LMFDB - Embedded newform 525.2.bo.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(4,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 3, 20]))

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

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

chi := DirichletCharacter("525.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bo (of order $30$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	525.4
Dual form			525.2.bo.a.394.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.576680 - 2.71307i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-5.20107 + 2.31567i) q^{4} +(0.442104 - 2.19193i) q^{5} +(2.24395 - 1.63033i) q^{6} +(1.97794 + 1.75720i) q^{7} +(6.02126 + 8.28755i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.576680 - 2.71307i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-5.20107 + 2.31567i) q^{4} +(0.442104 - 2.19193i) q^{5} +(2.24395 - 1.63033i) q^{6} +(1.97794 + 1.75720i) q^{7} +(6.02126 + 8.28755i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(-6.20179 + 0.0645817i) q^{10} +(3.95270 + 4.38992i) q^{11} +(-4.23093 - 3.80955i) q^{12} +(-1.69479 + 0.550670i) q^{13} +(3.62675 - 6.37963i) q^{14} +(2.18224 - 0.487654i) q^{15} +(11.3932 - 12.6535i) q^{16} +(1.05623 - 0.111014i) q^{17} +(2.40207 + 1.38684i) q^{18} +(2.80100 + 1.24708i) q^{19} +(2.77636 + 12.4241i) q^{20} +(-0.800777 + 2.52166i) q^{21} +(9.63070 - 13.2555i) q^{22} +(0.186011 + 0.875114i) q^{23} +(-5.12199 + 8.87154i) q^{24} +(-4.60909 - 1.93812i) q^{25} +(2.47136 + 4.28051i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(-14.3565 - 4.55905i) q^{28} +(5.67658 + 4.12428i) q^{29} +(-2.58150 - 5.63935i) q^{30} +(-0.138454 - 1.31730i) q^{31} +(-23.1568 - 13.3696i) q^{32} +(-2.40268 + 5.39652i) q^{33} +(-0.910295 - 2.80160i) q^{34} +(4.72610 - 3.55864i) q^{35} +(1.75932 - 5.41463i) q^{36} +(-2.85562 - 2.57121i) q^{37} +(1.76814 - 8.31846i) q^{38} +(-1.19240 - 1.32429i) q^{39} +(20.8277 - 9.53419i) q^{40} +(-2.22233 - 6.83962i) q^{41} +(7.30321 + 0.718372i) q^{42} -3.18781i q^{43} +(-30.7239 - 13.6792i) q^{44} +(1.33309 + 1.79523i) q^{45} +(2.26697 - 1.00932i) q^{46} +(7.36211 + 0.773789i) q^{47} +(16.1936 + 5.26161i) q^{48} +(0.824518 + 6.95127i) q^{49} +(-2.60028 + 13.6224i) q^{50} +(0.531024 + 0.919760i) q^{51} +(7.53955 - 6.78865i) q^{52} +(-1.19009 - 2.67298i) q^{53} +(-0.289928 + 2.75848i) q^{54} +(11.3699 - 6.72324i) q^{55} +(-2.65315 + 26.9728i) q^{56} +3.06607i q^{57} +(7.91586 - 17.7793i) q^{58} +(-1.08159 - 0.229898i) q^{59} +(-10.2208 + 7.58968i) q^{60} +(-13.1309 + 2.79105i) q^{61} +(-3.49408 + 1.13530i) q^{62} +(-2.62935 + 0.294104i) q^{63} +(-12.3953 + 38.1489i) q^{64} +(0.457755 + 3.95831i) q^{65} +(16.0267 + 3.40658i) q^{66} +(6.51058 - 0.684290i) q^{67} +(-5.23646 + 3.02327i) q^{68} +(-0.723799 + 0.525871i) q^{69} +(-12.3803 - 10.7700i) q^{70} +(2.66243 + 1.93437i) q^{71} +(-10.1879 - 1.07079i) q^{72} +(5.12282 - 4.61261i) q^{73} +(-5.32908 + 9.23024i) q^{74} +(-0.104123 - 4.99892i) q^{75} -17.4560 q^{76} +(0.104266 + 15.6287i) q^{77} +(-2.90525 + 3.99874i) q^{78} +(-1.64105 + 15.6135i) q^{79} +(-22.6985 - 30.5673i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-17.2748 + 9.97358i) q^{82} +(0.236448 + 0.325442i) q^{83} +(-1.67442 - 14.9697i) q^{84} +(0.223629 - 2.36426i) q^{85} +(-8.64873 + 1.83834i) q^{86} +(-1.45884 + 6.86331i) q^{87} +(-12.5815 + 59.1911i) q^{88} +(13.4035 - 2.84900i) q^{89} +(4.10182 - 4.65204i) q^{90} +(-4.31983 - 1.88888i) q^{91} +(-2.99393 - 4.12079i) q^{92} +(1.14710 - 0.662278i) q^{93} +(-2.14624 - 20.4201i) q^{94} +(3.97185 - 5.58824i) q^{95} +(2.79501 - 26.5927i) q^{96} +(4.20973 - 5.79420i) q^{97} +(18.3838 - 6.24563i) q^{98} -5.90722 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.576680	−	2.71307i	−0.407774	−	1.91843i	−0.395413	−	0.918503i	$-0.629399\pi$
$2$	−0.576680	−	2.71307i	−0.407774	−	1.91843i	−0.0123612	−	0.999924i	$-0.503935\pi$
$3$	0.406737	+	0.913545i	0.234830	+	0.527436i
$3$	0.406737	+	0.913545i	0.234830	+	0.527436i
$4$	−5.20107	+	2.31567i	−2.60054	+	1.15783i
$5$	0.442104	−	2.19193i	0.197715	−	0.980260i
$5$	0.442104	−	2.19193i	0.197715	−	0.980260i
$6$	2.24395	−	1.63033i	0.916089	−	0.665578i
$7$	1.97794	+	1.75720i	0.747592	+	0.664158i
$7$	1.97794	+	1.75720i	0.747592	+	0.664158i
$8$	6.02126	+	8.28755i	2.12884	+	2.93009i
$9$	−0.669131	+	0.743145i	−0.223044	+	0.247715i
$10$	−6.20179	+	0.0645817i	−1.96118	+	0.0204225i
$11$	3.95270	+	4.38992i	1.19179	+	1.32361i	0.933942	+	0.357425i	$0.116345\pi$
$11$	3.95270	+	4.38992i	1.19179	+	1.32361i	0.257844	+	0.966187i	$0.416988\pi$
$12$	−4.23093	−	3.80955i	−1.22137	−	1.09972i
$13$	−1.69479	+	0.550670i	−0.470050	+	0.152729i	−0.534458	−	0.845195i	$-0.679484\pi$
$13$	−1.69479	+	0.550670i	−0.470050	+	0.152729i	0.0644078	+	0.997924i	$0.479484\pi$
$14$	3.62675	−	6.37963i	0.969290	−	1.70503i
$15$	2.18224	−	0.487654i	0.563453	−	0.125912i
$16$	11.3932	−	12.6535i	2.84831	−	3.16337i
$17$	1.05623	−	0.111014i	0.256173	−	0.0269249i	0.0244287	−	0.999702i	$-0.492223\pi$
$17$	1.05623	−	0.111014i	0.256173	−	0.0269249i	0.231745	+	0.972777i	$0.425557\pi$
$18$	2.40207	+	1.38684i	0.566174	+	0.326881i
$19$	2.80100	+	1.24708i	0.642593	+	0.286101i	0.702047	−	0.712130i	$-0.252269\pi$
$19$	2.80100	+	1.24708i	0.642593	+	0.286101i	−0.0594544	+	0.998231i	$0.518936\pi$
$20$	2.77636	+	12.4241i	0.620812	+	2.77812i
$21$	−0.800777	+	2.52166i	−0.174744	+	0.550271i
$22$	9.63070	−	13.2555i	2.05327	−	2.82609i
$23$	0.186011	+	0.875114i	0.0387860	+	0.182474i	0.993276	−	0.115768i	$-0.0369330\pi$
$23$	0.186011	+	0.875114i	0.0387860	+	0.182474i	−0.954490	+	0.298242i	$0.903600\pi$
$24$	−5.12199	+	8.87154i	−1.04552	+	1.81090i
$25$	−4.60909	−	1.93812i	−0.921817	−	0.387624i
$26$	2.47136	+	4.28051i	0.484673	+	0.839478i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	−14.3565	−	4.55905i	−2.71313	−	0.861580i
$29$	5.67658	+	4.12428i	1.05411	+	0.765859i	0.972990	−	0.230845i	$-0.0741491\pi$
$29$	5.67658	+	4.12428i	1.05411	+	0.765859i	0.0811237	+	0.996704i	$0.474149\pi$
$30$	−2.58150	−	5.63935i	−0.471314	−	1.02960i
$31$	−0.138454	−	1.31730i	−0.0248671	−	0.236594i	−0.999895	−	0.0145108i	$-0.995381\pi$
$31$	−0.138454	−	1.31730i	−0.0248671	−	0.236594i	0.975028	−	0.222083i	$-0.0712857\pi$
$32$	−23.1568	−	13.3696i	−4.09359	−	2.36343i
$33$	−2.40268	+	5.39652i	−0.418254	+	0.939413i
$34$	−0.910295	−	2.80160i	−0.156114	−	0.480471i
$35$	4.72610	−	3.55864i	0.798857	−	0.601520i
$36$	1.75932	−	5.41463i	0.293220	−	0.902439i
$37$	−2.85562	−	2.57121i	−0.469461	−	0.422704i	0.400145	−	0.916452i	$-0.368960\pi$
$37$	−2.85562	−	2.57121i	−0.469461	−	0.422704i	−0.869605	+	0.493748i	$0.835627\pi$
$38$	1.76814	−	8.31846i	0.286831	−	1.34943i
$39$	−1.19240	−	1.32429i	−0.190936	−	0.212056i
$40$	20.8277	−	9.53419i	3.29315	−	1.50749i
$41$	−2.22233	−	6.83962i	−0.347069	−	1.06817i	−0.960467	−	0.278394i	$-0.910198\pi$
$41$	−2.22233	−	6.83962i	−0.347069	−	1.06817i	0.613398	−	0.789774i	$-0.289802\pi$
$42$	7.30321	+	0.718372i	1.12691	+	0.110847i
$43$		−	3.18781i		−	0.486136i	−0.970009	−	0.243068i	$-0.921846\pi$
$43$		−	3.18781i		−	0.486136i	0.970009	−	0.243068i	$-0.0781538\pi$
$44$	−30.7239	−	13.6792i	−4.63180	−	2.06221i
$45$	1.33309	+	1.79523i	0.198726	+	0.267618i
$46$	2.26697	−	1.00932i	0.334247	−	0.148816i
$47$	7.36211	+	0.773789i	1.07387	+	0.112869i	0.624922	−	0.780687i	$-0.285131\pi$
$47$	7.36211	+	0.773789i	1.07387	+	0.112869i	0.448952	+	0.893556i	$0.351797\pi$
$48$	16.1936	+	5.26161i	2.33734	+	0.759447i
$49$	0.824518	+	6.95127i	0.117788	+	0.993039i
$50$	−2.60028	+	13.6224i	−0.367735	+	1.92650i
$51$	0.531024	+	0.919760i	0.0743582	+	0.128792i
$52$	7.53955	−	6.78865i	1.04555	−	0.941416i
$53$	−1.19009	−	2.67298i	−0.163471	−	0.367161i	0.813174	−	0.582020i	$-0.197738\pi$
$53$	−1.19009	−	2.67298i	−0.163471	−	0.367161i	−0.976645	+	0.214859i	$0.931071\pi$
$54$	−0.289928	+	2.75848i	−0.0394542	+	0.375382i
$55$	11.3699	−	6.72324i	1.53312	−	0.906561i
$56$	−2.65315	+	26.9728i	−0.354542	+	3.60440i
$57$			3.06607i			0.406111i
$58$	7.91586	−	17.7793i	1.03940	−	2.33454i
$59$	−1.08159	−	0.229898i	−0.140810	−	0.0299302i	0.136967	−	0.990576i	$-0.456265\pi$
$59$	−1.08159	−	0.229898i	−0.140810	−	0.0299302i	−0.277778	+	0.960645i	$0.589598\pi$
$60$	−10.2208	+	7.58968i	−1.31950	+	0.979823i
$61$	−13.1309	+	2.79105i	−1.68123	+	0.357357i	−0.946924	−	0.321458i	$-0.895827\pi$
$61$	−13.1309	+	2.79105i	−1.68123	+	0.357357i	−0.734309	+	0.678815i	$0.762494\pi$
$62$	−3.49408	+	1.13530i	−0.443749	+	0.144183i
$63$	−2.62935	+	0.294104i	−0.331267	+	0.0370536i
$64$	−12.3953	+	38.1489i	−1.54941	+	4.76861i
$65$	0.457755	+	3.95831i	0.0567776	+	0.490968i
$66$	16.0267	+	3.40658i	1.97275	+	0.419321i
$67$	6.51058	−	0.684290i	0.795394	−	0.0835993i	0.301890	−	0.953343i	$-0.402382\pi$
$67$	6.51058	−	0.684290i	0.795394	−	0.0835993i	0.493504	+	0.869743i	$0.335716\pi$
$68$	−5.23646	+	3.02327i	−0.635014	+	0.366625i
$69$	−0.723799	+	0.525871i	−0.0871352	+	0.0633074i
$70$	−12.3803	−	10.7700i	−1.47973	−	1.28727i
$71$	2.66243	+	1.93437i	0.315973	+	0.229568i	0.734455	−	0.678657i	$-0.237438\pi$
$71$	2.66243	+	1.93437i	0.315973	+	0.229568i	−0.418482	+	0.908225i	$0.637438\pi$
$72$	−10.1879	−	1.07079i	−1.20065	−	0.126193i
$73$	5.12282	−	4.61261i	0.599581	−	0.539865i	−0.312477	−	0.949925i	$-0.601159\pi$
$73$	5.12282	−	4.61261i	0.599581	−	0.539865i	0.912059	+	0.410060i	$0.134492\pi$
$74$	−5.32908	+	9.23024i	−0.619493	+	1.07299i
$75$	−0.104123	−	4.99892i	−0.0120230	−	0.577225i
$76$	−17.4560			−2.00234
$77$	0.104266	+	15.6287i	0.0118822	+	1.78106i
$78$	−2.90525	+	3.99874i	−0.328955	+	0.452768i
$79$	−1.64105	+	15.6135i	−0.184632	+	1.75666i	0.374174	+	0.927359i	$0.377926\pi$
$79$	−1.64105	+	15.6135i	−0.184632	+	1.75666i	−0.558806	+	0.829298i	$0.688740\pi$
$80$	−22.6985	−	30.5673i	−2.53777	−	3.41753i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	−17.2748	+	9.97358i	−1.90768	+	1.10140i
$83$	0.236448	+	0.325442i	0.0259535	+	0.0357219i	0.821797	−	0.569781i	$-0.192972\pi$
$83$	0.236448	+	0.325442i	0.0259535	+	0.0357219i	−0.795843	+	0.605503i	$0.792972\pi$
$84$	−1.67442	−	14.9697i	−0.182694	−	1.63332i
$85$	0.223629	−	2.36426i	0.0242560	−	0.256440i
$86$	−8.64873	+	1.83834i	−0.932616	+	0.198234i
$87$	−1.45884	+	6.86331i	−0.156404	+	0.735824i
$88$	−12.5815	+	59.1911i	−1.34119	+	6.30979i
$89$	13.4035	−	2.84900i	1.42077	−	0.301993i	0.567459	−	0.823401i	$-0.307926\pi$
$89$	13.4035	−	2.84900i	1.42077	−	0.301993i	0.853307	+	0.521408i	$0.174593\pi$
$90$	4.10182	−	4.65204i	0.432369	−	0.490369i
$91$	−4.31983	−	1.88888i	−0.452842	−	0.198009i
$92$	−2.99393	−	4.12079i	−0.312139	−	0.429622i
$93$	1.14710	−	0.662278i	0.118949	−	0.0686751i
$94$	−2.14624	−	20.4201i	−0.221368	−	2.10617i
$95$	3.97185	−	5.58824i	0.407504	−	0.573342i
$96$	2.79501	−	26.5927i	0.285264	−	2.71411i
$97$	4.20973	−	5.79420i	0.427433	−	0.588312i	−0.539928	−	0.841711i	$-0.681549\pi$
$97$	4.20973	−	5.79420i	0.427433	−	0.588312i	0.967362	+	0.253399i	$0.0815487\pi$
$98$	18.3838	−	6.24563i	1.85704	−	0.630904i
$99$	−5.90722			−0.593698
$100$	28.4602	−	0.592800i	2.84602	−	0.0592800i
$101$	−1.93488	+	3.35132i	−0.192528	+	0.333468i	−0.946087	−	0.323912i	$-0.895002\pi$
$101$	−1.93488	+	3.35132i	−0.192528	+	0.333468i	0.753559	+	0.657380i	$0.228335\pi$
$102$	2.18914	−	1.97111i	0.216757	−	0.195169i
$103$	8.17226	+	0.858939i	0.805237	+	0.0846338i	0.498198	−	0.867063i	$-0.333995\pi$
$103$	8.17226	+	0.858939i	0.805237	+	0.0846338i	0.307039	+	0.951697i	$0.400662\pi$
$104$	−14.7685	−	10.7299i	−1.44817	−	1.05216i
$105$	5.17326	+	2.87008i	0.504859	+	0.280091i
$106$	−6.56566	+	4.77023i	−0.637713	+	0.463326i
$107$	4.61144	−	2.66241i	0.445804	−	0.257385i	−0.260252	−	0.965541i	$-0.583806\pi$
$107$	4.61144	−	2.66241i	0.445804	−	0.257385i	0.706057	+	0.708155i	$0.250472\pi$
$108$	5.66210	−	0.595110i	0.544835	−	0.0572645i
$109$	−1.44599	−	0.307354i	−0.138501	−	0.0294392i	0.138140	−	0.990413i	$-0.455888\pi$
$109$	−1.44599	−	0.307354i	−0.138501	−	0.0294392i	−0.276640	+	0.960974i	$0.589221\pi$
$110$	−24.7974	−	26.9701i	−2.36434	−	2.57150i
$111$	1.18743	−	3.65454i	0.112706	−	0.346874i
$112$	44.7698	−	5.00768i	4.23035	−	0.473182i
$113$	0.0380239	−	0.0123547i	0.00357699	−	0.00116223i	−0.307228	−	0.951636i	$-0.599401\pi$
$113$	0.0380239	−	0.0123547i	0.00357699	−	0.00116223i	0.310805	+	0.950474i	$0.399401\pi$
$114$	8.31846	−	1.76814i	0.779095	−	0.165602i
$115$	2.00042	−	0.0208312i	0.186540	−	0.00194252i
$116$	−39.0748	−	8.30560i	−3.62800	−	0.771155i
$117$	0.724808	−	1.62794i	0.0670085	−	0.150504i
$118$			3.06699i			0.282339i
$119$	2.28424	+	1.63642i	0.209396	+	0.150011i
$120$	17.1813	+	15.1492i	1.56843	+	1.38292i
$121$	−2.49774	+	23.7644i	−0.227067	+	2.16040i
$122$	15.1446	+	34.0153i	1.37113	+	3.07960i
$123$	5.34440	−	4.81212i	0.481888	−	0.433894i
$124$	3.77054	+	6.53077i	0.338604	+	0.586480i
$125$	−6.28592	+	9.24593i	−0.562230	+	0.826981i
$126$	2.31422	+	6.96401i	0.206167	+	0.620403i
$127$	−15.7827	−	5.12811i	−1.40049	−	0.455046i	−0.491139	−	0.871081i	$-0.663419\pi$
$127$	−15.7827	−	5.12811i	−1.40049	−	0.455046i	−0.909349	+	0.416035i	$0.863419\pi$
$128$	57.4631	+	6.03961i	5.07906	+	0.533831i
$129$	2.91221	−	1.29660i	0.256405	−	0.114159i
$130$	10.4752	−	3.52460i	0.918733	−	0.309128i
$131$	−3.39428	−	1.51123i	−0.296560	−	0.132037i	0.253063	−	0.967450i	$-0.418562\pi$
$131$	−3.39428	−	1.51123i	−0.296560	−	0.132037i	−0.549623	+	0.835413i	$0.685229\pi$
$132$		−	33.6315i		−	2.92725i
$133$	3.34884	+	7.38857i	0.290381	+	0.640670i
$134$	−5.61104	−	17.2690i	−0.484720	−	1.49182i
$135$	−1.09781	+	1.94803i	−0.0944844	+	0.167660i
$136$	7.27987	+	8.08511i	0.624243	+	0.693293i
$137$	0.502536	−	2.36425i	0.0429346	−	0.201991i	−0.951452	−	0.307796i	$-0.900409\pi$
$137$	0.502536	−	2.36425i	0.0429346	−	0.201991i	0.994387	+	0.105805i	$0.0337419\pi$
$138$	1.84412	+	1.66046i	0.156982	+	0.141347i
$139$	1.96047	−	6.03372i	0.166285	−	0.511773i	−0.832843	−	0.553509i	$-0.813289\pi$
$139$	1.96047	−	6.03372i	0.166285	−	0.511773i	0.999129	+	0.0417352i	$0.0132886\pi$
$140$	−16.3402	+	29.4528i	−1.38100	+	2.48922i
$141$	2.28755	+	7.04035i	0.192646	+	0.592904i
$142$	3.71270	−	8.33887i	0.311563	−	0.699782i
$143$	−9.11640	−	5.26336i	−0.762352	−	0.440144i
$144$	1.77980	+	16.9336i	0.148316	+	1.41114i
$145$	11.5498	−	10.6193i	0.959155	−	0.881884i
$146$	−15.4685	−	11.2386i	−1.28019	−	0.930110i
$147$	−6.01494	+	3.58057i	−0.496104	+	0.295321i
$148$	20.8063	+	6.76039i	1.71027	+	0.555701i
$149$	−2.55241	−	4.42090i	−0.209102	−	0.362175i	0.742330	−	0.670034i	$-0.233721\pi$
$149$	−2.55241	−	4.42090i	−0.209102	−	0.362175i	−0.951432	+	0.307860i	$0.900387\pi$
$150$	−13.5023	+	3.16527i	−1.10246	+	0.258443i
$151$	1.60032	−	2.77184i	0.130232	−	0.225569i	−0.793534	−	0.608526i	$-0.791761\pi$
$151$	1.60032	−	2.77184i	0.130232	−	0.225569i	0.923766	+	0.382957i	$0.125094\pi$
$152$	6.53026	+	30.7224i	0.529674	+	2.49192i
$153$	−0.624256	+	0.859215i	−0.0504681	+	0.0694634i
$154$	42.3416	−	9.29564i	3.41198	−	0.749064i
$155$	−2.94864	−	0.278904i	−0.236840	−	0.0224021i
$156$	9.26835	+	4.12654i	0.742062	+	0.330387i
$157$	−1.62466	−	0.937998i	−0.129662	−	0.0748604i	0.433766	−	0.901026i	$-0.357184\pi$
$157$	−1.62466	−	0.937998i	−0.129662	−	0.0748604i	−0.563428	+	0.826165i	$0.690518\pi$
$158$	43.3068	−	4.55173i	3.44531	−	0.362116i
$159$	1.95783	−	2.17439i	0.155266	−	0.172441i
$160$	−39.5429	+	44.8473i	−3.12614	+	3.54549i
$161$	−1.16983	+	2.05778i	−0.0921954	+	0.162176i
$162$	−2.63792	+	0.857113i	−0.207255	+	0.0673412i
$163$	−13.3573	−	12.0269i	−1.04622	−	0.942022i	−0.0478373	−	0.998855i	$-0.515233\pi$
$163$	−13.3573	−	12.0269i	−1.04622	−	0.942022i	−0.998384	+	0.0568336i	$0.981900\pi$
$164$	27.3968	+	30.4272i	2.13933	+	2.37596i
$165$	10.7665	+	7.65233i	0.838174	+	0.595733i
$166$	0.746591	−	0.829174i	0.0579467	−	0.0643564i
$167$	−12.9156	−	17.7768i	−0.999438	−	1.37561i	−0.925670	−	0.378333i	$-0.876498\pi$
$167$	−12.9156	−	17.7768i	−0.999438	−	1.37561i	−0.0737680	−	0.997275i	$-0.523502\pi$
$168$	−25.7201	+	8.54707i	−1.98435	+	0.659421i
$169$	−7.94815	+	5.77467i	−0.611396	+	0.444205i
$170$	−6.54335	+	0.756700i	−0.501852	+	0.0580363i
$171$	−2.80100	+	1.24708i	−0.214198	+	0.0953670i
$172$	7.38190	+	16.5800i	0.562864	+	1.26421i
$173$	1.49435	+	7.03038i	0.113614	+	0.534510i	0.997736	+	0.0672542i	$0.0214238\pi$
$173$	1.49435	+	7.03038i	0.113614	+	0.534510i	−0.884122	+	0.467256i	$0.845243\pi$
$174$	19.4619			1.47540
$175$	−5.71085	−	11.9326i	−0.431700	−	0.902017i
$176$	100.582			7.58164
$177$	−0.229898	−	1.08159i	−0.0172802	−	0.0812969i
$178$	−15.4590	−	34.7216i	−1.15870	−	2.60249i
$179$	4.38126	−	1.95066i	0.327471	−	0.145799i	−0.236415	−	0.971652i	$-0.575972\pi$
$179$	4.38126	−	1.95066i	0.327471	−	0.145799i	0.563886	+	0.825853i	$0.309306\pi$
$180$	−11.0907	−	6.25014i	−0.826650	−	0.465858i
$181$	7.38985	−	5.36904i	0.549283	−	0.399078i	−0.278238	−	0.960512i	$-0.589750\pi$
$181$	7.38985	−	5.36904i	0.549283	−	0.399078i	0.827521	+	0.561435i	$0.189750\pi$
$182$	−2.63350	+	12.8093i	−0.195208	+	0.949486i
$183$	−7.89055	−	10.8604i	−0.583286	−	0.802824i
$184$	−6.13253	+	6.81087i	−0.452096	+	0.502104i
$185$	−6.89838	+	5.12256i	−0.507179	+	0.376618i
$186$	−2.45831	−	2.73023i	−0.180252	−	0.200191i
$187$	4.66231	+	4.19796i	0.340942	+	0.306985i
$188$	−40.0827	+	13.0237i	−2.92333	+	0.949848i
$189$	−1.33813	−	2.28241i	−0.0973348	−	0.166021i
$190$	−17.4518	−	7.55327i	−1.26608	−	0.547972i
$191$	−11.4250	+	12.6887i	−0.826682	+	0.918123i	−0.997744	−	0.0671371i	$-0.978613\pi$
$191$	−11.4250	+	12.6887i	−0.826682	+	0.918123i	0.171062	+	0.985260i	$0.445280\pi$
$192$	−39.8924	+	4.19286i	−2.87898	+	0.302593i
$193$	−20.4596	−	11.8124i	−1.47272	−	0.850273i	−0.473187	−	0.880962i	$-0.656897\pi$
$193$	−20.4596	−	11.8124i	−1.47272	−	0.850273i	−0.999529	+	0.0306889i	$0.990230\pi$
$194$	−18.1477	−	8.07988i	−1.30293	−	0.580101i
$195$	−3.42991	+	2.02817i	−0.245621	+	0.145240i
$196$	−20.3852	−	34.2448i	−1.45609	−	2.44605i
$197$	5.78960	−	7.96870i	0.412492	−	0.567746i	−0.551332	−	0.834286i	$-0.685880\pi$
$197$	5.78960	−	7.96870i	0.412492	−	0.567746i	0.963824	+	0.266539i	$0.0858803\pi$
$198$	3.40658	+	16.0267i	0.242095	+	1.13897i
$199$	−9.91383	+	17.1713i	−0.702773	+	1.21724i	0.264717	+	0.964326i	$0.414721\pi$
$199$	−9.91383	+	17.1713i	−0.702773	+	1.21724i	−0.967489	+	0.252912i	$0.918612\pi$
$200$	−11.6902	−	49.8680i	−0.826624	−	3.52620i
$201$	3.27322	+	5.66939i	0.230875	+	0.399888i
$202$	10.2081	+	3.31683i	0.718243	+	0.233371i
$203$	3.98079	+	18.1324i	0.279396	+	1.27265i
$204$	−4.89175	−	3.55407i	−0.342491	−	0.248834i
$205$	−15.9744	+	1.84735i	−1.11570	+	0.129025i
$206$	−2.38242	−	22.6672i	−0.165991	−	1.57930i
$207$	−0.774802	−	0.447332i	−0.0538525	−	0.0310918i
$208$	−12.3412	+	27.7189i	−0.855711	+	1.92196i
$209$	5.59691	+	17.2255i	0.387147	+	1.19151i
$210$	4.80340	−	15.6905i	0.331466	−	1.08275i
$211$	−3.60631	+	11.0991i	−0.248268	+	0.764092i	0.746813	+	0.665034i	$0.231583\pi$
$211$	−3.60631	+	11.0991i	−0.248268	+	0.764092i	−0.995082	+	0.0990579i	$0.968417\pi$
$212$	12.3794	+	11.1465i	0.850224	+	0.765545i
$213$	−0.684227	+	3.21903i	−0.0468824	+	0.220564i
$214$	−9.88263	−	10.9758i	−0.675562	−	0.750288i
$215$	−6.98744	−	1.40934i	−0.476539	−	0.0961164i
$216$	−3.16556	−	9.74260i	−0.215389	−	0.662900i
$217$	2.04090	−	2.84884i	0.138546	−	0.193392i
$218$			4.10031i			0.277708i
$219$	6.29747	+	2.80381i	0.425544	+	0.189464i
$220$	−43.5669	+	61.2969i	−2.93728	+	4.13264i
$221$	−1.72895	+	0.769780i	−0.116302	+	0.0517810i
$222$	−10.5998	−	1.11408i	−0.711410	−	0.0747723i
$223$	−20.8405	−	6.77150i	−1.39558	−	0.453453i	−0.487824	−	0.872942i	$-0.662209\pi$
$223$	−20.8405	−	6.77150i	−1.39558	−	0.453453i	−0.907760	+	0.419489i	$0.862209\pi$
$224$	−22.3099	−	67.1354i	−1.49064	−	4.48567i
$225$	4.52439	−	2.12836i	0.301626	−	0.141891i
$226$	−0.0554468	−	0.0960367i	−0.00368827	−	0.00638826i
$227$	9.96784	−	8.97508i	0.661589	−	0.595697i	−0.268390	−	0.963310i	$-0.586492\pi$
$227$	9.96784	−	8.97508i	0.661589	−	0.595697i	0.929979	+	0.367613i	$0.119825\pi$
$228$	−7.10001	−	15.9469i	−0.470210	−	1.05611i
$229$	3.11385	−	29.6263i	0.205769	−	1.95776i	−0.0728059	−	0.997346i	$-0.523195\pi$
$229$	3.11385	−	29.6263i	0.205769	−	1.95776i	0.278575	−	0.960415i	$-0.410138\pi$
$230$	−1.21012	−	5.41527i	−0.0797929	−	0.357072i
$231$	−14.2351	+	6.45202i	−0.936602	+	0.424512i
$232$			71.8783i			4.71904i
$233$	0.430924	−	0.967870i	0.0282307	−	0.0634073i	−0.898880	−	0.438195i	$-0.855618\pi$
$233$	0.430924	−	0.967870i	0.0282307	−	0.0634073i	0.927111	+	0.374788i	$0.122285\pi$
$234$	−4.83470	−	1.02765i	−0.316054	−	0.0671794i
$235$	4.95091	−	15.7951i	0.322962	−	1.03036i
$236$	6.15777	−	1.30887i	0.400837	−	0.0852005i
$237$	−14.9311	+	4.85142i	−0.969881	+	0.315133i
$238$	3.12245	−	7.14097i	0.202398	−	0.462881i
$239$	−0.181849	+	0.559674i	−0.0117628	+	0.0362023i	−0.956766	−	0.290860i	$-0.906059\pi$
$239$	−0.181849	+	0.559674i	−0.0117628	+	0.0362023i	0.945003	+	0.327062i	$0.106059\pi$
$240$	18.6923	−	33.1689i	1.20658	−	2.14104i
$241$	−1.76220	−	0.374568i	−0.113513	−	0.0241280i	0.150805	−	0.988564i	$-0.451814\pi$
$241$	−1.76220	−	0.374568i	−0.113513	−	0.0241280i	−0.264318	+	0.964436i	$0.585147\pi$
$242$	65.9148	−	6.92792i	4.23716	−	0.445344i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	61.8314	−	44.9231i	3.95835	−	2.87591i
$245$	15.6012	+	1.26590i	0.996724	+	0.0808756i
$246$	−16.1376	−	11.7247i	−1.02890	−	0.747537i
$247$	−5.43384	−	0.571119i	−0.345747	−	0.0363394i
$248$	10.0835	−	9.07925i	0.640305	−	0.576533i
$249$	−0.201134	+	0.348375i	−0.0127464	+	0.0220774i
$250$	28.7098	+	11.7222i	1.81577	+	0.741375i
$251$	−2.27594			−0.143656			−0.0718281	−	0.997417i	$-0.522883\pi$
$251$	−2.27594			−0.143656			−0.0718281	+	0.997417i	$0.522883\pi$
$252$	12.9944	−	7.61837i	0.818571	−	0.479912i
$253$	−3.10644	+	4.27564i	−0.195300	+	0.268807i
$254$	−4.81133	+	45.7768i	−0.301890	+	2.87229i
$255$	2.25082	−	0.757335i	0.140952	−	0.0474262i
$256$	−8.36622	−	79.5992i	−0.522889	−	4.97495i
$257$	18.5990	−	10.7382i	1.16018	−	0.669828i	0.208830	−	0.977952i	$-0.433034\pi$
$257$	18.5990	−	10.7382i	1.16018	−	0.669828i	0.951346	+	0.308124i	$0.0997011\pi$
$258$	−5.19716	−	7.15328i	−0.323561	−	0.445344i
$259$	−1.13013	−	10.1036i	−0.0702227	−	0.627806i
$260$	−11.5469	−	19.5274i	−0.716111	−	1.21104i
$261$	−6.86331	+	1.45884i	−0.424828	+	0.0903000i
$262$	−2.14266	+	10.0804i	−0.132374	+	0.622769i
$263$	−2.05057	+	9.64717i	−0.126443	+	0.594870i	0.868607	+	0.495501i	$0.165016\pi$
$263$	−2.05057	+	9.64717i	−0.126443	+	0.594870i	−0.995051	+	0.0993685i	$0.968318\pi$
$264$	−59.1911	+	12.5815i	−3.64296	+	0.774335i
$265$	−6.38511	+	1.42685i	−0.392234	+	0.0876504i
$266$	18.1145	−	13.3465i	1.11067	−	0.818324i
$267$	8.05438	+	11.0859i	0.492920	+	0.678446i
$268$	−32.2774	+	18.6354i	−1.97166	+	1.13834i
$269$	3.16804	+	30.1419i	0.193159	+	1.83778i	0.476989	+	0.878909i	$0.341728\pi$
$269$	3.16804	+	30.1419i	0.193159	+	1.83778i	−0.283831	+	0.958874i	$0.591605\pi$
$270$	5.91821	+	1.85504i	0.360171	+	0.112894i
$271$	0.466565	−	4.43907i	0.0283418	−	0.269654i	−0.971169	−	0.238390i	$-0.923380\pi$
$271$	0.466565	−	4.43907i	0.0283418	−	0.269654i	0.999511	−	0.0312636i	$-0.00995312\pi$
$272$	10.6292	−	14.6298i	0.644487	−	0.887060i
$273$	−0.0314534	−	4.71464i	−0.00190365	−	0.285343i
$274$	−6.70416			−0.405013
$275$	−9.71016	−	27.8944i	−0.585544	−	1.68209i
$276$	2.54679	−	4.41117i	0.153299	−	0.265521i
$277$	−5.66809	+	5.10357i	−0.340563	+	0.306644i	−0.821609	−	0.570051i	$-0.806923\pi$
$277$	−5.66809	+	5.10357i	−0.340563	+	0.306644i	0.481047	+	0.876695i	$0.340257\pi$
$278$	−17.5004	−	1.83937i	−1.04961	−	0.110318i
$279$	1.07159	+	0.778555i	0.0641544	+	0.0466109i
$280$	57.9495	+	17.7403i	3.46315	+	1.06019i
$281$	9.86096	−	7.16441i	0.588256	−	0.427393i	−0.253435	−	0.967352i	$-0.581560\pi$
$281$	9.86096	−	7.16441i	0.588256	−	0.427393i	0.841691	+	0.539960i	$0.181560\pi$
$282$	17.7817	−	10.2663i	1.05889	−	0.611349i
$283$	−10.0296	+	1.05415i	−0.596196	+	0.0626627i	−0.397820	−	0.917463i	$-0.630233\pi$
$283$	−10.0296	+	1.05415i	−0.596196	+	0.0626627i	−0.198376	+	0.980126i	$0.563567\pi$
$284$	−18.3269	−	3.89550i	−1.08750	−	0.231155i
$285$	6.72061	+	1.35553i	0.398095	+	0.0802944i
$286$	−9.02259	+	27.7687i	−0.533517	+	1.64200i
$287$	7.62292	−	17.4334i	0.449967	−	1.02906i
$288$	25.4305	−	8.26287i	1.49851	−	0.486894i
$289$	−15.5252	+	3.29999i	−0.913248	+	0.194117i
$290$	−35.4713	−	25.2113i	−2.08295	−	1.48046i
$291$	7.00551	+	1.48907i	0.410671	+	0.0872907i
$292$	−15.9629	+	35.8533i	−0.934159	+	2.09816i
$293$		−	1.72539i		−	0.100798i	−0.998729	−	0.0503991i	$-0.983951\pi$
$293$		−	1.72539i		−	0.100798i	0.998729	−	0.0503991i	$-0.0160493\pi$
$294$	13.1830	+	14.2541i	0.768849	+	0.831315i
$295$	−0.982093	+	2.26912i	−0.0571797	+	0.132113i
$296$	4.11462	−	39.1480i	0.239157	−	2.27543i
$297$	−2.40268	−	5.39652i	−0.139418	−	0.313138i
$298$	−10.5223	+	9.47430i	−0.609539	+	0.548832i
$299$	−0.797149	−	1.38070i	−0.0461003	−	0.0798481i
$300$	12.1174	+	25.7586i	0.699597	+	1.48717i
$301$	5.60160	−	6.30530i	0.322871	−	0.363431i
$302$	−8.44305	−	2.74331i	−0.485843	−	0.157860i
$303$	−3.84857	−	0.404501i	−0.221094	−	0.0232380i
$304$	47.6924	−	21.2340i	2.73534	−	1.21785i
$305$	0.312566	+	30.0158i	0.0178975	+	1.71870i
$306$	2.69110	+	1.19816i	0.153840	+	0.0684940i
$307$		−	8.97272i		−	0.512100i	−0.966664	−	0.256050i	$-0.917579\pi$
$307$		−	8.97272i		−	0.512100i	0.966664	−	0.256050i	$-0.0824212\pi$
$308$	−36.7332	−	81.0446i	−2.09307	−	4.61794i
$309$	2.53928	+	7.81509i	0.144454	+	0.444585i
$310$	0.943736	+	8.16069i	0.0536006	+	0.463496i
$311$	−12.6726	−	14.0743i	−0.718595	−	0.798080i	0.267625	−	0.963523i	$-0.413761\pi$
$311$	−12.6726	−	14.0743i	−0.718595	−	0.798080i	−0.986219	+	0.165443i	$0.947095\pi$
$312$	3.79539	−	17.8559i	0.214872	−	1.01089i
$313$	−21.0304	−	18.9359i	−1.18871	−	1.07032i	−0.996026	−	0.0890588i	$-0.971614\pi$
$313$	−21.0304	−	18.9359i	−1.18871	−	1.07032i	−0.192684	−	0.981261i	$-0.561719\pi$
$314$	−1.60794	+	4.94874i	−0.0907414	+	0.279273i
$315$	−0.517795	+	5.89338i	−0.0291744	+	0.332054i
$316$	−27.6205	−	85.0071i	−1.55377	−	4.78202i
$317$	−8.93719	+	20.0732i	−0.501962	+	1.12743i	0.467902	+	0.883780i	$0.345010\pi$
$317$	−8.93719	+	20.0732i	−0.501962	+	1.12743i	−0.969864	+	0.243646i	$0.921657\pi$
$318$	−7.02832	−	4.05780i	−0.394129	−	0.227550i
$319$	4.33258	+	41.2218i	0.242578	+	2.30798i
$320$	78.1395	+	44.0354i	4.36813	+	2.46165i
$321$	4.30788	+	3.12986i	0.240442	+	0.174692i
$322$	6.25752	+	1.98714i	0.348718	+	0.110739i
$323$	3.09694	+	1.00626i	0.172318	+	0.0559897i
$324$	2.84664	+	4.93053i	0.158147	+	0.273918i
$325$	8.87870	+	0.746620i	0.492502	+	0.0414150i
$326$	−24.9270	+	43.1748i	−1.38058	+	2.39123i
$327$	−0.307354	−	1.44599i	−0.0169967	−	0.0799634i
$328$	43.3025	−	59.6007i	2.39098	−	3.29090i
$329$	13.2021	+	14.4672i	0.727857	+	0.797602i
$330$	14.5524	−	33.6233i	0.801085	−	1.85090i
$331$	11.9236	+	5.30871i	0.655378	+	0.291793i	0.707359	−	0.706855i	$-0.249887\pi$
$331$	11.9236	+	5.30871i	0.655378	+	0.291793i	−0.0519802	+	0.998648i	$0.516553\pi$
$332$	−1.98340	−	1.14511i	−0.108853	−	0.0628463i
$333$	3.82156	−	0.401662i	0.209420	−	0.0220110i
$334$	−40.7814	+	45.2923i	−2.23146	+	2.47829i
$335$	1.37844	−	14.5732i	0.0753125	−	0.796221i
$336$	22.7843	+	38.8624i	1.24298	+	2.12012i
$337$	8.52369	−	2.76952i	0.464315	−	0.150865i	−0.0675114	−	0.997719i	$-0.521506\pi$
$337$	8.52369	−	2.76952i	0.464315	−	0.150865i	0.531826	+	0.846853i	$0.321506\pi$
$338$	20.2506	+	18.2337i	1.10149	+	0.991783i
$339$	0.0267523	+	0.0297115i	0.00145299	+	0.00161370i
$340$	4.31172	+	12.8145i	0.233836	+	0.694965i
$341$	5.23558	−	5.81470i	0.283523	−	0.314884i
$342$	4.99870	+	6.88012i	0.270299	+	0.372034i
$343$	−10.5839	+	15.1981i	−0.571477	+	0.820618i
$344$	26.4191	−	19.1946i	1.42442	−	1.03490i
$345$	0.832676	+	1.81900i	0.0448297	+	0.0979319i
$346$	18.2121	−	8.10855i	0.979089	−	0.435919i
$347$	4.10112	+	9.21126i	0.220159	+	0.494486i	0.989532	−	0.144314i	$-0.0460976\pi$
$347$	4.10112	+	9.21126i	0.220159	+	0.494486i	−0.769372	+	0.638800i	$0.779431\pi$
$348$	−8.30560	−	39.0748i	−0.445227	−	2.09463i
$349$	24.3984			1.30601			0.653007	−	0.757351i	$-0.273507\pi$
$349$	24.3984			1.30601			0.653007	+	0.757351i	$0.273507\pi$
$350$	−29.0805	+	22.3752i	−1.55442	+	1.19600i
$351$	1.78201			0.0951165
$352$	−32.8406	−	154.503i	−1.75041	−	8.23503i
$353$	−11.3194	−	25.4237i	−0.602468	−	1.35317i	−0.915075	−	0.403283i	$-0.867869\pi$
$353$	−11.3194	−	25.4237i	−0.602468	−	1.35317i	0.312607	−	0.949883i	$-0.398798\pi$
$354$	−2.80183	+	1.24746i	−0.148916	+	0.0663016i
$355$	5.41707	−	4.98066i	0.287508	−	0.264346i
$356$	−63.1152	+	45.8559i	−3.34510	+	2.43036i
$357$	−0.565865	+	2.75235i	−0.0299487	+	0.145670i
$358$	−7.81886	−	10.7617i	−0.413240	−	0.568776i
$359$	−10.8513	+	12.0516i	−0.572712	+	0.636061i	−0.958011	−	0.286730i	$-0.907432\pi$
$359$	−10.8513	+	12.0516i	−0.572712	+	0.636061i	0.385299	+	0.922792i	$0.374098\pi$
$360$	−6.85119	+	21.8576i	−0.361089	+	1.15200i
$361$	−6.42311	−	7.13359i	−0.338058	−	0.375452i
$362$	−18.8281	−	16.9529i	−0.989585	−	0.891026i
$363$	−22.7258	+	7.38406i	−1.19279	+	0.387562i
$364$	26.8418	−	0.179073i	1.40689	−	0.00938599i
$365$	−7.84568	−	13.2681i	−0.410662	−	0.694485i
$366$	−24.9147	+	27.6706i	−1.30231	+	1.44636i
$367$	−1.32116	+	0.138859i	−0.0689639	+	0.00724840i	−0.138948	−	0.990300i	$-0.544372\pi$
$367$	−1.32116	+	0.138859i	−0.0689639	+	0.00724840i	0.0699837	+	0.997548i	$0.477705\pi$
$368$	13.1925	+	7.61669i	0.687706	+	0.397047i
$369$	6.56985	+	2.92509i	0.342013	+	0.152274i
$370$	17.8760	+	15.7617i	0.929329	+	0.819411i
$371$	2.34302	−	7.37821i	0.121644	−	0.383058i
$372$	−4.43253	+	6.10086i	−0.229816	+	0.316315i
$373$	5.03088	+	23.6684i	0.260489	+	1.22550i	0.892680	+	0.450691i	$0.148823\pi$
$373$	5.03088	+	23.6684i	0.260489	+	1.22550i	−0.632191	+	0.774813i	$0.717844\pi$
$374$	8.70068	−	15.0700i	0.449902	−	0.779252i
$375$	−11.0033	−	1.98181i	−0.568208	−	0.102340i
$376$	37.9163	+	65.6730i	1.95539	+	3.38683i
$377$	−11.8917	−	3.86385i	−0.612455	−	0.198999i
$378$	−5.42066	+	4.94666i	−0.278809	+	0.254429i
$379$	−18.4240	−	13.3858i	−0.946378	−	0.687584i	0.00356918	−	0.999994i	$-0.498864\pi$
$379$	−18.4240	−	13.3858i	−0.946378	−	0.687584i	−0.949948	+	0.312410i	$0.898864\pi$
$380$	−7.71739	+	38.2623i	−0.395894	+	1.96282i
$381$	−1.73464	−	16.5040i	−0.0888683	−	0.845525i
$382$	41.0139	+	23.6794i	2.09845	+	1.21154i
$383$	−8.77019	+	19.6982i	−0.448136	+	1.00653i	0.538356	+	0.842718i	$0.319046\pi$
$383$	−8.77019	+	19.6982i	−0.448136	+	1.00653i	−0.986492	+	0.163812i	$0.947621\pi$
$384$	17.8549	+	54.9516i	0.911153	+	2.80424i
$385$	34.3031	+	6.68098i	1.74825	+	0.340494i
$386$	−20.2491	+	62.3203i	−1.03065	+	3.17202i
$387$	2.36900	+	2.13306i	0.120423	+	0.108429i
$388$	−8.47769	+	39.8844i	−0.430389	+	2.02482i
$389$	−10.9472	−	12.1581i	−0.555045	−	0.616440i	0.398691	−	0.917085i	$-0.369465\pi$
$389$	−10.9472	−	12.1581i	−0.555045	−	0.616440i	−0.953736	+	0.300645i	$0.902798\pi$
$390$	7.48052	+	8.13596i	0.378791	+	0.411980i
$391$	0.293621	+	0.903672i	0.0148490	+	0.0457006i
$392$	−52.6444	+	48.6886i	−2.65894	+	2.45915i
$393$		−	3.71550i		−	0.187422i
$394$	−24.9584	−	11.1122i	−1.25738	−	0.559823i
$395$	33.4982	+	10.4999i	1.68548	+	0.528305i
$396$	30.7239	−	13.6792i	1.54393	−	0.687404i
$397$	0.681421	+	0.0716202i	0.0341995	+	0.00359452i	0.121613	−	0.992578i	$-0.461193\pi$
$397$	0.681421	+	0.0716202i	0.0341995	+	0.00359452i	−0.0874132	+	0.996172i	$0.527860\pi$
$398$	52.3038	+	16.9945i	2.62175	+	0.851860i
$399$	−5.38770	+	6.06452i	−0.269722	+	0.303606i
$400$	−77.0363	+	36.2395i	−3.85182	+	1.81197i
$401$	−7.49185	−	12.9763i	−0.374125	−	0.648004i	0.616071	−	0.787691i	$-0.288724\pi$
$401$	−7.49185	−	12.9763i	−0.374125	−	0.648004i	−0.990196	+	0.139687i	$0.955390\pi$
$402$	13.4938	−	12.1499i	0.673010	−	0.605981i
$403$	0.960049	+	2.15630i	0.0478234	+	0.107413i
$404$	2.30294	−	21.9110i	0.114575	−	1.09011i
$405$	−2.22613	−	0.210564i	−0.110617	−	0.0104630i
$406$	46.8989	−	21.2568i	2.32755	−	1.05495i
$407$		−	22.6992i		−	1.12516i
$408$	−4.42513	+	9.93900i	−0.219077	+	0.492054i
$409$	−8.72737	−	1.85506i	−0.431541	−	0.0917268i	−0.0129803	−	0.999916i	$-0.504132\pi$
$409$	−8.72737	−	1.85506i	−0.431541	−	0.0917268i	−0.418560	+	0.908189i	$0.637465\pi$
$410$	14.2241	+	42.2744i	0.702479	+	2.08778i
$411$	2.36425	−	0.502536i	0.116620	−	0.0247883i
$412$	−44.4935	+	14.4568i	−2.19204	+	0.712237i
$413$	−1.73534	−	2.35528i	−0.0853904	−	0.115896i
$414$	−0.766829	+	2.36006i	−0.0376876	+	0.115990i
$415$	0.817880	−	0.374396i	0.0401481	−	0.0183784i
$416$	46.6082	+	9.90688i	2.28516	+	0.485725i
$417$	6.30947	−	0.663152i	0.308976	−	0.0324747i
$418$	43.5064	−	25.1184i	2.12797	−	1.22858i
$419$	−0.413755	+	0.300611i	−0.0202133	+	0.0146858i	−0.597846	−	0.801611i	$-0.703977\pi$
$419$	−0.413755	+	0.300611i	−0.0202133	+	0.0146858i	0.577633	+	0.816297i	$0.303977\pi$
$420$	−33.5527	−	2.94795i	−1.63720	−	0.143845i
$421$	23.1072	+	16.7884i	1.12618	+	0.818214i	0.985134	−	0.171789i	$-0.0549549\pi$
$421$	23.1072	+	16.7884i	1.12618	+	0.818214i	0.141042	+	0.990004i	$0.454955\pi$
$422$	32.1922	+	3.38354i	1.56709	+	0.164708i
$423$	−5.50125	+	4.95335i	−0.267480	+	0.240840i
$424$	14.9866	−	25.9576i	0.727814	−	1.26061i
$425$	−5.08341	−	1.53543i	−0.246582	−	0.0744792i
$426$	9.12803			0.442254
$427$	−30.8765	−	17.5530i	−1.49422	−	0.849447i
$428$	−17.8192	+	24.5260i	−0.861322	+	1.18551i
$429$	1.10034	−	10.4690i	0.0531250	−	0.505450i
$430$	0.205874	+	19.7701i	0.00992812	+	0.953400i
$431$	−2.34285	−	22.2908i	−0.112851	−	1.07371i	−0.893600	−	0.448864i	$-0.851829\pi$
$431$	−2.34285	−	22.2908i	−0.112851	−	1.07371i	0.780749	−	0.624845i	$-0.214838\pi$
$432$	−14.7457	+	8.51346i	−0.709455	+	0.409604i
$433$	16.1763	+	22.2647i	0.777382	+	1.06997i	0.995566	+	0.0940663i	$0.0299866\pi$
$433$	16.1763	+	22.2647i	0.777382	+	1.06997i	−0.218184	+	0.975908i	$0.570013\pi$
$434$	−8.90603	−	3.89424i	−0.427503	−	0.186929i
$435$	14.3989	+	6.23197i	0.690375	+	0.298800i
$436$	8.23242	−	1.74986i	0.394262	−	0.0838029i
$437$	−0.570324	+	2.68317i	−0.0272823	+	0.128353i
$438$	3.97531	−	18.7024i	0.189948	−	0.893633i
$439$	19.4158	−	4.12695i	0.926665	−	0.196969i	0.280226	−	0.959934i	$-0.409591\pi$
$439$	19.4158	−	4.12695i	0.926665	−	0.196969i	0.646439	+	0.762965i	$0.276257\pi$
$440$	124.180	+	53.7463i	5.92006	+	2.56225i
$441$	−5.71751	−	4.03857i	−0.272262	−	0.192313i
$442$	3.08552	+	4.24685i	0.146763	+	0.202002i
$443$	33.1499	−	19.1391i	1.57500	−	0.909326i	0.579456	−	0.815003i	$-0.303265\pi$
$443$	33.1499	−	19.1391i	1.57500	−	0.909326i	0.995542	−	0.0943223i	$-0.0300684\pi$
$444$	2.28678	+	21.7572i	0.108526	+	1.03255i
$445$	−0.319056	−	30.6390i	−0.0151247	−	1.45243i
$446$	−6.35320	+	60.4467i	−0.300833	+	2.86223i
$447$	3.00054	−	4.12989i	0.141921	−	0.195337i
$448$	−91.5523	+	53.6753i	−4.32544	+	2.53592i
$449$	4.52594			0.213592			0.106796	−	0.994281i	$-0.465941\pi$
$449$	4.52594			0.213592			0.106796	+	0.994281i	$0.465941\pi$
$450$	−8.38351	−	11.0476i	−0.395202	−	0.520788i
$451$	21.2412	−	36.7908i	1.00021	−	1.73241i
$452$	−0.169156	+	0.152309i	−0.00795642	+	0.00716399i
$453$	3.18311	+	0.334558i	0.149556	+	0.0157189i
$454$	−30.0982	−	21.8676i	−1.41258	−	1.02630i
$455$	−6.05011	+	8.63368i	−0.283634	+	0.404753i
$456$	−25.4102	+	18.4616i	−1.18994	+	0.864545i
$457$	11.7532	−	6.78574i	0.549794	−	0.317424i	−0.199245	−	0.979950i	$-0.563849\pi$
$457$	11.7532	−	6.78574i	0.549794	−	0.317424i	0.749039	+	0.662526i	$0.230516\pi$
$458$	−82.1738	+	8.63681i	−3.83973	+	0.403572i
$459$	−1.03884	−	0.220812i	−0.0484889	−	0.0103066i
$460$	−10.3561	+	4.74066i	−0.482856	+	0.221034i
$461$	9.65979	−	29.7298i	0.449901	−	1.38465i	−0.427117	−	0.904196i	$-0.640471\pi$
$461$	9.65979	−	29.7298i	0.449901	−	1.38465i	0.877018	−	0.480457i	$-0.159529\pi$
$462$	25.7138	+	34.9001i	1.19632	+	1.62370i
$463$	2.61420	−	0.849405i	0.121492	−	0.0394752i	−0.247640	−	0.968852i	$-0.579655\pi$
$463$	2.61420	−	0.849405i	0.121492	−	0.0394752i	0.369132	+	0.929377i	$0.379655\pi$
$464$	116.861	−	24.8396i	5.42513	−	1.15315i
$465$	−0.944528	−	2.80716i	−0.0438014	−	0.130179i
$466$	−2.87440	−	0.610973i	−0.133154	−	0.0283028i
$467$	10.1107	−	22.7090i	0.467868	−	1.05085i	−0.513391	−	0.858155i	$-0.671611\pi$
$467$	10.1107	−	22.7090i	0.467868	−	1.05085i	0.981259	−	0.192694i	$-0.0617224\pi$
$468$			10.1455i			0.468975i
$469$	14.0800	+	10.0869i	0.650154	+	0.465769i
$470$	−45.7083	−	4.32342i	−2.10836	−	0.199425i
$471$	0.196095	−	1.86572i	0.00903558	−	0.0859678i
$472$	−4.60721	−	10.3480i	−0.212064	−	0.476304i
$473$	13.9942	−	12.6005i	0.643455	−	0.579370i
$474$	21.7727	+	37.7114i	1.00005	+	1.73214i
$475$	−10.4930	−	11.1766i	−0.481454	−	0.512817i
$476$	−15.6699	−	3.22163i	−0.718228	−	0.147663i
$477$	2.78273	+	0.904164i	0.127412	+	0.0413988i
$478$	1.62330	+	0.170616i	0.0742481	+	0.00780379i
$479$	−12.6049	+	5.61208i	−0.575934	+	0.256422i	−0.673968	−	0.738761i	$-0.735411\pi$
$479$	−12.6049	+	5.61208i	−0.575934	+	0.256422i	0.0980338	+	0.995183i	$0.468745\pi$
$480$	−57.0536	−	17.8832i	−2.60413	−	0.816254i
$481$	6.25556	+	2.78515i	0.285229	+	0.126992i
$482$			4.99698i			0.227606i
$483$	−2.35569	−	0.231715i	−0.107188	−	0.0105434i
$484$	−42.0395	−	129.384i	−1.91089	−	5.88111i
$485$	−10.8393	−	11.7891i	−0.492188	−	0.535314i
$486$	−1.85595	−	2.06124i	−0.0841877	−	0.0934999i
$487$	0.554581	−	2.60910i	0.0251305	−	0.118230i	−0.963794	−	0.266646i	$-0.914084\pi$
$487$	0.554581	−	2.60910i	0.0251305	−	0.118230i	0.988925	+	0.148417i	$0.0474177\pi$
$488$	−102.195	−	92.0170i	−4.62616	−	4.16541i
$489$	5.55426	−	17.0943i	0.251172	−	0.773029i
$490$	−5.56242	−	43.0571i	−0.251284	−	1.94512i
$491$	−6.77214	−	20.8425i	−0.305622	−	0.940609i	−0.979444	−	0.201715i	$-0.935349\pi$
$491$	−6.77214	−	20.8425i	−0.305622	−	0.940609i	0.673822	−	0.738894i	$-0.264651\pi$
$492$	−16.6533	+	37.4040i	−0.750791	+	1.68630i
$493$	6.45362	+	3.72600i	0.290657	+	0.167811i
$494$	1.58410	+	15.0717i	0.0712720	+	0.678108i
$495$	−2.61161	+	12.9482i	−0.117383	+	0.581979i
$496$	−18.2459	−	13.2564i	−0.819263	−	0.595229i
$497$	1.86707	+	8.50449i	0.0837496	+	0.381479i
$498$	1.06115	+	0.344790i	0.0475514	+	0.0154504i
$499$	10.5793	+	18.3239i	0.473596	+	0.820292i	0.999543	−	0.0302253i	$-0.00962246\pi$
$499$	10.5793	+	18.3239i	0.473596	+	0.820292i	−0.525947	+	0.850517i	$0.676289\pi$
$500$	11.2830	−	62.6449i	0.504592	−	2.80156i
$501$	10.9866	−	19.0294i	0.490847	−	0.850172i
$502$	1.31249	+	6.17478i	0.0585793	+	0.275594i
$503$	19.5034	−	26.8442i	0.869616	−	1.19692i	−0.109574	−	0.993979i	$-0.534949\pi$
$503$	19.5034	−	26.8442i	0.869616	−	1.19692i	0.979190	−	0.202945i	$-0.0650512\pi$
$504$	−18.2694	−	20.0200i	−0.813785	−	0.891763i
$505$	6.49042	+	5.72275i	0.288820	+	0.254659i
$506$	13.3915	+	5.96229i	0.595326	+	0.265056i
$507$	−8.50822	−	4.91223i	−0.377864	−	0.218160i
$508$	93.9620	−	9.87580i	4.16889	−	0.438168i
$509$	−7.30323	+	8.11106i	−0.323710	+	0.359516i	−0.882931	−	0.469502i	$-0.844433\pi$
$509$	−7.30323	+	8.11106i	−0.323710	+	0.359516i	0.559221	+	0.829018i	$0.311100\pi$
$510$	−3.35270	−	5.66987i	−0.148460	−	0.251066i
$511$	18.2379	−	0.121673i	0.806798	−	0.00538250i
$512$	−101.230	+	32.8916i	−4.47378	+	1.45362i
$513$	−2.27854	−	2.05160i	−0.100600	−	0.0905805i
$514$	−39.8590	−	44.2679i	−1.75811	−	1.95257i
$515$	5.49572	−	17.5333i	0.242171	−	0.772608i
$516$	−12.1441	+	13.4874i	−0.534615	+	0.593750i
$517$	25.7034	+	35.3777i	1.13043	+	1.55591i
$518$	−26.7600	+	8.89265i	−1.17577	+	0.390720i
$519$	−5.81476	+	4.22467i	−0.255240	+	0.185442i
$520$	−30.0484	+	27.6277i	−1.31771	+	1.21155i
$521$	10.9669	−	4.88280i	0.480471	−	0.213919i	−0.152186	−	0.988352i	$-0.548631\pi$
$521$	10.9669	−	4.88280i	0.480471	−	0.213919i	0.632656	+	0.774433i	$0.281965\pi$
$522$	7.91586	+	17.7793i	0.346468	+	0.778180i
$523$	1.36476	+	6.42071i	0.0596770	+	0.280758i	0.997860	−	0.0653803i	$-0.0208261\pi$
$523$	1.36476	+	6.42071i	0.0596770	+	0.280758i	−0.938183	+	0.346139i	$0.887493\pi$
$524$	21.1534			0.924091
$525$	8.57813	−	10.0705i	0.374380	−	0.439514i
$526$	27.3559			1.19277
$527$	−0.292478	−	1.37600i	−0.0127406	−	0.0599396i
$528$	40.9103	+	91.8861i	1.78039	+	3.99883i
$529$	20.2803	−	9.02938i	0.881753	−	0.392582i
$530$	7.55329	+	16.5004i	0.328094	+	0.716731i
$531$	0.894569	−	0.649943i	0.0388210	−	0.0282051i
$532$	−34.5270	−	30.6737i	−1.49694	−	1.32987i
$533$	7.53275	+	10.3679i	0.326280	+	0.449085i
$534$	25.4320	−	28.2451i	1.10055	−	1.22228i
$535$	−3.79708	−	11.2850i	−0.164162	−	0.487893i
$536$	44.8730	+	49.8365i	1.93822	+	2.15261i
$537$	3.56404	+	3.20908i	0.153800	+	0.138482i
$538$	79.9500	−	25.9773i	3.44689	−	1.11996i
$539$	−27.2565	+	31.0959i	−1.17402	+	1.33940i
$540$	1.19880	−	12.6740i	0.0515881	−	0.545402i
$541$	−6.49877	+	7.21762i	−0.279404	+	0.310310i	−0.866470	−	0.499230i	$-0.833616\pi$
$541$	−6.49877	+	7.21762i	−0.279404	+	0.310310i	0.587066	+	0.809539i	$0.300283\pi$
$542$	−12.3125	+	1.29410i	−0.528869	+	0.0555863i
$543$	7.91058	+	4.56718i	0.339476	+	0.195996i
$544$	−25.9431	−	11.5506i	−1.11230	−	0.495229i
$545$	−1.31298	+	3.03362i	−0.0562417	+	0.129946i
$546$	−12.7730	+	2.80417i	−0.546634	+	0.120008i
$547$	−10.0894	+	13.8869i	−0.431392	+	0.593760i	−0.968272	−	0.249898i	$-0.919603\pi$
$547$	−10.0894	+	13.8869i	−0.431392	+	0.593760i	0.536880	+	0.843659i	$0.319603\pi$
$548$	2.86108	+	13.4603i	0.122219	+	0.574997i
$549$	6.71210	−	11.6257i	0.286465	−	0.496173i
$550$	−70.0796	+	42.4304i	−2.98820	+	1.80924i
$551$	10.7568	+	18.6313i	0.458254	+	0.793719i
$552$	−8.71636	−	2.83212i	−0.370993	−	0.120543i
$553$	−30.6819	+	27.9990i	−1.30473	+	1.19064i
$554$	17.1150	+	12.4348i	0.727146	+	0.528303i
$555$	−7.48552	−	4.21845i	−0.317743	−	0.179063i
$556$	3.77551	+	35.9216i	0.160117	+	1.52342i
$557$	−30.5138	−	17.6171i	−1.29291	−	0.746462i	−0.313742	−	0.949508i	$-0.601583\pi$
$557$	−30.5138	−	17.6171i	−1.29291	−	0.746462i	−0.979169	+	0.203046i	$0.934916\pi$
$558$	1.49431	−	3.35627i	0.0632591	−	0.142082i
$559$	1.75543	+	5.40266i	0.0742468	+	0.228508i
$560$	8.81645	−	100.346i	0.372563	−	4.24039i
$561$	−1.93870	+	5.96669i	−0.0818518	+	0.251914i
$562$	−25.1241	−	22.6219i	−1.05980	−	0.954246i
$563$	0.530110	−	2.49397i	0.0223415	−	0.105108i	−0.965564	−	0.260166i	$-0.916223\pi$
$563$	0.530110	−	2.49397i	0.0223415	−	0.105108i	0.987905	+	0.155057i	$0.0495562\pi$
$564$	−28.2008	−	31.3202i	−1.18747	−	1.31882i
$565$	−0.0102701	−	0.0888077i	−0.000432066	−	0.00373617i
$566$	8.64383	+	26.6030i	0.363327	+	1.11821i
$567$	1.54082	−	2.15078i	0.0647083	−	0.0903245i
$568$			33.7124i			1.41454i
$569$	6.43700	+	2.86594i	0.269853	+	0.120146i	0.537202	−	0.843453i	$-0.319481\pi$
$569$	6.43700	+	2.86594i	0.269853	+	0.120146i	−0.267349	+	0.963600i	$0.586148\pi$
$570$	−0.198012	−	19.0152i	−0.00829382	−	0.796458i
$571$	−32.2454	+	14.3566i	−1.34943	+	0.600804i	−0.948928	−	0.315492i	$-0.897830\pi$
$571$	−32.2454	+	14.3566i	−1.34943	+	0.600804i	−0.400500	+	0.916297i	$0.631164\pi$
$572$	59.6033	+	6.26456i	2.49214	+	0.261934i
$573$	−16.2387	−	5.27626i	−0.678380	−	0.220419i
$574$	−51.6940	−	10.6280i	−2.15767	−	0.443603i
$575$	0.838736	−	4.39399i	0.0349777	−	0.183242i
$576$	−20.0560	−	34.7381i	−0.835669	−	1.44742i
$577$	−15.6773	+	14.1159i	−0.652656	+	0.587654i	−0.927495	−	0.373836i	$-0.878042\pi$
$577$	−15.6773	+	14.1159i	−0.652656	+	0.587654i	0.274839	+	0.961490i	$0.411376\pi$
$578$	17.9062	+	40.2179i	0.744798	+	1.67284i
$579$	2.46946	−	23.4953i	0.102627	−	0.976432i
$580$	−35.4804	+	81.9771i	−1.47324	+	3.40391i
$581$	−0.104186	+	1.05919i	−0.00432237	+	0.0439426i
$582$		−	19.8651i		−	0.823436i
$583$	7.03010	−	15.7899i	0.291157	−	0.653950i
$584$	69.0731	+	14.6819i	2.85827	+	0.607543i
$585$	−3.24789	−	2.30845i	−0.134284	−	0.0954425i
$586$	−4.68108	+	0.994995i	−0.193374	+	0.0411029i
$587$	43.4984	−	14.1335i	1.79537	−	0.583351i	0.795622	−	0.605794i	$-0.207144\pi$
$587$	43.4984	−	14.1335i	1.79537	−	0.583351i	0.999748	+	0.0224425i	$0.00714427\pi$
$588$	22.9927	−	32.5514i	0.948204	−	1.34240i
$589$	1.25498	−	3.86242i	0.0517104	−	0.159148i
$590$	6.72262	+	1.35593i	0.276766	+	0.0558227i
$591$	9.63461	+	2.04790i	0.396315	+	0.0842394i
$592$	−65.0694	+	6.83907i	−2.67434	+	0.281084i
$593$	−20.8662	+	12.0471i	−0.856873	+	0.494716i	−0.862964	−	0.505266i	$-0.831395\pi$
$593$	−20.8662	+	12.0471i	−0.856873	+	0.494716i	0.00609089	+	0.999981i	$0.498061\pi$
$594$	−13.2555	+	9.63070i	−0.543881	+	0.395153i
$595$	4.59679	−	4.28341i	0.188450	−	0.175603i
$596$	23.5126	+	17.0829i	0.963114	+	0.699744i
$597$	−19.7190	−	2.07255i	−0.807046	−	0.0848240i
$598$	−3.28624	+	2.95894i	−0.134384	+	0.121000i
$599$	11.4686	−	19.8641i	0.468593	−	0.811627i	−0.530762	−	0.847521i	$-0.678094\pi$
$599$	11.4686	−	19.8641i	0.468593	−	0.811627i	0.999356	+	0.0358935i	$0.0114277\pi$
$600$	40.8018	−	30.9627i	1.66573	−	1.26405i
$601$	−7.20390			−0.293853			−0.146927	−	0.989147i	$-0.546938\pi$
$601$	−7.20390			−0.293853			−0.146927	+	0.989147i	$0.546938\pi$
$602$	−20.3370	−	11.5614i	−0.828875	−	0.471207i
$603$	−3.84790	+	5.29618i	−0.156699	+	0.215677i
$604$	−1.90474	+	18.1223i	−0.0775026	+	0.737388i
$605$	50.9856	+	15.9812i	2.07286	+	0.649729i
$606$	1.12195	+	10.6747i	0.0455763	+	0.433629i
$607$	18.1985	−	10.5069i	0.738654	−	0.426462i	−0.0829254	−	0.996556i	$-0.526426\pi$
$607$	18.1985	−	10.5069i	0.738654	−	0.426462i	0.821580	+	0.570093i	$0.193093\pi$
$608$	−48.1892	−	66.3268i	−1.95433	−	2.68991i
$609$	−14.9457	+	11.0118i	−0.605630	+	0.446219i
$610$	81.2546	−	18.1575i	3.28990	−	0.735177i
$611$	−12.9033	+	2.74269i	−0.522013	+	0.110957i
$612$	1.25715	−	5.91441i	0.0508171	−	0.239076i
$613$	−7.45996	+	35.0963i	−0.301305	+	1.41753i	0.523459	+	0.852051i	$0.324641\pi$
$613$	−7.45996	+	35.0963i	−0.301305	+	1.41753i	−0.824764	+	0.565477i	$0.808692\pi$
$614$	−24.3436	+	5.17439i	−0.982426	+	0.208821i
$615$	−8.18503	−	13.8420i	−0.330052	−	0.558163i
$616$	−128.896	+	94.9686i	−5.19336	+	3.82639i
$617$	−10.8278	−	14.9031i	−0.435909	−	0.599977i	0.533388	−	0.845871i	$-0.320919\pi$
$617$	−10.8278	−	14.9031i	−0.435909	−	0.599977i	−0.969297	+	0.245893i	$0.920919\pi$
$618$	19.7385	−	11.3960i	0.793999	−	0.458416i
$619$	2.08092	+	19.7987i	0.0836393	+	0.795775i	0.953280	+	0.302089i	$0.0976841\pi$
$619$	2.08092	+	19.7987i	0.0836393	+	0.795775i	−0.869640	+	0.493686i	$0.835649\pi$
$620$	15.9819	−	5.37747i	0.641850	−	0.215964i
$621$	0.0935179	−	0.889764i	0.00375275	−	0.0357050i
$622$	−30.8765	+	42.4978i	−1.23803	+	1.70401i
$623$	31.5176	+	17.9174i	1.26273	+	0.717846i
$624$	−30.3421			−1.21466
$625$	17.4874	+	17.8659i	0.699495	+	0.714638i
$626$	−39.2465	+	67.9769i	−1.56860	+	2.71690i
$627$	−13.4598	+	12.1193i	−0.537534	+	0.483998i
$628$	10.6221	+	1.11642i	0.423867	+	0.0445502i
$629$	−3.30163	−	2.39877i	−0.131645	−	0.0956454i
$630$	16.2877	−	1.99378i	0.648918	−	0.0794341i
$631$	−31.6753	+	23.0135i	−1.26098	+	0.916152i	−0.998805	−	0.0488694i	$-0.984438\pi$
$631$	−31.6753	+	23.0135i	−1.26098	+	0.916152i	−0.262170	+	0.965022i	$0.584438\pi$
$632$	−139.279	+	80.4127i	−5.54022	+	3.19865i
$633$	−11.6063	+	1.21987i	−0.461310	+	0.0484856i
$634$	59.6139	+	12.6713i	2.36757	+	0.503243i
$635$	−18.2180	+	32.3274i	−0.722961	+	1.28287i
$636$	−5.14766	+	15.8429i	−0.204118	+	0.628211i
$637$	−5.22524	−	11.3269i	−0.207032	−	0.448788i
$638$	109.339	−	35.5264i	4.32877	−	1.40650i
$639$	−3.21903	+	0.684227i	−0.127343	+	0.0270676i
$640$	38.6431	−	123.285i	1.52750	−	4.87326i
$641$	10.3764	+	2.20557i	0.409844	+	0.0871150i	0.408220	−	0.912884i	$-0.366150\pi$
$641$	10.3764	+	2.20557i	0.409844	+	0.0871150i	0.00162398	+	0.999999i	$0.499483\pi$
$642$	6.00724	−	13.4925i	0.237087	−	0.532506i
$643$		−	13.8928i		−	0.547880i	−0.961747	−	0.273940i	$-0.911673\pi$
$643$		−	13.8928i		−	0.547880i	0.961747	−	0.273940i	$-0.0883270\pi$
$644$	1.31922	−	13.4116i	0.0519845	−	0.528492i
$645$	−1.55455	−	6.95657i	−0.0612103	−	0.273915i
$646$	0.944098	−	8.98249i	0.0371450	−	0.353411i
$647$	−12.9124	−	29.0018i	−0.507639	−	1.14018i	−0.967658	−	0.252267i	$-0.918824\pi$
$647$	−12.9124	−	29.0018i	−0.507639	−	1.14018i	0.460018	−	0.887910i	$-0.347843\pi$
$648$	7.61276	−	6.85456i	0.299057	−	0.269272i
$649$	−3.26595	−	5.65680i	−0.128200	−	0.222049i
$650$	−3.09454	−	24.5191i	−0.121378	−	0.961716i
$651$	3.43265	+	0.705731i	0.134536	+	0.0276598i
$652$	97.3224	+	31.6220i	3.81144	+	1.23841i
$653$	17.2858	+	1.81681i	0.676446	+	0.0710973i	0.436521	−	0.899694i	$-0.356211\pi$
$653$	17.2858	+	1.81681i	0.676446	+	0.0710973i	0.239925	+	0.970791i	$0.422877\pi$
$654$	−3.74582	+	1.66774i	−0.146473	+	0.0652140i
$655$	−4.81313	+	6.77189i	−0.188065	+	0.264600i
$656$	−111.864	−	49.8052i	−4.36757	−	1.94457i
$657$			6.89344i			0.268939i
$658$	31.6370	−	44.1612i	1.23334	−	1.72158i
$659$	10.5900	+	32.5927i	0.412528	+	1.26963i	0.914443	+	0.404714i	$0.132629\pi$
$659$	10.5900	+	32.5927i	0.412528	+	1.26963i	−0.501915	+	0.864917i	$0.667371\pi$
$660$	−73.7178	−	14.8686i	−2.86946	−	0.578761i
$661$	0.658914	+	0.731798i	0.0256288	+	0.0284636i	0.755823	−	0.654776i	$-0.227237\pi$
$661$	0.658914	+	0.731798i	0.0256288	+	0.0284636i	−0.730194	+	0.683240i	$0.760570\pi$
$662$	7.52681	−	35.4108i	0.292538	−	1.37628i
$663$	−1.40646	−	1.26638i	−0.0546223	−	0.0491822i
$664$	−1.27341	+	3.91914i	−0.0494178	+	0.152092i
$665$	17.6757	−	4.07390i	0.685436	−	0.157979i
$666$	−3.29355	−	10.1365i	−0.127623	−	0.392782i
$667$	−2.55330	+	5.73482i	−0.0988644	+	0.222053i
$668$	108.340	+	62.5501i	4.19180	+	2.42014i
$669$	−2.29053	−	21.7930i	−0.0885572	−	0.842565i
$670$	−40.3331	+	4.66429i	−1.55820	+	0.180197i
$671$	−64.1549	−	46.6112i	−2.47667	−	1.79941i
$672$	52.2570	−	47.6875i	2.01586	−	1.83959i
$673$	−17.8880	−	5.81216i	−0.689532	−	0.224042i	−0.0567681	−	0.998387i	$-0.518080\pi$
$673$	−17.8880	−	5.81216i	−0.689532	−	0.224042i	−0.632764	+	0.774345i	$0.718080\pi$
$674$	−12.4293	−	21.5282i	−0.478759	−	0.829236i
$675$	3.78459	+	3.26755i	0.145669	+	0.125768i
$676$	27.9667	−	48.4397i	1.07564	−	1.86307i
$677$	8.81196	+	41.4570i	0.338671	+	1.59332i	0.736877	+	0.676026i	$0.236299\pi$
$677$	8.81196	+	41.4570i	0.338671	+	1.59332i	−0.398206	+	0.917296i	$0.630367\pi$
$678$	0.0651816	−	0.0897148i	0.00250328	−	0.00344548i
$679$	18.5082	−	4.06327i	0.710278	−	0.155934i
$680$	20.9404	−	12.3825i	0.803029	−	0.474846i
$681$	12.2534	+	5.45558i	0.469552	+	0.209058i
$682$	−18.7949	−	10.8513i	−0.719695	−	0.415516i
$683$	−15.8599	+	1.66694i	−0.606861	+	0.0637836i	−0.402975	−	0.915211i	$-0.632024\pi$
$683$	−15.8599	+	1.66694i	−0.606861	+	0.0637836i	−0.203886	+	0.978995i	$0.565357\pi$
$684$	11.6804	−	12.9724i	0.446610	−	0.496011i
$685$	−4.96008	−	2.14677i	−0.189515	−	0.0820238i
$686$	47.3369	+	19.9504i	1.80733	+	0.761710i
$687$	28.3315	−	9.20546i	1.08091	−	0.351210i
$688$	−40.3368	−	36.3194i	−1.53783	−	1.38466i
$689$	3.48887	+	3.87479i	0.132915	+	0.147618i
$690$	4.45489	−	3.30809i	0.169595	−	0.125937i
$691$	7.77213	−	8.63183i	0.295666	−	0.328370i	−0.576948	−	0.816781i	$-0.695757\pi$
$691$	7.77213	−	8.63183i	0.295666	−	0.328370i	0.872614	+	0.488411i	$0.162423\pi$
$692$	−24.0523	−	33.1051i	−0.914330	−	1.25847i
$693$	−11.6842	−	10.3802i	−0.443844	−	0.394310i
$694$	22.6257	−	16.4385i	0.858860	−	0.623999i
$695$	−12.3587	−	6.96475i	−0.468794	−	0.264188i
$696$	−65.6641	+	29.2355i	−2.48899	+	1.10817i
$697$	−3.10658	−	6.97750i	−0.117670	−	0.264291i
$698$	−14.0701	−	66.1944i	−0.532559	−	2.50549i
$699$	1.05947			0.0400727
$700$	57.3344	+	48.8377i	2.16704	+	1.84589i
$701$	−30.7205			−1.16030			−0.580148	−	0.814511i	$-0.697005\pi$
$701$	−30.7205			−1.16030			−0.580148	+	0.814511i	$0.697005\pi$
$702$	−1.02765	−	4.83470i	−0.0387861	−	0.182474i
$703$	−4.79206	−	10.7631i	−0.180736	−	0.405940i
$704$	−216.466	+	96.3767i	−8.15836	+	3.63233i
$705$	16.4433	−	1.90157i	0.619289	−	0.0716172i
$706$	−62.4485	+	45.3715i	−2.35028	+	1.70758i
$707$	−9.71601	+	3.22874i	−0.365408	+	0.121429i
$708$	3.70031	+	5.09304i	0.139066	+	0.191408i
$709$	30.4250	−	33.7903i	1.14263	−	1.26902i	0.184458	−	0.982840i	$-0.440947\pi$
$709$	30.4250	−	33.7903i	1.14263	−	1.26902i	0.958175	−	0.286182i	$-0.0923862\pi$
$710$	−16.6368	−	11.8246i	−0.624367	−	0.443770i
$711$	−10.5050	−	11.6670i	−0.393969	−	0.437547i
$712$	104.317	+	93.9275i	3.90945	+	3.52008i
$713$	1.12703	−	0.366196i	0.0422078	−	0.0137141i
$714$	7.79362	−	0.0519946i	0.291669	−	0.00194585i
$715$	−15.5673	+	17.6555i	−0.582184	+	0.660280i
$716$	−18.2702	+	20.2911i	−0.682789	+	0.758314i
$717$	−0.585252	+	0.0615125i	−0.0218567	+	0.00229723i
$718$	38.9546	+	22.4905i	1.45377	+	0.839337i
$719$	−23.8575	−	10.6221i	−0.889736	−	0.396136i	−0.0896160	−	0.995976i	$-0.528564\pi$
$719$	−23.8575	−	10.6221i	−0.889736	−	0.396136i	−0.800120	+	0.599841i	$0.795231\pi$
$720$	37.9042	+	3.58525i	1.41260	+	0.133614i
$721$	14.6549	+	16.0592i	0.545779	+	0.598076i
$722$	−15.6498	+	21.5401i	−0.582426	+	0.801640i
$723$	−0.374568	−	1.76220i	−0.0139303	−	0.0655370i
$724$	−26.0022	+	45.0372i	−0.966366	+	1.67379i
$725$	−18.1705	−	30.0110i	−0.674835	−	1.11458i
$726$	33.1389	+	57.3983i	1.22990	+	2.13025i
$727$	18.2676	+	5.93551i	0.677508	+	0.220136i	0.627504	−	0.778613i	$-0.284077\pi$
$727$	18.2676	+	5.93551i	0.677508	+	0.220136i	0.0500040	+	0.998749i	$0.484077\pi$
$728$	−10.3566	−	47.1743i	−0.383842	−	1.74840i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−31.4728	+	28.9373i	−1.16486	+	1.07102i
$731$	−0.353892	−	3.36706i	−0.0130892	−	0.124535i
$732$	66.1884	+	38.2139i	2.44639	+	1.41243i
$733$	8.40347	−	18.8745i	0.310389	−	0.697146i	−0.689235	−	0.724537i	$-0.742053\pi$
$733$	8.40347	−	18.8745i	0.310389	−	0.697146i	0.999625	+	0.0273916i	$0.00872012\pi$
$734$	1.13862	+	3.50431i	0.0420272	+	0.129346i
$735$	5.18912	+	14.7673i	0.191404	+	0.544700i
$736$	7.39250	−	22.7518i	0.272491	−	0.838641i
$737$	28.7384	+	25.8762i	1.05859	+	0.953161i
$738$	4.14725	−	19.5113i	0.152662	−	0.718220i
$739$	24.6295	+	27.3539i	0.906012	+	1.00623i	0.999943	+	0.0106491i	$0.00338979\pi$
$739$	24.6295	+	27.3539i	0.906012	+	1.00623i	−0.0939317	+	0.995579i	$0.529944\pi$
$740$	24.0169	−	42.6172i	0.882877	−	1.56664i
$741$	−1.68840	−	5.19635i	−0.0620248	−	0.190893i
$742$	−21.3687	−	2.10191i	−0.784471	−	0.0771636i
$743$			0.773807i			0.0283882i	0.999899	+	0.0141941i	$0.00451828\pi$
$743$			0.773807i			0.0283882i	−0.999899	+	0.0141941i	$0.995482\pi$
$744$	12.3957	+	5.51890i	0.454447	+	0.202333i
$745$	−10.8187	+	3.64020i	−0.396368	+	0.133366i
$746$	61.3128	−	27.2982i	2.24482	−	0.999458i
$747$	−0.400065	−	0.0420485i	−0.0146376	−	0.00153848i
$748$	−33.9701	−	11.0376i	−1.24207	−	0.403573i
$749$	13.7995	+	2.83710i	0.504224	+	0.103665i
$750$	0.968585	+	30.9955i	0.0353677	+	1.13180i
$751$	3.29980	+	5.71542i	0.120411	+	0.208559i	0.919930	−	0.392083i	$-0.128245\pi$
$751$	3.29980	+	5.71542i	0.120411	+	0.208559i	−0.799519	+	0.600641i	$0.794912\pi$
$752$	93.6693	−	84.3402i	3.41577	−	3.07557i
$753$	−0.925709	−	2.07918i	−0.0337347	−	0.0757694i
$754$	−3.62517	+	34.4912i	−0.132021	+	1.25610i
$755$	−5.36816	−	4.73323i	−0.195367	−	0.172260i
$756$	12.2450	+	8.77232i	0.445347	+	0.319046i
$757$		−	32.8389i		−	1.19355i	−0.802409	−	0.596774i	$-0.796449\pi$
$757$		−	32.8389i		−	1.19355i	0.802409	−	0.596774i	$-0.203551\pi$
$758$	−25.6919	+	57.7049i	−0.933171	+	2.09594i
$759$	−5.16950	−	1.09881i	−0.187641	−	0.0398843i
$760$	70.2284	−	0.731316i	2.54745	−	0.0265276i
$761$	23.5348	−	5.00248i	0.853136	−	0.181340i	0.239469	−	0.970904i	$-0.423027\pi$
$761$	23.5348	−	5.00248i	0.853136	−	0.181340i	0.613668	+	0.789564i	$0.289693\pi$
$762$	−43.7761	+	14.2237i	−1.58584	+	0.515271i
$763$	−2.32000	−	3.14882i	−0.0839897	−	0.113995i
$764$	30.0393	−	92.4514i	1.08678	−	3.34477i
$765$	1.60735	+	1.74819i	0.0581138	+	0.0632058i
$766$	58.5000	+	12.4346i	2.11369	+	0.449279i
$767$	1.95966	−	0.205968i	0.0707591	−	0.00743708i
$768$	69.3147	−	40.0189i	2.50118	−	1.44406i
$769$	−30.8364	+	22.4040i	−1.11199	+	0.807908i	−0.982976	−	0.183735i	$-0.941181\pi$
$769$	−30.8364	+	22.4040i	−1.11199	+	0.807908i	−0.129014	+	0.991643i	$0.541181\pi$
$770$	−1.65596	−	96.9192i	−0.0596768	−	3.49273i
$771$	17.3747	+	12.6235i	0.625735	+	0.454623i
$772$	133.766	+	14.0593i	4.81433	+	0.506006i
$773$	−35.7112	+	32.1545i	−1.28444	+	1.15652i	−0.305542	+	0.952179i	$0.598838\pi$
$773$	−35.7112	+	32.1545i	−1.28444	+	1.15652i	−0.978900	+	0.204339i	$0.934496\pi$
$774$	4.42097	−	7.65735i	0.158909	−	0.275238i
$775$	−1.91494	+	6.33990i	−0.0687868	+	0.227736i
$776$	73.3676			2.63374
$777$	8.77042	−	5.14192i	0.314637	−	0.184465i
$778$	−26.6727	+	36.7118i	−0.956262	+	1.31618i
$779$	2.30485	−	21.9292i	0.0825798	−	0.785695i
$780$	13.1426	−	18.4912i	0.470582	−	0.662091i
$781$	2.03207	+	19.3339i	0.0727133	+	0.691820i
$782$	2.28240	−	1.31774i	0.0816183	−	0.0471223i
$783$	−4.12428	−	5.67658i	−0.147390	−	0.202864i
$784$	97.3516	+	68.7644i	3.47684	+	2.45587i
$785$	−2.77429	+	3.14644i	−0.0990188	+	0.112301i
$786$	−10.0804	+	2.14266i	−0.359556	+	0.0764260i
$787$	10.8623	−	51.1031i	0.387199	−	1.82163i	−0.163039	−	0.986620i	$-0.552130\pi$
$787$	10.8623	−	51.1031i	0.387199	−	1.82163i	0.550238	−	0.835008i	$-0.314537\pi$
$788$	−11.6593	+	54.8526i	−0.415345	+	1.95404i
$789$	−9.64717	+	2.05057i	−0.343448	+	0.0730022i
$790$	9.16908	−	96.9377i	0.326221	−	3.44889i
$791$	0.0969188	+	0.0423786i	0.00344604	+	0.00150681i
$792$	−35.5689	−	48.9564i	−1.26389	−	1.73959i
$793$	20.7171	−	11.9610i	0.735685	−	0.424748i
$794$	−0.198651	−	1.89004i	−0.00704987	−	0.0670750i
$795$	−3.90055	−	5.25274i	−0.138338	−	0.186295i
$796$	11.7996	−	112.266i	0.418227	−	3.97917i
$797$	−31.1243	+	42.8390i	−1.10248	+	1.51743i	−0.270425	+	0.962741i	$0.587164\pi$
$797$	−31.1243	+	42.8390i	−1.10248	+	1.51743i	−0.832055	+	0.554693i	$0.812836\pi$
$798$	19.5604	+	11.1199i	0.692431	+	0.393640i
$799$	7.86198			0.278137
$800$	80.8199	+	106.502i	2.85742	+	3.76543i
$801$	−6.85146	+	11.8671i	−0.242085	+	0.419303i
$802$	−30.8851	+	27.8090i	−1.09059	+	0.981971i
$803$	40.4980	+	4.25651i	1.42914	+	0.150209i
$804$	−30.1527	−	21.9072i	−1.06340	−	0.772608i
$805$	3.99333	+	3.47393i	0.140746	+	0.122440i
$806$	5.29656	−	3.84817i	0.186563	−	0.135546i
$807$	−26.2474	+	15.1540i	−0.923953	+	0.533445i
$808$	−39.4246	+	4.14370i	−1.38695	+	0.145775i
$809$	−12.4133	−	2.63852i	−0.436428	−	0.0927656i	−0.0155419	−	0.999879i	$-0.504947\pi$
$809$	−12.4133	−	2.63852i	−0.436428	−	0.0927656i	−0.420886	+	0.907114i	$0.638281\pi$
$810$	0.712492	+	6.16107i	0.0250344	+	0.216478i
$811$	−4.30210	+	13.2405i	−0.151067	+	0.464937i	−0.997741	−	0.0671750i	$-0.978601\pi$
$811$	−4.30210	+	13.2405i	−0.151067	+	0.464937i	0.846674	+	0.532112i	$0.178601\pi$
$812$	−62.6931	−	85.0900i	−2.20010	−	2.98607i
$813$	4.24506	−	1.37930i	0.148881	−	0.0483743i
$814$	−61.5843	+	13.0902i	−2.15853	+	0.458810i
$815$	−32.2674	+	23.9610i	−1.13028	+	0.839316i
$816$	17.6882	+	3.75975i	0.619212	+	0.131618i
$817$	3.97546	−	8.92904i	0.139084	−	0.312388i
$818$			24.7477i			0.865283i
$819$	4.29425	−	1.94635i	0.150053	−	0.0680110i
$820$	78.8064	−	46.5997i	2.75204	−	1.62733i
$821$	0.550330	−	5.23604i	0.0192066	−	0.182739i	−0.980713	−	0.195456i	$-0.937381\pi$
$821$	0.550330	−	5.23604i	0.0192066	−	0.182739i	0.999919	+	0.0127169i	$0.00404804\pi$
$822$	−2.72683	−	6.12456i	−0.0951091	−	0.213618i
$823$	−4.78461	+	4.30808i	−0.166781	+	0.150170i	−0.748295	−	0.663366i	$-0.769127\pi$
$823$	−4.78461	+	4.30808i	−0.166781	+	0.150170i	0.581514	+	0.813536i	$0.302461\pi$
$824$	42.0888	+	72.8999i	1.46623	+	2.53959i
$825$	21.5333	−	20.2163i	0.749693	−	0.703842i
$826$	−5.38930	+	6.06633i	−0.187518	+	0.211075i
$827$	30.2452	+	9.82725i	1.05173	+	0.341727i	0.783346	−	0.621586i	$-0.213511\pi$
$827$	30.2452	+	9.82725i	1.05173	+	0.341727i	0.268381	+	0.963313i	$0.413511\pi$
$828$	5.06568	+	0.532424i	0.176044	+	0.0185030i
$829$	16.1107	−	7.17296i	0.559549	−	0.249127i	−0.107419	−	0.994214i	$-0.534259\pi$
$829$	16.1107	−	7.17296i	0.559549	−	0.249127i	0.666968	+	0.745087i	$0.267592\pi$
$830$	−1.48742	−	2.00306i	−0.0516290	−	0.0695271i
$831$	−6.96776	−	3.10225i	−0.241709	−	0.107616i
$832$		−	71.4800i		−	2.47812i
$833$	1.64257	+	7.25061i	0.0569117	+	0.251219i
$834$	−5.43772	−	16.7356i	−0.188293	−	0.579506i
$835$	−44.6754	+	20.4508i	−1.54606	+	0.707730i
$836$	−68.9985	−	76.6306i	−2.38636	−	2.65033i
$837$	−0.275391	+	1.29561i	−0.00951890	+	0.0447829i
$838$	1.05418	+	0.949189i	0.0364161	+	0.0327892i
$839$	14.4676	−	44.5267i	0.499477	−	1.53723i	−0.310384	−	0.950611i	$-0.600458\pi$
$839$	14.4676	−	44.5267i	0.499477	−	1.53723i	0.809861	−	0.586622i	$-0.199542\pi$
$840$	7.36360	+	60.1552i	0.254068	+	2.07555i
$841$	6.25240	+	19.2429i	0.215600	+	0.663549i
$842$	32.2225	−	72.3728i	1.11046	−	2.49413i
$843$	10.5558	+	6.09441i	0.363562	+	0.209903i
$844$	−6.94509	−	66.0781i	−0.239060	−	2.27450i
$845$	9.14374	+	19.9748i	0.314554	+	0.687153i
$846$	16.6112	+	12.0688i	0.571105	+	0.414932i
$847$	−46.6991	+	42.6156i	−1.60460	+	1.46429i
$848$	−47.3813	−	15.3951i	−1.62708	−	0.528671i
$849$	−5.04241	−	8.73370i	−0.173055	−	0.299740i
$850$	−1.23421	+	14.6771i	−0.0423331	+	0.503420i
$851$	1.71892	−	2.97727i	0.0589240	−	0.102059i
$852$	−3.89550	−	18.3269i	−0.133457	−	0.627868i
$853$	17.2020	−	23.6765i	0.588984	−	0.810666i	−0.405661	−	0.914024i	$-0.632959\pi$
$853$	17.2020	−	23.6765i	0.588984	−	0.810666i	0.994644	+	0.103357i	$0.0329585\pi$
$854$	−29.8165	+	93.8924i	−1.02030	+	3.21293i
$855$	1.49518	+	6.69093i	0.0511342	+	0.228825i
$856$	49.8315	+	22.1864i	1.70321	+	0.758317i
$857$	−21.5081	−	12.4177i	−0.734702	−	0.424180i	0.0854378	−	0.996344i	$-0.472771\pi$
$857$	−21.5081	−	12.4177i	−0.734702	−	0.424180i	−0.820140	+	0.572163i	$0.806104\pi$
$858$	−29.0378	+	3.05199i	−0.991333	+	0.104193i
$859$	−7.60433	+	8.44546i	−0.259456	+	0.288155i	−0.858773	−	0.512357i	$-0.828773\pi$
$859$	−7.60433	+	8.44546i	−0.259456	+	0.288155i	0.599316	+	0.800512i	$0.295439\pi$
$860$	39.6058	−	8.85048i	1.35054	−	0.301799i
$861$	19.0268	−	0.126936i	0.648430	−	0.00432596i
$862$	−59.1252	+	19.2110i	−2.01381	+	0.654328i
$863$	−10.8556	−	9.77445i	−0.369530	−	0.332726i	0.463355	−	0.886173i	$-0.346646\pi$
$863$	−10.8556	−	9.77445i	−0.369530	−	0.332726i	−0.832885	+	0.553447i	$0.813312\pi$
$864$	17.8920	+	19.8711i	0.608699	+	0.676029i
$865$	16.0707	−	0.167351i	0.546421	−	0.00569010i
$866$	51.0771	−	56.7269i	1.73567	−	1.92766i
$867$	−9.32936	−	12.8408i	−0.316842	−	0.436095i
$868$	−4.01793	+	19.5431i	−0.136377	+	0.663335i
$869$	−75.0287	+	54.5115i	−2.54517	+	1.84918i
$870$	8.60419	−	42.6590i	0.291709	−	1.44628i
$871$	−10.6572	+	4.74491i	−0.361107	+	0.160775i
$872$	−6.15946	−	13.8344i	−0.208585	−	0.468491i
$873$	1.48907	+	7.00551i	0.0503973	+	0.237101i
$874$	7.60850			0.257361
$875$	−28.6801	+	7.24233i	−0.969565	+	0.244835i
$876$	−39.2463			−1.32601
$877$	11.1897	+	52.6433i	0.377849	+	1.77764i	0.597302	+	0.802016i	$0.296239\pi$
$877$	11.1897	+	52.6433i	0.377849	+	1.77764i	−0.219453	+	0.975623i	$0.570427\pi$
$878$	−22.3934	−	50.2964i	−0.755740	−	1.69742i
$879$	1.57622	−	0.701778i	0.0531645	−	0.0236704i
$880$	44.4677	−	220.468i	1.49900	−	7.43197i
$881$	29.9817	−	21.7830i	1.01011	−	0.733888i	0.0458778	−	0.998947i	$-0.485392\pi$
$881$	29.9817	−	21.7830i	1.01011	−	0.733888i	0.964232	+	0.265059i	$0.0853915\pi$
$882$	−7.65974	+	17.8409i	−0.257917	+	0.600736i
$883$	2.09491	+	2.88340i	0.0704994	+	0.0970342i	0.842811	−	0.538210i	$-0.180899\pi$
$883$	2.09491	+	2.88340i	0.0704994	+	0.0970342i	−0.772311	+	0.635244i	$0.780899\pi$
$884$	7.20987	−	8.00737i	0.242494	−	0.269317i
$885$	−2.47239	+	0.0257460i	−0.0831086	+	0.000865443i
$886$	−71.0425	−	78.9007i	−2.38672	−	2.65072i
$887$	−29.5996	−	26.6516i	−0.993856	−	0.894872i	0.000602665	−	1.00000i	$-0.499808\pi$
$887$	−29.5996	−	26.6516i	−0.993856	−	0.894872i	−0.994459	+	0.105128i	$0.966475\pi$
$888$	37.4370	−	12.1640i	1.25630	−	0.408198i
$889$	−22.2062	−	37.8764i	−0.744771	−	1.27033i
$890$	−82.9417	+	18.5345i	−2.78021	+	0.621279i
$891$	3.95270	−	4.38992i	0.132421	−	0.147068i
$892$	124.074	−	13.0407i	4.15429	−	0.436634i
$893$	19.6563	+	11.3486i	0.657772	+	0.379765i
$894$	−12.9350	−	5.75903i	−0.432611	−	0.192611i
$895$	−2.33874	−	10.4658i	−0.0781753	−	0.349833i
$896$	103.046	+	112.920i	3.44252	+	3.77239i
$897$	0.937105	−	1.28981i	0.0312890	−	0.0430657i
$898$	−2.61002	−	12.2792i	−0.0870974	−	0.409761i
$899$	4.64697	−	8.04878i	0.154985	−	0.268442i
$900$	−18.6031	+	21.5467i	−0.620103	+	0.718225i
$901$	−1.55374	−	2.69116i	−0.0517626	−	0.0896555i
$902$	−112.065	−	36.4122i	−3.73137	−	1.21239i
$903$	8.03855	+	2.55272i	0.267506	+	0.0849493i
$904$	0.331342	+	0.240734i	0.0110203	+	0.00800670i
$905$	−8.50146	−	18.5717i	−0.282598	−	0.617344i
$906$	−0.927956	−	8.82892i	−0.0308293	−	0.293321i
$907$	4.05096	+	2.33882i	0.134510	+	0.0776593i	0.565745	−	0.824580i	$-0.308589\pi$
$907$	4.05096	+	2.33882i	0.134510	+	0.0776593i	−0.431235	+	0.902240i	$0.641922\pi$
$908$	−31.0602	+	69.7623i	−1.03077	+	2.31514i
$909$	−1.19582	−	3.68037i	−0.0396630	−	0.122070i
$910$	26.9127	+	11.4355i	0.892147	+	0.379083i
$911$	10.3322	−	31.7991i	0.342320	−	1.05355i	−0.620683	−	0.784062i	$-0.713145\pi$
$911$	10.3322	−	31.7991i	0.342320	−	1.05355i	0.963003	−	0.269491i	$-0.0868555\pi$
$912$	38.7965	+	34.9325i	1.28468	+	1.15673i
$913$	−0.494059	+	2.32436i	−0.0163510	+	0.0769252i
$914$	−25.1880	−	27.9741i	−0.833146	−	0.925302i
$915$	−27.2937	+	12.4941i	−0.902301	+	0.413041i
$916$	52.4093	+	161.299i	1.73165	+	5.32948i
$917$	−4.05816	−	8.95355i	−0.134012	−	0.295672i
$918$			2.94578i			0.0972251i
$919$	10.6585	+	4.74545i	0.351590	+	0.156538i	0.574930	−	0.818203i	$-0.305029\pi$
$919$	10.6585	+	4.74545i	0.351590	+	0.156538i	−0.223340	+	0.974741i	$0.571696\pi$
$920$	12.2177	+	16.4532i	0.402806	+	0.542445i
$921$	8.19698	−	3.64953i	0.270100	−	0.120256i
$922$	−86.2294	−	9.06308i	−2.83981	−	0.298477i
$923$	−5.57746	−	1.81223i	−0.183584	−	0.0596502i
$924$	59.0972	−	66.5212i	1.94415	−	2.18839i
$925$	8.17847	+	17.3855i	0.268907	+	0.571630i
$926$	−3.81205	−	6.60266i	−0.125272	−	0.216977i
$927$	−6.10663	+	5.49843i	−0.200568	+	0.180592i
$928$	−76.3117	−	171.399i	−2.50505	−	5.62644i
$929$	−0.583508	+	5.55171i	−0.0191443	+	0.182146i	−0.999915	−	0.0130165i	$-0.995857\pi$
$929$	−0.583508	+	5.55171i	−0.0191443	+	0.182146i	0.980771	+	0.195162i	$0.0625233\pi$
$930$	−7.07131	+	4.18140i	−0.231877	+	0.137113i
$931$	−6.35935	+	20.4987i	−0.208419	+	0.671819i
$932$			6.03184i			0.197579i
$933$	7.70312	−	17.3015i	0.252189	−	0.566425i
$934$	−67.4417	−	14.3352i	−2.20676	−	0.469061i
$935$	11.2629	−	8.36350i	0.368335	−	0.273516i
$936$	17.8559	−	3.79539i	0.583639	−	0.124056i
$937$	−16.4983	+	5.36061i	−0.538975	+	0.175123i	−0.565839	−	0.824516i	$-0.691448\pi$
$937$	−16.4983	+	5.36061i	−0.538975	+	0.175123i	0.0268646	+	0.999639i	$0.491448\pi$
$938$	19.2467	−	44.0168i	0.628428	−	1.43720i
$939$	8.74495	−	26.9142i	0.285381	−	0.878311i
$940$	10.8262	+	93.6162i	0.353111	+	3.05342i
$941$	25.1224	+	5.33993i	0.818966	+	0.174077i	0.598299	−	0.801273i	$-0.295843\pi$
$941$	25.1224	+	5.33993i	0.818966	+	0.174077i	0.220667	+	0.975349i	$0.429177\pi$
$942$	−5.17490	+	0.543904i	−0.168607	+	0.0177214i
$943$	5.57207	−	3.21703i	0.181451	−	0.104761i
$944$	−15.2318	+	11.0665i	−0.495751	+	0.360185i
$945$	−5.59447	+	1.92402i	−0.181988	+	0.0625885i
$946$	−42.2561	−	30.7008i	−1.37386	−	0.998170i
$947$	32.1605	+	3.38021i	1.04508	+	0.109842i	0.611476	−	0.791263i	$-0.290576\pi$
$947$	32.1605	+	3.38021i	1.04508	+	0.109842i	0.433600	+	0.901105i	$0.357243\pi$
$948$	66.4236	−	59.8081i	2.15734	−	1.94248i
$949$	−6.14208	+	10.6384i	−0.199380	+	0.345337i
$950$	−24.2717	+	34.9136i	−0.787478	+	1.13275i
$951$	−21.9729			−0.712520
$952$	0.192031	+	28.7841i	0.00622376	+	0.932896i
$953$	−29.3999	+	40.4654i	−0.952355	+	1.31080i	−0.00188128	+	0.999998i	$0.500599\pi$
$953$	−29.3999	+	40.4654i	−0.952355	+	1.31080i	−0.950473	+	0.310806i	$0.899401\pi$
$954$	0.848311	−	8.07114i	0.0274651	−	0.261313i
$955$	22.7617	+	30.6524i	0.736551	+	0.991890i
$956$	−0.350208	−	3.33201i	−0.0113265	−	0.107765i
$957$	−35.8958	+	20.7244i	−1.16035	+	0.669926i
$958$	22.4949	+	30.9616i	0.726778	+	1.00032i
$959$	5.14844	−	3.79329i	0.166252	−	0.122492i
$960$	−8.44616	+	89.2948i	−0.272599	+	2.88198i
$961$	28.6065	−	6.08049i	0.922789	−	0.196145i
$962$	3.94885	−	18.5779i	0.127316	−	0.598975i
$963$	−1.10709	+	5.20847i	−0.0356756	+	0.167841i
$964$	10.0327	−	2.13252i	0.323132	−	0.0686839i
$965$	−34.9371	+	39.6237i	−1.12467	+	1.27553i
$966$	0.729822	+	6.52477i	0.0234817	+	0.209931i
$967$	−2.27676	−	3.13369i	−0.0732157	−	0.100773i	0.770839	−	0.637031i	$-0.219838\pi$
$967$	−2.27676	−	3.13369i	−0.0732157	−	0.100773i	−0.844054	+	0.536258i	$0.819838\pi$
$968$	−211.988	+	122.391i	−6.81356	+	3.93381i
$969$	0.340378	+	3.23848i	0.0109345	+	0.104035i
$970$	−25.7337	+	36.2063i	−0.826259	+	1.16251i
$971$	4.59839	−	43.7508i	0.147569	−	1.40403i	−0.630665	−	0.776055i	$-0.717218\pi$
$971$	4.59839	−	43.7508i	0.147569	−	1.40403i	0.778234	−	0.627974i	$-0.216115\pi$
$972$	−3.34643	+	4.60596i	−0.107337	+	0.147736i
$973$	14.4801	−	8.48941i	0.464212	−	0.272158i
$974$	−7.39847			−0.237062
$975$	2.92922	+	8.41477i	0.0938102	+	0.269488i
$976$	−114.286	+	197.950i	−3.65822	+	6.33622i
$977$	−4.21098	+	3.79158i	−0.134721	+	0.121303i	−0.733737	−	0.679434i	$-0.762225\pi$
$977$	−4.21098	+	3.79158i	−0.134721	+	0.121303i	0.599016	+	0.800737i	$0.295559\pi$
$978$	−49.5809	−	5.21116i	−1.58542	−	0.166634i
$979$	65.4869	+	47.5790i	2.09297	+	1.52063i
$980$	−84.0744	+	29.5431i	−2.68566	+	0.943721i
$981$	1.19596	−	0.868919i	0.0381842	−	0.0277424i
$982$	−52.6417	+	30.3927i	−1.67986	+	0.969870i
$983$	37.6274	−	3.95480i	1.20013	−	0.126139i	0.516706	−	0.856163i	$-0.327158\pi$
$983$	37.6274	−	3.95480i	1.20013	−	0.126139i	0.683421	+	0.730024i	$0.260491\pi$
$984$	72.0607	+	15.3170i	2.29721	+	0.488287i
$985$	−14.9072	−	16.2134i	−0.474983	−	0.516601i
$986$	6.38721	−	19.6578i	0.203410	−	0.626032i
$987$	−7.84664	+	17.9451i	−0.249761	+	0.571198i
$988$	29.5843	−	9.61252i	0.941202	−	0.305815i
$989$	2.78969	−	0.592968i	0.0887071	−	0.0188553i
$990$	36.6354	−	0.381499i	1.16435	−	0.0121248i
$991$	−11.7630	−	2.50030i	−0.373663	−	0.0794246i	0.0172522	−	0.999851i	$-0.494508\pi$
$991$	−11.7630	−	2.50030i	−0.373663	−	0.0794246i	−0.390915	+	0.920427i	$0.627842\pi$
$992$	−14.4056	+	32.3556i	−0.457379	+	1.02729i
$993$			13.0520i			0.414192i
$994$	21.9965	−	9.96986i	0.697688	−	0.316225i
$995$	33.2552	+	29.3219i	1.05426	+	0.929566i
$996$	0.239394	−	2.27768i	0.00758549	−	0.0721712i
$997$	11.7473	+	26.3849i	0.372041	+	0.835618i	0.998425	+	0.0561035i	$0.0178677\pi$
$997$	11.7473	+	26.3849i	0.372041	+	0.835618i	−0.626384	+	0.779515i	$0.715466\pi$
$998$	43.6131	−	39.2694i	1.38055	−	1.24305i
$999$	1.92131	+	3.32780i	0.0607874	+	0.105287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bo.a.4.1	✓	320
7.2	even	3	inner	525.2.bo.a.79.1	yes	320
25.19	even	10	inner	525.2.bo.a.319.1	yes	320
175.44	even	30	inner	525.2.bo.a.394.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bo.a.4.1	✓	320	1.1	even	1	trivial
525.2.bo.a.79.1	yes	320	7.2	even	3	inner
525.2.bo.a.319.1	yes	320	25.19	even	10	inner
525.2.bo.a.394.1	yes	320	175.44	even	30	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bo (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576680 - 2.71307i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-5.20107 + 2.31567i) q^{4} +(0.442104 - 2.19193i) q^{5} +(2.24395 - 1.63033i) q^{6} +(1.97794 + 1.75720i) q^{7} +(6.02126 + 8.28755i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.576680 - 2.71307i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-5.20107 + 2.31567i) q^{4} +(0.442104 - 2.19193i) q^{5} +(2.24395 - 1.63033i) q^{6} +(1.97794 + 1.75720i) q^{7} +(6.02126 + 8.28755i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(-6.20179 + 0.0645817i) q^{10} +(3.95270 + 4.38992i) q^{11} +(-4.23093 - 3.80955i) q^{12} +(-1.69479 + 0.550670i) q^{13} +(3.62675 - 6.37963i) q^{14} +(2.18224 - 0.487654i) q^{15} +(11.3932 - 12.6535i) q^{16} +(1.05623 - 0.111014i) q^{17} +(2.40207 + 1.38684i) q^{18} +(2.80100 + 1.24708i) q^{19} +(2.77636 + 12.4241i) q^{20} +(-0.800777 + 2.52166i) q^{21} +(9.63070 - 13.2555i) q^{22} +(0.186011 + 0.875114i) q^{23} +(-5.12199 + 8.87154i) q^{24} +(-4.60909 - 1.93812i) q^{25} +(2.47136 + 4.28051i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(-14.3565 - 4.55905i) q^{28} +(5.67658 + 4.12428i) q^{29} +(-2.58150 - 5.63935i) q^{30} +(-0.138454 - 1.31730i) q^{31} +(-23.1568 - 13.3696i) q^{32} +(-2.40268 + 5.39652i) q^{33} +(-0.910295 - 2.80160i) q^{34} +(4.72610 - 3.55864i) q^{35} +(1.75932 - 5.41463i) q^{36} +(-2.85562 - 2.57121i) q^{37} +(1.76814 - 8.31846i) q^{38} +(-1.19240 - 1.32429i) q^{39} +(20.8277 - 9.53419i) q^{40} +(-2.22233 - 6.83962i) q^{41} +(7.30321 + 0.718372i) q^{42} -3.18781i q^{43} +(-30.7239 - 13.6792i) q^{44} +(1.33309 + 1.79523i) q^{45} +(2.26697 - 1.00932i) q^{46} +(7.36211 + 0.773789i) q^{47} +(16.1936 + 5.26161i) q^{48} +(0.824518 + 6.95127i) q^{49} +(-2.60028 + 13.6224i) q^{50} +(0.531024 + 0.919760i) q^{51} +(7.53955 - 6.78865i) q^{52} +(-1.19009 - 2.67298i) q^{53} +(-0.289928 + 2.75848i) q^{54} +(11.3699 - 6.72324i) q^{55} +(-2.65315 + 26.9728i) q^{56} +3.06607i q^{57} +(7.91586 - 17.7793i) q^{58} +(-1.08159 - 0.229898i) q^{59} +(-10.2208 + 7.58968i) q^{60} +(-13.1309 + 2.79105i) q^{61} +(-3.49408 + 1.13530i) q^{62} +(-2.62935 + 0.294104i) q^{63} +(-12.3953 + 38.1489i) q^{64} +(0.457755 + 3.95831i) q^{65} +(16.0267 + 3.40658i) q^{66} +(6.51058 - 0.684290i) q^{67} +(-5.23646 + 3.02327i) q^{68} +(-0.723799 + 0.525871i) q^{69} +(-12.3803 - 10.7700i) q^{70} +(2.66243 + 1.93437i) q^{71} +(-10.1879 - 1.07079i) q^{72} +(5.12282 - 4.61261i) q^{73} +(-5.32908 + 9.23024i) q^{74} +(-0.104123 - 4.99892i) q^{75} -17.4560 q^{76} +(0.104266 + 15.6287i) q^{77} +(-2.90525 + 3.99874i) q^{78} +(-1.64105 + 15.6135i) q^{79} +(-22.6985 - 30.5673i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-17.2748 + 9.97358i) q^{82} +(0.236448 + 0.325442i) q^{83} +(-1.67442 - 14.9697i) q^{84} +(0.223629 - 2.36426i) q^{85} +(-8.64873 + 1.83834i) q^{86} +(-1.45884 + 6.86331i) q^{87} +(-12.5815 + 59.1911i) q^{88} +(13.4035 - 2.84900i) q^{89} +(4.10182 - 4.65204i) q^{90} +(-4.31983 - 1.88888i) q^{91} +(-2.99393 - 4.12079i) q^{92} +(1.14710 - 0.662278i) q^{93} +(-2.14624 - 20.4201i) q^{94} +(3.97185 - 5.58824i) q^{95} +(2.79501 - 26.5927i) q^{96} +(4.20973 - 5.79420i) q^{97} +(18.3838 - 6.24563i) q^{98} -5.90722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Introduction

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