LMFDB - Embedded newform 722.2.e.o.423.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [722,2,Mod(99,722)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(722, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("722.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,-6,6,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.186694177220038656.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 343x^{6} + 117649 $ x^12 + 343*x^6 + 117649
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			423.1
Root			$2.48619 - 0.904900i$ of defining polynomial
Character	$\chi$	$=$	722.423
Dual form			722.2.e.o.99.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.459430 + 2.60556i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.26072 - 1.05787i) q^{5} +(0.459430 + 2.60556i) q^{6} +(-1.82288 - 3.15731i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-3.75877 - 1.36808i) q^{9} +(-1.54650 - 0.562880i) q^{10} +(2.32288 - 4.02334i) q^{11} +(1.32288 + 2.29129i) q^{12} +(-0.347296 - 1.96962i) q^{13} +(-2.79281 - 2.34344i) q^{14} +(3.33555 - 2.79886i) q^{15} +(0.173648 - 0.984808i) q^{16} -4.00000 q^{18} -1.64575 q^{20} +(9.06404 - 3.29904i) q^{21} +(0.806726 - 4.57517i) q^{22} +(-1.26072 + 1.05787i) q^{23} +(2.02676 + 1.70066i) q^{24} +(-0.397915 - 2.25669i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(1.32288 - 2.29129i) q^{27} +(-3.42589 - 1.24692i) q^{28} +(1.54650 + 0.562880i) q^{29} +(2.17712 - 3.77089i) q^{30} +(-2.82288 - 4.88936i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(9.41584 + 7.90083i) q^{33} +(-1.04189 + 5.90885i) q^{35} +(-3.75877 + 1.36808i) q^{36} -0.354249 q^{37} +5.29150 q^{39} +(-1.54650 + 0.562880i) q^{40} +(0.0506189 - 0.287074i) q^{41} +(7.38907 - 6.20017i) q^{42} +(8.64979 + 7.25804i) q^{43} +(-0.806726 - 4.57517i) q^{44} +(3.29150 + 5.70105i) q^{45} +(-0.822876 + 1.42526i) q^{46} +(-4.09166 - 1.48924i) q^{47} +(2.48619 + 0.904900i) q^{48} +(-3.14575 + 5.44860i) q^{49} +(-1.14575 - 1.98450i) q^{50} +(-1.53209 - 1.28558i) q^{52} +(9.63914 - 8.08820i) q^{53} +(0.459430 - 2.60556i) q^{54} +(-7.18466 + 2.61500i) q^{55} -3.64575 q^{56} +1.64575 q^{58} +(-7.45858 + 2.71470i) q^{59} +(0.756107 - 4.28810i) q^{60} +(0.717978 - 0.602455i) q^{61} +(-4.32490 - 3.62902i) q^{62} +(2.53231 + 14.3615i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.64575 + 2.85052i) q^{65} +(11.5502 + 4.20394i) q^{66} +(0.606808 + 0.220860i) q^{67} +(-2.17712 - 3.77089i) q^{69} +(1.04189 + 5.90885i) q^{70} +(2.07483 + 1.74099i) q^{71} +(-3.06418 + 2.57115i) q^{72} +(0.296677 - 1.68254i) q^{73} +(-0.332885 + 0.121160i) q^{74} +6.06275 q^{75} -16.9373 q^{77} +(4.97239 - 1.80980i) q^{78} +(0.694593 - 3.93923i) q^{79} +(-1.26072 + 1.05787i) q^{80} +(-3.83022 - 3.21394i) q^{81} +(-0.0506189 - 0.287074i) q^{82} +(-3.96863 - 6.87386i) q^{83} +(4.82288 - 8.35347i) q^{84} +(10.6105 + 3.86192i) q^{86} +(-2.17712 + 3.77089i) q^{87} +(-2.32288 - 4.02334i) q^{88} +(5.04287 + 4.23147i) q^{90} +(-5.58562 + 4.68689i) q^{91} +(-0.285782 + 1.62075i) q^{92} +(14.0364 - 5.10884i) q^{93} -4.35425 q^{94} +2.64575 q^{96} +(-3.48485 + 1.26838i) q^{97} +(-1.09251 + 6.19592i) q^{98} +(-14.2354 + 11.9449i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} + 6 q^{8} + 12 q^{11} - 48 q^{18} + 12 q^{20} - 12 q^{26} + 42 q^{30} - 18 q^{31} - 36 q^{37} - 24 q^{45} + 6 q^{46} - 6 q^{49} + 18 q^{50} - 12 q^{56} - 12 q^{58} - 6 q^{64} + 12 q^{65}+ \cdots - 84 q^{94}+O(q^{100}) $ 12 * q - 6 * q^7 + 6 * q^8 + 12 * q^11 - 48 * q^18 + 12 * q^20 - 12 * q^26 + 42 * q^30 - 18 * q^31 - 36 * q^37 - 24 * q^45 + 6 * q^46 - 6 * q^49 + 18 * q^50 - 12 * q^56 - 12 * q^58 - 6 * q^64 + 12 * q^65 - 42 * q^69 + 168 * q^75 - 108 * q^77 + 42 * q^84 - 42 * q^87 - 12 * q^88 - 84 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−0.459430	+	2.60556i	−0.265252	+	1.50432i	0.503065	+	0.864249i	$0.332206\pi$
$3$	−0.459430	+	2.60556i	−0.265252	+	1.50432i	−0.768317	+	0.640070i	$0.778905\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−1.26072	−	1.05787i	−0.563811	−	0.473093i	0.315775	−	0.948834i	$-0.397736\pi$
$5$	−1.26072	−	1.05787i	−0.563811	−	0.473093i	−0.879585	+	0.475741i	$0.842180\pi$
$6$	0.459430	+	2.60556i	0.187561	+	1.06371i
$7$	−1.82288	−	3.15731i	−0.688982	−	1.19335i	−0.972167	−	0.234287i	$-0.924724\pi$
$7$	−1.82288	−	3.15731i	−0.688982	−	1.19335i	0.283185	−	0.959065i	$-0.408609\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−3.75877	−	1.36808i	−1.25292	−	0.456027i
$10$	−1.54650	−	0.562880i	−0.489046	−	0.177998i
$11$	2.32288	−	4.02334i	0.700373	−	1.21308i	−0.267962	−	0.963429i	$-0.586350\pi$
$11$	2.32288	−	4.02334i	0.700373	−	1.21308i	0.968335	−	0.249653i	$-0.0803165\pi$
$12$	1.32288	+	2.29129i	0.381881	+	0.661438i
$13$	−0.347296	−	1.96962i	−0.0963227	−	0.546273i	−0.994334	−	0.106301i	$-0.966099\pi$
$13$	−0.347296	−	1.96962i	−0.0963227	−	0.546273i	0.898011	−	0.439972i	$-0.145012\pi$
$14$	−2.79281	−	2.34344i	−0.746409	−	0.626312i
$15$	3.33555	−	2.79886i	0.861235	−	0.722662i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$17$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$18$	−4.00000			−0.942809
$19$		0			0
$19$		0			0
$20$	−1.64575			−0.368001
$21$	9.06404	−	3.29904i	1.97794	−	0.719910i
$22$	0.806726	−	4.57517i	0.171995	−	0.975430i
$23$	−1.26072	+	1.05787i	−0.262878	+	0.220581i	−0.764694	−	0.644394i	$-0.777110\pi$
$23$	−1.26072	+	1.05787i	−0.262878	+	0.220581i	0.501816	+	0.864974i	$0.332665\pi$
$24$	2.02676	+	1.70066i	0.413711	+	0.347145i
$25$	−0.397915	−	2.25669i	−0.0795831	−	0.451338i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	1.32288	−	2.29129i	0.254588	−	0.440959i
$28$	−3.42589	−	1.24692i	−0.647432	−	0.235646i
$29$	1.54650	+	0.562880i	0.287178	+	0.104524i	0.481593	−	0.876395i	$-0.340059\pi$
$29$	1.54650	+	0.562880i	0.287178	+	0.104524i	−0.194415	+	0.980919i	$0.562281\pi$
$30$	2.17712	−	3.77089i	0.397487	−	0.688467i
$31$	−2.82288	−	4.88936i	−0.507003	−	0.878156i	−0.999967	−	0.00810584i	$-0.997420\pi$
$31$	−2.82288	−	4.88936i	−0.507003	−	0.878156i	0.492964	−	0.870050i	$-0.335914\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	9.41584	+	7.90083i	1.63909	+	1.37536i
$34$		0			0
$35$	−1.04189	+	5.90885i	−0.176111	+	0.998777i
$36$	−3.75877	+	1.36808i	−0.626462	+	0.228013i
$37$	−0.354249			−0.0582381			−0.0291191	−	0.999576i	$-0.509270\pi$
$37$	−0.354249			−0.0582381			−0.0291191	+	0.999576i	$0.509270\pi$
$38$		0			0
$39$	5.29150			0.847319
$40$	−1.54650	+	0.562880i	−0.244523	+	0.0889992i
$41$	0.0506189	−	0.287074i	0.00790534	−	0.0448334i	−0.980600	−	0.196020i	$-0.937198\pi$
$41$	0.0506189	−	0.287074i	0.00790534	−	0.0448334i	0.988505	+	0.151186i	$0.0483094\pi$
$42$	7.38907	−	6.20017i	1.14016	−	0.956707i
$43$	8.64979	+	7.25804i	1.31908	+	1.10684i	0.986499	+	0.163766i	$0.0523642\pi$
$43$	8.64979	+	7.25804i	1.31908	+	1.10684i	0.332582	+	0.943074i	$0.392080\pi$
$44$	−0.806726	−	4.57517i	−0.121619	−	0.689733i
$45$	3.29150	+	5.70105i	0.490668	+	0.849862i
$46$	−0.822876	+	1.42526i	−0.121326	+	0.210143i
$47$	−4.09166	−	1.48924i	−0.596829	−	0.217228i	0.0259012	−	0.999665i	$-0.491754\pi$
$47$	−4.09166	−	1.48924i	−0.596829	−	0.217228i	−0.622730	+	0.782436i	$0.713977\pi$
$48$	2.48619	+	0.904900i	0.358851	+	0.130611i
$49$	−3.14575	+	5.44860i	−0.449393	+	0.778372i
$50$	−1.14575	−	1.98450i	−0.162034	−	0.280651i
$51$		0			0
$52$	−1.53209	−	1.28558i	−0.212463	−	0.178277i
$53$	9.63914	−	8.08820i	1.32404	−	1.11100i	0.338606	−	0.940928i	$-0.390045\pi$
$53$	9.63914	−	8.08820i	1.32404	−	1.11100i	0.985432	−	0.170071i	$-0.0543999\pi$
$54$	0.459430	−	2.60556i	0.0625205	−	0.354571i
$55$	−7.18466	+	2.61500i	−0.968779	+	0.352607i
$56$	−3.64575			−0.487184
$57$		0			0
$58$	1.64575			0.216098
$59$	−7.45858	+	2.71470i	−0.971024	+	0.353424i	−0.778344	−	0.627838i	$-0.783940\pi$
$59$	−7.45858	+	2.71470i	−0.971024	+	0.353424i	−0.192680	+	0.981262i	$0.561718\pi$
$60$	0.756107	−	4.28810i	0.0976130	−	0.553591i
$61$	0.717978	−	0.602455i	0.0919277	−	0.0771365i	−0.595666	−	0.803232i	$-0.703112\pi$
$61$	0.717978	−	0.602455i	0.0919277	−	0.0771365i	0.687593	+	0.726096i	$0.258667\pi$
$62$	−4.32490	−	3.62902i	−0.549262	−	0.460886i
$63$	2.53231	+	14.3615i	0.319041	+	1.80937i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.64575	+	2.85052i	−0.204130	+	0.353564i
$66$	11.5502	+	4.20394i	1.42174	+	0.517469i
$67$	0.606808	+	0.220860i	0.0741334	+	0.0269823i	0.378821	−	0.925470i	$-0.376330\pi$
$67$	0.606808	+	0.220860i	0.0741334	+	0.0269823i	−0.304687	+	0.952452i	$0.598552\pi$
$68$		0			0
$69$	−2.17712	−	3.77089i	−0.262095	−	0.453962i
$70$	1.04189	+	5.90885i	0.124530	+	0.706242i
$71$	2.07483	+	1.74099i	0.246237	+	0.206617i	0.757550	−	0.652777i	$-0.226396\pi$
$71$	2.07483	+	1.74099i	0.246237	+	0.206617i	−0.511313	+	0.859395i	$0.670841\pi$
$72$	−3.06418	+	2.57115i	−0.361117	+	0.303013i
$73$	0.296677	−	1.68254i	0.0347235	−	0.196927i	−0.962511	−	0.271241i	$-0.912566\pi$
$73$	0.296677	−	1.68254i	0.0347235	−	0.196927i	0.997235	+	0.0743148i	$0.0236770\pi$
$74$	−0.332885	+	0.121160i	−0.0386971	+	0.0140846i
$75$	6.06275			0.700066
$76$		0			0
$77$	−16.9373			−1.93018
$78$	4.97239	−	1.80980i	0.563012	−	0.204920i
$79$	0.694593	−	3.93923i	0.0781478	−	0.443198i	−0.920478	−	0.390794i	$-0.872200\pi$
$79$	0.694593	−	3.93923i	0.0781478	−	0.443198i	0.998626	−	0.0524041i	$-0.0166884\pi$
$80$	−1.26072	+	1.05787i	−0.140953	+	0.118273i
$81$	−3.83022	−	3.21394i	−0.425580	−	0.357104i
$82$	−0.0506189	−	0.287074i	−0.00558992	−	0.0317020i
$83$	−3.96863	−	6.87386i	−0.435613	−	0.754505i	0.561732	−	0.827319i	$-0.310135\pi$
$83$	−3.96863	−	6.87386i	−0.435613	−	0.754505i	−0.997345	+	0.0728147i	$0.976802\pi$
$84$	4.82288	−	8.35347i	0.526219	−	0.911438i
$85$		0			0
$86$	10.6105	+	3.86192i	1.14416	+	0.416442i
$87$	−2.17712	+	3.77089i	−0.233412	+	0.404282i
$88$	−2.32288	−	4.02334i	−0.247619	−	0.428889i
$89$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$89$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$90$	5.04287	+	4.23147i	0.531566	+	0.446037i
$91$	−5.58562	+	4.68689i	−0.585532	+	0.491319i
$92$	−0.285782	+	1.62075i	−0.0297948	+	0.168975i
$93$	14.0364	−	5.10884i	1.45551	−	0.529762i
$94$	−4.35425			−0.449106
$95$		0			0
$96$	2.64575			0.270031
$97$	−3.48485	+	1.26838i	−0.353833	+	0.128785i	−0.512820	−	0.858496i	$-0.671399\pi$
$97$	−3.48485	+	1.26838i	−0.353833	+	0.128785i	0.158988	+	0.987281i	$0.449177\pi$
$98$	−1.09251	+	6.19592i	−0.110360	+	0.625882i
$99$	−14.2354	+	11.9449i	−1.43071	+	1.20051i
$100$	−1.75539	−	1.47295i	−0.175539	−	0.147295i
$101$	−2.36956	−	13.4384i	−0.235780	−	1.33717i	−0.840965	−	0.541090i	$-0.818012\pi$
$101$	−2.36956	−	13.4384i	−0.235780	−	1.33717i	0.605185	−	0.796085i	$-0.293099\pi$
$102$		0			0
$103$	−6.64575	+	11.5108i	−0.654825	+	1.13419i	0.327112	+	0.944985i	$0.393924\pi$
$103$	−6.64575	+	11.5108i	−0.654825	+	1.13419i	−0.981938	+	0.189205i	$0.939409\pi$
$104$	−1.87939	−	0.684040i	−0.184289	−	0.0670757i
$105$	−14.9172	−	5.42940i	−1.45577	−	0.529855i
$106$	6.29150	−	10.8972i	0.611085	−	1.05843i
$107$	7.64575	+	13.2428i	0.739143	+	1.28023i	0.952882	+	0.303342i	$0.0981024\pi$
$107$	7.64575	+	13.2428i	0.739143	+	1.28023i	−0.213739	+	0.976891i	$0.568564\pi$
$108$	−0.459430	−	2.60556i	−0.0442087	−	0.250720i
$109$	−11.1712	−	9.37378i	−1.07001	−	0.897845i	−0.0749564	−	0.997187i	$-0.523882\pi$
$109$	−11.1712	−	9.37378i	−1.07001	−	0.897845i	−0.995053	+	0.0993420i	$0.968326\pi$
$110$	−5.85699	+	4.91459i	−0.558442	+	0.468588i
$111$	0.162752	−	0.923015i	0.0154478	−	0.0876087i
$112$	−3.42589	+	1.24692i	−0.323716	+	0.117823i
$113$	15.5830			1.46593			0.732963	−	0.680269i	$-0.238137\pi$
$113$	15.5830			1.46593			0.732963	+	0.680269i	$0.238137\pi$
$114$		0			0
$115$	2.70850			0.252569
$116$	1.54650	−	0.562880i	0.143589	−	0.0522621i
$117$	−1.38919	+	7.87846i	−0.128430	+	0.728364i
$118$	−6.08029	+	5.10197i	−0.559736	+	0.469674i
$119$		0			0
$120$	−0.756107	−	4.28810i	−0.0690228	−	0.391448i
$121$	−5.29150	−	9.16515i	−0.481046	−	0.833196i
$122$	0.468627	−	0.811686i	0.0424275	−	0.0734866i
$123$	0.724732	+	0.263781i	0.0653469	+	0.0237843i
$124$	−5.30527	−	1.93096i	−0.476427	−	0.173405i
$125$	−6.00000	+	10.3923i	−0.536656	+	0.929516i
$126$	7.29150	+	12.6293i	0.649579	+	1.12510i
$127$	2.30805	+	13.0896i	0.204806	+	1.16151i	0.897745	+	0.440516i	$0.145204\pi$
$127$	2.30805	+	13.0896i	0.204806	+	1.16151i	−0.692939	+	0.720996i	$0.743684\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−22.8852	+	19.2030i	−2.01493	+	1.69073i
$130$	−0.571563	+	3.24150i	−0.0501294	+	0.284298i
$131$	−1.82042	+	0.662580i	−0.159051	+	0.0578899i	−0.420319	−	0.907377i	$-0.638082\pi$
$131$	−1.82042	+	0.662580i	−0.159051	+	0.0578899i	0.261268	+	0.965266i	$0.415860\pi$
$132$	12.2915			1.06984
$133$		0			0
$134$	0.645751			0.0557844
$135$	−4.09166	+	1.48924i	−0.352154	+	0.128173i
$136$		0			0
$137$	11.9373	−	10.0166i	1.01987	−	0.855773i	0.0302590	−	0.999542i	$-0.490367\pi$
$137$	11.9373	−	10.0166i	1.01987	−	0.855773i	0.989611	+	0.143769i	$0.0459224\pi$
$138$	−3.33555	−	2.79886i	−0.283941	−	0.238255i
$139$	3.23780	+	18.3625i	0.274627	+	1.55749i	0.740145	+	0.672447i	$0.234757\pi$
$139$	3.23780	+	18.3625i	0.274627	+	1.55749i	−0.465518	+	0.885038i	$0.654132\pi$
$140$	3.00000	+	5.19615i	0.253546	+	0.439155i
$141$	5.76013	−	9.97684i	0.485090	−	0.840201i
$142$	2.54515	+	0.926361i	0.213585	+	0.0777385i
$143$	−8.73116	−	3.17788i	−0.730136	−	0.265748i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	−1.35425	−	2.34563i	−0.112464	−	0.194794i
$146$	−0.296677	−	1.68254i	−0.0245532	−	0.139248i
$147$	−12.7514	−	10.6997i	−1.05172	−	0.882495i
$148$	−0.271370	+	0.227707i	−0.0223065	+	0.0187174i
$149$	1.89923	−	10.7711i	0.155591	−	0.882402i	−0.802652	−	0.596448i	$-0.796578\pi$
$149$	1.89923	−	10.7711i	0.155591	−	0.882402i	0.958243	−	0.285954i	$-0.0923106\pi$
$150$	5.69712	−	2.07358i	0.465168	−	0.169307i
$151$	−12.9373			−1.05282			−0.526409	−	0.850231i	$-0.676462\pi$
$151$	−12.9373			−1.05282			−0.526409	+	0.850231i	$0.676462\pi$
$152$		0			0
$153$		0			0
$154$	−15.9158	+	5.79288i	−1.28253	+	0.466804i
$155$	−1.61345	+	9.15034i	−0.129596	+	0.734973i
$156$	4.05353	−	3.40131i	0.324542	−	0.272323i
$157$	−8.10705	−	6.80262i	−0.647013	−	0.542909i	0.259150	−	0.965837i	$-0.416558\pi$
$157$	−8.10705	−	6.80262i	−0.647013	−	0.542909i	−0.906163	+	0.422929i	$0.861002\pi$
$158$	−0.694593	−	3.93923i	−0.0552588	−	0.313388i
$159$	16.6458	+	28.8313i	1.32009	+	2.28647i
$160$	−0.822876	+	1.42526i	−0.0650540	+	0.112677i
$161$	5.63816	+	2.05212i	0.444349	+	0.161730i
$162$	−4.69846	−	1.71010i	−0.369146	−	0.134358i
$163$	−1.96863	+	3.40976i	−0.154195	+	0.267073i	−0.932766	−	0.360484i	$-0.882612\pi$
$163$	−1.96863	+	3.40976i	−0.154195	+	0.267073i	0.778571	+	0.627557i	$0.215945\pi$
$164$	−0.145751	−	0.252449i	−0.0113813	−	0.0197129i
$165$	−3.51269	−	19.9214i	−0.273462	−	1.55088i
$166$	−6.08029	−	5.10197i	−0.471922	−	0.395990i
$167$	9.19253	−	7.71345i	0.711340	−	0.596885i	−0.213635	−	0.976914i	$-0.568530\pi$
$167$	9.19253	−	7.71345i	0.711340	−	0.596885i	0.924975	+	0.380029i	$0.124086\pi$
$168$	1.67497	−	9.49921i	0.129227	−	0.732880i
$169$	8.45723	−	3.07818i	0.650556	−	0.236783i
$170$		0			0
$171$		0			0
$172$	11.2915			0.860969
$173$	−5.63816	+	2.05212i	−0.428661	+	0.156020i	−0.547335	−	0.836913i	$-0.684358\pi$
$173$	−5.63816	+	2.05212i	−0.428661	+	0.156020i	0.118674	+	0.992933i	$0.462136\pi$
$174$	−0.756107	+	4.28810i	−0.0573204	+	0.325080i
$175$	−6.39973	+	5.37001i	−0.483774	+	0.405934i
$176$	−3.55885	−	2.98623i	−0.268259	−	0.225096i
$177$	−3.64661	−	20.6810i	−0.274096	−	1.55448i
$178$		0			0
$179$	2.03137	−	3.51844i	0.151832	−	0.262981i	−0.780069	−	0.625693i	$-0.784816\pi$
$179$	2.03137	−	3.51844i	0.151832	−	0.262981i	0.931901	+	0.362713i	$0.118149\pi$
$180$	6.18600	+	2.25152i	0.461077	+	0.167818i
$181$	20.8882	+	7.60268i	1.55261	+	0.565103i	0.969028	−	0.246953i	$-0.0794292\pi$
$181$	20.8882	+	7.60268i	1.55261	+	0.565103i	0.583580	+	0.812056i	$0.301651\pi$
$182$	−3.64575	+	6.31463i	−0.270241	+	0.468071i
$183$	1.23987	+	2.14752i	0.0916539	+	0.158749i
$184$	0.285782	+	1.62075i	0.0210681	+	0.119483i
$185$	0.446608	+	0.374749i	0.0328353	+	0.0275521i
$186$	11.4426	−	9.60148i	0.839012	−	0.704015i
$187$		0			0
$188$	−4.09166	+	1.48924i	−0.298415	+	0.108614i
$189$	−9.64575			−0.701625
$190$		0			0
$191$	6.58301			0.476330			0.238165	−	0.971225i	$-0.423454\pi$
$191$	6.58301			0.476330			0.238165	+	0.971225i	$0.423454\pi$
$192$	2.48619	−	0.904900i	0.179426	−	0.0653055i
$193$	−2.53231	+	14.3615i	−0.182280	+	1.03376i	0.747121	+	0.664688i	$0.231436\pi$
$193$	−2.53231	+	14.3615i	−0.182280	+	1.03376i	−0.929401	+	0.369072i	$0.879676\pi$
$194$	−2.84087	+	2.38378i	−0.203963	+	0.171145i
$195$	−6.67110	−	5.59771i	−0.477727	−	0.400861i
$196$	1.09251	+	6.19592i	0.0780363	+	0.442566i
$197$	3.82288	+	6.62141i	0.272369	+	0.471756i	0.969468	−	0.245218i	$-0.0788597\pi$
$197$	3.82288	+	6.62141i	0.272369	+	0.471756i	−0.697099	+	0.716975i	$0.745526\pi$
$198$	−9.29150	+	16.0934i	−0.660318	+	1.14370i
$199$	18.6759	+	6.79748i	1.32390	+	0.481861i	0.904706	−	0.426035i	$-0.140090\pi$
$199$	18.6759	+	6.79748i	1.32390	+	0.481861i	0.419195	+	0.907896i	$0.362312\pi$
$200$	−2.15331	−	0.783740i	−0.152262	−	0.0554188i
$201$	−0.854249	+	1.47960i	−0.0602541	+	0.104363i
$202$	−6.82288	−	11.8176i	−0.480056	−	0.831481i
$203$	−1.04189	−	5.90885i	−0.0731263	−	0.414720i
$204$		0			0
$205$	−0.367503	+	0.308371i	−0.0256675	+	0.0215376i
$206$	−2.30805	+	13.0896i	−0.160809	+	0.911994i
$207$	6.18600	−	2.25152i	0.429957	−	0.156491i
$208$	−2.00000			−0.138675
$209$		0			0
$210$	−15.8745			−1.09545
$211$	−12.4899	+	4.54596i	−0.859842	+	0.312957i	−0.734046	−	0.679099i	$-0.762371\pi$
$211$	−12.4899	+	4.54596i	−0.859842	+	0.312957i	−0.125796	+	0.992056i	$0.540148\pi$
$212$	2.18502	−	12.3918i	0.150068	−	0.851075i
$213$	−5.48948	+	4.60622i	−0.376133	+	0.315613i
$214$	11.7140	+	9.82919i	0.800751	+	0.671909i
$215$	−3.22690	−	18.3007i	−0.220073	−	1.24810i
$216$	−1.32288	−	2.29129i	−0.0900103	−	0.155902i
$217$	−10.2915	+	17.8254i	−0.698633	+	1.21007i
$218$	−13.7035	−	4.98768i	−0.928121	−	0.337808i
$219$	4.24765	+	1.54602i	0.287030	+	0.104470i
$220$	−3.82288	+	6.62141i	−0.257738	+	0.446416i
$221$		0			0
$222$	−0.162752	−	0.923015i	−0.0109232	−	0.0619487i
$223$	14.4106	+	12.0920i	0.965008	+	0.809738i	0.981761	−	0.190122i	$-0.0608882\pi$
$223$	14.4106	+	12.0920i	0.965008	+	0.809738i	−0.0167523	+	0.999860i	$0.505333\pi$
$224$	−2.79281	+	2.34344i	−0.186602	+	0.156578i
$225$	−1.59166	+	9.02676i	−0.106111	+	0.601784i
$226$	14.6432	−	5.32970i	0.974054	−	0.354526i
$227$	7.35425			0.488119			0.244059	−	0.969760i	$-0.421521\pi$
$227$	7.35425			0.488119			0.244059	+	0.969760i	$0.421521\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	2.54515	−	0.926361i	0.167823	−	0.0610824i
$231$	7.78148	−	44.1310i	0.511984	−	2.90360i
$232$	1.26072	−	1.05787i	0.0827702	−	0.0694525i
$233$	14.4587	+	12.1323i	0.947222	+	0.794813i	0.978827	−	0.204687i	$-0.0656177\pi$
$233$	14.4587	+	12.1323i	0.947222	+	0.794813i	−0.0316058	+	0.999500i	$0.510062\pi$
$234$	1.38919	+	7.87846i	0.0908139	+	0.515031i
$235$	3.58301	+	6.20595i	0.233729	+	0.404831i
$236$	−3.96863	+	6.87386i	−0.258336	+	0.447450i
$237$	9.94477	+	3.61960i	0.645982	+	0.235118i
$238$		0			0
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$	−2.17712	−	3.77089i	−0.140533	−	0.243410i
$241$	1.31678	+	7.46780i	0.0848209	+	0.481043i	0.997395	+	0.0721322i	$0.0229803\pi$
$241$	1.31678	+	7.46780i	0.0848209	+	0.481043i	−0.912574	+	0.408911i	$0.865909\pi$
$242$	−8.10705	−	6.80262i	−0.521141	−	0.437289i
$243$	16.2141	−	13.6052i	1.04014	−	0.872777i
$244$	0.162752	−	0.923015i	0.0104192	−	0.0590900i
$245$	9.72981	−	3.54136i	0.621615	−	0.226249i
$246$	0.771243			0.0491727
$247$		0			0
$248$	−5.64575			−0.358506
$249$	19.7335	−	7.18242i	1.25056	−	0.455168i
$250$	−2.08378	+	11.8177i	−0.131790	+	0.747417i
$251$	22.3905	−	18.7879i	1.41328	−	1.18588i	0.458450	−	0.888720i	$-0.348405\pi$
$251$	22.3905	−	18.7879i	1.41328	−	1.18588i	0.954828	−	0.297160i	$-0.0960396\pi$
$252$	11.1712	+	9.37378i	0.703721	+	0.590492i
$253$	1.32767	+	7.52960i	0.0834699	+	0.473382i
$254$	6.64575	+	11.5108i	0.416992	+	0.722251i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	11.5502	+	4.20394i	0.720484	+	0.262235i	0.676131	−	0.736781i	$-0.263655\pi$
$257$	11.5502	+	4.20394i	0.720484	+	0.262235i	0.0443527	+	0.999016i	$0.485877\pi$
$258$	−14.9373	+	25.8721i	−0.929953	+	1.61073i
$259$	0.645751	+	1.11847i	0.0401250	+	0.0694986i
$260$	0.571563	+	3.24150i	0.0354469	+	0.201029i
$261$	−5.04287	−	4.23147i	−0.312146	−	0.261922i
$262$	−1.48402	+	1.24524i	−0.0916832	+	0.0769314i
$263$	−1.89923	+	10.7711i	−0.117112	+	0.664174i	0.868571	+	0.495565i	$0.165039\pi$
$263$	−1.89923	+	10.7711i	−0.117112	+	0.664174i	−0.985683	+	0.168609i	$0.946072\pi$
$264$	11.5502	−	4.20394i	0.710868	−	0.258735i
$265$	−20.7085			−1.27211
$266$		0			0
$267$		0			0
$268$	0.606808	−	0.220860i	0.0370667	−	0.0134912i
$269$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$269$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$270$	−3.33555	+	2.79886i	−0.202995	+	0.170333i
$271$	9.46390	+	7.94116i	0.574891	+	0.482391i	0.883265	−	0.468874i	$-0.155340\pi$
$271$	9.46390	+	7.94116i	0.574891	+	0.482391i	−0.308374	+	0.951265i	$0.599785\pi$
$272$		0			0
$273$	−9.64575	−	16.7069i	−0.583787	−	1.01115i
$274$	7.79150	−	13.4953i	0.470702	−	0.815280i
$275$	−10.0037	−	3.64106i	−0.603248	−	0.219564i
$276$	−4.09166	−	1.48924i	−0.246289	−	0.0896418i
$277$	13.7601	−	23.8332i	0.826766	−	1.43200i	−0.0737960	−	0.997273i	$-0.523511\pi$
$277$	13.7601	−	23.8332i	0.826766	−	1.43200i	0.900562	−	0.434727i	$-0.143155\pi$
$278$	9.32288	+	16.1477i	0.559149	+	0.968474i
$279$	3.92150	+	22.2399i	0.234774	+	1.33147i
$280$	4.59627	+	3.85673i	0.274679	+	0.230483i
$281$	−19.5016	+	16.3638i	−1.16337	+	0.976181i	−0.999946	−	0.0103755i	$-0.996697\pi$
$281$	−19.5016	+	16.3638i	−1.16337	+	0.976181i	−0.163421	+	0.986556i	$0.552253\pi$
$282$	2.00047	−	11.3452i	0.119126	−	0.675599i
$283$	−28.7976	+	10.4815i	−1.71184	+	0.623058i	−0.997084	−	0.0763164i	$-0.975684\pi$
$283$	−28.7976	+	10.4815i	−1.71184	+	0.623058i	−0.714755	+	0.699375i	$0.753462\pi$
$284$	2.70850			0.160720
$285$		0			0
$286$	−9.29150			−0.549418
$287$	−0.998655	+	0.363481i	−0.0589487	+	0.0214556i
$288$	−0.694593	+	3.93923i	−0.0409293	+	0.232121i
$289$	−13.0228	+	10.9274i	−0.766044	+	0.642788i
$290$	−2.07483	−	1.74099i	−0.121838	−	0.102234i
$291$	−1.70379	−	9.66270i	−0.0998782	−	0.566437i
$292$	−0.854249	−	1.47960i	−0.0499911	−	0.0865872i
$293$	14.4686	−	25.0604i	0.845266	−	1.46404i	−0.0401236	−	0.999195i	$-0.512775\pi$
$293$	14.4686	−	25.0604i	0.845266	−	1.46404i	0.885390	−	0.464849i	$-0.153891\pi$
$294$	−15.6419	−	5.69318i	−0.912254	−	0.332033i
$295$	12.2750	+	4.46772i	0.714676	+	0.260121i
$296$	−0.177124	+	0.306788i	−0.0102951	+	0.0178317i
$297$	−6.14575	−	10.6448i	−0.356613	−	0.617671i
$298$	−1.89923	−	10.7711i	−0.110020	−	0.623953i
$299$	2.52144	+	2.11574i	0.145818	+	0.122356i
$300$	4.64433	−	3.89706i	0.268141	−	0.224997i
$301$	7.14840	−	40.5406i	0.412027	−	2.33672i
$302$	−12.1570	+	4.42480i	−0.699559	+	0.254619i
$303$	36.1033			2.07408
$304$		0			0
$305$	−1.54249			−0.0883225
$306$		0			0
$307$	−0.112134	+	0.635941i	−0.00639980	+	0.0362951i	−0.987840	−	0.155471i	$-0.950310\pi$
$307$	−0.112134	+	0.635941i	−0.00639980	+	0.0362951i	0.981441	+	0.191766i	$0.0614215\pi$
$308$	−12.9747	+	10.8871i	−0.739302	+	0.620348i
$309$	−26.9387	−	22.6043i	−1.53249	−	1.28591i
$310$	1.61345	+	9.15034i	0.0916379	+	0.519705i
$311$	−6.82288	−	11.8176i	−0.386890	−	0.670113i	0.605140	−	0.796119i	$-0.293117\pi$
$311$	−6.82288	−	11.8176i	−0.386890	−	0.670113i	−0.992029	+	0.126007i	$0.959784\pi$
$312$	2.64575	−	4.58258i	0.149786	−	0.259437i
$313$	−8.33931	−	3.03526i	−0.471366	−	0.171563i	0.0954052	−	0.995439i	$-0.469585\pi$
$313$	−8.33931	−	3.03526i	−0.471366	−	0.171563i	−0.566771	+	0.823875i	$0.691808\pi$
$314$	−9.94477	−	3.61960i	−0.561216	−	0.204266i
$315$	12.0000	−	20.7846i	0.676123	−	1.17108i
$316$	−2.00000	−	3.46410i	−0.112509	−	0.194871i
$317$	1.04189	+	5.90885i	0.0585183	+	0.331874i	0.999986	−	0.00522845i	$-0.00166427\pi$
$317$	1.04189	+	5.90885i	0.0585183	+	0.331874i	−0.941468	+	0.337102i	$0.890553\pi$
$318$	25.5028	+	21.3994i	1.43012	+	1.20002i
$319$	5.85699	−	4.91459i	0.327928	−	0.275164i
$320$	−0.285782	+	1.62075i	−0.0159757	+	0.0906026i
$321$	−38.0176	+	13.8373i	−2.12194	+	0.772322i
$322$	6.00000			0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$	−4.30662	+	1.56748i	−0.238888	+	0.0869482i
$326$	−0.683697	+	3.87744i	−0.0378665	+	0.214751i
$327$	29.5563	−	24.8007i	1.63447	−	1.37148i
$328$	−0.223304	−	0.187374i	−0.0123299	−	0.0103460i
$329$	2.75658	+	15.6333i	0.151975	+	0.861894i
$330$	−10.1144	−	17.5186i	−0.556778	−	0.964368i
$331$	9.90588	−	17.1575i	0.544476	−	0.943061i	−0.454163	−	0.890919i	$-0.650062\pi$
$331$	9.90588	−	17.1575i	0.544476	−	0.943061i	0.998640	−	0.0521424i	$-0.0166050\pi$
$332$	−7.45858	−	2.71470i	−0.409343	−	0.148989i
$333$	1.33154	+	0.484641i	0.0729679	+	0.0265581i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	−0.531373	−	0.920365i	−0.0290320	−	0.0502849i
$336$	−1.67497	−	9.49921i	−0.0913769	−	0.518224i
$337$	7.43714	+	6.24050i	0.405127	+	0.339942i	0.822471	−	0.568807i	$-0.192595\pi$
$337$	7.43714	+	6.24050i	0.405127	+	0.339942i	−0.417344	+	0.908748i	$0.637039\pi$
$338$	6.89440	−	5.78509i	0.375006	−	0.314667i
$339$	−7.15930	+	40.6024i	−0.388840	+	2.20522i
$340$		0			0
$341$	−26.2288			−1.42037
$342$		0			0
$343$	−2.58301			−0.139469
$344$	10.6105	−	3.86192i	0.572082	−	0.208221i
$345$	−1.24436	+	7.05714i	−0.0669943	+	0.379944i
$346$	−4.59627	+	3.85673i	−0.247097	+	0.207339i
$347$	−17.7943	−	14.9312i	−0.955246	−	0.801546i	0.0249272	−	0.999689i	$-0.492065\pi$
$347$	−17.7943	−	14.9312i	−0.955246	−	0.801546i	−0.980173	+	0.198143i	$0.936509\pi$
$348$	0.756107	+	4.28810i	0.0405316	+	0.229866i
$349$	−10.5830	−	18.3303i	−0.566495	−	0.981199i	−0.996909	−	0.0785668i	$-0.974966\pi$
$349$	−10.5830	−	18.3303i	−0.566495	−	0.981199i	0.430414	−	0.902632i	$-0.358368\pi$
$350$	−4.17712	+	7.23499i	−0.223277	+	0.386727i
$351$	−4.97239	−	1.80980i	−0.265406	−	0.0966000i
$352$	−4.36558	−	1.58894i	−0.232686	−	0.0846908i
$353$	−6.43725	+	11.1497i	−0.342620	+	0.593436i	−0.984918	−	0.173019i	$-0.944648\pi$
$353$	−6.43725	+	11.1497i	−0.342620	+	0.593436i	0.642298	+	0.766455i	$0.277981\pi$
$354$	−10.5000	−	18.1865i	−0.558069	−	0.966603i
$355$	−0.774039	−	4.38979i	−0.0410817	−	0.232986i
$356$		0			0
$357$		0			0
$358$	0.705488	−	4.00102i	0.0372862	−	0.211461i
$359$	4.63950	−	1.68864i	0.244864	−	0.0891230i	−0.216673	−	0.976244i	$-0.569521\pi$
$359$	4.63950	−	1.68864i	0.244864	−	0.0891230i	0.461537	+	0.887121i	$0.347298\pi$
$360$	6.58301			0.346955
$361$		0			0
$362$	22.2288			1.16832
$363$	26.3114	−	9.57656i	1.38099	−	0.502639i
$364$	−1.26616	+	7.18073i	−0.0663646	+	0.376372i
$365$	−2.15393	+	1.80737i	−0.112742	+	0.0946018i
$366$	1.89959	+	1.59395i	0.0992932	+	0.0833169i
$367$	2.81809	+	15.9822i	0.147103	+	0.834264i	0.965654	+	0.259830i	$0.0836667\pi$
$367$	2.81809	+	15.9822i	0.147103	+	0.834264i	−0.818551	+	0.574434i	$0.805222\pi$
$368$	0.822876	+	1.42526i	0.0428954	+	0.0742969i
$369$	−0.583005	+	1.00979i	−0.0303500	+	0.0525678i
$370$	0.547846	+	0.199400i	0.0284811	+	0.0103663i
$371$	−43.1079	−	15.6900i	−2.23805	−	0.814585i
$372$	7.46863	−	12.9360i	0.387230	−	0.670703i
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$		0			0
$375$	−24.3212	−	20.4079i	−1.25594	−	1.05386i
$376$	−3.33555	+	2.79886i	−0.172018	+	0.144340i
$377$	0.571563	−	3.24150i	0.0294370	−	0.166946i
$378$	−9.06404	+	3.29904i	−0.466204	+	0.169684i
$379$	−10.7085			−0.550059			−0.275029	−	0.961436i	$-0.588688\pi$
$379$	−10.7085			−0.550059			−0.275029	+	0.961436i	$0.588688\pi$
$380$		0			0
$381$	−35.1660			−1.80161
$382$	6.18600	−	2.25152i	0.316503	−	0.115198i
$383$	−0.958583	+	5.43639i	−0.0489813	+	0.277787i	−0.999455	−	0.0330191i	$-0.989488\pi$
$383$	−0.958583	+	5.43639i	−0.0489813	+	0.277787i	0.950473	+	0.310806i	$0.100599\pi$
$384$	2.02676	−	1.70066i	0.103428	−	0.0867862i
$385$	21.3531	+	17.9174i	1.08826	+	0.913155i
$386$	2.53231	+	14.3615i	0.128891	+	0.730979i
$387$	−22.5830	−	39.1149i	−1.14796	−	1.98832i
$388$	−1.85425	+	3.21165i	−0.0941352	+	0.163047i
$389$	−11.2763	−	4.10424i	−0.571732	−	0.208093i	0.0399440	−	0.999202i	$-0.487282\pi$
$389$	−11.2763	−	4.10424i	−0.571732	−	0.208093i	−0.611676	+	0.791109i	$0.709504\pi$
$390$	−8.18331	−	2.97848i	−0.414378	−	0.150821i
$391$		0			0
$392$	3.14575	+	5.44860i	0.158884	+	0.275196i
$393$	−0.890032	−	5.04762i	−0.0448962	−	0.254619i
$394$	5.85699	+	4.91459i	0.295071	+	0.247594i
$395$	−5.04287	+	4.23147i	−0.253735	+	0.212909i
$396$	−3.22690	+	18.3007i	−0.162158	+	0.919644i
$397$	−19.7925	+	7.20388i	−0.993357	+	0.361553i	−0.787019	−	0.616928i	$-0.788377\pi$
$397$	−19.7925	+	7.20388i	−0.993357	+	0.361553i	−0.206338	+	0.978481i	$0.566155\pi$
$398$	19.8745			0.996219
$399$		0			0
$400$	−2.29150			−0.114575
$401$	25.9195	−	9.43394i	1.29436	−	0.471109i	0.399205	−	0.916862i	$-0.369286\pi$
$401$	25.9195	−	9.43394i	1.29436	−	0.471109i	0.895156	+	0.445753i	$0.147064\pi$
$402$	−0.296677	+	1.68254i	−0.0147969	+	0.0839175i
$403$	−8.64979	+	7.25804i	−0.430877	+	0.361549i
$404$	−10.4533	−	8.77132i	−0.520069	−	0.436389i
$405$	1.42891	+	8.10374i	0.0710030	+	0.402678i
$406$	−3.00000	−	5.19615i	−0.148888	−	0.257881i
$407$	−0.822876	+	1.42526i	−0.0407884	+	0.0706476i
$408$		0			0
$409$	−7.12569	−	2.59354i	−0.352343	−	0.128242i	0.159784	−	0.987152i	$-0.448920\pi$
$409$	−7.12569	−	2.59354i	−0.352343	−	0.128242i	−0.512127	+	0.858910i	$0.671142\pi$
$410$	−0.239870	+	0.415468i	−0.0118464	+	0.0205185i
$411$	20.6144	+	35.7052i	1.01683	+	1.76121i
$412$	2.30805	+	13.0896i	0.113709	+	0.644877i
$413$	22.1672	+	18.6005i	1.09078	+	0.915271i
$414$	5.04287	−	4.23147i	0.247844	−	0.207966i
$415$	−2.26832	+	12.8643i	−0.111348	+	0.631483i
$416$	−1.87939	+	0.684040i	−0.0921444	+	0.0335378i
$417$	−49.3320			−2.41580
$418$		0			0
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$	−14.9172	+	5.42940i	−0.727883	+	0.264928i
$421$	4.30852	−	24.4348i	0.209984	−	1.19088i	−0.679417	−	0.733752i	$-0.737767\pi$
$421$	4.30852	−	24.4348i	0.209984	−	1.19088i	0.889401	−	0.457128i	$-0.151122\pi$
$422$	−10.1819	+	8.54361i	−0.495646	+	0.415897i
$423$	13.3422	+	11.1954i	0.648720	+	0.544340i
$424$	−2.18502	−	12.3918i	−0.106114	−	0.601801i
$425$		0			0
$426$	−3.58301	+	6.20595i	−0.173597	+	0.300679i
$427$	−3.21092	−	1.16868i	−0.155388	−	0.0565564i
$428$	14.3693	+	5.23000i	0.694567	+	0.252802i
$429$	12.2915	−	21.2895i	0.593439	−	1.02787i
$430$	−9.29150	−	16.0934i	−0.448076	−	0.776090i
$431$	−4.84036	−	27.4510i	−0.233152	−	1.32227i	−0.846471	−	0.532435i	$-0.821277\pi$
$431$	−4.84036	−	27.4510i	−0.233152	−	1.32227i	0.613319	−	0.789835i	$-0.289834\pi$
$432$	−2.02676	−	1.70066i	−0.0975127	−	0.0818229i
$433$	−13.6927	+	11.4895i	−0.658028	+	0.552151i	−0.909495	−	0.415715i	$-0.863531\pi$
$433$	−13.6927	+	11.4895i	−0.658028	+	0.552151i	0.251467	+	0.967866i	$0.419087\pi$
$434$	−3.57420	+	20.2703i	−0.171567	+	0.973006i
$435$	6.73385	−	2.45092i	0.322863	−	0.117513i
$436$	−14.5830			−0.698399
$437$		0			0
$438$	4.52026			0.215986
$439$	10.1597	−	3.69784i	0.484898	−	0.176488i	−0.0879914	−	0.996121i	$-0.528045\pi$
$439$	10.1597	−	3.69784i	0.484898	−	0.176488i	0.572889	+	0.819633i	$0.305823\pi$
$440$	−1.32767	+	7.52960i	−0.0632942	+	0.358959i
$441$	19.2783	−	16.1764i	0.918013	−	0.770305i
$442$		0			0
$443$	1.84862	+	10.4840i	0.0878304	+	0.498111i	0.996710	+	0.0810520i	$0.0258280\pi$
$443$	1.84862	+	10.4840i	0.0878304	+	0.498111i	−0.908880	+	0.417059i	$0.863061\pi$
$444$	−0.468627	−	0.811686i	−0.0222401	−	0.0385209i
$445$		0			0
$446$	17.6773	+	6.43400i	0.837043	+	0.304659i
$447$	27.1921	+	9.89712i	1.28614	+	0.468118i
$448$	−1.82288	+	3.15731i	−0.0861228	+	0.149169i
$449$	−12.1458	−	21.0371i	−0.573193	−	0.992800i	−0.996235	−	0.0866900i	$-0.972371\pi$
$449$	−12.1458	−	21.0371i	−0.573193	−	0.992800i	0.423042	−	0.906110i	$-0.360962\pi$
$450$	1.59166	+	9.02676i	0.0750316	+	0.425525i
$451$	−1.03741	−	0.870494i	−0.0488499	−	0.0409900i
$452$	11.9373	−	10.0166i	0.561482	−	0.471139i
$453$	5.94376	−	33.7087i	0.279262	−	1.58377i
$454$	6.91073	−	2.51530i	0.324337	−	0.118049i
$455$	12.0000			0.562569
$456$		0			0
$457$	32.8745			1.53780			0.768902	−	0.639366i	$-0.220803\pi$
$457$	32.8745			1.53780			0.768902	+	0.639366i	$0.220803\pi$
$458$	18.7939	−	6.84040i	0.878179	−	0.319631i
$459$		0			0
$460$	2.07483	−	1.74099i	0.0967394	−	0.0811740i
$461$	14.6820	+	12.3197i	0.683810	+	0.573784i	0.917117	−	0.398619i	$-0.130510\pi$
$461$	14.6820	+	12.3197i	0.683810	+	0.573784i	−0.233307	+	0.972403i	$0.574955\pi$
$462$	−7.78148	−	44.1310i	−0.362027	−	2.05316i
$463$	19.2288	+	33.3052i	0.893636	+	1.54782i	0.835484	+	0.549515i	$0.185188\pi$
$463$	19.2288	+	33.3052i	0.893636	+	1.54782i	0.0581525	+	0.998308i	$0.481479\pi$
$464$	0.822876	−	1.42526i	0.0382010	−	0.0661661i
$465$	−23.1005	−	8.40788i	−1.07126	−	0.389906i
$466$	17.7362	+	6.45546i	0.821615	+	0.299043i
$467$	9.67712	−	16.7613i	0.447804	−	0.775619i	−0.550439	−	0.834875i	$-0.685540\pi$
$467$	9.67712	−	16.7613i	0.447804	−	0.775619i	0.998243	+	0.0592563i	$0.0188729\pi$
$468$	4.00000	+	6.92820i	0.184900	+	0.320256i
$469$	−0.408811	−	2.31848i	−0.0188771	−	0.107058i
$470$	5.48948	+	4.60622i	0.253211	+	0.212469i
$471$	21.4492	−	17.9981i	0.988329	−	0.829307i
$472$	−1.37829	+	7.81667i	−0.0634409	+	0.359791i
$473$	49.2939	−	17.9415i	2.26654	−	0.824952i
$474$	10.5830			0.486094
$475$		0			0
$476$		0			0
$477$	−47.2966	+	17.2146i	−2.16556	+	0.788201i
$478$	2.08378	−	11.8177i	0.0953098	−	0.540529i
$479$	5.04287	−	4.23147i	0.230415	−	0.193341i	−0.520269	−	0.854002i	$-0.674168\pi$
$479$	5.04287	−	4.23147i	0.230415	−	0.193341i	0.750684	+	0.660661i	$0.229724\pi$
$480$	−3.33555	−	2.79886i	−0.152246	−	0.127750i
$481$	0.123029	+	0.697734i	0.00560965	+	0.0318139i
$482$	3.79150	+	6.56708i	0.172698	+	0.299122i
$483$	−7.93725	+	13.7477i	−0.361158	+	0.625543i
$484$	−9.94477	−	3.61960i	−0.452035	−	0.164527i
$485$	5.73519	+	2.08744i	0.260422	+	0.0947857i
$486$	10.5830	−	18.3303i	0.480055	−	0.831479i
$487$	2.11438	+	3.66221i	0.0958116	+	0.165951i	0.909947	−	0.414724i	$-0.136122\pi$
$487$	2.11438	+	3.66221i	0.0958116	+	0.165951i	−0.814135	+	0.580675i	$0.802789\pi$
$488$	−0.162752	−	0.923015i	−0.00736746	−	0.0417829i
$489$	−7.97988	−	6.69592i	−0.360863	−	0.302800i
$490$	7.93181	−	6.65558i	0.358323	−	0.300669i
$491$	6.82290	−	38.6946i	0.307913	−	1.74626i	−0.301553	−	0.953449i	$-0.597505\pi$
$491$	6.82290	−	38.6946i	0.307913	−	1.74626i	0.609466	−	0.792812i	$-0.291384\pi$
$492$	0.724732	−	0.263781i	0.0326734	−	0.0118922i
$493$		0			0
$494$		0			0
$495$	30.5830			1.37460
$496$	−5.30527	+	1.93096i	−0.238214	+	0.0867027i
$497$	1.71469	−	9.72449i	0.0769144	−	0.436203i
$498$	16.0869	−	13.4985i	0.720873	−	0.604884i
$499$	−3.65498	−	3.06690i	−0.163620	−	0.137293i	0.557302	−	0.830310i	$-0.311837\pi$
$499$	−3.65498	−	3.06690i	−0.163620	−	0.137293i	−0.720921	+	0.693017i	$0.756281\pi$
$500$	2.08378	+	11.8177i	0.0931894	+	0.528503i
$501$	15.8745	+	27.4955i	0.709221	+	1.22841i
$502$	14.6144	−	25.3128i	0.652272	−	1.12977i
$503$	38.4684	+	14.0014i	1.71522	+	0.624290i	0.997409	−	0.0719447i	$-0.0229205\pi$
$503$	38.4684	+	14.0014i	1.71522	+	0.624290i	0.717814	+	0.696235i	$0.245143\pi$
$504$	13.7035	+	4.98768i	0.610404	+	0.222169i
$505$	−11.2288	+	19.4488i	−0.499673	+	0.865459i
$506$	3.82288	+	6.62141i	0.169948	+	0.294358i
$507$	4.13487	+	23.4500i	0.183636	+	1.04145i
$508$	10.1819	+	8.54361i	0.451748	+	0.379062i
$509$	24.3212	−	20.4079i	1.07802	−	0.904563i	0.0822617	−	0.996611i	$-0.473786\pi$
$509$	24.3212	−	20.4079i	1.07802	−	0.904563i	0.995755	+	0.0920477i	$0.0293412\pi$
$510$		0			0
$511$	−5.85312	+	2.13036i	−0.258927	+	0.0942416i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	12.2915			0.542155
$515$	20.5553	−	7.48152i	0.905775	−	0.329675i
$516$	−5.18765	+	29.4206i	−0.228374	+	1.29517i
$517$	−15.4961	+	13.0028i	−0.681519	+	0.571862i
$518$	0.989348	+	0.830162i	0.0434695	+	0.0364752i
$519$	−2.75658	−	15.6333i	−0.121000	−	0.686227i
$520$	1.64575	+	2.85052i	0.0721710	+	0.125004i
$521$	−5.85425	+	10.1399i	−0.256479	+	0.444235i	−0.965296	−	0.261157i	$-0.915896\pi$
$521$	−5.85425	+	10.1399i	−0.256479	+	0.444235i	0.708817	+	0.705392i	$0.249229\pi$
$522$	−6.18600	−	2.25152i	−0.270754	−	0.0985464i
$523$	−1.76146	−	0.641119i	−0.0770233	−	0.0280342i	0.303221	−	0.952920i	$-0.401938\pi$
$523$	−1.76146	−	0.641119i	−0.0770233	−	0.0280342i	−0.380244	+	0.924886i	$0.624160\pi$
$524$	−0.968627	+	1.67771i	−0.0423147	+	0.0732912i
$525$	−11.0516	−	19.1420i	−0.482333	−	0.835425i
$526$	1.89923	+	10.7711i	0.0828105	+	0.469642i
$527$		0			0
$528$	9.41584	−	7.90083i	0.409772	−	0.343839i
$529$	−3.52358	+	19.9832i	−0.153199	+	0.868836i
$530$	−19.4596	+	7.08272i	−0.845272	+	0.307654i
$531$	31.7490			1.37779
$532$		0			0
$533$	−0.583005			−0.0252528
$534$		0			0
$535$	4.37003	−	24.7837i	0.188933	−	1.07149i
$536$	0.494674	−	0.415081i	0.0213667	−	0.0179288i
$537$	8.23422	+	6.90933i	0.355333	+	0.298160i
$538$		0			0
$539$	14.6144	+	25.3128i	0.629486	+	1.09030i
$540$	−2.17712	+	3.77089i	−0.0936885	+	0.162273i
$541$	−7.51754	−	2.73616i	−0.323204	−	0.117637i	0.175322	−	0.984511i	$-0.443903\pi$
$541$	−7.51754	−	2.73616i	−0.323204	−	0.117637i	−0.498527	+	0.866874i	$0.666125\pi$
$542$	11.6092	+	4.22540i	0.498658	+	0.181497i
$543$	−29.4059	+	50.9325i	−1.26193	+	2.18572i
$544$		0			0
$545$	4.16756	+	23.6354i	0.178518	+	1.01243i
$546$	−14.7781	−	12.4003i	−0.632446	−	0.530686i
$547$	−8.64979	+	7.25804i	−0.369838	+	0.310331i	−0.808698	−	0.588225i	$-0.799827\pi$
$547$	−8.64979	+	7.25804i	−0.369838	+	0.310331i	0.438859	+	0.898556i	$0.355383\pi$
$548$	2.70596	−	15.3463i	0.115593	−	0.655560i
$549$	−3.52292	+	1.28224i	−0.150355	+	0.0547246i
$550$	−10.6458			−0.453936
$551$		0			0
$552$	−4.35425			−0.185329
$553$	−13.7035	+	4.98768i	−0.582734	+	0.212098i
$554$	4.77884	−	27.1022i	0.203034	−	1.15146i
$555$	−1.18161	+	0.991491i	−0.0501567	+	0.0420865i
$556$	14.2835	+	11.9853i	0.605754	+	0.508288i
$557$	−0.940651	−	5.33470i	−0.0398567	−	0.226038i	0.958373	−	0.285520i	$-0.0921663\pi$
$557$	−0.940651	−	5.33470i	−0.0398567	−	0.226038i	−0.998229	+	0.0594817i	$0.981055\pi$
$558$	11.2915	+	19.5575i	0.478007	+	0.827933i
$559$	11.2915	−	19.5575i	0.477580	−	0.827192i
$560$	5.63816	+	2.05212i	0.238256	+	0.0867179i
$561$		0			0
$562$	−12.7288	+	22.0469i	−0.536930	+	0.929990i
$563$	5.03137	+	8.71459i	0.212047	+	0.367276i	0.952355	−	0.304992i	$-0.0986536\pi$
$563$	5.03137	+	8.71459i	0.212047	+	0.367276i	−0.740308	+	0.672268i	$0.765320\pi$
$564$	−2.00047	−	11.3452i	−0.0842351	−	0.477721i
$565$	−19.6458	−	16.4848i	−0.826504	−	0.693520i
$566$	−23.4760	+	19.6987i	−0.986770	+	0.827999i
$567$	−3.16539	+	17.9518i	−0.132934	+	0.753906i
$568$	2.54515	−	0.926361i	0.106792	−	0.0388692i
$569$	−6.58301			−0.275974			−0.137987	−	0.990434i	$-0.544063\pi$
$569$	−6.58301			−0.275974			−0.137987	+	0.990434i	$0.544063\pi$
$570$		0			0
$571$	7.81176			0.326912			0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176			0.326912			0.163456	+	0.986551i	$0.447736\pi$
$572$	−8.73116	+	3.17788i	−0.365068	+	0.132874i
$573$	−3.02443	+	17.1524i	−0.126347	+	0.716551i
$574$	−0.814111	+	0.683120i	−0.0339803	+	0.0285129i
$575$	2.88894	+	2.42411i	0.120477	+	0.101092i
$576$	0.694593	+	3.93923i	0.0289414	+	0.164135i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$	−36.2562	−	13.1962i	−1.50675	−	0.548414i
$580$	−2.54515	−	0.926361i	−0.105682	−	0.0384650i
$581$	−14.4686	+	25.0604i	−0.600260	+	1.03968i
$582$	−4.90588	−	8.49723i	−0.203355	−	0.352222i
$583$	−10.1510	−	57.5694i	−0.420413	−	2.38428i
$584$	−1.30878	−	1.09820i	−0.0541579	−	0.0454439i
$585$	10.0857	−	8.46295i	0.416994	−	0.349900i
$586$	5.02490	−	28.4976i	0.207577	−	1.17723i
$587$	13.2736	−	4.83120i	0.547861	−	0.199405i	−0.0532349	−	0.998582i	$-0.516953\pi$
$587$	13.2736	−	4.83120i	0.547861	−	0.199405i	0.601096	+	0.799177i	$0.294731\pi$
$588$	−16.6458			−0.686459
$589$		0			0
$590$	13.0627			0.537785
$591$	−19.0088	+	6.91864i	−0.781918	+	0.284595i
$592$	−0.0615146	+	0.348867i	−0.00252824	+	0.0143383i
$593$	22.7580	−	19.0963i	0.934560	−	0.784189i	−0.0420702	−	0.999115i	$-0.513395\pi$
$593$	22.7580	−	19.0963i	0.934560	−	0.784189i	0.976630	+	0.214925i	$0.0689509\pi$
$594$	−9.41584	−	7.90083i	−0.386336	−	0.324175i
$595$		0			0
$596$	−5.46863	−	9.47194i	−0.224004	−	0.387986i
$597$	−26.2915	+	45.5382i	−1.07604	+	1.86376i
$598$	3.09300	+	1.12576i	0.126482	+	0.0460358i
$599$	−15.9158	−	5.79288i	−0.650302	−	0.236691i	−0.00425849	−	0.999991i	$-0.501356\pi$
$599$	−15.9158	−	5.79288i	−0.650302	−	0.236691i	−0.646044	+	0.763300i	$0.723578\pi$
$600$	3.03137	−	5.25049i	0.123755	−	0.214350i
$601$	5.20850	+	9.02138i	0.212459	+	0.367990i	0.952484	−	0.304590i	$-0.0985195\pi$
$601$	5.20850	+	9.02138i	0.212459	+	0.367990i	−0.740025	+	0.672580i	$0.765186\pi$
$602$	−7.14840	−	40.5406i	−0.291347	−	1.65231i
$603$	−1.97870	−	1.66032i	−0.0805788	−	0.0676136i
$604$	−9.91051	+	8.31591i	−0.403253	+	0.338369i
$605$	−3.02443	+	17.1524i	−0.122961	+	0.697344i
$606$	33.9260	−	12.3480i	1.37815	−	0.501605i
$607$	−6.93725			−0.281574			−0.140787	−	0.990040i	$-0.544963\pi$
$607$	−6.93725			−0.281574			−0.140787	+	0.990040i	$0.544963\pi$
$608$		0			0
$609$	15.8745			0.643268
$610$	−1.44946	+	0.527562i	−0.0586871	+	0.0213603i
$611$	−1.51221	+	8.57620i	−0.0611777	+	0.346956i
$612$		0			0
$613$	5.68175	+	4.76755i	0.229484	+	0.192560i	0.750278	−	0.661123i	$-0.229920\pi$
$613$	5.68175	+	4.76755i	0.229484	+	0.192560i	−0.520794	+	0.853682i	$0.674364\pi$
$614$	0.112134	+	0.635941i	0.00452534	+	0.0256645i
$615$	−0.634637	−	1.09922i	−0.0255911	−	0.0443250i
$616$	−8.46863	+	14.6681i	−0.341211	+	0.590994i
$617$	29.0125	+	10.5597i	1.16800	+	0.425118i	0.851949	−	0.523624i	$-0.175420\pi$
$617$	29.0125	+	10.5597i	1.16800	+	0.425118i	0.316052	+	0.948742i	$0.397643\pi$
$618$	−33.0452	−	12.0275i	−1.32927	−	0.483816i
$619$	4.22876	−	7.32442i	0.169968	−	0.294393i	−0.768440	−	0.639921i	$-0.778967\pi$
$619$	4.22876	−	7.32442i	0.169968	−	0.294393i	0.938408	+	0.345528i	$0.112300\pi$
$620$	4.64575	+	8.04668i	0.186578	+	0.323162i
$621$	0.756107	+	4.28810i	0.0303415	+	0.172075i
$622$	−10.4533	−	8.77132i	−0.419137	−	0.351698i
$623$		0			0
$624$	0.918860	−	5.21111i	0.0367838	−	0.208611i
$625$	7.79146	−	2.83586i	0.311659	−	0.113434i
$626$	−8.87451			−0.354697
$627$		0			0
$628$	−10.5830			−0.422308
$629$		0			0
$630$	4.16756	−	23.6354i	0.166039	−	0.941656i
$631$	−19.0069	+	15.9487i	−0.756653	+	0.634907i	−0.937253	−	0.348649i	$-0.886640\pi$
$631$	−19.0069	+	15.9487i	−0.756653	+	0.634907i	0.180600	+	0.983557i	$0.442196\pi$
$632$	−3.06418	−	2.57115i	−0.121886	−	0.102275i
$633$	−6.10651	−	34.6318i	−0.242712	−	1.37649i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	10.9373	−	18.9439i	0.434032	−	0.751765i
$636$	31.2838	+	11.3864i	1.24048	+	0.451499i
$637$	11.8242	+	4.30364i	0.468490	+	0.170516i
$638$	3.82288	−	6.62141i	0.151349	−	0.262144i
$639$	−5.41699	−	9.38251i	−0.214293	−	0.371166i
$640$	0.285782	+	1.62075i	0.0112965	+	0.0640657i
$641$	−9.86245	−	8.27557i	−0.389543	−	0.326866i	0.426892	−	0.904303i	$-0.359608\pi$
$641$	−9.86245	−	8.27557i	−0.389543	−	0.326866i	−0.816435	+	0.577437i	$0.804053\pi$
$642$	−30.9923	+	26.0056i	−1.22317	+	1.02636i
$643$	−1.13223	+	6.42120i	−0.0446508	+	0.253227i	−0.998960	−	0.0455933i	$-0.985482\pi$
$643$	−1.13223	+	6.42120i	−0.0446508	+	0.253227i	0.954309	+	0.298821i	$0.0965933\pi$
$644$	5.63816	−	2.05212i	0.222174	−	0.0808649i
$645$	49.1660			1.93591
$646$		0			0
$647$	−22.4575			−0.882896			−0.441448	−	0.897287i	$-0.645535\pi$
$647$	−22.4575			−0.882896			−0.441448	+	0.897287i	$0.645535\pi$
$648$	−4.69846	+	1.71010i	−0.184573	+	0.0671791i
$649$	−6.40319	+	36.3143i	−0.251347	+	1.42546i
$650$	−3.51079	+	2.94590i	−0.137704	+	0.115548i
$651$	−41.7169	−	35.0046i	−1.63501	−	1.37194i
$652$	0.683697	+	3.87744i	0.0267756	+	0.151852i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$	19.2915	−	33.4139i	0.754357	−	1.30659i
$655$	2.99596	+	1.09044i	0.117062	+	0.0426071i
$656$	−0.273923	−	0.0996998i	−0.0106949	−	0.00389262i
$657$	−3.41699	+	5.91841i	−0.133310	+	0.230899i
$658$	7.93725	+	13.7477i	0.309426	+	0.535942i
$659$	3.22690	+	18.3007i	0.125702	+	0.712894i	0.980888	+	0.194572i	$0.0623318\pi$
$659$	3.22690	+	18.3007i	0.125702	+	0.712894i	−0.855186	+	0.518321i	$0.826557\pi$
$660$	−15.4961	−	13.0028i	−0.603186	−	0.506133i
$661$	−12.4319	+	10.4316i	−0.483547	+	0.405744i	−0.851707	−	0.524018i	$-0.824432\pi$
$661$	−12.4319	+	10.4316i	−0.483547	+	0.405744i	0.368160	+	0.929762i	$0.379988\pi$
$662$	3.44028	−	19.5108i	0.133710	−	0.758308i
$663$		0			0
$664$	−7.93725			−0.308025
$665$		0			0
$666$	1.41699			0.0549074
$667$	−2.54515	+	0.926361i	−0.0985488	+	0.0358688i
$668$	2.08378	−	11.8177i	0.0806238	−	0.457240i
$669$	−38.1270	+	31.9923i	−1.47407	+	1.23690i
$670$	−0.814111	−	0.683120i	−0.0314518	−	0.0263912i
$671$	−0.756107	−	4.28810i	−0.0291892	−	0.165540i
$672$	−4.82288	−	8.35347i	−0.186046	−	0.322242i
$673$	−6.93725	+	12.0157i	−0.267411	+	0.463170i	−0.968193	−	0.250206i	$-0.919502\pi$
$673$	−6.93725	+	12.0157i	−0.267411	+	0.463170i	0.700781	+	0.713376i	$0.252835\pi$
$674$	9.12300	+	3.32050i	0.351405	+	0.127901i
$675$	−5.69712	−	2.07358i	−0.219282	−	0.0798122i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−5.70850	−	9.88741i	−0.219395	−	0.380004i	0.735228	−	0.677820i	$-0.237075\pi$
$677$	−5.70850	−	9.88741i	−0.219395	−	0.380004i	−0.954623	+	0.297816i	$0.903742\pi$
$678$	7.15930	+	40.6024i	0.274951	+	1.55933i
$679$	10.3571	+	8.69066i	0.397470	+	0.333517i
$680$		0			0
$681$	−3.37876	+	19.1619i	−0.129474	+	0.734286i
$682$	−24.6470	+	8.97076i	−0.943781	+	0.343508i
$683$	5.41699			0.207276			0.103638	−	0.994615i	$-0.466952\pi$
$683$	5.41699			0.207276			0.103638	+	0.994615i	$0.466952\pi$
$684$		0			0
$685$	−25.6458			−0.979874
$686$	−2.42723	+	0.883440i	−0.0926721	+	0.0337299i
$687$	−9.18860	+	52.1111i	−0.350567	+	1.98816i
$688$	8.64979	−	7.25804i	0.329770	−	0.276710i
$689$	−19.2783	−	16.1764i	−0.734444	−	0.616272i
$690$	1.24436	+	7.05714i	0.0473722	+	0.268661i
$691$	−1.29150	−	2.23695i	−0.0491311	−	0.0850975i	0.840414	−	0.541945i	$-0.182312\pi$
$691$	−1.29150	−	2.23695i	−0.0491311	−	0.0850975i	−0.889545	+	0.456847i	$0.848979\pi$
$692$	−3.00000	+	5.19615i	−0.114043	+	0.197528i
$693$	63.6633	+	23.1715i	2.41837	+	0.880214i
$694$	−21.8279	−	7.94470i	−0.828575	−	0.301577i
$695$	15.3431	−	26.5751i	0.581998	−	1.00805i
$696$	2.17712	+	3.77089i	0.0825237	+	0.142935i
$697$		0			0
$698$	−16.2141	−	13.6052i	−0.613713	−	0.514966i
$699$	−38.2542	+	32.0990i	−1.44691	+	1.21410i
$700$	−1.45070	+	8.22733i	−0.0548313	+	0.310964i
$701$	−9.72981	+	3.54136i	−0.367490	+	0.133755i	−0.519163	−	0.854675i	$-0.673756\pi$
$701$	−9.72981	+	3.54136i	−0.367490	+	0.133755i	0.151673	+	0.988431i	$0.451534\pi$
$702$	−5.29150			−0.199715
$703$		0			0
$704$	−4.64575			−0.175093
$705$	−17.8161	+	6.48452i	−0.670993	+	0.244221i
$706$	−2.23563	+	12.6789i	−0.0841392	+	0.477177i
$707$	−38.1100	+	31.9781i	−1.43327	+	1.20266i
$708$	−16.0869	−	13.4985i	−0.604584	−	0.507306i
$709$	0.633078	+	3.59036i	0.0237757	+	0.134839i	0.994385	−	0.105821i	$-0.0337472\pi$
$709$	0.633078	+	3.59036i	0.0237757	+	0.134839i	−0.970609	+	0.240660i	$0.922636\pi$
$710$	−2.22876	−	3.86032i	−0.0836437	−	0.144875i
$711$	−8.00000	+	13.8564i	−0.300023	+	0.519656i
$712$		0			0
$713$	8.73116	+	3.17788i	0.326984	+	0.119013i
$714$		0			0
$715$	7.64575	+	13.2428i	0.285935	+	0.495254i
$716$	−0.705488	−	4.00102i	−0.0263653	−	0.149525i
$717$	24.3212	+	20.4079i	0.908290	+	0.762146i
$718$	3.78216	−	3.17361i	0.141149	−	0.118438i
$719$	0.470326	−	2.66735i	0.0175402	−	0.0994753i	−0.974781	−	0.223164i	$-0.928361\pi$
$719$	0.470326	−	2.66735i	0.0175402	−	0.0994753i	0.992321	+	0.123689i	$0.0394725\pi$
$720$	6.18600	−	2.25152i	0.230539	−	0.0839092i
$721$	48.4575			1.80465
$722$		0			0
$723$	−20.0627			−0.746142
$724$	20.8882	−	7.60268i	0.776304	−	0.282551i
$725$	0.654870	−	3.71395i	0.0243212	−	0.137933i
$726$	21.4492	−	17.9981i	0.796056	−	0.667970i
$727$	1.08548	+	0.910827i	0.0402583	+	0.0337807i	0.662695	−	0.748890i	$-0.269413\pi$
$727$	1.08548	+	0.910827i	0.0402583	+	0.0337807i	−0.622437	+	0.782670i	$0.713857\pi$
$728$	1.26616	+	7.18073i	0.0469269	+	0.266135i
$729$	20.5000	+	35.5070i	0.759259	+	1.31508i
$730$	−1.40588	+	2.43506i	−0.0520340	+	0.0901255i
$731$		0			0
$732$	2.33019	+	0.848121i	0.0861265	+	0.0313475i
$733$	8.05163	−	13.9458i	0.297394	−	0.515101i	−0.678145	−	0.734928i	$-0.737216\pi$
$733$	8.05163	−	13.9458i	0.297394	−	0.515101i	0.975539	+	0.219827i	$0.0705492\pi$
$734$	8.11438	+	14.0545i	0.299507	+	0.518762i
$735$	4.75705	+	26.9786i	0.175466	+	0.995120i
$736$	1.26072	+	1.05787i	0.0464707	+	0.0389936i
$737$	2.29813	−	1.92836i	0.0846528	−	0.0710322i
$738$	−0.202476	+	1.14830i	−0.00745323	+	0.0422694i
$739$	31.7727	−	11.5643i	1.16878	−	0.425400i	0.316551	−	0.948575i	$-0.397475\pi$
$739$	31.7727	−	11.5643i	1.16878	−	0.425400i	0.852225	+	0.523176i	$0.175253\pi$
$740$	0.583005			0.0214317
$741$		0			0
$742$	−45.8745			−1.68411
$743$	−44.6544	+	16.2529i	−1.63821	+	0.596261i	−0.986725	−	0.162399i	$-0.948077\pi$
$743$	−44.6544	+	16.2529i	−1.63821	+	0.596261i	−0.651487	+	0.758660i	$0.725855\pi$
$744$	2.59383	−	14.7103i	0.0950943	−	0.539307i
$745$	−13.7888	+	11.5702i	−0.505183	+	0.423898i
$746$	−3.06418	−	2.57115i	−0.112188	−	0.0941365i
$747$	5.51316	+	31.2667i	0.201716	+	1.14399i
$748$		0			0
$749$	27.8745	−	48.2801i	1.01851	−	1.76412i
$750$	−29.8343	−	10.8588i	−1.08940	−	0.396507i
$751$	−7.39962	−	2.69324i	−0.270016	−	0.0982777i	0.203464	−	0.979082i	$-0.434780\pi$
$751$	−7.39962	−	2.69324i	−0.270016	−	0.0982777i	−0.473480	+	0.880805i	$0.657002\pi$
$752$	−2.17712	+	3.77089i	−0.0793916	+	0.137510i
$753$	38.6660	+	66.9715i	1.40907	+	2.44058i
$754$	−0.571563	−	3.24150i	−0.0208151	−	0.118048i
$755$	16.3102	+	13.6859i	0.593590	+	0.498081i
$756$	−7.38907	+	6.20017i	−0.268738	+	0.225498i
$757$	−0.795831	+	4.51338i	−0.0289250	+	0.164042i	−0.995849	−	0.0910241i	$-0.970986\pi$
$757$	−0.795831	+	4.51338i	−0.0289250	+	0.164042i	0.966924	+	0.255066i	$0.0820971\pi$
$758$	−10.0627	+	3.66252i	−0.365494	+	0.133029i
$759$	−20.2288			−0.734257
$760$		0			0
$761$	42.8745			1.55420			0.777100	−	0.629377i	$-0.216690\pi$
$761$	42.8745			1.55420			0.777100	+	0.629377i	$0.216690\pi$
$762$	−33.0452	+	12.0275i	−1.19710	+	0.435710i
$763$	−9.23218	+	52.3583i	−0.334227	+	1.89550i
$764$	5.04287	−	4.23147i	0.182445	−	0.153089i
$765$		0			0
$766$	0.958583	+	5.43639i	0.0346350	+	0.196425i
$767$	7.93725	+	13.7477i	0.286598	+	0.496402i
$768$	1.32288	−	2.29129i	0.0477352	−	0.0826797i
$769$	−33.1632	−	12.0704i	−1.19589	−	0.435270i	−0.334105	−	0.942536i	$-0.608434\pi$
$769$	−33.1632	−	12.0704i	−1.19589	−	0.435270i	−0.861790	+	0.507266i	$0.830656\pi$
$770$	26.1935	+	9.53364i	0.943947	+	0.343569i
$771$	−16.2601	+	28.1634i	−0.585594	+	1.01428i
$772$	7.29150	+	12.6293i	0.262427	+	0.454537i
$773$	0.857345	+	4.86225i	0.0308366	+	0.174883i	0.996336	−	0.0855209i	$-0.0272554\pi$
$773$	0.857345	+	4.86225i	0.0308366	+	0.174883i	−0.965500	+	0.260404i	$0.916144\pi$
$774$	−34.5992	−	29.0322i	−1.24364	−	1.04354i
$775$	−9.91051	+	8.31591i	−0.355996	+	0.298716i
$776$	−0.643974	+	3.65216i	−0.0231173	+	0.131105i
$777$	−3.21092	+	1.16868i	−0.115191	+	0.0419262i
$778$	−12.0000			−0.430221
$779$		0			0
$780$	−8.70850			−0.311814
$781$	11.8242	−	4.30364i	0.423102	−	0.153996i
$782$		0			0
$783$	3.33555	−	2.79886i	0.119203	−	0.100023i
$784$	4.81957	+	4.04410i	0.172128	+	0.144432i
$785$	3.02443	+	17.1524i	0.107947	+	0.612195i
$786$	−2.56275	−	4.43881i	−0.0914101	−	0.158327i
$787$	−21.2601	+	36.8236i	−0.757842	+	1.31262i	0.186107	+	0.982529i	$0.440413\pi$
$787$	−21.2601	+	36.8236i	−0.757842	+	1.31262i	−0.943949	+	0.330091i	$0.892921\pi$
$788$	7.18466	+	2.61500i	0.255943	+	0.0931556i
$789$	−27.1921	−	9.89712i	−0.968065	−	0.352347i
$790$	−3.29150	+	5.70105i	−0.117106	+	0.202834i
$791$	−28.4059	−	49.2004i	−1.01000	−	1.74937i
$792$	3.22690	+	18.3007i	0.114663	+	0.650287i
$793$	−1.43596	−	1.20491i	−0.0509923	−	0.0427876i
$794$	−16.1350	+	13.5389i	−0.572610	+	0.480477i
$795$	9.51410	−	53.9572i	0.337430	−	1.91366i
$796$	18.6759	−	6.79748i	0.661951	−	0.240930i
$797$	44.8118			1.58731			0.793657	−	0.608365i	$-0.208174\pi$
$797$	44.8118			1.58731			0.793657	+	0.608365i	$0.208174\pi$
$798$		0			0
$799$		0			0
$800$	−2.15331	+	0.783740i	−0.0761309	+	0.0277094i
$801$		0			0
$802$	21.1298	−	17.7300i	0.746119	−	0.626069i
$803$	−6.08029	−	5.10197i	−0.214569	−	0.180045i
$804$	0.296677	+	1.68254i	0.0104630	+	0.0593387i
$805$	−4.93725	−	8.55157i	−0.174015	−	0.301403i
$806$	−5.64575	+	9.77873i	−0.198863	+	0.344441i
$807$		0			0
$808$	−12.8228	−	4.66712i	−0.451105	−	0.164189i
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$	4.11438	+	7.12631i	0.144565	+	0.250393i
$811$	5.43371	+	30.8161i	0.190803	+	1.08210i	0.918269	+	0.395956i	$0.129587\pi$
$811$	5.43371	+	30.8161i	0.190803	+	1.08210i	−0.727466	+	0.686144i	$0.759302\pi$
$812$	−4.59627	−	3.85673i	−0.161297	−	0.135345i
$813$	−25.0391	+	21.0103i	−0.878161	+	0.736864i
$814$	−0.285782	+	1.62075i	−0.0100166	+	0.0568072i
$815$	6.08896	−	2.21620i	0.213287	−	0.0776302i
$816$		0			0
$817$		0			0
$818$	−7.58301			−0.265134
$819$	27.4071	−	9.97536i	0.957681	−	0.348567i
$820$	−0.0833061	+	0.472452i	−0.00290918	+	0.0164988i
$821$	−4.59627	+	3.85673i	−0.160411	+	0.134601i	−0.719460	−	0.694534i	$-0.755611\pi$
$821$	−4.59627	+	3.85673i	−0.160411	+	0.134601i	0.559049	+	0.829134i	$0.311166\pi$
$822$	31.5831	+	26.5013i	1.10159	+	0.924340i
$823$	−5.53495	−	31.3903i	−0.192936	−	1.09420i	−0.915327	−	0.402711i	$-0.868068\pi$
$823$	−5.53495	−	31.3903i	−0.192936	−	1.09420i	0.722391	−	0.691485i	$-0.243043\pi$
$824$	6.64575	+	11.5108i	0.231516	+	0.400997i
$825$	14.0830	−	24.3925i	0.490307	−	0.849237i
$826$	27.1921	+	9.89712i	0.946135	+	0.344365i
$827$	−49.4708	−	18.0059i	−1.72027	−	0.626127i	−0.722406	−	0.691469i	$-0.756964\pi$
$827$	−49.4708	−	18.0059i	−1.72027	−	0.626127i	−0.997863	+	0.0653422i	$0.979186\pi$
$828$	3.29150	−	5.70105i	0.114388	−	0.198125i
$829$	−8.58301	−	14.8662i	−0.298100	−	0.516325i	0.677601	−	0.735430i	$-0.263020\pi$
$829$	−8.58301	−	14.8662i	−0.298100	−	0.516325i	−0.975701	+	0.219105i	$0.929686\pi$
$830$	2.26832	+	12.8643i	0.0787346	+	0.446526i
$831$	55.7770	+	46.8025i	1.93488	+	1.62356i
$832$	−1.53209	+	1.28558i	−0.0531156	+	0.0445693i
$833$		0			0
$834$	−46.3569	+	16.8725i	−1.60521	+	0.584248i
$835$	−19.7490			−0.683443
$836$		0			0
$837$	−14.9373			−0.516307
$838$	−29.8343	+	10.8588i	−1.03061	+	0.375111i
$839$	7.20992	−	40.8895i	0.248914	−	1.41166i	−0.562310	−	0.826926i	$-0.690087\pi$
$839$	7.20992	−	40.8895i	0.248914	−	1.41166i	0.811224	−	0.584735i	$-0.198802\pi$
$840$	−12.1606	+	10.2039i	−0.419580	+	0.352069i
$841$	−20.1405	−	16.8999i	−0.694499	−	0.582754i
$842$	−4.30852	−	24.4348i	−0.148481	−	0.842079i
$843$	−33.6771	−	58.3305i	−1.15990	−	2.00901i
$844$	−6.64575	+	11.5108i	−0.228756	+	0.396217i
$845$	−13.9185	−	5.06592i	−0.478811	−	0.174273i
$846$	16.3666	+	5.95696i	0.562696	+	0.204805i
$847$	−19.2915	+	33.4139i	−0.662864	+	1.14811i
$848$	−6.29150	−	10.8972i	−0.216051	−	0.374211i
$849$	−14.0796	−	79.8492i	−0.483210	−	2.74042i
$850$		0			0
$851$	0.446608	−	0.374749i	0.0153095	−	0.0128462i
$852$	−1.24436	+	7.05714i	−0.0426312	+	0.241774i
$853$	−8.06539	+	2.93556i	−0.276154	+	0.100512i	−0.476385	−	0.879237i	$-0.658053\pi$
$853$	−8.06539	+	2.93556i	−0.276154	+	0.100512i	0.200231	+	0.979749i	$0.435831\pi$
$854$	−3.41699			−0.116927
$855$		0			0
$856$	15.2915			0.522653
$857$	19.7335	−	7.18242i	0.674085	−	0.245347i	0.0177793	−	0.999842i	$-0.494340\pi$
$857$	19.7335	−	7.18242i	0.674085	−	0.245347i	0.656306	+	0.754495i	$0.272118\pi$
$858$	4.26879	−	24.2095i	0.145734	−	0.826500i
$859$	10.1338	−	8.50328i	0.345761	−	0.290128i	−0.453324	−	0.891346i	$-0.649762\pi$
$859$	10.1338	−	8.50328i	0.345761	−	0.290128i	0.799085	+	0.601218i	$0.205318\pi$
$860$	−14.2354	−	11.9449i	−0.485423	−	0.407319i
$861$	−0.488257	−	2.76904i	−0.0166398	−	0.0943688i
$862$	−13.9373	−	24.1400i	−0.474705	−	0.822213i
$863$	−15.5314	+	26.9011i	−0.528694	+	0.915725i	0.470746	+	0.882269i	$0.343985\pi$
$863$	−15.5314	+	26.9011i	−0.528694	+	0.915725i	−0.999440	+	0.0334563i	$0.989349\pi$
$864$	−2.48619	−	0.904900i	−0.0845820	−	0.0307853i
$865$	9.27900	+	3.37728i	0.315496	+	0.114831i
$866$	−8.93725	+	15.4798i	−0.303700	+	0.526024i
$867$	−22.4889	−	38.9519i	−0.763763	−	1.32288i
$868$	3.57420	+	20.2703i	0.121316	+	0.688019i
$869$	−14.2354	−	11.9449i	−0.482903	−	0.405204i
$870$	5.48948	−	4.60622i	0.186111	−	0.156166i
$871$	0.224267	−	1.27188i	0.00759900	−	0.0430961i
$872$	−13.7035	+	4.98768i	−0.464061	+	0.168904i
$873$	14.8340			0.502054
$874$		0			0
$875$	43.7490			1.47899
$876$	4.24765	−	1.54602i	0.143515	−	0.0522352i
$877$	7.23171	−	41.0131i	0.244197	−	1.38491i	−0.578152	−	0.815929i	$-0.696226\pi$
$877$	7.23171	−	41.0131i	0.244197	−	1.38491i	0.822349	−	0.568983i	$-0.192663\pi$
$878$	8.28229	−	6.94967i	0.279514	−	0.234540i
$879$	58.6490	+	49.2123i	1.97818	+	1.65989i
$880$	1.32767	+	7.52960i	0.0447558	+	0.253823i
$881$	18.4373	+	31.9343i	0.621167	+	1.07589i	0.989269	+	0.146107i	$0.0466744\pi$
$881$	18.4373	+	31.9343i	0.621167	+	1.07589i	−0.368102	+	0.929785i	$0.619992\pi$
$882$	12.5830	−	21.7944i	0.423692	−	0.733856i
$883$	26.6824	+	9.71158i	0.897933	+	0.326821i	0.749424	−	0.662090i	$-0.230330\pi$
$883$	26.6824	+	9.71158i	0.897933	+	0.326821i	0.148509	+	0.988911i	$0.452553\pi$
$884$		0			0
$885$	−17.2804	+	29.9305i	−0.580874	+	1.00610i
$886$	5.32288	+	9.21949i	0.178826	+	0.309735i
$887$	3.02443	+	17.1524i	0.101550	+	0.575921i	0.992542	+	0.121902i	$0.0388992\pi$
$887$	3.02443	+	17.1524i	0.101550	+	0.575921i	−0.890992	+	0.454019i	$0.849990\pi$
$888$	−0.717978	−	0.602455i	−0.0240938	−	0.0202171i
$889$	37.1206	−	31.1479i	1.24499	−	1.04467i
$890$		0			0
$891$	−21.8279	+	7.94470i	−0.731262	+	0.266158i
$892$	18.8118			0.629864
$893$		0			0
$894$	28.9373			0.967807
$895$	−6.28304	+	2.28684i	−0.210019	+	0.0764406i
$896$	−0.633078	+	3.59036i	−0.0211497	+	0.119946i
$897$	−6.67110	+	5.59771i	−0.222741	+	0.186902i
$898$	−18.6084	−	15.6143i	−0.620969	−	0.521055i
$899$	−1.61345	−	9.15034i	−0.0538117	−	0.305181i
$900$	4.58301	+	7.93800i	0.152767	+	0.264600i
$901$		0			0
$902$	−1.27258	−	0.463180i	−0.0423722	−	0.0154222i
$903$	102.347	+	37.2511i	3.40588	+	1.23964i
$904$	7.79150	−	13.4953i	0.259142	−	0.448846i
$905$	−18.2915	−	31.6818i	−0.608030	−	1.05314i
$906$	−5.94376	−	33.7087i	−0.197468	−	1.11990i
$907$	−30.5937	−	25.6712i	−1.01585	−	0.852397i	−0.0267475	−	0.999642i	$-0.508515\pi$
$907$	−30.5937	−	25.6712i	−1.01585	−	0.852397i	−0.989100	+	0.147245i	$0.952959\pi$
$908$	5.63368	−	4.72722i	0.186960	−	0.156878i
$909$	−9.47824	+	53.7538i	−0.314373	+	1.78290i
$910$	11.2763	−	4.10424i	0.373806	−	0.136054i
$911$	−16.9373			−0.561156			−0.280578	−	0.959831i	$-0.590526\pi$
$911$	−16.9373			−0.561156			−0.280578	+	0.959831i	$0.590526\pi$
$912$		0			0
$913$	−36.8745			−1.22037
$914$	30.8919	−	11.2437i	1.02181	−	0.371910i
$915$	0.708665	−	4.01904i	0.0234277	−	0.132865i
$916$	15.3209	−	12.8558i	0.506216	−	0.424766i
$917$	5.41038	+	4.53985i	0.178666	+	0.149919i
$918$		0			0
$919$	9.93725	+	17.2118i	0.327800	+	0.567766i	0.982075	−	0.188491i	$-0.0603595\pi$
$919$	9.93725	+	17.2118i	0.327800	+	0.567766i	−0.654275	+	0.756257i	$0.727026\pi$
$920$	1.35425	−	2.34563i	0.0446483	−	0.0773330i
$921$	−1.60546	−	0.584341i	−0.0529018	−	0.0192547i
$922$	18.0102	+	6.55516i	0.593133	+	0.215883i
$923$	2.70850	−	4.69126i	0.0891513	−	0.154415i
$924$	−22.4059	−	38.8081i	−0.737099	−	1.27669i
$925$	0.140961	+	0.799429i	0.00463477	+	0.0262851i
$926$	29.4602	+	24.7200i	0.968121	+	0.812350i
$927$	40.7275	−	34.1745i	1.33767	−	1.12244i
$928$	0.285782	−	1.62075i	0.00938124	−	0.0532037i
$929$	9.00508	−	3.27758i	0.295447	−	0.107534i	−0.190044	−	0.981776i	$-0.560863\pi$
$929$	9.00508	−	3.27758i	0.295447	−	0.107534i	0.485491	+	0.874242i	$0.338641\pi$
$930$	−24.5830			−0.806108
$931$		0			0
$932$	18.8745			0.618255
$933$	33.9260	−	12.3480i	1.11069	−	0.404257i
$934$	3.36083	−	19.0602i	0.109970	−	0.623669i
$935$		0			0
$936$	6.12836	+	5.14230i	0.200312	+	0.168081i
$937$	1.23733	+	7.01724i	0.0404218	+	0.229243i	0.998325	−	0.0578464i	$-0.0184234\pi$
$937$	1.23733	+	7.01724i	0.0404218	+	0.229243i	−0.957904	+	0.287090i	$0.907312\pi$
$938$	−1.17712	−	2.03884i	−0.0384345	−	0.0665705i
$939$	11.7399	−	20.3341i	0.383116	−	0.663577i
$940$	6.73385	+	2.45092i	0.219634	+	0.0799402i
$941$	15.8188	+	5.75756i	0.515677	+	0.187691i	0.586732	−	0.809781i	$-0.300414\pi$
$941$	15.8188	+	5.75756i	0.515677	+	0.187691i	−0.0710546	+	0.997472i	$0.522636\pi$
$942$	14.0000	−	24.2487i	0.456145	−	0.790066i
$943$	0.239870	+	0.415468i	0.00781126	+	0.0135295i
$944$	1.37829	+	7.81667i	0.0448595	+	0.254411i
$945$	12.1606	+	10.2039i	0.395584	+	0.331934i
$946$	40.1848	−	33.7190i	1.30652	−	1.09630i
$947$	−1.34560	+	7.63129i	−0.0437262	+	0.247984i	−0.998834	−	0.0482745i	$-0.984628\pi$
$947$	−1.34560	+	7.63129i	−0.0437262	+	0.247984i	0.955108	+	0.296258i	$0.0957389\pi$
$948$	9.94477	−	3.61960i	0.322991	−	0.117559i
$949$	−3.41699			−0.110920
$950$		0			0
$951$	−15.8745			−0.514766
$952$		0			0
$953$	2.33687	−	13.2531i	0.0756987	−	0.429309i	−0.923280	−	0.384127i	$-0.874502\pi$
$953$	2.33687	−	13.2531i	0.0756987	−	0.429309i	0.998979	−	0.0451814i	$-0.0143866\pi$
$954$	−38.5566	+	32.3528i	−1.24831	+	1.04746i
$955$	−8.29932	−	6.96395i	−0.268560	−	0.225348i
$956$	−2.08378	−	11.8177i	−0.0673942	−	0.382212i
$957$	10.1144	+	17.5186i	0.326951	+	0.566296i
$958$	3.29150	−	5.70105i	0.106344	−	0.184193i
$959$	−53.3856	−	19.4308i	−1.72391	−	0.627452i
$960$	−4.09166	−	1.48924i	−0.132058	−	0.0480650i
$961$	−0.437254	+	0.757346i	−0.0141050	+	0.0244305i
$962$	0.354249	+	0.613577i	0.0114214	+	0.0197825i
$963$	−10.6214	−	60.2368i	−0.342269	−	1.94110i
$964$	5.80892	+	4.87426i	0.187093	+	0.156989i
$965$	18.3851	−	15.4269i	0.591836	−	0.496610i
$966$	−2.75658	+	15.6333i	−0.0886915	+	0.502994i
$967$	12.4899	−	4.54596i	0.401649	−	0.146188i	−0.133294	−	0.991077i	$-0.542555\pi$
$967$	12.4899	−	4.54596i	0.401649	−	0.146188i	0.534943	+	0.844888i	$0.320333\pi$
$968$	−10.5830			−0.340151
$969$		0			0
$970$	6.10326			0.195964
$971$	−51.1144	+	18.6041i	−1.64034	+	0.597034i	−0.987098	−	0.160117i	$-0.948813\pi$
$971$	−51.1144	+	18.6041i	−1.64034	+	0.597034i	−0.653240	+	0.757151i	$0.726591\pi$
$972$	3.67544	−	20.8445i	0.117890	−	0.668586i
$973$	52.0740	−	43.6953i	1.66942	−	1.40081i
$974$	3.23942	+	2.71819i	0.103798	+	0.0870965i
$975$	−2.10557	−	11.9413i	−0.0674322	−	0.382427i
$976$	−0.468627	−	0.811686i	−0.0150004	−	0.0259814i
$977$	−3.72876	+	6.45840i	−0.119293	+	0.206622i	−0.919488	−	0.393118i	$-0.871396\pi$
$977$	−3.72876	+	6.45840i	−0.119293	+	0.206622i	0.800194	+	0.599741i	$0.204730\pi$
$978$	−9.78877	−	3.56282i	−0.313010	−	0.113926i
$979$		0			0
$980$	5.17712	−	8.96704i	0.165377	−	0.286442i
$981$	29.1660	+	50.5170i	0.931199	+	1.61288i
$982$	−6.82290	−	38.6946i	−0.217727	−	1.23479i
$983$	−24.3212	−	20.4079i	−0.775724	−	0.650910i	0.166444	−	0.986051i	$-0.446772\pi$
$983$	−24.3212	−	20.4079i	−0.775724	−	0.650910i	−0.942168	+	0.335141i	$0.891216\pi$
$984$	0.590807	−	0.495746i	0.0188342	−	0.0158038i
$985$	2.18502	−	12.3918i	0.0696204	−	0.394837i
$986$		0			0
$987$	−42.0000			−1.33687
$988$		0			0
$989$	−18.5830			−0.590905
$990$	28.7386	−	10.4600i	0.913373	−	0.332441i
$991$	0.492117	−	2.79093i	0.0156326	−	0.0886570i	−0.975993	−	0.217801i	$-0.930112\pi$
$991$	0.492117	−	2.79093i	0.0156326	−	0.0886570i	0.991626	+	0.129144i	$0.0412228\pi$
$992$	−4.32490	+	3.62902i	−0.137316	+	0.115221i
$993$	40.1537	+	33.6930i	1.27424	+	1.06921i
$994$	−1.71469	−	9.72449i	−0.0543867	−	0.308442i
$995$	−16.3542	−	28.3264i	−0.518465	−	0.898007i
$996$	10.5000	−	18.1865i	0.332705	−	0.576262i
$997$	−15.2500	−	5.55056i	−0.482974	−	0.175788i	0.0890467	−	0.996027i	$-0.471618\pi$
$997$	−15.2500	−	5.55056i	−0.482974	−	0.175788i	−0.572020	+	0.820239i	$0.693840\pi$
$998$	−4.48350	−	1.63186i	−0.141923	−	0.0516557i
$999$	−0.468627	+	0.811686i	−0.0148267	+	0.0256806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.o.423.1		12
19.2	odd	18		722.2.a.j.1.2		2
19.3	odd	18		38.2.c.b.7.1	✓	4
19.4	even	9	inner	722.2.e.o.99.1		12
19.5	even	9		722.2.c.j.429.2		4
19.6	even	9	inner	722.2.e.o.389.1		12
19.7	even	3	inner	722.2.e.o.245.1		12
19.8	odd	6		722.2.e.n.415.1		12
19.9	even	9	inner	722.2.e.o.595.2		12
19.10	odd	18		722.2.e.n.595.1		12
19.11	even	3	inner	722.2.e.o.415.2		12
19.12	odd	6		722.2.e.n.245.2		12
19.13	odd	18		722.2.e.n.389.2		12
19.14	odd	18		38.2.c.b.11.1	yes	4
19.15	odd	18		722.2.e.n.99.2		12
19.16	even	9		722.2.c.j.653.2		4
19.17	even	9		722.2.a.g.1.1		2
19.18	odd	2		722.2.e.n.423.2		12
57.2	even	18		6498.2.a.ba.1.2		2
57.14	even	18		342.2.g.f.163.1		4
57.17	odd	18		6498.2.a.bg.1.2		2
57.41	even	18		342.2.g.f.235.1		4
76.3	even	18		304.2.i.e.273.2		4
76.55	odd	18		5776.2.a.z.1.2		2
76.59	even	18		5776.2.a.ba.1.1		2
76.71	even	18		304.2.i.e.49.2		4
95.3	even	36		950.2.j.g.349.2		8
95.14	odd	18		950.2.e.k.201.2		4
95.22	even	36		950.2.j.g.349.3		8
95.33	even	36		950.2.j.g.49.3		8
95.52	even	36		950.2.j.g.49.2		8
95.79	odd	18		950.2.e.k.501.2		4
152.3	even	18		1216.2.i.k.577.1		4
152.109	odd	18		1216.2.i.l.961.2		4
152.117	odd	18		1216.2.i.l.577.2		4
152.147	even	18		1216.2.i.k.961.1		4
228.71	odd	18		2736.2.s.v.1873.1		4
228.155	odd	18		2736.2.s.v.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	19.3	odd	18
38.2.c.b.11.1	yes	4	19.14	odd	18
304.2.i.e.49.2		4	76.71	even	18
304.2.i.e.273.2		4	76.3	even	18
342.2.g.f.163.1		4	57.14	even	18
342.2.g.f.235.1		4	57.41	even	18
722.2.a.g.1.1		2	19.17	even	9
722.2.a.j.1.2		2	19.2	odd	18
722.2.c.j.429.2		4	19.5	even	9
722.2.c.j.653.2		4	19.16	even	9
722.2.e.n.99.2		12	19.15	odd	18
722.2.e.n.245.2		12	19.12	odd	6
722.2.e.n.389.2		12	19.13	odd	18
722.2.e.n.415.1		12	19.8	odd	6
722.2.e.n.423.2		12	19.18	odd	2
722.2.e.n.595.1		12	19.10	odd	18
722.2.e.o.99.1		12	19.4	even	9	inner
722.2.e.o.245.1		12	19.7	even	3	inner
722.2.e.o.389.1		12	19.6	even	9	inner
722.2.e.o.415.2		12	19.11	even	3	inner
722.2.e.o.423.1		12	1.1	even	1	trivial
722.2.e.o.595.2		12	19.9	even	9	inner
950.2.e.k.201.2		4	95.14	odd	18
950.2.e.k.501.2		4	95.79	odd	18
950.2.j.g.49.2		8	95.52	even	36
950.2.j.g.49.3		8	95.33	even	36
950.2.j.g.349.2		8	95.3	even	36
950.2.j.g.349.3		8	95.22	even	36
1216.2.i.k.577.1		4	152.3	even	18
1216.2.i.k.961.1		4	152.147	even	18
1216.2.i.l.577.2		4	152.117	odd	18
1216.2.i.l.961.2		4	152.109	odd	18
2736.2.s.v.577.1		4	228.155	odd	18
2736.2.s.v.1873.1		4	228.71	odd	18
5776.2.a.z.1.2		2	76.55	odd	18
5776.2.a.ba.1.1		2	76.59	even	18
6498.2.a.ba.1.2		2	57.2	even	18
6498.2.a.bg.1.2		2	57.17	odd	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.459430 + 2.60556i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.26072 - 1.05787i) q^{5} +(0.459430 + 2.60556i) q^{6} +(-1.82288 - 3.15731i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-3.75877 - 1.36808i) q^{9} +(-1.54650 - 0.562880i) q^{10} +(2.32288 - 4.02334i) q^{11} +(1.32288 + 2.29129i) q^{12} +(-0.347296 - 1.96962i) q^{13} +(-2.79281 - 2.34344i) q^{14} +(3.33555 - 2.79886i) q^{15} +(0.173648 - 0.984808i) q^{16} -4.00000 q^{18} -1.64575 q^{20} +(9.06404 - 3.29904i) q^{21} +(0.806726 - 4.57517i) q^{22} +(-1.26072 + 1.05787i) q^{23} +(2.02676 + 1.70066i) q^{24} +(-0.397915 - 2.25669i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(1.32288 - 2.29129i) q^{27} +(-3.42589 - 1.24692i) q^{28} +(1.54650 + 0.562880i) q^{29} +(2.17712 - 3.77089i) q^{30} +(-2.82288 - 4.88936i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(9.41584 + 7.90083i) q^{33} +(-1.04189 + 5.90885i) q^{35} +(-3.75877 + 1.36808i) q^{36} -0.354249 q^{37} +5.29150 q^{39} +(-1.54650 + 0.562880i) q^{40} +(0.0506189 - 0.287074i) q^{41} +(7.38907 - 6.20017i) q^{42} +(8.64979 + 7.25804i) q^{43} +(-0.806726 - 4.57517i) q^{44} +(3.29150 + 5.70105i) q^{45} +(-0.822876 + 1.42526i) q^{46} +(-4.09166 - 1.48924i) q^{47} +(2.48619 + 0.904900i) q^{48} +(-3.14575 + 5.44860i) q^{49} +(-1.14575 - 1.98450i) q^{50} +(-1.53209 - 1.28558i) q^{52} +(9.63914 - 8.08820i) q^{53} +(0.459430 - 2.60556i) q^{54} +(-7.18466 + 2.61500i) q^{55} -3.64575 q^{56} +1.64575 q^{58} +(-7.45858 + 2.71470i) q^{59} +(0.756107 - 4.28810i) q^{60} +(0.717978 - 0.602455i) q^{61} +(-4.32490 - 3.62902i) q^{62} +(2.53231 + 14.3615i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.64575 + 2.85052i) q^{65} +(11.5502 + 4.20394i) q^{66} +(0.606808 + 0.220860i) q^{67} +(-2.17712 - 3.77089i) q^{69} +(1.04189 + 5.90885i) q^{70} +(2.07483 + 1.74099i) q^{71} +(-3.06418 + 2.57115i) q^{72} +(0.296677 - 1.68254i) q^{73} +(-0.332885 + 0.121160i) q^{74} +6.06275 q^{75} -16.9373 q^{77} +(4.97239 - 1.80980i) q^{78} +(0.694593 - 3.93923i) q^{79} +(-1.26072 + 1.05787i) q^{80} +(-3.83022 - 3.21394i) q^{81} +(-0.0506189 - 0.287074i) q^{82} +(-3.96863 - 6.87386i) q^{83} +(4.82288 - 8.35347i) q^{84} +(10.6105 + 3.86192i) q^{86} +(-2.17712 + 3.77089i) q^{87} +(-2.32288 - 4.02334i) q^{88} +(5.04287 + 4.23147i) q^{90} +(-5.58562 + 4.68689i) q^{91} +(-0.285782 + 1.62075i) q^{92} +(14.0364 - 5.10884i) q^{93} -4.35425 q^{94} +2.64575 q^{96} +(-3.48485 + 1.26838i) q^{97} +(-1.09251 + 6.19592i) q^{98} +(-14.2354 + 11.9449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} + 6 q^{8} + 12 q^{11} - 48 q^{18} + 12 q^{20} - 12 q^{26} + 42 q^{30} - 18 q^{31} - 36 q^{37} - 24 q^{45} + 6 q^{46} - 6 q^{49} + 18 q^{50} - 12 q^{56} - 12 q^{58} - 6 q^{64} + 12 q^{65}+ \cdots - 84 q^{94}+O(q^{100}) \) 12 * q - 6 * q^7 + 6 * q^8 + 12 * q^11 - 48 * q^18 + 12 * q^20 - 12 * q^26 + 42 * q^30 - 18 * q^31 - 36 * q^37 - 24 * q^45 + 6 * q^46 - 6 * q^49 + 18 * q^50 - 12 * q^56 - 12 * q^58 - 6 * q^64 + 12 * q^65 - 42 * q^69 + 168 * q^75 - 108 * q^77 + 42 * q^84 - 42 * q^87 - 12 * q^88 - 84 * q^94

Introduction

L-functions

Modular forms

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