LMFDB - Embedded newform 529.2.c.d.266.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,2,Mod(118,529)] 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("529.118"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$529 = 23^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	529.c (of order $11$ , degree $10$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [10,4,-7,8,-3,-5,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			266.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	529.266
Dual form			529.2.c.d.177.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44306 - 1.66538i) q^{2} +(-2.11435 - 1.35881i) q^{3} +(-0.406440 + 2.82685i) q^{4} +(-0.513652 + 1.12474i) q^{5} +(0.788201 + 5.48206i) q^{6} +(2.27667 + 0.668491i) q^{7} +(1.58671 - 1.01971i) q^{8} +(1.37787 + 3.01713i) q^{9} +(2.61435 - 0.767644i) q^{10} +(1.25199 - 1.44488i) q^{11} +(4.70052 - 5.42469i) q^{12} +(-0.188515 + 0.0553531i) q^{13} +(-2.17208 - 4.75620i) q^{14} +(2.61435 - 1.68014i) q^{15} +(1.49254 + 0.438250i) q^{16} +(0.221998 + 1.54403i) q^{17} +(3.03631 - 6.64858i) q^{18} +(1.13631 - 7.90319i) q^{19} +(-2.97071 - 1.90916i) q^{20} +(-3.90533 - 4.50700i) q^{21} -4.21297 q^{22} -4.74046 q^{24} +(2.27310 + 2.62330i) q^{25} +(0.364223 + 0.234072i) q^{26} +(0.113337 - 0.788278i) q^{27} +(-2.81506 + 6.16411i) q^{28} +(-0.708346 - 4.92665i) q^{29} +(-6.57075 - 1.92935i) q^{30} +(1.49969 - 0.963789i) q^{31} +(-2.99103 - 6.54943i) q^{32} +(-4.61047 + 1.35376i) q^{33} +(2.25104 - 2.59784i) q^{34} +(-1.92130 + 2.21729i) q^{35} +(-9.08899 + 2.66877i) q^{36} +(1.61315 + 3.53231i) q^{37} +(-14.8016 + 9.51240i) q^{38} +(0.473802 + 0.139121i) q^{39} +(0.331900 + 2.30841i) q^{40} +(0.177173 - 0.387954i) q^{41} +(-1.87023 + 13.0077i) q^{42} +(3.74625 + 2.40757i) q^{43} +(3.57559 + 4.12645i) q^{44} -4.10123 q^{45} -2.58842 q^{47} +(-2.56026 - 2.95470i) q^{48} +(-1.15242 - 0.740618i) q^{49} +(1.08857 - 7.57116i) q^{50} +(1.62866 - 3.56627i) q^{51} +(-0.0798548 - 0.555402i) q^{52} +(-9.42164 - 2.76644i) q^{53} +(-1.47634 + 0.948784i) q^{54} +(0.982022 + 2.15033i) q^{55} +(4.29408 - 1.26086i) q^{56} +(-13.1415 + 15.1661i) q^{57} +(-7.18257 + 8.28913i) q^{58} +(6.92649 - 2.03380i) q^{59} +(3.68694 + 8.07327i) q^{60} +(6.25023 - 4.01678i) q^{61} +(-3.76921 - 1.10674i) q^{62} +(1.12005 + 7.79010i) q^{63} +(-5.29867 + 11.6025i) q^{64} +(0.0345733 - 0.240463i) q^{65} +(8.90771 + 5.72464i) q^{66} +(-4.75855 - 5.49165i) q^{67} -4.45497 q^{68} +6.46519 q^{70} +(0.478234 + 0.551912i) q^{71} +(5.26289 + 3.38226i) q^{72} +(0.917125 - 6.37875i) q^{73} +(3.55476 - 7.78385i) q^{74} +(-1.24157 - 8.63530i) q^{75} +(21.8793 + 6.42434i) q^{76} +(3.81626 - 2.45256i) q^{77} +(-0.452036 - 0.989821i) q^{78} +(5.44808 - 1.59970i) q^{79} +(-1.25957 + 1.45362i) q^{80} +(5.20549 - 6.00746i) q^{81} +(-0.901763 + 0.264782i) q^{82} +(-5.35459 - 11.7249i) q^{83} +(14.3279 - 9.20798i) q^{84} +(-1.85066 - 0.543403i) q^{85} +(-1.39655 - 9.71319i) q^{86} +(-5.19671 + 11.3792i) q^{87} +(0.513183 - 3.56927i) q^{88} +(-11.6936 - 7.51503i) q^{89} +(5.91833 + 6.83012i) q^{90} -0.466190 q^{91} -4.48047 q^{93} +(3.73525 + 4.31070i) q^{94} +(8.30537 + 5.33754i) q^{95} +(-2.57536 + 17.9121i) q^{96} +(1.79616 - 3.93304i) q^{97} +(0.429607 + 2.98798i) q^{98} +(6.08446 + 1.78656i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - 3 q^{5} - 5 q^{6} + 6 q^{7} + 15 q^{8} - 2 q^{9} + 12 q^{10} + 7 q^{11} - 10 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{15} + 12 q^{16} + q^{17} - 3 q^{18} + 2 q^{19} + 2 q^{20}+ \cdots + 25 q^{99}+O(q^{100})$ 10 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - 3 * q^5 - 5 * q^6 + 6 * q^7 + 15 * q^8 - 2 * q^9 + 12 * q^10 + 7 * q^11 - 10 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^15 + 12 * q^16 + q^17 - 3 * q^18 + 2 * q^19 + 2 * q^20 - 24 * q^21 - 6 * q^22 - 38 * q^24 + 18 * q^25 - 10 * q^26 - 4 * q^27 - 26 * q^28 - 8 * q^29 - 4 * q^30 - 12 * q^31 - 23 * q^32 - 17 * q^33 - 26 * q^34 + 18 * q^35 - 6 * q^36 + 25 * q^37 - 52 * q^38 + 12 * q^39 + 12 * q^40 - 26 * q^41 - 14 * q^42 + 22 * q^43 + 32 * q^44 - 6 * q^45 - 18 * q^47 - 15 * q^48 + 15 * q^49 + 5 * q^50 + 18 * q^51 + 13 * q^52 - 48 * q^53 - 17 * q^54 + 32 * q^55 - 2 * q^56 - 8 * q^57 - q^58 + q^59 - 8 * q^60 + 36 * q^61 - 18 * q^62 - 21 * q^63 + 13 * q^64 + 13 * q^65 + 2 * q^66 - 10 * q^67 - 30 * q^68 + 38 * q^70 - 14 * q^71 - 3 * q^72 - 3 * q^73 + 32 * q^74 - 6 * q^75 + 50 * q^76 + 13 * q^77 + 7 * q^78 + 18 * q^79 + 14 * q^80 + 11 * q^81 - 6 * q^82 - 15 * q^83 + 16 * q^84 - 19 * q^85 + 22 * q^86 + 10 * q^87 + 16 * q^88 - 19 * q^89 + 24 * q^90 - 4 * q^91 + 4 * q^93 - 5 * q^94 + 28 * q^95 - 7 * q^96 + 21 * q^97 + 39 * q^98 + 25 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$ .

$n$	$5$
$\chi(n)$	$e\left(\frac{7}{11}\right)$

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

)

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

$2$	−1.44306	−	1.66538i	−1.02040	−	1.17760i	−0.983982	−	0.178266i	$-0.942951\pi$
$2$	−1.44306	−	1.66538i	−1.02040	−	1.17760i	−0.0364161	−	0.999337i	$-0.511594\pi$
$3$	−2.11435	−	1.35881i	−1.22072	−	0.784511i	−0.238302	−	0.971191i	$-0.576591\pi$
$3$	−2.11435	−	1.35881i	−1.22072	−	0.784511i	−0.982421	+	0.186680i	$0.940227\pi$
$4$	−0.406440	+	2.82685i	−0.203220	+	1.41343i
$5$	−0.513652	+	1.12474i	−0.229712	+	0.502999i	−0.989029	−	0.147722i	$-0.952806\pi$
$5$	−0.513652	+	1.12474i	−0.229712	+	0.502999i	0.759317	+	0.650721i	$0.225533\pi$
$6$	0.788201	+	5.48206i	0.321782	+	2.23804i
$7$	2.27667	+	0.668491i	0.860501	+	0.252666i	0.682070	−	0.731287i	$-0.261080\pi$
$7$	2.27667	+	0.668491i	0.860501	+	0.252666i	0.178431	+	0.983953i	$0.442898\pi$
$8$	1.58671	−	1.01971i	0.560986	−	0.360524i
$9$	1.37787	+	3.01713i	0.459292	+	1.00571i
$10$	2.61435	−	0.767644i	0.826731	−	0.242750i
$11$	1.25199	−	1.44488i	0.377490	−	0.435646i	−0.534934	−	0.844894i	$-0.679663\pi$
$11$	1.25199	−	1.44488i	0.377490	−	0.435646i	0.912423	+	0.409248i	$0.134209\pi$
$12$	4.70052	−	5.42469i	1.35692	−	1.56597i
$13$	−0.188515	+	0.0553531i	−0.0522847	+	0.0153522i	−0.307770	−	0.951461i	$-0.599583\pi$
$13$	−0.188515	+	0.0553531i	−0.0522847	+	0.0153522i	0.255486	+	0.966813i	$0.417765\pi$
$14$	−2.17208	−	4.75620i	−0.580514	−	1.27115i
$15$	2.61435	−	1.68014i	0.675023	−	0.433811i
$16$	1.49254	+	0.438250i	0.373136	+	0.109563i
$17$	0.221998	+	1.54403i	0.0538424	+	0.374482i	0.998871	+	0.0474955i	$0.0151240\pi$
$17$	0.221998	+	1.54403i	0.0538424	+	0.374482i	−0.945029	+	0.326986i	$0.893967\pi$
$18$	3.03631	−	6.64858i	0.715664	−	1.56709i
$19$	1.13631	−	7.90319i	0.260687	−	1.81312i	−0.267023	−	0.963690i	$-0.586040\pi$
$19$	1.13631	−	7.90319i	0.260687	−	1.81312i	0.527709	−	0.849425i	$-0.323051\pi$
$20$	−2.97071	−	1.90916i	−0.664270	−	0.426901i
$21$	−3.90533	−	4.50700i	−0.852214	−	0.983507i
$22$	−4.21297			−0.898208
$23$		0			0
$23$		0			0
$24$	−4.74046			−0.967643
$25$	2.27310	+	2.62330i	0.454620	+	0.524659i
$26$	0.364223	+	0.234072i	0.0714300	+	0.0459053i
$27$	0.113337	−	0.788278i	0.0218118	−	0.151704i
$28$	−2.81506	+	6.16411i	−0.531996	+	1.16491i
$29$	−0.708346	−	4.92665i	−0.131537	−	0.914857i	−0.943553	−	0.331222i	$-0.892539\pi$
$29$	−0.708346	−	4.92665i	−0.131537	−	0.914857i	0.812016	−	0.583635i	$-0.198370\pi$
$30$	−6.57075	−	1.92935i	−1.19965	−	0.352249i
$31$	1.49969	−	0.963789i	0.269351	−	0.173102i	−0.398992	−	0.916954i	$-0.630640\pi$
$31$	1.49969	−	0.963789i	0.269351	−	0.173102i	0.668344	+	0.743853i	$0.267004\pi$
$32$	−2.99103	−	6.54943i	−0.528744	−	1.15779i
$33$	−4.61047	+	1.35376i	−0.802579	+	0.235659i
$34$	2.25104	−	2.59784i	0.386050	−	0.445526i
$35$	−1.92130	+	2.21729i	−0.324758	+	0.374791i
$36$	−9.08899	+	2.66877i	−1.51483	+	0.444795i
$37$	1.61315	+	3.53231i	0.265200	+	0.580708i	0.994647	−	0.103330i	$-0.0329497\pi$
$37$	1.61315	+	3.53231i	0.265200	+	0.580708i	−0.729447	+	0.684037i	$0.760222\pi$
$38$	−14.8016	+	9.51240i	−2.40113	+	1.54311i
$39$	0.473802	+	0.139121i	0.0758691	+	0.0222772i
$40$	0.331900	+	2.30841i	0.0524779	+	0.364992i
$41$	0.177173	−	0.387954i	0.0276697	−	0.0605883i	−0.895293	−	0.445479i	$-0.853033\pi$
$41$	0.177173	−	0.387954i	0.0276697	−	0.0605883i	0.922962	+	0.384890i	$0.125761\pi$
$42$	−1.87023	+	13.0077i	−0.288583	+	2.00714i
$43$	3.74625	+	2.40757i	0.571297	+	0.367150i	0.794169	−	0.607698i	$-0.207907\pi$
$43$	3.74625	+	2.40757i	0.571297	+	0.367150i	−0.222872	+	0.974848i	$0.571543\pi$
$44$	3.57559	+	4.12645i	0.539041	+	0.622086i
$45$	−4.10123			−0.611375
$46$		0			0
$47$	−2.58842			−0.377559			−0.188780	−	0.982019i	$-0.560453\pi$
$47$	−2.58842			−0.377559			−0.188780	+	0.982019i	$0.560453\pi$
$48$	−2.56026	−	2.95470i	−0.369542	−	0.426475i
$49$	−1.15242	−	0.740618i	−0.164632	−	0.105803i
$50$	1.08857	−	7.57116i	0.153947	−	1.07072i
$51$	1.62866	−	3.56627i	0.228058	−	0.499378i
$52$	−0.0798548	−	0.555402i	−0.0110739	−	0.0770204i
$53$	−9.42164	−	2.76644i	−1.29416	−	0.380000i	−0.439059	−	0.898458i	$-0.644688\pi$
$53$	−9.42164	−	2.76644i	−1.29416	−	0.380000i	−0.855103	+	0.518458i	$0.826506\pi$
$54$	−1.47634	+	0.948784i	−0.200904	+	0.129113i
$55$	0.982022	+	2.15033i	0.132416	+	0.289950i
$56$	4.29408	−	1.26086i	0.573821	−	0.168489i
$57$	−13.1415	+	15.1661i	−1.74063	+	2.00880i
$58$	−7.18257	+	8.28913i	−0.943118	+	1.08842i
$59$	6.92649	−	2.03380i	0.901752	−	0.264778i	0.202187	−	0.979347i	$-0.435195\pi$
$59$	6.92649	−	2.03380i	0.901752	−	0.264778i	0.699565	+	0.714569i	$0.253377\pi$
$60$	3.68694	+	8.07327i	0.475982	+	1.04225i
$61$	6.25023	−	4.01678i	0.800260	−	0.514296i	−0.0754408	−	0.997150i	$-0.524036\pi$
$61$	6.25023	−	4.01678i	0.800260	−	0.514296i	0.875701	+	0.482855i	$0.160400\pi$
$62$	−3.76921	−	1.10674i	−0.478691	−	0.140556i
$63$	1.12005	+	7.79010i	0.141113	+	0.981460i
$64$	−5.29867	+	11.6025i	−0.662334	+	1.45031i
$65$	0.0345733	−	0.240463i	0.00428830	−	0.0298258i
$66$	8.90771	+	5.72464i	1.09646	+	0.704654i
$67$	−4.75855	−	5.49165i	−0.581349	−	0.670912i	0.386545	−	0.922270i	$-0.373668\pi$
$67$	−4.75855	−	5.49165i	−0.581349	−	0.670912i	−0.967894	+	0.251358i	$0.919123\pi$
$68$	−4.45497			−0.540244
$69$		0			0
$70$	6.46519			0.772738
$71$	0.478234	+	0.551912i	0.0567559	+	0.0654999i	0.783418	−	0.621496i	$-0.213475\pi$
$71$	0.478234	+	0.551912i	0.0567559	+	0.0654999i	−0.726662	+	0.686996i	$0.758929\pi$
$72$	5.26289	+	3.38226i	0.620238	+	0.398603i
$73$	0.917125	−	6.37875i	0.107341	−	0.746576i	−0.863064	−	0.505094i	$-0.831458\pi$
$73$	0.917125	−	6.37875i	0.107341	−	0.746576i	0.970405	−	0.241481i	$-0.0776332\pi$
$74$	3.55476	−	7.78385i	0.413233	−	0.904854i
$75$	−1.24157	−	8.63530i	−0.143364	−	0.997118i
$76$	21.8793	+	6.42434i	2.50973	+	0.736923i
$77$	3.81626	−	2.45256i	0.434903	−	0.279495i
$78$	−0.452036	−	0.989821i	−0.0511830	−	0.112075i
$79$	5.44808	−	1.59970i	0.612957	−	0.179980i	0.0395047	−	0.999219i	$-0.487422\pi$
$79$	5.44808	−	1.59970i	0.612957	−	0.179980i	0.573452	+	0.819239i	$0.305604\pi$
$80$	−1.25957	+	1.45362i	−0.140824	+	0.162519i
$81$	5.20549	−	6.00746i	0.578388	−	0.667495i
$82$	−0.901763	+	0.264782i	−0.0995831	+	0.0292402i
$83$	−5.35459	−	11.7249i	−0.587743	−	1.28698i	−0.936797	−	0.349874i	$-0.886224\pi$
$83$	−5.35459	−	11.7249i	−0.587743	−	1.28698i	0.349054	−	0.937103i	$-0.386503\pi$
$84$	14.3279	−	9.20798i	1.56330	−	1.00467i
$85$	−1.85066	−	0.543403i	−0.200732	−	0.0589403i
$86$	−1.39655	−	9.71319i	−0.150593	−	1.04740i
$87$	−5.19671	+	11.3792i	−0.557145	+	1.21998i
$88$	0.513183	−	3.56927i	0.0547055	−	0.380485i
$89$	−11.6936	−	7.51503i	−1.23952	−	0.796592i	−0.254175	−	0.967158i	$-0.581804\pi$
$89$	−11.6936	−	7.51503i	−1.23952	−	0.796592i	−0.985346	+	0.170567i	$0.945440\pi$
$90$	5.91833	+	6.83012i	0.623847	+	0.719957i
$91$	−0.466190			−0.0488700
$92$		0			0
$93$	−4.48047			−0.464603
$94$	3.73525	+	4.31070i	0.385261	+	0.444615i
$95$	8.30537	+	5.33754i	0.852113	+	0.547620i
$96$	−2.57536	+	17.9121i	−0.262847	+	1.82814i
$97$	1.79616	−	3.93304i	0.182372	−	0.399340i	−0.796261	−	0.604953i	$-0.793192\pi$
$97$	1.79616	−	3.93304i	0.182372	−	0.399340i	0.978633	+	0.205614i	$0.0659190\pi$
$98$	0.429607	+	2.98798i	0.0433969	+	0.301832i
$99$	6.08446	+	1.78656i	0.611511	+	0.179556i
$100$	−8.33955	+	5.35951i	−0.833955	+	0.535951i
$101$	−0.756171	−	1.65578i	−0.0752418	−	0.164757i	0.868273	−	0.496086i	$-0.165230\pi$
$101$	−0.756171	−	1.65578i	−0.0752418	−	0.164757i	−0.943515	+	0.331330i	$0.892503\pi$
$102$	−8.28947	+	2.43401i	−0.820780	+	0.241003i
$103$	10.0280	−	11.5730i	0.988091	−	1.14032i	−0.00201469	−	0.999998i	$-0.500641\pi$
$103$	10.0280	−	11.5730i	0.988091	−	1.14032i	0.990106	−	0.140320i	$-0.0448132\pi$
$104$	−0.242674	+	0.280061i	−0.0237962	+	0.0274622i
$105$	7.07518	−	2.07746i	0.690467	−	0.202739i
$106$	8.98882	+	19.6828i	0.873071	+	1.91176i
$107$	1.67269	−	1.07497i	0.161705	−	0.103921i	−0.457286	−	0.889320i	$-0.651178\pi$
$107$	1.67269	−	1.07497i	0.161705	−	0.103921i	0.618990	+	0.785398i	$0.287542\pi$
$108$	2.18228	+	0.640776i	0.209990	+	0.0616587i
$109$	−2.21937	−	15.4360i	−0.212577	−	1.47851i	−0.764507	−	0.644615i	$-0.777018\pi$
$109$	−2.21937	−	15.4360i	−0.212577	−	1.47851i	0.551930	−	0.833890i	$-0.313891\pi$
$110$	2.16400	−	4.73850i	0.206329	−	0.451798i
$111$	1.38897	−	9.66051i	0.131835	−	0.916935i
$112$	3.10506	+	1.99550i	0.293401	+	0.188557i
$113$	0.974593	+	1.12474i	0.0916820	+	0.105807i	0.799737	−	0.600351i	$-0.204972\pi$
$113$	0.974593	+	1.12474i	0.0916820	+	0.105807i	−0.708055	+	0.706158i	$0.750427\pi$
$114$	44.2213			4.14171
$115$		0			0
$116$	14.2148			1.31981
$117$	−0.426757	−	0.492504i	−0.0394537	−	0.0455320i
$118$	−13.3824	−	8.60035i	−1.23195	−	0.791726i
$119$	−0.526753	+	3.66365i	−0.0482874	+	0.335846i
$120$	2.43495	−	5.33179i	0.222279	−	0.486724i
$121$	1.04528	+	7.27009i	0.0950256	+	0.660917i
$122$	−15.7089	−	4.61256i	−1.42222	−	0.417601i
$123$	−0.901763	+	0.579528i	−0.0813092	+	0.0522543i
$124$	2.11496	+	4.63111i	0.189929	+	0.415886i
$125$	−10.0501	+	2.95097i	−0.898906	+	0.263943i
$126$	11.3572	−	13.1069i	1.01178	−	1.16766i
$127$	−3.92548	+	4.53024i	−0.348330	+	0.401994i	−0.902696	−	0.430279i	$-0.858415\pi$
$127$	−3.92548	+	4.53024i	−0.348330	+	0.401994i	0.554366	+	0.832273i	$0.312961\pi$
$128$	13.1520	−	3.86177i	1.16248	−	0.341335i
$129$	−4.64946	−	10.1809i	−0.409362	−	0.896377i
$130$	−0.450354	+	0.289425i	−0.0394987	+	0.0253842i
$131$	12.2516	+	3.59739i	1.07043	+	0.314306i	0.769043	−	0.639197i	$-0.220733\pi$
$131$	12.2516	+	3.59739i	1.07043	+	0.314306i	0.301384	+	0.953503i	$0.402551\pi$
$132$	−1.95299	−	13.5833i	−0.169986	−	1.18228i
$133$	7.87021	−	17.2333i	0.682433	−	1.49432i
$134$	−2.27883	+	15.8496i	−0.196861	+	1.36920i
$135$	0.828393	+	0.532376i	0.0712967	+	0.0458196i
$136$	1.92671	+	2.22355i	0.165214	+	0.190668i
$137$	0.697560			0.0595966			0.0297983	−	0.999556i	$-0.490514\pi$
$137$	0.697560			0.0595966			0.0297983	+	0.999556i	$0.490514\pi$
$138$		0			0
$139$	13.9559			1.18372			0.591862	−	0.806039i	$-0.298393\pi$
$139$	13.9559			1.18372			0.591862	+	0.806039i	$0.298393\pi$
$140$	−5.48707	−	6.33242i	−0.463742	−	0.535187i
$141$	5.47283	+	3.51717i	0.460895	+	0.296200i
$142$	0.229022	−	1.59288i	0.0192191	−	0.133672i
$143$	−0.156041	+	0.341683i	−0.0130488	+	0.0285729i
$144$	0.734282	+	5.10704i	0.0611902	+	0.425587i
$145$	5.90505	+	1.73388i	0.490388	+	0.143991i
$146$	−11.9465	+	7.67756i	−0.988700	+	0.635399i
$147$	1.43027	+	3.13186i	0.117967	+	0.258311i
$148$	−10.6410	+	3.12447i	−0.874681	+	0.256830i
$149$	10.8962	−	12.5749i	0.892655	−	1.03018i	−0.106700	−	0.994291i	$-0.534029\pi$
$149$	10.8962	−	12.5749i	0.892655	−	1.03018i	0.999356	−	0.0358880i	$-0.0114260\pi$
$150$	−12.5894	+	14.5289i	−1.02792	+	1.18628i
$151$	−12.6557	+	3.71604i	−1.02990	+	0.302407i	−0.752672	−	0.658396i	$-0.771235\pi$
$151$	−12.6557	+	3.71604i	−1.02990	+	0.302407i	−0.277233	+	0.960803i	$0.589417\pi$
$152$	−6.25601	−	13.6988i	−0.507430	−	1.11112i
$153$	−4.35264	+	2.79727i	−0.351890	+	0.226146i
$154$	−9.59155	−	2.81633i	−0.772909	−	0.226946i
$155$	0.313697	+	2.18181i	0.0251967	+	0.175247i
$156$	−0.585846	+	1.28282i	−0.0469053	+	0.102708i
$157$	−0.587572	+	4.08665i	−0.0468933	+	0.326150i	0.952849	+	0.303445i	$0.0981369\pi$
$157$	−0.587572	+	4.08665i	−0.0468933	+	0.326150i	−0.999742	+	0.0227050i	$0.992772\pi$
$158$	−10.5260	−	6.76467i	−0.837406	−	0.538168i
$159$	16.1616	+	18.6515i	1.28170	+	1.47916i
$160$	8.90276			0.703825
$161$		0			0
$162$	−17.5166			−1.37623
$163$	9.68494	+	11.1770i	0.758583	+	0.875451i	0.995371	−	0.0961100i	$-0.0306401\pi$
$163$	9.68494	+	11.1770i	0.758583	+	0.875451i	−0.236788	+	0.971561i	$0.576095\pi$
$164$	1.02468	+	0.658522i	0.0800140	+	0.0514219i
$165$	0.845552	−	5.88094i	0.0658261	−	0.457831i
$166$	−11.7995	+	25.8372i	−0.915816	+	2.00536i
$167$	−0.189242	−	1.31621i	−0.0146440	−	0.101851i	0.981189	−	0.193052i	$-0.0618386\pi$
$167$	−0.189242	−	1.31621i	−0.0146440	−	0.101851i	−0.995833	+	0.0912007i	$0.970930\pi$
$168$	−10.7925	−	3.16896i	−0.832657	−	0.244490i
$169$	−10.9038	+	7.00746i	−0.838756	+	0.539035i
$170$	1.76564	+	3.86622i	0.135419	+	0.296526i
$171$	25.4106	−	7.46122i	1.94320	−	0.570574i
$172$	−8.32846	+	9.61155i	−0.635039	+	0.732874i
$173$	11.0908	−	12.7994i	0.843214	−	0.973121i	−0.156680	−	0.987649i	$-0.550079\pi$
$173$	11.0908	−	12.7994i	0.843214	−	0.973121i	0.999894	+	0.0145281i	$0.00462459\pi$
$174$	26.4499	−	7.76638i	2.00516	−	0.588768i
$175$	3.42145	+	7.49193i	0.258637	+	0.566337i
$176$	2.50187	−	1.60785i	0.188585	−	0.121197i
$177$	−17.4086	−	5.11163i	−1.30851	−	0.384213i
$178$	4.35921	+	30.3190i	0.326737	+	2.27250i
$179$	−0.594604	+	1.30200i	−0.0444428	+	0.0973162i	−0.930551	−	0.366162i	$-0.880672\pi$
$179$	−0.594604	+	1.30200i	−0.0444428	+	0.0973162i	0.886108	+	0.463478i	$0.153399\pi$
$180$	1.66690	−	11.5936i	0.124244	−	0.864134i
$181$	−13.5706	−	8.72127i	−1.00869	−	0.648247i	−0.0716377	−	0.997431i	$-0.522823\pi$
$181$	−13.5706	−	8.72127i	−1.00869	−	0.648247i	−0.937054	+	0.349184i	$0.886459\pi$
$182$	0.672741	+	0.776384i	0.0498669	+	0.0575494i
$183$	−18.6732			−1.38037
$184$		0			0
$185$	−4.80153			−0.353015
$186$	6.46560	+	7.46170i	0.474081	+	0.547118i
$187$	2.50887	+	1.61235i	0.183467	+	0.117907i
$188$	1.05204	−	7.31707i	0.0767276	−	0.533653i
$189$	0.784989	−	1.71889i	0.0570995	−	0.125031i
$190$	−3.09612	−	21.5340i	−0.224616	−	1.56224i
$191$	19.9042	+	5.84440i	1.44022	+	0.422886i	0.906294	−	0.422647i	$-0.138899\pi$
$191$	19.9042	+	5.84440i	1.44022	+	0.422886i	0.533923	+	0.845533i	$0.320717\pi$
$192$	26.9688	−	17.3318i	1.94631	−	1.25082i
$193$	6.08677	+	13.3282i	0.438135	+	0.959382i	0.991937	+	0.126733i	$0.0404493\pi$
$193$	6.08677	+	13.3282i	0.438135	+	0.959382i	−0.553802	+	0.832649i	$0.686823\pi$
$194$	−9.14198	+	2.68433i	−0.656356	+	0.192723i
$195$	−0.399844	+	0.461445i	−0.0286334	+	0.0330448i
$196$	2.56201	−	2.95671i	0.183001	−	0.211194i
$197$	−11.2049	+	3.29004i	−0.798313	+	0.234406i	−0.655353	−	0.755322i	$-0.727480\pi$
$197$	−11.2049	+	3.29004i	−0.798313	+	0.234406i	−0.142960	+	0.989728i	$0.545662\pi$
$198$	−5.80494	−	12.7111i	−0.412539	−	0.903335i
$199$	−4.81484	+	3.09431i	−0.341315	+	0.219350i	−0.700057	−	0.714087i	$-0.746842\pi$
$199$	−4.81484	+	3.09431i	−0.341315	+	0.219350i	0.358742	+	0.933437i	$0.383206\pi$
$200$	6.28176	+	1.84449i	0.444188	+	0.130425i
$201$	2.59912	+	18.0773i	0.183328	+	1.27507i
$202$	−1.66631	+	3.64871i	−0.117241	+	0.256722i
$203$	1.68075	−	11.6899i	0.117966	−	0.820470i
$204$	9.41938	+	6.05347i	0.659488	+	0.423827i
$205$	0.345343	+	0.398547i	0.0241198	+	0.0278357i
$206$	−33.7445			−2.35109
$207$		0			0
$208$	−0.305626			−0.0211913
$209$	−9.99647	−	11.5365i	−0.691471	−	0.798000i
$210$	−13.6697	−	8.78498i	−0.943298	−	0.606221i
$211$	2.00205	−	13.9245i	0.137827	−	0.958606i	−0.797121	−	0.603820i	$-0.793645\pi$
$211$	2.00205	−	13.9245i	0.137827	−	0.958606i	0.934948	−	0.354786i	$-0.115446\pi$
$212$	11.6497	−	25.5092i	0.800102	−	1.75198i
$213$	−0.261212	−	1.81677i	−0.0178979	−	0.124483i
$214$	−4.20403	−	1.23441i	−0.287381	−	0.0843828i
$215$	−4.63215	+	2.97690i	−0.315910	+	0.203023i
$216$	−0.623986	−	1.36634i	−0.0424569	−	0.0929676i
$217$	4.05857	−	1.19170i	0.275514	−	0.0808982i
$218$	−22.5042	+	25.9713i	−1.52418	+	1.75900i
$219$	−10.6066	+	12.2407i	−0.716731	+	0.827151i
$220$	−6.47780	+	1.90205i	−0.436733	+	0.128236i
$221$	−0.127317	−	0.278784i	−0.00856424	−	0.0187531i
$222$	−18.0928	+	11.6275i	−1.21431	+	0.780390i
$223$	4.03331	+	1.18429i	0.270090	+	0.0793057i	0.413973	−	0.910289i	$-0.364141\pi$
$223$	4.03331	+	1.18429i	0.270090	+	0.0793057i	−0.143883	+	0.989595i	$0.545959\pi$
$224$	−2.43134	−	16.9104i	−0.162451	−	1.12987i
$225$	−4.78277	+	10.4728i	−0.318851	+	0.698187i
$226$	0.466724	−	3.24614i	0.0310460	−	0.215930i
$227$	15.5049	+	9.96443i	1.02910	+	0.661362i	0.942268	−	0.334861i	$-0.108689\pi$
$227$	15.5049	+	9.96443i	1.02910	+	0.661362i	0.0868320	+	0.996223i	$0.472326\pi$
$228$	−37.5311	−	43.3132i	−2.48556	−	2.86849i
$229$	10.9247			0.721923			0.360961	−	0.932581i	$-0.382449\pi$
$229$	10.9247			0.721923			0.360961	+	0.932581i	$0.382449\pi$
$230$		0			0
$231$	−11.4015			−0.750163
$232$	−6.14772	−	7.09485i	−0.403618	−	0.465799i
$233$	3.50368	+	2.25168i	0.229533	+	0.147512i	0.650353	−	0.759632i	$-0.274621\pi$
$233$	3.50368	+	2.25168i	0.229533	+	0.147512i	−0.420819	+	0.907144i	$0.638257\pi$
$234$	−0.204370	+	1.42143i	−0.0133601	+	0.0929216i
$235$	1.32955	−	2.91130i	0.0867300	−	0.189912i
$236$	2.93405	+	20.4068i	0.190990	+	1.32837i
$237$	−13.6929	−	4.02059i	−0.889447	−	0.261165i
$238$	6.86151	−	4.40962i	0.444765	−	0.285833i
$239$	−9.35396	−	20.4823i	−0.605057	−	1.32489i	−0.925904	−	0.377760i	$-0.876695\pi$
$239$	−9.35396	−	20.4823i	−0.605057	−	1.32489i	0.320846	−	0.947131i	$-0.396033\pi$
$240$	4.63836	−	1.36195i	0.299405	−	0.0879132i
$241$	−3.88276	+	4.48094i	−0.250110	+	0.288643i	−0.866897	−	0.498488i	$-0.833889\pi$
$241$	−3.88276	+	4.48094i	−0.250110	+	0.288643i	0.616786	+	0.787131i	$0.288434\pi$
$242$	10.5991	−	12.2320i	0.681334	−	0.786302i
$243$	−21.4616	+	6.30171i	−1.37676	+	0.404255i
$244$	8.81450	+	19.3011i	0.564290	+	1.23562i
$245$	1.42495	−	0.915758i	0.0910365	−	0.0585056i
$246$	2.26643	+	0.665485i	0.144503	+	0.0424298i
$247$	0.223254	+	1.55277i	0.0142053	+	0.0988003i
$248$	1.39677	−	3.05850i	0.0886951	−	0.194215i
$249$	−4.61047	+	32.0665i	−0.292177	+	2.03213i
$250$	19.4174	+	12.4788i	1.22806	+	0.789227i
$251$	1.01543	+	1.17187i	0.0640937	+	0.0739681i	0.786891	−	0.617092i	$-0.211689\pi$
$251$	1.01543	+	1.17187i	0.0640937	+	0.0739681i	−0.722797	+	0.691060i	$0.757144\pi$
$252$	−22.4767			−1.41590
$253$		0			0
$254$	13.2093			0.828824
$255$	3.17457	+	3.66365i	0.198799	+	0.229426i
$256$	−3.94983	−	2.53840i	−0.246864	−	0.158650i
$257$	−3.90766	+	27.1784i	−0.243753	+	1.69534i	0.389201	+	0.921153i	$0.372751\pi$
$257$	−3.90766	+	27.1784i	−0.243753	+	1.69534i	−0.632954	+	0.774189i	$0.718158\pi$
$258$	−10.2456	+	22.4348i	−0.637864	+	1.39673i
$259$	1.31130	+	9.12028i	0.0814801	+	0.566706i
$260$	0.665701	+	0.195468i	0.0412850	+	0.0121224i
$261$	13.8883	−	8.92548i	0.859665	−	0.552473i
$262$	−11.6888	−	25.5948i	−0.722135	−	1.58125i
$263$	12.4165	−	3.64582i	0.765635	−	0.224811i	0.124480	−	0.992222i	$-0.460274\pi$
$263$	12.4165	−	3.64582i	0.765635	−	0.224811i	0.641155	+	0.767412i	$0.278456\pi$
$264$	−5.93502	+	6.84938i	−0.365275	+	0.421550i
$265$	7.95097	−	9.17591i	0.488424	−	0.563672i
$266$	−40.0573	+	11.7619i	−2.45607	+	0.721167i
$267$	14.5129	+	31.7789i	0.888176	+	1.94483i
$268$	17.4582	−	11.2197i	1.06643	−	0.685351i
$269$	9.59269	+	2.81667i	0.584876	+	0.171735i	0.560766	−	0.827974i	$-0.310507\pi$
$269$	9.59269	+	2.81667i	0.584876	+	0.171735i	0.0241100	+	0.999709i	$0.492325\pi$
$270$	−0.308813	−	2.14784i	−0.0187938	−	0.130713i
$271$	1.83256	−	4.01274i	0.111320	−	0.243757i	−0.845770	−	0.533548i	$-0.820858\pi$
$271$	1.83256	−	4.01274i	0.111320	−	0.243757i	0.957090	+	0.289791i	$0.0935858\pi$
$272$	−0.345329	+	2.40182i	−0.0209387	+	0.145632i
$273$	0.985691	+	0.633465i	0.0596567	+	0.0383390i
$274$	−1.00662	−	1.16170i	−0.0608122	−	0.0701811i
$275$	6.63624			0.400180
$276$		0			0
$277$	−30.8042			−1.85085			−0.925423	−	0.378935i	$-0.876290\pi$
$277$	−30.8042			−1.85085			−0.925423	+	0.378935i	$0.876290\pi$
$278$	−20.1392	−	23.2419i	−1.20787	−	1.39396i
$279$	4.97425	+	3.19676i	0.297801	+	0.191385i
$280$	−0.787527	+	5.47737i	−0.0470637	+	0.327335i
$281$	−1.48690	+	3.25585i	−0.0887009	+	0.194228i	−0.948784	−	0.315927i	$-0.897685\pi$
$281$	−1.48690	+	3.25585i	−0.0887009	+	0.194228i	0.860083	+	0.510155i	$0.170412\pi$
$282$	−2.04019	−	14.1898i	−0.121492	−	0.844993i
$283$	−14.1817	−	4.16412i	−0.843014	−	0.247531i	−0.168416	−	0.985716i	$-0.553865\pi$
$283$	−14.1817	−	4.16412i	−0.843014	−	0.247531i	−0.674599	+	0.738185i	$0.735683\pi$
$284$	−1.75455	+	1.12758i	−0.104113	+	0.0669095i
$285$	−10.3078	−	22.5709i	−0.610580	−	1.33698i
$286$	0.794209	−	0.233201i	0.0469625	−	0.0137894i
$287$	0.662708	−	0.764806i	0.0391184	−	0.0451451i
$288$	15.6392	−	18.0486i	0.921548	−	1.06352i
$289$	13.9766	−	4.10391i	0.822155	−	0.241407i
$290$	−5.63378	−	12.3363i	−0.330827	−	0.724410i
$291$	−9.14198	+	5.87519i	−0.535912	+	0.344410i
$292$	17.6590	+	5.18516i	1.03342	+	0.303438i
$293$	−3.06168	−	21.2945i	−0.178866	−	1.24404i	−0.859393	−	0.511315i	$-0.829159\pi$
$293$	−3.06168	−	21.2945i	−0.178866	−	1.24404i	0.680528	−	0.732722i	$-0.261750\pi$
$294$	3.15177	−	6.90141i	0.183815	−	0.402498i
$295$	−1.27031	+	8.83517i	−0.0739600	+	0.514403i
$296$	6.16154	+	3.95978i	0.358132	+	0.230158i
$297$	−0.997067	−	1.15068i	−0.0578557	−	0.0667690i
$298$	−36.6660			−2.12401
$299$		0			0
$300$	24.9153			1.43849
$301$	6.91953	+	7.98557i	0.398835	+	0.460280i
$302$	24.4516	+	15.7141i	1.40703	+	0.904242i
$303$	−0.651086	+	4.52840i	−0.0374039	+	0.260150i
$304$	5.15956	−	11.2979i	0.295921	−	0.647977i
$305$	1.30739	+	9.09311i	0.0748611	+	0.520670i
$306$	10.9397	+	3.21217i	0.625378	+	0.183628i
$307$	11.8995	−	7.64733i	0.679139	−	0.436456i	−0.155071	−	0.987903i	$-0.549561\pi$
$307$	11.8995	−	7.64733i	0.679139	−	0.436456i	0.834210	+	0.551447i	$0.185924\pi$
$308$	5.38195	+	11.7848i	0.306665	+	0.671503i
$309$	−36.9283	+	10.8431i	−2.10078	+	0.616844i
$310$	3.18086	−	3.67091i	0.180661	−	0.208494i
$311$	−0.373362	+	0.430883i	−0.0211714	+	0.0244331i	−0.766237	−	0.642559i	$-0.777873\pi$
$311$	−0.373362	+	0.430883i	−0.0211714	+	0.0244331i	0.745065	+	0.666992i	$0.232418\pi$
$312$	0.893649	−	0.262399i	0.0505929	−	0.0148554i
$313$	−8.77886	−	19.2230i	−0.496210	−	1.08655i	−0.977683	−	0.210088i	$-0.932625\pi$
$313$	−8.77886	−	19.2230i	−0.496210	−	1.08655i	0.481472	−	0.876461i	$-0.340102\pi$
$314$	7.65373	−	4.91876i	0.431925	−	0.277582i
$315$	−9.33716	−	2.74164i	−0.526089	−	0.154474i
$316$	2.30780	+	16.0511i	0.129824	+	0.902945i
$317$	−3.66069	+	8.01580i	−0.205605	+	0.450212i	−0.984141	−	0.177388i	$-0.943235\pi$
$317$	−3.66069	+	8.01580i	−0.205605	+	0.450212i	0.778536	+	0.627600i	$0.215963\pi$
$318$	7.73965	−	53.8305i	0.434018	−	3.01866i
$319$	−8.00524	−	5.14466i	−0.448208	−	0.288046i
$320$	−10.3281	−	11.9193i	−0.577358	−	0.666307i
$321$	−4.99734			−0.278924
$322$		0			0
$323$	12.4550			0.693015
$324$	14.8665	+	17.1568i	0.825916	+	0.953157i
$325$	−0.573721	−	0.368708i	−0.0318243	−	0.0204523i
$326$	4.63803	−	32.2582i	0.256877	−	1.78662i
$327$	−16.2822	+	35.6530i	−0.900406	+	1.97161i
$328$	−0.114481	−	0.796236i	−0.00632118	−	0.0439648i
$329$	−5.89298	−	1.73033i	−0.324890	−	0.0953964i
$330$	−11.0142	+	7.07839i	−0.606311	+	0.389653i
$331$	12.5403	+	27.4595i	0.689279	+	1.50931i	0.852503	+	0.522722i	$0.175084\pi$
$331$	12.5403	+	27.4595i	0.689279	+	1.50931i	−0.163224	+	0.986589i	$0.552189\pi$
$332$	35.3209	−	10.3712i	1.93849	−	0.569191i
$333$	−8.43469	+	9.73415i	−0.462218	+	0.533428i
$334$	−1.91890	+	2.21453i	−0.104998	+	0.121174i
$335$	8.62092	−	2.53133i	0.471011	−	0.138301i
$336$	−3.85369	−	8.43840i	−0.210236	−	0.460352i
$337$	−4.16906	+	2.67929i	−0.227103	+	0.145950i	−0.649245	−	0.760580i	$-0.724915\pi$
$337$	−4.16906	+	2.67929i	−0.227103	+	0.145950i	0.422142	+	0.906530i	$0.361278\pi$
$338$	27.4050	+	8.04683i	1.49063	+	0.437690i
$339$	−0.532323	−	3.70239i	−0.0289118	−	0.201086i
$340$	2.28830	−	5.01068i	0.124101	−	0.271743i
$341$	0.485038	−	3.37351i	0.0262663	−	0.182686i
$342$	−49.0948	−	31.5513i	−2.65474	−	1.70610i
$343$	−13.0055	−	15.0091i	−0.702231	−	0.810418i
$344$	8.39923			0.452856
$345$		0			0
$346$	−37.3205			−2.00636
$347$	4.43141	+	5.11412i	0.237891	+	0.274541i	0.862124	−	0.506698i	$-0.169134\pi$
$347$	4.43141	+	5.11412i	0.237891	+	0.274541i	−0.624233	+	0.781238i	$0.714588\pi$
$348$	−30.0552	−	19.3153i	−1.61113	−	1.03541i
$349$	−1.43622	+	9.98913i	−0.0768791	+	0.534706i	0.914592	+	0.404378i	$0.132512\pi$
$349$	−1.43622	+	9.98913i	−0.0768791	+	0.534706i	−0.991471	+	0.130328i	$0.958397\pi$
$350$	7.53956	−	16.5093i	0.403007	−	0.882461i
$351$	0.0222678	+	0.154876i	0.00118857	+	0.00826667i
$352$	−13.2079	−	3.87817i	−0.703981	−	0.206707i
$353$	20.5849	−	13.2291i	1.09562	−	0.704113i	0.137507	−	0.990501i	$-0.456091\pi$
$353$	20.5849	−	13.2291i	1.09562	−	0.704113i	0.958114	+	0.286388i	$0.0924546\pi$
$354$	16.6089	+	36.3683i	0.882751	+	1.93296i
$355$	−0.866403	+	0.254399i	−0.0459839	+	0.0135021i
$356$	25.9966	−	30.0017i	1.37782	−	1.59009i
$357$	6.09195	−	7.03049i	0.322420	−	0.372093i
$358$	3.02638	−	0.888625i	0.159949	−	0.0469653i
$359$	0.173981	+	0.380966i	0.00918237	+	0.0201066i	0.914168	−	0.405336i	$-0.132846\pi$
$359$	0.173981	+	0.380966i	0.00918237	+	0.0201066i	−0.904985	+	0.425443i	$0.860118\pi$
$360$	−6.50745	+	4.18209i	−0.342973	+	0.220415i
$361$	−42.9388	−	12.6080i	−2.25994	−	0.663577i
$362$	5.05891	+	35.1855i	0.265890	+	1.84931i
$363$	7.66860	−	16.7919i	0.402497	−	0.881346i
$364$	0.189478	−	1.31785i	0.00993136	−	0.0690741i
$365$	6.70335	+	4.30798i	0.350869	+	0.225490i
$366$	26.9466	+	31.0981i	1.40852	+	1.62552i
$367$	28.5682			1.49125			0.745624	−	0.666367i	$-0.232151\pi$
$367$	28.5682			1.49125			0.745624	+	0.666367i	$0.232151\pi$
$368$		0			0
$369$	1.41463			0.0736426
$370$	6.92890	+	7.99637i	0.360216	+	0.415712i
$371$	−19.6006	−	12.5966i	−1.01761	−	0.653981i
$372$	1.82104	−	12.6656i	0.0944167	−	0.656683i
$373$	5.98520	−	13.1058i	0.309902	−	0.678591i	−0.689033	−	0.724730i	$-0.741964\pi$
$373$	5.98520	−	13.1058i	0.309902	−	0.678591i	0.998935	+	0.0461391i	$0.0146918\pi$
$374$	−0.935270	−	6.50494i	−0.0483616	−	0.336363i
$375$	25.2592	+	7.41678i	1.30438	+	0.383001i
$376$	−4.10706	+	2.63945i	−0.211806	+	0.136119i
$377$	0.406239	+	0.889540i	0.0209224	+	0.0458136i
$378$	−3.99539	+	1.17315i	−0.205501	+	0.0603404i
$379$	3.68498	−	4.25270i	0.189285	−	0.218446i	−0.653173	−	0.757209i	$-0.726563\pi$
$379$	3.68498	−	4.25270i	0.189285	−	0.218446i	0.842458	+	0.538762i	$0.181108\pi$
$380$	−18.4641	+	21.3087i	−0.947187	+	1.09311i
$381$	14.4556	−	4.24455i	0.740582	−	0.217455i
$382$	−18.9898	−	41.5819i	−0.971604	−	2.12752i
$383$	0.194885	−	0.125245i	0.00995815	−	0.00639971i	−0.535652	−	0.844439i	$-0.679934\pi$
$383$	0.194885	−	0.125245i	0.00995815	−	0.00639971i	0.545610	+	0.838039i	$0.316298\pi$
$384$	−33.0553	−	9.70592i	−1.68685	−	0.495303i
$385$	0.798266	+	5.55206i	0.0406834	+	0.282959i
$386$	13.4129	−	29.3701i	0.682698	−	1.49490i
$387$	−2.10207	+	14.6202i	−0.106854	+	0.743187i
$388$	10.3881	+	6.67602i	0.527376	+	0.338924i
$389$	19.7570	+	22.8008i	1.00172	+	1.15605i	0.987734	+	0.156146i	$0.0499069\pi$
$389$	19.7570	+	22.8008i	1.00172	+	1.15605i	0.0139870	+	0.999902i	$0.495548\pi$
$390$	1.34548			0.0681311
$391$		0			0
$392$	−2.58378			−0.130500
$393$	−21.0160	−	24.2538i	−1.06012	−	1.22344i
$394$	21.6485	+	13.9126i	1.09063	+	0.700909i
$395$	−0.999168	+	6.94937i	−0.0502736	+	0.349661i
$396$	−7.52330	+	16.4737i	−0.378060	+	0.827836i
$397$	1.85654	+	12.9125i	0.0931768	+	0.648059i	0.981870	+	0.189556i	$0.0607050\pi$
$397$	1.85654	+	12.9125i	0.0931768	+	0.648059i	−0.888693	+	0.458503i	$0.848386\pi$
$398$	12.1013	+	3.55327i	0.606584	+	0.178109i
$399$	−40.0573	+	25.7433i	−2.00537	+	1.28877i
$400$	2.24304	+	4.91157i	0.112152	+	0.245579i
$401$	20.4619	−	6.00816i	1.02182	−	0.300033i	0.272439	−	0.962173i	$-0.412170\pi$
$401$	20.4619	−	6.00816i	1.02182	−	0.300033i	0.749380	+	0.662140i	$0.230352\pi$
$402$	26.3549	−	30.4151i	1.31446	−	1.51697i
$403$	−0.229365	+	0.264701i	−0.0114255	+	0.0131857i
$404$	4.98799	−	1.46461i	0.248162	−	0.0728669i
$405$	4.08302	+	8.94057i	0.202887	+	0.444261i
$406$	−21.8936	+	14.0701i	−1.08656	+	0.698289i
$407$	7.12339	+	2.09162i	0.353093	+	0.103678i
$408$	−1.05237	−	7.31941i	−0.0521002	−	0.362365i
$409$	−3.80064	+	8.32224i	−0.187930	+	0.411509i	−0.980021	−	0.198894i	$-0.936265\pi$
$409$	−3.80064	+	8.32224i	−0.187930	+	0.411509i	0.792091	+	0.610403i	$0.208992\pi$
$410$	0.165382	−	1.15026i	0.00816762	−	0.0568071i
$411$	−1.47489	−	0.947853i	−0.0727509	−	0.0467542i
$412$	28.6393	+	33.0515i	1.41096	+	1.62833i
$413$	17.1289			0.842859
$414$		0			0
$415$	15.9379			0.782360
$416$	0.926385	+	1.06910i	0.0454197	+	0.0524172i
$417$	−29.5077	−	18.9635i	−1.44500	−	0.928645i
$418$	−4.78723	+	33.2959i	−0.234151	+	1.62855i
$419$	−3.72802	+	8.16322i	−0.182125	+	0.398799i	−0.978571	−	0.205912i	$-0.933984\pi$
$419$	−3.72802	+	8.16322i	−0.182125	+	0.398799i	0.796445	+	0.604711i	$0.206711\pi$
$420$	2.99704	+	20.8449i	0.146241	+	1.01713i
$421$	−30.1974	−	8.86677i	−1.47173	−	0.432140i	−0.555071	−	0.831803i	$-0.687309\pi$
$421$	−30.1974	−	8.86677i	−1.47173	−	0.432140i	−0.916662	+	0.399663i	$0.869127\pi$
$422$	−26.0788	+	16.7598i	−1.26949	+	0.815855i
$423$	−3.56652	−	7.80958i	−0.173410	−	0.379715i
$424$	−17.7704	+	5.21785i	−0.863005	+	0.253401i
$425$	−3.54582	+	4.09210i	−0.171998	+	0.198496i
$426$	−2.64867	+	3.05672i	−0.128328	+	0.148099i
$427$	16.9149	−	4.96666i	0.818569	−	0.240354i
$428$	2.35894	+	5.16535i	0.114024	+	0.249677i
$429$	0.794209	−	0.510407i	0.0383448	−	0.0246427i
$430$	11.6422	+	3.41845i	0.561435	+	0.164852i
$431$	3.14550	+	21.8774i	0.151513	+	1.05380i	0.913685	+	0.406423i	$0.133224\pi$
$431$	3.14550	+	21.8774i	0.151513	+	1.05380i	−0.762171	+	0.647375i	$0.775867\pi$
$432$	0.514624	−	1.12687i	0.0247599	−	0.0542165i
$433$	−1.80672	+	12.5660i	−0.0868255	+	0.603885i	0.899231	+	0.437474i	$0.144127\pi$
$433$	−1.80672	+	12.5660i	−0.0868255	+	0.603885i	−0.986057	+	0.166411i	$0.946782\pi$
$434$	−7.84142	−	5.03937i	−0.376400	−	0.241898i
$435$	−10.1293	−	11.6899i	−0.485665	−	0.560487i
$436$	44.5375			2.13296
$437$		0			0
$438$	35.6915			1.70541
$439$	−12.0632	−	13.9217i	−0.575745	−	0.664445i	0.390940	−	0.920416i	$-0.372150\pi$
$439$	−12.0632	−	13.9217i	−0.575745	−	0.664445i	−0.966684	+	0.255971i	$0.917605\pi$
$440$	3.75090	+	2.41056i	0.178817	+	0.114919i
$441$	0.646641	−	4.49748i	0.0307924	−	0.214166i
$442$	−0.280557	+	0.614334i	−0.0133447	+	0.0292209i
$443$	1.98000	+	13.7712i	0.0940724	+	0.654288i	0.981233	+	0.192827i	$0.0617656\pi$
$443$	1.98000	+	13.7712i	0.0940724	+	0.654288i	−0.887160	+	0.461461i	$0.847325\pi$
$444$	26.7443	+	7.85284i	1.26923	+	0.372679i
$445$	14.4589	−	9.29218i	0.685418	−	0.440491i
$446$	−3.84803	−	8.42600i	−0.182209	−	0.398983i
$447$	−40.1255	+	11.7819i	−1.89787	+	0.557265i
$448$	−19.8195	+	22.8729i	−0.936382	+	1.08064i
$449$	−19.7064	+	22.7424i	−0.930001	+	1.07328i	0.0671417	+	0.997743i	$0.478612\pi$
$449$	−19.7064	+	22.7424i	−0.930001	+	1.07328i	−0.997143	+	0.0755354i	$0.975933\pi$
$450$	24.3430	−	7.14776i	1.14754	−	0.336949i
$451$	−0.338727	−	0.741708i	−0.0159500	−	0.0349257i
$452$	−3.57559	+	2.29789i	−0.168182	+	0.108084i
$453$	31.8080	+	9.33967i	1.49447	+	0.438816i
$454$	−5.78002	−	40.2009i	−0.271270	−	1.88672i
$455$	0.239459	−	0.524343i	0.0112260	−	0.0245816i
$456$	−5.38662	+	37.4648i	−0.252252	+	1.75445i
$457$	32.0076	+	20.5701i	1.49725	+	0.962227i	0.995249	+	0.0973617i	$0.0310404\pi$
$457$	32.0076	+	20.5701i	1.49725	+	0.962227i	0.502005	+	0.864865i	$0.332596\pi$
$458$	−15.7650	−	18.1938i	−0.736649	−	0.850138i
$459$	1.24228			0.0579849
$460$		0			0
$461$	8.76016			0.408001			0.204001	−	0.978971i	$-0.434606\pi$
$461$	8.76016			0.408001			0.204001	+	0.978971i	$0.434606\pi$
$462$	16.4531	+	18.9878i	0.765465	+	0.883394i
$463$	−23.4177	−	15.0497i	−1.08831	−	0.699417i	−0.131851	−	0.991270i	$-0.542092\pi$
$463$	−23.4177	−	15.0497i	−1.08831	−	0.699417i	−0.956463	+	0.291852i	$0.905728\pi$
$464$	1.10187	−	7.66368i	0.0511530	−	0.355777i
$465$	2.30140	−	5.03937i	0.106725	−	0.233695i
$466$	−1.30612	−	9.08426i	−0.0605048	−	0.420820i
$467$	16.6629	+	4.89266i	0.771066	+	0.226406i	0.643522	−	0.765427i	$-0.277472\pi$
$467$	16.6629	+	4.89266i	0.771066	+	0.226406i	0.127544	+	0.991833i	$0.459291\pi$
$468$	1.56569	−	1.00621i	0.0723740	−	0.0465119i
$469$	−7.16252	−	15.6837i	−0.330735	−	0.724208i
$470$	−6.76704	+	1.98698i	−0.312140	+	0.0916526i
$471$	6.79533	−	7.84223i	0.313112	−	0.361351i
$472$	8.91641	−	10.2901i	0.410411	−	0.473640i
$473$	8.16890	−	2.39861i	0.375606	−	0.110288i
$474$	13.0638	+	28.6058i	0.600042	+	1.31391i
$475$	23.3153	−	14.9839i	1.06978	−	0.687507i
$476$	−10.1425	−	2.97811i	−0.464881	−	0.136501i
$477$	−4.63513	−	32.2381i	−0.212228	−	1.47608i
$478$	−20.6125	+	45.1352i	−0.942795	+	2.06443i
$479$	3.62587	−	25.2185i	0.165670	−	1.15226i	−0.722038	−	0.691854i	$-0.756794\pi$
$479$	3.62587	−	25.2185i	0.165670	−	1.15226i	0.887708	−	0.460407i	$-0.152297\pi$
$480$	−18.8236	−	12.0972i	−0.859175	−	0.552158i
$481$	−0.499627	−	0.576601i	−0.0227810	−	0.0262907i
$482$	13.0655			0.595119
$483$		0			0
$484$	−20.9763			−0.953469
$485$	3.50105	+	4.04043i	0.158974	+	0.183466i
$486$	41.4652	+	26.6481i	1.88090	+	1.20878i
$487$	0.876812	−	6.09836i	0.0397321	−	0.276343i	−0.960264	−	0.279093i	$-0.909966\pi$
$487$	0.876812	−	6.09836i	0.0397321	−	0.276343i	0.999996	+	0.00274985i	$0.000875307\pi$
$488$	5.82132	−	12.7469i	0.263519	−	0.577025i
$489$	−5.28992	−	36.7922i	−0.239218	−	1.66380i
$490$	−3.58137	−	1.05159i	−0.161790	−	0.0475058i
$491$	−27.4649	+	17.6506i	−1.23947	+	0.796562i	−0.985339	−	0.170607i	$-0.945427\pi$
$491$	−27.4649	+	17.6506i	−1.23947	+	0.796562i	−0.254135	+	0.967169i	$0.581791\pi$
$492$	−1.27173	−	2.78469i	−0.0573339	−	0.125544i
$493$	7.44964	−	2.18741i	0.335515	−	0.0985161i
$494$	2.26378	−	2.61254i	0.101852	−	0.117544i
$495$	−5.13471	+	5.92577i	−0.230788	+	0.266343i
$496$	2.66073	−	0.781260i	0.119470	−	0.0350796i
$497$	0.719834	+	1.57622i	0.0322890	+	0.0707030i
$498$	60.0562	−	38.5958i	2.69118	−	1.72952i
$499$	8.22640	+	2.41549i	0.368264	+	0.108132i	0.460628	−	0.887593i	$-0.347624\pi$
$499$	8.22640	+	2.41549i	0.368264	+	0.108132i	−0.0923641	+	0.995725i	$0.529442\pi$
$500$	−4.25720	−	29.6095i	−0.190388	−	1.32418i
$501$	−1.38836	+	3.04008i	−0.0620272	+	0.135821i
$502$	0.486283	−	3.38217i	0.0217039	−	0.150954i
$503$	5.68312	+	3.65232i	0.253398	+	0.162849i	0.661173	−	0.750233i	$-0.270059\pi$
$503$	5.68312	+	3.65232i	0.253398	+	0.162849i	−0.407775	+	0.913082i	$0.633695\pi$
$504$	9.72087	+	11.2185i	0.433002	+	0.499711i
$505$	2.25073			0.100156
$506$		0			0
$507$	32.5764			1.44677
$508$	−11.2109	−	12.9380i	−0.497401	−	0.574032i
$509$	34.4683	+	22.1514i	1.52778	+	0.981845i	0.990358	+	0.138532i	$0.0442384\pi$
$509$	34.4683	+	22.1514i	1.52778	+	0.981845i	0.537423	+	0.843313i	$0.319398\pi$
$510$	1.52027	−	10.5737i	0.0673188	−	0.468213i
$511$	6.35213	−	13.9092i	0.281001	−	0.615307i
$512$	−2.42904	−	16.8943i	−0.107349	−	0.746631i
$513$	−6.10112	−	1.79145i	−0.269371	−	0.0790945i
$514$	50.9014	−	32.7124i	2.24517	−	1.44288i
$515$	7.86567	+	17.2234i	0.346603	+	0.758954i
$516$	30.6696	−	9.00541i	1.35015	−	0.396441i
$517$	−3.24068	+	3.73994i	−0.142525	+	0.164482i
$518$	13.2965	−	15.3449i	0.584213	−	0.674217i
$519$	−40.8418	+	11.9922i	−1.79276	+	0.526400i
$520$	−0.190346	−	0.416799i	−0.00834722	−	0.0182779i
$521$	−15.7540	+	10.1245i	−0.690196	+	0.443562i	−0.838156	−	0.545431i	$-0.816366\pi$
$521$	−15.7540	+	10.1245i	−0.690196	+	0.443562i	0.147959	+	0.988993i	$0.452730\pi$
$522$	−34.9060	−	10.2493i	−1.52780	−	0.448601i
$523$	−3.35351	−	23.3242i	−0.146639	−	1.01989i	−0.921671	−	0.387973i	$-0.873176\pi$
$523$	−3.35351	−	23.3242i	−0.146639	−	1.01989i	0.775032	−	0.631922i	$-0.217734\pi$
$524$	−15.1488	+	33.1713i	−0.661780	+	1.44910i
$525$	2.94597	−	20.4897i	0.128573	−	0.894244i
$526$	−23.9895	−	15.4171i	−1.04599	−	0.672217i
$527$	1.82104	+	2.10160i	0.0793259	+	0.0915470i
$528$	−7.47461			−0.325291
$529$		0			0
$530$	−26.7551			−1.16217
$531$	15.6801	+	18.0958i	0.680457	+	0.785289i
$532$	45.5174	+	29.2522i	1.97343	+	1.26825i
$533$	−0.0119253	+	0.0829423i	−0.000516542	+	0.00359263i
$534$	31.9809	−	70.0284i	1.38395	−	3.03043i
$535$	0.349885	+	2.43350i	0.0151268	+	0.105209i
$536$	−13.1503	−	3.86129i	−0.568008	−	0.166782i
$537$	3.02638	−	1.94494i	0.130598	−	0.0839302i
$538$	−9.15201	−	20.0401i	−0.394571	−	0.863990i
$539$	−2.51292	+	0.737861i	−0.108239	+	0.0317819i
$540$	−1.84164	+	2.12537i	−0.0792516	+	0.0914612i
$541$	−0.624271	+	0.720447i	−0.0268395	+	0.0309744i	−0.769011	−	0.639236i	$-0.779251\pi$
$541$	−0.624271	+	0.720447i	−0.0268395	+	0.0309744i	0.742171	+	0.670210i	$0.233796\pi$
$542$	−9.32724	+	2.73873i	−0.400639	+	0.117638i
$543$	16.8424	+	36.8797i	0.722776	+	1.58266i
$544$	9.44850	−	6.07218i	0.405101	−	0.260343i
$545$	18.5015	+	5.43254i	0.792519	+	0.232704i
$546$	−0.367451	−	2.55568i	−0.0157255	−	0.109373i
$547$	12.3736	−	27.0943i	0.529055	−	1.15847i	−0.436841	−	0.899539i	$-0.643903\pi$
$547$	12.3736	−	27.0943i	0.529055	−	1.15847i	0.965896	−	0.258930i	$-0.0833700\pi$
$548$	−0.283516	+	1.97190i	−0.0121112	+	0.0842354i
$549$	20.7312	+	13.3231i	0.884784	+	0.568616i
$550$	−9.57650	−	11.0519i	−0.408343	−	0.471253i
$551$	−39.7412			−1.69303
$552$		0			0
$553$	13.4729			0.572925
$554$	44.4524	+	51.3008i	1.88860	+	2.17956i
$555$	10.1521	+	6.52437i	0.430934	+	0.276944i
$556$	−5.67224	+	39.4513i	−0.240557	+	1.67311i
$557$	−2.49611	+	5.46572i	−0.105764	+	0.231590i	−0.955113	−	0.296240i	$-0.904267\pi$
$557$	−2.49611	+	5.46572i	−0.105764	+	0.231590i	0.849350	+	0.527830i	$0.176994\pi$
$558$	−1.85433	−	12.8971i	−0.0785000	−	0.545980i
$559$	−0.839490	−	0.246497i	−0.0355067	−	0.0104257i
$560$	−3.83935	+	2.46740i	−0.162242	+	0.104267i
$561$	−3.11375	−	6.81816i	−0.131463	−	0.287863i
$562$	7.56792	−	2.22214i	0.319234	−	0.0937354i
$563$	−0.0584071	+	0.0674053i	−0.00246156	+	0.00284080i	−0.756979	−	0.653439i	$-0.773326\pi$
$563$	−0.0584071	+	0.0674053i	−0.00246156	+	0.00284080i	0.754517	+	0.656280i	$0.227871\pi$
$564$	−12.1669	+	14.0414i	−0.512319	+	0.591248i
$565$	−1.76564	+	0.518440i	−0.0742812	+	0.0218109i
$566$	13.5302	+	29.6270i	0.568717	+	1.24532i
$567$	15.8671	−	10.1972i	0.666357	−	0.428241i
$568$	1.32161	+	0.388060i	0.0554535	+	0.0162826i
$569$	5.88608	+	40.9386i	0.246757	+	1.71623i	0.616715	+	0.787186i	$0.288463\pi$
$569$	5.88608	+	40.9386i	0.246757	+	1.71623i	−0.369958	+	0.929049i	$0.620628\pi$
$570$	−22.7144	+	49.7376i	−0.951401	+	2.08328i
$571$	−3.67037	+	25.5280i	−0.153600	+	1.06831i	0.756521	+	0.653970i	$0.226898\pi$
$571$	−3.67037	+	25.5280i	−0.153600	+	1.06831i	−0.910121	+	0.414343i	$0.864011\pi$
$572$	−0.902465	−	0.579979i	−0.0377339	−	0.0242501i
$573$	−34.1431	−	39.4032i	−1.42635	−	1.64609i
$574$	−2.23002			−0.0930793
$575$		0			0
$576$	−42.3070			−1.76279
$577$	−17.7757	−	20.5142i	−0.740011	−	0.854018i	0.253549	−	0.967323i	$-0.418402\pi$
$577$	−17.7757	−	20.5142i	−0.740011	−	0.854018i	−0.993560	+	0.113304i	$0.963857\pi$
$578$	−27.0037	−	17.3542i	−1.12321	−	0.721841i
$579$	5.24089	−	36.4512i	0.217804	−	1.51486i
$580$	−7.30147	+	15.9880i	−0.303177	+	0.663865i
$581$	−4.35264	−	30.2733i	−0.180578	−	1.25595i
$582$	22.9769	+	6.74662i	0.952422	+	0.279656i
$583$	−15.7930	+	10.1495i	−0.654078	+	0.420351i
$584$	−5.04929	−	11.0564i	−0.208941	−	0.457517i
$585$	0.773144	−	0.227016i	0.0319656	−	0.00938594i
$586$	−31.0452	+	35.8281i	−1.28247	+	1.48005i
$587$	−20.7164	+	23.9080i	−0.855057	+	0.986788i	−0.999996	−	0.00265257i	$-0.999156\pi$
$587$	−20.7164	+	23.9080i	−0.855057	+	0.986788i	0.144940	+	0.989440i	$0.453701\pi$
$588$	−9.43461	+	2.77025i	−0.389077	+	0.114243i
$589$	−5.91290	−	12.9475i	−0.243637	−	0.533490i
$590$	16.5471	−	10.6341i	0.681231	−	0.437801i
$591$	28.1616	+	8.26899i	1.15841	+	0.340141i
$592$	0.859662	+	5.97908i	0.0353319	+	0.245739i
$593$	−10.6953	+	23.4194i	−0.439202	+	0.961718i	0.552542	+	0.833485i	$0.313658\pi$
$593$	−10.6953	+	23.4194i	−0.439202	+	0.961718i	−0.991744	+	0.128233i	$0.959069\pi$
$594$	−0.477487	+	3.32099i	−0.0195915	+	0.136262i
$595$	−3.85009	−	2.47430i	−0.157838	−	0.101436i
$596$	31.1188	+	35.9130i	1.27468	+	1.47106i
$597$	14.3849			0.588733
$598$		0			0
$599$	16.9434			0.692289			0.346144	−	0.938181i	$-0.387491\pi$
$599$	16.9434			0.692289			0.346144	+	0.938181i	$0.387491\pi$
$600$	−10.7755	−	12.4356i	−0.439910	−	0.507683i
$601$	−8.12227	−	5.21986i	−0.331314	−	0.212923i	0.364398	−	0.931243i	$-0.381275\pi$
$601$	−8.12227	−	5.21986i	−0.331314	−	0.212923i	−0.695712	+	0.718321i	$0.744911\pi$
$602$	3.31370	−	23.0473i	0.135057	−	0.939339i
$603$	10.0123	−	21.9239i	0.407734	−	0.892812i
$604$	−5.36093	−	37.2861i	−0.218133	−	1.51715i
$605$	−8.71388	−	2.55863i	−0.354270	−	0.104023i
$606$	8.48108	−	5.45046i	0.344520	−	0.221410i
$607$	1.34813	+	2.95200i	0.0547191	+	0.119818i	0.935017	−	0.354604i	$-0.115384\pi$
$607$	1.34813	+	2.95200i	0.0547191	+	0.119818i	−0.880297	+	0.474422i	$0.842657\pi$
$608$	−55.1601	+	16.1965i	−2.23704	+	0.656853i
$609$	−19.4381	+	22.4327i	−0.787671	+	0.909020i
$610$	13.2569	−	15.2992i	0.536754	−	0.619448i
$611$	0.487956	−	0.143277i	0.0197406	−	0.00579636i
$612$	−6.13839	−	13.4412i	−0.248130	−	0.543328i
$613$	−27.6893	+	17.7948i	−1.11836	+	0.718726i	−0.963099	−	0.269148i	$-0.913258\pi$
$613$	−27.6893	+	17.7948i	−1.11836	+	0.718726i	−0.155260	+	0.987874i	$0.549622\pi$
$614$	−29.9074	−	8.78161i	−1.20696	−	0.354397i
$615$	−0.188626	−	1.31193i	−0.00760615	−	0.0529019i
$616$	3.55437	−	7.78299i	0.143210	−	0.313586i
$617$	−0.430421	+	2.99364i	−0.0173281	+	0.120519i	−0.996649	−	0.0817912i	$-0.973936\pi$
$617$	−0.430421	+	2.99364i	−0.0173281	+	0.120519i	0.979321	+	0.202311i	$0.0648450\pi$
$618$	71.3478	+	45.8524i	2.87003	+	1.84445i
$619$	−6.82521	−	7.87671i	−0.274328	−	0.316592i	0.601822	−	0.798631i	$-0.294442\pi$
$619$	−6.82521	−	7.87671i	−0.274328	−	0.316592i	−0.876150	+	0.482039i	$0.839896\pi$
$620$	−6.29515			−0.252819
$621$		0			0
$622$	1.25637			0.0503758
$623$	−21.5988	−	24.9263i	−0.865337	−	0.998652i
$624$	0.646201	+	0.415288i	0.0258687	+	0.0166248i
$625$	−0.626794	+	4.35944i	−0.0250717	+	0.174378i
$626$	−19.3452	+	42.3601i	−0.773191	+	1.69305i
$627$	5.46008	+	37.9757i	0.218054	+	1.51660i
$628$	−11.3135	−	3.32196i	−0.451460	−	0.132561i
$629$	−5.09586	+	3.27491i	−0.203185	+	0.130579i
$630$	8.90822	+	19.5063i	0.354912	+	0.777149i
$631$	−32.7200	+	9.60745i	−1.30256	+	0.382466i	−0.858170	−	0.513366i	$-0.828398\pi$
$631$	−32.7200	+	9.60745i	−1.30256	+	0.382466i	−0.444392	+	0.895833i	$0.646580\pi$
$632$	7.01327	−	8.09375i	0.278973	−	0.321952i
$633$	−23.1539	+	26.7210i	−0.920285	+	1.06206i
$634$	18.6320	−	5.47084i	0.739970	−	0.217275i
$635$	−3.07902	−	6.74211i	−0.122187	−	0.267552i
$636$	−59.2937	+	38.1057i	−2.35115	+	1.51099i
$637$	0.258245	+	0.0758275i	0.0102320	+	0.00300440i
$638$	2.98424	+	20.7558i	0.118147	+	0.821732i
$639$	−1.00624	+	2.20336i	−0.0398062	+	0.0871635i
$640$	−2.41205	+	16.7762i	−0.0953445	+	0.663136i
$641$	−7.57605	−	4.86883i	−0.299236	−	0.192307i	0.382404	−	0.923995i	$-0.375096\pi$
$641$	−7.57605	−	4.86883i	−0.299236	−	0.192307i	−0.681640	+	0.731688i	$0.738733\pi$
$642$	7.21146	+	8.32247i	0.284614	+	0.328462i
$643$	−22.9522			−0.905146			−0.452573	−	0.891727i	$-0.649494\pi$
$643$	−22.9522			−0.905146			−0.452573	+	0.891727i	$0.649494\pi$
$644$		0			0
$645$	13.8391			0.544913
$646$	−17.9733	−	20.7423i	−0.707151	−	0.816096i
$647$	−37.8180	−	24.3041i	−1.48678	−	0.955495i	−0.996470	−	0.0839454i	$-0.973248\pi$
$647$	−37.8180	−	24.3041i	−1.48678	−	0.955495i	−0.490308	−	0.871549i	$-0.663116\pi$
$648$	2.13370	−	14.8402i	0.0838196	−	0.582978i
$649$	5.73332	−	12.5542i	0.225052	−	0.492796i
$650$	0.213875	+	1.48753i	0.00838887	+	0.0583459i
$651$	−10.2006	−	2.99516i	−0.399792	−	0.117389i
$652$	−35.5321	+	22.8351i	−1.39155	+	0.894292i
$653$	−12.1980	−	26.7099i	−0.477344	−	1.04524i	−0.983185	−	0.182611i	$-0.941545\pi$
$653$	−12.1980	−	26.7099i	−0.477344	−	1.04524i	0.505841	−	0.862627i	$-0.331182\pi$
$654$	82.8720	−	24.3334i	3.24055	−	0.951511i
$655$	−10.3392	+	11.9321i	−0.403986	+	0.466224i
$656$	0.434459	−	0.501393i	0.0169628	−	0.0195761i
$657$	20.5092	−	6.02203i	0.800138	−	0.234942i
$658$	5.62226	+	12.3110i	0.219178	+	0.479934i
$659$	−33.7794	+	21.7087i	−1.31586	+	0.845652i	−0.994844	−	0.101421i	$-0.967661\pi$
$659$	−33.7794	+	21.7087i	−1.31586	+	0.845652i	−0.321017	+	0.947073i	$0.604025\pi$
$660$	16.2809	+	4.78050i	0.633733	+	0.186081i
$661$	−1.41839	−	9.86515i	−0.0551692	−	0.383710i	−0.998635	−	0.0522391i	$-0.983364\pi$
$661$	−1.41839	−	9.86515i	−0.0551692	−	0.383710i	0.943465	−	0.331471i	$-0.107545\pi$
$662$	27.6341	−	60.5102i	1.07403	−	2.35180i
$663$	−0.109624	+	0.762448i	−0.00425742	+	0.0296110i
$664$	−20.4522	−	13.1439i	−0.793701	−	0.510081i
$665$	15.3405	+	17.7039i	0.594879	+	0.686527i
$666$	28.3829			1.09981
$667$		0			0
$668$	3.79764			0.146935
$669$	−6.91862	−	7.98451i	−0.267489	−	0.308699i
$670$	−16.6562	−	10.7043i	−0.643483	−	0.413542i
$671$	2.02149	−	14.0598i	0.0780388	−	0.542772i
$672$	−17.8373	+	39.0583i	−0.688089	+	1.50670i
$673$	4.84678	+	33.7101i	0.186830	+	1.29943i	0.840153	+	0.542349i	$0.182465\pi$
$673$	4.84678	+	33.7101i	0.186830	+	1.29943i	−0.653323	+	0.757079i	$0.726626\pi$
$674$	10.4782	+	3.07669i	0.403607	+	0.118510i
$675$	2.32552	−	1.49452i	0.0895091	−	0.0575240i
$676$	−15.3773	−	33.6716i	−0.591435	−	1.29506i
$677$	23.9788	−	7.04081i	0.921580	−	0.270600i	0.213672	−	0.976905i	$-0.431458\pi$
$677$	23.9788	−	7.04081i	0.921580	−	0.270600i	0.707907	+	0.706305i	$0.249639\pi$
$678$	−5.39772	+	6.22930i	−0.207298	+	0.239235i
$679$	6.71847	−	7.75352i	0.257831	−	0.297553i
$680$	−3.49057	+	1.02492i	−0.133857	+	0.0393041i
$681$	−19.2432	−	42.1366i	−0.737399	−	1.61468i
$682$	−6.31813	+	4.06041i	−0.241934	+	0.155481i
$683$	−33.0796	−	9.71306i	−1.26576	−	0.371660i	−0.421123	−	0.907004i	$-0.638364\pi$
$683$	−33.0796	−	9.71306i	−1.26576	−	0.371660i	−0.844634	+	0.535344i	$0.820182\pi$
$684$	10.7639	+	74.8645i	0.411568	+	2.86252i
$685$	−0.358303	+	0.784574i	−0.0136901	+	0.0299770i
$686$	−6.22822	+	43.3182i	−0.237795	+	1.65390i
$687$	−23.0986	−	14.8446i	−0.881267	−	0.566356i
$688$	4.53632	+	5.23519i	0.172945	+	0.199590i
$689$	1.92925			0.0734987
$690$		0			0
$691$	−21.2259			−0.807470			−0.403735	−	0.914876i	$-0.632288\pi$
$691$	−21.2259			−0.807470			−0.403735	+	0.914876i	$0.632288\pi$
$692$	31.6743	+	36.5541i	1.20408	+	1.38958i
$693$	12.6580	+	8.13481i	0.480838	+	0.309016i
$694$	2.12217	−	14.7600i	0.0805563	−	0.560282i
$695$	−7.16848	+	15.6968i	−0.271916	+	0.595413i
$696$	3.35789	+	23.3546i	0.127280	+	0.885254i
$697$	0.638344	+	0.187435i	0.0241790	+	0.00709960i
$698$	18.7083	−	12.0231i	0.708118	−	0.455080i
$699$	−4.34841	−	9.52168i	−0.164472	−	0.360143i
$700$	−22.5692	+	6.62692i	−0.853036	+	0.250474i
$701$	15.7993	−	18.2333i	0.596730	−	0.688663i	−0.374386	−	0.927273i	$-0.622146\pi$
$701$	15.7993	−	18.2333i	0.596730	−	0.688663i	0.971115	+	0.238610i	$0.0766918\pi$
$702$	0.225794	−	0.260580i	0.00852204	−	0.00983496i
$703$	29.7495	−	8.73524i	1.12202	−	0.329456i
$704$	10.1302	+	22.1821i	0.381797	+	0.836020i
$705$	−6.76704	+	4.34891i	−0.254861	+	0.163789i
$706$	−51.7367	−	15.1913i	−1.94714	−	0.571731i
$707$	−0.614676	−	4.27517i	−0.0231173	−	0.160784i
$708$	21.5254	−	47.1340i	0.808973	−	1.77140i
$709$	−1.00146	+	6.96530i	−0.0376106	+	0.261587i	−0.999947	−	0.0102732i	$-0.996730\pi$
$709$	−1.00146	+	6.96530i	−0.0376106	+	0.261587i	0.962337	+	0.271861i	$0.0876390\pi$
$710$	1.67394	+	1.07578i	0.0628220	+	0.0403733i
$711$	12.3333	+	14.2334i	0.462534	+	0.533792i
$712$	−26.2175			−0.982544
$713$		0			0
$714$	−20.4995			−0.767175
$715$	−0.304153	−	0.351012i	−0.0113747	−	0.0131271i
$716$	−3.43890	−	2.21004i	−0.128518	−	0.0825932i
$717$	−8.05405	+	56.0171i	−0.300784	+	2.09200i
$718$	0.383388	−	0.839502i	0.0143079	−	0.0313299i
$719$	−3.78106	−	26.2978i	−0.141010	−	0.980743i	−0.930320	−	0.366749i	$-0.880471\pi$
$719$	−3.78106	−	26.2978i	−0.141010	−	0.980743i	0.789310	−	0.613994i	$-0.210438\pi$
$720$	−6.12127	−	1.79737i	−0.228126	−	0.0669839i
$721$	30.5670	−	19.6442i	1.13837	−	0.731588i
$722$	40.9662	+	89.7036i	1.52461	+	3.33842i
$723$	14.2983	−	4.19835i	0.531759	−	0.156138i
$724$	30.1694	−	34.8173i	1.12124	−	1.29398i
$725$	11.3139	−	13.0570i	0.420189	−	0.484924i
$726$	−39.0312	+	11.4606i	−1.44858	+	0.425342i
$727$	−2.17161	−	4.75515i	−0.0805404	−	0.176359i	0.865078	−	0.501638i	$-0.167269\pi$
$727$	−2.17161	−	4.75515i	−0.0805404	−	0.176359i	−0.945618	+	0.325279i	$0.894542\pi$
$728$	−0.739707	+	0.475381i	−0.0274154	+	0.0176188i
$729$	31.0593	+	9.11983i	1.15034	+	0.337771i
$730$	−2.49891	−	17.3803i	−0.0924889	−	0.643275i
$731$	−2.88569	+	6.31878i	−0.106731	+	0.233709i
$732$	7.58955	−	52.7865i	0.280518	−	1.95105i
$733$	−22.4521	−	14.4291i	−0.829288	−	0.532951i	0.0557637	−	0.998444i	$-0.482241\pi$
$733$	−22.4521	−	14.4291i	−0.829288	−	0.532951i	−0.885052	+	0.465493i	$0.845877\pi$
$734$	−41.2257	−	47.5770i	−1.52167	−	1.75610i
$735$	−4.25719			−0.157029
$736$		0			0
$737$	−13.8924			−0.511734
$738$	−2.04140	−	2.35590i	−0.0751448	−	0.0867217i
$739$	−1.88403	−	1.21079i	−0.0693051	−	0.0445397i	0.505529	−	0.862809i	$-0.331297\pi$
$739$	−1.88403	−	1.21079i	−0.0693051	−	0.0445397i	−0.574835	+	0.818270i	$0.694934\pi$
$740$	1.95153	−	13.5732i	0.0717398	−	0.498961i
$741$	1.63788	−	3.58646i	0.0601691	−	0.131752i
$742$	7.30683	+	50.8201i	0.268242	+	1.86567i
$743$	−17.4053	−	5.11067i	−0.638540	−	0.187492i	−0.0535916	−	0.998563i	$-0.517067\pi$
$743$	−17.4053	−	5.11067i	−0.638540	−	0.187492i	−0.584948	+	0.811071i	$0.698885\pi$
$744$	−7.10920	+	4.56881i	−0.260636	+	0.167501i
$745$	8.54667	+	18.7146i	0.313126	+	0.685650i
$746$	−30.4631	+	8.94478i	−1.11533	+	0.327492i
$747$	27.9976	−	32.3109i	1.02438	−	1.18220i
$748$	−5.57758	+	6.43687i	−0.203937	+	0.235355i
$749$	4.52677	−	1.32918i	0.165405	−	0.0485671i
$750$	−24.0988	−	52.7691i	−0.879966	−	1.92686i
$751$	23.7458	−	15.2605i	0.866497	−	0.556864i	−0.0301825	−	0.999544i	$-0.509609\pi$
$751$	23.7458	−	15.2605i	0.866497	−	0.556864i	0.896679	+	0.442681i	$0.145972\pi$
$752$	−3.86333	−	1.13437i	−0.140881	−	0.0413664i
$753$	−0.554631	−	3.85754i	−0.0202119	−	0.140577i
$754$	0.895195	−	1.96020i	0.0326011	−	0.0713864i
$755$	2.32103	−	16.1431i	0.0844709	−	0.587508i
$756$	4.53999	+	2.91767i	0.165118	+	0.106115i
$757$	−0.0799019	−	0.0922117i	−0.00290408	−	0.00335149i	0.754296	−	0.656535i	$-0.227979\pi$
$757$	−0.0799019	−	0.0922117i	−0.00290408	−	0.00335149i	−0.757200	+	0.653183i	$0.773433\pi$
$758$	−12.4000			−0.450389
$759$		0			0
$760$	18.6210			0.675453
$761$	17.4883	+	20.1826i	0.633951	+	0.731618i	0.978293	−	0.207226i	$-0.0664435\pi$
$761$	17.4883	+	20.1826i	0.633951	+	0.731618i	−0.344342	+	0.938844i	$0.611898\pi$
$762$	−27.9291	−	17.9489i	−1.01176	−	0.650221i
$763$	5.26609	−	36.6264i	0.190645	−	1.32597i
$764$	−24.6111	+	53.8908i	−0.890399	+	1.94970i
$765$	−0.910464	−	6.33242i	−0.0329179	−	0.228949i
$766$	−0.489811	−	0.143822i	−0.0176976	−	0.00519648i
$767$	−1.19317	+	0.766804i	−0.0430829	+	0.0276877i
$768$	4.90212	+	10.7342i	0.176890	+	0.387335i
$769$	7.53302	−	2.21189i	0.271648	−	0.0797629i	−0.143072	−	0.989712i	$-0.545698\pi$
$769$	7.53302	−	2.21189i	0.271648	−	0.0797629i	0.414719	+	0.909949i	$0.363880\pi$
$770$	8.09436	−	9.34139i	0.291700	−	0.336640i
$771$	45.1925	−	52.1550i	1.62757	−	1.87832i
$772$	−40.1507	+	11.7893i	−1.44505	+	0.424306i
$773$	−14.2411	−	31.1837i	−0.512218	−	1.12160i	−0.972303	−	0.233725i	$-0.924908\pi$
$773$	−14.2411	−	31.1837i	−0.512218	−	1.12160i	0.460085	−	0.887875i	$-0.347819\pi$
$774$	27.3816	−	17.5971i	0.984213	−	0.632515i
$775$	5.93724	+	1.74333i	0.213272	+	0.0626223i
$776$	−1.16060	−	8.07215i	−0.0416631	−	0.289773i
$777$	9.62020	−	21.0653i	0.345123	−	0.755713i
$778$	9.46147	−	65.8060i	0.339210	−	2.35926i
$779$	−2.86475	−	1.84106i	−0.102640	−	0.0659630i
$780$	−1.14192	−	1.31785i	−0.0408874	−	0.0471866i
$781$	1.39619			0.0499596
$782$		0			0
$783$	−3.96386			−0.141657
$784$	−1.39547	−	1.61045i	−0.0498381	−	0.0575162i
$785$	−4.29462	−	2.75998i	−0.153281	−	0.0985080i
$786$	−10.0644	+	69.9994i	−0.358985	+	2.49680i
$787$	6.65184	−	14.5655i	0.237113	−	0.519204i	−0.753245	−	0.657740i	$-0.771512\pi$
$787$	6.65184	−	14.5655i	0.237113	−	0.519204i	0.990357	+	0.138536i	$0.0442397\pi$
$788$	−4.74637	−	33.0117i	−0.169082	−	1.17599i
$789$	−31.2069	−	9.16316i	−1.11099	−	0.326217i
$790$	13.0152	−	8.36437i	0.463060	−	0.297591i
$791$	1.46695	+	3.21217i	0.0521587	+	0.114212i
$792$	11.4760	−	3.36967i	0.407783	−	0.119736i
$793$	−0.955922	+	1.10319i	−0.0339458	+	0.0391755i
$794$	18.8251	−	21.7254i	0.668079	−	0.771004i
$795$	−29.2795	+	8.59724i	−1.03844	+	0.304913i
$796$	−6.79021	−	14.8685i	−0.240673	−	0.527000i
$797$	18.1069	−	11.6366i	0.641380	−	0.412190i	−0.179128	−	0.983826i	$-0.557328\pi$
$797$	18.1069	−	11.6366i	0.641380	−	0.412190i	0.820507	+	0.571636i	$0.193691\pi$
$798$	100.677	+	29.5616i	3.56394	+	1.04647i
$799$	−0.574623	−	3.99659i	−0.0203287	−	0.141389i
$800$	10.3822	−	22.7339i	0.367066	−	0.803763i
$801$	6.56145	−	45.6359i	0.231837	−	1.61246i
$802$	−39.5337	−	25.4067i	−1.39598	−	0.897143i
$803$	−8.06826	−	9.31127i	−0.284723	−	0.328587i
$804$	−52.1582			−1.83948
$805$		0			0
$806$	0.771816			0.0271860
$807$	−16.4550	−	18.9901i	−0.579244	−	0.668483i
$808$	−2.88825	−	1.85616i	−0.101608	−	0.0652996i
$809$	−3.43336	+	23.8796i	−0.120711	+	0.839561i	0.836044	+	0.548663i	$0.184863\pi$
$809$	−3.43336	+	23.8796i	−0.120711	+	0.839561i	−0.956754	+	0.290898i	$0.906046\pi$
$810$	8.99741	−	19.7016i	0.316137	−	0.692243i
$811$	−2.04055	−	14.1923i	−0.0716535	−	0.498361i	−0.993770	−	0.111449i	$-0.964451\pi$
$811$	−2.04055	−	14.1923i	−0.0716535	−	0.498361i	0.922117	−	0.386912i	$-0.126458\pi$
$812$	32.3625	+	9.50248i	1.13570	+	0.333472i
$813$	−9.32724	+	5.99426i	−0.327121	+	0.210228i
$814$	−6.79615	−	14.8815i	−0.238205	−	0.521596i
$815$	−17.5459	+	5.15195i	−0.614607	+	0.180465i
$816$	3.99377	−	4.60906i	0.139810	−	0.161349i
$817$	23.2843	−	26.8715i	0.814615	−	0.940116i
$818$	19.3443	−	5.67999i	0.676357	−	0.198596i
$819$	−0.642352	−	1.40655i	−0.0224456	−	0.0491490i
$820$	−1.26699	+	0.814248i	−0.0442454	+	0.0284348i
$821$	−13.6329	−	4.00299i	−0.475792	−	0.139705i	0.0350395	−	0.999386i	$-0.488844\pi$
$821$	−13.6329	−	4.00299i	−0.475792	−	0.139705i	−0.510832	+	0.859681i	$0.670662\pi$
$822$	0.549817	+	3.82406i	0.0191771	+	0.133379i
$823$	6.65624	−	14.5751i	0.232022	−	0.508057i	−0.757430	−	0.652916i	$-0.773546\pi$
$823$	6.65624	−	14.5751i	0.232022	−	0.508057i	0.989452	+	0.144859i	$0.0462728\pi$
$824$	4.11043	−	28.5886i	0.143194	−	0.995933i
$825$	−14.0314	−	9.01741i	−0.488509	−	0.313946i
$826$	−24.7181	−	28.5262i	−0.860052	−	0.992552i
$827$	35.1240			1.22138			0.610690	−	0.791870i	$-0.290892\pi$
$827$	35.1240			1.22138			0.610690	+	0.791870i	$0.290892\pi$
$828$		0			0
$829$	−2.29604			−0.0797447			−0.0398723	−	0.999205i	$-0.512695\pi$
$829$	−2.29604			−0.0797447			−0.0398723	+	0.999205i	$0.512695\pi$
$830$	−22.9994	−	26.5427i	−0.798319	−	0.921309i
$831$	65.1310	+	41.8572i	2.25937	+	1.45201i
$832$	0.356648	−	2.48054i	0.0123645	−	0.0859972i
$833$	0.887699	−	1.94379i	0.0307569	−	0.0673483i
$834$	11.0001	+	76.5071i	0.380901	+	2.64922i
$835$	1.57760	+	0.463225i	0.0545950	+	0.0160306i
$836$	36.6751	−	23.5696i	1.26843	−	0.815173i
$837$	−0.589764	−	1.29140i	−0.0203852	−	0.0446374i
$838$	18.9746	−	5.57145i	0.655468	−	0.192463i
$839$	−25.2853	+	29.1808i	−0.872944	+	1.00743i	0.126935	+	0.991911i	$0.459486\pi$
$839$	−25.2853	+	29.1808i	−0.872944	+	1.00743i	−0.999880	+	0.0155205i	$0.995059\pi$
$840$	9.10783	−	10.5110i	0.314250	−	0.362664i
$841$	4.05514	−	1.19070i	0.139832	−	0.0410585i
$842$	28.8102	+	63.0855i	0.992865	+	2.17407i
$843$	7.56792	−	4.86361i	0.260653	−	0.167512i
$844$	38.5489	+	11.3190i	1.32691	+	0.389616i
$845$	−2.28081	−	15.8634i	−0.0784622	−	0.545716i
$846$	−7.85923	+	17.2093i	−0.270206	+	0.591668i
$847$	−2.48023	+	17.2504i	−0.0852217	+	0.592730i
$848$	−12.8498	−	8.25807i	−0.441264	−	0.283583i
$849$	24.3269	+	28.0747i	0.834896	+	0.963521i
$850$	11.9317			0.409255
$851$		0			0
$852$	5.24190			0.179584
$853$	25.1659	+	29.0430i	0.861664	+	0.994413i	0.999992	+	0.00402649i	$0.00128168\pi$
$853$	25.1659	+	29.0430i	0.861664	+	0.994413i	−0.138328	+	0.990386i	$0.544173\pi$
$854$	−32.6806	−	21.0026i	−1.11831	−	0.718693i
$855$	−4.66026	+	32.4128i	−0.159377	+	1.10849i
$856$	1.55790	−	3.41133i	0.0532480	−	0.116597i
$857$	7.24233	+	50.3715i	0.247393	+	1.72066i	0.613167	+	0.789953i	$0.289895\pi$
$857$	7.24233	+	50.3715i	0.247393	+	1.72066i	−0.365774	+	0.930704i	$0.619196\pi$
$858$	−1.99611	−	0.586112i	−0.0681462	−	0.0200095i
$859$	7.69504	−	4.94530i	0.262551	−	0.168731i	−0.402742	−	0.915313i	$-0.631943\pi$
$859$	7.69504	−	4.94530i	0.262551	−	0.168731i	0.665293	+	0.746582i	$0.268306\pi$
$860$	−6.53258	−	14.3043i	−0.222759	−	0.487774i
$861$	−2.44043	+	0.716574i	−0.0831695	+	0.0244208i
$862$	31.8951	−	36.8089i	1.08635	−	1.25372i
$863$	−8.08023	+	9.32508i	−0.275054	+	0.317430i	−0.876423	−	0.481542i	$-0.840077\pi$
$863$	−8.08023	+	9.32508i	−0.275054	+	0.317430i	0.601369	+	0.798972i	$0.294622\pi$
$864$	−5.50177	+	1.61547i	−0.187174	+	0.0549592i
$865$	8.69923	+	19.0487i	0.295783	+	0.647674i
$866$	23.5344	−	15.1247i	0.799733	−	0.513957i
$867$	−35.1280	−	10.3145i	−1.19301	−	0.350299i
$868$	1.71921	+	11.9573i	0.0583537	+	0.405859i
$869$	4.50958	−	9.87461i	0.152977	−	0.334973i
$870$	−4.85086	+	33.7385i	−0.164460	+	1.14384i
$871$	1.20104	+	0.771860i	0.0406956	+	0.0261535i
$872$	−19.2619	−	22.2294i	−0.652289	−	0.752781i
$873$	14.3414			0.485381
$874$		0			0
$875$	−24.8534			−0.840199
$876$	−30.2918	−	34.9585i	−1.02346	−	1.18114i
$877$	1.94094	+	1.24737i	0.0655409	+	0.0421205i	0.573001	−	0.819555i	$-0.305779\pi$
$877$	1.94094	+	1.24737i	0.0655409	+	0.0421205i	−0.507460	+	0.861675i	$0.669416\pi$
$878$	−5.77696	+	40.1796i	−0.194963	+	1.35600i
$879$	−22.4617	+	49.1843i	−0.757615	+	1.65895i
$880$	0.523329	+	3.63983i	0.0176414	+	0.122699i
$881$	34.1583	+	10.0298i	1.15082	+	0.337912i	0.800860	−	0.598852i	$-0.204376\pi$
$881$	34.1583	+	10.0298i	1.15082	+	0.337912i	0.349962	+	0.936764i	$0.386194\pi$
$882$	−8.42317	+	5.41324i	−0.283623	+	0.182273i
$883$	12.6596	+	27.7206i	0.426029	+	0.932873i	0.993954	+	0.109793i	$0.0350188\pi$
$883$	12.6596	+	27.7206i	0.426029	+	0.932873i	−0.567926	+	0.823080i	$0.692254\pi$
$884$	0.839829	−	0.246596i	0.0282465	−	0.00829392i
$885$	14.6912	−	16.9546i	0.493840	−	0.569921i
$886$	20.0770	−	23.1701i	0.674500	−	0.778414i
$887$	−19.9490	+	5.85755i	−0.669821	+	0.196677i	−0.598923	−	0.800806i	$-0.704405\pi$
$887$	−19.9490	+	5.85755i	−0.669821	+	0.196677i	−0.0708976	+	0.997484i	$0.522586\pi$
$888$	−7.64708	−	16.7448i	−0.256619	−	0.561917i
$889$	−11.9654	+	7.68972i	−0.401308	+	0.257905i
$890$	−36.3401	−	10.6704i	−1.21812	−	0.357673i
$891$	−2.16280	−	15.0426i	−0.0724564	−	0.503945i
$892$	−4.98710	+	10.9202i	−0.166981	+	0.365636i
$893$	−2.94124	+	20.4567i	−0.0984247	+	0.684559i
$894$	77.5250	+	49.8223i	2.59282	+	1.66631i
$895$	−1.15899	−	1.33755i	−0.0387409	−	0.0447094i
$896$	32.5243			1.08656
$897$		0			0
$898$	66.3122			2.21287
$899$	−5.81055	−	6.70573i	−0.193793	−	0.223649i
$900$	−27.6612	−	17.7767i	−0.922039	−	0.592558i
$901$	2.17988	−	15.1614i	0.0726224	−	0.505100i
$902$	−0.746424	+	1.63444i	−0.0248532	+	0.0544209i
$903$	−3.77945	−	26.2867i	−0.125772	−	0.874765i
$904$	2.69331	+	0.790827i	0.0895781	+	0.0263025i
$905$	16.7797	−	10.7837i	0.557777	−	0.358461i
$906$	−30.3468	−	66.4502i	−1.00820	−	2.20766i
$907$	21.7918	−	6.39866i	0.723586	−	0.212464i	0.100856	−	0.994901i	$-0.467842\pi$
$907$	21.7918	−	6.39866i	0.723586	−	0.212464i	0.622730	+	0.782437i	$0.286024\pi$
$908$	−34.4698	+	39.7803i	−1.14392	+	1.32015i
$909$	3.95379	−	4.56292i	0.131139	−	0.151343i
$910$	−1.21879	+	0.357868i	−0.0404024	+	0.0118632i
$911$	0.346474	+	0.758673i	0.0114792	+	0.0251359i	0.915285	−	0.402807i	$-0.131966\pi$
$911$	0.346474	+	0.758673i	0.0114792	+	0.0251359i	−0.903806	+	0.427943i	$0.859238\pi$
$912$	−26.2608	+	16.8768i	−0.869582	+	0.558847i
$913$	−23.6449	−	6.94278i	−0.782534	−	0.229773i
$914$	−11.9320	−	82.9888i	−0.394675	−	2.74502i
$915$	9.59155	−	21.0026i	0.317087	−	0.694323i
$916$	−4.44022	+	30.8824i	−0.146709	+	1.02038i
$917$	25.4880	+	16.3802i	0.841689	+	0.540921i
$918$	−1.79269	−	2.06888i	−0.0591677	−	0.0682831i
$919$	−45.3320			−1.49537			−0.747683	−	0.664056i	$-0.768834\pi$
$919$	−45.3320			−1.49537			−0.747683	+	0.664056i	$0.768834\pi$
$920$		0			0
$921$	−35.5510			−1.17145
$922$	−12.6414	−	14.5890i	−0.416324	−	0.480463i
$923$	−0.120704	−	0.0775720i	−0.00397303	−	0.00255331i
$924$	4.63402	−	32.2303i	0.152448	−	1.06030i
$925$	−5.59944	+	12.2611i	−0.184108	+	0.403141i
$926$	8.72979	+	60.7170i	0.286879	+	1.99529i
$927$	48.7345	+	14.3097i	1.60065	+	0.469993i
$928$	−30.1481	+	19.3750i	−0.989660	+	0.636016i
$929$	−7.35584	−	16.1070i	−0.241337	−	0.528455i	0.749742	−	0.661731i	$-0.230178\pi$
$929$	−7.35584	−	16.1070i	−0.241337	−	0.528455i	−0.991079	+	0.133276i	$0.957450\pi$
$930$	−11.7135	+	3.43941i	−0.384102	+	0.112783i
$931$	−7.16275	+	8.26625i	−0.234750	+	0.270915i
$932$	−7.78919	+	8.98921i	−0.255143	+	0.294451i
$933$	1.37491	−	0.403709i	0.0450125	−	0.0132169i
$934$	−15.8974	−	34.8105i	−0.520179	−	1.13903i
$935$	−3.10216	+	1.99364i	−0.101452	+	0.0651989i
$936$	−1.17935	−	0.346289i	−0.0385484	−	0.0113188i
$937$	3.31964	+	23.0886i	0.108448	+	0.754272i	0.969382	+	0.245556i	$0.0789705\pi$
$937$	3.31964	+	23.0886i	0.108448	+	0.754272i	−0.860935	+	0.508716i	$0.830120\pi$
$938$	−15.7834	+	34.5609i	−0.515348	+	1.12845i
$939$	−7.55887	+	52.5731i	−0.246674	+	1.71566i
$940$	7.68943	+	4.94170i	0.250802	+	0.161180i
$941$	−7.60605	−	8.77785i	−0.247950	−	0.286150i	0.618108	−	0.786093i	$-0.287900\pi$
$941$	−7.60605	−	8.77785i	−0.247950	−	0.286150i	−0.866058	+	0.499944i	$0.833354\pi$
$942$	−22.8664			−0.745027
$943$		0			0
$944$	11.2294			0.365486
$945$	1.53009	+	1.76582i	0.0497738	+	0.0574421i
$946$	−15.7828	−	10.1430i	−0.513144	−	0.329777i
$947$	−0.853596	+	5.93689i	−0.0277381	+	0.192923i	−0.998979	−	0.0451760i	$-0.985615\pi$
$947$	−0.853596	+	5.93689i	−0.0277381	+	0.192923i	0.971241	+	0.238099i	$0.0765242\pi$
$948$	16.9309	−	37.0736i	0.549891	−	1.20409i
$949$	0.180191	+	1.25326i	0.00584925	+	0.0406824i
$950$	−58.5993	−	17.2063i	−1.90121	−	0.558247i
$951$	18.6320	−	11.9740i	0.604183	−	0.388285i
$952$	2.90007	+	6.35027i	0.0939919	+	0.205814i
$953$	17.1813	−	5.04489i	0.556558	−	0.163420i	0.00865552	−	0.999963i	$-0.497245\pi$
$953$	17.1813	−	5.04489i	0.556558	−	0.163420i	0.547902	+	0.836542i	$0.315427\pi$
$954$	−46.9999	+	54.2408i	−1.52168	+	1.75611i
$955$	−16.7973	+	19.3851i	−0.543547	+	0.627286i
$956$	61.7023	−	18.1174i	1.99560	−	0.585960i
$957$	9.93529	+	21.7553i	0.321162	+	0.703247i
$958$	−47.2307	+	30.3533i	−1.52595	+	0.980671i
$959$	1.58811	+	0.466312i	0.0512829	+	0.0150580i
$960$	5.64121	+	39.2355i	0.182069	+	1.26632i
$961$	−11.5577	+	25.3078i	−0.372829	+	0.816382i
$962$	−0.239267	+	1.66414i	−0.00771428	+	0.0536540i
$963$	5.54808	+	3.56553i	0.178784	+	0.114898i
$964$	−11.0889	−	12.7972i	−0.357148	−	0.412171i
$965$	−18.1172			−0.583213
$966$		0			0
$967$	33.5068			1.07751			0.538753	−	0.842464i	$-0.318896\pi$
$967$	33.5068			1.07751			0.538753	+	0.842464i	$0.318896\pi$
$968$	9.07198	+	10.4696i	0.291584	+	0.336506i
$969$	−26.3343	−	16.9240i	−0.845979	−	0.543678i
$970$	1.67662	−	11.6612i	0.0538331	−	0.374418i
$971$	24.6283	−	53.9284i	0.790360	−	1.73065i	0.114740	−	0.993396i	$-0.463397\pi$
$971$	24.6283	−	53.9284i	0.790360	−	1.73065i	0.675620	−	0.737250i	$-0.263876\pi$
$972$	−9.09112	−	63.2302i	−0.291598	−	2.02811i
$973$	31.7730	+	9.32940i	1.01860	+	0.299087i
$974$	−11.4214	+	7.34008i	−0.365965	+	0.235191i
$975$	0.712044	+	1.55916i	0.0228037	+	0.0499331i
$976$	11.0891	−	3.25605i	0.354953	−	0.104224i
$977$	8.27873	−	9.55416i	0.264860	−	0.305665i	−0.607705	−	0.794163i	$-0.707910\pi$
$977$	8.27873	−	9.55416i	0.264860	−	0.305665i	0.872565	+	0.488498i	$0.162455\pi$
$978$	−53.6393	+	61.9031i	−1.71520	+	1.97944i
$979$	−25.4986	+	7.48706i	−0.814938	+	0.239288i
$980$	2.00956	+	4.40032i	0.0641930	+	0.140563i
$981$	43.5145	−	27.9651i	1.38931	−	0.892856i
$982$	69.0286	+	20.2686i	2.20279	+	0.646798i
$983$	8.30621	+	57.7710i	0.264927	+	1.84261i	0.494328	+	0.869275i	$0.335414\pi$
$983$	8.30621	+	57.7710i	0.264927	+	1.84261i	−0.229401	+	0.973332i	$0.573677\pi$
$984$	−0.839881	+	1.83908i	−0.0267744	+	0.0586278i
$985$	2.05495	−	14.2925i	0.0654762	−	0.455397i
$986$	−14.3932	−	9.24992i	−0.458372	−	0.294578i
$987$	10.1086	+	11.6660i	0.321761	+	0.371332i
$988$	−4.48019			−0.142534
$989$		0			0
$990$	17.2784			0.549142
$991$	29.9868	+	34.6066i	0.952561	+	1.09931i	0.994966	+	0.100214i	$0.0319526\pi$
$991$	29.9868	+	34.6066i	0.952561	+	1.09931i	−0.0424048	+	0.999101i	$0.513502\pi$
$992$	−10.7979	−	6.93937i	−0.342833	−	0.220325i
$993$	10.7976	−	75.0991i	0.342652	−	2.38320i
$994$	1.58624	−	3.47337i	0.0503124	−	0.110169i
$995$	−1.00714	−	7.00484i	−0.0319286	−	0.222068i
$996$	−88.7734	−	26.0662i	−2.81289	−	0.825940i
$997$	−33.1051	+	21.2753i	−1.04845	+	0.673797i	−0.947062	−	0.321050i	$-0.895964\pi$
$997$	−33.1051	+	21.2753i	−1.04845	+	0.673797i	−0.101386	+	0.994847i	$0.532328\pi$
$998$	−7.84848	−	17.1858i	−0.248439	−	0.544006i
$999$	2.96727	−	0.871269i	0.0938803	−	0.0275657i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.d.266.1		10
23.2	even	11		529.2.c.g.466.1		10
23.3	even	11		529.2.c.i.255.1		10
23.4	even	11		529.2.a.i.1.5		5
23.5	odd	22		529.2.c.a.118.1		10
23.6	even	11		23.2.c.a.8.1	yes	10
23.7	odd	22		529.2.c.e.177.1		10
23.8	even	11		529.2.c.g.487.1		10
23.9	even	11		529.2.c.b.501.1		10
23.10	odd	22		529.2.c.h.334.1		10
23.11	odd	22		529.2.c.c.170.1		10
23.12	even	11		529.2.c.b.170.1		10
23.13	even	11		529.2.c.i.334.1		10
23.14	odd	22		529.2.c.c.501.1		10
23.15	odd	22		529.2.c.f.487.1		10
23.16	even	11	inner	529.2.c.d.177.1		10
23.17	odd	22		529.2.c.a.399.1		10
23.18	even	11		23.2.c.a.3.1	✓	10
23.19	odd	22		529.2.a.j.1.5		5
23.20	odd	22		529.2.c.h.255.1		10
23.21	odd	22		529.2.c.f.466.1		10
23.22	odd	2		529.2.c.e.266.1		10
69.29	odd	22		207.2.i.c.100.1		10
69.41	odd	22		207.2.i.c.118.1		10
69.50	odd	22		4761.2.a.bo.1.1		5
69.65	even	22		4761.2.a.bn.1.1		5
92.19	even	22		8464.2.a.bt.1.5		5
92.27	odd	22		8464.2.a.bs.1.5		5
92.75	odd	22		368.2.m.c.353.1		10
92.87	odd	22		368.2.m.c.49.1		10
115.18	odd	44		575.2.p.b.49.1		20
115.29	even	22		575.2.k.b.376.1		10
115.52	odd	44		575.2.p.b.399.1		20
115.64	even	22		575.2.k.b.26.1		10
115.87	odd	44		575.2.p.b.49.2		20
115.98	odd	44		575.2.p.b.399.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	23.18	even	11
23.2.c.a.8.1	yes	10	23.6	even	11
207.2.i.c.100.1		10	69.29	odd	22
207.2.i.c.118.1		10	69.41	odd	22
368.2.m.c.49.1		10	92.87	odd	22
368.2.m.c.353.1		10	92.75	odd	22
529.2.a.i.1.5		5	23.4	even	11
529.2.a.j.1.5		5	23.19	odd	22
529.2.c.a.118.1		10	23.5	odd	22
529.2.c.a.399.1		10	23.17	odd	22
529.2.c.b.170.1		10	23.12	even	11
529.2.c.b.501.1		10	23.9	even	11
529.2.c.c.170.1		10	23.11	odd	22
529.2.c.c.501.1		10	23.14	odd	22
529.2.c.d.177.1		10	23.16	even	11	inner
529.2.c.d.266.1		10	1.1	even	1	trivial
529.2.c.e.177.1		10	23.7	odd	22
529.2.c.e.266.1		10	23.22	odd	2
529.2.c.f.466.1		10	23.21	odd	22
529.2.c.f.487.1		10	23.15	odd	22
529.2.c.g.466.1		10	23.2	even	11
529.2.c.g.487.1		10	23.8	even	11
529.2.c.h.255.1		10	23.20	odd	22
529.2.c.h.334.1		10	23.10	odd	22
529.2.c.i.255.1		10	23.3	even	11
529.2.c.i.334.1		10	23.13	even	11
575.2.k.b.26.1		10	115.64	even	22
575.2.k.b.376.1		10	115.29	even	22
575.2.p.b.49.1		20	115.18	odd	44
575.2.p.b.49.2		20	115.87	odd	44
575.2.p.b.399.1		20	115.52	odd	44
575.2.p.b.399.2		20	115.98	odd	44
4761.2.a.bn.1.1		5	69.65	even	22
4761.2.a.bo.1.1		5	69.50	odd	22
8464.2.a.bs.1.5		5	92.27	odd	22
8464.2.a.bt.1.5		5	92.19	even	22

Overview	Random
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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

Introduction

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Newspace parameters

Newform invariants

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	529.2.c.d.266.1

Level	$529$
Weight	$2$
Character	529.266
Analytic conductor	$4.224$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$