LMFDB - Embedded newform 75.2.l.a.62.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(2,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("75.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.l (of order $20$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			62.8
Character	$\chi$	$=$	75.62
Dual form			75.2.l.a.23.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.07952 - 0.329364i) q^{2} +(-1.22169 - 1.22779i) q^{3} +(2.31381 - 0.751802i) q^{4} +(-2.11007 + 0.740012i) q^{5} +(-2.94492 - 2.15084i) q^{6} +(1.98257 + 1.98257i) q^{7} +(0.812071 - 0.413771i) q^{8} +(-0.0149544 + 2.99996i) q^{9} +O(q^{10})$	\(q+(2.07952 - 0.329364i) q^{2} +(-1.22169 - 1.22779i) q^{3} +(2.31381 - 0.751802i) q^{4} +(-2.11007 + 0.740012i) q^{5} +(-2.94492 - 2.15084i) q^{6} +(1.98257 + 1.98257i) q^{7} +(0.812071 - 0.413771i) q^{8} +(-0.0149544 + 2.99996i) q^{9} +(-4.14419 + 2.23385i) q^{10} +(-0.542989 + 0.747360i) q^{11} +(-3.74981 - 1.92241i) q^{12} +(0.794440 - 5.01590i) q^{13} +(4.77577 + 3.46980i) q^{14} +(3.48643 + 1.68666i) q^{15} +(-2.38405 + 1.73211i) q^{16} +(-2.38204 - 4.67502i) q^{17} +(0.956980 + 6.24341i) q^{18} +(-0.201787 - 0.0655644i) q^{19} +(-4.32595 + 3.29860i) q^{20} +(0.0121038 - 4.85626i) q^{21} +(-0.883003 + 1.73299i) q^{22} +(0.0321047 + 0.202701i) q^{23} +(-1.50012 - 0.491557i) q^{24} +(3.90476 - 3.12295i) q^{25} -10.6923i q^{26} +(3.70160 - 3.64666i) q^{27} +(6.07778 + 3.09678i) q^{28} +(0.160641 + 0.494401i) q^{29} +(7.80562 + 2.35915i) q^{30} +(-2.03788 + 6.27196i) q^{31} +(-5.67611 + 5.67611i) q^{32} +(1.58097 - 0.246363i) q^{33} +(-6.49329 - 8.93724i) q^{34} +(-5.65047 - 2.71623i) q^{35} +(2.22078 + 6.95258i) q^{36} +(2.33693 + 0.370134i) q^{37} +(-0.441214 - 0.0698814i) q^{38} +(-7.12905 + 5.15246i) q^{39} +(-1.40733 + 1.47403i) q^{40} +(4.36217 + 6.00401i) q^{41} +(-1.57431 - 10.1027i) q^{42} +(-0.516864 + 0.516864i) q^{43} +(-0.694506 + 2.13747i) q^{44} +(-2.18845 - 6.34119i) q^{45} +(0.133525 + 0.410946i) q^{46} +(8.19208 + 4.17408i) q^{47} +(5.03924 + 0.811018i) q^{48} +0.861150i q^{49} +(7.09145 - 7.78032i) q^{50} +(-2.82985 + 8.63608i) q^{51} +(-1.93278 - 12.2031i) q^{52} +(5.30087 - 10.4035i) q^{53} +(6.49648 - 8.80247i) q^{54} +(0.592688 - 1.97880i) q^{55} +(2.43031 + 0.789657i) q^{56} +(0.166021 + 0.327852i) q^{57} +(0.496893 + 0.975208i) q^{58} +(-0.0415323 + 0.0301750i) q^{59} +(9.33496 + 1.28151i) q^{60} +(-3.17882 - 2.30955i) q^{61} +(-2.17206 + 13.7139i) q^{62} +(-5.97728 + 5.91798i) q^{63} +(-6.46985 + 8.90499i) q^{64} +(2.03550 + 11.1718i) q^{65} +(3.20651 - 1.03303i) q^{66} +(-4.08589 + 2.08186i) q^{67} +(-9.02628 - 9.02628i) q^{68} +(0.209653 - 0.287055i) q^{69} +(-12.6449 - 3.78739i) q^{70} +(3.13172 - 1.01756i) q^{71} +(1.22915 + 2.44237i) q^{72} +(-11.2465 + 1.78126i) q^{73} +4.98160 q^{74} +(-8.60474 - 0.978973i) q^{75} -0.516187 q^{76} +(-2.55821 + 0.405180i) q^{77} +(-13.1280 + 13.0627i) q^{78} +(3.90882 - 1.27005i) q^{79} +(3.74872 - 5.41910i) q^{80} +(-8.99955 - 0.0897252i) q^{81} +(11.0487 + 11.0487i) q^{82} +(-13.9694 + 7.11778i) q^{83} +(-3.62294 - 11.2456i) q^{84} +(8.48584 + 8.10187i) q^{85} +(-0.904592 + 1.24506i) q^{86} +(0.410770 - 0.801238i) q^{87} +(-0.131710 + 0.831583i) q^{88} +(-6.24638 - 4.53826i) q^{89} +(-6.63949 - 12.4658i) q^{90} +(11.5194 - 8.36933i) q^{91} +(0.226675 + 0.444875i) q^{92} +(10.1903 - 5.16028i) q^{93} +(18.4104 + 5.98190i) q^{94} +(0.474302 - 0.0109792i) q^{95} +(13.9035 + 0.0346533i) q^{96} +(-4.00961 + 7.86930i) q^{97} +(0.283631 + 1.79078i) q^{98} +(-2.23393 - 1.64012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	2.07952	−	0.329364i	1.47044	−	0.232895i	0.630762	−	0.775976i	$-0.282742\pi$
$2$	2.07952	−	0.329364i	1.47044	−	0.232895i	0.839680	+	0.543081i	$0.182742\pi$
$3$	−1.22169	−	1.22779i	−0.705342	−	0.708867i
$3$	−1.22169	−	1.22779i	−0.705342	−	0.708867i
$4$	2.31381	−	0.751802i	1.15690	−	0.375901i
$5$	−2.11007	+	0.740012i	−0.943651	+	0.330943i
$5$	−2.11007	+	0.740012i	−0.943651	+	0.330943i
$6$	−2.94492	−	2.15084i	−1.20226	−	0.878077i
$7$	1.98257	+	1.98257i	0.749340	+	0.749340i	0.974355	−	0.225015i	$-0.0722431\pi$
$7$	1.98257	+	1.98257i	0.749340	+	0.749340i	−0.225015	+	0.974355i	$0.572243\pi$
$8$	0.812071	−	0.413771i	0.287110	−	0.146290i
$9$	−0.0149544	+	2.99996i	−0.00498479	+	0.999988i
$10$	−4.14419	+	2.23385i	−1.31051	+	0.706405i
$11$	−0.542989	+	0.747360i	−0.163717	+	0.225338i	−0.882992	−	0.469388i	$-0.844474\pi$
$11$	−0.542989	+	0.747360i	−0.163717	+	0.225338i	0.719274	+	0.694726i	$0.244474\pi$
$12$	−3.74981	−	1.92241i	−1.08248	−	0.554952i
$13$	0.794440	−	5.01590i	0.220338	−	1.39116i	−0.591042	−	0.806641i	$-0.701283\pi$
$13$	0.794440	−	5.01590i	0.220338	−	1.39116i	0.811380	−	0.584519i	$-0.198717\pi$
$14$	4.77577	+	3.46980i	1.27638	+	0.927344i
$15$	3.48643	+	1.68666i	0.900191	+	0.435494i
$16$	−2.38405	+	1.73211i	−0.596012	+	0.433028i
$17$	−2.38204	−	4.67502i	−0.577730	−	1.13386i	−0.976239	−	0.216695i	$-0.930472\pi$
$17$	−2.38204	−	4.67502i	−0.577730	−	1.13386i	0.398509	−	0.917164i	$-0.369528\pi$
$18$	0.956980	+	6.24341i	0.225562	+	1.47159i
$19$	−0.201787	−	0.0655644i	−0.0462930	−	0.0150415i	0.285779	−	0.958296i	$-0.407748\pi$
$19$	−0.201787	−	0.0655644i	−0.0462930	−	0.0150415i	−0.332072	+	0.943254i	$0.607748\pi$
$20$	−4.32595	+	3.29860i	−0.967312	+	0.737589i
$21$	0.0121038	−	4.85626i	0.00264127	−	1.05972i
$22$	−0.883003	+	1.73299i	−0.188257	+	0.369475i
$23$	0.0321047	+	0.202701i	0.00669428	+	0.0422660i	0.990809	−	0.135266i	$-0.0431888\pi$
$23$	0.0321047	+	0.202701i	0.00669428	+	0.0422660i	−0.984115	+	0.177532i	$0.943189\pi$
$24$	−1.50012	−	0.491557i	−0.306211	−	0.100339i
$25$	3.90476	−	3.12295i	0.780953	−	0.624590i
$26$		−	10.6923i		−	2.09694i
$27$	3.70160	−	3.64666i	0.712374	−	0.701800i
$28$	6.07778	+	3.09678i	1.14859	+	0.585237i
$29$	0.160641	+	0.494401i	0.0298302	+	0.0918080i	0.964863	−	0.262753i	$-0.0846304\pi$
$29$	0.160641	+	0.494401i	0.0298302	+	0.0918080i	−0.935033	+	0.354561i	$0.884630\pi$
$30$	7.80562	+	2.35915i	1.42510	+	0.430719i
$31$	−2.03788	+	6.27196i	−0.366015	+	1.12648i	0.583329	+	0.812236i	$0.301750\pi$
$31$	−2.03788	+	6.27196i	−0.366015	+	1.12648i	−0.949343	+	0.314241i	$0.898250\pi$
$32$	−5.67611	+	5.67611i	−1.00340	+	1.00340i
$33$	1.58097	−	0.246363i	0.275211	−	0.0428863i
$34$	−6.49329	−	8.93724i	−1.11359	−	1.53272i
$35$	−5.65047	−	2.71623i	−0.955105	−	0.459126i
$36$	2.22078	+	6.95258i	0.370129	+	1.15876i
$37$	2.33693	+	0.370134i	0.384189	+	0.0608496i	0.345542	−	0.938403i	$-0.387695\pi$
$37$	2.33693	+	0.370134i	0.384189	+	0.0608496i	0.0386473	+	0.999253i	$0.487695\pi$
$38$	−0.441214	−	0.0698814i	−0.0715743	−	0.0113363i
$39$	−7.12905	+	5.15246i	−1.14156	+	0.825053i
$40$	−1.40733	+	1.47403i	−0.222518	+	0.233064i
$41$	4.36217	+	6.00401i	0.681256	+	0.937668i	0.999948	−	0.0101899i	$-0.00324361\pi$
$41$	4.36217	+	6.00401i	0.681256	+	0.937668i	−0.318692	+	0.947858i	$0.603244\pi$
$42$	−1.57431	−	10.1027i	−0.242921	−	1.55888i
$43$	−0.516864	+	0.516864i	−0.0788210	+	0.0788210i	−0.745418	−	0.666597i	$-0.767750\pi$
$43$	−0.516864	+	0.516864i	−0.0788210	+	0.0788210i	0.666597	+	0.745418i	$0.267750\pi$
$44$	−0.694506	+	2.13747i	−0.104701	+	0.322236i
$45$	−2.18845	−	6.34119i	−0.326235	−	0.945289i
$46$	0.133525	+	0.410946i	0.0196871	+	0.0605907i
$47$	8.19208	+	4.17408i	1.19494	+	0.608851i	0.934266	−	0.356576i	$-0.116056\pi$
$47$	8.19208	+	4.17408i	1.19494	+	0.608851i	0.260672	+	0.965427i	$0.416056\pi$
$48$	5.03924	+	0.811018i	0.727352	+	0.117060i
$49$			0.861150i			0.123021i
$50$	7.09145	−	7.78032i	1.00288	−	1.10030i
$51$	−2.82985	+	8.63608i	−0.396258	+	1.20929i
$52$	−1.93278	−	12.2031i	−0.268028	−	1.69226i
$53$	5.30087	−	10.4035i	0.728130	−	1.42904i	−0.168248	−	0.985745i	$-0.553811\pi$
$53$	5.30087	−	10.4035i	0.728130	−	1.42904i	0.896378	−	0.443291i	$-0.146189\pi$
$54$	6.49648	−	8.80247i	0.884059	−	1.19786i
$55$	0.592688	−	1.97880i	0.0799180	−	0.266821i
$56$	2.43031	+	0.789657i	0.324764	+	0.105522i
$57$	0.166021	+	0.327852i	0.0219900	+	0.0434250i
$58$	0.496893	+	0.975208i	0.0652453	+	0.128051i
$59$	−0.0415323	+	0.0301750i	−0.00540705	+	0.00392845i	−0.590485	−	0.807048i	$-0.701064\pi$
$59$	−0.0415323	+	0.0301750i	−0.00540705	+	0.00392845i	0.585078	+	0.810977i	$0.301064\pi$
$60$	9.33496	+	1.28151i	1.20514	+	0.165442i
$61$	−3.17882	−	2.30955i	−0.407006	−	0.295707i	0.365382	−	0.930857i	$-0.380938\pi$
$61$	−3.17882	−	2.30955i	−0.407006	−	0.295707i	−0.772389	+	0.635150i	$0.780938\pi$
$62$	−2.17206	+	13.7139i	−0.275852	+	1.74166i
$63$	−5.97728	+	5.91798i	−0.753066	+	0.745596i
$64$	−6.46985	+	8.90499i	−0.808731	+	1.11312i
$65$	2.03550	+	11.1718i	0.252473	+	1.38569i
$66$	3.20651	−	1.03303i	0.394694	−	0.127157i
$67$	−4.08589	+	2.08186i	−0.499170	+	0.254340i	−0.685401	−	0.728166i	$-0.740373\pi$
$67$	−4.08589	+	2.08186i	−0.499170	+	0.254340i	0.186230	+	0.982506i	$0.440373\pi$
$68$	−9.02628	−	9.02628i	−1.09460	−	1.09460i
$69$	0.209653	−	0.287055i	0.0252392	−	0.0345574i
$70$	−12.6449	−	3.78739i	−1.51135	−	0.452679i
$71$	3.13172	−	1.01756i	0.371667	−	0.120762i	−0.117227	−	0.993105i	$-0.537400\pi$
$71$	3.13172	−	1.01756i	0.371667	−	0.120762i	0.488894	+	0.872343i	$0.337400\pi$
$72$	1.22915	+	2.44237i	0.144857	+	0.287836i
$73$	−11.2465	+	1.78126i	−1.31630	+	0.208481i	−0.774792	−	0.632216i	$-0.782145\pi$
$73$	−11.2465	+	1.78126i	−1.31630	+	0.208481i	−0.541505	+	0.840697i	$0.682145\pi$
$74$	4.98160			0.579100
$75$	−8.60474	−	0.978973i	−0.993590	−	0.113042i
$76$	−0.516187			−0.0592107
$77$	−2.55821	+	0.405180i	−0.291535	+	0.0461745i
$78$	−13.1280	+	13.0627i	−1.48645	+	1.47906i
$79$	3.90882	−	1.27005i	0.439776	−	0.142892i	−0.0807561	−	0.996734i	$-0.525733\pi$
$79$	3.90882	−	1.27005i	0.439776	−	0.142892i	0.520532	+	0.853842i	$0.325733\pi$
$80$	3.74872	−	5.41910i	0.419120	−	0.605874i
$81$	−8.99955	−	0.0897252i	−0.999950	−	0.00996946i
$82$	11.0487	+	11.0487i	1.22013	+	1.22013i
$83$	−13.9694	+	7.11778i	−1.53335	+	0.781278i	−0.997991	−	0.0633496i	$-0.979822\pi$
$83$	−13.9694	+	7.11778i	−1.53335	+	0.781278i	−0.535354	+	0.844628i	$0.679822\pi$
$84$	−3.62294	−	11.2456i	−0.395296	−	1.22699i
$85$	8.48584	+	8.10187i	0.920419	+	0.878771i
$86$	−0.904592	+	1.24506i	−0.0975447	+	0.134259i
$87$	0.410770	−	0.801238i	0.0440391	−	0.0859017i
$88$	−0.131710	+	0.831583i	−0.0140403	+	0.0886470i
$89$	−6.24638	−	4.53826i	−0.662115	−	0.481054i	0.205262	−	0.978707i	$-0.434195\pi$
$89$	−6.24638	−	4.53826i	−0.662115	−	0.481054i	−0.867376	+	0.497653i	$0.834195\pi$
$90$	−6.63949	−	12.4658i	−0.699864	−	1.31401i
$91$	11.5194	−	8.36933i	1.20756	−	0.877344i
$92$	0.226675	+	0.444875i	0.0236325	+	0.0463814i
$93$	10.1903	−	5.16028i	1.05669	−	0.535096i
$94$	18.4104	+	5.98190i	1.89889	+	0.616986i
$95$	0.474302	−	0.0109792i	0.0486623	−	0.00112644i
$96$	13.9035	+	0.0346533i	1.41902	+	0.00353679i
$97$	−4.00961	+	7.86930i	−0.407114	+	0.799006i	−0.999980	−	0.00629464i	$-0.997996\pi$
$97$	−4.00961	+	7.86930i	−0.407114	+	0.799006i	0.592866	+	0.805301i	$0.297996\pi$
$98$	0.283631	+	1.79078i	0.0286511	+	0.180896i
$99$	−2.23393	−	1.64012i	−0.224519	−	0.164839i
$100$	6.68704	−	10.1615i	0.668704	−	1.01615i
$101$		−	5.72257i		−	0.569417i	−0.958614	−	0.284709i	$-0.908103\pi$
$101$		−	5.72257i		−	0.569417i	0.958614	−	0.284709i	$-0.0918969\pi$
$102$	−3.04032	+	18.8909i	−0.301036	+	1.87048i
$103$	−2.02479	−	1.03168i	−0.199508	−	0.101655i	0.351382	−	0.936232i	$-0.385712\pi$
$103$	−2.02479	−	1.03168i	−0.199508	−	0.101655i	−0.550891	+	0.834578i	$0.685712\pi$
$104$	−1.43029	−	4.40198i	−0.140252	−	0.431650i
$105$	3.56815	+	10.2560i	0.348216	+	1.00088i
$106$	7.59671	−	23.3803i	0.737858	−	2.27089i
$107$	0.338061	−	0.338061i	0.0326816	−	0.0326816i	−0.690577	−	0.723259i	$-0.742643\pi$
$107$	0.338061	−	0.338061i	0.0326816	−	0.0326816i	0.723259	+	0.690577i	$0.242643\pi$
$108$	5.82324	−	11.2205i	0.560341	−	1.07970i
$109$	−2.94311	−	4.05085i	−0.281899	−	0.388001i	0.644463	−	0.764636i	$-0.277081\pi$
$109$	−2.94311	−	4.05085i	−0.281899	−	0.388001i	−0.926362	+	0.376635i	$0.877081\pi$
$110$	0.580761	−	4.31016i	0.0553734	−	0.410958i
$111$	−2.40055	−	3.32146i	−0.227851	−	0.315259i
$112$	−8.16057	−	1.29251i	−0.771102	−	0.122131i
$113$	5.72305	+	0.906443i	0.538380	+	0.0852710i	0.419702	−	0.907662i	$-0.362135\pi$
$113$	5.72305	+	0.906443i	0.538380	+	0.0852710i	0.118678	+	0.992933i	$0.462135\pi$
$114$	0.453226	+	0.627093i	0.0424485	+	0.0587326i
$115$	−0.217744	−	0.403955i	−0.0203047	−	0.0376690i
$116$	0.743383	+	1.02318i	0.0690214	+	0.0949998i
$117$	15.0356	+	2.45830i	1.39004	+	0.227270i
$118$	−0.0764287	+	0.0764287i	−0.00703583	+	0.00703583i
$119$	4.54599	−	13.9911i	0.416730	−	1.28256i
$120$	3.52912	−	0.0728920i	0.322163	−	0.00665410i
$121$	3.13548	+	9.65000i	0.285043	+	0.877273i
$122$	−7.37110	−	3.75576i	−0.667348	−	0.340031i
$123$	2.04247	−	12.6909i	0.184164	−	1.14430i
$124$			16.0442i			1.44081i
$125$	−5.92829	+	9.47921i	−0.530243	+	0.847846i
$126$	−10.4807	+	14.2753i	−0.933695	+	1.27174i
$127$	−2.03459	−	12.8459i	−0.180541	−	1.13989i	−0.896924	−	0.442184i	$-0.854204\pi$
$127$	−2.03459	−	12.8459i	−0.180541	−	1.13989i	0.716383	−	0.697707i	$-0.245796\pi$
$128$	−3.23263	+	6.34440i	−0.285727	+	0.560771i
$129$	1.26605	+	0.00315552i	0.111469	+	0.000277828i
$130$	7.91245	+	22.5615i	0.693967	+	1.97878i
$131$	19.2637	+	6.25917i	1.68308	+	0.546866i	0.985505	−	0.169646i	$-0.0542624\pi$
$131$	19.2637	+	6.25917i	1.68308	+	0.546866i	0.697575	+	0.716512i	$0.254262\pi$
$132$	3.47284	−	1.75861i	0.302272	−	0.153068i
$133$	−0.270070	−	0.530041i	−0.0234180	−	0.0459604i
$134$	−7.81099	+	5.67502i	−0.674767	+	0.490247i
$135$	−5.11206	+	10.4339i	−0.439976	+	0.898009i
$136$	−3.86878	−	2.81083i	−0.331745	−	0.241027i
$137$	1.75026	−	11.0507i	0.149534	−	0.944123i	−0.792808	−	0.609472i	$-0.791381\pi$
$137$	1.75026	−	11.0507i	0.149534	−	0.944123i	0.942342	−	0.334651i	$-0.108619\pi$
$138$	0.341432	−	0.665989i	0.0290646	−	0.0566927i
$139$	2.00883	−	2.76492i	0.170387	−	0.234517i	−0.715281	−	0.698837i	$-0.753701\pi$
$139$	2.00883	−	2.76492i	0.170387	−	0.234517i	0.885668	+	0.464320i	$0.153701\pi$
$140$	−15.1162	−	2.03679i	−1.27755	−	0.172140i
$141$	−4.88327	−	15.1576i	−0.411246	−	1.27650i
$142$	6.17734	−	3.14751i	0.518391	−	0.264133i
$143$	3.31731	+	3.31731i	0.277408	+	0.277408i
$144$	−5.16062	−	7.17796i	−0.430052	−	0.598164i
$145$	−0.704825	−	0.924343i	−0.0585326	−	0.0767625i
$146$	−22.8005	+	7.40834i	−1.88699	+	0.613119i
$147$	1.05731	−	1.05206i	0.0872058	−	0.0867722i
$148$	5.68548	−	0.900492i	0.467344	−	0.0740199i
$149$	4.86008			0.398153			0.199077	−	0.979984i	$-0.436206\pi$
$149$	4.86008			0.398153			0.199077	+	0.979984i	$0.436206\pi$
$150$	−18.2162	+	0.798296i	−1.48734	+	0.0651806i
$151$	8.48112			0.690184			0.345092	−	0.938569i	$-0.387848\pi$
$151$	8.48112			0.690184			0.345092	+	0.938569i	$0.387848\pi$
$152$	−0.190994	+	0.0302504i	−0.0154916	+	0.00245363i
$153$	14.0605	−	7.07613i	1.13673	−	0.572071i
$154$	−5.18639	+	1.68516i	−0.417931	+	0.135794i
$155$	−0.341256	−	14.7423i	−0.0274103	−	1.18413i
$156$	−12.6216	+	17.2814i	−1.01054	+	1.38362i
$157$	−10.9610	−	10.9610i	−0.874786	−	0.874786i	0.118204	−	0.992989i	$-0.462286\pi$
$157$	−10.9610	−	10.9610i	−0.874786	−	0.874786i	−0.992989	+	0.118204i	$0.962286\pi$
$158$	7.71015	−	3.92852i	0.613387	−	0.312536i
$159$	−19.2494	+	6.20151i	−1.52658	+	0.491812i
$160$	7.77658	−	16.1774i	0.614793	−	1.27893i
$161$	−0.338219	+	0.465518i	−0.0266554	+	0.0366879i
$162$	−18.7443	+	2.77754i	−1.47269	+	0.218224i
$163$	−2.79341	+	17.6369i	−0.218797	+	1.38143i	0.596605	+	0.802535i	$0.296516\pi$
$163$	−2.79341	+	17.6369i	−0.218797	+	1.38143i	−0.815402	+	0.578895i	$0.803484\pi$
$164$	14.6070	+	10.6126i	1.14062	+	0.828708i
$165$	−3.15364	+	1.68978i	−0.245510	+	0.131549i
$166$	−26.7054	+	19.4026i	−2.07274	+	1.50593i
$167$	4.18368	+	8.21094i	0.323743	+	0.635381i	0.994317	−	0.106461i	$-0.0339521\pi$
$167$	4.18368	+	8.21094i	0.323743	+	0.635381i	−0.670574	+	0.741843i	$0.733952\pi$
$168$	−1.99955	−	3.94864i	−0.154269	−	0.304644i
$169$	−12.1644	−	3.95244i	−0.935721	−	0.304034i
$170$	20.3149	+	14.0531i	1.55808	+	1.07782i
$171$	0.199708	−	0.604372i	0.0152721	−	0.0462175i
$172$	−0.807345	+	1.58450i	−0.0615595	+	0.120817i
$173$	1.96990	+	12.4375i	0.149769	+	0.945602i	0.942056	+	0.335454i	$0.108890\pi$
$173$	1.96990	+	12.4375i	0.149769	+	0.945602i	−0.792288	+	0.610148i	$0.791110\pi$
$174$	0.590305	−	1.80148i	0.0447509	−	0.136570i
$175$	13.9329	+	1.55000i	1.05323	+	0.117169i
$176$		−	2.72226i		−	0.205198i
$177$	0.0877882	+	0.0141287i	0.00659857	+	0.00106198i
$178$	−14.4842	−	7.38007i	−1.08564	−	0.553160i
$179$	3.09902	+	9.53780i	0.231631	+	0.712888i	0.997550	+	0.0699512i	$0.0222844\pi$
$179$	3.09902	+	9.53780i	0.231631	+	0.712888i	−0.765919	+	0.642937i	$0.777716\pi$
$180$	−9.83098	−	13.0270i	−0.732758	−	0.970976i
$181$	−1.02409	+	3.15183i	−0.0761202	+	0.234274i	−0.981875	−	0.189527i	$-0.939304\pi$
$181$	−1.02409	+	3.15183i	−0.0761202	+	0.234274i	0.905755	+	0.423801i	$0.139304\pi$
$182$	21.1982	−	21.1982i	1.57132	−	1.57132i
$183$	1.04788	+	6.72448i	0.0774615	+	0.497088i
$184$	0.109943	+	0.151324i	0.00810510	+	0.0111557i
$185$	−5.20499	+	0.948351i	−0.382678	+	0.0697241i
$186$	19.4914	−	14.0872i	1.42918	−	1.03293i
$187$	4.78735	+	0.758242i	0.350086	+	0.0554481i
$188$	22.0930	+	3.49919i	1.61130	+	0.255204i
$189$	14.5684	+	0.108933i	1.05970	+	0.00792374i
$190$	0.982703	−	0.179049i	0.0712928	−	0.0129896i
$191$	−5.50332	−	7.57467i	−0.398206	−	0.548084i	0.562086	−	0.827079i	$-0.309999\pi$
$191$	−5.50332	−	7.57467i	−0.398206	−	0.548084i	−0.960293	+	0.278995i	$0.909999\pi$
$192$	18.8376	−	2.93548i	1.35949	−	0.211850i
$193$	1.55757	−	1.55757i	0.112116	−	0.112116i	−0.648823	−	0.760939i	$-0.724738\pi$
$193$	1.55757	−	1.55757i	0.112116	−	0.112116i	0.760939	+	0.648823i	$0.224738\pi$
$194$	−5.74620	+	17.6850i	−0.412553	+	1.26971i
$195$	11.2299	−	16.1476i	0.804189	−	1.15635i
$196$	0.647414	+	1.99254i	0.0462439	+	0.142324i
$197$	−13.7702	−	7.01627i	−0.981087	−	0.499889i	−0.111551	−	0.993759i	$-0.535582\pi$
$197$	−13.7702	−	7.01627i	−0.981087	−	0.499889i	−0.869536	+	0.493870i	$0.835582\pi$
$198$	−5.18571	−	2.67489i	−0.368532	−	0.190096i
$199$		−	6.87281i		−	0.487200i	−0.969876	−	0.243600i	$-0.921672\pi$
$199$		−	6.87281i		−	0.487200i	0.969876	−	0.243600i	$-0.0783285\pi$
$200$	1.87876	−	4.15173i	0.132848	−	0.293572i
$201$	7.54778	+	2.47324i	0.532379	+	0.174449i
$202$	−1.88481	−	11.9002i	−0.132615	−	0.837295i
$203$	−0.661703	+	1.29866i	−0.0464424	+	0.0911484i
$204$	−0.0551065	+	22.1097i	−0.00385823	+	1.54799i
$205$	−13.6475	−	9.44080i	−0.953183	−	0.659374i
$206$	−4.55039	−	1.47851i	−0.317041	−	0.103013i
$207$	−0.608575	+	0.0932815i	−0.0422989	+	0.00648351i
$208$	6.79412	+	13.3342i	0.471088	+	0.924561i
$209$	0.158568	−	0.115207i	0.0109684	−	0.00796900i
$210$	10.7980	+	20.1523i	0.745133	+	1.39064i
$211$	−3.79498	−	2.75721i	−0.261257	−	0.189814i	0.449444	−	0.893309i	$-0.351622\pi$
$211$	−3.79498	−	2.75721i	−0.261257	−	0.189814i	−0.710701	+	0.703494i	$0.751622\pi$
$212$	4.44379	−	28.0570i	0.305201	−	1.92696i
$213$	−5.07534	−	2.60197i	−0.347757	−	0.178284i
$214$	0.591659	−	0.814349i	0.0404450	−	0.0556677i
$215$	0.708132	−	1.47310i	0.0482942	−	0.100465i
$216$	1.49708	−	4.49296i	0.101864	−	0.305707i
$217$	−16.4748	+	8.39434i	−1.11838	+	0.569845i
$218$	−7.45447	−	7.45447i	−0.504880	−	0.504880i
$219$	15.9267	+	11.6322i	1.07623	+	0.786029i
$220$	−0.116299	−	5.02415i	−0.00784089	−	0.338728i
$221$	−25.3418	+	8.23406i	−1.70468	+	0.553883i
$222$	−6.08597	−	6.11638i	−0.408463	−	0.410505i
$223$	16.4719	−	2.60889i	1.10304	−	0.174704i	0.421745	−	0.906715i	$-0.361418\pi$
$223$	16.4719	−	2.60889i	1.10304	−	0.174704i	0.681293	+	0.732010i	$0.261418\pi$
$224$	−22.5065			−1.50378
$225$	9.31034	+	11.7608i	0.620689	+	0.784057i
$226$	12.1998			0.811516
$227$	−21.5699	+	3.41634i	−1.43164	+	0.226750i	−0.823608	−	0.567159i	$-0.808042\pi$
$227$	−21.5699	+	3.41634i	−1.43164	+	0.226750i	−0.608036	+	0.793909i	$0.708042\pi$
$228$	0.630620	+	0.633771i	0.0417638	+	0.0419725i
$229$	14.7727	−	4.79995i	0.976209	−	0.317190i	0.222889	−	0.974844i	$-0.428451\pi$
$229$	14.7727	−	4.79995i	0.976209	−	0.317190i	0.753320	+	0.657654i	$0.228451\pi$
$230$	−0.585851	−	0.768314i	−0.0386299	−	0.0506612i
$231$	3.62281	+	2.64594i	0.238363	+	0.174090i
$232$	0.335020	+	0.335020i	0.0219952	+	0.0219952i
$233$	4.97593	−	2.53536i	0.325984	−	0.166097i	−0.283338	−	0.959020i	$-0.591442\pi$
$233$	4.97593	−	2.53536i	0.325984	−	0.166097i	0.609322	+	0.792923i	$0.291442\pi$
$234$	32.0766	+	0.159897i	2.09691	+	0.0104528i
$235$	−20.3747	−	2.74534i	−1.32910	−	0.179086i
$236$	−0.0734122	+	0.101043i	−0.00477873	+	0.00657735i
$237$	−6.33472	−	3.24761i	−0.411484	−	0.210955i
$238$	4.84531	−	30.5921i	0.314075	−	1.98299i
$239$	−14.9846	−	10.8869i	−0.969271	−	0.704217i	−0.0139860	−	0.999902i	$-0.504452\pi$
$239$	−14.9846	−	10.8869i	−0.969271	−	0.704217i	−0.955285	+	0.295685i	$0.904452\pi$
$240$	−11.2333	+	2.01780i	−0.725107	+	0.130248i
$241$	−10.4630	+	7.60183i	−0.673982	+	0.489677i	−0.871356	−	0.490651i	$-0.836759\pi$
$241$	−10.4630	+	7.60183i	−0.673982	+	0.489677i	0.197373	+	0.980328i	$0.436759\pi$
$242$	9.69864	+	19.0347i	0.623453	+	1.22359i
$243$	10.8845	+	11.1592i	0.698240	+	0.715864i
$244$	−9.09151	−	2.95401i	−0.582024	−	0.189111i
$245$	−0.637262	−	1.81708i	−0.0407131	−	0.116089i
$246$	0.0674537	−	27.0636i	0.00430069	−	1.72551i
$247$	−0.489172	+	0.960054i	−0.0311253	+	0.0610868i
$248$	0.940248	+	5.93649i	0.0597058	+	0.376968i
$249$	25.8055	+	8.45587i	1.63536	+	0.535869i
$250$	−9.20590	+	21.6648i	−0.582232	+	1.37020i
$251$		−	4.70685i		−	0.297094i	−0.988905	−	0.148547i	$-0.952540\pi$
$251$		−	4.70685i		−	0.297094i	0.988905	−	0.148547i	$-0.0474596\pi$
$252$	−9.38113	+	18.1868i	−0.590955	+	1.14566i
$253$	−0.168923	−	0.0860706i	−0.0106201	−	0.00541121i
$254$	−8.46195	−	26.0432i	−0.530950	−	1.63410i
$255$	−0.419633	−	20.3168i	−0.0262784	−	1.27229i
$256$	2.17010	−	6.67887i	0.135631	−	0.417429i
$257$	11.3472	−	11.3472i	0.707820	−	0.707820i	−0.258256	−	0.966076i	$-0.583148\pi$
$257$	11.3472	−	11.3472i	0.707820	−	0.707820i	0.966076	+	0.258256i	$0.0831479\pi$
$258$	2.63381	−	0.410428i	0.163974	−	0.0255522i
$259$	3.89931	+	5.36694i	0.242291	+	0.333485i
$260$	13.1087	+	24.3191i	0.812969	+	1.50820i
$261$	−1.48559	+	0.474522i	−0.0919555	+	0.0293722i
$262$	42.1209	+	6.67129i	2.60223	+	0.412154i
$263$	−7.06296	−	1.11866i	−0.435521	−	0.0689797i	−0.0651753	−	0.997874i	$-0.520761\pi$
$263$	−7.06296	−	1.11866i	−0.435521	−	0.0689797i	−0.370345	+	0.928894i	$0.620761\pi$
$264$	1.18192	−	0.854223i	0.0727422	−	0.0525738i
$265$	−3.48644	+	25.8749i	−0.214170	+	1.58948i
$266$	−0.736191	−	1.01328i	−0.0451388	−	0.0621282i
$267$	2.05908	+	13.2136i	0.126014	+	0.808659i
$268$	−7.88881	+	7.88881i	−0.481886	+	0.481886i
$269$	0.354740	−	1.09178i	0.0216289	−	0.0665668i	−0.939660	−	0.342111i	$-0.888858\pi$
$269$	0.354740	−	1.09178i	0.0216289	−	0.0665668i	0.961288	+	0.275544i	$0.0888581\pi$
$270$	−7.19408	+	23.3813i	−0.437818	+	1.42294i
$271$	−2.97307	−	9.15016i	−0.180601	−	0.555832i	0.819244	−	0.573445i	$-0.194393\pi$
$271$	−2.97307	−	9.15016i	−0.180601	−	0.555832i	−0.999845	+	0.0176127i	$0.994393\pi$
$272$	13.7766	+	7.01952i	0.835328	+	0.425621i
$273$	−24.3489	−	3.91872i	−1.47366	−	0.237172i
$274$		−	23.5566i		−	1.42310i
$275$	0.213725	+	4.61399i	0.0128881	+	0.278234i
$276$	0.269288	−	0.821808i	0.0162092	−	0.0494670i
$277$	3.59160	+	22.6764i	0.215798	+	1.36250i	0.823042	+	0.567980i	$0.192275\pi$
$277$	3.59160	+	22.6764i	0.215798	+	1.36250i	−0.607244	+	0.794515i	$0.707725\pi$
$278$	3.26674	−	6.41134i	0.195926	−	0.384527i
$279$	−18.7852	−	6.20737i	−1.12464	−	0.371625i
$280$	−5.71248	+	0.132233i	−0.341386	+	0.00790242i
$281$	8.86944	+	2.88186i	0.529107	+	0.171917i	0.561374	−	0.827562i	$-0.310273\pi$
$281$	8.86944	+	2.88186i	0.529107	+	0.171917i	−0.0322675	+	0.999479i	$0.510273\pi$
$282$	−15.1472	−	29.9122i	−0.902004	−	1.78124i
$283$	−15.1028	−	29.6409i	−0.897769	−	1.76197i	−0.582143	−	0.813087i	$-0.697786\pi$
$283$	−15.1028	−	29.6409i	−0.897769	−	1.76197i	−0.315626	−	0.948884i	$-0.602214\pi$
$284$	6.48121	−	4.70887i	0.384589	−	0.279420i
$285$	−0.592929	−	0.568931i	−0.0351221	−	0.0337006i
$286$	7.99102	+	5.80581i	0.472519	+	0.343305i
$287$	−3.25506	+	20.5516i	−0.192140	+	1.21313i
$288$	−16.9432	−	17.1130i	−0.998390	−	1.00839i
$289$	−6.18935	+	8.51891i	−0.364080	+	0.501112i
$290$	−1.77014	−	1.69005i	−0.103946	−	0.0992429i
$291$	14.5604	−	4.69086i	0.853544	−	0.274983i
$292$	−24.6830	+	12.5766i	−1.44446	+	0.735990i
$293$	19.5495	+	19.5495i	1.14209	+	1.14209i	0.988067	+	0.154025i	$0.0492235\pi$
$293$	19.5495	+	19.5495i	1.14209	+	1.14209i	0.154025	+	0.988067i	$0.450776\pi$
$294$	1.85220	−	2.53601i	0.108022	−	0.147903i
$295$	0.0653061	−	0.0944057i	0.00380227	−	0.00549651i
$296$	2.05090	−	0.666379i	0.119206	−	0.0387325i
$297$	0.715438	+	4.74653i	0.0415139	+	0.275422i
$298$	10.1066	−	1.60073i	0.585462	−	0.0927280i
$299$	1.04223			0.0602738
$300$	−20.6457	+	4.20391i	−1.19198	+	0.242713i
$301$	−2.04944			−0.118127
$302$	17.6367	−	2.79337i	1.01488	−	0.160741i
$303$	−7.02614	+	6.99120i	−0.403641	+	0.401634i
$304$	0.594634	−	0.193208i	0.0341046	−	0.0110813i
$305$	8.41662	+	2.52094i	0.481934	+	0.144348i
$306$	26.9085	−	19.3460i	1.53826	−	1.10594i
$307$	16.9428	+	16.9428i	0.966975	+	0.966975i	0.999472	−	0.0324970i	$-0.0103459\pi$
$307$	16.9428	+	16.9428i	0.966975	+	0.966975i	−0.0324970	+	0.999472i	$0.510346\pi$
$308$	−5.61458	+	2.86077i	−0.319921	+	0.163008i
$309$	1.20697	+	3.74642i	0.0686621	+	0.213126i
$310$	−5.56523	−	30.5445i	−0.316084	−	1.73481i
$311$	1.70402	−	2.34539i	0.0966263	−	0.132995i	−0.757966	−	0.652294i	$-0.773807\pi$
$311$	1.70402	−	2.34539i	0.0966263	−	0.132995i	0.854593	+	0.519299i	$0.173807\pi$
$312$	−3.65736	+	7.13395i	−0.207057	+	0.403881i
$313$	−2.13060	+	13.4521i	−0.120429	+	0.760357i	0.851374	+	0.524560i	$0.175770\pi$
$313$	−2.13060	+	13.4521i	−0.120429	+	0.760357i	−0.971802	+	0.235797i	$0.924230\pi$
$314$	−26.4038	−	19.1835i	−1.49006	−	1.08259i
$315$	8.23308	−	16.9106i	0.463881	−	0.952804i
$316$	8.08943	−	5.87731i	0.455066	−	0.330625i
$317$	−13.7296	−	26.9459i	−0.771132	−	1.51343i	−0.855963	−	0.517037i	$-0.827035\pi$
$317$	−13.7296	−	26.9459i	−0.771132	−	1.51343i	0.0848304	−	0.996395i	$-0.472965\pi$
$318$	−37.9870	+	19.2362i	−2.13020	+	1.07871i
$319$	−0.456722	−	0.148398i	−0.0255715	−	0.00830869i
$320$	7.06202	−	23.5779i	0.394779	−	1.31804i
$321$	−0.828074	−	0.00206390i	−0.0462186	−	0.000115196i
$322$	−0.550007	+	1.07945i	−0.0306507	+	0.0601554i
$323$	0.174149	+	1.09953i	0.00968991	+	0.0611797i
$324$	−20.8907	+	6.55828i	−1.16059	+	0.364349i
$325$	−12.5623	−	22.0669i	−0.696831	−	1.22405i
$326$			37.5964i			2.08227i
$327$	−1.37804	+	8.56241i	−0.0762057	+	0.473503i
$328$	6.02667	+	3.07074i	0.332767	+	0.169553i
$329$	7.96597	+	24.5167i	0.439178	+	1.35165i
$330$	−6.00150	+	4.55262i	−0.330372	+	0.250613i
$331$	−2.97741	+	9.16351i	−0.163653	+	0.503672i	−0.998935	−	0.0461504i	$-0.985305\pi$
$331$	−2.97741	+	9.16351i	−0.163653	+	0.503672i	0.835282	+	0.549823i	$0.185305\pi$
$332$	−26.9714	+	26.9714i	−1.48025	+	1.48025i
$333$	−1.14533	+	7.00517i	−0.0627639	+	0.383881i
$334$	11.4044	+	15.6969i	0.624023	+	0.858894i
$335$	7.08089	−	7.41647i	0.386870	−	0.405205i
$336$	8.38275	+	11.5985i	0.457316	+	0.632752i
$337$	7.78320	+	1.23274i	0.423978	+	0.0671515i	0.364778	−	0.931095i	$-0.381145\pi$
$337$	7.78320	+	1.23274i	0.423978	+	0.0671515i	0.0592003	+	0.998246i	$0.481145\pi$
$338$	−26.5978	−	4.21268i	−1.44673	−	0.229140i
$339$	−5.87887	−	8.13412i	−0.319296	−	0.441785i
$340$	25.7256	+	12.3665i	1.39517	+	0.670668i
$341$	−3.58087	−	4.92864i	−0.193915	−	0.266901i
$342$	0.216240	−	1.32258i	0.0116929	−	0.0715169i
$343$	12.1707	−	12.1707i	0.657155	−	0.657155i
$344$	−0.205867	+	0.633593i	−0.0110996	+	0.0341611i
$345$	−0.229957	+	0.760851i	−0.0123805	+	0.0409629i
$346$	8.19289	+	25.2151i	0.440452	+	1.35557i
$347$	−2.91927	−	1.48744i	−0.156715	−	0.0798502i	0.373874	−	0.927479i	$-0.378029\pi$
$347$	−2.91927	−	1.48744i	−0.156715	−	0.0798502i	−0.530589	+	0.847629i	$0.678029\pi$
$348$	0.348070	−	2.16273i	0.0186585	−	0.115934i
$349$		−	10.1798i		−	0.544913i	−0.962168	−	0.272457i	$-0.912164\pi$
$349$		−	10.1798i		−	0.544913i	0.962168	−	0.272457i	$-0.0878361\pi$
$350$	29.4843	−	1.36574i	1.57600	−	0.0730019i
$351$	−15.3506	−	21.4639i	−0.819353	−	1.14566i
$352$	−1.16003	−	7.32417i	−0.0618300	−	0.390379i
$353$	−0.838034	+	1.64473i	−0.0446041	+	0.0875404i	−0.912233	−	0.409672i	$-0.865643\pi$
$353$	−0.838034	+	1.64473i	−0.0446041	+	0.0875404i	0.867629	+	0.497213i	$0.165643\pi$
$354$	0.187211		0.000466606i	0.00995014		2.47999e-5i
$355$	−5.85514	+	4.46463i	−0.310759	+	0.236958i
$356$	−17.8648	−	5.80462i	−0.946832	−	0.307644i
$357$	−22.7320	+	11.5112i	−1.20310	+	0.609240i
$358$	9.58587	+	18.8133i	0.506629	+	0.994315i
$359$	21.6017	−	15.6946i	1.14009	−	0.828327i	0.152962	−	0.988232i	$-0.451119\pi$
$359$	21.6017	−	15.6946i	1.14009	−	0.828327i	0.987132	+	0.159905i	$0.0511187\pi$
$360$	−4.40098	−	4.24398i	−0.231952	−	0.223677i
$361$	−15.3349	−	11.1415i	−0.807100	−	0.586393i
$362$	−1.09152	+	6.89160i	−0.0573691	+	0.362214i
$363$	8.01764	−	15.6390i	0.420817	−	0.820836i
$364$	20.3616	−	28.0253i	1.06724	−	1.46893i
$365$	22.4126	−	12.0811i	1.17313	−	0.632353i
$366$	4.39389	+	13.6386i	0.229672	+	0.712899i
$367$	27.2917	−	13.9058i	1.42461	−	0.725877i	0.439575	−	0.898206i	$-0.355129\pi$
$367$	27.2917	−	13.9058i	1.42461	−	0.725877i	0.985040	+	0.172328i	$0.0551290\pi$
$368$	−0.427640	−	0.427640i	−0.0222923	−	0.0222923i
$369$	−18.0770	+	12.9966i	−0.941053	+	0.676573i
$370$	−10.5115	+	3.68645i	−0.546468	+	0.191649i
$371$	31.1350	−	10.1164i	1.61645	−	0.525217i
$372$	19.6990	−	19.6010i	1.02134	−	1.01627i
$373$	1.84979	−	0.292978i	0.0957785	−	0.0151698i	−0.108361	−	0.994112i	$-0.534560\pi$
$373$	1.84979	−	0.292978i	0.0957785	−	0.0151698i	0.204140	+	0.978942i	$0.434560\pi$
$374$	10.2051			0.527694
$375$	18.8810	−	4.30192i	0.975013	−	0.222150i
$376$	8.37966			0.432148
$377$	2.60749	−	0.412985i	0.134292	−	0.0212698i
$378$	30.3312	−	4.57178i	1.56007	−	0.235147i
$379$	−22.0932	+	7.17851i	−1.13485	+	0.368735i	−0.815417	−	0.578874i	$-0.803492\pi$
$379$	−22.0932	+	7.17851i	−1.13485	+	0.368735i	−0.319433	+	0.947609i	$0.603492\pi$
$380$	1.08919	−	0.381985i	0.0558742	−	0.0195954i
$381$	−13.2865	+	18.1918i	−0.680688	+	0.931992i
$382$	−13.9391	−	13.9391i	−0.713186	−	0.713186i
$383$	−29.5378	+	15.0503i	−1.50931	+	0.769032i	−0.996016	−	0.0891798i	$-0.971575\pi$
$383$	−29.5378	+	15.0503i	−1.50931	+	0.769032i	−0.513295	+	0.858212i	$0.671575\pi$
$384$	11.7389	−	3.78187i	0.599047	−	0.192993i
$385$	5.09815	−	2.74806i	0.259826	−	0.140054i
$386$	2.72599	−	3.75201i	0.138749	−	0.190972i
$387$	−1.54284	−	1.55830i	−0.0784271	−	0.0792129i
$388$	−3.36131	+	21.2225i	−0.170645	+	1.07741i
$389$	24.6907	+	17.9388i	1.25187	+	0.909534i	0.998329	−	0.0577917i	$-0.0184059\pi$
$389$	24.6907	+	17.9388i	1.25187	+	0.909534i	0.253537	+	0.967326i	$0.418406\pi$
$390$	18.0343	−	37.2780i	0.913204	−	1.88764i
$391$	0.871156	−	0.632932i	0.0440563	−	0.0320087i
$392$	0.356319	+	0.699315i	0.0179968	+	0.0353207i
$393$	−15.8493	−	31.2986i	−0.799492	−	1.57881i
$394$	−30.9463	−	10.0551i	−1.55905	−	0.506567i
$395$	−7.30801	+	5.57247i	−0.367706	+	0.280381i
$396$	−6.40194	−	2.11546i	−0.321710	−	0.106306i
$397$	15.9894	−	31.3810i	0.802487	−	1.57497i	−0.0156032	−	0.999878i	$-0.504967\pi$
$397$	15.9894	−	31.3810i	0.802487	−	1.57497i	0.818090	−	0.575090i	$-0.195033\pi$
$398$	−2.26365	−	14.2921i	−0.113467	−	0.716400i
$399$	−0.320841	+	0.979135i	−0.0160621	+	0.0490181i
$400$	−3.89985	+	14.2088i	−0.194992	+	0.710438i
$401$			1.91078i			0.0954199i	0.998861	+	0.0477099i	$0.0151923\pi$
$401$			1.91078i			0.0954199i	−0.998861	+	0.0477099i	$0.984808\pi$
$402$	16.5103	+	2.65718i	0.823461	+	0.132528i
$403$	29.8405	+	15.2045i	1.48646	+	0.757391i
$404$	−4.30224	−	13.2409i	−0.214045	−	0.658761i
$405$	19.0561	−	6.47045i	0.946903	−	0.321519i
$406$	−0.948291	+	2.91854i	−0.0470629	+	0.144845i
$407$	−1.54555	+	1.54555i	−0.0766102	+	0.0766102i
$408$	1.27532	+	8.18402i	0.0631377	+	0.405169i
$409$	21.1310	+	29.0844i	1.04486	+	1.43813i	0.893179	+	0.449701i	$0.148469\pi$
$409$	21.1310	+	29.0844i	1.04486	+	1.43813i	0.151683	+	0.988429i	$0.451531\pi$
$410$	−31.4897	−	15.1373i	−1.55517	−	0.747580i
$411$	−15.7062	+	11.3515i	−0.774731	+	0.559930i
$412$	−5.46060	−	0.864873i	−0.269024	−	0.0426093i
$413$	−0.142165	−	0.0225167i	−0.00699546	−	0.00110797i
$414$	−1.23482	+	0.394423i	−0.0606881	+	0.0193848i
$415$	24.2092	−	25.3566i	1.18838	−	1.24470i
$416$	23.9615	+	32.9801i	1.17481	+	1.61698i
$417$	−5.84892	+	0.911440i	−0.286423	+	0.0446334i
$418$	0.291801	−	0.291801i	0.0142724	−	0.0142724i
$419$	6.87568	−	21.1612i	0.335899	−	1.03379i	−0.630378	−	0.776288i	$-0.717100\pi$
$419$	6.87568	−	21.1612i	0.335899	−	1.03379i	0.966277	−	0.257503i	$-0.0828998\pi$
$420$	15.9665	+	21.0479i	0.779086	+	1.02703i
$421$	5.74528	+	17.6821i	0.280008	+	0.861775i	0.987851	+	0.155405i	$0.0496684\pi$
$421$	5.74528	+	17.6821i	0.280008	+	0.861775i	−0.707843	+	0.706370i	$0.750332\pi$
$422$	−8.79986	−	4.48375i	−0.428371	−	0.218266i
$423$	−12.6446	+	24.5135i	−0.614800	+	1.19189i
$424$		−	10.6418i		−	0.516809i
$425$	−23.9012	−	10.8159i	−1.15938	−	0.524646i
$426$	−11.4113	−	3.73922i	−0.552878	−	0.181166i
$427$	−1.72339	−	10.8811i	−0.0834007	−	0.526572i
$428$	0.528053	−	1.03636i	0.0255244	−	0.0500945i
$429$	0.0202526	−	8.12570i	0.000977804	−	0.392312i
$430$	0.987388	−	3.29658i	0.0476161	−	0.158975i
$431$	−14.0978	−	4.58064i	−0.679065	−	0.220642i	−0.0508791	−	0.998705i	$-0.516202\pi$
$431$	−14.0978	−	4.58064i	−0.679065	−	0.220642i	−0.628186	+	0.778063i	$0.716202\pi$
$432$	−2.50838	+	15.1054i	−0.120685	+	0.726760i
$433$	−3.87588	−	7.60685i	−0.186263	−	0.365562i	0.778926	−	0.627116i	$-0.215765\pi$
$433$	−3.87588	−	7.60685i	−0.186263	−	0.365562i	−0.965189	+	0.261554i	$0.915765\pi$
$434$	−31.4949	+	22.8824i	−1.51181	+	1.09839i
$435$	−0.273826	+	1.99464i	−0.0131289	+	0.0956356i
$436$	−9.85524	−	7.16025i	−0.471980	−	0.342914i
$437$	0.00681168	−	0.0430072i	0.000325847	−	0.00205731i
$438$	36.9511	+	18.9437i	1.76559	+	0.905163i
$439$	−4.12954	+	5.68383i	−0.197092	+	0.271274i	−0.896112	−	0.443828i	$-0.853620\pi$
$439$	−4.12954	+	5.68383i	−0.197092	+	0.271274i	0.699020	+	0.715103i	$0.253620\pi$
$440$	−0.337465	−	1.85216i	−0.0160880	−	0.0882984i
$441$	−2.58342	−	0.0128780i	−0.123020	−	0.000613237i
$442$	−49.9868	+	25.4696i	−2.37763	+	1.21146i
$443$	−4.70856	−	4.70856i	−0.223711	−	0.223711i	0.586348	−	0.810059i	$-0.300565\pi$
$443$	−4.70856	−	4.70856i	−0.223711	−	0.223711i	−0.810059	+	0.586348i	$0.800565\pi$
$444$	−8.05150	−	5.88048i	−0.382107	−	0.279075i
$445$	16.5386	+	4.95363i	0.784007	+	0.234825i
$446$	33.3943	−	10.8505i	1.58127	−	0.513785i
$447$	−5.93750	−	5.96718i	−0.280834	−	0.282238i
$448$	−30.4817	+	4.82782i	−1.44012	+	0.228093i
$449$	−27.1755			−1.28249			−0.641245	−	0.767336i	$-0.721582\pi$
$449$	−27.1755			−1.28249			−0.641245	+	0.767336i	$0.721582\pi$
$450$	23.2346	+	21.3904i	1.09529	+	1.00835i
$451$	−6.85577			−0.322825
$452$	13.9235	−	2.20527i	0.654907	−	0.103727i
$453$	−10.3613	−	10.4131i	−0.486816	−	0.489249i
$454$	−43.7298	+	14.2087i	−2.05234	+	0.666846i
$455$	−18.1133	+	26.1843i	−0.849164	+	1.22754i
$456$	0.270476	+	0.197544i	0.0126662	+	0.00925085i
$457$	2.13051	+	2.13051i	0.0996610	+	0.0996610i	0.755179	−	0.655518i	$-0.227550\pi$
$457$	2.13051	+	2.13051i	0.0996610	+	0.0996610i	−0.655518	+	0.755179i	$0.727550\pi$
$458$	29.1392	−	14.8472i	1.36159	−	0.693764i
$459$	−25.8656	−	8.61859i	−1.20730	−	0.402281i
$460$	−0.807512	−	0.770973i	−0.0376504	−	0.0359468i
$461$	−19.4302	+	26.7433i	−0.904953	+	1.24556i	0.0639082	+	0.997956i	$0.479644\pi$
$461$	−19.4302	+	26.7433i	−0.904953	+	1.24556i	−0.968861	+	0.247605i	$0.920356\pi$
$462$	8.40518	+	4.30907i	0.391044	+	0.200476i
$463$	−2.29527	+	14.4917i	−0.106670	+	0.673488i	0.875175	+	0.483806i	$0.160746\pi$
$463$	−2.29527	+	14.4917i	−0.106670	+	0.673488i	−0.981845	+	0.189683i	$0.939254\pi$
$464$	−1.23933	−	0.900429i	−0.0575346	−	0.0418014i
$465$	−17.6836	+	18.4295i	−0.820058	+	0.854648i
$466$	9.51249	−	6.91123i	0.440658	−	0.320156i
$467$	0.0206689	+	0.0405649i	0.000956441	+	0.00187712i	0.891484	−	0.453052i	$-0.149665\pi$
$467$	0.0206689	+	0.0405649i	0.000956441	+	0.00187712i	−0.890528	+	0.454929i	$0.849665\pi$
$468$	36.6377	−	5.61578i	1.69358	−	0.259589i
$469$	−12.2280	−	3.97311i	−0.564636	−	0.183461i
$470$	−43.2738	+	1.00170i	−1.99607	+	0.0462052i
$471$	−0.0669184	+	26.8489i	−0.00308344	+	1.23713i
$472$	−0.0212417	+	0.0416891i	−0.000977726	+	0.00191890i
$473$	−0.105632	−	0.666935i	−0.00485697	−	0.0306657i
$474$	−14.2428	−	4.66705i	−0.654194	−	0.214365i
$475$	−0.992683	+	0.374156i	−0.0455474	+	0.0171674i
$476$		−	35.7904i		−	1.64045i
$477$	31.1309	+	16.0580i	1.42539	+	0.735244i
$478$	−34.7465	−	17.7042i	−1.58927	−	0.809772i
$479$	1.78148	+	5.48284i	0.0813980	+	0.250517i	0.983471	−	0.181067i	$-0.0579549\pi$
$479$	1.78148	+	5.48284i	0.0813980	+	0.250517i	−0.902073	+	0.431584i	$0.857955\pi$
$480$	−29.3630	+	10.2157i	−1.34023	+	0.466279i
$481$	3.71311	−	11.4278i	0.169303	−	0.521061i
$482$	−19.2543	+	19.2543i	−0.877009	+	0.877009i
$483$	0.984758	−	0.153455i	0.0448080	−	0.00698246i
$484$	14.5098	+	19.9710i	0.659536	+	0.907773i
$485$	2.63717	−	19.5719i	0.119748	−	0.888715i
$486$	26.3099	+	19.6208i	1.19344	+	0.890020i
$487$	−8.22938	−	1.30341i	−0.372909	−	0.0590629i	−0.0328326	−	0.999461i	$-0.510453\pi$
$487$	−8.22938	−	1.30341i	−0.372909	−	0.0590629i	−0.340076	+	0.940398i	$0.610453\pi$
$488$	−3.53705	−	0.560214i	−0.160115	−	0.0253597i
$489$	25.0672	−	18.1171i	1.13358	−	0.819283i
$490$	−1.92368	−	3.56877i	−0.0869030	−	0.161221i
$491$	−1.38128	−	1.90117i	−0.0623362	−	0.0857985i	0.776711	−	0.629858i	$-0.216887\pi$
$491$	−1.38128	−	1.90117i	−0.0623362	−	0.0857985i	−0.839047	+	0.544059i	$0.816887\pi$
$492$	−4.81513	−	30.8998i	−0.217083	−	1.39307i
$493$	1.92868	−	1.92868i	0.0868635	−	0.0868635i
$494$	−0.701036	+	2.15757i	−0.0315411	+	0.0970735i
$495$	5.92746	+	1.80763i	0.266420	+	0.0812470i
$496$	−6.00533	−	18.4825i	−0.269647	−	0.829889i
$497$	8.22624	+	4.19148i	0.368997	+	0.188013i
$498$	56.4480	+	9.08477i	2.52950	+	0.407098i
$499$			14.4704i			0.647786i	0.946094	+	0.323893i	$0.104992\pi$
$499$			14.4704i			0.647786i	−0.946094	+	0.323893i	$0.895008\pi$
$500$	−6.59045	+	26.3900i	−0.294734	+	1.18020i
$501$	4.97018	−	15.1679i	0.222051	−	0.677652i
$502$	−1.55026	−	9.78798i	−0.0691917	−	0.436859i
$503$	−3.62024	+	7.10512i	−0.161419	+	0.316802i	−0.957523	−	0.288358i	$-0.906891\pi$
$503$	−3.62024	+	7.10512i	−0.161419	+	0.316802i	0.796104	+	0.605160i	$0.206891\pi$
$504$	−2.40529	+	7.27904i	−0.107140	+	0.324234i
$505$	4.23477	+	12.0750i	0.188445	+	0.537331i
$506$	−0.379627	−	0.123348i	−0.0168765	−	0.00548351i
$507$	10.0083	+	19.7640i	0.444484	+	0.877750i
$508$	−14.3652	−	28.1934i	−0.637355	−	1.25088i
$509$	31.5666	−	22.9345i	1.39917	−	1.01655i	0.404377	−	0.914592i	$-0.367488\pi$
$509$	31.5666	−	22.9345i	1.39917	−	1.01655i	0.994788	−	0.101961i	$-0.0325115\pi$
$510$	−7.56426	−	42.1110i	−0.334951	−	1.86471i
$511$	−25.8283	−	18.7654i	−1.14258	−	0.830131i
$512$	4.54076	−	28.6692i	0.200675	−	1.26701i
$513$	−0.986025	+	0.493153i	−0.0435341	+	0.0217732i
$514$	19.8594	−	27.3341i	0.875961	−	1.20566i
$515$	5.03590	+	0.678549i	0.221908	+	0.0299004i
$516$	2.93177	−	0.944517i	0.129064	−	0.0415800i
$517$	−7.56775	+	3.85596i	−0.332829	+	0.169585i
$518$	9.87637	+	9.87637i	0.433943	+	0.433943i
$519$	12.8640	−	17.6133i	0.564668	−	0.773139i
$520$	6.27553	+	8.23004i	0.275200	+	0.360911i
$521$	19.4591	−	6.32266i	0.852521	−	0.277001i	0.150019	−	0.988683i	$-0.452066\pi$
$521$	19.4591	−	6.32266i	0.852521	−	0.277001i	0.702501	+	0.711682i	$0.252066\pi$
$522$	−2.93302	+	1.47608i	−0.128375	+	0.0646061i
$523$	−10.1716	+	1.61103i	−0.444775	+	0.0704454i	−0.374805	−	0.927104i	$-0.622290\pi$
$523$	−10.1716	+	1.61103i	−0.444775	+	0.0704454i	−0.0699699	+	0.997549i	$0.522290\pi$
$524$	49.2782			2.15273
$525$	−15.1186	−	19.0004i	−0.659830	−	0.829244i
$526$	−15.0560			−0.656473
$527$	34.1759	−	5.41293i	1.48872	−	0.235791i
$528$	−3.34238	+	3.32576i	−0.145458	+	0.144735i
$529$	21.8342	−	7.09438i	0.949315	−	0.308451i
$530$	1.27211	+	54.9556i	0.0552571	+	2.38712i
$531$	−0.0899028	−	0.125047i	−0.00390145	−	0.00542656i
$532$	−1.02338	−	1.02338i	−0.0443690	−	0.0443690i
$533$	33.5810	−	17.1104i	1.45455	−	0.741132i
$534$	8.63398	+	26.7998i	0.373629	+	1.15974i
$535$	−0.463162	+	0.963500i	−0.0200242	+	0.0416557i
$536$	−2.45662	+	3.38124i	−0.106110	+	0.146047i
$537$	7.92441	−	15.4572i	0.341964	−	0.667026i
$538$	0.378097	−	2.38721i	0.0163009	−	0.102920i
$539$	−0.643590	−	0.467595i	−0.0277214	−	0.0201408i
$540$	−3.98409	+	27.9854i	−0.171448	+	1.20430i
$541$	25.8243	−	18.7625i	1.11028	−	0.806662i	0.127568	−	0.991830i	$-0.459283\pi$
$541$	25.8243	−	18.7625i	1.11028	−	0.806662i	0.982707	+	0.185167i	$0.0592827\pi$
$542$	−9.19628	−	18.0487i	−0.395014	−	0.775259i
$543$	5.12092	−	2.59318i	0.219760	−	0.111284i
$544$	40.0567	+	13.0152i	1.71742	+	0.558022i
$545$	9.20785	+	6.36962i	0.394421	+	0.272845i
$546$	−51.9247	−	0.129418i	−2.22217	−	0.00553857i
$547$	−14.1351	+	27.7417i	−0.604373	+	1.18615i	0.362761	+	0.931882i	$0.381834\pi$
$547$	−14.1351	+	27.7417i	−0.604373	+	1.18615i	−0.967134	+	0.254267i	$0.918166\pi$
$548$	−4.25817	−	26.8850i	−0.181900	−	1.14847i
$549$	6.97610	−	9.50181i	0.297733	−	0.405527i
$550$	1.96413	+	9.52450i	0.0837506	+	0.406126i
$551$		−	0.110296i		−	0.00469876i
$552$	0.0514780	−	0.319857i	0.00219105	−	0.0136140i
$553$	10.2675	+	5.23153i	0.436617	+	0.222467i
$554$	14.9376	+	45.9732i	0.634637	+	1.95321i
$555$	7.52325	+	5.23206i	0.319344	+	0.222089i
$556$	2.56938	−	7.90774i	0.108966	−	0.335363i
$557$	−13.9418	+	13.9418i	−0.590734	+	0.590734i	−0.937830	−	0.347096i	$-0.887168\pi$
$557$	−13.9418	+	13.9418i	−0.590734	+	0.590734i	0.347096	+	0.937830i	$0.387168\pi$
$558$	−41.1086	−	6.72119i	−1.74027	−	0.284531i
$559$	2.18192	+	3.00315i	0.0922854	+	0.127020i
$560$	18.1758	−	3.31164i	0.768069	−	0.139943i
$561$	−4.91769	−	6.80421i	−0.207625	−	0.287274i
$562$	19.3934	+	3.07161i	0.818060	+	0.129568i
$563$	4.18439	+	0.662743i	0.176351	+	0.0279313i	0.243985	−	0.969779i	$-0.421545\pi$
$563$	4.18439	+	0.662743i	0.176351	+	0.0279313i	−0.0676342	+	0.997710i	$0.521545\pi$
$564$	−22.6945	−	31.4006i	−0.955610	−	1.32220i
$565$	−12.7468	+	2.32247i	−0.536262	+	0.0977072i
$566$	−41.1692	−	56.6646i	−1.73047	−	2.38179i
$567$	−17.6643	−	18.0201i	−0.741832	−	0.756773i
$568$	2.12215	−	2.12215i	0.0890433	−	0.0890433i
$569$	−11.0678	+	34.0631i	−0.463985	+	1.42800i	0.396270	+	0.918134i	$0.370304\pi$
$569$	−11.0678	+	34.0631i	−0.463985	+	1.42800i	−0.860255	+	0.509864i	$0.829696\pi$
$570$	−1.42039	−	0.987815i	−0.0594937	−	0.0413750i
$571$	−7.59320	−	23.3695i	−0.317766	−	0.977982i	−0.974601	−	0.223948i	$-0.928105\pi$
$571$	−7.59320	−	23.3695i	−0.317766	−	0.977982i	0.656835	−	0.754034i	$-0.271895\pi$
$572$	10.1696	+	5.18166i	0.425212	+	0.216656i
$573$	−2.57679	+	16.0108i	−0.107647	+	0.668862i
$574$			43.8096i			1.82858i
$575$	0.758386	+	0.691238i	0.0316269	+	0.0288266i
$576$	−26.6179	−	19.5425i	−1.10908	−	0.814270i
$577$	−4.38472	−	27.6840i	−0.182538	−	1.15250i	−0.893431	−	0.449200i	$-0.851709\pi$
$577$	−4.38472	−	27.6840i	−0.182538	−	1.15250i	0.710893	−	0.703300i	$-0.248291\pi$
$578$	−10.0651	+	19.7538i	−0.418651	+	0.821649i
$579$	−3.81524	−	0.00950915i	−0.158556	−	0.000395187i
$580$	−2.32575	−	1.60886i	−0.0965717	−	0.0668045i
$581$	−41.8069	−	13.5839i	−1.73444	−	0.563554i
$582$	28.7336	−	14.5504i	1.19105	−	0.603133i
$583$	4.89688	+	9.61066i	0.202808	+	0.398033i
$584$	−8.39588	+	6.09997i	−0.347424	+	0.252418i
$585$	−33.5454	+	5.93937i	−1.38693	+	0.245563i
$586$	47.0924	+	34.2146i	1.94537	+	1.41339i
$587$	−5.73646	+	36.2186i	−0.236769	+	1.49490i	0.527252	+	0.849709i	$0.323222\pi$
$587$	−5.73646	+	36.2186i	−0.236769	+	1.49490i	−0.764021	+	0.645191i	$0.776778\pi$
$588$	1.65549	−	3.22915i	0.0682711	−	0.133168i
$589$	0.822435	−	1.13198i	0.0338878	−	0.0466426i
$590$	0.104712	−	0.217828i	0.00431091	−	0.00896783i
$591$	8.20837	+	25.4787i	0.337647	+	1.04805i
$592$	−6.21248	+	3.16541i	−0.255331	+	0.130098i
$593$	−18.0099	−	18.0099i	−0.739577	−	0.739577i	0.232919	−	0.972496i	$-0.425172\pi$
$593$	−18.0099	−	18.0099i	−0.739577	−	0.739577i	−0.972496	+	0.232919i	$0.925172\pi$
$594$	3.05110	+	9.63486i	0.125188	+	0.395323i
$595$	0.761253	+	32.8863i	0.0312083	+	1.34821i
$596$	11.2453	−	3.65382i	0.460625	−	0.149666i
$597$	−8.43839	+	8.39643i	−0.345360	+	0.343643i
$598$	2.16734	−	0.343273i	0.0886292	−	0.0140375i
$599$	−16.9050			−0.690719			−0.345360	−	0.938470i	$-0.612243\pi$
$599$	−16.9050			−0.690719			−0.345360	+	0.938470i	$0.612243\pi$
$600$	−7.39273	+	2.76540i	−0.301807	+	0.112897i
$601$	23.5312			0.959857			0.479929	−	0.877308i	$-0.340663\pi$
$601$	23.5312			0.959857			0.479929	+	0.877308i	$0.340663\pi$
$602$	−4.26184	+	0.675009i	−0.173700	+	0.0275113i
$603$	−6.18441	−	12.2886i	−0.251849	−	0.500432i
$604$	19.6237	−	6.37613i	0.798477	−	0.259441i
$605$	−13.7572	−	18.0419i	−0.559309	−	0.733506i
$606$	−12.3083	+	16.8525i	−0.499992	+	0.684586i
$607$	−17.3958	−	17.3958i	−0.706072	−	0.706072i	0.259635	−	0.965707i	$-0.416398\pi$
$607$	−17.3958	−	17.3958i	−0.706072	−	0.706072i	−0.965707	+	0.259635i	$0.916398\pi$
$608$	1.51751	−	0.773212i	0.0615433	−	0.0313579i
$609$	2.40289	−	0.774129i	0.0973699	−	0.0313693i
$610$	18.3328	+	2.47021i	0.742274	+	0.100016i
$611$	27.4449	−	37.7746i	1.11030	−	1.52820i
$612$	27.2135	−	26.9435i	1.10004	−	1.08913i
$613$	4.24641	−	26.8108i	0.171511	−	1.08288i	−0.740303	−	0.672273i	$-0.765318\pi$
$613$	4.24641	−	26.8108i	0.171511	−	1.08288i	0.911814	−	0.410604i	$-0.134682\pi$
$614$	40.8132	+	29.6525i	1.64708	+	1.19668i
$615$	5.08164	+	28.2900i	0.204911	+	1.14076i
$616$	−1.90979	+	1.38755i	−0.0769478	+	0.0559058i
$617$	−4.36406	−	8.56494i	−0.175690	−	0.344812i	0.786322	−	0.617816i	$-0.211983\pi$
$617$	−4.36406	−	8.56494i	−0.175690	−	0.344812i	−0.962013	+	0.273005i	$0.911983\pi$
$618$	3.74385	+	7.39322i	0.150600	+	0.297399i
$619$	34.6660	+	11.2637i	1.39334	+	0.452725i	0.907032	−	0.421061i	$-0.138342\pi$
$619$	34.6660	+	11.2637i	1.39334	+	0.452725i	0.486311	+	0.873786i	$0.338342\pi$
$620$	−11.8729	−	33.8543i	−0.476827	−	1.35962i
$621$	0.858020	+	0.633244i	0.0344311	+	0.0254112i
$622$	2.77106	−	5.43852i	0.111110	−	0.218065i
$623$	−3.38646	−	21.3813i	−0.135676	−	0.856622i
$624$	8.07136	−	24.6320i	0.323113	−	0.986071i
$625$	5.49437	−	24.3888i	0.219775	−	0.975551i
$626$			28.6756i			1.14611i
$627$	−0.335171	−	0.0539425i	−0.0133854	−	0.00215426i
$628$	−33.6023	−	17.1212i	−1.34088	−	0.683210i
$629$	−3.83629	−	11.8069i	−0.152963	−	0.470771i
$630$	11.5511	−	37.8776i	0.460207	−	1.50908i
$631$	−3.21512	+	9.89511i	−0.127992	+	0.393918i	−0.994434	−	0.105359i	$-0.966401\pi$
$631$	−3.21512	+	9.89511i	−0.127992	+	0.393918i	0.866443	+	0.499277i	$0.166401\pi$
$632$	2.64873	−	2.64873i	0.105361	−	0.105361i
$633$	1.25099	+	8.02791i	0.0497225	+	0.319081i
$634$	−37.4260	−	51.5125i	−1.48638	−	2.04582i
$635$	13.7993	+	25.6001i	0.547607	+	1.01591i
$636$	−39.8771	+	28.8208i	−1.58123	+	1.14282i
$637$	4.31944	+	0.684132i	0.171143	+	0.0271063i
$638$	−0.998639	−	0.158169i	−0.0395365	−	0.00626197i
$639$	3.00581	+	9.41027i	0.118908	+	0.372265i
$640$	2.12614	−	15.7793i	0.0840430	−	0.623731i
$641$	4.96036	+	6.82734i	0.195922	+	0.269664i	0.895663	−	0.444733i	$-0.146701\pi$
$641$	4.96036	+	6.82734i	0.195922	+	0.269664i	−0.699741	+	0.714397i	$0.746701\pi$
$642$	−1.72267	+	0.268445i	−0.0679886	+	0.0105947i
$643$	−32.9970	+	32.9970i	−1.30127	+	1.30127i	−0.373739	+	0.927534i	$0.621924\pi$
$643$	−32.9970	+	32.9970i	−1.30127	+	1.30127i	−0.927534	+	0.373739i	$0.878076\pi$
$644$	−0.432596	+	1.33139i	−0.0170467	+	0.0524642i
$645$	−2.67378	+	0.930233i	−0.105280	+	0.0366279i
$646$	0.724293	+	2.22914i	0.0284969	+	0.0877045i
$647$	27.7853	+	14.1573i	1.09235	+	0.556582i	0.904871	−	0.425686i	$-0.139967\pi$
$647$	27.7853	+	14.1573i	1.09235	+	0.556582i	0.187482	+	0.982268i	$0.439967\pi$
$648$	−7.34540	+	3.65089i	−0.288555	+	0.143420i
$649$		−	0.0474243i		−	0.00186157i
$650$	−33.3916	−	41.7510i	−1.30973	−	1.63761i
$651$	30.4336	+	9.97242i	1.19279	+	0.390850i
$652$	6.79605	+	42.9085i	0.266154	+	1.68043i
$653$	−8.99906	+	17.6616i	−0.352160	+	0.691153i	−0.997341	−	0.0728766i	$-0.976782\pi$
$653$	−8.99906	+	17.6616i	−0.352160	+	0.691153i	0.645181	+	0.764030i	$0.276782\pi$
$654$	−0.0455104	+	18.2596i	−0.00177960	+	0.714006i
$655$	−45.2796	+	1.04814i	−1.76922	+	0.0409540i
$656$	−20.7992	−	6.75808i	−0.812074	−	0.263859i
$657$	−5.17554	−	33.7656i	−0.201917	−	1.31732i
$658$	24.6403	+	48.3594i	0.960580	+	1.88524i
$659$	−25.0740	+	18.2173i	−0.976745	+	0.709647i	−0.956979	−	0.290158i	$-0.906292\pi$
$659$	−25.0740	+	18.2173i	−0.976745	+	0.709647i	−0.0197663	+	0.999805i	$0.506292\pi$
$660$	−6.02653	+	6.28073i	−0.234583	+	0.244477i
$661$	4.14459	+	3.01122i	0.161206	+	0.117123i	0.665464	−	0.746430i	$-0.268234\pi$
$661$	4.14459	+	3.01122i	0.161206	+	0.117123i	−0.504258	+	0.863553i	$0.668234\pi$
$662$	−3.17345	+	20.0364i	−0.123339	+	0.778735i
$663$	41.0695	+	21.0551i	1.59501	+	0.817711i
$664$	−8.39904	+	11.5603i	−0.325946	+	0.448626i
$665$	0.962102	+	0.918568i	0.0373087	+	0.0356205i
$666$	−0.0744968	+	14.9446i	−0.00288669	+	0.579092i
$667$	−0.0950582	+	0.0484346i	−0.00368067	+	0.00187539i
$668$	15.8532	+	15.8532i	0.613380	+	0.613380i
$669$	−23.3267	−	17.0368i	−0.901861	−	0.658681i
$670$	12.2821	−	17.7549i	0.474500	−	0.685931i
$671$	3.45213	−	1.12167i	0.133268	−	0.0433014i
$672$	27.4960	+	27.6334i	1.06068	+	1.06598i
$673$	18.2947	−	2.89759i	0.705208	−	0.111694i	0.206478	−	0.978451i	$-0.433800\pi$
$673$	18.2947	−	2.89759i	0.705208	−	0.111694i	0.498730	+	0.866757i	$0.333800\pi$
$674$	16.5913			0.639075
$675$	3.06556	−	25.7993i	0.117993	−	0.993014i
$676$	−31.1175			−1.19683
$677$	−22.5569	+	3.57266i	−0.866931	+	0.137308i	−0.574030	−	0.818834i	$-0.694621\pi$
$677$	−22.5569	+	3.57266i	−0.866931	+	0.137308i	−0.292901	+	0.956143i	$0.594621\pi$
$678$	−14.9043	−	14.9788i	−0.572396	−	0.575257i
$679$	−23.5507	+	7.65210i	−0.903795	+	0.293661i
$680$	10.2434	+	3.06810i	0.392817	+	0.117656i
$681$	30.5462	+	22.3097i	1.17053	+	0.854909i
$682$	−9.06980	−	9.06980i	−0.347300	−	0.347300i
$683$	33.3574	−	16.9964i	1.27639	−	0.650351i	0.321383	−	0.946949i	$-0.395852\pi$
$683$	33.3574	−	16.9964i	1.27639	−	0.650351i	0.955002	+	0.296598i	$0.0958523\pi$
$684$	0.00771926	−	1.54854i	0.000295153	−	0.0592100i
$685$	4.48448	+	24.6129i	0.171343	+	0.940410i
$686$	21.3006	−	29.3178i	0.813261	−	1.11936i
$687$	−23.9410	−	12.2738i	−0.913407	−	0.468275i
$688$	0.336962	−	2.12750i	0.0128466	−	0.0811100i
$689$	−47.9719	−	34.8536i	−1.82758	−	1.32782i
$690$	−0.227604	+	1.65794i	−0.00866474	+	0.0631169i
$691$	−27.2396	+	19.7907i	−1.03624	+	0.752875i	−0.969549	−	0.244899i	$-0.921245\pi$
$691$	−27.2396	+	19.7907i	−1.03624	+	0.752875i	−0.0666945	+	0.997773i	$0.521245\pi$
$692$	13.9085	+	27.2969i	0.528721	+	1.03767i
$693$	−1.17727	−	7.68058i	−0.0447207	−	0.291761i
$694$	−6.56060	−	2.13167i	−0.249037	−	0.0809170i
$695$	−2.19270	+	7.32072i	−0.0831737	+	0.277691i
$696$	0.00204534	−	0.820626i	7.75284e−5	−	0.0311058i
$697$	17.6780	−	34.6950i	0.669602	−	1.31417i
$698$	−3.35286	−	21.1691i	−0.126908	−	0.801263i
$699$	−9.19194	−	3.01199i	−0.347671	−	0.113924i
$700$	33.4034	−	6.88839i	1.26253	−	0.260357i
$701$			41.4824i			1.56677i	0.621538	+	0.783384i	$0.286508\pi$
$701$			41.4824i			1.56677i	−0.621538	+	0.783384i	$0.713492\pi$
$702$	−38.9912	−	39.5787i	−1.47163	−	1.49380i
$703$	−0.447294	−	0.227908i	−0.0168700	−	0.00859570i
$704$	−3.14218	−	9.67062i	−0.118425	−	0.364475i
$705$	21.5208	+	28.3699i	0.810522	+	1.06847i
$706$	−1.20099	+	3.69628i	−0.0452000	+	0.139111i
$707$	11.3454	−	11.3454i	0.426687	−	0.426687i
$708$	0.213747	−	0.0333083i	0.00803311	−	0.00125180i
$709$	−12.5345	−	17.2522i	−0.470742	−	0.647921i	0.505951	−	0.862562i	$-0.331142\pi$
$709$	−12.5345	−	17.2522i	−0.470742	−	0.647921i	−0.976693	+	0.214641i	$0.931142\pi$
$710$	−10.7054	+	11.2128i	−0.401766	+	0.420807i
$711$	3.75165	+	11.7453i	0.140698	+	0.440483i
$712$	−6.95030	−	1.10082i	−0.260474	−	0.0412550i
$713$	−1.33676	−	0.211722i	−0.0500620	−	0.00792903i
$714$	−43.4802	+	31.4249i	−1.62721	+	1.17605i
$715$	−9.45460	−	4.54490i	−0.353582	−	0.169970i
$716$	14.3411	+	19.7388i	0.535951	+	0.737673i
$717$	4.93958	+	31.6984i	0.184472	+	1.18380i
$718$	39.7520	−	39.7520i	1.48353	−	1.48353i
$719$	−8.68648	+	26.7342i	−0.323951	+	0.997019i	0.647961	+	0.761674i	$0.275622\pi$
$719$	−8.68648	+	26.7342i	−0.323951	+	0.997019i	−0.971912	+	0.235345i	$0.924378\pi$
$720$	16.2010	+	11.3271i	0.603777	+	0.422135i
$721$	−1.96890	−	6.05966i	−0.0733258	−	0.225674i
$722$	−35.5588	−	18.1181i	−1.32336	−	0.674287i
$723$	22.1160	+	3.55936i	0.822504	+	0.132374i
$724$			8.06265i			0.299646i
$725$	2.17125	+	1.42885i	0.0806383	+	0.0530660i
$726$	11.5219	−	35.1624i	0.427618	−	1.30500i
$727$	2.81844	+	17.7949i	0.104530	+	0.659977i	0.983198	+	0.182543i	$0.0584330\pi$
$727$	2.81844	+	17.7949i	0.104530	+	0.659977i	−0.878668	+	0.477434i	$0.841567\pi$
$728$	5.89158	−	11.5629i	0.218356	−	0.428549i
$729$	0.403755	−	26.9970i	0.0149539	−	0.999888i
$730$	42.6284	−	32.5048i	1.57775	−	1.20306i
$731$	3.64754	+	1.18516i	0.134909	+	0.0438347i
$732$	7.48007	+	14.7714i	0.276472	+	0.545966i
$733$	10.3267	+	20.2674i	0.381427	+	0.748592i	0.999289	−	0.0376939i	$-0.0120012\pi$
$733$	10.3267	+	20.2674i	0.381427	+	0.748592i	−0.617863	+	0.786286i	$0.712001\pi$
$734$	52.1735	−	37.9063i	1.92576	−	1.39915i
$735$	−1.45247	+	3.00234i	−0.0535752	+	0.110743i
$736$	−1.33278	−	0.968323i	−0.0491270	−	0.0356929i
$737$	0.662690	−	4.18406i	0.0244105	−	0.154122i
$738$	−33.3110	+	32.9805i	−1.22619	+	1.21403i
$739$	−17.5716	+	24.1852i	−0.646382	+	0.889669i	−0.998936	−	0.0461231i	$-0.985313\pi$
$739$	−17.5716	+	24.1852i	−0.646382	+	0.889669i	0.352554	+	0.935792i	$0.385313\pi$
$740$	−11.3304	+	6.10742i	−0.416513	+	0.224513i
$741$	1.77636	−	0.572285i	0.0652563	−	0.0210234i
$742$	61.4140	−	31.2920i	2.25458	−	1.14876i
$743$	−35.7229	−	35.7229i	−1.31055	−	1.31055i	−0.921011	−	0.389537i	$-0.872635\pi$
$743$	−35.7229	−	35.7229i	−1.31055	−	1.31055i	−0.389537	−	0.921011i	$-0.627365\pi$
$744$	6.14010	−	8.40698i	0.225107	−	0.308215i
$745$	−10.2551	+	3.59652i	−0.375718	+	0.131766i
$746$	3.75018	−	1.21851i	0.137304	−	0.0446127i
$747$	−21.1442	−	42.0142i	−0.773625	−	1.53722i
$748$	11.6471	−	1.84471i	0.425859	−	0.0674494i
$749$	1.34046			0.0489792
$750$	37.8466	−	15.1646i	1.38196	−	0.553735i
$751$	43.1672			1.57520			0.787598	−	0.616190i	$-0.211325\pi$
$751$	43.1672			1.57520			0.787598	+	0.616190i	$0.211325\pi$
$752$	−26.7603	+	4.23842i	−0.975848	+	0.154559i
$753$	−5.77904	+	5.75030i	−0.210600	+	0.209553i
$754$	5.28629	−	1.71762i	0.192515	−	0.0625521i
$755$	−17.8957	+	6.27613i	−0.651293	+	0.228412i
$756$	33.7905	−	10.7005i	1.22895	−	0.389174i
$757$	12.8580	+	12.8580i	0.467331	+	0.467331i	0.901049	−	0.433718i	$-0.142798\pi$
$757$	12.8580	+	12.8580i	0.467331	+	0.467331i	−0.433718	+	0.901049i	$0.642798\pi$
$758$	−43.5789	+	22.2045i	−1.58286	+	0.806505i
$759$	0.100694	+	0.312554i	0.00365498	+	0.0113450i
$760$	0.380624	−	0.205168i	0.0138067	−	0.00744223i
$761$	−8.40118	+	11.5632i	−0.304543	+	0.419167i	−0.933670	−	0.358136i	$-0.883413\pi$
$761$	−8.40118	+	11.5632i	−0.304543	+	0.419167i	0.629127	+	0.777303i	$0.283413\pi$
$762$	−21.6378	+	42.2062i	−0.783856	+	1.52897i
$763$	2.19616	−	13.8660i	0.0795063	−	0.501983i
$764$	−18.4283	−	13.3889i	−0.666712	−	0.484395i
$765$	−24.4322	+	25.3360i	−0.883348	+	0.916027i
$766$	−56.4674	+	41.0260i	−2.04025	+	1.48233i
$767$	0.118360	+	0.232294i	0.00427372	+	0.00838765i
$768$	−10.8515	+	5.49507i	−0.391568	+	0.198286i
$769$	−27.6008	−	8.96803i	−0.995309	−	0.323395i	−0.234319	−	0.972160i	$-0.575286\pi$
$769$	−27.6008	−	8.96803i	−0.995309	−	0.323395i	−0.760989	+	0.648764i	$0.775286\pi$
$770$	9.69659	−	7.39379i	0.349441	−	0.266454i
$771$	−27.7948	−	0.0692761i	−1.00101	−	0.00249492i
$772$	2.43294	−	4.77491i	0.0875633	−	0.171853i
$773$	1.42015	+	8.96649i	0.0510793	+	0.322502i	0.999976	+	0.00691550i	$0.00220129\pi$
$773$	1.42015	+	8.96649i	0.0510793	+	0.322502i	−0.948897	+	0.315587i	$0.897799\pi$
$774$	−3.72162	−	2.73236i	−0.133771	−	0.0982128i
$775$	11.6296	+	30.8547i	0.417746	+	1.10833i
$776$			8.04949i			0.288960i
$777$	1.82575	−	11.3443i	0.0654985	−	0.406974i
$778$	57.2531	+	29.1719i	2.05262	+	1.04586i
$779$	−0.486577	−	1.49753i	−0.0174334	−	0.0536546i
$780$	13.8440	−	45.8051i	0.495695	−	1.64009i
$781$	−0.940009	+	2.89305i	−0.0336362	+	0.103522i
$782$	1.60312	−	1.60312i	0.0573275	−	0.0573275i
$783$	2.39754	+	1.24428i	0.0856811	+	0.0444668i
$784$	−1.49161	−	2.05303i	−0.0532718	−	0.0733223i
$785$	31.2398	+	15.0172i	1.11500	+	0.535987i
$786$	−43.2676	−	59.8660i	−1.54330	−	2.13535i
$787$	−33.9240	−	5.37304i	−1.20926	−	0.191528i	−0.480934	−	0.876757i	$-0.659702\pi$
$787$	−33.9240	−	5.37304i	−1.20926	−	0.191528i	−0.728328	+	0.685229i	$0.759702\pi$
$788$	−37.1365	−	5.88184i	−1.32293	−	0.209532i
$789$	7.25525	+	10.0385i	0.258294	+	0.357381i
$790$	−13.3618	+	13.9950i	−0.475391	+	0.497921i
$791$	9.54926	+	13.1434i	0.339533	+	0.467327i
$792$	−2.49275	−	0.407560i	−0.0885759	−	0.0144820i
$793$	−14.1098	+	14.1098i	−0.501055	+	0.501055i
$794$	22.9146	−	70.5238i	0.813208	−	2.50280i
$795$	36.0283	−	27.3304i	1.27779	−	0.969309i
$796$	−5.16699	−	15.9024i	−0.183139	−	0.563644i
$797$	−12.2061	−	6.21933i	−0.432363	−	0.220300i	0.224244	−	0.974533i	$-0.428009\pi$
$797$	−12.2061	−	6.21933i	−0.432363	−	0.220300i	−0.656607	+	0.754233i	$0.728009\pi$
$798$	−0.344703	+	2.14180i	−0.0122023	+	0.0758190i
$799$		−	48.2410i		−	1.70664i
$800$	−4.43767	+	39.8901i	−0.156895	+	1.41033i
$801$	13.7080	−	18.6710i	0.484349	−	0.659708i
$802$	0.629342	+	3.97351i	0.0222228	+	0.140309i
$803$	4.77546	−	9.37236i	0.168522	−	0.330743i
$804$	19.3235	+	0.0481621i	0.681487	+	0.00169855i
$805$	0.369175	−	1.23256i	0.0130117	−	0.0434420i
$806$	67.0618	+	21.7897i	2.36215	+	0.767509i
$807$	−1.77386	+	0.898264i	−0.0624428	+	0.0316204i
$808$	−2.36783	−	4.64714i	−0.0833001	−	0.163486i
$809$	−15.4929	+	11.2563i	−0.544702	+	0.395749i	−0.825828	−	0.563922i	$-0.809292\pi$
$809$	−15.4929	+	11.2563i	−0.544702	+	0.395749i	0.281126	+	0.959671i	$0.409292\pi$
$810$	37.4963	−	19.7318i	1.31749	−	0.693305i
$811$	24.0863	+	17.4997i	0.845785	+	0.614499i	0.923981	−	0.382439i	$-0.124916\pi$
$811$	24.0863	+	17.4997i	0.845785	+	0.614499i	−0.0781955	+	0.996938i	$0.524916\pi$
$812$	−0.554715	+	3.50233i	−0.0194667	+	0.122908i
$813$	−7.60234	+	14.8290i	−0.266626	+	0.520074i
$814$	−2.70496	+	3.72305i	−0.0948087	+	0.130493i
$815$	−7.15724	−	39.2822i	−0.250707	−	1.37600i
$816$	−8.21217	−	25.4905i	−0.287483	−	0.892344i
$817$	0.138184	−	0.0704083i	0.00483445	−	0.00246327i
$818$	53.5217	+	53.5217i	1.87134	+	1.87134i
$819$	24.9354	+	34.6829i	0.871314	+	1.21192i
$820$	−38.6753	−	11.5840i	−1.35060	−	0.404530i
$821$	12.5951	−	4.09240i	0.439572	−	0.142826i	−0.0808659	−	0.996725i	$-0.525769\pi$
$821$	12.5951	−	4.09240i	0.439572	−	0.142826i	0.520438	+	0.853899i	$0.325769\pi$
$822$	−28.9226	+	28.7788i	−1.00879	+	1.00378i
$823$	1.69091	−	0.267813i	0.0589413	−	0.00933539i	−0.126894	−	0.991916i	$-0.540501\pi$
$823$	1.69091	−	0.267813i	0.0589413	−	0.00933539i	0.185835	+	0.982581i	$0.440501\pi$
$824$	−2.07115			−0.0721520
$825$	5.40393	−	5.89927i	0.188141	−	0.205386i
$826$	−0.303050			−0.0105445
$827$	−26.1282	+	4.13831i	−0.908568	+	0.143903i	−0.593189	−	0.805063i	$-0.702132\pi$
$827$	−26.1282	+	4.13831i	−0.908568	+	0.143903i	−0.315379	+	0.948966i	$0.602132\pi$
$828$	−1.33800	+	0.673364i	−0.0464986	+	0.0234010i
$829$	17.9708	−	5.83907i	0.624152	−	0.202799i	0.0201694	−	0.999797i	$-0.493579\pi$
$829$	17.9708	−	5.83907i	0.624152	−	0.202799i	0.603983	+	0.796997i	$0.293579\pi$
$830$	41.9920	−	60.7031i	1.45756	−	2.10703i
$831$	23.4542	−	32.1133i	0.813617	−	1.11400i
$832$	39.5266	+	39.5266i	1.37034	+	1.37034i
$833$	4.02590	−	2.05130i	0.139489	−	0.0710732i
$834$	−11.8627	+	3.82178i	−0.410773	+	0.132337i
$835$	−14.9040	−	14.2297i	−0.515776	−	0.492437i
$836$	0.280284	−	0.385778i	0.00969382	−	0.0133424i
$837$	15.3283	+	30.6478i	0.529822	+	1.05934i
$838$	7.32840	−	46.2697i	0.253155	−	1.59836i
$839$	42.3961	+	30.8026i	1.46368	+	1.06342i	0.982386	+	0.186863i	$0.0598322\pi$
$839$	42.3961	+	30.8026i	1.46368	+	1.06342i	0.481292	+	0.876561i	$0.340168\pi$
$840$	7.14123	+	6.85220i	0.246396	+	0.236423i
$841$	23.2429	−	16.8869i	0.801478	−	0.582308i
$842$	17.7713	+	34.8781i	0.612439	+	1.20198i
$843$	−7.29737	−	14.4106i	−0.251335	−	0.496327i
$844$	−10.8537	−	3.52659i	−0.373601	−	0.121390i
$845$	28.5925	−	0.661861i	0.983612	−	0.0227687i
$846$	−18.2208	+	55.1410i	−0.626444	+	1.89579i
$847$	−12.9155	+	25.3481i	−0.443782	+	0.870970i
$848$	5.38258	+	33.9842i	0.184838	+	1.16702i
$849$	−17.9420	+	54.7551i	−0.615768	+	1.87919i
$850$	−53.2653	−	14.6196i	−1.82699	−	0.501449i
$851$			0.485581i			0.0166455i
$852$	−13.6995	−	2.20481i	−0.469339	−	0.0755355i
$853$	9.96838	+	5.07914i	0.341311	+	0.173906i	0.616241	−	0.787558i	$-0.288655\pi$
$853$	9.96838	+	5.07914i	0.341311	+	0.173906i	−0.274930	+	0.961464i	$0.588655\pi$
$854$	−7.16765	−	22.0598i	−0.245272	−	0.754870i
$855$	0.0258442	+	1.42305i	0.000883852	+	0.0486673i
$856$	0.134650	−	0.414409i	0.00460223	−	0.0141642i
$857$	37.2269	−	37.2269i	1.27165	−	1.27165i	0.326423	−	0.945224i	$-0.394157\pi$
$857$	37.2269	−	37.2269i	1.27165	−	1.27165i	0.945224	−	0.326423i	$-0.105843\pi$
$858$	−2.63419	−	16.9042i	−0.0899299	−	0.577100i
$859$	−24.6352	−	33.9074i	−0.840542	−	1.15691i	−0.985868	−	0.167523i	$-0.946423\pi$
$859$	−24.6352	−	33.9074i	−0.840542	−	1.15691i	0.145326	−	0.989384i	$-0.453577\pi$
$860$	0.531000	−	3.94085i	0.0181069	−	0.134382i
$861$	29.2098	−	21.1112i	0.995469	−	0.719466i
$862$	−30.8253	−	4.88224i	−1.04991	−	0.166290i
$863$	−10.1944	−	1.61464i	−0.347023	−	0.0549630i	−0.0195098	−	0.999810i	$-0.506211\pi$
$863$	−10.1944	−	1.61464i	−0.347023	−	0.0549630i	−0.327513	+	0.944847i	$0.606211\pi$
$864$	−0.311877	+	41.7096i	−0.0106103	+	1.41899i
$865$	−13.3605	−	24.7861i	−0.454270	−	0.842753i
$866$	−10.5654	−	14.5420i	−0.359027	−	0.494158i
$867$	18.0209	−	2.80821i	0.612023	−	0.0953718i
$868$	−31.8087	+	31.8087i	−1.07966	+	1.07966i
$869$	−1.17326	+	3.61092i	−0.0398001	+	0.122492i
$870$	0.0875352	+	4.23808i	0.00296772	+	0.143684i
$871$	7.19642	+	22.1483i	0.243841	+	0.750467i
$872$	−4.06614	−	2.07180i	−0.137697	−	0.0701601i
$873$	−23.5476	−	12.1464i	−0.796967	−	0.411092i
$874$		−	0.0916779i		−	0.00310105i
$875$	−30.5464	+	7.03992i	−1.03266	+	0.237993i
$876$	45.5964	+	14.9409i	1.54056	+	0.504807i
$877$	5.32972	+	33.6506i	0.179972	+	1.13630i	0.897906	+	0.440187i	$0.145088\pi$
$877$	5.32972	+	33.6506i	0.179972	+	1.13630i	−0.717934	+	0.696111i	$0.754912\pi$
$878$	−6.71542	+	13.1797i	−0.226634	+	0.444795i
$879$	0.119352	−	47.8861i	0.00402564	−	1.61516i
$880$	2.01451	+	5.74416i	0.0679091	+	0.193636i
$881$	28.3863	+	9.22328i	0.956360	+	0.310740i	0.745297	−	0.666732i	$-0.232308\pi$
$881$	28.3863	+	9.22328i	0.956360	+	0.310740i	0.211063	+	0.977472i	$0.432308\pi$
$882$	−5.37651	+	0.824104i	−0.181037	+	0.0277490i
$883$	−25.5428	−	50.1305i	−0.859583	−	1.68703i	−0.716806	−	0.697272i	$-0.754397\pi$
$883$	−25.5428	−	50.1305i	−0.859583	−	1.68703i	−0.142777	−	0.989755i	$-0.545603\pi$
$884$	−52.4458	+	38.1041i	−1.76394	+	1.28158i
$885$	−0.195694	+	0.0351519i	−0.00657819	+	0.00118162i
$886$	−11.3424	−	8.24072i	−0.381055	−	0.276852i
$887$	5.96616	−	37.6688i	0.200324	−	1.26480i	−0.658522	−	0.752562i	$-0.728818\pi$
$887$	5.96616	−	37.6688i	0.200324	−	1.26480i	0.858846	−	0.512234i	$-0.171182\pi$
$888$	−3.32374	−	1.70398i	−0.111538	−	0.0571818i
$889$	21.4342	−	29.5016i	0.718879	−	0.989452i
$890$	36.0240	+	4.85396i	1.20753	+	0.162705i
$891$	4.95372	−	6.67719i	0.165956	−	0.223694i
$892$	36.1514	−	18.4201i	1.21044	−	0.616749i
$893$	−1.37938	−	1.37938i	−0.0461592	−	0.0461592i
$894$	−14.3125	−	10.4533i	−0.478683	−	0.349609i
$895$	−13.5972	−	17.8321i	−0.454505	−	0.596061i
$896$	−18.9871	+	6.16928i	−0.634315	+	0.206101i
$897$	−1.27328	−	1.27965i	−0.0425137	−	0.0427261i
$898$	−56.5119	+	8.95061i	−1.88583	+	0.298686i
$899$	−3.42823			−0.114338
$900$	30.3842	+	20.2128i	1.01281	+	0.673761i
$901$	−61.2636			−2.04099
$902$	−14.2567	+	2.25804i	−0.474696	+	0.0751845i
$903$	2.50377	+	2.51628i	0.0833203	+	0.0837367i
$904$	5.02259	−	1.63194i	0.167049	−	0.0542774i
$905$	−0.171490	−	7.40842i	−0.00570054	−	0.246264i
$906$	−24.9762	−	18.2416i	−0.829779	−	0.606035i
$907$	−9.39707	−	9.39707i	−0.312024	−	0.312024i	0.533669	−	0.845693i	$-0.320813\pi$
$907$	−9.39707	−	9.39707i	−0.312024	−	0.312024i	−0.845693	+	0.533669i	$0.820813\pi$
$908$	−47.3402	+	24.1210i	−1.57104	+	0.800485i
$909$	17.1675	+	0.0855775i	0.569410	+	0.00283843i
$910$	−29.0428	+	60.4167i	−0.962758	+	2.00279i
$911$	−16.0441	+	22.0828i	−0.531566	+	0.731637i	−0.987368	−	0.158444i	$-0.949352\pi$
$911$	−16.0441	+	22.0828i	−0.531566	+	0.731637i	0.455802	+	0.890081i	$0.349352\pi$
$912$	−0.963678	−	0.494048i	−0.0319106	−	0.0163596i
$913$	2.26570	−	14.3051i	0.0749838	−	0.473429i
$914$	5.13214	+	3.72872i	0.169756	+	0.123335i
$915$	−7.18730	−	13.4137i	−0.237605	−	0.443442i
$916$	30.5727	−	22.2123i	1.01015	−	0.733916i
$917$	25.7824	+	50.6009i	0.851411	+	1.67099i
$918$	−56.6267	−	9.40333i	−1.86896	−	0.310356i
$919$	34.4230	+	11.1847i	1.13551	+	0.368949i	0.815667	−	0.578521i	$-0.196370\pi$
$919$	34.4230	+	11.1847i	1.13551	+	0.368949i	0.319842	+	0.947471i	$0.396370\pi$
$920$	−0.343968	−	0.237944i	−0.0113403	−	0.00784477i
$921$	0.103438	−	41.5010i	0.00340839	−	1.36750i
$922$	−31.5971	+	62.0129i	−1.04060	+	2.04228i
$923$	−2.61600	−	16.5168i	−0.0861068	−	0.543657i
$924$	10.3717	+	3.39858i	0.341204	+	0.111805i
$925$	10.2811	−	5.85284i	0.338040	−	0.192440i
$926$			30.8918i			1.01517i
$927$	3.12529	−	6.05886i	0.102648	−	0.198999i
$928$	−3.71809	−	1.89446i	−0.122052	−	0.0621887i
$929$	−13.7579	−	42.3425i	−0.451383	−	1.38921i	−0.875330	−	0.483526i	$-0.839356\pi$
$929$	−13.7579	−	42.3425i	−0.451383	−	1.38921i	0.423948	−	0.905687i	$-0.360644\pi$
$930$	−30.7034	+	44.1489i	−1.00680	+	1.44770i
$931$	0.0564608	−	0.173769i	0.00185043	−	0.00569503i
$932$	9.60726	−	9.60726i	0.314696	−	0.314696i
$933$	−4.96143	+	0.773143i	−0.162430	+	0.0253116i
$934$	0.0563419	+	0.0775480i	0.00184356	+	0.00253745i
$935$	−10.6627	+	1.94276i	−0.348709	+	0.0635349i
$936$	13.2272	−	4.22499i	0.432344	−	0.138098i
$937$	−19.1179	−	3.02798i	−0.624554	−	0.0989196i	−0.163867	−	0.986482i	$-0.552397\pi$
$937$	−19.1179	−	3.02798i	−0.624554	−	0.0989196i	−0.460687	+	0.887563i	$0.652397\pi$
$938$	−26.7369	−	4.23471i	−0.872992	−	0.138268i
$939$	19.1193	−	13.8183i	0.623935	−	0.450944i
$940$	−49.2071	+	8.96556i	−1.60496	+	0.292424i
$941$	−21.8140	−	30.0244i	−0.711116	−	0.978767i	−0.999772	−	0.0213346i	$-0.993208\pi$
$941$	−21.8140	−	30.0244i	−0.711116	−	0.978767i	0.288656	−	0.957433i	$-0.406792\pi$
$942$	8.70388	+	55.8548i	0.283588	+	1.81985i
$943$	−1.07697	+	1.07697i	−0.0350710	+	0.0350710i
$944$	0.0467486	−	0.143877i	0.00152154	−	0.00468281i
$945$	−30.8210	+	10.5510i	−1.00261	+	0.343223i
$946$	−0.439328	−	1.35211i	−0.0142838	−	0.0439610i
$947$	37.8632	+	19.2923i	1.23039	+	0.626915i	0.943603	−	0.331080i	$-0.107413\pi$
$947$	37.8632	+	19.2923i	1.23039	+	0.626915i	0.286787	+	0.957994i	$0.407413\pi$
$948$	−17.0989	−	2.75190i	−0.555346	−	0.0893776i
$949$			57.8262i			1.87712i
$950$	−1.94107	+	1.10502i	−0.0629767	+	0.0358515i
$951$	−16.3107	+	49.7766i	−0.528910	+	1.61412i
$952$	−2.09745	−	13.2428i	−0.0679787	−	0.429201i
$953$	2.66087	−	5.22226i	0.0861942	−	0.169166i	−0.843886	−	0.536523i	$-0.819737\pi$
$953$	2.66087	−	5.22226i	0.0861942	−	0.169166i	0.930080	+	0.367357i	$0.119737\pi$
$954$	70.0263	+	23.1395i	2.26719	+	0.749168i
$955$	17.2177	+	11.9105i	0.557152	+	0.385416i
$956$	−42.8562	−	13.9248i	−1.38607	−	0.450361i
$957$	0.375770	+	0.742056i	0.0121469	+	0.0239873i
$958$	5.51047	+	10.8149i	0.178035	+	0.349414i
$959$	25.3787	−	18.4387i	0.819522	−	0.595417i
$960$	−37.5764	+	20.1341i	−1.21277	+	0.649826i
$961$	−10.1050	−	7.34170i	−0.325967	−	0.236829i
$962$	3.95759	−	24.9872i	0.127598	−	0.805620i
$963$	1.00911	+	1.01922i	0.0325182	+	0.0328441i
$964$	−18.4944	+	25.4553i	−0.595663	+	0.819860i
$965$	−2.13396	+	4.43920i	−0.0686945	+	0.142903i
$966$	1.99728	−	0.643456i	0.0642614	−	0.0207029i
$967$	49.2268	−	25.0823i	1.58303	−	0.806593i	0.583045	−	0.812440i	$-0.301861\pi$
$967$	49.2268	−	25.0823i	1.58303	−	0.806593i	0.999983	+	0.00584637i	$0.00186097\pi$
$968$	6.53912	+	6.53912i	0.210175	+	0.210175i
$969$	1.13724	−	1.55711i	0.0365336	−	0.0500215i
$970$	−0.962236	−	41.5688i	−0.0308955	−	1.33469i
$971$	−50.9146	+	16.5432i	−1.63393	+	0.530895i	−0.975169	−	0.221460i	$-0.928918\pi$
$971$	−50.9146	+	16.5432i	−1.63393	+	0.530895i	−0.658758	+	0.752355i	$0.728918\pi$
$972$	33.5741	+	17.6373i	1.07689	+	0.565717i
$973$	9.46429	−	1.49900i	0.303411	−	0.0480556i
$974$	−17.5424			−0.562096
$975$	−11.7464	+	42.3828i	−0.376185	+	1.35734i
$976$	11.5789			0.370631
$977$	17.7277	−	2.80780i	0.567161	−	0.0898294i	0.133732	−	0.991017i	$-0.457304\pi$
$977$	17.7277	−	2.80780i	0.567161	−	0.0898294i	0.433428	+	0.901188i	$0.357304\pi$
$978$	46.1606	−	45.9310i	1.47605	−	1.46871i
$979$	6.78343	−	2.20407i	0.216799	−	0.0704424i
$980$	−2.84059	−	3.72529i	−0.0907393	−	0.119000i
$981$	12.1964	−	8.76866i	0.389401	−	0.279962i
$982$	−3.49857	−	3.49857i	−0.111644	−	0.111644i
$983$	17.3894	−	8.86036i	0.554637	−	0.282602i	−0.154123	−	0.988052i	$-0.549255\pi$
$983$	17.3894	−	8.86036i	0.554637	−	0.282602i	0.708760	+	0.705450i	$0.249255\pi$
$984$	−3.59248	−	11.1510i	−0.114524	−	0.355481i
$985$	34.2482	+	4.61468i	1.09124	+	0.147036i
$986$	3.37550	−	4.64597i	0.107498	−	0.147958i
$987$	20.3696	−	39.7324i	0.648370	−	1.26470i
$988$	−0.410080	+	2.58914i	−0.0130464	+	0.0823716i
$989$	−0.121362	−	0.0881750i	−0.00385910	−	0.00280380i
$990$	12.9216	+	1.80672i	0.410677	+	0.0574213i
$991$	12.9781	−	9.42911i	0.412262	−	0.299526i	−0.362255	−	0.932079i	$-0.617993\pi$
$991$	12.9781	−	9.42911i	0.412262	−	0.299526i	0.774517	+	0.632553i	$0.217993\pi$
$992$	−24.0331	−	47.1676i	−0.763051	−	1.49757i
$993$	14.8884	−	7.53932i	0.472468	−	0.239253i
$994$	18.4871	+	6.00684i	0.586376	+	0.190525i
$995$	5.08596	+	14.5021i	0.161236	+	0.459747i
$996$	66.0661	+	0.164664i	2.09338	+	0.00521757i
$997$	−5.47711	+	10.7494i	−0.173462	+	0.340438i	−0.961327	−	0.275410i	$-0.911186\pi$
$997$	−5.47711	+	10.7494i	−0.173462	+	0.340438i	0.787865	+	0.615848i	$0.211186\pi$
$998$	4.76603	+	30.0915i	0.150866	+	0.952531i
$999$	10.0001	−	7.15190i	0.316391	−	0.226276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.l.a.62.8	yes	64
3.2	odd	2	inner	75.2.l.a.62.1	yes	64
5.2	odd	4		375.2.l.b.293.8		64
5.3	odd	4		375.2.l.a.293.1		64
5.4	even	2		375.2.l.c.332.1		64
15.2	even	4		375.2.l.b.293.1		64
15.8	even	4		375.2.l.a.293.8		64
15.14	odd	2		375.2.l.c.332.8		64
25.2	odd	20		375.2.l.c.218.8		64
25.11	even	5		375.2.l.a.32.8		64
25.14	even	10		375.2.l.b.32.1		64
25.23	odd	20	inner	75.2.l.a.23.1	✓	64
75.2	even	20		375.2.l.c.218.1		64
75.11	odd	10		375.2.l.a.32.1		64
75.14	odd	10		375.2.l.b.32.8		64
75.23	even	20	inner	75.2.l.a.23.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.23.1	✓	64	25.23	odd	20	inner
75.2.l.a.23.8	yes	64	75.23	even	20	inner
75.2.l.a.62.1	yes	64	3.2	odd	2	inner
75.2.l.a.62.8	yes	64	1.1	even	1	trivial
375.2.l.a.32.1		64	75.11	odd	10
375.2.l.a.32.8		64	25.11	even	5
375.2.l.a.293.1		64	5.3	odd	4
375.2.l.a.293.8		64	15.8	even	4
375.2.l.b.32.1		64	25.14	even	10
375.2.l.b.32.8		64	75.14	odd	10
375.2.l.b.293.1		64	15.2	even	4
375.2.l.b.293.8		64	5.2	odd	4
375.2.l.c.218.1		64	75.2	even	20
375.2.l.c.218.8		64	25.2	odd	20
375.2.l.c.332.1		64	5.4	even	2
375.2.l.c.332.8		64	15.14	odd	2

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.07952 - 0.329364i) q^{2} +(-1.22169 - 1.22779i) q^{3} +(2.31381 - 0.751802i) q^{4} +(-2.11007 + 0.740012i) q^{5} +(-2.94492 - 2.15084i) q^{6} +(1.98257 + 1.98257i) q^{7} +(0.812071 - 0.413771i) q^{8} +(-0.0149544 + 2.99996i) q^{9} +O(q^{10})\)	\(q+(2.07952 - 0.329364i) q^{2} +(-1.22169 - 1.22779i) q^{3} +(2.31381 - 0.751802i) q^{4} +(-2.11007 + 0.740012i) q^{5} +(-2.94492 - 2.15084i) q^{6} +(1.98257 + 1.98257i) q^{7} +(0.812071 - 0.413771i) q^{8} +(-0.0149544 + 2.99996i) q^{9} +(-4.14419 + 2.23385i) q^{10} +(-0.542989 + 0.747360i) q^{11} +(-3.74981 - 1.92241i) q^{12} +(0.794440 - 5.01590i) q^{13} +(4.77577 + 3.46980i) q^{14} +(3.48643 + 1.68666i) q^{15} +(-2.38405 + 1.73211i) q^{16} +(-2.38204 - 4.67502i) q^{17} +(0.956980 + 6.24341i) q^{18} +(-0.201787 - 0.0655644i) q^{19} +(-4.32595 + 3.29860i) q^{20} +(0.0121038 - 4.85626i) q^{21} +(-0.883003 + 1.73299i) q^{22} +(0.0321047 + 0.202701i) q^{23} +(-1.50012 - 0.491557i) q^{24} +(3.90476 - 3.12295i) q^{25} -10.6923i q^{26} +(3.70160 - 3.64666i) q^{27} +(6.07778 + 3.09678i) q^{28} +(0.160641 + 0.494401i) q^{29} +(7.80562 + 2.35915i) q^{30} +(-2.03788 + 6.27196i) q^{31} +(-5.67611 + 5.67611i) q^{32} +(1.58097 - 0.246363i) q^{33} +(-6.49329 - 8.93724i) q^{34} +(-5.65047 - 2.71623i) q^{35} +(2.22078 + 6.95258i) q^{36} +(2.33693 + 0.370134i) q^{37} +(-0.441214 - 0.0698814i) q^{38} +(-7.12905 + 5.15246i) q^{39} +(-1.40733 + 1.47403i) q^{40} +(4.36217 + 6.00401i) q^{41} +(-1.57431 - 10.1027i) q^{42} +(-0.516864 + 0.516864i) q^{43} +(-0.694506 + 2.13747i) q^{44} +(-2.18845 - 6.34119i) q^{45} +(0.133525 + 0.410946i) q^{46} +(8.19208 + 4.17408i) q^{47} +(5.03924 + 0.811018i) q^{48} +0.861150i q^{49} +(7.09145 - 7.78032i) q^{50} +(-2.82985 + 8.63608i) q^{51} +(-1.93278 - 12.2031i) q^{52} +(5.30087 - 10.4035i) q^{53} +(6.49648 - 8.80247i) q^{54} +(0.592688 - 1.97880i) q^{55} +(2.43031 + 0.789657i) q^{56} +(0.166021 + 0.327852i) q^{57} +(0.496893 + 0.975208i) q^{58} +(-0.0415323 + 0.0301750i) q^{59} +(9.33496 + 1.28151i) q^{60} +(-3.17882 - 2.30955i) q^{61} +(-2.17206 + 13.7139i) q^{62} +(-5.97728 + 5.91798i) q^{63} +(-6.46985 + 8.90499i) q^{64} +(2.03550 + 11.1718i) q^{65} +(3.20651 - 1.03303i) q^{66} +(-4.08589 + 2.08186i) q^{67} +(-9.02628 - 9.02628i) q^{68} +(0.209653 - 0.287055i) q^{69} +(-12.6449 - 3.78739i) q^{70} +(3.13172 - 1.01756i) q^{71} +(1.22915 + 2.44237i) q^{72} +(-11.2465 + 1.78126i) q^{73} +4.98160 q^{74} +(-8.60474 - 0.978973i) q^{75} -0.516187 q^{76} +(-2.55821 + 0.405180i) q^{77} +(-13.1280 + 13.0627i) q^{78} +(3.90882 - 1.27005i) q^{79} +(3.74872 - 5.41910i) q^{80} +(-8.99955 - 0.0897252i) q^{81} +(11.0487 + 11.0487i) q^{82} +(-13.9694 + 7.11778i) q^{83} +(-3.62294 - 11.2456i) q^{84} +(8.48584 + 8.10187i) q^{85} +(-0.904592 + 1.24506i) q^{86} +(0.410770 - 0.801238i) q^{87} +(-0.131710 + 0.831583i) q^{88} +(-6.24638 - 4.53826i) q^{89} +(-6.63949 - 12.4658i) q^{90} +(11.5194 - 8.36933i) q^{91} +(0.226675 + 0.444875i) q^{92} +(10.1903 - 5.16028i) q^{93} +(18.4104 + 5.98190i) q^{94} +(0.474302 - 0.0109792i) q^{95} +(13.9035 + 0.0346533i) q^{96} +(-4.00961 + 7.86930i) q^{97} +(0.283631 + 1.79078i) q^{98} +(-2.23393 - 1.64012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Introduction

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