LMFDB - Embedded newform 456.2.bm.b.89.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(41,456)] 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("456.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bm (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.5
Character	$\chi$	$=$	456.89
Dual form			456.2.bm.b.41.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.144474 + 1.72601i) q^{3} +(2.45783 - 0.433381i) q^{5} +(-2.29577 + 3.97638i) q^{7} +(-2.95825 + 0.498730i) q^{9} +(-3.74180 + 2.16033i) q^{11} +(-0.651848 - 1.79094i) q^{13} +(1.10312 + 4.17963i) q^{15} +(2.81708 + 3.35726i) q^{17} +(1.87753 - 3.93381i) q^{19} +(-7.19497 - 3.38804i) q^{21} +(3.57273 + 0.629969i) q^{23} +(1.15463 - 0.420253i) q^{25} +(-1.28821 - 5.03394i) q^{27} +(3.18868 + 2.67562i) q^{29} +(-2.29253 - 1.32359i) q^{31} +(-4.26936 - 6.14630i) q^{33} +(-3.91931 + 10.7682i) q^{35} +5.26569i q^{37} +(2.99701 - 1.38384i) q^{39} +(2.84993 + 1.03729i) q^{41} +(1.24668 + 7.07025i) q^{43} +(-7.05474 + 2.50784i) q^{45} +(2.70628 - 3.22521i) q^{47} +(-7.04108 - 12.1955i) q^{49} +(-5.38768 + 5.34735i) q^{51} +(-1.64899 + 9.35187i) q^{53} +(-8.26046 + 6.93135i) q^{55} +(7.06107 + 2.67232i) q^{57} +(4.98221 - 4.18057i) q^{59} +(1.49179 - 8.46035i) q^{61} +(4.80832 - 12.9081i) q^{63} +(-2.37829 - 4.11932i) q^{65} +(9.62058 - 11.4654i) q^{67} +(-0.571168 + 6.25761i) q^{69} +(0.219681 + 1.24587i) q^{71} +(-2.29219 - 0.834290i) q^{73} +(0.892177 + 1.93220i) q^{75} -19.8385i q^{77} +(-4.31964 + 11.8681i) q^{79} +(8.50254 - 2.95074i) q^{81} +(15.5265 + 8.96425i) q^{83} +(8.37886 + 7.03070i) q^{85} +(-4.15748 + 5.89027i) q^{87} +(10.0104 - 3.64348i) q^{89} +(8.61794 + 1.51957i) q^{91} +(1.95333 - 4.14817i) q^{93} +(2.90981 - 10.4823i) q^{95} +(1.02401 + 1.22036i) q^{97} +(9.99179 - 8.25696i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{9} + 3 q^{13} - 3 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{25} + 3 q^{27} + 6 q^{29} + 24 q^{35} + 18 q^{39} + 3 q^{41} - 21 q^{43} + 63 q^{45} - 18 q^{47} - 30 q^{49} + 33 q^{51} - 36 q^{53} + 18 q^{55}+ \cdots - 39 q^{99}+O(q^{100}) $ 60 * q - 6 * q^9 + 3 * q^13 - 3 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^25 + 3 * q^27 + 6 * q^29 + 24 * q^35 + 18 * q^39 + 3 * q^41 - 21 * q^43 + 63 * q^45 - 18 * q^47 - 30 * q^49 + 33 * q^51 - 36 * q^53 + 18 * q^55 - 24 * q^57 - 21 * q^59 - 6 * q^61 - 24 * q^63 + 24 * q^65 - 48 * q^67 - 21 * q^69 + 36 * q^71 - 57 * q^73 - 36 * q^79 + 6 * q^81 - 36 * q^83 + 6 * q^85 + 72 * q^87 - 24 * q^89 - 18 * q^91 + 108 * q^93 + 30 * q^95 + 15 * q^97 - 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$	$1$

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
$3$	0.144474	+	1.72601i	0.0834123	+	0.996515i
$3$	0.144474	+	1.72601i	0.0834123	+	0.996515i
$4$		0			0
$5$	2.45783	−	0.433381i	1.09917	−	0.193814i	0.405494	−	0.914098i	$-0.367099\pi$
$5$	2.45783	−	0.433381i	1.09917	−	0.193814i	0.693680	+	0.720284i	$0.255988\pi$
$6$		0			0
$7$	−2.29577	+	3.97638i	−0.867718	+	1.50293i	−0.00339458	+	0.999994i	$0.501081\pi$
$7$	−2.29577	+	3.97638i	−0.867718	+	1.50293i	−0.864323	+	0.502937i	$0.832253\pi$
$8$		0			0
$9$	−2.95825	+	0.498730i	−0.986085	+	0.166243i
$10$		0			0
$11$	−3.74180	+	2.16033i	−1.12820	+	0.651365i	−0.943481	−	0.331427i	$-0.892470\pi$
$11$	−3.74180	+	2.16033i	−1.12820	+	0.651365i	−0.184716	+	0.982792i	$0.559136\pi$
$12$		0			0
$13$	−0.651848	−	1.79094i	−0.180790	−	0.496716i	0.815883	−	0.578217i	$-0.196251\pi$
$13$	−0.651848	−	1.79094i	−0.180790	−	0.496716i	−0.996673	+	0.0815001i	$0.974029\pi$
$14$		0			0
$15$	1.10312	+	4.17963i	0.284823	+	1.07918i
$16$		0			0
$17$	2.81708	+	3.35726i	0.683241	+	0.814255i	0.990521	−	0.137364i	$-0.0438631\pi$
$17$	2.81708	+	3.35726i	0.683241	+	0.814255i	−0.307279	+	0.951619i	$0.599419\pi$
$18$		0			0
$19$	1.87753	−	3.93381i	0.430736	−	0.902478i
$19$	1.87753	−	3.93381i	0.430736	−	0.902478i
$20$		0			0
$21$	−7.19497	−	3.38804i	−1.57007	−	0.739331i
$22$		0			0
$23$	3.57273	+	0.629969i	0.744967	+	0.131358i	0.533231	−	0.845969i	$-0.320977\pi$
$23$	3.57273	+	0.629969i	0.744967	+	0.131358i	0.211735	+	0.977327i	$0.432089\pi$
$24$		0			0
$25$	1.15463	−	0.420253i	0.230927	−	0.0840505i
$26$		0			0
$27$	−1.28821	−	5.03394i	−0.247915	−	0.968782i
$28$		0			0
$29$	3.18868	+	2.67562i	0.592124	+	0.496851i	0.888903	−	0.458095i	$-0.151468\pi$
$29$	3.18868	+	2.67562i	0.592124	+	0.496851i	−0.296779	+	0.954946i	$0.595913\pi$
$30$		0			0
$31$	−2.29253	−	1.32359i	−0.411750	−	0.237724i	0.279791	−	0.960061i	$-0.409735\pi$
$31$	−2.29253	−	1.32359i	−0.411750	−	0.237724i	−0.691542	+	0.722337i	$0.743068\pi$
$32$		0			0
$33$	−4.26936	−	6.14630i	−0.743200	−	1.06993i
$34$		0			0
$35$	−3.91931	+	10.7682i	−0.662484	+	1.82016i
$36$		0			0
$37$			5.26569i			0.865674i	0.901472	+	0.432837i	$0.142487\pi$
$37$			5.26569i			0.865674i	−0.901472	+	0.432837i	$0.857513\pi$
$38$		0			0
$39$	2.99701	−	1.38384i	0.479905	−	0.221592i
$40$		0			0
$41$	2.84993	+	1.03729i	0.445084	+	0.161997i	0.554832	−	0.831962i	$-0.312782\pi$
$41$	2.84993	+	1.03729i	0.445084	+	0.161997i	−0.109749	+	0.993959i	$0.535005\pi$
$42$		0			0
$43$	1.24668	+	7.07025i	0.190116	+	1.07820i	0.919204	+	0.393782i	$0.128834\pi$
$43$	1.24668	+	7.07025i	0.190116	+	1.07820i	−0.729088	+	0.684420i	$0.760055\pi$
$44$		0			0
$45$	−7.05474	+	2.50784i	−1.05166	+	0.373847i
$46$		0			0
$47$	2.70628	−	3.22521i	0.394751	−	0.470446i	−0.531661	−	0.846957i	$-0.678432\pi$
$47$	2.70628	−	3.22521i	0.394751	−	0.470446i	0.926412	+	0.376511i	$0.122876\pi$
$48$		0			0
$49$	−7.04108	−	12.1955i	−1.00587	−	1.74221i
$50$		0			0
$51$	−5.38768	+	5.34735i	−0.754427	+	0.748779i
$52$		0			0
$53$	−1.64899	+	9.35187i	−0.226506	+	1.28458i	0.633279	+	0.773923i	$0.281708\pi$
$53$	−1.64899	+	9.35187i	−0.226506	+	1.28458i	−0.859785	+	0.510656i	$0.829403\pi$
$54$		0			0
$55$	−8.26046	+	6.93135i	−1.11384	+	0.934623i
$56$		0			0
$57$	7.06107	+	2.67232i	0.935262	+	0.353957i
$58$		0			0
$59$	4.98221	−	4.18057i	0.648628	−	0.544264i	−0.258026	−	0.966138i	$-0.583072\pi$
$59$	4.98221	−	4.18057i	0.648628	−	0.544264i	0.906654	+	0.421874i	$0.138628\pi$
$60$		0			0
$61$	1.49179	−	8.46035i	0.191004	−	1.08324i	−0.726992	−	0.686646i	$-0.759082\pi$
$61$	1.49179	−	8.46035i	0.191004	−	1.08324i	0.917996	−	0.396590i	$-0.129807\pi$
$62$		0			0
$63$	4.80832	−	12.9081i	0.605791	−	1.62627i
$64$		0			0
$65$	−2.37829	−	4.11932i	−0.294990	−	0.510938i
$66$		0			0
$67$	9.62058	−	11.4654i	1.17534	−	1.40072i	0.277312	−	0.960780i	$-0.410556\pi$
$67$	9.62058	−	11.4654i	1.17534	−	1.40072i	0.898029	−	0.439937i	$-0.144999\pi$
$68$		0			0
$69$	−0.571168	+	6.25761i	−0.0687606	+	0.753327i
$70$		0			0
$71$	0.219681	+	1.24587i	0.0260714	+	0.147858i	0.995065	−	0.0992292i	$-0.0316377\pi$
$71$	0.219681	+	1.24587i	0.0260714	+	0.147858i	−0.968993	+	0.247087i	$0.920527\pi$
$72$		0			0
$73$	−2.29219	−	0.834290i	−0.268281	−	0.0976463i	0.204377	−	0.978892i	$-0.434483\pi$
$73$	−2.29219	−	0.834290i	−0.268281	−	0.0976463i	−0.472658	+	0.881246i	$0.656705\pi$
$74$		0			0
$75$	0.892177	+	1.93220i	0.103020	+	0.223111i
$76$		0			0
$77$		−	19.8385i		−	2.26080i
$78$		0			0
$79$	−4.31964	+	11.8681i	−0.485998	+	1.33527i	0.418278	+	0.908319i	$0.362634\pi$
$79$	−4.31964	+	11.8681i	−0.485998	+	1.33527i	−0.904276	+	0.426949i	$0.859588\pi$
$80$		0			0
$81$	8.50254	−	2.95074i	0.944726	−	0.327860i
$82$		0			0
$83$	15.5265	+	8.96425i	1.70426	+	0.983954i	0.941339	+	0.337461i	$0.109568\pi$
$83$	15.5265	+	8.96425i	1.70426	+	0.983954i	0.762920	+	0.646493i	$0.223765\pi$
$84$		0			0
$85$	8.37886	+	7.03070i	0.908815	+	0.762586i
$86$		0			0
$87$	−4.15748	+	5.89027i	−0.445729	+	0.631504i
$88$		0			0
$89$	10.0104	−	3.64348i	1.06110	−	0.386208i	0.248258	−	0.968694i	$-0.420142\pi$
$89$	10.0104	−	3.64348i	1.06110	−	0.386208i	0.812841	+	0.582486i	$0.197920\pi$
$90$		0			0
$91$	8.61794	+	1.51957i	0.903405	+	0.159295i
$92$		0			0
$93$	1.95333	−	4.14817i	0.202551	−	0.430145i
$94$		0			0
$95$	2.90981	−	10.4823i	0.298540	−	1.07546i
$96$		0			0
$97$	1.02401	+	1.22036i	0.103972	+	0.123909i	0.815521	−	0.578727i	$-0.196450\pi$
$97$	1.02401	+	1.22036i	0.103972	+	0.123909i	−0.711549	+	0.702637i	$0.752006\pi$
$98$		0			0
$99$	9.99179	−	8.25696i	1.00421	−	0.829856i
$100$		0			0
$101$	−3.14558	−	8.64241i	−0.312997	−	0.859952i	−0.992048	−	0.125861i	$-0.959831\pi$
$101$	−3.14558	−	8.64241i	−0.312997	−	0.859952i	0.679051	−	0.734091i	$-0.262392\pi$
$102$		0			0
$103$	−7.73101	+	4.46350i	−0.761759	+	0.439802i	−0.829927	−	0.557872i	$-0.811618\pi$
$103$	−7.73101	+	4.46350i	−0.761759	+	0.439802i	0.0681681	+	0.997674i	$0.478285\pi$
$104$		0			0
$105$	−19.1523	−	5.20905i	−1.86907	−	0.508351i
$106$		0			0
$107$	7.80705	−	13.5222i	0.754736	−	1.30724i	−0.190769	−	0.981635i	$-0.561098\pi$
$107$	7.80705	−	13.5222i	0.754736	−	1.30724i	0.945505	−	0.325607i	$-0.105569\pi$
$108$		0			0
$109$	5.80872	−	1.02423i	0.556374	−	0.0981038i	0.111611	−	0.993752i	$-0.464399\pi$
$109$	5.80872	−	1.02423i	0.556374	−	0.0981038i	0.444763	+	0.895648i	$0.353288\pi$
$110$		0			0
$111$	−9.08866	+	0.760757i	−0.862657	+	0.0722078i
$112$		0			0
$113$	11.5473			1.08628			0.543142	−	0.839641i	$-0.317235\pi$
$113$	11.5473			1.08628			0.543142	+	0.839641i	$0.317235\pi$
$114$		0			0
$115$	9.05418			0.844307
$116$		0			0
$117$	2.82152	+	4.97295i	0.260850	+	0.459749i
$118$		0			0
$119$	−19.8171	+	3.49429i	−1.81663	+	0.320321i
$120$		0			0
$121$	3.83407	−	6.64080i	0.348552	−	0.603709i
$122$		0			0
$123$	−1.37863	+	5.06888i	−0.124307	+	0.457045i
$124$		0			0
$125$	−8.15112	+	4.70605i	−0.729059	+	0.420922i
$126$		0			0
$127$	−5.29301	−	14.5424i	−0.469679	−	1.29043i	−0.918008	−	0.396563i	$-0.870203\pi$
$127$	−5.29301	−	14.5424i	−0.469679	−	1.29043i	0.448329	−	0.893869i	$-0.352019\pi$
$128$		0			0
$129$	−12.0232	+	3.17325i	−1.05859	+	0.279389i
$130$		0			0
$131$	−3.79397	−	4.52148i	−0.331481	−	0.395043i	0.574401	−	0.818574i	$-0.305235\pi$
$131$	−3.79397	−	4.52148i	−0.331481	−	0.395043i	−0.905882	+	0.423531i	$0.860791\pi$
$132$		0			0
$133$	11.3320	+	16.4969i	0.982606	+	1.43046i
$134$		0			0
$135$	−5.34780	−	11.8143i	−0.460266	−	1.01681i
$136$		0			0
$137$	−13.5569	−	2.39045i	−1.15825	−	0.204230i	−0.438673	−	0.898647i	$-0.644551\pi$
$137$	−13.5569	−	2.39045i	−1.15825	−	0.204230i	−0.719573	+	0.694417i	$0.755663\pi$
$138$		0			0
$139$	−11.2261	+	4.08596i	−0.952183	+	0.346566i	−0.770966	−	0.636877i	$-0.780226\pi$
$139$	−11.2261	+	4.08596i	−0.952183	+	0.346566i	−0.181218	+	0.983443i	$0.558004\pi$
$140$		0			0
$141$	5.95775	+	4.20511i	0.501733	+	0.354134i
$142$		0			0
$143$	6.30810	+	5.29313i	0.527510	+	0.442634i
$144$		0			0
$145$	8.99680	+	5.19430i	0.747143	+	0.431363i
$146$		0			0
$147$	20.0324	−	13.9149i	1.65224	−	1.14768i
$148$		0			0
$149$	−6.82022	+	18.7384i	−0.558735	+	1.53511i	0.262741	+	0.964866i	$0.415374\pi$
$149$	−6.82022	+	18.7384i	−0.558735	+	1.53511i	−0.821475	+	0.570244i	$0.806849\pi$
$150$		0			0
$151$			2.58955i			0.210735i	0.994433	+	0.105367i	$0.0336018\pi$
$151$			2.58955i			0.210735i	−0.994433	+	0.105367i	$0.966398\pi$
$152$		0			0
$153$	−10.0080	−	8.52667i	−0.809098	−	0.689340i
$154$		0			0
$155$	−6.20826	−	2.25962i	−0.498660	−	0.181497i
$156$		0			0
$157$	−0.383416	−	2.17446i	−0.0305999	−	0.173541i	0.965678	−	0.259743i	$-0.0836379\pi$
$157$	−0.383416	−	2.17446i	−0.0305999	−	0.173541i	−0.996278	+	0.0862025i	$0.972527\pi$
$158$		0			0
$159$	−16.3797	−	1.49507i	−1.29900	−	0.118567i
$160$		0			0
$161$	−10.7072	+	12.7603i	−0.843842	+	1.00565i
$162$		0			0
$163$	−7.10780	−	12.3111i	−0.556726	−	0.964277i	−0.997767	−	0.0667904i	$-0.978724\pi$
$163$	−7.10780	−	12.3111i	−0.556726	−	0.964277i	0.441041	−	0.897487i	$-0.354609\pi$
$164$		0			0
$165$	−13.1570	−	13.2563i	−1.02427	−	1.03200i
$166$		0			0
$167$	2.76178	−	15.6628i	0.213713	−	1.21203i	−0.669413	−	0.742891i	$-0.733454\pi$
$167$	2.76178	−	15.6628i	0.213713	−	1.21203i	0.883126	−	0.469136i	$-0.155435\pi$
$168$		0			0
$169$	7.17603	−	6.02140i	0.552002	−	0.463185i
$170$		0			0
$171$	−3.59231	+	12.5736i	−0.274711	+	0.961527i
$172$		0			0
$173$	11.6673	−	9.79004i	0.887049	−	0.744323i	−0.0805667	−	0.996749i	$-0.525673\pi$
$173$	11.6673	−	9.79004i	0.887049	−	0.744323i	0.967616	+	0.252426i	$0.0812286\pi$
$174$		0			0
$175$	−0.979685	+	5.55607i	−0.0740572	+	0.419999i
$176$		0			0
$177$	7.93552	+	7.99538i	0.596470	+	0.600969i
$178$		0			0
$179$	4.58725	+	7.94535i	0.342867	+	0.593863i	0.984964	−	0.172760i	$-0.0552686\pi$
$179$	4.58725	+	7.94535i	0.342867	+	0.593863i	−0.642097	+	0.766624i	$0.721935\pi$
$180$		0			0
$181$	−6.79399	+	8.09676i	−0.504993	+	0.601828i	−0.956965	−	0.290205i	$-0.906277\pi$
$181$	−6.79399	+	8.09676i	−0.504993	+	0.601828i	0.451971	+	0.892033i	$0.350721\pi$
$182$		0			0
$183$	14.8182	+	1.35254i	1.09539	+	0.0999830i
$184$		0			0
$185$	2.28205	+	12.9422i	0.167780	+	0.951526i
$186$		0			0
$187$	−17.7937	−	6.47639i	−1.30121	−	0.473601i
$188$		0			0
$189$	22.9743	+	6.43434i	1.67113	+	0.468029i
$190$		0			0
$191$		−	5.81299i		−	0.420613i	−0.977636	−	0.210306i	$-0.932554\pi$
$191$		−	5.81299i		−	0.420613i	0.977636	−	0.210306i	$-0.0674462\pi$
$192$		0			0
$193$	1.86644	−	5.12800i	0.134349	−	0.369122i	−0.854215	−	0.519919i	$-0.825962\pi$
$193$	1.86644	−	5.12800i	0.134349	−	0.369122i	0.988565	+	0.150798i	$0.0481842\pi$
$194$		0			0
$195$	6.76640	−	4.70010i	0.484552	−	0.336581i
$196$		0			0
$197$	17.1165	+	9.88223i	1.21950	+	0.704080i	0.964812	−	0.262942i	$-0.0846929\pi$
$197$	17.1165	+	9.88223i	1.21950	+	0.704080i	0.254691	+	0.967023i	$0.418026\pi$
$198$		0			0
$199$	−19.8707	−	16.6735i	−1.40859	−	1.18195i	−0.957129	−	0.289660i	$-0.906458\pi$
$199$	−19.8707	−	16.6735i	−1.40859	−	1.18195i	−0.451464	−	0.892290i	$-0.649098\pi$
$200$		0			0
$201$	21.1793	+	14.9488i	1.49387	+	1.05441i
$202$		0			0
$203$	−17.9598	+	6.53682i	−1.26053	+	0.458795i
$204$		0			0
$205$	7.45417	+	1.31437i	0.520622	+	0.0917997i
$206$		0			0
$207$	−10.8832	−	0.0817814i	−0.756438	−	0.00568420i
$208$		0			0
$209$	1.47298	+	18.7756i	0.101888	+	1.29874i
$210$		0			0
$211$	18.0319	+	21.4896i	1.24137	+	1.47941i	0.819841	+	0.572592i	$0.194062\pi$
$211$	18.0319	+	21.4896i	1.24137	+	1.47941i	0.421529	+	0.906815i	$0.361494\pi$
$212$		0			0
$213$	−2.11866	+	0.559170i	−0.145168	+	0.0383137i
$214$		0			0
$215$	6.12823	+	16.8372i	0.417942	+	1.14828i
$216$		0			0
$217$	10.5262	−	6.07732i	0.714566	−	0.412555i
$218$		0			0
$219$	1.10883	−	4.07689i	0.0749281	−	0.275491i
$220$		0			0
$221$	4.17634	−	7.23363i	0.280931	−	0.486586i
$222$		0			0
$223$	−12.1785	+	2.14739i	−0.815531	+	0.143800i	−0.565829	−	0.824523i	$-0.691444\pi$
$223$	−12.1785	+	2.14739i	−0.815531	+	0.143800i	−0.249702	+	0.968323i	$0.580333\pi$
$224$		0			0
$225$	−3.20611	+	1.81906i	−0.213741	+	0.121271i
$226$		0			0
$227$	22.7402			1.50932			0.754661	−	0.656115i	$-0.227801\pi$
$227$	22.7402			1.50932			0.754661	+	0.656115i	$0.227801\pi$
$228$		0			0
$229$	−4.80165			−0.317302			−0.158651	−	0.987335i	$-0.550714\pi$
$229$	−4.80165			−0.317302			−0.158651	+	0.987335i	$0.550714\pi$
$230$		0			0
$231$	34.2415	−	2.86615i	2.25292	−	0.188579i
$232$		0			0
$233$	−16.4340	+	2.89777i	−1.07663	+	0.189839i	−0.683725	−	0.729740i	$-0.739641\pi$
$233$	−16.4340	+	2.89777i	−1.07663	+	0.189839i	−0.392905	+	0.919579i	$0.628530\pi$
$234$		0			0
$235$	5.25381	−	9.09987i	0.342721	−	0.593610i
$236$		0			0
$237$	−21.1086	−	5.74113i	−1.37115	−	0.372926i
$238$		0			0
$239$	−18.5367	+	10.7022i	−1.19904	+	0.692266i	−0.960341	−	0.278827i	$-0.910054\pi$
$239$	−18.5367	+	10.7022i	−1.19904	+	0.692266i	−0.238699	+	0.971094i	$0.576721\pi$
$240$		0			0
$241$	2.43271	+	6.68382i	0.156705	+	0.430543i	0.993055	−	0.117653i	$-0.0375371\pi$
$241$	2.43271	+	6.68382i	0.156705	+	0.430543i	−0.836350	+	0.548196i	$0.815315\pi$
$242$		0			0
$243$	6.32142	+	14.2492i	0.405519	+	0.914087i
$244$		0			0
$245$	−22.5911	−	26.9230i	−1.44329	−	1.72005i
$246$		0			0
$247$	−8.26907	−	0.798297i	−0.526148	−	0.0507944i
$248$		0			0
$249$	−13.2292	+	28.0941i	−0.838369	+	1.78039i
$250$		0			0
$251$	0.626296	+	0.110433i	0.0395314	+	0.00697046i	0.193379	−	0.981124i	$-0.438055\pi$
$251$	0.626296	+	0.110433i	0.0395314	+	0.00697046i	−0.153847	+	0.988095i	$0.549166\pi$
$252$		0			0
$253$	−14.7294	+	5.36107i	−0.926030	+	0.337048i
$254$		0			0
$255$	−10.9246	+	15.4778i	−0.684122	+	0.969257i
$256$		0			0
$257$	−18.7785	−	15.7571i	−1.17137	−	0.982898i	−0.171375	−	0.985206i	$-0.554821\pi$
$257$	−18.7785	−	15.7571i	−1.17137	−	0.982898i	−0.999997	+	0.00230758i	$0.999265\pi$
$258$		0			0
$259$	−20.9384	−	12.0888i	−1.30105	−	0.751161i
$260$		0			0
$261$	−10.7673	−	6.32488i	−0.666482	−	0.391500i
$262$		0			0
$263$	−1.49037	+	4.09475i	−0.0919001	+	0.252493i	−0.977123	−	0.212673i	$-0.931783\pi$
$263$	−1.49037	+	4.09475i	−0.0919001	+	0.252493i	0.885223	+	0.465166i	$0.154005\pi$
$264$		0			0
$265$			23.6999i			1.45588i
$266$		0			0
$267$	7.73495	+	16.7517i	0.473371	+	1.02519i
$268$		0			0
$269$	−5.86725	−	2.13550i	−0.357732	−	0.130204i	0.156901	−	0.987614i	$-0.449850\pi$
$269$	−5.86725	−	2.13550i	−0.357732	−	0.130204i	−0.514633	+	0.857410i	$0.672072\pi$
$270$		0			0
$271$	1.51875	+	8.61329i	0.0922578	+	0.523220i	0.995553	+	0.0942008i	$0.0300296\pi$
$271$	1.51875	+	8.61329i	0.0922578	+	0.523220i	−0.903295	+	0.429019i	$0.858859\pi$
$272$		0			0
$273$	−1.37774	+	15.0942i	−0.0833845	+	0.913544i
$274$		0			0
$275$	−3.41253	+	4.06690i	−0.205783	+	0.245243i
$276$		0			0
$277$	6.13311	+	10.6229i	0.368503	+	0.638266i	0.989332	−	0.145680i	$-0.0465371\pi$
$277$	6.13311	+	10.6229i	0.368503	+	0.638266i	−0.620829	+	0.783946i	$0.713204\pi$
$278$		0			0
$279$	7.44200	+	2.77217i	0.445541	+	0.165966i
$280$		0			0
$281$	1.62709	−	9.22769i	0.0970641	−	0.550478i	−0.897031	−	0.441967i	$-0.854281\pi$
$281$	1.62709	−	9.22769i	0.0970641	−	0.550478i	0.994095	−	0.108511i	$-0.0346081\pi$
$282$		0			0
$283$	19.1635	−	16.0801i	1.13915	−	0.955861i	0.139740	−	0.990188i	$-0.455373\pi$
$283$	19.1635	−	16.0801i	1.13915	−	0.955861i	0.999411	+	0.0343277i	$0.0109290\pi$
$284$		0			0
$285$	18.5130	+	3.50795i	1.09662	+	0.207793i
$286$		0			0
$287$	−10.6674	+	8.95102i	−0.629678	+	0.528362i
$288$		0			0
$289$	−0.383260	+	2.17358i	−0.0225447	+	0.127857i
$290$		0			0
$291$	−1.95842	+	1.94376i	−0.114805	+	0.113945i
$292$		0			0
$293$	6.85167	+	11.8674i	0.400279	+	0.693304i	0.993759	−	0.111545i	$-0.0355799\pi$
$293$	6.85167	+	11.8674i	0.400279	+	0.693304i	−0.593480	+	0.804848i	$0.702247\pi$
$294$		0			0
$295$	10.4336	−	12.4343i	0.607469	−	0.723954i
$296$		0			0
$297$	15.6952	+	16.0531i	0.910727	+	0.931493i
$298$		0			0
$299$	−1.20064	−	6.80918i	−0.0694350	−	0.393785i
$300$		0			0
$301$	−30.9761	−	11.2744i	−1.78543	−	0.649844i
$302$		0			0
$303$	14.4625	−	6.67793i	0.830848	−	0.383637i
$304$		0			0
$305$		−	21.4406i		−	1.22768i
$306$		0			0
$307$	−1.95864	+	5.38131i	−0.111785	+	0.307128i	−0.982953	−	0.183858i	$-0.941141\pi$
$307$	−1.95864	+	5.38131i	−0.111785	+	0.307128i	0.871167	+	0.490986i	$0.163363\pi$
$308$		0			0
$309$	−8.82100	−	12.6990i	−0.501809	−	0.722419i
$310$		0			0
$311$	−18.2229	−	10.5210i	−1.03333	−	0.596592i	−0.115391	−	0.993320i	$-0.536812\pi$
$311$	−18.2229	−	10.5210i	−1.03333	−	0.596592i	−0.917936	+	0.396728i	$0.870146\pi$
$312$		0			0
$313$	2.99001	+	2.50892i	0.169006	+	0.141812i	0.723368	−	0.690463i	$-0.242593\pi$
$313$	2.99001	+	2.50892i	0.169006	+	0.141812i	−0.554362	+	0.832276i	$0.687038\pi$
$314$		0			0
$315$	6.22388	−	33.8098i	0.350676	−	1.90496i
$316$		0			0
$317$	−14.1115	+	5.13616i	−0.792580	+	0.288475i	−0.706408	−	0.707805i	$-0.749686\pi$
$317$	−14.1115	+	5.13616i	−0.792580	+	0.288475i	−0.0861718	+	0.996280i	$0.527463\pi$
$318$		0			0
$319$	−17.7117	−	3.12304i	−0.991663	−	0.174857i
$320$		0			0
$321$	24.4675	+	11.5215i	1.36564	+	0.643066i
$322$		0			0
$323$	18.4960	−	4.77848i	1.02914	−	0.265882i
$324$		0			0
$325$	−1.50529	−	1.79394i	−0.0834985	−	0.0995097i
$326$		0			0
$327$	2.60705	+	9.87796i	0.144170	+	0.546252i
$328$		0			0
$329$	6.61171	+	18.1655i	0.364515	+	1.00150i
$330$		0			0
$331$	−4.64775	+	2.68338i	−0.255463	+	0.147492i	−0.622263	−	0.782808i	$-0.713787\pi$
$331$	−4.64775	+	2.68338i	−0.255463	+	0.147492i	0.366800	+	0.930300i	$0.380453\pi$
$332$		0			0
$333$	−2.62615	−	15.5772i	−0.143912	−	0.853628i
$334$		0			0
$335$	18.6769	−	32.3493i	1.02043	−	1.76743i
$336$		0			0
$337$	5.31074	−	0.936426i	0.289294	−	0.0510104i	−0.0271178	−	0.999632i	$-0.508633\pi$
$337$	5.31074	−	0.936426i	0.289294	−	0.0510104i	0.316412	+	0.948622i	$0.397522\pi$
$338$		0			0
$339$	1.66830	+	19.9309i	0.0906094	+	1.08250i
$340$		0			0
$341$	11.4376			0.619381
$342$		0			0
$343$	32.5179			1.75580
$344$		0			0
$345$	1.30810	+	15.6277i	0.0704256	+	0.841365i
$346$		0			0
$347$	−33.0387	+	5.82562i	−1.77361	+	0.312735i	−0.962322	−	0.271911i	$-0.912344\pi$
$347$	−33.0387	+	5.82562i	−1.77361	+	0.312735i	−0.811288	+	0.584646i	$0.801233\pi$
$348$		0			0
$349$	7.23111	−	12.5246i	0.387072	−	0.670429i	−0.604982	−	0.796239i	$-0.706820\pi$
$349$	7.23111	−	12.5246i	0.387072	−	0.670429i	0.992054	+	0.125810i	$0.0401530\pi$
$350$		0			0
$351$	−8.17575	+	5.58846i	−0.436389	+	0.298290i
$352$		0			0
$353$	−7.95771	+	4.59438i	−0.423546	+	0.244534i	−0.696593	−	0.717466i	$-0.745302\pi$
$353$	−7.95771	+	4.59438i	−0.423546	+	0.244534i	0.273047	+	0.962001i	$0.411968\pi$
$354$		0			0
$355$	1.07988	+	2.96694i	0.0573139	+	0.157469i
$356$		0			0
$357$	−8.89425	−	33.6998i	−0.470734	−	1.78358i
$358$		0			0
$359$	5.30188	+	6.31854i	0.279823	+	0.333480i	0.887589	−	0.460636i	$-0.152379\pi$
$359$	5.30188	+	6.31854i	0.279823	+	0.333480i	−0.607766	+	0.794116i	$0.707934\pi$
$360$		0			0
$361$	−11.9497	−	14.7717i	−0.628934	−	0.777459i
$362$		0			0
$363$	12.0160	+	5.65823i	0.630679	+	0.296980i
$364$		0			0
$365$	−5.99538	−	1.05715i	−0.313813	−	0.0553336i
$366$		0			0
$367$	16.4716	−	5.99517i	0.859811	−	0.312946i	0.125777	−	0.992059i	$-0.459858\pi$
$367$	16.4716	−	5.99517i	0.859811	−	0.312946i	0.734034	+	0.679113i	$0.237635\pi$
$368$		0			0
$369$	−8.94813	−	1.64722i	−0.465821	−	0.0857508i
$370$		0			0
$371$	−33.4009	−	28.0267i	−1.73409	−	1.45507i
$372$		0			0
$373$	−5.05993	−	2.92135i	−0.261993	−	0.151262i	0.363250	−	0.931692i	$-0.381667\pi$
$373$	−5.05993	−	2.92135i	−0.261993	−	0.151262i	−0.625244	+	0.780430i	$0.715000\pi$
$374$		0			0
$375$	−9.30035	−	13.3891i	−0.480268	−	0.691408i
$376$		0			0
$377$	2.71334	−	7.45483i	0.139744	−	0.383943i
$378$		0			0
$379$			19.4099i			0.997020i	0.866884	+	0.498510i	$0.166119\pi$
$379$			19.4099i			0.997020i	−0.866884	+	0.498510i	$0.833881\pi$
$380$		0			0
$381$	24.3357	−	11.2368i	1.24676	−	0.575680i
$382$		0			0
$383$	1.85317	+	0.674499i	0.0946926	+	0.0344653i	0.388932	−	0.921266i	$-0.372844\pi$
$383$	1.85317	+	0.674499i	0.0946926	+	0.0344653i	−0.294239	+	0.955732i	$0.595066\pi$
$384$		0			0
$385$	−8.59762	−	48.7595i	−0.438175	−	2.48502i
$386$		0			0
$387$	−7.21412	−	20.2938i	−0.366715	−	1.03159i
$388$		0			0
$389$	8.92735	−	10.6392i	0.452635	−	0.539429i	−0.490675	−	0.871343i	$-0.663250\pi$
$389$	8.92735	−	10.6392i	0.452635	−	0.539429i	0.943310	+	0.331914i	$0.107694\pi$
$390$		0			0
$391$	7.94969	+	13.7693i	0.402033	+	0.696342i
$392$		0			0
$393$	7.25601	−	7.20169i	0.366017	−	0.363277i
$394$		0			0
$395$	−5.47352	+	31.0419i	−0.275403	+	1.56189i
$396$		0			0
$397$	8.93894	−	7.50066i	0.448633	−	0.376447i	−0.390296	−	0.920690i	$-0.627627\pi$
$397$	8.93894	−	7.50066i	0.448633	−	0.376447i	0.838928	+	0.544242i	$0.183183\pi$
$398$		0			0
$399$	−26.8367	+	21.9425i	−1.34352	+	1.09850i
$400$		0			0
$401$	12.7300	−	10.6818i	0.635707	−	0.533422i	−0.266989	−	0.963700i	$-0.586029\pi$
$401$	12.7300	−	10.6818i	0.635707	−	0.533422i	0.902697	+	0.430278i	$0.141584\pi$
$402$		0			0
$403$	−0.876091	+	4.96856i	−0.0436412	+	0.247501i
$404$		0			0
$405$	19.6190	−	10.9372i	0.974875	−	0.543476i
$406$		0			0
$407$	−11.3756	−	19.7032i	−0.563869	−	0.976650i
$408$		0			0
$409$	−0.596254	+	0.710588i	−0.0294829	+	0.0351363i	−0.780584	−	0.625050i	$-0.785078\pi$
$409$	−0.596254	+	0.710588i	−0.0294829	+	0.0351363i	0.751102	+	0.660187i	$0.229523\pi$
$410$		0			0
$411$	2.16733	−	23.7448i	0.106906	−	1.17125i
$412$		0			0
$413$	5.18556	+	29.4088i	0.255165	+	1.44711i
$414$		0			0
$415$	42.0465	+	15.3037i	2.06398	+	0.751228i
$416$		0			0
$417$	−8.67430	−	18.7861i	−0.424782	−	0.919957i
$418$		0			0
$419$			4.32431i			0.211256i	0.994406	+	0.105628i	$0.0336853\pi$
$419$			4.32431i			0.211256i	−0.994406	+	0.105628i	$0.966315\pi$
$420$		0			0
$421$	−7.48696	+	20.5703i	−0.364892	+	1.00253i	0.612383	+	0.790561i	$0.290211\pi$
$421$	−7.48696	+	20.5703i	−0.364892	+	1.00253i	−0.977276	+	0.211972i	$0.932011\pi$
$422$		0			0
$423$	−6.39734	+	10.8907i	−0.311049	+	0.529524i
$424$		0			0
$425$	4.66359	+	2.69252i	0.226217	+	0.130607i
$426$		0			0
$427$	30.2168	+	25.3549i	1.46229	+	1.22701i
$428$		0			0
$429$	−8.22466	+	11.6526i	−0.397090	+	0.562593i
$430$		0			0
$431$	−2.08390	+	0.758478i	−0.100378	+	0.0365346i	−0.391721	−	0.920084i	$-0.628120\pi$
$431$	−2.08390	+	0.758478i	−0.100378	+	0.0365346i	0.291343	+	0.956619i	$0.405898\pi$
$432$		0			0
$433$	−19.0991	−	3.36769i	−0.917845	−	0.161841i	−0.305282	−	0.952262i	$-0.598751\pi$
$433$	−19.0991	−	3.36769i	−0.917845	−	0.161841i	−0.612564	+	0.790421i	$0.709862\pi$
$434$		0			0
$435$	−7.66564	+	16.2791i	−0.367539	+	0.780521i
$436$		0			0
$437$	9.18611	−	12.8717i	0.439431	−	0.615736i
$438$		0			0
$439$	0.642464	+	0.765659i	0.0306631	+	0.0365429i	0.781158	−	0.624333i	$-0.214629\pi$
$439$	0.642464	+	0.765659i	0.0306631	+	0.0365429i	−0.750495	+	0.660876i	$0.770185\pi$
$440$		0			0
$441$	26.9116	+	32.5658i	1.28150	+	1.55075i
$442$		0			0
$443$	−4.15661	−	11.4202i	−0.197486	−	0.542589i	0.800935	−	0.598751i	$-0.204336\pi$
$443$	−4.15661	−	11.4202i	−0.197486	−	0.542589i	−0.998422	+	0.0561615i	$0.982114\pi$
$444$		0			0
$445$	23.0248	−	13.2934i	1.09148	−	0.630166i
$446$		0			0
$447$	−33.3281	−	9.06459i	−1.57637	−	0.428740i
$448$		0			0
$449$	13.6316	−	23.6107i	0.643316	−	1.11426i	−0.341371	−	0.939929i	$-0.610891\pi$
$449$	13.6316	−	23.6107i	0.643316	−	1.11426i	0.984688	−	0.174328i	$-0.0557753\pi$
$450$		0			0
$451$	−12.9048	+	2.27546i	−0.607661	+	0.107147i
$452$		0			0
$453$	−4.46960	+	0.374124i	−0.210000	+	0.0175779i
$454$		0			0
$455$	21.8400			1.02387
$456$		0			0
$457$	−21.5286			−1.00706			−0.503532	−	0.863976i	$-0.667967\pi$
$457$	−21.5286			−1.00706			−0.503532	+	0.863976i	$0.667967\pi$
$458$		0			0
$459$	13.2713	−	18.5058i	0.619449	−	0.863778i
$460$		0			0
$461$	11.7710	−	2.07554i	0.548230	−	0.0966677i	0.107329	−	0.994224i	$-0.465770\pi$
$461$	11.7710	−	2.07554i	0.548230	−	0.0966677i	0.440901	+	0.897556i	$0.354659\pi$
$462$		0			0
$463$	−17.2125	+	29.8130i	−0.799935	+	1.38553i	0.119723	+	0.992807i	$0.461799\pi$
$463$	−17.2125	+	29.8130i	−0.799935	+	1.38553i	−0.919658	+	0.392720i	$0.871534\pi$
$464$		0			0
$465$	3.00321	−	11.0420i	0.139270	−	0.512061i
$466$		0			0
$467$	10.1222	−	5.84403i	0.468398	−	0.270430i	−0.247171	−	0.968972i	$-0.579501\pi$
$467$	10.1222	−	5.84403i	0.468398	−	0.270430i	0.715569	+	0.698542i	$0.246168\pi$
$468$		0			0
$469$	23.5041	+	64.5769i	1.08532	+	2.98188i
$470$		0			0
$471$	3.69775	−	0.975934i	0.170383	−	0.0449687i
$472$		0			0
$473$	−19.9389	−	23.7623i	−0.916791	−	1.09259i
$474$		0			0
$475$	0.514670	−	5.33115i	0.0236147	−	0.244610i
$476$		0			0
$477$	0.214068	−	28.4876i	0.00980151	−	1.30436i
$478$		0			0
$479$	10.5999	+	1.86905i	0.484322	+	0.0853990i	0.410477	−	0.911871i	$-0.365362\pi$
$479$	10.5999	+	1.86905i	0.484322	+	0.0853990i	0.0738444	+	0.997270i	$0.476473\pi$
$480$		0			0
$481$	9.43051	−	3.43243i	0.429994	−	0.156505i
$482$		0			0
$483$	−23.5714	−	16.6372i	−1.07253	−	0.757018i
$484$		0			0
$485$	3.04572	+	2.55566i	0.138299	+	0.116047i
$486$		0			0
$487$	19.0096	+	10.9752i	0.861406	+	0.497333i	0.864483	−	0.502663i	$-0.167646\pi$
$487$	19.0096	+	10.9752i	0.861406	+	0.497333i	−0.00307718	+	0.999995i	$0.500979\pi$
$488$		0			0
$489$	20.2222	−	14.0468i	0.914479	−	0.635218i
$490$		0			0
$491$	5.65914	−	15.5484i	0.255393	−	0.701688i	−0.744043	−	0.668131i	$-0.767094\pi$
$491$	5.65914	−	15.5484i	0.255393	−	0.701688i	0.999437	−	0.0335565i	$-0.0106834\pi$
$492$		0			0
$493$			18.2427i			0.821608i
$494$		0			0
$495$	20.9797	−	24.6244i	0.942967	−	1.10679i
$496$		0			0
$497$	−5.45841	−	1.98670i	−0.244843	−	0.0891156i
$498$		0			0
$499$	0.0513797	+	0.291389i	0.00230007	+	0.0130443i	0.985936	−	0.167122i	$-0.0534474\pi$
$499$	0.0513797	+	0.291389i	0.00230007	+	0.0130443i	−0.983636	+	0.180167i	$0.942336\pi$
$500$		0			0
$501$	27.4333	+	2.50400i	1.22563	+	0.111870i
$502$		0			0
$503$	−6.11833	+	7.29154i	−0.272803	+	0.325114i	−0.885000	−	0.465592i	$-0.845842\pi$
$503$	−6.11833	+	7.29154i	−0.272803	+	0.325114i	0.612197	+	0.790705i	$0.290286\pi$
$504$		0			0
$505$	−11.4768	−	19.8783i	−0.510709	−	0.884574i
$506$		0			0
$507$	11.4298	+	11.5160i	0.507614	+	0.511443i
$508$		0			0
$509$	−4.18871	+	23.7553i	−0.185661	+	1.05294i	0.739442	+	0.673220i	$0.235089\pi$
$509$	−4.18871	+	23.7553i	−0.185661	+	1.05294i	−0.925103	+	0.379716i	$0.876022\pi$
$510$		0			0
$511$	8.57979	−	7.19930i	0.379548	−	0.318478i
$512$		0			0
$513$	−22.2212	−	4.38382i	−0.981090	−	0.193550i
$514$		0			0
$515$	−17.0671	+	14.3210i	−0.752066	+	0.631058i
$516$		0			0
$517$	−3.15882	+	17.9146i	−0.138925	+	0.787882i
$518$		0			0
$519$	18.5834	+	18.7235i	0.815720	+	0.821872i
$520$		0			0
$521$	−5.76706	−	9.98884i	−0.252659	−	0.437619i	0.711598	−	0.702587i	$-0.247972\pi$
$521$	−5.76706	−	9.98884i	−0.252659	−	0.437619i	−0.964257	+	0.264968i	$0.914639\pi$
$522$		0			0
$523$	7.64855	−	9.11518i	0.334448	−	0.398579i	−0.572444	−	0.819944i	$-0.694004\pi$
$523$	7.64855	−	9.11518i	0.334448	−	0.398579i	0.906891	+	0.421365i	$0.138449\pi$
$524$		0			0
$525$	−9.73140	−	0.888241i	−0.424713	−	0.0387660i
$526$		0			0
$527$	−2.01458	−	11.4253i	−0.0877567	−	0.497693i
$528$		0			0
$529$	−9.24536	−	3.36504i	−0.401972	−	0.146306i
$530$		0			0
$531$	−12.6537	+	14.8520i	−0.549122	+	0.644520i
$532$		0			0
$533$		−	5.78019i		−	0.250368i
$534$		0			0
$535$	13.3281	−	36.6187i	0.576225	−	1.58316i
$536$		0			0
$537$	−13.0511	+	9.06556i	−0.563194	+	0.391208i
$538$		0			0
$539$	52.6927	+	30.4221i	2.26963	+	1.31037i
$540$		0			0
$541$	−31.5118	−	26.4416i	−1.35480	−	1.13681i	−0.977551	−	0.210699i	$-0.932426\pi$
$541$	−31.5118	−	26.4416i	−1.35480	−	1.13681i	−0.377248	−	0.926112i	$-0.623130\pi$
$542$		0			0
$543$	−14.9567	−	10.5568i	−0.641853	−	0.453034i
$544$		0			0
$545$	13.8329	−	5.03478i	0.592538	−	0.215666i
$546$		0			0
$547$	−24.2128	−	4.26937i	−1.03526	−	0.182545i	−0.369906	−	0.929069i	$-0.620610\pi$
$547$	−24.2128	−	4.26937i	−1.03526	−	0.182545i	−0.665358	+	0.746524i	$0.731721\pi$
$548$		0			0
$549$	−0.193661	+	25.7719i	−0.00826525	+	1.09992i
$550$		0			0
$551$	16.5123	−	7.52011i	0.703446	−	0.320367i
$552$		0			0
$553$	−37.2753	−	44.4230i	−1.58511	−	1.88906i
$554$		0			0
$555$	−22.0087	+	5.80866i	−0.934215	+	0.246564i
$556$		0			0
$557$	−2.52133	−	6.92729i	−0.106832	−	0.293519i	0.874746	−	0.484582i	$-0.161028\pi$
$557$	−2.52133	−	6.92729i	−0.106832	−	0.293519i	−0.981578	+	0.191064i	$0.938806\pi$
$558$		0			0
$559$	11.8497	−	6.84144i	0.501190	−	0.289362i
$560$		0			0
$561$	8.60761	−	31.6479i	0.363414	−	1.33618i
$562$		0			0
$563$	−7.18491	+	12.4446i	−0.302808	+	0.524478i	−0.976771	−	0.214287i	$-0.931257\pi$
$563$	−7.18491	+	12.4446i	−0.302808	+	0.524478i	0.673963	+	0.738765i	$0.264591\pi$
$564$		0			0
$565$	28.3814	−	5.00441i	1.19401	−	0.210537i
$566$		0			0
$567$	−7.78657	+	40.5835i	−0.327005	+	1.70435i
$568$		0			0
$569$	−23.8628			−1.00038			−0.500190	−	0.865916i	$-0.666737\pi$
$569$	−23.8628			−1.00038			−0.500190	+	0.865916i	$0.666737\pi$
$570$		0			0
$571$	16.7519			0.701045			0.350523	−	0.936554i	$-0.386004\pi$
$571$	16.7519			0.701045			0.350523	+	0.936554i	$0.386004\pi$
$572$		0			0
$573$	10.0333	−	0.839827i	0.419147	−	0.0350843i
$574$		0			0
$575$	4.38995	−	0.774066i	0.183073	−	0.0322808i
$576$		0			0
$577$	14.0202	−	24.2838i	0.583670	−	1.01095i	−0.411369	−	0.911469i	$-0.634949\pi$
$577$	14.0202	−	24.2838i	0.583670	−	1.01095i	0.995040	−	0.0994781i	$-0.0317173\pi$
$578$		0			0
$579$	9.12066	+	2.48064i	0.379042	+	0.103092i
$580$		0			0
$581$	−71.2906	+	41.1596i	−2.95763	+	1.70759i
$582$		0			0
$583$	−14.0330	−	38.5552i	−0.581186	−	1.59680i
$584$		0			0
$585$	9.09000	+	10.9999i	0.375825	+	0.454788i
$586$		0			0
$587$	−10.8980	−	12.9877i	−0.449808	−	0.536060i	0.492720	−	0.870188i	$-0.336003\pi$
$587$	−10.8980	−	12.9877i	−0.449808	−	0.536060i	−0.942528	+	0.334128i	$0.891558\pi$
$588$		0			0
$589$	−9.51106	+	6.53329i	−0.391897	+	0.269200i
$590$		0			0
$591$	−14.5840	+	30.9711i	−0.599905	+	1.27398i
$592$		0			0
$593$	44.9926	+	7.93341i	1.84763	+	0.325786i	0.983975	−	0.178305i	$-0.0570614\pi$
$593$	44.9926	+	7.93341i	1.84763	+	0.325786i	0.863650	+	0.504091i	$0.168172\pi$
$594$		0			0
$595$	−47.1926	+	17.1767i	−1.93471	+	0.704177i
$596$		0			0
$597$	25.9078	−	36.7059i	1.06034	−	1.50227i
$598$		0			0
$599$	19.8093	+	16.6220i	0.809387	+	0.679156i	0.950461	−	0.310843i	$-0.100611\pi$
$599$	19.8093	+	16.6220i	0.809387	+	0.679156i	−0.141075	+	0.989999i	$0.545056\pi$
$600$		0			0
$601$	20.8635	+	12.0455i	0.851040	+	0.491348i	0.861002	−	0.508602i	$-0.169838\pi$
$601$	20.8635	+	12.0455i	0.851040	+	0.491348i	−0.00996176	+	0.999950i	$0.503171\pi$
$602$		0			0
$603$	−22.7420	+	38.7155i	−0.926126	+	1.57662i
$604$		0			0
$605$	6.54548	−	17.9836i	0.266112	−	0.731136i
$606$		0			0
$607$		−	21.8193i		−	0.885617i	−0.896616	−	0.442809i	$-0.853982\pi$
$607$		−	21.8193i		−	0.885617i	0.896616	−	0.442809i	$-0.146018\pi$
$608$		0			0
$609$	−13.8774	−	30.0544i	−0.562340	−	1.21787i
$610$		0			0
$611$	−7.54023	−	2.74442i	−0.305045	−	0.111027i
$612$		0			0
$613$	0.146818	+	0.832646i	0.00592992	+	0.0336302i	0.987629	−	0.156808i	$-0.0501203\pi$
$613$	0.146818	+	0.832646i	0.00592992	+	0.0336302i	−0.981699	+	0.190438i	$0.939009\pi$
$614$		0			0
$615$	−1.19169	+	13.0559i	−0.0480535	+	0.526465i
$616$		0			0
$617$	13.6787	−	16.3016i	0.550683	−	0.656279i	−0.416864	−	0.908969i	$-0.636871\pi$
$617$	13.6787	−	16.3016i	0.550683	−	0.656279i	0.967547	+	0.252690i	$0.0813153\pi$
$618$		0			0
$619$	−18.9506	−	32.8233i	−0.761688	−	1.31928i	−0.941980	−	0.335669i	$-0.891038\pi$
$619$	−18.9506	−	32.8233i	−0.761688	−	1.31928i	0.180293	−	0.983613i	$-0.442296\pi$
$620$		0			0
$621$	−1.43119	−	18.7965i	−0.0574318	−	0.754276i
$622$		0			0
$623$	−8.49361	+	48.1697i	−0.340289	+	1.92988i
$624$		0			0
$625$	−22.7009	+	19.0483i	−0.908035	+	0.761932i
$626$		0			0
$627$	−32.1942	+	5.25498i	−1.28571	+	0.209864i
$628$		0			0
$629$	−17.6783	+	14.8338i	−0.704879	+	0.591464i
$630$		0			0
$631$	−3.72763	+	21.1405i	−0.148395	+	0.841588i	0.816184	+	0.577792i	$0.196086\pi$
$631$	−3.72763	+	21.1405i	−0.148395	+	0.841588i	−0.964579	+	0.263796i	$0.915025\pi$
$632$		0			0
$633$	−34.4863	+	34.2281i	−1.37071	+	1.36044i
$634$		0			0
$635$	−19.3117	−	33.4489i	−0.766362	−	1.32738i
$636$		0			0
$637$	−17.2517	+	20.5597i	−0.683536	+	0.814606i
$638$		0			0
$639$	−1.27123	−	3.57605i	−0.0502890	−	0.141466i
$640$		0			0
$641$	0.890484	+	5.05019i	0.0351720	+	0.199470i	0.997330	−	0.0730202i	$-0.0232638\pi$
$641$	0.890484	+	5.05019i	0.0351720	+	0.199470i	−0.962158	+	0.272491i	$0.912153\pi$
$642$		0			0
$643$	26.2317	+	9.54757i	1.03448	+	0.376519i	0.802785	−	0.596269i	$-0.203351\pi$
$643$	26.2317	+	9.54757i	1.03448	+	0.376519i	0.231694	+	0.972789i	$0.425573\pi$
$644$		0			0
$645$	−28.1758	+	13.0099i	−1.10942	+	0.512266i
$646$		0			0
$647$			2.13623i			0.0839837i	0.999118	+	0.0419919i	$0.0133704\pi$
$647$			2.13623i			0.0839837i	−0.999118	+	0.0419919i	$0.986630\pi$
$648$		0			0
$649$	−9.61103	+	26.4061i	−0.377266	+	1.03653i
$650$		0			0
$651$	12.0103	+	17.2904i	0.470721	+	0.677664i
$652$		0			0
$653$	−0.500626	−	0.289037i	−0.0195910	−	0.0113109i	0.490173	−	0.871625i	$-0.336934\pi$
$653$	−0.500626	−	0.289037i	−0.0195910	−	0.0113109i	−0.509764	+	0.860315i	$0.670267\pi$
$654$		0			0
$655$	−11.2845	−	9.46878i	−0.440920	−	0.369976i
$656$		0			0
$657$	7.19698	+	1.32486i	0.280781	+	0.0516876i
$658$		0			0
$659$	23.0584	−	8.39258i	0.898229	−	0.326929i	0.148686	−	0.988884i	$-0.452496\pi$
$659$	23.0584	−	8.39258i	0.898229	−	0.326929i	0.749543	+	0.661956i	$0.230273\pi$
$660$		0			0
$661$	−13.9639	−	2.46222i	−0.543133	−	0.0957691i	−0.104651	−	0.994509i	$-0.533373\pi$
$661$	−13.9639	−	2.46222i	−0.543133	−	0.0957691i	−0.438482	+	0.898740i	$0.644484\pi$
$662$		0			0
$663$	13.0887	+	6.16334i	0.508324	+	0.239364i
$664$		0			0
$665$	35.0015	+	35.6355i	1.35730	+	1.38188i
$666$		0			0
$667$	9.70676	+	11.5681i	0.375847	+	0.447917i
$668$		0			0
$669$	−5.46591	−	20.7100i	−0.211324	−	0.800694i
$670$		0			0
$671$	12.6952	+	34.8797i	0.490092	+	1.34652i
$672$		0			0
$673$	−0.452127	+	0.261035i	−0.0174282	+	0.0100622i	−0.508689	−	0.860950i	$-0.669870\pi$
$673$	−0.452127	+	0.261035i	−0.0174282	+	0.0100622i	0.491261	+	0.871013i	$0.336536\pi$
$674$		0			0
$675$	−3.60293	−	5.27099i	−0.138677	−	0.202880i
$676$		0			0
$677$	22.3175	−	38.6550i	0.857730	−	1.48563i	−0.0163583	−	0.999866i	$-0.505207\pi$
$677$	22.3175	−	38.6550i	0.857730	−	1.48563i	0.874089	−	0.485766i	$-0.161459\pi$
$678$		0			0
$679$	−7.20351	+	1.27017i	−0.276446	+	0.0487448i
$680$		0			0
$681$	3.28538	+	39.2500i	0.125896	+	1.50406i
$682$		0			0
$683$	6.04064			0.231139			0.115569	−	0.993299i	$-0.463131\pi$
$683$	6.04064			0.231139			0.115569	+	0.993299i	$0.463131\pi$
$684$		0			0
$685$	−34.3566			−1.31270
$686$		0			0
$687$	−0.693715	−	8.28772i	−0.0264669	−	0.316196i
$688$		0			0
$689$	17.8235	−	3.14276i	0.679021	−	0.119730i
$690$		0			0
$691$	2.37454	−	4.11282i	0.0903316	−	0.156459i	−0.817319	−	0.576185i	$-0.804541\pi$
$691$	2.37454	−	4.11282i	0.0903316	−	0.156459i	0.907651	+	0.419726i	$0.137874\pi$
$692$		0			0
$693$	9.89403	+	58.6872i	0.375843	+	2.22934i
$694$		0			0
$695$	−25.8210	+	14.9077i	−0.979446	+	0.565483i
$696$		0			0
$697$	4.54601	+	12.4901i	0.172192	+	0.473095i
$698$		0			0
$699$	−7.37588	−	27.9468i	−0.278982	−	1.05704i
$700$		0			0
$701$	18.1636	+	21.6466i	0.686030	+	0.817579i	0.990869	−	0.134825i	$-0.0430471\pi$
$701$	18.1636	+	21.6466i	0.686030	+	0.817579i	−0.304839	+	0.952404i	$0.598603\pi$
$702$		0			0
$703$	20.7142	+	9.88650i	0.781252	+	0.372877i
$704$		0			0
$705$	16.4655	+	7.75346i	0.620128	+	0.292012i
$706$		0			0
$707$	41.5871	+	7.33292i	1.56404	+	0.275783i
$708$		0			0
$709$	23.2838	−	8.47462i	0.874443	−	0.318271i	0.134478	−	0.990917i	$-0.457064\pi$
$709$	23.2838	−	8.47462i	0.874443	−	0.318271i	0.739965	+	0.672645i	$0.234842\pi$
$710$		0			0
$711$	6.85962	−	37.2633i	0.257256	−	1.39748i
$712$		0			0
$713$	−7.35678	−	6.17307i	−0.275513	−	0.231183i
$714$		0			0
$715$	17.7982	+	10.2758i	0.665614	+	0.384292i
$716$		0			0
$717$	−21.1502	−	30.4485i	−0.789869	−	1.13712i
$718$		0			0
$719$	5.45833	−	14.9966i	0.203561	−	0.559280i	−0.795339	−	0.606165i	$-0.792707\pi$
$719$	5.45833	−	14.9966i	0.203561	−	0.559280i	0.998900	+	0.0468847i	$0.0149293\pi$
$720$		0			0
$721$		−	40.9886i		−	1.52649i
$722$		0			0
$723$	−11.1849	+	5.16453i	−0.415971	+	0.192071i
$724$		0			0
$725$	4.80620	+	1.74931i	0.178498	+	0.0649679i
$726$		0			0
$727$	0.0763752	+	0.433145i	0.00283260	+	0.0160645i	0.986191	−	0.165610i	$-0.0529593\pi$
$727$	0.0763752	+	0.433145i	0.00283260	+	0.0160645i	−0.983359	+	0.181675i	$0.941848\pi$
$728$		0			0
$729$	−23.6810	+	12.9695i	−0.877076	+	0.480352i
$730$		0			0
$731$	−20.2247	+	24.1028i	−0.748037	+	0.891475i
$732$		0			0
$733$	15.8181	+	27.3978i	0.584256	+	1.01196i	0.994968	+	0.100195i	$0.0319468\pi$
$733$	15.8181	+	27.3978i	0.584256	+	1.01196i	−0.410712	+	0.911765i	$0.634720\pi$
$734$		0			0
$735$	43.2056	−	42.8822i	1.59366	−	1.58173i
$736$		0			0
$737$	−11.2293	+	63.6848i	−0.413638	+	2.34586i
$738$		0			0
$739$	−20.1981	+	16.9482i	−0.742998	+	0.623449i	−0.933641	−	0.358210i	$-0.883387\pi$
$739$	−20.1981	+	16.9482i	−0.742998	+	0.623449i	0.190643	+	0.981659i	$0.438943\pi$
$740$		0			0
$741$	0.183204	−	14.3879i	0.00673018	−	0.528552i
$742$		0			0
$743$	23.4319	−	19.6617i	0.859633	−	0.721318i	−0.102256	−	0.994758i	$-0.532606\pi$
$743$	23.4319	−	19.6617i	0.859633	−	0.721318i	0.961889	+	0.273440i	$0.0881617\pi$
$744$		0			0
$745$	−8.64206	+	49.0115i	−0.316621	+	1.79564i
$746$		0			0
$747$	−50.4022	−	18.7750i	−1.84412	−	0.686941i
$748$		0			0
$749$	35.8463	+	62.0876i	1.30980	+	2.26863i
$750$		0			0
$751$	27.4205	−	32.6785i	1.00059	−	1.19245i	0.0193183	−	0.999813i	$-0.493850\pi$
$751$	27.4205	−	32.6785i	1.00059	−	1.19245i	0.981269	−	0.192641i	$-0.0617052\pi$
$752$		0			0
$753$	−0.100125	+	1.09695i	−0.00364876	+	0.0399751i
$754$		0			0
$755$	1.12226	+	6.36467i	0.0408433	+	0.231634i
$756$		0			0
$757$	−18.6067	−	6.77229i	−0.676272	−	0.246143i	−0.0190261	−	0.999819i	$-0.506057\pi$
$757$	−18.6067	−	6.77229i	−0.676272	−	0.246143i	−0.657246	+	0.753676i	$0.728279\pi$
$758$		0			0
$759$	−11.3813	−	24.6487i	−0.413115	−	0.894689i
$760$		0			0
$761$			21.0263i			0.762202i	0.924533	+	0.381101i	$0.124455\pi$
$761$			21.0263i			0.762202i	−0.924533	+	0.381101i	$0.875545\pi$
$762$		0			0
$763$	−9.26271	+	25.4491i	−0.335332	+	0.921318i
$764$		0			0
$765$	−28.2932	−	16.6198i	−1.02294	−	0.600890i
$766$		0			0
$767$	−10.7348	−	6.19772i	−0.387610	−	0.223787i
$768$		0			0
$769$	9.84253	+	8.25886i	0.354931	+	0.297822i	0.802766	−	0.596294i	$-0.203361\pi$
$769$	9.84253	+	8.25886i	0.354931	+	0.297822i	−0.447836	+	0.894116i	$0.647805\pi$
$770$		0			0
$771$	24.4839	−	34.6885i	0.881766	−	1.24928i
$772$		0			0
$773$	−48.7230	+	17.7337i	−1.75245	+	0.637838i	−0.999788	−	0.0205750i	$-0.993450\pi$
$773$	−48.7230	+	17.7337i	−1.75245	+	0.637838i	−0.752657	+	0.658413i	$0.771228\pi$
$774$		0			0
$775$	−3.20328	−	0.564824i	−0.115065	−	0.0202891i
$776$		0			0
$777$	17.8404	−	37.8865i	0.640019	−	1.35917i
$778$		0			0
$779$	9.43133	−	9.26353i	0.337912	−	0.331900i
$780$		0			0
$781$	−3.51351	−	4.18723i	−0.125723	−	0.149831i
$782$		0			0
$783$	9.36123	−	19.4984i	0.334543	−	0.696815i
$784$		0			0
$785$	−1.88474	−	5.17828i	−0.0672692	−	0.184821i
$786$		0			0
$787$	23.1195	−	13.3480i	0.824120	−	0.475806i	−0.0277150	−	0.999616i	$-0.508823\pi$
$787$	23.1195	−	13.3480i	0.824120	−	0.475806i	0.851835	+	0.523810i	$0.175490\pi$
$788$		0			0
$789$	−7.28293	−	1.98081i	−0.259279	−	0.0705187i
$790$		0			0
$791$	−26.5100	+	45.9167i	−0.942587	+	1.63261i
$792$		0			0
$793$	−16.1244	+	2.84316i	−0.572593	+	0.100964i
$794$		0			0
$795$	−40.9064	+	3.42403i	−1.45080	+	0.121438i
$796$		0			0
$797$	39.6576			1.40474			0.702372	−	0.711810i	$-0.252124\pi$
$797$	39.6576			1.40474			0.702372	+	0.711810i	$0.252124\pi$
$798$		0			0
$799$	18.4517			0.652773
$800$		0			0
$801$	−27.7961	+	15.7708i	−0.982128	+	0.557234i
$802$		0			0
$803$	10.3793	−	1.83015i	0.366277	−	0.0645845i
$804$		0			0
$805$	−20.7863	+	36.0029i	−0.732620	+	1.26894i
$806$		0			0
$807$	2.83824	−	10.4355i	0.0999109	−	0.367346i
$808$		0			0
$809$	−13.1404	+	7.58659i	−0.461990	+	0.266730i	−0.712881	−	0.701285i	$-0.752610\pi$
$809$	−13.1404	+	7.58659i	−0.461990	+	0.266730i	0.250890	+	0.968015i	$0.419277\pi$
$810$		0			0
$811$	−4.48250	−	12.3156i	−0.157402	−	0.432458i	0.835776	−	0.549071i	$-0.185018\pi$
$811$	−4.48250	−	12.3156i	−0.157402	−	0.432458i	−0.993177	+	0.116613i	$0.962796\pi$
$812$		0			0
$813$	−14.6472	+	3.86579i	−0.513701	+	0.135579i
$814$		0			0
$815$	−22.8051	−	27.1781i	−0.798829	−	0.952007i
$816$		0			0
$817$	30.1537	+	8.37044i	1.05494	+	0.292845i
$818$		0			0
$819$	−26.2519	−	0.197268i	−0.917316	−	0.00689311i
$820$		0			0
$821$	13.0469	+	2.30053i	0.455341	+	0.0802890i	0.396615	−	0.917985i	$-0.370185\pi$
$821$	13.0469	+	2.30053i	0.455341	+	0.0802890i	0.0587266	+	0.998274i	$0.481296\pi$
$822$		0			0
$823$	−20.4461	+	7.44178i	−0.712707	+	0.259404i	−0.672827	−	0.739800i	$-0.734920\pi$
$823$	−20.4461	+	7.44178i	−0.712707	+	0.259404i	−0.0398806	+	0.999204i	$0.512698\pi$
$824$		0			0
$825$	−7.51255	−	5.30252i	−0.261553	−	0.184610i
$826$		0			0
$827$	20.5471	+	17.2410i	0.714492	+	0.599530i	0.925855	−	0.377878i	$-0.123346\pi$
$827$	20.5471	+	17.2410i	0.714492	+	0.599530i	−0.211364	+	0.977407i	$0.567791\pi$
$828$		0			0
$829$	25.5289	+	14.7391i	0.886655	+	0.511910i	0.872847	−	0.487994i	$-0.162271\pi$
$829$	25.5289	+	14.7391i	0.886655	+	0.511910i	0.0138079	+	0.999905i	$0.495605\pi$
$830$		0			0
$831$	−17.4491	+	12.1206i	−0.605304	+	0.420458i
$832$		0			0
$833$	21.1082	−	57.9944i	0.731357	−	2.00939i
$834$		0			0
$835$		−	39.6935i		−	1.37365i
$836$		0			0
$837$	−3.70963	+	13.2455i	−0.128224	+	0.457832i
$838$		0			0
$839$	−12.8095	−	4.66226i	−0.442232	−	0.160959i	0.111301	−	0.993787i	$-0.464498\pi$
$839$	−12.8095	−	4.66226i	−0.442232	−	0.160959i	−0.553532	+	0.832828i	$0.686720\pi$
$840$		0			0
$841$	−2.02705	−	11.4960i	−0.0698984	−	0.396414i
$842$		0			0
$843$	16.1622	+	1.47522i	0.556656	+	0.0508092i
$844$		0			0
$845$	15.0279	−	17.9095i	0.516975	−	0.616107i
$846$		0			0
$847$	17.6042	+	30.4914i	0.604889	+	1.04770i
$848$		0			0
$849$	30.5231	+	30.7533i	1.04755	+	1.05545i
$850$		0			0
$851$	−3.31722	+	18.8129i	−0.113713	+	0.644898i
$852$		0			0
$853$	24.3461	−	20.4288i	0.833595	−	0.699470i	−0.122518	−	0.992466i	$-0.539097\pi$
$853$	24.3461	−	20.4288i	0.833595	−	0.699470i	0.956113	+	0.292997i	$0.0946525\pi$
$854$		0			0
$855$	−3.38012	+	32.4606i	−0.115598	+	1.11013i
$856$		0			0
$857$	5.73136	−	4.80918i	0.195780	−	0.164279i	−0.539628	−	0.841904i	$-0.681435\pi$
$857$	5.73136	−	4.80918i	0.195780	−	0.164279i	0.735408	+	0.677625i	$0.236991\pi$
$858$		0			0
$859$	6.61755	−	37.5300i	0.225788	−	1.28051i	−0.635386	−	0.772195i	$-0.719159\pi$
$859$	6.61755	−	37.5300i	0.225788	−	1.28051i	0.861173	−	0.508311i	$-0.169730\pi$
$860$		0			0
$861$	−16.9908	−	17.1189i	−0.579044	−	0.583411i
$862$		0			0
$863$	17.8990	+	31.0020i	0.609289	+	1.05532i	0.991358	+	0.131185i	$0.0418783\pi$
$863$	17.8990	+	31.0020i	0.609289	+	1.05532i	−0.382069	+	0.924134i	$0.624788\pi$
$864$		0			0
$865$	24.4334	−	29.1186i	0.830761	−	0.990063i
$866$		0			0
$867$	−3.80699	−	0.347487i	−0.129292	−	0.0118013i
$868$		0			0
$869$	−9.47582	−	53.7401i	−0.321445	−	1.82301i
$870$		0			0
$871$	−26.8049	−	9.75618i	−0.908249	−	0.330576i
$872$		0			0
$873$	−3.63791	−	3.09945i	−0.123124	−	0.104900i
$874$		0			0
$875$		−	43.2160i		−	1.46097i
$876$		0			0
$877$	10.5187	−	28.8998i	0.355190	−	0.975876i	−0.625486	−	0.780235i	$-0.715099\pi$
$877$	10.5187	−	28.8998i	0.355190	−	0.975876i	0.980676	−	0.195640i	$-0.0626786\pi$
$878$		0			0
$879$	−19.4935	+	13.5406i	−0.657499	+	0.456714i
$880$		0			0
$881$	−8.15736	−	4.70966i	−0.274829	−	0.158672i	0.356251	−	0.934390i	$-0.384055\pi$
$881$	−8.15736	−	4.70966i	−0.274829	−	0.158672i	−0.631080	+	0.775718i	$0.717388\pi$
$882$		0			0
$883$	8.55501	+	7.17850i	0.287899	+	0.241576i	0.775286	−	0.631610i	$-0.217606\pi$
$883$	8.55501	+	7.17850i	0.287899	+	0.241576i	−0.487387	+	0.873186i	$0.662050\pi$
$884$		0			0
$885$	22.9692	+	16.2122i	0.772101	+	0.544966i
$886$		0			0
$887$	41.5278	−	15.1149i	1.39437	−	0.507509i	0.467867	−	0.883799i	$-0.345023\pi$
$887$	41.5278	−	15.1149i	1.39437	−	0.507509i	0.926502	+	0.376291i	$0.122801\pi$
$888$		0			0
$889$	69.9777	+	12.3390i	2.34698	+	0.413835i
$890$		0			0
$891$	−25.4403	+	29.4094i	−0.852281	+	0.985252i
$892$		0			0
$893$	−7.60626	−	16.7014i	−0.254534	−	0.558892i
$894$		0			0
$895$	14.7180	+	17.5403i	0.491970	+	0.586307i
$896$		0			0
$897$	11.5793	−	3.05608i	0.386621	−	0.102040i
$898$		0			0
$899$	−3.76872	−	10.3545i	−0.125694	−	0.345341i
$900$		0			0
$901$	−36.0420	+	20.8089i	−1.20073	+	0.693243i
$902$		0			0
$903$	14.9845	−	55.0940i	0.498652	−	1.83341i
$904$		0			0
$905$	−13.1895	+	22.8448i	−0.438433	+	0.759388i
$906$		0			0
$907$	4.51072	−	0.795362i	0.149776	−	0.0264096i	−0.0982573	−	0.995161i	$-0.531327\pi$
$907$	4.51072	−	0.795362i	0.149776	−	0.0264096i	0.248033	+	0.968751i	$0.420216\pi$
$908$		0			0
$909$	13.6157	+	23.9977i	0.451603	+	0.795952i
$910$		0			0
$911$	−13.1488			−0.435640			−0.217820	−	0.975989i	$-0.569895\pi$
$911$	−13.1488			−0.435640			−0.217820	+	0.975989i	$0.569895\pi$
$912$		0			0
$913$	−77.4630			−2.56365
$914$		0			0
$915$	37.0068	−	3.09761i	1.22341	−	0.102404i
$916$		0			0
$917$	26.6892	−	4.70602i	0.881355	−	0.155407i
$918$		0			0
$919$	−9.31748	+	16.1383i	−0.307355	+	0.532355i	−0.977783	−	0.209620i	$-0.932777\pi$
$919$	−9.31748	+	16.1383i	−0.307355	+	0.532355i	0.670428	+	0.741975i	$0.266111\pi$
$920$		0			0
$921$	−9.57119	−	2.60317i	−0.315382	−	0.0857775i
$922$		0			0
$923$	2.08808	−	1.20556i	0.0687301	−	0.0396813i
$924$		0			0
$925$	2.21292	+	6.07995i	0.0727603	+	0.199907i
$926$		0			0
$927$	20.6442	−	17.0598i	0.678045	−	0.560319i
$928$		0			0
$929$	4.43968	+	5.29101i	0.145661	+	0.173592i	0.833942	−	0.551852i	$-0.186079\pi$
$929$	4.43968	+	5.29101i	0.145661	+	0.173592i	−0.688281	+	0.725444i	$0.741634\pi$
$930$		0			0
$931$	−61.1947	+	4.80081i	−2.00557	+	0.157340i
$932$		0			0
$933$	15.5267	−	32.9731i	0.508321	−	1.07949i
$934$		0			0
$935$	−46.5407	−	8.20638i	−1.52204	−	0.268377i
$936$		0			0
$937$	45.1480	−	16.4325i	1.47492	−	0.536827i	0.525488	−	0.850801i	$-0.323883\pi$
$937$	45.1480	−	16.4325i	1.47492	−	0.536827i	0.949431	+	0.313974i	$0.101661\pi$
$938$		0			0
$939$	−3.89845	+	5.52328i	−0.127221	+	0.180245i
$940$		0			0
$941$	−33.8655	−	28.4165i	−1.10398	−	0.926352i	−0.106297	−	0.994334i	$-0.533899\pi$
$941$	−33.8655	−	28.4165i	−1.10398	−	0.926352i	−0.997687	+	0.0679825i	$0.978344\pi$
$942$		0			0
$943$	9.52857	+	5.50132i	0.310293	+	0.179148i
$944$		0			0
$945$	59.2553	+	5.85787i	1.92758	+	0.190556i
$946$		0			0
$947$	10.5950	−	29.1095i	0.344291	−	0.945931i	−0.639843	−	0.768505i	$-0.721001\pi$
$947$	10.5950	−	29.1095i	0.344291	−	0.945931i	0.984134	−	0.177426i	$-0.0567770\pi$
$948$		0			0
$949$			4.64900i			0.150913i
$950$		0			0
$951$	−10.9038	−	23.6146i	−0.353581	−	0.765755i
$952$		0			0
$953$	−20.7542	−	7.55393i	−0.672296	−	0.244696i	−0.0167598	−	0.999860i	$-0.505335\pi$
$953$	−20.7542	−	7.55393i	−0.672296	−	0.244696i	−0.655536	+	0.755164i	$0.727557\pi$
$954$		0			0
$955$	−2.51924	−	14.2873i	−0.0815207	−	0.462327i
$956$		0			0
$957$	2.83154	−	31.0218i	0.0915307	−	1.00279i
$958$		0			0
$959$	40.6289	−	48.4196i	1.31197	−	1.56355i
$960$		0			0
$961$	−11.9962	−	20.7780i	−0.386974	−	0.670259i
$962$		0			0
$963$	−16.3513	+	43.8958i	−0.526914	+	1.41452i
$964$		0			0
$965$	2.36501	−	13.4126i	0.0761323	−	0.431768i
$966$		0			0
$967$	−23.5446	+	19.7562i	−0.757143	+	0.635318i	−0.937381	−	0.348305i	$-0.886757\pi$
$967$	−23.5446	+	19.7562i	−0.757143	+	0.635318i	0.180239	+	0.983623i	$0.442313\pi$
$968$		0			0
$969$	10.9199	+	31.2340i	0.350798	+	1.00338i
$970$		0			0
$971$	−6.71056	+	5.63083i	−0.215352	+	0.180702i	−0.744082	−	0.668088i	$-0.767113\pi$
$971$	−6.71056	+	5.63083i	−0.215352	+	0.180702i	0.528730	+	0.848790i	$0.322668\pi$
$972$		0			0
$973$	9.52511	−	54.0196i	0.305361	−	1.73179i
$974$		0			0
$975$	2.87889	−	2.85733i	0.0921981	−	0.0915079i
$976$		0			0
$977$	−19.0522	−	32.9995i	−0.609535	−	1.05575i	−0.991317	−	0.131493i	$-0.958023\pi$
$977$	−19.0522	−	32.9995i	−0.609535	−	1.05575i	0.381782	−	0.924252i	$-0.375311\pi$
$978$		0			0
$979$	−29.5858	+	35.2589i	−0.945565	+	1.12688i
$980$		0			0
$981$	−16.6728	+	5.92692i	−0.532323	+	0.189232i
$982$		0			0
$983$	−1.05201	−	5.96622i	−0.0335538	−	0.190293i	0.963424	−	0.267982i	$-0.0863569\pi$
$983$	−1.05201	−	5.96622i	−0.0335538	−	0.190293i	−0.996978	+	0.0776894i	$0.975246\pi$
$984$		0			0
$985$	46.3523	+	16.8708i	1.47691	+	0.537550i
$986$		0			0
$987$	−30.3987	+	14.0364i	−0.967602	+	0.446782i
$988$		0			0
$989$			26.0455i			0.828198i
$990$		0			0
$991$	14.3275	−	39.3644i	0.455127	−	1.25045i	−0.473945	−	0.880555i	$-0.657170\pi$
$991$	14.3275	−	39.3644i	0.455127	−	1.25045i	0.929072	−	0.369898i	$-0.120607\pi$
$992$		0			0
$993$	−5.30303	−	7.63440i	−0.168287	−	0.242270i
$994$		0			0
$995$	−56.0646	−	32.3689i	−1.77737	−	1.02616i
$996$		0			0
$997$	−15.7307	−	13.1996i	−0.498196	−	0.418036i	0.358757	−	0.933431i	$-0.383201\pi$
$997$	−15.7307	−	13.1996i	−0.498196	−	0.418036i	−0.856953	+	0.515395i	$0.827645\pi$
$998$		0			0
$999$	26.5071	−	6.78329i	0.838649	−	0.214614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bm.b.89.5	yes	60
3.2	odd	2		456.2.bm.a.89.4	yes	60
4.3	odd	2		912.2.cc.g.545.6		60
12.11	even	2		912.2.cc.h.545.7		60
19.3	odd	18		456.2.bm.a.41.4	✓	60
57.41	even	18	inner	456.2.bm.b.41.5	yes	60
76.3	even	18		912.2.cc.h.497.7		60
228.155	odd	18		912.2.cc.g.497.6		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bm.a.41.4	✓	60	19.3	odd	18
456.2.bm.a.89.4	yes	60	3.2	odd	2
456.2.bm.b.41.5	yes	60	57.41	even	18	inner
456.2.bm.b.89.5	yes	60	1.1	even	1	trivial
912.2.cc.g.497.6		60	228.155	odd	18
912.2.cc.g.545.6		60	4.3	odd	2
912.2.cc.h.497.7		60	76.3	even	18
912.2.cc.h.545.7		60	12.11	even	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bm (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.144474 + 1.72601i) q^{3} +(2.45783 - 0.433381i) q^{5} +(-2.29577 + 3.97638i) q^{7} +(-2.95825 + 0.498730i) q^{9} +(-3.74180 + 2.16033i) q^{11} +(-0.651848 - 1.79094i) q^{13} +(1.10312 + 4.17963i) q^{15} +(2.81708 + 3.35726i) q^{17} +(1.87753 - 3.93381i) q^{19} +(-7.19497 - 3.38804i) q^{21} +(3.57273 + 0.629969i) q^{23} +(1.15463 - 0.420253i) q^{25} +(-1.28821 - 5.03394i) q^{27} +(3.18868 + 2.67562i) q^{29} +(-2.29253 - 1.32359i) q^{31} +(-4.26936 - 6.14630i) q^{33} +(-3.91931 + 10.7682i) q^{35} +5.26569i q^{37} +(2.99701 - 1.38384i) q^{39} +(2.84993 + 1.03729i) q^{41} +(1.24668 + 7.07025i) q^{43} +(-7.05474 + 2.50784i) q^{45} +(2.70628 - 3.22521i) q^{47} +(-7.04108 - 12.1955i) q^{49} +(-5.38768 + 5.34735i) q^{51} +(-1.64899 + 9.35187i) q^{53} +(-8.26046 + 6.93135i) q^{55} +(7.06107 + 2.67232i) q^{57} +(4.98221 - 4.18057i) q^{59} +(1.49179 - 8.46035i) q^{61} +(4.80832 - 12.9081i) q^{63} +(-2.37829 - 4.11932i) q^{65} +(9.62058 - 11.4654i) q^{67} +(-0.571168 + 6.25761i) q^{69} +(0.219681 + 1.24587i) q^{71} +(-2.29219 - 0.834290i) q^{73} +(0.892177 + 1.93220i) q^{75} -19.8385i q^{77} +(-4.31964 + 11.8681i) q^{79} +(8.50254 - 2.95074i) q^{81} +(15.5265 + 8.96425i) q^{83} +(8.37886 + 7.03070i) q^{85} +(-4.15748 + 5.89027i) q^{87} +(10.0104 - 3.64348i) q^{89} +(8.61794 + 1.51957i) q^{91} +(1.95333 - 4.14817i) q^{93} +(2.90981 - 10.4823i) q^{95} +(1.02401 + 1.22036i) q^{97} +(9.99179 - 8.25696i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{9} + 3 q^{13} - 3 q^{15} - 6 q^{17} + 3 q^{19} + 6 q^{25} + 3 q^{27} + 6 q^{29} + 24 q^{35} + 18 q^{39} + 3 q^{41} - 21 q^{43} + 63 q^{45} - 18 q^{47} - 30 q^{49} + 33 q^{51} - 36 q^{53} + 18 q^{55}+ \cdots - 39 q^{99}+O(q^{100}) \) 60 * q - 6 * q^9 + 3 * q^13 - 3 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^25 + 3 * q^27 + 6 * q^29 + 24 * q^35 + 18 * q^39 + 3 * q^41 - 21 * q^43 + 63 * q^45 - 18 * q^47 - 30 * q^49 + 33 * q^51 - 36 * q^53 + 18 * q^55 - 24 * q^57 - 21 * q^59 - 6 * q^61 - 24 * q^63 + 24 * q^65 - 48 * q^67 - 21 * q^69 + 36 * q^71 - 57 * q^73 - 36 * q^79 + 6 * q^81 - 36 * q^83 + 6 * q^85 + 72 * q^87 - 24 * q^89 - 18 * q^91 + 108 * q^93 + 30 * q^95 + 15 * q^97 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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