LMFDB - Embedded newform 370.2.ba.a.87.2

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			87.2
Character	$\chi$	$=$	370.87
Dual form			370.2.ba.a.353.2

$q$-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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{4}\right)$

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	0.148529	+	0.988908i	$0.452546\pi$
$3$	−1.44027	+	2.05692i	−0.831541	+	1.18756i	−0.980069	+	0.198655i	$0.936343\pi$
$4$	−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	0.385487	−	0.922713i	$-0.374033\pi$
$7$	1.60039	+	0.140016i	0.604891	+	0.0529211i	0.219403	+	0.975634i	$0.429589\pi$
$8$	−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	−0.0398936	−	0.999204i	$-0.512702\pi$
$11$	−3.06846	−	1.77158i	−0.925176	−	0.534151i	−0.885283	+	0.465053i	$0.846035\pi$
$12$	2.05692	−	1.44027i	0.593782	−	0.415770i
$13$	−4.50501	−	1.63969i	−1.24946	−	0.454768i	−0.369244	−	0.929333i	$-0.620383\pi$
$13$	−4.50501	−	1.63969i	−1.24946	−	0.454768i	−0.880221	+	0.474565i	$0.842605\pi$
$14$	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	0.967423	−	0.253167i	$-0.0814722\pi$
$17$	0.262235	+	0.720486i	0.0636014	+	0.174743i	−0.903821	+	0.427910i	$0.859250\pi$
$18$	−3.25509	+	0.573960i	−0.767231	+	0.135284i
$19$	−4.90656	−	3.43561i	−1.12564	−	0.788183i	−0.146069	−	0.989274i	$-0.546662\pi$
$19$	−4.90656	−	3.43561i	−1.12564	−	0.788183i	−0.979572	+	0.201092i	$0.935551\pi$
$20$	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	0.917626	+	0.397445i	$0.130103\pi$
$23$	3.85110	+	6.67031i	0.803011	+	1.39086i	−0.114615	+	0.993410i	$0.536563\pi$
$24$	−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	−0.267164	−	0.963651i	$-0.586086\pi$
$29$	−0.0899791	+	0.0241098i	−0.0167087	+	0.00447708i	0.250455	+	0.968128i	$0.419420\pi$
$30$	−5.28006	+	1.90983i	−0.964003	+	0.348686i
$31$	−6.67231	+	6.67231i	−1.19838	+	1.19838i	−0.223731	+	0.974651i	$0.571824\pi$
$31$	−6.67231	+	6.67231i	−1.19838	+	1.19838i	−0.974651	+	0.223731i	$0.928176\pi$
$32$	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	−0.867245	−	0.497881i	$-0.834111\pi$
$41$	0.750031	−	2.06069i	0.117135	−	0.321826i	0.984380	+	0.176055i	$0.0563337\pi$
$42$	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	−0.999722	−	0.0235911i	$-0.992490\pi$
$47$	−0.837362	+	3.12508i	−0.122142	+	0.455839i	0.877580	+	0.479430i	$0.159157\pi$
$48$	−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	0.549588	−	0.835436i	$-0.314785\pi$
$53$	8.99748	−	0.787177i	1.23590	−	0.108127i	0.686311	+	0.727309i	$0.259229\pi$
$54$	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	−6.73760e−5	−	1.00000i	$-0.500021\pi$
$59$	1.33279	−	0.116604i	0.173514	−	0.0151805i	0.173582	+	0.984819i	$0.444466\pi$
$60$	0.963942	+	5.53148i	0.124444	+	0.714112i
$61$	0.635806	−	0.296481i	0.0814066	−	0.0379605i	−0.381489	−	0.924374i	$-0.624588\pi$
$61$	0.635806	−	0.296481i	0.0814066	−	0.0379605i	0.462895	+	0.886413i	$0.346811\pi$
$62$	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	0.760325	+	0.649543i	$0.225040\pi$
$67$	−0.828692	+	9.47199i	−0.101241	+	1.15719i	−0.861566	+	0.507645i	$0.830516\pi$
$68$		−	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	−0.935005	−	0.354634i	$-0.884606\pi$
$71$	−1.49715	−	8.49078i	−0.177680	−	1.00767i	0.757326	−	0.653037i	$-0.226505\pi$
$72$	3.25509	+	0.573960i	0.383616	+	0.0676418i
$73$	4.69493	+	4.69493i	0.549500	+	0.549500i	0.926296	−	0.376796i	$-0.122974\pi$
$73$	4.69493	+	4.69493i	0.549500	+	0.549500i	−0.376796	+	0.926296i	$0.622974\pi$
$74$	−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	0.466220	+	0.884669i	$0.345616\pi$
$79$	−1.30246	+	14.8872i	−0.146538	+	1.67494i	−0.612758	+	0.790270i	$0.709940\pi$
$80$	−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	0.0789149	+	0.996881i	$0.474854\pi$
$83$	−6.70041	+	14.3691i	−0.735466	+	1.57721i	−0.814381	+	0.580331i	$0.802923\pi$
$84$	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	0.700071	+	0.714073i	$0.253152\pi$
$89$	1.27013	+	14.5176i	0.134633	+	1.53886i	−0.565438	+	0.824791i	$0.691293\pi$
$90$	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	−0.598862	−	0.800852i	$-0.704380\pi$
$97$	−2.01640	+	1.16417i	−0.204734	+	0.118203i	0.394127	+	0.919056i	$0.371047\pi$
$98$	−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	−0.571072	−	0.820900i	$-0.693472\pi$
$101$	−1.46415	+	0.845327i	−0.145688	+	0.0841132i	0.425384	+	0.905013i	$0.360139\pi$
$102$	−0.813656	+	1.74489i	−0.0805639	+	0.172770i
$103$	9.06370	+	5.23293i	0.893073	+	0.515616i	0.874946	−	0.484220i	$-0.160897\pi$
$103$	9.06370	+	5.23293i	0.893073	+	0.515616i	0.0181263	+	0.999836i	$0.494230\pi$
$104$	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	0.800808	−	0.598922i	$-0.204404\pi$
$107$	−1.78686	−	3.83193i	−0.172742	−	0.370447i	−0.973550	+	0.228475i	$0.926626\pi$
$108$	−0.627981	−	0.439717i	−0.0604275	−	0.0423118i
$109$	−4.61706	−	6.59384i	−0.442234	−	0.631575i	0.534719	−	0.845030i	$-0.320417\pi$
$109$	−4.61706	−	6.59384i	−0.442234	−	0.631575i	−0.976953	+	0.213455i	$0.931528\pi$
$110$	−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	0.181147	−	0.983456i	$-0.442019\pi$
$113$	0.159526	+	0.0281287i	0.0150069	+	0.00264612i	−0.166140	+	0.986102i	$0.553130\pi$
$114$	−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	−0.957656	−	0.287915i	$-0.907038\pi$
$127$	−0.727384	−	8.31404i	−0.0645449	−	0.737752i	0.893111	−	0.449837i	$-0.148518\pi$
$128$	−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	−0.681096	−	0.732194i	$-0.738496\pi$
$131$	3.63507	−	7.79543i	0.317597	−	0.681090i	0.998693	+	0.0511044i	$0.0162741\pi$
$132$	−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	0.263936	−	0.964540i	$-0.414979\pi$
$137$	11.4095	−	3.05717i	0.974781	−	0.261192i	0.710845	+	0.703349i	$0.248313\pi$
$138$	−5.00570	+	18.6815i	−0.426113	+	1.59028i
$139$	−4.29233	+	1.56228i	−0.364070	+	0.132511i	−0.517577	−	0.855637i	$-0.673166\pi$
$139$	−4.29233	+	1.56228i	−0.364070	+	0.132511i	0.153506	+	0.988148i	$0.450944\pi$
$140$	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	$0.149412\pi$
$149$			11.0431i			0.904687i	−0.891844	+	0.452344i	$0.850588\pi$
$150$	1.14430	−	12.5029i	0.0934315	−	1.02086i
$151$	−22.2433	+	3.92209i	−1.81013	+	0.319175i	−0.973517	−	0.228614i	$-0.926581\pi$
$151$	−22.2433	+	3.92209i	−1.81013	+	0.319175i	−0.836616	+	0.547789i	$0.815470\pi$
$152$	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	0.337543	−	0.941310i	$-0.390404\pi$
$157$	−2.08717	−	0.973262i	−0.166574	−	0.0776748i	−0.504117	+	0.863635i	$0.668182\pi$
$158$	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	−0.845401	−	0.534133i	$-0.820638\pi$
$163$	−2.20336	+	2.62586i	−0.172580	+	0.205673i	0.672820	+	0.739806i	$0.265083\pi$
$164$	−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	−0.390115	−	0.920766i	$-0.627565\pi$
$167$	−5.70910	+	1.00667i	−0.441784	+	0.0778984i	−0.0516681	+	0.998664i	$0.516454\pi$
$168$	−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	−0.967964	−	0.251088i	$-0.919212\pi$
$173$	−13.9827	+	9.79077i	−1.06308	+	0.744378i	−0.0951178	+	0.995466i	$0.530323\pi$
$174$	−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	0.816391	−	0.577500i	$-0.195971\pi$
$179$	3.19615	+	3.19615i	0.238891	+	0.238891i	−0.577500	+	0.816391i	$0.695971\pi$
$180$	−6.69215	−	3.13692i	−0.498803	−	0.233812i
$181$	−6.09554	−	2.21860i	−0.453078	−	0.164907i	0.105394	−	0.994431i	$-0.466390\pi$
$181$	−6.09554	−	2.21860i	−0.453078	−	0.164907i	−0.558471	+	0.829524i	$0.688612\pi$
$182$	−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	0.948136	−	0.317863i	$-0.102965\pi$
$191$	8.71055	+	8.71055i	0.630273	+	0.630273i	−0.317863	+	0.948136i	$0.602965\pi$
$192$	2.50148	+	0.218851i	0.180529	+	0.0157942i
$193$	2.46596	−	4.27118i	0.177504	−	0.307446i	−0.763521	−	0.645783i	$-0.776531\pi$
$193$	2.46596	−	4.27118i	0.177504	−	0.307446i	0.941025	+	0.338337i	$0.109864\pi$
$194$	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	−0.846096	−	0.533031i	$-0.821053\pi$
$197$	−8.90692	+	6.23669i	−0.634592	+	0.444346i	0.211504	+	0.977377i	$0.432164\pi$
$198$	11.0049	+	4.00547i	0.782086	+	0.284656i
$199$	4.74610	−	17.7127i	0.336442	−	1.25562i	−0.565856	−	0.824504i	$-0.691454\pi$
$199$	4.74610	−	17.7127i	0.336442	−	1.25562i	0.902298	−	0.431114i	$-0.141879\pi$
$200$	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	−0.289518	−	0.957173i	$-0.593495\pi$
$211$	9.93824	−	17.2135i	0.684177	−	1.18503i	0.973695	−	0.227857i	$-0.0731717\pi$
$212$	−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	−0.916009	−	0.401158i	$-0.868608\pi$
$223$	−7.68835	+	7.68835i	−0.514850	+	0.514850i	0.401158	+	0.916009i	$0.368608\pi$
$224$	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	0.990187	−	0.139746i	$-0.0446285\pi$
$227$	10.2546	+	12.2209i	0.680621	+	0.811132i	−0.309567	+	0.950878i	$0.600184\pi$
$228$	−15.0406			−0.996088
$229$	2.41996	+	2.88399i	0.159915	+	0.190580i	0.840052	−	0.542505i	$-0.182524\pi$
$229$	2.41996	+	2.88399i	0.159915	+	0.190580i	−0.680137	+	0.733085i	$0.738080\pi$
$230$	−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	−0.345485	−	0.938424i	$-0.612286\pi$
$233$	−2.67847	+	0.717694i	−0.175472	+	0.0470177i	0.170013	+	0.985442i	$0.445619\pi$
$234$	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	−0.818955	−	0.573857i	$-0.805446\pi$
$239$	2.27348	−	4.87549i	0.147059	−	0.315369i	0.966014	+	0.258488i	$0.0832242\pi$
$240$	0.986070	−	5.52758i	0.0636505	−	0.356804i
$241$	5.34121	−	7.62803i	0.344057	−	0.491365i	−0.609412	−	0.792853i	$-0.708595\pi$
$241$	5.34121	−	7.62803i	0.344057	−	0.491365i	0.953470	+	0.301489i	$0.0974835\pi$
$242$	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	0.992947	+	0.118556i	$0.0378264\pi$
$251$	3.04672	+	11.3705i	0.192308	+	0.717701i	−0.800640	+	0.599146i	$0.795507\pi$
$252$	−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	−0.744021	−	0.668157i	$-0.767084\pi$
$257$	−26.7993	−	4.72544i	−1.67169	−	0.294765i	−0.927674	+	0.373392i	$0.878195\pi$
$258$	−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	−0.777359	−	0.629058i	$-0.783441\pi$
$263$	−12.3181	−	26.4163i	−0.759568	−	1.62890i	0.0177904	−	0.999842i	$-0.494337\pi$
$264$	−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	0.559492	−	0.828836i	$-0.310996\pi$
$269$	25.5372	−	14.7439i	1.55703	−	0.898952i	0.997539	−	0.0701167i	$-0.0223372\pi$
$270$	1.09925	+	1.31537i	0.0668982	+	0.0800510i
$271$	4.86429	−	27.5868i	0.295485	−	1.67578i	−0.369742	−	0.929135i	$-0.620554\pi$
$271$	4.86429	−	27.5868i	0.295485	−	1.67578i	0.665226	−	0.746642i	$-0.268335\pi$
$272$	−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	−0.911138	−	0.412101i	$-0.864795\pi$
$277$	−3.26035	−	18.4904i	−0.195895	−	1.11098i	0.715243	−	0.698876i	$-0.246316\pi$
$278$	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	0.998872	−	0.0474852i	$-0.0151207\pi$
$281$	0.116158	+	1.32769i	0.00692938	+	0.0792032i	−0.991943	+	0.126688i	$0.959565\pi$
$282$	−7.03559	+	4.06200i	−0.418963	+	0.241888i
$283$	−7.09619	+	19.4966i	−0.421825	+	1.15895i	0.528837	+	0.848724i	$0.322628\pi$
$283$	−7.09619	+	19.4966i	−0.421825	+	1.15895i	−0.950661	+	0.310230i	$0.899594\pi$
$284$	−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	−0.240962	−	0.970534i	$-0.577463\pi$
$293$	−21.1463	−	14.8068i	−1.23538	−	0.865023i	−0.994418	+	0.105512i	$0.966352\pi$
$294$	−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	0.954301	−	0.298847i	$-0.0966020\pi$
$307$	−0.377961	−	1.41057i	−0.0215714	−	0.0805055i	−0.975872	+	0.218341i	$0.929935\pi$
$308$	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	0.267207	−	0.963639i	$-0.413899\pi$
$311$	12.3039	−	1.07645i	0.697689	−	0.0610399i	0.430482	+	0.902599i	$0.358344\pi$
$312$	1.04920	+	11.9924i	0.0593993	+	0.678937i
$313$	0.440890	−	0.160471i	0.0249206	−	0.00907036i	−0.329530	−	0.944145i	$-0.606890\pi$
$313$	0.440890	−	0.160471i	0.0249206	−	0.00907036i	0.354450	+	0.935075i	$0.384668\pi$
$314$	−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	−0.0189085	−	0.999821i	$-0.506019\pi$
$317$	2.42297	−	0.211982i	0.136087	−	0.0119061i	0.154996	+	0.987915i	$0.450464\pi$
$318$	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	0.473354	−	0.880872i	$-0.343043\pi$
$331$	26.6169	−	18.6374i	1.46300	−	1.02440i	0.989646	−	0.143531i	$-0.0458458\pi$
$332$	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	−0.621176	−	0.783671i	$-0.713345\pi$
$337$	−7.71264	+	3.59646i	−0.420134	+	0.195912i	0.201042	+	0.979583i	$0.435567\pi$
$338$	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	0.951139	+	0.308765i	$0.0999155\pi$
$347$	13.8399	+	23.9715i	0.742967	+	1.28686i	−0.208171	+	0.978092i	$0.566751\pi$
$348$	−0.150355	+	0.179186i	−0.00805988	+	0.00960539i
$349$	−9.40756	+	11.2115i	−0.503575	+	0.600137i	−0.956616	−	0.291353i	$-0.905895\pi$
$349$	−9.40756	+	11.2115i	−0.503575	+	0.600137i	0.453041	+	0.891490i	$0.350339\pi$
$350$	−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	0.868360	+	0.495934i	$0.165174\pi$
$353$	9.80632	+	26.9426i	0.521938	+	1.43401i	−0.346422	+	0.938079i	$0.612604\pi$
$354$	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	0.390815	−	0.920469i	$-0.372193\pi$
$359$	−3.99651	−	2.30739i	−0.210928	−	0.121779i	−0.601743	+	0.798690i	$0.705527\pi$
$360$	−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	−0.0280916	−	0.999605i	$-0.508943\pi$
$367$	17.6407	−	25.1936i	0.920838	−	1.31509i	0.948930	−	0.315488i	$-0.102168\pi$
$368$	−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	−0.981954	−	0.189118i	$-0.939437\pi$
$373$	−9.04618	+	12.9193i	−0.468393	+	0.668935i	0.513561	+	0.858053i	$0.328326\pi$
$374$	−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	0.886029	+	0.463631i	$0.153454\pi$
$379$	9.83728	+	27.0277i	0.505307	+	1.38832i	−0.380721	+	0.924690i	$0.624324\pi$
$380$	−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	−0.133865	−	0.991000i	$-0.542739\pi$
$383$	−17.0930	−	6.22136i	−0.873414	−	0.317897i	−0.739549	+	0.673103i	$0.764961\pi$
$384$	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	0.991617	−	0.129215i	$-0.0412457\pi$
$389$	23.8521	+	16.7014i	1.20935	+	0.846794i	0.217731	+	0.976009i	$0.430135\pi$
$390$	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	0.999159	−	0.0410113i	$-0.0130580\pi$
$397$	36.7404	+	9.84457i	1.84395	+	0.494085i	0.844791	+	0.535096i	$0.179725\pi$
$398$	−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	−0.814502	−	0.580161i	$-0.802990\pi$
$401$	−4.69266	+	4.69266i	−0.234340	+	0.234340i	0.580161	+	0.814502i	$0.302990\pi$
$402$	−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	−0.454793	−	0.890597i	$-0.650287\pi$
$409$	4.58162	−	3.20808i	0.226546	−	0.158629i	0.681339	+	0.731968i	$0.261398\pi$
$410$	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	−0.590334	−	0.807159i	$-0.701004\pi$
$419$	−29.0898	−	5.12932i	−1.42113	−	0.250584i	−0.830797	+	0.556576i	$0.812115\pi$
$420$	0.768187	+	8.98750i	0.0374837	+	0.438545i
$421$	−33.0452	−	8.85443i	−1.61052	−	0.431538i	−0.662324	−	0.749217i	$-0.730430\pi$
$421$	−33.0452	−	8.85443i	−1.61052	−	0.431538i	−0.948198	+	0.317679i	$0.897097\pi$
$422$	−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	−0.646362	−	0.763031i	$-0.723710\pi$
$431$	−9.90941	+	4.62083i	−0.477319	+	0.222578i	0.169042	+	0.985609i	$0.445933\pi$
$432$	0.439717	+	0.627981i	0.0211559	+	0.0302137i
$433$	−9.88051	−	36.8746i	−0.474827	−	1.77208i	−0.622052	−	0.782976i	$-0.713701\pi$
$433$	−9.88051	−	36.8746i	−0.474827	−	1.77208i	0.147225	−	0.989103i	$-0.452966\pi$
$434$	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	−0.116076	−	0.993240i	$-0.537031\pi$
$439$	−8.44090	−	0.738483i	−0.402862	−	0.0352459i	−0.286787	+	0.957995i	$0.592587\pi$
$440$	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	0.813457	−	0.581625i	$-0.197583\pi$
$443$	4.87950	+	4.87950i	0.231832	+	0.231832i	−0.581625	+	0.813457i	$0.697583\pi$
$444$	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	0.941128	+	0.338052i	$0.109768\pi$
$449$	−0.940909	+	10.7546i	−0.0444042	+	0.507543i	−0.985532	+	0.169491i	$0.945788\pi$
$450$	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	−0.996473	−	0.0839175i	$-0.973257\pi$
$457$	−3.83063	+	10.5246i	−0.179189	+	0.492318i	0.817284	+	0.576236i	$0.195479\pi$
$458$	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	0.864977	−	0.501812i	$-0.167333\pi$
$461$	22.2559	+	10.3781i	1.03656	+	0.483357i	0.171586	+	0.985169i	$0.445111\pi$
$462$	−2.48196	−	14.0759i	−0.115471	−	0.654870i
$463$	1.85997	+	10.5484i	0.0864403	+	0.490227i	0.997036	+	0.0769300i	$0.0245118\pi$
$463$	1.85997	+	10.5484i	0.0864403	+	0.490227i	−0.910596	+	0.413297i	$0.864377\pi$
$464$	−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	−0.998556	−	0.0537121i	$-0.982895\pi$
$467$	−31.3633	+	18.1076i	−1.45132	+	0.837919i	−0.452762	+	0.891631i	$0.649561\pi$
$468$	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	−0.989567	−	0.144070i	$-0.953981\pi$
$479$	−17.2133	−	24.5832i	−0.786497	−	1.12323i	0.203070	−	0.979164i	$-0.434908\pi$
$480$	−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	$0.0753354\pi$
$487$			10.3486i			0.468939i	−0.972123	+	0.234470i	$0.924665\pi$
$488$	−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	0.701206	−	0.712959i	$-0.252645\pi$
$491$	−5.91272	−	10.2411i	−0.266837	−	0.462176i	−0.968043	+	0.250783i	$0.919312\pi$
$492$	−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	−0.996124	−	0.0879544i	$-0.971967\pi$
$499$	−12.7949	+	18.2731i	−0.572780	+	0.818014i	0.423345	+	0.905969i	$0.360856\pi$
$500$	−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	0.902762	−	0.430140i	$-0.141536\pi$
$503$	14.2622	+	11.9674i	0.635920	+	0.533601i	−0.266842	+	0.963740i	$0.585980\pi$
$504$	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	0.515510	−	0.856884i	$-0.327603\pi$
$509$	32.9663	−	11.9988i	1.46121	−	0.531836i	0.945698	+	0.325048i	$0.105380\pi$
$510$	−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	−0.559279	−	0.828980i	$-0.688922\pi$
$521$	−18.2900	+	3.22503i	−0.801301	+	0.141291i	−0.242023	+	0.970271i	$0.577811\pi$
$522$	0.279052	−	0.130124i	0.0122138	−	0.00569537i
$523$	6.97043	−	5.84888i	0.304796	−	0.255754i	−0.477541	−	0.878609i	$-0.658472\pi$
$523$	6.97043	−	5.84888i	0.304796	−	0.255754i	0.782337	+	0.622855i	$0.214028\pi$
$524$	−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	−0.999168	−	0.0407759i	$-0.987017\pi$
$541$	−2.63937	+	9.85025i	−0.113475	+	0.423495i	0.885693	+	0.464271i	$0.153684\pi$
$542$	−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	−0.498656	−	0.866800i	$-0.666173\pi$
$547$	11.7254	−	20.3090i	0.501343	−	0.868351i	0.999999	−	0.00155089i	$-0.000493663\pi$
$548$	−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	0.756479	+	0.654018i	$0.226918\pi$
$557$	−4.20251	+	23.8336i	−0.178066	+	1.00986i	−0.934545	+	0.355845i	$0.884193\pi$
$558$	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	−0.900492	−	0.434873i	$-0.856793\pi$
$563$	−1.74717	+	3.02619i	−0.0736346	+	0.127539i	0.826857	+	0.562412i	$0.190127\pi$
$564$	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	−0.772037	−	0.635578i	$-0.780762\pi$
$569$	5.11318	−	19.0827i	0.214356	−	0.799986i	0.986392	−	0.164408i	$-0.0525715\pi$
$570$	32.4684	+	8.76954i	1.35995	+	0.367315i
$571$	−8.61188	−	7.22622i	−0.360396	−	0.302408i	0.444553	−	0.895753i	$-0.353363\pi$
$571$	−8.61188	−	7.22622i	−0.360396	−	0.302408i	−0.804948	+	0.593345i	$0.797807\pi$
$572$	−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	−0.0696835	+	0.997569i	$0.522199\pi$
$577$	−24.9816	+	29.7719i	−1.04000	+	1.23942i	−0.970313	+	0.241851i	$0.922246\pi$
$578$	−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	−0.843519	−	0.537100i	$-0.819520\pi$
$587$	−11.1705	+	9.37314i	−0.461055	+	0.386871i	0.382464	+	0.923970i	$0.375076\pi$
$588$	−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	−0.0409222	−	0.999162i	$-0.513030\pi$
$593$	23.3347	−	23.3347i	0.958240	−	0.958240i	0.999162	+	0.0409222i	$0.0130296\pi$
$594$	−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	0.868441	−	0.495792i	$-0.165122\pi$
$599$	5.61392	+	6.69041i	0.229379	+	0.273363i	−0.639063	+	0.769155i	$0.720678\pi$
$600$	−5.35154	+	11.3575i	−0.218476	+	0.463669i
$601$	−22.7086	+	8.26527i	−0.926304	+	0.337147i	−0.760744	−	0.649052i	$-0.775166\pi$
$601$	−22.7086	+	8.26527i	−0.926304	+	0.337147i	−0.165561	+	0.986200i	$0.552943\pi$
$602$	−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	−0.951136	−	0.308772i	$-0.900082\pi$
$607$	−34.9944	−	29.3638i	−1.42038	−	1.19184i	−0.469244	−	0.883069i	$-0.655474\pi$
$608$	−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	0.989603	−	0.143823i	$-0.0459395\pi$
$613$	−0.246109	−	2.81304i	−0.00994025	−	0.113618i	−0.999544	+	0.0302051i	$0.990384\pi$
$614$	−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	0.984194	+	0.177095i	$0.0566700\pi$
$617$	20.2192	+	28.8760i	0.813995	+	1.16250i	−0.170199	+	0.985410i	$0.554441\pi$
$618$	6.80180	+	25.3847i	0.273609	+	1.02112i
$619$	13.0900	+	22.6726i	0.526132	+	0.911287i	0.999537	+	0.0304418i	$0.00969143\pi$
$619$	13.0900	+	22.6726i	0.526132	+	0.911287i	−0.473405	+	0.880845i	$0.656975\pi$
$620$	−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	0.999911	−	0.0133729i	$-0.00425686\pi$
$631$	16.2111	+	23.1519i	0.645355	+	0.921662i	−0.354556	+	0.935035i	$0.615368\pi$
$632$	−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	−0.968765	−	0.247979i	$-0.920234\pi$
$641$	0.668146	−	3.78924i	0.0263902	−	0.149666i	0.995156	+	0.0983131i	$0.0313447\pi$
$642$	3.63117	−	9.97656i	0.143311	−	0.393743i
$643$	36.7030	−	21.1905i	1.44742	−	0.835671i	0.449097	−	0.893483i	$-0.351746\pi$
$643$	36.7030	−	21.1905i	1.44742	−	0.835671i	0.998327	+	0.0578124i	$0.0184125\pi$
$644$	−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	0.974634	+	0.223806i	$0.0718483\pi$
$647$	3.44212	+	19.5213i	0.135324	+	0.767460i	−0.839310	+	0.543653i	$0.817041\pi$
$648$	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	−0.781939	−	0.623355i	$-0.785769\pi$
$653$	5.56426	−	15.2877i	0.217746	−	0.598253i	0.999685	+	0.0251026i	$0.00799123\pi$
$654$	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	−0.316449	+	0.948610i	$0.602490\pi$
$659$	−33.5160	+	28.1233i	−1.30560	+	1.09553i	−0.989149	+	0.146917i	$0.953065\pi$
$660$	6.84164	−	18.6809i	0.266310	−	0.727151i
$661$	−2.90064	+	33.1545i	−0.112822	+	1.28956i	0.702972	+	0.711218i	$0.251856\pi$
$661$	−2.90064	+	33.1545i	−0.112822	+	1.28956i	−0.815794	+	0.578343i	$0.803700\pi$
$662$	−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	0.979338	+	0.202229i	$0.0648185\pi$
$673$	−0.525028	+	6.00110i	−0.0202384	+	0.231325i	−0.999577	+	0.0290964i	$0.990737\pi$
$674$	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	0.795675	+	0.605724i	$0.207116\pi$
$677$	10.6539	+	39.7608i	0.409462	+	1.52813i	−0.386213	+	0.922410i	$0.626217\pi$
$678$	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	−0.690822	−	0.723025i	$-0.742751\pi$
$683$	−19.7385	+	7.18421i	−0.755271	+	0.274896i	−0.0644492	+	0.997921i	$0.520529\pi$
$684$	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	0.747641	−	0.664103i	$-0.231186\pi$
$691$	32.1504	+	5.66898i	1.22306	+	0.215658i	0.475416	+	0.879761i	$0.342297\pi$
$692$	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	−0.218259	−	0.975891i	$-0.570038\pi$
$701$	16.5247	−	11.5707i	0.624130	−	0.437021i	0.842389	+	0.538870i	$0.181149\pi$
$702$	−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	−0.465769	−	0.884906i	$-0.654222\pi$
$709$	11.1604	−	11.1604i	0.419137	−	0.419137i	0.884906	+	0.465769i	$0.154222\pi$
$710$	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	−0.860436	−	0.509558i	$-0.829809\pi$
$719$	−5.60968	+	6.68536i	−0.209206	+	0.249322i	0.651230	+	0.758880i	$0.274253\pi$
$720$	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	0.805803	−	0.592184i	$-0.201734\pi$
$727$	28.1071	+	10.2302i	1.04244	+	0.379415i	0.236632	+	0.971599i	$0.423956\pi$
$728$	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	0.843579	−	0.537005i	$-0.180445\pi$
$733$	42.8064	+	3.74508i	1.58109	+	0.138328i	0.737513	+	0.675333i	$0.236000\pi$
$734$	−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	−0.814818	−	0.579717i	$-0.803163\pi$
$743$	0.235002	−	0.335617i	0.00862138	−	0.0123126i	0.823440	+	0.567404i	$0.192052\pi$
$744$	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	−0.248933	−	0.968521i	$-0.580080\pi$
$751$	−33.2186	−	19.1788i	−1.21216	−	0.699843i	−0.963230	+	0.268678i	$0.913413\pi$
$752$	−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	−0.996819	−	0.0797046i	$-0.974602\pi$
$757$	−7.82610	−	21.5020i	−0.284444	−	0.781505i	0.712374	−	0.701800i	$-0.247620\pi$
$758$	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	−0.643388	−	0.765540i	$-0.722472\pi$
$761$	6.13090	−	7.30652i	0.222245	−	0.264861i	0.865633	+	0.500679i	$0.166916\pi$
$762$	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	−0.995453	−	0.0952522i	$-0.969634\pi$
$769$	−50.1905	+	13.4485i	−1.80991	+	0.484965i	−0.814462	+	0.580217i	$0.802968\pi$
$770$	−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	−0.702708	−	0.711478i	$-0.748026\pi$
$773$	−16.9424	+	7.90039i	−0.609377	+	0.284157i	0.0933314	+	0.995635i	$0.470248\pi$
$774$	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	−0.981514	−	0.191389i	$-0.938701\pi$
$787$	−1.00442	+	3.74853i	−0.0358036	+	0.133621i	0.945711	+	0.325010i	$0.105368\pi$
$788$	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	−0.293180	−	0.956057i	$-0.594713\pi$
$797$	2.73204	−	0.994380i	0.0967737	−	0.0352228i	0.389953	+	0.920835i	$0.372491\pi$
$798$	−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	−0.244887	−	0.969552i	$-0.578751\pi$
$809$	−18.6134	−	1.62846i	−0.654414	−	0.0572538i	−0.409527	+	0.912298i	$0.634306\pi$
$810$	17.8033	−	1.52169i	0.625543	−	0.0534669i
$811$	4.29645	+	24.3664i	0.150869	+	0.855619i	0.962466	+	0.271402i	$0.0874872\pi$
$811$	4.29645	+	24.3664i	0.150869	+	0.855619i	−0.811597	+	0.584217i	$0.801402\pi$
$812$	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	−0.822753	−	0.568399i	$-0.807563\pi$
$821$	−11.6291	+	9.75797i	−0.405858	+	0.340555i	0.416895	+	0.908955i	$0.363118\pi$
$822$	25.6866	+	14.8302i	0.895924	+	0.517262i
$823$	−5.13453	+	11.0110i	−0.178978	+	0.383820i	−0.975246	−	0.221125i	$-0.929027\pi$
$823$	−5.13453	+	11.0110i	−0.178978	+	0.383820i	0.796267	+	0.604945i	$0.206805\pi$
$824$	−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	−0.970366	−	0.241638i	$-0.922315\pi$
$827$	−2.06194	+	5.66513i	−0.0717007	+	0.196996i	0.898666	+	0.438634i	$0.144538\pi$
$828$	−22.0474	+	12.7291i	−0.766199	+	0.442365i
$829$	1.64207	+	18.7689i	0.0570313	+	0.651871i	0.969882	+	0.243577i	$0.0783207\pi$
$829$	1.64207	+	18.7689i	0.0570313	+	0.651871i	−0.912850	+	0.408294i	$0.866124\pi$
$830$	−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	−0.765009	−	0.644020i	$-0.777265\pi$
$839$	5.04382	−	28.6049i	0.174132	−	0.987552i	0.939141	−	0.343532i	$-0.111623\pi$
$840$	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	−0.669260	−	0.743028i	$-0.733389\pi$
$853$	−45.3364	−	7.99403i	−1.55229	−	0.273710i	−0.883029	+	0.469318i	$0.844500\pi$
$854$	−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	$-0.969597\pi$
$857$		−	5.58369i		−	0.190735i	0.995442	−	0.0953677i	$-0.0304027\pi$
$858$	−3.71748	+	42.4910i	−0.126913	+	1.45062i
$859$	−6.47211	−	24.1542i	−0.220825	−	0.824132i	−0.984034	−	0.177980i	$-0.943044\pi$
$859$	−6.47211	−	24.1542i	−0.220825	−	0.824132i	0.763209	−	0.646152i	$-0.223623\pi$
$860$	−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	0.946417	−	0.322947i	$-0.104673\pi$
$863$	9.37865	+	13.3941i	0.319253	+	0.455940i	−0.627164	+	0.778887i	$0.715785\pi$
$864$	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	−0.260159	−	0.965566i	$-0.583775\pi$
$877$	−0.0793615	+	0.0212649i	−0.00267985	+	0.000718063i	0.257479	+	0.966284i	$0.417108\pi$
$878$	−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	0.990850	−	0.134965i	$-0.0430922\pi$
$881$	20.3579	+	24.2616i	0.685876	+	0.817396i	−0.304974	+	0.952361i	$0.598648\pi$
$882$	14.6066			0.491830
$883$	−17.3121	−	20.6318i	−0.582600	−	0.694316i	0.391566	−	0.920150i	$-0.371934\pi$
$883$	−17.3121	−	20.6318i	−0.582600	−	0.694316i	−0.974166	+	0.225835i	$0.927489\pi$
$884$	−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	−0.780006	−	0.625773i	$-0.784784\pi$
$887$	−4.59345	+	4.59345i	−0.154233	+	0.154233i	0.625773	+	0.780006i	$0.284784\pi$
$888$	−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	0.465166	−	0.885224i	$-0.345995\pi$
$907$	36.2916	−	6.39919i	1.20504	−	0.212482i	0.739877	+	0.672742i	$0.234884\pi$
$908$	−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	−0.513238	−	0.858246i	$-0.671554\pi$
$911$	10.8767	−	40.5925i	0.360362	−	1.34489i	0.873600	−	0.486644i	$-0.161779\pi$
$912$	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	0.906341	−	0.422547i	$-0.138864\pi$
$919$	14.6662	+	14.6662i	0.483794	+	0.483794i	−0.422547	+	0.906341i	$0.638864\pi$
$920$	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	0.135239	−	0.990813i	$-0.456820\pi$
$929$	−12.1322	−	4.41576i	−0.398045	−	0.144876i	−0.533283	+	0.845937i	$0.679042\pi$
$930$	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	−0.786530	−	0.617552i	$-0.788125\pi$
$937$	−14.5470	+	10.1859i	−0.475230	+	0.332760i	0.311300	+	0.950312i	$0.399236\pi$
$938$	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	−0.0857315	−	0.996318i	$-0.527323\pi$
$941$	−33.1850	−	27.8455i	−1.08180	−	0.907738i	−0.996069	+	0.0885798i	$0.971767\pi$
$942$	−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	−0.497447	−	0.867494i	$-0.665729\pi$
$947$	13.6402	−	16.2558i	0.443248	−	0.528243i	0.940696	+	0.339251i	$0.110174\pi$
$948$	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	0.302251	−	0.953228i	$-0.402262\pi$
$953$	−7.21388	−	3.36389i	−0.233680	−	0.108967i	−0.535932	+	0.844261i	$0.680040\pi$
$954$	−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	0.897697	−	0.440613i	$-0.145239\pi$
$967$	9.57450	+	11.4104i	0.307895	+	0.366935i	−0.589802	+	0.807548i	$0.700794\pi$
$968$	−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	−0.754577	−	0.656211i	$-0.772158\pi$
$971$	−28.3817	+	10.3301i	−0.910812	+	0.331508i	−0.156235	+	0.987720i	$0.549936\pi$
$972$	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	0.940675	−	0.339309i	$-0.110193\pi$
$977$	24.0638	+	20.1919i	0.769868	+	0.645996i	−0.170807	+	0.985304i	$0.554638\pi$
$978$	−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	−0.998897	−	0.0469570i	$-0.985048\pi$
$983$	−0.731446	−	8.36046i	−0.0233295	−	0.266657i	0.975567	−	0.219700i	$-0.0705079\pi$
$984$	−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	−0.988499	−	0.151226i	$-0.951678\pi$
$991$	−6.54934	−	24.4425i	−0.208047	−	0.776441i	0.780453	−	0.625215i	$-0.214989\pi$
$992$	−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	0.704445	−	0.709759i	$-0.251196\pi$
$997$	35.4797	+	6.25603i	1.12365	+	0.198131i	0.419210	+	0.907889i	$0.362307\pi$
$998$	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.87.2	✓	108
5.3	odd	4		370.2.bd.a.13.2	yes	108
37.20	odd	36		370.2.bd.a.57.2	yes	108
185.168	even	36	inner	370.2.ba.a.353.2	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.ba.a.87.2	✓	108	1.1	even	1	trivial
370.2.ba.a.353.2	yes	108	185.168	even	36	inner
370.2.bd.a.13.2	yes	108	5.3	odd	4
370.2.bd.a.57.2	yes	108	37.20	odd	36

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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