LMFDB - Embedded newform 348.2.t.a.35.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, 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:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			35.18
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.834189 + 1.14198i) q^{2} +(1.21862 - 1.23084i) q^{3} +(-0.608258 - 1.90526i) q^{4} +(-0.252365 - 0.201255i) q^{5} +(0.389050 + 2.41840i) q^{6} +(-3.46126 - 0.790009i) q^{7} +(2.68318 + 0.894727i) q^{8} +(-0.0299545 - 2.99985i) q^{9} +O(q^{10})$	\(q+(-0.834189 + 1.14198i) q^{2} +(1.21862 - 1.23084i) q^{3} +(-0.608258 - 1.90526i) q^{4} +(-0.252365 - 0.201255i) q^{5} +(0.389050 + 2.41840i) q^{6} +(-3.46126 - 0.790009i) q^{7} +(2.68318 + 0.894727i) q^{8} +(-0.0299545 - 2.99985i) q^{9} +(0.440350 - 0.120313i) q^{10} +(-0.320018 - 0.664525i) q^{11} +(-3.08631 - 1.57311i) q^{12} +(3.28982 - 1.58429i) q^{13} +(3.78952 - 3.29368i) q^{14} +(-0.555249 + 0.0653704i) q^{15} +(-3.26004 + 2.31778i) q^{16} -0.499932 q^{17} +(3.45077 + 2.46823i) q^{18} +(-1.43177 - 6.27298i) q^{19} +(-0.229939 + 0.603236i) q^{20} +(-5.19032 + 3.29755i) q^{21} +(1.02583 + 0.188883i) q^{22} +(-2.29001 - 2.87158i) q^{23} +(4.37103 - 2.21225i) q^{24} +(-1.08942 - 4.77306i) q^{25} +(-0.935092 + 5.07853i) q^{26} +(-3.72885 - 3.61879i) q^{27} +(0.600163 + 7.07513i) q^{28} +(-2.28754 + 4.87516i) q^{29} +(0.388530 - 0.688617i) q^{30} +(3.05971 - 3.83676i) q^{31} +(0.0726220 - 5.65639i) q^{32} +(-1.20791 - 0.415907i) q^{33} +(0.417038 - 0.570915i) q^{34} +(0.714508 + 0.895964i) q^{35} +(-5.69728 + 1.88175i) q^{36} +(-1.90809 + 3.96219i) q^{37} +(8.35801 + 3.59780i) q^{38} +(2.05901 - 5.97990i) q^{39} +(-0.497074 - 0.765800i) q^{40} +7.55503 q^{41} +(0.563953 - 8.67804i) q^{42} +(4.09169 + 5.13082i) q^{43} +(-1.07144 + 1.01392i) q^{44} +(-0.596174 + 0.763086i) q^{45} +(5.18960 - 0.219715i) q^{46} +(2.12415 + 4.41085i) q^{47} +(-1.11991 + 6.83709i) q^{48} +(5.04940 + 2.43166i) q^{49} +(6.35954 + 2.73753i) q^{50} +(-0.609225 + 0.615338i) q^{51} +(-5.01956 - 5.30431i) q^{52} +(8.28539 + 6.60738i) q^{53} +(7.24317 - 1.23953i) q^{54} +(-0.0529771 + 0.232108i) q^{55} +(-8.58034 - 5.21662i) q^{56} +(-9.46584 - 5.88207i) q^{57} +(-3.65912 - 6.67913i) q^{58} -4.97485 q^{59} +(0.462282 + 1.01813i) q^{60} +(9.83324 + 2.24437i) q^{61} +(1.82914 + 6.69473i) q^{62} +(-2.26623 + 10.4069i) q^{63} +(6.39893 + 4.80143i) q^{64} +(-1.14908 - 0.262271i) q^{65} +(1.48258 - 1.03246i) q^{66} +(2.56551 - 5.32735i) q^{67} +(0.304088 + 0.952501i) q^{68} +(-6.32510 - 0.680707i) q^{69} +(-1.61921 + 0.0685534i) q^{70} +(-11.6763 + 5.62299i) q^{71} +(2.60367 - 8.07594i) q^{72} +(2.23386 - 1.78145i) q^{73} +(-2.93305 - 5.48422i) q^{74} +(-7.20248 - 4.47562i) q^{75} +(-11.0808 + 6.54348i) q^{76} +(0.582685 + 2.55291i) q^{77} +(5.11136 + 7.33972i) q^{78} +(5.79611 + 2.79126i) q^{79} +(1.28919 + 0.0711714i) q^{80} +(-8.99821 + 0.179718i) q^{81} +(-6.30232 + 8.62773i) q^{82} +(-1.07201 - 4.69678i) q^{83} +(9.43975 + 7.88315i) q^{84} +(0.126165 + 0.100614i) q^{85} +(-9.27255 + 0.392577i) q^{86} +(3.21294 + 8.75654i) q^{87} +(-0.264099 - 2.06937i) q^{88} +(-2.08812 + 2.61842i) q^{89} +(-0.374111 - 1.31738i) q^{90} +(-12.6385 + 2.88466i) q^{91} +(-4.07819 + 6.10972i) q^{92} +(-0.993840 - 8.44156i) q^{93} +(-6.80907 - 1.25373i) q^{94} +(-0.901138 + 1.87123i) q^{95} +(-6.87363 - 6.98235i) q^{96} +(0.496272 - 0.113271i) q^{97} +(-6.98907 + 3.73787i) q^{98} +(-1.98389 + 0.979913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$	$-1$

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 $

$2$	−0.834189	+	1.14198i	−0.589861	+	0.807505i
$2$	−0.834189	+	1.14198i	−0.589861	+	0.807505i
$3$	1.21862	−	1.23084i	0.703568	−	0.710628i
$3$	1.21862	−	1.23084i	0.703568	−	0.710628i
$4$	−0.608258	−	1.90526i	−0.304129	−	0.952631i
$5$	−0.252365	−	0.201255i	−0.112861	−	0.0900038i	0.565433	−	0.824794i	$-0.308709\pi$
$5$	−0.252365	−	0.201255i	−0.112861	−	0.0900038i	−0.678294	+	0.734790i	$0.737280\pi$
$6$	0.389050	+	2.41840i	0.158829	+	0.987306i
$7$	−3.46126	−	0.790009i	−1.30823	−	0.298595i	−0.489114	−	0.872220i	$-0.662680\pi$
$7$	−3.46126	−	0.790009i	−1.30823	−	0.298595i	−0.819118	+	0.573625i	$0.805537\pi$
$8$	2.68318	+	0.894727i	0.948648	+	0.316334i
$9$	−0.0299545	−	2.99985i	−0.00998482	−	0.999950i
$10$	0.440350	−	0.120313i	0.139251	−	0.0380463i
$11$	−0.320018	−	0.664525i	−0.0964891	−	0.200362i	0.847137	−	0.531374i	$-0.178324\pi$
$11$	−0.320018	−	0.664525i	−0.0964891	−	0.200362i	−0.943626	+	0.331012i	$0.892610\pi$
$12$	−3.08631	−	1.57311i	−0.890942	−	0.454118i
$13$	3.28982	−	1.58429i	0.912432	−	0.439404i	0.0820691	−	0.996627i	$-0.473847\pi$
$13$	3.28982	−	1.58429i	0.912432	−	0.439404i	0.830363	+	0.557222i	$0.188133\pi$
$14$	3.78952	−	3.29368i	1.01279	−	0.880274i
$15$	−0.555249	+	0.0653704i	−0.143365	+	0.0168786i
$16$	−3.26004	+	2.31778i	−0.815011	+	0.579445i
$17$	−0.499932			−0.121251			−0.0606256	−	0.998161i	$-0.519310\pi$
$17$	−0.499932			−0.121251			−0.0606256	+	0.998161i	$0.519310\pi$
$18$	3.45077	+	2.46823i	0.813355	+	0.581768i
$19$	−1.43177	−	6.27298i	−0.328470	−	1.43912i	−0.822047	−	0.569419i	$-0.807168\pi$
$19$	−1.43177	−	6.27298i	−0.328470	−	1.43912i	0.493577	−	0.869702i	$-0.335689\pi$
$20$	−0.229939	+	0.603236i	−0.0514160	+	0.134888i
$21$	−5.19032	+	3.29755i	−1.13262	+	0.719584i
$22$	1.02583	+	0.188883i	0.218708	+	0.0402700i
$23$	−2.29001	−	2.87158i	−0.477499	−	0.598765i	0.483490	−	0.875350i	$-0.339369\pi$
$23$	−2.29001	−	2.87158i	−0.477499	−	0.598765i	−0.960990	+	0.276584i	$0.910797\pi$
$24$	4.37103	−	2.21225i	0.892234	−	0.451574i
$25$	−1.08942	−	4.77306i	−0.217884	−	0.954612i
$26$	−0.935092	+	5.07853i	−0.183387	+	0.995981i
$27$	−3.72885	−	3.61879i	−0.717618	−	0.696437i
$28$	0.600163	+	7.07513i	0.113420	+	1.33707i
$29$	−2.28754	+	4.87516i	−0.424785	+	0.905294i
$29$	−2.28754	+	4.87516i	−0.424785	+	0.905294i
$30$	0.388530	−	0.688617i	0.0709356	−	0.125724i
$31$	3.05971	−	3.83676i	0.549541	−	0.689102i	−0.427045	−	0.904230i	$-0.640445\pi$
$31$	3.05971	−	3.83676i	0.549541	−	0.689102i	0.976586	+	0.215128i	$0.0690169\pi$
$32$	0.0726220	−	5.65639i	0.0128379	−	0.999918i
$33$	−1.20791	−	0.415907i	−0.210269	−	0.0724002i
$34$	0.417038	−	0.570915i	0.0715214	−	0.0979110i
$35$	0.714508	+	0.895964i	0.120774	+	0.151446i
$36$	−5.69728	+	1.88175i	−0.949547	+	0.313626i
$37$	−1.90809	+	3.96219i	−0.313688	+	0.651380i	−0.996886	−	0.0788531i	$-0.974874\pi$
$37$	−1.90809	+	3.96219i	−0.313688	+	0.651380i	0.683198	+	0.730233i	$0.260588\pi$
$38$	8.35801	+	3.59780i	1.35585	+	0.583639i
$39$	2.05901	−	5.97990i	0.329705	−	0.957551i
$40$	−0.497074	−	0.765800i	−0.0785943	−	0.121084i
$41$	7.55503			1.17990			0.589949	−	0.807441i	$-0.299148\pi$
$41$	7.55503			1.17990			0.589949	+	0.807441i	$0.299148\pi$
$42$	0.563953	−	8.67804i	0.0870199	−	1.33905i
$43$	4.09169	+	5.13082i	0.623977	+	0.782442i	0.988898	−	0.148596i	$-0.0474755\pi$
$43$	4.09169	+	5.13082i	0.623977	+	0.782442i	−0.364921	+	0.931038i	$0.618904\pi$
$44$	−1.07144	+	1.01392i	−0.161526	+	0.152854i
$45$	−0.596174	+	0.763086i	−0.0888724	+	0.113754i
$46$	5.18960	−	0.219715i	0.765164	−	0.0323951i
$47$	2.12415	+	4.41085i	0.309840	+	0.643389i	0.996500	−	0.0835893i	$-0.0266384\pi$
$47$	2.12415	+	4.41085i	0.309840	+	0.643389i	−0.686661	+	0.726978i	$0.740924\pi$
$48$	−1.11991	+	6.83709i	−0.161645	+	0.986849i
$49$	5.04940	+	2.43166i	0.721343	+	0.347380i
$50$	6.35954	+	2.73753i	0.899375	+	0.387146i
$51$	−0.609225	+	0.615338i	−0.0853085	+	0.0861646i
$52$	−5.01956	−	5.30431i	−0.696087	−	0.735576i
$53$	8.28539	+	6.60738i	1.13809	+	0.907594i	0.996604	−	0.0823470i	$-0.0262416\pi$
$53$	8.28539	+	6.60738i	1.13809	+	0.907594i	0.141483	+	0.989941i	$0.454813\pi$
$54$	7.24317	−	1.23953i	0.985671	−	0.168679i
$55$	−0.0529771	+	0.232108i	−0.00714344	+	0.0312974i
$56$	−8.58034	−	5.21662i	−1.14660	−	0.697100i
$57$	−9.46584	−	5.88207i	−1.25378	−	0.779099i
$58$	−3.65912	−	6.67913i	−0.480466	−	0.877013i
$59$	−4.97485			−0.647670			−0.323835	−	0.946113i	$-0.604972\pi$
$59$	−4.97485			−0.647670			−0.323835	+	0.946113i	$0.604972\pi$
$60$	0.462282	+	1.01813i	0.0596804	+	0.131440i
$61$	9.83324	+	2.24437i	1.25902	+	0.287362i	0.799424	−	0.600767i	$-0.205138\pi$
$61$	9.83324	+	2.24437i	1.25902	+	0.287362i	0.459593	+	0.888130i	$0.347995\pi$
$62$	1.82914	+	6.69473i	0.232301	+	0.850231i
$63$	−2.26623	+	10.4069i	−0.285518	+	1.31115i
$64$	6.39893	+	4.80143i	0.799866	+	0.600179i
$65$	−1.14908	−	0.262271i	−0.142526	−	0.0325307i
$66$	1.48258	−	1.03246i	0.182493	−	0.127088i
$67$	2.56551	−	5.32735i	0.313428	−	0.650839i	−0.683433	−	0.730013i	$-0.739514\pi$
$67$	2.56551	−	5.32735i	0.313428	−	0.650839i	0.996861	+	0.0791740i	$0.0252283\pi$
$68$	0.304088	+	0.952501i	0.0368760	+	0.115508i
$69$	−6.32510	−	0.680707i	−0.761453	−	0.0819474i
$70$	−1.61921	+	0.0685534i	−0.193533	+	0.00819370i
$71$	−11.6763	+	5.62299i	−1.38572	+	0.667326i	−0.970210	−	0.242264i	$-0.922110\pi$
$71$	−11.6763	+	5.62299i	−1.38572	+	0.667326i	−0.415506	+	0.909590i	$0.636396\pi$
$72$	2.60367	−	8.07594i	0.306846	−	0.951759i
$73$	2.23386	−	1.78145i	0.261454	−	0.208503i	−0.483985	−	0.875076i	$-0.660811\pi$
$73$	2.23386	−	1.78145i	0.261454	−	0.208503i	0.745439	+	0.666573i	$0.232240\pi$
$74$	−2.93305	−	5.48422i	−0.340960	−	0.637528i
$75$	−7.20248	−	4.47562i	−0.831670	−	0.516800i
$76$	−11.0808	+	6.54348i	−1.27105	+	0.750589i
$77$	0.582685	+	2.55291i	0.0664031	+	0.290931i
$78$	5.11136	+	7.33972i	0.578747	+	0.831060i
$79$	5.79611	+	2.79126i	0.652114	+	0.314041i	0.730531	−	0.682879i	$-0.239272\pi$
$79$	5.79611	+	2.79126i	0.652114	+	0.314041i	−0.0784176	+	0.996921i	$0.524987\pi$
$80$	1.28919	+	0.0711714i	0.144135	+	0.00795720i
$81$	−8.99821	+	0.179718i	−0.999801	+	0.0199686i
$82$	−6.30232	+	8.62773i	−0.695975	+	0.952773i
$83$	−1.07201	−	4.69678i	−0.117668	−	0.515538i	−0.999068	−	0.0431670i	$-0.986255\pi$
$83$	−1.07201	−	4.69678i	−0.117668	−	0.515538i	0.881400	−	0.472371i	$-0.156602\pi$
$84$	9.43975	+	7.88315i	1.02996	+	0.860122i
$85$	0.126165	+	0.100614i	0.0136846	+	0.0109131i
$86$	−9.27255	+	0.392577i	−0.999885	+	0.0423327i
$87$	3.21294	+	8.75654i	0.344463	+	0.938800i
$88$	−0.264099	−	2.06937i	−0.0281531	−	0.220596i
$89$	−2.08812	+	2.61842i	−0.221340	+	0.277552i	−0.880087	−	0.474813i	$-0.842516\pi$
$89$	−2.08812	+	2.61842i	−0.221340	+	0.277552i	0.658746	+	0.752365i	$0.271087\pi$
$90$	−0.374111	−	1.31738i	−0.0394348	−	0.138864i
$91$	−12.6385	+	2.88466i	−1.32488	+	0.302395i
$92$	−4.07819	+	6.10972i	−0.425181	+	0.636983i
$93$	−0.993840	−	8.44156i	−0.103056	−	0.875349i
$94$	−6.80907	−	1.25373i	−0.702302	−	0.129313i
$95$	−0.901138	+	1.87123i	−0.0924548	+	0.191984i
$96$	−6.87363	−	6.98235i	−0.701537	−	0.712633i
$97$	0.496272	−	0.113271i	0.0503888	−	0.0115009i	−0.197252	−	0.980353i	$-0.563202\pi$
$97$	0.496272	−	0.113271i	0.0503888	−	0.0115009i	0.247641	+	0.968852i	$0.420345\pi$
$98$	−6.98907	+	3.73787i	−0.706003	+	0.377582i
$99$	−1.98389	+	0.979913i	−0.199388	+	0.0984849i
$100$	−8.43128	+	4.97888i	−0.843128	+	0.497888i
$101$	−11.7409	−	14.7227i	−1.16827	−	1.46496i	−0.857507	−	0.514472i	$-0.827988\pi$
$101$	−11.7409	−	14.7227i	−1.16827	−	1.46496i	−0.310760	−	0.950488i	$-0.600584\pi$
$102$	−0.194499	−	1.20903i	−0.0192582	−	0.119712i
$103$	5.46701	+	11.3524i	0.538681	+	1.11858i	0.975696	+	0.219128i	$0.0703212\pi$
$103$	5.46701	+	11.3524i	0.538681	+	1.11858i	−0.437015	+	0.899454i	$0.643965\pi$
$104$	10.2447	−	1.30746i	1.00458	−	0.128207i
$105$	1.97350	+	0.212388i	0.192594	+	0.0207270i
$106$	−14.4571	+	3.94999i	−1.40420	+	0.383657i
$107$	14.9982	+	7.22275i	1.44993	+	0.698249i	0.982583	−	0.185825i	$-0.0594958\pi$
$107$	14.9982	+	7.22275i	1.44993	+	0.698249i	0.467347	+	0.884074i	$0.345210\pi$
$108$	−4.62665	+	9.30560i	−0.445199	+	0.895432i
$109$	−1.61185	+	7.06197i	−0.154387	+	0.676414i	0.837192	+	0.546909i	$0.184196\pi$
$109$	−1.61185	+	7.06197i	−0.154387	+	0.676414i	−0.991579	+	0.129505i	$0.958661\pi$
$110$	−0.220871	−	0.254121i	−0.0210592	−	0.0242295i
$111$	2.55161	+	7.17694i	0.242188	+	0.681205i
$112$	13.1149	−	5.44697i	1.23924	−	0.514690i
$113$	1.59193	−	6.97471i	0.149756	−	0.656125i	−0.843196	−	0.537607i	$-0.819328\pi$
$113$	1.59193	−	6.97471i	0.149756	−	0.656125i	0.992952	−	0.118518i	$-0.0378144\pi$
$114$	14.6135	−	5.90308i	1.36868	−	0.552874i
$115$			1.18556i			0.110554i
$116$	10.6799	+	1.39300i	0.991601	+	0.129337i
$117$	−4.85119	−	9.82152i	−0.448493	−	0.908000i
$118$	4.14997	−	5.68120i	0.382035	−	0.522997i
$119$	1.73039	+	0.394951i	0.158625	+	0.0362051i
$120$	−1.54832	−	0.321395i	−0.141342	−	0.0293393i
$121$	6.51921	−	8.17483i	0.592655	−	0.743166i
$122$	−10.7658	+	9.35718i	−0.974691	+	0.847159i
$123$	9.20667	−	9.29906i	0.830138	−	0.838468i
$124$	−9.17113	−	3.49582i	−0.823591	−	0.313933i
$125$	−1.38593	+	2.87791i	−0.123961	+	0.257408i
$126$	−9.99408	−	11.2693i	−0.890343	−	1.00395i
$127$	−1.90169	+	0.915807i	−0.168748	+	0.0812647i	−0.516351	−	0.856377i	$-0.672710\pi$
$127$	−1.90169	+	0.915807i	−0.168748	+	0.0812647i	0.347603	+	0.937642i	$0.386996\pi$
$128$	−10.8211	+	3.30218i	−0.956457	+	0.291874i
$129$	11.3014	+	1.21626i	0.995035	+	0.107086i
$130$	1.25806	−	1.09345i	0.110339	−	0.0959021i
$131$	13.8620	−	11.0546i	1.21113	−	0.965841i	0.211193	−	0.977444i	$-0.432265\pi$
$131$	13.8620	−	11.0546i	1.21113	−	0.965841i	0.999933	+	0.0116034i	$0.00369357\pi$
$132$	−0.0576942	+	2.55436i	−0.00502163	+	0.222328i
$133$			22.8435i			1.98078i
$134$	3.94362	+	7.37379i	0.340677	+	0.636999i
$135$	0.212734	+	1.66371i	0.0183092	+	0.143189i
$136$	−1.34141	−	0.447302i	−0.115025	−	0.0383559i
$137$	6.27367	+	3.02124i	0.535996	+	0.258122i	0.682242	−	0.731126i	$-0.261005\pi$
$137$	6.27367	+	3.02124i	0.535996	+	0.258122i	−0.146246	+	0.989248i	$0.546719\pi$
$138$	6.05368	−	6.65533i	0.515324	−	0.566539i
$139$	−5.23403	+	4.17400i	−0.443945	+	0.354034i	−0.819805	−	0.572642i	$-0.805918\pi$
$139$	−5.23403	+	4.17400i	−0.443945	+	0.354034i	0.375861	+	0.926676i	$0.377347\pi$
$140$	1.27244	−	1.90630i	0.107541	−	0.161112i
$141$	8.01760	+	2.76063i	0.675204	+	0.232487i
$142$	3.31884	−	18.0247i	0.278510	−	1.51260i
$143$	−2.10561	−	1.67917i	−0.176080	−	0.140419i
$144$	7.05065	+	9.71022i	0.587554	+	0.809185i
$145$	1.55844	−	0.769944i	0.129422	−	0.0639403i
$146$	0.170921	+	4.03710i	0.0141455	+	0.334113i
$147$	9.14627	−	3.25176i	0.754372	−	0.268201i
$148$	8.70962	+	1.22538i	0.715926	+	0.100725i
$149$	−13.8295	+	3.15649i	−1.13296	+	0.258590i	−0.747582	−	0.664170i	$-0.768785\pi$
$149$	−13.8295	+	3.15649i	−1.13296	+	0.258590i	−0.385375	+	0.922760i	$0.625928\pi$
$150$	11.1193	−	4.49161i	0.907888	−	0.366738i
$151$	10.4312	−	8.31863i	0.848881	−	0.676960i	−0.0991726	−	0.995070i	$-0.531620\pi$
$151$	10.4312	−	8.31863i	0.848881	−	0.676960i	0.948054	+	0.318110i	$0.103048\pi$
$152$	1.77091	−	18.1126i	0.143640	−	1.46913i
$153$	0.0149752	+	1.49972i	0.00121067	+	0.121245i
$154$	−3.40145	−	1.46419i	−0.274097	−	0.117988i
$155$	−1.54433	+	0.352483i	−0.124044	+	0.0283121i
$156$	−12.6457	−	0.285623i	−1.01247	−	0.0228681i
$157$		−	6.75806i		−	0.539352i	−0.962951	−	0.269676i	$-0.913083\pi$
$157$		−	6.75806i		−	0.539352i	0.962951	−	0.269676i	$-0.0869166\pi$
$158$	−8.02263	+	4.29063i	−0.638246	+	0.341344i
$159$	18.2294	−	2.14617i	1.44568	−	0.170203i
$160$	−1.15670	+	1.41286i	−0.0914452	+	0.111696i
$161$	5.65773	+	11.7484i	0.445891	+	0.925903i
$162$	7.30097	−	10.4257i	0.573618	−	0.819123i
$163$	−17.6894	+	8.51876i	−1.38554	+	0.667241i	−0.970173	−	0.242413i	$-0.922061\pi$
$163$	−17.6894	+	8.51876i	−1.38554	+	0.667241i	−0.415367	+	0.909654i	$0.636347\pi$
$164$	−4.59541	−	14.3943i	−0.358841	−	1.12401i
$165$	0.221130	+	0.348057i	0.0172150	+	0.0270962i
$166$	6.25791	+	2.69378i	0.485708	+	0.209078i
$167$	−2.44513	+	10.7128i	−0.189210	+	0.828981i	0.787825	+	0.615899i	$0.211207\pi$
$167$	−2.44513	+	10.7128i	−0.189210	+	0.828981i	−0.977034	+	0.213082i	$0.931650\pi$
$168$	−16.8770	+	4.20401i	−1.30209	+	0.324346i
$169$	0.207571	−	0.260286i	0.0159670	−	0.0200220i
$170$	−0.220145	+	0.0601483i	−0.0168843	+	0.00461316i
$171$	−18.7751	+	4.48299i	−1.43577	+	0.342823i
$172$	7.28674	−	10.9166i	0.555609	−	0.832383i
$173$		−	24.4511i		−	1.85898i	−0.368845	−	0.929491i	$-0.620247\pi$
$173$		−	24.4511i		−	1.85898i	0.368845	−	0.929491i	$-0.379753\pi$
$174$	−12.6800	−	3.63549i	−0.961271	−	0.275606i
$175$			17.3814i			1.31391i
$176$	2.58350	+	1.42465i	0.194738	+	0.107387i
$177$	−6.06243	+	6.12327i	−0.455680	+	0.460253i
$178$	−1.24831	−	4.56886i	−0.0935647	−	0.342451i
$179$	14.4929	−	18.1735i	1.08325	−	1.35835i	0.154348	−	0.988017i	$-0.450672\pi$
$179$	14.4929	−	18.1735i	1.08325	−	1.35835i	0.928899	−	0.370332i	$-0.120756\pi$
$180$	1.81651	+	0.671714i	0.135394	+	0.0500666i
$181$	3.79453	−	16.6249i	0.282045	−	1.23572i	−0.613121	−	0.789989i	$-0.710086\pi$
$181$	3.79453	−	16.6249i	0.282045	−	1.23572i	0.895166	−	0.445733i	$-0.147057\pi$
$182$	7.24868	−	16.8394i	0.537308	−	1.24822i
$183$	14.7454	−	9.36816i	1.09001	−	0.692514i
$184$	−3.57523	−	9.75389i	−0.263569	−	0.719067i
$185$	1.27894	−	0.615907i	0.0940298	−	0.0452824i
$186$	10.4692	+	5.90691i	0.767638	+	0.433116i
$187$	0.159987	+	0.332217i	0.0116994	+	0.0242941i
$188$	7.11179	−	6.73001i	0.518681	−	0.490836i
$189$	10.0476	+	15.4714i	0.730858	+	1.12538i
$190$	−1.38520	−	2.59005i	−0.100493	−	0.187902i
$191$		−	9.09714i		−	0.658246i	−0.944287	−	0.329123i	$-0.893247\pi$
$191$		−	9.09714i		−	0.658246i	0.944287	−	0.329123i	$-0.106753\pi$
$192$	13.7076	−	2.02499i	0.989264	−	0.146141i
$193$	12.1491	−	2.77296i	0.874512	−	0.199602i	0.238371	−	0.971174i	$-0.423387\pi$
$193$	12.1491	−	2.77296i	0.874512	−	0.199602i	0.636141	+	0.771573i	$0.280530\pi$
$194$	−0.284631	+	0.661224i	−0.0204353	+	0.0474731i
$195$	−1.72310	+	1.09474i	−0.123394	+	0.0783956i
$196$	1.56162	−	11.0995i	0.111544	−	0.792822i
$197$	0.531566	−	0.423910i	0.0378725	−	0.0302023i	−0.604371	−	0.796703i	$-0.706575\pi$
$197$	0.531566	−	0.423910i	0.0378725	−	0.0302023i	0.642243	+	0.766501i	$0.278004\pi$
$198$	0.535893	−	3.08300i	0.0380843	−	0.219099i
$199$	13.4846	−	3.07777i	0.955898	−	0.218177i	0.284003	−	0.958824i	$-0.408338\pi$
$199$	13.4846	−	3.07777i	0.955898	−	0.218177i	0.671895	+	0.740646i	$0.265480\pi$
$200$	1.34747	−	13.7817i	0.0952808	−	0.974515i
$201$	−3.43076	−	9.64973i	−0.241987	−	0.680640i
$202$	26.6072	−	1.12648i	1.87208	−	0.0792591i
$203$	11.7692	−	15.0670i	0.826034	−	1.05750i
$204$	1.54295	+	0.786448i	0.108028	+	0.0550624i
$205$	−1.90663	−	1.52048i	−0.133165	−	0.106195i
$206$	−17.5247	−	3.22677i	−1.22101	−	0.224820i
$207$	−8.54571	+	6.95569i	−0.593968	+	0.483454i
$208$	−7.05292	+	12.7900i	−0.489032	+	0.886824i
$209$	−3.71036	+	2.95891i	−0.256651	+	0.204672i
$210$	−1.88882	+	2.07654i	−0.130341	+	0.143295i
$211$	−4.85052	−	2.33588i	−0.333923	−	0.160809i	0.259407	−	0.965768i	$-0.416473\pi$
$211$	−4.85052	−	2.33588i	−0.333923	−	0.160809i	−0.593330	+	0.804959i	$0.702187\pi$
$212$	7.54913	−	19.8048i	0.518477	−	1.36020i
$213$	−7.30784	+	21.2239i	−0.500725	+	1.45424i
$214$	−20.7596	+	11.1026i	−1.41910	+	0.758956i
$215$		−	2.11831i		−	0.144468i
$216$	−6.76735	−	13.0462i	−0.460460	−	0.887680i
$217$	−13.6215	+	10.8628i	−0.924690	+	0.737415i
$218$	−6.72008	−	7.73172i	−0.455141	−	0.523658i
$219$	0.529537	−	4.92044i	0.0357828	−	0.332492i
$220$	0.474450	−	0.0402462i	0.0319874	−	0.00271340i
$221$	−1.64469	+	0.792039i	−0.110634	+	0.0532783i
$222$	−10.3245	−	3.07303i	−0.692934	−	0.206248i
$223$	−2.90255	+	6.02721i	−0.194369	+	0.403612i	−0.975262	−	0.221054i	$-0.929050\pi$
$223$	−2.90255	+	6.02721i	−0.194369	+	0.403612i	0.780892	+	0.624666i	$0.214765\pi$
$224$	−4.71996	+	19.5208i	−0.315366	+	1.30429i
$225$	−14.2858	+	3.41107i	−0.952389	+	0.227405i
$226$	6.63704	+	7.63618i	0.441489	+	0.507951i
$227$	−0.533717	+	0.669259i	−0.0354240	+	0.0444203i	−0.799228	−	0.601028i	$-0.794758\pi$
$227$	−0.533717	+	0.669259i	−0.0354240	+	0.0444203i	0.763804	+	0.645448i	$0.223329\pi$
$228$	−5.44921	+	21.6127i	−0.360883	+	1.43134i
$229$	−16.0488	−	3.66303i	−1.06053	−	0.242060i	−0.343538	−	0.939139i	$-0.611625\pi$
$229$	−16.0488	−	3.66303i	−1.06053	−	0.242060i	−0.716994	+	0.697079i	$0.754483\pi$
$230$	−1.35389	−	0.988981i	−0.0892730	−	0.0652115i
$231$	3.85230	+	2.39382i	0.253463	+	0.157502i
$232$	−10.4998	+	11.0342i	−0.689346	+	0.724432i
$233$			11.1762i			0.732179i	0.930580	+	0.366090i	$0.119304\pi$
$233$			11.1762i			0.732179i	−0.930580	+	0.366090i	$0.880696\pi$
$234$	15.2628	+	2.65301i	0.997763	+	0.173433i
$235$	0.351641	−	1.54064i	0.0229385	−	0.100500i
$236$	3.02599	+	9.47839i	0.196975	+	0.616991i
$237$	10.4988	−	3.73264i	0.681973	−	0.242461i
$238$	−1.89450	+	1.64662i	−0.122802	+	0.106734i
$239$	−4.35430	+	19.0774i	−0.281656	+	1.23402i	0.614013	+	0.789296i	$0.289554\pi$
$239$	−4.35430	+	19.0774i	−0.281656	+	1.23402i	−0.895669	+	0.444721i	$0.853303\pi$
$240$	1.65862	−	1.50006i	0.107064	−	0.0968282i
$241$	15.3694	+	7.40151i	0.990030	+	0.476773i	0.857544	−	0.514411i	$-0.171990\pi$
$241$	15.3694	+	7.40151i	0.990030	+	0.476773i	0.132487	+	0.991185i	$0.457704\pi$
$242$	3.89728	+	14.2642i	0.250526	+	0.916936i
$243$	−10.7441	+	11.2944i	−0.689237	+	0.724536i
$244$	−1.70503	−	20.1000i	−0.109153	−	1.28677i
$245$	−0.784909	−	1.62988i	−0.0501460	−	0.104129i
$246$	2.93928	+	18.2711i	0.187402	+	1.16492i
$247$	−14.6485	−	18.3687i	−0.932063	−	1.16877i
$248$	11.6426	−	7.55711i	0.739307	−	0.479877i
$249$	−7.08737	−	4.40409i	−0.449144	−	0.279098i
$250$	−2.13040	−	3.98343i	−0.134739	−	0.251934i
$251$	−21.4035	+	4.88521i	−1.35098	+	0.308352i	−0.835943	−	0.548817i	$-0.815078\pi$
$251$	−21.4035	+	4.88521i	−1.35098	+	0.308352i	−0.515036	+	0.857169i	$0.672221\pi$
$252$	21.2064	−	2.01233i	1.33587	−	0.126765i
$253$	−1.17539	+	2.44072i	−0.0738962	+	0.153447i
$254$	0.540533	−	2.93566i	0.0339161	−	0.184200i
$255$	0.277587	−	0.0326807i	0.0173832	−	0.00204655i
$256$	5.25578	−	15.1121i	0.328486	−	0.944509i
$257$	4.97743	−	1.13607i	0.310484	−	0.0708659i	−0.0644399	−	0.997922i	$-0.520526\pi$
$257$	4.97743	−	1.13607i	0.310484	−	0.0708659i	0.374924	+	0.927056i	$0.377669\pi$
$258$	−10.8165	+	11.8915i	−0.673404	+	0.740331i
$259$	9.73455	−	12.2067i	0.604876	−	0.758490i
$260$	0.199245	+	2.34883i	0.0123566	+	0.145668i
$261$	14.6933	+	6.71623i	0.909491	+	0.415724i
$262$	1.06063	+	25.0517i	0.0655259	+	1.54770i
$263$	22.5861	+	18.0118i	1.39272	+	1.11065i	0.979821	+	0.199875i	$0.0640535\pi$
$263$	22.5861	+	18.0118i	1.39272	+	1.11065i	0.412894	+	0.910779i	$0.364518\pi$
$264$	−2.86891	−	2.19670i	−0.176569	−	0.135198i
$265$	−0.761180	−	3.33495i	−0.0467589	−	0.204864i
$266$	−26.0869	−	19.0558i	−1.59949	−	1.16839i
$267$	0.678252	+	5.76100i	0.0415084	+	0.352567i
$268$	−11.7105	−	1.64758i	−0.715332	−	0.100642i
$269$	−7.35074	−	3.53993i	−0.448182	−	0.215833i	0.196158	−	0.980572i	$-0.437154\pi$
$269$	−7.35074	−	3.53993i	−0.448182	−	0.215833i	−0.644340	+	0.764739i	$0.722868\pi$
$270$	−2.07739	−	1.14491i	−0.126426	−	0.0696768i
$271$	−2.00199	−	8.77131i	−0.121613	−	0.532819i	−0.998628	−	0.0523578i	$-0.983326\pi$
$271$	−2.00199	−	8.77131i	−0.121613	−	0.532819i	0.877016	−	0.480461i	$-0.159531\pi$
$272$	1.62980	−	1.15873i	0.0988212	−	0.0702585i
$273$	−11.8509	+	19.0713i	−0.717251	+	1.15425i
$274$	−8.68364	+	4.64415i	−0.524598	+	0.280563i
$275$	−2.82318	+	2.25141i	−0.170244	+	0.135765i
$276$	2.55037	+	12.4650i	0.153514	+	0.750306i
$277$	7.01096	−	3.37630i	0.421248	−	0.202862i	−0.211237	−	0.977435i	$-0.567749\pi$
$277$	7.01096	−	3.37630i	0.421248	−	0.202862i	0.632485	+	0.774573i	$0.282035\pi$
$278$	−0.400474	−	9.45908i	−0.0240188	−	0.567318i
$279$	−11.6014	−	9.06375i	−0.694555	−	0.542633i
$280$	1.11551	+	3.04332i	0.0666645	+	0.181873i
$281$	2.58459	−	5.36695i	0.154183	−	0.320165i	−0.809541	−	0.587063i	$-0.800284\pi$
$281$	2.58459	−	5.36695i	0.154183	−	0.320165i	0.963725	+	0.266897i	$0.0859985\pi$
$282$	−9.84079	+	6.85309i	−0.586010	+	0.408095i
$283$	28.7354	+	6.55866i	1.70814	+	0.389872i	0.961381	−	0.275222i	$-0.0887513\pi$
$283$	28.7354	+	6.55866i	1.70814	+	0.389872i	0.746760	+	0.665094i	$0.231608\pi$
$284$	17.8154	+	18.8261i	1.05715	+	1.11712i
$285$	1.20505	+	3.38947i	0.0713813	+	0.200775i
$286$	3.67405	−	1.00383i	0.217251	−	0.0593577i
$287$	−26.1499	−	5.96854i	−1.54358	−	0.352312i
$288$	−16.9705	−	0.0484212i	−0.999996	−	0.00285324i
$289$	−16.7501			−0.985298
$290$	−0.420771	+	2.42200i	−0.0247085	+	0.142224i
$291$	0.465346	−	0.748867i	0.0272791	−	0.0438994i
$292$	−4.75289	−	3.17252i	−0.278142	−	0.185658i
$293$	4.42992	−	19.4087i	0.258799	−	1.13387i	−0.663739	−	0.747964i	$-0.731032\pi$
$293$	4.42992	−	19.4087i	0.258799	−	1.13387i	0.922538	−	0.385907i	$-0.126111\pi$
$294$	−3.91625	+	13.1575i	−0.228401	+	0.767360i
$295$	1.25548	+	1.00121i	0.0730968	+	0.0582928i
$296$	−8.66483	+	8.92405i	−0.503633	+	0.518700i
$297$	−1.21148	+	3.63599i	−0.0702971	+	0.210982i
$298$	7.93175	−	18.4262i	0.459474	−	1.06740i
$299$	−12.0831	−	5.81893i	−0.698786	−	0.336518i
$300$	−4.14626	+	16.4449i	−0.239384	+	0.949449i
$301$	−10.1090	−	20.9915i	−0.582673	−	1.20993i
$302$	0.798130	+	18.8516i	0.0459272	+	1.08479i
$303$	−32.4290	−	3.49000i	−1.86300	−	0.200496i
$304$	19.2070	+	17.1317i	1.10160	+	0.982569i
$305$	−2.02988	−	2.54538i	−0.116230	−	0.145748i
$306$	−1.72515	−	1.23395i	−0.0986203	−	0.0705402i
$307$	−0.824590			−0.0470618			−0.0235309	−	0.999723i	$-0.507491\pi$
$307$	−0.824590			−0.0470618			−0.0235309	+	0.999723i	$0.507491\pi$
$308$	4.50954	−	2.66299i	0.256955	−	0.151738i
$309$	20.6352	+	7.10513i	1.17389	+	0.404197i
$310$	0.885733	−	2.05764i	0.0503062	−	0.116866i
$311$	−9.81515	+	20.3814i	−0.556566	+	1.15572i	0.412963	+	0.910748i	$0.364494\pi$
$311$	−9.81515	+	20.3814i	−0.556566	+	1.15572i	−0.969530	+	0.244974i	$0.921221\pi$
$312$	10.8751	−	14.2029i	0.615680	−	0.804082i
$313$	12.2263	+	15.3313i	0.691072	+	0.866577i	0.996321	−	0.0856951i	$-0.0273111\pi$
$313$	12.2263	+	15.3313i	0.691072	+	0.866577i	−0.305249	+	0.952273i	$0.598740\pi$
$314$	7.71760	+	5.63750i	0.435530	+	0.318142i
$315$	2.66636	−	2.17025i	0.150232	−	0.122280i
$316$	1.79255	−	12.7409i	0.100839	−	0.716733i
$317$	−2.25457	+	2.82714i	−0.126629	+	0.158788i	−0.841104	−	0.540873i	$-0.818094\pi$
$317$	−2.25457	+	2.82714i	−0.126629	+	0.158788i	0.714475	+	0.699661i	$0.246666\pi$
$318$	−12.7558	+	22.6080i	−0.715312	+	1.26779i
$319$	3.97172	−	0.0400161i	0.222374	−	0.00224047i
$320$	−0.648557	−	2.49953i	−0.0362555	−	0.139728i
$321$	27.1671	−	9.65868i	1.51632	−	0.539095i
$322$	−18.1361	−	3.33934i	−1.01069	−	0.186094i
$323$	0.715786	+	3.13606i	0.0398274	+	0.174495i
$324$	5.81564	+	17.0346i	0.323091	+	0.946368i
$325$	−11.1459	−	13.9766i	−0.618265	−	0.775280i
$326$	5.02800	−	27.3073i	0.278475	−	1.51241i
$327$	6.72796	+	10.5898i	0.372057	+	0.585615i
$328$	20.2715	+	6.75969i	1.11931	+	0.373241i
$329$	−3.86763	−	16.9452i	−0.213229	−	0.934219i
$330$	−0.581940	−	0.0378181i	−0.0320347	−	0.00208182i
$331$	−23.7698			−1.30651			−0.653253	−	0.757139i	$-0.726596\pi$
$331$	−23.7698			−1.30651			−0.653253	+	0.757139i	$0.726596\pi$
$332$	−8.29653	+	4.89931i	−0.455331	+	0.268885i
$333$	11.9431	+	5.60530i	0.654480	+	0.307168i
$334$	−10.1942	−	11.7288i	−0.557799	−	0.641771i
$335$	−1.71960	+	0.828115i	−0.0939517	+	0.0452448i
$336$	9.27767	−	22.7802i	0.506138	−	1.24276i
$337$	−6.26978	−	13.0193i	−0.341537	−	0.709208i	0.657483	−	0.753469i	$-0.271621\pi$
$337$	−6.26978	−	13.0193i	−0.341537	−	0.709208i	−0.999020	+	0.0442607i	$0.985907\pi$
$338$	0.124089	+	0.454171i	0.00674957	+	0.0247037i
$339$	−6.64482	−	10.4589i	−0.360897	−	0.568050i
$340$	0.114954	−	0.301577i	0.00623426	−	0.0163553i
$341$	−3.52879	−	0.805422i	−0.191094	−	0.0436161i
$342$	10.5425	−	25.1806i	0.570073	−	1.36161i
$343$	3.87375	+	3.08922i	0.209163	+	0.166802i
$344$	6.38807	+	17.4279i	0.344421	+	0.939647i
$345$	1.45924	+	1.44474i	0.0785628	+	0.0777823i
$346$	27.9228	+	20.3968i	1.50114	+	1.09654i
$347$	17.4812			0.938439			0.469219	−	0.883082i	$-0.344535\pi$
$347$	17.4812			0.938439			0.469219	+	0.883082i	$0.344535\pi$
$348$	14.7292	−	11.4477i	0.789569	−	0.613662i
$349$	22.0072			1.17802			0.589010	−	0.808126i	$-0.299518\pi$
$349$	22.0072			1.17802			0.589010	+	0.808126i	$0.299518\pi$
$350$	−19.8493	−	14.4994i	−1.06099	−	0.775026i
$351$	−18.0005	−	5.99759i	−0.960795	−	0.320128i
$352$	−3.78205	+	1.76189i	−0.201584	+	0.0939090i
$353$	2.17527	+	1.73472i	0.115778	+	0.0923300i	0.679667	−	0.733520i	$-0.262124\pi$
$353$	2.17527	+	1.73472i	0.115778	+	0.0923300i	−0.563889	+	0.825850i	$0.690696\pi$
$354$	−1.93547	−	12.0312i	−0.102869	−	0.639449i
$355$	4.07833	+	0.930853i	0.216455	+	0.0494045i
$356$	6.25889	+	2.38574i	0.331721	+	0.126444i
$357$	2.59481	−	1.64855i	0.137332	−	0.0872505i
$358$	8.66404	+	31.7107i	0.457909	+	1.67596i
$359$	3.97191	+	8.24775i	0.209629	+	0.435300i	0.979099	−	0.203383i	$-0.0651938\pi$
$359$	3.97191	+	8.24775i	0.209629	+	0.435300i	−0.769470	+	0.638683i	$0.779480\pi$
$360$	−2.28240	+	1.51409i	−0.120293	+	0.0797994i
$361$	−20.1819	+	9.71911i	−1.06221	+	0.511532i
$362$	15.8201	+	18.2016i	0.831484	+	0.956657i
$363$	−2.11753	−	17.9861i	−0.111142	−	0.944025i
$364$	13.1835	+	22.3251i	0.691004	+	1.17015i
$365$	−0.922274			−0.0482740
$366$	−1.60216	+	24.6538i	−0.0837463	+	1.28868i
$367$	2.84740	+	12.4753i	0.148633	+	0.651204i	0.993266	+	0.115858i	$0.0369616\pi$
$367$	2.84740	+	12.4753i	0.148633	+	0.651204i	−0.844633	+	0.535346i	$0.820181\pi$
$368$	14.1212	+	4.05374i	0.736119	+	0.211316i
$369$	−0.226307	−	22.6640i	−0.0117811	−	1.17984i
$370$	−0.363524	+	1.97432i	−0.0188987	+	0.102640i
$371$	−23.4580	−	29.4154i	−1.21788	−	1.52717i
$372$	−15.4789	+	7.02817i	−0.802542	+	0.364394i
$373$	−2.07715	−	9.10061i	−0.107551	−	0.471212i	−0.999806	−	0.0196804i	$-0.993735\pi$
$373$	−2.07715	−	9.10061i	−0.107551	−	0.471212i	0.892255	−	0.451531i	$-0.149122\pi$
$374$	−0.512847	−	0.0944287i	−0.0265187	−	0.00488279i
$375$	1.85335	+	5.21293i	0.0957064	+	0.269194i
$376$	1.75298	+	13.7357i	0.0904033	+	0.708362i
$377$	0.198105	+	19.6625i	0.0102029	+	1.01267i
$378$	−26.0497	−	1.43183i	−1.33985	−	0.0736454i
$379$	23.8967	−	29.9655i	1.22749	−	1.53923i	0.476062	−	0.879412i	$-0.342064\pi$
$379$	23.8967	−	29.9655i	1.22749	−	1.53923i	0.751430	−	0.659813i	$-0.229365\pi$
$380$	4.11331	+	0.578712i	0.211008	+	0.0296873i
$381$	−1.19022	+	3.45670i	−0.0609766	+	0.177092i
$382$	10.3888	+	7.58873i	0.531537	+	0.388273i
$383$	−1.71540	−	2.15105i	−0.0876531	−	0.109914i	0.736071	−	0.676904i	$-0.236679\pi$
$383$	−1.71540	−	2.15105i	−0.0876531	−	0.109914i	−0.823724	+	0.566991i	$0.808107\pi$
$384$	−9.12225	+	17.3431i	−0.465518	+	0.885038i
$385$	0.366735	−	0.761533i	0.0186905	−	0.0388113i
$386$	−6.96798	+	16.1873i	−0.354661	+	0.823910i
$387$	15.2691	−	12.4281i	0.776173	−	0.631758i
$388$	−0.517672	−	0.876630i	−0.0262808	−	0.0445041i
$389$	−13.3945			−0.679128			−0.339564	−	0.940583i	$-0.610279\pi$
$389$	−13.3945			−0.679128			−0.339564	+	0.940583i	$0.610279\pi$
$390$	0.187224	−	2.88097i	0.00948044	−	0.145884i
$391$	1.14485	+	1.43559i	0.0578974	+	0.0726011i
$392$	11.3728	+	11.0424i	0.574412	+	0.557727i
$393$	3.28598	−	30.5332i	0.165756	−	1.54019i
$394$	0.0406720	+	0.960661i	0.00204903	+	0.0483974i
$395$	−0.900983	−	1.87091i	−0.0453334	−	0.0941357i
$396$	3.07371	+	3.18379i	0.154460	+	0.159991i
$397$	19.6973	+	9.48574i	0.988581	+	0.476076i	0.857048	−	0.515236i	$-0.172296\pi$
$397$	19.6973	+	9.48574i	0.988581	+	0.476076i	0.131533	+	0.991312i	$0.458010\pi$
$398$	−7.73393	+	17.9667i	−0.387667	+	0.900587i
$399$	28.1168	+	27.8374i	1.40760	+	1.39362i
$400$	14.6145	+	13.0354i	0.730723	+	0.651768i
$401$	−8.64731	−	6.89600i	−0.431826	−	0.344370i	0.383330	−	0.923612i	$-0.374777\pi$
$401$	−8.64731	−	6.89600i	−0.431826	−	0.344370i	−0.815156	+	0.579242i	$0.803349\pi$
$402$	13.8817	+	4.13183i	0.692359	+	0.206077i
$403$	3.98735	−	17.4697i	0.198624	−	0.870230i
$404$	−20.9090	+	31.3247i	−1.04026	+	1.55846i
$405$	2.30700	+	1.76557i	0.114636	+	0.0877321i
$406$	7.38858	+	26.0089i	0.366689	+	1.29080i
$407$	3.24360			0.160779
$408$	−2.18522	+	1.10597i	−0.108185	+	0.0547539i
$409$	−32.4008	−	7.39528i	−1.60212	−	0.365673i	−0.674227	−	0.738524i	$-0.735523\pi$
$409$	−32.4008	−	7.39528i	−1.60212	−	0.365673i	−0.927891	+	0.372851i	$0.878380\pi$
$410$	3.32686	−	0.908968i	0.164302	−	0.0448907i
$411$	11.3639	−	4.04018i	0.560538	−	0.199287i
$412$	18.3039	−	17.3213i	0.901767	−	0.853357i
$413$	17.2192	+	3.93018i	0.847303	+	0.193391i
$414$	−0.814562	−	15.5614i	−0.0400336	−	0.764802i
$415$	−0.674710	+	1.40105i	−0.0331202	+	0.0687748i
$416$	−8.72247	−	18.7236i	−0.427654	−	0.917998i
$417$	−1.24072	+	11.5288i	−0.0607586	+	0.564566i
$418$	−0.283893	−	6.70547i	−0.0138857	−	0.327975i
$419$	−15.7047	+	7.56301i	−0.767227	+	0.369477i	−0.776203	−	0.630483i	$-0.782857\pi$
$419$	−15.7047	+	7.56301i	−0.767227	+	0.369477i	0.00897634	+	0.999960i	$0.497143\pi$
$420$	−0.795744	−	3.88922i	−0.0388283	−	0.189775i
$421$	−17.5131	+	13.9662i	−0.853536	+	0.680672i	−0.949177	−	0.314744i	$-0.898082\pi$
$421$	−17.5131	+	13.9662i	−0.853536	+	0.680672i	0.0956405	+	0.995416i	$0.469510\pi$
$422$	6.71379	−	3.59064i	0.326822	−	0.174790i
$423$	13.1683	−	6.50427i	0.640263	−	0.316248i
$424$	16.3194	+	25.1420i	0.792541	+	1.22100i
$425$	0.544636	+	2.38621i	0.0264187	+	0.115748i
$426$	−18.1413	−	26.0502i	−0.878947	−	1.26214i
$427$	−32.2623	−	15.5367i	−1.56128	−	0.751873i
$428$	4.63845	−	32.9688i	0.224208	−	1.59361i
$429$	−4.63271	+	0.545417i	−0.223670	+	0.0263330i
$430$	2.41908	+	1.76707i	0.116658	+	0.0852157i
$431$	−4.91082	−	21.5157i	−0.236546	−	1.03638i	−0.944085	−	0.329702i	$-0.893052\pi$
$431$	−4.91082	−	21.5157i	−0.236546	−	1.03638i	0.707539	−	0.706674i	$-0.249805\pi$
$432$	20.5438	+	3.15477i	0.988414	+	0.151784i
$433$	−8.29721	−	6.61681i	−0.398739	−	0.317983i	0.403508	−	0.914976i	$-0.367791\pi$
$433$	−8.29721	−	6.61681i	−0.398739	−	0.317983i	−0.802247	+	0.596993i	$0.796362\pi$
$434$	−1.04223	−	24.6172i	−0.0500287	−	1.18166i
$435$	0.951461	−	2.85646i	0.0456190	−	0.136957i
$436$	14.4353	−	1.22451i	0.691326	−	0.0586432i
$437$	−14.7346	+	18.4766i	−0.704851	+	0.883856i
$438$	5.17733	+	4.70930i	0.247382	+	0.225019i
$439$	−1.44167	+	0.329052i	−0.0688073	+	0.0157048i	−0.256786	−	0.966468i	$-0.582664\pi$
$439$	−1.44167	+	0.329052i	−0.0688073	+	0.0157048i	0.187979	+	0.982173i	$0.439806\pi$
$440$	−0.349821	+	0.575388i	−0.0166770	+	0.0274305i
$441$	7.14337	−	15.2203i	0.340161	−	0.724775i
$442$	0.467483	−	2.53892i	0.0222359	−	0.120764i
$443$	−11.7045	+	24.3046i	−0.556097	+	1.15475i	0.413605	+	0.910457i	$0.364270\pi$
$443$	−11.7045	+	24.3046i	−0.556097	+	1.15475i	−0.969702	+	0.244291i	$0.921445\pi$
$444$	12.1219	−	9.22692i	0.575281	−	0.437890i
$445$	1.05394	−	0.240555i	0.0499615	−	0.0114034i
$446$	−4.46171	−	8.34250i	−0.211268	−	0.395029i
$447$	−12.9677	+	20.8685i	−0.613351	+	0.987047i
$448$	−18.3552	−	21.6742i	−0.867200	−	1.02401i
$449$	7.60580	+	9.53737i	0.358940	+	0.450096i	0.928211	−	0.372053i	$-0.121346\pi$
$449$	7.60580	+	9.53737i	0.358940	+	0.450096i	−0.569272	+	0.822150i	$0.692775\pi$
$450$	8.02169	−	19.1597i	0.378146	−	0.903196i
$451$	−2.41775	−	5.02051i	−0.113847	−	0.236406i
$452$	−14.2569	+	1.20938i	−0.670590	+	0.0568842i
$453$	2.47272	−	22.9764i	0.116178	−	1.07953i
$454$	−0.319064	−	1.16778i	−0.0149744	−	0.0548069i
$455$	3.77007	+	1.81557i	0.176744	+	0.0851153i
$456$	−20.1357	−	24.2520i	−0.942941	−	1.13570i
$457$	−5.48242	+	24.0200i	−0.256457	+	1.12361i	0.668553	+	0.743665i	$0.266914\pi$
$457$	−5.48242	+	24.0200i	−0.256457	+	1.12361i	−0.925009	+	0.379945i	$0.875943\pi$
$458$	17.5708	−	15.2718i	0.821030	−	0.713604i
$459$	1.86417	+	1.80915i	0.0870121	+	0.0844439i
$460$	2.25880	−	0.721127i	0.105317	−	0.0336227i
$461$	−0.756735	+	3.31547i	−0.0352447	+	0.154417i	−0.989488	−	0.144614i	$-0.953806\pi$
$461$	−0.756735	+	3.31547i	−0.0352447	+	0.154417i	0.954244	+	0.299031i	$0.0966633\pi$
$462$	−5.94725	+	2.40237i	−0.276691	+	0.111768i
$463$		−	27.5849i		−	1.28198i	−0.767550	−	0.640989i	$-0.778524\pi$
$463$		−	27.5849i		−	1.28198i	0.767550	−	0.640989i	$-0.221476\pi$
$464$	−3.84209	−	21.1952i	−0.178364	−	0.983965i
$465$	−1.44809	+	2.33037i	−0.0671537	+	0.108068i
$466$	−12.7631	−	9.32309i	−0.591239	−	0.431884i
$467$	39.1575	+	8.93744i	1.81199	+	0.413575i	0.988181	−	0.153289i	$-0.0489865\pi$
$467$	39.1575	+	8.93744i	1.81199	+	0.413575i	0.823811	+	0.566864i	$0.191844\pi$
$468$	−15.7618	+	15.2168i	−0.728589	+	0.703397i
$469$	−13.0886	+	16.4125i	−0.604373	+	0.757860i
$470$	1.46605	+	1.68675i	0.0676240	+	0.0778042i
$471$	−8.31812	−	8.23548i	−0.383279	−	0.379471i
$472$	−13.3484	−	4.45113i	−0.614411	−	0.204880i
$473$	2.10014	−	4.36098i	0.0965645	−	0.200518i
$474$	−4.49540	+	15.1032i	−0.206480	+	0.693715i
$475$	−28.3815	+	13.6678i	−1.30223	+	0.627123i
$476$	−0.300040	−	3.53708i	−0.0137523	−	0.162122i
$477$	19.5730	−	25.0529i	0.896185	−	1.14709i
$478$	−18.1538	−	20.8867i	−0.830337	−	0.955337i
$479$	−1.09334	+	0.871909i	−0.0499560	+	0.0398385i	−0.648150	−	0.761513i	$-0.724457\pi$
$479$	−1.09334	+	0.871909i	−0.0499560	+	0.0398385i	0.598194	+	0.801352i	$0.295885\pi$
$480$	0.329437	+	3.14545i	0.0150367	+	0.143570i
$481$			16.0579i			0.732176i
$482$	−21.2734	+	11.3774i	−0.968977	+	0.518225i
$483$	21.3550	+	7.35299i	0.971688	+	0.334573i
$484$	−19.5405	−	7.44839i	−0.888206	−	0.338563i
$485$	−0.148038	−	0.0712914i	−0.00672206	−	0.00323717i
$486$	−3.93538	−	21.6913i	−0.178512	−	0.983938i
$487$	−8.93741	+	7.12735i	−0.404993	+	0.322971i	−0.804711	−	0.593667i	$-0.797680\pi$
$487$	−8.93741	+	7.12735i	−0.404993	+	0.322971i	0.399718	+	0.916638i	$0.369108\pi$
$488$	24.3763	+	14.8201i	1.10346	+	0.670875i
$489$	−11.0713	+	32.1540i	−0.500661	+	1.45405i
$490$	2.51606	+	0.463274i	0.113664	+	0.0209286i
$491$	−28.6863	−	22.8766i	−1.29459	−	1.03240i	−0.996975	−	0.0777204i	$-0.975236\pi$
$491$	−28.6863	−	22.8766i	−1.29459	−	1.03240i	−0.297620	−	0.954685i	$-0.596193\pi$
$492$	−23.3172	−	11.8849i	−1.05122	−	0.535812i
$493$	1.14361	−	2.43725i	0.0515057	−	0.109768i
$494$	33.1963	−	1.40545i	1.49357	−	0.0632342i
$495$	0.697876	+	0.151971i	0.0313672	+	0.00683058i
$496$	−1.08203	+	19.5998i	−0.0485847	+	0.880055i
$497$	44.8567	−	10.2383i	2.01210	−	0.459249i
$498$	10.9416	−	4.41982i	0.490305	−	0.198057i
$499$	0.634462	−	0.505967i	0.0284024	−	0.0226502i	−0.609186	−	0.793028i	$-0.708504\pi$
$499$	0.634462	−	0.505967i	0.0284024	−	0.0226502i	0.637588	+	0.770377i	$0.279932\pi$
$500$	6.32618	+	0.890045i	0.282915	+	0.0398040i
$501$	10.2061	+	16.0643i	0.455976	+	0.717702i
$502$	12.2757	−	28.5177i	0.547893	−	1.27281i
$503$	25.0099	−	5.70836i	1.11514	−	0.254523i	0.375031	−	0.927012i	$-0.377632\pi$
$503$	25.0099	−	5.70836i	1.11514	−	0.254523i	0.740107	+	0.672489i	$0.234775\pi$
$504$	−15.3921	+	25.8960i	−0.685616	+	1.15350i
$505$			6.07841i			0.270486i
$506$	−1.80677	−	3.37830i	−0.0803208	−	0.150184i
$507$	−0.0674222	−	0.572677i	−0.00299433	−	0.0254335i
$508$	2.90157	+	3.06617i	0.128736	+	0.136039i
$509$	4.54692	+	9.44178i	0.201539	+	0.418499i	0.977102	−	0.212770i	$-0.0682485\pi$
$509$	4.54692	+	9.44178i	0.201539	+	0.418499i	−0.775564	+	0.631269i	$0.782534\pi$
$510$	−0.194239	+	0.344262i	−0.00860104	+	0.0152442i
$511$	−9.13934	+	4.40127i	−0.404301	+	0.194701i
$512$	12.8735	+	18.6084i	0.568935	+	0.822383i
$513$	−17.3618	+	28.5723i	−0.766541	+	1.26150i
$514$	−2.85475	+	6.63184i	−0.125918	+	0.292518i
$515$	0.905032	−	3.96520i	0.0398805	−	0.174728i
$516$	−4.55689	−	22.2720i	−0.200606	−	0.980469i
$517$	2.25135	−	2.82311i	0.0990144	−	0.124160i
$518$	5.81946	+	21.2994i	0.255692	+	0.935844i
$519$	−30.0955	−	29.7965i	−1.32104	−	1.30792i
$520$	−2.84854	−	1.73184i	−0.124917	−	0.0759460i
$521$			37.9747i			1.66370i	0.554999	+	0.831851i	$0.312719\pi$
$521$			37.9747i			1.66370i	−0.554999	+	0.831851i	$0.687281\pi$
$522$	−19.9268	+	11.1769i	−0.872172	+	0.489199i
$523$			38.7627i			1.69498i	0.530814	+	0.847488i	$0.321886\pi$
$523$			38.7627i			1.69498i	−0.530814	+	0.847488i	$0.678114\pi$
$524$	−29.4935	−	19.6867i	−1.28843	−	0.860016i
$525$	21.3938	+	21.1813i	0.933704	+	0.924427i
$526$	−39.4102	+	10.7677i	−1.71837	+	0.469494i
$527$	−1.52965	+	1.91812i	−0.0666325	+	0.0835545i
$528$	4.90181	−	1.44378i	0.213324	−	0.0628327i
$529$	2.11615	−	9.27148i	0.0920067	−	0.403108i
$530$	4.44343	+	1.91272i	0.193010	+	0.0830832i
$531$	0.149019	+	14.9238i	0.00646687	+	0.647638i
$532$	43.5229	−	13.8947i	1.88696	−	0.602414i
$533$	24.8547	−	11.9694i	1.07658	−	0.518452i
$534$	−7.14476	−	4.03121i	−0.309184	−	0.174447i
$535$	−2.33141	−	4.84122i	−0.100796	−	0.209304i
$536$	11.6503	−	11.9988i	0.503215	−	0.518269i
$537$	−4.70749	−	39.9849i	−0.203143	−	1.72548i
$538$	10.1744	−	5.44146i	0.438652	−	0.234598i
$539$		−	4.13363i		−	0.178048i
$540$	3.04040	−	1.41728i	0.130838	−	0.0609898i
$541$	−19.8375	+	4.52779i	−0.852882	+	0.194665i	−0.626546	−	0.779385i	$-0.715532\pi$
$541$	−19.8375	+	4.52779i	−0.852882	+	0.194665i	−0.226336	+	0.974049i	$0.572675\pi$
$542$	11.6867	+	5.03068i	0.501989	+	0.216086i
$543$	−15.8386	−	24.9299i	−0.679701	−	1.06984i
$544$	−0.0363061	+	2.82781i	−0.00155661	+	0.121241i
$545$	1.82803	−	1.45780i	0.0783041	−	0.0624454i
$546$	−11.8933	−	29.4427i	−0.508985	−	1.26003i
$547$	−16.6244	+	3.79440i	−0.710807	+	0.162237i	−0.562612	−	0.826721i	$-0.690203\pi$
$547$	−16.6244	+	3.79440i	−0.710807	+	0.162237i	−0.148195	+	0.988958i	$0.547346\pi$
$548$	1.94024	−	13.7907i	0.0828831	−	0.589109i
$549$	6.43823	−	29.5655i	0.274777	−	1.26182i
$550$	−0.216012	−	5.10214i	−0.00921077	−	0.217556i
$551$	33.8570	+	7.36958i	1.44236	+	0.313954i
$552$	−16.3623	−	7.48570i	−0.696428	−	0.318612i
$553$	−17.8567	−	14.2403i	−0.759345	−	0.605557i
$554$	−1.99278	+	10.8229i	−0.0846652	+	0.459820i
$555$	0.800455	−	2.32473i	0.0339774	−	0.0986795i
$556$	11.1362	+	7.43333i	0.472280	+	0.315243i
$557$	−22.2721	+	17.7614i	−0.943701	+	0.752576i	−0.968989	−	0.247104i	$-0.920521\pi$
$557$	−22.2721	+	17.7614i	−0.943701	+	0.752576i	0.0252880	+	0.999680i	$0.491950\pi$
$558$	20.0284	−	5.68769i	0.847869	−	0.240779i
$559$	21.5897	+	10.3970i	0.913145	+	0.439747i
$560$	−4.40598	−	1.26481i	−0.186186	−	0.0534480i
$561$	0.603871	+	0.207925i	0.0254954	+	0.00877862i
$562$	3.97294	+	7.42861i	0.167588	+	0.313357i
$563$		−	32.5999i		−	1.37392i	−0.726694	−	0.686961i	$-0.758944\pi$
$563$		−	32.5999i		−	1.37392i	0.726694	−	0.686961i	$-0.241056\pi$
$564$	0.382951	−	16.9548i	0.0161251	−	0.713926i
$565$	−1.80544	+	1.43979i	−0.0759554	+	0.0605724i
$566$	−31.4606	+	27.3442i	−1.32239	+	1.14936i
$567$	31.2871	+	6.48662i	1.31393	+	0.272412i
$568$	−36.3606	+	4.64044i	−1.52565	+	0.194709i
$569$	17.8144	−	8.57896i	0.746818	−	0.359649i	−0.0214560	−	0.999770i	$-0.506830\pi$
$569$	17.8144	−	8.57896i	0.746818	−	0.359649i	0.768274	+	0.640121i	$0.221116\pi$
$570$	−4.87597	−	1.45131i	−0.204232	−	0.0607885i
$571$	−2.32917	+	4.83657i	−0.0974728	+	0.202404i	−0.944003	−	0.329936i	$-0.892973\pi$
$571$	−2.32917	+	4.83657i	−0.0974728	+	0.202404i	0.846531	+	0.532340i	$0.178687\pi$
$572$	−1.91850	+	5.03310i	−0.0802164	+	0.210444i
$573$	−11.1972	−	11.0859i	−0.467768	−	0.463120i
$574$	28.6299	−	24.8839i	1.19499	−	1.03863i
$575$	−11.2114	+	14.0587i	−0.467549	+	0.586288i
$576$	14.2119	−	19.3397i	0.592162	−	0.805819i
$577$	18.0841	+	4.12758i	0.752851	+	0.171833i	0.581691	−	0.813410i	$-0.302391\pi$
$577$	18.0841	+	4.12758i	0.752851	+	0.171833i	0.171160	+	0.985243i	$0.445249\pi$
$578$	13.9727	−	19.1283i	0.581189	−	0.795633i
$579$	11.3920	−	18.3328i	0.473436	−	0.761886i
$580$	−2.41488	−	2.50092i	−0.100272	−	0.103845i
$581$			17.1037i			0.709579i
$582$	0.467008	+	1.15611i	0.0193581	+	0.0479225i
$583$	1.73929	−	7.62033i	0.0720341	−	0.315602i
$584$	7.58777	−	2.78125i	0.313984	−	0.115089i
$585$	−0.752353	+	3.45493i	−0.0311060	+	0.142844i
$586$	18.4691	+	21.2495i	0.762951	+	0.877807i
$587$	−6.36740	+	27.8974i	−0.262811	+	1.15145i	0.655376	+	0.755303i	$0.272510\pi$
$587$	−6.36740	+	27.8974i	−0.262811	+	1.15145i	−0.918187	+	0.396147i	$0.870347\pi$
$588$	−11.7588	−	15.4481i	−0.484923	−	0.637070i
$589$	−28.4487	−	13.7002i	−1.17221	−	0.564506i
$590$	−2.19067	+	0.598539i	−0.0901887	+	0.0246415i
$591$	0.126008	−	1.17086i	0.00518326	−	0.0481626i
$592$	−2.96303	−	17.3394i	−0.121780	−	0.712647i
$593$	8.21662	+	17.0620i	0.337416	+	0.700652i	0.998778	−	0.0494146i	$-0.0157356\pi$
$593$	8.21662	+	17.0620i	0.337416	+	0.700652i	−0.661362	+	0.750067i	$0.730021\pi$
$594$	−3.14165	−	4.41660i	−0.128903	−	0.181215i
$595$	−0.357205	−	0.447921i	−0.0146440	−	0.0183630i
$596$	14.4259	+	24.4289i	0.590906	+	1.00065i
$597$	12.6443	−	20.3481i	0.517496	−	0.832791i
$598$	16.7248	−	8.94467i	0.683926	−	0.365775i
$599$	30.6401	−	6.99341i	1.25192	−	0.285743i	0.455364	−	0.890305i	$-0.349509\pi$
$599$	30.6401	−	6.99341i	1.25192	−	0.285743i	0.796558	+	0.604562i	$0.206652\pi$
$600$	−15.3211	−	18.4531i	−0.625481	−	0.753346i
$601$	7.07105	−	14.6832i	0.288434	−	0.598940i	−0.705526	−	0.708685i	$-0.749289\pi$
$601$	7.07105	−	14.6832i	0.288434	−	0.598940i	0.993960	+	0.109744i	$0.0350033\pi$
$602$	32.4048	+	5.96659i	1.32072	+	0.243180i
$603$	−16.0581	−	7.53658i	−0.653936	−	0.306913i
$604$	−22.1940	−	14.8143i	−0.903062	−	0.602787i
$605$	−3.29044	+	0.751022i	−0.133775	+	0.0305334i
$606$	31.0374	−	34.1221i	1.26081	−	1.38612i
$607$	−0.0998902	+	0.125258i	−0.00405442	+	0.00508408i	−0.783855	−	0.620944i	$-0.786749\pi$
$607$	−0.0998902	+	0.125258i	−0.00405442	+	0.00508408i	0.779800	+	0.626029i	$0.215321\pi$
$608$	−35.5864	+	7.64307i	−1.44322	+	0.309968i
$609$	−4.20305	−	32.8469i	−0.170316	−	1.33102i
$610$	4.60009	−	0.194756i	0.186252	−	0.00788546i
$611$	13.9762	+	11.1456i	0.565416	+	0.450904i
$612$	2.84825	−	0.940749i	0.115134	−	0.0380275i
$613$	−9.18942	−	40.2615i	−0.371157	−	1.62614i	−0.723535	−	0.690287i	$-0.757484\pi$
$613$	−9.18942	−	40.2615i	−0.371157	−	1.62614i	0.352378	−	0.935858i	$-0.385373\pi$
$614$	0.687863	−	0.941669i	0.0277599	−	0.0380027i
$615$	−4.19492	+	0.493875i	−0.169156	+	0.0199150i
$616$	−0.720707	+	7.37126i	−0.0290381	+	0.296997i
$617$	−33.5737	−	16.1682i	−1.35163	−	0.650909i	−0.388873	−	0.921291i	$-0.627136\pi$
$617$	−33.5737	−	16.1682i	−1.35163	−	0.650909i	−0.962753	+	0.270382i	$0.912850\pi$
$618$	−25.3276	+	17.6380i	−1.01882	+	0.709506i
$619$	−1.49912	−	6.56809i	−0.0602549	−	0.263994i	0.935823	−	0.352469i	$-0.114658\pi$
$619$	−1.49912	−	6.56809i	−0.0602549	−	0.263994i	−0.996078	+	0.0884750i	$0.971801\pi$
$620$	1.61092	+	2.72795i	0.0646963	+	0.109557i
$621$	−1.85255	+	18.9947i	−0.0743404	+	0.762233i
$622$	−15.0875	−	28.2107i	−0.604955	−	1.13114i
$623$	9.29610	−	7.41339i	0.372440	−	0.297011i
$624$	7.14765	+	24.2671i	0.286135	+	0.971461i
$625$	−21.1259	+	10.1737i	−0.845036	+	0.406948i
$626$	−27.7072	+	1.17305i	−1.10740	+	0.0468847i
$627$	−0.879540	+	8.17265i	−0.0351254	+	0.326384i
$628$	−12.8759	+	4.11064i	−0.513803	+	0.164033i
$629$	0.953915	−	1.98082i	0.0380351	−	0.0789807i
$630$	0.254153	+	4.85534i	0.0101257	+	0.193441i
$631$	33.3217	+	7.60546i	1.32652	+	0.302769i	0.826348	−	0.563160i	$-0.190414\pi$
$631$	33.3217	+	7.60546i	1.32652	+	0.302769i	0.500168	+	0.865928i	$0.333272\pi$
$632$	13.0546	+	12.6754i	0.519284	+	0.504200i
$633$	−8.78602	+	3.12368i	−0.349213	+	0.124155i
$634$	−1.34781	−	4.93305i	−0.0535286	−	0.195917i
$635$	0.664231	+	0.151606i	0.0263592	+	0.00601632i
$636$	−15.1772	−	33.4263i	−0.601814	−	1.32544i
$637$	20.4641			0.810817
$638$	−3.26746	+	4.56902i	−0.129360	+	0.180889i
$639$	17.2179	+	34.8586i	0.681129	+	1.37898i
$640$	3.39544	+	1.34443i	0.134217	+	0.0531434i
$641$	−1.87562	+	8.21763i	−0.0740826	+	0.324577i	−0.998367	−	0.0571278i	$-0.981806\pi$
$641$	−1.87562	+	8.21763i	−0.0740826	+	0.324577i	0.924284	+	0.381705i	$0.124663\pi$
$642$	−11.6324	+	39.0816i	−0.459095	+	1.54243i
$643$	30.1332	+	24.0305i	1.18834	+	0.947669i	0.999411	−	0.0343224i	$-0.0109273\pi$
$643$	30.1332	+	24.0305i	1.18834	+	0.947669i	0.188928	+	0.981991i	$0.439499\pi$
$644$	18.9424	−	17.9255i	0.746435	−	0.706364i
$645$	−2.60731	−	2.58140i	−0.102663	−	0.101643i
$646$	−4.17844	−	1.79865i	−0.164398	−	0.0707670i
$647$	−2.43121	−	1.17081i	−0.0955809	−	0.0460293i	0.385482	−	0.922715i	$-0.374035\pi$
$647$	−2.43121	−	1.17081i	−0.0955809	−	0.0460293i	−0.481063	+	0.876686i	$0.659749\pi$
$648$	−24.3046	−	7.56872i	−0.954776	−	0.297327i
$649$	1.59204	+	3.30591i	0.0624932	+	0.129768i
$650$	25.2588	−	1.06940i	0.990733	−	0.0419452i
$651$	−3.22898	+	30.0036i	−0.126554	+	1.17593i
$652$	26.9902	+	28.5213i	1.05702	+	1.11698i
$653$	−7.69131	−	9.64460i	−0.300984	−	0.377422i	0.608223	−	0.793766i	$-0.291883\pi$
$653$	−7.69131	−	9.64460i	−0.300984	−	0.377422i	−0.909207	+	0.416344i	$0.863311\pi$
$654$	−17.7057	−	1.15063i	−0.692349	−	0.0449932i
$655$	−5.72306			−0.223618
$656$	−24.6297	+	17.5109i	−0.961630	+	0.683686i
$657$	−5.41099	−	6.64790i	−0.211103	−	0.259359i
$658$	22.5775	+	9.71872i	0.880162	+	0.378875i
$659$	10.6820	−	22.1813i	0.416110	−	0.864061i	−0.582574	−	0.812777i	$-0.697955\pi$
$659$	10.6820	−	22.1813i	0.416110	−	0.864061i	0.998684	−	0.0512834i	$-0.0163312\pi$
$660$	0.528636	−	0.633019i	0.0205771	−	0.0246402i
$661$	15.6274	+	19.5962i	0.607837	+	0.762204i	0.986577	−	0.163300i	$-0.0522138\pi$
$661$	15.6274	+	19.5962i	0.607837	+	0.762204i	−0.378739	+	0.925503i	$0.623642\pi$
$662$	19.8285	−	27.1448i	0.770657	−	1.05501i
$663$	−1.02936	+	2.98954i	−0.0399772	+	0.116104i
$664$	1.32594	−	13.5615i	0.0514564	−	0.526287i
$665$	4.59736	−	5.76491i	0.178278	−	0.223553i
$666$	−16.3640	+	8.96299i	−0.634092	+	0.347309i
$667$	19.2379	−	4.59531i	0.744893	−	0.177931i
$668$	21.8980	−	1.85754i	0.847257	−	0.0718704i
$669$	3.88147	+	10.9174i	0.150066	+	0.422093i
$670$	0.488775	−	2.65456i	0.0188830	−	0.102555i
$671$	−1.65537	−	7.25267i	−0.0639050	−	0.279986i
$672$	18.2753	+	29.5979i	0.704985	+	1.14176i
$673$	29.7939	+	37.3604i	1.14847	+	1.44014i	0.878803	+	0.477185i	$0.158343\pi$
$673$	29.7939	+	37.3604i	1.14847	+	1.44014i	0.269669	+	0.962953i	$0.413086\pi$
$674$	20.0981	+	3.70059i	0.774149	+	0.142541i
$675$	−13.2104	+	21.7404i	−0.508470	+	0.836789i
$676$	−0.622171	−	0.237157i	−0.0239296	−	0.00912141i
$677$	−7.10149	−	31.1137i	−0.272932	−	1.19579i	−0.906533	−	0.422135i	$-0.861281\pi$
$677$	−7.10149	−	31.1137i	−0.272932	−	1.19579i	0.633601	−	0.773660i	$-0.281576\pi$
$678$	17.4869	+	1.13641i	0.671582	+	0.0436436i
$679$	−1.80721			−0.0693543
$680$	0.248503	+	0.382848i	0.00952966	+	0.0146816i
$681$	0.173359	+	1.47249i	0.00664313	+	0.0564260i
$682$	3.86345	−	3.35795i	0.147939	−	0.128582i
$683$	−38.1589	+	18.3763i	−1.46011	+	0.703151i	−0.984317	−	0.176407i	$-0.943553\pi$
$683$	−38.1589	+	18.3763i	−1.46011	+	0.703151i	−0.475792	+	0.879558i	$0.657838\pi$
$684$	19.9614	+	33.0447i	0.763243	+	1.26350i
$685$	−0.975218	−	2.02506i	−0.0372612	−	0.0773736i
$686$	−6.75928	+	1.84678i	−0.258071	+	0.0705103i
$687$	−24.0659	+	15.2897i	−0.918170	+	0.583339i
$688$	−25.2312	−	7.24305i	−0.961930	−	0.276139i
$689$	37.7255	+	8.61060i	1.43723	+	0.328038i
$690$	−2.86715	+	0.461242i	−0.109151	+	0.0175592i
$691$	26.5589	+	21.1801i	1.01035	+	0.805727i	0.981033	−	0.193843i	$-0.0620952\pi$
$691$	26.5589	+	21.1801i	1.01035	+	0.805727i	0.0293174	+	0.999570i	$0.490667\pi$
$692$	−46.5857	+	14.8726i	−1.77092	+	0.565370i
$693$	7.64089	−	1.82444i	0.290253	−	0.0693047i
$694$	−14.5826	+	19.9632i	−0.553548	+	0.757794i
$695$	2.16092			0.0819685
$696$	0.786178	+	26.3701i	0.0298000	+	0.999556i
$697$	−3.77700			−0.143064
$698$	−18.3582	+	25.1319i	−0.694867	+	0.951257i
$699$	13.7562	+	13.6195i	0.520307	+	0.515138i
$700$	33.1162	−	10.5724i	1.25167	−	0.399599i
$701$	−5.26734	−	4.20056i	−0.198945	−	0.158653i	0.518951	−	0.854804i	$-0.326323\pi$
$701$	−5.26734	−	4.20056i	−0.198945	−	0.158653i	−0.717895	+	0.696151i	$0.754894\pi$
$702$	21.8650	−	15.5532i	0.825240	−	0.587016i
$703$	27.5867	+	6.29648i	1.04045	+	0.237476i
$704$	1.14289	−	5.78879i	0.0430745	−	0.218173i
$705$	−1.46777	−	2.31026i	−0.0552796	−	0.0870096i
$706$	−3.79562	+	1.03704i	−0.142850	+	0.0390296i
$707$	29.0074	+	60.2344i	1.09093	+	2.26535i
$708$	15.3539	+	7.82599i	0.577037	+	0.294119i
$709$	8.88152	−	4.27712i	0.333553	−	0.160630i	−0.259609	−	0.965714i	$-0.583594\pi$
$709$	8.88152	−	4.27712i	0.333553	−	0.160630i	0.593162	+	0.805083i	$0.297879\pi$
$710$	−4.46512	+	3.88089i	−0.167573	+	0.145647i
$711$	8.19975	−	17.4711i	0.307515	−	0.655217i
$712$	−7.94558	+	5.15740i	−0.297773	+	0.193282i
$713$	−18.0243			−0.675016
$714$	−0.281938	+	4.33843i	−0.0105513	+	0.162362i
$715$	0.193442	+	0.847526i	0.00723433	+	0.0316957i
$716$	−43.4406	−	16.5585i	−1.62345	−	0.618821i
$717$	18.1751	+	28.6075i	0.678763	+	1.06837i
$718$	−12.7321	−	2.34432i	−0.475159	−	0.0874894i
$719$	−16.6797	−	20.9157i	−0.622048	−	0.780023i	0.366583	−	0.930385i	$-0.380527\pi$
$719$	−16.6797	−	20.9157i	−0.622048	−	0.780023i	−0.988631	+	0.150362i	$0.951956\pi$
$720$	0.174887	−	3.86950i	0.00651764	−	0.144208i
$721$	−9.95425	−	43.6124i	−0.370716	−	1.62421i
$722$	5.73647	−	31.1550i	0.213489	−	1.15947i
$723$	27.8395	−	9.89774i	1.03536	−	0.368101i
$724$	−33.9829	+	2.88267i	−1.26297	+	0.107134i
$725$	25.7615	+	5.60745i	0.956759	+	0.208255i
$726$	22.3063	+	12.5856i	0.827863	+	0.467096i
$727$	−12.5844	+	15.7803i	−0.466729	+	0.585260i	−0.958367	−	0.285540i	$-0.907827\pi$
$727$	−12.5844	+	15.7803i	−0.466729	+	0.585260i	0.491638	+	0.870800i	$0.336398\pi$
$728$	−36.4924	−	3.56796i	−1.35250	−	0.132237i
$729$	0.808663	+	26.9879i	0.0299505	+	0.999551i
$730$	0.769351	−	1.05322i	0.0284749	−	0.0389815i
$731$	−2.04557	−	2.56506i	−0.0756580	−	0.0948721i
$732$	−26.8178	−	22.3956i	−0.991214	−	0.827765i
$733$	−15.6083	+	32.4109i	−0.576505	+	1.19713i	0.385147	+	0.922855i	$0.374151\pi$
$733$	−15.6083	+	32.4109i	−0.576505	+	1.19713i	−0.961653	+	0.274271i	$0.911564\pi$
$734$	−16.6218	−	7.15504i	−0.613523	−	0.264097i
$735$	−2.96263	−	1.02010i	−0.109278	−	0.0376268i
$736$	−16.4091	+	12.7446i	−0.604846	+	0.469773i
$737$	−4.36117			−0.160646
$738$	26.0707	+	18.6476i	0.959675	+	0.686427i
$739$	5.05270	+	6.33589i	0.185867	+	0.233069i	0.866031	−	0.499990i	$-0.166663\pi$
$739$	5.05270	+	6.33589i	0.185867	+	0.233069i	−0.680164	+	0.733060i	$0.738092\pi$
$740$	−1.95139	−	2.06209i	−0.0717346	−	0.0758040i
$741$	−40.4598	−	4.35428i	−1.48633	−	0.159959i
$742$	53.1603	−	2.25068i	1.95158	−	0.0826249i
$743$	−12.8327	−	26.6475i	−0.470788	−	0.977601i	−0.992242	−	0.124322i	$-0.960325\pi$
$743$	−12.8327	−	26.6475i	−0.470788	−	0.977601i	0.521454	−	0.853279i	$-0.325390\pi$
$744$	4.88624	−	23.5395i	0.179138	−	0.862999i
$745$	4.12534	+	1.98666i	0.151141	+	0.0727856i
$746$	12.1255	+	5.21955i	0.443946	+	0.191101i
$747$	−14.0575	+	3.35656i	−0.514338	+	0.122810i
$748$	0.535647	−	0.506892i	0.0195852	−	0.0185338i
$749$	−46.2065	−	36.8485i	−1.68835	−	1.34641i
$750$	−7.49912	−	2.23207i	−0.273829	−	0.0815038i
$751$	−7.26063	+	31.8109i	−0.264944	+	1.16080i	0.650869	+	0.759190i	$0.274405\pi$
$751$	−7.26063	+	31.8109i	−0.264944	+	1.16080i	−0.915813	+	0.401605i	$0.868452\pi$
$752$	−17.1482	−	9.45625i	−0.625332	−	0.344834i
$753$	−20.0697	+	32.2976i	−0.731381	+	1.17699i
$754$	−22.6196	−	16.1760i	−0.823756	−	0.589097i
$755$	−4.30664			−0.156735
$756$	23.3655	−	28.5540i	0.849796	−	1.03850i
$757$	1.76930	+	0.403831i	0.0643063	+	0.0146775i	0.254553	−	0.967059i	$-0.418072\pi$
$757$	1.76930	+	0.403831i	0.0643063	+	0.0146775i	−0.190247	+	0.981736i	$0.560929\pi$
$758$	14.2858	+	52.2866i	0.518884	+	1.89913i
$759$	1.57180	+	4.42103i	0.0570528	+	0.160473i
$760$	−4.09216	+	4.21458i	−0.148438	+	0.152879i
$761$	−2.24766	−	0.513013i	−0.0814775	−	0.0185967i	0.181588	−	0.983375i	$-0.441876\pi$
$761$	−2.24766	−	0.513013i	−0.0814775	−	0.0185967i	−0.263065	+	0.964778i	$0.584733\pi$
$762$	−2.95464	−	4.24275i	−0.107035	−	0.153699i
$763$	11.1580	−	23.1699i	0.403948	−	0.838807i
$764$	−17.3324	+	5.53341i	−0.627065	+	0.200192i
$765$	0.298046	−	0.381491i	0.0107759	−	0.0137928i
$766$	3.88744	−	0.164584i	0.140459	−	0.00594668i
$767$	−16.3664	+	7.88163i	−0.590956	+	0.284589i
$768$	−12.1959	−	24.8849i	−0.440082	−	0.897957i
$769$	4.27488	−	3.40910i	0.154156	−	0.122935i	−0.543374	−	0.839490i	$-0.682854\pi$
$769$	4.27488	−	3.40910i	0.154156	−	0.122935i	0.697531	+	0.716555i	$0.254282\pi$
$770$	0.563733	+	1.05407i	0.0203155	+	0.0379860i
$771$	4.66725	−	7.51087i	0.168087	−	0.270497i
$772$	−12.6730	−	21.4606i	−0.456111	−	0.772383i
$773$	−5.47793	−	24.0004i	−0.197027	−	0.863233i	−0.972694	−	0.232091i	$-0.925443\pi$
$773$	−5.47793	−	24.0004i	−0.197027	−	0.863233i	0.775667	−	0.631143i	$-0.217414\pi$
$774$	1.45543	+	27.8045i	0.0523142	+	0.999413i
$775$	−21.6464	−	10.4244i	−0.777562	−	0.374454i
$776$	1.43293	+	0.140102i	0.0514393	+	0.00502935i
$777$	−3.16193	−	26.8570i	−0.113433	−	0.963491i
$778$	11.1735	−	15.2963i	0.400591	−	0.548399i
$779$	−10.8170	−	47.3926i	−0.387561	−	1.69802i
$780$	3.13385	+	2.61708i	0.112210	+	0.0937066i
$781$	7.47323	+	5.95970i	0.267413	+	0.213255i
$782$	−2.59444	+	0.109842i	−0.0927771	+	0.00392795i
$783$	26.1721	−	9.90063i	0.935314	−	0.353819i
$784$	−22.0973	+	3.77608i	−0.789190	+	0.134860i
$785$	−1.36009	+	1.70550i	−0.0485437	+	0.0608719i
$786$	32.1273	+	29.2230i	1.14594	+	1.04235i
$787$	−36.7634	+	8.39101i	−1.31047	+	0.299107i	−0.820007	−	0.572353i	$-0.806031\pi$
$787$	−36.7634	+	8.39101i	−1.31047	+	0.299107i	−0.490466	+	0.871460i	$0.663174\pi$
$788$	−1.13099	−	0.754926i	−0.0402898	−	0.0268931i
$789$	49.6934	−	5.85049i	1.76913	−	0.208283i
$790$	2.88814	+	0.531784i	0.102755	+	0.0189200i
$791$	−11.0202	+	22.8836i	−0.391832	+	0.813647i
$792$	−6.19989	+	0.854245i	−0.220303	+	0.0303543i
$793$	35.9053	−	8.19516i	1.27504	−	0.291019i
$794$	−27.2639	+	14.5812i	−0.967558	+	0.517466i
$795$	−5.03238	−	3.12712i	−0.178480	−	0.110908i
$796$	−14.0661	−	23.8196i	−0.498559	−	0.844264i
$797$	5.58545	+	7.00393i	0.197847	+	0.248092i	0.870852	−	0.491546i	$-0.163568\pi$
$797$	5.58545	+	7.00393i	0.197847	+	0.248092i	−0.673005	+	0.739638i	$0.734997\pi$
$798$	−55.2447	+	8.88727i	−1.95564	+	0.314606i
$799$	−1.06193	−	2.20513i	−0.0375685	−	0.0780117i
$800$	−27.0774	+	5.81555i	−0.957331	+	0.205611i
$801$	7.91742	+	6.18562i	0.279748	+	0.218558i
$802$	15.0886	−	4.12253i	0.532798	−	0.145572i
$803$	−1.89869	−	0.914363i	−0.0670034	−	0.0322672i
$804$	−16.2985	+	12.4060i	−0.574803	+	0.437527i
$805$	0.936604	−	4.10353i	0.0330109	−	0.144630i
$806$	16.6240	+	19.1266i	0.585554	+	0.673704i
$807$	−13.3148	+	4.73380i	−0.468704	+	0.166638i
$808$	−18.3303	−	50.0085i	−0.644858	−	1.75929i
$809$	−5.02237	+	22.0044i	−0.176577	+	0.773635i	0.806617	+	0.591074i	$0.201296\pi$
$809$	−5.02237	+	22.0044i	−0.176577	+	0.773635i	−0.983195	+	0.182561i	$0.941561\pi$
$810$	−3.94074	+	1.16174i	−0.138463	+	0.0408193i
$811$			27.8239i			0.977029i	0.872556	+	0.488515i	$0.162461\pi$
$811$			27.8239i			0.977029i	−0.872556	+	0.488515i	$0.837539\pi$
$812$	−35.8653	−	13.2587i	−1.25862	−	0.465290i
$813$	−13.2358	−	8.22471i	−0.464199	−	0.288453i
$814$	−2.70577	+	3.70414i	−0.0948373	+	0.129830i
$815$	6.17862	+	1.41023i	0.216428	+	0.0493982i
$816$	0.559880	−	3.41808i	0.0195997	−	0.119657i
$817$	26.3272	−	33.0132i	0.921071	−	1.15499i
$818$	35.4737	−	30.8322i	1.24031	−	1.07802i
$819$	9.03213	+	37.8273i	0.315608	+	1.32179i
$820$	−1.73720	+	4.55747i	−0.0606656	+	0.159154i
$821$	−12.6171	+	26.1997i	−0.440341	+	0.914377i	0.556182	+	0.831060i	$0.312266\pi$
$821$	−12.6171	+	26.1997i	−0.440341	+	0.914377i	−0.996523	+	0.0833166i	$0.973449\pi$
$822$	−4.86579	+	16.3476i	−0.169714	+	0.570189i
$823$	5.11301	−	2.46229i	0.178228	−	0.0858302i	−0.342642	−	0.939466i	$-0.611322\pi$
$823$	5.11301	−	2.46229i	0.178228	−	0.0858302i	0.520870	+	0.853636i	$0.325608\pi$
$824$	4.51172	+	35.3519i	0.157173	+	1.23154i
$825$	−0.669235	+	6.21850i	−0.0232998	+	0.216501i
$826$	−18.8523	+	16.3856i	−0.655955	+	0.570128i
$827$	−0.639941	+	0.510336i	−0.0222529	+	0.0177461i	−0.634553	−	0.772879i	$-0.718816\pi$
$827$	−0.639941	+	0.510336i	−0.0222529	+	0.0177461i	0.612300	+	0.790625i	$0.290244\pi$
$828$	18.4504	+	12.0510i	0.641196	+	0.418800i
$829$		−	5.04869i		−	0.175348i	−0.996149	−	0.0876741i	$-0.972057\pi$
$829$		−	5.04869i		−	0.175348i	0.996149	−	0.0876741i	$-0.0279434\pi$
$830$	−1.03714	−	1.93925i	−0.0359997	−	0.0673123i
$831$	4.38796	−	12.7438i	0.152217	−	0.442078i
$832$	28.6582	+	5.65806i	0.993545	+	0.196158i
$833$	−2.52436	−	1.21567i	−0.0874637	−	0.0421203i
$834$	−12.1307	−	11.0341i	−0.420051	−	0.382078i
$835$	2.77306	−	2.21144i	0.0959658	−	0.0765302i
$836$	7.89436	+	5.26943i	0.273032	+	0.182247i
$837$	−25.2937	+	3.23423i	−0.874277	+	0.111791i
$838$	4.46389	−	24.2436i	0.154202	−	0.837480i
$839$	26.6586	+	21.2595i	0.920356	+	0.733959i	0.964227	−	0.265078i	$-0.0853977\pi$
$839$	26.6586	+	21.2595i	0.920356	+	0.733959i	−0.0438713	+	0.999037i	$0.513969\pi$
$840$	5.10524	+	2.33562i	0.176147	+	0.0805866i
$841$	−18.5344	−	22.3042i	−0.639116	−	0.769110i
$842$	−1.33999	−	31.6502i	−0.0461791	−	1.09074i
$843$	−3.45626	−	9.72147i	−0.119040	−	0.334825i
$844$	−1.50011	+	10.6623i	−0.0516358	+	0.367012i
$845$	−0.104768	+	0.0239125i	−0.00360412	+	0.000822616i
$846$	−3.55705	+	20.4638i	−0.122294	+	0.703558i
$847$	−29.0228	+	23.1449i	−0.997236	+	0.795269i
$848$	−42.3252	−	2.33663i	−1.45345	−	0.0802401i
$849$	43.0900	−	27.3763i	1.47885	−	0.939551i
$850$	−3.17934	−	1.36858i	−0.109050	−	0.0469419i
$851$	15.7473	−	3.59421i	0.539809	−	0.123208i
$852$	44.8822	+	1.01373i	1.53764	+	0.0347300i
$853$		−	19.1447i		−	0.655503i	−0.944764	−	0.327751i	$-0.893709\pi$
$853$		−	19.1447i		−	0.655503i	0.944764	−	0.327751i	$-0.106291\pi$
$854$	44.6555	−	23.8825i	1.52808	−	0.817242i
$855$	5.64041	+	2.64723i	0.192898	+	0.0905332i
$856$	33.7805	+	32.7992i	1.15459	+	1.12105i
$857$	14.5555	+	30.2248i	0.497206	+	1.03246i	0.987015	+	0.160629i	$0.0513521\pi$
$857$	14.5555	+	30.2248i	0.497206	+	1.03246i	−0.489809	+	0.871830i	$0.662934\pi$
$858$	3.24170	−	5.74547i	0.110670	−	0.196147i
$859$	−6.35465	+	3.06024i	−0.216818	+	0.104414i	−0.539140	−	0.842216i	$-0.681251\pi$
$859$	−6.35465	+	3.06024i	−0.216818	+	0.104414i	0.322323	+	0.946630i	$0.395536\pi$
$860$	−4.03594	+	1.28848i	−0.137624	+	0.0439368i
$861$	−39.2130	+	24.9131i	−1.33638	+	0.849036i
$862$	28.6672	+	12.3401i	0.976408	+	0.420305i
$863$	−2.00702	+	8.79335i	−0.0683199	+	0.299329i	−0.997532	−	0.0702188i	$-0.977630\pi$
$863$	−2.00702	+	8.79335i	−0.0683199	+	0.299329i	0.929212	+	0.369548i	$0.120487\pi$
$864$	−20.7401	+	20.8290i	−0.705592	+	0.708618i
$865$	−4.92089	+	6.17060i	−0.167315	+	0.209807i
$866$	14.4777	−	3.95562i	0.491973	−	0.134418i
$867$	−20.4119	+	20.6167i	−0.693224	+	0.700181i
$868$	28.9819	+	19.3452i	0.983710	+	0.656618i
$869$		−	4.74492i		−	0.160960i
$870$	2.46834	+	3.46938i	0.0836846	+	0.117623i
$871$		−	21.5906i		−	0.731568i
$872$	−10.6434	+	17.5064i	−0.360432	+	0.592841i
$873$	−0.354661	−	1.48535i	−0.0120035	−	0.0502714i
$874$	−8.80856	−	32.2397i	−0.297954	−	1.09052i
$875$	7.07063	−	8.86629i	0.239031	−	0.299735i
$876$	−9.69682	+	1.98399i	−0.327625	+	0.0670328i
$877$	−7.07577	+	31.0010i	−0.238932	+	1.04683i	0.703043	+	0.711147i	$0.251824\pi$
$877$	−7.07577	+	31.0010i	−0.238932	+	1.04683i	−0.941975	+	0.335682i	$0.891033\pi$
$878$	0.826854	−	1.92086i	0.0279050	−	0.0648259i
$879$	−18.4908	−	29.1043i	−0.623678	−	0.981664i
$880$	−0.365268	−	0.879472i	−0.0123132	−	0.0296470i
$881$	14.7482	−	7.10235i	0.496879	−	0.239284i	−0.168623	−	0.985681i	$-0.553932\pi$
$881$	14.7482	−	7.10235i	0.496879	−	0.239284i	0.665502	+	0.746396i	$0.268218\pi$
$882$	11.4224	+	20.8542i	0.384612	+	0.702198i
$883$	−21.5873	−	44.8264i	−0.726470	−	1.50853i	−0.856012	−	0.516956i	$-0.827065\pi$
$883$	−21.5873	−	44.8264i	−0.726470	−	1.50853i	0.129542	−	0.991574i	$-0.458649\pi$
$884$	2.50944	+	2.65179i	0.0844015	+	0.0891895i
$885$	2.76228	−	0.325208i	0.0928531	−	0.0109317i
$886$	−17.9918	−	33.6410i	−0.604445	−	1.13019i
$887$			11.7555i			0.394711i	0.980332	+	0.197355i	$0.0632352\pi$
$887$			11.7555i			0.394711i	−0.980332	+	0.197355i	$0.936765\pi$
$888$	0.425029	+	21.5400i	0.0142631	+	0.722836i
$889$	7.30574	−	1.66749i	0.245027	−	0.0559257i
$890$	−0.604474	+	1.40425i	−0.0202620	+	0.0470705i
$891$	2.99902	+	5.92202i	0.100471	+	0.198395i
$892$	13.2489	+	1.86402i	0.443607	+	0.0624121i
$893$	24.6279	−	19.6401i	0.824141	−	0.657231i
$894$	−13.0140	−	32.2172i	−0.435254	−	1.07750i
$895$	−7.31499	+	1.66960i	−0.244513	+	0.0558085i
$896$	40.0633	−	2.88094i	1.33842	−	0.0962455i
$897$	−21.8869	+	7.78142i	−0.730782	+	0.259814i
$898$	−17.2362	+	0.729738i	−0.575180	+	0.0243517i
$899$	11.7056	+	23.6933i	0.390404	+	0.790216i
$900$	15.1885	+	25.1434i	0.506282	+	0.838115i
$901$	−4.14213	−	3.30324i	−0.137994	−	0.110047i
$902$	7.75020	+	1.42702i	0.258053	+	0.0475145i
$903$	−38.1563	−	13.1380i	−1.26976	−	0.437206i
$904$	10.5119	−	17.2901i	0.349620	−	0.575059i
$905$	−4.30345	+	3.43189i	−0.143052	+	0.114080i
$906$	24.1760	+	21.9905i	0.803194	+	0.730585i
$907$	20.2470	+	9.75046i	0.672292	+	0.323759i	0.738700	−	0.674034i	$-0.235440\pi$
$907$	20.2470	+	9.75046i	0.672292	+	0.323759i	−0.0664086	+	0.997793i	$0.521154\pi$
$908$	1.59975	+	0.609787i	0.0530896	+	0.0202365i
$909$	−43.8141	+	35.6621i	−1.45322	+	1.18284i
$910$	−5.21831	+	2.79084i	−0.172985	+	0.0925154i
$911$			12.6274i			0.418365i	0.977877	+	0.209183i	$0.0670803\pi$
$911$			12.6274i			0.418365i	−0.977877	+	0.209183i	$0.932920\pi$
$912$	44.4924	−	2.76393i	1.47329	−	0.0915230i
$913$	−2.77806	+	2.21543i	−0.0919405	+	0.0733201i
$914$	−22.8571	−	26.2981i	−0.756047	−	0.869863i
$915$	−5.60661	−	0.603383i	−0.185349	−	0.0199472i
$916$	2.78277	+	32.8052i	0.0919452	+	1.08391i
$917$	−56.7130	+	27.3116i	−1.87283	+	0.901907i
$918$	−3.62109	+	0.619682i	−0.119514	+	0.0204526i
$919$	3.41521	−	7.09176i	0.112658	−	0.233936i	−0.837015	−	0.547180i	$-0.815701\pi$
$919$	3.41521	−	7.09176i	0.112658	−	0.233936i	0.949673	+	0.313244i	$0.101416\pi$
$920$	−1.06075	+	3.18107i	−0.0349720	+	0.104877i
$921$	−1.00486	+	1.01494i	−0.0331112	+	0.0334434i
$922$	−3.15496	−	3.62991i	−0.103903	−	0.119545i
$923$	−29.5043	+	36.9973i	−0.971147	+	1.21778i
$924$	2.21766	−	8.79570i	0.0729556	−	0.289357i
$925$	20.9905	+	4.79094i	0.690163	+	0.157525i
$926$	31.5015	+	23.0110i	1.03520	+	0.756188i
$927$	33.8916	−	16.7403i	1.11315	−	0.549823i
$928$	27.4097	+	13.2932i	0.899766	+	0.436372i
$929$			27.6787i			0.908109i	0.890974	+	0.454054i	$0.150023\pi$
$929$			27.6787i			0.908109i	−0.890974	+	0.454054i	$0.849977\pi$
$930$	−1.45327	−	3.59767i	−0.0476545	−	0.117972i
$931$	8.02421	−	35.1564i	0.262983	−	1.15220i
$932$	21.2936	−	6.79803i	0.697497	−	0.222677i
$933$	13.1254	+	36.9180i	0.429706	+	1.20864i
$934$	−42.8712	+	37.2617i	−1.40279	+	1.21924i
$935$	0.0264850	−	0.116038i	0.000866151	−	0.00379486i
$936$	−4.22906	−	30.6934i	−0.138231	−	1.00325i
$937$	14.2963	+	6.88472i	0.467038	+	0.224914i	0.652576	−	0.757723i	$-0.273688\pi$
$937$	14.2963	+	6.88472i	0.467038	+	0.224914i	−0.185538	+	0.982637i	$0.559403\pi$
$938$	−7.82453	−	28.6381i	−0.255480	−	0.935067i
$939$	33.7696	+	3.63428i	1.10203	+	0.118600i
$940$	−3.14921	+	0.267139i	−0.102716	+	0.00871310i
$941$	−21.6635	−	44.9847i	−0.706210	−	1.46646i	−0.876668	−	0.481095i	$-0.840239\pi$
$941$	−21.6635	−	44.9847i	−0.706210	−	1.46646i	0.170459	−	0.985365i	$-0.445475\pi$
$942$	16.3437	−	2.62922i	0.532506	−	0.0856647i
$943$	−17.3011	−	21.6949i	−0.563400	−	0.706482i
$944$	16.2182	−	11.5306i	0.527859	−	0.375290i
$945$	0.578017	−	5.92657i	0.0188029	−	0.192791i
$946$	3.22826	+	6.03621i	0.104960	+	0.196254i
$947$	4.35848	−	0.994794i	0.141631	−	0.0323265i	−0.151117	−	0.988516i	$-0.548287\pi$
$947$	4.35848	−	0.994794i	0.141631	−	0.0323265i	0.292749	+	0.956189i	$0.405430\pi$
$948$	−13.4977	−	17.7326i	−0.438383	−	0.575929i
$949$	4.52668	−	9.39975i	0.146942	−	0.305129i
$950$	8.06711	−	43.8128i	0.261732	−	1.42148i
$951$	0.732317	+	6.22022i	0.0237470	+	0.201704i
$952$	4.28958	+	2.60795i	0.139026	+	0.0845242i
$953$	43.8211	−	10.0019i	1.41951	−	0.323993i	0.557199	−	0.830379i	$-0.311876\pi$
$953$	43.8211	−	10.0019i	1.41951	−	0.323993i	0.862307	+	0.506386i	$0.169019\pi$
$954$	12.2824	+	43.2509i	0.397658	+	1.40030i
$955$	−1.83084	+	2.29580i	−0.0592446	+	0.0742903i
$956$	38.9960	−	3.30792i	1.26122	−	0.106986i
$957$	4.79074	−	4.93733i	0.154863	−	0.159601i
$958$	−0.0836553	−	1.97591i	−0.00270278	−	0.0638389i
$959$	−19.3280	−	15.4135i	−0.624133	−	0.497729i
$960$	−3.86687	−	2.24769i	−0.124803	−	0.0725438i
$961$	1.53927	+	6.74400i	0.0496540	+	0.217548i
$962$	−18.3378	−	13.3953i	−0.591236	−	0.431882i
$963$	21.2179	−	45.2087i	0.683737	−	1.45683i
$964$	4.75326	−	33.7848i	0.153092	−	1.08813i
$965$	−3.62408	−	1.74527i	−0.116663	−	0.0561821i
$966$	−26.2111	+	18.2533i	−0.843329	+	0.587292i
$967$	−5.18627	−	22.7225i	−0.166779	−	0.730707i	−0.987271	−	0.159048i	$-0.949157\pi$
$967$	−5.18627	−	22.7225i	−0.166779	−	0.730707i	0.820492	−	0.571658i	$-0.193700\pi$
$968$	24.8065	−	16.1016i	0.797310	−	0.517526i
$969$	4.73227	+	2.94063i	0.152023	+	0.0944668i
$970$	0.204905	−	0.109587i	0.00657911	−	0.00351862i
$971$	−15.1012	+	12.0428i	−0.484619	+	0.386471i	−0.835099	−	0.550099i	$-0.814590\pi$
$971$	−15.1012	+	12.0428i	−0.484619	+	0.386471i	0.350480	+	0.936570i	$0.386018\pi$
$972$	28.0540	+	13.6005i	0.899832	+	0.436236i
$973$	21.4138	−	10.3123i	0.686495	−	0.330599i
$974$	−0.683833	−	16.1519i	−0.0219114	−	0.517541i
$975$	−30.7856	−	3.31314i	−0.985927	−	0.106105i
$976$	−37.2588	+	15.4745i	−1.19262	+	0.495328i
$977$	19.1705	−	39.8080i	0.613319	−	1.27357i	−0.330717	−	0.943730i	$-0.607291\pi$
$977$	19.1705	−	39.8080i	0.613319	−	1.27357i	0.944037	−	0.329841i	$-0.106995\pi$
$978$	−27.4838	−	39.4657i	−0.878835	−	1.26197i
$979$	2.40824	+	0.549666i	0.0769678	+	0.0175674i
$980$	−2.62792	+	2.48685i	−0.0839459	+	0.0794394i
$981$	21.2331	+	4.62377i	0.677922	+	0.147626i
$982$	50.0545	−	13.6759i	1.59730	−	0.436417i
$983$	−55.1181	−	12.5803i	−1.75799	−	0.401251i	−0.782742	−	0.622347i	$-0.786179\pi$
$983$	−55.1181	−	12.5803i	−1.75799	−	0.401251i	−0.975252	+	0.221096i	$0.929036\pi$
$984$	33.0233	−	16.7136i	1.05274	−	0.532811i
$985$	−0.219462			−0.00699266
$986$	1.82931	+	3.33911i	0.0582571	+	0.106339i
$987$	−25.5700	−	15.8892i	−0.813903	−	0.505759i
$988$	−26.0870	+	39.0821i	−0.829939	+	1.24337i
$989$	5.36354	−	23.4992i	0.170551	−	0.747231i
$990$	−0.755709	+	0.670192i	−0.0240180	+	0.0213001i
$991$	−43.7862	−	34.9184i	−1.39092	−	1.10922i	−0.980323	−	0.197400i	$-0.936750\pi$
$991$	−43.7862	−	34.9184i	−1.39092	−	1.10922i	−0.410593	−	0.911819i	$-0.634678\pi$
$992$	−21.4800	−	17.5856i	−0.681991	−	0.558342i
$993$	−28.9662	+	29.2569i	−0.919216	+	0.928441i
$994$	−25.7270	+	59.7663i	−0.816012	+	1.89567i
$995$	−4.02246	−	1.93711i	−0.127521	−	0.0614106i
$996$	−4.07999	+	16.1821i	−0.129280	+	0.512750i
$997$	22.5347	+	46.7938i	0.713682	+	1.48198i	0.869366	+	0.494169i	$0.164527\pi$
$997$	22.5347	+	46.7938i	0.713682	+	1.48198i	−0.155684	+	0.987807i	$0.549758\pi$
$998$	0.0485450	+	1.14662i	0.00153666	+	0.0362956i
$999$	21.4533	−	7.86943i	0.678753	−	0.248978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.18	yes	336
3.2	odd	2	inner	348.2.t.a.35.39	yes	336
4.3	odd	2	inner	348.2.t.a.35.16	✓	336
12.11	even	2	inner	348.2.t.a.35.41	yes	336
29.5	even	14	inner	348.2.t.a.179.41	yes	336
87.5	odd	14	inner	348.2.t.a.179.16	yes	336
116.63	odd	14	inner	348.2.t.a.179.39	yes	336
348.179	even	14	inner	348.2.t.a.179.18	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.16	✓	336	4.3	odd	2	inner
348.2.t.a.35.18	yes	336	1.1	even	1	trivial
348.2.t.a.35.39	yes	336	3.2	odd	2	inner
348.2.t.a.35.41	yes	336	12.11	even	2	inner
348.2.t.a.179.16	yes	336	87.5	odd	14	inner
348.2.t.a.179.18	yes	336	348.179	even	14	inner
348.2.t.a.179.39	yes	336	116.63	odd	14	inner
348.2.t.a.179.41	yes	336	29.5	even	14	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:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.834189 + 1.14198i) q^{2} +(1.21862 - 1.23084i) q^{3} +(-0.608258 - 1.90526i) q^{4} +(-0.252365 - 0.201255i) q^{5} +(0.389050 + 2.41840i) q^{6} +(-3.46126 - 0.790009i) q^{7} +(2.68318 + 0.894727i) q^{8} +(-0.0299545 - 2.99985i) q^{9} +O(q^{10})\)	\(q+(-0.834189 + 1.14198i) q^{2} +(1.21862 - 1.23084i) q^{3} +(-0.608258 - 1.90526i) q^{4} +(-0.252365 - 0.201255i) q^{5} +(0.389050 + 2.41840i) q^{6} +(-3.46126 - 0.790009i) q^{7} +(2.68318 + 0.894727i) q^{8} +(-0.0299545 - 2.99985i) q^{9} +(0.440350 - 0.120313i) q^{10} +(-0.320018 - 0.664525i) q^{11} +(-3.08631 - 1.57311i) q^{12} +(3.28982 - 1.58429i) q^{13} +(3.78952 - 3.29368i) q^{14} +(-0.555249 + 0.0653704i) q^{15} +(-3.26004 + 2.31778i) q^{16} -0.499932 q^{17} +(3.45077 + 2.46823i) q^{18} +(-1.43177 - 6.27298i) q^{19} +(-0.229939 + 0.603236i) q^{20} +(-5.19032 + 3.29755i) q^{21} +(1.02583 + 0.188883i) q^{22} +(-2.29001 - 2.87158i) q^{23} +(4.37103 - 2.21225i) q^{24} +(-1.08942 - 4.77306i) q^{25} +(-0.935092 + 5.07853i) q^{26} +(-3.72885 - 3.61879i) q^{27} +(0.600163 + 7.07513i) q^{28} +(-2.28754 + 4.87516i) q^{29} +(0.388530 - 0.688617i) q^{30} +(3.05971 - 3.83676i) q^{31} +(0.0726220 - 5.65639i) q^{32} +(-1.20791 - 0.415907i) q^{33} +(0.417038 - 0.570915i) q^{34} +(0.714508 + 0.895964i) q^{35} +(-5.69728 + 1.88175i) q^{36} +(-1.90809 + 3.96219i) q^{37} +(8.35801 + 3.59780i) q^{38} +(2.05901 - 5.97990i) q^{39} +(-0.497074 - 0.765800i) q^{40} +7.55503 q^{41} +(0.563953 - 8.67804i) q^{42} +(4.09169 + 5.13082i) q^{43} +(-1.07144 + 1.01392i) q^{44} +(-0.596174 + 0.763086i) q^{45} +(5.18960 - 0.219715i) q^{46} +(2.12415 + 4.41085i) q^{47} +(-1.11991 + 6.83709i) q^{48} +(5.04940 + 2.43166i) q^{49} +(6.35954 + 2.73753i) q^{50} +(-0.609225 + 0.615338i) q^{51} +(-5.01956 - 5.30431i) q^{52} +(8.28539 + 6.60738i) q^{53} +(7.24317 - 1.23953i) q^{54} +(-0.0529771 + 0.232108i) q^{55} +(-8.58034 - 5.21662i) q^{56} +(-9.46584 - 5.88207i) q^{57} +(-3.65912 - 6.67913i) q^{58} -4.97485 q^{59} +(0.462282 + 1.01813i) q^{60} +(9.83324 + 2.24437i) q^{61} +(1.82914 + 6.69473i) q^{62} +(-2.26623 + 10.4069i) q^{63} +(6.39893 + 4.80143i) q^{64} +(-1.14908 - 0.262271i) q^{65} +(1.48258 - 1.03246i) q^{66} +(2.56551 - 5.32735i) q^{67} +(0.304088 + 0.952501i) q^{68} +(-6.32510 - 0.680707i) q^{69} +(-1.61921 + 0.0685534i) q^{70} +(-11.6763 + 5.62299i) q^{71} +(2.60367 - 8.07594i) q^{72} +(2.23386 - 1.78145i) q^{73} +(-2.93305 - 5.48422i) q^{74} +(-7.20248 - 4.47562i) q^{75} +(-11.0808 + 6.54348i) q^{76} +(0.582685 + 2.55291i) q^{77} +(5.11136 + 7.33972i) q^{78} +(5.79611 + 2.79126i) q^{79} +(1.28919 + 0.0711714i) q^{80} +(-8.99821 + 0.179718i) q^{81} +(-6.30232 + 8.62773i) q^{82} +(-1.07201 - 4.69678i) q^{83} +(9.43975 + 7.88315i) q^{84} +(0.126165 + 0.100614i) q^{85} +(-9.27255 + 0.392577i) q^{86} +(3.21294 + 8.75654i) q^{87} +(-0.264099 - 2.06937i) q^{88} +(-2.08812 + 2.61842i) q^{89} +(-0.374111 - 1.31738i) q^{90} +(-12.6385 + 2.88466i) q^{91} +(-4.07819 + 6.10972i) q^{92} +(-0.993840 - 8.44156i) q^{93} +(-6.80907 - 1.25373i) q^{94} +(-0.901138 + 1.87123i) q^{95} +(-6.87363 - 6.98235i) q^{96} +(0.496272 - 0.113271i) q^{97} +(-6.98907 + 3.73787i) q^{98} +(-1.98389 + 0.979913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

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