LMFDB - Embedded newform 462.2.bc.a.95.8

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			95.8
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.a.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(0.0618530 - 1.73095i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.30191 - 2.92414i) q^{5} +(-1.71500 - 0.242447i) q^{6} +(-2.04556 + 1.67800i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.99235 - 0.214128i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(0.0618530 - 1.73095i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.30191 - 2.92414i) q^{5} +(-1.71500 - 0.242447i) q^{6} +(-2.04556 + 1.67800i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.99235 - 0.214128i) q^{9} +(-2.77204 - 1.60044i) q^{10} +(-0.980906 - 3.16825i) q^{11} +(-0.420385 + 1.68026i) q^{12} +(-0.203849 + 0.280574i) q^{13} +(1.45499 + 2.20975i) q^{14} +(-4.98101 - 2.43441i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.764996 + 7.27845i) q^{17} +(-0.525741 + 2.95357i) q^{18} +(-1.45757 - 6.85733i) q^{19} +(-1.88143 + 2.58956i) q^{20} +(2.77800 + 3.64455i) q^{21} +(-3.25343 + 0.644360i) q^{22} +(6.50747 - 3.75709i) q^{23} +(1.62711 + 0.593717i) q^{24} +(-3.50999 - 3.89823i) q^{25} +(0.257729 + 0.232060i) q^{26} +(-0.555730 + 5.16635i) q^{27} +(2.34974 - 1.21603i) q^{28} +(-0.673371 - 2.07242i) q^{29} +(-2.94173 + 4.69926i) q^{30} +(-0.996173 + 0.443525i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.54475 + 1.50193i) q^{33} +7.31854 q^{34} +(2.24357 + 8.16612i) q^{35} +(2.88244 + 0.831593i) q^{36} +(0.821546 - 0.912419i) q^{37} +(-6.97212 + 0.732799i) q^{38} +(0.473050 + 0.370206i) q^{39} +(2.37871 + 2.14180i) q^{40} +(-1.62090 + 4.98861i) q^{41} +(3.91496 - 2.38182i) q^{42} +1.84972i q^{43} +(0.300754 + 3.30296i) q^{44} +(-4.52192 + 8.47128i) q^{45} +(-3.05629 - 6.86454i) q^{46} +(-0.790295 - 3.71805i) q^{47} +(0.760545 - 1.55614i) q^{48} +(1.36864 - 6.86490i) q^{49} +(-4.24377 + 3.08328i) q^{50} +(12.6459 - 0.873973i) q^{51} +(0.257729 - 0.232060i) q^{52} +(-2.42620 - 5.44933i) q^{53} +(5.07996 + 1.09272i) q^{54} +(-10.5415 - 1.25648i) q^{55} +(-0.963758 - 2.46397i) q^{56} +(-11.9598 + 2.09883i) q^{57} +(-2.13146 + 0.453055i) q^{58} +(1.23315 - 5.80153i) q^{59} +(4.36602 + 3.41682i) q^{60} +(0.0447633 - 0.100540i) q^{61} +(0.336967 + 1.03708i) q^{62} +(6.48034 - 4.58314i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.555045 + 0.961366i) q^{65} +(0.914118 + 5.67137i) q^{66} +(5.60173 - 9.70248i) q^{67} +(0.764996 - 7.27845i) q^{68} +(-6.10081 - 11.4965i) q^{69} +(8.35590 - 1.37768i) q^{70} +(3.42260 + 4.71081i) q^{71} +(1.12833 - 2.77972i) q^{72} +(-0.794456 + 3.73762i) q^{73} +(-0.821546 - 0.912419i) q^{74} +(-6.96474 + 5.83448i) q^{75} +7.01052i q^{76} +(7.32283 + 4.83490i) q^{77} +(0.417625 - 0.431761i) q^{78} +(-6.66607 - 0.700632i) q^{79} +(2.37871 - 2.14180i) q^{80} +(8.90830 + 1.28149i) q^{81} +(4.79185 + 2.13347i) q^{82} +(9.88760 - 7.18376i) q^{83} +(-1.95955 - 4.14248i) q^{84} +(22.2792 + 7.23895i) q^{85} +(1.83959 + 0.193349i) q^{86} +(-3.62890 + 1.03738i) q^{87} +(3.31630 + 0.0461467i) q^{88} +(1.06962 - 0.617544i) q^{89} +(7.95220 + 5.38264i) q^{90} +(-0.0538172 - 0.915989i) q^{91} +(-7.14641 + 2.32201i) q^{92} +(0.706101 + 1.75175i) q^{93} +(-3.78029 + 0.397324i) q^{94} +(-21.9494 - 4.66550i) q^{95} +(-1.46812 - 0.919039i) q^{96} +(-8.00898 - 5.81887i) q^{97} +(-6.68423 - 2.07872i) q^{98} +(2.25680 + 9.69055i) 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
$3$	0.0618530	−	1.73095i	0.0357108	−	0.999362i
$3$	0.0618530	−	1.73095i	0.0357108	−	0.999362i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	1.30191	−	2.92414i	0.582233	−	1.30772i	−0.346876	−	0.937911i	$-0.612758\pi$
$5$	1.30191	−	2.92414i	0.582233	−	1.30772i	0.929109	−	0.369806i	$-0.120576\pi$
$6$	−1.71500	−	0.242447i	−0.700145	−	0.0989787i
$7$	−2.04556	+	1.67800i	−0.773150	+	0.634224i
$7$	−2.04556	+	1.67800i	−0.773150	+	0.634224i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.99235	−	0.214128i	−0.997449	−	0.0713761i
$10$	−2.77204	−	1.60044i	−0.876595	−	0.506103i
$11$	−0.980906	−	3.16825i	−0.295754	−	0.955264i
$11$	−0.980906	−	3.16825i	−0.295754	−	0.955264i
$12$	−0.420385	+	1.68026i	−0.121355	+	0.485050i
$13$	−0.203849	+	0.280574i	−0.0565375	+	0.0778172i	−0.836350	−	0.548196i	$-0.815315\pi$
$13$	−0.203849	+	0.280574i	−0.0565375	+	0.0778172i	0.779812	+	0.626014i	$0.215315\pi$
$14$	1.45499	+	2.20975i	0.388862	+	0.590582i
$15$	−4.98101	−	2.43441i	−1.28609	−	0.628561i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.764996	+	7.27845i	0.185539	+	1.76528i	0.551046	+	0.834475i	$0.314229\pi$
$17$	0.764996	+	7.27845i	0.185539	+	1.76528i	−0.365507	+	0.930809i	$0.619104\pi$
$18$	−0.525741	+	2.95357i	−0.123918	+	0.696164i
$19$	−1.45757	−	6.85733i	−0.334389	−	1.57318i	−0.748616	−	0.663004i	$-0.769281\pi$
$19$	−1.45757	−	6.85733i	−0.334389	−	1.57318i	0.414226	−	0.910174i	$-0.364052\pi$
$20$	−1.88143	+	2.58956i	−0.420700	+	0.579043i
$21$	2.77800	+	3.64455i	0.606209	+	0.795305i
$22$	−3.25343	+	0.644360i	−0.693633	+	0.137378i
$23$	6.50747	−	3.75709i	1.35690	−	0.783407i	0.367696	−	0.929946i	$-0.380147\pi$
$23$	6.50747	−	3.75709i	1.35690	−	0.783407i	0.989205	+	0.146539i	$0.0468133\pi$
$24$	1.62711	+	0.593717i	0.332133	+	0.121192i
$25$	−3.50999	−	3.89823i	−0.701997	−	0.779647i
$26$	0.257729	+	0.232060i	0.0505448	+	0.0455107i
$27$	−0.555730	+	5.16635i	−0.106950	+	0.994264i
$28$	2.34974	−	1.21603i	0.444058	−	0.229809i
$29$	−0.673371	−	2.07242i	−0.125042	−	0.384840i	0.868867	−	0.495046i	$-0.164849\pi$
$29$	−0.673371	−	2.07242i	−0.125042	−	0.384840i	−0.993909	+	0.110206i	$0.964849\pi$
$30$	−2.94173	+	4.69926i	−0.537084	+	0.857963i
$31$	−0.996173	+	0.443525i	−0.178918	+	0.0796594i	−0.494241	−	0.869325i	$-0.664554\pi$
$31$	−0.996173	+	0.443525i	−0.178918	+	0.0796594i	0.315323	+	0.948984i	$0.397887\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−5.54475	+	1.50193i	−0.965216	+	0.261452i
$34$	7.31854			1.25512
$35$	2.24357	+	8.16612i	0.379232	+	1.38033i
$36$	2.88244	+	0.831593i	0.480406	+	0.138599i
$37$	0.821546	−	0.912419i	0.135061	−	0.150001i	−0.671820	−	0.740715i	$-0.734487\pi$
$37$	0.821546	−	0.912419i	0.135061	−	0.150001i	0.806881	+	0.590714i	$0.201154\pi$
$38$	−6.97212	+	0.732799i	−1.13103	+	0.118876i
$39$	0.473050	+	0.370206i	0.0757485	+	0.0592803i
$40$	2.37871	+	2.14180i	0.376107	+	0.338649i
$41$	−1.62090	+	4.98861i	−0.253141	+	0.779089i	0.741049	+	0.671451i	$0.234329\pi$
$41$	−1.62090	+	4.98861i	−0.253141	+	0.779089i	−0.994190	+	0.107638i	$0.965671\pi$
$42$	3.91496	−	2.38182i	0.604092	−	0.367523i
$43$			1.84972i			0.282080i	0.990004	+	0.141040i	$0.0450446\pi$
$43$			1.84972i			0.282080i	−0.990004	+	0.141040i	$0.954955\pi$
$44$	0.300754	+	3.30296i	0.0453404	+	0.497940i
$45$	−4.52192	+	8.47128i	−0.674088	+	1.26282i
$46$	−3.05629	−	6.86454i	−0.450626	−	1.01212i
$47$	−0.790295	−	3.71805i	−0.115276	−	0.542333i	−0.997447	−	0.0714039i	$-0.977252\pi$
$47$	−0.790295	−	3.71805i	−0.115276	−	0.542333i	0.882171	−	0.470929i	$-0.156081\pi$
$48$	0.760545	−	1.55614i	0.109775	−	0.224609i
$49$	1.36864	−	6.86490i	0.195520	−	0.980700i
$50$	−4.24377	+	3.08328i	−0.600160	+	0.436042i
$51$	12.6459	−	0.873973i	1.77078	−	0.122381i
$52$	0.257729	−	0.232060i	0.0357406	−	0.0321809i
$53$	−2.42620	−	5.44933i	−0.333264	−	0.748524i	−0.999995	−	0.00322489i	$-0.998973\pi$
$53$	−2.42620	−	5.44933i	−0.333264	−	0.748524i	0.666731	−	0.745299i	$-0.267693\pi$
$54$	5.07996	+	1.09272i	0.691295	+	0.148700i
$55$	−10.5415	−	1.25648i	−1.42141	−	0.169423i
$56$	−0.963758	−	2.46397i	−0.128788	−	0.329262i
$57$	−11.9598	+	2.09883i	−1.58412	+	0.277997i
$58$	−2.13146	+	0.453055i	−0.279874	+	0.0594891i
$59$	1.23315	−	5.80153i	0.160543	−	0.755295i	−0.822034	−	0.569438i	$-0.807161\pi$
$59$	1.23315	−	5.80153i	0.160543	−	0.755295i	0.982577	−	0.185856i	$-0.0595060\pi$
$60$	4.36602	+	3.41682i	0.563651	+	0.441109i
$61$	0.0447633	−	0.100540i	0.00573135	−	0.0128728i	−0.910657	−	0.413163i	$-0.864424\pi$
$61$	0.0447633	−	0.100540i	0.00573135	−	0.0128728i	0.916388	+	0.400290i	$0.131091\pi$
$62$	0.336967	+	1.03708i	0.0427948	+	0.131709i
$63$	6.48034	−	4.58314i	0.816446	−	0.577422i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.555045	+	0.961366i	0.0688448	+	0.119243i
$66$	0.914118	+	5.67137i	0.112520	+	0.698097i
$67$	5.60173	−	9.70248i	0.684361	−	1.18535i	−0.289277	−	0.957245i	$-0.593415\pi$
$67$	5.60173	−	9.70248i	0.684361	−	1.18535i	0.973637	−	0.228102i	$-0.0732519\pi$
$68$	0.764996	−	7.27845i	0.0927694	−	0.882642i
$69$	−6.10081	−	11.4965i	−0.734451	−	1.38401i
$70$	8.35590	−	1.37768i	0.998722	−	0.164665i
$71$	3.42260	+	4.71081i	0.406188	+	0.559070i	0.962284	−	0.272048i	$-0.0877011\pi$
$71$	3.42260	+	4.71081i	0.406188	+	0.559070i	−0.556095	+	0.831119i	$0.687701\pi$
$72$	1.12833	−	2.77972i	0.132976	−	0.327594i
$73$	−0.794456	+	3.73762i	−0.0929841	+	0.437456i	0.906887	+	0.421375i	$0.138452\pi$
$73$	−0.794456	+	3.73762i	−0.0929841	+	0.437456i	−0.999871	+	0.0160809i	$0.994881\pi$
$74$	−0.821546	−	0.912419i	−0.0955028	−	0.106067i
$75$	−6.96474	+	5.83448i	−0.804219	+	0.673708i
$76$			7.01052i			0.804162i
$77$	7.32283	+	4.83490i	0.834513	+	0.550987i
$78$	0.417625	−	0.431761i	0.0472867	−	0.0488873i
$79$	−6.66607	−	0.700632i	−0.749991	−	0.0788273i	−0.278183	−	0.960528i	$-0.589732\pi$
$79$	−6.66607	−	0.700632i	−0.749991	−	0.0788273i	−0.471809	+	0.881701i	$0.656399\pi$
$80$	2.37871	−	2.14180i	0.265948	−	0.239461i
$81$	8.90830	+	1.28149i	0.989811	+	0.142388i
$82$	4.79185	+	2.13347i	0.529171	+	0.235602i
$83$	9.88760	−	7.18376i	1.08530	−	0.788520i	0.106705	−	0.994291i	$-0.465970\pi$
$83$	9.88760	−	7.18376i	1.08530	−	0.788520i	0.978600	+	0.205771i	$0.0659701\pi$
$84$	−1.95955	−	4.14248i	−0.213805	−	0.451982i
$85$	22.2792	+	7.23895i	2.41652	+	0.785174i
$86$	1.83959	+	0.193349i	0.198368	+	0.0208493i
$87$	−3.62890	+	1.03738i	−0.389059	+	0.111219i
$88$	3.31630	+	0.0461467i	0.353519	+	0.00491926i
$89$	1.06962	−	0.617544i	0.113379	−	0.0654595i	−0.442238	−	0.896898i	$-0.645815\pi$
$89$	1.06962	−	0.617544i	0.113379	−	0.0654595i	0.555617	+	0.831438i	$0.312482\pi$
$90$	7.95220	+	5.38264i	0.838236	+	0.567380i
$91$	−0.0538172	−	0.915989i	−0.00564158	−	0.0960217i
$92$	−7.14641	+	2.32201i	−0.745064	+	0.242086i
$93$	0.706101	+	1.75175i	0.0732193	+	0.181648i
$94$	−3.78029	+	0.397324i	−0.389907	+	0.0409809i
$95$	−21.9494	−	4.66550i	−2.25196	−	0.478670i
$96$	−1.46812	−	0.919039i	−0.149839	−	0.0937991i
$97$	−8.00898	−	5.81887i	−0.813189	−	0.590816i	0.101564	−	0.994829i	$-0.467615\pi$
$97$	−8.00898	−	5.81887i	−0.813189	−	0.590816i	−0.914753	+	0.404013i	$0.867615\pi$
$98$	−6.68423	−	2.07872i	−0.675209	−	0.209983i
$99$	2.25680	+	9.69055i	0.226817	+	0.973937i
$100$	2.62280	+	4.54282i	0.262280	+	0.454282i
$101$	6.49419	−	2.89140i	0.646196	−	0.287705i	−0.0573507	−	0.998354i	$-0.518265\pi$
$101$	6.49419	−	2.89140i	0.646196	−	0.287705i	0.703547	+	0.710649i	$0.251599\pi$
$102$	0.452673	−	12.6680i	0.0448213	−	1.25432i
$103$	−4.83164	+	5.36608i	−0.476076	+	0.528736i	−0.932569	−	0.360991i	$-0.882439\pi$
$103$	−4.83164	+	5.36608i	−0.476076	+	0.528736i	0.456493	+	0.889727i	$0.349105\pi$
$104$	−0.203849	−	0.280574i	−0.0199890	−	0.0275125i
$105$	14.2739	−	3.37839i	1.39299	−	0.329697i
$106$	−5.67309	+	1.84330i	−0.551019	+	0.179037i
$107$	14.5556	−	3.09389i	1.40715	−	0.299098i	0.559135	−	0.829077i	$-0.311133\pi$
$107$	14.5556	−	3.09389i	1.40715	−	0.299098i	0.848011	+	0.529979i	$0.177800\pi$
$108$	1.61773	−	4.93791i	0.155666	−	0.475151i
$109$	13.8199	+	7.97890i	1.32370	+	0.764240i	0.984317	−	0.176407i	$-0.0564476\pi$
$109$	13.8199	+	7.97890i	1.32370	+	0.764240i	0.339385	+	0.940647i	$0.389781\pi$
$110$	−2.35148	+	10.3524i	−0.224205	+	0.987062i
$111$	−1.52853	−	1.47849i	−0.145082	−	0.140332i
$112$	−2.55122	+	0.700923i	−0.241067	+	0.0662310i
$113$	10.0711	+	3.27230i	0.947409	+	0.307832i	0.741662	−	0.670774i	$-0.234038\pi$
$113$	10.0711	+	3.27230i	0.947409	+	0.307832i	0.205747	+	0.978605i	$0.434038\pi$
$114$	0.837190	+	12.1137i	0.0784100	+	1.13455i
$115$	−2.51411	−	23.9202i	−0.234442	−	2.23057i
$116$	0.227775	+	2.16714i	0.0211484	+	0.201214i
$117$	0.670066	−	0.795925i	0.0619476	−	0.0735833i
$118$	−5.64085	−	1.83282i	−0.519282	−	0.168725i
$119$	−13.7781	−	13.6049i	−1.26303	−	1.24715i
$120$	3.85447	−	3.98495i	0.351864	−	0.363774i
$121$	−9.07565	+	6.21552i	−0.825059	+	0.565047i
$122$	−0.0953101	−	0.0550273i	−0.00862898	−	0.00498194i
$123$	8.53475	+	3.11424i	0.769552	+	0.280802i
$124$	1.06662	−	0.226717i	0.0957851	−	0.0203598i
$125$	−0.747634	+	0.242921i	−0.0668704	+	0.0217275i
$126$	−3.88066	−	6.92391i	−0.345716	−	0.616831i
$127$	−11.1208	−	15.3064i	−0.986808	−	1.35823i	−0.933080	−	0.359670i	$-0.882889\pi$
$127$	−11.1208	−	15.3064i	−0.986808	−	1.35823i	−0.0537288	−	0.998556i	$-0.517111\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	3.20177	+	0.114411i	0.281900	+	0.0100733i
$130$	1.01412	−	0.451514i	0.0889440	−	0.0396004i
$131$	−5.64476	−	9.77700i	−0.493185	−	0.854221i	0.506785	−	0.862073i	$-0.330834\pi$
$131$	−5.64476	−	9.77700i	−0.493185	−	0.854221i	−0.999969	+	0.00785196i	$0.997501\pi$
$132$	5.73585	−	0.316291i	0.499242	−	0.0275296i
$133$	14.4881	+	11.5813i	1.25628	+	1.00422i
$134$	−9.06379	−	6.58523i	−0.782992	−	0.568877i
$135$	14.3836	+	8.35117i	1.23795	+	0.718754i
$136$	−7.15861	−	1.52161i	−0.613846	−	0.130477i
$137$	15.8434	−	1.66520i	1.35359	−	0.142268i	0.600204	−	0.799847i	$-0.295086\pi$
$137$	15.8434	−	1.66520i	1.35359	−	0.142268i	0.753385	+	0.657579i	$0.228420\pi$
$138$	−12.0712	+	4.86568i	−1.02757	+	0.414194i
$139$	−2.90927	+	0.945281i	−0.246761	+	0.0801777i	−0.429786	−	0.902931i	$-0.641411\pi$
$139$	−2.90927	+	0.945281i	−0.246761	+	0.0801777i	0.183025	+	0.983108i	$0.441411\pi$
$140$	−0.496707	−	8.45414i	−0.0419794	−	0.714505i
$141$	−6.48462	+	1.13799i	−0.546104	+	0.0958358i
$142$	5.04276	−	2.91144i	0.423179	−	0.244323i
$143$	1.08889	+	0.370628i	0.0910572	+	0.0309935i
$144$	−2.64655	−	1.41271i	−0.220546	−	0.117726i
$145$	−6.93674	−	0.729080i	−0.576065	−	0.0605468i
$146$	3.63410	+	1.18079i	0.300761	+	0.0977230i
$147$	−11.7981	−	2.79366i	−0.973092	−	0.230417i
$148$	−0.993296	+	0.721672i	−0.0816484	+	0.0593210i
$149$	3.09258	+	1.37691i	0.253354	+	0.112801i	0.529484	−	0.848320i	$-0.322385\pi$
$149$	3.09258	+	1.37691i	0.253354	+	0.112801i	−0.276130	+	0.961120i	$0.589052\pi$
$150$	5.07450	+	7.53645i	0.414332	+	0.615349i
$151$	0.746498	−	0.672150i	0.0607491	−	0.0546988i	−0.638197	−	0.769873i	$-0.720319\pi$
$151$	0.746498	−	0.672150i	0.0607491	−	0.0546988i	0.698946	+	0.715174i	$0.253653\pi$
$152$	6.97212	+	0.732799i	0.565513	+	0.0594379i
$153$	−0.730613	−	21.9435i	−0.0590665	−	1.77402i
$154$	5.57385	−	6.77733i	0.449154	−	0.546133i
$155$			3.49038i			0.280354i
$156$	−0.385742	−	0.460468i	−0.0308841	−	0.0368670i
$157$	−0.0390587	−	0.0433791i	−0.00311723	−	0.00346203i	0.741584	−	0.670860i	$-0.234075\pi$
$157$	−0.0390587	−	0.0433791i	−0.00311723	−	0.00346203i	−0.744701	+	0.667398i	$0.767408\pi$
$158$	−1.39359	+	6.55632i	−0.110868	+	0.521593i
$159$	−9.58257	+	3.86256i	−0.759947	+	0.306321i
$160$	−1.88143	−	2.58956i	−0.148740	−	0.204723i
$161$	−7.00704	+	18.6049i	−0.552232	+	1.46627i
$162$	2.20564	−	8.72555i	0.173292	−	0.685544i
$163$	−1.00407	+	9.55311i	−0.0786450	+	0.748257i	0.882145	+	0.470979i	$0.156099\pi$
$163$	−1.00407	+	9.55311i	−0.0786450	+	0.748257i	−0.960790	+	0.277278i	$0.910568\pi$
$164$	2.62266	−	4.54259i	0.204796	−	0.354717i
$165$	−2.82692	+	18.1690i	−0.220075	+	1.41446i
$166$	−6.11087	−	10.5843i	−0.474296	−	0.821504i
$167$	10.6721	+	7.75371i	0.825830	+	0.600000i	0.918376	−	0.395708i	$-0.129501\pi$
$167$	10.6721	+	7.75371i	0.825830	+	0.600000i	−0.0925466	+	0.995708i	$0.529501\pi$
$168$	−4.32462	+	1.51581i	−0.333652	+	0.116947i
$169$	3.98005	+	12.2493i	0.306158	+	0.942257i
$170$	9.52810	−	21.4005i	0.730772	−	1.64134i
$171$	2.89321	+	20.8316i	0.221249	+	1.59303i
$172$	0.384579	−	1.80930i	0.0293239	−	0.137958i
$173$	−4.08955	+	0.869261i	−0.310923	+	0.0660887i	−0.360730	−	0.932670i	$-0.617473\pi$
$173$	−4.08955	+	0.869261i	−0.310923	+	0.0660887i	0.0498075	+	0.998759i	$0.484139\pi$
$174$	0.652377	+	3.71746i	0.0494566	+	0.281820i
$175$	13.7211	+	2.08433i	1.03722	+	0.157560i
$176$	0.392542	−	3.29331i	0.0295890	−	0.248243i
$177$	−9.96586	−	2.49336i	−0.749080	−	0.187413i
$178$	−0.502355	−	1.12831i	−0.0376531	−	0.0845703i
$179$	−10.1448	+	9.13442i	−0.758258	+	0.682739i	−0.954631	−	0.297790i	$-0.903750\pi$
$179$	−10.1448	+	9.13442i	−0.758258	+	0.682739i	0.196373	+	0.980529i	$0.437084\pi$
$180$	6.18438	−	7.34600i	0.460957	−	0.547539i
$181$	−18.7407	+	13.6159i	−1.39299	+	1.01206i	−0.397456	+	0.917621i	$0.630107\pi$
$181$	−18.7407	+	13.6159i	−1.39299	+	1.01206i	−0.995530	+	0.0944427i	$0.969893\pi$
$182$	−0.916597	−	0.0422245i	−0.0679427	−	0.00312989i
$183$	−0.171260	−	0.0837015i	−0.0126599	−	0.00618739i
$184$	1.56229	+	7.34997i	0.115173	+	0.541847i
$185$	−1.59846	−	3.59021i	−0.117521	−	0.263957i
$186$	1.81597	−	0.519125i	0.133153	−	0.0380641i
$187$	22.3096	−	9.56318i	1.63144	−	0.699329i
$188$			3.80111i			0.277225i
$189$	−7.53235	−	11.5006i	−0.547898	−	0.836545i
$190$	−6.93428	+	21.3415i	−0.503065	+	1.54828i
$191$	13.6384	+	12.2801i	0.986839	+	0.888554i	0.993773	−	0.111422i	$-0.0355406\pi$
$191$	13.6384	+	12.2801i	0.986839	+	0.888554i	−0.00693423	+	0.999976i	$0.502207\pi$
$192$	−1.06746	+	1.36401i	−0.0770376	+	0.0984388i
$193$	11.4479	−	1.20322i	0.824036	−	0.0866097i	0.316882	−	0.948465i	$-0.397364\pi$
$193$	11.4479	−	1.20322i	0.824036	−	0.0866097i	0.507154	+	0.861855i	$0.330697\pi$
$194$	−6.62416	+	7.35687i	−0.475587	+	0.528193i
$195$	1.69840	−	0.901289i	0.121625	−	0.0645427i
$196$	−2.76603	+	6.43033i	−0.197573	+	0.459309i
$197$	−13.7636			−0.980618			−0.490309	−	0.871549i	$-0.663116\pi$
$197$	−13.7636			−0.980618			−0.490309	+	0.871549i	$0.663116\pi$
$198$	9.87337	−	1.23150i	0.701670	−	0.0875188i
$199$	−11.2114	+	19.4186i	−0.794752	+	1.37655i	0.128244	+	0.991743i	$0.459066\pi$
$199$	−11.2114	+	19.4186i	−0.794752	+	1.37655i	−0.922996	+	0.384808i	$0.874268\pi$
$200$	4.79209	−	2.13357i	0.338852	−	0.150866i
$201$	−16.4480	−	10.2964i	−1.16015	−	0.726254i
$202$	−2.19673	−	6.76084i	−0.154562	−	0.475691i
$203$	4.85495	+	3.10935i	0.340750	+	0.218234i
$204$	−12.5513	−	1.77436i	−0.878766	−	0.124230i
$205$	12.4771	+	11.2345i	0.871441	+	0.784649i
$206$	4.83164	+	5.36608i	0.336637	+	0.373873i
$207$	−20.2771	+	9.84909i	−1.40936	+	0.684559i
$208$	−0.300345	+	0.173404i	−0.0208252	+	0.0120234i
$209$	−20.2960	+	11.3443i	−1.40390	+	0.784704i
$210$	−1.86786	−	14.5488i	−0.128894	−	1.00396i
$211$	15.4237	−	21.2289i	1.06181	−	1.46146i	0.183708	−	0.982981i	$-0.441190\pi$
$211$	15.4237	−	21.2289i	1.06181	−	1.46146i	0.878102	−	0.478474i	$-0.158810\pi$
$212$	1.24020	+	5.83469i	0.0851774	+	0.400728i
$213$	8.36585	−	5.63296i	0.573219	−	0.385964i
$214$	−1.55547	−	14.7993i	−0.106330	−	1.01166i
$215$	5.40886	+	2.40818i	0.368881	+	0.164236i
$216$	−4.74176	−	2.12502i	−0.322636	−	0.144589i
$217$	1.29350	−	2.57883i	0.0878084	−	0.175063i
$218$	9.37976	−	12.9101i	0.635278	−	0.874385i
$219$	6.42048	+	1.60634i	0.433856	+	0.108547i
$220$	10.0499	+	3.42072i	0.677563	+	0.230625i
$221$	−2.19809	−	1.26907i	−0.147859	−	0.0853666i
$222$	−1.63016	+	1.36562i	−0.109409	+	0.0916541i
$223$	1.06351	−	3.27315i	0.0712179	−	0.219186i	−0.909112	−	0.416552i	$-0.863239\pi$
$223$	1.06351	−	3.27315i	0.0712179	−	0.219186i	0.980330	+	0.197365i	$0.0632386\pi$
$224$	0.430409	+	2.61051i	0.0287579	+	0.174422i
$225$	9.66838	+	12.4165i	0.644559	+	0.827764i
$226$	4.30709	−	9.67387i	0.286503	−	0.643497i
$227$	−18.1882	−	3.86603i	−1.20720	−	0.256597i	−0.439993	−	0.898001i	$-0.645019\pi$
$227$	−18.1882	−	3.86603i	−1.20720	−	0.256597i	−0.767203	+	0.641404i	$0.778352\pi$
$228$	12.1348	+	0.433621i	0.803649	+	0.0287173i
$229$	0.210429	−	2.00209i	0.0139055	−	0.132302i	−0.985367	−	0.170448i	$-0.945479\pi$
$229$	0.210429	−	2.00209i	0.0139055	−	0.132302i	0.999272	+	0.0381459i	$0.0121452\pi$
$230$	−24.0519			−1.58594
$231$	8.82188	−	12.3764i	0.580437	−	0.814305i
$232$	2.17908			0.143063
$233$	1.16626	−	11.0963i	0.0764045	−	0.726940i	−0.887521	−	0.460767i	$-0.847574\pi$
$233$	1.16626	−	11.0963i	0.0764045	−	0.726940i	0.963925	−	0.266173i	$-0.0857591\pi$
$234$	−0.721524	−	0.749592i	−0.0471675	−	0.0490023i
$235$	−11.9010	−	2.52964i	−0.776336	−	0.165015i
$236$	−2.41241	+	5.41837i	−0.157035	+	0.352706i
$237$	−1.62507	+	11.4953i	−0.105560	+	0.746698i
$238$	−14.9705	+	12.2805i	−0.970395	+	0.796027i
$239$	−5.83958	+	17.9724i	−0.377731	+	1.16254i	0.563886	+	0.825853i	$0.309306\pi$
$239$	−5.83958	+	17.9724i	−0.377731	+	1.16254i	−0.941617	+	0.336685i	$0.890694\pi$
$240$	−3.56021	−	4.24990i	−0.229811	−	0.274330i
$241$	20.1296	+	11.6218i	1.29666	+	0.748629i	0.979826	−	0.199851i	$-0.0640458\pi$
$241$	20.1296	+	11.6218i	1.29666	+	0.748629i	0.316837	+	0.948480i	$0.397379\pi$
$242$	5.23280	+	9.67563i	0.336377	+	0.621973i
$243$	2.76920	−	15.3405i	0.177644	−	0.984095i
$244$	−0.0646885	+	0.0890361i	−0.00414126	+	0.00569995i
$245$	−18.2921	−	12.9396i	−1.16864	−	0.826681i
$246$	3.98931	−	8.16247i	0.254349	−	0.520420i
$247$	2.22111	+	0.988902i	0.141326	+	0.0629223i
$248$	−0.113983	−	1.08447i	−0.00723791	−	0.0688641i
$249$	−11.8231	−	17.5592i	−0.749260	−	1.11277i
$250$	0.163441	+	0.768930i	0.0103369	+	0.0486314i
$251$	−15.7226	+	21.6403i	−0.992400	+	1.36592i	−0.0625255	+	0.998043i	$0.519915\pi$
$251$	−15.7226	+	21.6403i	−0.992400	+	1.36592i	−0.929874	+	0.367878i	$0.880085\pi$
$252$	−7.29162	+	3.13565i	−0.459329	+	0.197528i
$253$	−18.2866	−	16.9320i	−1.14967	−	1.06450i
$254$	−16.3850	+	9.45989i	−1.02809	+	0.593566i
$255$	13.9083	−	38.1163i	0.870969	−	2.38694i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	4.41774	+	3.97775i	0.275571	+	0.248125i	0.795314	−	0.606197i	$-0.207306\pi$
$257$	4.41774	+	3.97775i	0.275571	+	0.248125i	−0.519743	+	0.854322i	$0.673972\pi$
$258$	0.448460	−	3.17227i	0.0279199	−	0.197497i
$259$	−0.149485	+	3.24496i	−0.00928852	+	0.201632i
$260$	−0.343037	−	1.05576i	−0.0212742	−	0.0654753i
$261$	1.57120	+	6.34560i	0.0972547	+	0.392783i
$262$	−10.3135	+	4.59186i	−0.637169	+	0.283686i
$263$	9.09839	−	15.7589i	0.561031	−	0.971734i	−0.436376	−	0.899764i	$-0.643738\pi$
$263$	9.09839	−	15.7589i	0.561031	−	0.971734i	0.997407	−	0.0719694i	$-0.0229284\pi$
$264$	0.285001	−	5.73749i	0.0175406	−	0.353118i
$265$	−19.0933			−1.17289
$266$	13.0323	−	13.1982i	0.799059	−	0.809233i
$267$	−1.00278	−	1.88965i	−0.0613689	−	0.115644i
$268$	−7.49658	+	8.32580i	−0.457927	+	0.508579i
$269$	−2.03144	+	0.213513i	−0.123859	+	0.0130181i	−0.166255	−	0.986083i	$-0.553167\pi$
$269$	−2.03144	+	0.213513i	−0.123859	+	0.0130181i	0.0423962	+	0.999101i	$0.486501\pi$
$270$	9.80892	−	13.4319i	0.596952	−	0.817440i
$271$	12.0678	+	10.8659i	0.733066	+	0.660056i	0.948613	−	0.316438i	$-0.102487\pi$
$271$	12.0678	+	10.8659i	0.733066	+	0.660056i	−0.215547	+	0.976493i	$0.569153\pi$
$272$	−2.26155	+	6.96035i	−0.137127	+	0.422033i
$273$	−1.58886	+	0.0364980i	−0.0961620	+	0.00220896i
$274$		−	15.9306i		−	0.962404i
$275$	−8.90762	+	14.9443i	−0.537150	+	0.901177i
$276$	3.57725	+	12.5137i	0.215325	+	0.753234i
$277$	0.0916738	+	0.205903i	0.00550814	+	0.0123715i	0.916279	−	0.400542i	$-0.131178\pi$
$277$	0.0916738	+	0.205903i	0.00550814	+	0.0123715i	−0.910770	+	0.412913i	$0.864511\pi$
$278$	0.636000	+	2.99215i	0.0381448	+	0.179457i
$279$	3.07587	−	1.11387i	0.184147	−	0.0666858i
$280$	−8.45974	−	0.389712i	−0.505566	−	0.0232898i
$281$	3.41644	−	2.48219i	0.203808	−	0.148075i	−0.481200	−	0.876611i	$-0.659799\pi$
$281$	3.41644	−	2.48219i	0.203808	−	0.148075i	0.685008	+	0.728536i	$0.259799\pi$
$282$	0.453925	+	6.56805i	0.0270308	+	0.391122i
$283$	−22.0978	+	19.8969i	−1.31358	+	1.18275i	−0.343720	+	0.939072i	$0.611687\pi$
$283$	−22.0978	+	19.8969i	−1.31358	+	1.18275i	−0.969856	+	0.243677i	$0.921646\pi$
$284$	−2.36838	−	5.31947i	−0.140537	−	0.315652i
$285$	−9.43336	+	37.7047i	−0.558784	+	2.23343i
$286$	0.482417	−	1.04418i	0.0285259	−	0.0617436i
$287$	−5.05523	−	12.9244i	−0.298401	−	0.762901i
$288$	−1.68161	+	2.48439i	−0.0990901	+	0.146394i
$289$	−35.7621	+	7.60147i	−2.10365	+	0.447145i
$290$	−1.45017	+	6.82253i	−0.0851571	+	0.400633i
$291$	−10.5675	+	13.5032i	−0.619479	+	0.791572i
$292$	1.55419	−	3.49077i	0.0909521	−	0.204282i
$293$	3.12179	+	9.60789i	0.182377	+	0.561299i	0.999893	−	0.0146066i	$-0.00464961\pi$
$293$	3.12179	+	9.60789i	0.182377	+	0.561299i	−0.817516	+	0.575906i	$0.804650\pi$
$294$	−4.01159	+	11.4415i	−0.233961	+	0.667280i
$295$	−15.3590	−	11.1590i	−0.894238	−	0.649702i
$296$	0.613891	+	1.06329i	0.0356817	+	0.0618025i
$297$	16.9134	−	3.30701i	0.981416	−	0.191892i
$298$	1.69263	−	2.93172i	0.0980513	−	0.169830i
$299$	−0.272399	+	2.59170i	−0.0157532	+	0.149882i
$300$	8.02560	−	4.25893i	0.463358	−	0.245890i
$301$	−3.10383	−	3.78372i	−0.178902	−	0.218090i
$302$	−0.590437	−	0.812667i	−0.0339758	−	0.0467637i
$303$	−4.60317	−	11.4199i	−0.264445	−	0.656058i
$304$	1.45757	−	6.85733i	0.0835973	−	0.393295i
$305$	−0.235715	−	0.261788i	−0.0134970	−	0.0149900i
$306$	−21.8996	−	1.56711i	−1.25192	−	0.0895855i
$307$			17.8891i			1.02098i	0.859883	+	0.510491i	$0.170537\pi$
$307$			17.8891i			1.02098i	−0.859883	+	0.510491i	$0.829463\pi$
$308$	−6.15757	−	6.25174i	−0.350860	−	0.356226i
$309$	8.98955	+	8.69522i	0.511398	+	0.494654i
$310$	3.47126	+	0.364844i	0.197154	+	0.0207218i
$311$	13.0736	−	11.7715i	0.741336	−	0.667502i	−0.209285	−	0.977855i	$-0.567114\pi$
$311$	13.0736	−	11.7715i	0.741336	−	0.667502i	0.950622	+	0.310353i	$0.100447\pi$
$312$	−0.498267	+	0.335497i	−0.0282088	+	0.0189938i
$313$	20.4749	+	9.11601i	1.15731	+	0.515267i	0.893392	−	0.449278i	$-0.148319\pi$
$313$	20.4749	+	9.11601i	1.15731	+	0.515267i	0.263917	+	0.964545i	$0.414985\pi$
$314$	−0.0472242	+	0.0343104i	−0.00266502	+	0.00193625i
$315$	−4.96493	−	24.9163i	−0.279742	−	1.40387i
$316$	6.37473	+	2.07128i	0.358607	+	0.116518i
$317$	11.7788	+	1.23800i	0.661564	+	0.0695332i	0.429359	−	0.903134i	$-0.358739\pi$
$317$	11.7788	+	1.23800i	0.661564	+	0.0695332i	0.232205	+	0.972667i	$0.425406\pi$
$318$	2.83975	+	9.93383i	0.159245	+	0.557061i
$319$	−5.90545	+	4.16626i	−0.330642	+	0.233266i
$320$	−2.77204	+	1.60044i	−0.154962	+	0.0894671i
$321$	−4.45506	−	25.3864i	−0.248657	−	1.41693i
$322$	17.7705	+	8.91339i	0.990313	+	0.496724i
$323$	48.7957	−	15.8547i	2.71506	−	0.882178i
$324$	−8.44719	−	3.10563i	−0.469289	−	0.172535i
$325$	1.80925	−	0.190160i	0.100359	−	0.0105482i
$326$	9.39582	+	1.99714i	0.520386	+	0.110612i
$327$	14.6658	−	23.4279i	0.811023	−	1.29557i
$328$	−4.24356	−	3.08313i	−0.234311	−	0.170237i
$329$	7.85548	+	6.27938i	0.433086	+	0.346193i
$330$	17.7740	+	4.71061i	0.978426	+	0.259311i
$331$	5.81463	+	10.0712i	0.319601	+	0.553566i	0.980405	−	0.196993i	$-0.0631177\pi$
$331$	5.81463	+	10.0712i	0.319601	+	0.553566i	−0.660804	+	0.750559i	$0.729784\pi$
$332$	−11.1651	+	4.97103i	−0.612765	+	0.272821i
$333$	−2.65373	+	2.55436i	−0.145423	+	0.139978i
$334$	8.82677	−	9.80313i	0.482980	−	0.536403i
$335$	−21.0785	−	29.0121i	−1.15164	−	1.58510i
$336$	1.05546	+	4.45937i	0.0575801	+	0.243279i
$337$	5.37493	−	1.74642i	0.292791	−	0.0951337i	−0.158938	−	0.987288i	$-0.550807\pi$
$337$	5.37493	−	1.74642i	0.292791	−	0.0951337i	0.451730	+	0.892155i	$0.350807\pi$
$338$	12.5983	−	2.67785i	0.685256	−	0.145656i
$339$	6.28710	−	17.2301i	0.341468	−	0.935812i
$340$	−20.2873	−	11.7129i	−1.10023	−	0.635219i
$341$	2.38235	+	2.72107i	0.129011	+	0.147354i
$342$	21.0199	−	0.699863i	1.13663	−	0.0378442i
$343$	8.71965	+	16.3391i	0.470817	+	0.882231i
$344$	−1.75919	−	0.571596i	−0.0948492	−	0.0308184i
$345$	−41.5600	+	2.87226i	−2.23752	+	0.154637i
$346$	0.437025	+	4.15801i	0.0234946	+	0.223536i
$347$	−0.703447	−	6.69285i	−0.0377630	−	0.359291i	−0.997044	−	0.0768364i	$-0.975518\pi$
$347$	−0.703447	−	6.69285i	−0.0377630	−	0.359291i	0.959281	−	0.282454i	$-0.0911486\pi$
$348$	3.76529	−	0.260223i	0.201841	−	0.0139494i
$349$	0.797395	+	0.259089i	0.0426836	+	0.0138687i	0.330281	−	0.943883i	$-0.392856\pi$
$349$	0.797395	+	0.259089i	0.0426836	+	0.0138687i	−0.287597	+	0.957751i	$0.592856\pi$
$350$	3.50716	−	13.4281i	0.187465	−	0.717761i
$351$	−1.33626	−	1.20908i	−0.0713242	−	0.0645358i
$352$	−3.23424	−	0.734637i	−0.172386	−	0.0391563i
$353$	22.8385	+	13.1858i	1.21557	+	0.701811i	0.963968	−	0.266019i	$-0.0857084\pi$
$353$	22.8385	+	13.1858i	1.21557	+	0.701811i	0.251605	+	0.967830i	$0.419042\pi$
$354$	−3.52142	+	9.65064i	−0.187161	+	0.512926i
$355$	18.2310	−	3.87512i	0.967602	−	0.205670i
$356$	−1.17464	+	0.381663i	−0.0622557	+	0.0202281i
$357$	−24.4015	+	23.0076i	−1.29146	+	1.21769i
$358$	8.02396	+	11.0440i	0.424080	+	0.583696i
$359$	−6.28209	+	6.97696i	−0.331556	+	0.368230i	−0.885754	−	0.464155i	$-0.846358\pi$
$359$	−6.28209	+	6.97696i	−0.331556	+	0.368230i	0.554198	+	0.832385i	$0.313025\pi$
$360$	−6.65932	−	6.91837i	−0.350977	−	0.364630i
$361$	−27.5410	+	12.2621i	−1.44953	+	0.645372i
$362$	11.5824	+	20.0613i	0.608757	+	1.05440i
$363$	10.1974	+	16.0939i	0.535223	+	0.844711i
$364$	−0.137804	+	0.907162i	−0.00722287	+	0.0475482i
$365$	9.89503	+	7.18916i	0.517930	+	0.376298i
$366$	−0.101145	+	0.161573i	−0.00528691	+	0.00844556i
$367$	21.7579	+	4.62479i	1.13575	+	0.241412i	0.737162	−	0.675716i	$-0.236166\pi$
$367$	21.7579	+	4.62479i	1.13575	+	0.241412i	0.398592	+	0.917128i	$0.369499\pi$
$368$	7.47301	−	0.785445i	0.389558	−	0.0409442i
$369$	5.91849	−	14.5806i	0.308104	−	0.759034i
$370$	−3.73763	+	1.21443i	−0.194310	+	0.0631351i
$371$	14.1069	+	7.07579i	0.732395	+	0.367357i
$372$	−0.326461	−	1.86028i	−0.0169262	−	0.0964511i
$373$	1.91568	−	1.10602i	0.0991902	−	0.0572675i	−0.449584	−	0.893238i	$-0.648428\pi$
$373$	1.91568	−	1.10602i	0.0991902	−	0.0572675i	0.548775	+	0.835970i	$0.315095\pi$
$374$	−7.17880	−	23.1870i	−0.371207	−	1.19897i
$375$	0.374240	+	1.30914i	0.0193257	+	0.0676036i
$376$	3.78029	+	0.397324i	0.194953	+	0.0204904i
$377$	0.718734	+	0.233531i	0.0370167	+	0.0120275i
$378$	−12.2249	+	6.28894i	−0.628783	+	0.323468i
$379$	12.9776	−	9.42879i	0.666615	−	0.484324i	−0.202275	−	0.979329i	$-0.564834\pi$
$379$	12.9776	−	9.42879i	0.666615	−	0.484324i	0.868890	+	0.495004i	$0.164834\pi$
$380$	20.4998	+	9.12709i	1.05162	+	0.468210i
$381$	−27.1824	+	18.3027i	−1.39260	+	0.937676i
$382$	13.6384	−	12.2801i	0.697800	−	0.628302i
$383$	−17.0563	−	1.79269i	−0.871537	−	0.0916023i	−0.341809	−	0.939770i	$-0.611040\pi$
$383$	−17.0563	−	1.79269i	−0.871537	−	0.0916023i	−0.529728	+	0.848167i	$0.677706\pi$
$384$	1.24496	+	1.20419i	0.0635314	+	0.0614513i
$385$	23.6716	−	15.1184i	1.20642	−	0.770504i
$386$		−	11.5109i		−	0.585891i
$387$	0.396078	−	5.53502i	0.0201338	−	0.281361i
$388$	6.62416	+	7.35687i	0.336291	+	0.373489i
$389$	−5.69708	+	26.8026i	−0.288853	+	1.35895i	0.559198	+	0.829034i	$0.311109\pi$
$389$	−5.69708	+	26.8026i	−0.288853	+	1.35895i	−0.848052	+	0.529914i	$0.822224\pi$
$390$	−0.718820	−	1.78331i	−0.0363989	−	0.0903014i
$391$	32.3240	+	44.4901i	1.63469	+	2.24996i
$392$	6.10597	+	3.42303i	0.308398	+	0.172889i
$393$	−17.2726	+	9.16603i	−0.871288	+	0.462365i
$394$	−1.43869	+	13.6882i	−0.0724802	+	0.689603i
$395$	−10.7274	+	18.5804i	−0.539754	+	0.934881i
$396$	−0.192704	−	9.94801i	−0.00968375	−	0.499906i
$397$	−12.3272	−	21.3513i	−0.618683	−	1.07159i	−0.989726	−	0.142975i	$-0.954333\pi$
$397$	−12.3272	−	21.3513i	−0.618683	−	1.07159i	0.371043	−	0.928616i	$-0.379000\pi$
$398$	18.1404	+	13.1797i	0.909294	+	0.660641i
$399$	20.9427	−	24.3618i	1.04845	−	1.21962i
$400$	−1.62098	−	4.98885i	−0.0810489	−	0.249443i
$401$	13.4144	−	30.1293i	0.669884	−	1.50458i	−0.183345	−	0.983049i	$-0.558693\pi$
$401$	13.4144	−	30.1293i	0.669884	−	1.50458i	0.853229	−	0.521536i	$-0.174641\pi$
$402$	−11.9593	+	15.2816i	−0.596476	+	0.762178i
$403$	0.0786272	−	0.369912i	0.00391670	−	0.0184266i
$404$	−6.95343	+	1.47800i	−0.345946	+	0.0735331i
$405$	15.3451	−	24.3808i	0.762504	−	1.21149i
$406$	3.59980	−	4.50334i	0.178655	−	0.223497i
$407$	−3.69663	−	1.70787i	−0.183235	−	0.0846558i
$408$	−3.07661	+	12.2971i	−0.152315	+	0.608795i
$409$	−11.7883	−	26.4769i	−0.582892	−	1.30920i	−0.928679	−	0.370884i	$-0.879055\pi$
$409$	−11.7883	−	26.4769i	−0.582892	−	1.30920i	0.345787	−	0.938313i	$-0.387612\pi$
$410$	12.4771	−	11.2345i	0.616202	−	0.554830i
$411$	−1.90242	−	27.5270i	−0.0938394	−	1.35781i
$412$	5.84173	−	4.24427i	0.287801	−	0.209100i
$413$	7.21247	+	13.9366i	0.354902	+	0.685776i
$414$	7.67560	+	21.1955i	0.377235	+	1.04170i
$415$	−8.13356	−	38.2654i	−0.399261	−	1.87837i
$416$	0.141060	+	0.316825i	0.00691602	+	0.0155336i
$417$	1.45628	+	5.09427i	0.0713145	+	0.249467i
$418$	9.16068	+	21.3706i	0.448064	+	1.04527i
$419$		−	23.8655i		−	1.16590i	−0.812506	−	0.582952i	$-0.801897\pi$
$419$		−	23.8655i		−	1.16590i	0.812506	−	0.582952i	$-0.198103\pi$
$420$	−14.6644	+	0.336859i	−0.715548	+	0.0164371i
$421$	−5.71242	+	17.5810i	−0.278406	+	0.856847i	0.709892	+	0.704311i	$0.248744\pi$
$421$	−5.71242	+	17.5810i	−0.278406	+	0.856847i	−0.988298	+	0.152536i	$0.951256\pi$
$422$	−19.5004	−	17.5582i	−0.949263	−	0.854720i
$423$	1.56870	+	11.2949i	0.0762728	+	0.549178i
$424$	5.93236	−	0.623516i	0.288101	−	0.0302806i
$425$	25.6880	−	28.5294i	1.24605	−	1.38388i
$426$	−4.72764	−	8.90883i	−0.229055	−	0.431634i
$427$	0.0771399	+	0.280773i	0.00373306	+	0.0135876i
$428$	−14.8808			−0.719291
$429$	0.708888	−	1.86188i	0.0342254	−	0.0898923i
$430$	2.96036	−	5.12750i	0.142761	−	0.247270i
$431$	8.66387	−	3.85740i	0.417324	−	0.185805i	−0.187323	−	0.982298i	$-0.559981\pi$
$431$	8.66387	−	3.85740i	0.417324	−	0.185805i	0.604647	+	0.796494i	$0.293314\pi$
$432$	−2.60903	+	4.49366i	−0.125527	+	0.216201i
$433$	−1.63950	−	5.04587i	−0.0787895	−	0.242489i	0.903902	−	0.427740i	$-0.140690\pi$
$433$	−1.63950	−	5.04587i	−0.0787895	−	0.242489i	−0.982691	+	0.185251i	$0.940690\pi$
$434$	−2.42950	−	1.55597i	−0.116620	−	0.0746892i
$435$	−1.69106	+	11.9620i	−0.0810800	+	0.573535i
$436$	−11.8590	−	10.6779i	−0.567941	−	0.511376i
$437$	−35.2487	−	39.1476i	−1.68617	−	1.87268i
$438$	2.26867	−	6.21740i	0.108401	−	0.297079i
$439$	−35.1312	+	20.2830i	−1.67672	+	0.968056i	−0.712995	+	0.701169i	$0.752662\pi$
$439$	−35.1312	+	20.2830i	−1.67672	+	0.968056i	−0.963728	+	0.266887i	$0.914005\pi$
$440$	4.45248	−	9.63727i	0.212264	−	0.459439i
$441$	−5.56542	+	20.2491i	−0.265020	+	0.964243i
$442$	−1.49188	+	2.05339i	−0.0709613	+	0.0976699i
$443$	−4.11953	−	19.3809i	−0.195725	−	0.920812i	−0.960880	−	0.276966i	$-0.910671\pi$
$443$	−4.11953	−	19.3809i	−0.195725	−	0.920812i	0.765155	−	0.643846i	$-0.222662\pi$
$444$	1.18774	+	1.76398i	0.0563675	+	0.0837147i
$445$	−0.413239	−	3.93170i	−0.0195894	−	0.186381i
$446$	−3.14405	−	1.39982i	−0.148875	−	0.0662834i
$447$	2.57464	−	5.26793i	0.121776	−	0.249165i
$448$	2.64120	−	0.155179i	0.124785	−	0.00733150i
$449$	21.0414	−	28.9611i	0.993007	−	1.36676i	0.0634877	−	0.997983i	$-0.479778\pi$
$449$	21.0414	−	28.9611i	0.993007	−	1.36676i	0.929519	−	0.368774i	$-0.120222\pi$
$450$	13.3591	−	8.31754i	0.629752	−	0.392093i
$451$	17.3951	+	0.242055i	0.819104	+	0.0113979i
$452$	−9.17067	−	5.29469i	−0.431352	−	0.249041i
$453$	−1.11728	−	1.33372i	−0.0524945	−	0.0626637i
$454$	−5.74604	+	17.6845i	−0.269675	+	0.829974i
$455$	−2.74855	−	1.03517i	−0.128854	−	0.0485294i
$456$	1.69968	−	12.0230i	0.0795949	−	0.563030i
$457$	7.05936	−	15.8556i	0.330223	−	0.741693i	−0.669777	−	0.742563i	$-0.733610\pi$
$457$	7.05936	−	15.8556i	0.330223	−	0.741693i	1.00000		0.000869771i	$0.000276857\pi$
$458$	−1.96913	−	0.418552i	−0.0920114	−	0.0195576i
$459$	−38.0281	−	0.0926172i	−1.77500	−	0.00432300i
$460$	−2.51411	+	23.9202i	−0.117221	+	1.11528i
$461$	21.4592			0.999457			0.499728	−	0.866182i	$-0.333433\pi$
$461$	21.4592			0.999457			0.499728	+	0.866182i	$0.333433\pi$
$462$	−11.3864	−	10.0672i	−0.529745	−	0.468370i
$463$	−8.82749			−0.410248			−0.205124	−	0.978736i	$-0.565760\pi$
$463$	−8.82749			−0.410248			−0.205124	+	0.978736i	$0.565760\pi$
$464$	0.227775	−	2.16714i	0.0105742	−	0.100607i
$465$	6.04166	+	0.215890i	0.280175	+	0.0100117i
$466$	−10.9136	−	2.31975i	−0.505561	−	0.107460i
$467$	8.37593	−	18.8126i	0.387592	−	0.870545i	−0.609387	−	0.792873i	$-0.708584\pi$
$467$	8.37593	−	18.8126i	0.387592	−	0.870545i	0.996979	−	0.0776725i	$-0.0247489\pi$
$468$	−0.820905	+	0.639218i	−0.0379464	+	0.0295478i
$469$	4.82207	+	29.2467i	0.222662	+	1.35049i
$470$	−3.75977	+	11.5714i	−0.173425	+	0.533748i
$471$	−0.0775028	+	0.0649255i	−0.00357114	+	0.00299161i
$472$	5.13652	+	2.96557i	0.236427	+	0.136501i
$473$	5.86039	−	1.81440i	0.269461	−	0.0834264i
$474$	11.2624	+	2.81775i	0.517301	+	0.129424i
$475$	−21.6154	+	29.7511i	−0.991783	+	1.36507i
$476$	10.6484	+	16.1722i	0.488068	+	0.741251i
$477$	6.09318	+	16.8258i	0.278988	+	0.770402i
$478$	17.2635	+	7.68622i	0.789616	+	0.351560i
$479$	3.13898	+	29.8654i	0.143424	+	1.36458i	0.795280	+	0.606242i	$0.207324\pi$
$479$	3.13898	+	29.8654i	0.143424	+	1.36458i	−0.651857	+	0.758342i	$0.726010\pi$
$480$	−4.59876	+	3.09648i	−0.209904	+	0.141334i
$481$	0.0885298	+	0.416500i	0.00403661	+	0.0189908i
$482$	13.6623	−	18.8045i	0.622301	−	0.856523i
$483$	31.7706	+	13.2796i	1.44561	+	0.604241i
$484$	10.1696	−	4.19276i	0.462255	−	0.190580i
$485$	−27.4422	+	15.8438i	−1.24609	+	0.719428i
$486$	−14.9670	−	4.35755i	−0.678918	−	0.197662i
$487$	2.50287	+	2.77972i	0.113416	+	0.125961i	0.797179	−	0.603743i	$-0.206325\pi$
$487$	2.50287	+	2.77972i	0.113416	+	0.125961i	−0.683763	+	0.729704i	$0.739658\pi$
$488$	0.0817866	+	0.0736410i	0.00370230	+	0.00333357i
$489$	16.4738	+	2.32888i	0.744971	+	0.105316i
$490$	−14.7808	+	16.8393i	−0.667727	+	0.760723i
$491$	−6.49039	−	19.9754i	−0.292907	−	0.901476i	−0.983916	−	0.178630i	$-0.942834\pi$
$491$	−6.49039	−	19.9754i	−0.292907	−	0.901476i	0.691009	−	0.722846i	$-0.257166\pi$
$492$	−7.70076	−	4.82066i	−0.347177	−	0.217332i
$493$	14.5689	−	6.48650i	0.656151	−	0.292137i
$494$	1.21565	−	2.10557i	0.0546948	−	0.0947343i
$495$	31.2747	+	6.01705i	1.40569	+	0.270446i
$496$	−1.09045			−0.0489625
$497$	−14.9059	−	3.89313i	−0.668620	−	0.174631i
$498$	−18.6989	+	9.92292i	−0.837918	+	0.444657i
$499$	15.2981	−	16.9903i	0.684839	−	0.760590i	−0.296048	−	0.955173i	$-0.595669\pi$
$499$	15.2981	−	16.9903i	0.684839	−	0.760590i	0.980886	+	0.194583i	$0.0623353\pi$
$500$	0.781802	−	0.0821707i	0.0349633	−	0.00367479i
$501$	14.0814	−	17.9932i	0.629109	−	0.803877i
$502$	19.8783	+	17.8985i	0.887210	+	0.798847i
$503$	−7.56056	+	23.2690i	−0.337109	+	1.03751i	0.628565	+	0.777757i	$0.283643\pi$
$503$	−7.56056	+	23.2690i	−0.337109	+	1.03751i	−0.965674	+	0.259757i	$0.916357\pi$
$504$	2.35629	+	7.57944i	0.104958	+	0.337615i
$505$		−	22.7543i		−	1.01255i
$506$	−18.7507	+	16.4166i	−0.833569	+	0.729806i
$507$	21.4491	−	6.13160i	0.952589	−	0.272314i
$508$	7.69537	+	17.2841i	0.341427	+	0.766857i
$509$	−1.60028	−	7.52872i	−0.0709312	−	0.333705i	0.928346	−	0.371717i	$-0.121231\pi$
$509$	−1.60028	−	7.52872i	−0.0709312	−	0.333705i	−0.999277	+	0.0380121i	$0.987897\pi$
$510$	−36.4537	−	17.8163i	−1.61420	−	0.788920i
$511$	−4.64662	−	8.97863i	−0.205554	−	0.397191i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	36.2374	−	3.71949i	1.59992	−	0.164220i
$514$	4.41774	−	3.97775i	0.194858	−	0.175451i
$515$	9.40082	+	21.1146i	0.414250	+	0.930420i
$516$	−3.10802	−	0.777596i	−0.136823	−	0.0342318i
$517$	−11.0045	+	6.15091i	−0.483978	+	0.270517i
$518$	3.21156	+	0.487857i	0.141108	+	0.0214352i
$519$	1.25169	+	7.13256i	0.0549432	+	0.313085i
$520$	−1.08583	+	0.230801i	−0.0476169	+	0.0101213i
$521$	−5.50931	+	25.9192i	−0.241367	+	1.13554i	0.675814	+	0.737072i	$0.263792\pi$
$521$	−5.50931	+	25.9192i	−0.241367	+	1.13554i	−0.917181	+	0.398471i	$0.869541\pi$
$522$	6.47508	−	0.899294i	0.283406	−	0.0393610i
$523$	−2.84477	+	6.38945i	−0.124393	+	0.279391i	−0.964998	−	0.262258i	$-0.915533\pi$
$523$	−2.84477	+	6.38945i	−0.124393	+	0.279391i	0.840605	+	0.541649i	$0.182200\pi$
$524$	3.48865	+	10.7370i	0.152402	+	0.469046i
$525$	4.45655	−	23.6216i	0.194500	−	1.03093i
$526$	−14.7215	−	10.6958i	−0.641888	−	0.466359i
$527$	−3.99024	−	6.91130i	−0.173818	−	0.301061i
$528$	−5.67627	−	0.883170i	−0.247028	−	0.0384351i
$529$	16.7314	−	28.9797i	0.727454	−	1.25999i
$530$	−1.99580	+	18.9887i	−0.0866919	+	0.824818i
$531$	−4.93230	+	17.0961i	−0.214043	+	0.741910i
$532$	−11.7636	−	14.3405i	−0.510019	−	0.621737i
$533$	−1.06925	−	1.47170i	−0.0463145	−	0.0637465i
$534$	−1.98411	+	0.799761i	−0.0858610	+	0.0346090i
$535$	9.90317	−	46.5907i	0.428151	−	2.01429i
$536$	7.49658	+	8.32580i	0.323803	+	0.359620i
$537$	15.1837	+	18.1251i	0.655225	+	0.782156i
$538$			2.04263i			0.0880639i
$539$	−23.0922	+	2.39762i	−0.994653	+	0.103273i
$540$	−12.3330	−	11.1592i	−0.530728	−	0.480216i
$541$	−9.63592	−	1.01278i	−0.414281	−	0.0435426i	−0.104904	−	0.994482i	$-0.533454\pi$
$541$	−9.63592	−	1.01278i	−0.414281	−	0.0435426i	−0.309376	+	0.950940i	$0.600120\pi$
$542$	12.0678	−	10.8659i	0.518356	−	0.466730i
$543$	22.4093	+	33.2814i	0.961674	+	1.42824i
$544$	6.68582	+	2.97672i	0.286652	+	0.127626i
$545$	41.3237	−	30.0234i	1.77011	−	1.28606i
$546$	−0.129783	+	1.58397i	−0.00555418	+	0.0677876i
$547$	30.5840	+	9.93733i	1.30768	+	0.424890i	0.878245	−	0.478210i	$-0.158714\pi$
$547$	30.5840	+	9.93733i	1.30768	+	0.424890i	0.429430	+	0.903100i	$0.358714\pi$
$548$	−15.8434	−	1.66520i	−0.676794	−	0.0711340i
$549$	−0.155476	+	0.291265i	−0.00663554	+	0.0124309i
$550$	13.9314	+	10.4209i	0.594035	+	0.444350i
$551$	−13.2298	+	7.63823i	−0.563608	+	0.325400i
$552$	12.8190	−	2.24961i	0.545615	−	0.0957499i
$553$	14.8115	−	9.75247i	0.629850	−	0.414717i
$554$	0.214357	−	0.0696489i	0.00910717	−	0.00295910i
$555$	−6.31333	+	2.54479i	−0.267986	+	0.108020i
$556$	3.04223	−	0.319752i	0.129019	−	0.0135605i
$557$	0.113199	+	0.0240611i	0.00479637	+	0.00101950i	0.210309	−	0.977635i	$-0.432553\pi$
$557$	0.113199	+	0.0240611i	0.00479637	+	0.00101950i	−0.205513	+	0.978654i	$0.565886\pi$
$558$	−0.786254	−	3.17545i	−0.0332848	−	0.134427i
$559$	−0.518984	−	0.377064i	−0.0219507	−	0.0159481i
$560$	−1.27186	+	8.37266i	−0.0537459	+	0.353810i
$561$	−15.1734	−	39.2082i	−0.640623	−	1.65537i
$562$	−2.11148	−	3.65718i	−0.0890672	−	0.154269i
$563$	−24.2189	+	10.7829i	−1.02070	+	0.454447i	−0.847701	−	0.530474i	$-0.822014\pi$
$563$	−24.2189	+	10.7829i	−1.02070	+	0.454447i	−0.173003	+	0.984921i	$0.555347\pi$
$564$	6.57952	+	0.235110i	0.277048	+	0.00989991i
$565$	22.6803	−	25.1891i	0.954169	−	1.05971i
$566$	17.4781	+	24.0565i	0.734659	+	1.01117i
$567$	−20.3728	+	12.3267i	−0.855578	+	0.517674i
$568$	−5.53789	+	1.79937i	−0.232365	+	0.0754998i
$569$	−20.2079	+	4.29532i	−0.847158	+	0.180069i	−0.610985	−	0.791642i	$-0.709226\pi$
$569$	−20.2079	+	4.29532i	−0.847158	+	0.180069i	−0.236173	+	0.971711i	$0.575893\pi$
$570$	36.5121	+	13.3229i	1.52932	+	0.558035i
$571$	−6.31699	−	3.64712i	−0.264358	−	0.152627i	0.361963	−	0.932192i	$-0.382107\pi$
$571$	−6.31699	−	3.64712i	−0.264358	−	0.152627i	−0.626321	+	0.779565i	$0.715440\pi$
$572$	−0.988033	−	0.588921i	−0.0413117	−	0.0246240i
$573$	22.0997	−	22.8478i	0.923228	−	0.954479i
$574$	−13.3820	+	3.67657i	−0.558553	+	0.153457i
$575$	−37.4871	−	12.1803i	−1.56332	−	0.507954i
$576$	2.29500	+	1.93209i	0.0956250	+	0.0805038i
$577$	1.22504	+	11.6555i	0.0509992	+	0.485225i	0.989975	+	0.141242i	$0.0451095\pi$
$577$	1.22504	+	11.6555i	0.0509992	+	0.485225i	−0.938976	+	0.343983i	$0.888224\pi$
$578$	3.82167	+	36.3608i	0.158961	+	1.51241i
$579$	−1.37462	−	19.8901i	−0.0571275	−	0.826604i
$580$	6.63357	+	2.15538i	0.275444	+	0.0894972i
$581$	−8.17135	+	31.2862i	−0.339005	+	1.29797i
$582$	12.3246	+	11.9211i	0.510872	+	0.494146i
$583$	−14.8850	+	13.0321i	−0.616473	+	0.539734i
$584$	−3.30919	−	1.91056i	−0.136935	−	0.0790596i
$585$	−1.45503	−	2.99559i	−0.0601582	−	0.123853i
$586$	9.88157	−	2.10039i	0.408204	−	0.0867664i
$587$	12.4049	−	4.03060i	0.512006	−	0.166361i	−0.0416085	−	0.999134i	$-0.513248\pi$
$587$	12.4049	−	4.03060i	0.512006	−	0.166361i	0.553614	+	0.832773i	$0.313248\pi$
$588$	10.9595	+	5.18558i	0.451961	+	0.213850i
$589$	4.49338	+	6.18461i	0.185147	+	0.254833i
$590$	−12.7033	+	14.1085i	−0.522988	+	0.580837i
$591$	−0.851321	+	23.8241i	−0.0350187	+	0.979993i
$592$	1.12163	−	0.499384i	0.0460989	−	0.0205245i
$593$	−6.76636	−	11.7197i	−0.277861	−	0.481270i	0.692992	−	0.720946i	$-0.256292\pi$
$593$	−6.76636	−	11.7197i	−0.277861	−	0.481270i	−0.970853	+	0.239676i	$0.922959\pi$
$594$	−1.52096	−	17.1664i	−0.0624058	−	0.704348i
$595$	−57.7204	+	22.5767i	−2.36631	+	0.925556i
$596$	−2.73873	−	1.98980i	−0.112183	−	0.0815055i
$597$	32.9192	+	20.6074i	1.34729	+	0.843403i
$598$	2.54903	+	0.541814i	0.104238	+	0.0221564i
$599$	−15.0296	+	1.57967i	−0.614092	+	0.0645437i	−0.406468	−	0.913665i	$-0.633240\pi$
$599$	−15.0296	+	1.57967i	−0.614092	+	0.0645437i	−0.207624	+	0.978209i	$0.566573\pi$
$600$	−3.39670	−	8.42681i	−0.138670	−	0.344023i
$601$	21.8028	−	7.08415i	0.889354	−	0.288969i	0.171518	−	0.985181i	$-0.445133\pi$
$601$	21.8028	−	7.08415i	0.889354	−	0.288969i	0.717836	+	0.696212i	$0.245133\pi$
$602$	−4.08743	+	2.69132i	−0.166591	+	0.109690i
$603$	−18.8399	+	27.8337i	−0.767220	+	1.13348i
$604$	−0.869933	+	0.502256i	−0.0353971	+	0.0204365i
$605$	6.35936	+	34.6306i	0.258545	+	1.40793i
$606$	−11.8385	+	3.38425i	−0.480907	+	0.137476i
$607$	−2.97486	−	0.312671i	−0.120746	−	0.0126909i	0.0439627	−	0.999033i	$-0.486002\pi$
$607$	−2.97486	−	0.312671i	−0.120746	−	0.0126909i	−0.164709	+	0.986342i	$0.552668\pi$
$608$	−6.66740	−	2.16637i	−0.270399	−	0.0878579i
$609$	5.68242	−	8.21133i	0.230263	−	0.332740i
$610$	−0.284993	+	0.207060i	−0.0115390	+	0.00838360i
$611$	1.20429	+	0.536183i	0.0487203	+	0.0216917i
$612$	−3.84766	+	21.6159i	−0.155532	+	0.873769i
$613$	−21.5858	+	19.4359i	−0.871841	+	0.785009i	−0.977839	−	0.209357i	$-0.932863\pi$
$613$	−21.5858	+	19.4359i	−0.871841	+	0.785009i	0.105998	+	0.994366i	$0.466196\pi$
$614$	17.7911	+	1.86992i	0.717989	+	0.0754637i
$615$	20.2180	−	20.9024i	0.815268	−	0.842864i
$616$	−6.86114	+	5.47036i	−0.276443	+	0.220407i
$617$			27.1148i			1.09160i	0.837916	+	0.545800i	$0.183774\pi$
$617$			27.1148i			1.09160i	−0.837916	+	0.545800i	$0.816226\pi$
$618$	9.58725	−	8.03141i	0.385656	−	0.323070i
$619$	−32.8535	−	36.4875i	−1.32049	−	1.46656i	−0.780940	−	0.624606i	$-0.785260\pi$
$619$	−32.8535	−	36.4875i	−1.32049	−	1.46656i	−0.539554	−	0.841951i	$-0.681407\pi$
$620$	0.725691	−	3.41411i	0.0291445	−	0.137114i
$621$	15.7940	+	35.7078i	0.633793	+	1.43290i
$622$	−10.3405	−	14.2324i	−0.414615	−	0.570669i
$623$	−1.15173	+	3.05804i	−0.0461431	+	0.122518i
$624$	0.281576	+	0.530606i	0.0112721	+	0.0212413i
$625$	2.47855	−	23.5818i	0.0991420	−	0.943273i
$626$	11.2063	−	19.4098i	0.447893	−	0.775773i
$627$	18.3811	+	35.8330i	0.734069	+	1.43103i
$628$	0.0291862	+	0.0505520i	0.00116466	+	0.00201724i
$629$	7.26948	+	5.28158i	0.289853	+	0.210591i
$630$	−25.2988	+	2.33327i	−1.00793	+	0.0929599i
$631$	5.32433	+	16.3866i	0.211958	+	0.652341i	0.999356	+	0.0358949i	$0.0114281\pi$
$631$	5.32433	+	16.3866i	0.211958	+	0.652341i	−0.787397	+	0.616446i	$0.788572\pi$
$632$	2.72627	−	6.12330i	0.108445	−	0.243572i
$633$	−35.7920	−	28.0106i	−1.42260	−	1.11332i
$634$	2.46244	−	11.5849i	0.0977961	−	0.460094i
$635$	−59.2364	+	12.5911i	−2.35073	+	0.499662i
$636$	10.1762	−	1.78583i	0.403514	−	0.0708127i
$637$	1.64711	+	1.78341i	0.0652611	+	0.0706611i
$638$	3.52615	+	6.30859i	0.139602	+	0.249760i
$639$	−9.23290	−	14.8293i	−0.365248	−	0.586636i
$640$	1.30191	+	2.92414i	0.0514626	+	0.115587i
$641$	10.0703	−	9.06731i	0.397752	−	0.358137i	−0.445849	−	0.895108i	$-0.647098\pi$
$641$	10.0703	−	9.06731i	0.397752	−	0.358137i	0.843601	+	0.536971i	$0.180431\pi$
$642$	−25.7130	+	1.77705i	−1.01481	+	0.0701346i
$643$	8.50492	−	6.17919i	0.335401	−	0.243683i	−0.407318	−	0.913287i	$-0.633536\pi$
$643$	8.50492	−	6.17919i	0.335401	−	0.243683i	0.742719	+	0.669603i	$0.233536\pi$
$644$	10.7221	−	16.7415i	0.422509	−	0.659706i
$645$	4.50298	−	9.21348i	0.177305	−	0.362781i
$646$	−10.6673	−	50.1856i	−0.419699	−	1.97453i
$647$	−4.09139	−	9.18942i	−0.160849	−	0.361273i	0.815084	−	0.579343i	$-0.196691\pi$
$647$	−4.09139	−	9.18942i	−0.160849	−	0.361273i	−0.975933	+	0.218070i	$0.930024\pi$
$648$	−3.97159	+	8.07629i	−0.156019	+	0.317267i
$649$	−19.5903	+	1.78382i	−0.768987	+	0.0700209i
$650$		−	1.81922i		−	0.0713555i
$651$	−4.38381	−	2.39849i	−0.171815	−	0.0940040i
$652$	2.96833	−	9.13559i	0.116249	−	0.357777i
$653$	−18.4484	−	16.6110i	−0.721941	−	0.650039i	0.223921	−	0.974607i	$-0.428114\pi$
$653$	−18.4484	−	16.6110i	−0.721941	−	0.650039i	−0.945862	+	0.324569i	$0.894781\pi$
$654$	−21.7666	−	17.0344i	−0.851141	−	0.666097i
$655$	−35.9383	+	3.77727i	−1.40423	+	0.147590i
$656$	−3.50981	+	3.89804i	−0.137035	+	0.152193i
$657$	3.17762	−	11.0142i	0.123971	−	0.429703i
$658$	7.06610	−	7.15607i	0.275465	−	0.278973i
$659$	−4.79076			−0.186621			−0.0933107	−	0.995637i	$-0.529745\pi$
$659$	−4.79076			−0.186621			−0.0933107	+	0.995637i	$0.529745\pi$
$660$	6.54269	−	17.1842i	0.254674	−	0.668895i
$661$	−18.4155	+	31.8966i	−0.716281	+	1.24063i	0.246183	+	0.969223i	$0.420824\pi$
$661$	−18.4155	+	31.8966i	−0.716281	+	1.24063i	−0.962464	+	0.271411i	$0.912510\pi$
$662$	10.6239	−	4.73005i	0.412908	−	0.183839i
$663$	−2.33264	+	3.72627i	−0.0905923	+	0.144716i
$664$	3.77673	+	11.6236i	0.146565	+	0.451082i
$665$	52.7276	−	27.2876i	2.04469	−	1.05817i
$666$	2.26298	+	2.90619i	0.0876886	+	0.112613i
$667$	−12.1682	−	10.9563i	−0.471156	−	0.424230i
$668$	−8.82677	−	9.80313i	−0.341518	−	0.379294i
$669$	−5.59986	−	2.04333i	−0.216503	−	0.0789998i
$670$	−31.0564	+	17.9304i	−1.19981	+	0.692713i
$671$	−0.362444	−	0.0432011i	−0.0139920	−	0.00166776i
$672$	4.54527	−	0.583547i	0.175338	−	0.0225108i
$673$	−8.44748	+	11.6270i	−0.325626	+	0.448186i	−0.940175	−	0.340693i	$-0.889338\pi$
$673$	−8.44748	+	11.6270i	−0.325626	+	0.448186i	0.614548	+	0.788879i	$0.289338\pi$
$674$	−1.17502	−	5.52804i	−0.0452601	−	0.212932i
$675$	22.0902	−	15.9674i	0.850254	−	0.614587i
$676$	−1.34630	−	12.8092i	−0.0517807	−	0.492660i
$677$	−8.40774	−	3.74336i	−0.323136	−	0.143869i	0.238757	−	0.971079i	$-0.423260\pi$
$677$	−8.40774	−	3.74336i	−0.323136	−	0.143869i	−0.561893	+	0.827210i	$0.689927\pi$
$678$	−16.4785	−	8.05369i	−0.632855	−	0.309300i
$679$	26.1469	−	1.53621i	1.00343	−	0.0589544i
$680$	−13.7693	+	18.9518i	−0.528028	+	0.726769i
$681$	−7.81689	+	31.2437i	−0.299544	+	1.19726i
$682$	2.95519	−	2.08487i	0.113160	−	0.0798338i
$683$	14.8962	+	8.60034i	0.569988	+	0.329083i	0.757145	−	0.653247i	$-0.226594\pi$
$683$	14.8962	+	8.60034i	0.569988	+	0.329083i	−0.187157	+	0.982330i	$0.559927\pi$
$684$	1.50115	−	20.9779i	0.0573979	−	0.802111i
$685$	15.7574	−	48.4962i	0.602058	−	1.85294i
$686$	17.1611	−	6.96397i	0.655214	−	0.265886i
$687$	−3.45250	−	0.488076i	−0.131721	−	0.0186213i
$688$	−0.752350	+	1.68981i	−0.0286831	+	0.0644232i
$689$	2.02352	+	0.430112i	0.0770899	+	0.0163860i
$690$	−1.48768	+	41.6326i	−0.0566351	+	1.58493i
$691$	−3.04268	+	28.9492i	−0.115749	+	1.10128i	0.770298	+	0.637684i	$0.220108\pi$
$691$	−3.04268	+	28.9492i	−0.115749	+	1.10128i	−0.886047	+	0.463595i	$0.846559\pi$
$692$	4.18091			0.158935
$693$	−20.8772	−	16.0357i	−0.793058	−	0.609146i
$694$	−6.72971			−0.255456
$695$	−1.02349	+	9.73781i	−0.0388230	+	0.369376i
$696$	0.134782	−	3.77186i	0.00510891	−	0.142972i
$697$	−37.5493	−	7.98135i	−1.42228	−	0.302315i
$698$	0.341021	−	0.765945i	0.0129078	−	0.0289914i
$699$	−19.1349	−	2.70508i	−0.723748	−	0.102315i
$700$	−12.9879	−	4.89156i	−0.490898	−	0.184884i
$701$	1.46579	−	4.51124i	0.0553622	−	0.170387i	−0.919552	−	0.392968i	$-0.871448\pi$
$701$	1.46579	−	4.51124i	0.0553622	−	0.170387i	0.974914	+	0.222581i	$0.0714482\pi$
$702$	−1.34213	+	1.20255i	−0.0506555	+	0.0453875i
$703$	−7.45422	−	4.30369i	−0.281141	−	0.162317i
$704$	−1.06868	+	3.13973i	−0.0402775	+	0.118333i
$705$	−5.11478	+	20.4435i	−0.192634	+	0.769948i
$706$	15.5009	−	21.3351i	0.583383	−	0.802958i
$707$	−8.43250	+	16.8118i	−0.317137	+	0.632272i
$708$	9.22968	+	4.51090i	0.346873	+	0.169530i
$709$	−36.2745	−	16.1505i	−1.36232	−	0.606543i	−0.410122	−	0.912030i	$-0.634514\pi$
$709$	−36.2745	−	16.1505i	−1.36232	−	0.606543i	−0.952196	+	0.305487i	$0.901181\pi$
$710$	−1.94823	−	18.5362i	−0.0731159	−	0.695651i
$711$	19.7972	+	3.52393i	0.742452	+	0.132158i
$712$	0.256789	+	1.20810i	0.00962358	+	0.0452754i
$713$	−4.81620	+	6.62893i	−0.180368	+	0.248255i
$714$	20.3309	+	26.6728i	0.760865	+	0.998203i
$715$	2.50140	−	2.70153i	0.0935472	−	0.101032i
$716$	11.8223	−	6.82559i	0.441819	−	0.255084i
$717$	30.7480	+	11.2197i	1.14831	+	0.419006i
$718$	6.28209	+	6.97696i	0.234445	+	0.260378i
$719$	−1.57133	−	1.41483i	−0.0586008	−	0.0527644i	0.639310	−	0.768949i	$-0.279220\pi$
$719$	−1.57133	−	1.41483i	−0.0586008	−	0.0527644i	−0.697911	+	0.716185i	$0.745887\pi$
$720$	−7.57656	+	5.89967i	−0.282362	+	0.219868i
$721$	0.879143	−	19.0841i	0.0327410	−	0.710731i
$722$	9.31606	+	28.6719i	0.346708	+	1.06706i
$723$	21.3619	−	34.1245i	0.794456	−	1.26910i
$724$	21.1621	−	9.42197i	0.786483	−	0.350165i
$725$	−5.71527	+	9.89914i	−0.212260	+	0.367645i
$726$	17.0717	−	8.45923i	0.633588	−	0.313952i
$727$	−3.15728			−0.117097			−0.0585486	−	0.998285i	$-0.518647\pi$
$727$	−3.15728			−0.117097			−0.0585486	+	0.998285i	$0.518647\pi$
$728$	0.887788	+	0.231873i	0.0329036	+	0.00859378i
$729$	−26.3823	−	5.74219i	−0.977123	−	0.212674i
$730$	8.18409	−	9.08935i	0.302907	−	0.336412i
$731$	−13.4631	+	1.41503i	−0.497951	+	0.0523368i
$732$	0.150116	+	0.117479i	0.00554843	+	0.00434217i
$733$	−29.0301	−	26.1388i	−1.07225	−	0.965460i	−0.0727607	−	0.997349i	$-0.523181\pi$
$733$	−29.0301	−	26.1388i	−1.07225	−	0.965460i	−0.999491	+	0.0318893i	$0.989848\pi$
$734$	6.87377	−	21.1553i	0.253716	−	0.780856i
$735$	−23.5292	+	30.8623i	−0.867887	+	1.13837i
$736$		−	7.51418i		−	0.276976i
$737$	−36.2347	−	8.23048i	−1.33472	−	0.303173i
$738$	−13.8820	−	7.41015i	−0.511005	−	0.272771i
$739$	−7.04919	−	15.8328i	−0.259309	−	0.582417i	0.736234	−	0.676727i	$-0.236602\pi$
$739$	−7.04919	−	15.8328i	−0.259309	−	0.582417i	−0.995543	+	0.0943098i	$0.969936\pi$
$740$	0.817087	+	3.84409i	0.0300367	+	0.141312i
$741$	1.84912	−	3.78346i	0.0679290	−	0.138989i
$742$	8.51160	−	13.2900i	0.312471	−	0.487892i
$743$	−27.5929	+	20.0474i	−1.01229	+	0.735469i	−0.964687	−	0.263398i	$-0.915157\pi$
$743$	−27.5929	+	20.0474i	−1.01229	+	0.735469i	−0.0475989	+	0.998867i	$0.515157\pi$
$744$	−1.88421	+	0.130220i	−0.0690787	+	0.00477410i
$745$	8.05255	−	7.25055i	0.295023	−	0.265639i
$746$	−0.899717	−	2.02080i	−0.0329410	−	0.0739866i
$747$	−31.1254	+	19.3791i	−1.13882	+	0.709044i
$748$	−23.8104	+	4.71578i	−0.870593	+	0.172426i
$749$	−24.5829	+	30.7531i	−0.898239	+	1.12369i
$750$	1.34109	−	0.235347i	0.0489695	−	0.00859367i
$751$	21.3815	−	4.54477i	0.780221	−	0.165841i	0.199450	−	0.979908i	$-0.436084\pi$
$751$	21.3815	−	4.54477i	0.780221	−	0.165841i	0.580771	+	0.814067i	$0.302751\pi$
$752$	0.790295	−	3.71805i	0.0288191	−	0.135583i
$753$	36.4856	+	28.5534i	1.32961	+	1.04054i
$754$	0.307380	−	0.690386i	0.0111941	−	0.0251424i
$755$	−0.993587	−	3.05795i	−0.0361603	−	0.111290i
$756$	4.97664	+	12.8153i	0.180999	+	0.466090i
$757$	−9.32957	−	6.77833i	−0.339089	−	0.246363i	0.405188	−	0.914233i	$-0.367206\pi$
$757$	−9.32957	−	6.77833i	−0.339089	−	0.246363i	−0.744277	+	0.667871i	$0.767206\pi$
$758$	−8.02060	−	13.8921i	−0.291321	−	0.504584i
$759$	−30.4394	+	30.6059i	−1.10488	+	1.11092i
$760$	11.2199	−	19.4334i	0.406988	−	0.704925i
$761$	0.0732676	−	0.697095i	0.00265595	−	0.0252697i	−0.993114	−	0.117155i	$-0.962623\pi$
$761$	0.0732676	−	0.697095i	0.00265595	−	0.0252697i	0.995770	+	0.0918852i	$0.0292893\pi$
$762$	15.3611	+	28.9467i	0.556474	+	1.04863i
$763$	−41.6580	+	6.86838i	−1.50812	+	0.248652i
$764$	−10.7872	−	14.8473i	−0.390267	−	0.537156i
$765$	−65.1170	−	26.4321i	−2.35431	−	0.955653i
$766$	−3.56574	+	16.7755i	−0.128835	+	0.606123i
$767$	1.37638	+	1.52863i	0.0496982	+	0.0551955i
$768$	1.32773	−	1.11226i	0.0479104	−	0.0401353i
$769$			3.10127i			0.111835i	0.998435	+	0.0559174i	$0.0178084\pi$
$769$			3.10127i			0.111835i	−0.998435	+	0.0559174i	$0.982192\pi$
$770$	−12.5612	−	25.1222i	−0.452674	−	0.905342i
$771$	7.15853	−	7.40084i	0.257808	−	0.266535i
$772$	−11.4479	−	1.20322i	−0.412018	−	0.0433049i
$773$	−0.711863	+	0.640964i	−0.0256039	+	0.0230539i	−0.681833	−	0.731508i	$-0.738817\pi$
$773$	−0.711863	+	0.640964i	−0.0256039	+	0.0230539i	0.656229	+	0.754561i	$0.272150\pi$
$774$	−5.46329	−	0.972475i	−0.196374	−	0.0349549i
$775$	5.22552	+	2.32655i	0.187706	+	0.0835721i
$776$	8.00898	−	5.81887i	0.287506	−	0.208885i
$777$	5.60761	+	0.459460i	0.201172	+	0.0164830i
$778$	26.0603	+	8.46750i	0.934307	+	0.303575i
$779$	36.5711	+	3.84377i	1.31029	+	0.137717i
$780$	−1.84868	+	0.528476i	−0.0661933	+	0.0189225i
$781$	11.5678	−	15.4645i	0.413928	−	0.553364i
$782$	47.6252	−	27.4964i	1.70307	−	0.983270i
$783$	11.0811	−	2.32716i	0.396005	−	0.0831660i
$784$	4.04252	−	5.71472i	0.144376	−	0.204097i
$785$	−0.177698	+	0.0577375i	−0.00634231	+	0.00206074i
$786$	7.31034	+	18.1361i	0.260751	+	0.646893i
$787$	15.1421	−	1.59150i	0.539759	−	0.0567309i	0.169273	−	0.985569i	$-0.445858\pi$
$787$	15.1421	−	1.59150i	0.539759	−	0.0567309i	0.370486	+	0.928838i	$0.379191\pi$
$788$	13.4629	+	2.86162i	0.479595	+	0.101941i
$789$	−26.7150	−	16.7236i	−0.951079	−	0.595374i
$790$	17.3573	+	12.6108i	0.617544	+	0.448672i
$791$	−26.0919	+	10.2056i	−0.927723	+	0.362869i
$792$	−9.91365	−	0.848201i	−0.352266	−	0.0301395i
$793$	0.0190839	+	0.0330544i	0.000677691	+	0.00117379i
$794$	−22.5229	+	10.0278i	−0.799307	+	0.355874i
$795$	−1.18098	+	33.0495i	−0.0418850	+	1.17215i
$796$	15.0037	−	16.6633i	0.531793	−	0.590616i
$797$	−22.9804	−	31.6298i	−0.814006	−	1.12038i	−0.990693	−	0.136116i	$-0.956538\pi$
$797$	−22.9804	−	31.6298i	−0.814006	−	1.12038i	0.176687	−	0.984267i	$-0.443462\pi$
$798$	−22.0393	−	23.3745i	−0.780182	−	0.827448i
$799$	26.4571	−	8.59642i	0.935983	−	0.304119i
$800$	−5.13096	+	1.09062i	−0.181407	+	0.0385592i
$801$	−3.33290	+	1.61887i	−0.117762	+	0.0572000i
$802$	−28.5620	−	16.4903i	−1.00856	−	0.582293i
$803$	12.6210	−	1.14922i	0.445386	−	0.0405550i
$804$	13.9478	+	13.4912i	0.491902	+	0.475796i
$805$	45.2808	+	44.7115i	1.59594	+	1.57587i
$806$	−0.359667	−	0.116863i	−0.0126687	−	0.00411632i
$807$	0.243928	+	3.52951i	0.00858669	+	0.124245i
$808$	0.743069	+	7.06983i	0.0261411	+	0.248716i
$809$	−0.976088	−	9.28686i	−0.0343174	−	0.326509i	−0.998190	−	0.0601438i	$-0.980844\pi$
$809$	−0.976088	−	9.28686i	−0.0343174	−	0.326509i	0.963872	−	0.266365i	$-0.0858226\pi$
$810$	−22.6432	−	17.8095i	−0.795601	−	0.625763i
$811$	−11.4327	−	3.71472i	−0.401457	−	0.130441i	0.101327	−	0.994853i	$-0.467691\pi$
$811$	−11.4327	−	3.71472i	−0.401457	−	0.130441i	−0.502785	+	0.864412i	$0.667691\pi$
$812$	−4.10238	−	4.05081i	−0.143965	−	0.142155i
$813$	19.5547	−	20.2166i	0.685813	−	0.709028i
$814$	−2.08491	+	3.49786i	−0.0730762	+	0.122600i
$815$	26.6274	+	15.3734i	0.932719	+	0.538505i
$816$	11.9081	+	4.34515i	0.416867	+	0.152111i
$817$	12.6842	−	2.69610i	0.443762	−	0.0943246i
$818$	−27.5640	+	8.95610i	−0.963754	+	0.313143i
$819$	−0.0350993	+	2.75248i	−0.00122647	+	0.0961795i
$820$	−9.86870	−	13.5831i	−0.344630	−	0.474343i
$821$	−0.417810	+	0.464025i	−0.0145817	+	0.0161946i	−0.750392	−	0.660994i	$-0.770135\pi$
$821$	−0.417810	+	0.464025i	−0.0145817	+	0.0161946i	0.735810	+	0.677188i	$0.236802\pi$
$822$	−27.5750	−	0.985356i	−0.961790	−	0.0343682i
$823$	44.6899	−	19.8972i	1.55779	−	0.693574i	0.566355	−	0.824161i	$-0.308353\pi$
$823$	44.6899	−	19.8972i	1.55779	−	0.693574i	0.991437	+	0.130588i	$0.0416865\pi$
$824$	−3.61039	−	6.25338i	−0.125774	−	0.217847i
$825$	25.3169	+	16.3430i	0.881420	+	0.568989i
$826$	14.6142	−	5.71618i	0.508492	−	0.198891i
$827$	−14.5018	−	10.5362i	−0.504277	−	0.366378i	0.306372	−	0.951912i	$-0.400885\pi$
$827$	−14.5018	−	10.5362i	−0.504277	−	0.366378i	−0.810648	+	0.585534i	$0.800885\pi$
$828$	21.8817	−	5.41801i	0.760443	−	0.188289i
$829$	−4.76426	−	1.01267i	−0.165470	−	0.0351717i	0.124432	−	0.992228i	$-0.460289\pi$
$829$	−4.76426	−	1.01267i	−0.165470	−	0.0351717i	−0.289901	+	0.957057i	$0.593623\pi$
$830$	−38.9060	+	4.08918i	−1.35045	+	0.141938i
$831$	0.362077	−	0.145947i	0.0125603	−	0.00506283i
$832$	0.329834	−	0.107170i	0.0114349	−	0.00371544i
$833$	51.0128	+	4.70998i	1.76749	+	0.163191i
$834$	5.21858	−	0.915809i	0.180705	−	0.0317119i
$835$	36.5671	−	21.1120i	1.26546	−	0.730611i
$836$	22.2111	−	6.87666i	0.768187	−	0.237834i
$837$	−1.73780	−	5.39306i	−0.0600672	−	0.186411i
$838$	−23.7347	−	2.49462i	−0.819903	−	0.0861752i
$839$	−19.0746	−	6.19773i	−0.658530	−	0.213969i	−0.0393585	−	0.999225i	$-0.512531\pi$
$839$	−19.0746	−	6.19773i	−0.658530	−	0.213969i	−0.619171	+	0.785256i	$0.712531\pi$
$840$	−1.19783	+	14.6193i	−0.0413291	+	0.504412i
$841$	19.6200	−	14.2547i	0.676551	−	0.491543i
$842$	16.8876	+	7.51885i	0.581985	+	0.259117i
$843$	−4.08522	−	6.06720i	−0.140702	−	0.208966i
$844$	−19.5004	+	17.5582i	−0.671230	+	0.604378i
$845$	41.0005	+	4.30933i	1.41046	+	0.148245i
$846$	11.3970	−	0.379466i	0.391838	−	0.0130463i
$847$	8.13517	−	27.9431i	0.279528	−	0.960138i
$848$		−	5.96504i		−	0.204840i
$849$	33.0737	+	39.4807i	1.13509	+	1.35498i
$850$	−25.6880	−	28.5294i	−0.881090	−	0.978550i
$851$	1.91814	−	9.02416i	0.0657531	−	0.309344i
$852$	−9.35420	+	3.77051i	−0.320470	+	0.129176i
$853$	1.37703	+	1.89532i	0.0471486	+	0.0648945i	0.831940	−	0.554865i	$-0.187230\pi$
$853$	1.37703	+	1.89532i	0.0471486	+	0.0648945i	−0.784792	+	0.619760i	$0.787230\pi$
$854$	0.287299	−	0.0473685i	0.00983115	−	0.00162092i
$855$	64.6813	+	18.6608i	2.21205	+	0.638185i
$856$	−1.55547	+	14.7993i	−0.0531648	+	0.505829i
$857$	28.4617	−	49.2970i	0.972232	−	1.68395i	0.283449	−	0.958987i	$-0.408521\pi$
$857$	28.4617	−	49.2970i	0.972232	−	1.68395i	0.688783	−	0.724968i	$-0.258145\pi$
$858$	−1.77758	−	0.899624i	−0.0606855	−	0.0307126i
$859$	5.79738	+	10.0414i	0.197804	+	0.342607i	0.947816	−	0.318817i	$-0.103286\pi$
$859$	5.79738	+	10.0414i	0.197804	+	0.342607i	−0.750012	+	0.661424i	$0.769952\pi$
$860$	−4.78997	−	3.48012i	−0.163337	−	0.118671i
$861$	−22.6840	+	7.95092i	−0.773070	+	0.270967i
$862$	−2.93065	−	9.01962i	−0.0998184	−	0.307209i
$863$	−18.3456	+	41.2049i	−0.624491	+	1.40263i	0.273179	+	0.961963i	$0.411925\pi$
$863$	−18.3456	+	41.2049i	−0.624491	+	1.40263i	−0.897671	+	0.440667i	$0.854742\pi$
$864$	4.19632	+	3.06445i	0.142762	+	0.104255i
$865$	−2.78239	+	13.0901i	−0.0946043	+	0.445078i
$866$	−5.18961	+	1.10308i	−0.176350	+	0.0374843i
$867$	10.9457	+	62.3725i	0.371737	+	2.11828i
$868$	−1.80140	+	2.25355i	−0.0611436	+	0.0764903i
$869$	4.31901	+	21.8070i	0.146512	+	0.739753i
$870$	11.7197	+	2.93216i	0.397336	+	0.0994097i
$871$	1.58036	+	3.54954i	0.0535484	+	0.120272i
$872$	−11.8590	+	10.6779i	−0.401595	+	0.361598i
$873$	22.7197	+	19.1270i	0.768945	+	0.647352i
$874$	−42.6176	+	30.9635i	−1.44156	+	1.04736i
$875$	1.12171	−	1.75144i	0.0379207	−	0.0592094i
$876$	−5.94620	−	2.90613i	−0.200904	−	0.0981892i
$877$	9.49300	+	44.6611i	0.320556	+	1.50810i	0.783322	+	0.621616i	$0.213524\pi$
$877$	9.49300	+	44.6611i	0.320556	+	1.50810i	−0.462766	+	0.886480i	$0.653143\pi$
$878$	16.4997	+	37.0589i	0.556838	+	1.25068i
$879$	16.8238	−	4.80938i	0.567454	−	0.162216i
$880$	−9.11906	−	5.43546i	−0.307404	−	0.183229i
$881$		−	16.8915i		−	0.569088i	−0.958663	−	0.284544i	$-0.908158\pi$
$881$		−	16.8915i		−	0.569088i	0.958663	−	0.284544i	$-0.0918421\pi$
$882$	19.5564	+	7.65154i	0.658499	+	0.257641i
$883$	−11.7006	+	36.0106i	−0.393755	+	1.21185i	0.536171	+	0.844109i	$0.319870\pi$
$883$	−11.7006	+	36.0106i	−0.393755	+	1.21185i	−0.929927	+	0.367745i	$0.880130\pi$
$884$	1.88620	+	1.69834i	0.0634397	+	0.0571214i
$885$	−20.2656	+	25.8955i	−0.681222	+	0.870467i
$886$	−19.7053	+	2.07111i	−0.662012	+	0.0695803i
$887$	−22.3383	+	24.8092i	−0.750047	+	0.833012i	−0.990480	−	0.137654i	$-0.956044\pi$
$887$	−22.3383	+	24.8092i	−0.750047	+	0.833012i	0.240433	+	0.970666i	$0.422711\pi$
$888$	1.87847	−	0.996844i	0.0630373	−	0.0334519i
$889$	48.4324	+	12.6496i	1.62437	+	0.424254i
$890$	−3.95336			−0.132517
$891$	−4.67811	−	29.4808i	−0.156723	−	0.987643i
$892$	−1.72079	+	2.98050i	−0.0576165	+	0.0997947i
$893$	−24.3440	+	10.8386i	−0.814639	+	0.362701i
$894$	−4.96995	−	3.11118i	−0.166220	−	0.104053i
$895$	13.5027	+	41.5571i	0.451346	+	1.38910i
$896$	0.121752	−	2.64295i	0.00406744	−	0.0882947i
$897$	4.46925	+	0.631813i	0.149224	+	0.0210956i
$898$	−26.6030	−	23.9534i	−0.887753	−	0.799336i
$899$	1.58997	+	1.76584i	0.0530283	+	0.0588939i
$900$	−6.87557	−	14.1553i	−0.229186	−	0.471843i
$901$	37.8067	−	21.8277i	1.25952	−	0.727186i
$902$	2.05901	−	17.2745i	0.0685576	−	0.575178i
$903$	−6.74140	+	5.13853i	−0.224340	+	0.171000i
$904$	−6.22428	+	8.56698i	−0.207016	+	0.284934i
$905$	15.4162	+	72.5273i	0.512450	+	2.41089i
$906$	−1.44320	+	0.971749i	−0.0479472	+	0.0322842i
$907$	0.0737341	+	0.701533i	0.00244830	+	0.0232940i	0.995678	−	0.0928743i	$-0.0296055\pi$
$907$	0.0737341	+	0.701533i	0.00244830	+	0.0232940i	−0.993230	+	0.116168i	$0.962939\pi$
$908$	16.9870	+	7.56310i	0.563733	+	0.250990i
$909$	−20.0520	+	7.26148i	−0.665083	+	0.240848i
$910$	−1.31680	+	2.62529i	−0.0436515	+	0.0870274i
$911$	32.5498	−	44.8009i	1.07842	−	1.48432i	0.217175	−	0.976133i	$-0.430316\pi$
$911$	32.5498	−	44.8009i	1.07842	−	1.48432i	0.861246	−	0.508187i	$-0.169684\pi$
$912$	−11.7795	−	2.94712i	−0.390058	−	0.0975889i
$913$	−32.4588	−	24.2798i	−1.07423	−	0.803544i
$914$	−15.0308	−	8.67805i	−0.497175	−	0.287044i
$915$	−0.467721	+	0.391818i	−0.0154624	+	0.0129531i
$916$	−0.622089	+	1.91459i	−0.0205544	+	0.0632599i
$917$	27.9525	+	10.5276i	0.923073	+	0.347651i
$918$	−4.06713	+	37.8101i	−0.134235	+	1.24792i
$919$	10.8432	−	24.3542i	0.357684	−	0.803370i	−0.641655	−	0.766994i	$-0.721752\pi$
$919$	10.8432	−	24.3542i	0.357684	−	0.803370i	0.999338	−	0.0363767i	$-0.0115816\pi$
$920$	23.5263	+	5.00068i	0.775640	+	0.164867i
$921$	30.9650	+	1.10649i	1.02033	+	0.0364601i
$922$	2.24310	−	21.3417i	0.0738726	−	0.702851i
$923$	−2.01942			−0.0664701
$924$	−11.2023	+	10.2717i	−0.368528	+	0.337915i
$925$	−6.44044			−0.211760
$926$	−0.922724	+	8.77913i	−0.0303226	+	0.288500i
$927$	15.6070	−	15.0226i	0.512601	−	0.493407i
$928$	−2.13146	−	0.453055i	−0.0699685	−	0.0148723i
$929$	15.6942	−	35.2497i	0.514910	−	1.15651i	−0.449785	−	0.893137i	$-0.648499\pi$
$929$	15.6942	−	35.2497i	0.514910	−	1.15651i	0.964695	−	0.263370i	$-0.0848338\pi$
$930$	0.846234	−	5.98600i	0.0277491	−	0.196289i
$931$	−49.0697	+	0.620840i	−1.60820	+	0.0203472i
$932$	−3.44782	+	10.6113i	−0.112937	+	0.347585i
$933$	−19.5672	−	23.3578i	−0.640603	−	0.764700i
$934$	−17.8341	−	10.2965i	−0.583548	−	0.336912i
$935$	1.08102	−	77.6868i	0.0353532	−	2.54063i
$936$	0.549908	+	0.883225i	0.0179743	+	0.0288691i
$937$	−10.4302	+	14.3560i	−0.340740	+	0.468989i	−0.944657	−	0.328058i	$-0.893606\pi$
$937$	−10.4302	+	14.3560i	−0.340740	+	0.468989i	0.603917	+	0.797047i	$0.293606\pi$
$938$	29.5906	−	1.73854i	0.966166	−	0.0567652i
$939$	17.0458	−	34.8771i	0.556267	−	1.13817i
$940$	11.1150	+	4.94871i	0.362531	+	0.161409i
$941$	−4.36807	−	41.5594i	−0.142395	−	1.35480i	−0.799349	−	0.600867i	$-0.794822\pi$
$941$	−4.36807	−	41.5594i	−0.142395	−	1.35480i	0.656954	−	0.753931i	$-0.271845\pi$
$942$	0.0564685	+	0.0838648i	0.00183984	+	0.00273246i
$943$	8.19470	+	38.5530i	0.266856	+	1.25546i
$944$	3.48624	−	4.79839i	0.113467	−	0.156174i
$945$	−43.4359	+	7.05289i	−1.41297	+	0.229430i
$946$	−1.19189	−	6.01794i	−0.0387516	−	0.195660i
$947$	2.93327	−	1.69353i	0.0953185	−	0.0550322i	−0.451583	−	0.892229i	$-0.649141\pi$
$947$	2.93327	−	1.69353i	0.0953185	−	0.0550322i	0.546902	+	0.837197i	$0.315807\pi$
$948$	3.97956	−	10.9062i	0.129250	−	0.354217i
$949$	−0.886730	−	0.984814i	−0.0287845	−	0.0319684i
$950$	27.3287	+	24.6068i	0.886659	+	0.798351i
$951$	2.87147	−	20.3119i	0.0931138	−	0.658659i
$952$	17.1966	−	8.89960i	0.557346	−	0.288438i
$953$	3.55178	+	10.9313i	0.115053	+	0.354098i	0.991958	−	0.126566i	$-0.0403956\pi$
$953$	3.55178	+	10.9313i	0.115053	+	0.354098i	−0.876905	+	0.480664i	$0.840396\pi$
$954$	17.3706	−	4.30102i	0.562393	−	0.139251i
$955$	53.6646	−	23.8930i	1.73655	−	0.773160i
$956$	9.44865	−	16.3655i	0.305591	−	0.529299i
$957$	6.84631	+	10.4797i	0.221310	+	0.338761i
$958$	30.0299			0.970221
$959$	−29.6143	+	29.9914i	−0.956297	+	0.968473i
$960$	2.59881	+	4.89724i	0.0838763	+	0.158058i
$961$	−19.9474	+	22.1538i	−0.643465	+	0.714640i
$962$	0.423472	−	0.0445087i	0.0136533	−	0.00143502i
$963$	−44.2180	+	6.14124i	−1.42491	+	0.197899i
$964$	−17.2734	−	15.5531i	−0.556340	−	0.500931i
$965$	11.3857	−	35.0417i	0.366520	−	1.12803i
$966$	16.5278	−	30.2085i	0.531772	−	0.971942i
$967$			44.2037i			1.42149i	0.703448	+	0.710747i	$0.251643\pi$
$967$			44.2037i			1.42149i	−0.703448	+	0.710747i	$0.748357\pi$
$968$	−3.10678	−	10.5522i	−0.0998556	−	0.339159i
$969$	−24.4254	−	85.4433i	−0.784658	−	2.74483i
$970$	12.8885	+	28.9480i	0.413824	+	0.929464i
$971$	6.19444	+	29.1425i	0.198789	+	0.935228i	0.958528	+	0.285000i	$0.0919935\pi$
$971$	6.19444	+	29.1425i	0.198789	+	0.935228i	−0.759739	+	0.650229i	$0.774673\pi$
$972$	−5.89816	+	14.4295i	−0.189184	+	0.462828i
$973$	4.36492	−	6.81539i	0.139933	−	0.218491i
$974$	3.02612	−	2.19860i	0.0969630	−	0.0704478i
$975$	−0.217249	−	3.14347i	−0.00695753	−	0.100672i
$976$	0.0817866	−	0.0736410i	0.00261792	−	0.00235719i
$977$	14.4435	+	32.4406i	0.462088	+	1.03787i	0.982891	+	0.184190i	$0.0589662\pi$
$977$	14.4435	+	32.4406i	0.462088	+	1.03787i	−0.520802	+	0.853677i	$0.674367\pi$
$978$	4.03811	−	16.1401i	0.129124	−	0.516104i
$979$	−3.00573	−	2.78306i	−0.0960635	−	0.0889471i
$980$	15.2021	+	16.4600i	0.485612	+	0.525795i
$981$	−39.6453	−	26.8349i	−1.26578	−	0.856772i
$982$	−20.5444	+	4.36684i	−0.655597	+	0.139352i
$983$	6.94411	−	32.6695i	0.221483	−	1.04199i	−0.717108	−	0.696962i	$-0.754535\pi$
$983$	6.94411	−	32.6695i	0.221483	−	1.04199i	0.938591	−	0.345032i	$-0.112132\pi$
$984$	−5.59920	+	7.15467i	−0.178496	+	0.228083i
$985$	−17.9190	+	40.2468i	−0.570948	+	1.28237i
$986$	−4.92810	−	15.1671i	−0.156943	−	0.483020i
$987$	11.3552	−	13.2090i	0.361438	−	0.420447i
$988$	−1.96697	−	1.42909i	−0.0625776	−	0.0454653i
$989$	6.94957	+	12.0370i	0.220984	+	0.382755i
$990$	9.25318	−	30.4745i	0.294086	−	0.968542i
$991$	7.29221	−	12.6305i	0.231645	−	0.401220i	−0.726648	−	0.687010i	$-0.758923\pi$
$991$	7.29221	−	12.6305i	0.231645	−	0.401220i	0.958292	+	0.285790i	$0.0922560\pi$
$992$	−0.113983	+	1.08447i	−0.00361896	+	0.0344321i
$993$	17.7924	−	9.44188i	0.564626	−	0.299629i
$994$	−5.42989	+	14.4173i	−0.172226	+	0.457288i
$995$	42.1867	+	58.0650i	1.33741	+	1.84078i
$996$	7.91399	+	19.6337i	0.250764	+	0.622117i
$997$	−3.66956	+	17.2639i	−0.116216	+	0.546754i	0.881061	+	0.473003i	$0.156830\pi$
$997$	−3.66956	+	17.2639i	−0.116216	+	0.546754i	−0.997277	+	0.0737505i	$0.976503\pi$
$998$	−15.2981	−	16.9903i	−0.484254	−	0.537819i
$999$	4.25732	+	4.75145i	0.134696	+	0.150329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.95.8	✓	128
3.2	odd	2		462.2.bc.b.95.1	yes	128
7.2	even	3	inner	462.2.bc.a.359.13	yes	128
11.8	odd	10		462.2.bc.b.305.11	yes	128
21.2	odd	6		462.2.bc.b.359.11	yes	128
33.8	even	10	inner	462.2.bc.a.305.13	yes	128
77.30	odd	30		462.2.bc.b.107.1	yes	128
231.107	even	30	inner	462.2.bc.a.107.8	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.8	✓	128	1.1	even	1	trivial
462.2.bc.a.107.8	yes	128	231.107	even	30	inner
462.2.bc.a.305.13	yes	128	33.8	even	10	inner
462.2.bc.a.359.13	yes	128	7.2	even	3	inner
462.2.bc.b.95.1	yes	128	3.2	odd	2
462.2.bc.b.107.1	yes	128	77.30	odd	30
462.2.bc.b.305.11	yes	128	11.8	odd	10
462.2.bc.b.359.11	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)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.0618530 - 1.73095i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.30191 - 2.92414i) q^{5} +(-1.71500 - 0.242447i) q^{6} +(-2.04556 + 1.67800i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.99235 - 0.214128i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.0618530 - 1.73095i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.30191 - 2.92414i) q^{5} +(-1.71500 - 0.242447i) q^{6} +(-2.04556 + 1.67800i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.99235 - 0.214128i) q^{9} +(-2.77204 - 1.60044i) q^{10} +(-0.980906 - 3.16825i) q^{11} +(-0.420385 + 1.68026i) q^{12} +(-0.203849 + 0.280574i) q^{13} +(1.45499 + 2.20975i) q^{14} +(-4.98101 - 2.43441i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.764996 + 7.27845i) q^{17} +(-0.525741 + 2.95357i) q^{18} +(-1.45757 - 6.85733i) q^{19} +(-1.88143 + 2.58956i) q^{20} +(2.77800 + 3.64455i) q^{21} +(-3.25343 + 0.644360i) q^{22} +(6.50747 - 3.75709i) q^{23} +(1.62711 + 0.593717i) q^{24} +(-3.50999 - 3.89823i) q^{25} +(0.257729 + 0.232060i) q^{26} +(-0.555730 + 5.16635i) q^{27} +(2.34974 - 1.21603i) q^{28} +(-0.673371 - 2.07242i) q^{29} +(-2.94173 + 4.69926i) q^{30} +(-0.996173 + 0.443525i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.54475 + 1.50193i) q^{33} +7.31854 q^{34} +(2.24357 + 8.16612i) q^{35} +(2.88244 + 0.831593i) q^{36} +(0.821546 - 0.912419i) q^{37} +(-6.97212 + 0.732799i) q^{38} +(0.473050 + 0.370206i) q^{39} +(2.37871 + 2.14180i) q^{40} +(-1.62090 + 4.98861i) q^{41} +(3.91496 - 2.38182i) q^{42} +1.84972i q^{43} +(0.300754 + 3.30296i) q^{44} +(-4.52192 + 8.47128i) q^{45} +(-3.05629 - 6.86454i) q^{46} +(-0.790295 - 3.71805i) q^{47} +(0.760545 - 1.55614i) q^{48} +(1.36864 - 6.86490i) q^{49} +(-4.24377 + 3.08328i) q^{50} +(12.6459 - 0.873973i) q^{51} +(0.257729 - 0.232060i) q^{52} +(-2.42620 - 5.44933i) q^{53} +(5.07996 + 1.09272i) q^{54} +(-10.5415 - 1.25648i) q^{55} +(-0.963758 - 2.46397i) q^{56} +(-11.9598 + 2.09883i) q^{57} +(-2.13146 + 0.453055i) q^{58} +(1.23315 - 5.80153i) q^{59} +(4.36602 + 3.41682i) q^{60} +(0.0447633 - 0.100540i) q^{61} +(0.336967 + 1.03708i) q^{62} +(6.48034 - 4.58314i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.555045 + 0.961366i) q^{65} +(0.914118 + 5.67137i) q^{66} +(5.60173 - 9.70248i) q^{67} +(0.764996 - 7.27845i) q^{68} +(-6.10081 - 11.4965i) q^{69} +(8.35590 - 1.37768i) q^{70} +(3.42260 + 4.71081i) q^{71} +(1.12833 - 2.77972i) q^{72} +(-0.794456 + 3.73762i) q^{73} +(-0.821546 - 0.912419i) q^{74} +(-6.96474 + 5.83448i) q^{75} +7.01052i q^{76} +(7.32283 + 4.83490i) q^{77} +(0.417625 - 0.431761i) q^{78} +(-6.66607 - 0.700632i) q^{79} +(2.37871 - 2.14180i) q^{80} +(8.90830 + 1.28149i) q^{81} +(4.79185 + 2.13347i) q^{82} +(9.88760 - 7.18376i) q^{83} +(-1.95955 - 4.14248i) q^{84} +(22.2792 + 7.23895i) q^{85} +(1.83959 + 0.193349i) q^{86} +(-3.62890 + 1.03738i) q^{87} +(3.31630 + 0.0461467i) q^{88} +(1.06962 - 0.617544i) q^{89} +(7.95220 + 5.38264i) q^{90} +(-0.0538172 - 0.915989i) q^{91} +(-7.14641 + 2.32201i) q^{92} +(0.706101 + 1.75175i) q^{93} +(-3.78029 + 0.397324i) q^{94} +(-21.9494 - 4.66550i) q^{95} +(-1.46812 - 0.919039i) q^{96} +(-8.00898 - 5.81887i) q^{97} +(-6.68423 - 2.07872i) q^{98} +(2.25680 + 9.69055i) 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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