LMFDB - Embedded newform 462.2.bc.a.95.4

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			95.4
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.a.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(-1.41798 - 0.994648i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.12093 + 2.51765i) q^{5} +(-1.13742 + 1.30625i) q^{6} +(2.40939 - 1.09308i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.02135 + 2.82079i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(-1.41798 - 0.994648i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.12093 + 2.51765i) q^{5} +(-1.13742 + 1.30625i) q^{6} +(2.40939 - 1.09308i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.02135 + 2.82079i) q^{9} +(2.38669 + 1.37795i) q^{10} +(3.22424 - 0.777358i) q^{11} +(1.18020 + 1.26773i) q^{12} +(0.533779 - 0.734683i) q^{13} +(-0.835242 - 2.51045i) q^{14} +(4.09363 - 2.45505i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.233441 + 2.22105i) q^{17} +(2.91210 - 0.720902i) q^{18} +(-1.38320 - 6.50747i) q^{19} +(1.61988 - 2.22958i) q^{20} +(-4.50371 - 0.846530i) q^{21} +(-0.436075 - 3.28783i) q^{22} +(4.85329 - 2.80205i) q^{23} +(1.38415 - 1.04122i) q^{24} +(-1.73642 - 1.92849i) q^{25} +(-0.674863 - 0.607650i) q^{26} +(1.35744 - 5.01571i) q^{27} +(-2.58401 + 0.568253i) q^{28} +(1.35518 + 4.17081i) q^{29} +(-2.01370 - 4.32783i) q^{30} +(-0.217640 + 0.0968995i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.34511 - 2.10470i) q^{33} +2.23328 q^{34} +(0.0512330 + 7.29127i) q^{35} +(-0.412556 - 2.97150i) q^{36} +(7.25637 - 8.05901i) q^{37} +(-6.61640 + 0.695412i) q^{38} +(-1.48764 + 0.510846i) q^{39} +(-2.04804 - 1.84406i) q^{40} +(1.32308 - 4.07202i) q^{41} +(-1.31266 + 4.39055i) q^{42} +8.42414i q^{43} +(-3.31540 + 0.0900140i) q^{44} +(-8.24661 - 0.590505i) q^{45} +(-2.27939 - 5.11959i) q^{46} +(2.18126 + 10.2620i) q^{47} +(-0.890832 - 1.48540i) q^{48} +(4.61035 - 5.26732i) q^{49} +(-2.09943 + 1.52532i) q^{50} +(1.87814 - 3.38160i) q^{51} +(-0.674863 + 0.607650i) q^{52} +(-1.15816 - 2.60126i) q^{53} +(-4.84634 - 1.87429i) q^{54} +(-1.65703 + 8.98886i) q^{55} +(0.295038 + 2.62925i) q^{56} +(-4.51128 + 10.6033i) q^{57} +(4.28962 - 0.911786i) q^{58} +(1.31314 - 6.17786i) q^{59} +(-4.51461 + 1.55029i) q^{60} +(1.19589 - 2.68601i) q^{61} +(0.0736192 + 0.226576i) q^{62} +(5.54418 + 5.67997i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.25135 + 2.16739i) q^{65} +(-2.65189 + 5.09583i) q^{66} +(2.80878 - 4.86495i) q^{67} +(0.233441 - 2.22105i) q^{68} +(-9.66893 - 0.854061i) q^{69} +(7.25668 + 0.711193i) q^{70} +(2.57763 + 3.54780i) q^{71} +(-2.99834 + 0.0996895i) q^{72} +(-2.21647 + 10.4277i) q^{73} +(-7.25637 - 8.05901i) q^{74} +(0.544043 + 4.46168i) q^{75} +6.65285i q^{76} +(6.91874 - 5.39731i) q^{77} +(0.352547 + 1.53289i) q^{78} +(4.75825 + 0.500112i) q^{79} +(-2.04804 + 1.84406i) q^{80} +(-6.91369 + 5.76202i) q^{81} +(-3.91141 - 1.74147i) q^{82} +(-3.07387 + 2.23330i) q^{83} +(4.22929 + 1.76440i) q^{84} +(-5.85348 - 1.90191i) q^{85} +(8.37800 + 0.880563i) q^{86} +(2.22687 - 7.26206i) q^{87} +(-0.257033 + 3.30665i) q^{88} +(3.00107 - 1.73267i) q^{89} +(-1.44928 + 8.13971i) q^{90} +(0.483015 - 2.35360i) q^{91} +(-5.32981 + 1.73176i) q^{92} +(0.404991 + 0.0790733i) q^{93} +(10.4338 - 1.09664i) q^{94} +(17.9340 + 3.81199i) q^{95} +(-1.57038 + 0.730685i) q^{96} +(14.4550 + 10.5022i) q^{97} +(-4.75655 - 5.13568i) q^{98} +(5.48584 + 8.30094i) 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
$3$	−1.41798	−	0.994648i	−0.818673	−	0.574260i
$3$	−1.41798	−	0.994648i	−0.818673	−	0.574260i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−1.12093	+	2.51765i	−0.501295	+	1.12593i	0.468823	+	0.883292i	$0.344678\pi$
$5$	−1.12093	+	2.51765i	−0.501295	+	1.12593i	−0.970118	+	0.242634i	$0.921988\pi$
$6$	−1.13742	+	1.30625i	−0.464349	+	0.533273i
$7$	2.40939	−	1.09308i	0.910665	−	0.413146i
$7$	2.40939	−	1.09308i	0.910665	−	0.413146i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	1.02135	+	2.82079i	0.340450	+	0.940263i
$10$	2.38669	+	1.37795i	0.754737	+	0.435747i
$11$	3.22424	−	0.777358i	0.972145	−	0.234382i
$11$	3.22424	−	0.777358i	0.972145	−	0.234382i
$12$	1.18020	+	1.26773i	0.340694	+	0.365962i
$13$	0.533779	−	0.734683i	0.148044	−	0.203764i	−0.728554	−	0.684988i	$-0.759807\pi$
$13$	0.533779	−	0.734683i	0.148044	−	0.203764i	0.876598	+	0.481224i	$0.159807\pi$
$14$	−0.835242	−	2.51045i	−0.223228	−	0.670947i
$15$	4.09363	−	2.45505i	1.05697	−	0.633891i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.233441	+	2.22105i	0.0566178	+	0.538683i	0.985664	+	0.168719i	$0.0539631\pi$
$17$	0.233441	+	2.22105i	0.0566178	+	0.538683i	−0.929046	+	0.369963i	$0.879370\pi$
$18$	2.91210	−	0.720902i	0.686388	−	0.169918i
$19$	−1.38320	−	6.50747i	−0.317329	−	1.49291i	−0.790783	−	0.612097i	$-0.790326\pi$
$19$	−1.38320	−	6.50747i	−0.317329	−	1.49291i	0.473454	−	0.880818i	$-0.343007\pi$
$20$	1.61988	−	2.22958i	0.362217	−	0.498549i
$21$	−4.50371	−	0.846530i	−0.982790	−	0.184728i
$22$	−0.436075	−	3.28783i	−0.0929715	−	0.700968i
$23$	4.85329	−	2.80205i	1.01198	−	0.584267i	0.100209	−	0.994966i	$-0.468049\pi$
$23$	4.85329	−	2.80205i	1.01198	−	0.584267i	0.911771	+	0.410699i	$0.134715\pi$
$24$	1.38415	−	1.04122i	0.282538	−	0.212538i
$25$	−1.73642	−	1.92849i	−0.347283	−	0.385697i
$26$	−0.674863	−	0.607650i	−0.132352	−	0.119170i
$27$	1.35744	−	5.01571i	0.261239	−	0.965274i
$28$	−2.58401	+	0.568253i	−0.488331	+	0.107390i
$29$	1.35518	+	4.17081i	0.251650	+	0.774500i	0.994471	+	0.105010i	$0.0334874\pi$
$29$	1.35518	+	4.17081i	0.251650	+	0.774500i	−0.742821	+	0.669490i	$0.766513\pi$
$30$	−2.01370	−	4.32783i	−0.367650	−	0.790150i
$31$	−0.217640	+	0.0968995i	−0.0390893	+	0.0174037i	−0.426188	−	0.904635i	$-0.640144\pi$
$31$	−0.217640	+	0.0968995i	−0.0390893	+	0.0174037i	0.387099	+	0.922038i	$0.373477\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−5.34511	−	2.10470i	−0.930465	−	0.366382i
$34$	2.23328			0.383004
$35$	0.0512330	+	7.29127i	0.00865996	+	1.23245i
$36$	−0.412556	−	2.97150i	−0.0687593	−	0.495250i
$37$	7.25637	−	8.05901i	1.19294	−	1.32489i	0.259678	−	0.965695i	$-0.416383\pi$
$37$	7.25637	−	8.05901i	1.19294	−	1.32489i	0.933261	−	0.359199i	$-0.116950\pi$
$38$	−6.61640	+	0.695412i	−1.07332	+	0.112811i
$39$	−1.48764	+	0.510846i	−0.238213	+	0.0818008i
$40$	−2.04804	−	1.84406i	−0.323823	−	0.291572i
$41$	1.32308	−	4.07202i	0.206630	−	0.635942i	−0.793012	−	0.609205i	$-0.791488\pi$
$41$	1.32308	−	4.07202i	0.206630	−	0.635942i	0.999643	−	0.0267365i	$-0.00851151\pi$
$42$	−1.31266	+	4.39055i	−0.202548	+	0.677477i
$43$			8.42414i			1.28467i	0.766424	+	0.642335i	$0.222034\pi$
$43$			8.42414i			1.28467i	−0.766424	+	0.642335i	$0.777966\pi$
$44$	−3.31540	+	0.0900140i	−0.499816	+	0.0135701i
$45$	−8.24661	−	0.590505i	−1.22933	−	0.0880273i
$46$	−2.27939	−	5.11959i	−0.336078	−	0.754843i
$47$	2.18126	+	10.2620i	0.318169	+	1.49687i	0.788862	+	0.614571i	$0.210671\pi$
$47$	2.18126	+	10.2620i	0.318169	+	1.49687i	−0.470692	+	0.882297i	$0.655996\pi$
$48$	−0.890832	−	1.48540i	−0.128580	−	0.214399i
$49$	4.61035	−	5.26732i	0.658621	−	0.752474i
$50$	−2.09943	+	1.52532i	−0.296904	+	0.215713i
$51$	1.87814	−	3.38160i	0.262993	−	0.473518i
$52$	−0.674863	+	0.607650i	−0.0935867	+	0.0842659i
$53$	−1.15816	−	2.60126i	−0.159085	−	0.357311i	0.816364	−	0.577538i	$-0.195987\pi$
$53$	−1.15816	−	2.60126i	−0.159085	−	0.357311i	−0.975448	+	0.220228i	$0.929320\pi$
$54$	−4.84634	−	1.87429i	−0.659504	−	0.255058i
$55$	−1.65703	+	8.98886i	−0.223434	+	1.21206i
$56$	0.295038	+	2.62925i	0.0394261	+	0.351348i
$57$	−4.51128	+	10.6033i	−0.597534	+	1.40444i
$58$	4.28962	−	0.911786i	0.563254	−	0.119723i
$59$	1.31314	−	6.17786i	0.170957	−	0.804288i	−0.806179	−	0.591672i	$-0.798468\pi$
$59$	1.31314	−	6.17786i	0.170957	−	0.804288i	0.977136	−	0.212617i	$-0.0681985\pi$
$60$	−4.51461	+	1.55029i	−0.582834	+	0.200141i
$61$	1.19589	−	2.68601i	0.153118	−	0.343909i	−0.820657	−	0.571421i	$-0.806392\pi$
$61$	1.19589	−	2.68601i	0.153118	−	0.343909i	0.973775	+	0.227512i	$0.0730591\pi$
$62$	0.0736192	+	0.226576i	0.00934964	+	0.0287752i
$63$	5.54418	+	5.67997i	0.698501	+	0.715609i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.25135	+	2.16739i	0.155210	+	0.268832i
$66$	−2.65189	+	5.09583i	−0.326425	+	0.627253i
$67$	2.80878	−	4.86495i	0.343147	−	0.594348i	−0.641868	−	0.766815i	$-0.721840\pi$
$67$	2.80878	−	4.86495i	0.343147	−	0.594348i	0.985015	+	0.172467i	$0.0551737\pi$
$68$	0.233441	−	2.22105i	0.0283089	−	0.269341i
$69$	−9.66893	−	0.854061i	−1.16400	−	0.102817i
$70$	7.25668	+	0.711193i	0.867339	+	0.0850038i
$71$	2.57763	+	3.54780i	0.305909	+	0.421047i	0.934100	−	0.357012i	$-0.116204\pi$
$71$	2.57763	+	3.54780i	0.305909	+	0.421047i	−0.628191	+	0.778059i	$0.716204\pi$
$72$	−2.99834	+	0.0996895i	−0.353358	+	0.0117485i
$73$	−2.21647	+	10.4277i	−0.259418	+	1.22047i	0.634744	+	0.772722i	$0.281105\pi$
$73$	−2.21647	+	10.4277i	−0.259418	+	1.22047i	−0.894162	+	0.447743i	$0.852228\pi$
$74$	−7.25637	−	8.05901i	−0.843536	−	0.936841i
$75$	0.544043	+	4.46168i	0.0628207	+	0.515191i
$76$			6.65285i			0.763134i
$77$	6.91874	−	5.39731i	0.788464	−	0.615081i
$78$	0.352547	+	1.53289i	0.0399181	+	0.173565i
$79$	4.75825	+	0.500112i	0.535345	+	0.0562670i	0.368344	−	0.929690i	$-0.379925\pi$
$79$	4.75825	+	0.500112i	0.535345	+	0.0562670i	0.167001	+	0.985957i	$0.446592\pi$
$80$	−2.04804	+	1.84406i	−0.228978	+	0.206173i
$81$	−6.91369	+	5.76202i	−0.768188	+	0.640224i
$82$	−3.91141	−	1.74147i	−0.431943	−	0.192313i
$83$	−3.07387	+	2.23330i	−0.337402	+	0.245137i	−0.743565	−	0.668664i	$-0.766866\pi$
$83$	−3.07387	+	2.23330i	−0.337402	+	0.245137i	0.406163	+	0.913801i	$0.366866\pi$
$84$	4.22929	+	1.76440i	0.461453	+	0.192512i
$85$	−5.85348	−	1.90191i	−0.634899	−	0.206291i
$86$	8.37800	+	0.880563i	0.903423	+	0.0949535i
$87$	2.22687	−	7.26206i	0.238745	−	0.778575i
$88$	−0.257033	+	3.30665i	−0.0273998	+	0.352490i
$89$	3.00107	−	1.73267i	0.318112	−	0.183662i	−0.332439	−	0.943125i	$-0.607871\pi$
$89$	3.00107	−	1.73267i	0.318112	−	0.183662i	0.650551	+	0.759463i	$0.274538\pi$
$90$	−1.44928	+	8.13971i	−0.152767	+	0.858001i
$91$	0.483015	−	2.35360i	0.0506337	−	0.246725i
$92$	−5.32981	+	1.73176i	−0.555671	+	0.180548i
$93$	0.404991	+	0.0790733i	0.0419956	+	0.00819952i
$94$	10.4338	−	1.09664i	1.07616	−	0.113109i
$95$	17.9340	+	3.81199i	1.83999	+	0.391101i
$96$	−1.57038	+	0.730685i	−0.160276	+	0.0745752i
$97$	14.4550	+	10.5022i	1.46768	+	1.06633i	0.981277	+	0.192603i	$0.0616928\pi$
$97$	14.4550	+	10.5022i	1.46768	+	1.06633i	0.486407	+	0.873732i	$0.338307\pi$
$98$	−4.75655	−	5.13568i	−0.480484	−	0.518782i
$99$	5.48584	+	8.30094i	0.551347	+	0.834276i
$100$	1.29752	+	2.24736i	0.129752	+	0.224736i
$101$	−13.8161	+	6.15131i	−1.37475	+	0.612078i	−0.955283	−	0.295692i	$-0.904450\pi$
$101$	−13.8161	+	6.15131i	−1.37475	+	0.612078i	−0.419467	+	0.907770i	$0.637783\pi$
$102$	−3.16675	−	2.22133i	−0.313555	−	0.219944i
$103$	−0.929037	+	1.03180i	−0.0915408	+	0.101666i	−0.787175	−	0.616730i	$-0.788457\pi$
$103$	−0.929037	+	1.03180i	−0.0915408	+	0.101666i	0.695634	+	0.718397i	$0.255124\pi$
$104$	0.533779	+	0.734683i	0.0523413	+	0.0720416i
$105$	7.17960	−	10.3899i	0.700657	−	1.01395i
$106$	−2.70807	+	0.879905i	−0.263031	+	0.0854640i
$107$	3.96332	−	0.842430i	0.383149	−	0.0814408i	−0.0123107	−	0.999924i	$-0.503919\pi$
$107$	3.96332	−	0.842430i	0.383149	−	0.0814408i	0.395459	+	0.918483i	$0.370585\pi$
$108$	−2.37060	+	4.62388i	−0.228111	+	0.444933i
$109$	0.347989	+	0.200911i	0.0333313	+	0.0192438i	0.516573	−	0.856243i	$-0.327207\pi$
$109$	0.347989	+	0.200911i	0.0333313	+	0.0192438i	−0.483242	+	0.875487i	$0.660541\pi$
$110$	8.76641	+	2.58754i	0.835845	+	0.246713i
$111$	−18.3053	+	4.21001i	−1.73746	+	0.399596i
$112$	2.64569	−	0.0185902i	0.249994	−	0.00175661i
$113$	−17.6802	−	5.74465i	−1.66321	−	0.540411i	−0.681672	−	0.731658i	$-0.738747\pi$
$113$	−17.6802	−	5.74465i	−1.66321	−	0.540411i	−0.981542	+	0.191247i	$0.938747\pi$
$114$	10.0736	+	5.59491i	0.943482	+	0.524011i
$115$	1.61438	+	15.3598i	0.150541	+	1.43231i
$116$	−0.458404	−	4.36142i	−0.0425618	−	0.404948i
$117$	2.61756	+	0.755308i	0.241993	+	0.0698282i
$118$	−6.00675	−	1.95171i	−0.552966	−	0.179670i
$119$	2.99023	+	5.09620i	0.274114	+	0.467168i
$120$	1.06989	+	4.65193i	0.0976672	+	0.424661i
$121$	9.79143	−	5.01278i	0.890130	−	0.455707i
$122$	−2.54629	−	1.47010i	−0.230531	−	0.133097i
$123$	−5.92632	+	4.45805i	−0.534359	+	0.401969i
$124$	0.233031	−	0.0495322i	0.0209268	−	0.00444812i
$125$	−6.30348	+	2.04812i	−0.563800	+	0.183190i
$126$	6.22838	−	4.92009i	0.554868	−	0.438316i
$127$	−3.41705	−	4.70316i	−0.303214	−	0.417338i	0.630036	−	0.776566i	$-0.283040\pi$
$127$	−3.41705	−	4.70316i	−0.303214	−	0.417338i	−0.933250	+	0.359228i	$0.883040\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	8.37906	−	11.9453i	0.737735	−	1.05172i
$130$	2.28632	−	1.01794i	0.200524	−	0.0892789i
$131$	−8.02200	−	13.8945i	−0.700885	−	1.21397i	−0.968156	−	0.250347i	$-0.919455\pi$
$131$	−8.02200	−	13.8945i	−0.700885	−	1.21397i	0.267271	−	0.963621i	$-0.413878\pi$
$132$	4.79072	+	3.17002i	0.416978	+	0.275915i
$133$	−10.4459	−	14.1671i	−0.905771	−	1.22844i
$134$	−4.54470	−	3.30192i	−0.392602	−	0.285242i
$135$	11.1062	+	9.03980i	0.955870	+	0.778023i
$136$	−2.18448	−	0.464325i	−0.187317	−	0.0398155i
$137$	−9.04595	+	0.950767i	−0.772848	+	0.0812295i	−0.482739	−	0.875764i	$-0.660358\pi$
$137$	−9.04595	+	0.950767i	−0.772848	+	0.0812295i	−0.290108	+	0.956994i	$0.593691\pi$
$138$	−1.86006	+	9.52669i	−0.158339	+	0.810965i
$139$	−15.7296	+	5.11087i	−1.33417	+	0.433498i	−0.887338	−	0.461119i	$-0.847448\pi$
$139$	−15.7296	+	5.11087i	−1.33417	+	0.433498i	−0.446832	+	0.894618i	$0.647448\pi$
$140$	1.46583	−	7.14259i	0.123885	−	0.603659i
$141$	7.11411	−	16.7209i	0.599116	−	1.40816i
$142$	3.79781	−	2.19266i	0.318705	−	0.184004i
$143$	1.14992	−	2.78373i	0.0961609	−	0.232787i
$144$	−0.214269	+	2.99234i	−0.0178557	+	0.249362i
$145$	−12.0197	−	1.26332i	−0.998181	−	0.104913i
$146$	10.1389	+	3.29431i	0.839097	+	0.272639i
$147$	−11.7765	+	2.88329i	−0.971312	+	0.237810i
$148$	−8.77336	+	6.37422i	−0.721166	+	0.523958i
$149$	−13.6840	−	6.09250i	−1.12104	−	0.499117i	−0.239340	−	0.970936i	$-0.576931\pi$
$149$	−13.6840	−	6.09250i	−1.12104	−	0.499117i	−0.881696	+	0.471818i	$0.843598\pi$
$150$	4.49411	−	0.0746899i	0.366942	−	0.00609840i
$151$	−3.87172	+	3.48611i	−0.315076	+	0.283696i	−0.811461	−	0.584407i	$-0.801327\pi$
$151$	−3.87172	+	3.48611i	−0.315076	+	0.283696i	0.496385	+	0.868103i	$0.334661\pi$
$152$	6.61640	+	0.695412i	0.536661	+	0.0564053i
$153$	−6.02667	+	2.92695i	−0.487228	+	0.236630i
$154$	−4.64454	−	7.44501i	−0.374268	−	0.599936i
$155$		−	0.656558i		−	0.0527360i
$156$	1.56134	−	0.190385i	0.125007	−	0.0152430i
$157$	0.797111	+	0.885281i	0.0636164	+	0.0706532i	0.774113	−	0.633048i	$-0.218196\pi$
$157$	0.797111	+	0.885281i	0.0636164	+	0.0706532i	−0.710497	+	0.703701i	$0.751530\pi$
$158$	0.994745	−	4.67991i	0.0791377	−	0.372314i
$159$	−0.945094	+	4.84050i	−0.0749509	+	0.383877i
$160$	1.61988	+	2.22958i	0.128063	+	0.176264i
$161$	8.63061	−	12.0563i	0.680188	−	0.950167i
$162$	5.00778	+	7.47811i	0.393448	+	0.587536i
$163$	−1.19889	+	11.4067i	−0.0939045	+	0.893441i	0.841594	+	0.540111i	$0.181618\pi$
$163$	−1.19889	+	11.4067i	−0.0939045	+	0.893441i	−0.935499	+	0.353331i	$0.885049\pi$
$164$	−2.14079	+	3.70795i	−0.167167	+	0.289542i
$165$	11.2904	−	11.0979i	0.878956	−	0.863969i
$166$	1.89976	+	3.29048i	0.147450	+	0.255391i
$167$	13.4155	+	9.74696i	1.03813	+	0.754243i	0.969919	−	0.243429i	$-0.0782721\pi$
$167$	13.4155	+	9.74696i	1.03813	+	0.754243i	0.0682071	+	0.997671i	$0.478272\pi$
$168$	2.19682	−	4.02169i	0.169488	−	0.310280i
$169$	3.76238	+	11.5794i	0.289414	+	0.890725i
$170$	−2.50335	+	5.62261i	−0.191998	+	0.431235i
$171$	16.9434	−	10.5481i	1.29570	−	0.806635i
$172$	1.75148	−	8.24006i	0.133549	−	0.628298i
$173$	−11.1481	+	2.36959i	−0.847572	+	0.180157i	−0.611171	−	0.791499i	$-0.709301\pi$
$173$	−11.1481	+	2.36959i	−0.847572	+	0.180157i	−0.236401	+	0.971656i	$0.575968\pi$
$174$	−6.98951	−	2.97376i	−0.529873	−	0.225440i
$175$	−6.29170	−	2.74844i	−0.475608	−	0.207762i
$176$	3.26167	+	0.601264i	0.245858	+	0.0453220i
$177$	−8.00681	+	7.45398i	−0.601829	+	0.560275i
$178$	−1.40948	−	3.16574i	−0.105645	−	0.237282i
$179$	−7.34748	+	6.61570i	−0.549176	+	0.494481i	−0.896366	−	0.443314i	$-0.853803\pi$
$179$	−7.34748	+	6.61570i	−0.549176	+	0.494481i	0.347190	+	0.937795i	$0.387136\pi$
$180$	7.94363	+	2.29217i	0.592083	+	0.170848i
$181$	12.4958	−	9.07875i	0.928807	−	0.674818i	−0.0168932	−	0.999857i	$-0.505378\pi$
$181$	12.4958	−	9.07875i	0.928807	−	0.674818i	0.945701	+	0.325039i	$0.105378\pi$
$182$	−2.29022	−	0.726387i	−0.169762	−	0.0538434i
$183$	−4.36739	+	2.61923i	−0.322847	+	0.193619i
$184$	1.16516	+	5.48163i	0.0858965	+	0.404111i
$185$	12.1559	+	27.3026i	0.893718	+	2.00732i
$186$	0.120973	−	0.394507i	0.00887019	−	0.0289266i
$187$	2.47922	+	6.97971i	0.181298	+	0.510407i
$188$		−	10.4913i		−	0.765155i
$189$	−2.21198	−	13.5686i	−0.160898	−	0.986971i
$190$	5.66571	−	17.4373i	0.411034	−	1.26503i
$191$	−15.2558	−	13.7364i	−1.10387	−	0.993932i	−0.103873	−	0.994591i	$-0.533124\pi$
$191$	−15.2558	−	13.7364i	−1.10387	−	0.993932i	−1.00000		0.000658696i	$0.999790\pi$
$192$	0.562532	+	1.63816i	0.0405973	+	0.118224i
$193$	−23.7227	+	2.49336i	−1.70760	+	0.179476i	−0.907403	−	0.420263i	$-0.861938\pi$
$193$	−23.7227	+	2.49336i	−1.70760	+	0.179476i	−0.800196	+	0.599738i	$0.795271\pi$
$194$	11.9556	−	13.2780i	0.858363	−	0.953308i
$195$	0.381409	−	4.31798i	0.0273132	−	0.309217i
$196$	−5.60474	+	4.19367i	−0.400339	+	0.299548i
$197$	16.7596			1.19407			0.597037	−	0.802214i	$-0.296344\pi$
$197$	16.7596			1.19407			0.597037	+	0.802214i	$0.296344\pi$
$198$	8.82889	−	4.58810i	0.627442	−	0.326062i
$199$	11.4850	−	19.8927i	0.814152	−	1.41015i	−0.0957828	−	0.995402i	$-0.530535\pi$
$199$	11.4850	−	19.8927i	0.814152	−	1.41015i	0.909935	−	0.414751i	$-0.136131\pi$
$200$	2.37068	−	1.05550i	0.167632	−	0.0746348i
$201$	−8.82171	+	4.10467i	−0.622236	+	0.289521i
$202$	4.67344	+	14.3834i	0.328822	+	1.01201i
$203$	7.82419	+	8.56780i	0.549150	+	0.601342i
$204$	−2.54018	+	2.91721i	−0.177848	+	0.204246i
$205$	8.76882	+	7.89548i	0.612441	+	0.551445i
$206$	0.929037	+	1.03180i	0.0647291	+	0.0718889i
$207$	12.8609	+	10.8282i	0.893893	+	0.752614i
$208$	0.786453	−	0.454059i	0.0545307	−	0.0314833i
$209$	−9.51841	−	19.9064i	−0.658402	−	1.37695i
$210$	−9.58246	−	8.22631i	−0.661253	−	0.567669i
$211$	14.6884	−	20.2169i	1.01119	−	1.39179i	0.0929963	−	0.995666i	$-0.470356\pi$
$211$	14.6884	−	20.2169i	1.01119	−	1.39179i	0.918198	−	0.396123i	$-0.129644\pi$
$212$	0.592015	+	2.78521i	0.0406597	+	0.191289i
$213$	−0.126218	−	7.59456i	−0.00864831	−	0.520371i
$214$	−0.423535	−	4.02967i	−0.0289523	−	0.275462i
$215$	−21.2090	−	9.44287i	−1.44644	−	0.643998i
$216$	4.35075	+	2.84094i	0.296031	+	0.193301i
$217$	−0.418461	+	0.471367i	−0.0284070	+	0.0319985i
$218$	0.236186	−	0.325082i	0.0159965	−	0.0220173i
$219$	13.5148	−	12.5816i	0.913243	−	0.850188i
$220$	3.48971	−	8.44792i	0.235276	−	0.569558i
$221$	1.75637	+	1.01404i	0.118146	+	0.0682118i
$222$	2.27352	+	18.6451i	0.152589	+	1.25138i
$223$	−6.29557	+	19.3758i	−0.421582	+	1.29750i	0.484646	+	0.874710i	$0.338948\pi$
$223$	−6.29557	+	19.3758i	−0.421582	+	1.29750i	−0.906229	+	0.422787i	$0.861052\pi$
$224$	0.258061	−	2.63314i	0.0172424	−	0.175934i
$225$	3.66636	−	6.86772i	0.244424	−	0.457848i
$226$	−7.56126	+	16.9829i	−0.502968	+	1.12968i
$227$	−3.61620	−	0.768647i	−0.240016	−	0.0510169i	0.0863331	−	0.996266i	$-0.472485\pi$
$227$	−3.61620	−	0.768647i	−0.240016	−	0.0510169i	−0.326349	+	0.945249i	$0.605818\pi$
$228$	6.61724	−	9.43362i	0.438238	−	0.624757i
$229$	1.37888	−	13.1192i	0.0911190	−	0.866940i	−0.849526	−	0.527547i	$-0.823112\pi$
$229$	1.37888	−	13.1192i	0.0911190	−	0.866940i	0.940645	−	0.339392i	$-0.110221\pi$
$230$	15.4444			1.01837
$231$	−15.1791	+	0.771580i	−0.998711	+	0.0507662i
$232$	−4.38545			−0.287919
$233$	−1.32065	+	12.5652i	−0.0865188	+	0.823171i	0.862098	+	0.506742i	$0.169150\pi$
$233$	−1.32065	+	12.5652i	−0.0865188	+	0.823171i	−0.948616	+	0.316429i	$0.897516\pi$
$234$	1.02478	−	2.52427i	0.0669920	−	0.165017i
$235$	−28.2812	−	6.01135i	−1.84486	−	0.392137i
$236$	−2.56890	+	5.76984i	−0.167221	+	0.375584i
$237$	−6.24968	−	5.44194i	−0.405960	−	0.353492i
$238$	5.38085	−	2.44115i	0.348789	−	0.158237i
$239$	−1.36443	+	4.19929i	−0.0882578	+	0.271630i	−0.985438	−	0.170035i	$-0.945612\pi$
$239$	−1.36443	+	4.19929i	−0.0882578	+	0.271630i	0.897180	+	0.441665i	$0.145612\pi$
$240$	4.73828	−	0.577770i	0.305855	−	0.0372949i
$241$	−9.65705	−	5.57550i	−0.622065	−	0.359150i	0.155607	−	0.987819i	$-0.450267\pi$
$241$	−9.65705	−	5.57550i	−0.622065	−	0.359150i	−0.777673	+	0.628669i	$0.783600\pi$
$242$	−3.96183	−	10.2618i	−0.254676	−	0.659651i
$243$	15.5347	−	1.29375i	0.996550	−	0.0829943i
$244$	−1.72821	+	2.37868i	−0.110637	+	0.152279i
$245$	8.09338	+	17.5115i	0.517067	+	1.11877i
$246$	3.81416	+	6.35985i	0.243182	+	0.405489i
$247$	−5.51925	−	2.45733i	−0.351181	−	0.156356i
$248$	−0.0249025	−	0.236932i	−0.00158131	−	0.0150452i
$249$	6.58005	−	0.109357i	0.416994	−	0.00693023i
$250$	1.37801	+	6.48303i	0.0871531	+	0.410023i
$251$	−14.1993	+	19.5437i	−0.896252	+	1.23359i	0.0753957	+	0.997154i	$0.475978\pi$
$251$	−14.1993	+	19.5437i	−0.896252	+	1.23359i	−0.971648	+	0.236432i	$0.924022\pi$
$252$	−4.24209	−	6.70855i	−0.267227	−	0.422599i
$253$	13.4700	−	12.8072i	0.846849	−	0.805182i
$254$	−5.03457	+	2.90671i	−0.315897	+	0.182383i
$255$	6.40840	+	8.51904i	0.401310	+	0.533483i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	3.99776	+	3.59960i	0.249373	+	0.224537i	0.784332	−	0.620342i	$-0.213006\pi$
$257$	3.99776	+	3.59960i	0.249373	+	0.224537i	−0.534958	+	0.844878i	$0.679673\pi$
$258$	−11.0040	−	9.58178i	−0.685079	−	0.596536i
$259$	8.67429	−	27.3491i	0.538994	−	1.69939i
$260$	−0.773374	−	2.38020i	−0.0479626	−	0.147614i
$261$	−10.3809	+	8.08252i	−0.642559	+	0.500296i
$262$	−14.6569	+	6.52568i	−0.905507	+	0.403158i
$263$	6.87941	−	11.9155i	0.424203	−	0.734740i	−0.572143	−	0.820154i	$-0.693888\pi$
$263$	6.87941	−	11.9155i	0.424203	−	0.734740i	0.996346	+	0.0854134i	$0.0272211\pi$
$264$	3.65342	−	4.43311i	0.224853	−	0.272839i
$265$	7.84727			0.482054
$266$	−15.1814	+	8.90778i	−0.930830	+	0.546171i
$267$	−5.97885	−	0.528115i	−0.365900	−	0.0323201i
$268$	−3.75888	+	4.17466i	−0.229610	+	0.255008i
$269$	−6.29328	+	0.661450i	−0.383708	+	0.0403293i	−0.294419	−	0.955676i	$-0.595126\pi$
$269$	−6.29328	+	0.661450i	−0.383708	+	0.0403293i	−0.0892889	+	0.996006i	$0.528459\pi$
$270$	10.1512	−	10.1004i	0.617782	−	0.614694i
$271$	1.69848	+	1.52932i	0.103175	+	0.0928996i	0.719104	−	0.694902i	$-0.244552\pi$
$271$	1.69848	+	1.52932i	0.103175	+	0.0928996i	−0.615929	+	0.787802i	$0.711219\pi$
$272$	−0.690122	+	2.12398i	−0.0418448	+	0.128785i
$273$	−3.02591	+	2.85694i	−0.183137	+	0.172910i
$274$			9.09578i			0.549496i
$275$	−7.09774	−	4.86808i	−0.428010	−	0.293556i
$276$	9.28007	+	2.84568i	0.558594	+	0.171290i
$277$	−3.73663	−	8.39261i	−0.224512	−	0.504263i	0.765807	−	0.643071i	$-0.222340\pi$
$277$	−3.73663	−	8.39261i	−0.224512	−	0.504263i	−0.990319	+	0.138807i	$0.955673\pi$
$278$	3.43868	+	16.1777i	0.206238	+	0.970274i
$279$	−0.495620	−	0.514948i	−0.0296720	−	0.0308291i
$280$	−6.95024	−	2.20440i	−0.415356	−	0.131738i
$281$	5.24984	−	3.81423i	0.313179	−	0.227538i	−0.420080	−	0.907487i	$-0.637998\pi$
$281$	5.24984	−	3.81423i	0.313179	−	0.227538i	0.733259	+	0.679949i	$0.237998\pi$
$282$	−15.8857	−	8.82295i	−0.945981	−	0.525399i
$283$	−4.90246	+	4.41420i	−0.291421	+	0.262397i	−0.801853	−	0.597521i	$-0.796152\pi$
$283$	−4.90246	+	4.41420i	−0.291421	+	0.262397i	0.510432	+	0.859918i	$0.329486\pi$
$284$	−1.78367	−	4.00620i	−0.105842	−	0.237724i
$285$	−21.6385	−	23.2433i	−1.28175	−	1.37682i
$286$	−2.64828	−	1.43460i	−0.156596	−	0.0848295i
$287$	−1.26323	−	11.2573i	−0.0745658	−	0.664498i
$288$	2.95355	+	0.525880i	0.174040	+	0.0309877i
$289$	11.7500	−	2.49753i	0.691174	−	0.146914i
$290$	−2.51280	+	11.8218i	−0.147557	+	0.694199i
$291$	−10.0510	−	29.2696i	−0.589199	−	1.71581i
$292$	4.33606	−	9.73896i	0.253749	−	0.569929i
$293$	−3.95822	−	12.1821i	−0.231241	−	0.711688i	−0.997598	−	0.0692722i	$-0.977932\pi$
$293$	−3.95822	−	12.1821i	−0.231241	−	0.711688i	0.766356	−	0.642416i	$-0.222068\pi$
$294$	1.63652	+	12.0134i	0.0954435	+	0.700636i
$295$	14.0817	+	10.2310i	0.819870	+	0.595670i
$296$	5.42224	+	9.39159i	0.315161	+	0.545875i
$297$	0.477695	−	17.2271i	0.0277187	−	0.999616i
$298$	−7.48949	+	12.9722i	−0.433855	+	0.751459i
$299$	0.531964	−	5.06130i	0.0307643	−	0.292703i
$300$	0.395482	−	4.47730i	0.0228331	−	0.258497i
$301$	9.20827	+	20.2971i	0.530756	+	1.16990i
$302$	3.06231	+	4.21491i	0.176216	+	0.242541i
$303$	25.7093	+	5.01968i	1.47696	+	0.288373i
$304$	1.38320	−	6.50747i	0.0793322	−	0.373229i
$305$	5.42193	+	6.02166i	0.310459	+	0.344799i
$306$	2.28096	+	6.29961i	0.130394	+	0.360125i
$307$		−	13.7899i		−	0.787032i	−0.919318	−	0.393516i	$-0.871259\pi$
$307$		−	13.7899i		−	0.787032i	0.919318	−	0.393516i	$-0.128741\pi$
$308$	−7.88972	+	3.84088i	−0.449558	+	0.218855i
$309$	2.34364	−	0.539010i	0.133325	−	0.0306632i
$310$	−0.652962	−	0.0686290i	−0.0370857	−	0.00389787i
$311$	22.7419	−	20.4769i	1.28957	−	1.16114i	0.312105	−	0.950048i	$-0.398966\pi$
$311$	22.7419	−	20.4769i	1.28957	−	1.16114i	0.977467	−	0.211089i	$-0.0677009\pi$
$312$	−0.0261373	−	1.57269i	−0.00147973	−	0.0890360i
$313$	−9.47181	−	4.21712i	−0.535379	−	0.238366i	0.121194	−	0.992629i	$-0.461328\pi$
$313$	−9.47181	−	4.21712i	−0.535379	−	0.238366i	−0.656572	+	0.754263i	$0.727994\pi$
$314$	0.963753	−	0.700207i	0.0543877	−	0.0395150i
$315$	−20.5148	+	7.59145i	−1.15588	+	0.427730i
$316$	−4.55029	−	1.47848i	−0.255974	−	0.0831710i
$317$	23.2914	+	2.44802i	1.30817	+	0.137495i	0.732827	−	0.680415i	$-0.238200\pi$
$317$	23.2914	+	2.44802i	1.30817	+	0.137495i	0.575347	+	0.817910i	$0.304867\pi$
$318$	4.71519	+	1.44589i	0.264415	+	0.0810813i
$319$	7.61163	+	12.3942i	0.426169	+	0.693943i
$320$	2.38669	−	1.37795i	0.133420	−	0.0770300i
$321$	−6.45784	−	2.74756i	−0.360442	−	0.153354i
$322$	−11.0881	−	9.84356i	−0.617914	−	0.548560i
$323$	14.1305	−	4.59127i	0.786241	−	0.255465i
$324$	7.96060	−	4.19867i	0.442256	−	0.233259i
$325$	−2.34369	+	0.246331i	−0.130004	+	0.0136640i
$326$	11.2189	+	2.38465i	0.621357	+	0.132073i
$327$	−0.293606	−	0.631016i	−0.0162364	−	0.0348952i
$328$	3.46386	+	2.51664i	0.191260	+	0.138958i
$329$	16.4727	+	22.3409i	0.908170	+	1.23170i
$330$	−9.85692	−	12.3886i	−0.542606	−	0.681969i
$331$	5.45074	+	9.44095i	0.299600	+	0.518922i	0.976044	−	0.217572i	$-0.0698136\pi$
$331$	5.45074	+	9.44095i	0.299600	+	0.518922i	−0.676445	+	0.736493i	$0.736480\pi$
$332$	3.47103	−	1.54540i	0.190498	−	0.0848150i
$333$	30.1441	+	12.2376i	1.65188	+	0.670617i
$334$	11.0959	−	12.3232i	0.607139	−	0.674296i
$335$	9.09979	+	12.5248i	0.497174	+	0.684302i
$336$	−3.77003	−	2.60517i	−0.205672	−	0.142123i
$337$	−24.0108	+	7.80159i	−1.30795	+	0.424979i	−0.878341	−	0.478034i	$-0.841349\pi$
$337$	−24.0108	+	7.80159i	−1.30795	+	0.424979i	−0.429611	+	0.903014i	$0.641349\pi$
$338$	11.9093	−	2.53139i	0.647778	−	0.137690i
$339$	19.3563	+	25.7314i	1.05129	+	1.39754i
$340$	5.33014	+	3.07736i	0.289067	+	0.166893i
$341$	−0.626397	+	0.481611i	−0.0339213	+	0.0260807i
$342$	−8.71927	−	17.9532i	−0.471484	−	0.970798i
$343$	5.35054	−	17.7305i	0.288902	−	0.957359i
$344$	−8.01184	−	2.60320i	−0.431969	−	0.140355i
$345$	12.9884	−	23.3856i	0.699272	−	1.25904i
$346$	1.19132	+	11.3347i	0.0640459	+	0.609356i
$347$	0.936447	+	8.90970i	0.0502711	+	0.478298i	0.990476	+	0.137688i	$0.0439670\pi$
$347$	0.936447	+	8.90970i	0.0502711	+	0.478298i	−0.940205	+	0.340610i	$0.889366\pi$
$348$	−3.68807	+	6.64038i	−0.197702	+	0.355961i
$349$	−3.82596	−	1.24313i	−0.204799	−	0.0665433i	0.204821	−	0.978799i	$-0.434339\pi$
$349$	−3.82596	−	1.24313i	−0.204799	−	0.0665433i	−0.409620	+	0.912256i	$0.634339\pi$
$350$	−3.39104	+	5.96994i	−0.181259	+	0.319107i
$351$	−2.96039	−	3.67456i	−0.158014	−	0.196134i
$352$	0.938908	−	3.18095i	0.0500439	−	0.169545i
$353$	20.7273	+	11.9669i	1.10320	+	0.636935i	0.937061	−	0.349167i	$-0.113535\pi$
$353$	20.7273	+	11.9669i	1.10320	+	0.636935i	0.166143	+	0.986102i	$0.446869\pi$
$354$	6.57620	+	8.74210i	0.349521	+	0.464637i
$355$	−11.8215	+	2.51273i	−0.627418	+	0.133362i
$356$	−3.29573	+	1.07085i	−0.174673	+	0.0567548i
$357$	0.828830	−	10.2006i	0.0438663	−	0.539871i
$358$	5.81144	+	7.99876i	0.307144	+	0.422748i
$359$	17.7065	−	19.6650i	0.934512	−	1.03788i	−0.0646884	−	0.997906i	$-0.520605\pi$
$359$	17.7065	−	19.6650i	0.934512	−	1.03788i	0.999201	−	0.0399755i	$-0.0127280\pi$
$360$	3.10995	−	7.66052i	0.163909	−	0.403745i
$361$	−23.0765	+	10.2743i	−1.21455	+	0.540753i
$362$	−7.72284	−	13.3764i	−0.405904	−	0.703046i
$363$	−18.8700	−	2.63100i	−0.990419	−	0.138092i
$364$	−0.961801	+	2.20175i	−0.0504121	+	0.115403i
$365$	−23.7687	−	17.2689i	−1.24411	−	0.903898i
$366$	2.14836	+	4.61725i	0.112297	+	0.241347i
$367$	−9.15707	−	1.94640i	−0.477995	−	0.101601i	−0.0373877	−	0.999301i	$-0.511904\pi$
$367$	−9.15707	−	1.94640i	−0.477995	−	0.101601i	−0.440608	+	0.897700i	$0.645237\pi$
$368$	5.57339	−	0.585787i	0.290533	−	0.0305363i
$369$	12.8376	−	0.426828i	0.668300	−	0.0222198i
$370$	28.4236	−	9.23540i	1.47767	−	0.480126i
$371$	−5.63384	−	5.00150i	−0.292494	−	0.259665i
$372$	−0.379700	−	0.161548i	−0.0196865	−	0.00837586i
$373$	−21.2488	+	12.2680i	−1.10022	+	0.635214i	−0.936279	−	0.351256i	$-0.885755\pi$
$373$	−21.2488	+	12.2680i	−1.10022	+	0.635214i	−0.163943	+	0.986470i	$0.552421\pi$
$374$	7.20063	−	1.73606i	0.372336	−	0.0897694i
$375$	10.9754	+	3.36554i	0.566766	+	0.173796i
$376$	−10.4338	−	1.09664i	−0.538082	−	0.0565547i
$377$	3.78759	+	1.23066i	0.195071	+	0.0633823i
$378$	−13.7255	+	0.781555i	−0.705963	+	0.0401989i
$379$	−19.2969	+	14.0200i	−0.991217	+	0.720161i	−0.960187	−	0.279357i	$-0.909879\pi$
$379$	−19.2969	+	14.0200i	−0.991217	+	0.720161i	−0.0310297	+	0.999518i	$0.509879\pi$
$380$	−16.7495	−	7.45737i	−0.859232	−	0.382555i
$381$	0.167321	+	10.0678i	0.00857212	+	0.515787i
$382$	−15.2558	+	13.7364i	−0.780556	+	0.702816i
$383$	−19.3608	−	2.03491i	−0.989293	−	0.103979i	−0.403964	−	0.914775i	$-0.632368\pi$
$383$	−19.3608	−	2.03491i	−0.989293	−	0.103979i	−0.585329	+	0.810796i	$0.699035\pi$
$384$	1.68798	−	0.388217i	0.0861395	−	0.0198111i
$385$	5.83311	+	23.4690i	0.297283	+	1.19609i
$386$			23.8534i			1.21411i
$387$	−23.7627	+	8.60399i	−1.20793	+	0.437366i
$388$	−11.9556	−	13.2780i	−0.606954	−	0.674091i
$389$	−3.11706	+	14.6646i	−0.158041	+	0.743526i	0.825725	+	0.564073i	$0.190766\pi$
$389$	−3.11706	+	14.6646i	−0.158041	+	0.743526i	−0.983766	+	0.179454i	$0.942567\pi$
$390$	−4.25445	−	0.830671i	−0.215433	−	0.0420626i
$391$	7.35643	+	10.1253i	0.372031	+	0.512056i
$392$	3.58484	+	6.01240i	0.181062	+	0.303672i
$393$	−2.44510	+	27.6812i	−0.123339	+	1.39633i
$394$	1.75186	−	16.6678i	0.0882574	−	0.839713i
$395$	−6.59277	+	11.4190i	−0.331718	+	0.574553i
$396$	−3.64010	−	9.26011i	−0.182922	−	0.465338i
$397$	12.3184	+	21.3361i	0.618243	+	1.07083i	0.989806	+	0.142421i	$0.0454887\pi$
$397$	12.3184	+	21.3361i	0.618243	+	1.07083i	−0.371563	+	0.928408i	$0.621178\pi$
$398$	−18.5832	−	13.5015i	−0.931490	−	0.676767i
$399$	0.720786	+	30.4786i	0.0360844	+	1.52584i
$400$	−0.801909	−	2.46802i	−0.0400955	−	0.123401i
$401$	−9.87635	+	22.1827i	−0.493202	+	1.10775i	0.479890	+	0.877329i	$0.340677\pi$
$401$	−9.87635	+	22.1827i	−0.493202	+	1.10775i	−0.973091	+	0.230420i	$0.925990\pi$
$402$	3.16006	+	9.20244i	0.157609	+	0.458976i
$403$	−0.0449811	+	0.211619i	−0.00224067	+	0.0105415i
$404$	14.7931	−	3.14437i	0.735984	−	0.156438i
$405$	−6.75698	−	23.8651i	−0.335757	−	1.18586i
$406$	9.33872	−	6.88575i	0.463473	−	0.341734i
$407$	17.1315	−	31.6250i	0.849178	−	1.56759i
$408$	2.63571	+	2.83119i	0.130487	+	0.140165i
$409$	10.9353	+	24.5611i	0.540715	+	1.21447i	0.952877	+	0.303356i	$0.0981070\pi$
$409$	10.9353	+	24.5611i	0.540715	+	1.21447i	−0.412162	+	0.911110i	$0.635226\pi$
$410$	8.76882	−	7.89548i	0.433061	−	0.389930i
$411$	13.7727	+	7.64937i	0.679356	+	0.377315i
$412$	1.12326	−	0.816095i	0.0553390	−	0.0402061i
$413$	−3.58901	−	16.3203i	−0.176604	−	0.803067i
$414$	12.1132	−	11.6586i	0.595333	−	0.572987i
$415$	−2.17707	−	10.2423i	−0.106868	−	0.502775i
$416$	−0.369365	−	0.829607i	−0.0181096	−	0.0406748i
$417$	27.3879	+	8.39833i	1.34119	+	0.411268i
$418$	−20.7923	+	7.38549i	−1.01698	+	0.361236i
$419$			9.11719i			0.445404i	0.974887	+	0.222702i	$0.0714877\pi$
$419$			9.11719i			0.445404i	−0.974887	+	0.222702i	$0.928512\pi$
$420$	−9.18288	+	8.67009i	−0.448079	+	0.423057i
$421$	−5.30508	+	16.3274i	−0.258554	+	0.795747i	0.734555	+	0.678550i	$0.237391\pi$
$421$	−5.30508	+	16.3274i	−0.258554	+	0.795747i	−0.993109	+	0.117198i	$0.962609\pi$
$422$	−18.5708	−	16.7212i	−0.904012	−	0.813976i
$423$	−26.7191	+	16.6340i	−1.29913	+	0.808771i
$424$	2.83184	−	0.297638i	0.137526	−	0.0144546i
$425$	3.87790	−	4.30685i	0.188106	−	0.208913i
$426$	−7.56615	−	0.668321i	−0.366581	−	0.0323803i
$427$	−0.0546591	−	7.77886i	−0.00264514	−	0.376446i
$428$	−4.05186			−0.195854
$429$	−4.39940	+	2.80352i	−0.212405	+	0.135355i
$430$	−11.6081	+	20.1058i	−0.559792	+	0.969588i
$431$	−35.8153	+	15.9460i	−1.72516	+	0.768092i	−0.728629	+	0.684909i	$0.759842\pi$
$431$	−35.8153	+	15.9460i	−1.72516	+	0.768092i	−0.996534	+	0.0831836i	$0.973491\pi$
$432$	3.28015	−	4.02996i	0.157816	−	0.193892i
$433$	−2.30058	−	7.08046i	−0.110559	−	0.340265i	0.880436	−	0.474165i	$-0.157250\pi$
$433$	−2.30058	−	7.08046i	−0.110559	−	0.340265i	−0.990995	+	0.133900i	$0.957250\pi$
$434$	0.425044	+	0.465440i	0.0204028	+	0.0223418i
$435$	15.7871	+	13.7467i	0.756936	+	0.659105i
$436$	−0.298613	−	0.268872i	−0.0143010	−	0.0128766i
$437$	−24.9473	−	27.7068i	−1.19339	−	1.32540i
$438$	−11.1000	−	14.7559i	−0.530380	−	0.705063i
$439$	24.1794	−	13.9600i	1.15402	−	0.666273i	0.204155	−	0.978939i	$-0.434555\pi$
$439$	24.1794	−	13.9600i	1.15402	−	0.666273i	0.949863	+	0.312666i	$0.101222\pi$
$440$	−8.03686	−	4.35364i	−0.383142	−	0.207552i
$441$	19.5668	+	7.62505i	0.931751	+	0.363097i
$442$	1.19208	−	1.64075i	0.0567013	−	0.0780427i
$443$	−1.21132	−	5.69881i	−0.0575516	−	0.270759i	0.939958	−	0.341290i	$-0.110864\pi$
$443$	−1.21132	−	5.69881i	−0.0575516	−	0.270759i	−0.997510	+	0.0705313i	$0.977531\pi$
$444$	18.7806	−	0.312124i	0.891287	−	0.0148128i
$445$	0.998261	+	9.49782i	0.0473221	+	0.450240i
$446$	18.6116	+	8.28640i	0.881283	+	0.392372i
$447$	13.3438	+	22.2498i	0.631138	+	1.05238i
$448$	−2.59174	−	0.531885i	−0.122448	−	0.0251292i
$449$	6.92207	−	9.52742i	0.326673	−	0.449627i	−0.613817	−	0.789448i	$-0.710367\pi$
$449$	6.92207	−	9.52742i	0.326673	−	0.449627i	0.940490	+	0.339822i	$0.110367\pi$
$450$	−6.44686	−	4.36415i	−0.303908	−	0.205728i
$451$	1.10051	−	14.1577i	0.0518208	−	0.666658i
$452$	16.0995	+	9.29503i	0.757255	+	0.437202i
$453$	8.95749	−	1.09225i	0.420860	−	0.0513183i
$454$	−1.14243	+	3.51604i	−0.0536170	+	0.165016i
$455$	5.38412	+	3.85428i	0.252411	+	0.180692i
$456$	−8.69025	−	7.56707i	−0.406958	−	0.354361i
$457$	−12.2727	+	27.5649i	−0.574092	+	1.28943i	0.360185	+	0.932881i	$0.382714\pi$
$457$	−12.2727	+	27.5649i	−0.574092	+	1.28943i	−0.934276	+	0.356550i	$0.883953\pi$
$458$	−12.9032	−	2.74265i	−0.602926	−	0.128156i
$459$	11.4570	+	1.84405i	0.534767	+	0.0860731i
$460$	1.61438	−	15.3598i	0.0752707	−	0.716153i
$461$	11.0690			0.515533			0.257767	−	0.966207i	$-0.417013\pi$
$461$	11.0690			0.515533			0.257767	+	0.966207i	$0.417013\pi$
$462$	−0.819294	+	15.1766i	−0.0381170	+	0.706079i
$463$	2.93172			0.136249			0.0681243	−	0.997677i	$-0.478299\pi$
$463$	2.93172			0.136249			0.0681243	+	0.997677i	$0.478299\pi$
$464$	−0.458404	+	4.36142i	−0.0212809	+	0.202474i
$465$	−0.653045	+	0.930988i	−0.0302842	+	0.0431735i
$466$	12.3583	+	2.62683i	0.572486	+	0.121686i
$467$	−14.5556	+	32.6924i	−0.673552	+	1.51282i	0.175480	+	0.984483i	$0.443852\pi$
$467$	−14.5556	+	32.6924i	−0.673552	+	1.51282i	−0.849033	+	0.528341i	$0.822814\pi$
$468$	−2.40332	−	1.28302i	−0.111094	−	0.0593078i
$469$	1.44967	−	14.7918i	0.0669397	−	0.683022i
$470$	−8.93461	+	27.4979i	−0.412123	+	1.26838i
$471$	−0.249746	−	2.04816i	−0.0115077	−	0.0943742i
$472$	5.46971	+	3.15794i	0.251764	+	0.145356i
$473$	6.54858	+	27.1615i	0.301104	+	1.24888i
$474$	−6.06540	+	5.64661i	−0.278593	+	0.259357i
$475$	−10.1477	+	13.9672i	−0.465610	+	0.640857i
$476$	−1.86533	−	5.60654i	−0.0854973	−	0.256975i
$477$	6.15472	−	5.92371i	0.281805	−	0.271228i
$478$	4.03367	+	1.79590i	0.184496	+	0.0821427i
$479$	−2.02764	−	19.2917i	−0.0926454	−	0.881462i	−0.937855	−	0.347027i	$-0.887191\pi$
$479$	−2.02764	−	19.2917i	−0.0926454	−	0.881462i	0.845210	−	0.534435i	$-0.179475\pi$
$480$	−0.0793202	−	4.77271i	−0.00362045	−	0.217844i
$481$	−2.04753	−	9.63286i	−0.0933592	−	0.439221i
$482$	−6.55440	+	9.02135i	−0.298545	+	0.410911i
$483$	−24.2298	+	8.51115i	−1.10249	+	0.387271i
$484$	−10.6197	+	2.86748i	−0.482713	+	0.130340i
$485$	−42.6438	+	24.6204i	−1.93636	+	1.11796i
$486$	0.337150	−	15.5848i	0.0152934	−	0.706941i
$487$	−5.39572	−	5.99255i	−0.244503	−	0.271548i	0.608385	−	0.793642i	$-0.291818\pi$
$487$	−5.39572	−	5.99255i	−0.244503	−	0.271548i	−0.852888	+	0.522094i	$0.825151\pi$
$488$	2.18500	+	1.96738i	0.0989103	+	0.0890592i
$489$	13.0457	−	14.9820i	0.589945	−	0.677510i
$490$	18.2616	−	6.21859i	0.824975	−	0.280927i
$491$	−8.27669	−	25.4730i	−0.373522	−	1.14958i	−0.944470	−	0.328597i	$-0.893424\pi$
$491$	−8.27669	−	25.4730i	−0.373522	−	1.14958i	0.570948	−	0.820986i	$-0.306576\pi$
$492$	6.72370	−	3.12848i	0.303128	−	0.141043i
$493$	−8.94720	+	3.98355i	−0.402962	+	0.179410i
$494$	−3.02079	+	5.23215i	−0.135912	+	0.235406i
$495$	−27.0481	+	4.50664i	−1.21572	+	0.202558i
$496$	−0.238237			−0.0106971
$497$	10.0886	+	5.73050i	0.452534	+	0.257048i
$498$	0.579044	−	6.55543i	0.0259476	−	0.293756i
$499$	−6.22535	+	6.91395i	−0.278685	+	0.309511i	−0.866195	−	0.499706i	$-0.833441\pi$
$499$	−6.22535	+	6.91395i	−0.278685	+	0.309511i	0.587510	+	0.809217i	$0.300108\pi$
$500$	6.59156	−	0.692801i	0.294784	−	0.0309830i
$501$	−9.32821	−	27.1648i	−0.416754	−	1.21363i
$502$	17.9524	+	16.1644i	0.801254	+	0.721452i
$503$	1.28741	−	3.96225i	0.0574029	−	0.176668i	−0.918244	−	0.396015i	$-0.870393\pi$
$503$	1.28741	−	3.96225i	0.0574029	−	0.176668i	0.975647	+	0.219347i	$0.0703928\pi$
$504$	−7.11522	+	3.51762i	−0.316937	+	0.156687i
$505$		−	41.6792i		−	1.85470i
$506$	−11.3291	−	14.7349i	−0.503638	−	0.655046i
$507$	6.18246	−	20.1617i	0.274573	−	0.895411i
$508$	2.36453	+	5.31083i	0.104909	+	0.235630i
$509$	−3.84990	−	18.1123i	−0.170644	−	0.802815i	−0.977311	−	0.211809i	$-0.932064\pi$
$509$	−3.84990	−	18.1123i	−0.170644	−	0.802815i	0.806667	−	0.591006i	$-0.201269\pi$
$510$	9.14223	−	5.48282i	0.404825	−	0.242783i
$511$	6.05793	+	27.5471i	0.267987	+	1.21861i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−34.5172	−	1.89572i	−1.52397	−	0.0836979i
$514$	3.99776	−	3.59960i	0.176334	−	0.158771i
$515$	−1.55633	−	3.49556i	−0.0685799	−	0.154033i
$516$	−10.6795	+	9.94215i	−0.470140	+	0.437679i
$517$	15.0102	+	31.3916i	0.660146	+	1.38060i
$518$	−26.2926	−	11.4855i	−1.15523	−	0.504646i
$519$	18.1647	+	7.72836i	0.797341	+	0.339237i
$520$	−2.44800	+	0.520339i	−0.107352	+	0.0228184i
$521$	−2.41312	+	11.3528i	−0.105721	+	0.497377i	0.893145	+	0.449768i	$0.148493\pi$
$521$	−2.41312	+	11.3528i	−0.105721	+	0.497377i	−0.998866	+	0.0476089i	$0.984840\pi$
$522$	6.95315	+	11.1688i	0.304331	+	0.488847i
$523$	−3.45369	+	7.75711i	−0.151019	+	0.339195i	−0.973174	−	0.230069i	$-0.926105\pi$
$523$	−3.45369	+	7.75711i	−0.151019	+	0.339195i	0.822155	+	0.569263i	$0.192772\pi$
$524$	4.95787	+	15.2587i	0.216585	+	0.666581i
$525$	6.18779	+	10.1553i	0.270057	+	0.443212i
$526$	−11.1311	−	8.08723i	−0.485340	−	0.352620i
$527$	−0.266025	−	0.460768i	−0.0115882	−	0.0200714i
$528$	−4.02694	−	4.09680i	−0.175250	−	0.178290i
$529$	4.20293	−	7.27968i	0.182736	−	0.316508i
$530$	0.820263	−	7.80428i	0.0356299	−	0.338996i
$531$	18.7676	−	2.60565i	0.814445	−	0.113076i
$532$	7.27210	+	16.0293i	0.315285	+	0.694959i
$533$	−2.28541	−	3.14560i	−0.0989921	−	0.136251i
$534$	−1.15018	+	5.89090i	−0.0497732	+	0.254924i
$535$	−2.32166	+	10.9226i	−0.100374	+	0.472223i
$536$	3.75888	+	4.17466i	0.162359	+	0.180318i
$537$	16.9989	−	2.07279i	0.733556	−	0.0894475i
$538$			6.32794i			0.272817i
$539$	10.7703	−	20.5670i	0.463909	−	0.885883i
$540$	−8.98403	−	11.1514i	−0.386611	−	0.479879i
$541$	−39.5292	−	4.15468i	−1.69949	−	0.178624i	−0.795436	−	0.606038i	$-0.792758\pi$
$541$	−39.5292	−	4.15468i	−1.69949	−	0.178624i	−0.904056	+	0.427414i	$0.859425\pi$
$542$	1.69848	−	1.52932i	0.0729560	−	0.0656899i
$543$	−26.7490	+	0.444556i	−1.14791	+	0.0190777i
$544$	2.04020	+	0.908357i	0.0874730	+	0.0389455i
$545$	−0.895895	+	0.650906i	−0.0383759	+	0.0278818i
$546$	2.52499	+	3.30797i	0.108060	+	0.141568i
$547$	−8.50536	−	2.76356i	−0.363663	−	0.118161i	0.121485	−	0.992593i	$-0.461234\pi$
$547$	−8.50536	−	2.76356i	−0.363663	−	0.118161i	−0.485148	+	0.874432i	$0.661234\pi$
$548$	9.04595	+	0.950767i	0.386424	+	0.0406148i
$549$	8.79809	+	0.629995i	0.375493	+	0.0268875i
$550$	−5.58333	+	6.55001i	−0.238074	+	0.279293i
$551$	25.2669	−	14.5879i	1.07641	−	0.621464i
$552$	3.80012	−	8.93178i	0.161744	−	0.380162i
$553$	12.0112	−	3.99618i	0.510766	−	0.169935i
$554$	−8.73722	+	2.83890i	−0.371209	+	0.120613i
$555$	9.91962	−	50.8054i	0.421064	−	2.15657i
$556$	16.4485	−	1.72881i	0.697572	−	0.0733178i
$557$	−14.2055	−	3.01946i	−0.601904	−	0.127939i	−0.103126	−	0.994668i	$-0.532885\pi$
$557$	−14.2055	−	3.01946i	−0.601904	−	0.127939i	−0.498778	+	0.866730i	$0.666218\pi$
$558$	−0.563933	+	0.439078i	−0.0238732	+	0.0185876i
$559$	6.18908	+	4.49663i	0.261770	+	0.190187i
$560$	−2.91882	+	6.68174i	−0.123343	+	0.282355i
$561$	3.42687	−	12.3631i	0.144683	−	0.521969i
$562$	−3.24458	−	5.61977i	−0.136864	−	0.237056i
$563$	31.7810	−	14.1498i	1.33941	−	0.596344i	0.393069	−	0.919509i	$-0.371413\pi$
$563$	31.7810	−	14.1498i	1.33941	−	0.596344i	0.946343	+	0.323165i	$0.104747\pi$
$564$	−10.4351	+	14.8764i	−0.439398	+	0.626411i
$565$	34.2812	−	38.0732i	1.44222	−	1.60175i
$566$	3.87757	+	5.33702i	0.162986	+	0.224331i
$567$	−10.3594	+	21.4402i	−0.435056	+	0.900403i
$568$	−4.17069	+	1.35514i	−0.174998	+	0.0568604i
$569$	39.3585	−	8.36592i	1.65000	−	0.350717i	0.713299	−	0.700859i	$-0.247200\pi$
$569$	39.3585	−	8.36592i	1.65000	−	0.350717i	0.936697	+	0.350142i	$0.113867\pi$
$570$	−25.3778	+	19.0904i	−1.06296	+	0.799607i
$571$	13.0787	+	7.55102i	0.547328	+	0.316000i	0.748044	−	0.663649i	$-0.230993\pi$
$571$	13.0787	+	7.55102i	0.547328	+	0.316000i	−0.200715	+	0.979650i	$0.564327\pi$
$572$	−1.70356	+	2.48382i	−0.0712294	+	0.103854i
$573$	7.96960	+	34.6522i	0.332935	+	1.44762i
$574$	−11.3277	+	0.0795954i	−0.472809	+	0.00332225i
$575$	−13.8310	−	4.49397i	−0.576794	−	0.187412i
$576$	0.831729	−	2.88240i	0.0346554	−	0.120100i
$577$	−1.60227	−	15.2446i	−0.0667034	−	0.634640i	−0.975892	−	0.218255i	$-0.929964\pi$
$577$	−1.60227	−	15.2446i	−0.0667034	−	0.634640i	0.909188	−	0.416385i	$-0.136703\pi$
$578$	−1.25564	−	11.9467i	−0.0522279	−	0.496915i
$579$	36.1184	+	20.0602i	1.50103	+	0.833674i
$580$	11.4944	+	3.73475i	0.477278	+	0.155077i
$581$	−4.96499	+	8.74089i	−0.205983	+	0.362633i
$582$	−30.1598	+	6.93642i	−1.25017	+	0.287524i
$583$	−5.75628	−	7.48678i	−0.238401	−	0.310071i
$584$	−9.23237	−	5.33031i	−0.382038	−	0.220570i
$585$	−4.83570	+	5.74345i	−0.199932	+	0.237462i
$586$	−12.5291	+	2.66315i	−0.517574	+	0.110014i
$587$	5.75326	−	1.86935i	0.237462	−	0.0771562i	−0.187868	−	0.982194i	$-0.560158\pi$
$587$	5.75326	−	1.86935i	0.237462	−	0.0771562i	0.425331	+	0.905038i	$0.360158\pi$
$588$	12.1187	−	0.371808i	0.499765	−	0.0153331i
$589$	0.931611	+	1.28225i	0.0383864	+	0.0528343i
$590$	11.6469	−	12.9352i	0.479494	−	0.532532i
$591$	−23.7649	−	16.6699i	−0.977556	−	0.685710i
$592$	9.90692	−	4.41084i	0.407172	−	0.181285i
$593$	6.96755	+	12.0681i	0.286123	+	0.495579i	0.972881	−	0.231307i	$-0.0743001\pi$
$593$	6.96755	+	12.0681i	0.286123	+	0.495579i	−0.686758	+	0.726886i	$0.740967\pi$
$594$	−17.0828	−	2.27580i	−0.700914	−	0.0933771i
$595$	−16.1823	+	1.81587i	−0.663409	+	0.0744436i
$596$	12.1183	+	8.80443i	0.496383	+	0.360643i
$597$	−36.0718	+	16.7839i	−1.47632	+	0.686918i
$598$	−4.97797	−	1.05810i	−0.203564	−	0.0432689i
$599$	−24.6676	+	2.59267i	−1.00789	+	0.105933i	−0.594060	−	0.804421i	$-0.702476\pi$
$599$	−24.6676	+	2.59267i	−1.00789	+	0.105933i	−0.413830	+	0.910354i	$0.635809\pi$
$600$	−4.41143	−	0.861320i	−0.180096	−	0.0351632i
$601$	3.63278	−	1.18036i	0.148184	−	0.0481479i	−0.233986	−	0.972240i	$-0.575177\pi$
$601$	3.63278	−	1.18036i	0.148184	−	0.0481479i	0.382170	+	0.924092i	$0.375177\pi$
$602$	21.1484	−	7.03620i	0.861945	−	0.286774i
$603$	16.5917	+	2.95416i	0.675668	+	0.120303i
$604$	4.51192	−	2.60496i	0.183587	−	0.105994i
$605$	1.64491	+	30.2703i	0.0668749	+	1.23066i
$606$	7.67954	−	25.0438i	0.311960	−	1.01734i
$607$	10.2443	+	1.07672i	0.415802	+	0.0437026i	0.310120	−	0.950697i	$-0.399631\pi$
$607$	10.2443	+	1.07672i	0.415802	+	0.0437026i	0.105682	+	0.994400i	$0.466297\pi$
$608$	−6.32723	−	2.05584i	−0.256603	−	0.0833754i
$609$	−2.57261	−	19.9313i	−0.104248	−	0.807657i
$610$	6.55542	−	4.76279i	0.265421	−	0.192840i
$611$	8.70364	+	3.87511i	0.352111	+	0.156770i
$612$	6.50353	−	1.60998i	0.262889	−	0.0650794i
$613$	−19.8888	+	17.9080i	−0.803302	+	0.723297i	−0.964631	−	0.263604i	$-0.915089\pi$
$613$	−19.8888	+	17.9080i	−0.803302	+	0.723297i	0.161329	+	0.986901i	$0.448422\pi$
$614$	−13.7144	−	1.44144i	−0.553467	−	0.0581717i
$615$	−4.58081	−	19.9176i	−0.184716	−	0.803153i
$616$	2.99514	+	8.24798i	0.120678	+	0.332320i
$617$		−	0.534245i		−	0.0215079i	−0.999942	−	0.0107539i	$-0.996577\pi$
$617$		−	0.534245i		−	0.0215079i	0.999942	−	0.0107539i	$-0.00342315\pi$
$618$	−0.291080	−	2.38714i	−0.0117090	−	0.0960249i
$619$	6.98455	+	7.75712i	0.280733	+	0.311785i	0.866976	−	0.498350i	$-0.166060\pi$
$619$	6.98455	+	7.75712i	0.280733	+	0.311785i	−0.586243	+	0.810135i	$0.699394\pi$
$620$	−0.136506	+	0.642211i	−0.00548222	+	0.0257918i
$621$	−7.46623	−	28.1463i	−0.299609	−	1.12947i
$622$	−17.9875	−	24.7577i	−0.721234	−	0.992693i
$623$	5.33680	−	7.45508i	0.213815	−	0.298681i
$624$	−1.56681	−	0.138397i	−0.0627225	−	0.00554030i
$625$	3.26557	−	31.0698i	0.130623	−	1.24279i
$626$	−5.18410	+	8.97912i	−0.207198	+	0.358878i
$627$	−6.30290	+	37.6944i	−0.251714	+	1.50537i
$628$	−0.595632	−	1.03166i	−0.0237683	−	0.0411679i
$629$	19.5934	+	14.2354i	0.781239	+	0.567603i
$630$	5.40548	+	21.1959i	0.215360	+	0.844466i
$631$	−9.40698	−	28.9517i	−0.374486	−	1.15255i	−0.943825	−	0.330446i	$-0.892801\pi$
$631$	−9.40698	−	28.9517i	−0.374486	−	1.15255i	0.569339	−	0.822103i	$-0.307199\pi$
$632$	−1.94602	+	4.37082i	−0.0774083	+	0.173862i
$633$	−40.9367	+	14.0574i	−1.62709	+	0.558731i
$634$	4.86922	−	22.9079i	0.193382	−	0.909789i
$635$	15.6712	−	3.33101i	0.621891	−	0.132187i
$636$	1.93084	−	4.53823i	0.0765627	−	0.179952i
$637$	−1.40891	−	6.19873i	−0.0558229	−	0.245603i
$638$	13.1220	−	6.27438i	0.519503	−	0.248405i
$639$	−7.37494	+	10.8945i	−0.291748	+	0.430980i
$640$	−1.12093	−	2.51765i	−0.0443086	−	0.0995188i
$641$	−2.88041	+	2.59353i	−0.113769	+	0.102438i	−0.724052	−	0.689745i	$-0.757723\pi$
$641$	−2.88041	+	2.59353i	−0.113769	+	0.102438i	0.610283	+	0.792184i	$0.291056\pi$
$642$	−3.40754	+	6.13527i	−0.134485	+	0.242140i
$643$	36.1152	−	26.2392i	1.42425	−	1.03477i	0.433193	−	0.901301i	$-0.357387\pi$
$643$	36.1152	−	26.2392i	1.42425	−	1.03477i	0.991052	−	0.133473i	$-0.0426131\pi$
$644$	−10.9487	+	9.99840i	−0.431437	+	0.393992i
$645$	20.6817	+	34.4854i	0.814341	+	1.35786i
$646$	−3.08908	−	14.5330i	−0.121538	−	0.571793i
$647$	−8.39624	−	18.8583i	−0.330090	−	0.741395i	0.669909	−	0.742443i	$-0.266333\pi$
$647$	−8.39624	−	18.8583i	−0.330090	−	0.741395i	−0.999999	+	0.00104834i	$0.999666\pi$
$648$	−3.34356	−	8.35587i	−0.131347	−	0.328250i
$649$	−0.568517	−	20.9397i	−0.0223162	−	0.821954i
$650$			2.35660i			0.0924333i
$651$	1.06222	−	0.252169i	0.0416315	−	0.00988327i
$652$	3.54428	−	10.9082i	0.138805	−	0.427197i
$653$	−1.51251	−	1.36187i	−0.0591891	−	0.0532941i	0.639005	−	0.769202i	$-0.279346\pi$
$653$	−1.51251	−	1.36187i	−0.0591891	−	0.0532941i	−0.698194	+	0.715908i	$0.746013\pi$
$654$	−0.658249	+	0.226038i	−0.0257396	+	0.00883880i
$655$	43.9736	−	4.62181i	1.71819	−	0.180589i
$656$	2.86493	−	3.18183i	0.111857	−	0.124229i
$657$	−31.6780	+	4.39810i	−1.23588	+	0.171586i
$658$	23.9404	−	14.0472i	0.933295	−	0.547617i
$659$	42.4842			1.65495			0.827475	−	0.561503i	$-0.189777\pi$
$659$	42.4842			1.65495			0.827475	+	0.561503i	$0.189777\pi$
$660$	−13.3511	+	8.50797i	−0.519689	+	0.331172i
$661$	3.30366	−	5.72211i	0.128498	−	0.222564i	−0.794597	−	0.607137i	$-0.792318\pi$
$661$	3.30366	−	5.72211i	0.128498	−	0.222564i	0.923095	+	0.384573i	$0.125651\pi$
$662$	9.95899	−	4.43403i	0.387067	−	0.172333i
$663$	−1.48189	−	3.18486i	−0.0575518	−	0.123690i
$664$	−1.17412	−	3.61356i	−0.0455645	−	0.140233i
$665$	47.3768	−	10.4187i	1.83719	−	0.404020i
$666$	15.3215	−	28.6997i	0.593695	−	1.11209i
$667$	18.2639	+	16.4449i	0.707180	+	0.636748i
$668$	−11.0959	−	12.3232i	−0.429312	−	0.476800i
$669$	28.1991	−	21.2126i	1.09024	−	0.820128i
$670$	13.4074	−	7.74074i	0.517971	−	0.299051i
$671$	1.76784	−	9.58998i	0.0682467	−	0.370217i
$672$	−2.98497	+	3.47706i	−0.115148	+	0.134131i
$673$	−7.43753	+	10.2369i	−0.286696	+	0.394603i	−0.927937	−	0.372736i	$-0.878420\pi$
$673$	−7.43753	+	10.2369i	−0.286696	+	0.394603i	0.641242	+	0.767339i	$0.278420\pi$
$674$	5.24903	+	24.6948i	0.202185	+	0.951207i
$675$	−12.0298	+	6.09157i	−0.463027	+	0.234464i
$676$	−1.27267	−	12.1086i	−0.0489488	−	0.465716i
$677$	−35.4891	−	15.8007i	−1.36396	−	0.607272i	−0.411349	−	0.911478i	$-0.634942\pi$
$677$	−35.4891	−	15.8007i	−1.36396	−	0.607272i	−0.952606	+	0.304206i	$0.901609\pi$
$678$	27.6137	−	16.5606i	1.06050	−	0.636007i
$679$	46.3075	+	9.50339i	1.77712	+	0.364707i
$680$	3.61765	−	4.97927i	0.138731	−	0.190946i
$681$	4.36318	+	4.68678i	0.167197	+	0.179598i
$682$	0.413497	+	0.673308i	0.0158336	+	0.0257823i
$683$	−16.8137	−	9.70740i	−0.643359	−	0.371443i	0.142549	−	0.989788i	$-0.454470\pi$
$683$	−16.8137	−	9.70740i	−0.643359	−	0.371443i	−0.785907	+	0.618345i	$0.787804\pi$
$684$	−18.7663	+	6.79488i	−0.717546	+	0.259809i
$685$	7.74617	−	23.8403i	0.295966	−	0.910889i
$686$	−17.0741	−	7.17457i	−0.651893	−	0.273927i
$687$	−15.0042	+	17.2313i	−0.572446	+	0.657414i
$688$	−3.42641	+	7.69584i	−0.130631	+	0.293401i
$689$	−2.52930	−	0.537619i	−0.0963587	−	0.0204817i
$690$	−21.8998	−	15.3617i	−0.833713	−	0.584811i
$691$	−0.0343623	+	0.326935i	−0.00130720	+	0.0124372i	−0.995156	−	0.0983078i	$-0.968657\pi$
$691$	−0.0343623	+	0.326935i	−0.00130720	+	0.0124372i	0.993849	+	0.110745i	$0.0353237\pi$
$692$	11.3971			0.433253
$693$	22.2911	+	14.0038i	0.846770	+	0.531959i
$694$	8.95878			0.340071
$695$	4.76444	−	45.3306i	0.180725	−	1.71949i
$696$	6.21849	+	4.36198i	0.235711	+	0.165340i
$697$	9.35299	+	1.98804i	0.354270	+	0.0753024i
$698$	−1.63624	+	3.67506i	−0.0619327	+	0.139103i
$699$	14.3706	−	16.5036i	0.543545	−	0.624223i
$700$	5.58278	+	3.99649i	0.211009	+	0.151053i
$701$	−9.58667	+	29.5047i	−0.362084	+	1.11438i	0.589704	+	0.807620i	$0.299245\pi$
$701$	−9.58667	+	29.5047i	−0.362084	+	1.11438i	−0.951787	+	0.306759i	$0.900755\pi$
$702$	−3.96388	+	2.56007i	−0.149607	+	0.0966238i
$703$	−62.4808	−	36.0733i	−2.35651	−	1.36053i
$704$	−3.06538	−	1.26626i	−0.115531	−	0.0477241i
$705$	34.1230	+	36.6538i	1.28515	+	1.38046i
$706$	14.0680	−	19.3629i	0.529454	−	0.728732i
$707$	−26.5645	+	29.9230i	−0.999060	+	1.12537i
$708$	9.38161	−	5.62638i	0.352583	−	0.211452i
$709$	−38.1680	−	16.9935i	−1.43343	−	0.638204i	−0.464508	−	0.885569i	$-0.653769\pi$
$709$	−38.1680	−	16.9935i	−1.43343	−	0.638204i	−0.968923	+	0.247364i	$0.920436\pi$
$710$	1.26329	+	12.0194i	0.0474103	+	0.451078i
$711$	3.44913	+	13.9328i	0.129352	+	0.522521i
$712$	0.720483	+	3.38961i	0.0270012	+	0.127031i
$713$	−0.784752	+	1.08012i	−0.0293892	+	0.0404508i
$714$	−10.0580	−	1.89054i	−0.376413	−	0.0707516i
$715$	5.71948	+	6.01545i	0.213896	+	0.224965i
$716$	8.56240	−	4.94350i	0.319992	−	0.184747i
$717$	6.11156	−	4.59739i	0.228240	−	0.171693i
$718$	−17.7065	−	19.6650i	−0.660800	−	0.733893i
$719$	7.76133	+	6.98833i	0.289449	+	0.260621i	0.801044	−	0.598606i	$-0.204278\pi$
$719$	7.76133	+	6.98833i	0.289449	+	0.260621i	−0.511595	+	0.859227i	$0.670945\pi$
$720$	−7.29347	−	3.89365i	−0.271812	−	0.145108i
$721$	−1.11057	+	3.50152i	−0.0413600	+	0.130404i
$722$	7.80588	+	24.0240i	0.290505	+	0.894082i
$723$	8.14787	+	17.5113i	0.303022	+	0.651254i
$724$	−14.1103	+	6.28233i	−0.524407	+	0.233481i
$725$	5.69019	−	9.85570i	0.211328	−	0.366032i
$726$	−4.58904	+	18.4916i	−0.170315	+	0.686289i
$727$	40.2565			1.49303			0.746515	−	0.665368i	$-0.231725\pi$
$727$	40.2565			1.49303			0.746515	+	0.665368i	$0.231725\pi$
$728$	2.08915	+	1.18668i	0.0774290	+	0.0439812i
$729$	−23.3147	−	13.6170i	−0.863509	−	0.504334i
$730$	−19.6589	+	21.8334i	−0.727607	+	0.808089i
$731$	−18.7104	+	1.96654i	−0.692030	+	0.0727352i
$732$	4.81652	−	1.65396i	0.178024	−	0.0611322i
$733$	−4.49741	−	4.04948i	−0.166115	−	0.149571i	0.581881	−	0.813274i	$-0.302317\pi$
$733$	−4.49741	−	4.04948i	−0.166115	−	0.149571i	−0.747996	+	0.663703i	$0.768984\pi$
$734$	−2.89291	+	8.90345i	−0.106779	+	0.328633i
$735$	5.94154	−	32.8811i	0.219157	−	1.21284i
$736$		−	5.60409i		−	0.206570i
$737$	5.27437	−	17.8692i	0.194284	−	0.658220i
$738$	0.917407	−	12.8119i	0.0337702	−	0.471613i
$739$	7.30925	+	16.4169i	0.268875	+	0.603904i	0.996639	−	0.0819247i	$-0.0261067\pi$
$739$	7.30925	+	16.4169i	0.268875	+	0.603904i	−0.727763	+	0.685828i	$0.759440\pi$
$740$	−6.21373	−	29.2333i	−0.228421	−	1.07464i
$741$	5.38202	+	8.97416i	0.197714	+	0.329674i
$742$	−5.56300	+	5.08018i	−0.204224	+	0.186499i
$743$	−27.5255	+	19.9984i	−1.00981	+	0.733672i	−0.964170	−	0.265286i	$-0.914534\pi$
$743$	−27.5255	+	19.9984i	−1.00981	+	0.733672i	−0.0456429	+	0.998958i	$0.514534\pi$
$744$	−0.200352	+	0.360734i	−0.00734527	+	0.0132251i
$745$	30.6776	−	27.6222i	1.12394	−	1.01200i
$746$	9.97970	+	22.4148i	0.365383	+	0.820663i
$747$	−9.43917	−	6.38977i	−0.345361	−	0.233789i
$748$	−0.973877	−	7.34265i	−0.0356085	−	0.268474i
$749$	8.62835	−	6.36197i	0.315273	−	0.232461i
$750$	4.49434	−	10.5635i	0.164110	−	0.385723i
$751$	1.92014	−	0.408137i	0.0700667	−	0.0148931i	−0.172745	−	0.984967i	$-0.555264\pi$
$751$	1.92014	−	0.408137i	0.0700667	−	0.0148931i	0.242812	+	0.970073i	$0.421930\pi$
$752$	−2.18126	+	10.2620i	−0.0795423	+	0.374217i
$753$	39.5735	−	13.5893i	1.44214	−	0.495220i
$754$	1.61983	−	3.63820i	0.0589908	−	0.132495i
$755$	−4.43688	−	13.6553i	−0.161475	−	0.496968i
$756$	−0.657431	+	13.7320i	−0.0239105	+	0.499428i
$757$	14.6142	+	10.6179i	0.531163	+	0.385913i	0.820793	−	0.571226i	$-0.193532\pi$
$757$	14.6142	+	10.6179i	0.531163	+	0.385913i	−0.289629	+	0.957139i	$0.593532\pi$
$758$	11.9262	+	20.6567i	0.433178	+	0.750286i
$759$	−31.8388	+	4.76252i	−1.15568	+	0.172869i
$760$	−9.16732	+	15.8783i	−0.332534	+	0.575965i
$761$	0.925539	−	8.80591i	0.0335507	−	0.319214i	−0.964856	−	0.262781i	$-0.915360\pi$
$761$	0.925539	−	8.80591i	0.0335507	−	0.319214i	0.998406	−	0.0564334i	$-0.0179729\pi$
$762$	10.0301	+	0.885963i	0.363352	+	0.0320950i
$763$	1.05805	+	0.103695i	0.0383041	+	0.00375401i
$764$	12.0665	+	16.6081i	0.436550	+	0.600860i
$765$	−0.613561	−	18.4540i	−0.0221833	−	0.667204i
$766$	−4.04752	+	19.0421i	−0.146243	+	0.688018i
$767$	−3.83784	−	4.26235i	−0.138576	−	0.153905i
$768$	−0.209648	−	1.71932i	−0.00756501	−	0.0620405i
$769$		−	5.92488i		−	0.213657i	−0.994277	−	0.106828i	$-0.965930\pi$
$769$		−	5.92488i		−	0.213657i	0.994277	−	0.106828i	$-0.0340695\pi$
$770$	23.9501	−	3.34798i	0.863103	−	0.120653i
$771$	−2.08842	−	9.08053i	−0.0752125	−	0.327027i
$772$	23.7227	+	2.49336i	0.853799	+	0.0897379i
$773$	24.0733	−	21.6757i	0.865855	−	0.779619i	−0.110933	−	0.993828i	$-0.535384\pi$
$773$	24.0733	−	21.6757i	0.865855	−	0.779619i	0.976788	+	0.214209i	$0.0687172\pi$
$774$	6.07298	+	24.5319i	0.218289	+	0.881781i
$775$	0.564783	+	0.251458i	0.0202876	+	0.00903262i
$776$	−14.4550	+	10.5022i	−0.518905	+	0.377006i
$777$	−39.5028	+	30.1527i	−1.41715	+	1.08172i
$778$	14.2585	+	4.63286i	0.511191	+	0.166096i
$779$	−28.3286	−	2.97745i	−1.01498	−	0.106678i
$780$	−1.27083	+	4.14432i	−0.0455031	+	0.148390i
$781$	11.0688	+	9.43523i	0.396073	+	0.337619i
$782$	10.8387	−	6.25775i	0.387593	−	0.223777i
$783$	22.7591	−	1.13557i	0.813346	−	0.0405821i
$784$	6.35418	−	2.93674i	0.226935	−	0.104884i
$785$	−3.12233	+	1.01451i	−0.111441	+	0.0362093i
$786$	27.2740	+	5.32518i	0.972832	+	0.189943i
$787$	5.51325	−	0.579466i	0.196526	−	0.0206557i	−0.00575389	−	0.999983i	$-0.501832\pi$
$787$	5.51325	−	0.579466i	0.196526	−	0.0206557i	0.202280	+	0.979328i	$0.435165\pi$
$788$	−16.3934	−	3.48452i	−0.583990	−	0.124131i
$789$	−21.6066	+	10.0534i	−0.769215	+	0.357909i
$790$	10.6673	+	7.75026i	0.379526	+	0.275742i
$791$	−48.8779	+	5.48477i	−1.73790	+	0.195016i
$792$	−9.58988	+	2.65221i	−0.340762	+	0.0942421i
$793$	−1.33503	−	2.31234i	−0.0474082	−	0.0821134i
$794$	22.5069	−	10.0207i	0.798739	−	0.355621i
$795$	−11.1273	−	7.80527i	−0.394644	−	0.276824i
$796$	−15.3700	+	17.0701i	−0.544774	+	0.605033i
$797$	−12.1374	−	16.7057i	−0.429929	−	0.591747i	0.538008	−	0.842940i	$-0.319177\pi$
$797$	−12.1374	−	16.7057i	−0.429929	−	0.591747i	−0.967937	+	0.251193i	$0.919177\pi$
$798$	30.3870	+	2.46905i	1.07569	+	0.0874034i
$799$	−22.2832	+	7.24025i	−0.788323	+	0.256142i
$800$	−2.53833	+	0.539538i	−0.0897434	+	0.0190755i
$801$	7.95262	+	6.69571i	0.280992	+	0.236581i
$802$	21.0288	+	12.1410i	0.742552	+	0.428712i
$803$	0.959605	+	35.3442i	0.0338637	+	1.24727i
$804$	9.48235	−	2.18083i	0.334417	−	0.0769120i
$805$	20.6791	+	35.2431i	0.728843	+	1.24215i
$806$	0.205758	+	0.0668549i	0.00724752	+	0.00235486i
$807$	9.58167	+	5.32167i	0.337291	+	0.187332i
$808$	−1.58084	−	15.0407i	−0.0556139	−	0.529131i
$809$	3.70144	+	35.2168i	0.130136	+	1.23816i	0.843409	+	0.537272i	$0.180545\pi$
$809$	3.70144	+	35.2168i	0.130136	+	1.23816i	−0.713273	+	0.700886i	$0.752788\pi$
$810$	−24.4406	+	4.22539i	−0.858756	+	0.148465i
$811$	9.00660	+	2.92642i	0.316265	+	0.102761i	0.462848	−	0.886438i	$-0.346828\pi$
$811$	9.00660	+	2.92642i	0.316265	+	0.102761i	−0.146583	+	0.989198i	$0.546828\pi$
$812$	−5.87186	−	10.0073i	−0.206062	−	0.351188i
$813$	−0.887282	−	3.85794i	−0.0311183	−	0.135304i
$814$	−29.6610	−	20.3434i	−1.03962	−	0.713035i
$815$	−27.3742	−	15.8045i	−0.958875	−	0.553607i
$816$	3.09119	−	2.32533i	0.108213	−	0.0814029i
$817$	54.8198	−	11.6523i	1.91790	−	0.407663i
$818$	25.5696	−	8.30805i	0.894019	−	0.290484i
$819$	7.13234	−	1.04137i	0.249224	−	0.0363884i
$820$	−6.93564	−	9.54609i	−0.242203	−	0.333364i
$821$	−14.3879	+	15.9794i	−0.502141	+	0.557684i	−0.939918	−	0.341399i	$-0.889099\pi$
$821$	−14.3879	+	15.9794i	−0.502141	+	0.557684i	0.437777	+	0.899083i	$0.355766\pi$
$822$	9.04710	−	12.8977i	0.315554	−	0.449857i
$823$	−5.99816	+	2.67055i	−0.209083	+	0.0930896i	−0.508606	−	0.860999i	$-0.669839\pi$
$823$	−5.99816	+	2.67055i	−0.209083	+	0.0930896i	0.299523	+	0.954089i	$0.403172\pi$
$824$	−0.694212	−	1.20241i	−0.0241840	−	0.0418880i
$825$	5.22245	+	13.9626i	0.181822	+	0.486116i
$826$	−16.6060	+	1.86342i	−0.577797	+	0.0648367i
$827$	−39.8068	−	28.9213i	−1.38422	−	1.00569i	−0.996472	−	0.0839259i	$-0.973254\pi$
$827$	−39.8068	−	28.9213i	−1.38422	−	1.00569i	−0.387745	−	0.921767i	$-0.626746\pi$
$828$	−10.3285	−	13.2655i	−0.358941	−	0.461009i
$829$	−0.584827	−	0.124309i	−0.0203119	−	0.00431743i	0.197745	−	0.980254i	$-0.436638\pi$
$829$	−0.584827	−	0.124309i	−0.0203119	−	0.00431743i	−0.218056	+	0.975936i	$0.569972\pi$
$830$	−10.4138	+	1.09453i	−0.361467	+	0.0379917i
$831$	−3.04922	+	15.6172i	−0.105776	+	0.541755i
$832$	−0.863672	+	0.280624i	−0.0299424	+	0.00972889i
$833$	12.7752	+	9.01019i	0.442635	+	0.312185i
$834$	11.2151	−	26.3600i	0.388349	−	0.912771i
$835$	−39.5773	+	22.8500i	−1.36963	+	0.790756i
$836$	5.17164	+	21.4504i	0.178865	+	0.741876i
$837$	0.190588	+	1.22315i	0.00658768	+	0.0422784i
$838$	9.06724	+	0.953006i	0.313223	+	0.0329210i
$839$	−35.2570	−	11.4557i	−1.21721	−	0.395494i	−0.371142	−	0.928576i	$-0.621034\pi$
$839$	−35.2570	−	11.4557i	−1.21721	−	0.395494i	−0.846063	+	0.533082i	$0.821034\pi$
$840$	7.66272	+	10.0388i	0.264389	+	0.346373i
$841$	7.90235	−	5.74139i	0.272495	−	0.197979i
$842$	15.6834	+	6.98270i	0.540485	+	0.240640i
$843$	−11.2380	+	0.186770i	−0.387057	+	0.00643270i
$844$	−18.5708	+	16.7212i	−0.639233	+	0.575568i
$845$	−33.3703	−	3.50736i	−1.14797	−	0.120657i
$846$	13.7499	+	28.3115i	0.472732	+	0.973369i
$847$	18.1120	−	22.7806i	0.622337	−	0.782750i
$848$		−	2.84743i		−	0.0977813i
$849$	11.3422	−	1.38303i	0.389263	−	0.0474654i
$850$	−3.87790	−	4.30685i	−0.133011	−	0.147724i
$851$	12.6355	−	59.4454i	0.433140	−	2.03776i
$852$	−1.45554	+	7.45485i	−0.0498659	+	0.255399i
$853$	−3.16081	−	4.35048i	−0.108224	−	0.148958i	0.751469	−	0.659768i	$-0.229345\pi$
$853$	−3.16081	−	4.35048i	−0.108224	−	0.148958i	−0.859693	+	0.510810i	$0.829345\pi$
$854$	−7.74196	−	0.758753i	−0.264925	−	0.0259640i
$855$	7.56406	+	54.4813i	0.258685	+	1.86322i
$856$	−0.423535	+	4.02967i	−0.0144761	+	0.137731i
$857$	10.1726	−	17.6194i	0.347488	−	0.601867i	−0.638315	−	0.769776i	$-0.720368\pi$
$857$	10.1726	−	17.6194i	0.347488	−	0.601867i	0.985803	+	0.167909i	$0.0537014\pi$
$858$	2.32830	+	4.66834i	0.0794868	+	0.159375i
$859$	−17.2318	−	29.8464i	−0.587941	−	1.01834i	−0.994502	−	0.104721i	$-0.966605\pi$
$859$	−17.2318	−	29.8464i	−0.587941	−	1.01834i	0.406560	−	0.913624i	$-0.366728\pi$
$860$	18.7823	+	13.6461i	0.640470	+	0.465329i
$861$	−9.40584	+	17.2191i	−0.320550	+	0.586827i
$862$	12.1149	+	37.2859i	0.412636	+	1.26996i
$863$	18.0794	−	40.6070i	0.615430	−	1.38228i	−0.289689	−	0.957121i	$-0.593552\pi$
$863$	18.0794	−	40.6070i	0.615430	−	1.38228i	0.905119	−	0.425158i	$-0.139781\pi$
$864$	−3.66502	−	3.68343i	−0.124686	−	0.125313i
$865$	6.53039	−	30.7230i	0.222040	−	1.04461i
$866$	−7.28215	+	1.54787i	−0.247458	+	0.0525987i
$867$	−19.1454	−	8.14562i	−0.650212	−	0.276640i
$868$	0.507320	−	0.374064i	0.0172195	−	0.0126965i
$869$	15.7305	−	2.08638i	0.533621	−	0.0707757i
$870$	15.3216	−	14.2637i	0.519452	−	0.483586i
$871$	−2.07493	−	4.66037i	−0.0703063	−	0.157911i
$872$	−0.298613	+	0.268872i	−0.0101123	+	0.00910516i
$873$	−14.8608	+	51.5009i	−0.502962	+	1.74304i
$874$	−30.1627	+	21.9145i	−1.02027	+	0.741269i
$875$	−12.9488	+	11.8249i	−0.437749	+	0.399756i
$876$	−15.8353	+	9.49682i	−0.535025	+	0.320868i
$877$	3.80533	+	17.9027i	0.128497	+	0.604530i	0.994522	+	0.104529i	$0.0333336\pi$
$877$	3.80533	+	17.9027i	0.128497	+	0.604530i	−0.866025	+	0.500001i	$0.833333\pi$
$878$	−11.3561	−	25.5061i	−0.383248	−	0.860790i
$879$	−6.50426	+	21.2111i	−0.219383	+	0.715432i
$880$	−5.16987	+	7.53776i	−0.174276	+	0.254098i
$881$		−	10.9054i		−	0.367412i	−0.982981	−	0.183706i	$-0.941191\pi$
$881$		−	10.9054i		−	0.367412i	0.982981	−	0.183706i	$-0.0588094\pi$
$882$	9.62856	−	18.6626i	0.324210	−	0.628401i
$883$	−1.16254	+	3.57794i	−0.0391227	+	0.120407i	−0.968710	−	0.248194i	$-0.920163\pi$
$883$	−1.16254	+	3.57794i	−0.0391227	+	0.120407i	0.929588	+	0.368601i	$0.120163\pi$
$884$	−1.50716	−	1.35705i	−0.0506912	−	0.0456426i
$885$	−9.79142	−	28.5137i	−0.329135	−	0.958478i
$886$	−5.79421	+	0.608996i	−0.194660	+	0.0204596i
$887$	−30.2166	+	33.5589i	−1.01457	+	1.12680i	−0.0226791	+	0.999743i	$0.507220\pi$
$887$	−30.2166	+	33.5589i	−1.01457	+	1.12680i	−0.991895	+	0.127056i	$0.959447\pi$
$888$	1.65269	−	18.7103i	0.0554607	−	0.627877i
$889$	−13.3739	−	7.59665i	−0.448547	−	0.254784i
$890$	9.55014			0.320121
$891$	−17.8122	+	23.9525i	−0.596732	+	0.802440i
$892$	10.1864	−	17.6434i	0.341067	−	0.590746i
$893$	63.7626	−	28.3889i	2.13373	−	0.949999i
$894$	23.5227	−	10.9449i	0.786718	−	0.366053i
$895$	−8.42000	−	25.9141i	−0.281450	−	0.866213i
$896$	−0.799882	+	2.52194i	−0.0267222	+	0.0842522i
$897$	−5.78853	+	6.64772i	−0.193273	+	0.221961i
$898$	−8.75167	−	7.88004i	−0.292047	−	0.262960i
$899$	−0.699090	−	0.776419i	−0.0233160	−	0.0258950i
$900$	−5.01412	+	5.95536i	−0.167137	+	0.198512i
$901$	5.50716	−	3.17956i	0.183470	−	0.105926i
$902$	−13.9651	−	2.57435i	−0.464986	−	0.0857166i
$903$	7.13129	−	37.9399i	0.237314	−	1.26256i
$904$	10.9270	−	15.0397i	0.363425	−	0.500212i
$905$	8.85016	+	41.6367i	0.294189	+	1.38405i
$906$	−0.149951	−	9.02259i	−0.00498179	−	0.299756i
$907$	5.58670	+	53.1539i	0.185503	+	1.76495i	0.551352	+	0.834273i	$0.314112\pi$
$907$	5.58670	+	53.1539i	0.185503	+	1.76495i	−0.365848	+	0.930675i	$0.619221\pi$
$908$	3.37737	+	1.50370i	0.112082	+	0.0499021i
$909$	−31.4626	−	32.6896i	−1.04355	−	1.08424i
$910$	4.39596	−	4.95174i	0.145725	−	0.164149i
$911$	18.7287	−	25.7778i	0.620509	−	0.854057i	−0.376881	−	0.926262i	$-0.623003\pi$
$911$	18.7287	−	25.7778i	0.620509	−	0.854057i	0.997390	+	0.0722044i	$0.0230034\pi$
$912$	−8.43400	+	7.85167i	−0.279278	+	0.259995i
$913$	−8.17483	+	9.59019i	−0.270547	+	0.317389i
$914$	26.1310	+	15.0868i	0.864338	+	0.499026i
$915$	−1.69876	−	13.9315i	−0.0561594	−	0.460562i
$916$	−4.07638	+	12.5458i	−0.134687	+	0.414525i
$917$	−34.5160	−	24.7086i	−1.13982	−	0.815951i
$918$	3.03154	−	11.2015i	0.100056	−	0.369704i
$919$	9.71005	−	21.8091i	0.320305	−	0.719417i	−0.679595	−	0.733588i	$-0.737844\pi$
$919$	9.71005	−	21.8091i	0.320305	−	0.719417i	0.999900	+	0.0141710i	$0.00451093\pi$
$920$	−15.1069	−	3.21106i	−0.498059	−	0.105866i
$921$	−13.7161	+	19.5539i	−0.451961	+	0.644322i
$922$	1.15702	−	11.0083i	0.0381045	−	0.362540i
$923$	3.98240			0.131082
$924$	15.0078	+	2.40119i	0.493721	+	0.0789934i
$925$	−28.1418			−0.925296
$926$	0.306448	−	2.91566i	0.0100705	−	0.0958145i
$927$	−3.85936	−	1.56679i	−0.126758	−	0.0514601i
$928$	4.28962	+	0.911786i	0.140814	+	0.0299308i
$929$	−18.7080	+	42.0189i	−0.613790	+	1.37859i	0.292634	+	0.956225i	$0.405468\pi$
$929$	−18.7080	+	42.0189i	−0.613790	+	1.37859i	−0.906424	+	0.422370i	$0.861198\pi$
$930$	0.857626	+	0.746782i	0.0281227	+	0.0244879i
$931$	−40.6540	−	22.7159i	−1.33238	−	0.744484i
$932$	3.90424	−	12.0160i	0.127887	−	0.393597i
$933$	−52.6148	+	6.41568i	−1.72253	+	0.210040i
$934$	30.9918	+	17.8931i	1.01408	+	0.585481i
$935$	−20.3515	−	1.58197i	−0.665565	−	0.0517358i
$936$	−1.52721	+	2.25604i	−0.0499185	+	0.0737411i
$937$	−1.10579	+	1.52199i	−0.0361246	+	0.0497213i	−0.826697	−	0.562647i	$-0.809783\pi$
$937$	−1.10579	+	1.52199i	−0.0361246	+	0.0497213i	0.790573	+	0.612368i	$0.209783\pi$
$938$	−14.5592	−	2.98790i	−0.475376	−	0.0975583i
$939$	9.23631	+	15.4009i	0.301416	+	0.502590i
$940$	26.4133	+	11.7600i	0.861508	+	0.383568i
$941$	3.01561	+	28.6916i	0.0983062	+	0.935321i	0.926859	+	0.375410i	$0.122498\pi$
$941$	3.01561	+	28.6916i	0.0983062	+	0.935321i	−0.828553	+	0.559911i	$0.810835\pi$
$942$	−2.06304	+	0.0342868i	−0.0672176	+	0.00111712i
$943$	−4.98870	−	23.4700i	−0.162454	−	0.764288i
$944$	3.71238	−	5.10965i	0.120828	−	0.166305i
$945$	36.6405	+	9.64047i	1.19191	+	0.313604i
$946$	27.6972	−	3.67356i	0.900513	−	0.119438i
$947$	14.5984	−	8.42840i	0.474385	−	0.273886i	−0.243689	−	0.969853i	$-0.578358\pi$
$947$	14.5984	−	8.42840i	0.474385	−	0.273886i	0.718073	+	0.695967i	$0.245024\pi$
$948$	4.98167	+	6.62240i	0.161797	+	0.215086i
$949$	6.47792	+	7.19446i	0.210282	+	0.233542i
$950$	12.8299	+	11.5521i	0.416257	+	0.374800i
$951$	−30.5918	−	26.6380i	−0.992008	−	0.863796i
$952$	−5.77081	+	1.26907i	−0.187033	+	0.0411307i
$953$	9.78823	+	30.1251i	0.317072	+	0.975847i	0.974893	+	0.222673i	$0.0714782\pi$
$953$	9.78823	+	30.1251i	0.317072	+	0.975847i	−0.657821	+	0.753174i	$0.728522\pi$
$954$	−5.24791	−	6.74020i	−0.169907	−	0.218222i
$955$	51.6842	−	23.0113i	1.67246	−	0.744627i
$956$	2.20770	−	3.82385i	0.0714021	−	0.123672i
$957$	1.53474	−	25.1457i	0.0496110	−	0.812845i
$958$	−19.3980			−0.626721
$959$	−20.7560	+	12.1787i	−0.670246	+	0.393271i
$960$	−4.75486	−	0.419999i	−0.153462	−	0.0135554i
$961$	−20.7051	+	22.9953i	−0.667906	+	0.741784i
$962$	−9.79411	+	1.02940i	−0.315775	+	0.0331893i
$963$	6.42425	+	10.3193i	0.207019	+	0.332534i
$964$	8.28681	+	7.46148i	0.266900	+	0.240318i
$965$	20.3141	−	62.5203i	0.653934	−	2.01260i
$966$	5.93182	+	24.9867i	0.190853	+	0.803935i
$967$			0.0899523i			0.00289267i	0.999999	+	0.00144634i	$0.000460383\pi$
$967$			0.0899523i			0.00289267i	−0.999999	+	0.00144634i	$0.999540\pi$
$968$	1.74171	+	10.8612i	0.0559808	+	0.349093i
$969$	−24.6035	−	7.54452i	−0.790378	−	0.242365i
$970$	20.0281	+	44.9838i	0.643062	+	1.44434i
$971$	−1.22134	−	5.74596i	−0.0391947	−	0.184397i	0.954195	−	0.299184i	$-0.0967145\pi$
$971$	−1.22134	−	5.74596i	−0.0391947	−	0.184397i	−0.993390	+	0.114788i	$0.963381\pi$
$972$	−15.4642	−	1.96436i	−0.496014	−	0.0630069i
$973$	−32.3123	+	29.5079i	−1.03588	+	0.945978i
$974$	−6.52373	+	4.73977i	−0.209034	+	0.151872i
$975$	3.56832	+	1.98185i	0.114278	+	0.0634700i
$976$	2.18500	−	1.96738i	0.0699401	−	0.0629744i
$977$	−14.8825	−	33.4266i	−0.476133	−	1.06941i	−0.978779	−	0.204920i	$-0.934307\pi$
$977$	−14.8825	−	33.4266i	−0.476133	−	1.06941i	0.502646	−	0.864493i	$-0.332360\pi$
$978$	−13.5363	−	14.5402i	−0.432843	−	0.464946i
$979$	8.32925	−	7.91943i	0.266204	−	0.253106i
$980$	−4.27567	−	18.8116i	−0.136581	−	0.600914i
$981$	−0.211310	+	1.18680i	−0.00674662	+	0.0378917i
$982$	−26.1987	+	5.56870i	−0.836033	+	0.177704i
$983$	−8.19645	+	38.5613i	−0.261426	+	1.22991i	0.629945	+	0.776640i	$0.283077\pi$
$983$	−8.19645	+	38.5613i	−0.261426	+	1.22991i	−0.891371	+	0.453274i	$0.850256\pi$
$984$	−2.40852	−	7.01388i	−0.0767809	−	0.223594i
$985$	−18.7864	+	42.1949i	−0.598583	+	1.34444i
$986$	3.02649	+	9.31459i	0.0963832	+	0.296637i
$987$	−1.13665	−	48.0636i	−0.0361800	−	1.52988i
$988$	4.88773	+	3.55115i	0.155500	+	0.112977i
$989$	23.6048	+	40.8848i	0.750590	+	1.30006i
$990$	1.65466	+	27.3710i	0.0525885	+	0.869907i
$991$	0.245349	−	0.424956i	0.00779376	−	0.0134992i	−0.862102	−	0.506734i	$-0.830852\pi$
$991$	0.245349	−	0.424956i	0.00779376	−	0.0134992i	0.869896	+	0.493235i	$0.164186\pi$
$992$	−0.0249025	+	0.236932i	−0.000790655	+	0.00752258i
$993$	1.66138	−	18.8087i	0.0527222	−	0.596875i
$994$	6.75365	−	9.43430i	0.214213	−	0.299238i
$995$	37.2088	+	51.2135i	1.17960	+	1.62358i
$996$	−6.45900	−	1.26110i	−0.204661	−	0.0399595i
$997$	4.98138	−	23.4356i	0.157762	−	0.742212i	−0.826135	−	0.563473i	$-0.809465\pi$
$997$	4.98138	−	23.4356i	0.157762	−	0.742212i	0.983897	−	0.178739i	$-0.0572018\pi$
$998$	6.22535	+	6.91395i	0.197060	+	0.218857i
$999$	−30.5716	−	47.3355i	−0.967244	−	1.49763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.95.4	✓	128
3.2	odd	2		462.2.bc.b.95.6	yes	128
7.2	even	3	inner	462.2.bc.a.359.15	yes	128
11.8	odd	10		462.2.bc.b.305.16	yes	128
21.2	odd	6		462.2.bc.b.359.16	yes	128
33.8	even	10	inner	462.2.bc.a.305.15	yes	128
77.30	odd	30		462.2.bc.b.107.6	yes	128
231.107	even	30	inner	462.2.bc.a.107.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.4	✓	128	1.1	even	1	trivial
462.2.bc.a.107.4	yes	128	231.107	even	30	inner
462.2.bc.a.305.15	yes	128	33.8	even	10	inner
462.2.bc.a.359.15	yes	128	7.2	even	3	inner
462.2.bc.b.95.6	yes	128	3.2	odd	2
462.2.bc.b.107.6	yes	128	77.30	odd	30
462.2.bc.b.305.16	yes	128	11.8	odd	10
462.2.bc.b.359.16	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)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(-1.41798 - 0.994648i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.12093 + 2.51765i) q^{5} +(-1.13742 + 1.30625i) q^{6} +(2.40939 - 1.09308i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.02135 + 2.82079i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(-1.41798 - 0.994648i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.12093 + 2.51765i) q^{5} +(-1.13742 + 1.30625i) q^{6} +(2.40939 - 1.09308i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.02135 + 2.82079i) q^{9} +(2.38669 + 1.37795i) q^{10} +(3.22424 - 0.777358i) q^{11} +(1.18020 + 1.26773i) q^{12} +(0.533779 - 0.734683i) q^{13} +(-0.835242 - 2.51045i) q^{14} +(4.09363 - 2.45505i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.233441 + 2.22105i) q^{17} +(2.91210 - 0.720902i) q^{18} +(-1.38320 - 6.50747i) q^{19} +(1.61988 - 2.22958i) q^{20} +(-4.50371 - 0.846530i) q^{21} +(-0.436075 - 3.28783i) q^{22} +(4.85329 - 2.80205i) q^{23} +(1.38415 - 1.04122i) q^{24} +(-1.73642 - 1.92849i) q^{25} +(-0.674863 - 0.607650i) q^{26} +(1.35744 - 5.01571i) q^{27} +(-2.58401 + 0.568253i) q^{28} +(1.35518 + 4.17081i) q^{29} +(-2.01370 - 4.32783i) q^{30} +(-0.217640 + 0.0968995i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.34511 - 2.10470i) q^{33} +2.23328 q^{34} +(0.0512330 + 7.29127i) q^{35} +(-0.412556 - 2.97150i) q^{36} +(7.25637 - 8.05901i) q^{37} +(-6.61640 + 0.695412i) q^{38} +(-1.48764 + 0.510846i) q^{39} +(-2.04804 - 1.84406i) q^{40} +(1.32308 - 4.07202i) q^{41} +(-1.31266 + 4.39055i) q^{42} +8.42414i q^{43} +(-3.31540 + 0.0900140i) q^{44} +(-8.24661 - 0.590505i) q^{45} +(-2.27939 - 5.11959i) q^{46} +(2.18126 + 10.2620i) q^{47} +(-0.890832 - 1.48540i) q^{48} +(4.61035 - 5.26732i) q^{49} +(-2.09943 + 1.52532i) q^{50} +(1.87814 - 3.38160i) q^{51} +(-0.674863 + 0.607650i) q^{52} +(-1.15816 - 2.60126i) q^{53} +(-4.84634 - 1.87429i) q^{54} +(-1.65703 + 8.98886i) q^{55} +(0.295038 + 2.62925i) q^{56} +(-4.51128 + 10.6033i) q^{57} +(4.28962 - 0.911786i) q^{58} +(1.31314 - 6.17786i) q^{59} +(-4.51461 + 1.55029i) q^{60} +(1.19589 - 2.68601i) q^{61} +(0.0736192 + 0.226576i) q^{62} +(5.54418 + 5.67997i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.25135 + 2.16739i) q^{65} +(-2.65189 + 5.09583i) q^{66} +(2.80878 - 4.86495i) q^{67} +(0.233441 - 2.22105i) q^{68} +(-9.66893 - 0.854061i) q^{69} +(7.25668 + 0.711193i) q^{70} +(2.57763 + 3.54780i) q^{71} +(-2.99834 + 0.0996895i) q^{72} +(-2.21647 + 10.4277i) q^{73} +(-7.25637 - 8.05901i) q^{74} +(0.544043 + 4.46168i) q^{75} +6.65285i q^{76} +(6.91874 - 5.39731i) q^{77} +(0.352547 + 1.53289i) q^{78} +(4.75825 + 0.500112i) q^{79} +(-2.04804 + 1.84406i) q^{80} +(-6.91369 + 5.76202i) q^{81} +(-3.91141 - 1.74147i) q^{82} +(-3.07387 + 2.23330i) q^{83} +(4.22929 + 1.76440i) q^{84} +(-5.85348 - 1.90191i) q^{85} +(8.37800 + 0.880563i) q^{86} +(2.22687 - 7.26206i) q^{87} +(-0.257033 + 3.30665i) q^{88} +(3.00107 - 1.73267i) q^{89} +(-1.44928 + 8.13971i) q^{90} +(0.483015 - 2.35360i) q^{91} +(-5.32981 + 1.73176i) q^{92} +(0.404991 + 0.0790733i) q^{93} +(10.4338 - 1.09664i) q^{94} +(17.9340 + 3.81199i) q^{95} +(-1.57038 + 0.730685i) q^{96} +(14.4550 + 10.5022i) q^{97} +(-4.75655 - 5.13568i) q^{98} +(5.48584 + 8.30094i) 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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