LMFDB - Embedded newform 507.2.t.a.127.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.9
Character	$\chi$	$=$	507.127
Dual form			507.2.t.a.4.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.756241 - 0.0304755i) q^{2} +(0.278217 + 0.960518i) q^{3} +(-1.42254 + 0.114840i) q^{4} +(-1.80244 + 0.683575i) q^{5} +(0.239672 + 0.717904i) q^{6} +(0.988668 - 2.32049i) q^{7} +(-2.57496 + 0.312656i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})$	\(q+(0.756241 - 0.0304755i) q^{2} +(0.278217 + 0.960518i) q^{3} +(-1.42254 + 0.114840i) q^{4} +(-1.80244 + 0.683575i) q^{5} +(0.239672 + 0.717904i) q^{6} +(0.988668 - 2.32049i) q^{7} +(-2.57496 + 0.312656i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(-1.34225 + 0.571877i) q^{10} +(-3.17644 + 5.02314i) q^{11} +(-0.506082 - 1.33443i) q^{12} +(0.984160 - 3.46863i) q^{13} +(0.676953 - 1.78498i) q^{14} +(-1.15806 - 1.54109i) q^{15} +(0.879621 - 0.142952i) q^{16} +(-6.63268 - 2.82592i) q^{17} +(-0.622879 + 0.429942i) q^{18} +(-4.97273 - 2.87100i) q^{19} +(2.48555 - 1.17941i) q^{20} +(2.50394 + 0.304033i) q^{21} +(-2.24907 + 3.89551i) q^{22} +(2.77663 + 4.80926i) q^{23} +(-1.01671 - 2.38631i) q^{24} +(-0.961042 + 0.851409i) q^{25} +(0.638554 - 2.65312i) q^{26} +(-0.748511 - 0.663123i) q^{27} +(-1.13994 + 3.41453i) q^{28} +(-0.236964 - 5.88019i) q^{29} +(-0.922735 - 1.13014i) q^{30} +(-6.21270 + 7.01269i) q^{31} +(5.74375 - 1.17259i) q^{32} +(-5.70856 - 1.65350i) q^{33} +(-5.10202 - 1.93494i) q^{34} +(-0.195785 + 4.85837i) q^{35} +(1.14094 - 0.857362i) q^{36} +(5.74704 + 1.17327i) q^{37} +(-3.84807 - 2.01962i) q^{38} +(3.60550 - 0.0197311i) q^{39} +(4.42748 - 2.32372i) q^{40} +(-3.28934 + 0.952768i) q^{41} +(1.90284 + 0.153613i) q^{42} +(-1.59494 - 7.81251i) q^{43} +(3.94177 - 7.51042i) q^{44} +(1.15806 - 1.54109i) q^{45} +(2.24636 + 3.55234i) q^{46} +(4.44238 + 3.06635i) q^{47} +(0.382034 + 0.805120i) q^{48} +(0.441869 + 0.460034i) q^{49} +(-0.700832 + 0.673158i) q^{50} +(0.869021 - 7.15703i) q^{51} +(-1.00167 + 5.04730i) q^{52} +(1.15493 + 9.51172i) q^{53} +(-0.586263 - 0.478669i) q^{54} +(2.29165 - 11.2252i) q^{55} +(-1.82026 + 6.28427i) q^{56} +(1.37415 - 5.57516i) q^{57} +(-0.358403 - 4.43962i) q^{58} +(0.547602 - 3.36953i) q^{59} +(1.82436 + 2.05928i) q^{60} +(0.266815 + 0.200498i) q^{61} +(-4.48458 + 5.49261i) q^{62} +(0.404610 + 2.48966i) q^{63} +(2.57739 - 0.635269i) q^{64} +(0.597183 + 6.92475i) q^{65} +(-4.36743 - 1.07648i) q^{66} +(-0.813674 + 10.0792i) q^{67} +(9.75980 + 3.25830i) q^{68} +(-3.84688 + 4.00502i) q^{69} +3.68006i q^{70} +(-2.56094 - 2.45981i) q^{71} +(2.00922 - 1.64048i) q^{72} +(2.44727 + 4.66288i) q^{73} +(4.38190 + 0.712128i) q^{74} +(-1.08517 - 0.686222i) q^{75} +(7.40362 + 3.51306i) q^{76} +(8.51569 + 12.3371i) q^{77} +(2.72602 - 0.124801i) q^{78} +(0.769740 - 1.11516i) q^{79} +(-1.48774 + 0.858949i) q^{80} +(0.428693 - 0.903450i) q^{81} +(-2.45849 + 0.820766i) q^{82} +(2.02625 + 8.22083i) q^{83} +(-3.59687 - 0.144949i) q^{84} +(13.8867 + 0.559616i) q^{85} +(-1.44425 - 5.85953i) q^{86} +(5.58210 - 1.86358i) q^{87} +(6.60868 - 13.9275i) q^{88} +(-0.207571 + 0.119841i) q^{89} +(0.828804 - 1.20073i) q^{90} +(-7.07592 - 5.71306i) q^{91} +(-4.50217 - 6.52252i) q^{92} +(-8.46429 - 4.01636i) q^{93} +(3.45295 + 2.18352i) q^{94} +(10.9256 + 1.77558i) q^{95} +(2.72431 + 5.19074i) q^{96} +(0.273825 - 0.223571i) q^{97} +(0.348179 + 0.334430i) q^{98} -5.94321i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{77}{78}\right)$

Coefficient data

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

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

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

$2$	0.756241	−	0.0304755i	0.534743	−	0.0215494i	0.228574	−	0.973527i	$-0.426594\pi$
$2$	0.756241	−	0.0304755i	0.534743	−	0.0215494i	0.306169	+	0.951977i	$0.400953\pi$
$3$	0.278217	+	0.960518i	0.160629	+	0.554555i
$3$	0.278217	+	0.960518i	0.160629	+	0.554555i
$4$	−1.42254	+	0.114840i	−0.711272	+	0.0574198i
$5$	−1.80244	+	0.683575i	−0.806075	+	0.305704i	−0.723008	−	0.690840i	$-0.757241\pi$
$5$	−1.80244	+	0.683575i	−0.806075	+	0.305704i	−0.0830675	+	0.996544i	$0.526472\pi$
$6$	0.239672	+	0.717904i	0.0978455	+	0.293083i
$7$	0.988668	−	2.32049i	0.373681	−	0.877062i	−0.621895	−	0.783101i	$-0.713637\pi$
$7$	0.988668	−	2.32049i	0.373681	−	0.877062i	0.995576	−	0.0939612i	$-0.0299530\pi$
$8$	−2.57496	+	0.312656i	−0.910385	+	0.110541i
$9$	−0.845190	+	0.534466i	−0.281730	+	0.178155i
$10$	−1.34225	+	0.571877i	−0.424455	+	0.180843i
$11$	−3.17644	+	5.02314i	−0.957733	+	1.51453i	−0.103509	+	0.994629i	$0.533007\pi$
$11$	−3.17644	+	5.02314i	−0.957733	+	1.51453i	−0.854224	+	0.519905i	$0.825967\pi$
$12$	−0.506082	−	1.33443i	−0.146093	−	0.385216i
$13$	0.984160	−	3.46863i	0.272957	−	0.962026i
$13$	0.984160	−	3.46863i	0.272957	−	0.962026i
$14$	0.676953	−	1.78498i	0.180923	−	0.477055i
$15$	−1.15806	−	1.54109i	−0.299009	−	0.397908i
$16$	0.879621	−	0.142952i	0.219905	−	0.0357381i
$17$	−6.63268	−	2.82592i	−1.60866	−	0.685387i	−0.614070	−	0.789252i	$-0.710469\pi$
$17$	−6.63268	−	2.82592i	−1.60866	−	0.685387i	−0.994591	+	0.103865i	$0.966879\pi$
$18$	−0.622879	+	0.429942i	−0.146814	+	0.101338i
$19$	−4.97273	−	2.87100i	−1.14082	−	0.658654i	−0.194188	−	0.980964i	$-0.562207\pi$
$19$	−4.97273	−	2.87100i	−1.14082	−	0.658654i	−0.946634	+	0.322311i	$0.895540\pi$
$20$	2.48555	−	1.17941i	0.555785	−	0.263723i
$21$	2.50394	+	0.304033i	0.546404	+	0.0663454i
$22$	−2.24907	+	3.89551i	−0.479504	+	0.830525i
$23$	2.77663	+	4.80926i	0.578967	+	1.00280i	0.995598	+	0.0937245i	$0.0298773\pi$
$23$	2.77663	+	4.80926i	0.578967	+	1.00280i	−0.416631	+	0.909076i	$0.636789\pi$
$24$	−1.01671	−	2.38631i	−0.207535	−	0.487103i
$25$	−0.961042	+	0.851409i	−0.192208	+	0.170282i
$26$	0.638554	−	2.65312i	0.125231	−	0.520319i
$27$	−0.748511	−	0.663123i	−0.144051	−	0.127618i
$28$	−1.13994	+	3.41453i	−0.215428	+	0.645286i
$29$	−0.236964	−	5.88019i	−0.0440030	−	1.09192i	−0.858843	−	0.512238i	$-0.828816\pi$
$29$	−0.236964	−	5.88019i	−0.0440030	−	1.09192i	0.814840	−	0.579686i	$-0.196825\pi$
$30$	−0.922735	−	1.13014i	−0.168468	−	0.206335i
$31$	−6.21270	+	7.01269i	−1.11583	+	1.25952i	−0.153351	+	0.988172i	$0.549007\pi$
$31$	−6.21270	+	7.01269i	−1.11583	+	1.25952i	−0.962482	+	0.271344i	$0.912532\pi$
$32$	5.74375	−	1.17259i	1.01536	−	0.207287i
$33$	−5.70856	−	1.65350i	−0.993732	−	0.287838i
$34$	−5.10202	−	1.93494i	−0.874990	−	0.331840i
$35$	−0.195785	+	4.85837i	−0.0330938	+	0.821214i
$36$	1.14094	−	0.857362i	0.190157	−	0.142894i
$37$	5.74704	+	1.17327i	0.944808	+	0.192884i	0.647644	−	0.761943i	$-0.275754\pi$
$37$	5.74704	+	1.17327i	0.944808	+	0.192884i	0.297163	+	0.954827i	$0.403959\pi$
$38$	−3.84807	−	2.01962i	−0.624240	−	0.327626i
$39$	3.60550	−	0.0197311i	0.577342	−	0.00315950i
$40$	4.42748	−	2.32372i	0.700046	−	0.367412i
$41$	−3.28934	+	0.952768i	−0.513708	+	0.148797i	−0.524940	−	0.851140i	$-0.675912\pi$
$41$	−3.28934	+	0.952768i	−0.513708	+	0.148797i	0.0112313	+	0.999937i	$0.496425\pi$
$42$	1.90284	+	0.153613i	0.293615	+	0.0237031i
$43$	−1.59494	−	7.81251i	−0.243225	−	1.19140i	−0.899516	−	0.436889i	$-0.856080\pi$
$43$	−1.59494	−	7.81251i	−0.243225	−	1.19140i	0.656290	−	0.754509i	$-0.272125\pi$
$44$	3.94177	−	7.51042i	0.594244	−	1.13224i
$45$	1.15806	−	1.54109i	0.172633	−	0.229733i
$46$	2.24636	+	3.55234i	0.331208	+	0.523764i
$47$	4.44238	+	3.06635i	0.647987	+	0.447273i	0.846185	−	0.532889i	$-0.178894\pi$
$47$	4.44238	+	3.06635i	0.647987	+	0.447273i	−0.198198	+	0.980162i	$0.563509\pi$
$48$	0.382034	+	0.805120i	0.0551419	+	0.116209i
$49$	0.441869	+	0.460034i	0.0631241	+	0.0657191i
$50$	−0.700832	+	0.673158i	−0.0991126	+	0.0951990i
$51$	0.869021	−	7.15703i	0.121687	−	1.00218i
$52$	−1.00167	+	5.04730i	−0.138907	+	0.699935i
$53$	1.15493	+	9.51172i	0.158642	+	1.30654i	0.826792	+	0.562508i	$0.190164\pi$
$53$	1.15493	+	9.51172i	0.158642	+	1.30654i	−0.668149	+	0.744027i	$0.732913\pi$
$54$	−0.586263	−	0.478669i	−0.0797803	−	0.0651386i
$55$	2.29165	−	11.2252i	0.309006	−	1.51361i
$56$	−1.82026	+	6.28427i	−0.243243	+	0.839771i
$57$	1.37415	−	5.57516i	0.182011	−	0.738447i
$58$	−0.358403	−	4.43962i	−0.0470606	−	0.582950i
$59$	0.547602	−	3.36953i	0.0712917	−	0.438676i	−0.926726	−	0.375738i	$-0.877389\pi$
$59$	0.547602	−	3.36953i	0.0712917	−	0.438676i	0.998017	−	0.0629372i	$-0.0200468\pi$
$60$	1.82436	+	2.05928i	0.235524	+	0.265852i
$61$	0.266815	+	0.200498i	0.0341622	+	0.0256712i	0.617686	−	0.786425i	$-0.288070\pi$
$61$	0.266815	+	0.200498i	0.0341622	+	0.0256712i	−0.583524	+	0.812096i	$0.698327\pi$
$62$	−4.48458	+	5.49261i	−0.569542	+	0.697563i
$63$	0.404610	+	2.48966i	0.0509760	+	0.313668i
$64$	2.57739	−	0.635269i	0.322174	−	0.0794086i
$65$	0.597183	+	6.92475i	0.0740715	+	0.858910i
$66$	−4.36743	−	1.07648i	−0.537594	−	0.132505i
$67$	−0.813674	+	10.0792i	−0.0994061	+	1.23137i	0.734172	+	0.678964i	$0.237571\pi$
$67$	−0.813674	+	10.0792i	−0.0994061	+	1.23137i	−0.833578	+	0.552402i	$0.813711\pi$
$68$	9.75980	+	3.25830i	1.18355	+	0.395127i
$69$	−3.84688	+	4.00502i	−0.463109	+	0.482148i
$70$			3.68006i			0.439851i
$71$	−2.56094	−	2.45981i	−0.303927	−	0.291926i	0.525208	−	0.850974i	$-0.323987\pi$
$71$	−2.56094	−	2.45981i	−0.303927	−	0.291926i	−0.829136	+	0.559048i	$0.811167\pi$
$72$	2.00922	−	1.64048i	0.236789	−	0.193333i
$73$	2.44727	+	4.66288i	0.286431	+	0.545749i	0.985576	−	0.169231i	$-0.0541284\pi$
$73$	2.44727	+	4.66288i	0.286431	+	0.545749i	−0.699146	+	0.714979i	$0.746436\pi$
$74$	4.38190	+	0.712128i	0.509386	+	0.0827832i
$75$	−1.08517	−	0.686222i	−0.125305	−	0.0792380i
$76$	7.40362	+	3.51306i	0.849254	+	0.402976i
$77$	8.51569	+	12.3371i	0.970453	+	1.40594i
$78$	2.72602	−	0.124801i	0.308661	−	0.0141309i
$79$	0.769740	−	1.11516i	0.0866025	−	0.125465i	−0.777288	−	0.629145i	$-0.783405\pi$
$79$	0.769740	−	1.11516i	0.0866025	−	0.125465i	0.863891	+	0.503679i	$0.168021\pi$
$80$	−1.48774	+	0.858949i	−0.166335	+	0.0960335i
$81$	0.428693	−	0.903450i	0.0476325	−	0.100383i
$82$	−2.45849	+	0.820766i	−0.271495	+	0.0906385i
$83$	2.02625	+	8.22083i	0.222410	+	0.902353i	0.970954	+	0.239268i	$0.0769074\pi$
$83$	2.02625	+	8.22083i	0.222410	+	0.902353i	−0.748543	+	0.663086i	$0.769246\pi$
$84$	−3.59687	−	0.144949i	−0.392451	−	0.0158152i
$85$	13.8867	+	0.559616i	1.50623	+	0.0606989i
$86$	−1.44425	−	5.85953i	−0.155737	−	0.631850i
$87$	5.58210	−	1.86358i	0.598464	−	0.199797i
$88$	6.60868	−	13.9275i	0.704488	−	1.48468i
$89$	−0.207571	+	0.119841i	−0.0220025	+	0.0127032i	−0.510961	−	0.859604i	$-0.670710\pi$
$89$	−0.207571	+	0.119841i	−0.0220025	+	0.0127032i	0.488958	+	0.872307i	$0.337377\pi$
$90$	0.828804	−	1.20073i	0.0873636	−	0.126568i
$91$	−7.07592	−	5.71306i	−0.741758	−	0.598891i
$92$	−4.50217	−	6.52252i	−0.469383	−	0.680019i
$93$	−8.46429	−	4.01636i	−0.877706	−	0.416477i
$94$	3.45295	+	2.18352i	0.356145	+	0.225213i
$95$	10.9256	+	1.77558i	1.12094	+	0.182171i
$96$	2.72431	+	5.19074i	0.278049	+	0.529777i
$97$	0.273825	−	0.223571i	0.0278027	−	0.0227002i	−0.618442	−	0.785830i	$-0.712236\pi$
$97$	0.273825	−	0.223571i	0.0278027	−	0.0227002i	0.646245	+	0.763130i	$0.276338\pi$
$98$	0.348179	+	0.334430i	0.0351714	+	0.0337826i
$99$		−	5.94321i		−	0.597315i
$100$	1.26935	−	1.32153i	0.126935	−	0.132153i
$101$	−12.0265	−	4.01505i	−1.19669	−	0.399512i	−0.352628	−	0.935764i	$-0.614712\pi$
$101$	−12.0265	−	4.01505i	−1.19669	−	0.399512i	−0.844058	+	0.536251i	$0.819840\pi$
$102$	0.439075	−	5.43892i	0.0434749	−	0.538533i
$103$	−14.9643	−	3.68836i	−1.47447	−	0.363425i	−0.581504	−	0.813544i	$-0.697535\pi$
$103$	−14.9643	−	3.68836i	−1.47447	−	0.363425i	−0.892969	+	0.450119i	$0.851382\pi$
$104$	−1.44968	+	9.23929i	−0.142153	+	0.905987i
$105$	−4.72102	+	1.16363i	−0.460724	+	0.113558i
$106$	1.16328	+	7.15795i	0.112988	+	0.695242i
$107$	1.18625	−	1.45290i	0.114679	−	0.140457i	−0.714075	−	0.700069i	$-0.753152\pi$
$107$	1.18625	−	1.45290i	0.114679	−	0.140457i	0.828755	+	0.559612i	$0.189050\pi$
$108$	1.14094	+	0.857362i	0.109787	+	0.0824997i
$109$	−0.706928	−	0.797957i	−0.0677114	−	0.0764304i	0.713679	−	0.700473i	$-0.247028\pi$
$109$	−0.706928	−	0.797957i	−0.0677114	−	0.0764304i	−0.781390	+	0.624043i	$0.785489\pi$
$110$	1.39094	−	8.55882i	0.132621	−	0.816051i
$111$	0.471983	+	5.84656i	0.0447987	+	0.554931i
$112$	0.537933	−	2.18248i	0.0508299	−	0.206225i
$113$	−0.834545	+	2.88118i	−0.0785074	+	0.271039i	−0.990164	−	0.139915i	$-0.955317\pi$
$113$	−0.834545	+	2.88118i	−0.0785074	+	0.271039i	0.911656	+	0.410954i	$0.134804\pi$
$114$	0.869285	−	4.25804i	0.0814160	−	0.398802i
$115$	−8.29219	−	6.77036i	−0.773251	−	0.631340i
$116$	1.01237	+	8.33762i	0.0939962	+	0.774128i
$117$	1.02206	+	3.45766i	0.0944899	+	0.319660i
$118$	0.311431	−	2.56486i	0.0286695	−	0.236115i
$119$	−13.1150	+	12.5972i	−1.20225	+	1.15478i
$120$	3.46378	+	3.60617i	0.316198	+	0.329197i
$121$	−10.4265	−	21.9735i	−0.947867	−	1.99759i
$122$	0.207887	+	0.143494i	0.0188212	+	0.0129913i
$123$	−1.83030	−	2.89439i	−0.165033	−	0.260978i
$124$	8.03250	−	10.6893i	0.721340	−	0.959929i
$125$	5.62947	−	10.7261i	0.503515	−	0.959368i
$126$	0.381856	+	1.87045i	0.0340184	+	0.166633i
$127$	10.0877	+	0.814360i	0.895135	+	0.0722628i	0.519466	−	0.854491i	$-0.326131\pi$
$127$	10.0877	+	0.814360i	0.895135	+	0.0722628i	0.375669	+	0.926754i	$0.377413\pi$
$128$	−9.33177	+	2.70298i	−0.824820	+	0.238912i
$129$	7.06032	−	3.70554i	0.621627	−	0.326255i
$130$	0.662649	+	5.21858i	0.0581182	+	0.457700i
$131$	−2.37100	−	1.24439i	−0.207155	−	0.108723i	0.357955	−	0.933739i	$-0.383474\pi$
$131$	−2.37100	−	1.24439i	−0.207155	−	0.108723i	−0.565110	+	0.825015i	$0.691166\pi$
$132$	8.31056	+	1.69661i	0.723341	+	0.147671i
$133$	−11.5785	+	8.70068i	−1.00398	+	0.754445i
$134$	−0.308166	+	7.64707i	−0.0266215	+	0.660606i
$135$	1.80244	+	0.683575i	0.155129	+	0.0588328i
$136$	17.9624	+	5.20288i	1.54026	+	0.446143i
$137$	2.41866	−	0.493774i	0.206640	−	0.0421859i	−0.0955903	−	0.995421i	$-0.530474\pi$
$137$	2.41866	−	0.493774i	0.206640	−	0.0421859i	0.302231	+	0.953235i	$0.402269\pi$
$138$	−2.78711	+	3.14599i	−0.237254	+	0.267805i
$139$	−2.34882	−	2.87678i	−0.199224	−	0.244006i	0.665324	−	0.746554i	$-0.268293\pi$
$139$	−2.34882	−	2.87678i	−0.199224	−	0.244006i	−0.864549	+	0.502549i	$0.832396\pi$
$140$	−0.279419	−	6.93372i	−0.0236153	−	0.586006i
$141$	−1.70934	+	5.12010i	−0.143952	+	0.431190i
$142$	−2.01165	−	1.78216i	−0.168814	−	0.149556i
$143$	14.2973	+	15.9615i	1.19560	+	1.33477i
$144$	−0.667044	+	0.590949i	−0.0555870	+	0.0492458i
$145$	4.44666	+	10.4367i	0.369275	+	0.866721i
$146$	1.99283	+	3.45168i	0.164927	+	0.285663i
$147$	−0.318935	+	0.552412i	−0.0263053	+	0.0455622i
$148$	−8.31015	−	1.00904i	−0.683091	−	0.0829422i
$149$	−4.96604	+	2.35642i	−0.406834	+	0.193045i	−0.621102	−	0.783730i	$-0.713315\pi$
$149$	−4.96604	+	2.35642i	−0.406834	+	0.193045i	0.214268	+	0.976775i	$0.431263\pi$
$150$	−0.841564	−	0.485877i	−0.0687135	−	0.0396717i
$151$	2.48946	−	1.71835i	0.202589	−	0.139837i	−0.462451	−	0.886645i	$-0.653030\pi$
$151$	2.48946	−	1.71835i	0.202589	−	0.139837i	0.665040	+	0.746808i	$0.268414\pi$
$152$	13.7022	+	5.83796i	1.11139	+	0.473521i
$153$	7.11623	−	1.15650i	0.575313	−	0.0934975i
$154$	6.81589	+	9.07030i	0.549240	+	0.730906i
$155$	6.40431	−	16.8868i	0.514407	−	1.35638i
$156$	−5.12671	+	0.442122i	−0.410465	+	0.0353981i
$157$	−5.81673	−	15.3375i	−0.464226	−	1.22406i	−0.938988	−	0.343949i	$-0.888235\pi$
$157$	−5.81673	−	15.3375i	−0.464226	−	1.22406i	0.474763	−	0.880114i	$-0.342534\pi$
$158$	0.548123	−	0.866788i	0.0436064	−	0.0689579i
$159$	−8.81486	+	3.75566i	−0.699064	+	0.297843i
$160$	−9.55120	+	6.03981i	−0.755088	+	0.477489i
$161$	13.9050	−	1.68837i	1.09587	−	0.133062i
$162$	0.296662	−	0.696290i	0.0233079	−	0.0547057i
$163$	2.39570	+	7.17601i	0.187646	+	0.562068i	0.999771	−	0.0214157i	$-0.00681736\pi$
$163$	2.39570	+	7.17601i	0.187646	+	0.562068i	−0.812125	+	0.583484i	$0.801689\pi$
$164$	4.56981	−	1.73310i	0.356842	−	0.135332i
$165$	11.4196	−	0.921887i	0.889016	−	0.0717688i
$166$	1.78287	+	6.15518i	0.138377	+	0.477734i
$167$	6.84155	−	0.275705i	0.529415	−	0.0213347i	0.225880	−	0.974155i	$-0.427474\pi$
$167$	6.84155	−	0.275705i	0.529415	−	0.0213347i	0.303535	+	0.952820i	$0.401833\pi$
$168$	−6.54259			−0.504771
$169$	−11.0629	−	6.82739i	−0.850989	−	0.525183i
$170$	10.5188			0.806752
$171$	5.73735	−	0.231207i	0.438746	−	0.0176809i
$172$	3.16605	+	10.9305i	0.241409	+	0.833441i
$173$	−21.0388	+	1.69843i	−1.59955	+	0.129129i	−0.847799	−	0.530318i	$-0.822073\pi$
$173$	−21.0388	+	1.69843i	−1.59955	+	0.129129i	−0.751751	+	0.659447i	$0.770790\pi$
$174$	4.16462	−	1.57943i	0.315719	−	0.119736i
$175$	1.02553	+	3.07185i	0.0775230	+	0.232210i
$176$	−2.07599	+	4.87254i	−0.156484	+	0.367281i
$177$	3.38885	−	0.411481i	0.254721	−	0.0309288i
$178$	−0.153322	+	0.0969547i	−0.0114919	+	0.00726706i
$179$	−17.5553	+	7.47961i	−1.31214	+	0.559052i	−0.930850	−	0.365402i	$-0.880931\pi$
$179$	−17.5553	+	7.47961i	−1.31214	+	0.559052i	−0.381293	+	0.924454i	$0.624521\pi$
$180$	−1.47041	+	2.32526i	−0.109598	+	0.173315i
$181$	−5.08876	−	13.4180i	−0.378245	−	0.997349i	−0.980058	−	0.198712i	$-0.936324\pi$
$181$	−5.08876	−	13.4180i	−0.378245	−	0.997349i	0.601813	−	0.798637i	$-0.294445\pi$
$182$	−5.52521	−	4.10481i	−0.409555	−	0.304268i
$183$	−0.118350	+	0.312063i	−0.00874867	+	0.0230683i
$184$	−8.65334	−	11.5155i	−0.637933	−	0.848935i
$185$	−11.1607	+	1.81379i	−0.820552	+	0.133353i
$186$	−6.52344	−	2.77938i	−0.478322	−	0.203794i
$187$	35.2633	−	24.3405i	2.57871	−	1.77995i
$188$	−6.67161	−	3.85186i	−0.486577	−	0.280926i
$189$	−2.27880	+	1.08130i	−0.165758	+	0.0786532i
$190$	8.31648	+	1.00980i	0.603341	+	0.0732588i
$191$	11.8971	−	20.6063i	0.860841	−	1.49102i	−0.0102764	−	0.999947i	$-0.503271\pi$
$191$	11.8971	−	20.6063i	0.860841	−	1.49102i	0.871118	−	0.491074i	$-0.163396\pi$
$192$	1.32726	+	2.29889i	0.0957869	+	0.165908i
$193$	−1.39204	−	3.26725i	−0.100202	−	0.235182i	0.862333	−	0.506342i	$-0.169003\pi$
$193$	−1.39204	−	3.26725i	−0.100202	−	0.235182i	−0.962534	+	0.271161i	$0.912593\pi$
$194$	0.200264	−	0.177418i	0.0143781	−	0.0127379i
$195$	−6.48520	+	2.50019i	−0.464415	+	0.179042i
$196$	−0.681407	−	0.603674i	−0.0486720	−	0.0431196i
$197$	1.71465	−	5.13600i	0.122164	−	0.365925i	−0.869642	−	0.493684i	$-0.835650\pi$
$197$	1.71465	−	5.13600i	0.122164	−	0.365925i	0.991805	+	0.127759i	$0.0407783\pi$
$198$	−0.181122	−	4.49449i	−0.0128718	−	0.319410i
$199$	10.6201	+	13.0073i	0.752839	+	0.922061i	0.998886	−	0.0471971i	$-0.0150289\pi$
$199$	10.6201	+	13.0073i	0.752839	+	0.922061i	−0.246046	+	0.969258i	$0.579131\pi$
$200$	2.20844	−	2.49282i	0.156161	−	0.176269i
$201$	−9.90760	+	2.02265i	−0.698828	+	0.142667i
$202$	−9.21732	−	2.66983i	−0.648529	−	0.187849i
$203$	−13.8792	−	5.26368i	−0.974128	−	0.369438i
$204$	−0.414310	+	10.2810i	−0.0290075	+	0.719813i
$205$	5.27754	−	3.96582i	0.368600	−	0.276985i
$206$	−11.4290	−	2.33324i	−0.796295	−	0.162565i
$207$	−4.91716	−	2.58073i	−0.341766	−	0.179373i
$208$	0.369838	−	3.19177i	0.0256437	−	0.221310i
$209$	30.2170	−	15.8591i	2.09016	−	1.09700i
$210$	−3.53477	+	1.02386i	−0.243922	+	0.0706529i
$211$	10.4985	+	0.847524i	0.722744	+	0.0583460i	0.436364	−	0.899770i	$-0.356266\pi$
$211$	10.4985	+	0.847524i	0.722744	+	0.0583460i	0.286380	+	0.958116i	$0.407548\pi$
$212$	−2.73526	−	13.3982i	−0.187859	−	0.920193i
$213$	1.65020	−	3.14419i	0.113070	−	0.215436i
$214$	0.852815	−	1.13489i	0.0582973	−	0.0775796i
$215$	8.21521	+	12.9913i	0.560273	+	0.886001i
$216$	2.13471	+	1.47349i	0.145249	+	0.100258i
$217$	10.1306	+	21.3497i	0.687708	+	1.44931i
$218$	−0.558926	−	0.581904i	−0.0378552	−	0.0394115i
$219$	−3.79791	+	3.64794i	−0.256639	+	0.246505i
$220$	−1.97087	+	16.2316i	−0.132876	+	1.09433i
$221$	−16.3297	+	20.2252i	−1.09846	+	1.36049i
$222$	0.535109	+	4.40702i	0.0359142	+	0.295780i
$223$	−6.34238	−	5.17839i	−0.424717	−	0.346771i	0.395856	−	0.918313i	$-0.370448\pi$
$223$	−6.34238	−	5.17839i	−0.424717	−	0.346771i	−0.820573	+	0.571542i	$0.806345\pi$
$224$	2.95767	−	14.4876i	0.197617	−	0.967994i
$225$	0.357214	−	1.23325i	0.0238143	−	0.0822164i
$226$	−0.543312	+	2.20430i	−0.0361405	+	0.146628i
$227$	−2.24673	−	27.8307i	−0.149120	−	1.84719i	−0.449393	−	0.893334i	$-0.648360\pi$
$227$	−2.24673	−	27.8307i	−0.149120	−	1.84719i	0.300273	−	0.953853i	$-0.402922\pi$
$228$	−1.31454	+	8.08871i	−0.0870577	+	0.535688i
$229$	−0.172303	−	0.194490i	−0.0113861	−	0.0128523i	0.742790	−	0.669524i	$-0.233502\pi$
$229$	−0.172303	−	0.194490i	−0.0113861	−	0.0128523i	−0.754176	+	0.656672i	$0.771964\pi$
$230$	−6.47722	−	4.86732i	−0.427095	−	0.320941i
$231$	−9.48080	+	11.6119i	−0.623791	+	0.764005i
$232$	2.44865	+	15.0672i	0.160762	+	0.989207i
$233$	−3.76625	+	0.928298i	−0.246735	+	0.0608148i	−0.360744	−	0.932665i	$-0.617477\pi$
$233$	−3.76625	+	0.928298i	−0.246735	+	0.0608148i	0.114008	+	0.993480i	$0.463631\pi$
$234$	0.878300	+	2.58367i	0.0574163	+	0.168900i
$235$	−10.1032	−	2.49021i	−0.659060	−	0.162444i
$236$	−0.392032	+	4.85619i	−0.0255191	+	0.316111i
$237$	1.28529	+	0.429092i	0.0834884	+	0.0278725i
$238$	−9.53422	+	9.92617i	−0.618011	+	0.643418i
$239$			20.0145i			1.29463i	0.762223	+	0.647314i	$0.224108\pi$
$239$			20.0145i			1.29463i	−0.762223	+	0.647314i	$0.775892\pi$
$240$	−1.23895	−	1.19003i	−0.0799741	−	0.0768161i
$241$	−19.8372	+	16.1966i	−1.27783	+	1.04331i	−0.281334	+	0.959610i	$0.590777\pi$
$241$	−19.8372	+	16.1966i	−1.27783	+	1.04331i	−0.996491	+	0.0837021i	$0.973326\pi$
$242$	−8.55462	−	16.2995i	−0.549912	−	1.04777i
$243$	0.987050	+	0.160411i	0.0633193	+	0.0102904i
$244$	−0.402581	−	0.254577i	−0.0257726	−	0.0162976i
$245$	−1.11091	−	0.527133i	−0.0709734	−	0.0336773i
$246$	−1.47236	−	2.13308i	−0.0938740	−	0.136000i
$247$	−14.8524	+	14.4230i	−0.945037	+	0.917716i
$248$	13.8049	−	19.9998i	0.876610	−	1.26999i
$249$	−7.33252	+	4.23343i	−0.464679	+	0.268283i
$250$	3.93035	−	8.28305i	0.248577	−	0.523866i
$251$	0.331067	−	0.110526i	0.0208968	−	0.00697636i	−0.306200	−	0.951967i	$-0.599058\pi$
$251$	0.331067	−	0.110526i	0.0208968	−	0.00697636i	0.327097	+	0.944991i	$0.393930\pi$
$252$	−0.861487	−	3.49519i	−0.0542686	−	0.220176i
$253$	−32.9774	−	1.32894i	−2.07327	−	0.0835499i
$254$	7.65352	+	0.308426i	0.480224	+	0.0193524i
$255$	3.32601	+	13.4942i	0.208283	+	0.845037i
$256$	−12.0105	+	4.00970i	−0.750657	+	0.250606i
$257$	−3.97917	+	8.38593i	−0.248214	+	0.523100i	−0.988870	−	0.148785i	$-0.952464\pi$
$257$	−3.97917	+	8.38593i	−0.248214	+	0.523100i	0.740656	+	0.671885i	$0.234515\pi$
$258$	5.22637	−	3.01745i	0.325380	−	0.187858i
$259$	8.40447	−	12.1760i	0.522228	−	0.756578i
$260$	−1.64475	−	9.78218i	−0.102003	−	0.606665i
$261$	3.34304	+	4.84323i	0.206929	+	0.299788i
$262$	−1.83097	−	0.868805i	−0.113118	−	0.0536749i
$263$	−1.05436	−	0.666734i	−0.0650144	−	0.0411126i	0.501563	−	0.865121i	$-0.332758\pi$
$263$	−1.05436	−	0.666734i	−0.0650144	−	0.0411126i	−0.566578	+	0.824008i	$0.691733\pi$
$264$	15.2163	+	2.47288i	0.936497	+	0.152196i
$265$	−8.58367	−	16.3548i	−0.527291	−	1.00467i
$266$	−8.49098	+	6.93267i	−0.520615	+	0.425069i
$267$	−0.172860	−	0.166034i	−0.0105788	−	0.0101611i
$268$		−	14.4315i		−	0.881544i
$269$	−7.78430	+	8.10431i	−0.474617	+	0.494129i	−0.914872	−	0.403744i	$-0.867709\pi$
$269$	−7.78430	+	8.10431i	−0.474617	+	0.494129i	0.440255	+	0.897873i	$0.354888\pi$
$270$	1.38391	+	0.462017i	0.0842221	+	0.0281175i
$271$	−2.33865	+	28.9693i	−0.142063	+	1.75976i	0.397300	+	0.917689i	$0.369947\pi$
$271$	−2.33865	+	28.9693i	−0.142063	+	1.75976i	−0.539363	+	0.842074i	$0.681335\pi$
$272$	−6.23822	−	1.53758i	−0.378247	−	0.0932296i
$273$	3.51885	−	8.38602i	0.212971	−	0.507545i
$274$	1.81404	−	0.447121i	0.109590	−	0.0270116i
$275$	−1.22405	−	7.53190i	−0.0738132	−	0.454191i
$276$	5.01241	−	6.13909i	0.301712	−	0.369530i
$277$	−16.5290	−	12.4208i	−0.993132	−	0.746291i	−0.0257649	−	0.999668i	$-0.508202\pi$
$277$	−16.5290	−	12.4208i	−0.993132	−	0.746291i	−0.967367	+	0.253377i	$0.918459\pi$
$278$	−1.86395	−	2.10396i	−0.111792	−	0.126187i
$279$	1.50287	−	9.24753i	0.0899745	−	0.553635i
$280$	−1.01486	−	12.5713i	−0.0606495	−	0.751279i
$281$	1.93924	−	7.86781i	0.115685	−	0.469354i	−0.884312	−	0.466897i	$-0.845372\pi$
$281$	1.93924	−	7.86781i	0.115685	−	0.469354i	0.999997	−	0.00245699i	$-0.000782084\pi$
$282$	−1.13663	+	3.92412i	−0.0676856	+	0.233678i
$283$	6.55475	−	32.1073i	0.389639	−	1.90858i	−0.0272636	−	0.999628i	$-0.508679\pi$
$283$	6.55475	−	32.1073i	0.389639	−	1.90858i	0.416903	−	0.908951i	$-0.363116\pi$
$284$	3.92553	+	3.20509i	0.232937	+	0.190187i
$285$	1.33421	+	10.9882i	0.0790318	+	0.650886i
$286$	11.2986	+	11.6350i	0.668103	+	0.687992i
$287$	−1.04117	+	8.57484i	−0.0614586	+	0.506157i
$288$	−4.22785	+	4.06090i	−0.249128	+	0.239291i
$289$	24.2303	+	25.2264i	1.42531	+	1.48391i
$290$	3.68081	+	7.75714i	0.216145	+	0.455515i
$291$	0.290927	+	0.200812i	0.0170544	+	0.0117718i
$292$	−4.01683	−	6.35210i	−0.235067	−	0.371729i
$293$	−9.14001	+	12.1631i	−0.533965	+	0.710579i	−0.983138	−	0.182866i	$-0.941462\pi$
$293$	−9.14001	+	12.1631i	−0.533965	+	0.710579i	0.449173	+	0.893445i	$0.351719\pi$
$294$	−0.224357	+	0.427476i	−0.0130848	+	0.0249309i
$295$	1.31631	+	6.44770i	0.0766384	+	0.375400i
$296$	−15.1652	−	1.22426i	−0.881460	−	0.0711588i
$297$	5.70856	−	1.65350i	0.331244	−	0.0959460i
$298$	−3.68371	+	1.93336i	−0.213392	+	0.111997i
$299$	19.4142	−	4.89802i	1.12275	−	0.283260i
$300$	1.62251	+	0.851559i	0.0936757	+	0.0491648i
$301$	−19.7057	−	4.02295i	−1.13582	−	0.231879i
$302$	1.83026	−	1.37535i	0.105320	−	0.0791427i
$303$	0.510534	−	12.6688i	0.0293294	−	0.727802i
$304$	−4.78453	−	1.81453i	−0.274412	−	0.104071i
$305$	−0.617973	−	0.178998i	−0.0353851	−	0.0102494i
$306$	5.34634	−	1.09146i	0.305630	−	0.0623948i
$307$	−17.1523	+	19.3610i	−0.978934	+	1.10499i	0.0155270	+	0.999879i	$0.495057\pi$
$307$	−17.1523	+	19.3610i	−0.978934	+	1.10499i	−0.994461	+	0.105108i	$0.966481\pi$
$308$	−13.5307	−	16.5721i	−0.770985	−	0.944285i
$309$	−0.620583	−	15.3996i	−0.0353037	−	0.876053i
$310$	4.32857	−	12.9656i	0.245846	−	0.736399i
$311$	25.4003	+	22.5027i	1.44032	+	1.27601i	0.900937	+	0.433950i	$0.142881\pi$
$311$	25.4003	+	22.5027i	1.44032	+	1.27601i	0.539382	+	0.842061i	$0.318658\pi$
$312$	−9.27783	+	1.17809i	−0.525254	+	0.0666961i
$313$	−1.31137	+	1.16178i	−0.0741232	+	0.0656675i	−0.699371	−	0.714759i	$-0.746536\pi$
$313$	−1.31137	+	1.16178i	−0.0741232	+	0.0656675i	0.625248	+	0.780426i	$0.284998\pi$
$314$	−4.86626	−	11.4215i	−0.274619	−	0.644555i
$315$	−2.43116	−	4.21088i	−0.136980	−	0.237256i
$316$	−0.966924	+	1.67476i	−0.0543937	+	0.0942127i
$317$	−21.6736	−	2.63165i	−1.21731	−	0.147808i	−0.513434	−	0.858129i	$-0.671627\pi$
$317$	−21.6736	−	2.63165i	−1.21731	−	0.147808i	−0.703878	+	0.710321i	$0.748550\pi$
$318$	−6.55170	+	3.10882i	−0.367401	+	0.174334i
$319$	30.2897	+	17.4878i	1.69590	+	0.979128i
$320$	−4.21133	+	2.90687i	−0.235421	+	0.162499i
$321$	1.72557	+	0.735197i	0.0963119	+	0.0410347i
$322$	10.4641	−	1.70058i	0.583140	−	0.0947694i
$323$	24.8693	+	33.0950i	1.38376	+	1.84145i
$324$	−0.506082	+	1.33443i	−0.0281157	+	0.0741349i
$325$	2.00741	+	4.17143i	0.111351	+	0.231389i
$326$	2.03042	+	5.35378i	0.112455	+	0.296518i
$327$	0.569772	−	0.901023i	0.0315085	−	0.0498267i
$328$	8.17202	−	3.48177i	0.451224	−	0.192249i
$329$	11.5075	−	7.27688i	0.634427	−	0.401187i
$330$	8.60789	−	1.04519i	0.473849	−	0.0575356i
$331$	−11.8623	+	27.8418i	−0.652010	+	1.53032i	0.184767	+	0.982782i	$0.440847\pi$
$331$	−11.8623	+	27.8418i	−0.652010	+	1.53032i	−0.836778	+	0.547543i	$0.815563\pi$
$332$	−3.82651	−	11.4618i	−0.210007	−	0.629048i
$333$	−5.48441	+	2.07996i	−0.300544	+	0.113981i
$334$	5.16546	−	0.416999i	0.282641	−	0.0228172i
$335$	−5.42327	−	18.7233i	−0.296305	−	1.02296i
$336$	2.24598	−	0.0905097i	0.122528	−	0.00493771i
$337$	31.2104			1.70014			0.850070	−	0.526670i	$-0.176560\pi$
$337$	31.2104			1.70014			0.850070	+	0.526670i	$0.176560\pi$
$338$	−8.57425	−	4.82600i	−0.466378	−	0.262500i
$339$	−2.99961			−0.162917
$340$	−19.8187	+	0.798668i	−1.07482	+	0.0433139i
$341$	−15.4914	−	53.4826i	−0.838908	−	2.89625i
$342$	4.33177	−	0.349697i	0.234235	−	0.0189094i
$343$	18.0133	−	6.83153i	0.972625	−	0.368868i
$344$	6.54953	+	19.6182i	0.353127	+	1.05774i
$345$	4.19603	−	9.84843i	0.225906	−	0.530222i
$346$	−15.8586	+	1.92559i	−0.852565	+	0.103520i
$347$	−12.0390	+	7.61303i	−0.646290	+	0.408689i	−0.817004	−	0.576631i	$-0.804367\pi$
$347$	−12.0390	+	7.61303i	−0.646290	+	0.408689i	0.170714	+	0.985321i	$0.445392\pi$
$348$	−7.72677	+	3.29207i	−0.414198	+	0.176473i
$349$	6.74596	−	10.6679i	0.361103	−	0.571039i	−0.614951	−	0.788565i	$-0.710824\pi$
$349$	6.74596	−	10.6679i	0.361103	−	0.571039i	0.976055	+	0.217526i	$0.0697987\pi$
$350$	0.869166	+	2.29180i	0.0464589	+	0.122502i
$351$	−3.03678	+	1.94369i	−0.162092	+	0.103747i
$352$	−12.3546	+	32.5763i	−0.658501	+	1.73632i
$353$	−13.4521	−	17.9015i	−0.715983	−	0.952800i	0.283999	−	0.958824i	$-0.408339\pi$
$353$	−13.4521	−	17.9015i	−0.715983	−	0.952800i	−0.999982	+	0.00602480i	$0.998082\pi$
$354$	2.55024	−	0.414455i	0.135544	−	0.0220280i
$355$	6.29740	+	2.68307i	0.334231	+	0.142403i
$356$	0.281517	−	0.194317i	0.0149204	−	0.0102988i
$357$	−15.7486	−	9.09248i	−0.833506	−	0.481225i
$358$	−13.0481	+	6.19139i	−0.689612	+	0.327225i
$359$	−15.7432	−	1.91157i	−0.830893	−	0.100889i	−0.305973	−	0.952040i	$-0.598982\pi$
$359$	−15.7432	−	1.91157i	−0.830893	−	0.100889i	−0.524920	+	0.851152i	$0.675905\pi$
$360$	−2.50011	+	4.33032i	−0.131768	+	0.228228i
$361$	6.98533	+	12.0989i	0.367649	+	0.636787i
$362$	−4.25724	−	9.99212i	−0.223756	−	0.525174i
$363$	18.2051	−	16.1283i	0.955518	−	0.846515i
$364$	10.7219	+	7.31448i	0.561980	+	0.383383i
$365$	−7.59848	−	6.73166i	−0.397722	−	0.352351i
$366$	−0.0799907	+	0.239601i	−0.00418118	+	0.0125242i
$367$	−0.134917	−	3.34794i	−0.00704264	−	0.174761i	−0.998882	−	0.0472689i	$-0.984948\pi$
$367$	−0.134917	−	3.34794i	−0.00704264	−	0.174761i	0.991840	−	0.127492i	$-0.0406928\pi$
$368$	3.12987	+	3.83340i	0.163156	+	0.199830i
$369$	2.27089	−	2.56331i	0.118218	−	0.133441i
$370$	−8.38490	+	1.71179i	−0.435910	+	0.0889918i
$371$	23.2137	+	6.72393i	1.20519	+	0.349089i
$372$	12.5021	+	4.74141i	0.648202	+	0.245831i
$373$	−0.624197	+	15.4893i	−0.0323197	+	0.802006i	0.899032	+	0.437884i	$0.144272\pi$
$373$	−0.624197	+	15.4893i	−0.0323197	+	0.802006i	−0.931351	+	0.364122i	$0.881369\pi$
$374$	25.9258	−	19.4819i	1.34059	−	1.00739i
$375$	11.8688	+	2.42303i	0.612902	+	0.125125i
$376$	−12.3976	−	6.50679i	−0.639360	−	0.335562i
$377$	−20.6294	−	4.96511i	−1.06247	−	0.255716i
$378$	−1.69037	+	0.887172i	−0.0869430	+	0.0456312i
$379$	22.9619	−	6.65099i	1.17947	−	0.341638i	0.370132	−	0.928979i	$-0.379312\pi$
$379$	22.9619	−	6.65099i	1.17947	−	0.341638i	0.809340	+	0.587341i	$0.199825\pi$
$380$	−15.7460	−	1.27115i	−0.807754	−	0.0652086i
$381$	2.02436	+	9.91595i	0.103711	+	0.508009i
$382$	8.36906	−	15.9459i	0.428198	−	0.815864i
$383$	3.42361	−	4.55599i	0.174938	−	0.232800i	−0.703454	−	0.710740i	$-0.748360\pi$
$383$	3.42361	−	4.55599i	0.174938	−	0.232800i	0.878392	+	0.477940i	$0.158616\pi$
$384$	−5.19252	−	8.21132i	−0.264980	−	0.419032i
$385$	−23.7824	−	16.4158i	−1.21206	−	0.836625i
$386$	−1.15229	−	2.42840i	−0.0586501	−	0.123602i
$387$	5.52355	+	5.75062i	0.280778	+	0.292320i
$388$	−0.363853	+	0.349485i	−0.0184718	+	0.0177424i
$389$	2.51038	−	20.6748i	0.127281	−	1.04825i	−0.779426	−	0.626494i	$-0.784489\pi$
$389$	2.51038	−	20.6748i	0.127281	−	1.04825i	0.906707	−	0.421761i	$-0.138588\pi$
$390$	−4.82818	+	2.08839i	−0.244484	+	0.105750i
$391$	−4.82589	−	39.7448i	−0.244056	−	2.00998i
$392$	−1.28163	−	1.04641i	−0.0647319	−	0.0528519i
$393$	0.535611	−	2.62360i	0.0270180	−	0.132343i
$394$	1.14016	−	3.93630i	0.0574407	−	0.198308i
$395$	−0.625113	+	2.53618i	−0.0314529	+	0.127609i
$396$	0.682515	+	8.45447i	0.0342977	+	0.424853i
$397$	−0.297525	+	1.83075i	−0.0149324	+	0.0918826i	−0.993447	−	0.114296i	$-0.963539\pi$
$397$	−0.297525	+	1.83075i	−0.0149324	+	0.0918826i	0.978514	+	0.206179i	$0.0661028\pi$
$398$	8.42776	+	9.51297i	0.422445	+	0.476842i
$399$	−11.5785	−	8.70068i	−0.579650	−	0.435579i
$400$	−0.723642	+	0.886300i	−0.0361821	+	0.0443150i
$401$	2.20811	+	13.5871i	0.110268	+	0.678506i	0.982051	+	0.188614i	$0.0603996\pi$
$401$	2.20811	+	13.5871i	0.110268	+	0.678506i	−0.871783	+	0.489892i	$0.837036\pi$
$402$	−7.43089	+	1.83155i	−0.370619	+	0.0913494i
$403$	18.2102	+	28.4512i	0.907113	+	1.41725i
$404$	17.5694	+	4.33046i	0.874109	+	0.215448i
$405$	−0.155116	+	1.92146i	−0.00770778	+	0.0954780i
$406$	−10.6564	−	3.55764i	−0.528869	−	0.176563i
$407$	−24.1486	+	25.1414i	−1.19700	+	1.24621i
$408$			18.7008i			0.925825i
$409$	1.31462	+	1.26271i	0.0650039	+	0.0624371i	0.724523	−	0.689251i	$-0.242060\pi$
$409$	1.31462	+	1.26271i	0.0650039	+	0.0624371i	−0.659519	+	0.751688i	$0.729240\pi$
$410$	3.87023	−	3.15995i	0.191137	−	0.156059i
$411$	1.14719	+	2.18579i	0.0565868	+	0.107817i
$412$	21.7109	+	3.52836i	1.06962	+	0.173830i
$413$	−7.27756	−	4.60205i	−0.358105	−	0.226452i
$414$	−3.79721	−	1.80180i	−0.186623	−	0.0885535i
$415$	−9.27175	−	13.4325i	−0.455132	−	0.659373i
$416$	1.58547	−	21.0770i	0.0777339	−	1.03338i
$417$	2.10972	−	3.05646i	0.103313	−	0.149675i
$418$	22.3680	−	12.9142i	1.09406	−	0.631653i
$419$	−3.01888	+	6.36214i	−0.147482	+	0.310811i	−0.963725	−	0.266897i	$-0.914002\pi$
$419$	−3.01888	+	6.36214i	−0.147482	+	0.310811i	0.816243	+	0.577708i	$0.196053\pi$
$420$	6.58223	−	2.19747i	0.321180	−	0.107226i
$421$	3.11877	+	12.6533i	0.151999	+	0.616686i	0.996680	+	0.0814156i	$0.0259441\pi$
$421$	3.11877	+	12.6533i	0.151999	+	0.616686i	−0.844681	+	0.535270i	$0.820210\pi$
$422$	7.96520	+	0.320986i	0.387740	+	0.0156254i
$423$	−5.39351	−	0.217351i	−0.262242	−	0.0105680i
$424$	−5.94780	−	24.1312i	−0.288851	−	1.17191i
$425$	8.78030	−	2.93130i	0.425907	−	0.142189i
$426$	1.15213	−	2.42805i	0.0558207	−	0.117640i
$427$	0.729046	−	0.420915i	0.0352810	−	0.0203695i
$428$	−1.52065	+	2.20304i	−0.0735033	+	0.106488i
$429$	−11.3535	+	18.1736i	−0.548154	+	0.877429i
$430$	6.60860	+	9.57420i	0.318695	+	0.461709i
$431$	12.8694	+	6.10661i	0.619898	+	0.294145i	0.712624	−	0.701547i	$-0.247507\pi$
$431$	12.8694	+	6.10661i	0.619898	+	0.294145i	−0.0927259	+	0.995692i	$0.529558\pi$
$432$	−0.753200	−	0.476295i	−0.0362384	−	0.0229158i
$433$	−4.99258	−	0.811374i	−0.239928	−	0.0389921i	0.0392580	−	0.999229i	$-0.487501\pi$
$433$	−4.99258	−	0.811374i	−0.239928	−	0.0389921i	−0.279186	+	0.960237i	$0.590065\pi$
$434$	8.31179	+	15.8368i	0.398979	+	0.760190i
$435$	−8.78750	+	7.17477i	−0.421329	+	0.344004i
$436$	1.09727	+	1.05395i	0.0525499	+	0.0504748i
$437$		−	31.8868i		−	1.52535i
$438$	−2.76096	+	2.87446i	−0.131924	+	0.137347i
$439$	5.89299	+	1.96737i	0.281257	+	0.0938973i	0.453797	−	0.891105i	$-0.350069\pi$
$439$	5.89299	+	1.96737i	0.281257	+	0.0938973i	−0.172540	+	0.985003i	$0.555197\pi$
$440$	−2.39126	+	29.6210i	−0.113999	+	1.41213i
$441$	−0.619335	−	0.152652i	−0.0294922	−	0.00726917i
$442$	−11.7328	+	15.7928i	−0.558073	+	0.751185i
$443$	−8.33812	+	2.05516i	−0.396156	+	0.0976436i	−0.432361	−	0.901701i	$-0.642319\pi$
$443$	−8.33812	+	2.05516i	−0.396156	+	0.0976436i	0.0362049	+	0.999344i	$0.488473\pi$
$444$	−1.34283	−	8.26279i	−0.0637281	−	0.392134i
$445$	0.292214	−	0.357897i	0.0138523	−	0.0169660i
$446$	−4.95418	−	3.72282i	−0.234587	−	0.176281i
$447$	−3.64502	−	4.11438i	−0.172404	−	0.194603i
$448$	1.07405	−	6.60887i	0.0507439	−	0.312240i
$449$	0.542835	+	6.72421i	0.0256179	+	0.317335i	0.996857	+	0.0792271i	$0.0252452\pi$
$449$	0.542835	+	6.72421i	0.0256179	+	0.317335i	−0.971239	+	0.238108i	$0.923473\pi$
$450$	0.232556	−	0.943518i	0.0109628	−	0.0444778i
$451$	5.66250	−	19.5492i	0.266637	−	0.920537i
$452$	0.856303	−	4.19445i	0.0402771	−	0.197290i
$453$	2.34312	+	1.91310i	0.110089	+	0.0898851i
$454$	−2.54722	−	20.9782i	−0.119547	−	0.984557i
$455$	16.6592	+	5.46052i	0.780996	+	0.255993i
$456$	−1.79528	+	14.7854i	−0.0840715	+	0.692391i
$457$	−16.7882	+	16.1253i	−0.785319	+	0.754309i	−0.973712	−	0.227785i	$-0.926852\pi$
$457$	−16.7882	+	16.1253i	−0.785319	+	0.754309i	0.188392	+	0.982094i	$0.439672\pi$
$458$	−0.136230	−	0.141830i	−0.00636560	−	0.00662729i
$459$	3.09070	+	6.51351i	0.144262	+	0.304025i
$460$	12.5735	+	8.67887i	0.586243	+	0.404654i
$461$	4.63538	+	7.33026i	0.215891	+	0.341404i	0.935718	−	0.352749i	$-0.114753\pi$
$461$	4.63538	+	7.33026i	0.215891	+	0.341404i	−0.719827	+	0.694154i	$0.755779\pi$
$462$	−6.81589	+	9.07030i	−0.317104	+	0.421989i
$463$	−12.1422	+	23.1350i	−0.564295	+	1.07517i	0.421438	+	0.906857i	$0.361525\pi$
$463$	−12.1422	+	23.1350i	−0.564295	+	1.07517i	−0.985733	+	0.168316i	$0.946167\pi$
$464$	−1.04902	−	5.13846i	−0.0486998	−	0.238547i
$465$	18.0019	+	1.45326i	0.834816	+	0.0673933i
$466$	−2.81990	+	0.816795i	−0.130629	+	0.0378373i
$467$	24.1228	−	12.6606i	1.11627	−	0.585864i	0.197361	−	0.980331i	$-0.436763\pi$
$467$	24.1228	−	12.6606i	1.11627	−	0.585864i	0.918910	+	0.394467i	$0.129071\pi$
$468$	−1.85101	−	4.80129i	−0.0855628	−	0.221940i
$469$	22.5841	+	11.8531i	1.04284	+	0.547324i
$470$	−7.71634	−	1.57530i	−0.355928	−	0.0726632i
$471$	13.1136	−	9.85422i	0.604242	−	0.454059i
$472$	−0.356547	+	8.84761i	−0.0164114	+	0.407244i
$473$	44.3096	+	16.8044i	2.03736	+	0.772667i
$474$	0.985063	+	0.285327i	0.0452454	+	0.0131055i
$475$	7.22340	−	1.47467i	0.331432	−	0.0676624i
$476$	17.2101	−	19.4261i	0.788821	−	0.890395i
$477$	−6.05983	−	7.42194i	−0.277460	−	0.339827i
$478$	0.609950	+	15.1357i	0.0278985	+	0.692293i
$479$	1.81495	−	5.43644i	0.0829272	−	0.248397i	−0.898907	−	0.438140i	$-0.855637\pi$
$479$	1.81495	−	5.43644i	0.0829272	−	0.248397i	0.981834	+	0.189743i	$0.0607655\pi$
$480$	−8.45866	−	7.49372i	−0.386083	−	0.342040i
$481$	9.72565	−	18.7797i	0.443451	−	0.856281i
$482$	−14.5081	+	12.8530i	−0.660825	+	0.585440i
$483$	5.49032	+	12.8863i	0.249818	+	0.586345i
$484$	17.3556	+	30.0608i	0.788892	+	1.36640i
$485$	−0.340725	+	0.590153i	−0.0154715	+	0.0267975i
$486$	0.751336	+	0.0912287i	0.0340813	+	0.00413822i
$487$	33.9785	−	16.1230i	1.53971	−	0.730602i	0.545507	−	0.838106i	$-0.316337\pi$
$487$	33.9785	−	16.1230i	1.53971	−	0.730602i	0.994205	+	0.107504i	$0.0342857\pi$
$488$	−0.749724	−	0.432854i	−0.0339384	−	0.0195944i
$489$	−6.22616	+	4.29761i	−0.281557	+	0.194344i
$490$	−0.856179	−	0.364784i	−0.0386782	−	0.0164793i
$491$	−1.65240	+	0.268541i	−0.0745717	+	0.0121191i	−0.197583	−	0.980286i	$-0.563309\pi$
$491$	−1.65240	+	0.268541i	−0.0745717	+	0.0121191i	0.123011	+	0.992405i	$0.460745\pi$
$492$	2.93608	+	3.90721i	0.132369	+	0.176150i
$493$	−15.0453	+	39.6711i	−0.677604	+	1.78670i
$494$	−10.7925	+	11.3599i	−0.485576	+	0.511107i
$495$	4.06263	+	10.7123i	0.182602	+	0.481481i
$496$	−4.46234	+	7.05662i	−0.200365	+	0.316852i
$497$	−8.23988	+	3.51068i	−0.369609	+	0.157476i
$498$	−5.41613	+	3.42495i	−0.242703	+	0.153476i
$499$	−16.8282	+	2.04331i	−0.753333	+	0.0914712i	−0.488189	−	0.872738i	$-0.662342\pi$
$499$	−16.8282	+	2.04331i	−0.753333	+	0.0914712i	−0.265144	+	0.964209i	$0.585419\pi$
$500$	−6.77639	+	15.9048i	−0.303050	+	0.711283i
$501$	2.16826	+	6.49473i	0.0968707	+	0.290163i
$502$	0.246998	−	0.0936740i	0.0110241	−	0.00418087i
$503$	1.66683	−	0.134561i	0.0743204	−	0.00599977i	−0.0432504	−	0.999064i	$-0.513771\pi$
$503$	1.66683	−	0.134561i	0.0743204	−	0.00599977i	0.117571	+	0.993064i	$0.462489\pi$
$504$	−1.82026	−	6.28427i	−0.0810809	−	0.279924i
$505$	24.4217	−	0.984161i	1.08675	−	0.0437946i
$506$	−24.9793			−1.11047
$507$	3.47995	−	12.5256i	0.154550	−	0.556280i
$508$	−14.4437			−0.640834
$509$	17.5624	−	0.707742i	0.778441	−	0.0313701i	0.352135	−	0.935949i	$-0.385456\pi$
$509$	17.5624	−	0.707742i	0.778441	−	0.0313701i	0.426306	+	0.904579i	$0.359815\pi$
$510$	2.92650	+	10.1035i	0.129588	+	0.447389i
$511$	13.2397	−	1.06882i	0.585689	−	0.0472817i
$512$	9.20738	−	3.49190i	0.406912	−	0.154322i
$513$	1.81831	+	5.44650i	0.0802804	+	0.240469i
$514$	−2.75365	+	6.46305i	−0.121458	+	0.285073i
$515$	29.4934	−	3.58115i	1.29964	−	0.157804i
$516$	−9.61807	+	6.08210i	−0.423412	+	0.267750i
$517$	−29.5137	+	12.5746i	−1.29801	+	0.553030i
$518$	5.98473	−	9.46409i	0.262954	−	0.415828i
$519$	−7.48473	−	19.7356i	−0.328543	−	0.866297i
$520$	−3.70279	−	17.6442i	−0.162378	−	0.773750i
$521$	8.18196	−	21.5740i	0.358458	−	0.945176i	−0.627565	−	0.778564i	$-0.715948\pi$
$521$	8.18196	−	21.5740i	0.358458	−	0.945176i	0.986023	−	0.166612i	$-0.0532826\pi$
$522$	2.67574	+	3.56077i	0.117114	+	0.155851i
$523$	23.8892	−	3.88237i	1.04460	−	0.169764i	0.386187	−	0.922421i	$-0.373792\pi$
$523$	23.8892	−	3.88237i	1.04460	−	0.169764i	0.658413	+	0.752657i	$0.271228\pi$
$524$	3.51575	+	1.49792i	0.153586	+	0.0654370i
$525$	−2.66524	+	1.83969i	−0.116321	+	0.0802904i
$526$	−0.817666	−	0.472079i	−0.0356519	−	0.0205836i
$527$	61.0242	−	28.9563i	2.65825	−	1.26136i
$528$	−5.25774	−	0.638405i	−0.228814	−	0.0277830i
$529$	−3.91932	+	6.78846i	−0.170405	+	0.295151i
$530$	−6.98974	−	12.1066i	−0.303615	−	0.525876i
$531$	1.33807	+	3.14057i	0.0580673	+	0.136289i
$532$	15.4717	−	13.7068i	0.670785	−	0.594264i
$533$	0.0675700	+	12.3472i	0.00292678	+	0.534816i
$534$	−0.135783	−	0.120294i	−0.00587593	−	0.00520562i
$535$	−1.14499	+	3.42965i	−0.0495021	+	0.148277i
$536$	−1.05614	−	26.2078i	−0.0456183	−	1.13201i
$537$	−12.0685	−	14.7812i	−0.520793	−	0.637856i
$538$	−5.63982	+	6.36604i	−0.243150	+	0.274459i
$539$	−3.71438	+	0.758297i	−0.159990	+	0.0326622i
$540$	−2.64255	−	0.765424i	−0.113717	−	0.0329386i
$541$	−21.4297	−	8.12722i	−0.921335	−	0.349416i	−0.152088	−	0.988367i	$-0.548600\pi$
$541$	−21.4297	−	8.12722i	−0.921335	−	0.349416i	−0.769248	+	0.638951i	$0.779369\pi$
$542$	−0.885726	+	21.9791i	−0.0380452	+	0.944082i
$543$	11.4724	−	8.62096i	0.492328	−	0.369961i
$544$	−41.4101	−	8.45393i	−1.77544	−	0.362459i
$545$	1.81966	+	0.955030i	0.0779456	+	0.0409090i
$546$	2.40553	−	6.44909i	0.102947	−	0.275996i
$547$	30.3113	−	15.9086i	1.29602	−	0.680204i	0.331311	−	0.943522i	$-0.392509\pi$
$547$	30.3113	−	15.9086i	1.29602	−	0.680204i	0.964709	+	0.263318i	$0.0848169\pi$
$548$	−3.38395	+	0.980173i	−0.144555	+	0.0418709i
$549$	−0.332669	−	0.0268558i	−0.0141980	−	0.00114618i
$550$	−1.15522	−	5.65862i	−0.0492586	−	0.241285i
$551$	−15.7037	+	29.9209i	−0.669000	+	1.27467i
$552$	8.65334	−	11.5155i	0.368311	−	0.490133i
$553$	−1.82670	−	2.88870i	−0.0776792	−	0.122840i
$554$	−12.8784	−	8.88935i	−0.547153	−	0.377672i
$555$	−4.84728	−	10.2154i	−0.205756	−	0.433621i
$556$	3.67167	+	3.82261i	0.155713	+	0.162115i
$557$	−17.7417	+	17.0411i	−0.751738	+	0.722054i	−0.967077	−	0.254485i	$-0.918094\pi$
$557$	−17.7417	+	17.0411i	−0.751738	+	0.722054i	0.215338	+	0.976539i	$0.430915\pi$
$558$	0.854709	−	7.03916i	0.0361827	−	0.297991i
$559$	−28.6684	−	2.15651i	−1.21255	−	0.0912108i
$560$	0.522298	+	4.30151i	0.0220711	+	0.181772i
$561$	33.1904	+	27.0991i	1.40130	+	1.14412i
$562$	1.22676	−	6.00906i	0.0517477	−	0.253477i
$563$	−2.59202	+	8.94870i	−0.109241	+	0.377143i	−0.996446	−	0.0842319i	$-0.973156\pi$
$563$	−2.59202	+	8.94870i	−0.109241	+	0.377143i	0.887205	+	0.461374i	$0.152644\pi$
$564$	1.84362	−	7.47986i	0.0776304	−	0.314959i
$565$	−0.465289	−	5.76363i	−0.0195748	−	0.242478i
$566$	3.97848	−	24.4806i	0.167228	−	1.02900i
$567$	−1.67261	−	1.88799i	−0.0702431	−	0.0792881i
$568$	7.36338	+	5.53322i	0.308960	+	0.232169i
$569$	5.04678	−	6.18119i	0.211572	−	0.259129i	−0.657906	−	0.753100i	$-0.728558\pi$
$569$	5.04678	−	6.18119i	0.211572	−	0.259129i	0.869478	+	0.493971i	$0.164455\pi$
$570$	1.34386	+	8.26907i	0.0562879	+	0.346353i
$571$	4.61636	−	1.13783i	0.193189	−	0.0476167i	−0.141534	−	0.989933i	$-0.545204\pi$
$571$	4.61636	−	1.13783i	0.193189	−	0.0476167i	0.334723	+	0.942317i	$0.391357\pi$
$572$	−22.1716	−	21.0640i	−0.927039	−	0.880731i
$573$	23.1027	+	5.69431i	0.965130	+	0.237883i
$574$	−0.526056	+	6.51637i	−0.0219572	+	0.271988i
$575$	−6.76310	−	2.25786i	−0.282041	−	0.0941591i
$576$	−1.83885	+	1.91445i	−0.0766189	+	0.0797687i
$577$			17.1026i			0.711992i	0.934487	+	0.355996i	$0.115858\pi$
$577$			17.1026i			0.711992i	−0.934487	+	0.355996i	$0.884142\pi$
$578$	19.0927	+	18.3388i	0.794153	+	0.762794i
$579$	2.75096	−	2.24609i	0.114326	−	0.0933443i
$580$	−7.52412	−	14.3360i	−0.312422	−	0.595271i
$581$	21.0796	+	3.42577i	0.874531	+	0.142125i
$582$	0.226131	+	0.142996i	0.00937341	+	0.00592739i
$583$	−51.4473	−	24.4120i	−2.13073	−	1.01104i
$584$	−7.75949	−	11.2416i	−0.321090	−	0.465179i
$585$	−4.20578	−	5.53356i	−0.173887	−	0.228784i
$586$	−6.54137	+	9.47681i	−0.270222	+	0.391484i
$587$	−16.3642	+	9.44790i	−0.675424	+	0.389956i	−0.798129	−	0.602487i	$-0.794177\pi$
$587$	−16.3642	+	9.44790i	−0.675424	+	0.389956i	0.122704	+	0.992443i	$0.460843\pi$
$588$	0.390261	−	0.822457i	0.0160941	−	0.0339176i
$589$	51.0275	−	17.0355i	2.10255	−	0.701935i
$590$	1.19194	+	4.83590i	0.0490715	+	0.199091i
$591$	5.41026	+	0.218026i	0.222549	+	0.00896840i
$592$	5.22294	+	0.210477i	0.214661	+	0.00865056i
$593$	5.64488	+	22.9022i	0.231808	+	0.940480i	0.965376	+	0.260864i	$0.0840074\pi$
$593$	5.64488	+	22.9022i	0.231808	+	0.940480i	−0.733568	+	0.679616i	$0.762146\pi$
$594$	4.26665	−	1.42442i	0.175063	−	0.0584446i
$595$	15.0279	−	31.6707i	0.616086	−	1.29837i
$596$	6.79380	−	3.92240i	0.278285	−	0.160668i
$597$	−9.53902	+	13.8197i	−0.390406	+	0.565601i
$598$	14.5325	−	4.29574i	0.594280	−	0.175666i
$599$	−24.0129	−	34.7887i	−0.981140	−	1.42143i	−0.905527	−	0.424289i	$-0.860524\pi$
$599$	−24.0129	−	34.7887i	−0.981140	−	1.42143i	−0.0756127	−	0.997137i	$-0.524091\pi$
$600$	3.00882	+	1.42771i	0.122835	+	0.0582858i
$601$	8.93104	+	5.64765i	0.364305	+	0.230372i	0.704058	−	0.710142i	$-0.251369\pi$
$601$	8.93104	+	5.64765i	0.364305	+	0.230372i	−0.339754	+	0.940515i	$0.610344\pi$
$602$	−15.0249	−	2.44178i	−0.612368	−	0.0995194i
$603$	−4.69926	−	8.95369i	−0.191369	−	0.364623i
$604$	−3.34403	+	2.73032i	−0.136067	+	0.111095i
$605$	33.8137	+	32.4785i	1.37472	+	1.32044i
$606$		−	9.59620i		−	0.389819i
$607$	4.92212	−	5.12446i	0.199782	−	0.207996i	−0.613774	−	0.789482i	$-0.710349\pi$
$607$	4.92212	−	5.12446i	0.199782	−	0.207996i	0.813556	+	0.581487i	$0.197529\pi$
$608$	−31.9286	−	10.6593i	−1.29488	−	0.432293i
$609$	1.19443	−	14.7957i	0.0484007	−	0.599551i
$610$	−0.472792	−	0.116533i	−0.0191428	−	0.00471827i
$611$	15.0081	−	12.3912i	0.607161	−	0.501294i
$612$	−9.99034	+	2.46240i	−0.403836	+	0.0995365i
$613$	7.82061	+	48.1221i	0.315871	+	1.94364i	0.330675	+	0.943745i	$0.392724\pi$
$613$	7.82061	+	48.1221i	0.315871	+	1.94364i	−0.0148038	+	0.999890i	$0.504712\pi$
$614$	−12.3812	+	15.1643i	−0.499666	+	0.611980i
$615$	5.27754	+	3.96582i	0.212811	+	0.159917i
$616$	−25.7848	−	29.1050i	−1.03890	−	1.17268i
$617$	−3.42976	+	21.1042i	−0.138077	+	0.849622i	0.821918	+	0.569606i	$0.192904\pi$
$617$	−3.42976	+	21.1042i	−0.138077	+	0.849622i	−0.959995	+	0.280017i	$0.909660\pi$
$618$	−0.938620	−	11.6269i	−0.0377568	−	0.467702i
$619$	−6.65639	+	27.0060i	−0.267543	+	1.08546i	0.671319	+	0.741169i	$0.265728\pi$
$619$	−6.65639	+	27.0060i	−0.267543	+	1.08546i	−0.938861	+	0.344295i	$0.888118\pi$
$620$	−7.17114	+	24.7577i	−0.288000	+	0.994291i
$621$	1.11079	−	5.44103i	0.0445746	−	0.218341i
$622$	19.8945	+	16.2434i	0.797698	+	0.651300i
$623$	0.0728714	+	0.600150i	0.00291953	+	0.0240445i
$624$	3.16865	−	0.532770i	0.126847	−	0.0213279i
$625$	−2.04090	+	16.8084i	−0.0816361	+	0.672334i
$626$	−0.956308	+	0.918547i	−0.0382218	+	0.0367125i
$627$	23.6399	+	24.6117i	0.944086	+	0.982897i
$628$	10.0359	+	21.1502i	0.400476	+	0.843985i
$629$	−34.8027	−	24.0226i	−1.38768	−	0.957844i
$630$	−1.96687	−	3.11035i	−0.0783618	−	0.123919i
$631$	10.4705	−	13.9337i	0.416825	−	0.554694i	−0.541379	−	0.840779i	$-0.682098\pi$
$631$	10.4705	−	13.9337i	0.416825	−	0.554694i	0.958204	+	0.286085i	$0.0923540\pi$
$632$	−1.63339	+	3.11216i	−0.0649726	+	0.123795i
$633$	2.10680	+	10.3198i	0.0837376	+	0.410174i
$634$	−16.4707	−	1.32965i	−0.654134	−	0.0528072i
$635$	−18.7391	+	5.42784i	−0.743637	+	0.215397i
$636$	12.1082	−	6.35488i	0.480122	−	0.251988i
$637$	2.03056	−	1.07993i	0.0804537	−	0.0427885i
$638$	23.4393	+	12.3019i	0.927969	+	0.487036i
$639$	3.47916	+	0.710276i	0.137634	+	0.0280981i
$640$	14.9723	−	11.2509i	0.591830	−	0.444732i
$641$	−1.06469	+	26.4201i	−0.0420528	+	1.04353i	0.831112	+	0.556105i	$0.187705\pi$
$641$	−1.06469	+	26.4201i	−0.0420528	+	1.04353i	−0.873165	+	0.487425i	$0.837936\pi$
$642$	1.32735	+	0.503398i	0.0523864	+	0.0198675i
$643$	15.2928	+	4.42960i	0.603087	+	0.174686i	0.565695	−	0.824614i	$-0.308608\pi$
$643$	15.2928	+	4.42960i	0.603087	+	0.174686i	0.0373920	+	0.999301i	$0.488095\pi$
$644$	−19.5866	+	3.99863i	−0.771819	+	0.157568i
$645$	−10.1928	+	11.5053i	−0.401340	+	0.453020i
$646$	19.8157	+	24.2699i	0.779640	+	0.954885i
$647$	0.608634	+	15.1031i	0.0239279	+	0.593764i	0.966029	+	0.258434i	$0.0832066\pi$
$647$	0.608634	+	15.1031i	0.0239279	+	0.593764i	−0.942101	+	0.335329i	$0.891152\pi$
$648$	−0.821396	+	2.46038i	−0.0322675	+	0.0966529i
$649$	15.1862	+	13.4538i	0.596110	+	0.528108i
$650$	1.64521	+	3.09343i	0.0645304	+	0.121334i
$651$	−17.6883	+	15.6705i	−0.693259	+	0.614173i
$652$	−4.23208	−	9.93306i	−0.165741	−	0.389009i
$653$	4.87256	+	8.43952i	0.190678	+	0.330264i	0.945475	−	0.325694i	$-0.105598\pi$
$653$	4.87256	+	8.43952i	0.190678	+	0.330264i	−0.754797	+	0.655958i	$0.772265\pi$
$654$	0.403426	−	0.698754i	0.0157752	−	0.0273235i
$655$	5.12421	+	0.622192i	0.200220	+	0.0243111i
$656$	−2.75717	+	1.30829i	−0.107649	+	0.0510803i
$657$	−4.56055	−	2.63304i	−0.177924	−	0.102725i
$658$	8.48065	−	5.85377i	0.330610	−	0.228204i
$659$	2.11106	+	0.899440i	0.0822353	+	0.0350372i	0.432693	−	0.901542i	$-0.357564\pi$
$659$	2.11106	+	0.899440i	0.0822353	+	0.0350372i	−0.350457	+	0.936579i	$0.613974\pi$
$660$	−16.1390	+	2.62285i	−0.628211	+	0.102094i
$661$	−30.2622	−	40.2717i	−1.17706	−	1.56639i	−0.748895	−	0.662689i	$-0.769415\pi$
$661$	−30.2622	−	40.2717i	−1.17706	−	1.56639i	−0.428169	−	0.903699i	$-0.640841\pi$
$662$	−8.12225	+	21.4166i	−0.315680	+	0.832381i
$663$	−23.9699	−	10.0580i	−0.930913	−	0.390620i
$664$	−7.78781	−	20.5348i	−0.302226	−	0.796904i
$665$	14.9220	−	23.5972i	0.578650	−	0.915061i
$666$	−4.08415	+	1.74009i	−0.158258	+	0.0674272i
$667$	27.6214	−	17.4667i	1.06951	−	0.676314i
$668$	−9.70075	+	1.17788i	−0.375333	+	0.0455737i
$669$	3.20938	−	7.53269i	0.124082	−	0.291231i
$670$	−4.67190	−	13.9940i	−0.180491	−	0.540637i
$671$	−1.85465	+	0.703377i	−0.0715981	+	0.0271536i
$672$	14.7385	−	1.18981i	0.568549	−	0.0458980i
$673$	−7.00434	−	24.1818i	−0.269997	−	0.932139i	−0.974864	−	0.222800i	$-0.928480\pi$
$673$	−7.00434	−	24.1818i	−0.269997	−	0.932139i	0.704867	−	0.709340i	$-0.251007\pi$
$674$	23.6026	−	0.951151i	0.909137	−	0.0366370i
$675$	1.28394			0.0494188
$676$	16.5214	+	8.44180i	0.635440	+	0.324685i
$677$	−23.2861			−0.894956			−0.447478	−	0.894295i	$-0.647678\pi$
$677$	−23.2861			−0.894956			−0.447478	+	0.894295i	$0.647678\pi$
$678$	−2.26843	+	0.0914146i	−0.0871185	+	0.00351076i
$679$	−0.248072	−	0.856445i	−0.00952014	−	0.0328673i
$680$	−35.9327	+	2.90079i	−1.37796	+	0.111240i
$681$	26.1068	−	9.90100i	1.00041	−	0.379407i
$682$	−13.3452	−	39.9736i	−0.511013	−	1.53067i
$683$	3.23064	−	7.58259i	0.123617	−	0.290140i	−0.846661	−	0.532133i	$-0.821391\pi$
$683$	3.23064	−	7.58259i	0.123617	−	0.290140i	0.970278	+	0.241993i	$0.0778011\pi$
$684$	−8.13508	+	0.987778i	−0.311053	+	0.0377686i
$685$	−4.02196	+	2.54333i	−0.153671	+	0.0971758i
$686$	13.4142	−	5.71525i	0.512156	−	0.218209i
$687$	0.138874	−	0.219611i	0.00529836	−	0.00837868i
$688$	−2.51976	−	6.64405i	−0.0960648	−	0.253302i
$689$	34.1293	+	5.35502i	1.30022	+	0.204010i
$690$	2.87307	−	7.57566i	0.109376	−	0.288400i
$691$	−13.3990	−	17.8308i	−0.509722	−	0.678317i	0.469073	−	0.883160i	$-0.344588\pi$
$691$	−13.3990	−	17.8308i	−0.509722	−	0.678317i	−0.978795	+	0.204842i	$0.934332\pi$
$692$	29.7336	−	4.83217i	1.13030	−	0.183692i
$693$	−13.7911	−	5.87586i	−0.523882	−	0.223205i
$694$	−8.87241	+	6.12418i	−0.336792	+	0.232471i
$695$	6.20010	+	3.57963i	0.235183	+	0.135783i
$696$	−13.7910	+	6.54392i	−0.522747	+	0.248047i
$697$	24.5096	+	2.97600i	0.928366	+	0.112724i
$698$	4.77646	−	8.27308i	0.180792	−	0.313141i
$699$	−1.93948	−	3.35928i	−0.0733580	−	0.127060i
$700$	−1.81164	−	4.25207i	−0.0684734	−	0.160713i
$701$	18.3895	−	16.2917i	0.694562	−	0.615328i	−0.240150	−	0.970736i	$-0.577196\pi$
$701$	18.3895	−	16.2917i	0.694562	−	0.615328i	0.934711	+	0.355408i	$0.115658\pi$
$702$	−2.23731	+	1.56245i	−0.0844416	+	0.0589707i
$703$	−25.2100	−	22.3341i	−0.950813	−	0.842347i
$704$	−4.99588	+	14.9645i	−0.188289	+	0.563995i
$705$	−0.418990	−	10.3971i	−0.0157801	−	0.391578i
$706$	−10.7186	−	13.1279i	−0.403399	−	0.494074i
$707$	−21.2071	+	23.9379i	−0.797576	+	0.900278i
$708$	−4.77353	+	0.974523i	−0.179400	+	0.0366248i
$709$	−30.0175	−	8.69467i	−1.12733	−	0.326535i	−0.338390	−	0.941006i	$-0.609882\pi$
$709$	−30.0175	−	8.69467i	−1.12733	−	0.326535i	−0.788940	+	0.614471i	$0.789370\pi$
$710$	4.84411	+	1.83713i	0.181796	+	0.0689463i
$711$	−0.0545612	+	1.35392i	−0.00204620	+	0.0507761i
$712$	0.497018	−	0.373485i	0.0186265	−	0.0139969i
$713$	−50.9762	−	10.4069i	−1.90907	−	0.389740i
$714$	−12.1869	−	6.39615i	−0.456081	−	0.239370i
$715$	−36.6809	−	18.9963i	−1.37179	−	0.710422i
$716$	24.1142	−	12.6561i	0.901190	−	0.472981i
$717$	−19.2243	+	5.56837i	−0.717943	+	0.207955i
$718$	−11.9639	−	0.965825i	−0.446488	−	0.0360443i
$719$	2.30134	+	11.2727i	0.0858254	+	0.420401i	0.999890	+	0.0148320i	$0.00472133\pi$
$719$	2.30134	+	11.2727i	0.0858254	+	0.420401i	−0.914065	+	0.405569i	$0.867074\pi$
$720$	0.798347	−	1.52112i	0.0297527	−	0.0566889i
$721$	−23.3535	+	31.0778i	−0.869729	+	1.15740i
$722$	5.65131	+	8.93683i	0.210320	+	0.332594i
$723$	−21.0761	−	14.5478i	−0.783830	−	0.541039i
$724$	8.77989	+	18.5032i	0.326302	+	0.687667i
$725$	5.23418	+	5.44936i	0.194393	+	0.202384i
$726$	13.2759	−	12.7517i	0.492714	−	0.473259i
$727$	1.58192	−	13.0283i	0.0586702	−	0.483193i	−0.933526	−	0.358509i	$-0.883285\pi$
$727$	1.58192	−	13.0283i	0.0586702	−	0.483193i	0.992197	−	0.124684i	$-0.0397917\pi$
$728$	20.0064	+	12.4986i	0.741487	+	0.463227i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−5.95143	−	4.85919i	−0.220272	−	0.179847i
$731$	−11.4988	+	56.3251i	−0.425300	+	2.08326i
$732$	0.132521	−	0.457514i	0.00489810	−	0.0169102i
$733$	−5.56717	+	22.5869i	−0.205628	+	0.834267i	0.773957	+	0.633238i	$0.218275\pi$
$733$	−5.56717	+	22.5869i	−0.205628	+	0.834267i	−0.979585	+	0.201029i	$0.935572\pi$
$734$	−0.204060	−	2.52774i	−0.00753200	−	0.0933005i
$735$	0.197246	−	1.21371i	0.00727554	−	0.0447682i
$736$	21.5876	+	24.3673i	0.795728	+	0.898191i
$737$	−48.0445	−	36.1031i	−1.76974	−	1.32987i
$738$	1.63922	−	2.00768i	0.0603407	−	0.0739039i
$739$	−7.19348	−	44.2633i	−0.264617	−	1.62825i	−0.690402	−	0.723426i	$-0.742566\pi$
$739$	−7.19348	−	44.2633i	−0.264617	−	1.62825i	0.425785	−	0.904824i	$-0.359998\pi$
$740$	15.6683	−	3.86189i	0.575978	−	0.141966i
$741$	−17.9858	−	10.2533i	−0.660725	−	0.376664i
$742$	17.7600	+	4.37746i	0.651992	+	0.160702i
$743$	2.65942	−	32.9429i	0.0975648	−	1.20856i	−0.743917	−	0.668272i	$-0.767034\pi$
$743$	2.65942	−	32.9429i	0.0975648	−	1.20856i	0.841482	−	0.540285i	$-0.181684\pi$
$744$	23.0509	+	7.69553i	0.845088	+	0.282132i
$745$	7.34020	−	7.64196i	0.268924	−	0.279980i
$746$			11.7327i			0.429563i
$747$	−6.10632	−	5.86520i	−0.223419	−	0.214597i
$748$	−47.3683	+	38.6751i	−1.73196	+	1.41410i
$749$	−2.19862	−	4.18912i	−0.0803358	−	0.153067i
$750$	9.04951	+	1.47069i	0.330441	+	0.0537019i
$751$	1.08966	+	0.689059i	0.0397622	+	0.0251441i	0.554199	−	0.832384i	$-0.313025\pi$
$751$	1.08966	+	0.689059i	0.0397622	+	0.0251441i	−0.514437	+	0.857528i	$0.671999\pi$
$752$	4.34595	+	2.06218i	0.158480	+	0.0751999i
$753$	0.198271	+	0.287245i	0.00722541	+	0.0104678i
$754$	−15.7521	−	3.12613i	−0.573659	−	0.113847i
$755$	−3.31248	+	4.79895i	−0.120553	+	0.174652i
$756$	3.11751	−	1.79990i	0.113383	−	0.0654616i
$757$	1.15621	−	2.43665i	0.0420230	−	0.0885616i	−0.881353	−	0.472458i	$-0.843367\pi$
$757$	1.15621	−	2.43665i	0.0420230	−	0.0885616i	0.923376	+	0.383897i	$0.125418\pi$
$758$	17.1620	−	5.72952i	0.623352	−	0.208106i
$759$	−7.89841	−	32.0451i	−0.286694	−	1.16316i
$760$	−28.6881	−	1.15609i	−1.04062	−	0.0419358i
$761$	−50.1861	−	2.02243i	−1.81925	−	0.0733131i	−0.892960	−	0.450136i	$-0.851375\pi$
$761$	−50.1861	−	2.02243i	−1.81925	−	0.0733131i	−0.926285	+	0.376823i	$0.877016\pi$
$762$	1.83309	+	7.43715i	0.0664059	+	0.269419i
$763$	−2.55057	+	0.851504i	−0.0923367	+	0.0308265i
$764$	−14.5577	+	30.6796i	−0.526678	+	1.10995i
$765$	−12.0360	+	6.94900i	−0.435163	+	0.251242i
$766$	2.45022	−	3.54976i	0.0885302	−	0.128258i
$767$	−11.1487	−	5.21559i	−0.402558	−	0.188324i
$768$	−7.19292	−	10.4207i	−0.259552	−	0.376026i
$769$	41.4833	+	19.6841i	1.49592	+	0.709825i	0.988409	−	0.151817i	$-0.0485125\pi$
$769$	41.4833	+	19.6841i	1.49592	+	0.709825i	0.507516	+	0.861642i	$0.330564\pi$
$770$	−18.4855	−	11.6895i	−0.666170	−	0.421260i
$771$	−9.16191	−	1.48896i	−0.329958	−	0.0536234i
$772$	2.35545	+	4.48794i	0.0847746	+	0.161524i
$773$	−3.02296	+	2.46817i	−0.108728	+	0.0887740i	−0.685250	−	0.728308i	$-0.740307\pi$
$773$	−3.02296	+	2.46817i	−0.108728	+	0.0887740i	0.576522	+	0.817082i	$0.304410\pi$
$774$	4.35238	+	4.18052i	0.156443	+	0.150266i
$775$		−	12.0290i		−	0.432096i
$776$	−0.635186	+	0.661299i	−0.0228019	+	0.0237393i
$777$	14.0335	+	4.68507i	0.503449	+	0.168076i
$778$	1.26837	−	15.7116i	0.0454734	−	0.563290i
$779$	19.0924	+	4.70585i	0.684055	+	0.168604i
$780$	8.93836	−	4.30139i	0.320045	−	0.154014i
$781$	20.4906	−	5.05049i	0.733213	−	0.180721i
$782$	−4.86078	−	29.9096i	−0.173821	−	1.06956i
$783$	−3.72192	+	4.55852i	−0.133011	+	0.162908i
$784$	0.454440	+	0.341489i	0.0162300	+	0.0121960i
$785$	20.9686	+	23.6687i	0.748401	+	0.844771i
$786$	0.325096	−	2.00039i	0.0115958	−	0.0713517i
$787$	−2.25433	−	27.9249i	−0.0803583	−	0.995417i	−0.903783	−	0.427991i	$-0.859221\pi$
$787$	−2.25433	−	27.9249i	−0.0803583	−	0.995417i	0.823425	−	0.567426i	$-0.192061\pi$
$788$	−1.84935	+	7.50309i	−0.0658802	+	0.267287i
$789$	0.347070	−	1.19822i	0.0123560	−	0.0426579i
$790$	−0.395445	+	1.93702i	−0.0140693	+	0.0689159i
$791$	5.86067	+	4.78509i	0.208381	+	0.170138i
$792$	1.85818	+	15.3035i	0.0660276	+	0.543786i
$793$	0.958044	−	0.728161i	0.0340212	−	0.0258578i
$794$	−0.169208	+	1.39355i	−0.00600497	+	0.0494553i
$795$	13.3210	−	12.7950i	0.472446	−	0.453791i
$796$	−16.6013	−	17.2838i	−0.588418	−	0.612608i
$797$	−16.3232	−	34.4005i	−0.578198	−	1.21853i	−0.956198	−	0.292721i	$-0.905439\pi$
$797$	−16.3232	−	34.4005i	−0.578198	−	1.21853i	0.377999	−	0.925806i	$-0.376612\pi$
$798$	−9.02129	−	6.22695i	−0.319350	−	0.220432i
$799$	−20.7996	−	32.8919i	−0.735837	−	1.16363i
$800$	−4.52163	+	6.01719i	−0.159864	+	0.212740i
$801$	0.111386	−	0.212228i	0.00393563	−	0.00749872i
$802$	2.08394	+	10.2078i	0.0735864	+	0.360450i
$803$	−31.1959	−	2.51839i	−1.10088	−	0.0888721i
$804$	13.8617	−	4.01509i	0.488865	−	0.141601i
$805$	−23.9088	+	12.5483i	−0.842674	+	0.442269i
$806$	14.6383	+	20.9610i	0.515613	+	0.738319i
$807$	−9.95007	−	5.22220i	−0.350259	−	0.183830i
$808$	32.2232	+	6.57841i	1.13361	+	0.231428i
$809$	−13.4925	+	10.1390i	−0.474372	+	0.356467i	−0.810879	−	0.585213i	$-0.801011\pi$
$809$	−13.4925	+	10.1390i	−0.474372	+	0.356467i	0.336507	+	0.941681i	$0.390754\pi$
$810$	−0.0587478	+	1.45781i	−0.00206419	+	0.0512223i
$811$	−10.0773	−	3.82183i	−0.353863	−	0.134203i	0.171267	−	0.985225i	$-0.445214\pi$
$811$	−10.0773	−	3.82183i	−0.353863	−	0.134203i	−0.525130	+	0.851022i	$0.675983\pi$
$812$	20.3482	+	5.89394i	0.714083	+	0.206837i
$813$	−28.4762	+	5.81347i	−0.998705	+	0.203887i
$814$	−17.4960	+	19.7489i	−0.613234	+	0.692198i
$815$	−9.22345	−	11.2967i	−0.323083	−	0.395705i
$816$	−0.258705	−	6.41970i	−0.00905649	−	0.224734i
$817$	−14.4986	+	43.4286i	−0.507241	+	1.51937i
$818$	1.03265	+	0.914851i	0.0361059	+	0.0319870i
$819$	9.03393	+	1.04678i	0.315671	+	0.0365776i
$820$	−7.05210	+	6.24762i	−0.246270	+	0.218176i
$821$	−7.46669	−	17.5250i	−0.260589	−	0.611625i	0.737369	−	0.675490i	$-0.236068\pi$
$821$	−7.46669	−	17.5250i	−0.260589	−	0.611625i	−0.997959	+	0.0638644i	$0.979657\pi$
$822$	0.934167	+	1.61802i	0.0325828	+	0.0564351i
$823$	−25.2470	+	43.7290i	−0.880054	+	1.52430i	−0.0287742	+	0.999586i	$0.509160\pi$
$823$	−25.2470	+	43.7290i	−0.880054	+	1.52430i	−0.851280	+	0.524712i	$0.824173\pi$
$824$	39.6855	+	4.81869i	1.38251	+	0.167867i
$825$	6.89397	−	3.27123i	0.240017	−	0.113890i
$826$	−5.64384	−	3.25847i	−0.196374	−	0.113377i
$827$	−26.3869	+	18.2135i	−0.917561	+	0.633347i	−0.930390	−	0.366571i	$-0.880532\pi$
$827$	−26.3869	+	18.2135i	−0.917561	+	0.633347i	0.0128290	+	0.999918i	$0.495916\pi$
$828$	7.29125	+	3.10651i	0.253388	+	0.107959i
$829$	3.33646	−	0.542228i	0.115880	−	0.0188323i	−0.102195	−	0.994764i	$-0.532586\pi$
$829$	3.33646	−	0.542228i	0.115880	−	0.0188323i	0.218075	+	0.975932i	$0.430022\pi$
$830$	−7.42104	−	9.87560i	−0.257588	−	0.342787i
$831$	7.33169	−	19.3321i	0.254334	−	0.670623i
$832$	0.333046	−	9.56523i	0.0115463	−	0.331615i
$833$	−1.63075	−	4.29994i	−0.0565023	−	0.148984i
$834$	1.50231	−	2.37571i	0.0520207	−	0.0822642i
$835$	−12.1430	+	5.17366i	−0.420227	+	0.179042i
$836$	−41.1638	+	26.0304i	−1.42368	+	0.900280i
$837$	9.30054	−	1.12929i	0.321474	−	0.0390340i
$838$	−2.08911	+	4.90331i	−0.0721670	+	0.169382i
$839$	14.0802	+	42.1752i	0.486101	+	1.45605i	0.851080	+	0.525035i	$0.175948\pi$
$839$	14.0802	+	42.1752i	0.486101	+	1.45605i	−0.364979	+	0.931016i	$0.618924\pi$
$840$	11.7926	−	4.47235i	0.406884	−	0.154311i
$841$	−5.61454	+	0.453252i	−0.193605	+	0.0156294i
$842$	2.74415	+	9.47392i	0.0945698	+	0.326493i
$843$	8.09671	−	0.326286i	0.278865	−	0.0112379i
$844$	−15.0319			−0.517418
$845$	24.6072	+	4.74365i	0.846512	+	0.163187i
$846$	−4.08542			−0.140460
$847$	−61.2975	+	2.47021i	−2.10621	+	0.0848773i
$848$	2.37562	+	8.20161i	0.0815793	+	0.281644i
$849$	32.6633	−	2.63685i	1.12100	−	0.0904965i
$850$	6.55069	−	2.48435i	0.224687	−	0.0852124i
$851$	10.3148	+	30.8967i	0.353588	+	1.05913i
$852$	−1.98640	+	4.66225i	−0.0680529	+	0.159726i
$853$	17.6351	−	2.14129i	0.603813	−	0.0733162i	0.187079	−	0.982345i	$-0.440098\pi$
$853$	17.6351	−	2.14129i	0.603813	−	0.0733162i	0.416734	+	0.909029i	$0.363175\pi$
$854$	0.538506	−	0.340531i	0.0184273	−	0.0116527i
$855$	−10.1832	+	4.33865i	−0.348257	+	0.148379i
$856$	−2.60030	+	4.11204i	−0.0888763	+	0.140547i
$857$	−0.971190	−	2.56082i	−0.0331752	−	0.0874758i	0.917405	−	0.397955i	$-0.130280\pi$
$857$	−0.971190	−	2.56082i	−0.0331752	−	0.0874758i	−0.950580	+	0.310479i	$0.899511\pi$
$858$	−8.03216	+	14.0896i	−0.274213	+	0.481011i
$859$	−7.70079	+	20.3053i	−0.262748	+	0.692808i	0.737107	+	0.675776i	$0.236191\pi$
$859$	−7.70079	+	20.3053i	−0.262748	+	0.692808i	−0.999855	+	0.0170327i	$0.994578\pi$
$860$	−13.1784	−	17.5373i	−0.449380	−	0.598017i
$861$	−8.52596	+	1.38560i	−0.290564	+	0.0472212i
$862$	9.91847	+	4.22587i	0.337825	+	0.143934i
$863$	−3.37284	+	2.32810i	−0.114813	+	0.0792494i	−0.624087	−	0.781355i	$-0.714529\pi$
$863$	−3.37284	+	2.32810i	−0.114813	+	0.0792494i	0.509275	+	0.860604i	$0.329914\pi$
$864$	−5.07683	−	2.93111i	−0.172717	−	0.0997184i
$865$	36.7601	−	17.4429i	1.24988	−	0.593076i
$866$	−3.80032	−	0.461443i	−0.129140	−	0.0156805i
$867$	−17.4891	+	30.2921i	−0.593962	+	1.02877i
$868$	−16.8630	−	29.2075i	−0.572366	−	0.991367i
$869$	3.15657	+	7.40875i	0.107079	+	0.251325i
$870$	−6.42681	+	5.69366i	−0.217889	+	0.193033i
$871$	34.1602	+	12.7419i	1.15747	+	0.431741i
$872$	2.06980	+	1.83368i	0.0700922	+	0.0620962i
$873$	−0.111943	+	0.335310i	−0.00378869	+	0.0113485i
$874$	−0.971766	−	24.1141i	−0.0328705	−	0.815672i
$875$	−19.3240	−	23.6676i	−0.653271	−	0.800112i
$876$	4.98376	−	5.62550i	0.168386	−	0.190068i
$877$	−12.9102	+	2.63563i	−0.435946	+	0.0889990i	−0.412986	−	0.910737i	$-0.635514\pi$
$877$	−12.9102	+	2.63563i	−0.435946	+	0.0889990i	−0.0229599	+	0.999736i	$0.507309\pi$
$878$	4.51647	+	1.30821i	0.152424	+	0.0441500i
$879$	−14.2258	−	5.39515i	−0.479826	−	0.181974i
$880$	0.411108	−	10.2015i	0.0138585	−	0.343894i
$881$	−18.5841	+	13.9650i	−0.626114	+	0.470494i	−0.865823	−	0.500351i	$-0.833204\pi$
$881$	−18.5841	+	13.9650i	−0.626114	+	0.470494i	0.239709	+	0.970845i	$0.422948\pi$
$882$	−0.473019	−	0.0965675i	−0.0159274	−	0.00325160i
$883$	47.2165	+	24.7811i	1.58896	+	0.833951i	0.999661	+	0.0260366i	$0.00828866\pi$
$883$	47.2165	+	24.7811i	1.58896	+	0.833951i	0.589300	+	0.807914i	$0.299404\pi$
$884$	20.9071	−	30.6465i	0.703181	−	1.03075i
$885$	−5.82691	+	3.05820i	−0.195870	+	0.102800i
$886$	−6.24299	+	1.80830i	−0.209737	+	0.0607512i
$887$	18.1137	+	1.46229i	0.608200	+	0.0490990i	0.380730	−	0.924686i	$-0.375673\pi$
$887$	18.1137	+	1.46229i	0.608200	+	0.0490990i	0.227470	+	0.973785i	$0.426955\pi$
$888$	−3.04330	−	14.9071i	−0.102127	−	0.500249i
$889$	11.8631	−	22.6032i	0.397874	−	0.758086i
$890$	0.210077	−	0.279562i	0.00704180	−	0.00937093i
$891$	3.17644	+	5.02314i	0.106415	+	0.168282i
$892$	9.61700	+	6.63813i	0.322001	+	0.222261i
$893$	−13.2872	−	28.0022i	−0.444640	−	0.937058i
$894$	−2.88190	−	3.00038i	−0.0963851	−	0.100348i
$895$	26.5294	−	25.4819i	0.886782	−	0.851765i
$896$	−2.95379	+	24.3266i	−0.0986790	+	0.812695i
$897$	10.1060	+	17.2850i	0.337430	+	0.577129i
$898$	0.615437	+	5.06858i	0.0205374	+	0.169141i
$899$	42.7081	+	34.8701i	1.42440	+	1.16298i
$900$	−0.366527	+	1.79537i	−0.0122176	+	0.0598457i
$901$	19.2191	−	66.3520i	0.640280	−	2.21050i
$902$	3.68644	−	14.9565i	0.122745	−	0.497996i
$903$	−1.61836	−	20.0469i	−0.0538555	−	0.667121i
$904$	1.24810	−	7.67985i	0.0415111	−	0.255428i
$905$	18.3444	+	20.7065i	0.609787	+	0.688307i
$906$	1.83026	+	1.37535i	0.0608064	+	0.0456931i
$907$	−11.7677	+	14.4128i	−0.390741	+	0.478571i	−0.932090	−	0.362227i	$-0.882016\pi$
$907$	−11.7677	+	14.4128i	−0.390741	+	0.478571i	0.541349	+	0.840798i	$0.317914\pi$
$908$	6.39213	+	39.3323i	0.212130	+	1.30529i
$909$	12.3106	−	3.03430i	0.408318	−	0.100641i
$910$	12.7648	+	3.62177i	0.423149	+	0.120060i
$911$	8.60825	+	2.12174i	0.285204	+	0.0702965i	0.379323	−	0.925265i	$-0.376157\pi$
$911$	8.60825	+	2.12174i	0.285204	+	0.0702965i	−0.0941184	+	0.995561i	$0.530003\pi$
$912$	0.411752	−	5.10046i	0.0136345	−	0.168893i
$913$	−47.7307	−	15.9348i	−1.57965	−	0.527366i
$914$	−12.2045	+	12.7062i	−0.403689	+	0.420285i
$915$		−	0.643375i		−	0.0212693i
$916$	0.267444	+	0.256883i	0.00883660	+	0.00848767i
$917$	−5.23173	+	4.27158i	−0.172767	+	0.141060i
$918$	2.53582	+	4.83159i	0.0836944	+	0.159466i
$919$	−37.5469	−	6.10197i	−1.23856	−	0.201285i	−0.494368	−	0.869253i	$-0.664601\pi$
$919$	−37.5469	−	6.10197i	−1.23856	−	0.201285i	−0.744191	+	0.667967i	$0.767165\pi$
$920$	23.4688	+	14.8408i	0.773745	+	0.489287i
$921$	−23.3686	−	11.0885i	−0.770022	−	0.365380i
$922$	3.72885	+	5.40218i	0.122803	+	0.177911i
$923$	−11.0526	+	6.46210i	−0.363800	+	0.212703i
$924$	12.1534	−	17.6072i	0.399816	−	0.579233i
$925$	−6.52208	+	3.76552i	−0.214445	+	0.123810i
$926$	−8.47735	+	17.8656i	−0.278583	+	0.587102i
$927$	14.6189	−	4.88052i	0.480149	−	0.160297i
$928$	−8.25614	−	33.4965i	−0.271021	−	1.09958i
$929$	22.1309	+	0.891845i	0.726092	+	0.0292605i	0.400560	−	0.916271i	$-0.368816\pi$
$929$	22.1309	+	0.891845i	0.726092	+	0.0292605i	0.325532	+	0.945531i	$0.394457\pi$
$930$	13.6580	+	0.550400i	0.447864	+	0.0180483i
$931$	−0.876532	−	3.55623i	−0.0287272	−	0.116551i
$932$	5.25105	−	1.75306i	0.172004	−	0.0574233i
$933$	−14.5474	+	30.6581i	−0.476262	+	1.00370i
$934$	17.8568	−	10.3096i	0.584293	−	0.337342i
$935$	−46.9214	+	67.9774i	−1.53449	+	2.22310i
$936$	−3.71283	−	8.58376i	−0.121358	−	0.280569i
$937$	−18.0171	−	26.1022i	−0.588592	−	0.852722i	0.409635	−	0.912249i	$-0.365656\pi$
$937$	−18.0171	−	26.1022i	−0.588592	−	0.852722i	−0.998227	+	0.0595274i	$0.981041\pi$
$938$	17.4403	+	8.27551i	0.569445	+	0.270205i
$939$	−1.48075	−	0.936372i	−0.0483226	−	0.0305573i
$940$	14.6582	+	2.38219i	0.478098	+	0.0776985i
$941$	−2.92901	−	5.58077i	−0.0954831	−	0.181928i	0.833030	−	0.553228i	$-0.186604\pi$
$941$	−2.92901	−	5.58077i	−0.0954831	−	0.181928i	−0.928513	+	0.371300i	$0.878912\pi$
$942$	9.61672	−	7.85181i	0.313330	−	0.255826i
$943$	−13.7154	−	13.1738i	−0.446634	−	0.428998i
$944$		−	3.04219i		−	0.0990149i
$945$	3.36824	−	3.50671i	0.109569	−	0.114073i
$946$	34.0208	+	11.3578i	1.10611	+	0.369275i
$947$	1.74301	−	21.5910i	0.0566401	−	0.701614i	−0.904664	−	0.426125i	$-0.859878\pi$
$947$	1.74301	−	21.5910i	0.0566401	−	0.701614i	0.961304	−	0.275489i	$-0.0888396\pi$
$948$	−1.87765	−	0.462800i	−0.0609833	−	0.0150310i
$949$	18.5823	−	3.89966i	0.603208	−	0.126588i
$950$	5.41769	−	1.33534i	0.175773	−	0.0433241i
$951$	−3.50223	−	21.5501i	−0.113568	−	0.698809i
$952$	29.8321	−	36.5377i	0.966863	−	1.18419i
$953$	−12.4165	−	9.33043i	−0.402211	−	0.302242i	0.380318	−	0.924856i	$-0.375815\pi$
$953$	−12.4165	−	9.33043i	−0.402211	−	0.302242i	−0.782530	+	0.622613i	$0.786071\pi$
$954$	−4.80887	−	5.42810i	−0.155693	−	0.175741i
$955$	−7.35777	+	45.2742i	−0.238092	+	1.46504i
$956$	−2.29845	−	28.4714i	−0.0743373	−	0.920832i
$957$	−8.37020	+	33.9592i	−0.270570	+	1.09775i
$958$	1.20686	−	4.16657i	0.0389919	−	0.134616i
$959$	1.24546	−	6.10066i	0.0402179	−	0.197000i
$960$	−3.96377	−	3.23632i	−0.127930	−	0.104452i
$961$	−6.84352	−	56.3615i	−0.220759	−	1.81811i
$962$	6.78261	−	14.4984i	0.218680	−	0.467446i
$963$	−0.226086	+	1.86199i	−0.00728552	+	0.0600017i
$964$	26.3592	−	25.3184i	0.848974	−	0.815451i
$965$	4.74248	+	4.93745i	0.152666	+	0.158942i
$966$	4.54472	+	9.57780i	0.146224	+	0.308161i
$967$	12.1684	+	8.39926i	0.391310	+	0.270102i	0.747433	−	0.664337i	$-0.231286\pi$
$967$	12.1684	+	8.39926i	0.391310	+	0.270102i	−0.356123	+	0.934439i	$0.615902\pi$
$968$	33.7180	+	53.3208i	1.08374	+	1.71380i
$969$	−24.8693	+	33.0950i	−0.798916	+	1.06316i
$970$	−0.239685	+	0.456681i	−0.00769582	+	0.0146632i
$971$	−9.17194	−	44.9271i	−0.294341	−	1.44178i	−0.810727	−	0.585424i	$-0.800928\pi$
$971$	−9.17194	−	44.9271i	−0.294341	−	1.44178i	0.516386	−	0.856356i	$-0.327277\pi$
$972$	−1.42254	−	0.114840i	−0.0456281	−	0.00368348i
$973$	−8.99775	+	2.60623i	−0.288455	+	0.0835519i
$974$	25.2046	−	13.2284i	0.807606	−	0.423864i
$975$	−3.44824	+	3.08872i	−0.110432	+	0.0989181i
$976$	0.263358	+	0.138221i	0.00842987	+	0.00442434i
$977$	22.0494	+	4.50141i	0.705421	+	0.144013i	0.539326	−	0.842097i	$-0.318679\pi$
$977$	22.0494	+	4.50141i	0.705421	+	0.144013i	0.166095	+	0.986110i	$0.446884\pi$
$978$	−4.57750	+	3.43977i	−0.146372	+	0.109992i
$979$	0.0573582	−	1.42333i	0.00183317	−	0.0454898i
$980$	1.64085	+	0.622293i	0.0524151	+	0.0198784i
$981$	1.02397	+	0.296596i	0.0326928	+	0.00946959i
$982$	−1.24143	+	0.253439i	−0.0396155	+	0.00808756i
$983$	−5.60869	+	6.33090i	−0.178889	+	0.201924i	−0.831115	−	0.556101i	$-0.812297\pi$
$983$	−5.60869	+	6.33090i	−0.178889	+	0.201924i	0.652226	+	0.758025i	$0.273835\pi$
$984$	5.61790	+	6.88068i	0.179092	+	0.219348i
$985$	0.420291	+	10.4294i	0.0133916	+	0.332309i
$986$	−10.1688	+	30.4594i	−0.323842	+	0.970024i
$987$	10.1912	+	9.02858i	0.324388	+	0.287383i
$988$	19.4719	−	22.2230i	0.619483	−	0.707009i
$989$	33.1439	−	29.3629i	1.05391	−	0.933686i
$990$	3.39878	+	7.97724i	0.108020	+	0.253533i
$991$	17.5632	+	30.4204i	0.557914	+	0.966335i	0.997670	+	0.0682178i	$0.0217313\pi$
$991$	17.5632	+	30.4204i	0.557914	+	0.966335i	−0.439757	+	0.898117i	$0.644935\pi$
$992$	−27.4611	+	47.5641i	−0.871892	+	1.51016i
$993$	−30.0429	−	3.64786i	−0.953382	−	0.115761i
$994$	−6.12434	+	2.90604i	−0.194252	+	0.0921739i
$995$	−28.0335	−	16.1852i	−0.888723	−	0.513104i
$996$	9.94466	−	6.86430i	0.315109	−	0.217504i
$997$	−11.2602	−	4.79752i	−0.356614	−	0.151939i	0.206227	−	0.978504i	$-0.433881\pi$
$997$	−11.2602	−	4.79752i	−0.356614	−	0.151939i	−0.562841	+	0.826565i	$0.690292\pi$
$998$	−12.6639	+	2.05808i	−0.400868	+	0.0651474i
$999$	−3.52370	−	4.68920i	−0.111485	−	0.148360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.127.9	yes	336
169.4	even	78	inner	507.2.t.a.4.9	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.4.9	✓	336	169.4	even	78	inner
507.2.t.a.127.9	yes	336	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.756241 - 0.0304755i) q^{2} +(0.278217 + 0.960518i) q^{3} +(-1.42254 + 0.114840i) q^{4} +(-1.80244 + 0.683575i) q^{5} +(0.239672 + 0.717904i) q^{6} +(0.988668 - 2.32049i) q^{7} +(-2.57496 + 0.312656i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})\)	\(q+(0.756241 - 0.0304755i) q^{2} +(0.278217 + 0.960518i) q^{3} +(-1.42254 + 0.114840i) q^{4} +(-1.80244 + 0.683575i) q^{5} +(0.239672 + 0.717904i) q^{6} +(0.988668 - 2.32049i) q^{7} +(-2.57496 + 0.312656i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(-1.34225 + 0.571877i) q^{10} +(-3.17644 + 5.02314i) q^{11} +(-0.506082 - 1.33443i) q^{12} +(0.984160 - 3.46863i) q^{13} +(0.676953 - 1.78498i) q^{14} +(-1.15806 - 1.54109i) q^{15} +(0.879621 - 0.142952i) q^{16} +(-6.63268 - 2.82592i) q^{17} +(-0.622879 + 0.429942i) q^{18} +(-4.97273 - 2.87100i) q^{19} +(2.48555 - 1.17941i) q^{20} +(2.50394 + 0.304033i) q^{21} +(-2.24907 + 3.89551i) q^{22} +(2.77663 + 4.80926i) q^{23} +(-1.01671 - 2.38631i) q^{24} +(-0.961042 + 0.851409i) q^{25} +(0.638554 - 2.65312i) q^{26} +(-0.748511 - 0.663123i) q^{27} +(-1.13994 + 3.41453i) q^{28} +(-0.236964 - 5.88019i) q^{29} +(-0.922735 - 1.13014i) q^{30} +(-6.21270 + 7.01269i) q^{31} +(5.74375 - 1.17259i) q^{32} +(-5.70856 - 1.65350i) q^{33} +(-5.10202 - 1.93494i) q^{34} +(-0.195785 + 4.85837i) q^{35} +(1.14094 - 0.857362i) q^{36} +(5.74704 + 1.17327i) q^{37} +(-3.84807 - 2.01962i) q^{38} +(3.60550 - 0.0197311i) q^{39} +(4.42748 - 2.32372i) q^{40} +(-3.28934 + 0.952768i) q^{41} +(1.90284 + 0.153613i) q^{42} +(-1.59494 - 7.81251i) q^{43} +(3.94177 - 7.51042i) q^{44} +(1.15806 - 1.54109i) q^{45} +(2.24636 + 3.55234i) q^{46} +(4.44238 + 3.06635i) q^{47} +(0.382034 + 0.805120i) q^{48} +(0.441869 + 0.460034i) q^{49} +(-0.700832 + 0.673158i) q^{50} +(0.869021 - 7.15703i) q^{51} +(-1.00167 + 5.04730i) q^{52} +(1.15493 + 9.51172i) q^{53} +(-0.586263 - 0.478669i) q^{54} +(2.29165 - 11.2252i) q^{55} +(-1.82026 + 6.28427i) q^{56} +(1.37415 - 5.57516i) q^{57} +(-0.358403 - 4.43962i) q^{58} +(0.547602 - 3.36953i) q^{59} +(1.82436 + 2.05928i) q^{60} +(0.266815 + 0.200498i) q^{61} +(-4.48458 + 5.49261i) q^{62} +(0.404610 + 2.48966i) q^{63} +(2.57739 - 0.635269i) q^{64} +(0.597183 + 6.92475i) q^{65} +(-4.36743 - 1.07648i) q^{66} +(-0.813674 + 10.0792i) q^{67} +(9.75980 + 3.25830i) q^{68} +(-3.84688 + 4.00502i) q^{69} +3.68006i q^{70} +(-2.56094 - 2.45981i) q^{71} +(2.00922 - 1.64048i) q^{72} +(2.44727 + 4.66288i) q^{73} +(4.38190 + 0.712128i) q^{74} +(-1.08517 - 0.686222i) q^{75} +(7.40362 + 3.51306i) q^{76} +(8.51569 + 12.3371i) q^{77} +(2.72602 - 0.124801i) q^{78} +(0.769740 - 1.11516i) q^{79} +(-1.48774 + 0.858949i) q^{80} +(0.428693 - 0.903450i) q^{81} +(-2.45849 + 0.820766i) q^{82} +(2.02625 + 8.22083i) q^{83} +(-3.59687 - 0.144949i) q^{84} +(13.8867 + 0.559616i) q^{85} +(-1.44425 - 5.85953i) q^{86} +(5.58210 - 1.86358i) q^{87} +(6.60868 - 13.9275i) q^{88} +(-0.207571 + 0.119841i) q^{89} +(0.828804 - 1.20073i) q^{90} +(-7.07592 - 5.71306i) q^{91} +(-4.50217 - 6.52252i) q^{92} +(-8.46429 - 4.01636i) q^{93} +(3.45295 + 2.18352i) q^{94} +(10.9256 + 1.77558i) q^{95} +(2.72431 + 5.19074i) q^{96} +(0.273825 - 0.223571i) q^{97} +(0.348179 + 0.334430i) q^{98} -5.94321i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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