LMFDB - Embedded newform 462.2.bf.a.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(5,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 12]))

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

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

chi := DirichletCharacter("462.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bf (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	462.5
Dual form			462.2.bf.a.185.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207912 - 0.978148i) q^{2} +(-1.62450 + 0.600840i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.383830 - 0.426287i) q^{5} +(0.249958 + 1.71392i) q^{6} +(-2.12466 + 1.57664i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.27798 - 1.95213i) q^{9} +O(q^{10})$	\(q+(0.207912 - 0.978148i) q^{2} +(-1.62450 + 0.600840i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.383830 - 0.426287i) q^{5} +(0.249958 + 1.71392i) q^{6} +(-2.12466 + 1.57664i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.27798 - 1.95213i) q^{9} +(-0.496774 + 0.286813i) q^{10} +(2.05262 + 2.60514i) q^{11} +(1.72844 + 0.111848i) q^{12} +(5.25730 - 1.70820i) q^{13} +(1.10045 + 2.40604i) q^{14} +(0.879662 + 0.461881i) q^{15} +(0.669131 + 0.743145i) q^{16} +(1.80521 - 0.383709i) q^{17} +(-1.43585 - 2.63407i) q^{18} +(-2.38460 - 5.35590i) q^{19} +(0.177260 + 0.545550i) q^{20} +(2.50420 - 3.83784i) q^{21} +(2.97498 - 1.46612i) q^{22} +(6.17919 + 3.56755i) q^{23} +(0.468766 - 1.66741i) q^{24} +(0.488248 - 4.64537i) q^{25} +(-0.577817 - 5.49757i) q^{26} +(-2.52766 + 4.53993i) q^{27} +(2.58226 - 0.576157i) q^{28} +(4.25665 + 5.85878i) q^{29} +(0.634680 - 0.764409i) q^{30} +(1.57061 + 1.41418i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.89974 - 2.99875i) q^{33} -1.84554i q^{34} +(1.48761 + 0.300553i) q^{35} +(-2.87504 + 0.856816i) q^{36} +(-0.0798338 - 0.759568i) q^{37} +(-5.73465 + 1.21894i) q^{38} +(-7.51411 + 5.93376i) q^{39} +(0.570483 - 0.0599602i) q^{40} +(1.20627 + 0.876408i) q^{41} +(-3.23332 - 3.24741i) q^{42} +7.77598 q^{43} +(-0.815553 - 3.21479i) q^{44} +(-1.70652 - 0.221789i) q^{45} +(4.77432 - 5.30242i) q^{46} +(0.407668 - 0.181505i) q^{47} +(-1.53351 - 0.805196i) q^{48} +(2.02839 - 6.69967i) q^{49} +(-4.44234 - 1.44340i) q^{50} +(-2.70201 + 1.70797i) q^{51} +(-5.49757 - 0.577817i) q^{52} +(2.59005 + 2.33210i) q^{53} +(3.91519 + 3.41633i) q^{54} +(0.322681 - 1.87494i) q^{55} +(-0.0266852 - 2.64562i) q^{56} +(7.09182 + 7.26788i) q^{57} +(6.61576 - 2.94552i) q^{58} +(-9.56549 - 4.25883i) q^{59} +(-0.615747 - 0.779740i) q^{60} +(-0.468853 + 0.422157i) q^{61} +(1.70983 - 1.24226i) q^{62} +(-1.76214 + 7.73918i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-2.74609 - 1.58546i) q^{65} +(-3.95194 + 4.16920i) q^{66} +(2.30807 + 3.99770i) q^{67} +(-1.80521 - 0.383709i) q^{68} +(-12.1816 - 2.08278i) q^{69} +(0.603277 - 1.39262i) q^{70} +(7.77727 + 2.52699i) q^{71} +(0.240338 + 2.99036i) q^{72} +(-5.15099 + 11.5693i) q^{73} +(-0.759568 - 0.0798338i) q^{74} +(1.99796 + 7.83974i) q^{75} +5.86276i q^{76} +(-8.46850 - 2.29880i) q^{77} +(4.24182 + 8.58360i) q^{78} +(-10.3411 - 2.19806i) q^{79} +(0.0599602 - 0.570483i) q^{80} +(1.37841 - 8.89382i) q^{81} +(1.10805 - 0.997697i) q^{82} +(1.54533 - 4.75602i) q^{83} +(-3.84869 + 2.48749i) q^{84} +(-0.856463 - 0.622257i) q^{85} +(1.61672 - 7.60606i) q^{86} +(-10.4351 - 6.96000i) q^{87} +(-3.31410 + 0.129338i) q^{88} +(-6.63333 + 11.4893i) q^{89} +(-0.571749 + 1.62312i) q^{90} +(-8.47676 + 11.9182i) q^{91} +(-4.19391 - 5.77243i) q^{92} +(-3.40114 - 1.35365i) q^{93} +(-0.0927802 - 0.436497i) q^{94} +(-1.36787 + 3.07228i) q^{95} +(-1.10644 + 1.33259i) q^{96} +(3.18905 - 1.03619i) q^{97} +(-6.13154 - 3.37701i) q^{98} +(9.76139 + 1.92750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$3$	−1.62450	+	0.600840i	−0.937904	+	0.346895i
$3$	−1.62450	+	0.600840i	−0.937904	+	0.346895i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	−0.383830	−	0.426287i	−0.171654	−	0.190641i	0.651179	−	0.758924i	$-0.274275\pi$
$5$	−0.383830	−	0.426287i	−0.171654	−	0.190641i	−0.822833	+	0.568283i	$0.807608\pi$
$6$	0.249958	+	1.71392i	0.102045	+	0.699705i
$7$	−2.12466	+	1.57664i	−0.803047	+	0.595915i
$7$	−2.12466	+	1.57664i	−0.803047	+	0.595915i
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	2.27798	−	1.95213i	0.759328	−	0.650709i
$10$	−0.496774	+	0.286813i	−0.157094	+	0.0906982i
$11$	2.05262	+	2.60514i	0.618887	+	0.785480i
$11$	2.05262	+	2.60514i	0.618887	+	0.785480i
$12$	1.72844	+	0.111848i	0.498956	+	0.0322877i
$13$	5.25730	−	1.70820i	1.45811	−	0.473769i	0.530619	−	0.847611i	$-0.321960\pi$
$13$	5.25730	−	1.70820i	1.45811	−	0.473769i	0.927493	+	0.373841i	$0.121960\pi$
$14$	1.10045	+	2.40604i	0.294107	+	0.643041i
$15$	0.879662	+	0.461881i	0.227128	+	0.119257i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	1.80521	−	0.383709i	0.437827	−	0.0930630i	0.0162757	−	0.999868i	$-0.494819\pi$
$17$	1.80521	−	0.383709i	0.437827	−	0.0930630i	0.421551	+	0.906805i	$0.361486\pi$
$18$	−1.43585	−	2.63407i	−0.338433	−	0.620857i
$19$	−2.38460	−	5.35590i	−0.547065	−	1.22873i	−0.949641	−	0.313341i	$-0.898552\pi$
$19$	−2.38460	−	5.35590i	−0.547065	−	1.22873i	0.402576	−	0.915387i	$-0.368115\pi$
$20$	0.177260	+	0.545550i	0.0396366	+	0.121989i
$21$	2.50420	−	3.83784i	0.546461	−	0.837484i
$22$	2.97498	−	1.46612i	0.634267	−	0.312579i
$23$	6.17919	+	3.56755i	1.28845	+	0.743887i	0.978378	−	0.206827i	$-0.0663136\pi$
$23$	6.17919	+	3.56755i	1.28845	+	0.743887i	0.310072	+	0.950713i	$0.399647\pi$
$24$	0.468766	−	1.66741i	0.0956864	−	0.340359i
$25$	0.488248	−	4.64537i	0.0976495	−	0.929073i
$26$	−0.577817	−	5.49757i	−0.113319	−	1.07816i
$27$	−2.52766	+	4.53993i	−0.486449	+	0.873709i
$28$	2.58226	−	0.576157i	0.488000	−	0.108883i
$29$	4.25665	+	5.85878i	0.790440	+	1.08795i	0.994053	+	0.108896i	$0.0347316\pi$
$29$	4.25665	+	5.85878i	0.790440	+	1.08795i	−0.203613	+	0.979051i	$0.565268\pi$
$30$	0.634680	−	0.764409i	0.115876	−	0.139561i
$31$	1.57061	+	1.41418i	0.282089	+	0.253994i	0.798013	−	0.602640i	$-0.205885\pi$
$31$	1.57061	+	1.41418i	0.282089	+	0.253994i	−0.515924	+	0.856635i	$0.672551\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−4.89974	−	2.99875i	−0.852936	−	0.522016i
$34$		−	1.84554i		−	0.316507i
$35$	1.48761	+	0.300553i	0.251453	+	0.0508027i
$36$	−2.87504	+	0.856816i	−0.479174	+	0.142803i
$37$	−0.0798338	−	0.759568i	−0.0131246	−	0.124872i	0.985998	−	0.166758i	$-0.0533300\pi$
$37$	−0.0798338	−	0.759568i	−0.0131246	−	0.124872i	−0.999122	+	0.0418862i	$0.986663\pi$
$38$	−5.73465	+	1.21894i	−0.930283	+	0.197738i
$39$	−7.51411	+	5.93376i	−1.20322	+	0.950162i
$40$	0.570483	−	0.0599602i	0.0902013	−	0.00948054i
$41$	1.20627	+	0.876408i	0.188388	+	0.136872i	0.677982	−	0.735079i	$-0.262855\pi$
$41$	1.20627	+	0.876408i	0.188388	+	0.136872i	−0.489594	+	0.871951i	$0.662855\pi$
$42$	−3.23332	−	3.24741i	−0.498912	−	0.501086i
$43$	7.77598			1.18583			0.592913	−	0.805267i	$-0.297978\pi$
$43$	7.77598			1.18583			0.592913	+	0.805267i	$0.297978\pi$
$44$	−0.815553	−	3.21479i	−0.122949	−	0.484648i
$45$	−1.70652	−	0.221789i	−0.254394	−	0.0330623i
$46$	4.77432	−	5.30242i	0.703935	−	0.781799i
$47$	0.407668	−	0.181505i	0.0594645	−	0.0264753i	−0.376789	−	0.926299i	$-0.622972\pi$
$47$	0.407668	−	0.181505i	0.0594645	−	0.0264753i	0.436253	+	0.899824i	$0.356305\pi$
$48$	−1.53351	−	0.805196i	−0.221343	−	0.116220i
$49$	2.02839	−	6.69967i	0.289770	−	0.957096i
$50$	−4.44234	−	1.44340i	−0.628242	−	0.204128i
$51$	−2.70201	+	1.70797i	−0.378357	+	0.239164i
$52$	−5.49757	−	0.577817i	−0.762375	−	0.0801289i
$53$	2.59005	+	2.33210i	0.355771	+	0.320338i	0.827564	−	0.561372i	$-0.189726\pi$
$53$	2.59005	+	2.33210i	0.355771	+	0.320338i	−0.471792	+	0.881710i	$0.656393\pi$
$54$	3.91519	+	3.41633i	0.532789	+	0.464904i
$55$	0.322681	−	1.87494i	0.0435103	−	0.252816i
$56$	−0.0266852	−	2.64562i	−0.00356596	−	0.353535i
$57$	7.09182	+	7.26788i	0.939334	+	0.962655i
$58$	6.61576	−	2.94552i	0.868691	−	0.386766i
$59$	−9.56549	−	4.25883i	−1.24532	−	0.554453i	−0.325036	−	0.945702i	$-0.605376\pi$
$59$	−9.56549	−	4.25883i	−1.24532	−	0.554453i	−0.920285	+	0.391249i	$0.872043\pi$
$60$	−0.615747	−	0.779740i	−0.0794926	−	0.100664i
$61$	−0.468853	+	0.422157i	−0.0600304	+	0.0540516i	−0.698600	−	0.715513i	$-0.746193\pi$
$61$	−0.468853	+	0.422157i	−0.0600304	+	0.0540516i	0.638569	+	0.769564i	$0.279527\pi$
$62$	1.70983	−	1.24226i	0.217148	−	0.157767i
$63$	−1.76214	+	7.73918i	−0.222009	+	0.975045i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−2.74609	−	1.58546i	−0.340611	−	0.196652i
$66$	−3.95194	+	4.16920i	−0.486450	+	0.513193i
$67$	2.30807	+	3.99770i	0.281976	+	0.488396i	0.971871	−	0.235513i	$-0.0756769\pi$
$67$	2.30807	+	3.99770i	0.281976	+	0.488396i	−0.689896	+	0.723909i	$0.742344\pi$
$68$	−1.80521	−	0.383709i	−0.218913	−	0.0465315i
$69$	−12.1816	−	2.08278i	−1.46649	−	0.250737i
$70$	0.603277	−	1.39262i	0.0721054	−	0.166450i
$71$	7.77727	+	2.52699i	0.922992	+	0.299898i	0.731694	−	0.681634i	$-0.238730\pi$
$71$	7.77727	+	2.52699i	0.922992	+	0.299898i	0.191299	+	0.981532i	$0.438730\pi$
$72$	0.240338	+	2.99036i	0.0283241	+	0.352417i
$73$	−5.15099	+	11.5693i	−0.602878	+	1.35409i	0.311895	+	0.950117i	$0.399036\pi$
$73$	−5.15099	+	11.5693i	−0.602878	+	1.35409i	−0.914773	+	0.403969i	$0.867630\pi$
$74$	−0.759568	−	0.0798338i	−0.0882979	−	0.00928049i
$75$	1.99796	+	7.83974i	0.230705	+	0.905255i
$76$			5.86276i			0.672505i
$77$	−8.46850	−	2.29880i	−0.965075	−	0.261973i
$78$	4.24182	+	8.58360i	0.480291	+	0.971902i
$79$	−10.3411	−	2.19806i	−1.16346	−	0.247301i	−0.414584	−	0.910011i	$-0.636073\pi$
$79$	−10.3411	−	2.19806i	−1.16346	−	0.247301i	−0.748876	+	0.662710i	$0.769406\pi$
$80$	0.0599602	−	0.570483i	0.00670376	−	0.0637820i
$81$	1.37841	−	8.89382i	0.153157	−	0.988202i
$82$	1.10805	−	0.997697i	0.122364	−	0.110177i
$83$	1.54533	−	4.75602i	0.169622	−	0.522041i	−0.829726	−	0.558172i	$-0.811503\pi$
$83$	1.54533	−	4.75602i	0.169622	−	0.522041i	0.999347	+	0.0361301i	$0.0115031\pi$
$84$	−3.84869	+	2.48749i	−0.419926	+	0.271407i
$85$	−0.856463	−	0.622257i	−0.0928965	−	0.0674933i
$86$	1.61672	−	7.60606i	0.174335	−	0.820182i
$87$	−10.4351	−	6.96000i	−1.11876	−	0.746190i
$88$	−3.31410	+	0.129338i	−0.353284	+	0.0137875i
$89$	−6.63333	+	11.4893i	−0.703132	+	1.21786i	0.264229	+	0.964460i	$0.414882\pi$
$89$	−6.63333	+	11.4893i	−0.703132	+	1.21786i	−0.967361	+	0.253401i	$0.918451\pi$
$90$	−0.571749	+	1.62312i	−0.0602676	+	0.171092i
$91$	−8.47676	+	11.9182i	−0.888606	+	1.24937i
$92$	−4.19391	−	5.77243i	−0.437246	−	0.601817i
$93$	−3.40114	−	1.35365i	−0.352682	−	0.140367i
$94$	−0.0927802	−	0.436497i	−0.00956955	−	0.0450212i
$95$	−1.36787	+	3.07228i	−0.140340	+	0.315210i
$96$	−1.10644	+	1.33259i	−0.112925	+	0.136007i
$97$	3.18905	−	1.03619i	0.323799	−	0.105209i	−0.142607	−	0.989779i	$-0.545549\pi$
$97$	3.18905	−	1.03619i	0.323799	−	0.105209i	0.466406	+	0.884571i	$0.345549\pi$
$98$	−6.13154	−	3.37701i	−0.619379	−	0.341129i
$99$	9.76139	+	1.92750i	0.981057	+	0.193721i
$100$	−2.33548	+	4.04516i	−0.233548	+	0.404516i
$101$	11.5500	−	12.8275i	1.14926	−	1.27639i	0.193878	−	0.981026i	$-0.437893\pi$
$101$	11.5500	−	12.8275i	1.14926	−	1.27639i	0.955386	−	0.295361i	$-0.0954400\pi$
$102$	1.10887	+	2.99807i	0.109795	+	0.296853i
$103$	8.74670	−	0.919315i	0.861838	−	0.0905828i	0.336712	−	0.941608i	$-0.390685\pi$
$103$	8.74670	−	0.919315i	0.861838	−	0.0905828i	0.525125	+	0.851025i	$0.324018\pi$
$104$	−1.70820	+	5.25730i	−0.167503	+	0.515520i
$105$	−2.59721	+	0.405570i	−0.253462	+	0.0395796i
$106$	2.81964	−	2.04859i	0.273867	−	0.198976i
$107$	6.01554	+	13.5111i	0.581544	+	1.30617i	0.929557	+	0.368680i	$0.120190\pi$
$107$	6.01554	+	13.5111i	0.581544	+	1.30617i	−0.348012	+	0.937490i	$0.613143\pi$
$108$	4.15569	−	3.11934i	0.399881	−	0.300158i
$109$	−8.50953	−	14.7389i	−0.815065	−	1.41173i	−0.909281	−	0.416182i	$-0.863368\pi$
$109$	−8.50953	−	14.7389i	−0.815065	−	1.41173i	0.0942163	−	0.995552i	$-0.469965\pi$
$110$	−1.76688	−	0.705451i	−0.168465	−	0.0672621i
$111$	0.586068	+	1.18595i	0.0556271	+	0.112565i
$112$	−2.59335	−	0.523953i	−0.245049	−	0.0495089i
$113$	−3.84599	+	5.29355i	−0.361800	+	0.497975i	−0.950649	−	0.310268i	$-0.899581\pi$
$113$	−3.84599	+	5.29355i	−0.361800	+	0.497975i	0.588849	+	0.808243i	$0.299581\pi$
$114$	8.58353	−	5.42577i	0.803922	−	0.508170i
$115$	−0.850958	−	4.00344i	−0.0793522	−	0.373323i
$116$	−1.50566	−	7.08359i	−0.139797	−	0.657695i
$117$	8.64141	−	14.1541i	0.798899	−	1.30855i
$118$	−6.15454	+	8.47100i	−0.566572	+	0.779819i
$119$	−3.23049	+	3.66142i	−0.296138	+	0.335642i
$120$	−0.890722	+	0.440174i	−0.0813114	+	0.0401822i
$121$	−2.57352	+	10.6947i	−0.233957	+	0.972247i
$122$	0.315452	+	0.546378i	0.0285597	+	0.0494668i
$123$	−2.48617	−	0.698946i	−0.224170	−	0.0630218i
$124$	−0.859622	−	1.93074i	−0.0771963	−	0.173386i
$125$	−4.48803	+	3.26074i	−0.401421	+	0.291650i
$126$	7.20369	+	3.33270i	0.641755	+	0.296901i
$127$	−3.76408	+	11.5846i	−0.334008	+	1.02797i	0.633201	+	0.773987i	$0.281741\pi$
$127$	−3.76408	+	11.5846i	−0.334008	+	1.02797i	−0.967209	+	0.253983i	$0.918259\pi$
$128$	−0.994522	+	0.104528i	−0.0879041	+	0.00923910i
$129$	−12.6321	+	4.67212i	−1.11219	+	0.411357i
$130$	−2.12176	+	2.35645i	−0.186090	+	0.206674i
$131$	1.36096	−	2.35725i	0.118908	−	0.205954i	−0.800427	−	0.599430i	$-0.795394\pi$
$131$	1.36096	−	2.35725i	0.118908	−	0.205954i	0.919335	+	0.393476i	$0.128727\pi$
$132$	3.25644	+	4.73240i	0.283436	+	0.411903i
$133$	13.5108	+	7.61982i	1.17154	+	0.660723i
$134$	4.39021	−	1.42647i	0.379256	−	0.123228i
$135$	2.90550	−	0.665053i	0.250066	−	0.0572386i
$136$	−0.750647	+	1.68598i	−0.0643675	+	0.144572i
$137$	−1.48542	−	6.98837i	−0.126908	−	0.597057i	−0.994933	−	0.100537i	$-0.967944\pi$
$137$	−1.48542	−	6.98837i	−0.126908	−	0.597057i	0.868025	−	0.496521i	$-0.165389\pi$
$138$	−4.56996	+	11.4824i	−0.389021	+	0.977444i
$139$	−4.87086	−	6.70416i	−0.413141	−	0.568639i	0.550840	−	0.834611i	$-0.314307\pi$
$139$	−4.87086	−	6.70416i	−0.413141	−	0.568639i	−0.963981	+	0.265971i	$0.914307\pi$
$140$	−1.23676	−	0.879635i	−0.104525	−	0.0743428i
$141$	−0.553200	+	0.539798i	−0.0465878	+	0.0454592i
$142$	4.08875	−	7.08193i	0.343121	−	0.594302i
$143$	15.2413	+	10.1897i	1.27454	+	0.852107i
$144$	2.97498	+	0.386644i	0.247915	+	0.0322203i
$145$	0.863688	−	4.06333i	0.0717254	−	0.337441i
$146$	10.2455	+	7.44382i	0.847927	+	0.616055i
$147$	0.730314	+	12.1023i	0.0602353	+	0.998184i
$148$	−0.236012	+	0.726371i	−0.0194001	+	0.0597073i
$149$	9.17923	−	8.26501i	0.751991	−	0.677096i	−0.201171	−	0.979556i	$-0.564475\pi$
$149$	9.17923	−	8.26501i	0.751991	−	0.677096i	0.953162	+	0.302460i	$0.0978079\pi$
$150$	8.08383	−	0.324330i	0.660042	−	0.0264814i
$151$	2.43691	−	23.1856i	0.198313	−	1.88682i	−0.215567	−	0.976489i	$-0.569160\pi$
$151$	2.43691	−	23.1856i	0.198313	−	1.88682i	0.413880	−	0.910331i	$-0.364173\pi$
$152$	5.73465	+	1.21894i	0.465141	+	0.0988689i
$153$	3.36318	−	4.39807i	0.271897	−	0.355563i
$154$	−4.00927	+	7.80549i	−0.323076	+	0.628985i
$155$		−	1.21234i		−	0.0973771i
$156$	9.27796	−	2.36449i	0.742831	−	0.189311i
$157$	10.9913	+	1.15523i	0.877201	+	0.0921975i	0.532415	−	0.846484i	$-0.321285\pi$
$157$	10.9913	+	1.15523i	0.877201	+	0.0921975i	0.344786	+	0.938681i	$0.387951\pi$
$158$	−4.30005	+	9.65808i	−0.342094	+	0.768355i
$159$	−5.60875	−	2.23227i	−0.444803	−	0.177031i
$160$	−0.545550	−	0.177260i	−0.0431295	−	0.0140136i
$161$	−18.7535	+	2.16252i	−1.47798	+	0.170430i
$162$	−8.41288	−	3.19742i	−0.660978	−	0.251213i
$163$	7.47060	+	1.58793i	0.585143	+	0.124376i	0.490965	−	0.871179i	$-0.336644\pi$
$163$	7.47060	+	1.58793i	0.585143	+	0.124376i	0.0941779	+	0.995555i	$0.469978\pi$
$164$	−0.745517	−	1.29127i	−0.0582151	−	0.100832i
$165$	0.602343	+	3.23971i	0.0468923	+	0.252211i
$166$	−4.33080	−	2.50039i	−0.336135	−	0.194068i
$167$	−4.73526	−	14.5736i	−0.366425	−	1.12774i	−0.949084	−	0.315024i	$-0.897988\pi$
$167$	−4.73526	−	14.5736i	−0.366425	−	1.12774i	0.582659	−	0.812717i	$-0.302012\pi$
$168$	1.63294	+	4.28176i	0.125984	+	0.330345i
$169$	14.2040	−	10.3198i	1.09261	−	0.793831i
$170$	−0.786728	+	0.708373i	−0.0603393	+	0.0543297i
$171$	−15.8875	−	7.54561i	−1.21495	−	0.577027i
$172$	−7.10371	−	3.16278i	−0.541653	−	0.241159i
$173$	−7.41533	+	3.30152i	−0.563777	+	0.251010i	−0.668778	−	0.743462i	$-0.733182\pi$
$173$	−7.41533	+	3.30152i	−0.563777	+	0.251010i	0.105001	+	0.994472i	$0.466516\pi$
$174$	−8.97749	+	8.76001i	−0.680582	+	0.664094i
$175$	6.28672	+	10.6396i	0.475232	+	0.804281i
$176$	−0.562528	+	3.26857i	−0.0424022	+	0.246378i
$177$	18.0980	+	1.17113i	1.36033	+	0.0880276i
$178$	9.85906	+	8.87713i	0.738968	+	0.665369i
$179$	10.7035	+	1.12498i	0.800016	+	0.0840851i	0.495709	−	0.868489i	$-0.334908\pi$
$179$	10.7035	+	1.12498i	0.800016	+	0.0840851i	0.304307	+	0.952574i	$0.401575\pi$
$180$	1.46878	+	0.896721i	0.109476	+	0.0668376i
$181$	0.702191	+	0.228156i	0.0521934	+	0.0169587i	0.334997	−	0.942219i	$-0.391265\pi$
$181$	0.702191	+	0.228156i	0.0521934	+	0.0169587i	−0.282804	+	0.959178i	$0.591265\pi$
$182$	9.89537	+	10.7695i	0.733493	+	0.798286i
$183$	0.508001	−	0.967498i	0.0375525	−	0.0715195i
$184$	−6.51825	+	2.90211i	−0.480532	+	0.213946i
$185$	−0.293151	+	0.325577i	−0.0215529	+	0.0239369i
$186$	−2.03121	+	3.04538i	−0.148935	+	0.223298i
$187$	4.70501	+	3.91521i	0.344065	+	0.286309i
$188$	−0.446248			−0.0325460
$189$	−1.78741	−	13.6310i	−0.130015	−	0.991512i
$190$	2.72075	+	1.97674i	0.197384	+	0.143408i
$191$	−20.5339	+	2.15820i	−1.48578	+	0.156162i	−0.812386	−	0.583121i	$-0.801832\pi$
$191$	−20.5339	+	2.15820i	−1.48578	+	0.156162i	−0.673395	+	0.739282i	$0.735165\pi$
$192$	1.07343	+	1.35932i	0.0774681	+	0.0981004i
$193$	−7.45383	+	1.58436i	−0.536539	+	0.114045i	−0.468209	−	0.883618i	$-0.655100\pi$
$193$	−7.45383	+	1.58436i	−0.536539	+	0.114045i	−0.0683300	+	0.997663i	$0.521767\pi$
$194$	−0.350501	−	3.33480i	−0.0251645	−	0.239425i
$195$	5.41363	+	0.925609i	0.387678	+	0.0662842i
$196$	−4.57803	+	5.29543i	−0.327002	+	0.378245i
$197$		−	24.7824i		−	1.76567i	−0.469683	−	0.882835i	$-0.655632\pi$
$197$		−	24.7824i		−	1.76567i	0.469683	−	0.882835i	$-0.344368\pi$
$198$	3.91489	−	9.14733i	0.278219	−	0.650072i
$199$	−22.2678	+	12.8563i	−1.57852	+	0.911360i	−0.583456	+	0.812144i	$0.698300\pi$
$199$	−22.2678	+	12.8563i	−1.57852	+	0.911360i	−0.995066	+	0.0992159i	$0.968367\pi$
$200$	3.47119	+	3.12548i	0.245451	+	0.221005i
$201$	−6.15143	−	5.10746i	−0.433888	−	0.360253i
$202$	−10.1458	−	13.9646i	−0.713859	−	0.982543i
$203$	−18.2812	−	5.73671i	−1.28309	−	0.402638i
$204$	3.16310	−	0.461307i	0.221461	−	0.0322979i
$205$	−0.0894027	−	0.850610i	−0.00624416	−	0.0594092i
$206$	0.919315	−	8.74670i	0.0640517	−	0.609411i
$207$	21.0404	−	3.93572i	1.46241	−	0.273551i
$208$	4.78726	+	2.76392i	0.331937	+	0.191644i
$209$	9.05821	−	17.2058i	0.626569	−	1.19015i
$210$	−0.143282	+	2.62478i	−0.00988740	+	0.181127i
$211$	1.12878	+	3.47402i	0.0777082	+	0.239161i	0.982363	−	0.186984i	$-0.0598713\pi$
$211$	1.12878	+	3.47402i	0.0777082	+	0.239161i	−0.904655	+	0.426145i	$0.859871\pi$
$212$	−1.41758	−	3.18395i	−0.0973600	−	0.218674i
$213$	−14.1525	+	0.567809i	−0.969711	+	0.0389056i
$214$	14.4666	−	3.07497i	0.988915	−	0.210200i
$215$	−2.98466	−	3.31480i	−0.203552	−	0.226067i
$216$	−2.18715	−	4.71342i	−0.148817	−	0.320708i
$217$	−5.56667	−	0.528372i	−0.377890	−	0.0358682i
$218$	−16.1861	+	5.25918i	−1.09626	+	0.356196i
$219$	1.41646	−	21.8892i	0.0957158	−	1.47914i
$220$	−1.05739	+	1.58159i	−0.0712892	+	0.106631i
$221$	8.83506	−	5.10092i	0.594310	−	0.343125i
$222$	1.28188	−	0.326689i	0.0860343	−	0.0219259i
$223$	7.56718	−	10.4153i	0.506736	−	0.697462i	−0.476629	−	0.879105i	$-0.658141\pi$
$223$	7.56718	−	10.4153i	0.506736	−	0.697462i	0.983365	+	0.181643i	$0.0581414\pi$
$224$	−1.05169	+	2.42774i	−0.0702691	+	0.162211i
$225$	−7.95612	−	11.5352i	−0.530408	−	0.769012i
$226$	4.37825	+	4.86254i	0.291237	+	0.323451i
$227$	−8.77515	−	3.90695i	−0.582427	−	0.259313i	0.0943042	−	0.995543i	$-0.469937\pi$
$227$	−8.77515	−	3.90695i	−0.582427	−	0.259313i	−0.676731	+	0.736230i	$0.736604\pi$
$228$	−3.52258	−	9.52404i	−0.233289	−	0.630745i
$229$	3.22100	−	15.1536i	0.212850	−	1.00138i	−0.733862	−	0.679298i	$-0.762284\pi$
$229$	3.22100	−	15.1536i	0.212850	−	1.00138i	0.946712	−	0.322081i	$-0.104382\pi$
$230$	−4.09288			−0.269877
$231$	15.1383	−	1.35381i	0.996025	−	0.0890742i
$232$	−7.24185			−0.475450
$233$	−3.82624	+	18.0010i	−0.250665	+	1.17929i	0.655112	+	0.755532i	$0.272622\pi$
$233$	−3.82624	+	18.0010i	−0.250665	+	1.17929i	−0.905777	+	0.423755i	$0.860712\pi$
$234$	−12.0482	−	11.3954i	−0.787615	−	0.744940i
$235$	−0.233849	−	0.104116i	−0.0152546	−	0.00679179i
$236$	7.00629	+	7.78127i	0.456071	+	0.506518i
$237$	18.1197	−	2.64258i	1.17700	−	0.171654i
$238$	2.90975	+	3.92114i	0.188611	+	0.254170i
$239$	1.03027	−	1.41805i	0.0666429	−	0.0917261i	−0.774394	−	0.632703i	$-0.781945\pi$
$239$	1.03027	−	1.41805i	0.0666429	−	0.0917261i	0.841037	+	0.540977i	$0.181945\pi$
$240$	0.245364	+	0.962775i	0.0158382	+	0.0621469i
$241$	6.56869	−	3.79244i	0.423127	−	0.244292i	−0.273287	−	0.961932i	$-0.588111\pi$
$241$	6.56869	−	3.79244i	0.423127	−	0.244292i	0.696414	+	0.717640i	$0.254778\pi$
$242$	9.92595	+	4.74084i	0.638064	+	0.304753i
$243$	3.10454	+	15.2762i	0.199156	+	0.979968i
$244$	0.600025	−	0.194960i	0.0384127	−	0.0124810i
$245$	−3.63454	+	1.70686i	−0.232202	+	0.109047i
$246$	−1.20058	+	2.28652i	−0.0765459	+	0.145783i
$247$	−21.6855	−	24.0842i	−1.37982	−	1.53244i
$248$	−2.06728	+	0.439413i	−0.131272	+	0.0279028i
$249$	0.347231	+	8.65464i	0.0220049	+	0.548466i
$250$	2.25637	+	5.06790i	0.142706	+	0.320522i
$251$	2.79881	+	8.61385i	0.176659	+	0.543701i	0.999705	−	0.0242733i	$-0.00772720\pi$
$251$	2.79881	+	8.61385i	0.176659	+	0.543701i	−0.823046	+	0.567975i	$0.807727\pi$
$252$	4.75760	−	6.35336i	0.299701	−	0.400224i
$253$	3.38952	+	23.4205i	0.213097	+	1.47243i
$254$	10.5489	+	6.09040i	0.661896	+	0.382146i
$255$	1.76520	+	0.496258i	0.110541	+	0.0310769i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	2.55936	+	24.3507i	0.159649	+	1.51896i	0.721904	+	0.691993i	$0.243267\pi$
$257$	2.55936	+	24.3507i	0.159649	+	1.51896i	−0.562256	+	0.826964i	$0.690066\pi$
$258$	1.94367	+	13.3274i	0.121008	+	0.829728i
$259$	1.36719	+	1.48796i	0.0849529	+	0.0924571i
$260$	1.86382	+	2.56532i	0.115589	+	0.159095i
$261$	21.1336	+	5.03668i	1.30814	+	0.311762i
$262$	−2.02278	−	1.82132i	−0.124968	−	0.112522i
$263$	−6.50504	+	3.75568i	−0.401118	+	0.231585i	−0.686966	−	0.726689i	$-0.741058\pi$
$263$	−6.50504	+	3.75568i	−0.401118	+	0.231585i	0.285848	+	0.958275i	$0.407725\pi$
$264$	5.30604	−	2.20135i	0.326564	−	0.135484i
$265$		−	1.99924i		−	0.122812i
$266$	10.2624	−	11.6313i	0.629226	−	0.713162i
$267$	3.87262	−	22.6499i	0.237001	−	1.38615i
$268$	−0.482518	−	4.59085i	−0.0294745	−	0.280431i
$269$	−0.526248	+	0.111857i	−0.0320859	+	0.00682007i	−0.223927	−	0.974606i	$-0.571888\pi$
$269$	−0.526248	+	0.111857i	−0.0320859	+	0.00682007i	0.191841	+	0.981426i	$0.438554\pi$
$270$	−0.0464313	−	2.98028i	−0.00282572	−	0.181374i
$271$	−10.0781	+	1.05925i	−0.612202	+	0.0643450i	−0.405555	−	0.914071i	$-0.632922\pi$
$271$	−10.0781	+	1.05925i	−0.612202	+	0.0643450i	−0.206647	+	0.978416i	$0.566255\pi$
$272$	1.49307	+	1.08478i	0.0905307	+	0.0657744i
$273$	6.60953	−	24.4543i	0.400027	−	1.48004i
$274$	−7.14450			−0.431615
$275$	13.1040	−	8.26320i	0.790202	−	0.498290i
$276$	10.2813	+	6.85742i	0.618862	+	0.412768i
$277$	1.54921	−	1.72058i	0.0930833	−	0.103379i	−0.694803	−	0.719200i	$-0.744509\pi$
$277$	1.54921	−	1.72058i	0.0930833	−	0.103379i	0.787887	+	0.615820i	$0.211175\pi$
$278$	−7.57037	+	3.37054i	−0.454040	+	0.202152i
$279$	6.33848	+	0.155458i	0.379475	+	0.00930700i
$280$	−1.11755	+	1.02684i	−0.0667863	+	0.0613657i
$281$	8.20269	+	2.66521i	0.489331	+	0.158993i	0.543282	−	0.839550i	$-0.317181\pi$
$281$	8.20269	+	2.66521i	0.489331	+	0.158993i	−0.0539508	+	0.998544i	$0.517181\pi$
$282$	0.412986	+	0.653341i	0.0245929	+	0.0389059i
$283$	18.0712	+	1.89936i	1.07422	+	0.112905i	0.625085	−	0.780557i	$-0.285064\pi$
$283$	18.0712	+	1.89936i	1.07422	+	0.112905i	0.449139	+	0.893462i	$0.351731\pi$
$284$	−6.07707	−	5.47182i	−0.360608	−	0.324693i
$285$	0.376148	−	5.81278i	0.0222811	−	0.344320i
$286$	13.1359	−	12.7897i	0.776742	−	0.756270i
$287$	−3.94471	+	0.0397885i	−0.232849	+	0.00234864i
$288$	0.996728	−	2.82958i	0.0587328	−	0.166735i
$289$	−12.4187	+	5.52918i	−0.730514	+	0.325246i
$290$	−3.79497	−	1.68963i	−0.222848	−	0.0992184i
$291$	−4.55802	+	3.59939i	−0.267196	+	0.211000i
$292$	9.41132	−	8.47400i	0.550756	−	0.495903i
$293$	16.5539	−	12.0271i	0.967088	−	0.702630i	0.0123016	−	0.999924i	$-0.496084\pi$
$293$	16.5539	−	12.0271i	0.967088	−	0.702630i	0.954786	+	0.297294i	$0.0960842\pi$
$294$	11.9897	+	1.80186i	0.699254	+	0.105087i
$295$	1.85604	+	5.71231i	0.108063	+	0.332584i
$296$	0.661428	+	0.381876i	0.0384447	+	0.0221961i
$297$	−17.0155	+	2.73381i	−0.987338	+	0.158632i
$298$	−6.17593	−	10.6970i	−0.357762	−	0.619662i
$299$	38.5799	+	8.20041i	2.23113	+	0.474242i
$300$	1.36348	−	7.97461i	0.0787205	−	0.460414i
$301$	−16.5213	+	12.2599i	−0.952274	+	0.706651i
$302$	−22.1723	−	7.20422i	−1.27587	−	0.414556i
$303$	−11.0556	+	27.7780i	−0.635127	+	1.59580i
$304$	2.38460	−	5.35590i	0.136766	−	0.307182i
$305$	0.359920	+	0.0378291i	0.0206090	+	0.00216609i
$306$	−3.60272	−	4.20410i	−0.205954	−	0.240332i
$307$		−	12.1207i		−	0.691765i	−0.938278	−	0.345882i	$-0.887580\pi$
$307$		−	12.1207i		−	0.691765i	0.938278	−	0.345882i	$-0.112420\pi$
$308$	6.80135	+	5.54451i	0.387543	+	0.315928i
$309$	−13.6566	+	6.74879i	−0.776898	+	0.383925i
$310$	−1.18584	−	0.252059i	−0.0673513	−	0.0143160i
$311$	−3.41274	+	32.4701i	−0.193519	+	1.84121i	0.279486	+	0.960150i	$0.409836\pi$
$311$	−3.41274	+	32.4701i	−0.193519	+	1.84121i	−0.473005	+	0.881060i	$0.656831\pi$
$312$	−0.383829	−	9.56682i	−0.0217300	−	0.541614i
$313$	−12.7162	+	11.4497i	−0.718761	+	0.647175i	−0.945065	−	0.326881i	$-0.894002\pi$
$313$	−12.7162	+	11.4497i	−0.718761	+	0.647175i	0.226304	+	0.974057i	$0.427336\pi$
$314$	3.41521	−	10.5109i	0.192731	−	0.593166i
$315$	3.97547	−	2.21935i	0.223993	−	0.125046i
$316$	8.55299	+	6.21411i	0.481143	+	0.349571i
$317$	−0.777025	+	3.65561i	−0.0436421	+	0.205320i	−0.994566	−	0.104104i	$-0.966803\pi$
$317$	−0.777025	+	3.65561i	−0.0436421	+	0.205320i	0.950924	+	0.309423i	$0.100136\pi$
$318$	−3.34962	+	5.02207i	−0.187837	+	0.281624i
$319$	−6.52567	+	23.1150i	−0.365367	+	1.29419i
$320$	−0.286813	+	0.496774i	−0.0160333	+	0.0277705i
$321$	−17.8902	−	18.3344i	−0.998536	−	1.02333i
$322$	−1.78380	+	18.7933i	−0.0994073	+	1.04731i
$323$	−6.35980	−	8.75352i	−0.353869	−	0.487059i
$324$	−4.87668	+	7.56426i	−0.270927	+	0.420236i
$325$	−5.36835	−	25.2561i	−0.297782	−	1.40096i
$326$	3.10645	−	6.97720i	0.172050	−	0.386431i
$327$	22.6794	+	18.8305i	1.25418	+	1.04133i
$328$	−1.41806	+	0.460755i	−0.0782991	+	0.0254409i
$329$	−0.579988	+	1.02838i	−0.0319758	+	0.0566967i
$330$	3.29415	+	0.0843932i	0.181337	+	0.00464569i
$331$	−1.63784	+	2.83683i	−0.0900240	+	0.155926i	−0.907521	−	0.420007i	$-0.862028\pi$
$331$	−1.63784	+	2.83683i	−0.0900240	+	0.155926i	0.817497	+	0.575933i	$0.195361\pi$
$332$	−3.34617	+	3.71630i	−0.183645	+	0.203959i
$333$	−1.66463	−	1.57444i	−0.0912212	−	0.0862786i
$334$	−15.2397	+	1.60175i	−0.833878	+	0.0876441i
$335$	0.818258	−	2.51834i	0.0447062	−	0.137591i
$336$	4.52770	−	0.707030i	0.247007	−	0.0385716i
$337$	8.60418	−	6.25130i	0.468699	−	0.340530i	−0.328235	−	0.944596i	$-0.606454\pi$
$337$	8.60418	−	6.25130i	0.468699	−	0.340530i	0.796934	+	0.604066i	$0.206454\pi$
$338$	−7.14111	−	16.0392i	−0.388425	−	0.872418i
$339$	3.06722	−	10.9102i	0.166589	−	0.592560i
$340$	0.529323	+	0.916815i	0.0287066	+	0.0497213i
$341$	−0.460286	+	6.99443i	−0.0249259	+	0.378769i
$342$	−10.6839	+	13.9715i	−0.577720	+	0.755491i
$343$	6.25334	+	17.4326i	0.337649	+	0.941272i
$344$	−4.57061	+	6.29090i	−0.246431	+	0.339183i
$345$	3.78781	+	5.99229i	0.203929	+	0.322614i
$346$	1.68764	+	7.93971i	0.0907279	+	0.426841i
$347$	−5.41764	−	25.4880i	−0.290834	−	1.36827i	−0.844513	−	0.535536i	$-0.820110\pi$
$347$	−5.41764	−	25.4880i	−0.290834	−	1.36827i	0.553679	−	0.832730i	$-0.313224\pi$
$348$	6.70205	+	10.6026i	0.359268	+	0.568360i
$349$	−8.75870	+	12.0553i	−0.468843	+	0.645307i	−0.976313	−	0.216363i	$-0.930581\pi$
$349$	−8.75870	+	12.0553i	−0.468843	+	0.645307i	0.507470	+	0.861669i	$0.330581\pi$
$350$	11.7142	−	3.93724i	0.626151	−	0.210454i
$351$	−5.53357	+	28.1855i	−0.295360	+	1.50443i
$352$	3.08019	+	1.22981i	0.164175	+	0.0655491i
$353$	9.61706	+	16.6572i	0.511864	+	0.886575i	0.999905	+	0.0137543i	$0.00437825\pi$
$353$	9.61706	+	16.6572i	0.511864	+	0.886575i	−0.488041	+	0.872821i	$0.662288\pi$
$354$	4.90832	−	17.4590i	0.260874	−	0.927936i
$355$	−1.90793	−	4.28528i	−0.101262	−	0.227439i
$356$	10.7330	−	7.79795i	0.568846	−	0.413291i
$357$	3.04799	−	7.88897i	0.161317	−	0.417529i
$358$	3.32578	−	10.2357i	0.175773	−	0.540973i
$359$	5.17692	−	0.544117i	0.273228	−	0.0287174i	0.0330762	−	0.999453i	$-0.489470\pi$
$359$	5.17692	−	0.544117i	0.273228	−	0.0287174i	0.240151	+	0.970735i	$0.422803\pi$
$360$	1.18250	−	1.25024i	0.0623233	−	0.0658936i
$361$	−10.2859	+	11.4236i	−0.541362	+	0.601243i
$362$	0.369163	−	0.639410i	0.0194028	−	0.0336066i
$363$	−2.24513	−	18.9198i	−0.117839	−	0.993033i
$364$	12.5915	−	7.44003i	0.659973	−	0.389964i
$365$	6.90895	−	2.24485i	0.361631	−	0.117501i
$366$	−0.840736	−	0.698054i	−0.0439460	−	0.0364879i
$367$	4.49807	−	10.1028i	0.234797	−	0.527363i	−0.757266	−	0.653107i	$-0.773465\pi$
$367$	4.49807	−	10.1028i	0.234797	−	0.527363i	0.992063	+	0.125744i	$0.0401318\pi$
$368$	1.48347	+	6.97919i	0.0773314	+	0.363815i
$369$	4.45873	−	0.358352i	0.232112	−	0.0186551i
$370$	0.257513	+	0.354436i	0.0133875	+	0.0184263i
$371$	−9.17988	−	0.871327i	−0.476595	−	0.0452370i
$372$	2.55652	+	2.61999i	0.132549	+	0.135840i
$373$	−7.93738	+	13.7479i	−0.410982	+	0.711842i	−0.994997	−	0.0999008i	$-0.968147\pi$
$373$	−7.93738	+	13.7479i	−0.410982	+	0.711842i	0.584015	+	0.811743i	$0.301481\pi$
$374$	4.80788	−	3.78818i	0.248610	−	0.195882i
$375$	5.33160	−	7.99365i	0.275323	−	0.412791i
$376$	−0.0927802	+	0.436497i	−0.00478477	+	0.0225106i
$377$	32.3864	+	23.5301i	1.66799	+	1.21186i
$378$	−13.7048	−	1.08570i	−0.704898	−	0.0558423i
$379$	1.08677	−	3.34472i	0.0558235	−	0.171807i	−0.919257	−	0.393657i	$-0.871210\pi$
$379$	1.08677	−	3.34472i	0.0558235	−	0.171807i	0.975081	+	0.221850i	$0.0712097\pi$
$380$	2.49922	−	2.25031i	0.128207	−	0.115438i
$381$	−0.845780	−	21.0808i	−0.0433306	−	1.08000i
$382$	−2.15820	+	20.5339i	−0.110423	+	1.05061i
$383$	−0.670465	−	0.142512i	−0.0342591	−	0.00728201i	0.190750	−	0.981639i	$-0.438908\pi$
$383$	−0.670465	−	0.142512i	−0.0342591	−	0.00728201i	−0.225009	+	0.974357i	$0.572241\pi$
$384$	1.55279	−	0.767355i	0.0792406	−	0.0391589i
$385$	2.27052	+	4.49236i	0.115716	+	0.228952i
$386$			7.62036i			0.387866i
$387$	17.7135	−	15.1797i	0.900430	−	0.771627i
$388$	−3.33480	−	0.350501i	−0.169299	−	0.0177940i
$389$	−0.975881	+	2.19186i	−0.0494791	+	0.111132i	−0.936594	−	0.350418i	$-0.886040\pi$
$389$	−0.975881	+	2.19186i	−0.0494791	+	0.111132i	0.887114	+	0.461550i	$0.152706\pi$
$390$	2.03094	−	5.10288i	0.102841	−	0.258394i
$391$	12.5236	+	4.06917i	0.633346	+	0.205787i
$392$	4.22789	+	5.57897i	0.213541	+	0.281781i
$393$	−0.794545	+	4.64707i	−0.0400795	+	0.234414i
$394$	−24.2408	−	5.15254i	−1.22123	−	0.259581i
$395$	3.03221	+	5.25194i	0.152567	+	0.264254i
$396$	−8.13349	−	5.73117i	−0.408723	−	0.288002i
$397$	−14.0038	−	8.08509i	−0.702830	−	0.405779i	0.105570	−	0.994412i	$-0.466333\pi$
$397$	−14.0038	−	8.08509i	−0.702830	−	0.405779i	−0.808401	+	0.588633i	$0.799667\pi$
$398$	7.94564	+	24.4542i	0.398279	+	1.22578i
$399$	−26.5266	−	4.26054i	−1.32799	−	0.213294i
$400$	3.77888	−	2.74552i	0.188944	−	0.137276i
$401$	−26.1642	+	23.5583i	−1.30658	+	1.17645i	−0.334338	+	0.942453i	$0.608513\pi$
$401$	−26.1642	+	23.5583i	−1.30658	+	1.17645i	−0.972238	+	0.233994i	$0.924821\pi$
$402$	−6.27481	+	4.95510i	−0.312959	+	0.247138i
$403$	10.6728	+	4.75186i	0.531652	+	0.236707i
$404$	−15.7688	+	7.02074i	−0.784529	+	0.349295i
$405$	−4.32039	+	2.82612i	−0.214682	+	0.140431i
$406$	−9.41222	+	16.6889i	−0.467120	+	0.828258i
$407$	1.81491	−	1.76708i	0.0899619	−	0.0875909i
$408$	0.206420	−	3.18989i	0.0102193	−	0.157923i
$409$	2.70993	+	2.44003i	0.133998	+	0.120652i	0.733404	−	0.679793i	$-0.237930\pi$
$409$	2.70993	+	2.44003i	0.133998	+	0.120652i	−0.599407	+	0.800444i	$0.704597\pi$
$410$	−0.850610	−	0.0894027i	−0.0420086	−	0.00441529i
$411$	6.61196	+	10.4601i	0.326144	+	0.515958i
$412$	−8.36443	−	2.71777i	−0.412086	−	0.133895i
$413$	27.0381	−	6.03278i	1.33046	−	0.296854i
$414$	0.524830	−	21.3989i	0.0257940	−	1.05170i
$415$	−2.62057	+	1.16675i	−0.128639	+	0.0572737i
$416$	3.69885	−	4.10799i	0.181351	−	0.201411i
$417$	11.9408	+	7.96428i	0.584745	+	0.390013i
$418$	−14.9465	−	12.4376i	−0.731059	−	0.608341i
$419$	−23.5510			−1.15054			−0.575271	−	0.817963i	$-0.695103\pi$
$419$	−23.5510			−1.15054			−0.575271	+	0.817963i	$0.695103\pi$
$420$	2.53763	+	0.685872i	0.123824	+	0.0334672i
$421$	16.0972	+	11.6953i	0.784527	+	0.569993i	0.906334	−	0.422561i	$-0.138869\pi$
$421$	16.0972	+	11.6953i	0.784527	+	0.569993i	−0.121807	+	0.992554i	$0.538869\pi$
$422$	3.63279	−	0.381821i	0.176841	−	0.0185868i
$423$	0.574339	−	1.20929i	0.0279253	−	0.0587975i
$424$	−3.40910	+	0.724627i	−0.165561	+	0.0351910i
$425$	−0.901079	−	8.57319i	−0.0437087	−	0.415861i
$426$	−2.38706	+	13.9613i	−0.115654	+	0.676425i
$427$	0.330564	−	1.63615i	0.0159971	−	0.0791791i
$428$		−	14.7898i		−	0.714890i
$429$	−30.8819	−	7.39558i	−1.49099	−	0.357062i
$430$	−3.86291	+	2.23025i	−0.186286	+	0.107552i
$431$	−24.1786	−	21.7705i	−1.16464	−	1.04865i	−0.998037	−	0.0626232i	$-0.980053\pi$
$431$	−24.1786	−	21.7705i	−1.16464	−	1.04865i	−0.166603	−	0.986024i	$-0.553280\pi$
$432$	−5.06516	+	1.15938i	−0.243698	+	0.0557809i
$433$	18.8256	+	25.9113i	0.904702	+	1.24522i	0.968944	+	0.247281i	$0.0795371\pi$
$433$	18.8256	+	25.9113i	0.904702	+	1.24522i	−0.0642418	+	0.997934i	$0.520463\pi$
$434$	−1.67420	+	5.33517i	−0.0803643	+	0.256096i
$435$	1.03835	+	7.11981i	0.0497852	+	0.341369i
$436$	1.77898	+	16.9258i	0.0851975	+	0.810600i
$437$	4.37258	−	41.6023i	0.209169	−	1.99011i
$438$	−21.1164	−	5.93654i	−1.00898	−	0.283659i
$439$	0.295939	+	0.170861i	0.0141244	+	0.00815473i	0.507046	−	0.861919i	$-0.330738\pi$
$439$	0.295939	+	0.170861i	0.0141244	+	0.00815473i	−0.492921	+	0.870074i	$0.664071\pi$
$440$	1.32719	+	1.36311i	0.0632712	+	0.0649839i
$441$	−8.45796	−	19.2214i	−0.402760	−	0.915306i
$442$	−3.15254	−	9.70253i	−0.149951	−	0.461502i
$443$	−11.6830	−	26.2405i	−0.555078	−	1.24673i	−0.945359	−	0.326030i	$-0.894289\pi$
$443$	−11.6830	−	26.2405i	−0.555078	−	1.24673i	0.390281	−	0.920696i	$-0.372378\pi$
$444$	−0.0530314	−	1.32179i	−0.00251676	−	0.0627295i
$445$	7.44380	−	1.58223i	0.352870	−	0.0750049i
$446$	−8.61443	−	9.56729i	−0.407905	−	0.453024i
$447$	−9.94568	+	18.9417i	−0.470414	+	0.895913i
$448$	2.15603	+	1.53347i	0.101863	+	0.0724494i
$449$	−13.1851	+	4.28409i	−0.622242	+	0.202179i	−0.603135	−	0.797639i	$-0.706082\pi$
$449$	−13.1851	+	4.28409i	−0.622242	+	0.202179i	−0.0191065	+	0.999817i	$0.506082\pi$
$450$	−12.9373	+	5.38396i	−0.609869	+	0.253802i
$451$	0.192848	+	4.94144i	0.00908086	+	0.232683i
$452$	5.66657	−	3.27159i	0.266533	−	0.153883i
$453$	9.97211	+	39.1292i	0.468530	+	1.83845i
$454$	−5.64603	+	7.77109i	−0.264981	+	0.364715i
$455$	8.33423	−	0.961045i	0.390715	−	0.0450545i
$456$	−10.0483	+	1.46545i	−0.470555	+	0.0686258i
$457$	−17.1929	−	19.0946i	−0.804248	−	0.893208i	0.191854	−	0.981424i	$-0.438550\pi$
$457$	−17.1929	−	19.0946i	−0.804248	−	0.893208i	−0.996101	+	0.0882159i	$0.971883\pi$
$458$	−14.1528	−	6.30123i	−0.661317	−	0.294437i
$459$	−2.82094	+	9.16539i	−0.131670	+	0.427804i
$460$	−0.850958	+	4.00344i	−0.0396761	+	0.186661i
$461$	−38.8494			−1.80940			−0.904699	−	0.426050i	$-0.859905\pi$
$461$	−38.8494			−1.80940			−0.904699	+	0.426050i	$0.859905\pi$
$462$	1.82320	−	15.0889i	0.0848228	−	0.702001i
$463$	−36.2859			−1.68635			−0.843175	−	0.537639i	$-0.819316\pi$
$463$	−36.2859			−1.68635			−0.843175	+	0.537639i	$0.819316\pi$
$464$	−1.50566	+	7.08359i	−0.0698987	+	0.328848i
$465$	0.728419	+	1.96944i	0.0337796	+	0.0913304i
$466$	16.8122	+	7.48525i	0.778808	+	0.346748i
$467$	−1.81869	−	2.01986i	−0.0841590	−	0.0934680i	0.699594	−	0.714540i	$-0.253364\pi$
$467$	−1.81869	−	2.01986i	−0.0841590	−	0.0934680i	−0.783753	+	0.621072i	$0.786697\pi$
$468$	−13.6513	+	9.41568i	−0.631033	+	0.435240i
$469$	−11.2068	−	4.85475i	−0.517483	−	0.224172i
$470$	−0.150461	+	0.207092i	−0.00694024	+	0.00955243i
$471$	−18.5494	+	4.72734i	−0.854713	+	0.217824i
$472$	9.06792	−	5.23537i	0.417385	−	0.240977i
$473$	15.9611	+	20.2575i	0.733893	+	0.931442i
$474$	1.18247	−	18.2732i	0.0543125	−	0.839314i
$475$	−26.0444	+	8.46234i	−1.19500	+	0.388279i
$476$	4.44043	−	2.03092i	0.203527	−	0.0930869i
$477$	10.4526	+	0.256362i	0.478594	+	0.0117380i
$478$	−1.17286	−	1.30259i	−0.0536452	−	0.0595791i
$479$	5.60978	−	1.19239i	0.256317	−	0.0544819i	−0.0779608	−	0.996956i	$-0.524841\pi$
$479$	5.60978	−	1.19239i	0.256317	−	0.0544819i	0.334278	+	0.942475i	$0.391508\pi$
$480$	0.992750	−	0.0398300i	0.0453126	−	0.00181798i
$481$	−1.71720	−	3.85690i	−0.0782977	−	0.175859i
$482$	−2.34386	−	7.21364i	−0.106760	−	0.328573i
$483$	29.1656	−	14.7808i	1.32708	−	0.672551i
$484$	6.70097	−	8.72336i	0.304589	−	0.396517i
$485$	−1.66577	−	0.961731i	−0.0756386	−	0.0436700i
$486$	15.5878	+	0.139404i	0.707079	+	0.00632349i
$487$	−1.87629	+	17.8517i	−0.0850228	+	0.808938i	0.866047	+	0.499962i	$0.166653\pi$
$487$	−1.87629	+	17.8517i	−0.0850228	+	0.808938i	−0.951070	+	0.308976i	$0.900014\pi$
$488$	−0.0659474	−	0.627447i	−0.00298530	−	0.0284032i
$489$	−13.0901	+	1.90905i	−0.591953	+	0.0863304i
$490$	0.913899	+	3.91000i	0.0412858	+	0.176636i
$491$	7.86498	+	10.8252i	0.354942	+	0.488535i	0.948731	−	0.316085i	$-0.102369\pi$
$491$	7.86498	+	10.8252i	0.354942	+	0.488535i	−0.593789	+	0.804621i	$0.702369\pi$
$492$	1.98694	+	1.64973i	0.0895781	+	0.0743757i
$493$	9.93220	+	8.94299i	0.447324	+	0.402772i
$494$	−28.0666	+	16.2042i	−1.26277	+	0.729063i
$495$	−2.92505	−	4.90099i	−0.131471	−	0.220283i
$496$			2.11346i			0.0948972i
$497$	−20.5082	+	6.89298i	−0.919921	+	0.309192i
$498$	8.53771	+	1.45976i	0.382584	+	0.0654133i
$499$	−0.100890	−	0.959905i	−0.00451646	−	0.0429712i	0.992032	−	0.125990i	$-0.0402106\pi$
$499$	−0.100890	−	0.959905i	−0.00451646	−	0.0429712i	−0.996548	+	0.0830184i	$0.973544\pi$
$500$	5.42628	−	1.15339i	0.242671	−	0.0515812i
$501$	16.4488	+	20.8297i	0.734879	+	0.930601i
$502$	9.00752	−	0.946728i	0.402025	−	0.0422546i
$503$	−11.2682	−	8.18686i	−0.502426	−	0.365034i	0.307517	−	0.951543i	$-0.400502\pi$
$503$	−11.2682	−	8.18686i	−0.502426	−	0.365034i	−0.809943	+	0.586509i	$0.800502\pi$
$504$	−5.22536	−	5.97458i	−0.232756	−	0.266129i
$505$	−9.90144			−0.440608
$506$	23.6134	+	1.55394i	1.04974	+	0.0690811i
$507$	−16.8738	+	25.2988i	−0.749391	+	1.12356i
$508$	8.15055	−	9.05210i	0.361622	−	0.401622i
$509$	−8.78650	+	3.91200i	−0.389455	+	0.173396i	−0.592116	−	0.805852i	$-0.701707\pi$
$509$	−8.78650	+	3.91200i	−0.389455	+	0.173396i	0.202662	+	0.979249i	$0.435041\pi$
$510$	0.852419	−	1.62345i	0.0377457	−	0.0718875i
$511$	−7.29656	−	32.7022i	−0.322781	−	1.44666i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	30.3429	+	2.71200i	1.33967	+	0.119738i
$514$	24.3507	+	2.55936i	1.07406	+	0.112889i
$515$	−3.74914	−	3.37574i	−0.165207	−	0.148753i
$516$	13.4403	+	0.869728i	0.591675	+	0.0382876i
$517$	1.30963	+	0.689471i	0.0575976	+	0.0303229i
$518$	1.73970	−	1.02795i	0.0764378	−	0.0451654i
$519$	10.0625	−	9.81873i	0.441695	−	0.430994i
$520$	2.89678	−	1.28973i	0.127032	−	0.0565583i
$521$	−13.3346	−	5.93696i	−0.584201	−	0.260103i	0.0932842	−	0.995640i	$-0.470263\pi$
$521$	−13.3346	−	5.93696i	−0.584201	−	0.260103i	−0.677485	+	0.735537i	$0.736930\pi$
$522$	9.32054	−	19.6246i	0.407949	−	0.858947i
$523$	−15.8982	+	14.3148i	−0.695181	+	0.625944i	−0.939016	−	0.343873i	$-0.888261\pi$
$523$	−15.8982	+	14.3148i	−0.695181	+	0.625944i	0.243835	+	0.969817i	$0.421594\pi$
$524$	−2.20208	+	1.59990i	−0.0961983	+	0.0698922i
$525$	−16.6055	−	13.5067i	−0.724723	−	0.589482i
$526$	2.32114	+	7.14374i	0.101207	+	0.311482i
$527$	3.37790	+	1.95023i	0.147144	+	0.0849535i
$528$	−1.05006	−	5.64778i	−0.0456981	−	0.245788i
$529$	13.9549	+	24.1706i	0.606735	+	1.05090i
$530$	−1.95555	−	0.415664i	−0.0849436	−	0.0180553i
$531$	−30.1038	+	8.97150i	−1.30639	+	0.389330i
$532$	−9.24349	−	12.4564i	−0.400756	−	0.540054i
$533$	7.83881	+	2.54698i	0.339536	+	0.110322i
$534$	−21.3497	−	8.49717i	−0.923894	−	0.367708i
$535$	3.45067	−	7.75033i	0.149185	−	0.335076i
$536$	−4.59085	−	0.482518i	−0.198295	−	0.0208416i
$537$	−18.0637	+	4.60355i	−0.779507	+	0.198658i
$538$			0.538005i			0.0231950i
$539$	21.6171	−	8.46762i	0.931115	−	0.364726i
$540$	−2.92481	−	0.574219i	−0.125864	−	0.0247105i
$541$	−7.99242	−	1.69884i	−0.343621	−	0.0730389i	0.0328688	−	0.999460i	$-0.489536\pi$
$541$	−7.99242	−	1.69884i	−0.343621	−	0.0730389i	−0.376490	+	0.926421i	$0.622869\pi$
$542$	−1.05925	+	10.0781i	−0.0454988	+	0.432892i
$543$	−1.27779	+	0.0512661i	−0.0548353	+	0.00220004i
$544$	1.37150	−	1.23490i	0.0588026	−	0.0529461i
$545$	−3.01680	+	9.28475i	−0.129225	+	0.397715i
$546$	−22.5457	−	11.5494i	−0.964868	−	0.494270i
$547$	13.6251	+	9.89924i	0.582569	+	0.423261i	0.839649	−	0.543129i	$-0.182761\pi$
$547$	13.6251	+	9.89924i	0.582569	+	0.423261i	−0.257081	+	0.966390i	$0.582761\pi$
$548$	−1.48542	+	6.98837i	−0.0634542	+	0.298529i
$549$	−0.243935	+	1.87693i	−0.0104109	+	0.0801052i
$550$	−5.35815	−	14.5357i	−0.228472	−	0.619804i
$551$	21.2286	−	36.7690i	0.904370	−	1.56641i
$552$	8.84517	−	8.63089i	0.376475	−	0.367355i
$553$	25.4368	−	11.6340i	1.08168	−	0.494729i
$554$	−1.36088	−	1.87309i	−0.0578182	−	0.0795799i
$555$	0.280603	−	0.705036i	0.0119109	−	0.0299271i
$556$	1.72292	+	8.10571i	0.0730682	+	0.343759i
$557$	−14.5394	+	32.6559i	−0.616053	+	1.38368i	0.288568	+	0.957459i	$0.406821\pi$
$557$	−14.5394	+	32.6559i	−0.616053	+	1.38368i	−0.904621	+	0.426217i	$0.859846\pi$
$558$	1.46990	−	6.16764i	0.0622260	−	0.261097i
$559$	40.8806	−	13.2829i	1.72907	−	0.561808i
$560$	0.772053	+	1.30662i	0.0326252	+	0.0552148i
$561$	−9.99570	−	3.53329i	−0.422019	−	0.149176i
$562$	4.31241	−	7.46931i	0.181908	−	0.315074i
$563$	−20.5504	+	22.8235i	−0.866097	+	0.961898i	−0.999575	−	0.0291539i	$-0.990719\pi$
$563$	−20.5504	+	22.8235i	−0.866097	+	0.961898i	0.133478	+	0.991052i	$0.457385\pi$
$564$	0.724929	−	0.268124i	0.0305250	−	0.0112900i
$565$	3.73278	−	0.392331i	0.157039	−	0.0165055i
$566$	5.61508	−	17.2814i	0.236019	−	0.726393i
$567$	11.0937	+	21.0696i	0.465892	+	0.884841i
$568$	−6.61574	+	4.80662i	−0.277590	+	0.201681i
$569$	1.49417	+	3.35596i	0.0626389	+	0.140689i	0.942153	−	0.335184i	$-0.108799\pi$
$569$	1.49417	+	3.35596i	0.0626389	+	0.140689i	−0.879514	+	0.475874i	$0.842132\pi$
$570$	−5.60756	−	1.57647i	−0.234875	−	0.0660312i
$571$	−11.4258	−	19.7901i	−0.478157	−	0.828192i	0.521530	−	0.853233i	$-0.325362\pi$
$571$	−11.4258	−	19.7901i	−0.478157	−	0.828192i	−0.999686	+	0.0250415i	$0.992028\pi$
$572$	−9.77910	−	15.5080i	−0.408885	−	0.648421i
$573$	32.0605	−	15.8436i	1.33935	−	0.661875i
$574$	−0.781231	+	3.86678i	−0.0326080	+	0.161396i
$575$	19.5896	−	26.9627i	0.816942	−	1.12442i
$576$	−2.56052	−	1.56325i	−0.106688	−	0.0651354i
$577$	7.86768	+	37.0145i	0.327536	+	1.54094i	0.766389	+	0.642376i	$0.222051\pi$
$577$	7.86768	+	37.0145i	0.327536	+	1.54094i	−0.438853	+	0.898559i	$0.644615\pi$
$578$	2.82635	+	13.2969i	0.117561	+	0.553080i
$579$	11.1568	−	7.05235i	0.463660	−	0.293086i
$580$	−2.44172	+	3.36074i	−0.101387	+	0.139547i
$581$	4.21526	+	12.5414i	0.174878	+	0.520304i
$582$	2.57307	+	5.20678i	0.106657	+	0.215828i
$583$	−0.759048	+	11.5344i	−0.0314366	+	0.477704i
$584$	−6.33209	−	10.9675i	−0.262024	−	0.453839i
$585$	−9.35057	+	1.74907i	−0.386598	+	0.0723153i
$586$	−8.32253	−	18.6927i	−0.343800	−	0.772188i
$587$	−5.50217	+	3.99756i	−0.227099	+	0.164997i	−0.695516	−	0.718510i	$-0.744824\pi$
$587$	−5.50217	+	3.99756i	−0.227099	+	0.164997i	0.468417	+	0.883507i	$0.344824\pi$
$588$	4.25529	−	11.3531i	0.175485	−	0.468193i
$589$	3.82894	−	11.7843i	0.157769	−	0.485563i
$590$	5.97338	−	0.627827i	0.245920	−	0.0258472i
$591$	14.8902	+	40.2589i	0.612502	+	1.65603i
$592$	0.511050	−	0.567578i	0.0210040	−	0.0233273i
$593$	6.60072	−	11.4328i	0.271059	−	0.469488i	−0.698074	−	0.716025i	$-0.745959\pi$
$593$	6.60072	−	11.4328i	0.271059	−	0.469488i	0.969133	+	0.246537i	$0.0792928\pi$
$594$	−0.863643	+	17.2120i	−0.0354357	+	0.706218i
$595$	2.80077	−	0.0282502i	0.114821	−	0.00115814i
$596$	−11.7473	+	3.81694i	−0.481189	+	0.156348i
$597$	28.4494	−	34.2644i	1.16436	−	1.40235i
$598$	16.0424	−	36.0319i	0.656024	−	1.47345i
$599$	−4.50314	−	21.1856i	−0.183993	−	0.865621i	−0.969179	−	0.246360i	$-0.920766\pi$
$599$	−4.50314	−	21.1856i	−0.183993	−	0.865621i	0.785185	−	0.619261i	$-0.212568\pi$
$600$	−7.51686	−	2.99170i	−0.306874	−	0.122136i
$601$	−16.6129	−	22.8657i	−0.677655	−	0.932712i	0.322248	−	0.946655i	$-0.395561\pi$
$601$	−16.6129	−	22.8657i	−0.677655	−	0.932712i	−0.999903	+	0.0139435i	$0.995561\pi$
$602$	8.55706	+	18.7093i	0.348760	+	0.762534i
$603$	13.0617	+	4.60104i	0.531916	+	0.187369i
$604$	−11.6567	+	20.1900i	−0.474303	+	0.821518i
$605$	5.54682	−	3.00790i	0.225510	−	0.122288i
$606$	24.8724	+	16.5894i	1.01037	+	0.673897i
$607$	3.93471	−	18.5114i	0.159705	−	0.751353i	−0.823275	−	0.567642i	$-0.807856\pi$
$607$	3.93471	−	18.5114i	0.159705	−	0.751353i	0.982980	−	0.183711i	$-0.0588109\pi$
$608$	−4.74308	−	3.44605i	−0.192357	−	0.139756i
$609$	33.1445	−	1.66477i	1.34308	−	0.0674600i
$610$	0.111834	−	0.344190i	0.00452803	−	0.0139358i
$611$	1.83318	−	1.65061i	0.0741627	−	0.0667764i
$612$	−4.86128	+	2.64991i	−0.196505	+	0.107116i
$613$	2.29983	−	21.8815i	0.0928894	−	0.883784i	−0.844513	−	0.535535i	$-0.820110\pi$
$613$	2.29983	−	21.8815i	0.0928894	−	0.883784i	0.937402	−	0.348249i	$-0.113224\pi$
$614$	−11.8558	−	2.52003i	−0.478462	−	0.101700i
$615$	0.656315	+	1.32810i	0.0264652	+	0.0535540i
$616$	6.83743	−	5.49996i	0.275488	−	0.221600i
$617$			24.4514i			0.984375i	0.870489	+	0.492187i	$0.163803\pi$
$617$			24.4514i			0.984375i	−0.870489	+	0.492187i	$0.836197\pi$
$618$	3.76194	+	14.7613i	0.151327	+	0.593788i
$619$	10.3453	+	1.08734i	0.415813	+	0.0437037i	0.310125	−	0.950696i	$-0.399629\pi$
$619$	10.3453	+	1.08734i	0.415813	+	0.0437037i	0.105688	+	0.994399i	$0.466296\pi$
$620$	−0.493101	+	1.10752i	−0.0198034	+	0.0444792i
$621$	−31.8153	+	19.0355i	−1.27671	+	0.763867i
$622$	31.0510	+	10.0891i	1.24503	+	0.404535i
$623$	−4.02088	−	34.8692i	−0.161093	−	1.39701i
$624$	−9.43756	−	1.61361i	−0.377805	−	0.0645962i
$625$	−19.7318	−	4.19411i	−0.789270	−	0.167765i
$626$	8.55565	+	14.8188i	0.341953	+	0.592279i
$627$	−4.37708	+	33.3934i	−0.174804	+	1.33360i
$628$	−9.57117	−	5.52592i	−0.381931	−	0.220508i
$629$	−0.435569	−	1.34054i	−0.0173673	−	0.0534510i
$630$	−1.34431	−	4.35003i	−0.0535585	−	0.173309i
$631$	−10.0220	+	7.28140i	−0.398969	+	0.289868i	−0.769121	−	0.639103i	$-0.779306\pi$
$631$	−10.0220	+	7.28140i	−0.398969	+	0.289868i	0.370152	+	0.928971i	$0.379306\pi$
$632$	7.85659	−	7.07410i	0.312518	−	0.281393i
$633$	−3.92102	−	4.96532i	−0.155847	−	0.197354i
$634$	3.41418	+	1.52009i	0.135594	+	0.0603705i
$635$	6.38315	−	2.84196i	0.253307	−	0.112780i
$636$	4.21590	+	4.32057i	0.167171	+	0.171322i
$637$	−0.780519	−	38.6871i	−0.0309253	−	1.53284i
$638$	21.2531	+	11.1889i	0.841419	+	0.442975i
$639$	22.6495	−	9.42577i	0.896000	−	0.372878i
$640$	0.426287	+	0.383830i	0.0168505	+	0.0151722i
$641$	26.7676	+	2.81338i	1.05726	+	0.111122i	0.617167	−	0.786832i	$-0.288280\pi$
$641$	26.7676	+	2.81338i	1.05726	+	0.111122i	0.440089	+	0.897954i	$0.354947\pi$
$642$	−21.6533	+	13.6874i	−0.854589	+	0.540197i
$643$	19.9480	+	6.48148i	0.786670	+	0.255605i	0.674686	−	0.738105i	$-0.264279\pi$
$643$	19.9480	+	6.48148i	0.786670	+	0.255605i	0.111985	+	0.993710i	$0.464279\pi$
$644$	18.0117	+	5.65216i	0.709761	+	0.222726i
$645$	6.84023	+	3.59158i	0.269334	+	0.141418i
$646$	−9.88451	+	4.40087i	−0.388901	+	0.173150i
$647$	14.0408	−	15.5939i	0.552001	−	0.613059i	−0.400981	−	0.916086i	$-0.631331\pi$
$647$	14.0408	−	15.5939i	0.552001	−	0.613059i	0.952982	+	0.303027i	$0.0979973\pi$
$648$	6.38504	+	6.34281i	0.250828	+	0.249169i
$649$	−8.53944	−	33.6612i	−0.335202	−	1.32132i
$650$	−25.8203			−1.01276
$651$	9.36051	−	2.48634i	0.366867	−	0.0974473i
$652$	−6.17887	−	4.48921i	−0.241983	−	0.175811i
$653$	−36.6591	+	3.85303i	−1.43458	+	0.150781i	−0.789696	−	0.613499i	$-0.789762\pi$
$653$	−36.6591	+	3.85303i	−1.43458	+	0.150781i	−0.644886	+	0.764279i	$0.723095\pi$
$654$	23.1343	−	18.2688i	0.904624	−	0.714365i
$655$	−1.52724	+	0.324626i	−0.0596744	+	0.0126842i
$656$	0.155856	+	1.48287i	0.00608514	+	0.0578962i
$657$	10.8509	+	36.4101i	0.423333	+	1.42049i
$658$	0.885326	+	0.781127i	0.0345136	+	0.0304515i
$659$		−	1.19425i		−	0.0465212i	−0.999729	−	0.0232606i	$-0.992595\pi$
$659$		−	1.19425i		−	0.0465212i	0.999729	−	0.0232606i	$-0.00740475\pi$
$660$	0.767441	−	3.20462i	0.0298726	−	0.124740i
$661$	39.1889	−	22.6257i	1.52427	−	0.880038i	0.524684	−	0.851297i	$-0.324184\pi$
$661$	39.1889	−	22.6257i	1.52427	−	0.880038i	0.999587	−	0.0287410i	$-0.00914982\pi$
$662$	2.43431	+	2.19186i	0.0946121	+	0.0851892i
$663$	−11.2877	+	13.5949i	−0.438377	+	0.527982i
$664$	2.93938	+	4.04572i	0.114070	+	0.157004i
$665$	−1.93763	−	8.68421i	−0.0751382	−	0.336759i
$666$	−1.88613	+	1.30091i	−0.0730860	+	0.0504093i
$667$	5.40113	+	51.3883i	0.209133	+	1.98976i
$668$	−1.60175	+	15.2397i	−0.0619737	+	0.589640i
$669$	−6.03492	+	21.4663i	−0.233323	+	0.829937i
$670$	−2.29318	−	1.32397i	−0.0885933	−	0.0511494i
$671$	−2.06215	−	0.354901i	−0.0796085	−	0.0137008i
$672$	0.249783	−	4.57576i	0.00963560	−	0.176514i
$673$	−13.3737	−	41.1600i	−0.515518	−	1.58660i	−0.782338	−	0.622854i	$-0.785973\pi$
$673$	−13.3737	−	41.1600i	−0.515518	−	1.58660i	0.266820	−	0.963746i	$-0.414027\pi$
$674$	−4.32578	−	9.71587i	−0.166623	−	0.374241i
$675$	19.8555	+	13.9585i	0.764238	+	0.537264i
$676$	−17.1734	+	3.65033i	−0.660517	+	0.140397i
$677$	7.58063	+	8.41914i	0.291347	+	0.323574i	0.870994	−	0.491294i	$-0.163476\pi$
$677$	7.58063	+	8.41914i	0.291347	+	0.323574i	−0.579647	+	0.814868i	$0.696809\pi$
$678$	−10.0341	−	5.26855i	−0.385356	−	0.202338i
$679$	−5.14197	+	7.22954i	−0.197331	+	0.277444i
$680$	1.00683	−	0.327140i	0.0386103	−	0.0125452i
$681$	16.6027	+	1.07437i	0.636215	+	0.0411698i
$682$	6.74588	+	1.90445i	0.258313	+	0.0729252i
$683$	3.95212	−	2.28176i	0.151224	−	0.0873091i	−0.422479	−	0.906373i	$-0.638840\pi$
$683$	3.95212	−	2.28176i	0.151224	−	0.0873091i	0.573703	+	0.819064i	$0.305507\pi$
$684$	11.4449	+	13.3553i	0.437605	+	0.510652i
$685$	−2.40890	+	3.31557i	−0.0920394	+	0.126681i
$686$	18.3518	−	2.49225i	0.700675	−	0.0951546i
$687$	3.87239	+	26.5523i	0.147741	+	1.01303i
$688$	5.20315	+	5.77868i	0.198368	+	0.220310i
$689$	17.6004	+	7.83619i	0.670520	+	0.298535i
$690$	6.64888	−	2.45917i	0.253118	−	0.0936189i
$691$	5.64101	−	26.5389i	0.214594	−	1.00959i	−0.730532	−	0.682879i	$-0.760728\pi$
$691$	5.64101	−	26.5389i	0.214594	−	1.00959i	0.945126	−	0.326707i	$-0.105939\pi$
$692$	8.11709			0.308565
$693$	−23.7787	+	11.2949i	−0.903276	+	0.429059i
$694$	−26.0574			−0.989125
$695$	−0.988312	+	4.64964i	−0.0374888	+	0.176371i
$696$	11.7644	−	4.35119i	0.445927	−	0.164931i
$697$	2.51386	+	1.11924i	0.0952191	+	0.0423943i
$698$	9.97085	+	11.0737i	0.377402	+	0.419147i
$699$	−4.60003	−	31.5416i	−0.173989	−	1.19301i
$700$	−1.41568	−	12.2768i	−0.0535076	−	0.464020i
$701$	14.6754	−	20.1989i	0.554281	−	0.762903i	−0.436304	−	0.899799i	$-0.643713\pi$
$701$	14.6754	−	20.1989i	0.554281	−	0.762903i	0.990585	+	0.136897i	$0.0437128\pi$
$702$	26.4191	+	11.2727i	0.997123	+	0.425462i
$703$	−3.87780	+	2.23885i	−0.146254	+	0.0844397i
$704$	1.84334	−	2.75719i	0.0694736	−	0.103915i
$705$	0.442444	+	0.0286308i	0.0166634	+	0.00107830i
$706$	18.2927	−	5.94367i	0.688456	−	0.223693i
$707$	−4.31534	+	45.4644i	−0.162295	+	1.70986i
$708$	−16.0570	−	8.43100i	−0.603459	−	0.316856i
$709$	23.7216	+	26.3455i	0.890882	+	0.989424i	0.999989	−	0.00460566i	$-0.00146603\pi$
$709$	23.7216	+	26.3455i	0.890882	+	0.989424i	−0.109108	+	0.994030i	$0.534799\pi$
$710$	−4.58832	+	0.975278i	−0.172197	+	0.0366015i
$711$	−27.8476	+	15.1799i	−1.04437	+	0.569291i
$712$	−5.39604	−	12.1197i	−0.202225	−	0.454205i
$713$	4.65991	+	14.3417i	0.174515	+	0.537101i
$714$	−7.08286	−	4.62159i	−0.265070	−	0.172959i
$715$	−1.50634	−	10.4083i	−0.0563338	−	0.389248i
$716$	−9.32055	−	5.38122i	−0.348325	−	0.201106i
$717$	−0.821656	+	2.92265i	−0.0306853	+	0.109148i
$718$	0.544117	−	5.17692i	0.0203063	−	0.193201i
$719$	0.463987	+	4.41454i	0.0173038	+	0.164634i	0.999761	−	0.0218525i	$-0.00695643\pi$
$719$	0.463987	+	4.41454i	0.0173038	+	0.164634i	−0.982457	+	0.186487i	$0.940290\pi$
$720$	−0.977067	−	1.41660i	−0.0364131	−	0.0527936i
$721$	−17.1344	+	15.7437i	−0.638117	+	0.586324i
$722$	9.03544	+	12.4362i	0.336264	+	0.462828i
$723$	−8.39218	+	10.1075i	−0.312108	+	0.375903i
$724$	−0.548684	−	0.494037i	−0.0203917	−	0.0183607i
$725$	29.2945	−	16.9132i	1.08797	−	0.628139i
$726$	−18.9732	−	1.73758i	−0.704160	−	0.0644878i
$727$		−	8.22143i		−	0.304916i	−0.988310	−	0.152458i	$-0.951281\pi$
$727$		−	8.22143i		−	0.304916i	0.988310	−	0.152458i	$-0.0487189\pi$
$728$	−4.65953	−	13.8632i	−0.172694	−	0.513805i
$729$	−14.2219	−	22.9508i	−0.526735	−	0.850029i
$730$	−0.759347	−	7.22471i	−0.0281047	−	0.267398i
$731$	14.0373	−	2.98371i	0.519186	−	0.110356i
$732$	−0.857599	+	0.677231i	−0.0316978	+	0.0250312i
$733$	20.0982	−	2.11241i	0.742344	−	0.0780235i	0.274197	−	0.961674i	$-0.411588\pi$
$733$	20.0982	−	2.11241i	0.742344	−	0.0780235i	0.468148	+	0.883650i	$0.344921\pi$
$734$	−8.94685	−	6.50027i	−0.330234	−	0.239929i
$735$	4.87875	−	4.95657i	0.179956	−	0.182826i
$736$	7.13511			0.263004
$737$	−5.67698	+	14.2186i	−0.209114	+	0.523748i
$738$	0.576500	−	4.43580i	0.0212212	−	0.163284i
$739$	8.64362	−	9.59971i	0.317961	−	0.353131i	−0.562884	−	0.826536i	$-0.690308\pi$
$739$	8.64362	−	9.59971i	0.317961	−	0.353131i	0.880845	+	0.473404i	$0.156975\pi$
$740$	0.400231	−	0.178194i	0.0147128	−	0.00655056i
$741$	49.6988	+	26.0952i	1.82573	+	0.958630i
$742$	−2.76089	+	8.79812i	−0.101355	+	0.322989i
$743$	−8.24475	−	2.67888i	−0.302471	−	0.0982787i	0.153850	−	0.988094i	$-0.450833\pi$
$743$	−8.24475	−	2.67888i	−0.302471	−	0.0982787i	−0.456320	+	0.889816i	$0.650833\pi$
$744$	3.09427	−	1.95593i	0.113441	−	0.0717078i
$745$	−7.04653	−	0.740620i	−0.258165	−	0.0271342i
$746$	11.7972	+	10.6223i	0.431928	+	0.388910i
$747$	−5.76413	−	13.8508i	−0.210899	−	0.506775i
$748$	−2.70578	−	5.49043i	−0.0989332	−	0.200750i
$749$	−34.0832	−	19.2222i	−1.24537	−	0.702365i
$750$	−6.71047	−	6.87707i	−0.245032	−	0.251115i
$751$	30.5349	−	13.5950i	1.11424	−	0.496090i	0.234770	−	0.972051i	$-0.424566\pi$
$751$	30.5349	−	13.5950i	1.11424	−	0.496090i	0.879466	+	0.475961i	$0.157900\pi$
$752$	0.407668	+	0.181505i	0.0148661	+	0.00661882i
$753$	−9.72220	−	12.3115i	−0.354297	−	0.448657i
$754$	29.7494	−	26.7865i	1.08341	−	0.975507i
$755$	−10.8191	+	7.86053i	−0.393747	+	0.286074i
$756$	−3.91136	+	13.1796i	−0.142255	+	0.479337i
$757$	3.45829	+	10.6435i	0.125694	+	0.386845i	0.994027	−	0.109136i	$-0.0348084\pi$
$757$	3.45829	+	10.6435i	0.125694	+	0.386845i	−0.868333	+	0.495981i	$0.834808\pi$
$758$	−3.04568	−	1.75843i	−0.110624	−	0.0638689i
$759$	−19.5782	−	36.0099i	−0.710644	−	1.30708i
$760$	−1.68152	−	2.91247i	−0.0609950	−	0.105646i
$761$	7.20633	+	1.53175i	0.261229	+	0.0555260i	0.336664	−	0.941625i	$-0.390701\pi$
$761$	7.20633	+	1.53175i	0.261229	+	0.0555260i	−0.0754351	+	0.997151i	$0.524035\pi$
$762$	−20.7960	−	3.55565i	−0.753360	−	0.128808i
$763$	41.3179	+	17.8988i	1.49581	+	0.647980i
$764$	19.6365	+	6.38028i	0.710423	+	0.230830i
$765$	−3.16573	+	0.254433i	−0.114457	+	0.00919905i
$766$	−0.278795	+	0.626184i	−0.0100733	+	0.0226249i
$767$	−57.5635	−	6.05017i	−2.07850	−	0.218459i
$768$	−0.427742	−	1.67840i	−0.0154348	−	0.0605642i
$769$		−	15.1564i		−	0.546554i	−0.961935	−	0.273277i	$-0.911892\pi$
$769$		−	15.1564i		−	0.546554i	0.961935	−	0.273277i	$-0.0881075\pi$
$770$	4.86626	−	1.28689i	0.175368	−	0.0463762i
$771$	−18.7886	−	38.0199i	−0.676654	−	1.36925i
$772$	7.45383	+	1.58436i	0.268269	+	0.0570224i
$773$	1.29864	−	12.3557i	0.0467088	−	0.444405i	−0.946027	−	0.324089i	$-0.894942\pi$
$773$	1.29864	−	12.3557i	0.0467088	−	0.444405i	0.992736	−	0.120316i	$-0.0383909\pi$
$774$	−11.1651	−	20.4825i	−0.401322	−	0.736228i
$775$	7.33623	−	6.60557i	0.263525	−	0.237279i
$776$	−1.03619	+	3.18905i	−0.0371969	+	0.114480i
$777$	−3.11502	−	1.59572i	−0.111751	−	0.0572462i
$778$	1.94107	+	1.41027i	0.0695907	+	0.0505606i
$779$	1.81748	−	8.55056i	0.0651179	−	0.306356i
$780$	−4.56912	−	3.04751i	−0.163601	−	0.109118i
$781$	9.38060	+	25.4478i	0.335664	+	0.910595i
$782$	6.58405	−	11.4039i	0.235445	−	0.407803i
$783$	−37.3578	+	4.51587i	−1.33506	+	0.161384i
$784$	6.33609	−	2.97557i	0.226289	−	0.106270i
$785$	−3.72633	−	5.12886i	−0.132999	−	0.183057i
$786$	4.38032	+	1.74336i	0.156241	+	0.0621837i
$787$	−11.1937	−	52.6621i	−0.399011	−	1.87720i	−0.474827	−	0.880079i	$-0.657489\pi$
$787$	−11.1937	−	52.6621i	−0.399011	−	1.87720i	0.0758157	−	0.997122i	$-0.475844\pi$
$788$	−10.0799	+	22.6398i	−0.359081	+	0.806510i
$789$	8.31085	−	10.0096i	0.295874	−	0.356351i
$790$	5.76760	−	1.87401i	0.205202	−	0.0666742i
$791$	−0.174606	−	17.3108i	−0.00620828	−	0.615500i
$792$	−7.29698	+	6.76417i	−0.259287	+	0.240354i
$793$	−1.74377	+	3.02030i	−0.0619231	+	0.107254i
$794$	−10.8200	+	12.0168i	−0.383986	+	0.426460i
$795$	1.20122	+	3.24775i	0.0426029	+	0.115186i
$796$	25.5718	−	2.68770i	0.906368	−	0.0952631i
$797$	−10.4230	+	32.0786i	−0.369201	+	1.13628i	0.578108	+	0.815960i	$0.303791\pi$
$797$	−10.4230	+	32.0786i	−0.369201	+	1.13628i	−0.947308	+	0.320323i	$0.896209\pi$
$798$	−9.68263	+	25.0611i	−0.342761	+	0.887153i
$799$	0.666280	−	0.484081i	0.0235713	−	0.0171255i
$800$	−1.89985	−	4.26713i	−0.0671698	−	0.150866i
$801$	7.31788	+	39.1215i	0.258565	+	1.38229i
$802$	17.6037	+	30.4905i	0.621608	+	1.07666i
$803$	−40.7127	+	10.3283i	−1.43672	+	0.364478i
$804$	3.54222	+	7.16791i	0.124924	+	0.252793i
$805$	8.12000	+	7.16431i	0.286192	+	0.252509i
$806$	6.86703	−	9.45165i	0.241881	−	0.332920i
$807$	0.787680	−	0.497903i	0.0277276	−	0.0175270i
$808$	3.58879	+	16.8839i	0.126253	+	0.593975i
$809$	−3.35620	−	15.7897i	−0.117998	−	0.555136i	−0.996937	−	0.0782031i	$-0.975082\pi$
$809$	−3.35620	−	15.7897i	−0.117998	−	0.555136i	0.878940	−	0.476933i	$-0.158252\pi$
$810$	1.86610	+	4.81357i	0.0655681	+	0.169131i
$811$	13.6610	−	18.8028i	0.479704	−	0.660256i	−0.498744	−	0.866749i	$-0.666205\pi$
$811$	13.6610	−	18.8028i	0.479704	−	0.660256i	0.978448	+	0.206493i	$0.0662052\pi$
$812$	14.3673	+	12.6764i	0.504195	+	0.444853i
$813$	15.7354	−	7.77609i	0.551866	−	0.272719i
$814$	−1.35112	−	2.14265i	−0.0473568	−	0.0750998i
$815$	−2.19053	−	3.79411i	−0.0767310	−	0.132902i
$816$	−3.07727	−	0.865124i	−0.107726	−	0.0302854i
$817$	−18.5426	−	41.6474i	−0.648724	−	1.45706i
$818$	2.95014	−	2.14340i	0.103149	−	0.0749423i
$819$	3.95595	+	43.6972i	0.138232	+	1.52690i
$820$	−0.264301	+	0.813434i	−0.00922979	+	0.0284064i
$821$	18.6031	−	1.95526i	0.649252	−	0.0682391i	0.225823	−	0.974168i	$-0.427493\pi$
$821$	18.6031	−	1.95526i	0.649252	−	0.0682391i	0.423429	+	0.905929i	$0.360826\pi$
$822$	11.6062	−	4.29270i	0.404813	−	0.149725i
$823$	5.16585	−	5.73725i	0.180070	−	0.199988i	−0.646352	−	0.763040i	$-0.723706\pi$
$823$	5.16585	−	5.73725i	0.180070	−	0.199988i	0.826422	+	0.563052i	$0.190373\pi$
$824$	−4.39744	+	7.61659i	−0.153192	+	0.265336i
$825$	−16.3226	+	21.2970i	−0.568279	+	0.741465i
$826$	−0.279414	−	27.7016i	−0.00972204	−	0.963860i
$827$	−54.5386	+	17.7206i	−1.89649	+	0.616207i	−0.924505	+	0.381170i	$0.875521\pi$
$827$	−54.5386	+	17.7206i	−1.89649	+	0.616207i	−0.971986	+	0.235037i	$0.924479\pi$
$828$	−20.8222	−	4.96244i	−0.723620	−	0.172457i
$829$	4.16299	−	9.35023i	0.144587	−	0.324747i	−0.826706	−	0.562634i	$-0.809788\pi$
$829$	4.16299	−	9.35023i	0.144587	−	0.324747i	0.971293	+	0.237887i	$0.0764548\pi$
$830$	0.596410	+	2.80589i	0.0207017	+	0.0973939i
$831$	−1.48290	+	3.72590i	−0.0514414	+	0.129250i
$832$	−3.24919	−	4.47212i	−0.112645	−	0.155043i
$833$	1.09095	−	12.8726i	0.0377990	−	0.446009i
$834$	10.2729	−	10.0240i	0.355721	−	0.347103i
$835$	−4.39501	+	7.61238i	−0.152096	+	0.263437i
$836$	−15.2733	+	12.0340i	−0.528239	+	0.416205i
$837$	−10.3902	+	3.55587i	−0.359139	+	0.122909i
$838$	−4.89653	+	23.0363i	−0.169148	+	0.795777i
$839$	7.93550	+	5.76548i	0.273964	+	0.199046i	0.716280	−	0.697813i	$-0.245843\pi$
$839$	7.93550	+	5.76548i	0.273964	+	0.199046i	−0.442316	+	0.896859i	$0.645843\pi$
$840$	1.19849	−	2.33957i	0.0413517	−	0.0807230i
$841$	−7.24470	+	22.2969i	−0.249817	+	0.768858i
$842$	14.7865	−	13.3138i	0.509576	−	0.458824i
$843$	−14.9266	+	0.598868i	−0.514100	+	0.0206261i
$844$	0.381821	−	3.63279i	0.0131428	−	0.125046i
$845$	−9.85112	−	2.09392i	−0.338889	−	0.0720331i
$846$	−1.06345	−	0.813213i	−0.0365621	−	0.0279588i
$847$	−11.3939	−	26.7802i	−0.391498	−	0.920179i
$848$			3.48526i			0.119684i
$849$	−30.4979	+	7.77241i	−1.04668	+	0.266748i
$850$	−8.57319	−	0.901079i	−0.294058	−	0.0309067i
$851$	2.21649	−	4.97832i	0.0759804	−	0.170655i
$852$	13.1599	+	5.23761i	0.450850	+	0.179438i
$853$	35.1011	+	11.4050i	1.20184	+	0.390501i	0.840437	−	0.541910i	$-0.182299\pi$
$853$	35.1011	+	11.4050i	1.20184	+	0.390501i	0.361401	+	0.932411i	$0.382299\pi$
$854$	−1.53167	−	0.663516i	−0.0524128	−	0.0227050i
$855$	2.88150	+	9.66886i	0.0985453	+	0.330668i
$856$	−14.4666	−	3.07497i	−0.494457	−	0.105100i
$857$	14.4523	+	25.0321i	0.493682	+	0.855081i	0.999973	−	0.00728067i	$-0.00231753\pi$
$857$	14.4523	+	25.0321i	0.493682	+	0.855081i	−0.506292	+	0.862362i	$0.668984\pi$
$858$	−13.6547	+	28.6694i	−0.466163	+	0.978757i
$859$	18.6851	+	10.7878i	0.637527	+	0.368076i	0.783661	−	0.621188i	$-0.213350\pi$
$859$	18.6851	+	10.7878i	0.637527	+	0.368076i	−0.146134	+	0.989265i	$0.546683\pi$
$860$	1.37837	+	4.24219i	0.0470021	+	0.144657i
$861$	6.38426	−	2.43477i	0.217575	−	0.0829768i
$862$	−26.3218	+	19.1239i	−0.896522	+	0.651362i
$863$	36.4741	−	32.8415i	1.24159	−	1.11794i	0.252979	−	0.967472i	$-0.418590\pi$
$863$	36.4741	−	32.8415i	1.24159	−	1.11794i	0.988615	−	0.150465i	$-0.0480769\pi$
$864$	0.0809435	+	5.19552i	0.00275376	+	0.176755i
$865$	4.25362	+	1.89383i	0.144627	+	0.0643923i
$866$	29.2591	−	13.0270i	0.994265	−	0.442675i
$867$	16.8520	−	16.4438i	0.572326	−	0.558461i
$868$	4.87050	+	2.74686i	0.165316	+	0.0932345i
$869$	−15.5000	−	31.4517i	−0.525801	−	1.06693i
$870$	7.18011	+	0.464629i	0.243429	+	0.0157524i
$871$	18.9631	+	17.0744i	0.642539	+	0.578545i
$872$	16.9258	+	1.77898i	0.573181	+	0.0602437i
$873$	5.24184	−	8.58584i	0.177409	−	0.290587i
$874$	−39.7841	−	12.9266i	−1.34572	−	0.437250i
$875$	4.39452	−	14.0040i	0.148562	−	0.473422i
$876$	−10.1972	+	19.4207i	−0.344530	+	0.656164i
$877$	−9.65588	+	4.29907i	−0.326056	+	0.145169i	−0.563236	−	0.826296i	$-0.690444\pi$
$877$	−9.65588	+	4.29907i	−0.326056	+	0.145169i	0.237180	+	0.971466i	$0.423777\pi$
$878$	0.228656	−	0.253948i	0.00771677	−	0.00857034i
$879$	−19.6654	+	29.4842i	−0.663296	+	0.994478i
$880$	1.60927	−	1.01478i	0.0542483	−	0.0342082i
$881$	−46.2099			−1.55685			−0.778425	−	0.627738i	$-0.783981\pi$
$881$	−46.2099			−1.55685			−0.778425	+	0.627738i	$0.783981\pi$
$882$	−20.5599	+	4.27678i	−0.692288	+	0.144007i
$883$	−38.3024	−	27.8283i	−1.28898	−	0.936498i	−0.289195	−	0.957270i	$-0.593388\pi$
$883$	−38.3024	−	27.8283i	−1.28898	−	0.936498i	−0.999784	+	0.0207721i	$0.993388\pi$
$884$	−10.1460	+	1.06638i	−0.341245	+	0.0358663i
$885$	−6.44732	−	8.16445i	−0.216724	−	0.274445i
$886$	−28.0962	+	5.97202i	−0.943909	+	0.200634i
$887$	−6.17824	−	58.7820i	−0.207445	−	1.97371i	−0.226988	−	0.973898i	$-0.572888\pi$
$887$	−6.17824	−	58.7820i	−0.207445	−	1.97371i	0.0195430	−	0.999809i	$-0.493779\pi$
$888$	−1.30393	−	0.222944i	−0.0437572	−	0.00748150i
$889$	−10.2674	−	30.5481i	−0.344359	−	1.02455i
$890$		−	7.61010i		−	0.255091i
$891$	25.9990	−	14.6646i	0.870999	−	0.491284i
$892$	−11.1493	+	6.43703i	−0.373305	+	0.215528i
$893$	−1.94425	−	1.75061i	−0.0650619	−	0.0585820i
$894$	16.4600	+	13.6665i	0.550504	+	0.457078i
$895$	−3.62876	−	4.99456i	−0.121296	−	0.166950i
$896$	1.94822	−	1.79009i	0.0650855	−	0.0598028i
$897$	−67.6001	+	9.85880i	−2.25710	+	0.329176i
$898$	1.44914	+	13.7877i	0.0483585	+	0.460100i
$899$	−1.59985	+	15.2215i	−0.0533578	+	0.507666i
$900$	2.57649	+	13.7740i	0.0858831	+	0.459132i
$901$	5.57043	+	3.21609i	0.185578	+	0.107143i
$902$	4.87355	+	0.838749i	0.162272	+	0.0279273i
$903$	19.4726	−	29.8429i	0.648008	−	0.993110i
$904$	−2.02196	−	6.22294i	−0.0672493	−	0.206972i
$905$	−0.172262	−	0.386908i	−0.00572620	−	0.0128612i
$906$	40.3474	−	1.61877i	1.34045	−	0.0537801i
$907$	26.2737	−	5.58465i	0.872405	−	0.185435i	0.250109	−	0.968218i	$-0.419533\pi$
$907$	26.2737	−	5.58465i	0.872405	−	0.185435i	0.622296	+	0.782782i	$0.286200\pi$
$908$	6.42740	+	7.13835i	0.213301	+	0.236894i
$909$	1.26966	−	51.7679i	0.0421120	−	1.71703i
$910$	0.792739	−	8.35192i	0.0262790	−	0.276863i
$911$	6.76232	−	2.19721i	0.224046	−	0.0727968i	−0.194843	−	0.980834i	$-0.562420\pi$
$911$	6.76232	−	2.19721i	0.224046	−	0.0727968i	0.418889	+	0.908038i	$0.362420\pi$
$912$	−0.655738	+	10.1334i	−0.0217137	+	0.335551i
$913$	15.5621	−	5.73650i	0.515030	−	0.189851i
$914$	−22.2519	+	12.8472i	−0.736028	+	0.424946i
$915$	−0.607418	+	0.154801i	−0.0200806	+	0.00511756i
$916$	−9.10607	+	12.5334i	−0.300873	+	0.414116i
$917$	0.824963	+	7.15412i	0.0272427	+	0.236250i
$918$	8.37860	+	4.66489i	0.276535	+	0.153964i
$919$	5.04750	+	5.60582i	0.166502	+	0.184919i	0.820621	−	0.571472i	$-0.193627\pi$
$919$	5.04750	+	5.60582i	0.166502	+	0.184919i	−0.654120	+	0.756391i	$0.726961\pi$
$920$	3.73903	+	1.66473i	0.123272	+	0.0548844i
$921$	7.28260	+	19.6900i	0.239970	+	0.648809i
$922$	−8.07725	+	38.0005i	−0.266010	+	1.25148i
$923$	45.2040			1.48791
$924$	−14.3801	−	4.92052i	−0.473072	−	0.161873i
$925$	−3.56745			−0.117297
$926$	−7.54427	+	35.4930i	−0.247920	+	1.16637i
$927$	18.1302	−	19.1688i	0.595474	−	0.629587i
$928$	6.61576	+	2.94552i	0.217173	+	0.0966916i
$929$	−2.06133	−	2.28934i	−0.0676302	−	0.0751109i	0.708380	−	0.705831i	$-0.249426\pi$
$929$	−2.06133	−	2.28934i	−0.0676302	−	0.0751109i	−0.776010	+	0.630720i	$0.782760\pi$
$930$	2.07785	−	0.303033i	0.0681352	−	0.00993685i
$931$	−40.7197	+	5.11218i	−1.33453	+	0.167545i
$932$	10.8171	−	14.8885i	0.354327	−	0.487689i
$933$	−13.9653	−	54.7981i	−0.457204	−	1.79401i
$934$	−2.35385	+	1.35900i	−0.0770203	+	0.0444677i
$935$	−0.136924	−	3.50846i	−0.00447789	−	0.114739i
$936$	6.37165	+	15.3106i	0.208264	+	0.500444i
$937$	−48.7972	+	15.8552i	−1.59414	+	0.517966i	−0.965648	−	0.259854i	$-0.916326\pi$
$937$	−48.7972	+	15.8552i	−1.59414	+	0.517966i	−0.628487	+	0.777820i	$0.716326\pi$
$938$	−7.07869	+	9.95256i	−0.231128	+	0.324963i
$939$	13.7780	−	26.2404i	0.449627	−	0.856323i
$940$	0.171284	+	0.190230i	0.00558666	+	0.00620461i
$941$	7.36912	−	1.56635i	0.240226	−	0.0510617i	−0.0862250	−	0.996276i	$-0.527480\pi$
$941$	7.36912	−	1.56635i	0.240226	−	0.0510617i	0.326451	+	0.945214i	$0.394147\pi$
$942$	0.767390	+	19.1270i	0.0250029	+	0.623190i
$943$	4.32715	+	9.71893i	0.140911	+	0.316492i
$944$	−3.23563	−	9.95826i	−0.105311	−	0.324114i
$945$	−5.12467	+	5.99396i	−0.166706	+	0.194983i
$946$	23.1334	−	11.4005i	0.752130	−	0.370664i
$947$	−22.7672	−	13.1446i	−0.739834	−	0.427143i	0.0821750	−	0.996618i	$-0.473813\pi$
$947$	−22.7672	−	13.1446i	−0.739834	−	0.427143i	−0.822009	+	0.569475i	$0.807147\pi$
$948$	−17.6280	−	4.95583i	−0.572531	−	0.160958i
$949$	−7.31759	+	69.6222i	−0.237539	+	2.26003i
$950$	2.86248	+	27.2347i	0.0928711	+	0.883610i
$951$	−0.934164	−	6.40540i	−0.0302924	−	0.207709i
$952$	−1.06332	−	4.76565i	−0.0344623	−	0.154455i
$953$	31.2377	+	42.9950i	1.01189	+	1.39275i	0.917737	+	0.397188i	$0.130014\pi$
$953$	31.2377	+	42.9950i	1.01189	+	1.39275i	0.0941521	+	0.995558i	$0.469986\pi$
$954$	2.42399	−	10.1709i	0.0784794	−	0.329296i
$955$	8.80155	+	7.92495i	0.284811	+	0.256445i
$956$	−1.51798	+	0.876404i	−0.0490949	+	0.0283449i
$957$	−3.28749	−	41.4711i	−0.106269	−	1.34057i
$958$		−	5.73510i		−	0.185293i
$959$	14.1742	+	12.5060i	0.457709	+	0.403838i
$960$	0.167445	−	0.979337i	0.00540426	−	0.0316080i
$961$	−2.77348	−	26.3879i	−0.0894672	−	0.851224i
$962$	−4.12964	+	0.877783i	−0.133145	+	0.0283009i
$963$	40.0787	+	19.0350i	1.29152	+	0.613395i
$964$	−7.54332	+	0.792835i	−0.242954	+	0.0255355i
$965$	3.53640	+	2.56935i	0.113841	+	0.0827102i
$966$	−8.39396	−	31.6014i	−0.270071	−	1.01676i
$967$	28.6148			0.920191			0.460096	−	0.887869i	$-0.347815\pi$
$967$	28.6148			0.920191			0.460096	+	0.887869i	$0.347815\pi$
$968$	−7.13953	−	8.36822i	−0.229473	−	0.268965i
$969$	15.5909	+	10.3988i	0.500853	+	0.334059i
$970$	−1.28705	+	1.42941i	−0.0413246	+	0.0458956i
$971$	−44.7759	+	19.9355i	−1.43693	+	0.639761i	−0.969683	−	0.244368i	$-0.921420\pi$
$971$	−44.7759	+	19.9355i	−1.43693	+	0.639761i	−0.467244	+	0.884129i	$0.654753\pi$
$972$	3.37725	−	15.2182i	0.108325	−	0.488125i
$973$	20.9190	+	6.56448i	0.670632	+	0.210448i
$974$	17.0715	+	5.54687i	0.547006	+	0.177733i
$975$	23.8957	+	37.8029i	0.765276	+	1.21066i
$976$	−0.627447	−	0.0659474i	−0.0200841	−	0.00211092i
$977$	22.9222	+	20.6393i	0.733347	+	0.660309i	0.948682	−	0.316231i	$-0.102418\pi$
$977$	22.9222	+	20.6393i	0.733347	+	0.660309i	−0.215335	+	0.976540i	$0.569084\pi$
$978$	−0.854239	+	13.2009i	−0.0273155	+	0.422119i
$979$	−43.5469	+	6.30230i	−1.39176	+	0.201422i
$980$	4.01456	−	0.0809945i	0.128241	−	0.00258728i
$981$	−48.1568	−	16.9634i	−1.53753	−	0.541599i
$982$	12.2239	−	5.44243i	0.390080	−	0.173675i
$983$	−35.8825	−	15.9759i	−1.14447	−	0.509553i	−0.255182	−	0.966893i	$-0.582136\pi$
$983$	−35.8825	−	15.9759i	−1.14447	−	0.509553i	−0.889292	+	0.457340i	$0.848802\pi$
$984$	2.02679	−	1.60052i	0.0646117	−	0.0510227i
$985$	−10.5644	+	9.51223i	−0.336610	+	0.303085i
$986$	10.8126	−	7.85580i	0.344343	−	0.250180i
$987$	0.324294	−	2.01909i	0.0103224	−	0.0642683i
$988$	10.0148	+	30.8223i	0.318612	+	0.980587i
$989$	48.0492	+	27.7412i	1.52788	+	0.882120i
$990$	−5.40204	+	1.84216i	−0.171688	+	0.0585477i
$991$	1.31178	+	2.27207i	0.0416701	+	0.0721748i	0.886108	−	0.463478i	$-0.153399\pi$
$991$	1.31178	+	2.27207i	0.0416701	+	0.0721748i	−0.844438	+	0.535653i	$0.820065\pi$
$992$	2.06728	+	0.439413i	0.0656361	+	0.0139514i
$993$	0.956193	−	5.59250i	0.0303439	−	0.177473i
$994$	2.47845	+	21.4932i	0.0786116	+	0.681724i
$995$	14.0275	+	4.55782i	0.444703	+	0.144493i
$996$	3.20295	−	8.04764i	0.101489	−	0.254999i
$997$	1.73262	−	3.89152i	0.0548725	−	0.123246i	−0.884028	−	0.467433i	$-0.845179\pi$
$997$	1.73262	−	3.89152i	0.0548725	−	0.123246i	0.938901	+	0.344187i	$0.111846\pi$
$998$	−0.959905	−	0.100890i	−0.0303853	−	0.00319362i
$999$	3.65017	+	1.55749i	0.115486	+	0.0492768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bf.a.5.18	yes	256
3.2	odd	2	inner	462.2.bf.a.5.3	✓	256
7.3	odd	6	inner	462.2.bf.a.269.20	yes	256
11.9	even	5	inner	462.2.bf.a.383.9	yes	256
21.17	even	6	inner	462.2.bf.a.269.9	yes	256
33.20	odd	10	inner	462.2.bf.a.383.20	yes	256
77.31	odd	30	inner	462.2.bf.a.185.3	yes	256
231.185	even	30	inner	462.2.bf.a.185.18	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bf.a.5.3	✓	256	3.2	odd	2	inner
462.2.bf.a.5.18	yes	256	1.1	even	1	trivial
462.2.bf.a.185.3	yes	256	77.31	odd	30	inner
462.2.bf.a.185.18	yes	256	231.185	even	30	inner
462.2.bf.a.269.9	yes	256	21.17	even	6	inner
462.2.bf.a.269.20	yes	256	7.3	odd	6	inner
462.2.bf.a.383.9	yes	256	11.9	even	5	inner
462.2.bf.a.383.20	yes	256	33.20	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bf (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207912 - 0.978148i) q^{2} +(-1.62450 + 0.600840i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.383830 - 0.426287i) q^{5} +(0.249958 + 1.71392i) q^{6} +(-2.12466 + 1.57664i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.27798 - 1.95213i) q^{9} +O(q^{10})\)	\(q+(0.207912 - 0.978148i) q^{2} +(-1.62450 + 0.600840i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-0.383830 - 0.426287i) q^{5} +(0.249958 + 1.71392i) q^{6} +(-2.12466 + 1.57664i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.27798 - 1.95213i) q^{9} +(-0.496774 + 0.286813i) q^{10} +(2.05262 + 2.60514i) q^{11} +(1.72844 + 0.111848i) q^{12} +(5.25730 - 1.70820i) q^{13} +(1.10045 + 2.40604i) q^{14} +(0.879662 + 0.461881i) q^{15} +(0.669131 + 0.743145i) q^{16} +(1.80521 - 0.383709i) q^{17} +(-1.43585 - 2.63407i) q^{18} +(-2.38460 - 5.35590i) q^{19} +(0.177260 + 0.545550i) q^{20} +(2.50420 - 3.83784i) q^{21} +(2.97498 - 1.46612i) q^{22} +(6.17919 + 3.56755i) q^{23} +(0.468766 - 1.66741i) q^{24} +(0.488248 - 4.64537i) q^{25} +(-0.577817 - 5.49757i) q^{26} +(-2.52766 + 4.53993i) q^{27} +(2.58226 - 0.576157i) q^{28} +(4.25665 + 5.85878i) q^{29} +(0.634680 - 0.764409i) q^{30} +(1.57061 + 1.41418i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.89974 - 2.99875i) q^{33} -1.84554i q^{34} +(1.48761 + 0.300553i) q^{35} +(-2.87504 + 0.856816i) q^{36} +(-0.0798338 - 0.759568i) q^{37} +(-5.73465 + 1.21894i) q^{38} +(-7.51411 + 5.93376i) q^{39} +(0.570483 - 0.0599602i) q^{40} +(1.20627 + 0.876408i) q^{41} +(-3.23332 - 3.24741i) q^{42} +7.77598 q^{43} +(-0.815553 - 3.21479i) q^{44} +(-1.70652 - 0.221789i) q^{45} +(4.77432 - 5.30242i) q^{46} +(0.407668 - 0.181505i) q^{47} +(-1.53351 - 0.805196i) q^{48} +(2.02839 - 6.69967i) q^{49} +(-4.44234 - 1.44340i) q^{50} +(-2.70201 + 1.70797i) q^{51} +(-5.49757 - 0.577817i) q^{52} +(2.59005 + 2.33210i) q^{53} +(3.91519 + 3.41633i) q^{54} +(0.322681 - 1.87494i) q^{55} +(-0.0266852 - 2.64562i) q^{56} +(7.09182 + 7.26788i) q^{57} +(6.61576 - 2.94552i) q^{58} +(-9.56549 - 4.25883i) q^{59} +(-0.615747 - 0.779740i) q^{60} +(-0.468853 + 0.422157i) q^{61} +(1.70983 - 1.24226i) q^{62} +(-1.76214 + 7.73918i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-2.74609 - 1.58546i) q^{65} +(-3.95194 + 4.16920i) q^{66} +(2.30807 + 3.99770i) q^{67} +(-1.80521 - 0.383709i) q^{68} +(-12.1816 - 2.08278i) q^{69} +(0.603277 - 1.39262i) q^{70} +(7.77727 + 2.52699i) q^{71} +(0.240338 + 2.99036i) q^{72} +(-5.15099 + 11.5693i) q^{73} +(-0.759568 - 0.0798338i) q^{74} +(1.99796 + 7.83974i) q^{75} +5.86276i q^{76} +(-8.46850 - 2.29880i) q^{77} +(4.24182 + 8.58360i) q^{78} +(-10.3411 - 2.19806i) q^{79} +(0.0599602 - 0.570483i) q^{80} +(1.37841 - 8.89382i) q^{81} +(1.10805 - 0.997697i) q^{82} +(1.54533 - 4.75602i) q^{83} +(-3.84869 + 2.48749i) q^{84} +(-0.856463 - 0.622257i) q^{85} +(1.61672 - 7.60606i) q^{86} +(-10.4351 - 6.96000i) q^{87} +(-3.31410 + 0.129338i) q^{88} +(-6.63333 + 11.4893i) q^{89} +(-0.571749 + 1.62312i) q^{90} +(-8.47676 + 11.9182i) q^{91} +(-4.19391 - 5.77243i) q^{92} +(-3.40114 - 1.35365i) q^{93} +(-0.0927802 - 0.436497i) q^{94} +(-1.36787 + 3.07228i) q^{95} +(-1.10644 + 1.33259i) q^{96} +(3.18905 - 1.03619i) q^{97} +(-6.13154 - 3.37701i) q^{98} +(9.76139 + 1.92750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Introduction

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