LMFDB - Embedded newform 272.2.l.b.205.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [272,2,Mod(69,272)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(272, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("272.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.1
Character	$\chi$	$=$	272.205
Dual form			272.2.l.b.69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 + 0.00186943i) q^{2} +(-0.274984 - 0.274984i) q^{3} +(1.99999 - 0.00528753i) q^{4} +(-2.33984 + 2.33984i) q^{5} +(0.389399 + 0.388371i) q^{6} +0.445993i q^{7} +(-2.82840 + 0.0112165i) q^{8} -2.84877i q^{9} +(3.30466 - 3.31341i) q^{10} +(-0.541659 + 0.541659i) q^{11} +(-0.551420 - 0.548512i) q^{12} +(-3.22546 - 3.22546i) q^{13} +(-0.000833751 - 0.630728i) q^{14} +1.28684 q^{15} +(3.99994 - 0.0211501i) q^{16} -1.00000 q^{17} +(0.00532556 + 4.02876i) q^{18} +(-5.38194 - 5.38194i) q^{19} +(-4.66729 + 4.69204i) q^{20} +(0.122641 - 0.122641i) q^{21} +(0.765008 - 0.767033i) q^{22} +7.35616i q^{23} +(0.780850 + 0.774681i) q^{24} -5.94972i q^{25} +(4.56751 + 4.55545i) q^{26} +(-1.60832 + 1.60832i) q^{27} +(0.00235820 + 0.891982i) q^{28} +(-4.91877 - 4.91877i) q^{29} +(-1.81986 + 0.00240565i) q^{30} -4.01205 q^{31} +(-5.65673 + 0.0373883i) q^{32} +0.297895 q^{33} +(1.41421 - 0.00186943i) q^{34} +(-1.04355 - 1.04355i) q^{35} +(-0.0150630 - 5.69752i) q^{36} +(-2.25691 + 2.25691i) q^{37} +(7.62127 + 7.60115i) q^{38} +1.77390i q^{39} +(6.59177 - 6.64426i) q^{40} -8.61863i q^{41} +(-0.173211 + 0.173669i) q^{42} +(-2.61250 + 2.61250i) q^{43} +(-1.08045 + 1.08618i) q^{44} +(6.66567 + 6.66567i) q^{45} +(-0.0137518 - 10.4032i) q^{46} +0.997504 q^{47} +(-1.10574 - 1.09410i) q^{48} +6.80109 q^{49} +(0.0111226 + 8.41416i) q^{50} +(0.274984 + 0.274984i) q^{51} +(-6.46795 - 6.43384i) q^{52} +(2.69710 - 2.69710i) q^{53} +(2.27149 - 2.27751i) q^{54} -2.53479i q^{55} +(-0.00500249 - 1.26145i) q^{56} +2.95989i q^{57} +(6.96538 + 6.94699i) q^{58} +(-8.74827 + 8.74827i) q^{59} +(2.57366 - 0.00680419i) q^{60} +(7.55364 + 7.55364i) q^{61} +(5.67389 - 0.00750023i) q^{62} +1.27053 q^{63} +(7.99975 - 0.0634498i) q^{64} +15.0941 q^{65} +(-0.421286 + 0.000556892i) q^{66} +(9.29067 + 9.29067i) q^{67} +(-1.99999 + 0.00528753i) q^{68} +(2.02282 - 2.02282i) q^{69} +(1.47776 + 1.47385i) q^{70} +2.68411i q^{71} +(0.0319533 + 8.05747i) q^{72} -0.113478i q^{73} +(3.18753 - 3.19597i) q^{74} +(-1.63608 + 1.63608i) q^{75} +(-10.7923 - 10.7354i) q^{76} +(-0.241576 - 0.241576i) q^{77} +(-0.00331617 - 2.50867i) q^{78} +5.48610 q^{79} +(-9.30975 + 9.40872i) q^{80} -7.66178 q^{81} +(0.0161119 + 12.1886i) q^{82} +(-4.04204 - 4.04204i) q^{83} +(0.244632 - 0.245929i) q^{84} +(2.33984 - 2.33984i) q^{85} +(3.68974 - 3.69951i) q^{86} +2.70516i q^{87} +(1.52595 - 1.53811i) q^{88} -12.6504i q^{89} +(-9.43913 - 9.41421i) q^{90} +(1.43853 - 1.43853i) q^{91} +(0.0388959 + 14.7123i) q^{92} +(1.10325 + 1.10325i) q^{93} +(-1.41068 + 0.00186476i) q^{94} +25.1858 q^{95} +(1.56579 + 1.54523i) q^{96} -14.5443 q^{97} +(-9.61819 + 0.0127141i) q^{98} +(1.54306 + 1.54306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.41421	+	0.00186943i	−0.999999	+	0.00132188i
$2$	−1.41421	+	0.00186943i	−0.999999	+	0.00132188i
$3$	−0.274984	−	0.274984i	−0.158762	−	0.158762i	0.623256	−	0.782018i	$-0.285809\pi$
$3$	−0.274984	−	0.274984i	−0.158762	−	0.158762i	−0.782018	+	0.623256i	$0.785809\pi$
$4$	1.99999	−	0.00528753i	0.999997	−	0.00264377i
$5$	−2.33984	+	2.33984i	−1.04641	+	1.04641i	−0.0475396	+	0.998869i	$0.515138\pi$
$5$	−2.33984	+	2.33984i	−1.04641	+	1.04641i	−0.998869	+	0.0475396i	$0.984862\pi$
$6$	0.389399	+	0.388371i	0.158972	+	0.158552i
$7$			0.445993i			0.168569i	0.996442	+	0.0842847i	$0.0268605\pi$
$7$			0.445993i			0.168569i	−0.996442	+	0.0842847i	$0.973139\pi$
$8$	−2.82840	+	0.0112165i	−0.999992	+	0.00396564i
$9$		−	2.84877i		−	0.949589i
$10$	3.30466	−	3.31341i	1.04502	−	1.04779i
$11$	−0.541659	+	0.541659i	−0.163316	+	0.163316i	−0.784034	−	0.620718i	$-0.786841\pi$
$11$	−0.541659	+	0.541659i	−0.163316	+	0.163316i	0.620718	+	0.784034i	$0.286841\pi$
$12$	−0.551420	−	0.548512i	−0.159181	−	0.158342i
$13$	−3.22546	−	3.22546i	−0.894581	−	0.894581i	0.100369	−	0.994950i	$-0.467998\pi$
$13$	−3.22546	−	3.22546i	−0.894581	−	0.894581i	−0.994950	+	0.100369i	$0.967998\pi$
$14$	−0.000833751	−	0.630728i	−0.000222829	−	0.168569i
$15$	1.28684			0.332260
$16$	3.99994	−	0.0211501i	0.999986	−	0.00528751i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	0.00532556	+	4.02876i	0.00125525	+	0.949588i
$19$	−5.38194	−	5.38194i	−1.23470	−	1.23470i	−0.962138	−	0.272564i	$-0.912128\pi$
$19$	−5.38194	−	5.38194i	−1.23470	−	1.23470i	−0.272564	−	0.962138i	$-0.587872\pi$
$20$	−4.66729	+	4.69204i	−1.04364	+	1.04917i
$21$	0.122641	−	0.122641i	0.0267624	−	0.0267624i
$22$	0.765008	−	0.767033i	0.163100	−	0.163532i
$23$			7.35616i			1.53387i	0.641727	+	0.766933i	$0.278218\pi$
$23$			7.35616i			1.53387i	−0.641727	+	0.766933i	$0.721782\pi$
$24$	0.780850	+	0.774681i	0.159390	+	0.158131i
$25$		−	5.94972i		−	1.18994i
$26$	4.56751	+	4.55545i	0.895763	+	0.893398i
$27$	−1.60832	+	1.60832i	−0.309521	+	0.309521i
$28$	0.00235820	+	0.891982i	0.000445658	+	0.168569i
$29$	−4.91877	−	4.91877i	−0.913392	−	0.913392i	0.0831451	−	0.996537i	$-0.473504\pi$
$29$	−4.91877	−	4.91877i	−0.913392	−	0.913392i	−0.996537	+	0.0831451i	$0.973504\pi$
$30$	−1.81986	+	0.00240565i	−0.332259	+	0.000439209i
$31$	−4.01205			−0.720585			−0.360293	−	0.932839i	$-0.617323\pi$
$31$	−4.01205			−0.720585			−0.360293	+	0.932839i	$0.617323\pi$
$32$	−5.65673	+	0.0373883i	−0.999978	+	0.00660938i
$33$	0.297895			0.0518568
$34$	1.41421	−	0.00186943i	0.242535	−	0.000320604i
$35$	−1.04355	−	1.04355i	−0.176393	−	0.176393i
$36$	−0.0150630	−	5.69752i	−0.00251049	−	0.949586i
$37$	−2.25691	+	2.25691i	−0.371034	+	0.371034i	−0.867854	−	0.496820i	$-0.834501\pi$
$37$	−2.25691	+	2.25691i	−0.371034	+	0.371034i	0.496820	+	0.867854i	$0.334501\pi$
$38$	7.62127	+	7.60115i	1.23633	+	1.23307i
$39$			1.77390i			0.284051i
$40$	6.59177	−	6.64426i	1.04225	−	1.05055i
$41$		−	8.61863i		−	1.34600i	−0.739641	−	0.673002i	$-0.765005\pi$
$41$		−	8.61863i		−	1.34600i	0.739641	−	0.673002i	$-0.234995\pi$
$42$	−0.173211	+	0.173669i	−0.0267270	+	0.0267978i
$43$	−2.61250	+	2.61250i	−0.398402	+	0.398402i	−0.877669	−	0.479267i	$-0.840903\pi$
$43$	−2.61250	+	2.61250i	−0.398402	+	0.398402i	0.479267	+	0.877669i	$0.340903\pi$
$44$	−1.08045	+	1.08618i	−0.162884	+	0.163747i
$45$	6.66567	+	6.66567i	0.993659	+	0.993659i
$46$	−0.0137518	−	10.4032i	−0.00202759	−	1.53386i
$47$	0.997504			0.145501			0.0727504	−	0.997350i	$-0.476822\pi$
$47$	0.997504			0.145501			0.0727504	+	0.997350i	$0.476822\pi$
$48$	−1.10574	−	1.09410i	−0.159599	−	0.157920i
$49$	6.80109			0.971584
$50$	0.0111226	+	8.41416i	0.00157297	+	1.18994i
$51$	0.274984	+	0.274984i	0.0385054	+	0.0385054i
$52$	−6.46795	−	6.43384i	−0.896943	−	0.892213i
$53$	2.69710	−	2.69710i	0.370475	−	0.370475i	−0.497175	−	0.867650i	$-0.665629\pi$
$53$	2.69710	−	2.69710i	0.370475	−	0.370475i	0.867650	+	0.497175i	$0.165629\pi$
$54$	2.27149	−	2.27751i	0.309111	−	0.309929i
$55$		−	2.53479i		−	0.341791i
$56$	−0.00500249	−	1.26145i	−0.000668486	−	0.168568i
$57$			2.95989i			0.392047i
$58$	6.96538	+	6.94699i	0.914599	+	0.912184i
$59$	−8.74827	+	8.74827i	−1.13893	+	1.13893i	−0.150285	+	0.988643i	$0.548019\pi$
$59$	−8.74827	+	8.74827i	−1.13893	+	1.13893i	−0.988643	+	0.150285i	$0.951981\pi$
$60$	2.57366	−	0.00680419i	0.332259	−	0.000878417i
$61$	7.55364	+	7.55364i	0.967145	+	0.967145i	0.999477	−	0.0323326i	$-0.0102936\pi$
$61$	7.55364	+	7.55364i	0.967145	+	0.967145i	−0.0323326	+	0.999477i	$0.510294\pi$
$62$	5.67389	−	0.00750023i	0.720585	−	0.000952530i
$63$	1.27053			0.160072
$64$	7.99975	−	0.0634498i	0.999969	−	0.00793123i
$65$	15.0941			1.87219
$66$	−0.421286		0.000556892i	−0.0518568		6.85487e-5i
$67$	9.29067	+	9.29067i	1.13504	+	1.13504i	0.989328	+	0.145708i	$0.0465459\pi$
$67$	9.29067	+	9.29067i	1.13504	+	1.13504i	0.145708	+	0.989328i	$0.453454\pi$
$68$	−1.99999	+	0.00528753i	−0.242535	+	0.000641208i
$69$	2.02282	−	2.02282i	0.243519	−	0.243519i
$70$	1.47776	+	1.47385i	0.176626	+	0.176159i
$71$			2.68411i			0.318546i	0.987235	+	0.159273i	$0.0509150\pi$
$71$			2.68411i			0.318546i	−0.987235	+	0.159273i	$0.949085\pi$
$72$	0.0319533	+	8.05747i	0.00376573	+	0.949582i
$73$		−	0.113478i		−	0.0132816i	−0.999978	−	0.00664079i	$-0.997886\pi$
$73$		−	0.113478i		−	0.0132816i	0.999978	−	0.00664079i	$-0.00211384\pi$
$74$	3.18753	−	3.19597i	0.370543	−	0.371524i
$75$	−1.63608	+	1.63608i	−0.188918	+	0.188918i
$76$	−10.7923	−	10.7354i	−1.23796	−	1.23143i
$77$	−0.241576	−	0.241576i	−0.0275301	−	0.0275301i
$78$	−0.00331617	−	2.50867i	−0.000375482	−	0.284051i
$79$	5.48610			0.617234			0.308617	−	0.951186i	$-0.400134\pi$
$79$	5.48610			0.617234			0.308617	+	0.951186i	$0.400134\pi$
$80$	−9.30975	+	9.40872i	−1.04086	+	1.05193i
$81$	−7.66178			−0.851309
$82$	0.0161119	+	12.1886i	0.00177926	+	1.34600i
$83$	−4.04204	−	4.04204i	−0.443671	−	0.443671i	0.449573	−	0.893244i	$-0.351576\pi$
$83$	−4.04204	−	4.04204i	−0.443671	−	0.443671i	−0.893244	+	0.449573i	$0.851576\pi$
$84$	0.244632	−	0.245929i	0.0266916	−	0.0268331i
$85$	2.33984	−	2.33984i	0.253791	−	0.253791i
$86$	3.68974	−	3.69951i	0.397875	−	0.398928i
$87$			2.70516i			0.290024i
$88$	1.52595	−	1.53811i	0.162667	−	0.163963i
$89$		−	12.6504i		−	1.34094i	−0.741936	−	0.670471i	$-0.766092\pi$
$89$		−	12.6504i		−	1.34094i	0.741936	−	0.670471i	$-0.233908\pi$
$90$	−9.43913	−	9.41421i	−0.994971	−	0.992344i
$91$	1.43853	−	1.43853i	0.150799	−	0.150799i
$92$	0.0388959	+	14.7123i	0.00405518	+	1.53386i
$93$	1.10325	+	1.10325i	0.114402	+	0.114402i
$94$	−1.41068	+	0.00186476i	−0.145501	+	0.000192335i
$95$	25.1858			2.58401
$96$	1.56579	+	1.54523i	0.159808	+	0.157709i
$97$	−14.5443			−1.47675			−0.738375	−	0.674390i	$-0.764407\pi$
$97$	−14.5443			−1.47675			−0.738375	+	0.674390i	$0.764407\pi$
$98$	−9.61819	+	0.0127141i	−0.971584	+	0.00128432i
$99$	1.54306	+	1.54306i	0.155083	+	0.155083i
$100$	−0.0314593	−	11.8994i	−0.00314593	−	1.18994i
$101$	0.486673	−	0.486673i	0.0484258	−	0.0484258i	−0.682479	−	0.730905i	$-0.739098\pi$
$101$	0.486673	−	0.486673i	0.0484258	−	0.0484258i	0.730905	+	0.682479i	$0.239098\pi$
$102$	−0.389399	−	0.388371i	−0.0385563	−	0.0384545i
$103$		−	4.48234i		−	0.441658i	−0.975313	−	0.220829i	$-0.929124\pi$
$103$		−	4.48234i		−	0.441658i	0.975313	−	0.220829i	$-0.0708762\pi$
$104$	9.15908	+	9.08672i	0.898121	+	0.891026i
$105$			0.573920i			0.0560088i
$106$	−3.80923	+	3.81931i	−0.369985	+	0.370965i
$107$	3.57883	−	3.57883i	0.345978	−	0.345978i	−0.512631	−	0.858609i	$-0.671329\pi$
$107$	3.57883	−	3.57883i	0.345978	−	0.345978i	0.858609	+	0.512631i	$0.171329\pi$
$108$	−3.20812	+	3.22512i	−0.308701	+	0.310338i
$109$	−0.841902	−	0.841902i	−0.0806396	−	0.0806396i	0.665637	−	0.746276i	$-0.268160\pi$
$109$	−0.841902	−	0.841902i	−0.0806396	−	0.0806396i	−0.746276	+	0.665637i	$0.768160\pi$
$110$	0.00473861	+	3.58473i	0.000451808	+	0.341791i
$111$	1.24123			0.117812
$112$	0.00943277	+	1.78395i	0.000891313	+	0.168567i
$113$	−6.86840			−0.646124			−0.323062	−	0.946378i	$-0.604712\pi$
$113$	−6.86840			−0.646124			−0.323062	+	0.946378i	$0.604712\pi$
$114$	−0.00553330	−	4.18592i	−0.000518241	−	0.392047i
$115$	−17.2122	−	17.2122i	−1.60505	−	1.60505i
$116$	−9.86351	−	9.81149i	−0.915804	−	0.910974i
$117$	−9.18858	+	9.18858i	−0.849484	+	0.849484i
$118$	12.3556	−	12.3883i	1.13742	−	1.14043i
$119$		−	0.445993i		−	0.0408841i
$120$	−3.63969	+	0.0144338i	−0.332257	+	0.00131762i
$121$			10.4132i			0.946656i
$122$	−10.6966	−	10.6683i	−0.968422	−	0.965865i
$123$	−2.36998	+	2.36998i	−0.213694	+	0.213694i
$124$	−8.02407	+	0.0212138i	−0.720583	+	0.00190506i
$125$	2.22219	+	2.22219i	0.198758	+	0.198758i
$126$	−1.79680	+	0.00237516i	−0.160072	+	0.000211596i
$127$	−13.9483			−1.23771			−0.618857	−	0.785504i	$-0.712404\pi$
$127$	−13.9483			−1.23771			−0.618857	+	0.785504i	$0.712404\pi$
$128$	−11.3132	+	0.104686i	−0.999957	+	0.00925306i
$129$	1.43679			0.126502
$130$	−21.3463	+	0.0282173i	−1.87219	+	0.00247483i
$131$	6.97302	+	6.97302i	0.609235	+	0.609235i	0.942746	−	0.333511i	$-0.108233\pi$
$131$	6.97302	+	6.97302i	0.609235	+	0.609235i	−0.333511	+	0.942746i	$0.608233\pi$
$132$	0.595787	−	0.00157513i	0.0518566	−	0.000137097i
$133$	2.40031	−	2.40031i	0.208133	−	0.208133i
$134$	−13.1563	−	13.1216i	−1.13653	−	1.13353i
$135$		−	7.52641i		−	0.647770i
$136$	2.82840	−	0.0112165i	0.242534	−	0.000961810i
$137$		−	5.51851i		−	0.471478i	−0.971816	−	0.235739i	$-0.924249\pi$
$137$		−	5.51851i		−	0.471478i	0.971816	−	0.235739i	$-0.0757510\pi$
$138$	−2.85692	+	2.86448i	−0.243197	+	0.243841i
$139$	10.8272	−	10.8272i	0.918347	−	0.918347i	−0.0785622	−	0.996909i	$-0.525033\pi$
$139$	10.8272	−	10.8272i	0.918347	−	0.918347i	0.996909	+	0.0785622i	$0.0250329\pi$
$140$	−2.09261	−	2.08158i	−0.176858	−	0.175926i
$141$	−0.274297	−	0.274297i	−0.0231000	−	0.0231000i
$142$	−0.00501776	−	3.79591i	−0.000421081	−	0.318545i
$143$	3.49419			0.292199
$144$	−0.0602516	−	11.3949i	−0.00502097	−	0.949576i
$145$	23.0183			1.91156
$146$	0.000212139		0.160482i	1.75567e−5		0.0132816i
$147$	−1.87019	−	1.87019i	−0.154251	−	0.154251i
$148$	−4.50187	+	4.52574i	−0.370052	+	0.372014i
$149$	−13.3812	+	13.3812i	−1.09623	+	1.09623i	−0.101384	+	0.994847i	$0.532327\pi$
$149$	−13.3812	+	13.3812i	−1.09623	+	1.09623i	−0.994847	+	0.101384i	$0.967673\pi$
$150$	2.31070	−	2.31682i	0.188668	−	0.189167i
$151$			14.3363i			1.16667i	0.812233	+	0.583334i	$0.198252\pi$
$151$			14.3363i			1.16667i	−0.812233	+	0.583334i	$0.801748\pi$
$152$	15.2827	+	15.1619i	1.23959	+	1.22980i
$153$			2.84877i			0.230309i
$154$	0.342091	+	0.341188i	0.0275665	+	0.0274937i
$155$	9.38756	−	9.38756i	0.754027	−	0.754027i
$156$	0.00937954	+	3.54778i	0.000750964	+	0.284050i
$157$	−1.53680	−	1.53680i	−0.122650	−	0.122650i	0.643118	−	0.765767i	$-0.277641\pi$
$157$	−1.53680	−	1.53680i	−0.122650	−	0.122650i	−0.765767	+	0.643118i	$0.777641\pi$
$158$	−7.75850	+	0.0102559i	−0.617233	+	0.000815912i
$159$	−1.48332			−0.117635
$160$	13.1484	−	13.3233i	1.03947	−	1.05330i
$161$	−3.28079			−0.258563
$162$	10.8354	−	0.0143231i	0.851308	−	0.00112533i
$163$	11.3536	+	11.3536i	0.889285	+	0.889285i	0.994454	−	0.105169i	$-0.0335385\pi$
$163$	11.3536	+	11.3536i	0.889285	+	0.889285i	−0.105169	+	0.994454i	$0.533539\pi$
$164$	−0.0455713	−	17.2372i	−0.00355852	−	1.34600i
$165$	−0.697026	+	0.697026i	−0.0542634	+	0.0542634i
$166$	5.72385	+	5.70874i	0.444257	+	0.443084i
$167$			18.0679i			1.39813i	0.715057	+	0.699067i	$0.246401\pi$
$167$			18.0679i			1.39813i	−0.715057	+	0.699067i	$0.753599\pi$
$168$	−0.345502	+	0.348253i	−0.0266561	+	0.0268683i
$169$			7.80715i			0.600550i
$170$	−3.30466	+	3.31341i	−0.253456	+	0.254127i
$171$	−15.3319	+	15.3319i	−1.17246	+	1.17246i
$172$	−5.21116	+	5.23879i	−0.397347	+	0.399454i
$173$	−6.14057	−	6.14057i	−0.466859	−	0.466859i	0.434037	−	0.900895i	$-0.357089\pi$
$173$	−6.14057	−	6.14057i	−0.466859	−	0.466859i	−0.900895	+	0.434037i	$0.857089\pi$
$174$	−0.00505710	−	3.82567i	−0.000383378	−	0.290024i
$175$	2.65353			0.200588
$176$	−2.15515	+	2.17806i	−0.162450	+	0.164178i
$177$	4.81126			0.361637
$178$	0.0236490	+	17.8904i	0.00177257	+	1.34094i
$179$	−3.60205	−	3.60205i	−0.269230	−	0.269230i	0.559560	−	0.828790i	$-0.310970\pi$
$179$	−3.60205	−	3.60205i	−0.269230	−	0.269230i	−0.828790	+	0.559560i	$0.810970\pi$
$180$	13.3665	+	13.2960i	0.996282	+	0.991028i
$181$	0.0188640	−	0.0188640i	0.00140215	−	0.00140215i	−0.706405	−	0.707808i	$-0.749684\pi$
$181$	0.0188640	−	0.0188640i	0.00140215	−	0.00140215i	0.707808	+	0.706405i	$0.249684\pi$
$182$	−2.03170	+	2.03708i	−0.150599	+	0.150998i
$183$		−	4.15426i		−	0.307091i
$184$	−0.0825106	−	20.8062i	−0.00608276	−	1.53385i
$185$		−	10.5616i		−	0.776506i
$186$	−1.56229	−	1.55816i	−0.114553	−	0.114250i
$187$	0.541659	−	0.541659i	0.0396100	−	0.0396100i
$188$	1.99500	−	0.00527433i	0.145500	−	0.000384670i
$189$	−0.717297	−	0.717297i	−0.0521757	−	0.0521757i
$190$	−35.6180	+	0.0470830i	−2.58400	+	0.00341576i
$191$	−8.19518			−0.592983			−0.296491	−	0.955036i	$-0.595817\pi$
$191$	−8.19518			−0.592983			−0.296491	+	0.955036i	$0.595817\pi$
$192$	−2.21725	−	2.18235i	−0.160016	−	0.157498i
$193$	−1.99586			−0.143665			−0.0718325	−	0.997417i	$-0.522885\pi$
$193$	−1.99586			−0.143665			−0.0718325	+	0.997417i	$0.522885\pi$
$194$	20.5687	−	0.0271895i	1.47675	−	0.00195209i
$195$	−4.15064	−	4.15064i	−0.297233	−	0.297233i
$196$	13.6021	−	0.0359610i	0.971581	−	0.00256864i
$197$	−3.33429	+	3.33429i	−0.237558	+	0.237558i	−0.815838	−	0.578280i	$-0.803724\pi$
$197$	−3.33429	+	3.33429i	−0.237558	+	0.237558i	0.578280	+	0.815838i	$0.303724\pi$
$198$	−2.18510	−	2.17933i	−0.155288	−	0.154878i
$199$		−	21.2711i		−	1.50787i	−0.656950	−	0.753934i	$-0.728154\pi$
$199$		−	21.2711i		−	1.50787i	0.656950	−	0.753934i	$-0.271846\pi$
$200$	0.0667352	+	16.8282i	0.00471889	+	1.18993i
$201$		−	5.10956i		−	0.360401i
$202$	−0.687349	+	0.689169i	−0.0483617	+	0.0484898i
$203$	2.19373	−	2.19373i	0.153970	−	0.153970i
$204$	0.551420	+	0.548512i	0.0386071	+	0.0384035i
$205$	20.1662	+	20.1662i	1.40847	+	1.40847i
$206$	0.00837940	+	6.33898i	0.000583821	+	0.441657i
$207$	20.9560			1.45654
$208$	−12.9699	−	12.8334i	−0.899298	−	0.889838i
$209$	5.83035			0.403294
$210$	−0.00107290	−	0.811644i	−7.40372e−5	−	0.0560088i
$211$	−17.5179	−	17.5179i	−1.20598	−	1.20598i	−0.972318	−	0.233661i	$-0.924929\pi$
$211$	−17.5179	−	17.5179i	−1.20598	−	1.20598i	−0.233661	−	0.972318i	$-0.575071\pi$
$212$	5.37992	−	5.40844i	0.369494	−	0.371453i
$213$	0.738088	−	0.738088i	0.0505729	−	0.0505729i
$214$	−5.05453	+	5.06791i	−0.345520	+	0.346435i
$215$		−	12.2257i		−	0.833783i
$216$	4.53093	−	4.56701i	0.308291	−	0.310746i
$217$		−	1.78934i		−	0.121469i
$218$	1.19220	+	1.18905i	0.0807461	+	0.0805329i
$219$	−0.0312046	+	0.0312046i	−0.00210861	+	0.00210861i
$220$	−0.0134028	−	5.06957i	−0.000903616	−	0.341790i
$221$	3.22546	+	3.22546i	0.216968	+	0.216968i
$222$	−1.75536	+	0.00232038i	−0.117812	+	0.000155734i
$223$	−7.76046			−0.519679			−0.259839	−	0.965652i	$-0.583670\pi$
$223$	−7.76046			−0.519679			−0.259839	+	0.965652i	$0.583670\pi$
$224$	−0.0166749	−	2.52286i	−0.00111414	−	0.168566i
$225$	−16.9494			−1.12996
$226$	9.71337	−	0.0128400i	0.646124	−	0.000854102i
$227$	−18.8044	−	18.8044i	−1.24809	−	1.24809i	−0.956562	−	0.291531i	$-0.905835\pi$
$227$	−18.8044	−	18.8044i	−1.24809	−	1.24809i	−0.291531	−	0.956562i	$-0.594165\pi$
$228$	0.0156505	+	5.91976i	0.00103648	+	0.392046i
$229$	11.5509	−	11.5509i	0.763308	−	0.763308i	−0.213611	−	0.976919i	$-0.568522\pi$
$229$	11.5509	−	11.5509i	0.763308	−	0.763308i	0.976919	+	0.213611i	$0.0685224\pi$
$230$	24.3740	+	24.3096i	1.60717	+	1.60293i
$231$			0.132859i			0.00874147i
$232$	13.9674	+	13.8571i	0.917007	+	0.909763i
$233$			9.25433i			0.606271i	0.952947	+	0.303136i	$0.0980336\pi$
$233$			9.25433i			0.606271i	−0.952947	+	0.303136i	$0.901966\pi$
$234$	12.9774	−	13.0118i	0.848361	−	0.850607i
$235$	−2.33400	+	2.33400i	−0.152253	+	0.152253i
$236$	−17.4502	+	17.5427i	−1.13591	+	1.14193i
$237$	−1.50859	−	1.50859i	−0.0979933	−	0.0979933i
$238$	0.000833751		0.630728i	5.40440e−5		0.0408840i
$239$	17.7138			1.14581			0.572906	−	0.819621i	$-0.305816\pi$
$239$	17.7138			1.14581			0.572906	+	0.819621i	$0.305816\pi$
$240$	5.14727	−	0.0272167i	0.332255	−	0.00175683i
$241$	3.29924			0.212523			0.106261	−	0.994338i	$-0.466112\pi$
$241$	3.29924			0.212523			0.106261	+	0.994338i	$0.466112\pi$
$242$	−0.0194667	−	14.7265i	−0.00125137	−	0.946655i
$243$	6.93181	+	6.93181i	0.444676	+	0.444676i
$244$	15.1472	+	15.0673i	0.969698	+	0.964584i
$245$	−15.9135	+	15.9135i	−1.01667	+	1.01667i
$246$	3.34723	−	3.35609i	0.213411	−	0.213976i
$247$			34.7184i			2.20908i
$248$	11.3477	−	0.0450013i	0.720580	−	0.00285758i
$249$			2.22299i			0.140876i
$250$	−3.14680	−	3.13849i	−0.199021	−	0.198495i
$251$	10.7213	−	10.7213i	0.676722	−	0.676722i	−0.282535	−	0.959257i	$-0.591175\pi$
$251$	10.7213	−	10.7213i	0.676722	−	0.676722i	0.959257	+	0.282535i	$0.0911754\pi$
$252$	2.54105	−	0.00671797i	0.160071	−	0.000423192i
$253$	−3.98453	−	3.98453i	−0.250505	−	0.250505i
$254$	19.7259	−	0.0260754i	1.23771	−	0.00163611i
$255$	−1.28684			−0.0805848
$256$	15.9991	−	0.169198i	0.999944	−	0.0105749i
$257$	7.10412			0.443143			0.221572	−	0.975144i	$-0.428881\pi$
$257$	7.10412			0.443143			0.221572	+	0.975144i	$0.428881\pi$
$258$	−2.03192	+	0.00268597i	−0.126502	+	0.000167221i
$259$	−1.00657	−	1.00657i	−0.0625450	−	0.0625450i
$260$	30.1881	−	0.0798106i	1.87219	−	0.00494965i
$261$	−14.0124	+	14.0124i	−0.867348	+	0.867348i
$262$	−9.87436	−	9.84829i	−0.610040	−	0.608429i
$263$		−	20.6451i		−	1.27303i	−0.771264	−	0.636515i	$-0.780375\pi$
$263$		−	20.6451i		−	1.27303i	0.771264	−	0.636515i	$-0.219625\pi$
$264$	−0.842567	+	0.00334135i	−0.0518564	+	0.000205646i
$265$			12.6216i			0.775337i
$266$	−3.39006	+	3.39903i	−0.207858	+	0.208408i
$267$	−3.47866	+	3.47866i	−0.212890	+	0.212890i
$268$	18.6304	+	18.5321i	1.13803	+	1.13203i
$269$	−6.99084	−	6.99084i	−0.426239	−	0.426239i	0.461106	−	0.887345i	$-0.347453\pi$
$269$	−6.99084	−	6.99084i	−0.426239	−	0.426239i	−0.887345	+	0.461106i	$0.847453\pi$
$270$	0.0140701	+	10.6439i	0.000856277	+	0.647770i
$271$	−9.59290			−0.582727			−0.291364	−	0.956612i	$-0.594109\pi$
$271$	−9.59290			−0.582727			−0.291364	+	0.956612i	$0.594109\pi$
$272$	−3.99994	+	0.0211501i	−0.242532	+	0.00128241i
$273$	−0.791145			−0.0478823
$274$	0.0103164	+	7.80434i	0.000623239	+	0.471478i
$275$	3.22272	+	3.22272i	0.194337	+	0.194337i
$276$	4.03494	−	4.05633i	0.242875	−	0.244162i
$277$	−3.54839	+	3.54839i	−0.213202	+	0.213202i	−0.805626	−	0.592424i	$-0.798171\pi$
$277$	−3.54839	+	3.54839i	−0.213202	+	0.213202i	0.592424	+	0.805626i	$0.298171\pi$
$278$	−15.2917	+	15.3321i	−0.917132	+	0.919560i
$279$			11.4294i			0.684260i
$280$	2.96329	+	2.93988i	0.177091	+	0.175692i
$281$		−	5.02976i		−	0.300050i	−0.988682	−	0.150025i	$-0.952065\pi$
$281$		−	5.02976i		−	0.300050i	0.988682	−	0.150025i	$-0.0479354\pi$
$282$	0.388427	+	0.387402i	0.0231305	+	0.0230694i
$283$	3.29569	−	3.29569i	0.195908	−	0.195908i	−0.602335	−	0.798243i	$-0.705763\pi$
$283$	3.29569	−	3.29569i	0.195908	−	0.195908i	0.798243	+	0.602335i	$0.205763\pi$
$284$	0.0141923	+	5.36821i	0.000842161	+	0.318545i
$285$	−6.92568	−	6.92568i	−0.410242	−	0.410242i
$286$	−4.94153	+	0.00653214i	−0.292199	+	0.000386254i
$287$	3.84384			0.226895
$288$	0.106511	+	16.1147i	0.00627619	+	0.949569i
$289$	1.00000			0.0588235
$290$	−32.5527	+	0.0430310i	−1.91156	+	0.00252687i
$291$	3.99945	+	3.99945i	0.234452	+	0.234452i
$292$	−0.000600018	−	0.226955i	−3.51134e−5	−	0.0132815i
$293$	17.3070	−	17.3070i	1.01108	−	1.01108i	0.0111460	−	0.999938i	$-0.496452\pi$
$293$	17.3070	−	17.3070i	1.01108	−	1.01108i	0.999938	−	0.0111460i	$-0.00354794\pi$
$294$	2.64834	+	2.64135i	0.154454	+	0.154047i
$295$		−	40.9391i		−	2.38357i
$296$	6.35814	−	6.40877i	0.369560	−	0.372502i
$297$		−	1.74232i		−	0.101099i
$298$	18.8989	−	18.9489i	1.09478	−	1.09768i
$299$	23.7270	−	23.7270i	1.37217	−	1.37217i
$300$	−3.26349	+	3.28079i	−0.188418	+	0.189416i
$301$	−1.16515	−	1.16515i	−0.0671584	−	0.0671584i
$302$	−0.0268006	−	20.2745i	−0.00154220	−	1.16667i
$303$	−0.267654			−0.0153763
$304$	−21.6413	−	21.4136i	−1.24121	−	1.22816i
$305$	−35.3486			−2.02406
$306$	−0.00532556	−	4.02876i	−0.000304442	−	0.230309i
$307$	11.0046	+	11.0046i	0.628067	+	0.628067i	0.947581	−	0.319514i	$-0.103520\pi$
$307$	11.0046	+	11.0046i	0.628067	+	0.628067i	−0.319514	+	0.947581i	$0.603520\pi$
$308$	−0.484427	−	0.481873i	−0.0276028	−	0.0274572i
$309$	−1.23257	+	1.23257i	−0.0701184	+	0.0701184i
$310$	−13.2585	+	13.2936i	−0.753029	+	0.755023i
$311$			1.58558i			0.0899101i	0.998989	+	0.0449551i	$0.0143145\pi$
$311$			1.58558i			0.0899101i	−0.998989	+	0.0449551i	$0.985686\pi$
$312$	−0.0198970	−	5.01730i	−0.00112644	−	0.284049i
$313$			0.967233i			0.0546712i	0.999626	+	0.0273356i	$0.00870228\pi$
$313$			0.967233i			0.0546712i	−0.999626	+	0.0273356i	$0.991298\pi$
$314$	2.17623	+	2.17049i	0.122812	+	0.122488i
$315$	−2.97284	+	2.97284i	−0.167500	+	0.167500i
$316$	10.9722	−	0.0290079i	0.617232	−	0.00163182i
$317$	−5.64282	−	5.64282i	−0.316932	−	0.316932i	0.530655	−	0.847588i	$-0.321946\pi$
$317$	−5.64282	−	5.64282i	−0.316932	−	0.316932i	−0.847588	+	0.530655i	$0.821946\pi$
$318$	2.09773	−	0.00277295i	0.117635	−	0.000155499i
$319$	5.32859			0.298344
$320$	−18.5697	+	18.8666i	−1.03808	+	1.05468i
$321$	−1.96824			−0.109856
$322$	4.63974	−	0.00613320i	0.258563	−	0.000341790i
$323$	5.38194	+	5.38194i	0.299459	+	0.299459i
$324$	−15.3235	+	0.0405119i	−0.851306	+	0.00225066i
$325$	−19.1906	+	19.1906i	−1.06450	+	1.06450i
$326$	−16.0777	−	16.0352i	−0.890460	−	0.888109i
$327$			0.463019i			0.0256050i
$328$	0.0966711	+	24.3770i	0.00533777	+	1.34599i
$329$			0.444879i			0.0245270i
$330$	0.984440	−	0.987046i	0.0541917	−	0.0543351i
$331$	−15.1155	+	15.1155i	−0.830822	+	0.830822i	−0.987629	−	0.156808i	$-0.949880\pi$
$331$	−15.1155	+	15.1155i	−0.830822	+	0.830822i	0.156808	+	0.987629i	$0.449880\pi$
$332$	−8.10542	−	8.06267i	−0.444843	−	0.442497i
$333$	6.42942	+	6.42942i	0.352330	+	0.352330i
$334$	−0.0337765	−	25.5518i	−0.00184817	−	1.39813i
$335$	−43.4774			−2.37542
$336$	0.487962	−	0.493150i	0.0266205	−	0.0269035i
$337$	12.4658			0.679053			0.339526	−	0.940597i	$-0.389733\pi$
$337$	12.4658			0.679053			0.339526	+	0.940597i	$0.389733\pi$
$338$	−0.0145949	−	11.0410i	−0.000793857	−	0.600549i
$339$	1.88870	+	1.88870i	0.102580	+	0.102580i
$340$	4.66729	−	4.69204i	0.253120	−	0.254462i
$341$	2.17316	−	2.17316i	0.117683	−	0.117683i
$342$	21.6539	−	21.7112i	1.17091	−	1.17401i
$343$			6.15519i			0.332349i
$344$	7.35989	−	7.41850i	0.396819	−	0.399979i
$345$			9.46618i			0.509642i
$346$	8.69554	+	8.67259i	0.467475	+	0.466241i
$347$	4.94973	−	4.94973i	0.265716	−	0.265716i	−0.561656	−	0.827371i	$-0.689835\pi$
$347$	4.94973	−	4.94973i	0.265716	−	0.265716i	0.827371	+	0.561656i	$0.189835\pi$
$348$	0.0143036	+	5.41031i	0.000766755	+	0.290023i
$349$	−9.77844	−	9.77844i	−0.523428	−	0.523428i	0.395177	−	0.918605i	$-0.370683\pi$
$349$	−9.77844	−	9.77844i	−0.523428	−	0.523428i	−0.918605	+	0.395177i	$0.870683\pi$
$350$	−3.75265	+	0.00496058i	−0.200588	+	0.000265154i
$351$	10.3751			0.553782
$352$	3.04377	−	3.08427i	0.162233	−	0.164392i
$353$	−8.85342			−0.471220			−0.235610	−	0.971848i	$-0.575709\pi$
$353$	−8.85342			−0.471220			−0.235610	+	0.971848i	$0.575709\pi$
$354$	−6.80415	+	0.00899430i	−0.361636	+	0.000478042i
$355$	−6.28040	−	6.28040i	−0.333329	−	0.333329i
$356$	−0.0668895	−	25.3007i	−0.00354514	−	1.34094i
$357$	−0.122641	+	0.122641i	−0.00649084	+	0.00649084i
$358$	5.10079	+	5.08733i	0.269585	+	0.268874i
$359$		−	24.0430i		−	1.26894i	−0.772947	−	0.634470i	$-0.781218\pi$
$359$		−	24.0430i		−	1.26894i	0.772947	−	0.634470i	$-0.218782\pi$
$360$	−18.9280	−	18.7784i	−0.997591	−	0.989710i
$361$			38.9306i			2.04898i
$362$	−0.0266425	+	0.0267130i	−0.00140030	+	0.00140400i
$363$	2.86346	−	2.86346i	0.150293	−	0.150293i
$364$	2.86944	−	2.88466i	0.150400	−	0.151197i
$365$	0.265520	+	0.265520i	0.0138980	+	0.0138980i
$366$	0.00776608	+	5.87500i	0.000405939	+	0.307091i
$367$	−31.5283			−1.64577			−0.822883	−	0.568211i	$-0.807636\pi$
$367$	−31.5283			−1.64577			−0.822883	+	0.568211i	$0.807636\pi$
$368$	0.155583	+	29.4242i	0.00811034	+	1.53384i
$369$	−24.5525			−1.27815
$370$	0.0197442	+	14.9364i	0.00102645	+	0.776506i
$371$	1.20289	+	1.20289i	0.0624508	+	0.0624508i
$372$	2.21232	+	2.20066i	0.114704	+	0.114099i
$373$	26.9953	−	26.9953i	1.39777	−	1.39777i	0.591351	−	0.806414i	$-0.298595\pi$
$373$	26.9953	−	26.9953i	1.39777	−	1.39777i	0.806414	−	0.591351i	$-0.201405\pi$
$374$	−0.765008	+	0.767033i	−0.0395576	+	0.0396623i
$375$		−	1.22213i		−	0.0631105i
$376$	−2.82134	+	0.0111885i	−0.145500	+	0.000577005i
$377$			31.7306i			1.63421i
$378$	1.01575	+	1.01307i	0.0522446	+	0.0521067i
$379$	11.2644	−	11.2644i	0.578611	−	0.578611i	−0.355909	−	0.934520i	$-0.615829\pi$
$379$	11.2644	−	11.2644i	0.578611	−	0.578611i	0.934520	+	0.355909i	$0.115829\pi$
$380$	50.3714	−	0.133171i	2.58400	−	0.00683151i
$381$	3.83556	+	3.83556i	0.196502	+	0.196502i
$382$	11.5897	−	0.0153203i	0.592982	−	0.000783855i
$383$	−9.53049			−0.486985			−0.243493	−	0.969903i	$-0.578293\pi$
$383$	−9.53049			−0.486985			−0.243493	+	0.969903i	$0.578293\pi$
$384$	3.13974	+	3.08217i	0.160224	+	0.157286i
$385$	1.13050			0.0576155
$386$	2.82257	−	0.00373111i	0.143665	−	0.000189909i
$387$	7.44240	+	7.44240i	0.378318	+	0.378318i
$388$	−29.0885	+	0.0769035i	−1.47675	+	0.00390418i
$389$	1.68160	−	1.68160i	0.0852605	−	0.0852605i	−0.663190	−	0.748451i	$-0.730798\pi$
$389$	1.68160	−	1.68160i	0.0852605	−	0.0852605i	0.748451	+	0.663190i	$0.230798\pi$
$390$	5.87764	+	5.86212i	0.297626	+	0.296840i
$391$		−	7.35616i		−	0.372017i
$392$	−19.2362	+	0.0762847i	−0.971577	+	0.00385296i
$393$		−	3.83493i		−	0.193447i
$394$	4.70916	−	4.72163i	0.237244	−	0.237872i
$395$	−12.8366	+	12.8366i	−0.645879	+	0.645879i
$396$	3.09427	+	3.07795i	0.155493	+	0.154673i
$397$	−23.4716	−	23.4716i	−1.17801	−	1.17801i	−0.980252	−	0.197754i	$-0.936635\pi$
$397$	−23.4716	−	23.4716i	−1.17801	−	1.17801i	−0.197754	−	0.980252i	$-0.563365\pi$
$398$	0.0397648	+	30.0818i	0.00199323	+	1.50787i
$399$	−1.32009			−0.0660872
$400$	−0.125837	−	23.7985i	−0.00629184	−	1.18993i
$401$	33.2764			1.66174			0.830871	−	0.556464i	$-0.187842\pi$
$401$	33.2764			1.66174			0.830871	+	0.556464i	$0.187842\pi$
$402$	0.00955196	+	7.22601i	0.000476408	+	0.360401i
$403$	12.9407	+	12.9407i	0.644622	+	0.644622i
$404$	0.970770	−	0.975916i	0.0482976	−	0.0485537i
$405$	17.9274	−	17.9274i	0.890817	−	0.890817i
$406$	−3.09831	+	3.10651i	−0.153766	+	0.154173i
$407$		−	2.44495i		−	0.121192i
$408$	−0.780850	−	0.774681i	−0.0386578	−	0.0383524i
$409$		−	6.14234i		−	0.303719i	−0.988402	−	0.151859i	$-0.951474\pi$
$409$		−	6.14234i		−	0.303719i	0.988402	−	0.151859i	$-0.0485261\pi$
$410$	−28.5570	−	28.4816i	−1.41033	−	1.40661i
$411$	−1.51750	+	1.51750i	−0.0748527	+	0.0748527i
$412$	−0.0237005	−	8.96464i	−0.00116764	−	0.441656i
$413$	−3.90166	−	3.90166i	−0.191988	−	0.191988i
$414$	−29.6362	+	0.0391757i	−1.45654	+	0.00192538i
$415$	18.9155			0.928523
$416$	18.3661	+	18.1249i	0.900474	+	0.888649i
$417$	−5.95458			−0.291597
$418$	−8.24536	+	0.0108994i	−0.403293	+	0.000533108i
$419$	25.8823	+	25.8823i	1.26443	+	1.26443i	0.948921	+	0.315514i	$0.102177\pi$
$419$	25.8823	+	25.8823i	1.26443	+	1.26443i	0.315514	+	0.948921i	$0.397823\pi$
$420$	0.00303462	+	1.14784i	0.000148074	+	0.0560086i
$421$	−15.1813	+	15.1813i	−0.739891	+	0.739891i	−0.972557	−	0.232666i	$-0.925255\pi$
$421$	−15.1813	+	15.1813i	−0.739891	+	0.739891i	0.232666	+	0.972557i	$0.425255\pi$
$422$	24.8067	+	24.7412i	1.20757	+	1.20438i
$423$		−	2.84166i		−	0.138166i
$424$	−7.59824	+	7.65874i	−0.369003	+	0.371941i
$425$			5.94972i			0.288604i
$426$	−1.04243	+	1.04519i	−0.0505060	+	0.0506397i
$427$	−3.36887	+	3.36887i	−0.163031	+	0.163031i
$428$	7.13870	−	7.17655i	0.345062	−	0.346892i
$429$	−0.960847	−	0.960847i	−0.0463901	−	0.0463901i
$430$	0.0228550	+	17.2897i	0.00110216	+	0.833782i
$431$	−28.0733			−1.35224			−0.676122	−	0.736790i	$-0.736341\pi$
$431$	−28.0733			−1.35224			−0.676122	+	0.736790i	$0.736341\pi$
$432$	−6.39916	+	6.46719i	−0.307880	+	0.311153i
$433$	−23.2394			−1.11681			−0.558406	−	0.829568i	$-0.688587\pi$
$433$	−23.2394			−1.11681			−0.558406	+	0.829568i	$0.688587\pi$
$434$	0.00334505	+	2.53051i	0.000160567	+	0.121469i
$435$	−6.32965	−	6.32965i	−0.303484	−	0.303484i
$436$	−1.68825	−	1.67935i	−0.0808525	−	0.0804261i
$437$	39.5904	−	39.5904i	1.89387	−	1.89387i
$438$	0.0440715	−	0.0441882i	0.00210582	−	0.00211139i
$439$			19.0017i			0.906900i	0.891282	+	0.453450i	$0.149807\pi$
$439$			19.0017i			0.906900i	−0.891282	+	0.453450i	$0.850193\pi$
$440$	0.0284316	+	7.16942i	0.00135542	+	0.341789i
$441$		−	19.3747i		−	0.922606i
$442$	−4.56751	−	4.55545i	−0.217254	−	0.216681i
$443$	19.3884	−	19.3884i	0.921171	−	0.921171i	−0.0759413	−	0.997112i	$-0.524196\pi$
$443$	19.3884	−	19.3884i	0.921171	−	0.921171i	0.997112	+	0.0759413i	$0.0241962\pi$
$444$	2.48245	−	0.00656303i	0.117812	−	0.000311468i
$445$	29.6000	+	29.6000i	1.40317	+	1.40317i
$446$	10.9749	−	0.0145076i	0.519679	−	0.000686956i
$447$	7.35923			0.348080
$448$	0.0282981	+	3.56783i	0.00133696	+	0.168564i
$449$	5.79770			0.273610			0.136805	−	0.990598i	$-0.456317\pi$
$449$	5.79770			0.273610			0.136805	+	0.990598i	$0.456317\pi$
$450$	23.9700	−	0.0316856i	1.12996	−	0.00149367i
$451$	4.66835	+	4.66835i	0.219824	+	0.219824i
$452$	−13.7367	+	0.0363169i	−0.646122	+	0.00170820i
$453$	3.94224	−	3.94224i	0.185222	−	0.185222i
$454$	26.6286	+	26.5583i	1.24974	+	1.24644i
$455$			6.73187i			0.315595i
$456$	−0.0331997	−	8.37177i	−0.00155472	−	0.392044i
$457$		−	30.3420i		−	1.41934i	−0.704534	−	0.709670i	$-0.748844\pi$
$457$		−	30.3420i		−	1.41934i	0.704534	−	0.709670i	$-0.251156\pi$
$458$	−16.3139	+	16.3571i	−0.762299	+	0.764317i
$459$	1.60832	−	1.60832i	0.0750698	−	0.0750698i
$460$	−34.5154	−	34.3334i	−1.60929	−	1.60080i
$461$	2.04864	+	2.04864i	0.0954145	+	0.0954145i	0.753203	−	0.657788i	$-0.228508\pi$
$461$	2.04864	+	2.04864i	0.0954145	+	0.0954145i	−0.657788	+	0.753203i	$0.728508\pi$
$462$	−0.000248370	−	0.187891i	−1.15552e−5	−	0.00874146i
$463$	−36.6070			−1.70127			−0.850635	−	0.525757i	$-0.823782\pi$
$463$	−36.6070			−1.70127			−0.850635	+	0.525757i	$0.823782\pi$
$464$	−19.7788	−	19.5708i	−0.918209	−	0.908550i
$465$	−5.16285			−0.239422
$466$	−0.0173003	−	13.0876i	−0.000801421	−	0.606271i
$467$	−0.987469	−	0.987469i	−0.0456946	−	0.0456946i	0.683890	−	0.729585i	$-0.260287\pi$
$467$	−0.987469	−	0.987469i	−0.0456946	−	0.0456946i	−0.729585	+	0.683890i	$0.760287\pi$
$468$	−18.3285	+	18.4257i	−0.847236	+	0.851727i
$469$	−4.14357	+	4.14357i	−0.191332	+	0.191332i
$470$	3.29641	−	3.30513i	0.152052	−	0.152455i
$471$			0.845189i			0.0389443i
$472$	24.6455	−	24.8418i	1.13440	−	1.14343i
$473$		−	2.83016i		−	0.130131i
$474$	2.13628	+	2.13064i	0.0981227	+	0.0978636i
$475$	−32.0210	+	32.0210i	−1.46923	+	1.46923i
$476$	−0.00235820	−	0.891982i	−0.000108088	−	0.0408839i
$477$	−7.68341	−	7.68341i	−0.351799	−	0.351799i
$478$	−25.0511	+	0.0331147i	−1.14581	+	0.00151463i
$479$	2.70723			0.123696			0.0618482	−	0.998086i	$-0.480301\pi$
$479$	2.70723			0.123696			0.0618482	+	0.998086i	$0.480301\pi$
$480$	−7.27929	+	0.0481126i	−0.332253	+	0.00219603i
$481$	14.5591			0.663840
$482$	−4.66583	+	0.00616770i	−0.212523	+	0.000280931i
$483$	0.902165	+	0.902165i	0.0410499	+	0.0410499i
$484$	0.0550602	+	20.8264i	0.00250274	+	0.946652i
$485$	34.0314	−	34.0314i	1.54529	−	1.54529i
$486$	−9.81601	−	9.79010i	−0.445263	−	0.444088i
$487$		−	14.3550i		−	0.650488i	−0.945630	−	0.325244i	$-0.894554\pi$
$487$		−	14.3550i		−	0.650488i	0.945630	−	0.325244i	$-0.105446\pi$
$488$	−21.4495	−	21.2800i	−0.970972	−	0.963302i
$489$		−	6.24413i		−	0.282369i
$490$	22.4753	−	22.5348i	1.01533	−	1.01802i
$491$	−6.46532	+	6.46532i	−0.291776	+	0.291776i	−0.837781	−	0.546006i	$-0.816148\pi$
$491$	−6.46532	+	6.46532i	−0.291776	+	0.291776i	0.546006	+	0.837781i	$0.316148\pi$
$492$	−4.72742	+	4.75248i	−0.213128	+	0.214258i
$493$	4.91877	+	4.91877i	0.221530	+	0.221530i
$494$	−0.0649036	−	49.0992i	−0.00292015	−	2.20908i
$495$	−7.22103			−0.324561
$496$	−16.0480	+	0.0848551i	−0.720575	+	0.00381011i
$497$	−1.19710			−0.0536971
$498$	−0.00415571	−	3.14378i	−0.000186222	−	0.140876i
$499$	11.6037	+	11.6037i	0.519455	+	0.519455i	0.917406	−	0.397952i	$-0.130279\pi$
$499$	11.6037	+	11.6037i	0.519455	+	0.519455i	−0.397952	+	0.917406i	$0.630279\pi$
$500$	4.45610	+	4.43260i	0.199283	+	0.198232i
$501$	4.96837	−	4.96837i	0.221970	−	0.221970i
$502$	−15.1421	+	15.1822i	−0.675826	+	0.677615i
$503$		−	23.7063i		−	1.05701i	−0.848930	−	0.528506i	$-0.822752\pi$
$503$		−	23.7063i		−	1.05701i	0.848930	−	0.528506i	$-0.177248\pi$
$504$	−3.59357	+	0.0142509i	−0.160070	+	0.000634787i
$505$			2.27748i			0.101346i
$506$	5.64242	+	5.62752i	0.250836	+	0.250174i
$507$	2.14684	−	2.14684i	0.0953444	−	0.0953444i
$508$	−27.8965	+	0.0737522i	−1.23771	+	0.00327222i
$509$	−5.57748	−	5.57748i	−0.247217	−	0.247217i	0.572610	−	0.819828i	$-0.305931\pi$
$509$	−5.57748	−	5.57748i	−0.247217	−	0.247217i	−0.819828	+	0.572610i	$0.805931\pi$
$510$	1.81986	−	0.00240565i	0.0805848	−	0.000106524i
$511$	0.0506103			0.00223887
$512$	−22.6258	+	0.269191i	−0.999929	+	0.0118967i
$513$	17.3117			0.764331
$514$	−10.0467	+	0.0132806i	−0.443143	+	0.000585784i
$515$	10.4880	+	10.4880i	0.462155	+	0.462155i
$516$	2.87357	−	0.00759706i	0.126502	−	0.000334442i
$517$	−0.540307	+	0.540307i	−0.0237627	+	0.0237627i
$518$	1.42538	+	1.42162i	0.0626276	+	0.0624622i
$519$			3.37711i			0.148239i
$520$	−42.6923	+	0.169304i	−1.87218	+	0.00742446i
$521$			30.3640i			1.33027i	0.746723	+	0.665135i	$0.231626\pi$
$521$			30.3640i			1.33027i	−0.746723	+	0.665135i	$0.768374\pi$
$522$	19.7904	−	19.8427i	0.866200	−	0.868493i
$523$	−12.9934	+	12.9934i	−0.568160	+	0.568160i	−0.931613	−	0.363452i	$-0.881598\pi$
$523$	−12.9934	+	12.9934i	−0.568160	+	0.568160i	0.363452	+	0.931613i	$0.381598\pi$
$524$	13.9829	+	13.9091i	0.610844	+	0.607622i
$525$	−0.729677	−	0.729677i	−0.0318457	−	0.0318457i
$526$	0.0385945	+	29.1965i	0.00168280	+	1.27303i
$527$	4.01205			0.174768
$528$	1.19156	−	0.00630049i	0.0518561	−	0.000274194i
$529$	−31.1131			−1.35274
$530$	−0.0235951	−	17.8496i	−0.00102491	−	0.775336i
$531$	24.9218	+	24.9218i	1.08151	+	1.08151i
$532$	4.78790	−	4.81329i	0.207582	−	0.208682i
$533$	−27.7990	+	27.7990i	−1.20411	+	1.20411i
$534$	4.91306	−	4.92606i	0.212609	−	0.213172i
$535$			16.7478i			0.724069i
$536$	−26.3820	−	26.1736i	−1.13953	−	1.13053i
$537$			1.98101i			0.0854869i
$538$	9.89960	+	9.87346i	0.426802	+	0.425675i
$539$	−3.68387	+	3.68387i	−0.158676	+	0.158676i
$540$	−0.0397961	−	15.0528i	−0.00171255	−	0.647768i
$541$	21.4030	+	21.4030i	0.920185	+	0.920185i	0.997042	−	0.0768571i	$-0.0244885\pi$
$541$	21.4030	+	21.4030i	0.920185	+	0.920185i	−0.0768571	+	0.997042i	$0.524489\pi$
$542$	13.5664	−	0.0179332i	0.582727	−	0.000770298i
$543$	−0.0103746			−0.000445217
$544$	5.65673	−	0.0373883i	0.242530	−	0.00160301i
$545$	3.93983			0.168764
$546$	1.11885	−	0.00147899i	0.0478822	−	6.32948e-5i
$547$	8.09835	+	8.09835i	0.346260	+	0.346260i	0.858715	−	0.512454i	$-0.171264\pi$
$547$	8.09835	+	8.09835i	0.346260	+	0.346260i	−0.512454	+	0.858715i	$0.671264\pi$
$548$	−0.0291793	−	11.0370i	−0.00124648	−	0.471476i
$549$	21.5186	−	21.5186i	0.918390	−	0.918390i
$550$	−4.56363	−	4.55158i	−0.194594	−	0.194080i
$551$			52.9450i			2.25553i
$552$	−5.69868	+	5.74406i	−0.242552	+	0.244483i
$553$			2.44676i			0.104047i
$554$	5.01154	−	5.02481i	0.212920	−	0.213484i
$555$	−2.90428	+	2.90428i	−0.123280	+	0.123280i
$556$	21.5970	−	21.7115i	0.915916	−	0.920772i
$557$	0.593641	+	0.593641i	0.0251534	+	0.0251534i	0.719572	−	0.694418i	$-0.244338\pi$
$557$	0.593641	+	0.593641i	0.0251534	+	0.0251534i	−0.694418	+	0.719572i	$0.744338\pi$
$558$	−0.0213664	−	16.1636i	−0.000904513	−	0.684259i
$559$	16.8530			0.712806
$560$	−4.19622	−	4.15208i	−0.177323	−	0.175457i
$561$	−0.297895			−0.0125771
$562$	0.00940276	+	7.11314i	0.000396632	+	0.300050i
$563$	−0.476645	−	0.476645i	−0.0200882	−	0.0200882i	0.696991	−	0.717080i	$-0.254522\pi$
$563$	−0.476645	−	0.476645i	−0.0200882	−	0.0200882i	−0.717080	+	0.696991i	$0.754522\pi$
$564$	−0.550043	−	0.547142i	−0.0231610	−	0.0230388i
$565$	16.0710	−	16.0710i	0.676110	−	0.676110i
$566$	−4.65464	+	4.66697i	−0.195649	+	0.196167i
$567$		−	3.41710i		−	0.143505i
$568$	−0.0301065	−	7.59176i	−0.00126324	−	0.318543i
$569$		−	13.8256i		−	0.579598i	−0.957087	−	0.289799i	$-0.906411\pi$
$569$		−	13.8256i		−	0.579598i	0.957087	−	0.289799i	$-0.0935885\pi$
$570$	9.80733	+	9.78143i	0.410784	+	0.409699i
$571$	−17.5093	+	17.5093i	−0.732740	+	0.732740i	−0.971162	−	0.238422i	$-0.923370\pi$
$571$	−17.5093	+	17.5093i	−0.732740	+	0.732740i	0.238422	+	0.971162i	$0.423370\pi$
$572$	6.98836	−	0.0184757i	0.292198	−	0.000772507i
$573$	2.25354	+	2.25354i	0.0941431	+	0.0941431i
$574$	−5.43601	+	0.00718579i	−0.226895	+	0.000299929i
$575$	43.7671			1.82521
$576$	−0.180754	−	22.7894i	−0.00753141	−	0.949559i
$577$	3.52413			0.146712			0.0733558	−	0.997306i	$-0.476629\pi$
$577$	3.52413			0.146712			0.0733558	+	0.997306i	$0.476629\pi$
$578$	−1.41421	+	0.00186943i	−0.0588235	+	7.77579e-5i
$579$	0.548829	+	0.548829i	0.0228085	+	0.0228085i
$580$	46.0364	−	0.121710i	1.91156	−	0.00505373i
$581$	1.80272	−	1.80272i	0.0747894	−	0.0747894i
$582$	−5.66355	−	5.64859i	−0.234762	−	0.234142i
$583$			2.92182i			0.121009i
$584$	0.00127283	+	0.320961i	5.26700e−5	+	0.0132815i
$585$		−	42.9996i		−	1.77782i
$586$	−24.4434	+	24.5081i	−1.00975	+	1.01242i
$587$	13.3710	−	13.3710i	0.551880	−	0.551880i	−0.375103	−	0.926983i	$-0.622393\pi$
$587$	13.3710	−	13.3710i	0.551880	−	0.551880i	0.926983	+	0.375103i	$0.122393\pi$
$588$	−3.75025	−	3.73048i	−0.154658	−	0.153842i
$589$	21.5926	+	21.5926i	0.889708	+	0.889708i
$590$	0.0765327	+	57.8966i	0.00315080	+	2.38357i
$591$	1.83375			0.0754305
$592$	−8.97978	+	9.07525i	−0.369067	+	0.372991i
$593$	47.3833			1.94580			0.972900	−	0.231225i	$-0.0742735\pi$
$593$	47.3833			1.94580			0.972900	+	0.231225i	$0.0742735\pi$
$594$	0.00325713	+	2.46401i	0.000133642	+	0.101099i
$595$	1.04355	+	1.04355i	0.0427815	+	0.0427815i
$596$	−26.6916	+	26.8331i	−1.09333	+	1.09913i
$597$	−5.84921	+	5.84921i	−0.239392	+	0.239392i
$598$	−33.5106	+	33.5993i	−1.37035	+	1.37398i
$599$			15.4256i			0.630273i	0.949046	+	0.315137i	$0.102050\pi$
$599$			15.4256i			0.630273i	−0.949046	+	0.315137i	$0.897950\pi$
$600$	4.60913	−	4.64583i	0.188167	−	0.189665i
$601$			25.3809i			1.03531i	0.855590	+	0.517655i	$0.173195\pi$
$601$			25.3809i			1.03531i	−0.855590	+	0.517655i	$0.826805\pi$
$602$	1.64995	+	1.64560i	0.0672471	+	0.0670695i
$603$	26.4669	−	26.4669i	1.07782	−	1.07782i
$604$	0.0758034	+	28.6724i	0.00308440	+	1.16666i
$605$	−24.3653	−	24.3653i	−0.990589	−	0.990589i
$606$	0.378520		0.000500360i	0.0153763		2.03258e-5i
$607$	−17.2036			−0.698271			−0.349135	−	0.937072i	$-0.613525\pi$
$607$	−17.2036			−0.698271			−0.349135	+	0.937072i	$0.613525\pi$
$608$	30.6454	+	30.2430i	1.24284	+	1.22651i
$609$	−1.20648			−0.0488891
$610$	49.9905	−	0.0660817i	2.02406	−	0.00267557i
$611$	−3.21740	−	3.21740i	−0.130162	−	0.130162i
$612$	0.0150630	+	5.69752i	0.000608884	+	0.230308i
$613$	0.883507	−	0.883507i	0.0356845	−	0.0356845i	−0.689039	−	0.724724i	$-0.741967\pi$
$613$	0.883507	−	0.883507i	0.0356845	−	0.0356845i	0.724724	+	0.689039i	$0.241967\pi$
$614$	−15.5835	−	15.5423i	−0.628897	−	0.627237i
$615$		−	11.0908i		−	0.447223i
$616$	0.685984	+	0.680565i	0.0276391	+	0.0274207i
$617$			32.5417i			1.31008i	0.755594	+	0.655040i	$0.227348\pi$
$617$			32.5417i			1.31008i	−0.755594	+	0.655040i	$0.772652\pi$
$618$	1.74081	−	1.74542i	0.0700257	−	0.0702111i
$619$	−23.9736	+	23.9736i	−0.963582	+	0.963582i	−0.999360	−	0.0357779i	$-0.988609\pi$
$619$	−23.9736	+	23.9736i	−0.963582	+	0.963582i	0.0357779	+	0.999360i	$0.488609\pi$
$620$	18.7254	−	18.8247i	0.752031	−	0.756018i
$621$	−11.8310	−	11.8310i	−0.474763	−	0.474763i
$622$	−0.00296413	−	2.24235i	−0.000118851	−	0.0899100i
$623$	5.64199			0.226042
$624$	0.0375180	+	7.09549i	0.00150192	+	0.284047i
$625$	19.3495			0.773978
$626$	−0.00180817	−	1.36787i	−7.22690e−5	−	0.0546712i
$627$	−1.60325	−	1.60325i	−0.0640277	−	0.0640277i
$628$	−3.08171	−	3.06546i	−0.122974	−	0.122325i
$629$	2.25691	−	2.25691i	0.0899889	−	0.0899889i
$630$	4.19867	−	4.20978i	0.167279	−	0.167722i
$631$		−	21.4294i		−	0.853092i	−0.904466	−	0.426546i	$-0.859730\pi$
$631$		−	21.4294i		−	0.853092i	0.904466	−	0.426546i	$-0.140270\pi$
$632$	−15.5169	+	0.0615350i	−0.617229	+	0.00244773i
$633$			9.63425i			0.382927i
$634$	7.99069	+	7.96959i	0.317351	+	0.316513i
$635$	32.6369	−	32.6369i	1.29515	−	1.29515i
$636$	−2.96662	+	0.00784309i	−0.117634	+	0.000310999i
$637$	−21.9366	−	21.9366i	−0.869161	−	0.869161i
$638$	−7.53576	+	0.00996141i	−0.298343	+	0.000394376i
$639$	7.64642			0.302488
$640$	26.2262	−	26.7161i	1.03668	−	1.05605i
$641$	38.0752			1.50388			0.751940	−	0.659231i	$-0.229118\pi$
$641$	38.0752			1.50388			0.751940	+	0.659231i	$0.229118\pi$
$642$	2.78351	−	0.00367948i	0.109856	−	0.000145217i
$643$	3.46845	+	3.46845i	0.136782	+	0.136782i	0.772183	−	0.635400i	$-0.219165\pi$
$643$	3.46845	+	3.46845i	0.136782	+	0.136782i	−0.635400	+	0.772183i	$0.719165\pi$
$644$	−6.56156	+	0.0173473i	−0.258562	+	0.000683580i
$645$	−3.36186	+	3.36186i	−0.132373	+	0.132373i
$646$	−7.62127	−	7.60115i	−0.299855	−	0.299063i
$647$			38.7740i			1.52436i	0.647364	+	0.762181i	$0.275871\pi$
$647$			38.7740i			1.52436i	−0.647364	+	0.762181i	$0.724129\pi$
$648$	21.6706	−	0.0859387i	0.851302	−	0.00337599i
$649$		−	9.47715i		−	0.372011i
$650$	27.1036	−	27.1754i	1.06309	−	1.06591i
$651$	−0.492041	+	0.492041i	−0.0192846	+	0.0192846i
$652$	22.7672	+	22.6471i	0.891633	+	0.886931i
$653$	−27.9698	−	27.9698i	−1.09454	−	1.09454i	−0.995037	−	0.0995044i	$-0.968274\pi$
$653$	−27.9698	−	27.9698i	−1.09454	−	1.09454i	−0.0995044	−	0.995037i	$-0.531726\pi$
$654$	−0.000865579	−	0.654807i	−3.38468e−5	−	0.0256050i
$655$	−32.6315			−1.27502
$656$	−0.182284	−	34.4740i	−0.00711701	−	1.34598i
$657$	−0.323272			−0.0126120
$658$	−0.000831669	−	0.629154i	−3.24218e−5	−	0.0245270i
$659$	−25.7456	−	25.7456i	−1.00290	−	1.00290i	−0.999996	−	0.00290880i	$-0.999074\pi$
$659$	−25.7456	−	25.7456i	−1.00290	−	1.00290i	−0.00290880	−	0.999996i	$-0.500926\pi$
$660$	−1.39036	+	1.39773i	−0.0541198	+	0.0544067i
$661$	8.74713	−	8.74713i	0.340224	−	0.340224i	−0.516228	−	0.856451i	$-0.672664\pi$
$661$	8.74713	−	8.74713i	0.340224	−	0.340224i	0.856451	+	0.516228i	$0.172664\pi$
$662$	21.3482	−	21.4047i	0.829723	−	0.831919i
$663$		−	1.77390i		−	0.0688924i
$664$	11.4779	+	11.3872i	0.445427	+	0.441908i
$665$			11.2327i			0.435584i
$666$	−9.10458	−	9.08054i	−0.352795	−	0.351864i
$667$	36.1833	−	36.1833i	1.40102	−	1.40102i
$668$	0.0955344	+	36.1356i	0.00369634	+	1.39813i
$669$	2.13400	+	2.13400i	0.0825052	+	0.0825052i
$670$	61.4862	−	0.0812778i	2.37542	−	0.00314003i
$671$	−8.18299			−0.315901
$672$	−0.689160	+	0.698331i	−0.0265849	+	0.0269387i
$673$	−42.6197			−1.64287			−0.821434	−	0.570303i	$-0.806826\pi$
$673$	−42.6197			−1.64287			−0.821434	+	0.570303i	$0.806826\pi$
$674$	−17.6292	+	0.0233038i	−0.679052	+	0.000897629i
$675$	9.56902	+	9.56902i	0.368312	+	0.368312i
$676$	0.0412806	+	15.6142i	0.00158771	+	0.600548i
$677$	−27.1401	+	27.1401i	−1.04308	+	1.04308i	−0.0440513	+	0.999029i	$0.514027\pi$
$677$	−27.1401	+	27.1401i	−1.04308	+	1.04308i	−0.999029	+	0.0440513i	$0.985973\pi$
$678$	−2.67455	−	2.66749i	−0.102715	−	0.102444i
$679$		−	6.48666i		−	0.248935i
$680$	−6.59177	+	6.64426i	−0.252783	+	0.254796i
$681$			10.3418i			0.396299i
$682$	−3.06925	+	3.07737i	−0.117528	+	0.117839i
$683$	9.46120	−	9.46120i	0.362023	−	0.362023i	−0.502534	−	0.864557i	$-0.667599\pi$
$683$	9.46120	−	9.46120i	0.362023	−	0.362023i	0.864557	+	0.502534i	$0.167599\pi$
$684$	−30.5826	+	30.7448i	−1.16936	+	1.17556i
$685$	12.9124	+	12.9124i	0.493359	+	0.493359i
$686$	−0.0115067	−	8.70474i	−0.000439327	−	0.332348i
$687$	−6.35265			−0.242369
$688$	−10.3946	+	10.5051i	−0.396290	+	0.400503i
$689$	−17.3988			−0.662840
$690$	−0.0176963	−	13.3872i	−0.000673688	−	0.509641i
$691$	−28.3148	−	28.3148i	−1.07715	−	1.07715i	−0.996764	−	0.0803833i	$-0.974386\pi$
$691$	−28.3148	−	28.3148i	−1.07715	−	1.07715i	−0.0803833	−	0.996764i	$-0.525614\pi$
$692$	−12.3136	−	12.2486i	−0.468091	−	0.465623i
$693$	−0.688194	+	0.688194i	−0.0261423	+	0.0261423i
$694$	−6.99072	+	7.00923i	−0.265364	+	0.266067i
$695$			50.6676i			1.92193i
$696$	−0.0303426	−	7.65130i	−0.00115013	−	0.290022i
$697$			8.61863i			0.326454i
$698$	13.8471	+	13.8105i	0.524119	+	0.522735i
$699$	2.54479	−	2.54479i	0.0962528	−	0.0962528i
$700$	5.30704	−	0.0140306i	0.200587	−	0.000530308i
$701$	−23.2180	−	23.2180i	−0.876933	−	0.876933i	0.116283	−	0.993216i	$-0.462902\pi$
$701$	−23.2180	−	23.2180i	−0.876933	−	0.876933i	−0.993216	+	0.116283i	$0.962902\pi$
$702$	−14.6726	+	0.0193955i	−0.553782	+	0.000732036i
$703$	24.2931			0.916233
$704$	−4.29877	+	4.36750i	−0.162016	+	0.164606i
$705$	1.28362			0.0483441
$706$	12.5206	−	0.0165508i	0.471220	−	0.000622898i
$707$	0.217053	+	0.217053i	0.00816311	+	0.00816311i
$708$	9.62249	−	0.0254397i	0.361635	−	0.000956083i
$709$	33.6444	−	33.6444i	1.26354	−	1.26354i	0.314178	−	0.949364i	$-0.398271\pi$
$709$	33.6444	−	33.6444i	1.26354	−	1.26354i	0.949364	−	0.314178i	$-0.101729\pi$
$710$	8.89356	+	8.87008i	0.333769	+	0.332888i
$711$		−	15.6286i		−	0.586119i
$712$	0.141894	+	35.7805i	0.00531770	+	1.34093i
$713$		−	29.5133i		−	1.10528i
$714$	0.173211	−	0.173669i	0.00648225	−	0.00649941i
$715$	−8.17586	+	8.17586i	−0.305760	+	0.305760i
$716$	−7.22312	−	7.18503i	−0.269941	−	0.268517i
$717$	−4.87101	−	4.87101i	−0.181911	−	0.181911i
$718$	0.0449466	+	34.0019i	0.00167739	+	1.26894i
$719$	−49.2239			−1.83574			−0.917870	−	0.396880i	$-0.870093\pi$
$719$	−49.2239			−1.83574			−0.917870	+	0.396880i	$0.870093\pi$
$720$	26.8033	+	26.5213i	0.998899	+	0.988391i
$721$	1.99909			0.0744500
$722$	−0.0727779	−	55.0561i	−0.00270851	−	2.04898i
$723$	−0.907238	−	0.907238i	−0.0337406	−	0.0337406i
$724$	0.0376282	−	0.0378277i	0.00139844	−	0.00140585i
$725$	−29.2653	+	29.2653i	−1.08689	+	1.08689i
$726$	−4.04419	+	4.05490i	−0.150094	+	0.150491i
$727$		−	20.7067i		−	0.767971i	−0.923339	−	0.383985i	$-0.874551\pi$
$727$		−	20.7067i		−	0.767971i	0.923339	−	0.383985i	$-0.125449\pi$
$728$	−4.05261	+	4.08488i	−0.150200	+	0.151396i
$729$			19.1731i			0.710114i
$730$	−0.375998	−	0.375006i	−0.0139163	−	0.0138796i
$731$	2.61250	−	2.61250i	0.0966267	−	0.0966267i
$732$	−0.0219658	−	8.30848i	−0.000811878	−	0.307090i
$733$	19.4338	+	19.4338i	0.717803	+	0.717803i	0.968155	−	0.250352i	$-0.0805462\pi$
$733$	19.4338	+	19.4338i	0.717803	+	0.717803i	−0.250352	+	0.968155i	$0.580546\pi$
$734$	44.5878	−	0.0589399i	1.64576	−	0.00217551i
$735$	8.75189			0.322818
$736$	−0.275034	−	41.6118i	−0.0101379	−	1.53383i
$737$	−10.0647			−0.370740
$738$	34.7224	−	0.0458990i	1.27815	−	0.00168957i
$739$	20.4702	+	20.4702i	0.753008	+	0.753008i	0.975040	−	0.222031i	$-0.0712687\pi$
$739$	20.4702	+	20.4702i	0.753008	+	0.753008i	−0.222031	+	0.975040i	$0.571269\pi$
$740$	−0.0558450	−	21.1232i	−0.00205290	−	0.776504i
$741$	9.54701	−	9.54701i	0.350718	−	0.350718i
$742$	−1.70339	−	1.69889i	−0.0625333	−	0.0623682i
$743$			32.1087i			1.17796i	0.808149	+	0.588978i	$0.200469\pi$
$743$			32.1087i			1.17796i	−0.808149	+	0.588978i	$0.799531\pi$
$744$	−3.13281	−	3.10806i	−0.114854	−	0.113947i
$745$		−	62.6198i		−	2.29421i
$746$	−38.1267	+	38.2276i	−1.39592	+	1.39961i
$747$	−11.5148	+	11.5148i	−0.421305	+	0.421305i
$748$	1.08045	−	1.08618i	0.0395052	−	0.0397146i
$749$	1.59613	+	1.59613i	0.0583213	+	0.0583213i
$750$	0.00228468	+	1.72835i	8.34248e−5	+	0.0631104i
$751$	−11.9497			−0.436049			−0.218025	−	0.975943i	$-0.569961\pi$
$751$	−11.9497			−0.436049			−0.218025	+	0.975943i	$0.569961\pi$
$752$	3.98996	−	0.0210973i	0.145499	−	0.000769338i
$753$	−5.89636			−0.214875
$754$	−0.0593180	−	44.8737i	−0.00216023	−	1.63421i
$755$	−33.5446	−	33.5446i	−1.22081	−	1.22081i
$756$	−1.43838	−	1.43080i	−0.0523134	−	0.0520376i
$757$	−7.68332	+	7.68332i	−0.279255	+	0.279255i	−0.832812	−	0.553556i	$-0.813270\pi$
$757$	−7.68332	+	7.68332i	−0.279255	+	0.279255i	0.553556	+	0.832812i	$0.313270\pi$
$758$	−15.9091	+	15.9513i	−0.577846	+	0.579375i
$759$			2.19136i			0.0795414i
$760$	−71.2356	+	0.282497i	−2.58399	+	0.0102472i
$761$			10.8724i			0.394123i	0.980391	+	0.197061i	$0.0631398\pi$
$761$			10.8724i			0.394123i	−0.980391	+	0.197061i	$0.936860\pi$
$762$	−5.43147	−	5.41713i	−0.196761	−	0.196242i
$763$	0.375482	−	0.375482i	0.0135934	−	0.0135934i
$764$	−16.3903	+	0.0433323i	−0.592981	+	0.00156771i
$765$	−6.66567	−	6.66567i	−0.240998	−	0.240998i
$766$	13.4781	−	0.0178166i	0.486985	−	0.000643738i
$767$	56.4343			2.03773
$768$	−4.44602	−	4.35297i	−0.160432	−	0.157074i
$769$	−15.8455			−0.571402			−0.285701	−	0.958319i	$-0.592226\pi$
$769$	−15.8455			−0.571402			−0.285701	+	0.958319i	$0.592226\pi$
$770$	−1.59876	+	0.00211338i	−0.0576155	+	7.61611e-5i
$771$	−1.95352	−	1.95352i	−0.0703543	−	0.0703543i
$772$	−3.99170	+	0.0105532i	−0.143665	+	0.000379817i
$773$	−38.2552	+	38.2552i	−1.37595	+	1.37595i	−0.524590	+	0.851355i	$0.675781\pi$
$773$	−38.2552	+	38.2552i	−1.37595	+	1.37595i	−0.851355	+	0.524590i	$0.824219\pi$
$774$	−10.5390	−	10.5112i	−0.378818	−	0.377818i
$775$			23.8706i			0.857456i
$776$	41.1372	−	0.163137i	1.47674	−	0.00585627i
$777$			0.553578i			0.0198595i
$778$	−2.37500	+	2.38128i	−0.0851477	+	0.0853731i
$779$	−46.3849	+	46.3849i	−1.66191	+	1.66191i
$780$	−8.32319	−	8.27930i	−0.298018	−	0.296446i
$781$	−1.45387	−	1.45387i	−0.0520237	−	0.0520237i
$782$	0.0137518	+	10.4032i	0.000491764	+	0.372017i
$783$	15.8219			0.565427
$784$	27.2040	−	0.143843i	0.971571	−	0.00513727i
$785$	7.19173			0.256684
$786$	0.00716912	+	5.42341i	0.000255714	+	0.193447i
$787$	7.55567	+	7.55567i	0.269331	+	0.269331i	0.828830	−	0.559500i	$-0.189007\pi$
$787$	7.55567	+	7.55567i	0.269331	+	0.269331i	−0.559500	+	0.828830i	$0.689007\pi$
$788$	−6.65093	+	6.68619i	−0.236930	+	0.238186i
$789$	−5.67706	+	5.67706i	−0.202109	+	0.202109i
$790$	18.1297	−	18.1777i	0.645025	−	0.646732i
$791$		−	3.06325i		−	0.108917i
$792$	−4.38171	−	4.34709i	−0.155697	−	0.154467i
$793$		−	48.7279i		−	1.73038i
$794$	33.2377	+	33.1499i	1.17956	+	1.17645i
$795$	3.47073	−	3.47073i	0.123094	−	0.123094i
$796$	−0.112472	−	42.5420i	−0.00398645	−	1.50786i
$797$	1.80416	+	1.80416i	0.0639067	+	0.0639067i	0.738338	−	0.674431i	$-0.235611\pi$
$797$	1.80416	+	1.80416i	0.0639067	+	0.0639067i	−0.674431	+	0.738338i	$0.735611\pi$
$798$	1.86689	−	0.00246781i	0.0660871	−	8.73596e-5i
$799$	−0.997504			−0.0352891
$800$	0.222450	+	33.6559i	0.00786478	+	1.18992i
$801$	−36.0381			−1.27334
$802$	−47.0599	+	0.0622078i	−1.66174	+	0.00219663i
$803$	0.0614663	+	0.0614663i	0.00216910	+	0.00216910i
$804$	−0.0270170	−	10.2191i	−0.000952816	−	0.360400i
$805$	7.67654	−	7.67654i	0.270562	−	0.270562i
$806$	−18.3251	−	18.2767i	−0.645473	−	0.643769i
$807$			3.84473i			0.135341i
$808$	−1.37105	+	1.38197i	−0.0482334	+	0.0486175i
$809$			17.6231i			0.619594i	0.950803	+	0.309797i	$0.100261\pi$
$809$			17.6231i			0.619594i	−0.950803	+	0.309797i	$0.899739\pi$
$810$	−25.3196	+	25.3866i	−0.889639	+	0.891994i
$811$	−20.4928	+	20.4928i	−0.719598	+	0.719598i	−0.968523	−	0.248925i	$-0.919923\pi$
$811$	−20.4928	+	20.4928i	−0.719598	+	0.719598i	0.248925	+	0.968523i	$0.419923\pi$
$812$	4.37585	−	4.39905i	0.153562	−	0.154377i
$813$	2.63789	+	2.63789i	0.0925149	+	0.0925149i
$814$	0.00457066	+	3.45768i	0.000160201	+	0.121192i
$815$	−53.1314			−1.86111
$816$	1.10574	+	1.09410i	0.0387085	+	0.0383013i
$817$	28.1206			0.983815
$818$	0.0114826	+	8.68657i	0.000401481	+	0.303719i
$819$	−4.09804	−	4.09804i	−0.143197	−	0.143197i
$820$	40.4389	+	40.2257i	1.41219	+	1.40474i
$821$	0.0774244	−	0.0774244i	0.00270213	−	0.00270213i	−0.705754	−	0.708457i	$-0.749392\pi$
$821$	0.0774244	−	0.0774244i	0.00270213	−	0.00270213i	0.708457	+	0.705754i	$0.249392\pi$
$822$	2.14323	−	2.14890i	0.0747537	−	0.0749516i
$823$		−	34.7866i		−	1.21259i	−0.795242	−	0.606293i	$-0.792656\pi$
$823$		−	34.7866i		−	1.21259i	0.795242	−	0.606293i	$-0.207344\pi$
$824$	0.0502763	+	12.6779i	0.00175146	+	0.441654i
$825$		−	1.77239i		−	0.0617067i
$826$	5.52507	+	5.51049i	0.192242	+	0.191734i
$827$	8.23602	−	8.23602i	0.286395	−	0.286395i	−0.549258	−	0.835653i	$-0.685090\pi$
$827$	8.23602	−	8.23602i	0.286395	−	0.286395i	0.835653	+	0.549258i	$0.185090\pi$
$828$	41.9118	−	0.110806i	1.45654	−	0.00385076i
$829$	24.5554	+	24.5554i	0.852843	+	0.852843i	0.990482	−	0.137640i	$-0.0439516\pi$
$829$	24.5554	+	24.5554i	0.852843	+	0.852843i	−0.137640	+	0.990482i	$0.543952\pi$
$830$	−26.7505	+	0.0353611i	−0.928522	+	0.00122740i
$831$	1.95150			0.0676967
$832$	−26.0075	−	25.5982i	−0.901648	−	0.887458i
$833$	−6.80109			−0.235644
$834$	8.42104	−	0.0111317i	0.291597	−	0.000385458i
$835$	−42.2759	−	42.2759i	−1.46302	−	1.46302i
$836$	11.6607	−	0.0308282i	0.403292	−	0.00106621i
$837$	6.45264	−	6.45264i	0.223036	−	0.223036i
$838$	−36.6515	−	36.5547i	−1.26611	−	1.26276i
$839$		−	27.8393i		−	0.961119i	−0.876962	−	0.480559i	$-0.840434\pi$
$839$		−	27.8393i		−	0.961119i	0.876962	−	0.480559i	$-0.159566\pi$
$840$	−0.00643739	−	1.62328i	−0.000222111	−	0.0560084i
$841$			19.3886i			0.668571i
$842$	21.4412	−	21.4980i	0.738913	−	0.740869i
$843$	−1.38310	+	1.38310i	−0.0476365	+	0.0476365i
$844$	−35.1282	−	34.9430i	−1.20916	−	1.20279i
$845$	−18.2675	−	18.2675i	−0.628421	−	0.628421i
$846$	0.00531227	+	4.01870i	0.000182640	+	0.138166i
$847$	−4.64422			−0.159577
$848$	10.7312	−	10.8453i	0.368511	−	0.372429i
$849$	−1.81252			−0.0622056
$850$	−0.0111226	−	8.41416i	−0.000381501	−	0.288603i
$851$	−16.6022	−	16.6022i	−0.569116	−	0.569116i
$852$	1.47227	−	1.48007i	0.0504391	−	0.0507065i
$853$	7.08858	−	7.08858i	0.242708	−	0.242708i	−0.575261	−	0.817970i	$-0.695100\pi$
$853$	7.08858	−	7.08858i	0.242708	−	0.242708i	0.817970	+	0.575261i	$0.195100\pi$
$854$	4.75800	−	4.77059i	0.162815	−	0.163246i
$855$		−	71.7484i		−	2.45374i
$856$	−10.0822	+	10.1625i	−0.344603	+	0.347347i
$857$		−	20.5844i		−	0.703150i	−0.936160	−	0.351575i	$-0.885646\pi$
$857$		−	20.5844i		−	0.703150i	0.936160	−	0.351575i	$-0.114354\pi$
$858$	1.36064	+	1.35704i	0.0464514	+	0.0463287i
$859$	−36.2617	+	36.2617i	−1.23723	+	1.23723i	−0.276106	+	0.961127i	$0.589044\pi$
$859$	−36.2617	+	36.2617i	−1.23723	+	1.23723i	−0.961127	+	0.276106i	$0.910956\pi$
$860$	−0.0646436	−	24.4512i	−0.00220433	−	0.833780i
$861$	−1.05699	−	1.05699i	−0.0360223	−	0.0360223i
$862$	39.7016	−	0.0524810i	1.35224	−	0.00178751i
$863$	−27.5125			−0.936538			−0.468269	−	0.883586i	$-0.655122\pi$
$863$	−27.5125			−0.936538			−0.468269	+	0.883586i	$0.655122\pi$
$864$	9.03768	−	9.15794i	0.307468	−	0.311560i
$865$	28.7359			0.977050
$866$	32.8654	−	0.0434443i	1.11681	−	0.00147630i
$867$	−0.274984	−	0.274984i	−0.00933894	−	0.00933894i
$868$	−0.00946122	−	3.57868i	−0.000321135	−	0.121468i
$869$	−2.97159	+	2.97159i	−0.100804	+	0.100804i
$870$	8.96330	+	8.93964i	0.303884	+	0.303082i
$871$		−	59.9333i		−	2.03076i
$872$	2.39068	+	2.37180i	0.0809587	+	0.0803192i
$873$			41.4334i			1.40231i
$874$	−55.9153	+	56.0633i	−1.89136	+	1.89637i
$875$	−0.991078	+	0.991078i	−0.0335046	+	0.0335046i
$876$	−0.0622439	+	0.0625739i	−0.00210303	+	0.00211418i
$877$	11.8758	+	11.8758i	0.401018	+	0.401018i	0.878592	−	0.477573i	$-0.158484\pi$
$877$	11.8758	+	11.8758i	0.401018	+	0.401018i	−0.477573	+	0.878592i	$0.658484\pi$
$878$	−0.0355222	−	26.8724i	−0.00119882	−	0.906900i
$879$	−9.51827			−0.321043
$880$	−0.0536110	−	10.1390i	−0.00180723	−	0.341786i
$881$	−38.5265			−1.29799			−0.648996	−	0.760792i	$-0.724811\pi$
$881$	−38.5265			−1.29799			−0.648996	+	0.760792i	$0.724811\pi$
$882$	0.0362196	+	27.4000i	0.00121958	+	0.922605i
$883$	−13.7995	−	13.7995i	−0.464389	−	0.464389i	0.435702	−	0.900091i	$-0.356500\pi$
$883$	−13.7995	−	13.7995i	−0.464389	−	0.464389i	−0.900091	+	0.435702i	$0.856500\pi$
$884$	6.46795	+	6.43384i	0.217541	+	0.216393i
$885$	−11.2576	+	11.2576i	−0.378420	+	0.378420i
$886$	−27.3831	+	27.4556i	−0.919952	+	0.922388i
$887$			36.9295i			1.23997i	0.784613	+	0.619986i	$0.212862\pi$
$887$			36.9295i			1.23997i	−0.784613	+	0.619986i	$0.787138\pi$
$888$	−3.51069	+	0.0139223i	−0.117811	+	0.000467201i
$889$		−	6.22085i		−	0.208641i
$890$	−41.9160	−	41.8053i	−1.40503	−	1.40132i
$891$	4.15007	−	4.15007i	0.139033	−	0.139033i
$892$	−15.5209	+	0.0410337i	−0.519677	+	0.00137391i
$893$	−5.36851	−	5.36851i	−0.179650	−	0.179650i
$894$	−10.4075	+	0.0137575i	−0.348079	+	0.000460121i
$895$	16.8564			0.563449
$896$	−0.0466894	−	5.04562i	−0.00155978	−	0.168562i
$897$	−13.0491			−0.435696
$898$	−8.19918	+	0.0108384i	−0.273610	+	0.000361681i
$899$	19.7343	+	19.7343i	0.658177	+	0.658177i
$900$	−33.8986	+	0.0896203i	−1.12995	+	0.00298734i
$901$	−2.69710	+	2.69710i	−0.0898534	+	0.0898534i
$902$	−6.61077	−	6.59332i	−0.220115	−	0.219533i
$903$			0.640797i			0.0213244i
$904$	19.4266	−	0.0770396i	0.646119	−	0.00256230i
$905$			0.0882777i			0.00293445i
$906$	−5.56779	+	5.58253i	−0.184977	+	0.185467i
$907$	16.3104	−	16.3104i	0.541579	−	0.541579i	−0.382413	−	0.923992i	$-0.624907\pi$
$907$	16.3104	−	16.3104i	0.541579	−	0.541579i	0.923992	+	0.382413i	$0.124907\pi$
$908$	−37.7081	−	37.5092i	−1.25139	−	1.24479i
$909$	−1.38642	−	1.38642i	−0.0459846	−	0.0459846i
$910$	−0.0125847	−	9.52029i	−0.000417180	−	0.315594i
$911$	−21.6882			−0.718562			−0.359281	−	0.933229i	$-0.616978\pi$
$911$	−21.6882			−0.718562			−0.359281	+	0.933229i	$0.616978\pi$
$912$	0.0626019	+	11.8394i	0.00207296	+	0.392042i
$913$	4.37881			0.144917
$914$	0.0567222	+	42.9101i	0.00187620	+	1.41934i
$915$	9.72030	+	9.72030i	0.321343	+	0.321343i
$916$	23.0407	−	23.1629i	0.761288	−	0.765324i
$917$	−3.10991	+	3.10991i	−0.102698	+	0.102698i
$918$	−2.27149	+	2.27751i	−0.0749705	+	0.0751689i
$919$			8.10831i			0.267468i	0.991017	+	0.133734i	$0.0426968\pi$
$919$			8.10831i			0.267468i	−0.991017	+	0.133734i	$0.957303\pi$
$920$	48.8763	+	48.4901i	1.61140	+	1.59867i
$921$		−	6.05219i		−	0.199426i
$922$	−2.90104	−	2.89338i	−0.0955406	−	0.0952883i
$923$	8.65750	−	8.65750i	0.284965	−	0.284965i
$924$	0.000702496		0.265717i	2.31104e−5		0.00874144i
$925$	13.4280	+	13.4280i	0.441509	+	0.441509i
$926$	51.7700	−	0.0684340i	1.70127	−	0.00224888i
$927$	−12.7691			−0.419394
$928$	28.0081	+	27.6402i	0.919409	+	0.907335i
$929$	−5.04169			−0.165413			−0.0827063	−	0.996574i	$-0.526356\pi$
$929$	−5.04169			−0.165413			−0.0827063	+	0.996574i	$0.526356\pi$
$930$	7.30137	−	0.00965157i	0.239421	−	0.000316488i
$931$	−36.6031	−	36.6031i	−1.19962	−	1.19962i
$932$	0.0489326	+	18.5086i	0.00160284	+	0.606269i
$933$	0.436009	−	0.436009i	0.0142743	−	0.0142743i
$934$	1.39834	+	1.39465i	0.0457550	+	0.0456342i
$935$			2.53479i			0.0828965i
$936$	25.8860	−	26.0921i	0.846109	−	0.852846i
$937$			32.4923i			1.06148i	0.847535	+	0.530739i	$0.178085\pi$
$937$			32.4923i			1.06148i	−0.847535	+	0.530739i	$0.821915\pi$
$938$	5.85214	−	5.86763i	0.191079	−	0.191585i
$939$	0.265973	−	0.265973i	0.00867971	−	0.00867971i
$940$	−4.65564	+	4.68032i	−0.151850	+	0.152655i
$941$	32.1813	+	32.1813i	1.04908	+	1.04908i	0.998732	+	0.0503486i	$0.0160332\pi$
$941$	32.1813	+	32.1813i	1.04908	+	1.04908i	0.0503486	+	0.998732i	$0.483967\pi$
$942$	−0.00158002	−	1.19528i	−5.14798e−5	−	0.0389442i
$943$	63.4000			2.06459
$944$	−34.8076	+	35.1776i	−1.13289	+	1.14493i
$945$	3.35672			0.109194
$946$	0.00529078	+	4.00245i	0.000172018	+	0.130131i
$947$	34.2541	+	34.2541i	1.11311	+	1.11311i	0.992728	+	0.120380i	$0.0384113\pi$
$947$	34.2541	+	34.2541i	1.11311	+	1.11311i	0.120380	+	0.992728i	$0.461589\pi$
$948$	−3.02514	−	3.00919i	−0.0982520	−	0.0977338i
$949$	−0.366018	+	0.366018i	−0.0118814	+	0.0118814i
$950$	45.2247	−	45.3444i	1.46728	−	1.47117i
$951$			3.10337i			0.100634i
$952$	0.00500249	+	1.26145i	0.000162132	+	0.0408838i
$953$		−	54.3582i		−	1.76084i	−0.474199	−	0.880418i	$-0.657262\pi$
$953$		−	54.3582i		−	1.76084i	0.474199	−	0.880418i	$-0.342738\pi$
$954$	10.8803	+	10.8516i	0.352264	+	0.351334i
$955$	19.1754	−	19.1754i	0.620502	−	0.620502i
$956$	35.4275	−	0.0936624i	1.14581	−	0.00302926i
$957$	−1.46528	−	1.46528i	−0.0473656	−	0.0473656i
$958$	−3.82860	+	0.00506097i	−0.123696	+	0.000163512i
$959$	2.46121			0.0794767
$960$	10.2944	−	0.0816495i	0.332249	−	0.00263523i
$961$	−14.9035			−0.480757
$962$	−20.5897	+	0.0272172i	−0.663839	+	0.000877519i
$963$	−10.1952	−	10.1952i	−0.328537	−	0.328537i
$964$	6.59846	−	0.0174449i	0.212522	−	0.000561861i
$965$	4.66999	−	4.66999i	0.150332	−	0.150332i
$966$	−1.27754	−	1.27417i	−0.0411042	−	0.0409956i
$967$		−	7.33112i		−	0.235753i	−0.993028	−	0.117876i	$-0.962391\pi$
$967$		−	7.33112i		−	0.235753i	0.993028	−	0.117876i	$-0.0376087\pi$
$968$	−0.116800	−	29.4528i	−0.00375410	−	0.946648i
$969$		−	2.95989i		−	0.0950854i
$970$	−48.0640	+	48.1912i	−1.54324	+	1.54733i
$971$	17.0216	−	17.0216i	0.546249	−	0.546249i	−0.379105	−	0.925354i	$-0.623768\pi$
$971$	17.0216	−	17.0216i	0.546249	−	0.546249i	0.925354	+	0.379105i	$0.123768\pi$
$972$	13.9002	+	13.8269i	0.445850	+	0.443499i
$973$	4.82883	+	4.82883i	0.154805	+	0.154805i
$974$	0.0268357	+	20.3010i	0.000859870	+	0.650487i
$975$	10.5542			0.338004
$976$	30.3739	+	30.0544i	0.972245	+	0.962017i
$977$	33.7368			1.07934			0.539669	−	0.841877i	$-0.318550\pi$
$977$	33.7368			1.07934			0.539669	+	0.841877i	$0.318550\pi$
$978$	0.0116729	+	8.83052i	0.000373259	+	0.282369i
$979$	6.85221	+	6.85221i	0.218998	+	0.218998i
$980$	−31.7427	+	31.9110i	−1.01398	+	1.01936i
$981$	−2.39838	+	2.39838i	−0.0765745	+	0.0765745i
$982$	9.13125	−	9.15542i	0.291390	−	0.292161i
$983$		−	20.4547i		−	0.652405i	−0.945300	−	0.326202i	$-0.894231\pi$
$983$		−	20.4547i		−	0.652405i	0.945300	−	0.326202i	$-0.105769\pi$
$984$	6.67669	−	6.72985i	0.212845	−	0.214540i
$985$		−	15.6034i		−	0.497166i
$986$	−6.96538	−	6.94699i	−0.221823	−	0.221237i
$987$	0.122335	−	0.122335i	0.00389395	−	0.00389395i
$988$	0.183575	+	69.4366i	0.00584030	+	2.20907i
$989$	−19.2179	−	19.2179i	−0.611095	−	0.611095i
$990$	10.2121	−	0.0134992i	0.324561	−	0.000429032i
$991$	22.8027			0.724350			0.362175	−	0.932110i	$-0.382034\pi$
$991$	22.8027			0.724350			0.362175	+	0.932110i	$0.382034\pi$
$992$	22.6951	−	0.150004i	0.720570	−	0.00476262i
$993$	8.31302			0.263806
$994$	1.69295	−	0.00223788i	0.0536970	−	7.09813e-5i
$995$	49.7710	+	49.7710i	1.57785	+	1.57785i
$996$	0.0117541	+	4.44596i	0.000372444	+	0.140876i
$997$	−23.0821	+	23.0821i	−0.731017	+	0.731017i	−0.970821	−	0.239804i	$-0.922917\pi$
$997$	−23.0821	+	23.0821i	−0.731017	+	0.731017i	0.239804	+	0.970821i	$0.422917\pi$
$998$	−16.4318	−	16.3885i	−0.520141	−	0.518768i
$999$		−	7.25965i		−	0.229685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.b.205.1	yes	30
4.3	odd	2		1088.2.l.b.273.9		30
16.5	even	4	inner	272.2.l.b.69.1	✓	30
16.11	odd	4		1088.2.l.b.817.9		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.1	✓	30	16.5	even	4	inner
272.2.l.b.205.1	yes	30	1.1	even	1	trivial
1088.2.l.b.273.9		30	4.3	odd	2
1088.2.l.b.817.9		30	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 0.00186943i) q^{2} +(-0.274984 - 0.274984i) q^{3} +(1.99999 - 0.00528753i) q^{4} +(-2.33984 + 2.33984i) q^{5} +(0.389399 + 0.388371i) q^{6} +0.445993i q^{7} +(-2.82840 + 0.0112165i) q^{8} -2.84877i q^{9} +(3.30466 - 3.31341i) q^{10} +(-0.541659 + 0.541659i) q^{11} +(-0.551420 - 0.548512i) q^{12} +(-3.22546 - 3.22546i) q^{13} +(-0.000833751 - 0.630728i) q^{14} +1.28684 q^{15} +(3.99994 - 0.0211501i) q^{16} -1.00000 q^{17} +(0.00532556 + 4.02876i) q^{18} +(-5.38194 - 5.38194i) q^{19} +(-4.66729 + 4.69204i) q^{20} +(0.122641 - 0.122641i) q^{21} +(0.765008 - 0.767033i) q^{22} +7.35616i q^{23} +(0.780850 + 0.774681i) q^{24} -5.94972i q^{25} +(4.56751 + 4.55545i) q^{26} +(-1.60832 + 1.60832i) q^{27} +(0.00235820 + 0.891982i) q^{28} +(-4.91877 - 4.91877i) q^{29} +(-1.81986 + 0.00240565i) q^{30} -4.01205 q^{31} +(-5.65673 + 0.0373883i) q^{32} +0.297895 q^{33} +(1.41421 - 0.00186943i) q^{34} +(-1.04355 - 1.04355i) q^{35} +(-0.0150630 - 5.69752i) q^{36} +(-2.25691 + 2.25691i) q^{37} +(7.62127 + 7.60115i) q^{38} +1.77390i q^{39} +(6.59177 - 6.64426i) q^{40} -8.61863i q^{41} +(-0.173211 + 0.173669i) q^{42} +(-2.61250 + 2.61250i) q^{43} +(-1.08045 + 1.08618i) q^{44} +(6.66567 + 6.66567i) q^{45} +(-0.0137518 - 10.4032i) q^{46} +0.997504 q^{47} +(-1.10574 - 1.09410i) q^{48} +6.80109 q^{49} +(0.0111226 + 8.41416i) q^{50} +(0.274984 + 0.274984i) q^{51} +(-6.46795 - 6.43384i) q^{52} +(2.69710 - 2.69710i) q^{53} +(2.27149 - 2.27751i) q^{54} -2.53479i q^{55} +(-0.00500249 - 1.26145i) q^{56} +2.95989i q^{57} +(6.96538 + 6.94699i) q^{58} +(-8.74827 + 8.74827i) q^{59} +(2.57366 - 0.00680419i) q^{60} +(7.55364 + 7.55364i) q^{61} +(5.67389 - 0.00750023i) q^{62} +1.27053 q^{63} +(7.99975 - 0.0634498i) q^{64} +15.0941 q^{65} +(-0.421286 + 0.000556892i) q^{66} +(9.29067 + 9.29067i) q^{67} +(-1.99999 + 0.00528753i) q^{68} +(2.02282 - 2.02282i) q^{69} +(1.47776 + 1.47385i) q^{70} +2.68411i q^{71} +(0.0319533 + 8.05747i) q^{72} -0.113478i q^{73} +(3.18753 - 3.19597i) q^{74} +(-1.63608 + 1.63608i) q^{75} +(-10.7923 - 10.7354i) q^{76} +(-0.241576 - 0.241576i) q^{77} +(-0.00331617 - 2.50867i) q^{78} +5.48610 q^{79} +(-9.30975 + 9.40872i) q^{80} -7.66178 q^{81} +(0.0161119 + 12.1886i) q^{82} +(-4.04204 - 4.04204i) q^{83} +(0.244632 - 0.245929i) q^{84} +(2.33984 - 2.33984i) q^{85} +(3.68974 - 3.69951i) q^{86} +2.70516i q^{87} +(1.52595 - 1.53811i) q^{88} -12.6504i q^{89} +(-9.43913 - 9.41421i) q^{90} +(1.43853 - 1.43853i) q^{91} +(0.0388959 + 14.7123i) q^{92} +(1.10325 + 1.10325i) q^{93} +(-1.41068 + 0.00186476i) q^{94} +25.1858 q^{95} +(1.56579 + 1.54523i) q^{96} -14.5443 q^{97} +(-9.61819 + 0.0127141i) q^{98} +(1.54306 + 1.54306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Introduction

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