LMFDB - Embedded newform 756.2.bt.a.103.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.2
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41407 + 0.0203430i) q^{2} +(1.63923 - 0.559403i) q^{3} +(1.99917 - 0.0575327i) q^{4} +(-1.49077 - 0.262863i) q^{5} +(-2.30660 + 0.824380i) q^{6} +(1.66611 - 2.05525i) q^{7} +(-2.82579 + 0.122024i) q^{8} +(2.37414 - 1.83398i) q^{9} +O(q^{10})$	\(q+(-1.41407 + 0.0203430i) q^{2} +(1.63923 - 0.559403i) q^{3} +(1.99917 - 0.0575327i) q^{4} +(-1.49077 - 0.262863i) q^{5} +(-2.30660 + 0.824380i) q^{6} +(1.66611 - 2.05525i) q^{7} +(-2.82579 + 0.122024i) q^{8} +(2.37414 - 1.83398i) q^{9} +(2.11340 + 0.341379i) q^{10} +(-3.02942 + 0.534168i) q^{11} +(3.24492 - 1.21265i) q^{12} +(2.09650 - 2.49852i) q^{13} +(-2.31419 + 2.94016i) q^{14} +(-2.59076 + 0.403049i) q^{15} +(3.99338 - 0.230036i) q^{16} -1.88674i q^{17} +(-3.31988 + 2.64167i) q^{18} -1.64419 q^{19} +(-2.99543 - 0.439740i) q^{20} +(1.58143 - 4.30106i) q^{21} +(4.27293 - 0.816977i) q^{22} +(-1.15541 + 1.37696i) q^{23} +(-4.56386 + 1.78078i) q^{24} +(-2.54517 - 0.926365i) q^{25} +(-2.91377 + 3.57572i) q^{26} +(2.86582 - 4.33441i) q^{27} +(3.21261 - 4.20466i) q^{28} +(8.13107 - 6.82278i) q^{29} +(3.65530 - 0.622642i) q^{30} +(-5.68712 + 2.06994i) q^{31} +(-5.64223 + 0.406523i) q^{32} +(-4.66709 + 2.57029i) q^{33} +(0.0383820 + 2.66798i) q^{34} +(-3.02404 + 2.62595i) q^{35} +(4.64079 - 3.80303i) q^{36} +(-1.32913 - 2.30213i) q^{37} +(2.32500 - 0.0334478i) q^{38} +(2.03897 - 5.26843i) q^{39} +(4.24468 + 0.560886i) q^{40} +(1.18751 - 1.41521i) q^{41} +(-2.14875 + 6.11415i) q^{42} +(1.00225 - 2.75367i) q^{43} +(-6.02560 + 1.24218i) q^{44} +(-4.02137 + 2.10997i) q^{45} +(1.60581 - 1.97062i) q^{46} +(4.23350 + 1.54087i) q^{47} +(6.41738 - 2.61099i) q^{48} +(-1.44812 - 6.84857i) q^{49} +(3.61788 + 1.25817i) q^{50} +(-1.05545 - 3.09280i) q^{51} +(4.04753 - 5.11558i) q^{52} +(4.36596 + 7.56206i) q^{53} +(-3.96428 + 6.18744i) q^{54} +4.65657 q^{55} +(-4.45731 + 6.01103i) q^{56} +(-2.69521 + 0.919768i) q^{57} +(-11.3591 + 9.81328i) q^{58} +(-3.94099 - 3.30688i) q^{59} +(-5.15618 + 0.954817i) q^{60} +(-4.04017 + 11.1003i) q^{61} +(7.99986 - 3.04273i) q^{62} +(0.186295 - 7.93507i) q^{63} +(7.97022 - 0.689631i) q^{64} +(-3.78217 + 3.17362i) q^{65} +(6.54729 - 3.72950i) q^{66} +(6.19801 + 1.09288i) q^{67} +(-0.108549 - 3.77193i) q^{68} +(-1.12370 + 2.90349i) q^{69} +(4.22278 - 3.77478i) q^{70} +(-10.4391 - 6.02700i) q^{71} +(-6.48503 + 5.47215i) q^{72} +(-1.94716 - 1.12419i) q^{73} +(1.92632 + 3.22832i) q^{74} +(-4.69032 - 0.0947491i) q^{75} +(-3.28703 + 0.0945950i) q^{76} +(-3.94951 + 7.11620i) q^{77} +(-2.77607 + 7.49139i) q^{78} +(9.56286 - 1.68619i) q^{79} +(-6.01367 - 0.706781i) q^{80} +(2.27305 - 8.70823i) q^{81} +(-1.65042 + 2.02537i) q^{82} +(7.14197 - 5.99283i) q^{83} +(2.91409 - 8.68954i) q^{84} +(-0.495955 + 2.81270i) q^{85} +(-1.36123 + 3.91426i) q^{86} +(9.51200 - 15.7326i) q^{87} +(8.49533 - 1.87911i) q^{88} -11.6381i q^{89} +(5.64357 - 3.06544i) q^{90} +(-1.64207 - 8.47166i) q^{91} +(-2.23064 + 2.81925i) q^{92} +(-8.16455 + 6.57450i) q^{93} +(-6.01781 - 2.09277i) q^{94} +(2.45111 + 0.432198i) q^{95} +(-9.02149 + 3.82266i) q^{96} +(4.13324 - 11.3560i) q^{97} +(2.18707 + 9.65488i) q^{98} +(-6.21260 + 6.82407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.41407	+	0.0203430i	−0.999897	+	0.0143847i
$2$	−1.41407	+	0.0203430i	−0.999897	+	0.0143847i
$3$	1.63923	−	0.559403i	0.946409	−	0.322972i
$3$	1.63923	−	0.559403i	0.946409	−	0.322972i
$4$	1.99917	−	0.0575327i	0.999586	−	0.0287663i
$5$	−1.49077	−	0.262863i	−0.666692	−	0.117556i	−0.169948	−	0.985453i	$-0.554360\pi$
$5$	−1.49077	−	0.262863i	−0.666692	−	0.117556i	−0.496744	+	0.867897i	$0.665471\pi$
$6$	−2.30660	+	0.824380i	−0.941665	+	0.336552i
$7$	1.66611	−	2.05525i	0.629732	−	0.776812i
$7$	1.66611	−	2.05525i	0.629732	−	0.776812i
$8$	−2.82579	+	0.122024i	−0.999069	+	0.0431421i
$9$	2.37414	−	1.83398i	0.791379	−	0.611326i
$10$	2.11340	+	0.341379i	0.668314	+	0.107954i
$11$	−3.02942	+	0.534168i	−0.913404	+	0.161058i	−0.610549	−	0.791979i	$-0.709051\pi$
$11$	−3.02942	+	0.534168i	−0.913404	+	0.161058i	−0.302855	+	0.953037i	$0.597940\pi$
$12$	3.24492	−	1.21265i	0.936726	−	0.350063i
$13$	2.09650	−	2.49852i	0.581466	−	0.692964i	−0.392476	−	0.919762i	$-0.628381\pi$
$13$	2.09650	−	2.49852i	0.581466	−	0.692964i	0.973942	+	0.226798i	$0.0728258\pi$
$14$	−2.31419	+	2.94016i	−0.618493	+	0.785790i
$15$	−2.59076	+	0.403049i	−0.668930	+	0.104067i
$16$	3.99338	−	0.230036i	0.998345	−	0.0575089i
$17$		−	1.88674i		−	0.457603i	−0.973473	−	0.228801i	$-0.926519\pi$
$17$		−	1.88674i		−	0.457603i	0.973473	−	0.228801i	$-0.0734806\pi$
$18$	−3.31988	+	2.64167i	−0.782503	+	0.622647i
$19$	−1.64419			−0.377204			−0.188602	−	0.982054i	$-0.560396\pi$
$19$	−1.64419			−0.377204			−0.188602	+	0.982054i	$0.560396\pi$
$20$	−2.99543	−	0.439740i	−0.669798	−	0.0983289i
$21$	1.58143	−	4.30106i	0.345096	−	0.938568i
$22$	4.27293	−	0.816977i	0.910993	−	0.174180i
$23$	−1.15541	+	1.37696i	−0.240919	+	0.287116i	−0.872932	−	0.487842i	$-0.837784\pi$
$23$	−1.15541	+	1.37696i	−0.240919	+	0.287116i	0.632013	+	0.774958i	$0.282229\pi$
$24$	−4.56386	+	1.78078i	−0.931594	+	0.363501i
$25$	−2.54517	−	0.926365i	−0.509034	−	0.185273i
$26$	−2.91377	+	3.57572i	−0.571437	+	0.701256i
$27$	2.86582	−	4.33441i	0.551527	−	0.834157i
$28$	3.21261	−	4.20466i	0.607125	−	0.794606i
$29$	8.13107	−	6.82278i	1.50990	−	1.26696i	0.645955	−	0.763375i	$-0.276459\pi$
$29$	8.13107	−	6.82278i	1.50990	−	1.26696i	0.863947	−	0.503583i	$-0.167985\pi$
$30$	3.65530	−	0.622642i	0.667364	−	0.113678i
$31$	−5.68712	+	2.06994i	−1.02144	+	0.371772i	−0.797814	−	0.602903i	$-0.794010\pi$
$31$	−5.68712	+	2.06994i	−1.02144	+	0.371772i	−0.223622	+	0.974676i	$0.571788\pi$
$32$	−5.64223	+	0.406523i	−0.997414	+	0.0718638i
$33$	−4.66709	+	2.57029i	−0.812436	+	0.447430i
$34$	0.0383820	+	2.66798i	0.00658246	+	0.457555i
$35$	−3.02404	+	2.62595i	−0.511156	+	0.443866i
$36$	4.64079	−	3.80303i	0.773466	−	0.633838i
$37$	−1.32913	−	2.30213i	−0.218508	−	0.378467i	0.735844	−	0.677151i	$-0.236786\pi$
$37$	−1.32913	−	2.30213i	−0.218508	−	0.378467i	−0.954352	+	0.298684i	$0.903452\pi$
$38$	2.32500	−	0.0334478i	0.377165	−	0.00542595i
$39$	2.03897	−	5.26843i	0.326497	−	0.843624i
$40$	4.24468	+	0.560886i	0.671143	+	0.0886839i
$41$	1.18751	−	1.41521i	0.185457	−	0.221019i	−0.665303	−	0.746574i	$-0.731698\pi$
$41$	1.18751	−	1.41521i	0.185457	−	0.221019i	0.850760	+	0.525554i	$0.176142\pi$
$42$	−2.14875	+	6.11415i	−0.331559	+	0.943434i
$43$	1.00225	−	2.75367i	0.152842	−	0.419930i	−0.839514	−	0.543338i	$-0.817160\pi$
$43$	1.00225	−	2.75367i	0.152842	−	0.419930i	0.992356	+	0.123408i	$0.0393824\pi$
$44$	−6.02560	+	1.24218i	−0.908393	+	0.187266i
$45$	−4.02137	+	2.10997i	−0.599471	+	0.314535i
$46$	1.60581	−	1.97062i	0.236764	−	0.290552i
$47$	4.23350	+	1.54087i	0.617520	+	0.224759i	0.631790	−	0.775139i	$-0.282320\pi$
$47$	4.23350	+	1.54087i	0.617520	+	0.224759i	−0.0142704	+	0.999898i	$0.504543\pi$
$48$	6.41738	−	2.61099i	0.926269	−	0.376864i
$49$	−1.44812	−	6.84857i	−0.206875	−	0.978367i
$50$	3.61788	+	1.25817i	0.511646	+	0.177932i
$51$	−1.05545	−	3.09280i	−0.147793	−	0.433079i
$52$	4.04753	−	5.11558i	0.561291	−	0.709404i
$53$	4.36596	+	7.56206i	0.599710	+	1.03873i	0.992864	+	0.119255i	$0.0380508\pi$
$53$	4.36596	+	7.56206i	0.599710	+	1.03873i	−0.393154	+	0.919473i	$0.628616\pi$
$54$	−3.96428	+	6.18744i	−0.539471	+	0.842004i
$55$	4.65657			0.627892
$56$	−4.45731	+	6.01103i	−0.595632	+	0.803257i
$57$	−2.69521	+	0.919768i	−0.356989	+	0.121826i
$58$	−11.3591	+	9.81328i	−1.49152	+	1.28855i
$59$	−3.94099	−	3.30688i	−0.513073	−	0.430519i	0.349136	−	0.937072i	$-0.386475\pi$
$59$	−3.94099	−	3.30688i	−0.513073	−	0.430519i	−0.862209	+	0.506553i	$0.830920\pi$
$60$	−5.15618	+	0.954817i	−0.665660	+	0.123266i
$61$	−4.04017	+	11.1003i	−0.517291	+	1.42125i	0.356202	+	0.934409i	$0.384072\pi$
$61$	−4.04017	+	11.1003i	−0.517291	+	1.42125i	−0.873493	+	0.486837i	$0.838151\pi$
$62$	7.99986	−	3.04273i	1.01598	−	0.386427i
$63$	0.186295	−	7.93507i	0.0234709	−	0.999725i
$64$	7.97022	−	0.689631i	0.996278	−	0.0862038i
$65$	−3.78217	+	3.17362i	−0.469121	+	0.393639i
$66$	6.54729	−	3.72950i	0.805916	−	0.459070i
$67$	6.19801	+	1.09288i	0.757207	+	0.133516i	0.538907	−	0.842365i	$-0.318838\pi$
$67$	6.19801	+	1.09288i	0.757207	+	0.133516i	0.218301	+	0.975882i	$0.429949\pi$
$68$	−0.108549	−	3.77193i	−0.0131636	−	0.457413i
$69$	−1.12370	+	2.90349i	−0.135277	+	0.349539i
$70$	4.22278	−	3.77478i	0.504719	−	0.451173i
$71$	−10.4391	−	6.02700i	−1.23889	−	0.715273i	−0.270022	−	0.962854i	$-0.587031\pi$
$71$	−10.4391	−	6.02700i	−1.23889	−	0.715273i	−0.968867	+	0.247581i	$0.920364\pi$
$72$	−6.48503	+	5.47215i	−0.764268	+	0.644899i
$73$	−1.94716	−	1.12419i	−0.227898	−	0.131577i	0.381704	−	0.924285i	$-0.375337\pi$
$73$	−1.94716	−	1.12419i	−0.227898	−	0.131577i	−0.609602	+	0.792708i	$0.708671\pi$
$74$	1.92632	+	3.22832i	0.223930	+	0.375285i
$75$	−4.69032	−	0.0947491i	−0.541592	−	0.0109407i
$76$	−3.28703	+	0.0945950i	−0.377048	+	0.0108508i
$77$	−3.94951	+	7.11620i	−0.450088	+	0.810967i
$78$	−2.77607	+	7.49139i	−0.314328	+	0.848233i
$79$	9.56286	−	1.68619i	1.07591	−	0.189711i	0.392501	−	0.919751i	$-0.371610\pi$
$79$	9.56286	−	1.68619i	1.07591	−	0.189711i	0.683404	+	0.730040i	$0.260499\pi$
$80$	−6.01367	−	0.706781i	−0.672349	−	0.0790205i
$81$	2.27305	−	8.70823i	0.252561	−	0.967581i
$82$	−1.65042	+	2.02537i	−0.182259	+	0.223664i
$83$	7.14197	−	5.99283i	0.783933	−	0.657798i	−0.160302	−	0.987068i	$-0.551247\pi$
$83$	7.14197	−	5.99283i	0.783933	−	0.657798i	0.944236	+	0.329270i	$0.106803\pi$
$84$	2.91409	−	8.68954i	0.317954	−	0.948106i
$85$	−0.495955	+	2.81270i	−0.0537938	+	0.305080i
$86$	−1.36123	+	3.91426i	−0.146786	+	0.422085i
$87$	9.51200	−	15.7326i	1.01979	−	1.68672i
$88$	8.49533	−	1.87911i	0.905605	−	0.200314i
$89$		−	11.6381i		−	1.23364i	−0.787104	−	0.616820i	$-0.788421\pi$
$89$		−	11.6381i		−	1.23364i	0.787104	−	0.616820i	$-0.211579\pi$
$90$	5.64357	−	3.06544i	0.594884	−	0.323126i
$91$	−1.64207	−	8.47166i	−0.172135	−	0.888071i
$92$	−2.23064	+	2.81925i	−0.232560	+	0.293927i
$93$	−8.16455	+	6.57450i	−0.846624	+	0.681744i
$94$	−6.01781	−	2.09277i	−0.620689	−	0.215853i
$95$	2.45111	+	0.432198i	0.251479	+	0.0443425i
$96$	−9.02149	+	3.82266i	−0.920752	+	0.390149i
$97$	4.13324	−	11.3560i	0.419666	−	1.15302i	−0.532229	−	0.846601i	$-0.678645\pi$
$97$	4.13324	−	11.3560i	0.419666	−	1.15302i	0.951895	−	0.306424i	$-0.0991324\pi$
$98$	2.18707	+	9.65488i	0.220927	+	0.975290i
$99$	−6.21260	+	6.82407i	−0.624390	+	0.685845i
$100$	−5.14153	−	1.70553i	−0.514153	−	0.170553i
$101$	−1.81769	−	2.16623i	−0.180866	−	0.215548i	0.667992	−	0.744168i	$-0.267154\pi$
$101$	−1.81769	−	2.16623i	−0.180866	−	0.215548i	−0.848858	+	0.528620i	$0.822710\pi$
$102$	1.55539	+	4.35196i	0.154007	+	0.430908i
$103$	−0.282617	+	1.60280i	−0.0278470	+	0.157928i	−0.995560	−	0.0941249i	$-0.969995\pi$
$103$	−0.282617	+	1.60280i	−0.0278470	+	0.157928i	0.967713	+	0.252053i	$0.0811058\pi$
$104$	−5.61941	+	7.31612i	−0.551028	+	0.717404i
$105$	−3.48813	+	5.99618i	−0.340407	+	0.585168i
$106$	−6.32759	−	10.6044i	−0.614590	−	1.02999i
$107$	−2.83255	−	1.63537i	−0.273833	−	0.158097i	0.356795	−	0.934183i	$-0.383869\pi$
$107$	−2.83255	−	1.63537i	−0.273833	−	0.158097i	−0.630628	+	0.776085i	$0.717203\pi$
$108$	5.47989	−	8.83011i	0.527303	−	0.849677i
$109$	8.82069	+	15.2779i	0.844869	+	1.46336i	0.885735	+	0.464191i	$0.153655\pi$
$109$	8.82069	+	15.2779i	0.844869	+	1.46336i	−0.0408659	+	0.999165i	$0.513012\pi$
$110$	−6.58471	+	0.0947286i	−0.627827	+	0.00903202i
$111$	−3.46657	−	3.03019i	−0.329032	−	0.287613i
$112$	6.18065	−	8.59067i	0.584016	−	0.811742i
$113$	5.35397	−	1.94869i	0.503659	−	0.183317i	−0.0776798	−	0.996978i	$-0.524751\pi$
$113$	5.35397	−	1.94869i	0.503659	−	0.183317i	0.581339	+	0.813661i	$0.302529\pi$
$114$	3.79250	−	1.35544i	0.355200	−	0.126949i
$115$	2.08440	−	1.74902i	0.194371	−	0.163097i
$116$	15.8629	−	14.1077i	1.47283	−	1.30987i
$117$	0.395162	−	9.77676i	0.0365327	−	0.903862i
$118$	5.64010	+	4.59598i	0.519213	+	0.423095i
$119$	−3.87773	−	3.14353i	−0.355471	−	0.288167i
$120$	7.27176	−	1.45507i	0.663818	−	0.132829i
$121$	−1.44458	+	0.525785i	−0.131326	+	0.0477987i
$122$	5.48726	−	15.7787i	0.496794	−	1.42854i
$123$	1.15492	−	2.98415i	0.104135	−	0.269072i
$124$	−11.2504	+	4.46536i	−1.01032	+	0.401002i
$125$	10.1056	+	5.83444i	0.903868	+	0.521848i
$126$	−0.102010	+	11.2245i	−0.00908779	+	0.999959i
$127$	−1.47968	+	0.854292i	−0.131300	+	0.0758062i	−0.564211	−	0.825630i	$-0.690820\pi$
$127$	−1.47968	+	0.854292i	−0.131300	+	0.0758062i	0.432911	+	0.901437i	$0.357486\pi$
$128$	−11.2564	+	1.13732i	−0.994934	+	0.100526i
$129$	0.102511	−	5.07455i	0.00902558	−	0.446789i
$130$	5.28368	−	4.56465i	0.463410	−	0.400346i
$131$	3.68958	+	3.09592i	0.322360	+	0.270492i	0.789578	−	0.613650i	$-0.210299\pi$
$131$	3.68958	+	3.09592i	0.322360	+	0.270492i	−0.467218	+	0.884142i	$0.654744\pi$
$132$	−9.18244	+	5.40696i	−0.799229	+	0.470616i
$133$	−2.73942	+	3.37924i	−0.237538	+	0.293017i
$134$	−8.78663	−	1.41931i	−0.759050	−	0.122610i
$135$	−5.41163	+	5.70828i	−0.465759	+	0.491291i
$136$	0.230228	+	5.33155i	0.0197419	+	0.457176i
$137$	5.83450	+	2.12358i	0.498475	+	0.181430i	0.579008	−	0.815322i	$-0.303440\pi$
$137$	5.83450	+	2.12358i	0.498475	+	0.181430i	−0.0805331	+	0.996752i	$0.525662\pi$
$138$	1.52992	−	4.12859i	0.130235	−	0.351449i
$139$	−0.539562	+	3.06001i	−0.0457650	+	0.259546i	−0.999102	−	0.0423607i	$-0.986512\pi$
$139$	−0.539562	+	3.06001i	−0.0457650	+	0.259546i	0.953337	+	0.301907i	$0.0976232\pi$
$140$	−5.89450	+	5.42370i	−0.498176	+	0.458386i
$141$	7.80165	+	0.157601i	0.657017	+	0.0132724i
$142$	14.8841	+	8.31022i	1.24905	+	0.697378i
$143$	−5.01656	+	8.68894i	−0.419506	+	0.726605i
$144$	9.05895	−	7.86991i	0.754912	−	0.655826i
$145$	−13.9150	+	8.03383i	−1.15558	+	0.667173i
$146$	2.77629	+	1.55008i	0.229767	+	0.128285i
$147$	−6.20492	−	10.4163i	−0.511773	−	0.859121i
$148$	−2.78962	−	4.52588i	−0.229305	−	0.372025i
$149$	−12.3989	+	4.51284i	−1.01576	+	0.369707i	−0.795642	−	0.605767i	$-0.792867\pi$
$149$	−12.3989	+	4.51284i	−1.01576	+	0.369707i	−0.220118	+	0.975473i	$0.570644\pi$
$150$	6.63436	+	0.0385665i	0.541693	+	0.00314894i
$151$	18.5431	−	3.26965i	1.50901	−	0.266080i	0.642910	−	0.765942i	$-0.277727\pi$
$151$	18.5431	−	3.26965i	1.50901	−	0.266080i	0.866105	+	0.499862i	$0.166616\pi$
$152$	4.64616	−	0.200632i	0.376853	−	0.0162734i
$153$	−3.46025	−	4.47939i	−0.279744	−	0.362137i
$154$	5.44010	−	10.1431i	0.438376	−	0.817357i
$155$	9.02229	−	1.59087i	0.724688	−	0.127782i
$156$	3.77315	−	10.6498i	0.302093	−	0.852667i
$157$	−12.2313	+	14.5767i	−0.976166	+	1.16335i	0.0103931	+	0.999946i	$0.496692\pi$
$157$	−12.2313	+	14.5767i	−0.976166	+	1.16335i	−0.986559	+	0.163404i	$0.947753\pi$
$158$	−13.4882	+	2.57892i	−1.07307	+	0.205168i
$159$	11.3870	+	9.95361i	0.903051	+	0.789372i
$160$	8.51812	+	0.877100i	0.673416	+	0.0693408i
$161$	0.904960	+	4.66882i	0.0713209	+	0.367955i
$162$	−3.03709	+	12.3603i	−0.238616	+	0.971114i
$163$	7.01583	+	4.05059i	0.549523	+	0.317267i	0.748929	−	0.662650i	$-0.230568\pi$
$163$	7.01583	+	4.05059i	0.549523	+	0.317267i	−0.199407	+	0.979917i	$0.563902\pi$
$164$	2.29261	−	2.89758i	0.179023	−	0.226263i
$165$	7.63319	−	2.60490i	0.594243	−	0.202791i
$166$	−9.97732	+	8.61955i	−0.774390	+	0.669007i
$167$	−9.23106	+	3.35983i	−0.714321	+	0.259991i	−0.673513	−	0.739176i	$-0.735215\pi$
$167$	−9.23106	+	3.35983i	−0.714321	+	0.259991i	−0.0408078	+	0.999167i	$0.512993\pi$
$168$	−3.94395	+	12.3469i	−0.304283	+	0.952582i
$169$	0.410172	+	2.32620i	0.0315517	+	0.178938i
$170$	0.644095	−	3.98743i	0.0493998	−	0.305822i
$171$	−3.90354	+	3.01542i	−0.298511	+	0.230595i
$172$	1.84525	−	5.56272i	0.140699	−	0.424153i
$173$	13.7597	+	16.3982i	1.04613	+	1.24673i	0.968307	+	0.249762i	$0.0803524\pi$
$173$	13.7597	+	16.3982i	1.04613	+	1.24673i	0.0778229	+	0.996967i	$0.475203\pi$
$174$	−13.1306	+	22.4405i	−0.995425	+	1.70121i
$175$	−6.14446	+	3.68753i	−0.464477	+	0.278751i
$176$	−11.9747	+	2.83001i	−0.902630	+	0.213320i
$177$	−8.31006	−	3.21613i	−0.624622	−	0.241739i
$178$	0.236754	+	16.4571i	0.0177455	+	1.23351i
$179$			11.9302i			0.891702i	0.895107	+	0.445851i	$0.147099\pi$
$179$			11.9302i			0.891702i	−0.895107	+	0.445851i	$0.852901\pi$
$180$	−7.91803	+	4.44955i	−0.590175	+	0.331650i
$181$	7.58264	−	4.37784i	0.563613	−	0.325402i	−0.190981	−	0.981594i	$-0.561167\pi$
$181$	7.58264	−	4.37784i	0.563613	−	0.325402i	0.754594	+	0.656191i	$0.227834\pi$
$182$	2.49433	+	11.9461i	0.184892	+	0.885503i
$183$	−0.413231	+	20.4560i	−0.0305469	+	1.51215i
$184$	3.09692	−	4.03199i	0.228308	−	0.297242i
$185$	1.37629	+	3.78132i	0.101187	+	0.278008i
$186$	11.4115	−	9.46287i	0.836730	−	0.693851i
$187$	1.00784	+	5.71573i	0.0737004	+	0.417976i
$188$	8.55215	+	2.83690i	0.623730	+	0.206902i
$189$	−4.13352	−	13.1116i	−0.300669	−	0.953728i
$190$	−3.47483	−	0.561294i	−0.252091	−	0.0407205i
$191$	17.6780	−	3.11710i	1.27913	−	0.225546i	0.507521	−	0.861639i	$-0.330562\pi$
$191$	17.6780	−	3.11710i	1.27913	−	0.225546i	0.771612	+	0.636094i	$0.219451\pi$
$192$	12.6792	−	5.58903i	0.915044	−	0.403353i
$193$	−24.9137	+	9.06784i	−1.79333	+	0.652717i	−0.794351	+	0.607460i	$0.792189\pi$
$193$	−24.9137	+	9.06784i	−1.79333	+	0.652717i	−0.998975	+	0.0452576i	$0.985589\pi$
$194$	−5.61366	+	16.1422i	−0.403037	+	1.15894i
$195$	−4.42451	+	7.31804i	−0.316846	+	0.524056i
$196$	−3.28907	−	13.6082i	−0.234933	−	0.972011i
$197$	8.77450	+	15.1979i	0.625157	+	1.08280i	0.988510	+	0.151152i	$0.0482984\pi$
$197$	8.77450	+	15.1979i	0.625157	+	1.08280i	−0.363354	+	0.931651i	$0.618368\pi$
$198$	8.64621	−	9.77608i	0.614459	−	0.694756i
$199$	−1.56796			−0.111150			−0.0555750	−	0.998455i	$-0.517699\pi$
$199$	−1.56796			−0.111150			−0.0555750	+	0.998455i	$0.517699\pi$
$200$	7.30516	+	2.30715i	0.516553	+	0.163140i
$201$	10.7713	−	1.67571i	0.759749	−	0.118196i
$202$	2.61440	+	3.02622i	0.183948	+	0.212924i
$203$	−0.475237	−	28.0789i	−0.0333551	−	1.97076i
$204$	−2.28796	−	6.12232i	−0.160190	−	0.428648i
$205$	−2.14230	+	1.79761i	−0.149625	+	0.125550i
$206$	0.367033	−	2.27221i	0.0255724	−	0.158313i
$207$	−0.217778	+	5.38808i	−0.0151366	+	0.374497i
$208$	7.79739	−	10.4598i	0.540652	−	0.725256i
$209$	4.98095	−	0.878276i	0.344540	−	0.0607517i
$210$	4.81047	−	8.54997i	0.331954	−	0.590004i
$211$	3.30773	+	9.08792i	0.227714	+	0.625638i	0.999953	−	0.00969347i	$-0.00308558\pi$
$211$	3.30773	+	9.08792i	0.227714	+	0.625638i	−0.772239	+	0.635332i	$0.780863\pi$
$212$	9.16336	+	14.8667i	0.629342	+	1.02105i
$213$	−20.4835	−	4.03998i	−1.40351	−	0.276815i
$214$	4.03868	+	2.25490i	0.276078	+	0.154142i
$215$	−2.21796	+	3.84162i	−0.151264	+	0.261997i
$216$	−7.56931	+	12.5978i	−0.515026	+	0.857175i
$217$	−5.22114	+	15.1372i	−0.354434	+	1.02758i
$218$	−12.7838	−	21.4245i	−0.865831	−	1.45105i
$219$	−3.82072	−	0.753563i	−0.258180	−	0.0509211i
$220$	9.30930	−	0.267905i	0.627633	−	0.0180622i
$221$	−4.71406	−	3.95557i	−0.317102	−	0.266080i
$222$	4.96361	+	4.21437i	0.333135	+	0.282850i
$223$	3.61655	+	20.5105i	0.242182	+	1.37348i	0.826947	+	0.562280i	$0.190076\pi$
$223$	3.61655	+	20.5105i	0.242182	+	1.37348i	−0.584765	+	0.811203i	$0.698813\pi$
$224$	−8.56509	+	12.2735i	−0.572279	+	0.820059i
$225$	−7.74151	+	2.46847i	−0.516101	+	0.164564i
$226$	−7.53124	+	2.86449i	−0.500970	+	0.190543i
$227$	3.59218	+	20.3723i	0.238421	+	1.35215i	0.835287	+	0.549814i	$0.185301\pi$
$227$	3.59218	+	20.3723i	0.238421	+	1.35215i	−0.596866	+	0.802341i	$0.703588\pi$
$228$	−5.33527	+	1.99384i	−0.353337	+	0.132045i
$229$	7.09579	+	19.4955i	0.468903	+	1.28830i	0.918625	+	0.395131i	$0.129301\pi$
$229$	7.09579	+	19.4955i	0.468903	+	1.28830i	−0.449722	+	0.893169i	$0.648477\pi$
$230$	−2.91190	+	2.51563i	−0.192005	+	0.165876i
$231$	−2.49332	+	13.8744i	−0.164048	+	0.912871i
$232$	−22.1442	+	20.2720i	−1.45384	+	1.33092i
$233$	7.64807	+	13.2468i	0.501042	+	0.867830i	0.999999	+	0.00120338i	$0.000383048\pi$
$233$	7.64807	+	13.2468i	0.501042	+	0.867830i	−0.498957	+	0.866626i	$0.666284\pi$
$234$	−0.359897	+	13.8330i	−0.0235272	+	0.904294i
$235$	−5.90614	−	3.40991i	−0.385274	−	0.222438i
$236$	−8.06897	−	6.38429i	−0.525245	−	0.415582i
$237$	14.7324	−	8.11354i	0.956975	−	0.527031i
$238$	5.54733	+	4.36628i	0.359580	+	0.283024i
$239$	−28.9303	−	5.10119i	−1.87134	−	0.329968i	−0.881506	−	0.472172i	$-0.843470\pi$
$239$	−28.9303	−	5.10119i	−1.87134	−	0.329968i	−0.989837	+	0.142204i	$0.954581\pi$
$240$	−10.2532	+	2.20549i	−0.661839	+	0.142364i
$241$	3.59654	−	9.88142i	0.231674	−	0.636518i	−0.768320	−	0.640066i	$-0.778907\pi$
$241$	3.59654	−	9.88142i	0.231674	−	0.636518i	0.999994	+	0.00354764i	$0.00112925\pi$
$242$	2.03204	−	0.772883i	0.130625	−	0.0496828i
$243$	−1.14537	−	15.5463i	−0.0734755	−	0.997297i
$244$	−7.43837	+	22.4238i	−0.476193	+	1.43554i
$245$	0.358585	+	10.5903i	0.0229091	+	0.676589i
$246$	−1.57242	+	4.24329i	−0.100254	+	0.270542i
$247$	−3.44706	+	4.10805i	−0.219331	+	0.261389i
$248$	15.8180	−	6.54319i	1.00445	−	0.415493i
$249$	8.35492	−	13.8189i	0.529471	−	0.875734i
$250$	−14.4086	−	8.04472i	−0.911281	−	0.508793i
$251$	−8.80967	−	15.2588i	−0.556061	−	0.963126i	−0.997820	−	0.0659925i	$-0.978979\pi$
$251$	−8.80967	−	15.2588i	−0.556061	−	0.963126i	0.441759	−	0.897134i	$-0.354355\pi$
$252$	−0.0840907	−	15.8743i	−0.00529722	−	0.999986i
$253$	2.76468	−	4.78857i	0.173814	−	0.301055i
$254$	2.07498	−	1.23813i	0.130196	−	0.0776870i
$255$	0.760450	+	4.88809i	0.0476212	+	0.306104i
$256$	15.8942	−	1.83724i	0.993385	−	0.114827i
$257$	−2.23066	−	6.12869i	−0.139145	−	0.382297i	0.850474	−	0.526018i	$-0.176315\pi$
$257$	−2.23066	−	6.12869i	−0.139145	−	0.382297i	−0.989618	+	0.143721i	$0.954093\pi$
$258$	−0.0417258	+	7.17784i	−0.00259774	+	0.446873i
$259$	−6.94594	−	1.10390i	−0.431600	−	0.0685932i
$260$	−7.37862	+	6.56221i	−0.457603	+	0.406971i
$261$	6.79144	−	31.1104i	0.420380	−	1.92569i
$262$	−5.28029	−	4.30279i	−0.326217	−	0.265827i
$263$	17.4649	+	20.8138i	1.07693	+	1.28344i	0.956822	+	0.290674i	$0.0938796\pi$
$263$	17.4649	+	20.8138i	1.07693	+	1.28344i	0.120108	+	0.992761i	$0.461676\pi$
$264$	12.8746	−	7.83260i	0.792377	−	0.482063i
$265$	−4.52085	−	12.4209i	−0.277713	−	0.763011i
$266$	3.80498	−	4.83419i	0.233298	−	0.296403i
$267$	−6.51041	−	19.0775i	−0.398430	−	1.16753i
$268$	12.4538	+	1.82826i	0.760735	+	0.111679i
$269$	22.2404	−	12.8405i	1.35602	−	0.782901i	0.366939	−	0.930245i	$-0.380406\pi$
$269$	22.2404	−	12.8405i	1.35602	−	0.782901i	0.989085	+	0.147344i	$0.0470726\pi$
$270$	7.53628	−	8.18199i	0.458643	−	0.497940i
$271$	3.67612	−	6.36723i	0.223309	−	0.386782i	−0.732502	−	0.680765i	$-0.761648\pi$
$271$	3.67612	−	6.36723i	0.223309	−	0.386782i	0.955811	+	0.293983i	$0.0949809\pi$
$272$	−0.434018	−	7.53448i	−0.0263162	−	0.456845i
$273$	−7.43079	−	12.9684i	−0.449732	−	0.784884i
$274$	−8.29357	−	2.88420i	−0.501033	−	0.174241i
$275$	8.20521	+	1.44680i	0.494793	+	0.0872453i
$276$	−2.07942	+	5.86922i	−0.125167	+	0.353286i
$277$	17.4535	−	14.6453i	1.04868	−	0.879949i	0.0557276	−	0.998446i	$-0.482252\pi$
$277$	17.4535	−	14.6453i	1.04868	−	0.879949i	0.992954	+	0.118497i	$0.0378077\pi$
$278$	0.700727	−	4.33803i	0.0420268	−	0.260178i
$279$	−9.70576	+	15.3444i	−0.581069	+	0.918644i
$280$	8.22489	−	7.78939i	0.491531	−	0.465505i
$281$	18.0713	+	6.57741i	1.07804	+	0.392375i	0.819179	−	0.573538i	$-0.194430\pi$
$281$	18.0713	+	6.57741i	1.07804	+	0.392375i	0.258864	+	0.965914i	$0.416652\pi$
$282$	−11.0353	−	0.0641496i	−0.657140	−	0.00382005i
$283$	0.783050	−	4.44090i	0.0465475	−	0.263984i	−0.952649	−	0.304073i	$-0.901653\pi$
$283$	0.783050	−	4.44090i	0.0465475	−	0.263984i	0.999196	+	0.0400894i	$0.0127643\pi$
$284$	−21.2162	−	11.4484i	−1.25895	−	0.679339i
$285$	4.25971	−	0.662691i	0.252323	−	0.0392544i
$286$	6.91699	−	12.3888i	0.409010	−	0.732565i
$287$	−0.930102	−	4.79853i	−0.0549022	−	0.283249i
$288$	−12.6499	+	11.3129i	−0.745400	+	0.666617i
$289$	13.4402			0.790600
$290$	19.5133	−	11.6435i	1.14586	−	0.683727i
$291$	0.422749	−	20.9272i	0.0247820	−	1.22677i
$292$	−3.95739	−	2.13543i	−0.231589	−	0.124967i
$293$	−1.76422	−	0.311080i	−0.103067	−	0.0181735i	0.121877	−	0.992545i	$-0.461109\pi$
$293$	−1.76422	−	0.311080i	−0.103067	−	0.0181735i	−0.224944	+	0.974372i	$0.572220\pi$
$294$	8.98607	+	14.6031i	0.524078	+	0.851670i
$295$	5.00585	+	5.96574i	0.291452	+	0.347339i
$296$	4.03677	+	6.34315i	0.234633	+	0.368688i
$297$	−6.36646	+	14.6616i	−0.369419	+	0.850750i
$298$	17.4411	−	6.63370i	1.01034	−	0.384280i
$299$	1.01804	+	5.77360i	0.0588749	+	0.333896i
$300$	−9.38221	+	0.0804270i	−0.541682	+	0.00464346i
$301$	−3.98961	−	6.64780i	−0.229957	−	0.383173i
$302$	−26.1547	+	5.00072i	−1.50503	+	0.287759i
$303$	−4.19140	−	2.53413i	−0.240790	−	0.145582i
$304$	−6.56590	+	0.378223i	−0.376580	+	0.0216926i
$305$	8.94082	−	15.4859i	0.511950	−	0.886723i
$306$	4.98415	+	6.26376i	0.284925	+	0.358075i
$307$	−8.84262	+	15.3159i	−0.504675	+	0.874123i	0.495310	+	0.868716i	$0.335054\pi$
$307$	−8.84262	+	15.3159i	−0.504675	+	0.874123i	−0.999985	+	0.00540654i	$0.998279\pi$
$308$	−7.48633	+	14.4537i	−0.426573	+	0.823578i
$309$	0.433337	+	2.78545i	0.0246517	+	0.158459i
$310$	−12.7258	+	2.43314i	−0.722775	+	0.138193i
$311$	3.67660	−	20.8510i	0.208481	−	1.18235i	−0.683387	−	0.730056i	$-0.739494\pi$
$311$	3.67660	−	20.8510i	0.208481	−	1.18235i	0.891868	−	0.452296i	$-0.149395\pi$
$312$	−5.11883	+	15.1363i	−0.289797	+	0.856924i
$313$	−18.9543	−	22.5888i	−1.07136	−	1.27680i	−0.959085	−	0.283119i	$-0.908631\pi$
$313$	−18.9543	−	22.5888i	−1.07136	−	1.27680i	−0.112275	−	0.993677i	$-0.535814\pi$
$314$	16.9994	−	20.8613i	0.959331	−	1.17727i
$315$	−2.36356	+	11.7804i	−0.133171	+	0.663749i
$316$	19.0208	−	3.92116i	1.07000	−	0.220583i
$317$	−14.3475	−	5.22206i	−0.805835	−	0.293300i	−0.0939326	−	0.995579i	$-0.529944\pi$
$317$	−14.3475	−	5.22206i	−0.805835	−	0.293300i	−0.711902	+	0.702279i	$0.752166\pi$
$318$	−16.3045	−	13.8434i	−0.914312	−	0.776300i
$319$	−20.9879	+	25.0124i	−1.17510	+	1.40043i
$320$	−12.0630	−	1.06699i	−0.674344	−	0.0596468i
$321$	−5.55802	−	1.09621i	−0.310219	−	0.0611846i
$322$	−1.37465	−	6.58362i	−0.0766064	−	0.366891i
$323$			3.10217i			0.172610i
$324$	4.04320	−	17.5400i	0.224622	−	0.974446i
$325$	−7.65049	+	4.41702i	−0.424373	+	0.245012i
$326$	−10.0033	−	5.58509i	−0.554030	−	0.309329i
$327$	23.0056	+	20.1096i	1.27221	+	1.11206i
$328$	−3.18296	+	4.14401i	−0.175749	+	0.228815i
$329$	10.2204	−	6.13365i	0.563468	−	0.338159i
$330$	−10.7408	+	3.83879i	−0.591264	+	0.211318i
$331$	8.18494	−	22.4879i	0.449885	−	1.23605i	−0.482919	−	0.875665i	$-0.660423\pi$
$331$	8.18494	−	22.4879i	0.449885	−	1.23605i	0.932804	−	0.360384i	$-0.117354\pi$
$332$	13.9333	−	12.3916i	0.764687	−	0.680077i
$333$	−7.37760	−	3.02796i	−0.404290	−	0.165931i
$334$	12.9850	−	4.93881i	0.710507	−	0.270240i
$335$	−8.95252	−	3.25845i	−0.489129	−	0.178028i
$336$	5.32584	−	17.5395i	0.290549	−	0.956860i
$337$	10.8834	+	9.13222i	0.592854	+	0.497464i	0.889140	−	0.457636i	$-0.151304\pi$
$337$	10.8834	+	9.13222i	0.592854	+	0.497464i	−0.296285	+	0.955099i	$0.595748\pi$
$338$	−0.627332	−	3.28106i	−0.0341224	−	0.178466i
$339$	7.68628	−	6.18937i	0.417461	−	0.336160i
$340$	−0.829677	+	5.65160i	−0.0449955	+	0.306501i
$341$	16.1230	−	9.30859i	0.873107	−	0.504089i
$342$	5.45853	−	4.34341i	0.295163	−	0.234865i
$343$	−16.4883	−	8.43424i	−0.890284	−	0.455406i
$344$	−2.49614	+	7.90359i	−0.134583	+	0.426133i
$345$	2.43839	−	4.03305i	0.131279	−	0.217132i
$346$	−19.7907	−	22.9082i	−1.06396	−	1.23155i
$347$	3.99776	+	10.9838i	0.214611	+	0.589640i	0.999552	−	0.0299313i	$-0.00952885\pi$
$347$	3.99776	+	10.9838i	0.214611	+	0.589640i	−0.784941	+	0.619571i	$0.787307\pi$
$348$	18.1110	−	31.9995i	0.970850	−	1.71535i
$349$	−10.5102	−	12.5256i	−0.562600	−	0.670481i	0.407494	−	0.913208i	$-0.366403\pi$
$349$	−10.5102	−	12.5256i	−0.562600	−	0.670481i	−0.970095	+	0.242727i	$0.921958\pi$
$350$	8.61366	−	5.33941i	0.460419	−	0.285404i
$351$	−4.82139	−	16.2474i	−0.257347	−	0.867222i
$352$	16.8755	−	4.24543i	0.899468	−	0.226282i
$353$	−2.05589	+	5.64851i	−0.109424	+	0.300640i	−0.982304	−	0.187296i	$-0.940028\pi$
$353$	−2.05589	+	5.64851i	−0.109424	+	0.300640i	0.872880	+	0.487936i	$0.162250\pi$
$354$	11.8164	+	4.37878i	0.628035	+	0.232729i
$355$	13.9780	+	11.7289i	0.741873	+	0.622505i
$356$	−0.669573	−	23.2666i	−0.0354873	−	1.23313i
$357$	−8.11499	−	2.98375i	−0.429491	−	0.157917i
$358$	−0.242695	−	16.8700i	−0.0128268	−	0.891610i
$359$			24.6853i			1.30284i	0.758718	+	0.651419i	$0.225826\pi$
$359$			24.6853i			1.30284i	−0.758718	+	0.651419i	$0.774174\pi$
$360$	11.1061	−	6.45303i	0.585343	−	0.340105i
$361$	−16.2966			−0.857717
$362$	−10.6333	+	6.34481i	−0.558874	+	0.333476i
$363$	−2.07387	+	1.66999i	−0.108850	+	0.0876515i
$364$	−3.77017	−	16.8418i	−0.197611	−	0.882752i
$365$	2.60726	+	2.18775i	0.136470	+	0.114512i
$366$	0.168201	−	28.9345i	0.00879199	−	1.51243i
$367$	−5.51393	−	31.2711i	−0.287825	−	1.63234i	−0.695016	−	0.718994i	$-0.744603\pi$
$367$	−5.51393	−	31.2711i	−0.287825	−	1.63234i	0.407191	−	0.913343i	$-0.366508\pi$
$368$	−4.29723	+	5.76451i	−0.224008	+	0.300496i
$369$	0.223828	−	5.53777i	0.0116520	−	0.288285i
$370$	−2.02309	−	5.31904i	−0.105175	−	0.276524i
$371$	22.8161	+	3.62611i	1.18455	+	0.188258i
$372$	−15.9441	+	13.6133i	−0.826663	+	0.705816i
$373$	−4.29481	+	24.3571i	−0.222377	+	1.26116i	0.645260	+	0.763963i	$0.276749\pi$
$373$	−4.29481	+	24.3571i	−0.222377	+	1.26116i	−0.867637	+	0.497199i	$0.834362\pi$
$374$	−1.54143	−	8.06193i	−0.0797052	−	0.416872i
$375$	19.8291	+	3.91090i	1.02397	+	0.201958i
$376$	−12.1510	−	3.83759i	−0.626642	−	0.197909i
$377$		−	34.6196i		−	1.78300i
$378$	6.11181	+	18.4566i	0.314357	+	0.949305i
$379$		−	23.7987i		−	1.22246i	−0.791454	−	0.611229i	$-0.790675\pi$
$379$		−	23.7987i		−	1.22246i	0.791454	−	0.611229i	$-0.209325\pi$
$380$	4.92507	+	0.723018i	0.252651	+	0.0370901i
$381$	−1.94763	+	2.22812i	−0.0997803	+	0.114150i
$382$	−24.9344	+	4.76741i	−1.27576	+	0.243922i
$383$	2.39190	−	13.5651i	0.122220	−	0.693145i	−0.860700	−	0.509113i	$-0.829974\pi$
$383$	2.39190	−	13.5651i	0.122220	−	0.693145i	0.982920	−	0.184033i	$-0.0589152\pi$
$384$	−17.8156	+	8.16119i	−0.909148	+	0.416474i
$385$	7.75839	−	9.57044i	0.395404	−	0.487755i
$386$	35.0452	−	13.3294i	1.78375	−	0.678446i
$387$	−2.67068	−	8.37569i	−0.135758	−	0.425760i
$388$	7.60971	−	22.9403i	0.386324	−	1.16462i
$389$	2.50784	+	14.2227i	0.127153	+	0.721119i	0.980006	+	0.198968i	$0.0637590\pi$
$389$	2.50784	+	14.2227i	0.127153	+	0.721119i	−0.852853	+	0.522151i	$0.825130\pi$
$390$	6.10768	−	10.4382i	0.309274	−	0.528559i
$391$	2.59797	+	2.17996i	0.131385	+	0.110245i
$392$	4.92779	+	19.1759i	0.248891	+	0.968531i
$393$	7.77993	+	3.01096i	0.392445	+	0.151883i
$394$	−12.7169	−	21.3123i	−0.640668	−	1.07370i
$395$	−14.6992			−0.739600
$396$	−12.0274	+	13.9999i	−0.604402	+	0.703523i
$397$			32.8542i			1.64891i	0.565930	+	0.824453i	$0.308517\pi$
$397$			32.8542i			1.64891i	−0.565930	+	0.824453i	$0.691483\pi$
$398$	2.21721	−	0.0318971i	0.111138	−	0.00159885i
$399$	−2.60017	+	7.07178i	−0.130172	+	0.354032i
$400$	−10.3769	−	3.11385i	−0.518846	−	0.155692i
$401$	−12.6996	−	10.6562i	−0.634187	−	0.532146i	0.268040	−	0.963408i	$-0.413624\pi$
$401$	−12.6996	−	10.6562i	−0.634187	−	0.532146i	−0.902227	+	0.431262i	$0.858068\pi$
$402$	−15.1973	+	2.58869i	−0.757971	+	0.129112i
$403$	−6.75128	+	18.5490i	−0.336305	+	0.923991i
$404$	−3.75850	−	4.22610i	−0.186992	−	0.210256i
$405$	−5.67766	+	12.3845i	−0.282125	+	0.615389i
$406$	1.24323	+	39.6958i	0.0617003	+	1.97007i
$407$	5.25622	+	6.26412i	0.260541	+	0.310501i
$408$	3.35988	+	8.61083i	0.166339	+	0.426300i
$409$	−4.40827	−	12.1116i	−0.217975	−	0.598881i	0.781719	−	0.623631i	$-0.214343\pi$
$409$	−4.40827	−	12.1116i	−0.217975	−	0.598881i	−0.999694	+	0.0247500i	$0.992121\pi$
$410$	2.99279	−	2.58552i	0.147804	−	0.127690i
$411$	10.7520	+	0.217201i	0.530358	+	0.0107137i
$412$	−0.472786	+	3.22053i	−0.0232925	+	0.158664i
$413$	−13.3626	+	2.59008i	−0.657531	+	0.127450i
$414$	0.198343	−	7.62354i	0.00974803	−	0.374676i
$415$	−12.2223	+	7.05656i	−0.599970	+	0.346393i
$416$	−10.8133	+	14.9495i	−0.530163	+	0.732958i
$417$	0.827313	+	5.31788i	0.0405137	+	0.260418i
$418$	−7.02554	+	1.34327i	−0.343630	+	0.0657015i
$419$	19.0332	+	15.9708i	0.929835	+	0.780224i	0.975788	−	0.218719i	$-0.0701879\pi$
$419$	19.0332	+	15.9708i	0.929835	+	0.780224i	−0.0459527	+	0.998944i	$0.514632\pi$
$420$	−6.62840	+	12.1881i	−0.323433	+	0.594718i
$421$	8.73263	+	3.17842i	0.425602	+	0.154907i	0.545936	−	0.837827i	$-0.316174\pi$
$421$	8.73263	+	3.17842i	0.425602	+	0.154907i	−0.120334	+	0.992734i	$0.538396\pi$
$422$	−4.86223	−	12.7836i	−0.236690	−	0.622298i
$423$	12.8768	−	4.10592i	0.626093	−	0.199637i
$424$	−13.2600	−	20.8361i	−0.643965	−	1.01189i
$425$	−1.74781	+	4.80208i	−0.0847814	+	0.232935i
$426$	29.0473	+	5.29610i	1.40734	+	0.256597i
$427$	16.0825	+	26.7979i	0.778287	+	1.29684i
$428$	−5.75684	−	3.10643i	−0.278267	−	0.150155i
$429$	−3.36267	+	17.0494i	−0.162351	+	0.823154i
$430$	3.05820	−	5.47744i	0.147479	−	0.264145i
$431$	7.08658	−	4.09144i	0.341349	−	0.197078i	−0.319520	−	0.947580i	$-0.603522\pi$
$431$	7.08658	−	4.09144i	0.341349	−	0.197078i	0.660868	+	0.750502i	$0.270188\pi$
$432$	10.4472	−	17.9682i	0.502643	−	0.864494i
$433$			5.44181i			0.261517i	0.991414	+	0.130758i	$0.0417412\pi$
$433$			5.44181i			0.261517i	−0.991414	+	0.130758i	$0.958259\pi$
$434$	7.07510	−	21.5113i	0.339616	−	1.03257i
$435$	−18.3157	+	20.9534i	−0.878171	+	1.00464i
$436$	18.5131	+	30.0356i	0.886615	+	1.43845i
$437$	1.89971	−	2.26399i	0.0908756	−	0.108301i
$438$	5.41809	+	0.987864i	0.258886	+	0.0472019i
$439$	−33.5083	−	12.1960i	−1.59926	−	0.582084i	−0.619986	−	0.784613i	$-0.712862\pi$
$439$	−33.5083	−	12.1960i	−1.59926	−	0.582084i	−0.979276	+	0.202530i	$0.935084\pi$
$440$	−13.1585	+	0.568215i	−0.627308	+	0.0270886i
$441$	−15.9982	−	13.6036i	−0.761818	−	0.647791i
$442$	6.74647	+	5.49754i	0.320897	+	0.261491i
$443$	−3.18699	−	3.79810i	−0.151418	−	0.180453i	0.685003	−	0.728540i	$-0.259801\pi$
$443$	−3.18699	−	3.79810i	−0.151418	−	0.180453i	−0.836422	+	0.548087i	$0.815356\pi$
$444$	−7.10461	−	5.85843i	−0.337170	−	0.278029i
$445$	−3.05923	+	17.3498i	−0.145021	+	0.822458i
$446$	−5.53129	−	28.9296i	−0.261914	−	1.36986i
$447$	−17.8002	+	14.3336i	−0.841920	+	0.677955i
$448$	11.8619	−	17.5298i	0.560424	−	0.828206i
$449$	−5.14391	+	8.90952i	−0.242756	+	0.420466i	−0.961498	−	0.274811i	$-0.911385\pi$
$449$	−5.14391	+	8.90952i	−0.242756	+	0.420466i	0.718742	+	0.695277i	$0.244718\pi$
$450$	10.8968	−	3.64806i	0.513680	−	0.171971i
$451$	−2.84149	+	4.92160i	−0.133801	+	0.231749i
$452$	10.5914	−	4.20379i	0.498178	−	0.197730i
$453$	28.5673	−	15.7328i	1.34221	−	0.739189i
$454$	−5.49402	−	28.7347i	−0.257847	−	1.34859i
$455$	0.221056	+	13.0609i	0.0103633	+	0.612306i
$456$	7.50387	−	2.92795i	0.351401	−	0.137114i
$457$	3.71246	+	21.0544i	0.173662	+	0.984884i	0.939677	+	0.342062i	$0.111125\pi$
$457$	3.71246	+	21.0544i	0.173662	+	0.984884i	−0.766016	+	0.642822i	$0.777764\pi$
$458$	−10.4305	−	27.4236i	−0.487386	−	1.28142i
$459$	−8.17792	−	5.40706i	−0.381712	−	0.252380i
$460$	4.06644	−	3.61650i	0.189599	−	0.168620i
$461$	−5.76147	−	6.86626i	−0.268339	−	0.319793i	0.615002	−	0.788526i	$-0.289155\pi$
$461$	−5.76147	−	6.86626i	−0.268339	−	0.319793i	−0.883340	+	0.468732i	$0.844711\pi$
$462$	3.24347	−	19.6701i	0.150900	−	0.915137i
$463$	25.8910	+	4.56529i	1.20326	+	0.212167i	0.739106	−	0.673589i	$-0.235248\pi$
$463$	25.8910	+	4.56529i	1.20326	+	0.212167i	0.464152	+	0.885756i	$0.346359\pi$
$464$	30.9010	−	29.1164i	1.43454	−	1.35169i
$465$	13.8996	−	7.65490i	0.644581	−	0.354987i
$466$	−11.0844	−	18.5763i	−0.513473	−	0.860533i
$467$	−35.8839			−1.66051			−0.830255	−	0.557384i	$-0.811805\pi$
$467$	−35.8839			−1.66051			−0.830255	+	0.557384i	$0.811805\pi$
$468$	0.227513	−	19.5682i	0.0105168	−	0.904539i
$469$	12.5727	−	10.9176i	0.580555	−	0.504129i
$470$	8.42105	+	4.70170i	0.388434	+	0.216873i
$471$	−11.8957	+	30.7368i	−0.548123	+	1.41628i
$472$	11.5399	+	8.86367i	0.531169	+	0.407984i
$473$	−1.56532	+	8.87738i	−0.0719735	+	0.408182i
$474$	−20.6676	+	11.7728i	−0.949295	+	0.540742i
$475$	4.18475	+	1.52313i	0.192010	+	0.0698858i
$476$	−7.93311	−	6.06136i	−0.363614	−	0.277822i
$477$	24.2340	+	9.94629i	1.10960	+	0.455409i
$478$	41.0131	+	6.62489i	1.87590	+	0.303016i
$479$	11.8776	−	9.96649i	0.542701	−	0.455381i	−0.329759	−	0.944065i	$-0.606968\pi$
$479$	11.8776	−	9.96649i	0.542701	−	0.455381i	0.872461	+	0.488685i	$0.162523\pi$
$480$	14.4538	−	3.32730i	0.659722	−	0.151870i
$481$	−8.53844	−	1.50556i	−0.389319	−	0.0686475i
$482$	−4.88474	+	14.0462i	−0.222494	+	0.639785i
$483$	4.09519	+	7.14703i	0.186338	+	0.325201i
$484$	−2.85772	+	1.13425i	−0.129896	+	0.0515566i
$485$	−9.14676	+	15.8427i	−0.415333	+	0.719378i
$486$	1.93589	+	21.9602i	0.0878136	+	0.996137i
$487$	−12.3044	+	7.10394i	−0.557565	+	0.321910i	−0.752167	−	0.658972i	$-0.770992\pi$
$487$	−12.3044	+	7.10394i	−0.557565	+	0.321910i	0.194603	+	0.980882i	$0.437658\pi$
$488$	10.0622	−	31.8601i	0.455494	−	1.44224i
$489$	13.7665	+	2.71517i	0.622541	+	0.122784i
$490$	−0.722501	−	14.9681i	−0.0326393	−	0.676190i
$491$	−4.09168	−	11.2418i	−0.184655	−	0.507336i	0.812479	−	0.582991i	$-0.198118\pi$
$491$	−4.09168	−	11.2418i	−0.184655	−	0.507336i	−0.997134	+	0.0756548i	$0.975895\pi$
$492$	2.13719	−	6.03228i	0.0963521	−	0.271956i
$493$	−12.8728	−	15.3412i	−0.579763	−	0.690935i
$494$	4.79081	−	5.87918i	0.215549	−	0.264517i
$495$	11.0553	−	8.54006i	0.496901	−	0.383847i
$496$	−22.2347	+	9.57430i	−0.998366	+	0.429899i
$497$	−29.7797	+	11.4132i	−1.33580	+	0.511954i
$498$	−11.5333	+	19.7108i	−0.516819	+	0.883260i
$499$	1.56224	+	4.29223i	0.0699357	+	0.192147i	0.969736	−	0.244155i	$-0.0785104\pi$
$499$	1.56224	+	4.29223i	0.0699357	+	0.192147i	−0.899801	+	0.436301i	$0.856288\pi$
$500$	20.5384	+	11.0827i	0.918506	+	0.495631i
$501$	−13.2523	+	10.6714i	−0.592069	+	0.476763i
$502$	12.7679	+	21.3977i	0.569858	+	0.955028i
$503$	19.0846	−	33.0555i	0.850940	−	1.47387i	−0.0294203	−	0.999567i	$-0.509366\pi$
$503$	19.0846	−	33.0555i	0.850940	−	1.47387i	0.880361	−	0.474305i	$-0.157301\pi$
$504$	0.441840	+	22.4456i	0.0196811	+	0.999806i
$505$	2.14033	+	3.70716i	0.0952433	+	0.164966i
$506$	−3.81203	+	6.82760i	−0.169465	+	0.303524i
$507$	1.97365	+	3.58372i	0.0876528	+	0.159159i
$508$	−2.90898	+	1.79301i	−0.129065	+	0.0795518i
$509$	24.6021	−	29.3196i	1.09047	−	1.29957i	0.139518	−	0.990220i	$-0.455445\pi$
$509$	24.6021	−	29.3196i	1.09047	−	1.29957i	0.950949	−	0.309348i	$-0.100111\pi$
$510$	−1.17477	−	6.89662i	−0.0520195	−	0.305388i
$511$	−5.55470	+	2.12887i	−0.245725	+	0.0941758i
$512$	−22.4380	+	2.92131i	−0.991631	+	0.129105i
$513$	−4.71196	+	7.12661i	−0.208038	+	0.314648i
$514$	3.27898	+	8.62100i	0.144630	+	0.380256i
$515$	0.842632	−	2.31511i	0.0371308	−	0.102016i
$516$	−0.0870155	−	10.1508i	−0.00383065	−	0.446864i
$517$	−13.6481	−	2.40653i	−0.600244	−	0.105839i
$518$	9.84449	+	1.41969i	0.432542	+	0.0623776i
$519$	31.7285	+	19.1831i	1.39272	+	0.842045i
$520$	10.3004	−	9.42951i	0.451701	−	0.413511i
$521$	−13.2945	−	7.67556i	−0.582441	−	0.336272i	0.179662	−	0.983728i	$-0.442500\pi$
$521$	−13.2945	−	7.67556i	−0.582441	−	0.336272i	−0.762103	+	0.647456i	$0.775833\pi$
$522$	−8.97068	+	44.1304i	−0.392636	+	1.93153i
$523$	−19.5944	−	33.9385i	−0.856803	−	1.48403i	−0.874962	−	0.484191i	$-0.839114\pi$
$523$	−19.5944	−	33.9385i	−0.856803	−	1.48403i	0.0181592	−	0.999835i	$-0.494219\pi$
$524$	7.55422	+	5.97701i	0.330007	+	0.261107i
$525$	−8.00935	+	9.48193i	−0.349557	+	0.413825i
$526$	−25.1199	−	29.0769i	−1.09528	−	1.26781i
$527$	3.90545	+	10.7301i	0.170124	+	0.467412i
$528$	−18.0462	+	11.3377i	−0.785360	+	0.493412i
$529$	3.43285	+	19.4687i	0.149255	+	0.846464i
$530$	6.64546	+	17.4721i	0.288660	+	0.758938i
$531$	−15.4212	−	0.623301i	−0.669223	−	0.0270490i
$532$	−5.28215	+	6.91328i	−0.229010	+	0.299729i
$533$	−1.04633	−	5.93401i	−0.0453214	−	0.257030i
$534$	9.59425	+	26.8445i	0.415184	+	1.16167i
$535$	3.79279	+	3.18253i	0.163977	+	0.137593i
$536$	−17.6477	−	2.33194i	−0.762262	−	0.100724i
$537$	6.67377	+	19.5562i	0.287994	+	0.843914i
$538$	−31.1883	+	18.6098i	−1.34462	+	0.802326i
$539$	8.04526	+	19.9736i	0.346534	+	0.860326i
$540$	−10.4904	+	11.7232i	−0.451433	+	0.504486i
$541$	−4.25478	+	7.36950i	−0.182927	+	0.316840i	−0.942876	−	0.333143i	$-0.891891\pi$
$541$	−4.25478	+	7.36950i	−0.182927	+	0.316840i	0.759949	+	0.649983i	$0.225224\pi$
$542$	−5.06876	+	9.07848i	−0.217722	+	0.389954i
$543$	9.98070	−	11.4180i	0.428313	−	0.489995i
$544$	0.767005	+	10.6454i	0.0328851	+	0.456419i
$545$	−9.13363	−	25.0944i	−0.391242	−	1.07493i
$546$	10.7715	+	18.1870i	0.460976	+	0.778333i
$547$	10.8801	−	1.91845i	0.465197	−	0.0820268i	0.0638634	−	0.997959i	$-0.479658\pi$
$547$	10.8801	−	1.91845i	0.465197	−	0.0820268i	0.401334	+	0.915932i	$0.368547\pi$
$548$	11.7863	+	3.90974i	0.503488	+	0.167016i
$549$	10.7658	+	33.7632i	0.459471	+	1.44098i
$550$	−11.6322	−	1.87895i	−0.495997	−	0.0801189i
$551$	−13.3691	+	11.2180i	−0.569541	+	0.477902i
$552$	2.82105	−	8.34178i	0.120072	−	0.355050i
$553$	12.4673	−	22.4635i	0.530162	−	0.955244i
$554$	−24.3826	+	21.0644i	−1.03592	+	0.894943i
$555$	4.37133	+	5.42855i	0.185553	+	0.230429i
$556$	−0.902627	+	6.14852i	−0.0382799	+	0.260756i
$557$	6.77296			0.286980			0.143490	−	0.989652i	$-0.454168\pi$
$557$	6.77296			0.286980			0.143490	+	0.989652i	$0.454168\pi$
$558$	13.4125	−	21.8954i	0.567794	−	0.926907i
$559$	−4.77885	−	8.27722i	−0.202124	−	0.350089i
$560$	−11.4721	+	11.1820i	−0.484784	+	0.472527i
$561$	4.84948	+	8.80560i	0.204745	+	0.371773i
$562$	−25.6878	−	8.93328i	−1.08358	−	0.376828i
$563$	20.8660	−	7.59460i	0.879397	−	0.320074i	0.137430	−	0.990511i	$-0.456116\pi$
$563$	20.8660	−	7.59460i	0.879397	−	0.320074i	0.741966	+	0.670437i	$0.233893\pi$
$564$	15.6059	−	0.133778i	0.657127	−	0.00563308i
$565$	−8.49377	+	1.49768i	−0.357336	+	0.0630079i
$566$	−1.01694	+	6.29566i	−0.0427454	+	0.264626i
$567$	−14.1105	−	19.1806i	−0.592583	−	0.805509i
$568$	30.2341	+	15.7572i	1.26859	+	0.661159i
$569$	−2.23459	−	12.6730i	−0.0936788	−	0.531279i	−0.995144	−	0.0984277i	$-0.968619\pi$
$569$	−2.23459	−	12.6730i	−0.0936788	−	0.531279i	0.901465	−	0.432851i	$-0.142492\pi$
$570$	−6.01003	+	1.02374i	−0.251733	+	0.0428799i
$571$	1.71735	+	4.71837i	0.0718687	+	0.197458i	0.970426	−	0.241398i	$-0.0776061\pi$
$571$	1.71735	+	4.71837i	0.0718687	+	0.197458i	−0.898557	+	0.438856i	$0.855384\pi$
$572$	−9.52907	+	17.6593i	−0.398430	+	0.738372i
$573$	27.2345	−	14.9987i	1.13774	−	0.626582i
$574$	1.41284	+	6.76653i	0.0589710	+	0.282429i
$575$	4.21627	−	2.43427i	0.175831	−	0.101516i
$576$	17.6576	−	16.2545i	0.735734	−	0.677270i
$577$		−	14.5222i		−	0.604568i	−0.953218	−	0.302284i	$-0.902251\pi$
$577$		−	14.5222i		−	0.604568i	0.953218	−	0.302284i	$-0.0977491\pi$
$578$	−19.0053	+	0.273414i	−0.790518	+	0.0113725i
$579$	−35.7666	+	28.8010i	−1.48641	+	1.19693i
$580$	−27.3563	+	16.8616i	−1.13591	+	0.700139i
$581$	−0.417427	−	24.6633i	−0.0173178	−	1.02321i
$582$	−0.172075	+	29.6010i	−0.00713274	+	1.22700i
$583$	−17.2657	−	20.5765i	−0.715073	−	0.852190i
$584$	5.63946	+	2.93914i	0.233362	+	0.121623i
$585$	−3.15904	+	14.4710i	−0.130610	+	0.598303i
$586$	2.50106	+	0.403999i	0.103318	+	0.0166890i
$587$	−1.50792	−	8.55185i	−0.0622386	−	0.352973i	−0.999984	−	0.00564940i	$-0.998202\pi$
$587$	−1.50792	−	8.55185i	−0.0622386	−	0.352973i	0.937745	−	0.347323i	$-0.112909\pi$
$588$	−13.0040	−	20.4670i	−0.536275	−	0.844043i
$589$	9.35073	−	3.40339i	0.385290	−	0.140234i
$590$	−7.19997	−	8.33412i	−0.296418	−	0.343110i
$591$	22.8851	+	20.0043i	0.941369	+	0.822867i
$592$	−5.83731	−	8.88752i	−0.239912	−	0.365275i
$593$	5.26258	+	3.03835i	0.216108	+	0.124770i	0.604147	−	0.796873i	$-0.293514\pi$
$593$	5.26258	+	3.03835i	0.216108	+	0.124770i	−0.388039	+	0.921643i	$0.626847\pi$
$594$	8.70434	−	20.8619i	0.357143	−	0.855976i
$595$	4.95449	+	5.70559i	0.203114	+	0.233906i
$596$	−24.5280	+	9.73530i	−1.00471	+	0.398773i
$597$	−2.57025	+	0.877124i	−0.105193	+	0.0358983i
$598$	−1.55703	−	8.14355i	−0.0636718	−	0.333015i
$599$	25.1782	−	30.0062i	1.02875	−	1.22602i	0.0549834	−	0.998487i	$-0.482489\pi$
$599$	25.1782	−	30.0062i	1.02875	−	1.22602i	0.973770	−	0.227534i	$-0.0730661\pi$
$600$	13.2654	−	0.304591i	0.541559	−	0.0124349i
$601$	6.69655	−	1.18078i	0.273158	−	0.0481652i	−0.0353910	−	0.999374i	$-0.511268\pi$
$601$	6.69655	−	1.18078i	0.273158	−	0.0481652i	0.308549	+	0.951208i	$0.400157\pi$
$602$	5.77681	+	9.31928i	0.235445	+	0.379826i
$603$	16.7192	−	8.77238i	0.680860	−	0.357239i
$604$	36.8827	−	7.60342i	1.50074	−	0.309379i
$605$	2.29175	−	0.404097i	0.0931728	−	0.0164289i
$606$	5.97847	+	3.49817i	0.242859	+	0.142103i
$607$	−25.4956	+	9.27962i	−1.03483	+	0.376648i	−0.802919	−	0.596088i	$-0.796721\pi$
$607$	−25.4956	+	9.27962i	−1.03483	+	0.376648i	−0.231914	+	0.972736i	$0.574499\pi$
$608$	9.27692	−	0.668403i	0.376229	−	0.0271073i
$609$	−16.4865	−	45.7619i	−0.668065	−	1.85437i
$610$	−12.3279	+	22.0801i	−0.499142	+	0.893995i
$611$	12.7254	−	7.34704i	0.514817	−	0.297229i
$612$	−7.17534	−	8.75599i	−0.290046	−	0.353940i
$613$	16.3180	−	28.2636i	0.659078	−	1.14156i	−0.321776	−	0.946816i	$-0.604280\pi$
$613$	16.3180	−	28.2636i	0.659078	−	1.14156i	0.980855	−	0.194741i	$-0.0623868\pi$
$614$	12.1925	−	21.8375i	0.492049	−	0.881292i
$615$	−2.50614	+	4.14510i	−0.101057	+	0.167147i
$616$	10.2921	−	20.5909i	0.414682	−	0.829629i
$617$	−5.33923	+	30.2803i	−0.214949	+	1.21904i	0.666045	+	0.745911i	$0.267986\pi$
$617$	−5.33923	+	30.2803i	−0.214949	+	1.21904i	−0.880994	+	0.473127i	$0.843125\pi$
$618$	−0.669432	−	3.93000i	−0.0269285	−	0.158088i
$619$	−42.1321	−	15.3348i	−1.69343	−	0.616360i	−0.698383	−	0.715724i	$-0.746097\pi$
$619$	−42.1321	−	15.3348i	−1.69343	−	0.616360i	−0.995051	+	0.0993647i	$0.968319\pi$
$620$	17.9456	−	3.69951i	0.720712	−	0.148576i
$621$	2.65712	+	8.95412i	0.106627	+	0.359316i
$622$	−4.77478	+	29.5595i	−0.191451	+	1.18523i
$623$	−23.9193	−	19.3905i	−0.958306	−	0.776862i
$624$	6.93046	−	21.5079i	0.277440	−	0.861004i
$625$	−3.15719	−	2.64919i	−0.126287	−	0.105968i
$626$	27.2622	+	31.5565i	1.08962	+	1.26125i
$627$	7.67361	−	4.22606i	0.306454	−	0.168772i
$628$	−23.6139	+	29.8451i	−0.942297	+	1.19095i
$629$	−4.34352	+	2.50773i	−0.173188	+	0.0999899i
$630$	3.10258	−	16.7063i	0.123610	−	0.665596i
$631$	−25.5089	−	14.7276i	−1.01549	−	0.586295i	−0.102698	−	0.994713i	$-0.532748\pi$
$631$	−25.5089	−	14.7276i	−1.01549	−	0.586295i	−0.912795	+	0.408417i	$0.866081\pi$
$632$	−26.8169	+	5.93173i	−1.06672	+	0.235951i
$633$	10.5059	+	13.0468i	0.417574	+	0.518564i
$634$	20.3945	+	7.09247i	0.809970	+	0.281678i
$635$	2.43042	−	0.884600i	0.0964482	−	0.0351043i
$636$	23.3373	+	19.2438i	0.925384	+	0.763068i
$637$	−20.1473	−	10.7399i	−0.798264	−	0.425530i
$638$	29.1695	−	35.7962i	1.15483	−	1.41718i
$639$	−35.8371	+	4.83611i	−1.41770	+	0.191313i
$640$	17.0796	+	1.26340i	0.675132	+	0.0499404i
$641$	10.2789	−	8.62503i	0.405992	−	0.340668i	−0.416812	−	0.908993i	$-0.636853\pi$
$641$	10.2789	−	8.62503i	0.405992	−	0.340668i	0.822804	+	0.568325i	$0.192408\pi$
$642$	7.88172	+	1.43705i	0.311067	+	0.0567158i
$643$	42.2788	−	15.3882i	1.66731	−	0.606853i	0.675828	−	0.737060i	$-0.263786\pi$
$643$	42.2788	−	15.3882i	1.66731	−	0.606853i	0.991487	+	0.130207i	$0.0415641\pi$
$644$	2.07778	+	9.28172i	0.0818761	+	0.365751i
$645$	−1.48673	+	7.53803i	−0.0585399	+	0.296810i
$646$	−0.0631075	−	4.38668i	−0.00248293	−	0.172592i
$647$	8.85875	+	15.3438i	0.348273	+	0.603227i	0.985943	−	0.167083i	$-0.0534348\pi$
$647$	8.85875	+	15.3438i	0.348273	+	0.603227i	−0.637670	+	0.770310i	$0.720101\pi$
$648$	−5.36055	+	24.8850i	−0.210582	+	0.977576i
$649$	13.7053	+	7.91278i	0.537981	+	0.310604i
$650$	10.7285	−	6.40159i	0.420805	−	0.251091i
$651$	−0.0908249	+	27.7341i	−0.00355971	+	1.08698i
$652$	14.2589	+	7.69420i	0.558422	+	0.301328i
$653$	−5.69659	+	32.3069i	−0.222925	+	1.26427i	0.643688	+	0.765288i	$0.277403\pi$
$653$	−5.69659	+	32.3069i	−0.222925	+	1.26427i	−0.866613	+	0.498981i	$0.833708\pi$
$654$	−32.9406	−	27.9683i	−1.28808	−	1.09365i
$655$	−4.68650	−	5.58516i	−0.183117	−	0.218230i
$656$	4.41661	−	5.92466i	0.172440	−	0.231319i
$657$	−6.68458	+	0.902062i	−0.260790	+	0.0351928i
$658$	−14.3275	+	8.88131i	−0.558545	+	0.346230i
$659$	−9.49768	+	26.0947i	−0.369977	+	1.01650i	0.605393	+	0.795927i	$0.293016\pi$
$659$	−9.49768	+	26.0947i	−0.369977	+	1.01650i	−0.975370	+	0.220577i	$0.929206\pi$
$660$	15.1102	−	5.64681i	0.588163	−	0.219802i
$661$	34.6053	+	6.10186i	1.34599	+	0.237335i	0.799770	−	0.600306i	$-0.204955\pi$
$661$	34.6053	+	6.10186i	1.34599	+	0.237335i	0.546221	+	0.837641i	$0.316066\pi$
$662$	−11.1166	+	31.9660i	−0.432058	+	1.24239i
$663$	−9.94018	−	3.84701i	−0.386044	−	0.149406i
$664$	−19.4505	+	17.8060i	−0.754825	+	0.691006i
$665$	4.97211	−	4.31757i	0.192810	−	0.167428i
$666$	10.4940	+	4.13166i	0.406635	+	0.160099i
$667$			19.0792i			0.738751i
$668$	−18.2612	+	7.24797i	−0.706546	+	0.280432i
$669$	17.4020	+	31.5982i	0.672799	+	1.22166i
$670$	12.7258	+	4.42555i	0.491639	+	0.170974i
$671$	6.30995	−	35.7855i	0.243593	−	1.38149i
$672$	−7.17429	+	24.9104i	−0.276754	+	0.960941i
$673$	−5.64162	+	4.73388i	−0.217468	+	0.182478i	−0.745013	−	0.667049i	$-0.767557\pi$
$673$	−5.64162	+	4.73388i	−0.217468	+	0.182478i	0.527545	+	0.849527i	$0.323113\pi$
$674$	−15.5756	−	12.6922i	−0.599949	−	0.488884i
$675$	−11.3092	+	8.37700i	−0.435293	+	0.322431i
$676$	0.953836	+	4.62687i	0.0366860	+	0.177957i
$677$	−34.9626	+	6.16486i	−1.34372	+	0.236935i	−0.798823	−	0.601566i	$-0.794544\pi$
$677$	−34.9626	+	6.16486i	−1.34372	+	0.236935i	−0.544900	+	0.838501i	$0.683432\pi$
$678$	−10.7430	+	8.90855i	−0.412583	+	0.342131i
$679$	−16.4529	−	27.4152i	−0.631406	−	1.05210i
$680$	1.05825	−	8.00863i	0.0405820	−	0.307117i
$681$	17.2847	+	31.3853i	0.662352	+	1.20269i
$682$	−22.6096	+	13.4910i	−0.865766	+	0.516596i
$683$	−4.65548	−	2.68784i	−0.178137	−	0.102847i	0.408280	−	0.912857i	$-0.366129\pi$
$683$	−4.65548	−	2.68784i	−0.178137	−	0.102847i	−0.586417	+	0.810009i	$0.699462\pi$
$684$	−7.63037	+	6.25292i	−0.291754	+	0.239086i
$685$	−8.13968	−	4.69944i	−0.311001	−	0.179557i
$686$	23.4871	+	11.5912i	0.896742	+	0.442553i
$687$	22.5375	+	27.9882i	0.859858	+	1.06782i
$688$	3.36893	−	11.2270i	0.128439	−	0.428025i
$689$	28.0472	+	4.94547i	1.06851	+	0.188407i
$690$	−3.36601	+	5.75261i	−0.128142	+	0.218998i
$691$	33.2630	−	27.9110i	1.26538	−	1.06178i	0.270296	−	0.962777i	$-0.412878\pi$
$691$	33.2630	−	27.9110i	1.26538	−	1.06178i	0.995087	−	0.0990054i	$-0.0315661\pi$
$692$	28.4514	+	31.9911i	1.08156	+	1.21612i
$693$	3.67430	+	24.1381i	0.139575	+	0.916932i
$694$	−5.87655	−	15.4505i	−0.223071	−	0.586491i
$695$	1.60872	−	4.41993i	0.0610224	−	0.167658i
$696$	−24.9592	+	45.6179i	−0.946075	+	1.72914i
$697$	−2.67015	−	2.24052i	−0.101139	−	0.0848657i
$698$	15.1170	+	17.4983i	0.572187	+	0.662319i
$699$	19.9473	+	17.4362i	0.754475	+	0.659499i
$700$	−12.0717	+	7.72552i	−0.456266	+	0.291997i
$701$	−30.0965			−1.13673			−0.568364	−	0.822777i	$-0.692423\pi$
$701$	−30.0965			−1.13673			−0.568364	+	0.822777i	$0.692423\pi$
$702$	7.14829	+	22.8768i	0.269795	+	0.863430i
$703$	2.18536	+	3.78515i	0.0824222	+	0.142759i
$704$	−23.7767	+	6.34662i	−0.896120	+	0.239197i
$705$	−11.5890	−	2.28571i	−0.436468	−	0.0860848i
$706$	2.79226	−	8.02920i	0.105088	−	0.302183i
$707$	−7.48063	+	0.126610i	−0.281338	+	0.00476165i
$708$	−16.7983	−	5.95150i	−0.631318	−	0.223671i
$709$	3.30447	+	1.20273i	0.124102	+	0.0451694i	0.403325	−	0.915057i	$-0.367855\pi$
$709$	3.30447	+	1.20273i	0.124102	+	0.0451694i	−0.279223	+	0.960226i	$0.590077\pi$
$710$	−20.0044	−	16.3011i	−0.750751	−	0.611769i
$711$	19.6111	−	21.5413i	0.735473	−	0.807863i
$712$	1.42013	+	32.8870i	0.0532218	+	1.23249i
$713$	3.72071	−	10.2226i	0.139342	−	0.382838i
$714$	11.5358	+	4.05414i	0.431718	+	0.151722i
$715$	9.76253	−	11.6345i	0.365098	−	0.435107i
$716$	0.686374	+	23.8504i	0.0256510	+	0.891333i
$717$	−50.2769	+	7.82168i	−1.87763	+	0.292106i
$718$	−0.502172	−	34.9066i	−0.0187409	−	1.30270i
$719$	−9.46490	−	16.3937i	−0.352981	−	0.611382i	0.633789	−	0.773506i	$-0.281499\pi$
$719$	−9.46490	−	16.3937i	−0.352981	−	0.611382i	−0.986770	+	0.162124i	$0.948165\pi$
$720$	−15.5735	+	9.35095i	−0.580390	+	0.348490i
$721$	2.82328	+	3.25129i	0.105145	+	0.121085i
$722$	23.0445	−	0.331522i	0.857628	−	0.0123380i
$723$	0.367856	−	18.2098i	0.0136807	−	0.677230i
$724$	14.9071	−	9.18831i	0.554019	−	0.341481i
$725$	−27.0153	+	9.83278i	−1.00332	+	0.365180i
$726$	2.89863	−	2.40366i	0.107578	−	0.0892082i
$727$	16.1604	−	13.5602i	0.599357	−	0.502920i	−0.291882	−	0.956454i	$-0.594281\pi$
$727$	16.1604	−	13.5602i	0.599357	−	0.502920i	0.891239	+	0.453534i	$0.149837\pi$
$728$	5.67389	+	23.7388i	0.210288	+	0.879818i
$729$	−10.5742	−	24.8432i	−0.391636	−	0.920120i
$730$	−3.73135	−	3.04059i	−0.138103	−	0.112537i
$731$	−5.19546	−	1.89099i	−0.192161	−	0.0699409i
$732$	0.350768	+	40.9188i	0.0129648	+	1.51240i
$733$	16.4501	−	19.6044i	0.607597	−	0.724105i	−0.371288	−	0.928518i	$-0.621084\pi$
$733$	16.4501	−	19.6044i	0.607597	−	0.724105i	0.978885	+	0.204412i	$0.0655283\pi$
$734$	8.43322	+	44.1072i	0.311276	+	1.62803i
$735$	6.51205	+	17.1593i	0.240200	+	0.632931i
$736$	5.95930	−	8.23882i	0.219663	−	0.303687i
$737$	−19.3601			−0.713140
$738$	−0.203853	+	7.83534i	−0.00750395	+	0.288423i
$739$			3.49532i			0.128577i	0.997931	+	0.0642887i	$0.0204778\pi$
$739$			3.49532i			0.128577i	−0.997931	+	0.0642887i	$0.979522\pi$
$740$	2.96899	+	7.48033i	0.109142	+	0.274982i
$741$	−3.35247	+	8.66233i	−0.123156	+	0.318218i
$742$	−32.3373	−	4.66342i	−1.18714	−	0.171199i
$743$	6.53363	−	7.78648i	0.239696	−	0.285658i	−0.632763	−	0.774345i	$-0.718079\pi$
$743$	6.53363	−	7.78648i	0.239696	−	0.285658i	0.872459	+	0.488687i	$0.162524\pi$
$744$	22.2691	−	19.5744i	0.816424	−	0.717634i
$745$	19.6702	−	3.46839i	0.720661	−	0.127072i
$746$	5.57766	−	34.5299i	0.204213	−	1.26423i
$747$	5.96530	−	27.3260i	0.218259	−	0.999807i
$748$	2.34368	+	11.3688i	0.0856936	+	0.415683i
$749$	−8.08045	+	3.09688i	−0.295253	+	0.113158i
$750$	−28.1193	−	5.12690i	−1.02677	−	0.187208i
$751$	8.72160	+	1.53785i	0.318256	+	0.0561171i	0.330494	−	0.943808i	$-0.392785\pi$
$751$	8.72160	+	1.53785i	0.318256	+	0.0561171i	−0.0122384	+	0.999925i	$0.503896\pi$
$752$	17.2604	+	5.17942i	0.629424	+	0.188874i
$753$	−22.9769	−	20.0845i	−0.837324	−	0.731919i
$754$	0.704266	+	48.9545i	0.0256479	+	1.78282i
$755$	−28.5029			−1.03733
$756$	−9.01797	−	25.9745i	−0.327980	−	0.944685i
$757$	8.71196			0.316641			0.158321	−	0.987388i	$-0.449392\pi$
$757$	8.71196			0.316641			0.158321	+	0.987388i	$0.449392\pi$
$758$	0.484137	+	33.6530i	0.0175846	+	1.22233i
$759$	1.85320	−	9.39612i	0.0672670	−	0.341058i
$760$	−6.97908	−	0.922206i	−0.253158	−	0.0334519i
$761$	−38.8647	−	6.85289i	−1.40884	−	0.248417i	−0.583071	−	0.812421i	$-0.698149\pi$
$761$	−38.8647	−	6.85289i	−1.40884	−	0.248417i	−0.825772	+	0.564004i	$0.809260\pi$
$762$	2.70876	−	3.19033i	0.0981280	−	0.115573i
$763$	46.0962	+	7.32596i	1.66879	+	0.265218i
$764$	35.1620	−	7.24869i	1.27212	−	0.262248i
$765$	3.98096	+	7.58730i	0.143932	+	0.274319i
$766$	−3.10635	+	19.2306i	−0.112237	+	0.694831i
$767$	−16.5246	+	2.91373i	−0.596669	+	0.105209i
$768$	25.0264	−	11.9029i	0.903063	−	0.429509i
$769$	−8.06555	+	9.61215i	−0.290851	+	0.346623i	−0.891607	−	0.452809i	$-0.850422\pi$
$769$	−8.06555	+	9.61215i	−0.290851	+	0.346623i	0.600756	+	0.799432i	$0.294866\pi$
$770$	−10.7762	+	13.6911i	−0.388347	+	0.493392i
$771$	−7.08497	−	8.79848i	−0.255159	−	0.316869i
$772$	−49.2850	+	19.5615i	−1.77381	+	0.704035i
$773$			12.1701i			0.437729i	0.975755	+	0.218865i	$0.0702353\pi$
$773$			12.1701i			0.437729i	−0.975755	+	0.218865i	$0.929765\pi$
$774$	3.94691	+	11.7895i	0.141869	+	0.423763i
$775$	16.3922			0.588825
$776$	−10.2940	+	32.5940i	−0.369532	+	1.17006i
$777$	−12.0035	+	2.07603i	−0.430623	+	0.0744773i
$778$	−3.83559	−	20.0608i	−0.137513	−	0.719215i
$779$	−1.95249	+	2.32689i	−0.0699553	+	0.0833695i
$780$	−8.42433	+	14.8846i	−0.301639	+	0.532953i
$781$	34.8437	+	12.6821i	1.24681	+	0.453800i
$782$	−3.71805	−	3.02975i	−0.132957	−	0.108344i
$783$	−6.27054	−	54.7962i	−0.224091	−	1.95826i
$784$	−7.35833	−	27.0158i	−0.262797	−	0.964851i
$785$	22.0658	−	18.5154i	0.787561	−	0.660842i
$786$	−11.0626	−	4.09944i	−0.394589	−	0.146222i
$787$	22.0752	−	8.03471i	0.786895	−	0.286406i	0.0828504	−	0.996562i	$-0.473598\pi$
$787$	22.0752	−	8.03471i	0.786895	−	0.286406i	0.704045	+	0.710156i	$0.251375\pi$
$788$	18.4161	+	29.8783i	0.656047	+	1.06437i
$789$	40.2722	+	24.3487i	1.43373	+	0.866836i
$790$	20.7857	−	0.299027i	0.739523	−	0.0106389i
$791$	4.91529	−	14.2505i	0.174768	−	0.506689i
$792$	16.7228	−	20.0415i	0.594219	−	0.712144i
$793$	19.2640	+	33.3662i	0.684085	+	1.18487i
$794$	−0.668353	−	46.4581i	−0.0237190	−	1.64874i
$795$	−14.3590	−	17.8318i	−0.509261	−	0.632427i
$796$	−3.13463	+	0.0902092i	−0.111104	+	0.00319738i
$797$	−1.85594	+	2.21182i	−0.0657408	+	0.0783468i	−0.797913	−	0.602773i	$-0.794062\pi$
$797$	−1.85594	+	2.21182i	−0.0657408	+	0.0783468i	0.732172	+	0.681120i	$0.238507\pi$
$798$	3.53296	−	10.0529i	0.125065	−	0.355867i
$799$	2.90723	−	7.98754i	0.102850	−	0.282579i
$800$	14.7370	+	4.19210i	0.521032	+	0.148213i
$801$	−21.3441	−	27.6305i	−0.754156	−	0.976276i
$802$	18.1748	+	14.8103i	0.641776	+	0.522968i
$803$	6.49928	+	2.36554i	0.229355	+	0.0834782i
$804$	21.4373	−	3.96974i	0.756035	−	0.140002i
$805$	−0.121827	−	7.19802i	−0.00429382	−	0.253697i
$806$	9.16943	−	26.3669i	0.322979	−	0.928733i
$807$	29.2741	−	33.4899i	1.03050	−	1.17890i
$808$	5.40074	+	5.89953i	0.189997	+	0.207545i
$809$	−8.11352	−	14.0530i	−0.285256	−	0.494078i	0.687415	−	0.726265i	$-0.258745\pi$
$809$	−8.11352	−	14.0530i	−0.285256	−	0.494078i	−0.972671	+	0.232187i	$0.925412\pi$
$810$	7.77665	−	17.6280i	0.273244	−	0.619383i
$811$	−3.21142			−0.112768			−0.0563842	−	0.998409i	$-0.517957\pi$
$811$	−3.21142			−0.112768			−0.0563842	+	0.998409i	$0.517957\pi$
$812$	−2.56554	−	56.1073i	−0.0900327	−	1.96898i
$813$	2.46415	−	12.4938i	0.0864217	−	0.438176i
$814$	−7.56009	−	8.75097i	−0.264981	−	0.306721i
$815$	−9.39424	−	7.88270i	−0.329066	−	0.276119i
$816$	−4.92627	−	12.1079i	−0.172454	−	0.423863i
$817$	−1.64790	+	4.52756i	−0.0576527	+	0.158399i
$818$	6.47998	+	17.0370i	0.226567	+	0.595684i
$819$	−19.4353	−	17.1014i	−0.679125	−	0.597570i
$820$	−4.17942	+	3.71698i	−0.145952	+	0.129803i
$821$	4.71406	−	3.95557i	0.164522	−	0.138050i	−0.556810	−	0.830640i	$-0.687975\pi$
$821$	4.71406	−	3.95557i	0.164522	−	0.138050i	0.721332	+	0.692590i	$0.243530\pi$
$822$	−15.2085	−	0.0884091i	−0.530457	−	0.00308362i
$823$	−46.8529	−	8.26144i	−1.63319	−	0.287976i	−0.719532	−	0.694459i	$-0.755644\pi$
$823$	−46.8529	−	8.26144i	−1.63319	−	0.287976i	−0.913658	+	0.406483i	$0.866755\pi$
$824$	0.603036	−	4.56366i	0.0210078	−	0.158983i
$825$	14.2596	−	2.21839i	0.496454	−	0.0772343i
$826$	18.8429	−	3.93439i	0.655630	−	0.136895i
$827$	3.52015	+	2.03236i	0.122408	+	0.0706720i	0.559954	−	0.828524i	$-0.310819\pi$
$827$	3.52015	+	2.03236i	0.122408	+	0.0706720i	−0.437546	+	0.899196i	$0.644152\pi$
$828$	−0.125385	+	10.7842i	−0.00435743	+	0.374778i
$829$	−35.0692	−	20.2472i	−1.21801	−	0.703216i	−0.253514	−	0.967332i	$-0.581587\pi$
$829$	−35.0692	−	20.2472i	−1.21801	−	0.703216i	−0.964491	+	0.264116i	$0.914920\pi$
$830$	17.1396	−	10.2271i	0.594926	−	0.354988i
$831$	20.4177	−	33.7705i	0.708283	−	1.17149i
$832$	14.9865	−	21.3595i	0.519565	−	0.740509i
$833$	−12.9215	+	2.73224i	−0.447703	+	0.0946665i
$834$	−1.27806	−	7.50301i	−0.0442555	−	0.259808i
$835$	14.6445	−	2.58223i	0.506795	−	0.0893617i
$836$	9.90725	−	2.04239i	0.342650	−	0.0706377i
$837$	−7.32627	+	30.5824i	−0.253233	+	1.05708i
$838$	−27.2392	−	22.1966i	−0.940962	−	0.766768i
$839$	9.66543	−	8.11026i	0.333688	−	0.279997i	−0.460513	−	0.887653i	$-0.652334\pi$
$839$	9.66543	−	8.11026i	0.333688	−	0.279997i	0.794201	+	0.607656i	$0.207890\pi$
$840$	9.12506	−	17.3696i	0.314844	−	0.599309i
$841$	14.5282	−	82.3936i	0.500973	−	2.84116i
$842$	−12.4132	−	4.31685i	−0.427787	−	0.148768i
$843$	33.3024	+	0.672741i	1.14699	+	0.0231704i
$844$	7.13558	+	17.9780i	0.245617	+	0.618829i
$845$		−	3.57564i		−	0.123006i
$846$	−18.1252	+	6.06800i	−0.623157	+	0.208622i
$847$	−1.32622	+	3.84500i	−0.0455694	+	0.132116i
$848$	19.1745	+	29.1938i	0.658454	+	1.00252i
$849$	−1.20066	−	7.71769i	−0.0412064	−	0.264870i
$850$	2.37384	−	6.82602i	0.0814220	−	0.234130i
$851$	4.70563	+	0.829729i	0.161307	+	0.0284427i
$852$	−41.1825	−	6.89814i	−1.41089	−	0.236326i
$853$	−9.49903	+	26.0984i	−0.325241	+	0.893591i	0.664057	+	0.747682i	$0.268833\pi$
$853$	−9.49903	+	26.0984i	−0.325241	+	0.893591i	−0.989298	+	0.145910i	$0.953389\pi$
$854$	−23.2869	−	37.5669i	−0.796861	−	1.28551i
$855$	6.61192	−	3.46920i	0.226123	−	0.118644i
$856$	8.20375	+	4.27558i	0.280398	+	0.146136i
$857$	15.7032	+	18.7143i	0.536410	+	0.639268i	0.964379	−	0.264525i	$-0.0852152\pi$
$857$	15.7032	+	18.7143i	0.536410	+	0.639268i	−0.427969	+	0.903793i	$0.640771\pi$
$858$	4.40820	−	24.1774i	0.150493	−	0.825404i
$859$	−3.08981	+	17.5232i	−0.105423	+	0.597883i	0.885628	+	0.464396i	$0.153729\pi$
$859$	−3.08981	+	17.5232i	−0.105423	+	0.597883i	−0.991051	+	0.133487i	$0.957383\pi$
$860$	−4.21307	+	7.80768i	−0.143665	+	0.266240i
$861$	−4.20896	−	7.34559i	−0.143441	−	0.250337i
$862$	−9.93767	+	5.92973i	−0.338478	+	0.201968i
$863$	4.38030	+	2.52897i	0.149107	+	0.0860871i	0.572697	−	0.819767i	$-0.305897\pi$
$863$	4.38030	+	2.52897i	0.149107	+	0.0860871i	−0.423590	+	0.905854i	$0.639230\pi$
$864$	−14.4076	+	25.6207i	−0.490155	+	0.871635i
$865$	−16.2021	−	28.0628i	−0.550886	−	0.954163i
$866$	−0.110703	−	7.69509i	−0.00376183	−	0.261490i
$867$	22.0315	−	7.51849i	0.748231	−	0.255341i
$868$	−9.56707	+	30.5623i	−0.324727	+	1.03735i
$869$	−28.0692	+	10.2163i	−0.952182	+	0.346566i
$870$	25.4734	−	30.0021i	0.863629	−	1.01717i
$871$	15.7247	−	13.1946i	0.532812	−	0.447082i
$872$	−26.7897	−	42.0958i	−0.907215	−	1.42554i
$873$	−11.0137	−	34.5409i	−0.372759	−	1.16903i
$874$	−2.64027	+	3.24008i	−0.0893083	+	0.109597i
$875$	28.8283	−	11.0486i	0.974573	−	0.373511i
$876$	−7.68163	−	1.28669i	−0.259538	−	0.0434731i
$877$	32.2508	−	11.7383i	1.08903	−	0.396376i	0.265771	−	0.964036i	$-0.414374\pi$
$877$	32.2508	−	11.7383i	1.08903	−	0.396376i	0.823263	+	0.567660i	$0.192151\pi$
$878$	47.6310	+	16.5643i	1.60747	+	0.559019i
$879$	−3.06598	+	0.476981i	−0.103413	+	0.0160882i
$880$	18.5955	−	1.07118i	0.626853	−	0.0361094i
$881$	−30.5804	−	17.6556i	−1.03028	−	0.594832i	−0.113215	−	0.993571i	$-0.536115\pi$
$881$	−30.5804	−	17.6556i	−1.03028	−	0.594832i	−0.917065	+	0.398738i	$0.869448\pi$
$882$	22.8992	+	18.9110i	0.771057	+	0.636766i
$883$	−22.7270	+	13.1215i	−0.764826	+	0.441572i	−0.831026	−	0.556234i	$-0.812246\pi$
$883$	−22.7270	+	13.1215i	−0.764826	+	0.441572i	0.0662000	+	0.997806i	$0.478912\pi$
$884$	−9.65179	−	7.63665i	−0.324625	−	0.256848i
$885$	11.5430	+	6.97892i	0.388013	+	0.234594i
$886$	4.58388	+	5.30594i	0.153998	+	0.178257i
$887$	−1.48749	−	1.24815i	−0.0499451	−	0.0419089i	0.617473	−	0.786592i	$-0.288156\pi$
$887$	−1.48749	−	1.24815i	−0.0499451	−	0.0419089i	−0.667419	+	0.744683i	$0.732601\pi$
$888$	10.1656	+	8.13969i	0.341134	+	0.273150i
$889$	−0.709526	+	4.46446i	−0.0237967	+	0.149733i
$890$	3.97301	−	24.5960i	0.133176	−	0.824459i
$891$	−2.23435	+	27.5951i	−0.0748535	+	0.924469i
$892$	8.41013	+	40.7959i	0.281592	+	1.36595i
$893$	−6.96071	−	2.53349i	−0.232931	−	0.0847800i
$894$	24.8791	−	20.6308i	0.832081	−	0.689996i
$895$	3.13599	−	17.7851i	0.104825	−	0.594491i
$896$	−16.4170	+	25.0296i	−0.548452	+	0.836182i
$897$	4.89858	+	8.89476i	0.163559	+	0.296987i
$898$	7.09259	−	12.7033i	0.236683	−	0.423915i
$899$	−32.1196	+	55.6328i	−1.07125	+	1.85546i
$900$	−15.3346	+	5.38028i	−0.511153	+	0.179343i
$901$	14.2677	−	8.23744i	0.475325	−	0.274429i
$902$	3.91794	−	7.01728i	0.130453	−	0.233650i
$903$	−10.2587	−	8.66547i	−0.341388	−	0.288369i
$904$	−14.8914	+	6.15990i	−0.495282	+	0.204875i
$905$	−12.4547	+	4.53315i	−0.414009	+	0.150687i
$906$	−40.0760	+	22.8283i	−1.33144	+	0.758420i
$907$	−15.0343	+	2.65095i	−0.499206	+	0.0880234i	−0.417581	−	0.908640i	$-0.637122\pi$
$907$	−15.0343	+	2.65095i	−0.499206	+	0.0880234i	−0.0816247	+	0.996663i	$0.526011\pi$
$908$	8.35346	+	40.5210i	0.277219	+	1.34474i
$909$	−8.28826	−	1.80934i	−0.274904	−	0.0600119i
$910$	−0.578287	−	18.4645i	−0.0191700	−	0.612093i
$911$	31.5401	−	5.56137i	1.04497	−	0.184256i	0.375291	−	0.926907i	$-0.377543\pi$
$911$	31.5401	−	5.56137i	1.04497	−	0.184256i	0.669679	+	0.742651i	$0.266432\pi$
$912$	−10.5514	+	4.29298i	−0.349392	+	0.142155i
$913$	−18.4348	+	21.9698i	−0.610104	+	0.727094i
$914$	−5.67798	−	29.6968i	−0.187811	−	0.982284i
$915$	5.99315	−	30.3865i	0.198127	−	1.00455i
$916$	15.3073	+	38.5667i	0.505769	+	1.27428i
$917$	12.5102	−	2.42485i	0.413122	−	0.0800756i
$918$	11.6741	+	7.47959i	0.385303	+	0.246863i
$919$	31.9233	+	18.4309i	1.05305	+	0.607981i	0.923503	−	0.383592i	$-0.125313\pi$
$919$	31.9233	+	18.4309i	1.05305	+	0.607981i	0.129551	+	0.991573i	$0.458646\pi$
$920$	−5.67665	+	5.19670i	−0.187154	+	0.171330i
$921$	−5.92732	+	30.0528i	−0.195312	+	0.990273i
$922$	8.28679	+	9.59214i	0.272911	+	0.315900i
$923$	−36.9441	+	13.4465i	−1.21603	+	0.442599i
$924$	−4.18633	+	27.8809i	−0.137720	+	0.917213i
$925$	1.25026	+	7.09056i	0.0411082	+	0.233136i
$926$	−36.7045	−	5.92892i	−1.20619	−	0.194836i
$927$	2.26853	+	4.32357i	0.0745082	+	0.142005i
$928$	−43.1037	+	41.8011i	−1.41495	+	1.37219i
$929$	−32.5683	−	38.8134i	−1.06853	−	1.27343i	−0.960201	−	0.279311i	$-0.909894\pi$
$929$	−32.5683	−	38.8134i	−1.06853	−	1.27343i	−0.108331	−	0.994115i	$-0.534551\pi$
$930$	−19.4993	+	11.1073i	−0.639408	+	0.364223i
$931$	2.38100	+	11.2604i	0.0780341	+	0.369044i
$932$	16.0519	+	26.0427i	0.525799	+	0.853058i
$933$	−5.63734	−	36.2363i	−0.184558	−	1.18632i
$934$	50.7423	−	0.729986i	1.66034	−	0.0238859i
$935$		−	8.78576i		−	0.287325i
$936$	0.0763564	+	27.6753i	0.00249579	+	0.904597i
$937$	35.3825	−	20.4281i	1.15590	−	0.667358i	0.205580	−	0.978640i	$-0.434092\pi$
$937$	35.3825	−	20.4281i	1.15590	−	0.667358i	0.950317	+	0.311283i	$0.100759\pi$
$938$	−17.5566	+	15.6940i	−0.573243	+	0.512428i
$939$	−43.7067	−	26.4252i	−1.42631	−	0.862353i
$940$	−12.0036	−	6.47720i	−0.391513	−	0.211263i
$941$	7.00116	+	19.2355i	0.228231	+	0.627060i	0.999960	−	0.00889121i	$-0.00283020\pi$
$941$	7.00116	+	19.2355i	0.228231	+	0.627060i	−0.771729	+	0.635951i	$0.780608\pi$
$942$	16.1960	−	43.7059i	0.527694	−	1.42402i
$943$	0.576642	+	3.27030i	0.0187780	+	0.106496i
$944$	−16.4986	−	12.2991i	−0.536983	−	0.400301i
$945$	2.71558	+	20.6329i	0.0883377	+	0.671189i
$946$	2.03288	−	12.5850i	0.0660945	−	0.409175i
$947$	−36.5598	+	6.44649i	−1.18803	+	0.209483i	−0.732520	−	0.680746i	$-0.761656\pi$
$947$	−36.5598	+	6.44649i	−1.18803	+	0.209483i	−0.455515	+	0.890228i	$0.650545\pi$
$948$	28.9859	−	17.0680i	0.941418	−	0.554342i
$949$	−6.89105	+	2.50814i	−0.223693	+	0.0814176i
$950$	−5.94851	−	2.06867i	−0.192995	−	0.0671166i
$951$	−26.4400	−	0.534115i	−0.857376	−	0.0173198i
$952$	11.3413	+	8.40979i	0.367572	+	0.272563i
$953$	15.6463	+	27.1002i	0.506833	+	0.877860i	0.999969	+	0.00790808i	$0.00251725\pi$
$953$	15.6463	+	27.1002i	0.506833	+	0.877860i	−0.493136	+	0.869952i	$0.664149\pi$
$954$	−34.4709	−	13.5717i	−1.11604	−	0.439401i
$955$	−27.1731			−0.879302
$956$	−58.1301	−	8.53372i	−1.88006	−	0.276000i
$957$	−20.4119	+	52.7417i	−0.659824	+	1.70490i
$958$	−16.5930	+	14.3349i	−0.536095	+	0.463140i
$959$	14.0854	−	8.45323i	0.454843	−	0.272969i
$960$	−20.3709	+	4.99905i	−0.657469	+	0.161344i
$961$	4.31127	−	3.61758i	0.139073	−	0.116696i
$962$	12.1046	+	1.95526i	0.390266	+	0.0630402i
$963$	−9.72409	+	1.31223i	−0.313354	+	0.0422862i
$964$	6.62160	−	19.9616i	0.213268	−	0.642919i
$965$	39.5241	−	6.96917i	1.27233	−	0.224346i
$966$	−5.93627	−	10.0231i	−0.190996	−	0.322487i
$967$	5.31254	+	14.5961i	0.170840	+	0.469378i	0.995334	−	0.0964923i	$-0.0307623\pi$
$967$	5.31254	+	14.5961i	0.170840	+	0.469378i	−0.824494	+	0.565871i	$0.808540\pi$
$968$	4.01793	−	1.66203i	0.129141	−	0.0534198i
$969$	1.73537	+	5.08517i	0.0557480	+	0.163359i
$970$	12.6118	−	22.5887i	0.404942	−	0.725278i
$971$	−20.2453	+	35.0659i	−0.649703	+	1.12532i	0.333491	+	0.942753i	$0.391773\pi$
$971$	−20.2453	+	35.0659i	−0.649703	+	1.12532i	−0.983194	+	0.182565i	$0.941560\pi$
$972$	−3.18421	−	31.0139i	−0.102134	−	0.994771i
$973$	5.39012	+	6.20726i	0.172799	+	0.198996i
$974$	17.2547	−	10.2958i	0.552876	−	0.329897i
$975$	−10.0700	+	11.5202i	−0.322498	+	0.368942i
$976$	−13.5805	+	45.2570i	−0.434701	+	1.44864i
$977$	7.49186	+	6.28642i	0.239686	+	0.201120i	0.754716	−	0.656052i	$-0.227775\pi$
$977$	7.49186	+	6.28642i	0.239686	+	0.201120i	−0.515030	+	0.857172i	$0.672219\pi$
$978$	−19.5219	−	3.55938i	−0.624243	−	0.113816i
$979$	6.21672	+	35.2568i	0.198687	+	1.12681i
$980$	1.32616	+	21.1512i	0.0423627	+	0.675650i
$981$	48.9608	+	20.0948i	1.56320	+	0.641578i
$982$	6.01461	+	15.8134i	0.191934	+	0.504627i
$983$	7.75026	+	43.9539i	0.247195	+	1.40191i	0.815340	+	0.578983i	$0.196550\pi$
$983$	7.75026	+	43.9539i	0.247195	+	1.40191i	−0.568145	+	0.822928i	$0.692339\pi$
$984$	−2.89942	+	8.57353i	−0.0924301	+	0.273314i
$985$	−9.08579	−	24.9630i	−0.289497	−	0.795387i
$986$	18.5151	+	21.4317i	0.589642	+	0.682524i
$987$	13.3223	−	15.7718i	0.424055	−	0.502021i
$988$	−6.65492	+	8.41102i	−0.211721	+	0.267590i
$989$	2.63368	+	4.56166i	0.0837461	+	0.145052i
$990$	−15.4593	+	12.3011i	−0.491328	+	0.390955i
$991$	−42.6128	−	24.6025i	−1.35364	−	0.781524i	−0.364882	−	0.931054i	$-0.618891\pi$
$991$	−42.6128	−	24.6025i	−1.35364	−	0.781524i	−0.988757	+	0.149530i	$0.952224\pi$
$992$	31.2465	−	13.9910i	0.992078	−	0.444216i
$993$	0.837160	−	41.4415i	0.0265665	−	1.31511i
$994$	41.8783	−	16.7449i	1.32830	−	0.531116i
$995$	2.33747	+	0.412159i	0.0741028	+	0.0130663i
$996$	15.9079	−	28.1069i	0.504061	−	0.890603i
$997$	3.00227	−	8.24866i	0.0950828	−	0.261238i	−0.883029	−	0.469319i	$-0.844500\pi$
$997$	3.00227	−	8.24866i	0.0950828	−	0.261238i	0.978112	+	0.208081i	$0.0667218\pi$
$998$	−2.29644	−	6.03772i	−0.0726924	−	0.191121i
$999$	−13.7874	−	0.836468i	−0.436214	−	0.0264647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.103.2	✓	840
4.3	odd	2	inner	756.2.bt.a.103.124	yes	840
7.3	odd	6		756.2.cd.a.535.96	yes	840
27.16	even	9		756.2.cd.a.691.63	yes	840
28.3	even	6		756.2.cd.a.535.63	yes	840
108.43	odd	18		756.2.cd.a.691.96	yes	840
189.178	odd	18	inner	756.2.bt.a.367.124	yes	840
756.367	even	18	inner	756.2.bt.a.367.2	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.2	✓	840	1.1	even	1	trivial
756.2.bt.a.103.124	yes	840	4.3	odd	2	inner
756.2.bt.a.367.2	yes	840	756.367	even	18	inner
756.2.bt.a.367.124	yes	840	189.178	odd	18	inner
756.2.cd.a.535.63	yes	840	28.3	even	6
756.2.cd.a.535.96	yes	840	7.3	odd	6
756.2.cd.a.691.63	yes	840	27.16	even	9
756.2.cd.a.691.96	yes	840	108.43	odd	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41407 + 0.0203430i) q^{2} +(1.63923 - 0.559403i) q^{3} +(1.99917 - 0.0575327i) q^{4} +(-1.49077 - 0.262863i) q^{5} +(-2.30660 + 0.824380i) q^{6} +(1.66611 - 2.05525i) q^{7} +(-2.82579 + 0.122024i) q^{8} +(2.37414 - 1.83398i) q^{9} +O(q^{10})\)	\(q+(-1.41407 + 0.0203430i) q^{2} +(1.63923 - 0.559403i) q^{3} +(1.99917 - 0.0575327i) q^{4} +(-1.49077 - 0.262863i) q^{5} +(-2.30660 + 0.824380i) q^{6} +(1.66611 - 2.05525i) q^{7} +(-2.82579 + 0.122024i) q^{8} +(2.37414 - 1.83398i) q^{9} +(2.11340 + 0.341379i) q^{10} +(-3.02942 + 0.534168i) q^{11} +(3.24492 - 1.21265i) q^{12} +(2.09650 - 2.49852i) q^{13} +(-2.31419 + 2.94016i) q^{14} +(-2.59076 + 0.403049i) q^{15} +(3.99338 - 0.230036i) q^{16} -1.88674i q^{17} +(-3.31988 + 2.64167i) q^{18} -1.64419 q^{19} +(-2.99543 - 0.439740i) q^{20} +(1.58143 - 4.30106i) q^{21} +(4.27293 - 0.816977i) q^{22} +(-1.15541 + 1.37696i) q^{23} +(-4.56386 + 1.78078i) q^{24} +(-2.54517 - 0.926365i) q^{25} +(-2.91377 + 3.57572i) q^{26} +(2.86582 - 4.33441i) q^{27} +(3.21261 - 4.20466i) q^{28} +(8.13107 - 6.82278i) q^{29} +(3.65530 - 0.622642i) q^{30} +(-5.68712 + 2.06994i) q^{31} +(-5.64223 + 0.406523i) q^{32} +(-4.66709 + 2.57029i) q^{33} +(0.0383820 + 2.66798i) q^{34} +(-3.02404 + 2.62595i) q^{35} +(4.64079 - 3.80303i) q^{36} +(-1.32913 - 2.30213i) q^{37} +(2.32500 - 0.0334478i) q^{38} +(2.03897 - 5.26843i) q^{39} +(4.24468 + 0.560886i) q^{40} +(1.18751 - 1.41521i) q^{41} +(-2.14875 + 6.11415i) q^{42} +(1.00225 - 2.75367i) q^{43} +(-6.02560 + 1.24218i) q^{44} +(-4.02137 + 2.10997i) q^{45} +(1.60581 - 1.97062i) q^{46} +(4.23350 + 1.54087i) q^{47} +(6.41738 - 2.61099i) q^{48} +(-1.44812 - 6.84857i) q^{49} +(3.61788 + 1.25817i) q^{50} +(-1.05545 - 3.09280i) q^{51} +(4.04753 - 5.11558i) q^{52} +(4.36596 + 7.56206i) q^{53} +(-3.96428 + 6.18744i) q^{54} +4.65657 q^{55} +(-4.45731 + 6.01103i) q^{56} +(-2.69521 + 0.919768i) q^{57} +(-11.3591 + 9.81328i) q^{58} +(-3.94099 - 3.30688i) q^{59} +(-5.15618 + 0.954817i) q^{60} +(-4.04017 + 11.1003i) q^{61} +(7.99986 - 3.04273i) q^{62} +(0.186295 - 7.93507i) q^{63} +(7.97022 - 0.689631i) q^{64} +(-3.78217 + 3.17362i) q^{65} +(6.54729 - 3.72950i) q^{66} +(6.19801 + 1.09288i) q^{67} +(-0.108549 - 3.77193i) q^{68} +(-1.12370 + 2.90349i) q^{69} +(4.22278 - 3.77478i) q^{70} +(-10.4391 - 6.02700i) q^{71} +(-6.48503 + 5.47215i) q^{72} +(-1.94716 - 1.12419i) q^{73} +(1.92632 + 3.22832i) q^{74} +(-4.69032 - 0.0947491i) q^{75} +(-3.28703 + 0.0945950i) q^{76} +(-3.94951 + 7.11620i) q^{77} +(-2.77607 + 7.49139i) q^{78} +(9.56286 - 1.68619i) q^{79} +(-6.01367 - 0.706781i) q^{80} +(2.27305 - 8.70823i) q^{81} +(-1.65042 + 2.02537i) q^{82} +(7.14197 - 5.99283i) q^{83} +(2.91409 - 8.68954i) q^{84} +(-0.495955 + 2.81270i) q^{85} +(-1.36123 + 3.91426i) q^{86} +(9.51200 - 15.7326i) q^{87} +(8.49533 - 1.87911i) q^{88} -11.6381i q^{89} +(5.64357 - 3.06544i) q^{90} +(-1.64207 - 8.47166i) q^{91} +(-2.23064 + 2.81925i) q^{92} +(-8.16455 + 6.57450i) q^{93} +(-6.01781 - 2.09277i) q^{94} +(2.45111 + 0.432198i) q^{95} +(-9.02149 + 3.82266i) q^{96} +(4.13324 - 11.3560i) q^{97} +(2.18707 + 9.65488i) q^{98} +(-6.21260 + 6.82407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

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