LMFDB - Embedded newform 78.2.g.a.47.3

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			47.3
Root			$-0.0980500 + 1.72927i$ of defining polynomial
Character	$\chi$	$=$	78.47
Dual form			78.2.g.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.29211 + 1.15345i) q^{3} -1.00000i q^{4} +(1.82732 - 1.82732i) q^{5} +(-1.72927 + 0.0980500i) q^{6} +(-2.63122 + 2.63122i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.339111 + 2.98077i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.29211 + 1.15345i) q^{3} -1.00000i q^{4} +(1.82732 - 1.82732i) q^{5} +(-1.72927 + 0.0980500i) 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} +(4.46883 - 0.253383i) q^{15} -1.00000 q^{16} -1.34775 q^{17} +(-2.34751 - 1.86794i) q^{18} +(-3.58423 - 3.58423i) q^{19} +(-1.82732 - 1.82732i) q^{20} +(-6.43482 + 0.364855i) q^{21} +3.26245 q^{22} +3.65465 q^{23} +(0.0980500 + 1.72927i) 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} +(-0.319883 - 5.64166i) 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} +(5.81658 - 2.27319i) 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} +(6.06650 + 4.82717i) 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} +(-0.878680 - 5.12132i) q^{54} -8.43090 q^{55} -3.72111 q^{56} +(-0.497002 - 8.76544i) q^{57} +(2.58423 + 2.58423i) q^{58} +(-3.65465 - 3.65465i) q^{59} +(-0.253383 - 4.46883i) q^{60} +6.52489 q^{61} -0.455064 q^{62} +(-8.73535 - 6.95080i) 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} +(-1.86794 + 2.34751i) 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} +(-2.50556 + 5.72033i) 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} +(0.364855 + 6.43482i) 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} +(0.0446190 + 0.786930i) q^{93} -6.67822 q^{94} -13.0991 q^{95} +(1.72927 - 0.0980500i) q^{96} +(0.168451 + 0.168451i) q^{97} +(4.84133 + 4.84133i) q^{98} +(6.09404 - 7.65863i) 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	−0.168498	−	0.985702i	$-0.553892\pi$
$5$	1.82732	−	1.82732i	0.817204	−	0.817204i	0.985702	+	0.168498i	$0.0538917\pi$
$6$	−1.72927	+	0.0980500i	−0.705973	+	0.0400288i
$7$	−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	0.267893	−	0.963449i	$-0.413673\pi$
$11$	−2.30690	−	2.30690i	−0.695556	−	0.695556i	−0.963449	+	0.267893i	$0.913673\pi$
$12$	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
$15$	4.46883	−	0.253383i	1.15385	−	0.0654233i
$16$	−1.00000			−0.250000
$17$	−1.34775			−0.326877			−0.163439	−	0.986554i	$-0.552259\pi$
$17$	−1.34775			−0.326877			−0.163439	+	0.986554i	$0.552259\pi$
$18$	−2.34751	−	1.86794i	−0.553314	−	0.440277i
$19$	−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
$21$	−6.43482	+	0.364855i	−1.40419	+	0.0796179i
$22$	3.26245			0.695556
$23$	3.65465			0.762047			0.381023	−	0.924565i	$-0.375572\pi$
$23$	3.65465			0.762047			0.381023	+	0.924565i	$0.375572\pi$
$24$	0.0980500	+	1.72927i	0.0200144	+	0.352986i
$25$		−	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	$-0.889801\pi$
$29$		−	3.65465i		−	0.678651i	0.940669	−	0.339325i	$-0.110199\pi$
$30$	−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
$33$	−0.319883	−	5.64166i	−0.0556845	−	0.982087i
$34$	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
$39$	5.81658	−	2.27319i	0.931398	−	0.364002i
$40$	2.58423			0.408602
$41$	−7.89729	+	7.89729i	−1.23335	+	1.23335i	−0.270680	+	0.962670i	$0.587248\pi$
$41$	−7.89729	+	7.89729i	−1.23335	+	1.23335i	−0.962670	+	0.270680i	$0.912752\pi$
$42$	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
$45$	6.06650	+	4.82717i	0.904340	+	0.719592i
$46$	−2.58423	+	2.58423i	−0.381023	+	0.381023i
$47$	4.72222	+	4.72222i	0.688806	+	0.688806i	0.961968	−	0.273162i	$-0.0880695\pi$
$47$	4.72222	+	4.72222i	0.688806	+	0.688806i	−0.273162	+	0.961968i	$0.588070\pi$
$48$	−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	$-0.995259\pi$
$53$		−	0.216838i		−	0.0297851i	0.999889	−	0.0148925i	$-0.00474061\pi$
$54$	−0.878680	−	5.12132i	−0.119573	−	0.696923i
$55$	−8.43090			−1.13682
$56$	−3.72111			−0.497254
$57$	−0.497002	−	8.76544i	−0.0658295	−	1.16101i
$58$	2.58423	+	2.58423i	0.339325	+	0.339325i
$59$	−3.65465	−	3.65465i	−0.475794	−	0.475794i	0.427989	−	0.903784i	$-0.359222\pi$
$59$	−3.65465	−	3.65465i	−0.475794	−	0.475794i	−0.903784	+	0.427989i	$0.859222\pi$
$60$	−0.253383	−	4.46883i	−0.0327117	−	0.576924i
$61$	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
$63$	−8.73535	−	6.95080i	−1.10055	−	0.875719i
$64$			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	−0.700644	−	0.713511i	$-0.747104\pi$
$71$	0.108419	−	0.108419i	0.0128670	−	0.0128670i	0.713511	+	0.700644i	$0.247104\pi$
$72$	−1.86794	+	2.34751i	−0.220138	+	0.276657i
$73$	−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
$78$	−2.50556	+	5.72033i	−0.283698	+	0.647700i
$79$	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	$-0.443525\pi$
$83$	10.5753	−	10.5753i	1.16079	−	1.16079i	0.984302	−	0.176492i	$-0.0564751\pi$
$84$	0.364855	+	6.43482i	0.0398090	+	0.702096i
$85$	−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	0.998231	−	0.0594508i	$-0.0189349\pi$
$89$	8.85644	+	8.85644i	0.938780	+	0.938780i	−0.0594508	+	0.998231i	$0.518935\pi$
$90$	−7.70299	+	0.876338i	−0.811966	+	0.0923742i
$91$	4.16845	+	12.7527i	0.436972	+	1.33684i
$92$		−	3.65465i		−	0.381023i
$93$	0.0446190	+	0.786930i	0.00462678	+	0.0816008i
$94$	−6.67822			−0.688806
$95$	−13.0991			−1.34394
$96$	1.72927	−	0.0980500i	0.176493	−	0.0100072i
$97$	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
$99$	6.09404	−	7.65863i	0.612475	−	0.769721i
$100$	−1.67822			−0.167822
$101$	−17.7129			−1.76250			−0.881248	−	0.472653i	$-0.843296\pi$
$101$	−17.7129			−1.76250			−0.881248	+	0.472653i	$0.843296\pi$
$102$	2.33063	−	0.132147i	0.230766	−	0.0130845i
$103$		−	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	$0.0715903\pi$
$107$			4.61380i			0.446033i	−0.974815	+	0.223016i	$0.928410\pi$
$108$	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
$111$	4.77619	−	0.270810i	0.453336	−	0.0257042i
$112$	2.63122	−	2.63122i	0.248627	−	0.248627i
$113$		−	3.43781i		−	0.323402i	−0.986840	−	0.161701i	$-0.948302\pi$
$113$		−	3.43781i		−	0.323402i	0.986840	−	0.161701i	$-0.0516980\pi$
$114$	6.54954	+	5.84667i	0.613421	+	0.547591i
$115$	6.67822	−	6.67822i	0.622747	−	0.622747i
$116$	−3.65465			−0.339325
$117$	10.1377	+	3.77191i	0.937229	+	0.348713i
$118$	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
$123$	−19.3133	+	1.09507i	−1.74142	+	0.0987389i
$124$	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	$-0.709682\pi$
$131$		−	18.1015i		−	1.58153i	0.612118	−	0.790767i	$-0.290318\pi$
$132$	−5.64166	+	0.319883i	−0.491044	+	0.0278422i
$133$	18.8618			1.63553
$134$	−3.19958			−0.276402
$135$	2.27071	+	13.2346i	0.195431	+	1.13906i
$136$	−0.953002	−	0.953002i	−0.0817193	−	0.0817193i
$137$	0.976593	+	0.976593i	0.0834360	+	0.0834360i	0.747593	−	0.664157i	$-0.231209\pi$
$137$	0.976593	+	0.976593i	0.0834360	+	0.0834360i	−0.664157	+	0.747593i	$0.731209\pi$
$138$	−6.31988	+	0.358338i	−0.537984	+	0.0305038i
$139$	−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
$141$	0.654800	+	11.5485i	0.0551441	+	0.972557i
$142$			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	−0.244182	−	0.969729i	$-0.578519\pi$
$149$	8.85644	−	8.85644i	0.725548	−	0.725548i	0.969729	+	0.244182i	$0.0785194\pi$
$150$	0.164550	+	2.90210i	0.0134354	+	0.236956i
$151$	−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
$156$	−2.27319	−	5.81658i	−0.182001	−	0.465699i
$157$	−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
$162$	4.77183	−	7.63084i	0.374910	−	0.599535i
$163$	−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	0.669022	−	0.743243i	$-0.266713\pi$
$167$	−0.959150	−	0.959150i	−0.0742212	−	0.0742212i	−0.743243	+	0.669022i	$0.766713\pi$
$168$	−4.80810	−	4.29211i	−0.370953	−	0.331144i
$169$	−7.67822	−	10.4902i	−0.590632	−	0.806941i
$170$		−	3.48289i		−	0.267125i
$171$	9.46831	−	11.8992i	0.724060	−	0.909955i
$172$	9.10912			0.694564
$173$	17.4960			1.33020			0.665099	−	0.746755i	$-0.268389\pi$
$173$	17.4960			1.33020			0.665099	+	0.746755i	$0.268389\pi$
$174$	0.358338	+	6.31988i	0.0271655	+	0.479109i
$175$	4.41577	+	4.41577i	0.333801	+	0.333801i
$176$	2.30690	+	2.30690i	0.173889	+	0.173889i
$177$	−0.506767	−	8.93766i	−0.0380909	−	0.671796i
$178$	−12.5249			−0.938780
$179$	−18.1015			−1.35297			−0.676484	−	0.736458i	$-0.736497\pi$
$179$	−18.1015			−1.35297			−0.676484	+	0.736458i	$0.736497\pi$
$180$	4.82717	−	6.06650i	0.359796	−	0.452170i
$181$		−	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
$189$	−3.26967	−	19.0570i	−0.237833	−	1.38619i
$190$	9.26245	−	9.26245i	0.671969	−	0.671969i
$191$		−	6.35014i		−	0.459480i	−0.973252	−	0.229740i	$-0.926212\pi$
$191$		−	6.35014i		−	0.459480i	0.973252	−	0.229740i	$-0.0737876\pi$
$192$	−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
$195$	6.47492	−	14.7826i	0.463679	−	1.05861i
$196$	−6.84667			−0.489048
$197$	−2.78647	+	2.78647i	−0.198528	+	0.198528i	−0.799369	−	0.600841i	$-0.794833\pi$
$197$	−2.78647	+	2.78647i	−0.198528	+	0.198528i	0.600841	+	0.799369i	$0.294833\pi$
$198$	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
$201$	0.313719	+	5.53295i	0.0221280	+	0.390264i
$202$	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
$210$	−0.942868	−	16.6290i	−0.0650641	−	1.14751i
$211$	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
$213$	0.265146	−	0.0150338i	0.0181675	−	0.00103010i
$214$	−3.26245	−	3.26245i	−0.223016	−	0.223016i
$215$	16.6453	+	16.6453i	1.13520	+	1.13520i
$216$	−5.12132	+	0.878680i	−0.348462	+	0.0597866i
$217$	−1.69334			−0.114952
$218$	−13.0326			−0.882680
$219$	−8.76544	+	0.497002i	−0.592314	+	0.0335843i
$220$			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	−0.943586	−	0.331129i	$-0.892571\pi$
$227$	−9.22759	+	9.22759i	−0.612457	+	0.612457i	0.331129	+	0.943586i	$0.392571\pi$
$228$	−8.76544	+	0.497002i	−0.580506	+	0.0329148i
$229$	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	$-0.526344\pi$
$233$	−2.52374			−0.165335			−0.0826677	+	0.996577i	$0.526344\pi$
$234$	−9.83557	+	4.50128i	−0.642971	+	0.294258i
$235$	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	−0.900546	−	0.434760i	$-0.856833\pi$
$239$	−7.20087	+	7.20087i	−0.465786	+	0.465786i	0.434760	+	0.900546i	$0.356833\pi$
$240$	−4.46883	+	0.253383i	−0.288462	+	0.0163558i
$241$	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
$249$	25.8626	−	1.46642i	1.63898	−	0.0929303i
$250$	−8.58423			−0.542914
$251$	18.4901			1.16708			0.583541	−	0.812083i	$-0.301667\pi$
$251$	18.4901			1.16708			0.583541	+	0.812083i	$0.301667\pi$
$252$	−6.95080	+	8.73535i	−0.437859	+	0.550276i
$253$	−8.43090	−	8.43090i	−0.530046	−	0.530046i
$254$	7.83082	+	7.83082i	0.491349	+	0.491349i
$255$	−6.02286	+	0.341497i	−0.377166	+	0.0213854i
$256$	1.00000			0.0625000
$257$	13.6696			0.852688			0.426344	−	0.904561i	$-0.359801\pi$
$257$	13.6696			0.852688			0.426344	+	0.904561i	$0.359801\pi$
$258$	−0.893149	−	15.7522i	−0.0556050	−	0.980686i
$259$			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	$0.148829\pi$
$263$			14.6186i			0.901421i	−0.892670	+	0.450710i	$0.851171\pi$
$264$	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
$267$	1.22807	+	21.6590i	0.0751564	+	1.32551i
$268$	2.26245	−	2.26245i	0.138201	−	0.138201i
$269$		−	15.7946i		−	0.963012i	−0.876443	−	0.481506i	$-0.840090\pi$
$269$		−	15.7946i		−	0.963012i	0.876443	−	0.481506i	$-0.159910\pi$
$270$	−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
$273$	−9.32345	+	21.2860i	−0.564281	+	1.28829i
$274$	−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
$279$	−0.850031	+	1.06827i	−0.0508900	+	0.0639555i
$280$	−6.79967	+	6.79967i	−0.406358	+	0.406358i
$281$	−3.06665	−	3.06665i	−0.182941	−	0.182941i	0.609695	−	0.792636i	$-0.291292\pi$
$281$	−3.06665	−	3.06665i	−0.182941	−	0.182941i	−0.792636	+	0.609695i	$0.791292\pi$
$282$	−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
$288$	2.34751	+	1.86794i	0.138328	+	0.110069i
$289$	−15.1836			−0.893151
$290$	9.44443			0.554596
$291$	0.0233580	+	0.411957i	0.00136927	+	0.0241493i
$292$	3.58423	+	3.58423i	0.209751	+	0.209751i
$293$	−3.00331	−	3.00331i	−0.175455	−	0.175455i	0.613916	−	0.789371i	$-0.289593\pi$
$293$	−3.00331	−	3.00331i	−0.175455	−	0.175455i	−0.789371	+	0.613916i	$0.789593\pi$
$294$	0.671316	+	11.8398i	0.0391520	+	0.690509i
$295$	−13.3564			−0.777642
$296$	2.76196			0.160536
$297$	16.7080	−	2.86665i	0.969498	−	0.166340i
$298$			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
$306$	3.16386	+	2.51751i	0.180866	+	0.143916i
$307$	−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	$-0.531075\pi$
$311$	−3.43781			−0.194940			−0.0974701	+	0.995238i	$0.531075\pi$
$312$	5.72033	+	2.50556i	0.323850	+	0.141849i
$313$	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	−0.996107	−	0.0881494i	$-0.971905\pi$
$317$	−16.1657	+	16.1657i	−0.907958	+	0.907958i	0.0881494	+	0.996107i	$0.471905\pi$
$318$	0.0212610	+	0.374973i	0.00119226	+	0.0210274i
$319$	−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
$327$	1.27785	+	22.5369i	0.0706652	+	1.24630i
$328$	−11.1685			−0.616675
$329$	−24.8504			−1.37005
$330$	14.5793	−	0.826650i	0.802565	−	0.0455056i
$331$	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
$333$	6.48374	+	5.15917i	0.355307	+	0.282721i
$334$	1.35644			0.0742212
$335$	8.26844			0.451753
$336$	6.43482	−	0.364855i	0.351048	−	0.0199045i
$337$			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
$345$	16.3320	−	0.926027i	0.879285	−	0.0498556i
$346$	−12.3716	+	12.3716i	−0.665099	+	0.665099i
$347$			29.2823i			1.57195i	0.618256	+	0.785977i	$0.287840\pi$
$347$			29.2823i			1.57195i	−0.618256	+	0.785977i	$0.712160\pi$
$348$	−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
$351$	8.74832	+	16.5670i	0.466951	+	0.884283i
$352$	−3.26245			−0.173889
$353$	5.59039	−	5.59039i	0.297546	−	0.297546i	−0.542506	−	0.840052i	$-0.682524\pi$
$353$	5.59039	−	5.59039i	0.297546	−	0.297546i	0.840052	+	0.542506i	$0.182524\pi$
$354$	6.67822	+	5.96154i	0.354943	+	0.316853i
$355$		−	0.396234i		−	0.0210299i
$356$	8.85644	−	8.85644i	0.469390	−	0.469390i
$357$	8.67252	−	0.491733i	0.458998	−	0.0260253i
$358$	12.7997	−	12.7997i	0.676484	−	0.676484i
$359$	−12.8822	−	12.8822i	−0.679899	−	0.679899i	0.280079	−	0.959977i	$-0.409639\pi$
$359$	−12.8822	−	12.8822i	−0.679899	−	0.679899i	−0.959977	+	0.280079i	$0.909639\pi$
$360$	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
$366$	−11.2833	+	0.639766i	−0.589789	+	0.0334411i
$367$	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
$369$	−26.2181	−	20.8620i	−1.36486	−	1.08603i
$370$	5.04700	+	5.04700i	0.262381	+	0.262381i
$371$	0.570551	+	0.570551i	0.0296215	+	0.0296215i
$372$	0.786930	−	0.0446190i	0.0408004	−	0.00231339i
$373$	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
$375$	0.841683	+	14.8445i	0.0434643	+	0.766565i
$376$			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	−0.373100	−	0.927791i	$-0.621705\pi$
$383$	10.8555	−	10.8555i	0.554691	−	0.554691i	0.927791	+	0.373100i	$0.121705\pi$
$384$	−0.0980500	−	1.72927i	−0.00500359	−	0.0882466i
$385$	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	$-0.462684\pi$
$389$	4.61380			0.233929			0.116964	+	0.993136i	$0.462684\pi$
$390$	5.87443	+	15.0314i	0.297464	+	0.761142i
$391$	−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
$396$	−7.65863	−	6.09404i	−0.384861	−	0.306237i
$397$	−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	0.792067	−	0.610434i	$-0.209005\pi$
$401$	3.63720	+	3.63720i	0.181633	+	0.181633i	−0.610434	+	0.792067i	$0.709005\pi$
$402$	−4.13422	−	3.69056i	−0.206196	−	0.184068i
$403$	1.55956	−	0.509770i	0.0776870	−	0.0253935i
$404$			17.7129i			0.881248i
$405$	−12.3315	+	19.7198i	−0.612756	+	0.979885i
$406$	−13.5993			−0.674924
$407$	−9.01075			−0.446646
$408$	−0.132147	−	2.33063i	−0.00654224	−	0.115383i
$409$	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
$411$	0.135418	+	2.38832i	0.00667968	+	0.117807i
$412$	−7.90600			−0.389501
$413$	19.2324			0.946364
$414$	−8.57933	−	6.82665i	−0.421651	−	0.335512i
$415$		−	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	$0.00275023\pi$
$419$			0.353712i			0.0172800i	−0.999963	+	0.00863998i	$0.997250\pi$
$420$	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
$423$	−12.4745	+	15.6772i	−0.606531	+	0.762252i
$424$	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
$429$	−18.6623	−	8.17424i	−0.901023	−	0.394656i
$430$	−23.5400			−1.13520
$431$	5.89820	−	5.89820i	0.284106	−	0.284106i	−0.550638	−	0.834744i	$-0.685615\pi$
$431$	5.89820	−	5.89820i	0.284106	−	0.284106i	0.834744	+	0.550638i	$0.185615\pi$
$432$	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
$435$	−0.926027	−	16.3320i	−0.0443996	−	0.783060i
$436$	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	$0.261281\pi$
$443$			30.8018i			1.46344i	−0.681608	+	0.731718i	$0.738719\pi$
$444$	−0.270810	−	4.77619i	−0.0128521	−	0.226668i
$445$	32.3671			1.53435
$446$	8.33491			0.394669
$447$	21.6590	−	1.22807i	1.02443	−	0.0580855i
$448$	−2.63122	−	2.63122i	−0.124314	−	0.124314i
$449$	−19.2149	−	19.2149i	−0.906809	−	0.906809i	0.0892043	−	0.996013i	$-0.471568\pi$
$449$	−19.2149	−	19.2149i	−0.906809	−	0.906809i	−0.996013	+	0.0892043i	$0.971568\pi$
$450$	−3.13481	+	3.93964i	−0.147776	+	0.185717i
$451$	36.4365			1.71573
$452$	−3.43781			−0.161701
$453$	−28.8568	+	1.63619i	−1.35581	+	0.0768747i
$454$		−	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	−0.765153	−	0.643848i	$-0.777337\pi$
$461$	−2.60452	+	2.60452i	−0.121305	+	0.121305i	0.643848	+	0.765153i	$0.277337\pi$
$462$	−20.9933	+	1.19032i	−0.976695	+	0.0553787i
$463$	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	$-0.676538\pi$
$467$	−22.7603			−1.05322			−0.526612	+	0.850106i	$0.676538\pi$
$468$	3.77191	−	10.1377i	0.174357	−	0.468615i
$469$	−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
$474$	−7.07964	+	0.401416i	−0.325179	+	0.0184377i
$475$	−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	0.982216	−	0.187755i	$-0.0601212\pi$
$479$	17.3876	+	17.3876i	0.794460	+	0.794460i	−0.187755	+	0.982216i	$0.560121\pi$
$480$	2.98077	−	3.33911i	0.136053	−	0.152409i
$481$	−3.09400	−	9.46556i	−0.141074	−	0.431592i
$482$			28.9150i			1.31704i
$483$	−23.5170	+	1.33342i	−1.07006	+	0.0606725i
$484$	−0.356442			−0.0162019
$485$	0.615628			0.0279542
$486$	14.9675	−	4.35584i	0.678941	−	0.197585i
$487$	−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
$489$	−6.87694	+	0.389923i	−0.310986	+	0.0176329i
$490$	17.6933			0.799304
$491$	0.822276			0.0371088			0.0185544	−	0.999828i	$-0.494094\pi$
$491$	0.822276			0.0371088			0.0185544	+	0.999828i	$0.494094\pi$
$492$	1.09507	+	19.3133i	0.0493694	+	0.870711i
$493$			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
$501$	−0.132999	−	2.34566i	−0.00594197	−	0.104796i
$502$	−13.0745	+	13.0745i	−0.583541	+	0.583541i
$503$		−	38.1212i		−	1.69974i	−0.526991	−	0.849871i	$-0.676680\pi$
$503$		−	38.1212i		−	1.69974i	0.526991	−	0.849871i	$-0.323320\pi$
$504$	−1.26187	−	11.0918i	−0.0562081	−	0.494067i
$505$	−32.3671	+	32.3671i	−1.44032	+	1.44032i
$506$	11.9231			0.530046
$507$	2.17882	−	22.4110i	0.0967647	−	0.995307i
$508$	−11.0745			−0.491349
$509$	−20.7795	+	20.7795i	−0.921036	+	0.921036i	−0.997103	−	0.0760664i	$-0.975764\pi$
$509$	−20.7795	+	20.7795i	−0.921036	+	0.921036i	0.0760664	+	0.997103i	$0.475764\pi$
$510$	4.01733	−	4.50028i	0.177890	−	0.199276i
$511$		−	18.8618i		−	0.834397i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	25.9593	−	4.45390i	1.14613	−	0.196645i
$514$	−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	$-0.998802\pi$
$521$		−	0.171761i		−	0.00752497i	0.999993	−	0.00376248i	$-0.00119764\pi$
$522$	−6.82665	+	8.57933i	−0.298794	+	0.375507i
$523$	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
$525$	0.612308	+	10.7990i	0.0267233	+	0.471309i
$526$	−10.3369	−	10.3369i	−0.450710	−	0.450710i
$527$	−0.433677	−	0.433677i	−0.0188913	−	0.0188913i
$528$	0.319883	+	5.64166i	0.0139211	+	0.245522i
$529$	−9.64356			−0.419285
$530$	0.560360			0.0243405
$531$	9.65434	−	12.1330i	0.418963	−	0.526527i
$532$		−	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
$540$	13.2346	−	2.27071i	0.569528	−	0.0977156i
$541$	−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
$546$	−8.45879	−	21.6441i	−0.362003	−	0.926284i
$547$	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
$552$	0.358338	+	6.31988i	0.0152519	+	0.268992i
$553$	−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	0.532727	−	0.846287i	$-0.321167\pi$
$557$	−7.40027	−	7.40027i	−0.313559	−	0.313559i	−0.846287	+	0.532727i	$0.821167\pi$
$558$	−0.154317	−	1.35644i	−0.00653276	−	0.0574228i
$559$	29.2899	+	14.8590i	1.23883	+	0.628469i
$560$		−	9.61619i		−	0.406358i
$561$	0.431122	+	7.60354i	0.0182020	+	0.321022i
$562$	4.33690			0.182941
$563$	−38.1111			−1.60619			−0.803095	−	0.595851i	$-0.796815\pi$
$563$	−38.1111			−1.60619			−0.803095	+	0.595851i	$0.796815\pi$
$564$	11.5485	−	0.654800i	0.486278	−	0.0275720i
$565$	−6.28199	−	6.28199i	−0.264285	−	0.264285i
$566$	6.61600	+	6.61600i	0.278091	+	0.278091i
$567$	17.7565	−	28.3952i	0.745703	−	1.19249i
$568$	0.153328			0.00643350
$569$	38.2930			1.60533			0.802663	−	0.596433i	$-0.203416\pi$
$569$	38.2930			1.60533			0.802663	+	0.596433i	$0.203416\pi$
$570$	22.6519	−	1.28436i	0.948783	−	0.0537961i
$571$		−	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
$579$	−10.4241	+	0.591046i	−0.433210	+	0.0245631i
$580$	−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
$585$	25.4173	−	11.6323i	1.05088	−	0.480937i
$586$	4.24732			0.175455
$587$	11.0090	−	11.0090i	0.454391	−	0.454391i	−0.442418	−	0.896809i	$-0.645879\pi$
$587$	11.0090	−	11.0090i	0.454391	−	0.454391i	0.896809	+	0.442418i	$0.145879\pi$
$588$	−8.84667	−	7.89729i	−0.364831	−	0.325679i
$589$		−	2.30666i		−	0.0950441i
$590$	9.44443	−	9.44443i	0.388821	−	0.388821i
$591$	−6.81449	+	0.386383i	−0.280311	+	0.0158937i
$592$	−1.95300	+	1.95300i	−0.0802679	+	0.0802679i
$593$	8.06905	+	8.06905i	0.331356	+	0.331356i	0.853101	−	0.521745i	$-0.174719\pi$
$593$	8.06905	+	8.06905i	0.331356	+	0.331356i	−0.521745	+	0.853101i	$0.674719\pi$
$594$	−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	$0.148511\pi$
$599$			22.0180i			0.899633i	−0.893121	+	0.449816i	$0.851489\pi$
$600$	2.90210	−	0.164550i	0.118478	−	0.00671771i
$601$	−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
$603$	−5.97662	+	7.51106i	−0.243387	+	0.305874i
$604$	11.7997	+	11.7997i	0.480122	+	0.480122i
$605$	−0.651335	−	0.651335i	−0.0264805	−	0.0264805i
$606$	30.6304	−	1.73675i	1.24427	−	0.0705506i
$607$	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
$609$	1.33342	+	23.5170i	0.0540328	+	0.952957i
$610$			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	$0.636519\pi$
$617$	−32.9195	+	32.9195i	−1.32529	+	1.32529i	−0.909430	+	0.415858i	$0.863481\pi$
$618$	0.775184	+	13.6716i	0.0311825	+	0.549954i
$619$	−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
$624$	−5.81658	+	2.27319i	−0.232850	+	0.0910004i
$625$	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
$630$	17.9624	−	22.5741i	0.715641	−	0.899375i
$631$	−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
$639$	0.359939	+	0.286407i	0.0142390	+	0.0113301i
$640$	−2.58423			−0.102150
$641$	34.2846			1.35416			0.677081	−	0.735908i	$-0.263245\pi$
$641$	34.2846			1.35416			0.677081	+	0.735908i	$0.263245\pi$
$642$	−0.452383	−	7.97851i	−0.0178541	−	0.314887i
$643$	−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
$645$	2.30810	+	40.7071i	0.0908813	+	1.60284i
$646$	−6.83155			−0.268784
$647$	−2.69550			−0.105971			−0.0529855	−	0.998595i	$-0.516874\pi$
$647$	−2.69550			−0.105971			−0.0529855	+	0.998595i	$0.516874\pi$
$648$	−7.63084	−	4.77183i	−0.299768	−	0.187455i
$649$			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	$-0.676178\pi$
$653$		−	43.4774i		−	1.70140i	0.525651	−	0.850700i	$-0.323822\pi$
$654$	−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
$657$	−11.8992	−	9.46831i	−0.464232	−	0.369394i
$658$	17.5719	−	17.5719i	0.685024	−	0.685024i
$659$		−	39.2972i		−	1.53080i	−0.643553	−	0.765401i	$-0.722540\pi$
$659$		−	39.2972i		−	1.53080i	0.643553	−	0.765401i	$-0.277460\pi$
$660$	−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
$663$	−7.83929	+	3.06369i	−0.304453	+	0.118984i
$664$	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
$669$	−0.817238	−	14.4133i	−0.0315962	−	0.557252i
$670$	−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	$-0.898460\pi$
$677$		−	16.3200i		−	0.627230i	0.949550	−	0.313615i	$-0.101540\pi$
$678$	0.337077	+	5.94491i	0.0129454	+	0.228313i
$679$	−0.886464			−0.0340194
$680$	−3.48289			−0.133563
$681$	−22.5666	+	1.27953i	−0.864756	+	0.0490318i
$682$	1.04979	+	1.04979i	0.0401984	+	0.0401984i
$683$	−0.171761	−	0.171761i	−0.00657223	−	0.00657223i	0.703813	−	0.710385i	$-0.251479\pi$
$683$	−0.171761	−	0.171761i	−0.00657223	−	0.00657223i	−0.710385	+	0.703813i	$0.751479\pi$
$684$	−11.8992	−	9.46831i	−0.454978	−	0.362030i
$685$	3.56910			0.136368
$686$	0.570551			0.0217837
$687$	22.5369	−	1.27785i	0.859838	−	0.0487529i
$688$		−	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
$696$	6.31988	−	0.358338i	0.239555	−	0.0135828i
$697$	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	$-0.719773\pi$
$701$	−33.7243			−1.27375			−0.636874	+	0.770968i	$0.719773\pi$
$702$	−17.9007	−	5.52867i	−0.675617	−	0.208666i
$703$	−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
$708$	−8.93766	+	0.506767i	−0.335898	+	0.0190455i
$709$	−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
$717$	−17.6102	+	0.998500i	−0.657664	+	0.0372897i
$718$	18.2182			0.679899
$719$	30.6300			1.14231			0.571153	−	0.820844i	$-0.306496\pi$
$719$	30.6300			1.14231			0.571153	+	0.820844i	$0.306496\pi$
$720$	−6.06650	−	4.82717i	−0.226085	−	0.179898i
$721$	20.8025	+	20.8025i	0.774724	+	0.774724i
$722$	−4.73291	−	4.73291i	−0.176141	−	0.176141i
$723$	50.0020	−	2.83512i	1.85959	−	0.105439i
$724$	−1.90600			−0.0708361
$725$	−6.13331			−0.227785
$726$	0.0349492	+	0.616386i	0.00129709	+	0.0228762i
$727$			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
$735$	−1.73483	−	30.5966i	−0.0639903	−	1.12857i
$736$	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
$741$	−28.9956	−	12.7003i	−1.06518	−	0.466558i
$742$	−0.806880			−0.0296215
$743$	−1.06757	+	1.06757i	−0.0391653	+	0.0391653i	−0.726418	−	0.687253i	$-0.758816\pi$
$743$	−1.06757	+	1.06757i	−0.0391653	+	0.0391653i	0.687253	+	0.726418i	$0.258816\pi$
$744$	−0.524893	+	0.587994i	−0.0192435	+	0.0215569i
$745$		−	32.3671i		−	1.18584i
$746$	−11.1808	+	11.1808i	−0.409357	+	0.409357i
$747$	35.1089	+	27.9365i	1.28457	+	1.02214i
$748$	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
$756$	−19.0570	+	3.26967i	−0.693097	+	0.118917i
$757$	−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
$759$	−1.16906	−	20.6183i	−0.0424342	−	0.748396i
$760$	−9.26245	−	9.26245i	−0.335984	−	0.335984i
$761$	−30.4408	−	30.4408i	−1.10348	−	1.10348i	−0.993988	−	0.109490i	$-0.965078\pi$
$761$	−30.4408	−	30.4408i	−1.10348	−	1.10348i	−0.109490	−	0.993988i	$-0.534922\pi$
$762$	1.08585	+	19.1508i	0.0393362	+	0.693759i
$763$	−48.4958			−1.75567
$764$	−6.35014			−0.229740
$765$	−8.17612	−	6.50581i	−0.295608	−	0.235218i
$766$			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	−0.585527	−	0.810653i	$-0.699112\pi$
$773$	6.25917	−	6.25917i	0.225127	−	0.225127i	0.810653	+	0.585527i	$0.199112\pi$
$774$	17.0153	−	21.3838i	0.611601	−	0.768623i
$775$	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
$780$	−14.7826	−	6.47492i	−0.529303	−	0.231839i
$781$	−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
$786$	1.77485	+	31.3024i	0.0633068	+	1.11652i
$787$	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
$795$	−0.0549433	−	0.969015i	−0.00194864	−	0.0343674i
$796$	−17.2927			−0.612923
$797$	28.0263			0.992742			0.496371	−	0.868110i	$-0.334665\pi$
$797$	28.0263			0.992742			0.496371	+	0.868110i	$0.334665\pi$
$798$	−32.6172	+	1.84940i	−1.15464	+	0.0654680i
$799$	−6.36436	−	6.36436i	−0.225155	−	0.225155i
$800$	−1.18668	−	1.18668i	−0.0419555	−	0.0419555i
$801$	−23.3957	+	29.4023i	−0.826647	+	1.03888i
$802$	−5.14378			−0.181633
$803$	16.5369			0.583574
$804$	5.53295	−	0.313719i	0.195132	−	0.0110640i
$805$			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	$0.212116\pi$
$809$			35.1638i			1.23629i	−0.786062	+	0.618147i	$0.787884\pi$
$810$	−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
$813$	39.6929	−	2.25059i	1.39209	−	0.0789317i
$814$	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
$819$	−36.5993	+	16.7498i	−1.27888	+	0.585284i
$820$	28.8618			1.00790
$821$	13.0081	−	13.0081i	0.453986	−	0.453986i	−0.442689	−	0.896675i	$-0.645976\pi$
$821$	13.0081	−	13.0081i	0.453986	−	0.453986i	0.896675	+	0.442689i	$0.145976\pi$
$822$	−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
$825$	−9.46796	+	0.536834i	−0.329632	+	0.0186902i
$826$	−13.5993	+	13.5993i	−0.473182	+	0.473182i
$827$	18.6720	+	18.6720i	0.649290	+	0.649290i	0.952821	−	0.303532i	$-0.0981658\pi$
$827$	18.6720	+	18.6720i	0.649290	+	0.649290i	−0.303532	+	0.952821i	$0.598166\pi$
$828$	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
$834$	12.2936	−	0.697049i	0.425693	−	0.0241368i
$835$	−3.50535			−0.121308
$836$	16.5369			0.571940
$837$	−2.33053	+	0.399856i	−0.0805549	+	0.0138210i
$838$	−0.250112	−	0.250112i	−0.00863998	−	0.00863998i
$839$	35.2438	+	35.2438i	1.21675	+	1.21675i	0.968763	+	0.247988i	$0.0797693\pi$
$839$	35.2438	+	35.2438i	1.21675	+	1.21675i	0.247988	+	0.968763i	$0.420231\pi$
$840$	−16.6290	+	0.942868i	−0.573756	+	0.0325320i
$841$	15.6436			0.539433
$842$	32.3979			1.11651
$843$	−0.425233	−	7.49969i	−0.0146458	−	0.258303i
$844$		−	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
$852$	−0.0150338	−	0.265146i	−0.000515050	−	0.00908375i
$853$	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	$-0.622397\pi$
$857$	−21.9628			−0.750234			−0.375117	+	0.926978i	$0.622397\pi$
$858$	18.9763	−	7.41616i	0.647840	−	0.253183i
$859$	−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	$0.593999\pi$
$863$	−36.6549	+	36.6549i	−1.24775	+	1.24775i	−0.956713	+	0.291034i	$0.906001\pi$
$864$	0.878680	+	5.12132i	0.0298933	+	0.174231i
$865$	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
$873$	−0.444990	+	0.559237i	−0.0150606	+	0.0189273i
$874$	18.5249			0.626614
$875$	−31.9429			−1.07987
$876$	0.497002	+	8.76544i	0.0167921	+	0.296157i
$877$	−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
$879$	−0.416450	−	7.34478i	−0.0140465	−	0.247733i
$880$	8.43090			0.284205
$881$	−40.6450			−1.36936			−0.684682	−	0.728842i	$-0.740059\pi$
$881$	−40.6450			−1.36936			−0.684682	+	0.728842i	$0.740059\pi$
$882$	−12.7892	+	16.0726i	−0.430633	+	0.541194i
$883$			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	$0.0936850\pi$
$887$			17.2792i			0.580179i	−0.957000	+	0.290089i	$0.906315\pi$
$888$	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
$891$	24.8952	+	15.5678i	0.834020	+	0.521542i
$892$	−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
$897$	21.2575	−	8.30770i	0.709769	−	0.277386i
$898$	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
$903$	−3.32351	−	58.6155i	−0.110599	−	1.95060i
$904$	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	$-0.953953\pi$
$911$		−	8.70212i		−	0.288314i	0.989555	−	0.144157i	$-0.0460470\pi$
$912$	0.497002	+	8.76544i	0.0164574	+	0.290253i
$913$	−48.7925			−1.61480
$914$	−16.2148			−0.536336
$915$	29.1587	−	1.65330i	0.963955	−	0.0546564i
$916$	−9.21545	−	9.21545i	−0.304487	−	0.304487i
$917$	47.6290	+	47.6290i	1.57285	+	1.57285i
$918$	1.18424	+	6.90225i	0.0390857	+	0.227808i
$919$	−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
$921$	−7.94153	+	0.450286i	−0.261682	+	0.0148374i
$922$		−	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	−0.455438	−	0.890268i	$-0.650517\pi$
$929$	13.2534	−	13.2534i	0.434830	−	0.434830i	0.890268	+	0.455438i	$0.150517\pi$
$930$	−2.03360	+	0.115306i	−0.0666845	+	0.00378102i
$931$	−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
$936$	4.50128	+	9.83557i	0.147129	+	0.321486i
$937$	−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	−0.0469563	−	0.998897i	$-0.514952\pi$
$941$	29.2015	−	29.2015i	0.951941	−	0.951941i	0.998897	+	0.0469563i	$0.0149522\pi$
$942$	32.6172	−	1.84940i	1.06273	−	0.0602567i
$943$	−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	0.403285	−	0.915075i	$-0.367868\pi$
$947$	−15.7495	−	15.7495i	−0.511790	−	0.511790i	−0.915075	+	0.403285i	$0.867868\pi$
$948$	4.72222	−	5.28990i	0.153370	−	0.171808i
$949$	5.67822	+	17.3716i	0.184323	+	0.563905i
$950$		−	8.50667i		−	0.275993i
$951$	−39.5343	+	2.24160i	−1.28199	+	0.0726888i
$952$	5.01512			0.162541
$953$	−11.6612			−0.377742			−0.188871	−	0.982002i	$-0.560483\pi$
$953$	−11.6612			−0.377742			−0.188871	+	0.982002i	$0.560483\pi$
$954$	−0.405041	+	0.509031i	−0.0131137	+	0.0164805i
$955$	−11.6038	−	11.6038i	−0.375489	−	0.375489i
$956$	7.20087	+	7.20087i	0.232893	+	0.232893i
$957$	−20.6183	+	1.16906i	−0.666494	+	0.0377903i
$958$	−24.5898			−0.794460
$959$	−5.13927			−0.165956
$960$	0.253383	+	4.46883i	0.00817791	+	0.144231i
$961$		−	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
$969$	0.669834	+	11.8136i	0.0215182	+	0.379508i
$970$	−0.435315	+	0.435315i	−0.0139771	+	0.0139771i
$971$			8.74884i			0.280764i	0.990097	+	0.140382i	$0.0448330\pi$
$971$			8.74884i			0.280764i	−0.990097	+	0.140382i	$0.955167\pi$
$972$	−7.50359	+	13.6637i	−0.240678	+	0.438263i
$973$	18.7057	−	18.7057i	0.599677	−	0.599677i
$974$	14.1635			0.453829
$975$	−3.81491	−	9.76151i	−0.122175	−	0.312618i
$976$	−6.52489			−0.208857
$977$	10.7297	−	10.7297i	0.343272	−	0.343272i	−0.514324	−	0.857596i	$-0.671957\pi$
$977$	10.7297	−	10.7297i	0.343272	−	0.343272i	0.857596	+	0.514324i	$0.171957\pi$
$978$	4.58701	−	5.13845i	0.146677	−	0.164309i
$979$		−	40.8618i		−	1.30595i
$980$	−12.5111	+	12.5111i	−0.399652	+	0.399652i
$981$	−24.3441	+	30.5942i	−0.777247	+	0.976798i
$982$	−0.581437	+	0.581437i	−0.0185544	+	0.0185544i
$983$	12.8087	+	12.8087i	0.408534	+	0.408534i	0.881227	−	0.472693i	$-0.156718\pi$
$983$	12.8087	+	12.8087i	0.408534	+	0.408534i	−0.472693	+	0.881227i	$0.656718\pi$
$984$	−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
$990$	19.7916	+	15.7484i	0.629019	+	0.500517i
$991$	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
$993$	0.766102	+	13.5115i	0.0243115	+	0.428773i
$994$	−0.403440	−	0.403440i	−0.0127963	−	0.0127963i
$995$	−31.5993	−	31.5993i	−1.00177	−	1.00177i
$996$	−1.46642	−	25.8626i	−0.0464652	−	0.819489i
$997$	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
$999$	2.42688	+	14.1449i	0.0767831	+	0.447525i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.29211 + 1.15345i) q^{3} -1.00000i q^{4} +(1.82732 - 1.82732i) q^{5} +(-1.72927 + 0.0980500i) q^{6} +(-2.63122 + 2.63122i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.339111 + 2.98077i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.29211 + 1.15345i) q^{3} -1.00000i q^{4} +(1.82732 - 1.82732i) q^{5} +(-1.72927 + 0.0980500i) 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} +(4.46883 - 0.253383i) q^{15} -1.00000 q^{16} -1.34775 q^{17} +(-2.34751 - 1.86794i) q^{18} +(-3.58423 - 3.58423i) q^{19} +(-1.82732 - 1.82732i) q^{20} +(-6.43482 + 0.364855i) q^{21} +3.26245 q^{22} +3.65465 q^{23} +(0.0980500 + 1.72927i) 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} +(-0.319883 - 5.64166i) 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} +(5.81658 - 2.27319i) 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} +(6.06650 + 4.82717i) 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} +(-0.878680 - 5.12132i) q^{54} -8.43090 q^{55} -3.72111 q^{56} +(-0.497002 - 8.76544i) q^{57} +(2.58423 + 2.58423i) q^{58} +(-3.65465 - 3.65465i) q^{59} +(-0.253383 - 4.46883i) q^{60} +6.52489 q^{61} -0.455064 q^{62} +(-8.73535 - 6.95080i) 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} +(-1.86794 + 2.34751i) 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} +(-2.50556 + 5.72033i) 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} +(0.364855 + 6.43482i) 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} +(0.0446190 + 0.786930i) q^{93} -6.67822 q^{94} -13.0991 q^{95} +(1.72927 - 0.0980500i) q^{96} +(0.168451 + 0.168451i) q^{97} +(4.84133 + 4.84133i) q^{98} +(6.09404 - 7.65863i) 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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