LMFDB - Embedded newform 1456.2.cc.c.225.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.5
Root			$-1.30089 - 0.554694i$ of defining polynomial
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.c.673.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13082 - 1.95864i) q^{3} -3.60178i q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.05753 - 1.83169i) q^{9} +O(q^{10})$	\(q+(1.13082 - 1.95864i) q^{3} -3.60178i q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.05753 - 1.83169i) q^{9} +(-0.767631 - 0.443192i) q^{11} +(-1.17349 + 3.40924i) q^{13} +(-7.05461 - 4.07298i) q^{15} +(-2.48008 - 4.29563i) q^{17} +(-2.06008 + 1.18939i) q^{19} -2.26165i q^{21} +(1.92926 - 3.34157i) q^{23} -7.97282 q^{25} +2.00144 q^{27} +(-0.640986 + 1.11022i) q^{29} -8.46921i q^{31} +(-1.73611 + 1.00234i) q^{33} +(-1.80089 - 3.11923i) q^{35} +(-8.34686 - 4.81906i) q^{37} +(5.35049 + 6.15370i) q^{39} +(10.4652 + 6.04207i) q^{41} +(1.82125 + 3.15450i) q^{43} +(-6.59734 + 3.80898i) q^{45} +2.98229i q^{47} +(0.500000 - 0.866025i) q^{49} -11.2181 q^{51} +4.92032 q^{53} +(-1.59628 + 2.76484i) q^{55} +5.37995i q^{57} +(-6.34577 + 3.66373i) q^{59} +(0.769632 + 1.33304i) q^{61} +(-1.83169 - 1.05753i) q^{63} +(12.2793 + 4.22664i) q^{65} +(-7.29756 - 4.21325i) q^{67} +(-4.36330 - 7.55745i) q^{69} +(5.58490 - 3.22444i) q^{71} +7.14859i q^{73} +(-9.01585 + 15.6159i) q^{75} -0.886384 q^{77} -0.757551 q^{79} +(5.43585 - 9.41518i) q^{81} +4.76766i q^{83} +(-15.4719 + 8.93270i) q^{85} +(1.44969 + 2.51093i) q^{87} +(3.13400 + 1.80942i) q^{89} +(0.688351 + 3.53923i) q^{91} +(-16.5882 - 9.57719i) q^{93} +(4.28391 + 7.41995i) q^{95} +(-0.401229 + 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^9	$ 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.13082	−	1.95864i	0.652882	−	1.13082i	−0.329539	−	0.944142i	$-0.606893\pi$
$3$	1.13082	−	1.95864i	0.652882	−	1.13082i	0.982420	−	0.186682i	$-0.0597734\pi$
$4$		0			0
$5$		−	3.60178i		−	1.61076i	−0.592756	−	0.805382i	$-0.701960\pi$
$5$		−	3.60178i		−	1.61076i	0.592756	−	0.805382i	$-0.298040\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		0			0
$9$	−1.05753	−	1.83169i	−0.352509	−	0.610563i
$10$		0			0
$11$	−0.767631	−	0.443192i	−0.231450	−	0.133627i	0.379791	−	0.925072i	$-0.375996\pi$
$11$	−0.767631	−	0.443192i	−0.231450	−	0.133627i	−0.611241	+	0.791445i	$0.709329\pi$
$12$		0			0
$13$	−1.17349	+	3.40924i	−0.325467	+	0.945553i
$13$	−1.17349	+	3.40924i	−0.325467	+	0.945553i
$14$		0			0
$15$	−7.05461	−	4.07298i	−1.82149	−	1.05164i
$16$		0			0
$17$	−2.48008	−	4.29563i	−0.601508	−	1.04184i	−0.992593	−	0.121488i	$-0.961233\pi$
$17$	−2.48008	−	4.29563i	−0.601508	−	1.04184i	0.391085	−	0.920355i	$-0.372100\pi$
$18$		0			0
$19$	−2.06008	+	1.18939i	−0.472615	+	0.272864i	−0.717334	−	0.696730i	$-0.754638\pi$
$19$	−2.06008	+	1.18939i	−0.472615	+	0.272864i	0.244719	+	0.969594i	$0.421304\pi$
$20$		0			0
$21$		−	2.26165i		−	0.493532i
$22$		0			0
$23$	1.92926	−	3.34157i	0.402278	−	0.696765i	−0.591723	−	0.806142i	$-0.701552\pi$
$23$	1.92926	−	3.34157i	0.402278	−	0.696765i	0.994000	+	0.109376i	$0.0348853\pi$
$24$		0			0
$25$	−7.97282			−1.59456
$26$		0			0
$27$	2.00144			0.385177
$28$		0			0
$29$	−0.640986	+	1.11022i	−0.119028	+	0.206163i	−0.919383	−	0.393364i	$-0.871311\pi$
$29$	−0.640986	+	1.11022i	−0.119028	+	0.206163i	0.800355	+	0.599527i	$0.204645\pi$
$30$		0			0
$31$		−	8.46921i		−	1.52111i	−0.649271	−	0.760557i	$-0.724926\pi$
$31$		−	8.46921i		−	1.52111i	0.649271	−	0.760557i	$-0.275074\pi$
$32$		0			0
$33$	−1.73611	+	1.00234i	−0.302218	+	0.174486i
$34$		0			0
$35$	−1.80089	−	3.11923i	−0.304406	−	0.527247i
$36$		0			0
$37$	−8.34686	−	4.81906i	−1.37222	−	0.792249i	−0.381009	−	0.924571i	$-0.624423\pi$
$37$	−8.34686	−	4.81906i	−1.37222	−	0.792249i	−0.991207	+	0.132323i	$0.957757\pi$
$38$		0			0
$39$	5.35049	+	6.15370i	0.856763	+	0.985380i
$40$		0			0
$41$	10.4652	+	6.04207i	1.63438	+	0.943612i	0.982719	+	0.185106i	$0.0592628\pi$
$41$	10.4652	+	6.04207i	1.63438	+	0.943612i	0.651666	+	0.758506i	$0.274071\pi$
$42$		0			0
$43$	1.82125	+	3.15450i	0.277738	+	0.481056i	0.970822	−	0.239800i	$-0.0770820\pi$
$43$	1.82125	+	3.15450i	0.277738	+	0.481056i	−0.693084	+	0.720856i	$0.743749\pi$
$44$		0			0
$45$	−6.59734	+	3.80898i	−0.983474	+	0.567809i
$46$		0			0
$47$			2.98229i			0.435012i	0.976059	+	0.217506i	$0.0697922\pi$
$47$			2.98229i			0.435012i	−0.976059	+	0.217506i	$0.930208\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	−11.2181			−1.57085
$52$		0			0
$53$	4.92032			0.675858			0.337929	−	0.941172i	$-0.390274\pi$
$53$	4.92032			0.675858			0.337929	+	0.941172i	$0.390274\pi$
$54$		0			0
$55$	−1.59628	+	2.76484i	−0.215242	+	0.372811i
$56$		0			0
$57$			5.37995i			0.712592i
$58$		0			0
$59$	−6.34577	+	3.66373i	−0.826148	+	0.476977i	−0.852532	−	0.522675i	$-0.824934\pi$
$59$	−6.34577	+	3.66373i	−0.826148	+	0.476977i	0.0263837	+	0.999652i	$0.491601\pi$
$60$		0			0
$61$	0.769632	+	1.33304i	0.0985412	+	0.170678i	0.911081	−	0.412227i	$-0.135249\pi$
$61$	0.769632	+	1.33304i	0.0985412	+	0.170678i	−0.812540	+	0.582906i	$0.801916\pi$
$62$		0			0
$63$	−1.83169	−	1.05753i	−0.230771	−	0.133236i
$64$		0			0
$65$	12.2793	+	4.22664i	1.52306	+	0.524250i
$66$		0			0
$67$	−7.29756	−	4.21325i	−0.891539	−	0.514730i	−0.0170931	−	0.999854i	$-0.505441\pi$
$67$	−7.29756	−	4.21325i	−0.891539	−	0.514730i	−0.874445	+	0.485124i	$0.838775\pi$
$68$		0			0
$69$	−4.36330	−	7.55745i	−0.525279	−	0.909811i
$70$		0			0
$71$	5.58490	−	3.22444i	0.662805	−	0.382671i	−0.130540	−	0.991443i	$-0.541671\pi$
$71$	5.58490	−	3.22444i	0.662805	−	0.382671i	0.793345	+	0.608772i	$0.208338\pi$
$72$		0			0
$73$			7.14859i			0.836679i	0.908291	+	0.418340i	$0.137388\pi$
$73$			7.14859i			0.836679i	−0.908291	+	0.418340i	$0.862612\pi$
$74$		0			0
$75$	−9.01585	+	15.6159i	−1.04106	+	1.80317i
$76$		0			0
$77$	−0.886384			−0.101013
$78$		0			0
$79$	−0.757551			−0.0852311			−0.0426156	−	0.999092i	$-0.513569\pi$
$79$	−0.757551			−0.0852311			−0.0426156	+	0.999092i	$0.513569\pi$
$80$		0			0
$81$	5.43585	−	9.41518i	0.603984	−	1.04613i
$82$		0			0
$83$			4.76766i			0.523319i	0.965160	+	0.261659i	$0.0842697\pi$
$83$			4.76766i			0.523319i	−0.965160	+	0.261659i	$0.915730\pi$
$84$		0			0
$85$	−15.4719	+	8.93270i	−1.67816	+	0.968888i
$86$		0			0
$87$	1.44969	+	2.51093i	0.155423	+	0.269200i
$88$		0			0
$89$	3.13400	+	1.80942i	0.332204	+	0.191798i	0.656819	−	0.754048i	$-0.271902\pi$
$89$	3.13400	+	1.80942i	0.332204	+	0.191798i	−0.324615	+	0.945846i	$0.605235\pi$
$90$		0			0
$91$	0.688351	+	3.53923i	0.0721588	+	0.371012i
$92$		0			0
$93$	−16.5882	−	9.57719i	−1.72011	−	0.993108i
$94$		0			0
$95$	4.28391	+	7.41995i	0.439520	+	0.761271i
$96$		0			0
$97$	−0.401229	+	0.231650i	−0.0407386	+	0.0235205i	−0.520231	−	0.854026i	$-0.674154\pi$
$97$	−0.401229	+	0.231650i	−0.0407386	+	0.0235205i	0.479492	+	0.877546i	$0.340821\pi$
$98$		0			0
$99$			1.87475i			0.188419i
$100$		0			0
$101$	2.91152	−	5.04289i	0.289707	−	0.501787i	−0.684033	−	0.729451i	$-0.739776\pi$
$101$	2.91152	−	5.04289i	0.289707	−	0.501787i	0.973740	+	0.227664i	$0.0731089\pi$
$102$		0			0
$103$	8.23888			0.811801			0.405901	−	0.913917i	$-0.366958\pi$
$103$	8.23888			0.811801			0.405901	+	0.913917i	$0.366958\pi$
$104$		0			0
$105$	−8.14596			−0.794964
$106$		0			0
$107$	−1.91630	+	3.31913i	−0.185256	+	0.320872i	−0.943663	−	0.330909i	$-0.892645\pi$
$107$	−1.91630	+	3.31913i	−0.185256	+	0.320872i	0.758407	+	0.651781i	$0.225978\pi$
$108$		0			0
$109$		−	10.4180i		−	0.997867i	−0.866640	−	0.498934i	$-0.833725\pi$
$109$		−	10.4180i		−	0.997867i	0.866640	−	0.498934i	$-0.166275\pi$
$110$		0			0
$111$	−18.8777	+	10.8990i	−1.79179	+	1.03449i
$112$		0			0
$113$	2.45505	+	4.25228i	0.230952	+	0.400021i	0.958089	−	0.286472i	$-0.0924826\pi$
$113$	2.45505	+	4.25228i	0.230952	+	0.400021i	−0.727136	+	0.686493i	$0.759149\pi$
$114$		0			0
$115$	−12.0356	−	6.94875i	−1.12233	−	0.647975i
$116$		0			0
$117$	7.48567	−	1.45590i	0.692050	−	0.134598i
$118$		0			0
$119$	−4.29563	−	2.48008i	−0.393779	−	0.227349i
$120$		0			0
$121$	−5.10716	−	8.84586i	−0.464287	−	0.804169i
$122$		0			0
$123$	23.6685	−	13.6650i	2.13412	−	1.23213i
$124$		0			0
$125$			10.7074i			0.957702i
$126$		0			0
$127$	6.15508	−	10.6609i	0.546175	−	0.946003i	−0.452357	−	0.891837i	$-0.649417\pi$
$127$	6.15508	−	10.6609i	0.546175	−	0.946003i	0.998532	−	0.0541658i	$-0.0172500\pi$
$128$		0			0
$129$	8.23805			0.725320
$130$		0			0
$131$	8.20265			0.716669			0.358335	−	0.933593i	$-0.383345\pi$
$131$	8.20265			0.716669			0.358335	+	0.933593i	$0.383345\pi$
$132$		0			0
$133$	−1.18939	+	2.06008i	−0.103133	+	0.178632i
$134$		0			0
$135$		−	7.20874i		−	0.620429i
$136$		0			0
$137$	6.45670	−	3.72778i	0.551633	−	0.318485i	−0.198147	−	0.980172i	$-0.563492\pi$
$137$	6.45670	−	3.72778i	0.551633	−	0.318485i	0.749780	+	0.661687i	$0.230159\pi$
$138$		0			0
$139$	8.34028	+	14.4458i	0.707413	+	1.22528i	0.965813	+	0.259238i	$0.0834714\pi$
$139$	8.34028	+	14.4458i	0.707413	+	1.22528i	−0.258400	+	0.966038i	$0.583195\pi$
$140$		0			0
$141$	5.84125	+	3.37245i	0.491922	+	0.284011i
$142$		0			0
$143$	2.41175	−	2.09696i	0.201681	−	0.175357i
$144$		0			0
$145$	3.99877	+	2.30869i	0.332080	+	0.191726i
$146$		0			0
$147$	−1.13082	−	1.95864i	−0.0932688	−	0.161546i
$148$		0			0
$149$	−2.18380	+	1.26082i	−0.178904	+	0.103290i	−0.586777	−	0.809748i	$-0.699604\pi$
$149$	−2.18380	+	1.26082i	−0.178904	+	0.103290i	0.407874	+	0.913038i	$0.366270\pi$
$150$		0			0
$151$		−	15.8972i		−	1.29370i	−0.762618	−	0.646849i	$-0.776086\pi$
$151$		−	15.8972i		−	1.29370i	0.762618	−	0.646849i	$-0.223914\pi$
$152$		0			0
$153$	−5.24550	+	9.08548i	−0.424074	+	0.734517i
$154$		0			0
$155$	−30.5042			−2.45016
$156$		0			0
$157$	12.9831			1.03616			0.518082	−	0.855331i	$-0.326646\pi$
$157$	12.9831			1.03616			0.518082	+	0.855331i	$0.326646\pi$
$158$		0			0
$159$	5.56402	−	9.63717i	0.441256	−	0.764277i
$160$		0			0
$161$		−	3.85851i		−	0.304093i
$162$		0			0
$163$	2.00873	−	1.15974i	0.157336	−	0.0908378i	−0.419265	−	0.907864i	$-0.637712\pi$
$163$	2.00873	−	1.15974i	0.157336	−	0.0908378i	0.576601	+	0.817026i	$0.304379\pi$
$164$		0			0
$165$	3.61023	+	6.25309i	0.281056	+	0.486803i
$166$		0			0
$167$	11.9441	+	6.89591i	0.924260	+	0.533622i	0.884992	−	0.465607i	$-0.154164\pi$
$167$	11.9441	+	6.89591i	0.924260	+	0.533622i	0.0392682	+	0.999229i	$0.487497\pi$
$168$		0			0
$169$	−10.2459	−	8.00140i	−0.788143	−	0.615493i
$170$		0			0
$171$	4.35718	+	2.51562i	0.333202	+	0.192374i
$172$		0			0
$173$	−1.84216	−	3.19071i	−0.140057	−	0.242585i	0.787461	−	0.616364i	$-0.211395\pi$
$173$	−1.84216	−	3.19071i	−0.140057	−	0.242585i	−0.927518	+	0.373779i	$0.878062\pi$
$174$		0			0
$175$	−6.90466	+	3.98641i	−0.521943	+	0.301344i
$176$		0			0
$177$			16.5721i			1.24564i
$178$		0			0
$179$	2.94638	−	5.10328i	0.220223	−	0.381437i	−0.734653	−	0.678443i	$-0.762655\pi$
$179$	2.94638	−	5.10328i	0.220223	−	0.381437i	0.954876	+	0.297006i	$0.0959882\pi$
$180$		0			0
$181$	−2.11543			−0.157239			−0.0786193	−	0.996905i	$-0.525051\pi$
$181$	−2.11543			−0.157239			−0.0786193	+	0.996905i	$0.525051\pi$
$182$		0			0
$183$	3.48127			0.257343
$184$		0			0
$185$	−17.3572	+	30.0635i	−1.27613	+	2.21032i
$186$		0			0
$187$			4.39661i			0.321512i
$188$		0			0
$189$	1.73330	−	1.00072i	0.126079	−	0.0727916i
$190$		0			0
$191$	−5.68333	−	9.84381i	−0.411231	−	0.712273i	0.583794	−	0.811902i	$-0.301568\pi$
$191$	−5.68333	−	9.84381i	−0.411231	−	0.712273i	−0.995025	+	0.0996290i	$0.968234\pi$
$192$		0			0
$193$	12.2017	+	7.04468i	0.878301	+	0.507087i	0.870098	−	0.492879i	$-0.164055\pi$
$193$	12.2017	+	7.04468i	0.878301	+	0.507087i	0.00820314	+	0.999966i	$0.497389\pi$
$194$		0			0
$195$	22.1643	−	19.2713i	1.58722	−	1.38004i
$196$		0			0
$197$	−19.8815	−	11.4786i	−1.41650	−	0.817814i	−0.420507	−	0.907289i	$-0.638148\pi$
$197$	−19.8815	−	11.4786i	−1.41650	−	0.817814i	−0.995989	+	0.0894753i	$0.971481\pi$
$198$		0			0
$199$	1.57492	+	2.72785i	0.111643	+	0.193372i	0.916433	−	0.400188i	$-0.131055\pi$
$199$	1.57492	+	2.72785i	0.111643	+	0.193372i	−0.804790	+	0.593560i	$0.797722\pi$
$200$		0			0
$201$	−16.5045	+	9.52888i	−1.16414	+	0.672116i
$202$		0			0
$203$			1.28197i			0.0899768i
$204$		0			0
$205$	21.7622	−	37.6932i	1.51994	−	2.63261i
$206$		0			0
$207$	−8.16096			−0.567226
$208$		0			0
$209$	2.10851			0.145849
$210$		0			0
$211$	−7.43191	+	12.8725i	−0.511634	+	0.886176i	0.488275	+	0.872690i	$0.337626\pi$
$211$	−7.43191	+	12.8725i	−0.511634	+	0.886176i	−0.999909	+	0.0134864i	$0.995707\pi$
$212$		0			0
$213$		−	14.5851i		−	0.999355i
$214$		0			0
$215$	11.3618	−	6.55974i	0.774868	−	0.447370i
$216$		0			0
$217$	−4.23460	−	7.33455i	−0.287464	−	0.497902i
$218$		0			0
$219$	14.0016	+	8.08380i	0.946137	+	0.546253i
$220$		0			0
$221$	17.5552	−	3.41433i	1.18089	−	0.229673i
$222$		0			0
$223$	−3.79396	−	2.19044i	−0.254062	−	0.146683i	0.367561	−	0.930000i	$-0.380193\pi$
$223$	−3.79396	−	2.19044i	−0.254062	−	0.146683i	−0.621623	+	0.783317i	$0.713526\pi$
$224$		0			0
$225$	8.43147	+	14.6037i	0.562098	+	0.973582i
$226$		0			0
$227$	−11.7488	+	6.78316i	−0.779793	+	0.450214i	−0.836357	−	0.548185i	$-0.815319\pi$
$227$	−11.7488	+	6.78316i	−0.779793	+	0.450214i	0.0565636	+	0.998399i	$0.481986\pi$
$228$		0			0
$229$		−	16.5180i		−	1.09154i	−0.837935	−	0.545770i	$-0.816237\pi$
$229$		−	16.5180i		−	1.09154i	0.837935	−	0.545770i	$-0.183763\pi$
$230$		0			0
$231$	−1.00234	+	1.73611i	−0.0659494	+	0.114228i
$232$		0			0
$233$	16.5026			1.08112			0.540561	−	0.841305i	$-0.318212\pi$
$233$	16.5026			1.08112			0.540561	+	0.841305i	$0.318212\pi$
$234$		0			0
$235$	10.7416			0.700702
$236$		0			0
$237$	−0.856657	+	1.48377i	−0.0556458	+	0.0963814i
$238$		0			0
$239$		−	30.4210i		−	1.96777i	−0.178796	−	0.983886i	$-0.557220\pi$
$239$		−	30.4210i		−	1.96777i	0.178796	−	0.983886i	$-0.442780\pi$
$240$		0			0
$241$	−25.5602	+	14.7572i	−1.64648	+	0.950593i	−0.668018	+	0.744145i	$0.732857\pi$
$241$	−25.5602	+	14.7572i	−1.64648	+	0.950593i	−0.978458	+	0.206448i	$0.933810\pi$
$242$		0			0
$243$	−9.29184	−	16.0939i	−0.596072	−	1.03243i
$244$		0			0
$245$	−3.11923	−	1.80089i	−0.199280	−	0.115055i
$246$		0			0
$247$	−1.63743	−	8.41904i	−0.104187	−	0.535691i
$248$		0			0
$249$	9.33816	+	5.39139i	0.591782	+	0.341665i
$250$		0			0
$251$	6.49134	+	11.2433i	0.409730	+	0.709673i	0.994859	−	0.101267i	$-0.0322897\pi$
$251$	6.49134	+	11.2433i	0.409730	+	0.709673i	−0.585130	+	0.810940i	$0.698956\pi$
$252$		0			0
$253$	−2.96191	+	1.71006i	−0.186214	+	0.107511i
$254$		0			0
$255$			40.4053i			2.53028i
$256$		0			0
$257$	−2.29261	+	3.97091i	−0.143009	+	0.247698i	−0.928628	−	0.371011i	$-0.879011\pi$
$257$	−2.29261	+	3.97091i	−0.143009	+	0.247698i	0.785620	+	0.618710i	$0.212344\pi$
$258$		0			0
$259$	−9.63812			−0.598884
$260$		0			0
$261$	2.71144			0.167834
$262$		0			0
$263$	−1.33250	+	2.30795i	−0.0821652	+	0.142314i	−0.904180	−	0.427152i	$-0.859517\pi$
$263$	−1.33250	+	2.30795i	−0.0821652	+	0.142314i	0.822015	+	0.569466i	$0.192850\pi$
$264$		0			0
$265$		−	17.7219i		−	1.08865i
$266$		0			0
$267$	7.08801	−	4.09227i	0.433779	−	0.250443i
$268$		0			0
$269$	−5.96282	−	10.3279i	−0.363559	−	0.629703i	0.624984	−	0.780637i	$-0.285105\pi$
$269$	−5.96282	−	10.3279i	−0.363559	−	0.629703i	−0.988544	+	0.150934i	$0.951772\pi$
$270$		0			0
$271$	11.2828	+	6.51416i	0.685384	+	0.395707i	0.801881	−	0.597484i	$-0.203833\pi$
$271$	11.2828	+	6.51416i	0.685384	+	0.395707i	−0.116496	+	0.993191i	$0.537166\pi$
$272$		0			0
$273$	7.71051	+	2.65402i	0.466661	+	0.160628i
$274$		0			0
$275$	6.12018	+	3.53349i	0.369061	+	0.213077i
$276$		0			0
$277$	10.6824	+	18.5025i	0.641846	+	1.11171i	0.985020	+	0.172438i	$0.0551646\pi$
$277$	10.6824	+	18.5025i	0.641846	+	1.11171i	−0.343174	+	0.939272i	$0.611502\pi$
$278$		0			0
$279$	−15.5130	+	8.95641i	−0.928737	+	0.536206i
$280$		0			0
$281$		−	17.2678i		−	1.03011i	−0.857158	−	0.515054i	$-0.827772\pi$
$281$		−	17.2678i		−	1.03011i	0.857158	−	0.515054i	$-0.172228\pi$
$282$		0			0
$283$	10.6201	−	18.3946i	0.631299	−	1.09344i	−0.355987	−	0.934491i	$-0.615855\pi$
$283$	10.6201	−	18.3946i	0.631299	−	1.09344i	0.987286	−	0.158952i	$-0.0508114\pi$
$284$		0			0
$285$	19.3774			1.14782
$286$		0			0
$287$	12.0841			0.713304
$288$		0			0
$289$	−3.80160	+	6.58457i	−0.223624	+	0.387327i
$290$		0			0
$291$			1.04782i			0.0614243i
$292$		0			0
$293$	−0.363782	+	0.210030i	−0.0212524	+	0.0122701i	−0.510589	−	0.859825i	$-0.670572\pi$
$293$	−0.363782	+	0.210030i	−0.0212524	+	0.0122701i	0.489336	+	0.872095i	$0.337239\pi$
$294$		0			0
$295$	13.1959	+	22.8561i	0.768298	+	1.33073i
$296$		0			0
$297$	−1.53637	−	0.887022i	−0.0891490	−	0.0514702i
$298$		0			0
$299$	9.12826	+	10.4986i	0.527901	+	0.607149i
$300$		0			0
$301$	3.15450	+	1.82125i	0.181822	+	0.104975i
$302$		0			0
$303$	−6.58482	−	11.4053i	−0.378288	−	0.655215i
$304$		0			0
$305$	4.80132	−	2.77204i	0.274923	−	0.158727i
$306$		0			0
$307$		−	14.0807i		−	0.803628i	−0.915721	−	0.401814i	$-0.868380\pi$
$307$		−	14.0807i		−	0.803628i	0.915721	−	0.401814i	$-0.131620\pi$
$308$		0			0
$309$	9.31673	−	16.1370i	0.530010	−	0.918004i
$310$		0			0
$311$	10.3848			0.588867			0.294434	−	0.955672i	$-0.404869\pi$
$311$	10.3848			0.588867			0.294434	+	0.955672i	$0.404869\pi$
$312$		0			0
$313$	6.84759			0.387048			0.193524	−	0.981096i	$-0.438008\pi$
$313$	6.84759			0.387048			0.193524	+	0.981096i	$0.438008\pi$
$314$		0			0
$315$	−3.80898	+	6.59734i	−0.214612	+	0.371718i
$316$		0			0
$317$		−	0.701249i		−	0.0393861i	−0.999806	−	0.0196930i	$-0.993731\pi$
$317$		−	0.701249i		−	0.0393861i	0.999806	−	0.0196930i	$-0.00626889\pi$
$318$		0			0
$319$	0.984082	−	0.568160i	0.0550980	−	0.0318109i
$320$		0			0
$321$	4.33400	+	7.50670i	0.241900	+	0.418983i
$322$		0			0
$323$	10.2183	+	5.89956i	0.568563	+	0.328260i
$324$		0			0
$325$	9.35600	−	27.1813i	0.518977	−	1.50774i
$326$		0			0
$327$	−20.4052	−	11.7810i	−1.12841	−	0.651489i
$328$		0			0
$329$	1.49115	+	2.58274i	0.0822095	+	0.142391i
$330$		0			0
$331$	−3.63613	+	2.09932i	−0.199860	+	0.115389i	−0.596590	−	0.802546i	$-0.703478\pi$
$331$	−3.63613	+	2.09932i	−0.199860	+	0.115389i	0.396730	+	0.917935i	$0.370145\pi$
$332$		0			0
$333$			20.3851i			1.11710i
$334$		0			0
$335$	−15.1752	+	26.2842i	−0.829109	+	1.43606i
$336$		0			0
$337$	−20.4278			−1.11278			−0.556388	−	0.830923i	$-0.687813\pi$
$337$	−20.4278			−1.11278			−0.556388	+	0.830923i	$0.687813\pi$
$338$		0			0
$339$	11.1049			0.603138
$340$		0			0
$341$	−3.75349	+	6.50123i	−0.203263	+	0.352061i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	−27.2203	+	15.7156i	−1.46549	+	0.846102i
$346$		0			0
$347$	3.98500	+	6.90222i	0.213926	+	0.370531i	0.952940	−	0.303160i	$-0.0980415\pi$
$347$	3.98500	+	6.90222i	0.213926	+	0.370531i	−0.739014	+	0.673690i	$0.764708\pi$
$348$		0			0
$349$	18.7038	+	10.7986i	1.00119	+	0.578037i	0.908600	−	0.417668i	$-0.137152\pi$
$349$	18.7038	+	10.7986i	1.00119	+	0.578037i	0.0925892	+	0.995704i	$0.470486\pi$
$350$		0			0
$351$	−2.34866	+	6.82338i	−0.125362	+	0.364205i
$352$		0			0
$353$	18.7214	+	10.8088i	0.996439	+	0.575295i	0.907193	−	0.420715i	$-0.138221\pi$
$353$	18.7214	+	10.8088i	0.996439	+	0.575295i	0.0892465	+	0.996010i	$0.471554\pi$
$354$		0			0
$355$	−11.6137	−	20.1156i	−0.616393	−	1.06762i
$356$		0			0
$357$	−9.71520	+	5.60907i	−0.514183	+	0.296863i
$358$		0			0
$359$			13.6834i			0.722180i	0.932531	+	0.361090i	$0.117595\pi$
$359$			13.6834i			0.722180i	−0.932531	+	0.361090i	$0.882405\pi$
$360$		0			0
$361$	−6.67071	+	11.5540i	−0.351090	+	0.608106i
$362$		0			0
$363$	−23.1012			−1.21250
$364$		0			0
$365$	25.7477			1.34769
$366$		0			0
$367$	−5.70638	+	9.88374i	−0.297871	+	0.515927i	−0.975649	−	0.219339i	$-0.929610\pi$
$367$	−5.70638	+	9.88374i	−0.297871	+	0.515927i	0.677778	+	0.735267i	$0.262943\pi$
$368$		0			0
$369$		−	25.5586i		−	1.33053i
$370$		0			0
$371$	4.26112	−	2.46016i	0.221227	−	0.127725i
$372$		0			0
$373$	15.6404	+	27.0900i	0.809830	+	1.40267i	0.912981	+	0.408002i	$0.133774\pi$
$373$	15.6404	+	27.0900i	0.809830	+	1.40267i	−0.103151	+	0.994666i	$0.532892\pi$
$374$		0			0
$375$	20.9721	+	12.1082i	1.08299	+	0.625266i
$376$		0			0
$377$	−3.03282	−	3.48811i	−0.156198	−	0.179647i
$378$		0			0
$379$	−23.7421	−	13.7075i	−1.21955	−	0.704108i	−0.254729	−	0.967012i	$-0.581986\pi$
$379$	−23.7421	−	13.7075i	−1.21955	−	0.704108i	−0.964822	+	0.262904i	$0.915320\pi$
$380$		0			0
$381$	−13.9206	−	24.1112i	−0.713175	−	1.23526i
$382$		0			0
$383$	−13.9436	+	8.05032i	−0.712483	+	0.411352i	−0.811980	−	0.583686i	$-0.801610\pi$
$383$	−13.9436	+	8.05032i	−0.712483	+	0.411352i	0.0994967	+	0.995038i	$0.468277\pi$
$384$		0			0
$385$			3.19256i			0.162708i
$386$		0			0
$387$	3.85204	−	6.67193i	0.195810	−	0.339153i
$388$		0			0
$389$	−21.1380			−1.07174			−0.535870	−	0.844301i	$-0.680016\pi$
$389$	−21.1380			−1.07174			−0.535870	+	0.844301i	$0.680016\pi$
$390$		0			0
$391$	−19.1388			−0.967893
$392$		0			0
$393$	9.27576	−	16.0661i	0.467900	−	0.810427i
$394$		0			0
$395$			2.72853i			0.137287i
$396$		0			0
$397$	11.3436	−	6.54921i	0.569317	−	0.328695i	−0.187560	−	0.982253i	$-0.560058\pi$
$397$	11.3436	−	6.54921i	0.569317	−	0.328695i	0.756876	+	0.653558i	$0.226724\pi$
$398$		0			0
$399$	2.68998	+	4.65918i	0.134667	+	0.233251i
$400$		0			0
$401$	16.8396	+	9.72236i	0.840930	+	0.485511i	0.857580	−	0.514350i	$-0.171967\pi$
$401$	16.8396	+	9.72236i	0.840930	+	0.485511i	−0.0166501	+	0.999861i	$0.505300\pi$
$402$		0			0
$403$	28.8736	+	9.93851i	1.43830	+	0.495072i
$404$		0			0
$405$	−33.9114	−	19.5788i	−1.68507	−	0.972876i
$406$		0			0
$407$	4.27154	+	7.39853i	0.211732	+	0.366731i
$408$		0			0
$409$	20.8330	−	12.0279i	1.03013	−	0.594743i	0.113105	−	0.993583i	$-0.463921\pi$
$409$	20.8330	−	12.0279i	1.03013	−	0.594743i	0.917020	+	0.398840i	$0.130587\pi$
$410$		0			0
$411$		−	16.8618i		−	0.831733i
$412$		0			0
$413$	−3.66373	+	6.34577i	−0.180280	+	0.312255i
$414$		0			0
$415$	17.1721			0.842944
$416$		0			0
$417$	37.7256			1.84743
$418$		0			0
$419$	19.5119	−	33.7956i	0.953218	−	1.65102i	0.214825	−	0.976653i	$-0.431082\pi$
$419$	19.5119	−	33.7956i	0.953218	−	1.65102i	0.738394	−	0.674370i	$-0.235585\pi$
$420$		0			0
$421$			22.0284i			1.07360i	0.843710	+	0.536799i	$0.180367\pi$
$421$			22.0284i			1.07360i	−0.843710	+	0.536799i	$0.819633\pi$
$422$		0			0
$423$	5.46263	−	3.15385i	0.265602	−	0.153346i
$424$		0			0
$425$	19.7732	+	34.2482i	0.959142	+	1.66128i
$426$		0			0
$427$	1.33304	+	0.769632i	0.0645104	+	0.0372451i
$428$		0			0
$429$	−1.37993	−	7.09506i	−0.0666237	−	0.342553i
$430$		0			0
$431$	31.0727	+	17.9398i	1.49672	+	0.864131i	0.999993	−	0.00377645i	$-0.00120209\pi$
$431$	31.0727	+	17.9398i	1.49672	+	0.864131i	0.496726	+	0.867907i	$0.334535\pi$
$432$		0			0
$433$	6.10678	+	10.5773i	0.293473	+	0.508310i	0.974629	−	0.223828i	$-0.0718555\pi$
$433$	6.10678	+	10.5773i	0.293473	+	0.508310i	−0.681155	+	0.732139i	$0.738522\pi$
$434$		0			0
$435$	9.04381	−	5.22145i	0.433618	−	0.250349i
$436$		0			0
$437$			9.17853i			0.439069i
$438$		0			0
$439$	7.87765	−	13.6445i	0.375980	−	0.651216i	−0.614493	−	0.788922i	$-0.710639\pi$
$439$	7.87765	−	13.6445i	0.375980	−	0.651216i	0.990473	+	0.137706i	$0.0439728\pi$
$440$		0			0
$441$	−2.11505			−0.100717
$442$		0			0
$443$	15.0706			0.716028			0.358014	−	0.933716i	$-0.383454\pi$
$443$	15.0706			0.716028			0.358014	+	0.933716i	$0.383454\pi$
$444$		0			0
$445$	6.51712	−	11.2880i	0.308941	−	0.535102i
$446$		0			0
$447$			5.70305i			0.269745i
$448$		0			0
$449$	26.6585	−	15.3913i	1.25809	−	0.726360i	0.285388	−	0.958412i	$-0.407877\pi$
$449$	26.6585	−	15.3913i	1.25809	−	0.726360i	0.972703	+	0.232052i	$0.0745441\pi$
$450$		0			0
$451$	−5.35559	−	9.27616i	−0.252185	−	0.436797i
$452$		0			0
$453$	−31.1370	−	17.9770i	−1.46295	−	0.844632i
$454$		0			0
$455$	12.7475	−	2.47929i	0.597614	−	0.116231i
$456$		0			0
$457$	−6.71687	−	3.87799i	−0.314202	−	0.181405i	0.334603	−	0.942359i	$-0.391398\pi$
$457$	−6.71687	−	3.87799i	−0.314202	−	0.181405i	−0.648805	+	0.760955i	$0.724731\pi$
$458$		0			0
$459$	−4.96373	−	8.59743i	−0.231687	−	0.401294i
$460$		0			0
$461$	1.27498	−	0.736110i	0.0593817	−	0.0342840i	−0.470015	−	0.882658i	$-0.655752\pi$
$461$	1.27498	−	0.736110i	0.0593817	−	0.0342840i	0.529397	+	0.848374i	$0.322418\pi$
$462$		0			0
$463$		−	14.0366i		−	0.652335i	−0.945312	−	0.326168i	$-0.894243\pi$
$463$		−	14.0366i		−	0.652335i	0.945312	−	0.326168i	$-0.105757\pi$
$464$		0			0
$465$	−34.4949	+	59.7469i	−1.59966	+	2.77070i
$466$		0			0
$467$	31.3806			1.45212			0.726060	−	0.687631i	$-0.241349\pi$
$467$	31.3806			1.45212			0.726060	+	0.687631i	$0.241349\pi$
$468$		0			0
$469$	−8.42649			−0.389099
$470$		0			0
$471$	14.6816	−	25.4293i	0.676492	−	1.17172i
$472$		0			0
$473$		−	3.22865i		−	0.148454i
$474$		0			0
$475$	16.4246	−	9.48277i	0.753614	−	0.435099i
$476$		0			0
$477$	−5.20337	−	9.01251i	−0.238246	−	0.412654i
$478$		0			0
$479$	−35.6760	−	20.5975i	−1.63008	−	0.941125i	−0.984068	−	0.177795i	$-0.943104\pi$
$479$	−35.6760	−	20.5975i	−1.63008	−	0.941125i	−0.646009	−	0.763330i	$-0.723563\pi$
$480$		0			0
$481$	26.2243	−	22.8014i	1.19572	−	1.03965i
$482$		0			0
$483$	−7.55745	−	4.36330i	−0.343876	−	0.198537i
$484$		0			0
$485$	0.834351	+	1.44514i	0.0378859	+	0.0656204i
$486$		0			0
$487$	−24.5314	+	14.1632i	−1.11163	+	0.641798i	−0.939250	−	0.343234i	$-0.888478\pi$
$487$	−24.5314	+	14.1632i	−1.11163	+	0.641798i	−0.172376	+	0.985031i	$0.555144\pi$
$488$		0			0
$489$		−	5.24584i		−	0.237225i
$490$		0			0
$491$	−17.3931	+	30.1258i	−0.784941	+	1.35956i	0.144094	+	0.989564i	$0.453973\pi$
$491$	−17.3931	+	30.1258i	−0.784941	+	1.35956i	−0.929034	+	0.369993i	$0.879360\pi$
$492$		0			0
$493$	6.35879			0.286386
$494$		0			0
$495$	6.75244			0.303499
$496$		0			0
$497$	3.22444	−	5.58490i	0.144636	−	0.250517i
$498$		0			0
$499$		−	0.0694885i		−	0.00311073i	−0.999999	−	0.00155537i	$-0.999505\pi$
$499$		−	0.0694885i		−	0.00311073i	0.999999	−	0.00155537i	$-0.000495089\pi$
$500$		0			0
$501$	27.0133	−	15.5961i	1.20686	−	0.696783i
$502$		0			0
$503$	12.8686	+	22.2891i	0.573782	+	0.993820i	0.996173	+	0.0874060i	$0.0278578\pi$
$503$	12.8686	+	22.2891i	0.573782	+	0.993820i	−0.422391	+	0.906414i	$0.638809\pi$
$504$		0			0
$505$	−18.1634	−	10.4866i	−0.808260	−	0.466649i
$506$		0			0
$507$	−27.2582	+	11.0198i	−1.21058	+	0.489407i
$508$		0			0
$509$	−6.09682	−	3.52000i	−0.270237	−	0.156021i	0.358759	−	0.933430i	$-0.383200\pi$
$509$	−6.09682	−	3.52000i	−0.270237	−	0.156021i	−0.628995	+	0.777409i	$0.716533\pi$
$510$		0			0
$511$	3.57430	+	6.19086i	0.158118	+	0.273868i
$512$		0			0
$513$	−4.12312	+	2.38049i	−0.182040	+	0.105101i
$514$		0			0
$515$		−	29.6746i		−	1.30762i
$516$		0			0
$517$	1.32173	−	2.28930i	0.0581295	−	0.100683i
$518$		0			0
$519$	−8.33263			−0.365762
$520$		0			0
$521$	16.3253			0.715225			0.357613	−	0.933870i	$-0.383591\pi$
$521$	16.3253			0.715225			0.357613	+	0.933870i	$0.383591\pi$
$522$		0			0
$523$	−3.54473	+	6.13965i	−0.155000	+	0.268468i	−0.933059	−	0.359723i	$-0.882871\pi$
$523$	−3.54473	+	6.13965i	−0.155000	+	0.268468i	0.778059	+	0.628191i	$0.216204\pi$
$524$		0			0
$525$			18.0317i			0.786968i
$526$		0			0
$527$	−36.3805	+	21.0043i	−1.58476	+	0.914963i
$528$		0			0
$529$	4.05594	+	7.02510i	0.176345	+	0.305439i
$530$		0			0
$531$	13.4216	+	7.74899i	0.582449	+	0.336277i
$532$		0			0
$533$	−32.8796	+	28.5880i	−1.42417	+	1.23828i
$534$		0			0
$535$	11.9548	+	6.90209i	0.516850	+	0.298403i
$536$		0			0
$537$	−6.66368	−	11.5418i	−0.287559	−	0.498067i
$538$		0			0
$539$	−0.767631	+	0.443192i	−0.0330642	+	0.0190896i
$540$		0			0
$541$			25.5162i			1.09703i	0.836141	+	0.548515i	$0.184806\pi$
$541$			25.5162i			1.09703i	−0.836141	+	0.548515i	$0.815194\pi$
$542$		0			0
$543$	−2.39218	+	4.14338i	−0.102658	+	0.177809i
$544$		0			0
$545$	−37.5235			−1.60733
$546$		0			0
$547$	13.3073			0.568978			0.284489	−	0.958679i	$-0.408176\pi$
$547$	13.3073			0.568978			0.284489	+	0.958679i	$0.408176\pi$
$548$		0			0
$549$	1.62781	−	2.81945i	0.0694733	−	0.120331i
$550$		0			0
$551$		−	3.04952i		−	0.129914i
$552$		0			0
$553$	−0.656058	+	0.378775i	−0.0278984	+	0.0161072i
$554$		0			0
$555$	39.2559	+	67.9932i	1.66632	+	2.88615i
$556$		0			0
$557$	−14.7285	−	8.50353i	−0.624069	−	0.360306i	0.154383	−	0.988011i	$-0.450661\pi$
$557$	−14.7285	−	8.50353i	−0.624069	−	0.360306i	−0.778451	+	0.627705i	$0.783994\pi$
$558$		0			0
$559$	−12.8916	+	2.50732i	−0.545259	+	0.106048i
$560$		0			0
$561$	8.61140	+	4.97179i	0.363573	+	0.209909i
$562$		0			0
$563$	12.4596	+	21.5807i	0.525111	+	0.909519i	0.999572	+	0.0292428i	$0.00930961\pi$
$563$	12.4596	+	21.5807i	0.525111	+	0.909519i	−0.474461	+	0.880276i	$0.657357\pi$
$564$		0			0
$565$	15.3158	−	8.84257i	0.644340	−	0.372010i
$566$		0			0
$567$		−	10.8717i		−	0.456569i
$568$		0			0
$569$	2.94065	−	5.09335i	0.123278	−	0.213524i	−0.797780	−	0.602948i	$-0.793993\pi$
$569$	2.94065	−	5.09335i	0.123278	−	0.213524i	0.921059	+	0.389424i	$0.127326\pi$
$570$		0			0
$571$	8.92622			0.373551			0.186775	−	0.982403i	$-0.440196\pi$
$571$	8.92622			0.373551			0.186775	+	0.982403i	$0.440196\pi$
$572$		0			0
$573$	−25.7074			−1.07394
$574$		0			0
$575$	−15.3816	+	26.6417i	−0.641457	+	1.11104i
$576$		0			0
$577$		−	36.1933i		−	1.50675i	−0.657592	−	0.753374i	$-0.728425\pi$
$577$		−	36.1933i		−	1.50675i	0.657592	−	0.753374i	$-0.271575\pi$
$578$		0			0
$579$	27.5961	−	15.9326i	1.14685	−	0.662136i
$580$		0			0
$581$	2.38383	+	4.12892i	0.0988980	+	0.171296i
$582$		0			0
$583$	−3.77699	−	2.18065i	−0.156427	−	0.0903132i
$584$		0			0
$585$	−5.24383	−	26.9617i	−0.216806	−	1.11473i
$586$		0			0
$587$	−31.6008	−	18.2447i	−1.30431	−	0.753041i	−0.323166	−	0.946342i	$-0.604747\pi$
$587$	−31.6008	−	18.2447i	−1.30431	−	0.753041i	−0.981139	+	0.193301i	$0.938080\pi$
$588$		0			0
$589$	10.0732	+	17.4472i	0.415058	+	0.718901i
$590$		0			0
$591$	−44.9649	+	25.9605i	−1.84961	+	1.06787i
$592$		0			0
$593$			34.9930i			1.43699i	0.695533	+	0.718495i	$0.255168\pi$
$593$			34.9930i			1.43699i	−0.695533	+	0.718495i	$0.744832\pi$
$594$		0			0
$595$	−8.93270	+	15.4719i	−0.366205	+	0.634286i
$596$		0			0
$597$	7.12385			0.291560
$598$		0			0
$599$	32.5052			1.32812			0.664062	−	0.747677i	$-0.268831\pi$
$599$	32.5052			1.32812			0.664062	+	0.747677i	$0.268831\pi$
$600$		0			0
$601$	−10.0390	+	17.3881i	−0.409500	+	0.709275i	−0.994834	−	0.101518i	$-0.967630\pi$
$601$	−10.0390	+	17.3881i	−0.409500	+	0.709275i	0.585334	+	0.810792i	$0.300963\pi$
$602$		0			0
$603$			17.8225i			0.725788i
$604$		0			0
$605$	−31.8608	+	18.3949i	−1.29533	+	0.747858i
$606$		0			0
$607$	4.85800	+	8.41431i	0.197180	+	0.341526i	0.947613	−	0.319420i	$-0.103488\pi$
$607$	4.85800	+	8.41431i	0.197180	+	0.341526i	−0.750433	+	0.660947i	$0.770155\pi$
$608$		0			0
$609$	2.51093	+	1.44969i	0.101748	+	0.0587442i
$610$		0			0
$611$	−10.1674	−	3.49968i	−0.411327	−	0.141582i
$612$		0			0
$613$	−10.2898	−	5.94080i	−0.415600	−	0.239947i	0.277593	−	0.960699i	$-0.410463\pi$
$613$	−10.2898	−	5.94080i	−0.415600	−	0.239947i	−0.693193	+	0.720752i	$0.743797\pi$
$614$		0			0
$615$	−49.2184	−	85.2488i	−1.98468	−	3.43756i
$616$		0			0
$617$	−17.3105	+	9.99422i	−0.696895	+	0.402352i	−0.806190	−	0.591657i	$-0.798474\pi$
$617$	−17.3105	+	9.99422i	−0.696895	+	0.402352i	0.109295	+	0.994009i	$0.465141\pi$
$618$		0			0
$619$		−	41.7176i		−	1.67677i	−0.545078	−	0.838386i	$-0.683500\pi$
$619$		−	41.7176i		−	1.67677i	0.545078	−	0.838386i	$-0.316500\pi$
$620$		0			0
$621$	3.86129	−	6.68794i	0.154948	−	0.268378i
$622$		0			0
$623$	3.61884			0.144986
$624$		0			0
$625$	−1.29828			−0.0519312
$626$		0			0
$627$	2.38435	−	4.12982i	0.0952219	−	0.164929i
$628$		0			0
$629$			47.8066i			1.90618i
$630$		0			0
$631$	−15.2780	+	8.82074i	−0.608206	+	0.351148i	−0.772263	−	0.635303i	$-0.780875\pi$
$631$	−15.2780	+	8.82074i	−0.608206	+	0.351148i	0.164057	+	0.986451i	$0.447542\pi$
$632$		0			0
$633$	16.8084	+	29.1130i	0.668073	+	1.15714i
$634$		0			0
$635$	−38.3982	−	22.1692i	−1.52379	−	0.879759i
$636$		0			0
$637$	2.36575	+	2.72089i	0.0937343	+	0.107806i
$638$		0			0
$639$	−11.8124	−	6.81987i	−0.467290	−	0.269790i
$640$		0			0
$641$	−5.46012	−	9.45721i	−0.215662	−	0.373537i	0.737815	−	0.675003i	$-0.235858\pi$
$641$	−5.46012	−	9.45721i	−0.215662	−	0.373537i	−0.953477	+	0.301465i	$0.902524\pi$
$642$		0			0
$643$	−15.2725	+	8.81757i	−0.602288	+	0.347731i	−0.769941	−	0.638115i	$-0.779714\pi$
$643$	−15.2725	+	8.81757i	−0.602288	+	0.347731i	0.167653	+	0.985846i	$0.446381\pi$
$644$		0			0
$645$		−	29.6716i		−	1.16832i
$646$		0			0
$647$	−8.33632	+	14.4389i	−0.327735	+	0.567653i	−0.982062	−	0.188558i	$-0.939619\pi$
$647$	−8.33632	+	14.4389i	−0.327735	+	0.567653i	0.654327	+	0.756211i	$0.272952\pi$
$648$		0			0
$649$	6.49495			0.254949
$650$		0			0
$651$	−19.1544			−0.750719
$652$		0			0
$653$	3.38664	−	5.86584i	0.132530	−	0.229548i	−0.792121	−	0.610364i	$-0.791023\pi$
$653$	3.38664	−	5.86584i	0.132530	−	0.229548i	0.924651	+	0.380816i	$0.124357\pi$
$654$		0			0
$655$		−	29.5441i		−	1.15439i
$656$		0			0
$657$	13.0940	−	7.55983i	0.510846	−	0.294937i
$658$		0			0
$659$	16.7680	+	29.0431i	0.653190	+	1.13136i	0.982344	+	0.187082i	$0.0599031\pi$
$659$	16.7680	+	29.0431i	0.653190	+	1.13136i	−0.329154	+	0.944276i	$0.606764\pi$
$660$		0			0
$661$	−21.7945	−	12.5830i	−0.847707	−	0.489424i	0.0121696	−	0.999926i	$-0.496126\pi$
$661$	−21.7945	−	12.5830i	−0.847707	−	0.489424i	−0.859876	+	0.510502i	$0.829460\pi$
$662$		0			0
$663$	13.1643	−	38.2454i	0.511261	−	1.48533i
$664$		0			0
$665$	7.41995	+	4.28391i	0.287733	+	0.166123i
$666$		0			0
$667$	2.47325	+	4.28380i	0.0957647	+	0.165869i
$668$		0			0
$669$	−8.58060	+	4.95401i	−0.331745	+	0.191533i
$670$		0			0
$671$		−	1.36438i		−	0.0526713i
$672$		0			0
$673$	−0.927341	+	1.60620i	−0.0357464	+	0.0619145i	−0.883345	−	0.468723i	$-0.844714\pi$
$673$	−0.927341	+	1.60620i	−0.0357464	+	0.0619145i	0.847599	+	0.530638i	$0.178048\pi$
$674$		0			0
$675$	−15.9571			−0.614189
$676$		0			0
$677$	−14.7209			−0.565770			−0.282885	−	0.959154i	$-0.591291\pi$
$677$	−14.7209			−0.565770			−0.282885	+	0.959154i	$0.591291\pi$
$678$		0			0
$679$	−0.231650	+	0.401229i	−0.00888990	+	0.0153978i
$680$		0			0
$681$			30.6822i			1.17575i
$682$		0			0
$683$	−6.87930	+	3.97177i	−0.263229	+	0.151975i	−0.625807	−	0.779978i	$-0.715230\pi$
$683$	−6.87930	+	3.97177i	−0.263229	+	0.151975i	0.362578	+	0.931954i	$0.381897\pi$
$684$		0			0
$685$	−13.4266	−	23.2556i	−0.513005	−	0.888551i
$686$		0			0
$687$	−32.3529	−	18.6790i	−1.23434	−	0.712647i
$688$		0			0
$689$	−5.77394	+	16.7746i	−0.219969	+	0.639060i
$690$		0			0
$691$	−8.86002	−	5.11534i	−0.337051	−	0.194597i	0.321916	−	0.946768i	$-0.395673\pi$
$691$	−8.86002	−	5.11534i	−0.337051	−	0.194597i	−0.658967	+	0.752172i	$0.729006\pi$
$692$		0			0
$693$	0.937375	+	1.62358i	0.0356079	+	0.0616748i
$694$		0			0
$695$	52.0306	−	30.0399i	1.97363	−	1.13948i
$696$		0			0
$697$		−	59.9392i		−	2.27036i
$698$		0			0
$699$	18.6616	−	32.3228i	0.705845	−	1.22256i
$700$		0			0
$701$	−16.5978			−0.626891			−0.313445	−	0.949606i	$-0.601483\pi$
$701$	−16.5978			−0.626891			−0.313445	+	0.949606i	$0.601483\pi$
$702$		0			0
$703$	22.9269			0.864706
$704$		0			0
$705$	12.1468	−	21.0389i	0.457475	−	0.792371i
$706$		0			0
$707$		−	5.82303i		−	0.218998i
$708$		0			0
$709$	41.4531	−	23.9329i	1.55680	−	0.898820i	0.559242	−	0.829004i	$-0.311092\pi$
$709$	41.4531	−	23.9329i	1.55680	−	0.898820i	0.997560	−	0.0698158i	$-0.0222412\pi$
$710$		0			0
$711$	0.801130	+	1.38760i	0.0300447	+	0.0520390i
$712$		0			0
$713$	−28.3004	−	16.3393i	−1.05986	−	0.611910i
$714$		0			0
$715$	−7.55279	−	8.68661i	−0.282458	−	0.324861i
$716$		0			0
$717$	−59.5840	−	34.4008i	−2.22520	−	1.28472i
$718$		0			0
$719$	19.0461	+	32.9888i	0.710300	+	1.23028i	0.964744	+	0.263188i	$0.0847741\pi$
$719$	19.0461	+	32.9888i	0.710300	+	1.23028i	−0.254444	+	0.967087i	$0.581893\pi$
$720$		0			0
$721$	7.13508	−	4.11944i	0.265724	−	0.153416i
$722$		0			0
$723$			66.7511i			2.48250i
$724$		0			0
$725$	5.11047	−	8.85159i	0.189798	−	0.328740i
$726$		0			0
$727$	−15.4059			−0.571374			−0.285687	−	0.958323i	$-0.592222\pi$
$727$	−15.4059			−0.571374			−0.285687	+	0.958323i	$0.592222\pi$
$728$		0			0
$729$	−9.41460			−0.348689
$730$		0			0
$731$	9.03369	−	15.6468i	0.334123	−	0.578718i
$732$		0			0
$733$			11.6298i			0.429557i	0.976663	+	0.214778i	$0.0689029\pi$
$733$			11.6298i			0.429557i	−0.976663	+	0.214778i	$0.931097\pi$
$734$		0			0
$735$	−7.05461	+	4.07298i	−0.260213	+	0.150234i
$736$		0			0
$737$	3.73456	+	6.46844i	0.137564	+	0.238268i
$738$		0			0
$739$	−2.32875	−	1.34451i	−0.0856645	−	0.0494584i	0.456556	−	0.889695i	$-0.349083\pi$
$739$	−2.32875	−	1.34451i	−0.0856645	−	0.0494584i	−0.542220	+	0.840236i	$0.682416\pi$
$740$		0			0
$741$	−18.3416	−	6.31331i	−0.673794	−	0.231925i
$742$		0			0
$743$	2.13665	+	1.23360i	0.0783862	+	0.0452563i	0.538681	−	0.842510i	$-0.318923\pi$
$743$	2.13665	+	1.23360i	0.0783862	+	0.0452563i	−0.460295	+	0.887766i	$0.652256\pi$
$744$		0			0
$745$	4.54118	+	7.86556i	0.166376	+	0.288172i
$746$		0			0
$747$	8.73288	−	5.04193i	0.319519	−	0.184475i
$748$		0			0
$749$			3.83260i			0.140040i
$750$		0			0
$751$	18.9592	−	32.8383i	0.691832	−	1.19829i	−0.279405	−	0.960173i	$-0.590137\pi$
$751$	18.9592	−	32.8383i	0.691832	−	1.19829i	0.971237	−	0.238115i	$-0.0765295\pi$
$752$		0			0
$753$	29.3623			1.07002
$754$		0			0
$755$	−57.2583			−2.08384
$756$		0			0
$757$	−17.3225	+	30.0035i	−0.629598	+	1.09050i	0.358034	+	0.933709i	$0.383447\pi$
$757$	−17.3225	+	30.0035i	−0.629598	+	1.09050i	−0.987632	+	0.156788i	$0.949886\pi$
$758$		0			0
$759$			7.73512i			0.280767i
$760$		0			0
$761$	19.7969	−	11.4297i	0.717636	−	0.414328i	−0.0962458	−	0.995358i	$-0.530683\pi$
$761$	19.7969	−	11.4297i	0.717636	−	0.414328i	0.813882	+	0.581030i	$0.197350\pi$
$762$		0			0
$763$	−5.20902	−	9.02229i	−0.188579	−	0.326629i
$764$		0			0
$765$	32.7239	+	18.8931i	1.18313	+	0.683083i
$766$		0			0
$767$	−5.04386	−	25.9336i	−0.182123	−	0.936408i
$768$		0			0
$769$	−44.8839	−	25.9137i	−1.61855	−	0.934473i	−0.987294	−	0.158902i	$-0.949205\pi$
$769$	−44.8839	−	25.9137i	−1.61855	−	0.934473i	−0.631260	−	0.775571i	$-0.717462\pi$
$770$		0			0
$771$	5.18507	+	8.98080i	0.186736	+	0.323436i
$772$		0			0
$773$	−4.93605	+	2.84983i	−0.177538	+	0.102501i	−0.586135	−	0.810213i	$-0.699351\pi$
$773$	−4.93605	+	2.84983i	−0.177538	+	0.102501i	0.408598	+	0.912715i	$0.366018\pi$
$774$		0			0
$775$			67.5234i			2.42551i
$776$		0			0
$777$	−10.8990	+	18.8777i	−0.391000	+	0.677232i
$778$		0			0
$779$	−28.7454			−1.02991
$780$		0			0
$781$	−5.71619			−0.204541
$782$		0			0
$783$	−1.28289	+	2.22204i	−0.0458469	+	0.0794092i
$784$		0			0
$785$		−	46.7622i		−	1.66902i
$786$		0			0
$787$	14.5614	−	8.40705i	0.519059	−	0.299679i	−0.217490	−	0.976062i	$-0.569787\pi$
$787$	14.5614	−	8.40705i	0.519059	−	0.299679i	0.736550	+	0.676384i	$0.236454\pi$
$788$		0			0
$789$	3.01364	+	5.21977i	0.107288	+	0.185829i
$790$		0			0
$791$	4.25228	+	2.45505i	0.151194	+	0.0872917i
$792$		0			0
$793$	−5.44781	+	1.05955i	−0.193457	+	0.0376258i
$794$		0			0
$795$	−34.7109	−	20.0404i	−1.23107	−	0.710759i
$796$		0			0
$797$	21.0651	+	36.4858i	0.746163	+	1.29239i	0.949650	+	0.313314i	$0.101439\pi$
$797$	21.0651	+	36.4858i	0.746163	+	1.29239i	−0.203487	+	0.979078i	$0.565227\pi$
$798$		0			0
$799$	12.8108	−	7.39632i	0.453214	−	0.261663i
$800$		0			0
$801$		−	7.65403i		−	0.270442i
$802$		0			0
$803$	3.16820	−	5.48748i	0.111803	−	0.193649i
$804$		0			0
$805$	−13.8975			−0.489823
$806$		0			0
$807$	−26.9716			−0.949445
$808$		0			0
$809$	15.0843	−	26.1268i	0.530336	−	0.918569i	−0.469037	−	0.883178i	$-0.655399\pi$
$809$	15.0843	−	26.1268i	0.530336	−	0.918569i	0.999374	−	0.0353910i	$-0.0112677\pi$
$810$		0			0
$811$			23.7929i			0.835480i	0.908567	+	0.417740i	$0.137178\pi$
$811$			23.7929i			0.835480i	−0.908567	+	0.417740i	$0.862822\pi$
$812$		0			0
$813$	25.5178	−	14.7327i	0.894950	−	0.516699i
$814$		0			0
$815$	−4.17712	−	7.23499i	−0.146318	−	0.253431i
$816$		0			0
$817$	−7.50384	−	4.33234i	−0.262526	−	0.151569i
$818$		0			0
$819$	5.75483	−	5.00368i	0.201090	−	0.174843i
$820$		0			0
$821$	−31.0771	−	17.9424i	−1.08460	−	0.626193i	−0.152465	−	0.988309i	$-0.548721\pi$
$821$	−31.0771	−	17.9424i	−1.08460	−	0.626193i	−0.932133	+	0.362116i	$0.882054\pi$
$822$		0			0
$823$	6.11728	+	10.5954i	0.213235	+	0.369334i	0.952725	−	0.303833i	$-0.0982666\pi$
$823$	6.11728	+	10.5954i	0.213235	+	0.369334i	−0.739490	+	0.673167i	$0.764933\pi$
$824$		0			0
$825$	13.8417	−	7.99151i	0.481906	−	0.278229i
$826$		0			0
$827$		−	27.3474i		−	0.950962i	−0.879726	−	0.475481i	$-0.842274\pi$
$827$		−	27.3474i		−	0.950962i	0.879726	−	0.475481i	$-0.157726\pi$
$828$		0			0
$829$	11.7869	−	20.4155i	0.409376	−	0.709060i	−0.585444	−	0.810713i	$-0.699080\pi$
$829$	11.7869	−	20.4155i	0.409376	−	0.709060i	0.994820	+	0.101653i	$0.0324132\pi$
$830$		0			0
$831$	48.3199			1.67620
$832$		0			0
$833$	−4.96016			−0.171859
$834$		0			0
$835$	24.8376	−	43.0199i	0.859539	−	1.48877i
$836$		0			0
$837$		−	16.9506i		−	0.585898i
$838$		0			0
$839$	−9.16975	+	5.29416i	−0.316575	+	0.182775i	−0.649865	−	0.760050i	$-0.725175\pi$
$839$	−9.16975	+	5.29416i	−0.316575	+	0.182775i	0.333290	+	0.942824i	$0.391841\pi$
$840$		0			0
$841$	13.6783	+	23.6915i	0.471665	+	0.816947i
$842$		0			0
$843$	−33.8214	−	19.5268i	−1.16487	−	0.672538i
$844$		0			0
$845$	−28.8193	+	36.9033i	−0.991414	+	1.26951i
$846$		0			0
$847$	−8.84586	−	5.10716i	−0.303947	−	0.175484i
$848$		0			0
$849$	−24.0189	−	41.6020i	−0.824328	−	1.42778i
$850$		0			0
$851$	−32.2065	+	18.5944i	−1.10402	+	0.637408i
$852$		0			0
$853$			21.3925i			0.732464i	0.930524	+	0.366232i	$0.119352\pi$
$853$			21.3925i			0.732464i	−0.930524	+	0.366232i	$0.880648\pi$
$854$		0			0
$855$	9.06070	−	15.6936i	0.309870	−	0.536710i
$856$		0			0
$857$	−7.22129			−0.246675			−0.123337	−	0.992365i	$-0.539360\pi$
$857$	−7.22129			−0.246675			−0.123337	+	0.992365i	$0.539360\pi$
$858$		0			0
$859$	−57.1073			−1.94848			−0.974238	−	0.225524i	$-0.927590\pi$
$859$	−57.1073			−1.94848			−0.974238	+	0.225524i	$0.927590\pi$
$860$		0			0
$861$	13.6650	−	23.6685i	0.465703	−	0.806621i
$862$		0			0
$863$			51.3361i			1.74750i	0.486374	+	0.873751i	$0.338319\pi$
$863$			51.3361i			1.74750i	−0.486374	+	0.873751i	$0.661681\pi$
$864$		0			0
$865$	−11.4922	+	6.63505i	−0.390748	+	0.225598i
$866$		0			0
$867$	8.59788	+	14.8920i	0.291999	+	0.505758i
$868$		0			0
$869$	0.581520	+	0.335741i	0.0197267	+	0.0113892i
$870$		0			0
$871$	22.9276	−	19.9349i	0.776871	−	0.675470i
$872$		0			0
$873$	0.848621	+	0.489952i	0.0287215	+	0.0165824i
$874$		0			0
$875$	5.35371	+	9.27291i	0.180989	+	0.313481i
$876$		0			0
$877$	−18.5570	+	10.7139i	−0.626624	+	0.361781i	−0.779443	−	0.626473i	$-0.784498\pi$
$877$	−18.5570	+	10.7139i	−0.626624	+	0.361781i	0.152820	+	0.988254i	$0.451165\pi$
$878$		0			0
$879$			0.950027i			0.0320436i
$880$		0			0
$881$	14.5309	−	25.1683i	0.489560	−	0.847943i	−0.510368	−	0.859956i	$-0.670491\pi$
$881$	14.5309	−	25.1683i	0.489560	−	0.847943i	0.999928	+	0.0120134i	$0.00382406\pi$
$882$		0			0
$883$	−4.83594			−0.162742			−0.0813711	−	0.996684i	$-0.525930\pi$
$883$	−4.83594			−0.162742			−0.0813711	+	0.996684i	$0.525930\pi$
$884$		0			0
$885$	59.6892			2.00643
$886$		0			0
$887$	−12.4949	+	21.6418i	−0.419538	+	0.726660i	−0.995893	−	0.0905387i	$-0.971141\pi$
$887$	−12.4949	+	21.6418i	−0.419538	+	0.726660i	0.576355	+	0.817199i	$0.304474\pi$
$888$		0			0
$889$		−	12.3102i		−	0.412869i
$890$		0			0
$891$	−8.34546	+	4.81826i	−0.279584	+	0.161418i
$892$		0			0
$893$	−3.54710	−	6.14376i	−0.118699	−	0.205593i
$894$		0			0
$895$	−18.3809	−	10.6122i	−0.614406	−	0.354727i
$896$		0			0
$897$	30.8855	−	6.00696i	1.03124	−	0.200567i
$898$		0			0
$899$	9.40269	+	5.42865i	0.313597	+	0.181055i
$900$		0			0
$901$	−12.2028	−	21.1359i	−0.406534	−	0.704138i
$902$		0			0
$903$	7.13436	−	4.11902i	0.237417	−	0.137073i
$904$		0			0
$905$			7.61931i			0.253274i
$906$		0			0
$907$	−7.52060	+	13.0261i	−0.249717	+	0.432523i	−0.963447	−	0.267898i	$-0.913671\pi$
$907$	−7.52060	+	13.0261i	−0.249717	+	0.432523i	0.713730	+	0.700421i	$0.247004\pi$
$908$		0			0
$909$	−12.3160			−0.408497
$910$		0			0
$911$	9.22150			0.305522			0.152761	−	0.988263i	$-0.451184\pi$
$911$	9.22150			0.305522			0.152761	+	0.988263i	$0.451184\pi$
$912$		0			0
$913$	2.11299	−	3.65981i	0.0699298	−	0.121122i
$914$		0			0
$915$		−	12.5388i		−	0.414519i
$916$		0			0
$917$	7.10371	−	4.10133i	0.234585	−	0.135438i
$918$		0			0
$919$	−22.5402	−	39.0407i	−0.743531	−	1.28783i	−0.950878	−	0.309567i	$-0.899816\pi$
$919$	−22.5402	−	39.0407i	−0.743531	−	1.28783i	0.207346	−	0.978268i	$-0.433517\pi$
$920$		0			0
$921$	−27.5791	−	15.9228i	−0.908762	−	0.524674i
$922$		0			0
$923$	4.43910	+	22.8241i	0.146115	+	0.751265i
$924$		0			0
$925$	66.5480	+	38.4215i	2.18808	+	1.26329i
$926$		0			0
$927$	−8.71284	−	15.0911i	−0.286167	−	0.495656i
$928$		0			0
$929$	−40.6313	+	23.4585i	−1.33307	+	0.769647i	−0.985769	−	0.168107i	$-0.946235\pi$
$929$	−40.6313	+	23.4585i	−1.33307	+	0.769647i	−0.347300	+	0.937754i	$0.612901\pi$
$930$		0			0
$931$			2.37878i			0.0779612i
$932$		0			0
$933$	11.7434	−	20.3401i	0.384461	−	0.665906i
$934$		0			0
$935$	15.8356			0.517880
$936$		0			0
$937$	−28.3912			−0.927501			−0.463750	−	0.885966i	$-0.653497\pi$
$937$	−28.3912			−0.927501			−0.463750	+	0.885966i	$0.653497\pi$
$938$		0			0
$939$	7.74342	−	13.4120i	0.252697	−	0.437684i
$940$		0			0
$941$		−	17.8718i		−	0.582603i	−0.956631	−	0.291302i	$-0.905912\pi$
$941$		−	17.8718i		−	0.582603i	0.956631	−	0.291302i	$-0.0940883\pi$
$942$		0			0
$943$	40.3800	−	23.3134i	1.31495	−	0.759188i
$944$		0			0
$945$	−3.60437	−	6.24295i	−0.117250	−	0.203083i
$946$		0			0
$947$	−8.24659	−	4.76117i	−0.267978	−	0.154717i	0.359990	−	0.932956i	$-0.382780\pi$
$947$	−8.24659	−	4.76117i	−0.267978	−	0.154717i	−0.627969	+	0.778239i	$0.716113\pi$
$948$		0			0
$949$	−24.3713	−	8.38878i	−0.791125	−	0.272311i
$950$		0			0
$951$	−1.37350	−	0.792989i	−0.0445387	−	0.0257144i
$952$		0			0
$953$	−6.70900	−	11.6203i	−0.217326	−	0.376419i	0.736664	−	0.676259i	$-0.236400\pi$
$953$	−6.70900	−	11.6203i	−0.217326	−	0.376419i	−0.953990	+	0.299840i	$0.903067\pi$
$954$		0			0
$955$	−35.4552	+	20.4701i	−1.14730	+	0.662397i
$956$		0			0
$957$		−	2.56996i		−	0.0830749i
$958$		0			0
$959$	3.72778	−	6.45670i	0.120376	−	0.208498i
$960$		0			0
$961$	−40.7275			−1.31379
$962$		0			0
$963$	8.10615			0.261217
$964$		0			0
$965$	25.3734	−	43.9480i	0.816798	−	1.41474i
$966$		0			0
$967$		−	12.9316i		−	0.415851i	−0.978145	−	0.207926i	$-0.933329\pi$
$967$		−	12.9316i		−	0.415851i	0.978145	−	0.207926i	$-0.0666712\pi$
$968$		0			0
$969$	23.1103	−	13.3427i	0.742409	−	0.428630i
$970$		0			0
$971$	23.7607	+	41.1547i	0.762516	+	1.32072i	0.941550	+	0.336874i	$0.109370\pi$
$971$	23.7607	+	41.1547i	0.762516	+	1.32072i	−0.179034	+	0.983843i	$0.557297\pi$
$972$		0			0
$973$	14.4458	+	8.34028i	0.463111	+	0.267377i
$974$		0			0
$975$	−42.6584	−	49.0623i	−1.36616	−	1.57125i
$976$		0			0
$977$	31.6049	+	18.2471i	1.01113	+	0.583776i	0.911522	−	0.411251i	$-0.134908\pi$
$977$	31.6049	+	18.2471i	1.01113	+	0.583776i	0.0996074	+	0.995027i	$0.468241\pi$
$978$		0			0
$979$	−1.60384	−	2.77793i	−0.0512589	−	0.0887831i
$980$		0			0
$981$	−19.0826	+	11.0174i	−0.609261	+	0.351757i
$982$		0			0
$983$			44.1843i			1.40926i	0.709576	+	0.704629i	$0.248887\pi$
$983$			44.1843i			1.40926i	−0.709576	+	0.704629i	$0.751113\pi$
$984$		0			0
$985$	−41.3433	+	71.6087i	−1.31731	+	2.28164i
$986$		0			0
$987$	6.74490			0.214692
$988$		0			0
$989$	14.0546			0.446911
$990$		0			0
$991$	−25.3549	+	43.9159i	−0.805424	+	1.39504i	0.110581	+	0.993867i	$0.464729\pi$
$991$	−25.3549	+	43.9159i	−0.805424	+	1.39504i	−0.916005	+	0.401168i	$0.868604\pi$
$992$		0			0
$993$			9.49586i			0.301342i
$994$		0			0
$995$	9.82511	−	5.67253i	0.311477	−	0.179831i
$996$		0			0
$997$	25.1384	+	43.5410i	0.796141	+	1.37896i	0.922112	+	0.386923i	$0.126462\pi$
$997$	25.1384	+	43.5410i	0.796141	+	1.37896i	−0.125971	+	0.992034i	$0.540205\pi$
$998$		0			0
$999$	−16.7057	−	9.64505i	−0.528546	−	0.305156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.c.225.5		12
4.3	odd	2		91.2.q.a.43.6	yes	12
12.11	even	2		819.2.ct.a.316.1		12
13.10	even	6	inner	1456.2.cc.c.673.5		12
28.3	even	6		637.2.u.i.30.1		12
28.11	odd	6		637.2.u.h.30.1		12
28.19	even	6		637.2.k.g.459.1		12
28.23	odd	6		637.2.k.h.459.1		12
28.27	even	2		637.2.q.h.589.6		12
52.7	even	12		1183.2.a.p.1.5		6
52.19	even	12		1183.2.a.m.1.2		6
52.23	odd	6		91.2.q.a.36.6	✓	12
52.35	odd	6		1183.2.c.i.337.2		12
52.43	odd	6		1183.2.c.i.337.11		12
156.23	even	6		819.2.ct.a.127.1		12
364.23	odd	6		637.2.u.h.361.1		12
364.75	even	6		637.2.u.i.361.1		12
364.111	odd	12		8281.2.a.ch.1.5		6
364.179	odd	6		637.2.k.h.569.6		12
364.279	odd	12		8281.2.a.by.1.2		6
364.283	even	6		637.2.k.g.569.6		12
364.335	even	6		637.2.q.h.491.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.6	✓	12	52.23	odd	6
91.2.q.a.43.6	yes	12	4.3	odd	2
637.2.k.g.459.1		12	28.19	even	6
637.2.k.g.569.6		12	364.283	even	6
637.2.k.h.459.1		12	28.23	odd	6
637.2.k.h.569.6		12	364.179	odd	6
637.2.q.h.491.6		12	364.335	even	6
637.2.q.h.589.6		12	28.27	even	2
637.2.u.h.30.1		12	28.11	odd	6
637.2.u.h.361.1		12	364.23	odd	6
637.2.u.i.30.1		12	28.3	even	6
637.2.u.i.361.1		12	364.75	even	6
819.2.ct.a.127.1		12	156.23	even	6
819.2.ct.a.316.1		12	12.11	even	2
1183.2.a.m.1.2		6	52.19	even	12
1183.2.a.p.1.5		6	52.7	even	12
1183.2.c.i.337.2		12	52.35	odd	6
1183.2.c.i.337.11		12	52.43	odd	6
1456.2.cc.c.225.5		12	1.1	even	1	trivial
1456.2.cc.c.673.5		12	13.10	even	6	inner
8281.2.a.by.1.2		6	364.279	odd	12
8281.2.a.ch.1.5		6	364.111	odd	12

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.13082 - 1.95864i) q^{3} -3.60178i q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.05753 - 1.83169i) q^{9} +O(q^{10})\)	\(q+(1.13082 - 1.95864i) q^{3} -3.60178i q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.05753 - 1.83169i) q^{9} +(-0.767631 - 0.443192i) q^{11} +(-1.17349 + 3.40924i) q^{13} +(-7.05461 - 4.07298i) q^{15} +(-2.48008 - 4.29563i) q^{17} +(-2.06008 + 1.18939i) q^{19} -2.26165i q^{21} +(1.92926 - 3.34157i) q^{23} -7.97282 q^{25} +2.00144 q^{27} +(-0.640986 + 1.11022i) q^{29} -8.46921i q^{31} +(-1.73611 + 1.00234i) q^{33} +(-1.80089 - 3.11923i) q^{35} +(-8.34686 - 4.81906i) q^{37} +(5.35049 + 6.15370i) q^{39} +(10.4652 + 6.04207i) q^{41} +(1.82125 + 3.15450i) q^{43} +(-6.59734 + 3.80898i) q^{45} +2.98229i q^{47} +(0.500000 - 0.866025i) q^{49} -11.2181 q^{51} +4.92032 q^{53} +(-1.59628 + 2.76484i) q^{55} +5.37995i q^{57} +(-6.34577 + 3.66373i) q^{59} +(0.769632 + 1.33304i) q^{61} +(-1.83169 - 1.05753i) q^{63} +(12.2793 + 4.22664i) q^{65} +(-7.29756 - 4.21325i) q^{67} +(-4.36330 - 7.55745i) q^{69} +(5.58490 - 3.22444i) q^{71} +7.14859i q^{73} +(-9.01585 + 15.6159i) q^{75} -0.886384 q^{77} -0.757551 q^{79} +(5.43585 - 9.41518i) q^{81} +4.76766i q^{83} +(-15.4719 + 8.93270i) q^{85} +(1.44969 + 2.51093i) q^{87} +(3.13400 + 1.80942i) q^{89} +(0.688351 + 3.53923i) q^{91} +(-16.5882 - 9.57719i) q^{93} +(4.28391 + 7.41995i) q^{95} +(-0.401229 + 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^9	\( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

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Database

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