LMFDB - Embedded newform 456.2.bk.a.253.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] 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("456.61"); 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, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.16
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453922 + 1.33939i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-1.58791 - 1.21595i) q^{4} +(-2.07565 + 0.365992i) q^{5} +(1.10336 + 0.884644i) q^{6} +(0.994443 - 1.72243i) q^{7} +(2.34942 - 1.57487i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(0.451977 - 2.94622i) q^{10} +(-4.64743 + 2.68320i) q^{11} +(-1.68572 + 1.07627i) q^{12} +(2.31010 + 6.34696i) q^{13} +(1.85559 + 2.11379i) q^{14} +(-0.365992 + 2.07565i) q^{15} +(1.04291 + 3.86165i) q^{16} +(-4.80442 + 4.03138i) q^{17} +(1.20867 - 0.734254i) q^{18} +(1.64951 + 4.03474i) q^{19} +(3.74097 + 1.94273i) q^{20} +(-1.27843 - 1.52358i) q^{21} +(-1.48426 - 7.44267i) q^{22} +(0.307565 - 1.74429i) q^{23} +(-0.676350 - 2.74637i) q^{24} +(-0.524107 + 0.190759i) q^{25} +(-9.54963 + 0.213096i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-3.67348 + 1.52586i) q^{28} +(1.05844 - 1.26140i) q^{29} +(-2.61396 - 1.43239i) q^{30} +(1.98429 - 3.43688i) q^{31} +(-5.64564 - 0.356026i) q^{32} +(0.931865 + 5.28487i) q^{33} +(-3.21875 - 8.26490i) q^{34} +(-1.43372 + 3.93910i) q^{35} +(0.434809 + 1.95216i) q^{36} -0.502359i q^{37} +(-6.15282 + 0.377879i) q^{38} +6.75429 q^{39} +(-4.30017 + 4.12875i) q^{40} +(0.821603 + 0.299039i) q^{41} +(2.62096 - 1.02073i) q^{42} +(-11.4809 + 2.02439i) q^{43} +(10.6423 + 1.39039i) q^{44} +(1.82529 + 1.05383i) q^{45} +(2.19667 + 1.20372i) q^{46} +(4.46708 + 3.74833i) q^{47} +(3.98546 + 0.340745i) q^{48} +(1.52217 + 2.63647i) q^{49} +(-0.0175966 - 0.788571i) q^{50} +(2.14506 + 5.89349i) q^{51} +(4.04937 - 12.8874i) q^{52} +(-5.86117 - 1.03348i) q^{53} +(-0.276585 - 1.38690i) q^{54} +(8.66440 - 7.27029i) q^{55} +(-0.376242 - 5.61282i) q^{56} +(4.35558 - 0.170075i) q^{57} +(1.20905 + 1.99024i) q^{58} +(0.834265 + 0.994239i) q^{59} +(3.10505 - 2.85091i) q^{60} +(-8.23216 - 1.45155i) q^{61} +(3.70260 + 4.21780i) q^{62} +(-1.86894 + 0.680239i) q^{63} +(3.03954 - 7.40008i) q^{64} +(-7.11789 - 12.3286i) q^{65} +(-7.50147 - 1.15079i) q^{66} +(9.53108 - 11.3587i) q^{67} +(12.5310 - 0.559523i) q^{68} +(-1.53390 - 0.885599i) q^{69} +(-4.62519 - 3.70835i) q^{70} +(1.34103 + 7.60533i) q^{71} +(-2.81207 - 0.303753i) q^{72} +(-12.5965 - 4.58476i) q^{73} +(0.672853 + 0.228032i) q^{74} +0.557743i q^{75} +(2.28678 - 8.41253i) q^{76} +10.6731i q^{77} +(-3.06592 + 9.04660i) q^{78} +(7.19001 + 2.61695i) q^{79} +(-3.57805 - 7.63372i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.773472 + 0.964703i) q^{82} +(5.16182 + 2.98018i) q^{83} +(0.177436 + 3.97381i) q^{84} +(8.49681 - 10.1261i) q^{85} +(2.49998 - 16.2962i) q^{86} +(-0.823322 - 1.42604i) q^{87} +(-6.69307 + 13.6231i) q^{88} +(-2.36013 + 0.859017i) q^{89} +(-2.24003 + 1.96641i) q^{90} +(13.2294 + 2.33270i) q^{91} +(-2.60936 + 2.39579i) q^{92} +(-2.55095 - 3.04010i) q^{93} +(-7.04816 + 4.28170i) q^{94} +(-4.90049 - 7.77098i) q^{95} +(-2.26548 + 5.18340i) q^{96} +(-10.5547 + 8.85648i) q^{97} +(-4.22220 + 0.842016i) q^{98} +(5.28487 + 0.931865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

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

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	−0.453922	+	1.33939i	−0.320971	+	0.947089i
$2$	−0.453922	+	1.33939i	−0.320971	+	0.947089i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$4$	−1.58791	−	1.21595i	−0.793955	−	0.607977i
$5$	−2.07565	+	0.365992i	−0.928257	+	0.163677i	−0.617283	−	0.786741i	$-0.711766\pi$
$5$	−2.07565	+	0.365992i	−0.928257	+	0.163677i	−0.310975	+	0.950418i	$0.600655\pi$
$6$	1.10336	+	0.884644i	0.450445	+	0.361155i
$7$	0.994443	−	1.72243i	0.375864	−	0.651016i	−0.614592	−	0.788845i	$-0.710679\pi$
$7$	0.994443	−	1.72243i	0.375864	−	0.651016i	0.990456	+	0.137830i	$0.0440126\pi$
$8$	2.34942	−	1.57487i	0.830645	−	0.556802i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	0.451977	−	2.94622i	0.142928	−	0.931678i
$11$	−4.64743	+	2.68320i	−1.40125	+	0.809015i	−0.994521	−	0.104533i	$-0.966665\pi$
$11$	−4.64743	+	2.68320i	−1.40125	+	0.809015i	−0.406733	+	0.913547i	$0.633332\pi$
$12$	−1.68572	+	1.07627i	−0.486625	+	0.310691i
$13$	2.31010	+	6.34696i	0.640707	+	1.76033i	0.649493	+	0.760367i	$0.274981\pi$
$13$	2.31010	+	6.34696i	0.640707	+	1.76033i	−0.00878576	+	0.999961i	$0.502797\pi$
$14$	1.85559	+	2.11379i	0.495928	+	0.564934i
$15$	−0.365992	+	2.07565i	−0.0944988	+	0.535930i
$16$	1.04291	+	3.86165i	0.260728	+	0.965412i
$17$	−4.80442	+	4.03138i	−1.16524	+	0.977754i	−0.999964	−	0.00849248i	$-0.997297\pi$
$17$	−4.80442	+	4.03138i	−1.16524	+	0.977754i	−0.165278	+	0.986247i	$0.552852\pi$
$18$	1.20867	−	0.734254i	0.284885	−	0.173065i
$19$	1.64951	+	4.03474i	0.378424	+	0.925632i
$19$	1.64951	+	4.03474i	0.378424	+	0.925632i
$20$	3.74097	+	1.94273i	0.836506	+	0.434407i
$21$	−1.27843	−	1.52358i	−0.278977	−	0.332471i
$22$	−1.48426	−	7.44267i	−0.316446	−	1.58678i
$23$	0.307565	−	1.74429i	0.0641318	−	0.363710i	−0.935806	−	0.352517i	$-0.885326\pi$
$23$	0.307565	−	1.74429i	0.0641318	−	0.363710i	0.999937	−	0.0111929i	$-0.00356289\pi$
$24$	−0.676350	−	2.74637i	−0.138059	−	0.560601i
$25$	−0.524107	+	0.190759i	−0.104821	+	0.0381519i
$26$	−9.54963	+	0.213096i	−1.87284	+	0.0417915i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−3.67348	+	1.52586i	−0.694222	+	0.288360i
$29$	1.05844	−	1.26140i	0.196548	−	0.234237i	−0.658765	−	0.752349i	$-0.728921\pi$
$29$	1.05844	−	1.26140i	0.196548	−	0.234237i	0.855312	+	0.518112i	$0.173365\pi$
$30$	−2.61396	−	1.43239i	−0.477241	−	0.261517i
$31$	1.98429	−	3.43688i	0.356388	−	0.617282i	−0.630966	−	0.775810i	$-0.717341\pi$
$31$	1.98429	−	3.43688i	0.356388	−	0.617282i	0.987355	+	0.158528i	$0.0506748\pi$
$32$	−5.64564	−	0.356026i	−0.998017	−	0.0629372i
$33$	0.931865	+	5.28487i	0.162217	+	0.919977i
$34$	−3.21875	−	8.26490i	−0.552011	−	1.41742i
$35$	−1.43372	+	3.93910i	−0.242342	+	0.665830i
$36$	0.434809	+	1.95216i	0.0724682	+	0.325361i
$37$		−	0.502359i		−	0.0825874i	−0.999147	−	0.0412937i	$-0.986852\pi$
$37$		−	0.502359i		−	0.0825874i	0.999147	−	0.0412937i	$-0.0131479\pi$
$38$	−6.15282	+	0.377879i	−0.998119	+	0.0613001i
$39$	6.75429			1.08155
$40$	−4.30017	+	4.12875i	−0.679917	+	0.652813i
$41$	0.821603	+	0.299039i	0.128313	+	0.0467020i	0.405378	−	0.914149i	$-0.367140\pi$
$41$	0.821603	+	0.299039i	0.128313	+	0.0467020i	−0.277066	+	0.960851i	$0.589362\pi$
$42$	2.62096	−	1.02073i	0.404423	−	0.157502i
$43$	−11.4809	+	2.02439i	−1.75082	+	0.308716i	−0.954952	−	0.296760i	$-0.904094\pi$
$43$	−11.4809	+	2.02439i	−1.75082	+	0.308716i	−0.795863	+	0.605476i	$0.792983\pi$
$44$	10.6423	+	1.39039i	1.60439	+	0.209609i
$45$	1.82529	+	1.05383i	0.272099	+	0.157096i
$46$	2.19667	+	1.20372i	0.323881	+	0.177479i
$47$	4.46708	+	3.74833i	0.651591	+	0.546749i	0.907553	−	0.419937i	$-0.137948\pi$
$47$	4.46708	+	3.74833i	0.651591	+	0.546749i	−0.255963	+	0.966687i	$0.582392\pi$
$48$	3.98546	+	0.340745i	0.575252	+	0.0491823i
$49$	1.52217	+	2.63647i	0.217452	+	0.376639i
$50$	−0.0175966	−	0.788571i	−0.00248854	−	0.111521i
$51$	2.14506	+	5.89349i	0.300368	+	0.825254i
$52$	4.04937	−	12.8874i	0.561547	−	1.78716i
$53$	−5.86117	−	1.03348i	−0.805093	−	0.141960i	−0.244068	−	0.969758i	$-0.578482\pi$
$53$	−5.86117	−	1.03348i	−0.805093	−	0.141960i	−0.561026	+	0.827798i	$0.689593\pi$
$54$	−0.276585	−	1.38690i	−0.0376384	−	0.188734i
$55$	8.66440	−	7.27029i	1.16831	−	0.980326i
$56$	−0.376242	−	5.61282i	−0.0502775	−	0.750045i
$57$	4.35558	−	0.170075i	0.576911	−	0.0225270i
$58$	1.20905	+	1.99024i	0.158757	+	0.261332i
$59$	0.834265	+	0.994239i	0.108612	+	0.129439i	0.817612	−	0.575770i	$-0.195298\pi$
$59$	0.834265	+	0.994239i	0.108612	+	0.129439i	−0.709000	+	0.705209i	$0.750853\pi$
$60$	3.10505	−	2.85091i	0.400861	−	0.368051i
$61$	−8.23216	−	1.45155i	−1.05402	−	0.185852i	−0.380318	−	0.924856i	$-0.624186\pi$
$61$	−8.23216	−	1.45155i	−1.05402	−	0.185852i	−0.673701	+	0.739004i	$0.735297\pi$
$62$	3.70260	+	4.21780i	0.470231	+	0.535661i
$63$	−1.86894	+	0.680239i	−0.235464	+	0.0857021i
$64$	3.03954	−	7.40008i	0.379942	−	0.925010i
$65$	−7.11789	−	12.3286i	−0.882866	−	1.52917i
$66$	−7.50147	−	1.15079i	−0.923367	−	0.141653i
$67$	9.53108	−	11.3587i	1.16441	−	1.38769i	0.257541	−	0.966267i	$-0.417088\pi$
$67$	9.53108	−	11.3587i	1.16441	−	1.38769i	0.906866	−	0.421419i	$-0.138468\pi$
$68$	12.5310	−	0.559523i	1.51960	−	0.0678522i
$69$	−1.53390	−	0.885599i	−0.184660	−	0.106614i
$70$	−4.62519	−	3.70835i	−0.552815	−	0.443232i
$71$	1.34103	+	7.60533i	0.159150	+	0.902587i	0.954893	+	0.296951i	$0.0959699\pi$
$71$	1.34103	+	7.60533i	0.159150	+	0.902587i	−0.795742	+	0.605635i	$0.792919\pi$
$72$	−2.81207	−	0.303753i	−0.331406	−	0.0357976i
$73$	−12.5965	−	4.58476i	−1.47431	−	0.536606i	−0.525044	−	0.851075i	$-0.675951\pi$
$73$	−12.5965	−	4.58476i	−1.47431	−	0.536606i	−0.949268	+	0.314469i	$0.898173\pi$
$74$	0.672853	+	0.228032i	0.0782176	+	0.0265082i
$75$			0.557743i			0.0644026i
$76$	2.28678	−	8.41253i	0.262311	−	0.964983i
$77$			10.6731i			1.21632i
$78$	−3.06592	+	9.04660i	−0.347147	+	1.02433i
$79$	7.19001	+	2.61695i	0.808940	+	0.294430i	0.713186	−	0.700975i	$-0.247252\pi$
$79$	7.19001	+	2.61695i	0.808940	+	0.294430i	0.0957540	+	0.995405i	$0.469474\pi$
$80$	−3.57805	−	7.63372i	−0.400038	−	0.853476i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−0.773472	+	0.964703i	−0.0854157	+	0.106534i
$83$	5.16182	+	2.98018i	0.566583	+	0.327117i	0.755784	−	0.654822i	$-0.227256\pi$
$83$	5.16182	+	2.98018i	0.566583	+	0.327117i	−0.189200	+	0.981939i	$0.560590\pi$
$84$	0.177436	+	3.97381i	0.0193598	+	0.433578i
$85$	8.49681	−	10.1261i	0.921609	−	1.09833i
$86$	2.49998	−	16.2962i	0.269580	−	1.75727i
$87$	−0.823322	−	1.42604i	−0.0882694	−	0.152887i
$88$	−6.69307	+	13.6231i	−0.713484	+	1.45223i
$89$	−2.36013	+	0.859017i	−0.250173	+	0.0910557i	−0.464063	−	0.885802i	$-0.653609\pi$
$89$	−2.36013	+	0.859017i	−0.250173	+	0.0910557i	0.213890	+	0.976858i	$0.431387\pi$
$90$	−2.24003	+	1.96641i	−0.236120	+	0.207278i
$91$	13.2294	+	2.33270i	1.38682	+	0.244534i
$92$	−2.60936	+	2.39579i	−0.272045	+	0.249778i
$93$	−2.55095	−	3.04010i	−0.264521	−	0.315244i
$94$	−7.04816	+	4.28170i	−0.726962	+	0.441623i
$95$	−4.90049	−	7.77098i	−0.502780	−	0.797285i
$96$	−2.26548	+	5.18340i	−0.231219	+	0.529028i
$97$	−10.5547	+	8.85648i	−1.07167	+	0.899240i	−0.995203	−	0.0978324i	$-0.968809\pi$
$97$	−10.5547	+	8.85648i	−1.07167	+	0.899240i	−0.0764690	+	0.997072i	$0.524365\pi$
$98$	−4.22220	+	0.842016i	−0.426506	+	0.0850565i
$99$	5.28487	+	0.931865i	0.531149	+	0.0936559i
$100$	1.06419	+	0.334381i	0.106419	+	0.0334381i
$101$	−3.03030	−	8.32569i	−0.301527	−	0.828437i	−0.994235	−	0.107220i	$-0.965805\pi$
$101$	−3.03030	−	8.32569i	−0.301527	−	0.828437i	0.692709	−	0.721217i	$-0.256417\pi$
$102$	−8.86735	+	0.197871i	−0.877998	+	0.0195921i
$103$	4.63948	+	8.03581i	0.457141	+	0.791792i	0.998809	−	0.0488010i	$-0.0155400\pi$
$103$	4.63948	+	8.03581i	0.457141	+	0.791792i	−0.541667	+	0.840593i	$0.682207\pi$
$104$	15.4231	+	11.2735i	1.51236	+	1.10546i
$105$	3.21119	+	2.69451i	0.313380	+	0.262957i
$106$	4.04475	−	7.38125i	0.392860	−	0.716930i
$107$	0.168395	+	0.0972228i	0.0162793	+	0.00939888i	0.508118	−	0.861288i	$-0.330342\pi$
$107$	0.168395	+	0.0972228i	0.0162793	+	0.00939888i	−0.491838	+	0.870687i	$0.663675\pi$
$108$	1.98315	+	0.259092i	0.190828	+	0.0249312i
$109$	−8.84563	+	1.55972i	−0.847258	+	0.149394i	−0.580390	−	0.814339i	$-0.697100\pi$
$109$	−8.84563	+	1.55972i	−0.847258	+	0.149394i	−0.266868	+	0.963733i	$0.585989\pi$
$110$	5.80477	+	14.9051i	0.553463	+	1.42115i
$111$	−0.472063	−	0.171817i	−0.0448063	−	0.0163082i
$112$	7.68852	+	2.04385i	0.726497	+	0.193126i
$113$	9.73778			0.916053			0.458026	−	0.888939i	$-0.348557\pi$
$113$	9.73778			0.916053			0.458026	+	0.888939i	$0.348557\pi$
$114$	−1.74930	+	5.91100i	−0.163837	+	0.553616i
$115$			3.73309i			0.348113i
$116$	−3.21452	+	0.715976i	−0.298461	+	0.0664767i
$117$	2.31010	−	6.34696i	0.213569	−	0.586776i
$118$	−1.71036	+	0.666096i	−0.157451	+	0.0613191i
$119$	2.16604	+	12.2842i	0.198561	+	1.12609i
$120$	2.40901	+	5.45295i	0.219912	+	0.497784i
$121$	8.89910	−	15.4137i	0.809009	−	1.40124i
$122$	5.68095	−	10.3671i	0.514329	−	0.938597i
$123$	0.562009	−	0.669777i	0.0506747	−	0.0603917i
$124$	−7.32996	+	3.04466i	−0.658249	+	0.273418i
$125$	10.1445	−	5.85693i	0.907352	−	0.523860i
$126$	−0.0627487	−	2.81201i	−0.00559010	−	0.250514i
$127$	13.6204	−	4.95742i	1.20862	−	0.439900i	0.342393	−	0.939557i	$-0.388763\pi$
$127$	13.6204	−	4.95742i	1.20862	−	0.439900i	0.866223	+	0.499657i	$0.166541\pi$
$128$	8.53185	+	7.43018i	0.754116	+	0.656741i
$129$	−2.02439	+	11.4809i	−0.178237	+	1.01083i
$130$	19.7437	−	3.93740i	1.73163	−	0.345333i
$131$	7.74363	+	9.22850i	0.676564	+	0.806297i	0.989661	−	0.143424i	$-0.0458111\pi$
$131$	7.74363	+	9.22850i	0.676564	+	0.806297i	−0.313097	+	0.949721i	$0.601367\pi$
$132$	4.94644	−	9.52500i	0.430532	−	0.829044i
$133$	8.58988	+	1.17115i	0.744837	+	0.101552i
$134$	10.8873	+	17.9218i	0.940521	+	1.54820i
$135$	1.61457	−	1.35478i	0.138960	−	0.116601i
$136$	−4.93866	+	17.0378i	−0.423487	+	1.46098i
$137$	−0.409824	+	2.32423i	−0.0350136	+	0.198572i	−0.997297	−	0.0734775i	$-0.976590\pi$
$137$	−0.409824	+	2.32423i	−0.0350136	+	0.198572i	0.962283	+	0.272049i	$0.0877014\pi$
$138$	1.88243	−	1.65249i	0.160243	−	0.140670i
$139$	−3.61144	−	9.92236i	−0.306319	−	0.841603i	−0.993366	−	0.114991i	$-0.963316\pi$
$139$	−3.61144	−	9.92236i	−0.306319	−	0.841603i	0.687048	−	0.726612i	$-0.258906\pi$
$140$	7.06638	−	4.51161i	0.597218	−	0.381300i
$141$	5.05011	−	2.91568i	0.425296	−	0.245545i
$142$	−10.7952	−	1.65608i	−0.905913	−	0.138975i
$143$	−27.7662	−	23.2986i	−2.32193	−	1.94833i
$144$	1.68330	−	3.62857i	0.140275	−	0.302380i
$145$	−1.73529	+	3.00561i	−0.144108	+	0.249602i
$146$	11.8586	−	14.7905i	0.981425	−	1.22407i
$147$	2.99808	−	0.528643i	0.247278	−	0.0436017i
$148$	−0.610846	+	0.797701i	−0.0502112	+	0.0655706i
$149$	4.95568	−	13.6156i	0.405985	−	1.11543i	−0.553297	−	0.832984i	$-0.686631\pi$
$149$	4.95568	−	13.6156i	0.405985	−	1.11543i	0.959282	−	0.282450i	$-0.0911471\pi$
$150$	−0.747033	−	0.253172i	−0.0609950	−	0.0206714i
$151$	−15.2722			−1.24283			−0.621415	−	0.783481i	$-0.713442\pi$
$151$	−15.2722			−1.24283			−0.621415	+	0.783481i	$0.713442\pi$
$152$	10.2296	+	6.88151i	0.829731	+	0.558164i
$153$	6.27172			0.507039
$154$	−14.2955	−	4.84478i	−1.15196	−	0.390403i
$155$	−2.86080	+	7.85999i	−0.229785	+	0.631329i
$156$	−10.7252	−	8.21290i	−0.858703	−	0.657559i
$157$	−0.613975	+	0.108260i	−0.0490006	+	0.00864012i	−0.198095	−	0.980183i	$-0.563475\pi$
$157$	−0.613975	+	0.108260i	−0.0490006	+	0.00864012i	0.149094	+	0.988823i	$0.452364\pi$
$158$	−6.76881	+	8.44231i	−0.538498	+	0.671634i
$159$	−2.97579	+	5.15423i	−0.235996	+	0.408757i
$160$	11.8487	−	1.32728i	0.936718	−	0.104930i
$161$	−2.69855	−	2.26435i	−0.212676	−	0.178456i
$162$	−1.39786	−	0.214444i	−0.109826	−	0.0168483i
$163$	−3.05698	+	1.76495i	−0.239441	+	0.138241i	−0.614920	−	0.788590i	$-0.710812\pi$
$163$	−3.05698	+	1.76495i	−0.239441	+	0.138241i	0.375479	+	0.926831i	$0.377478\pi$
$164$	−0.941013	−	1.47388i	−0.0734808	−	0.115091i
$165$	−3.86844	−	10.6285i	−0.301158	−	0.827424i
$166$	−6.33467	+	5.56090i	−0.491666	+	0.431609i
$167$	2.55363	−	14.4823i	0.197606	−	1.12068i	−0.711053	−	0.703138i	$-0.751782\pi$
$167$	2.55363	−	14.4823i	0.197606	−	1.12068i	0.908659	−	0.417539i	$-0.137107\pi$
$168$	−5.40301	−	1.56615i	−0.416851	−	0.120831i
$169$	−24.9887	+	20.9680i	−1.92221	+	1.61292i
$170$	9.70588	+	15.9770i	0.744407	+	1.22538i
$171$	1.32988	−	4.15108i	0.101698	−	0.317441i
$172$	20.6921	+	10.7457i	1.57776	+	0.819349i
$173$	8.59540	+	10.2436i	0.653496	+	0.778807i	0.986437	−	0.164141i	$-0.0524853\pi$
$173$	8.59540	+	10.2436i	0.653496	+	0.778807i	−0.332940	+	0.942948i	$0.608041\pi$
$174$	2.28374	−	0.455437i	0.173130	−	0.0345266i
$175$	−0.192626	+	1.09243i	−0.0145611	+	0.0825803i
$176$	−15.2084	−	15.1484i	−1.14638	−	1.14186i
$177$	1.21961	−	0.443903i	0.0916718	−	0.0333658i
$178$	−0.0792401	−	3.55105i	−0.00593929	−	0.266163i
$179$	−16.9986	+	9.81414i	−1.27053	+	0.733543i	−0.975088	−	0.221816i	$-0.928801\pi$
$179$	−16.9986	+	9.81414i	−1.27053	+	0.733543i	−0.295446	+	0.955360i	$0.595468\pi$
$180$	−1.61699	−	3.89286i	−0.120523	−	0.290157i
$181$	−9.98884	+	11.9042i	−0.742465	+	0.884835i	−0.996605	−	0.0823323i	$-0.973763\pi$
$181$	−9.98884	+	11.9042i	−0.742465	+	0.884835i	0.254140	+	0.967167i	$0.418208\pi$
$182$	−9.12952	+	16.6604i	−0.676725	+	1.23495i
$183$	−4.17958	+	7.23924i	−0.308963	+	0.535140i
$184$	−2.02444	−	4.58244i	−0.149244	−	0.337822i
$185$	0.183860	+	1.04272i	0.0135176	+	0.0766623i
$186$	5.22980	−	2.03673i	0.383468	−	0.149341i
$187$	11.5112	−	31.6268i	0.841783	−	2.31278i
$188$	−2.53553	−	11.3838i	−0.184922	−	0.830246i
$189$			1.98889i			0.144670i
$190$	12.6328	−	3.03623i	0.916478	−	0.220271i
$191$	−6.87291			−0.497306			−0.248653	−	0.968593i	$-0.579988\pi$
$191$	−6.87291			−0.497306			−0.248653	+	0.968593i	$0.579988\pi$
$192$	−5.91422	−	5.38721i	−0.426822	−	0.388788i
$193$	9.77009	+	3.55602i	0.703267	+	0.255968i	0.668805	−	0.743438i	$-0.266806\pi$
$193$	9.77009	+	3.55602i	0.703267	+	0.255968i	0.0344617	+	0.999406i	$0.489028\pi$
$194$	−7.07122	−	18.1570i	−0.507684	−	1.30360i
$195$	−14.0195	+	2.47202i	−1.00396	+	0.177025i
$196$	0.788763	−	6.03736i	0.0563402	−	0.431240i
$197$	6.30148	+	3.63816i	0.448962	+	0.259208i	0.707392	−	0.706822i	$-0.249872\pi$
$197$	6.30148	+	3.63816i	0.448962	+	0.259208i	−0.258430	+	0.966030i	$0.583205\pi$
$198$	−3.64705	+	6.65548i	−0.259184	+	0.472985i
$199$	14.6902	+	12.3266i	1.04136	+	0.873807i	0.992159	−	0.124982i	$-0.0398874\pi$
$199$	14.6902	+	12.3266i	1.04136	+	0.873807i	0.0492031	+	0.998789i	$0.484332\pi$
$200$	−0.930925	+	1.27358i	−0.0658263	+	0.0900555i
$201$	−7.41387	−	12.8412i	−0.522934	−	0.905748i
$202$	12.5268	−	0.279531i	0.881385	−	0.0196677i
$203$	−1.12011	−	3.07748i	−0.0786164	−	0.215997i
$204$	3.76006	−	11.9666i	0.263257	−	0.837831i
$205$	−1.81480	−	0.319999i	−0.126751	−	0.0223497i
$206$	−12.8690	+	2.56642i	−0.896627	+	0.178811i
$207$	−1.35682	+	1.13850i	−0.0943053	+	0.0791315i
$208$	−22.1005	+	15.5401i	−1.53239	+	1.07751i
$209$	−18.4920	−	14.3252i	−1.27912	−	0.990895i
$210$	−5.06661	+	3.07792i	−0.349630	+	0.212397i
$211$	−4.46641	−	5.32286i	−0.307480	−	0.366440i	0.590071	−	0.807352i	$-0.299100\pi$
$211$	−4.46641	−	5.32286i	−0.307480	−	0.366440i	−0.897551	+	0.440911i	$0.854655\pi$
$212$	8.05034	+	8.76799i	0.552899	+	0.602188i
$213$	7.60533	+	1.34103i	0.521109	+	0.0918855i
$214$	−0.206657	+	0.181414i	−0.0141268	+	0.0124012i
$215$	23.0893	−	8.40382i	1.57468	−	0.573136i
$216$	−1.24722	+	2.53859i	−0.0848625	+	0.172729i
$217$	−3.94652	−	6.83557i	−0.267907	−	0.464029i
$218$	1.92616	−	12.5557i	0.130456	−	0.850380i
$219$	−8.61653	+	10.2688i	−0.582251	+	0.693900i
$220$	−22.5986	+	1.00906i	−1.52360	+	0.0680307i
$221$	−36.6857	−	21.1805i	−2.46775	−	1.42476i
$222$	0.444409	−	0.554284i	0.0298268	−	0.0372011i
$223$	1.16963	+	6.63329i	0.0783241	+	0.444198i	0.998599	+	0.0529245i	$0.0168543\pi$
$223$	1.16963	+	6.63329i	0.0783241	+	0.444198i	−0.920274	+	0.391274i	$0.872035\pi$
$224$	−6.22750	+	9.37015i	−0.416092	+	0.626069i
$225$	0.524107	+	0.190759i	0.0349405	+	0.0127173i
$226$	−4.42019	+	13.0426i	−0.294027	+	0.867583i
$227$		−	8.74782i		−	0.580613i	−0.956934	−	0.290307i	$-0.906243\pi$
$227$		−	8.74782i		−	0.580613i	0.956934	−	0.290307i	$-0.0937573\pi$
$228$	−7.12307	−	5.02612i	−0.471737	−	0.332863i
$229$			22.2254i			1.46869i	0.678774	+	0.734347i	$0.262512\pi$
$229$			22.2254i			1.46869i	−0.678774	+	0.734347i	$0.737488\pi$
$230$	−5.00005	−	1.69453i	−0.329694	−	0.111734i
$231$	10.0295	+	3.65043i	0.659891	+	0.240181i
$232$	0.500173	−	4.63048i	0.0328380	−	0.304006i
$233$	1.52893	+	8.67101i	0.100164	+	0.568057i	0.993042	+	0.117759i	$0.0375710\pi$
$233$	1.52893	+	8.67101i	0.100164	+	0.568057i	−0.892879	+	0.450298i	$0.851318\pi$
$234$	7.45242	+	5.97514i	0.487180	+	0.390607i
$235$	−10.6439	−	6.14528i	−0.694334	−	0.400874i
$236$	−0.115789	−	2.59319i	−0.00753724	−	0.168802i
$237$	4.91826	−	5.86135i	0.319475	−	0.380736i
$238$	−17.4365	−	2.67492i	−1.13024	−	0.173389i
$239$	−10.3434	−	17.9154i	−0.669061	−	1.15885i	−0.978167	−	0.207821i	$-0.933363\pi$
$239$	−10.3434	−	17.9154i	−0.669061	−	1.15885i	0.309106	−	0.951028i	$-0.399970\pi$
$240$	−8.39711	+	0.751382i	−0.542031	+	0.0485015i
$241$	12.0595	−	4.38929i	0.776819	−	0.282739i	0.0769734	−	0.997033i	$-0.475474\pi$
$241$	12.0595	−	4.38929i	0.776819	−	0.282739i	0.699846	+	0.714294i	$0.253252\pi$
$242$	16.6054	+	18.9159i	1.06743	+	1.21596i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	11.3069	+	12.3149i	0.723850	+	0.788378i
$245$	−4.12441	−	4.91528i	−0.263499	−	0.314025i
$246$	0.641981	+	1.05677i	0.0409312	+	0.0673774i
$247$	−21.7978	+	19.7901i	−1.38696	+	1.25921i
$248$	−0.750744	−	11.1997i	−0.0476723	−	0.711180i
$249$	4.56590	−	3.83124i	0.289352	−	0.242795i
$250$	3.23988	+	16.2460i	0.204908	+	1.02749i
$251$	12.3491	+	2.17748i	0.779470	+	0.137442i	0.549206	−	0.835687i	$-0.314930\pi$
$251$	12.3491	+	2.17748i	0.779470	+	0.137442i	0.230263	+	0.973128i	$0.426041\pi$
$252$	3.79485	+	1.19239i	0.239053	+	0.0751134i
$253$	3.25088	+	8.93173i	0.204381	+	0.561533i
$254$	0.457298	+	20.4933i	0.0286934	+	1.28586i
$255$	−6.60935	−	11.4477i	−0.413893	−	0.716884i
$256$	−13.8247	+	8.05472i	−0.864042	+	0.503420i
$257$	−8.03156	−	6.73928i	−0.500995	−	0.420385i	0.356952	−	0.934123i	$-0.383816\pi$
$257$	−8.03156	−	6.73928i	−0.500995	−	0.420385i	−0.857947	+	0.513738i	$0.828260\pi$
$258$	−14.4584	−	7.92285i	−0.900140	−	0.493255i
$259$	−0.865277	−	0.499568i	−0.0537657	−	0.0310416i
$260$	−3.68838	+	28.2317i	−0.228744	+	1.75085i
$261$	−1.62163	+	0.285937i	−0.100376	+	0.0176990i
$262$	−15.8755	+	6.18269i	−0.980793	+	0.381968i
$263$	5.64346	+	2.05405i	0.347991	+	0.126658i	0.510101	−	0.860114i	$-0.329608\pi$
$263$	5.64346	+	2.05405i	0.347991	+	0.126658i	−0.162111	+	0.986773i	$0.551830\pi$
$264$	10.5123	+	10.9488i	0.646990	+	0.673852i
$265$	12.5440			0.770569
$266$	−5.46776	+	10.9736i	−0.335250	+	0.672832i
$267$			2.51160i			0.153707i
$268$	−28.9462	+	6.44723i	−1.76817	+	0.393827i
$269$	7.83529	−	21.5273i	0.477726	−	1.31254i	−0.433692	−	0.901061i	$-0.642789\pi$
$269$	7.83529	−	21.5273i	0.477726	−	1.31254i	0.911418	−	0.411481i	$-0.134988\pi$
$270$	1.08169	+	2.77749i	0.0658295	+	0.169033i
$271$	−2.78811	−	15.8122i	−0.169366	−	0.960521i	−0.944448	−	0.328661i	$-0.893403\pi$
$271$	−2.78811	−	15.8122i	−0.169366	−	0.960521i	0.775082	−	0.631861i	$-0.217708\pi$
$272$	−20.5784	−	14.3486i	−1.24775	−	0.870011i
$273$	6.71676	−	11.6338i	0.406517	−	0.704107i
$274$	−2.92701	−	1.60393i	−0.176827	−	0.0968969i
$275$	1.92391	−	2.29282i	0.116016	−	0.138263i
$276$	1.35885	+	3.27141i	0.0817932	+	0.196915i
$277$	24.1532	−	13.9449i	1.45123	−	0.837865i	0.452674	−	0.891676i	$-0.350470\pi$
$277$	24.1532	−	13.9449i	1.45123	−	0.837865i	0.998551	+	0.0538110i	$0.0171369\pi$
$278$	14.9292	−	0.333138i	0.895393	−	0.0199803i
$279$	−3.72924	+	1.35733i	−0.223264	+	0.0812613i
$280$	2.83520	+	11.5125i	0.169435	+	0.688005i
$281$	−1.61880	+	9.18064i	−0.0965692	+	0.547671i	0.897686	+	0.440636i	$0.145247\pi$
$281$	−1.61880	+	9.18064i	−0.0965692	+	0.547671i	−0.994255	+	0.107036i	$0.965864\pi$
$282$	1.61287	+	8.08753i	0.0960447	+	0.481605i
$283$	−5.29301	−	6.30796i	−0.314637	−	0.374969i	0.585429	−	0.810724i	$-0.300926\pi$
$283$	−5.29301	−	6.30796i	−0.314637	−	0.374969i	−0.900066	+	0.435754i	$0.856482\pi$
$284$	7.11831	−	13.7072i	0.422394	−	0.813373i
$285$	−8.97840	+	1.94712i	−0.531834	+	0.115338i
$286$	43.8095	−	26.6139i	2.59051	−	1.57371i
$287$	1.33211	−	1.11777i	0.0786319	−	0.0659800i
$288$	4.09596	+	3.90168i	0.241357	+	0.229909i
$289$	3.87834	−	21.9952i	0.228138	−	1.29383i
$290$	−3.23798	−	3.68853i	−0.190141	−	0.216598i
$291$	4.71244	+	12.9473i	0.276248	+	0.758985i
$292$	14.4273	+	22.5970i	0.844293	+	1.32239i
$293$	−16.3695	+	9.45096i	−0.956319	+	0.552131i	−0.895038	−	0.445990i	$-0.852852\pi$
$293$	−16.3695	+	9.45096i	−0.956319	+	0.552131i	−0.0612808	+	0.998121i	$0.519519\pi$
$294$	−0.652839	+	4.25555i	−0.0380744	+	0.248189i
$295$	−2.09552	−	1.75835i	−0.122006	−	0.102375i
$296$	−0.791153	−	1.18025i	−0.0459849	−	0.0686008i
$297$	2.68320	−	4.64743i	0.155695	−	0.269672i
$298$	15.9871	+	12.8180i	0.926106	+	0.742526i
$299$	11.7814	−	2.07739i	0.681338	−	0.120138i
$300$	0.678190	−	0.885645i	0.0391553	−	0.0511328i
$301$	−7.93021	+	21.7881i	−0.457090	+	1.25584i
$302$	6.93237	−	20.4553i	0.398913	−	1.17707i
$303$	−8.86002			−0.508995
$304$	−13.8604	+	10.5777i	−0.794951	+	0.606674i
$305$	17.6183			1.00882
$306$	−2.84687	+	8.40026i	−0.162745	+	0.480211i
$307$	−0.909379	+	2.49850i	−0.0519010	+	0.142597i	−0.962934	−	0.269736i	$-0.913064\pi$
$307$	−0.909379	+	2.49850i	−0.0519010	+	0.142597i	0.911033	+	0.412333i	$0.135286\pi$
$308$	12.9781	−	16.9480i	0.739493	−	0.965701i
$309$	9.13799	−	1.61127i	0.519842	−	0.0916622i
$310$	−9.22897	−	7.39954i	−0.524170	−	0.420265i
$311$	−0.766706	+	1.32797i	−0.0434759	+	0.0753025i	−0.886945	−	0.461876i	$-0.847177\pi$
$311$	−0.766706	+	1.32797i	−0.0434759	+	0.0753025i	0.843469	+	0.537178i	$0.180510\pi$
$312$	15.8687	−	10.6372i	0.898386	−	0.602211i
$313$	9.05730	+	7.59998i	0.511949	+	0.429576i	0.861814	−	0.507224i	$-0.169328\pi$
$313$	9.05730	+	7.59998i	0.511949	+	0.429576i	−0.349866	+	0.936800i	$0.613773\pi$
$314$	0.133695	−	0.871492i	0.00754482	−	0.0491811i
$315$	3.63030	−	2.09595i	0.204544	−	0.118094i
$316$	−8.23500	−	12.8982i	−0.463255	−	0.725581i
$317$	3.04664	+	8.37058i	0.171116	+	0.470138i	0.995374	−	0.0960766i	$-0.0306294\pi$
$317$	3.04664	+	8.37058i	0.171116	+	0.470138i	−0.824258	+	0.566215i	$0.808407\pi$
$318$	−5.55272	−	6.32535i	−0.311381	−	0.354708i
$319$	−1.53445	+	8.70230i	−0.0859127	+	0.487235i
$320$	−3.60063	+	16.4724i	−0.201281	+	0.920835i
$321$	0.148954	−	0.124987i	0.00831380	−	0.00697610i
$322$	4.25778	−	2.58656i	0.237277	−	0.144144i
$323$	−24.1905	−	12.7347i	−1.34600	−	0.708580i
$324$	0.921743	−	1.77493i	0.0512080	−	0.0986074i
$325$	−2.42148	−	2.88581i	−0.134320	−	0.160076i
$326$	−0.976315	−	4.89562i	−0.0540731	−	0.271143i
$327$	−1.55972	+	8.84563i	−0.0862529	+	0.489165i
$328$	2.40124	−	0.591354i	0.132586	−	0.0326521i
$329$	10.8985	−	3.96672i	0.600852	−	0.218692i
$330$	15.9916	−	0.356845i	0.880308	−	0.0196436i
$331$	1.14528	−	0.661225i	0.0629500	−	0.0363442i	−0.468195	−	0.883625i	$-0.655095\pi$
$331$	1.14528	−	0.661225i	0.0629500	−	0.0363442i	0.531145	+	0.847281i	$0.321762\pi$
$332$	−4.57274	−	11.0088i	−0.250962	−	0.604186i
$333$	−0.322910	+	0.384830i	−0.0176954	+	0.0210885i
$334$	18.2383	+	9.99415i	0.997955	+	0.546856i
$335$	−15.6260	+	27.0650i	−0.853737	+	1.47872i
$336$	4.55022	−	6.52581i	0.248235	−	0.356012i
$337$	3.19248	+	18.1054i	0.173905	+	0.986266i	0.939400	+	0.342823i	$0.111383\pi$
$337$	3.19248	+	18.1054i	0.173905	+	0.986266i	−0.765495	+	0.643442i	$0.777506\pi$
$338$	−16.7413	−	42.9874i	−0.910608	−	2.33820i
$339$	3.33052	−	9.15052i	0.180889	−	0.496988i
$340$	−25.8051	+	5.74761i	−1.39948	+	0.311708i
$341$			21.2969i			1.15329i
$342$	4.95623	+	3.66548i	0.268002	+	0.198207i
$343$	19.9770			1.07866
$344$	−23.7852	+	22.8371i	−1.28241	+	1.23129i
$345$	3.50796	+	1.27679i	0.188862	+	0.0687402i
$346$	−17.6218	+	6.86276i	−0.947353	+	0.368944i
$347$	24.3324	−	4.29046i	1.30623	−	0.230324i	0.523150	−	0.852241i	$-0.324757\pi$
$347$	24.3324	−	4.29046i	1.30623	−	0.230324i	0.783083	+	0.621917i	$0.213646\pi$
$348$	−0.426633	+	3.26554i	−0.0228699	+	0.175051i
$349$	−1.41980	−	0.819724i	−0.0760003	−	0.0438788i	0.461518	−	0.887131i	$-0.347305\pi$
$349$	−1.41980	−	0.819724i	−0.0760003	−	0.0438788i	−0.537519	+	0.843252i	$0.680638\pi$
$350$	−1.37575	−	0.753880i	−0.0735372	−	0.0402966i
$351$	−5.17409	−	4.34157i	−0.276172	−	0.231736i
$352$	27.1930	−	13.4938i	1.44939	−	0.719220i
$353$	14.5379	+	25.1804i	0.773776	+	1.34022i	0.935480	+	0.353380i	$0.114968\pi$
$353$	14.5379	+	25.1804i	0.773776	+	1.34022i	−0.161704	+	0.986839i	$0.551699\pi$
$354$	0.0409479	+	1.83503i	0.00217635	+	0.0975308i
$355$	−5.56699	−	15.2952i	−0.295465	−	0.811783i
$356$	4.79220	+	1.50577i	0.253986	+	0.0798056i
$357$	12.2842	+	2.16604i	0.650151	+	0.114639i
$358$	−5.42888	−	27.2225i	−0.286925	−	1.43876i
$359$	−24.3303	+	20.4156i	−1.28410	+	1.07749i	−0.291440	+	0.956589i	$0.594134\pi$
$359$	−24.3303	+	20.4156i	−1.28410	+	1.07749i	−0.992664	+	0.120903i	$0.961421\pi$
$360$	5.94803	−	0.398712i	0.313489	−	0.0210140i
$361$	−13.5582	+	13.3107i	−0.713590	+	0.700564i
$362$	−11.4102	−	18.7825i	−0.599707	−	0.987187i
$363$	−11.4405	−	13.6342i	−0.600468	−	0.715610i
$364$	−18.1707	−	19.7905i	−0.952402	−	1.03730i
$365$	27.8239	+	4.90611i	1.45637	+	0.256797i
$366$	−7.79893	−	8.88411i	−0.407657	−	0.464380i
$367$	10.3920	−	3.78237i	0.542457	−	0.197438i	−0.0562349	−	0.998418i	$-0.517910\pi$
$367$	10.3920	−	3.78237i	0.542457	−	0.197438i	0.598692	+	0.800979i	$0.295687\pi$
$368$	7.05660	−	0.631431i	0.367851	−	0.0329156i
$369$	−0.437166	−	0.757193i	−0.0227579	−	0.0394179i
$370$	−1.48006	−	0.227055i	−0.0769448	−	0.0118040i
$371$	−7.60869	+	9.06769i	−0.395024	+	0.470771i
$372$	0.354051	+	7.92924i	0.0183567	+	0.411112i
$373$	16.3350	+	9.43099i	0.845792	+	0.488318i	0.859229	−	0.511591i	$-0.170944\pi$
$373$	16.3350	+	9.43099i	0.845792	+	0.488318i	−0.0134367	+	0.999910i	$0.504277\pi$
$374$	37.1353	+	29.7741i	1.92022	+	1.53958i
$375$	−2.03409	−	11.5359i	−0.105040	−	0.595712i
$376$	16.3982	+	1.77129i	0.845672	+	0.0913475i
$377$	10.4512	+	3.80392i	0.538263	+	0.195912i
$378$	−2.66389	−	0.902799i	−0.137016	−	0.0464350i
$379$		−	2.77702i		−	0.142646i	−0.997453	−	0.0713230i	$-0.977278\pi$
$379$		−	2.77702i		−	0.142646i	0.997453	−	0.0713230i	$-0.0227221\pi$
$380$	−1.66761	+	18.2984i	−0.0855468	+	0.938687i
$381$		−	14.4945i		−	0.742578i
$382$	3.11977	−	9.20548i	0.159621	−	0.470993i
$383$	10.6875	+	3.88993i	0.546105	+	0.198766i	0.600315	−	0.799764i	$-0.295042\pi$
$383$	10.6875	+	3.88993i	0.546105	+	0.198766i	−0.0542101	+	0.998530i	$0.517264\pi$
$384$	9.90015	−	5.47605i	0.505215	−	0.279448i
$385$	−3.90629	−	22.1537i	−0.199083	−	1.12906i
$386$	−9.19775	+	11.4718i	−0.468153	+	0.583898i
$387$	10.0961	+	5.82899i	0.513214	+	0.296304i
$388$	27.5291	−	1.22921i	1.39758	−	0.0624036i
$389$	−18.3957	+	21.9231i	−0.932697	+	1.11155i	0.0608522	+	0.998147i	$0.480618\pi$
$389$	−18.3957	+	21.9231i	−0.932697	+	1.11155i	−0.993550	+	0.113399i	$0.963826\pi$
$390$	3.05278	−	19.8996i	0.154584	−	1.00766i
$391$	5.55423	+	9.62021i	0.280890	+	0.486515i
$392$	7.72832	+	3.79695i	0.390339	+	0.191775i
$393$	11.3204	−	4.12030i	0.571040	−	0.207842i
$394$	−7.73328	+	6.78867i	−0.389597	+	0.342008i
$395$	−15.8817	−	2.80037i	−0.799095	−	0.140902i
$396$	−7.25879	−	7.90587i	−0.364768	−	0.397285i
$397$	11.5196	+	13.7285i	0.578150	+	0.689013i	0.973282	−	0.229611i	$-0.0737455\pi$
$397$	11.5196	+	13.7285i	0.578150	+	0.689013i	−0.395132	+	0.918624i	$0.629301\pi$
$398$	−23.1782	+	14.0806i	−1.16182	+	0.705795i
$399$	4.03843	−	7.67129i	0.202175	−	0.384045i
$400$	−1.28324	−	1.82497i	−0.0641622	−	0.0912486i
$401$	−10.7221	+	8.99691i	−0.535436	+	0.449284i	−0.869974	−	0.493098i	$-0.835864\pi$
$401$	−10.7221	+	8.99691i	−0.535436	+	0.449284i	0.334538	+	0.942382i	$0.391420\pi$
$402$	20.5646	−	4.10113i	1.02567	−	0.204546i
$403$	26.3976	+	4.65462i	1.31496	+	0.231863i
$404$	−5.31181	+	16.9052i	−0.264272	+	0.841063i
$405$	−0.720864	−	1.98056i	−0.0358200	−	0.0984147i
$406$	4.63038	−	0.103325i	0.229802	−	0.00512792i
$407$	1.34793	+	2.33468i	0.0668144	+	0.115726i
$408$	14.3211	+	10.4681i	0.709002	+	0.518247i
$409$	−3.85056	−	3.23100i	−0.190398	−	0.159763i	0.542606	−	0.839988i	$-0.317438\pi$
$409$	−3.85056	−	3.23100i	−0.190398	−	0.159763i	−0.733004	+	0.680225i	$0.761882\pi$
$410$	1.25238	−	2.28547i	0.0618507	−	0.112871i
$411$	2.04389	+	1.18004i	0.100818	+	0.0582071i
$412$	2.40411	−	18.4015i	0.118442	−	0.906578i
$413$	2.54213	−	0.448246i	0.125090	−	0.0220568i
$414$	−0.909007	−	2.33409i	−0.0446753	−	0.114714i
$415$	−11.8048	−	4.29661i	−0.579476	−	0.210912i
$416$	−10.7823	−	36.6551i	−0.528647	−	1.79716i
$417$	−10.5592			−0.517084
$418$	27.5809	−	18.2654i	1.34903	−	0.893390i
$419$		−	19.0602i		−	0.931153i	−0.885008	−	0.465577i	$-0.845847\pi$
$419$		−	19.0602i		−	0.931153i	0.885008	−	0.465577i	$-0.154153\pi$
$420$	−1.82268	−	8.18329i	−0.0889376	−	0.399304i
$421$	−9.61166	+	26.4078i	−0.468443	+	1.28704i	0.450545	+	0.892754i	$0.351230\pi$
$421$	−9.61166	+	26.4078i	−0.468443	+	1.28704i	−0.918989	+	0.394284i	$0.870993\pi$
$422$	9.15676	−	3.56608i	0.445744	−	0.173594i
$423$	−1.01260	−	5.74277i	−0.0492345	−	0.279223i
$424$	−15.3979	+	6.80253i	−0.747790	+	0.330360i
$425$	1.74900	−	3.02936i	0.0848392	−	0.146946i
$426$	−5.24838	+	9.57775i	−0.254285	+	0.464044i
$427$	−10.6866	+	12.7358i	−0.517161	+	0.616328i
$428$	−0.149177	−	0.359141i	−0.00721075	−	0.0173597i
$429$	−31.3901	+	18.1231i	−1.51553	+	0.874991i
$430$	0.775210	+	34.7402i	0.0373840	+	1.67532i
$431$	−6.22856	+	2.26701i	−0.300019	+	0.109198i	−0.487644	−	0.873043i	$-0.662143\pi$
$431$	−6.22856	+	2.26701i	−0.300019	+	0.109198i	0.187624	+	0.982241i	$0.439921\pi$
$432$	−2.83401	−	2.82283i	−0.136352	−	0.135813i
$433$	−1.08310	+	6.14256i	−0.0520504	+	0.295192i	−0.999710	−	0.0240907i	$-0.992331\pi$
$433$	−1.08310	+	6.14256i	−0.0520504	+	0.295192i	0.947659	+	0.319283i	$0.103442\pi$
$434$	10.9469	−	2.18309i	0.525467	−	0.104792i
$435$	2.23084	+	2.65862i	0.106961	+	0.127471i
$436$	15.9426	+	8.27918i	0.763513	+	0.396501i
$437$	7.54508	−	1.63629i	0.360930	−	0.0782741i
$438$	−9.84263	−	16.2021i	−0.470299	−	0.774166i
$439$	11.0737	−	9.29194i	0.528519	−	0.443480i	−0.339071	−	0.940761i	$-0.610113\pi$
$439$	11.0737	−	9.29194i	0.528519	−	0.443480i	0.867590	+	0.497281i	$0.165668\pi$
$440$	8.90650	−	30.7263i	0.424601	−	1.46482i
$441$	0.528643	−	2.99808i	0.0251735	−	0.142766i
$442$	45.0213	−	39.5220i	2.14145	−	1.87987i
$443$	7.70857	+	21.1791i	0.366245	+	1.00625i	0.976777	+	0.214259i	$0.0687335\pi$
$443$	7.70857	+	21.1791i	0.366245	+	1.00625i	−0.610532	+	0.791992i	$0.709044\pi$
$444$	0.540672	+	0.846837i	0.0256592	+	0.0401891i
$445$	4.58440	−	2.64681i	0.217321	−	0.125471i
$446$	−9.41546	−	1.44441i	−0.445835	−	0.0683950i
$447$	−11.0995	−	9.31362i	−0.524990	−	0.440519i
$448$	−9.72344	−	12.5943i	−0.459390	−	0.595026i
$449$	5.92877	−	10.2689i	0.279796	−	0.484621i	−0.691538	−	0.722340i	$-0.743066\pi$
$449$	5.92877	−	10.2689i	0.279796	−	0.484621i	0.971334	+	0.237719i	$0.0763998\pi$
$450$	−0.493404	+	0.615392i	−0.0232593	+	0.0290098i
$451$	−4.62073	+	0.814759i	−0.217581	+	0.0383655i
$452$	−15.4627	−	11.8407i	−0.727304	−	0.556939i
$453$	−5.22338	+	14.3511i	−0.245416	+	0.674275i
$454$	11.7167	+	3.97083i	0.549892	+	0.186360i
$455$	−28.3134			−1.32735
$456$	9.96523	−	7.25907i	0.466665	−	0.339937i
$457$	−28.7204			−1.34348			−0.671741	−	0.740786i	$-0.734453\pi$
$457$	−28.7204			−1.34348			−0.671741	+	0.740786i	$0.734453\pi$
$458$	−29.7684	−	10.0886i	−1.39098	−	0.471409i
$459$	2.14506	−	5.89349i	0.100123	−	0.275085i
$460$	4.53927	−	5.92782i	0.211645	−	0.276386i
$461$	−0.500581	+	0.0882659i	−0.0233144	+	0.00411095i	−0.185293	−	0.982683i	$-0.559323\pi$
$461$	−0.500581	+	0.0882659i	−0.0233144	+	0.00411095i	0.161979	+	0.986794i	$0.448212\pi$
$462$	−9.44194	+	11.7763i	−0.439279	+	0.547884i
$463$	−6.07174	+	10.5166i	−0.282178	+	0.488746i	−0.971921	−	0.235308i	$-0.924390\pi$
$463$	−6.07174	+	10.5166i	−0.282178	+	0.488746i	0.689743	+	0.724054i	$0.257724\pi$
$464$	5.97496	+	2.77180i	0.277380	+	0.128678i
$465$	6.40752	+	5.37655i	0.297142	+	0.249331i
$466$	−12.3078	−	1.88813i	−0.570150	−	0.0874660i
$467$	17.9975	−	10.3909i	0.832827	−	0.480833i	−0.0219928	−	0.999758i	$-0.507001\pi$
$467$	17.9975	−	10.3909i	0.832827	−	0.480833i	0.854820	+	0.518925i	$0.173668\pi$
$468$	−11.3858	+	7.26941i	−0.526311	+	0.336029i
$469$	−10.0864	−	27.7122i	−0.465747	−	1.27963i
$470$	13.0624	−	11.4669i	0.602524	−	0.528927i
$471$	−0.108260	+	0.613975i	−0.00498838	+	0.0282905i
$472$	3.52584	+	1.02202i	0.162290	+	0.0470423i
$473$	47.9247	−	40.2136i	2.20358	−	1.84902i
$474$	5.61811	+	9.24805i	0.258048	+	0.424777i
$475$	−1.63419	−	1.79997i	−0.0749816	−	0.0825885i
$476$	11.4976	−	22.1401i	0.526991	−	1.01479i
$477$	3.82561	+	4.55918i	0.175162	+	0.208751i
$478$	28.6907	−	5.72168i	1.31228	−	0.261703i
$479$	1.69095	−	9.58985i	0.0772614	−	0.438171i	−0.921498	−	0.388382i	$-0.873034\pi$
$479$	1.69095	−	9.58985i	0.0772614	−	0.438171i	0.998760	−	0.0497890i	$-0.0158549\pi$
$480$	2.80525	−	11.5880i	0.128041	−	0.528920i
$481$	3.18845	−	1.16050i	0.145381	−	0.0529143i
$482$	0.404890	+	18.1447i	0.0184422	+	0.826468i
$483$	−3.05076	+	1.76136i	−0.138814	+	0.0801444i
$484$	−32.8733	+	13.6547i	−1.49424	+	0.620666i
$485$	18.6665	−	22.2459i	0.847602	−	1.01013i
$486$	−0.679608	+	1.24021i	−0.0308276	+	0.0562573i
$487$	−1.66796	+	2.88899i	−0.0755825	+	0.130913i	−0.901339	−	0.433113i	$-0.857415\pi$
$487$	−1.66796	+	2.88899i	−0.0755825	+	0.130913i	0.825757	+	0.564026i	$0.190748\pi$
$488$	−21.6268	+	9.55432i	−0.978999	+	0.432504i
$489$	0.612960	+	3.47627i	0.0277190	+	0.157202i
$490$	8.45561	−	3.29302i	0.381986	−	0.148763i
$491$	−4.80671	+	13.2063i	−0.216924	+	0.595994i	−0.999652	−	0.0263700i	$-0.991605\pi$
$491$	−4.80671	+	13.2063i	−0.216924	+	0.595994i	0.782728	+	0.622364i	$0.213827\pi$
$492$	−1.70684	+	0.380167i	−0.0769502	+	0.0171393i
$493$			10.3273i			0.465118i
$494$	−16.6120	−	38.1787i	−0.747411	−	1.71774i
$495$	−11.3106			−0.508372
$496$	15.3415	+	4.07825i	0.688852	+	0.183119i
$497$	14.4332	+	5.25325i	0.647417	+	0.235641i
$498$	3.05895	+	7.85458i	0.137075	+	0.351972i
$499$	−6.65084	+	1.17272i	−0.297732	+	0.0524983i	−0.320519	−	0.947242i	$-0.603857\pi$
$499$	−6.65084	+	1.17272i	−0.297732	+	0.0524983i	0.0227866	+	0.999740i	$0.492746\pi$
$500$	−23.2303	−	3.03497i	−1.03889	−	0.135728i
$501$	−12.7356	−	7.35288i	−0.568983	−	0.328502i
$502$	−8.52203	+	15.5518i	−0.380357	+	0.694112i
$503$	14.4204	+	12.1002i	0.642974	+	0.539519i	0.904930	−	0.425560i	$-0.139923\pi$
$503$	14.4204	+	12.1002i	0.642974	+	0.539519i	−0.261956	+	0.965080i	$0.584367\pi$
$504$	−3.31963	+	4.54152i	−0.147868	+	0.202295i
$505$	9.33698	+	16.1721i	0.415490	+	0.719650i
$506$	−13.4387	+	0.299878i	−0.597422	+	0.0133312i
$507$	11.1568	+	30.6532i	0.495493	+	1.36136i
$508$	−27.6560	−	8.68985i	−1.22704	−	0.385550i
$509$	30.9072	+	5.44978i	1.36994	+	0.241557i	0.809734	−	0.586797i	$-0.199611\pi$
$509$	30.9072	+	5.44978i	1.36994	+	0.241557i	0.560205	+	0.828354i	$0.310722\pi$
$510$	18.3331	−	3.65609i	0.811801	−	0.161894i
$511$	−20.4234	+	17.1373i	−0.903480	+	0.758109i
$512$	−4.51306	−	22.1728i	−0.199451	−	0.979908i
$513$	−3.44589	−	2.66943i	−0.152140	−	0.117858i
$514$	12.6722	−	7.69825i	0.558947	−	0.339555i
$515$	−12.5710	−	14.9815i	−0.553943	−	0.660163i
$516$	17.1747	−	15.7690i	0.756076	−	0.694192i
$517$	−30.8180	−	5.43404i	−1.35537	−	0.238989i
$518$	1.06188	−	0.932175i	0.0466564	−	0.0409574i
$519$	12.5656	−	4.57352i	0.551570	−	0.200755i
$520$	−36.1388	−	17.7551i	−1.58479	−	0.778615i
$521$	0.0663700	+	0.114956i	0.00290772	+	0.00503632i	0.867476	−	0.497480i	$-0.165741\pi$
$521$	0.0663700	+	0.114956i	0.00290772	+	0.00503632i	−0.864568	+	0.502516i	$0.832408\pi$
$522$	0.353113	−	2.30178i	0.0154553	−	0.100746i
$523$	−18.4618	+	22.0019i	−0.807276	+	0.962074i	−0.999815	−	0.0192149i	$-0.993883\pi$
$523$	−18.4618	+	22.0019i	−0.807276	+	0.962074i	0.192539	+	0.981289i	$0.438328\pi$
$524$	−1.07475	−	24.0699i	−0.0469508	−	1.05150i
$525$	0.960671	+	0.554644i	0.0419271	+	0.0242066i
$526$	−5.31286	+	6.62639i	−0.231652	+	0.288924i
$527$	4.32206	+	24.5116i	0.188272	+	1.06774i
$528$	−19.4365	+	9.11019i	−0.845863	+	0.396470i
$529$	18.6650	+	6.79350i	0.811521	+	0.295369i
$530$	−5.69398	+	16.8012i	−0.247331	+	0.729798i
$531$		−	1.29789i		−	0.0563235i
$532$	−12.2159	−	12.3046i	−0.529626	−	0.533471i
$533$			5.90549i			0.255795i
$534$	−3.36400	−	1.14007i	−0.145575	−	0.0493357i
$535$	−0.385111	−	0.140169i	−0.0166498	−	0.00606003i
$536$	4.50397	−	41.6966i	0.194542	−	1.80102i
$537$	3.40841	+	19.3301i	0.147084	+	0.834155i
$538$	25.2767	+	20.2662i	1.08976	+	0.873738i
$539$	−14.1483	−	8.16855i	−0.609412	−	0.351844i
$540$	−4.21114	+	0.188033i	−0.181218	+	0.00809164i
$541$	0.862571	−	1.02797i	0.0370848	−	0.0441960i	−0.747183	−	0.664618i	$-0.768594\pi$
$541$	0.862571	−	1.02797i	0.0370848	−	0.0441960i	0.784268	+	0.620422i	$0.213039\pi$
$542$	22.4442	+	3.44314i	0.964061	+	0.147895i
$543$	7.76994	+	13.4579i	0.333440	+	0.577535i
$544$	28.5593	−	21.0492i	1.22447	−	0.902479i
$545$	17.7896	−	6.47487i	0.762021	−	0.277353i
$546$	12.5332	+	14.2772i	0.536372	+	0.611006i
$547$	−0.168798	−	0.0297637i	−0.00721728	−	0.00127260i	0.170038	−	0.985437i	$-0.445611\pi$
$547$	−0.168798	−	0.0297637i	−0.00721728	−	0.00127260i	−0.177256	+	0.984165i	$0.556722\pi$
$548$	3.47691	−	3.19233i	0.148526	−	0.136370i
$549$	5.37316	+	6.40348i	0.229321	+	0.273294i
$550$	2.19767	+	3.61762i	0.0937091	+	0.154256i
$551$	6.83534	+	2.18984i	0.291195	+	0.0932901i
$552$	−4.99849	+	0.335062i	−0.212750	+	0.0142612i
$553$	11.6576	−	9.78186i	0.495730	−	0.415967i
$554$	7.71387	+	38.6803i	0.327731	+	1.64337i
$555$	1.04272	+	0.183860i	0.0442610	+	0.00780441i
$556$	−6.33049	+	20.1472i	−0.268472	+	0.854430i
$557$	−13.8202	−	37.9707i	−0.585581	−	1.60887i	−0.778492	−	0.627654i	$-0.784015\pi$
$557$	−13.8202	−	37.9707i	−0.585581	−	1.60887i	0.192911	−	0.981216i	$-0.438207\pi$
$558$	−0.125207	−	5.61101i	−0.00530044	−	0.237533i
$559$	−39.3707	−	68.1920i	−1.66520	−	2.88421i
$560$	−16.7067	−	1.42837i	−0.705986	−	0.0603597i
$561$	−25.7824	−	21.6340i	−1.08853	−	0.913388i
$562$	−11.5616	−	6.33549i	−0.487697	−	0.267247i
$563$	14.6535	+	8.46022i	0.617573	+	0.356556i	0.775923	−	0.630827i	$-0.217284\pi$
$563$	14.6535	+	8.46022i	0.617573	+	0.356556i	−0.158351	+	0.987383i	$0.550618\pi$
$564$	−11.5644	−	1.51086i	−0.486951	−	0.0636187i
$565$	−20.2122	+	3.56395i	−0.850333	+	0.149937i
$566$	10.8514	−	4.22606i	0.456119	−	0.177634i
$567$	1.86894	+	0.680239i	0.0784882	+	0.0285674i
$568$	15.1281	+	15.7562i	0.634760	+	0.661114i
$569$	−8.85097			−0.371052			−0.185526	−	0.982639i	$-0.559399\pi$
$569$	−8.85097			−0.371052			−0.185526	+	0.982639i	$0.559399\pi$
$570$	1.46754	−	12.9094i	0.0614686	−	0.540714i
$571$			6.83340i			0.285969i	0.989725	+	0.142984i	$0.0456699\pi$
$571$			6.83340i			0.285969i	−0.989725	+	0.142984i	$0.954330\pi$
$572$	15.7602	+	70.7585i	0.658966	+	2.95856i
$573$	−2.35067	+	6.45842i	−0.0982008	+	0.269805i
$574$	0.892455	+	2.29159i	0.0372503	+	0.0956491i
$575$	0.171542	+	0.972865i	0.00715381	+	0.0405713i
$576$	−7.08510	+	3.71501i	−0.295213	+	0.154792i
$577$	21.3538	−	36.9858i	0.888969	−	1.53974i	0.0478721	−	0.998853i	$-0.484756\pi$
$577$	21.3538	−	36.9858i	0.888969	−	1.53974i	0.841096	−	0.540885i	$-0.181911\pi$
$578$	27.6996	+	15.1787i	1.15215	+	0.631351i
$579$	6.68314	−	7.96465i	0.277742	−	0.331000i
$580$	6.41016	−	2.66260i	0.266167	−	0.110559i
$581$	10.2663	−	5.92723i	0.425917	−	0.245903i
$582$	−19.4805	+	0.434699i	−0.807494	+	0.0180188i
$583$	30.0124	−	10.9236i	1.24299	−	0.452411i
$584$	−36.8149	+	9.06643i	−1.52341	+	0.375172i
$585$	−2.47202	+	14.0195i	−0.102205	+	0.579636i
$586$	−5.22798	−	26.2151i	−0.215966	−	1.08294i
$587$	2.41542	+	2.87858i	0.0996949	+	0.118812i	0.813585	−	0.581446i	$-0.197513\pi$
$587$	2.41542	+	2.87858i	0.0996949	+	0.118812i	−0.713890	+	0.700258i	$0.753068\pi$
$588$	−5.40349	−	2.80609i	−0.222836	−	0.115721i
$589$	17.1400	+	2.33688i	0.706242	+	0.0962896i
$590$	3.30632	−	2.00856i	0.136119	−	0.0826911i
$591$	5.57398	−	4.67713i	0.229283	−	0.192391i
$592$	1.93994	−	0.523917i	0.0797309	−	0.0215328i
$593$	2.19378	−	12.4415i	0.0900876	−	0.510912i	−0.906055	−	0.423160i	$-0.860921\pi$
$593$	2.19378	−	12.4415i	0.0900876	−	0.510912i	0.996142	−	0.0877516i	$-0.0279682\pi$
$594$	5.00675	+	5.70341i	0.205429	+	0.234014i
$595$	−8.99187	−	24.7050i	−0.368631	−	1.01280i
$596$	−24.4251	+	15.5945i	−1.00049	+	0.638775i
$597$	16.6075	−	9.58836i	0.679701	−	0.392425i
$598$	−2.56543	+	16.7229i	−0.104908	+	0.683849i
$599$	25.9726	+	21.7936i	1.06121	+	0.890462i	0.994228	−	0.107292i	$-0.0342181\pi$
$599$	25.9726	+	21.7936i	1.06121	+	0.890462i	0.0669834	+	0.997754i	$0.478663\pi$
$600$	0.878376	+	1.31037i	0.0358595	+	0.0534957i
$601$	−2.89454	+	5.01348i	−0.118071	+	0.204504i	−0.919003	−	0.394251i	$-0.871004\pi$
$601$	−2.89454	+	5.01348i	−0.118071	+	0.204504i	0.800932	+	0.598755i	$0.204338\pi$
$602$	−25.5829	−	20.5117i	−1.04268	−	0.835994i
$603$	−14.6025	+	2.57481i	−0.594658	+	0.104854i
$604$	24.2508	+	18.5702i	0.986751	+	0.755612i
$605$	−12.8301	+	35.2504i	−0.521617	+	1.43313i
$606$	4.02176	−	11.8670i	0.163373	−	0.482063i
$607$	−14.4722			−0.587410			−0.293705	−	0.955896i	$-0.594888\pi$
$607$	−14.4722			−0.587410			−0.293705	+	0.955896i	$0.594888\pi$
$608$	−7.87609	−	23.3659i	−0.319418	−	0.947614i
$609$	−3.27499			−0.132709
$610$	−7.99734	+	23.5977i	−0.323803	+	0.955443i
$611$	−13.4710	+	37.0114i	−0.544980	+	1.49732i
$612$	−9.95893	−	7.62612i	−0.402566	−	0.308268i
$613$	−9.82585	+	1.73256i	−0.396862	+	0.0699776i	−0.368518	−	0.929621i	$-0.620135\pi$
$613$	−9.82585	+	1.73256i	−0.396862	+	0.0699776i	−0.0283446	+	0.999598i	$0.509024\pi$
$614$	−2.93367	−	2.35213i	−0.118393	−	0.0949244i
$615$	−0.921399	+	1.59591i	−0.0371544	+	0.0643533i
$616$	16.8089	+	25.0757i	0.677249	+	1.01033i
$617$	11.5242	+	9.66992i	0.463945	+	0.389296i	0.844580	−	0.535429i	$-0.179850\pi$
$617$	11.5242	+	9.66992i	0.463945	+	0.389296i	−0.380635	+	0.924725i	$0.624295\pi$
$618$	−1.98982	+	12.9707i	−0.0800422	+	0.521758i
$619$	−8.08677	+	4.66890i	−0.325035	+	0.187659i	−0.653634	−	0.756810i	$-0.726757\pi$
$619$	−8.08677	+	4.66890i	−0.325035	+	0.187659i	0.328600	+	0.944469i	$0.393423\pi$
$620$	14.1001	−	9.00234i	0.566273	−	0.361543i
$621$	0.605785	+	1.66438i	0.0243093	+	0.0667893i
$622$	−1.43064	−	1.62971i	−0.0573636	−	0.0653455i
$623$	−0.867422	+	4.91939i	−0.0347525	+	0.197091i
$624$	7.04413	+	26.0827i	0.281991	+	1.04414i
$625$	−16.7765	+	14.0772i	−0.671061	+	0.563087i
$626$	−14.2906	+	8.68142i	−0.571168	+	0.346979i
$627$	−19.7859	+	12.4773i	−0.790174	+	0.498295i
$628$	1.10658	+	0.574658i	0.0441572	+	0.0229313i
$629$	2.02520	+	2.41354i	0.0807502	+	0.0962343i
$630$	1.15942	+	5.81377i	0.0461923	+	0.231626i
$631$	−1.12600	+	6.38584i	−0.0448252	+	0.254216i	−0.998983	−	0.0450876i	$-0.985643\pi$
$631$	−1.12600	+	6.38584i	−0.0448252	+	0.254216i	0.954158	+	0.299304i	$0.0967544\pi$
$632$	21.0137	−	5.17506i	0.835881	−	0.205853i
$633$	−6.52945	+	2.37652i	−0.259522	+	0.0944584i
$634$	−12.5944	+	0.281037i	−0.500186	+	0.0111614i
$635$	−26.4568	+	15.2748i	−1.04990	+	0.606163i
$636$	10.9926	−	4.56601i	0.435885	−	0.181054i
$637$	−13.2172	+	15.7516i	−0.523684	+	0.624103i
$638$	−10.9592	−	6.00539i	−0.433879	−	0.237755i
$639$	3.86133	−	6.68802i	0.152752	−	0.264574i
$640$	−20.4285	−	12.2998i	−0.807507	−	0.486193i
$641$	7.18062	+	40.7233i	0.283617	+	1.60847i	0.710183	+	0.704017i	$0.248612\pi$
$641$	7.18062	+	40.7233i	0.283617	+	1.60847i	−0.426565	+	0.904457i	$0.640277\pi$
$642$	0.0997926	+	0.256241i	0.00393850	+	0.0101130i
$643$	7.49302	−	20.5869i	0.295496	−	0.811868i	−0.699743	−	0.714395i	$-0.746702\pi$
$643$	7.49302	−	20.5869i	0.295496	−	0.811868i	0.995238	−	0.0974726i	$-0.0310758\pi$
$644$	1.53171	+	6.87691i	0.0603577	+	0.270988i
$645$		−	24.5711i		−	0.967487i
$646$	28.0373	−	26.6199i	1.10311	−	1.04735i
$647$	32.9049			1.29363			0.646813	−	0.762649i	$-0.276101\pi$
$647$	32.9049			1.29363			0.646813	+	0.762649i	$0.276101\pi$
$648$	1.95892	+	2.04025i	0.0769537	+	0.0801487i
$649$	−6.54493	−	2.38216i	−0.256911	−	0.0935080i
$650$	4.96438	−	1.93337i	0.194719	−	0.0758329i
$651$	−7.77312	+	1.37061i	−0.304653	+	0.0537185i
$652$	7.00030	+	0.914569i	0.274153	+	0.0358173i
$653$	−1.22144	−	0.705201i	−0.0477988	−	0.0275966i	0.475910	−	0.879494i	$-0.342119\pi$
$653$	−1.22144	−	0.705201i	−0.0477988	−	0.0275966i	−0.523709	+	0.851897i	$0.675452\pi$
$654$	−11.1397	−	6.10430i	−0.435598	−	0.238697i
$655$	−19.4506	−	16.3210i	−0.759997	−	0.637714i
$656$	−0.297924	+	3.48461i	−0.0116320	+	0.136051i
$657$	6.70247	+	11.6090i	0.261488	+	0.452911i
$658$	0.365910	+	16.3978i	0.0142647	+	0.639254i
$659$	−8.21365	−	22.5668i	−0.319958	−	0.879078i	−0.990538	−	0.137241i	$-0.956177\pi$
$659$	−8.21365	−	22.5668i	−0.319958	−	0.879078i	0.670579	−	0.741838i	$-0.266046\pi$
$660$	−6.78098	+	21.5809i	−0.263949	+	0.840035i
$661$	41.5332	+	7.32343i	1.61546	+	0.284848i	0.907071	−	0.420978i	$-0.138313\pi$
$661$	41.5332	+	7.32343i	1.61546	+	0.284848i	0.708385	+	0.705827i	$0.249424\pi$
$662$	0.365770	+	1.83411i	0.0142160	+	0.0712847i
$663$	−32.4504	+	27.2291i	−1.26027	+	1.05749i
$664$	16.8207	−	1.12753i	0.652769	−	0.0437568i
$665$	−18.2582	+	0.712938i	−0.708022	+	0.0276466i
$666$	−0.368859	−	0.607184i	−0.0142930	−	0.0235279i
$667$	−1.87471	−	2.23419i	−0.0725891	−	0.0865083i
$668$	−21.6648	+	19.8916i	−0.838236	+	0.769627i
$669$	6.63329	+	1.16963i	0.256458	+	0.0452204i
$670$	−29.1574	−	33.2146i	−1.12645	−	1.28319i
$671$	42.1532	−	15.3425i	1.62731	−	0.592291i
$672$	6.67513	+	9.05671i	0.257499	+	0.349370i
$673$	−9.08098	−	15.7287i	−0.350046	−	0.606298i	0.636211	−	0.771515i	$-0.280501\pi$
$673$	−9.08098	−	15.7287i	−0.350046	−	0.606298i	−0.986257	+	0.165217i	$0.947167\pi$
$674$	−25.6993	−	3.94250i	−0.989900	−	0.151859i
$675$	0.358510	−	0.427256i	0.0137991	−	0.0164451i
$676$	65.1759	−	2.91019i	2.50677	−	0.111930i
$677$	−16.7758	−	9.68552i	−0.644747	−	0.372245i	0.141694	−	0.989910i	$-0.454745\pi$
$677$	−16.7758	−	9.68552i	−0.644747	−	0.372245i	−0.786441	+	0.617666i	$0.788078\pi$
$678$	10.7443	+	8.61447i	0.412631	+	0.330837i
$679$	4.75854	+	26.9870i	0.182616	+	1.03567i
$680$	4.01522	−	37.1719i	0.153977	−	1.42548i
$681$	−8.22026	−	2.99193i	−0.315001	−	0.114651i
$682$	−28.5248	−	9.66714i	−1.09227	−	0.370174i
$683$			14.0659i			0.538216i	0.963110	+	0.269108i	$0.0867289\pi$
$683$			14.0659i			0.538216i	−0.963110	+	0.269108i	$0.913271\pi$
$684$	−7.15924	+	4.97446i	−0.273740	+	0.190203i
$685$		−	4.97426i		−	0.190057i
$686$	−9.06802	+	26.7570i	−0.346219	+	1.02159i
$687$	20.8850	+	7.60153i	0.796814	+	0.290016i
$688$	−19.7910	−	42.2238i	−0.754525	−	1.60977i
$689$	−6.98044	−	39.5880i	−0.265934	−	1.50818i
$690$	−3.30246	+	4.11895i	−0.125723	+	0.156806i
$691$	7.71228	+	4.45269i	0.293389	+	0.169388i	0.639469	−	0.768817i	$-0.279154\pi$
$691$	7.71228	+	4.45269i	0.293389	+	0.169388i	−0.346080	+	0.938205i	$0.612488\pi$
$692$	−1.19297	−	26.7175i	−0.0453500	−	1.01565i
$693$	6.86057	−	8.17611i	0.260611	−	0.310585i
$694$	−5.29844	+	34.5380i	−0.201126	+	1.31105i
$695$	11.1276	+	19.2735i	0.422093	+	0.731087i
$696$	−4.18016	−	2.05373i	−0.158448	−	0.0778463i
$697$	−5.15286	+	1.87549i	−0.195179	+	0.0710392i
$698$	1.74241	−	1.52957i	0.0659510	−	0.0578952i
$699$	8.67101	+	1.52893i	0.327968	+	0.0578295i
$700$	1.63422	−	1.50046i	0.0617678	−	0.0567122i
$701$	17.4052	+	20.7427i	0.657386	+	0.783442i	0.987008	−	0.160671i	$-0.0513657\pi$
$701$	17.4052	+	20.7427i	0.657386	+	0.783442i	−0.329622	+	0.944113i	$0.606921\pi$
$702$	8.16368	−	4.95936i	0.308118	−	0.187179i
$703$	2.02689	−	0.828649i	0.0764455	−	0.0312531i
$704$	5.72983	+	42.5471i	0.215951	+	1.60355i
$705$	−9.41511	+	7.90022i	−0.354594	+	0.297539i
$706$	−40.3254	+	8.04194i	−1.51767	+	0.302662i
$707$	−17.3539	−	3.05995i	−0.652659	−	0.115081i
$708$	−2.47640	−	0.778117i	−0.0930689	−	0.0292434i
$709$	−15.3822	−	42.2622i	−0.577690	−	1.58719i	−0.792064	−	0.610438i	$-0.790993\pi$
$709$	−15.3822	−	42.2622i	−0.577690	−	1.58719i	0.214374	−	0.976752i	$-0.431229\pi$
$710$	23.0131	−	0.513527i	0.863667	−	0.0192723i
$711$	−3.82573	−	6.62635i	−0.143476	−	0.248508i
$712$	−4.19209	+	5.73510i	−0.157105	+	0.214932i
$713$	−5.38462	−	4.51823i	−0.201656	−	0.169209i
$714$	−8.47725	+	15.4701i	−0.317253	+	0.578955i
$715$	66.1599	+	38.1974i	2.47424	+	1.42850i
$716$	38.9258	+	5.08554i	1.45472	+	0.190055i
$717$	−20.3726	+	3.59224i	−0.760829	+	0.134155i
$718$	−16.3002	−	41.8548i	−0.608320	−	1.56201i
$719$	−27.1463	−	9.88044i	−1.01239	−	0.368478i	−0.218037	−	0.975940i	$-0.569965\pi$
$719$	−27.1463	−	9.88044i	−1.01239	−	0.368478i	−0.794349	+	0.607462i	$0.792188\pi$
$720$	−2.16591	+	8.14769i	−0.0807189	+	0.303647i
$721$	18.4548			0.687292
$722$	−11.6738	−	24.2017i	−0.434454	−	0.900694i
$723$		−	12.8334i		−	0.477280i
$724$	30.3364	−	6.75688i	1.12744	−	0.251117i
$725$	−0.314113	+	0.863018i	−0.0116659	+	0.0320517i
$726$	23.4545	−	9.13432i	0.870480	−	0.339006i
$727$	−1.28103	−	7.26508i	−0.0475108	−	0.269447i	0.951794	−	0.306739i	$-0.0992379\pi$
$727$	−1.28103	−	7.26508i	−0.0475108	−	0.269447i	−0.999304	+	0.0372921i	$0.988127\pi$
$728$	34.7552	−	15.3542i	1.28811	−	0.569064i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−19.2011	+	35.0400i	−0.710663	+	1.29689i
$731$	46.9978	−	56.0098i	1.73828	−	2.07160i
$732$	15.4394	−	6.41308i	0.570655	−	0.237034i
$733$	−12.2319	+	7.06208i	−0.451795	+	0.260844i	−0.708588	−	0.705623i	$-0.750667\pi$
$733$	−12.2319	+	7.06208i	−0.451795	+	0.260844i	0.256793	+	0.966466i	$0.417334\pi$
$734$	0.348905	+	15.6358i	0.0128783	+	0.577127i
$735$	−6.02948	+	2.19455i	−0.222401	+	0.0809472i
$736$	−2.35742	+	9.73813i	−0.0868955	+	0.358952i
$737$	−13.8174	+	78.3626i	−0.508972	+	2.88652i
$738$	1.21261	−	0.241827i	0.0446369	−	0.00890177i
$739$	−5.51010	−	6.56668i	−0.202692	−	0.241559i	0.655117	−	0.755527i	$-0.272619\pi$
$739$	−5.51010	−	6.56668i	−0.202692	−	0.241559i	−0.857809	+	0.513968i	$0.828175\pi$
$740$	0.975947	−	1.87931i	0.0358765	−	0.0690848i
$741$	11.1413	+	27.2518i	0.409286	+	1.00112i
$742$	−8.69138	−	14.3070i	−0.319071	−	0.525227i
$743$	−0.578500	+	0.485420i	−0.0212231	+	0.0178083i	−0.653337	−	0.757067i	$-0.726632\pi$
$743$	−0.578500	+	0.485420i	−0.0212231	+	0.0178083i	0.632114	+	0.774875i	$0.282187\pi$
$744$	−10.7810	−	3.12505i	−0.395252	−	0.114570i
$745$	−5.30302	+	30.0749i	−0.194288	+	1.10186i
$746$	−20.0465	+	17.5979i	−0.733956	+	0.644304i
$747$	−2.03856	−	5.60090i	−0.0745871	−	0.204926i
$748$	−56.7355	+	36.2234i	−2.07446	+	1.32446i
$749$	0.334918	−	0.193365i	0.0122376	−	0.00706540i
$750$	16.3744	+	2.51197i	0.597907	+	0.0917242i
$751$	−7.69813	−	6.45950i	−0.280909	−	0.235710i	0.491437	−	0.870913i	$-0.336472\pi$
$751$	−7.69813	−	6.45950i	−0.280909	−	0.235710i	−0.772345	+	0.635203i	$0.780916\pi$
$752$	−9.81595	+	21.1595i	−0.357951	+	0.771607i
$753$	6.26981	−	10.8596i	0.228485	−	0.395747i
$754$	−9.83894	+	12.2715i	−0.358313	+	0.446901i
$755$	31.6996	−	5.58949i	1.15367	−	0.203422i
$756$	2.41839	−	3.15817i	0.0879561	−	0.114862i
$757$	−6.60249	+	18.1402i	−0.239972	+	0.659317i	0.759984	+	0.649941i	$0.225207\pi$
$757$	−6.60249	+	18.1402i	−0.239972	+	0.659317i	−0.999956	+	0.00937542i	$0.997016\pi$
$758$	3.71950	+	1.26055i	0.135098	+	0.0457853i
$759$	9.50495			0.345008
$760$	−23.7516	−	10.5396i	−0.861562	−	0.382312i
$761$	−51.4676			−1.86570			−0.932849	−	0.360267i	$-0.882686\pi$
$761$	−51.4676			−1.86570			−0.932849	+	0.360267i	$0.882686\pi$
$762$	19.4138	+	6.57939i	0.703287	+	0.238346i
$763$	−6.10997	+	16.7870i	−0.221196	+	0.607730i
$764$	10.9136	+	8.35714i	0.394839	+	0.302351i
$765$	−13.0179	+	2.29540i	−0.470662	+	0.0829905i
$766$	−10.0614	+	12.5489i	−0.363533	+	0.453412i
$767$	−4.38315	+	7.59184i	−0.158266	+	0.274125i
$768$	2.84065	+	15.7458i	0.102503	+	0.568178i
$769$	2.68332	+	2.25158i	0.0967631	+	0.0811939i	0.689886	−	0.723918i	$-0.257661\pi$
$769$	2.68332	+	2.25158i	0.0967631	+	0.0811939i	−0.593123	+	0.805112i	$0.702105\pi$
$770$	31.4455	+	4.82401i	1.13322	+	0.173845i
$771$	−9.07981	+	5.24223i	−0.327001	+	0.188794i
$772$	−11.1901	−	17.5266i	−0.402739	−	0.630797i
$773$	2.25269	+	6.18920i	0.0810235	+	0.222610i	0.973589	−	0.228307i	$-0.0733191\pi$
$773$	2.25269	+	6.18920i	0.0810235	+	0.222610i	−0.892566	+	0.450918i	$0.851097\pi$
$774$	−12.3901	+	10.8767i	−0.445353	+	0.390954i
$775$	−0.384360	+	2.17982i	−0.0138066	+	0.0783013i
$776$	−10.8497	+	37.4300i	−0.389480	+	1.34366i
$777$	−0.765382	+	0.642232i	−0.0274579	+	0.0230399i
$778$	−21.0133	−	34.5903i	−0.753363	−	1.24012i
$779$	0.148702	+	3.80822i	0.00532780	+	0.136444i
$780$	25.2676	+	13.1217i	0.904724	+	0.469834i
$781$	−26.6389	−	31.7470i	−0.953216	−	1.13600i
$782$	−15.4064	+	3.07243i	−0.550930	+	0.109870i
$783$	−0.285937	+	1.62163i	−0.0102185	+	0.0579523i
$784$	−8.59363	+	8.62768i	−0.306916	+	0.308131i
$785$	1.23477	−	0.449421i	0.0440709	−	0.0160405i
$786$	0.380077	+	17.0327i	0.0135569	+	0.607537i
$787$	−15.2734	+	8.81812i	−0.544439	+	0.314332i	−0.746876	−	0.664963i	$-0.768447\pi$
$787$	−15.2734	+	8.81812i	−0.544439	+	0.314332i	0.202437	+	0.979295i	$0.435114\pi$
$788$	−5.58234	−	13.4394i	−0.198863	−	0.478758i
$789$	3.86035	−	4.60059i	0.137432	−	0.163785i
$790$	10.9598	−	20.0006i	0.389934	−	0.711589i
$791$	9.68366	−	16.7726i	0.344311	−	0.596365i
$792$	13.8839	−	6.13367i	0.493344	−	0.217950i
$793$	−9.80420	−	55.6024i	−0.348157	−	1.97450i
$794$	−23.6167	+	9.19748i	−0.838126	+	0.326406i
$795$	4.29029	−	11.7875i	0.152161	−	0.418058i
$796$	−8.33821	−	37.4361i	−0.295540	−	1.32689i
$797$		−	30.4027i		−	1.07692i	−0.842652	−	0.538459i	$-0.819007\pi$
$797$		−	30.4027i		−	1.07692i	0.842652	−	0.538459i	$-0.180993\pi$
$798$	8.44169	+	8.89119i	0.298832	+	0.314745i
$799$	−36.5727			−1.29385
$800$	3.02683	−	0.890363i	0.107015	−	0.0314791i
$801$	2.36013	+	0.859017i	0.0833911	+	0.0303519i
$802$	−7.18334	−	18.4449i	−0.253652	−	0.651313i
$803$	70.8433	−	12.4916i	2.50001	−	0.440819i
$804$	−3.84175	+	29.4056i	−0.135488	+	1.03705i
$805$	6.42998	+	3.71235i	0.226627	+	0.130843i
$806$	−18.2168	+	33.2438i	−0.641660	+	1.17096i
$807$	−17.5492	−	14.7255i	−0.617761	−	0.518363i
$808$	−20.2314	−	14.7882i	−0.711737	−	0.520247i
$809$	16.2377	+	28.1246i	0.570888	+	0.988807i	0.996475	+	0.0838894i	$0.0267342\pi$
$809$	16.2377	+	28.1246i	0.570888	+	0.988807i	−0.425587	+	0.904917i	$0.639932\pi$
$810$	2.97995	−	0.0664961i	0.104705	−	0.00233644i
$811$	−13.9300	−	38.2724i	−0.489148	−	1.34392i	−0.901452	−	0.432878i	$-0.857498\pi$
$811$	−13.9300	−	38.2724i	−0.489148	−	1.34392i	0.412304	−	0.911046i	$-0.364724\pi$
$812$	−1.96344	+	6.24877i	−0.0689032	+	0.219289i
$813$	−15.8122	−	2.78811i	−0.554557	−	0.0977834i
$814$	−3.73890	+	0.745634i	−0.131048	+	0.0261345i
$815$	5.69925	−	4.78224i	0.199636	−	0.167514i
$816$	−20.5215	+	14.4298i	−0.718396	+	0.505146i
$817$	−27.1057	−	42.9830i	−0.948309	−	1.50379i
$818$	6.07542	−	3.69076i	0.212422	−	0.129044i
$819$	−8.63489	−	10.2907i	−0.301728	−	0.359585i
$820$	2.49264	+	2.71484i	0.0870467	+	0.0948065i
$821$	−52.7896	−	9.30824i	−1.84237	−	0.324860i	−0.859783	−	0.510659i	$-0.829401\pi$
$821$	−52.7896	−	9.30824i	−1.84237	−	0.324860i	−0.982588	+	0.185800i	$0.940512\pi$
$822$	−2.50830	+	2.20191i	−0.0874869	+	0.0768004i
$823$	−6.01987	+	2.19105i	−0.209840	+	0.0763753i	−0.444801	−	0.895629i	$-0.646726\pi$
$823$	−6.01987	+	2.19105i	−0.209840	+	0.0763753i	0.234962	+	0.972005i	$0.424503\pi$
$824$	23.5555	+	11.5729i	0.820594	+	0.403161i
$825$	−1.49653	−	2.59207i	−0.0521027	−	0.0902444i
$826$	−0.553555	+	3.60836i	−0.0192606	+	0.125551i
$827$	−8.17462	+	9.74213i	−0.284259	+	0.338767i	−0.889213	−	0.457494i	$-0.848747\pi$
$827$	−8.17462	+	9.74213i	−0.284259	+	0.338767i	0.604954	+	0.796261i	$0.293192\pi$
$828$	3.53887	−	0.158015i	0.122984	−	0.00549141i
$829$	2.01722	+	1.16464i	0.0700609	+	0.0404497i	0.534621	−	0.845092i	$-0.320454\pi$
$829$	2.01722	+	1.16464i	0.0700609	+	0.0404497i	−0.464560	+	0.885541i	$0.653788\pi$
$830$	11.1133	−	13.8609i	0.385748	−	0.481119i
$831$	−4.84300	−	27.4660i	−0.168002	−	0.952785i
$832$	53.9896	+	2.19686i	1.87175	+	0.0761624i
$833$	−17.9417	−	6.53026i	−0.621645	−	0.226260i
$834$	4.79303	−	14.1428i	0.165969	−	0.489724i
$835$			30.9948i			1.07262i
$836$	11.9448	+	45.2326i	0.413121	+	1.56440i
$837$			3.96857i			0.137174i
$838$	25.5290	+	8.65186i	0.881885	+	0.298874i
$839$	−17.4809	−	6.36252i	−0.603507	−	0.219659i	0.0221528	−	0.999755i	$-0.492948\pi$
$839$	−17.4809	−	6.36252i	−0.603507	−	0.219659i	−0.625660	+	0.780096i	$0.715170\pi$
$840$	11.7879	+	1.27330i	0.406722	+	0.0439332i
$841$	4.56496	+	25.8892i	0.157412	+	0.892730i
$842$	−31.0073	−	24.8608i	−1.06858	−	0.856760i
$843$	8.07332	+	4.66114i	0.278060	+	0.160538i
$844$	0.619901	+	13.8832i	0.0213379	+	0.477878i
$845$	44.1936	−	52.6678i	1.52030	−	1.81183i
$846$	8.15143	+	1.25050i	0.280252	+	0.0429931i
$847$	−17.6993	−	30.6561i	−0.608155	−	1.05336i
$848$	−2.12174	−	23.7116i	−0.0728608	−	0.814260i
$849$	−7.73786	+	2.81635i	−0.265563	+	0.0966569i
$850$	3.26358	+	3.71769i	0.111940	+	0.127516i
$851$	−0.876260	−	0.154508i	−0.0300378	−	0.00529648i
$852$	−10.4460	−	11.3772i	−0.357872	−	0.389775i
$853$	−2.19128	−	2.61146i	−0.0750280	−	0.0894149i	0.727225	−	0.686399i	$-0.240810\pi$
$853$	−2.19128	−	2.61146i	−0.0750280	−	0.0894149i	−0.802253	+	0.596985i	$0.796365\pi$
$854$	−12.2073	−	20.0945i	−0.417724	−	0.687621i
$855$	−1.24109	+	9.10289i	−0.0424445	+	0.311312i
$856$	0.548743	−	0.0367837i	0.0187557	−	0.00125724i
$857$	24.0191	−	20.1545i	0.820478	−	0.688463i	−0.132606	−	0.991169i	$-0.542334\pi$
$857$	24.0191	−	20.1545i	0.820478	−	0.688463i	0.953084	+	0.302706i	$0.0978900\pi$
$858$	−10.0251	−	50.2700i	−0.342253	−	1.71619i
$859$	24.1248	+	4.25385i	0.823127	+	0.145140i	0.569321	−	0.822115i	$-0.307206\pi$
$859$	24.1248	+	4.25385i	0.823127	+	0.145140i	0.253807	+	0.967255i	$0.418317\pi$
$860$	−46.8824	−	14.7310i	−1.59868	−	0.502324i
$861$	−0.594754	−	1.63407i	−0.0202692	−	0.0556891i
$862$	−0.209120	−	9.37149i	−0.00712267	−	0.319194i
$863$	−27.0413	−	46.8369i	−0.920497	−	1.59435i	−0.798648	−	0.601798i	$-0.794451\pi$
$863$	−27.0413	−	46.8369i	−0.920497	−	1.59435i	−0.121849	−	0.992549i	$-0.538882\pi$
$864$	5.06728	−	2.51449i	0.172392	−	0.0855448i
$865$	−21.5901	−	18.1162i	−0.734085	−	0.615971i
$866$	−7.73561	−	4.23893i	−0.262867	−	0.144045i
$867$	−19.3422	−	11.1672i	−0.656897	−	0.379260i
$868$	−2.04502	+	15.6530i	−0.0694126	+	0.531299i
$869$	−40.4369	+	7.13012i	−1.37173	+	0.241873i
$870$	−4.57354	+	1.78116i	−0.155058	+	0.0603868i
$871$	94.1110	+	34.2536i	3.18883	+	1.16064i
$872$	−18.3257	+	17.5952i	−0.620588	+	0.595849i
$873$	13.7782			0.466323
$874$	−1.23326	+	10.8485i	−0.0417157	+	0.366957i
$875$		−	23.2975i		−	0.787601i
$876$	26.1686	−	5.82859i	0.884156	−	0.196930i
$877$	8.03060	−	22.0639i	0.271174	−	0.745044i	−0.727112	−	0.686519i	$-0.759138\pi$
$877$	8.03060	−	22.0639i	0.271174	−	0.745044i	0.998286	−	0.0585255i	$-0.0186399\pi$
$878$	7.41889	+	19.0498i	0.250375	+	0.642899i
$879$	3.28228	+	18.6148i	0.110709	+	0.627860i
$880$	37.1115	+	25.8766i	1.25103	+	0.872300i
$881$	−1.58911	+	2.75242i	−0.0535385	+	0.0927314i	−0.891553	−	0.452917i	$-0.850383\pi$
$881$	−1.58911	+	2.75242i	−0.0535385	+	0.0927314i	0.838014	+	0.545649i	$0.183717\pi$
$882$	3.77563	+	2.06895i	0.127132	+	0.0696653i
$883$	−20.0195	+	23.8583i	−0.673709	+	0.802895i	−0.989284	−	0.146006i	$-0.953358\pi$
$883$	−20.0195	+	23.8583i	−0.673709	+	0.802895i	0.315575	+	0.948901i	$0.397803\pi$
$884$	32.4991	+	78.2409i	1.09306	+	2.63153i
$885$	−2.36902	+	1.36776i	−0.0796338	+	0.0459766i
$886$	−31.8661	+	0.711077i	−1.07056	+	0.0238891i
$887$	44.3807	−	16.1533i	1.49016	−	0.542373i	0.536667	−	0.843794i	$-0.319683\pi$
$887$	44.3807	−	16.1533i	1.49016	−	0.542373i	0.953491	+	0.301421i	$0.0974609\pi$
$888$	−1.37967	+	0.339771i	−0.0462985	+	0.0114020i
$889$	5.00593	−	28.3900i	0.167893	−	0.952171i
$890$	1.46413	+	7.34173i	0.0490778	+	0.246095i
$891$	−3.44945	−	4.11090i	−0.115561	−	0.137720i
$892$	6.20851	−	11.9553i	0.207876	−	0.400292i
$893$	−7.75500	+	24.2064i	−0.259511	+	0.810037i
$894$	17.5129	−	10.6389i	0.585718	−	0.355818i
$895$	31.6912	−	26.5920i	1.05932	−	0.888874i
$896$	21.2824	−	7.30660i	0.710994	−	0.244096i
$897$	2.07739	−	11.7814i	0.0693619	−	0.393371i
$898$	11.0629	+	12.6022i	0.369173	+	0.420541i
$899$	−2.23504	−	6.14072i	−0.0745428	−	0.204805i
$900$	−0.600280	−	0.940199i	−0.0200093	−	0.0313400i
$901$	32.3259	−	18.6633i	1.07693	−	0.621766i
$902$	1.00617	−	6.55877i	0.0335019	−	0.218383i
$903$	17.7618	+	14.9039i	0.591076	+	0.495971i
$904$	22.8781	−	15.3358i	0.760915	−	0.510060i
$905$	16.3764	−	28.3648i	0.544371	−	0.942879i
$906$	−16.8507	−	13.5104i	−0.559827	−	0.448854i
$907$	6.98120	−	1.23097i	0.231807	−	0.0408738i	−0.0565379	−	0.998400i	$-0.518006\pi$
$907$	6.98120	−	1.23097i	0.231807	−	0.0408738i	0.288345	+	0.957527i	$0.406895\pi$
$908$	−10.6369	+	13.8907i	−0.353000	+	0.460981i
$909$	−3.03030	+	8.32569i	−0.100509	+	0.276146i
$910$	12.8521	−	37.9225i	0.426042	−	1.25712i
$911$	11.3498			0.376037			0.188018	−	0.982166i	$-0.439794\pi$
$911$	11.3498			0.376037			0.188018	+	0.982166i	$0.439794\pi$
$912$	5.19926	+	16.6423i	0.172165	+	0.551083i
$913$	−31.9856			−1.05857
$914$	13.0368	−	38.4677i	0.431219	−	1.27240i
$915$	6.02581	−	16.5558i	0.199207	−	0.547317i
$916$	27.0250	−	35.2919i	0.892933	−	1.16608i
$917$	23.5960	−	4.16061i	0.779208	−	0.137395i
$918$	6.91997	+	5.54824i	0.228393	+	0.183119i
$919$	5.49311	−	9.51434i	0.181201	−	0.313849i	−0.761089	−	0.648648i	$-0.775335\pi$
$919$	5.49311	−	9.51434i	0.181201	−	0.313849i	0.942290	+	0.334798i	$0.108668\pi$
$920$	5.87916	+	8.77060i	0.193830	+	0.289158i
$921$	2.03679	+	1.70907i	0.0671146	+	0.0563159i
$922$	0.109003	−	0.710537i	0.00358981	−	0.0234003i
$923$	−45.1728	+	26.0805i	−1.48688	+	0.858451i
$924$	−11.4871	−	17.9919i	−0.377899	−	0.591891i
$925$	0.0958298	+	0.263290i	0.00315086	+	0.00865693i
$926$	−11.3296	−	12.9061i	−0.372315	−	0.424121i
$927$	1.61127	−	9.13799i	0.0529212	−	0.300131i
$928$	−6.42468	+	6.74459i	−0.210900	+	0.221402i
$929$	−41.6485	+	34.9472i	−1.36644	+	1.14658i	−0.392508	+	0.919749i	$0.628393\pi$
$929$	−41.6485	+	34.9472i	−1.36644	+	1.14658i	−0.973934	+	0.226832i	$0.927163\pi$
$930$	−10.1098	+	6.14161i	−0.331513	+	0.201391i
$931$	−8.12663	+	10.4904i	−0.266339	+	0.343810i
$932$	8.11574	−	15.6279i	0.265840	−	0.511908i
$933$	0.985658	+	1.17466i	0.0322690	+	0.0384567i
$934$	5.74792	+	28.8223i	0.188078	+	0.943095i
$935$	−12.3180	+	69.8591i	−0.402843	+	2.28464i
$936$	−4.56826	−	18.5498i	−0.149318	−	0.606319i
$937$	12.7757	−	4.64998i	0.417364	−	0.151908i	−0.124798	−	0.992182i	$-0.539828\pi$
$937$	12.7757	−	4.64998i	0.417364	−	0.151908i	0.542162	+	0.840274i	$0.317606\pi$
$938$	41.6957	−	0.930421i	1.36141	−	0.0303793i
$939$	10.2394	−	5.91173i	0.334151	−	0.192922i
$940$	9.42923	+	22.7007i	0.307548	+	0.740415i
$941$	31.5029	−	37.5436i	1.02696	−	1.22389i	0.0526685	−	0.998612i	$-0.483227\pi$
$941$	31.5029	−	37.5436i	1.02696	−	1.22389i	0.974295	−	0.225276i	$-0.0723282\pi$
$942$	−0.773208	−	0.423699i	−0.0251925	−	0.0138049i
$943$	0.774307	−	1.34114i	0.0252149	−	0.0436735i
$944$	−2.96934	+	4.25854i	−0.0966436	+	0.138604i
$945$	−0.727917	−	4.12822i	−0.0236791	−	0.134291i
$946$	32.1075	+	82.4436i	1.04390	+	2.68047i
$947$	1.14309	−	3.14062i	0.0371455	−	0.102057i	−0.919733	−	0.392544i	$-0.871595\pi$
$947$	1.14309	−	3.14062i	0.0371455	−	0.102057i	0.956879	+	0.290487i	$0.0938174\pi$
$948$	−14.9369	+	3.32692i	−0.485127	+	0.108053i
$949$		−	90.5409i		−	2.93908i
$950$	3.15265	−	1.37176i	0.102286	−	0.0445057i
$951$	8.90778			0.288855
$952$	24.4351	+	25.4496i	0.791945	+	0.824825i
$953$	−12.1919	−	4.43747i	−0.394933	−	0.143744i	0.136917	−	0.990583i	$-0.456281\pi$
$953$	−12.1919	−	4.43747i	−0.394933	−	0.143744i	−0.531850	+	0.846839i	$0.678503\pi$
$954$	−7.84303	+	3.05445i	−0.253927	+	0.0988915i
$955$	14.2657	−	2.51543i	0.461628	−	0.0813975i
$956$	−5.35981	+	41.0251i	−0.173349	+	1.32685i
$957$	7.65267	+	4.41827i	0.247376	+	0.142822i
$958$	12.0769	+	6.61788i	0.390188	+	0.213814i
$959$	3.59576	+	3.01720i	0.116113	+	0.0974305i
$960$	14.2475	+	9.01738i	0.459836	+	0.291035i
$961$	7.62523	+	13.2073i	0.245975	+	0.426041i
$962$	0.107051	+	4.79735i	0.00345145	+	0.154673i
$963$	−0.0665043	−	0.182719i	−0.00214307	−	0.00588804i
$964$	−24.4865	−	7.69397i	−0.788658	−	0.247806i
$965$	−21.5807	−	3.80527i	−0.694708	−	0.122496i
$966$	−0.974328	−	4.88566i	−0.0313485	−	0.157194i
$967$	19.4560	−	16.3255i	0.625662	−	0.524992i	−0.273916	−	0.961754i	$-0.588319\pi$
$967$	19.4560	−	16.3255i	0.625662	−	0.524992i	0.899577	+	0.436761i	$0.143875\pi$
$968$	−3.36693	−	50.2282i	−0.108217	−	1.61440i
$969$	−20.2404	+	18.3761i	−0.650215	+	0.590326i
$970$	21.3227	+	35.0996i	0.684630	+	1.12698i
$971$	27.0066	+	32.1853i	0.866685	+	1.03287i	0.999131	+	0.0416843i	$0.0132724\pi$
$971$	27.0066	+	32.1853i	0.866685	+	1.03287i	−0.132446	+	0.991190i	$0.542283\pi$
$972$	−1.35264	−	1.47322i	−0.0433859	−	0.0472535i
$973$	−20.6819	−	3.64678i	−0.663031	−	0.116910i
$974$	−3.11235	−	3.54542i	−0.0997261	−	0.113603i
$975$	−3.53997	+	1.28844i	−0.113370	+	0.0412632i
$976$	−2.98003	−	33.3035i	−0.0953886	−	1.06602i
$977$	14.0246	+	24.2913i	0.448686	+	0.777148i	0.998301	−	0.0582709i	$-0.0185587\pi$
$977$	14.0246	+	24.2913i	0.448686	+	0.777148i	−0.549614	+	0.835418i	$0.685225\pi$
$978$	−4.93430	−	0.756965i	−0.157782	−	0.0242051i
$979$	8.66364	−	10.3249i	0.276891	−	0.329986i
$980$	0.572434	+	12.8201i	0.0182857	+	0.409523i
$981$	7.77872	+	4.49105i	0.248355	+	0.143388i
$982$	−15.5065	−	12.4327i	−0.494832	−	0.396743i
$983$	−1.92629	−	10.9245i	−0.0614392	−	0.348439i	−0.999995	−	0.00331006i	$-0.998946\pi$
$983$	−1.92629	−	10.9245i	−0.0614392	−	0.348439i	0.938555	−	0.345129i	$-0.112165\pi$
$984$	0.265581	−	2.45868i	0.00846641	−	0.0783799i
$985$	−14.4112	−	5.24524i	−0.459178	−	0.167127i
$986$	−13.8322	−	4.68779i	−0.440508	−	0.149290i
$987$		−	11.5979i		−	0.369165i
$988$	58.6766	−	4.91975i	1.86675	−	0.156518i
$989$			20.6486i			0.656587i
$990$	5.13412	−	15.1492i	0.163173	−	0.481474i
$991$	10.3929	+	3.78271i	0.330142	+	0.120162i	0.501773	−	0.865000i	$-0.332681\pi$
$991$	10.3929	+	3.78271i	0.330142	+	0.120162i	−0.171631	+	0.985161i	$0.554904\pi$
$992$	−12.4262	+	18.6969i	−0.394532	+	0.593629i
$993$	−0.229641	−	1.30236i	−0.00728744	−	0.0413291i
$994$	−13.5877	+	16.9470i	−0.430975	+	0.537528i
$995$	−35.0031	−	20.2091i	−1.10967	−	0.640670i
$996$	−11.9088	+	0.531745i	−0.377346	+	0.0168490i
$997$	15.7754	−	18.8004i	0.499613	−	0.595415i	−0.456022	−	0.889968i	$-0.650726\pi$
$997$	15.7754	−	18.8004i	0.499613	−	0.595415i	0.955635	+	0.294553i	$0.0951707\pi$
$998$	1.44824	−	9.44036i	0.0458431	−	0.298829i
$999$	0.251180	+	0.435056i	0.00794697	+	0.0137646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.16	yes	240
8.5	even	2	inner	456.2.bk.a.253.5	✓	240
19.16	even	9	inner	456.2.bk.a.301.5	yes	240
152.149	even	18	inner	456.2.bk.a.301.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.5	✓	240	8.5	even	2	inner
456.2.bk.a.253.16	yes	240	1.1	even	1	trivial
456.2.bk.a.301.5	yes	240	19.16	even	9	inner
456.2.bk.a.301.16	yes	240	152.149	even	18	inner

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.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453922 + 1.33939i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-1.58791 - 1.21595i) q^{4} +(-2.07565 + 0.365992i) q^{5} +(1.10336 + 0.884644i) q^{6} +(0.994443 - 1.72243i) q^{7} +(2.34942 - 1.57487i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(0.451977 - 2.94622i) q^{10} +(-4.64743 + 2.68320i) q^{11} +(-1.68572 + 1.07627i) q^{12} +(2.31010 + 6.34696i) q^{13} +(1.85559 + 2.11379i) q^{14} +(-0.365992 + 2.07565i) q^{15} +(1.04291 + 3.86165i) q^{16} +(-4.80442 + 4.03138i) q^{17} +(1.20867 - 0.734254i) q^{18} +(1.64951 + 4.03474i) q^{19} +(3.74097 + 1.94273i) q^{20} +(-1.27843 - 1.52358i) q^{21} +(-1.48426 - 7.44267i) q^{22} +(0.307565 - 1.74429i) q^{23} +(-0.676350 - 2.74637i) q^{24} +(-0.524107 + 0.190759i) q^{25} +(-9.54963 + 0.213096i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-3.67348 + 1.52586i) q^{28} +(1.05844 - 1.26140i) q^{29} +(-2.61396 - 1.43239i) q^{30} +(1.98429 - 3.43688i) q^{31} +(-5.64564 - 0.356026i) q^{32} +(0.931865 + 5.28487i) q^{33} +(-3.21875 - 8.26490i) q^{34} +(-1.43372 + 3.93910i) q^{35} +(0.434809 + 1.95216i) q^{36} -0.502359i q^{37} +(-6.15282 + 0.377879i) q^{38} +6.75429 q^{39} +(-4.30017 + 4.12875i) q^{40} +(0.821603 + 0.299039i) q^{41} +(2.62096 - 1.02073i) q^{42} +(-11.4809 + 2.02439i) q^{43} +(10.6423 + 1.39039i) q^{44} +(1.82529 + 1.05383i) q^{45} +(2.19667 + 1.20372i) q^{46} +(4.46708 + 3.74833i) q^{47} +(3.98546 + 0.340745i) q^{48} +(1.52217 + 2.63647i) q^{49} +(-0.0175966 - 0.788571i) q^{50} +(2.14506 + 5.89349i) q^{51} +(4.04937 - 12.8874i) q^{52} +(-5.86117 - 1.03348i) q^{53} +(-0.276585 - 1.38690i) q^{54} +(8.66440 - 7.27029i) q^{55} +(-0.376242 - 5.61282i) q^{56} +(4.35558 - 0.170075i) q^{57} +(1.20905 + 1.99024i) q^{58} +(0.834265 + 0.994239i) q^{59} +(3.10505 - 2.85091i) q^{60} +(-8.23216 - 1.45155i) q^{61} +(3.70260 + 4.21780i) q^{62} +(-1.86894 + 0.680239i) q^{63} +(3.03954 - 7.40008i) q^{64} +(-7.11789 - 12.3286i) q^{65} +(-7.50147 - 1.15079i) q^{66} +(9.53108 - 11.3587i) q^{67} +(12.5310 - 0.559523i) q^{68} +(-1.53390 - 0.885599i) q^{69} +(-4.62519 - 3.70835i) q^{70} +(1.34103 + 7.60533i) q^{71} +(-2.81207 - 0.303753i) q^{72} +(-12.5965 - 4.58476i) q^{73} +(0.672853 + 0.228032i) q^{74} +0.557743i q^{75} +(2.28678 - 8.41253i) q^{76} +10.6731i q^{77} +(-3.06592 + 9.04660i) q^{78} +(7.19001 + 2.61695i) q^{79} +(-3.57805 - 7.63372i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.773472 + 0.964703i) q^{82} +(5.16182 + 2.98018i) q^{83} +(0.177436 + 3.97381i) q^{84} +(8.49681 - 10.1261i) q^{85} +(2.49998 - 16.2962i) q^{86} +(-0.823322 - 1.42604i) q^{87} +(-6.69307 + 13.6231i) q^{88} +(-2.36013 + 0.859017i) q^{89} +(-2.24003 + 1.96641i) q^{90} +(13.2294 + 2.33270i) q^{91} +(-2.60936 + 2.39579i) q^{92} +(-2.55095 - 3.04010i) q^{93} +(-7.04816 + 4.28170i) q^{94} +(-4.90049 - 7.77098i) q^{95} +(-2.26548 + 5.18340i) q^{96} +(-10.5547 + 8.85648i) q^{97} +(-4.22220 + 0.842016i) q^{98} +(5.28487 + 0.931865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more