LMFDB - Embedded newform 370.2.ba.a.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(17,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("370.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.ba (of order $36$, degree $12$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			353.2
Character	$\chi$	$=$	370.353
Dual form			370.2.ba.a.87.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-1.44027 - 2.05692i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.949056 - 2.02467i) q^{5} +(1.77557 - 1.77557i) q^{6} +(1.60039 - 0.140016i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.13048 + 3.10597i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-1.44027 - 2.05692i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.949056 - 2.02467i) q^{5} +(1.77557 - 1.77557i) q^{6} +(1.60039 - 0.140016i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.13048 + 3.10597i) q^{9} +(1.82911 - 1.28622i) q^{10} +(-3.06846 + 1.77158i) q^{11} +(2.05692 + 1.44027i) q^{12} +(-4.50501 + 1.63969i) q^{13} +(0.415794 + 1.55176i) q^{14} +(-2.79769 + 4.86821i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.262235 - 0.720486i) q^{17} +(-3.25509 - 0.573960i) q^{18} +(-4.90656 + 3.43561i) q^{19} +(1.58430 + 1.57797i) q^{20} +(-2.59300 - 3.09021i) q^{21} +(-2.27750 - 2.71421i) q^{22} +(3.85110 - 6.67031i) q^{23} +(-1.06121 + 2.27577i) q^{24} +(-3.19859 + 3.84305i) q^{25} +(-2.39706 - 4.15184i) q^{26} +(0.740501 - 0.198417i) q^{27} +(-1.45599 + 0.678938i) q^{28} +(-0.0899791 - 0.0241098i) q^{29} +(-5.28006 - 1.90983i) q^{30} +(-6.67231 - 6.67231i) q^{31} +(0.766044 + 0.642788i) q^{32} +(8.06341 + 3.76003i) q^{33} +(0.755077 + 0.133140i) q^{34} +(-1.80235 - 3.10738i) q^{35} -3.30530i q^{36} +(5.79641 + 1.84434i) q^{37} +(-4.23543 - 4.23543i) q^{38} +(9.86114 + 6.90484i) q^{39} +(-1.27889 + 1.83424i) q^{40} +(0.750031 + 2.06069i) q^{41} +(2.59300 - 3.09021i) q^{42} -6.81877 q^{43} +(2.27750 - 2.71421i) q^{44} +(7.36145 - 0.658888i) q^{45} +(7.23771 + 2.63431i) q^{46} +(-0.837362 - 3.12508i) q^{47} +(-2.42547 - 0.649904i) q^{48} +(-4.35201 + 0.767377i) q^{49} +(-4.34010 - 2.48265i) q^{50} +(-1.85967 + 0.498297i) q^{51} +(3.67252 - 3.08161i) q^{52} +(8.99748 + 0.787177i) q^{53} +(0.323989 + 0.694796i) q^{54} +(6.49901 + 4.53130i) q^{55} +(-0.921452 - 1.31597i) q^{56} +(14.1335 + 5.14419i) q^{57} +(0.00811884 - 0.0927988i) q^{58} +(1.33279 + 0.116604i) q^{59} +(0.963942 - 5.53148i) q^{60} +(0.635806 + 0.296481i) q^{61} +(5.41231 - 7.72958i) q^{62} +(-1.37432 + 5.12904i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(7.59533 + 7.56500i) q^{65} +(-2.30271 + 8.59383i) q^{66} +(-0.828692 - 9.47199i) q^{67} +0.766725i q^{68} +(-19.2669 + 1.68564i) q^{69} +(2.74720 - 2.31456i) q^{70} +(-1.49715 + 8.49078i) q^{71} +(3.25509 - 0.573960i) q^{72} +(4.69493 - 4.69493i) q^{73} +(-0.809786 + 6.02862i) q^{74} +(12.5117 + 1.04420i) q^{75} +(3.43561 - 4.90656i) q^{76} +(-4.66269 + 3.26485i) q^{77} +(-5.08758 + 10.9103i) q^{78} +(-1.30246 - 14.8872i) q^{79} +(-2.02845 - 0.940946i) q^{80} +(6.12137 + 5.13644i) q^{81} +(-1.89914 + 1.09647i) q^{82} +(-6.70041 - 14.3691i) q^{83} +(3.49354 + 2.01699i) q^{84} +(-1.70762 + 0.152841i) q^{85} +(-1.18407 - 6.71518i) q^{86} +(0.0800023 + 0.219805i) q^{87} +(3.06846 + 1.77158i) q^{88} +(1.27013 - 14.5176i) q^{89} +(1.92718 + 7.13520i) q^{90} +(-6.98019 + 3.25491i) q^{91} +(-1.33747 + 7.58519i) q^{92} +(-4.11447 + 23.3343i) q^{93} +(2.93219 - 1.36730i) q^{94} +(11.6126 + 6.67358i) q^{95} +(0.218851 - 2.50148i) q^{96} +(-2.01640 - 1.16417i) q^{97} +(-1.51144 - 4.15264i) q^{98} +(-2.03363 - 11.5333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) $ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8	$ 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−1.44027	−	2.05692i	−0.831541	−	1.18756i	−0.980069	−	0.198655i	$-0.936343\pi$
$3$	−1.44027	−	2.05692i	−0.831541	−	1.18756i	0.148529	−	0.988908i	$-0.452546\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.949056	−	2.02467i	−0.424431	−	0.905460i
$5$	−0.949056	−	2.02467i	−0.424431	−	0.905460i
$6$	1.77557	−	1.77557i	0.724874	−	0.724874i
$7$	1.60039	−	0.140016i	0.604891	−	0.0529211i	0.219403	−	0.975634i	$-0.429589\pi$
$7$	1.60039	−	0.140016i	0.604891	−	0.0529211i	0.385487	+	0.922713i	$0.374033\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−1.13048	+	3.10597i	−0.376827	+	1.03532i
$10$	1.82911	−	1.28622i	0.578415	−	0.406738i
$11$	−3.06846	+	1.77158i	−0.925176	+	0.534151i	−0.885283	−	0.465053i	$-0.846035\pi$
$11$	−3.06846	+	1.77158i	−0.925176	+	0.534151i	−0.0398936	+	0.999204i	$0.512702\pi$
$12$	2.05692	+	1.44027i	0.593782	+	0.415770i
$13$	−4.50501	+	1.63969i	−1.24946	+	0.454768i	−0.880221	−	0.474565i	$-0.842605\pi$
$13$	−4.50501	+	1.63969i	−1.24946	+	0.454768i	−0.369244	+	0.929333i	$0.620383\pi$
$14$	0.415794	+	1.55176i	0.111126	+	0.414726i
$15$	−2.79769	+	4.86821i	−0.722360	+	1.25697i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.262235	−	0.720486i	0.0636014	−	0.174743i	−0.903821	−	0.427910i	$-0.859250\pi$
$17$	0.262235	−	0.720486i	0.0636014	−	0.174743i	0.967423	+	0.253167i	$0.0814722\pi$
$18$	−3.25509	−	0.573960i	−0.767231	−	0.135284i
$19$	−4.90656	+	3.43561i	−1.12564	+	0.788183i	−0.979572	−	0.201092i	$-0.935551\pi$
$19$	−4.90656	+	3.43561i	−1.12564	+	0.788183i	−0.146069	+	0.989274i	$0.546662\pi$
$20$	1.58430	+	1.57797i	0.354260	+	0.352845i
$21$	−2.59300	−	3.09021i	−0.565838	−	0.674340i
$22$	−2.27750	−	2.71421i	−0.485564	−	0.578673i
$23$	3.85110	−	6.67031i	0.803011	−	1.39086i	−0.114615	−	0.993410i	$-0.536563\pi$
$23$	3.85110	−	6.67031i	0.803011	−	1.39086i	0.917626	−	0.397445i	$-0.130103\pi$
$24$	−1.06121	+	2.27577i	−0.216619	+	0.464540i
$25$	−3.19859	+	3.84305i	−0.639717	+	0.768611i
$26$	−2.39706	−	4.15184i	−0.470103	−	0.814242i
$27$	0.740501	−	0.198417i	0.142509	−	0.0381853i
$28$	−1.45599	+	0.678938i	−0.275156	+	0.128307i
$29$	−0.0899791	−	0.0241098i	−0.0167087	−	0.00447708i	0.250455	−	0.968128i	$-0.419420\pi$
$29$	−0.0899791	−	0.0241098i	−0.0167087	−	0.00447708i	−0.267164	+	0.963651i	$0.586086\pi$
$30$	−5.28006	−	1.90983i	−0.964003	−	0.348686i
$31$	−6.67231	−	6.67231i	−1.19838	−	1.19838i	−0.974651	−	0.223731i	$-0.928176\pi$
$31$	−6.67231	−	6.67231i	−1.19838	−	1.19838i	−0.223731	−	0.974651i	$-0.571824\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	8.06341	+	3.76003i	1.40366	+	0.654537i
$34$	0.755077	+	0.133140i	0.129495	+	0.0228334i
$35$	−1.80235	−	3.10738i	−0.304652	−	0.525243i
$36$		−	3.30530i		−	0.550884i
$37$	5.79641	+	1.84434i	0.952924	+	0.303208i
$37$	5.79641	+	1.84434i	0.952924	+	0.303208i
$38$	−4.23543	−	4.23543i	−0.687077	−	0.687077i
$39$	9.86114	+	6.90484i	1.57905	+	1.10566i
$40$	−1.27889	+	1.83424i	−0.202210	+	0.290019i
$41$	0.750031	+	2.06069i	0.117135	+	0.321826i	0.984380	−	0.176055i	$-0.0563337\pi$
$41$	0.750031	+	2.06069i	0.117135	+	0.321826i	−0.867245	+	0.497881i	$0.834111\pi$
$42$	2.59300	−	3.09021i	0.400108	−	0.476830i
$43$	−6.81877			−1.03985			−0.519926	−	0.854211i	$-0.674041\pi$
$43$	−6.81877			−1.03985			−0.519926	+	0.854211i	$0.674041\pi$
$44$	2.27750	−	2.71421i	0.343346	−	0.409183i
$45$	7.36145	−	0.658888i	1.09738	−	0.0982212i
$46$	7.23771	+	2.63431i	1.06714	+	0.388408i
$47$	−0.837362	−	3.12508i	−0.122142	−	0.455839i	0.877580	−	0.479430i	$-0.159157\pi$
$47$	−0.837362	−	3.12508i	−0.122142	−	0.455839i	−0.999722	+	0.0235911i	$0.992490\pi$
$48$	−2.42547	−	0.649904i	−0.350087	−	0.0938056i
$49$	−4.35201	+	0.767377i	−0.621716	+	0.109625i
$50$	−4.34010	−	2.48265i	−0.613782	−	0.351100i
$51$	−1.85967	+	0.498297i	−0.260406	+	0.0697756i
$52$	3.67252	−	3.08161i	0.509286	−	0.427342i
$53$	8.99748	+	0.787177i	1.23590	+	0.108127i	0.686311	−	0.727309i	$-0.259229\pi$
$53$	8.99748	+	0.787177i	1.23590	+	0.108127i	0.549588	+	0.835436i	$0.314785\pi$
$54$	0.323989	+	0.694796i	0.0440893	+	0.0945498i
$55$	6.49901	+	4.53130i	0.876326	+	0.611001i
$56$	−0.921452	−	1.31597i	−0.123134	−	0.175854i
$57$	14.1335	+	5.14419i	1.87203	+	0.681365i
$58$	0.00811884	−	0.0927988i	0.00106606	−	0.0121851i
$59$	1.33279	+	0.116604i	0.173514	+	0.0151805i	0.173582	−	0.984819i	$-0.444466\pi$
$59$	1.33279	+	0.116604i	0.173514	+	0.0151805i	−6.73760e−5		1.00000i	$0.500021\pi$
$60$	0.963942	−	5.53148i	0.124444	−	0.714112i
$61$	0.635806	+	0.296481i	0.0814066	+	0.0379605i	0.462895	−	0.886413i	$-0.346811\pi$
$61$	0.635806	+	0.296481i	0.0814066	+	0.0379605i	−0.381489	+	0.924374i	$0.624588\pi$
$62$	5.41231	−	7.72958i	0.687364	−	0.981657i
$63$	−1.37432	+	5.12904i	−0.173148	+	0.646199i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	7.59533	+	7.56500i	0.942085	+	0.938323i
$66$	−2.30271	+	8.59383i	−0.283444	+	1.05783i
$67$	−0.828692	−	9.47199i	−0.101241	−	1.15719i	−0.861566	−	0.507645i	$-0.830516\pi$
$67$	−0.828692	−	9.47199i	−0.101241	−	1.15719i	0.760325	−	0.649543i	$-0.225040\pi$
$68$			0.766725i			0.0929790i
$69$	−19.2669	+	1.68564i	−2.31947	+	0.202927i
$70$	2.74720	−	2.31456i	0.328353	−	0.276642i
$71$	−1.49715	+	8.49078i	−0.177680	+	1.00767i	0.757326	+	0.653037i	$0.226505\pi$
$71$	−1.49715	+	8.49078i	−0.177680	+	1.00767i	−0.935005	+	0.354634i	$0.884606\pi$
$72$	3.25509	−	0.573960i	0.383616	−	0.0676418i
$73$	4.69493	−	4.69493i	0.549500	−	0.549500i	−0.376796	−	0.926296i	$-0.622974\pi$
$73$	4.69493	−	4.69493i	0.549500	−	0.549500i	0.926296	+	0.376796i	$0.122974\pi$
$74$	−0.809786	+	6.02862i	−0.0941358	+	0.700813i
$75$	12.5117	+	1.04420i	1.44472	+	0.120573i
$76$	3.43561	−	4.90656i	0.394091	−	0.562821i
$77$	−4.66269	+	3.26485i	−0.531363	+	0.372064i
$78$	−5.08758	+	10.9103i	−0.576054	+	1.23535i
$79$	−1.30246	−	14.8872i	−0.146538	−	1.67494i	−0.612758	−	0.790270i	$-0.709940\pi$
$79$	−1.30246	−	14.8872i	−0.146538	−	1.67494i	0.466220	−	0.884669i	$-0.345616\pi$
$80$	−2.02845	−	0.940946i	−0.226788	−	0.105201i
$81$	6.12137	+	5.13644i	0.680153	+	0.570716i
$82$	−1.89914	+	1.09647i	−0.209725	+	0.121085i
$83$	−6.70041	−	14.3691i	−0.735466	−	1.57721i	−0.814381	−	0.580331i	$-0.802923\pi$
$83$	−6.70041	−	14.3691i	−0.735466	−	1.57721i	0.0789149	−	0.996881i	$-0.474854\pi$
$84$	3.49354	+	2.01699i	0.381176	+	0.220072i
$85$	−1.70762	+	0.152841i	−0.185218	+	0.0165779i
$86$	−1.18407	−	6.71518i	−0.127681	−	0.724116i
$87$	0.0800023	+	0.219805i	0.00857715	+	0.0235655i
$88$	3.06846	+	1.77158i	0.327099	+	0.188851i
$89$	1.27013	−	14.5176i	0.134633	−	1.53886i	−0.565438	−	0.824791i	$-0.691293\pi$
$89$	1.27013	−	14.5176i	0.134633	−	1.53886i	0.700071	−	0.714073i	$-0.253152\pi$
$90$	1.92718	+	7.13520i	0.203143	+	0.752116i
$91$	−6.98019	+	3.25491i	−0.731722	+	0.341208i
$92$	−1.33747	+	7.58519i	−0.139441	+	0.790811i
$93$	−4.11447	+	23.3343i	−0.426651	+	2.41966i
$94$	2.93219	−	1.36730i	0.302433	−	0.141027i
$95$	11.6126	+	6.67358i	1.19143	+	0.684695i
$96$	0.218851	−	2.50148i	0.0223364	−	0.255306i
$97$	−2.01640	−	1.16417i	−0.204734	−	0.118203i	0.394127	−	0.919056i	$-0.371047\pi$
$97$	−2.01640	−	1.16417i	−0.204734	−	0.118203i	−0.598862	+	0.800852i	$0.704380\pi$
$98$	−1.51144	−	4.15264i	−0.152678	−	0.419480i
$99$	−2.03363	−	11.5333i	−0.204387	−	1.15914i
$100$	1.69129	−	4.70527i	0.169129	−	0.470527i
$101$	−1.46415	−	0.845327i	−0.145688	−	0.0841132i	0.425384	−	0.905013i	$-0.360139\pi$
$101$	−1.46415	−	0.845327i	−0.145688	−	0.0841132i	−0.571072	+	0.820900i	$0.693472\pi$
$102$	−0.813656	−	1.74489i	−0.0805639	−	0.172770i
$103$	9.06370	−	5.23293i	0.893073	−	0.515616i	0.0181263	−	0.999836i	$-0.494230\pi$
$103$	9.06370	−	5.23293i	0.893073	−	0.515616i	0.874946	+	0.484220i	$0.160897\pi$
$104$	3.67252	+	3.08161i	0.360120	+	0.302176i
$105$	−3.79577	+	8.18275i	−0.370429	+	0.798555i
$106$	0.787177	+	8.99748i	0.0764574	+	0.873912i
$107$	−1.78686	+	3.83193i	−0.172742	+	0.370447i	−0.973550	−	0.228475i	$-0.926626\pi$
$107$	−1.78686	+	3.83193i	−0.172742	+	0.370447i	0.800808	+	0.598922i	$0.204404\pi$
$108$	−0.627981	+	0.439717i	−0.0604275	+	0.0423118i
$109$	−4.61706	+	6.59384i	−0.442234	+	0.631575i	−0.976953	−	0.213455i	$-0.931528\pi$
$109$	−4.61706	+	6.59384i	−0.442234	+	0.631575i	0.534719	+	0.845030i	$0.320417\pi$
$110$	−3.33392	+	7.18712i	−0.317877	+	0.685265i
$111$	−4.55474	−	14.5791i	−0.432317	−	1.38379i
$112$	1.13597	−	1.13597i	0.107339	−	0.107339i
$113$	0.159526	−	0.0281287i	0.0150069	−	0.00264612i	−0.166140	−	0.986102i	$-0.553130\pi$
$113$	0.159526	−	0.0281287i	0.0150069	−	0.00264612i	0.181147	+	0.983456i	$0.442019\pi$
$114$	−2.61177	+	14.8121i	−0.244615	+	1.38728i
$115$	−17.1601	−	1.46672i	−1.60019	−	0.136773i
$116$	0.0927988	−	0.00811884i	0.00861615	−	0.000753815i
$117$		−	15.8460i		−	1.46497i
$118$	0.116604	+	1.33279i	0.0107343	+	0.122693i
$119$	0.318799	−	1.18978i	0.0292243	−	0.109067i
$120$	5.61484	−	0.0112344i	0.512562	−	0.00102556i
$121$	0.776977	−	1.34576i	0.0706343	−	0.122342i
$122$	−0.181570	+	0.677630i	−0.0164386	+	0.0613497i
$123$	3.15843	−	4.51071i	0.284786	−	0.406717i
$124$	8.55198	+	3.98786i	0.767991	+	0.358120i
$125$	10.8166	+	2.82881i	0.967462	+	0.253016i
$126$	−5.28977	−	0.462795i	−0.471250	−	0.0412291i
$127$	−0.727384	+	8.31404i	−0.0645449	+	0.737752i	0.893111	+	0.449837i	$0.148518\pi$
$127$	−0.727384	+	8.31404i	−0.0645449	+	0.737752i	−0.957656	+	0.287915i	$0.907038\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	9.82088	+	14.0257i	0.864680	+	1.23489i
$130$	−6.13116	+	8.79359i	−0.537738	+	0.771249i
$131$	3.63507	+	7.79543i	0.317597	+	0.681090i	0.998693	−	0.0511044i	$-0.0162741\pi$
$131$	3.63507	+	7.79543i	0.317597	+	0.681090i	−0.681096	+	0.732194i	$0.738496\pi$
$132$	−8.86314	−	0.775424i	−0.771437	−	0.0674920i
$133$	−7.37136	+	6.18531i	−0.639178	+	0.536334i
$134$	9.18419	−	2.46090i	0.793393	−	0.212589i
$135$	−1.10451	−	1.31096i	−0.0950607	−	0.112830i
$136$	−0.755077	+	0.133140i	−0.0647473	+	0.0114167i
$137$	11.4095	+	3.05717i	0.974781	+	0.261192i	0.710845	−	0.703349i	$-0.248313\pi$
$137$	11.4095	+	3.05717i	0.974781	+	0.261192i	0.263936	+	0.964540i	$0.414979\pi$
$138$	−5.00570	−	18.6815i	−0.426113	−	1.59028i
$139$	−4.29233	−	1.56228i	−0.364070	−	0.132511i	0.153506	−	0.988148i	$-0.450944\pi$
$139$	−4.29233	−	1.56228i	−0.364070	−	0.132511i	−0.517577	+	0.855637i	$0.673166\pi$
$140$	2.75644	+	2.30354i	0.232962	+	0.194685i
$141$	−5.22200	+	6.22334i	−0.439772	+	0.524100i
$142$	−8.62177			−0.723523
$143$	10.9186	−	13.0123i	0.913060	−	1.08814i
$144$	1.13048	+	3.10597i	0.0942066	+	0.258831i
$145$	0.0365808	+	0.205060i	0.00303787	+	0.0170293i
$146$	5.43887	+	3.80834i	0.450124	+	0.315180i
$147$	7.84651	+	7.84651i	0.647169	+	0.647169i
$148$	−6.07765	+	0.249375i	−0.499580	+	0.0204985i
$149$		−	11.0431i		−	0.904687i	−0.891844	−	0.452344i	$-0.850588\pi$
$149$		−	11.0431i		−	0.904687i	0.891844	−	0.452344i	$-0.149412\pi$
$150$	1.14430	+	12.5029i	0.0934315	+	1.02086i
$151$	−22.2433	−	3.92209i	−1.81013	−	0.319175i	−0.836616	−	0.547789i	$-0.815470\pi$
$151$	−22.2433	−	3.92209i	−1.81013	−	0.319175i	−0.973517	+	0.228614i	$0.926581\pi$
$152$	5.42860	+	2.53140i	0.440318	+	0.205324i
$153$	1.94135	+	1.62899i	0.156949	+	0.131696i
$154$	−4.02492	−	4.02492i	−0.324337	−	0.324337i
$155$	−7.17683	+	19.8416i	−0.576457	+	1.59372i
$156$	−11.6280	−	3.11572i	−0.930988	−	0.249457i
$157$	−2.08717	+	0.973262i	−0.166574	+	0.0776748i	−0.504117	−	0.863635i	$-0.668182\pi$
$157$	−2.08717	+	0.973262i	−0.166574	+	0.0776748i	0.337543	+	0.941310i	$0.390404\pi$
$158$	14.4348	−	3.86781i	1.14837	−	0.307706i
$159$	−11.3396	−	19.6408i	−0.899293	−	1.55762i
$160$	0.574414	−	2.16103i	0.0454114	−	0.170844i
$161$	5.22932	−	11.2143i	0.412128	−	0.883812i
$162$	−3.99544	+	6.92031i	−0.313912	+	0.543711i
$163$	−2.20336	−	2.62586i	−0.172580	−	0.205673i	0.672820	−	0.739806i	$-0.265083\pi$
$163$	−2.20336	−	2.62586i	−0.172580	−	0.205673i	−0.845401	+	0.534133i	$0.820638\pi$
$164$	−1.40960	−	1.67989i	−0.110071	−	0.131178i
$165$	−0.0398053	−	19.8942i	−0.00309884	−	1.54876i
$166$	12.9873	−	9.09379i	1.00801	−	0.705815i
$167$	−5.70910	−	1.00667i	−0.441784	−	0.0778984i	−0.0516681	−	0.998664i	$-0.516454\pi$
$167$	−5.70910	−	1.00667i	−0.441784	−	0.0778984i	−0.390115	+	0.920766i	$0.627565\pi$
$168$	−1.37970	+	3.79071i	−0.106447	+	0.292459i
$169$	7.64793	−	6.41738i	0.588302	−	0.493644i
$170$	−0.447045	−	1.65514i	−0.0342868	−	0.126943i
$171$	−5.12412	−	19.1235i	−0.391852	−	1.46241i
$172$	6.40755	−	2.33216i	0.488571	−	0.177825i
$173$	−13.9827	−	9.79077i	−1.06308	−	0.744378i	−0.0951178	−	0.995466i	$-0.530323\pi$
$173$	−13.9827	−	9.79077i	−1.06308	−	0.744378i	−0.967964	+	0.251088i	$0.919212\pi$
$174$	−0.202573	+	0.116956i	−0.0153570	+	0.00886638i
$175$	−4.58089	+	6.59824i	−0.346283	+	0.498780i
$176$	−1.21183	+	3.32948i	−0.0913452	+	0.250969i
$177$	−1.67973	−	2.90938i	−0.126256	−	0.218683i
$178$	14.5176	−	1.27013i	1.08814	−	0.0952000i
$179$	3.19615	−	3.19615i	0.238891	−	0.238891i	−0.577500	−	0.816391i	$-0.695971\pi$
$179$	3.19615	−	3.19615i	0.238891	−	0.238891i	0.816391	+	0.577500i	$0.195971\pi$
$180$	−6.69215	+	3.13692i	−0.498803	+	0.233812i
$181$	−6.09554	+	2.21860i	−0.453078	+	0.164907i	−0.558471	−	0.829524i	$-0.688612\pi$
$181$	−6.09554	+	2.21860i	−0.453078	+	0.164907i	0.105394	+	0.994431i	$0.466390\pi$
$182$	−4.41756	−	6.30893i	−0.327451	−	0.467649i
$183$	−0.305895	−	1.73481i	−0.0226124	−	0.128241i
$184$	−7.70221			−0.567814
$185$	−1.76693	−	13.4862i	−0.129908	−	0.991526i
$186$	−23.6943			−1.73735
$187$	0.471737	+	2.67535i	0.0344968	+	0.195641i
$188$	1.85570	+	2.65022i	0.135341	+	0.193287i
$189$	1.15731	−	0.421226i	0.0841818	−	0.0306397i
$190$	−4.55569	+	12.5950i	−0.330504	+	0.913738i
$191$	8.71055	−	8.71055i	0.630273	−	0.630273i	−0.317863	−	0.948136i	$-0.602965\pi$
$191$	8.71055	−	8.71055i	0.630273	−	0.630273i	0.948136	+	0.317863i	$0.102965\pi$
$192$	2.50148	−	0.218851i	0.180529	−	0.0157942i
$193$	2.46596	+	4.27118i	0.177504	+	0.307446i	0.941025	−	0.338337i	$-0.109864\pi$
$193$	2.46596	+	4.27118i	0.177504	+	0.307446i	−0.763521	+	0.645783i	$0.776531\pi$
$194$	0.796339	−	2.18792i	0.0571738	−	0.157084i
$195$	4.62126	−	26.5186i	0.330936	−	1.89904i
$196$	3.82709	−	2.20957i	0.273364	−	0.157827i
$197$	−8.90692	−	6.23669i	−0.634592	−	0.444346i	0.211504	−	0.977377i	$-0.432164\pi$
$197$	−8.90692	−	6.23669i	−0.634592	−	0.444346i	−0.846096	+	0.533031i	$0.821053\pi$
$198$	11.0049	−	4.00547i	0.782086	−	0.284656i
$199$	4.74610	+	17.7127i	0.336442	+	1.25562i	0.902298	+	0.431114i	$0.141879\pi$
$199$	4.74610	+	17.7127i	0.336442	+	1.25562i	−0.565856	+	0.824504i	$0.691454\pi$
$200$	4.92747	+	0.848530i	0.348425	+	0.0600001i
$201$	−18.2896	+	15.3468i	−1.29005	+	1.08248i
$202$	0.578238	−	1.58869i	0.0406847	−	0.111780i
$203$	−0.147377	−	0.0259866i	−0.0103439	−	0.00182390i
$204$	1.57709	−	1.10429i	0.110419	−	0.0773159i
$205$	3.46040	−	3.47428i	0.241685	−	0.242654i
$206$	6.72732	+	8.01731i	0.468715	+	0.558592i
$207$	16.3642	+	19.5021i	1.13739	+	1.35549i
$208$	−2.39706	+	4.15184i	−0.166206	+	0.287878i
$209$	8.96914	−	19.2344i	0.620408	−	1.33047i
$210$	−8.71757	−	2.31718i	−0.601569	−	0.159901i
$211$	9.93824	+	17.2135i	0.684177	+	1.18503i	0.973695	+	0.227857i	$0.0731717\pi$
$211$	9.93824	+	17.2135i	0.684177	+	1.18503i	−0.289518	+	0.957173i	$0.593495\pi$
$212$	−8.72410	+	2.33761i	−0.599173	+	0.160548i
$213$	19.6212	−	9.14950i	1.34442	−	0.626914i
$214$	−4.08400	−	1.09430i	−0.279177	−	0.0748051i
$215$	6.47140	+	13.8058i	0.441346	+	0.941545i
$216$	−0.542084	−	0.542084i	−0.0368842	−	0.0368842i
$217$	−11.6125	−	9.74407i	−0.788310	−	0.661470i
$218$	−7.29541	−	3.40190i	−0.494107	−	0.230406i
$219$	−16.4191	−	2.89512i	−1.10950	−	0.195634i
$220$	−7.65686	−	2.03524i	−0.516226	−	0.137216i
$221$			3.67578i			0.247260i
$222$	13.5667	−	7.01718i	0.910537	−	0.470962i
$223$	−7.68835	−	7.68835i	−0.514850	−	0.514850i	0.401158	−	0.916009i	$-0.368608\pi$
$223$	−7.68835	−	7.68835i	−0.514850	−	0.514850i	−0.916009	+	0.401158i	$0.868608\pi$
$224$	1.31597	+	0.921452i	0.0879270	+	0.0615671i
$225$	−8.32046	−	14.2792i	−0.554697	−	0.951946i
$226$	0.0554026	+	0.152217i	0.00368533	+	0.0101254i
$227$	10.2546	−	12.2209i	0.680621	−	0.811132i	−0.309567	−	0.950878i	$-0.600184\pi$
$227$	10.2546	−	12.2209i	0.680621	−	0.811132i	0.990187	+	0.139746i	$0.0446285\pi$
$228$	−15.0406			−0.996088
$229$	2.41996	−	2.88399i	0.159915	−	0.190580i	−0.680137	−	0.733085i	$-0.738080\pi$
$229$	2.41996	−	2.88399i	0.159915	−	0.190580i	0.840052	+	0.542505i	$0.182524\pi$
$230$	−1.53538	−	17.1541i	−0.101240	−	1.13111i
$231$	13.4311	+	4.88851i	0.883700	+	0.321640i
$232$	0.0241098	+	0.0899791i	0.00158289	+	0.00590742i
$233$	−2.67847	−	0.717694i	−0.175472	−	0.0470177i	0.170013	−	0.985442i	$-0.445619\pi$
$233$	−2.67847	−	0.717694i	−0.175472	−	0.0470177i	−0.345485	+	0.938424i	$0.612286\pi$
$234$	15.6053	−	2.75164i	1.02015	−	0.179880i
$235$	−5.53255	+	4.66125i	−0.360904	+	0.304067i
$236$	−1.29229	+	0.346269i	−0.0841212	+	0.0225402i
$237$	−28.7459	+	24.1206i	−1.86724	+	1.56680i
$238$	1.22706	+	0.107354i	0.0795384	+	0.00695871i
$239$	2.27348	+	4.87549i	0.147059	+	0.315369i	0.966014	−	0.258488i	$-0.0832242\pi$
$239$	2.27348	+	4.87549i	0.147059	+	0.315369i	−0.818955	+	0.573857i	$0.805446\pi$
$240$	0.986070	+	5.52758i	0.0636505	+	0.356804i
$241$	5.34121	+	7.62803i	0.344057	+	0.491365i	0.953470	−	0.301489i	$-0.0974835\pi$
$241$	5.34121	+	7.62803i	0.344057	+	0.491365i	−0.609412	+	0.792853i	$0.708595\pi$
$242$	1.46024	+	0.531484i	0.0938677	+	0.0341651i
$243$	1.94926	−	22.2802i	0.125045	−	1.42927i
$244$	−0.698864	−	0.0611427i	−0.0447402	−	0.00391426i
$245$	5.68399	+	8.08311i	0.363137	+	0.516411i
$246$	4.99064	+	2.32717i	0.318191	+	0.148375i
$247$	16.4707	−	23.5227i	1.04801	−	1.49671i
$248$	−2.44223	+	9.11454i	−0.155082	+	0.578774i
$249$	−19.9056	+	34.4776i	−1.26147	+	2.18493i
$250$	−0.907559	+	11.1434i	−0.0573991	+	0.704773i
$251$	3.04672	−	11.3705i	0.192308	−	0.717701i	−0.800640	−	0.599146i	$-0.795507\pi$
$251$	3.04672	−	11.3705i	0.192308	−	0.717701i	0.992947	−	0.118556i	$-0.0378264\pi$
$252$	−0.462795	−	5.28977i	−0.0291533	−	0.333224i
$253$			27.2901i			1.71572i
$254$	−8.31404	+	0.727384i	−0.521669	+	0.0456402i
$255$	2.77382	+	3.29231i	0.173703	+	0.206172i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−26.7993	+	4.72544i	−1.67169	+	0.294765i	−0.927674	−	0.373392i	$-0.878195\pi$
$257$	−26.7993	+	4.72544i	−1.67169	+	0.294765i	−0.744021	+	0.668157i	$0.767084\pi$
$258$	−12.1072	+	12.1072i	−0.753762	+	0.753762i
$259$	9.53476	+	2.14008i	0.592461	+	0.132978i
$260$	−9.72466	−	4.51102i	−0.603098	−	0.279761i
$261$	0.176604	−	0.252217i	0.0109315	−	0.0156118i
$262$	−7.04578	+	4.93351i	−0.435290	+	0.304793i
$263$	−12.3181	+	26.4163i	−0.759568	+	1.62890i	0.0177904	+	0.999842i	$0.494337\pi$
$263$	−12.3181	+	26.4163i	−0.759568	+	1.62890i	−0.777359	+	0.629058i	$0.783441\pi$
$264$	−0.775424	−	8.86314i	−0.0477240	−	0.545488i
$265$	−6.94534	−	18.9640i	−0.426649	−	1.16495i
$266$	−7.37136	−	6.18531i	−0.451967	−	0.379246i
$267$	−31.6909	+	18.2967i	−1.93945	+	1.11974i
$268$	4.01833	+	8.61733i	0.245458	+	0.526387i
$269$	25.5372	+	14.7439i	1.55703	+	0.898952i	0.997539	+	0.0701167i	$0.0223372\pi$
$269$	25.5372	+	14.7439i	1.55703	+	0.898952i	0.559492	+	0.828836i	$0.310996\pi$
$270$	1.09925	−	1.31537i	0.0668982	−	0.0800510i
$271$	4.86429	+	27.5868i	0.295485	+	1.67578i	0.665226	+	0.746642i	$0.268335\pi$
$271$	4.86429	+	27.5868i	0.295485	+	1.67578i	−0.369742	+	0.929135i	$0.620554\pi$
$272$	−0.262235	−	0.720486i	−0.0159004	−	0.0436859i
$273$	16.7485	+	9.66973i	1.01366	+	0.585238i
$274$	−1.02948	+	11.7671i	−0.0621934	+	0.710874i
$275$	3.00647	−	17.4588i	0.181297	−	1.05281i
$276$	17.5285	−	8.17366i	1.05509	−	0.491996i
$277$	−3.26035	+	18.4904i	−0.195895	+	1.11098i	0.715243	+	0.698876i	$0.246316\pi$
$277$	−3.26035	+	18.4904i	−0.195895	+	1.11098i	−0.911138	+	0.412101i	$0.864795\pi$
$278$	0.793190	−	4.49840i	0.0475724	−	0.269796i
$279$	28.2669	−	13.1811i	1.69229	−	0.789130i
$280$	−1.78990	+	3.11457i	−0.106967	+	0.186131i
$281$	0.116158	−	1.32769i	0.00692938	−	0.0792032i	−0.991943	−	0.126688i	$-0.959565\pi$
$281$	0.116158	−	1.32769i	0.00692938	−	0.0792032i	0.998872	+	0.0474852i	$0.0151207\pi$
$282$	−7.03559	−	4.06200i	−0.418963	−	0.241888i
$283$	−7.09619	−	19.4966i	−0.421825	−	1.15895i	−0.950661	−	0.310230i	$-0.899594\pi$
$283$	−7.09619	−	19.4966i	−0.421825	−	1.15895i	0.528837	−	0.848724i	$-0.322628\pi$
$284$	−1.49715	−	8.49078i	−0.0888398	−	0.503835i
$285$	−2.99824	−	33.4979i	−0.177600	−	1.98424i
$286$	14.7106	+	8.49317i	0.869856	+	0.502212i
$287$	1.48887	+	3.19290i	0.0878853	+	0.188471i
$288$	−2.86248	+	1.65265i	−0.168673	+	0.0973834i
$289$	12.5724	+	10.5495i	0.739554	+	0.620560i
$290$	−0.195592	+	0.0716332i	−0.0114856	+	0.00420645i
$291$	0.509560	+	5.82429i	0.0298709	+	0.341426i
$292$	−2.80603	+	6.01755i	−0.164211	+	0.352151i
$293$	−21.1463	+	14.8068i	−1.23538	+	0.865023i	−0.994418	−	0.105512i	$-0.966352\pi$
$293$	−21.1463	+	14.8068i	−1.23538	+	0.865023i	−0.240962	+	0.970534i	$0.577463\pi$
$294$	−6.36477	+	9.08983i	−0.371201	+	0.530130i
$295$	−1.02881	−	2.80912i	−0.0598995	−	0.163554i
$296$	−1.30096	−	5.94201i	−0.0756167	−	0.345372i
$297$	−1.92069	+	1.92069i	−0.111450	+	0.111450i
$298$	10.8753	−	1.91762i	0.629992	−	0.111085i
$299$	−6.41202	+	36.3644i	−0.370817	+	2.10301i
$300$	−12.1143	+	3.29802i	−0.699418	+	0.190411i
$301$	−10.9127	+	0.954737i	−0.628997	+	0.0550301i
$302$		−	22.5864i		−	1.29970i
$303$	0.370002	+	4.22914i	0.0212560	+	0.242958i
$304$	−1.55027	+	5.78570i	−0.0889143	+	0.331833i
$305$	−0.00313867	−	1.56867i	−0.000179720	−	0.0898220i
$306$	−1.26713	+	2.19473i	−0.0724369	+	0.125464i
$307$	−0.377961	+	1.41057i	−0.0215714	+	0.0805055i	−0.975872	−	0.218341i	$-0.929935\pi$
$307$	−0.377961	+	1.41057i	−0.0215714	+	0.0805055i	0.954301	+	0.298847i	$0.0966020\pi$
$308$	3.26485	−	4.66269i	0.186032	−	0.265681i
$309$	−23.8179	−	11.1065i	−1.35495	−	0.631825i
$310$	−20.7864	−	3.62234i	−1.18059	−	0.205735i
$311$	12.3039	+	1.07645i	0.697689	+	0.0610399i	0.430482	−	0.902599i	$-0.358344\pi$
$311$	12.3039	+	1.07645i	0.697689	+	0.0610399i	0.267207	+	0.963639i	$0.413899\pi$
$312$	1.04920	−	11.9924i	0.0593993	−	0.678937i
$313$	0.440890	+	0.160471i	0.0249206	+	0.00907036i	0.354450	−	0.935075i	$-0.384668\pi$
$313$	0.440890	+	0.160471i	0.0249206	+	0.00907036i	−0.329530	+	0.944145i	$0.606890\pi$
$314$	−1.32091	−	1.88645i	−0.0745432	−	0.106459i
$315$	11.6889	−	2.08520i	0.658597	−	0.117488i
$316$	6.31563	+	13.5439i	0.355282	+	0.761905i
$317$	2.42297	+	0.211982i	0.136087	+	0.0119061i	0.154996	−	0.987915i	$-0.450464\pi$
$317$	2.42297	+	0.211982i	0.136087	+	0.0119061i	−0.0189085	+	0.999821i	$0.506019\pi$
$318$	17.3733	−	14.5780i	0.974249	−	0.817492i
$319$	0.318810	−	0.0854249i	0.0178499	−	0.00478288i
$320$	2.22794	+	0.190429i	0.124546	+	0.0106453i
$321$	10.4555	−	1.84359i	0.583571	−	0.102899i
$322$	11.9520	+	3.20253i	0.666059	+	0.178470i
$323$	1.18863	+	4.43604i	0.0661374	+	0.246828i
$324$	−7.50898	−	2.73304i	−0.417165	−	0.151836i
$325$	8.10824	−	22.5577i	0.449764	−	1.25127i
$326$	2.20336	−	2.62586i	0.122033	−	0.145433i
$327$	20.2128			1.11777
$328$	1.40960	−	1.67989i	0.0778320	−	0.0927565i
$329$	−1.77767	−	4.88410i	−0.0980059	−	0.269269i
$330$	19.5851	−	3.49380i	1.07812	−	0.192327i
$331$	26.6169	+	18.6374i	1.46300	+	1.02440i	0.989646	+	0.143531i	$0.0458458\pi$
$331$	26.6169	+	18.6374i	1.46300	+	1.02440i	0.473354	+	0.880872i	$0.343043\pi$
$332$	11.2108	+	11.2108i	0.615275	+	0.615275i
$333$	−12.2812	+	15.9185i	−0.673005	+	0.872327i
$334$		−	5.79717i		−	0.317207i
$335$	−18.3912	+	10.6673i	−1.00482	+	0.582816i
$336$	−3.97270	−	0.700495i	−0.216729	−	0.0382151i
$337$	−7.71264	−	3.59646i	−0.420134	−	0.195912i	0.201042	−	0.979583i	$-0.435567\pi$
$337$	−7.71264	−	3.59646i	−0.420134	−	0.195912i	−0.621176	+	0.783671i	$0.713345\pi$
$338$	7.64793	+	6.41738i	0.415993	+	0.349059i
$339$	−0.287618	−	0.287618i	−0.0156213	−	0.0156213i
$340$	1.55237	−	0.727665i	0.0841888	−	0.0394632i
$341$	32.2942	+	8.65322i	1.74883	+	0.468598i
$342$	17.9432	−	8.36704i	0.970255	−	0.452438i
$343$	−17.7198	+	4.74801i	−0.956780	+	0.256368i
$344$	3.40939	+	5.90523i	0.183822	+	0.318389i
$345$	21.6983	+	37.4094i	1.16819	+	2.01406i
$346$	7.21396	−	15.4704i	0.387825	−	0.831693i
$347$	13.8399	−	23.9715i	0.742967	−	1.28686i	−0.208171	−	0.978092i	$-0.566751\pi$
$347$	13.8399	−	23.9715i	0.742967	−	1.28686i	0.951139	−	0.308765i	$-0.0999155\pi$
$348$	−0.150355	−	0.179186i	−0.00805988	−	0.00960539i
$349$	−9.40756	−	11.2115i	−0.503575	−	0.600137i	0.453041	−	0.891490i	$-0.350339\pi$
$349$	−9.40756	−	11.2115i	−0.503575	−	0.600137i	−0.956616	+	0.291353i	$0.905895\pi$
$350$	−7.29346	−	3.36553i	−0.389852	−	0.179895i
$351$	−3.01062	+	2.10806i	−0.160695	+	0.112520i
$352$	−3.48933	−	0.615263i	−0.185982	−	0.0327936i
$353$	9.80632	−	26.9426i	0.521938	−	1.43401i	−0.346422	−	0.938079i	$-0.612604\pi$
$353$	9.80632	−	26.9426i	0.521938	−	1.43401i	0.868360	−	0.495934i	$-0.165174\pi$
$354$	2.57350	−	2.15942i	0.136780	−	0.114772i
$355$	18.6119	−	5.02699i	0.987819	−	0.266805i
$356$	3.77179	+	14.0765i	0.199904	+	0.746053i
$357$	−2.90643	+	1.05785i	−0.153825	+	0.0559876i
$358$	3.70260	+	2.59259i	0.195688	+	0.137022i
$359$	−3.99651	+	2.30739i	−0.210928	+	0.121779i	−0.601743	−	0.798690i	$-0.705527\pi$
$359$	−3.99651	+	2.30739i	−0.210928	+	0.121779i	0.390815	+	0.920469i	$0.372193\pi$
$360$	−4.25134	−	6.04576i	−0.224065	−	0.318639i
$361$	5.77252	−	15.8599i	0.303817	−	0.834729i
$362$	−3.24337	−	5.61768i	−0.170468	−	0.295259i
$363$	−3.88719	+	0.340085i	−0.204024	+	0.0178498i
$364$	5.44598	−	5.44598i	0.285447	−	0.285447i
$365$	−13.9614	−	5.04994i	−0.730775	−	0.264326i
$366$	1.65534	−	0.602495i	0.0865261	−	0.0314929i
$367$	17.6407	+	25.1936i	0.920838	+	1.31509i	0.948930	+	0.315488i	$0.102168\pi$
$367$	17.6407	+	25.1936i	0.920838	+	1.31509i	−0.0280916	+	0.999605i	$0.508943\pi$
$368$	−1.33747	−	7.58519i	−0.0697207	−	0.395406i
$369$	−7.24834			−0.377334
$370$	12.9745	−	4.08195i	0.674512	−	0.212210i
$371$	14.5097			0.753306
$372$	−4.11447	−	23.3343i	−0.213326	−	1.20983i
$373$	−9.04618	−	12.9193i	−0.468393	−	0.668935i	0.513561	−	0.858053i	$-0.328326\pi$
$373$	−9.04618	−	12.9193i	−0.468393	−	0.668935i	−0.981954	+	0.189118i	$0.939437\pi$
$374$	−2.55279	+	0.929141i	−0.132002	+	0.0480447i
$375$	−9.76013	−	26.3230i	−0.504011	−	1.35932i
$376$	−2.28771	+	2.28771i	−0.117980	+	0.117980i
$377$	0.444889	−	0.0389228i	0.0229130	−	0.00200462i
$378$	0.615791	+	1.06658i	0.0316729	+	0.0548590i
$379$	9.83728	−	27.0277i	0.505307	−	1.38832i	−0.380721	−	0.924690i	$-0.624324\pi$
$379$	9.83728	−	27.0277i	0.505307	−	1.38832i	0.886029	−	0.463631i	$-0.153454\pi$
$380$	−13.1947	−	2.29938i	−0.676876	−	0.117956i
$381$	18.1490	−	10.4783i	0.929799	−	0.536820i
$382$	10.0908	+	7.06564i	0.516289	+	0.361510i
$383$	−17.0930	+	6.22136i	−0.873414	+	0.317897i	−0.739549	−	0.673103i	$-0.764961\pi$
$383$	−17.0930	+	6.22136i	−0.873414	+	0.317897i	−0.133865	+	0.991000i	$0.542739\pi$
$384$	0.649904	+	2.42547i	0.0331653	+	0.123774i
$385$	11.0354	+	6.34188i	0.562416	+	0.323212i
$386$	−3.77808	+	3.17018i	−0.192299	+	0.161358i
$387$	7.70848	−	21.1789i	0.391844	−	1.07658i
$388$	2.29297	+	0.404312i	0.116408	+	0.0205258i
$389$	23.8521	−	16.7014i	1.20935	−	0.846794i	0.217731	−	0.976009i	$-0.430135\pi$
$389$	23.8521	−	16.7014i	1.20935	−	0.846794i	0.991617	+	0.129215i	$0.0412457\pi$
$390$	26.9182	−	0.0538592i	1.36306	−	0.00272727i
$391$	−3.79597	−	4.52386i	−0.191970	−	0.228781i
$392$	2.84057	+	3.38526i	0.143471	+	0.170982i
$393$	10.7991	−	18.7046i	0.544742	−	0.943521i
$394$	4.59527	−	9.85459i	0.231506	−	0.496467i
$395$	−28.9055	+	16.7658i	−1.45440	+	0.843580i
$396$	5.85560	+	10.1422i	0.294255	+	0.509664i
$397$	36.7404	−	9.84457i	1.84395	−	0.494085i	0.844791	−	0.535096i	$-0.179725\pi$
$397$	36.7404	−	9.84457i	1.84395	−	0.494085i	0.999159	+	0.0410113i	$0.0130580\pi$
$398$	−16.6194	+	7.74977i	−0.833057	+	0.388461i
$399$	23.3395	+	6.25379i	1.16843	+	0.313081i
$400$	0.0200084	+	4.99996i	0.00100042	+	0.249998i
$401$	−4.69266	−	4.69266i	−0.234340	−	0.234340i	0.580161	−	0.814502i	$-0.302990\pi$
$401$	−4.69266	−	4.69266i	−0.234340	−	0.234340i	−0.814502	+	0.580161i	$0.802990\pi$
$402$	−18.2896	−	15.3468i	−0.912202	−	0.765428i
$403$	40.9993	+	19.1183i	2.04232	+	0.952350i
$404$	1.66497	+	0.293579i	0.0828353	+	0.0146061i
$405$	4.59008	−	17.2685i	0.228083	−	0.858081i
$406$		−	0.149651i		−	0.00742705i
$407$	−21.0535	+	4.60950i	−1.04358	+	0.228484i
$408$	1.36137	+	1.36137i	0.0673981	+	0.0673981i
$409$	4.58162	+	3.20808i	0.226546	+	0.158629i	0.681339	−	0.731968i	$-0.261398\pi$
$409$	4.58162	+	3.20808i	0.226546	+	0.158629i	−0.454793	+	0.890597i	$0.650287\pi$
$410$	4.02239	+	2.80453i	0.198652	+	0.138506i
$411$	−10.1444	−	27.8716i	−0.500388	−	1.37481i
$412$	−6.72732	+	8.01731i	−0.331431	+	0.394985i
$413$	2.14931			0.105761
$414$	−16.3642	+	19.5021i	−0.804255	+	0.958474i
$415$	−22.7336	+	27.2032i	−1.11595	+	1.33535i
$416$	−4.50501	−	1.63969i	−0.220876	−	0.0803923i
$417$	2.96863	+	11.0791i	0.145374	+	0.542545i
$418$	20.4996	+	5.49286i	1.00267	+	0.268665i
$419$	−29.0898	+	5.12932i	−1.42113	+	0.250584i	−0.830797	−	0.556576i	$-0.812115\pi$
$419$	−29.0898	+	5.12932i	−1.42113	+	0.250584i	−0.590334	+	0.807159i	$0.701004\pi$
$420$	0.768187	−	8.98750i	0.0374837	−	0.438545i
$421$	−33.0452	+	8.85443i	−1.61052	+	0.431538i	−0.948198	−	0.317679i	$-0.897097\pi$
$421$	−33.0452	+	8.85443i	−1.61052	+	0.431538i	−0.662324	+	0.749217i	$0.730430\pi$
$422$	−15.2263	+	12.7764i	−0.741203	+	0.621943i
$423$	10.6530	+	0.932017i	0.517967	+	0.0453162i
$424$	−3.81702	−	8.18563i	−0.185371	−	0.397530i
$425$	1.93008	+	3.31232i	0.0936227	+	0.160671i
$426$	12.4177	+	17.7343i	0.601639	+	0.859229i
$427$	1.05905	+	0.385462i	0.0512510	+	0.0186538i
$428$	0.368501	−	4.21198i	0.0178121	−	0.203594i
$429$	−42.4910	−	3.71748i	−2.05149	−	0.179482i
$430$	−12.4723	+	8.77043i	−0.601467	+	0.422948i
$431$	−9.90941	−	4.62083i	−0.477319	−	0.222578i	0.169042	−	0.985609i	$-0.445933\pi$
$431$	−9.90941	−	4.62083i	−0.477319	−	0.222578i	−0.646362	+	0.763031i	$0.723710\pi$
$432$	0.439717	−	0.627981i	0.0211559	−	0.0302137i
$433$	−9.88051	+	36.8746i	−0.474827	+	1.77208i	0.147225	+	0.989103i	$0.452966\pi$
$433$	−9.88051	+	36.8746i	−0.474827	+	1.77208i	−0.622052	+	0.782976i	$0.713701\pi$
$434$	7.57954	−	13.1281i	0.363829	−	0.630171i
$435$	0.369105	−	0.370585i	0.0176972	−	0.0177682i
$436$	2.08339	−	7.77531i	0.0997761	−	0.372370i
$437$	4.02090	+	45.9591i	0.192346	+	2.19852i
$438$		−	16.6724i		−	0.796636i
$439$	−8.44090	+	0.738483i	−0.402862	+	0.0352459i	−0.286787	−	0.957995i	$-0.592587\pi$
$439$	−8.44090	+	0.738483i	−0.402862	+	0.0352459i	−0.116076	+	0.993240i	$0.537031\pi$
$440$	0.674719	−	7.89396i	0.0321660	−	0.376330i
$441$	2.53641	−	14.3847i	0.120782	−	0.684986i
$442$	−3.61993	+	0.638292i	−0.172183	+	0.0303605i
$443$	4.87950	−	4.87950i	0.231832	−	0.231832i	−0.581625	−	0.813457i	$-0.697583\pi$
$443$	4.87950	−	4.87950i	0.231832	−	0.231832i	0.813457	+	0.581625i	$0.197583\pi$
$444$	9.26641	+	12.1421i	0.439764	+	0.576237i
$445$	−30.5988	+	11.2064i	−1.45052	+	0.531236i
$446$	6.23648	−	8.90662i	0.295306	−	0.421741i
$447$	−22.7148	+	15.9051i	−1.07437	+	0.752284i
$448$	−0.678938	+	1.45599i	−0.0320768	+	0.0687889i
$449$	−0.940909	−	10.7546i	−0.0444042	−	0.507543i	−0.985532	−	0.169491i	$-0.945788\pi$
$449$	−0.940909	−	10.7546i	−0.0444042	−	0.507543i	0.941128	−	0.338052i	$-0.109768\pi$
$450$	12.6174	−	10.6736i	0.594791	−	0.503159i
$451$	−5.95212	−	4.99442i	−0.280274	−	0.235178i
$452$	−0.140284	+	0.0809932i	−0.00659842	+	0.00380960i
$453$	23.9689	+	51.4016i	1.12616	+	2.41506i
$454$	13.8160	+	7.97665i	0.648415	+	0.374363i
$455$	13.2147	+	11.0435i	0.619516	+	0.517726i
$456$	−2.61177	−	14.8121i	−0.122307	−	0.693640i
$457$	−3.83063	−	10.5246i	−0.179189	−	0.492318i	0.817284	−	0.576236i	$-0.195479\pi$
$457$	−3.83063	−	10.5246i	−0.179189	−	0.492318i	−0.996473	+	0.0839175i	$0.973257\pi$
$458$	3.26040	+	1.88239i	0.152349	+	0.0879585i
$459$	0.0512292	−	0.585552i	0.00239117	−	0.0273312i
$460$	16.6269	−	4.49083i	0.775231	−	0.209386i
$461$	22.2559	−	10.3781i	1.03656	−	0.483357i	0.171586	−	0.985169i	$-0.445111\pi$
$461$	22.2559	−	10.3781i	1.03656	−	0.483357i	0.864977	+	0.501812i	$0.167333\pi$
$462$	−2.48196	+	14.0759i	−0.115471	+	0.654870i
$463$	1.85997	−	10.5484i	0.0864403	−	0.490227i	−0.910596	−	0.413297i	$-0.864377\pi$
$463$	1.85997	−	10.5484i	0.0864403	−	0.490227i	0.997036	−	0.0769300i	$-0.0245118\pi$
$464$	−0.0844255	+	0.0393683i	−0.00391936	+	0.00182763i
$465$	51.1492	−	13.8151i	2.37199	−	0.640662i
$466$	0.241679	−	2.76241i	0.0111956	−	0.127966i
$467$	−31.3633	−	18.1076i	−1.45132	−	0.837919i	−0.452762	−	0.891631i	$-0.649561\pi$
$467$	−31.3633	−	18.1076i	−1.45132	−	0.837919i	−0.998556	+	0.0537121i	$0.982895\pi$
$468$	5.41966	+	14.8904i	0.250524	+	0.688309i
$469$	−2.65246	−	15.0429i	−0.122479	−	0.694614i
$470$	−5.55116	−	4.63908i	−0.256056	−	0.213985i
$471$	5.00801	+	2.89138i	0.230757	+	0.133228i
$472$	−0.565413	−	1.21253i	−0.0260252	−	0.0558113i
$473$	20.9231	−	12.0800i	0.962047	−	0.555438i
$474$	−28.7459	−	24.1206i	−1.32034	−	1.10790i
$475$	2.49082	−	29.8452i	0.114287	−	1.36939i
$476$	0.107354	+	1.22706i	0.00492055	+	0.0562421i
$477$	−12.6164	+	27.0560i	−0.577666	+	1.23881i
$478$	−4.40664	+	3.08556i	−0.201555	+	0.141130i
$479$	−17.2133	+	24.5832i	−0.786497	+	1.12323i	0.203070	+	0.979164i	$0.434908\pi$
$479$	−17.2133	+	24.5832i	−0.786497	+	1.12323i	−0.989567	+	0.144070i	$0.953981\pi$
$480$	−5.27238	+	1.93094i	−0.240650	+	0.0881351i
$481$	−29.1370	+	1.19553i	−1.32853	+	0.0545117i
$482$	−6.58466	+	6.58466i	−0.299923	+	0.299923i
$483$	−30.5986	+	5.39536i	−1.39228	+	0.245497i
$484$	−0.269841	+	1.53035i	−0.0122655	+	0.0695612i
$485$	−0.443383	+	5.18741i	−0.0201330	+	0.235548i
$486$	22.2802	−	1.94926i	1.01065	−	0.0884203i
$487$		−	10.3486i		−	0.468939i	−0.972123	−	0.234470i	$-0.924665\pi$
$487$		−	10.3486i		−	0.468939i	0.972123	−	0.234470i	$-0.0753354\pi$
$488$	−0.0611427	−	0.698864i	−0.00276780	−	0.0316361i
$489$	−2.22775	+	8.31407i	−0.100742	+	0.375975i
$490$	−6.97329	+	7.00125i	−0.315021	+	0.316284i
$491$	−5.91272	+	10.2411i	−0.266837	+	0.462176i	−0.968043	−	0.250783i	$-0.919312\pi$
$491$	−5.91272	+	10.2411i	−0.266837	+	0.462176i	0.701206	+	0.712959i	$0.252645\pi$
$492$	−1.42520	+	5.31893i	−0.0642531	+	0.239796i
$493$	−0.0409665	+	0.0585062i	−0.00184504	+	0.00263499i
$494$	26.0254	+	12.1359i	1.17094	+	0.546018i
$495$	−21.4211	+	15.0632i	−0.962805	+	0.677039i
$496$	−9.40016	−	0.822408i	−0.422080	−	0.0369272i
$497$	−1.20719	+	13.7982i	−0.0541497	+	0.618933i
$498$	−37.4104	−	13.6163i	−1.67640	−	0.610159i
$499$	−12.7949	−	18.2731i	−0.572780	−	0.818014i	0.423345	−	0.905969i	$-0.360856\pi$
$499$	−12.7949	−	18.2731i	−0.572780	−	0.818014i	−0.996124	+	0.0879544i	$0.971967\pi$
$500$	−11.1317	+	1.04127i	−0.497827	+	0.0465669i
$501$	6.15202	+	13.1930i	0.274852	+	0.589422i
$502$	11.7268	+	1.02597i	0.523395	+	0.0457911i
$503$	14.2622	−	11.9674i	0.635920	−	0.533601i	−0.266842	−	0.963740i	$-0.585980\pi$
$503$	14.2622	−	11.9674i	0.635920	−	0.533601i	0.902762	+	0.430140i	$0.141536\pi$
$504$	5.12904	−	1.37432i	0.228466	−	0.0612172i
$505$	−0.321949	+	3.76668i	−0.0143265	+	0.167615i
$506$	−26.8755	+	4.73888i	−1.19476	+	0.210669i
$507$	−24.2151	−	6.48842i	−1.07543	−	0.288161i
$508$	−2.16005	−	8.06142i	−0.0958368	−	0.357668i
$509$	32.9663	+	11.9988i	1.46121	+	0.531836i	0.945698	−	0.325048i	$-0.105380\pi$
$509$	32.9663	+	11.9988i	1.46121	+	0.531836i	0.515510	+	0.856884i	$0.327603\pi$
$510$	−2.76062	+	3.30338i	−0.122242	+	0.146276i
$511$	6.85635	−	8.17108i	0.303307	−	0.361467i
$512$	1.00000			0.0441942
$513$	−2.95163	+	3.51761i	−0.130318	+	0.155306i
$514$	−9.30730	−	25.5716i	−0.410527	−	1.12791i
$515$	−19.1969	−	13.3847i	−0.845917	−	0.589799i
$516$	−14.0257	−	9.82088i	−0.617446	−	0.432340i
$517$	8.10573	+	8.10573i	0.356490	+	0.356490i
$518$	−0.451871	+	9.76152i	−0.0198541	+	0.428897i
$519$			42.8626i			1.88146i
$520$	2.75382	−	10.3603i	0.120763	−	0.454327i
$521$	−18.2900	−	3.22503i	−0.801301	−	0.141291i	−0.242023	−	0.970271i	$-0.577811\pi$
$521$	−18.2900	−	3.22503i	−0.801301	−	0.141291i	−0.559279	+	0.828980i	$0.688922\pi$
$522$	0.279052	+	0.130124i	0.0122138	+	0.00569537i
$523$	6.97043	+	5.84888i	0.304796	+	0.255754i	0.782337	−	0.622855i	$-0.214028\pi$
$523$	6.97043	+	5.84888i	0.304796	+	0.255754i	−0.477541	+	0.878609i	$0.658472\pi$
$524$	−6.08204	−	6.08204i	−0.265695	−	0.265695i
$525$	20.1698	−	0.0807135i	0.880281	−	0.00352263i
$526$	−28.1540	−	7.54384i	−1.22757	−	0.328927i
$527$	−6.55702	+	3.05759i	−0.285628	+	0.133191i
$528$	8.59383	−	2.30271i	0.373999	−	0.100213i
$529$	−18.1620	−	31.4575i	−0.789653	−	1.36772i
$530$	17.4699	−	10.1329i	0.758842	−	0.440145i
$531$	−1.86886	+	4.00778i	−0.0811016	+	0.173923i
$532$	4.81132	−	8.33345i	0.208597	−	0.361301i
$533$	−6.75779	−	8.05362i	−0.292712	−	0.348841i
$534$	−23.5218	−	28.0322i	−1.01789	−	1.21307i
$535$	9.45423	−	0.0189165i	0.408742	−	0.000817830i
$536$	−7.78864	+	5.45366i	−0.336418	+	0.235562i
$537$	−11.1775	−	1.97090i	−0.482347	−	0.0850507i
$538$	−10.0854	+	27.7095i	−0.434814	+	1.19464i
$539$	11.9945	−	10.0646i	0.516640	−	0.433513i
$540$	1.48627	+	0.854138i	0.0639589	+	0.0367563i
$541$	−2.63937	−	9.85025i	−0.113475	−	0.423495i	0.885693	−	0.464271i	$-0.153684\pi$
$541$	−2.63937	−	9.85025i	−0.113475	−	0.423495i	−0.999168	+	0.0407759i	$0.987017\pi$
$542$	−26.3230	+	9.58078i	−1.13067	+	0.411530i
$543$	13.3427	+	9.34266i	0.572590	+	0.400932i
$544$	0.664003	−	0.383362i	0.0284689	−	0.0164365i
$545$	17.7322	+	3.09010i	0.759564	+	0.132365i
$546$	−6.61448	+	18.1731i	−0.283074	+	0.777739i
$547$	11.7254	+	20.3090i	0.501343	+	0.868351i	0.999999	+	0.00155089i	$0.000493663\pi$
$547$	11.7254	+	20.3090i	0.501343	+	0.868351i	−0.498656	+	0.866800i	$0.666173\pi$
$548$	−11.7671	+	1.02948i	−0.502664	+	0.0439774i
$549$	−1.63963	+	1.63963i	−0.0699775	+	0.0699775i
$550$	17.7156	−	0.0708928i	0.755397	−	0.00302288i
$551$	0.524320	−	0.190837i	0.0223368	−	0.00812992i
$552$	11.0933	+	15.8428i	0.472161	+	0.674316i
$553$	−4.16889	−	23.6429i	−0.177279	−	1.00540i
$554$	−18.7756			−0.797699
$555$	−25.1952	+	23.0582i	−1.06948	+	0.978768i
$556$	4.56780			0.193718
$557$	−4.20251	−	23.8336i	−0.178066	−	1.00986i	−0.934545	−	0.355845i	$-0.884193\pi$
$557$	−4.20251	−	23.8336i	−0.178066	−	1.00986i	0.756479	−	0.654018i	$-0.226918\pi$
$558$	17.8893	+	25.5486i	0.757315	+	1.08156i
$559$	30.7186	−	11.1807i	1.29926	−	0.472892i
$560$	−3.37806	−	1.22187i	−0.142749	−	0.0516332i
$561$	4.82356	−	4.82356i	0.203651	−	0.203651i
$562$	1.32769	−	0.116158i	0.0560051	−	0.00489981i
$563$	−1.74717	−	3.02619i	−0.0736346	−	0.127539i	0.826857	−	0.562412i	$-0.190127\pi$
$563$	−1.74717	−	3.02619i	−0.0736346	−	0.127539i	−0.900492	+	0.434873i	$0.856793\pi$
$564$	2.77857	−	7.63406i	0.116999	−	0.321452i
$565$	−0.208350	−	0.296291i	−0.00876535	−	0.0124651i
$566$	17.9682	−	10.3739i	0.755259	−	0.436049i
$567$	10.5158	+	7.36322i	0.441621	+	0.309226i
$568$	8.10181	−	2.94882i	0.339944	−	0.123730i
$569$	5.11318	+	19.0827i	0.214356	+	0.799986i	0.986392	+	0.164408i	$0.0525715\pi$
$569$	5.11318	+	19.0827i	0.214356	+	0.799986i	−0.772037	+	0.635578i	$0.780762\pi$
$570$	32.4684	−	8.76954i	1.35995	−	0.367315i
$571$	−8.61188	+	7.22622i	−0.360396	+	0.302408i	−0.804948	−	0.593345i	$-0.797807\pi$
$571$	−8.61188	+	7.22622i	−0.360396	+	0.302408i	0.444553	+	0.895753i	$0.353363\pi$
$572$	−5.80967	+	15.9619i	−0.242915	+	0.667402i
$573$	−30.4624	−	5.37135i	−1.27259	−	0.224391i
$574$	−2.88585	+	2.02069i	−0.120453	+	0.0843421i
$575$	13.3163	+	36.1355i	0.555327	+	1.50696i
$576$	−2.12461	−	2.53201i	−0.0885253	−	0.105500i
$577$	−24.9816	−	29.7719i	−1.04000	−	1.23942i	−0.970313	−	0.241851i	$-0.922246\pi$
$577$	−24.9816	−	29.7719i	−1.04000	−	1.23942i	−0.0696835	−	0.997569i	$-0.522199\pi$
$578$	−8.20607	+	14.2133i	−0.341327	+	0.591196i
$579$	5.23381	−	11.2239i	0.217510	−	0.466451i
$580$	−0.104509	−	0.180182i	−0.00433951	−	0.00748164i
$581$	−12.7352	−	22.0580i	−0.528344	−	0.915119i
$582$	−5.64733	+	1.51320i	−0.234089	+	0.0627240i
$583$	−29.0030	+	13.5243i	−1.20118	+	0.560120i
$584$	−6.41339	−	1.71846i	−0.265388	−	0.0711105i
$585$	−32.0830	+	15.0388i	−1.32647	+	0.621777i
$586$	−18.2539	−	18.2539i	−0.754060	−	0.754060i
$587$	−11.1705	−	9.37314i	−0.461055	−	0.386871i	0.382464	−	0.923970i	$-0.375076\pi$
$587$	−11.1705	−	9.37314i	−0.461055	−	0.386871i	−0.843519	+	0.537100i	$0.819520\pi$
$588$	−10.0570	−	4.68964i	−0.414742	−	0.193398i
$589$	55.6615	+	9.81463i	2.29349	+	0.404405i
$590$	2.58780	−	1.50098i	0.106538	−	0.0617942i
$591$			27.3033i			1.12311i
$592$	5.62583	−	2.31301i	0.231220	−	0.0950643i
$593$	23.3347	+	23.3347i	0.958240	+	0.958240i	0.999162	−	0.0409222i	$-0.0130296\pi$
$593$	23.3347	+	23.3347i	0.958240	+	0.958240i	−0.0409222	+	0.999162i	$0.513030\pi$
$594$	−2.22503	−	1.55799i	−0.0912942	−	0.0639249i
$595$	−2.71146	+	0.483700i	−0.111159	+	0.0198298i
$596$	3.77697	+	10.3771i	0.154711	+	0.425064i
$597$	29.5979	−	35.2734i	1.21136	−	1.44364i
$598$	−36.9254			−1.50999
$599$	5.61392	−	6.69041i	0.229379	−	0.273363i	−0.639063	−	0.769155i	$-0.720678\pi$
$599$	5.61392	−	6.69041i	0.229379	−	0.273363i	0.868441	+	0.495792i	$0.165122\pi$
$600$	−5.35154	−	11.3575i	−0.218476	−	0.463669i
$601$	−22.7086	−	8.26527i	−0.926304	−	0.337147i	−0.165561	−	0.986200i	$-0.552943\pi$
$601$	−22.7086	−	8.26527i	−0.926304	−	0.337147i	−0.760744	+	0.649052i	$0.775166\pi$
$602$	−2.83520	−	10.5811i	−0.115554	−	0.431254i
$603$	30.3565	+	8.13400i	1.23621	+	0.331242i
$604$	22.2433	−	3.92209i	0.905067	−	0.159588i
$605$	−3.46212	−	0.295918i	−0.140755	−	0.0120308i
$606$	−4.10064	+	1.09876i	−0.166577	+	0.0446342i
$607$	−34.9944	+	29.3638i	−1.42038	+	1.19184i	−0.469244	+	0.883069i	$0.655474\pi$
$607$	−34.9944	+	29.3638i	−1.42038	+	1.19184i	−0.951136	+	0.308772i	$0.900082\pi$
$608$	−5.96701	−	0.522046i	−0.241994	−	0.0211717i
$609$	0.158811	+	0.340571i	0.00643535	+	0.0138006i
$610$	1.54430	−	0.275488i	0.0625268	−	0.0111542i
$611$	8.89647	+	12.7055i	0.359913	+	0.514009i
$612$	−2.38142	−	0.866767i	−0.0962633	−	0.0350370i
$613$	−0.246109	+	2.81304i	−0.00994025	+	0.113618i	−0.999544	−	0.0302051i	$-0.990384\pi$
$613$	−0.246109	+	2.81304i	−0.00994025	+	0.113618i	0.989603	+	0.143823i	$0.0459395\pi$
$614$	−1.45477	−	0.127276i	−0.0587099	−	0.00513645i
$615$	−12.1302	−	2.11387i	−0.489138	−	0.0852395i
$616$	5.15879	+	2.40558i	0.207853	+	0.0969237i
$617$	20.2192	−	28.8760i	0.813995	−	1.16250i	−0.170199	−	0.985410i	$-0.554441\pi$
$617$	20.2192	−	28.8760i	0.813995	−	1.16250i	0.984194	−	0.177095i	$-0.0566700\pi$
$618$	6.80180	−	25.3847i	0.273609	−	1.02112i
$619$	13.0900	−	22.6726i	0.526132	−	0.911287i	−0.473405	−	0.880845i	$-0.656975\pi$
$619$	13.0900	−	22.6726i	0.526132	−	0.911287i	0.999537	−	0.0304418i	$-0.00969143\pi$
$620$	−0.0422171	−	21.0997i	−0.00169548	−	0.847382i
$621$	1.52825	−	5.70349i	0.0613264	−	0.228873i
$622$	1.07645	+	12.3039i	0.0431617	+	0.493341i
$623$		−	23.4117i		−	0.937969i
$624$	11.9924	−	1.04920i	0.480081	−	0.0420016i
$625$	−4.53811	−	24.5847i	−0.181524	−	0.983386i
$626$	−0.0814733	+	0.462058i	−0.00325633	+	0.0184675i
$627$	−52.4816	+	9.25392i	−2.09591	+	0.369566i
$628$	1.62842	−	1.62842i	0.0649810	−	0.0649810i
$629$	2.84885	−	3.69258i	0.113591	−	0.147233i
$630$	4.08328	+	11.1493i	0.162682	+	0.444197i
$631$	16.2111	−	23.1519i	0.645355	−	0.921662i	−0.354556	−	0.935035i	$-0.615368\pi$
$631$	16.2111	−	23.1519i	0.645355	−	0.921662i	0.999911	+	0.0133729i	$0.00425686\pi$
$632$	−12.2415	+	8.57156i	−0.486939	+	0.340958i
$633$	21.0931	−	45.2343i	0.838376	−	1.79790i
$634$	0.211982	+	2.42297i	0.00841889	+	0.0962284i
$635$	17.5235	−	6.41778i	0.695400	−	0.254682i
$636$	17.3733	+	14.5780i	0.688898	+	0.578054i
$637$	18.3476	−	10.5930i	0.726958	−	0.419709i
$638$	0.139488	+	0.299133i	0.00552238	+	0.0118428i
$639$	−24.6796	−	14.2488i	−0.976310	−	0.563673i
$640$	0.199343	+	2.22716i	0.00787971	+	0.0880364i
$641$	0.668146	+	3.78924i	0.0263902	+	0.149666i	0.995156	−	0.0983131i	$-0.0313447\pi$
$641$	0.668146	+	3.78924i	0.0263902	+	0.149666i	−0.968765	+	0.247979i	$0.920234\pi$
$642$	3.63117	+	9.97656i	0.143311	+	0.393743i
$643$	36.7030	+	21.1905i	1.44742	+	0.835671i	0.998327	−	0.0578124i	$-0.0184125\pi$
$643$	36.7030	+	21.1905i	1.44742	+	0.835671i	0.449097	+	0.893483i	$0.351746\pi$
$644$	−1.07843	+	12.3265i	−0.0424962	+	0.485734i
$645$	19.0768	−	33.1952i	0.751148	−	1.30706i
$646$	−4.16224	+	1.94089i	−0.163761	+	0.0763632i
$647$	3.44212	−	19.5213i	0.135324	−	0.767460i	−0.839310	−	0.543653i	$-0.817041\pi$
$647$	3.44212	−	19.5213i	0.135324	−	0.767460i	0.974634	−	0.223806i	$-0.0718483\pi$
$648$	1.38760	−	7.86949i	0.0545102	−	0.309143i
$649$	−4.29619	+	2.00335i	−0.168640	+	0.0786382i
$650$	23.6229	+	4.06796i	0.926568	+	0.159558i
$651$	−3.31758	+	37.9201i	−0.130026	+	1.48621i
$652$	2.96857	+	1.71391i	0.116258	+	0.0671217i
$653$	5.56426	+	15.2877i	0.217746	+	0.598253i	0.999685	−	0.0251026i	$-0.00799123\pi$
$653$	5.56426	+	15.2877i	0.217746	+	0.598253i	−0.781939	+	0.623355i	$0.785769\pi$
$654$	3.50992	+	19.9057i	0.137249	+	0.778376i
$655$	12.3333	−	14.7581i	0.481902	−	0.576647i
$656$	1.89914	+	1.09647i	0.0741492	+	0.0428100i
$657$	9.27478	+	19.8898i	0.361843	+	0.775976i
$658$	4.50121	−	2.59877i	0.175475	−	0.101311i
$659$	−33.5160	−	28.1233i	−1.30560	−	1.09553i	−0.989149	−	0.146917i	$-0.953065\pi$
$659$	−33.5160	−	28.1233i	−1.30560	−	1.09553i	−0.316449	−	0.948610i	$-0.602490\pi$
$660$	6.84164	+	18.6809i	0.266310	+	0.727151i
$661$	−2.90064	−	33.1545i	−0.112822	−	1.28956i	−0.815794	−	0.578343i	$-0.803700\pi$
$661$	−2.90064	−	33.1545i	−0.112822	−	1.28956i	0.702972	−	0.711218i	$-0.251856\pi$
$662$	−13.7323	+	29.4489i	−0.533719	+	1.14457i
$663$	7.56078	−	5.29412i	0.293636	−	0.205606i
$664$	−9.09379	+	12.9873i	−0.352907	+	0.504004i
$665$	19.5191	+	9.05438i	0.756917	+	0.351114i
$666$	−17.8092	−	9.33040i	−0.690094	−	0.361546i
$667$	−0.507339	+	0.507339i	−0.0196442	+	0.0196442i
$668$	5.70910	−	1.00667i	0.220892	−	0.0389492i
$669$	−4.74102	+	26.8876i	−0.183298	+	1.03954i
$670$	−13.6988	−	16.2594i	−0.529231	−	0.628157i
$671$	−2.47619	+	0.216638i	−0.0955921	+	0.00836322i
$672$		−	4.03399i		−	0.155614i
$673$	−0.525028	−	6.00110i	−0.0202384	−	0.231325i	−0.999577	−	0.0290964i	$-0.990737\pi$
$673$	−0.525028	−	6.00110i	−0.0202384	−	0.231325i	0.979338	−	0.202229i	$-0.0648185\pi$
$674$	2.20254	−	8.21998i	0.0848386	−	0.316622i
$675$	−1.60603	+	3.48044i	−0.0618161	+	0.133962i
$676$	−4.99183	+	8.64611i	−0.191994	+	0.332543i
$677$	10.6539	−	39.7608i	0.409462	−	1.52813i	−0.386213	−	0.922410i	$-0.626217\pi$
$677$	10.6539	−	39.7608i	0.409462	−	1.52813i	0.795675	−	0.605724i	$-0.207116\pi$
$678$	0.233304	−	0.333193i	0.00896000	−	0.0127962i
$679$	−3.39003	−	1.58080i	−0.130097	−	0.0606654i
$680$	0.986175	+	1.40242i	0.0378181	+	0.0537805i
$681$	−39.9069	−	3.49140i	−1.52923	−	0.133791i
$682$	−2.91392	+	33.3062i	−0.111580	+	1.27536i
$683$	−19.7385	−	7.18421i	−0.755271	−	0.274896i	−0.0644492	−	0.997921i	$-0.520529\pi$
$683$	−19.7385	−	7.18421i	−0.755271	−	0.274896i	−0.690822	+	0.723025i	$0.742751\pi$
$684$	11.3557	+	16.2177i	0.434197	+	0.620097i
$685$	−4.63851	−	26.0019i	−0.177228	−	0.993483i
$686$	−7.75289	−	16.6261i	−0.296007	−	0.634788i
$687$	−9.41754	−	0.823928i	−0.359302	−	0.0314348i
$688$	−5.22348	+	4.38302i	−0.199143	+	0.167101i
$689$	−41.8244	+	11.2068i	−1.59338	+	0.426946i
$690$	−33.0732	+	27.8647i	−1.25908	+	1.06079i
$691$	32.1504	−	5.66898i	1.22306	−	0.215658i	0.475416	−	0.879761i	$-0.342297\pi$
$691$	32.1504	−	5.66898i	1.22306	−	0.215658i	0.747641	+	0.664103i	$0.231186\pi$
$692$	16.4880	+	4.41796i	0.626781	+	0.167946i
$693$	−4.86944	−	18.1730i	−0.184975	−	0.690335i
$694$	26.0106	+	9.46708i	0.987348	+	0.359365i
$695$	0.910558	+	10.1732i	0.0345394	+	0.385893i
$696$	0.150355	−	0.179186i	0.00569920	−	0.00679204i
$697$	1.68138			0.0636870
$698$	9.40756	−	11.2115i	0.356081	−	0.424361i
$699$	2.38148	+	6.54307i	0.0900760	+	0.247482i
$700$	2.04790	−	7.76707i	0.0774035	−	0.293568i
$701$	16.5247	+	11.5707i	0.624130	+	0.437021i	0.842389	−	0.538870i	$-0.181149\pi$
$701$	16.5247	+	11.5707i	0.624130	+	0.437021i	−0.218259	+	0.975891i	$0.570038\pi$
$702$	−2.59882	−	2.59882i	−0.0980862	−	0.0980862i
$703$	−34.7769	+	10.8648i	−1.31163	+	0.409775i
$704$		−	3.54316i		−	0.133538i
$705$	17.5562	+	4.66654i	0.661205	+	0.175752i
$706$	28.2362	+	4.97880i	1.06268	+	0.187380i
$707$	−2.46157	−	1.14785i	−0.0925768	−	0.0431693i
$708$	2.57350	+	2.15942i	0.0967181	+	0.0811561i
$709$	11.1604	+	11.1604i	0.419137	+	0.419137i	0.884906	−	0.465769i	$-0.154222\pi$
$709$	11.1604	+	11.1604i	0.419137	+	0.419137i	−0.465769	+	0.884906i	$0.654222\pi$
$710$	8.18254	+	17.4562i	0.307085	+	0.655121i
$711$	47.7115	+	12.7843i	1.78932	+	0.479447i
$712$	−13.2077	+	6.15884i	−0.494979	+	0.230812i
$713$	−70.2021	+	18.8106i	−2.62909	+	0.704462i
$714$	−1.54648	−	2.67858i	−0.0578755	−	0.100243i
$715$	−36.7080	−	9.75720i	−1.37280	−	0.364899i
$716$	−1.91025	+	4.09654i	−0.0713894	+	0.153095i
$717$	6.75407	−	11.6984i	0.252235	−	0.436885i
$718$	−2.96632	−	3.53512i	−0.110702	−	0.131930i
$719$	−5.60968	−	6.68536i	−0.209206	−	0.249322i	0.651230	−	0.758880i	$-0.274253\pi$
$719$	−5.60968	−	6.68536i	−0.209206	−	0.249322i	−0.860436	+	0.509558i	$0.829809\pi$
$720$	5.21567	−	5.23659i	0.194377	−	0.195156i
$721$	13.7728	−	9.64379i	0.512924	−	0.359153i
$722$	16.6213	+	2.93078i	0.618581	+	0.109072i
$723$	7.99747	−	21.9729i	0.297429	−	0.817180i
$724$	4.96913	−	4.16959i	0.184676	−	0.154962i
$725$	0.380461	−	0.268677i	0.0141300	−	0.00997842i
$726$	−1.00992	−	3.76908i	−0.0374817	−	0.139884i
$727$	28.1071	−	10.2302i	1.04244	−	0.379415i	0.236632	−	0.971599i	$-0.423956\pi$
$727$	28.1071	−	10.2302i	1.04244	−	0.379415i	0.805803	+	0.592184i	$0.201734\pi$
$728$	6.30893	+	4.41756i	0.233825	+	0.163726i
$729$	−27.8751	+	16.0937i	−1.03241	+	0.596062i
$730$	2.54884	−	14.6262i	0.0943367	−	0.541342i
$731$	−1.78812	+	4.91283i	−0.0661361	+	0.181707i
$732$	0.880788	+	1.52557i	0.0325549	+	0.0563867i
$733$	42.8064	−	3.74508i	1.58109	−	0.138328i	0.737513	−	0.675333i	$-0.236000\pi$
$733$	42.8064	−	3.74508i	1.58109	−	0.138328i	0.843579	+	0.537005i	$0.180445\pi$
$734$	−21.7475	+	21.7475i	−0.802716	+	0.802716i
$735$	8.43982	−	23.3334i	0.311307	−	0.860664i
$736$	7.23771	−	2.63431i	0.266785	−	0.0971020i
$737$	19.3232	+	27.5964i	0.711779	+	1.01653i
$738$	−1.25866	−	7.13822i	−0.0463320	−	0.262762i
$739$	6.93311			0.255038			0.127519	−	0.991836i	$-0.459299\pi$
$739$	6.93311			0.255038			0.127519	+	0.991836i	$0.459299\pi$
$740$	6.27293	+	12.0686i	0.230598	+	0.443649i
$741$	−72.1066			−2.64890
$742$	2.51958	+	14.2893i	0.0924968	+	0.524575i
$743$	0.235002	+	0.335617i	0.00862138	+	0.0123126i	0.823440	−	0.567404i	$-0.192052\pi$
$743$	0.235002	+	0.335617i	0.00862138	+	0.0123126i	−0.814818	+	0.579717i	$0.803163\pi$
$744$	22.2654	−	8.10393i	0.816288	−	0.297105i
$745$	−22.3587	+	10.4805i	−0.819158	+	0.383977i
$746$	11.1522	−	11.1522i	0.408309	−	0.408309i
$747$	52.2046	−	4.56731i	1.91007	−	0.167109i
$748$	−1.35831	−	2.35267i	−0.0496648	−	0.0860220i
$749$	−2.32314	+	6.38277i	−0.0848857	+	0.233222i
$750$	24.2283	−	14.1828i	0.884693	−	0.517883i
$751$	−33.2186	+	19.1788i	−1.21216	+	0.699843i	−0.963230	−	0.268678i	$-0.913413\pi$
$751$	−33.2186	+	19.1788i	−1.21216	+	0.699843i	−0.248933	+	0.968521i	$0.580080\pi$
$752$	−2.65022	−	1.85570i	−0.0966434	−	0.0676705i
$753$	−27.7764	+	10.1098i	−1.01223	+	0.368421i
$754$	0.115586	+	0.431371i	0.00420938	+	0.0157096i
$755$	13.1692	+	48.7576i	0.479276	+	1.77447i
$756$	−0.943447	+	0.791646i	−0.0343128	+	0.0287919i
$757$	−7.82610	+	21.5020i	−0.284444	+	0.781505i	0.712374	+	0.701800i	$0.247620\pi$
$757$	−7.82610	+	21.5020i	−0.284444	+	0.781505i	−0.996819	+	0.0797046i	$0.974602\pi$
$758$	28.3253	+	4.99452i	1.02882	+	0.181409i
$759$	56.1336	−	39.3052i	2.03752	−	1.42669i
$760$	−0.0267985	−	13.3936i	−0.000972082	−	0.485836i
$761$	6.13090	+	7.30652i	0.222245	+	0.264861i	0.865633	−	0.500679i	$-0.166916\pi$
$761$	6.13090	+	7.30652i	0.222245	+	0.264861i	−0.643388	+	0.765540i	$0.722472\pi$
$762$	13.4706	+	16.0537i	0.487990	+	0.581564i
$763$	−6.46585	+	11.1992i	−0.234079	+	0.405437i
$764$	−5.20605	+	11.1644i	−0.188348	+	0.403914i
$765$	1.45571	−	5.47660i	0.0526314	−	0.198007i
$766$	−9.09502	−	15.7530i	−0.328616	−	0.569180i
$767$	−6.19542	+	1.66006i	−0.223704	+	0.0599412i
$768$	−2.27577	+	1.06121i	−0.0821198	+	0.0382931i
$769$	−50.1905	−	13.4485i	−1.80991	−	0.484965i	−0.814462	−	0.580217i	$-0.802968\pi$
$769$	−50.1905	−	13.4485i	−1.80991	−	0.484965i	−0.995453	+	0.0952522i	$0.969634\pi$
$770$	−4.32926	+	11.9690i	−0.156016	+	0.431333i
$771$	48.3181	+	48.3181i	1.74013	+	1.74013i
$772$	−3.77808	−	3.17018i	−0.135976	−	0.114097i
$773$	−16.9424	−	7.90039i	−0.609377	−	0.284157i	0.0933314	−	0.995635i	$-0.470248\pi$
$773$	−16.9424	−	7.90039i	−0.609377	−	0.284157i	−0.702708	+	0.711478i	$0.748026\pi$
$774$	22.1957	+	3.91370i	0.797808	+	0.140675i
$775$	46.9840	−	4.30009i	1.68771	−	0.154464i
$776$			2.32834i			0.0835825i
$777$	−9.33067	−	22.6945i	−0.334736	−	0.814162i
$778$	20.5895	+	20.5895i	0.738170	+	0.738170i
$779$	−10.7598	−	7.53410i	−0.385510	−	0.269937i
$780$	4.72734	+	26.4999i	0.169266	+	0.948850i
$781$	−10.4481	−	28.7060i	−0.373863	−	1.02718i
$782$	3.79597	−	4.52386i	0.135743	−	0.161773i
$783$	−0.0714134			−0.00255211
$784$	−2.84057	+	3.38526i	−0.101449	+	0.120902i
$785$	3.95137	+	3.30215i	0.141031	+	0.117859i
$786$	20.2957	+	7.38701i	0.723922	+	0.263486i
$787$	−1.00442	−	3.74853i	−0.0358036	−	0.133621i	0.945711	−	0.325010i	$-0.105368\pi$
$787$	−1.00442	−	3.74853i	−0.0358036	−	0.133621i	−0.981514	+	0.191389i	$0.938701\pi$
$788$	10.5028	+	2.81423i	0.374148	+	0.100253i
$789$	72.0777	−	12.7092i	2.56603	−	0.452461i
$790$	−21.5305	−	25.5550i	−0.766021	−	0.909208i
$791$	0.251365	−	0.0673529i	0.00893750	−	0.00239479i
$792$	−8.97130	+	7.52781i	−0.318781	+	0.267489i
$793$	−3.35045	−	0.293126i	−0.118978	−	0.0104092i
$794$	16.0749	+	34.4728i	0.570478	+	1.22339i
$795$	−29.0043	+	41.5993i	−1.02868	+	1.47538i
$796$	−10.5180	−	15.0212i	−0.372799	−	0.532413i
$797$	2.73204	+	0.994380i	0.0967737	+	0.0352228i	0.389953	−	0.920835i	$-0.372491\pi$
$797$	2.73204	+	0.994380i	0.0967737	+	0.0352228i	−0.293180	+	0.956057i	$0.594713\pi$
$798$	−2.10592	+	24.0708i	−0.0745489	+	0.852098i
$799$	−2.47116	−	0.216198i	−0.0874233	−	0.00764855i
$800$	−4.92052	+	0.887938i	−0.173967	+	0.0313934i
$801$	43.6554	+	20.3568i	1.54249	+	0.719273i
$802$	3.80650	−	5.43624i	0.134412	−	0.191960i
$803$	−6.08878	+	22.7237i	−0.214869	+	0.801900i
$804$	11.9377	−	20.6767i	0.421010	−	0.729210i
$805$	−27.6682	+	0.0553598i	−0.975176	+	0.00195118i
$806$	−11.7084	+	43.6963i	−0.412410	+	1.53914i
$807$	−6.45345	−	73.7632i	−0.227172	−	2.59659i
$808$			1.69065i			0.0594770i
$809$	−18.6134	+	1.62846i	−0.654414	+	0.0572538i	−0.409527	−	0.912298i	$-0.634306\pi$
$809$	−18.6134	+	1.62846i	−0.654414	+	0.0572538i	−0.244887	+	0.969552i	$0.578751\pi$
$810$	17.8033	+	1.52169i	0.625543	+	0.0534669i
$811$	4.29645	−	24.3664i	0.150869	−	0.855619i	−0.811597	−	0.584217i	$-0.801402\pi$
$811$	4.29645	−	24.3664i	0.150869	−	0.855619i	0.962466	−	0.271402i	$-0.0874872\pi$
$812$	0.147377	−	0.0259866i	0.00517193	−	0.000911951i
$813$	49.7379	−	49.7379i	1.74438	−	1.74438i
$814$	−8.19537	−	19.9332i	−0.287248	−	0.698658i
$815$	−3.22539	+	6.95315i	−0.112980	+	0.243558i
$816$	−1.10429	+	1.57709i	−0.0386579	+	0.0552093i
$817$	33.4567	−	23.4266i	1.17050	−	0.819594i
$818$	−2.36375	+	5.06909i	−0.0826467	+	0.177237i
$819$	−2.21870	−	25.3598i	−0.0775276	−	0.886145i
$820$	−2.06344	+	4.44828i	−0.0720585	+	0.155341i
$821$	−11.6291	−	9.75797i	−0.405858	−	0.340555i	0.416895	−	0.908955i	$-0.363118\pi$
$821$	−11.6291	−	9.75797i	−0.405858	−	0.340555i	−0.822753	+	0.568399i	$0.807563\pi$
$822$	25.6866	−	14.8302i	0.895924	−	0.517262i
$823$	−5.13453	−	11.0110i	−0.178978	−	0.383820i	0.796267	−	0.604945i	$-0.206805\pi$
$823$	−5.13453	−	11.0110i	−0.178978	−	0.383820i	−0.975246	+	0.221125i	$0.929027\pi$
$824$	−9.06370	−	5.23293i	−0.315749	−	0.182298i
$825$	−40.2415	+	18.9613i	−1.40103	+	0.660149i
$826$	0.373224	+	2.11666i	0.0129861	+	0.0736479i
$827$	−2.06194	−	5.66513i	−0.0717007	−	0.196996i	0.898666	−	0.438634i	$-0.144538\pi$
$827$	−2.06194	−	5.66513i	−0.0717007	−	0.196996i	−0.970366	+	0.241638i	$0.922315\pi$
$828$	−22.0474	−	12.7291i	−0.766199	−	0.442365i
$829$	1.64207	−	18.7689i	0.0570313	−	0.651871i	−0.912850	−	0.408294i	$-0.866124\pi$
$829$	1.64207	−	18.7689i	0.0570313	−	0.651871i	0.969882	−	0.243577i	$-0.0783207\pi$
$830$	−30.7376	−	17.6644i	−1.06692	−	0.613142i
$831$	42.7290	−	19.9248i	1.48225	−	0.691185i
$832$	0.832492	−	4.72129i	0.0288615	−	0.163681i
$833$	−0.588367	+	3.33679i	−0.0203857	+	0.115613i
$834$	−10.3953	+	4.84739i	−0.359959	+	0.167851i
$835$	3.38009	+	12.5144i	0.116973	+	0.433080i
$836$	−1.84969	+	21.1420i	−0.0639728	+	0.731213i
$837$	−6.26475	−	3.61695i	−0.216541	−	0.125020i
$838$	−10.1028	−	27.7572i	−0.348995	−	0.958856i
$839$	5.04382	+	28.6049i	0.174132	+	0.987552i	0.939141	+	0.343532i	$0.111623\pi$
$839$	5.04382	+	28.6049i	0.174132	+	0.987552i	−0.765009	+	0.644020i	$0.777265\pi$
$840$	8.98435	−	0.804146i	0.309990	−	0.0277457i
$841$	−25.1072	−	14.4957i	−0.865766	−	0.499850i
$842$	−14.4581	−	31.0056i	−0.498260	−	1.06852i
$843$	−2.89825	+	1.67330i	−0.0998209	+	0.0576316i
$844$	−15.2263	−	12.7764i	−0.524110	−	0.439780i
$845$	−20.2514	−	9.39410i	−0.696669	−	0.323167i
$846$	0.932017	+	10.6530i	0.0320434	+	0.366258i
$847$	1.05504	−	2.26254i	0.0362515	−	0.0777417i
$848$	7.39846	−	5.18046i	0.254064	−	0.177898i
$849$	−29.8826	+	42.6767i	−1.02557	+	1.46466i
$850$	−2.92684	+	2.47594i	−0.100390	+	0.0849240i
$851$	34.6249	−	31.5611i	1.18693	−	1.08190i
$852$	−15.3086	+	15.3086i	−0.524463	+	0.524463i
$853$	−45.3364	+	7.99403i	−1.55229	+	0.273710i	−0.883029	−	0.469318i	$-0.844500\pi$
$853$	−45.3364	+	7.99403i	−1.55229	+	0.273710i	−0.669260	+	0.743028i	$0.733389\pi$
$854$	−0.195704	+	1.10989i	−0.00669687	+	0.0379798i
$855$	−33.8557	+	28.5239i	−1.15784	+	0.975498i
$856$	4.21198	−	0.368501i	0.143963	−	0.0125951i
$857$			5.58369i			0.190735i	0.995442	+	0.0953677i	$0.0304027\pi$
$857$			5.58369i			0.190735i	−0.995442	+	0.0953677i	$0.969597\pi$
$858$	−3.71748	−	42.4910i	−0.126913	−	1.45062i
$859$	−6.47211	+	24.1542i	−0.220825	+	0.824132i	0.763209	+	0.646152i	$0.223623\pi$
$859$	−6.47211	+	24.1542i	−0.220825	+	0.824132i	−0.984034	+	0.177980i	$0.943044\pi$
$860$	−10.8030	−	10.7598i	−0.368378	−	0.366907i
$861$	4.42315	−	7.66113i	0.150741	−	0.261090i
$862$	2.82988	−	10.5613i	0.0963861	−	0.359718i
$863$	9.37865	−	13.3941i	0.319253	−	0.455940i	−0.627164	−	0.778887i	$-0.715785\pi$
$863$	9.37865	−	13.3941i	0.319253	−	0.455940i	0.946417	+	0.322947i	$0.104673\pi$
$864$	0.694796	+	0.323989i	0.0236374	+	0.0110223i
$865$	−6.55275	+	37.6023i	−0.222800	+	1.27852i
$866$	−38.0301	−	3.32720i	−1.29232	−	0.113063i
$867$	3.59182	−	41.0546i	0.121984	−	1.39429i
$868$	14.2449	+	5.18471i	0.483502	+	0.175981i
$869$	30.3704	+	43.3734i	1.03024	+	1.47134i
$870$	0.429050	+	0.299146i	0.0145461	+	0.0101420i
$871$	19.2644	+	41.3126i	0.652749	+	1.39982i
$872$	8.01896	+	0.701568i	0.271556	+	0.0237581i
$873$	5.89537	−	4.94680i	0.199528	−	0.167424i
$874$	−44.5627	+	11.9405i	−1.50736	+	0.403895i
$875$	17.7068	+	3.01271i	0.598599	+	0.101848i
$876$	16.4191	−	2.89512i	0.554749	−	0.0978172i
$877$	−0.0793615	−	0.0212649i	−0.00267985	−	0.000718063i	0.257479	−	0.966284i	$-0.417108\pi$
$877$	−0.0793615	−	0.0212649i	−0.00267985	−	0.000718063i	−0.260159	+	0.965566i	$0.583775\pi$
$878$	−2.19301	−	8.18443i	−0.0740105	−	0.276211i
$879$	60.9128	+	22.1705i	2.05454	+	0.747791i
$880$	7.89119	−	0.706303i	0.266012	−	0.0238095i
$881$	20.3579	−	24.2616i	0.685876	−	0.817396i	−0.304974	−	0.952361i	$-0.598648\pi$
$881$	20.3579	−	24.2616i	0.685876	−	0.817396i	0.990850	+	0.134965i	$0.0430922\pi$
$882$	14.6066			0.491830
$883$	−17.3121	+	20.6318i	−0.582600	+	0.694316i	−0.974166	−	0.225835i	$-0.927489\pi$
$883$	−17.3121	+	20.6318i	−0.582600	+	0.694316i	0.391566	+	0.920150i	$0.371934\pi$
$884$	−1.25719	−	3.45410i	−0.0422839	−	0.116174i
$885$	−4.29638	+	6.16208i	−0.144421	+	0.207136i
$886$	5.65268	+	3.95805i	0.189906	+	0.132973i
$887$	−4.59345	−	4.59345i	−0.154233	−	0.154233i	0.625773	−	0.780006i	$-0.284784\pi$
$887$	−4.59345	−	4.59345i	−0.154233	−	0.154233i	−0.780006	+	0.625773i	$0.784784\pi$
$888$	−10.3485	+	11.2341i	−0.347273	+	0.376991i
$889$			13.4076i			0.449675i
$890$	−16.3496	−	28.1880i	−0.548040	−	0.944863i
$891$	−27.8828	−	4.91649i	−0.934110	−	0.164709i
$892$	9.85426	+	4.59512i	0.329945	+	0.153856i
$893$	14.8451	+	12.4565i	0.496772	+	0.416841i
$894$	−19.6078	−	19.6078i	−0.655784	−	0.655784i
$895$	−9.50447	−	3.43783i	−0.317700	−	0.114914i
$896$	−1.55176	−	0.415794i	−0.0518408	−	0.0138907i
$897$	84.0337	−	39.1856i	2.80580	−	1.30837i
$898$	10.4279	−	2.79414i	0.347982	−	0.0932416i
$899$	0.439500	+	0.761237i	0.0146582	+	0.0253887i
$900$	12.7024	+	10.5723i	0.423415	+	0.352410i
$901$	2.92661	−	6.27613i	0.0974994	−	0.209088i
$902$	3.88497	−	6.72897i	0.129355	−	0.224050i
$903$	17.6811	+	21.0715i	0.588389	+	0.701214i
$904$	−0.104123	−	0.124089i	−0.00346308	−	0.00412713i
$905$	10.2769	+	10.2359i	0.341617	+	0.340253i
$906$	−46.4585	+	32.5306i	−1.54348	+	1.08076i
$907$	36.2916	+	6.39919i	1.20504	+	0.212482i	0.739877	−	0.672742i	$-0.234884\pi$
$907$	36.2916	+	6.39919i	1.20504	+	0.212482i	0.465166	+	0.885224i	$0.345995\pi$
$908$	−5.45635	+	14.9912i	−0.181075	+	0.497500i
$909$	4.28075	−	3.59197i	0.141983	−	0.119138i
$910$	−8.58100	+	14.9316i	−0.284457	+	0.494979i
$911$	10.8767	+	40.5925i	0.360362	+	1.34489i	0.873600	+	0.486644i	$0.161779\pi$
$911$	10.8767	+	40.5925i	0.360362	+	1.34489i	−0.513238	+	0.858246i	$0.671554\pi$
$912$	14.1335	−	5.14419i	0.468008	−	0.170341i
$913$	46.0159	+	32.2207i	1.52291	+	1.06635i
$914$	9.69949	−	5.60000i	0.320831	−	0.185232i
$915$	−3.22212	+	2.26577i	−0.106520	+	0.0749041i
$916$	−1.28763	+	3.53774i	−0.0425446	+	0.116890i
$917$	6.90901	+	11.9668i	0.228156	+	0.395177i
$918$	0.585552	−	0.0512292i	0.0193261	−	0.00169081i
$919$	14.6662	−	14.6662i	0.483794	−	0.483794i	−0.422547	−	0.906341i	$-0.638864\pi$
$919$	14.6662	−	14.6662i	0.483794	−	0.483794i	0.906341	+	0.422547i	$0.138864\pi$
$920$	7.30983	+	15.5944i	0.240998	+	0.514133i
$921$	3.44580	−	1.25417i	0.113543	−	0.0413262i
$922$	14.0852	+	20.1157i	0.463870	+	0.662475i
$923$	−7.17755	−	40.7059i	−0.236252	−	1.33985i
$924$	−14.2930			−0.470207
$925$	−25.6282	+	16.3766i	−0.842651	+	0.538460i
$926$	10.7112			0.351990
$927$	6.00698	+	34.0673i	0.197295	+	1.11892i
$928$	−0.0534305	−	0.0763067i	−0.00175394	−	0.00250489i
$929$	−12.1322	+	4.41576i	−0.398045	+	0.144876i	−0.533283	−	0.845937i	$-0.679042\pi$
$929$	−12.1322	+	4.41576i	−0.398045	+	0.144876i	0.135239	+	0.990813i	$0.456820\pi$
$930$	22.4872	+	47.9732i	0.737385	+	1.57310i
$931$	18.7170	−	18.7170i	0.613424	−	0.613424i
$932$	2.76241	−	0.241679i	0.0904856	−	0.00791646i
$933$	−15.5068	−	26.8585i	−0.507668	−	0.879307i
$934$	12.3863	−	34.0311i	0.405293	−	1.11353i
$935$	4.96901	−	3.49417i	0.162504	−	0.114272i
$936$	−13.7231	+	7.92302i	−0.448553	+	0.258972i
$937$	−14.5470	−	10.1859i	−0.475230	−	0.332760i	0.311300	−	0.950312i	$-0.399236\pi$
$937$	−14.5470	−	10.1859i	−0.475230	−	0.332760i	−0.786530	+	0.617552i	$0.788125\pi$
$938$	14.3537	−	5.22433i	0.468666	−	0.170580i
$939$	−0.304926	−	1.13800i	−0.00995087	−	0.0371372i
$940$	3.60465	−	6.27239i	0.117571	−	0.204583i
$941$	−33.1850	+	27.8455i	−1.08180	+	0.907738i	−0.996069	−	0.0885798i	$-0.971767\pi$
$941$	−33.1850	+	27.8455i	−1.08180	+	0.907738i	−0.0857315	+	0.996318i	$0.527323\pi$
$942$	−1.97782	+	5.43401i	−0.0644408	+	0.177050i
$943$	16.6339	+	2.93301i	0.541674	+	0.0955118i
$944$	1.09593	−	0.767377i	0.0356694	−	0.0249760i
$945$	−1.95119	−	1.94340i	−0.0634724	−	0.0632189i
$946$	15.5297	+	18.5076i	0.504915	+	0.601734i
$947$	13.6402	+	16.2558i	0.443248	+	0.528243i	0.940696	−	0.339251i	$-0.110174\pi$
$947$	13.6402	+	16.2558i	0.443248	+	0.528243i	−0.497447	+	0.867494i	$0.665729\pi$
$948$	18.7625	−	32.4976i	0.609379	−	1.05547i
$949$	−13.4525	+	28.8489i	−0.436686	+	0.936475i
$950$	29.8244	−	2.72960i	0.967630	−	0.0885598i
$951$	−3.05370	−	5.28916i	−0.0990230	−	0.171513i
$952$	−1.18978	+	0.318799i	−0.0385608	+	0.0103323i
$953$	−7.21388	+	3.36389i	−0.233680	+	0.108967i	−0.535932	−	0.844261i	$-0.680040\pi$
$953$	−7.21388	+	3.36389i	−0.233680	+	0.108967i	0.302251	+	0.953228i	$0.402262\pi$
$954$	−28.8358	−	7.72652i	−0.933592	−	0.250155i
$955$	−25.9028	−	9.36919i	−0.838195	−	0.303180i
$956$	−3.80389	−	3.80389i	−0.123027	−	0.123027i
$957$	−0.634885	−	0.532732i	−0.0205229	−	0.0172208i
$958$	−27.1988	−	12.6830i	−0.878753	−	0.409769i
$959$	18.6877	+	3.29515i	0.603458	+	0.106406i
$960$	−2.81715	−	4.85697i	−0.0909230	−	0.156758i
$961$			58.0394i			1.87224i
$962$	−6.23696	−	28.4868i	−0.201088	−	0.918450i
$963$	−9.88185	−	9.88185i	−0.318438	−	0.318438i
$964$	−7.62803	−	5.34121i	−0.245682	−	0.172029i
$965$	6.30739	−	9.04635i	0.203042	−	0.291212i
$966$	−10.6268	−	29.1968i	−0.341911	−	0.939392i
$967$	9.57450	−	11.4104i	0.307895	−	0.366935i	−0.589802	−	0.807548i	$-0.700794\pi$
$967$	9.57450	−	11.4104i	0.307895	−	0.366935i	0.897697	+	0.440613i	$0.145239\pi$
$968$	−1.55395			−0.0499460
$969$	7.41263	−	8.83403i	0.238128	−	0.283790i
$970$	−5.18559	+	0.464137i	−0.166499	+	0.0149026i
$971$	−28.3817	−	10.3301i	−0.910812	−	0.331508i	−0.156235	−	0.987720i	$-0.549936\pi$
$971$	−28.3817	−	10.3301i	−0.910812	−	0.331508i	−0.754577	+	0.656211i	$0.772158\pi$
$972$	5.78856	+	21.6032i	0.185668	+	0.692923i
$973$	−7.08814	−	1.89926i	−0.227235	−	0.0608875i
$974$	10.1914	−	1.79701i	0.326553	−	0.0575800i
$975$	−58.0774	+	15.8111i	−1.85996	+	0.506362i
$976$	0.677630	−	0.181570i	0.0216904	−	0.00581193i
$977$	24.0638	−	20.1919i	0.769868	−	0.645996i	−0.170807	−	0.985304i	$-0.554638\pi$
$977$	24.0638	−	20.1919i	0.769868	−	0.645996i	0.940675	+	0.339309i	$0.110193\pi$
$978$	−8.57461	−	0.750181i	−0.274186	−	0.0239881i
$979$	21.8217	+	46.7969i	0.697426	+	1.49563i
$980$	−8.10579	−	5.65160i	−0.258930	−	0.180534i
$981$	−15.2608	−	21.7946i	−0.487239	−	0.695849i
$982$	−11.1123	−	4.04454i	−0.354607	−	0.129066i
$983$	−0.731446	+	8.36046i	−0.0233295	+	0.266657i	0.975567	+	0.219700i	$0.0705079\pi$
$983$	−0.731446	+	8.36046i	−0.0233295	+	0.266657i	−0.998897	+	0.0469570i	$0.985048\pi$
$984$	−5.48561	−	0.479928i	−0.174875	−	0.0152996i
$985$	−4.17408	+	23.9526i	−0.132997	+	0.763192i
$986$	−0.0647311	−	0.0301846i	−0.00206146	−	0.000961274i
$987$	−7.48588	+	10.6909i	−0.238278	+	0.340296i
$988$	−7.43221	+	27.7374i	−0.236450	+	0.882444i
$989$	−26.2598	+	45.4833i	−0.835013	+	1.44628i
$990$	−18.5540	−	18.4799i	−0.589686	−	0.587331i
$991$	−6.54934	+	24.4425i	−0.208047	+	0.776441i	0.780453	+	0.625215i	$0.214989\pi$
$991$	−6.54934	+	24.4425i	−0.208047	+	0.776441i	−0.988499	+	0.151226i	$0.951678\pi$
$992$	−0.822408	−	9.40016i	−0.0261115	−	0.298455i
$993$		−	81.5918i		−	2.58924i
$994$	−13.7982	+	1.20719i	−0.437652	+	0.0382896i
$995$	31.3580	−	26.4196i	0.994116	−	0.837558i
$996$	6.91316	−	39.2065i	0.219052	−	1.24230i
$997$	35.4797	−	6.25603i	1.12365	−	0.198131i	0.419210	−	0.907889i	$-0.362307\pi$
$997$	35.4797	−	6.25603i	1.12365	−	0.198131i	0.704445	+	0.709759i	$0.251196\pi$
$998$	15.7736	−	15.7736i	0.499305	−	0.499305i
$999$	4.65820	+	0.215633i	0.147379	+	0.00682232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.ba.a.353.2	yes	108
5.2	odd	4		370.2.bd.a.57.2	yes	108
37.13	odd	36		370.2.bd.a.13.2	yes	108
185.87	even	36	inner	370.2.ba.a.87.2	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.ba.a.87.2	✓	108	185.87	even	36	inner
370.2.ba.a.353.2	yes	108	1.1	even	1	trivial
370.2.bd.a.13.2	yes	108	37.13	odd	36
370.2.bd.a.57.2	yes	108	5.2	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.44027 - 2.05692i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.949056 - 2.02467i) q^{5} +(1.77557 - 1.77557i) q^{6} +(1.60039 - 0.140016i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.13048 + 3.10597i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.44027 - 2.05692i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.949056 - 2.02467i) q^{5} +(1.77557 - 1.77557i) q^{6} +(1.60039 - 0.140016i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.13048 + 3.10597i) q^{9} +(1.82911 - 1.28622i) q^{10} +(-3.06846 + 1.77158i) q^{11} +(2.05692 + 1.44027i) q^{12} +(-4.50501 + 1.63969i) q^{13} +(0.415794 + 1.55176i) q^{14} +(-2.79769 + 4.86821i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.262235 - 0.720486i) q^{17} +(-3.25509 - 0.573960i) q^{18} +(-4.90656 + 3.43561i) q^{19} +(1.58430 + 1.57797i) q^{20} +(-2.59300 - 3.09021i) q^{21} +(-2.27750 - 2.71421i) q^{22} +(3.85110 - 6.67031i) q^{23} +(-1.06121 + 2.27577i) q^{24} +(-3.19859 + 3.84305i) q^{25} +(-2.39706 - 4.15184i) q^{26} +(0.740501 - 0.198417i) q^{27} +(-1.45599 + 0.678938i) q^{28} +(-0.0899791 - 0.0241098i) q^{29} +(-5.28006 - 1.90983i) q^{30} +(-6.67231 - 6.67231i) q^{31} +(0.766044 + 0.642788i) q^{32} +(8.06341 + 3.76003i) q^{33} +(0.755077 + 0.133140i) q^{34} +(-1.80235 - 3.10738i) q^{35} -3.30530i q^{36} +(5.79641 + 1.84434i) q^{37} +(-4.23543 - 4.23543i) q^{38} +(9.86114 + 6.90484i) q^{39} +(-1.27889 + 1.83424i) q^{40} +(0.750031 + 2.06069i) q^{41} +(2.59300 - 3.09021i) q^{42} -6.81877 q^{43} +(2.27750 - 2.71421i) q^{44} +(7.36145 - 0.658888i) q^{45} +(7.23771 + 2.63431i) q^{46} +(-0.837362 - 3.12508i) q^{47} +(-2.42547 - 0.649904i) q^{48} +(-4.35201 + 0.767377i) q^{49} +(-4.34010 - 2.48265i) q^{50} +(-1.85967 + 0.498297i) q^{51} +(3.67252 - 3.08161i) q^{52} +(8.99748 + 0.787177i) q^{53} +(0.323989 + 0.694796i) q^{54} +(6.49901 + 4.53130i) q^{55} +(-0.921452 - 1.31597i) q^{56} +(14.1335 + 5.14419i) q^{57} +(0.00811884 - 0.0927988i) q^{58} +(1.33279 + 0.116604i) q^{59} +(0.963942 - 5.53148i) q^{60} +(0.635806 + 0.296481i) q^{61} +(5.41231 - 7.72958i) q^{62} +(-1.37432 + 5.12904i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(7.59533 + 7.56500i) q^{65} +(-2.30271 + 8.59383i) q^{66} +(-0.828692 - 9.47199i) q^{67} +0.766725i q^{68} +(-19.2669 + 1.68564i) q^{69} +(2.74720 - 2.31456i) q^{70} +(-1.49715 + 8.49078i) q^{71} +(3.25509 - 0.573960i) q^{72} +(4.69493 - 4.69493i) q^{73} +(-0.809786 + 6.02862i) q^{74} +(12.5117 + 1.04420i) q^{75} +(3.43561 - 4.90656i) q^{76} +(-4.66269 + 3.26485i) q^{77} +(-5.08758 + 10.9103i) q^{78} +(-1.30246 - 14.8872i) q^{79} +(-2.02845 - 0.940946i) q^{80} +(6.12137 + 5.13644i) q^{81} +(-1.89914 + 1.09647i) q^{82} +(-6.70041 - 14.3691i) q^{83} +(3.49354 + 2.01699i) q^{84} +(-1.70762 + 0.152841i) q^{85} +(-1.18407 - 6.71518i) q^{86} +(0.0800023 + 0.219805i) q^{87} +(3.06846 + 1.77158i) q^{88} +(1.27013 - 14.5176i) q^{89} +(1.92718 + 7.13520i) q^{90} +(-6.98019 + 3.25491i) q^{91} +(-1.33747 + 7.58519i) q^{92} +(-4.11447 + 23.3343i) q^{93} +(2.93219 - 1.36730i) q^{94} +(11.6126 + 6.67358i) q^{95} +(0.218851 - 2.50148i) q^{96} +(-2.01640 - 1.16417i) q^{97} +(-1.51144 - 4.15264i) q^{98} +(-2.03363 - 11.5333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) \) 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8	\( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Introduction

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