LMFDB - Embedded newform 804.2.u.b.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(43,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 3]))

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

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

chi := DirichletCharacter("804.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.u (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$340$
Relative dimension:	$34$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	804.43
Dual form			804.2.u.b.187.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34334 - 0.442069i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(1.60915 + 1.18770i) q^{4} +(-1.70218 - 0.244737i) q^{5} +(1.36909 - 0.354375i) q^{6} +(1.89274 - 4.14453i) q^{7} +(-1.63660 - 2.30685i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.34334 - 0.442069i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(1.60915 + 1.18770i) q^{4} +(-1.70218 - 0.244737i) q^{5} +(1.36909 - 0.354375i) q^{6} +(1.89274 - 4.14453i) q^{7} +(-1.63660 - 2.30685i) q^{8} +(0.415415 - 0.909632i) q^{9} +(2.17843 + 1.08125i) q^{10} +(-0.121666 + 0.846203i) q^{11} +(-1.99582 - 0.129187i) q^{12} +(0.789845 - 2.68997i) q^{13} +(-4.37478 + 4.73081i) q^{14} +(1.56428 - 0.714383i) q^{15} +(1.17873 + 3.82238i) q^{16} +(-0.288131 + 0.332520i) q^{17} +(-0.960166 + 1.03831i) q^{18} +(-2.28170 + 1.04202i) q^{19} +(-2.44839 - 2.41550i) q^{20} +(0.648425 + 4.50990i) q^{21} +(0.537519 - 1.08296i) q^{22} +(3.59624 + 5.59585i) q^{23} +(2.62397 + 1.05583i) q^{24} +(-1.95994 - 0.575491i) q^{25} +(-2.25019 + 3.26439i) q^{26} +(0.142315 + 0.989821i) q^{27} +(7.96818 - 4.42115i) q^{28} -7.55983 q^{29} +(-2.41717 + 0.268142i) q^{30} +(4.36528 - 1.28176i) q^{31} +(0.106323 - 5.65585i) q^{32} +(-0.355140 - 0.777648i) q^{33} +(0.534056 - 0.319316i) q^{34} +(-4.23611 + 6.59152i) q^{35} +(1.74884 - 0.970345i) q^{36} -5.23184 q^{37} +(3.52575 - 0.391119i) q^{38} +(0.789845 + 2.68997i) q^{39} +(2.22121 + 4.32721i) q^{40} +(-5.49960 - 4.76543i) q^{41} +(1.12263 - 6.34499i) q^{42} +(2.11680 - 2.44291i) q^{43} +(-1.20082 + 1.21716i) q^{44} +(-0.929732 + 1.44669i) q^{45} +(-2.35723 - 9.10694i) q^{46} +(-3.87793 - 6.03417i) q^{47} +(-3.05814 - 2.57833i) q^{48} +(-9.01063 - 10.3988i) q^{49} +(2.37847 + 1.63951i) q^{50} +(0.0626168 - 0.435509i) q^{51} +(4.46586 - 3.39046i) q^{52} +(6.92027 - 5.99645i) q^{53} +(0.246392 - 1.39258i) q^{54} +(0.414194 - 1.41061i) q^{55} +(-12.6585 + 2.41665i) q^{56} +(1.35613 - 2.11018i) q^{57} +(10.1555 + 3.34197i) q^{58} +(0.742335 + 2.52816i) q^{59} +(3.36564 + 0.708351i) q^{60} +(-9.19134 + 1.32151i) q^{61} +(-6.43070 - 0.207908i) q^{62} +(-2.98372 - 3.44340i) q^{63} +(-2.64311 + 7.55076i) q^{64} +(-2.00279 + 4.38551i) q^{65} +(0.133301 + 1.20165i) q^{66} +(-7.83768 + 2.36025i) q^{67} +(-0.858581 + 0.192862i) q^{68} +(-6.05069 - 2.76326i) q^{69} +(8.60446 - 6.98203i) q^{70} +(5.95655 - 5.16138i) q^{71} +(-2.77825 + 0.530400i) q^{72} +(-0.760568 - 5.28987i) q^{73} +(7.02816 + 2.31283i) q^{74} +(1.95994 - 0.575491i) q^{75} +(-4.90920 - 1.03322i) q^{76} +(3.27683 + 2.10589i) q^{77} +(0.128117 - 3.96272i) q^{78} +(-2.11367 - 0.620630i) q^{79} +(-1.07093 - 6.79486i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(5.28121 + 8.83282i) q^{82} +(-8.17325 - 1.17514i) q^{83} +(-4.31300 + 8.02723i) q^{84} +(0.571830 - 0.495494i) q^{85} +(-3.92352 + 2.34590i) q^{86} +(6.35973 - 4.08715i) q^{87} +(2.15118 - 1.10423i) q^{88} +(-5.87443 - 3.77526i) q^{89} +(1.88849 - 1.53240i) q^{90} +(-9.65367 - 8.36496i) q^{91} +(-0.859326 + 13.2758i) q^{92} +(-2.97933 + 3.43834i) q^{93} +(2.54187 + 9.82028i) q^{94} +(4.13888 - 1.21529i) q^{95} +(2.96834 + 4.81549i) q^{96} +2.27994i q^{97} +(7.50738 + 17.9525i) q^{98} +(0.719191 + 0.462196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 34 q^{3} - 2 q^{4} - 11 q^{6} + 4 q^{7} + 27 q^{8} - 34 q^{9}+O(q^{10}) $ 340 * q + 34 * q^3 - 2 * q^4 - 11 * q^6 + 4 * q^7 + 27 * q^8 - 34 * q^9	$ 340 q + 34 q^{3} - 2 q^{4} - 11 q^{6} + 4 q^{7} + 27 q^{8} - 34 q^{9} - 27 q^{10} - 9 q^{12} + 4 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 6 q^{24} + 34 q^{25} - 10 q^{26} + 34 q^{27} + 47 q^{28} + 16 q^{29} - 6 q^{30} - 4 q^{31} - 55 q^{32} + 9 q^{36} - 12 q^{37} + 26 q^{38} - 37 q^{40} - 4 q^{42} - 4 q^{43} - 51 q^{44} - 103 q^{46} + 2 q^{48} - 46 q^{49} - 51 q^{50} + 32 q^{52} - 14 q^{56} + 66 q^{57} + 92 q^{58} + 67 q^{60} + 2 q^{62} - 18 q^{63} + 7 q^{64} - 8 q^{66} - 18 q^{67} - 208 q^{68} + 56 q^{70} - 6 q^{72} + 54 q^{73} + 22 q^{74} - 34 q^{75} - 56 q^{76} + 8 q^{77} + 10 q^{78} + 10 q^{79} - 68 q^{80} - 34 q^{81} + 84 q^{82} + 8 q^{84} + 104 q^{86} - 16 q^{87} - 82 q^{88} - 27 q^{90} + 134 q^{92} + 4 q^{93} + 32 q^{94} - 40 q^{95} - 7 q^{98}+O(q^{100}) $ 340 * q + 34 * q^3 - 2 * q^4 - 11 * q^6 + 4 * q^7 + 27 * q^8 - 34 * q^9 - 27 * q^10 - 9 * q^12 + 4 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 6 * q^24 + 34 * q^25 - 10 * q^26 + 34 * q^27 + 47 * q^28 + 16 * q^29 - 6 * q^30 - 4 * q^31 - 55 * q^32 + 9 * q^36 - 12 * q^37 + 26 * q^38 - 37 * q^40 - 4 * q^42 - 4 * q^43 - 51 * q^44 - 103 * q^46 + 2 * q^48 - 46 * q^49 - 51 * q^50 + 32 * q^52 - 14 * q^56 + 66 * q^57 + 92 * q^58 + 67 * q^60 + 2 * q^62 - 18 * q^63 + 7 * q^64 - 8 * q^66 - 18 * q^67 - 208 * q^68 + 56 * q^70 - 6 * q^72 + 54 * q^73 + 22 * q^74 - 34 * q^75 - 56 * q^76 + 8 * q^77 + 10 * q^78 + 10 * q^79 - 68 * q^80 - 34 * q^81 + 84 * q^82 + 8 * q^84 + 104 * q^86 - 16 * q^87 - 82 * q^88 - 27 * q^90 + 134 * q^92 + 4 * q^93 + 32 * q^94 - 40 * q^95 - 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.34334	−	0.442069i	−0.949888	−	0.312590i
$2$	−1.34334	−	0.442069i	−0.949888	−	0.312590i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	1.60915	+	1.18770i	0.804575	+	0.593851i
$5$	−1.70218	−	0.244737i	−0.761238	−	0.109450i	−0.249247	−	0.968440i	$-0.580183\pi$
$5$	−1.70218	−	0.244737i	−0.761238	−	0.109450i	−0.511992	+	0.858990i	$0.671092\pi$
$6$	1.36909	−	0.354375i	0.558930	−	0.144673i
$7$	1.89274	−	4.14453i	0.715390	−	1.56649i	−0.104864	−	0.994487i	$-0.533441\pi$
$7$	1.89274	−	4.14453i	0.715390	−	1.56649i	0.820254	−	0.571999i	$-0.193832\pi$
$8$	−1.63660	−	2.30685i	−0.578624	−	0.815594i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	2.17843	+	1.08125i	0.688878	+	0.341920i
$11$	−0.121666	+	0.846203i	−0.0366836	+	0.255140i	−0.999908	−	0.0135581i	$-0.995684\pi$
$11$	−0.121666	+	0.846203i	−0.0366836	+	0.255140i	0.963225	+	0.268698i	$0.0865933\pi$
$12$	−1.99582	−	0.129187i	−0.576145	−	0.0372931i
$13$	0.789845	−	2.68997i	0.219064	−	0.746063i	−0.774479	−	0.632600i	$-0.781988\pi$
$13$	0.789845	−	2.68997i	0.219064	−	0.746063i	0.993542	−	0.113462i	$-0.0361941\pi$
$14$	−4.37478	+	4.73081i	−1.16921	+	1.26436i
$15$	1.56428	−	0.714383i	0.403895	−	0.184453i
$16$	1.17873	+	3.82238i	0.294681	+	0.955596i
$17$	−0.288131	+	0.332520i	−0.0698819	+	0.0806480i	−0.789614	−	0.613604i	$-0.789719\pi$
$17$	−0.288131	+	0.332520i	−0.0698819	+	0.0806480i	0.719732	+	0.694252i	$0.244265\pi$
$18$	−0.960166	+	1.03831i	−0.226313	+	0.244731i
$19$	−2.28170	+	1.04202i	−0.523457	+	0.239055i	−0.659576	−	0.751638i	$-0.729264\pi$
$19$	−2.28170	+	1.04202i	−0.523457	+	0.239055i	0.136119	+	0.990692i	$0.456537\pi$
$20$	−2.44839	−	2.41550i	−0.547477	−	0.540123i
$21$	0.648425	+	4.50990i	0.141498	+	0.984140i
$22$	0.537519	−	1.08296i	0.114599	−	0.230887i
$23$	3.59624	+	5.59585i	0.749867	+	1.16682i	0.981022	+	0.193899i	$0.0621134\pi$
$23$	3.59624	+	5.59585i	0.749867	+	1.16682i	−0.231154	+	0.972917i	$0.574250\pi$
$24$	2.62397	+	1.05583i	0.535615	+	0.215521i
$25$	−1.95994	−	0.575491i	−0.391988	−	0.115098i
$26$	−2.25019	+	3.26439i	−0.441298	+	0.640199i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	7.96818	−	4.42115i	1.50584	−	0.835520i
$29$	−7.55983			−1.40382			−0.701912	−	0.712263i	$-0.747670\pi$
$29$	−7.55983			−1.40382			−0.701912	+	0.712263i	$0.747670\pi$
$30$	−2.41717	+	0.268142i	−0.441314	+	0.0489559i
$31$	4.36528	−	1.28176i	0.784027	−	0.230211i	0.134868	−	0.990864i	$-0.456939\pi$
$31$	4.36528	−	1.28176i	0.784027	−	0.230211i	0.649159	+	0.760652i	$0.275121\pi$
$32$	0.106323	−	5.65585i	0.0187954	−	0.999823i
$33$	−0.355140	−	0.777648i	−0.0618220	−	0.135371i
$34$	0.534056	−	0.319316i	0.0915898	−	0.0547622i
$35$	−4.23611	+	6.59152i	−0.716033	+	1.11417i
$36$	1.74884	−	0.970345i	0.291473	−	0.161724i
$37$	−5.23184			−0.860109			−0.430054	−	0.902803i	$-0.641506\pi$
$37$	−5.23184			−0.860109			−0.430054	+	0.902803i	$0.641506\pi$
$38$	3.52575	−	0.391119i	0.571952	−	0.0634479i
$39$	0.789845	+	2.68997i	0.126476	+	0.430739i
$40$	2.22121	+	4.32721i	0.351204	+	0.684192i
$41$	−5.49960	−	4.76543i	−0.858893	−	0.744235i	0.109414	−	0.993996i	$-0.465102\pi$
$41$	−5.49960	−	4.76543i	−0.858893	−	0.744235i	−0.968308	+	0.249761i	$0.919648\pi$
$42$	1.12263	−	6.34499i	0.173225	−	0.979054i
$43$	2.11680	−	2.44291i	0.322808	−	0.372541i	−0.571031	−	0.820929i	$-0.693456\pi$
$43$	2.11680	−	2.44291i	0.322808	−	0.372541i	0.893839	+	0.448388i	$0.148002\pi$
$44$	−1.20082	+	1.21716i	−0.181030	+	0.183494i
$45$	−0.929732	+	1.44669i	−0.138596	+	0.215660i
$46$	−2.35723	−	9.10694i	−0.347555	−	1.34275i
$47$	−3.87793	−	6.03417i	−0.565654	−	0.880174i	0.434133	−	0.900849i	$-0.357055\pi$
$47$	−3.87793	−	6.03417i	−0.565654	−	0.880174i	−0.999786	+	0.0206747i	$0.993419\pi$
$48$	−3.05814	−	2.57833i	−0.441405	−	0.372149i
$49$	−9.01063	−	10.3988i	−1.28723	−	1.48555i
$50$	2.37847	+	1.63951i	0.336366	+	0.231862i
$51$	0.0626168	−	0.435509i	0.00876810	−	0.0609835i
$52$	4.46586	−	3.39046i	0.619303	−	0.470172i
$53$	6.92027	−	5.99645i	0.950572	−	0.823675i	−0.0338625	−	0.999426i	$-0.510781\pi$
$53$	6.92027	−	5.99645i	0.950572	−	0.823675i	0.984435	+	0.175751i	$0.0562354\pi$
$54$	0.246392	−	1.39258i	0.0335297	−	0.189507i
$55$	0.414194	−	1.41061i	0.0558499	−	0.190207i
$56$	−12.6585	+	2.41665i	−1.69156	+	0.322938i
$57$	1.35613	−	2.11018i	0.179624	−	0.279500i
$58$	10.1555	+	3.34197i	1.33348	+	0.438822i
$59$	0.742335	+	2.52816i	0.0966438	+	0.329139i	0.993596	−	0.112988i	$-0.0360423\pi$
$59$	0.742335	+	2.52816i	0.0966438	+	0.329139i	−0.896953	+	0.442127i	$0.854224\pi$
$60$	3.36564	+	0.708351i	0.434502	+	0.0914477i
$61$	−9.19134	+	1.32151i	−1.17683	+	0.169203i	−0.702853	−	0.711335i	$-0.748091\pi$
$61$	−9.19134	+	1.32151i	−1.17683	+	0.169203i	−0.473977	+	0.880537i	$0.657182\pi$
$62$	−6.43070	−	0.207908i	−0.816700	−	0.0264043i
$63$	−2.98372	−	3.44340i	−0.375914	−	0.433828i
$64$	−2.64311	+	7.55076i	−0.330388	+	0.943845i
$65$	−2.00279	+	4.38551i	−0.248416	+	0.543955i
$66$	0.133301	+	1.20165i	0.0164082	+	0.147912i
$67$	−7.83768	+	2.36025i	−0.957525	+	0.288351i
$67$	−7.83768	+	2.36025i	−0.957525	+	0.288351i
$68$	−0.858581	+	0.192862i	−0.104118	+	0.0233879i
$69$	−6.05069	−	2.76326i	−0.728418	−	0.332657i
$70$	8.60446	−	6.98203i	1.02843	−	0.834512i
$71$	5.95655	−	5.16138i	0.706912	−	0.612543i	−0.225371	−	0.974273i	$-0.572359\pi$
$71$	5.95655	−	5.16138i	0.706912	−	0.612543i	0.932283	+	0.361730i	$0.117814\pi$
$72$	−2.77825	+	0.530400i	−0.327420	+	0.0625083i
$73$	−0.760568	−	5.28987i	−0.0890177	−	0.619132i	−0.984677	−	0.174390i	$-0.944205\pi$
$73$	−0.760568	−	5.28987i	−0.0890177	−	0.619132i	0.895659	−	0.444742i	$-0.146705\pi$
$74$	7.02816	+	2.31283i	0.817007	+	0.268861i
$75$	1.95994	−	0.575491i	0.226315	−	0.0664519i
$76$	−4.90920	−	1.03322i	−0.563124	−	0.118518i
$77$	3.27683	+	2.10589i	0.373430	+	0.239989i
$78$	0.128117	−	3.96272i	0.0145064	−	0.448690i
$79$	−2.11367	−	0.620630i	−0.237807	−	0.0698263i	0.160658	−	0.987010i	$-0.448639\pi$
$79$	−2.11367	−	0.620630i	−0.237807	−	0.0698263i	−0.398464	+	0.917184i	$0.630457\pi$
$80$	−1.07093	−	6.79486i	−0.119733	−	0.759689i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	5.28121	+	8.83282i	0.583212	+	0.975422i
$83$	−8.17325	−	1.17514i	−0.897131	−	0.128988i	−0.321703	−	0.946841i	$-0.604255\pi$
$83$	−8.17325	−	1.17514i	−0.897131	−	0.128988i	−0.575428	+	0.817853i	$0.695164\pi$
$84$	−4.31300	+	8.02723i	−0.470587	+	0.875843i
$85$	0.571830	−	0.495494i	0.0620237	−	0.0537438i
$86$	−3.92352	+	2.34590i	−0.423084	+	0.252965i
$87$	6.35973	−	4.08715i	0.681835	−	0.438189i
$88$	2.15118	−	1.10423i	0.229317	−	0.117711i
$89$	−5.87443	−	3.77526i	−0.622688	−	0.400177i	0.190908	−	0.981608i	$-0.438857\pi$
$89$	−5.87443	−	3.77526i	−0.622688	−	0.400177i	−0.813596	+	0.581431i	$0.802493\pi$
$90$	1.88849	−	1.53240i	0.199064	−	0.161529i
$91$	−9.65367	−	8.36496i	−1.01198	−	0.876886i
$92$	−0.859326	+	13.2758i	−0.0895909	+	1.38410i
$93$	−2.97933	+	3.43834i	−0.308943	+	0.356539i
$94$	2.54187	+	9.82028i	0.262174	+	1.01288i
$95$	4.13888	−	1.21529i	0.424640	−	0.124686i
$96$	2.96834	+	4.81549i	0.302955	+	0.491479i
$97$			2.27994i			0.231493i	0.993279	+	0.115746i	$0.0369260\pi$
$97$			2.27994i			0.231493i	−0.993279	+	0.115746i	$0.963074\pi$
$98$	7.50738	+	17.9525i	0.758360	+	1.81348i
$99$	0.719191	+	0.462196i	0.0722814	+	0.0464525i
$100$	−2.47033	−	3.25388i	−0.247033	−	0.325388i
$101$	−8.86816	+	4.04995i	−0.882414	+	0.402985i	−0.804484	−	0.593974i	$-0.797558\pi$
$101$	−8.86816	+	4.04995i	−0.882414	+	0.402985i	−0.0779299	+	0.996959i	$0.524831\pi$
$102$	−0.276641	+	0.557358i	−0.0273915	+	0.0551867i
$103$	3.67230	+	12.5067i	0.361843	+	1.23232i	0.916429	+	0.400197i	$0.131058\pi$
$103$	3.67230	+	12.5067i	0.361843	+	1.23232i	−0.554587	+	0.832126i	$0.687124\pi$
$104$	−7.49801	+	2.58033i	−0.735240	+	0.253023i
$105$		−	7.83535i		−	0.764652i
$106$	−11.9472	+	4.99606i	−1.16041	+	0.485260i
$107$	−0.741261	+	0.106577i	−0.0716604	+	0.0103032i	−0.178052	−	0.984021i	$-0.556979\pi$
$107$	−0.741261	+	0.106577i	−0.0716604	+	0.0103032i	0.106391	+	0.994324i	$0.466070\pi$
$108$	−0.946608	+	1.76180i	−0.0910874	+	0.169529i
$109$	−2.60033	+	8.85591i	−0.249066	+	0.848242i	0.736134	+	0.676836i	$0.236649\pi$
$109$	−2.60033	+	8.85591i	−0.249066	+	0.848242i	−0.985200	+	0.171406i	$0.945169\pi$
$110$	−1.17999	+	1.71184i	−0.112508	+	0.163217i
$111$	4.40130	−	2.82854i	0.417753	−	0.268474i
$112$	18.0730	+	2.34953i	1.70774	+	0.222009i
$113$	−17.5618	+	2.52500i	−1.65207	+	0.237532i	−0.904446	−	0.426589i	$-0.859715\pi$
$113$	−17.5618	+	2.52500i	−1.65207	+	0.237532i	−0.747625	+	0.664121i	$0.768806\pi$
$114$	−2.75459	+	2.23519i	−0.257991	+	0.209345i
$115$	−4.75193	−	10.4053i	−0.443120	−	0.970298i
$116$	−12.1649	−	8.97883i	−1.12948	−	0.833663i
$117$	−2.11877	−	1.83592i	−0.195880	−	0.169731i
$118$	0.120410	−	3.72436i	0.0110847	−	0.342855i
$119$	0.832784	+	1.82354i	0.0763412	+	0.167164i
$120$	−4.20807	−	2.43940i	−0.384142	−	0.222686i
$121$	9.85317	+	2.89315i	0.895742	+	0.263014i
$122$	12.9313	+	2.28796i	1.17075	+	0.207142i
$123$	7.20294	+	1.03563i	0.649468	+	0.0933794i
$124$	8.54674	+	3.12211i	0.767520	+	0.280374i
$125$	11.0167	+	5.03117i	0.985366	+	0.450002i
$126$	2.48595	+	5.94469i	0.221466	+	0.529595i
$127$	10.1188	+	4.62108i	0.897894	+	0.410054i	0.810241	−	0.586097i	$-0.199336\pi$
$127$	10.1188	+	4.62108i	0.897894	+	0.410054i	0.0876528	+	0.996151i	$0.472063\pi$
$128$	6.88856	−	8.97484i	0.608869	−	0.793271i
$129$	−0.460024	+	3.19953i	−0.0405028	+	0.281703i
$130$	4.62914	−	5.00587i	0.406002	−	0.439044i
$131$	−9.27431	−	14.4311i	−0.810300	−	1.26085i	−0.962170	−	0.272451i	$-0.912166\pi$
$131$	−9.27431	−	14.4311i	−0.810300	−	1.26085i	0.151870	−	0.988401i	$-0.451471\pi$
$132$	0.352141	−	1.67315i	0.0306500	−	0.145629i
$133$			11.4288i			0.991006i
$134$	11.5721	+	0.294161i	0.999677	+	0.0254116i
$135$		−	1.71968i		−	0.148007i
$136$	1.23863	+	0.120472i	0.106211	+	0.0103304i
$137$	−7.08963	−	11.0317i	−0.605708	−	0.942500i	−0.999726	−	0.0233977i	$-0.992552\pi$
$137$	−7.08963	−	11.0317i	−0.605708	−	0.942500i	0.394018	−	0.919103i	$-0.371085\pi$
$138$	6.90661	+	6.38683i	0.587930	+	0.543683i
$139$	0.141050	−	0.981023i	0.0119637	−	0.0832093i	−0.982965	−	0.183794i	$-0.941162\pi$
$139$	0.141050	−	0.981023i	0.0119637	−	0.0832093i	0.994929	+	0.100584i	$0.0320713\pi$
$140$	−14.6453	+	5.57550i	−1.23775	+	0.471216i
$141$	6.52464	+	2.97970i	0.549474	+	0.250936i
$142$	−10.2834	+	4.30030i	−0.862963	+	0.360874i
$143$	2.18016	+	0.995646i	0.182314	+	0.0832601i
$144$	3.96662	+	0.515669i	0.330552	+	0.0429724i
$145$	12.8682	+	1.85017i	1.06865	+	0.153648i
$146$	−1.31678	+	7.44234i	−0.108978	+	0.615932i
$147$	13.2023	+	3.87653i	1.08890	+	0.319731i
$148$	−8.41881	−	6.21387i	−0.692022	−	0.510777i
$149$	−6.90399	−	15.1176i	−0.565597	−	1.23848i	−0.949109	−	0.314948i	$-0.898013\pi$
$149$	−6.90399	−	15.1176i	−0.565597	−	1.23848i	0.383512	−	0.923536i	$-0.374714\pi$
$150$	−2.88728	−	0.0933473i	−0.235746	−	0.00762177i
$151$	−14.4044	−	12.4815i	−1.17222	−	1.01573i	−0.999527	−	0.0307544i	$-0.990209\pi$
$151$	−14.4044	−	12.4815i	−1.17222	−	1.01573i	−0.172689	−	0.984976i	$-0.555246\pi$
$152$	6.13799	+	3.55817i	0.497857	+	0.288606i
$153$	0.182777	+	0.400227i	0.0147767	+	0.0323564i
$154$	−3.47096	−	4.27752i	−0.279698	−	0.344693i
$155$	−7.74419	+	1.11345i	−0.622028	+	0.0894342i
$156$	−1.92390	+	5.26666i	−0.154035	+	0.421670i
$157$	5.87429	−	3.77517i	0.468819	−	0.301292i	−0.284819	−	0.958581i	$-0.591934\pi$
$157$	5.87429	−	3.77517i	0.468819	−	0.301292i	0.753638	+	0.657290i	$0.228297\pi$
$158$	2.56503	+	1.76811i	0.204063	+	0.140663i
$159$	−2.57978	+	8.78591i	−0.204590	+	0.696768i
$160$	−1.56518	+	9.60127i	−0.123738	+	0.759047i
$161$	29.9989	−	4.31320i	2.36425	−	0.339927i
$162$	0.545610	+	1.30473i	0.0428672	+	0.102509i
$163$		−	3.11407i		−	0.243913i	−0.992535	−	0.121956i	$-0.961083\pi$
$163$		−	3.11407i		−	0.243913i	0.992535	−	0.121956i	$-0.0389168\pi$
$164$	−3.18977	−	14.2002i	−0.249079	−	1.10885i
$165$	0.414194	+	1.41061i	0.0322449	+	0.109816i
$166$	10.4600	+	5.19176i	0.811854	+	0.402959i
$167$	9.32446	−	4.25834i	0.721549	−	0.329520i	−0.0205703	−	0.999788i	$-0.506548\pi$
$167$	9.32446	−	4.25834i	0.721549	−	0.329520i	0.742119	+	0.670268i	$0.233821\pi$
$168$	9.34244	−	8.87670i	0.720785	−	0.684852i
$169$	4.32423	+	2.77901i	0.332633	+	0.213770i
$170$	−0.987208	+	0.412830i	−0.0757154	+	0.0316626i
$171$			2.50837i			0.191820i
$172$	6.30769	−	1.41689i	0.480957	−	0.108037i
$173$	16.5259	−	4.85245i	1.25644	−	0.368925i	0.415273	−	0.909697i	$-0.363686\pi$
$173$	16.5259	−	4.85245i	1.25644	−	0.368925i	0.841169	+	0.540772i	$0.181868\pi$
$174$	−10.3501	+	2.67901i	−0.784640	+	0.203095i
$175$	−6.09481	+	7.03378i	−0.460724	+	0.531704i
$176$	−3.37792	+	0.532388i	−0.254620	+	0.0401303i
$177$	−1.99132	−	1.72549i	−0.149677	−	0.129696i
$178$	6.22245	+	7.66838i	0.466392	+	0.574770i
$179$	9.89813	+	6.36114i	0.739821	+	0.475454i	0.855481	−	0.517835i	$-0.173262\pi$
$179$	9.89813	+	6.36114i	0.739821	+	0.475454i	−0.115660	+	0.993289i	$0.536898\pi$
$180$	−3.21432	+	1.22370i	−0.239581	+	0.0912090i
$181$	−9.98149	+	6.41472i	−0.741919	+	0.476802i	−0.856199	−	0.516646i	$-0.827180\pi$
$181$	−9.98149	+	6.41472i	−0.741919	+	0.476802i	0.114280	+	0.993449i	$0.463544\pi$
$182$	9.27032	+	15.5046i	0.687162	+	1.14928i
$183$	7.01778	−	6.08094i	0.518769	−	0.449516i
$184$	7.02320	−	17.4541i	0.517757	−	1.28674i
$185$	8.90553	+	1.28042i	0.654748	+	0.0941385i
$186$	5.52225	−	3.30180i	0.404911	−	0.242100i
$187$	−0.246324	−	0.284273i	−0.0180130	−	0.0207881i
$188$	0.926636	−	14.3157i	0.0675819	−	1.04408i
$189$	4.37171	+	1.28365i	0.317995	+	0.0933718i
$190$	−6.09718	−	0.197125i	−0.442336	−	0.0143009i
$191$	7.77668	+	4.99777i	0.562701	+	0.361626i	0.790859	−	0.611998i	$-0.209634\pi$
$191$	7.77668	+	4.99777i	0.562701	+	0.361626i	−0.228158	+	0.973624i	$0.573270\pi$
$192$	−1.85873	−	7.78108i	−0.134142	−	0.561551i
$193$	25.0110	−	7.34389i	1.80033	−	0.528624i	0.802634	−	0.596472i	$-0.203431\pi$
$193$	25.0110	−	7.34389i	1.80033	−	0.528624i	0.997696	+	0.0678474i	$0.0216131\pi$
$194$	1.00789	−	3.06275i	0.0723624	−	0.219892i
$195$	−0.686126	−	4.77211i	−0.0491345	−	0.341738i
$196$	−2.14875	−	27.4352i	−0.153482	−	1.95966i
$197$	−1.84802	+	1.60132i	−0.131666	+	0.114089i	−0.718204	−	0.695832i	$-0.755036\pi$
$197$	−1.84802	+	1.60132i	−0.131666	+	0.114089i	0.586539	+	0.809921i	$0.300490\pi$
$198$	−0.761799	−	0.938821i	−0.0541387	−	0.0667191i
$199$	−13.8885	−	6.34265i	−0.984527	−	0.449618i	−0.142935	−	0.989732i	$-0.545654\pi$
$199$	−13.8885	−	6.34265i	−0.984527	−	0.449618i	−0.841592	+	0.540114i	$0.818381\pi$
$200$	1.88006	+	5.46313i	0.132940	+	0.386302i
$201$	5.31742	−	6.22294i	0.375062	−	0.438932i
$202$	13.7033	−	1.52014i	0.964164	−	0.106957i
$203$	−14.3088	+	31.3319i	−1.00428	+	2.19907i
$204$	0.618015	−	0.626429i	0.0432697	−	0.0438588i
$205$	8.19504	+	9.45758i	0.572366	+	0.660546i
$206$	0.595664	−	18.4242i	0.0415019	−	1.28368i
$207$	6.58410	−	0.946650i	0.457626	−	0.0657967i
$208$	11.2131	−	0.151641i	0.777488	−	0.0105144i
$209$	−0.604153	−	2.05756i	−0.0417901	−	0.142324i
$210$	−3.46377	+	10.5256i	−0.239023	+	0.726334i
$211$	−10.5454	+	16.4090i	−0.725978	+	1.12964i	0.260457	+	0.965486i	$0.416127\pi$
$211$	−10.5454	+	16.4090i	−0.725978	+	1.12964i	−0.986434	+	0.164158i	$0.947509\pi$
$212$	18.2577	−	1.42996i	1.25395	−	0.0982101i
$213$	−2.22052	+	7.56238i	−0.152147	+	0.518166i
$214$	1.04288	+	0.184519i	0.0712900	+	0.0126134i
$215$	−4.20104	+	3.64022i	−0.286508	+	0.248261i
$216$	2.05046	−	1.94824i	0.139516	−	0.132561i
$217$	2.95006	−	20.5181i	0.200263	−	1.39286i
$218$	7.40806	−	10.7470i	0.501737	−	0.727880i
$219$	3.49975	+	4.03892i	0.236491	+	0.272925i
$220$	2.34189	−	1.77795i	0.157890	−	0.119869i
$221$	0.666890	+	1.03770i	0.0448599	+	0.0698034i
$222$	−7.16288	+	1.85403i	−0.480741	+	0.124434i
$223$	−9.00937	+	14.0188i	−0.603312	+	0.938771i	0.396473	+	0.918046i	$0.370234\pi$
$223$	−9.00937	+	14.0188i	−0.603312	+	0.938771i	−0.999785	+	0.0207253i	$0.993402\pi$
$224$	−23.2396	−	11.1457i	−1.55276	−	0.744706i
$225$	−1.33767	+	1.54376i	−0.0891782	+	0.102917i
$226$	24.7077	+	4.37157i	1.64353	+	0.290792i
$227$	1.30005	+	1.12650i	0.0862872	+	0.0747682i	0.696936	−	0.717133i	$-0.254546\pi$
$227$	1.30005	+	1.12650i	0.0862872	+	0.0747682i	−0.610649	+	0.791901i	$0.709091\pi$
$228$	4.68848	−	1.78491i	0.310502	−	0.118209i
$229$	5.99985	+	20.4336i	0.396481	+	1.35029i	0.880007	+	0.474961i	$0.157538\pi$
$229$	5.99985	+	20.4336i	0.396481	+	1.35029i	−0.483525	+	0.875330i	$0.660644\pi$
$230$	1.78363	+	16.0786i	0.117609	+	1.06019i
$231$	−3.89518			−0.256284
$232$	12.3724	+	17.4394i	0.812287	+	1.14495i
$233$	−5.45207	+	8.48359i	−0.357177	+	0.555778i	−0.972619	−	0.232404i	$-0.925341\pi$
$233$	−5.45207	+	8.48359i	−0.357177	+	0.555778i	0.615442	+	0.788182i	$0.288977\pi$
$234$	2.03463	+	3.40292i	0.133008	+	0.222456i
$235$	5.12415	+	11.2203i	0.334263	+	0.731933i
$236$	−1.80818	+	4.94986i	−0.117702	+	0.322209i
$237$	2.11367	−	0.620630i	0.137298	−	0.0403143i
$238$	−0.312584	−	2.81779i	−0.0202618	−	0.182650i
$239$	−0.415139			−0.0268531			−0.0134265	−	0.999910i	$-0.504274\pi$
$239$	−0.415139			−0.0268531			−0.0134265	+	0.999910i	$0.504274\pi$
$240$	4.57450	+	5.13722i	0.295283	+	0.331606i
$241$	−3.01900	−	20.9976i	−0.194471	−	1.35257i	−0.819996	−	0.572369i	$-0.806024\pi$
$241$	−3.01900	−	20.9976i	−0.194471	−	1.35257i	0.625525	−	0.780204i	$-0.284885\pi$
$242$	−11.9572	−	8.24228i	−0.768640	−	0.529834i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	−16.3598	−	8.79006i	−1.04733	−	0.562726i
$245$	12.7928	+	19.9059i	0.817299	+	1.27174i
$246$	−9.21822	−	4.57540i	−0.587732	−	0.291717i
$247$	1.00080	+	6.96072i	0.0636794	+	0.442900i
$248$	−10.1010	−	7.97232i	−0.641416	−	0.506243i
$249$	7.51111	−	3.43021i	0.475997	−	0.217381i
$250$	−12.5751	−	11.6288i	−0.795322	−	0.735467i
$251$	13.7775	−	15.9001i	0.869631	−	1.00361i	−0.130296	−	0.991475i	$-0.541593\pi$
$251$	13.7775	−	15.9001i	0.869631	−	1.00361i	0.999926	−	0.0121322i	$-0.00386188\pi$
$252$	−0.711522	−	9.08472i	−0.0448217	−	0.572284i
$253$	−5.17276	+	2.36232i	−0.325209	+	0.148518i
$254$	−11.5501	−	10.6809i	−0.724720	−	0.670179i
$255$	−0.213170	+	0.725991i	−0.0133492	+	0.0454633i
$256$	−13.2212	+	9.01108i	−0.826326	+	0.563192i
$257$	−1.75372	+	12.1974i	−0.109394	+	0.760852i	0.859099	+	0.511810i	$0.171025\pi$
$257$	−1.75372	+	12.1974i	−0.109394	+	0.760852i	−0.968493	+	0.249042i	$0.919884\pi$
$258$	2.03239	−	4.09472i	0.126531	−	0.254926i
$259$	−9.90253	+	21.6835i	−0.615313	+	1.34735i
$260$	−8.43147	+	4.67821i	−0.522898	+	0.290130i
$261$	−3.14047	+	6.87666i	−0.194390	+	0.425655i
$262$	6.07904	+	23.4858i	0.375565	+	1.45096i
$263$	0.844074	+	0.121359i	0.0520478	+	0.00748335i	0.168290	−	0.985738i	$-0.446176\pi$
$263$	0.844074	+	0.121359i	0.0520478	+	0.00748335i	−0.116242	+	0.993221i	$0.537085\pi$
$264$	−1.21270	+	2.09195i	−0.0746363	+	0.128751i
$265$	−13.2471	+	8.51339i	−0.813763	+	0.522974i
$266$	5.05234	−	15.3529i	0.309779	−	0.941344i
$267$	6.98294			0.427349
$268$	−15.4153	−	5.51083i	−0.941638	−	0.336627i
$269$	−8.06384			−0.491661			−0.245830	−	0.969313i	$-0.579061\pi$
$269$	−8.06384			−0.491661			−0.245830	+	0.969313i	$0.579061\pi$
$270$	−0.760220	+	2.31013i	−0.0462655	+	0.140590i
$271$	19.4751	−	12.5159i	1.18303	−	0.760287i	0.207088	−	0.978322i	$-0.433601\pi$
$271$	19.4751	−	12.5159i	1.18303	−	0.760287i	0.975941	+	0.218036i	$0.0699649\pi$
$272$	−1.61065	−	0.709395i	−0.0976598	−	0.0430134i
$273$	12.6436	+	1.81788i	0.765227	+	0.110023i
$274$	4.64705	+	17.9535i	0.280739	+	1.08461i
$275$	0.725439	−	1.58849i	0.0437456	−	0.0957896i
$276$	−6.45454	−	11.6329i	−0.388518	−	0.700220i
$277$	3.47236	−	7.60342i	0.208634	−	0.456845i	−0.776168	−	0.630526i	$-0.782839\pi$
$277$	3.47236	−	7.60342i	0.208634	−	0.456845i	0.984802	+	0.173681i	$0.0555663\pi$
$278$	−0.623158	+	1.25550i	−0.0373746	+	0.0752998i
$279$	0.647471	−	4.50326i	0.0387631	−	0.269603i
$280$	22.1384	−	1.01558i	1.32302	−	0.0606926i
$281$	4.93656	−	16.8124i	0.294490	−	1.00294i	−0.670773	−	0.741663i	$-0.734037\pi$
$281$	4.93656	−	16.8124i	0.294490	−	1.00294i	0.965263	−	0.261279i	$-0.0841444\pi$
$282$	−7.44760	−	6.88711i	−0.443498	−	0.410121i
$283$	1.34719	−	0.615243i	0.0800824	−	0.0365724i	−0.374971	−	0.927036i	$-0.622347\pi$
$283$	1.34719	−	0.615243i	0.0800824	−	0.0365724i	0.455054	+	0.890464i	$0.349620\pi$
$284$	15.7152	−	1.23082i	0.932523	−	0.0730359i
$285$	−2.82482	+	3.26001i	−0.167328	+	0.193106i
$286$	−2.48856	−	2.30128i	−0.147152	−	0.136077i
$287$	−30.1598	+	13.7735i	−1.78028	+	0.813025i
$288$	−5.10058	−	2.44624i	−0.300554	−	0.144146i
$289$	2.39180	+	16.6353i	0.140694	+	0.978550i
$290$	−16.4685	−	8.17404i	−0.967065	−	0.479996i
$291$	−1.23263	−	1.91801i	−0.0722580	−	0.112436i
$292$	5.05892	−	9.41551i	0.296051	−	0.551001i
$293$	−1.86861	−	0.548675i	−0.109166	−	0.0320539i	0.226694	−	0.973966i	$-0.427208\pi$
$293$	−1.86861	−	0.548675i	−0.109166	−	0.0320539i	−0.335859	+	0.941912i	$0.609027\pi$
$294$	−16.0215	−	11.0438i	−0.934392	−	0.644089i
$295$	−0.644855	−	4.48506i	−0.0375449	−	0.261131i
$296$	8.56240	+	12.0691i	0.497680	+	0.701500i
$297$	−0.854904			−0.0496066
$298$	2.59140	+	23.3602i	0.150116	+	1.35322i
$299$	17.8931	−	5.25390i	1.03479	−	0.303841i
$300$	3.83735	+	1.40178i	0.221550	+	0.0809316i
$301$	−6.11817	−	13.3969i	−0.352646	−	0.772186i
$302$	13.8324	+	23.1347i	0.795967	+	1.33125i
$303$	5.27080	−	8.20152i	0.302799	−	0.471165i
$304$	−6.67248	−	7.49327i	−0.382693	−	0.429768i
$305$	15.9687			0.914367
$306$	−0.0686052	−	0.618443i	−0.00392190	−	0.0353540i
$307$	−5.40742	−	18.4160i	−0.308618	−	1.05106i	−0.957084	−	0.289812i	$-0.906407\pi$
$307$	−5.40742	−	18.4160i	−0.308618	−	1.05106i	0.648466	−	0.761244i	$-0.275411\pi$
$308$	2.77174	+	7.28060i	0.157935	+	0.414850i
$309$	−9.85097	−	8.53592i	−0.560402	−	0.485591i
$310$	10.8953	+	1.92773i	0.618814	+	0.109487i
$311$	11.2113	−	12.9385i	0.635733	−	0.733675i	−0.342882	−	0.939379i	$-0.611403\pi$
$311$	11.2113	−	12.9385i	0.635733	−	0.733675i	0.978614	+	0.205704i	$0.0659484\pi$
$312$	4.91269	−	6.22444i	0.278126	−	0.352390i
$313$	8.13046	−	12.6512i	0.459561	−	0.715091i	−0.531711	−	0.846926i	$-0.678451\pi$
$313$	8.13046	−	12.6512i	0.459561	−	0.715091i	0.991272	+	0.131835i	$0.0420870\pi$
$314$	−9.56008	+	2.47452i	−0.539506	+	0.139645i
$315$	4.23611	+	6.59152i	0.238678	+	0.371390i
$316$	−2.66409	−	3.50910i	−0.149867	−	0.197402i
$317$	17.7251	+	20.4559i	0.995542	+	1.14892i	0.988846	+	0.148939i	$0.0475857\pi$
$317$	17.7251	+	20.4559i	0.995542	+	1.14892i	0.00669530	+	0.999978i	$0.497869\pi$
$318$	7.34951	−	10.6621i	0.412140	−	0.597899i
$319$	0.919771	−	6.39715i	0.0514973	−	0.358171i
$320$	6.34699	−	12.2059i	0.354808	−	0.682330i
$321$	0.565968	−	0.490414i	0.0315893	−	0.0273723i
$322$	−42.2056	−	7.46750i	−2.35203	−	0.416147i
$323$	0.310935	−	1.05895i	0.0173009	−	0.0589214i
$324$	−0.156163	−	1.99389i	−0.00867574	−	0.110772i
$325$	−3.09610	+	4.81763i	−0.171741	+	0.267234i
$326$	−1.37664	+	4.18327i	−0.0762448	+	0.231690i
$327$	−2.60033	−	8.85591i	−0.143799	−	0.489733i
$328$	−1.99251	+	20.4858i	−0.110018	+	1.13114i
$329$	−32.3487	+	4.65105i	−1.78344	+	0.256420i
$330$	0.0671842	−	2.07804i	0.00369837	−	0.114393i
$331$	0.493088	+	0.569054i	0.0271026	+	0.0312780i	0.769139	−	0.639081i	$-0.220685\pi$
$331$	0.493088	+	0.569054i	0.0271026	+	0.0312780i	−0.742036	+	0.670360i	$0.766140\pi$
$332$	−11.7563	−	11.5984i	−0.645210	−	0.636543i
$333$	−2.17338	+	4.75905i	−0.119101	+	0.260794i
$334$	−14.4085	+	1.59836i	−0.788395	+	0.0874584i
$335$	13.9188	−	2.09941i	0.760465	−	0.114703i
$336$	−16.4742	+	7.79446i	−0.898743	+	0.425223i
$337$	−24.8452	−	11.3464i	−1.35340	−	0.618079i	−0.399098	−	0.916908i	$-0.630677\pi$
$337$	−24.8452	−	11.3464i	−1.35340	−	0.618079i	−0.954307	+	0.298829i	$0.903404\pi$
$338$	−4.58042	−	5.64478i	−0.249142	−	0.307036i
$339$	13.4088	−	11.6188i	0.728264	−	0.631045i
$340$	1.50866	−	0.118159i	0.0818186	−	0.00640809i
$341$	0.553526	+	3.84986i	0.0299751	+	0.208481i
$342$	1.10887	−	3.36961i	0.0599611	−	0.182208i
$343$	−29.5511	+	8.67698i	−1.59561	+	0.468513i
$344$	−9.09977	−	0.885068i	−0.490627	−	0.0477197i
$345$	9.62310	+	6.18439i	0.518090	+	0.332957i
$346$	−24.3451	−	0.787090i	−1.30880	−	0.0423142i
$347$	14.1483	+	4.15430i	0.759518	+	0.223015i	0.638485	−	0.769634i	$-0.279561\pi$
$347$	14.1483	+	4.15430i	0.759518	+	0.223015i	0.121033	+	0.992649i	$0.461379\pi$
$348$	15.0881	+	0.976631i	0.808806	+	0.0523529i
$349$	−8.30672	−	9.58646i	−0.444648	−	0.513152i	0.488539	−	0.872542i	$-0.337530\pi$
$349$	−8.30672	−	9.58646i	−0.444648	−	0.513152i	−0.933187	+	0.359391i	$0.882985\pi$
$350$	11.2968	−	6.75447i	0.603842	−	0.361041i
$351$	2.77499	+	0.398984i	0.148118	+	0.0212962i
$352$	4.77306	+	0.778094i	0.254405	+	0.0414725i
$353$	9.04871	−	7.84075i	0.481614	−	0.417321i	−0.379921	−	0.925019i	$-0.624049\pi$
$353$	9.04871	−	7.84075i	0.481614	−	0.417321i	0.861535	+	0.507698i	$0.169503\pi$
$354$	1.91224	+	3.19823i	0.101635	+	0.169984i
$355$	−11.4023	+	7.32782i	−0.605171	+	0.388920i
$356$	−4.96894	−	13.0520i	−0.263353	−	0.691756i
$357$	−1.68646	−	1.08382i	−0.0892571	−	0.0573621i
$358$	−10.4845	−	12.9209i	−0.554125	−	0.682889i
$359$	−21.2044	−	18.3737i	−1.11913	−	0.969729i	−0.119395	−	0.992847i	$-0.538095\pi$
$359$	−21.2044	−	18.3737i	−1.11913	−	0.969729i	−0.999733	+	0.0231176i	$0.992641\pi$
$360$	4.85889	−	0.222897i	0.256086	−	0.0117477i
$361$	−8.32201	+	9.60411i	−0.438000	+	0.505480i
$362$	16.2443	−	4.20466i	0.853783	−	0.220992i
$363$	−9.85317	+	2.89315i	−0.517157	+	0.151851i
$364$	−5.59913	−	24.9262i	−0.293474	−	1.30649i
$365$			9.19045i			0.481050i
$366$	−12.1155	+	5.06645i	−0.633287	+	0.264828i
$367$	−22.7057	−	14.5921i	−1.18523	−	0.761701i	−0.208889	−	0.977939i	$-0.566985\pi$
$367$	−22.7057	−	14.5921i	−1.18523	−	0.761701i	−0.976341	+	0.216239i	$0.930621\pi$
$368$	−17.1505	+	20.3422i	−0.894032	+	1.06041i
$369$	−6.61940	+	3.02298i	−0.344592	+	0.157370i
$370$	−11.3972	−	5.65691i	−0.592510	−	0.294089i
$371$	−11.7542	−	40.0310i	−0.610246	−	2.07831i
$372$	−8.87791	+	1.99423i	−0.460298	+	0.103396i
$373$			23.7946i			1.23204i	0.787732	+	0.616018i	$0.211255\pi$
$373$			23.7946i			1.23204i	−0.787732	+	0.616018i	$0.788745\pi$
$374$	0.205230	+	0.490769i	0.0106122	+	0.0253771i
$375$	−11.9879	+	1.72360i	−0.619054	+	0.0890065i
$376$	−7.57332	+	18.8213i	−0.390564	+	0.970634i
$377$	−5.97110	+	20.3357i	−0.307527	+	1.04734i
$378$	−5.30525	−	3.65698i	−0.272873	−	0.188095i
$379$	22.9731	−	14.7639i	1.18005	−	0.758372i	0.204654	−	0.978834i	$-0.434393\pi$
$379$	22.9731	−	14.7639i	1.18005	−	0.758372i	0.975396	+	0.220462i	$0.0707566\pi$
$380$	8.10348	+	2.96018i	0.415700	+	0.151854i
$381$	−11.0108	+	1.58311i	−0.564099	+	0.0811052i
$382$	−8.23740	−	10.1516i	−0.421462	−	0.519399i
$383$	10.8842	+	23.8331i	0.556157	+	1.21781i	0.953846	+	0.300295i	$0.0970850\pi$
$383$	10.8842	+	23.8331i	0.556157	+	1.21781i	−0.397689	+	0.917520i	$0.630188\pi$
$384$	−0.942864	+	11.2744i	−0.0481153	+	0.575342i
$385$	−5.06237	−	4.38657i	−0.258002	−	0.223560i
$386$	−36.8449	−	1.19121i	−1.87535	−	0.0606311i
$387$	−1.34280	−	2.94033i	−0.0682585	−	0.149465i
$388$	−2.70789	+	3.66877i	−0.137472	+	0.186253i
$389$	−16.7707	−	4.92432i	−0.850308	−	0.249673i	−0.172589	−	0.984994i	$-0.555213\pi$
$389$	−16.7707	−	4.92432i	−0.850308	−	0.249673i	−0.677719	+	0.735321i	$0.737031\pi$
$390$	−1.18790	+	6.71391i	−0.0601517	+	0.339972i
$391$	−2.89692	−	0.416514i	−0.146504	−	0.0210640i
$392$	−9.24176	+	37.8048i	−0.466779	+	1.90943i
$393$	15.6041	+	7.12615i	0.787122	+	0.359467i
$394$	3.19041	−	1.33417i	0.160731	−	0.0672144i
$395$	3.44596	+	1.57372i	0.173385	+	0.0791823i
$396$	0.608335	+	1.59793i	0.0305700	+	0.0802989i
$397$	3.55705	−	24.7398i	0.178523	−	1.24166i	−0.681659	−	0.731670i	$-0.738741\pi$
$397$	3.55705	−	24.7398i	0.178523	−	1.24166i	0.860183	−	0.509986i	$-0.170350\pi$
$398$	15.8531	+	14.6600i	0.794644	+	0.734841i
$399$	−6.17889	−	9.61455i	−0.309332	−	0.481329i
$400$	−0.110487	−	8.16999i	−0.00552436	−	0.408499i
$401$			37.5080i			1.87306i	0.350586	+	0.936531i	$0.385982\pi$
$401$			37.5080i			1.87306i	−0.350586	+	0.936531i	$0.614018\pi$
$402$	−9.89410	+	6.00889i	−0.493473	+	0.299696i
$403$		−	12.7549i		−	0.635364i
$404$	−19.0803	−	4.01575i	−0.949282	−	0.199791i
$405$	0.929732	+	1.44669i	0.0461987	+	0.0718866i
$406$	33.0726	−	35.7641i	1.64136	−	1.77494i
$407$	0.636534	−	4.42719i	0.0315518	−	0.219448i
$408$	−1.10713	+	0.568305i	−0.0548112	+	0.0281353i
$409$	3.76026	+	1.71725i	0.185933	+	0.0849127i	0.506206	−	0.862412i	$-0.331047\pi$
$409$	3.76026	+	1.71725i	0.185933	+	0.0849127i	−0.320273	+	0.947325i	$0.603775\pi$
$410$	−6.82786	−	16.3276i	−0.337204	−	0.806361i
$411$	11.9284	+	5.44750i	0.588382	+	0.268705i
$412$	−8.94497	+	24.4868i	−0.440687	+	1.20638i
$413$	11.8831	+	1.70853i	0.584729	+	0.0840713i
$414$	−9.26320	−	1.63895i	−0.455261	−	0.0805499i
$415$	13.6248	+	4.00059i	0.668813	+	0.196381i
$416$	−15.1301	−	4.75326i	−0.741813	−	0.233048i
$417$	0.411722	+	0.901546i	0.0201621	+	0.0441489i
$418$	−0.0979964	+	3.03108i	−0.00479316	+	0.148255i
$419$	20.2786	+	17.5715i	0.990675	+	0.858425i	0.989928	−	0.141575i	$-0.0452166\pi$
$419$	20.2786	+	17.5715i	0.990675	+	0.858425i	0.000747617		1.00000i	$0.499762\pi$
$420$	9.30607	−	12.6083i	0.454090	−	0.615220i
$421$	−5.49029	−	12.0221i	−0.267580	−	0.585919i	0.727375	−	0.686241i	$-0.240740\pi$
$421$	−5.49029	−	12.0221i	−0.267580	−	0.585919i	−0.994955	+	0.100321i	$0.968013\pi$
$422$	21.4201	−	17.3811i	1.04271	−	0.846101i
$423$	−7.09982	+	1.02080i	−0.345205	+	0.0496330i
$424$	−25.1586	−	6.15026i	−1.22181	−	0.298683i
$425$	0.756081	−	0.485904i	0.0366753	−	0.0235698i
$426$	6.32601	−	9.17726i	0.306496	−	0.444640i
$427$	−11.9198	+	40.5951i	−0.576839	+	1.96453i
$428$	−1.31938	−	0.708899i	−0.0637747	−	0.0342659i
$429$	−2.37235	+	0.341093i	−0.114538	+	0.0164681i
$430$	7.25267	−	3.03292i	0.349755	−	0.146260i
$431$			34.2327i			1.64893i	0.565911	+	0.824466i	$0.308525\pi$
$431$			34.2327i			1.64893i	−0.565911	+	0.824466i	$0.691475\pi$
$432$	−3.61573	+	1.71071i	−0.173962	+	0.0823065i
$433$	−9.43207	−	32.1227i	−0.453276	−	1.54372i	−0.796604	−	0.604502i	$-0.793372\pi$
$433$	−9.43207	−	32.1227i	−0.453276	−	1.54372i	0.343328	−	0.939216i	$-0.388446\pi$
$434$	−13.0334	+	26.2587i	−0.625621	+	1.26046i
$435$	−11.8257	+	5.40061i	−0.566998	+	0.258940i
$436$	−14.7025	+	11.1621i	−0.704122	+	0.534566i
$437$	−14.0365	−	9.02071i	−0.671456	−	0.431519i
$438$	−2.91588	−	6.97280i	−0.139326	−	0.333173i
$439$		−	8.57484i		−	0.409255i	−0.978840	−	0.204627i	$-0.934402\pi$
$439$		−	8.57484i		−	0.409255i	0.978840	−	0.204627i	$-0.0655983\pi$
$440$	−3.93194	+	1.35312i	−0.187448	+	0.0645076i
$441$	−13.2023	+	3.87653i	−0.628679	+	0.184597i
$442$	−0.437128	−	1.68880i	−0.0207920	−	0.0803281i
$443$	17.5506	−	20.2545i	0.833855	−	0.962320i	−0.165861	−	0.986149i	$-0.553040\pi$
$443$	17.5506	−	20.2545i	0.833855	−	0.962320i	0.999716	+	0.0238290i	$0.00758573\pi$
$444$	10.4418	+	0.675885i	0.495547	+	0.0320761i
$445$	9.07539	+	7.86387i	0.430215	+	0.372783i
$446$	18.3000	−	14.8494i	0.866529	−	0.703139i
$447$	13.9812	+	8.98518i	0.661289	+	0.424984i
$448$	26.2916	+	25.2461i	1.24216	+	1.19277i
$449$	9.46052	−	6.07991i	0.446469	−	0.286928i	−0.298024	−	0.954558i	$-0.596328\pi$
$449$	9.46052	−	6.07991i	0.446469	−	0.286928i	0.744493	+	0.667630i	$0.232691\pi$
$450$	2.47940	−	1.48245i	0.116880	−	0.0698836i
$451$	4.70163	−	4.07399i	0.221391	−	0.191837i
$452$	−31.2584	−	16.7950i	−1.47027	−	0.789972i
$453$	18.8658	+	2.71249i	0.886392	+	0.127444i
$454$	−1.24842	−	2.08798i	−0.0585913	−	0.0979940i
$455$	14.3851	+	16.6013i	0.674383	+	0.778280i
$456$	−7.08730	+	0.325123i	−0.331893	+	0.0152253i
$457$	23.2276	+	6.82023i	1.08654	+	0.319037i	0.775492	−	0.631357i	$-0.217502\pi$
$457$	23.2276	+	6.82023i	1.08654	+	0.319037i	0.311048	+	0.950394i	$0.399320\pi$
$458$	0.973204	−	30.1017i	0.0454748	−	1.40656i
$459$	−0.370141	−	0.237875i	−0.0172767	−	0.0111031i
$460$	4.71181	−	22.3875i	0.219689	−	1.04382i
$461$	25.7696	−	7.56665i	1.20021	−	0.352414i	0.380278	−	0.924872i	$-0.375828\pi$
$461$	25.7696	−	7.56665i	1.20021	−	0.352414i	0.819934	+	0.572459i	$0.194010\pi$
$462$	5.23257	+	1.72194i	0.243441	+	0.0801118i
$463$	4.87551	+	33.9099i	0.226584	+	1.57593i	0.712341	+	0.701833i	$0.247635\pi$
$463$	4.87551	+	33.9099i	0.226584	+	1.57593i	−0.485757	+	0.874094i	$0.661456\pi$
$464$	−8.91096	−	28.8966i	−0.413681	−	1.34149i
$465$	5.91285	−	5.12352i	0.274202	−	0.237597i
$466$	11.0743	−	8.98619i	0.513009	−	0.416277i
$467$	25.1038	+	11.4645i	1.16167	+	0.530515i	0.900533	−	0.434788i	$-0.143177\pi$
$467$	25.1038	+	11.4645i	1.16167	+	0.530515i	0.261133	+	0.965303i	$0.415904\pi$
$468$	−1.22888	−	5.47074i	−0.0568052	−	0.252885i
$469$	−5.05257	+	36.9509i	−0.233306	+	1.70623i
$470$	−1.92334	−	17.3380i	−0.0887171	−	0.799742i
$471$	−2.90075	+	6.35176i	−0.133660	+	0.292673i
$472$	4.61718	−	5.85003i	0.212523	−	0.269270i
$473$	1.80966	+	2.08846i	0.0832081	+	0.0960273i
$474$	−3.11375	−	0.100669i	−0.143019	−	0.00462389i
$475$	5.07166	−	0.729195i	0.232704	−	0.0334578i
$476$	−0.825752	+	3.92345i	−0.0378483	+	0.179831i
$477$	−2.57978	−	8.78591i	−0.118120	−	0.402279i
$478$	0.557674	+	0.183520i	0.0255074	+	0.00839401i
$479$	11.0074	−	17.1279i	0.502943	−	0.782595i	−0.493239	−	0.869894i	$-0.664187\pi$
$479$	11.0074	−	17.1279i	0.502943	−	0.782595i	0.996182	+	0.0872990i	$0.0278236\pi$
$480$	−3.87413	−	8.92330i	−0.176829	−	0.407291i
$481$	−4.13234	+	14.0735i	−0.188419	+	0.641695i
$482$	−5.22683	+	29.5416i	−0.238076	+	1.34558i
$483$	−22.9048	+	19.8471i	−1.04221	+	0.903076i
$484$	12.4190	+	16.3581i	0.564501	+	0.743552i
$485$	0.557985	−	3.88087i	0.0253368	−	0.176221i
$486$	−1.16438	−	0.802626i	−0.0528176	−	0.0364079i
$487$	−17.9653	−	20.7330i	−0.814084	−	0.939503i	0.184981	−	0.982742i	$-0.440778\pi$
$487$	−17.9653	−	20.7330i	−0.814084	−	0.939503i	−0.999065	+	0.0432391i	$0.986232\pi$
$488$	18.0910	+	19.0402i	0.818943	+	0.861911i
$489$	1.68359	+	2.61972i	0.0761348	+	0.118468i
$490$	−8.38529	−	32.3958i	−0.378809	−	1.46349i
$491$	1.25077	−	1.94623i	0.0564463	−	0.0878322i	−0.811883	−	0.583820i	$-0.801557\pi$
$491$	1.25077	−	1.94623i	0.0564463	−	0.0878322i	0.868330	+	0.495988i	$0.165194\pi$
$492$	10.3606	+	10.2214i	0.467092	+	0.460818i
$493$	2.17822	−	2.51380i	0.0981020	−	0.113216i
$494$	1.73270	−	9.79307i	0.0779579	−	0.440611i
$495$	−1.11108	−	0.962754i	−0.0499392	−	0.0432726i
$496$	10.0449	+	15.1749i	0.451027	+	0.681374i
$497$	−10.1173	−	34.4563i	−0.453822	−	1.54557i
$498$	−11.6064	+	1.28752i	−0.520095	+	0.0576952i
$499$	−34.0576			−1.52463			−0.762314	−	0.647208i	$-0.775937\pi$
$499$	−34.0576			−1.52463			−0.762314	+	0.647208i	$0.775937\pi$
$500$	11.7520	+	21.1805i	0.525567	+	0.947221i
$501$	−5.54201	+	8.62353i	−0.247599	+	0.385271i
$502$	−25.5369	+	15.2687i	−1.13977	+	0.681477i
$503$	−5.65040	−	12.3727i	−0.251939	−	0.551669i	0.740833	−	0.671690i	$-0.234431\pi$
$503$	−5.65040	−	12.3727i	−0.251939	−	0.551669i	−0.992771	+	0.120021i	$0.961704\pi$
$504$	−3.06026	+	12.5185i	−0.136315	+	0.557616i
$505$	16.0864	−	4.72339i	0.715834	−	0.210188i
$506$	7.99311	−	0.886693i	0.355337	−	0.0394183i
$507$	−5.14022			−0.228285
$508$	10.7941	+	19.4541i	0.478912	+	0.863135i
$509$	−2.78501	−	19.3702i	−0.123443	−	0.858568i	−0.953608	−	0.301050i	$-0.902663\pi$
$509$	−2.78501	−	19.3702i	−0.123443	−	0.858568i	0.830165	−	0.557518i	$-0.188246\pi$
$510$	0.607299	−	0.881020i	0.0268917	−	0.0390122i
$511$	−23.3636	−	6.86016i	−1.03354	−	0.303476i
$512$	21.7442	−	6.26029i	0.960965	−	0.276668i
$513$	−1.35613	−	2.11018i	−0.0598746	−	0.0931667i
$514$	7.74794	−	15.6100i	0.341747	−	0.688529i
$515$	−3.19007	−	22.1874i	−0.140571	−	0.977695i
$516$	−4.54034	+	4.60216i	−0.199877	+	0.202599i
$517$	5.57794	−	2.54736i	0.245318	−	0.112033i
$518$	22.8881	−	24.7508i	1.00565	−	1.08749i
$519$	−11.2791	+	13.0167i	−0.495096	+	0.571371i
$520$	13.3945	−	2.55716i	0.587386	−	0.112139i
$521$	10.5012	−	4.79574i	0.460066	−	0.210105i	−0.171879	−	0.985118i	$-0.554984\pi$
$521$	10.5012	−	4.79574i	0.460066	−	0.210105i	0.631945	+	0.775013i	$0.282257\pi$
$522$	7.25869	−	7.84942i	0.317704	−	0.343560i
$523$	−9.13439	+	31.1089i	−0.399419	+	1.36030i	0.477066	+	0.878867i	$0.341700\pi$
$523$	−9.13439	+	31.1089i	−0.399419	+	1.36030i	−0.876485	+	0.481429i	$0.840118\pi$
$524$	2.21611	−	34.2369i	0.0968112	−	1.49565i
$525$	1.32453	−	9.21229i	0.0578071	−	0.402057i
$526$	−1.08023	−	0.536167i	−0.0471004	−	0.0233780i
$527$	−0.831559	+	1.82086i	−0.0362233	+	0.0793179i
$528$	2.55386	−	2.27412i	0.111142	−	0.0989682i
$529$	−8.82611	+	19.3265i	−0.383744	+	0.840282i
$530$	21.5589	−	5.58029i	0.936460	−	0.242392i
$531$	2.60807	+	0.374984i	0.113181	+	0.0162729i
$532$	−13.5741	+	18.3907i	−0.588510	+	0.797338i
$533$	−17.1627	+	11.0298i	−0.743398	+	0.477753i
$534$	−9.38050	−	3.08694i	−0.405934	−	0.133585i
$535$	1.28784			0.0556783
$536$	18.2719	+	14.2176i	0.789224	+	0.614105i
$537$	−11.7659			−0.507737
$538$	10.8325	+	3.56477i	0.467023	+	0.153688i
$539$	9.89580	−	6.35964i	0.426242	−	0.273929i
$540$	2.04247	−	2.76723i	0.0878941	−	0.119083i
$541$	33.1925	+	4.77236i	1.42706	+	0.205180i	0.812163	−	0.583431i	$-0.198290\pi$
$541$	33.1925	+	4.77236i	1.42706	+	0.205180i	0.614893	+	0.788611i	$0.289199\pi$
$542$	−31.6947	+	8.20381i	−1.36140	+	0.352384i
$543$	4.92891	−	10.7928i	0.211520	−	0.463164i
$544$	1.85005	+	1.66498i	0.0793203	+	0.0713854i
$545$	6.59360	−	14.4380i	0.282439	−	0.618454i
$546$	−16.1811	−	8.03139i	−0.692488	−	0.343712i
$547$	6.23126	−	43.3393i	0.266429	−	1.85306i	−0.215056	−	0.976602i	$-0.568993\pi$
$547$	6.23126	−	43.3393i	0.266429	−	1.85306i	0.481485	−	0.876454i	$-0.340098\pi$
$548$	1.69408	−	26.1720i	0.0723674	−	1.11801i
$549$	−2.61613	+	8.90971i	−0.111654	+	0.380257i
$550$	−1.67674	+	1.81320i	−0.0714963	+	0.0773149i
$551$	17.2492	−	7.87746i	0.734842	−	0.335591i
$552$	3.52812	+	18.4804i	0.150167	+	0.786577i
$553$	−6.57286	+	7.58549i	−0.279506	+	0.322568i
$554$	−8.02582	+	8.67898i	−0.340984	+	0.368735i
$555$	−8.18406	+	3.73753i	−0.347394	+	0.158649i
$556$	1.39213	−	1.41109i	0.0590396	−	0.0598434i
$557$	4.71748	+	32.8108i	0.199886	+	1.39024i	0.804610	+	0.593803i	$0.202374\pi$
$557$	4.71748	+	32.8108i	0.199886	+	1.39024i	−0.604724	+	0.796435i	$0.706717\pi$
$558$	−2.86053	+	5.76321i	−0.121096	+	0.243976i
$559$	−4.89941	−	7.62363i	−0.207223	−	0.322445i
$560$	−30.1885	−	8.42245i	−1.27570	−	0.355913i
$561$	0.360911	+	0.105973i	0.0152377	+	0.00447418i
$562$	−14.0637	+	20.4025i	−0.593243	+	0.860628i
$563$	−2.69902	−	18.7721i	−0.113750	−	0.791149i	−0.964216	−	0.265119i	$-0.914589\pi$
$563$	−2.69902	−	18.7721i	−0.113750	−	0.791149i	0.850466	−	0.526030i	$-0.176320\pi$
$564$	6.96012	+	12.5441i	0.293074	+	0.528203i
$565$	30.5112			1.28362
$566$	−2.08173	+	0.230930i	−0.0875015	+	0.00970673i
$567$	−4.37171	+	1.28365i	−0.183595	+	0.0539082i
$568$	−21.6550	−	5.29377i	−0.908623	−	0.222122i
$569$	−4.57789	−	10.0242i	−0.191915	−	0.420236i	0.789074	−	0.614298i	$-0.210561\pi$
$569$	−4.57789	−	10.0242i	−0.191915	−	0.420236i	−0.980989	+	0.194063i	$0.937834\pi$
$570$	5.23585	−	3.13055i	0.219306	−	0.131124i
$571$	1.22969	−	1.91344i	0.0514610	−	0.0800749i	−0.814570	−	0.580066i	$-0.803027\pi$
$571$	1.22969	−	1.91344i	0.0514610	−	0.0800749i	0.866031	+	0.499991i	$0.166663\pi$
$572$	2.32567	+	4.19152i	0.0972413	+	0.175256i
$573$	−9.24416			−0.386180
$574$	46.6039	−	5.16987i	1.94521	−	0.215786i
$575$	−3.82805	−	13.0371i	−0.159641	−	0.543686i
$576$	5.77043	+	5.54095i	0.240434	+	0.230873i
$577$	−15.3916	−	13.3369i	−0.640760	−	0.555221i	0.272726	−	0.962092i	$-0.412075\pi$
$577$	−15.3916	−	13.3369i	−0.640760	−	0.555221i	−0.913486	+	0.406870i	$0.866620\pi$
$578$	4.14096	−	23.4043i	0.172241	−	0.973492i
$579$	−17.0702	+	19.7000i	−0.709412	+	0.818705i
$580$	18.5094	+	18.2608i	0.768561	+	0.758238i
$581$	−20.3403	+	31.6501i	−0.843856	+	1.31307i
$582$	0.807953	+	3.12145i	0.0334907	+	0.129388i
$583$	4.23225	+	6.58551i	0.175282	+	0.272744i
$584$	−10.9582	+	10.4119i	−0.453453	+	0.430847i
$585$	3.15721	+	3.64361i	0.130534	+	0.150645i
$586$	2.26764	+	1.56312i	0.0936754	+	0.0645717i
$587$	3.86813	−	26.9034i	0.159655	−	1.11042i	−0.739615	−	0.673030i	$-0.764993\pi$
$587$	3.86813	−	26.9034i	0.159655	−	1.11042i	0.899270	−	0.437394i	$-0.144098\pi$
$588$	16.6402	+	21.9183i	0.686232	+	0.903894i
$589$	−8.62463	+	7.47328i	−0.355372	+	0.307931i
$590$	−1.11645	+	6.31006i	−0.0459634	+	0.259781i
$591$	0.688914	−	2.34623i	0.0283381	−	0.0965108i
$592$	−6.16690	−	19.9981i	−0.253458	−	0.821916i
$593$	14.9123	−	23.2040i	0.612376	−	0.952876i	−0.387148	−	0.922018i	$-0.626540\pi$
$593$	14.9123	−	23.2040i	0.612376	−	0.952876i	0.999524	−	0.0308583i	$-0.00982405\pi$
$594$	1.14843	+	0.377927i	0.0471207	+	0.0155065i
$595$	−0.971261	−	3.30781i	−0.0398178	−	0.135607i
$596$	6.84569	−	32.5264i	0.280410	−	1.33233i
$597$	15.1128	−	2.17289i	0.618526	−	0.0889307i
$598$	−26.3592	−	0.852207i	−1.07791	−	0.0348493i
$599$	15.2329	+	17.5797i	0.622398	+	0.718286i	0.976161	−	0.217050i	$-0.0696433\pi$
$599$	15.2329	+	17.5797i	0.622398	+	0.718286i	−0.353762	+	0.935335i	$0.615098\pi$
$600$	−4.53520	−	3.57944i	−0.185149	−	0.146130i
$601$	6.99812	−	15.3237i	0.285459	−	0.625069i	−0.711526	−	0.702660i	$-0.751996\pi$
$601$	6.99812	−	15.3237i	0.285459	−	0.625069i	0.996985	+	0.0775912i	$0.0247229\pi$
$602$	2.29645	+	20.7014i	0.0935961	+	0.843724i
$603$	−1.10893	+	8.10989i	−0.0451590	+	0.330260i
$604$	−8.35456	−	37.1928i	−0.339942	−	1.51335i
$605$	−16.0638	−	7.33610i	−0.653087	−	0.298255i
$606$	−10.7061	+	8.68741i	−0.434907	+	0.352902i
$607$	−0.470732	+	0.407892i	−0.0191064	+	0.0165558i	−0.664362	−	0.747411i	$-0.731296\pi$
$607$	−0.470732	+	0.407892i	−0.0191064	+	0.0165558i	0.645255	+	0.763967i	$0.276751\pi$
$608$	5.65090	+	13.0157i	0.229174	+	0.527858i
$609$	−4.90198	−	34.0940i	−0.198638	−	1.38156i
$610$	−21.4515	−	7.05929i	−0.868547	−	0.285822i
$611$	−19.2947	+	5.66543i	−0.780579	+	0.229199i
$612$	−0.181234	+	0.861110i	−0.00732595	+	0.0348083i
$613$	26.4427	+	16.9937i	1.06801	+	0.686368i	0.951757	−	0.306852i	$-0.0992755\pi$
$613$	26.4427	+	16.9937i	1.06801	+	0.686368i	0.116252	+	0.993220i	$0.462912\pi$
$614$	−0.877109	+	27.1295i	−0.0353972	+	1.09486i
$615$	−12.0073	−	3.52565i	−0.484179	−	0.142168i
$616$	−0.504874	−	11.0057i	−0.0203420	−	0.443430i
$617$	−8.48392	−	9.79096i	−0.341550	−	0.394169i	0.558824	−	0.829286i	$-0.311253\pi$
$617$	−8.48392	−	9.79096i	−0.341550	−	0.394169i	−0.900374	+	0.435117i	$0.856707\pi$
$618$	9.45978	+	15.8215i	0.380528	+	0.636434i
$619$	35.9460	+	5.16826i	1.44479	+	0.207730i	0.819687	−	0.572811i	$-0.194147\pi$
$619$	35.9460	+	5.16826i	1.44479	+	0.207730i	0.625105	+	0.780541i	$0.285056\pi$
$620$	−13.7840	−	7.40609i	−0.553579	−	0.297436i
$621$	−5.02710	+	4.35600i	−0.201730	+	0.174800i
$622$	−20.7803	+	12.4247i	−0.833214	+	0.498185i
$623$	−26.7655	+	17.2011i	−1.07234	+	0.689149i
$624$	−9.35107	+	6.18982i	−0.374342	+	0.247791i
$625$	−8.92908	−	5.73837i	−0.357163	−	0.229535i
$626$	−16.5147	+	13.4008i	−0.660062	+	0.535602i
$627$	1.62064	+	1.40430i	0.0647223	+	0.0560822i
$628$	13.9364	+	0.902083i	0.556122	+	0.0359971i
$629$	1.50745	−	1.73969i	0.0601060	−	0.0693661i
$630$	−2.77665	−	10.7273i	−0.110624	−	0.427387i
$631$	32.4508	−	9.52840i	1.29184	−	0.379320i	0.437590	−	0.899175i	$-0.355832\pi$
$631$	32.4508	−	9.52840i	1.29184	−	0.379320i	0.854255	+	0.519855i	$0.174014\pi$
$632$	2.02753	+	5.89164i	0.0806507	+	0.234357i
$633$		−	19.5054i		−	0.775271i
$634$	−14.7680	−	35.3150i	−0.586513	−	1.40254i
$635$	−16.0930	−	10.3423i	−0.638631	−	0.410423i
$636$	−14.5863	+	11.0738i	−0.578384	+	0.439106i
$637$	−35.0895	+	16.0248i	−1.39030	+	0.634927i
$638$	−4.06355	+	8.18697i	−0.160878	+	0.324125i
$639$	−2.22052	−	7.56238i	−0.0878422	−	0.299163i
$640$	−13.9221	+	13.5909i	−0.550317	+	0.537228i
$641$			31.0876i			1.22789i	0.789351	+	0.613943i	$0.210417\pi$
$641$			31.0876i			1.22789i	−0.789351	+	0.613943i	$0.789583\pi$
$642$	−0.977088	+	0.408598i	−0.0385626	+	0.0161261i
$643$	28.9068	−	4.15617i	1.13997	−	0.163903i	0.453636	−	0.891187i	$-0.350126\pi$
$643$	28.9068	−	4.15617i	1.13997	−	0.163903i	0.686337	+	0.727283i	$0.259217\pi$
$644$	53.3956	+	28.6892i	2.10408	+	1.13051i
$645$	1.56609	−	5.33360i	0.0616646	−	0.210010i
$646$	−0.885821	+	1.28508i	−0.0348522	+	0.0505607i
$647$	19.8358	−	12.7477i	0.779827	−	0.501165i	−0.0891490	−	0.996018i	$-0.528415\pi$
$647$	19.8358	−	12.7477i	0.779827	−	0.501165i	0.868976	+	0.494854i	$0.164778\pi$
$648$	−0.671658	+	2.74752i	−0.0263852	+	0.107933i
$649$	−2.22965	+	0.320576i	−0.0875216	+	0.0125837i
$650$	6.28886	−	5.10304i	0.246669	−	0.200158i
$651$	8.61117	+	18.8558i	0.337498	+	0.739018i
$652$	3.69859	−	5.01101i	0.144848	−	0.196246i
$653$	22.4042	+	19.4134i	0.876745	+	0.759704i	0.971810	−	0.235767i	$-0.0757603\pi$
$653$	22.4042	+	19.4134i	0.876745	+	0.759704i	−0.0950647	+	0.995471i	$0.530306\pi$
$654$	−0.421786	+	13.0461i	−0.0164931	+	0.510141i
$655$	12.2547	+	26.8341i	0.478832	+	1.04850i
$656$	11.7328	−	26.6387i	0.458088	−	1.04007i
$657$	−5.12778	−	1.50565i	−0.200054	−	0.0587411i
$658$	45.5116	+	8.05242i	1.77423	+	0.313916i
$659$	−16.8831	−	2.42743i	−0.657673	−	0.0945591i	−0.194605	−	0.980882i	$-0.562342\pi$
$659$	−16.8831	−	2.42743i	−0.657673	−	0.0945591i	−0.463068	+	0.886323i	$0.653251\pi$
$660$	−1.00889	+	2.76183i	−0.0392710	+	0.107504i
$661$	−44.3240	−	20.2421i	−1.72400	−	0.787326i	−0.994663	−	0.103174i	$-0.967100\pi$
$661$	−44.3240	−	20.2421i	−1.72400	−	0.787326i	−0.729339	−	0.684152i	$-0.760172\pi$
$662$	−0.410826	−	0.982414i	−0.0159672	−	0.0381826i
$663$	−1.12205	−	0.512422i	−0.0435767	−	0.0199008i
$664$	10.6655	+	20.7777i	0.413900	+	0.806331i
$665$	2.79705	−	19.4539i	0.108465	−	0.754392i
$666$	5.02343	−	5.43225i	0.194654	−	0.210496i
$667$	−27.1869	−	42.3037i	−1.05268	−	1.63801i
$668$	20.0621	+	4.22238i	0.776226	+	0.163369i
$669$		−	16.6642i		−	0.644277i
$670$	−19.6258	−	3.33283i	−0.758211	−	0.128759i
$671$		−	7.93852i		−	0.306463i
$672$	25.5763	−	3.18789i	0.986626	−	0.122976i
$673$	−8.85947	−	13.7856i	−0.341507	−	0.531396i	0.627439	−	0.778666i	$-0.284103\pi$
$673$	−8.85947	−	13.7856i	−0.341507	−	0.531396i	−0.968947	+	0.247269i	$0.920467\pi$
$674$	28.3598	+	26.2255i	1.09238	+	1.01017i
$675$	0.290704	−	2.02189i	0.0111892	−	0.0778227i
$676$	3.65769	+	9.60775i	0.140680	+	0.369529i
$677$	4.78829	+	2.18674i	0.184029	+	0.0840433i	0.505299	−	0.862944i	$-0.331382\pi$
$677$	4.78829	+	2.18674i	0.184029	+	0.0840433i	−0.321270	+	0.946988i	$0.604110\pi$
$678$	−23.1489	+	9.68040i	−0.889028	+	0.371774i
$679$	9.44929	+	4.31534i	0.362630	+	0.165608i
$680$	−2.07888	−	0.508203i	−0.0797216	−	0.0194887i
$681$	−1.70270	−	0.244811i	−0.0652476	−	0.00938119i
$682$	0.958327	−	5.41638i	0.0366963	−	0.207404i
$683$	−23.8947	−	7.01611i	−0.914304	−	0.268464i	−0.209453	−	0.977819i	$-0.567168\pi$
$683$	−23.8947	−	7.01611i	−0.914304	−	0.268464i	−0.704851	+	0.709355i	$0.748986\pi$
$684$	−2.97920	+	4.03635i	−0.113913	+	0.154334i
$685$	9.36798	+	20.5130i	0.357932	+	0.783762i
$686$	43.5331	+	1.40745i	1.66210	+	0.0537366i
$687$	−16.0946	−	13.9461i	−0.614049	−	0.532077i
$688$	11.8329	+	5.21168i	0.451124	+	0.198693i
$689$	−10.6643	−	23.3516i	−0.406277	−	0.889624i
$690$	−10.1932	−	12.5618i	−0.388049	−	0.478221i
$691$	7.18433	−	1.03295i	0.273305	−	0.0392953i	−0.00429975	−	0.999991i	$-0.501369\pi$
$691$	7.18433	−	1.03295i	0.273305	−	0.0392953i	0.277604	+	0.960695i	$0.410460\pi$
$692$	32.3559	+	11.8196i	1.22999	+	0.449312i
$693$	3.27683	−	2.10589i	0.124477	−	0.0799962i
$694$	−17.1695	−	11.8352i	−0.651745	−	0.449257i
$695$	−0.480185	+	1.63536i	−0.0182144	+	0.0620327i
$696$	−19.8368	−	7.98193i	−0.751910	−	0.302554i
$697$	3.16921	−	0.455663i	0.120042	−	0.0172595i
$698$	6.92090	+	16.5501i	0.261960	+	0.626429i
$699$		−	10.0845i		−	0.381429i
$700$	−18.1615	+	4.07959i	−0.686440	+	0.154194i
$701$	−9.35596	−	31.8635i	−0.353370	−	1.20347i	−0.924043	−	0.382289i	$-0.875136\pi$
$701$	−9.35596	−	31.8635i	−0.353370	−	1.20347i	0.570673	−	0.821177i	$-0.306682\pi$
$702$	−3.55139	−	1.76271i	−0.134039	−	0.0665293i
$703$	11.9375	−	5.45166i	0.450230	−	0.205613i
$704$	−6.06790	−	3.15527i	−0.228693	−	0.118919i
$705$	−10.3769	−	6.66881i	−0.390816	−	0.251162i
$706$	−15.6217	+	6.53267i	−0.587930	+	0.245860i
$707$			44.4199i			1.67058i
$708$	−1.15496	−	5.14166i	−0.0434062	−	0.193236i
$709$	−6.25495	+	1.83662i	−0.234909	+	0.0689756i	−0.397068	−	0.917789i	$-0.629972\pi$
$709$	−6.25495	+	1.83662i	−0.234909	+	0.0689756i	0.162159	+	0.986765i	$0.448154\pi$
$710$	18.5566	−	4.80317i	0.696418	−	0.180260i
$711$	−1.44260	+	1.66484i	−0.0541016	+	0.0624366i
$712$	0.905096	+	19.7300i	0.0339199	+	0.739413i
$713$	22.8711	+	19.8179i	0.856531	+	0.742188i
$714$	1.78638	+	2.20148i	0.0668535	+	0.0823884i
$715$	−3.46736	−	2.22833i	−0.129672	−	0.0833350i
$716$	8.37243	+	21.9921i	0.312892	+	0.821882i
$717$	0.349237	−	0.224441i	0.0130425	−	0.00838190i
$718$	20.3624	+	34.0561i	0.759918	+	1.27096i
$719$	9.13367	−	7.91437i	0.340628	−	0.295156i	−0.467701	−	0.883887i	$-0.654918\pi$
$719$	9.13367	−	7.91437i	0.340628	−	0.295156i	0.808329	+	0.588731i	$0.200372\pi$
$720$	−6.62570	−	1.84854i	−0.246925	−	0.0688910i
$721$	58.7852	+	8.45203i	2.18927	+	0.314770i
$722$	15.4250	−	9.22273i	0.574059	−	0.343234i
$723$	13.8919	+	16.0321i	0.516645	+	0.596240i
$724$	−23.6805	−	1.53281i	−0.880079	−	0.0569663i
$725$	14.8168	+	4.35061i	0.550283	+	0.161578i
$726$	14.5152	+	0.469283i	0.538709	+	0.0174167i
$727$	20.7140	+	13.3121i	0.768238	+	0.493717i	0.865111	−	0.501580i	$-0.167248\pi$
$727$	20.7140	+	13.3121i	0.768238	+	0.493717i	−0.0968731	+	0.995297i	$0.530884\pi$
$728$	−3.49753	+	35.9596i	−0.129627	+	1.33275i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	4.06281	−	12.3459i	0.150371	−	0.456944i
$731$	0.202405	+	1.40776i	0.00748621	+	0.0520677i
$732$	18.5150	−	1.45011i	0.684334	−	0.0535976i
$733$	20.0286	−	17.3548i	0.739772	−	0.641016i	−0.201181	−	0.979554i	$-0.564478\pi$
$733$	20.0286	−	17.3548i	0.739772	−	0.641016i	0.940953	+	0.338538i	$0.109932\pi$
$734$	24.0509	+	29.6397i	0.887735	+	1.09402i
$735$	−21.5239	−	9.82963i	−0.793921	−	0.362572i
$736$	32.0317	−	19.7448i	1.18070	−	0.727804i
$737$	−1.04368	−	6.91943i	−0.0384444	−	0.254880i
$738$	10.2285	−	1.13467i	0.376517	−	0.0417678i
$739$	8.81245	−	19.2966i	0.324171	−	0.709836i	−0.675449	−	0.737407i	$-0.736050\pi$
$739$	8.81245	−	19.2966i	0.324171	−	0.709836i	0.999620	+	0.0275710i	$0.00877725\pi$
$740$	12.8096	+	12.6375i	0.470889	+	0.464564i
$741$	−4.60518	−	5.31466i	−0.169175	−	0.195239i
$742$	−1.90658	+	58.9716i	−0.0699928	+	2.16492i
$743$	−16.6753	+	2.39754i	−0.611756	+	0.0879573i	−0.441227	−	0.897395i	$-0.645457\pi$
$743$	−16.6753	+	2.39754i	−0.611756	+	0.0879573i	−0.170529	+	0.985353i	$0.554548\pi$
$744$	12.8077	+	1.24571i	0.469553	+	0.0456699i
$745$	8.05200	+	27.4226i	0.295002	+	1.00469i
$746$	10.5188	−	31.9643i	0.385122	−	1.17030i
$747$	−4.46423	+	6.94648i	−0.163338	+	0.254159i
$748$	−0.0587404	−	0.749998i	−0.00214776	−	0.0274226i
$749$	−0.961304	+	3.27390i	−0.0351253	+	0.119626i
$750$	16.8659	+	2.98410i	0.615854	+	0.108964i
$751$	−28.7525	+	24.9142i	−1.04919	+	0.909132i	−0.995991	−	0.0894520i	$-0.971488\pi$
$751$	−28.7525	+	24.9142i	−1.04919	+	0.909132i	−0.0532028	+	0.998584i	$0.516943\pi$
$752$	18.4939	−	21.9355i	0.674403	−	0.799907i
$753$	−2.99415	+	20.8247i	−0.109113	+	0.758896i
$754$	17.0110	−	24.6782i	0.619505	−	0.898727i
$755$	21.4643	+	24.7711i	0.781164	+	0.901512i
$756$	5.51014	+	7.25788i	0.200402	+	0.263966i
$757$	−15.4045	−	23.9699i	−0.559886	−	0.871200i	0.439752	−	0.898119i	$-0.355066\pi$
$757$	−15.4045	−	23.9699i	−0.559886	−	0.871200i	−0.999638	+	0.0269199i	$0.991430\pi$
$758$	−37.3875	+	9.67734i	−1.35798	+	0.351497i
$759$	3.07444	−	4.78392i	0.111595	−	0.173645i
$760$	−9.57716	−	7.55884i	−0.347400	−	0.274188i
$761$	−3.64071	+	4.20161i	−0.131976	+	0.152308i	−0.817891	−	0.575373i	$-0.804857\pi$
$761$	−3.64071	+	4.20161i	−0.131976	+	0.152308i	0.685915	+	0.727682i	$0.259402\pi$
$762$	15.4911	+	2.74086i	0.561184	+	0.0992910i
$763$	31.7818	+	27.5391i	1.15058	+	0.996983i
$764$	6.57798	+	17.2785i	0.237983	+	0.625116i
$765$	−0.213170	−	0.725991i	−0.00770718	−	0.0262482i
$766$	−4.08537	−	36.8277i	−0.147610	−	1.33064i
$767$	7.38700			0.266729
$768$	6.25064	−	14.7285i	0.225550	−	0.531470i
$769$	1.80686	−	2.81153i	0.0651571	−	0.101386i	−0.807146	−	0.590352i	$-0.798989\pi$
$769$	1.80686	−	2.81153i	0.0651571	−	0.101386i	0.872303	+	0.488965i	$0.162625\pi$
$770$	4.86134	+	8.13059i	0.175191	+	0.293006i
$771$	−5.11908	−	11.2092i	−0.184359	−	0.403691i
$772$	48.9688	+	17.8882i	1.76242	+	0.643810i
$773$	−8.71766	+	2.55973i	−0.313552	+	0.0920673i	−0.434722	−	0.900564i	$-0.643154\pi$
$773$	−8.71766	+	2.55973i	−0.313552	+	0.0920673i	0.121170	+	0.992632i	$0.461335\pi$
$774$	0.504018	+	4.54348i	0.0181166	+	0.163312i
$775$	−9.29333			−0.333826
$776$	5.25948	−	3.73134i	0.188804	−	0.133947i
$777$	−3.39245	−	23.5950i	−0.121704	−	0.846467i
$778$	20.3519	+	14.0289i	0.729652	+	0.502959i
$779$	17.5141	+	5.14260i	0.627507	+	0.184253i
$780$	4.56377	−	8.49396i	0.163409	−	0.304133i
$781$	3.64287	+	5.66841i	0.130352	+	0.202832i
$782$	3.70744	+	1.84016i	0.132578	+	0.0658041i
$783$	−1.07588	−	7.48288i	−0.0384487	−	0.267416i
$784$	29.1272	−	46.6994i	1.04026	−	1.66784i
$785$	−10.9230	+	4.98838i	−0.389859	+	0.178043i
$786$	−17.8114	−	16.4710i	−0.635312	−	0.587500i
$787$	31.7329	−	36.6217i	1.13116	−	1.30542i	0.184624	−	0.982809i	$-0.440893\pi$
$787$	31.7329	−	36.6217i	1.13116	−	1.30542i	0.946531	−	0.322613i	$-0.104561\pi$
$788$	−4.87562	+	0.381862i	−0.173687	+	0.0136033i
$789$	−0.775692	+	0.354247i	−0.0276154	+	0.0126115i
$790$	−3.93342	−	3.63740i	−0.139945	−	0.129413i
$791$	−22.7750	+	77.5644i	−0.809785	+	2.75787i
$792$	−0.110809	−	2.41549i	−0.00393741	−	0.0858309i
$793$	−3.70490	+	25.7682i	−0.131565	+	0.915055i
$794$	−15.7151	+	31.6616i	−0.557706	+	1.12363i
$795$	6.54148	−	14.3238i	0.232002	−	0.508014i
$796$	−14.8154	−	26.7016i	−0.525119	−	0.946414i
$797$	22.8594	−	50.0550i	0.809720	−	1.77304i	0.201113	−	0.979568i	$-0.435544\pi$
$797$	22.8594	−	50.0550i	0.809720	−	1.77304i	0.608607	−	0.793471i	$-0.291728\pi$
$798$	4.05009	+	15.6471i	0.143372	+	0.553903i
$799$	3.12383	+	0.449140i	0.110513	+	0.0158894i
$800$	−3.46328	+	11.0240i	−0.122445	+	0.389756i
$801$	−5.87443	+	3.77526i	−0.207563	+	0.133392i
$802$	16.5811	−	50.3862i	0.585500	−	1.77920i
$803$	4.56883			0.161231
$804$	15.9475	−	3.69813i	0.562426	−	0.130423i
$805$	−52.1192			−1.83696
$806$	−5.63853	+	17.1342i	−0.198609	+	0.603525i
$807$	6.78373	−	4.35964i	0.238799	−	0.153467i
$808$	23.8562	+	13.8294i	0.839259	+	0.486515i
$809$	−28.2606	−	4.06326i	−0.993589	−	0.142856i	−0.373703	−	0.927549i	$-0.621912\pi$
$809$	−28.2606	−	4.06326i	−0.993589	−	0.142856i	−0.619886	+	0.784692i	$0.712821\pi$
$810$	−0.609413	−	2.35441i	−0.0214126	−	0.0827255i
$811$	−17.3838	+	38.0653i	−0.610429	+	1.33665i	0.311851	+	0.950131i	$0.399051\pi$
$811$	−17.3838	+	38.0653i	−0.610429	+	1.33665i	−0.922280	+	0.386522i	$0.873676\pi$
$812$	−60.2381	+	33.4232i	−2.11394	+	1.17292i
$813$	−9.61691	+	21.0581i	−0.337280	+	0.738539i
$814$	−2.81221	+	5.66586i	−0.0985679	+	0.198588i
$815$	−0.762128	+	5.30071i	−0.0266962	+	0.185676i
$816$	1.73849	−	0.274001i	0.0608593	−	0.00959194i
$817$	−2.28433	+	7.77972i	−0.0799187	+	0.272178i
$818$	−4.29218	−	3.96916i	−0.150073	−	0.138778i
$819$	−11.6193	+	5.30636i	−0.406012	+	0.185419i
$820$	1.95425	+	24.9519i	0.0682455	+	0.871359i
$821$	−21.4604	+	24.7666i	−0.748974	+	0.864362i	−0.994468	−	0.105036i	$-0.966504\pi$
$821$	−21.4604	+	24.7666i	−0.748974	+	0.864362i	0.245495	+	0.969398i	$0.421050\pi$
$822$	−13.6157	−	12.5910i	−0.474903	−	0.439163i
$823$	46.2783	−	21.1346i	1.61316	−	0.736705i	0.614523	−	0.788899i	$-0.289349\pi$
$823$	46.2783	−	21.1346i	1.61316	−	0.736705i	0.998637	+	0.0521936i	$0.0166213\pi$
$824$	22.8410	−	28.9399i	0.795704	−	1.00817i
$825$	0.248524	+	1.72852i	0.00865251	+	0.0601795i
$826$	−15.2078	−	7.54830i	−0.529147	−	0.262639i
$827$	−8.23058	−	12.8070i	−0.286205	−	0.445344i	0.668146	−	0.744030i	$-0.267088\pi$
$827$	−8.23058	−	12.8070i	−0.286205	−	0.445344i	−0.954351	+	0.298686i	$0.903452\pi$
$828$	11.7191	+	6.29665i	0.407268	+	0.218824i
$829$	−32.1780	−	9.44832i	−1.11759	−	0.328154i	−0.329770	−	0.944061i	$-0.606971\pi$
$829$	−32.1780	−	9.44832i	−1.11759	−	0.328154i	−0.787818	+	0.615908i	$0.788789\pi$
$830$	−16.5342	−	11.3973i	−0.573911	−	0.395605i
$831$	1.18958	+	8.27370i	0.0412660	+	0.287012i
$832$	18.2236	+	13.0738i	0.631791	+	0.453253i
$833$	6.05406			0.209761
$834$	−0.154539	−	1.39310i	−0.00535126	−	0.0482390i
$835$	−16.9141	+	4.96643i	−0.585336	+	0.171870i
$836$	1.47159	−	4.02847i	0.0508961	−	0.139328i
$837$	1.88996	+	4.13843i	0.0653266	+	0.143045i
$838$	−19.4733	−	32.5692i	−0.672695	−	1.12508i
$839$	0.138744	−	0.215890i	0.00478998	−	0.00745335i	−0.838850	−	0.544362i	$-0.816772\pi$
$839$	0.138744	−	0.215890i	0.00478998	−	0.00745335i	0.843640	+	0.536909i	$0.180408\pi$
$840$	−18.0750	+	12.8233i	−0.623646	+	0.442446i
$841$	28.1510			0.970724
$842$	2.06077	+	18.5769i	0.0710188	+	0.640201i
$843$	4.93656	+	16.8124i	0.170024	+	0.579049i
$844$	−36.4582	+	13.8797i	−1.25494	+	0.477760i
$845$	−6.68050	−	5.78868i	−0.229816	−	0.199137i
$846$	9.98877	+	1.76733i	0.343421	+	0.0607619i
$847$	30.6403	−	35.3608i	1.05281	−	1.21501i
$848$	31.0778	+	19.3837i	1.06722	+	0.665641i
$849$	−0.800706	+	1.24592i	−0.0274802	+	0.0427600i
$850$	−1.23048	+	0.318496i	−0.0422052	+	0.0109243i
$851$	−18.8149	−	29.2766i	−0.644967	−	1.00359i
$852$	−12.5550	+	9.53169i	−0.430127	+	0.326550i
$853$	9.51323	+	10.9788i	0.325727	+	0.375909i	0.894868	−	0.446331i	$-0.147270\pi$
$853$	9.51323	+	10.9788i	0.325727	+	0.375909i	−0.569141	+	0.822240i	$0.692724\pi$
$854$	33.9582	−	49.2638i	1.16203	−	1.68577i
$855$	0.613891	−	4.26971i	0.0209946	−	0.146021i
$856$	1.45900	+	1.53555i	0.0498677	+	0.0524841i
$857$	16.8604	−	14.6097i	0.575942	−	0.499057i	−0.317486	−	0.948263i	$-0.602839\pi$
$857$	16.8604	−	14.6097i	0.575942	−	0.499057i	0.893428	+	0.449206i	$0.148293\pi$
$858$	3.33768	+	0.590539i	0.113946	+	0.0201607i
$859$	−2.33008	+	7.93551i	−0.0795012	+	0.270756i	−0.989645	−	0.143536i	$-0.954153\pi$
$859$	−2.33008	+	7.93551i	−0.0795012	+	0.270756i	0.910144	+	0.414292i	$0.135971\pi$
$860$	−11.0836	+	0.868076i	−0.377948	+	0.0296011i
$861$	17.9255	−	27.8927i	0.610900	−	0.950579i
$862$	15.1332	−	45.9864i	0.515440	−	1.56630i
$863$	9.18470	+	31.2802i	0.312651	+	1.06479i	0.954562	+	0.298012i	$0.0963235\pi$
$863$	9.18470	+	31.2802i	0.312651	+	1.06479i	−0.641911	+	0.766779i	$0.721858\pi$
$864$	5.61342	−	0.699671i	0.190972	−	0.0238033i
$865$	−29.3177	+	4.21525i	−0.996831	+	0.143323i
$866$	−1.52993	+	47.3215i	−0.0519890	+	1.60805i
$867$	−11.0059	−	12.7014i	−0.373779	−	0.431363i
$868$	29.1165	−	29.5129i	0.988277	−	1.00173i
$869$	0.782340	−	1.71309i	0.0265391	−	0.0581125i
$870$	18.2734	−	2.02711i	0.619527	−	0.0687255i
$871$	0.158451	+	22.9473i	0.00536891	+	0.777541i
$872$	24.6849	−	8.49498i	0.835937	−	0.287676i
$873$	2.07391	+	0.947122i	0.0701911	+	0.0320552i
$874$	14.8681	+	18.3230i	0.502920	+	0.619785i
$875$	41.7037	−	36.1365i	1.40984	−	1.22164i
$876$	0.834578	+	10.6559i	0.0281978	+	0.360029i
$877$	−3.39517	−	23.6139i	−0.114647	−	0.797385i	−0.963298	−	0.268433i	$-0.913494\pi$
$877$	−3.39517	−	23.6139i	−0.114647	−	0.797385i	0.848652	−	0.528952i	$-0.177415\pi$
$878$	−3.79067	+	11.5190i	−0.127929	+	0.388746i
$879$	1.86861	−	0.548675i	0.0630268	−	0.0185063i
$880$	5.88013	−	0.0795202i	0.198219	−	0.00268062i
$881$	−14.9984	−	9.63891i	−0.505310	−	0.324743i	0.263027	−	0.964788i	$-0.415279\pi$
$881$	−14.9984	−	9.63891i	−0.505310	−	0.324743i	−0.768337	+	0.640045i	$0.778916\pi$
$882$	19.4489	+	0.628792i	0.654878	+	0.0211725i
$883$	5.55269	+	1.63042i	0.186863	+	0.0548679i	0.373825	−	0.927499i	$-0.378046\pi$
$883$	5.55269	+	1.63042i	0.186863	+	0.0548679i	−0.186962	+	0.982367i	$0.559864\pi$
$884$	−0.159354	+	2.46188i	−0.00535967	+	0.0828021i
$885$	2.96730	+	3.42444i	0.0997445	+	0.115111i
$886$	−32.5304	+	19.4502i	−1.09288	+	0.653442i
$887$	−43.3533	−	6.23326i	−1.45566	−	0.209292i	−0.631380	−	0.775474i	$-0.717511\pi$
$887$	−43.3533	−	6.23326i	−1.45566	−	0.209292i	−0.824281	+	0.566181i	$0.808420\pi$
$888$	−13.7282	−	5.52395i	−0.460687	−	0.185372i
$889$	38.3044	−	33.1910i	1.28469	−	1.11319i
$890$	−8.71500	−	14.5758i	−0.292128	−	0.488583i
$891$	0.719191	−	0.462196i	0.0240938	−	0.0154842i
$892$	−31.1476	+	11.8580i	−1.04290	+	0.397034i
$893$	15.1360	+	9.72729i	0.506506	+	0.325511i
$894$	−14.8095	−	18.2509i	−0.495304	−	0.610400i
$895$	−15.2916	−	13.2502i	−0.511142	−	0.442907i
$896$	−24.1582	−	45.5369i	−0.807069	−	1.52128i
$897$	−12.2122	+	14.0936i	−0.407753	+	0.470572i
$898$	−15.3965	+	3.98521i	−0.513787	+	0.132988i
$899$	−33.0008	+	9.68990i	−1.10064	+	0.323176i
$900$	−3.98604	+	0.895379i	−0.132868	+	0.0298460i
$901$			4.02889i			0.134222i
$902$	−8.11690	+	3.39432i	−0.270263	+	0.113019i
$903$	12.3899	+	7.96248i	0.412309	+	0.264975i
$904$	34.5663	+	36.3799i	1.14966	+	1.20998i
$905$	18.5602	−	8.47617i	0.616963	−	0.281757i
$906$	−24.1442	−	11.9838i	−0.802136	−	0.398135i
$907$	11.4625	+	39.0376i	0.380605	+	1.29622i	0.897819	+	0.440366i	$0.145151\pi$
$907$	11.4625	+	39.0376i	0.380605	+	1.29622i	−0.517213	+	0.855856i	$0.673031\pi$
$908$	0.754027	+	3.35677i	0.0250233	+	0.111398i
$909$			9.74917i			0.323359i
$910$	−11.9852	−	28.6604i	−0.397306	−	0.950084i
$911$	11.6841	−	1.67992i	0.387112	−	0.0556584i	0.0539888	−	0.998542i	$-0.482806\pi$
$911$	11.6841	−	1.67992i	0.387112	−	0.0556584i	0.333124	+	0.942883i	$0.391897\pi$
$912$	9.66441	+	2.69632i	0.320021	+	0.0892842i
$913$	1.98881	−	6.77326i	0.0658199	−	0.224162i
$914$	−28.1876	−	19.4301i	−0.932364	−	0.642691i
$915$	−13.4338	+	8.63335i	−0.444106	+	0.285410i
$916$	−14.6144	+	40.0068i	−0.482873	+	1.32186i
$917$	−77.3640	+	11.1233i	−2.55479	+	0.367323i
$918$	0.392070	+	0.483176i	0.0129402	+	0.0159472i
$919$	5.80791	+	12.7175i	0.191585	+	0.419513i	0.980910	−	0.194463i	$-0.0622964\pi$
$919$	5.80791	+	12.7175i	0.191585	+	0.419513i	−0.789325	+	0.613976i	$0.789569\pi$
$920$	−16.2264	+	27.9912i	−0.534969	+	0.922844i
$921$	14.5054	+	12.5690i	0.477970	+	0.414164i
$922$	−37.9625	−	1.22735i	−1.25023	−	0.0404205i
$923$	−9.17918	−	20.0996i	−0.302137	−	0.661587i
$924$	−6.26792	−	4.62631i	−0.206200	−	0.152194i
$925$	10.2541	+	3.01087i	0.337152	+	0.0989969i
$926$	8.44104	−	47.7080i	0.277390	−	1.56778i
$927$	12.9020	+	1.85503i	0.423758	+	0.0609272i
$928$	−0.803783	+	42.7573i	−0.0263855	+	1.40358i
$929$	−0.963878	−	0.440188i	−0.0316238	−	0.0144421i	0.399540	−	0.916716i	$-0.369170\pi$
$929$	−0.963878	−	0.440188i	−0.0316238	−	0.0144421i	−0.431164	+	0.902274i	$0.641897\pi$
$930$	−10.2079	+	4.26876i	−0.334732	+	0.139978i
$931$	31.3953	+	14.3377i	1.02894	+	0.469901i
$932$	−18.8492	+	7.17592i	−0.617425	+	0.235055i
$933$	−2.43644	+	16.9458i	−0.0797655	+	0.554781i
$934$	−28.6550	−	26.4984i	−0.937619	−	0.867055i
$935$	0.349716	+	0.544169i	0.0114369	+	0.0177962i
$936$	−0.767630	+	7.89234i	−0.0250908	+	0.257969i
$937$		−	48.3071i		−	1.57812i	−0.614313	−	0.789062i	$-0.710567\pi$
$937$		−	48.3071i		−	1.57812i	0.614313	−	0.789062i	$-0.289433\pi$
$938$	23.1222	−	47.4042i	0.754966	−	1.54780i
$939$			15.0386i			0.490765i
$940$	−5.08088	+	24.1411i	−0.165720	+	0.787397i
$941$	−8.10791	−	12.6162i	−0.264310	−	0.411275i	0.683578	−	0.729877i	$-0.260423\pi$
$941$	−8.10791	−	12.6162i	−0.264310	−	0.411275i	−0.947888	+	0.318602i	$0.896787\pi$
$942$	6.70462	−	7.25027i	0.218448	−	0.236226i
$943$	6.88879	−	47.9126i	0.224330	−	1.56025i
$944$	−8.78859	+	5.81750i	−0.286044	+	0.189343i
$945$	−7.12729	−	3.25492i	−0.231851	−	0.105883i
$946$	−1.50775	−	3.60551i	−0.0490212	−	0.117225i
$947$	−38.2637	−	17.4745i	−1.24340	−	0.567844i	−0.318456	−	0.947938i	$-0.603164\pi$
$947$	−38.2637	−	17.4745i	−1.24340	−	0.567844i	−0.924948	+	0.380094i	$0.875892\pi$
$948$	4.13834	+	1.51173i	0.134407	+	0.0490986i
$949$	−14.8303	−	2.13227i	−0.481412	−	0.0692166i
$950$	−7.13535	−	1.26247i	−0.231501	−	0.0409598i
$951$	−25.9706	−	7.62566i	−0.842154	−	0.247279i
$952$	2.84371	−	4.90551i	0.0921651	−	0.158988i
$953$	−0.811222	−	1.77633i	−0.0262781	−	0.0575409i	0.896038	−	0.443978i	$-0.146433\pi$
$953$	−0.811222	−	1.77633i	−0.0262781	−	0.0575409i	−0.922316	+	0.386437i	$0.873706\pi$
$954$	−0.418452	+	12.9429i	−0.0135479	+	0.419043i
$955$	−12.0142	−	10.4103i	−0.388770	−	0.336871i
$956$	−0.668020	−	0.493061i	−0.0216053	−	0.0159467i
$957$	2.68480	+	5.87889i	0.0867872	+	0.190037i
$958$	−22.3585	+	18.1427i	−0.722371	+	0.586162i
$959$	−59.1400	+	8.50305i	−1.90973	+	0.274578i
$960$	1.25957	+	13.6997i	0.0406525	+	0.442156i
$961$	−8.66610	+	5.56937i	−0.279552	+	0.179657i
$962$	11.7726	−	17.0787i	0.379564	−	0.550640i
$963$	−0.210985	+	0.718548i	−0.00679889	+	0.0231549i
$964$	20.0809	−	37.3739i	0.646761	−	1.20373i
$965$	−44.3705	+	6.37952i	−1.42834	+	0.205364i
$966$	39.5429	−	16.5360i	1.27227	−	0.532038i
$967$			54.4401i			1.75068i	0.483512	+	0.875338i	$0.339361\pi$
$967$			54.4401i			1.75068i	−0.483512	+	0.875338i	$0.660639\pi$
$968$	−9.45159	−	27.4647i	−0.303786	−	0.882749i
$969$	0.310935	+	1.05895i	0.00998867	+	0.0340183i
$970$	−2.46518	+	4.96668i	−0.0791522	+	0.159471i
$971$	−28.7436	+	13.1267i	−0.922424	+	0.421257i	−0.819270	−	0.573408i	$-0.805621\pi$
$971$	−28.7436	+	13.1267i	−0.922424	+	0.421257i	−0.103155	+	0.994665i	$0.532894\pi$
$972$	1.20935	+	1.59294i	0.0387900	+	0.0510936i
$973$	−3.79891	−	2.44141i	−0.121787	−	0.0782680i
$974$	14.9681	+	35.7935i	0.479609	+	1.14690i
$975$		−	5.72673i		−	0.183402i
$976$	−15.8854	−	33.5751i	−0.508479	−	1.07471i
$977$	−4.65728	+	1.36750i	−0.149000	+	0.0437502i	−0.355382	−	0.934721i	$-0.615649\pi$
$977$	−4.65728	+	1.36750i	−0.149000	+	0.0437502i	0.206382	+	0.978471i	$0.433831\pi$
$978$	−1.10355	−	4.26346i	−0.0352876	−	0.136330i
$979$	3.90935	−	4.51164i	0.124943	−	0.144192i
$980$	−3.05685	+	47.2256i	−0.0976474	+	1.50857i
$981$	6.97540	+	6.04422i	0.222707	+	0.192977i
$982$	−2.54058	+	2.06153i	−0.0810731	+	0.0657862i
$983$	0.858959	+	0.552020i	0.0273965	+	0.0176067i	0.554267	−	0.832339i	$-0.312998\pi$
$983$	0.858959	+	0.552020i	0.0273965	+	0.0176067i	−0.526871	+	0.849945i	$0.676635\pi$
$984$	−9.39927	−	18.3110i	−0.299638	−	0.583734i
$985$	3.53756	−	2.27345i	0.112716	−	0.0724382i
$986$	−4.03737	+	2.41397i	−0.128576	+	0.0768766i
$987$	24.6989	−	21.4018i	0.786176	−	0.681225i
$988$	−6.65683	+	12.3895i	−0.211782	+	0.394162i
$989$	21.2827	+	3.05999i	0.676750	+	0.0973019i
$990$	1.06696	+	1.78448i	0.0339101	+	0.0567146i
$991$	7.40177	+	8.54210i	0.235125	+	0.271349i	0.861034	−	0.508547i	$-0.169817\pi$
$991$	7.40177	+	8.54210i	0.235125	+	0.271349i	−0.625909	+	0.779896i	$0.715272\pi$
$992$	−6.78533	−	24.8257i	−0.215434	−	0.788216i
$993$	−0.722466	−	0.212135i	−0.0229268	−	0.00673190i
$994$	−1.64107	+	50.7592i	−0.0520516	+	1.60998i
$995$	22.0884	+	14.1954i	0.700249	+	0.450023i
$996$	16.1606	+	3.40124i	0.512067	+	0.107772i
$997$	−31.1416	+	9.14399i	−0.986263	+	0.289593i	−0.734807	−	0.678276i	$-0.762727\pi$
$997$	−31.1416	+	9.14399i	−0.986263	+	0.289593i	−0.251456	+	0.967869i	$0.580909\pi$
$998$	45.7511	+	15.0558i	1.44823	+	0.476584i
$999$	−0.744568	−	5.17858i	−0.0235571	−	0.163843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.u.b.43.5	yes	340
4.3	odd	2		804.2.u.a.43.6	✓	340
67.53	odd	22		804.2.u.a.187.6	yes	340
268.187	even	22	inner	804.2.u.b.187.5	yes	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.u.a.43.6	✓	340	4.3	odd	2
804.2.u.a.187.6	yes	340	67.53	odd	22
804.2.u.b.43.5	yes	340	1.1	even	1	trivial
804.2.u.b.187.5	yes	340	268.187	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34334 - 0.442069i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(1.60915 + 1.18770i) q^{4} +(-1.70218 - 0.244737i) q^{5} +(1.36909 - 0.354375i) q^{6} +(1.89274 - 4.14453i) q^{7} +(-1.63660 - 2.30685i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.34334 - 0.442069i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(1.60915 + 1.18770i) q^{4} +(-1.70218 - 0.244737i) q^{5} +(1.36909 - 0.354375i) q^{6} +(1.89274 - 4.14453i) q^{7} +(-1.63660 - 2.30685i) q^{8} +(0.415415 - 0.909632i) q^{9} +(2.17843 + 1.08125i) q^{10} +(-0.121666 + 0.846203i) q^{11} +(-1.99582 - 0.129187i) q^{12} +(0.789845 - 2.68997i) q^{13} +(-4.37478 + 4.73081i) q^{14} +(1.56428 - 0.714383i) q^{15} +(1.17873 + 3.82238i) q^{16} +(-0.288131 + 0.332520i) q^{17} +(-0.960166 + 1.03831i) q^{18} +(-2.28170 + 1.04202i) q^{19} +(-2.44839 - 2.41550i) q^{20} +(0.648425 + 4.50990i) q^{21} +(0.537519 - 1.08296i) q^{22} +(3.59624 + 5.59585i) q^{23} +(2.62397 + 1.05583i) q^{24} +(-1.95994 - 0.575491i) q^{25} +(-2.25019 + 3.26439i) q^{26} +(0.142315 + 0.989821i) q^{27} +(7.96818 - 4.42115i) q^{28} -7.55983 q^{29} +(-2.41717 + 0.268142i) q^{30} +(4.36528 - 1.28176i) q^{31} +(0.106323 - 5.65585i) q^{32} +(-0.355140 - 0.777648i) q^{33} +(0.534056 - 0.319316i) q^{34} +(-4.23611 + 6.59152i) q^{35} +(1.74884 - 0.970345i) q^{36} -5.23184 q^{37} +(3.52575 - 0.391119i) q^{38} +(0.789845 + 2.68997i) q^{39} +(2.22121 + 4.32721i) q^{40} +(-5.49960 - 4.76543i) q^{41} +(1.12263 - 6.34499i) q^{42} +(2.11680 - 2.44291i) q^{43} +(-1.20082 + 1.21716i) q^{44} +(-0.929732 + 1.44669i) q^{45} +(-2.35723 - 9.10694i) q^{46} +(-3.87793 - 6.03417i) q^{47} +(-3.05814 - 2.57833i) q^{48} +(-9.01063 - 10.3988i) q^{49} +(2.37847 + 1.63951i) q^{50} +(0.0626168 - 0.435509i) q^{51} +(4.46586 - 3.39046i) q^{52} +(6.92027 - 5.99645i) q^{53} +(0.246392 - 1.39258i) q^{54} +(0.414194 - 1.41061i) q^{55} +(-12.6585 + 2.41665i) q^{56} +(1.35613 - 2.11018i) q^{57} +(10.1555 + 3.34197i) q^{58} +(0.742335 + 2.52816i) q^{59} +(3.36564 + 0.708351i) q^{60} +(-9.19134 + 1.32151i) q^{61} +(-6.43070 - 0.207908i) q^{62} +(-2.98372 - 3.44340i) q^{63} +(-2.64311 + 7.55076i) q^{64} +(-2.00279 + 4.38551i) q^{65} +(0.133301 + 1.20165i) q^{66} +(-7.83768 + 2.36025i) q^{67} +(-0.858581 + 0.192862i) q^{68} +(-6.05069 - 2.76326i) q^{69} +(8.60446 - 6.98203i) q^{70} +(5.95655 - 5.16138i) q^{71} +(-2.77825 + 0.530400i) q^{72} +(-0.760568 - 5.28987i) q^{73} +(7.02816 + 2.31283i) q^{74} +(1.95994 - 0.575491i) q^{75} +(-4.90920 - 1.03322i) q^{76} +(3.27683 + 2.10589i) q^{77} +(0.128117 - 3.96272i) q^{78} +(-2.11367 - 0.620630i) q^{79} +(-1.07093 - 6.79486i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(5.28121 + 8.83282i) q^{82} +(-8.17325 - 1.17514i) q^{83} +(-4.31300 + 8.02723i) q^{84} +(0.571830 - 0.495494i) q^{85} +(-3.92352 + 2.34590i) q^{86} +(6.35973 - 4.08715i) q^{87} +(2.15118 - 1.10423i) q^{88} +(-5.87443 - 3.77526i) q^{89} +(1.88849 - 1.53240i) q^{90} +(-9.65367 - 8.36496i) q^{91} +(-0.859326 + 13.2758i) q^{92} +(-2.97933 + 3.43834i) q^{93} +(2.54187 + 9.82028i) q^{94} +(4.13888 - 1.21529i) q^{95} +(2.96834 + 4.81549i) q^{96} +2.27994i q^{97} +(7.50738 + 17.9525i) q^{98} +(0.719191 + 0.462196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 34 q^{3} - 2 q^{4} - 11 q^{6} + 4 q^{7} + 27 q^{8} - 34 q^{9}+O(q^{10}) \) 340 * q + 34 * q^3 - 2 * q^4 - 11 * q^6 + 4 * q^7 + 27 * q^8 - 34 * q^9	\( 340 q + 34 q^{3} - 2 q^{4} - 11 q^{6} + 4 q^{7} + 27 q^{8} - 34 q^{9} - 27 q^{10} - 9 q^{12} + 4 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 6 q^{24} + 34 q^{25} - 10 q^{26} + 34 q^{27} + 47 q^{28} + 16 q^{29} - 6 q^{30} - 4 q^{31} - 55 q^{32} + 9 q^{36} - 12 q^{37} + 26 q^{38} - 37 q^{40} - 4 q^{42} - 4 q^{43} - 51 q^{44} - 103 q^{46} + 2 q^{48} - 46 q^{49} - 51 q^{50} + 32 q^{52} - 14 q^{56} + 66 q^{57} + 92 q^{58} + 67 q^{60} + 2 q^{62} - 18 q^{63} + 7 q^{64} - 8 q^{66} - 18 q^{67} - 208 q^{68} + 56 q^{70} - 6 q^{72} + 54 q^{73} + 22 q^{74} - 34 q^{75} - 56 q^{76} + 8 q^{77} + 10 q^{78} + 10 q^{79} - 68 q^{80} - 34 q^{81} + 84 q^{82} + 8 q^{84} + 104 q^{86} - 16 q^{87} - 82 q^{88} - 27 q^{90} + 134 q^{92} + 4 q^{93} + 32 q^{94} - 40 q^{95} - 7 q^{98}+O(q^{100}) \) 340 * q + 34 * q^3 - 2 * q^4 - 11 * q^6 + 4 * q^7 + 27 * q^8 - 34 * q^9 - 27 * q^10 - 9 * q^12 + 4 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 6 * q^24 + 34 * q^25 - 10 * q^26 + 34 * q^27 + 47 * q^28 + 16 * q^29 - 6 * q^30 - 4 * q^31 - 55 * q^32 + 9 * q^36 - 12 * q^37 + 26 * q^38 - 37 * q^40 - 4 * q^42 - 4 * q^43 - 51 * q^44 - 103 * q^46 + 2 * q^48 - 46 * q^49 - 51 * q^50 + 32 * q^52 - 14 * q^56 + 66 * q^57 + 92 * q^58 + 67 * q^60 + 2 * q^62 - 18 * q^63 + 7 * q^64 - 8 * q^66 - 18 * q^67 - 208 * q^68 + 56 * q^70 - 6 * q^72 + 54 * q^73 + 22 * q^74 - 34 * q^75 - 56 * q^76 + 8 * q^77 + 10 * q^78 + 10 * q^79 - 68 * q^80 - 34 * q^81 + 84 * q^82 + 8 * q^84 + 104 * q^86 - 16 * q^87 - 82 * q^88 - 27 * q^90 + 134 * q^92 + 4 * q^93 + 32 * q^94 - 40 * q^95 - 7 * q^98

Introduction

L-functions

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