LMFDB - Embedded newform 800.2.be.a.209.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(209,800)] 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("800.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			209.20
Character	$\chi$	$=$	800.209
Dual form			800.2.be.a.689.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.423859 + 1.30450i) q^{3} +(1.11400 - 1.93881i) q^{5} -0.927462i q^{7} +(0.904979 - 0.657506i) q^{9} +(-1.54449 + 2.12581i) q^{11} +(2.08531 - 1.51507i) q^{13} +(3.00137 + 0.631440i) q^{15} +(0.893539 + 0.290328i) q^{17} +(-0.336558 - 0.109354i) q^{19} +(1.20988 - 0.393113i) q^{21} +(4.22031 - 5.80876i) q^{23} +(-2.51799 - 4.31969i) q^{25} +(4.57033 + 3.32054i) q^{27} +(1.33062 - 0.432345i) q^{29} +(1.34398 - 4.13636i) q^{31} +(-3.42777 - 1.11375i) q^{33} +(-1.79818 - 1.03320i) q^{35} +(-7.47195 + 5.42869i) q^{37} +(2.86029 + 2.07812i) q^{39} +(7.67997 - 5.57982i) q^{41} +5.59241 q^{43} +(-0.266630 - 2.48705i) q^{45} +(-7.85457 + 2.55210i) q^{47} +6.13981 q^{49} +1.28868i q^{51} +(3.01052 + 9.26543i) q^{53} +(2.40098 + 5.36264i) q^{55} -0.485392i q^{57} +(2.55804 + 3.52083i) q^{59} +(-2.14775 + 2.95612i) q^{61} +(-0.609812 - 0.839334i) q^{63} +(-0.614386 - 5.73082i) q^{65} +(-0.325879 + 1.00295i) q^{67} +(9.36636 + 3.04331i) q^{69} +(-3.56365 - 10.9678i) q^{71} +(-9.25671 + 12.7408i) q^{73} +(4.56778 - 5.11566i) q^{75} +(1.97161 + 1.43246i) q^{77} +(1.73030 + 5.32530i) q^{79} +(-1.35747 + 4.17785i) q^{81} +(2.17829 - 6.70408i) q^{83} +(1.55830 - 1.40898i) q^{85} +(1.12799 + 1.55254i) q^{87} +(7.12799 + 5.17879i) q^{89} +(-1.40517 - 1.93405i) q^{91} +5.96555 q^{93} +(-0.586945 + 0.530702i) q^{95} +(1.52791 - 0.496446i) q^{97} +2.93933i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$	0.423859	+	1.30450i	0.244715	+	0.753155i	0.995683	+	0.0928169i	$0.0295871\pi$
$3$	0.423859	+	1.30450i	0.244715	+	0.753155i	−0.750968	+	0.660338i	$0.770413\pi$
$4$		0			0
$5$	1.11400	−	1.93881i	0.498198	−	0.867063i
$5$	1.11400	−	1.93881i	0.498198	−	0.867063i
$6$		0			0
$7$		−	0.927462i		−	0.350548i	−0.984520	−	0.175274i	$-0.943919\pi$
$7$		−	0.927462i		−	0.350548i	0.984520	−	0.175274i	$-0.0560811\pi$
$8$		0			0
$9$	0.904979	−	0.657506i	0.301660	−	0.219169i
$10$		0			0
$11$	−1.54449	+	2.12581i	−0.465682	+	0.640956i	−0.975675	−	0.219222i	$-0.929648\pi$
$11$	−1.54449	+	2.12581i	−0.465682	+	0.640956i	0.509993	+	0.860179i	$0.329648\pi$
$12$		0			0
$13$	2.08531	−	1.51507i	0.578362	−	0.420204i	−0.259771	−	0.965670i	$-0.583647\pi$
$13$	2.08531	−	1.51507i	0.578362	−	0.420204i	0.838133	+	0.545466i	$0.183647\pi$
$14$		0			0
$15$	3.00137	+	0.631440i	0.774950	+	0.163037i
$16$		0			0
$17$	0.893539	+	0.290328i	0.216715	+	0.0704150i	0.415362	−	0.909656i	$-0.363655\pi$
$17$	0.893539	+	0.290328i	0.216715	+	0.0704150i	−0.198647	+	0.980071i	$0.563655\pi$
$18$		0			0
$19$	−0.336558	−	0.109354i	−0.0772118	−	0.0250876i	0.270156	−	0.962816i	$-0.412925\pi$
$19$	−0.336558	−	0.109354i	−0.0772118	−	0.0250876i	−0.347368	+	0.937729i	$0.612925\pi$
$20$		0			0
$21$	1.20988	−	0.393113i	0.264017	−	0.0857843i
$22$		0			0
$23$	4.22031	−	5.80876i	0.879995	−	1.21121i	−0.0964270	−	0.995340i	$-0.530741\pi$
$23$	4.22031	−	5.80876i	0.879995	−	1.21121i	0.976422	−	0.215869i	$-0.0692586\pi$
$24$		0			0
$25$	−2.51799	−	4.31969i	−0.503598	−	0.863938i
$26$		0			0
$27$	4.57033	+	3.32054i	0.879561	+	0.639038i
$28$		0			0
$29$	1.33062	−	0.432345i	0.247090	−	0.0802844i	−0.182854	−	0.983140i	$-0.558533\pi$
$29$	1.33062	−	0.432345i	0.247090	−	0.0802844i	0.429944	+	0.902856i	$0.358533\pi$
$30$		0			0
$31$	1.34398	−	4.13636i	0.241387	−	0.742911i	−0.754823	−	0.655928i	$-0.772277\pi$
$31$	1.34398	−	4.13636i	0.241387	−	0.742911i	0.996210	−	0.0869831i	$-0.0277226\pi$
$32$		0			0
$33$	−3.42777	−	1.11375i	−0.596699	−	0.193879i
$34$		0			0
$35$	−1.79818	−	1.03320i	−0.303947	−	0.174642i
$36$		0			0
$37$	−7.47195	+	5.42869i	−1.22838	+	0.892471i	−0.996768	−	0.0803370i	$-0.974400\pi$
$37$	−7.47195	+	5.42869i	−1.22838	+	0.892471i	−0.231613	+	0.972808i	$0.574400\pi$
$38$		0			0
$39$	2.86029	+	2.07812i	0.458013	+	0.332766i
$40$		0			0
$41$	7.67997	−	5.57982i	1.19941	−	0.871422i	0.205183	−	0.978724i	$-0.434221\pi$
$41$	7.67997	−	5.57982i	1.19941	−	0.871422i	0.994227	+	0.107301i	$0.0342210\pi$
$42$		0			0
$43$	5.59241			0.852834			0.426417	−	0.904527i	$-0.359776\pi$
$43$	5.59241			0.852834			0.426417	+	0.904527i	$0.359776\pi$
$44$		0			0
$45$	−0.266630	−	2.48705i	−0.0397468	−	0.370747i
$46$		0			0
$47$	−7.85457	+	2.55210i	−1.14571	+	0.372263i	−0.819524	−	0.573044i	$-0.805762\pi$
$47$	−7.85457	+	2.55210i	−1.14571	+	0.372263i	−0.326182	+	0.945307i	$0.605762\pi$
$48$		0			0
$49$	6.13981			0.877116
$50$		0			0
$51$			1.28868i			0.180452i
$52$		0			0
$53$	3.01052	+	9.26543i	0.413527	+	1.27270i	0.913562	+	0.406699i	$0.133320\pi$
$53$	3.01052	+	9.26543i	0.413527	+	1.27270i	−0.500035	+	0.866005i	$0.666680\pi$
$54$		0			0
$55$	2.40098	+	5.36264i	0.323748	+	0.723099i
$56$		0			0
$57$		−	0.485392i		−	0.0642918i
$58$		0			0
$59$	2.55804	+	3.52083i	0.333028	+	0.458374i	0.942389	−	0.334519i	$-0.108574\pi$
$59$	2.55804	+	3.52083i	0.333028	+	0.458374i	−0.609361	+	0.792893i	$0.708574\pi$
$60$		0			0
$61$	−2.14775	+	2.95612i	−0.274991	+	0.378492i	−0.924067	−	0.382231i	$-0.875156\pi$
$61$	−2.14775	+	2.95612i	−0.274991	+	0.378492i	0.649076	+	0.760724i	$0.275156\pi$
$62$		0			0
$63$	−0.609812	−	0.839334i	−0.0768291	−	0.105746i
$64$		0			0
$65$	−0.614386	−	5.73082i	−0.0762052	−	0.710821i
$66$		0			0
$67$	−0.325879	+	1.00295i	−0.0398124	+	0.122530i	−0.968987	−	0.247110i	$-0.920519\pi$
$67$	−0.325879	+	1.00295i	−0.0398124	+	0.122530i	0.929175	+	0.369640i	$0.120519\pi$
$68$		0			0
$69$	9.36636	+	3.04331i	1.12758	+	0.366372i
$70$		0			0
$71$	−3.56365	−	10.9678i	−0.422927	−	1.30164i	−0.904965	−	0.425486i	$-0.860103\pi$
$71$	−3.56365	−	10.9678i	−0.422927	−	1.30164i	0.482038	−	0.876151i	$-0.339897\pi$
$72$		0			0
$73$	−9.25671	+	12.7408i	−1.08342	+	1.49119i	−0.227712	+	0.973729i	$0.573124\pi$
$73$	−9.25671	+	12.7408i	−1.08342	+	1.49119i	−0.855704	+	0.517466i	$0.826876\pi$
$74$		0			0
$75$	4.56778	−	5.11566i	0.527442	−	0.590706i
$76$		0			0
$77$	1.97161	+	1.43246i	0.224686	+	0.163244i
$78$		0			0
$79$	1.73030	+	5.32530i	0.194673	+	0.599143i	0.999980	+	0.00628500i	$0.00200059\pi$
$79$	1.73030	+	5.32530i	0.194673	+	0.599143i	−0.805307	+	0.592858i	$0.797999\pi$
$80$		0			0
$81$	−1.35747	+	4.17785i	−0.150830	+	0.464206i
$82$		0			0
$83$	2.17829	−	6.70408i	0.239098	−	0.735868i	−0.757453	−	0.652889i	$-0.773557\pi$
$83$	2.17829	−	6.70408i	0.239098	−	0.735868i	0.996551	−	0.0829787i	$-0.0264433\pi$
$84$		0			0
$85$	1.55830	−	1.40898i	0.169021	−	0.152825i
$86$		0			0
$87$	1.12799	+	1.55254i	0.120933	+	0.166450i
$88$		0			0
$89$	7.12799	+	5.17879i	0.755566	+	0.548951i	0.897547	−	0.440919i	$-0.145347\pi$
$89$	7.12799	+	5.17879i	0.755566	+	0.548951i	−0.141981	+	0.989869i	$0.545347\pi$
$90$		0			0
$91$	−1.40517	−	1.93405i	−0.147302	−	0.202743i
$92$		0			0
$93$	5.96555			0.618598
$94$		0			0
$95$	−0.586945	+	0.530702i	−0.0602193	+	0.0544489i
$96$		0			0
$97$	1.52791	−	0.496446i	0.155135	−	0.0504065i	−0.230420	−	0.973091i	$-0.574010\pi$
$97$	1.52791	−	0.496446i	0.155135	−	0.0504065i	0.385555	+	0.922685i	$0.374010\pi$
$98$		0			0
$99$			2.93933i			0.295414i
$100$		0			0
$101$			7.75829i			0.771979i	0.922503	+	0.385989i	$0.126140\pi$
$101$			7.75829i			0.771979i	−0.922503	+	0.385989i	$0.873860\pi$
$102$		0			0
$103$	−1.34359	+	0.436559i	−0.132388	+	0.0430155i	−0.374462	−	0.927242i	$-0.622172\pi$
$103$	−1.34359	+	0.436559i	−0.132388	+	0.0430155i	0.242074	+	0.970258i	$0.422172\pi$
$104$		0			0
$105$	0.585636	−	2.78365i	0.0571523	−	0.271657i
$106$		0			0
$107$	−16.9717			−1.64071			−0.820357	−	0.571852i	$-0.806225\pi$
$107$	−16.9717			−1.64071			−0.820357	+	0.571852i	$0.806225\pi$
$108$		0			0
$109$	−6.86530	−	9.44928i	−0.657577	−	0.905077i	0.341822	−	0.939765i	$-0.388956\pi$
$109$	−6.86530	−	9.44928i	−0.657577	−	0.905077i	−0.999398	+	0.0346883i	$0.988956\pi$
$110$		0			0
$111$	−10.2488	−	7.44618i	−0.972772	−	0.706760i
$112$		0			0
$113$	−0.532915	−	0.733494i	−0.0501324	−	0.0690013i	0.783215	−	0.621751i	$-0.213578\pi$
$113$	−0.532915	−	0.733494i	−0.0501324	−	0.0690013i	−0.833347	+	0.552750i	$0.813578\pi$
$114$		0			0
$115$	−6.56065	−	14.6534i	−0.611784	−	1.36643i
$116$		0			0
$117$	0.890998	−	2.74221i	0.0823728	−	0.253517i
$118$		0			0
$119$	0.269269	−	0.828724i	0.0246838	−	0.0759690i
$120$		0			0
$121$	1.26557	+	3.89502i	0.115052	+	0.354093i
$122$		0			0
$123$	10.5341	+	7.65349i	0.949830	+	0.690092i
$124$		0			0
$125$	−11.1801	+	0.0697518i	−0.999981	+	0.00623879i
$126$		0			0
$127$	−9.56787	+	13.1690i	−0.849012	+	1.16856i	0.135068	+	0.990836i	$0.456875\pi$
$127$	−9.56787	+	13.1690i	−0.849012	+	1.16856i	−0.984080	+	0.177728i	$0.943125\pi$
$128$		0			0
$129$	2.37039	+	7.29531i	0.208701	+	0.642317i
$130$		0			0
$131$	−15.6123	−	5.07274i	−1.36405	−	0.443207i	−0.466657	−	0.884438i	$-0.654542\pi$
$131$	−15.6123	−	5.07274i	−1.36405	−	0.443207i	−0.897393	+	0.441231i	$0.854542\pi$
$132$		0			0
$133$	−0.101422	+	0.312145i	−0.00879441	+	0.0270664i
$134$		0			0
$135$	11.5293	−	5.16192i	0.992282	−	0.444267i
$136$		0			0
$137$	−13.1690	−	18.1256i	−1.12510	−	1.54857i	−0.797051	−	0.603913i	$-0.793608\pi$
$137$	−13.1690	−	18.1256i	−1.12510	−	1.54857i	−0.328053	−	0.944659i	$-0.606392\pi$
$138$		0			0
$139$	6.92525	−	9.53178i	0.587392	−	0.808475i	−0.407090	−	0.913388i	$-0.633456\pi$
$139$	6.92525	−	9.53178i	0.587392	−	0.808475i	0.994481	+	0.104913i	$0.0334564\pi$
$140$		0			0
$141$	−6.65845	−	9.16457i	−0.560743	−	0.771796i
$142$		0			0
$143$			6.77299i			0.566386i
$144$		0			0
$145$	0.644081	−	3.06146i	0.0534880	−	0.254240i
$146$		0			0
$147$	2.60241	+	8.00941i	0.214643	+	0.660605i
$148$		0			0
$149$		−	13.3102i		−	1.09041i	−0.838302	−	0.545207i	$-0.816451\pi$
$149$		−	13.3102i		−	1.09041i	0.838302	−	0.545207i	$-0.183549\pi$
$150$		0			0
$151$	21.1864			1.72412			0.862062	−	0.506802i	$-0.169173\pi$
$151$	21.1864			1.72412			0.862062	+	0.506802i	$0.169173\pi$
$152$		0			0
$153$	0.999527	−	0.324766i	0.0808069	−	0.0262558i
$154$		0			0
$155$	−6.52241	−	7.21365i	−0.523893	−	0.579414i
$156$		0			0
$157$	−3.41079			−0.272211			−0.136105	−	0.990694i	$-0.543459\pi$
$157$	−3.41079			−0.272211			−0.136105	+	0.990694i	$0.543459\pi$
$158$		0			0
$159$	−10.8107	+	7.85446i	−0.857348	+	0.622900i
$160$		0			0
$161$	−5.38740	−	3.91418i	−0.424587	−	0.308480i
$162$		0			0
$163$	−15.7109	+	11.4146i	−1.23057	+	0.894062i	−0.996933	−	0.0782611i	$-0.975063\pi$
$163$	−15.7109	+	11.4146i	−1.23057	+	0.894062i	−0.233639	+	0.972324i	$0.575063\pi$
$164$		0			0
$165$	−5.97791	+	5.40509i	−0.465380	+	0.420785i
$166$		0			0
$167$	2.68999	+	0.874029i	0.208157	+	0.0676344i	0.411240	−	0.911527i	$-0.365096\pi$
$167$	2.68999	+	0.874029i	0.208157	+	0.0676344i	−0.203082	+	0.979162i	$0.565096\pi$
$168$		0			0
$169$	−1.96412	+	6.04495i	−0.151087	+	0.464997i
$170$		0			0
$171$	−0.376479	+	0.122326i	−0.0287901	+	0.00935447i
$172$		0			0
$173$	−0.694928	−	0.504895i	−0.0528344	−	0.0383864i	0.561055	−	0.827779i	$-0.310396\pi$
$173$	−0.694928	−	0.504895i	−0.0528344	−	0.0383864i	−0.613889	+	0.789392i	$0.710396\pi$
$174$		0			0
$175$	−4.00635	+	2.33534i	−0.302852	+	0.176535i
$176$		0			0
$177$	−3.50869	+	4.82930i	−0.263730	+	0.362993i
$178$		0			0
$179$	21.7579	−	7.06957i	1.62626	−	0.528404i	0.652854	−	0.757484i	$-0.273572\pi$
$179$	21.7579	−	7.06957i	1.62626	−	0.528404i	0.973408	+	0.229079i	$0.0735715\pi$
$180$		0			0
$181$	−18.5330	−	6.02173i	−1.37754	−	0.447591i	−0.475683	−	0.879617i	$-0.657799\pi$
$181$	−18.5330	−	6.02173i	−1.37754	−	0.447591i	−0.901862	+	0.432025i	$0.857799\pi$
$182$		0			0
$183$	−4.76661	−	1.54876i	−0.352358	−	0.114488i
$184$		0			0
$185$	2.20143	+	20.5343i	0.161852	+	1.50971i
$186$		0			0
$187$	−1.99725	+	1.45109i	−0.146053	+	0.106114i
$188$		0			0
$189$	3.07968	−	4.23881i	0.224013	−	0.308328i
$190$		0			0
$191$	−10.2038	+	7.41347i	−0.738318	+	0.536420i	−0.892184	−	0.451672i	$-0.850828\pi$
$191$	−10.2038	+	7.41347i	−0.738318	+	0.536420i	0.153866	+	0.988092i	$0.450828\pi$
$192$		0			0
$193$			8.48402i			0.610693i	0.952241	+	0.305347i	$0.0987723\pi$
$193$			8.48402i			0.610693i	−0.952241	+	0.305347i	$0.901228\pi$
$194$		0			0
$195$	7.21546	−	3.23053i	0.516710	−	0.231343i
$196$		0			0
$197$	4.55285	+	14.0122i	0.324377	+	0.998331i	0.971721	+	0.236132i	$0.0758799\pi$
$197$	4.55285	+	14.0122i	0.324377	+	0.998331i	−0.647344	+	0.762198i	$0.724120\pi$
$198$		0			0
$199$	−5.70622			−0.404503			−0.202252	−	0.979334i	$-0.564826\pi$
$199$	−5.70622			−0.404503			−0.202252	+	0.979334i	$0.564826\pi$
$200$		0			0
$201$	−1.44648			−0.102027
$202$		0			0
$203$	−0.400983	−	1.23410i	−0.0281435	−	0.0866168i
$204$		0			0
$205$	−2.26271	−	21.1060i	−0.158035	−	1.47411i
$206$		0			0
$207$		−	8.03168i		−	0.558240i
$208$		0			0
$209$	0.752279	−	0.546562i	0.0520362	−	0.0378065i
$210$		0			0
$211$	−7.99954	+	11.0104i	−0.550711	+	0.757989i	−0.990108	−	0.140304i	$-0.955192\pi$
$211$	−7.99954	+	11.0104i	−0.550711	+	0.757989i	0.439398	+	0.898293i	$0.355192\pi$
$212$		0			0
$213$	12.7970	−	9.29758i	0.876838	−	0.637060i
$214$		0			0
$215$	6.22997	−	10.8426i	0.424880	−	0.739461i
$216$		0			0
$217$	−3.83631	−	1.24649i	−0.260426	−	0.0846175i
$218$		0			0
$219$	−20.5439	−	6.67512i	−1.38823	−	0.451063i
$220$		0			0
$221$	2.30318	−	0.748347i	0.154928	−	0.0503393i
$222$		0			0
$223$	−13.3402	+	18.3612i	−0.893328	+	1.22956i	0.0792204	+	0.996857i	$0.474757\pi$
$223$	−13.3402	+	18.3612i	−0.893328	+	1.22956i	−0.972548	+	0.232703i	$0.925243\pi$
$224$		0			0
$225$	−5.11895	−	2.25364i	−0.341263	−	0.150243i
$226$		0			0
$227$	11.1188	+	8.07830i	0.737983	+	0.536176i	0.892079	−	0.451880i	$-0.149247\pi$
$227$	11.1188	+	8.07830i	0.737983	+	0.536176i	−0.154096	+	0.988056i	$0.549247\pi$
$228$		0			0
$229$	−6.28758	+	2.04296i	−0.415495	+	0.135002i	−0.509302	−	0.860588i	$-0.670096\pi$
$229$	−6.28758	+	2.04296i	−0.415495	+	0.135002i	0.0938071	+	0.995590i	$0.470096\pi$
$230$		0			0
$231$	−1.03296	+	3.17913i	−0.0679639	+	0.209171i
$232$		0			0
$233$	−13.6940	−	4.44945i	−0.897123	−	0.291493i	−0.176074	−	0.984377i	$-0.556340\pi$
$233$	−13.6940	−	4.44945i	−0.897123	−	0.291493i	−0.721049	+	0.692884i	$0.756340\pi$
$234$		0			0
$235$	−3.80197	+	18.0716i	−0.248013	+	1.17886i
$236$		0			0
$237$	−6.21347	+	4.51435i	−0.403608	+	0.293239i
$238$		0			0
$239$	0.520809	+	0.378390i	0.0336883	+	0.0244760i	0.604502	−	0.796604i	$-0.293372\pi$
$239$	0.520809	+	0.378390i	0.0336883	+	0.0244760i	−0.570814	+	0.821080i	$0.693372\pi$
$240$		0			0
$241$	−18.0169	+	13.0900i	−1.16057	+	0.843202i	−0.989850	−	0.142118i	$-0.954609\pi$
$241$	−18.0169	+	13.0900i	−1.16057	+	0.843202i	−0.170719	+	0.985320i	$0.554609\pi$
$242$		0			0
$243$	10.9223			0.700668
$244$		0			0
$245$	6.83978	−	11.9039i	0.436977	−	0.760515i
$246$		0			0
$247$	−0.867509	+	0.281871i	−0.0551983	+	0.0179350i
$248$		0			0
$249$	9.66877			0.612734
$250$		0			0
$251$		−	5.01412i		−	0.316488i	−0.987400	−	0.158244i	$-0.949417\pi$
$251$		−	5.01412i		−	0.316488i	0.987400	−	0.158244i	$-0.0505833\pi$
$252$		0			0
$253$	5.83009	+	17.9432i	0.366534	+	1.12808i
$254$		0			0
$255$	2.49851	+	1.43560i	0.156463	+	0.0899006i
$256$		0			0
$257$		−	4.08455i		−	0.254787i	−0.991852	−	0.127394i	$-0.959339\pi$
$257$		−	4.08455i		−	0.254787i	0.991852	−	0.127394i	$-0.0406611\pi$
$258$		0			0
$259$	5.03490	+	6.92995i	0.312854	+	0.430606i
$260$		0			0
$261$	0.919914	−	1.26615i	0.0569412	−	0.0783729i
$262$		0			0
$263$	14.0516	+	19.3404i	0.866458	+	1.19258i	0.979991	+	0.199043i	$0.0637834\pi$
$263$	14.0516	+	19.3404i	0.866458	+	1.19258i	−0.113532	+	0.993534i	$0.536217\pi$
$264$		0			0
$265$	21.3177	+	4.48489i	1.30953	+	0.275505i
$266$		0			0
$267$	−3.73448	+	11.4936i	−0.228547	+	0.703395i
$268$		0			0
$269$	28.5572	+	9.27879i	1.74116	+	0.565738i	0.994986	−	0.100011i	$-0.0318876\pi$
$269$	28.5572	+	9.27879i	1.74116	+	0.565738i	0.746176	+	0.665749i	$0.231888\pi$
$270$		0			0
$271$	−1.45987	−	4.49301i	−0.0886807	−	0.272931i	0.896875	−	0.442285i	$-0.145832\pi$
$271$	−1.45987	−	4.49301i	−0.0886807	−	0.272931i	−0.985555	+	0.169354i	$0.945832\pi$
$272$		0			0
$273$	1.92738	−	2.65281i	0.116650	−	0.160555i
$274$		0			0
$275$	13.0719	+	1.31896i	0.788263	+	0.0795364i
$276$		0			0
$277$	3.00568	+	2.18376i	0.180594	+	0.131209i	0.674410	−	0.738357i	$-0.264398\pi$
$277$	3.00568	+	2.18376i	0.180594	+	0.131209i	−0.493816	+	0.869567i	$0.664398\pi$
$278$		0			0
$279$	−1.50340	−	4.62699i	−0.0900062	−	0.277011i
$280$		0			0
$281$	4.25051	−	13.0817i	0.253564	−	0.780389i	−0.740545	−	0.672006i	$-0.765433\pi$
$281$	4.25051	−	13.0817i	0.253564	−	0.780389i	0.994109	−	0.108383i	$-0.0345673\pi$
$282$		0			0
$283$	−0.460617	+	1.41763i	−0.0273808	+	0.0842695i	−0.963813	−	0.266579i	$-0.914107\pi$
$283$	−0.460617	+	1.41763i	−0.0273808	+	0.0842695i	0.936432	+	0.350848i	$0.114107\pi$
$284$		0			0
$285$	−0.941084	−	0.540729i	−0.0557450	−	0.0320300i
$286$		0			0
$287$	−5.17508	−	7.12288i	−0.305475	−	0.420450i
$288$		0			0
$289$	−13.0392	−	9.47351i	−0.767010	−	0.557265i
$290$		0			0
$291$	1.29523	+	1.78273i	0.0759278	+	0.104506i
$292$		0			0
$293$	−7.33412			−0.428464			−0.214232	−	0.976783i	$-0.568725\pi$
$293$	−7.33412			−0.428464			−0.214232	+	0.976783i	$0.568725\pi$
$294$		0			0
$295$	9.67590	−	1.03733i	0.563353	−	0.0603955i
$296$		0			0
$297$	−14.1177	+	4.58711i	−0.819191	+	0.266171i
$298$		0			0
$299$		−	18.5071i		−	1.07029i
$300$		0			0
$301$		−	5.18675i		−	0.298959i
$302$		0			0
$303$	−10.1207	+	3.28842i	−0.581420	+	0.188915i
$304$		0			0
$305$	3.33876	+	7.45721i	0.191177	+	0.426998i
$306$		0			0
$307$	3.91344			0.223352			0.111676	−	0.993745i	$-0.464378\pi$
$307$	3.91344			0.223352			0.111676	+	0.993745i	$0.464378\pi$
$308$		0			0
$309$	−1.13899	−	1.56768i	−0.0647947	−	0.0891822i
$310$		0			0
$311$	−5.35582	−	3.89123i	−0.303701	−	0.220652i	0.425488	−	0.904964i	$-0.360102\pi$
$311$	−5.35582	−	3.89123i	−0.303701	−	0.220652i	−0.729189	+	0.684312i	$0.760102\pi$
$312$		0			0
$313$	12.0592	+	16.5981i	0.681628	+	0.938180i	0.999952	−	0.00980162i	$-0.00312000\pi$
$313$	12.0592	+	16.5981i	0.681628	+	0.938180i	−0.318324	+	0.947982i	$0.603120\pi$
$314$		0			0
$315$	−2.30664	+	0.247289i	−0.129965	+	0.0139332i
$316$		0			0
$317$	1.53918	−	4.73712i	0.0864492	−	0.266063i	−0.898482	−	0.439011i	$-0.855329\pi$
$317$	1.53918	−	4.73712i	0.0864492	−	0.266063i	0.984931	+	0.172947i	$0.0553290\pi$
$318$		0			0
$319$	−1.13605	+	3.49640i	−0.0636065	+	0.195761i
$320$		0			0
$321$	−7.19359	−	22.1396i	−0.401507	−	1.23571i
$322$		0			0
$323$	−0.268979	−	0.195425i	−0.0149664	−	0.0108737i
$324$		0			0
$325$	−11.7954	−	5.19298i	−0.654292	−	0.288055i
$326$		0			0
$327$	9.41669	−	12.9610i	0.520744	−	0.716743i
$328$		0			0
$329$	2.36698	+	7.28481i	0.130496	+	0.401625i
$330$		0			0
$331$	−18.8854	−	6.13623i	−1.03803	−	0.337278i	−0.260072	−	0.965589i	$-0.583746\pi$
$331$	−18.8854	−	6.13623i	−1.03803	−	0.337278i	−0.777962	+	0.628311i	$0.783746\pi$
$332$		0			0
$333$	−3.19256	+	9.82570i	−0.174951	+	0.538445i
$334$		0			0
$335$	1.58151	+	1.74911i	0.0864069	+	0.0955641i
$336$		0			0
$337$	8.18761	+	11.2693i	0.446007	+	0.613876i	0.971534	−	0.236901i	$-0.0761317\pi$
$337$	8.18761	+	11.2693i	0.446007	+	0.613876i	−0.525527	+	0.850777i	$0.676132\pi$
$338$		0			0
$339$	0.730965	−	1.00609i	0.0397005	−	0.0546431i
$340$		0			0
$341$	6.71734	+	9.24562i	0.363764	+	0.500679i
$342$		0			0
$343$		−	12.1867i		−	0.658019i
$344$		0			0
$345$	16.3346	−	14.7693i	0.879424	−	0.795155i
$346$		0			0
$347$	−0.983057	−	3.02554i	−0.0527733	−	0.162419i	0.921196	−	0.389098i	$-0.127213\pi$
$347$	−0.983057	−	3.02554i	−0.0527733	−	0.162419i	−0.973970	+	0.226679i	$0.927213\pi$
$348$		0			0
$349$			17.7286i			0.948990i	0.880258	+	0.474495i	$0.157369\pi$
$349$			17.7286i			0.948990i	−0.880258	+	0.474495i	$0.842631\pi$
$350$		0			0
$351$	14.5614			0.777231
$352$		0			0
$353$	23.9311	−	7.77568i	1.27372	−	0.413858i	0.407358	−	0.913269i	$-0.366450\pi$
$353$	23.9311	−	7.77568i	1.27372	−	0.413858i	0.866365	+	0.499411i	$0.166450\pi$
$354$		0			0
$355$	−25.2344	−	5.30891i	−1.33930	−	0.281768i
$356$		0			0
$357$	1.19520			0.0632569
$358$		0			0
$359$	24.3831	−	17.7154i	1.28689	−	0.934983i	0.287156	−	0.957884i	$-0.407290\pi$
$359$	24.3831	−	17.7154i	1.28689	−	0.934983i	0.999738	+	0.0229013i	$0.00729034\pi$
$360$		0			0
$361$	−15.2700	−	11.0943i	−0.803685	−	0.583911i
$362$		0			0
$363$	−4.54465	+	3.30188i	−0.238532	+	0.173304i
$364$		0			0
$365$	14.3899	+	32.1403i	0.753204	+	1.68230i
$366$		0			0
$367$	−6.38802	−	2.07559i	−0.333452	−	0.108345i	0.137506	−	0.990501i	$-0.456091\pi$
$367$	−6.38802	−	2.07559i	−0.333452	−	0.108345i	−0.470957	+	0.882156i	$0.656091\pi$
$368$		0			0
$369$	3.28144	−	10.0992i	0.170825	−	0.525746i
$370$		0			0
$371$	8.59333	−	2.79214i	0.446144	−	0.144961i
$372$		0			0
$373$	−19.6096	−	14.2472i	−1.01535	−	0.737692i	−0.0500223	−	0.998748i	$-0.515929\pi$
$373$	−19.6096	−	14.2472i	−1.01535	−	0.737692i	−0.965324	+	0.261056i	$0.915929\pi$
$374$		0			0
$375$	−4.82978	−	14.5549i	−0.249409	−	0.751614i
$376$		0			0
$377$	2.11973	−	2.91755i	0.109171	−	0.150262i
$378$		0			0
$379$	7.74403	−	2.51619i	0.397784	−	0.129248i	−0.103292	−	0.994651i	$-0.532938\pi$
$379$	7.74403	−	2.51619i	0.397784	−	0.129248i	0.501076	+	0.865403i	$0.332938\pi$
$380$		0			0
$381$	−21.2345	−	6.89950i	−1.08788	−	0.353472i
$382$		0			0
$383$	−8.59217	−	2.79177i	−0.439040	−	0.142653i	0.0811529	−	0.996702i	$-0.474140\pi$
$383$	−8.59217	−	2.79177i	−0.439040	−	0.142653i	−0.520192	+	0.854049i	$0.674140\pi$
$384$		0			0
$385$	4.97365	−	2.22682i	0.253481	−	0.113489i
$386$		0			0
$387$	5.06101	−	3.67704i	0.257266	−	0.186914i
$388$		0			0
$389$	7.45733	−	10.2641i	0.378102	−	0.520412i	−0.576979	−	0.816759i	$-0.695768\pi$
$389$	7.45733	−	10.2641i	0.378102	−	0.520412i	0.955080	+	0.296347i	$0.0957685\pi$
$390$		0			0
$391$	5.45746	−	3.96507i	0.275995	−	0.200522i
$392$		0			0
$393$		−	22.5164i		−	1.13580i
$394$		0			0
$395$	12.2523	+	2.57769i	0.616481	+	0.129698i
$396$		0			0
$397$	4.22625	+	13.0071i	0.212109	+	0.652805i	0.999346	+	0.0361546i	$0.0115109\pi$
$397$	4.22625	+	13.0071i	0.212109	+	0.652805i	−0.787237	+	0.616651i	$0.788489\pi$
$398$		0			0
$399$	−0.450183			−0.0225373
$400$		0			0
$401$	34.7894			1.73730			0.868649	−	0.495428i	$-0.164989\pi$
$401$	34.7894			1.73730			0.868649	+	0.495428i	$0.164989\pi$
$402$		0			0
$403$	−3.46424	−	10.6618i	−0.172566	−	0.531103i
$404$		0			0
$405$	6.58785	+	7.28602i	0.327353	+	0.362045i
$406$		0			0
$407$		−	24.2685i		−	1.20295i
$408$		0			0
$409$	−13.3846	+	9.72446i	−0.661824	+	0.480843i	−0.867278	−	0.497823i	$-0.834133\pi$
$409$	−13.3846	+	9.72446i	−0.661824	+	0.480843i	0.205454	+	0.978667i	$0.434133\pi$
$410$		0			0
$411$	18.0631	−	24.8617i	0.890985	−	1.22634i
$412$		0			0
$413$	3.26544	−	2.37248i	0.160682	−	0.116742i
$414$		0			0
$415$	−10.5713	−	11.6917i	−0.518926	−	0.573921i
$416$		0			0
$417$	15.3696	+	4.99387i	0.752651	+	0.244551i
$418$		0			0
$419$	2.26155	+	0.734822i	0.110484	+	0.0358984i	0.363737	−	0.931502i	$-0.381501\pi$
$419$	2.26155	+	0.734822i	0.110484	+	0.0358984i	−0.253253	+	0.967400i	$0.581501\pi$
$420$		0			0
$421$	5.82497	−	1.89265i	0.283892	−	0.0922420i	−0.163610	−	0.986525i	$-0.552314\pi$
$421$	5.82497	−	1.89265i	0.283892	−	0.0922420i	0.447502	+	0.894283i	$0.352314\pi$
$422$		0			0
$423$	−5.43020	+	7.47402i	−0.264025	+	0.363399i
$424$		0			0
$425$	−0.995791	−	4.59086i	−0.0483030	−	0.222689i
$426$		0			0
$427$	2.74169	+	1.99195i	0.132680	+	0.0963974i
$428$		0			0
$429$	−8.83539	+	2.87079i	−0.426577	+	0.138603i
$430$		0			0
$431$	−9.67194	+	29.7672i	−0.465881	+	1.43383i	0.391990	+	0.919970i	$0.371787\pi$
$431$	−9.67194	+	29.7672i	−0.465881	+	1.43383i	−0.857871	+	0.513865i	$0.828213\pi$
$432$		0			0
$433$	14.1827	+	4.60823i	0.681575	+	0.221457i	0.629285	−	0.777175i	$-0.283348\pi$
$433$	14.1827	+	4.60823i	0.681575	+	0.221457i	0.0522905	+	0.998632i	$0.483348\pi$
$434$		0			0
$435$	4.26668	−	0.457419i	0.204572	−	0.0219316i
$436$		0			0
$437$	−2.05559	+	1.49348i	−0.0983324	+	0.0714426i
$438$		0			0
$439$	26.3874	+	19.1715i	1.25940	+	0.915008i	0.998728	−	0.0504195i	$-0.0160558\pi$
$439$	26.3874	+	19.1715i	1.25940	+	0.915008i	0.260672	+	0.965427i	$0.416056\pi$
$440$		0			0
$441$	5.55640	−	4.03696i	0.264591	−	0.192236i
$442$		0			0
$443$	24.4310			1.16075			0.580375	−	0.814349i	$-0.302906\pi$
$443$	24.4310			1.16075			0.580375	+	0.814349i	$0.302906\pi$
$444$		0			0
$445$	17.9813	−	8.05065i	0.852396	−	0.381637i
$446$		0			0
$447$	17.3632	−	5.64164i	0.821251	−	0.266841i
$448$		0			0
$449$	−11.0987			−0.523780			−0.261890	−	0.965098i	$-0.584346\pi$
$449$	−11.0987			−0.523780			−0.261890	+	0.965098i	$0.584346\pi$
$450$		0			0
$451$			24.9442i			1.17457i
$452$		0			0
$453$	8.98004	+	27.6377i	0.421919	+	1.29853i
$454$		0			0
$455$	−5.31512	+	0.569820i	−0.249177	+	0.0267136i
$456$		0			0
$457$		−	10.7162i		−	0.501281i	−0.968080	−	0.250641i	$-0.919359\pi$
$457$		−	10.7162i		−	0.501281i	0.968080	−	0.250641i	$-0.0806412\pi$
$458$		0			0
$459$	3.11972	+	4.29393i	0.145616	+	0.200423i
$460$		0			0
$461$	−9.05653	+	12.4652i	−0.421804	+	0.580564i	−0.966048	−	0.258363i	$-0.916817\pi$
$461$	−9.05653	+	12.4652i	−0.421804	+	0.580564i	0.544243	+	0.838927i	$0.316817\pi$
$462$		0			0
$463$	1.08285	+	1.49042i	0.0503245	+	0.0692657i	0.833438	−	0.552614i	$-0.186369\pi$
$463$	1.08285	+	1.49042i	0.0503245	+	0.0692657i	−0.783113	+	0.621879i	$0.786369\pi$
$464$		0			0
$465$	6.64565	−	11.5661i	0.308184	−	0.536364i
$466$		0			0
$467$	6.50123	−	20.0087i	0.300841	−	0.925894i	−0.680355	−	0.732883i	$-0.738174\pi$
$467$	6.50123	−	20.0087i	0.300841	−	0.925894i	0.981196	−	0.193012i	$-0.0618255\pi$
$468$		0			0
$469$	0.930200	+	0.302240i	0.0429527	+	0.0139562i
$470$		0			0
$471$	−1.44569	−	4.44939i	−0.0666140	−	0.205017i
$472$		0			0
$473$	−8.63743	+	11.8884i	−0.397150	+	0.546630i
$474$		0			0
$475$	0.375073	+	1.72918i	0.0172095	+	0.0793403i
$476$		0			0
$477$	8.81653	+	6.40558i	0.403681	+	0.293292i
$478$		0			0
$479$	−0.641151	−	1.97326i	−0.0292949	−	0.0901606i	0.935340	−	0.353750i	$-0.115094\pi$
$479$	−0.641151	−	1.97326i	−0.0292949	−	0.0901606i	−0.964635	+	0.263589i	$0.915094\pi$
$480$		0			0
$481$	−7.35651	+	22.6410i	−0.335428	+	1.03234i
$482$		0			0
$483$	2.82256	−	8.68694i	0.128431	−	0.395270i
$484$		0			0
$485$	0.739576	−	3.51537i	0.0335824	−	0.159625i
$486$		0			0
$487$	−2.86770	−	3.94704i	−0.129948	−	0.178858i	0.739085	−	0.673612i	$-0.235258\pi$
$487$	−2.86770	−	3.94704i	−0.129948	−	0.178858i	−0.869033	+	0.494754i	$0.835258\pi$
$488$		0			0
$489$	−21.5496	−	15.6567i	−0.974507	−	0.708021i
$490$		0			0
$491$	11.2000	+	15.4154i	0.505447	+	0.695688i	0.983143	−	0.182837i	$-0.0585280\pi$
$491$	11.2000	+	15.4154i	0.505447	+	0.695688i	−0.477696	+	0.878525i	$0.658528\pi$
$492$		0			0
$493$	1.31448			0.0592013
$494$		0			0
$495$	5.69881	+	3.27442i	0.256142	+	0.147174i
$496$		0			0
$497$	−10.1722	+	3.30515i	−0.456286	+	0.148256i
$498$		0			0
$499$			12.8562i			0.575522i	0.957702	+	0.287761i	$0.0929108\pi$
$499$			12.8562i			0.575522i	−0.957702	+	0.287761i	$0.907089\pi$
$500$		0			0
$501$			3.87956i			0.173326i
$502$		0			0
$503$	23.8717	−	7.75639i	1.06439	−	0.345840i	0.276088	−	0.961132i	$-0.410962\pi$
$503$	23.8717	−	7.75639i	1.06439	−	0.345840i	0.788299	+	0.615292i	$0.210962\pi$
$504$		0			0
$505$	15.0419	+	8.64277i	0.669354	+	0.384598i
$506$		0			0
$507$	−8.71817			−0.387188
$508$		0			0
$509$	−7.89183	−	10.8622i	−0.349799	−	0.481457i	0.597472	−	0.801890i	$-0.296172\pi$
$509$	−7.89183	−	10.8622i	−0.349799	−	0.481457i	−0.947271	+	0.320432i	$0.896172\pi$
$510$		0			0
$511$	11.8166	+	8.58525i	0.522735	+	0.379789i
$512$		0			0
$513$	−1.17507	−	1.61734i	−0.0518805	−	0.0714074i
$514$		0			0
$515$	−0.650360	+	3.09130i	−0.0286583	+	0.136219i
$516$		0			0
$517$	6.70603	−	20.6390i	0.294931	−	0.907704i
$518$		0			0
$519$	0.364086	−	1.12054i	0.0159816	−	0.0491862i
$520$		0			0
$521$	−7.91688	−	24.3656i	−0.346845	−	1.06748i	−0.960589	−	0.277973i	$-0.910337\pi$
$521$	−7.91688	−	24.3656i	−0.346845	−	1.06748i	0.613744	−	0.789505i	$-0.289663\pi$
$522$		0			0
$523$	21.7366	+	15.7926i	0.950476	+	0.690562i	0.950919	−	0.309438i	$-0.100141\pi$
$523$	21.7366	+	15.7926i	0.950476	+	0.690562i	−0.000443114		1.00000i	$0.500141\pi$
$524$		0			0
$525$	−4.74458	−	4.23644i	−0.207071	−	0.184894i
$526$		0			0
$527$	2.40180	−	3.30580i	0.104624	−	0.144003i
$528$		0			0
$529$	−8.82326	−	27.1552i	−0.383620	−	1.18066i
$530$		0			0
$531$	4.62994	+	1.50436i	0.200922	+	0.0652836i
$532$		0			0
$533$	7.56132	−	23.2714i	0.327517	−	1.00799i
$534$		0			0
$535$	−18.9065	+	32.9049i	−0.817400	+	1.42260i
$536$		0			0
$537$	18.4446	+	25.3867i	0.795941	+	1.09552i
$538$		0			0
$539$	−9.48290	+	13.0521i	−0.408457	+	0.562193i
$540$		0			0
$541$	11.1415	+	15.3350i	0.479011	+	0.659302i	0.978314	−	0.207125i	$-0.0664108\pi$
$541$	11.1415	+	15.3350i	0.479011	+	0.659302i	−0.499304	+	0.866427i	$0.666411\pi$
$542$		0			0
$543$		−	26.7287i		−	1.14704i
$544$		0			0
$545$	−25.9684	+	2.78400i	−1.11236	+	0.119253i
$546$		0			0
$547$	−4.69413	−	14.4470i	−0.200706	−	0.617711i	−0.999862	−	0.0165870i	$-0.994720\pi$
$547$	−4.69413	−	14.4470i	−0.200706	−	0.617711i	0.799156	−	0.601124i	$-0.205280\pi$
$548$		0			0
$549$			4.08738i			0.174445i
$550$		0			0
$551$	−0.495110			−0.0210924
$552$		0			0
$553$	4.93902	−	1.60478i	0.210028	−	0.0682424i
$554$		0			0
$555$	−25.8540	+	11.5754i	−1.09744	+	0.491349i
$556$		0			0
$557$	−1.85471			−0.0785867			−0.0392933	−	0.999228i	$-0.512511\pi$
$557$	−1.85471			−0.0785867			−0.0392933	+	0.999228i	$0.512511\pi$
$558$		0			0
$559$	11.6619	−	8.47288i	0.493247	−	0.358365i
$560$		0			0
$561$	−2.73950	−	1.99036i	−0.115662	−	0.0840331i
$562$		0			0
$563$	−30.3261	+	22.0332i	−1.27809	+	0.928587i	−0.999494	−	0.0318207i	$-0.989869\pi$
$563$	−30.3261	+	22.0332i	−1.27809	+	0.928587i	−0.278597	+	0.960408i	$0.589869\pi$
$564$		0			0
$565$	−2.01578	+	0.216106i	−0.0848044	+	0.00909164i
$566$		0			0
$567$	3.87480	+	1.25900i	0.162726	+	0.0528730i
$568$		0			0
$569$	−8.05065	+	24.7774i	−0.337501	+	1.03872i	0.627976	+	0.778233i	$0.283884\pi$
$569$	−8.05065	+	24.7774i	−0.337501	+	1.03872i	−0.965477	+	0.260488i	$0.916116\pi$
$570$		0			0
$571$	31.4963	−	10.2338i	1.31808	−	0.428270i	0.436244	−	0.899828i	$-0.356308\pi$
$571$	31.4963	−	10.2338i	1.31808	−	0.428270i	0.881835	+	0.471558i	$0.156308\pi$
$572$		0			0
$573$	−13.9958	−	10.1686i	−0.584685	−	0.424798i
$574$		0			0
$575$	−35.7187	−	3.60405i	−1.48957	−	0.150299i
$576$		0			0
$577$	−10.2228	+	14.0705i	−0.425580	+	0.585761i	−0.966932	−	0.255035i	$-0.917913\pi$
$577$	−10.2228	+	14.0705i	−0.425580	+	0.585761i	0.541351	+	0.840796i	$0.317913\pi$
$578$		0			0
$579$	−11.0674	+	3.59603i	−0.459947	+	0.149446i
$580$		0			0
$581$	−6.21778	−	2.02028i	−0.257957	−	0.0838153i
$582$		0			0
$583$	−24.3463	−	7.91058i	−1.00832	−	0.327623i
$584$		0			0
$585$	−4.32405	−	4.78231i	−0.178778	−	0.197724i
$586$		0			0
$587$	−27.1271	+	19.7090i	−1.11965	+	0.813476i	−0.984157	−	0.177301i	$-0.943263\pi$
$587$	−27.1271	+	19.7090i	−1.11965	+	0.813476i	−0.135497	+	0.990778i	$0.543263\pi$
$588$		0			0
$589$	−0.904658	+	1.24515i	−0.0372758	+	0.0513057i
$590$		0			0
$591$	−16.3492	+	11.8784i	−0.672518	+	0.488613i
$592$		0			0
$593$		−	19.5523i		−	0.802917i	−0.915877	−	0.401458i	$-0.868503\pi$
$593$		−	19.5523i		−	0.802917i	0.915877	−	0.401458i	$-0.131497\pi$
$594$		0			0
$595$	−1.30677	−	1.44526i	−0.0535725	−	0.0592500i
$596$		0			0
$597$	−2.41863	−	7.44379i	−0.0989880	−	0.304654i
$598$		0			0
$599$	15.7131			0.642018			0.321009	−	0.947076i	$-0.395978\pi$
$599$	15.7131			0.642018			0.321009	+	0.947076i	$0.395978\pi$
$600$		0			0
$601$	44.4894			1.81476			0.907380	−	0.420310i	$-0.138079\pi$
$601$	44.4894			1.81476			0.907380	+	0.420310i	$0.138079\pi$
$602$		0			0
$603$	0.364533	+	1.12192i	0.0148449	+	0.0456880i
$604$		0			0
$605$	8.96157	+	1.88537i	0.364340	+	0.0766512i
$606$		0			0
$607$			21.4173i			0.869301i	0.900599	+	0.434651i	$0.143128\pi$
$607$			21.4173i			0.869301i	−0.900599	+	0.434651i	$0.856872\pi$
$608$		0			0
$609$	1.43993	−	1.04617i	0.0583488	−	0.0423929i
$610$		0			0
$611$	−12.5126	+	17.2221i	−0.506206	+	0.696733i
$612$		0			0
$613$	1.93251	−	1.40405i	0.0780532	−	0.0567090i	−0.548074	−	0.836430i	$-0.684639\pi$
$613$	1.93251	−	1.40405i	0.0780532	−	0.0567090i	0.626128	+	0.779721i	$0.284639\pi$
$614$		0			0
$615$	26.5737	−	11.8977i	1.07156	−	0.479760i
$616$		0			0
$617$	9.76545	+	3.17299i	0.393142	+	0.127740i	0.498915	−	0.866651i	$-0.333732\pi$
$617$	9.76545	+	3.17299i	0.393142	+	0.127740i	−0.105773	+	0.994390i	$0.533732\pi$
$618$		0			0
$619$	−22.9711	−	7.46375i	−0.923285	−	0.299994i	−0.191471	−	0.981498i	$-0.561326\pi$
$619$	−22.9711	−	7.46375i	−0.923285	−	0.299994i	−0.731814	+	0.681505i	$0.761326\pi$
$620$		0			0
$621$	38.5764	−	12.5342i	1.54802	−	0.502982i
$622$		0			0
$623$	4.80313	−	6.61094i	0.192433	−	0.264862i
$624$		0			0
$625$	−12.3195	+	21.7539i	−0.492779	+	0.870155i
$626$		0			0
$627$	1.03185	+	0.749685i	0.0412082	+	0.0299395i
$628$		0			0
$629$	−8.25258	+	2.68143i	−0.329052	+	0.106915i
$630$		0			0
$631$	−5.14314	+	15.8289i	−0.204745	+	0.630140i	0.794979	+	0.606637i	$0.207482\pi$
$631$	−5.14314	+	15.8289i	−0.204745	+	0.630140i	−0.999724	+	0.0235031i	$0.992518\pi$
$632$		0			0
$633$	−17.7538	−	5.76856i	−0.705650	−	0.229280i
$634$		0			0
$635$	14.8737	+	33.2207i	0.590243	+	1.31832i
$636$		0			0
$637$	12.8034	−	9.30224i	0.507290	−	0.368568i
$638$		0			0
$639$	−10.4364	−	7.58250i	−0.412858	−	0.299959i
$640$		0			0
$641$	−11.9869	+	8.70898i	−0.473454	+	0.343984i	−0.798786	−	0.601616i	$-0.794524\pi$
$641$	−11.9869	+	8.70898i	−0.473454	+	0.343984i	0.325332	+	0.945600i	$0.394524\pi$
$642$		0			0
$643$	−17.1919			−0.677981			−0.338990	−	0.940790i	$-0.610085\pi$
$643$	−17.1919			−0.677981			−0.338990	+	0.940790i	$0.610085\pi$
$644$		0			0
$645$	16.7849	+	3.53127i	0.660904	+	0.139044i
$646$		0			0
$647$	7.49201	−	2.43430i	0.294541	−	0.0957023i	−0.158019	−	0.987436i	$-0.550511\pi$
$647$	7.49201	−	2.43430i	0.294541	−	0.0957023i	0.452560	+	0.891734i	$0.350511\pi$
$648$		0			0
$649$	−11.4355			−0.448882
$650$		0			0
$651$		−	5.53282i		−	0.216848i
$652$		0			0
$653$	−11.8930	−	36.6029i	−0.465409	−	1.43238i	−0.858467	−	0.512869i	$-0.828583\pi$
$653$	−11.8930	−	36.6029i	−0.465409	−	1.43238i	0.393057	−	0.919514i	$-0.371417\pi$
$654$		0			0
$655$	−27.2272	+	24.6182i	−1.06386	+	0.961914i
$656$		0			0
$657$			17.6165i			0.687284i
$658$		0			0
$659$	20.8965	+	28.7616i	0.814013	+	1.12039i	0.990692	+	0.136124i	$0.0434646\pi$
$659$	20.8965	+	28.7616i	0.814013	+	1.12039i	−0.176679	+	0.984269i	$0.556535\pi$
$660$		0			0
$661$	17.1104	−	23.5504i	0.665516	−	0.916005i	−0.334132	−	0.942526i	$-0.608443\pi$
$661$	17.1104	−	23.5504i	0.665516	−	0.916005i	0.999648	+	0.0265217i	$0.00844310\pi$
$662$		0			0
$663$	1.95244	+	2.68731i	0.0758266	+	0.104366i
$664$		0			0
$665$	0.492206	+	0.544370i	0.0190869	+	0.0211097i
$666$		0			0
$667$	3.10424	−	9.55387i	0.120197	−	0.369927i
$668$		0			0
$669$	−29.6067	−	9.61979i	−1.14466	−	0.371923i
$670$		0			0
$671$	−2.96697	−	9.13141i	−0.114539	−	0.352514i
$672$		0			0
$673$	−1.94169	+	2.67251i	−0.0748467	+	0.103018i	−0.844799	−	0.535084i	$-0.820280\pi$
$673$	−1.94169	+	2.67251i	−0.0748467	+	0.103018i	0.769952	+	0.638102i	$0.220280\pi$
$674$		0			0
$675$	2.83567	−	28.1035i	0.109145	−	1.08170i
$676$		0			0
$677$	−17.2107	−	12.5043i	−0.661460	−	0.480579i	0.205696	−	0.978616i	$-0.434054\pi$
$677$	−17.2107	−	12.5043i	−0.661460	−	0.480579i	−0.867156	+	0.498037i	$0.834054\pi$
$678$		0			0
$679$	−0.460435	−	1.41707i	−0.0176699	−	0.0543823i
$680$		0			0
$681$	−5.82536	+	17.9286i	−0.223228	+	0.687026i
$682$		0			0
$683$	3.92453	−	12.0784i	0.150168	−	0.462169i	−0.847471	−	0.530841i	$-0.821876\pi$
$683$	3.92453	−	12.0784i	0.150168	−	0.462169i	0.997639	+	0.0686719i	$0.0218762\pi$
$684$		0			0
$685$	−49.8124	+	5.34025i	−1.90323	+	0.204041i
$686$		0			0
$687$	−5.33009	−	7.33624i	−0.203356	−	0.279895i
$688$		0			0
$689$	20.3156	+	14.7602i	0.773964	+	0.562318i
$690$		0			0
$691$	−22.6417	−	31.1636i	−0.861329	−	1.18552i	−0.981251	−	0.192734i	$-0.938264\pi$
$691$	−22.6417	−	31.1636i	−0.861329	−	1.18552i	0.119922	−	0.992783i	$-0.461736\pi$
$692$		0			0
$693$	2.72612			0.103557
$694$		0			0
$695$	−10.7656	−	24.0452i	−0.408362	−	0.912086i
$696$		0			0
$697$	8.48233	−	2.75608i	0.321291	−	0.104394i
$698$		0			0
$699$		−	19.7498i		−	0.747006i
$700$		0			0
$701$			39.6154i			1.49625i	0.663555	+	0.748127i	$0.269047\pi$
$701$			39.6154i			1.49625i	−0.663555	+	0.748127i	$0.730953\pi$
$702$		0			0
$703$	3.10840	−	1.00998i	0.117235	−	0.0380921i
$704$		0			0
$705$	−25.1859	+	2.70012i	−0.948557	+	0.101692i
$706$		0			0
$707$	7.19552			0.270615
$708$		0			0
$709$	5.04361	+	6.94194i	0.189417	+	0.260710i	0.893154	−	0.449750i	$-0.148487\pi$
$709$	5.04361	+	6.94194i	0.189417	+	0.260710i	−0.703738	+	0.710460i	$0.748487\pi$
$710$		0			0
$711$	5.06730	+	3.68161i	0.190039	+	0.138071i
$712$		0			0
$713$	−18.3551	−	25.2636i	−0.687402	−	0.946128i
$714$		0			0
$715$	13.1316	+	7.54514i	0.491093	+	0.282172i
$716$		0			0
$717$	−0.272861	+	0.839780i	−0.0101902	+	0.0313622i
$718$		0			0
$719$	−2.74075	+	8.43517i	−0.102213	+	0.314579i	−0.989066	−	0.147472i	$-0.952886\pi$
$719$	−2.74075	+	8.43517i	−0.102213	+	0.314579i	0.886853	+	0.462051i	$0.152886\pi$
$720$		0			0
$721$	0.404892	+	1.24613i	0.0150790	+	0.0464083i
$722$		0			0
$723$	−24.7126	−	17.9547i	−0.919071	−	0.667744i
$724$		0			0
$725$	−5.21808	−	4.65923i	−0.193795	−	0.173039i
$726$		0			0
$727$	−19.5205	+	26.8677i	−0.723976	+	0.996468i	0.275406	+	0.961328i	$0.411188\pi$
$727$	−19.5205	+	26.8677i	−0.723976	+	0.996468i	−0.999382	+	0.0351397i	$0.988812\pi$
$728$		0			0
$729$	8.70192	+	26.7818i	0.322293	+	0.991917i
$730$		0			0
$731$	4.99703	+	1.62364i	0.184822	+	0.0600523i
$732$		0			0
$733$	−0.186051	+	0.572607i	−0.00687196	+	0.0211497i	−0.954434	−	0.298423i	$-0.903539\pi$
$733$	−0.186051	+	0.572607i	−0.00687196	+	0.0211497i	0.947562	+	0.319573i	$0.103539\pi$
$734$		0			0
$735$	18.4278	+	3.87692i	0.679721	+	0.143002i
$736$		0			0
$737$	−1.62877	−	2.24181i	−0.0599965	−	0.0825781i
$738$		0			0
$739$	−21.4919	+	29.5811i	−0.790594	+	1.08816i	0.203440	+	0.979087i	$0.434788\pi$
$739$	−21.4919	+	29.5811i	−0.790594	+	1.08816i	−0.994034	+	0.109072i	$0.965212\pi$
$740$		0			0
$741$	−0.735402	−	1.01219i	−0.0270157	−	0.0371839i
$742$		0			0
$743$			0.112858i			0.00414038i	0.999998	+	0.00207019i	$0.000658962\pi$
$743$			0.112858i			0.00414038i	−0.999998	+	0.00207019i	$0.999341\pi$
$744$		0			0
$745$	−25.8060	−	14.8276i	−0.945458	−	0.543242i
$746$		0			0
$747$	−2.43667	−	7.49929i	−0.0891529	−	0.274385i
$748$		0			0
$749$			15.7406i			0.575149i
$750$		0			0
$751$	21.9164			0.799742			0.399871	−	0.916571i	$-0.369055\pi$
$751$	21.9164			0.799742			0.399871	+	0.916571i	$0.369055\pi$
$752$		0			0
$753$	6.54093	−	2.12528i	0.238365	−	0.0774495i
$754$		0			0
$755$	23.6017	−	41.0765i	0.858955	−	1.49493i
$756$		0			0
$757$	−16.3710			−0.595014			−0.297507	−	0.954720i	$-0.596155\pi$
$757$	−16.3710			−0.595014			−0.297507	+	0.954720i	$0.596155\pi$
$758$		0			0
$759$	−20.9358	+	15.2107i	−0.759921	+	0.552115i
$760$		0			0
$761$	−5.84229	−	4.24467i	−0.211783	−	0.153869i	0.476837	−	0.878992i	$-0.341783\pi$
$761$	−5.84229	−	4.24467i	−0.211783	−	0.153869i	−0.688620	+	0.725122i	$0.741783\pi$
$762$		0			0
$763$	−8.76385	+	6.36731i	−0.317273	+	0.230512i
$764$		0			0
$765$	0.483817	−	2.29969i	0.0174924	−	0.0831453i
$766$		0			0
$767$	10.6686	+	3.46644i	0.385221	+	0.125166i
$768$		0			0
$769$	12.3133	−	37.8964i	0.444028	−	1.36658i	−0.439518	−	0.898234i	$-0.644851\pi$
$769$	12.3133	−	37.8964i	0.444028	−	1.36658i	0.883546	−	0.468344i	$-0.155149\pi$
$770$		0			0
$771$	5.32830	−	1.73127i	0.191894	−	0.0623502i
$772$		0			0
$773$	−40.6107	−	29.5054i	−1.46066	−	1.06123i	−0.983189	−	0.182590i	$-0.941552\pi$
$773$	−40.6107	−	29.5054i	−1.46066	−	1.06123i	−0.477475	−	0.878645i	$-0.658448\pi$
$774$		0			0
$775$	−21.2519	+	4.60970i	−0.763391	+	0.165585i
$776$		0			0
$777$	−6.90605	+	9.50537i	−0.247753	+	0.341003i
$778$		0			0
$779$	−3.19494	+	1.03810i	−0.114470	+	0.0371937i
$780$		0			0
$781$	28.8195	+	9.36401i	1.03124	+	0.335071i
$782$		0			0
$783$	7.51699	+	2.44242i	0.268635	+	0.0872849i
$784$		0			0
$785$	−3.79964	+	6.61288i	−0.135615	+	0.236024i
$786$		0			0
$787$	33.6522	−	24.4497i	1.19957	−	0.871539i	0.205329	−	0.978693i	$-0.434174\pi$
$787$	33.6522	−	24.4497i	1.19957	−	0.871539i	0.994242	+	0.107154i	$0.0341737\pi$
$788$		0			0
$789$	−19.2737	+	26.5279i	−0.686161	+	0.944419i
$790$		0			0
$791$	−0.680288	+	0.494258i	−0.0241883	+	0.0175738i
$792$		0			0
$793$			9.41841i			0.334458i
$794$		0			0
$795$	3.18512	+	29.7099i	0.112965	+	1.05370i
$796$		0			0
$797$	−10.9651	−	33.7472i	−0.388404	−	1.19539i	−0.933980	−	0.357324i	$-0.883689\pi$
$797$	−10.9651	−	33.7472i	−0.388404	−	1.19539i	0.545576	−	0.838061i	$-0.316311\pi$
$798$		0			0
$799$	−7.75931			−0.274505
$800$		0			0
$801$	9.85577			0.348236
$802$		0			0
$803$	−12.7876	−	39.3560i	−0.451263	−	1.38884i
$804$		0			0
$805$	−13.5904	+	6.08475i	−0.479000	+	0.214459i
$806$		0			0
$807$			41.1858i			1.44981i
$808$		0			0
$809$	15.2356	−	11.0693i	0.535656	−	0.389177i	−0.286813	−	0.957986i	$-0.592596\pi$
$809$	15.2356	−	11.0693i	0.535656	−	0.389177i	0.822469	+	0.568810i	$0.192596\pi$
$810$		0			0
$811$	30.8789	−	42.5012i	1.08431	−	1.49242i	0.229616	−	0.973281i	$-0.426253\pi$
$811$	30.8789	−	42.5012i	1.08431	−	1.49242i	0.854690	−	0.519138i	$-0.173747\pi$
$812$		0			0
$813$	5.24237	−	3.80881i	0.183858	−	0.133581i
$814$		0			0
$815$	4.62882	+	43.1764i	0.162141	+	1.51240i
$816$		0			0
$817$	−1.88217	−	0.611555i	−0.0658489	−	0.0213956i
$818$		0			0
$819$	−2.54330	−	0.826367i	−0.0888700	−	0.0288756i
$820$		0			0
$821$	4.70172	−	1.52768i	0.164091	−	0.0533164i	−0.225819	−	0.974169i	$-0.572506\pi$
$821$	4.70172	−	1.52768i	0.164091	−	0.0533164i	0.389910	+	0.920853i	$0.372506\pi$
$822$		0			0
$823$	3.18730	−	4.38694i	0.111102	−	0.152919i	−0.749845	−	0.661614i	$-0.769872\pi$
$823$	3.18730	−	4.38694i	0.111102	−	0.152919i	0.860947	+	0.508695i	$0.169872\pi$
$824$		0			0
$825$	3.82003	+	17.6113i	0.132996	+	0.613148i
$826$		0			0
$827$	−33.7010	−	24.4852i	−1.17190	−	0.851435i	−0.180664	−	0.983545i	$-0.557825\pi$
$827$	−33.7010	−	24.4852i	−1.17190	−	0.851435i	−0.991235	+	0.132110i	$0.957825\pi$
$828$		0			0
$829$	−27.3761	+	8.89503i	−0.950811	+	0.308937i	−0.743045	−	0.669241i	$-0.766619\pi$
$829$	−27.3761	+	8.89503i	−0.950811	+	0.308937i	−0.207766	+	0.978179i	$0.566619\pi$
$830$		0			0
$831$	−1.57473	+	4.84653i	−0.0546268	+	0.168124i
$832$		0			0
$833$	5.48616	+	1.78256i	0.190084	+	0.0617621i
$834$		0			0
$835$	4.69124	−	4.24171i	0.162347	−	0.146790i
$836$		0			0
$837$	19.8774	−	14.4418i	0.687063	−	0.499180i
$838$		0			0
$839$	−43.0983	−	31.3128i	−1.48792	−	1.08104i	−0.974895	−	0.222663i	$-0.928525\pi$
$839$	−43.0983	−	31.3128i	−1.48792	−	1.08104i	−0.513024	−	0.858374i	$-0.671475\pi$
$840$		0			0
$841$	−21.8779	+	15.8952i	−0.754409	+	0.548110i
$842$		0			0
$843$	18.8667			0.649805
$844$		0			0
$845$	9.53199	+	10.5422i	0.327910	+	0.362662i
$846$		0			0
$847$	3.61249	−	1.17377i	0.124126	−	0.0403311i
$848$		0			0
$849$	−2.04454			−0.0701685
$850$		0			0
$851$			66.3135i			2.27320i
$852$		0			0
$853$	16.1501	+	49.7048i	0.552968	+	1.70186i	0.701250	+	0.712915i	$0.252625\pi$
$853$	16.1501	+	49.7048i	0.552968	+	1.70186i	−0.148283	+	0.988945i	$0.547375\pi$
$854$		0			0
$855$	−0.182233	+	0.866194i	−0.00623225	+	0.0296232i
$856$		0			0
$857$		−	6.32615i		−	0.216097i	−0.994146	−	0.108049i	$-0.965540\pi$
$857$		−	6.32615i		−	0.216097i	0.994146	−	0.108049i	$-0.0344602\pi$
$858$		0			0
$859$	−31.4567	−	43.2964i	−1.07329	−	1.47726i	−0.866701	−	0.498827i	$-0.833764\pi$
$859$	−31.4567	−	43.2964i	−1.07329	−	1.47726i	−0.206588	−	0.978428i	$-0.566236\pi$
$860$		0			0
$861$	7.09832	−	9.77000i	0.241910	−	0.332961i
$862$		0			0
$863$	25.6168	+	35.2585i	0.872007	+	1.20021i	0.978571	+	0.205909i	$0.0660150\pi$
$863$	25.6168	+	35.2585i	0.872007	+	1.20021i	−0.106564	+	0.994306i	$0.533985\pi$
$864$		0			0
$865$	−1.75305	+	0.784880i	−0.0596055	+	0.0266867i
$866$		0			0
$867$	6.83146	−	21.0251i	0.232008	−	0.714049i
$868$		0			0
$869$	−13.9930	−	4.54661i	−0.474681	−	0.154233i
$870$		0			0
$871$	0.839981	+	2.58520i	0.0284617	+	0.0875961i
$872$		0			0
$873$	1.05631	−	1.45388i	0.0357505	−	0.0492064i
$874$		0			0
$875$	0.0646922	+	10.3691i	0.00218700	+	0.350541i
$876$		0			0
$877$	−3.02353	−	2.19672i	−0.102097	−	0.0741781i	0.535565	−	0.844494i	$-0.320099\pi$
$877$	−3.02353	−	2.19672i	−0.102097	−	0.0741781i	−0.637663	+	0.770316i	$0.720099\pi$
$878$		0			0
$879$	−3.10863	−	9.56738i	−0.104851	−	0.322700i
$880$		0			0
$881$	−13.5548	+	41.7174i	−0.456673	+	1.40549i	0.412487	+	0.910963i	$0.364660\pi$
$881$	−13.5548	+	41.7174i	−0.456673	+	1.40549i	−0.869160	+	0.494531i	$0.835340\pi$
$882$		0			0
$883$	6.00720	−	18.4883i	0.202158	−	0.622179i	−0.797660	−	0.603108i	$-0.793929\pi$
$883$	6.00720	−	18.4883i	0.202158	−	0.622179i	0.999818	−	0.0190716i	$-0.00607105\pi$
$884$		0			0
$885$	5.45441	+	12.1826i	0.183348	+	0.409512i
$886$		0			0
$887$	10.5570	+	14.5304i	0.354468	+	0.487883i	0.948597	−	0.316486i	$-0.102503\pi$
$887$	10.5570	+	14.5304i	0.354468	+	0.487883i	−0.594129	+	0.804370i	$0.702503\pi$
$888$		0			0
$889$	12.2138	+	8.87384i	0.409638	+	0.297619i
$890$		0			0
$891$	−6.78473	−	9.33838i	−0.227297	−	0.312847i
$892$		0			0
$893$	2.92260			0.0978012
$894$		0			0
$895$	10.5318	−	50.0600i	0.352040	−	1.67332i
$896$		0			0
$897$	24.1426	−	7.84441i	0.806098	−	0.261917i
$898$		0			0
$899$		−	6.08498i		−	0.202945i
$900$		0			0
$901$			9.15306i			0.304933i
$902$		0			0
$903$	6.76613	−	2.19845i	0.225163	−	0.0731598i
$904$		0			0
$905$	−32.3208	+	29.2237i	−1.07438	+	0.971429i
$906$		0			0
$907$	14.9961			0.497938			0.248969	−	0.968511i	$-0.419908\pi$
$907$	14.9961			0.497938			0.248969	+	0.968511i	$0.419908\pi$
$908$		0			0
$909$	5.10112	+	7.02109i	0.169193	+	0.232875i
$910$		0			0
$911$	−28.4325	−	20.6574i	−0.942011	−	0.684411i	0.00689309	−	0.999976i	$-0.497806\pi$
$911$	−28.4325	−	20.6574i	−0.942011	−	0.684411i	−0.948904	+	0.315565i	$0.897806\pi$
$912$		0			0
$913$	10.8873	+	14.9850i	0.360316	+	0.495932i
$914$		0			0
$915$	−8.31278	+	7.51623i	−0.274812	+	0.248479i
$916$		0			0
$917$	−4.70477	+	14.4798i	−0.155365	+	0.478165i
$918$		0			0
$919$	−1.49412	+	4.59844i	−0.0492866	+	0.151689i	−0.972671	−	0.232188i	$-0.925411\pi$
$919$	−1.49412	+	4.59844i	−0.0492866	+	0.151689i	0.923384	+	0.383877i	$0.125411\pi$
$920$		0			0
$921$	1.65874	+	5.10509i	0.0546575	+	0.168218i
$922$		0			0
$923$	−24.0483	−	17.4721i	−0.791558	−	0.575101i
$924$		0			0
$925$	42.2645	+	18.6071i	1.38965	+	0.611799i
$926$		0			0
$927$	−0.928882	+	1.27850i	−0.0305085	+	0.0419913i
$928$		0			0
$929$	−1.73466	−	5.33873i	−0.0569124	−	0.175158i	0.918559	−	0.395283i	$-0.129354\pi$
$929$	−1.73466	−	5.33873i	−0.0569124	−	0.175158i	−0.975472	+	0.220125i	$0.929354\pi$
$930$		0			0
$931$	−2.06641	−	0.671416i	−0.0677237	−	0.0220048i
$932$		0			0
$933$	2.80601	−	8.63602i	0.0918648	−	0.282731i
$934$		0			0
$935$	0.588440	+	5.48880i	0.0192440	+	0.179503i
$936$		0			0
$937$	−20.3931	−	28.0687i	−0.666213	−	0.916964i	0.333454	−	0.942767i	$-0.391786\pi$
$937$	−20.3931	−	28.0687i	−0.666213	−	0.916964i	−0.999667	+	0.0258024i	$0.991786\pi$
$938$		0			0
$939$	−16.5409	+	22.7666i	−0.539791	+	0.742958i
$940$		0			0
$941$	−27.7263	−	38.1620i	−0.903853	−	1.24405i	−0.969223	−	0.246185i	$-0.920823\pi$
$941$	−27.7263	−	38.1620i	−0.903853	−	1.24405i	0.0653703	−	0.997861i	$-0.479177\pi$
$942$		0			0
$943$		−	68.1597i		−	2.21958i
$944$		0			0
$945$	−4.78749	−	10.6930i	−0.155737	−	0.347842i
$946$		0			0
$947$	−1.10237	−	3.39273i	−0.0358221	−	0.110249i	0.931547	−	0.363622i	$-0.118460\pi$
$947$	−1.10237	−	3.39273i	−0.0358221	−	0.110249i	−0.967369	+	0.253373i	$0.918460\pi$
$948$		0			0
$949$			40.5930i			1.31771i
$950$		0			0
$951$	6.83199			0.221542
$952$		0			0
$953$	26.4322	−	8.58834i	0.856222	−	0.278204i	0.152172	−	0.988354i	$-0.451373\pi$
$953$	26.4322	−	8.58834i	0.856222	−	0.278204i	0.704050	+	0.710150i	$0.251373\pi$
$954$		0			0
$955$	3.00629	+	28.0418i	0.0972812	+	0.907412i
$956$		0			0
$957$	−5.04259			−0.163004
$958$		0			0
$959$	−16.8108	+	12.2137i	−0.542848	+	0.394402i
$960$		0			0
$961$	9.77638	+	7.10296i	0.315367	+	0.229128i
$962$		0			0
$963$	−15.3590	+	11.1590i	−0.494937	+	0.359593i
$964$		0			0
$965$	16.4489	+	9.45124i	0.529510	+	0.304246i
$966$		0			0
$967$	23.8022	+	7.73379i	0.765426	+	0.248702i	0.665606	−	0.746304i	$-0.268173\pi$
$967$	23.8022	+	7.73379i	0.765426	+	0.248702i	0.0998201	+	0.995006i	$0.468173\pi$
$968$		0			0
$969$	0.140923	−	0.433717i	0.00452710	−	0.0139330i
$970$		0			0
$971$	23.8687	−	7.75540i	0.765982	−	0.248883i	0.100138	−	0.994974i	$-0.468072\pi$
$971$	23.8687	−	7.75540i	0.765982	−	0.248883i	0.665844	+	0.746091i	$0.268072\pi$
$972$		0			0
$973$	−8.84037	−	6.42290i	−0.283409	−	0.205909i
$974$		0			0
$975$	1.77467	−	17.5883i	0.0568349	−	0.563275i
$976$		0			0
$977$	20.3216	−	27.9703i	0.650146	−	0.894850i	−0.348959	−	0.937138i	$-0.613465\pi$
$977$	20.3216	−	27.9703i	0.650146	−	0.894850i	0.999105	+	0.0422882i	$0.0134648\pi$
$978$		0			0
$979$	−22.0183	+	7.15417i	−0.703707	+	0.228648i
$980$		0			0
$981$	−12.4259	−	4.03742i	−0.396729	−	0.128905i
$982$		0			0
$983$	−16.4679	−	5.35074i	−0.525244	−	0.170662i	0.0343798	−	0.999409i	$-0.489054\pi$
$983$	−16.4679	−	5.35074i	−0.525244	−	0.170662i	−0.559624	+	0.828747i	$0.689054\pi$
$984$		0			0
$985$	32.2390	+	6.78257i	1.02722	+	0.216111i
$986$		0			0
$987$	−8.49980	+	6.17546i	−0.270552	+	0.196567i
$988$		0			0
$989$	23.6017	−	32.4849i	0.750490	−	1.03296i
$990$		0			0
$991$	45.0802	−	32.7527i	1.43202	−	1.04042i	0.442385	−	0.896825i	$-0.354132\pi$
$991$	45.0802	−	32.7527i	1.43202	−	1.04042i	0.989636	−	0.143599i	$-0.0458676\pi$
$992$		0			0
$993$		−	27.2369i		−	0.864338i
$994$		0			0
$995$	−6.35676	+	11.0633i	−0.201523	+	0.350730i
$996$		0			0
$997$	−5.97548	−	18.3906i	−0.189245	−	0.582438i	0.810750	−	0.585392i	$-0.199060\pi$
$997$	−5.97548	−	18.3906i	−0.189245	−	0.582438i	−0.999996	+	0.00295465i	$0.999060\pi$
$998$		0			0
$999$	−52.1755			−1.65076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.209.20		112
4.3	odd	2		200.2.o.a.109.15	yes	112
8.3	odd	2		200.2.o.a.109.2	✓	112
8.5	even	2	inner	800.2.be.a.209.9		112
20.3	even	4		1000.2.t.b.701.55		224
20.7	even	4		1000.2.t.b.701.2		224
20.19	odd	2		1000.2.o.a.549.14		112
25.14	even	10	inner	800.2.be.a.689.9		112
40.3	even	4		1000.2.t.b.701.32		224
40.19	odd	2		1000.2.o.a.549.27		112
40.27	even	4		1000.2.t.b.701.25		224
100.11	odd	10		1000.2.o.a.949.27		112
100.23	even	20		1000.2.t.b.301.32		224
100.27	even	20		1000.2.t.b.301.25		224
100.39	odd	10		200.2.o.a.189.2	yes	112
200.11	odd	10		1000.2.o.a.949.14		112
200.27	even	20		1000.2.t.b.301.2		224
200.123	even	20		1000.2.t.b.301.55		224
200.139	odd	10		200.2.o.a.189.15	yes	112
200.189	even	10	inner	800.2.be.a.689.20		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.2	✓	112	8.3	odd	2
200.2.o.a.109.15	yes	112	4.3	odd	2
200.2.o.a.189.2	yes	112	100.39	odd	10
200.2.o.a.189.15	yes	112	200.139	odd	10
800.2.be.a.209.9		112	8.5	even	2	inner
800.2.be.a.209.20		112	1.1	even	1	trivial
800.2.be.a.689.9		112	25.14	even	10	inner
800.2.be.a.689.20		112	200.189	even	10	inner
1000.2.o.a.549.14		112	20.19	odd	2
1000.2.o.a.549.27		112	40.19	odd	2
1000.2.o.a.949.14		112	200.11	odd	10
1000.2.o.a.949.27		112	100.11	odd	10
1000.2.t.b.301.2		224	200.27	even	20
1000.2.t.b.301.25		224	100.27	even	20
1000.2.t.b.301.32		224	100.23	even	20
1000.2.t.b.301.55		224	200.123	even	20
1000.2.t.b.701.2		224	20.7	even	4
1000.2.t.b.701.25		224	40.27	even	4
1000.2.t.b.701.32		224	40.3	even	4
1000.2.t.b.701.55		224	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.423859 + 1.30450i) q^{3} +(1.11400 - 1.93881i) q^{5} -0.927462i q^{7} +(0.904979 - 0.657506i) q^{9} +(-1.54449 + 2.12581i) q^{11} +(2.08531 - 1.51507i) q^{13} +(3.00137 + 0.631440i) q^{15} +(0.893539 + 0.290328i) q^{17} +(-0.336558 - 0.109354i) q^{19} +(1.20988 - 0.393113i) q^{21} +(4.22031 - 5.80876i) q^{23} +(-2.51799 - 4.31969i) q^{25} +(4.57033 + 3.32054i) q^{27} +(1.33062 - 0.432345i) q^{29} +(1.34398 - 4.13636i) q^{31} +(-3.42777 - 1.11375i) q^{33} +(-1.79818 - 1.03320i) q^{35} +(-7.47195 + 5.42869i) q^{37} +(2.86029 + 2.07812i) q^{39} +(7.67997 - 5.57982i) q^{41} +5.59241 q^{43} +(-0.266630 - 2.48705i) q^{45} +(-7.85457 + 2.55210i) q^{47} +6.13981 q^{49} +1.28868i q^{51} +(3.01052 + 9.26543i) q^{53} +(2.40098 + 5.36264i) q^{55} -0.485392i q^{57} +(2.55804 + 3.52083i) q^{59} +(-2.14775 + 2.95612i) q^{61} +(-0.609812 - 0.839334i) q^{63} +(-0.614386 - 5.73082i) q^{65} +(-0.325879 + 1.00295i) q^{67} +(9.36636 + 3.04331i) q^{69} +(-3.56365 - 10.9678i) q^{71} +(-9.25671 + 12.7408i) q^{73} +(4.56778 - 5.11566i) q^{75} +(1.97161 + 1.43246i) q^{77} +(1.73030 + 5.32530i) q^{79} +(-1.35747 + 4.17785i) q^{81} +(2.17829 - 6.70408i) q^{83} +(1.55830 - 1.40898i) q^{85} +(1.12799 + 1.55254i) q^{87} +(7.12799 + 5.17879i) q^{89} +(-1.40517 - 1.93405i) q^{91} +5.96555 q^{93} +(-0.586945 + 0.530702i) q^{95} +(1.52791 - 0.496446i) q^{97} +2.93933i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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