LMFDB - Embedded newform 675.2.ba.b.518.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] 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("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			518.14
Character	$\chi$	$=$	675.518
Dual form			675.2.ba.b.632.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.19031 + 0.191628i) q^{2} +(1.58451 - 0.699511i) q^{3} +(2.79113 + 0.492152i) q^{4} +(3.60463 - 1.22851i) q^{6} +(-0.000530458 - 0.000371431i) q^{7} +(1.77162 + 0.474704i) q^{8} +(2.02137 - 2.21677i) q^{9} +(0.925209 - 2.54199i) q^{11} +(4.76685 - 1.17261i) q^{12} +(0.277011 + 3.16625i) q^{13} +(-0.00109069 - 0.000915200i) q^{14} +(-1.53710 - 0.559459i) q^{16} +(-6.58840 + 1.76536i) q^{17} +(4.85222 - 4.46807i) q^{18} +(1.52337 - 0.879517i) q^{19} +(-0.00110034 - 0.000217476i) q^{21} +(2.51361 - 5.39046i) q^{22} +(2.93096 + 4.18584i) q^{23} +(3.13922 - 0.487092i) q^{24} +6.98815i q^{26} +(1.65223 - 4.92647i) q^{27} +(-0.00129778 - 0.00129778i) q^{28} +(-4.37718 + 3.67289i) q^{29} +(-0.944975 + 5.35922i) q^{31} +(-6.58407 - 3.07020i) q^{32} +(-0.312144 - 4.67501i) q^{33} +(-14.7689 + 2.60416i) q^{34} +(6.73289 - 5.19248i) q^{36} +(0.0678960 + 0.253391i) q^{37} +(3.50519 - 1.63450i) q^{38} +(2.65375 + 4.82319i) q^{39} +(7.56097 - 9.01082i) q^{41} +(-0.00236841 - 0.000687195i) q^{42} +(3.67622 + 7.88368i) q^{43} +(3.83342 - 6.63969i) q^{44} +(5.61759 + 9.72995i) q^{46} +(0.403711 - 0.576559i) q^{47} +(-2.82690 + 0.188748i) q^{48} +(-2.39414 - 6.57785i) q^{49} +(-9.20452 + 7.40589i) q^{51} +(-0.785101 + 8.97374i) q^{52} +(-5.73786 + 5.73786i) q^{53} +(4.56295 - 10.4739i) q^{54} +(-0.000763450 - 0.000909845i) q^{56} +(1.79857 - 2.45922i) q^{57} +(-10.2912 + 7.20599i) q^{58} +(-2.11198 + 0.768697i) q^{59} +(-1.14333 - 6.48417i) q^{61} +(-3.09676 + 11.5573i) q^{62} +(-0.00189563 + 0.000425105i) q^{63} +(-10.9996 - 6.35064i) q^{64} +(0.212168 - 10.2996i) q^{66} +(-2.47165 + 0.216242i) q^{67} +(-19.2579 + 1.68485i) q^{68} +(7.57218 + 4.58228i) q^{69} +(-10.4316 - 6.02267i) q^{71} +(4.63341 - 2.96772i) q^{72} +(0.375408 - 1.40104i) q^{73} +(0.100157 + 0.568017i) q^{74} +(4.68478 - 1.70512i) q^{76} +(-0.00143496 + 0.00100477i) q^{77} +(4.88829 + 11.0728i) q^{78} +(3.36157 + 4.00616i) q^{79} +(-0.828138 - 8.96182i) q^{81} +(18.2876 - 18.2876i) q^{82} +(1.39592 - 15.9554i) q^{83} +(-0.00296416 - 0.00114854i) q^{84} +(6.54134 + 17.9722i) q^{86} +(-4.36647 + 8.88163i) q^{87} +(2.84581 - 4.06424i) q^{88} +(2.99426 + 5.18621i) q^{89} +(0.00102910 - 0.00178245i) q^{91} +(6.12062 + 13.1257i) q^{92} +(2.25151 + 9.15278i) q^{93} +(0.994737 - 1.18548i) q^{94} +(-12.5802 - 0.259149i) q^{96} +(-7.62753 + 3.55678i) q^{97} +(-3.98342 - 14.8663i) q^{98} +(-3.76482 - 7.18927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.19031	+	0.191628i	1.54878	+	0.135501i	0.829219	−	0.558923i	$-0.188785\pi$
$2$	2.19031	+	0.191628i	1.54878	+	0.135501i	0.719566	+	0.694425i	$0.244341\pi$
$3$	1.58451	−	0.699511i	0.914820	−	0.403863i
$3$	1.58451	−	0.699511i	0.914820	−	0.403863i
$4$	2.79113	+	0.492152i	1.39557	+	0.246076i
$5$		0			0
$5$		0			0
$6$	3.60463	−	1.22851i	1.47158	−	0.501538i
$7$	−0.000530458	0	0.000371431i	−0.000200494	0	0.000140388i	0.573476	−	0.819222i	$-0.305595\pi$
$7$	−0.000530458	0	0.000371431i	−0.000200494	0	0.000140388i	−0.573677	+	0.819082i	$0.694483\pi$
$8$	1.77162	+	0.474704i	0.626362	+	0.167833i
$9$	2.02137	−	2.21677i	0.673790	−	0.738923i
$10$		0			0
$11$	0.925209	−	2.54199i	0.278961	−	0.766439i	−0.718520	−	0.695506i	$-0.755180\pi$
$11$	0.925209	−	2.54199i	0.278961	−	0.766439i	0.997481	−	0.0709326i	$-0.0225975\pi$
$12$	4.76685	−	1.17261i	1.37607	−	0.338502i
$13$	0.277011	+	3.16625i	0.0768289	+	0.878159i	0.932625	+	0.360846i	$0.117512\pi$
$13$	0.277011	+	3.16625i	0.0768289	+	0.878159i	−0.855797	+	0.517313i	$0.826932\pi$
$14$	−0.00109069		0.000915200i	−0.000291500		0.000244597i
$15$		0			0
$16$	−1.53710	−	0.559459i	−0.384275	−	0.139865i
$17$	−6.58840	+	1.76536i	−1.59792	+	0.428162i	−0.944414	−	0.328759i	$-0.893370\pi$
$17$	−6.58840	+	1.76536i	−1.59792	+	0.428162i	−0.653507	+	0.756921i	$0.726703\pi$
$18$	4.85222	−	4.46807i	1.14368	−	1.05313i
$19$	1.52337	−	0.879517i	0.349485	−	0.201775i	−0.314974	−	0.949100i	$-0.601996\pi$
$19$	1.52337	−	0.879517i	0.349485	−	0.201775i	0.664458	+	0.747325i	$0.268662\pi$
$20$		0			0
$21$	−0.00110034		0.000217476i	−0.000240113		4.74571e-5i
$22$	2.51361	−	5.39046i	0.535904	−	1.14925i
$23$	2.93096	+	4.18584i	0.611147	+	0.872808i	0.998799	−	0.0489979i	$-0.0156028\pi$
$23$	2.93096	+	4.18584i	0.611147	+	0.872808i	−0.387652	+	0.921806i	$0.626714\pi$
$24$	3.13922	−	0.487092i	0.640790	−	0.0994273i
$25$		0			0
$26$			6.98815i			1.37049i
$27$	1.65223	−	4.92647i	0.317972	−	0.948100i
$28$	−0.00129778	−	0.00129778i	−0.000245257	−	0.000245257i
$29$	−4.37718	+	3.67289i	−0.812822	+	0.682038i	−0.951279	−	0.308330i	$-0.900230\pi$
$29$	−4.37718	+	3.67289i	−0.812822	+	0.682038i	0.138458	+	0.990368i	$0.455785\pi$
$30$		0			0
$31$	−0.944975	+	5.35922i	−0.169723	+	0.962544i	0.774338	+	0.632772i	$0.218083\pi$
$31$	−0.944975	+	5.35922i	−0.169723	+	0.962544i	−0.944061	+	0.329772i	$0.893028\pi$
$32$	−6.58407	−	3.07020i	−1.16391	−	0.542740i
$33$	−0.312144	−	4.67501i	−0.0543373	−	0.813815i
$34$	−14.7689	+	2.60416i	−2.53285	+	0.446610i
$35$		0			0
$36$	6.73289	−	5.19248i	1.12215	−	0.865413i
$37$	0.0678960	+	0.253391i	0.0111620	+	0.0416573i	0.971282	−	0.237930i	$-0.0764690\pi$
$37$	0.0678960	+	0.253391i	0.0111620	+	0.0416573i	−0.960120	+	0.279587i	$0.909802\pi$
$38$	3.50519	−	1.63450i	0.568617	−	0.265151i
$39$	2.65375	+	4.82319i	0.424940	+	0.772328i
$40$		0			0
$41$	7.56097	−	9.01082i	1.18083	−	1.40725i	0.287537	−	0.957770i	$-0.407164\pi$
$41$	7.56097	−	9.01082i	1.18083	−	1.40725i	0.893289	−	0.449483i	$-0.148392\pi$
$42$	−0.00236841		0.000687195i	−0.000365454		0.000106037i
$43$	3.67622	+	7.88368i	0.560618	+	1.20225i	0.958574	+	0.284845i	$0.0919421\pi$
$43$	3.67622	+	7.88368i	0.560618	+	1.20225i	−0.397955	+	0.917405i	$0.630280\pi$
$44$	3.83342	−	6.63969i	0.577910	−	1.00097i
$45$		0			0
$46$	5.61759	+	9.72995i	0.828268	+	1.43460i
$47$	0.403711	−	0.576559i	0.0588873	−	0.0840997i	−0.788628	−	0.614870i	$-0.789208\pi$
$47$	0.403711	−	0.576559i	0.0588873	−	0.0840997i	0.847516	+	0.530770i	$0.178097\pi$
$48$	−2.82690	+	0.188748i	−0.408028	+	0.0272435i
$49$	−2.39414	−	6.57785i	−0.342020	−	0.939693i
$50$		0			0
$51$	−9.20452	+	7.40589i	−1.28889	+	1.03703i
$52$	−0.785101	+	8.97374i	−0.108874	+	1.24443i
$53$	−5.73786	+	5.73786i	−0.788156	+	0.788156i	−0.981192	−	0.193036i	$-0.938167\pi$
$53$	−5.73786	+	5.73786i	−0.788156	+	0.788156i	0.193036	+	0.981192i	$0.438167\pi$
$54$	4.56295	−	10.4739i	0.620939	−	1.42532i
$55$		0			0
$56$	−0.000763450	0	0.000909845i	−0.000102020	0	0.000121583i
$57$	1.79857	−	2.45922i	0.238226	−	0.325732i
$58$	−10.2912	+	7.20599i	−1.35130	+	0.946193i
$59$	−2.11198	+	0.768697i	−0.274956	+	0.100076i	−0.475818	−	0.879544i	$-0.657848\pi$
$59$	−2.11198	+	0.768697i	−0.274956	+	0.100076i	0.200862	+	0.979620i	$0.435626\pi$
$60$		0			0
$61$	−1.14333	−	6.48417i	−0.146389	−	0.830213i	−0.966241	−	0.257638i	$-0.917056\pi$
$61$	−1.14333	−	6.48417i	−0.146389	−	0.830213i	0.819852	−	0.572575i	$-0.194055\pi$
$62$	−3.09676	+	11.5573i	−0.393290	+	1.46778i
$63$	−0.00189563		0.000425105i	−0.000238827		5.35582e-5i
$64$	−10.9996	−	6.35064i	−1.37495	−	0.793830i
$65$		0			0
$66$	0.212168	−	10.2996i	0.0261161	−	1.26779i
$67$	−2.47165	+	0.216242i	−0.301960	+	0.0264181i	−0.237129	−	0.971478i	$-0.576206\pi$
$67$	−2.47165	+	0.216242i	−0.301960	+	0.0264181i	−0.0648313	+	0.997896i	$0.520651\pi$
$68$	−19.2579	+	1.68485i	−2.33536	+	0.204318i
$69$	7.57218	+	4.58228i	0.911583	+	0.551642i
$70$		0			0
$71$	−10.4316	−	6.02267i	−1.23800	−	0.714759i	−0.269314	−	0.963052i	$-0.586797\pi$
$71$	−10.4316	−	6.02267i	−1.23800	−	0.714759i	−0.968685	+	0.248294i	$0.920130\pi$
$72$	4.63341	−	2.96772i	0.546052	−	0.349749i
$73$	0.375408	−	1.40104i	0.0439381	−	0.163979i	−0.940471	−	0.339875i	$-0.889615\pi$
$73$	0.375408	−	1.40104i	0.0439381	−	0.163979i	0.984409	+	0.175895i	$0.0562820\pi$
$74$	0.100157	+	0.568017i	0.0116430	+	0.0660306i
$75$		0			0
$76$	4.68478	−	1.70512i	0.537381	−	0.195591i
$77$	−0.00143496	+	0.00100477i	−0.000163529	+	0.000114504i
$78$	4.88829	+	11.0728i	0.553490	+	1.25375i
$79$	3.36157	+	4.00616i	0.378206	+	0.450729i	0.921247	−	0.388978i	$-0.127172\pi$
$79$	3.36157	+	4.00616i	0.378206	+	0.450729i	−0.543041	+	0.839706i	$0.682727\pi$
$80$		0			0
$81$	−0.828138	−	8.96182i	−0.0920153	−	0.995758i
$82$	18.2876	−	18.2876i	2.01953	−	2.01953i
$83$	1.39592	−	15.9554i	0.153222	−	1.75134i	−0.398372	−	0.917224i	$-0.630425\pi$
$83$	1.39592	−	15.9554i	0.153222	−	1.75134i	0.551594	−	0.834113i	$-0.314020\pi$
$84$	−0.00296416	−	0.00114854i	−0.000323416	−	0.000125316i
$85$		0			0
$86$	6.54134	+	17.9722i	0.705371	+	1.93799i
$87$	−4.36647	+	8.88163i	−0.468135	+	0.952211i
$88$	2.84581	−	4.06424i	0.303364	−	0.433249i
$89$	2.99426	+	5.18621i	0.317391	+	0.549737i	0.979943	−	0.199279i	$-0.0638600\pi$
$89$	2.99426	+	5.18621i	0.317391	+	0.549737i	−0.662552	+	0.749016i	$0.730527\pi$
$90$		0			0
$91$	0.00102910	−	0.00178245i	0.000107879	−	0.000186852i
$92$	6.12062	+	13.1257i	0.638118	+	1.36845i
$93$	2.25151	+	9.15278i	0.233470	+	0.949099i
$94$	0.994737	−	1.18548i	0.102599	−	0.122273i
$95$		0			0
$96$	−12.5802	−	0.259149i	−1.28396	−	0.0264492i
$97$	−7.62753	+	3.55678i	−0.774459	+	0.361136i	−0.769331	−	0.638851i	$-0.779410\pi$
$97$	−7.62753	+	3.55678i	−0.774459	+	0.361136i	−0.00512815	+	0.999987i	$0.501632\pi$
$98$	−3.98342	−	14.8663i	−0.402386	−	1.50173i
$99$	−3.76482	−	7.18927i	−0.378378	−	0.722549i
$100$		0			0
$101$	11.3335	−	1.99841i	1.12773	−	0.198849i	0.421496	−	0.906830i	$-0.361505\pi$
$101$	11.3335	−	1.99841i	1.12773	−	0.198849i	0.706231	+	0.707981i	$0.250394\pi$
$102$	−21.5799	+	14.4574i	−2.13673	+	1.43149i
$103$	−6.21507	−	2.89813i	−0.612389	−	0.285562i	0.0915740	−	0.995798i	$-0.470810\pi$
$103$	−6.21507	−	2.89813i	−0.612389	−	0.285562i	−0.703963	+	0.710237i	$0.748588\pi$
$104$	−1.01227	+	5.74088i	−0.0992615	+	0.562940i
$105$		0			0
$106$	−13.6672	+	11.4682i	−1.32748	+	1.11389i
$107$	9.67551	+	9.67551i	0.935367	+	0.935367i	0.998034	−	0.0626673i	$-0.0199607\pi$
$107$	9.67551	+	9.67551i	0.935367	+	0.935367i	−0.0626673	+	0.998034i	$0.519961\pi$
$108$	7.03617	−	12.9373i	0.677056	−	1.24489i
$109$			3.73835i			0.358069i	0.983843	+	0.179034i	$0.0572974\pi$
$109$			3.73835i			0.358069i	−0.983843	+	0.179034i	$0.942703\pi$
$110$		0			0
$111$	0.284832	+	0.354008i	0.0270351	+	0.0336010i
$112$	0.000607567	0	0.000867696i	5.74097e−5	0	8.19895e-5i
$113$	0.472320	−	1.01289i	0.0444322	−	0.0952851i	−0.882839	−	0.469676i	$-0.844371\pi$
$113$	0.472320	−	1.01289i	0.0444322	−	0.0952851i	0.927271	+	0.374391i	$0.122148\pi$
$114$	4.41068	−	5.04180i	0.413098	−	0.472208i
$115$		0			0
$116$	−14.0249	+	8.09728i	−1.30218	+	0.751814i
$117$	7.57878	+	5.78608i	0.700658	+	0.534923i
$118$	−4.77320	+	1.27897i	−0.439408	+	0.117739i
$119$	0.00415058	+	0.00151069i	0.000380483	+	0.000138484i
$120$		0			0
$121$	2.82079	+	2.36692i	0.256435	+	0.215175i
$122$	−1.26171	−	14.4215i	−0.114230	−	1.30566i
$123$	5.67730	−	19.5667i	0.511905	−	1.76427i
$124$	−5.27510	+	14.4932i	−0.473718	+	1.30153i
$125$		0			0
$126$	−0.00423348		0.000567858i	−0.000377148		5.05889e-5i
$127$	10.0914	+	2.70398i	0.895467	+	0.239940i	0.677068	−	0.735920i	$-0.263250\pi$
$127$	10.0914	+	2.70398i	0.895467	+	0.239940i	0.218398	+	0.975860i	$0.429917\pi$
$128$	−10.9739	−	7.68398i	−0.969962	−	0.679175i
$129$	11.3397	+	9.92024i	0.998409	+	0.873429i
$130$		0			0
$131$	−14.3376	−	2.52811i	−1.25269	−	0.220882i	−0.492341	−	0.870402i	$-0.663859\pi$
$131$	−14.3376	−	2.52811i	−1.25269	−	0.220882i	−0.760345	+	0.649520i	$0.774970\pi$
$132$	1.42958	−	13.2022i	0.124429	−	1.14910i
$133$	−0.00113476		9.92788e-5i	−9.83964e−5		8.60857e-6i
$134$	−5.45513			−0.471251
$135$		0			0
$136$	−12.5102			−1.07274
$137$	7.28394	+	0.637262i	0.622309	+	0.0544450i	0.393950	−	0.919132i	$-0.371108\pi$
$137$	7.28394	+	0.637262i	0.622309	+	0.0544450i	0.228359	+	0.973577i	$0.426664\pi$
$138$	15.7074	+	11.4877i	1.33710	+	0.977896i
$139$	3.00586	+	0.530014i	0.254953	+	0.0449552i	0.299664	−	0.954045i	$-0.403125\pi$
$139$	3.00586	+	0.530014i	0.254953	+	0.0449552i	−0.0447106	+	0.999000i	$0.514237\pi$
$140$		0			0
$141$	0.236376	−	1.19597i	0.0199065	−	0.100718i
$142$	−21.6943	−	15.1905i	−1.82054	−	1.27476i
$143$	8.30486	+	2.22528i	0.694487	+	0.186087i
$144$	−4.34724	+	2.27652i	−0.362270	+	0.189710i
$145$		0			0
$146$	1.09074	−	2.99678i	0.0902701	−	0.248015i
$147$	−8.39483	−	8.74796i	−0.692394	−	0.721520i
$148$	0.0647997	+	0.740664i	0.00532650	+	0.0608822i
$149$	−7.76525	−	6.51582i	−0.636154	−	0.533797i	0.266680	−	0.963785i	$-0.414073\pi$
$149$	−7.76525	−	6.51582i	−0.636154	−	0.533797i	−0.902834	+	0.429988i	$0.858518\pi$
$150$		0			0
$151$	17.4779	+	6.36142i	1.42233	+	0.517685i	0.934722	−	0.355379i	$-0.115648\pi$
$151$	17.4779	+	6.36142i	1.42233	+	0.517685i	0.487605	+	0.873064i	$0.337870\pi$
$152$	3.11634	−	0.835020i	0.252768	−	0.0677291i
$153$	−9.40419	+	18.1734i	−0.760284	+	1.46923i
$154$	−0.00333555	+	0.00192578i	−0.000268786	+	0.000155184i
$155$		0			0
$156$	5.03323	+	14.7682i	0.402981	+	1.18240i
$157$	0.136723	−	0.293204i	0.0109117	−	0.0234002i	−0.900776	−	0.434283i	$-0.857002\pi$
$157$	0.136723	−	0.293204i	0.0109117	−	0.0234002i	0.911688	+	0.410883i	$0.134780\pi$
$158$	6.59520	+	9.41892i	0.524686	+	0.749329i
$159$	−5.07803	+	13.1054i	−0.402714	+	1.03933i
$160$		0			0
$161$		−	0.00330906i		−	0.000260790i
$162$	−0.0965494	−	19.7879i	−0.00758564	−	1.55468i
$163$	3.86594	+	3.86594i	0.302804	+	0.302804i	0.842110	−	0.539306i	$-0.181313\pi$
$163$	3.86594	+	3.86594i	0.302804	+	0.302804i	−0.539306	+	0.842110i	$0.681313\pi$
$164$	25.5384	−	21.4292i	1.99421	−	1.67334i
$165$		0			0
$166$	6.11500	−	34.6799i	0.474616	−	2.69168i
$167$	−16.6893	−	7.78235i	−1.29146	−	0.602217i	−0.349182	−	0.937055i	$-0.613541\pi$
$167$	−16.6893	−	7.78235i	−1.29146	−	0.602217i	−0.942276	+	0.334838i	$0.891318\pi$
$168$	−0.00184614		0.000907620i	−0.000142433		7.00244e-5i
$169$	2.85412	−	0.503259i	0.219548	−	0.0387122i
$170$		0			0
$171$	1.12960	−	5.15478i	0.0863828	−	0.394196i
$172$	6.38085	+	23.8136i	0.486535	+	1.81577i
$173$	2.69896	−	1.25855i	0.205198	−	0.0956855i	−0.317302	−	0.948324i	$-0.602777\pi$
$173$	2.69896	−	1.25855i	0.205198	−	0.0956855i	0.522501	+	0.852639i	$0.324999\pi$
$174$	−11.2659	+	18.6168i	−0.854066	+	1.41134i
$175$		0			0
$176$	−2.84428	+	3.38968i	−0.214395	+	0.255506i
$177$	−2.80875	+	2.69536i	−0.211118	+	0.202596i
$178$	5.56454	+	11.9332i	0.417080	+	0.894431i
$179$	8.26245	−	14.3110i	0.617564	−	1.06965i	−0.372365	−	0.928087i	$-0.621453\pi$
$179$	8.26245	−	14.3110i	0.617564	−	1.06965i	0.989929	−	0.141566i	$-0.0452138\pi$
$180$		0			0
$181$	4.81540	+	8.34051i	0.357926	+	0.619945i	0.987614	−	0.156902i	$-0.0501508\pi$
$181$	4.81540	+	8.34051i	0.357926	+	0.619945i	−0.629688	+	0.776848i	$0.716817\pi$
$182$	0.00259561	−	0.00370692i	0.000192400	−	0.000274775i
$183$	−6.34738	−	9.47449i	−0.469212	−	0.700374i
$184$	3.20550	+	8.80705i	0.236313	+	0.649264i
$185$		0			0
$186$	3.17758	+	20.4789i	0.232992	+	1.50159i
$187$	−1.60813	+	18.3810i	−0.117598	+	1.34415i
$188$	1.41056	−	1.41056i	0.102876	−	0.102876i
$189$	−0.00270628	+	0.00199960i	−0.000196853	+	0.000145449i
$190$		0			0
$191$	0.797244	+	0.950119i	0.0576866	+	0.0687482i	0.794116	−	0.607766i	$-0.207934\pi$
$191$	0.797244	+	0.950119i	0.0576866	+	0.0687482i	−0.736430	+	0.676514i	$0.763490\pi$
$192$	−21.8714	−	2.36831i	−1.57843	−	0.170918i
$193$	14.5052	−	10.1567i	1.04411	−	0.731093i	0.0800524	−	0.996791i	$-0.474491\pi$
$193$	14.5052	−	10.1567i	1.04411	−	0.731093i	0.964056	+	0.265698i	$0.0856023\pi$
$194$	−17.3883	+	6.32881i	−1.24840	+	0.454382i
$195$		0			0
$196$	−3.44506	−	19.5379i	−0.246076	−	1.39557i
$197$	4.39615	−	16.4067i	0.313213	−	1.16893i	−0.612429	−	0.790526i	$-0.709807\pi$
$197$	4.39615	−	16.4067i	0.313213	−	1.16893i	0.925642	−	0.378401i	$-0.123526\pi$
$198$	−6.86847	−	16.4682i	−0.488121	−	1.17034i
$199$	9.13371	+	5.27335i	0.647472	+	0.373818i	0.787487	−	0.616331i	$-0.211382\pi$
$199$	9.13371	+	5.27335i	0.647472	+	0.373818i	−0.140015	+	0.990149i	$0.544715\pi$
$200$		0			0
$201$	−3.76510	+	2.07159i	−0.265570	+	0.146118i
$202$	25.2069	−	2.20532i	1.77355	−	0.155166i
$203$	0.00368613		0.000322495i	0.000258716		2.26347e-5i
$204$	−29.3358	+	16.1408i	−2.05392	+	1.13008i
$205$		0			0
$206$	−13.0576	−	7.53880i	−0.909765	−	0.525253i
$207$	15.2036	+	1.96387i	1.05672	+	0.136498i
$208$	1.34559	−	5.02181i	0.0932999	−	0.348200i
$209$	−0.826290	−	4.68612i	−0.0571557	−	0.324146i
$210$		0			0
$211$	0.169003	−	0.0615119i	0.0116346	−	0.00423465i	−0.336196	−	0.941792i	$-0.609141\pi$
$211$	0.169003	−	0.0615119i	0.0116346	−	0.00423465i	0.347831	+	0.937557i	$0.386918\pi$
$212$	−18.8390	+	13.1912i	−1.29387	+	0.905978i
$213$	−20.7419	−	2.24600i	−1.42121	−	0.153894i
$214$	19.3383	+	23.0465i	1.32194	+	1.57543i
$215$		0			0
$216$	5.26574	−	7.94351i	0.358288	−	0.540488i
$217$	0.00249185	−	0.00249185i	0.000169158	−	0.000169158i
$218$	−0.716371	+	8.18815i	−0.0485187	+	0.554572i
$219$	−0.385205	−	2.48257i	−0.0260297	−	0.167757i
$220$		0			0
$221$	−7.41460	−	20.3715i	−0.498760	−	1.37033i
$222$	0.556034	+	0.829970i	0.0373185	+	0.0557039i
$223$	−10.5728	+	15.0996i	−0.708010	+	1.01114i	0.290516	+	0.956870i	$0.406173\pi$
$223$	−10.5728	+	15.0996i	−0.708010	+	1.01114i	−0.998526	+	0.0542728i	$0.982716\pi$
$224$	0.00235221	+	0.00407414i	0.000157163	+	0.000272215i
$225$		0			0
$226$	1.22863	−	2.12804i	0.0817271	−	0.141555i
$227$	−6.61613	−	14.1883i	−0.439128	−	0.941713i	−0.993959	−	0.109750i	$-0.964995\pi$
$227$	−6.61613	−	14.1883i	−0.439128	−	0.941713i	0.554831	−	0.831963i	$-0.312783\pi$
$228$	6.23034	−	5.97884i	0.412615	−	0.395958i
$229$	4.54463	−	5.41608i	0.300318	−	0.357904i	−0.594690	−	0.803955i	$-0.702725\pi$
$229$	4.54463	−	5.41608i	0.300318	−	0.357904i	0.895008	+	0.446050i	$0.147170\pi$
$230$		0			0
$231$	−0.00157086	+	0.00259584i	−0.000103355	+	0.000170794i
$232$	−9.49823	+	4.42910i	−0.623590	+	0.290785i
$233$	−0.591957	−	2.20921i	−0.0387804	−	0.144730i	0.943821	−	0.330457i	$-0.107203\pi$
$233$	−0.591957	−	2.20921i	−0.0387804	−	0.144730i	−0.982601	+	0.185726i	$0.940536\pi$
$234$	15.4911	+	14.1256i	1.01269	+	0.923421i
$235$		0			0
$236$	−6.27313	+	1.10612i	−0.408346	+	0.0720024i
$237$	8.12881	+	3.99637i	0.528023	+	0.259592i
$238$	0.00880157	+	0.00410424i	0.000570521	+	0.000266038i
$239$	1.33675	−	7.58107i	0.0864670	−	0.490379i	−0.910563	−	0.413369i	$-0.864352\pi$
$239$	1.33675	−	7.58107i	0.0864670	−	0.490379i	0.997030	−	0.0770092i	$-0.0245371\pi$
$240$		0			0
$241$	−7.35154	+	6.16868i	−0.473555	+	0.397359i	−0.848089	−	0.529853i	$-0.822247\pi$
$241$	−7.35154	+	6.16868i	−0.473555	+	0.397359i	0.374535	+	0.927213i	$0.377802\pi$
$242$	5.72484	+	5.72484i	0.368007	+	0.368007i
$243$	−7.58109	−	13.6208i	−0.486327	−	0.873777i
$244$		−	18.6609i		−	1.19464i
$245$		0			0
$246$	16.1846	−	41.7694i	1.03189	−	2.66312i
$247$	3.20676	+	4.57972i	0.204041	+	0.291401i
$248$	−4.21818	+	9.04592i	−0.267855	+	0.574416i
$249$	−8.94915	−	26.2581i	−0.567129	−	1.66404i
$250$		0			0
$251$	−4.10987	+	2.37283i	−0.259413	+	0.149772i	−0.624067	−	0.781371i	$-0.714521\pi$
$251$	−4.10987	+	2.37283i	−0.259413	+	0.149772i	0.364654	+	0.931143i	$0.381187\pi$
$252$	−0.00550016		0.000253588i	−0.000346478		1.59745e-5i
$253$	13.3521	−	3.57769i	0.839440	−	0.224927i
$254$	21.5852	+	7.85635i	1.35437	+	0.492951i
$255$		0			0
$256$	−3.10423	−	2.60476i	−0.194015	−	0.162798i
$257$	−1.05277	−	12.0332i	−0.0656701	−	0.750612i	−0.955629	−	0.294572i	$-0.904823\pi$
$257$	−1.05277	−	12.0332i	−0.0656701	−	0.750612i	0.889959	−	0.456040i	$-0.150733\pi$
$258$	22.9366	+	23.9014i	1.42797	+	1.48804i
$259$	5.81013e−5	0	0.000159632i	3.61024e−6	0	9.91906e-6i
$260$		0			0
$261$	−0.705942	+	17.1275i	−0.0436967	+	1.06016i
$262$	−30.9195	−	8.28485i	−1.91021	−	0.511840i
$263$	7.01542	+	4.91225i	0.432589	+	0.302902i	0.769515	−	0.638629i	$-0.220498\pi$
$263$	7.01542	+	4.91225i	0.432589	+	0.302902i	−0.336926	+	0.941531i	$0.609387\pi$
$264$	1.66625	−	8.43052i	0.102550	−	0.518863i
$265$		0			0
$266$	−0.00246646		0.000434903i	−0.000151228		2.66656e-5i
$267$	8.37225	+	6.12310i	0.512374	+	0.374728i
$268$	−7.00513	−	0.612870i	−0.427907	−	0.0374370i
$269$	−17.3406			−1.05728			−0.528638	−	0.848847i	$-0.677297\pi$
$269$	−17.3406			−1.05728			−0.528638	+	0.848847i	$0.677297\pi$
$270$		0			0
$271$	−11.8573			−0.720278			−0.360139	−	0.932899i	$-0.617271\pi$
$271$	−11.8573			−0.720278			−0.360139	+	0.932899i	$0.617271\pi$
$272$	11.1147	+	0.972407i	0.673926	+	0.0589609i
$273$	0.000383777	−	0.00354418i	2.32272e−5	−	0.000214504i
$274$	15.8320	+	2.79161i	0.956446	+	0.168647i
$275$		0			0
$276$	18.8798	+	16.5164i	1.13643	+	0.994172i
$277$	16.3872	+	11.4745i	0.984613	+	0.689433i	0.950739	−	0.309993i	$-0.100327\pi$
$277$	16.3872	+	11.4745i	0.984613	+	0.689433i	0.0338740	+	0.999426i	$0.489216\pi$
$278$	6.48220	+	1.73690i	0.388776	+	0.104172i
$279$	9.97002	+	12.9278i	0.596889	+	0.773964i
$280$		0			0
$281$	−2.66069	+	7.31019i	−0.158724	+	0.436089i	−0.993407	−	0.114641i	$-0.963428\pi$
$281$	−2.66069	+	7.31019i	−0.158724	+	0.436089i	0.834683	+	0.550730i	$0.185651\pi$
$282$	0.746917	−	2.57424i	0.0444783	−	0.153294i
$283$	−1.30970	−	14.9700i	−0.0778538	−	0.889873i	−0.930238	−	0.366957i	$-0.880400\pi$
$283$	−1.30970	−	14.9700i	−0.0778538	−	0.889873i	0.852384	−	0.522916i	$-0.175156\pi$
$284$	−26.1518	−	21.9440i	−1.55182	−	1.30213i
$285$		0			0
$286$	17.7638	+	6.46550i	1.05040	+	0.382313i
$287$	−0.00735767	+	0.00197148i	−0.000434310	+	0.000116373i
$288$	−20.1148	+	8.38936i	−1.18527	+	0.494348i
$289$	25.5680	−	14.7617i	1.50400	−	0.868336i
$290$		0			0
$291$	−9.59793	+	10.9713i	−0.562641	+	0.643150i
$292$	1.73734	−	3.72573i	0.101670	−	0.218032i
$293$	−12.9347	−	18.4726i	−0.755651	−	1.07918i	−0.994147	−	0.108038i	$-0.965543\pi$
$293$	−12.9347	−	18.4726i	−0.755651	−	1.07918i	0.238495	−	0.971144i	$-0.423346\pi$
$294$	−16.7109	−	20.7695i	−0.974602	−	1.21130i
$295$		0			0
$296$			0.481143i			0.0279659i
$297$	−10.9944	−	8.75797i	−0.637959	−	0.508189i
$298$	−15.7597	−	15.7597i	−0.912936	−	0.912936i
$299$	−12.4415	+	10.4396i	−0.719510	+	0.603740i
$300$		0			0
$301$	0.000978160	−	0.00554742i	5.63802e−5	−	0.000319748i
$302$	37.0629	+	17.2827i	2.13273	+	0.994510i
$303$	16.5602	−	11.0944i	0.951360	−	0.637358i
$304$	−2.83362	+	0.499644i	−0.162519	+	0.0286566i
$305$		0			0
$306$	−24.0806	+	38.0033i	−1.37660	+	2.17250i
$307$	1.30818	+	4.88220i	0.0746619	+	0.278642i	0.993156	−	0.116792i	$-0.0372610\pi$
$307$	1.30818	+	4.88220i	0.0746619	+	0.278642i	−0.918495	+	0.395434i	$0.870594\pi$
$308$	−0.00449965	+	0.00209822i	−0.000256392	+	0.000119557i
$309$	−11.8751	−	0.244625i	−0.675553	−	0.0139162i
$310$		0			0
$311$	12.6744	−	15.1048i	0.718699	−	0.856512i	−0.275805	−	0.961214i	$-0.588944\pi$
$311$	12.6744	−	15.1048i	0.718699	−	0.856512i	0.994504	+	0.104702i	$0.0333888\pi$
$312$	2.41185	+	9.80460i	0.136544	+	0.555076i
$313$	11.4671	+	24.5912i	0.648157	+	1.38998i	0.905787	+	0.423734i	$0.139281\pi$
$313$	11.4671	+	24.5912i	0.648157	+	1.38998i	−0.257629	+	0.966244i	$0.582941\pi$
$314$	0.355652	−	0.616007i	0.0200706	−	0.0347633i
$315$		0			0
$316$	7.41094	+	12.8361i	0.416898	+	0.722089i
$317$	−0.143177	+	0.204479i	−0.00804165	+	0.0114847i	−0.823153	−	0.567820i	$-0.807787\pi$
$317$	−0.143177	+	0.204479i	−0.00804165	+	0.0114847i	0.815111	+	0.579305i	$0.196676\pi$
$318$	−13.6338	+	27.7319i	−0.764547	+	1.55513i
$319$	5.28664	+	14.5249i	0.295995	+	0.813240i
$320$		0			0
$321$	22.0991	+	8.56286i	1.23345	+	0.477932i
$322$	0.000634107	−	0.00724787i	3.53374e−5	−	0.000403908i
$323$	−8.48389	+	8.48389i	−0.472056	+	0.472056i
$324$	2.09913	−	25.4212i	0.116619	−	1.41229i
$325$		0			0
$326$	7.72680	+	9.20844i	0.427948	+	0.510009i
$327$	2.61502	+	5.92347i	0.144611	+	0.327569i
$328$	17.6726	−	12.3745i	0.975808	−	0.683268i
$329$	−0.000428303	0	0.000155890i	−2.36131e−5	0	8.59448e-6i
$330$		0			0
$331$	0.820786	+	4.65491i	0.0451145	+	0.255857i	0.999021	−	0.0442484i	$-0.0140893\pi$
$331$	0.820786	+	4.65491i	0.0451145	+	0.255857i	−0.953906	+	0.300105i	$0.902978\pi$
$332$	11.7487	−	43.8467i	0.644794	−	2.40640i
$333$	0.698953	+	0.361687i	0.0383024	+	0.0198203i
$334$	−35.0635	−	20.2439i	−1.91859	−	1.10770i
$335$		0			0
$336$	0.00156966		0.000949876i	8.56320e−5		5.18200e-5i
$337$	−10.7791	+	0.943046i	−0.587173	+	0.0513710i	−0.376872	−	0.926266i	$-0.623000\pi$
$337$	−10.7791	+	0.943046i	−0.587173	+	0.0513710i	−0.210302	+	0.977637i	$0.567445\pi$
$338$	6.34786	−	0.555366i	0.345278	−	0.0302079i
$339$	0.0398674	−	1.93534i	0.00216530	−	0.105113i
$340$		0			0
$341$	12.7488	+	7.36051i	0.690385	+	0.398594i
$342$	3.46198	−	11.0741i	0.187202	−	0.598820i
$343$	−0.00234645	+	0.00875706i	−0.000126696	+	0.000472837i
$344$	2.77045	+	15.7120i	0.149373	+	0.847134i
$345$		0			0
$346$	6.15274	−	2.23942i	0.330774	−	0.120392i
$347$	−19.7058	+	13.7981i	−1.05786	+	0.740723i	−0.966906	−	0.255132i	$-0.917881\pi$
$347$	−19.7058	+	13.7981i	−1.05786	+	0.740723i	−0.0909561	+	0.995855i	$0.528992\pi$
$348$	−16.5585	+	22.6408i	−0.887630	+	1.21368i
$349$	0.752338	+	0.896601i	0.0402717	+	0.0479940i	0.785804	−	0.618475i	$-0.212249\pi$
$349$	0.752338	+	0.896601i	0.0402717	+	0.0479940i	−0.745533	+	0.666469i	$0.767805\pi$
$350$		0			0
$351$	16.0561	+	3.86669i	0.857012	+	0.206388i
$352$	−13.8961	+	13.8961i	−0.740662	+	0.740662i
$353$	−1.76656	+	20.1919i	−0.0940245	+	1.07470i	0.791830	+	0.610741i	$0.209129\pi$
$353$	−1.76656	+	20.1919i	−0.0940245	+	1.07470i	−0.885855	+	0.463963i	$0.846427\pi$
$354$	−6.66854	+	5.36546i	−0.354429	+	0.285171i
$355$		0			0
$356$	5.80497	+	15.9490i	0.307663	+	0.845296i
$357$	0.00763339		0.000509670i	0.000404002		2.69746e-5i
$358$	20.8397	−	29.7622i	1.10141	−	1.57298i
$359$	−13.1082	−	22.7040i	−0.691823	−	1.19827i	−0.971240	−	0.238102i	$-0.923475\pi$
$359$	−13.1082	−	22.7040i	−0.691823	−	1.19827i	0.279418	−	0.960170i	$-0.409859\pi$
$360$		0			0
$361$	−7.95290	+	13.7748i	−0.418574	+	0.724991i
$362$	8.94895	+	19.1911i	0.470347	+	1.00866i
$363$	6.12527	+	1.77725i	0.321493	+	0.0932814i
$364$	0.00374959	−	0.00446858i	0.000196532	−	0.000234217i
$365$		0			0
$366$	−12.0872	−	21.9684i	−0.631807	−	1.14831i
$367$	19.0178	−	8.86817i	0.992723	−	0.462914i	0.142761	−	0.989757i	$-0.454402\pi$
$367$	19.0178	−	8.86817i	0.992723	−	0.462914i	0.849963	+	0.526843i	$0.176624\pi$
$368$	−2.16337	−	8.07380i	−0.112773	−	0.420876i
$369$	−4.69139	−	34.9751i	−0.244224	−	1.82073i
$370$		0			0
$371$	0.00517492		0.000912477i	0.000268668		4.73735e-5i
$372$	1.77970	+	26.6547i	0.0922730	+	1.38198i
$373$	1.52296	+	0.710169i	0.0788560	+	0.0367712i	0.461646	−	0.887064i	$-0.347259\pi$
$373$	1.52296	+	0.710169i	0.0788560	+	0.0367712i	−0.382790	+	0.923835i	$0.625037\pi$
$374$	−7.04459	+	39.9519i	−0.364267	+	2.06586i
$375$		0			0
$376$	0.988917	−	0.829800i	0.0509995	−	0.0427937i
$377$	−12.8418	−	12.8418i	−0.661386	−	0.661386i
$378$	−0.00631078	+	0.00386115i	−0.000324592	+	0.000198596i
$379$			11.6637i			0.599126i	0.954077	+	0.299563i	$0.0968408\pi$
$379$			11.6637i			0.599126i	−0.954077	+	0.299563i	$0.903159\pi$
$380$		0			0
$381$	17.8814	−	2.77455i	0.916093	−	0.142144i
$382$	1.56415	+	2.23383i	0.0800286	+	0.114293i
$383$	4.44907	−	9.54105i	0.227337	−	0.487525i	−0.759243	−	0.650808i	$-0.774430\pi$
$383$	4.44907	−	9.54105i	0.227337	−	0.487525i	0.986579	+	0.163283i	$0.0522082\pi$
$384$	−22.7633	−	4.49904i	−1.16163	−	0.229591i
$385$		0			0
$386$	33.7173	−	19.4667i	1.71616	−	0.990828i
$387$	24.9073	+	7.78649i	1.26611	+	0.395809i
$388$	−23.0399	+	6.17353i	−1.16968	+	0.313414i
$389$	36.8621	+	13.4167i	1.86898	+	0.680254i	0.970427	+	0.241396i	$0.0776054\pi$
$389$	36.8621	+	13.4167i	1.86898	+	0.680254i	0.898557	+	0.438858i	$0.144617\pi$
$390$		0			0
$391$	−26.6998	−	22.4038i	−1.35027	−	1.13301i
$392$	−1.11898	−	12.7900i	−0.0565168	−	0.645990i
$393$	−24.4866	+	6.02351i	−1.23519	+	0.303846i
$394$	12.7729	−	35.0933i	0.643491	−	1.76798i
$395$		0			0
$396$	−6.96989	−	21.9191i	−0.350250	−	1.10147i
$397$	10.0653	+	2.69699i	0.505162	+	0.135358i	0.502395	−	0.864638i	$-0.332452\pi$
$397$	10.0653	+	2.69699i	0.505162	+	0.135358i	0.00276748	+	0.999996i	$0.499119\pi$
$398$	18.9952	+	13.3006i	0.952141	+	0.666697i
$399$	−0.00186749		0.000636470i	−9.34916e−5		3.18634e-5i
$400$		0			0
$401$	26.3401	+	4.64448i	1.31536	+	0.231934i	0.786931	−	0.617041i	$-0.211669\pi$
$401$	26.3401	+	4.64448i	1.31536	+	0.231934i	0.528433	+	0.848975i	$0.322780\pi$
$402$	−8.64373	+	3.81592i	−0.431110	+	0.190321i
$403$	−17.2304	−	1.50746i	−0.858306	−	0.0750921i
$404$	32.6169			1.62275
$405$		0			0
$406$	0.00813559			0.000403762
$407$	0.706936	+	0.0618489i	0.0350415	+	0.00306574i
$408$	−19.8225	+	8.75099i	−0.981361	+	0.433239i
$409$	−33.6400	−	5.93165i	−1.66339	−	0.293301i	−0.738705	−	0.674028i	$-0.764562\pi$
$409$	−33.6400	−	5.93165i	−1.66339	−	0.293301i	−0.924687	+	0.380727i	$0.875674\pi$
$410$		0			0
$411$	11.9873	−	4.08545i	0.591289	−	0.201520i
$412$	−15.9208	−	11.1478i	−0.784359	−	0.549214i
$413$	0.00140583		0.000376692i	6.91766e−5		1.85358e-5i
$414$	32.9243	+	7.21491i	1.61814	+	0.354594i
$415$		0			0
$416$	7.89716	−	21.6973i	0.387190	−	1.06380i
$417$	5.13357	−	1.26282i	0.251392	−	0.0618403i
$418$	−0.911843	−	10.4224i	−0.0445997	−	0.509777i
$419$	12.2431	+	10.2731i	0.598112	+	0.501876i	0.890838	−	0.454321i	$-0.150118\pi$
$419$	12.2431	+	10.2731i	0.598112	+	0.501876i	−0.292726	+	0.956196i	$0.594562\pi$
$420$		0			0
$421$	29.9345	+	10.8953i	1.45892	+	0.531002i	0.945067	−	0.326878i	$-0.105997\pi$
$421$	29.9345	+	10.8953i	1.45892	+	0.531002i	0.513850	+	0.857880i	$0.328219\pi$
$422$	0.381956	−	0.102345i	0.0185933	−	0.00498206i
$423$	−0.462050	−	2.06037i	−0.0224656	−	0.100179i
$424$	−12.8891	+	7.44152i	−0.625950	+	0.361392i
$425$		0			0
$426$	−45.0008	−	8.89416i	−2.18030	−	0.430924i
$427$	−0.00180193	+	0.00386425i	−8.72015e−5	+	0.000187004i
$428$	22.2438	+	31.7675i	1.07520	+	1.53554i
$429$	14.7158	−	2.28335i	0.710484	−	0.110241i
$430$		0			0
$431$			5.93676i			0.285963i	0.989725	+	0.142982i	$0.0456690\pi$
$431$			5.93676i			0.285963i	−0.989725	+	0.142982i	$0.954331\pi$
$432$	−5.29580	+	6.64813i	−0.254794	+	0.319858i
$433$	7.73933	+	7.73933i	0.371929	+	0.371929i	0.868179	−	0.496251i	$-0.165290\pi$
$433$	7.73933	+	7.73933i	0.371929	+	0.371929i	−0.496251	+	0.868179i	$0.665290\pi$
$434$	0.00593543	−	0.00498042i	0.000284910	−	0.000239068i
$435$		0			0
$436$	−1.83984	+	10.4342i	−0.0881122	+	0.499709i
$437$	8.14644	+	3.79875i	0.389697	+	0.181719i
$438$	−0.367990	−	5.51142i	−0.0175832	−	0.263346i
$439$	−28.6483	+	5.05146i	−1.36731	+	0.241093i	−0.808642	−	0.588300i	$-0.799797\pi$
$439$	−28.6483	+	5.05146i	−1.36731	+	0.241093i	−0.558665	+	0.829394i	$0.688686\pi$
$440$		0			0
$441$	−19.4210	−	7.98900i	−0.924810	−	0.380428i
$442$	−12.3366	−	46.0407i	−0.586791	−	2.18993i
$443$	−24.6030	+	11.4725i	−1.16892	+	0.545077i	−0.907461	−	0.420137i	$-0.861982\pi$
$443$	−24.6030	+	11.4725i	−1.16892	+	0.545077i	−0.261461	+	0.965214i	$0.584204\pi$
$444$	0.620778	+	1.12826i	0.0294608	+	0.0535450i
$445$		0			0
$446$	−26.0513	+	31.0468i	−1.23357	+	1.47011i
$447$	−16.8620	−	4.89253i	−0.797547	−	0.231409i
$448$	0.00347602	+	0.00745435i	0.000164227	+	0.000352185i
$449$	−1.73698	+	3.00854i	−0.0819733	+	0.141982i	−0.904097	−	0.427326i	$-0.859456\pi$
$449$	−1.73698	+	3.00854i	−0.0819733	+	0.141982i	0.822124	+	0.569308i	$0.192789\pi$
$450$		0			0
$451$	−15.9099	−	27.5568i	−0.749169	−	1.29760i
$452$	1.81681	−	2.59467i	0.0854554	−	0.122043i
$453$	32.1438	−	2.14620i	1.51025	−	0.100837i
$454$	−11.7725	−	32.3447i	−0.552511	−	1.51801i
$455$		0			0
$456$	4.35378	−	3.50301i	0.203884	−	0.164044i
$457$	2.05624	−	23.5029i	0.0961868	−	1.09942i	−0.782703	−	0.622395i	$-0.786160\pi$
$457$	2.05624	−	23.5029i	0.0961868	−	1.09942i	0.878890	−	0.477025i	$-0.158285\pi$
$458$	10.9920	−	10.9920i	0.513624	−	0.513624i
$459$	−2.18858	+	35.3743i	−0.102154	+	1.65113i
$460$		0			0
$461$	5.14645	+	6.13330i	0.239694	+	0.285656i	0.872459	−	0.488688i	$-0.162524\pi$
$461$	5.14645	+	6.13330i	0.239694	+	0.285656i	−0.632765	+	0.774344i	$0.718080\pi$
$462$	−0.00393812	+	0.00538467i	−0.000183218	+	0.000250518i
$463$	−1.93475	+	1.35473i	−0.0899154	+	0.0629594i	−0.617670	−	0.786438i	$-0.711923\pi$
$463$	−1.93475	+	1.35473i	−0.0899154	+	0.0629594i	0.527754	+	0.849397i	$0.323034\pi$
$464$	8.78299	−	3.19675i	0.407740	−	0.148405i
$465$		0			0
$466$	−0.873225	−	4.95230i	−0.0404514	−	0.229411i
$467$	−5.32380	+	19.8687i	−0.246356	+	0.919414i	0.726341	+	0.687335i	$0.241220\pi$
$467$	−5.32380	+	19.8687i	−0.246356	+	0.919414i	−0.972697	+	0.232079i	$0.925447\pi$
$468$	18.3057	+	19.8796i	0.846183	+	0.918936i
$469$	0.00139143		0.000803341i	6.42501e−5		3.70948e-5i
$470$		0			0
$471$	0.0115405	−	0.560224i	0.000531757	−	0.0258138i
$472$	−4.10653	+	0.359274i	−0.189018	+	0.0165369i
$473$	23.4415	−	2.05087i	1.07784	−	0.0942989i
$474$	17.0388	+	10.3110i	0.782619	+	0.473600i
$475$		0			0
$476$	0.0108413	+	0.00625924i	0.000496911	+	0.000286892i
$477$	1.12119	+	24.3179i	0.0513356	+	1.11344i
$478$	4.38064	−	16.3488i	0.200366	−	0.747775i
$479$	3.74161	+	21.2197i	0.170958	+	0.969553i	0.942706	+	0.333624i	$0.108272\pi$
$479$	3.74161	+	21.2197i	0.170958	+	0.969553i	−0.771748	+	0.635929i	$0.780617\pi$
$480$		0			0
$481$	−0.783491	+	0.285167i	−0.0357241	+	0.0130025i
$482$	−17.2843	+	12.1026i	−0.787277	+	0.551257i
$483$	−0.00231472	−	0.00524325i	−0.000105324	−	0.000238576i
$484$	6.70831	+	7.99465i	0.304923	+	0.363393i
$485$		0			0
$486$	−13.9948	−	31.2866i	−0.634818	−	1.41919i
$487$	−2.20133	+	2.20133i	−0.0997518	+	0.0997518i	−0.755221	−	0.655470i	$-0.772471\pi$
$487$	−2.20133	+	2.20133i	−0.0997518	+	0.0997518i	0.655470	+	0.755221i	$0.272471\pi$
$488$	1.05251	−	12.0302i	0.0476449	−	0.544583i
$489$	8.82991	+	3.42137i	0.399302	+	0.154720i
$490$		0			0
$491$	−2.81965	−	7.74693i	−0.127249	−	0.349614i	0.859666	−	0.510857i	$-0.170672\pi$
$491$	−2.81965	−	7.74693i	−0.127249	−	0.349614i	−0.986915	+	0.161243i	$0.948450\pi$
$492$	25.4759	−	51.8193i	1.14854	−	2.33619i
$493$	22.3546	−	31.9257i	1.00680	−	1.43786i
$494$	6.14620	+	10.6455i	0.276530	+	0.478965i
$495$		0			0
$496$	4.45078	−	7.70898i	0.199846	−	0.346144i
$497$	0.00329650	+	0.00706937i	0.000147868	+	0.000317105i
$498$	−14.5697	−	59.2283i	−0.652882	−	2.65408i
$499$	16.9583	−	20.2101i	0.759156	−	0.904727i	−0.238638	−	0.971109i	$-0.576701\pi$
$499$	16.9583	−	20.2101i	0.759156	−	0.904727i	0.997794	+	0.0663815i	$0.0211454\pi$
$500$		0			0
$501$	−31.8883	−	0.656890i	−1.42466	−	0.0293477i
$502$	−9.45659	+	4.40968i	−0.422068	+	0.196814i
$503$	−2.01259	−	7.51109i	−0.0897370	−	0.334903i	0.906432	−	0.422352i	$-0.138795\pi$
$503$	−2.01259	−	7.51109i	−0.0897370	−	0.334903i	−0.996169	+	0.0874487i	$0.972129\pi$
$504$	−0.00356013		0.000146738i	−0.000158581		6.53622e-6i
$505$		0			0
$506$	29.9309	−	5.27762i	1.33059	−	0.234619i
$507$	4.17036	−	2.79391i	0.185212	−	0.124082i
$508$	26.8357	+	12.5137i	1.19064	+	0.555204i
$509$	−5.25087	+	29.7791i	−0.232741	+	1.31994i	0.614580	+	0.788855i	$0.289326\pi$
$509$	−5.25087	+	29.7791i	−0.232741	+	1.31994i	−0.847320	+	0.531082i	$0.821785\pi$
$510$		0			0
$511$	−0.000719528	0	0.000603755i	−3.18300e−5	0	2.67086e-5i
$512$	12.6456	+	12.6456i	0.558861	+	0.558861i
$513$	−1.81596	−	8.95800i	−0.0801765	−	0.395505i
$514$		−	26.5583i		−	1.17144i
$515$		0			0
$516$	26.7684	+	33.2696i	1.17842	+	1.46461i
$517$	−1.09209	−	1.55967i	−0.0480300	−	0.0685940i
$518$	0.000157850	0	0.000338510i	6.93553e−6	0	1.48733e-5i
$519$	3.39618	−	3.88214i	0.149076	−	0.170407i
$520$		0			0
$521$	2.44020	−	1.40885i	0.106907	−	0.0617227i	−0.445593	−	0.895236i	$-0.647007\pi$
$521$	2.44020	−	1.40885i	0.106907	−	0.0617227i	0.552500	+	0.833513i	$0.313674\pi$
$522$	−4.82833	+	37.3792i	−0.211330	+	1.63604i
$523$	−12.7481	+	3.41584i	−0.557436	+	0.149364i	−0.526528	−	0.850158i	$-0.676506\pi$
$523$	−12.7481	+	3.41584i	−0.557436	+	0.149364i	−0.0309077	+	0.999522i	$0.509840\pi$
$524$	−38.7741	−	14.1126i	−1.69385	−	0.616512i
$525$		0			0
$526$	14.4246	+	12.1037i	0.628944	+	0.527747i
$527$	−3.23506	−	36.9769i	−0.140921	−	1.61074i
$528$	−2.13568	+	7.36059i	−0.0929435	+	0.320329i
$529$	−1.06428	+	2.92409i	−0.0462731	+	0.127134i
$530$		0			0
$531$	−2.56506	+	6.23559i	−0.111314	+	0.270602i
$532$	−0.00311841		0.000835576i	−0.000135200		3.62268e-5i
$533$	30.6249	+	21.4438i	1.32651	+	0.928834i
$534$	17.1645	+	15.0159i	0.742780	+	0.649800i
$535$		0			0
$536$	−4.48148	−	0.790206i	−0.193570	−	0.0341317i
$537$	3.08127	−	28.4556i	0.132967	−	1.22795i
$538$	−37.9814	−	3.32294i	−1.63749	−	0.143262i
$539$	−18.9359			−0.815627
$540$		0			0
$541$	−11.4416			−0.491911			−0.245956	−	0.969281i	$-0.579102\pi$
$541$	−11.4416			−0.491911			−0.245956	+	0.969281i	$0.579102\pi$
$542$	−25.9711	−	2.27218i	−1.11556	−	0.0975985i
$543$	13.4643	+	9.84723i	0.577810	+	0.422585i
$544$	48.7984	+	8.60448i	2.09222	+	0.368914i
$545$		0			0
$546$	0.00151975	−	0.00768933i	6.50395e−5	−	0.000329073i
$547$	−26.2542	−	18.3834i	−1.12255	−	0.786018i	−0.143503	−	0.989650i	$-0.545837\pi$
$547$	−26.2542	−	18.3834i	−1.12255	−	0.786018i	−0.979048	+	0.203632i	$0.934726\pi$
$548$	20.0168	+	5.36349i	0.855076	+	0.229117i
$549$	−16.6850	−	10.5724i	−0.712099	−	0.451219i
$550$		0			0
$551$	−3.43769	+	9.44496i	−0.146450	+	0.402369i
$552$	11.2398	+	11.7126i	0.478398	+	0.498522i
$553$	−0.000295160	−	0.00337369i	−1.25515e−5	−	0.000143464i
$554$	33.6943	+	28.2729i	1.43153	+	1.20120i
$555$		0			0
$556$	8.12889	+	2.95868i	0.344742	+	0.125476i
$557$	28.6955	−	7.68893i	1.21587	−	0.325791i	0.406806	−	0.913515i	$-0.366643\pi$
$557$	28.6955	−	7.68893i	1.21587	−	0.325791i	0.809061	+	0.587724i	$0.199976\pi$
$558$	19.3601	+	30.2263i	0.819580	+	1.27958i
$559$	−23.9433	+	13.8237i	−1.01269	+	0.584679i
$560$		0			0
$561$	10.3096	+	30.2498i	0.435271	+	1.27715i
$562$	−7.22858	+	15.5017i	−0.304919	+	0.653902i
$563$	−3.43987	−	4.91264i	−0.144973	−	0.207043i	0.740098	−	0.672499i	$-0.234779\pi$
$563$	−3.43987	−	4.91264i	−0.144973	−	0.207043i	−0.885071	+	0.465456i	$0.845890\pi$
$564$	1.24835	−	3.22176i	0.0525652	−	0.135661i
$565$		0			0
$566$		−	33.0399i		−	1.38877i
$567$	−0.00288940	+	0.00506147i	−0.000121344	+	0.000212562i
$568$	−15.6218	−	15.6218i	−0.655475	−	0.655475i
$569$	−8.00903	+	6.72037i	−0.335756	+	0.281733i	−0.795040	−	0.606557i	$-0.792550\pi$
$569$	−8.00903	+	6.72037i	−0.335756	+	0.281733i	0.459284	+	0.888289i	$0.348106\pi$
$570$		0			0
$571$	−1.98699	+	11.2688i	−0.0831531	+	0.471584i	0.914587	+	0.404390i	$0.132516\pi$
$571$	−1.98699	+	11.2688i	−0.0831531	+	0.471584i	−0.997740	+	0.0671948i	$0.978595\pi$
$572$	22.0848	+	10.2983i	0.923411	+	0.430594i
$573$	1.92786	+	0.947795i	0.0805376	+	0.0395947i
$574$	−0.0164934	+	0.00290823i	−0.000688421	+	0.000121387i
$575$		0			0
$576$	−36.3122	+	11.5467i	−1.51301	+	0.481111i
$577$	−11.8211	−	44.1170i	−0.492120	−	1.83662i	−0.545597	−	0.838047i	$-0.683697\pi$
$577$	−11.8211	−	44.1170i	−0.492120	−	1.83662i	0.0534774	−	0.998569i	$-0.482969\pi$
$578$	58.8308	−	27.4332i	2.44704	−	1.14107i
$579$	15.8790	−	26.2399i	0.659910	−	1.09049i
$580$		0			0
$581$	−0.00666682	+	0.00794521i	−0.000276586	+	0.000329623i
$582$	−23.1249	+	22.1914i	−0.958557	+	0.919862i
$583$	9.27687	+	19.8943i	0.384209	+	0.823938i
$584$	1.33016	−	2.30390i	0.0550424	−	0.0953362i
$585$		0			0
$586$	−24.7911	−	42.9394i	−1.02411	−	1.77381i
$587$	−15.9259	+	22.7446i	−0.657334	+	0.938770i	−1.00000		0.000687603i	$-0.999781\pi$
$587$	−15.9259	+	22.7446i	−0.657334	+	0.938770i	0.342666	+	0.939457i	$0.388670\pi$
$588$	−19.1257	−	28.5483i	−0.788732	−	1.17731i
$589$	3.27398	+	8.99519i	0.134902	+	0.370640i
$590$		0			0
$591$	−4.51088	−	29.0718i	−0.185553	−	1.19585i
$592$	0.0373990	−	0.427473i	0.00153709	−	0.0175690i
$593$	−12.5526	+	12.5526i	−0.515474	+	0.515474i	−0.916199	−	0.400725i	$-0.868758\pi$
$593$	−12.5526	+	12.5526i	−0.515474	+	0.515474i	0.400725	+	0.916199i	$0.368758\pi$
$594$	−22.4029	−	21.2895i	−0.919201	−	0.873519i
$595$		0			0
$596$	−18.4671	−	22.0082i	−0.756441	−	0.901491i
$597$	18.1613	+	1.96657i	0.743291	+	0.0804862i
$598$	−29.2513	+	20.4820i	−1.19617	+	0.837570i
$599$	9.47392	−	3.44823i	0.387094	−	0.140891i	−0.141140	−	0.989990i	$-0.545077\pi$
$599$	9.47392	−	3.44823i	0.387094	−	0.140891i	0.528234	+	0.849099i	$0.322854\pi$
$600$		0			0
$601$	−0.977209	−	5.54203i	−0.0398612	−	0.226064i	0.958369	−	0.285533i	$-0.0921705\pi$
$601$	−0.977209	−	5.54203i	−0.0398612	−	0.226064i	−0.998230	+	0.0594686i	$0.981059\pi$
$602$	0.00320552	−	0.0119631i	0.000130647	−	0.000487581i
$603$	−4.51676	+	5.91619i	−0.183937	+	0.240926i
$604$	45.6522	+	26.3573i	1.85756	+	1.07246i
$605$		0			0
$606$	38.3980	−	21.1269i	1.55981	−	0.858220i
$607$	−12.1412	+	1.06222i	−0.492796	+	0.0431140i	−0.330846	−	0.943685i	$-0.607334\pi$
$607$	−12.1412	+	1.06222i	−0.492796	+	0.0431140i	−0.161950	+	0.986799i	$0.551778\pi$
$608$	−12.7303	+	1.11375i	−0.516280	+	0.0451686i
$609$	0.00561514	−	0.00308949i	0.000227537	−	0.000125192i
$610$		0			0
$611$	1.93736	+	1.11853i	0.0783771	+	0.0452511i
$612$	−35.1924	+	46.0960i	−1.42257	+	1.86332i
$613$	−5.69311	+	21.2470i	−0.229942	+	0.858157i	0.750422	+	0.660960i	$0.229851\pi$
$613$	−5.69311	+	21.2470i	−0.229942	+	0.858157i	−0.980364	+	0.197197i	$0.936816\pi$
$614$	1.92976	+	10.9442i	0.0778789	+	0.441673i
$615$		0			0
$616$	−0.00301917	+	0.00109889i	−0.000121646	+	4.42754e-5i
$617$	5.87642	−	4.11472i	0.236576	−	0.165652i	−0.449277	−	0.893393i	$-0.648318\pi$
$617$	5.87642	−	4.11472i	0.236576	−	0.165652i	0.685853	+	0.727740i	$0.259429\pi$
$618$	−25.9634	−	2.81141i	−1.04440	−	0.113091i
$619$	−0.611202	−	0.728403i	−0.0245663	−	0.0292770i	0.753621	−	0.657309i	$-0.228305\pi$
$619$	−0.611202	−	0.728403i	−0.0245663	−	0.0292770i	−0.778188	+	0.628032i	$0.783861\pi$
$620$		0			0
$621$	25.4640	−	7.52330i	1.02184	−	0.301900i
$622$	30.6554	−	30.6554i	1.22917	−	1.22917i
$623$	0.000337988	−	0.00386323i	1.35412e−5	−	0.000154777i
$624$	−1.38071	−	8.89839i	−0.0552725	−	0.356221i
$625$		0			0
$626$	20.4041	+	56.0599i	0.815513	+	2.24060i
$627$	−4.58726	−	6.84723i	−0.183198	−	0.273452i
$628$	0.525913	−	0.751081i	0.0209862	−	0.0299714i
$629$	−0.894651	−	1.54958i	−0.0356721	−	0.0617859i
$630$		0			0
$631$	−19.0880	+	33.0615i	−0.759883	+	1.31616i	0.183027	+	0.983108i	$0.441411\pi$
$631$	−19.0880	+	33.0615i	−0.759883	+	1.31616i	−0.942910	+	0.333048i	$0.891923\pi$
$632$	4.05368	+	8.69315i	0.161247	+	0.345795i
$633$	0.224759	−	0.215686i	0.00893335	−	0.00857273i
$634$	−0.352787	+	0.420435i	−0.0140110	+	0.0166976i
$635$		0			0
$636$	−20.6233	+	34.0798i	−0.817767	+	1.35135i
$637$	20.1639	−	9.40257i	0.798922	−	0.372543i
$638$	8.79602	+	32.8272i	0.348238	+	1.29964i
$639$	−34.4369	+	10.9503i	−1.36230	+	0.433189i
$640$		0			0
$641$	−24.5606	+	4.33069i	−0.970084	+	0.171052i	−0.636168	−	0.771551i	$-0.719481\pi$
$641$	−24.5606	+	4.33069i	−0.970084	+	0.171052i	−0.333916	+	0.942603i	$0.608370\pi$
$642$	46.7631	+	22.9901i	1.84559	+	0.907348i
$643$	−40.2010	−	18.7461i	−1.58537	−	0.739272i	−0.587808	−	0.809000i	$-0.700009\pi$
$643$	−40.2010	−	18.7461i	−1.58537	−	0.739272i	−0.997566	+	0.0697279i	$0.977787\pi$
$644$	0.00162856	−	0.00923602i	6.41742e−5	−	0.000363950i
$645$		0			0
$646$	−20.2081	+	16.9566i	−0.795078	+	0.667149i
$647$	−4.55768	−	4.55768i	−0.179181	−	0.179181i	0.611818	−	0.790999i	$-0.290439\pi$
$647$	−4.55768	−	4.55768i	−0.179181	−	0.179181i	−0.790999	+	0.611818i	$0.790439\pi$
$648$	2.78707	−	16.2701i	0.109486	−	0.639148i
$649$			6.07983i			0.238654i
$650$		0			0
$651$	0.00220529	−	0.00569145i	8.64323e−5	−	0.000223065i
$652$	8.88773	+	12.6930i	0.348070	+	0.497096i
$653$	2.85735	−	6.12762i	0.111817	−	0.239792i	−0.842434	−	0.538800i	$-0.818878\pi$
$653$	2.85735	−	6.12762i	0.111817	−	0.239792i	0.954251	+	0.299008i	$0.0966557\pi$
$654$	4.59261	+	13.4754i	0.179585	+	0.526928i
$655$		0			0
$656$	−16.6632	+	9.62047i	−0.650587	+	0.375616i
$657$	−2.34695	−	3.66421i	−0.0915631	−	0.142955i
$658$	−0.000967991	0	0.000259372i	−3.77362e−5	0	1.01114e-5i
$659$	−29.5176	−	10.7435i	−1.14984	−	0.418508i	−0.304383	−	0.952550i	$-0.598450\pi$
$659$	−29.5176	−	10.7435i	−1.14984	−	0.418508i	−0.845458	+	0.534042i	$0.820673\pi$
$660$		0			0
$661$	−12.6918	−	10.6497i	−0.493654	−	0.414225i	0.361680	−	0.932302i	$-0.382203\pi$
$661$	−12.6918	−	10.6497i	−0.493654	−	0.414225i	−0.855334	+	0.518078i	$0.826648\pi$
$662$	0.905769	+	10.3530i	0.0352037	+	0.402380i
$663$	−25.9986	−	27.0923i	−1.00970	−	1.05218i
$664$	10.0472	−	27.6043i	0.389905	−	1.07126i
$665$		0			0
$666$	1.46162	+	0.926147i	0.0566365	+	0.0358875i
$667$	−28.2034	−	7.55709i	−1.09204	−	0.292612i
$668$	−42.7520	−	29.9353i	−1.65412	−	1.15823i
$669$	−6.19049	+	31.3213i	−0.239338	+	1.21095i
$670$		0			0
$671$	−17.5405	−	3.09287i	−0.677144	−	0.119399i
$672$	0.00657701	+	0.00481014i	0.000253714	+	0.000185555i
$673$	−7.80022	−	0.682431i	−0.300676	−	0.0263058i	−0.0641806	−	0.997938i	$-0.520443\pi$
$673$	−7.80022	−	0.682431i	−0.300676	−	0.0263058i	−0.236496	+	0.971633i	$0.575999\pi$
$674$	−23.7902			−0.916366
$675$		0			0
$676$	8.21392			0.315920
$677$	−30.1802	−	2.64043i	−1.15992	−	0.101480i	−0.509097	−	0.860709i	$-0.670021\pi$
$677$	−30.1802	−	2.64043i	−1.15992	−	0.101480i	−0.650823	+	0.759229i	$0.725576\pi$
$678$	0.458186	−	4.23136i	0.0175965	−	0.162504i
$679$	0.00536718		0.000946379i	0.000205974		3.63187e-5i
$680$		0			0
$681$	−20.4082	−	17.8536i	−0.782045	−	0.684150i
$682$	26.5133	+	18.5648i	1.01525	+	0.710885i
$683$	−30.0707	−	8.05741i	−1.15062	−	0.308308i	−0.367408	−	0.930060i	$-0.619755\pi$
$683$	−30.0707	−	8.05741i	−1.15062	−	0.308308i	−0.783214	+	0.621752i	$0.786421\pi$
$684$	5.68980	−	13.8317i	0.217555	−	0.528870i
$685$		0			0
$686$	−0.00681755	+	0.0187311i	−0.000260295	+	0.000715155i
$687$	3.41242	−	11.7609i	0.130192	−	0.448705i
$688$	−1.24013	−	14.1747i	−0.0472793	−	0.540405i
$689$	−19.7569	−	16.5780i	−0.752679	−	0.631573i
$690$		0			0
$691$	6.70424	+	2.44014i	0.255041	+	0.0928274i	0.466377	−	0.884586i	$-0.345559\pi$
$691$	6.70424	+	2.44014i	0.255041	+	0.0928274i	−0.211336	+	0.977414i	$0.567781\pi$
$692$	8.15256	−	2.18447i	0.309914	−	0.0830411i
$693$	−0.000673238		0.00521198i	−2.55742e−5		0.000197987i
$694$	−45.8059	+	26.4461i	−1.73877	+	1.00388i
$695$		0			0
$696$	−11.9519	+	13.6621i	−0.453035	+	0.517860i
$697$	−33.9074	+	72.7146i	−1.28433	+	2.75426i
$698$	1.47604	+	2.10801i	0.0558690	+	0.0797892i
$699$	−2.48333	−	3.08645i	−0.0939283	−	0.116740i
$700$		0			0
$701$			18.1226i			0.684482i	0.939612	+	0.342241i	$0.111186\pi$
$701$			18.1226i			0.684482i	−0.939612	+	0.342241i	$0.888814\pi$
$702$	34.4269	+	11.5460i	1.29936	+	0.435777i
$703$	0.326292	+	0.326292i	0.0123064	+	0.0123064i
$704$	−26.3202	+	22.0853i	−0.991981	+	0.832371i
$705$		0			0
$706$	−7.73863	+	43.8880i	−0.291247	+	1.65175i
$707$	−0.00675423	−	0.00314955i	−0.000254019	−	0.000118451i
$708$	−9.16611	+	6.14079i	−0.344484	+	0.230785i
$709$	−20.6080	+	3.63375i	−0.773951	+	0.136469i	−0.546656	−	0.837357i	$-0.684099\pi$
$709$	−20.6080	+	3.63375i	−0.773951	+	0.136469i	−0.227296	+	0.973826i	$0.572988\pi$
$710$		0			0
$711$	15.6757	+	0.646105i	0.587885	+	0.0242308i
$712$	2.84277	+	10.6094i	0.106537	+	0.397603i
$713$	−25.2025	+	11.7521i	−0.943842	+	0.440121i
$714$	0.0168172		0.000346429i	0.000629367		1.29648e-5i
$715$		0			0
$716$	30.1048	−	35.8774i	1.12507	−	1.34080i
$717$	−3.18495	−	12.9474i	−0.118944	−	0.483529i
$718$	−24.3603	−	52.2408i	−0.909117	−	1.94961i
$719$	4.36807	−	7.56572i	0.162902	−	0.282154i	−0.773007	−	0.634398i	$-0.781248\pi$
$719$	4.36807	−	7.56572i	0.162902	−	0.282154i	0.935908	+	0.352244i	$0.114581\pi$
$720$		0			0
$721$	0.00222038	+	0.00384581i	8.26912e−5	+	0.000143225i
$722$	−20.0590	+	28.6472i	−0.746518	+	1.06614i
$723$	−7.33357	+	14.9168i	−0.272738	+	0.554763i
$724$	9.33561	+	25.6494i	0.346955	+	0.953252i
$725$		0			0
$726$	13.0757	+	5.06650i	0.485284	+	0.188035i
$727$	−3.90529	+	44.6377i	−0.144839	+	1.65552i	0.481851	+	0.876253i	$0.339965\pi$
$727$	−3.90529	+	44.6377i	−0.144839	+	1.65552i	−0.626690	+	0.779268i	$0.715591\pi$
$728$	0.00266931	−	0.00266931i	9.89311e−5	−	9.89311e-5i
$729$	−21.5403	−	16.2793i	−0.797787	−	0.602939i
$730$		0			0
$731$	−38.1379	−	45.4510i	−1.41058	−	1.68106i
$732$	−13.0535	−	29.5684i	−0.482471	−	1.09288i
$733$	18.4458	−	12.9159i	0.681312	−	0.477060i	−0.180970	−	0.983489i	$-0.557924\pi$
$733$	18.4458	−	12.9159i	0.681312	−	0.477060i	0.862282	+	0.506429i	$0.169035\pi$
$734$	43.3544	−	15.7797i	1.60024	−	0.582440i
$735$		0			0
$736$	−6.44625	−	36.5585i	−0.237612	−	1.34756i
$737$	−1.73711	+	6.48298i	−0.0639873	+	0.238804i
$738$	−3.57342	−	77.5054i	−0.131540	−	2.85301i
$739$	−29.3820	−	16.9637i	−1.08084	−	0.624020i	−0.149714	−	0.988729i	$-0.547835\pi$
$739$	−29.3820	−	16.9637i	−1.08084	−	0.624020i	−0.931122	+	0.364709i	$0.881168\pi$
$740$		0			0
$741$	8.28471	+	5.01347i	0.304347	+	0.184174i
$742$	0.0115095	−	0.00100695i	0.000422528	−	3.69664e-5i
$743$	−25.4881	+	2.22992i	−0.935068	+	0.0818078i	−0.544495	−	0.838764i	$-0.683279\pi$
$743$	−25.4881	+	2.22992i	−0.935068	+	0.0818078i	−0.390573	+	0.920572i	$0.627723\pi$
$744$	−0.356047	+	17.2840i	−0.0130533	+	0.633664i
$745$		0			0
$746$	3.19968	+	1.84733i	0.117148	+	0.0676357i
$747$	−32.5479	−	35.3463i	−1.19086	−	1.29325i
$748$	−13.5347	+	50.5122i	−0.494878	+	1.84691i
$749$	−0.00153867	−	0.00872624i	−5.62218e−5	−	0.000318850i
$750$		0			0
$751$	−18.3171	+	6.66687i	−0.668400	+	0.243278i	−0.653859	−	0.756617i	$-0.726851\pi$
$751$	−18.3171	+	6.66687i	−0.668400	+	0.243278i	−0.0145411	+	0.999894i	$0.504629\pi$
$752$	−0.943105	+	0.660369i	−0.0343915	+	0.0240812i
$753$	−4.85232	+	6.63468i	−0.176828	+	0.241781i
$754$	−25.6667	−	30.5884i	−0.934726	−	1.11396i
$755$		0			0
$756$	−0.00853770	+	0.00424924i	−0.000310513	+	0.000154543i
$757$	−37.3446	+	37.3446i	−1.35731	+	1.35731i	−0.480097	+	0.877215i	$0.659399\pi$
$757$	−37.3446	+	37.3446i	−1.35731	+	1.35731i	−0.877215	+	0.480097i	$0.840601\pi$
$758$	−2.23509	+	25.5472i	−0.0811822	+	0.927917i
$759$	18.6540	−	15.0088i	0.677096	−	0.544786i
$760$		0			0
$761$	13.8978	+	38.1838i	0.503793	+	1.38416i	0.887543	+	0.460724i	$0.152410\pi$
$761$	13.8978	+	38.1838i	0.503793	+	1.38416i	−0.383750	+	0.923437i	$0.625368\pi$
$762$	39.6976	−	2.65055i	1.43809	−	0.0960194i
$763$	0.00138854	−	0.00198304i	5.02685e−5	−	7.17908e-5i
$764$	1.75761	+	3.04427i	0.0635881	+	0.110138i
$765$		0			0
$766$	11.5732	−	20.0453i	0.418156	−	0.724267i
$767$	−3.01892	−	6.47410i	−0.109007	−	0.233766i
$768$	−6.74076	−	1.95584i	−0.243236	−	0.0705751i
$769$	1.03060	−	1.22823i	0.0371646	−	0.0442910i	−0.747142	−	0.664664i	$-0.768575\pi$
$769$	1.03060	−	1.22823i	0.0371646	−	0.0442910i	0.784307	+	0.620373i	$0.213019\pi$
$770$		0			0
$771$	−10.0855	−	18.3304i	−0.363221	−	0.660153i
$772$	45.4846	−	21.2098i	1.63703	−	0.763358i
$773$	8.72934	+	32.5784i	0.313973	+	1.17176i	0.924942	+	0.380108i	$0.124113\pi$
$773$	8.72934	+	32.5784i	0.313973	+	1.17176i	−0.610970	+	0.791654i	$0.709220\pi$
$774$	53.0627	+	21.8278i	1.90730	+	0.784583i
$775$		0			0
$776$	−15.2015	+	2.68044i	−0.545702	+	0.0962220i
$777$	−1.96020e−5	0	0.000293582i	−7.03220e−7	0	1.05322e-5i
$778$	78.1685	+	36.4506i	2.80248	+	1.30682i
$779$	3.59298	−	20.3768i	0.128732	−	0.730074i
$780$		0			0
$781$	−24.9609	+	20.9447i	−0.893172	+	0.749460i
$782$	−54.1877	−	54.1877i	−1.93775	−	1.93775i
$783$	10.8623	+	27.6325i	0.388186	+	0.987506i
$784$			11.4502i			0.408937i
$785$		0			0
$786$	−54.7877	+	8.50106i	−1.95421	+	0.303223i
$787$	1.32801	+	1.89659i	0.0473384	+	0.0676063i	0.842123	−	0.539285i	$-0.181305\pi$
$787$	1.32801	+	1.89659i	0.0473384	+	0.0676063i	−0.794785	+	0.606891i	$0.792416\pi$
$788$	20.3448	−	43.6296i	0.724754	−	1.55424i
$789$	14.5522	+	2.87616i	0.518072	+	0.102394i
$790$		0			0
$791$	−0.000626766	0	0.000361864i	−2.22852e−5	0	1.28664e-5i
$792$	−3.25705	−	14.5238i	−0.115734	−	0.516082i
$793$	20.2138	−	5.41626i	0.717812	−	0.192337i
$794$	21.5293	+	7.83603i	0.764047	+	0.278090i
$795$		0			0
$796$	22.8981	+	19.2138i	0.811602	+	0.681015i
$797$	1.45181	+	16.5943i	0.0514259	+	0.587801i	0.977567	+	0.210624i	$0.0675495\pi$
$797$	1.45181	+	16.5943i	0.0514259	+	0.587801i	−0.926141	+	0.377177i	$0.876895\pi$
$798$	−0.00421236	+	0.00103621i	−0.000149116	+	3.66813e-5i
$799$	−1.64198	+	4.51129i	−0.0580889	+	0.159598i
$800$		0			0
$801$	17.5491	+	3.84565i	0.620068	+	0.135880i
$802$	56.8031	+	15.2204i	2.00579	+	0.537449i
$803$	−3.21410	−	2.25054i	−0.113423	−	0.0794197i
$804$	−11.5284	+	3.92907i	−0.406577	+	0.138568i
$805$		0			0
$806$	−37.4510	−	6.60363i	−1.31916	−	0.232603i
$807$	−27.4765	+	12.1300i	−0.967217	+	0.426995i
$808$	21.0273	+	1.83965i	0.739739	+	0.0647188i
$809$	38.2899			1.34620			0.673100	−	0.739551i	$-0.264962\pi$
$809$	38.2899			1.34620			0.673100	+	0.739551i	$0.264962\pi$
$810$		0			0
$811$	48.1974			1.69244			0.846220	−	0.532833i	$-0.178873\pi$
$811$	48.1974			1.69244			0.846220	+	0.532833i	$0.178873\pi$
$812$	0.0104472		0.000914012i	0.000366625		3.20755e-5i
$813$	−18.7880	+	8.29429i	−0.658924	+	0.290894i
$814$	1.53656	+	0.270937i	0.0538564	+	0.00949633i
$815$		0			0
$816$	18.2916	−	6.23404i	0.640332	−	0.218235i
$817$	12.5341	+	8.77644i	0.438511	+	0.307049i
$818$	−72.5455	−	19.4385i	−2.53649	−	0.679652i
$819$	−0.00187110	−	0.00588427i	−6.53814e−5	−	0.000205613i
$820$		0			0
$821$	5.73809	−	15.7653i	0.200261	−	0.550212i	−0.798390	−	0.602141i	$-0.794315\pi$
$821$	5.73809	−	15.7653i	0.200261	−	0.550212i	0.998651	+	0.0519288i	$0.0165369\pi$
$822$	27.0388	−	6.65131i	0.943086	−	0.231991i
$823$	3.01595	+	34.4725i	0.105130	+	1.20164i	0.847185	+	0.531298i	$0.178295\pi$
$823$	3.01595	+	34.4725i	0.105130	+	1.20164i	−0.742056	+	0.670338i	$0.766149\pi$
$824$	−9.63498	−	8.08471i	−0.335651	−	0.281644i
$825$		0			0
$826$	0.00300703	+	0.00109447i	0.000104628	+	3.80815e-5i
$827$	−19.5339	+	5.23409i	−0.679261	+	0.182007i	−0.581923	−	0.813244i	$-0.697699\pi$
$827$	−19.5339	+	5.23409i	−0.679261	+	0.182007i	−0.0973378	+	0.995251i	$0.531033\pi$
$828$	41.4687	+	12.9639i	1.44114	+	0.450526i
$829$	45.7476	−	26.4124i	1.58888	−	0.917340i	0.595387	−	0.803439i	$-0.296999\pi$
$829$	45.7476	−	26.4124i	1.58888	−	0.917340i	0.993492	−	0.113900i	$-0.0363344\pi$
$830$		0			0
$831$	33.9923	+	6.71839i	1.17918	+	0.233059i
$832$	17.0607	−	36.5867i	0.591473	−	1.26842i
$833$	27.3858	+	39.1110i	0.948861	+	1.35511i
$834$	11.4861	−	1.78223i	0.397732	−	0.0617135i
$835$		0			0
$836$		−	13.4862i		−	0.466432i
$837$	24.8407	+	13.5101i	0.858621	+	0.466976i
$838$	24.8475	+	24.8475i	0.858342	+	0.858342i
$839$	−1.94021	+	1.62803i	−0.0669835	+	0.0562059i	−0.675665	−	0.737209i	$-0.736143\pi$
$839$	−1.94021	+	1.62803i	−0.0669835	+	0.0562059i	0.608681	+	0.793415i	$0.291699\pi$
$840$		0			0
$841$	0.633784	−	3.59437i	0.0218546	−	0.123944i
$842$	63.4780	+	29.6003i	2.18760	+	1.02009i
$843$	0.897656	+	13.4443i	0.0309169	+	0.463046i
$844$	0.501982	−	0.0885129i	0.0172789	−	0.00304674i
$845$		0			0
$846$	−0.617209	−	4.60140i	−0.0212201	−	0.158199i
$847$	−0.000617162	−	0.00230328i	−2.12059e−5	−	7.91417e-5i
$848$	12.0298	−	5.60957i	0.413104	−	0.192634i
$849$	−12.5469	−	22.8040i	−0.430609	−	0.782631i
$850$		0			0
$851$	−0.861655	+	1.02688i	−0.0295371	+	0.0352010i
$852$	−56.7879	−	16.4770i	−1.94552	−	0.564494i
$853$	−17.6637	−	37.8798i	−0.604792	−	1.29698i	−0.935526	−	0.353257i	$-0.885074\pi$
$853$	−17.6637	−	37.8798i	−0.604792	−	1.29698i	0.330734	−	0.943724i	$-0.392704\pi$
$854$	−0.00468729	+	0.00811862i	−0.000160396	+	0.000277813i
$855$		0			0
$856$	12.5483	+	21.7343i	0.428893	+	0.742864i
$857$	15.3891	−	21.9778i	0.525680	−	0.750749i	−0.465242	−	0.885183i	$-0.654033\pi$
$857$	15.3891	−	21.9778i	0.525680	−	0.750749i	0.990923	+	0.134434i	$0.0429217\pi$
$858$	32.6697	−	2.18131i	1.11532	−	0.0744687i
$859$	7.80591	+	21.4466i	0.266334	+	0.731747i	0.998707	+	0.0508429i	$0.0161908\pi$
$859$	7.80591	+	21.4466i	0.266334	+	0.731747i	−0.732372	+	0.680904i	$0.761587\pi$
$860$		0			0
$861$	−0.0102793	+	0.00827062i	−0.000350316	+	0.000281862i
$862$	−1.13765	+	13.0034i	−0.0387484	+	0.442896i
$863$	7.93097	−	7.93097i	0.269973	−	0.269973i	−0.559116	−	0.829089i	$-0.688859\pi$
$863$	7.93097	−	7.93097i	0.269973	−	0.269973i	0.829089	+	0.559116i	$0.188859\pi$
$864$	−26.0037	+	27.3635i	−0.884663	+	0.930927i
$865$		0			0
$866$	15.4685	+	18.4346i	0.525641	+	0.626434i
$867$	30.1869	−	41.2753i	1.02520	−	1.40178i
$868$	0.00818145	−	0.00572871i	0.000277696	−	0.000194445i
$869$	13.2938	−	4.83854i	0.450961	−	0.164136i
$870$		0			0
$871$	−1.36935	−	7.76596i	−0.0463986	−	0.263139i
$872$	−1.77461	+	6.62293i	−0.0600959	+	0.224281i
$873$	−7.53350	+	24.0980i	−0.254970	+	0.815595i
$874$	17.1153	+	9.88153i	0.578934	+	0.334248i
$875$		0			0
$876$	0.146645	−	7.11876i	0.00495466	−	0.240521i
$877$	−0.977840	+	0.0855499i	−0.0330193	+	0.00288882i	−0.103653	−	0.994613i	$-0.533053\pi$
$877$	−0.977840	+	0.0855499i	−0.0330193	+	0.00288882i	0.0706341	+	0.997502i	$0.477498\pi$
$878$	−63.7167	+	5.57448i	−2.15033	+	0.188130i
$879$	−33.4170	−	20.2222i	−1.12713	−	0.682077i
$880$		0			0
$881$	22.3414	+	12.8988i	0.752701	+	0.434572i	0.826669	−	0.562689i	$-0.190233\pi$
$881$	22.3414	+	12.8988i	0.752701	+	0.434572i	−0.0739682	+	0.997261i	$0.523566\pi$
$882$	−41.0072	−	21.2200i	−1.38078	−	0.714515i
$883$	12.4224	−	46.3611i	0.418048	−	1.56018i	−0.360604	−	0.932719i	$-0.617429\pi$
$883$	12.4224	−	46.3611i	0.418048	−	1.56018i	0.778652	−	0.627457i	$-0.215904\pi$
$884$	−10.6693	−	60.5085i	−0.358847	−	2.03512i
$885$		0			0
$886$	−56.0866	+	20.4139i	−1.88427	+	0.685817i
$887$	5.46649	−	3.82768i	0.183547	−	0.128521i	−0.478192	−	0.878255i	$-0.658708\pi$
$887$	5.46649	−	3.82768i	0.183547	−	0.128521i	0.661739	+	0.749734i	$0.269819\pi$
$888$	0.336565	+	0.762379i	0.0112944	+	0.0255837i
$889$	−0.00434872	−	0.00518260i	−0.000145851	−	0.000173819i
$890$		0			0
$891$	−23.5470	−	6.18643i	−0.788856	−	0.207253i
$892$	−36.9415	+	36.9415i	−1.23689	+	1.23689i
$893$	0.107907	−	1.23338i	0.00361097	−	0.0412735i
$894$	−35.9956	−	13.9474i	−1.20387	−	0.466471i
$895$		0			0
$896$	0.00296711	+	0.00815206i	9.91241e−5	+	0.000272341i
$897$	−12.4111	+	25.2447i	−0.414393	+	0.842897i
$898$	−4.38105	+	6.25679i	−0.146198	+	0.208792i
$899$	−15.5475	−	26.9291i	−0.518538	−	0.898134i
$900$		0			0
$901$	27.6739	−	47.9327i	0.921953	−	1.59687i
$902$	−29.5671	−	63.4068i	−0.984476	−	2.11121i
$903$	−0.00233057	−	0.00947420i	−7.75567e−5	−	0.000315282i
$904$	1.31760	−	1.57025i	0.0438226	−	0.0522258i
$905$		0			0
$906$	70.8162	+	1.45879i	2.35271	+	0.0484652i
$907$	−1.07303	+	0.500360i	−0.0356292	+	0.0166142i	−0.440351	−	0.897826i	$-0.645146\pi$
$907$	−1.07303	+	0.500360i	−0.0356292	+	0.0166142i	0.404722	+	0.914440i	$0.367368\pi$
$908$	−11.4837	−	42.8576i	−0.381099	−	1.42228i
$909$	18.4792	−	29.1633i	0.612917	−	0.967286i
$910$		0			0
$911$	−27.0446	+	4.76870i	−0.896028	+	0.157994i	−0.602653	−	0.798003i	$-0.705890\pi$
$911$	−27.0446	+	4.76870i	−0.896028	+	0.157994i	−0.293375	+	0.955997i	$0.594779\pi$
$912$	−4.14041	+	2.77384i	−0.137103	+	0.0918511i
$913$	−39.2670	−	18.3105i	−1.29955	−	0.605990i
$914$	9.00761	−	51.0847i	0.297945	−	1.68973i
$915$		0			0
$916$	15.3502	−	12.8803i	0.507185	−	0.425578i
$917$	0.00666650	+	0.00666650i	0.000220147	+	0.000220147i
$918$	−11.5724	+	77.0614i	−0.381945	+	2.54341i
$919$			21.2332i			0.700419i	0.936671	+	0.350209i	$0.113890\pi$
$919$			21.2332i			0.700419i	−0.936671	+	0.350209i	$0.886110\pi$
$920$		0			0
$921$	5.48799	+	6.82083i	0.180835	+	0.224754i
$922$	10.0970	+	14.4200i	0.332528	+	0.474899i
$923$	16.1796	−	34.6972i	0.532557	−	1.14207i
$924$	−0.00566203	+	0.00647222i	−0.000186267	+	0.000212920i
$925$		0			0
$926$	−4.49731	+	2.59652i	−0.147791	+	0.0853270i
$927$	−18.9874	+	7.91918i	−0.623630	+	0.260100i
$928$	40.0962	−	10.7437i	1.31622	−	0.352680i
$929$	−28.3403	−	10.3150i	−0.929816	−	0.338425i	−0.167679	−	0.985842i	$-0.553627\pi$
$929$	−28.3403	−	10.3150i	−0.929816	−	0.338425i	−0.762136	+	0.647416i	$0.775850\pi$
$930$		0			0
$931$	−9.43249	−	7.91479i	−0.309137	−	0.259397i
$932$	−0.564962	−	6.45754i	−0.0185059	−	0.211524i
$933$	9.51681	−	32.7996i	0.311566	−	1.07381i
$934$	−15.4682	+	42.4985i	−0.506135	+	1.39059i
$935$		0			0
$936$	10.6800	+	13.8484i	0.349088	+	0.452650i
$937$	−16.5394	−	4.43173i	−0.540320	−	0.144778i	−0.0216704	−	0.999765i	$-0.506898\pi$
$937$	−16.5394	−	4.43173i	−0.540320	−	0.144778i	−0.518650	+	0.854987i	$0.673565\pi$
$938$	0.00289372	+	0.00202620i	9.44832e−5	+	6.61579e-5i
$939$	35.3716	+	30.9438i	1.15431	+	1.00981i
$940$		0			0
$941$	−21.0459	−	3.71097i	−0.686078	−	0.120974i	−0.180266	−	0.983618i	$-0.557696\pi$
$941$	−21.0459	−	3.71097i	−0.686078	−	0.120974i	−0.505812	+	0.862644i	$0.668807\pi$
$942$	0.132632	−	1.22485i	0.00432137	−	0.0399079i
$943$	59.8787	+	5.23871i	1.94992	+	0.170596i
$944$	3.67638			0.119656
$945$		0			0
$946$	51.7372			1.68212
$947$	28.3818	+	2.48308i	0.922284	+	0.0806894i	0.538398	−	0.842691i	$-0.319030\pi$
$947$	28.3818	+	2.48308i	0.922284	+	0.0806894i	0.383886	+	0.923380i	$0.374585\pi$
$948$	20.7218	+	15.1550i	0.673012	+	0.492211i
$949$	4.54003	+	0.800530i	0.147376	+	0.0259863i
$950$		0			0
$951$	−0.0838316	+	0.424153i	−0.00271843	+	0.0137541i
$952$	0.00663611	+	0.00464666i	0.000215078	+	0.000150599i
$953$	−48.9558	−	13.1177i	−1.58583	−	0.424923i	−0.645108	−	0.764091i	$-0.723188\pi$
$953$	−48.9558	−	13.1177i	−1.58583	−	0.424923i	−0.940726	+	0.339169i	$0.889854\pi$
$954$	−2.20422	+	53.4786i	−0.0713644	+	1.73143i
$955$		0			0
$956$	7.46208	−	20.5019i	0.241341	−	0.663078i
$957$	18.5371	+	19.3169i	0.599220	+	0.624426i
$958$	4.12901	+	47.1948i	0.133402	+	1.52479i
$959$	−0.00362713	−	0.00304352i	−0.000117126	−	9.82804e-5i
$960$		0			0
$961$	1.30221	+	0.473965i	0.0420067	+	0.0152892i
$962$	−1.77074	+	0.474467i	−0.0570908	+	0.0152974i
$963$	41.0062	−	1.89061i	1.32141	−	0.0609240i
$964$	−23.5551	+	13.5995i	−0.758657	+	0.438011i
$965$		0			0
$966$	−0.00406522	−	0.0119279i	−0.000130796	−	0.000383775i
$967$	22.4321	−	48.1057i	0.721366	−	1.54697i	−0.111663	−	0.993746i	$-0.535618\pi$
$967$	22.4321	−	48.1057i	0.721366	−	1.54697i	0.833029	−	0.553229i	$-0.186604\pi$
$968$	3.87378	+	5.53233i	0.124508	+	0.177816i
$969$	−7.50827	+	19.3774i	−0.241200	+	0.622492i
$970$		0			0
$971$			12.4548i			0.399695i	0.979827	+	0.199847i	$0.0640447\pi$
$971$			12.4548i			0.399695i	−0.979827	+	0.199847i	$0.935955\pi$
$972$	−14.4563	−	41.7486i	−0.463686	−	1.33909i
$973$	−0.00139762	−	0.00139762i	−4.48056e−5	−	4.48056e-5i
$974$	−5.24344	+	4.39976i	−0.168011	+	0.140978i
$975$		0			0
$976$	−1.87021	+	10.6065i	−0.0598639	+	0.339505i
$977$	17.1398	+	7.99244i	0.548352	+	0.255701i	0.676992	−	0.735991i	$-0.263283\pi$
$977$	17.1398	+	7.99244i	0.548352	+	0.255701i	−0.128639	+	0.991691i	$0.541061\pi$
$978$	18.6846	+	9.18592i	0.597469	+	0.293733i
$979$	15.9536	−	2.81305i	0.509879	−	0.0899055i
$980$		0			0
$981$	8.28706	+	7.55658i	0.264586	+	0.241263i
$982$	−4.69139	−	17.5085i	−0.149708	−	0.558719i
$983$	−12.0933	+	5.63921i	−0.385717	+	0.179863i	−0.605798	−	0.795619i	$-0.707146\pi$
$983$	−12.0933	+	5.63921i	−0.385717	+	0.179863i	0.220080	+	0.975482i	$0.429368\pi$
$984$	19.3464	−	31.9698i	0.616742	−	1.01916i
$985$		0			0
$986$	55.0815	−	65.6436i	1.75415	−	2.09052i
$987$	−0.000569606	0	0.000546612i	−1.81308e−5	0	1.73989e-5i
$988$	6.69656	+	14.3608i	0.213046	+	0.456878i
$989$	−22.2250	+	38.4948i	−0.706713	+	1.22406i
$990$		0			0
$991$	−2.99736	−	5.19158i	−0.0952142	−	0.164916i	0.814484	−	0.580186i	$-0.197020\pi$
$991$	−2.99736	−	5.19158i	−0.0952142	−	0.164916i	−0.909698	+	0.415270i	$0.863687\pi$
$992$	22.6757	−	32.3842i	0.719953	−	1.02820i
$993$	4.55670	+	6.80161i	0.144603	+	0.215843i
$994$	0.00586569	+	0.0161158i	0.000186048	+	0.000511163i
$995$		0			0
$996$	−12.0553	−	77.6941i	−0.381987	−	2.46183i
$997$	3.98279	−	45.5235i	0.126136	−	1.44174i	−0.624498	−	0.781026i	$-0.714696\pi$
$997$	3.98279	−	45.5235i	0.126136	−	1.44174i	0.750634	−	0.660718i	$-0.229748\pi$
$998$	41.0167	−	41.0167i	1.29836	−	1.29836i
$999$	1.36051	+	0.0841734i	0.0430445	+	0.00266313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.518.14		192
5.2	odd	4	inner	675.2.ba.b.32.3		192
5.3	odd	4		135.2.q.a.32.14	✓	192
5.4	even	2		135.2.q.a.113.3	yes	192
15.8	even	4		405.2.r.a.287.3		192
15.14	odd	2		405.2.r.a.368.14		192
27.11	odd	18	inner	675.2.ba.b.443.3		192
135.38	even	36		135.2.q.a.92.3	yes	192
135.43	odd	36		405.2.r.a.197.14		192
135.92	even	36	inner	675.2.ba.b.632.14		192
135.119	odd	18		135.2.q.a.38.14	yes	192
135.124	even	18		405.2.r.a.278.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.14	✓	192	5.3	odd	4
135.2.q.a.38.14	yes	192	135.119	odd	18
135.2.q.a.92.3	yes	192	135.38	even	36
135.2.q.a.113.3	yes	192	5.4	even	2
405.2.r.a.197.14		192	135.43	odd	36
405.2.r.a.278.3		192	135.124	even	18
405.2.r.a.287.3		192	15.8	even	4
405.2.r.a.368.14		192	15.14	odd	2
675.2.ba.b.32.3		192	5.2	odd	4	inner
675.2.ba.b.443.3		192	27.11	odd	18	inner
675.2.ba.b.518.14		192	1.1	even	1	trivial
675.2.ba.b.632.14		192	135.92	even	36	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19031 + 0.191628i) q^{2} +(1.58451 - 0.699511i) q^{3} +(2.79113 + 0.492152i) q^{4} +(3.60463 - 1.22851i) q^{6} +(-0.000530458 - 0.000371431i) q^{7} +(1.77162 + 0.474704i) q^{8} +(2.02137 - 2.21677i) q^{9} +(0.925209 - 2.54199i) q^{11} +(4.76685 - 1.17261i) q^{12} +(0.277011 + 3.16625i) q^{13} +(-0.00109069 - 0.000915200i) q^{14} +(-1.53710 - 0.559459i) q^{16} +(-6.58840 + 1.76536i) q^{17} +(4.85222 - 4.46807i) q^{18} +(1.52337 - 0.879517i) q^{19} +(-0.00110034 - 0.000217476i) q^{21} +(2.51361 - 5.39046i) q^{22} +(2.93096 + 4.18584i) q^{23} +(3.13922 - 0.487092i) q^{24} +6.98815i q^{26} +(1.65223 - 4.92647i) q^{27} +(-0.00129778 - 0.00129778i) q^{28} +(-4.37718 + 3.67289i) q^{29} +(-0.944975 + 5.35922i) q^{31} +(-6.58407 - 3.07020i) q^{32} +(-0.312144 - 4.67501i) q^{33} +(-14.7689 + 2.60416i) q^{34} +(6.73289 - 5.19248i) q^{36} +(0.0678960 + 0.253391i) q^{37} +(3.50519 - 1.63450i) q^{38} +(2.65375 + 4.82319i) q^{39} +(7.56097 - 9.01082i) q^{41} +(-0.00236841 - 0.000687195i) q^{42} +(3.67622 + 7.88368i) q^{43} +(3.83342 - 6.63969i) q^{44} +(5.61759 + 9.72995i) q^{46} +(0.403711 - 0.576559i) q^{47} +(-2.82690 + 0.188748i) q^{48} +(-2.39414 - 6.57785i) q^{49} +(-9.20452 + 7.40589i) q^{51} +(-0.785101 + 8.97374i) q^{52} +(-5.73786 + 5.73786i) q^{53} +(4.56295 - 10.4739i) q^{54} +(-0.000763450 - 0.000909845i) q^{56} +(1.79857 - 2.45922i) q^{57} +(-10.2912 + 7.20599i) q^{58} +(-2.11198 + 0.768697i) q^{59} +(-1.14333 - 6.48417i) q^{61} +(-3.09676 + 11.5573i) q^{62} +(-0.00189563 + 0.000425105i) q^{63} +(-10.9996 - 6.35064i) q^{64} +(0.212168 - 10.2996i) q^{66} +(-2.47165 + 0.216242i) q^{67} +(-19.2579 + 1.68485i) q^{68} +(7.57218 + 4.58228i) q^{69} +(-10.4316 - 6.02267i) q^{71} +(4.63341 - 2.96772i) q^{72} +(0.375408 - 1.40104i) q^{73} +(0.100157 + 0.568017i) q^{74} +(4.68478 - 1.70512i) q^{76} +(-0.00143496 + 0.00100477i) q^{77} +(4.88829 + 11.0728i) q^{78} +(3.36157 + 4.00616i) q^{79} +(-0.828138 - 8.96182i) q^{81} +(18.2876 - 18.2876i) q^{82} +(1.39592 - 15.9554i) q^{83} +(-0.00296416 - 0.00114854i) q^{84} +(6.54134 + 17.9722i) q^{86} +(-4.36647 + 8.88163i) q^{87} +(2.84581 - 4.06424i) q^{88} +(2.99426 + 5.18621i) q^{89} +(0.00102910 - 0.00178245i) q^{91} +(6.12062 + 13.1257i) q^{92} +(2.25151 + 9.15278i) q^{93} +(0.994737 - 1.18548i) q^{94} +(-12.5802 - 0.259149i) q^{96} +(-7.62753 + 3.55678i) q^{97} +(-3.98342 - 14.8663i) q^{98} +(-3.76482 - 7.18927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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