LMFDB - Embedded newform 756.2.ci.a.191.85

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (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			191.85
Character	$\chi$	$=$	756.191
Dual form			756.2.ci.a.95.85

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.400135 + 1.35643i) q^{2} +(-1.04908 + 1.37820i) q^{3} +(-1.67978 + 1.08551i) q^{4} +(0.0136217 - 0.00240188i) q^{5} +(-2.28920 - 0.871530i) q^{6} +(2.34832 - 1.21877i) q^{7} +(-2.14455 - 1.84415i) q^{8} +(-0.798872 - 2.89168i) q^{9} +O(q^{10})$	\(q+(0.400135 + 1.35643i) q^{2} +(-1.04908 + 1.37820i) q^{3} +(-1.67978 + 1.08551i) q^{4} +(0.0136217 - 0.00240188i) q^{5} +(-2.28920 - 0.871530i) q^{6} +(2.34832 - 1.21877i) q^{7} +(-2.14455 - 1.84415i) q^{8} +(-0.798872 - 2.89168i) q^{9} +(0.00870850 + 0.0175158i) q^{10} +(0.989827 - 5.61359i) q^{11} +(0.266177 - 3.45386i) q^{12} +(-0.373911 - 2.12055i) q^{13} +(2.59281 + 2.69765i) q^{14} +(-0.0109800 + 0.0212932i) q^{15} +(1.64335 - 3.64684i) q^{16} +(-4.46911 - 2.58024i) q^{17} +(3.60269 - 2.24067i) q^{18} +(1.67374 - 0.966334i) q^{19} +(-0.0202743 + 0.0188211i) q^{20} +(-0.783868 + 4.51504i) q^{21} +(8.01048 - 0.903566i) q^{22} +(5.57999 - 4.68217i) q^{23} +(4.79141 - 1.02096i) q^{24} +(-4.69828 + 1.71004i) q^{25} +(2.72676 - 1.35569i) q^{26} +(4.82339 + 1.93259i) q^{27} +(-2.62169 + 4.59638i) q^{28} +(-6.57796 - 1.15987i) q^{29} +(-0.0332762 - 0.00637337i) q^{30} +(-7.43341 + 1.31071i) q^{31} +(5.60422 + 0.769853i) q^{32} +(6.69824 + 7.25327i) q^{33} +(1.71166 - 7.09446i) q^{34} +(0.0290609 - 0.0222421i) q^{35} +(4.48087 + 3.99021i) q^{36} -1.62487 q^{37} +(1.98048 + 1.88364i) q^{38} +(3.31481 + 1.70930i) q^{39} +(-0.0336419 - 0.0199696i) q^{40} +(0.819613 - 0.144520i) q^{41} +(-6.43797 + 0.743364i) q^{42} +(-3.59069 + 4.27922i) q^{43} +(4.43089 + 10.5041i) q^{44} +(-0.0178275 - 0.0374709i) q^{45} +(8.58376 + 5.69534i) q^{46} +(0.133348 - 0.756257i) q^{47} +(3.30207 + 6.09068i) q^{48} +(4.02922 - 5.72410i) q^{49} +(-4.19948 - 5.68863i) q^{50} +(8.24453 - 3.45245i) q^{51} +(2.92997 + 3.15619i) q^{52} +(2.00935 - 1.16010i) q^{53} +(-0.691407 + 7.31587i) q^{54} -0.0788442i q^{55} +(-7.28368 - 1.71696i) q^{56} +(-0.424081 + 3.32051i) q^{57} +(-1.05879 - 9.38662i) q^{58} +(10.3506 + 3.76730i) q^{59} +(-0.00466996 - 0.0476869i) q^{60} +(-1.50186 + 8.51747i) q^{61} +(-4.75225 - 9.55841i) q^{62} +(-5.40028 - 5.81695i) q^{63} +(1.19820 + 7.90976i) q^{64} +(-0.0101866 - 0.0279875i) q^{65} +(-7.15832 + 11.9880i) q^{66} +(0.900117 + 1.07272i) q^{67} +(10.3080 - 0.517003i) q^{68} +(0.599121 + 12.6023i) q^{69} +(0.0417980 + 0.0305191i) q^{70} +(-6.87368 - 11.9056i) q^{71} +(-3.61948 + 7.67459i) q^{72} -0.975165 q^{73} +(-0.650168 - 2.20402i) q^{74} +(2.57209 - 8.26914i) q^{75} +(-1.76256 + 3.44009i) q^{76} +(-4.51721 - 14.3889i) q^{77} +(-0.992170 + 5.18024i) q^{78} +(2.27083 - 2.70627i) q^{79} +(0.0136260 - 0.0536233i) q^{80} +(-7.72361 + 4.62016i) q^{81} +(0.523986 + 1.05392i) q^{82} +(-0.761271 + 4.31738i) q^{83} +(-3.58438 - 8.43518i) q^{84} +(-0.0670745 - 0.0244131i) q^{85} +(-7.24120 - 3.15824i) q^{86} +(8.49933 - 7.84895i) q^{87} +(-12.4750 + 10.2132i) q^{88} +(12.6403 - 7.29787i) q^{89} +(0.0436931 - 0.0391751i) q^{90} +(-3.46252 - 4.52403i) q^{91} +(-4.29065 + 13.9221i) q^{92} +(5.99180 - 11.6198i) q^{93} +(1.07916 - 0.121727i) q^{94} +(0.0204782 - 0.0171833i) q^{95} +(-6.94028 + 6.91611i) q^{96} +(1.44343 + 1.21118i) q^{97} +(9.37656 + 3.17493i) q^{98} +(-17.0234 + 1.62228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.400135	+	1.35643i	0.282938	+	0.959138i
$2$	0.400135	+	1.35643i	0.282938	+	0.959138i
$3$	−1.04908	+	1.37820i	−0.605685	+	0.795704i
$3$	−1.04908	+	1.37820i	−0.605685	+	0.795704i
$4$	−1.67978	+	1.08551i	−0.839892	+	0.542754i
$5$	0.0136217	−	0.00240188i	0.00609182	−	0.00107415i	−0.170601	−	0.985340i	$-0.554571\pi$
$5$	0.0136217	−	0.00240188i	0.00609182	−	0.00107415i	0.176693	+	0.984266i	$0.443460\pi$
$6$	−2.28920	−	0.871530i	−0.934562	−	0.355801i
$7$	2.34832	−	1.21877i	0.887582	−	0.460650i
$7$	2.34832	−	1.21877i	0.887582	−	0.460650i
$8$	−2.14455	−	1.84415i	−0.758213	−	0.652007i
$9$	−0.798872	−	2.89168i	−0.266291	−	0.963893i
$10$	0.00870850	+	0.0175158i	0.00275387	+	0.00553898i
$11$	0.989827	−	5.61359i	0.298444	−	1.69256i	−0.354421	−	0.935086i	$-0.615322\pi$
$11$	0.989827	−	5.61359i	0.298444	−	1.69256i	0.652865	−	0.757474i	$-0.273567\pi$
$12$	0.266177	−	3.45386i	0.0768388	−	0.997044i
$13$	−0.373911	−	2.12055i	−0.103704	−	0.588136i	−0.991730	−	0.128342i	$-0.959034\pi$
$13$	−0.373911	−	2.12055i	−0.103704	−	0.588136i	0.888026	−	0.459794i	$-0.152077\pi$
$14$	2.59281	+	2.69765i	0.692958	+	0.720978i
$15$	−0.0109800	+	0.0212932i	−0.00283502	+	0.00549789i
$16$	1.64335	−	3.64684i	0.410837	−	0.911709i
$17$	−4.46911	−	2.58024i	−1.08392	−	0.625801i	−0.151968	−	0.988385i	$-0.548561\pi$
$17$	−4.46911	−	2.58024i	−1.08392	−	0.625801i	−0.931951	+	0.362585i	$0.881894\pi$
$18$	3.60269	−	2.24067i	0.849163	−	0.528132i
$19$	1.67374	−	0.966334i	0.383982	−	0.221692i	−0.295567	−	0.955322i	$-0.595509\pi$
$19$	1.67374	−	0.966334i	0.383982	−	0.221692i	0.679549	+	0.733630i	$0.262175\pi$
$20$	−0.0202743	+	0.0188211i	−0.00453347	+	0.00420853i
$21$	−0.783868	+	4.51504i	−0.171054	+	0.985262i
$22$	8.01048	−	0.903566i	1.70784	−	0.192641i
$23$	5.57999	−	4.68217i	1.16351	−	0.976299i	0.163560	−	0.986533i	$-0.447702\pi$
$23$	5.57999	−	4.68217i	1.16351	−	0.976299i	0.999948	+	0.0102344i	$0.00325778\pi$
$24$	4.79141	−	1.02096i	0.978043	−	0.208403i
$25$	−4.69828	+	1.71004i	−0.939657	+	0.342007i
$26$	2.72676	−	1.35569i	0.534761	−	0.265873i
$27$	4.82339	+	1.93259i	0.928262	+	0.371927i
$28$	−2.62169	+	4.59638i	−0.495453	+	0.868635i
$29$	−6.57796	−	1.15987i	−1.22150	−	0.215383i	−0.474527	−	0.880241i	$-0.657381\pi$
$29$	−6.57796	−	1.15987i	−1.22150	−	0.215383i	−0.746970	+	0.664858i	$0.768492\pi$
$30$	−0.0332762	−	0.00637337i	−0.00607537	−	0.00116361i
$31$	−7.43341	+	1.31071i	−1.33508	+	0.235411i	−0.795208	−	0.606336i	$-0.792638\pi$
$31$	−7.43341	+	1.31071i	−1.33508	+	0.235411i	−0.539872	+	0.841747i	$0.681527\pi$
$32$	5.60422	+	0.769853i	0.990696	+	0.136092i
$33$	6.69824	+	7.25327i	1.16601	+	1.26263i
$34$	1.71166	−	7.09446i	0.293547	−	1.21669i
$35$	0.0290609	−	0.0222421i	0.00491218	−	0.00375960i
$36$	4.48087	+	3.99021i	0.746812	+	0.665036i
$37$	−1.62487			−0.267127			−0.133564	−	0.991040i	$-0.542642\pi$
$37$	−1.62487			−0.267127			−0.133564	+	0.991040i	$0.542642\pi$
$38$	1.98048	+	1.88364i	0.321277	+	0.305567i
$39$	3.31481	+	1.70930i	0.530794	+	0.273707i
$40$	−0.0336419	−	0.0199696i	−0.00531926	−	0.00315747i
$41$	0.819613	−	0.144520i	0.128002	−	0.0225702i	−0.109280	−	0.994011i	$-0.534855\pi$
$41$	0.819613	−	0.144520i	0.128002	−	0.0225702i	0.237282	+	0.971441i	$0.423743\pi$
$42$	−6.43797	+	0.743364i	−0.993400	+	0.114704i
$43$	−3.59069	+	4.27922i	−0.547575	+	0.652574i	−0.966868	−	0.255277i	$-0.917833\pi$
$43$	−3.59069	+	4.27922i	−0.547575	+	0.652574i	0.419293	+	0.907851i	$0.362278\pi$
$44$	4.43089	+	10.5041i	0.667983	+	1.58355i
$45$	−0.0178275	−	0.0374709i	−0.00265756	−	0.00558583i
$46$	8.58376	+	5.69534i	1.26561	+	0.839732i
$47$	0.133348	−	0.756257i	0.0194509	−	0.110311i	−0.973537	−	0.228531i	$-0.926608\pi$
$47$	0.133348	−	0.756257i	0.0194509	−	0.110311i	0.992987	+	0.118220i	$0.0377188\pi$
$48$	3.30207	+	6.09068i	0.476613	+	0.879113i
$49$	4.02922	−	5.72410i	0.575603	−	0.817729i
$50$	−4.19948	−	5.68863i	−0.593897	−	0.804494i
$51$	8.24453	−	3.45245i	1.15447	−	0.483440i
$52$	2.92997	+	3.15619i	0.406313	+	0.437685i
$53$	2.00935	−	1.16010i	0.276005	−	0.159352i	−0.355608	−	0.934635i	$-0.615726\pi$
$53$	2.00935	−	1.16010i	0.276005	−	0.159352i	0.631614	+	0.775283i	$0.282393\pi$
$54$	−0.691407	+	7.31587i	−0.0940886	+	0.995564i
$55$		−	0.0788442i		−	0.0106314i
$56$	−7.28368	−	1.71696i	−0.973323	−	0.229438i
$57$	−0.424081	+	3.32051i	−0.0561709	+	0.439812i
$58$	−1.05879	−	9.38662i	−0.139026	−	1.23252i
$59$	10.3506	+	3.76730i	1.34753	+	0.490461i	0.912176	−	0.409799i	$-0.134401\pi$
$59$	10.3506	+	3.76730i	1.34753	+	0.490461i	0.435354	+	0.900260i	$0.356623\pi$
$60$	−0.00466996	−	0.0476869i	−0.000602889	−	0.00615635i
$61$	−1.50186	+	8.51747i	−0.192293	+	1.09055i	0.723927	+	0.689876i	$0.242335\pi$
$61$	−1.50186	+	8.51747i	−0.192293	+	1.09055i	−0.916221	+	0.400674i	$0.868776\pi$
$62$	−4.75225	−	9.55841i	−0.603537	−	1.21392i
$63$	−5.40028	−	5.81695i	−0.680372	−	0.732867i
$64$	1.19820	+	7.90976i	0.149775	+	0.988720i
$65$	−0.0101866	−	0.0279875i	−0.00126350	−	0.00347142i
$66$	−7.15832	+	11.9880i	−0.881128	+	1.47562i
$67$	0.900117	+	1.07272i	0.109967	+	0.131053i	0.818220	−	0.574905i	$-0.194961\pi$
$67$	0.900117	+	1.07272i	0.109967	+	0.131053i	−0.708253	+	0.705958i	$0.750517\pi$
$68$	10.3080	−	0.517003i	1.25003	−	0.0626958i
$69$	0.599121	+	12.6023i	0.0721257	+	1.51714i
$70$	0.0417980	+	0.0305191i	0.00499582	+	0.00364773i
$71$	−6.87368	−	11.9056i	−0.815755	−	1.41293i	−0.908784	−	0.417266i	$-0.862988\pi$
$71$	−6.87368	−	11.9056i	−0.815755	−	1.41293i	0.0930288	−	0.995663i	$-0.470345\pi$
$72$	−3.61948	+	7.67459i	−0.426559	+	0.904460i
$73$	−0.975165			−0.114134			−0.0570672	−	0.998370i	$-0.518175\pi$
$73$	−0.975165			−0.114134			−0.0570672	+	0.998370i	$0.518175\pi$
$74$	−0.650168	−	2.20402i	−0.0755805	−	0.256212i
$75$	2.57209	−	8.26914i	0.297000	−	0.954837i
$76$	−1.76256	+	3.44009i	−0.202179	+	0.394605i
$77$	−4.51721	−	14.3889i	−0.514784	−	1.63976i
$78$	−0.992170	+	5.18024i	−0.112341	+	0.586547i
$79$	2.27083	−	2.70627i	0.255489	−	0.304479i	−0.623020	−	0.782206i	$-0.714095\pi$
$79$	2.27083	−	2.70627i	0.255489	−	0.304479i	0.878509	+	0.477726i	$0.158539\pi$
$80$	0.0136260	−	0.0536233i	0.00152343	−	0.00599527i
$81$	−7.72361	+	4.62016i	−0.858179	+	0.513351i
$82$	0.523986	+	1.05392i	0.0578646	+	0.116386i
$83$	−0.761271	+	4.31738i	−0.0835604	+	0.473894i	0.914098	+	0.405494i	$0.132901\pi$
$83$	−0.761271	+	4.31738i	−0.0835604	+	0.473894i	−0.997658	+	0.0684002i	$0.978211\pi$
$84$	−3.58438	−	8.43518i	−0.391087	−	0.920354i
$85$	−0.0670745	−	0.0244131i	−0.00727525	−	0.00264797i
$86$	−7.24120	−	3.15824i	−0.780839	−	0.340562i
$87$	8.49933	−	7.84895i	0.911223	−	0.841496i
$88$	−12.4750	+	10.2132i	−1.32984	+	1.08873i
$89$	12.6403	−	7.29787i	1.33987	−	0.773573i	0.353081	−	0.935593i	$-0.385134\pi$
$89$	12.6403	−	7.29787i	1.33987	−	0.773573i	0.986788	+	0.162020i	$0.0518008\pi$
$90$	0.0436931	−	0.0391751i	0.00460565	−	0.00412942i
$91$	−3.46252	−	4.52403i	−0.362971	−	0.474247i
$92$	−4.29065	+	13.9221i	−0.447331	+	1.45148i
$93$	5.99180	−	11.6198i	0.621321	−	1.20491i
$94$	1.07916	−	0.121727i	0.111307	−	0.0125552i
$95$	0.0204782	−	0.0171833i	0.00210102	−	0.00176296i
$96$	−6.94028	+	6.91611i	−0.708339	+	0.705872i
$97$	1.44343	+	1.21118i	0.146558	+	0.122977i	0.713119	−	0.701043i	$-0.247282\pi$
$97$	1.44343	+	1.21118i	0.146558	+	0.122977i	−0.566561	+	0.824020i	$0.691726\pi$
$98$	9.37656	+	3.17493i	0.947175	+	0.320716i
$99$	−17.0234	+	1.62228i	−1.71092	+	0.163045i
$100$	6.03584	−	7.97251i	0.603584	−	0.797251i
$101$	−7.25909	+	8.65105i	−0.722307	+	0.860812i	−0.994853	−	0.101331i	$-0.967690\pi$
$101$	−7.25909	+	8.65105i	−0.722307	+	0.860812i	0.272546	+	0.962143i	$0.412134\pi$
$102$	7.98193	+	9.80165i	0.790329	+	0.970508i
$103$	7.42134	−	1.30858i	0.731247	−	0.128939i	0.204386	−	0.978890i	$-0.434480\pi$
$103$	7.42134	−	1.30858i	0.731247	−	0.128939i	0.526861	+	0.849952i	$0.323369\pi$
$104$	−3.10875	+	5.23718i	−0.304838	+	0.513548i
$105$	0.000166923		0.0633854i	1.62900e−5		0.00618578i
$106$	2.37760	+	2.26134i	0.230933	+	0.219641i
$107$	6.91667	−	11.9800i	0.668660	−	1.15815i	−0.309620	−	0.950861i	$-0.600202\pi$
$107$	6.91667	−	11.9800i	0.668660	−	1.15815i	0.978279	−	0.207292i	$-0.0664650\pi$
$108$	−10.2001	+	1.98949i	−0.981504	+	0.191439i
$109$	4.23706	+	7.33880i	0.405837	+	0.702930i	0.994418	−	0.105508i	$-0.0336469\pi$
$109$	4.23706	+	7.33880i	0.405837	+	0.702930i	−0.588582	+	0.808438i	$0.700314\pi$
$110$	0.106946	−	0.0315483i	0.0101969	−	0.00300802i
$111$	1.70462	−	2.23940i	0.161795	−	0.212554i
$112$	−0.585528	−	10.5668i	−0.0553272	−	0.998468i
$113$	−2.64126	−	3.14773i	−0.248468	−	0.296113i	0.627366	−	0.778724i	$-0.284133\pi$
$113$	−2.64126	−	3.14773i	−0.248468	−	0.296113i	−0.875835	+	0.482611i	$0.839688\pi$
$114$	−4.67371	+	0.753417i	−0.437733	+	0.0705639i
$115$	0.0647631	−	0.0771816i	0.00603919	−	0.00719723i
$116$	12.3086	−	5.19209i	1.14282	−	0.482073i
$117$	−5.83325	+	2.77528i	−0.539284	+	0.256575i
$118$	−0.968437	+	15.5472i	−0.0891519	+	1.43124i
$119$	−13.6396	−	0.612440i	−1.25034	−	0.0561423i
$120$	0.0628151	−	0.0254156i	0.00573421	−	0.00232012i
$121$	−20.1960	−	7.35074i	−1.83600	−	0.668249i
$122$	−12.1543	+	1.37098i	−1.10040	+	0.124122i
$123$	−0.660660	+	1.28120i	−0.0595697	+	0.115522i
$124$	11.0637	−	10.2707i	0.993553	−	0.922339i
$125$	−0.119785	+	0.0691580i	−0.0107139	+	0.00618568i
$126$	5.72942	−	9.65265i	0.510417	−	0.859927i
$127$	−4.35663	−	2.51530i	−0.386588	−	0.223197i	0.294093	−	0.955777i	$-0.404983\pi$
$127$	−4.35663	−	2.51530i	−0.386588	−	0.223197i	−0.680681	+	0.732580i	$0.738316\pi$
$128$	−10.2496	+	4.79024i	−0.905942	+	0.423401i
$129$	−2.13071	−	9.43792i	−0.187598	−	0.830962i
$130$	0.0338870	−	0.0250162i	0.00297208	−	0.00219407i
$131$	−12.0272	+	10.0920i	−1.05082	+	0.881741i	−0.993179	−	0.116596i	$-0.962802\pi$
$131$	−12.0272	+	10.0920i	−1.05082	+	0.881741i	−0.0576387	+	0.998338i	$0.518357\pi$
$132$	−19.1251	−	4.91293i	−1.66462	−	0.427616i
$133$	2.75274	−	4.30916i	0.238693	−	0.373651i
$134$	−1.09489	+	1.65017i	−0.0945845	+	0.142553i
$135$	0.0703448	+	0.0147400i	0.00605431	+	0.00126862i
$136$	4.82587	+	13.7752i	0.413815	+	1.18121i
$137$	−4.84376	−	13.3081i	−0.413830	−	1.13699i	−0.955137	−	0.296164i	$-0.904292\pi$
$137$	−4.84376	−	13.3081i	−0.413830	−	1.13699i	0.541307	−	0.840825i	$-0.317930\pi$
$138$	−16.8544	+	5.85528i	−1.43474	+	0.498435i
$139$	−1.08536	+	2.98199i	−0.0920587	+	0.252929i	−0.977173	−	0.212444i	$-0.931858\pi$
$139$	−1.08536	+	2.98199i	−0.0920587	+	0.252929i	0.885115	+	0.465373i	$0.154080\pi$
$140$	−0.0246720	+	0.0689077i	−0.00208517	+	0.00582376i
$141$	0.902380	+	0.977153i	0.0759941	+	0.0822911i
$142$	13.3986	−	14.0875i	1.12439	−	1.18219i
$143$	−12.2740			−1.02640
$144$	−11.8583	−	1.83868i	−0.988192	−	0.153223i
$145$	−0.0923891			−0.00767249
$146$	−0.390198	−	1.32274i	−0.0322930	−	0.109471i
$147$	3.66199	+	11.5581i	0.302036	+	0.953296i
$148$	2.72943	−	1.76381i	0.224358	−	0.144984i
$149$	3.14028	−	8.62786i	0.257262	−	0.706822i	−0.742072	−	0.670321i	$-0.766157\pi$
$149$	3.14028	−	8.62786i	0.257262	−	0.706822i	0.999334	−	0.0365009i	$-0.0116212\pi$
$150$	12.2457	+	0.180083i	0.999854	+	0.0147037i
$151$	14.3646	+	2.53287i	1.16897	+	0.206122i	0.724245	−	0.689543i	$-0.242189\pi$
$151$	14.3646	+	2.53287i	1.16897	+	0.206122i	0.444730	+	0.895665i	$0.353300\pi$
$152$	−5.37149	−	1.01428i	−0.435685	−	0.0822689i
$153$	−3.89098	+	14.9845i	−0.314567	+	1.21143i
$154$	17.7099	−	11.8848i	1.42711	−	0.957701i
$155$	−0.0981078	+	0.0357083i	−0.00788021	+	0.00286816i
$156$	−7.42362	+	0.726992i	−0.594365	+	0.0582060i
$157$	9.63440	+	3.50664i	0.768909	+	0.279860i	0.696540	−	0.717518i	$-0.254722\pi$
$157$	9.63440	+	3.50664i	0.768909	+	0.279860i	0.0723691	+	0.997378i	$0.476944\pi$
$158$	4.57950	+	1.99734i	0.364325	+	0.158900i
$159$	−0.509116	+	3.98632i	−0.0403755	+	0.316136i
$160$	0.0781883	−	0.00297393i	0.00618133	−	0.000235110i
$161$	7.39714	−	17.7959i	0.582976	−	1.40252i
$162$	−9.35739	−	8.62781i	−0.735186	−	0.677865i
$163$	11.3722	+	6.56577i	0.890743	+	0.514271i	0.874186	−	0.485592i	$-0.161396\pi$
$163$	11.3722	+	6.56577i	0.890743	+	0.514271i	0.0165578	+	0.999863i	$0.494729\pi$
$164$	−1.21990	+	1.13246i	−0.0952578	+	0.0884301i
$165$	0.108663	+	0.0827137i	0.00845941	+	0.00643925i
$166$	−6.16082	+	0.694928i	−0.478173	+	0.0539369i
$167$	8.76693	−	7.35633i	0.678405	−	0.569250i	−0.237135	−	0.971477i	$-0.576208\pi$
$167$	8.76693	−	7.35633i	0.678405	−	0.569250i	0.915540	+	0.402227i	$0.131764\pi$
$168$	10.0075	−	8.23715i	0.772093	−	0.635510i
$169$	7.85907	−	2.86047i	0.604544	−	0.220036i
$170$	0.00627573	−	0.100750i	0.000481327	−	0.00772718i
$171$	−4.13143	−	4.06794i	−0.315938	−	0.311083i
$172$	1.38646	−	11.0859i	0.105717	−	0.845290i
$173$	1.72866	+	4.74947i	0.131428	+	0.361095i	0.987899	−	0.155100i	$-0.0495700\pi$
$173$	1.72866	+	4.74947i	0.131428	+	0.361095i	−0.856471	+	0.516195i	$0.827348\pi$
$174$	14.0474	+	8.38807i	1.06493	+	0.635898i
$175$	−8.94895	+	9.74182i	−0.676477	+	0.736412i
$176$	−18.8452	−	12.8348i	−1.42051	−	0.967460i
$177$	−16.0506	+	10.3130i	−1.20644	+	0.775170i
$178$	14.9569	+	14.2255i	1.12106	+	1.06625i
$179$	1.34848	−	2.33564i	0.100790	−	0.174574i	−0.811220	−	0.584741i	$-0.801196\pi$
$179$	1.34848	−	2.33564i	0.100790	−	0.174574i	0.912010	+	0.410167i	$0.134530\pi$
$180$	0.0706212	+	0.0435911i	0.00526379	+	0.00324909i
$181$	4.79202	−	8.30002i	0.356188	−	0.616936i	−0.631132	−	0.775675i	$-0.717410\pi$
$181$	4.79202	−	8.30002i	0.356188	−	0.616936i	0.987321	+	0.158739i	$0.0507429\pi$
$182$	4.75104	−	6.50688i	0.352170	−	0.482322i
$183$	−10.1632	−	11.0054i	−0.751286	−	0.813539i
$184$	−20.6012	−	0.249210i	−1.51874	−	0.0183720i
$185$	−0.0221336	+	0.00390275i	−0.00162729	+	0.000286936i
$186$	18.1589	+	3.47796i	1.33147	+	0.255017i
$187$	−18.9081	+	22.5337i	−1.38269	+	1.64783i
$188$	0.596926	+	1.41510i	0.0435353	+	0.103207i
$189$	13.6822	−	1.34024i	0.995237	−	0.0974881i
$190$	0.0315019	+	0.0209015i	0.00228539	+	0.00151636i
$191$	−19.7220	−	16.5487i	−1.42703	−	1.19742i	−0.947441	−	0.319932i	$-0.896340\pi$
$191$	−19.7220	−	16.5487i	−1.42703	−	1.19742i	−0.479592	−	0.877491i	$-0.659215\pi$
$192$	−12.1582	−	6.64660i	−0.877445	−	0.479677i
$193$	−2.42579	−	13.7573i	−0.174612	−	0.990274i	−0.938591	−	0.345032i	$-0.887868\pi$
$193$	−2.42579	−	13.7573i	−0.174612	−	0.990274i	0.763979	−	0.645241i	$-0.223243\pi$
$194$	−1.06531	+	2.44255i	−0.0764850	+	0.175365i
$195$	0.0492590	+	0.0153219i	0.00352751	+	0.00109722i
$196$	−0.554666	+	13.9890i	−0.0396190	+	0.999215i
$197$	18.1556	+	10.4821i	1.29353	+	0.746820i	0.979278	−	0.202520i	$-0.0649130\pi$
$197$	18.1556	+	10.4821i	1.29353	+	0.746820i	0.314252	+	0.949340i	$0.398246\pi$
$198$	−9.01217	−	22.4419i	−0.640467	−	1.59488i
$199$	20.8338	+	12.0284i	1.47687	+	0.852671i	0.999659	−	0.0261181i	$-0.00831459\pi$
$199$	20.8338	+	12.0284i	1.47687	+	0.852671i	0.477211	+	0.878789i	$0.341648\pi$
$200$	13.2293	+	4.99710i	0.935451	+	0.353348i
$201$	−2.42271	+	0.115177i	−0.170885	+	0.00812399i
$202$	−14.6391	−	6.38484i	−1.03001	−	0.449236i
$203$	−16.8608	+	5.29324i	−1.18339	+	0.371512i
$204$	−10.1014	+	14.7489i	−0.707237	+	1.03263i
$205$	0.0108174	−	0.00393722i	0.000755522	−	0.000274987i
$206$	4.74454	+	9.54290i	0.330568	+	0.664885i
$207$	−17.9970	−	12.3951i	−1.25088	−	0.861517i
$208$	−8.34777	−	2.12122i	−0.578814	−	0.147080i
$209$	−3.76789	−	10.3522i	−0.260630	−	0.716075i
$210$	−0.0859108	+	0.0255891i	−0.00592841	+	0.00176582i
$211$	11.6247	+	13.8537i	0.800275	+	0.953731i	0.999657	−	0.0261913i	$-0.00833790\pi$
$211$	11.6247	+	13.8537i	0.800275	+	0.953731i	−0.199382	+	0.979922i	$0.563893\pi$
$212$	−2.11598	+	4.12988i	−0.145326	+	0.283641i
$213$	23.6193	+	3.01655i	1.61837	+	0.206691i
$214$	19.0176	+	4.58832i	1.30002	+	0.313651i
$215$	−0.0386332	+	0.0669147i	−0.00263476	+	0.00456355i
$216$	−6.78002	−	13.0396i	−0.461322	−	0.887233i
$217$	−15.8586	+	12.1376i	−1.07655	+	0.823951i
$218$	−8.25914	+	8.68377i	−0.559380	+	0.588139i
$219$	1.02302	−	1.34397i	0.0691295	−	0.0908172i
$220$	0.0855860	+	0.132441i	0.00577021	+	0.00892919i
$221$	−3.80049	+	10.4418i	−0.255649	+	0.702389i
$222$	3.71966	+	1.41612i	0.249647	+	0.0950441i
$223$	−3.17794	−	8.73133i	−0.212811	−	0.584693i	0.786654	−	0.617394i	$-0.211811\pi$
$223$	−3.17794	−	8.73133i	−0.212811	−	0.584693i	−0.999465	+	0.0327008i	$0.989589\pi$
$224$	14.0988	−	5.02237i	0.942015	−	0.335571i
$225$	8.69820	+	12.2198i	0.579880	+	0.814655i
$226$	3.21280	−	4.84218i	0.213712	−	0.322097i
$227$	−0.618441	+	3.50735i	−0.0410474	+	0.232791i	−0.998429	−	0.0560355i	$-0.982154\pi$
$227$	−0.618441	+	3.50735i	−0.0410474	+	0.232791i	0.957381	+	0.288827i	$0.0932651\pi$
$228$	−2.89207	−	6.03808i	−0.191532	−	0.399881i
$229$	15.5815	+	5.67119i	1.02965	+	0.374763i	0.800949	−	0.598733i	$-0.204329\pi$
$229$	15.5815	+	5.67119i	1.02965	+	0.374763i	0.228704	+	0.973496i	$0.426551\pi$
$230$	0.130605	+	0.0569633i	0.00861185	+	0.00375605i
$231$	24.5697	+	8.86942i	1.61656	+	0.583565i
$232$	11.9678	+	14.6182i	0.785724	+	0.959730i
$233$			5.77554i			0.378368i	0.981942	+	0.189184i	$0.0605843\pi$
$233$			5.77554i			0.378368i	−0.981942	+	0.189184i	$0.939416\pi$
$234$	−6.09855	−	6.80189i	−0.398675	−	0.444653i
$235$		−	0.0106218i		−	0.000692891i
$236$	−21.4762	+	4.90737i	−1.39798	+	0.319443i
$237$	1.34751	+	5.96875i	0.0875299	+	0.387712i
$238$	−4.62696	−	18.7462i	−0.299921	−	1.21514i
$239$	11.8566	+	4.31546i	0.766941	+	0.279144i	0.695716	−	0.718317i	$-0.255087\pi$
$239$	11.8566	+	4.31546i	0.766941	+	0.279144i	0.0712245	+	0.997460i	$0.477309\pi$
$240$	0.0596090	+	0.0750344i	0.00384774	+	0.00484345i
$241$	−21.6170	+	7.86793i	−1.39247	+	0.506818i	−0.925934	−	0.377684i	$-0.876720\pi$
$241$	−21.6170	+	7.86793i	−1.39247	+	0.506818i	−0.466536	+	0.884502i	$0.654498\pi$
$242$	1.88961	−	30.3356i	0.121469	−	1.95005i
$243$	1.73516	−	15.4916i	0.111310	−	0.993786i
$244$	−6.72298	−	15.9378i	−0.430395	−	1.02031i
$245$	0.0411364	−	0.0876499i	0.00262811	−	0.00559975i
$246$	−2.00221	−	0.383483i	−0.127656	−	0.0244500i
$247$	−2.67499	−	3.18793i	−0.170206	−	0.202843i
$248$	18.3585	+	10.8975i	1.16576	+	0.691990i
$249$	−5.15159	−	5.57845i	−0.326469	−	0.353520i
$250$	−0.141738	−	0.134807i	−0.00896430	−	0.00852596i
$251$	−14.4420	+	25.0143i	−0.911572	+	1.57889i	−0.0997284	+	0.995015i	$0.531797\pi$
$251$	−14.4420	+	25.0143i	−0.911572	+	1.57889i	−0.811844	+	0.583875i	$0.801536\pi$
$252$	15.3857	+	3.90917i	0.969205	+	0.246255i
$253$	−20.7605	−	35.9583i	−1.30520	−	2.26068i
$254$	1.66858	−	6.91590i	0.104696	−	0.433942i
$255$	0.104012	−	0.0668308i	0.00651351	−	0.00418511i
$256$	−10.5988	−	11.9860i	−0.662426	−	0.749127i
$257$	5.28642	−	14.5243i	0.329758	−	0.906002i	−0.658415	−	0.752655i	$-0.728773\pi$
$257$	5.28642	−	14.5243i	0.329758	−	0.906002i	0.988172	−	0.153346i	$-0.0490051\pi$
$258$	11.9493	−	6.66659i	0.743929	−	0.415043i
$259$	−3.81572	+	1.98034i	−0.237097	+	0.123052i
$260$	0.0474920	+	0.0359553i	0.00294533	+	0.00222985i
$261$	1.90097	+	19.9479i	0.117667	+	1.23475i
$262$	−18.5015	−	12.2758i	−1.14303	−	0.758401i
$263$	17.4428	+	14.6362i	1.07557	+	0.902508i	0.995545	−	0.0942847i	$-0.0300564\pi$
$263$	17.4428	+	14.6362i	1.07557	+	0.902508i	0.0800223	+	0.996793i	$0.474501\pi$
$264$	−0.988583	−	27.9076i	−0.0608431	−	1.71759i
$265$	0.0245844	−	0.0206288i	0.00151021	−	0.00126721i
$266$	6.94652	+	2.00965i	0.425918	+	0.123219i
$267$	−3.20271	+	25.0769i	−0.196003	+	1.53468i
$268$	−2.67645	−	0.824851i	−0.163490	−	0.0503858i
$269$	−16.1987	+	9.35233i	−0.987653	+	0.570222i	−0.904572	−	0.426321i	$-0.859809\pi$
$269$	−16.1987	+	9.35233i	−0.987653	+	0.570222i	−0.0830813	+	0.996543i	$0.526476\pi$
$270$	0.00815367	+	0.101315i	0.000496216	+	0.00616586i
$271$	20.0590	+	11.5811i	1.21850	+	0.703499i	0.964596	−	0.263731i	$-0.0849533\pi$
$271$	20.0590	+	11.5811i	1.21850	+	0.703499i	0.253900	+	0.967230i	$0.418287\pi$
$272$	−16.7540	+	12.0579i	−1.01586	+	0.731116i
$273$	9.86747	−	0.0259856i	0.597207	−	0.00157272i
$274$	16.1133	−	11.8952i	0.973441	−	0.718618i
$275$	4.94894	+	28.0669i	0.298433	+	1.69250i
$276$	−14.6863	−	20.5188i	−0.884010	−	1.23509i
$277$	−12.8292	−	10.7650i	−0.770834	−	0.646807i	0.170088	−	0.985429i	$-0.445595\pi$
$277$	−12.8292	−	10.7650i	−0.770834	−	0.646807i	−0.940922	+	0.338622i	$0.890039\pi$
$278$	−4.47914	−	0.279006i	−0.268641	−	0.0167337i
$279$	9.72850	+	20.4479i	0.582430	+	1.22419i
$280$	−0.103340	−	0.00589344i	−0.00617576	−	0.000352200i
$281$	3.21906	−	3.83632i	0.192033	−	0.228856i	−0.661433	−	0.750004i	$-0.730052\pi$
$281$	3.21906	−	3.83632i	0.192033	−	0.228856i	0.853466	+	0.521148i	$0.174496\pi$
$282$	−0.964362	+	1.61501i	−0.0574269	+	0.0961722i
$283$	−18.4885	−	22.0337i	−1.09903	−	1.30977i	−0.946943	−	0.321400i	$-0.895846\pi$
$283$	−18.4885	−	22.0337i	−1.09903	−	1.30977i	−0.152083	−	0.988368i	$-0.548598\pi$
$284$	24.4699	+	12.5373i	1.45202	+	0.743954i
$285$	0.00219874	+	0.0462496i	0.000130242	+	0.00273959i
$286$	−4.91126	−	16.6488i	−0.290409	−	0.984464i
$287$	1.74858	−	1.33829i	0.103215	−	0.0789970i
$288$	−2.25089	−	16.8206i	−0.132635	−	0.991165i
$289$	4.81530	+	8.34034i	0.283253	+	0.490608i
$290$	−0.0369681	−	0.125319i	−0.00217084	−	0.00735898i
$291$	−3.18353	+	0.718713i	−0.186622	+	0.0421317i
$292$	1.63807	−	1.05855i	0.0958606	−	0.0619469i
$293$	4.42501	−	12.1576i	0.258512	−	0.710256i	−0.740748	−	0.671783i	$-0.765529\pi$
$293$	4.42501	−	12.1576i	0.258512	−	0.710256i	0.999260	−	0.0384727i	$-0.0122492\pi$
$294$	−14.2124	+	9.59203i	−0.828885	+	0.559418i
$295$	0.150041	+	0.0264563i	0.00873574	+	0.00154035i
$296$	3.48462	+	2.99651i	0.202539	+	0.174169i
$297$	15.6231	−	25.1636i	0.906543	−	1.46014i
$298$	12.9596	+	0.807254i	0.750729	+	0.0467630i
$299$	−12.0152	−	10.0819i	−0.694857	−	0.583054i
$300$	4.65565	+	16.6824i	0.268794	+	0.963158i
$301$	−3.21673	+	14.4252i	−0.185409	+	0.831453i
$302$	2.31213	+	20.4980i	0.133048	+	1.17953i
$303$	−4.30753	−	19.0801i	−0.247461	−	1.09612i
$304$	−0.773525	−	7.69187i	−0.0443647	−	0.441159i
$305$			0.119630i			0.00684999i
$306$	−21.8823	+	0.717998i	−1.25093	+	0.0410452i
$307$	20.8425	−	12.0334i	1.18954	−	0.686782i	0.231339	−	0.972873i	$-0.425689\pi$
$307$	20.8425	−	12.0334i	1.18954	−	0.686782i	0.958202	+	0.286091i	$0.0923559\pi$
$308$	23.2072	+	19.2667i	1.32235	+	1.09782i
$309$	−5.98208	+	11.6009i	−0.340308	+	0.659952i
$310$	−0.0876920	−	0.118788i	−0.00498057	−	0.00674669i
$311$	12.0906	−	10.1452i	0.685597	−	0.575284i	−0.232039	−	0.972706i	$-0.574540\pi$
$311$	12.0906	−	10.1452i	0.685597	−	0.575284i	0.917636	+	0.397422i	$0.130095\pi$
$312$	−3.95656	−	9.77870i	−0.223996	−	0.553610i
$313$	2.06531	−	0.751712i	0.116738	−	0.0424893i	−0.282991	−	0.959123i	$-0.591327\pi$
$313$	2.06531	−	0.751712i	0.116738	−	0.0424893i	0.399729	+	0.916633i	$0.369104\pi$
$314$	−0.901430	+	14.4715i	−0.0508707	+	0.816673i
$315$	−0.0875328	−	0.0662661i	−0.00493192	−	0.00373367i
$316$	−0.876829	+	7.01096i	−0.0493255	+	0.394397i
$317$	−4.17377	−	0.735948i	−0.234422	−	0.0413350i	0.0552028	−	0.998475i	$-0.482419\pi$
$317$	−4.17377	−	0.735948i	−0.234422	−	0.0413350i	−0.289625	+	0.957140i	$0.593531\pi$
$318$	−5.61086	+	0.904488i	−0.314642	+	0.0507212i
$319$	−13.0221	+	35.7779i	−0.729097	+	2.00318i
$320$	0.0353198	+	0.104867i	0.00197444	+	0.00586223i
$321$	9.25475	+	22.1005i	0.516550	+	1.23353i
$322$	27.0987	+	2.91290i	1.51015	+	0.162330i
$323$	−9.97350			−0.554940
$324$	7.95877	−	16.1449i	0.442154	−	0.896939i
$325$	5.38296	+	9.32356i	0.298593	+	0.517178i
$326$	−4.35555	+	18.0528i	−0.241232	+	0.999853i
$327$	−14.5593	−	1.85946i	−0.805133	−	0.102828i
$328$	−2.02422	−	1.20156i	−0.111769	−	0.0663451i
$329$	−0.608554	−	1.93845i	−0.0335507	−	0.106870i
$330$	−0.0687151	+	0.180490i	−0.00378264	+	0.00993566i
$331$	−18.9659	−	3.34420i	−1.04246	−	0.183814i	−0.373899	−	0.927470i	$-0.621979\pi$
$331$	−18.9659	−	3.34420i	−1.04246	−	0.183814i	−0.668563	+	0.743656i	$0.733090\pi$
$332$	−3.40778	−	8.07864i	−0.187026	−	0.443373i
$333$	1.29806	+	4.69861i	0.0711335	+	0.257482i
$334$	13.4863	+	8.94817i	0.737936	+	0.489622i
$335$	0.0148377	+	0.0124503i	0.000810670	+	0.000680233i
$336$	15.1774	+	10.2784i	0.827996	+	0.560733i
$337$	2.39033	+	13.5562i	0.130210	+	0.738455i	0.978077	+	0.208246i	$0.0667754\pi$
$337$	2.39033	+	13.5562i	0.130210	+	0.738455i	−0.847867	+	0.530209i	$0.822113\pi$
$338$	7.02470	+	9.51567i	0.382093	+	0.517584i
$339$	7.10908	−	0.337970i	0.386112	−	0.0183560i
$340$	0.139171	−	0.0318011i	0.00754762	−	0.00172466i
$341$			43.0255i			2.32996i
$342$	3.86473	−	7.23170i	0.208981	−	0.391046i
$343$	2.48557	−	18.3527i	0.134208	−	0.990953i
$344$	15.5919	−	2.55522i	0.840661	−	0.137768i
$345$	0.0384303	+	0.170226i	0.00206902	+	0.00916466i
$346$	−5.75060	+	4.24523i	−0.309154	+	0.228225i
$347$	4.98051	+	28.2459i	0.267368	+	1.51632i	0.762208	+	0.647333i	$0.224116\pi$
$347$	4.98051	+	28.2459i	0.267368	+	1.51632i	−0.494840	+	0.868984i	$0.664773\pi$
$348$	−5.75694	+	22.4106i	−0.308604	+	1.20134i
$349$	−3.14734	+	17.8495i	−0.168473	+	0.955460i	0.776937	+	0.629578i	$0.216772\pi$
$349$	−3.14734	+	17.8495i	−0.168473	+	0.955460i	−0.945411	+	0.325882i	$0.894339\pi$
$350$	−16.7948	−	8.24054i	−0.897722	−	0.440475i
$351$	2.29464	−	10.9509i	0.122479	−	0.584514i
$352$	9.86885	−	30.6978i	0.526011	−	1.63620i
$353$	−6.55109	−	17.9990i	−0.348679	−	0.957988i	−0.982787	−	0.184743i	$-0.940855\pi$
$353$	−6.55109	−	17.9990i	−0.348679	−	0.957988i	0.634108	−	0.773245i	$-0.281368\pi$
$354$	−20.4112	−	17.6449i	−1.08484	−	0.937818i
$355$	−0.122227	−	0.145665i	−0.00648714	−	0.00773107i
$356$	−13.3111	+	25.9800i	−0.705485	+	1.37694i
$357$	15.1531	−	18.1556i	0.801986	−	0.960898i
$358$	3.70769	+	0.894544i	0.195958	+	0.0472781i
$359$	7.52617	+	13.0357i	0.397216	+	0.687998i	0.993381	−	0.114864i	$-0.0366431\pi$
$359$	7.52617	+	13.0357i	0.397216	+	0.687998i	−0.596165	+	0.802862i	$0.703310\pi$
$360$	−0.0308701	+	0.113235i	−0.00162700	+	0.00596800i
$361$	−7.63240	+	13.2197i	−0.401705	+	0.695774i
$362$	13.1758	+	3.17889i	0.692506	+	0.167079i
$363$	31.3179	−	20.1226i	1.64377	−	1.05616i
$364$	10.7272	+	3.84080i	0.562256	+	0.201313i
$365$	−0.0132834	+	0.00234223i	−0.000695287	+	0.000122598i
$366$	10.8613	−	18.1893i	0.567729	−	0.950769i
$367$	−9.62497	−	1.69714i	−0.502419	−	0.0885901i	−0.0833060	−	0.996524i	$-0.526548\pi$
$367$	−9.62497	−	1.69714i	−0.502419	−	0.0885901i	−0.419113	+	0.907934i	$0.637659\pi$
$368$	−7.90523	−	28.0437i	−0.412088	−	1.46188i
$369$	−1.07267	−	2.25460i	−0.0558410	−	0.117370i
$370$	−0.0141502	−	0.0284609i	−0.000735634	−	0.00147961i
$371$	3.30471	−	5.17321i	0.171572	−	0.268580i
$372$	2.54841	+	26.0228i	0.132129	+	1.34922i
$373$	−3.35172	−	19.0086i	−0.173546	−	0.984226i	−0.939809	−	0.341700i	$-0.888997\pi$
$373$	−3.35172	−	19.0086i	−0.173546	−	0.984226i	0.766263	−	0.642527i	$-0.222114\pi$
$374$	−38.1311	−	16.6308i	−1.97171	−	0.859960i
$375$	0.0303504	−	0.237640i	0.00156729	−	0.0122717i
$376$	−1.68063	+	1.37592i	−0.0866717	+	0.0709575i
$377$			14.3826i			0.740742i
$378$	7.29268	+	18.0227i	0.375095	+	0.926986i
$379$		−	30.5848i		−	1.57104i	−0.618838	−	0.785519i	$-0.712396\pi$
$379$		−	30.5848i		−	1.57104i	0.618838	−	0.785519i	$-0.287604\pi$
$380$	−0.0157464	+	0.0510934i	−0.000807774	+	0.00262104i
$381$	8.03702	−	3.36556i	0.411749	−	0.172423i
$382$	14.5556	−	33.3731i	0.744732	−	1.70752i
$383$	−5.15207	−	29.2188i	−0.263258	−	1.49301i	−0.773949	−	0.633248i	$-0.781721\pi$
$383$	−5.15207	−	29.2188i	−0.263258	−	1.49301i	0.510691	−	0.859764i	$-0.329390\pi$
$384$	4.15068	−	19.1513i	0.211814	−	0.977310i
$385$	−0.0960926	−	0.185152i	−0.00489733	−	0.00943620i
$386$	17.6902	−	8.79519i	0.900405	−	0.447663i
$387$	15.2426	+	6.96457i	0.774826	+	0.354029i
$388$	−3.73940	−	0.467670i	−0.189839	−	0.0237424i
$389$	−1.14509	−	0.201910i	−0.0580584	−	0.0102373i	0.144544	−	0.989498i	$-0.453829\pi$
$389$	−1.14509	−	0.201910i	−0.0580584	−	0.0102373i	−0.202602	+	0.979261i	$0.564940\pi$
$390$	−0.00107275	+	0.0729470i	−5.43209e−5	+	0.00369381i
$391$	−37.0187	+	6.52740i	−1.87212	+	0.330105i
$392$	−19.1970	+	4.84513i	−0.969595	+	0.244716i
$393$	−1.29135	−	27.1631i	−0.0651401	−	1.37020i
$394$	−6.95354	+	28.8209i	−0.350314	+	1.45198i
$395$	0.0244325	−	0.0423184i	0.00122933	−	0.00212927i
$396$	26.8347	−	21.2041i	1.34849	−	1.06555i
$397$	12.2364	+	21.1941i	0.614127	+	1.06370i	0.990537	+	0.137246i	$0.0438252\pi$
$397$	12.2364	+	21.1941i	0.614127	+	1.06370i	−0.376410	+	0.926453i	$0.622841\pi$
$398$	−7.97931	+	33.0725i	−0.399966	+	1.65777i
$399$	3.05104	+	8.31447i	0.152743	+	0.416244i
$400$	−1.48470	+	19.9440i	−0.0742348	+	0.997202i
$401$	−0.963922	−	1.14876i	−0.0481360	−	0.0573662i	0.741439	−	0.671020i	$-0.234144\pi$
$401$	−0.963922	−	1.14876i	−0.0481360	−	0.0573662i	−0.789575	+	0.613654i	$0.789699\pi$
$402$	−1.12564	−	3.24015i	−0.0561419	−	0.161604i
$403$	5.55887	+	15.2729i	0.276907	+	0.760795i
$404$	2.80293	−	22.4117i	0.139451	−	1.11502i
$405$	−0.0941118	+	0.0814858i	−0.00467645	+	0.00404906i
$406$	−13.9265	−	20.7524i	−0.691159	−	1.02992i
$407$	−1.60834	+	9.12136i	−0.0797225	+	0.452129i
$408$	−24.0477	−	7.80022i	−1.19054	−	0.386168i
$409$	3.33542	+	18.9161i	0.164926	+	0.935340i	0.949141	+	0.314851i	$0.101955\pi$
$409$	3.33542	+	18.9161i	0.164926	+	0.935340i	−0.784215	+	0.620489i	$0.786934\pi$
$410$	0.00966898	+	0.0130976i	0.000477517	+	0.000646845i
$411$	23.4227	+	7.28558i	1.15536	+	0.359371i
$412$	−11.0458	+	10.2541i	−0.544186	+	0.505181i
$413$	28.8979	−	3.76809i	1.42197	−	0.185415i
$414$	9.61177	−	29.3713i	0.472393	−	1.44352i
$415$			0.0606387i			0.00297664i
$416$	−0.462965	−	12.1719i	−0.0226987	−	0.596777i
$417$	−2.97116	−	4.62418i	−0.145498	−	0.226447i
$418$	12.5343	−	9.25313i	0.613073	−	0.452585i
$419$	−1.32687	−	7.52504i	−0.0648217	−	0.367622i	−0.999913	−	0.0132144i	$-0.995794\pi$
$419$	−1.32687	−	7.52504i	−0.0648217	−	0.367622i	0.935091	−	0.354408i	$-0.115318\pi$
$420$	−0.0690857	−	0.106293i	−0.00337104	−	0.00518654i
$421$	−4.57960	−	3.84274i	−0.223196	−	0.187284i	0.524332	−	0.851514i	$-0.324315\pi$
$421$	−4.57960	−	3.84274i	−0.223196	−	0.187284i	−0.747528	+	0.664230i	$0.768759\pi$
$422$	−14.1401	+	21.3114i	−0.688331	+	1.03742i
$423$	−2.29338	+	0.218551i	−0.111508	+	0.0106263i
$424$	−6.44855	−	1.21766i	−0.313169	−	0.0591347i
$425$	25.4095	+	4.48037i	1.23254	+	0.217330i
$426$	5.35917	+	33.2448i	0.259652	+	1.61072i
$427$	6.85395	+	21.8322i	0.331686	+	1.05653i
$428$	1.38589	+	27.6319i	0.0669897	+	1.33564i
$429$	12.8764	−	16.9161i	0.621678	−	0.816715i
$430$	−0.106223	−	0.0256282i	−0.00512255	−	0.00123590i
$431$	2.53108	+	4.38396i	0.121918	+	0.211168i	0.920524	−	0.390686i	$-0.127762\pi$
$431$	2.53108	+	4.38396i	0.121918	+	0.211168i	−0.798606	+	0.601854i	$0.794429\pi$
$432$	14.9743	−	14.4142i	0.720453	−	0.693503i
$433$	−29.5886			−1.42194			−0.710968	−	0.703225i	$-0.751743\pi$
$433$	−29.5886			−1.42194			−0.710968	+	0.703225i	$0.751743\pi$
$434$	−22.8093	−	16.6543i	−1.09488	−	0.799434i
$435$	0.0969233	−	0.127331i	0.00464712	−	0.00610504i
$436$	−15.0837	−	7.72824i	−0.722376	−	0.370116i
$437$	4.81491	−	13.2288i	0.230328	−	0.632822i
$438$	2.23235	+	0.849886i	0.106666	+	0.0406091i
$439$	40.5976	+	7.15845i	1.93762	+	0.341654i	0.999982	−	0.00596909i	$-0.00190003\pi$
$439$	40.5976	+	7.15845i	1.93762	+	0.341654i	0.937634	+	0.347623i	$0.113011\pi$
$440$	−0.145401	+	0.169085i	−0.00693171	+	0.00806083i
$441$	−19.7711	−	7.07839i	−0.941481	−	0.337066i
$442$	−15.6842	−	0.976970i	−0.746021	−	0.0464697i
$443$	−2.65490	+	0.966303i	−0.126138	+	0.0459105i	−0.404318	−	0.914619i	$-0.632491\pi$
$443$	−2.65490	+	0.966303i	−0.126138	+	0.0459105i	0.278180	+	0.960529i	$0.410269\pi$
$444$	−0.432504	+	5.61208i	−0.0205257	+	0.266338i
$445$	0.154654	−	0.129770i	0.00733130	−	0.00615169i
$446$	10.5718	−	7.80435i	0.500589	−	0.369547i
$447$	8.59651	+	13.3792i	0.406601	+	0.632816i
$448$	12.4539	+	17.1143i	0.588391	+	0.808576i
$449$	28.5786	−	16.4999i	1.34871	−	0.778677i	0.360642	−	0.932704i	$-0.382558\pi$
$449$	28.5786	−	16.4999i	1.34871	−	0.778677i	0.988067	+	0.154027i	$0.0492243\pi$
$450$	−13.0948	+	16.6880i	−0.617296	+	0.786682i
$451$		−	4.74402i		−	0.223387i
$452$	7.85362	+	2.42040i	0.369403	+	0.113846i
$453$	−18.5604	+	17.1401i	−0.872043	+	0.805313i
$454$	−5.00493	+	0.564545i	−0.234893	+	0.0264954i
$455$	−0.0580317	−	0.0533086i	−0.00272057	−	0.00249914i
$456$	7.03299	−	6.33892i	0.329350	−	0.296847i
$457$	−5.75563	−	4.82954i	−0.269237	−	0.225917i	0.498166	−	0.867082i	$-0.334007\pi$
$457$	−5.75563	−	4.82954i	−0.269237	−	0.225917i	−0.767403	+	0.641165i	$0.778451\pi$
$458$	−1.45786	+	23.4044i	−0.0681213	+	1.09361i
$459$	−16.5697	−	21.0825i	−0.773408	−	0.984046i
$460$	−0.0250068	+	0.199949i	−0.00116595	+	0.00932268i
$461$	23.5584	+	4.15398i	1.09722	+	0.193470i	0.692820	−	0.721110i	$-0.256368\pi$
$461$	23.5584	+	4.15398i	1.09722	+	0.193470i	0.404404	+	0.914581i	$0.367479\pi$
$462$	−2.19953	+	36.8759i	−0.102331	+	1.71562i
$463$	−2.52793	+	6.94544i	−0.117483	+	0.322782i	−0.984471	−	0.175547i	$-0.943831\pi$
$463$	−2.52793	+	6.94544i	−0.117483	+	0.322782i	0.866988	+	0.498329i	$0.166053\pi$
$464$	−15.0397	+	22.0827i	−0.698202	+	1.02516i
$465$	0.0537095	−	0.172673i	0.00249072	−	0.00800752i
$466$	−7.83409	+	2.31100i	−0.362907	+	0.107055i
$467$	−6.92839	−	12.0003i	−0.320608	−	0.555309i	0.660006	−	0.751260i	$-0.270554\pi$
$467$	−6.92839	−	12.0003i	−0.320608	−	0.555309i	−0.980614	+	0.195952i	$0.937220\pi$
$468$	6.78601	−	10.9939i	0.313684	−	0.508194i
$469$	3.42116	+	1.42205i	0.157974	+	0.0656644i
$470$	0.0144077	−	0.00425016i	0.000664578	−	0.000196045i
$471$	−14.9401	+	9.59940i	−0.688403	+	0.442317i
$472$	−15.2498	−	27.1672i	−0.701931	−	1.25047i
$473$	20.4676	+	24.3923i	0.941101	+	1.12156i
$474$	−7.55699	+	4.21610i	−0.347104	+	0.193652i
$475$	−6.21123	+	7.40226i	−0.284991	+	0.339639i
$476$	23.5764	−	13.7771i	1.08062	−	0.631474i
$477$	−4.95985	−	4.88362i	−0.227096	−	0.223606i
$478$	−1.10935	+	17.8094i	−0.0507404	+	0.814582i
$479$	−16.1509	−	13.5522i	−0.737952	−	0.619215i	0.194335	−	0.980935i	$-0.437745\pi$
$479$	−16.1509	−	13.5522i	−0.737952	−	0.619215i	−0.932287	+	0.361720i	$0.882190\pi$
$480$	−0.0779270	+	0.110879i	−0.00355686	+	0.00506091i
$481$	0.607557	+	3.44563i	0.0277022	+	0.157107i
$482$	−19.3220	−	26.1736i	−0.880091	−	1.19217i
$483$	16.7662	+	28.8640i	0.762887	+	1.31336i
$484$	41.9042	−	9.57524i	1.90473	−	0.435238i
$485$	0.0225712	+	0.0130315i	0.00102490	+	0.000591728i
$486$	21.7075	−	3.84512i	0.984672	−	0.174418i
$487$	−4.59642	+	2.65375i	−0.208284	+	0.120253i	−0.600514	−	0.799615i	$-0.705037\pi$
$487$	−4.59642	+	2.65375i	−0.208284	+	0.120253i	0.392230	+	0.919867i	$0.371704\pi$
$488$	18.9283	−	15.4965i	0.856846	−	0.701493i
$489$	−20.9793	+	8.78523i	−0.948718	+	0.397282i
$490$	0.135351	+	0.0207267i	0.00611452	+	0.000936335i
$491$	30.4604	−	25.5593i	1.37466	−	1.15348i	0.403520	−	0.914971i	$-0.367787\pi$
$491$	30.4604	−	25.5593i	1.37466	−	1.15348i	0.971141	−	0.238506i	$-0.0766578\pi$
$492$	−0.280989	−	2.86930i	−0.0126680	−	0.129358i
$493$	26.4049	+	22.1563i	1.18922	+	0.997871i
$494$	3.25383	−	4.90403i	0.146397	−	0.220643i
$495$	−0.227992	+	0.0629864i	−0.0102475	+	0.00283103i
$496$	−7.43573	+	29.2624i	−0.333874	+	1.31392i
$497$	−30.6517	−	19.5807i	−1.37492	−	0.878313i
$498$	5.50543	−	9.21988i	0.246704	−	0.413153i
$499$	3.57679	−	9.82714i	0.160119	−	0.439923i	−0.833526	−	0.552480i	$-0.813682\pi$
$499$	3.57679	−	9.82714i	0.160119	−	0.439923i	0.993645	+	0.112557i	$0.0359039\pi$
$500$	0.126142	−	0.246198i	0.00564123	−	0.0110103i
$501$	0.941302	+	19.7999i	0.0420543	+	0.884596i
$502$	−39.7088	−	9.58043i	−1.77229	−	0.427596i
$503$	7.56216	+	13.0980i	0.337180	+	0.584013i	0.983901	−	0.178714i	$-0.0571936\pi$
$503$	7.56216	+	13.0980i	0.337180	+	0.584013i	−0.646721	+	0.762727i	$0.723860\pi$
$504$	0.853837	+	22.4337i	0.0380329	+	0.999276i
$505$	−0.0781027	+	0.135278i	−0.00347552	+	0.00601978i
$506$	40.4677	−	42.5483i	1.79901	−	1.89150i
$507$	−4.30248	+	13.8322i	−0.191080	+	0.614310i
$508$	10.0486	−	0.503990i	0.445833	−	0.0223610i
$509$	10.3805	+	12.3710i	0.460108	+	0.548335i	0.945355	−	0.326042i	$-0.105715\pi$
$509$	10.3805	+	12.3710i	0.460108	+	0.548335i	−0.485248	+	0.874377i	$0.661271\pi$
$510$	0.132270	+	0.114344i	0.00585702	+	0.00506323i
$511$	−2.29000	+	1.18850i	−0.101304	+	0.0525760i
$512$	12.0172	−	19.1725i	0.531091	−	0.847315i
$513$	9.94062	−	1.42635i	0.438889	−	0.0629751i
$514$	21.8164	+	1.35895i	0.962282	+	0.0599406i
$515$	0.0979485	−	0.0356503i	0.00431613	−	0.00157094i
$516$	13.8241	+	13.5408i	0.608570	+	0.596099i
$517$	−4.11332	−	1.49713i	−0.180904	−	0.0658436i
$518$	−4.21299	−	4.38334i	−0.185108	−	0.192593i
$519$	−8.35922	−	2.60011i	−0.366929	−	0.114132i
$520$	−0.0297675	+	0.0788064i	−0.00130539	+	0.00345589i
$521$			14.2206i			0.623018i	0.950243	+	0.311509i	$0.100834\pi$
$521$			14.2206i			0.623018i	−0.950243	+	0.311509i	$0.899166\pi$
$522$	−26.2972	+	10.5604i	−1.15100	+	0.462216i
$523$		−	21.2863i		−	0.930786i	−0.885104	−	0.465393i	$-0.845913\pi$
$523$		−	21.2863i		−	0.930786i	0.885104	−	0.465393i	$-0.154087\pi$
$524$	9.24811	−	30.0079i	0.404005	−	1.31090i
$525$	−4.03803	−	22.5534i	−0.176234	−	0.984309i
$526$	−12.8735	+	29.5163i	−0.561311	+	1.28697i
$527$	36.6027	+	13.3223i	1.59444	+	0.580328i
$528$	37.4590	−	12.5077i	1.63019	−	0.544330i
$529$	5.21968	−	29.6023i	0.226943	−	1.28705i
$530$	0.0378185	+	0.0250926i	0.00164273	+	0.00108995i
$531$	2.62504	−	32.9401i	0.113917	−	1.42948i
$532$	0.0536086	+	10.2266i	0.00232423	+	0.443378i
$533$	−0.612924	−	1.68400i	−0.0265487	−	0.0729419i
$534$	−35.2965	+	5.68990i	−1.52743	+	0.246226i
$535$	0.0654424	−	0.179802i	0.00282932	−	0.00777350i
$536$	0.0479090	−	3.96045i	0.00206935	−	0.171066i
$537$	1.80431	+	4.30874i	0.0778619	+	0.185936i
$538$	−19.1674	−	18.2302i	−0.826366	−	0.785958i
$539$	−28.1445	−	28.2843i	−1.21227	−	1.21829i
$540$	−0.134164	+	0.0515997i	−0.00577352	+	0.00222050i
$541$	8.54769	−	14.8050i	0.367494	−	0.636518i	−0.621679	−	0.783272i	$-0.713549\pi$
$541$	8.54769	−	14.8050i	0.367494	−	0.636518i	0.989173	+	0.146754i	$0.0468826\pi$
$542$	−7.68255	+	31.8425i	−0.329994	+	1.36775i
$543$	6.41189	+	15.3117i	0.275161	+	0.657089i
$544$	−23.0595	−	17.9008i	−0.988667	−	0.767491i
$545$	0.0753430	+	0.0897903i	0.00322734	+	0.00384619i
$546$	3.98357	+	13.3741i	0.170481	+	0.572359i
$547$	−15.6179	−	42.9099i	−0.667774	−	1.83469i	−0.537594	−	0.843204i	$-0.680667\pi$
$547$	−15.6179	−	42.9099i	−0.667774	−	1.83469i	−0.130180	−	0.991490i	$-0.541556\pi$
$548$	22.5825	+	17.0968i	0.964678	+	0.730340i
$549$	25.8296	−	2.46147i	1.10238	−	0.105053i
$550$	−36.0904	+	17.9434i	−1.53890	+	0.765110i
$551$	−12.1306	+	4.41518i	−0.516781	+	0.188093i
$552$	21.9557	−	28.1311i	0.934497	−	1.19734i
$553$	2.03433	−	9.12281i	0.0865086	−	0.387941i
$554$	9.46851	−	21.7094i	0.402278	−	0.922343i
$555$	0.0178411	−	0.0345988i	0.000757311	−	0.00146864i
$556$	−1.41381	−	6.18726i	−0.0599589	−	0.262398i
$557$	0.203736	+	0.117627i	0.00863257	+	0.00498402i	0.504310	−	0.863523i	$-0.331747\pi$
$557$	0.203736	+	0.117627i	0.00863257	+	0.00498402i	−0.495678	+	0.868507i	$0.665080\pi$
$558$	−23.8434	+	21.3779i	−1.00937	+	0.905000i
$559$	10.4169	+	6.01420i	0.440588	+	0.254374i
$560$	−0.0333561	−	0.142532i	−0.00140955	−	0.00602306i
$561$	−11.2200	−	49.6987i	−0.473709	−	2.09828i
$562$	6.49175	+	2.83137i	0.273838	+	0.119434i
$563$	−2.49355	−	14.1416i	−0.105091	−	0.595998i	−0.991184	−	0.132492i	$-0.957702\pi$
$563$	−2.49355	−	14.1416i	−0.105091	−	0.595998i	0.886094	−	0.463506i	$-0.153409\pi$
$564$	−2.57651	−	0.661865i	−0.108491	−	0.0278696i
$565$	−0.0435389	−	0.0365335i	−0.00183170	−	0.00153698i
$566$	22.4892	−	33.8947i	0.945292	−	1.42470i
$567$	−12.5066	+	20.2629i	−0.525228	+	0.850961i
$568$	−7.21472	+	38.2082i	−0.302723	+	1.60318i
$569$	−6.42183	+	7.65324i	−0.269217	+	0.320841i	−0.883668	−	0.468115i	$-0.844933\pi$
$569$	−6.42183	+	7.65324i	−0.269217	+	0.320841i	0.614450	+	0.788955i	$0.289378\pi$
$570$	−0.0618544	+	0.0214885i	−0.00259080	+	0.000900055i
$571$	8.40632	−	1.48226i	0.351794	−	0.0620307i	0.00504093	−	0.999987i	$-0.498395\pi$
$571$	8.40632	−	1.48226i	0.351794	−	0.0620307i	0.346753	+	0.937957i	$0.387284\pi$
$572$	20.6177	−	13.3235i	0.862069	−	0.557085i
$573$	43.4973	−	9.81997i	1.81713	−	0.410235i
$574$	2.51497	+	1.83632i	0.104973	+	0.0766465i
$575$	−18.2097	+	31.5401i	−0.759397	+	1.31531i
$576$	21.9153	−	9.78369i	0.913137	−	0.407654i
$577$	5.95537	−	10.3150i	0.247925	−	0.429419i	−0.715025	−	0.699099i	$-0.753585\pi$
$577$	5.95537	−	10.3150i	0.247925	−	0.429419i	0.962950	+	0.269680i	$0.0869179\pi$
$578$	−9.38629	+	9.86886i	−0.390418	+	0.410491i
$579$	21.5052	+	11.0893i	0.893725	+	0.460855i
$580$	0.155194	−	0.100289i	0.00644407	−	0.00416427i
$581$	3.47417	+	11.0664i	0.144133	+	0.459112i
$582$	−2.24872	−	4.03064i	−0.0932125	−	0.167075i
$583$	−4.52341	−	12.4280i	−0.187340	−	0.514713i
$584$	2.09129	+	1.79835i	0.0865382	+	0.0744164i
$585$	−0.0727931	+	0.0518149i	−0.00300962	+	0.00214228i
$586$	18.2615	+	1.13751i	0.754377	+	0.0469902i
$587$	−32.8836	+	11.9686i	−1.35725	+	0.493999i	−0.915203	−	0.402993i	$-0.867970\pi$
$587$	−32.8836	+	11.9686i	−1.35725	+	0.493999i	−0.442047	+	0.896992i	$0.645748\pi$
$588$	−18.6978	−	15.4400i	−0.771083	−	0.636735i
$589$	−11.1750	+	9.37694i	−0.460458	+	0.386370i
$590$	0.0241507	+	0.214106i	0.000994270	+	0.00881460i
$591$	−33.4931	+	14.0254i	−1.37772	+	0.576930i
$592$	−2.67023	+	5.92564i	−0.109746	+	0.243542i
$593$	−31.0652	−	17.9355i	−1.27570	−	0.736523i	−0.299642	−	0.954052i	$-0.596867\pi$
$593$	−31.0652	−	17.9355i	−1.27570	−	0.736523i	−0.976054	+	0.217528i	$0.930201\pi$
$594$	40.3839	+	11.1227i	1.65697	+	0.456371i
$595$	−0.187266	+	0.0244182i	−0.00767717	+	0.00100105i
$596$	4.09060	+	17.9017i	0.167558	+	0.733284i
$597$	−38.4338	+	16.0944i	−1.57299	+	0.658701i
$598$	8.86772	−	20.3319i	0.362628	−	0.831432i
$599$	−6.79622	−	2.47362i	−0.277686	−	0.101070i	0.199423	−	0.979913i	$-0.436093\pi$
$599$	−6.79622	−	2.47362i	−0.277686	−	0.101070i	−0.477109	+	0.878844i	$0.658315\pi$
$600$	−20.7655	+	12.9902i	−0.847750	+	0.530325i
$601$	−35.5366	+	12.9343i	−1.44957	+	0.527599i	−0.942470	−	0.334290i	$-0.891504\pi$
$601$	−35.5366	+	12.9343i	−1.44957	+	0.527599i	−0.507097	+	0.861889i	$0.669281\pi$
$602$	−20.8538	+	1.40876i	−0.849938	+	0.0574169i
$603$	2.38288	−	3.45981i	0.0970383	−	0.140895i
$604$	−26.8789	+	11.3382i	−1.09369	+	0.461345i
$605$	−0.292760	−	0.0516215i	−0.0119024	−	0.00209871i
$606$	24.1572	−	13.4775i	0.981318	−	0.547485i
$607$	3.27497	−	8.99792i	0.132927	−	0.365214i	−0.855316	−	0.518107i	$-0.826637\pi$
$607$	3.27497	−	8.99792i	0.132927	−	0.365214i	0.988243	+	0.152893i	$0.0488590\pi$
$608$	10.1239	−	4.12702i	0.410580	−	0.167373i
$609$	10.3931	−	28.7905i	0.421150	−	1.16665i
$610$	−0.162269	+	0.0478682i	−0.00657009	+	0.00193813i
$611$	−1.65354			−0.0668952
$612$	−9.72979	−	29.3944i	−0.393303	−	1.18820i
$613$	−16.2468			−0.656202			−0.328101	−	0.944643i	$-0.606409\pi$
$613$	−16.2468			−0.656202			−0.328101	+	0.944643i	$0.606409\pi$
$614$	24.6622	+	23.4563i	0.995286	+	0.946618i
$615$	−0.00592204	+	0.0190390i	−0.000238800	+	0.000767728i
$616$	−16.8479	+	39.1881i	−0.678821	+	1.57893i
$617$	−6.34195	+	17.4244i	−0.255317	+	0.701479i	0.744123	+	0.668042i	$0.232867\pi$
$617$	−6.34195	+	17.4244i	−0.255317	+	0.701479i	−0.999441	+	0.0334366i	$0.989355\pi$
$618$	−18.1294	−	3.47232i	−0.729272	−	0.139677i
$619$	−0.355165	−	0.975807i	−0.0142753	−	0.0392210i	0.932350	−	0.361556i	$-0.117754\pi$
$619$	−0.355165	−	0.975807i	−0.0142753	−	0.0392210i	−0.946626	+	0.322335i	$0.895532\pi$
$620$	0.126038	−	0.166479i	0.00506182	−	0.00668596i
$621$	35.9632	−	11.8001i	1.44315	−	0.473521i
$622$	18.5992	+	12.3406i	0.745758	+	0.494812i
$623$	20.7891	−	32.5433i	0.832896	−	1.30382i
$624$	11.6809	−	9.27959i	0.467611	−	0.371481i
$625$	19.1489	−	16.0678i	0.765957	−	0.642714i
$626$	1.84605	+	2.50066i	0.0737828	+	0.0999463i
$627$	18.2202	+	5.66734i	0.727644	+	0.226332i
$628$	−19.9902	+	4.56783i	−0.797696	+	0.182276i
$629$	7.26173	+	4.19256i	0.289544	+	0.167168i
$630$	0.0548601	−	0.145247i	0.00218568	−	0.00578679i
$631$	24.6697	−	14.2431i	0.982085	−	0.567007i	0.0791861	−	0.996860i	$-0.474768\pi$
$631$	24.6697	−	14.2431i	0.982085	−	0.567007i	0.902899	+	0.429853i	$0.141435\pi$
$632$	−9.86070	+	1.61598i	−0.392238	+	0.0642801i
$633$	−31.2884	+	1.48747i	−1.24360	+	0.0591217i
$634$	−0.671812	−	5.95589i	−0.0266811	−	0.236538i
$635$	−0.0653862	−	0.0237986i	−0.00259477	−	0.000944420i
$636$	−3.47197	−	7.24880i	−0.137673	−	0.287434i
$637$	−13.6448	−	6.40388i	−0.540628	−	0.253731i
$638$	−53.7406	−	3.34751i	−2.12761	−	0.132529i
$639$	−28.9359	+	29.3875i	−1.14468	+	1.16255i
$640$	−0.128111	+	0.0898696i	−0.00506404	+	0.00355241i
$641$	−29.6346	+	35.3172i	−1.17050	+	1.39495i	−0.268459	+	0.963291i	$0.586514\pi$
$641$	−29.6346	+	35.3172i	−1.17050	+	1.39495i	−0.902039	+	0.431654i	$0.857930\pi$
$642$	−26.2746	+	21.3966i	−1.03698	+	0.844455i
$643$	0.865546	+	1.03152i	0.0341338	+	0.0406791i	0.782841	−	0.622221i	$-0.213770\pi$
$643$	0.865546	+	1.03152i	0.0341338	+	0.0406791i	−0.748707	+	0.662901i	$0.769325\pi$
$644$	6.89201	+	37.9230i	0.271583	+	1.49437i
$645$	−0.0516926	−	0.123443i	−0.00203540	−	0.00486057i
$646$	−3.99075	−	13.5283i	−0.157014	−	0.532264i
$647$	−15.3895	−	26.6554i	−0.605024	−	1.04793i	−0.992048	−	0.125863i	$-0.959830\pi$
$647$	−15.3895	−	26.6554i	−0.605024	−	1.04793i	0.387023	−	0.922070i	$-0.373503\pi$
$648$	25.0840	+	4.33534i	0.985391	+	0.170308i
$649$	31.3933	−	54.3748i	1.23230	−	2.13440i
$650$	−10.4928	+	11.0323i	−0.411562	+	0.432721i
$651$	−0.0910904	−	34.5896i	−0.00357011	−	1.35567i
$652$	−26.2301	+	1.31558i	−1.02725	+	0.0515222i
$653$	−2.68956	+	0.474242i	−0.105251	+	0.0185585i	−0.226025	−	0.974121i	$-0.572573\pi$
$653$	−2.68956	+	0.474242i	−0.105251	+	0.0185585i	0.120775	+	0.992680i	$0.461462\pi$
$654$	−3.30349	−	20.4927i	−0.129177	−	0.801328i
$655$	−0.139591	+	0.166358i	−0.00545427	+	0.00650015i
$656$	0.819869	−	3.22649i	0.0320105	−	0.125973i
$657$	0.779032	+	2.81986i	0.0303929	+	0.110013i
$658$	2.38587	−	1.60110i	0.0930107	−	0.0624175i
$659$	−12.7083	−	10.6635i	−0.495043	−	0.415391i	0.360786	−	0.932649i	$-0.382508\pi$
$659$	−12.7083	−	10.6635i	−0.495043	−	0.415391i	−0.855830	+	0.517258i	$0.826953\pi$
$660$	−0.272317	−	0.0209865i	−0.0105999	−	0.000816900i
$661$	3.18720	−	2.67438i	0.123968	−	0.104021i	−0.578696	−	0.815543i	$-0.696438\pi$
$661$	3.18720	−	2.67438i	0.123968	−	0.104021i	0.702664	+	0.711522i	$0.251994\pi$
$662$	−3.05277	−	27.0640i	−0.118649	−	1.05187i
$663$	−10.4038	−	16.1921i	−0.404051	−	0.628848i
$664$	9.59450	−	7.85495i	0.372339	−	0.304831i
$665$	0.0271470	−	0.0653099i	0.00105272	−	0.00253261i
$666$	−5.85391	+	3.64081i	−0.226834	+	0.141078i
$667$	−42.1356	+	24.3270i	−1.63150	+	0.941946i
$668$	−6.74120	+	21.8736i	−0.260825	+	0.846315i
$669$	15.3674	+	4.78000i	0.594139	+	0.184805i
$670$	−0.0109508	+	0.0251080i	−0.000423068	+	0.000970008i
$671$	46.3270	+	16.8616i	1.78843	+	0.650937i
$672$	−7.86889	+	24.6998i	−0.303549	+	0.952816i
$673$	−1.93250	+	10.9598i	−0.0744925	+	0.422468i	0.924641	+	0.380840i	$0.124365\pi$
$673$	−1.93250	+	10.9598i	−0.0744925	+	0.422468i	−0.999133	+	0.0416272i	$0.986746\pi$
$674$	−17.4316	+	8.66663i	−0.671439	+	0.333826i
$675$	−25.9665	−	0.831685i	−0.999449	−	0.0320116i
$676$	−10.0965	+	13.3360i	−0.388326	+	0.512925i
$677$	−2.59808	+	3.09627i	−0.0998524	+	0.118999i	−0.813656	−	0.581346i	$-0.802526\pi$
$677$	−2.59808	+	3.09627i	−0.0998524	+	0.118999i	0.713804	+	0.700345i	$0.246971\pi$
$678$	3.30302	+	9.50771i	0.126852	+	0.365141i
$679$	4.86579	+	1.08504i	0.186732	+	0.0416401i
$680$	0.0988231	+	0.176051i	0.00378969	+	0.00675124i
$681$	−4.18504	−	4.53182i	−0.160371	−	0.173660i
$682$	−58.3609	+	17.2160i	−2.23475	+	0.659235i
$683$	21.7031			0.830446			0.415223	−	0.909720i	$-0.363704\pi$
$683$	21.7031			0.830446			0.415223	+	0.909720i	$0.363704\pi$
$684$	11.3557	+	2.34856i	0.434195	+	0.0897994i
$685$	−0.0979449	−	0.169646i	−0.00374228	−	0.00648182i
$686$	25.8887	−	3.97207i	0.988434	−	0.151654i
$687$	−24.1622	+	15.5249i	−0.921846	+	0.592311i
$688$	9.70485	+	20.1269i	0.369994	+	0.767330i
$689$	−3.21137	−	3.82716i	−0.122343	−	0.145803i
$690$	−0.215522	+	0.120241i	−0.00820477	+	0.00457750i
$691$	−5.61793	−	15.4351i	−0.213716	−	0.587180i	0.785794	−	0.618489i	$-0.212255\pi$
$691$	−5.61793	−	15.4351i	−0.213716	−	0.587180i	−0.999510	+	0.0313085i	$0.990033\pi$
$692$	−8.05936	−	6.10160i	−0.306371	−	0.231948i
$693$	−37.9993	+	24.5572i	−1.44347	+	0.932851i
$694$	−36.3205	+	18.0578i	−1.37871	+	0.685466i
$695$	−0.00762205	+	0.0432268i	−0.000289121	+	0.00163969i
$696$	−32.7019	+	1.15841i	−1.23956	+	0.0439096i
$697$	−4.03584	−	1.46892i	−0.152868	−	0.0556395i
$698$	−25.4708	+	2.87306i	−0.964085	+	0.108747i
$699$	−7.95985	−	6.05899i	−0.301069	−	0.229172i
$700$	4.45748	−	26.0783i	0.168477	−	0.985667i
$701$		−	32.0058i		−	1.20884i	−0.796664	−	0.604422i	$-0.793404\pi$
$701$		−	32.0058i		−	1.20884i	0.796664	−	0.604422i	$-0.206596\pi$
$702$	15.7722	−	1.26932i	0.595284	−	0.0479073i
$703$	−2.71961	+	1.57017i	−0.102572	+	0.0592200i
$704$	45.5881	+	1.10311i	1.71817	+	0.0415749i
$705$	0.0146390	+	0.0111431i	0.000551336	+	0.000419674i
$706$	21.7929	−	16.0881i	0.820188	−	0.605483i
$707$	−6.50308	+	29.1626i	−0.244574	+	1.09677i
$708$	15.7668	−	34.7466i	0.592553	−	1.30586i
$709$	−5.32213	+	30.1833i	−0.199877	+	1.13356i	0.705424	+	0.708786i	$0.250757\pi$
$709$	−5.32213	+	30.1833i	−0.199877	+	1.13356i	−0.905301	+	0.424771i	$0.860354\pi$
$710$	0.148676	−	0.224078i	0.00557971	−	0.00840948i
$711$	−9.63978	−	4.40455i	−0.361520	−	0.165184i
$712$	−40.5661	−	7.65997i	−1.52028	−	0.287069i
$713$	−35.3414	+	42.1182i	−1.32355	+	1.57734i
$714$	30.6900	+	13.2893i	1.14855	+	0.497341i
$715$	−0.167193	+	0.0294807i	−0.00625268	+	0.00110252i
$716$	0.270195	+	5.38715i	0.0100977	+	0.201327i
$717$	−18.3861	+	11.8135i	−0.686640	+	0.441185i
$718$	−14.6705	+	15.4247i	−0.547498	+	0.575646i
$719$	−18.3973			−0.686104			−0.343052	−	0.939316i	$-0.611461\pi$
$719$	−18.3973			−0.686104			−0.343052	+	0.939316i	$0.611461\pi$
$720$	−0.165947	+	0.00343622i	−0.00618447	+	0.000128060i
$721$	15.8328	−	12.1179i	0.589646	−	0.451292i
$722$	−20.9855	−	5.06312i	−0.781001	−	0.188430i
$723$	11.8343	−	38.0466i	0.440122	−	1.41497i
$724$	0.960177	+	19.1440i	0.0356847	+	0.711482i
$725$	32.8885	−	5.79914i	1.22145	−	0.215375i
$726$	39.8263	+	34.4287i	1.47809	+	1.27777i
$727$	−46.6327	−	8.22260i	−1.72951	−	0.304959i	−0.781667	−	0.623695i	$-0.785631\pi$
$727$	−46.6327	−	8.22260i	−1.72951	−	0.304959i	−0.947844	+	0.318736i	$0.896742\pi$
$728$	−0.917456	+	16.0874i	−0.0340032	+	0.596240i
$729$	19.5302	+	18.6433i	0.723341	+	0.690491i
$730$	−0.00849223	−	0.0170808i	−0.000314311	−	0.000632188i
$731$	27.0886	−	9.85944i	1.00191	−	0.364665i
$732$	29.0184	+	7.45437i	1.07255	+	0.275522i
$733$	3.53949	−	2.96999i	0.130734	−	0.109699i	−0.575076	−	0.818100i	$-0.695028\pi$
$733$	3.53949	−	2.96999i	0.130734	−	0.109699i	0.705810	+	0.708401i	$0.250583\pi$
$734$	−1.54924	−	13.7346i	−0.0571835	−	0.506955i
$735$	0.0776439	+	0.148646i	0.00286394	+	0.00548288i
$736$	34.8761	−	21.9441i	1.28555	−	0.808871i
$737$	6.91276	−	3.99108i	0.254635	−	0.147013i
$738$	2.62899	−	2.35714i	0.0967745	−	0.0867677i
$739$	11.5549	+	6.67122i	0.425054	+	0.245405i	0.697237	−	0.716841i	$-0.254412\pi$
$739$	11.5549	+	6.67122i	0.425054	+	0.245405i	−0.272184	+	0.962245i	$0.587746\pi$
$740$	0.0329432	−	0.0305819i	0.00121101	−	0.00112421i
$741$	7.19988	−	0.342287i	0.264494	−	0.0125742i
$742$	8.33941	+	2.41261i	0.306149	+	0.0885698i
$743$	5.07270	+	28.7687i	0.186099	+	1.05542i	0.924535	+	0.381098i	$0.124454\pi$
$743$	5.07270	+	28.7687i	0.186099	+	1.05542i	−0.738435	+	0.674324i	$0.764435\pi$
$744$	−34.2784	+	13.8694i	−1.25671	+	0.508476i
$745$	0.0220530	−	0.125069i	0.000807960	−	0.00458217i
$746$	24.4426	−	12.1524i	0.894906	−	0.444930i
$747$	13.0926	−	1.24769i	0.479035	−	0.0456504i
$748$	7.30091	−	58.3767i	0.266948	−	2.13446i
$749$	1.64172	−	36.5627i	0.0599873	−	1.33597i
$750$	0.334486	−	0.0539201i	0.0122137	−	0.00196888i
$751$	−9.48036	+	1.67164i	−0.345943	+	0.0609991i	−0.343920	−	0.938999i	$-0.611755\pi$
$751$	−9.48036	+	1.67164i	−0.345943	+	0.0609991i	−0.00202294	+	0.999998i	$0.500644\pi$
$752$	−2.53881	−	1.72909i	−0.0925807	−	0.0630535i
$753$	−19.3239	−	46.1460i	−0.704203	−	1.68165i
$754$	−19.5089	+	5.75498i	−0.710474	+	0.209584i
$755$	0.201754			0.00734259
$756$	−21.5284	+	17.1035i	−0.782979	+	0.622048i
$757$	18.1573			0.659939			0.329969	−	0.943992i	$-0.392962\pi$
$757$	18.1573			0.659939			0.329969	+	0.943992i	$0.392962\pi$
$758$	41.4861	−	12.2381i	1.50684	−	0.444507i
$759$	71.3371	+	9.11087i	2.58937	+	0.330704i
$760$	−0.0756051		0.000914584i	−0.00274249		3.31754e-5i
$761$	1.45089	−	0.255831i	0.0525947	−	0.00927386i	−0.147289	−	0.989094i	$-0.547055\pi$
$761$	1.45089	−	0.255831i	0.0525947	−	0.00927386i	0.199884	+	0.979820i	$0.435944\pi$
$762$	7.78103	+	9.55495i	0.281877	+	0.346139i
$763$	18.8942	+	12.0699i	0.684018	+	0.436959i
$764$	51.0924	+	6.38990i	1.84846	+	0.231178i
$765$	−0.0170109	+	0.213461i	−0.000615032	+	0.00771769i
$766$	37.5717	−	18.6799i	1.35752	−	0.674931i
$767$	4.11857	−	23.3576i	0.148713	−	0.843393i
$768$	27.6381	−	2.03301i	0.997306	−	0.0733599i
$769$	1.27700	+	7.24225i	0.0460499	+	0.261162i	0.999137	−	0.0415338i	$-0.0132244\pi$
$769$	1.27700	+	7.24225i	0.0460499	+	0.261162i	−0.953087	+	0.302696i	$0.902113\pi$
$770$	0.212694	−	0.204428i	0.00766497	−	0.00736708i
$771$	14.4715	+	22.5229i	0.521180	+	0.811142i
$772$	19.0085	+	20.4761i	0.684130	+	0.736952i
$773$	−9.62168	−	5.55508i	−0.346068	−	0.199802i	0.316884	−	0.948464i	$-0.397363\pi$
$773$	−9.62168	−	5.55508i	−0.346068	−	0.199802i	−0.662952	+	0.748662i	$0.730697\pi$
$774$	−3.34782	+	23.4623i	−0.120335	+	0.843333i
$775$	32.6829	−	18.8695i	1.17400	−	0.677812i
$776$	−0.861906	−	5.25935i	−0.0309406	−	0.188800i
$777$	1.27369	−	7.33636i	0.0456932	−	0.263190i
$778$	−0.184314	−	1.63402i	−0.00660799	−	0.0585825i
$779$	1.23216	−	1.03391i	0.0441468	−	0.0370436i
$780$	−0.0993764	+	0.0277335i	−0.00355825	+	0.000993020i
$781$	−73.6366	+	26.8015i	−2.63493	+	0.959035i
$782$	−23.6664	−	47.6013i	−0.846309	−	1.70222i
$783$	−29.4865	−	18.3070i	−1.05376	−	0.654239i
$784$	−14.2535	−	24.1006i	−0.509052	−	0.860736i
$785$	0.139660	+	0.0246258i	0.00498467	+	0.000878932i
$786$	36.3280	−	12.6205i	1.29578	−	0.450160i
$787$	−28.3277	+	4.99494i	−1.00977	+	0.178050i	−0.653978	−	0.756513i	$-0.726901\pi$
$787$	−28.3277	+	4.99494i	−1.00977	+	0.178050i	−0.355796	+	0.934564i	$0.615790\pi$
$788$	−41.8758	+	2.10030i	−1.49176	+	0.0748202i
$789$	−38.4705	+	8.68510i	−1.36959	+	0.309198i
$790$	0.0671781	+	0.0162079i	0.00239009	+	0.000576650i
$791$	−10.0389	−	4.17280i	−0.356941	−	0.148368i
$792$	39.4993	+	27.9148i	1.40355	+	0.991908i
$793$	18.6233			0.661333
$794$	−23.8520	+	25.0783i	−0.846475	+	0.889994i
$795$	0.00263962	+	0.0555234i	9.36176e−5	+	0.00196921i
$796$	−48.0532	+	2.41013i	−1.70320	+	0.0854248i
$797$	−30.5136	+	5.38037i	−1.08085	+	0.190582i	−0.685589	−	0.727988i	$-0.740455\pi$
$797$	−30.5136	+	5.38037i	−1.08085	+	0.190582i	−0.395257	+	0.918571i	$0.629344\pi$
$798$	−10.0571	+	7.46542i	−0.356019	+	0.264273i
$799$	−2.54727	+	3.03572i	−0.0901161	+	0.107396i
$800$	−27.6467	+	5.96643i	−0.977459	+	0.210945i
$801$	−31.2011	−	30.7216i	−1.10244	−	1.08549i
$802$	1.17251	−	1.76715i	0.0414026	−	0.0624001i
$803$	−0.965244	+	5.47417i	−0.0340627	+	0.193179i
$804$	3.94461	−	2.82335i	0.139116	−	0.0995717i
$805$	0.0580182	−	0.260178i	0.00204487	−	0.00917008i
$806$	−18.4922	+	13.6514i	−0.651360	+	0.480850i
$807$	4.10432	−	32.1364i	0.144479	−	1.13125i
$808$	31.5214	−	5.16574i	1.10892	−	0.181730i
$809$	−24.0954	+	13.9115i	−0.847148	+	0.489101i	−0.859687	−	0.510821i	$-0.829342\pi$
$809$	−24.0954	+	13.9115i	−0.847148	+	0.489101i	0.0125398	+	0.999921i	$0.496008\pi$
$810$	−0.148187	−	0.0950504i	−0.00520676	−	0.00333973i
$811$		−	34.3213i		−	1.20519i	−0.798049	−	0.602593i	$-0.794134\pi$
$811$		−	34.3213i		−	1.20519i	0.798049	−	0.602593i	$-0.205866\pi$
$812$	22.5766	−	27.1940i	0.792283	−	0.954322i
$813$	−37.0044	+	15.4959i	−1.29780	+	0.543464i
$814$	−13.0160	+	1.46818i	−0.456211	+	0.0514596i
$815$	0.170680	+	0.0621224i	0.00597866	+	0.00217605i
$816$	0.958102	−	35.7400i	0.0335403	−	1.25115i
$817$	−1.87472	+	10.6321i	−0.0655883	+	0.371970i
$818$	−24.3236	+	12.0932i	−0.850456	+	0.422830i
$819$	−10.3159	+	13.6266i	−0.360468	+	0.476152i
$820$	−0.0138971	+	0.0183561i	−0.000485306	+	0.000641022i
$821$	9.70850	+	26.6739i	0.338829	+	0.930925i	0.985727	+	0.168349i	$0.0538436\pi$
$821$	9.70850	+	26.6739i	0.338829	+	0.930925i	−0.646898	+	0.762576i	$0.723934\pi$
$822$	−0.510095	+	34.6864i	−0.0177916	+	1.20983i
$823$	11.7048	+	13.9493i	0.408005	+	0.486242i	0.930443	−	0.366435i	$-0.119422\pi$
$823$	11.7048	+	13.9493i	0.408005	+	0.486242i	−0.522438	+	0.852677i	$0.674977\pi$
$824$	−18.3287	−	10.8798i	−0.638510	−	0.379015i
$825$	−43.8736	−	22.6237i	−1.52748	−	0.787655i
$826$	16.6742	+	37.6901i	0.580170	+	1.31141i
$827$	20.7902	+	36.0096i	0.722944	+	1.25218i	0.959815	+	0.280635i	$0.0905451\pi$
$827$	20.7902	+	36.0096i	0.722944	+	1.25218i	−0.236870	+	0.971541i	$0.576122\pi$
$828$	43.6860	+	1.28516i	1.51819	+	0.0446625i
$829$	−24.6751			−0.857002			−0.428501	−	0.903541i	$-0.640958\pi$
$829$	−24.6751			−0.857002			−0.428501	+	0.903541i	$0.640958\pi$
$830$	−0.0822519	+	0.0242637i	−0.00285501	+	0.000842205i
$831$	28.2952	−	6.38793i	0.981550	−	0.221595i
$832$	16.3251	−	5.49839i	0.565969	−	0.190622i
$833$	−32.7766	+	15.1853i	−1.13564	+	0.526139i
$834$	5.08349	−	5.88045i	0.176027	−	0.203623i
$835$	0.101752	−	0.121263i	0.00352126	−	0.00419648i
$836$	17.5666	+	13.2994i	0.607554	+	0.459968i
$837$	−38.3873	−	8.04366i	−1.32686	−	0.278030i
$838$	9.67623	−	4.81083i	0.334260	−	0.166187i
$839$	−1.01814	+	5.77416i	−0.0351501	+	0.199346i	−0.997326	−	0.0730834i	$-0.976716\pi$
$839$	−1.01814	+	5.77416i	−0.0351501	+	0.199346i	0.962176	+	0.272430i	$0.0878272\pi$
$840$	0.116534	−	0.136241i	0.00402082	−	0.00470076i
$841$	14.6732	+	5.34059i	0.505971	+	0.184158i
$842$	3.37994	−	7.74950i	0.116480	−	0.267066i
$843$	1.91018	+	8.46111i	0.0657901	+	0.291416i
$844$	−34.5653	−	10.6526i	−1.18979	−	0.366678i
$845$	0.100184	−	0.0578410i	0.00344642	−	0.00198979i
$846$	−1.21411	−	3.02335i	−0.0417420	−	0.103945i
$847$	−56.3855	+	7.35227i	−1.93743	+	0.252627i
$848$	−0.928628	−	9.23421i	−0.0318892	−	0.317104i
$849$	49.7627	−	2.36575i	1.70785	−	0.0811924i
$850$	4.08992	+	36.2588i	0.140283	+	1.24367i
$851$	−9.06676	+	7.60792i	−0.310805	+	0.260796i
$852$	−42.9498	+	20.5717i	−1.47143	+	0.704776i
$853$	17.0863	+	14.3371i	0.585022	+	0.490892i	0.886592	−	0.462552i	$-0.153066\pi$
$853$	17.0863	+	14.3371i	0.585022	+	0.490892i	−0.301570	+	0.953444i	$0.597511\pi$
$854$	−26.8712	+	18.0327i	−0.919514	+	0.617066i
$855$	−0.0660479	−	0.0454892i	−0.00225879	−	0.00155570i
$856$	−36.9261	+	12.9364i	−1.26211	+	0.442156i
$857$	16.6234	−	19.8110i	0.567844	−	0.676730i	−0.403343	−	0.915049i	$-0.632152\pi$
$857$	16.6234	−	19.8110i	0.567844	−	0.676730i	0.971187	+	0.238319i	$0.0765963\pi$
$858$	28.0977	+	10.6972i	0.959239	+	0.365196i
$859$	44.1447	−	7.78391i	1.50620	−	0.265584i	0.641207	−	0.767368i	$-0.278434\pi$
$859$	44.1447	−	7.78391i	1.50620	−	0.265584i	0.864993	+	0.501785i	$0.167323\pi$
$860$	−0.00774094	−	0.154339i	−0.000263964	−	0.00526291i
$861$	0.0100437	+	3.81387i	0.000342288	+	0.129976i
$862$	−4.93374	+	5.18740i	−0.168044	+	0.176684i
$863$	2.41252	−	4.17861i	0.0821232	−	0.142242i	−0.822039	−	0.569432i	$-0.807163\pi$
$863$	2.41252	−	4.17861i	0.0821232	−	0.142242i	0.904162	+	0.427190i	$0.140497\pi$
$864$	25.5436	+	14.5440i	0.869009	+	0.494796i
$865$	0.0349550	+	0.0605439i	0.00118851	+	0.00205855i
$866$	−11.8394	−	40.1347i	−0.402320	−	1.36383i
$867$	−16.5463	−	2.11322i	−0.561941	−	0.0717688i
$868$	13.4636	−	37.6031i	0.456984	−	1.27633i
$869$	−12.9442	−	15.4263i	−0.439101	−	0.523300i
$870$	0.211497	+	0.0805199i	0.00717042	+	0.00272988i
$871$	1.93819	−	2.30985i	0.0656731	−	0.0782662i
$872$	4.44728	−	23.5522i	0.150604	−	0.797579i
$873$	2.34924	−	5.14152i	0.0795096	−	0.174014i
$874$	19.8706	+	1.23774i	0.672132	+	0.0418672i
$875$	−0.197007	+	0.308395i	−0.00666004	+	0.0104257i
$876$	−0.259567	+	3.36808i	−0.00876995	+	0.113797i
$877$	23.9288	+	8.70935i	0.808017	+	0.294094i	0.712804	−	0.701363i	$-0.247425\pi$
$877$	23.9288	+	8.70935i	0.808017	+	0.294094i	0.0952123	+	0.995457i	$0.469647\pi$
$878$	6.53461	+	57.9320i	0.220532	+	1.95511i
$879$	12.1135	+	18.8529i	0.408577	+	0.635891i
$880$	−0.287532	−	0.129568i	−0.00969270	−	0.00436775i
$881$	−17.4100	+	10.0517i	−0.586558	+	0.338649i	−0.763735	−	0.645529i	$-0.776637\pi$
$881$	−17.4100	+	10.0517i	−0.586558	+	0.338649i	0.177177	+	0.984179i	$0.443303\pi$
$882$	1.69020	−	29.6503i	0.0569120	−	0.998379i
$883$	31.6236	+	18.2579i	1.06422	+	0.614427i	0.926596	−	0.376057i	$-0.122720\pi$
$883$	31.6236	+	18.2579i	1.06422	+	0.614427i	0.137623	+	0.990485i	$0.456054\pi$
$884$	−4.95061	−	21.6654i	−0.166507	−	0.728685i
$885$	−0.193867	+	0.179032i	−0.00651677	+	0.00601810i
$886$	−2.37304	−	3.21452i	−0.0797237	−	0.107994i
$887$	22.3079	−	18.7185i	0.749024	−	0.628506i	−0.186220	−	0.982508i	$-0.559624\pi$
$887$	22.3079	−	18.7185i	0.749024	−	0.628506i	0.935245	+	0.354002i	$0.115179\pi$
$888$	−7.78543	+	1.65893i	−0.261262	+	0.0556701i
$889$	−13.2963	−	0.597025i	−0.445944	−	0.0200236i
$890$	0.237906	+	0.157851i	0.00797463	+	0.00529118i
$891$	18.2906	+	47.9303i	0.612760	+	1.60573i
$892$	14.8162	+	11.2171i	0.496082	+	0.375575i
$893$	−0.507606	−	1.39464i	−0.0169864	−	0.0466697i
$894$	−14.7082	+	17.0140i	−0.491915	+	0.569034i
$895$	0.0127587	−	0.0350543i	0.000426477	−	0.00117174i
$896$	−18.2311	+	23.7408i	−0.609058	+	0.793126i
$897$	26.4998	−	5.98260i	0.884803	−	0.199753i
$898$	33.8162	+	32.1626i	1.12846	+	1.07328i
$899$	50.4169			1.68150
$900$	−27.8758	−	11.0847i	−0.929193	−	0.369490i
$901$	−11.9733			−0.398890
$902$	6.43491	−	1.89825i	0.214259	−	0.0632047i
$903$	−16.5062	−	19.5664i	−0.549291	−	0.651130i
$904$	−0.140582	+	11.6213i	−0.00467567	+	0.386520i
$905$	0.0453400	−	0.124571i	0.00150715	−	0.00414087i
$906$	−30.6760	−	18.3174i	−1.01914	−	0.608556i
$907$	−25.4363	−	4.48511i	−0.844599	−	0.148926i	−0.265427	−	0.964131i	$-0.585513\pi$
$907$	−25.4363	−	4.48511i	−0.844599	−	0.148926i	−0.579172	+	0.815205i	$0.696624\pi$
$908$	−2.76841	−	6.56292i	−0.0918729	−	0.217798i
$909$	30.8151	+	14.0799i	1.02207	+	0.467000i
$910$	0.0490886	−	0.100046i	0.00162727	−	0.00331650i
$911$	32.8796	−	11.9672i	1.08935	−	0.396491i	0.265971	−	0.963981i	$-0.414308\pi$
$911$	32.8796	−	11.9672i	1.08935	−	0.396491i	0.823380	+	0.567490i	$0.192085\pi$
$912$	11.4124	+	7.00330i	0.377903	+	0.231902i
$913$	23.4825	+	8.54692i	0.777157	+	0.282862i
$914$	4.24789	−	9.73955i	0.140508	−	0.322156i
$915$	−0.164874	−	0.125501i	−0.00545057	−	0.00414894i
$916$	−32.3296	+	7.38743i	−1.06820	+	0.244087i
$917$	−15.9439	+	38.3575i	−0.526513	+	1.26668i
$918$	21.9667	−	30.9114i	0.725009	−	1.02023i
$919$	−14.0968	−	8.13879i	−0.465010	−	0.268474i	0.249138	−	0.968468i	$-0.419853\pi$
$919$	−14.0968	−	8.13879i	−0.465010	−	0.268474i	−0.714149	+	0.699994i	$0.753186\pi$
$920$	−0.281223	+	0.0460869i	−0.00927163	+	0.00151944i
$921$	−5.28092	+	41.3490i	−0.174012	+	1.36250i
$922$	3.79197	+	33.6174i	0.124882	+	1.10713i
$923$	−22.6762	+	19.0276i	−0.746397	+	0.626302i
$924$	−50.8995	+	11.7718i	−1.67447	+	0.387265i
$925$	7.63411	−	2.77859i	0.251008	−	0.0913594i
$926$	−10.4325	−	0.649841i	−0.342833	−	0.0213551i
$927$	−9.71271	−	20.4148i	−0.319007	−	0.670508i
$928$	−35.9714	−	11.5642i	−1.18082	−	0.379615i
$929$	7.53729	+	20.7085i	0.247290	+	0.679425i	0.999783	+	0.0208242i	$0.00662904\pi$
$929$	7.53729	+	20.7085i	0.247290	+	0.679425i	−0.752493	+	0.658601i	$0.771149\pi$
$930$	0.255709	+	0.00376043i	0.00838503	+	0.000123309i
$931$	1.21247	−	13.4742i	0.0397372	−	0.441600i
$932$	−6.26939	−	9.70166i	−0.205361	−	0.317788i
$933$	1.29817	+	27.3065i	0.0425001	+	0.893973i
$934$	13.5053	−	14.1996i	0.441906	−	0.464625i
$935$	−0.203437	+	0.352364i	−0.00665311	+	0.0115235i
$936$	17.6277	+	4.80568i	0.576181	+	0.157079i
$937$	25.8784	−	44.8227i	0.845410	−	1.46429i	−0.0398551	−	0.999205i	$-0.512690\pi$
$937$	25.8784	−	44.8227i	0.845410	−	1.46429i	0.885265	−	0.465087i	$-0.153977\pi$
$938$	−0.559988	+	5.20956i	−0.0182842	+	0.170098i
$939$	−1.13066	+	3.63502i	−0.0368978	+	0.118624i
$940$	0.0115301	+	0.0178424i	0.000376069	+	0.000581953i
$941$	18.4412	−	3.25167i	0.601164	−	0.106002i	0.135220	−	0.990816i	$-0.456826\pi$
$941$	18.4412	−	3.25167i	0.601164	−	0.106002i	0.465944	+	0.884814i	$0.345715\pi$
$942$	−18.9989	−	16.4241i	−0.619019	−	0.535125i
$943$	3.89676	−	4.64398i	0.126896	−	0.151229i
$944$	30.7483	−	31.5558i	1.00077	−	1.02706i
$945$	0.183157	−	0.0511195i	0.00595809	−	0.00166292i
$946$	−24.8966	+	37.5230i	−0.809458	+	1.21998i
$947$	20.7704	+	17.4285i	0.674948	+	0.566349i	0.914525	−	0.404529i	$-0.132564\pi$
$947$	20.7704	+	17.4285i	0.674948	+	0.566349i	−0.239577	+	0.970877i	$0.577009\pi$
$948$	−8.74264	−	8.56349i	−0.283948	−	0.278129i
$949$	0.364625	+	2.06789i	0.0118362	+	0.0671265i
$950$	−12.5260	−	5.46318i	−0.406396	−	0.177249i
$951$	5.39289	−	4.98022i	0.174876	−	0.161495i
$952$	28.1214	+	26.4670i	0.911420	+	0.857799i
$953$	−22.6738	−	13.0907i	−0.734476	−	0.424050i	0.0855811	−	0.996331i	$-0.472725\pi$
$953$	−22.6738	−	13.0907i	−0.734476	−	0.424050i	−0.820058	+	0.572281i	$0.806059\pi$
$954$	4.63967	−	8.68177i	0.150215	−	0.281083i
$955$	−0.308396	−	0.178052i	−0.00997945	−	0.00576164i
$956$	−24.6010	+	5.62141i	−0.795654	+	0.181809i
$957$	−35.6479	−	55.4808i	−1.15233	−	1.79344i
$958$	11.9200	−	27.3302i	0.385118	−	0.882997i
$959$	−27.5942	−	25.3483i	−0.891062	−	0.818540i
$960$	−0.181581	−	0.0613356i	−0.00586049	−	0.00197960i
$961$	24.4072	−	8.88349i	0.787329	−	0.286564i
$962$	−4.43063	+	2.20282i	−0.142849	+	0.0710219i
$963$	−40.1679	−	10.4303i	−1.29439	−	0.336111i
$964$	27.7711	−	36.6818i	0.894447	−	1.18144i
$965$	−0.0660868	−	0.181572i	−0.00212741	−	0.00584501i
$966$	−32.4432	+	34.2916i	−1.04384	+	1.10331i
$967$	10.6499	+	12.6921i	0.342479	+	0.408151i	0.909601	−	0.415483i	$-0.136388\pi$
$967$	10.6499	+	12.6921i	0.342479	+	0.408151i	−0.567122	+	0.823634i	$0.691943\pi$
$968$	29.7554	+	53.0085i	0.956376	+	1.70376i
$969$	10.4630	−	13.7455i	0.336119	−	0.441568i
$970$	−0.00864471	+	0.0358305i	−0.000277565	+	0.00115045i
$971$	−14.7715	+	25.5850i	−0.474040	+	0.821061i	−0.999558	−	0.0297209i	$-0.990538\pi$
$971$	−14.7715	+	25.5850i	−0.474040	+	0.821061i	0.525518	+	0.850782i	$0.323871\pi$
$972$	13.9015	+	27.9060i	0.445892	+	0.895087i
$973$	1.08558	+	8.32547i	0.0348022	+	0.266902i
$974$	−5.43880	−	5.17285i	−0.174270	−	0.165749i
$975$	−18.4969	−	2.36234i	−0.592374	−	0.0756555i
$976$	28.5937	+	19.4742i	0.915263	+	0.623354i
$977$	−3.40729	+	9.36146i	−0.109009	+	0.299500i	−0.982188	−	0.187899i	$-0.939832\pi$
$977$	−3.40729	+	9.36146i	−0.109009	+	0.299500i	0.873179	+	0.487399i	$0.162054\pi$
$978$	−20.3111	−	24.9416i	−0.649477	−	0.797545i
$979$	−28.4556	−	78.1810i	−0.909444	−	2.49868i
$980$	0.0260444	+	0.191887i	0.000831957	+	0.00612960i
$981$	17.8366	−	18.1150i	0.569478	−	0.578366i
$982$	46.8577	+	31.0902i	1.49529	+	0.992127i
$983$	3.96847	−	22.5063i	0.126574	−	0.717839i	−0.853786	−	0.520624i	$-0.825699\pi$
$983$	3.96847	−	22.5063i	0.126574	−	0.717839i	0.980360	−	0.197215i	$-0.0631897\pi$
$984$	3.77955	−	1.52925i	0.120488	−	0.0487506i
$985$	0.272487	+	0.0991771i	0.00868216	+	0.00316005i
$986$	−19.4879	+	44.6818i	−0.620621	+	1.42296i
$987$	3.31000	+	1.19488i	0.105358	+	0.0380334i
$988$	7.95393	+	2.45131i	0.253048	+	0.0779866i
$989$			40.6902i			1.29387i
$990$	−0.176664	−	0.284051i	−0.00561475	−	0.00902775i
$991$			6.91742i			0.219739i	0.993946	+	0.109870i	$0.0350433\pi$
$991$			6.91742i			0.219739i	−0.993946	+	0.109870i	$0.964957\pi$
$992$	−42.6676	+	1.62288i	−1.35470	+	0.0515266i
$993$	24.5057	−	22.6305i	0.777665	−	0.718158i
$994$	14.2949	−	49.4117i	0.453407	−	1.56724i
$995$	0.312683	+	0.113807i	0.00991273	+	0.00360794i
$996$	14.7090	+	3.77851i	0.466073	+	0.119727i
$997$	7.16060	−	2.60625i	0.226779	−	0.0825407i	−0.226132	−	0.974097i	$-0.572608\pi$
$997$	7.16060	−	2.60625i	0.226779	−	0.0825407i	0.452910	+	0.891556i	$0.350386\pi$
$998$	14.7610	+	0.919463i	0.467251	+	0.0291051i
$999$	−7.83739	−	3.14021i	−0.247964	−	0.0993519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.191.85	yes	840
4.3	odd	2	inner	756.2.ci.a.191.5	yes	840
7.4	even	3		756.2.bs.a.515.11	✓	840
27.14	odd	18		756.2.bs.a.527.99	yes	840
28.11	odd	6		756.2.bs.a.515.99	yes	840
108.95	even	18		756.2.bs.a.527.11	yes	840
189.95	odd	18	inner	756.2.ci.a.95.5	yes	840
756.95	even	18	inner	756.2.ci.a.95.85	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.11	✓	840	7.4	even	3
756.2.bs.a.515.99	yes	840	28.11	odd	6
756.2.bs.a.527.11	yes	840	108.95	even	18
756.2.bs.a.527.99	yes	840	27.14	odd	18
756.2.ci.a.95.5	yes	840	189.95	odd	18	inner
756.2.ci.a.95.85	yes	840	756.95	even	18	inner
756.2.ci.a.191.5	yes	840	4.3	odd	2	inner
756.2.ci.a.191.85	yes	840	1.1	even	1	trivial

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.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.400135 + 1.35643i) q^{2} +(-1.04908 + 1.37820i) q^{3} +(-1.67978 + 1.08551i) q^{4} +(0.0136217 - 0.00240188i) q^{5} +(-2.28920 - 0.871530i) q^{6} +(2.34832 - 1.21877i) q^{7} +(-2.14455 - 1.84415i) q^{8} +(-0.798872 - 2.89168i) q^{9} +O(q^{10})\)	\(q+(0.400135 + 1.35643i) q^{2} +(-1.04908 + 1.37820i) q^{3} +(-1.67978 + 1.08551i) q^{4} +(0.0136217 - 0.00240188i) q^{5} +(-2.28920 - 0.871530i) q^{6} +(2.34832 - 1.21877i) q^{7} +(-2.14455 - 1.84415i) q^{8} +(-0.798872 - 2.89168i) q^{9} +(0.00870850 + 0.0175158i) q^{10} +(0.989827 - 5.61359i) q^{11} +(0.266177 - 3.45386i) q^{12} +(-0.373911 - 2.12055i) q^{13} +(2.59281 + 2.69765i) q^{14} +(-0.0109800 + 0.0212932i) q^{15} +(1.64335 - 3.64684i) q^{16} +(-4.46911 - 2.58024i) q^{17} +(3.60269 - 2.24067i) q^{18} +(1.67374 - 0.966334i) q^{19} +(-0.0202743 + 0.0188211i) q^{20} +(-0.783868 + 4.51504i) q^{21} +(8.01048 - 0.903566i) q^{22} +(5.57999 - 4.68217i) q^{23} +(4.79141 - 1.02096i) q^{24} +(-4.69828 + 1.71004i) q^{25} +(2.72676 - 1.35569i) q^{26} +(4.82339 + 1.93259i) q^{27} +(-2.62169 + 4.59638i) q^{28} +(-6.57796 - 1.15987i) q^{29} +(-0.0332762 - 0.00637337i) q^{30} +(-7.43341 + 1.31071i) q^{31} +(5.60422 + 0.769853i) q^{32} +(6.69824 + 7.25327i) q^{33} +(1.71166 - 7.09446i) q^{34} +(0.0290609 - 0.0222421i) q^{35} +(4.48087 + 3.99021i) q^{36} -1.62487 q^{37} +(1.98048 + 1.88364i) q^{38} +(3.31481 + 1.70930i) q^{39} +(-0.0336419 - 0.0199696i) q^{40} +(0.819613 - 0.144520i) q^{41} +(-6.43797 + 0.743364i) q^{42} +(-3.59069 + 4.27922i) q^{43} +(4.43089 + 10.5041i) q^{44} +(-0.0178275 - 0.0374709i) q^{45} +(8.58376 + 5.69534i) q^{46} +(0.133348 - 0.756257i) q^{47} +(3.30207 + 6.09068i) q^{48} +(4.02922 - 5.72410i) q^{49} +(-4.19948 - 5.68863i) q^{50} +(8.24453 - 3.45245i) q^{51} +(2.92997 + 3.15619i) q^{52} +(2.00935 - 1.16010i) q^{53} +(-0.691407 + 7.31587i) q^{54} -0.0788442i q^{55} +(-7.28368 - 1.71696i) q^{56} +(-0.424081 + 3.32051i) q^{57} +(-1.05879 - 9.38662i) q^{58} +(10.3506 + 3.76730i) q^{59} +(-0.00466996 - 0.0476869i) q^{60} +(-1.50186 + 8.51747i) q^{61} +(-4.75225 - 9.55841i) q^{62} +(-5.40028 - 5.81695i) q^{63} +(1.19820 + 7.90976i) q^{64} +(-0.0101866 - 0.0279875i) q^{65} +(-7.15832 + 11.9880i) q^{66} +(0.900117 + 1.07272i) q^{67} +(10.3080 - 0.517003i) q^{68} +(0.599121 + 12.6023i) q^{69} +(0.0417980 + 0.0305191i) q^{70} +(-6.87368 - 11.9056i) q^{71} +(-3.61948 + 7.67459i) q^{72} -0.975165 q^{73} +(-0.650168 - 2.20402i) q^{74} +(2.57209 - 8.26914i) q^{75} +(-1.76256 + 3.44009i) q^{76} +(-4.51721 - 14.3889i) q^{77} +(-0.992170 + 5.18024i) q^{78} +(2.27083 - 2.70627i) q^{79} +(0.0136260 - 0.0536233i) q^{80} +(-7.72361 + 4.62016i) q^{81} +(0.523986 + 1.05392i) q^{82} +(-0.761271 + 4.31738i) q^{83} +(-3.58438 - 8.43518i) q^{84} +(-0.0670745 - 0.0244131i) q^{85} +(-7.24120 - 3.15824i) q^{86} +(8.49933 - 7.84895i) q^{87} +(-12.4750 + 10.2132i) q^{88} +(12.6403 - 7.29787i) q^{89} +(0.0436931 - 0.0391751i) q^{90} +(-3.46252 - 4.52403i) q^{91} +(-4.29065 + 13.9221i) q^{92} +(5.99180 - 11.6198i) q^{93} +(1.07916 - 0.121727i) q^{94} +(0.0204782 - 0.0171833i) q^{95} +(-6.94028 + 6.91611i) q^{96} +(1.44343 + 1.21118i) q^{97} +(9.37656 + 3.17493i) q^{98} +(-17.0234 + 1.62228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

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