LMFDB - Embedded newform 430.2.q.c.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	430.81
Dual form			430.2.q.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.974928i) q^{2} +(-1.65144 - 0.509401i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(-0.864108 + 1.49668i) q^{6} +(0.201072 + 0.348266i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-0.0109619 - 0.00747371i) q^{9} +O(q^{10})$	\(q+(0.222521 - 0.974928i) q^{2} +(-1.65144 - 0.509401i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(-0.864108 + 1.49668i) q^{6} +(0.201072 + 0.348266i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-0.0109619 - 0.00747371i) q^{9} +(0.988831 - 0.149042i) q^{10} +(-4.49171 + 2.16309i) q^{11} +(1.26687 + 1.17549i) q^{12} +(0.917668 + 0.138316i) q^{13} +(0.384277 - 0.118534i) q^{14} +(-0.129150 - 1.72338i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-2.42589 + 6.18105i) q^{17} +(-0.00972558 + 0.00902402i) q^{18} +(0.545614 - 0.371993i) q^{19} +(0.0747301 - 0.997204i) q^{20} +(-0.154650 - 0.677566i) q^{21} +(1.10936 + 4.86042i) q^{22} +(-0.468258 + 6.24846i) q^{23} +(1.42792 - 0.973539i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(0.339049 - 0.863882i) q^{26} +(3.24687 + 4.07145i) q^{27} +(-0.0300522 - 0.401019i) q^{28} +(7.42107 - 2.28910i) q^{29} +(-1.70891 - 0.257577i) q^{30} +(-4.50267 - 4.17787i) q^{31} +(0.900969 - 0.433884i) q^{32} +(8.51965 - 1.28413i) q^{33} +(5.48627 + 3.74048i) q^{34} +(-0.250732 + 0.314408i) q^{35} +(0.00663363 + 0.0114898i) q^{36} +(-0.529980 + 0.917952i) q^{37} +(-0.241256 - 0.614711i) q^{38} +(-1.44501 - 0.695881i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(-1.71682 + 7.52186i) q^{41} -0.694991 q^{42} +(-4.89137 + 4.36743i) q^{43} +4.98542 q^{44} +(0.00295224 - 0.0129346i) q^{45} +(5.98760 + 1.84693i) q^{46} +(-9.64143 - 4.64307i) q^{47} +(-0.631388 - 1.60875i) q^{48} +(3.41914 - 5.92212i) q^{49} +(0.500000 + 0.866025i) q^{50} +(7.15483 - 8.97187i) q^{51} +(-0.766777 - 0.522780i) q^{52} +(5.94819 - 0.896546i) q^{53} +(4.69187 - 2.25948i) q^{54} +(-3.65457 - 3.39095i) q^{55} +(-0.397652 - 0.0599363i) q^{56} +(-1.09054 + 0.336387i) q^{57} +(-0.580361 - 7.74438i) q^{58} +(-1.21881 - 1.52834i) q^{59} +(-0.631388 + 1.60875i) q^{60} +(-9.81177 + 9.10399i) q^{61} +(-5.07506 + 3.46012i) q^{62} +(0.000398710 - 0.00532042i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.206507 + 0.904765i) q^{65} +(0.643866 - 8.59179i) q^{66} +(-10.3050 + 7.02583i) q^{67} +(4.86751 - 4.51639i) q^{68} +(3.95627 - 10.0804i) q^{69} +(0.250732 + 0.314408i) q^{70} +(-0.838013 - 11.1825i) q^{71} +(0.0126778 - 0.00391059i) q^{72} +(-9.53047 - 1.43649i) q^{73} +(0.777005 + 0.720955i) q^{74} +(1.55707 - 0.749845i) q^{75} +(-0.652983 + 0.0984214i) q^{76} +(-1.65649 - 1.12937i) q^{77} +(-0.999979 + 1.25393i) q^{78} +(-2.64418 - 4.57985i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.27346 - 8.34065i) q^{81} +(6.95125 + 3.34754i) q^{82} +(5.75073 + 1.77386i) q^{83} +(-0.154650 + 0.677566i) q^{84} -6.64006 q^{85} +(3.16950 + 5.74058i) q^{86} -13.4215 q^{87} +(1.10936 - 4.86042i) q^{88} +(-4.95277 - 1.52773i) q^{89} +(-0.0119534 - 0.00575645i) q^{90} +(0.136346 + 0.347404i) q^{91} +(3.13299 - 5.42650i) q^{92} +(5.30767 + 9.19315i) q^{93} +(-6.67207 + 8.36652i) q^{94} +(0.545614 + 0.371993i) q^{95} +(-1.70891 + 0.257577i) q^{96} +(16.8154 - 8.09787i) q^{97} +(-5.01281 - 4.65121i) q^{98} +(0.0654040 + 0.00985807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{21}\right)$

Coefficient data

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

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

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

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$	−1.65144	−	0.509401i	−0.953457	−	0.294103i	−0.221275	−	0.975211i	$-0.571022\pi$
$3$	−1.65144	−	0.509401i	−0.953457	−	0.294103i	−0.732182	+	0.681109i	$0.761498\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	0.365341	+	0.930874i	0.163385	+	0.416299i
$5$	0.365341	+	0.930874i	0.163385	+	0.416299i
$6$	−0.864108	+	1.49668i	−0.352771	+	0.611017i
$7$	0.201072	+	0.348266i	0.0759979	+	0.131632i	0.901520	−	0.432738i	$-0.142452\pi$
$7$	0.201072	+	0.348266i	0.0759979	+	0.131632i	−0.825522	+	0.564370i	$0.809119\pi$
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$	−0.0109619	−	0.00747371i	−0.00365397	−	0.00249124i
$10$	0.988831	−	0.149042i	0.312696	−	0.0471313i
$11$	−4.49171	+	2.16309i	−1.35430	+	0.652197i	−0.963358	−	0.268218i	$-0.913565\pi$
$11$	−4.49171	+	2.16309i	−1.35430	+	0.652197i	−0.390942	+	0.920415i	$0.627851\pi$
$12$	1.26687	+	1.17549i	0.365715	+	0.339334i
$13$	0.917668	+	0.138316i	0.254515	+	0.0383620i	0.275060	−	0.961427i	$-0.411302\pi$
$13$	0.917668	+	0.138316i	0.254515	+	0.0383620i	−0.0205452	+	0.999789i	$0.506540\pi$
$14$	0.384277	−	0.118534i	0.102702	−	0.0316795i
$15$	−0.129150	−	1.72338i	−0.0333463	−	0.444976i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−2.42589	+	6.18105i	−0.588364	+	1.49913i	0.257798	+	0.966199i	$0.417003\pi$
$17$	−2.42589	+	6.18105i	−0.588364	+	1.49913i	−0.846161	+	0.532927i	$0.821092\pi$
$18$	−0.00972558	+	0.00902402i	−0.00229234	+	0.00212698i
$19$	0.545614	−	0.371993i	0.125172	−	0.0853412i	−0.499115	−	0.866536i	$-0.666342\pi$
$19$	0.545614	−	0.371993i	0.125172	−	0.0853412i	0.624288	+	0.781194i	$0.285389\pi$
$20$	0.0747301	−	0.997204i	0.0167102	−	0.222982i
$21$	−0.154650	−	0.677566i	−0.0337474	−	0.147857i
$22$	1.10936	+	4.86042i	0.236516	+	1.03625i
$23$	−0.468258	+	6.24846i	−0.0976384	+	1.30289i	0.706185	+	0.708027i	$0.250415\pi$
$23$	−0.468258	+	6.24846i	−0.0976384	+	1.30289i	−0.803824	+	0.594867i	$0.797205\pi$
$24$	1.42792	−	0.973539i	0.291473	−	0.198723i
$25$	−0.733052	+	0.680173i	−0.146610	+	0.136035i
$26$	0.339049	−	0.863882i	0.0664929	−	0.169421i
$27$	3.24687	+	4.07145i	0.624861	+	0.783551i
$28$	−0.0300522	−	0.401019i	−0.00567933	−	0.0757854i
$29$	7.42107	−	2.28910i	1.37806	−	0.425075i	0.484803	−	0.874624i	$-0.338891\pi$
$29$	7.42107	−	2.28910i	1.37806	−	0.425075i	0.893256	+	0.449549i	$0.148415\pi$
$30$	−1.70891	−	0.257577i	−0.312004	−	0.0470270i
$31$	−4.50267	−	4.17787i	−0.808704	−	0.750367i	0.162986	−	0.986628i	$-0.447887\pi$
$31$	−4.50267	−	4.17787i	−0.808704	−	0.750367i	−0.971690	+	0.236261i	$0.924078\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$	8.51965	−	1.28413i	1.48308	−	0.223538i
$34$	5.48627	+	3.74048i	0.940888	+	0.641487i
$35$	−0.250732	+	0.314408i	−0.0423815	+	0.0531447i
$36$	0.00663363	+	0.0114898i	0.00110560	+	0.00191496i
$37$	−0.529980	+	0.917952i	−0.0871281	+	0.150910i	−0.906296	−	0.422643i	$-0.861102\pi$
$37$	−0.529980	+	0.917952i	−0.0871281	+	0.150910i	0.819168	+	0.573554i	$0.194436\pi$
$38$	−0.241256	−	0.614711i	−0.0391369	−	0.0997193i
$39$	−1.44501	−	0.695881i	−0.231387	−	0.111430i
$40$	−0.955573	−	0.294755i	−0.151089	−	0.0466049i
$41$	−1.71682	+	7.52186i	−0.268122	+	1.17472i	0.644074	+	0.764963i	$0.277243\pi$
$41$	−1.71682	+	7.52186i	−0.268122	+	1.17472i	−0.912196	+	0.409755i	$0.865614\pi$
$42$	−0.694991			−0.107239
$43$	−4.89137	+	4.36743i	−0.745927	+	0.666027i
$43$	−4.89137	+	4.36743i	−0.745927	+	0.666027i
$44$	4.98542			0.751580
$45$	0.00295224	−	0.0129346i	0.000440094	−	0.00192818i
$46$	5.98760	+	1.84693i	0.882824	+	0.272315i
$47$	−9.64143	−	4.64307i	−1.40635	−	0.677261i	−0.431909	−	0.901917i	$-0.642160\pi$
$47$	−9.64143	−	4.64307i	−1.40635	−	0.677261i	−0.974438	+	0.224657i	$0.927874\pi$
$48$	−0.631388	−	1.60875i	−0.0911331	−	0.232203i
$49$	3.41914	−	5.92212i	0.488449	−	0.846018i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	7.15483	−	8.97187i	1.00188	−	1.25631i
$52$	−0.766777	−	0.522780i	−0.106333	−	0.0724965i
$53$	5.94819	−	0.896546i	0.817047	−	0.123150i	0.272796	−	0.962072i	$-0.412052\pi$
$53$	5.94819	−	0.896546i	0.817047	−	0.123150i	0.544252	+	0.838922i	$0.316814\pi$
$54$	4.69187	−	2.25948i	0.638482	−	0.307477i
$55$	−3.65457	−	3.39095i	−0.492782	−	0.457235i
$56$	−0.397652	−	0.0599363i	−0.0531384	−	0.00800933i
$57$	−1.09054	+	0.336387i	−0.144446	+	0.0445556i
$58$	−0.580361	−	7.74438i	−0.0762052	−	1.01689i
$59$	−1.21881	−	1.52834i	−0.158675	−	0.198972i	0.696138	−	0.717908i	$-0.254900\pi$
$59$	−1.21881	−	1.52834i	−0.158675	−	0.198972i	−0.854814	+	0.518935i	$0.826329\pi$
$60$	−0.631388	+	1.60875i	−0.0815119	+	0.207689i
$61$	−9.81177	+	9.10399i	−1.25627	+	1.16565i	−0.277489	+	0.960729i	$0.589502\pi$
$61$	−9.81177	+	9.10399i	−1.25627	+	1.16565i	−0.978779	+	0.204918i	$0.934307\pi$
$62$	−5.07506	+	3.46012i	−0.644533	+	0.439435i
$63$	0.000398710	−	0.00532042i	5.02328e−5	−	0.000670310i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	0.206507	+	0.904765i	0.0256140	+	0.112222i
$66$	0.643866	−	8.59179i	0.0792544	−	1.05758i
$67$	−10.3050	+	7.02583i	−1.25896	+	0.858342i	−0.994364	−	0.106019i	$-0.966190\pi$
$67$	−10.3050	+	7.02583i	−1.25896	+	0.858342i	−0.264592	+	0.964360i	$0.585237\pi$
$68$	4.86751	−	4.51639i	0.590272	−	0.547692i
$69$	3.95627	−	10.0804i	0.476279	−	1.21354i
$70$	0.250732	+	0.314408i	0.0299682	+	0.0375790i
$71$	−0.838013	−	11.1825i	−0.0994538	−	1.32712i	−0.794109	−	0.607776i	$-0.792062\pi$
$71$	−0.838013	−	11.1825i	−0.0994538	−	1.32712i	0.694655	−	0.719343i	$-0.255557\pi$
$72$	0.0126778	−	0.00391059i	0.00149410	−	0.000460868i
$73$	−9.53047	−	1.43649i	−1.11546	−	0.168128i	−0.434656	−	0.900596i	$-0.643130\pi$
$73$	−9.53047	−	1.43649i	−1.11546	−	0.168128i	−0.680801	+	0.732468i	$0.738368\pi$
$74$	0.777005	+	0.720955i	0.0903250	+	0.0838094i
$75$	1.55707	−	0.749845i	0.179795	−	0.0865847i
$76$	−0.652983	+	0.0984214i	−0.0749023	+	0.0112897i
$77$	−1.65649	−	1.12937i	−0.188774	−	0.128704i
$78$	−0.999979	+	1.25393i	−0.113225	+	0.141980i
$79$	−2.64418	−	4.57985i	−0.297493	−	0.515273i	0.678069	−	0.734999i	$-0.262817\pi$
$79$	−2.64418	−	4.57985i	−0.297493	−	0.515273i	−0.975562	+	0.219725i	$0.929484\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−3.27346	−	8.34065i	−0.363718	−	0.926739i
$82$	6.95125	+	3.34754i	0.767637	+	0.369674i
$83$	5.75073	+	1.77386i	0.631224	+	0.194707i	0.593826	−	0.804594i	$-0.297617\pi$
$83$	5.75073	+	1.77386i	0.631224	+	0.194707i	0.0373984	+	0.999300i	$0.488093\pi$
$84$	−0.154650	+	0.677566i	−0.0168737	+	0.0739285i
$85$	−6.64006			−0.720215
$86$	3.16950	+	5.74058i	0.341776	+	0.619023i
$87$	−13.4215			−1.43894
$88$	1.10936	−	4.86042i	0.118258	−	0.518123i
$89$	−4.95277	−	1.52773i	−0.524992	−	0.161939i	0.0209199	−	0.999781i	$-0.493341\pi$
$89$	−4.95277	−	1.52773i	−0.524992	−	0.161939i	−0.545912	+	0.837843i	$0.683817\pi$
$90$	−0.0119534	−	0.00575645i	−0.00126000	−	0.000606783i
$91$	0.136346	+	0.347404i	0.0142930	+	0.0364179i
$92$	3.13299	−	5.42650i	0.326637	−	0.565752i
$93$	5.30767	+	9.19315i	0.550379	+	0.953285i
$94$	−6.67207	+	8.36652i	−0.688172	+	0.862940i
$95$	0.545614	+	0.371993i	0.0559788	+	0.0381657i
$96$	−1.70891	+	0.257577i	−0.174415	+	0.0262889i
$97$	16.8154	−	8.09787i	1.70735	−	0.822214i	0.714943	−	0.699183i	$-0.246453\pi$
$97$	16.8154	−	8.09787i	1.70735	−	0.822214i	0.992403	−	0.123032i	$-0.0392616\pi$
$98$	−5.01281	−	4.65121i	−0.506371	−	0.469843i
$99$	0.0654040	+	0.00985807i	0.00657335	+	0.000990774i
$100$	0.955573	−	0.294755i	0.0955573	−	0.0294755i
$101$	0.0664251	+	0.886382i	0.00660955	+	0.0881983i	0.999533	−	0.0305578i	$-0.00972838\pi$
$101$	0.0664251	+	0.886382i	0.00660955	+	0.0881983i	−0.992923	+	0.118756i	$0.962109\pi$
$102$	−7.15483	−	8.97187i	−0.708434	−	0.888348i
$103$	−1.00121	+	2.55103i	−0.0986519	+	0.251361i	−0.971676	−	0.236315i	$-0.924060\pi$
$103$	−1.00121	+	2.55103i	−0.0986519	+	0.251361i	0.873025	+	0.487676i	$0.162155\pi$
$104$	−0.680296	+	0.631223i	−0.0667086	+	0.0618965i
$105$	0.574228	−	0.391502i	0.0560389	−	0.0382067i
$106$	0.449530	−	5.99856i	0.0436622	−	0.582632i
$107$	2.18048	+	9.55329i	0.210795	+	0.923551i	0.964029	+	0.265799i	$0.0856357\pi$
$107$	2.18048	+	9.55329i	0.210795	+	0.923551i	−0.753234	+	0.657753i	$0.771507\pi$
$108$	−1.15880	−	5.07701i	−0.111505	−	0.488536i
$109$	0.327853	−	4.37489i	0.0314026	−	0.419039i	−0.959243	−	0.282581i	$-0.908809\pi$
$109$	0.327853	−	4.37489i	0.0314026	−	0.419039i	0.990646	−	0.136457i	$-0.0435717\pi$
$110$	−4.11915	+	2.80839i	−0.392745	+	0.267769i
$111$	1.34283	−	1.24597i	0.127456	−	0.118262i
$112$	−0.146919	+	0.374345i	−0.0138826	+	0.0353722i
$113$	4.89944	+	6.14370i	0.460901	+	0.577951i	0.956917	−	0.290362i	$-0.0937758\pi$
$113$	4.89944	+	6.14370i	0.460901	+	0.577951i	−0.496016	+	0.868313i	$0.665204\pi$
$114$	0.0852852	+	1.13805i	0.00798769	+	0.106588i
$115$	−5.98760	+	1.84693i	−0.558347	+	0.172227i
$116$	−7.67936	−	1.15748i	−0.713010	−	0.107469i
$117$	−0.00902566	−	0.00837459i	−0.000834423	−	0.000774231i
$118$	−1.76123	+	0.848162i	−0.162134	+	0.0780797i
$119$	−2.64043	+	0.397981i	−0.242048	+	0.0364828i
$120$	1.42792	+	0.973539i	0.130351	+	0.0888716i
$121$	8.63807	−	10.8318i	0.785279	−	0.984709i
$122$	6.69241	+	11.5916i	0.605902	+	1.04945i
$123$	6.66686	−	11.5473i	0.601130	−	1.04119i
$124$	2.24406	+	5.71776i	0.201522	+	0.513470i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	−0.00509830	−	0.00157262i	−0.000454193	−	0.000140100i
$127$	2.43514	−	10.6690i	0.216083	−	0.946723i	−0.744257	−	0.667893i	$-0.767196\pi$
$127$	2.43514	−	10.6690i	0.216083	−	0.946723i	0.960341	−	0.278830i	$-0.0899466\pi$
$128$	−1.00000			−0.0883883
$129$	10.3026	−	4.72087i	0.907090	−	0.415650i
$130$	0.928033			0.0813939
$131$	−2.10973	+	9.24334i	−0.184328	+	0.807594i	0.795210	+	0.606334i	$0.207361\pi$
$131$	−2.10973	+	9.24334i	−0.184328	+	0.807594i	−0.979538	+	0.201260i	$0.935496\pi$
$132$	−8.23310	−	2.53958i	−0.716600	−	0.221042i
$133$	0.239260	+	0.115222i	0.0207465	+	0.00999099i
$134$	4.55660	+	11.6100i	0.393630	+	1.00295i
$135$	−2.60379	+	4.50990i	−0.224099	+	0.388150i
$136$	−3.32003	−	5.75046i	−0.284690	−	0.493098i
$137$	−4.16806	+	5.22658i	−0.356102	+	0.446537i	−0.927325	−	0.374257i	$-0.877898\pi$
$137$	−4.16806	+	5.22658i	−0.356102	+	0.446537i	0.571223	+	0.820795i	$0.306469\pi$
$138$	−8.94732	−	6.10018i	−0.761647	−	0.519282i
$139$	13.7629	−	2.07442i	1.16735	−	0.175950i	0.463367	−	0.886166i	$-0.346641\pi$
$139$	13.7629	−	2.07442i	1.16735	−	0.175950i	0.703983	+	0.710217i	$0.251403\pi$
$140$	0.362319	−	0.174483i	0.0306215	−	0.0147465i
$141$	13.5570	+	12.5791i	1.14171	+	1.05935i
$142$	−11.0886	−	1.67134i	−0.930536	−	0.140256i
$143$	−4.42108	+	1.36372i	−0.369710	+	0.114040i
$144$	−0.000991463	−	0.0132302i	−8.26219e−5	−	0.00110251i
$145$	4.84208	+	6.07178i	0.402113	+	0.504234i
$146$	−3.52120	+	8.97188i	−0.291417	+	0.742518i
$147$	−8.66323	+	8.03830i	−0.714531	+	0.662988i
$148$	0.875779	−	0.597096i	0.0719886	−	0.0490810i
$149$	−0.0388227	+	0.518054i	−0.00318048	+	0.0424406i	−0.998568	−	0.0534929i	$-0.982965\pi$
$149$	−0.0388227	+	0.518054i	−0.00318048	+	0.0424406i	0.995388	+	0.0959335i	$0.0305836\pi$
$150$	−0.384564	−	1.68489i	−0.0313996	−	0.137570i
$151$	−1.71265	−	7.50363i	−0.139374	−	0.610637i	−0.995573	−	0.0939910i	$-0.970038\pi$
$151$	−1.71265	−	7.50363i	−0.139374	−	0.610637i	0.856199	−	0.516646i	$-0.172820\pi$
$152$	−0.0493487	+	0.658512i	−0.00400271	+	0.0534124i
$153$	0.0727878	−	0.0496259i	0.00588454	−	0.00401201i
$154$	−1.46966	+	1.36365i	−0.118429	+	0.109886i
$155$	2.24406	−	5.71776i	0.180247	−	0.459262i
$156$	0.999979	+	1.25393i	0.0800624	+	0.100395i
$157$	0.909002	+	12.1298i	0.0725463	+	0.968063i	0.908127	+	0.418695i	$0.137512\pi$
$157$	0.909002	+	12.1298i	0.0725463	+	0.968063i	−0.835581	+	0.549368i	$0.814869\pi$
$158$	−5.05341	+	1.55877i	−0.402027	+	0.124009i
$159$	−10.2798	−	1.54943i	−0.815239	−	0.122877i
$160$	0.733052	+	0.680173i	0.0579528	+	0.0537724i
$161$	−2.27028	+	1.09331i	−0.178923	+	0.0861649i
$162$	−8.85995	+	1.33542i	−0.696103	+	0.104921i
$163$	−4.33721	−	2.95706i	−0.339716	−	0.231615i	0.381430	−	0.924398i	$-0.375432\pi$
$163$	−4.33721	−	2.95706i	−0.339716	−	0.231615i	−0.721146	+	0.692783i	$0.756384\pi$
$164$	4.81041	−	6.03207i	0.375630	−	0.471025i
$165$	4.30794	+	7.46157i	0.335373	+	0.580883i
$166$	3.00905	−	5.21182i	0.233547	−	0.404516i
$167$	1.99185	+	5.07516i	0.154134	+	0.392728i	0.986994	−	0.160756i	$-0.0513933\pi$
$167$	1.99185	+	5.07516i	0.154134	+	0.392728i	−0.832860	+	0.553484i	$0.813298\pi$
$168$	0.626165	+	0.301545i	0.0483097	+	0.0232647i
$169$	−11.5995	−	3.57796i	−0.892266	−	0.275228i
$170$	−1.47755	+	6.47358i	−0.113323	+	0.496501i
$171$	−0.00876115			−0.000669982
$172$	6.30193	−	1.81264i	0.480518	−	0.138212i
$173$	22.7587			1.73031			0.865155	−	0.501504i	$-0.167220\pi$
$173$	22.7587			1.73031			0.865155	+	0.501504i	$0.167220\pi$
$174$	−2.98656	+	13.0850i	−0.226411	+	0.991971i
$175$	−0.384277	−	0.118534i	−0.0290486	−	0.00896031i
$176$	−4.49171	−	2.16309i	−0.338575	−	0.163049i
$177$	1.23425	+	3.14481i	0.0927717	+	0.236378i
$178$	−2.59152	+	4.48864i	−0.194242	+	0.336438i
$179$	−1.47532	−	2.55532i	−0.110270	−	0.190994i	0.805609	−	0.592448i	$-0.201838\pi$
$179$	−1.47532	−	2.55532i	−0.110270	−	0.190994i	−0.915879	+	0.401454i	$0.868505\pi$
$180$	−0.00827200	+	0.0103728i	−0.000616558	+	0.000773140i
$181$	14.1028	+	9.61514i	1.04825	+	0.714688i	0.959598	−	0.281374i	$-0.0907903\pi$
$181$	14.1028	+	9.61514i	1.04825	+	0.714688i	0.0886564	+	0.996062i	$0.471743\pi$
$182$	0.369034	−	0.0556229i	0.0273546	−	0.00412304i
$183$	20.8411	−	10.0365i	1.54062	−	0.741923i
$184$	−4.59329	−	4.26195i	−0.338622	−	0.314195i
$185$	−1.04812	−	0.157979i	−0.0770593	−	0.0116148i
$186$	10.1437	−	3.12892i	0.743774	−	0.229424i
$187$	−2.47382	−	33.0109i	−0.180904	−	2.41400i
$188$	6.67207	+	8.36652i	0.486611	+	0.610191i
$189$	−0.765095	+	1.94943i	−0.0556524	+	0.141800i
$190$	0.484077	−	0.449158i	0.0351187	−	0.0325854i
$191$	1.84791	−	1.25988i	0.133710	−	0.0911621i	−0.494618	−	0.869111i	$-0.664692\pi$
$191$	1.84791	−	1.25988i	0.133710	−	0.0911621i	0.628328	+	0.777949i	$0.283740\pi$
$192$	−0.129150	+	1.72338i	−0.00932058	+	0.124375i
$193$	−4.77407	−	20.9166i	−0.343645	−	1.50561i	−0.791315	−	0.611408i	$-0.790603\pi$
$193$	−4.77407	−	20.9166i	−0.343645	−	1.50561i	0.447670	−	0.894199i	$-0.352254\pi$
$194$	−4.15306	−	18.1958i	−0.298172	−	1.30638i
$195$	0.119855	−	1.59936i	0.00858302	−	0.114532i
$196$	−5.65005	+	3.85214i	−0.403575	+	0.275153i
$197$	−11.0199	+	10.2250i	−0.785135	+	0.728499i	−0.966987	−	0.254827i	$-0.917981\pi$
$197$	−11.0199	+	10.2250i	−0.785135	+	0.728499i	0.181852	+	0.983326i	$0.441791\pi$
$198$	0.0241647	−	0.0615706i	0.00171731	−	0.00437563i
$199$	4.75210	+	5.95894i	0.336867	+	0.422418i	0.921196	−	0.389099i	$-0.127214\pi$
$199$	4.75210	+	5.95894i	0.336867	+	0.422418i	−0.584329	+	0.811517i	$0.698642\pi$
$200$	−0.0747301	−	0.997204i	−0.00528422	−	0.0705130i
$201$	20.5970	−	6.35334i	1.45280	−	0.448130i
$202$	0.878939	+	0.132479i	0.0618420	+	0.00932118i
$203$	2.28938	+	2.12424i	0.160683	+	0.149092i
$204$	−10.3390	+	4.97901i	−0.723877	+	0.348601i
$205$	−7.62913	+	1.14991i	−0.532842	+	0.0803129i
$206$	2.26429	+	1.54376i	0.157760	+	0.107559i
$207$	0.0518322	−	0.0649955i	0.00360259	−	0.00451750i
$208$	0.464017	+	0.803700i	0.0321738	+	0.0557266i
$209$	−1.64608	+	2.85110i	−0.113862	+	0.197215i
$210$	−0.253909	−	0.646949i	−0.0175214	−	0.0446437i
$211$	7.35424	+	3.54161i	0.506287	+	0.243815i	0.669549	−	0.742768i	$-0.266487\pi$
$211$	7.35424	+	3.54161i	0.506287	+	0.243815i	−0.163262	+	0.986583i	$0.552202\pi$
$212$	−5.74813	−	1.77306i	−0.394784	−	0.121775i
$213$	−4.31245	+	18.8941i	−0.295484	+	1.29460i
$214$	9.79897			0.669844
$215$	−5.85255	−	2.95765i	−0.399140	−	0.201710i
$216$	−5.20758			−0.354331
$217$	0.549651	−	2.40818i	0.0373128	−	0.163478i
$218$	−4.19225	−	1.29314i	−0.283935	−	0.0875824i
$219$	15.0072	+	7.22710i	1.01409	+	0.488362i
$220$	1.82138	+	4.64079i	0.122797	+	0.312882i
$221$	−3.08110	+	5.33662i	−0.207257	+	0.358980i
$222$	−0.915920	−	1.58642i	−0.0614725	−	0.106473i
$223$	1.94850	−	2.44334i	0.130481	−	0.163618i	−0.712299	−	0.701876i	$-0.752346\pi$
$223$	1.94850	−	2.44334i	0.130481	−	0.163618i	0.842780	+	0.538258i	$0.180917\pi$
$224$	0.332266	+	0.226535i	0.0222005	+	0.0151360i
$225$	0.0131191	−	0.00197738i	0.000874605	−	0.000131825i
$226$	7.07990	−	3.40950i	0.470948	−	0.226796i
$227$	9.72491	+	9.02340i	0.645465	+	0.598904i	0.933440	−	0.358734i	$-0.116791\pi$
$227$	9.72491	+	9.02340i	0.645465	+	0.598904i	−0.287975	+	0.957638i	$0.592982\pi$
$228$	1.12850	+	0.170094i	0.0747365	+	0.0112647i
$229$	−3.86089	+	1.19093i	−0.255135	+	0.0786986i	−0.419684	−	0.907670i	$-0.637859\pi$
$229$	−3.86089	+	1.19093i	−0.255135	+	0.0786986i	0.164549	+	0.986369i	$0.447383\pi$
$230$	0.468258	+	6.24846i	0.0308760	+	0.412011i
$231$	2.16028	+	2.70890i	0.142136	+	0.178233i
$232$	−2.83727	+	7.22926i	−0.186276	+	0.474624i
$233$	−11.2364	+	10.4258i	−0.736119	+	0.683019i	−0.956283	−	0.292444i	$-0.905531\pi$
$233$	−11.2364	+	10.4258i	−0.736119	+	0.683019i	0.220163	+	0.975463i	$0.429341\pi$
$234$	−0.0101730	+	0.00693585i	−0.000665031	+	0.000453411i
$235$	0.799700	−	10.6713i	0.0521667	−	0.696116i
$236$	0.434987	+	1.90580i	0.0283152	+	0.124057i
$237$	2.03371	+	8.91028i	0.132104	+	0.578785i
$238$	−0.199548	+	2.66279i	−0.0129348	+	0.172603i
$239$	−11.3002	+	7.70436i	−0.730951	+	0.498354i	−0.870688	−	0.491835i	$-0.836326\pi$
$239$	−11.3002	+	7.70436i	−0.730951	+	0.498354i	0.139738	+	0.990189i	$0.455374\pi$
$240$	1.26687	−	1.17549i	0.0817763	−	0.0758773i
$241$	−9.38584	+	23.9147i	−0.604595	+	1.54048i	0.220439	+	0.975401i	$0.429251\pi$
$241$	−9.38584	+	23.9147i	−0.604595	+	1.54048i	−0.825034	+	0.565083i	$0.808844\pi$
$242$	−8.63807	−	10.8318i	−0.555276	−	0.696295i
$243$	−0.0103035	−	0.137491i	−0.000660970	−	0.00882004i
$244$	12.7902	−	3.94525i	0.818807	−	0.252568i
$245$	6.76190	+	1.01919i	0.432002	+	0.0651138i
$246$	−9.77431	−	9.06923i	−0.623187	−	0.578233i
$247$	0.552145	−	0.265899i	0.0351322	−	0.0169188i
$248$	6.07376	−	0.915472i	0.385684	−	0.0581325i
$249$	−8.59335	−	5.85885i	−0.544582	−	0.371290i
$250$	−0.623490	+	0.781831i	−0.0394330	+	0.0494474i
$251$	7.20244	+	12.4750i	0.454614	+	0.787414i	0.998666	−	0.0516372i	$-0.0164439\pi$
$251$	7.20244	+	12.4750i	0.454614	+	0.787414i	−0.544052	+	0.839051i	$0.683111\pi$
$252$	−0.00266767	+	0.00462054i	−0.000168047	+	0.000291066i
$253$	−11.4127	−	29.0791i	−0.717512	−	1.82819i
$254$	−9.85966	−	4.74816i	−0.618650	−	0.297926i
$255$	10.9656	+	3.38245i	0.686695	+	0.211817i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	23.5975			1.47197			0.735987	−	0.676996i	$-0.236718\pi$
$257$	23.5975			1.47197			0.735987	+	0.676996i	$0.236718\pi$
$258$	−2.30997	−	11.0948i	−0.143813	−	0.690729i
$259$	−0.426255			−0.0264862
$260$	0.206507	−	0.904765i	0.0128070	−	0.0561112i
$261$	−0.0984572	−	0.0303700i	−0.00609435	−	0.00187986i
$262$	8.54213	+	4.11367i	0.527735	+	0.254144i
$263$	10.7035	+	27.2721i	0.660008	+	1.68167i	0.729404	+	0.684083i	$0.239797\pi$
$263$	10.7035	+	27.2721i	0.660008	+	1.68167i	−0.0693962	+	0.997589i	$0.522107\pi$
$264$	−4.30794	+	7.46157i	−0.265135	+	0.459228i
$265$	3.00769	+	5.20947i	0.184761	+	0.320015i
$266$	0.165573	−	0.207622i	0.0101519	−	0.0127301i
$267$	7.40095	+	5.04589i	0.452931	+	0.308803i
$268$	12.3329	−	1.85888i	0.753350	−	0.113549i
$269$	9.54087	−	4.59464i	0.581717	−	0.280140i	−0.119794	−	0.992799i	$-0.538223\pi$
$269$	9.54087	−	4.59464i	0.581717	−	0.280140i	0.701511	+	0.712659i	$0.252509\pi$
$270$	3.81743	+	3.54205i	0.232321	+	0.215562i
$271$	9.85341	+	1.48516i	0.598552	+	0.0902172i	0.441328	−	0.897346i	$-0.354508\pi$
$271$	9.85341	+	1.48516i	0.598552	+	0.0902172i	0.157224	+	0.987563i	$0.449746\pi$
$272$	−6.34506	+	1.95719i	−0.384726	+	0.118672i
$273$	−0.0481990	−	0.643171i	−0.00291714	−	0.0389265i
$274$	4.16806	+	5.22658i	0.251802	+	0.315750i
$275$	1.82138	−	4.64079i	0.109833	−	0.279850i
$276$	−7.93820	+	7.36557i	−0.477824	+	0.443356i
$277$	11.1328	−	7.59019i	0.668903	−	0.456050i	−0.180654	−	0.983547i	$-0.557822\pi$
$277$	11.1328	−	7.59019i	0.668903	−	0.456050i	0.849557	+	0.527496i	$0.176869\pi$
$278$	1.04012	−	13.8794i	0.0623821	−	0.832431i
$279$	0.0181337	+	0.0794491i	0.00108564	+	0.00475649i
$280$	−0.0894853	−	0.392061i	−0.00534777	−	0.0234301i
$281$	−0.490894	+	6.55053i	−0.0292843	+	0.390772i	0.963233	+	0.268668i	$0.0865833\pi$
$281$	−0.490894	+	6.55053i	−0.0292843	+	0.390772i	−0.992517	+	0.122104i	$0.961036\pi$
$282$	15.2804	−	10.4180i	0.909936	−	0.620384i
$283$	−14.4398	+	13.3982i	−0.858358	+	0.796439i	−0.980592	−	0.196062i	$-0.937185\pi$
$283$	−14.4398	+	13.3982i	−0.858358	+	0.796439i	0.122234	+	0.992501i	$0.460994\pi$
$284$	−4.09688	+	10.4387i	−0.243105	+	0.619422i
$285$	−0.711554	−	0.892260i	−0.0421488	−	0.0528529i
$286$	0.345749	+	4.61370i	0.0204446	+	0.272814i
$287$	−2.96481	+	0.914524i	−0.175007	+	0.0539827i
$288$	−0.0131191	−	0.00197738i	−0.000773049	−	0.000116518i
$289$	−19.8586	−	18.4261i	−1.16816	−	1.08389i
$290$	6.99701	−	3.36958i	0.410879	−	0.197869i
$291$	−31.8946	+	4.80734i	−1.86970	+	0.281811i
$292$	7.96339	+	5.42935i	0.466022	+	0.317729i
$293$	−10.4723	+	13.1319i	−0.611801	+	0.767174i	−0.987165	−	0.159703i	$-0.948946\pi$
$293$	−10.4723	+	13.1319i	−0.611801	+	0.767174i	0.375364	+	0.926877i	$0.377518\pi$
$294$	5.90902	+	10.2347i	0.344621	+	0.596901i
$295$	0.977407	−	1.69292i	0.0569068	−	0.0985655i
$296$	−0.387247	−	0.986688i	−0.0225082	−	0.0573501i
$297$	−23.3909	−	11.2645i	−1.35728	−	0.653631i
$298$	0.496426	+	0.153127i	0.0287572	+	0.00887042i
$299$	−1.29397	+	5.66925i	−0.0748321	+	0.327861i
$300$	−1.72822			−0.0997786
$301$	−2.50455	−	0.825333i	−0.144360	−	0.0475714i
$302$	−7.69660			−0.442890
$303$	0.341827	−	1.49764i	0.0196374	−	0.0860372i
$304$	0.631021	+	0.194644i	0.0361915	+	0.0111636i
$305$	−12.0593	−	5.80746i	−0.690514	−	0.332534i
$306$	−0.0321848	−	0.0820056i	−0.00183988	−	0.00468795i
$307$	4.50349	−	7.80027i	0.257028	−	0.445185i	−0.708417	−	0.705794i	$-0.750590\pi$
$307$	4.50349	−	7.80027i	0.257028	−	0.445185i	0.965444	+	0.260610i	$0.0839236\pi$
$308$	1.00243	+	1.73625i	0.0571185	+	0.0989322i
$309$	2.95293	−	3.70286i	0.167986	−	0.210648i
$310$	−5.07506	−	3.46012i	−0.288244	−	0.196521i
$311$	−14.0200	+	2.11317i	−0.795001	+	0.119827i	−0.533970	−	0.845503i	$-0.679300\pi$
$311$	−14.0200	+	2.11317i	−0.795001	+	0.119827i	−0.261031	+	0.965331i	$0.584062\pi$
$312$	1.44501	−	0.695881i	0.0818077	−	0.0393965i
$313$	3.18440	+	2.95469i	0.179993	+	0.167009i	0.765024	−	0.644002i	$-0.222727\pi$
$313$	3.18440	+	2.95469i	0.179993	+	0.167009i	−0.585031	+	0.811011i	$0.698918\pi$
$314$	12.0279	+	1.81292i	0.678776	+	0.102309i
$315$	0.00509830	−	0.00157262i	0.000287257	−	8.86070e-5i
$316$	0.395199	+	5.27357i	0.0222317	+	0.296661i
$317$	−13.4026	−	16.8064i	−0.752767	−	0.943941i	0.246918	−	0.969036i	$-0.420582\pi$
$317$	−13.4026	−	16.8064i	−0.752767	−	0.943941i	−0.999685	+	0.0250959i	$0.992011\pi$
$318$	−3.79804	+	9.67725i	−0.212984	+	0.542673i
$319$	−28.3817	+	26.3344i	−1.58907	+	1.47444i
$320$	0.826239	−	0.563320i	0.0461882	−	0.0314905i
$321$	1.26554	−	16.8874i	0.0706353	−	0.942562i
$322$	0.560713	+	2.45665i	0.0312473	+	0.136904i
$323$	0.975715	+	4.27488i	0.0542902	+	0.237861i
$324$	−0.669583	+	8.93497i	−0.0371991	+	0.496387i
$325$	−0.766777	+	0.522780i	−0.0425331	+	0.0289986i
$326$	−3.84804	+	3.57046i	−0.213123	+	0.197749i
$327$	−2.77000	+	7.05785i	−0.153182	+	0.390300i
$328$	−4.81041	−	6.03207i	−0.265611	−	0.333065i
$329$	−0.321594	−	4.29137i	−0.0177300	−	0.236591i
$330$	8.23310	−	2.53958i	0.453217	−	0.139799i
$331$	19.6289	+	2.95858i	1.07890	+	0.162618i	0.664361	−	0.747412i	$-0.268704\pi$
$331$	19.6289	+	2.95858i	1.07890	+	0.162618i	0.414541	+	0.910030i	$0.363942\pi$
$332$	−4.41158	−	4.09334i	−0.242117	−	0.224651i
$333$	0.0126701	−	0.00610160i	0.000694317	−	0.000334365i
$334$	5.39114	−	0.812584i	0.294990	−	0.0444626i
$335$	−10.3050	−	7.02583i	−0.563022	−	0.383862i
$336$	0.433320	−	0.543366i	0.0236395	−	0.0296430i
$337$	1.17877	+	2.04170i	0.0642119	+	0.111218i	0.896344	−	0.443359i	$-0.146213\pi$
$337$	1.17877	+	2.04170i	0.0642119	+	0.111218i	−0.832132	+	0.554577i	$0.812880\pi$
$338$	−6.06938	+	10.5125i	−0.330131	+	0.571803i
$339$	−4.96151	−	12.6417i	−0.269472	−	0.686604i
$340$	5.98248	+	2.88101i	0.324446	+	0.156245i
$341$	29.2618	+	9.02607i	1.58461	+	0.488789i
$342$	−0.00194954	+	0.00854149i	−0.000105419	+	0.000461871i
$343$	5.56497			0.300480
$344$	−0.364877	−	6.54728i	−0.0196728	−	0.353006i
$345$	10.8290			0.583013
$346$	5.06428	−	22.1881i	0.272258	−	1.19284i
$347$	−1.74541	−	0.538388i	−0.0936985	−	0.0289022i	0.247551	−	0.968875i	$-0.420374\pi$
$347$	−1.74541	−	0.538388i	−0.0936985	−	0.0289022i	−0.341250	+	0.939973i	$0.610850\pi$
$348$	12.0924	+	5.82337i	0.648218	+	0.312165i
$349$	7.02759	+	17.9060i	0.376178	+	0.958486i	0.986119	+	0.166039i	$0.0530978\pi$
$349$	7.02759	+	17.9060i	0.376178	+	0.958486i	−0.609941	+	0.792447i	$0.708807\pi$
$350$	−0.201072	+	0.348266i	−0.0107477	+	0.0186156i
$351$	2.41640	+	4.18533i	0.128978	+	0.223397i
$352$	−3.10836	+	3.89776i	−0.165676	+	0.207751i
$353$	−16.4845	−	11.2389i	−0.877379	−	0.598187i	0.0386706	−	0.999252i	$-0.487688\pi$
$353$	−16.4845	−	11.2389i	−0.877379	−	0.598187i	−0.916050	+	0.401065i	$0.868640\pi$
$354$	3.34061	−	0.503516i	0.177551	−	0.0267616i
$355$	10.1033	−	4.86551i	0.536230	−	0.258235i
$356$	3.79943	+	3.52536i	0.201369	+	0.186844i
$357$	4.56323	+	0.687797i	0.241512	+	0.0364021i
$358$	−2.81954	+	0.869713i	−0.149017	+	0.0459658i
$359$	−1.96796	−	26.2606i	−0.103865	−	1.38598i	−0.768995	−	0.639254i	$-0.779243\pi$
$359$	−1.96796	−	26.2606i	−0.103865	−	1.38598i	0.665130	−	0.746727i	$-0.268376\pi$
$360$	0.00827200	+	0.0103728i	0.000435972	+	0.000546692i
$361$	−6.78216	+	17.2807i	−0.356956	+	0.909509i
$362$	12.5122	−	11.6097i	0.657629	−	0.610190i
$363$	−19.7830	+	13.4878i	−1.03834	+	0.707926i
$364$	0.0278894	−	0.372159i	0.00146180	−	0.0195064i
$365$	−2.14468	−	9.39648i	−0.112258	−	0.491834i
$366$	−5.14733	−	22.5519i	−0.269055	−	1.17881i
$367$	0.0968623	−	1.29254i	0.00505617	−	0.0674699i	−0.994105	−	0.108422i	$-0.965420\pi$
$367$	0.0968623	−	1.29254i	0.00505617	−	0.0674699i	0.999161	+	0.0409524i	$0.0130392\pi$
$368$	−5.17720	+	3.52975i	−0.269880	+	0.184001i
$369$	0.0750358	−	0.0696231i	0.00390621	−	0.00362443i
$370$	−0.387247	+	0.986688i	−0.0201320	+	0.0512955i
$371$	1.50825	+	1.89129i	0.0783044	+	0.0981907i
$372$	−0.793285	−	10.5857i	−0.0411299	−	0.548840i
$373$	−6.33779	+	1.95495i	−0.328158	+	0.101223i	−0.454457	−	0.890769i	$-0.650167\pi$
$373$	−6.33779	+	1.95495i	−0.328158	+	0.101223i	0.126298	+	0.991992i	$0.459690\pi$
$374$	−32.7337	−	4.93381i	−1.69262	−	0.255121i
$375$	1.26687	+	1.17549i	0.0654210	+	0.0607018i
$376$	9.64143	−	4.64307i	0.497219	−	0.239448i
$377$	7.12670	−	1.07418i	0.367044	−	0.0553229i
$378$	1.73030	+	1.17970i	0.0889972	+	0.0606773i
$379$	20.7460	−	26.0147i	1.06565	−	1.33628i	0.126811	−	0.991927i	$-0.459526\pi$
$379$	20.7460	−	26.0147i	1.06565	−	1.33628i	0.938839	−	0.344356i	$-0.111903\pi$
$380$	−0.330179	−	0.571888i	−0.0169379	−	0.0293372i
$381$	−9.45628	+	16.3788i	−0.484460	+	0.839110i
$382$	−0.817098	−	2.08193i	−0.0418064	−	0.106521i
$383$	−7.51919	−	3.62105i	−0.384213	−	0.185027i	0.231800	−	0.972764i	$-0.425539\pi$
$383$	−7.51919	−	3.62105i	−0.384213	−	0.185027i	−0.616012	+	0.787737i	$0.711253\pi$
$384$	1.65144	+	0.509401i	0.0842745	+	0.0259953i
$385$	0.446122	−	1.95459i	0.0227365	−	0.0996150i
$386$	−21.4545			−1.09200
$387$	0.0862598	−	0.0113188i	0.00438483	−	0.000575365i
$388$	−18.6637			−0.947505
$389$	6.96834	−	30.5303i	0.353309	−	1.54795i	−0.416177	−	0.909284i	$-0.636630\pi$
$389$	6.96834	−	30.5303i	0.353309	−	1.54795i	0.769486	−	0.638664i	$-0.220513\pi$
$390$	−1.53259	−	0.472741i	−0.0776056	−	0.0239382i
$391$	−37.4862	−	18.0524i	−1.89576	−	0.912948i
$392$	2.49830	+	6.36558i	0.126183	+	0.321510i
$393$	8.19265	−	14.1901i	0.413265	−	0.715796i
$394$	7.51645	+	13.0189i	0.378673	+	0.655881i
$395$	3.29723	−	4.13460i	0.165902	−	0.208034i
$396$	−0.0546497	−	0.0372596i	−0.00274625	−	0.00187236i
$397$	11.8789	−	1.79046i	0.596186	−	0.0898606i	0.155985	−	0.987759i	$-0.450145\pi$
$397$	11.8789	−	1.79046i	0.596186	−	0.0898606i	0.440202	+	0.897899i	$0.354907\pi$
$398$	6.86698	−	3.30696i	0.344211	−	0.165763i
$399$	−0.336429	−	0.312161i	−0.0168425	−	0.0156276i
$400$	−0.988831	−	0.149042i	−0.0494415	−	0.00745211i
$401$	−10.0615	+	3.10356i	−0.502447	+	0.154984i	−0.535610	−	0.844466i	$-0.679918\pi$
$401$	−10.0615	+	3.10356i	−0.502447	+	0.154984i	0.0331627	+	0.999450i	$0.489442\pi$
$402$	−1.61078	−	21.4944i	−0.0803384	−	1.07204i
$403$	−3.55409	−	4.45669i	−0.177042	−	0.222003i
$404$	0.324740	−	0.827423i	0.0161564	−	0.0411658i
$405$	6.56816	−	6.09436i	0.326375	−	0.302831i
$406$	2.58041	−	1.75930i	0.128064	−	0.0873124i
$407$	0.394899	−	5.26956i	0.0195744	−	0.261203i
$408$	2.55353	+	11.1877i	0.126419	+	0.553876i
$409$	−0.912013	−	3.99579i	−0.0450962	−	0.197579i	0.947362	−	0.320165i	$-0.103738\pi$
$409$	−0.912013	−	3.99579i	−0.0450962	−	0.197579i	−0.992458	+	0.122586i	$0.960881\pi$
$410$	−0.576565	+	7.69373i	−0.0284745	+	0.379966i
$411$	9.54572	−	6.50816i	0.470856	−	0.321024i
$412$	2.00891	−	1.86400i	0.0989718	−	0.0918325i
$413$	0.287200	−	0.731774i	0.0141322	−	0.0360083i
$414$	−0.0518322	−	0.0649955i	−0.00254741	−	0.00319436i
$415$	0.449733	+	6.00127i	0.0220765	+	0.294591i
$416$	0.886803	−	0.273543i	0.0434791	−	0.0134115i
$417$	−23.7852	−	3.58504i	−1.16477	−	0.175560i
$418$	2.41333	+	2.23924i	0.118040	+	0.109525i
$419$	24.6125	−	11.8528i	1.20240	−	0.579045i	0.278041	−	0.960569i	$-0.410315\pi$
$419$	24.6125	−	11.8528i	1.20240	−	0.579045i	0.924359	+	0.381524i	$0.124601\pi$
$420$	−0.687228	+	0.103583i	−0.0335333	+	0.00505433i
$421$	−5.90280	−	4.02446i	−0.287685	−	0.196140i	0.410875	−	0.911692i	$-0.365223\pi$
$421$	−5.90280	−	4.02446i	−0.287685	−	0.196140i	−0.698560	+	0.715551i	$0.746176\pi$
$422$	5.08929	−	6.38177i	0.247743	−	0.310660i
$423$	0.0709876	+	0.122954i	0.00345154	+	0.00597823i
$424$	−3.00769	+	5.20947i	−0.146066	+	0.252994i
$425$	−2.42589	−	6.18105i	−0.117673	−	0.299825i
$426$	17.4608	+	8.40866i	0.845976	+	0.407401i
$427$	−5.14348	−	1.58655i	−0.248911	−	0.0767787i
$428$	2.18048	−	9.55329i	0.105397	−	0.461776i
$429$	7.99582			0.386042
$430$	−4.18581	+	5.04767i	−0.201858	+	0.243420i
$431$	33.1974			1.59906			0.799532	−	0.600624i	$-0.205081\pi$
$431$	33.1974			1.59906			0.799532	+	0.600624i	$0.205081\pi$
$432$	−1.15880	+	5.07701i	−0.0557526	+	0.244268i
$433$	0.355142	+	0.109547i	0.0170670	+	0.00526448i	0.303277	−	0.952902i	$-0.401919\pi$
$433$	0.355142	+	0.109547i	0.0170670	+	0.00526448i	−0.286210	+	0.958167i	$0.592395\pi$
$434$	−2.22549	−	1.07174i	−0.106827	−	0.0514452i
$435$	−4.90342	−	12.4937i	−0.235101	−	0.599028i
$436$	−2.19358	+	3.79939i	−0.105053	+	0.181958i
$437$	2.06890	+	3.58344i	0.0989689	+	0.171419i
$438$	10.3853	−	13.0228i	0.496230	−	0.622253i
$439$	20.5770	+	14.0292i	0.982088	+	0.669577i	0.944085	−	0.329701i	$-0.106948\pi$
$439$	20.5770	+	14.0292i	0.982088	+	0.669577i	0.0380030	+	0.999278i	$0.487900\pi$
$440$	4.92974	−	0.743038i	0.235016	−	0.0354229i
$441$	−0.0817406	+	0.0393642i	−0.00389241	+	0.00187449i
$442$	4.51721	+	4.19136i	0.214862	+	0.199362i
$443$	−9.17981	−	1.38363i	−0.436146	−	0.0657384i	−0.0727003	−	0.997354i	$-0.523162\pi$
$443$	−9.17981	−	1.38363i	−0.436146	−	0.0657384i	−0.363446	+	0.931615i	$0.618400\pi$
$444$	−1.75046	+	0.539944i	−0.0830729	+	0.0256246i
$445$	−0.387329	−	5.16854i	−0.0183611	−	0.245012i
$446$	−1.94850	−	2.44334i	−0.0922640	−	0.115695i
$447$	0.328010	−	0.835756i	0.0155143	−	0.0395299i
$448$	0.294792	−	0.273527i	0.0139276	−	0.0129229i
$449$	−19.2355	+	13.1145i	−0.907779	+	0.618913i	−0.924598	−	0.380945i	$-0.875599\pi$
$449$	−19.2355	+	13.1145i	−0.907779	+	0.618913i	0.0168185	+	0.999859i	$0.494646\pi$
$450$	0.000991463	−	0.0132302i	4.67380e−5	−	0.000623675i
$451$	−8.55905	−	37.4996i	−0.403030	−	1.76579i
$452$	−1.74859	−	7.66107i	−0.0822468	−	0.360347i
$453$	−0.994014	+	13.2642i	−0.0467029	+	0.623207i
$454$	10.9612	−	7.47319i	0.514433	−	0.350734i
$455$	−0.273577	+	0.253842i	−0.0128255	+	0.0119003i
$456$	0.416943	−	1.06235i	0.0195251	−	0.0497493i
$457$	−3.21657	−	4.03345i	−0.150465	−	0.188677i	0.700887	−	0.713273i	$-0.252788\pi$
$457$	−3.21657	−	4.03345i	−0.150465	−	0.188677i	−0.851351	+	0.524596i	$0.824216\pi$
$458$	0.301939	+	4.02909i	0.0141087	+	0.188267i
$459$	−33.0424	+	10.1922i	−1.54229	+	0.475732i
$460$	6.19600	+	0.933896i	0.288890	+	0.0435431i
$461$	−22.2770	−	20.6700i	−1.03754	−	0.962698i	−0.0382110	−	0.999270i	$-0.512166\pi$
$461$	−22.2770	−	20.6700i	−1.03754	−	0.962698i	−0.999331	+	0.0365714i	$0.988356\pi$
$462$	3.12169	−	1.50333i	0.145234	−	0.0699412i
$463$	−9.89347	+	1.49120i	−0.459789	+	0.0693020i	−0.374853	−	0.927084i	$-0.622307\pi$
$463$	−9.89347	+	1.49120i	−0.459789	+	0.0693020i	−0.0849361	+	0.996386i	$0.527069\pi$
$464$	6.41665	+	4.37480i	0.297886	+	0.203095i
$465$	−6.61855	+	8.29940i	−0.306928	+	0.384876i
$466$	7.66411	+	13.2746i	0.355033	+	0.614935i
$467$	7.15207	−	12.3877i	0.330958	−	0.573236i	−0.651742	−	0.758441i	$-0.725961\pi$
$467$	7.15207	−	12.3877i	0.330958	−	0.573236i	0.982700	+	0.185205i	$0.0592948\pi$
$468$	0.00449824	+	0.0114613i	0.000207931	+	0.000529800i
$469$	−4.51890	−	2.17619i	−0.208664	−	0.100487i
$470$	−10.2258	−	3.15423i	−0.471679	−	0.145494i
$471$	4.67776	−	20.4946i	0.215540	−	0.944343i
$472$	1.95481			0.0899776
$473$	12.5234	−	30.1977i	0.575829	−	1.38849i
$474$	9.13942			0.419787
$475$	−0.146944	+	0.643802i	−0.00674224	+	0.0295397i
$476$	2.55162	+	0.787071i	0.116953	+	0.0360754i
$477$	−0.0719041	−	0.0346272i	−0.00329226	−	0.00158547i
$478$	4.99666	+	12.7313i	0.228542	+	0.582315i
$479$	−4.64676	+	8.04843i	−0.212316	+	0.367742i	−0.952439	−	0.304730i	$-0.901434\pi$
$479$	−4.64676	+	8.04843i	−0.212316	+	0.367742i	0.740123	+	0.672472i	$0.234767\pi$
$480$	−0.864108	−	1.49668i	−0.0394410	−	0.0683138i
$481$	−0.613313	+	0.769070i	−0.0279647	+	0.0350666i
$482$	21.2266	+	14.4720i	0.966845	+	0.659184i
$483$	4.30616	−	0.649049i	0.195937	−	0.0295328i
$484$	−12.4824	+	6.01120i	−0.567381	+	0.273236i
$485$	13.6815	+	12.6945i	0.621243	+	0.576429i
$486$	−0.136336	−	0.0205494i	−0.00618434	−	0.000932140i
$487$	30.8850	−	9.52675i	1.39953	−	0.431698i	0.499043	−	0.866577i	$-0.333685\pi$
$487$	30.8850	−	9.52675i	1.39953	−	0.431698i	0.900489	+	0.434879i	$0.143209\pi$
$488$	−1.00025	−	13.3474i	−0.0452791	−	0.604208i
$489$	5.65630	+	7.09277i	0.255787	+	0.320746i
$490$	2.49830	−	6.36558i	0.112862	−	0.287567i
$491$	−31.2869	+	29.0300i	−1.41196	+	1.31011i	−0.522841	+	0.852430i	$0.675128\pi$
$491$	−31.2869	+	29.0300i	−1.41196	+	1.31011i	−0.889118	+	0.457677i	$0.848681\pi$
$492$	−11.0168	+	7.51115i	−0.496677	+	0.338629i
$493$	−3.85363	+	51.4231i	−0.173559	+	2.31598i
$494$	−0.136369	−	0.597470i	−0.00613551	−	0.0268814i
$495$	0.0147182	+	0.0644845i	0.000661532	+	0.00289836i
$496$	0.459019	−	6.12519i	0.0206106	−	0.275029i
$497$	3.72599	−	2.54034i	0.167133	−	0.113950i
$498$	−7.62416	+	7.07418i	−0.341647	+	0.317002i
$499$	−8.83303	+	22.5062i	−0.395421	+	1.00752i	0.585075	+	0.810979i	$0.301065\pi$
$499$	−8.83303	+	22.5062i	−0.395421	+	1.00752i	−0.980496	+	0.196537i	$0.937030\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	−0.704130	−	9.39596i	−0.0314582	−	0.419780i
$502$	13.7649	−	4.24591i	0.614358	−	0.189504i
$503$	−20.0891	−	3.02795i	−0.895731	−	0.135010i	−0.314987	−	0.949096i	$-0.602000\pi$
$503$	−20.0891	−	3.02795i	−0.895731	−	0.135010i	−0.580744	+	0.814086i	$0.697238\pi$
$504$	0.00391108	+	0.00362895i	0.000174213	+	0.000161646i
$505$	−0.800842	+	0.385665i	−0.0356370	+	0.0171619i
$506$	−30.8896	+	4.65586i	−1.37321	+	0.206978i
$507$	17.3332	+	11.8176i	0.769793	+	0.524836i
$508$	−6.82310	+	8.55590i	−0.302726	+	0.379606i
$509$	7.21107	+	12.4899i	0.319625	+	0.553607i	0.980410	−	0.196969i	$-0.0631097\pi$
$509$	7.21107	+	12.4899i	0.319625	+	0.553607i	−0.660785	+	0.750575i	$0.729776\pi$
$510$	5.73773	−	9.93804i	0.254071	−	0.440064i
$511$	−1.41603	−	3.60798i	−0.0626414	−	0.159608i
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$	3.28609	+	1.01363i	0.145085	+	0.0447526i
$514$	5.25095	−	23.0059i	0.231609	−	1.01475i
$515$	−2.74047			−0.120760
$516$	−11.3306	−	0.216757i	−0.498802	−	0.00954220i
$517$	53.3498			2.34632
$518$	−0.0948508	+	0.415568i	−0.00416750	+	0.0182590i
$519$	−37.5845	−	11.5933i	−1.64978	−	0.508889i
$520$	−0.836129	−	0.402658i	−0.0366667	−	0.0176577i
$521$	−8.27403	−	21.0819i	−0.362492	−	0.923614i	−0.989491	−	0.144594i	$-0.953812\pi$
$521$	−8.27403	−	21.0819i	−0.362492	−	0.923614i	0.626999	−	0.779020i	$-0.284283\pi$
$522$	−0.0515174	+	0.0892307i	−0.00225485	+	0.00390552i
$523$	−5.83538	−	10.1072i	−0.255163	−	0.441956i	0.709777	−	0.704427i	$-0.248796\pi$
$523$	−5.83538	−	10.1072i	−0.255163	−	0.441956i	−0.964940	+	0.262471i	$0.915463\pi$
$524$	5.91134	−	7.41258i	0.258238	−	0.323820i
$525$	0.574228	+	0.391502i	0.0250614	+	0.0170866i
$526$	28.9701	−	4.36654i	1.26316	−	0.190390i
$527$	36.7466	−	17.6962i	1.60071	−	0.770860i
$528$	6.31589	+	5.86029i	0.274864	+	0.255036i
$529$	−16.0809	−	2.42381i	−0.699170	−	0.105383i
$530$	5.74813	−	1.77306i	0.249683	−	0.0770170i
$531$	0.00193813	+	0.0258625i	8.41075e−5	+	0.00112234i
$532$	−0.165573	−	0.207622i	−0.00717851	−	0.00900157i
$533$	−2.61586	+	6.66511i	−0.113306	+	0.288698i
$534$	6.56624	−	6.09258i	0.284149	−	0.263652i
$535$	−8.09629	+	5.51996i	−0.350033	+	0.238649i
$536$	0.932047	−	12.4373i	0.0402583	−	0.537210i
$537$	1.13471	+	4.97148i	0.0489662	+	0.214535i
$538$	−2.35640	−	10.3241i	−0.101592	−	0.445102i
$539$	−2.54768	+	33.9964i	−0.109736	+	1.46433i
$540$	4.30270	−	2.93353i	0.185159	−	0.126239i
$541$	21.1564	−	19.6302i	0.909583	−	0.843970i	−0.0786534	−	0.996902i	$-0.525062\pi$
$541$	21.1564	−	19.6302i	0.909583	−	0.843970i	0.988237	+	0.152932i	$0.0488715\pi$
$542$	3.64052	−	9.27588i	0.156374	−	0.398433i
$543$	−18.3920	−	23.0628i	−0.789274	−	0.989719i
$544$	0.496212	+	6.62149i	0.0212749	+	0.283894i
$545$	4.19225	−	1.29314i	0.179576	−	0.0553920i
$546$	−0.637771	−	0.0961284i	−0.0272941	−	0.00411392i
$547$	−25.3502	−	23.5216i	−1.08390	−	1.00571i	−0.999957	−	0.00923813i	$-0.997059\pi$
$547$	−25.3502	−	23.5216i	−1.08390	−	1.00571i	−0.0839392	−	0.996471i	$-0.526750\pi$
$548$	6.02302	−	2.90054i	0.257291	−	0.123905i
$549$	0.175596	−	0.0264669i	0.00749427	−	0.00112958i
$550$	−4.11915	−	2.80839i	−0.175641	−	0.119750i
$551$	3.19751	−	4.00955i	0.136219	−	0.170813i
$552$	5.41449	+	9.37817i	0.230456	+	0.399161i
$553$	1.06334	−	1.84176i	0.0452177	−	0.0783194i
$554$	−4.92262	−	12.5426i	−0.209142	−	0.532885i
$555$	1.65043	+	0.794805i	0.0700568	+	0.0337376i
$556$	−13.3000	−	4.10250i	−0.564044	−	0.173985i
$557$	2.00315	−	8.77636i	0.0848760	−	0.371866i	−0.914596	−	0.404370i	$-0.867491\pi$
$557$	2.00315	−	8.77636i	0.0848760	−	0.371866i	0.999472	+	0.0325036i	$0.0103480\pi$
$558$	0.0814923			0.00344984
$559$	−5.09274	+	3.33130i	−0.215400	+	0.140899i
$560$	−0.402143			−0.0169937
$561$	−12.7304	+	55.7756i	−0.537478	+	2.35485i
$562$	6.27706	+	1.93622i	0.264782	+	0.0816744i
$563$	37.8603	+	18.2325i	1.59562	+	0.768410i	0.999408	−	0.0344167i	$-0.0109574\pi$
$563$	37.8603	+	18.2325i	1.59562	+	0.768410i	0.596212	+	0.802827i	$0.296672\pi$
$564$	−6.75660	−	17.2155i	−0.284504	−	0.724905i
$565$	−3.92905	+	6.80531i	−0.165296	+	0.286301i
$566$	9.84911	+	17.0592i	0.413989	+	0.717050i
$567$	2.24657	−	2.81711i	0.0943469	−	0.118307i
$568$	9.26533	+	6.31699i	0.388764	+	0.265055i
$569$	−39.1022	+	5.89371i	−1.63925	+	0.247077i	−0.903002	−	0.429636i	$-0.858642\pi$
$569$	−39.1022	+	5.89371i	−1.63925	+	0.247077i	−0.736247	+	0.676713i	$0.763404\pi$
$570$	−1.02822	+	0.495167i	−0.0430676	+	0.0207403i
$571$	17.1796	+	15.9404i	0.718946	+	0.667084i	0.952250	−	0.305320i	$-0.0987634\pi$
$571$	17.1796	+	15.9404i	0.718946	+	0.667084i	−0.233304	+	0.972404i	$0.574954\pi$
$572$	4.57496	+	0.689564i	0.191289	+	0.0288321i
$573$	−3.69350	+	1.13929i	−0.154298	+	0.0475946i
$574$	0.231862	+	3.09398i	0.00967773	+	0.129140i
$575$	−3.90678	−	4.89894i	−0.162924	−	0.204300i
$576$	−0.00484707	+	0.0123501i	−0.000201961	+	0.000514589i
$577$	21.3630	−	19.8219i	0.889352	−	0.825198i	−0.0960615	−	0.995375i	$-0.530625\pi$
$577$	21.3630	−	19.8219i	0.889352	−	0.825198i	0.985413	+	0.170177i	$0.0544341\pi$
$578$	−22.3831	+	15.2605i	−0.931014	+	0.634755i
$579$	−2.77084	+	36.9743i	−0.115152	+	1.53660i
$580$	−1.72812	−	7.57138i	−0.0717562	−	0.314385i
$581$	0.538531	+	2.35946i	0.0223420	+	0.0978868i
$582$	−2.41041	+	32.1647i	−0.0999148	+	1.33327i
$583$	−24.7782	+	16.8935i	−1.02621	+	0.699658i
$584$	7.06525	−	6.55559i	0.292362	−	0.271272i
$585$	0.00449824	−	0.0114613i	0.000185979	−	0.000473868i
$586$	10.4723	+	13.1319i	0.432609	+	0.542474i
$587$	2.68811	+	35.8703i	0.110950	+	1.48053i	0.723625	+	0.690193i	$0.242474\pi$
$587$	2.68811	+	35.8703i	0.110950	+	1.48053i	−0.612675	+	0.790335i	$0.709907\pi$
$588$	11.2930	−	3.48343i	0.465715	−	0.143654i
$589$	−4.01086	−	0.604540i	−0.165265	−	0.0249096i
$590$	−1.43298	−	1.32961i	−0.0589949	−	0.0547392i
$591$	23.4073	−	11.2723i	0.962846	−	0.463682i
$592$	−1.04812	+	0.157979i	−0.0430775	+	0.00649289i
$593$	10.7547	+	7.33244i	0.441643	+	0.301107i	0.763650	−	0.645630i	$-0.223405\pi$
$593$	10.7547	+	7.33244i	0.441643	+	0.301107i	−0.322007	+	0.946737i	$0.604357\pi$
$594$	−16.1870	+	20.2979i	−0.664161	+	0.832832i
$595$	−1.33513	−	2.31251i	−0.0547349	−	0.0948036i
$596$	0.259753	−	0.449906i	0.0106399	−	0.0184288i
$597$	−4.81230	−	12.2615i	−0.196954	−	0.501832i
$598$	5.23917	+	2.52305i	0.214246	+	0.103175i
$599$	28.3845	+	8.75546i	1.15976	+	0.357738i	0.814158	−	0.580643i	$-0.197199\pi$
$599$	28.3845	+	8.75546i	1.15976	+	0.357738i	0.345601	+	0.938382i	$0.387675\pi$
$600$	−0.384564	+	1.68489i	−0.0156998	+	0.0687852i
$601$	−25.9691			−1.05930			−0.529650	−	0.848216i	$-0.677677\pi$
$601$	−25.9691			−1.05930			−0.529650	+	0.848216i	$0.677677\pi$
$602$	−1.36195	+	2.25810i	−0.0555091	+	0.0920332i
$603$	0.165472			0.00673852
$604$	−1.71265	+	7.50363i	−0.0696869	+	0.305318i
$605$	13.2389	+	4.08365i	0.538237	+	0.166024i
$606$	−1.38403	−	0.666513i	−0.0562223	−	0.0270752i
$607$	14.0043	+	35.6823i	0.568416	+	1.44830i	0.869129	+	0.494585i	$0.164680\pi$
$607$	14.0043	+	35.6823i	0.568416	+	1.44830i	−0.300714	+	0.953714i	$0.597225\pi$
$608$	0.330179	−	0.571888i	0.0133905	−	0.0231931i
$609$	−2.69868	−	4.67426i	−0.109356	−	0.189410i
$610$	−8.34530	+	10.4647i	−0.337891	+	0.423702i
$611$	−8.20542	−	5.59436i	−0.331956	−	0.226323i
$612$	−0.0871114	+	0.0131299i	−0.00352127	+	0.000530746i
$613$	5.75488	−	2.77141i	0.232438	−	0.111936i	−0.314040	−	0.949410i	$-0.601683\pi$
$613$	5.75488	−	2.77141i	0.232438	−	0.111936i	0.546478	+	0.837474i	$0.315968\pi$
$614$	−6.60258	−	6.12630i	−0.266458	−	0.247237i
$615$	13.1848	+	1.98729i	0.531662	+	0.0801352i
$616$	1.91578	−	0.590941i	0.0771891	−	0.0238097i
$617$	−0.979021	−	13.0641i	−0.0394139	−	0.525942i	−0.981612	−	0.190886i	$-0.938864\pi$
$617$	−0.979021	−	13.0641i	−0.0394139	−	0.525942i	0.942198	−	0.335056i	$-0.108755\pi$
$618$	−2.95293	−	3.70286i	−0.118784	−	0.148951i
$619$	−14.8167	+	37.7524i	−0.595534	+	1.51740i	0.241587	+	0.970379i	$0.422332\pi$
$619$	−14.8167	+	37.7524i	−0.595534	+	1.51740i	−0.837121	+	0.547018i	$0.815763\pi$
$620$	−4.50267	+	4.17787i	−0.180832	+	0.167787i
$621$	−26.9607	+	18.3815i	−1.08189	+	0.737623i
$622$	−1.05955	+	14.1387i	−0.0424841	+	0.566910i
$623$	−0.463805	−	2.03206i	−0.0185820	−	0.0814129i
$624$	−0.356888	−	1.56363i	−0.0142870	−	0.0625953i
$625$	0.0747301	−	0.997204i	0.00298920	−	0.0398882i
$626$	3.58921	−	2.44708i	0.143454	−	0.0978050i
$627$	4.17075	−	3.86989i	0.166564	−	0.154549i
$628$	4.44394	−	11.3230i	0.177332	−	0.451835i
$629$	−4.38824	−	5.50268i	−0.174971	−	0.219406i
$630$	−0.000398710	−	0.00532042i	−1.58850e−5	−	0.000211971i
$631$	6.94245	−	2.14146i	0.276375	−	0.0852502i	−0.153470	−	0.988153i	$-0.549045\pi$
$631$	6.94245	−	2.14146i	0.276375	−	0.0852502i	0.429844	+	0.902903i	$0.358569\pi$
$632$	5.22929	+	0.788188i	0.208010	+	0.0313524i
$633$	−10.3410	−	9.59501i	−0.411016	−	0.381367i
$634$	−19.3674	+	9.32684i	−0.769177	+	0.370416i
$635$	10.8212	−	1.63103i	0.429425	−	0.0647254i
$636$	8.58948	+	5.85621i	0.340595	+	0.232214i
$637$	3.95676	−	4.96162i	0.156773	−	0.196587i
$638$	19.3586	+	33.5301i	0.766415	+	1.32747i
$639$	−0.0743886	+	0.128845i	−0.00294277	+	0.00509702i
$640$	−0.365341	−	0.930874i	−0.0144414	−	0.0367960i
$641$	−26.5807	−	12.8006i	−1.04987	−	0.505593i	−0.172305	−	0.985044i	$-0.555122\pi$
$641$	−26.5807	−	12.8006i	−1.04987	−	0.505593i	−0.877569	+	0.479451i	$0.840836\pi$
$642$	−16.1824	−	4.99160i	−0.638668	−	0.197003i
$643$	−4.46259	+	19.5519i	−0.175987	+	0.771051i	0.807470	+	0.589909i	$0.200836\pi$
$643$	−4.46259	+	19.5519i	−0.175987	+	0.771051i	−0.983457	+	0.181142i	$0.942021\pi$
$644$	2.51982			0.0992949
$645$	8.15849	+	7.86566i	0.321240	+	0.309710i
$646$	4.38482			0.172518
$647$	−9.12125	+	39.9628i	−0.358593	+	1.57110i	0.398108	+	0.917338i	$0.369667\pi$
$647$	−9.12125	+	39.9628i	−0.358593	+	1.57110i	−0.756701	+	0.653761i	$0.773190\pi$
$648$	8.56195	+	2.64101i	0.336345	+	0.103749i
$649$	8.78045	+	4.22844i	0.344663	+	0.165981i
$650$	0.339049	+	0.863882i	0.0132986	+	0.0338842i
$651$	−2.13444	+	3.69696i	−0.0836554	+	0.144895i
$652$	2.62467	+	4.54606i	0.102790	+	0.178038i
$653$	−1.84987	+	2.31967i	−0.0723911	+	0.0907755i	−0.816708	−	0.577051i	$-0.804204\pi$
$653$	−1.84987	+	2.31967i	−0.0723911	+	0.0907755i	0.744317	+	0.667826i	$0.232775\pi$
$654$	6.26451	+	4.27107i	0.244962	+	0.167012i
$655$	−9.37516	+	1.41308i	−0.366318	+	0.0552135i
$656$	−6.95125	+	3.34754i	−0.271401	+	0.130700i
$657$	0.0937364	+	0.0869747i	0.00365700	+	0.00339320i
$658$	−4.25534	−	0.641389i	−0.165890	−	0.0250040i
$659$	−30.4435	+	9.39057i	−1.18591	+	0.365805i	−0.824098	−	0.566447i	$-0.808318\pi$
$659$	−30.4435	+	9.39057i	−1.18591	+	0.365805i	−0.361811	+	0.932251i	$0.617841\pi$
$660$	−0.643866	−	8.59179i	−0.0250624	−	0.334435i
$661$	22.2797	+	27.9378i	0.866578	+	1.08666i	0.995478	+	0.0949973i	$0.0302842\pi$
$661$	22.2797	+	27.9378i	0.866578	+	1.08666i	−0.128899	+	0.991658i	$0.541144\pi$
$662$	7.25225	−	18.4784i	0.281867	−	0.718184i
$663$	7.80671	−	7.24357i	0.303188	−	0.281317i
$664$	−4.97238	+	3.39011i	−0.192966	+	0.131562i
$665$	−0.0198452	+	0.264816i	−0.000769566	+	0.0102691i
$666$	−0.00312926	−	0.0137102i	−0.000121256	−	0.000531258i
$667$	10.8284	+	47.4422i	0.419276	+	1.83697i
$668$	0.407431	−	5.43679i	0.0157640	−	0.210356i
$669$	−4.46246	+	3.04245i	−0.172529	+	0.117628i
$670$	−9.14275	+	8.48324i	−0.353215	+	0.327736i
$671$	24.3788	−	62.1162i	0.941134	−	2.39797i
$672$	−0.433320	−	0.543366i	−0.0167157	−	0.0209608i
$673$	−0.979187	−	13.0663i	−0.0377449	−	0.503671i	−0.983753	−	0.179528i	$-0.942543\pi$
$673$	−0.979187	−	13.0663i	−0.0377449	−	0.503671i	0.946008	−	0.324143i	$-0.105076\pi$
$674$	2.25281	−	0.694899i	0.0867750	−	0.0267665i
$675$	−5.14941	−	0.776149i	−0.198201	−	0.0298740i
$676$	8.89834	+	8.25645i	0.342244	+	0.317556i
$677$	−39.0867	+	18.8231i	−1.50222	+	0.723432i	−0.990729	−	0.135855i	$-0.956622\pi$
$677$	−39.0867	+	18.8231i	−1.50222	+	0.723432i	−0.511494	+	0.859287i	$0.670908\pi$
$678$	−13.4288	+	2.02407i	−0.515730	+	0.0777338i
$679$	6.20132	+	4.22799i	0.237985	+	0.162255i
$680$	4.14001	−	5.19141i	0.158762	−	0.199081i
$681$	−11.4636	−	19.8555i	−0.439284	−	0.760863i
$682$	15.3111	−	26.5196i	0.586293	−	1.01549i
$683$	−3.32534	−	8.47282i	−0.127241	−	0.324204i	0.853031	−	0.521861i	$-0.174762\pi$
$683$	−3.32534	−	8.47282i	−0.127241	−	0.324204i	−0.980271	+	0.197657i	$0.936667\pi$
$684$	0.00789352	+	0.00380132i	0.000301816	+	0.000145347i
$685$	−6.38805	−	1.97045i	−0.244075	−	0.0752872i
$686$	1.23832	−	5.42545i	0.0472794	−	0.207144i
$687$	6.98267			0.266406
$688$	−6.46432	−	1.10118i	−0.246450	−	0.0419820i
$689$	5.58247			0.212675
$690$	2.40967	−	10.5575i	0.0917347	−	0.401916i
$691$	20.0253	+	6.17697i	0.761797	+	0.234983i	0.651225	−	0.758885i	$-0.274256\pi$
$691$	20.0253	+	6.17697i	0.761797	+	0.234983i	0.110572	+	0.993868i	$0.464732\pi$
$692$	−20.5049	−	9.87462i	−0.779478	−	0.375377i
$693$	0.00971766	+	0.0247602i	0.000369143	+	0.000940562i
$694$	−0.913280	+	1.58185i	−0.0346676	+	0.0600461i
$695$	6.95916	+	12.0536i	0.263976	+	0.457220i
$696$	8.36817	−	10.4933i	0.317195	−	0.397749i
$697$	−42.3283	−	28.8589i	−1.60330	−	1.09311i
$698$	19.0208	−	2.86693i	0.719949	−	0.108515i
$699$	23.8671	−	11.4938i	0.902736	−	0.434735i
$700$	0.294792	+	0.273527i	0.0111421	+	0.0103383i
$701$	−30.5415	−	4.60339i	−1.15354	−	0.173868i	−0.455706	−	0.890130i	$-0.650613\pi$
$701$	−30.5415	−	4.60339i	−1.15354	−	0.173868i	−0.697831	+	0.716263i	$0.745851\pi$
$702$	4.61810	−	1.42449i	0.174299	−	0.0537641i
$703$	0.0523076	+	0.697996i	0.00197282	+	0.0263254i
$704$	3.10836	+	3.89776i	0.117151	+	0.146902i
$705$	−6.75660	+	17.2155i	−0.254468	+	0.648374i
$706$	−14.6253	+	13.5703i	−0.550429	+	0.510723i
$707$	−0.295341	+	0.201360i	−0.0111074	+	0.00757292i
$708$	0.252464	−	3.36890i	0.00948817	−	0.126611i
$709$	7.55087	+	33.0825i	0.283579	+	1.24244i	0.893168	+	0.449723i	$0.148477\pi$
$709$	7.55087	+	33.0825i	0.283579	+	1.24244i	−0.609589	+	0.792717i	$0.708666\pi$
$710$	−2.49532	−	10.9327i	−0.0936476	−	0.410297i
$711$	−0.00524321	+	0.0699657i	−0.000196636	+	0.00262392i
$712$	4.28242	−	2.91971i	0.160491	−	0.109421i
$713$	28.2137	−	26.1785i	1.05661	−	0.980391i
$714$	1.68597	−	4.29578i	0.0630958	−	0.160765i
$715$	−2.88466	−	3.61725i	−0.107880	−	0.135277i
$716$	0.220501	+	2.94238i	0.00824050	+	0.109962i
$717$	22.5862	−	6.96692i	0.843497	−	0.260184i
$718$	−26.0401	−	3.92491i	−0.971808	−	0.146476i
$719$	21.6019	+	20.0437i	0.805616	+	0.747503i	0.971091	−	0.238711i	$-0.0767250\pi$
$719$	21.6019	+	20.0437i	0.805616	+	0.747503i	−0.165474	+	0.986214i	$0.552915\pi$
$720$	0.0119534	−	0.00575645i	0.000445476	−	0.000214530i
$721$	−1.08975	+	0.164254i	−0.0405846	+	0.00611714i
$722$	15.3382	+	10.4574i	0.570830	+	0.389185i
$723$	27.6823	−	34.7125i	1.02952	−	1.29097i
$724$	−8.53435	−	14.7819i	−0.317177	−	0.549366i
$725$	−3.88305	+	6.72564i	−0.144213	+	0.249784i
$726$	8.74750	+	22.2883i	0.324650	+	0.827195i
$727$	−32.2333	−	15.5227i	−1.19547	−	0.575706i	−0.273086	−	0.961990i	$-0.588044\pi$
$727$	−32.2333	−	15.5227i	−1.19547	−	0.575706i	−0.922380	+	0.386283i	$0.873759\pi$
$728$	−0.356622	−	0.110003i	−0.0132173	−	0.00407699i
$729$	−6.03440	+	26.4384i	−0.223496	+	0.979201i
$730$	−9.63812			−0.356723
$731$	−15.1294	−	40.8287i	−0.559583	−	1.51011i
$732$	−23.1319			−0.854979
$733$	3.68286	−	16.1357i	0.136030	−	0.595985i	−0.860255	−	0.509864i	$-0.829696\pi$
$733$	3.68286	−	16.1357i	0.136030	−	0.595985i	0.996285	−	0.0861210i	$-0.0274472\pi$
$734$	−1.23858	−	0.382050i	−0.0457167	−	0.0141017i
$735$	−10.6477	−	5.12765i	−0.392746	−	0.189136i
$736$	2.28922	+	5.83284i	0.0843818	+	0.215001i
$737$	31.0895	−	53.8486i	1.14520	−	1.98354i
$738$	−0.0511804	−	0.0886471i	−0.00188398	−	0.00326315i
$739$	30.4155	−	38.1398i	1.11885	−	1.40300i	0.214228	−	0.976784i	$-0.431276\pi$
$739$	30.4155	−	38.1398i	1.11885	−	1.40300i	0.904623	−	0.426212i	$-0.140152\pi$
$740$	0.875779	+	0.597096i	0.0321943	+	0.0219497i
$741$	−1.04728	+	0.157852i	−0.0384729	+	0.00579885i
$742$	2.17948	−	1.04958i	0.0800114	−	0.0385315i
$743$	22.0874	+	20.4941i	0.810308	+	0.751856i	0.971999	−	0.234986i	$-0.0755043\pi$
$743$	22.0874	+	20.4941i	0.810308	+	0.751856i	−0.161691	+	0.986841i	$0.551695\pi$
$744$	−10.4968	−	1.58213i	−0.384830	−	0.0580038i
$745$	−0.496426	+	0.153127i	−0.0181876	+	0.00561014i
$746$	0.495644	+	6.61391i	0.0181468	+	0.242152i
$747$	−0.0497817	−	0.0624242i	−0.00182142	−	0.00228398i
$748$	−12.0941	+	30.8151i	−0.442202	+	1.12671i
$749$	−2.88866	+	2.68028i	−0.105549	+	0.0979354i
$750$	1.42792	−	0.973539i	0.0521403	−	0.0355486i
$751$	0.983123	−	13.1189i	0.0358747	−	0.478714i	−0.950114	−	0.311903i	$-0.899034\pi$
$751$	0.983123	−	13.1189i	0.0358747	−	0.478714i	0.985989	−	0.166812i	$-0.0533472\pi$
$752$	−2.38124	−	10.4329i	−0.0868347	−	0.380448i
$753$	−5.53960	−	24.2706i	−0.201874	−	0.884469i
$754$	0.538594	−	7.18704i	0.0196145	−	0.261737i
$755$	6.35923	−	4.33565i	0.231436	−	0.157790i
$756$	1.53515	−	1.42441i	0.0558329	−	0.0518054i
$757$	−15.4084	+	39.2600i	−0.560028	+	1.42693i	0.317895	+	0.948126i	$0.397024\pi$
$757$	−15.4084	+	39.2600i	−0.560028	+	1.42693i	−0.877923	+	0.478802i	$0.841071\pi$
$758$	−20.7460	−	26.0147i	−0.753528	−	0.944895i
$759$	4.03445	+	53.8360i	0.146441	+	1.95412i
$760$	−0.631021	+	0.194644i	−0.0228895	+	0.00706049i
$761$	7.54667	+	1.13748i	0.273567	+	0.0412335i	0.284393	−	0.958708i	$-0.408208\pi$
$761$	7.54667	+	1.13748i	0.273567	+	0.0412335i	−0.0108261	+	0.999941i	$0.503446\pi$
$762$	13.8639	+	12.8638i	0.502236	+	0.466007i
$763$	1.58955	−	0.765487i	0.0575456	−	0.0277125i
$764$	−2.21155	+	0.333338i	−0.0800112	+	0.0120598i
$765$	0.0727878	+	0.0496259i	0.00263165	+	0.00179423i
$766$	−5.20344	+	6.52491i	−0.188008	+	0.235754i
$767$	−0.907066	−	1.57108i	−0.0327523	−	0.0567286i
$768$	0.864108	−	1.49668i	0.0311808	−	0.0540068i
$769$	11.5782	+	29.5009i	0.417522	+	1.06383i	0.972694	+	0.232093i	$0.0745573\pi$
$769$	11.5782	+	29.5009i	0.417522	+	1.06383i	−0.555172	+	0.831736i	$0.687347\pi$
$770$	−1.80631	−	0.869873i	−0.0650949	−	0.0313480i
$771$	−38.9698	−	12.0206i	−1.40346	−	0.432912i
$772$	−4.77407	+	20.9166i	−0.171823	+	0.752804i
$773$	0.487882			0.0175479			0.00877394	−	0.999962i	$-0.497207\pi$
$773$	0.487882			0.0175479			0.00877394	+	0.999962i	$0.497207\pi$
$774$	0.00815963	−	0.0866157i	0.000293292	−	0.00311334i
$775$	6.14236			0.220640
$776$	−4.15306	+	18.1958i	−0.149086	+	0.653189i
$777$	0.703934	+	0.217135i	0.0252535	+	0.00778967i
$778$	−28.2142	−	13.5873i	−1.01153	−	0.487127i
$779$	1.86136	+	4.74268i	0.0666903	+	0.169924i
$780$	−0.801921	+	1.38897i	−0.0287134	+	0.0497330i
$781$	27.9529	+	48.4158i	1.00023	+	1.73245i
$782$	−25.9412	+	32.5293i	−0.927656	+	1.16324i
$783$	33.4152	+	22.7821i	1.19416	+	0.814166i
$784$	6.76190	−	1.01919i	0.241497	−	0.0363997i
$785$	−10.9592	+	5.27768i	−0.391151	+	0.188368i
$786$	−12.0113	−	11.1448i	−0.428428	−	0.397523i
$787$	−45.8479	−	6.91046i	−1.63430	−	0.246331i	−0.733224	−	0.679988i	$-0.761985\pi$
$787$	−45.8479	−	6.91046i	−1.63430	−	0.246331i	−0.901078	+	0.433656i	$0.857223\pi$
$788$	14.3650	−	4.43102i	0.511733	−	0.157849i
$789$	−3.78375	−	50.4906i	−0.134705	−	1.79751i
$790$	−3.29723	−	4.13460i	−0.117310	−	0.147103i
$791$	−1.15451	+	2.94163i	−0.0410495	+	0.104592i
$792$	−0.0484861	+	0.0449885i	−0.00172288	+	0.00159860i
$793$	−10.2632	+	6.99731i	−0.364456	+	0.248482i
$794$	0.897740	−	11.9795i	0.0318596	−	0.425137i
$795$	−2.31330	−	10.1352i	−0.0820443	−	0.359460i
$796$	−1.69600	−	7.43068i	−0.0601133	−	0.263374i
$797$	−0.367770	+	4.90755i	−0.0130271	+	0.173834i	0.986895	+	0.161363i	$0.0515889\pi$
$797$	−0.367770	+	4.90755i	−0.0130271	+	0.173834i	−0.999922	+	0.0124714i	$0.996030\pi$
$798$	−0.379197	+	0.258532i	−0.0134234	+	0.00915193i
$799$	52.0880	−	48.3306i	1.84274	−	1.70982i
$800$	−0.365341	+	0.930874i	−0.0129168	+	0.0329114i
$801$	0.0428740	+	0.0537623i	0.00151488	+	0.00189960i
$802$	0.786854	+	10.4998i	0.0277848	+	0.370762i
$803$	45.9153	−	14.1630i	1.62032	−	0.499802i
$804$	−21.3139	−	3.21255i	−0.751683	−	0.113298i
$805$	−1.84716	−	1.71392i	−0.0651039	−	0.0604076i
$806$	−5.13581	+	2.47327i	−0.180901	+	0.0871174i
$807$	−18.0967	+	2.72763i	−0.637033	+	0.0960172i
$808$	−0.734417	−	0.500717i	−0.0258367	−	0.0176152i
$809$	26.7011	−	33.4821i	0.938761	−	1.17717i	−0.0452340	−	0.998976i	$-0.514403\pi$
$809$	26.7011	−	33.4821i	0.938761	−	1.17717i	0.983996	−	0.178193i	$-0.0570252\pi$
$810$	−4.48001	−	7.75961i	−0.157412	−	0.272645i
$811$	16.6507	−	28.8398i	0.584684	−	1.01270i	−0.410230	−	0.911982i	$-0.634552\pi$
$811$	16.6507	−	28.8398i	0.584684	−	1.01270i	0.994915	−	0.100721i	$-0.0321149\pi$
$812$	−1.14099	−	2.90720i	−0.0400409	−	0.102023i
$813$	−15.5157	−	7.47198i	−0.544161	−	0.262054i
$814$	−5.04957	−	1.55759i	−0.176987	−	0.0545934i
$815$	1.16809	−	5.11773i	0.0409163	−	0.179266i
$816$	11.4755			0.401721
$817$	−1.04415	+	4.20249i	−0.0365300	+	0.147027i
$818$	−4.09855			−0.143302
$819$	0.00110178	−	0.00482723i	3.84994e−5	−	0.000168677i
$820$	7.37253	+	2.27413i	0.257460	+	0.0794159i
$821$	38.8582	+	18.7131i	1.35616	+	0.653093i	0.963777	−	0.266709i	$-0.0859363\pi$
$821$	38.8582	+	18.7131i	1.35616	+	0.653093i	0.392384	+	0.919802i	$0.371651\pi$
$822$	−4.22087	−	10.7546i	−0.147220	−	0.375109i
$823$	−16.1806	+	28.0256i	−0.564019	+	0.976909i	0.433121	+	0.901336i	$0.357412\pi$
$823$	−16.1806	+	28.0256i	−0.564019	+	0.976909i	−0.997140	+	0.0755737i	$0.975921\pi$
$824$	−1.37024	−	2.37332i	−0.0477345	−	0.0826785i
$825$	−5.37191	+	6.73617i	−0.187026	+	0.234523i
$826$	−0.649519	−	0.442835i	−0.0225997	−	0.0154082i
$827$	6.46091	−	0.973825i	0.224668	−	0.0338632i	−0.0357435	−	0.999361i	$-0.511380\pi$
$827$	6.46091	−	0.973825i	0.224668	−	0.0338632i	0.260411	+	0.965498i	$0.416142\pi$
$828$	−0.0748997	+	0.0360698i	−0.00260294	+	0.00125351i
$829$	−18.1791	−	16.8678i	−0.631387	−	0.585842i	0.298173	−	0.954512i	$-0.403623\pi$
$829$	−18.1791	−	16.8678i	−0.631387	−	0.585842i	−0.929560	+	0.368670i	$0.879813\pi$
$830$	5.95088	+	0.896950i	0.206558	+	0.0311336i
$831$	−22.2515	+	6.86368i	−0.771896	+	0.238098i
$832$	−0.0693520	−	0.925438i	−0.00240435	−	0.0320838i
$833$	28.3105	+	35.5003i	0.980902	+	1.23001i
$834$	−8.78786	+	22.3911i	−0.304299	+	0.775341i
$835$	−3.99663	+	3.70833i	−0.138309	+	0.128332i
$836$	2.72011	−	1.85454i	0.0940771	−	0.0641407i
$837$	2.39038	−	31.8974i	0.0826236	−	1.10254i
$838$	−6.07879	−	26.6329i	−0.209988	−	0.920019i
$839$	3.50917	+	15.3747i	0.121150	+	0.530793i	0.998684	+	0.0512791i	$0.0163298\pi$
$839$	3.50917	+	15.3747i	0.121150	+	0.530793i	−0.877534	+	0.479514i	$0.840813\pi$
$840$	−0.0519367	+	0.693047i	−0.00179199	+	0.0239124i
$841$	25.8714	−	17.6388i	0.892117	−	0.608235i
$842$	−5.23706	+	4.85928i	−0.180481	+	0.167462i
$843$	4.14753	−	10.5677i	0.142848	−	0.363972i
$844$	−5.08929	−	6.38177i	−0.175181	−	0.219670i
$845$	−0.907130	−	12.1048i	−0.0312062	−	0.416418i
$846$	0.135668	−	0.0418479i	0.00466435	−	0.00143876i
$847$	5.50922	+	0.830382i	0.189299	+	0.0285323i
$848$	4.40959	+	4.09150i	0.151426	+	0.140503i
$849$	30.6715	−	14.7706i	1.05264	−	0.506926i
$850$	−6.56589	+	0.989649i	−0.225208	+	0.0339447i
$851$	−5.48762	−	3.74140i	−0.188113	−	0.128253i
$852$	12.0832	−	15.1519i	0.413964	−	0.519095i
$853$	−11.7194	−	20.2986i	−0.401265	−	0.695012i	0.592614	−	0.805487i	$-0.298096\pi$
$853$	−11.7194	−	20.2986i	−0.401265	−	0.695012i	−0.993879	+	0.110475i	$0.964763\pi$
$854$	−2.69131	+	4.66148i	−0.0920947	+	0.159513i
$855$	−0.00320081	−	0.00815552i	−0.000109465	−	0.000278913i
$856$	−8.82857	−	4.25161i	−0.301754	−	0.145317i
$857$	−27.0229	−	8.33545i	−0.923083	−	0.284733i	−0.203448	−	0.979086i	$-0.565215\pi$
$857$	−27.0229	−	8.33545i	−0.923083	−	0.284733i	−0.719635	+	0.694352i	$0.755691\pi$
$858$	1.77924	−	7.79535i	0.0607422	−	0.266129i
$859$	−9.03667			−0.308327			−0.154164	−	0.988045i	$-0.549268\pi$
$859$	−9.03667			−0.308327			−0.154164	+	0.988045i	$0.549268\pi$
$860$	3.98969	+	5.20407i	0.136047	+	0.177457i
$861$	5.36206			0.182739
$862$	7.38712	−	32.3651i	0.251606	−	1.10236i
$863$	35.6094	+	10.9841i	1.21216	+	0.373902i	0.833961	−	0.551823i	$-0.186068\pi$
$863$	35.6094	+	10.9841i	1.21216	+	0.373902i	0.378198	+	0.925725i	$0.376544\pi$
$864$	4.69187	+	2.25948i	0.159621	+	0.0768692i
$865$	8.31468	+	21.1855i	0.282708	+	0.720327i
$866$	0.185827	−	0.321861i	0.00631465	−	0.0109373i
$867$	23.4090	+	40.5456i	0.795011	+	1.37700i
$868$	−1.54009	+	1.93121i	−0.0522740	+	0.0655495i
$869$	21.7835	+	14.8517i	0.738955	+	0.503811i
$870$	−13.2716	+	2.00037i	−0.449949	+	0.0678189i
$871$	−10.4284	+	5.02203i	−0.353351	+	0.170165i
$872$	3.21602	+	2.98403i	0.108908	+	0.101052i
$873$	−0.244850	−	0.0369052i	−0.00828693	−	0.00124905i
$874$	3.95397	−	1.21964i	0.133745	−	0.0412549i
$875$	−0.0300522	−	0.401019i	−0.00101595	−	0.0135569i
$876$	−10.3853	−	13.0228i	−0.350888	−	0.439999i
$877$	1.24684	−	3.17689i	0.0421027	−	0.107276i	−0.908276	−	0.418372i	$-0.862601\pi$
$877$	1.24684	−	3.17689i	0.0421027	−	0.107276i	0.950378	+	0.311096i	$0.100696\pi$
$878$	18.2563	−	16.9393i	0.616119	−	0.571675i
$879$	23.9838	−	16.3519i	0.808954	−	0.551536i
$880$	0.372561	−	4.97148i	0.0125590	−	0.167588i
$881$	0.0551761	+	0.241742i	0.00185893	+	0.00814451i	0.975849	−	0.218447i	$-0.0700990\pi$
$881$	0.0551761	+	0.241742i	0.00185893	+	0.00814451i	−0.973990	+	0.226591i	$0.927242\pi$
$882$	0.0201883	+	0.0884505i	0.000679774	+	0.00297828i
$883$	3.13005	−	41.7676i	0.105334	−	1.40559i	−0.654789	−	0.755812i	$-0.727243\pi$
$883$	3.13005	−	41.7676i	0.105334	−	1.40559i	0.760124	−	0.649779i	$-0.225138\pi$
$884$	5.09144	−	3.47129i	0.171244	−	0.116752i
$885$	−2.47650	+	2.29786i	−0.0832466	+	0.0772416i
$886$	−3.39164	+	8.64177i	−0.113944	+	0.290326i
$887$	−1.38562	−	1.73751i	−0.0465244	−	0.0583398i	0.758025	−	0.652226i	$-0.226165\pi$
$887$	−1.38562	−	1.73751i	−0.0465244	−	0.0583398i	−0.804549	+	0.593886i	$0.797593\pi$
$888$	0.136894	+	1.82672i	0.00459385	+	0.0613006i
$889$	4.20530	−	1.29716i	0.141041	−	0.0435055i
$890$	−5.12514	−	0.772491i	−0.171795	−	0.0258940i
$891$	32.7450	+	30.3829i	1.09700	+	1.01787i
$892$	−2.81566	+	1.35595i	−0.0942753	+	0.0454006i
$893$	−6.98769	+	1.05322i	−0.233834	+	0.0352448i
$894$	−0.741813	−	0.505760i	−0.0248099	−	0.0169151i
$895$	1.83969	−	2.30690i	0.0614940	−	0.0771110i
$896$	−0.201072	−	0.348266i	−0.00671733	−	0.0116348i
$897$	5.02482	−	8.70325i	0.167774	−	0.290593i
$898$	8.50543	+	21.6715i	0.283830	+	0.723187i
$899$	−42.9782	−	20.6972i	−1.43340	−	0.690290i
$900$	−0.0126778	−	0.00391059i	−0.000422594	−	0.000130353i
$901$	−8.88804	+	38.9410i	−0.296103	+	1.29731i
$902$	−38.4640			−1.28071
$903$	3.71567	+	2.63880i	0.123650	+	0.0878139i
$904$	−7.85809			−0.261356
$905$	−3.79814	+	16.6408i	−0.126255	+	0.553157i
$906$	12.7105	+	3.92065i	0.422276	+	0.130255i
$907$	−18.0913	−	8.71230i	−0.600711	−	0.289287i	0.108708	−	0.994074i	$-0.465329\pi$
$907$	−18.0913	−	8.71230i	−0.600711	−	0.289287i	−0.709420	+	0.704786i	$0.751043\pi$
$908$	−4.84674	−	12.3493i	−0.160845	−	0.409825i
$909$	0.00589641	−	0.0102129i	0.000195572	−	0.000338740i
$910$	0.186601	+	0.323203i	0.00618577	+	0.0107141i
$911$	27.4979	−	34.4813i	0.911046	−	1.14242i	−0.0783142	−	0.996929i	$-0.524954\pi$
$911$	27.4979	−	34.4813i	0.911046	−	1.14242i	0.989360	−	0.145487i	$-0.0464748\pi$
$912$	−0.942940	−	0.642885i	−0.0312238	−	0.0212881i
$913$	−29.6676	+	4.47167i	−0.981855	+	0.147991i
$914$	−4.64807	+	2.23839i	−0.153745	+	0.0740395i
$915$	16.9569	+	15.7337i	0.560577	+	0.520139i
$916$	3.99526	+	0.602189i	0.132007	+	0.0198969i
$917$	−3.64335	+	1.12383i	−0.120314	+	0.0371120i
$918$	2.58406	+	34.4819i	0.0852868	+	1.13807i
$919$	5.70142	+	7.14935i	0.188072	+	0.235835i	0.866924	−	0.498440i	$-0.166094\pi$
$919$	5.70142	+	7.14935i	0.188072	+	0.235835i	−0.678852	+	0.734275i	$0.737522\pi$
$920$	2.28922	−	5.83284i	0.0754734	−	0.192303i
$921$	−11.4107	+	10.5876i	−0.375995	+	0.348872i
$922$	−25.1089	+	17.1189i	−0.826916	+	0.563782i
$923$	0.777704	−	10.3777i	0.0255984	−	0.341587i
$924$	−0.770995	−	3.37795i	−0.0253639	−	0.111126i
$925$	−0.235863	−	1.03338i	−0.00775513	−	0.0339774i
$926$	−0.747691	+	9.97725i	−0.0245707	+	0.327873i
$927$	0.0300408	−	0.0204815i	0.000986671	−	0.000672701i
$928$	5.69295	−	5.28229i	0.186880	−	0.173400i
$929$	−0.769272	+	1.96007i	−0.0252390	+	0.0643079i	−0.942938	−	0.332969i	$-0.891950\pi$
$929$	−0.769272	+	1.96007i	−0.0252390	+	0.0643079i	0.917699	+	0.397277i	$0.130045\pi$
$930$	6.61855	+	8.29940i	0.217031	+	0.272148i
$931$	−0.337460	−	4.50309i	−0.0110598	−	0.147583i
$932$	14.6472	−	4.51807i	0.479786	−	0.147994i
$933$	24.2296	+	3.65202i	0.793241	+	0.119562i
$934$	−10.4857	−	9.72928i	−0.343102	−	0.318352i
$935$	29.8252	−	14.3631i	0.975388	−	0.469722i
$936$	0.0121749	−	0.00183508i	0.000397950	−	5.99813e-5i
$937$	−35.7216	−	24.3546i	−1.16697	−	0.795629i	−0.184646	−	0.982805i	$-0.559114\pi$
$937$	−35.7216	−	24.3546i	−1.16697	−	0.795629i	−0.982326	+	0.187176i	$0.940066\pi$
$938$	−3.12718	+	3.92136i	−0.102106	+	0.128037i
$939$	−3.75372	−	6.50163i	−0.122498	−	0.212173i
$940$	−5.35059	+	9.26749i	−0.174517	+	0.302272i
$941$	−5.84855	−	14.9019i	−0.190657	−	0.485787i	0.803297	−	0.595578i	$-0.203077\pi$
$941$	−5.84855	−	14.9019i	−0.190657	−	0.485787i	−0.993955	+	0.109791i	$0.964982\pi$
$942$	−18.9399	−	9.12097i	−0.617095	−	0.297177i
$943$	−46.1962	−	14.2496i	−1.50435	−	0.464032i
$944$	0.434987	−	1.90580i	0.0141576	−	0.0620286i
$945$	−2.09419			−0.0681241
$946$	−26.6539	−	18.9291i	−0.866592	−	0.615438i
$947$	18.1825			0.590852			0.295426	−	0.955366i	$-0.404538\pi$
$947$	18.1825			0.590852			0.295426	+	0.955366i	$0.404538\pi$
$948$	2.03371	−	8.91028i	0.0660519	−	0.289392i
$949$	−8.54712	−	2.63644i	−0.277451	−	0.0855824i
$950$	0.594963	+	0.286519i	0.0193031	+	0.00929590i
$951$	13.5724	+	34.5820i	0.440116	+	1.12140i
$952$	1.33513	−	2.31251i	0.0432717	−	0.0749488i
$953$	−28.6054	−	49.5461i	−0.926621	−	1.60495i	−0.788934	−	0.614478i	$-0.789367\pi$
$953$	−28.6054	−	49.5461i	−0.926621	−	1.60495i	−0.137687	−	0.990476i	$-0.543967\pi$
$954$	−0.0497592	+	0.0623961i	−0.00161101	+	0.00202015i
$955$	1.84791	+	1.25988i	0.0597970	+	0.0407689i
$956$	13.5239	−	2.03841i	0.437396	−	0.0659268i
$957$	60.2854	−	29.0319i	1.94875	−	0.938469i
$958$	6.81263	+	6.32120i	0.220106	+	0.204229i
$959$	−2.65832	−	0.400678i	−0.0858417	−	0.0129386i
$960$	−1.65144	+	0.509401i	−0.0532999	+	0.0164408i
$961$	0.502831	+	6.70981i	0.0162204	+	0.216446i
$962$	0.613313	+	0.769070i	0.0197740	+	0.0247958i
$963$	0.0474963	−	0.121019i	0.00153055	−	0.00389977i
$964$	18.8326	−	17.4741i	0.606556	−	0.562802i
$965$	17.7265	−	12.0857i	0.570637	−	0.389054i
$966$	0.325435	−	4.34262i	0.0104707	−	0.139722i
$967$	10.8388	+	47.4879i	0.348552	+	1.52711i	0.780469	+	0.625194i	$0.214980\pi$
$967$	10.8388	+	47.4879i	0.348552	+	1.52711i	−0.431917	+	0.901913i	$0.642163\pi$
$968$	3.08289	+	13.5070i	0.0990879	+	0.434133i
$969$	0.566299	−	7.55673i	0.0181921	−	0.242757i
$970$	15.4207	−	10.5136i	0.495128	−	0.337572i
$971$	−5.29144	+	4.90974i	−0.169811	+	0.157561i	−0.760500	−	0.649338i	$-0.775046\pi$
$971$	−5.29144	+	4.90974i	−0.169811	+	0.157561i	0.590690	+	0.806899i	$0.298856\pi$
$972$	−0.0503719	+	0.128345i	−0.00161568	+	0.00411668i
$973$	3.48977	+	4.37603i	0.111877	+	0.140289i
$974$	−2.41534	−	32.2305i	−0.0773926	−	1.03273i
$975$	1.53259	−	0.472741i	0.0490821	−	0.0151398i
$976$	−13.2353	−	1.99490i	−0.423652	−	0.0638553i
$977$	−24.0672	−	22.3311i	−0.769979	−	0.714436i	0.193829	−	0.981035i	$-0.437909\pi$
$977$	−24.0672	−	22.3311i	−0.769979	−	0.714436i	−0.963807	+	0.266600i	$0.914100\pi$
$978$	8.17359	−	3.93619i	0.261362	−	0.125866i
$979$	25.5510	−	3.85119i	0.816613	−	0.123085i
$980$	−5.65005	−	3.85214i	−0.180484	−	0.123052i
$981$	−0.0362906	+	0.0455070i	−0.00115867	+	0.00145293i
$982$	21.3402	+	36.9623i	0.680993	+	1.17951i
$983$	−20.3330	+	35.2177i	−0.648521	+	1.12327i	0.334955	+	0.942234i	$0.391279\pi$
$983$	−20.3330	+	35.2177i	−0.648521	+	1.12327i	−0.983476	+	0.181037i	$0.942055\pi$
$984$	4.87135	+	12.4120i	0.155293	+	0.395680i
$985$	−13.5442	−	6.52253i	−0.431553	−	0.207825i
$986$	49.2763	+	15.1997i	1.56928	+	0.484058i
$987$	−1.65494	+	7.25075i	−0.0526772	+	0.230794i
$988$	−0.612835			−0.0194969
$989$	−24.9993	−	32.6086i	−0.794932	−	1.03689i
$990$	0.0661428			0.00210216
$991$	4.62167	−	20.2489i	0.146812	−	0.643226i	−0.846947	−	0.531678i	$-0.821562\pi$
$991$	4.62167	−	20.2489i	0.146812	−	0.643226i	0.993759	−	0.111549i	$-0.0355811\pi$
$992$	−5.86948	−	1.81049i	−0.186356	−	0.0574832i
$993$	−30.9088	−	14.8849i	−0.980861	−	0.472358i
$994$	−1.64753	−	4.19785i	−0.0522566	−	0.133148i
$995$	−3.81089	+	6.60065i	−0.120813	+	0.209255i
$996$	5.20029	+	9.00716i	0.164777	+	0.285403i
$997$	−8.26461	+	10.3635i	−0.261743	+	0.328215i	−0.895286	−	0.445492i	$-0.853029\pi$
$997$	−8.26461	+	10.3635i	−0.261743	+	0.328215i	0.633543	+	0.773708i	$0.281600\pi$
$998$	19.9764	+	13.6197i	0.632342	+	0.431123i
$999$	−5.45817	+	0.822687i	−0.172689	+	0.0260287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.81.1	✓	48
43.17	even	21	inner	430.2.q.c.361.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.81.1	✓	48	1.1	even	1	trivial
430.2.q.c.361.1	yes	48	43.17	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(-1.65144 - 0.509401i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(-0.864108 + 1.49668i) q^{6} +(0.201072 + 0.348266i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-0.0109619 - 0.00747371i) q^{9} +O(q^{10})\)	\(q+(0.222521 - 0.974928i) q^{2} +(-1.65144 - 0.509401i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(-0.864108 + 1.49668i) q^{6} +(0.201072 + 0.348266i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-0.0109619 - 0.00747371i) q^{9} +(0.988831 - 0.149042i) q^{10} +(-4.49171 + 2.16309i) q^{11} +(1.26687 + 1.17549i) q^{12} +(0.917668 + 0.138316i) q^{13} +(0.384277 - 0.118534i) q^{14} +(-0.129150 - 1.72338i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-2.42589 + 6.18105i) q^{17} +(-0.00972558 + 0.00902402i) q^{18} +(0.545614 - 0.371993i) q^{19} +(0.0747301 - 0.997204i) q^{20} +(-0.154650 - 0.677566i) q^{21} +(1.10936 + 4.86042i) q^{22} +(-0.468258 + 6.24846i) q^{23} +(1.42792 - 0.973539i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(0.339049 - 0.863882i) q^{26} +(3.24687 + 4.07145i) q^{27} +(-0.0300522 - 0.401019i) q^{28} +(7.42107 - 2.28910i) q^{29} +(-1.70891 - 0.257577i) q^{30} +(-4.50267 - 4.17787i) q^{31} +(0.900969 - 0.433884i) q^{32} +(8.51965 - 1.28413i) q^{33} +(5.48627 + 3.74048i) q^{34} +(-0.250732 + 0.314408i) q^{35} +(0.00663363 + 0.0114898i) q^{36} +(-0.529980 + 0.917952i) q^{37} +(-0.241256 - 0.614711i) q^{38} +(-1.44501 - 0.695881i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(-1.71682 + 7.52186i) q^{41} -0.694991 q^{42} +(-4.89137 + 4.36743i) q^{43} +4.98542 q^{44} +(0.00295224 - 0.0129346i) q^{45} +(5.98760 + 1.84693i) q^{46} +(-9.64143 - 4.64307i) q^{47} +(-0.631388 - 1.60875i) q^{48} +(3.41914 - 5.92212i) q^{49} +(0.500000 + 0.866025i) q^{50} +(7.15483 - 8.97187i) q^{51} +(-0.766777 - 0.522780i) q^{52} +(5.94819 - 0.896546i) q^{53} +(4.69187 - 2.25948i) q^{54} +(-3.65457 - 3.39095i) q^{55} +(-0.397652 - 0.0599363i) q^{56} +(-1.09054 + 0.336387i) q^{57} +(-0.580361 - 7.74438i) q^{58} +(-1.21881 - 1.52834i) q^{59} +(-0.631388 + 1.60875i) q^{60} +(-9.81177 + 9.10399i) q^{61} +(-5.07506 + 3.46012i) q^{62} +(0.000398710 - 0.00532042i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.206507 + 0.904765i) q^{65} +(0.643866 - 8.59179i) q^{66} +(-10.3050 + 7.02583i) q^{67} +(4.86751 - 4.51639i) q^{68} +(3.95627 - 10.0804i) q^{69} +(0.250732 + 0.314408i) q^{70} +(-0.838013 - 11.1825i) q^{71} +(0.0126778 - 0.00391059i) q^{72} +(-9.53047 - 1.43649i) q^{73} +(0.777005 + 0.720955i) q^{74} +(1.55707 - 0.749845i) q^{75} +(-0.652983 + 0.0984214i) q^{76} +(-1.65649 - 1.12937i) q^{77} +(-0.999979 + 1.25393i) q^{78} +(-2.64418 - 4.57985i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.27346 - 8.34065i) q^{81} +(6.95125 + 3.34754i) q^{82} +(5.75073 + 1.77386i) q^{83} +(-0.154650 + 0.677566i) q^{84} -6.64006 q^{85} +(3.16950 + 5.74058i) q^{86} -13.4215 q^{87} +(1.10936 - 4.86042i) q^{88} +(-4.95277 - 1.52773i) q^{89} +(-0.0119534 - 0.00575645i) q^{90} +(0.136346 + 0.347404i) q^{91} +(3.13299 - 5.42650i) q^{92} +(5.30767 + 9.19315i) q^{93} +(-6.67207 + 8.36652i) q^{94} +(0.545614 + 0.371993i) q^{95} +(-1.70891 + 0.257577i) q^{96} +(16.8154 - 8.09787i) q^{97} +(-5.01281 - 4.65121i) q^{98} +(0.0654040 + 0.00985807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

L-functions

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