LMFDB - Embedded newform 672.3.bh.a.577.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,3,Mod(481,672)] 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("672.481"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	672.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-24,0,0,0,-12,0,24,0,-12,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$18.3106737650$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 76 x^{14} - 392 x^{13} + 1982 x^{12} - 7160 x^{11} + 23796 x^{10} - 61736 x^{9} + \cdots + 16807 $ x^16 - 8x^15 + 76x^14 - 392x^13 + 1982x^12 - 7160x^11 + 23796x^10 - 61736x^9 + 141869x^8 - 261520x^7 + 411696x^6 - 515296x^5 + 526280x^4 - 407176x^3 + 235396x^2 - 87808*x + 16807
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{18}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			577.5
Root			$0.500000 - 0.920550i$ of defining polynomial
Character	$\chi$	$=$	672.577
Dual form			672.3.bh.a.481.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{3} +(3.54218 - 2.04508i) q^{5} +(-3.04344 - 6.30377i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-10.0406 + 17.3908i) q^{11} -21.9625i q^{13} -7.08436 q^{15} +(-10.9033 - 6.29500i) q^{17} +(-4.58876 + 2.64932i) q^{19} +(-0.894071 + 12.0913i) q^{21} +(8.75901 + 15.1710i) q^{23} +(-4.13532 + 7.16258i) q^{25} -5.19615i q^{27} +1.81648 q^{29} +(-37.2378 - 21.4993i) q^{31} +(30.1218 - 17.3908i) q^{33} +(-23.6721 - 16.1050i) q^{35} +(19.1992 + 33.2540i) q^{37} +(-19.0200 + 32.9437i) q^{39} -8.75947i q^{41} +33.6352 q^{43} +(10.6265 + 6.13523i) q^{45} +(-45.2937 + 26.1504i) q^{47} +(-30.4750 + 38.3702i) q^{49} +(10.9033 + 18.8850i) q^{51} +(-7.44072 + 12.8877i) q^{53} +82.1352i q^{55} +9.17752 q^{57} +(-16.2209 - 9.36515i) q^{59} +(-14.1845 + 8.18944i) q^{61} +(11.8125 - 17.3627i) q^{63} +(-44.9149 - 77.7949i) q^{65} +(-56.5994 + 98.0330i) q^{67} -30.3421i q^{69} -77.8034 q^{71} +(-113.411 - 65.4779i) q^{73} +(12.4060 - 7.16258i) q^{75} +(140.186 + 10.3658i) q^{77} +(-56.9426 - 98.6274i) q^{79} +(-4.50000 + 7.79423i) q^{81} -70.7869i q^{83} -51.4951 q^{85} +(-2.72472 - 1.57312i) q^{87} +(-126.937 + 73.2873i) q^{89} +(-138.446 + 66.8413i) q^{91} +(37.2378 + 64.4978i) q^{93} +(-10.8361 + 18.7687i) q^{95} -22.0792i q^{97} -60.2436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 12 q^{7} + 24 q^{9} - 12 q^{11} - 48 q^{17} - 60 q^{19} + 24 q^{21} - 48 q^{23} + 52 q^{25} - 64 q^{29} - 60 q^{31} + 36 q^{33} - 4 q^{37} + 12 q^{39} + 72 q^{43} + 120 q^{47} - 8 q^{49}+ \cdots - 72 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 - 12 * q^7 + 24 * q^9 - 12 * q^11 - 48 * q^17 - 60 * q^19 + 24 * q^21 - 48 * q^23 + 52 * q^25 - 64 * q^29 - 60 * q^31 + 36 * q^33 - 4 * q^37 + 12 * q^39 + 72 * q^43 + 120 * q^47 - 8 * q^49 + 48 * q^51 - 72 * q^53 + 120 * q^57 - 228 * q^59 + 72 * q^61 - 36 * q^63 - 40 * q^65 + 12 * q^67 - 528 * q^71 - 36 * q^73 - 156 * q^75 - 96 * q^77 - 204 * q^79 - 72 * q^81 - 480 * q^85 + 96 * q^87 - 192 * q^89 - 276 * q^91 + 60 * q^93 - 48 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$		0			0
$5$	3.54218	−	2.04508i	0.708436	−	0.409015i	−0.102046	−	0.994780i	$-0.532539\pi$
$5$	3.54218	−	2.04508i	0.708436	−	0.409015i	0.810481	+	0.585764i	$0.199206\pi$
$6$		0			0
$7$	−3.04344	−	6.30377i	−0.434776	−	0.900538i
$7$	−3.04344	−	6.30377i	−0.434776	−	0.900538i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−10.0406	+	17.3908i	−0.912782	+	1.58098i	−0.102665	+	0.994716i	$0.532737\pi$
$11$	−10.0406	+	17.3908i	−0.912782	+	1.58098i	−0.810117	+	0.586268i	$0.800597\pi$
$12$		0			0
$13$		−	21.9625i		−	1.68942i	−0.535225	−	0.844710i	$-0.679773\pi$
$13$		−	21.9625i		−	1.68942i	0.535225	−	0.844710i	$-0.320227\pi$
$14$		0			0
$15$	−7.08436			−0.472290
$16$		0			0
$17$	−10.9033	−	6.29500i	−0.641368	−	0.370294i	0.143773	−	0.989611i	$-0.454076\pi$
$17$	−10.9033	−	6.29500i	−0.641368	−	0.370294i	−0.785141	+	0.619316i	$0.787410\pi$
$18$		0			0
$19$	−4.58876	+	2.64932i	−0.241514	+	0.139438i	−0.615872	−	0.787846i	$-0.711196\pi$
$19$	−4.58876	+	2.64932i	−0.241514	+	0.139438i	0.374359	+	0.927284i	$0.377863\pi$
$20$		0			0
$21$	−0.894071	+	12.0913i	−0.0425748	+	0.575778i
$22$		0			0
$23$	8.75901	+	15.1710i	0.380826	+	0.659611i	0.991181	−	0.132518i	$-0.0423062\pi$
$23$	8.75901	+	15.1710i	0.380826	+	0.659611i	−0.610354	+	0.792129i	$0.708973\pi$
$24$		0			0
$25$	−4.13532	+	7.16258i	−0.165413	+	0.286503i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	1.81648			0.0626374			0.0313187	−	0.999509i	$-0.490029\pi$
$29$	1.81648			0.0626374			0.0313187	+	0.999509i	$0.490029\pi$
$30$		0			0
$31$	−37.2378	−	21.4993i	−1.20122	−	0.693525i	−0.240394	−	0.970675i	$-0.577277\pi$
$31$	−37.2378	−	21.4993i	−1.20122	−	0.693525i	−0.960827	+	0.277150i	$0.910610\pi$
$32$		0			0
$33$	30.1218	−	17.3908i	0.912782	−	0.526995i
$34$		0			0
$35$	−23.6721	−	16.1050i	−0.676345	−	0.460143i
$36$		0			0
$37$	19.1992	+	33.2540i	0.518898	+	0.898758i	0.999759	+	0.0219609i	$0.00699093\pi$
$37$	19.1992	+	33.2540i	0.518898	+	0.898758i	−0.480861	+	0.876797i	$0.659676\pi$
$38$		0			0
$39$	−19.0200	+	32.9437i	−0.487693	+	0.844710i
$40$		0			0
$41$		−	8.75947i		−	0.213646i	−0.994278	−	0.106823i	$-0.965932\pi$
$41$		−	8.75947i		−	0.213646i	0.994278	−	0.106823i	$-0.0340678\pi$
$42$		0			0
$43$	33.6352			0.782213			0.391107	−	0.920345i	$-0.372092\pi$
$43$	33.6352			0.782213			0.391107	+	0.920345i	$0.372092\pi$
$44$		0			0
$45$	10.6265	+	6.13523i	0.236145	+	0.136338i
$46$		0			0
$47$	−45.2937	+	26.1504i	−0.963697	+	0.556391i	−0.897309	−	0.441403i	$-0.854481\pi$
$47$	−45.2937	+	26.1504i	−0.963697	+	0.556391i	−0.0663879	+	0.997794i	$0.521147\pi$
$48$		0			0
$49$	−30.4750	+	38.3702i	−0.621939	+	0.783066i
$50$		0			0
$51$	10.9033	+	18.8850i	0.213789	+	0.370294i
$52$		0			0
$53$	−7.44072	+	12.8877i	−0.140391	+	0.243164i	−0.927644	−	0.373466i	$-0.878169\pi$
$53$	−7.44072	+	12.8877i	−0.140391	+	0.243164i	0.787253	+	0.616630i	$0.211503\pi$
$54$		0			0
$55$			82.1352i			1.49337i
$56$		0			0
$57$	9.17752			0.161009
$58$		0			0
$59$	−16.2209	−	9.36515i	−0.274931	−	0.158731i	0.356195	−	0.934411i	$-0.384074\pi$
$59$	−16.2209	−	9.36515i	−0.274931	−	0.158731i	−0.631126	+	0.775680i	$0.717407\pi$
$60$		0			0
$61$	−14.1845	+	8.18944i	−0.232533	+	0.134253i	−0.611740	−	0.791059i	$-0.709530\pi$
$61$	−14.1845	+	8.18944i	−0.232533	+	0.134253i	0.379207	+	0.925312i	$0.376197\pi$
$62$		0			0
$63$	11.8125	−	17.3627i	0.187500	−	0.275599i
$64$		0			0
$65$	−44.9149	−	77.7949i	−0.690999	−	1.19684i
$66$		0			0
$67$	−56.5994	+	98.0330i	−0.844767	+	1.46318i	0.0410559	+	0.999157i	$0.486928\pi$
$67$	−56.5994	+	98.0330i	−0.844767	+	1.46318i	−0.885823	+	0.464023i	$0.846406\pi$
$68$		0			0
$69$		−	30.3421i		−	0.439740i
$70$		0			0
$71$	−77.8034			−1.09582			−0.547911	−	0.836537i	$-0.684577\pi$
$71$	−77.8034			−1.09582			−0.547911	+	0.836537i	$0.684577\pi$
$72$		0			0
$73$	−113.411	−	65.4779i	−1.55358	−	0.896958i	−0.997846	−	0.0655949i	$-0.979105\pi$
$73$	−113.411	−	65.4779i	−1.55358	−	0.896958i	−0.555730	−	0.831363i	$-0.687561\pi$
$74$		0			0
$75$	12.4060	−	7.16258i	0.165413	−	0.0955011i
$76$		0			0
$77$	140.186	+	10.3658i	1.82059	+	0.134620i
$78$		0			0
$79$	−56.9426	−	98.6274i	−0.720792	−	1.24845i	−0.960683	−	0.277648i	$-0.910445\pi$
$79$	−56.9426	−	98.6274i	−0.720792	−	1.24845i	0.239891	−	0.970800i	$-0.422888\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	70.7869i		−	0.852854i	−0.904522	−	0.426427i	$-0.859772\pi$
$83$		−	70.7869i		−	0.852854i	0.904522	−	0.426427i	$-0.140228\pi$
$84$		0			0
$85$	−51.4951			−0.605824
$86$		0			0
$87$	−2.72472	−	1.57312i	−0.0313187	−	0.0180818i
$88$		0			0
$89$	−126.937	+	73.2873i	−1.42626	+	0.823453i	−0.996823	−	0.0796430i	$-0.974622\pi$
$89$	−126.937	+	73.2873i	−1.42626	+	0.823453i	−0.429439	+	0.903096i	$0.641289\pi$
$90$		0			0
$91$	−138.446	+	66.8413i	−1.52139	+	0.734520i
$92$		0			0
$93$	37.2378	+	64.4978i	0.400407	+	0.693525i
$94$		0			0
$95$	−10.8361	+	18.7687i	−0.114065	+	0.197566i
$96$		0			0
$97$		−	22.0792i		−	0.227621i	−0.993502	−	0.113810i	$-0.963694\pi$
$97$		−	22.0792i		−	0.227621i	0.993502	−	0.113810i	$-0.0363057\pi$
$98$		0			0
$99$	−60.2436			−0.608521
$100$		0			0
$101$	158.719	+	91.6365i	1.57148	+	0.907292i	0.995989	+	0.0894806i	$0.0285207\pi$
$101$	158.719	+	91.6365i	1.57148	+	0.907292i	0.575487	+	0.817811i	$0.304813\pi$
$102$		0			0
$103$	−22.2167	+	12.8268i	−0.215696	+	0.124532i	−0.603956	−	0.797018i	$-0.706410\pi$
$103$	−22.2167	+	12.8268i	−0.215696	+	0.124532i	0.388260	+	0.921550i	$0.373076\pi$
$104$		0			0
$105$	21.5608	+	44.6581i	0.205341	+	0.425316i
$106$		0			0
$107$	8.66237	+	15.0037i	0.0809567	+	0.140221i	0.903661	−	0.428248i	$-0.140869\pi$
$107$	8.66237	+	15.0037i	0.0809567	+	0.140221i	−0.822704	+	0.568469i	$0.807536\pi$
$108$		0			0
$109$	−71.2088	+	123.337i	−0.653291	+	1.13153i	0.329028	+	0.944320i	$0.393279\pi$
$109$	−71.2088	+	123.337i	−0.653291	+	1.13153i	−0.982319	+	0.187214i	$0.940054\pi$
$110$		0			0
$111$		−	66.5081i		−	0.599172i
$112$		0			0
$113$	183.612			1.62488			0.812442	−	0.583042i	$-0.198138\pi$
$113$	183.612			1.62488			0.812442	+	0.583042i	$0.198138\pi$
$114$		0			0
$115$	62.0519	+	35.8257i	0.539582	+	0.311528i
$116$		0			0
$117$	57.0601	−	32.9437i	0.487693	−	0.281570i
$118$		0			0
$119$	−6.49886	+	87.8901i	−0.0546123	+	0.738572i
$120$		0			0
$121$	−141.127	−	244.439i	−1.16634	−	2.02016i
$122$		0			0
$123$	−7.58592	+	13.1392i	−0.0616742	+	0.106823i
$124$		0			0
$125$			136.082i			1.08866i
$126$		0			0
$127$	65.7409			0.517645			0.258822	−	0.965925i	$-0.416666\pi$
$127$	65.7409			0.517645			0.258822	+	0.965925i	$0.416666\pi$
$128$		0			0
$129$	−50.4528	−	29.1289i	−0.391107	−	0.225806i
$130$		0			0
$131$	9.90519	−	5.71876i	0.0756121	−	0.0436547i	−0.461717	−	0.887027i	$-0.652767\pi$
$131$	9.90519	−	5.71876i	0.0756121	−	0.0436547i	0.537329	+	0.843372i	$0.319433\pi$
$132$		0			0
$133$	30.6663	+	20.8634i	0.230574	+	0.156868i
$134$		0			0
$135$	−10.6265	−	18.4057i	−0.0787151	−	0.136338i
$136$		0			0
$137$	−13.8277	+	23.9504i	−0.100932	+	0.174820i	−0.912069	−	0.410037i	$-0.865516\pi$
$137$	−13.8277	+	23.9504i	−0.100932	+	0.174820i	0.811137	+	0.584857i	$0.198849\pi$
$138$		0			0
$139$		−	90.1235i		−	0.648370i	−0.945994	−	0.324185i	$-0.894910\pi$
$139$		−	90.1235i		−	0.648370i	0.945994	−	0.324185i	$-0.105090\pi$
$140$		0			0
$141$	90.5875			0.642464
$142$		0			0
$143$	381.945	+	220.516i	2.67095	+	1.54207i
$144$		0			0
$145$	6.43431	−	3.71485i	0.0443745	−	0.0256196i
$146$		0			0
$147$	78.9421	−	31.1632i	0.537021	−	0.211995i
$148$		0			0
$149$	−105.816	−	183.278i	−0.710171	−	1.23005i	−0.964793	−	0.263012i	$-0.915284\pi$
$149$	−105.816	−	183.278i	−0.710171	−	1.23005i	0.254621	−	0.967041i	$-0.418049\pi$
$150$		0			0
$151$	81.3619	−	140.923i	0.538821	−	0.933265i	−0.460147	−	0.887843i	$-0.652203\pi$
$151$	81.3619	−	140.923i	0.538821	−	0.933265i	0.998968	−	0.0454221i	$-0.0144633\pi$
$152$		0			0
$153$		−	37.7700i		−	0.246863i
$154$		0			0
$155$	−175.871			−1.13465
$156$		0			0
$157$	−132.476	−	76.4852i	−0.843798	−	0.487167i	0.0147552	−	0.999891i	$-0.495303\pi$
$157$	−132.476	−	76.4852i	−0.843798	−	0.487167i	−0.858554	+	0.512724i	$0.828636\pi$
$158$		0			0
$159$	22.3222	−	12.8877i	0.140391	−	0.0810548i
$160$		0			0
$161$	68.9773	−	101.387i	0.428430	−	0.629732i
$162$		0			0
$163$	1.80839	+	3.13222i	0.0110944	+	0.0192161i	0.871519	−	0.490361i	$-0.163135\pi$
$163$	1.80839	+	3.13222i	0.0110944	+	0.0192161i	−0.860425	+	0.509577i	$0.829802\pi$
$164$		0			0
$165$	71.1312	−	123.203i	0.431098	−	0.746684i
$166$		0			0
$167$		−	87.6077i		−	0.524597i	−0.964987	−	0.262298i	$-0.915520\pi$
$167$		−	87.6077i		−	0.524597i	0.964987	−	0.262298i	$-0.0844805\pi$
$168$		0			0
$169$	−313.349			−1.85414
$170$		0			0
$171$	−13.7663	−	7.94796i	−0.0805045	−	0.0464793i
$172$		0			0
$173$	255.529	−	147.530i	1.47705	−	0.852773i	0.477383	−	0.878695i	$-0.341585\pi$
$173$	255.529	−	147.530i	1.47705	−	0.852773i	0.999664	+	0.0259220i	$0.00825216\pi$
$174$		0			0
$175$	57.7368	+	4.26924i	0.329925	+	0.0243956i
$176$		0			0
$177$	16.2209	+	28.0955i	0.0916436	+	0.158731i
$178$		0			0
$179$	149.739	−	259.356i	0.836533	−	1.44892i	−0.0562429	−	0.998417i	$-0.517912\pi$
$179$	149.739	−	259.356i	0.836533	−	1.44892i	0.892776	−	0.450501i	$-0.148755\pi$
$180$		0			0
$181$			49.1016i			0.271280i	0.990758	+	0.135640i	$0.0433090\pi$
$181$			49.1016i			0.271280i	−0.990758	+	0.135640i	$0.956691\pi$
$182$		0			0
$183$	28.3690			0.155022
$184$		0			0
$185$	136.014	+	78.5278i	0.735212	+	0.424475i
$186$		0			0
$187$	218.951	−	126.411i	1.17086	−	0.675996i
$188$		0			0
$189$	−32.7553	+	15.8142i	−0.173309	+	0.0836728i
$190$		0			0
$191$	−74.0704	−	128.294i	−0.387803	−	0.671694i	0.604351	−	0.796718i	$-0.293433\pi$
$191$	−74.0704	−	128.294i	−0.387803	−	0.671694i	−0.992154	+	0.125024i	$0.960099\pi$
$192$		0			0
$193$	−86.8312	+	150.396i	−0.449903	+	0.779254i	−0.998379	−	0.0569118i	$-0.981875\pi$
$193$	−86.8312	+	150.396i	−0.449903	+	0.779254i	0.548477	+	0.836166i	$0.315208\pi$
$194$		0			0
$195$			155.590i			0.797897i
$196$		0			0
$197$	59.0342			0.299666			0.149833	−	0.988711i	$-0.452126\pi$
$197$	59.0342			0.299666			0.149833	+	0.988711i	$0.452126\pi$
$198$		0			0
$199$	7.52989	+	4.34738i	0.0378386	+	0.0218462i	0.518800	−	0.854896i	$-0.326379\pi$
$199$	7.52989	+	4.34738i	0.0378386	+	0.0218462i	−0.480961	+	0.876742i	$0.659712\pi$
$200$		0			0
$201$	169.798	−	98.0330i	0.844767	−	0.487727i
$202$		0			0
$203$	−5.52835	−	11.4507i	−0.0272332	−	0.0564073i
$204$		0			0
$205$	−17.9138	−	31.0276i	−0.0873844	−	0.151354i
$206$		0			0
$207$	−26.2770	+	45.5131i	−0.126942	+	0.219870i
$208$		0			0
$209$		−	106.403i		−	0.509106i
$210$		0			0
$211$	391.284			1.85443			0.927214	−	0.374532i	$-0.122196\pi$
$211$	391.284			1.85443			0.927214	+	0.374532i	$0.122196\pi$
$212$		0			0
$213$	116.705	+	67.3797i	0.547911	+	0.316337i
$214$		0			0
$215$	119.142	−	68.7865i	0.554148	−	0.319937i
$216$		0			0
$217$	−22.1955	+	300.170i	−0.102283	+	1.38327i
$218$		0			0
$219$	113.411	+	196.434i	0.517859	+	0.896958i
$220$		0			0
$221$	−138.254	+	239.462i	−0.625582	+	1.08354i
$222$		0			0
$223$		−	214.781i		−	0.963144i	−0.876406	−	0.481572i	$-0.840066\pi$
$223$		−	214.781i		−	0.963144i	0.876406	−	0.481572i	$-0.159934\pi$
$224$		0			0
$225$	−24.8119			−0.110275
$226$		0			0
$227$	−157.877	−	91.1502i	−0.695493	−	0.401543i	0.110174	−	0.993912i	$-0.464859\pi$
$227$	−157.877	−	91.1502i	−0.695493	−	0.401543i	−0.805666	+	0.592370i	$0.798193\pi$
$228$		0			0
$229$	172.572	−	99.6346i	0.753590	−	0.435086i	−0.0733993	−	0.997303i	$-0.523385\pi$
$229$	172.572	−	99.6346i	0.753590	−	0.435086i	0.826990	+	0.562217i	$0.190051\pi$
$230$		0			0
$231$	−201.301	−	136.953i	−0.871435	−	0.592870i
$232$		0			0
$233$	31.6667	+	54.8483i	0.135908	+	0.235400i	0.925944	−	0.377661i	$-0.123271\pi$
$233$	31.6667	+	54.8483i	0.135908	+	0.235400i	−0.790036	+	0.613061i	$0.789938\pi$
$234$		0			0
$235$	−106.959	+	185.258i	−0.455145	+	0.788334i
$236$		0			0
$237$			197.255i			0.832299i
$238$		0			0
$239$	226.373			0.947168			0.473584	−	0.880749i	$-0.342960\pi$
$239$	226.373			0.947168			0.473584	+	0.880749i	$0.342960\pi$
$240$		0			0
$241$	−237.975	−	137.395i	−0.987448	−	0.570103i	−0.0829373	−	0.996555i	$-0.526430\pi$
$241$	−237.975	−	137.395i	−0.987448	−	0.570103i	−0.904510	+	0.426452i	$0.859763\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−29.4778	+	198.238i	−0.120318	+	0.809134i
$246$		0			0
$247$	58.1856	+	100.780i	0.235569	+	0.408018i
$248$		0			0
$249$	−61.3033	+	106.180i	−0.246198	+	0.426427i
$250$		0			0
$251$			35.9601i			0.143267i	0.997431	+	0.0716336i	$0.0228212\pi$
$251$			35.9601i			0.143267i	−0.997431	+	0.0716336i	$0.977179\pi$
$252$		0			0
$253$	−351.783			−1.39045
$254$		0			0
$255$	77.2426	+	44.5960i	0.302912	+	0.174886i
$256$		0			0
$257$	294.047	−	169.768i	1.14415	−	0.660576i	0.196696	−	0.980465i	$-0.436979\pi$
$257$	294.047	−	169.768i	1.14415	−	0.660576i	0.947455	+	0.319889i	$0.103645\pi$
$258$		0			0
$259$	151.194	−	222.234i	0.583761	−	0.858046i
$260$		0			0
$261$	2.72472	+	4.71936i	0.0104396	+	0.0180818i
$262$		0			0
$263$	−62.0629	+	107.496i	−0.235981	+	0.408731i	−0.959557	−	0.281514i	$-0.909164\pi$
$263$	−62.0629	+	107.496i	−0.235981	+	0.408731i	0.723577	+	0.690244i	$0.242497\pi$
$264$		0			0
$265$			60.8674i			0.229688i
$266$		0			0
$267$	253.875			0.950842
$268$		0			0
$269$	−306.478	−	176.945i	−1.13932	−	0.657789i	−0.193061	−	0.981187i	$-0.561842\pi$
$269$	−306.478	−	176.945i	−1.13932	−	0.657789i	−0.946263	+	0.323397i	$0.895175\pi$
$270$		0			0
$271$	−189.549	+	109.436i	−0.699444	+	0.403824i	−0.807140	−	0.590360i	$-0.798986\pi$
$271$	−189.549	+	109.436i	−0.699444	+	0.403824i	0.107696	+	0.994184i	$0.465653\pi$
$272$		0			0
$273$	265.556	+	19.6360i	0.972731	+	0.0719267i
$274$		0			0
$275$	−83.0421	−	143.833i	−0.301971	−	0.523030i
$276$		0			0
$277$	29.2203	−	50.6111i	0.105488	−	0.182711i	−0.808449	−	0.588566i	$-0.799693\pi$
$277$	29.2203	−	50.6111i	0.105488	−	0.182711i	0.913938	+	0.405855i	$0.133026\pi$
$278$		0			0
$279$		−	128.996i		−	0.462350i
$280$		0			0
$281$	−485.027			−1.72607			−0.863037	−	0.505141i	$-0.831440\pi$
$281$	−485.027			−1.72607			−0.863037	+	0.505141i	$0.831440\pi$
$282$		0			0
$283$	−195.507	−	112.876i	−0.690838	−	0.398855i	0.113088	−	0.993585i	$-0.463926\pi$
$283$	−195.507	−	112.876i	−0.690838	−	0.398855i	−0.803926	+	0.594730i	$0.797259\pi$
$284$		0			0
$285$	32.5084	−	18.7687i	0.114065	−	0.0658552i
$286$		0			0
$287$	−55.2177	+	26.6589i	−0.192396	+	0.0928881i
$288$		0			0
$289$	−65.2459	−	113.009i	−0.225764	−	0.391035i
$290$		0			0
$291$	−19.1212	+	33.1189i	−0.0657085	+	0.113810i
$292$		0			0
$293$			312.862i			1.06779i	0.845552	+	0.533894i	$0.179272\pi$
$293$			312.862i			1.06779i	−0.845552	+	0.533894i	$0.820728\pi$
$294$		0			0
$295$	−76.6098			−0.259694
$296$		0			0
$297$	90.3654	+	52.1725i	0.304261	+	0.175665i
$298$		0			0
$299$	333.193	−	192.369i	1.11436	−	0.643376i
$300$		0			0
$301$	−102.366	−	212.028i	−0.340088	−	0.704413i
$302$		0			0
$303$	−158.719	−	274.909i	−0.523825	−	0.907292i
$304$		0			0
$305$	−33.4961	+	58.0169i	−0.109823	+	0.190219i
$306$		0			0
$307$		−	263.601i		−	0.858635i	−0.903154	−	0.429318i	$-0.858754\pi$
$307$		−	263.601i		−	0.858635i	0.903154	−	0.429318i	$-0.141246\pi$
$308$		0			0
$309$	44.4334			0.143797
$310$		0			0
$311$	273.433	+	157.866i	0.879204	+	0.507609i	0.870396	−	0.492352i	$-0.163863\pi$
$311$	273.433	+	157.866i	0.879204	+	0.507609i	0.00880827	+	0.999961i	$0.497196\pi$
$312$		0			0
$313$	137.826	−	79.5740i	0.440339	−	0.254230i	−0.263402	−	0.964686i	$-0.584845\pi$
$313$	137.826	−	79.5740i	0.440339	−	0.254230i	0.703741	+	0.710456i	$0.251511\pi$
$314$		0			0
$315$	6.33392	−	85.6594i	0.0201077	−	0.271935i
$316$		0			0
$317$	−117.031	−	202.703i	−0.369183	−	0.639443i	0.620255	−	0.784400i	$-0.287029\pi$
$317$	−117.031	−	202.703i	−0.369183	−	0.639443i	−0.989438	+	0.144957i	$0.953696\pi$
$318$		0			0
$319$	−18.2386	+	31.5901i	−0.0571742	+	0.0990287i
$320$		0			0
$321$		−	30.0073i		−	0.0934807i
$322$		0			0
$323$	66.7099			0.206532
$324$		0			0
$325$	157.308	+	90.8217i	0.484024	+	0.279452i
$326$		0			0
$327$	213.626	−	123.337i	0.653291	−	0.377178i
$328$		0			0
$329$	302.694	+	205.934i	0.920044	+	0.625940i
$330$		0			0
$331$	270.288	+	468.152i	0.816579	+	1.41436i	0.908189	+	0.418561i	$0.137465\pi$
$331$	270.288	+	468.152i	0.816579	+	1.41436i	−0.0916097	+	0.995795i	$0.529201\pi$
$332$		0			0
$333$	−57.5977	+	99.7621i	−0.172966	+	0.299586i
$334$		0			0
$335$			463.001i			1.38209i
$336$		0			0
$337$	233.419			0.692639			0.346319	−	0.938117i	$-0.387431\pi$
$337$	233.419			0.692639			0.346319	+	0.938117i	$0.387431\pi$
$338$		0			0
$339$	−275.418	−	159.013i	−0.812442	−	0.469064i
$340$		0			0
$341$	747.780	−	431.731i	2.19290	−	1.26607i
$342$		0			0
$343$	334.626	+	75.3301i	0.975585	+	0.219621i
$344$		0			0
$345$	−62.0519	−	107.477i	−0.179861	−	0.311528i
$346$		0			0
$347$	3.31307	−	5.73841i	0.00954776	−	0.0165372i	−0.861212	−	0.508246i	$-0.830294\pi$
$347$	3.31307	−	5.73841i	0.00954776	−	0.0165372i	0.870760	+	0.491709i	$0.163627\pi$
$348$		0			0
$349$			423.659i			1.21392i	0.794732	+	0.606961i	$0.207612\pi$
$349$			423.659i			1.21392i	−0.794732	+	0.606961i	$0.792388\pi$
$350$		0			0
$351$	−114.120			−0.325129
$352$		0			0
$353$	−131.570	−	75.9618i	−0.372719	−	0.215189i	0.301927	−	0.953331i	$-0.402370\pi$
$353$	−131.570	−	75.9618i	−0.372719	−	0.215189i	−0.674645	+	0.738142i	$0.735703\pi$
$354$		0			0
$355$	−275.593	+	159.114i	−0.776319	+	0.448208i
$356$		0			0
$357$	85.8633	−	126.207i	0.240514	−	0.353521i
$358$		0			0
$359$	134.228	+	232.490i	0.373895	+	0.647604i	0.990161	−	0.139933i	$-0.0446888\pi$
$359$	134.228	+	232.490i	0.373895	+	0.647604i	−0.616266	+	0.787538i	$0.711356\pi$
$360$		0			0
$361$	−166.462	+	288.321i	−0.461114	+	0.798673i
$362$		0			0
$363$			488.879i			1.34677i
$364$		0			0
$365$	−535.630			−1.46748
$366$		0			0
$367$	−311.896	−	180.073i	−0.849854	−	0.490663i	0.0107477	−	0.999942i	$-0.496579\pi$
$367$	−311.896	−	180.073i	−0.849854	−	0.490663i	−0.860602	+	0.509279i	$0.829912\pi$
$368$		0			0
$369$	22.7578	−	13.1392i	0.0616742	−	0.0356076i
$370$		0			0
$371$	103.886	+	7.68168i	0.280017	+	0.0207053i
$372$		0			0
$373$	−307.413	−	532.454i	−0.824163	−	1.42749i	−0.902558	−	0.430569i	$-0.858313\pi$
$373$	−307.413	−	532.454i	−0.824163	−	1.42749i	0.0783949	−	0.996922i	$-0.475021\pi$
$374$		0			0
$375$	117.851	−	204.123i	0.314268	−	0.544328i
$376$		0			0
$377$		−	39.8944i		−	0.105821i
$378$		0			0
$379$	−56.9607			−0.150292			−0.0751460	−	0.997173i	$-0.523942\pi$
$379$	−56.9607			−0.150292			−0.0751460	+	0.997173i	$0.523942\pi$
$380$		0			0
$381$	−98.6114	−	56.9333i	−0.258822	−	0.149431i
$382$		0			0
$383$	−159.734	+	92.2224i	−0.417060	+	0.240790i	−0.693819	−	0.720150i	$-0.744073\pi$
$383$	−159.734	+	92.2224i	−0.417060	+	0.240790i	0.276759	+	0.960939i	$0.410740\pi$
$384$		0			0
$385$	517.761	−	249.973i	1.34483	−	0.649281i
$386$		0			0
$387$	50.4528	+	87.3867i	0.130369	+	0.225806i
$388$		0			0
$389$	156.503	−	271.070i	0.402320	−	0.696839i	−0.591685	−	0.806169i	$-0.701537\pi$
$389$	156.503	−	271.070i	0.402320	−	0.696839i	0.994006	+	0.109330i	$0.0348705\pi$
$390$		0			0
$391$		−	220.552i		−	0.564071i
$392$		0			0
$393$	−19.8104			−0.0504081
$394$		0			0
$395$	−403.401	−	232.904i	−1.02127	−	0.589630i
$396$		0			0
$397$	−168.237	+	97.1315i	−0.423770	+	0.244664i	−0.696689	−	0.717373i	$-0.745344\pi$
$397$	−168.237	+	97.1315i	−0.423770	+	0.244664i	0.272919	+	0.962037i	$0.412011\pi$
$398$		0			0
$399$	−27.9312	−	57.8529i	−0.0700030	−	0.144995i
$400$		0			0
$401$	75.0503	+	129.991i	0.187158	+	0.324167i	0.944302	−	0.329081i	$-0.106739\pi$
$401$	75.0503	+	129.991i	0.187158	+	0.324167i	−0.757144	+	0.653248i	$0.773406\pi$
$402$		0			0
$403$	−472.177	+	817.834i	−1.17165	+	2.02937i
$404$		0			0
$405$			36.8114i			0.0908923i
$406$		0			0
$407$	−771.087			−1.89456
$408$		0			0
$409$	523.278	+	302.115i	1.27941	+	0.738666i	0.976739	−	0.214430i	$-0.0687893\pi$
$409$	523.278	+	302.115i	1.27941	+	0.738666i	0.302668	+	0.953096i	$0.402123\pi$
$410$		0			0
$411$	41.4832	−	23.9504i	0.100932	−	0.0582734i
$412$		0			0
$413$	−9.66844	+	130.755i	−0.0234103	+	0.316598i
$414$		0			0
$415$	−144.765	−	250.740i	−0.348831	−	0.604192i
$416$		0			0
$417$	−78.0492	+	135.185i	−0.187168	+	0.324185i
$418$		0			0
$419$		−	38.8085i		−	0.0926218i	−0.998927	−	0.0463109i	$-0.985254\pi$
$419$		−	38.8085i		−	0.0926218i	0.998927	−	0.0463109i	$-0.0147465\pi$
$420$		0			0
$421$	−576.869			−1.37023			−0.685117	−	0.728433i	$-0.740249\pi$
$421$	−576.869			−1.37023			−0.685117	+	0.728433i	$0.740249\pi$
$422$		0			0
$423$	−135.881	−	78.4511i	−0.321232	−	0.185464i
$424$		0			0
$425$	90.1769	−	52.0637i	0.212181	−	0.122503i
$426$		0			0
$427$	94.7940	+	64.4919i	0.222000	+	0.151035i
$428$		0			0
$429$	−381.945	−	661.548i	−0.890315	−	1.54207i
$430$		0			0
$431$	313.062	−	542.239i	0.726362	−	1.25810i	−0.232049	−	0.972704i	$-0.574543\pi$
$431$	313.062	−	542.239i	0.726362	−	1.25810i	0.958411	−	0.285392i	$-0.0921238\pi$
$432$		0			0
$433$			347.489i			0.802516i	0.915965	+	0.401258i	$0.131427\pi$
$433$			347.489i			0.802516i	−0.915965	+	0.401258i	$0.868573\pi$
$434$		0			0
$435$	−12.8686			−0.0295830
$436$		0			0
$437$	−80.3859	−	46.4108i	−0.183949	−	0.106203i
$438$		0			0
$439$	−582.157	+	336.109i	−1.32610	+	0.765623i	−0.984694	−	0.174293i	$-0.944236\pi$
$439$	−582.157	+	336.109i	−1.32610	+	0.765623i	−0.341404	+	0.939916i	$0.610903\pi$
$440$		0			0
$441$	−145.401	−	21.6210i	−0.329708	−	0.0490273i
$442$		0			0
$443$	−360.071	−	623.662i	−0.812802	−	1.40782i	−0.910895	−	0.412638i	$-0.864608\pi$
$443$	−360.071	−	623.662i	−0.812802	−	1.40782i	0.0980927	−	0.995177i	$-0.468726\pi$
$444$		0			0
$445$	−299.756	+	519.193i	−0.673610	+	1.16673i
$446$		0			0
$447$			366.556i			0.820035i
$448$		0			0
$449$	414.577			0.923335			0.461668	−	0.887053i	$-0.347251\pi$
$449$	414.577			0.923335			0.461668	+	0.887053i	$0.347251\pi$
$450$		0			0
$451$	152.334	+	87.9503i	0.337770	+	0.195012i
$452$		0			0
$453$	−244.086	+	140.923i	−0.538821	+	0.311088i
$454$		0			0
$455$	−353.706	+	519.897i	−0.777375	+	1.14263i
$456$		0			0
$457$	−253.059	−	438.311i	−0.553740	−	0.959106i	−0.998000	−	0.0632080i	$-0.979867\pi$
$457$	−253.059	−	438.311i	−0.553740	−	0.959106i	0.444260	−	0.895898i	$-0.353466\pi$
$458$		0			0
$459$	−32.7098	+	56.6550i	−0.0712632	+	0.123431i
$460$		0			0
$461$		−	219.010i		−	0.475076i	−0.971378	−	0.237538i	$-0.923660\pi$
$461$		−	219.010i		−	0.475076i	0.971378	−	0.237538i	$-0.0763405\pi$
$462$		0			0
$463$	−388.150			−0.838336			−0.419168	−	0.907909i	$-0.637678\pi$
$463$	−388.150			−0.838336			−0.419168	+	0.907909i	$0.637678\pi$
$464$		0			0
$465$	263.806	+	152.309i	0.567325	+	0.327545i
$466$		0			0
$467$	−644.058	+	371.847i	−1.37914	+	0.796246i	−0.992056	−	0.125799i	$-0.959851\pi$
$467$	−644.058	+	371.847i	−1.37914	+	0.796246i	−0.387083	+	0.922045i	$0.626517\pi$
$468$		0			0
$469$	790.234	+	58.4323i	1.68493	+	0.124589i
$470$		0			0
$471$	132.476	+	229.456i	0.281266	+	0.487167i
$472$		0			0
$473$	−337.717	+	584.943i	−0.713990	+	1.23667i
$474$		0			0
$475$		−	43.8231i		−	0.0922592i
$476$		0			0
$477$	−44.6443			−0.0935940
$478$		0			0
$479$	230.319	+	132.975i	0.480834	+	0.277609i	0.720764	−	0.693181i	$-0.243791\pi$
$479$	230.319	+	132.975i	0.480834	+	0.277609i	−0.239930	+	0.970790i	$0.577125\pi$
$480$		0			0
$481$	730.340	−	421.662i	1.51838	−	0.876637i
$482$		0			0
$483$	−191.270	+	92.3442i	−0.396003	+	0.191189i
$484$		0			0
$485$	−45.1537	−	78.2086i	−0.0931005	−	0.161255i
$486$		0			0
$487$	400.464	−	693.625i	0.822309	−	1.42428i	−0.0816502	−	0.996661i	$-0.526019\pi$
$487$	400.464	−	693.625i	0.822309	−	1.42428i	0.903959	−	0.427619i	$-0.140648\pi$
$488$		0			0
$489$		−	6.26445i		−	0.0128107i
$490$		0			0
$491$	−427.294			−0.870253			−0.435127	−	0.900369i	$-0.643296\pi$
$491$	−427.294			−0.870253			−0.435127	+	0.900369i	$0.643296\pi$
$492$		0			0
$493$	−19.8056	−	11.4348i	−0.0401736	−	0.0231943i
$494$		0			0
$495$	−213.393	+	123.203i	−0.431098	+	0.248895i
$496$		0			0
$497$	236.790	+	490.455i	0.476438	+	0.986830i
$498$		0			0
$499$	−160.559	−	278.096i	−0.321761	−	0.557306i	0.659091	−	0.752064i	$-0.270941\pi$
$499$	−160.559	−	278.096i	−0.321761	−	0.557306i	−0.980851	+	0.194757i	$0.937608\pi$
$500$		0			0
$501$	−75.8705	+	131.412i	−0.151438	+	0.262298i
$502$		0			0
$503$			641.788i			1.27592i	0.770069	+	0.637960i	$0.220222\pi$
$503$			641.788i			1.27592i	−0.770069	+	0.637960i	$0.779778\pi$
$504$		0			0
$505$	749.615			1.48439
$506$		0			0
$507$	470.024	+	271.369i	0.927069	+	0.535244i
$508$		0			0
$509$	−41.6196	+	24.0291i	−0.0817674	+	0.0472084i	−0.540326	−	0.841456i	$-0.681699\pi$
$509$	−41.6196	+	24.0291i	−0.0817674	+	0.0472084i	0.458559	+	0.888664i	$0.348366\pi$
$510$		0			0
$511$	−67.5984	+	914.195i	−0.132286	+	1.78903i
$512$		0			0
$513$	13.7663	+	23.8439i	0.0268348	+	0.0464793i
$514$		0			0
$515$	−52.4636	+	90.8697i	−0.101871	+	0.176446i
$516$		0			0
$517$		−	1050.26i		−	2.03145i
$518$		0			0
$519$	−511.058			−0.984698
$520$		0			0
$521$	−155.324	−	89.6762i	−0.298126	−	0.172123i	0.343475	−	0.939162i	$-0.388396\pi$
$521$	−155.324	−	89.6762i	−0.298126	−	0.172123i	−0.641601	+	0.767039i	$0.721729\pi$
$522$		0			0
$523$	−110.310	+	63.6876i	−0.210918	+	0.121774i	−0.601738	−	0.798694i	$-0.705525\pi$
$523$	−110.310	+	63.6876i	−0.210918	+	0.121774i	0.390820	+	0.920467i	$0.372192\pi$
$524$		0			0
$525$	−82.9080	−	56.4054i	−0.157920	−	0.107439i
$526$		0			0
$527$	270.676	+	468.825i	0.513617	+	0.889610i
$528$		0			0
$529$	111.060	−	192.361i	0.209943	−	0.363631i
$530$		0			0
$531$		−	56.1909i		−	0.105821i
$532$		0			0
$533$	−192.379			−0.360937
$534$		0			0
$535$	61.3673	+	35.4304i	0.114705	+	0.0662251i
$536$		0			0
$537$	−449.218	+	259.356i	−0.836533	+	0.482973i
$538$		0			0
$539$	−361.303	−	915.245i	−0.670320	−	1.69804i
$540$		0			0
$541$	−177.512	−	307.460i	−0.328118	−	0.568318i	0.654020	−	0.756477i	$-0.273081\pi$
$541$	−177.512	−	307.460i	−0.328118	−	0.568318i	−0.982139	+	0.188159i	$0.939748\pi$
$542$		0			0
$543$	42.5233	−	73.6525i	0.0783117	−	0.135640i
$544$		0			0
$545$			582.510i			1.06882i
$546$		0			0
$547$	446.489			0.816250			0.408125	−	0.912926i	$-0.366183\pi$
$547$	446.489			0.816250			0.408125	+	0.912926i	$0.366183\pi$
$548$		0			0
$549$	−42.5536	−	24.5683i	−0.0775110	−	0.0447510i
$550$		0			0
$551$	−8.33540	+	4.81245i	−0.0151278	+	0.00873402i
$552$		0			0
$553$	−448.423	+	659.119i	−0.810892	+	1.19190i
$554$		0			0
$555$	−136.014	−	235.583i	−0.245071	−	0.424475i
$556$		0			0
$557$	−278.305	+	482.039i	−0.499650	+	0.865419i	−1.00000		0.000403899i	$-0.999871\pi$
$557$	−278.305	+	482.039i	−0.499650	+	0.865419i	0.500350	+	0.865823i	$0.333205\pi$
$558$		0			0
$559$		−	738.711i		−	1.32149i
$560$		0			0
$561$	−437.901			−0.780572
$562$		0			0
$563$	−112.631	−	65.0276i	−0.200055	−	0.115502i	0.396626	−	0.917980i	$-0.370181\pi$
$563$	−112.631	−	65.0276i	−0.200055	−	0.115502i	−0.596681	+	0.802478i	$0.703514\pi$
$564$		0			0
$565$	650.386	−	375.501i	1.15113	−	0.664603i
$566$		0			0
$567$	62.8285	+	4.64573i	0.110809	+	0.00819353i
$568$		0			0
$569$	−375.545	−	650.462i	−0.660008	−	1.14317i	−0.980613	−	0.195955i	$-0.937219\pi$
$569$	−375.545	−	650.462i	−0.660008	−	1.14317i	0.320605	−	0.947213i	$-0.396114\pi$
$570$		0			0
$571$	68.4870	−	118.623i	0.119942	−	0.207746i	−0.799802	−	0.600263i	$-0.795062\pi$
$571$	68.4870	−	118.623i	0.119942	−	0.207746i	0.919745	+	0.392517i	$0.128396\pi$
$572$		0			0
$573$			256.587i			0.447796i
$574$		0			0
$575$	−144.885			−0.251974
$576$		0			0
$577$	−296.585	−	171.233i	−0.514012	−	0.296765i	0.220469	−	0.975394i	$-0.429241\pi$
$577$	−296.585	−	171.233i	−0.514012	−	0.296765i	−0.734481	+	0.678629i	$0.762574\pi$
$578$		0			0
$579$	260.494	−	150.396i	0.449903	−	0.259751i
$580$		0			0
$581$	−446.224	+	215.435i	−0.768028	+	0.370801i
$582$		0			0
$583$	−149.419	−	258.801i	−0.256293	−	0.443912i
$584$		0			0
$585$	134.745	−	233.385i	0.230333	−	0.398948i
$586$		0			0
$587$			375.727i			0.640080i	0.947404	+	0.320040i	$0.103696\pi$
$587$			375.727i			0.640080i	−0.947404	+	0.320040i	$0.896304\pi$
$588$		0			0
$589$	227.834			0.386815
$590$		0			0
$591$	−88.5512	−	51.1251i	−0.149833	−	0.0865061i
$592$		0			0
$593$	439.393	−	253.684i	0.740967	−	0.427797i	−0.0814540	−	0.996677i	$-0.525956\pi$
$593$	439.393	−	253.684i	0.740967	−	0.427797i	0.822421	+	0.568880i	$0.192623\pi$
$594$		0			0
$595$	156.722	+	324.613i	0.263398	+	0.545568i
$596$		0			0
$597$	−7.52989	−	13.0422i	−0.0126129	−	0.0218462i
$598$		0			0
$599$	367.805	−	637.057i	0.614031	−	1.06353i	−0.376522	−	0.926408i	$-0.622880\pi$
$599$	367.805	−	637.057i	0.614031	−	1.06353i	0.990554	−	0.137126i	$-0.0437865\pi$
$600$		0			0
$601$			963.641i			1.60340i	0.597729	+	0.801698i	$0.296070\pi$
$601$			963.641i			1.60340i	−0.597729	+	0.801698i	$0.703930\pi$
$602$		0			0
$603$	−339.596			−0.563178
$604$		0			0
$605$	−999.795	−	577.232i	−1.65255	−	0.954103i
$606$		0			0
$607$	151.792	−	87.6374i	0.250070	−	0.144378i	−0.369726	−	0.929141i	$-0.620549\pi$
$607$	151.792	−	87.6374i	0.250070	−	0.144378i	0.619796	+	0.784763i	$0.287215\pi$
$608$		0			0
$609$	−1.62406	+	21.9637i	−0.00266677	+	0.0360652i
$610$		0			0
$611$	574.326	+	994.762i	0.939977	+	1.62809i
$612$		0			0
$613$	−184.106	+	318.881i	−0.300336	+	0.520198i	−0.976212	−	0.216818i	$-0.930432\pi$
$613$	−184.106	+	318.881i	−0.300336	+	0.520198i	0.675876	+	0.737016i	$0.263766\pi$
$614$		0			0
$615$			62.0552i			0.100903i
$616$		0			0
$617$	−332.534			−0.538952			−0.269476	−	0.963007i	$-0.586851\pi$
$617$	−332.534			−0.538952			−0.269476	+	0.963007i	$0.586851\pi$
$618$		0			0
$619$	−831.973	−	480.340i	−1.34406	−	0.775994i	−0.356660	−	0.934234i	$-0.616085\pi$
$619$	−831.973	−	480.340i	−1.34406	−	0.775994i	−0.987401	+	0.158241i	$0.949418\pi$
$620$		0			0
$621$	78.8311	−	45.5131i	0.126942	−	0.0732901i
$622$		0			0
$623$	848.312	+	577.139i	1.36166	+	0.926386i
$624$		0			0
$625$	174.915	+	302.962i	0.279865	+	0.484740i
$626$		0			0
$627$	−92.1478	+	159.605i	−0.146966	+	0.254553i
$628$		0			0
$629$		−	483.437i		−	0.768580i
$630$		0			0
$631$	659.689			1.04547			0.522733	−	0.852496i	$-0.324912\pi$
$631$	659.689			1.04547			0.522733	+	0.852496i	$0.324912\pi$
$632$		0			0
$633$	−586.927	−	338.862i	−0.927214	−	0.535327i
$634$		0			0
$635$	232.866	−	134.445i	0.366718	−	0.211725i
$636$		0			0
$637$	842.704	+	669.306i	1.32293	+	1.05072i
$638$		0			0
$639$	−116.705	−	202.139i	−0.182637	−	0.316337i
$640$		0			0
$641$	91.1878	−	157.942i	0.142259	−	0.246399i	−0.786088	−	0.618114i	$-0.787897\pi$
$641$	91.1878	−	157.942i	0.142259	−	0.246399i	0.928347	+	0.371715i	$0.121230\pi$
$642$		0			0
$643$			640.479i			0.996080i	0.867154	+	0.498040i	$0.165947\pi$
$643$			640.479i			0.996080i	−0.867154	+	0.498040i	$0.834053\pi$
$644$		0			0
$645$	−238.283			−0.369432
$646$		0			0
$647$	203.913	+	117.729i	0.315168	+	0.181962i	0.649237	−	0.760587i	$-0.275089\pi$
$647$	203.913	+	117.729i	0.315168	+	0.181962i	−0.334069	+	0.942549i	$0.608422\pi$
$648$		0			0
$649$	325.735	−	188.063i	0.501904	−	0.289774i
$650$		0			0
$651$	293.248	−	431.034i	0.450458	−	0.662110i
$652$		0			0
$653$	534.325	+	925.477i	0.818261	+	1.41727i	0.906962	+	0.421212i	$0.138395\pi$
$653$	534.325	+	925.477i	0.818261	+	1.41727i	−0.0887013	+	0.996058i	$0.528272\pi$
$654$		0			0
$655$	23.3906	−	40.5138i	0.0357109	−	0.0618531i
$656$		0			0
$657$		−	392.867i		−	0.597972i
$658$		0			0
$659$	683.671			1.03744			0.518719	−	0.854945i	$-0.326409\pi$
$659$	683.671			1.03744			0.518719	+	0.854945i	$0.326409\pi$
$660$		0			0
$661$	651.096	+	375.911i	0.985017	+	0.568700i	0.903781	−	0.427995i	$-0.140780\pi$
$661$	651.096	+	375.911i	0.985017	+	0.568700i	0.0812359	+	0.996695i	$0.474113\pi$
$662$		0			0
$663$	414.761	−	239.462i	0.625582	−	0.361180i
$664$		0			0
$665$	151.293	+	11.1871i	0.227508	+	0.0168226i
$666$		0			0
$667$	15.9106	+	27.5579i	0.0238540	+	0.0413163i
$668$		0			0
$669$	−186.006	+	322.172i	−0.278036	+	0.481572i
$670$		0			0
$671$		−	328.907i		−	0.490175i
$672$		0			0
$673$	954.727			1.41861			0.709307	−	0.704900i	$-0.249008\pi$
$673$	954.727			1.41861			0.709307	+	0.704900i	$0.249008\pi$
$674$		0			0
$675$	37.2179	+	21.4877i	0.0551376	+	0.0318337i
$676$		0			0
$677$	−243.840	+	140.781i	−0.360177	+	0.207948i	−0.669158	−	0.743120i	$-0.733345\pi$
$677$	−243.840	+	140.781i	−0.360177	+	0.207948i	0.308981	+	0.951068i	$0.400012\pi$
$678$		0			0
$679$	−139.182	+	67.1967i	−0.204981	+	0.0989643i
$680$		0			0
$681$	157.877	+	273.451i	0.231831	+	0.401543i
$682$		0			0
$683$	−436.291	+	755.678i	−0.638786	+	1.10641i	0.346914	+	0.937897i	$0.387230\pi$
$683$	−436.291	+	755.678i	−0.638786	+	1.10641i	−0.985700	+	0.168512i	$0.946104\pi$
$684$		0			0
$685$			113.115i			0.165132i
$686$		0			0
$687$	−345.144			−0.502394
$688$		0			0
$689$	283.046	+	163.417i	0.410807	+	0.237179i
$690$		0			0
$691$	−1055.16	+	609.195i	−1.52700	+	0.881613i	−0.527513	+	0.849547i	$0.676875\pi$
$691$	−1055.16	+	609.195i	−1.52700	+	0.881613i	−0.999486	+	0.0320660i	$0.989791\pi$
$692$		0			0
$693$	183.347	+	379.762i	0.264571	+	0.547997i
$694$		0			0
$695$	−184.310	−	319.233i	−0.265194	−	0.459329i
$696$		0			0
$697$	−55.1409	+	95.5068i	−0.0791118	+	0.137026i
$698$		0			0
$699$		−	109.697i		−	0.156934i
$700$		0			0
$701$	−415.806			−0.593161			−0.296581	−	0.955008i	$-0.595846\pi$
$701$	−415.806			−0.593161			−0.296581	+	0.955008i	$0.595846\pi$
$702$		0			0
$703$	−176.201	−	101.730i	−0.250642	−	0.144708i
$704$		0			0
$705$	320.877	−	185.258i	0.455145	−	0.262778i
$706$		0			0
$707$	94.6040	−	1279.42i	0.133811	−	1.80964i
$708$		0			0
$709$	403.674	+	699.184i	0.569357	+	0.986155i	0.996630	+	0.0820319i	$0.0261410\pi$
$709$	403.674	+	699.184i	0.569357	+	0.986155i	−0.427273	+	0.904123i	$0.640526\pi$
$710$		0			0
$711$	170.828	−	295.882i	0.240264	−	0.416149i
$712$		0			0
$713$		−	753.249i		−	1.05645i
$714$		0			0
$715$	1803.89			2.52292
$716$		0			0
$717$	−339.560	−	196.045i	−0.473584	−	0.273424i
$718$		0			0
$719$	278.233	−	160.638i	0.386972	−	0.223418i	−0.293875	−	0.955844i	$-0.594945\pi$
$719$	278.233	−	160.638i	0.386972	−	0.223418i	0.680847	+	0.732425i	$0.261612\pi$
$720$		0			0
$721$	148.472	+	101.011i	0.205926	+	0.140099i
$722$		0			0
$723$	237.975	+	412.185i	0.329149	+	0.570103i
$724$		0			0
$725$	−7.51174	+	13.0107i	−0.0103610	+	0.0179458i
$726$		0			0
$727$		−	488.836i		−	0.672402i	−0.941790	−	0.336201i	$-0.890858\pi$
$727$		−	488.836i		−	0.672402i	0.941790	−	0.336201i	$-0.109142\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−366.733	−	211.733i	−0.501687	−	0.289649i
$732$		0			0
$733$	337.597	−	194.912i	0.460569	−	0.265910i	−0.251714	−	0.967802i	$-0.580994\pi$
$733$	337.597	−	194.912i	0.460569	−	0.265910i	0.712284	+	0.701892i	$0.247661\pi$
$734$		0			0
$735$	215.896	−	271.828i	0.293736	−	0.369834i
$736$		0			0
$737$	−1136.58	−	1968.62i	−1.54218	−	2.67113i
$738$		0			0
$739$	261.924	−	453.666i	0.354430	−	0.613891i	−0.632590	−	0.774487i	$-0.718008\pi$
$739$	261.924	−	453.666i	0.354430	−	0.613891i	0.987020	+	0.160596i	$0.0513415\pi$
$740$		0			0
$741$		−	201.561i		−	0.272012i
$742$		0			0
$743$	−575.858			−0.775044			−0.387522	−	0.921860i	$-0.626669\pi$
$743$	−575.858			−0.775044			−0.387522	+	0.921860i	$0.626669\pi$
$744$		0			0
$745$	−749.635	−	432.802i	−1.00622	−	0.580942i
$746$		0			0
$747$	183.910	−	106.180i	0.246198	−	0.142142i
$748$		0			0
$749$	68.2162	−	100.268i	0.0910764	−	0.133869i
$750$		0			0
$751$	−10.0940	−	17.4834i	−0.0134408	−	0.0232801i	0.859227	−	0.511595i	$-0.170945\pi$
$751$	−10.0940	−	17.4834i	−0.0134408	−	0.0232801i	−0.872668	+	0.488315i	$0.837612\pi$
$752$		0			0
$753$	31.1423	−	53.9401i	0.0413577	−	0.0716336i
$754$		0			0
$755$		−	665.566i		−	0.881544i
$756$		0			0
$757$	809.002			1.06870			0.534348	−	0.845265i	$-0.320557\pi$
$757$	809.002			1.06870			0.534348	+	0.845265i	$0.320557\pi$
$758$		0			0
$759$	527.674	+	304.653i	0.695223	+	0.401387i
$760$		0			0
$761$	−408.446	+	235.816i	−0.536723	+	0.309877i	−0.743750	−	0.668458i	$-0.766955\pi$
$761$	−408.446	+	235.816i	−0.536723	+	0.309877i	0.207027	+	0.978335i	$0.433621\pi$
$762$		0			0
$763$	994.208	+	73.5148i	1.30303	+	0.0963497i
$764$		0			0
$765$	−77.2426	−	133.788i	−0.100971	−	0.174886i
$766$		0			0
$767$	−205.682	+	356.251i	−0.268164	+	0.464474i
$768$		0			0
$769$		−	977.857i		−	1.27160i	−0.771856	−	0.635798i	$-0.780671\pi$
$769$		−	977.857i		−	1.27160i	0.771856	−	0.635798i	$-0.219329\pi$
$770$		0			0
$771$	−588.094			−0.762767
$772$		0			0
$773$	155.942	+	90.0329i	0.201736	+	0.116472i	0.597465	−	0.801895i	$-0.296175\pi$
$773$	155.942	+	90.0329i	0.201736	+	0.116472i	−0.395729	+	0.918367i	$0.629508\pi$
$774$		0			0
$775$	307.981	−	177.813i	0.397394	−	0.229436i
$776$		0			0
$777$	−419.252	+	202.413i	−0.539577	+	0.260506i
$778$		0			0
$779$	23.2067	+	40.1951i	0.0297903	+	0.0515983i
$780$		0			0
$781$	781.193	−	1353.07i	1.00025	−	1.73248i
$782$		0			0
$783$		−	9.43872i		−	0.0120546i
$784$		0			0
$785$	−625.673			−0.797036
$786$		0			0
$787$	−1256.76	−	725.590i	−1.59690	−	0.921969i	−0.992080	−	0.125605i	$-0.959913\pi$
$787$	−1256.76	−	725.590i	−1.59690	−	0.921969i	−0.604817	−	0.796364i	$-0.706754\pi$
$788$		0			0
$789$	186.189	−	107.496i	0.235981	−	0.136244i
$790$		0			0
$791$	−558.811	−	1157.45i	−0.706461	−	1.46327i
$792$		0			0
$793$	179.860	+	311.527i	0.226810	+	0.392846i
$794$		0			0
$795$	52.7127	−	91.3011i	0.0663053	−	0.114844i
$796$		0			0
$797$			29.2237i			0.0366671i	0.999832	+	0.0183336i	$0.00583608\pi$
$797$			29.2237i			0.0366671i	−0.999832	+	0.0183336i	$0.994164\pi$
$798$		0			0
$799$	658.466			0.824113
$800$		0			0
$801$	−380.812	−	219.862i	−0.475421	−	0.274484i
$802$		0			0
$803$	2277.43	−	1314.87i	2.83615	−	1.63745i
$804$		0			0
$805$	36.9859	−	500.194i	0.0459452	−	0.621359i
$806$		0			0
$807$	306.478	+	530.836i	0.379775	+	0.657789i
$808$		0			0
$809$	−584.425	+	1012.25i	−0.722404	+	1.25124i	0.237630	+	0.971356i	$0.423629\pi$
$809$	−584.425	+	1012.25i	−0.722404	+	1.25124i	−0.960034	+	0.279884i	$0.909704\pi$
$810$		0			0
$811$			538.766i			0.664323i	0.943222	+	0.332162i	$0.107778\pi$
$811$			538.766i			0.664323i	−0.943222	+	0.332162i	$0.892222\pi$
$812$		0			0
$813$	379.099			0.466296
$814$		0			0
$815$	12.8113	+	7.39660i	0.0157194	+	0.00907558i
$816$		0			0
$817$	−154.344	+	89.1104i	−0.188915	+	0.109070i
$818$		0			0
$819$	−381.328	−	259.432i	−0.465602	−	0.316767i
$820$		0			0
$821$	−641.644	−	1111.36i	−0.781540	−	1.35367i	−0.931045	−	0.364905i	$-0.881101\pi$
$821$	−641.644	−	1111.36i	−0.781540	−	1.35367i	0.149505	−	0.988761i	$-0.452232\pi$
$822$		0			0
$823$	−532.531	+	922.371i	−0.647061	+	1.12074i	0.336761	+	0.941590i	$0.390669\pi$
$823$	−532.531	+	922.371i	−0.647061	+	1.12074i	−0.983821	+	0.179152i	$0.942665\pi$
$824$		0			0
$825$			287.666i			0.348687i
$826$		0			0
$827$	645.796			0.780890			0.390445	−	0.920626i	$-0.372321\pi$
$827$	645.796			0.780890			0.390445	+	0.920626i	$0.372321\pi$
$828$		0			0
$829$	426.417	+	246.192i	0.514375	+	0.296975i	0.734630	−	0.678468i	$-0.237356\pi$
$829$	426.417	+	246.192i	0.514375	+	0.296975i	−0.220255	+	0.975442i	$0.570689\pi$
$830$		0			0
$831$	−87.6609	+	50.6111i	−0.105488	+	0.0609038i
$832$		0			0
$833$	573.818	−	226.520i	0.688857	−	0.271933i
$834$		0			0
$835$	−179.164	−	310.322i	−0.214568	−	0.371643i
$836$		0			0
$837$	−111.714	+	193.493i	−0.133469	+	0.231175i
$838$		0			0
$839$		−	72.1244i		−	0.0859647i	−0.999076	−	0.0429823i	$-0.986314\pi$
$839$		−	72.1244i		−	0.0859647i	0.999076	−	0.0429823i	$-0.0136859\pi$
$840$		0			0
$841$	−837.700			−0.996077
$842$		0			0
$843$	727.540	+	420.045i	0.863037	+	0.498274i
$844$		0			0
$845$	−1109.94	+	640.824i	−1.31354	+	0.758371i
$846$		0			0
$847$	−1111.38	+	1633.57i	−1.31214	+	1.92865i
$848$		0			0
$849$	195.507	+	338.628i	0.230279	+	0.398855i
$850$		0			0
$851$	−336.332	+	582.545i	−0.395220	+	0.684541i
$852$		0			0
$853$			620.734i			0.727707i	0.931456	+	0.363854i	$0.118539\pi$
$853$			620.734i			0.727707i	−0.931456	+	0.363854i	$0.881461\pi$
$854$		0			0
$855$	−65.0168			−0.0760430
$856$		0			0
$857$	490.638	+	283.270i	0.572506	+	0.330536i	0.758150	−	0.652081i	$-0.226104\pi$
$857$	490.638	+	283.270i	0.572506	+	0.330536i	−0.185644	+	0.982617i	$0.559437\pi$
$858$		0			0
$859$	843.713	−	487.118i	0.982204	−	0.567076i	0.0792691	−	0.996853i	$-0.474741\pi$
$859$	843.713	−	487.118i	0.982204	−	0.567076i	0.902935	+	0.429778i	$0.141408\pi$
$860$		0			0
$861$	105.914	+	7.83159i	0.123013	+	0.00909592i
$862$		0			0
$863$	−34.5370	−	59.8198i	−0.0400197	−	0.0693161i	0.845322	−	0.534258i	$-0.179409\pi$
$863$	−34.5370	−	59.8198i	−0.0400197	−	0.0693161i	−0.885341	+	0.464941i	$0.846075\pi$
$864$		0			0
$865$	603.420	−	1045.15i	0.697595	−	1.20827i
$866$		0			0
$867$			226.018i			0.260690i
$868$		0			0
$869$	2286.95			2.63170
$870$		0			0
$871$	2153.05	+	1243.06i	2.47192	+	1.42717i
$872$		0			0
$873$	57.3635	−	33.1189i	0.0657085	−	0.0379368i
$874$		0			0
$875$	857.830	−	414.157i	0.980377	−	0.473322i
$876$		0			0
$877$	89.0528	+	154.244i	0.101543	+	0.175877i	0.912320	−	0.409477i	$-0.134289\pi$
$877$	89.0528	+	154.244i	0.101543	+	0.175877i	−0.810778	+	0.585354i	$0.800956\pi$
$878$		0			0
$879$	270.946	−	469.292i	0.308244	−	0.533894i
$880$		0			0
$881$			1205.99i			1.36889i	0.729065	+	0.684445i	$0.239955\pi$
$881$			1205.99i			1.36889i	−0.729065	+	0.684445i	$0.760045\pi$
$882$		0			0
$883$	1610.13			1.82348			0.911740	−	0.410767i	$-0.134739\pi$
$883$	1610.13			1.82348			0.911740	+	0.410767i	$0.134739\pi$
$884$		0			0
$885$	114.915	+	66.3461i	0.129847	+	0.0749673i
$886$		0			0
$887$	87.7294	−	50.6506i	0.0989058	−	0.0571033i	−0.449731	−	0.893164i	$-0.648480\pi$
$887$	87.7294	−	50.6506i	0.0989058	−	0.0571033i	0.548637	+	0.836061i	$0.315147\pi$
$888$		0			0
$889$	−200.078	−	414.415i	−0.225060	−	0.466159i
$890$		0			0
$891$	−90.3654	−	156.517i	−0.101420	−	0.175665i
$892$		0			0
$893$	138.561	−	239.995i	0.155164	−	0.268752i
$894$		0			0
$895$		−	1224.91i		−	1.36862i
$896$		0			0
$897$	−666.387			−0.742906
$898$		0			0
$899$	−67.6419	−	39.0531i	−0.0752413	−	0.0434406i
$900$		0			0
$901$	162.256	−	93.6787i	0.180085	−	0.103972i
$902$		0			0
$903$	−30.0722	+	406.694i	−0.0333026	+	0.450381i
$904$		0			0
$905$	100.417	+	173.927i	0.110958	+	0.192184i
$906$		0			0
$907$	184.357	−	319.315i	0.203260	−	0.352056i	−0.746317	−	0.665591i	$-0.768180\pi$
$907$	184.357	−	319.315i	0.203260	−	0.352056i	0.949577	+	0.313534i	$0.101513\pi$
$908$		0			0
$909$			549.819i			0.604861i
$910$		0			0
$911$	−128.901			−0.141494			−0.0707470	−	0.997494i	$-0.522538\pi$
$911$	−128.901			−0.141494			−0.0707470	+	0.997494i	$0.522538\pi$
$912$		0			0
$913$	1231.04	+	710.743i	1.34835	+	0.778470i
$914$		0			0
$915$	100.488	−	58.0169i	0.109823	−	0.0634064i
$916$		0			0
$917$	−66.1956	−	45.0353i	−0.0721871	−	0.0491116i
$918$		0			0
$919$	−861.173	−	1491.59i	−0.937076	−	1.62306i	−0.770890	−	0.636968i	$-0.780188\pi$
$919$	−861.173	−	1491.59i	−0.937076	−	1.62306i	−0.166186	−	0.986094i	$-0.553145\pi$
$920$		0			0
$921$	−228.285	+	395.401i	−0.247867	+	0.429318i
$922$		0			0
$923$			1708.75i			1.85130i
$924$		0			0
$925$	−317.580			−0.343329
$926$		0			0
$927$	−66.6501	−	38.4804i	−0.0718987	−	0.0415107i
$928$		0			0
$929$	−1109.63	+	640.642i	−1.19443	+	0.689604i	−0.959308	−	0.282362i	$-0.908882\pi$
$929$	−1109.63	+	640.642i	−1.19443	+	0.689604i	−0.235122	+	0.971966i	$0.575549\pi$
$930$		0			0
$931$	38.1874	−	256.810i	0.0410176	−	0.275843i
$932$		0			0
$933$	−273.433	−	473.599i	−0.293068	−	0.507609i
$934$		0			0
$935$	517.041	−	895.542i	0.552985	−	0.957799i
$936$		0			0
$937$		−	996.293i		−	1.06328i	−0.846971	−	0.531640i	$-0.821576\pi$
$937$		−	996.293i		−	1.06328i	0.846971	−	0.531640i	$-0.178424\pi$
$938$		0			0
$939$	−275.652			−0.293559
$940$		0			0
$941$	1531.28	+	884.086i	1.62729	+	0.939517i	0.984897	+	0.173144i	$0.0553925\pi$
$941$	1531.28	+	884.086i	1.62729	+	0.939517i	0.642395	+	0.766374i	$0.277941\pi$
$942$		0			0
$943$	132.890	−	76.7243i	0.140923	−	0.0813619i
$944$		0			0
$945$	−83.6841	+	123.004i	−0.0885546	+	0.130163i
$946$		0			0
$947$	479.865	+	831.150i	0.506721	+	0.877667i	0.999970	+	0.00777830i	$0.00247593\pi$
$947$	479.865	+	831.150i	0.506721	+	0.877667i	−0.493249	+	0.869888i	$0.664191\pi$
$948$		0			0
$949$	−1438.06	+	2490.79i	−1.51534	+	2.62464i
$950$		0			0
$951$			405.407i			0.426295i
$952$		0			0
$953$	−881.308			−0.924772			−0.462386	−	0.886679i	$-0.653007\pi$
$953$	−881.308			−0.924772			−0.462386	+	0.886679i	$0.653007\pi$
$954$		0			0
$955$	−524.741	−	302.959i	−0.549467	−	0.317235i
$956$		0			0
$957$	54.7157	−	31.5901i	0.0571742	−	0.0330096i
$958$		0			0
$959$	193.061	+	14.2755i	0.201315	+	0.0148859i
$960$		0			0
$961$	443.938	+	768.923i	0.461954	+	0.800128i
$962$		0			0
$963$	−25.9871	+	45.0110i	−0.0269856	+	0.0467404i
$964$		0			0
$965$			710.306i			0.736068i
$966$		0			0
$967$	513.785			0.531319			0.265659	−	0.964067i	$-0.414410\pi$
$967$	513.785			0.531319			0.265659	+	0.964067i	$0.414410\pi$
$968$		0			0
$969$	−100.065	−	57.7725i	−0.103266	−	0.0596207i
$970$		0			0
$971$	−1637.84	+	945.609i	−1.68676	+	0.973851i	−0.729785	+	0.683677i	$0.760380\pi$
$971$	−1637.84	+	945.609i	−1.68676	+	0.973851i	−0.956974	+	0.290174i	$0.906287\pi$
$972$		0			0
$973$	−568.118	+	274.285i	−0.583883	+	0.281896i
$974$		0			0
$975$	−157.308	−	272.465i	−0.161341	−	0.279452i
$976$		0			0
$977$	−144.973	+	251.100i	−0.148386	+	0.257012i	−0.930631	−	0.365959i	$-0.880741\pi$
$977$	−144.973	+	251.100i	−0.148386	+	0.257012i	0.782245	+	0.622971i	$0.214074\pi$
$978$		0			0
$979$		−	2943.39i		−	3.00653i
$980$		0			0
$981$	−427.253			−0.435528
$982$		0			0
$983$	−82.7372	−	47.7683i	−0.0841680	−	0.0485944i	0.457325	−	0.889299i	$-0.348808\pi$
$983$	−82.7372	−	47.7683i	−0.0841680	−	0.0485944i	−0.541493	+	0.840705i	$0.682141\pi$
$984$		0			0
$985$	209.109	−	120.729i	0.212294	−	0.122568i
$986$		0			0
$987$	−275.697	−	571.043i	−0.279328	−	0.578564i
$988$		0			0
$989$	294.611	+	510.281i	0.297887	+	0.515956i
$990$		0			0
$991$	237.242	−	410.915i	0.239396	−	0.414647i	−0.721145	−	0.692784i	$-0.756384\pi$
$991$	237.242	−	410.915i	0.239396	−	0.414647i	0.960541	+	0.278138i	$0.0897171\pi$
$992$		0			0
$993$		−	936.304i		−	0.942904i
$994$		0			0
$995$	35.5629			0.0357417
$996$		0			0
$997$	−520.989	−	300.793i	−0.522557	−	0.301698i	0.215423	−	0.976521i	$-0.430887\pi$
$997$	−520.989	−	300.793i	−0.522557	−	0.301698i	−0.737980	+	0.674822i	$0.764220\pi$
$998$		0			0
$999$	172.793	−	99.7621i	0.172966	−	0.0998620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.3.bh.a.577.5	yes	16
4.3	odd	2		672.3.bh.c.577.5	yes	16
7.5	odd	6	inner	672.3.bh.a.481.5	✓	16
28.19	even	6		672.3.bh.c.481.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.3.bh.a.481.5	✓	16	7.5	odd	6	inner
672.3.bh.a.577.5	yes	16	1.1	even	1	trivial
672.3.bh.c.481.5	yes	16	28.19	even	6
672.3.bh.c.577.5	yes	16	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	672.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(3.54218 - 2.04508i) q^{5} +(-3.04344 - 6.30377i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-10.0406 + 17.3908i) q^{11} -21.9625i q^{13} -7.08436 q^{15} +(-10.9033 - 6.29500i) q^{17} +(-4.58876 + 2.64932i) q^{19} +(-0.894071 + 12.0913i) q^{21} +(8.75901 + 15.1710i) q^{23} +(-4.13532 + 7.16258i) q^{25} -5.19615i q^{27} +1.81648 q^{29} +(-37.2378 - 21.4993i) q^{31} +(30.1218 - 17.3908i) q^{33} +(-23.6721 - 16.1050i) q^{35} +(19.1992 + 33.2540i) q^{37} +(-19.0200 + 32.9437i) q^{39} -8.75947i q^{41} +33.6352 q^{43} +(10.6265 + 6.13523i) q^{45} +(-45.2937 + 26.1504i) q^{47} +(-30.4750 + 38.3702i) q^{49} +(10.9033 + 18.8850i) q^{51} +(-7.44072 + 12.8877i) q^{53} +82.1352i q^{55} +9.17752 q^{57} +(-16.2209 - 9.36515i) q^{59} +(-14.1845 + 8.18944i) q^{61} +(11.8125 - 17.3627i) q^{63} +(-44.9149 - 77.7949i) q^{65} +(-56.5994 + 98.0330i) q^{67} -30.3421i q^{69} -77.8034 q^{71} +(-113.411 - 65.4779i) q^{73} +(12.4060 - 7.16258i) q^{75} +(140.186 + 10.3658i) q^{77} +(-56.9426 - 98.6274i) q^{79} +(-4.50000 + 7.79423i) q^{81} -70.7869i q^{83} -51.4951 q^{85} +(-2.72472 - 1.57312i) q^{87} +(-126.937 + 73.2873i) q^{89} +(-138.446 + 66.8413i) q^{91} +(37.2378 + 64.4978i) q^{93} +(-10.8361 + 18.7687i) q^{95} -22.0792i q^{97} -60.2436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 12 q^{7} + 24 q^{9} - 12 q^{11} - 48 q^{17} - 60 q^{19} + 24 q^{21} - 48 q^{23} + 52 q^{25} - 64 q^{29} - 60 q^{31} + 36 q^{33} - 4 q^{37} + 12 q^{39} + 72 q^{43} + 120 q^{47} - 8 q^{49}+ \cdots - 72 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 12 * q^7 + 24 * q^9 - 12 * q^11 - 48 * q^17 - 60 * q^19 + 24 * q^21 - 48 * q^23 + 52 * q^25 - 64 * q^29 - 60 * q^31 + 36 * q^33 - 4 * q^37 + 12 * q^39 + 72 * q^43 + 120 * q^47 - 8 * q^49 + 48 * q^51 - 72 * q^53 + 120 * q^57 - 228 * q^59 + 72 * q^61 - 36 * q^63 - 40 * q^65 + 12 * q^67 - 528 * q^71 - 36 * q^73 - 156 * q^75 - 96 * q^77 - 204 * q^79 - 72 * q^81 - 480 * q^85 + 96 * q^87 - 192 * q^89 - 276 * q^91 + 60 * q^93 - 48 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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