			0
$22$	2.35723	+	2.07090i	0.502564	+	0.441518i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$		0			0
$25$	3.49050			0.698101
$26$	−5.12119	−	4.49913i	−1.00435	−	0.882351i
$27$		0			0
$28$	−6.76003	+	0.877898i	−1.27753	+	0.165907i
$29$			9.68395i			1.79826i	0.437677	+	0.899132i	$0.355801\pi$
$29$			9.68395i			1.79826i	−0.437677	+	0.899132i	$0.644199\pi$
$30$		0			0
$31$		−	3.37624i		−	0.606390i	−0.952929	−	0.303195i	$-0.901947\pi$
$31$		−	3.37624i		−	0.606390i	0.952929	−	0.303195i	$-0.0980534\pi$
$32$	−5.06244	−	2.52422i	−0.894922	−	0.446223i
$33$		0			0
$34$	−0.943523	+	1.07398i	−0.161813	+	0.184186i
$35$	−4.18761			−0.707836
$36$		0			0
$37$	4.73094			0.777761			0.388881	−	0.921288i	$-0.372862\pi$
$37$	4.73094			0.777761			0.388881	+	0.921288i	$0.372862\pi$
$38$	8.06079	−	9.17530i	1.30763	−	1.48843i
$39$		0			0
$40$	−2.88430	−	1.93824i	−0.456048	−	0.306463i
$41$			3.51413i			0.548814i	0.961614	+	0.274407i	$0.0884816\pi$
$41$			3.51413i			0.548814i	−0.961614	+	0.274407i	$0.911518\pi$
$42$		0			0
$43$			3.87111i			0.590339i	0.955445	+	0.295169i	$0.0953761\pi$
$43$			3.87111i			0.590339i	−0.955445	+	0.295169i	$0.904624\pi$
$44$	0.571466	+	4.40043i	0.0861518	+	0.663390i
$45$		0			0
$46$	−1.06244	−	0.933389i	−0.156649	−	0.137621i
$47$	2.64002			0.385087			0.192544	−	0.981288i	$-0.438326\pi$
$47$	2.64002			0.385087			0.192544	+	0.981288i	$0.438326\pi$
$48$		0			0
$49$	−4.61718			−0.659597
$50$	3.70846	+	3.25800i	0.524455	+	0.460750i
$51$		0			0
$52$	−1.24154	−	9.56013i	−0.172170	−	1.32575i
$53$			13.5760i			1.86481i	0.361414	+	0.932405i	$0.382294\pi$
$53$			13.5760i			1.86481i	−0.361414	+	0.932405i	$0.617706\pi$
$54$		0			0
$55$			2.72592i			0.367563i
$56$	−8.00157	−	5.37702i	−1.06925	−	0.718535i
$57$		0			0
$58$	−9.03890	+	10.2886i	−1.18687	+	1.35096i
$59$	−0.774720			−0.100860			−0.0504300	−	0.998728i	$-0.516059\pi$
$59$	−0.774720			−0.100860			−0.0504300	+	0.998728i	$0.516059\pi$
$60$		0			0
$61$	−9.56384			−1.22452			−0.612262	−	0.790655i	$-0.709740\pi$
$61$	−9.56384			−1.22452			−0.612262	+	0.790655i	$0.709740\pi$
$62$	3.15134	−	3.58706i	0.400221	−	0.455557i
$63$		0			0
$64$	−3.02248	−	7.40707i	−0.377810	−	0.925883i
$65$		−	5.92218i		−	0.734556i
$66$		0			0
$67$		−	8.78558i		−	1.07333i	−0.843796	−	0.536664i	$-0.819684\pi$
$67$		−	8.78558i		−	1.07333i	0.843796	−	0.536664i	$-0.180316\pi$
$68$	−2.00488	+	0.260365i	−0.243127	+	0.0315739i
$69$		0			0
$70$	−4.44910	−	3.90867i	−0.531769	−	0.467176i
$71$	15.6645			1.85904			0.929518	−	0.368777i	$-0.120223\pi$
$71$	15.6645			1.85904			0.929518	+	0.368777i	$0.120223\pi$
$72$		0			0
$73$	10.0471			1.17593			0.587964	−	0.808887i	$-0.299930\pi$
$73$	10.0471			1.17593			0.587964	+	0.808887i	$0.299930\pi$
$74$	5.02635	+	4.41581i	0.584301	+	0.513327i
$75$		0			0
$76$	17.1282	−	2.22438i	1.96474	−	0.255153i
$77$			7.56219i			0.861791i
$78$		0			0
$79$			8.25854i			0.929158i	0.885532	+	0.464579i	$0.153794\pi$
$79$			8.25854i			0.929158i	−0.885532	+	0.464579i	$0.846206\pi$
$80$	−1.25527	−	4.75145i	−0.140344	−	0.531228i
$81$		0			0
$82$	−3.28005	+	3.73356i	−0.362221	+	0.412302i
$83$	2.16629			0.237781			0.118891	−	0.992907i	$-0.462066\pi$
$83$	2.16629			0.237781			0.118891	+	0.992907i	$0.462066\pi$
$84$		0			0
$85$	−1.24195			−0.134709
$86$	−3.61325	+	4.11283i	−0.389627	+	0.443498i
$87$		0			0
$88$	−3.50017	+	5.20861i	−0.373119	+	0.555239i
$89$		−	4.80574i		−	0.509407i	−0.967019	−	0.254704i	$-0.918022\pi$
$89$		−	4.80574i		−	0.509407i	0.967019	−	0.254704i	$-0.0819779\pi$
$90$		0			0
$91$		−	16.4292i		−	1.72225i
$92$	−0.257569	−	1.98335i	−0.0268534	−	0.206778i
$93$		0			0
$94$	2.80487	+	2.46417i	0.289301	+	0.254160i
$95$	10.6104			1.08860
$96$		0			0
$97$	12.8144			1.30111			0.650554	−	0.759460i	$-0.274537\pi$
$97$	12.8144			1.30111			0.650554	+	0.759460i	$0.274537\pi$
$98$	−4.90549	−	4.30963i	−0.495529	−	0.435338i
$99$		0			0
$100$	0.899045	+	6.92287i	0.0899045	+	0.692287i
$101$		−	12.7990i		−	1.27354i	−0.771052	−	0.636772i	$-0.780269\pi$
$101$		−	12.7990i		−	1.27354i	0.771052	−	0.636772i	$-0.219731\pi$
$102$		0			0
$103$			6.07708i			0.598793i	0.954129	+	0.299396i	$0.0967853\pi$
$103$			6.07708i			0.598793i	−0.954129	+	0.299396i	$0.903215\pi$
$104$	7.60426	−	11.3159i	0.745659	−	1.10962i
$105$		0			0
$106$	−12.6717	+	14.4237i	−1.23079	+	1.40096i
$107$	15.8689			1.53410			0.767050	−	0.641587i	$-0.221724\pi$
$107$	15.8689			1.53410			0.767050	+	0.641587i	$0.221724\pi$
$108$		0			0
$109$	−14.6944			−1.40747			−0.703733	−	0.710465i	$-0.748485\pi$
$109$	−14.6944			−1.40747			−0.703733	+	0.710465i	$0.748485\pi$
$110$	−2.54434	+	2.89613i	−0.242594	+	0.276136i
$111$		0			0
$112$	−3.48235	−	13.1814i	−0.329051	−	1.24552i
$113$			6.82745i			0.642273i	0.947033	+	0.321136i	$0.104065\pi$
$113$			6.82745i			0.642273i	−0.947033	+	0.321136i	$0.895935\pi$
$114$		0			0
$115$		−	1.22862i		−	0.114569i
$116$	−19.2066	+	2.49429i	−1.78329	+	0.231589i
$117$		0			0
$118$	−0.823096	−	0.723116i	−0.0757721	−	0.0665682i
$119$	−3.44540			−0.315840
$120$		0			0
$121$	−6.07741			−0.552492
$122$	−10.1610	−	8.92679i	−0.919937	−	0.808194i
$123$		0			0
$124$	6.69624	−	0.869614i	0.601340	−	0.0780936i
$125$			10.4316i			0.933028i
$126$		0			0
$127$		−	15.3795i		−	1.36471i	−0.731020	−	0.682356i	$-0.760955\pi$
$127$		−	15.3795i		−	1.36471i	0.731020	−	0.682356i	$-0.239045\pi$
$128$	3.70247	−	10.6907i	0.327255	−	0.944936i
$129$		0			0
$130$	5.52770	−	6.29198i	0.484811	−	0.551843i
$131$	0.0770237			0.00672959			0.00336480	−	0.999994i	$-0.498929\pi$
$131$	0.0770237			0.00672959			0.00336480	+	0.999994i	$0.498929\pi$
$132$		0			0
$133$	29.4351			2.55234
$134$	8.20036	−	9.33417i	0.708403	−	0.806350i
$135$		0			0
$136$	−2.37309	−	1.59471i	−0.203491	−	0.136745i
$137$			3.89315i			0.332615i	0.986074	+	0.166307i	$0.0531844\pi$
$137$			3.89315i			0.332615i	−0.986074	+	0.166307i	$0.946816\pi$
$138$		0			0
$139$			10.0090i			0.848949i	0.905440	+	0.424475i	$0.139541\pi$
$139$			10.0090i			0.848949i	−0.905440	+	0.424475i	$0.860459\pi$
$140$	−1.07860	−	8.30548i	−0.0911583	−	0.701941i
$141$		0			0
$142$	16.6426	+	14.6211i	1.39662	+	1.22697i
$143$	−10.6945			−0.894323
$144$		0			0
$145$	−11.8979			−0.988063
$146$	10.6745	+	9.37788i	0.883428	+	0.776119i
$147$		0			0
$148$	1.21854	+	9.38308i	0.100164	+	0.771285i
$149$		−	17.8615i		−	1.46327i	−0.681697	−	0.731635i	$-0.738758\pi$
$149$		−	17.8615i		−	1.46327i	0.681697	−	0.731635i	$-0.261242\pi$
$150$		0			0
$151$		−	10.5463i		−	0.858243i	−0.903247	−	0.429121i	$-0.858823\pi$
$151$		−	10.5463i		−	0.858243i	0.903247	−	0.429121i	$-0.141177\pi$
$152$	20.2740	+	13.6240i	1.64444	+	1.10506i
$153$		0			0
$154$	−7.05846	+	8.03439i	−0.568787	+	0.647430i
$155$	4.14810			0.333183
$156$		0			0
$157$	16.4230			1.31070			0.655348	−	0.755327i	$-0.272522\pi$
$157$	16.4230			1.31070			0.655348	+	0.755327i	$0.272522\pi$
$158$	−7.70843	+	8.77422i	−0.613250	+	0.698040i
$159$		0			0
$160$	3.10129	−	6.21980i	0.245179	−	0.491718i
$161$		−	3.40840i		−	0.268619i
$162$		0			0
$163$		−	2.38240i		−	0.186604i	−0.995638	−	0.0933019i	$-0.970258\pi$
$163$		−	2.38240i		−	0.186604i	0.995638	−	0.0933019i	$-0.0297422\pi$
$164$	−6.96972	+	0.905130i	−0.544244	+	0.0706788i
$165$		0			0
$166$	2.30156	+	2.02199i	0.178636	+	0.156937i
$167$	−0.744061			−0.0575772			−0.0287886	−	0.999586i	$-0.509165\pi$
$167$	−0.744061			−0.0575772			−0.0287886	+	0.999586i	$0.509165\pi$
$168$		0			0
$169$	10.2344			0.787258
$170$	−1.31951	−	1.15923i	−0.101201	−	0.0889087i
$171$		0			0
$172$	−7.67775	+	0.997078i	−0.585423	+	0.0760265i
$173$		−	16.3823i		−	1.24552i	−0.782413	−	0.622760i	$-0.786011\pi$
$173$		−	16.3823i		−	1.24552i	0.782413	−	0.622760i	$-0.213989\pi$
$174$		0			0
$175$			11.8970i			0.899331i
$176$	−8.58038	+	2.26683i	−0.646771	+	0.170869i
$177$		0			0
$178$	4.48562	−	5.10582i	0.336212	−	0.382698i
$179$	5.87150			0.438857			0.219428	−	0.975629i	$-0.429581\pi$
$179$	5.87150			0.438857			0.219428	+	0.975629i	$0.429581\pi$
$180$		0			0
$181$	3.36353			0.250009			0.125005	−	0.992156i	$-0.460105\pi$
$181$	3.36353			0.250009			0.125005	+	0.992156i	$0.460105\pi$
$182$	15.3348	−	17.4551i	1.13669	−	1.29385i
$183$		0			0
$184$	1.57758	−	2.34760i	0.116301	−	0.173068i
$185$			5.81250i			0.427344i
$186$		0			0
$187$			2.24278i			0.164008i
$188$	0.679988	+	5.23608i	0.0495932	+	0.381880i
$189$		0			0
$190$	11.2729	+	9.90361i	0.817823	+	0.718483i
$191$	−3.15439			−0.228244			−0.114122	−	0.993467i	$-0.536405\pi$
$191$	−3.15439			−0.228244			−0.114122	+	0.993467i	$0.536405\pi$
$192$		0			0
$193$	2.64746			0.190568			0.0952840	−	0.995450i	$-0.469624\pi$
$193$	2.64746			0.190568			0.0952840	+	0.995450i	$0.469624\pi$
$194$	13.6146	+	11.9608i	0.977470	+	0.858738i
$195$		0			0
$196$	−1.18924	−	9.15746i	−0.0849459	−	0.654104i
$197$			2.78253i			0.198247i	0.995075	+	0.0991237i	$0.0316039\pi$
$197$			2.78253i			0.198247i	−0.995075	+	0.0991237i	$0.968396\pi$
$198$		0			0
$199$			13.8637i			0.982770i	0.870942	+	0.491385i	$0.163509\pi$
$199$			13.8637i			0.982770i	−0.870942	+	0.491385i	$0.836491\pi$
$200$	−5.50655	+	8.19431i	−0.389372	+	0.579426i
$201$		0			0
$202$	11.9464	−	13.5982i	0.840546	−	0.956763i
$203$	−33.0068			−2.31662
$204$		0			0
$205$	−4.31751			−0.301548
$206$	−5.67229	+	6.45655i	−0.395207	+	0.449849i
$207$		0			0
$208$	18.6413	−	4.92479i	1.29254	−	0.341472i
$209$		−	19.1607i		−	1.32537i
$210$		0			0
$211$		−	7.83831i		−	0.539611i	−0.962915	−	0.269806i	$-0.913041\pi$
$211$		−	7.83831i		−	0.539611i	0.962915	−	0.269806i	$-0.0869595\pi$
$212$	−26.9259	+	3.49676i	−1.84928	+	0.240159i
$213$		0			0
$214$	16.8597	+	14.8118i	1.15251	+	1.01252i
$215$	−4.75611			−0.324364
$216$		0			0
$217$	11.5076			0.781184
$218$	−15.6119	−	13.7156i	−1.05737	−	0.928935i
$219$		0			0
$220$	−5.40644	+	0.702113i	−0.364502	+	0.0473364i
$221$		−	4.87254i		−	0.327762i
$222$		0			0
$223$		−	4.17477i		−	0.279563i	−0.990182	−	0.139782i	$-0.955360\pi$
$223$		−	4.17477i		−	0.279563i	0.990182	−	0.139782i	$-0.0446401\pi$
$224$	8.60354	−	17.2548i	0.574848	−	1.15289i
$225$		0			0
$226$	−6.37267	+	7.25378i	−0.423904	+	0.482514i
$227$	−6.55743			−0.435232			−0.217616	−	0.976034i	$-0.569828\pi$
$227$	−6.55743			−0.435232			−0.217616	+	0.976034i	$0.569828\pi$
$228$		0			0
$229$	1.31455			0.0868676			0.0434338	−	0.999056i	$-0.486170\pi$
$229$	1.31455			0.0868676			0.0434338	+	0.999056i	$0.486170\pi$
$230$	1.14678	−	1.30533i	0.0756162	−	0.0860712i
$231$		0			0
$232$	−22.7341	−	15.2772i	−1.49256	−	1.00300i
$233$			17.4205i			1.14125i	0.821210	+	0.570627i	$0.193300\pi$
$233$			17.4205i			1.14125i	−0.821210	+	0.570627i	$0.806700\pi$
$234$		0			0
$235$			3.24357i			0.211587i
$236$	−0.199544	−	1.53654i	−0.0129892	−	0.100020i
$237$		0			0
$238$	−3.66054	−	3.21590i	−0.237278	−	0.208456i
$239$	−26.1161			−1.68931			−0.844655	−	0.535312i	$-0.820194\pi$
$239$	−26.1161			−1.68931			−0.844655	+	0.535312i	$0.820194\pi$
$240$		0			0
$241$	8.12251			0.523217			0.261608	−	0.965174i	$-0.415747\pi$
$241$	8.12251			0.523217			0.261608	+	0.965174i	$0.415747\pi$
$242$	−6.45690	−	5.67259i	−0.415065	−	0.364648i
$243$		0			0
$244$	−2.46335	−	18.9684i	−0.157700	−	1.21433i
$245$		−	5.67274i		−	0.362418i
$246$		0			0
$247$			41.6275i			2.64869i
$248$	7.92606	+	5.32629i	0.503306	+	0.338220i
$249$		0			0
$250$	−9.73671	+	11.0829i	−0.615804	+	0.700947i
$251$	−9.09053			−0.573789			−0.286895	−	0.957962i	$-0.592623\pi$
$251$	−9.09053			−0.573789			−0.286895	+	0.957962i	$0.592623\pi$
$252$		0			0
$253$	−2.21869			−0.139488
$254$	14.3551	−	16.3399i	0.900718	−	1.02525i
$255$		0			0
$256$	13.9123	−	7.90245i	0.869517	−	0.493903i
$257$			10.6947i			0.667115i	0.942730	+	0.333557i	$0.108249\pi$
$257$			10.6947i			0.667115i	−0.942730	+	0.333557i	$0.891751\pi$
$258$		0			0
$259$			16.1249i			1.00195i
$260$	11.7457	−	1.52537i	0.728439	−	0.0945994i
$261$		0			0
$262$	0.0818333	+	0.0718931i	0.00505568	+	0.00444157i
$263$	8.52116			0.525437			0.262719	−	0.964872i	$-0.415381\pi$
$263$	8.52116			0.525437			0.262719	+	0.964872i	$0.415381\pi$
$264$		0			0
$265$	−16.6797			−1.02463
$266$	31.2731	+	27.4744i	1.91747	+	1.68456i
$267$		0			0
$268$	17.4248	−	2.26289i	1.06439	−	0.138228i
$269$			6.47155i			0.394577i	0.980345	+	0.197289i	$0.0632136\pi$
$269$			6.47155i			0.394577i	−0.980345	+	0.197289i	$0.936786\pi$
$270$		0			0
$271$		−	8.63524i		−	0.524553i	−0.964993	−	0.262277i	$-0.915527\pi$
$271$		−	8.63524i		−	0.524553i	0.964993	−	0.262277i	$-0.0844733\pi$
$272$	−1.03279	−	3.90930i	−0.0626220	−	0.237036i
$273$		0			0
$274$	−3.63383	+	4.13625i	−0.219528	+	0.249880i
$275$	7.74435			0.467002
$276$		0			0
$277$	9.70835			0.583318			0.291659	−	0.956522i	$-0.405793\pi$
$277$	9.70835			0.583318			0.291659	+	0.956522i	$0.405793\pi$
$278$	−9.34226	+	10.6340i	−0.560312	+	0.637782i
$279$		0			0
$280$	6.60630	−	9.83085i	0.394802	−	0.587506i
$281$		−	0.885037i		−	0.0527969i	−0.999652	−	0.0263984i	$-0.991596\pi$
$281$		−	0.885037i		−	0.0527969i	0.999652	−	0.0263984i	$-0.00840386\pi$
$282$		0			0
$283$		−	8.95308i		−	0.532205i	−0.963945	−	0.266103i	$-0.914264\pi$
$283$		−	8.95308i		−	0.532205i	0.963945	−	0.266103i	$-0.0857360\pi$
$284$	4.03469	+	31.0681i	0.239415	+	1.84355i
$285$		0			0
$286$	−11.3623	−	9.98217i	−0.671869	−	0.590258i
$287$	−11.9775			−0.707012
$288$		0			0
$289$	15.9782			0.939892
$290$	−12.6408	−	11.1053i	−0.742293	−	0.652127i
$291$		0			0
$292$	2.58783	+	19.9269i	0.151441	+	1.16614i
$293$			6.85130i			0.400257i	0.979770	+	0.200129i	$0.0641360\pi$
$293$			6.85130i			0.400257i	−0.979770	+	0.200129i	$0.935864\pi$
$294$		0			0
$295$		−	0.951834i		−	0.0554179i
$296$	−7.46344	+	11.1064i	−0.433803	+	0.645544i
$297$		0			0
$298$	16.6717	−	18.9768i	0.965767	−	1.09930i
$299$	4.82020			0.278760
$300$		0			0
$301$	−13.1943			−0.760506
$302$	9.84377	−	11.2048i	0.566445	−	0.644764i
$303$		0			0
$304$	8.82341	+	33.3983i	0.506057	+	1.91552i
$305$		−	11.7503i		−	0.672820i
$306$		0			0
$307$		−	23.3952i		−	1.33523i	−0.744505	−	0.667617i	$-0.767314\pi$
$307$		−	23.3952i		−	1.33523i	0.744505	−	0.667617i	$-0.232686\pi$
$308$	−14.9984	+	1.94778i	−0.854615	+	0.110985i
$309$		0			0
$310$	4.40712	+	3.87179i	0.250307	+	0.219903i
$311$	28.3202			1.60589			0.802945	−	0.596053i	$-0.203265\pi$
$311$	28.3202			1.60589			0.802945	+	0.596053i	$0.203265\pi$
$312$		0			0
$313$	−15.0245			−0.849234			−0.424617	−	0.905373i	$-0.639591\pi$
$313$	−15.0245			−0.849234			−0.424617	+	0.905373i	$0.639591\pi$
$314$	17.4485	+	15.3290i	0.984674	+	0.865067i
$315$		0			0
$316$	−16.3795	+	2.12714i	−0.921421	+	0.119661i
$317$		−	23.9137i		−	1.34313i	−0.740947	−	0.671564i	$-0.765623\pi$
$317$		−	23.9137i		−	1.34313i	0.740947	−	0.671564i	$-0.234377\pi$
$318$		0			0
$319$			21.4857i			1.20297i
$320$	9.10044	−	3.71346i	0.508730	−	0.207589i
$321$		0			0
$322$	3.18136	−	3.62123i	0.177290	−	0.201803i
$323$	8.72980			0.485739
$324$		0			0
$325$	−16.8249			−0.933279
$326$	2.22370	−	2.53116i	0.123160	−	0.140188i
$327$		0			0
$328$	−8.24977	−	5.54382i	−0.455517	−	0.306106i
$329$			8.99825i			0.496090i
$330$		0			0
$331$		−	33.2140i		−	1.82561i	−0.408398	−	0.912804i	$-0.633913\pi$
$331$		−	33.2140i		−	1.82561i	0.408398	−	0.912804i	$-0.366087\pi$
$332$	0.557969	+	4.29650i	0.0306225	+	0.235801i
$333$		0			0
$334$	−0.790522	−	0.694498i	−0.0432554	−	0.0380013i
$335$	10.7941			0.589745
$336$		0			0
$337$	−15.3745			−0.837503			−0.418752	−	0.908101i	$-0.637532\pi$
$337$	−15.3745			−0.837503			−0.418752	+	0.908101i	$0.637532\pi$
$338$	10.8734	+	9.55264i	0.591436	+	0.519595i
$339$		0			0
$340$	−0.319889	−	2.46323i	−0.0173484	−	0.133587i
$341$		−	7.49083i		−	0.405651i
$342$		0			0
$343$			8.12160i			0.438525i
$344$	−9.08783	−	6.10699i	−0.489983	−	0.329267i
$345$		0			0
$346$	15.2910	−	17.4052i	0.822051	−	0.935710i
$347$	5.28524			0.283726			0.141863	−	0.989886i	$-0.454691\pi$
$347$	5.28524			0.283726			0.141863	+	0.989886i	$0.454691\pi$
$348$		0			0
$349$	−33.2573			−1.78022			−0.890111	−	0.455743i	$-0.849373\pi$
$349$	−33.2573			−1.78022			−0.890111	+	0.455743i	$0.849373\pi$
$350$	−11.1046	+	12.6399i	−0.593563	+	0.675631i
$351$		0			0
$352$	−11.2320	−	5.60046i	−0.598668	−	0.298506i
$353$		−	19.5365i		−	1.03982i	−0.854220	−	0.519912i	$-0.825965\pi$
$353$		−	19.5365i		−	1.03982i	0.854220	−	0.519912i	$-0.174035\pi$
$354$		0			0
$355$			19.2457i			1.02145i
$356$	9.53144	−	1.23781i	0.505165	−	0.0656038i
$357$		0			0
$358$	6.23814	+	5.48040i	0.329696	+	0.289648i
$359$	11.6023			0.612347			0.306173	−	0.951976i	$-0.400951\pi$
$359$	11.6023			0.612347			0.306173	+	0.951976i	$0.400951\pi$
$360$		0			0
$361$	−55.5812			−2.92533
$362$	3.57356	+	3.13948i	0.187822	+	0.165007i
$363$		0			0
$364$	32.5847	−	4.23165i	1.70790	−	0.221799i
$365$			12.3441i			0.646118i
$366$		0			0
$367$			23.1472i			1.20827i	0.796880	+	0.604137i	$0.206482\pi$
$367$			23.1472i			1.20827i	−0.796880	+	0.604137i	$0.793518\pi$
$368$	3.86732	−	1.02170i	0.201598	−	0.0532596i
$369$		0			0
$370$	−5.42533	+	6.17545i	−0.282049	+	0.321047i
$371$	−46.2725			−2.40235
$372$		0			0
$373$	−35.0879			−1.81678			−0.908391	−	0.418122i	$-0.862688\pi$
$373$	−35.0879			−1.81678			−0.908391	+	0.418122i	$0.862688\pi$
$374$	−2.09339	+	2.38283i	−0.108246	+	0.123213i
$375$		0			0
$376$	−4.16485	+	6.19773i	−0.214786	+	0.319623i
$377$		−	46.6786i		−	2.40407i
$378$		0			0
$379$			5.76564i			0.296161i	0.988975	+	0.148081i	$0.0473095\pi$
$379$			5.76564i			0.296161i	−0.988975	+	0.148081i	$0.952690\pi$
$380$	2.73290	+	21.0440i	0.140195	+	1.07954i
$381$		0			0
$382$	−3.35136	−	2.94427i	−0.171470	−	0.150642i
$383$	16.1602			0.825748			0.412874	−	0.910788i	$-0.364525\pi$
$383$	16.1602			0.825748			0.412874	+	0.910788i	$0.364525\pi$
$384$		0			0
$385$	−9.29102			−0.473514
$386$	2.81277	+	2.47111i	0.143166	+	0.125776i
$387$		0			0
$388$	3.30060	+	25.4154i	0.167562	+	1.29027i
$389$		−	14.3949i		−	0.729852i	−0.931037	−	0.364926i	$-0.881094\pi$
$389$		−	14.3949i		−	0.729852i	0.931037	−	0.364926i	$-0.118906\pi$
$390$		0			0
$391$		−	1.01086i		−	0.0511212i
$392$	7.28397	−	10.8393i	0.367896	−	0.547468i
$393$		0			0
$394$	−2.59719	+	2.95628i	−0.130844	+	0.148935i
$395$	−10.1466			−0.510529
$396$		0			0
$397$	20.8041			1.04413			0.522063	−	0.852907i	$-0.325162\pi$
$397$	20.8041			1.04413			0.522063	+	0.852907i	$0.325162\pi$
$398$	−12.9402	+	14.7294i	−0.648634	+	0.738316i
$399$		0			0
$400$	−13.4989	+	3.56623i	−0.674944	+	0.178312i
$401$			5.38087i			0.268708i	0.990933	+	0.134354i	$0.0428959\pi$
$401$			5.38087i			0.268708i	−0.990933	+	0.134354i	$0.957104\pi$
$402$		0			0
$403$			16.2741i			0.810673i
$404$	25.3847	−	3.29661i	1.26294	−	0.164013i
$405$		0			0
$406$	−35.0678	−	30.8082i	−1.74039	−	1.52898i
$407$	10.4965			0.520292
$408$		0			0
$409$	18.0534			0.892681			0.446341	−	0.894863i	$-0.352727\pi$
$409$	18.0534			0.892681			0.446341	+	0.894863i	$0.352727\pi$
$410$	−4.58711	−	4.02992i	−0.226541	−	0.199023i
$411$		0			0
$412$	−12.0530	+	1.56527i	−0.593807	+	0.0771153i
$413$		−	2.64056i		−	0.129933i
$414$		0			0
$415$			2.66154i			0.130650i
$416$	24.4020	+	12.1672i	1.19641	+	0.596548i
$417$		0			0
$418$	17.8844	−	20.3572i	0.874755	−	0.995701i
$419$	−25.6298			−1.25210			−0.626048	−	0.779784i	$-0.715329\pi$
$419$	−25.6298			−1.25210			−0.626048	+	0.779784i	$0.715329\pi$
$420$		0			0
$421$	−5.40133			−0.263245			−0.131622	−	0.991300i	$-0.542019\pi$
$421$	−5.40133			−0.263245			−0.131622	+	0.991300i	$0.542019\pi$
$422$	7.31619	−	8.32775i	0.356147	−	0.405389i
$423$		0			0
$424$	−31.8711	−	21.4173i	−1.54780	−	1.04011i
$425$			3.52840i			0.171152i
$426$		0			0
$427$		−	32.5974i		−	1.57750i
$428$	4.08733	+	31.4734i	0.197568	+	1.52133i
$429$		0			0
$430$	−5.05309	−	4.43930i	−0.243682	−	0.214082i
$431$	−9.54944			−0.459980			−0.229990	−	0.973193i	$-0.573869\pi$
$431$	−9.54944			−0.459980			−0.229990	+	0.973193i	$0.573869\pi$
$432$		0			0
$433$	14.8130			0.711868			0.355934	−	0.934511i	$-0.384163\pi$
$433$	14.8130			0.711868			0.355934	+	0.934511i	$0.384163\pi$
$434$	12.2261	+	10.7410i	0.586873	+	0.515586i
$435$		0			0
$436$	−3.78481	−	29.1440i	−0.181260	−	1.39574i
$437$			8.63604i			0.413118i
$438$		0			0
$439$		−	34.3506i		−	1.63946i	−0.572748	−	0.819731i	$-0.694123\pi$
$439$		−	34.3506i		−	1.63946i	0.572748	−	0.819731i	$-0.305877\pi$
$440$	−6.39938	−	4.30036i	−0.305078	−	0.205012i
$441$		0			0
$442$	4.54797	−	5.17679i	0.216325	−	0.246235i
$443$	−23.4751			−1.11533			−0.557667	−	0.830065i	$-0.688303\pi$
$443$	−23.4751			−1.11533			−0.557667	+	0.830065i	$0.688303\pi$
$444$		0			0
$445$	5.90441			0.279896
$446$	3.89668	−	4.43545i	0.184513	−	0.210025i
$447$		0			0
$448$	25.2462	−	10.3018i	1.19277	−	0.486715i
$449$			2.98969i			0.141092i	0.997509	+	0.0705460i	$0.0224742\pi$
$449$			2.98969i			0.141092i	−0.997509	+	0.0705460i	$0.977526\pi$
$450$		0			0
$451$			7.79676i			0.367135i
$452$	−13.5412	+	1.75854i	−0.636924	+	0.0827148i
$453$		0			0
$454$	−6.96689	−	6.12064i	−0.326973	−	0.287256i
$455$	20.1851			0.946294
$456$		0			0
$457$	−12.5595			−0.587507			−0.293753	−	0.955881i	$-0.594904\pi$
$457$	−12.5595			−0.587507			−0.293753	+	0.955881i	$0.594904\pi$
$458$	1.39663	+	1.22698i	0.0652602	+	0.0573331i
$459$		0			0
$460$	2.43677	−	0.316453i	0.113615	−	0.0147547i
$461$		−	11.6749i		−	0.543755i	−0.962332	−	0.271878i	$-0.912355\pi$
$461$		−	11.6749i		−	0.543755i	0.962332	−	0.271878i	$-0.0876446\pi$
$462$		0			0
$463$		−	18.4628i		−	0.858038i	−0.903296	−	0.429019i	$-0.858859\pi$
$463$		−	18.4628i		−	0.858038i	0.903296	−	0.429019i	$-0.141141\pi$
$464$	−9.89406	−	37.4509i	−0.459320	−	1.73861i
$465$		0			0
$466$	−16.2601	+	18.5083i	−0.753234	+	0.857379i
$467$	−27.2829			−1.26250			−0.631251	−	0.775579i	$-0.717458\pi$
$467$	−27.2829			−1.26250			−0.631251	+	0.775579i	$0.717458\pi$
$468$		0			0
$469$	29.9447			1.38272
$470$	−3.02752	+	3.44611i	−0.139649	+	0.158957i
$471$		0			0
$472$	1.22218	−	1.81874i	0.0562556	−	0.0837141i
$473$			8.58880i			0.394914i
$474$		0			0
$475$		−	30.1441i		−	1.38311i
$476$	−0.887429	−	6.83342i	−0.0406752	−	0.313209i
$477$		0			0
$478$	−27.7468	−	24.3765i	−1.26911	−	1.11495i
$479$	−13.4044			−0.612461			−0.306230	−	0.951957i	$-0.599068\pi$
$479$	−13.4044			−0.612461			−0.306230	+	0.951957i	$0.599068\pi$
$480$		0			0
$481$	−22.8041			−1.03978
$482$	8.62970	+	7.58146i	0.393072	+	0.345326i
$483$		0			0
$484$	−1.56535	−	12.0536i	−0.0711524	−	0.547891i
$485$			15.7440i			0.714898i
$486$		0			0
$487$		−	3.65427i		−	0.165591i	−0.996567	−	0.0827953i	$-0.973615\pi$
$487$		−	3.65427i		−	0.165591i	0.996567	−	0.0827953i	$-0.0263848\pi$
$488$	15.0877	−	22.4521i	0.682990	−	1.01636i
$489$		0			0
$490$	5.29488	−	6.02696i	0.239198	−	0.272270i
$491$	39.3521			1.77593			0.887967	−	0.459908i	$-0.152118\pi$
$491$	39.3521			1.77593			0.887967	+	0.459908i	$0.152118\pi$
$492$		0			0
$493$	−9.78909			−0.440878
$494$	−38.8546	+	44.2268i	−1.74815	+	1.98986i
$495$		0			0
$496$	3.44949	+	13.0570i	0.154887	+	0.586276i
$497$			53.3909i			2.39491i
$498$		0			0
$499$			20.9177i			0.936406i	0.883621	+	0.468203i	$0.155098\pi$
$499$			20.9177i			0.936406i	−0.883621	+	0.468203i	$0.844902\pi$
$500$	−20.6894	+	2.68685i	−0.925258	+	0.120160i
$501$		0			0
$502$	−9.65817	−	8.48500i	−0.431065	−	0.378704i
$503$	−31.2085			−1.39152			−0.695760	−	0.718275i	$-0.744932\pi$
$503$	−31.2085			−1.39152			−0.695760	+	0.718275i	$0.744932\pi$
$504$		0			0
$505$	15.7250			0.699753
$506$	−2.35723	−	2.07090i	−0.104792	−	0.0920629i
$507$		0			0
$508$	30.5029	−	3.96129i	1.35335	−	0.175754i
$509$		−	8.02365i		−	0.355642i	−0.984063	−	0.177821i	$-0.943095\pi$
$509$		−	8.02365i		−	0.355642i	0.984063	−	0.177821i	$-0.0569048\pi$
$510$		0			0
$511$			34.2446i			1.51489i
$512$	22.1571	+	4.58967i	0.979213	+	0.202837i
$513$		0			0
$514$	−9.98228	+	11.3625i	−0.440300	+	0.501177i
$515$	−7.46640			−0.329009
$516$		0			0
$517$	5.85740			0.257608
$518$	−15.0508	+	17.1318i	−0.661295	+	0.752728i
$519$		0			0
$520$	13.9029	+	9.34271i	0.609684	+	0.409705i
$521$			28.6574i			1.25550i	0.778413	+	0.627752i	$0.216025\pi$
$521$			28.6574i			1.25550i	−0.778413	+	0.627752i	$0.783975\pi$
$522$		0			0
$523$			11.5757i			0.506169i	0.967444	+	0.253084i	$0.0814450\pi$
$523$			11.5757i			0.506169i	−0.967444	+	0.253084i	$0.918555\pi$
$524$	0.0198389	+	0.152765i	0.000866668	+	0.00667355i
$525$		0			0
$526$	9.05325	+	7.95356i	0.394740	+	0.346792i
$527$	3.41289			0.148668
$528$		0			0
$529$	1.00000			0.0434783
$530$	−17.7212	−	15.5687i	−0.769762	−	0.676260i
$531$		0			0
$532$	7.58156	+	58.3799i	0.328702	+	2.53109i
$533$		−	16.9388i		−	0.733701i
$534$		0			0
$535$			19.4967i			0.842917i
$536$	20.6250	+	13.8600i	0.890866	+	0.598659i
$537$		0			0
$538$	−6.04047	+	6.87565i	−0.260423	+	0.296430i
$539$	−10.2441			−0.441245
$540$		0			0
$541$	30.4645			1.30977			0.654886	−	0.755728i	$-0.272717\pi$
$541$	30.4645			1.30977			0.654886	+	0.755728i	$0.272717\pi$
$542$	8.06004	−	9.17445i	0.346208	−	0.394076i
$543$		0			0
$544$	2.55162	−	5.11740i	0.109400	−	0.219407i
$545$		−	18.0537i		−	0.773337i
$546$		0			0
$547$		−	19.8944i		−	0.850623i	−0.905047	−	0.425312i	$-0.860164\pi$
$547$		−	19.8944i		−	0.850623i	0.905047	−	0.425312i	$-0.139836\pi$
$548$	−7.72147	+	1.00276i	−0.329845	+	0.0428356i
$549$		0			0
$550$	8.22793	+	7.22849i	0.350840	+	0.308224i
$551$	83.6310			3.56280
$552$		0			0
$553$	−28.1484			−1.19699
$554$	10.3146	+	9.06167i	0.438224	+	0.384993i
$555$		0			0
$556$	−19.8512	+	2.57800i	−0.841880	+	0.109332i
$557$			17.2707i			0.731781i	0.930658	+	0.365891i	$0.119236\pi$
$557$			17.2707i			0.731781i	−0.930658	+	0.365891i	$0.880764\pi$
$558$		0			0
$559$		−	18.6595i		−	0.789215i
$560$	16.1948	−	4.27847i	0.684356	−	0.180798i
$561$		0			0
$562$	0.826084	−	0.940301i	0.0348462	−	0.0396642i
$563$	−40.9920			−1.72761			−0.863803	−	0.503829i	$-0.831924\pi$
$563$	−40.9920			−1.72761			−0.863803	+	0.503829i	$0.831924\pi$
$564$		0			0
$565$	−8.38832			−0.352899
$566$	8.35671	−	9.51213i	0.351259	−	0.399825i
$567$		0			0
$568$	−24.7120	+	36.7741i	−1.03689	+	1.54301i
$569$		−	13.9433i		−	0.584534i	−0.956337	−	0.292267i	$-0.905590\pi$
$569$		−	13.9433i		−	0.584534i	0.956337	−	0.292267i	$-0.0944097\pi$
$570$		0			0
$571$			1.53194i			0.0641097i	0.999486	+	0.0320548i	$0.0102051\pi$
$571$			1.53194i			0.0641097i	−0.999486	+	0.0320548i	$0.989795\pi$
$572$	−2.75458	−	21.2110i	−0.115175	−	0.886875i
$573$		0			0
$574$	−12.7254	−	11.1797i	−0.531150	−	0.466632i
$575$	−3.49050			−0.145564
$576$		0			0
$577$	20.5495			0.855487			0.427744	−	0.903900i	$-0.359309\pi$
$577$	20.5495			0.855487			0.427744	+	0.903900i	$0.359309\pi$
$578$	16.9759	+	14.9139i	0.706104	+	0.620334i
$579$		0			0
$580$	−3.06452	−	23.5976i	−0.127247	−	0.979835i
$581$			7.38358i			0.306322i
$582$		0			0
$583$			30.1210i			1.24749i
$584$	−15.8502	+	23.5867i	−0.655884	+	0.976023i
$585$		0			0
$586$	−6.39493	+	7.27912i	−0.264172	+	0.300698i
$587$	−41.4352			−1.71021			−0.855107	−	0.518452i	$-0.826509\pi$
$587$	−41.4352			−1.71021			−0.855107	+	0.518452i	$0.826509\pi$
$588$		0			0
$589$	−29.1573			−1.20141
$590$	0.888431	−	1.01127i	0.0365761	−	0.0416333i
$591$		0			0
$592$	−18.2960	+	4.83358i	−0.751962	+	0.198659i
$593$		−	22.2632i		−	0.914239i	−0.889405	−	0.457120i	$-0.848881\pi$
$593$		−	22.2632i		−	0.914239i	0.889405	−	0.457120i	$-0.151119\pi$
$594$		0			0
$595$		−	4.23308i		−	0.173539i
$596$	35.4255	−	4.60056i	1.45108	−	0.188446i
$597$		0			0
$598$	5.12119	+	4.49913i	0.209421	+	0.183983i
$599$	−30.5243			−1.24719			−0.623594	−	0.781749i	$-0.714328\pi$
$599$	−30.5243			−1.24719			−0.623594	+	0.781749i	$0.714328\pi$
$600$		0			0
$601$	−34.5655			−1.40996			−0.704979	−	0.709228i	$-0.749044\pi$
$601$	−34.5655			−1.40996			−0.704979	+	0.709228i	$0.749044\pi$
$602$	−14.0182	−	12.3154i	−0.571338	−	0.501939i
$603$		0			0
$604$	20.9169	−	2.71639i	0.851096	−	0.110528i
$605$		−	7.46680i		−	0.303569i
$606$		0			0
$607$			43.5251i			1.76663i	0.468782	+	0.883314i	$0.344693\pi$
$607$			43.5251i			1.76663i	−0.468782	+	0.883314i	$0.655307\pi$
$608$	−21.7992	+	43.7195i	−0.884076	+	1.77306i
$609$		0			0
$610$	10.9676	−	12.4840i	0.444065	−	0.505463i
$611$	−12.7254			−0.514817
$612$		0			0
$613$	38.9189			1.57192			0.785959	−	0.618279i	$-0.212170\pi$
$613$	38.9189			1.57192			0.785959	+	0.618279i	$0.212170\pi$
$614$	21.8368	−	24.8561i	0.881263	−	1.00311i
$615$		0			0
$616$	−17.7530	−	11.9300i	−0.715289	−	0.480672i
$617$			28.4644i			1.14593i	0.819578	+	0.572967i	$0.194208\pi$
$617$			28.4644i			1.14593i	−0.819578	+	0.572967i	$0.805792\pi$
$618$		0			0
$619$		−	41.9668i		−	1.68679i	−0.537297	−	0.843393i	$-0.680554\pi$
$619$		−	41.9668i		−	1.68679i	0.537297	−	0.843393i	$-0.319446\pi$
$620$	1.06842	+	8.22711i	0.0429088	+	0.330409i
$621$		0			0
$622$	30.0886	+	26.4337i	1.20644	+	1.05990i
$623$	16.3799			0.656246
$624$		0			0
$625$	4.63613			0.185445
$626$	−15.9627	−	14.0237i	−0.637996	−	0.560500i
$627$		0			0
$628$	4.23005	+	32.5724i	0.168797	+	1.29978i
$629$			4.78230i			0.190683i
$630$		0			0
$631$			36.7177i			1.46171i	0.682534	+	0.730854i	$0.260878\pi$
$631$			36.7177i			1.46171i	−0.682534	+	0.730854i	$0.739122\pi$
$632$	−19.3878	−	13.0285i	−0.771204	−	0.518246i
$633$		0			0
$634$	22.3208	−	25.4069i	0.886472	−	1.00904i
$635$	18.8955			0.749846
$636$		0			0
$637$	22.2557			0.881805
$638$	−20.0545	+	22.8273i	−0.793966	+	0.903742i
$639$		0			0
$640$	13.1348	+	4.54891i	0.519199	+	0.179811i
$641$			12.3649i			0.488385i	0.969727	+	0.244193i	$0.0785229\pi$
$641$			12.3649i			0.488385i	−0.969727	+	0.244193i	$0.921477\pi$
$642$		0			0
$643$			23.0833i			0.910316i	0.890411	+	0.455158i	$0.150417\pi$
$643$			23.0833i			0.910316i	−0.890411	+	0.455158i	$0.849583\pi$
$644$	6.76003	−	0.877898i	0.266383	−	0.0345940i
$645$		0			0
$646$	9.27491	+	8.14830i	0.364917	+	0.320591i
$647$	40.5322			1.59349			0.796743	−	0.604318i	$-0.206554\pi$
$647$	40.5322			1.59349			0.796743	+	0.604318i	$0.206554\pi$
$648$		0			0
$649$	−1.71887			−0.0674714
$650$	−17.8755	−	15.7042i	−0.701136	−	0.615970i
$651$		0			0
$652$	4.72512	−	0.613632i	0.185050	−	0.0240317i
$653$			7.34537i			0.287447i	0.989618	+	0.143723i	$0.0459075\pi$
$653$			7.34537i			0.287447i	−0.989618	+	0.143723i	$0.954092\pi$
$654$		0			0
$655$			0.0946326i			0.00369760i
$656$	−3.59037	−	13.5902i	−0.140180	−	0.530610i
$657$		0			0
$658$	−8.39887	+	9.56013i	−0.327422	+	0.372693i
$659$	50.1737			1.95449			0.977245	−	0.212115i	$-0.0680352\pi$
$659$	50.1737			1.95449			0.977245	+	0.212115i	$0.0680352\pi$
$660$		0			0
$661$	13.0921			0.509225			0.254613	−	0.967043i	$-0.418052\pi$
$661$	13.0921			0.509225			0.254613	+	0.967043i	$0.418052\pi$
$662$	31.0016	−	35.2880i	1.20491	−	1.37151i
$663$		0			0
$664$	−3.41750	+	5.08559i	−0.132625	+	0.197359i
$665$			36.1644i			1.40239i
$666$		0			0
$667$		−	9.68395i		−	0.374964i
$668$	−0.191647	−	1.47573i	−0.00741505	−	0.0570977i
$669$		0			0
$670$	11.4681	+	10.0751i	0.443052	+	0.389235i
$671$	−21.2192			−0.819159
$672$		0			0
$673$	23.8992			0.921247			0.460624	−	0.887596i	$-0.347626\pi$
$673$	23.8992			0.921247			0.460624	+	0.887596i	$0.347626\pi$
$674$	−16.3345	−	14.3504i	−0.629183	−	0.552757i
$675$		0			0
$676$	2.63605	+	20.2983i	0.101387	+	0.780703i
$677$		−	37.7093i		−	1.44929i	−0.689125	−	0.724643i	$-0.742005\pi$
$677$		−	37.7093i		−	1.44929i	0.689125	−	0.724643i	$-0.257995\pi$
$678$		0			0
$679$			43.6766i			1.67616i
$680$	1.95928	−	2.91562i	0.0751351	−	0.111809i
$681$		0			0
$682$	6.99186	−	7.95858i	0.267732	−	0.304750i
$683$	−32.1564			−1.23043			−0.615216	−	0.788359i	$-0.710931\pi$
$683$	−32.1564			−1.23043			−0.615216	+	0.788359i	$0.710931\pi$
$684$		0			0
$685$	−4.78319			−0.182756
$686$	−7.58061	+	8.62873i	−0.289429	+	0.329447i
$687$		0			0
$688$	−3.95510	−	14.9708i	−0.150787	−	0.570757i
$689$		−	65.4392i		−	2.49304i
$690$		0			0
$691$		−	25.6114i		−	0.974304i	−0.873317	−	0.487152i	$-0.838036\pi$
$691$		−	25.6114i		−	0.974304i	0.873317	−	0.487152i	$-0.161964\pi$
$692$	32.4917	−	4.21956i	1.23515	−	0.160404i
$693$		0			0
$694$	5.61526	+	4.93318i	0.213152	+	0.187261i
$695$	−12.2972			−0.466458
$696$		0			0
$697$	−3.55228			−0.134552
$698$	−35.3340	−	31.0420i	−1.33741	−	1.17496i
$699$		0			0
$700$	−23.5959	+	3.06431i	−0.891841	+	0.115820i
$701$		−	15.2314i		−	0.575283i	−0.957738	−	0.287641i	$-0.907129\pi$
$701$		−	15.2314i		−	0.575283i	0.957738	−	0.287641i	$-0.0928711\pi$
$702$		0			0
$703$		−	40.8566i		−	1.54093i
$704$	−6.70595	−	16.4340i	−0.252740	−	0.619380i
$705$		0			0
$706$	18.2352	−	20.7565i	0.686291	−	0.781179i
$707$	43.6239			1.64065
$708$		0			0
$709$	−0.255381			−0.00959105			−0.00479552	−	0.999989i	$-0.501526\pi$
$709$	−0.255381			−0.00959105			−0.00479552	+	0.999989i	$0.501526\pi$
$710$	−17.9637	+	20.4474i	−0.674166	+	0.767378i
$711$		0			0
$712$	11.2820	+	7.58144i	0.422810	+	0.284127i
$713$			3.37624i			0.126441i
$714$		0			0
$715$		−	13.1395i		−	0.491389i
$716$	1.51232	+	11.6452i	0.0565180	+	0.435202i
$717$		0			0
$718$	12.3268	+	10.8295i	0.460032	+	0.404152i
$719$	25.2308			0.940949			0.470475	−	0.882414i	$-0.344083\pi$
$719$	25.2308			0.940949			0.470475	+	0.882414i	$0.344083\pi$
$720$		0			0
$721$	−20.7131			−0.771397
$722$	−59.0518	−	51.8789i	−2.19768	−	1.93073i
$723$		0			0
$724$	0.866341	+	6.67104i	0.0321973	+	0.247927i
$725$			33.8019i			1.25537i
$726$		0			0
$727$		−	20.9014i		−	0.775191i	−0.921830	−	0.387596i	$-0.873306\pi$
$727$		−	20.9014i		−	0.775191i	0.921830	−	0.387596i	$-0.126694\pi$
$728$	38.5692	+	25.9183i	1.42947	+	0.960598i
$729$		0			0
$730$	−11.5218	+	13.1149i	−0.426442	+	0.485403i
$731$	−3.91314			−0.144733
$732$		0			0
$733$	22.5200			0.831796			0.415898	−	0.909411i	$-0.363467\pi$
$733$	22.5200			0.831796			0.415898	+	0.909411i	$0.363467\pi$
$734$	−21.6054	+	24.5926i	−0.797468	+	0.907729i
$735$		0			0
$736$	5.06244	+	2.52422i	0.186604	+	0.0930439i
$737$		−	19.4925i		−	0.718015i
$738$		0			0
$739$		−	0.366071i		−	0.0134661i	−0.999977	−	0.00673307i	$-0.997857\pi$
$739$		−	0.366071i		−	0.0134661i	0.999977	−	0.00673307i	$-0.00214322\pi$
$740$	−11.5282	+	1.49712i	−0.423785	+	0.0550353i
$741$		0			0
$742$	−49.1619	−	43.1903i	−1.80479	−	1.58556i
$743$	9.67773			0.355042			0.177521	−	0.984117i	$-0.443192\pi$
$743$	9.67773			0.355042			0.177521	+	0.984117i	$0.443192\pi$
$744$		0			0
$745$	21.9449			0.803999
$746$	−37.2789	−	32.7506i	−1.36488	−	1.19909i
$747$		0			0
$748$	−4.44821	+	0.577671i	−0.162643	+	0.0211217i
$749$			54.0874i			1.97631i
$750$		0			0
$751$		−	2.92851i		−	0.106863i	−0.998572	−	0.0534314i	$-0.982984\pi$
$751$		−	2.92851i		−	0.106863i	0.998572	−	0.0534314i	$-0.0170158\pi$
$752$	−10.2098	+	2.69730i	−0.372313	+	0.0983605i
$753$		0			0
$754$	43.5693	−	49.5933i	1.58670	−	1.80608i
$755$	12.9573			0.471565
$756$		0			0
$757$	−6.07432			−0.220775			−0.110387	−	0.993889i	$-0.535209\pi$
$757$	−6.07432			−0.220775			−0.110387	+	0.993889i	$0.535209\pi$
$758$	−5.38159	+	6.12567i	−0.195468	+	0.222494i
$759$		0			0
$760$	−16.7387	+	24.9089i	−0.607177	+	0.903543i
$761$			8.37814i			0.303707i	0.988403	+	0.151854i	$0.0485243\pi$
$761$			8.37814i			0.303707i	−0.988403	+	0.151854i	$0.951476\pi$
$762$		0			0
$763$		−	50.0843i		−	1.81317i
$764$	−0.812473	−	6.25624i	−0.0293942	−	0.226343i
$765$		0			0
$766$	17.1693	+	15.0838i	0.620352	+	0.544999i
$767$	3.73431			0.134838
$768$		0			0
$769$	20.1540			0.726771			0.363385	−	0.931639i	$-0.381621\pi$
$769$	20.1540			0.726771			0.363385	+	0.931639i	$0.381621\pi$
$770$	−9.87118	−	8.67214i	−0.355733	−	0.312522i
$771$		0			0
$772$	0.681903	+	5.25082i	0.0245422	+	0.188981i
$773$		−	33.5388i		−	1.20631i	−0.797626	−	0.603153i	$-0.793911\pi$
$773$		−	33.5388i		−	1.20631i	0.797626	−	0.603153i	$-0.206089\pi$
$774$		0			0
$775$		−	11.7848i		−	0.423321i
$776$	−20.2158	+	30.0832i	−0.725704	+	1.07992i
$777$		0			0
$778$	13.4361	−	15.2938i	0.481706	−	0.548309i
$779$	30.3481			1.08733
$780$		0			0
$781$	34.7547			1.24362
$782$	0.943523	−	1.07398i	0.0337403	−	0.0384054i
$783$		0			0
$784$	17.8561	−	4.71736i	0.637718	−	0.168477i
$785$			20.1775i			0.720167i
$786$		0			0
$787$		−	11.2448i		−	0.400835i	−0.979711	−	0.200417i	$-0.935770\pi$
$787$		−	11.2448i		−	0.400835i	0.979711	−	0.200417i	$-0.0642299\pi$
$788$	−5.51873	+	0.716695i	−0.196596	+	0.0255312i
$789$		0			0
$790$	−10.7802	−	9.47070i	−0.383541	−	0.336952i
$791$	−23.2707			−0.827410
$792$		0			0
$793$	46.0997			1.63705
$794$	22.1031	+	19.4183i	0.784411	+	0.689130i
$795$		0			0
$796$	−27.4965	+	3.57085i	−0.974586	+	0.126566i
$797$		−	13.6921i		−	0.484998i	−0.970152	−	0.242499i	$-0.922033\pi$
$797$		−	13.6921i		−	0.484998i	0.970152	−	0.242499i	$-0.0779671\pi$
$798$		0			0
$799$			2.66869i			0.0944113i
$800$	−17.6705	−	8.81079i	−0.624745	−	0.311508i
$801$		0			0
$802$	−5.02245	+	5.71687i	−0.177349	+	0.201870i
$803$	22.2915			0.786649
$804$		0			0
$805$	4.18761			0.147594
$806$	−15.1901	+	17.2904i	−0.535049	+	0.609027i
$807$		0			0
$808$	30.0469	+	20.1914i	1.05704	+	0.710330i
$809$			5.56299i			0.195584i	0.995207	+	0.0977922i	$0.0311781\pi$
$809$			5.56299i			0.195584i	−0.995207	+	0.0977922i	$0.968822\pi$
$810$		0			0
$811$		−	11.5285i		−	0.404821i	−0.979301	−	0.202410i	$-0.935123\pi$
$811$		−	11.5285i		−	0.404821i	0.979301	−	0.202410i	$-0.0648775\pi$
$812$	−8.50152	−	65.4638i	−0.298345	−	2.29733i
$813$		0			0
$814$	11.1519	+	9.79731i	0.390875	+	0.343396i
$815$	2.92705			0.102530
$816$		0			0
$817$	33.4311			1.16961
$818$	19.1807	+	16.8508i	0.670636	+	0.589175i
$819$		0			0
$820$	−1.11206	−	8.56311i	−0.0388347	−	0.299037i
$821$			47.3041i			1.65092i	0.564458	+	0.825462i	$0.309085\pi$
$821$			47.3041i			1.65092i	−0.564458	+	0.825462i	$0.690915\pi$
$822$		0			0
$823$		−	5.49929i		−	0.191693i	−0.995396	−	0.0958466i	$-0.969444\pi$
$823$		−	5.49929i		−	0.191693i	0.995396	−	0.0958466i	$-0.0305558\pi$
$824$	−14.2666	−	9.58709i	−0.497000	−	0.333982i
$825$		0			0
$826$	2.46467	−	2.80544i	0.0857567	−	0.0976137i
$827$	14.1379			0.491624			0.245812	−	0.969318i	$-0.420945\pi$
$827$	14.1379			0.491624			0.245812	+	0.969318i	$0.420945\pi$
$828$		0			0
$829$	43.8496			1.52296			0.761480	−	0.648189i	$-0.224473\pi$
$829$	43.8496			1.52296			0.761480	+	0.648189i	$0.224473\pi$
$830$	−2.48425	+	2.82773i	−0.0862296	+	0.0981520i
$831$		0			0
$832$	14.5690	+	35.7036i	0.505088	+	1.23780i
$833$		−	4.66731i		−	0.161713i
$834$		0			0
$835$		−	0.914165i		−	0.0316360i
$836$	38.0023	−	4.93521i	1.31434	−	0.170688i
$837$		0			0
$838$	−27.2302	−	23.9226i	−0.940650	−	0.826391i
$839$	17.2099			0.594150			0.297075	−	0.954854i	$-0.403989\pi$
$839$	17.2099			0.594150			0.297075	+	0.954854i	$0.403989\pi$
$840$		0			0
$841$	−64.7789			−2.23375
$842$	−5.73860	−	5.04154i	−0.197765	−	0.173743i
$843$		0			0
$844$	15.5461	−	2.01891i	0.535118	−	0.0694936i
$845$			12.5741i			0.432562i
$846$		0			0
$847$		−	20.7142i		−	0.711749i
$848$	−13.8706	−	52.5028i	−0.476318	−	1.80295i
$849$		0			0
$850$	−3.29337	+	3.74872i	−0.112962	+	0.128580i
$851$	−4.73094			−0.162174
$852$		0			0
$853$	−35.7347			−1.22353			−0.611766	−	0.791039i	$-0.709541\pi$
$853$	−35.7347			−1.22353			−0.611766	+	0.791039i	$0.709541\pi$
$854$	30.4261	−	34.6329i	1.04116	−	1.18511i
$855$		0			0
$856$	−25.0344	+	37.2538i	−0.855658	+	1.27331i
$857$		−	23.3758i		−	0.798502i	−0.916842	−	0.399251i	$-0.869270\pi$
$857$		−	23.3758i		−	0.798502i	0.916842	−	0.399251i	$-0.130730\pi$
$858$		0			0
$859$		−	31.1150i		−	1.06163i	−0.847488	−	0.530815i	$-0.821886\pi$
$859$		−	31.1150i		−	1.06163i	0.847488	−	0.530815i	$-0.178114\pi$
$860$	−1.22503	−	9.43301i	−0.0417731	−	0.321663i
$861$		0			0
$862$	−10.1457	−	8.91335i	−0.345565	−	0.303590i
$863$	36.1125			1.22928			0.614642	−	0.788806i	$-0.289301\pi$
$863$	36.1125			1.22928			0.614642	+	0.788806i	$0.289301\pi$
$864$		0			0
$865$	20.1275			0.684356
$866$	15.7380	+	13.8263i	0.534798	+	0.469837i
$867$		0			0
$868$	2.96399	+	22.8235i	0.100604	+	0.774679i
$869$			18.3232i			0.621570i
$870$		0			0
$871$			42.3483i			1.43492i
$872$	23.1816	−	34.4965i	0.785027	−	1.16820i
$873$		0			0
$874$	−8.06079	+	9.17530i	−0.272660	+	0.310359i
$875$	−35.5549			−1.20198
$876$		0			0
$877$	−6.99544			−0.236219			−0.118110	−	0.993001i	$-0.537683\pi$
$877$	−6.99544			−0.236219			−0.118110	+	0.993001i	$0.537683\pi$
$878$	32.0624	−	36.4955i	1.08205	−	1.23166i
$879$		0			0
$880$	−2.78506	−	10.5420i	−0.0938845	−	0.355371i
$881$		−	25.1312i		−	0.846692i	−0.905968	−	0.423346i	$-0.860855\pi$
$881$		−	25.1312i		−	0.846692i	0.905968	−	0.423346i	$-0.139145\pi$
$882$		0			0
$883$			38.4680i			1.29455i	0.762256	+	0.647276i	$0.224092\pi$
$883$			38.4680i			1.29455i	−0.762256	+	0.647276i	$0.775908\pi$
$884$	9.66392	−	1.25501i	0.325033	−	0.0422107i
$885$		0			0
$886$	−24.9409	−	21.9114i	−0.837906	−	0.736127i
$887$	32.4015			1.08794			0.543969	−	0.839106i	$-0.316921\pi$
$887$	32.4015			1.08794			0.543969	+	0.839106i	$0.316921\pi$
$888$		0			0
$889$	52.4196			1.75810
$890$	6.27309	+	5.51111i	0.210275	+	0.184733i
$891$		0			0
$892$	8.28001	−	1.07529i	0.277235	−	0.0360034i
$893$		−	22.7993i		−	0.762951i
$894$		0			0
$895$			7.21382i			0.241132i
$896$	36.4383	+	12.6195i	1.21732	+	0.421587i
$897$		0			0
$898$	−2.79054	+	3.17637i	−0.0931216	+	0.105997i
$899$	32.6953			1.09045
$900$		0			0
$901$	−13.7234			−0.457193
$902$	−7.27741	+	8.28361i	−0.242311	+	0.275814i
$903$		0			0
$904$	−16.0281	−	10.7709i	−0.533088	−	0.358233i
$905$			4.13248i			0.137368i
$906$		0			0
$907$			30.7057i			1.01957i	0.860303	+	0.509783i	$0.170274\pi$
$907$			30.7057i			1.01957i	−0.860303	+	0.509783i	$0.829726\pi$
$908$	−1.68899	−	13.0056i	−0.0560511	−	0.431608i
$909$		0			0
$910$	21.4456	+	18.8406i	0.710913	+	0.624560i
$911$	3.34011			0.110663			0.0553314	−	0.998468i	$-0.482378\pi$
$911$	3.34011			0.110663			0.0553314	+	0.998468i	$0.482378\pi$
$912$		0			0
$913$	4.80633			0.159066
$914$	−13.3437	−	11.7229i	−0.441371	−	0.387758i
$915$		0			0
$916$	0.338586	+	2.60720i	0.0111872	+	0.0861443i
$917$			0.262528i			0.00866942i
$918$		0			0
$919$		−	20.5895i		−	0.679185i	−0.940573	−	0.339593i	$-0.889711\pi$
$919$		−	20.5895i		−	0.679185i	0.940573	−	0.339593i	$-0.110289\pi$
$920$	2.88430	+	1.93824i	0.0950926	+	0.0639019i
$921$		0			0
$922$	10.8972	−	12.4039i	0.358882	−	0.408502i
$923$	−75.5061			−2.48532
$924$		0			0
$925$	16.5134			0.542956
$926$	17.2330	−	19.6156i	0.566310	−	0.644610i
$927$		0			0
$928$	24.4444	−	49.0244i	0.802427	−	1.60931i
$929$			53.1268i			1.74303i	0.490365	+	0.871517i	$0.336863\pi$
$929$			53.1268i			1.74303i	−0.490365	+	0.871517i	$0.663137\pi$
$930$		0			0
$931$			39.8742i			1.30682i
$932$	−34.5508	+	4.48698i	−1.13175	+	0.146976i
$933$		0			0
$934$	−28.9865	−	25.4655i	−0.948467	−	0.833258i
$935$	−2.75551			−0.0901150
$936$		0			0
$937$	59.2470			1.93551			0.967757	−	0.251886i	$-0.0810508\pi$
$937$	59.2470			1.93551			0.967757	+	0.251886i	$0.0810508\pi$
$938$	31.8146	+	27.9501i	1.03878	+	0.912603i
$939$		0			0
$940$	−6.43313	+	0.835444i	−0.209826	+	0.0272492i
$941$			14.4291i			0.470375i	0.971950	+	0.235188i	$0.0755704\pi$
$941$			14.4291i			0.470375i	−0.971950	+	0.235188i	$0.924430\pi$
$942$		0			0
$943$		−	3.51413i		−	0.114436i
$944$	2.99609	−	0.791529i	0.0975144	−	0.0257621i
$945$		0			0
$946$	−8.01670	+	9.12511i	−0.260645	+	0.296683i
$947$	18.2275			0.592314			0.296157	−	0.955139i	$-0.404295\pi$
$947$	18.2275			0.592314			0.296157	+	0.955139i	$0.404295\pi$
$948$		0			0
$949$	−48.4292			−1.57208
$950$	28.1362	−	32.0264i	0.912859	−	1.03907i
$951$		0			0
$952$	5.43540	−	8.08844i	0.176162	−	0.262148i
$953$		−	17.6007i		−	0.570143i	−0.958506	−	0.285072i	$-0.907983\pi$
$953$		−	17.6007i		−	0.570143i	0.958506	−	0.285072i	$-0.0920174\pi$
$954$		0			0
$955$		−	3.87553i		−	0.125409i
$956$	−6.72669	−	51.7972i	−0.217557	−	1.67524i
$957$		0			0
$958$	−14.2414	−	12.5115i	−0.460118	−	0.404228i
$959$	−13.2694			−0.428492
$960$		0			0
$961$	19.6010			0.632291
$962$	−24.2280	−	21.2851i	−0.781143	−	0.686259i
$963$		0			0
$964$	2.09211	+	16.1097i	0.0673822	+	0.518860i
$965$			3.25271i			0.104708i
$966$		0			0
$967$		−	43.6238i		−	1.40285i	−0.712744	−	0.701424i	$-0.752548\pi$
$967$		−	43.6238i		−	1.40285i	0.712744	−	0.701424i	$-0.247452\pi$
$968$	9.58760	−	14.2673i	0.308157	−	0.458570i
$969$		0			0
$970$	−14.6953	+	16.7271i	−0.471837	+	0.537075i
$971$	−25.3544			−0.813662			−0.406831	−	0.913504i	$-0.633366\pi$
$971$	−25.3544			−0.813662			−0.406831	+	0.913504i	$0.633366\pi$
$972$		0			0
$973$	−34.1145			−1.09366
$974$	3.41085	−	3.88245i	0.109291	−	0.124402i
$975$		0			0
$976$	36.9864	−	9.77135i	1.18391	−	0.312773i
$977$		−	13.9548i		−	0.446455i	−0.974766	−	0.223228i	$-0.928341\pi$
$977$		−	13.9548i		−	0.446455i	0.974766	−	0.223228i	$-0.0716593\pi$
$978$		0			0
$979$		−	10.6625i		−	0.340773i
$980$	11.2510	−	1.46112i	0.359400	−	0.0466738i
$981$		0			0
$982$	41.8093	+	36.7308i	1.33419	+	1.17213i
$983$	−29.6731			−0.946425			−0.473213	−	0.880948i	$-0.656906\pi$
$983$	−29.6731			−0.946425			−0.473213	+	0.880948i	$0.656906\pi$
$984$		0			0
$985$	−3.41867			−0.108928
$986$	−10.4003	−	9.13703i	−0.331214	−	0.290982i
$987$		0			0
$988$	−82.5616	+	10.7219i	−2.62664	+	0.341111i
$989$		−	3.87111i		−	0.123094i
$990$		0			0
$991$			10.3399i			0.328457i	0.986422	+	0.164229i	$0.0525134\pi$
$991$			10.3399i			0.328457i	−0.986422	+	0.164229i	$0.947487\pi$
$992$	−8.52236	+	17.0920i	−0.270585	+	0.542672i
$993$		0			0
$994$	−49.8345	+	56.7248i	−1.58065	+	1.79920i
$995$	−17.0331			−0.539987
$996$		0			0
$997$	−6.35171			−0.201161			−0.100580	−	0.994929i	$-0.532070\pi$
$997$	−6.35171			−0.201161			−0.100580	+	0.994929i	$0.532070\pi$
$998$	−19.5244	+	22.2239i	−0.618034	+	0.703485i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.c.e.323.11	yes	12
3.2	odd	2		828.2.c.f.323.2	yes	12
4.3	odd	2		828.2.c.f.323.3	yes	12
12.11	even	2	inner	828.2.c.e.323.10	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
828.2.c.e.323.10	✓	12	12.11	even	2	inner
828.2.c.e.323.11	yes	12	1.1	even	1	trivial
828.2.c.f.323.2	yes	12	3.2	odd	2
828.2.c.f.323.3	yes	12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06244 + 0.933389i) q^{2} +(0.257569 + 1.98335i) q^{4} +1.22862i q^{5} +3.40840i q^{7} +(-1.57758 + 2.34760i) q^{8} +(-1.14678 + 1.30533i) q^{10} +2.21869 q^{11} -4.82020 q^{13} +(-3.18136 + 3.62123i) q^{14} +(-3.86732 + 1.02170i) q^{16} +1.01086i q^{17} -8.63604i q^{19} +(-2.43677 + 0.316453i) q^{20} +(2.35723 + 2.07090i) q^{22} -1.00000 q^{23} +3.49050 q^{25} +(-5.12119 - 4.49913i) q^{26} +(-6.76003 + 0.877898i) q^{28} +9.68395i q^{29} -3.37624i q^{31} +(-5.06244 - 2.52422i) q^{32} +(-0.943523 + 1.07398i) q^{34} -4.18761 q^{35} +4.73094 q^{37} +(8.06079 - 9.17530i) q^{38} +(-2.88430 - 1.93824i) q^{40} +3.51413i q^{41} +3.87111i q^{43} +(0.571466 + 4.40043i) q^{44} +(-1.06244 - 0.933389i) q^{46} +2.64002 q^{47} -4.61718 q^{49} +(3.70846 + 3.25800i) q^{50} +(-1.24154 - 9.56013i) q^{52} +13.5760i q^{53} +2.72592i q^{55} +(-8.00157 - 5.37702i) q^{56} +(-9.03890 + 10.2886i) q^{58} -0.774720 q^{59} -9.56384 q^{61} +(3.15134 - 3.58706i) q^{62} +(-3.02248 - 7.40707i) q^{64} -5.92218i q^{65} -8.78558i q^{67} +(-2.00488 + 0.260365i) q^{68} +(-4.44910 - 3.90867i) q^{70} +15.6645 q^{71} +10.0471 q^{73} +(5.02635 + 4.41581i) q^{74} +(17.1282 - 2.22438i) q^{76} +7.56219i q^{77} +8.25854i q^{79} +(-1.25527 - 4.75145i) q^{80} +(-3.28005 + 3.73356i) q^{82} +2.16629 q^{83} -1.24195 q^{85} +(-3.61325 + 4.11283i) q^{86} +(-3.50017 + 5.20861i) q^{88} -4.80574i q^{89} -16.4292i q^{91} +(-0.257569 - 1.98335i) q^{92} +(2.80487 + 2.46417i) q^{94} +10.6104 q^{95} +12.8144 q^{97} +(-4.90549 - 4.30963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 8 q^{10} - 12 q^{11} - 4 q^{13} + 12 q^{14} - 12 q^{16} - 20 q^{20} + 4 q^{22} - 12 q^{23} - 40 q^{25} - 8 q^{26} - 24 q^{28} - 44 q^{32} - 28 q^{34} - 40 q^{35} - 32 q^{37}+ \cdots + 20 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 8 * q^10 - 12 * q^11 - 4 * q^13 + 12 * q^14 - 12 * q^16 - 20 * q^20 + 4 * q^22 - 12 * q^23 - 40 * q^25 - 8 * q^26 - 24 * q^28 - 44 * q^32 - 28 * q^34 - 40 * q^35 - 32 * q^37 + 32 * q^38 - 12 * q^40 - 4 * q^44 + 4 * q^46 - 32 * q^49 + 20 * q^50 + 32 * q^52 + 8 * q^56 - 16 * q^58 + 24 * q^59 - 56 * q^61 + 28 * q^64 - 16 * q^68 + 64 * q^70 + 56 * q^71 + 8 * q^73 + 36 * q^74 - 28 * q^76 - 28 * q^80 + 24 * q^82 + 28 * q^83 - 12 * q^85 + 8 * q^86 + 4 * q^88 - 4 * q^92 + 16 * q^94 - 8 * q^95 - 4 * q^97 + 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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