LMFDB - Embedded newform 78.2.g.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(5,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("78.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.g (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:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.58498535041007616.52
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 $ x^12 - 12x^9 + 72x^6 - 324*x^3 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.6
Root			$1.72927 - 0.0980500i$ of defining polynomial
Character	$\chi$	$=$	78.47
Dual form			78.2.g.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.29211 - 1.15345i) q^{3} -1.00000i q^{4} +(-1.82732 + 1.82732i) q^{5} +(0.0980500 - 1.72927i) q^{6} +(-2.63122 + 2.63122i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.339111 - 2.98077i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.29211 - 1.15345i) q^{3} -1.00000i q^{4} +(-1.82732 + 1.82732i) q^{5} +(0.0980500 - 1.72927i) q^{6} +(-2.63122 + 2.63122i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.339111 - 2.98077i) q^{9} +2.58423i q^{10} +(2.30690 + 2.30690i) q^{11} +(-1.15345 - 1.29211i) q^{12} +(1.63122 - 3.21545i) q^{13} +3.72111i q^{14} +(-0.253383 + 4.46883i) q^{15} -1.00000 q^{16} +1.34775 q^{17} +(-1.86794 - 2.34751i) q^{18} +(-3.58423 - 3.58423i) q^{19} +(1.82732 + 1.82732i) q^{20} +(-0.364855 + 6.43482i) q^{21} +3.26245 q^{22} -3.65465 q^{23} +(-1.72927 - 0.0980500i) q^{24} -1.67822i q^{25} +(-1.12022 - 3.42711i) q^{26} +(-3.00000 - 4.24264i) q^{27} +(2.63122 + 2.63122i) q^{28} +3.65465i q^{29} +(2.98077 + 3.33911i) q^{30} +(0.321779 + 0.321779i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.64166 + 0.319883i) q^{33} +(0.953002 - 0.953002i) q^{34} -9.61619i q^{35} +(-2.98077 - 0.339111i) q^{36} +(1.95300 - 1.95300i) q^{37} -5.06886 q^{38} +(-1.60113 - 6.03626i) q^{39} +2.58423 q^{40} +(7.89729 - 7.89729i) q^{41} +(4.29211 + 4.80810i) q^{42} +9.10912i q^{43} +(2.30690 - 2.30690i) q^{44} +(4.82717 + 6.06650i) q^{45} +(-2.58423 + 2.58423i) q^{46} +(-4.72222 - 4.72222i) q^{47} +(-1.29211 + 1.15345i) q^{48} -6.84667i q^{49} +(-1.18668 - 1.18668i) q^{50} +(1.74144 - 1.55456i) q^{51} +(-3.21545 - 1.63122i) q^{52} +0.216838i q^{53} +(-5.12132 - 0.878680i) q^{54} -8.43090 q^{55} +3.72111 q^{56} +(-8.76544 - 0.497002i) q^{57} +(2.58423 + 2.58423i) q^{58} +(3.65465 + 3.65465i) q^{59} +(4.46883 + 0.253383i) q^{60} +6.52489 q^{61} +0.455064 q^{62} +(6.95080 + 8.73535i) q^{63} +1.00000i q^{64} +(2.89489 + 8.85644i) q^{65} +(4.21545 - 3.76307i) q^{66} +(2.26245 + 2.26245i) q^{67} -1.34775i q^{68} +(-4.72222 + 4.21545i) q^{69} +(-6.79967 - 6.79967i) q^{70} +(-0.108419 + 0.108419i) q^{71} +(-2.34751 + 1.86794i) q^{72} +(-3.58423 + 3.58423i) q^{73} -2.76196i q^{74} +(-1.93574 - 2.16845i) q^{75} +(-3.58423 + 3.58423i) q^{76} -12.1399 q^{77} +(-5.40045 - 3.13611i) q^{78} +4.09400 q^{79} +(1.82732 - 1.82732i) q^{80} +(-8.77001 - 2.02162i) q^{81} -11.1685i q^{82} +(-10.5753 + 10.5753i) q^{83} +(6.43482 + 0.364855i) q^{84} +(-2.46277 + 2.46277i) q^{85} +(6.44112 + 6.44112i) q^{86} +(4.21545 + 4.72222i) q^{87} -3.26245i q^{88} +(-8.85644 - 8.85644i) q^{89} +(7.70299 + 0.876338i) q^{90} +(4.16845 + 12.7527i) q^{91} +3.65465i q^{92} +(0.786930 + 0.0446190i) q^{93} -6.67822 q^{94} +13.0991 q^{95} +(-0.0980500 + 1.72927i) q^{96} +(0.168451 + 0.168451i) q^{97} +(-4.84133 - 4.84133i) q^{98} +(7.65863 - 6.09404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{7}+O(q^{10}) $ 12 * q - 12 * q^7	$ 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^7 - 12 * q^16 - 12 * q^19 - 36 * q^27 + 12 * q^28 + 12 * q^31 + 36 * q^33 + 12 * q^37 + 36 * q^42 + 36 * q^45 + 12 * q^52 - 36 * q^54 - 36 * q^57 - 36 * q^63 - 12 * q^67 - 12 * q^73 - 12 * q^76 - 36 * q^78 + 72 * q^79 - 72 * q^85 - 12 * q^91 + 36 * q^93 - 72 * q^94 - 60 * q^97 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.29211	−	1.15345i	0.746002	−	0.665944i
$3$	1.29211	−	1.15345i	0.746002	−	0.665944i
$4$		−	1.00000i		−	0.500000i
$5$	−1.82732	+	1.82732i	−0.817204	+	0.817204i	−0.985702	−	0.168498i	$-0.946108\pi$
$5$	−1.82732	+	1.82732i	−0.817204	+	0.817204i	0.168498	+	0.985702i	$0.446108\pi$
$6$	0.0980500	−	1.72927i	0.0400288	−	0.705973i
$7$	−2.63122	+	2.63122i	−0.994509	+	0.994509i	−0.999985	−	0.00547608i	$-0.998257\pi$
$7$	−2.63122	+	2.63122i	−0.994509	+	0.994509i	0.00547608	+	0.999985i	$0.498257\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.339111	−	2.98077i	0.113037	−	0.993591i
$10$			2.58423i			0.817204i
$11$	2.30690	+	2.30690i	0.695556	+	0.695556i	0.963449	−	0.267893i	$-0.0863273\pi$
$11$	2.30690	+	2.30690i	0.695556	+	0.695556i	−0.267893	+	0.963449i	$0.586327\pi$
$12$	−1.15345	−	1.29211i	−0.332972	−	0.373001i
$13$	1.63122	−	3.21545i	0.452420	−	0.891805i
$13$	1.63122	−	3.21545i	0.452420	−	0.891805i
$14$			3.72111i			0.994509i
$15$	−0.253383	+	4.46883i	−0.0654233	+	1.15385i
$16$	−1.00000			−0.250000
$17$	1.34775			0.326877			0.163439	−	0.986554i	$-0.447741\pi$
$17$	1.34775			0.326877			0.163439	+	0.986554i	$0.447741\pi$
$18$	−1.86794	−	2.34751i	−0.440277	−	0.553314i
$19$	−3.58423	−	3.58423i	−0.822278	−	0.822278i	0.164157	−	0.986434i	$-0.447510\pi$
$19$	−3.58423	−	3.58423i	−0.822278	−	0.822278i	−0.986434	+	0.164157i	$0.947510\pi$
$20$	1.82732	+	1.82732i	0.408602	+	0.408602i
$21$	−0.364855	+	6.43482i	−0.0796179	+	1.40419i
$22$	3.26245			0.695556
$23$	−3.65465			−0.762047			−0.381023	−	0.924565i	$-0.624428\pi$
$23$	−3.65465			−0.762047			−0.381023	+	0.924565i	$0.624428\pi$
$24$	−1.72927	−	0.0980500i	−0.352986	−	0.0200144i
$25$		−	1.67822i		−	0.335644i
$26$	−1.12022	−	3.42711i	−0.219693	−	0.672112i
$27$	−3.00000	−	4.24264i	−0.577350	−	0.816497i
$28$	2.63122	+	2.63122i	0.497254	+	0.497254i
$29$			3.65465i			0.678651i	0.940669	+	0.339325i	$0.110199\pi$
$29$			3.65465i			0.678651i	−0.940669	+	0.339325i	$0.889801\pi$
$30$	2.98077	+	3.33911i	0.544212	+	0.609635i
$31$	0.321779	+	0.321779i	0.0577932	+	0.0577932i	0.735413	−	0.677619i	$-0.236988\pi$
$31$	0.321779	+	0.321779i	0.0577932	+	0.0577932i	−0.677619	+	0.735413i	$0.736988\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	5.64166	+	0.319883i	0.982087	+	0.0556845i
$34$	0.953002	−	0.953002i	0.163439	−	0.163439i
$35$		−	9.61619i		−	1.62543i
$36$	−2.98077	−	0.339111i	−0.496795	−	0.0565184i
$37$	1.95300	−	1.95300i	0.321072	−	0.321072i	−0.528107	−	0.849178i	$-0.677098\pi$
$37$	1.95300	−	1.95300i	0.321072	−	0.321072i	0.849178	+	0.528107i	$0.177098\pi$
$38$	−5.06886			−0.822278
$39$	−1.60113	−	6.03626i	−0.256386	−	0.966574i
$40$	2.58423			0.408602
$41$	7.89729	−	7.89729i	1.23335	−	1.23335i	0.270680	−	0.962670i	$-0.412752\pi$
$41$	7.89729	−	7.89729i	1.23335	−	1.23335i	0.962670	−	0.270680i	$-0.0872484\pi$
$42$	4.29211	+	4.80810i	0.662287	+	0.741905i
$43$			9.10912i			1.38913i	0.719431	+	0.694564i	$0.244403\pi$
$43$			9.10912i			1.38913i	−0.719431	+	0.694564i	$0.755597\pi$
$44$	2.30690	−	2.30690i	0.347778	−	0.347778i
$45$	4.82717	+	6.06650i	0.719592	+	0.904340i
$46$	−2.58423	+	2.58423i	−0.381023	+	0.381023i
$47$	−4.72222	−	4.72222i	−0.688806	−	0.688806i	0.273162	−	0.961968i	$-0.411930\pi$
$47$	−4.72222	−	4.72222i	−0.688806	−	0.688806i	−0.961968	+	0.273162i	$0.911930\pi$
$48$	−1.29211	+	1.15345i	−0.186500	+	0.166486i
$49$		−	6.84667i		−	0.978096i
$50$	−1.18668	−	1.18668i	−0.167822	−	0.167822i
$51$	1.74144	−	1.55456i	0.243851	−	0.217682i
$52$	−3.21545	−	1.63122i	−0.445903	−	0.226210i
$53$			0.216838i			0.0297851i	0.999889	+	0.0148925i	$0.00474061\pi$
$53$			0.216838i			0.0297851i	−0.999889	+	0.0148925i	$0.995259\pi$
$54$	−5.12132	−	0.878680i	−0.696923	−	0.119573i
$55$	−8.43090			−1.13682
$56$	3.72111			0.497254
$57$	−8.76544	−	0.497002i	−1.16101	−	0.0658295i
$58$	2.58423	+	2.58423i	0.339325	+	0.339325i
$59$	3.65465	+	3.65465i	0.475794	+	0.475794i	0.903784	−	0.427989i	$-0.140778\pi$
$59$	3.65465	+	3.65465i	0.475794	+	0.475794i	−0.427989	+	0.903784i	$0.640778\pi$
$60$	4.46883	+	0.253383i	0.576924	+	0.0327117i
$61$	6.52489			0.835427			0.417713	−	0.908579i	$-0.362832\pi$
$61$	6.52489			0.835427			0.417713	+	0.908579i	$0.362832\pi$
$62$	0.455064			0.0577932
$63$	6.95080	+	8.73535i	0.875719	+	1.10055i
$64$			1.00000i			0.125000i
$65$	2.89489	+	8.85644i	0.359067	+	1.09851i
$66$	4.21545	−	3.76307i	0.518886	−	0.463201i
$67$	2.26245	+	2.26245i	0.276402	+	0.276402i	0.831671	−	0.555269i	$-0.187385\pi$
$67$	2.26245	+	2.26245i	0.276402	+	0.276402i	−0.555269	+	0.831671i	$0.687385\pi$
$68$		−	1.34775i		−	0.163439i
$69$	−4.72222	+	4.21545i	−0.568488	+	0.507480i
$70$	−6.79967	−	6.79967i	−0.812717	−	0.812717i
$71$	−0.108419	+	0.108419i	−0.0128670	+	0.0128670i	−0.713511	−	0.700644i	$-0.752896\pi$
$71$	−0.108419	+	0.108419i	−0.0128670	+	0.0128670i	0.700644	+	0.713511i	$0.252896\pi$
$72$	−2.34751	+	1.86794i	−0.276657	+	0.220138i
$73$	−3.58423	+	3.58423i	−0.419502	+	0.419502i	−0.885032	−	0.465530i	$-0.845864\pi$
$73$	−3.58423	+	3.58423i	−0.419502	+	0.419502i	0.465530	+	0.885032i	$0.345864\pi$
$74$		−	2.76196i		−	0.321072i
$75$	−1.93574	−	2.16845i	−0.223520	−	0.250391i
$76$	−3.58423	+	3.58423i	−0.411139	+	0.411139i
$77$	−12.1399			−1.38347
$78$	−5.40045	−	3.13611i	−0.611480	−	0.355094i
$79$	4.09400			0.460611			0.230305	−	0.973118i	$-0.426028\pi$
$79$	4.09400			0.460611			0.230305	+	0.973118i	$0.426028\pi$
$80$	1.82732	−	1.82732i	0.204301	−	0.204301i
$81$	−8.77001	−	2.02162i	−0.974445	−	0.224625i
$82$		−	11.1685i		−	1.23335i
$83$	−10.5753	+	10.5753i	−1.16079	+	1.16079i	−0.176492	+	0.984302i	$0.556475\pi$
$83$	−10.5753	+	10.5753i	−1.16079	+	1.16079i	−0.984302	+	0.176492i	$0.943525\pi$
$84$	6.43482	+	0.364855i	0.702096	+	0.0398090i
$85$	−2.46277	+	2.46277i	−0.267125	+	0.267125i
$86$	6.44112	+	6.44112i	0.694564	+	0.694564i
$87$	4.21545	+	4.72222i	0.451944	+	0.506275i
$88$		−	3.26245i		−	0.347778i
$89$	−8.85644	−	8.85644i	−0.938780	−	0.938780i	0.0594508	−	0.998231i	$-0.481065\pi$
$89$	−8.85644	−	8.85644i	−0.938780	−	0.938780i	−0.998231	+	0.0594508i	$0.981065\pi$
$90$	7.70299	+	0.876338i	0.811966	+	0.0923742i
$91$	4.16845	+	12.7527i	0.436972	+	1.33684i
$92$			3.65465i			0.381023i
$93$	0.786930	+	0.0446190i	0.0816008	+	0.00462678i
$94$	−6.67822			−0.688806
$95$	13.0991			1.34394
$96$	−0.0980500	+	1.72927i	−0.0100072	+	0.176493i
$97$	0.168451	+	0.168451i	0.0171036	+	0.0171036i	0.715607	−	0.698503i	$-0.246150\pi$
$97$	0.168451	+	0.168451i	0.0171036	+	0.0171036i	−0.698503	+	0.715607i	$0.746150\pi$
$98$	−4.84133	−	4.84133i	−0.489048	−	0.489048i
$99$	7.65863	−	6.09404i	0.769721	−	0.612475i
$100$	−1.67822			−0.167822
$101$	17.7129			1.76250			0.881248	−	0.472653i	$-0.156704\pi$
$101$	17.7129			1.76250			0.881248	+	0.472653i	$0.156704\pi$
$102$	0.132147	−	2.33063i	0.0130845	−	0.230766i
$103$		−	7.90600i		−	0.779002i	−0.921026	−	0.389501i	$-0.872648\pi$
$103$		−	7.90600i		−	0.779002i	0.921026	−	0.389501i	$-0.127352\pi$
$104$	−3.42711	+	1.12022i	−0.336056	+	0.109846i
$105$	−11.0918	−	12.4252i	−1.08245	−	1.21258i
$106$	0.153328	+	0.153328i	0.0148925	+	0.0148925i
$107$		−	4.61380i		−	0.446033i	−0.974815	−	0.223016i	$-0.928410\pi$
$107$		−	4.61380i		−	0.446033i	0.974815	−	0.223016i	$-0.0715903\pi$
$108$	−4.24264	+	3.00000i	−0.408248	+	0.288675i
$109$	9.21545	+	9.21545i	0.882680	+	0.882680i	0.993806	−	0.111126i	$-0.0354458\pi$
$109$	9.21545	+	9.21545i	0.882680	+	0.882680i	−0.111126	+	0.993806i	$0.535446\pi$
$110$	−5.96154	+	5.96154i	−0.568411	+	0.568411i
$111$	0.270810	−	4.77619i	0.0257042	−	0.453336i
$112$	2.63122	−	2.63122i	0.248627	−	0.248627i
$113$			3.43781i			0.323402i	0.986840	+	0.161701i	$0.0516980\pi$
$113$			3.43781i			0.323402i	−0.986840	+	0.161701i	$0.948302\pi$
$114$	−6.54954	+	5.84667i	−0.613421	+	0.547591i
$115$	6.67822	−	6.67822i	0.622747	−	0.622747i
$116$	3.65465			0.339325
$117$	−9.03136	−	5.95270i	−0.834949	−	0.550327i
$118$	5.16845			0.475794
$119$	−3.54623	+	3.54623i	−0.325082	+	0.325082i
$120$	3.33911	−	2.98077i	0.304818	−	0.272106i
$121$		−	0.356442i		−	0.0324038i
$122$	4.61380	−	4.61380i	0.417713	−	0.417713i
$123$	1.09507	−	19.3133i	0.0987389	−	1.74142i
$124$	0.321779	−	0.321779i	0.0288966	−	0.0288966i
$125$	−6.06996	−	6.06996i	−0.542914	−	0.542914i
$126$	11.0918	+	1.26187i	0.988135	+	0.112416i
$127$		−	11.0745i		−	0.982699i	−0.870962	−	0.491349i	$-0.836504\pi$
$127$		−	11.0745i		−	0.982699i	0.870962	−	0.491349i	$-0.163496\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	10.5069	+	11.7700i	0.925081	+	1.03629i
$130$	8.30944	+	4.21545i	0.728786	+	0.369719i
$131$			18.1015i			1.58153i	0.612118	+	0.790767i	$0.290318\pi$
$131$			18.1015i			1.58153i	−0.612118	+	0.790767i	$0.709682\pi$
$132$	0.319883	−	5.64166i	0.0278422	−	0.491044i
$133$	18.8618			1.63553
$134$	3.19958			0.276402
$135$	13.2346	+	2.27071i	1.13906	+	0.195431i
$136$	−0.953002	−	0.953002i	−0.0817193	−	0.0817193i
$137$	−0.976593	−	0.976593i	−0.0834360	−	0.0834360i	0.664157	−	0.747593i	$-0.268791\pi$
$137$	−0.976593	−	0.976593i	−0.0834360	−	0.0834360i	−0.747593	+	0.664157i	$0.768791\pi$
$138$	−0.358338	+	6.31988i	−0.0305038	+	0.537984i
$139$	−7.10912			−0.602988			−0.301494	−	0.953468i	$-0.597485\pi$
$139$	−7.10912			−0.602988			−0.301494	+	0.953468i	$0.597485\pi$
$140$	−9.61619			−0.812717
$141$	−11.5485	−	0.654800i	−0.972557	−	0.0551441i
$142$			0.153328i			0.0128670i
$143$	11.1808	−	3.65465i	0.934984	−	0.305617i
$144$	−0.339111	+	2.98077i	−0.0282592	+	0.248398i
$145$	−6.67822	−	6.67822i	−0.554596	−	0.554596i
$146$			5.06886i			0.419502i
$147$	−7.89729	−	8.84667i	−0.651357	−	0.729661i
$148$	−1.95300	−	1.95300i	−0.160536	−	0.160536i
$149$	−8.85644	+	8.85644i	−0.725548	+	0.725548i	−0.969729	−	0.244182i	$-0.921481\pi$
$149$	−8.85644	+	8.85644i	−0.725548	+	0.725548i	0.244182	+	0.969729i	$0.421481\pi$
$150$	−2.90210	−	0.164550i	−0.236956	−	0.0134354i
$151$	−11.7997	+	11.7997i	−0.960244	+	0.960244i	−0.999239	−	0.0389955i	$-0.987584\pi$
$151$	−11.7997	+	11.7997i	−0.960244	+	0.960244i	0.0389955	+	0.999239i	$0.487584\pi$
$152$			5.06886i			0.411139i
$153$	0.457036	−	4.01733i	0.0369492	−	0.324782i
$154$	−8.58423	+	8.58423i	−0.691737	+	0.691737i
$155$	−1.17599			−0.0944576
$156$	−6.03626	+	1.60113i	−0.483287	+	0.128193i
$157$	−18.8618			−1.50534			−0.752668	−	0.658401i	$-0.771233\pi$
$157$	−18.8618			−1.50534			−0.752668	+	0.658401i	$0.771233\pi$
$158$	2.89489	−	2.89489i	0.230305	−	0.230305i
$159$	0.250112	+	0.280180i	0.0198352	+	0.0222197i
$160$		−	2.58423i		−	0.204301i
$161$	9.61619	−	9.61619i	0.757862	−	0.757862i
$162$	−7.63084	+	4.77183i	−0.599535	+	0.374910i
$163$	−2.81201	+	2.81201i	−0.220254	+	0.220254i	−0.808605	−	0.588352i	$-0.799777\pi$
$163$	−2.81201	+	2.81201i	−0.220254	+	0.220254i	0.588352	+	0.808605i	$0.299777\pi$
$164$	−7.89729	−	7.89729i	−0.616675	−	0.616675i
$165$	−10.8937	+	9.72461i	−0.848071	+	0.757060i
$166$			14.9558i			1.16079i
$167$	0.959150	+	0.959150i	0.0742212	+	0.0742212i	0.743243	−	0.669022i	$-0.233287\pi$
$167$	0.959150	+	0.959150i	0.0742212	+	0.0742212i	−0.669022	+	0.743243i	$0.733287\pi$
$168$	4.80810	−	4.29211i	0.370953	−	0.331144i
$169$	−7.67822	−	10.4902i	−0.590632	−	0.806941i
$170$			3.48289i			0.267125i
$171$	−11.8992	+	9.46831i	−0.909955	+	0.724060i
$172$	9.10912			0.694564
$173$	−17.4960			−1.33020			−0.665099	−	0.746755i	$-0.731611\pi$
$173$	−17.4960			−1.33020			−0.665099	+	0.746755i	$0.731611\pi$
$174$	6.31988	+	0.358338i	0.479109	+	0.0271655i
$175$	4.41577	+	4.41577i	0.333801	+	0.333801i
$176$	−2.30690	−	2.30690i	−0.173889	−	0.173889i
$177$	8.93766	+	0.506767i	0.671796	+	0.0380909i
$178$	−12.5249			−0.938780
$179$	18.1015			1.35297			0.676484	−	0.736458i	$-0.263503\pi$
$179$	18.1015			1.35297			0.676484	+	0.736458i	$0.263503\pi$
$180$	6.06650	−	4.82717i	0.452170	−	0.359796i
$181$		−	1.90600i		−	0.141672i	−0.997488	−	0.0708361i	$-0.977433\pi$
$181$		−	1.90600i		−	0.141672i	0.997488	−	0.0708361i	$-0.0225667\pi$
$182$	11.9650	+	6.06996i	0.886908	+	0.449936i
$183$	8.43090	−	7.52613i	0.623230	−	0.556348i
$184$	2.58423	+	2.58423i	0.190512	+	0.190512i
$185$			7.13753i			0.524762i
$186$	0.587994	−	0.524893i	0.0431138	−	0.0384870i
$187$	3.10912	+	3.10912i	0.227361	+	0.227361i
$188$	−4.72222	+	4.72222i	−0.344403	+	0.344403i
$189$	19.0570	+	3.26967i	1.38619	+	0.237833i
$190$	9.26245	−	9.26245i	0.671969	−	0.671969i
$191$			6.35014i			0.459480i	0.973252	+	0.229740i	$0.0737876\pi$
$191$			6.35014i			0.459480i	−0.973252	+	0.229740i	$0.926212\pi$
$192$	1.15345	+	1.29211i	0.0832430	+	0.0932502i
$193$	−4.26245	+	4.26245i	−0.306818	+	0.306818i	−0.843674	−	0.536856i	$-0.819612\pi$
$193$	−4.26245	+	4.26245i	−0.306818	+	0.306818i	0.536856	+	0.843674i	$0.319612\pi$
$194$	0.238226			0.0171036
$195$	13.9560	+	8.10440i	0.999408	+	0.580368i
$196$	−6.84667			−0.489048
$197$	2.78647	−	2.78647i	0.198528	−	0.198528i	−0.600841	−	0.799369i	$-0.705167\pi$
$197$	2.78647	−	2.78647i	0.198528	−	0.198528i	0.799369	+	0.600841i	$0.205167\pi$
$198$	1.10633	−	9.72461i	0.0786235	−	0.691098i
$199$		−	17.2927i		−	1.22585i	−0.790142	−	0.612923i	$-0.789993\pi$
$199$		−	17.2927i		−	1.22585i	0.790142	−	0.612923i	$-0.210007\pi$
$200$	−1.18668	+	1.18668i	−0.0839111	+	0.0839111i
$201$	5.53295	+	0.313719i	0.390264	+	0.0221280i
$202$	12.5249	−	12.5249i	0.881248	−	0.881248i
$203$	−9.61619	−	9.61619i	−0.674924	−	0.674924i
$204$	−1.55456	−	1.74144i	−0.108841	−	0.121925i
$205$			28.8618i			2.01580i
$206$	−5.59039	−	5.59039i	−0.389501	−	0.389501i
$207$	−1.23933	+	10.8937i	−0.0861393	+	0.757162i
$208$	−1.63122	+	3.21545i	−0.113105	+	0.222951i
$209$		−	16.5369i		−	1.14388i
$210$	−16.6290	−	0.942868i	−1.14751	−	0.0650641i
$211$	9.41577			0.648209			0.324104	−	0.946021i	$-0.394937\pi$
$211$	9.41577			0.648209			0.324104	+	0.946021i	$0.394937\pi$
$212$	0.216838			0.0148925
$213$	−0.0150338	+	0.265146i	−0.00103010	+	0.0181675i
$214$	−3.26245	−	3.26245i	−0.223016	−	0.223016i
$215$	−16.6453	−	16.6453i	−1.13520	−	1.13520i
$216$	−0.878680	+	5.12132i	−0.0597866	+	0.348462i
$217$	−1.69334			−0.114952
$218$	13.0326			0.882680
$219$	−0.497002	+	8.76544i	−0.0335843	+	0.592314i
$220$			8.43090i			0.568411i
$221$	2.19848	−	4.33362i	0.147886	−	0.291511i
$222$	−3.18578	−	3.56877i	−0.213816	−	0.239520i
$223$	−5.89367	−	5.89367i	−0.394669	−	0.394669i	0.481679	−	0.876348i	$-0.340027\pi$
$223$	−5.89367	−	5.89367i	−0.394669	−	0.394669i	−0.876348	+	0.481679i	$0.840027\pi$
$224$		−	3.72111i		−	0.248627i
$225$	−5.00240	−	0.569103i	−0.333493	−	0.0379402i
$226$	2.43090	+	2.43090i	0.161701	+	0.161701i
$227$	9.22759	−	9.22759i	0.612457	−	0.612457i	−0.331129	−	0.943586i	$-0.607429\pi$
$227$	9.22759	−	9.22759i	0.612457	−	0.612457i	0.943586	+	0.331129i	$0.107429\pi$
$228$	−0.497002	+	8.76544i	−0.0329148	+	0.580506i
$229$	9.21545	−	9.21545i	0.608974	−	0.608974i	−0.333704	−	0.942678i	$-0.608299\pi$
$229$	9.21545	−	9.21545i	0.608974	−	0.608974i	0.942678	+	0.333704i	$0.108299\pi$
$230$		−	9.44443i		−	0.622747i
$231$	−15.6862	+	14.0028i	−1.03207	+	0.921316i
$232$	2.58423	−	2.58423i	0.169663	−	0.169663i
$233$	2.52374			0.165335			0.0826677	−	0.996577i	$-0.473656\pi$
$233$	2.52374			0.165335			0.0826677	+	0.996577i	$0.473656\pi$
$234$	−10.5953	+	2.17694i	−0.692638	+	0.142311i
$235$	17.2580			1.12579
$236$	3.65465	−	3.65465i	0.237897	−	0.237897i
$237$	5.28990	−	4.72222i	0.343616	−	0.306741i
$238$			5.01512i			0.325082i
$239$	7.20087	−	7.20087i	0.465786	−	0.465786i	−0.434760	−	0.900546i	$-0.643167\pi$
$239$	7.20087	−	7.20087i	0.465786	−	0.465786i	0.900546	+	0.434760i	$0.143167\pi$
$240$	0.253383	−	4.46883i	0.0163558	−	0.288462i
$241$	20.4460	−	20.4460i	1.31704	−	1.31704i	0.400939	−	0.916105i	$-0.368684\pi$
$241$	20.4460	−	20.4460i	1.31704	−	1.31704i	0.916105	−	0.400939i	$-0.131316\pi$
$242$	−0.252043	−	0.252043i	−0.0162019	−	0.0162019i
$243$	−13.6637	+	7.50359i	−0.876525	+	0.481356i
$244$		−	6.52489i		−	0.417713i
$245$	12.5111	+	12.5111i	0.799304	+	0.799304i
$246$	−12.8822	−	14.4309i	−0.821342	−	0.920080i
$247$	−17.3716	+	5.67822i	−1.10533	+	0.361297i
$248$		−	0.455064i		−	0.0288966i
$249$	−1.46642	+	25.8626i	−0.0929303	+	1.63898i
$250$	−8.58423			−0.542914
$251$	−18.4901			−1.16708			−0.583541	−	0.812083i	$-0.698333\pi$
$251$	−18.4901			−1.16708			−0.583541	+	0.812083i	$0.698333\pi$
$252$	8.73535	−	6.95080i	0.550276	−	0.437859i
$253$	−8.43090	−	8.43090i	−0.530046	−	0.530046i
$254$	−7.83082	−	7.83082i	−0.491349	−	0.491349i
$255$	−0.341497	+	6.02286i	−0.0213854	+	0.377166i
$256$	1.00000			0.0625000
$257$	−13.6696			−0.852688			−0.426344	−	0.904561i	$-0.640199\pi$
$257$	−13.6696			−0.852688			−0.426344	+	0.904561i	$0.640199\pi$
$258$	15.7522	+	0.893149i	0.980686	+	0.0556050i
$259$			10.2776i			0.638617i
$260$	8.85644	−	2.89489i	0.549253	−	0.179534i
$261$	10.8937	+	1.23933i	0.674301	+	0.0767126i
$262$	12.7997	+	12.7997i	0.790767	+	0.790767i
$263$		−	14.6186i		−	0.901421i	−0.892670	−	0.450710i	$-0.851171\pi$
$263$		−	14.6186i		−	0.901421i	0.892670	−	0.450710i	$-0.148829\pi$
$264$	−3.76307	−	4.21545i	−0.231601	−	0.259443i
$265$	−0.396234	−	0.396234i	−0.0243405	−	0.0243405i
$266$	13.3373	−	13.3373i	0.817763	−	0.817763i
$267$	−21.6590	−	1.22807i	−1.32551	−	0.0751564i
$268$	2.26245	−	2.26245i	0.138201	−	0.138201i
$269$			15.7946i			0.963012i	0.876443	+	0.481506i	$0.159910\pi$
$269$			15.7946i			0.963012i	−0.876443	+	0.481506i	$0.840090\pi$
$270$	10.9639	−	7.75268i	0.667244	−	0.471813i
$271$	16.2306	−	16.2306i	0.985937	−	0.985937i	−0.0139655	−	0.999902i	$-0.504445\pi$
$271$	16.2306	−	16.2306i	0.985937	−	0.985937i	0.999902	+	0.0139655i	$0.00444549\pi$
$272$	−1.34775			−0.0817193
$273$	20.0957	+	11.6698i	1.21625	+	0.706288i
$274$	−1.38111			−0.0834360
$275$	3.87149	−	3.87149i	0.233459	−	0.233459i
$276$	4.21545	+	4.72222i	0.253740	+	0.284244i
$277$			26.1489i			1.57114i	0.618775	+	0.785568i	$0.287629\pi$
$277$			26.1489i			1.57114i	−0.618775	+	0.785568i	$0.712371\pi$
$278$	−5.02691	+	5.02691i	−0.301494	+	0.301494i
$279$	1.06827	−	0.850031i	0.0639555	−	0.0508900i
$280$	−6.79967	+	6.79967i	−0.406358	+	0.406358i
$281$	3.06665	+	3.06665i	0.182941	+	0.182941i	0.792636	−	0.609695i	$-0.208708\pi$
$281$	3.06665	+	3.06665i	0.182941	+	0.182941i	−0.609695	+	0.792636i	$0.708708\pi$
$282$	−8.62901	+	7.70299i	−0.513850	+	0.458706i
$283$		−	9.35644i		−	0.556183i	−0.960555	−	0.278091i	$-0.910298\pi$
$283$		−	9.35644i		−	0.556183i	0.960555	−	0.278091i	$-0.0897018\pi$
$284$	0.108419	+	0.108419i	0.00643350	+	0.00643350i
$285$	16.9255	−	15.1091i	1.00258	−	0.894987i
$286$	5.32178	−	10.4902i	0.314683	−	0.620300i
$287$			41.5591i			2.45315i
$288$	1.86794	+	2.34751i	0.110069	+	0.138328i
$289$	−15.1836			−0.893151
$290$	−9.44443			−0.554596
$291$	0.411957	+	0.0233580i	0.0241493	+	0.00136927i
$292$	3.58423	+	3.58423i	0.209751	+	0.209751i
$293$	3.00331	+	3.00331i	0.175455	+	0.175455i	0.789371	−	0.613916i	$-0.210407\pi$
$293$	3.00331	+	3.00331i	0.175455	+	0.175455i	−0.613916	+	0.789371i	$0.710407\pi$
$294$	−11.8398	−	0.671316i	−0.690509	−	0.0391520i
$295$	−13.3564			−0.777642
$296$	−2.76196			−0.160536
$297$	2.86665	−	16.7080i	0.166340	−	0.969498i
$298$			12.5249i			0.725548i
$299$	−5.96154	+	11.7513i	−0.344765	+	0.679597i
$300$	−2.16845	+	1.93574i	−0.125196	+	0.111760i
$301$	−23.9681	−	23.9681i	−1.38150	−	1.38150i
$302$			16.6873i			0.960244i
$303$	22.8870	−	20.4309i	1.31483	−	1.17372i
$304$	3.58423	+	3.58423i	0.205569	+	0.205569i
$305$	−11.9231	+	11.9231i	−0.682714	+	0.682714i
$306$	−2.51751	−	3.16386i	−0.143916	−	0.180866i
$307$	−3.24732	+	3.24732i	−0.185335	+	0.185335i	−0.793676	−	0.608341i	$-0.791835\pi$
$307$	−3.24732	+	3.24732i	−0.185335	+	0.185335i	0.608341	+	0.793676i	$0.291835\pi$
$308$			12.1399i			0.691737i
$309$	−9.11917	−	10.2154i	−0.518772	−	0.581137i
$310$	−0.831549	+	0.831549i	−0.0472288	+	0.0472288i
$311$	3.43781			0.194940			0.0974701	−	0.995238i	$-0.468925\pi$
$311$	3.43781			0.194940			0.0974701	+	0.995238i	$0.468925\pi$
$312$	−3.13611	+	5.40045i	−0.177547	+	0.305740i
$313$	1.50977			0.0853373			0.0426686	−	0.999089i	$-0.486414\pi$
$313$	1.50977			0.0853373			0.0426686	+	0.999089i	$0.486414\pi$
$314$	−13.3373	+	13.3373i	−0.752668	+	0.752668i
$315$	−28.6637	−	3.26095i	−1.61502	−	0.183734i
$316$		−	4.09400i		−	0.230305i
$317$	16.1657	−	16.1657i	0.907958	−	0.907958i	−0.0881494	−	0.996107i	$-0.528095\pi$
$317$	16.1657	−	16.1657i	0.907958	−	0.907958i	0.996107	+	0.0881494i	$0.0280953\pi$
$318$	0.374973	+	0.0212610i	0.0210274	+	0.00119226i
$319$	−8.43090	+	8.43090i	−0.472040	+	0.472040i
$320$	−1.82732	−	1.82732i	−0.102150	−	0.102150i
$321$	−5.32178	−	5.96154i	−0.297033	−	0.332741i
$322$		−	13.5993i		−	0.757862i
$323$	−4.83063	−	4.83063i	−0.268784	−	0.268784i
$324$	−2.02162	+	8.77001i	−0.112312	+	0.487223i
$325$	−5.39623	−	2.73755i	−0.299329	−	0.151852i
$326$			3.97678i			0.220254i
$327$	22.5369	+	1.27785i	1.24630	+	0.0706652i
$328$	−11.1685			−0.616675
$329$	24.8504			1.37005
$330$	−0.826650	+	14.5793i	−0.0455056	+	0.802565i
$331$	5.52489	+	5.52489i	0.303676	+	0.303676i	0.842450	−	0.538774i	$-0.181112\pi$
$331$	5.52489	+	5.52489i	0.303676	+	0.303676i	−0.538774	+	0.842450i	$0.681112\pi$
$332$	10.5753	+	10.5753i	0.580397	+	0.580397i
$333$	−5.15917	−	6.48374i	−0.282721	−	0.355307i
$334$	1.35644			0.0742212
$335$	−8.26844			−0.451753
$336$	0.364855	−	6.43482i	0.0199045	−	0.351048i
$337$			18.8271i			1.02558i	0.858514	+	0.512790i	$0.171388\pi$
$337$			18.8271i			1.02558i	−0.858514	+	0.512790i	$0.828612\pi$
$338$	−12.8470	−	1.98839i	−0.698787	−	0.108154i
$339$	3.96534	+	4.44204i	0.215368	+	0.241258i
$340$	2.46277	+	2.46277i	0.133563	+	0.133563i
$341$			1.48462i			0.0803968i
$342$	−1.71890	+	15.1091i	−0.0929477	+	0.817008i
$343$	−0.403440	−	0.403440i	−0.0217837	−	0.0217837i
$344$	6.44112	−	6.44112i	0.347282	−	0.347282i
$345$	0.926027	−	16.3320i	0.0498556	−	0.879285i
$346$	−12.3716	+	12.3716i	−0.665099	+	0.665099i
$347$		−	29.2823i		−	1.57195i	−0.618256	−	0.785977i	$-0.712160\pi$
$347$		−	29.2823i		−	1.57195i	0.618256	−	0.785977i	$-0.287840\pi$
$348$	4.72222	−	4.21545i	0.253137	−	0.225972i
$349$	4.87855	−	4.87855i	0.261143	−	0.261143i	−0.564376	−	0.825518i	$-0.690883\pi$
$349$	4.87855	−	4.87855i	0.261143	−	0.261143i	0.825518	+	0.564376i	$0.190883\pi$
$350$	6.24485			0.333801
$351$	−18.5357	+	2.72565i	−0.989361	+	0.145485i
$352$	−3.26245			−0.173889
$353$	−5.59039	+	5.59039i	−0.297546	+	0.297546i	−0.840052	−	0.542506i	$-0.817476\pi$
$353$	−5.59039	+	5.59039i	−0.297546	+	0.297546i	0.542506	+	0.840052i	$0.317476\pi$
$354$	6.67822	−	5.96154i	0.354943	−	0.316853i
$355$		−	0.396234i		−	0.0210299i
$356$	−8.85644	+	8.85644i	−0.469390	+	0.469390i
$357$	−0.491733	+	8.67252i	−0.0260253	+	0.458998i
$358$	12.7997	−	12.7997i	0.676484	−	0.676484i
$359$	12.8822	+	12.8822i	0.679899	+	0.679899i	0.959977	−	0.280079i	$-0.0903605\pi$
$359$	12.8822	+	12.8822i	0.679899	+	0.679899i	−0.280079	+	0.959977i	$0.590361\pi$
$360$	0.876338	−	7.70299i	0.0461871	−	0.405983i
$361$			6.69334i			0.352281i
$362$	−1.34775	−	1.34775i	−0.0708361	−	0.0708361i
$363$	−0.411138	−	0.460564i	−0.0215791	−	0.0241733i
$364$	12.7527	−	4.16845i	0.668422	−	0.218486i
$365$		−	13.0991i		−	0.685637i
$366$	0.639766	−	11.2833i	0.0334411	−	0.589789i
$367$	7.56910			0.395104			0.197552	−	0.980292i	$-0.436701\pi$
$367$	7.56910			0.395104			0.197552	+	0.980292i	$0.436701\pi$
$368$	3.65465			0.190512
$369$	−20.8620	−	26.2181i	−1.08603	−	1.36486i
$370$	5.04700	+	5.04700i	0.262381	+	0.262381i
$371$	−0.570551	−	0.570551i	−0.0296215	−	0.0296215i
$372$	0.0446190	−	0.786930i	0.00231339	−	0.0408004i
$373$	15.8120			0.818715			0.409357	−	0.912374i	$-0.365753\pi$
$373$	15.8120			0.818715			0.409357	+	0.912374i	$0.365753\pi$
$374$	4.39696			0.227361
$375$	−14.8445	−	0.841683i	−0.766565	−	0.0434643i
$376$			6.67822i			0.344403i
$377$	11.7513	+	5.96154i	0.605224	+	0.307035i
$378$	15.7873	−	11.1633i	0.812013	−	0.574180i
$379$	5.33690	+	5.33690i	0.274138	+	0.274138i	0.830764	−	0.556625i	$-0.187904\pi$
$379$	5.33690	+	5.33690i	0.274138	+	0.274138i	−0.556625	+	0.830764i	$0.687904\pi$
$380$		−	13.0991i		−	0.671969i
$381$	−12.7738	−	14.3094i	−0.654423	−	0.733095i
$382$	4.49023	+	4.49023i	0.229740	+	0.229740i
$383$	−10.8555	+	10.8555i	−0.554691	+	0.554691i	−0.927791	−	0.373100i	$-0.878295\pi$
$383$	−10.8555	+	10.8555i	−0.554691	+	0.554691i	0.373100	+	0.927791i	$0.378295\pi$
$384$	1.72927	+	0.0980500i	0.0882466	+	0.00500359i
$385$	22.1836	−	22.1836i	1.13058	−	1.13058i
$386$			6.02801i			0.306818i
$387$	27.1522	+	3.08900i	1.38022	+	0.157023i
$388$	0.168451	−	0.168451i	0.00855180	−	0.00855180i
$389$	−4.61380			−0.233929			−0.116964	−	0.993136i	$-0.537316\pi$
$389$	−4.61380			−0.233929			−0.116964	+	0.993136i	$0.537316\pi$
$390$	15.5990	−	4.13769i	0.789888	−	0.209520i
$391$	−4.92554			−0.249096
$392$	−4.84133	+	4.84133i	−0.244524	+	0.244524i
$393$	20.8791	+	23.3891i	1.05321	+	1.17983i
$394$		−	3.94067i		−	0.198528i
$395$	−7.48105	+	7.48105i	−0.376413	+	0.376413i
$396$	−6.09404	−	7.65863i	−0.306237	−	0.384861i
$397$	−12.5400	+	12.5400i	−0.629365	+	0.629365i	−0.947908	−	0.318543i	$-0.896806\pi$
$397$	−12.5400	+	12.5400i	−0.629365	+	0.629365i	0.318543	+	0.947908i	$0.396806\pi$
$398$	−12.2278	−	12.2278i	−0.612923	−	0.612923i
$399$	24.3716	−	21.7561i	1.22010	−	1.08917i
$400$			1.67822i			0.0839111i
$401$	−3.63720	−	3.63720i	−0.181633	−	0.181633i	0.610434	−	0.792067i	$-0.290995\pi$
$401$	−3.63720	−	3.63720i	−0.181633	−	0.181633i	−0.792067	+	0.610434i	$0.790995\pi$
$402$	4.13422	−	3.69056i	0.206196	−	0.184068i
$403$	1.55956	−	0.509770i	0.0776870	−	0.0253935i
$404$		−	17.7129i		−	0.881248i
$405$	19.7198	−	12.3315i	0.979885	−	0.612756i
$406$	−13.5993			−0.674924
$407$	9.01075			0.446646
$408$	−2.33063	−	0.132147i	−0.115383	−	0.00654224i
$409$	18.5993	+	18.5993i	0.919679	+	0.919679i	0.997006	−	0.0773272i	$-0.0246386\pi$
$409$	18.5993	+	18.5993i	0.919679	+	0.919679i	−0.0773272	+	0.997006i	$0.524639\pi$
$410$	20.4084	+	20.4084i	1.00790	+	1.00790i
$411$	−2.38832	−	0.135418i	−0.117807	−	0.00667968i
$412$	−7.90600			−0.389501
$413$	−19.2324			−0.946364
$414$	6.82665	+	8.57933i	0.335512	+	0.421651i
$415$		−	38.6491i		−	1.89721i
$416$	1.12022	+	3.42711i	0.0549231	+	0.168028i
$417$	−9.18578	+	8.20001i	−0.449830	+	0.401556i
$418$	−11.6933	−	11.6933i	−0.571940	−	0.571940i
$419$		−	0.353712i		−	0.0172800i	−0.999963	−	0.00863998i	$-0.997250\pi$
$419$		−	0.353712i		−	0.0172800i	0.999963	−	0.00863998i	$-0.00275023\pi$
$420$	−12.4252	+	11.0918i	−0.606288	+	0.541224i
$421$	−22.9088	−	22.9088i	−1.11651	−	1.11651i	−0.992250	−	0.124256i	$-0.960346\pi$
$421$	−22.9088	−	22.9088i	−1.11651	−	1.11651i	−0.124256	−	0.992250i	$-0.539654\pi$
$422$	6.65796	−	6.65796i	0.324104	−	0.324104i
$423$	−15.6772	+	12.4745i	−0.762252	+	0.606531i
$424$	0.153328	−	0.153328i	0.00744626	−	0.00744626i
$425$		−	2.26182i		−	0.109714i
$426$	0.176856	+	0.198117i	0.00856870	+	0.00959880i
$427$	−17.1685	+	17.1685i	−0.830840	+	0.830840i
$428$	−4.61380			−0.223016
$429$	10.2314	−	17.6187i	0.493976	−	0.850638i
$430$	−23.5400			−1.13520
$431$	−5.89820	+	5.89820i	−0.284106	+	0.284106i	−0.834744	−	0.550638i	$-0.814385\pi$
$431$	−5.89820	+	5.89820i	−0.284106	+	0.284106i	0.550638	+	0.834744i	$0.314385\pi$
$432$	3.00000	+	4.24264i	0.144338	+	0.204124i
$433$			37.6093i			1.80739i	0.428177	+	0.903695i	$0.359156\pi$
$433$			37.6093i			1.80739i	−0.428177	+	0.903695i	$0.640844\pi$
$434$	−1.19738	+	1.19738i	−0.0574758	+	0.0574758i
$435$	−16.3320	−	0.926027i	−0.783060	−	0.0443996i
$436$	9.21545	−	9.21545i	0.441340	−	0.441340i
$437$	13.0991	+	13.0991i	0.626614	+	0.626614i
$438$	5.84667	+	6.54954i	0.279365	+	0.312949i
$439$			18.0000i			0.859093i	0.903045	+	0.429547i	$0.141327\pi$
$439$			18.0000i			0.859093i	−0.903045	+	0.429547i	$0.858673\pi$
$440$	5.96154	+	5.96154i	0.284205	+	0.284205i
$441$	−20.4084	−	2.32178i	−0.971827	−	0.110561i
$442$	−1.50977	−	4.61889i	−0.0718124	−	0.219698i
$443$		−	30.8018i		−	1.46344i	−0.681608	−	0.731718i	$-0.738719\pi$
$443$		−	30.8018i		−	1.46344i	0.681608	−	0.731718i	$-0.261281\pi$
$444$	−4.77619	−	0.270810i	−0.226668	−	0.0128521i
$445$	32.3671			1.53435
$446$	−8.33491			−0.394669
$447$	−1.22807	+	21.6590i	−0.0580855	+	1.02443i
$448$	−2.63122	−	2.63122i	−0.124314	−	0.124314i
$449$	19.2149	+	19.2149i	0.906809	+	0.906809i	0.996013	−	0.0892043i	$-0.0284324\pi$
$449$	19.2149	+	19.2149i	0.906809	+	0.906809i	−0.0892043	+	0.996013i	$0.528432\pi$
$450$	−3.93964	+	3.13481i	−0.185717	+	0.147776i
$451$	36.4365			1.71573
$452$	3.43781			0.161701
$453$	−1.63619	+	28.8568i	−0.0768747	+	1.35581i
$454$		−	13.0498i		−	0.612457i
$455$	−30.9204	−	15.6862i	−1.44957	−	0.735378i
$456$	5.84667	+	6.54954i	0.273796	+	0.306710i
$457$	11.4656	+	11.4656i	0.536336	+	0.536336i	0.922451	−	0.386115i	$-0.126183\pi$
$457$	11.4656	+	11.4656i	0.536336	+	0.536336i	−0.386115	+	0.922451i	$0.626183\pi$
$458$		−	13.0326i		−	0.608974i
$459$	−4.04325	−	5.71801i	−0.188723	−	0.266894i
$460$	−6.67822	−	6.67822i	−0.311374	−	0.311374i
$461$	2.60452	−	2.60452i	0.121305	−	0.121305i	−0.643848	−	0.765153i	$-0.722663\pi$
$461$	2.60452	−	2.60452i	0.121305	−	0.121305i	0.765153	+	0.643848i	$0.222663\pi$
$462$	−1.19032	+	20.9933i	−0.0553787	+	0.976695i
$463$	8.20311	−	8.20311i	0.381231	−	0.381231i	−0.490315	−	0.871546i	$-0.663118\pi$
$463$	8.20311	−	8.20311i	0.381231	−	0.381231i	0.871546	+	0.490315i	$0.163118\pi$
$464$		−	3.65465i		−	0.169663i
$465$	−1.51951	+	1.35644i	−0.0704655	+	0.0629035i
$466$	1.78455	−	1.78455i	0.0826677	−	0.0826677i
$467$	22.7603			1.05322			0.526612	−	0.850106i	$-0.323462\pi$
$467$	22.7603			1.05322			0.526612	+	0.850106i	$0.323462\pi$
$468$	−5.95270	+	9.03136i	−0.275164	+	0.417475i
$469$	−11.9060			−0.549768
$470$	12.2033	−	12.2033i	0.562895	−	0.562895i
$471$	−24.3716	+	21.7561i	−1.12298	+	1.00247i
$472$		−	5.16845i		−	0.237897i
$473$	−21.0138	+	21.0138i	−0.966216	+	0.966216i
$474$	0.401416	−	7.07964i	0.0184377	−	0.325179i
$475$	−6.01512	+	6.01512i	−0.275993	+	0.275993i
$476$	3.54623	+	3.54623i	0.162541	+	0.162541i
$477$	0.646346	+	0.0735322i	0.0295942	+	0.00336681i
$478$		−	10.1836i		−	0.465786i
$479$	−17.3876	−	17.3876i	−0.794460	−	0.794460i	0.187755	−	0.982216i	$-0.439879\pi$
$479$	−17.3876	−	17.3876i	−0.794460	−	0.794460i	−0.982216	+	0.187755i	$0.939879\pi$
$480$	−2.98077	−	3.33911i	−0.136053	−	0.152409i
$481$	−3.09400	−	9.46556i	−0.141074	−	0.431592i
$482$		−	28.9150i		−	1.31704i
$483$	1.33342	−	23.5170i	0.0606725	−	1.07006i
$484$	−0.356442			−0.0162019
$485$	−0.615628			−0.0279542
$486$	−4.35584	+	14.9675i	−0.197585	+	0.678941i
$487$	−10.0151	−	10.0151i	−0.453829	−	0.453829i	0.442795	−	0.896623i	$-0.353987\pi$
$487$	−10.0151	−	10.0151i	−0.453829	−	0.453829i	−0.896623	+	0.442795i	$0.853987\pi$
$488$	−4.61380	−	4.61380i	−0.208857	−	0.208857i
$489$	−0.389923	+	6.87694i	−0.0176329	+	0.310986i
$490$	17.6933			0.799304
$491$	−0.822276			−0.0371088			−0.0185544	−	0.999828i	$-0.505906\pi$
$491$	−0.822276			−0.0371088			−0.0185544	+	0.999828i	$0.505906\pi$
$492$	−19.3133	−	1.09507i	−0.870711	−	0.0493694i
$493$			4.92554i			0.221835i
$494$	−8.26844	+	16.2987i	−0.372015	+	0.733311i
$495$	−2.85901	+	25.1306i	−0.128503	+	1.12954i
$496$	−0.321779	−	0.321779i	−0.0144483	−	0.0144483i
$497$		−	0.570551i		−	0.0255927i
$498$	17.2507	+	19.3246i	0.773024	+	0.865955i
$499$	−4.32178	−	4.32178i	−0.193469	−	0.193469i	0.603724	−	0.797193i	$-0.293683\pi$
$499$	−4.32178	−	4.32178i	−0.193469	−	0.193469i	−0.797193	+	0.603724i	$0.793683\pi$
$500$	−6.06996	+	6.06996i	−0.271457	+	0.271457i
$501$	2.34566	+	0.132999i	0.104796	+	0.00594197i
$502$	−13.0745	+	13.0745i	−0.583541	+	0.583541i
$503$			38.1212i			1.69974i	0.526991	+	0.849871i	$0.323320\pi$
$503$			38.1212i			1.69974i	−0.526991	+	0.849871i	$0.676680\pi$
$504$	1.26187	−	11.0918i	0.0562081	−	0.494067i
$505$	−32.3671	+	32.3671i	−1.44032	+	1.44032i
$506$	−11.9231			−0.530046
$507$	−22.0211	−	4.69812i	−0.977990	−	0.208651i
$508$	−11.0745			−0.491349
$509$	20.7795	−	20.7795i	0.921036	−	0.921036i	−0.0760664	−	0.997103i	$-0.524236\pi$
$509$	20.7795	−	20.7795i	0.921036	−	0.921036i	0.997103	+	0.0760664i	$0.0242361\pi$
$510$	4.01733	+	4.50028i	0.177890	+	0.199276i
$511$		−	18.8618i		−	0.834397i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.45390	+	25.9593i	−0.196645	+	1.14613i
$514$	−9.66589	+	9.66589i	−0.426344	+	0.426344i
$515$	14.4468	+	14.4468i	0.636603	+	0.636603i
$516$	11.7700	−	10.5069i	0.518146	−	0.462541i
$517$		−	21.7873i		−	0.958206i
$518$	7.26734	+	7.26734i	0.319309	+	0.319309i
$519$	−22.6068	+	20.1808i	−0.992331	+	0.885838i
$520$	4.21545	−	8.30944i	0.184860	−	0.364393i
$521$			0.171761i			0.00752497i	0.999993	+	0.00376248i	$0.00119764\pi$
$521$			0.171761i			0.00752497i	−0.999993	+	0.00376248i	$0.998802\pi$
$522$	8.57933	−	6.82665i	0.375507	−	0.298794i
$523$	20.8618			0.912223			0.456111	−	0.889923i	$-0.349242\pi$
$523$	20.8618			0.912223			0.456111	+	0.889923i	$0.349242\pi$
$524$	18.1015			0.790767
$525$	10.7990	+	0.612308i	0.471309	+	0.0267233i
$526$	−10.3369	−	10.3369i	−0.450710	−	0.450710i
$527$	0.433677	+	0.433677i	0.0188913	+	0.0188913i
$528$	−5.64166	−	0.319883i	−0.245522	−	0.0139211i
$529$	−9.64356			−0.419285
$530$	−0.560360			−0.0243405
$531$	12.1330	−	9.65434i	0.526527	−	0.418963i
$532$		−	18.8618i		−	0.817763i
$533$	−12.5111	−	38.2756i	−0.541915	−	1.65790i
$534$	−16.1836	+	14.4468i	−0.700332	+	0.625175i
$535$	8.43090	+	8.43090i	0.364499	+	0.364499i
$536$		−	3.19958i		−	0.138201i
$537$	23.3891	−	20.8791i	1.00932	−	0.901001i
$538$	11.1685	+	11.1685i	0.481506	+	0.481506i
$539$	15.7946	−	15.7946i	0.680320	−	0.680320i
$540$	2.27071	−	13.2346i	0.0977156	−	0.569528i
$541$	−22.6021	+	22.6021i	−0.971742	+	0.971742i	−0.999612	−	0.0278698i	$-0.991128\pi$
$541$	−22.6021	+	22.6021i	−0.971742	+	0.971742i	0.0278698	+	0.999612i	$0.491128\pi$
$542$		−	22.9535i		−	0.985937i
$543$	−2.19848	−	2.46277i	−0.0943458	−	0.105688i
$544$	−0.953002	+	0.953002i	−0.0408596	+	0.0408596i
$545$	−33.6792			−1.44266
$546$	22.4616	−	5.95799i	0.961267	−	0.254978i
$547$	33.7527			1.44316			0.721580	−	0.692331i	$-0.243416\pi$
$547$	33.7527			1.44316			0.721580	+	0.692331i	$0.243416\pi$
$548$	−0.976593	+	0.976593i	−0.0417180	+	0.0417180i
$549$	2.21266	−	19.4492i	0.0944340	−	0.830073i
$550$		−	5.47511i		−	0.233459i
$551$	13.0991	−	13.0991i	0.558039	−	0.558039i
$552$	6.31988	+	0.358338i	0.268992	+	0.0152519i
$553$	−10.7722	+	10.7722i	−0.458081	+	0.458081i
$554$	18.4901	+	18.4901i	0.785568	+	0.785568i
$555$	8.23278	+	9.22250i	0.349462	+	0.391473i
$556$			7.10912i			0.301494i
$557$	7.40027	+	7.40027i	0.313559	+	0.313559i	0.846287	−	0.532727i	$-0.178833\pi$
$557$	7.40027	+	7.40027i	0.313559	+	0.313559i	−0.532727	+	0.846287i	$0.678833\pi$
$558$	0.154317	−	1.35644i	0.00653276	−	0.0574228i
$559$	29.2899	+	14.8590i	1.23883	+	0.628469i
$560$			9.61619i			0.406358i
$561$	7.60354	+	0.431122i	0.321022	+	0.0182020i
$562$	4.33690			0.182941
$563$	38.1111			1.60619			0.803095	−	0.595851i	$-0.203185\pi$
$563$	38.1111			1.60619			0.803095	+	0.595851i	$0.203185\pi$
$564$	−0.654800	+	11.5485i	−0.0275720	+	0.486278i
$565$	−6.28199	−	6.28199i	−0.264285	−	0.264285i
$566$	−6.61600	−	6.61600i	−0.278091	−	0.278091i
$567$	28.3952	−	17.7565i	1.19249	−	0.745703i
$568$	0.153328			0.00643350
$569$	−38.2930			−1.60533			−0.802663	−	0.596433i	$-0.796584\pi$
$569$	−38.2930			−1.60533			−0.802663	+	0.596433i	$0.796584\pi$
$570$	1.28436	−	22.6519i	0.0537961	−	0.948783i
$571$		−	34.6145i		−	1.44857i	−0.689500	−	0.724285i	$-0.742170\pi$
$571$		−	34.6145i		−	1.44857i	0.689500	−	0.724285i	$-0.257830\pi$
$572$	−3.65465	−	11.1808i	−0.152808	−	0.467492i
$573$	7.32457	+	8.20510i	0.305988	+	0.342773i
$574$	29.3867	+	29.3867i	1.22658	+	1.22658i
$575$			6.13331i			0.255777i
$576$	2.98077	+	0.339111i	0.124199	+	0.0141296i
$577$	4.72243	+	4.72243i	0.196597	+	0.196597i	0.798540	−	0.601942i	$-0.205606\pi$
$577$	4.72243	+	4.72243i	0.196597	+	0.196597i	−0.601942	+	0.798540i	$0.705606\pi$
$578$	−10.7364	+	10.7364i	−0.446576	+	0.446576i
$579$	−0.591046	+	10.4241i	−0.0245631	+	0.433210i
$580$	−6.67822	+	6.67822i	−0.277298	+	0.277298i
$581$		−	55.6522i		−	2.30884i
$582$	0.307814	−	0.274781i	0.0127593	−	0.0113900i
$583$	−0.500224	+	0.500224i	−0.0207172	+	0.0207172i
$584$	5.06886			0.209751
$585$	27.3807	−	5.62570i	1.13205	−	0.232594i
$586$	4.24732			0.175455
$587$	−11.0090	+	11.0090i	−0.454391	+	0.454391i	−0.896809	−	0.442418i	$-0.854121\pi$
$587$	−11.0090	+	11.0090i	−0.454391	+	0.454391i	0.442418	+	0.896809i	$0.354121\pi$
$588$	−8.84667	+	7.89729i	−0.364831	+	0.325679i
$589$		−	2.30666i		−	0.0950441i
$590$	−9.44443	+	9.44443i	−0.388821	+	0.388821i
$591$	0.386383	−	6.81449i	0.0158937	−	0.280311i
$592$	−1.95300	+	1.95300i	−0.0802679	+	0.0802679i
$593$	−8.06905	−	8.06905i	−0.331356	−	0.331356i	0.521745	−	0.853101i	$-0.325281\pi$
$593$	−8.06905	−	8.06905i	−0.331356	−	0.331356i	−0.853101	+	0.521745i	$0.825281\pi$
$594$	−9.78734	−	13.8414i	−0.401579	−	0.567919i
$595$		−	12.9602i		−	0.531317i
$596$	8.85644	+	8.85644i	0.362774	+	0.362774i
$597$	−19.9462	−	22.3441i	−0.816345	−	0.914483i
$598$	4.09400	+	12.5249i	0.167416	+	0.512181i
$599$		−	22.0180i		−	0.899633i	−0.893121	−	0.449816i	$-0.851489\pi$
$599$		−	22.0180i		−	0.899633i	0.893121	−	0.449816i	$-0.148511\pi$
$600$	−0.164550	+	2.90210i	−0.00671771	+	0.118478i
$601$	−38.2529			−1.56037			−0.780184	−	0.625550i	$-0.784875\pi$
$601$	−38.2529			−1.56037			−0.780184	+	0.625550i	$0.784875\pi$
$602$	−33.8960			−1.38150
$603$	7.51106	−	5.97662i	0.305874	−	0.243387i
$604$	11.7997	+	11.7997i	0.480122	+	0.480122i
$605$	0.651335	+	0.651335i	0.0264805	+	0.0264805i
$606$	1.73675	−	30.6304i	0.0705506	−	1.24427i
$607$	8.06933			0.327524			0.163762	−	0.986500i	$-0.447637\pi$
$607$	8.06933			0.327524			0.163762	+	0.986500i	$0.447637\pi$
$608$	5.06886			0.205569
$609$	−23.5170	−	1.33342i	−0.952957	−	0.0540328i
$610$			16.8618i			0.682714i
$611$	−22.8870	+	7.48105i	−0.925910	+	0.302651i
$612$	−4.01733	−	0.457036i	−0.162391	−	0.0184746i
$613$	−23.0896	−	23.0896i	−0.932579	−	0.932579i	0.0652872	−	0.997867i	$-0.479204\pi$
$613$	−23.0896	−	23.0896i	−0.932579	−	0.932579i	−0.997867	+	0.0652872i	$0.979204\pi$
$614$			4.59241i			0.185335i
$615$	33.2906	+	37.2927i	1.34241	+	1.50379i
$616$	8.58423	+	8.58423i	0.345868	+	0.345868i
$617$	32.9195	−	32.9195i	1.32529	−	1.32529i	0.415858	−	0.909430i	$-0.363481\pi$
$617$	32.9195	−	32.9195i	1.32529	−	1.32529i	0.909430	−	0.415858i	$-0.136519\pi$
$618$	−13.6716	−	0.775184i	−0.549954	−	0.0311825i
$619$	−25.3716	+	25.3716i	−1.01977	+	1.01977i	−0.0199687	+	0.999801i	$0.506357\pi$
$619$	−25.3716	+	25.3716i	−1.01977	+	1.01977i	−0.999801	+	0.0199687i	$0.993643\pi$
$620$			1.17599i			0.0472288i
$621$	10.9639	+	15.5054i	0.439968	+	0.622208i
$622$	2.43090	−	2.43090i	0.0974701	−	0.0974701i
$623$	46.6065			1.86725
$624$	1.60113	+	6.03626i	0.0640966	+	0.241644i
$625$	30.5747			1.22299
$626$	1.06757	−	1.06757i	0.0426686	−	0.0426686i
$627$	−19.0745	−	21.3675i	−0.761760	−	0.853337i
$628$			18.8618i			0.752668i
$629$	2.63216	−	2.63216i	0.104951	−	0.104951i
$630$	−22.5741	+	17.9624i	−0.899375	+	0.715641i
$631$	−0.200326	+	0.200326i	−0.00797485	+	0.00797485i	−0.711083	−	0.703108i	$-0.751795\pi$
$631$	−0.200326	+	0.200326i	−0.00797485	+	0.00797485i	0.703108	+	0.711083i	$0.251795\pi$
$632$	−2.89489	−	2.89489i	−0.115153	−	0.115153i
$633$	12.1662	−	10.8606i	0.483565	−	0.431671i
$634$		−	22.8618i		−	0.907958i
$635$	20.2366	+	20.2366i	0.803065	+	0.803065i
$636$	0.280180	−	0.250112i	0.0111099	−	0.00991759i
$637$	−22.0151	−	11.1685i	−0.872271	−	0.442510i
$638$			11.9231i			0.472040i
$639$	0.286407	+	0.359939i	0.0113301	+	0.0142390i
$640$	−2.58423			−0.102150
$641$	−34.2846			−1.35416			−0.677081	−	0.735908i	$-0.736755\pi$
$641$	−34.2846			−1.35416			−0.677081	+	0.735908i	$0.736755\pi$
$642$	−7.97851	−	0.452383i	−0.314887	−	0.0178541i
$643$	−10.7873	−	10.7873i	−0.425411	−	0.425411i	0.461651	−	0.887062i	$-0.347257\pi$
$643$	−10.7873	−	10.7873i	−0.425411	−	0.425411i	−0.887062	+	0.461651i	$0.847257\pi$
$644$	−9.61619	−	9.61619i	−0.378931	−	0.378931i
$645$	−40.7071	−	2.30810i	−1.60284	−	0.0908813i
$646$	−6.83155			−0.268784
$647$	2.69550			0.105971			0.0529855	−	0.998595i	$-0.483126\pi$
$647$	2.69550			0.105971			0.0529855	+	0.998595i	$0.483126\pi$
$648$	4.77183	+	7.63084i	0.187455	+	0.299768i
$649$			16.8618i			0.661883i
$650$	−5.75146	+	1.87997i	−0.225591	+	0.0737385i
$651$	−2.18799	+	1.95319i	−0.0857541	+	0.0765514i
$652$	2.81201	+	2.81201i	0.110127	+	0.110127i
$653$			43.4774i			1.70140i	0.525651	+	0.850700i	$0.323822\pi$
$653$			43.4774i			1.70140i	−0.525651	+	0.850700i	$0.676178\pi$
$654$	16.8396	−	15.0325i	0.658481	−	0.587815i
$655$	−33.0772	−	33.0772i	−1.29243	−	1.29243i
$656$	−7.89729	+	7.89729i	−0.308337	+	0.308337i
$657$	9.46831	+	11.8992i	0.369394	+	0.464232i
$658$	17.5719	−	17.5719i	0.685024	−	0.685024i
$659$			39.2972i			1.53080i	0.643553	+	0.765401i	$0.277460\pi$
$659$			39.2972i			1.53080i	−0.643553	+	0.765401i	$0.722540\pi$
$660$	9.72461	+	10.8937i	0.378530	+	0.424036i
$661$	27.4958	−	27.4958i	1.06946	−	1.06946i	0.0720628	−	0.997400i	$-0.477042\pi$
$661$	27.4958	−	27.4958i	1.06946	−	1.06946i	0.997400	−	0.0720628i	$-0.0229582\pi$
$662$	7.81338			0.303676
$663$	−2.15792	−	8.13535i	−0.0838068	−	0.315951i
$664$	14.9558			0.580397
$665$	−34.4666	+	34.4666i	−1.33656	+	1.33656i
$666$	−8.23278	−	0.936611i	−0.319014	−	0.0362929i
$667$		−	13.3564i		−	0.517164i
$668$	0.959150	−	0.959150i	0.0371106	−	0.0371106i
$669$	−14.4133	−	0.817238i	−0.557252	−	0.0315962i
$670$	−5.84667	+	5.84667i	−0.225877	+	0.225877i
$671$	15.0523	+	15.0523i	0.581086	+	0.581086i
$672$	−4.29211	−	4.80810i	−0.165572	−	0.185476i
$673$			7.29153i			0.281068i	0.990076	+	0.140534i	$0.0448819\pi$
$673$			7.29153i			0.281068i	−0.990076	+	0.140534i	$0.955118\pi$
$674$	13.3128	+	13.3128i	0.512790	+	0.512790i
$675$	−7.12009	+	5.03466i	−0.274052	+	0.193784i
$676$	−10.4902	+	7.67822i	−0.403470	+	0.295316i
$677$			16.3200i			0.627230i	0.949550	+	0.313615i	$0.101540\pi$
$677$			16.3200i			0.627230i	−0.949550	+	0.313615i	$0.898460\pi$
$678$	5.94491	+	0.337077i	0.228313	+	0.0129454i
$679$	−0.886464			−0.0340194
$680$	3.48289			0.133563
$681$	1.27953	−	22.5666i	0.0490318	−	0.864756i
$682$	1.04979	+	1.04979i	0.0401984	+	0.0401984i
$683$	0.171761	+	0.171761i	0.00657223	+	0.00657223i	0.710385	−	0.703813i	$-0.248521\pi$
$683$	0.171761	+	0.171761i	0.00657223	+	0.00657223i	−0.703813	+	0.710385i	$0.748521\pi$
$684$	9.46831	+	11.8992i	0.362030	+	0.454978i
$685$	3.56910			0.136368
$686$	−0.570551			−0.0217837
$687$	1.27785	−	22.5369i	0.0487529	−	0.859838i
$688$		−	9.10912i		−	0.347282i
$689$	0.697233	+	0.353712i	0.0265625	+	0.0134754i
$690$	−10.8937	−	12.2033i	−0.414715	−	0.464571i
$691$	18.3218	+	18.3218i	0.696993	+	0.696993i	0.963761	−	0.266768i	$-0.0859556\pi$
$691$	18.3218	+	18.3218i	0.696993	+	0.696993i	−0.266768	+	0.963761i	$0.585956\pi$
$692$			17.4960i			0.665099i
$693$	−4.11678	+	36.1864i	−0.156383	+	1.37461i
$694$	−20.7057	−	20.7057i	−0.785977	−	0.785977i
$695$	12.9907	−	12.9907i	0.492764	−	0.492764i
$696$	0.358338	−	6.31988i	0.0135828	−	0.239555i
$697$	10.6436	−	10.6436i	0.403153	−	0.403153i
$698$		−	6.89931i		−	0.261143i
$699$	3.26095	−	2.91100i	0.123341	−	0.110104i
$700$	4.41577	−	4.41577i	0.166901	−	0.166901i
$701$	33.7243			1.27375			0.636874	−	0.770968i	$-0.280227\pi$
$701$	33.7243			1.27375			0.636874	+	0.770968i	$0.280227\pi$
$702$	−11.1794	+	15.0340i	−0.421938	+	0.567423i
$703$	−14.0000			−0.528020
$704$	−2.30690	+	2.30690i	−0.0869445	+	0.0869445i
$705$	22.2993	−	19.9063i	0.839841	−	0.749713i
$706$			7.90600i			0.297546i
$707$	−46.6065	+	46.6065i	−1.75282	+	1.75282i
$708$	0.506767	−	8.93766i	0.0190455	−	0.335898i
$709$	−3.79689	+	3.79689i	−0.142595	+	0.142595i	−0.774801	−	0.632206i	$-0.782150\pi$
$709$	−3.79689	+	3.79689i	−0.142595	+	0.142595i	0.632206	+	0.774801i	$0.282150\pi$
$710$	−0.280180	−	0.280180i	−0.0105150	−	0.0105150i
$711$	1.38832	−	12.2033i	0.0520660	−	0.457658i
$712$			12.5249i			0.469390i
$713$	−1.17599	−	1.17599i	−0.0440411	−	0.0440411i
$714$	5.78469	+	6.48010i	0.216487	+	0.242512i
$715$	−13.7527	+	27.1091i	−0.514321	+	1.01382i
$716$		−	18.1015i		−	0.676484i
$717$	0.998500	−	17.6102i	0.0372897	−	0.657664i
$718$	18.2182			0.679899
$719$	−30.6300			−1.14231			−0.571153	−	0.820844i	$-0.693504\pi$
$719$	−30.6300			−1.14231			−0.571153	+	0.820844i	$0.693504\pi$
$720$	−4.82717	−	6.06650i	−0.179898	−	0.226085i
$721$	20.8025	+	20.8025i	0.774724	+	0.774724i
$722$	4.73291	+	4.73291i	0.176141	+	0.176141i
$723$	2.83512	−	50.0020i	0.105439	−	1.85959i
$724$	−1.90600			−0.0708361
$725$	6.13331			0.227785
$726$	−0.616386	−	0.0349492i	−0.0228762	−	0.00129709i
$727$			0.430897i			0.0159811i	0.999968	+	0.00799055i	$0.00254350\pi$
$727$			0.430897i			0.0159811i	−0.999968	+	0.00799055i	$0.997457\pi$
$728$	6.06996	−	11.9650i	0.224968	−	0.443454i
$729$	−9.00000	+	25.4558i	−0.333333	+	0.942809i
$730$	−9.26245	−	9.26245i	−0.342819	−	0.342819i
$731$			12.2768i			0.454074i
$732$	−7.52613	−	8.43090i	−0.278174	−	0.311615i
$733$	8.50256	+	8.50256i	0.314049	+	0.314049i	0.846476	−	0.532427i	$-0.178720\pi$
$733$	8.50256	+	8.50256i	0.314049	+	0.314049i	−0.532427	+	0.846476i	$0.678720\pi$
$734$	5.35216	−	5.35216i	0.197552	−	0.197552i
$735$	30.5966	+	1.73483i	1.12857	+	0.0639903i
$736$	2.58423	−	2.58423i	0.0952558	−	0.0952558i
$737$			10.4385i			0.384506i
$738$	−33.2906	−	3.78734i	−1.22544	−	0.139414i
$739$	15.1836	−	15.1836i	0.558537	−	0.558537i	−0.370354	−	0.928891i	$-0.620764\pi$
$739$	15.1836	−	15.1836i	0.558537	−	0.558537i	0.928891	+	0.370354i	$0.120764\pi$
$740$	7.13753			0.262381
$741$	−15.8965	+	27.3741i	−0.583972	+	1.00561i
$742$	−0.806880			−0.0296215
$743$	1.06757	−	1.06757i	0.0391653	−	0.0391653i	−0.687253	−	0.726418i	$-0.741184\pi$
$743$	1.06757	−	1.06757i	0.0391653	−	0.0391653i	0.726418	+	0.687253i	$0.241184\pi$
$744$	−0.524893	−	0.587994i	−0.0192435	−	0.0215569i
$745$		−	32.3671i		−	1.18584i
$746$	11.1808	−	11.1808i	0.409357	−	0.409357i
$747$	27.9365	+	35.1089i	1.02214	+	1.28457i
$748$	3.10912	−	3.10912i	0.113681	−	0.113681i
$749$	12.1399	+	12.1399i	0.443583	+	0.443583i
$750$	−11.0918	+	9.90147i	−0.405015	+	0.361550i
$751$			1.88134i			0.0686509i	0.999411	+	0.0343255i	$0.0109283\pi$
$751$			1.88134i			0.0686509i	−0.999411	+	0.0343255i	$0.989072\pi$
$752$	4.72222	+	4.72222i	0.172201	+	0.172201i
$753$	−23.8913	+	21.3274i	−0.870646	+	0.777212i
$754$	12.5249	−	4.09400i	0.456130	−	0.149095i
$755$		−	43.1236i		−	1.56943i
$756$	3.26967	−	19.0570i	0.118917	−	0.693097i
$757$	−28.6189			−1.04017			−0.520086	−	0.854114i	$-0.674100\pi$
$757$	−28.6189			−1.04017			−0.520086	+	0.854114i	$0.674100\pi$
$758$	7.54752			0.274138
$759$	−20.6183	−	1.16906i	−0.748396	−	0.0424342i
$760$	−9.26245	−	9.26245i	−0.335984	−	0.335984i
$761$	30.4408	+	30.4408i	1.10348	+	1.10348i	0.993988	+	0.109490i	$0.0349218\pi$
$761$	30.4408	+	30.4408i	1.10348	+	1.10348i	0.109490	+	0.993988i	$0.465078\pi$
$762$	−19.1508	−	1.08585i	−0.693759	−	0.0393362i
$763$	−48.4958			−1.75567
$764$	6.35014			0.229740
$765$	6.50581	+	8.17612i	0.235218	+	0.295608i
$766$			15.3520i			0.554691i
$767$	17.7129	−	5.78978i	0.639575	−	0.209057i
$768$	1.29211	−	1.15345i	0.0466251	−	0.0416215i
$769$	14.9956	+	14.9956i	0.540755	+	0.540755i	0.923750	−	0.382996i	$-0.125108\pi$
$769$	14.9956	+	14.9956i	0.540755	+	0.540755i	−0.382996	+	0.923750i	$0.625108\pi$
$770$		−	31.3723i		−	1.13058i
$771$	−17.6627	+	15.7672i	−0.636107	+	0.567843i
$772$	4.26245	+	4.26245i	0.153409	+	0.153409i
$773$	−6.25917	+	6.25917i	−0.225127	+	0.225127i	−0.810653	−	0.585527i	$-0.800888\pi$
$773$	−6.25917	+	6.25917i	−0.225127	+	0.225127i	0.585527	+	0.810653i	$0.300888\pi$
$774$	21.3838	−	17.0153i	0.768623	−	0.611601i
$775$	0.540016	−	0.540016i	0.0193980	−	0.0193980i
$776$		−	0.238226i		−	0.00855180i
$777$	11.8547	+	13.2798i	0.425283	+	0.476409i
$778$	−3.26245	+	3.26245i	−0.116964	+	0.116964i
$779$	−56.6113			−2.02831
$780$	8.10440	−	13.9560i	0.290184	−	0.499704i
$781$	−0.500224			−0.0178994
$782$	−3.48289	+	3.48289i	−0.124548	+	0.124548i
$783$	15.5054	−	10.9639i	0.554116	−	0.391819i
$784$			6.84667i			0.244524i
$785$	34.4666	−	34.4666i	1.23017	−	1.23017i
$786$	31.3024	+	1.77485i	1.11652	+	0.0633068i
$787$	7.15333	−	7.15333i	0.254989	−	0.254989i	−0.568024	−	0.823012i	$-0.692292\pi$
$787$	7.15333	−	7.15333i	0.254989	−	0.254989i	0.823012	+	0.568024i	$0.192292\pi$
$788$	−2.78647	−	2.78647i	−0.0992640	−	0.0992640i
$789$	−16.8618	−	18.8889i	−0.600296	−	0.672461i
$790$			10.5798i			0.376413i
$791$	−9.04564	−	9.04564i	−0.321626	−	0.321626i
$792$	−9.72461	−	1.10633i	−0.345549	−	0.0393117i
$793$	10.6436	−	20.9805i	0.377964	−	0.745038i
$794$			17.7343i			0.629365i
$795$	−0.969015	−	0.0549433i	−0.0343674	−	0.00194864i
$796$	−17.2927			−0.612923
$797$	−28.0263			−0.992742			−0.496371	−	0.868110i	$-0.665335\pi$
$797$	−28.0263			−0.992742			−0.496371	+	0.868110i	$0.665335\pi$
$798$	1.84940	−	32.6172i	0.0654680	−	1.15464i
$799$	−6.36436	−	6.36436i	−0.225155	−	0.225155i
$800$	1.18668	+	1.18668i	0.0419555	+	0.0419555i
$801$	−29.4023	+	23.3957i	−1.03888	+	0.826647i
$802$	−5.14378			−0.181633
$803$	−16.5369			−0.583574
$804$	0.313719	−	5.53295i	0.0110640	−	0.195132i
$805$			35.1438i			1.23866i
$806$	0.742311	−	1.46324i	0.0261468	−	0.0515403i
$807$	18.2182	+	20.4084i	0.641312	+	0.718409i
$808$	−12.5249	−	12.5249i	−0.440624	−	0.440624i
$809$		−	35.1638i		−	1.23629i	−0.786062	−	0.618147i	$-0.787884\pi$
$809$		−	35.1638i		−	1.23629i	0.786062	−	0.618147i	$-0.212116\pi$
$810$	5.22433	−	22.6637i	0.183564	−	0.796320i
$811$	31.2529	+	31.2529i	1.09744	+	1.09744i	0.994709	+	0.102728i	$0.0327572\pi$
$811$	31.2529	+	31.2529i	1.09744	+	1.09744i	0.102728	+	0.994709i	$0.467243\pi$
$812$	−9.61619	+	9.61619i	−0.337462	+	0.337462i
$813$	2.25059	−	39.6929i	0.0789317	−	1.39209i
$814$	6.37157	−	6.37157i	0.223323	−	0.223323i
$815$		−	10.2769i		−	0.359984i
$816$	−1.74144	+	1.55456i	−0.0609627	+	0.0544205i
$817$	32.6491	−	32.6491i	1.14225	−	1.14225i
$818$	26.3035			0.919679
$819$	39.4264	−	8.10064i	1.37767	−	0.283059i
$820$	28.8618			1.00790
$821$	−13.0081	+	13.0081i	−0.453986	+	0.453986i	−0.896675	−	0.442689i	$-0.854024\pi$
$821$	−13.0081	+	13.0081i	−0.453986	+	0.453986i	0.442689	+	0.896675i	$0.354024\pi$
$822$	−1.78455	+	1.59304i	−0.0622434	+	0.0555637i
$823$			19.5356i			0.680968i	0.940250	+	0.340484i	$0.110591\pi$
$823$			19.5356i			0.680968i	−0.940250	+	0.340484i	$0.889409\pi$
$824$	−5.59039	+	5.59039i	−0.194750	+	0.194750i
$825$	0.536834	−	9.46796i	0.0186902	−	0.329632i
$826$	−13.5993	+	13.5993i	−0.473182	+	0.473182i
$827$	−18.6720	−	18.6720i	−0.649290	−	0.649290i	0.303532	−	0.952821i	$-0.401834\pi$
$827$	−18.6720	−	18.6720i	−0.649290	−	0.649290i	−0.952821	+	0.303532i	$0.901834\pi$
$828$	10.8937	+	1.23933i	0.378581	+	0.0430697i
$829$		−	2.85622i		−	0.0992006i	−0.998769	−	0.0496003i	$-0.984205\pi$
$829$		−	2.85622i		−	0.0992006i	0.998769	−	0.0496003i	$-0.0157947\pi$
$830$	−27.3291	−	27.3291i	−0.948606	−	0.948606i
$831$	30.1614	+	33.7873i	1.04629	+	1.17207i
$832$	3.21545	+	1.63122i	0.111476	+	0.0565525i
$833$		−	9.22759i		−	0.319717i
$834$	−0.697049	+	12.2936i	−0.0241368	+	0.425693i
$835$	−3.50535			−0.121308
$836$	−16.5369			−0.571940
$837$	0.399856	−	2.33053i	0.0138210	−	0.0805549i
$838$	−0.250112	−	0.250112i	−0.00863998	−	0.00863998i
$839$	−35.2438	−	35.2438i	−1.21675	−	1.21675i	−0.968763	−	0.247988i	$-0.920231\pi$
$839$	−35.2438	−	35.2438i	−1.21675	−	1.21675i	−0.247988	−	0.968763i	$-0.579769\pi$
$840$	−0.942868	+	16.6290i	−0.0325320	+	0.573756i
$841$	15.6436			0.539433
$842$	−32.3979			−1.11651
$843$	7.49969	+	0.425233i	0.258303	+	0.0146458i
$844$		−	9.41577i		−	0.324104i
$845$	33.1996	+	5.13845i	1.14210	+	0.176768i
$846$	−2.26466	+	19.9063i	−0.0778605	+	0.684391i
$847$	0.937879	+	0.937879i	0.0322259	+	0.0322259i
$848$		−	0.216838i		−	0.00744626i
$849$	−10.7922	−	12.0896i	−0.370387	−	0.414913i
$850$	−1.59935	−	1.59935i	−0.0548572	−	0.0548572i
$851$	−7.13753	+	7.13753i	−0.244671	+	0.244671i
$852$	0.265146	+	0.0150338i	0.00908375	+	0.000515050i
$853$	31.6217	−	31.6217i	1.08271	−	1.08271i	0.0864494	−	0.996256i	$-0.472448\pi$
$853$	31.6217	−	31.6217i	1.08271	−	1.08271i	0.996256	−	0.0864494i	$-0.0275521\pi$
$854$			24.2799i			0.830840i
$855$	4.44204	−	39.0454i	0.151914	−	1.33532i
$856$	−3.26245	+	3.26245i	−0.111508	+	0.111508i
$857$	21.9628			0.750234			0.375117	−	0.926978i	$-0.377603\pi$
$857$	21.9628			0.750234			0.375117	+	0.926978i	$0.377603\pi$
$858$	−5.22361	−	19.6930i	−0.178331	−	0.672307i
$859$	−37.2680			−1.27157			−0.635784	−	0.771867i	$-0.719323\pi$
$859$	−37.2680			−1.27157			−0.635784	+	0.771867i	$0.719323\pi$
$860$	−16.6453	+	16.6453i	−0.567600	+	0.567600i
$861$	47.9363	+	53.6990i	1.63366	+	1.83006i
$862$			8.34132i			0.284106i
$863$	36.6549	−	36.6549i	1.24775	−	1.24775i	0.291034	−	0.956713i	$-0.406001\pi$
$863$	36.6549	−	36.6549i	1.24775	−	1.24775i	0.956713	−	0.291034i	$-0.0939993\pi$
$864$	5.12132	+	0.878680i	0.174231	+	0.0298933i
$865$	31.9709	−	31.9709i	1.08704	−	1.08704i
$866$	26.5938	+	26.5938i	0.903695	+	0.903695i
$867$	−19.6189	+	17.5135i	−0.666292	+	0.594789i
$868$			1.69334i			0.0574758i
$869$	9.44443	+	9.44443i	0.320380	+	0.320380i
$870$	−12.2033	+	10.8937i	−0.413730	+	0.369330i
$871$	10.9653	−	3.58423i	0.371546	−	0.121447i
$872$		−	13.0326i		−	0.441340i
$873$	0.559237	−	0.444990i	0.0189273	−	0.0150606i
$874$	18.5249			0.626614
$875$	31.9429			1.07987
$876$	8.76544	+	0.497002i	0.296157	+	0.0167921i
$877$	−9.24012	−	9.24012i	−0.312017	−	0.312017i	0.533674	−	0.845690i	$-0.320811\pi$
$877$	−9.24012	−	9.24012i	−0.312017	−	0.312017i	−0.845690	+	0.533674i	$0.820811\pi$
$878$	12.7279	+	12.7279i	0.429547	+	0.429547i
$879$	7.34478	+	0.416450i	0.247733	+	0.0140465i
$880$	8.43090			0.284205
$881$	40.6450			1.36936			0.684682	−	0.728842i	$-0.259941\pi$
$881$	40.6450			1.36936			0.684682	+	0.728842i	$0.259941\pi$
$882$	−16.0726	+	12.7892i	−0.541194	+	0.430633i
$883$			13.2580i			0.446168i	0.974799	+	0.223084i	$0.0716125\pi$
$883$			13.2580i			0.446168i	−0.974799	+	0.223084i	$0.928388\pi$
$884$	−4.33362	−	2.19848i	−0.145755	−	0.0739428i
$885$	−17.2580	+	15.4060i	−0.580122	+	0.517866i
$886$	−21.7801	−	21.7801i	−0.731718	−	0.731718i
$887$		−	17.2792i		−	0.580179i	−0.957000	−	0.290089i	$-0.906315\pi$
$887$		−	17.2792i		−	0.580179i	0.957000	−	0.290089i	$-0.0936850\pi$
$888$	−3.56877	+	3.18578i	−0.119760	+	0.106908i
$889$	29.1394	+	29.1394i	0.977303	+	0.977303i
$890$	22.8870	−	22.8870i	0.767175	−	0.767175i
$891$	−15.5678	−	24.8952i	−0.521542	−	0.834020i
$892$	−5.89367	+	5.89367i	−0.197335	+	0.197335i
$893$			33.8510i			1.13278i
$894$	14.4468	+	16.1836i	0.483174	+	0.541260i
$895$	−33.0772	+	33.0772i	−1.10565	+	1.10565i
$896$	−3.72111			−0.124314
$897$	5.85157	+	22.0604i	0.195378	+	0.736575i
$898$	27.1740			0.906809
$899$	−1.17599	+	1.17599i	−0.0392214	+	0.0392214i
$900$	−0.569103	+	5.00240i	−0.0189701	+	0.166747i
$901$			0.292244i			0.00973605i
$902$	25.7645	−	25.7645i	0.857863	−	0.857863i
$903$	−58.6155	−	3.32351i	−1.95060	−	0.110599i
$904$	2.43090	−	2.43090i	0.0808504	−	0.0808504i
$905$	3.48289	+	3.48289i	0.115775	+	0.115775i
$906$	19.2479	+	21.5618i	0.639469	+	0.716343i
$907$			12.4656i			0.413912i	0.978350	+	0.206956i	$0.0663557\pi$
$907$			12.4656i			0.413912i	−0.978350	+	0.206956i	$0.933644\pi$
$908$	−9.22759	−	9.22759i	−0.306228	−	0.306228i
$909$	6.00662	−	52.7980i	0.199227	−	1.75120i
$910$	−32.9558	+	10.7722i	−1.09247	+	0.357096i
$911$			8.70212i			0.288314i	0.989555	+	0.144157i	$0.0460470\pi$
$911$			8.70212i			0.288314i	−0.989555	+	0.144157i	$0.953953\pi$
$912$	8.76544	+	0.497002i	0.290253	+	0.0164574i
$913$	−48.7925			−1.61480
$914$	16.2148			0.536336
$915$	−1.65330	+	29.1587i	−0.0546564	+	0.963955i
$916$	−9.21545	−	9.21545i	−0.304487	−	0.304487i
$917$	−47.6290	−	47.6290i	−1.57285	−	1.57285i
$918$	−6.90225	−	1.18424i	−0.227808	−	0.0390857i
$919$	−50.9311			−1.68006			−0.840031	−	0.542538i	$-0.817463\pi$
$919$	−50.9311			−1.68006			−0.840031	+	0.542538i	$0.817463\pi$
$920$	−9.44443			−0.311374
$921$	−0.450286	+	7.94153i	−0.0148374	+	0.261682i
$922$		−	3.68335i		−	0.121305i
$923$	0.171761	+	0.525473i	0.00565357	+	0.0172961i
$924$	14.0028	+	15.6862i	0.460658	+	0.516037i
$925$	−3.27757	−	3.27757i	−0.107766	−	0.107766i
$926$		−	11.6010i		−	0.381231i
$927$	−23.5660	−	2.68101i	−0.774009	−	0.0880559i
$928$	−2.58423	−	2.58423i	−0.0848314	−	0.0848314i
$929$	−13.2534	+	13.2534i	−0.434830	+	0.434830i	−0.890268	−	0.455438i	$-0.849483\pi$
$929$	−13.2534	+	13.2534i	−0.434830	+	0.434830i	0.455438	+	0.890268i	$0.349483\pi$
$930$	−0.115306	+	2.03360i	−0.00378102	+	0.0666845i
$931$	−24.5400	+	24.5400i	−0.804267	+	0.804267i
$932$		−	2.52374i		−	0.0826677i
$933$	4.44204	−	3.96534i	0.145426	−	0.129819i
$934$	16.0940	−	16.0940i	0.526612	−	0.526612i
$935$	−11.3627			−0.371601
$936$	2.17694	+	10.5953i	0.0711555	+	0.346319i
$937$	−46.8227			−1.52963			−0.764816	−	0.644249i	$-0.777170\pi$
$937$	−46.8227			−1.52963			−0.764816	+	0.644249i	$0.777170\pi$
$938$	−8.41882	+	8.41882i	−0.274884	+	0.274884i
$939$	1.95079	−	1.74144i	0.0636617	−	0.0568298i
$940$		−	17.2580i		−	0.562895i
$941$	−29.2015	+	29.2015i	−0.951941	+	0.951941i	−0.998897	−	0.0469563i	$-0.985048\pi$
$941$	−29.2015	+	29.2015i	−0.951941	+	0.951941i	0.0469563	+	0.998897i	$0.485048\pi$
$942$	−1.84940	+	32.6172i	−0.0602567	+	1.06273i
$943$	−28.8618	+	28.8618i	−0.939869	+	0.939869i
$944$	−3.65465	−	3.65465i	−0.118949	−	0.118949i
$945$	−40.7980	+	28.8486i	−1.32716	+	0.938444i
$946$			29.7180i			0.966216i
$947$	15.7495	+	15.7495i	0.511790	+	0.511790i	0.915075	−	0.403285i	$-0.132132\pi$
$947$	15.7495	+	15.7495i	0.511790	+	0.511790i	−0.403285	+	0.915075i	$0.632132\pi$
$948$	−4.72222	−	5.28990i	−0.153370	−	0.171808i
$949$	5.67822	+	17.3716i	0.184323	+	0.563905i
$950$			8.50667i			0.275993i
$951$	2.24160	−	39.5343i	0.0726888	−	1.28199i
$952$	5.01512			0.162541
$953$	11.6612			0.377742			0.188871	−	0.982002i	$-0.439517\pi$
$953$	11.6612			0.377742			0.188871	+	0.982002i	$0.439517\pi$
$954$	0.509031	−	0.405041i	0.0164805	−	0.0131137i
$955$	−11.6038	−	11.6038i	−0.375489	−	0.375489i
$956$	−7.20087	−	7.20087i	−0.232893	−	0.232893i
$957$	−1.16906	+	20.6183i	−0.0377903	+	0.666494i
$958$	−24.5898			−0.794460
$959$	5.13927			0.165956
$960$	−4.46883	−	0.253383i	−0.144231	−	0.00817791i
$961$		−	30.7929i		−	0.993320i
$962$	−8.88095	−	4.50538i	−0.286333	−	0.145259i
$963$	−13.7527	−	1.56459i	−0.443174	−	0.0504181i
$964$	−20.4460	−	20.4460i	−0.658522	−	0.658522i
$965$		−	15.5777i		−	0.501465i
$966$	−15.6862	−	17.5719i	−0.504694	−	0.565366i
$967$	30.7857	+	30.7857i	0.990002	+	0.990002i	0.999951	−	0.00994880i	$-0.00316685\pi$
$967$	30.7857	+	30.7857i	0.990002	+	0.990002i	−0.00994880	+	0.999951i	$0.503167\pi$
$968$	−0.252043	+	0.252043i	−0.00810096	+	0.00810096i
$969$	−11.8136	−	0.669834i	−0.379508	−	0.0215182i
$970$	−0.435315	+	0.435315i	−0.0139771	+	0.0139771i
$971$		−	8.74884i		−	0.280764i	−0.990097	−	0.140382i	$-0.955167\pi$
$971$		−	8.74884i		−	0.280764i	0.990097	−	0.140382i	$-0.0448330\pi$
$972$	7.50359	+	13.6637i	0.240678	+	0.438263i
$973$	18.7057	−	18.7057i	0.599677	−	0.599677i
$974$	−14.1635			−0.453829
$975$	−10.1302	+	2.68705i	−0.324425	+	0.0860546i
$976$	−6.52489			−0.208857
$977$	−10.7297	+	10.7297i	−0.343272	+	0.343272i	−0.857596	−	0.514324i	$-0.828043\pi$
$977$	−10.7297	+	10.7297i	−0.343272	+	0.343272i	0.514324	+	0.857596i	$0.328043\pi$
$978$	4.58701	+	5.13845i	0.146677	+	0.164309i
$979$		−	40.8618i		−	1.30595i
$980$	12.5111	−	12.5111i	0.399652	−	0.399652i
$981$	30.5942	−	24.3441i	0.976798	−	0.777247i
$982$	−0.581437	+	0.581437i	−0.0185544	+	0.0185544i
$983$	−12.8087	−	12.8087i	−0.408534	−	0.408534i	0.472693	−	0.881227i	$-0.343282\pi$
$983$	−12.8087	−	12.8087i	−0.408534	−	0.408534i	−0.881227	+	0.472693i	$0.843282\pi$
$984$	−14.4309	+	12.8822i	−0.460040	+	0.410671i
$985$			10.1836i			0.324476i
$986$	3.48289	+	3.48289i	0.110918	+	0.110918i
$987$	32.1095	−	28.6637i	1.02206	−	0.912375i
$988$	5.67822	+	17.3716i	0.180648	+	0.552663i
$989$		−	33.2906i		−	1.05858i
$990$	15.7484	+	19.7916i	0.500517	+	0.629019i
$991$	45.2289			1.43674			0.718372	−	0.695659i	$-0.244887\pi$
$991$	45.2289			1.43674			0.718372	+	0.695659i	$0.244887\pi$
$992$	−0.455064			−0.0144483
$993$	13.5115	+	0.766102i	0.428773	+	0.0243115i
$994$	−0.403440	−	0.403440i	−0.0127963	−	0.0127963i
$995$	31.5993	+	31.5993i	1.00177	+	1.00177i
$996$	25.8626	+	1.46642i	0.819489	+	0.0464652i
$997$	49.4416			1.56583			0.782916	−	0.622128i	$-0.213732\pi$
$997$	49.4416			1.56583			0.782916	+	0.622128i	$0.213732\pi$
$998$	−6.11192			−0.193469
$999$	−14.1449	−	2.42688i	−0.447525	−	0.0767831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.g.a.47.6	yes	12
3.2	odd	2	inner	78.2.g.a.47.3	yes	12
4.3	odd	2		624.2.bf.f.593.2		12
12.11	even	2		624.2.bf.f.593.1		12
13.5	odd	4	inner	78.2.g.a.5.3	✓	12
13.8	odd	4		1014.2.g.b.239.6		12
13.12	even	2		1014.2.g.b.437.3		12
39.5	even	4	inner	78.2.g.a.5.6	yes	12
39.8	even	4		1014.2.g.b.239.3		12
39.38	odd	2		1014.2.g.b.437.6		12
52.31	even	4		624.2.bf.f.161.2		12
156.83	odd	4		624.2.bf.f.161.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.g.a.5.3	✓	12	13.5	odd	4	inner
78.2.g.a.5.6	yes	12	39.5	even	4	inner
78.2.g.a.47.3	yes	12	3.2	odd	2	inner
78.2.g.a.47.6	yes	12	1.1	even	1	trivial
624.2.bf.f.161.1		12	156.83	odd	4
624.2.bf.f.161.2		12	52.31	even	4
624.2.bf.f.593.1		12	12.11	even	2
624.2.bf.f.593.2		12	4.3	odd	2
1014.2.g.b.239.3		12	39.8	even	4
1014.2.g.b.239.6		12	13.8	odd	4
1014.2.g.b.437.3		12	13.12	even	2
1014.2.g.b.437.6		12	39.38	odd	2

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.29211 - 1.15345i) q^{3} -1.00000i q^{4} +(-1.82732 + 1.82732i) q^{5} +(0.0980500 - 1.72927i) q^{6} +(-2.63122 + 2.63122i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.339111 - 2.98077i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.29211 - 1.15345i) q^{3} -1.00000i q^{4} +(-1.82732 + 1.82732i) q^{5} +(0.0980500 - 1.72927i) q^{6} +(-2.63122 + 2.63122i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.339111 - 2.98077i) q^{9} +2.58423i q^{10} +(2.30690 + 2.30690i) q^{11} +(-1.15345 - 1.29211i) q^{12} +(1.63122 - 3.21545i) q^{13} +3.72111i q^{14} +(-0.253383 + 4.46883i) q^{15} -1.00000 q^{16} +1.34775 q^{17} +(-1.86794 - 2.34751i) q^{18} +(-3.58423 - 3.58423i) q^{19} +(1.82732 + 1.82732i) q^{20} +(-0.364855 + 6.43482i) q^{21} +3.26245 q^{22} -3.65465 q^{23} +(-1.72927 - 0.0980500i) q^{24} -1.67822i q^{25} +(-1.12022 - 3.42711i) q^{26} +(-3.00000 - 4.24264i) q^{27} +(2.63122 + 2.63122i) q^{28} +3.65465i q^{29} +(2.98077 + 3.33911i) q^{30} +(0.321779 + 0.321779i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.64166 + 0.319883i) q^{33} +(0.953002 - 0.953002i) q^{34} -9.61619i q^{35} +(-2.98077 - 0.339111i) q^{36} +(1.95300 - 1.95300i) q^{37} -5.06886 q^{38} +(-1.60113 - 6.03626i) q^{39} +2.58423 q^{40} +(7.89729 - 7.89729i) q^{41} +(4.29211 + 4.80810i) q^{42} +9.10912i q^{43} +(2.30690 - 2.30690i) q^{44} +(4.82717 + 6.06650i) q^{45} +(-2.58423 + 2.58423i) q^{46} +(-4.72222 - 4.72222i) q^{47} +(-1.29211 + 1.15345i) q^{48} -6.84667i q^{49} +(-1.18668 - 1.18668i) q^{50} +(1.74144 - 1.55456i) q^{51} +(-3.21545 - 1.63122i) q^{52} +0.216838i q^{53} +(-5.12132 - 0.878680i) q^{54} -8.43090 q^{55} +3.72111 q^{56} +(-8.76544 - 0.497002i) q^{57} +(2.58423 + 2.58423i) q^{58} +(3.65465 + 3.65465i) q^{59} +(4.46883 + 0.253383i) q^{60} +6.52489 q^{61} +0.455064 q^{62} +(6.95080 + 8.73535i) q^{63} +1.00000i q^{64} +(2.89489 + 8.85644i) q^{65} +(4.21545 - 3.76307i) q^{66} +(2.26245 + 2.26245i) q^{67} -1.34775i q^{68} +(-4.72222 + 4.21545i) q^{69} +(-6.79967 - 6.79967i) q^{70} +(-0.108419 + 0.108419i) q^{71} +(-2.34751 + 1.86794i) q^{72} +(-3.58423 + 3.58423i) q^{73} -2.76196i q^{74} +(-1.93574 - 2.16845i) q^{75} +(-3.58423 + 3.58423i) q^{76} -12.1399 q^{77} +(-5.40045 - 3.13611i) q^{78} +4.09400 q^{79} +(1.82732 - 1.82732i) q^{80} +(-8.77001 - 2.02162i) q^{81} -11.1685i q^{82} +(-10.5753 + 10.5753i) q^{83} +(6.43482 + 0.364855i) q^{84} +(-2.46277 + 2.46277i) q^{85} +(6.44112 + 6.44112i) q^{86} +(4.21545 + 4.72222i) q^{87} -3.26245i q^{88} +(-8.85644 - 8.85644i) q^{89} +(7.70299 + 0.876338i) q^{90} +(4.16845 + 12.7527i) q^{91} +3.65465i q^{92} +(0.786930 + 0.0446190i) q^{93} -6.67822 q^{94} +13.0991 q^{95} +(-0.0980500 + 1.72927i) q^{96} +(0.168451 + 0.168451i) q^{97} +(-4.84133 - 4.84133i) q^{98} +(7.65863 - 6.09404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{7}+O(q^{10}) \) 12 * q - 12 * q^7	\( 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^7 - 12 * q^16 - 12 * q^19 - 36 * q^27 + 12 * q^28 + 12 * q^31 + 36 * q^33 + 12 * q^37 + 36 * q^42 + 36 * q^45 + 12 * q^52 - 36 * q^54 - 36 * q^57 - 36 * q^63 - 12 * q^67 - 12 * q^73 - 12 * q^76 - 36 * q^78 + 72 * q^79 - 72 * q^85 - 12 * q^91 + 36 * q^93 - 72 * q^94 - 60 * q^97 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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