LMFDB - Embedded newform 483.2.bc.a.11.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(11,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([33, 44, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	483.11
Dual form			483.2.bc.a.44.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02175 + 1.98192i) q^{2} +(-1.59600 - 0.672881i) q^{3} +(-1.72392 - 2.42090i) q^{4} +(1.12079 + 1.06868i) q^{5} +(2.96432 - 2.47564i) q^{6} +(-2.59123 + 0.534343i) q^{7} +(2.14526 - 0.308441i) q^{8} +(2.09446 + 2.14784i) q^{9} +(-3.26320 + 1.12941i) q^{10} +(-1.24073 + 0.639643i) q^{11} +(1.12240 + 5.02377i) q^{12} +(-2.18676 + 2.52366i) q^{13} +(1.58857 - 5.68158i) q^{14} +(-1.06970 - 2.45977i) q^{15} +(0.363468 - 1.05017i) q^{16} +(1.08661 + 0.103758i) q^{17} +(-6.39687 + 1.95650i) q^{18} +(-0.586258 - 6.13957i) q^{19} +(0.655003 - 4.55565i) q^{20} +(4.49517 + 0.890776i) q^{21} -3.11259i q^{22} +(-4.79479 + 0.0999357i) q^{23} +(-3.63138 - 0.951229i) q^{24} +(-0.123796 - 2.59880i) q^{25} +(-2.76736 - 6.91253i) q^{26} +(-1.89753 - 4.83729i) q^{27} +(5.76066 + 5.35196i) q^{28} +(7.36662 - 3.36422i) q^{29} +(5.96804 + 0.393210i) q^{30} +(-4.36913 - 1.74913i) q^{31} +(4.70122 + 4.93050i) q^{32} +(2.41062 - 0.186007i) q^{33} +(-1.31588 + 2.04755i) q^{34} +(-3.47528 - 2.17030i) q^{35} +(1.58904 - 8.77320i) q^{36} +(0.348726 - 0.0846000i) q^{37} +(12.7672 + 5.11120i) q^{38} +(5.18820 - 2.55634i) q^{39} +(2.73402 + 1.94688i) q^{40} +(-0.252563 - 0.860149i) q^{41} +(-6.35839 + 7.99891i) q^{42} +(-0.627275 - 0.0901886i) q^{43} +(3.68744 + 1.90101i) q^{44} +(0.0521160 + 4.64559i) q^{45} +(4.70102 - 9.60500i) q^{46} +(8.99866 - 5.19538i) q^{47} +(-1.28674 + 1.43151i) q^{48} +(6.42896 - 2.76921i) q^{49} +(5.27711 + 2.40998i) q^{50} +(-1.66441 - 0.896756i) q^{51} +(9.87933 + 0.943362i) q^{52} +(-6.48218 + 1.24934i) q^{53} +(11.5259 + 1.18175i) q^{54} +(-2.07418 - 0.609034i) q^{55} +(-5.39404 + 1.94555i) q^{56} +(-3.19553 + 10.1933i) q^{57} +(-0.859229 + 18.0374i) q^{58} +(-7.10687 + 2.45971i) q^{59} +(-4.11080 + 6.83010i) q^{60} +(-7.04342 - 8.95643i) q^{61} +(7.93080 - 6.87208i) q^{62} +(-6.57492 - 4.44639i) q^{63} +(-12.4428 + 3.65353i) q^{64} +(-5.14788 + 0.491563i) q^{65} +(-2.09440 + 4.96771i) q^{66} +(6.52512 - 0.310830i) q^{67} +(-1.62203 - 2.80944i) q^{68} +(7.71975 + 3.06682i) q^{69} +(7.85222 - 4.67022i) q^{70} +(2.26853 + 3.52991i) q^{71} +(5.15564 + 3.96165i) q^{72} +(-7.65767 - 10.7537i) q^{73} +(-0.188641 + 0.777587i) q^{74} +(-1.55111 + 4.23100i) q^{75} +(-13.8527 + 12.0034i) q^{76} +(2.87324 - 2.32044i) q^{77} +(-0.234590 + 12.8945i) q^{78} +(-0.802689 + 4.16475i) q^{79} +(1.52967 - 0.788597i) q^{80} +(-0.226453 + 8.99715i) q^{81} +(1.96280 + 0.378299i) q^{82} +(-10.9295 - 3.20920i) q^{83} +(-5.59282 - 12.4180i) q^{84} +(1.10698 + 1.27752i) q^{85} +(0.819665 - 1.15106i) q^{86} +(-14.0209 + 0.412457i) q^{87} +(-2.46440 + 1.75489i) q^{88} +(-0.450725 + 0.180443i) q^{89} +(-9.26044 - 4.64335i) q^{90} +(4.31790 - 7.70786i) q^{91} +(8.50776 + 11.4354i) q^{92} +(5.79619 + 5.73153i) q^{93} +(1.10244 + 23.1430i) q^{94} +(5.90414 - 7.50772i) q^{95} +(-4.18553 - 11.0325i) q^{96} +(-1.87227 - 6.37637i) q^{97} +(-1.08043 + 15.5711i) q^{98} +(-3.97252 - 1.32519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) $ 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−1.02175	+	1.98192i	−0.722487	+	1.40143i	0.185591	+	0.982627i	$0.440580\pi$
$2$	−1.02175	+	1.98192i	−0.722487	+	1.40143i	−0.908078	+	0.418802i	$0.862450\pi$
$3$	−1.59600	−	0.672881i	−0.921454	−	0.388488i
$3$	−1.59600	−	0.672881i	−0.921454	−	0.388488i
$4$	−1.72392	−	2.42090i	−0.861959	−	1.21045i
$5$	1.12079	+	1.06868i	0.501235	+	0.477926i	0.898001	−	0.439993i	$-0.145019\pi$
$5$	1.12079	+	1.06868i	0.501235	+	0.477926i	−0.396766	+	0.917920i	$0.629868\pi$
$6$	2.96432	−	2.47564i	1.21018	−	1.01067i
$7$	−2.59123	+	0.534343i	−0.979393	+	0.201963i
$7$	−2.59123	+	0.534343i	−0.979393	+	0.201963i
$8$	2.14526	−	0.308441i	0.758463	−	0.109050i
$9$	2.09446	+	2.14784i	0.698154	+	0.715947i
$10$	−3.26320	+	1.12941i	−1.03192	+	0.357149i
$11$	−1.24073	+	0.639643i	−0.374095	+	0.192859i	−0.635013	−	0.772502i	$-0.719005\pi$
$11$	−1.24073	+	0.639643i	−0.374095	+	0.192859i	0.260918	+	0.965361i	$0.415975\pi$
$12$	1.12240	+	5.02377i	0.324009	+	1.45024i
$13$	−2.18676	+	2.52366i	−0.606498	+	0.699937i	−0.973085	−	0.230448i	$-0.925981\pi$
$13$	−2.18676	+	2.52366i	−0.606498	+	0.699937i	0.366586	+	0.930384i	$0.380526\pi$
$14$	1.58857	−	5.68158i	0.424562	−	1.51847i
$15$	−1.06970	−	2.45977i	−0.276196	−	0.635111i
$16$	0.363468	−	1.05017i	0.0908669	−	0.262543i
$17$	1.08661	+	0.103758i	0.263541	+	0.0251651i	0.225990	−	0.974130i	$-0.427438\pi$
$17$	1.08661	+	0.103758i	0.263541	+	0.0251651i	0.0375509	+	0.999295i	$0.488044\pi$
$18$	−6.39687	+	1.95650i	−1.50776	+	0.461151i
$19$	−0.586258	−	6.13957i	−0.134497	−	1.40851i	−0.770801	−	0.637076i	$-0.780144\pi$
$19$	−0.586258	−	6.13957i	−0.134497	−	1.40851i	0.636304	−	0.771439i	$-0.280462\pi$
$20$	0.655003	−	4.55565i	0.146463	−	1.01867i
$21$	4.49517	+	0.890776i	0.980926	+	0.194383i
$22$		−	3.11259i		−	0.663606i
$23$	−4.79479	+	0.0999357i	−0.999783	+	0.0208380i
$23$	−4.79479	+	0.0999357i	−0.999783	+	0.0208380i
$24$	−3.63138	−	0.951229i	−0.741253	−	0.194169i
$25$	−0.123796	−	2.59880i	−0.0247593	−	0.519761i
$26$	−2.76736	−	6.91253i	−0.542724	−	1.35566i
$27$	−1.89753	−	4.83729i	−0.365180	−	0.930937i
$28$	5.76066	+	5.35196i	1.08866	+	1.01143i
$29$	7.36662	−	3.36422i	1.36795	−	0.624720i	0.410110	−	0.912036i	$-0.365490\pi$
$29$	7.36662	−	3.36422i	1.36795	−	0.624720i	0.957836	+	0.287316i	$0.0927629\pi$
$30$	5.96804	+	0.393210i	1.08961	+	0.0717901i
$31$	−4.36913	−	1.74913i	−0.784718	−	0.314154i	−0.0555211	−	0.998458i	$-0.517682\pi$
$31$	−4.36913	−	1.74913i	−0.784718	−	0.314154i	−0.729197	+	0.684304i	$0.760106\pi$
$32$	4.70122	+	4.93050i	0.831066	+	0.871597i
$33$	2.41062	−	0.186007i	0.419635	−	0.0323796i
$34$	−1.31588	+	2.04755i	−0.225672	+	0.351153i
$35$	−3.47528	−	2.17030i	−0.587429	−	0.366847i
$36$	1.58904	−	8.77320i	0.264840	−	1.46220i
$37$	0.348726	−	0.0846000i	0.0573302	−	0.0139082i	−0.206991	−	0.978343i	$-0.566367\pi$
$37$	0.348726	−	0.0846000i	0.0573302	−	0.0139082i	0.264321	+	0.964435i	$0.414852\pi$
$38$	12.7672	+	5.11120i	2.07111	+	0.829146i
$39$	5.18820	−	2.55634i	0.830777	−	0.409342i
$40$	2.73402	+	1.94688i	0.432286	+	0.307830i
$41$	−0.252563	−	0.860149i	−0.0394436	−	0.134333i	0.937417	−	0.348208i	$-0.113210\pi$
$41$	−0.252563	−	0.860149i	−0.0394436	−	0.134333i	−0.976861	+	0.213875i	$0.931391\pi$
$42$	−6.35839	+	7.99891i	−0.981120	+	1.23426i
$43$	−0.627275	−	0.0901886i	−0.0956586	−	0.0137536i	0.0943193	−	0.995542i	$-0.469933\pi$
$43$	−0.627275	−	0.0901886i	−0.0956586	−	0.0137536i	−0.189978	+	0.981788i	$0.560842\pi$
$44$	3.68744	+	1.90101i	0.555902	+	0.286587i
$45$	0.0521160	+	4.64559i	0.00776899	+	0.692524i
$46$	4.70102	−	9.60500i	0.693127	−	1.41618i
$47$	8.99866	−	5.19538i	1.31259	−	0.757824i	0.330065	−	0.943958i	$-0.392929\pi$
$47$	8.99866	−	5.19538i	1.31259	−	0.757824i	0.982524	+	0.186134i	$0.0595960\pi$
$48$	−1.28674	+	1.43151i	−0.185724	+	0.206620i
$49$	6.42896	−	2.76921i	0.918422	−	0.395602i
$50$	5.27711	+	2.40998i	0.746296	+	0.340822i
$51$	−1.66441	−	0.896756i	−0.233065	−	0.125571i
$52$	9.87933	+	0.943362i	1.37002	+	0.130821i
$53$	−6.48218	+	1.24934i	−0.890395	+	0.171610i	−0.613880	−	0.789400i	$-0.710392\pi$
$53$	−6.48218	+	1.24934i	−0.890395	+	0.171610i	−0.276516	+	0.961009i	$0.589180\pi$
$54$	11.5259	+	1.18175i	1.56848	+	0.160816i
$55$	−2.07418	−	0.609034i	−0.279682	−	0.0821221i
$56$	−5.39404	+	1.94555i	−0.720809	+	0.259985i
$57$	−3.19553	+	10.1933i	−0.423258	+	1.35013i
$58$	−0.859229	+	18.0374i	−0.112822	+	2.36843i
$59$	−7.10687	+	2.45971i	−0.925236	+	0.320227i	−0.747815	−	0.663908i	$-0.768897\pi$
$59$	−7.10687	+	2.45971i	−0.925236	+	0.320227i	−0.177422	+	0.984135i	$0.556776\pi$
$60$	−4.11080	+	6.83010i	−0.530701	+	0.881761i
$61$	−7.04342	−	8.95643i	−0.901817	−	1.14675i	−0.988606	−	0.150527i	$-0.951903\pi$
$61$	−7.04342	−	8.95643i	−0.901817	−	1.14675i	0.0867886	−	0.996227i	$-0.472340\pi$
$62$	7.93080	−	6.87208i	1.00721	−	0.872755i
$63$	−6.57492	−	4.44639i	−0.828362	−	0.560193i
$64$	−12.4428	+	3.65353i	−1.55535	+	0.456691i
$65$	−5.14788	+	0.491563i	−0.638516	+	0.0609709i
$66$	−2.09440	+	4.96771i	−0.257803	+	0.611483i
$67$	6.52512	−	0.310830i	0.797170	−	0.0379739i	0.354956	−	0.934883i	$-0.384496\pi$
$67$	6.52512	−	0.310830i	0.797170	−	0.0379739i	0.442215	+	0.896909i	$0.354193\pi$
$68$	−1.62203	−	2.80944i	−0.196700	−	0.340695i
$69$	7.71975	+	3.06682i	0.929349	+	0.369202i
$70$	7.85222	−	4.67022i	0.938520	−	0.558198i
$71$	2.26853	+	3.52991i	0.269226	+	0.418923i	0.949372	−	0.314153i	$-0.101720\pi$
$71$	2.26853	+	3.52991i	0.269226	+	0.418923i	−0.680147	+	0.733076i	$0.738084\pi$
$72$	5.15564	+	3.96165i	0.607598	+	0.466885i
$73$	−7.65767	−	10.7537i	−0.896263	−	1.25863i	−0.965335	−	0.261013i	$-0.915943\pi$
$73$	−7.65767	−	10.7537i	−0.896263	−	1.25863i	0.0690722	−	0.997612i	$-0.477996\pi$
$74$	−0.188641	+	0.777587i	−0.0219290	+	0.0903927i
$75$	−1.55111	+	4.23100i	−0.179106	+	0.488554i
$76$	−13.8527	+	12.0034i	−1.58901	+	1.37688i
$77$	2.87324	−	2.32044i	0.327436	−	0.264439i
$78$	−0.234590	+	12.8945i	−0.0265621	+	1.46002i
$79$	−0.802689	+	4.16475i	−0.0903096	+	0.468570i	0.908415	+	0.418071i	$0.137294\pi$
$79$	−0.802689	+	4.16475i	−0.0903096	+	0.468570i	−0.998724	+	0.0504998i	$0.983919\pi$
$80$	1.52967	−	0.788597i	0.171022	−	0.0881679i
$81$	−0.226453	+	8.99715i	−0.0251614	+	0.999683i
$82$	1.96280	+	0.378299i	0.216755	+	0.0417761i
$83$	−10.9295	−	3.20920i	−1.19967	−	0.352256i	−0.379945	−	0.925009i	$-0.624057\pi$
$83$	−10.9295	−	3.20920i	−1.19967	−	0.352256i	−0.819728	+	0.572753i	$0.805875\pi$
$84$	−5.59282	−	12.4180i	−0.610226	−	1.35491i
$85$	1.10698	+	1.27752i	0.120069	+	0.138567i
$86$	0.819665	−	1.15106i	0.0883868	−	0.124122i
$87$	−14.0209	+	0.412457i	−1.50320	+	0.0442201i
$88$	−2.46440	+	1.75489i	−0.262706	+	0.187072i
$89$	−0.450725	+	0.180443i	−0.0477767	+	0.0191269i	−0.395428	−	0.918497i	$-0.629404\pi$
$89$	−0.450725	+	0.180443i	−0.0477767	+	0.0191269i	0.347651	+	0.937624i	$0.386979\pi$
$90$	−9.26044	−	4.64335i	−0.976136	−	0.489452i
$91$	4.31790	−	7.70786i	0.452639	−	0.808003i
$92$	8.50776	+	11.4354i	0.886995	+	1.19223i
$93$	5.79619	+	5.73153i	0.601037	+	0.594332i
$94$	1.10244	+	23.1430i	0.113708	+	2.38702i
$95$	5.90414	−	7.50772i	0.605752	−	0.770276i
$96$	−4.18553	−	11.0325i	−0.427184	−	1.12600i
$97$	−1.87227	−	6.37637i	−0.190100	−	0.647423i	−0.998288	−	0.0584970i	$-0.981369\pi$
$97$	−1.87227	−	6.37637i	−0.190100	−	0.647423i	0.808187	−	0.588926i	$-0.200449\pi$
$98$	−1.08043	+	15.5711i	−0.109140	+	1.57292i
$99$	−3.97252	−	1.32519i	−0.399253	−	0.133187i
$100$	−6.07804	+	4.77982i	−0.607804	+	0.477982i
$101$	2.60728	+	2.73444i	0.259434	+	0.272087i	0.840550	−	0.541734i	$-0.182232\pi$
$101$	2.60728	+	2.73444i	0.259434	+	0.272087i	−0.581116	+	0.813821i	$0.697384\pi$
$102$	3.47792	−	2.38247i	0.344365	−	0.235900i
$103$	7.21431	+	0.343660i	0.710847	+	0.0338618i	0.399891	−	0.916563i	$-0.369048\pi$
$103$	7.21431	+	0.343660i	0.710847	+	0.0338618i	0.310956	+	0.950424i	$0.399351\pi$
$104$	−3.91276	+	6.08838i	−0.383678	+	0.597015i
$105$	4.08621	+	5.80225i	0.398773	+	0.566242i
$106$	4.14708	−	14.1237i	0.402800	−	1.37181i
$107$	−0.429630	+	0.337865i	−0.0415339	+	0.0326627i	−0.638710	−	0.769447i	$-0.720532\pi$
$107$	−0.429630	+	0.337865i	−0.0415339	+	0.0326627i	0.597176	+	0.802110i	$0.296289\pi$
$108$	−8.43943	+	12.9328i	−0.812085	+	1.24446i
$109$	0.863632	−	9.04436i	0.0827209	−	0.866293i	−0.854937	−	0.518732i	$-0.826404\pi$
$109$	0.863632	−	9.04436i	0.0827209	−	0.866293i	0.937658	−	0.347560i	$-0.112990\pi$
$110$	3.32635	−	3.48857i	0.317155	−	0.332623i
$111$	−0.613494	−	0.0996291i	−0.0582303	−	0.00945637i
$112$	−0.380677	+	2.91545i	−0.0359706	+	0.275484i
$113$	−17.0014	+	10.9262i	−1.59936	+	1.02785i	−0.631824	+	0.775112i	$0.717693\pi$
$113$	−17.0014	+	10.9262i	−1.59936	+	1.02785i	−0.967536	+	0.252734i	$0.918670\pi$
$114$	−16.9372	−	16.7483i	−1.58632	−	1.56862i
$115$	−5.48078	−	5.01207i	−0.511085	−	0.467378i
$116$	−20.8439	−	12.0342i	−1.93531	−	1.11735i
$117$	−10.0005	+	0.588887i	−0.924547	+	0.0544426i
$118$	2.38650	−	16.5985i	0.219695	−	1.52801i
$119$	−2.87109	+	0.311759i	−0.263193	+	0.0285789i
$120$	−3.05348	−	4.94691i	−0.278744	−	0.451589i
$121$	−5.25035	+	7.37308i	−0.477304	+	0.670280i
$122$	24.9476	−	4.80825i	2.25865	−	0.435318i
$123$	−0.175687	+	1.54275i	−0.0158411	+	0.139105i
$124$	3.29753	+	13.5926i	0.296127	+	1.22065i
$125$	7.70921	−	8.89690i	0.689532	−	0.795763i
$126$	15.5303	−	8.48786i	1.38355	−	0.756159i
$127$	−5.93218	−	3.81238i	−0.526396	−	0.338294i	0.250302	−	0.968168i	$-0.419470\pi$
$127$	−5.93218	−	3.81238i	−0.526396	−	0.338294i	−0.776698	+	0.629874i	$0.783107\pi$
$128$	2.89384	−	15.0146i	0.255781	−	1.32712i
$129$	0.940448	+	0.566023i	0.0828018	+	0.0498355i
$130$	4.28561	−	10.7049i	0.375873	−	0.938886i
$131$	−17.7752	−	6.15207i	−1.55303	−	0.537509i	−0.590116	−	0.807319i	$-0.700918\pi$
$131$	−17.7752	−	6.15207i	−1.55303	−	0.537509i	−0.962914	+	0.269810i	$0.913039\pi$
$132$	−4.60602	−	5.51522i	−0.400902	−	0.480038i
$133$	4.79977	+	15.5958i	0.416193	+	1.35233i
$134$	−6.05101	+	13.2499i	−0.522727	+	1.14461i
$135$	3.04275	−	7.44946i	0.261878	−	0.641147i
$136$	2.36306	−	0.112566i	0.202630	−	0.00965247i
$137$	−1.91680	+	3.32000i	−0.163763	+	0.283646i	−0.936215	−	0.351427i	$-0.885697\pi$
$137$	−1.91680	+	3.32000i	−0.163763	+	0.283646i	0.772452	+	0.635073i	$0.219030\pi$
$138$	−13.9659	+	12.1664i	−1.18885	+	1.03567i
$139$	−5.47655			−0.464515			−0.232257	−	0.972654i	$-0.574611\pi$
$139$	−5.47655			−0.464515			−0.232257	+	0.972654i	$0.574611\pi$
$140$	0.737014	+	12.1547i	0.0622890	+	1.02726i
$141$	−17.8578	+	2.23682i	−1.50390	+	0.188374i
$142$	−9.31387	+	0.889367i	−0.781603	+	0.0746340i
$143$	1.09895	−	4.52993i	0.0918988	−	0.378812i
$144$	3.01687	−	1.41887i	0.251406	−	0.118239i
$145$	11.8517	+	4.10192i	0.984232	+	0.340646i
$146$	29.1372	−	4.18930i	2.41141	−	0.346709i
$147$	−12.1240	+	0.0937551i	−0.999970	+	0.00773279i
$148$	−0.805984	−	0.698389i	−0.0662515	−	0.0574072i
$149$	−0.761892	+	15.9941i	−0.0624167	+	1.31029i	0.722796	+	0.691061i	$0.242856\pi$
$149$	−0.761892	+	15.9941i	−0.0624167	+	1.31029i	−0.785213	+	0.619226i	$0.787447\pi$
$150$	−6.80067	−	7.39720i	−0.555272	−	0.603979i
$151$	−5.28831	−	15.2796i	−0.430356	−	1.24343i	−0.926863	−	0.375400i	$-0.877505\pi$
$151$	−5.28831	−	15.2796i	−0.430356	−	1.24343i	0.496507	−	0.868033i	$-0.334616\pi$
$152$	−3.15137	−	12.9901i	−0.255610	−	1.05364i
$153$	2.05300	+	2.55118i	0.165975	+	0.206251i
$154$	1.66319	+	8.06544i	0.134024	+	0.649932i
$155$	−3.02764	−	6.62960i	−0.243186	−	0.532502i
$156$	−15.1327	−	8.15322i	−1.21158	−	0.652780i
$157$	−7.95483	+	5.66461i	−0.634864	+	0.452085i	−0.851633	−	0.524138i	$-0.824388\pi$
$157$	−7.95483	+	5.66461i	−0.634864	+	0.452085i	0.216769	+	0.976223i	$0.430448\pi$
$158$	−7.43404	−	5.84620i	−0.591421	−	0.465098i
$159$	11.1862	+	2.36778i	0.887126	+	0.187778i
$160$			10.5502i			0.834063i
$161$	12.3710	−	2.82102i	0.974972	−	0.222327i
$162$	−17.6003	−	9.64166i	−1.38281	−	0.757520i
$163$	22.2151	+	11.4527i	1.74002	+	0.897045i	0.963816	+	0.266568i	$0.0858898\pi$
$163$	22.2151	+	11.4527i	1.74002	+	0.897045i	0.776208	+	0.630476i	$0.217140\pi$
$164$	−1.64694	+	2.09426i	−0.128604	+	0.163534i
$165$	2.90059	+	2.36770i	0.225811	+	0.184325i
$166$	17.5277	−	18.3825i	1.36041	−	1.42676i
$167$	−8.53976	+	3.89998i	−0.660826	+	0.301789i	−0.717454	−	0.696606i	$-0.754693\pi$
$167$	−8.53976	+	3.89998i	−0.660826	+	0.301789i	0.0566276	+	0.998395i	$0.481965\pi$
$168$	9.91804	+	0.524448i	0.765193	+	0.0404620i
$169$	0.263173	+	1.83041i	0.0202441	+	0.140801i
$170$	−3.66301	+	0.888636i	−0.280940	+	0.0681552i
$171$	11.9589	−	14.1183i	0.914523	−	1.07965i
$172$	0.863033	+	1.67405i	0.0658057	+	0.127645i
$173$	6.69285	+	0.318820i	0.508848	+	0.0242394i	0.300436	−	0.953802i	$-0.402868\pi$
$173$	6.69285	+	0.318820i	0.508848	+	0.0242394i	0.208411	+	0.978041i	$0.433171\pi$
$174$	13.5084	−	28.2097i	1.02407	−	2.13857i
$175$	1.70944	+	6.66795i	0.129221	+	0.504050i
$176$	0.220768	+	1.53547i	0.0166410	+	0.115741i
$177$	12.9977	+	0.856366i	0.976967	+	0.0643684i
$178$	0.102905	−	1.07767i	0.00771304	−	0.0807746i
$179$	1.56617	+	0.379949i	0.117061	+	0.0283987i	0.293862	−	0.955848i	$-0.405060\pi$
$179$	1.56617	+	0.379949i	0.117061	+	0.0283987i	−0.176800	+	0.984247i	$0.556575\pi$
$180$	11.1567	−	8.13479i	0.831571	−	0.606331i
$181$	12.4353	+	1.78792i	0.924308	+	0.132895i	0.588004	−	0.808858i	$-0.299914\pi$
$181$	12.4353	+	1.78792i	0.924308	+	0.132895i	0.336304	+	0.941753i	$0.390823\pi$
$182$	10.8645	+	16.4333i	0.805333	+	1.21811i
$183$	5.21472	+	19.0339i	0.385483	+	1.40703i
$184$	−10.2552	+	1.69330i	−0.756026	+	0.124832i
$185$	0.481261	+	0.277856i	0.0353830	+	0.0204284i
$186$	−17.2817	+	5.63139i	−1.26715	+	0.412913i
$187$	−1.41456	+	0.566304i	−0.103443	+	0.0414122i
$188$	−28.0905	−	12.8285i	−2.04871	−	0.935613i
$189$	7.50171	+	11.5206i	0.545669	+	0.838001i
$190$	8.84715	+	19.3726i	0.641840	+	1.40543i
$191$	−3.47838	+	10.0501i	−0.251687	+	0.727202i	0.746407	+	0.665490i	$0.231777\pi$
$191$	−3.47838	+	10.0501i	−0.251687	+	0.727202i	−0.998094	+	0.0617122i	$0.980344\pi$
$192$	22.3171	+	2.54146i	1.61060	+	0.183414i
$193$	−18.3718	+	17.5175i	−1.32243	+	1.26093i	−0.380644	+	0.924722i	$0.624298\pi$
$193$	−18.3718	+	17.5175i	−1.32243	+	1.26093i	−0.941786	+	0.336213i	$0.890854\pi$
$194$	14.5505	+	2.80437i	1.04466	+	0.201342i
$195$	8.54681	+	2.67937i	0.612050	+	0.191874i
$196$	−17.7870	−	10.7900i	−1.27050	−	0.770713i
$197$	−8.79139	−	7.61778i	−0.626361	−	0.542745i	0.282806	−	0.959177i	$-0.408735\pi$
$197$	−8.79139	−	7.61778i	−0.626361	−	0.542745i	−0.909167	+	0.416433i	$0.863280\pi$
$198$	6.68535	−	6.51920i	0.475107	−	0.463300i
$199$	3.83183	−	9.57145i	0.271631	−	0.678502i	−0.728346	−	0.685209i	$-0.759711\pi$
$199$	3.83183	−	9.57145i	0.271631	−	0.678502i	0.999978	+	0.00670700i	$0.00213492\pi$
$200$	−1.06715	−	5.53692i	−0.0754591	−	0.391519i
$201$	−10.6233	−	3.89454i	−0.749308	−	0.274700i
$202$	−8.08342	+	2.37351i	−0.568748	+	0.166999i
$203$	−17.2910	+	12.6538i	−1.21359	+	0.888121i
$204$	0.698352	+	5.57532i	0.0488944	+	0.390351i
$205$	0.636150	−	1.23396i	0.0444306	−	0.0861834i
$206$	−8.05233	+	13.9470i	−0.561032	+	0.971737i
$207$	−10.2572	−	10.0891i	−0.712922	−	0.701244i
$208$	1.85545	+	3.21374i	0.128653	+	0.222833i
$209$	4.65452	+	7.24258i	0.321960	+	0.500980i
$210$	−15.6747	+	2.17008i	−1.08166	+	0.149750i
$211$	0.651213	−	1.42596i	0.0448313	−	0.0981669i	−0.885891	−	0.463893i	$-0.846452\pi$
$211$	0.651213	−	1.42596i	0.0448313	−	0.0981669i	0.930722	+	0.365726i	$0.119179\pi$
$212$	14.1993	+	13.5390i	0.975210	+	0.929860i
$213$	−1.24538	−	7.16020i	−0.0853323	−	0.490609i
$214$	−0.230646	−	1.19671i	−0.0157667	−	0.0818052i
$215$	−0.606665	−	0.771437i	−0.0413742	−	0.0526116i
$216$	−5.56271	−	9.79195i	−0.378495	−	0.666258i
$217$	12.2561	+	2.19780i	0.831995	+	0.149196i
$218$	17.0428	+	10.9527i	1.15428	+	0.741812i
$219$	4.98573	+	22.3157i	0.336904	+	1.50795i
$220$	2.10130	+	6.07131i	0.141670	+	0.409328i
$221$	−2.63800	+	2.51533i	−0.177451	+	0.169199i
$222$	0.824295	−	1.11410i	0.0553231	−	0.0747735i
$223$	14.6914	+	16.9548i	0.983809	+	1.13538i	0.990791	+	0.135401i	$0.0432322\pi$
$223$	14.6914	+	16.9548i	0.983809	+	1.13538i	−0.00698165	+	0.999976i	$0.502222\pi$
$224$	−14.8165	−	10.2640i	−0.989971	−	0.685792i
$225$	5.32253	−	5.70899i	0.354836	−	0.380599i
$226$	−4.28354	−	44.8593i	−0.284937	−	2.98399i
$227$	2.45764	+	1.93271i	0.163120	+	0.128279i	0.696382	−	0.717671i	$-0.254792\pi$
$227$	2.45764	+	1.93271i	0.163120	+	0.128279i	−0.533263	+	0.845950i	$0.679034\pi$
$228$	30.1858	−	9.83629i	1.99910	−	0.651424i
$229$	11.8823	−	6.86025i	0.785205	−	0.453338i	−0.0530667	−	0.998591i	$-0.516900\pi$
$229$	11.8823	−	6.86025i	0.785205	−	0.453338i	0.838272	+	0.545253i	$0.183566\pi$
$230$	15.5335	−	5.74137i	1.02425	−	0.378575i
$231$	−6.14708	+	1.77008i	−0.404448	+	0.116463i
$232$	14.7656	−	9.48929i	0.969410	−	0.623002i
$233$	0.303829	+	0.758928i	0.0199045	+	0.0497191i	0.937987	−	0.346670i	$-0.112688\pi$
$233$	0.303829	+	0.758928i	0.0199045	+	0.0497191i	−0.918083	+	0.396389i	$0.870263\pi$
$234$	9.05090	−	20.4219i	0.591676	−	1.33502i
$235$	15.6378	+	3.79370i	1.02010	+	0.247473i
$236$	18.2064	+	12.9647i	1.18514	+	0.843931i
$237$	4.08347	−	6.10684i	0.265250	−	0.396682i
$238$	2.31566	−	6.00882i	0.150102	−	0.389494i
$239$	−2.45626	+	8.36524i	−0.158882	+	0.541103i	0.841118	+	0.540852i	$0.181898\pi$
$239$	−2.45626	+	8.36524i	−0.158882	+	0.541103i	−1.00000		0.000250807i	$0.999920\pi$
$240$	−2.97199	+	0.229322i	−0.191841	+	0.0148027i
$241$	0.347795	+	0.674629i	0.0224035	+	0.0434567i	0.899772	−	0.436361i	$-0.143733\pi$
$241$	0.347795	+	0.674629i	0.0224035	+	0.0434567i	−0.877368	+	0.479818i	$0.840703\pi$
$242$	−9.24831	−	17.9392i	−0.594504	−	1.15318i
$243$	6.41543	−	14.2071i	0.411550	−	0.911387i
$244$	−9.54039	+	32.4916i	−0.610761	+	2.08006i
$245$	10.1649	+	3.76675i	0.649414	+	0.240649i
$246$	−2.87809	−	1.92450i	−0.183500	−	0.122702i
$247$	16.7762	+	11.9463i	1.06744	+	0.760123i
$248$	−9.91240	−	2.40472i	−0.629438	−	0.152700i
$249$	15.2842	+	12.4762i	0.968596	+	0.790646i
$250$	9.75605	+	24.3694i	0.617027	+	1.54126i
$251$	−22.5901	+	14.5178i	−1.42588	+	0.916355i	−0.425944	+	0.904750i	$0.640058\pi$
$251$	−22.5901	+	14.5178i	−1.42588	+	0.916355i	−0.999933	+	0.0116055i	$0.996306\pi$
$252$	0.570331	+	23.5825i	0.0359275	+	1.48556i
$253$	5.88513	−	3.19095i	0.369995	−	0.200613i
$254$	13.6170	−	7.86180i	0.854409	−	0.493293i
$255$	−0.907125	−	2.78380i	−0.0568063	−	0.174328i
$256$	6.41385	+	5.04390i	0.400865	+	0.315244i
$257$	−0.603277	−	6.31780i	−0.0376314	−	0.394094i	−0.994591	−	0.103872i	$-0.966877\pi$
$257$	−0.603277	−	6.31780i	−0.0376314	−	0.394094i	0.956959	−	0.290222i	$-0.0937292\pi$
$258$	−2.08272	+	1.28556i	−0.129664	+	0.0800354i
$259$	−0.858424	+	0.405558i	−0.0533399	+	0.0252001i
$260$	10.0646	+	11.6151i	0.624177	+	0.720339i
$261$	22.6549	+	8.77609i	1.40230	+	0.543227i
$262$	30.3548	−	28.9432i	1.87532	−	1.78812i
$263$	−8.34369	−	24.1075i	−0.514494	−	1.48653i	−0.840840	−	0.541283i	$-0.817939\pi$
$263$	−8.34369	−	24.1075i	−0.514494	−	1.48653i	0.326346	−	0.945250i	$-0.394182\pi$
$264$	5.11403	−	1.14257i	0.314747	−	0.0703202i
$265$	−8.60033	−	5.52709i	−0.528314	−	0.339527i
$266$	−35.8138	−	6.42225i	−2.19588	−	0.393774i
$267$	0.840775	+	0.0152962i	0.0514546	+	0.000936114i
$268$	−12.0013	−	15.2608i	−0.733094	−	0.932205i
$269$	−5.36526	−	27.8376i	−0.327126	−	1.69729i	−0.657513	−	0.753443i	$-0.728391\pi$
$269$	−5.36526	−	27.8376i	−0.327126	−	1.69729i	0.330387	−	0.943845i	$-0.392821\pi$
$270$	11.6553	+	13.6420i	0.709318	+	0.830224i
$271$	4.25263	+	4.05487i	0.258329	+	0.246316i	0.808164	−	0.588957i	$-0.200461\pi$
$271$	4.25263	+	4.05487i	0.258329	+	0.246316i	−0.549836	+	0.835273i	$0.685310\pi$
$272$	0.503911	−	1.10341i	0.0305541	−	0.0669041i
$273$	−12.0779	+	9.39634i	−0.730986	+	0.568693i
$274$	−4.62147	−	7.19115i	−0.279193	−	0.434433i
$275$	1.81590	+	3.14524i	0.109503	+	0.189665i
$276$	−5.88373	−	23.9757i	−0.354159	−	1.44317i
$277$	2.51339	−	4.35332i	0.151015	−	0.261566i	−0.780586	−	0.625049i	$-0.785079\pi$
$277$	2.51339	−	4.35332i	0.151015	−	0.261566i	0.931601	+	0.363483i	$0.118412\pi$
$278$	5.59567	−	10.8541i	0.335606	−	0.650984i
$279$	−5.39411	−	13.0477i	−0.322937	−	0.781145i
$280$	−8.12477	−	3.58392i	−0.485548	−	0.214180i
$281$	18.8236	−	5.52710i	1.12292	−	0.329719i	0.332999	−	0.942927i	$-0.391939\pi$
$281$	18.8236	−	5.52710i	1.12292	−	0.329719i	0.789922	+	0.613208i	$0.210121\pi$
$282$	13.8130	−	37.6782i	0.822552	−	2.24370i
$283$	−3.49157	−	18.1160i	−0.207552	−	1.07688i	−0.924912	−	0.380181i	$-0.875862\pi$
$283$	−3.49157	−	18.1160i	−0.207552	−	1.07688i	0.717360	−	0.696703i	$-0.245350\pi$
$284$	4.63480	−	11.5772i	0.275025	−	0.686979i
$285$	−14.4748	+	8.00958i	−0.857415	+	0.474447i
$286$	7.85511	+	6.80649i	0.464482	+	0.402476i
$287$	1.11406	+	2.09389i	0.0657610	+	0.123598i
$288$	−0.743402	+	20.4242i	−0.0438054	+	1.20351i
$289$	−15.5228	−	2.99178i	−0.913108	−	0.175987i
$290$	−20.2392	+	19.2980i	−1.18849	+	1.13322i
$291$	−1.30238	+	11.4365i	−0.0763471	+	0.670422i
$292$	−12.8325	+	37.0770i	−0.750964	+	2.16977i
$293$	−12.5157	−	27.4056i	−0.731176	−	1.60105i	−0.797547	−	0.603256i	$-0.793870\pi$
$293$	−12.5157	−	27.4056i	−0.731176	−	1.60105i	0.0663717	−	0.997795i	$-0.478858\pi$
$294$	12.2019	−	24.1246i	0.711628	−	1.40697i
$295$	−10.5940	−	4.83811i	−0.616806	−	0.281686i
$296$	0.722013	−	0.289050i	0.0419662	−	0.0168007i
$297$	5.44847	+	4.78805i	0.316152	+	0.277831i
$298$	−30.9205	−	17.8520i	−1.79118	−	1.03414i
$299$	10.2329	−	12.3189i	0.591781	−	0.712423i
$300$	12.9168	−	3.53882i	0.745754	−	0.204314i
$301$	1.67361	−	0.101481i	0.0964651	−	0.00584925i
$302$	35.6862	+	5.13090i	2.05351	+	0.295250i
$303$	−2.32128	−	6.11856i	−0.133354	−	0.351502i
$304$	−6.66069	−	1.61587i	−0.382017	−	0.0926763i
$305$	1.67730	−	17.5655i	0.0960418	−	1.00580i
$306$	−7.15389	+	1.46222i	−0.408961	+	0.0835893i
$307$	0.720345	+	5.01011i	0.0411123	+	0.285942i	0.999998	+	0.00214858i	$0.000683915\pi$
$307$	0.720345	+	5.01011i	0.0411123	+	0.285942i	−0.958885	+	0.283793i	$0.908407\pi$
$308$	−10.5708	−	2.95559i	−0.602327	−	0.168410i
$309$	−11.2828	−	5.40285i	−0.641858	−	0.307358i
$310$	16.2328	+	0.773265i	0.921963	+	0.0439185i
$311$	−2.23364	−	4.33267i	−0.126658	−	0.245683i	0.816977	−	0.576671i	$-0.195648\pi$
$311$	−2.23364	−	4.33267i	−0.126658	−	0.245683i	−0.943635	+	0.330988i	$0.892618\pi$
$312$	10.3415	−	7.08426i	0.585475	−	0.401067i
$313$	−22.6263	+	5.48909i	−1.27892	+	0.310262i	−0.816988	−	0.576655i	$-0.804358\pi$
$313$	−22.6263	+	5.48909i	−1.27892	+	0.310262i	−0.461929	+	0.886917i	$0.652842\pi$
$314$	−3.09895	−	21.5536i	−0.174884	−	1.21634i
$315$	−2.61738	−	12.0100i	−0.147473	−	0.676684i
$316$	11.4662	−	5.23645i	0.645025	−	0.294573i
$317$	8.69779	−	9.12198i	0.488517	−	0.512342i	−0.432622	−	0.901575i	$-0.642412\pi$
$317$	8.69779	−	9.12198i	0.488517	−	0.512342i	0.921139	+	0.389234i	$0.127260\pi$
$318$	−16.1223	+	19.7509i	−0.904094	+	1.10758i
$319$	−6.98811	+	8.88610i	−0.391259	+	0.497526i
$320$	−17.8502	−	9.20244i	−0.997859	−	0.514432i
$321$	0.913035	−	0.250144i	0.0509607	−	0.0139617i
$322$	−7.04905	+	27.4007i	−0.392828	+	1.52698i
$323$		−	6.73214i		−	0.374586i
$324$	22.1716	−	14.9621i	1.23176	−	0.831229i
$325$	6.82920	+	5.37054i	0.378816	+	0.297904i
$326$	−45.3967	+	32.3268i	−2.51429	+	1.79042i
$327$	−7.46414	+	13.8537i	−0.412768	+	0.766113i
$328$	−0.807117	−	1.76734i	−0.0445656	−	0.0975850i
$329$	−20.5415	+	18.2708i	−1.13249	+	1.00730i
$330$	−7.65627	+	3.32955i	−0.421464	+	0.183285i
$331$	−7.58762	−	31.2766i	−0.417053	−	1.71912i	−0.661933	−	0.749563i	$-0.730264\pi$
$331$	−7.58762	−	31.2766i	−0.417053	−	1.71912i	0.244880	−	0.969553i	$-0.421251\pi$
$332$	11.0725	+	31.9918i	0.607680	+	1.75578i
$333$	0.912101	+	0.571817i	0.0499828	+	0.0313354i
$334$	0.996062	−	20.9099i	0.0545021	−	1.14414i
$335$	7.64550	+	6.62486i	0.417718	+	0.361955i
$336$	2.56932	−	4.39693i	0.140168	−	0.239872i
$337$	−19.3678	+	2.78467i	−1.05503	+	0.151691i	−0.647936	−	0.761695i	$-0.724367\pi$
$337$	−19.3678	+	2.78467i	−1.05503	+	0.151691i	−0.407095	+	0.913386i	$0.633458\pi$
$338$	−3.89662	−	1.34863i	−0.211948	−	0.0733559i
$339$	34.4864	−	5.99826i	1.87304	−	0.325781i
$340$	1.18442	−	4.88224i	0.0642341	−	0.264777i
$341$	6.53974	−	0.624470i	0.354147	−	0.0338169i
$342$	15.7623	+	38.1270i	0.852327	+	2.06167i
$343$	−15.1792	+	10.6109i	−0.819600	+	0.572937i
$344$	−1.37348			−0.0740533
$345$	5.37482	+	11.6872i	0.289371	+	0.629217i
$346$	−7.47030	+	12.9389i	−0.401606	+	0.695601i
$347$	28.7965	−	1.37175i	1.54588	−	0.0736391i	0.742799	−	0.669515i	$-0.233498\pi$
$347$	28.7965	−	1.37175i	1.54588	−	0.0736391i	0.803077	+	0.595876i	$0.203195\pi$
$348$	25.1694	+	33.2322i	1.34922	+	1.78143i
$349$	2.10946	−	4.61906i	0.112917	−	0.247253i	−0.844734	−	0.535187i	$-0.820241\pi$
$349$	2.10946	−	4.61906i	0.112917	−	0.247253i	0.957650	+	0.287934i	$0.0929684\pi$
$350$	−14.9620	−	3.42502i	−0.799751	−	0.183075i
$351$	16.3571	+	5.78928i	0.873078	+	0.309009i
$352$	−8.98672	−	3.11033i	−0.478994	−	0.165781i
$353$	0.275997	−	0.689407i	0.0146898	−	0.0366934i	−0.920842	−	0.389937i	$-0.872497\pi$
$353$	0.275997	−	0.689407i	0.0146898	−	0.0366934i	0.935532	+	0.353243i	$0.114921\pi$
$354$	−14.9777	+	24.8854i	−0.796053	+	1.32264i
$355$	−1.22977	+	6.38063i	−0.0652692	+	0.338649i
$356$	1.21385	+	0.780093i	0.0643338	+	0.0413448i
$357$	4.79206	+	1.43434i	0.253622	+	0.0759131i
$358$	−2.35327	+	2.71582i	−0.124374	+	0.143535i
$359$	2.59331	+	10.6898i	0.136870	+	0.564184i	0.998403	+	0.0564841i	$0.0179890\pi$
$359$	2.59331	+	10.6898i	0.136870	+	0.564184i	−0.861534	+	0.507700i	$0.830496\pi$
$360$	1.54470	+	9.94991i	0.0814126	+	0.524407i
$361$	−18.6940	+	3.60298i	−0.983896	+	0.189630i
$362$	−16.2493	+	22.8189i	−0.854044	+	1.19934i
$363$	13.3408	−	8.23462i	0.700210	−	0.432205i
$364$	−26.1037	+	2.83448i	−1.36821	+	0.148567i
$365$	2.90954	−	20.2363i	0.152292	−	1.05921i
$366$	−43.0518	−	9.11275i	−2.25035	−	0.476331i
$367$	−5.37771	−	3.10482i	−0.280714	−	0.162070i	0.353033	−	0.935611i	$-0.385150\pi$
$367$	−5.37771	−	3.10482i	−0.280714	−	0.162070i	−0.633747	+	0.773541i	$0.718484\pi$
$368$	−1.63780	+	5.07167i	−0.0853763	+	0.264379i
$369$	1.31848	−	2.34401i	0.0686374	−	0.122025i
$370$	−1.04242	+	0.669920i	−0.0541926	+	0.0348275i
$371$	16.1292	−	6.70103i	0.837388	−	0.347900i
$372$	3.88333	−	23.9127i	0.201341	−	1.23982i
$373$	2.81379	−	2.95102i	0.145693	−	0.152798i	−0.646844	−	0.762622i	$-0.723912\pi$
$373$	2.81379	−	2.95102i	0.145693	−	0.152798i	0.792537	+	0.609824i	$0.208760\pi$
$374$	0.322957	−	3.38216i	0.0166997	−	0.174888i
$375$	−18.2905	+	9.01212i	−0.944517	+	0.465384i
$376$	17.7020	−	13.9210i	0.912909	−	0.717920i
$377$	−7.61889	+	25.9476i	−0.392393	+	1.33637i
$378$	−30.4978	+	3.09661i	−1.56864	+	0.159272i
$379$	−1.18680	+	1.84669i	−0.0609616	+	0.0948581i	−0.870396	−	0.492352i	$-0.836137\pi$
$379$	−1.18680	+	1.84669i	−0.0609616	+	0.0948581i	0.809435	+	0.587210i	$0.199774\pi$
$380$	−28.3537	−	1.35065i	−1.45452	−	0.0692871i
$381$	6.90251	+	10.0762i	0.353626	+	0.516221i
$382$	−16.3645	−	17.1626i	−0.837281	−	0.878115i
$383$	−18.8983	+	14.8618i	−0.965660	+	0.759403i	−0.970628	−	0.240584i	$-0.922661\pi$
$383$	−18.8983	+	14.8618i	−0.965660	+	0.759403i	0.00496847	+	0.999988i	$0.498418\pi$
$384$	−14.7216	+	22.0162i	−0.751261	+	1.12351i
$385$	5.70011	+	0.469824i	0.290504	+	0.0239445i
$386$	−15.9468	−	54.3099i	−0.811672	−	2.76430i
$387$	−1.12009	−	1.53618i	−0.0569376	−	0.0780887i
$388$	−12.2089	+	15.5249i	−0.619815	+	0.788159i
$389$	−0.175118	−	3.67617i	−0.00887882	−	0.186389i	−0.998950	−	0.0458203i	$-0.985410\pi$
$389$	−0.175118	−	3.67617i	−0.00887882	−	0.186389i	0.990071	−	0.140569i	$-0.0448932\pi$
$390$	−14.0430	+	14.2014i	−0.711096	+	0.719118i
$391$	−5.22042	−	0.388909i	−0.264008	−	0.0196680i
$392$	12.9376	−	7.92363i	0.653449	−	0.400204i
$393$	24.2298	+	21.7793i	1.22223	+	1.09862i
$394$	24.0804	−	9.64036i	1.21316	−	0.485674i
$395$	−5.35041	+	3.81001i	−0.269208	+	0.191702i
$396$	3.64014	+	11.9016i	0.182924	+	0.598079i
$397$	−5.26466	+	7.39319i	−0.264226	+	0.371053i	−0.925280	−	0.379285i	$-0.876170\pi$
$397$	−5.26466	+	7.39319i	−0.264226	+	0.371053i	0.661054	+	0.750338i	$0.270109\pi$
$398$	15.0547	+	17.3740i	0.754623	+	0.870881i
$399$	2.83366	−	28.1206i	0.141860	−	1.40779i
$400$	−2.77418	−	0.814574i	−0.138709	−	0.0407287i
$401$	35.7168	+	6.88386i	1.78361	+	0.343763i	0.971007	−	0.239049i	$-0.0768357\pi$
$401$	35.7168	+	6.88386i	1.78361	+	0.343763i	0.812607	+	0.582813i	$0.198048\pi$
$402$	18.5730	−	17.0752i	0.926338	−	0.851635i
$403$	13.9684	−	7.20124i	0.695818	−	0.358719i
$404$	2.12507	−	11.0259i	0.105726	−	0.548560i
$405$	−9.86884	+	9.84196i	−0.490387	+	0.489051i
$406$	−7.41172	−	47.1983i	−0.367837	−	2.34241i
$407$	−0.378562	+	0.328026i	−0.0187646	+	0.0162597i
$408$	−3.84719	−	1.41040i	−0.190464	−	0.0698251i
$409$	6.16936	−	25.4305i	0.305055	−	1.25745i	−0.588498	−	0.808498i	$-0.700281\pi$
$409$	6.16936	−	25.4305i	0.305055	−	1.25745i	0.893554	−	0.448957i	$-0.148204\pi$
$410$	1.79562	+	2.52160i	0.0886793	+	0.124533i
$411$	5.29318	−	4.00895i	0.261094	−	0.197747i
$412$	−11.6049	−	18.0576i	−0.571733	−	0.889633i
$413$	17.1012	−	10.1712i	0.841496	−	0.500492i
$414$	30.4761	−	10.0203i	1.49782	−	0.492469i
$415$	−8.82018	−	15.2770i	−0.432966	−	0.749918i
$416$	−22.7233	+	1.08245i	−1.11410	+	0.0530713i
$417$	8.74060	+	3.68506i	0.428029	+	0.180458i
$418$	−19.1100	+	1.82478i	−0.934700	+	0.0892530i
$419$	−12.7097	+	3.73192i	−0.620911	+	0.182316i	−0.577033	−	0.816721i	$-0.695790\pi$
$419$	−12.7097	+	3.73192i	−0.620911	+	0.182316i	−0.0438785	+	0.999037i	$0.513971\pi$
$420$	7.00241	−	19.8949i	0.341682	−	0.970773i
$421$	0.703827	−	0.609869i	0.0343024	−	0.0297232i	−0.637541	−	0.770417i	$-0.720048\pi$
$421$	0.703827	−	0.609869i	0.0343024	−	0.0297232i	0.671843	+	0.740693i	$0.265503\pi$
$422$	2.16076	+	2.74762i	0.105184	+	0.133752i
$423$	30.0062	+	8.44617i	1.45895	+	0.410667i
$424$	−13.5206	+	4.67952i	−0.656618	+	0.227258i
$425$	0.135130	−	2.83672i	0.00655476	−	0.137601i
$426$	15.4634	+	4.84769i	0.749205	+	0.234871i
$427$	23.0369	+	19.4446i	1.11484	+	0.940990i
$428$	1.55859	+	0.457642i	0.0753371	+	0.0221210i
$429$	−4.80203	+	6.49033i	−0.231844	+	0.313356i
$430$	2.14879	−	0.414145i	0.103624	−	0.0199718i
$431$	20.0780	+	1.91722i	0.967126	+	0.0923493i	0.566650	−	0.823958i	$-0.308239\pi$
$431$	20.0780	+	1.91722i	0.967126	+	0.0923493i	0.400475	+	0.916308i	$0.368845\pi$
$432$	−5.76967	+	0.234532i	−0.277594	+	0.0112839i
$433$	27.4157	+	12.5203i	1.31752	+	0.601689i	0.945223	−	0.326426i	$-0.105845\pi$
$433$	27.4157	+	12.5203i	1.31752	+	0.601689i	0.372293	+	0.928115i	$0.378572\pi$
$434$	−16.8785	+	22.0449i	−0.810193	+	1.05819i
$435$	−16.1553	−	14.5215i	−0.774588	−	0.696252i
$436$	−23.3844	+	13.5010i	−1.11991	+	0.646579i
$437$	3.42455	+	29.3794i	0.163818	+	1.40541i
$438$	−49.3220	−	12.9197i	−2.35670	−	0.617328i
$439$	−10.7329	−	5.53320i	−0.512254	−	0.264085i	0.182663	−	0.983176i	$-0.441528\pi$
$439$	−10.7329	−	5.53320i	−0.512254	−	0.264085i	−0.694916	+	0.719090i	$0.744559\pi$
$440$	−4.63750	−	0.666771i	−0.221084	−	0.0317871i
$441$	19.4130	+	8.00837i	0.924430	+	0.381351i
$442$	−2.28980	−	7.79835i	−0.108915	−	0.370930i
$443$	−30.3166	−	21.5884i	−1.44039	−	1.02570i	−0.991216	−	0.132249i	$-0.957780\pi$
$443$	−30.3166	−	21.5884i	−1.44039	−	1.02570i	−0.449171	−	0.893446i	$-0.648281\pi$
$444$	0.816422	+	1.65696i	0.0387457	+	0.0786360i
$445$	−0.698005	−	0.279439i	−0.0330886	−	0.0132467i
$446$	−48.6140	+	11.7936i	−2.30194	+	0.558444i
$447$	11.9781	−	25.0140i	0.566545	−	1.18312i
$448$	30.2899	−	16.1159i	1.43106	−	0.761402i
$449$	6.80349	−	10.5864i	0.321077	−	0.499605i	−0.642771	−	0.766058i	$-0.722215\pi$
$449$	6.80349	−	10.5864i	0.321077	−	0.499605i	0.963848	+	0.266453i	$0.0858518\pi$
$450$	5.87646	+	16.3820i	0.277019	+	0.772255i
$451$	0.863551	+	0.905666i	0.0406630	+	0.0426461i
$452$	55.7602	+	22.3230i	2.62274	+	1.04999i
$453$	−1.84116	+	27.9446i	−0.0865053	+	1.31295i
$454$	−6.34158	+	2.89610i	−0.297625	+	0.135921i
$455$	13.0767	−	4.02449i	0.613045	−	0.188671i
$456$	−3.71121	+	22.8528i	−0.173793	+	1.07018i
$457$	−9.99094	−	24.9562i	−0.467356	−	1.16740i	−0.955593	−	0.294688i	$-0.904784\pi$
$457$	−9.99094	−	24.9562i	−0.467356	−	1.16740i	0.488237	−	0.872711i	$-0.337640\pi$
$458$	1.45572	+	30.5593i	0.0680212	+	1.42794i
$459$	−1.55996	−	5.45312i	−0.0728127	−	0.254530i
$460$	−2.68533	+	21.9088i	−0.125204	+	1.02150i
$461$			19.4053i			0.903796i	0.892070	+	0.451898i	$0.149253\pi$
$461$			19.4053i			0.903796i	−0.892070	+	0.451898i	$0.850747\pi$
$462$	2.77262	−	13.9916i	0.128994	−	0.650949i
$463$	−1.42970	+	9.94381i	−0.0664440	+	0.462128i	0.929252	+	0.369447i	$0.120453\pi$
$463$	−1.42970	+	9.94381i	−0.0664440	+	0.462128i	−0.995696	+	0.0926812i	$0.970456\pi$
$464$	−0.855480	−	8.95899i	−0.0397147	−	0.415911i
$465$	0.371192	+	12.6181i	0.0172136	+	0.585151i
$466$	−1.81457	−	0.173271i	−0.0840585	−	0.00802661i
$467$	13.6099	−	39.3231i	0.629790	−	1.81966i	0.0594783	−	0.998230i	$-0.481056\pi$
$467$	13.6099	−	39.3231i	0.629790	−	1.81966i	0.570312	−	0.821429i	$-0.306822\pi$
$468$	18.6657	+	23.1951i	0.862822	+	1.07219i
$469$	−16.7420	+	4.29208i	−0.773074	+	0.198190i
$470$	−23.4968	+	27.1167i	−1.08382	+	1.25080i
$471$	16.5075	−	3.68809i	0.760628	−	0.169938i
$472$	−14.4874	+	7.46877i	−0.666836	+	0.343778i
$473$	0.835970	−	0.289332i	0.0384379	−	0.0133035i
$474$	7.93098	+	14.3328i	0.364282	+	0.658327i
$475$	−15.8830	+	2.28363i	−0.728761	+	0.104780i
$476$	5.70427	+	6.41320i	0.261455	+	0.293948i
$477$	−16.2601	−	11.3060i	−0.744497	−	0.517666i
$478$	−14.0696	−	13.4153i	−0.643527	−	0.613601i
$479$	14.7483	+	20.7110i	0.673865	+	0.946311i	1.00000		0.000987888i	$0.000314455\pi$
$479$	14.7483	+	20.7110i	0.673865	+	0.946311i	−0.326134	+	0.945323i	$0.605746\pi$
$480$	7.09900	−	16.8381i	0.324024	−	0.768551i
$481$	−0.549079	+	1.06507i	−0.0250359	+	0.0485628i
$482$	−1.69242			−0.0770876
$483$	−21.6424	−	3.82186i	−0.984763	−	0.173900i
$484$	26.9007			1.22276
$485$	4.71584	−	9.14746i	0.214135	−	0.415365i
$486$	21.6024	+	27.2310i	0.979905	+	1.23522i
$487$	13.1946	+	18.5292i	0.597902	+	0.839636i	0.997010	−	0.0772676i	$-0.0246196\pi$
$487$	13.1946	+	18.5292i	0.597902	+	0.839636i	−0.399108	+	0.916904i	$0.630680\pi$
$488$	−17.8725	−	17.0414i	−0.809049	−	0.771427i
$489$	−27.7492	−	33.2267i	−1.25486	−	1.50256i
$490$	−17.8514	+	16.2974i	−0.806445	+	0.736241i
$491$	−2.48006	+	0.356579i	−0.111923	+	0.0160922i	−0.198049	−	0.980192i	$-0.563461\pi$
$491$	−2.48006	+	0.356579i	−0.111923	+	0.0160922i	0.0861255	+	0.996284i	$0.472551\pi$
$492$	4.03771	−	2.23425i	0.182034	−	0.100728i
$493$	8.35369	−	2.89124i	0.376231	−	0.130215i
$494$	−40.8176	+	21.0430i	−1.83647	+	0.946767i
$495$	−3.03618	−	5.73061i	−0.136466	−	0.257572i
$496$	−3.42493	+	3.95258i	−0.153784	+	0.177476i
$497$	−7.76448	−	7.93463i	−0.348284	−	0.355917i
$498$	−40.3434	+	17.5445i	−1.80783	+	0.786188i
$499$	9.48777	−	27.4131i	0.424731	−	1.22718i	−0.506338	−	0.862335i	$-0.669001\pi$
$499$	9.48777	−	27.4131i	0.424731	−	1.22718i	0.931069	−	0.364844i	$-0.118878\pi$
$500$	−34.8286	−	3.32573i	−1.55758	−	0.148731i
$501$	16.2537	−	0.478141i	0.726162	−	0.0213618i
$502$	−5.69163	−	59.6054i	−0.254030	−	2.66032i
$503$	−1.53277	+	10.6607i	−0.0683430	+	0.475336i	0.926693	+	0.375819i	$0.122639\pi$
$503$	−1.53277	+	10.6607i	−0.0683430	+	0.475336i	−0.995036	+	0.0995165i	$0.968270\pi$
$504$	−15.4763	−	7.51068i	−0.689371	−	0.334552i
$505$			5.85108i			0.260370i
$506$	0.311059	+	14.9242i	0.0138282	+	0.663462i
$507$	0.811621	−	3.09842i	0.0360454	−	0.137606i
$508$	0.997184	+	20.9335i	0.0442429	+	0.928773i
$509$	10.2756	+	25.6673i	0.455460	+	1.13768i	0.961410	+	0.275121i	$0.0887180\pi$
$509$	10.2756	+	25.6673i	0.455460	+	1.13768i	−0.505949	+	0.862563i	$0.668858\pi$
$510$	6.44412	+	1.04650i	0.285350	+	0.0463398i
$511$	25.5890	+	23.7735i	1.13199	+	1.05168i
$512$	11.2683	−	5.14608i	0.497995	−	0.227427i
$513$	−28.5865	+	14.4859i	−1.26212	+	0.639569i
$514$	13.1378	+	5.25957i	0.579483	+	0.231990i
$515$	7.71850	+	8.09493i	0.340118	+	0.356705i
$516$	−0.250968	−	3.25251i	−0.0110483	−	0.143184i
$517$	−7.84175	+	12.2020i	−0.344880	+	0.536644i
$518$	0.0733131	−	2.11571i	0.00322119	−	0.0929588i
$519$	−10.4673	−	5.01233i	−0.459463	−	0.220017i
$520$	−10.8919	+	2.64235i	−0.477642	+	0.115875i
$521$	−31.2671	−	12.5175i	−1.36984	−	0.548400i	−0.434026	−	0.900901i	$-0.642907\pi$
$521$	−31.2671	−	12.5175i	−1.36984	−	0.548400i	−0.935812	+	0.352500i	$0.885331\pi$
$522$	−40.5412	+	35.9333i	−1.77444	+	1.57276i
$523$	16.6973	+	11.8901i	0.730124	+	0.519919i	0.883605	−	0.468233i	$-0.155109\pi$
$523$	16.6973	+	11.8901i	0.730124	+	0.519919i	−0.153481	+	0.988152i	$0.549048\pi$
$524$	15.7495	+	53.6378i	0.688019	+	2.34318i
$525$	1.75847	−	11.7923i	0.0767458	−	0.514659i
$526$	56.3044	+	8.09534i	2.45499	+	0.352974i
$527$	−4.56604	−	2.35396i	−0.198900	−	0.102540i
$528$	0.680844	−	2.59917i	0.0296299	−	0.113114i
$529$	22.9800	−	0.958341i	0.999132	−	0.0416670i
$530$	19.7416	−	11.3978i	0.857522	−	0.495091i
$531$	−20.1682	−	10.1127i	−0.875223	−	0.438852i
$532$	29.4815	−	38.5056i	1.27819	−	1.66943i
$533$	2.72301	+	1.24356i	0.117947	+	0.0538645i
$534$	−0.889379	+	1.65072i	−0.0384872	+	0.0714337i
$535$	−0.842596	−	0.0804582i	−0.0364286	−	0.00347851i
$536$	13.9022	−	2.67943i	0.600483	−	0.115734i
$537$	−2.24396	−	1.66025i	−0.0968339	−	0.0716450i
$538$	60.6539	+	17.8096i	2.61497	+	0.767826i
$539$	−6.20531	+	7.54809i	−0.267282	+	0.325119i
$540$	−23.2799	+	5.47604i	−1.00181	+	0.235651i
$541$	0.595068	−	12.4920i	0.0255840	−	0.537074i	−0.949302	−	0.314367i	$-0.898208\pi$
$541$	0.595068	−	12.4920i	0.0255840	−	0.537074i	0.974885	−	0.222707i	$-0.0714892\pi$
$542$	−12.3816	+	4.28530i	−0.531833	+	0.184069i
$543$	−18.6437	−	11.2210i	−0.800079	−	0.481539i
$544$	4.59680	+	5.84531i	0.197086	+	0.250616i
$545$	10.6334	−	9.21393i	0.455487	−	0.394681i
$546$	−6.28223	−	33.5381i	−0.268855	−	1.43530i
$547$	−12.1305	+	3.56183i	−0.518662	+	0.152293i	−0.530578	−	0.847636i	$-0.678025\pi$
$547$	−12.1305	+	3.56183i	−0.518662	+	0.152293i	0.0119163	+	0.999929i	$0.496207\pi$
$548$	11.3418	−	1.08301i	0.484498	−	0.0462639i
$549$	4.48483	−	33.8871i	0.191408	−	1.44626i
$550$	−8.08901	+	0.385327i	−0.344917	+	0.0164304i
$551$	−24.9736	−	43.2556i	−1.06391	−	1.84275i
$552$	17.5068	+	4.19804i	0.745138	+	0.178680i
$553$	−0.145450	−	11.2207i	−0.00618518	−	0.477154i
$554$	6.05988	+	9.42935i	0.257459	+	0.400615i
$555$	−0.581130	−	0.767290i	−0.0246676	−	0.0325697i
$556$	9.44112	+	13.2582i	0.400393	+	0.562273i
$557$	−3.74171	+	15.4236i	−0.158542	+	0.653517i	0.835960	+	0.548791i	$0.184912\pi$
$557$	−3.74171	+	15.4236i	−0.158542	+	0.653517i	−0.994501	+	0.104726i	$0.966603\pi$
$558$	31.3709	+	2.64080i	1.32804	+	0.111794i
$559$	1.59931	−	1.38581i	0.0676435	−	0.0586134i
$560$	−3.54233	+	2.86080i	−0.149691	+	0.120891i
$561$	2.63870	+	0.0480058i	0.111406	+	0.00202681i
$562$	−8.27873	+	42.9541i	−0.349217	+	1.81191i
$563$	−6.31242	+	3.25428i	−0.266037	+	0.137152i	−0.586085	−	0.810250i	$-0.699331\pi$
$563$	−6.31242	+	3.25428i	−0.266037	+	0.137152i	0.320048	+	0.947401i	$0.396301\pi$
$564$	36.2005	+	39.3759i	1.52431	+	1.65802i
$565$	−30.7316	−	5.92304i	−1.29289	−	0.249184i
$566$	39.4720	+	11.5900i	1.65913	+	0.487165i
$567$	−4.22077	−	23.4347i	−0.177256	−	0.984165i
$568$	5.95536	+	6.87285i	0.249881	+	0.288378i
$569$	−13.0018	+	18.2585i	−0.545064	+	0.765435i	−0.991602	−	0.129330i	$-0.958718\pi$
$569$	−13.0018	+	18.2585i	−0.545064	+	0.765435i	0.446538	+	0.894765i	$0.352657\pi$
$570$	−1.08467	−	36.8718i	−0.0454319	−	1.54439i
$571$	−24.3558	+	17.3437i	−1.01926	+	0.725810i	−0.962139	−	0.272558i	$-0.912130\pi$
$571$	−24.3558	+	17.3437i	−1.01926	+	0.725810i	−0.0571179	+	0.998367i	$0.518191\pi$
$572$	−12.8610	+	5.14878i	−0.537747	+	0.215281i
$573$	12.3141	−	13.6995i	0.514427	−	0.572306i
$574$	−5.28822	+	0.0685493i	−0.220726	+	0.00286119i
$575$	0.853290	+	12.4483i	0.0355847	+	0.519132i
$576$	−33.9081	−	19.0729i	−1.41284	−	0.794706i
$577$	−0.231917	−	4.86854i	−0.00965484	−	0.202680i	−0.998541	−	0.0540037i	$-0.982802\pi$
$577$	−0.231917	−	4.86854i	−0.00965484	−	0.202680i	0.988886	−	0.148676i	$-0.0475013\pi$
$578$	21.7899	−	27.7082i	0.906342	−	1.15251i
$579$	41.1086	−	15.5959i	1.70842	−	0.648145i
$580$	−10.5010	−	35.7633i	−0.436032	−	1.48499i
$581$	30.0358	+	2.47566i	1.24609	+	0.102708i
$582$	−21.3356	−	14.2665i	−0.884389	−	0.591366i
$583$	7.24352	−	5.69637i	0.299996	−	0.235920i
$584$	−19.7446	−	20.7075i	−0.817036	−	0.856883i
$585$	−11.8378	−	10.0273i	−0.489435	−	0.414577i
$586$	67.1036	+	3.19654i	2.77202	+	0.132048i
$587$	−7.30459	+	11.3662i	−0.301493	+	0.469132i	−0.958636	−	0.284633i	$-0.908128\pi$
$587$	−7.30459	+	11.3662i	−0.301493	+	0.469132i	0.657144	+	0.753765i	$0.271764\pi$
$588$	21.1277	+	29.1894i	0.871293	+	1.20375i
$589$	−8.17750	+	27.8500i	−0.336948	+	1.14754i
$590$	20.4132	−	16.0531i	0.840396	−	0.660895i
$591$	8.90524	+	18.0736i	0.366313	+	0.743448i
$592$	0.0379062	−	0.396972i	0.00155793	−	0.0163154i
$593$	−13.3721	+	14.0242i	−0.549124	+	0.575905i	−0.938546	−	0.345155i	$-0.887826\pi$
$593$	−13.3721	+	14.0242i	−0.549124	+	0.575905i	0.389422	+	0.921060i	$0.372675\pi$
$594$	−15.0565	+	5.90623i	−0.617776	+	0.242336i
$595$	−3.55108	−	2.71885i	−0.145580	−	0.111462i
$596$	40.0336	−	25.7280i	1.63984	−	1.05386i
$597$	−12.5561	+	12.6977i	−0.513886	+	0.519683i
$598$	13.9597	+	32.8676i	0.570856	+	1.34406i
$599$	41.6440	+	24.0432i	1.70153	+	0.982378i	0.944216	+	0.329326i	$0.106822\pi$
$599$	41.6440	+	24.0432i	1.70153	+	0.982378i	0.757313	+	0.653052i	$0.226512\pi$
$600$	−2.02250	+	9.55501i	−0.0825684	+	0.390082i
$601$	−0.578861	+	4.02607i	−0.0236122	+	0.164227i	−0.998216	−	0.0597110i	$-0.980982\pi$
$601$	−0.578861	+	4.02607i	−0.0236122	+	0.164227i	0.974603	+	0.223938i	$0.0718912\pi$
$602$	−1.50888	+	3.42064i	−0.0614974	+	0.139415i
$603$	14.3342	+	13.3639i	0.583735	+	0.544220i
$604$	−27.8737	+	39.1432i	−1.13417	+	1.59271i
$605$	−13.7640	+	2.65279i	−0.559586	+	0.107851i
$606$	14.4983	+	1.65105i	0.588952	+	0.0670694i
$607$	−2.82719	−	11.6539i	−0.114752	−	0.473015i	−0.999969	−	0.00783710i	$-0.997505\pi$
$607$	−2.82719	−	11.6539i	−0.114752	−	0.473015i	0.885217	−	0.465178i	$-0.154010\pi$
$608$	27.5150	−	31.7540i	1.11588	−	1.28780i
$609$	36.1109	−	8.56073i	1.46329	−	0.346898i
$610$	33.0995	+	21.2718i	1.34016	+	0.861270i
$611$	−6.56657	+	34.0706i	−0.265655	+	1.37835i
$612$	2.63695	−	9.36815i	0.106593	−	0.378685i
$613$	6.16935	−	15.4103i	0.249178	−	0.622416i	−0.750063	−	0.661366i	$-0.769977\pi$
$613$	6.16935	−	15.4103i	0.249178	−	0.622416i	0.999241	+	0.0389501i	$0.0124013\pi$
$614$	−10.6656	−	3.69142i	−0.430431	−	0.148973i
$615$	−1.84560	+	1.54135i	−0.0744220	+	0.0621532i
$616$	5.44812	−	5.86416i	0.219511	−	0.236274i
$617$	−6.70776	+	14.6879i	−0.270044	+	0.591314i	−0.995265	−	0.0972026i	$-0.969011\pi$
$617$	−6.70776	+	14.6879i	−0.270044	+	0.591314i	0.725221	+	0.688517i	$0.241738\pi$
$618$	22.2363	−	16.8413i	0.894473	−	0.677456i
$619$	−43.0406	+	2.05028i	−1.72995	+	0.0824076i	−0.888771	−	0.458352i	$-0.848440\pi$
$619$	−43.0406	+	2.05028i	−1.72995	+	0.0824076i	−0.841177	+	0.540760i	$0.818137\pi$
$620$	−10.8302	+	18.7585i	−0.434952	+	0.753360i
$621$	9.58168	+	23.0042i	0.384499	+	0.923125i
$622$	10.8692			0.435816
$623$	1.07151	−	0.708411i	0.0429293	−	0.0283819i
$624$	−0.798849	−	6.37765i	−0.0319796	−	0.255310i
$625$	5.19849	−	0.496396i	0.207940	−	0.0198558i
$626$	12.2395	−	50.4521i	0.489190	−	2.01647i
$627$	−2.55525	−	14.6911i	−0.102047	−	0.586707i
$628$	27.4269	+	9.49255i	1.09445	+	0.378794i
$629$	0.387706	−	0.0557438i	0.0154589	−	0.00222265i
$630$	26.4771	+	7.08373i	1.05487	+	0.282223i
$631$	−5.86116	−	5.07873i	−0.233329	−	0.202181i	0.530346	−	0.847781i	$-0.322062\pi$
$631$	−5.86116	−	5.07873i	−0.233329	−	0.202181i	−0.763676	+	0.645600i	$0.776607\pi$
$632$	−0.437394	+	9.18203i	−0.0173986	+	0.365242i
$633$	−1.99884	+	1.83765i	−0.0794467	+	0.0730399i
$634$	9.19206	+	26.5587i	0.365064	+	1.05478i
$635$	−2.57456	−	10.6125i	−0.102168	−	0.421143i
$636$	−13.5520	−	31.1627i	−0.537371	−	1.23568i
$637$	−7.07005	+	22.2801i	−0.280125	+	0.882769i
$638$	−10.4714	−	22.9293i	−0.414568	−	0.907778i
$639$	−2.83033	+	12.2657i	−0.111966	+	0.485224i
$640$	19.2892	−	13.7358i	0.762472	−	0.542954i
$641$	0.517311	+	0.406818i	0.0204325	+	0.0160683i	0.628323	−	0.777953i	$-0.283742\pi$
$641$	0.517311	+	0.406818i	0.0204325	+	0.0160683i	−0.607891	+	0.794021i	$0.707984\pi$
$642$	−0.437129	+	2.06515i	−0.0172521	+	0.0815049i
$643$		−	35.9369i		−	1.41721i	−0.705604	−	0.708606i	$-0.749324\pi$
$643$		−	35.9369i		−	1.41721i	0.705604	−	0.708606i	$-0.250676\pi$
$644$	−28.1560	−	25.0858i	−1.10950	−	0.988520i
$645$	0.449155	+	1.63943i	0.0176854	+	0.0645525i
$646$	13.3426	+	6.87857i	0.524956	+	0.270634i
$647$	−6.23685	+	7.93080i	−0.245196	+	0.311792i	−0.893037	−	0.449984i	$-0.851430\pi$
$647$	−6.23685	+	7.93080i	−0.245196	+	0.311792i	0.647841	+	0.761776i	$0.275672\pi$
$648$	2.28929	+	19.3710i	0.0899320	+	0.760967i
$649$	7.24440	−	7.59771i	0.284368	−	0.298236i
$650$	−17.6217	+	8.04757i	−0.691181	+	0.315652i
$651$	−18.0819	−	11.7546i	−0.708684	−	0.460698i
$652$	−10.5712	−	73.5243i	−0.414000	−	2.87943i
$653$	36.9104	−	8.95436i	1.44441	−	0.350411i	0.564456	−	0.825463i	$-0.309086\pi$
$653$	36.9104	−	8.95436i	1.44441	−	0.350411i	0.879958	+	0.475052i	$0.157571\pi$
$654$	−19.8305	−	28.9484i	−0.775433	−	1.13197i
$655$	−13.3478	−	25.8912i	−0.521543	−	1.01165i
$656$	−0.995102	−	0.0474025i	−0.0388522	−	0.00185076i
$657$	7.05854	−	38.9707i	0.275380	−	1.52039i
$658$	−15.2230	−	59.3798i	−0.593453	−	2.31486i
$659$	0.363057	+	2.52512i	0.0141427	+	0.0983646i	0.995670	−	0.0929568i	$-0.0296318\pi$
$659$	0.363057	+	2.52512i	0.0141427	+	0.0983646i	−0.981527	+	0.191321i	$0.938723\pi$
$660$	0.731583	−	11.1038i	0.0284768	−	0.432214i
$661$	−4.15067	+	43.4677i	−0.161442	+	1.69070i	0.444968	+	0.895547i	$0.353215\pi$
$661$	−4.15067	+	43.4677i	−0.161442	+	1.69070i	−0.606410	+	0.795152i	$0.707391\pi$
$662$	69.7403	+	16.9188i	2.71053	+	0.657569i
$663$	5.90278	−	2.23942i	0.229245	−	0.0869718i
$664$	−24.4365	−	3.51344i	−0.948321	−	0.136348i
$665$	−11.2873	+	22.6091i	−0.437702	+	0.876743i
$666$	−2.06524	+	1.22346i	−0.0800263	+	0.0474080i
$667$	−34.9852	+	16.8669i	−1.35463	+	0.653090i
$668$	24.1633	+	13.9507i	0.934906	+	0.539768i
$669$	−12.0390	−	36.9455i	−0.465455	−	1.42839i
$670$	−20.9417	+	8.38381i	−0.809050	+	0.323895i
$671$	14.4679	+	6.60728i	0.558528	+	0.255071i
$672$	16.7408	+	26.3511i	0.645791	+	1.01652i
$673$	−2.05655	−	4.50322i	−0.0792742	−	0.173586i	0.865845	−	0.500313i	$-0.166782\pi$
$673$	−2.05655	−	4.50322i	−0.0792742	−	0.173586i	−0.945119	+	0.326727i	$0.894054\pi$
$674$	14.2701	−	41.2306i	0.549662	−	1.58815i
$675$	−12.3363	+	5.53015i	−0.474823	+	0.212855i
$676$	3.97755	−	3.79259i	0.152983	−	0.145869i
$677$	−14.7087	−	2.83487i	−0.565302	−	0.108953i	−0.101410	−	0.994845i	$-0.532335\pi$
$677$	−14.7087	−	2.83487i	−0.565302	−	0.108953i	−0.463892	+	0.885892i	$0.653547\pi$
$678$	−23.3484	+	74.4779i	−0.896690	+	2.86031i
$679$	8.25866	+	15.5222i	0.316938	+	0.595688i
$680$	2.76880	+	2.39918i	0.106179	+	0.0920042i
$681$	−2.62193	−	4.73832i	−0.100472	−	0.181573i
$682$	−5.44434	+	13.5993i	−0.208474	+	0.520744i
$683$	−8.31014	−	43.1171i	−0.317979	−	1.64983i	−0.691623	−	0.722258i	$-0.743104\pi$
$683$	−8.31014	−	43.1171i	−0.317979	−	1.64983i	0.373645	−	0.927572i	$-0.378108\pi$
$684$	−54.7953	−	4.61266i	−2.09515	−	0.176369i
$685$	−5.69634	+	1.67260i	−0.217646	+	0.0639066i
$686$	−5.52067	−	40.9257i	−0.210780	−	1.56255i
$687$	−23.5804	+	2.95362i	−0.899647	+	0.112688i
$688$	−0.322708	+	0.625966i	−0.0123031	+	0.0238647i
$689$	11.0221	−	19.0908i	0.419908	−	0.727301i
$690$	−28.6548	−	1.28894i	−1.09087	−	0.0490691i
$691$	6.13949	+	10.6339i	0.233557	+	0.404533i	0.958852	−	0.283905i	$-0.0916301\pi$
$691$	6.13949	+	10.6339i	0.233557	+	0.404533i	−0.725295	+	0.688438i	$0.758297\pi$
$692$	−10.7661	−	16.7524i	−0.409265	−	0.636829i
$693$	11.0018	+	1.31119i	0.417925	+	0.0498080i
$694$	−26.7041	+	58.4739i	−1.01367	+	2.21964i
$695$	−6.13809	−	5.85266i	−0.232831	−	0.222004i
$696$	−29.9512	+	5.20945i	−1.13530	+	0.197464i
$697$	−0.185189	−	0.960850i	−0.00701452	−	0.0363948i
$698$	6.99927	+	8.90030i	0.264926	+	0.336881i
$699$	0.0257557	−	1.41569i	0.000974171	−	0.0535465i
$700$	13.1955	−	15.6334i	0.498745	−	0.590886i
$701$	−41.3530	−	26.5760i	−1.56188	−	1.00376i	−0.981960	−	0.189087i	$-0.939447\pi$
$701$	−41.3530	−	26.5760i	−1.56188	−	1.00376i	−0.579921	−	0.814673i	$-0.696917\pi$
$702$	−28.1868	+	26.5033i	−1.06384	+	1.00030i
$703$	−0.723852	−	2.09143i	−0.0273006	−	0.0788799i
$704$	13.1012	−	12.4920i	0.493771	−	0.470810i
$705$	−22.4053	−	16.5772i	−0.843834	−	0.624332i
$706$	1.08435	+	1.25141i	0.0408100	+	0.0470973i
$707$	−8.21719	−	5.69237i	−0.309039	−	0.214084i
$708$	−20.3338	−	32.9425i	−0.764190	−	1.23805i
$709$	4.24869	+	44.4943i	0.159563	+	1.67102i	0.620973	+	0.783832i	$0.286738\pi$
$709$	4.24869	+	44.4943i	0.159563	+	1.67102i	−0.461410	+	0.887187i	$0.652656\pi$
$710$	−11.3894	−	8.95671i	−0.427436	−	0.336139i
$711$	−10.6264	+	6.99885i	−0.398522	+	0.262478i
$712$	−0.911264	+	0.526119i	−0.0341511	+	0.0197171i
$713$	21.1238	+	7.95010i	0.791094	+	0.297734i
$714$	−7.73902	+	8.03194i	−0.289626	+	0.300588i
$715$	6.07273	−	3.90270i	0.227107	−	0.145953i
$716$	−1.78013	−	4.44656i	−0.0665267	−	0.166176i
$717$	9.54901	−	11.6982i	0.356614	−	0.436877i
$718$	−23.8360	−	5.78254i	−0.889551	−	0.215803i
$719$	−4.32165	−	3.07744i	−0.161171	−	0.114769i	0.496626	−	0.867965i	$-0.334572\pi$
$719$	−4.32165	−	3.07744i	−0.161171	−	0.114769i	−0.657797	+	0.753196i	$0.728511\pi$
$720$	4.89761	+	1.63379i	0.182523	+	0.0608878i
$721$	−18.8776	+	2.96441i	−0.703037	+	0.110400i
$722$	11.9598	−	40.7314i	0.445099	−	1.51587i
$723$	−0.101138	−	1.31074i	−0.00376137	−	0.0487468i
$724$	−17.1090	−	33.1869i	−0.635852	−	1.23338i
$725$	−9.65491	−	18.7279i	−0.358574	−	0.695537i
$726$	2.68939	+	34.8541i	0.0998126	+	1.29356i
$727$	−8.08554	+	27.5368i	−0.299876	+	1.02128i	0.662387	+	0.749162i	$0.269544\pi$
$727$	−8.08554	+	27.5368i	−0.299876	+	1.02128i	−0.962263	+	0.272122i	$0.912275\pi$
$728$	6.88559	−	17.8672i	0.255197	−	0.662201i
$729$	−19.7988	+	18.3578i	−0.733287	+	0.679919i
$730$	37.1338	+	26.4429i	1.37438	+	0.978695i
$731$	−0.672244	−	0.163085i	−0.0248639	−	0.00603190i
$732$	37.0895	−	45.4372i	1.37087	−	1.67941i
$733$	−1.67815	−	4.19182i	−0.0619840	−	0.154829i	0.894143	−	0.447782i	$-0.147786\pi$
$733$	−1.67815	−	4.19182i	−0.0619840	−	0.154829i	−0.956127	+	0.292954i	$0.905362\pi$
$734$	11.6482	−	7.48583i	0.429942	−	0.276307i
$735$	−13.6887	−	12.8515i	−0.504915	−	0.474036i
$736$	−23.0341	−	23.1709i	−0.849048	−	0.854090i
$737$	−7.89712	+	4.55940i	−0.290894	+	0.167948i
$738$	3.29849	+	5.00812i	0.121419	+	0.184352i
$739$	38.6093	+	30.3627i	1.42027	+	1.11691i	0.975178	+	0.221424i	$0.0710705\pi$
$739$	38.6093	+	30.3627i	1.42027	+	1.11691i	0.445089	+	0.895486i	$0.353172\pi$
$740$	−0.156991	−	1.64409i	−0.00577111	−	0.0604378i
$741$	−18.7365	−	30.3547i	−0.688301	−	1.11511i
$742$	−3.19917	+	38.8136i	−0.117445	+	1.42489i
$743$	−13.2361	−	15.2753i	−0.485587	−	0.560397i	0.459094	−	0.888388i	$-0.348174\pi$
$743$	−13.2361	−	15.2753i	−0.485587	−	0.560397i	−0.944681	+	0.327991i	$0.893629\pi$
$744$	14.2021	+	10.5078i	0.520676	+	0.385235i
$745$	−17.9464	+	17.1119i	−0.657506	+	0.626931i
$746$	2.97369	+	8.59192i	0.108875	+	0.314573i
$747$	−15.9987	−	30.1965i	−0.585360	−	1.10483i
$748$	3.80955	+	2.44825i	0.139291	+	0.0895169i
$749$	0.932736	−	1.10506i	0.0340814	−	0.0403779i
$750$	0.827025	−	45.4584i	0.0301987	−	1.65991i
$751$	20.7845	+	26.4296i	0.758436	+	0.964430i	0.999982	−	0.00595898i	$-0.00189681\pi$
$751$	20.7845	+	26.4296i	0.758436	+	0.964430i	−0.241546	+	0.970389i	$0.577654\pi$
$752$	−2.18531	−	11.3385i	−0.0796902	−	0.413472i
$753$	45.8227	−	7.97000i	1.66987	−	0.290443i
$754$	−43.6414	−	41.6120i	−1.58933	−	1.51542i
$755$	10.4018	−	22.7767i	0.378560	−	0.828930i
$756$	14.9579	−	38.0215i	0.544015	−	1.38283i
$757$	−18.9965	−	29.5592i	−0.690440	−	1.07435i	−0.992640	−	0.121102i	$-0.961357\pi$
$757$	−18.9965	−	29.5592i	−0.690440	−	1.07435i	0.302200	−	0.953245i	$-0.402279\pi$
$758$	−2.44738	−	4.23899i	−0.0888929	−	0.153967i
$759$	−11.5398	+	1.13277i	−0.418869	+	0.0411170i
$760$	10.3502	−	17.9271i	0.375441	−	0.650283i
$761$	−4.78253	+	9.27681i	−0.173366	+	0.336284i	−0.959470	−	0.281811i	$-0.909065\pi$
$761$	−4.78253	+	9.27681i	−0.173366	+	0.336284i	0.786104	+	0.618095i	$0.212095\pi$
$762$	−27.0229	+	3.38483i	−0.978937	+	0.122619i
$763$	2.59492	+	23.8975i	0.0939425	+	0.865148i
$764$	30.3269	−	8.90477i	1.09719	−	0.322163i
$765$	−0.425390	+	5.05334i	−0.0153800	+	0.182704i
$766$	−10.1455	−	52.6401i	−0.366573	−	1.90196i
$767$	9.33356	−	23.3141i	0.337015	−	0.841824i
$768$	−6.84258	−	12.3659i	−0.246910	−	0.446214i
$769$	20.5564	+	17.8122i	0.741282	+	0.642325i	0.941340	−	0.337459i	$-0.109568\pi$
$769$	20.5564	+	17.8122i	0.741282	+	0.642325i	−0.200058	+	0.979784i	$0.564113\pi$
$770$	−6.75524	+	10.8171i	−0.243442	+	0.389822i
$771$	−3.28830	+	10.4892i	−0.118425	+	0.377759i
$772$	74.0796	+	14.2777i	2.66618	+	0.513864i
$773$	22.0117	−	20.9881i	0.791705	−	0.754889i	−0.181854	−	0.983326i	$-0.558210\pi$
$773$	22.0117	−	20.9881i	0.791705	−	0.754889i	0.973559	+	0.228437i	$0.0733614\pi$
$774$	4.18905	−	0.650338i	0.150572	−	0.0233759i
$775$	−4.00477	+	11.5710i	−0.143856	+	0.415644i
$776$	−5.98324	−	13.1015i	−0.214786	−	0.470316i
$777$	1.64294	−	0.0696545i	0.0589402	−	0.00249884i
$778$	7.46481	+	3.40906i	0.267626	+	0.122221i
$779$	−5.13288	+	2.05490i	−0.183905	+	0.0736243i
$780$	−8.24749	−	25.3100i	−0.295307	−	0.906244i
$781$	−5.07253	−	2.92862i	−0.181509	−	0.104794i
$782$	6.10476	−	9.94909i	0.218306	−	0.355779i
$783$	−30.2521	−	29.2508i	−1.08112	−	1.04534i
$784$	−0.571429	−	7.75802i	−0.0204082	−	0.277072i
$785$	−14.9694	−	2.15227i	−0.534279	−	0.0768178i
$786$	−67.9217	+	25.7684i	−2.42269	+	0.919127i
$787$	−1.32143	−	0.320576i	−0.0471040	−	0.0114273i	0.212138	−	0.977240i	$-0.431957\pi$
$787$	−1.32143	−	0.320576i	−0.0471040	−	0.0114273i	−0.259242	+	0.965812i	$0.583473\pi$
$788$	−3.28629	+	34.4155i	−0.117069	+	1.22600i
$789$	−2.90491	+	44.0900i	−0.103418	+	1.56965i
$790$	−2.08435	−	14.4970i	−0.0741578	−	0.515779i
$791$	38.2163	−	37.3968i	1.35882	−	1.32968i
$792$	−8.93082	−	1.61759i	−0.317343	−	0.0574785i
$793$	38.0052	+	1.81041i	1.34961	+	0.0642896i
$794$	−9.27353	−	17.9881i	−0.329105	−	0.638375i
$795$	10.0071	+	14.6083i	0.354915	+	0.518102i
$796$	−29.7773	+	7.22390i	−1.05543	+	0.256044i
$797$	−3.52246	−	24.4993i	−0.124772	−	0.867808i	−0.952034	−	0.305992i	$-0.901012\pi$
$797$	−3.52246	−	24.4993i	−0.124772	−	0.867808i	0.827262	−	0.561816i	$-0.189897\pi$
$798$	52.8376	+	34.3484i	1.87043	+	1.21592i
$799$	10.3171	−	4.71165i	0.364992	−	0.166686i
$800$	12.2314	−	12.8279i	0.432446	−	0.453536i
$801$	−1.33159	−	0.590155i	−0.0470494	−	0.0208521i
$802$	−50.1370	+	63.7543i	−1.77040	+	2.25124i
$803$	16.3797	+	8.44430i	0.578026	+	0.297993i
$804$	8.88534	+	32.4318i	0.313362	+	1.14378i
$805$	16.8801	+	10.0588i	0.594946	+	0.354527i
$806$			35.0422i			1.23431i
$807$	−10.1684	+	48.0391i	−0.357945	+	1.69106i
$808$	6.43670	+	5.06188i	0.226442	+	0.178076i
$809$	−29.6353	+	21.1032i	−1.04192	+	0.741948i	−0.966880	−	0.255233i	$-0.917848\pi$
$809$	−29.6353	+	21.1032i	−1.04192	+	0.741948i	−0.0750403	+	0.997181i	$0.523909\pi$
$810$	−9.42247	−	29.6153i	−0.331072	−	1.04058i
$811$	0.948965	+	2.07794i	0.0333227	+	0.0729665i	0.925561	−	0.378598i	$-0.123594\pi$
$811$	0.948965	+	2.07794i	0.0333227	+	0.0729665i	−0.892239	+	0.451564i	$0.850866\pi$
$812$	60.4418	+	20.0457i	2.12109	+	0.703465i
$813$	−4.05877	−	9.33310i	−0.142347	−	0.327326i
$814$	−0.263325	−	1.08544i	−0.00922954	−	0.0380447i
$815$	12.6594	+	36.5769i	0.443439	+	1.28123i
$816$	−1.54671	+	1.42198i	−0.0541456	+	0.0497792i
$817$	−0.185974	+	3.90408i	−0.00650641	+	0.136586i
$818$	44.0976	+	38.2108i	1.54184	+	1.33601i
$819$	25.5990	−	6.86964i	0.894500	−	0.240045i
$820$	−4.08396	+	0.587185i	−0.142618	+	0.0205054i
$821$	−19.6725	−	6.80872i	−0.686576	−	0.237626i	−0.0385635	−	0.999256i	$-0.512278\pi$
$821$	−19.6725	−	6.80872i	−0.686576	−	0.237626i	−0.648012	+	0.761630i	$0.724399\pi$
$822$	2.53710	+	14.5868i	0.0884917	+	0.508774i
$823$	6.90584	−	28.4663i	0.240723	−	0.992272i	−0.715262	−	0.698856i	$-0.753693\pi$
$823$	6.90584	−	28.4663i	0.240723	−	0.992272i	0.955985	−	0.293416i	$-0.0947920\pi$
$824$	15.5825	−	1.48795i	0.542844	−	0.0518353i
$825$	−0.781821	−	6.24170i	−0.0272195	−	0.217308i
$826$	2.68530	+	44.2857i	0.0934337	+	1.54090i
$827$	41.0955			1.42903			0.714516	−	0.699619i	$-0.246647\pi$
$827$	41.0955			1.42903			0.714516	+	0.699619i	$0.246647\pi$
$828$	−6.74235	+	42.2244i	−0.234313	+	1.46740i
$829$	6.78733	−	11.7560i	0.235734	−	0.408303i	−0.723752	−	0.690060i	$-0.757584\pi$
$829$	6.78733	−	11.7560i	0.235734	−	0.408303i	0.959486	+	0.281757i	$0.0909173\pi$
$830$	39.2898	−	1.87160i	1.36377	−	0.0649643i
$831$	−6.94065	+	5.25671i	−0.240769	+	0.182353i
$832$	17.9891	−	39.3907i	0.623661	−	1.36563i
$833$	7.27308	−	2.34199i	0.251997	−	0.0811451i
$834$	−16.2342	+	13.5579i	−0.562145	+	0.469473i
$835$	−13.7391	−	4.75516i	−0.475462	−	0.164559i
$836$	9.50958	−	23.7538i	0.328896	−	0.821541i
$837$	−0.170521	+	24.4538i	−0.00589408	+	0.845246i
$838$	5.58983	−	29.0028i	0.193097	−	1.00188i
$839$	13.0641	+	8.39580i	0.451023	+	0.289855i	0.746365	−	0.665537i	$-0.231797\pi$
$839$	13.0641	+	8.39580i	0.451023	+	0.289855i	−0.295342	+	0.955392i	$0.595434\pi$
$840$	10.5556	+	11.1870i	0.364204	+	0.385987i
$841$	23.9581	−	27.6491i	0.826141	−	0.953418i
$842$	0.489577	+	2.01806i	0.0168719	+	0.0695470i
$843$	−33.7616	−	3.84475i	−1.16281	−	0.132420i
$844$	−4.57474	+	0.881710i	−0.157469	+	0.0303497i
$845$	−1.66115	+	2.33276i	−0.0571453	+	0.0802493i
$846$	−47.3985	+	50.8400i	−1.62959	+	1.74792i
$847$	9.66511	−	21.9108i	0.332097	−	0.752866i
$848$	−1.04404	+	7.26149i	−0.0358526	+	0.249361i
$849$	−6.61734	+	31.2626i	−0.227107	+	1.07293i
$850$	5.48409	+	3.16624i	0.188103	+	0.108601i
$851$	−1.66361	+	0.440490i	−0.0570280	+	0.0150998i
$852$	−15.1872	+	15.3586i	−0.520306	+	0.526176i
$853$	17.6759	−	11.3596i	0.605213	−	0.388946i	−0.201847	−	0.979417i	$-0.564694\pi$
$853$	17.6759	−	11.3596i	0.605213	−	0.388946i	0.807059	+	0.590471i	$0.201058\pi$
$854$	−62.0756	+	25.7898i	−2.12418	+	0.882510i
$855$	28.4914	−	3.04349i	0.974386	−	0.104085i
$856$	−0.817456	+	0.857323i	−0.0279401	+	0.0293027i
$857$	−0.495280	+	5.18681i	−0.0169184	+	0.177178i	−0.999981	−	0.00608995i	$-0.998061\pi$
$857$	−0.495280	+	5.18681i	−0.0169184	+	0.177178i	0.983063	+	0.183268i	$0.0586676\pi$
$858$	−7.95683	−	16.1487i	−0.271642	−	0.551309i
$859$	13.3993	−	10.5373i	0.457179	−	0.359530i	−0.362854	−	0.931846i	$-0.618198\pi$
$859$	13.3993	−	10.5373i	0.457179	−	0.359530i	0.820033	+	0.572316i	$0.193955\pi$
$860$	−0.821735	+	2.79857i	−0.0280209	+	0.0954305i
$861$	−0.369111	−	4.09149i	−0.0125793	−	0.139438i
$862$	−24.3145	+	37.8342i	−0.828156	+	1.28864i
$863$	33.6189	+	1.60146i	1.14440	+	0.0545145i	0.611201	−	0.791476i	$-0.290687\pi$
$863$	33.6189	+	1.60146i	1.14440	+	0.0545145i	0.533199	+	0.845990i	$0.320990\pi$
$864$	14.9295	−	32.0969i	0.507914	−	1.09196i
$865$	7.16059	+	7.50981i	0.243467	+	0.255341i
$866$	−52.8263	+	41.5431i	−1.79511	+	1.41169i
$867$	22.7614	+	15.2199i	0.773018	+	0.516896i
$868$	−15.8078	−	33.4595i	−0.536551	−	1.13569i
$869$	−1.66803	−	5.68077i	−0.0565839	−	0.192707i
$870$	45.2871	−	17.1812i	1.53538	−	0.582497i
$871$	−13.4845	+	17.1469i	−0.456903	+	0.581000i
$872$	−0.936943	−	19.6689i	−0.0317289	−	0.666072i
$873$	9.77404	−	17.3764i	0.330801	−	0.588103i
$874$	−61.7266	−	23.2312i	−2.08793	−	0.785808i
$875$	−15.2223	+	27.1733i	−0.514609	+	0.918625i
$876$	45.4291	−	50.5403i	1.53491	−	1.70760i
$877$	40.5021	−	16.2146i	1.36766	−	0.547529i	0.432462	−	0.901652i	$-0.357645\pi$
$877$	40.5021	−	16.2146i	1.36766	−	0.547529i	0.935199	+	0.354124i	$0.115221\pi$
$878$	21.9327	−	15.6182i	0.740193	−	0.527089i
$879$	1.53444	+	52.1610i	0.0517554	+	1.75935i
$880$	−1.39349	+	1.95688i	−0.0469744	+	0.0659664i
$881$	−23.0949	−	26.6530i	−0.778088	−	0.897961i	0.218882	−	0.975751i	$-0.429759\pi$
$881$	−23.0949	−	26.6530i	−0.778088	−	0.897961i	−0.996970	+	0.0777904i	$0.975214\pi$
$882$	−35.7072	+	30.2925i	−1.20233	+	1.02000i
$883$	18.8606	+	5.53797i	0.634709	+	0.186367i	0.583230	−	0.812307i	$-0.301788\pi$
$883$	18.8606	+	5.53797i	0.634709	+	0.186367i	0.0514785	+	0.998674i	$0.483607\pi$
$884$	10.6371	+	2.05013i	0.357763	+	0.0689533i
$885$	13.6526	+	14.8501i	0.458926	+	0.499182i
$886$	73.7625	−	38.0272i	2.47810	−	1.27755i
$887$	−8.07170	+	41.8800i	−0.271021	+	1.40619i	0.549938	+	0.835205i	$0.314651\pi$
$887$	−8.07170	+	41.8800i	−0.271021	+	1.40619i	−0.820959	+	0.570987i	$0.806561\pi$
$888$	−1.34683	−	0.0245029i	−0.0451967	−	0.000822265i
$889$	17.4088	+	6.70894i	0.583871	+	0.225011i
$890$	1.26701	−	1.09787i	0.0424704	−	0.0368008i
$891$	−5.47399	−	11.3079i	−0.183386	−	0.378829i
$892$	15.7191	−	64.7951i	0.526315	−	2.16950i
$893$	−37.1729	−	52.2021i	−1.24395	−	1.74688i
$894$	37.3371	+	49.2977i	1.24874	+	1.64876i
$895$	1.34932	+	2.09958i	0.0451026	+	0.0701811i
$896$	0.524375	+	40.4527i	0.0175181	+	1.35143i
$897$	−24.6209	+	12.7756i	−0.822067	+	0.426565i
$898$	14.0300	+	24.3007i	0.468187	+	0.810924i
$899$	−38.0701	+	1.81350i	−1.26971	+	0.0604838i
$900$	−22.9965	−	3.04351i	−0.766551	−	0.101450i
$901$	−7.17321	+	0.684959i	−0.238974	+	0.0228193i
$902$	−2.67729	+	0.786123i	−0.0891440	+	0.0261750i
$903$	−2.73937	−	0.964174i	−0.0911605	−	0.0320857i
$904$	−33.1023	+	28.6833i	−1.10097	+	0.953994i
$905$	12.0267	+	15.2932i	0.399781	+	0.508363i
$906$	−53.5028	−	32.2015i	−1.77751	−	1.06982i
$907$	23.7927	−	8.23474i	0.790024	−	0.273430i	0.0978886	−	0.995197i	$-0.468791\pi$
$907$	23.7927	−	8.23474i	0.790024	−	0.273430i	0.692136	+	0.721767i	$0.256670\pi$
$908$	0.442135	−	9.28156i	0.0146728	−	0.308019i
$909$	−0.412288	+	11.3272i	−0.0136747	+	0.375699i
$910$	−5.38490	+	30.0290i	−0.178508	+	0.995451i
$911$	23.9419	+	7.02998i	0.793231	+	0.232914i	0.653152	−	0.757227i	$-0.273446\pi$
$911$	23.9419	+	7.02998i	0.793231	+	0.232914i	0.140079	+	0.990140i	$0.455264\pi$
$912$	9.54321	+	7.06078i	0.316007	+	0.233806i
$913$	15.6134	−	3.00924i	0.516728	−	0.0995912i
$914$	59.6693	+	5.69773i	1.97369	+	0.188464i
$915$	−14.4964	+	26.9059i	−0.479237	+	0.889483i
$916$	−37.0921	−	16.9394i	−1.22556	−	0.559694i
$917$	49.3471	+	6.44336i	1.62958	+	0.212778i
$918$	12.4015	+	2.48001i	0.409312	+	0.0818526i
$919$	−16.3121	+	9.41780i	−0.538087	+	0.310665i	−0.744303	−	0.667842i	$-0.767218\pi$
$919$	−16.3121	+	9.41780i	−0.538087	+	0.310665i	0.206216	+	0.978506i	$0.433885\pi$
$920$	−13.3036	−	9.06168i	−0.438607	−	0.298755i
$921$	2.22153	−	8.48086i	0.0732020	−	0.279454i
$922$	−38.4598	−	19.8274i	−1.26661	−	0.652981i
$923$	−13.8690	−	1.99406i	−0.456504	−	0.0656354i
$924$	14.8823	+	11.8300i	0.489591	+	0.389179i
$925$	−0.263030	−	0.895798i	−0.00864837	−	0.0294536i
$926$	−18.2470	−	12.9937i	−0.599635	−	0.426998i
$927$	14.3720	+	16.2150i	0.472037	+	0.532570i
$928$	51.2194	+	20.5051i	1.68136	+	0.673114i
$929$	8.58629	−	2.08301i	0.281707	−	0.0683414i	−0.0924160	−	0.995720i	$-0.529459\pi$
$929$	8.58629	−	2.08301i	0.281707	−	0.0683414i	0.374123	+	0.927379i	$0.377944\pi$
$930$	−25.3874	−	12.1569i	−0.832484	−	0.398640i
$931$	−20.7708	−	37.8476i	−0.680736	−	1.24040i
$932$	1.31352	−	2.04387i	0.0430257	−	0.0669492i
$933$	0.649539	+	8.41793i	0.0212650	+	0.275591i
$934$	64.0294	+	67.1521i	2.09511	+	2.19728i
$935$	−2.19063	−	0.876994i	−0.0716411	−	0.0286808i
$936$	−21.2720	+	4.34788i	−0.695298	+	0.142115i
$937$	−39.1439	+	17.8764i	−1.27877	+	0.583996i	−0.934864	−	0.355006i	$-0.884479\pi$
$937$	−39.1439	+	17.8764i	−1.27877	+	0.583996i	−0.343910	+	0.939003i	$0.611751\pi$
$938$	8.59959	−	37.5668i	0.280786	−	1.22660i
$939$	39.8053	+	6.46422i	1.29900	+	0.210952i
$940$	−17.7742	−	44.3977i	−0.579729	−	1.44809i
$941$	0.309038	+	6.48751i	0.0100744	+	0.211487i	0.998292	+	0.0584289i	$0.0186091\pi$
$941$	0.309038	+	6.48751i	0.0100744	+	0.211487i	−0.988217	+	0.153058i	$0.951088\pi$
$942$	−9.55710	+	36.4849i	−0.311387	+	1.18874i
$943$	1.29694	+	4.09899i	0.0422343	+	0.133482i
$944$			8.35746i			0.272012i
$945$	−3.90391	+	20.9291i	−0.126994	+	0.680825i
$946$	−0.280720	+	1.95245i	−0.00912700	+	0.0634796i
$947$	1.98219	+	20.7584i	0.0644124	+	0.674557i	0.968800	+	0.247845i	$0.0797223\pi$
$947$	1.98219	+	20.7584i	0.0644124	+	0.674557i	−0.904387	+	0.426712i	$0.859672\pi$
$948$	−21.8236	+	0.641994i	−0.708799	+	0.0208510i
$949$	43.8842	+	4.19043i	1.42454	+	0.136027i
$950$	11.7025	−	33.8121i	0.379678	−	1.09701i
$951$	−20.0197	+	8.70615i	−0.649184	+	0.282316i
$952$	−6.06307	+	1.55437i	−0.196505	+	0.0503773i
$953$	−35.9894	+	41.5340i	−1.16581	+	1.34542i	−0.238492	+	0.971145i	$0.576653\pi$
$953$	−35.9894	+	41.5340i	−1.16581	+	1.34542i	−0.927319	+	0.374272i	$0.877892\pi$
$954$	39.0213	−	20.6742i	1.26336	−	0.669352i
$955$	−14.6389	+	7.54687i	−0.473703	+	0.244211i
$956$	24.4858	−	8.47463i	0.791929	−	0.274089i
$957$	17.1323	−	9.48010i	0.553810	−	0.306448i
$958$	−56.1167	+	8.06836i	−1.81305	+	0.260677i
$959$	3.19286	−	9.62710i	0.103103	−	0.310875i
$960$	22.2969	+	26.6982i	0.719630	+	0.861682i
$961$	−6.40597	−	6.10808i	−0.206644	−	0.197035i
$962$	−1.54985	−	2.17646i	−0.0499692	−	0.0701720i
$963$	−1.62553	−	0.215133i	−0.0523818	−	0.00693255i
$964$	1.03364	−	2.00498i	0.0332913	−	0.0645762i
$965$	−39.3115			−1.26548
$966$	29.6877	−	38.9885i	0.955188	−	1.25443i
$967$	12.6369			0.406375			0.203187	−	0.979140i	$-0.434870\pi$
$967$	12.6369			0.406375			0.203187	+	0.979140i	$0.434870\pi$
$968$	−8.98918	+	17.4366i	−0.288923	+	0.560433i
$969$	−4.52993	+	10.7445i	−0.145522	+	0.345164i
$970$	13.3111	+	18.6928i	0.427394	+	0.600191i
$971$	13.2637	+	12.6469i	0.425652	+	0.405858i	0.872393	−	0.488805i	$-0.162567\pi$
$971$	13.2637	+	12.6469i	0.425652	+	0.405858i	−0.446741	+	0.894663i	$0.647415\pi$
$972$	−45.4538	+	8.96077i	−1.45793	+	0.287417i
$973$	14.1910	−	2.92636i	0.454943	−	0.0938147i
$974$	−50.2048	+	7.21837i	−1.60867	+	0.231291i
$975$	−7.28570	−	13.1667i	−0.233329	−	0.421670i
$976$	−11.9658	+	4.14142i	−0.383017	+	0.132564i
$977$	−34.5852	+	17.8299i	−1.10648	+	0.570430i	−0.911882	−	0.410453i	$-0.865371\pi$
$977$	−34.5852	+	17.8299i	−1.10648	+	0.570430i	−0.194598	+	0.980883i	$0.562340\pi$
$978$	94.2054	−	21.0472i	3.01236	−	0.673016i
$979$	0.443810	−	0.512184i	0.0141842	−	0.0163695i
$980$	−8.40457	−	31.1019i	−0.268474	−	0.993513i
$981$	21.2347	−	17.0881i	0.677972	−	0.545582i
$982$	1.82729	−	5.27961i	0.0583112	−	0.168479i
$983$	−16.0038	−	1.52818i	−0.510443	−	0.0487414i	−0.163342	−	0.986569i	$-0.552228\pi$
$983$	−16.0038	−	1.52818i	−0.510443	−	0.0487414i	−0.347100	+	0.937828i	$0.612834\pi$
$984$	0.0989535	+	3.36378i	0.00315452	+	0.107233i
$985$	−1.71241	−	17.9331i	−0.0545618	−	0.571397i
$986$	−2.80518	+	19.5105i	−0.0893352	+	0.621340i
$987$	45.0784	−	15.3383i	1.43486	−	0.488223i
$988$		−	61.2079i		−	1.94728i
$989$	3.01667	+	0.369748i	0.0959244	+	0.0117573i
$990$	14.4598	−	0.162216i	0.459563	−	0.00515555i
$991$	2.03854	+	42.7943i	0.0647565	+	1.35941i	0.764321	+	0.644837i	$0.223075\pi$
$991$	2.03854	+	42.7943i	0.0647565	+	1.35941i	−0.699564	+	0.714570i	$0.746622\pi$
$992$	−11.9161	−	29.7650i	−0.378337	−	0.945041i
$993$	−8.93554	+	55.0231i	−0.283561	+	1.74611i
$994$	23.6592	−	7.28136i	0.750423	−	0.230951i
$995$	14.5235	−	6.63265i	0.460425	−	0.210269i
$996$	3.85495	−	58.5095i	0.122149	−	1.85394i
$997$	−23.4173	−	9.37488i	−0.741634	−	0.296905i	−0.0300901	−	0.999547i	$-0.509579\pi$
$997$	−23.4173	−	9.37488i	−0.741634	−	0.296905i	−0.711544	+	0.702642i	$0.752004\pi$
$998$	44.6365	+	46.8134i	1.41294	+	1.48185i
$999$	−1.07095	−	1.52636i	−0.0338835	−	0.0482918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bc.a.11.8	✓	1200
3.2	odd	2	inner	483.2.bc.a.11.53	yes	1200
7.2	even	3	inner	483.2.bc.a.149.53	yes	1200
21.2	odd	6	inner	483.2.bc.a.149.8	yes	1200
23.21	odd	22	inner	483.2.bc.a.389.8	yes	1200
69.44	even	22	inner	483.2.bc.a.389.53	yes	1200
161.44	odd	66	inner	483.2.bc.a.44.53	yes	1200
483.44	even	66	inner	483.2.bc.a.44.8	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bc.a.11.8	✓	1200	1.1	even	1	trivial
483.2.bc.a.11.53	yes	1200	3.2	odd	2	inner
483.2.bc.a.44.8	yes	1200	483.44	even	66	inner
483.2.bc.a.44.53	yes	1200	161.44	odd	66	inner
483.2.bc.a.149.8	yes	1200	21.2	odd	6	inner
483.2.bc.a.149.53	yes	1200	7.2	even	3	inner
483.2.bc.a.389.8	yes	1200	23.21	odd	22	inner
483.2.bc.a.389.53	yes	1200	69.44	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02175 + 1.98192i) q^{2} +(-1.59600 - 0.672881i) q^{3} +(-1.72392 - 2.42090i) q^{4} +(1.12079 + 1.06868i) q^{5} +(2.96432 - 2.47564i) q^{6} +(-2.59123 + 0.534343i) q^{7} +(2.14526 - 0.308441i) q^{8} +(2.09446 + 2.14784i) q^{9} +(-3.26320 + 1.12941i) q^{10} +(-1.24073 + 0.639643i) q^{11} +(1.12240 + 5.02377i) q^{12} +(-2.18676 + 2.52366i) q^{13} +(1.58857 - 5.68158i) q^{14} +(-1.06970 - 2.45977i) q^{15} +(0.363468 - 1.05017i) q^{16} +(1.08661 + 0.103758i) q^{17} +(-6.39687 + 1.95650i) q^{18} +(-0.586258 - 6.13957i) q^{19} +(0.655003 - 4.55565i) q^{20} +(4.49517 + 0.890776i) q^{21} -3.11259i q^{22} +(-4.79479 + 0.0999357i) q^{23} +(-3.63138 - 0.951229i) q^{24} +(-0.123796 - 2.59880i) q^{25} +(-2.76736 - 6.91253i) q^{26} +(-1.89753 - 4.83729i) q^{27} +(5.76066 + 5.35196i) q^{28} +(7.36662 - 3.36422i) q^{29} +(5.96804 + 0.393210i) q^{30} +(-4.36913 - 1.74913i) q^{31} +(4.70122 + 4.93050i) q^{32} +(2.41062 - 0.186007i) q^{33} +(-1.31588 + 2.04755i) q^{34} +(-3.47528 - 2.17030i) q^{35} +(1.58904 - 8.77320i) q^{36} +(0.348726 - 0.0846000i) q^{37} +(12.7672 + 5.11120i) q^{38} +(5.18820 - 2.55634i) q^{39} +(2.73402 + 1.94688i) q^{40} +(-0.252563 - 0.860149i) q^{41} +(-6.35839 + 7.99891i) q^{42} +(-0.627275 - 0.0901886i) q^{43} +(3.68744 + 1.90101i) q^{44} +(0.0521160 + 4.64559i) q^{45} +(4.70102 - 9.60500i) q^{46} +(8.99866 - 5.19538i) q^{47} +(-1.28674 + 1.43151i) q^{48} +(6.42896 - 2.76921i) q^{49} +(5.27711 + 2.40998i) q^{50} +(-1.66441 - 0.896756i) q^{51} +(9.87933 + 0.943362i) q^{52} +(-6.48218 + 1.24934i) q^{53} +(11.5259 + 1.18175i) q^{54} +(-2.07418 - 0.609034i) q^{55} +(-5.39404 + 1.94555i) q^{56} +(-3.19553 + 10.1933i) q^{57} +(-0.859229 + 18.0374i) q^{58} +(-7.10687 + 2.45971i) q^{59} +(-4.11080 + 6.83010i) q^{60} +(-7.04342 - 8.95643i) q^{61} +(7.93080 - 6.87208i) q^{62} +(-6.57492 - 4.44639i) q^{63} +(-12.4428 + 3.65353i) q^{64} +(-5.14788 + 0.491563i) q^{65} +(-2.09440 + 4.96771i) q^{66} +(6.52512 - 0.310830i) q^{67} +(-1.62203 - 2.80944i) q^{68} +(7.71975 + 3.06682i) q^{69} +(7.85222 - 4.67022i) q^{70} +(2.26853 + 3.52991i) q^{71} +(5.15564 + 3.96165i) q^{72} +(-7.65767 - 10.7537i) q^{73} +(-0.188641 + 0.777587i) q^{74} +(-1.55111 + 4.23100i) q^{75} +(-13.8527 + 12.0034i) q^{76} +(2.87324 - 2.32044i) q^{77} +(-0.234590 + 12.8945i) q^{78} +(-0.802689 + 4.16475i) q^{79} +(1.52967 - 0.788597i) q^{80} +(-0.226453 + 8.99715i) q^{81} +(1.96280 + 0.378299i) q^{82} +(-10.9295 - 3.20920i) q^{83} +(-5.59282 - 12.4180i) q^{84} +(1.10698 + 1.27752i) q^{85} +(0.819665 - 1.15106i) q^{86} +(-14.0209 + 0.412457i) q^{87} +(-2.46440 + 1.75489i) q^{88} +(-0.450725 + 0.180443i) q^{89} +(-9.26044 - 4.64335i) q^{90} +(4.31790 - 7.70786i) q^{91} +(8.50776 + 11.4354i) q^{92} +(5.79619 + 5.73153i) q^{93} +(1.10244 + 23.1430i) q^{94} +(5.90414 - 7.50772i) q^{95} +(-4.18553 - 11.0325i) q^{96} +(-1.87227 - 6.37637i) q^{97} +(-1.08043 + 15.5711i) q^{98} +(-3.97252 - 1.32519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) \) 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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