LMFDB - Embedded newform 76.2.k.a.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.2
Character	$\chi$	$=$	76.51
Dual form			76.2.k.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32415 + 0.496616i) q^{2} +(-1.09089 - 0.397053i) q^{3} +(1.50675 - 1.31519i) q^{4} +(0.615920 + 3.49306i) q^{5} +(1.64169 - 0.0159973i) q^{6} +(3.53555 + 2.04125i) q^{7} +(-1.34202 + 2.48978i) q^{8} +(-1.26573 - 1.06208i) q^{9} +O(q^{10})$	\(q+(-1.32415 + 0.496616i) q^{2} +(-1.09089 - 0.397053i) q^{3} +(1.50675 - 1.31519i) q^{4} +(0.615920 + 3.49306i) q^{5} +(1.64169 - 0.0159973i) q^{6} +(3.53555 + 2.04125i) q^{7} +(-1.34202 + 2.48978i) q^{8} +(-1.26573 - 1.06208i) q^{9} +(-2.55028 - 4.31946i) q^{10} +(-0.260098 + 0.150167i) q^{11} +(-2.16590 + 0.836472i) q^{12} +(0.546397 + 1.50121i) q^{13} +(-5.69532 - 0.947113i) q^{14} +(0.715025 - 4.05511i) q^{15} +(0.540567 - 3.96331i) q^{16} +(3.58623 - 3.00920i) q^{17} +(2.20347 + 0.777766i) q^{18} +(-3.34958 - 2.78932i) q^{19} +(5.52206 + 4.45310i) q^{20} +(-3.04643 - 3.63059i) q^{21} +(0.269833 - 0.328013i) q^{22} +(-3.07108 - 0.541514i) q^{23} +(2.45257 - 2.18323i) q^{24} +(-7.12363 + 2.59279i) q^{25} +(-1.46904 - 1.71648i) q^{26} +(2.70044 + 4.67730i) q^{27} +(8.01181 - 1.57426i) q^{28} +(0.344669 - 0.410760i) q^{29} +(1.06703 + 5.72467i) q^{30} +(2.08054 - 3.60361i) q^{31} +(1.25245 + 5.51646i) q^{32} +(0.343363 - 0.0605442i) q^{33} +(-3.25429 + 5.76561i) q^{34} +(-4.95259 + 13.6071i) q^{35} +(-3.30397 + 0.0643968i) q^{36} -2.42729i q^{37} +(5.82057 + 2.03002i) q^{38} -1.85461i q^{39} +(-9.52351 - 3.15423i) q^{40} +(2.70395 - 7.42905i) q^{41} +(5.83694 + 3.29454i) q^{42} +(2.23149 - 0.393472i) q^{43} +(-0.194403 + 0.568341i) q^{44} +(2.93031 - 5.07544i) q^{45} +(4.33550 - 0.808100i) q^{46} +(2.11323 - 2.51844i) q^{47} +(-2.16334 + 4.10891i) q^{48} +(4.83342 + 8.37173i) q^{49} +(8.14514 - 6.97095i) q^{50} +(-5.10701 + 1.85880i) q^{51} +(2.79766 + 1.54333i) q^{52} +(-5.12508 - 0.903690i) q^{53} +(-5.89861 - 4.85236i) q^{54} +(-0.684743 - 0.816045i) q^{55} +(-9.82703 + 6.06335i) q^{56} +(2.54653 + 4.37281i) q^{57} +(-0.252403 + 0.715076i) q^{58} +(4.17166 - 3.50044i) q^{59} +(-4.25587 - 7.05041i) q^{60} +(-0.594383 + 3.37091i) q^{61} +(-0.965344 + 5.80494i) q^{62} +(-2.30710 - 6.33871i) q^{63} +(-4.39799 - 6.68264i) q^{64} +(-4.90729 + 2.83323i) q^{65} +(-0.424597 + 0.250689i) q^{66} +(5.29646 + 4.44426i) q^{67} +(1.44587 - 9.25066i) q^{68} +(3.13521 + 1.81012i) q^{69} +(-0.199541 - 20.4774i) q^{70} +(-0.743257 - 4.21522i) q^{71} +(4.34297 - 1.72607i) q^{72} +(-8.50411 - 3.09524i) q^{73} +(1.20543 + 3.21410i) q^{74} +8.80060 q^{75} +(-8.71544 + 0.202533i) q^{76} -1.22612 q^{77} +(0.921031 + 2.45579i) q^{78} +(0.187126 + 0.0681083i) q^{79} +(14.1770 - 0.552850i) q^{80} +(-0.228002 - 1.29306i) q^{81} +(0.108943 + 11.1800i) q^{82} +(-12.9034 - 7.44977i) q^{83} +(-9.36510 - 1.46376i) q^{84} +(12.7201 + 10.6735i) q^{85} +(-2.75942 + 1.62921i) q^{86} +(-0.539091 + 0.311244i) q^{87} +(-0.0248287 - 0.849113i) q^{88} +(2.26220 + 6.21534i) q^{89} +(-1.35962 + 8.17588i) q^{90} +(-1.13254 + 6.42296i) q^{91} +(-5.33953 + 3.22312i) q^{92} +(-3.70047 + 3.10507i) q^{93} +(-1.54753 + 4.38426i) q^{94} +(7.68017 - 13.4183i) q^{95} +(0.824040 - 6.51517i) q^{96} +(3.90012 + 4.64798i) q^{97} +(-10.5577 - 8.68508i) q^{98} +(0.488704 + 0.0861717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−1.32415	+	0.496616i	−0.936315	+	0.351160i
$2$	−1.32415	+	0.496616i	−0.936315	+	0.351160i
$3$	−1.09089	−	0.397053i	−0.629828	−	0.229239i	0.00732842	−	0.999973i	$-0.497667\pi$
$3$	−1.09089	−	0.397053i	−0.629828	−	0.229239i	−0.637156	+	0.770734i	$0.719889\pi$
$4$	1.50675	−	1.31519i	0.753373	−	0.657593i
$5$	0.615920	+	3.49306i	0.275448	+	1.56214i	0.737535	+	0.675309i	$0.235990\pi$
$5$	0.615920	+	3.49306i	0.275448	+	1.56214i	−0.462087	+	0.886834i	$0.652899\pi$
$6$	1.64169	−	0.0159973i	0.670217	−	0.00653089i
$7$	3.53555	+	2.04125i	1.33631	+	0.771521i	0.986259	−	0.165208i	$-0.0528297\pi$
$7$	3.53555	+	2.04125i	1.33631	+	0.771521i	0.350055	+	0.936729i	$0.386163\pi$
$8$	−1.34202	+	2.48978i	−0.474474	+	0.880270i
$9$	−1.26573	−	1.06208i	−0.421911	−	0.354026i
$10$	−2.55028	−	4.31946i	−0.806469	−	1.36593i
$11$	−0.260098	+	0.150167i	−0.0784224	+	0.0452772i	−0.538698	−	0.842499i	$-0.681084\pi$
$11$	−0.260098	+	0.150167i	−0.0784224	+	0.0452772i	0.460276	+	0.887776i	$0.347750\pi$
$12$	−2.16590	+	0.836472i	−0.625241	+	0.241469i
$13$	0.546397	+	1.50121i	0.151543	+	0.416362i	0.992114	−	0.125340i	$-0.0400023\pi$
$13$	0.546397	+	1.50121i	0.151543	+	0.416362i	−0.840570	+	0.541702i	$0.817780\pi$
$14$	−5.69532	−	0.947113i	−1.52214	−	0.253127i
$15$	0.715025	−	4.05511i	0.184619	−	1.04702i
$16$	0.540567	−	3.96331i	0.135142	−	0.990826i
$17$	3.58623	−	3.00920i	0.869788	−	0.729839i	−0.0942656	−	0.995547i	$-0.530050\pi$
$17$	3.58623	−	3.00920i	0.869788	−	0.729839i	0.964053	+	0.265708i	$0.0856058\pi$
$18$	2.20347	+	0.777766i	0.519362	+	0.183321i
$19$	−3.34958	−	2.78932i	−0.768447	−	0.639914i
$19$	−3.34958	−	2.78932i	−0.768447	−	0.639914i
$20$	5.52206	+	4.45310i	1.23477	+	0.995743i
$21$	−3.04643	−	3.63059i	−0.664785	−	0.792260i
$22$	0.269833	−	0.328013i	0.0575285	−	0.0699326i
$23$	−3.07108	−	0.541514i	−0.640365	−	0.112914i	−0.155968	−	0.987762i	$-0.549850\pi$
$23$	−3.07108	−	0.541514i	−0.640365	−	0.112914i	−0.484397	+	0.874849i	$0.660961\pi$
$24$	2.45257	−	2.18323i	0.500629	−	0.445651i
$25$	−7.12363	+	2.59279i	−1.42473	+	0.518558i
$26$	−1.46904	−	1.71648i	−0.288102	−	0.336630i
$27$	2.70044	+	4.67730i	0.519700	+	0.900146i
$28$	8.01181	−	1.57426i	1.51409	−	0.297508i
$29$	0.344669	−	0.410760i	0.0640034	−	0.0762762i	−0.733093	−	0.680129i	$-0.761924\pi$
$29$	0.344669	−	0.410760i	0.0640034	−	0.0762762i	0.797096	+	0.603852i	$0.206368\pi$
$30$	1.06703	+	5.72467i	0.194812	+	1.04518i
$31$	2.08054	−	3.60361i	0.373676	−	0.647227i	−0.616452	−	0.787393i	$-0.711430\pi$
$31$	2.08054	−	3.60361i	0.373676	−	0.647227i	0.990128	+	0.140166i	$0.0447637\pi$
$32$	1.25245	+	5.51646i	0.221404	+	0.975182i
$33$	0.343363	−	0.0605442i	0.0597719	−	0.0105394i
$34$	−3.25429	+	5.76561i	−0.558105	+	0.988794i
$35$	−4.95259	+	13.6071i	−0.837141	+	2.30003i
$36$	−3.30397	+	0.0643968i	−0.550662	+	0.0107328i
$37$		−	2.42729i		−	0.399044i	−0.979893	−	0.199522i	$-0.936061\pi$
$37$		−	2.42729i		−	0.399044i	0.979893	−	0.199522i	$-0.0639389\pi$
$38$	5.82057	+	2.03002i	0.944221	+	0.329313i
$39$		−	1.85461i		−	0.296976i
$40$	−9.52351	−	3.15423i	−1.50580	−	0.498728i
$41$	2.70395	−	7.42905i	0.422286	−	1.16022i	−0.528109	−	0.849177i	$-0.677099\pi$
$41$	2.70395	−	7.42905i	0.422286	−	1.16022i	0.950395	−	0.311045i	$-0.100679\pi$
$42$	5.83694	+	3.29454i	0.900659	+	0.508359i
$43$	2.23149	−	0.393472i	0.340299	−	0.0600039i	−0.000887115	−	1.00000i	$-0.500282\pi$
$43$	2.23149	−	0.393472i	0.340299	−	0.0600039i	0.341186	+	0.939996i	$0.389171\pi$
$44$	−0.194403	+	0.568341i	−0.0293073	+	0.0856807i
$45$	2.93031	−	5.07544i	0.436824	−	0.756602i
$46$	4.33550	−	0.808100i	0.639234	−	0.119148i
$47$	2.11323	−	2.51844i	0.308246	−	0.367353i	−0.589575	−	0.807713i	$-0.700705\pi$
$47$	2.11323	−	2.51844i	0.308246	−	0.367353i	0.897821	+	0.440360i	$0.145149\pi$
$48$	−2.16334	+	4.10891i	−0.312252	+	0.593070i
$49$	4.83342	+	8.37173i	0.690489	+	1.19596i
$50$	8.14514	−	6.97095i	1.15190	−	0.985841i
$51$	−5.10701	+	1.85880i	−0.715124	+	0.260284i
$52$	2.79766	+	1.54333i	0.387966	+	0.214022i
$53$	−5.12508	−	0.903690i	−0.703984	−	0.124131i	−0.189814	−	0.981820i	$-0.560789\pi$
$53$	−5.12508	−	0.903690i	−0.703984	−	0.124131i	−0.514169	+	0.857689i	$0.671900\pi$
$54$	−5.89861	−	4.85236i	−0.802699	−	0.660323i
$55$	−0.684743	−	0.816045i	−0.0923307	−	0.110035i
$56$	−9.82703	+	6.06335i	−1.31319	+	0.810249i
$57$	2.54653	+	4.37281i	0.337296	+	0.579193i
$58$	−0.252403	+	0.715076i	−0.0331422	+	0.0938941i
$59$	4.17166	−	3.50044i	0.543104	−	0.455719i	−0.329494	−	0.944158i	$-0.606878\pi$
$59$	4.17166	−	3.50044i	0.543104	−	0.455719i	0.872598	+	0.488439i	$0.162434\pi$
$60$	−4.25587	−	7.05041i	−0.549430	−	0.910204i
$61$	−0.594383	+	3.37091i	−0.0761029	+	0.431601i	0.922821	+	0.385228i	$0.125877\pi$
$61$	−0.594383	+	3.37091i	−0.0761029	+	0.431601i	−0.998924	+	0.0463728i	$0.985234\pi$
$62$	−0.965344	+	5.80494i	−0.122599	+	0.737229i
$63$	−2.30710	−	6.33871i	−0.290668	−	0.798603i
$64$	−4.39799	−	6.68264i	−0.549749	−	0.835330i
$65$	−4.90729	+	2.83323i	−0.608675	+	0.351418i
$66$	−0.424597	+	0.250689i	−0.0522643	+	0.0308577i
$67$	5.29646	+	4.44426i	0.647066	+	0.542953i	0.906179	−	0.422894i	$-0.138986\pi$
$67$	5.29646	+	4.44426i	0.647066	+	0.542953i	−0.259113	+	0.965847i	$0.583430\pi$
$68$	1.44587	−	9.25066i	0.175338	−	1.12181i
$69$	3.13521	+	1.81012i	0.377435	+	0.217912i
$70$	−0.199541	−	20.4774i	−0.0238497	−	2.44752i
$71$	−0.743257	−	4.21522i	−0.0882084	−	0.500254i	−0.996618	−	0.0821733i	$-0.973814\pi$
$71$	−0.743257	−	4.21522i	−0.0882084	−	0.500254i	0.908410	−	0.418081i	$-0.137297\pi$
$72$	4.34297	−	1.72607i	0.511824	−	0.203420i
$73$	−8.50411	−	3.09524i	−0.995331	−	0.362271i	−0.207549	−	0.978225i	$-0.566549\pi$
$73$	−8.50411	−	3.09524i	−0.995331	−	0.362271i	−0.787782	+	0.615954i	$0.788771\pi$
$74$	1.20543	+	3.21410i	0.140128	+	0.373631i
$75$	8.80060			1.01621
$76$	−8.71544	+	0.202533i	−0.999730	+	0.0232321i
$77$	−1.22612			−0.139729
$78$	0.921031	+	2.45579i	0.104286	+	0.278063i
$79$	0.187126	+	0.0681083i	0.0210533	+	0.00766278i	0.352525	−	0.935802i	$-0.385323\pi$
$79$	0.187126	+	0.0681083i	0.0210533	+	0.00766278i	−0.331472	+	0.943465i	$0.607545\pi$
$80$	14.1770	−	0.552850i	1.58504	−	0.0618105i
$81$	−0.228002	−	1.29306i	−0.0253336	−	0.143674i
$82$	0.108943	+	11.1800i	0.0120307	+	1.23462i
$83$	−12.9034	−	7.44977i	−1.41633	−	0.817719i	−0.420356	−	0.907359i	$-0.638095\pi$
$83$	−12.9034	−	7.44977i	−1.41633	−	0.817719i	−0.995974	+	0.0896401i	$0.971428\pi$
$84$	−9.36510	−	1.46376i	−1.02182	−	0.159709i
$85$	12.7201	+	10.6735i	1.37969	+	1.15770i
$86$	−2.75942	+	1.62921i	−0.297556	+	0.175682i
$87$	−0.539091	+	0.311244i	−0.0577966	+	0.0333689i
$88$	−0.0248287	−	0.849113i	−0.00264674	−	0.0905157i
$89$	2.26220	+	6.21534i	0.239793	+	0.658825i	0.999959	+	0.00909600i	$0.00289539\pi$
$89$	2.26220	+	6.21534i	0.239793	+	0.658825i	−0.760166	+	0.649729i	$0.774882\pi$
$90$	−1.35962	+	8.17588i	−0.143317	+	0.861813i
$91$	−1.13254	+	6.42296i	−0.118723	+	0.673309i
$92$	−5.33953	+	3.22312i	−0.556685	+	0.336034i
$93$	−3.70047	+	3.10507i	−0.383721	+	0.321980i
$94$	−1.54753	+	4.38426i	−0.159615	+	0.452202i
$95$	7.68017	−	13.4183i	0.787969	−	1.37669i
$96$	0.824040	−	6.51517i	0.0841033	−	0.664951i
$97$	3.90012	+	4.64798i	0.395997	+	0.471931i	0.926795	−	0.375567i	$-0.122552\pi$
$97$	3.90012	+	4.64798i	0.395997	+	0.471931i	−0.530798	+	0.847498i	$0.678108\pi$
$98$	−10.5577	−	8.68508i	−1.06649	−	0.877325i
$99$	0.488704	+	0.0861717i	0.0491166	+	0.00866058i
$100$	−7.32350	+	13.2756i	−0.732350	+	1.32756i
$101$	5.15199	−	1.87517i	0.512642	−	0.186586i	−0.0727293	−	0.997352i	$-0.523171\pi$
$101$	5.15199	−	1.87517i	0.512642	−	0.186586i	0.585371	+	0.810765i	$0.300949\pi$
$102$	5.83933	−	4.99755i	0.578180	−	0.494831i
$103$	9.18625	+	15.9110i	0.905148	+	1.56776i	0.820719	+	0.571333i	$0.193573\pi$
$103$	9.18625	+	15.9110i	0.905148	+	1.56776i	0.0844294	+	0.996429i	$0.473093\pi$
$104$	−4.47096	−	0.654244i	−0.438414	−	0.0641539i
$105$	10.8055	−	12.8775i	1.05451	−	1.25672i
$106$	7.23516	−	1.34857i	0.702741	−	0.130985i
$107$	−8.31778	+	14.4068i	−0.804110	+	1.39276i	0.112780	+	0.993620i	$0.464025\pi$
$107$	−8.31778	+	14.4068i	−0.804110	+	1.39276i	−0.916890	+	0.399140i	$0.869309\pi$
$108$	10.2204	+	3.49592i	0.983458	+	0.336395i
$109$	−8.39330	+	1.47996i	−0.803932	+	0.141755i	−0.560491	−	0.828161i	$-0.689387\pi$
$109$	−8.39330	+	1.47996i	−0.803932	+	0.141755i	−0.243441	+	0.969916i	$0.578276\pi$
$110$	1.31196	+	0.740512i	0.125091	+	0.0706050i
$111$	−0.963763	+	2.64792i	−0.0914763	+	0.251329i
$112$	10.0013	−	12.9090i	0.945035	−	1.21979i
$113$		−	10.6541i		−	1.00226i	−0.865373	−	0.501129i	$-0.832918\pi$
$113$		−	10.6541i		−	1.00226i	0.865373	−	0.501129i	$-0.167082\pi$
$114$	−5.54360	−	4.52561i	−0.519206	−	0.423862i
$115$		−	11.0610i		−	1.03144i
$116$	−0.0208982	−	1.07221i	−0.00194035	−	0.0995527i
$117$	0.902812	−	2.48046i	0.0834650	−	0.229318i
$118$	−3.78553	+	6.70682i	−0.348487	+	0.617413i
$119$	18.8218	−	3.31880i	1.72539	−	0.304234i
$120$	9.13675	+	7.22227i	0.834067	+	0.659300i
$121$	−5.45490	+	9.44816i	−0.495900	+	0.858924i
$122$	−0.886996	−	4.75877i	−0.0803048	−	0.430839i
$123$	−5.89945	+	7.03069i	−0.531935	+	0.633936i
$124$	−1.60457	−	8.16602i	−0.144094	−	0.733330i
$125$	−4.57699	−	7.92759i	−0.409379	−	0.709065i
$126$	6.20285	+	7.24766i	0.552594	+	0.645673i
$127$	−17.1851	+	6.25486i	−1.52493	+	0.555029i	−0.962373	−	0.271730i	$-0.912404\pi$
$127$	−17.1851	+	6.25486i	−1.52493	+	0.555029i	−0.562556	+	0.826759i	$0.690182\pi$
$128$	9.14230	+	6.66471i	0.808073	+	0.589082i
$129$	−2.59055	−	0.456784i	−0.228085	−	0.0402176i
$130$	5.09097	−	6.18865i	0.446507	−	0.542781i
$131$	−1.78093	−	2.12243i	−0.155601	−	0.185438i	0.682612	−	0.730781i	$-0.260844\pi$
$131$	−1.78093	−	2.12243i	−0.155601	−	0.185438i	−0.838213	+	0.545343i	$0.816399\pi$
$132$	0.437735	−	0.542812i	0.0380999	−	0.0472457i
$133$	−6.14892	−	16.6991i	−0.533179	−	1.44800i
$134$	−9.22040	−	3.25456i	−0.796521	−	0.281151i
$135$	−14.6748	+	12.3136i	−1.26301	+	1.05979i
$136$	2.67947	+	12.9673i	0.229763	+	1.11194i
$137$	−1.84783	+	10.4796i	−0.157871	+	0.895330i	0.798243	+	0.602335i	$0.205763\pi$
$137$	−1.84783	+	10.4796i	−0.157871	+	0.895330i	−0.956114	+	0.292995i	$0.905348\pi$
$138$	−5.05043	−	0.839870i	−0.429921	−	0.0714945i
$139$	−6.24308	−	17.1527i	−0.529531	−	1.45487i	−0.859624	−	0.510927i	$-0.829302\pi$
$139$	−6.24308	−	17.1527i	−0.529531	−	1.45487i	0.330093	−	0.943948i	$-0.392920\pi$
$140$	10.4336	+	27.0161i	0.881803	+	2.28328i
$141$	−3.30526	+	1.90829i	−0.278353	+	0.160707i
$142$	3.07753	+	5.21247i	0.258260	+	0.437421i
$143$	−0.367550	−	0.308411i	−0.0307361	−	0.0257906i
$144$	−4.89355	+	4.44237i	−0.407796	+	0.370197i
$145$	1.64710	+	0.950952i	0.136784	+	0.0789723i
$146$	12.7979	−	0.124708i	1.05916	−	0.0103209i
$147$	−1.94873	−	11.0518i	−0.160729	−	0.911537i
$148$	−3.19234	−	3.65731i	−0.262409	−	0.300629i
$149$	14.1321	+	5.14368i	1.15775	+	0.421387i	0.848293	−	0.529527i	$-0.177630\pi$
$149$	14.1321	+	5.14368i	1.15775	+	0.421387i	0.309457	+	0.950913i	$0.399853\pi$
$150$	−11.6533	+	4.37052i	−0.951489	+	0.356851i
$151$	15.0749			1.22678			0.613389	−	0.789781i	$-0.289806\pi$
$151$	15.0749			1.22678			0.613389	+	0.789781i	$0.289806\pi$
$152$	11.4400	−	4.59641i	0.927904	−	0.372818i
$153$	−7.73522			−0.625355
$154$	1.62356	−	0.608910i	0.130831	−	0.0490673i
$155$	13.8691	+	5.04792i	1.11399	+	0.405459i
$156$	−2.43917	−	2.79443i	−0.195290	−	0.223734i
$157$	−2.81624	−	15.9717i	−0.224761	−	1.27468i	−0.863142	−	0.504961i	$-0.831507\pi$
$157$	−2.81624	−	15.9717i	−0.224761	−	1.27468i	0.638381	−	0.769720i	$-0.279604\pi$
$158$	−0.281606	+	0.00274410i	−0.0224034	+	0.000218309i
$159$	5.23211	+	3.02076i	0.414933	+	0.239562i
$160$	−18.4979	+	7.77258i	−1.46239	+	0.614476i
$161$	−9.75260	−	8.18340i	−0.768613	−	0.644942i
$162$	0.944065	+	1.59898i	0.0741727	+	0.125628i
$163$	5.45589	−	3.14996i	0.427338	−	0.246724i	−0.270874	−	0.962615i	$-0.587313\pi$
$163$	5.45589	−	3.14996i	0.427338	−	0.246724i	0.698212	+	0.715891i	$0.253979\pi$
$164$	−5.69642	−	14.7499i	−0.444815	−	1.15177i
$165$	0.422969	+	1.16210i	0.0329281	+	0.0904692i
$166$	20.7857	+	3.45659i	1.61328	+	0.268284i
$167$	0.932562	−	5.28882i	0.0721638	−	0.409261i	−0.927231	−	0.374489i	$-0.877818\pi$
$167$	0.932562	−	5.28882i	0.0721638	−	0.409261i	0.999395	−	0.0347725i	$-0.0110707\pi$
$168$	13.1277	−	2.71262i	1.01283	−	0.209283i
$169$	8.00348	−	6.71572i	0.615653	−	0.516594i
$170$	−22.1440	−	7.81625i	−1.69837	−	0.599479i
$171$	1.27721	+	7.08805i	0.0976707	+	0.542037i
$172$	2.84480	−	3.52769i	0.216914	−	0.268984i
$173$	−9.95804	−	11.8675i	−0.757096	−	0.902271i	0.240565	−	0.970633i	$-0.422667\pi$
$173$	−9.95804	−	11.8675i	−0.757096	−	0.902271i	−0.997661	+	0.0683617i	$0.978223\pi$
$174$	0.559268	−	0.679855i	0.0423980	−	0.0515396i
$175$	−30.4785	−	5.37418i	−2.30396	−	0.406250i
$176$	0.454559	+	1.11202i	0.0342637	+	0.0838218i
$177$	−5.94070	+	2.16224i	−0.446531	+	0.162524i
$178$	−6.08213	−	7.10660i	−0.455875	−	0.532662i
$179$	−4.09294	−	7.08919i	−0.305921	−	0.529871i	0.671545	−	0.740964i	$-0.265631\pi$
$179$	−4.09294	−	7.08919i	−0.305921	−	0.529871i	−0.977466	+	0.211093i	$0.932298\pi$
$180$	−2.25992	−	11.5013i	−0.168445	−	0.857256i
$181$	−11.2531	+	13.4109i	−0.836434	+	0.996823i	0.163514	+	0.986541i	$0.447717\pi$
$181$	−11.2531	+	13.4109i	−0.836434	+	0.996823i	−0.999947	+	0.0102816i	$0.996727\pi$
$182$	−1.69009	−	9.06740i	−0.125278	−	0.672120i
$183$	1.98684	−	3.44131i	0.146871	−	0.254389i
$184$	5.46969	−	6.91959i	0.403231	−	0.510119i
$185$	8.47866	−	1.49502i	0.623364	−	0.109916i
$186$	3.35796	−	5.94929i	0.246217	−	0.436223i
$187$	−0.480885	+	1.32122i	−0.0351658	+	0.0966173i
$188$	−0.128131	−	6.57394i	−0.00934491	−	0.479454i
$189$			22.0491i			1.60384i
$190$	−3.50597	+	21.5819i	−0.254350	+	1.56572i
$191$			5.42765i			0.392731i	0.980531	+	0.196366i	$0.0629139\pi$
$191$			5.42765i			0.392731i	−0.980531	+	0.196366i	$0.937086\pi$
$192$	2.14438	+	9.03629i	0.154757	+	0.652138i
$193$	−3.00336	+	8.25165i	−0.216186	+	0.593967i	−0.999622	−	0.0275063i	$-0.991243\pi$
$193$	−3.00336	+	8.25165i	−0.216186	+	0.593967i	0.783435	+	0.621473i	$0.213466\pi$
$194$	−7.47260	−	4.21776i	−0.536502	−	0.302818i
$195$	6.47828	−	1.14230i	0.463919	−	0.0818014i
$196$	18.2931	+	6.25722i	1.30665	+	0.446944i
$197$	1.49191	−	2.58406i	0.106294	−	0.184107i	−0.807972	−	0.589221i	$-0.799435\pi$
$197$	1.49191	−	2.58406i	0.106294	−	0.184107i	0.914266	+	0.405114i	$0.132768\pi$
$198$	−0.689912	+	0.128594i	−0.0490299	+	0.00913876i
$199$	0.554813	−	0.661200i	0.0393297	−	0.0468713i	−0.746021	−	0.665922i	$-0.768038\pi$
$199$	0.554813	−	0.661200i	0.0393297	−	0.0468713i	0.785351	+	0.619051i	$0.212483\pi$
$200$	3.10455	−	21.2158i	0.219525	−	1.50019i
$201$	−4.01327	−	6.95119i	−0.283075	−	0.490299i
$202$	−5.89077	+	5.04157i	−0.414473	+	0.354723i
$203$	2.05706	−	0.748708i	0.144377	−	0.0525490i
$204$	−5.25029	+	9.51741i	−0.367594	+	0.666352i
$205$	27.6155	+	4.86936i	1.92875	+	0.340091i
$206$	−20.0656	−	16.5066i	−1.39804	−	1.15007i
$207$	3.31204	+	3.94714i	0.230203	+	0.274345i
$208$	6.24514	−	1.35403i	0.433022	−	0.0938853i
$209$	1.29008	+	0.222497i	0.0892369	+	0.0153904i
$210$	−7.91295	+	22.4179i	−0.546045	+	1.54698i
$211$	6.79371	−	5.70060i	0.467698	−	0.392446i	−0.378256	−	0.925701i	$-0.623476\pi$
$211$	6.79371	−	5.70060i	0.467698	−	0.392446i	0.845954	+	0.533256i	$0.179032\pi$
$212$	−8.91072	+	5.37881i	−0.611990	+	0.369418i
$213$	−0.862851	+	4.89347i	−0.0591216	+	0.335295i
$214$	3.85934	−	23.2075i	0.263819	−	1.58643i
$215$	2.74884	+	7.55238i	0.187469	+	0.515068i
$216$	−15.2695	+	0.446490i	−1.03896	+	0.0303798i
$217$	14.7117	−	8.49382i	0.998698	−	0.576598i
$218$	10.3790	−	6.12794i	0.702955	−	0.415036i
$219$	8.04811	+	6.75317i	0.543841	+	0.456337i
$220$	−2.10499	−	0.329007i	−0.141918	−	0.0221817i
$221$	6.47696	+	3.73948i	0.435688	+	0.251544i
$222$	−0.0388302	−	3.98486i	−0.00260611	−	0.267446i
$223$	2.08177	+	11.8063i	0.139406	+	0.790610i	0.971690	+	0.236260i	$0.0759218\pi$
$223$	2.08177	+	11.8063i	0.139406	+	0.790610i	−0.832284	+	0.554350i	$0.812967\pi$
$224$	−6.83240	+	22.0603i	−0.456509	+	1.47397i
$225$	11.7704	+	4.28406i	0.784691	+	0.285604i
$226$	5.29101	+	14.1077i	0.351953	+	0.938429i
$227$	3.59398			0.238541			0.119270	−	0.992862i	$-0.461944\pi$
$227$	3.59398			0.238541			0.119270	+	0.992862i	$0.461944\pi$
$228$	9.58804	+	3.23955i	0.634984	+	0.214545i
$229$	8.48334			0.560595			0.280297	−	0.959913i	$-0.409567\pi$
$229$	8.48334			0.560595			0.280297	+	0.959913i	$0.409567\pi$
$230$	5.49306	+	14.6464i	0.362202	+	0.965756i
$231$	1.33757	+	0.486834i	0.0880054	+	0.0320313i
$232$	0.560151	+	1.40939i	0.0367757	+	0.0925313i
$233$	3.62386	+	20.5519i	0.237407	+	1.34640i	0.837485	+	0.546461i	$0.184025\pi$
$233$	3.62386	+	20.5519i	0.237407	+	1.34640i	−0.600078	+	0.799942i	$0.704864\pi$
$234$	0.0363745	+	3.73284i	0.00237787	+	0.244024i
$235$	10.0987	+	5.83046i	0.658763	+	0.380337i
$236$	1.68190	−	10.7608i	0.109482	−	0.700468i
$237$	−0.177092	−	0.148598i	−0.0115034	−	0.00965247i
$238$	−23.2748	+	13.7418i	−1.50868	+	0.890749i
$239$	−22.9107	+	13.2275i	−1.48197	+	0.855617i	−0.999791	−	0.0204539i	$-0.993489\pi$
$239$	−22.9107	+	13.2275i	−1.48197	+	0.855617i	−0.482182	+	0.876071i	$0.660156\pi$
$240$	−15.6851	−	5.02592i	−1.01247	−	0.324422i
$241$	−5.36811	−	14.7488i	−0.345790	−	0.950051i	−0.983681	−	0.179924i	$-0.942415\pi$
$241$	−5.36811	−	14.7488i	−0.345790	−	0.950051i	0.637890	−	0.770127i	$-0.279807\pi$
$242$	2.53100	−	15.2198i	0.162699	−	0.978364i
$243$	2.54887	−	14.4554i	0.163510	−	0.927312i
$244$	3.53780	+	5.86083i	0.226484	+	0.375201i
$245$	−26.2659	+	22.0397i	−1.67807	+	1.40807i
$246$	4.32021	−	12.2394i	0.275446	−	0.780359i
$247$	2.35716	−	6.55252i	0.149983	−	0.416927i
$248$	6.18006	+	10.0162i	0.392434	+	0.636028i
$249$	11.1183	+	13.2502i	0.704592	+	0.839700i
$250$	9.99759	+	8.22431i	0.632303	+	0.520151i
$251$	1.99182	+	0.351211i	0.125722	+	0.0221682i	0.236155	−	0.971715i	$-0.424113\pi$
$251$	1.99182	+	0.351211i	0.125722	+	0.0221682i	−0.110433	+	0.993884i	$0.535224\pi$
$252$	−11.8128	−	6.51656i	−0.744137	−	0.410505i
$253$	0.880099	−	0.320330i	0.0553313	−	0.0201390i
$254$	19.6494	−	16.8167i	1.23291	−	1.05518i
$255$	−9.63840	−	16.6942i	−0.603580	−	1.04543i
$256$	−15.4156	−	4.28486i	−0.963473	−	0.267804i
$257$	−2.96164	+	3.52955i	−0.184742	+	0.220167i	−0.850465	−	0.526032i	$-0.823679\pi$
$257$	−2.96164	+	3.52955i	−0.184742	+	0.220167i	0.665722	+	0.746200i	$0.268124\pi$
$258$	3.65712	−	0.681657i	0.227683	−	0.0424381i
$259$	4.95471	−	8.58181i	0.307871	−	0.533248i
$260$	−3.66782	+	10.7230i	−0.227469	+	0.665010i
$261$	−0.872518	+	0.153848i	−0.0540075	+	0.00952298i
$262$	3.41225	+	1.92598i	0.210810	+	0.118987i
$263$	−3.03627	+	8.34207i	−0.187224	+	0.514394i	−0.997422	−	0.0717627i	$-0.977138\pi$
$263$	−3.03627	+	8.34207i	−0.187224	+	0.514394i	0.810198	+	0.586157i	$0.199360\pi$
$264$	−0.310057	+	0.936150i	−0.0190827	+	0.0576161i
$265$		−	18.4588i		−	1.13392i
$266$	16.4351	+	19.0585i	1.00770	+	1.16855i
$267$		−	7.67849i		−	0.469916i
$268$	13.8255	−	0.269468i	0.844524	−	0.0164604i
$269$	−2.44696	+	6.72295i	−0.149193	+	0.409906i	−0.991666	−	0.128833i	$-0.958877\pi$
$269$	−2.44696	+	6.72295i	−0.149193	+	0.409906i	0.842473	+	0.538739i	$0.181099\pi$
$270$	13.3165	−	23.5928i	0.810417	−	1.43581i
$271$	−31.4126	+	5.53889i	−1.90818	+	0.336464i	−0.997122	−	0.0758130i	$-0.975845\pi$
$271$	−31.4126	+	5.53889i	−1.90818	+	0.336464i	−0.911059	+	0.412277i	$0.864734\pi$
$272$	−9.98779	−	15.8400i	−0.605599	−	0.960440i
$273$	3.78574	−	6.55709i	0.229123	−	0.396853i
$274$	−2.75751	−	14.7942i	−0.166587	−	0.893750i
$275$	1.46349	−	1.74412i	0.0882516	−	0.105174i
$276$	7.10461	−	1.39601i	0.427647	−	0.0840297i
$277$	−5.16272	−	8.94209i	−0.310198	−	0.537278i	0.668207	−	0.743975i	$-0.267062\pi$
$277$	−5.16272	−	8.94209i	−0.310198	−	0.537278i	−0.978405	+	0.206697i	$0.933729\pi$
$278$	16.7851	+	19.6124i	1.00670	+	1.17627i
$279$	−6.46072	+	2.35151i	−0.386793	+	0.140781i
$280$	−27.2323	−	30.5918i	−1.62744	−	1.82821i
$281$	−24.7357	−	4.36157i	−1.47561	−	0.260190i	−0.622787	−	0.782391i	$-0.714000\pi$
$281$	−24.7357	−	4.36157i	−1.47561	−	0.260190i	−0.852822	+	0.522202i	$0.825111\pi$
$282$	3.42897	−	4.16831i	0.204192	−	0.248219i
$283$	9.40772	+	11.2117i	0.559231	+	0.666465i	0.969384	−	0.245552i	$-0.0789691\pi$
$283$	9.40772	+	11.2117i	0.559231	+	0.666465i	−0.410153	+	0.912017i	$0.634525\pi$
$284$	−6.66370	−	5.37374i	−0.395418	−	0.318873i
$285$	−13.7060	+	11.5885i	−0.811875	+	0.686443i
$286$	0.639854	+	0.225852i	0.0378353	+	0.0133549i
$287$	24.7245	−	20.7463i	1.45944	−	1.22462i
$288$	4.27364	−	8.31257i	0.251827	−	0.489823i
$289$	0.853710	−	4.84163i	0.0502183	−	0.284802i
$290$	−2.65326	−	0.441229i	−0.155805	−	0.0259099i
$291$	−2.40912	−	6.61901i	−0.141225	−	0.388013i
$292$	−16.8844	+	6.52075i	−0.988082	+	0.381598i
$293$	25.4984	−	14.7215i	1.48963	−	0.860039i	0.489701	−	0.871890i	$-0.337106\pi$
$293$	25.4984	−	14.7215i	1.48963	−	0.860039i	0.999930	+	0.0118513i	$0.00377249\pi$
$294$	8.06891	+	13.6665i	0.470588	+	0.797045i
$295$	14.7967	+	12.4159i	0.861494	+	0.722880i
$296$	6.04341	+	3.25746i	0.351266	+	0.189336i
$297$	−1.40476	−	0.811036i	−0.0815122	−	0.0470611i
$298$	−21.2675	+	0.207240i	−1.23199	+	0.0120051i
$299$	−0.865101	−	4.90623i	−0.0500301	−	0.283735i
$300$	13.2603	−	11.5744i	0.765582	−	0.668251i
$301$	8.69273	+	3.16390i	0.501041	+	0.182364i
$302$	−19.9614	+	7.48643i	−1.14865	+	0.430796i
$303$	−6.36482			−0.365649
$304$	−12.8656	+	11.7676i	−0.737892	+	0.674918i
$305$	−12.1409			−0.695185
$306$	10.2426	−	3.84143i	0.585530	−	0.219600i
$307$	−14.8744	−	5.41384i	−0.848926	−	0.308984i	−0.119324	−	0.992855i	$-0.538073\pi$
$307$	−14.8744	−	5.41384i	−0.848926	−	0.308984i	−0.729602	+	0.683872i	$0.760295\pi$
$308$	−1.84745	+	1.61258i	−0.105268	+	0.0918850i
$309$	−3.70369	−	21.0047i	−0.210696	−	1.19492i
$310$	−20.8716	+	0.203382i	−1.18543	+	0.0115513i
$311$	11.3865	+	6.57399i	0.645669	+	0.372777i	0.786795	−	0.617215i	$-0.211739\pi$
$311$	11.3865	+	6.57399i	0.645669	+	0.372777i	−0.141126	+	0.989992i	$0.545072\pi$
$312$	4.61758	+	2.48892i	0.261419	+	0.140907i
$313$	−15.0193	−	12.6027i	−0.848944	−	0.712348i	0.110613	−	0.993864i	$-0.464719\pi$
$313$	−15.0193	−	12.6027i	−0.848944	−	0.712348i	−0.959557	+	0.281515i	$0.909163\pi$
$314$	11.6609	+	19.7503i	0.658064	+	1.11458i
$315$	20.7205	−	11.9630i	1.16747	−	0.674038i
$316$	0.371526	−	0.143484i	0.0209000	−	0.00807159i
$317$	2.06718	+	5.67953i	0.116104	+	0.318994i	0.984110	−	0.177560i	$-0.0568205\pi$
$317$	2.06718	+	5.67953i	0.116104	+	0.318994i	−0.868005	+	0.496555i	$0.834598\pi$
$318$	−8.42825	−	1.40159i	−0.472633	−	0.0785973i
$319$	−0.0279647	+	0.158596i	−0.00156572	+	0.00887966i
$320$	20.6340	−	19.4784i	1.15348	−	1.08888i
$321$	14.7941	−	12.4137i	0.825726	−	0.692866i
$322$	16.9779	+	5.99276i	0.946142	+	0.333963i
$323$	−20.4060	+	0.0764404i	−1.13542	+	0.00425326i
$324$	−2.04416	−	1.64845i	−0.113565	−	0.0915808i
$325$	−7.78467	−	9.27741i	−0.431816	−	0.514618i
$326$	−5.66009	+	6.88050i	−0.313484	+	0.381075i
$327$	9.74382	+	1.71810i	0.538835	+	0.0950111i
$328$	14.8679	+	16.7021i	0.820944	+	0.922221i
$329$	12.6122	−	4.59047i	0.695333	−	0.253081i
$330$	−1.13719	−	1.32874i	−0.0626003	−	0.0731447i
$331$	−1.83555	−	3.17926i	−0.100891	−	0.174748i	0.811161	−	0.584823i	$-0.198836\pi$
$331$	−1.83555	−	3.17926i	−0.100891	−	0.174748i	−0.912052	+	0.410075i	$0.865503\pi$
$332$	−29.2400	+	5.74545i	−1.60475	+	0.315323i
$333$	−2.57797	+	3.07230i	−0.141272	+	0.168361i
$334$	1.39166	+	7.46632i	0.0761482	+	0.408539i
$335$	−12.2619	+	21.2382i	−0.669937	+	1.16036i
$336$	−16.0359	+	10.1113i	−0.874832	+	0.551619i
$337$	−17.7177	+	3.12412i	−0.965147	+	0.170181i	−0.633945	−	0.773378i	$-0.718565\pi$
$337$	−17.7177	+	3.12412i	−0.965147	+	0.170181i	−0.331202	+	0.943560i	$0.607454\pi$
$338$	−7.26268	+	12.8673i	−0.395038	+	0.699887i
$339$	−4.23026	+	11.6225i	−0.229756	+	0.631250i
$340$	33.2036	−	0.647163i	1.80072	−	0.0350973i
$341$			1.24972i			0.0676761i
$342$	−5.21125	−	8.75136i	−0.281792	−	0.473219i
$343$			10.8874i			0.587864i
$344$	−2.01504	+	6.08396i	−0.108644	+	0.328025i
$345$	−4.39180	+	12.0664i	−0.236447	+	0.649632i
$346$	19.0795	+	10.7691i	1.02572	+	0.578949i
$347$	−16.0384	+	2.82801i	−0.860988	+	0.151815i	−0.586672	−	0.809824i	$-0.699562\pi$
$347$	−16.0384	+	2.82801i	−0.860988	+	0.151815i	−0.274316	+	0.961640i	$0.588451\pi$
$348$	−0.402928	+	1.17797i	−0.0215992	+	0.0631459i
$349$	5.92019	−	10.2541i	0.316901	−	0.548888i	−0.662939	−	0.748673i	$-0.730691\pi$
$349$	5.92019	−	10.2541i	0.316901	−	0.548888i	0.979840	+	0.199785i	$0.0640245\pi$
$350$	43.0270	−	8.01988i	2.29989	−	0.428681i
$351$	−5.54611	+	6.60960i	−0.296030	+	0.352794i
$352$	−1.15415	−	1.24674i	−0.0615165	−	0.0664516i
$353$	12.9044	+	22.3511i	0.686833	+	1.18963i	0.972857	+	0.231408i	$0.0743331\pi$
$353$	12.9044	+	22.3511i	0.686833	+	1.18963i	−0.286023	+	0.958223i	$0.592334\pi$
$354$	6.79258	−	5.81337i	0.361021	−	0.308977i
$355$	14.2662	−	5.19248i	0.757172	−	0.275588i
$356$	11.5829	+	6.38973i	0.613892	+	0.338655i
$357$	−21.8504	−	3.85281i	−1.15644	−	0.203912i
$358$	8.94027	+	7.35453i	0.472508	+	0.388699i
$359$	−2.73656	−	3.26130i	−0.144430	−	0.172125i	0.688980	−	0.724781i	$-0.258059\pi$
$359$	−2.73656	−	3.26130i	−0.144430	−	0.172125i	−0.833410	+	0.552656i	$0.813614\pi$
$360$	8.70420	+	14.1071i	0.458752	+	0.743511i
$361$	3.43941	+	18.6861i	0.181021	+	0.983479i
$362$	8.24069	−	23.3465i	0.433121	−	1.22706i
$363$	9.70214	−	8.14106i	0.509230	−	0.427295i
$364$	6.74094	+	11.1673i	0.353321	+	0.585324i
$365$	5.57401	−	31.6118i	0.291757	−	1.65464i
$366$	−0.921867	+	5.54350i	−0.0481868	+	0.289764i
$367$	0.887138	+	2.43739i	0.0463082	+	0.127231i	0.960691	−	0.277620i	$-0.0895457\pi$
$367$	0.887138	+	2.43739i	0.0463082	+	0.127231i	−0.914383	+	0.404851i	$0.867323\pi$
$368$	−3.80631	+	11.8789i	−0.198418	+	0.619231i
$369$	−11.3127	+	6.53139i	−0.588916	+	0.340011i
$370$	−10.4846	+	6.19026i	−0.545067	+	0.321817i
$371$	−16.2753	−	13.6566i	−0.844973	−	0.709017i
$372$	−1.49193	+	9.54536i	−0.0773530	+	0.494904i
$373$	−32.6213	−	18.8339i	−1.68907	−	0.975183i	−0.955233	−	0.295854i	$-0.904396\pi$
$373$	−32.6213	−	18.8339i	−1.68907	−	0.975183i	−0.733833	−	0.679330i	$-0.762271\pi$
$374$	−0.0193750	−	1.98831i	−0.00100186	−	0.102813i
$375$	1.84534	+	10.4655i	0.0952932	+	0.540434i
$376$	3.43439	+	8.64126i	0.177115	+	0.445639i
$377$	0.804965	+	0.292983i	0.0414578	+	0.0150894i
$378$	−10.9499	−	29.1963i	−0.563204	−	1.50170i
$379$	−17.6837			−0.908353			−0.454177	−	0.890912i	$-0.650066\pi$
$379$	−17.6837			−0.908353			−0.454177	+	0.890912i	$0.650066\pi$
$380$	−6.07548	−	30.3188i	−0.311666	−	1.55532i
$381$	21.2306			1.08768
$382$	−2.69546	−	7.18703i	−0.137912	−	0.367720i
$383$	18.5485	+	6.75110i	0.947785	+	0.344965i	0.769235	−	0.638966i	$-0.220637\pi$
$383$	18.5485	+	6.75110i	0.947785	+	0.344965i	0.178549	+	0.983931i	$0.442860\pi$
$384$	−7.32704	−	10.9005i	−0.373907	−	0.556262i
$385$	−0.755191	−	4.28290i	−0.0384881	−	0.218277i
$386$	−0.121006	−	12.4179i	−0.00615904	−	0.632057i
$387$	−3.24237	−	1.87199i	−0.164819	−	0.0951584i
$388$	11.9895	+	1.87394i	0.608672	+	0.0951349i
$389$	15.7275	+	13.1970i	0.797418	+	0.669113i	0.947569	−	0.319550i	$-0.103532\pi$
$389$	15.7275	+	13.1970i	0.797418	+	0.669113i	−0.150152	+	0.988663i	$0.547976\pi$
$390$	−8.01093	+	4.72978i	−0.405649	+	0.239502i
$391$	−12.6431	+	7.29951i	−0.639390	+	0.369152i
$392$	−27.3303	+	0.799157i	−1.38039	+	0.0403635i
$393$	1.10009	+	3.02247i	0.0554922	+	0.152463i
$394$	−0.692225	+	4.16259i	−0.0348738	+	0.209708i
$395$	−0.122651	+	0.695591i	−0.00617127	+	0.0349990i
$396$	0.849685	−	0.512898i	0.0426983	−	0.0257741i
$397$	4.01047	−	3.36518i	0.201280	−	0.168894i	−0.536577	−	0.843852i	$-0.680283\pi$
$397$	4.01047	−	3.36518i	0.201280	−	0.168894i	0.737856	+	0.674958i	$0.235838\pi$
$398$	−0.406293	+	1.15106i	−0.0203656	+	0.0576973i
$399$	0.0773861	+	20.6584i	0.00387415	+	1.03421i
$400$	6.42522	+	29.6347i	0.321261	+	1.48174i
$401$	16.5098	+	19.6756i	0.824458	+	0.982550i	0.999998	−	0.00192191i	$-0.000611762\pi$
$401$	16.5098	+	19.6756i	0.824458	+	0.982550i	−0.175541	+	0.984472i	$0.556167\pi$
$402$	8.76625	+	7.21137i	0.437221	+	0.359670i
$403$	6.54659	+	1.15434i	0.326109	+	0.0575018i
$404$	5.29654	−	9.60124i	0.263513	−	0.477679i
$405$	4.37632	−	1.59285i	0.217461	−	0.0791493i
$406$	−2.35203	+	2.01297i	−0.116730	+	0.0999020i
$407$	0.364500	+	0.631333i	0.0180676	+	0.0312940i
$408$	2.22568	−	15.2099i	0.110188	−	0.753000i
$409$	15.6062	−	18.5987i	0.771676	−	0.919648i	−0.226850	−	0.973930i	$-0.572843\pi$
$409$	15.6062	−	18.5987i	0.771676	−	0.919648i	0.998526	+	0.0542822i	$0.0172871\pi$
$410$	−38.9853	+	7.26653i	−1.92535	+	0.358868i
$411$	6.17673	−	10.6984i	0.304676	−	0.527714i
$412$	34.7673	+	11.8923i	1.71286	+	0.585890i
$413$	21.8944	−	3.86058i	1.07735	−	0.189967i
$414$	−6.34585	−	3.58179i	−0.311882	−	0.176035i
$415$	18.0750	−	49.6607i	0.887268	−	2.43775i
$416$	−7.59706	+	4.89437i	−0.372477	+	0.239966i
$417$			21.1906i			1.03771i
$418$	−1.81876	+	0.346056i	−0.0889584	+	0.0169262i
$419$			3.51321i			0.171632i	0.996311	+	0.0858159i	$0.0273497\pi$
$419$			3.51321i			0.171632i	−0.996311	+	0.0858159i	$0.972650\pi$
$420$	−0.655169	−	33.6144i	−0.0319690	−	1.64021i
$421$	−0.483024	+	1.32710i	−0.0235412	+	0.0646788i	−0.950907	−	0.309478i	$-0.899846\pi$
$421$	−0.483024	+	1.32710i	−0.0235412	+	0.0646788i	0.927365	+	0.374157i	$0.122068\pi$
$422$	−6.16489	+	10.9223i	−0.300102	+	0.531690i
$423$	−5.34957	+	0.943273i	−0.260105	+	0.0458635i
$424$	9.12792	−	11.5475i	0.443291	−	0.560799i
$425$	−17.7447	+	30.7348i	−0.860746	+	1.49086i
$426$	−1.28763	−	6.90819i	−0.0623859	−	0.334703i
$427$	−8.98236	+	10.7048i	−0.434687	+	0.518039i
$428$	6.41488	+	32.6469i	0.310075	+	1.57805i
$429$	0.278503	+	0.482381i	0.0134462	+	0.0232896i
$430$	−7.39051	−	8.63537i	−0.356402	−	0.416434i
$431$	29.6032	−	10.7747i	1.42594	−	0.518998i	0.490172	−	0.871626i	$-0.336934\pi$
$431$	29.6032	−	10.7747i	1.42594	−	0.518998i	0.935764	+	0.352628i	$0.114712\pi$
$432$	19.9973	−	8.17427i	0.962122	−	0.393285i
$433$	32.3517	+	5.70447i	1.55472	+	0.274139i	0.883970	−	0.467543i	$-0.154861\pi$
$433$	32.3517	+	5.70447i	1.55472	+	0.274139i	0.670751	+	0.741683i	$0.265972\pi$
$434$	−15.2624	+	18.5532i	−0.732618	+	0.890581i
$435$	−1.41923	−	1.69137i	−0.0680469	−	0.0810951i
$436$	−10.7001	+	13.2687i	−0.512444	+	0.635455i
$437$	8.77638	+	10.3801i	0.419831	+	0.496546i
$438$	−14.0106	−	4.94539i	−0.669454	−	0.236300i
$439$	−1.21027	+	1.01554i	−0.0577630	+	0.0484689i	−0.671212	−	0.741265i	$-0.734226\pi$
$439$	−1.21027	+	1.01554i	−0.0577630	+	0.0484689i	0.613449	+	0.789734i	$0.289782\pi$
$440$	2.95071	−	0.609714i	0.140669	−	0.0290670i
$441$	2.77360	−	15.7299i	0.132076	−	0.749041i
$442$	−10.4336	−	1.73507i	−0.496273	−	0.0825287i
$443$	−0.331536	−	0.910886i	−0.0157517	−	0.0432775i	0.931568	−	0.363568i	$-0.118442\pi$
$443$	−0.331536	−	0.910886i	−0.0157517	−	0.0432775i	−0.947319	+	0.320291i	$0.896219\pi$
$444$	2.03036	+	5.25727i	0.0963566	+	0.249499i
$445$	−20.3172	+	11.7301i	−0.963128	+	0.556062i
$446$	−8.61978	−	14.5995i	−0.408159	−	0.691306i
$447$	−13.3744	−	11.2224i	−0.632586	−	0.530802i
$448$	−1.90837	−	32.6042i	−0.0901622	−	1.54041i
$449$	−18.7171	−	10.8063i	−0.883312	−	0.509981i	−0.0115631	−	0.999933i	$-0.503681\pi$
$449$	−18.7171	−	10.8063i	−0.883312	−	0.509981i	−0.871749	+	0.489953i	$0.837014\pi$
$450$	−17.7133	+	0.172606i	−0.835011	+	0.00813672i
$451$	0.412309	+	2.33832i	0.0194149	+	0.110107i
$452$	−14.0122	−	16.0531i	−0.659078	−	0.755074i
$453$	−16.4451	−	5.98554i	−0.772659	−	0.281225i
$454$	−4.75896	+	1.78483i	−0.223349	+	0.0837660i
$455$	−23.1333			−1.08451
$456$	−14.3048	+	0.471920i	−0.669885	+	0.0220997i
$457$	−14.8816			−0.696132			−0.348066	−	0.937470i	$-0.613162\pi$
$457$	−14.8816			−0.696132			−0.348066	+	0.937470i	$0.613162\pi$
$458$	−11.2332	+	4.21296i	−0.524893	+	0.196859i
$459$	23.7593	+	8.64769i	1.10899	+	0.403639i
$460$	−14.5473	−	16.6661i	−0.678270	−	0.777061i
$461$	0.538610	+	3.05461i	0.0250856	+	0.142267i	0.994778	−	0.102061i	$-0.0325437\pi$
$461$	0.538610	+	3.05461i	0.0250856	+	0.142267i	−0.969693	+	0.244328i	$0.921433\pi$
$462$	−2.01291	+	0.0196146i	−0.0936489	+	0.000912556i
$463$	−10.3891	−	5.99813i	−0.482821	−	0.278757i	0.238771	−	0.971076i	$-0.423256\pi$
$463$	−10.3891	−	5.99813i	−0.482821	−	0.278757i	−0.721591	+	0.692319i	$0.756589\pi$
$464$	−1.44165	−	1.58807i	−0.0669270	−	0.0737243i
$465$	−13.1254	−	11.0135i	−0.608675	−	0.510739i
$466$	−15.0050	−	25.4142i	−0.695091	−	1.17729i
$467$	−6.20648	+	3.58331i	−0.287202	+	0.165816i	−0.636679	−	0.771129i	$-0.719692\pi$
$467$	−6.20648	+	3.58331i	−0.287202	+	0.165816i	0.349478	+	0.936945i	$0.386359\pi$
$468$	−1.90195	−	4.92478i	−0.0879179	−	0.227648i
$469$	9.65407	+	26.5243i	0.445783	+	1.22478i
$470$	−16.2676	−	2.70525i	−0.750370	−	0.124784i
$471$	−3.26939	+	18.5416i	−0.150646	+	0.854354i
$472$	3.11689	+	15.0842i	0.143466	+	0.694305i
$473$	−0.521319	+	0.437439i	−0.0239703	+	0.0201134i
$474$	0.308292	+	0.108819i	0.0141603	+	0.00499823i
$475$	31.0933	+	11.1853i	1.42666	+	0.513217i
$476$	23.9949	−	29.7548i	1.09980	−	1.36381i
$477$	5.52720	+	6.58706i	0.253073	+	0.301601i
$478$	23.7683	−	28.8931i	1.08713	−	1.32154i
$479$	30.0195	+	5.29324i	1.37162	+	0.241854i	0.810433	−	0.585831i	$-0.199232\pi$
$479$	30.0195	+	5.29324i	1.37162	+	0.241854i	0.561192	+	0.827686i	$0.310343\pi$
$480$	23.2654	−	1.13440i	1.06192	−	0.0517782i
$481$	3.64388	−	1.32627i	0.166147	−	0.0604725i
$482$	14.4327	+	16.8637i	0.657389	+	0.768120i
$483$	7.38981	+	12.7995i	0.336248	+	0.582399i
$484$	4.20695	+	21.4102i	0.191225	+	0.973191i
$485$	−13.8335	+	16.4861i	−0.628147	+	0.748597i
$486$	3.80367	+	20.4069i	0.172538	+	0.925674i
$487$	14.6412	−	25.3593i	0.663455	−	1.14914i	−0.316246	−	0.948677i	$-0.602423\pi$
$487$	14.6412	−	25.3593i	0.663455	−	1.14914i	0.979702	−	0.200461i	$-0.0642440\pi$
$488$	−7.59516	−	6.00370i	−0.343817	−	0.271775i
$489$	−7.20250	+	1.26999i	−0.325708	+	0.0574311i
$490$	23.8348	−	42.2280i	1.07674	−	1.90767i
$491$	8.64980	−	23.7651i	0.390360	−	1.07250i	−0.576478	−	0.817113i	$-0.695573\pi$
$491$	8.64980	−	23.7651i	0.390360	−	1.07250i	0.966838	−	0.255392i	$-0.0822045\pi$
$492$	0.357701	+	18.3523i	0.0161264	+	0.827388i
$493$		−	2.51026i		−	0.113056i
$494$	0.132847	+	9.84712i	0.00597705	+	0.443043i
$495$			1.76015i			0.0791127i
$496$	−13.1575	−	10.1938i	−0.590790	−	0.457716i
$497$	5.97650	−	16.4203i	0.268083	−	0.736551i
$498$	−21.3025	−	12.0238i	−0.954590	−	0.538799i
$499$	19.5472	−	3.44669i	0.875052	−	0.154295i	0.281956	−	0.959427i	$-0.409017\pi$
$499$	19.5472	−	3.44669i	0.875052	−	0.154295i	0.593096	+	0.805132i	$0.297906\pi$
$500$	−17.3226	−	5.92526i	−0.774691	−	0.264986i
$501$	−3.11727	+	5.39927i	−0.139269	+	0.241221i
$502$	−2.81188	+	0.524111i	−0.125500	+	0.0233922i
$503$	10.8354	−	12.9131i	0.483127	−	0.575768i	−0.468329	−	0.883554i	$-0.655144\pi$
$503$	10.8354	−	12.9131i	0.483127	−	0.575768i	0.951456	+	0.307786i	$0.0995881\pi$
$504$	18.8782	+	2.76247i	0.840900	+	0.123050i
$505$	9.72330	+	16.8412i	0.432681	+	0.749425i
$506$	−1.00630	+	0.861235i	−0.0447356	+	0.0382866i
$507$	−11.3974	+	4.14833i	−0.506178	+	0.184234i
$508$	−17.6672	+	32.0261i	−0.783857	+	1.42093i
$509$	−5.53279	−	0.975580i	−0.245237	−	0.0432418i	0.0496786	−	0.998765i	$-0.484180\pi$
$509$	−5.53279	−	0.975580i	−0.245237	−	0.0432418i	−0.294915	+	0.955523i	$0.595291\pi$
$510$	21.0533	+	17.3190i	0.932255	+	0.766900i
$511$	−23.7486	−	28.3024i	−1.05057	−	1.25203i
$512$	22.5405	−	1.98182i	0.996157	−	0.0875848i
$513$	4.00113	−	23.1994i	0.176654	−	1.02428i
$514$	2.16883	−	6.14445i	0.0956630	−	0.271020i
$515$	−49.9202	+	41.8880i	−2.19975	+	1.84581i
$516$	−4.50406	+	2.71880i	−0.198280	+	0.119689i
$517$	−0.171457	+	0.972379i	−0.00754066	+	0.0427652i
$518$	−2.29892	+	13.8242i	−0.101009	+	0.607400i
$519$	6.15113	+	16.9001i	0.270005	+	0.741831i
$520$	−0.468445	−	16.0203i	−0.0205427	−	0.702537i
$521$	10.7604	−	6.21252i	0.471422	−	0.272175i	−0.245413	−	0.969419i	$-0.578924\pi$
$521$	10.7604	−	6.21252i	0.471422	−	0.272175i	0.716835	+	0.697243i	$0.245590\pi$
$522$	1.07894	−	0.637024i	0.0472240	−	0.0278818i
$523$	−9.51699	−	7.98570i	−0.416149	−	0.349190i	0.410547	−	0.911839i	$-0.365338\pi$
$523$	−9.51699	−	7.98570i	−0.416149	−	0.349190i	−0.826696	+	0.562649i	$0.809782\pi$
$524$	−5.47480	−	0.855706i	−0.239168	−	0.0373817i
$525$	31.1150	+	17.9643i	1.35797	+	0.784024i
$526$	−0.122332	−	12.5540i	−0.00533392	−	0.547381i
$527$	−3.38268	−	19.1841i	−0.147352	−	0.835673i
$528$	−0.0543445	−	1.39358i	−0.00236504	−	0.0606479i
$529$	−12.4746	−	4.54039i	−0.542375	−	0.197408i
$530$	9.16693	+	24.4422i	0.398186	+	1.06170i
$531$	−8.99795			−0.390478
$532$	−31.2273	−	17.0744i	−1.35388	−	0.740267i
$533$	12.6300			0.547067
$534$	3.81326	+	10.1675i	0.165016	+	0.439990i
$535$	−55.4469	−	20.1810i	−2.39718	−	0.872502i
$536$	−18.1732	+	7.22275i	−0.784961	+	0.311975i
$537$	1.65019	+	9.35867i	0.0712108	+	0.403856i
$538$	−0.0985883	−	10.1174i	−0.00425045	−	0.436192i
$539$	−2.51432	−	1.45165i	−0.108300	−	0.0625268i
$540$	−5.91649	+	37.8536i	−0.254605	+	1.62896i
$541$	1.32512	+	1.11191i	0.0569713	+	0.0478046i	0.670829	−	0.741612i	$-0.265939\pi$
$541$	1.32512	+	1.11191i	0.0569713	+	0.0478046i	−0.613857	+	0.789417i	$0.710383\pi$
$542$	38.8443	−	22.9343i	1.66851	−	0.985113i
$543$	17.6007	−	10.1618i	0.755320	−	0.436084i
$544$	21.0917	+	16.0144i	0.904300	+	0.686613i
$545$	−10.3392	−	28.4067i	−0.442883	−	1.21681i
$546$	−1.75653	+	10.5626i	−0.0751726	+	0.452039i
$547$	−1.45078	+	8.22779i	−0.0620309	+	0.351795i	0.937956	+	0.346753i	$0.112716\pi$
$547$	−1.45078	+	8.22779i	−0.0620309	+	0.351795i	−0.999987	+	0.00504147i	$0.998395\pi$
$548$	10.9984	+	18.2203i	0.469828	+	0.778333i
$549$	4.33250	−	3.63540i	0.184907	−	0.155155i
$550$	−1.07172	+	3.03626i	−0.0456983	+	0.129467i
$551$	−2.30024	+	0.414484i	−0.0979934	+	0.0176576i
$552$	−8.71429	+	5.37678i	−0.370905	+	0.228851i
$553$	0.522568	+	0.622772i	0.0222218	+	0.0264829i
$554$	11.2770	+	9.27678i	0.479114	+	0.394133i
$555$	−9.84293	−	1.73557i	−0.417809	−	0.0736710i
$556$	−31.9658	−	17.6340i	−1.35565	−	0.747847i
$557$	−29.6978	+	10.8091i	−1.25834	+	0.457997i	−0.883210	−	0.468977i	$-0.844623\pi$
$557$	−29.6978	+	10.8091i	−1.25834	+	0.457997i	−0.375126	+	0.926974i	$0.622400\pi$
$558$	7.38717	−	6.32225i	0.312724	−	0.267642i
$559$	1.80997	+	3.13496i	0.0765535	+	0.132594i
$560$	51.2520	+	26.9842i	2.16579	+	1.14029i
$561$	1.04919	−	1.25038i	0.0442968	−	0.0527909i
$562$	34.9198	−	6.50876i	1.47300	−	0.274556i
$563$	−6.50555	+	11.2679i	−0.274176	+	0.474887i	−0.969927	−	0.243396i	$-0.921739\pi$
$563$	−6.50555	+	11.2679i	−0.274176	+	0.474887i	0.695751	+	0.718283i	$0.255072\pi$
$564$	−2.47043	+	7.22235i	−0.104024	+	0.304116i
$565$	37.2155	−	6.56210i	1.56567	−	0.276070i
$566$	−18.0251	−	10.1739i	−0.757652	−	0.427642i
$567$	1.83336	−	5.03711i	0.0769938	−	0.211539i
$568$	11.4924	+	3.80634i	0.482211	+	0.159711i
$569$		−	36.1864i		−	1.51701i	−0.651665	−	0.758507i	$-0.725929\pi$
$569$		−	36.1864i		−	1.51701i	0.651665	−	0.758507i	$-0.274071\pi$
$570$	12.3938	−	22.1515i	0.519120	−	0.927825i
$571$			45.6728i			1.91135i	0.294430	+	0.955673i	$0.404870\pi$
$571$			45.6728i			1.91135i	−0.294430	+	0.955673i	$0.595130\pi$
$572$	−0.959423	+	0.0186999i	−0.0401155	+	0.000781880i
$573$	2.15507	−	5.92099i	0.0900292	−	0.247353i
$574$	−22.4360	+	39.7498i	−0.936461	+	1.65913i
$575$	23.2813	−	4.10512i	0.970896	−	0.171195i
$576$	−1.53079	+	13.1295i	−0.0637830	+	0.547061i
$577$	7.41053	−	12.8354i	0.308504	−	0.534345i	−0.669531	−	0.742784i	$-0.733505\pi$
$577$	7.41053	−	12.8354i	0.308504	−	0.534345i	0.978035	+	0.208439i	$0.0668383\pi$
$578$	1.27399	+	6.83501i	0.0529910	+	0.284299i
$579$	6.55269	−	7.80919i	0.272320	−	0.324539i
$580$	3.73244	−	0.733398i	0.154981	−	0.0304527i
$581$	−30.4137	−	52.6781i	−1.26177	−	2.18546i
$582$	6.47714	+	7.56815i	0.268486	+	0.313710i
$583$	1.46873	−	0.534573i	0.0608284	−	0.0221397i
$584$	19.1191	−	17.0195i	0.791155	−	0.704271i
$585$	9.22043	+	1.62581i	0.381218	+	0.0672190i
$586$	−26.4527	+	32.1564i	−1.09275	+	1.32837i
$587$	27.2045	+	32.4211i	1.12285	+	1.33816i	0.934460	+	0.356067i	$0.115883\pi$
$587$	27.2045	+	32.4211i	1.12285	+	1.33816i	0.188391	+	0.982094i	$0.439673\pi$
$588$	−17.4714	−	14.0893i	−0.720509	−	0.581033i
$589$	−17.0206	+	6.26728i	−0.701320	+	0.258239i
$590$	−25.7589	−	9.09222i	−1.06048	−	0.374321i
$591$	−2.65352	+	2.22657i	−0.109151	+	0.0915888i
$592$	−9.62009	−	1.31211i	−0.395383	−	0.0539275i
$593$	−4.25553	+	24.1343i	−0.174754	+	0.991077i	0.763674	+	0.645602i	$0.223393\pi$
$593$	−4.25553	+	24.1343i	−0.174754	+	0.991077i	−0.938428	+	0.345475i	$0.887718\pi$
$594$	2.26288	+	0.376310i	0.0928471	+	0.0154402i
$595$	23.1855	+	63.7016i	0.950513	+	2.61151i
$596$	28.0585	−	10.8362i	1.14932	−	0.443868i
$597$	−0.867774	+	0.501010i	−0.0355156	+	0.0205050i
$598$	3.58204	+	6.06697i	0.146480	+	0.248097i
$599$	−3.72253	−	3.12357i	−0.152098	−	0.127626i	0.563563	−	0.826073i	$-0.309430\pi$
$599$	−3.72253	−	3.12357i	−0.152098	−	0.127626i	−0.715661	+	0.698447i	$0.753875\pi$
$600$	−11.8105	+	21.9115i	−0.482163	+	0.894535i
$601$	13.4093	+	7.74187i	0.546978	+	0.315798i	0.747902	−	0.663809i	$-0.231061\pi$
$601$	13.4093	+	7.74187i	0.546978	+	0.315798i	−0.200925	+	0.979607i	$0.564395\pi$
$602$	−13.0817	+	0.127474i	−0.533171	+	0.00519545i
$603$	−1.98377	−	11.2505i	−0.0807853	−	0.458156i
$604$	22.7141	−	19.8263i	0.924222	−	0.806721i
$605$	−36.3628	−	13.2350i	−1.47836	−	0.538078i
$606$	8.42797	−	3.16087i	0.342363	−	0.128401i
$607$	18.2620			0.741230			0.370615	−	0.928787i	$-0.379147\pi$
$607$	18.2620			0.741230			0.370615	+	0.928787i	$0.379147\pi$
$608$	11.1920	−	21.9713i	0.453895	−	0.891055i
$609$	−2.54131			−0.102979
$610$	16.0764	−	6.02935i	0.650913	−	0.244121i
$611$	4.93539	+	1.79633i	0.199664	+	0.0726719i
$612$	−11.6550	+	10.1733i	−0.471126	+	0.411229i
$613$	7.49765	+	42.5213i	0.302827	+	1.71742i	0.633560	+	0.773694i	$0.281593\pi$
$613$	7.49765	+	42.5213i	0.302827	+	1.71742i	−0.330732	+	0.943725i	$0.607296\pi$
$614$	22.3845	−	0.218125i	0.903366	−	0.00880279i
$615$	−28.1922	−	16.2768i	−1.13682	−	0.656343i
$616$	1.64547	−	3.05276i	0.0662979	−	0.122999i
$617$	−2.81302	−	2.36041i	−0.113248	−	0.0950264i	0.584405	−	0.811462i	$-0.301328\pi$
$617$	−2.81302	−	2.36041i	−0.113248	−	0.0950264i	−0.697653	+	0.716436i	$0.745772\pi$
$618$	15.3355	+	25.9741i	0.616885	+	1.04483i
$619$	−13.5511	+	7.82373i	−0.544665	+	0.314462i	−0.746967	−	0.664861i	$-0.768491\pi$
$619$	−13.5511	+	7.82373i	−0.544665	+	0.314462i	0.202303	+	0.979323i	$0.435158\pi$
$620$	27.5361	−	10.6345i	1.10588	−	0.427090i
$621$	−5.76044	−	15.8267i	−0.231159	−	0.635103i
$622$	−18.3422	−	3.05024i	−0.735454	−	0.122304i
$623$	−4.68896	+	26.5924i	−0.187859	+	1.06540i
$624$	−7.35040	−	1.00254i	−0.294252	−	0.0401338i
$625$	−4.16373	+	3.49379i	−0.166549	+	0.139751i
$626$	26.1466	+	9.22906i	1.04503	+	0.368867i
$627$	−1.31900	−	0.754952i	−0.0526758	−	0.0301499i
$628$	−25.2491	−	20.3614i	−1.00755	−	0.812509i
$629$	−7.30421	−	8.70481i	−0.291238	−	0.347084i
$630$	−21.4960	+	26.1309i	−0.856423	+	1.04108i
$631$	38.6875	+	6.82166i	1.54013	+	0.271566i	0.878307	−	0.478097i	$-0.158673\pi$
$631$	38.6875	+	6.82166i	1.54013	+	0.271566i	0.661820	+	0.749663i	$0.269784\pi$
$632$	−0.420700	+	0.374500i	−0.0167346	+	0.0148968i
$633$	−9.67466	+	3.52129i	−0.384533	+	0.139959i
$634$	−5.55780	−	6.49396i	−0.220728	−	0.257908i
$635$	−32.4332	−	56.1760i	−1.28707	−	2.22928i
$636$	11.8563	−	2.32968i	0.470134	−	0.0923780i
$637$	−9.92680	+	11.8303i	−0.393314	+	0.468733i
$638$	−0.0417317	−	0.223892i	−0.00165217	−	0.00886398i
$639$	−3.53612	+	6.12474i	−0.139887	+	0.242291i
$640$	−17.6493	+	36.0395i	−0.697649	+	1.42459i
$641$	−34.0089	+	5.99669i	−1.34327	+	0.236855i	−0.798635	−	0.601816i	$-0.794444\pi$
$641$	−34.0089	+	5.99669i	−1.34327	+	0.236855i	−0.544638	+	0.838671i	$0.683333\pi$
$642$	−13.4247	+	23.7846i	−0.529833	+	0.938703i
$643$	8.89830	−	24.4479i	0.350915	−	0.964130i	−0.631162	−	0.775651i	$-0.717422\pi$
$643$	8.89830	−	24.4479i	0.350915	−	0.964130i	0.982077	−	0.188479i	$-0.0603559\pi$
$644$	−25.4574	+	0.496183i	−1.00316	+	0.0195524i
$645$		−	9.33028i		−	0.367380i
$646$	26.9826	−	10.2351i	1.06162	−	0.402697i
$647$		−	29.4173i		−	1.15651i	−0.815855	−	0.578256i	$-0.803733\pi$
$647$		−	29.4173i		−	1.15651i	0.815855	−	0.578256i	$-0.196267\pi$
$648$	3.52543	+	1.16764i	0.138492	+	0.0458691i
$649$	−0.559387	+	1.53690i	−0.0219579	+	0.0603288i
$650$	14.9154	+	8.41869i	0.585029	+	0.330208i
$651$	−19.4214	+	3.42452i	−0.761186	+	0.134218i
$652$	4.07785	−	11.9217i	0.159701	−	0.466890i
$653$	5.77812	−	10.0080i	0.226115	−	0.391643i	−0.730538	−	0.682872i	$-0.760731\pi$
$653$	5.77812	−	10.0080i	0.226115	−	0.391643i	0.956654	+	0.291229i	$0.0940640\pi$
$654$	−13.7555	+	2.56391i	−0.537883	+	0.100257i
$655$	6.31686	−	7.52814i	0.246820	−	0.294149i
$656$	−27.9819	−	14.7325i	−1.09251	−	0.575207i
$657$	7.47656	+	12.9498i	0.291688	+	0.505219i
$658$	−14.4208	+	12.3419i	−0.562179	+	0.481137i
$659$	7.45091	−	2.71191i	0.290246	−	0.105641i	−0.192794	−	0.981239i	$-0.561755\pi$
$659$	7.45091	−	2.71191i	0.290246	−	0.105641i	0.483040	+	0.875598i	$0.339533\pi$
$660$	2.16568	+	1.19470i	0.0842991	+	0.0465038i
$661$	8.97455	+	1.58246i	0.349070	+	0.0615504i	0.345434	−	0.938443i	$-0.387732\pi$
$661$	8.97455	+	1.58246i	0.349070	+	0.0615504i	0.00363550	+	0.999993i	$0.498843\pi$
$662$	4.00941	+	3.29826i	0.155830	+	0.128190i
$663$	−5.58091	−	6.65107i	−0.216745	−	0.258306i
$664$	35.8648	−	22.1289i	1.39183	−	0.858766i
$665$	54.5438	−	31.7639i	2.11512	−	1.23175i
$666$	1.88786	−	5.34845i	0.0731532	−	0.207248i
$667$	−1.28094	+	1.07483i	−0.0495981	+	0.0416178i
$668$	−5.55065	−	9.19540i	−0.214761	−	0.355781i
$669$	2.41674	−	13.7060i	0.0934366	−	0.529905i
$670$	5.68934	−	34.2119i	0.219798	−	1.32172i
$671$	−0.351604	−	0.966024i	−0.0135735	−	0.0372929i
$672$	16.2125	−	21.3526i	0.625412	−	0.823696i
$673$	−12.1210	+	6.99808i	−0.467231	+	0.269756i	−0.715080	−	0.699043i	$-0.753610\pi$
$673$	−12.1210	+	6.99808i	−0.467231	+	0.269756i	0.247849	+	0.968799i	$0.420276\pi$
$674$	21.9095	−	12.9357i	0.843921	−	0.498265i
$675$	−31.3642	−	26.3177i	−1.20721	−	1.01297i
$676$	3.22679	−	20.6450i	0.124107	−	0.794037i
$677$	38.4118	+	22.1771i	1.47629	+	0.852334i	0.999642	−	0.0267620i	$-0.00851964\pi$
$677$	38.4118	+	22.1771i	1.47629	+	0.852334i	0.476644	+	0.879096i	$0.341853\pi$
$678$	−0.170438	−	17.4908i	−0.00654563	−	0.671730i
$679$	4.30138	+	24.3943i	0.165072	+	0.936168i
$680$	−43.6452	+	17.3464i	−1.67372	+	0.665203i
$681$	−3.92065	−	1.42700i	−0.150240	−	0.0546827i
$682$	−0.620630	−	1.65482i	−0.0237652	−	0.0633662i
$683$	−31.4233			−1.20238			−0.601190	−	0.799106i	$-0.705307\pi$
$683$	−31.4233			−1.20238			−0.601190	+	0.799106i	$0.705307\pi$
$684$	11.2465	+	9.00012i	0.430022	+	0.344128i
$685$	−37.7439			−1.44212
$686$	−5.40685	−	14.4165i	−0.206435	−	0.550426i
$687$	−9.25442	−	3.36833i	−0.353078	−	0.128510i
$688$	−0.353181	−	9.05678i	−0.0134649	−	0.345287i
$689$	−1.44370	−	8.18762i	−0.0550005	−	0.311923i
$690$	−0.176947	−	18.1587i	−0.00673624	−	0.691291i
$691$	−1.99231	−	1.15026i	−0.0757911	−	0.0437580i	0.461626	−	0.887075i	$-0.347266\pi$
$691$	−1.99231	−	1.15026i	−0.0757911	−	0.0437580i	−0.537417	+	0.843317i	$0.680600\pi$
$692$	−30.6122	−	4.78467i	−1.16370	−	0.181886i
$693$	1.55194	+	1.30223i	0.0589533	+	0.0494677i
$694$	19.8329	−	11.7096i	0.752845	−	0.444492i
$695$	56.0702	−	32.3721i	2.12686	−	1.22795i
$696$	−0.0514610	−	1.75991i	−0.00195063	−	0.0667092i
$697$	−12.6585	−	34.7790i	−0.479475	−	1.31735i
$698$	−2.74689	+	16.5180i	−0.103971	+	0.625215i
$699$	4.20696	−	23.8589i	0.159122	−	0.902425i
$700$	−52.9914	+	31.9874i	−2.00289	+	1.20901i
$701$	21.6513	−	18.1676i	0.817757	−	0.686180i	−0.134689	−	0.990888i	$-0.543003\pi$
$701$	21.6513	−	18.1676i	0.817757	−	0.686180i	0.952446	+	0.304708i	$0.0985590\pi$
$702$	4.06146	−	11.5064i	0.153290	−	0.434281i
$703$	−6.77049	+	8.13041i	−0.255354	+	0.306644i
$704$	2.14742	+	1.07770i	0.0809340	+	0.0406175i
$705$	−8.70156	−	10.3701i	−0.327720	−	0.390561i
$706$	−28.1873	−	23.1877i	−1.06084	−	0.872681i
$707$	22.0428	+	3.88675i	0.829006	+	0.146176i
$708$	−6.10738	+	11.0711i	−0.229529	+	0.416077i
$709$	22.1340	−	8.05611i	0.831259	−	0.302553i	0.108883	−	0.994055i	$-0.465272\pi$
$709$	22.1340	−	8.05611i	0.831259	−	0.302553i	0.722375	+	0.691501i	$0.243050\pi$
$710$	−16.3119	+	13.9604i	−0.612176	+	0.523926i
$711$	−0.164516	−	0.284949i	−0.00616981	−	0.0106864i
$712$	−18.5107	−	2.70871i	−0.693719	−	0.101513i
$713$	−8.34092	+	9.94032i	−0.312370	+	0.372268i
$714$	30.8465	−	5.74954i	1.15440	−	0.215171i
$715$	0.850917	−	1.47383i	0.0318225	−	0.0551182i
$716$	−15.4906	−	5.29862i	−0.578912	−	0.198019i
$717$	30.2452	−	5.33305i	1.12953	−	0.199166i
$718$	5.24323	+	2.95944i	0.195675	+	0.110445i
$719$	−6.03096	+	16.5699i	−0.224917	+	0.617954i	−0.999902	−	0.0140260i	$-0.995535\pi$
$719$	−6.03096	+	16.5699i	−0.224917	+	0.617954i	0.774985	+	0.631980i	$0.217757\pi$
$720$	−18.5315	−	14.3573i	−0.690628	−	0.535065i
$721$			75.0058i			2.79336i
$722$	−13.8341	−	23.0351i	−0.514852	−	0.857279i
$723$			18.2208i			0.677638i
$724$	0.682305	+	35.0067i	0.0253577	+	1.30101i
$725$	−1.39028	+	3.81976i	−0.0516336	+	0.141862i
$726$	−8.80411	+	15.5982i	−0.326751	+	0.578904i
$727$	−4.39466	+	0.774896i	−0.162989	+	0.0287393i	−0.254547	−	0.967060i	$-0.581926\pi$
$727$	−4.39466	+	0.774896i	−0.162989	+	0.0287393i	0.0915582	+	0.995800i	$0.470815\pi$
$728$	−14.4719	−	11.4395i	−0.536363	−	0.423975i
$729$	−10.4896	+	18.1685i	−0.388504	+	0.672909i
$730$	8.31808	+	44.6269i	0.307866	+	1.65171i
$731$	6.81860	−	8.12609i	0.252195	−	0.300554i
$732$	−1.53230	−	7.79824i	−0.0566354	−	0.288231i
$733$	18.5155	+	32.0698i	0.683886	+	1.18453i	0.973785	+	0.227469i	$0.0730450\pi$
$733$	18.5155	+	32.0698i	0.683886	+	1.18453i	−0.289899	+	0.957057i	$0.593622\pi$
$734$	−2.38515	−	2.78690i	−0.0880375	−	0.102867i
$735$	37.4043	−	13.6141i	1.37968	−	0.502162i
$736$	−0.859124	−	17.6197i	−0.0316677	−	0.649472i
$737$	−2.04498	−	0.360585i	−0.0753279	−	0.0132823i
$738$	11.7361	−	14.2666i	0.432013	−	0.525161i
$739$	−33.1809	−	39.5434i	−1.22058	−	1.45463i	−0.850785	−	0.525513i	$-0.823873\pi$
$739$	−33.1809	−	39.5434i	−1.22058	−	1.45463i	−0.369792	−	0.929114i	$-0.620571\pi$
$740$	10.8090	−	13.4036i	0.397346	−	0.492728i
$741$	−5.17311	+	6.21219i	−0.190039	+	0.228210i
$742$	28.3331	+	10.0008i	1.04014	+	0.367142i
$743$	−1.13874	+	0.955514i	−0.0417762	+	0.0350544i	−0.663437	−	0.748232i	$-0.730903\pi$
$743$	−1.13874	+	0.955514i	−0.0417762	+	0.0350544i	0.621660	+	0.783287i	$0.286458\pi$
$744$	−2.76483	−	13.3804i	−0.101364	−	0.490549i
$745$	−9.26290	+	52.5325i	−0.339366	+	1.92464i
$746$	52.5487	+	8.73868i	1.92394	+	0.319946i
$747$	8.42002	+	23.1338i	0.308073	+	0.846423i
$748$	1.01308	+	2.62320i	0.0370419	+	0.0959136i
$749$	−58.8159	+	33.9574i	−2.14909	+	1.24078i
$750$	−7.64083	−	12.9414i	−0.279004	−	0.472554i
$751$	24.8869	+	20.8826i	0.908134	+	0.762015i	0.971763	−	0.235958i	$-0.0758229\pi$
$751$	24.8869	+	20.8826i	0.908134	+	0.762015i	−0.0636288	+	0.997974i	$0.520267\pi$
$752$	−8.83903	−	9.73675i	−0.322326	−	0.355063i
$753$	−2.03341	−	1.17399i	−0.0741016	−	0.0427826i
$754$	−1.21139	+	0.0118044i	−0.0441164	+	0.000429889i
$755$	9.28494	+	52.6575i	0.337914	+	1.91640i
$756$	28.9987	+	33.2224i	1.05467	+	1.20829i
$757$	−14.9991	−	5.45921i	−0.545150	−	0.198418i	0.0547403	−	0.998501i	$-0.482567\pi$
$757$	−14.9991	−	5.45921i	−0.545150	−	0.198418i	−0.599890	+	0.800082i	$0.704789\pi$
$758$	23.4159	−	8.78202i	0.850505	−	0.318978i
$759$	−1.08728			−0.0394659
$760$	23.1016	+	37.1295i	0.837984	+	1.34683i
$761$	37.3192			1.35282			0.676410	−	0.736526i	$-0.263535\pi$
$761$	37.3192			1.35282			0.676410	+	0.736526i	$0.263535\pi$
$762$	−28.1125	+	10.5435i	−1.01841	+	0.381949i
$763$	−32.6959	−	11.9003i	−1.18367	−	0.430821i
$764$	7.13838	+	8.17809i	0.258257	+	0.295873i
$765$	−4.76428	−	27.0196i	−0.172253	−	0.976894i
$766$	−27.9137	+	0.272003i	−1.00856	+	0.00982788i
$767$	7.53430	+	4.34993i	0.272048	+	0.157067i
$768$	15.1154	+	10.7951i	0.545432	+	0.389536i
$769$	0.934238	+	0.783919i	0.0336895	+	0.0282688i	0.659477	−	0.751725i	$-0.270778\pi$
$769$	0.934238	+	0.783919i	0.0336895	+	0.0282688i	−0.625787	+	0.779994i	$0.715222\pi$
$770$	3.12694	+	5.29617i	0.112687	+	0.190861i
$771$	4.63226	−	2.67443i	0.166827	−	0.0963174i
$772$	6.32717	+	16.3831i	0.227720	+	0.589641i
$773$	14.4258	+	39.6345i	0.518859	+	1.42555i	0.871778	+	0.489901i	$0.162967\pi$
$773$	14.4258	+	39.6345i	0.518859	+	1.42555i	−0.352919	+	0.935654i	$0.614811\pi$
$774$	5.22305	+	0.868576i	0.187738	+	0.0312203i
$775$	−5.47763	+	31.0652i	−0.196762	+	1.11589i
$776$	−16.8065	+	3.47277i	−0.603317	+	0.124665i
$777$	−8.81250	+	7.39457i	−0.316147	+	0.265279i
$778$	−27.3794	−	9.66423i	−0.981600	−	0.346479i
$779$	−29.7791	+	17.3420i	−1.06695	+	0.621342i
$780$	8.25879	−	10.2413i	0.295712	−	0.366697i
$781$	0.826308	+	0.984756i	0.0295676	+	0.0352373i
$782$	13.1163	−	15.9444i	0.469039	−	0.570171i
$783$	2.85200	+	0.502885i	0.101922	+	0.0179717i
$784$	35.7925	−	14.6308i	1.27830	−	0.522530i
$785$	54.0555	−	19.6746i	1.92932	−	0.702217i
$786$	−2.95769	−	3.45588i	−0.105497	−	0.123267i
$787$	18.2059	+	31.5336i	0.648972	+	1.12405i	0.983369	+	0.181620i	$0.0581340\pi$
$787$	18.2059	+	31.5336i	0.648972	+	1.12405i	−0.334397	+	0.942432i	$0.608533\pi$
$788$	−1.15060	−	5.85566i	−0.0409883	−	0.208599i
$789$	6.62449	−	7.89476i	0.235838	−	0.281061i
$790$	−0.183032	−	0.981978i	−0.00651200	−	0.0349372i
$791$	21.7478	−	37.6683i	0.773262	−	1.33933i
$792$	−0.870397	+	1.10112i	−0.0309282	+	0.0391266i
$793$	−5.38523	+	0.949562i	−0.191235	+	0.0337199i
$794$	−3.63926	+	6.44767i	−0.129152	+	0.228819i
$795$	−7.32912	+	20.1366i	−0.259937	+	0.714172i
$796$	−0.0336399	−	1.72594i	−0.00119233	−	0.0611745i
$797$		−	13.4658i		−	0.476984i	−0.971145	−	0.238492i	$-0.923347\pi$
$797$		−	13.4658i		−	0.476984i	0.971145	−	0.238492i	$-0.0766530\pi$
$798$	−10.3618	−	27.3164i	−0.366803	−	0.966991i
$799$		−	15.3908i		−	0.544489i
$800$	−23.2250	−	36.0499i	−0.821128	−	1.27456i
$801$	3.73783	−	10.2696i	0.132070	−	0.362859i
$802$	−31.6326	−	17.8544i	−1.11698	−	0.630460i
$803$	2.67670	−	0.471975i	0.0944588	−	0.0166556i
$804$	−15.1891	−	5.19548i	−0.535678	−	0.183230i
$805$	22.5783	−	39.1067i	0.795780	−	1.37833i
$806$	−9.24193	+	1.72262i	−0.325533	+	0.0606766i
$807$	5.33874	−	6.36246i	0.187932	−	0.223969i
$808$	−2.24529	+	15.3438i	−0.0789890	+	0.539794i
$809$	−9.76161	−	16.9076i	−0.343200	−	0.594440i	0.641825	−	0.766851i	$-0.278178\pi$
$809$	−9.76161	−	16.9076i	−0.343200	−	0.594440i	−0.985025	+	0.172411i	$0.944844\pi$
$810$	−5.00387	+	4.28252i	−0.175818	+	0.150472i
$811$	28.8297	−	10.4931i	1.01235	−	0.368464i	0.218013	−	0.975946i	$-0.430042\pi$
$811$	28.8297	−	10.4931i	1.01235	−	0.368464i	0.794334	+	0.607482i	$0.207820\pi$
$812$	2.11477	−	3.83353i	0.0742140	−	0.134531i
$813$	36.4671	+	6.43013i	1.27896	+	0.225514i
$814$	−0.796182	−	0.654963i	−0.0279062	−	0.0229564i
$815$	14.3634	+	17.1176i	0.503127	+	0.599604i
$816$	4.60631	+	21.2454i	0.161253	+	0.743739i
$817$	−8.57208	−	4.90637i	−0.299899	−	0.171652i
$818$	−11.4285	+	32.3778i	−0.399588	+	1.13206i
$819$	8.25517	−	6.92691i	0.288459	−	0.242046i
$820$	48.0137	−	28.9827i	1.67671	−	1.01212i
$821$	−0.782765	+	4.43928i	−0.0273187	+	0.154932i	−0.995416	−	0.0956441i	$-0.969509\pi$
$821$	−0.782765	+	4.43928i	−0.0273187	+	0.154932i	0.968097	+	0.250576i	$0.0806200\pi$
$822$	−2.86592	+	17.2338i	−0.0999605	+	0.601097i
$823$	−12.8016	−	35.1722i	−0.446237	−	1.22603i	−0.935325	−	0.353791i	$-0.884892\pi$
$823$	−12.8016	−	35.1722i	−0.446237	−	1.22603i	0.489088	−	0.872235i	$-0.337330\pi$
$824$	−51.9431	+	1.51885i	−1.80952	+	0.0529117i
$825$	−2.28902	+	1.32156i	−0.0796933	+	0.0460110i
$826$	−27.0743	+	15.9851i	−0.942034	+	0.556192i
$827$	−9.25002	−	7.76169i	−0.321655	−	0.269900i	0.467635	−	0.883922i	$-0.345106\pi$
$827$	−9.25002	−	7.76169i	−0.321655	−	0.269900i	−0.789289	+	0.614022i	$0.789551\pi$
$828$	10.1816	+	1.59138i	0.353836	+	0.0553043i
$829$	−30.8649	−	17.8198i	−1.07198	−	0.618909i	−0.143259	−	0.989685i	$-0.545758\pi$
$829$	−30.8649	−	17.8198i	−1.07198	−	0.618909i	−0.928722	+	0.370776i	$0.879092\pi$
$830$	0.728247	+	74.7346i	0.0252778	+	2.59408i
$831$	2.08150	+	11.8047i	0.0722063	+	0.409502i
$832$	7.62903	−	10.2537i	0.264489	−	0.355483i
$833$	42.5260	+	15.4782i	1.47344	+	0.536288i
$834$	−10.5236	−	28.0596i	−0.364402	−	0.971624i
$835$	19.0485			0.659202
$836$	2.23645	−	1.36145i	0.0773493	−	0.0470869i
$837$	22.4735			0.776798
$838$	−1.74472	−	4.65202i	−0.0602702	−	0.160701i
$839$	−35.3858	−	12.8794i	−1.22165	−	0.444646i	−0.350922	−	0.936405i	$-0.614132\pi$
$839$	−35.3858	−	12.8794i	−1.22165	−	0.444646i	−0.870731	+	0.491759i	$0.836354\pi$
$840$	17.5610	+	44.1851i	0.605911	+	1.52453i
$841$	4.98587	+	28.2763i	0.171927	+	0.975044i
$842$	−0.0194611	−	1.99715i	−0.000670675	−	0.0688265i
$843$	25.2523	+	14.5794i	0.869734	+	0.502141i
$844$	2.73904	−	17.5244i	0.0942817	−	0.603213i
$845$	28.3879	+	23.8203i	0.976574	+	0.819443i
$846$	6.61518	−	3.90571i	0.227435	−	0.134281i
$847$	−38.5722	+	22.2697i	−1.32536	+	0.765194i
$848$	−6.35205	+	19.8238i	−0.218130	+	0.680751i
$849$	−5.81119	−	15.9661i	−0.199440	−	0.547956i
$850$	8.23332	−	49.5098i	0.282400	−	1.69817i
$851$	−1.31441	+	7.45440i	−0.0450575	+	0.255534i
$852$	5.13573	+	8.50803i	0.175947	+	0.291480i
$853$	−19.0885	+	16.0172i	−0.653578	+	0.548417i	−0.908154	−	0.418636i	$-0.862508\pi$
$853$	−19.0885	+	16.0172i	−0.653578	+	0.548417i	0.254576	+	0.967053i	$0.418064\pi$
$854$	6.57784	−	18.6355i	0.225089	−	0.637693i
$855$	−23.9723	+	8.82704i	−0.819836	+	0.301879i
$856$	−24.7072	−	40.0436i	−0.844475	−	1.36866i
$857$	−17.9448	−	21.3858i	−0.612983	−	0.730525i	0.366864	−	0.930275i	$-0.380431\pi$
$857$	−17.9448	−	21.3858i	−0.612983	−	0.730525i	−0.979847	+	0.199750i	$0.935987\pi$
$858$	−0.608337	−	0.500436i	−0.0207683	−	0.0170846i
$859$	−19.9915	−	3.52504i	−0.682100	−	0.120273i	−0.178147	−	0.984004i	$-0.557010\pi$
$859$	−19.9915	−	3.52504i	−0.682100	−	0.120273i	−0.503953	+	0.863731i	$0.668122\pi$
$860$	14.0746	+	7.76428i	0.479940	+	0.264760i
$861$	−35.2092	+	12.8151i	−1.19993	+	0.436738i
$862$	−33.8482	+	28.9687i	−1.15287	+	0.986678i
$863$	−5.87734	−	10.1799i	−0.200067	−	0.346526i	0.748483	−	0.663154i	$-0.230783\pi$
$863$	−5.87734	−	10.1799i	−0.200067	−	0.346526i	−0.948550	+	0.316628i	$0.897449\pi$
$864$	−22.4200	+	20.7549i	−0.762743	+	0.706098i
$865$	35.3206	−	42.0934i	1.20094	−	1.43122i
$866$	−45.6714	+	8.51276i	−1.55198	+	0.289275i
$867$	−2.85369	+	4.94274i	−0.0969165	+	0.167864i
$868$	10.9959	−	32.1467i	0.373224	−	1.09113i
$869$	−0.0588987	+	0.0103854i	−0.00199800	+	0.000352301i
$870$	2.71924	+	1.53482i	0.0921907	+	0.0520353i
$871$	−3.77781	+	10.3795i	−0.128006	+	0.351695i
$872$	7.57915	−	22.8836i	0.256662	−	0.774936i
$873$		−	10.0253i		−	0.339306i
$874$	−16.7761	−	9.38628i	−0.567462	−	0.317496i
$875$		−	37.3712i		−	1.26338i
$876$	21.0081	−	0.409464i	0.709799	−	0.0138345i
$877$	1.10391	−	3.03297i	0.0372764	−	0.102416i	−0.919658	−	0.392720i	$-0.871534\pi$
$877$	1.10391	−	3.03297i	0.0372764	−	0.102416i	0.956935	+	0.290304i	$0.0937564\pi$
$878$	1.09825	−	1.94576i	0.0370640	−	0.0656662i
$879$	−33.6612	+	5.93539i	−1.13537	+	0.200196i
$880$	−3.60438	+	2.27272i	−0.121504	+	0.0766133i
$881$	−1.25716	+	2.17746i	−0.0423546	+	0.0733604i	−0.886426	−	0.462871i	$-0.846819\pi$
$881$	−1.25716	+	2.17746i	−0.0423546	+	0.0733604i	0.844071	+	0.536232i	$0.180153\pi$
$882$	4.13903	+	22.2061i	0.139368	+	0.747718i
$883$	32.5538	−	38.7961i	1.09552	−	1.30559i	0.146910	−	0.989150i	$-0.453067\pi$
$883$	32.5538	−	38.7961i	1.09552	−	1.30559i	0.948612	−	0.316442i	$-0.102488\pi$
$884$	14.6772	−	2.88398i	0.493649	−	0.0969986i
$885$	−11.2118	−	19.4194i	−0.376881	−	0.652778i
$886$	0.891363	+	1.04150i	0.0299459	+	0.0349900i
$887$	−3.33576	+	1.21412i	−0.112004	+	0.0407661i	−0.397414	−	0.917639i	$-0.630092\pi$
$887$	−3.33576	+	1.21412i	−0.112004	+	0.0407661i	0.285410	+	0.958405i	$0.407870\pi$
$888$	−5.29934	−	5.95310i	−0.177834	−	0.199773i
$889$	−73.5265	−	12.9647i	−2.46600	−	0.434822i
$890$	21.0777	−	25.6223i	0.706525	−	0.858862i
$891$	0.253479	+	0.302085i	0.00849187	+	0.0101202i
$892$	18.6642	+	15.0512i	0.624924	+	0.503952i
$893$	−14.1032	+	2.54128i	−0.471945	+	0.0850406i
$894$	23.2829	+	8.21825i	0.778696	+	0.274859i
$895$	22.2420	−	18.6633i	0.743468	−	0.623844i
$896$	18.7187	+	42.2252i	0.625349	+	1.41064i
$897$	−1.00430	+	5.69567i	−0.0335326	+	0.190173i
$898$	30.1508	+	5.01397i	1.00614	+	0.167318i
$899$	−0.763120	−	2.09665i	−0.0254515	−	0.0699273i
$900$	23.3693	−	9.02524i	0.778977	−	0.300841i
$901$	−21.0991	+	12.1816i	−0.702913	+	0.405827i
$902$	−1.70721	−	2.89153i	−0.0568438	−	0.0962774i
$903$	−8.22662	−	6.90295i	−0.273765	−	0.229716i
$904$	26.5264	+	14.2980i	0.882257	+	0.475545i
$905$	−53.7760	−	31.0476i	−1.78757	−	1.03206i
$906$	24.7483	−	0.241159i	0.822208	−	0.00801195i
$907$	3.97715	+	22.5555i	0.132059	+	0.748944i	0.976863	+	0.213867i	$0.0686060\pi$
$907$	3.97715	+	22.5555i	0.132059	+	0.748944i	−0.844804	+	0.535076i	$0.820283\pi$
$908$	5.41521	−	4.72675i	0.179710	−	0.156863i
$909$	−8.51263	−	3.09834i	−0.282346	−	0.102766i
$910$	30.6320	−	11.4884i	1.01544	−	0.380836i
$911$	−21.7119			−0.719347			−0.359673	−	0.933078i	$-0.617112\pi$
$911$	−21.7119			−0.719347			−0.359673	+	0.933078i	$0.617112\pi$
$912$	18.7074	−	7.72889i	0.619463	−	0.255929i
$913$	4.47485			0.148096
$914$	19.7055	−	7.39044i	0.651799	−	0.244454i
$915$	13.2444	+	4.82058i	0.437847	+	0.159363i
$916$	12.7822	−	11.1572i	0.422337	−	0.368643i
$917$	−1.96416	−	11.1393i	−0.0648622	−	0.367852i
$918$	−35.7555	+	0.348417i	−1.18011	+	0.0114995i
$919$	20.5068	+	11.8396i	0.676457	+	0.390552i	0.798519	−	0.601970i	$-0.205617\pi$
$919$	20.5068	+	11.8396i	0.676457	+	0.390552i	−0.122062	+	0.992522i	$0.538951\pi$
$920$	27.5394	+	14.8440i	0.907948	+	0.489393i
$921$	14.0768	+	11.8118i	0.463847	+	0.389213i
$922$	−2.23017	−	3.77728i	−0.0734467	−	0.124398i
$923$	5.92183	−	3.41897i	0.194920	−	0.112537i
$924$	2.65565	−	1.02561i	0.0873645	−	0.0337402i
$925$	6.29345	+	17.2911i	0.206927	+	0.568529i
$926$	16.7354	+	2.78305i	0.549961	+	0.0914567i
$927$	5.27141	−	29.8957i	0.173136	−	0.981903i
$928$	2.69762	+	1.38690i	0.0885538	+	0.0455271i
$929$	−14.5821	+	12.2359i	−0.478425	+	0.401446i	−0.849856	−	0.527014i	$-0.823311\pi$
$929$	−14.5821	+	12.2359i	−0.478425	+	0.401446i	0.371432	+	0.928460i	$0.378867\pi$
$930$	22.8494	+	8.06525i	0.749263	+	0.264470i
$931$	7.16148	−	41.5238i	0.234708	−	1.36089i
$932$	32.4899	+	26.2005i	1.06424	+	0.858226i
$933$	−9.81123	−	11.6926i	−0.321205	−	0.382798i
$934$	6.43878	−	7.82708i	0.210683	−	0.256110i
$935$	−4.91129	−	0.865993i	−0.160616	−	0.0283210i
$936$	4.96420	+	5.57661i	0.162260	+	0.182277i
$937$	28.0788	−	10.2198i	0.917294	−	0.333868i	0.160133	−	0.987095i	$-0.448808\pi$
$937$	28.0788	−	10.2198i	0.917294	−	0.333868i	0.757162	+	0.653228i	$0.226586\pi$
$938$	−25.9558	−	30.3278i	−0.847488	−	0.990239i
$939$	11.3806	+	19.7117i	0.371391	+	0.643268i
$940$	22.8842	−	4.49659i	0.746402	−	0.146663i
$941$	7.50705	−	8.94655i	0.244723	−	0.291649i	−0.629675	−	0.776858i	$-0.716812\pi$
$941$	7.50705	−	8.94655i	0.244723	−	0.291649i	0.874398	+	0.485209i	$0.161257\pi$
$942$	−4.87890	−	26.1755i	−0.158963	−	0.852845i
$943$	−12.3270	+	21.3510i	−0.401422	+	0.695283i
$944$	−11.6183	−	18.4258i	−0.378142	−	0.599708i
$945$	−77.0188	+	13.5805i	−2.50542	+	0.441774i
$946$	0.473066	−	0.838129i	0.0153807	−	0.0272499i
$947$	−4.69128	+	12.8892i	−0.152446	+	0.418843i	−0.992283	−	0.123997i	$-0.960429\pi$
$947$	−4.69128	+	12.8892i	−0.152446	+	0.418843i	0.839836	+	0.542840i	$0.182651\pi$
$948$	−0.462267	+	0.00900991i	−0.0150137	+	0.000292628i
$949$		−	14.4577i		−	0.469318i
$950$	−46.7270	+	0.630390i	−1.51602	+	0.0204525i
$951$		−	7.01655i		−	0.227527i
$952$	−16.9961	+	51.3161i	−0.550847	+	1.66316i
$953$	−3.90387	+	10.7258i	−0.126459	+	0.347443i	−0.986724	−	0.162403i	$-0.948075\pi$
$953$	−3.90387	+	10.7258i	−0.126459	+	0.347443i	0.860266	+	0.509846i	$0.170298\pi$
$954$	−10.5901	−	5.97736i	−0.342867	−	0.193524i
$955$	−18.9591	+	3.34300i	−0.613502	+	0.108177i
$956$	−17.1240	+	50.0624i	−0.553830	+	1.61913i
$957$	0.0934775	−	0.161908i	0.00302170	−	0.00523373i
$958$	−42.3790	+	7.89909i	−1.36920	+	0.255208i
$959$	−27.9246	+	33.2792i	−0.901731	+	1.07464i
$960$	−30.2435	+	13.0561i	−0.976105	+	0.421383i
$961$	6.84269	+	11.8519i	0.220732	+	0.382319i
$962$	−4.16640	+	3.56578i	−0.134330	+	0.114965i
$963$	25.8293	−	9.40108i	0.832336	−	0.302946i
$964$	−27.4858	−	15.1626i	−0.885257	−	0.488354i
$965$	−30.6733	−	5.40854i	−0.987409	−	0.174107i
$966$	−16.1417	−	13.2786i	−0.519349	−	0.427232i
$967$	−0.279271	−	0.332822i	−0.00898075	−	0.0107028i	0.761535	−	0.648123i	$-0.224446\pi$
$967$	−0.279271	−	0.332822i	−0.00898075	−	0.0107028i	−0.770516	+	0.637421i	$0.780001\pi$
$968$	−16.2033	−	26.2611i	−0.520793	−	0.844063i
$969$	22.2911	+	8.01887i	0.716094	+	0.257603i
$970$	10.1304	−	28.7000i	0.325266	−	0.921503i
$971$	−42.2441	+	35.4470i	−1.35568	+	1.13755i	−0.378388	+	0.925647i	$0.623521\pi$
$971$	−42.2441	+	35.4470i	−1.35568	+	1.13755i	−0.977291	+	0.211902i	$0.932034\pi$
$972$	−15.1710	−	25.1328i	−0.486610	−	0.806135i
$973$	12.9403	−	73.3881i	0.414847	−	2.35271i
$974$	−6.79331	+	40.8505i	−0.217672	+	1.30893i
$975$	4.80863	+	13.2116i	0.153999	+	0.423110i
$976$	13.0387	+	4.17792i	0.417357	+	0.133732i
$977$	50.6858	−	29.2635i	1.62158	−	0.936221i	0.635085	−	0.772442i	$-0.280965\pi$
$977$	50.6858	−	29.2635i	1.62158	−	0.936221i	0.986497	−	0.163779i	$-0.0523683\pi$
$978$	8.90649	−	5.25854i	0.284798	−	0.168149i
$979$	−1.52174	−	1.27689i	−0.0486349	−	0.0408095i
$980$	−10.5897	+	67.7529i	−0.338276	+	2.16429i
$981$	12.1955	+	7.04109i	0.389373	+	0.224805i
$982$	0.348502	+	35.7642i	0.0111211	+	1.14128i
$983$	−5.85032	−	33.1788i	−0.186596	−	1.05824i	−0.923887	−	0.382665i	$-0.875006\pi$
$983$	−5.85032	−	33.1788i	−0.186596	−	1.05824i	0.737291	−	0.675575i	$-0.236105\pi$
$984$	−9.58771	−	24.1236i	−0.305645	−	0.769033i
$985$	9.94517	+	3.61974i	0.316879	+	0.115335i
$986$	1.24663	+	3.32396i	0.0397009	+	0.105856i
$987$	−15.5812			−0.495956
$988$	−5.06614	−	12.9731i	−0.161175	−	0.412729i
$989$	−7.06616			−0.224691
$990$	−0.874116	−	2.33070i	−0.0277812	−	0.0740744i
$991$	41.2012	+	14.9960i	1.30880	+	0.476364i	0.899853	−	0.436193i	$-0.143674\pi$
$991$	41.2012	+	14.9960i	1.30880	+	0.476364i	0.408948	+	0.912558i	$0.365896\pi$
$992$	22.4849	+	6.96391i	0.713897	+	0.221104i
$993$	0.740052	+	4.19705i	0.0234849	+	0.133189i
$994$	0.240794	+	24.7110i	0.00763754	+	0.783784i
$995$	2.65133	+	1.53075i	0.0840529	+	0.0485279i
$996$	34.1790	+	5.34214i	1.08300	+	0.169272i
$997$	16.0473	+	13.4653i	0.508224	+	0.426451i	0.860504	−	0.509444i	$-0.170149\pi$
$997$	16.0473	+	13.4653i	0.508224	+	0.426451i	−0.352280	+	0.935895i	$0.614593\pi$
$998$	−24.1717	+	14.2714i	−0.765142	+	0.451752i
$999$	11.3532	−	6.55475i	0.359198	−	0.207383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.51.2	yes	48
3.2	odd	2		684.2.cf.a.127.7		48
4.3	odd	2	inner	76.2.k.a.51.6	yes	48
12.11	even	2		684.2.cf.a.127.3		48
19.3	odd	18	inner	76.2.k.a.3.6	yes	48
57.41	even	18		684.2.cf.a.307.3		48
76.3	even	18	inner	76.2.k.a.3.2	✓	48
228.155	odd	18		684.2.cf.a.307.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.3.2	✓	48	76.3	even	18	inner
76.2.k.a.3.6	yes	48	19.3	odd	18	inner
76.2.k.a.51.2	yes	48	1.1	even	1	trivial
76.2.k.a.51.6	yes	48	4.3	odd	2	inner
684.2.cf.a.127.3		48	12.11	even	2
684.2.cf.a.127.7		48	3.2	odd	2
684.2.cf.a.307.3		48	57.41	even	18
684.2.cf.a.307.7		48	228.155	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32415 + 0.496616i) q^{2} +(-1.09089 - 0.397053i) q^{3} +(1.50675 - 1.31519i) q^{4} +(0.615920 + 3.49306i) q^{5} +(1.64169 - 0.0159973i) q^{6} +(3.53555 + 2.04125i) q^{7} +(-1.34202 + 2.48978i) q^{8} +(-1.26573 - 1.06208i) q^{9} +O(q^{10})\)	\(q+(-1.32415 + 0.496616i) q^{2} +(-1.09089 - 0.397053i) q^{3} +(1.50675 - 1.31519i) q^{4} +(0.615920 + 3.49306i) q^{5} +(1.64169 - 0.0159973i) q^{6} +(3.53555 + 2.04125i) q^{7} +(-1.34202 + 2.48978i) q^{8} +(-1.26573 - 1.06208i) q^{9} +(-2.55028 - 4.31946i) q^{10} +(-0.260098 + 0.150167i) q^{11} +(-2.16590 + 0.836472i) q^{12} +(0.546397 + 1.50121i) q^{13} +(-5.69532 - 0.947113i) q^{14} +(0.715025 - 4.05511i) q^{15} +(0.540567 - 3.96331i) q^{16} +(3.58623 - 3.00920i) q^{17} +(2.20347 + 0.777766i) q^{18} +(-3.34958 - 2.78932i) q^{19} +(5.52206 + 4.45310i) q^{20} +(-3.04643 - 3.63059i) q^{21} +(0.269833 - 0.328013i) q^{22} +(-3.07108 - 0.541514i) q^{23} +(2.45257 - 2.18323i) q^{24} +(-7.12363 + 2.59279i) q^{25} +(-1.46904 - 1.71648i) q^{26} +(2.70044 + 4.67730i) q^{27} +(8.01181 - 1.57426i) q^{28} +(0.344669 - 0.410760i) q^{29} +(1.06703 + 5.72467i) q^{30} +(2.08054 - 3.60361i) q^{31} +(1.25245 + 5.51646i) q^{32} +(0.343363 - 0.0605442i) q^{33} +(-3.25429 + 5.76561i) q^{34} +(-4.95259 + 13.6071i) q^{35} +(-3.30397 + 0.0643968i) q^{36} -2.42729i q^{37} +(5.82057 + 2.03002i) q^{38} -1.85461i q^{39} +(-9.52351 - 3.15423i) q^{40} +(2.70395 - 7.42905i) q^{41} +(5.83694 + 3.29454i) q^{42} +(2.23149 - 0.393472i) q^{43} +(-0.194403 + 0.568341i) q^{44} +(2.93031 - 5.07544i) q^{45} +(4.33550 - 0.808100i) q^{46} +(2.11323 - 2.51844i) q^{47} +(-2.16334 + 4.10891i) q^{48} +(4.83342 + 8.37173i) q^{49} +(8.14514 - 6.97095i) q^{50} +(-5.10701 + 1.85880i) q^{51} +(2.79766 + 1.54333i) q^{52} +(-5.12508 - 0.903690i) q^{53} +(-5.89861 - 4.85236i) q^{54} +(-0.684743 - 0.816045i) q^{55} +(-9.82703 + 6.06335i) q^{56} +(2.54653 + 4.37281i) q^{57} +(-0.252403 + 0.715076i) q^{58} +(4.17166 - 3.50044i) q^{59} +(-4.25587 - 7.05041i) q^{60} +(-0.594383 + 3.37091i) q^{61} +(-0.965344 + 5.80494i) q^{62} +(-2.30710 - 6.33871i) q^{63} +(-4.39799 - 6.68264i) q^{64} +(-4.90729 + 2.83323i) q^{65} +(-0.424597 + 0.250689i) q^{66} +(5.29646 + 4.44426i) q^{67} +(1.44587 - 9.25066i) q^{68} +(3.13521 + 1.81012i) q^{69} +(-0.199541 - 20.4774i) q^{70} +(-0.743257 - 4.21522i) q^{71} +(4.34297 - 1.72607i) q^{72} +(-8.50411 - 3.09524i) q^{73} +(1.20543 + 3.21410i) q^{74} +8.80060 q^{75} +(-8.71544 + 0.202533i) q^{76} -1.22612 q^{77} +(0.921031 + 2.45579i) q^{78} +(0.187126 + 0.0681083i) q^{79} +(14.1770 - 0.552850i) q^{80} +(-0.228002 - 1.29306i) q^{81} +(0.108943 + 11.1800i) q^{82} +(-12.9034 - 7.44977i) q^{83} +(-9.36510 - 1.46376i) q^{84} +(12.7201 + 10.6735i) q^{85} +(-2.75942 + 1.62921i) q^{86} +(-0.539091 + 0.311244i) q^{87} +(-0.0248287 - 0.849113i) q^{88} +(2.26220 + 6.21534i) q^{89} +(-1.35962 + 8.17588i) q^{90} +(-1.13254 + 6.42296i) q^{91} +(-5.33953 + 3.22312i) q^{92} +(-3.70047 + 3.10507i) q^{93} +(-1.54753 + 4.38426i) q^{94} +(7.68017 - 13.4183i) q^{95} +(0.824040 - 6.51517i) q^{96} +(3.90012 + 4.64798i) q^{97} +(-10.5577 - 8.68508i) q^{98} +(0.488704 + 0.0861717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

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