LMFDB - Embedded newform 462.2.bc.a.95.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.5
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.a.107.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(-1.18732 - 1.26106i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.157991 + 0.354854i) q^{5} +(-1.37826 + 1.04900i) q^{6} +(0.106147 + 2.64362i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.180521 + 2.99456i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(-1.18732 - 1.26106i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.157991 + 0.354854i) q^{5} +(-1.37826 + 1.04900i) q^{6} +(0.106147 + 2.64362i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.180521 + 2.99456i) q^{9} +(0.336396 + 0.194218i) q^{10} +(-1.98544 + 2.65670i) q^{11} +(0.899191 + 1.48036i) q^{12} +(0.804816 - 1.10773i) q^{13} +(2.64023 + 0.170768i) q^{14} +(0.635078 - 0.222091i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.160755 + 1.52948i) q^{17} +(2.95929 + 0.492549i) q^{18} +(0.942435 + 4.43381i) q^{19} +(0.228317 - 0.314252i) q^{20} +(3.20772 - 3.27269i) q^{21} +(2.43461 + 2.25226i) q^{22} +(-6.74827 + 3.89611i) q^{23} +(1.56624 - 0.739525i) q^{24} +(3.24469 + 3.60360i) q^{25} +(-1.01754 - 0.916196i) q^{26} +(3.99065 - 3.32787i) q^{27} +(0.445812 - 2.60792i) q^{28} +(-2.83206 - 8.71618i) q^{29} +(-0.154491 - 0.654814i) q^{30} +(8.50830 - 3.78814i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.70760 - 0.650615i) q^{33} +1.53791 q^{34} +(-0.954870 - 0.380002i) q^{35} +(0.799181 - 2.89159i) q^{36} +(-0.538125 + 0.597649i) q^{37} +(4.50803 - 0.473813i) q^{38} +(-2.35249 + 0.300322i) q^{39} +(-0.288664 - 0.259915i) q^{40} +(-1.43120 + 4.40478i) q^{41} +(-2.91947 - 3.53224i) q^{42} +3.44350i q^{43} +(2.49441 - 2.18585i) q^{44} +(-1.03411 - 0.537173i) q^{45} +(3.16938 + 7.11855i) q^{46} +(2.18458 + 10.2777i) q^{47} +(-0.571758 - 1.63496i) q^{48} +(-6.97747 + 0.561225i) q^{49} +(3.92302 - 2.85024i) q^{50} +(1.73789 - 2.01871i) q^{51} +(-1.01754 + 0.916196i) q^{52} +(-2.94977 - 6.62530i) q^{53} +(-2.89251 - 4.31664i) q^{54} +(-0.629058 - 1.12428i) q^{55} +(-2.54703 - 0.715972i) q^{56} +(4.47230 - 6.45283i) q^{57} +(-8.96446 + 1.90545i) q^{58} +(-0.621978 + 2.92618i) q^{59} +(-0.667375 + 0.0851981i) q^{60} +(-2.71039 + 6.08764i) q^{61} +(-2.87803 - 8.85766i) q^{62} +(-7.93565 - 0.159364i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.265930 + 0.460604i) q^{65} +(-0.0504441 - 5.74434i) q^{66} +(-3.38743 + 5.86719i) q^{67} +(0.160755 - 1.52948i) q^{68} +(12.9256 + 3.88399i) q^{69} +(-0.477732 + 0.909918i) q^{70} +(5.48581 + 7.55057i) q^{71} +(-2.79222 - 1.09706i) q^{72} +(0.267020 - 1.25623i) q^{73} +(0.538125 + 0.597649i) q^{74} +(0.691831 - 8.37038i) q^{75} -4.53286i q^{76} +(-7.23405 - 4.96674i) q^{77} +(0.0527750 + 2.37100i) q^{78} +(-13.8845 - 1.45932i) q^{79} +(-0.288664 + 0.259915i) q^{80} +(-8.93482 - 1.08116i) q^{81} +(4.23105 + 1.88379i) q^{82} +(-5.34599 + 3.88409i) q^{83} +(-3.81806 + 2.53425i) q^{84} +(-0.568141 - 0.184600i) q^{85} +(3.42464 + 0.359944i) q^{86} +(-7.62901 + 13.9203i) q^{87} +(-1.91313 - 2.70923i) q^{88} +(8.67330 - 5.00753i) q^{89} +(-0.642325 + 0.972298i) q^{90} +(3.01386 + 2.01004i) q^{91} +(7.41085 - 2.40793i) q^{92} +(-14.8792 - 6.23168i) q^{93} +(10.4497 - 1.09831i) q^{94} +(-1.72225 - 0.366076i) q^{95} +(-1.68577 + 0.397726i) q^{96} +(-2.60672 - 1.89389i) q^{97} +(-0.171193 + 6.99791i) q^{98} +(-7.59724 - 6.42511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$3$	−1.18732	−	1.26106i	−0.685502	−	0.728071i
$3$	−1.18732	−	1.26106i	−0.685502	−	0.728071i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−0.157991	+	0.354854i	−0.0706558	+	0.158696i	−0.945421	−	0.325852i	$-0.894349\pi$
$5$	−0.157991	+	0.354854i	−0.0706558	+	0.158696i	0.874765	+	0.484547i	$0.161016\pi$
$6$	−1.37826	+	1.04900i	−0.562671	+	0.428254i
$7$	0.106147	+	2.64362i	0.0401198	+	0.999195i
$7$	0.106147	+	2.64362i	0.0401198	+	0.999195i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.180521	+	2.99456i	−0.0601736	+	0.998188i
$10$	0.336396	+	0.194218i	0.106378	+	0.0614172i
$11$	−1.98544	+	2.65670i	−0.598632	+	0.801024i
$11$	−1.98544	+	2.65670i	−0.598632	+	0.801024i
$12$	0.899191	+	1.48036i	0.259574	+	0.427342i
$13$	0.804816	−	1.10773i	0.223216	−	0.307230i	−0.682691	−	0.730707i	$-0.739191\pi$
$13$	0.804816	−	1.10773i	0.223216	−	0.307230i	0.905907	+	0.423477i	$0.139191\pi$
$14$	2.64023	+	0.170768i	0.705632	+	0.0456397i
$15$	0.635078	−	0.222091i	0.163976	−	0.0573438i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.160755	+	1.52948i	0.0389888	+	0.370954i	0.996568	+	0.0827823i	$0.0263806\pi$
$17$	0.160755	+	1.52948i	0.0389888	+	0.370954i	−0.957579	+	0.288171i	$0.906953\pi$
$18$	2.95929	+	0.492549i	0.697511	+	0.116095i
$19$	0.942435	+	4.43381i	0.216209	+	1.01718i	0.943632	+	0.330996i	$0.107385\pi$
$19$	0.942435	+	4.43381i	0.216209	+	1.01718i	−0.727423	+	0.686189i	$0.759282\pi$
$20$	0.228317	−	0.314252i	0.0510533	−	0.0702688i
$21$	3.20772	−	3.27269i	0.699982	−	0.714160i
$22$	2.43461	+	2.25226i	0.519060	+	0.480184i
$23$	−6.74827	+	3.89611i	−1.40711	+	0.812396i	−0.995109	−	0.0987868i	$-0.968504\pi$
$23$	−6.74827	+	3.89611i	−1.40711	+	0.812396i	−0.412002	+	0.911183i	$0.635170\pi$
$24$	1.56624	−	0.739525i	0.319707	−	0.150955i
$25$	3.24469	+	3.60360i	0.648939	+	0.720719i
$26$	−1.01754	−	0.916196i	−0.199556	−	0.179681i
$27$	3.99065	−	3.32787i	0.768000	−	0.640449i
$28$	0.445812	−	2.60792i	0.0842506	−	0.492851i
$29$	−2.83206	−	8.71618i	−0.525900	−	1.61855i	−0.762530	−	0.646953i	$-0.776043\pi$
$29$	−2.83206	−	8.71618i	−0.525900	−	1.61855i	0.236630	−	0.971600i	$-0.423957\pi$
$30$	−0.154491	−	0.654814i	−0.0282061	−	0.119552i
$31$	8.50830	−	3.78814i	1.52814	−	0.680370i	0.541113	−	0.840950i	$-0.318003\pi$
$31$	8.50830	−	3.78814i	1.52814	−	0.680370i	0.987023	+	0.160580i	$0.0513365\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	5.70760	−	0.650615i	0.993566	−	0.113258i
$34$	1.53791			0.263749
$35$	−0.954870	−	0.380002i	−0.161403	−	0.0642321i
$36$	0.799181	−	2.89159i	0.133197	−	0.481932i
$37$	−0.538125	+	0.597649i	−0.0884673	+	0.0982528i	−0.785753	−	0.618541i	$-0.787724\pi$
$37$	−0.538125	+	0.597649i	−0.0884673	+	0.0982528i	0.697286	+	0.716793i	$0.254391\pi$
$38$	4.50803	−	0.473813i	0.731299	−	0.0768626i
$39$	−2.35249	+	0.300322i	−0.376700	+	0.0480901i
$40$	−0.288664	−	0.259915i	−0.0456419	−	0.0410961i
$41$	−1.43120	+	4.40478i	−0.223516	+	0.687912i	0.774923	+	0.632056i	$0.217789\pi$
$41$	−1.43120	+	4.40478i	−0.223516	+	0.687912i	−0.998439	+	0.0558558i	$0.982211\pi$
$42$	−2.91947	−	3.53224i	−0.450484	−	0.545036i
$43$			3.44350i			0.525129i	0.964914	+	0.262564i	$0.0845682\pi$
$43$			3.44350i			0.525129i	−0.964914	+	0.262564i	$0.915432\pi$
$44$	2.49441	−	2.18585i	0.376046	−	0.329529i
$45$	−1.03411	−	0.537173i	−0.154156	−	0.0800771i
$46$	3.16938	+	7.11855i	0.467300	+	1.04957i
$47$	2.18458	+	10.2777i	0.318654	+	1.49915i	0.787745	+	0.616001i	$0.211248\pi$
$47$	2.18458	+	10.2777i	0.318654	+	1.49915i	−0.469091	+	0.883150i	$0.655418\pi$
$48$	−0.571758	−	1.63496i	−0.0825261	−	0.235986i
$49$	−6.97747	+	0.561225i	−0.996781	+	0.0801750i
$50$	3.92302	−	2.85024i	0.554799	−	0.403085i
$51$	1.73789	−	2.01871i	0.243354	−	0.282676i
$52$	−1.01754	+	0.916196i	−0.141107	+	0.127054i
$53$	−2.94977	−	6.62530i	−0.405183	−	0.910055i	−0.994750	−	0.102336i	$-0.967368\pi$
$53$	−2.94977	−	6.62530i	−0.405183	−	0.910055i	0.589567	−	0.807719i	$-0.299298\pi$
$54$	−2.89251	−	4.31664i	−0.393620	−	0.587421i
$55$	−0.629058	−	1.12428i	−0.0848222	−	0.151597i
$56$	−2.54703	−	0.715972i	−0.340362	−	0.0956758i
$57$	4.47230	−	6.45283i	0.592370	−	0.854698i
$58$	−8.96446	+	1.90545i	−1.17709	+	0.250198i
$59$	−0.621978	+	2.92618i	−0.0809746	+	0.380956i	−0.999909	−	0.0134537i	$-0.995717\pi$
$59$	−0.621978	+	2.92618i	−0.0809746	+	0.380956i	0.918935	+	0.394409i	$0.129051\pi$
$60$	−0.667375	+	0.0851981i	−0.0861578	+	0.0109990i
$61$	−2.71039	+	6.08764i	−0.347030	+	0.779442i	0.652731	+	0.757590i	$0.273623\pi$
$61$	−2.71039	+	6.08764i	−0.347030	+	0.779442i	−0.999761	+	0.0218526i	$0.993044\pi$
$62$	−2.87803	−	8.85766i	−0.365510	−	1.12492i
$63$	−7.93565	−	0.159364i	−0.999798	−	0.0200780i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.265930	+	0.460604i	0.0329846	+	0.0571310i
$66$	−0.0504441	−	5.74434i	−0.00620924	−	0.707080i
$67$	−3.38743	+	5.86719i	−0.413840	+	0.716792i	−0.995306	−	0.0967789i	$-0.969146\pi$
$67$	−3.38743	+	5.86719i	−0.413840	+	0.716792i	0.581466	+	0.813571i	$0.302479\pi$
$68$	0.160755	−	1.52948i	0.0194944	−	0.185477i
$69$	12.9256	+	3.88399i	1.55606	+	0.467577i
$70$	−0.477732	+	0.909918i	−0.0570999	+	0.108756i
$71$	5.48581	+	7.55057i	0.651046	+	0.896088i	0.999144	−	0.0413700i	$-0.0131722\pi$
$71$	5.48581	+	7.55057i	0.651046	+	0.896088i	−0.348098	+	0.937458i	$0.613172\pi$
$72$	−2.79222	−	1.09706i	−0.329066	−	0.129289i
$73$	0.267020	−	1.25623i	0.0312524	−	0.147031i	−0.959755	−	0.280839i	$-0.909387\pi$
$73$	0.267020	−	1.25623i	0.0312524	−	0.147031i	0.991007	+	0.133808i	$0.0427206\pi$
$74$	0.538125	+	0.597649i	0.0625558	+	0.0694752i
$75$	0.691831	−	8.37038i	0.0798857	−	0.966528i
$76$		−	4.53286i		−	0.519955i
$77$	−7.23405	−	4.96674i	−0.824396	−	0.566013i
$78$	0.0527750	+	2.37100i	0.00597559	+	0.268462i
$79$	−13.8845	−	1.45932i	−1.56213	−	0.164186i	−0.716356	−	0.697735i	$-0.754191\pi$
$79$	−13.8845	−	1.45932i	−1.56213	−	0.164186i	−0.845769	+	0.533549i	$0.820858\pi$
$80$	−0.288664	+	0.259915i	−0.0322737	+	0.0290593i
$81$	−8.93482	−	1.08116i	−0.992758	−	0.120129i
$82$	4.23105	+	1.88379i	0.467242	+	0.208029i
$83$	−5.34599	+	3.88409i	−0.586799	+	0.426334i	−0.841169	−	0.540773i	$-0.818132\pi$
$83$	−5.34599	+	3.88409i	−0.586799	+	0.426334i	0.254370	+	0.967107i	$0.418132\pi$
$84$	−3.81806	+	2.53425i	−0.416584	+	0.276510i
$85$	−0.568141	−	0.184600i	−0.0616235	−	0.0200227i
$86$	3.42464	+	0.359944i	0.369288	+	0.0388137i
$87$	−7.62901	+	13.9203i	−0.817915	+	1.49241i
$88$	−1.91313	−	2.70923i	−0.203941	−	0.288805i
$89$	8.67330	−	5.00753i	0.919368	−	0.530798i	0.0359348	−	0.999354i	$-0.488559\pi$
$89$	8.67330	−	5.00753i	0.919368	−	0.530798i	0.883433	+	0.468557i	$0.155226\pi$
$90$	−0.642325	+	0.972298i	−0.0677070	+	0.102489i
$91$	3.01386	+	2.01004i	0.315938	+	0.210710i
$92$	7.41085	−	2.40793i	0.772634	−	0.251044i
$93$	−14.8792	−	6.23168i	−1.54290	−	0.646196i
$94$	10.4497	−	1.09831i	1.07781	−	0.113282i
$95$	−1.72225	−	0.366076i	−0.176699	−	0.0375586i
$96$	−1.68577	+	0.397726i	−0.172053	+	0.0405927i
$97$	−2.60672	−	1.89389i	−0.264672	−	0.192296i	0.447532	−	0.894268i	$-0.352303\pi$
$97$	−2.60672	−	1.89389i	−0.264672	−	0.192296i	−0.712204	+	0.701972i	$0.752303\pi$
$98$	−0.171193	+	6.99791i	−0.0172931	+	0.706895i
$99$	−7.59724	−	6.42511i	−0.763551	−	0.645748i
$100$	−2.42456	−	4.19946i	−0.242456	−	0.419946i
$101$	10.4550	−	4.65488i	1.04031	−	0.463178i	0.185790	−	0.982589i	$-0.440516\pi$
$101$	10.4550	−	4.65488i	1.04031	−	0.463178i	0.854524	+	0.519412i	$0.173849\pi$
$102$	−1.82599	−	1.93938i	−0.180800	−	0.192028i
$103$	2.83725	−	3.15109i	0.279563	−	0.310486i	−0.586967	−	0.809610i	$-0.699678\pi$
$103$	2.83725	−	3.15109i	0.279563	−	0.310486i	0.866530	+	0.499125i	$0.166345\pi$
$104$	0.804816	+	1.10773i	0.0789187	+	0.108622i
$105$	0.654537	+	1.65533i	0.0638763	+	0.161544i
$106$	−6.89734	+	2.24108i	−0.669929	+	0.217673i
$107$	−10.9732	+	2.33242i	−1.06082	+	0.225483i	−0.705098	−	0.709110i	$-0.749097\pi$
$107$	−10.9732	+	2.33242i	−1.06082	+	0.225483i	−0.355718	+	0.934593i	$0.615764\pi$
$108$	−4.59535	+	2.42545i	−0.442187	+	0.233389i
$109$	16.3029	+	9.41250i	1.56154	+	0.901554i	0.997102	+	0.0760767i	$0.0242394\pi$
$109$	16.3029	+	9.41250i	1.56154	+	0.901554i	0.564435	+	0.825477i	$0.309094\pi$
$110$	−1.18387	+	0.508093i	−0.112878	+	0.0484448i
$111$	1.39260	−	0.0309973i	0.132179	−	0.00294213i
$112$	−0.978287	+	2.45824i	−0.0924395	+	0.232282i
$113$	−6.52879	−	2.12133i	−0.614177	−	0.199558i	−0.0146235	−	0.999893i	$-0.504655\pi$
$113$	−6.52879	−	2.12133i	−0.614177	−	0.199558i	−0.599553	+	0.800335i	$0.704655\pi$
$114$	−5.95000	−	5.12230i	−0.557268	−	0.479748i
$115$	−0.316385	−	3.01020i	−0.0295031	−	0.280703i
$116$	0.957975	+	9.11452i	0.0889458	+	0.846262i
$117$	3.17189	+	2.61004i	0.293242	+	0.241298i
$118$	2.84513	+	0.924439i	0.261916	+	0.0851015i
$119$	−4.02631	+	0.587325i	−0.369091	+	0.0538400i
$120$	0.0149717	+	0.672625i	0.00136672	+	0.0614020i
$121$	−3.11608	−	10.5494i	−0.283280	−	0.959037i
$122$	5.77098	+	3.33187i	0.522480	+	0.301654i
$123$	7.25398	−	3.42508i	0.654069	−	0.308829i
$124$	−9.10997	+	1.93638i	−0.818100	+	0.173892i
$125$	−3.63851	+	1.18222i	−0.325438	+	0.105741i
$126$	−0.987993	+	7.87552i	−0.0880174	+	0.701607i
$127$	−1.27062	−	1.74885i	−0.112749	−	0.155186i	0.748913	−	0.662668i	$-0.230576\pi$
$127$	−1.27062	−	1.74885i	−0.112749	−	0.155186i	−0.861662	+	0.507483i	$0.830576\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	4.34244	−	4.08855i	0.382331	−	0.359977i
$130$	0.485878	−	0.216327i	0.0426144	−	0.0189731i
$131$	−7.62265	−	13.2028i	−0.665994	−	1.15353i	−0.979015	−	0.203789i	$-0.934674\pi$
$131$	−7.62265	−	13.2028i	−0.665994	−	1.15353i	0.313021	−	0.949746i	$-0.398659\pi$
$132$	−5.71815	−	0.550279i	−0.497701	−	0.0478957i
$133$	−11.6213	+	2.96207i	−1.00769	+	0.256844i
$134$	5.48097	+	3.98216i	0.473484	+	0.344006i
$135$	0.550422	+	1.94187i	0.0473728	+	0.167130i
$136$	−1.50430	−	0.319749i	−0.128993	−	0.0274182i
$137$	2.24300	−	0.235749i	0.191632	−	0.0201414i	−0.00822607	−	0.999966i	$-0.502618\pi$
$137$	2.24300	−	0.235749i	0.191632	−	0.0201414i	0.199858	+	0.979825i	$0.435952\pi$
$138$	5.21380	−	12.4488i	0.443828	−	1.05971i
$139$	6.80831	−	2.21215i	0.577473	−	0.187633i	−0.00569493	−	0.999984i	$-0.501813\pi$
$139$	6.80831	−	2.21215i	0.577473	−	0.187633i	0.583168	+	0.812351i	$0.301813\pi$
$140$	0.854997	+	0.570227i	0.0722605	+	0.0481930i
$141$	10.3669	−	14.9578i	0.873050	−	1.25967i
$142$	8.08264	−	4.66651i	0.678280	−	0.391605i
$143$	1.34500	+	4.33749i	0.112475	+	0.362719i
$144$	−1.38291	+	2.66225i	−0.115243	+	0.221854i
$145$	3.54041	+	0.372112i	0.294015	+	0.0309022i
$146$	−1.22144	−	0.396869i	−0.101087	−	0.0328451i
$147$	8.99225	+	8.13261i	0.741668	+	0.670767i
$148$	0.650624	−	0.472706i	0.0534810	−	0.0388562i
$149$	14.2576	+	6.34788i	1.16803	+	0.520038i	0.896782	−	0.442473i	$-0.145899\pi$
$149$	14.2576	+	6.34788i	1.16803	+	0.520038i	0.271243	+	0.962511i	$0.412565\pi$
$150$	−8.25221	−	1.56298i	−0.673790	−	0.127617i
$151$	−3.85480	+	3.47088i	−0.313699	+	0.282456i	−0.810906	−	0.585176i	$-0.801026\pi$
$151$	−3.85480	+	3.47088i	−0.313699	+	0.282456i	0.497207	+	0.867632i	$0.334359\pi$
$152$	−4.50803	−	0.473813i	−0.365649	−	0.0384313i
$153$	−4.60915	+	0.205288i	−0.372628	+	0.0165966i
$154$	−5.69570	+	6.67525i	−0.458973	+	0.537907i
$155$			3.61770i			0.290581i
$156$	2.36352	+	0.195351i	0.189233	+	0.0156406i
$157$	−6.00138	−	6.66520i	−0.478962	−	0.531941i	0.454438	−	0.890778i	$-0.349840\pi$
$157$	−6.00138	−	6.66520i	−0.478962	−	0.531941i	−0.933400	+	0.358837i	$0.883173\pi$
$158$	−2.90265	+	13.6559i	−0.230922	+	1.08640i
$159$	−4.85253	+	11.5862i	−0.384831	+	0.918846i
$160$	0.228317	+	0.314252i	0.0180501	+	0.0248438i
$161$	−11.0162	−	17.4263i	−0.868195	−	1.37338i
$162$	−2.00918	+	8.77287i	−0.157856	+	0.689261i
$163$	1.55061	−	14.7530i	0.121453	−	1.15555i	−0.748750	−	0.662853i	$-0.769345\pi$
$163$	1.55061	−	14.7530i	0.121453	−	1.15555i	0.870203	−	0.492694i	$-0.163988\pi$
$164$	2.31573	−	4.01097i	0.180828	−	0.313204i
$165$	−0.670878	+	2.12816i	−0.0522278	+	0.165677i
$166$	3.30400	+	5.72270i	0.256440	+	0.444168i
$167$	16.8083	+	12.2120i	1.30067	+	0.944990i	0.999962	−	0.00872665i	$-0.00277781\pi$
$167$	16.8083	+	12.2120i	1.30067	+	0.944990i	0.300706	+	0.953717i	$0.402778\pi$
$168$	2.12128	+	4.06204i	0.163660	+	0.313393i
$169$	3.43788	+	10.5807i	0.264452	+	0.813899i
$170$	−0.242976	+	0.545733i	−0.0186354	+	0.0418558i
$171$	−13.4474	+	2.02179i	−1.02835	+	0.154610i
$172$	0.715944	−	3.36825i	0.0545902	−	0.256827i
$173$	4.18356	−	0.889242i	0.318070	−	0.0676078i	−0.0461103	−	0.998936i	$-0.514683\pi$
$173$	4.18356	−	0.889242i	0.318070	−	0.0676078i	0.364180	+	0.931329i	$0.381349\pi$
$174$	13.0466	+	9.04228i	0.989061	+	0.685494i
$175$	−9.18213	+	8.96025i	−0.694104	+	0.677331i
$176$	−2.89436	+	1.61946i	−0.218171	+	0.122072i
$177$	4.42856	−	2.68997i	0.332871	−	0.202191i
$178$	−4.07350	−	9.14922i	−0.305321	−	0.685763i
$179$	15.8161	−	14.2409i	1.18215	−	1.06441i	0.185497	−	0.982645i	$-0.440610\pi$
$179$	15.8161	−	14.2409i	1.18215	−	1.06441i	0.996651	−	0.0817668i	$-0.0260563\pi$
$180$	0.899830	+	0.740439i	0.0670694	+	0.0551891i
$181$	18.2773	−	13.2793i	1.35854	−	0.987040i	0.360009	−	0.932949i	$-0.382774\pi$
$181$	18.2773	−	13.2793i	1.35854	−	0.987040i	0.998536	−	0.0540915i	$-0.0172263\pi$
$182$	2.31407	−	2.78724i	0.171530	−	0.206604i
$183$	10.8950	−	3.81005i	0.805379	−	0.281647i
$184$	−1.62010	−	7.62195i	−0.119435	−	0.561898i
$185$	−0.127059	−	0.285379i	−0.00934157	−	0.0209815i
$186$	−7.75284	+	14.1463i	−0.568466	+	1.03725i
$187$	−4.38254	−	2.60961i	−0.320483	−	0.190834i
$188$		−	10.5073i		−	0.766322i
$189$	9.22123	+	10.1965i	0.670746	+	0.741687i
$190$	−0.544095	+	1.67455i	−0.0394728	+	0.121485i
$191$	−6.91052	−	6.22226i	−0.500027	−	0.450227i	0.380113	−	0.924940i	$-0.375885\pi$
$191$	−6.91052	−	6.22226i	−0.500027	−	0.450227i	−0.880140	+	0.474713i	$0.842552\pi$
$192$	0.219336	+	1.71811i	0.0158292	+	0.123994i
$193$	−4.60204	+	0.483694i	−0.331262	+	0.0348171i	−0.268700	−	0.963224i	$-0.586594\pi$
$193$	−4.60204	+	0.483694i	−0.331262	+	0.0348171i	−0.0625625	+	0.998041i	$0.519927\pi$
$194$	−2.15599	+	2.39447i	−0.154791	+	0.171913i
$195$	0.265102	−	0.882240i	0.0189844	−	0.0631785i
$196$	6.94168	+	0.901736i	0.495834	+	0.0644097i
$197$	−0.300354			−0.0213994			−0.0106997	−	0.999943i	$-0.503406\pi$
$197$	−0.300354			−0.0213994			−0.0106997	+	0.999943i	$0.503406\pi$
$198$	−7.18404	+	6.88401i	−0.510547	+	0.489225i
$199$	−3.60764	+	6.24861i	−0.255739	+	0.442953i	−0.965096	−	0.261897i	$-0.915652\pi$
$199$	−3.60764	+	6.24861i	−0.255739	+	0.442953i	0.709357	+	0.704849i	$0.248985\pi$
$200$	−4.42989	+	1.97231i	−0.313240	+	0.139464i
$201$	11.4208	−	2.69453i	0.805563	−	0.190058i
$202$	−3.53653	−	10.8843i	−0.248829	−	0.765818i
$203$	22.7417	−	8.41208i	1.59615	−	0.590412i
$204$	−2.11963	+	1.61327i	−0.148404	+	0.112951i
$205$	−1.33694	−	1.20379i	−0.0933759	−	0.0840760i
$206$	−2.83725	−	3.15109i	−0.197681	−	0.219547i
$207$	−10.4490	−	20.9114i	−0.726253	−	1.45345i
$208$	1.18579	−	0.684617i	0.0822198	−	0.0474697i
$209$	−13.6504	−	6.29928i	−0.944219	−	0.435730i
$210$	1.71468	−	0.477922i	0.118324	−	0.0329798i
$211$	−2.53059	+	3.48306i	−0.174213	+	0.239784i	−0.887191	−	0.461403i	$-0.847346\pi$
$211$	−2.53059	+	3.48306i	−0.174213	+	0.239784i	0.712977	+	0.701187i	$0.247346\pi$
$212$	1.50784	+	7.09381i	0.103559	+	0.487205i
$213$	3.00825	−	15.8829i	0.206122	−	1.08828i
$214$	1.17263	+	11.1569i	0.0801596	+	0.762667i
$215$	−1.22194	−	0.544043i	−0.0833357	−	0.0371034i
$216$	1.93182	+	4.82370i	0.131444	+	0.328211i
$217$	10.9175	+	22.0906i	0.741131	+	1.49961i
$218$	11.0651	−	15.2297i	0.749420	−	1.03149i
$219$	−1.90122	+	1.15483i	−0.128472	+	0.0780360i
$220$	0.381562	+	1.23050i	0.0257249	+	0.0829600i
$221$	1.82364	+	1.05288i	0.122671	+	0.0708242i
$222$	0.114739	−	1.38821i	0.00770075	−	0.0931705i
$223$	6.34276	−	19.5210i	0.424743	−	1.30722i	−0.478498	−	0.878089i	$-0.658819\pi$
$223$	6.34276	−	19.5210i	0.424743	−	1.30722i	0.903240	−	0.429135i	$-0.141181\pi$
$224$	2.34252	+	1.22988i	0.156516	+	0.0821751i
$225$	−11.3769	+	9.06592i	−0.758462	+	0.604394i
$226$	−2.79215	+	6.27128i	−0.185731	+	0.417159i
$227$	−22.8935	−	4.86617i	−1.51950	−	0.322979i	−0.628796	−	0.777570i	$-0.716452\pi$
$227$	−22.8935	−	4.86617i	−1.51950	−	0.322979i	−0.890700	+	0.454591i	$0.849785\pi$
$228$	−5.71619	+	5.38198i	−0.378564	+	0.356430i
$229$	−0.631283	+	6.00626i	−0.0417164	+	0.396905i	0.953662	+	0.300879i	$0.0972799\pi$
$229$	−0.631283	+	6.00626i	−0.0417164	+	0.396905i	−0.995379	+	0.0960260i	$0.969387\pi$
$230$	−3.02678			−0.199580
$231$	2.32582	+	15.0197i	0.153028	+	0.988222i
$232$	9.16473			0.601694
$233$	−0.206128	+	1.96118i	−0.0135039	+	0.128481i	−0.999197	−	0.0400696i	$-0.987242\pi$
$233$	−0.206128	+	1.96118i	−0.0135039	+	0.128481i	0.985693	+	0.168551i	$0.0539087\pi$
$234$	2.92730	−	2.88169i	0.191363	−	0.188382i
$235$	−3.99222	−	0.848572i	−0.260424	−	0.0553547i
$236$	1.21677	−	2.73291i	0.0792051	−	0.177898i
$237$	14.6451	+	19.2418i	0.951301	+	1.24989i
$238$	0.163244	+	4.06564i	0.0105815	+	0.263536i
$239$	−6.95528	+	21.4062i	−0.449900	+	1.38465i	0.427120	+	0.904195i	$0.359528\pi$
$239$	−6.95528	+	21.4062i	−0.449900	+	1.38465i	−0.877020	+	0.480454i	$0.840472\pi$
$240$	0.670505	+	0.0554188i	0.0432809	+	0.00357727i
$241$	−8.49753	−	4.90605i	−0.547374	−	0.316027i	0.200688	−	0.979655i	$-0.435682\pi$
$241$	−8.49753	−	4.90605i	−0.547374	−	0.316027i	−0.748062	+	0.663628i	$0.769016\pi$
$242$	−10.8173	+	1.99629i	−0.695365	+	0.128326i
$243$	9.24513	+	12.5510i	0.593076	+	0.805147i
$244$	3.91685	−	5.39109i	0.250751	−	0.345129i
$245$	0.903226	−	2.56465i	0.0577050	−	0.163850i
$246$	−2.64807	−	7.57226i	−0.168835	−	0.482789i
$247$	5.66996	+	2.52443i	0.360771	+	0.160626i
$248$	0.973525	+	9.26247i	0.0618189	+	0.588168i
$249$	11.2455	+	2.12991i	0.712653	+	0.134978i
$250$	0.795419	+	3.74215i	0.0503067	+	0.236675i
$251$	15.3742	−	21.1608i	0.970412	−	1.33566i	0.0285733	−	0.999592i	$-0.490904\pi$
$251$	15.3742	−	21.1608i	0.970412	−	1.33566i	0.941839	−	0.336066i	$-0.109096\pi$
$252$	7.72911	+	1.80580i	0.486888	+	0.113755i
$253$	3.04747	−	25.6636i	0.191593	−	1.61346i
$254$	−1.87209	+	1.08085i	−0.117465	+	0.0678186i
$255$	0.441777	+	0.935637i	0.0276651	+	0.0585919i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	14.8390	+	13.3611i	0.925634	+	0.833445i	0.986342	−	0.164711i	$-0.0526691\pi$
$257$	14.8390	+	13.3611i	0.925634	+	0.833445i	−0.0607076	+	0.998156i	$0.519336\pi$
$258$	−3.61225	−	4.74603i	−0.224889	−	0.295475i
$259$	−1.63708	−	1.35916i	−0.101723	−	0.0844541i
$260$	−0.164354	−	0.505829i	−0.0101928	−	0.0313702i
$261$	26.6124	−	6.90733i	1.64727	−	0.427553i
$262$	−13.9273	+	6.20082i	−0.860429	+	0.383088i
$263$	3.76932	−	6.52866i	0.232426	−	0.402574i	−0.726095	−	0.687594i	$-0.758667\pi$
$263$	3.76932	−	6.52866i	0.232426	−	0.402574i	0.958522	+	0.285020i	$0.0920002\pi$
$264$	−1.14497	+	5.62930i	−0.0704683	+	0.346460i
$265$	2.81705			0.173050
$266$	1.73110	+	11.8672i	0.106140	+	0.727626i
$267$	−16.6128	−	4.99195i	−1.01669	−	0.305502i
$268$	4.53326	−	5.03470i	0.276913	−	0.307543i
$269$	13.7344	−	1.44354i	0.837399	−	0.0880142i	0.323886	−	0.946096i	$-0.395010\pi$
$269$	13.7344	−	1.44354i	0.837399	−	0.0880142i	0.513513	+	0.858082i	$0.328344\pi$
$270$	1.98877	−	0.344426i	0.121033	−	0.0209611i
$271$	19.5177	+	17.5739i	1.18562	+	1.06754i	0.996328	+	0.0856144i	$0.0272853\pi$
$271$	19.5177	+	17.5739i	1.18562	+	1.06754i	0.189290	+	0.981921i	$0.439381\pi$
$272$	−0.475239	+	1.46264i	−0.0288156	+	0.0886853i
$273$	−1.04365	−	6.18722i	−0.0631645	−	0.374467i
$274$		−	2.25535i		−	0.136251i
$275$	−16.0158	+	1.46545i	−0.965789	+	0.0883699i
$276$	−11.8356	−	6.48649i	−0.712420	−	0.390441i
$277$	−0.0186608	−	0.0419128i	−0.00112122	−	0.00251830i	0.912984	−	0.407995i	$-0.133772\pi$
$277$	−0.0186608	−	0.0419128i	−0.00112122	−	0.00251830i	−0.914105	+	0.405477i	$0.867105\pi$
$278$	−1.48837	−	7.00225i	−0.0892667	−	0.419967i
$279$	9.80790	+	26.1625i	0.587184	+	1.56631i
$280$	0.656475	−	0.790709i	0.0392319	−	0.0472539i
$281$	−20.5942	+	14.9625i	−1.22855	+	0.892590i	−0.996780	−	0.0801814i	$-0.974450\pi$
$281$	−20.5942	+	14.9625i	−1.22855	+	0.892590i	−0.231765	+	0.972772i	$0.574450\pi$
$282$	−13.7922	−	11.8736i	−0.821315	−	0.707063i
$283$	1.80599	−	1.62612i	0.107355	−	0.0966631i	−0.613705	−	0.789535i	$-0.710322\pi$
$283$	1.80599	−	1.62612i	0.107355	−	0.0966631i	0.721060	+	0.692872i	$0.243655\pi$
$284$	−3.79608	−	8.52614i	−0.225256	−	0.505933i
$285$	1.58323	+	2.60650i	0.0937824	+	0.154396i
$286$	4.45432	−	0.884242i	0.263389	−	0.0522863i
$287$	−11.7965	−	3.31600i	−0.696325	−	0.195737i
$288$	2.50311	+	1.65362i	0.147497	+	0.0974403i
$289$	14.3150	−	3.04276i	0.842061	−	0.178986i
$290$	0.740148	−	3.48212i	0.0434630	−	0.204477i
$291$	0.706718	+	5.53588i	0.0414286	+	0.324519i
$292$	−0.522370	+	1.17326i	−0.0305694	+	0.0686600i
$293$	1.51892	+	4.67477i	0.0887365	+	0.273103i	0.985571	−	0.169264i	$-0.0541390\pi$
$293$	1.51892	+	4.67477i	0.0887365	+	0.273103i	−0.896834	+	0.442367i	$0.854139\pi$
$294$	9.02801	−	8.09290i	0.526524	−	0.471988i
$295$	−0.940099	−	0.683022i	−0.0547347	−	0.0397671i
$296$	−0.402108	−	0.696471i	−0.0233720	−	0.0404816i
$297$	0.917968	+	17.2092i	0.0532659	+	0.998580i
$298$	7.80342	−	13.5159i	0.452040	−	0.782957i
$299$	−1.11525	+	10.6109i	−0.0644968	+	0.613646i
$300$	−2.41701	+	8.04362i	−0.139546	+	0.464399i
$301$	−9.10331	+	0.365517i	−0.524706	+	0.0210681i
$302$	3.04893	+	4.19649i	0.175446	+	0.241481i
$303$	−18.2836	−	7.65751i	−1.05036	−	0.439913i
$304$	−0.942435	+	4.43381i	−0.0540523	+	0.254296i
$305$	−1.73201	−	1.92359i	−0.0991744	−	0.110144i
$306$	−0.277624	+	4.60536i	−0.0158707	+	0.263271i
$307$		−	7.27749i		−	0.415348i	−0.978198	−	0.207674i	$-0.933411\pi$
$307$		−	7.27749i		−	0.415348i	0.978198	−	0.207674i	$-0.0665893\pi$
$308$	6.04332	+	6.36225i	0.344350	+	0.362523i
$309$	−7.34243	+	0.163432i	−0.417696	+	0.00929733i
$310$	3.59788	+	0.378152i	0.204346	+	0.0214776i
$311$	16.3455	−	14.7176i	0.926870	−	0.834557i	−0.0596467	−	0.998220i	$-0.518997\pi$
$311$	16.3455	−	14.7176i	0.926870	−	0.834557i	0.986516	+	0.163662i	$0.0523307\pi$
$312$	0.441336	−	2.33016i	0.0249857	−	0.131919i
$313$	−18.1480	−	8.08001i	−1.02579	−	0.456709i	−0.176309	−	0.984335i	$-0.556416\pi$
$313$	−18.1480	−	8.08001i	−1.02579	−	0.456709i	−0.849477	+	0.527626i	$0.823082\pi$
$314$	−7.25601	+	5.27180i	−0.409480	+	0.297505i
$315$	1.31032	−	2.79082i	0.0738279	−	0.157245i
$316$	13.2777	+	4.31417i	0.746926	+	0.242691i
$317$	22.4116	+	2.35556i	1.25876	+	0.132301i	0.710315	−	0.703884i	$-0.248553\pi$
$317$	22.4116	+	2.35556i	1.25876	+	0.132301i	0.548447	+	0.836185i	$0.315219\pi$
$318$	11.0155	+	6.03704i	0.617719	+	0.338540i
$319$	28.7791	+	9.78151i	1.61132	+	0.547659i
$320$	0.336396	−	0.194218i	0.0188051	−	0.0108571i
$321$	15.9700	+	11.0684i	0.891360	+	0.617780i
$322$	−18.4823	+	9.13427i	−1.02998	+	0.509033i
$323$	−6.62992	+	2.15419i	−0.368899	+	0.119862i
$324$	8.51479	+	2.91519i	0.473044	+	0.161955i
$325$	6.60320	−	0.694025i	0.366280	−	0.0384976i
$326$	−14.5101	−	3.08422i	−0.803642	−	0.170819i
$327$	−7.48719	−	31.7346i	−0.414042	−	1.75493i
$328$	−3.74693	−	2.72231i	−0.206890	−	0.150314i
$329$	−26.9384	+	6.86616i	−1.48516	+	0.378544i
$330$	2.04637	+	0.889656i	0.112649	+	0.0489739i
$331$	−3.66218	−	6.34307i	−0.201291	−	0.348647i	0.747653	−	0.664089i	$-0.231180\pi$
$331$	−3.66218	−	6.34307i	−0.201291	−	0.348647i	−0.948945	+	0.315442i	$0.897847\pi$
$332$	6.03672	−	2.68772i	0.331308	−	0.147508i
$333$	−1.69255	−	1.71934i	−0.0927514	−	0.0942192i
$334$	13.9020	−	15.4398i	0.760685	−	0.844826i
$335$	−1.54681	−	2.12901i	−0.0845115	−	0.116320i
$336$	4.26152	−	1.68506i	0.232485	−	0.0919274i
$337$	2.82081	−	0.916537i	0.153659	−	0.0499269i	−0.231177	−	0.972912i	$-0.574258\pi$
$337$	2.82081	−	0.916537i	0.153659	−	0.0499269i	0.384837	+	0.922985i	$0.374258\pi$
$338$	10.8821	−	2.31306i	0.591907	−	0.125814i
$339$	5.07667	+	10.7519i	0.275727	+	0.583961i
$340$	0.517345	+	0.298689i	0.0280570	+	0.0161987i
$341$	−6.82876	+	30.1251i	−0.369798	+	1.63136i
$342$	0.605071	+	13.5851i	0.0327185	+	0.734599i
$343$	−2.22430	−	18.3862i	−0.120101	−	0.992762i
$344$	−3.27496	−	1.06410i	−0.176574	−	0.0573724i
$345$	−3.42038	+	3.97307i	−0.184147	+	0.213903i
$346$	−0.447070	−	4.25359i	−0.0240346	−	0.228674i
$347$	1.48644	+	14.1425i	0.0797963	+	0.759211i	0.959123	+	0.282991i	$0.0913267\pi$
$347$	1.48644	+	14.1425i	0.0797963	+	0.759211i	−0.879326	+	0.476220i	$0.842007\pi$
$348$	10.3565	−	12.0300i	0.555166	−	0.644873i
$349$	−12.7628	−	4.14689i	−0.683178	−	0.221978i	−0.0531920	−	0.998584i	$-0.516940\pi$
$349$	−12.7628	−	4.14689i	−0.683178	−	0.221978i	−0.629986	+	0.776606i	$0.716940\pi$
$350$	7.95137	+	10.0684i	0.425019	+	0.538180i
$351$	−0.474662	−	7.09890i	−0.0253356	−	0.378911i
$352$	1.30805	+	3.04779i	0.0697192	+	0.162448i
$353$	−14.0502	−	8.11192i	−0.747819	−	0.431754i	0.0770861	−	0.997024i	$-0.475438\pi$
$353$	−14.0502	−	8.11192i	−0.747819	−	0.431754i	−0.824905	+	0.565271i	$0.808772\pi$
$354$	−2.21233	−	4.68548i	−0.117584	−	0.249030i
$355$	−3.54606	+	0.753739i	−0.188206	+	0.0400043i
$356$	−9.52490	+	3.09483i	−0.504818	+	0.164025i
$357$	5.52118	+	4.38005i	0.292212	+	0.231817i
$358$	−12.5096	−	17.2180i	−0.661154	−	0.910000i
$359$	−7.47423	+	8.30098i	−0.394475	+	0.438109i	−0.907364	−	0.420346i	$-0.861909\pi$
$359$	−7.47423	+	8.30098i	−0.394475	+	0.438109i	0.512889	+	0.858455i	$0.328575\pi$
$360$	0.830441	−	0.817504i	0.0437681	−	0.0430862i
$361$	−1.41309	+	0.629147i	−0.0743730	+	0.0331130i
$362$	−11.2960	−	19.5653i	−0.593706	−	1.02833i
$363$	−9.60360	+	16.4551i	−0.504058	+	0.863670i
$364$	−2.53009	−	2.59274i	−0.132612	−	0.135896i
$365$	0.403592	+	0.293227i	0.0211250	+	0.0153482i
$366$	−2.65034	−	11.2335i	−0.138536	−	0.587186i
$367$	−1.80373	−	0.383394i	−0.0941537	−	0.0200130i	0.160594	−	0.987021i	$-0.448659\pi$
$367$	−1.80373	−	0.383394i	−0.0941537	−	0.0200130i	−0.254748	+	0.967008i	$0.581992\pi$
$368$	−7.74954	+	0.814510i	−0.403973	+	0.0424592i
$369$	−12.9320	−	5.08098i	−0.673215	−	0.264505i
$370$	−0.297097	+	0.0965328i	−0.0154454	+	0.00501850i
$371$	17.2017	−	8.50134i	0.893066	−	0.441368i
$372$	13.2584	+	9.18906i	0.687415	+	0.476431i
$373$	−13.3886	+	7.72994i	−0.693238	+	0.400241i	−0.804824	−	0.593514i	$-0.797740\pi$
$373$	−13.3886	+	7.72994i	−0.693238	+	0.400241i	0.111586	+	0.993755i	$0.464407\pi$
$374$	−3.05342	+	4.08575i	−0.157888	+	0.211269i
$375$	5.81094	+	3.18468i	0.300076	+	0.164456i
$376$	−10.4497	−	1.09831i	−0.538903	−	0.0566410i
$377$	−11.9345	−	3.87775i	−0.614657	−	0.199714i
$378$	11.1045	−	8.10489i	0.571156	−	0.416871i
$379$	6.28957	−	4.56964i	0.323074	−	0.234727i	−0.414412	−	0.910089i	$-0.636013\pi$
$379$	6.28957	−	4.56964i	0.323074	−	0.234727i	0.737486	+	0.675363i	$0.236013\pi$
$380$	1.60850	+	0.716152i	0.0825145	+	0.0367378i
$381$	−0.696766	+	3.67877i	−0.0356964	+	0.188469i
$382$	−6.91052	+	6.22226i	−0.353573	+	0.318358i
$383$	6.66340	+	0.700351i	0.340484	+	0.0357863i	0.273227	−	0.961949i	$-0.411909\pi$
$383$	6.66340	+	0.700351i	0.340484	+	0.0357863i	0.0672562	+	0.997736i	$0.478576\pi$
$384$	1.73162	−	0.0385435i	0.0883665	−	0.00196691i
$385$	2.90539	−	1.78233i	0.148072	−	0.0908360i
$386$			4.62739i			0.235528i
$387$	−10.3118	−	0.621623i	−0.524177	−	0.0315989i
$388$	2.15599	+	2.39447i	0.109454	+	0.121561i
$389$	−2.20390	+	10.3685i	−0.111742	+	0.525705i	0.886297	+	0.463117i	$0.153269\pi$
$389$	−2.20390	+	10.3685i	−0.111742	+	0.525705i	−0.998039	+	0.0625885i	$0.980064\pi$
$390$	−0.849696	−	0.355869i	−0.0430260	−	0.0180201i
$391$	−7.04385	−	9.69503i	−0.356223	−	0.490299i
$392$	1.62240	−	6.80939i	0.0819435	−	0.343926i
$393$	−7.59892	+	25.2886i	−0.383315	+	1.27564i
$394$	−0.0313956	+	0.298709i	−0.00158169	+	0.0150487i
$395$	2.71147	−	4.69640i	0.136429	−	0.236302i
$396$	6.09536	+	7.86426i	0.306303	+	0.395194i
$397$	−6.79549	−	11.7701i	−0.341056	−	0.590726i	0.643573	−	0.765385i	$-0.277451\pi$
$397$	−6.79549	−	11.7701i	−0.341056	−	0.590726i	−0.984629	+	0.174659i	$0.944118\pi$
$398$	5.83728	+	4.24103i	0.292597	+	0.212584i
$399$	17.5336	+	11.1381i	0.877776	+	0.557603i
$400$	1.49846	+	4.61178i	0.0749230	+	0.230589i
$401$	6.75797	−	15.1787i	0.337477	−	0.757986i	−0.662483	−	0.749077i	$-0.730497\pi$
$401$	6.75797	−	15.1787i	0.337477	−	0.757986i	0.999960	−	0.00890902i	$-0.00283587\pi$
$402$	−1.48597	−	11.6399i	−0.0741134	−	0.580546i
$403$	2.65136	−	12.4737i	0.132074	−	0.621358i
$404$	−11.1944	+	2.37944i	−0.556940	+	0.118381i
$405$	1.79528	−	2.99975i	0.0892081	−	0.149059i
$406$	−5.98885	−	23.4964i	−0.297222	−	1.16611i
$407$	−0.519357	−	2.61623i	−0.0257436	−	0.129682i
$408$	1.38287	+	2.27665i	0.0684623	+	0.112711i
$409$	7.79199	+	17.5011i	0.385289	+	0.865373i	0.997224	+	0.0744649i	$0.0237249\pi$
$409$	7.79199	+	17.5011i	0.385289	+	0.865373i	−0.611935	+	0.790908i	$0.709608\pi$
$410$	−1.33694	+	1.20379i	−0.0660267	+	0.0594507i
$411$	−2.96046	−	2.54863i	−0.146029	−	0.125715i
$412$	−3.43040	+	2.49233i	−0.169004	+	0.122788i
$413$	−7.80172	−	1.33367i	−0.383898	−	0.0656256i
$414$	−21.8891	+	8.20588i	−1.07579	+	0.403297i
$415$	−0.533666	−	2.51070i	−0.0261966	−	0.123245i
$416$	−0.556918	−	1.25086i	−0.0273051	−	0.0613283i
$417$	−10.8733	−	5.95911i	−0.532469	−	0.291819i
$418$	−7.69163	+	12.9172i	−0.376210	+	0.631800i
$419$		−	6.14360i		−	0.300135i	−0.988676	−	0.150067i	$-0.952051\pi$
$419$		−	6.14360i		−	0.300135i	0.988676	−	0.150067i	$-0.0479491\pi$
$420$	−0.296071	−	1.75524i	−0.0144468	−	0.0856471i
$421$	−5.46266	+	16.8123i	−0.266234	+	0.819383i	0.725173	+	0.688567i	$0.241760\pi$
$421$	−5.46266	+	16.8123i	−0.266234	+	0.819383i	−0.991407	+	0.130816i	$0.958240\pi$
$422$	3.19946	+	2.88081i	0.155747	+	0.140236i
$423$	−31.1715	+	4.68655i	−1.51561	+	0.227868i
$424$	7.21257	−	0.758071i	0.350273	−	0.0368152i
$425$	−4.99003	+	5.54199i	−0.242052	+	0.268826i
$426$	−15.4814	−	4.65199i	−0.750078	−	0.225389i
$427$	−16.3811	−	6.51906i	−0.792737	−	0.315480i
$428$	11.2183			0.542258
$429$	3.87286	−	6.84613i	0.186983	−	0.330534i
$430$	−0.668790	+	1.15838i	−0.0322519	+	0.0558620i
$431$	11.6672	−	5.19459i	0.561991	−	0.250214i	−0.106023	−	0.994364i	$-0.533812\pi$
$431$	11.6672	−	5.19459i	0.561991	−	0.250214i	0.668013	+	0.744149i	$0.267145\pi$
$432$	4.99921	−	1.41702i	0.240524	−	0.0681764i
$433$	−5.70278	−	17.5514i	−0.274058	−	0.843464i	−0.989467	−	0.144758i	$-0.953760\pi$
$433$	−5.70278	−	17.5514i	−0.274058	−	0.843464i	0.715409	−	0.698706i	$-0.246240\pi$
$434$	23.1108	−	8.54863i	1.10935	−	0.410347i
$435$	−3.73436	−	4.90647i	−0.179049	−	0.235247i
$436$	−13.9897	−	12.5964i	−0.669985	−	0.603257i
$437$	−23.6344	−	26.2487i	−1.13059	−	1.25564i
$438$	0.949770	+	2.01151i	0.0453817	+	0.0961139i
$439$	−27.5780	+	15.9222i	−1.31623	+	0.759924i	−0.983120	−	0.182964i	$-0.941431\pi$
$439$	−27.5780	+	15.9222i	−1.31623	+	0.759924i	−0.333108	+	0.942889i	$0.608097\pi$
$440$	1.26364	−	0.250850i	0.0602417	−	0.0119588i
$441$	−0.421047	−	20.9958i	−0.0200499	−	0.999799i
$442$	1.23773	−	1.70359i	0.0588729	−	0.0810315i
$443$	4.82241	+	22.6877i	0.229120	+	1.07792i	0.930828	+	0.365459i	$0.119088\pi$
$443$	4.82241	+	22.6877i	0.229120	+	1.07792i	−0.701708	+	0.712465i	$0.747579\pi$
$444$	−1.36861	−	0.259217i	−0.0649514	−	0.0123019i
$445$	0.406638	+	3.86891i	0.0192765	+	0.183404i
$446$	−18.7511	−	8.34852i	−0.887889	−	0.395314i
$447$	−8.92333	−	25.5166i	−0.422059	−	1.20689i
$448$	1.46801	−	2.20113i	0.0693568	−	0.103993i
$449$	17.7780	−	24.4693i	0.838994	−	1.15478i	−0.147188	−	0.989109i	$-0.547022\pi$
$449$	17.7780	−	24.4693i	0.838994	−	1.15478i	0.986182	−	0.165668i	$-0.0529779\pi$
$450$	7.82704	+	12.2623i	0.368970	+	0.578048i
$451$	−8.86061	−	12.5477i	−0.417230	−	0.590848i
$452$	5.94507	+	3.43239i	0.279632	+	0.161446i
$453$	8.95387	+	0.740058i	0.420689	+	0.0347709i
$454$	−7.23253	+	22.2595i	−0.339440	+	1.04469i
$455$	−1.18944	+	0.751910i	−0.0557616	+	0.0352501i
$456$	4.75499	+	6.24744i	0.222673	+	0.292563i
$457$	−0.149977	+	0.336854i	−0.00701562	+	0.0157573i	−0.917019	−	0.398843i	$-0.869412\pi$
$457$	−0.149977	+	0.336854i	−0.00701562	+	0.0157573i	0.910004	+	0.414600i	$0.136079\pi$
$458$	5.90737	+	1.25565i	0.276033	+	0.0586726i
$459$	5.73144	+	5.56865i	0.267521	+	0.259922i
$460$	−0.316385	+	3.01020i	−0.0147515	+	0.140351i
$461$	15.7878			0.735311			0.367656	−	0.929962i	$-0.380161\pi$
$461$	15.7878			0.735311			0.367656	+	0.929962i	$0.380161\pi$
$462$	15.1805	−	0.743100i	0.706261	−	0.0345721i
$463$	−22.3466			−1.03854			−0.519268	−	0.854611i	$-0.673795\pi$
$463$	−22.3466			−1.03854			−0.519268	+	0.854611i	$0.673795\pi$
$464$	0.957975	−	9.11452i	0.0444729	−	0.423131i
$465$	4.56212	−	4.29538i	0.211563	−	0.199194i
$466$	1.92889	+	0.409998i	0.0893540	+	0.0189928i
$467$	−3.11709	+	7.00110i	−0.144242	+	0.323972i	−0.971190	−	0.238305i	$-0.923408\pi$
$467$	−3.11709	+	7.00110i	−0.144242	+	0.323972i	0.826949	+	0.562278i	$0.190075\pi$
$468$	−2.55992	−	3.21248i	−0.118332	−	0.148497i
$469$	−15.8702	−	8.33229i	−0.732818	−	0.384749i
$470$	−1.26122	+	3.88165i	−0.0581759	+	0.179047i
$471$	−1.27961	+	15.4818i	−0.0589613	+	0.713365i
$472$	−2.59076	−	1.49577i	−0.119249	−	0.0688486i
$473$	−9.14834	−	6.83685i	−0.420641	−	0.314359i
$474$	20.6672	−	12.5536i	0.949276	−	0.576604i
$475$	−12.9197	+	17.7825i	−0.592798	+	0.815917i
$476$	4.06043	+	0.262625i	0.186110	+	0.0120374i
$477$	20.3724	−	7.63728i	0.932787	−	0.349687i
$478$	20.5619	+	9.15473i	0.940478	+	0.418728i
$479$	2.05551	+	19.5569i	0.0939186	+	0.893576i	0.935472	+	0.353402i	$0.114975\pi$
$479$	2.05551	+	19.5569i	0.0939186	+	0.893576i	−0.841553	+	0.540174i	$0.818358\pi$
$480$	0.125202	−	0.661039i	0.00571467	−	0.0301722i
$481$	0.228944	+	1.07710i	0.0104389	+	0.0491114i
$482$	−5.76741	+	7.93816i	−0.262698	+	0.361573i
$483$	−8.89577	+	34.5827i	−0.404772	+	1.57357i
$484$	0.854636	+	10.9667i	0.0388471	+	0.498489i
$485$	1.08389	−	0.625786i	0.0492171	−	0.0284155i
$486$	13.4486	−	7.88255i	0.610042	−	0.357560i
$487$	−2.73851	−	3.04142i	−0.124094	−	0.137820i	0.677896	−	0.735158i	$-0.262892\pi$
$487$	−2.73851	−	3.04142i	−0.124094	−	0.137820i	−0.801990	+	0.597338i	$0.796225\pi$
$488$	−4.95213	−	4.45892i	−0.224172	−	0.201846i
$489$	−20.4455	+	15.5612i	−0.924576	+	0.703704i
$490$	−2.45619	−	1.16636i	−0.110959	−	0.0526906i
$491$	3.00475	+	9.24766i	0.135602	+	0.417341i	0.995683	−	0.0928167i	$-0.0295871\pi$
$491$	3.00475	+	9.24766i	0.135602	+	0.417341i	−0.860081	+	0.510158i	$0.829587\pi$
$492$	−7.80757	+	1.84205i	−0.351993	+	0.0830461i
$493$	12.8760	−	5.73275i	0.579904	−	0.258190i
$494$	3.10327	−	5.37503i	0.139623	−	0.241834i
$495$	3.48027	−	1.68080i	0.156427	−	0.0755463i
$496$	9.31349			0.418188
$497$	−19.3786	+	15.3039i	−0.869247	+	0.686473i
$498$	3.29372	−	10.9612i	0.147595	−	0.491185i
$499$	0.363926	−	0.404181i	0.0162916	−	0.0180936i	−0.734944	−	0.678128i	$-0.762792\pi$
$499$	0.363926	−	0.404181i	0.0162916	−	0.0180936i	0.751236	+	0.660034i	$0.229458\pi$
$500$	3.80480	−	0.399900i	0.170156	−	0.0178841i
$501$	−4.55698	−	35.6958i	−0.203591	−	1.59477i
$502$	−19.4378	−	17.5019i	−0.867553	−	0.781148i
$503$	6.37132	−	19.6089i	0.284083	−	0.874318i	−0.702589	−	0.711596i	$-0.747973\pi$
$503$	6.37132	−	19.6089i	0.284083	−	0.874318i	0.986672	−	0.162722i	$-0.0520274\pi$
$504$	2.60382	−	7.49801i	0.115983	−	0.333988i
$505$			4.44544i			0.197819i
$506$	−25.2045	−	5.71335i	−1.12047	−	0.253989i
$507$	9.26096	−	16.8981i	0.411294	−	0.750469i
$508$	0.879243	+	1.97481i	0.0390101	+	0.0876181i
$509$	1.74950	+	8.23074i	0.0775451	+	0.364821i	0.999761	−	0.0218539i	$-0.00695686\pi$
$509$	1.74950	+	8.23074i	0.0775451	+	0.364821i	−0.922216	+	0.386675i	$0.873624\pi$
$510$	0.976690	−	0.341556i	0.0432486	−	0.0151243i
$511$	3.34934	+	0.572555i	0.148166	+	0.0253283i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	18.5161	+	14.5575i	0.817504	+	0.642727i
$514$	14.8390	−	13.3611i	0.654522	−	0.589335i
$515$	0.669915	+	1.50465i	0.0295200	+	0.0663030i
$516$	−5.09761	+	3.09636i	−0.224410	+	0.136310i
$517$	−31.6420	−	14.6019i	−1.39161	−	0.642190i
$518$	−1.52284	+	1.48604i	−0.0669096	+	0.0652928i
$519$	−6.08862	−	4.21988i	−0.267261	−	0.185232i
$520$	−0.520238	+	0.110580i	−0.0228139	+	0.00484925i
$521$	−6.76451	+	31.8245i	−0.296359	+	1.39426i	0.537958	+	0.842972i	$0.319196\pi$
$521$	−6.76451	+	31.8245i	−0.296359	+	1.39426i	−0.834316	+	0.551286i	$0.814137\pi$
$522$	−4.08773	−	27.1886i	−0.178915	−	1.19001i
$523$	−2.57403	+	5.78136i	−0.112554	+	0.252801i	−0.961036	−	0.276424i	$-0.910851\pi$
$523$	−2.57403	+	5.78136i	−0.112554	+	0.252801i	0.848481	+	0.529225i	$0.177517\pi$
$524$	4.71105	+	14.4991i	0.205803	+	0.633398i
$525$	22.2015	+	0.940448i	0.968955	+	0.0410445i
$526$	−6.09889	−	4.43110i	−0.265924	−	0.193205i
$527$	7.16164	+	12.4043i	0.311966	+	0.540341i
$528$	5.47878	+	1.72712i	0.238433	+	0.0751634i
$529$	18.8594	−	32.6655i	0.819974	−	1.42024i
$530$	0.294462	−	2.80162i	0.0127906	−	0.121695i
$531$	−8.65034	−	2.39079i	−0.375393	−	0.103751i
$532$	11.9832	−	0.481149i	0.519536	−	0.0208605i
$533$	3.72747	+	5.13043i	0.161455	+	0.222224i
$534$	−6.70111	+	16.0000i	−0.289985	+	0.692388i
$535$	0.905996	−	4.26238i	0.0391696	−	0.184279i
$536$	−4.53326	−	5.03470i	−0.195807	−	0.217466i
$537$	−36.7373	−	3.03642i	−1.58533	−	0.131031i
$538$		−	13.8100i		−	0.595392i
$539$	12.3623	−	19.6513i	0.532483	−	0.846441i
$540$	−0.134656	−	2.01388i	−0.00579468	−	0.0866635i
$541$	26.9883	+	2.83658i	1.16032	+	0.121954i	0.665058	−	0.746791i	$-0.268407\pi$
$541$	26.9883	+	2.83658i	1.16032	+	0.121954i	0.495259	+	0.868746i	$0.335073\pi$
$542$	19.5177	−	17.5739i	0.838359	−	0.754862i
$543$	−38.4470	−	7.28194i	−1.64992	−	0.312498i
$544$	1.40495	+	0.625523i	0.0602366	+	0.0268191i
$545$	−5.91579	+	4.29807i	−0.253404	+	0.184109i
$546$	−6.26241	+	0.391191i	−0.268007	+	0.0167414i
$547$	10.4112	+	3.38280i	0.445151	+	0.144638i	0.523011	−	0.852326i	$-0.324809\pi$
$547$	10.4112	+	3.38280i	0.445151	+	0.144638i	−0.0778600	+	0.996964i	$0.524809\pi$
$548$	−2.24300	−	0.235749i	−0.0958161	−	0.0100707i
$549$	−17.7405	−	9.21538i	−0.757148	−	0.393303i
$550$	−0.216686	+	16.0812i	−0.00923950	+	0.685706i
$551$	35.9768	−	20.7712i	1.53266	−	0.884884i
$552$	−7.68812	+	11.0928i	−0.327228	+	0.472139i
$553$	2.38409	−	36.8602i	0.101382	−	1.56745i
$554$	−0.0436338	+	0.0141775i	−0.00185382	+	0.000602343i
$555$	−0.209019	+	0.499066i	−0.00887235	+	0.0211842i
$556$	−7.11947	+	0.748286i	−0.301933	+	0.0317344i
$557$	−5.88022	−	1.24988i	−0.249153	−	0.0529591i	0.0816421	−	0.996662i	$-0.473984\pi$
$557$	−5.88022	−	1.24988i	−0.249153	−	0.0529591i	−0.330795	+	0.943703i	$0.607317\pi$
$558$	27.0444	−	7.01945i	1.14488	−	0.297157i
$559$	3.81448	+	2.77138i	0.161335	+	0.117217i
$560$	−0.717757	−	0.735530i	−0.0303308	−	0.0310818i
$561$	1.91263	+	8.62508i	0.0807512	+	0.364151i
$562$	12.7279	+	22.0454i	0.536894	+	0.929928i
$563$	−2.55236	+	1.13638i	−0.107569	+	0.0478929i	−0.459816	−	0.888014i	$-0.652085\pi$
$563$	−2.55236	+	1.13638i	−0.107569	+	0.0478929i	0.352247	+	0.935907i	$0.385418\pi$
$564$	−13.2503	+	12.4755i	−0.557936	+	0.525315i
$565$	1.78425	−	1.98162i	0.0750642	−	0.0833672i
$566$	−1.42844	−	1.96608i	−0.0600417	−	0.0826404i
$567$	1.90978	−	23.7351i	0.0802031	−	0.996779i
$568$	−8.87623	+	2.88406i	−0.372438	+	0.121013i
$569$	17.7351	−	3.76970i	0.743492	−	0.158034i	0.179435	−	0.983770i	$-0.442573\pi$
$569$	17.7351	−	3.76970i	0.743492	−	0.158034i	0.564057	+	0.825736i	$0.309240\pi$
$570$	2.75772	−	1.30210i	0.115508	−	0.0545391i
$571$	13.4912	+	7.78912i	0.564587	+	0.325965i	0.754985	−	0.655743i	$-0.227644\pi$
$571$	13.4912	+	7.78912i	0.564587	+	0.325965i	−0.190397	+	0.981707i	$0.560978\pi$
$572$	−0.413795	−	4.52234i	−0.0173017	−	0.189089i
$573$	0.358416	+	16.1024i	0.0149731	+	0.672687i
$574$	−4.53090	+	11.3853i	−0.189116	+	0.475212i
$575$	−35.9361	−	11.6763i	−1.49864	−	0.486937i
$576$	1.90620	−	2.31655i	0.0794252	−	0.0965227i
$577$	4.56790	+	43.4607i	0.190164	+	1.80929i	0.508227	+	0.861223i	$0.330301\pi$
$577$	4.56790	+	43.4607i	0.190164	+	1.80929i	−0.318062	+	0.948070i	$0.603032\pi$
$578$	−1.52976	−	14.5547i	−0.0636295	−	0.605395i
$579$	6.07408	+	5.22913i	0.252430	+	0.217315i
$580$	−3.38568	−	1.10007i	−0.140583	−	0.0456781i
$581$	−10.8355	−	13.7205i	−0.449533	−	0.569222i
$582$	5.57942	−	0.124190i	0.231275	−	0.00514785i
$583$	23.4580	+	5.31747i	0.971531	+	0.220227i
$584$	1.11223	+	0.642148i	0.0460245	+	0.0265723i
$585$	−1.42732	+	0.713196i	−0.0590122	+	0.0294870i
$586$	4.80793	−	1.02196i	0.198614	−	0.0422167i
$587$	21.9242	−	7.12361i	0.904909	−	0.294023i	0.180647	−	0.983548i	$-0.442181\pi$
$587$	21.9242	−	7.12361i	0.904909	−	0.294023i	0.724262	+	0.689525i	$0.242181\pi$
$588$	−7.10488	−	9.82449i	−0.293000	−	0.405155i
$589$	24.8144	+	34.1541i	1.02246	+	1.40729i
$590$	−0.777547	+	0.863553i	−0.0320111	+	0.0355519i
$591$	0.356618	+	0.378763i	0.0146693	+	0.0155802i
$592$	−0.734688	+	0.327104i	−0.0301955	+	0.0134439i
$593$	−11.9279	−	20.6598i	−0.489821	−	0.848396i	0.510110	−	0.860109i	$-0.329605\pi$
$593$	−11.9279	−	20.6598i	−0.489821	−	0.848396i	−0.999931	+	0.0117136i	$0.996271\pi$
$594$	17.2109	+	0.885914i	0.706172	+	0.0363495i
$595$	0.427706	−	1.52154i	0.0175343	−	0.0623772i
$596$	−12.6262	−	9.17347i	−0.517189	−	0.375760i
$597$	12.1633	−	2.86970i	0.497810	−	0.117449i
$598$	10.4362	+	2.21829i	0.426769	+	0.0907126i
$599$	29.3478	−	3.08458i	1.19912	−	0.126033i	0.516162	−	0.856491i	$-0.327360\pi$
$599$	29.3478	−	3.08458i	1.19912	−	0.126033i	0.682957	+	0.730458i	$0.260693\pi$
$600$	7.74691	+	3.24456i	0.316266	+	0.132459i
$601$	−12.0376	+	3.91124i	−0.491022	+	0.159543i	−0.544054	−	0.839050i	$-0.683111\pi$
$601$	−12.0376	+	3.91124i	−0.491022	+	0.159543i	0.0530321	+	0.998593i	$0.483111\pi$
$602$	−0.588040	+	9.09165i	−0.0239667	+	0.370548i
$603$	−16.9582	−	11.2030i	−0.690591	−	0.456222i
$604$	4.49220	−	2.59357i	0.182785	−	0.105531i
$605$	4.23582	+	0.560962i	0.172210	+	0.0228064i
$606$	−9.52672	+	17.3830i	−0.386997	+	0.706135i
$607$	−34.6715	−	3.64412i	−1.40727	−	0.147910i	−0.629766	−	0.776785i	$-0.716849\pi$
$607$	−34.6715	−	3.64412i	−1.40727	−	0.147910i	−0.777507	+	0.628874i	$0.783516\pi$
$608$	4.31101	+	1.40073i	0.174834	+	0.0568071i
$609$	−37.6098	−	18.6906i	−1.52403	−	0.757382i
$610$	−2.09409	+	1.52145i	−0.0847874	+	0.0616016i
$611$	13.1431	+	5.85169i	0.531713	+	0.236734i
$612$	4.55111	+	0.757494i	0.183968	+	0.0306199i
$613$	5.00337	−	4.50506i	0.202084	−	0.181957i	−0.561875	−	0.827222i	$-0.689920\pi$
$613$	5.00337	−	4.50506i	0.202084	−	0.181957i	0.763959	+	0.645265i	$0.223253\pi$
$614$	−7.23762	−	0.760704i	−0.292087	−	0.0306995i
$615$	0.0693408	+	3.11524i	0.00279609	+	0.125618i
$616$	6.95910	−	5.34518i	0.280390	−	0.215363i
$617$			20.0613i			0.807637i	0.914839	+	0.403818i	$0.132317\pi$
$617$			20.0613i			0.807637i	−0.914839	+	0.403818i	$0.867683\pi$
$618$	−0.604956	+	7.31929i	−0.0243349	+	0.294425i
$619$	29.9745	+	33.2901i	1.20478	+	1.33804i	0.925925	+	0.377706i	$0.123287\pi$
$619$	29.9745	+	33.2901i	1.20478	+	1.33804i	0.278852	+	0.960334i	$0.410046\pi$
$620$	0.752162	−	3.53864i	0.0302075	−	0.142115i
$621$	−13.9642	+	38.0054i	−0.560363	+	1.52510i
$622$	−12.9284	−	17.7944i	−0.518381	−	0.713490i
$623$	14.1587	+	22.3974i	0.567255	+	0.897333i
$624$	−2.27126	−	0.682486i	−0.0909231	−	0.0273213i
$625$	−2.37902	+	22.6348i	−0.0951607	+	0.905394i
$626$	−9.93273	+	17.2040i	−0.396992	+	0.687610i
$627$	8.26374	+	24.6932i	0.330022	+	0.986153i
$628$	4.48446	+	7.76731i	0.178949	+	0.309949i
$629$	−1.00060	−	0.726978i	−0.0398965	−	0.0289865i
$630$	−2.63857	−	1.59486i	−0.105123	−	0.0635406i
$631$	9.40701	+	28.9518i	0.374487	+	1.15255i	0.943824	+	0.330448i	$0.107200\pi$
$631$	9.40701	+	28.9518i	0.374487	+	1.15255i	−0.569337	+	0.822104i	$0.692800\pi$
$632$	5.67843	−	12.7540i	0.225876	−	0.507325i
$633$	7.39697	−	0.944308i	0.294003	−	0.0375329i
$634$	4.68530	−	22.0426i	0.186077	−	0.875424i
$635$	0.821334	−	0.174580i	0.0325936	−	0.00692799i
$636$	7.15540	−	10.3241i	0.283730	−	0.409378i
$637$	−4.99389	+	8.18086i	−0.197865	+	0.324137i
$638$	12.7362	−	27.5990i	0.504229	−	1.09266i
$639$	−23.6010	+	15.0646i	−0.933640	+	0.595946i
$640$	−0.157991	−	0.354854i	−0.00624515	−	0.0140268i
$641$	−9.36855	+	8.43548i	−0.370035	+	0.333181i	−0.833079	−	0.553154i	$-0.813424\pi$
$641$	−9.36855	+	8.43548i	−0.370035	+	0.333181i	0.463044	+	0.886336i	$0.346757\pi$
$642$	12.6771	−	14.7256i	0.500326	−	0.581172i
$643$	22.0166	−	15.9960i	0.868252	−	0.630822i	−0.0618656	−	0.998084i	$-0.519705\pi$
$643$	22.0166	−	15.9960i	0.868252	−	0.630822i	0.930117	+	0.367263i	$0.119705\pi$
$644$	7.15230	+	19.3359i	0.281840	+	0.761941i
$645$	0.764772	+	2.18689i	0.0301129	+	0.0861087i
$646$	1.44938	+	6.81878i	0.0570249	+	0.268281i
$647$	15.3244	+	34.4191i	0.602463	+	1.35316i	0.915079	+	0.403275i	$0.132128\pi$
$647$	15.3244	+	34.4191i	0.602463	+	1.35316i	−0.312615	+	0.949880i	$0.601205\pi$
$648$	3.78926	−	8.16343i	0.148856	−	0.320690i
$649$	−6.53906	−	7.46214i	−0.256681	−	0.292915i
$650$		−	6.63958i		−	0.260426i
$651$	14.8948	−	39.9963i	0.583775	−	1.56758i
$652$	−4.58405	+	14.1083i	−0.179525	+	0.552522i
$653$	−27.0901	−	24.3921i	−1.06012	−	0.954535i	−0.0610693	−	0.998134i	$-0.519451\pi$
$653$	−27.0901	−	24.3921i	−1.06012	−	0.954535i	−0.999049	+	0.0435986i	$0.986118\pi$
$654$	−32.3434	+	4.12900i	−1.26473	+	0.161457i
$655$	5.88938	−	0.618999i	0.230117	−	0.0241863i
$656$	−3.09905	+	3.44185i	−0.120998	+	0.134382i
$657$	3.71366	+	1.02638i	0.144884	+	0.0400431i
$658$	4.01272	+	27.5085i	0.156432	+	1.07239i
$659$	10.8321			0.421957			0.210979	−	0.977491i	$-0.432335\pi$
$659$	10.8321			0.421957			0.210979	+	0.977491i	$0.432335\pi$
$660$	1.09869	−	1.94217i	0.0427663	−	0.0755988i
$661$	6.10624	−	10.5763i	0.237505	−	0.411371i	−0.722493	−	0.691379i	$-0.757004\pi$
$661$	6.10624	−	10.5763i	0.237505	−	0.411371i	0.959998	+	0.280008i	$0.0903370\pi$
$662$	−6.69113	+	2.97908i	−0.260058	+	0.115785i
$663$	−0.837512	−	3.54981i	−0.0325263	−	0.137863i
$664$	−2.04199	−	6.28459i	−0.0792445	−	0.243889i
$665$	0.784954	−	4.59184i	0.0304392	−	0.178064i
$666$	−1.88684	+	1.50356i	−0.0731136	+	0.0582619i
$667$	53.0707	+	47.7851i	2.05491	+	1.85025i
$668$	−13.9020	−	15.4398i	−0.537885	−	0.597382i
$669$	−32.1480	+	15.1792i	−1.24291	+	0.586862i
$670$	−2.27903	+	1.31580i	−0.0880467	+	0.0508338i
$671$	−10.7917	−	19.2873i	−0.416609	−	0.744578i
$672$	−1.23038	−	4.41432i	−0.0474628	−	0.170286i
$673$	16.7246	−	23.0195i	0.644687	−	0.887335i	−0.354168	−	0.935182i	$-0.615236\pi$
$673$	16.7246	−	23.0195i	0.644687	−	0.887335i	0.998855	+	0.0478467i	$0.0152359\pi$
$674$	−0.616661	−	2.90116i	−0.0237529	−	0.111749i
$675$	24.9407	+	3.58276i	0.959969	+	0.137900i
$676$	−1.16290	−	11.0643i	−0.0447269	−	0.425548i
$677$	30.2692	+	13.4767i	1.16334	+	0.517953i	0.895304	−	0.445455i	$-0.146958\pi$
$677$	30.2692	+	13.4767i	1.16334	+	0.517953i	0.268038	+	0.963408i	$0.413625\pi$
$678$	11.2236	−	3.92499i	0.431041	−	0.150738i
$679$	4.73004	−	7.09220i	0.181522	−	0.272174i
$680$	0.351130	−	0.483289i	0.0134652	−	0.0185333i
$681$	21.0455	+	34.6477i	0.806467	+	1.32770i
$682$	29.2463	+	9.94028i	1.11990	+	0.380633i
$683$	20.4119	+	11.7848i	0.781041	+	0.450934i	0.836799	−	0.547510i	$-0.184424\pi$
$683$	20.4119	+	11.7848i	0.781041	+	0.450934i	−0.0557582	+	0.998444i	$0.517758\pi$
$684$	13.5739	+	0.818275i	0.519012	+	0.0312875i
$685$	−0.270718	+	0.833184i	−0.0103436	+	0.0318343i
$686$	−18.5180	+	0.290236i	−0.707020	+	0.0110813i
$687$	8.32376	−	6.33529i	0.317571	−	0.241706i
$688$	−1.40060	+	3.14579i	−0.0533973	+	0.119932i
$689$	−9.71309	−	2.06458i	−0.370039	−	0.0786543i
$690$	3.59378	+	3.81694i	0.136813	+	0.145309i
$691$	1.70486	−	16.2207i	0.0648560	−	0.617064i	−0.913025	−	0.407903i	$-0.866260\pi$
$691$	1.70486	−	16.2207i	0.0648560	−	0.617064i	0.977881	−	0.209161i	$-0.0670732\pi$
$692$	−4.27702			−0.162588
$693$	16.1791	−	20.7662i	0.614594	−	0.788843i
$694$	14.2204			0.539800
$695$	−0.290661	+	2.76546i	−0.0110254	+	0.104900i
$696$	−10.8815	−	11.5572i	−0.412463	−	0.438076i
$697$	−6.96711	−	1.48090i	−0.263898	−	0.0560933i
$698$	−5.45825	+	12.2594i	−0.206598	+	0.464027i
$699$	2.71789	−	2.06862i	0.102800	−	0.0782422i
$700$	10.8444	−	6.85537i	0.409880	−	0.259109i
$701$	−13.8751	+	42.7031i	−0.524054	+	1.61287i	0.242124	+	0.970245i	$0.422156\pi$
$701$	−13.8751	+	42.7031i	−0.524054	+	1.61287i	−0.766178	+	0.642628i	$0.777844\pi$
$702$	−7.10963	−	0.269976i	−0.268336	−	0.0101896i
$703$	−3.15701	−	1.82270i	−0.119069	−	0.0687444i
$704$	3.16782	−	0.982302i	0.119392	−	0.0370219i
$705$	3.66996	+	6.04194i	0.138219	+	0.227553i
$706$	−9.53613	+	13.1254i	−0.358897	+	0.493979i
$707$	13.4155	+	27.1450i	0.504542	+	1.02089i
$708$	−4.89106	+	1.71044i	−0.183817	+	0.0642823i
$709$	−8.06276	−	3.58977i	−0.302803	−	0.134817i	0.249710	−	0.968321i	$-0.419665\pi$
$709$	−8.06276	−	3.58977i	−0.302803	−	0.134817i	−0.552514	+	0.833504i	$0.686331\pi$
$710$	0.378945	+	3.60543i	0.0142216	+	0.135309i
$711$	6.87645	−	41.3145i	0.257887	−	1.54941i
$712$	2.08225	+	9.79621i	0.0780356	+	0.367129i
$713$	−42.6573	+	58.7127i	−1.59753	+	2.19881i
$714$	4.93317	−	5.03310i	0.184619	−	0.188359i
$715$	−1.75167	−	0.208006i	−0.0655089	−	0.00777897i
$716$	−18.4313	+	10.6413i	−0.688810	+	0.397685i
$717$	35.2525	−	16.6451i	1.31653	−	0.621621i
$718$	7.47423	+	8.30098i	0.278936	+	0.309790i
$719$	24.3963	+	21.9665i	0.909829	+	0.819214i	0.984025	−	0.178030i	$-0.0569724\pi$
$719$	24.3963	+	21.9665i	0.909829	+	0.819214i	−0.0741961	+	0.997244i	$0.523639\pi$
$720$	−0.726221	−	0.911344i	−0.0270647	−	0.0339638i
$721$	8.63145	+	7.16614i	0.321452	+	0.266881i
$722$	0.477993	+	1.47111i	0.0177890	+	0.0547491i
$723$	3.90253	+	16.5409i	0.145137	+	0.615164i
$724$	−20.6389	+	9.18901i	−0.767037	+	0.341507i
$725$	22.2204	−	38.4869i	0.825246	−	1.42937i
$726$	15.3611	+	11.2710i	0.570105	+	0.418307i
$727$	−35.3797			−1.31216			−0.656080	−	0.754692i	$-0.727786\pi$
$727$	−35.3797			−1.31216			−0.656080	+	0.754692i	$0.727786\pi$
$728$	−2.84300	+	2.24521i	−0.105369	+	0.0832130i
$729$	4.85053	−	26.5607i	0.179649	−	0.983731i
$730$	0.333807	−	0.370731i	0.0123548	−	0.0137214i
$731$	−5.26677	+	0.553560i	−0.194799	+	0.0204741i
$732$	−11.4490	+	1.46160i	−0.423168	+	0.0540223i
$733$	14.9620	+	13.4718i	0.552632	+	0.497592i	0.897473	−	0.441069i	$-0.145401\pi$
$733$	14.9620	+	13.4718i	0.552632	+	0.497592i	−0.344841	+	0.938661i	$0.612067\pi$
$734$	−0.569834	+	1.75377i	−0.0210330	+	0.0647328i
$735$	−4.30659	+	1.90606i	−0.158851	+	0.0703060i
$736$			7.79223i			0.287225i
$737$	−8.86183	−	20.6483i	−0.326430	−	0.760590i
$738$	−6.40491	+	12.3301i	−0.235768	+	0.453877i
$739$	7.54765	+	16.9523i	0.277645	+	0.623600i	0.997511	−	0.0705127i	$-0.0224635\pi$
$739$	7.54765	+	16.9523i	0.277645	+	0.623600i	−0.719866	+	0.694113i	$0.755797\pi$
$740$	0.0649488	+	0.305560i	0.00238757	+	0.0112326i
$741$	−3.54864	−	10.1475i	−0.130363	−	0.372776i
$742$	−6.65670	−	17.9961i	−0.244375	−	0.660657i
$743$	33.7771	−	24.5405i	1.23916	−	0.900302i	0.241618	−	0.970372i	$-0.422322\pi$
$743$	33.7771	−	24.5405i	1.23916	−	0.900302i	0.997542	+	0.0700692i	$0.0223220\pi$
$744$	10.5246	−	12.2252i	0.385851	−	0.448199i
$745$	−4.50514	+	4.05645i	−0.165056	+	0.148617i
$746$	6.28810	+	14.1233i	0.230224	+	0.517091i
$747$	−10.6661	−	16.7101i	−0.390252	−	0.611390i
$748$	3.74420	+	3.46377i	0.136901	+	0.126648i
$749$	−7.33080	−	28.7613i	−0.267862	−	1.05092i
$750$	3.77464	−	5.44622i	0.137830	−	0.198868i
$751$	−4.06447	+	0.863929i	−0.148315	+	0.0315252i	−0.281471	−	0.959570i	$-0.590822\pi$
$751$	−4.06447	+	0.863929i	−0.148315	+	0.0315252i	0.133156	+	0.991095i	$0.457489\pi$
$752$	−2.18458	+	10.2777i	−0.0796636	+	0.374788i
$753$	−44.9391	+	5.73699i	−1.63767	+	0.209068i
$754$	−5.10400	+	11.4638i	−0.185877	+	0.417486i
$755$	−0.622631	−	1.91626i	−0.0226599	−	0.0697399i
$756$	−6.89975	−	11.8909i	−0.250941	−	0.432468i
$757$	9.25325	+	6.72288i	0.336315	+	0.244347i	0.743105	−	0.669174i	$-0.233352\pi$
$757$	9.25325	+	6.72288i	0.336315	+	0.244347i	−0.406790	+	0.913522i	$0.633352\pi$
$758$	−3.88717	−	6.73278i	−0.141188	−	0.244545i
$759$	−35.9815	+	26.6280i	−1.30605	+	0.966535i
$760$	0.880364	−	1.52483i	0.0319341	−	0.0553116i
$761$	2.04131	−	19.4217i	0.0739973	−	0.704038i	−0.893139	−	0.449780i	$-0.851502\pi$
$761$	2.04131	−	19.4217i	0.0739973	−	0.704038i	0.967137	−	0.254257i	$-0.0818311\pi$
$762$	3.58579	+	1.07749i	0.129899	+	0.0390332i
$763$	−23.1526	+	44.0979i	−0.838180	+	1.59645i
$764$	5.46583	+	7.52306i	0.197747	+	0.272175i
$765$	0.655358	−	1.66801i	0.0236945	−	0.0603070i
$766$	1.39303	−	6.55369i	0.0503322	−	0.236794i
$767$	2.74085	+	3.04402i	0.0989662	+	0.109913i
$768$	0.142671	−	1.72616i	0.00514821	−	0.0622876i
$769$			38.6431i			1.39351i	0.717311	+	0.696753i	$0.245373\pi$
$769$			38.6431i			1.39351i	−0.717311	+	0.696753i	$0.754627\pi$
$770$	−1.46887	−	3.07577i	−0.0529344	−	0.110843i
$771$	−0.769632	−	34.5769i	−0.0277176	−	1.24526i
$772$	4.60204	+	0.483694i	0.165631	+	0.0174085i
$773$	28.5661	−	25.7210i	1.02745	−	0.925121i	0.0302246	−	0.999543i	$-0.490378\pi$
$773$	28.5661	−	25.7210i	1.02745	−	0.925121i	0.997227	+	0.0744216i	$0.0237111\pi$
$774$	−1.69609	+	10.1903i	−0.0609648	+	0.366283i
$775$	41.2577	+	18.3691i	1.48202	+	0.659839i
$776$	2.60672	−	1.89389i	0.0935757	−	0.0679867i
$777$	0.229765	+	3.67821i	0.00824277	+	0.131955i
$778$	10.0814	+	3.27563i	0.361434	+	0.117437i
$779$	−20.8788	−	2.19445i	−0.748060	−	0.0786242i
$780$	−0.442737	+	0.807843i	−0.0158525	+	0.0289254i
$781$	−30.9513	−	0.417051i	−1.10753	−	0.0149233i
$782$	−10.3782	+	5.99186i	−0.371124	+	0.214268i
$783$	−40.3081	−	25.3585i	−1.44049	−	0.906237i
$784$	−6.60250	−	2.32529i	−0.235804	−	0.0830459i
$785$	3.31334	−	1.07657i	0.118258	−	0.0384244i
$786$	24.3558	+	10.2007i	0.868741	+	0.363846i
$787$	−23.8060	+	2.50211i	−0.848591	+	0.0891905i	−0.518834	−	0.854875i	$-0.673634\pi$
$787$	−23.8060	+	2.50211i	−0.848591	+	0.0891905i	−0.329757	+	0.944066i	$0.606967\pi$
$788$	0.293791	+	0.0624472i	0.0104659	+	0.00222459i
$789$	−12.7084	+	2.99831i	−0.452431	+	0.106743i
$790$	−4.38725	−	3.18752i	−0.156091	−	0.113407i
$791$	4.91499	−	17.4848i	0.174757	−	0.621688i
$792$	8.45832	−	5.23993i	0.300553	−	0.186193i
$793$	4.56212	+	7.90182i	0.162005	+	0.280602i
$794$	−12.4160	+	5.52795i	−0.440626	+	0.196180i
$795$	−3.34476	−	3.55246i	−0.118626	−	0.125993i
$796$	4.82796	−	5.36200i	0.171123	−	0.190051i
$797$	−0.726696	−	1.00021i	−0.0257409	−	0.0354293i	0.795953	−	0.605359i	$-0.206970\pi$
$797$	−0.726696	−	1.00021i	−0.0257409	−	0.0354293i	−0.821693	+	0.569930i	$0.806970\pi$
$798$	12.9099	−	16.2733i	0.457004	−	0.576067i
$799$	−15.3683	+	4.99347i	−0.543692	+	0.176656i
$800$	4.74315	−	1.00819i	0.167696	−	0.0356448i
$801$	13.4297	+	26.8767i	0.474514	+	0.949642i
$802$	−14.3891	−	8.30755i	−0.508097	−	0.293350i
$803$	2.80727	+	3.20356i	0.0990665	+	0.113051i
$804$	−11.7315	+	0.261126i	−0.413737	+	0.00920921i
$805$	7.92425	−	1.15593i	0.279293	−	0.0407411i
$806$	−12.1282	−	3.94069i	−0.427198	−	0.138805i
$807$	−18.1275	−	15.6058i	−0.638120	−	0.549352i
$808$	1.19627	+	11.3818i	0.0420847	+	0.400409i
$809$	2.53355	+	24.1051i	0.0890749	+	0.847491i	0.944267	+	0.329180i	$0.106772\pi$
$809$	2.53355	+	24.1051i	0.0890749	+	0.847491i	−0.855192	+	0.518311i	$0.826561\pi$
$810$	−2.79566	−	2.09900i	−0.0982293	−	0.0737515i
$811$	−22.4032	−	7.27923i	−0.786681	−	0.255608i	−0.111991	−	0.993709i	$-0.535723\pi$
$811$	−22.4032	−	7.27923i	−0.786681	−	0.255608i	−0.674690	+	0.738101i	$0.735723\pi$
$812$	−23.9937	+	3.50000i	−0.842012	+	0.122826i
$813$	−1.01229	−	45.4788i	−0.0355027	−	1.59501i
$814$	−2.65619	+	0.243042i	−0.0930993	+	0.00851860i
$815$	4.99019	+	2.88109i	0.174799	+	0.100920i
$816$	2.40873	−	1.13732i	0.0843223	−	0.0398142i
$817$	−15.2678	+	3.24527i	−0.534153	+	0.113538i
$818$	18.2197	−	5.91994i	0.637037	−	0.206986i
$819$	−6.56327	+	8.66233i	−0.229339	+	0.302686i
$820$	1.05744	+	1.45544i	0.0369275	+	0.0508263i
$821$	4.21790	−	4.68446i	0.147206	−	0.163489i	−0.665032	−	0.746815i	$-0.731582\pi$
$821$	4.21790	−	4.68446i	0.147206	−	0.163489i	0.812238	+	0.583326i	$0.198249\pi$
$822$	−2.84413	+	2.67784i	−0.0992003	+	0.0934003i
$823$	16.4511	−	7.32451i	0.573450	−	0.255316i	−0.0994590	−	0.995042i	$-0.531711\pi$
$823$	16.4511	−	7.32451i	0.573450	−	0.255316i	0.672909	+	0.739725i	$0.265045\pi$
$824$	2.12010	+	3.67213i	0.0738573	+	0.127925i
$825$	20.8640	+	18.4568i	0.726390	+	0.642585i
$826$	−2.14186	+	7.61957i	−0.0745250	+	0.265119i
$827$	−40.6562	−	29.5385i	−1.41375	−	1.02715i	−0.992763	−	0.120088i	$-0.961682\pi$
$827$	−40.6562	−	29.5385i	−1.41375	−	1.02715i	−0.420991	−	0.907065i	$-0.638318\pi$
$828$	5.87289	+	22.6269i	0.204097	+	0.786341i
$829$	9.30846	+	1.97857i	0.323296	+	0.0687187i	0.366701	−	0.930339i	$-0.380487\pi$
$829$	9.30846	+	1.97857i	0.323296	+	0.0687187i	−0.0434048	+	0.999058i	$0.513821\pi$
$830$	−2.55273	+	0.268303i	−0.0886065	+	0.00931292i
$831$	−0.0306979	+	0.0732963i	−0.00106490	+	0.00254262i
$832$	−1.30222	+	0.423117i	−0.0451463	+	0.0146689i
$833$	−1.98005	−	10.5817i	−0.0686045	−	0.366634i
$834$	−7.06304	+	10.1909i	−0.244573	+	0.352881i
$835$	−6.98904	+	4.03512i	−0.241866	+	0.139641i
$836$	12.0424	+	8.99971i	0.416496	+	0.311261i
$837$	21.3472	−	43.4317i	0.737866	−	1.50122i
$838$	−6.10995	−	0.642182i	−0.211065	−	0.0221838i
$839$	25.4930	+	8.28318i	0.880117	+	0.285967i	0.714006	−	0.700140i	$-0.246879\pi$
$839$	25.4930	+	8.28318i	0.880117	+	0.285967i	0.166111	+	0.986107i	$0.446879\pi$
$840$	−1.77658	+	0.110977i	−0.0612977	+	0.00382905i
$841$	−44.4897	+	32.3236i	−1.53413	+	1.11461i
$842$	16.1492	+	7.19010i	0.556539	+	0.247787i
$843$	43.3206	+	8.20499i	1.49204	+	0.282595i
$844$	3.19946	−	2.88081i	0.110130	−	0.0991616i
$845$	−4.29776	−	0.451713i	−0.147847	−	0.0155394i
$846$	1.40257	+	31.4906i	0.0482213	+	1.08267i
$847$	27.5579	−	9.35751i	0.946900	−	0.321528i
$848$		−	7.25229i		−	0.249045i
$849$	−4.19493	−	0.346721i	−0.143970	−	0.0118994i
$850$	4.99003	+	5.54199i	0.171157	+	0.190089i
$851$	1.30291	−	6.12969i	0.0446630	−	0.210123i
$852$	−6.24475	+	14.9104i	−0.213942	+	0.510821i
$853$	23.7810	+	32.7318i	0.814246	+	1.12071i	0.990654	+	0.136397i	$0.0435523\pi$
$853$	23.7810	+	32.7318i	0.814246	+	1.12071i	−0.176408	+	0.984317i	$0.556448\pi$
$854$	−8.19564	+	15.6099i	−0.280449	+	0.534161i
$855$	1.40714	−	5.09131i	0.0481231	−	0.174119i
$856$	1.17263	−	11.1569i	0.0400798	−	0.381334i
$857$	5.08753	−	8.81186i	0.173787	−	0.301007i	−0.765954	−	0.642895i	$-0.777733\pi$
$857$	5.08753	−	8.81186i	0.173787	−	0.301007i	0.939741	+	0.341888i	$0.111066\pi$
$858$	−6.40380	−	4.56726i	−0.218622	−	0.155924i
$859$	−15.6123	−	27.0412i	−0.532683	−	0.922634i	−0.999272	−	0.0381598i	$-0.987850\pi$
$859$	−15.6123	−	27.0412i	−0.532683	−	0.922634i	0.466588	−	0.884475i	$-0.345483\pi$
$860$	1.08213	+	0.786210i	0.0369002	+	0.0268095i
$861$	9.82461	+	18.8132i	0.334822	+	0.641152i
$862$	−3.94657	−	12.1463i	−0.134421	−	0.413705i
$863$	7.69543	−	17.2842i	0.261956	−	0.588362i	−0.733905	−	0.679252i	$-0.762304\pi$
$863$	7.69543	−	17.2842i	0.261956	−	0.588362i	0.995861	+	0.0908898i	$0.0289711\pi$
$864$	−0.886699	−	5.11994i	−0.0301661	−	0.174184i
$865$	−0.345414	+	1.62504i	−0.0117444	+	0.0552532i
$866$	−18.0513	+	3.83692i	−0.613408	+	0.130384i
$867$	−20.8337	−	14.4393i	−0.707549	−	0.490385i
$868$	−6.08606	−	23.8778i	−0.206574	−	0.810464i
$869$	31.4437	−	33.9895i	1.06665	−	1.15301i
$870$	−5.26994	+	3.20104i	−0.178668	+	0.108525i
$871$	3.77303	+	8.47437i	0.127844	+	0.287143i
$872$	−13.9897	+	12.5964i	−0.473751	+	0.426567i
$873$	6.14194	−	7.46410i	0.207873	−	0.252621i
$874$	−28.5754	+	20.7612i	−0.966576	+	0.702258i
$875$	−3.51157	−	9.49335i	−0.118713	−	0.320934i
$876$	2.09977	−	0.734306i	0.0709447	−	0.0248099i
$877$	0.966292	+	4.54605i	0.0326294	+	0.153509i	0.991446	−	0.130516i	$-0.0416634\pi$
$877$	0.966292	+	4.54605i	0.0326294	+	0.153509i	−0.958817	+	0.284025i	$0.908330\pi$
$878$	12.9523	+	29.0913i	0.437118	+	0.981783i
$879$	4.09169	−	7.46592i	0.138009	−	0.251819i
$880$	−0.117389	−	1.28294i	−0.00395719	−	0.0432478i
$881$			21.9454i			0.739358i	0.929160	+	0.369679i	$0.120532\pi$
$881$			21.9454i			0.739358i	−0.929160	+	0.369679i	$0.879468\pi$
$882$	−20.9248	−	1.77592i	−0.704574	−	0.0597982i
$883$	7.05947	−	21.7268i	0.237570	−	0.731165i	−0.759200	−	0.650857i	$-0.774410\pi$
$883$	7.05947	−	21.7268i	0.237570	−	0.731165i	0.996770	−	0.0803080i	$-0.0255904\pi$
$884$	−1.56488	−	1.40902i	−0.0526326	−	0.0473906i
$885$	0.254874	+	1.99648i	0.00856750	+	0.0671111i
$886$	23.0675	−	2.42449i	0.774967	−	0.0814523i
$887$	37.5379	−	41.6901i	1.26040	−	1.39982i	0.380413	−	0.924817i	$-0.375782\pi$
$887$	37.5379	−	41.6901i	1.26040	−	1.39982i	0.879986	−	0.474999i	$-0.157552\pi$
$888$	−0.400856	+	1.33402i	−0.0134519	+	0.0447667i
$889$	4.48843	−	3.54466i	0.150537	−	0.118884i
$890$	3.89022			0.130400
$891$	20.6119	−	21.5905i	0.690523	−	0.723310i
$892$	−10.2628	+	17.7757i	−0.343624	+	0.595174i
$893$	−43.5103	+	19.3720i	−1.45602	+	0.648261i
$894$	−26.3095	+	6.20724i	−0.879922	+	0.207601i
$895$	2.55463	+	7.86233i	0.0853917	+	0.262809i
$896$	−2.03562	−	1.69005i	−0.0680053	−	0.0564604i
$897$	14.7051	−	11.1922i	0.490991	−	0.373698i
$898$	−22.4769	−	20.2383i	−0.750065	−	0.675361i
$899$	−57.1141	−	63.4316i	−1.90486	−	2.11556i
$900$	13.0132	−	6.50241i	0.433774	−	0.216747i
$901$	9.65908	−	5.57667i	0.321791	−	0.185786i
$902$	−13.4051	+	7.50048i	−0.446342	+	0.249739i
$903$	11.2695	+	11.0458i	0.375026	+	0.367581i
$904$	4.03501	−	5.55372i	0.134203	−	0.184714i
$905$	1.82454	+	8.58380i	0.0606499	+	0.285335i
$906$	1.67194	−	8.82746i	0.0555464	−	0.293273i
$907$	−4.88842	−	46.5102i	−0.162317	−	1.54435i	−0.707914	−	0.706299i	$-0.750363\pi$
$907$	−4.88842	−	46.5102i	−0.162317	−	1.54435i	0.545596	−	0.838048i	$-0.316303\pi$
$908$	21.3815	+	9.51966i	0.709570	+	0.315921i
$909$	12.0520	+	32.1485i	0.399739	+	1.06630i
$910$	0.623461	+	1.26152i	0.0206675	+	0.0418189i
$911$	17.3918	−	23.9377i	0.576216	−	0.793093i	−0.417058	−	0.908880i	$-0.636939\pi$
$911$	17.3918	−	23.9377i	0.576216	−	0.793093i	0.993274	+	0.115787i	$0.0369390\pi$
$912$	6.71025	−	4.07590i	0.222199	−	0.134967i
$913$	0.295283	−	21.9143i	0.00977243	−	0.725257i
$914$	0.319331	+	0.184366i	0.0105625	+	0.00609829i
$915$	−0.369297	+	4.46808i	−0.0122086	+	0.147710i
$916$	1.86626	−	5.74375i	0.0616629	−	0.189779i
$917$	34.0941	−	21.5528i	1.12589	−	0.711737i
$918$	6.13724	−	5.11796i	0.202559	−	0.168918i
$919$	19.1103	−	42.9225i	0.630392	−	1.41588i	−0.262198	−	0.965014i	$-0.584448\pi$
$919$	19.1103	−	42.9225i	0.630392	−	1.41588i	0.892590	−	0.450869i	$-0.148886\pi$
$920$	2.96064	+	0.629304i	0.0976095	+	0.0207475i
$921$	−9.17731	+	8.64074i	−0.302403	+	0.284722i
$922$	1.65027	−	15.7013i	0.0543489	−	0.517095i
$923$	12.7791			0.420629
$924$	0.847766	−	15.1750i	0.0278895	−	0.499222i
$925$	−3.89974			−0.128223
$926$	−2.33586	+	22.2242i	−0.0767611	+	0.730333i
$927$	8.92395	+	9.06517i	0.293101	+	0.297739i
$928$	−8.96446	−	1.90545i	−0.294273	−	0.0625496i
$929$	8.63051	−	19.3844i	0.283158	−	0.635983i	−0.714836	−	0.699292i	$-0.753499\pi$
$929$	8.63051	−	19.3844i	0.283158	−	0.635983i	0.997994	+	0.0633091i	$0.0201654\pi$
$930$	−3.79498	−	4.98612i	−0.124442	−	0.163501i
$931$	−9.06417	−	30.4078i	−0.297066	−	0.996576i
$932$	0.609376	−	1.87547i	0.0199608	−	0.0614329i
$933$	−37.9671	−	3.13807i	−1.24299	−	0.102736i
$934$	6.63692	+	3.83183i	0.217167	+	0.125381i
$935$	1.61843	−	1.14287i	0.0529285	−	0.0373757i
$936$	−3.46246	+	2.21010i	−0.113174	+	0.0722395i
$937$	14.0856	−	19.3872i	0.460158	−	0.633353i	−0.514383	−	0.857560i	$-0.671979\pi$
$937$	14.0856	−	19.3872i	0.460158	−	0.633353i	0.974542	+	0.224207i	$0.0719792\pi$
$938$	−9.94553	+	14.9123i	−0.324733	+	0.486904i
$939$	11.3582	+	32.4792i	0.370662	+	1.05992i
$940$	3.72855	+	1.66006i	0.121612	+	0.0541451i
$941$	−1.62859	−	15.4950i	−0.0530906	−	0.505124i	−0.988463	−	0.151460i	$-0.951602\pi$
$941$	−1.62859	−	15.4950i	−0.0530906	−	0.505124i	0.935373	−	0.353664i	$-0.115064\pi$
$942$	15.2633	+	2.89089i	0.497304	+	0.0941903i
$943$	−7.50341	−	35.3008i	−0.244345	−	1.14955i
$944$	−1.75839	+	2.42021i	−0.0572306	+	0.0787712i
$945$	−5.07515	+	1.66123i	−0.165095	+	0.0540399i
$946$	−7.75566	+	8.38357i	−0.252158	+	0.272574i
$947$	−43.7106	+	25.2363i	−1.42040	+	0.820071i	−0.996333	−	0.0855585i	$-0.972733\pi$
$947$	−43.7106	+	25.2363i	−1.42040	+	0.820071i	−0.424071	+	0.905629i	$0.639399\pi$
$948$	−10.3245	−	21.8662i	−0.335323	−	0.710180i
$949$	−1.17667	−	1.30682i	−0.0381962	−	0.0424212i
$950$	16.3346	+	14.7077i	0.529964	+	0.477182i
$951$	−23.6394	−	31.0591i	−0.766559	−	1.00716i
$952$	0.685618	−	4.01074i	0.0222210	−	0.129989i
$953$	15.4469	+	47.5407i	0.500375	+	1.53999i	0.808410	+	0.588620i	$0.200329\pi$
$953$	15.4469	+	47.5407i	0.500375	+	1.53999i	−0.308035	+	0.951375i	$0.599671\pi$
$954$	−5.46595	−	21.0591i	−0.176967	−	0.681813i
$955$	3.29980	−	1.46916i	0.106779	−	0.0475410i
$956$	11.2539	−	19.4923i	0.363977	−	0.630426i
$957$	−21.8351	−	47.9059i	−0.705829	−	1.54858i
$958$	19.6646			0.635334
$959$	0.861318	+	5.90461i	0.0278134	+	0.190670i
$960$	−0.644331	−	0.193614i	−0.0207957	−	0.00624885i
$961$	37.2981	−	41.4237i	1.20316	−	1.33625i
$962$	1.09513	−	0.115103i	0.0353083	−	0.00371105i
$963$	−5.00369	−	33.2809i	−0.161242	−	1.07246i
$964$	7.29182	+	6.56558i	0.234854	+	0.211463i
$965$	0.555441	−	1.70947i	0.0178803	−	0.0550299i
$966$	33.4634	+	12.4619i	1.07667	+	0.400956i
$967$			23.0772i			0.742114i	0.928610	+	0.371057i	$0.121005\pi$
$967$			23.0772i			0.742114i	−0.928610	+	0.371057i	$0.878995\pi$
$968$	10.9960	+	0.296384i	0.353425	+	0.00952613i
$969$	10.5884	+	5.80297i	0.340149	+	0.186418i
$970$	−0.509061	−	1.14337i	−0.0163449	−	0.0367114i
$971$	−7.45542	−	35.0750i	−0.239256	−	1.12561i	−0.919642	−	0.392757i	$-0.871521\pi$
$971$	−7.45542	−	35.0750i	−0.239256	−	1.12561i	0.680387	−	0.732853i	$-0.261812\pi$
$972$	−6.43361	−	14.1989i	−0.206358	−	0.455430i
$973$	6.57078	+	17.7638i	0.210650	+	0.569481i
$974$	−3.31101	+	2.40559i	−0.106092	+	0.0770801i
$975$	−8.71535	−	7.50297i	−0.279115	−	0.240287i
$976$	−4.95213	+	4.45892i	−0.158514	+	0.142727i
$977$	13.1205	+	29.4691i	0.419761	+	0.942799i	0.992407	+	0.122996i	$0.0392503\pi$
$977$	13.1205	+	29.4691i	0.419761	+	0.942799i	−0.572646	+	0.819803i	$0.694083\pi$
$978$	13.3389	+	21.9601i	0.426530	+	0.702205i
$979$	−3.91680	+	32.9845i	−0.125182	+	1.05419i
$980$	−1.41671	+	2.32082i	−0.0452551	+	0.0741358i
$981$	−31.1293	+	47.1210i	−0.993884	+	1.50446i
$982$	9.51108	−	2.02164i	0.303511	−	0.0645132i
$983$	−6.28849	+	29.5850i	−0.200572	+	0.943615i	0.756552	+	0.653934i	$0.226883\pi$
$983$	−6.28849	+	29.5850i	−0.200572	+	0.943615i	−0.957123	+	0.289681i	$0.906451\pi$
$984$	1.01585	+	7.95735i	0.0323840	+	0.253671i
$985$	0.0474533	−	0.106582i	0.00151199	−	0.00339598i
$986$	−4.35544	−	13.4047i	−0.138705	−	0.426891i
$987$	40.6432	+	25.8184i	1.29369	+	0.821809i
$988$	−5.02120	−	3.64812i	−0.159746	−	0.116062i
$989$	−13.4163	−	23.2377i	−0.426613	−	0.738915i
$990$	−1.30780	−	3.63690i	−0.0415648	−	0.115588i
$991$	−9.31508	+	16.1342i	−0.295903	+	0.512520i	−0.975195	−	0.221349i	$-0.928954\pi$
$991$	−9.31508	+	16.1342i	−0.295903	+	0.512520i	0.679291	+	0.733869i	$0.262287\pi$
$992$	0.973525	−	9.26247i	0.0309095	−	0.294084i
$993$	−3.65078	+	12.1495i	−0.115854	+	0.385553i
$994$	13.1944	+	20.8721i	0.418502	+	0.662022i
$995$	−1.64737	−	2.26741i	−0.0522252	−	0.0718818i
$996$	−10.5569	−	4.42144i	−0.334508	−	0.140099i
$997$	−8.62091	+	40.5582i	−0.273027	+	1.28449i	0.601249	+	0.799062i	$0.294670\pi$
$997$	−8.62091	+	40.5582i	−0.273027	+	1.28449i	−0.874276	+	0.485429i	$0.838663\pi$
$998$	−0.363926	−	0.404181i	−0.0115199	−	0.0127941i
$999$	−0.158569	+	4.17582i	−0.00501691	+	0.132117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.95.5	✓	128
3.2	odd	2		462.2.bc.b.95.5	yes	128
7.2	even	3	inner	462.2.bc.a.359.16	yes	128
11.8	odd	10		462.2.bc.b.305.14	yes	128
21.2	odd	6		462.2.bc.b.359.14	yes	128
33.8	even	10	inner	462.2.bc.a.305.16	yes	128
77.30	odd	30		462.2.bc.b.107.5	yes	128
231.107	even	30	inner	462.2.bc.a.107.5	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.5	✓	128	1.1	even	1	trivial
462.2.bc.a.107.5	yes	128	231.107	even	30	inner
462.2.bc.a.305.16	yes	128	33.8	even	10	inner
462.2.bc.a.359.16	yes	128	7.2	even	3	inner
462.2.bc.b.95.5	yes	128	3.2	odd	2
462.2.bc.b.107.5	yes	128	77.30	odd	30
462.2.bc.b.305.14	yes	128	11.8	odd	10
462.2.bc.b.359.14	yes	128	21.2	odd	6

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.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(-1.18732 - 1.26106i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.157991 + 0.354854i) q^{5} +(-1.37826 + 1.04900i) q^{6} +(0.106147 + 2.64362i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.180521 + 2.99456i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(-1.18732 - 1.26106i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.157991 + 0.354854i) q^{5} +(-1.37826 + 1.04900i) q^{6} +(0.106147 + 2.64362i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.180521 + 2.99456i) q^{9} +(0.336396 + 0.194218i) q^{10} +(-1.98544 + 2.65670i) q^{11} +(0.899191 + 1.48036i) q^{12} +(0.804816 - 1.10773i) q^{13} +(2.64023 + 0.170768i) q^{14} +(0.635078 - 0.222091i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.160755 + 1.52948i) q^{17} +(2.95929 + 0.492549i) q^{18} +(0.942435 + 4.43381i) q^{19} +(0.228317 - 0.314252i) q^{20} +(3.20772 - 3.27269i) q^{21} +(2.43461 + 2.25226i) q^{22} +(-6.74827 + 3.89611i) q^{23} +(1.56624 - 0.739525i) q^{24} +(3.24469 + 3.60360i) q^{25} +(-1.01754 - 0.916196i) q^{26} +(3.99065 - 3.32787i) q^{27} +(0.445812 - 2.60792i) q^{28} +(-2.83206 - 8.71618i) q^{29} +(-0.154491 - 0.654814i) q^{30} +(8.50830 - 3.78814i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.70760 - 0.650615i) q^{33} +1.53791 q^{34} +(-0.954870 - 0.380002i) q^{35} +(0.799181 - 2.89159i) q^{36} +(-0.538125 + 0.597649i) q^{37} +(4.50803 - 0.473813i) q^{38} +(-2.35249 + 0.300322i) q^{39} +(-0.288664 - 0.259915i) q^{40} +(-1.43120 + 4.40478i) q^{41} +(-2.91947 - 3.53224i) q^{42} +3.44350i q^{43} +(2.49441 - 2.18585i) q^{44} +(-1.03411 - 0.537173i) q^{45} +(3.16938 + 7.11855i) q^{46} +(2.18458 + 10.2777i) q^{47} +(-0.571758 - 1.63496i) q^{48} +(-6.97747 + 0.561225i) q^{49} +(3.92302 - 2.85024i) q^{50} +(1.73789 - 2.01871i) q^{51} +(-1.01754 + 0.916196i) q^{52} +(-2.94977 - 6.62530i) q^{53} +(-2.89251 - 4.31664i) q^{54} +(-0.629058 - 1.12428i) q^{55} +(-2.54703 - 0.715972i) q^{56} +(4.47230 - 6.45283i) q^{57} +(-8.96446 + 1.90545i) q^{58} +(-0.621978 + 2.92618i) q^{59} +(-0.667375 + 0.0851981i) q^{60} +(-2.71039 + 6.08764i) q^{61} +(-2.87803 - 8.85766i) q^{62} +(-7.93565 - 0.159364i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.265930 + 0.460604i) q^{65} +(-0.0504441 - 5.74434i) q^{66} +(-3.38743 + 5.86719i) q^{67} +(0.160755 - 1.52948i) q^{68} +(12.9256 + 3.88399i) q^{69} +(-0.477732 + 0.909918i) q^{70} +(5.48581 + 7.55057i) q^{71} +(-2.79222 - 1.09706i) q^{72} +(0.267020 - 1.25623i) q^{73} +(0.538125 + 0.597649i) q^{74} +(0.691831 - 8.37038i) q^{75} -4.53286i q^{76} +(-7.23405 - 4.96674i) q^{77} +(0.0527750 + 2.37100i) q^{78} +(-13.8845 - 1.45932i) q^{79} +(-0.288664 + 0.259915i) q^{80} +(-8.93482 - 1.08116i) q^{81} +(4.23105 + 1.88379i) q^{82} +(-5.34599 + 3.88409i) q^{83} +(-3.81806 + 2.53425i) q^{84} +(-0.568141 - 0.184600i) q^{85} +(3.42464 + 0.359944i) q^{86} +(-7.62901 + 13.9203i) q^{87} +(-1.91313 - 2.70923i) q^{88} +(8.67330 - 5.00753i) q^{89} +(-0.642325 + 0.972298i) q^{90} +(3.01386 + 2.01004i) q^{91} +(7.41085 - 2.40793i) q^{92} +(-14.8792 - 6.23168i) q^{93} +(10.4497 - 1.09831i) q^{94} +(-1.72225 - 0.366076i) q^{95} +(-1.68577 + 0.397726i) q^{96} +(-2.60672 - 1.89389i) q^{97} +(-0.171193 + 6.99791i) q^{98} +(-7.59724 - 6.42511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

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