LMFDB - Embedded newform 370.2.ba.a.257.5

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			257.5
Character	$\chi$	$=$	370.257
Dual form			370.2.ba.a.203.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-0.0484358 - 0.553623i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.704954 + 2.12204i) q^{5} +(-0.392966 - 0.392966i) q^{6} +(3.12914 + 1.45914i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.65027 - 0.467314i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-0.0484358 - 0.553623i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.704954 + 2.12204i) q^{5} +(-0.392966 - 0.392966i) q^{6} +(3.12914 + 1.45914i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.65027 - 0.467314i) q^{9} +(0.823993 + 2.07871i) q^{10} +(-0.568753 + 0.328369i) q^{11} +(-0.553623 - 0.0484358i) q^{12} +(0.291091 - 1.65086i) q^{13} +(3.33498 - 0.893604i) q^{14} +(1.20895 + 0.287497i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.34025 - 0.236322i) q^{17} +(1.72984 - 2.06154i) q^{18} +(0.124303 - 0.0108751i) q^{19} +(1.96738 + 1.06273i) q^{20} +(0.656252 - 1.80304i) q^{21} +(-0.224618 + 0.617133i) q^{22} +(0.0688371 - 0.119229i) q^{23} +(-0.455234 + 0.318758i) q^{24} +(-4.00608 - 2.99188i) q^{25} +(-0.838164 - 1.45174i) q^{26} +(-0.818591 - 3.05502i) q^{27} +(1.98034 - 2.82822i) q^{28} +(-1.18293 + 4.41477i) q^{29} +(1.11091 - 0.556866i) q^{30} +(6.05636 - 6.05636i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.209341 + 0.298970i) q^{33} +(0.874785 - 1.04253i) q^{34} +(-5.30225 + 5.61152i) q^{35} -2.69116i q^{36} +(-4.96671 + 3.51166i) q^{37} +(0.0882315 - 0.0882315i) q^{38} +(-0.928054 - 0.0811942i) q^{39} +(2.19021 - 0.450510i) q^{40} +(-7.18825 - 1.26748i) q^{41} +(-0.656252 - 1.80304i) q^{42} +2.76084 q^{43} +(0.224618 + 0.617133i) q^{44} +(-0.876661 + 5.95341i) q^{45} +(-0.0239069 - 0.135583i) q^{46} +(-8.69482 + 2.32977i) q^{47} +(-0.143836 + 0.536802i) q^{48} +(3.16289 + 3.76939i) q^{49} +(-4.99198 + 0.283147i) q^{50} +(-0.195749 - 0.730546i) q^{51} +(-1.57523 - 0.573338i) q^{52} +(-5.40524 + 2.52050i) q^{53} +(-2.59081 - 1.81410i) q^{54} +(-0.295868 - 1.43840i) q^{55} +(-0.300916 - 3.43948i) q^{56} +(-0.0120415 - 0.0682905i) q^{57} +(1.93158 + 4.14228i) q^{58} +(4.60467 - 2.14719i) q^{59} +(0.493062 - 1.14066i) q^{60} +(3.20031 + 4.57052i) q^{61} +(0.746488 - 8.53240i) q^{62} +(8.97494 + 2.40483i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.29798 + 1.78149i) q^{65} +(0.352539 + 0.0944624i) q^{66} +(-6.49836 + 13.9358i) q^{67} -1.36092i q^{68} +(-0.0693423 - 0.0323349i) q^{69} +(-0.454744 + 7.70689i) q^{70} +(6.45079 + 5.41286i) q^{71} +(-1.72984 - 2.06154i) q^{72} +(-10.7767 - 10.7767i) q^{73} +(-1.54747 + 5.88263i) q^{74} +(-1.46234 + 2.36277i) q^{75} +(0.0108751 - 0.124303i) q^{76} +(-2.25884 + 0.197623i) q^{77} +(-0.763121 + 0.534343i) q^{78} +(3.27766 - 7.02896i) q^{79} +(1.38822 - 1.75295i) q^{80} +(5.93489 - 2.16012i) q^{81} +(-6.32124 + 3.64957i) q^{82} +(2.39528 + 1.67719i) q^{83} +(-1.66169 - 0.959376i) q^{84} +(-0.443330 + 3.01065i) q^{85} +(2.11493 - 1.77463i) q^{86} +(2.50141 + 0.441067i) q^{87} +(0.568753 + 0.328369i) q^{88} +(-0.362181 - 0.776700i) q^{89} +(3.15521 + 5.12408i) q^{90} +(3.31970 - 4.74102i) q^{91} +(-0.105465 - 0.0884953i) q^{92} +(-3.64629 - 3.05960i) q^{93} +(-5.16307 + 7.37363i) q^{94} +(-0.0645507 + 0.271443i) q^{95} +(0.234865 + 0.503670i) q^{96} +(-14.9234 - 8.61604i) q^{97} +(4.84583 + 0.854451i) q^{98} +(-1.35390 + 1.13605i) 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−0.0484358	−	0.553623i	−0.0279644	−	0.319635i	−0.997274	−	0.0737904i	$-0.976490\pi$
$3$	−0.0484358	−	0.553623i	−0.0279644	−	0.319635i	0.969309	−	0.245844i	$-0.0790651\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.704954	+	2.12204i	−0.315265	+	0.949004i
$5$	−0.704954	+	2.12204i	−0.315265	+	0.949004i
$6$	−0.392966	−	0.392966i	−0.160428	−	0.160428i
$7$	3.12914	+	1.45914i	1.18270	+	0.551503i	0.911612	−	0.411051i	$-0.134838\pi$
$7$	3.12914	+	1.45914i	1.18270	+	0.551503i	0.271090	+	0.962554i	$0.412616\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.65027	−	0.467314i	0.883423	−	0.155771i
$10$	0.823993	+	2.07871i	0.260569	+	0.657346i
$11$	−0.568753	+	0.328369i	−0.171485	+	0.0990071i	−0.583286	−	0.812267i	$-0.698233\pi$
$11$	−0.568753	+	0.328369i	−0.171485	+	0.0990071i	0.411801	+	0.911274i	$0.364900\pi$
$12$	−0.553623	−	0.0484358i	−0.159817	−	0.0139822i
$13$	0.291091	−	1.65086i	0.0807342	−	0.457866i	−0.917462	−	0.397824i	$-0.869765\pi$
$13$	0.291091	−	1.65086i	0.0807342	−	0.457866i	0.998196	−	0.0600421i	$-0.0191235\pi$
$14$	3.33498	−	0.893604i	0.891310	−	0.238826i
$15$	1.20895	+	0.287497i	0.312151	+	0.0742313i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.34025	−	0.236322i	0.325058	−	0.0573165i	−0.00873808	−	0.999962i	$-0.502781\pi$
$17$	1.34025	−	0.236322i	0.325058	−	0.0573165i	0.333796	+	0.942645i	$0.391670\pi$
$18$	1.72984	−	2.06154i	0.407727	−	0.485911i
$19$	0.124303	−	0.0108751i	0.0285172	−	0.00249493i	−0.0728882	−	0.997340i	$-0.523222\pi$
$19$	0.124303	−	0.0108751i	0.0285172	−	0.00249493i	0.101405	+	0.994845i	$0.467666\pi$
$20$	1.96738	+	1.06273i	0.439920	+	0.237634i
$21$	0.656252	−	1.80304i	0.143206	−	0.393455i
$22$	−0.224618	+	0.617133i	−0.0478887	+	0.131573i
$23$	0.0688371	−	0.119229i	0.0143535	−	0.0248610i	−0.858759	−	0.512379i	$-0.828764\pi$
$23$	0.0688371	−	0.119229i	0.0143535	−	0.0248610i	0.873113	+	0.487518i	$0.162098\pi$
$24$	−0.455234	+	0.318758i	−0.0929243	+	0.0650663i
$25$	−4.00608	−	2.99188i	−0.801216	−	0.598375i
$26$	−0.838164	−	1.45174i	−0.164377	−	0.284710i
$27$	−0.818591	−	3.05502i	−0.157538	−	0.587939i
$28$	1.98034	−	2.82822i	0.374249	−	0.534484i
$29$	−1.18293	+	4.41477i	−0.219665	+	0.819802i	0.764807	+	0.644260i	$0.222834\pi$
$29$	−1.18293	+	4.41477i	−0.219665	+	0.819802i	−0.984472	+	0.175542i	$0.943832\pi$
$30$	1.11091	−	0.556866i	0.202824	−	0.101669i
$31$	6.05636	−	6.05636i	1.08775	−	1.08775i	0.0919951	−	0.995759i	$-0.470676\pi$
$31$	6.05636	−	6.05636i	1.08775	−	1.08775i	0.995759	−	0.0919951i	$-0.0293244\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.209341	+	0.298970i	0.0364416	+	0.0520440i
$34$	0.874785	−	1.04253i	0.150024	−	0.178792i
$35$	−5.30225	+	5.61152i	−0.896243	+	0.948519i
$36$		−	2.69116i		−	0.448526i
$37$	−4.96671	+	3.51166i	−0.816522	+	0.577314i
$37$	−4.96671	+	3.51166i	−0.816522	+	0.577314i
$38$	0.0882315	−	0.0882315i	0.0143130	−	0.0143130i
$39$	−0.928054	−	0.0811942i	−0.148608	−	0.0130015i
$40$	2.19021	−	0.450510i	0.346303	−	0.0712319i
$41$	−7.18825	−	1.26748i	−1.12262	−	0.197947i	−0.418627	−	0.908158i	$-0.637488\pi$
$41$	−7.18825	−	1.26748i	−1.12262	−	0.197947i	−0.703989	+	0.710211i	$0.748600\pi$
$42$	−0.656252	−	1.80304i	−0.101262	−	0.278215i
$43$	2.76084			0.421024			0.210512	−	0.977591i	$-0.432487\pi$
$43$	2.76084			0.421024			0.210512	+	0.977591i	$0.432487\pi$
$44$	0.224618	+	0.617133i	0.0338624	+	0.0930363i
$45$	−0.876661	+	5.95341i	−0.130685	+	0.887481i
$46$	−0.0239069	−	0.135583i	−0.00352488	−	0.0199906i
$47$	−8.69482	+	2.32977i	−1.26827	+	0.339832i	−0.829368	−	0.558703i	$-0.811299\pi$
$47$	−8.69482	+	2.32977i	−1.26827	+	0.339832i	−0.438902	+	0.898535i	$0.644633\pi$
$48$	−0.143836	+	0.536802i	−0.0207609	+	0.0774807i
$49$	3.16289	+	3.76939i	0.451842	+	0.538484i
$50$	−4.99198	+	0.283147i	−0.705972	+	0.0400431i
$51$	−0.195749	−	0.730546i	−0.0274104	−	0.102297i
$52$	−1.57523	−	0.573338i	−0.218445	−	0.0795076i
$53$	−5.40524	+	2.52050i	−0.742466	+	0.346218i	−0.756771	−	0.653680i	$-0.773224\pi$
$53$	−5.40524	+	2.52050i	−0.742466	+	0.346218i	0.0143047	+	0.999898i	$0.495447\pi$
$54$	−2.59081	−	1.81410i	−0.352564	−	0.246868i
$55$	−0.295868	−	1.43840i	−0.0398948	−	0.193954i
$56$	−0.300916	−	3.43948i	−0.0402115	−	0.459620i
$57$	−0.0120415	−	0.0682905i	−0.00159493	−	0.00904530i
$58$	1.93158	+	4.14228i	0.253629	+	0.543908i
$59$	4.60467	−	2.14719i	0.599477	−	0.279541i	−0.0990979	−	0.995078i	$-0.531596\pi$
$59$	4.60467	−	2.14719i	0.599477	−	0.279541i	0.698575	+	0.715537i	$0.253818\pi$
$60$	0.493062	−	1.14066i	0.0636540	−	0.147259i
$61$	3.20031	+	4.57052i	0.409758	+	0.585195i	0.969991	−	0.243140i	$-0.0781773\pi$
$61$	3.20031	+	4.57052i	0.409758	+	0.585195i	−0.560233	+	0.828335i	$0.689288\pi$
$62$	0.746488	−	8.53240i	0.0948041	−	1.08362i
$63$	8.97494	+	2.40483i	1.13074	+	0.302980i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	3.29798	+	1.78149i	0.409064	+	0.220966i
$66$	0.352539	+	0.0944624i	0.0433945	+	0.0116275i
$67$	−6.49836	+	13.9358i	−0.793901	+	1.70253i	−0.0859112	+	0.996303i	$0.527380\pi$
$67$	−6.49836	+	13.9358i	−0.793901	+	1.70253i	−0.707990	+	0.706223i	$0.750398\pi$
$68$		−	1.36092i		−	0.165036i
$69$	−0.0693423	−	0.0323349i	−0.00834784	−	0.00389266i
$70$	−0.454744	+	7.70689i	−0.0543523	+	0.921149i
$71$	6.45079	+	5.41286i	0.765568	+	0.642388i	0.939570	−	0.342357i	$-0.111225\pi$
$71$	6.45079	+	5.41286i	0.765568	+	0.642388i	−0.174001	+	0.984745i	$0.555670\pi$
$72$	−1.72984	−	2.06154i	−0.203864	−	0.242955i
$73$	−10.7767	−	10.7767i	−1.26131	−	1.26131i	−0.950456	−	0.310859i	$-0.899383\pi$
$73$	−10.7767	−	10.7767i	−1.26131	−	1.26131i	−0.310859	−	0.950456i	$-0.600617\pi$
$74$	−1.54747	+	5.88263i	−0.179890	+	0.683842i
$75$	−1.46234	+	2.36277i	−0.168856	+	0.272830i
$76$	0.0108751	−	0.124303i	0.00124746	−	0.0142586i
$77$	−2.25884	+	0.197623i	−0.257419	+	0.0225212i
$78$	−0.763121	+	0.534343i	−0.0864065	+	0.0605025i
$79$	3.27766	−	7.02896i	0.368765	−	0.790820i	−0.631120	−	0.775685i	$-0.717405\pi$
$79$	3.27766	−	7.02896i	0.368765	−	0.790820i	0.999885	−	0.0151346i	$-0.00481766\pi$
$80$	1.38822	−	1.75295i	0.155208	−	0.195986i
$81$	5.93489	−	2.16012i	0.659433	−	0.240014i
$82$	−6.32124	+	3.64957i	−0.698064	+	0.403027i
$83$	2.39528	+	1.67719i	0.262916	+	0.184096i	0.697600	−	0.716487i	$-0.254251\pi$
$83$	2.39528	+	1.67719i	0.262916	+	0.184096i	−0.434684	+	0.900583i	$0.643140\pi$
$84$	−1.66169	−	0.959376i	−0.181305	−	0.104677i
$85$	−0.443330	+	3.01065i	−0.0480859	+	0.326551i
$86$	2.11493	−	1.77463i	0.228058	−	0.191364i
$87$	2.50141	+	0.441067i	0.268180	+	0.0472873i
$88$	0.568753	+	0.328369i	0.0606292	+	0.0350043i
$89$	−0.362181	−	0.776700i	−0.0383911	−	0.0823300i	0.886177	−	0.463347i	$-0.153352\pi$
$89$	−0.362181	−	0.776700i	−0.0383911	−	0.0823300i	−0.924568	+	0.381017i	$0.875574\pi$
$90$	3.15521	+	5.12408i	0.332589	+	0.540126i
$91$	3.31970	−	4.74102i	0.347999	−	0.496994i
$92$	−0.105465	−	0.0884953i	−0.0109954	−	0.00922627i
$93$	−3.64629	−	3.05960i	−0.378102	−	0.317266i
$94$	−5.16307	+	7.37363i	−0.532530	+	0.760532i
$95$	−0.0645507	+	0.271443i	−0.00662277	+	0.0278494i
$96$	0.234865	+	0.503670i	0.0239708	+	0.0514056i
$97$	−14.9234	−	8.61604i	−1.51524	−	0.874826i	−0.999840	−	0.0178779i	$-0.994309\pi$
$97$	−14.9234	−	8.61604i	−1.51524	−	0.874826i	−0.515403	−	0.856948i	$-0.672358\pi$
$98$	4.84583	+	0.854451i	0.489503	+	0.0863126i
$99$	−1.35390	+	1.13605i	−0.136072	+	0.114178i
$100$	−3.64207	+	3.42568i	−0.364207	+	0.342568i
$101$	−6.22075	−	3.59155i	−0.618987	−	0.357373i	0.157487	−	0.987521i	$-0.449661\pi$
$101$	−6.22075	−	3.59155i	−0.618987	−	0.357373i	−0.776475	+	0.630148i	$0.782994\pi$
$102$	−0.619539	−	0.433806i	−0.0613435	−	0.0429532i
$103$	7.32022	−	4.22633i	0.721283	−	0.416433i	−0.0939419	−	0.995578i	$-0.529947\pi$
$103$	7.32022	−	4.22633i	0.721283	−	0.416433i	0.815225	+	0.579145i	$0.196613\pi$
$104$	−1.57523	+	0.573338i	−0.154464	+	0.0562204i
$105$	3.36348	+	2.66365i	0.328242	+	0.259946i
$106$	−2.52050	+	5.40524i	−0.244813	+	0.525003i
$107$	−14.1024	+	9.87463i	−1.36333	+	0.954617i	−0.363600	+	0.931555i	$0.618452\pi$
$107$	−14.1024	+	9.87463i	−1.36333	+	0.954617i	−0.999734	+	0.0230615i	$0.992659\pi$
$108$	−3.15076	+	0.275655i	−0.303182	+	0.0265250i
$109$	1.03142	−	11.7892i	0.0987920	−	1.12920i	−0.771355	−	0.636405i	$-0.780421\pi$
$109$	1.03142	−	11.7892i	0.0987920	−	1.12920i	0.870147	−	0.492792i	$-0.164024\pi$
$110$	−1.15123	−	0.911698i	−0.109766	−	0.0869270i
$111$	2.18470	+	2.57960i	0.207363	+	0.244845i
$112$	−2.44137	−	2.44137i	−0.230688	−	0.230688i
$113$	−4.81633	−	5.73988i	−0.453083	−	0.539963i	0.490351	−	0.871525i	$-0.336869\pi$
$113$	−4.81633	−	5.73988i	−0.453083	−	0.539963i	−0.943433	+	0.331562i	$0.892424\pi$
$114$	−0.0531206	−	0.0445735i	−0.00497520	−	0.00417469i
$115$	0.204482	+	0.230126i	0.0190681	+	0.0214594i
$116$	4.14228	+	1.93158i	0.384601	+	0.179343i
$117$		−	4.51126i		−	0.417066i
$118$	2.14719	−	4.60467i	0.197665	−	0.423894i
$119$	4.53865	+	1.21613i	0.416057	+	0.111482i
$120$	−0.355498	−	1.19073i	−0.0324523	−	0.108699i
$121$	−5.28435	+	9.15276i	−0.480395	+	0.832069i
$122$	5.38946	+	1.44410i	0.487939	+	0.130743i
$123$	−0.353539	+	4.04097i	−0.0318776	+	0.364362i
$124$	−4.91268	−	7.01603i	−0.441171	−	0.630058i
$125$	9.17298	−	6.39191i	0.820456	−	0.571710i
$126$	8.42099	−	3.92677i	0.750202	−	0.349825i
$127$	4.49881	+	9.64773i	0.399205	+	0.856097i	0.998457	+	0.0555369i	$0.0176870\pi$
$127$	4.49881	+	9.64773i	0.399205	+	0.856097i	−0.599252	+	0.800561i	$0.704535\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−0.133723	−	1.52847i	−0.0117737	−	0.134574i
$130$	3.67152	−	0.755202i	0.322013	−	0.0662356i
$131$	−5.62664	−	3.93982i	−0.491602	−	0.344223i	0.301344	−	0.953516i	$-0.402565\pi$
$131$	−5.62664	−	3.93982i	−0.491602	−	0.344223i	−0.792946	+	0.609292i	$0.791454\pi$
$132$	0.330780	−	0.154245i	0.0287907	−	0.0134253i
$133$	0.404831	+	0.147346i	0.0351033	+	0.0127765i
$134$	3.97971	+	14.8525i	0.343795	+	1.28306i
$135$	7.05994	+	0.416571i	0.607623	+	0.0358527i
$136$	−0.874785	−	1.04253i	−0.0750122	−	0.0893960i
$137$	3.87130	−	14.4479i	0.330748	−	1.23437i	−0.577659	−	0.816278i	$-0.696034\pi$
$137$	3.87130	−	14.4479i	0.330748	−	1.23437i	0.908406	−	0.418089i	$-0.137300\pi$
$138$	−0.0739038	+	0.0198025i	−0.00629111	+	0.00168570i
$139$	−0.703165	−	3.98785i	−0.0596417	−	0.338245i	0.940356	−	0.340191i	$-0.110492\pi$
$139$	−0.703165	−	3.98785i	−0.0596417	−	0.338245i	−0.999998	+	0.00194595i	$0.999381\pi$
$140$	4.60554	+	6.19612i	0.389239	+	0.523668i
$141$	1.71096	+	4.70081i	0.144088	+	0.395880i
$142$	8.42091			0.706667
$143$	0.376533	+	1.03452i	0.0314873	+	0.0865106i
$144$	−2.65027	−	0.467314i	−0.220856	−	0.0389428i
$145$	−8.53438	−	5.62244i	−0.708742	−	0.466918i
$146$	−15.1825	−	1.32830i	−1.25652	−	0.109931i
$147$	1.93362	−	1.93362i	0.159483	−	0.159483i
$148$	2.59585	+	5.50105i	0.213378	+	0.452184i
$149$			7.15574i			0.586221i	0.956079	+	0.293111i	$0.0946904\pi$
$149$			7.15574i			0.586221i	−0.956079	+	0.293111i	$0.905310\pi$
$150$	0.398547	+	2.74996i	0.0325412	+	0.224533i
$151$	3.42109	−	4.07709i	0.278404	−	0.331789i	−0.608664	−	0.793428i	$-0.708294\pi$
$151$	3.42109	−	4.07709i	0.278404	−	0.331789i	0.887068	+	0.461639i	$0.152739\pi$
$152$	−0.0715698	−	0.102212i	−0.00580508	−	0.00829051i
$153$	3.44158	−	1.25263i	0.278236	−	0.101269i
$154$	−1.60334	+	1.60334i	−0.129201	+	0.129201i
$155$	8.58236	+	17.1213i	0.689352	+	1.37521i
$156$	−0.241116	+	0.899855i	−0.0193047	+	0.0720461i
$157$	−1.05514	+	1.50690i	−0.0842094	+	0.120264i	−0.859047	−	0.511897i	$-0.828943\pi$
$157$	−1.05514	+	1.50690i	−0.0842094	+	0.120264i	0.774837	+	0.632161i	$0.217832\pi$
$158$	−2.00730	−	7.49133i	−0.159692	−	0.595978i
$159$	1.65722	+	2.87038i	0.131426	+	0.227636i
$160$	−0.0633391	−	2.23517i	−0.00500739	−	0.176706i
$161$	0.389373	−	0.272642i	0.0306869	−	0.0214872i
$162$	3.15789	−	5.46963i	0.248107	−	0.429735i
$163$	4.76707	−	13.0974i	0.373385	−	1.02587i	−0.600658	−	0.799506i	$-0.705095\pi$
$163$	4.76707	−	13.0974i	0.373385	−	1.02587i	0.974043	−	0.226362i	$-0.0726832\pi$
$164$	−2.49645	+	6.85894i	−0.194940	+	0.535594i
$165$	−0.782001	+	0.233469i	−0.0608787	+	0.0181756i
$166$	2.91297	−	0.254852i	0.226091	−	0.0197804i
$167$	3.00511	−	3.58136i	0.232543	−	0.277134i	−0.637136	−	0.770751i	$-0.719881\pi$
$167$	3.00511	−	3.58136i	0.232543	−	0.277134i	0.869679	+	0.493617i	$0.164326\pi$
$168$	−1.88960	+	0.333188i	−0.145786	+	0.0257060i
$169$	9.57540	+	3.48516i	0.736569	+	0.268089i
$170$	1.59560	+	2.59126i	0.122377	+	0.198741i
$171$	0.324356	−	0.0869108i	0.0248041	−	0.00664623i
$172$	0.479415	−	2.71890i	0.0365550	−	0.207314i
$173$	−15.3650	−	1.34427i	−1.16818	−	0.102203i	−0.513488	−	0.858097i	$-0.671647\pi$
$173$	−15.3650	−	1.34427i	−1.16818	−	0.102203i	−0.654694	+	0.755894i	$0.727202\pi$
$174$	2.19971	−	1.27000i	0.166759	−	0.0962785i
$175$	−8.17000	−	15.2074i	−0.617594	−	1.14957i
$176$	0.646762	−	0.114042i	0.0487515	−	0.00859620i
$177$	−1.41177	−	2.44525i	−0.106115	−	0.183796i
$178$	−0.776700	−	0.362181i	−0.0582161	−	0.0271466i
$179$	1.56494	+	1.56494i	0.116969	+	0.116969i	0.763169	−	0.646199i	$-0.223643\pi$
$179$	1.56494	+	1.56494i	0.116969	+	0.116969i	−0.646199	+	0.763169i	$0.723643\pi$
$180$	5.71073	+	1.89714i	0.425653	+	0.141405i
$181$	2.23135	−	12.6546i	0.165855	−	0.940608i	−0.782324	−	0.622871i	$-0.785966\pi$
$181$	2.23135	−	12.6546i	0.165855	−	0.940608i	0.948179	−	0.317737i	$-0.102923\pi$
$182$	−0.504433	−	5.76570i	−0.0373911	−	0.427382i
$183$	2.37534	−	1.99315i	0.175590	−	0.147338i
$184$	−0.137674			−0.0101495
$185$	−3.95057	−	13.0151i	−0.290452	−	0.956890i
$186$	−4.75989			−0.349012
$187$	−0.684669	+	0.574505i	−0.0500679	+	0.0420120i
$188$	0.784536	+	8.96729i	0.0572182	+	0.654007i
$189$	1.89622	−	10.7540i	0.137930	−	0.782240i
$190$	0.125031	+	0.249430i	0.00907073	+	0.0180955i
$191$	13.5381	+	13.5381i	0.979584	+	0.979584i	0.999796	−	0.0202117i	$-0.00643404\pi$
$191$	13.5381	+	13.5381i	0.979584	+	0.979584i	−0.0202117	+	0.999796i	$0.506434\pi$
$192$	0.503670	+	0.234865i	0.0363492	+	0.0169499i
$193$	3.63741	+	6.30018i	0.261827	+	0.453497i	0.966727	−	0.255809i	$-0.0823418\pi$
$193$	3.63741	+	6.30018i	0.261827	+	0.453497i	−0.704901	+	0.709306i	$0.749008\pi$
$194$	−16.9703	+	2.99232i	−1.21840	+	0.214836i
$195$	0.826533	−	1.91213i	0.0591892	−	0.136930i
$196$	4.26135	−	2.46029i	0.304382	−	0.175735i
$197$	5.99066	+	0.524115i	0.426817	+	0.0373416i	0.298541	−	0.954397i	$-0.403500\pi$
$197$	5.99066	+	0.524115i	0.426817	+	0.0373416i	0.128276	+	0.991739i	$0.459056\pi$
$198$	−0.306903	+	1.74054i	−0.0218107	+	0.123695i
$199$	15.0572	−	4.03457i	1.06738	−	0.286003i	0.317963	−	0.948103i	$-0.397001\pi$
$199$	15.0572	−	4.03457i	1.06738	−	0.286003i	0.749415	+	0.662100i	$0.230335\pi$
$200$	−0.588002	+	4.96531i	−0.0415780	+	0.351100i
$201$	8.02992	+	2.92265i	0.566387	+	0.206148i
$202$	−7.07397	+	1.24733i	−0.497723	+	0.0877620i
$203$	−10.1433	+	12.0883i	−0.711922	+	0.848435i
$204$	−0.753439	+	0.0659174i	−0.0527513	+	0.00461514i
$205$	7.75703	−	14.3602i	0.541774	−	1.00296i
$206$	2.89098	−	7.94290i	0.201424	−	0.553408i
$207$	0.126719	−	0.348159i	0.00880760	−	0.0241987i
$208$	−0.838164	+	1.45174i	−0.0581162	+	0.100660i
$209$	−0.0671268	+	0.0470027i	−0.00464326	+	0.00325125i
$210$	4.28874	−	0.121532i	0.295951	−	0.00838651i
$211$	−7.64052	−	13.2338i	−0.525995	−	0.911050i	−0.999541	−	0.0302810i	$-0.990360\pi$
$211$	−7.64052	−	13.2338i	−0.525995	−	0.911050i	0.473547	−	0.880769i	$-0.342974\pi$
$212$	1.54360	+	5.76080i	0.106015	+	0.395653i
$213$	2.68424	−	3.83349i	0.183921	−	0.262666i
$214$	−4.45580	+	16.6293i	−0.304592	+	1.13675i
$215$	−1.94627	+	5.85860i	−0.132734	+	0.399553i
$216$	−2.23643	+	2.23643i	−0.152170	+	0.152170i
$217$	27.7883	−	10.1141i	1.88639	−	0.686590i
$218$	−6.78782	−	9.69401i	−0.459729	−	0.656561i
$219$	−5.44424	+	6.48820i	−0.367888	+	0.438432i
$220$	−1.46792	+	0.0415972i	−0.0989674	+	0.00280449i
$221$		−	2.28135i		−	0.153460i
$222$	3.33171	+	0.571786i	0.223610	+	0.0383757i
$223$	−6.74350	+	6.74350i	−0.451578	+	0.451578i	−0.895878	−	0.444300i	$-0.853452\pi$
$223$	−6.74350	+	6.74350i	−0.451578	+	0.451578i	0.444300	+	0.895878i	$0.353452\pi$
$224$	−3.43948	−	0.300916i	−0.229810	−	0.0201058i
$225$	−12.0153	−	6.05719i	−0.801023	−	0.403812i
$226$	−7.37905	−	1.30113i	−0.490847	−	0.0865496i
$227$	−0.313884	−	0.862389i	−0.0208332	−	0.0572387i	0.928840	−	0.370481i	$-0.120807\pi$
$227$	−0.313884	−	0.862389i	−0.0208332	−	0.0572387i	−0.949673	+	0.313242i	$0.898585\pi$
$228$	−0.0693440			−0.00459242
$229$	3.52456	+	9.68364i	0.232909	+	0.639913i	0.999999	−	0.00162731i	$-0.000517991\pi$
$229$	3.52456	+	9.68364i	0.232909	+	0.639913i	−0.767089	+	0.641540i	$0.778296\pi$
$230$	0.304565	+	0.0448483i	0.0200824	+	0.00295721i
$231$	0.218817	+	1.24098i	0.0143971	+	0.0816502i
$232$	4.41477	−	1.18293i	0.289844	−	0.0776634i
$233$	−1.30485	+	4.86976i	−0.0854834	+	0.319028i	−0.995405	−	0.0957513i	$-0.969475\pi$
$233$	−1.30485	+	4.86976i	−0.0854834	+	0.319028i	0.909922	+	0.414780i	$0.136141\pi$
$234$	−2.89978	−	3.45582i	−0.189565	−	0.225914i
$235$	1.18559	−	20.0931i	0.0773395	−	1.31073i
$236$	−1.31498	−	4.90757i	−0.0855979	−	0.319456i
$237$	−4.05015	−	1.47413i	−0.263086	−	0.0957553i
$238$	4.25852	−	1.98578i	0.276039	−	0.128719i
$239$	4.94477	+	3.46236i	0.319850	+	0.223962i	0.722464	−	0.691408i	$-0.243009\pi$
$239$	4.94477	+	3.46236i	0.319850	+	0.223962i	−0.402614	+	0.915370i	$0.631898\pi$
$240$	−1.03772	−	0.683645i	−0.0669843	−	0.0441291i
$241$	0.838673	+	9.58607i	0.0540237	+	0.617493i	0.974155	+	0.225882i	$0.0725265\pi$
$241$	0.838673	+	9.58607i	0.0540237	+	0.617493i	−0.920131	+	0.391611i	$0.871918\pi$
$242$	1.83523	+	10.4081i	0.117973	+	0.669060i
$243$	−5.49332	−	11.7805i	−0.352396	−	0.755717i
$244$	5.05681	−	2.35803i	0.323729	−	0.150957i
$245$	−10.2285	+	4.05453i	−0.653473	+	0.259034i
$246$	2.32666	+	3.32282i	0.148342	+	0.211855i
$247$	0.0182303	−	0.208373i	0.00115997	−	0.0132585i
$248$	−8.27314	−	2.21678i	−0.525345	−	0.140766i
$249$	0.812517	−	1.40732i	0.0514912	−	0.0891853i
$250$	2.91827	−	10.7928i	0.184567	−	0.682594i
$251$	22.6381	+	6.06587i	1.42891	+	0.382874i	0.888634	−	0.458616i	$-0.151655\pi$
$251$	22.6381	+	6.06587i	1.42891	+	0.382874i	0.540272	+	0.841490i	$0.318321\pi$
$252$	3.92677	−	8.42099i	0.247363	−	0.530473i
$253$			0.0904160i			0.00568441i
$254$	9.64773	+	4.49881i	0.605352	+	0.282280i
$255$	1.68824	+	0.0996144i	0.105722	+	0.00623810i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.54954	+	1.84667i	0.0966577	+	0.115192i	0.812205	−	0.583372i	$-0.198267\pi$
$257$	1.54954	+	1.84667i	0.0966577	+	0.115192i	−0.715547	+	0.698564i	$0.753823\pi$
$258$	−1.08492	−	1.08492i	−0.0675440	−	0.0675440i
$259$	−20.6655	+	3.74134i	−1.28409	+	0.232475i
$260$	2.32711	−	2.93852i	0.144321	−	0.182240i
$261$	−1.07201	+	12.2531i	−0.0663557	+	0.758449i
$262$	−6.84272	+	0.598661i	−0.422745	+	0.0369854i
$263$	2.41379	−	1.69016i	0.148841	−	0.104219i	−0.496784	−	0.867874i	$-0.665486\pi$
$263$	2.41379	−	1.69016i	0.148841	−	0.104219i	0.645625	+	0.763655i	$0.276597\pi$
$264$	0.154245	−	0.330780i	0.00949313	−	0.0203581i
$265$	−1.53816	−	13.2470i	−0.0944882	−	0.813754i
$266$	0.404831	−	0.147346i	0.0248218	−	0.00903438i
$267$	−0.412457	+	0.238132i	−0.0252419	+	0.0145734i
$268$	12.5956	+	8.81955i	0.769401	+	0.538740i
$269$	14.9040	+	8.60483i	0.908713	+	0.524646i	0.880017	−	0.474943i	$-0.157531\pi$
$269$	14.9040	+	8.60483i	0.908713	+	0.524646i	0.0286960	+	0.999588i	$0.490865\pi$
$270$	5.67599	−	4.21893i	0.345430	−	0.256756i
$271$	8.37619	−	7.02846i	0.508817	−	0.426948i	−0.351895	−	0.936039i	$-0.614463\pi$
$271$	8.37619	−	7.02846i	0.508817	−	0.426948i	0.860713	+	0.509091i	$0.170018\pi$
$272$	−1.34025	−	0.236322i	−0.0812645	−	0.0143291i
$273$	−2.78553	−	1.60823i	−0.168588	−	0.0973344i
$274$	−6.32134	−	13.5562i	−0.381886	−	0.818957i
$275$	3.26091	+	0.386164i	0.196640	+	0.0232866i
$276$	−0.0438848	+	0.0626740i	−0.00264155	+	0.00377253i
$277$	9.25095	+	7.76247i	0.555836	+	0.466402i	0.876911	−	0.480652i	$-0.159600\pi$
$277$	9.25095	+	7.76247i	0.555836	+	0.466402i	−0.321076	+	0.947054i	$0.604044\pi$
$278$	−3.10200	−	2.60288i	−0.186045	−	0.156111i
$279$	13.2208	−	18.8812i	0.791507	−	1.13039i
$280$	7.51084	+	1.78612i	0.448858	+	0.106741i
$281$	7.42802	+	15.9294i	0.443119	+	0.950271i	0.993337	+	0.115250i	$0.0367669\pi$
$281$	7.42802	+	15.9294i	0.443119	+	0.950271i	−0.550218	+	0.835021i	$0.685455\pi$
$282$	4.33229	+	2.50125i	0.257984	+	0.148947i
$283$	17.8211	+	3.14234i	1.05935	+	0.186793i	0.676070	−	0.736838i	$-0.263682\pi$
$283$	17.8211	+	3.14234i	1.05935	+	0.186793i	0.383284	+	0.923630i	$0.374793\pi$
$284$	6.45079	−	5.41286i	0.382784	−	0.321194i
$285$	0.153404	+	0.0225893i	0.00908685	+	0.00133807i
$286$	0.953416	+	0.550455i	0.0563766	+	0.0325491i
$287$	−20.6436	−	14.4548i	−1.21855	−	0.853239i
$288$	−2.33061	+	1.34558i	−0.137332	+	0.0792889i
$289$	−14.2344	+	5.18088i	−0.837315	+	0.304758i
$290$	−10.1517	+	1.17876i	−0.596131	+	0.0692192i
$291$	−4.04721	+	8.67927i	−0.237252	+	0.508788i
$292$	−12.4843	+	8.74161i	−0.730589	+	0.511564i
$293$	−4.15014	+	0.363090i	−0.242454	+	0.0212120i	−0.207735	−	0.978185i	$-0.566609\pi$
$293$	−4.15014	+	0.363090i	−0.242454	+	0.0212120i	−0.0347188	+	0.999397i	$0.511054\pi$
$294$	0.238332	−	2.72415i	0.0138998	−	0.158876i
$295$	1.31034	+	11.2850i	0.0762910	+	0.657035i
$296$	5.52454	+	2.54547i	0.321108	+	0.147952i
$297$	1.46875	+	1.46875i	0.0852256	+	0.0852256i
$298$	4.59962	+	5.48161i	0.266449	+	0.317541i
$299$	−0.176793	−	0.148347i	−0.0102242	−	0.00857913i
$300$	2.07295	+	1.85041i	0.119682	+	0.106834i
$301$	8.63904	+	4.02845i	0.497946	+	0.232196i
$302$		−	5.32226i		−	0.306262i
$303$	−1.68706	+	3.61791i	−0.0969190	+	0.207843i
$304$	−0.120526	−	0.0322950i	−0.00691267	−	0.00185224i
$305$	−11.9549	+	3.56917i	−0.684535	+	0.204370i
$306$	1.83123	−	3.17178i	0.104684	−	0.181319i
$307$	28.9561	+	7.75876i	1.65261	+	0.442816i	0.960342	−	0.278823i	$-0.0899443\pi$
$307$	28.9561	+	7.75876i	1.65261	+	0.442816i	0.692269	+	0.721639i	$0.256611\pi$
$308$	−0.197623	+	2.25884i	−0.0112606	+	0.128709i
$309$	−2.69436	−	3.84794i	−0.153277	−	0.218902i
$310$	17.5798	+	7.59902i	0.998466	+	0.431595i
$311$	−30.4518	+	14.1999i	−1.72676	+	0.805202i	−0.734856	+	0.678223i	$0.762750\pi$
$311$	−30.4518	+	14.1999i	−1.72676	+	0.805202i	−0.991905	+	0.126979i	$0.959472\pi$
$312$	0.393711	+	0.844315i	0.0222895	+	0.0477999i
$313$	3.29580	+	18.6914i	0.186289	+	1.05650i	0.924288	+	0.381697i	$0.124660\pi$
$313$	3.29580	+	18.6914i	0.186289	+	1.05650i	−0.737998	+	0.674803i	$0.764229\pi$
$314$	0.160330	+	1.83258i	0.00904796	+	0.103419i
$315$	−11.4300	+	17.3498i	−0.644010	+	0.977553i
$316$	−6.35301	−	4.44843i	−0.357385	−	0.250244i
$317$	−7.92776	+	3.69677i	−0.445267	+	0.207631i	−0.632302	−	0.774722i	$-0.717890\pi$
$317$	−7.92776	+	3.69677i	−0.445267	+	0.207631i	0.187035	+	0.982353i	$0.440112\pi$
$318$	3.11455	+	1.13360i	0.174655	+	0.0635693i
$319$	−0.776878	−	2.89935i	−0.0434968	−	0.162332i
$320$	−1.48526	−	1.67153i	−0.0830286	−	0.0934412i
$321$	6.14989	+	7.32915i	0.343253	+	0.409073i
$322$	0.123026	−	0.459140i	0.00685598	−	0.0255869i
$323$	0.164027	−	0.0439510i	0.00912673	−	0.00244550i
$324$	−1.09672	−	6.21983i	−0.0609291	−	0.345546i
$325$	−6.10530	+	5.74257i	−0.338661	+	0.318540i
$326$	−4.76707	−	13.0974i	−0.264023	−	0.725398i
$327$	−6.57672			−0.363693
$328$	2.49645	+	6.85894i	0.137843	+	0.378722i
$329$	−30.6068	−	5.39680i	−1.68740	−	0.297535i
$330$	−0.448976	+	0.681508i	−0.0247153	+	0.0375158i
$331$	−16.7622	−	1.46650i	−0.921332	−	0.0806061i	−0.383388	−	0.923587i	$-0.625243\pi$
$331$	−16.7622	−	1.46650i	−0.921332	−	0.0806061i	−0.537943	+	0.842981i	$0.680799\pi$
$332$	2.06765	−	2.06765i	0.113477	−	0.113477i
$333$	−11.5221	+	11.6279i	−0.631406	+	0.637203i
$334$		−	4.67513i		−	0.255812i
$335$	−24.9912	−	23.6138i	−1.36541	−	1.29016i
$336$	−1.23335	+	1.46985i	−0.0672848	+	0.0801869i
$337$	19.7479	+	28.2029i	1.07573	+	1.53631i	0.822384	+	0.568933i	$0.192644\pi$
$337$	19.7479	+	28.2029i	1.07573	+	1.53631i	0.253350	+	0.967375i	$0.418467\pi$
$338$	9.57540	−	3.48516i	0.520833	−	0.189568i
$339$	−2.94445	+	2.94445i	−0.159921	+	0.159921i
$340$	2.88793	+	0.959389i	0.156620	+	0.0520302i
$341$	−1.45585	+	5.43330i	−0.0788385	+	0.294229i
$342$	0.192606	−	0.275069i	0.0104149	−	0.0148740i
$343$	−1.85817	−	6.93479i	−0.100332	−	0.374444i
$344$	−1.38042	−	2.39096i	−0.0744272	−	0.128912i
$345$	0.117499	−	0.124352i	0.00632593	−	0.00669491i
$346$	−12.6344	+	8.84669i	−0.679228	+	0.475601i
$347$	−6.63324	+	11.4891i	−0.356091	+	0.616768i	−0.987304	−	0.158842i	$-0.949224\pi$
$347$	−6.63324	+	11.4891i	−0.356091	+	0.616768i	0.631213	+	0.775610i	$0.282557\pi$
$348$	0.868732	−	2.38682i	0.0465689	−	0.127947i
$349$	6.00947	−	16.5109i	0.321679	−	0.883807i	−0.668463	−	0.743745i	$-0.733048\pi$
$349$	6.00947	−	16.5109i	0.321679	−	0.883807i	0.990143	−	0.140062i	$-0.0447301\pi$
$350$	−16.0337	−	6.39799i	−0.857039	−	0.341987i
$351$	−5.28170	+	0.462089i	−0.281916	+	0.0246645i
$352$	0.422144	−	0.503091i	0.0225003	−	0.0268149i
$353$	−33.2608	+	5.86479i	−1.77030	+	0.312151i	−0.961267	−	0.275618i	$-0.911118\pi$
$353$	−33.2608	+	5.86479i	−1.77030	+	0.312151i	−0.809029	+	0.587769i	$0.800007\pi$
$354$	−2.65325	−	0.965705i	−0.141019	−	0.0513267i
$355$	−16.0338	+	9.87301i	−0.850986	+	0.524005i
$356$	−0.827792	+	0.221806i	−0.0438729	+	0.0117557i
$357$	0.453443	−	2.57160i	0.0239988	−	0.136104i
$358$	2.20474	+	0.192890i	0.116524	+	0.0101945i
$359$	31.6055	−	18.2474i	1.66807	−	0.963062i	0.699396	−	0.714734i	$-0.253452\pi$
$359$	31.6055	−	18.2474i	1.66807	−	0.963062i	0.968676	−	0.248328i	$-0.0798811\pi$
$360$	5.59413	−	2.21749i	0.294837	−	0.116872i
$361$	−18.6960	+	3.29661i	−0.984001	+	0.173506i
$362$	−6.42491	−	11.1283i	−0.337686	−	0.584888i
$363$	5.32313	+	2.48222i	0.279392	+	0.130283i
$364$	−4.09254	−	4.09254i	−0.214507	−	0.214507i
$365$	30.4656	−	15.2714i	1.59464	−	0.799344i
$366$	0.538445	−	3.05368i	0.0281450	−	0.159618i
$367$	0.911774	+	10.4216i	0.0475942	+	0.544004i	0.982139	+	0.188158i	$0.0602518\pi$
$367$	0.911774	+	10.4216i	0.0475942	+	0.544004i	−0.934545	+	0.355846i	$0.884193\pi$
$368$	−0.105465	+	0.0884953i	−0.00549772	+	0.00461313i
$369$	−19.6431			−1.02258
$370$	−11.3923	−	7.43077i	−0.592255	−	0.386307i
$371$	−20.5915			−1.06906
$372$	−3.64629	+	3.05960i	−0.189051	+	0.158633i
$373$	−0.679626	−	7.76816i	−0.0351897	−	0.402220i	−0.993279	−	0.115749i	$-0.963073\pi$
$373$	−0.679626	−	7.76816i	−0.0351897	−	0.402220i	0.958089	−	0.286471i	$-0.0924823\pi$
$374$	−0.155202	+	0.880193i	−0.00802529	+	0.0455137i
$375$	−3.98301	−	4.76878i	−0.205682	−	0.246259i
$376$	6.36505	+	6.36505i	0.328253	+	0.328253i
$377$	6.94382	+	3.23796i	0.357625	+	0.166763i
$378$	−5.45996	−	9.45693i	−0.280830	−	0.486412i
$379$	−11.0092	+	1.94122i	−0.565504	+	0.0997136i	−0.449089	−	0.893487i	$-0.648251\pi$
$379$	−11.0092	+	1.94122i	−0.565504	+	0.0997136i	−0.116415	+	0.993201i	$0.537140\pi$
$380$	0.256110	+	0.110706i	0.0131382	+	0.00567908i
$381$	5.12330	−	2.95794i	0.262475	−	0.151540i
$382$	19.0729	+	1.66867i	0.975856	+	0.0853764i
$383$	1.63926	−	9.29671i	0.0837623	−	0.475040i	−0.913855	−	0.406042i	$-0.866909\pi$
$383$	1.63926	−	9.29671i	0.0837623	−	0.475040i	0.997617	−	0.0689978i	$-0.0219802\pi$
$384$	0.536802	−	0.143836i	0.0273936	−	0.00734008i
$385$	1.17302	−	4.93266i	0.0597825	−	0.251392i
$386$	6.83610	+	2.48814i	0.347948	+	0.126643i
$387$	7.31697	−	1.29018i	0.371943	−	0.0655835i
$388$	−11.0766	+	13.2005i	−0.562327	+	0.670156i
$389$	−6.65855	+	0.582548i	−0.337602	+	0.0295364i	−0.254696	−	0.967021i	$-0.581976\pi$
$389$	−6.65855	+	0.582548i	−0.337602	+	0.0295364i	−0.0829056	+	0.996557i	$0.526420\pi$
$390$	−0.595930	−	1.99606i	−0.0301761	−	0.101074i
$391$	0.0640823	−	0.176065i	0.00324078	−	0.00890397i
$392$	1.68294	−	4.62384i	0.0850013	−	0.233539i
$393$	−1.90864	+	3.30587i	−0.0962783	+	0.166759i
$394$	4.92600	−	3.44923i	0.248169	−	0.173769i
$395$	12.6051	+	11.9104i	0.634232	+	0.599277i
$396$	0.883693	+	1.53060i	0.0444073	+	0.0769156i
$397$	−3.81485	−	14.2372i	−0.191462	−	0.714546i	−0.993154	−	0.116809i	$-0.962733\pi$
$397$	−3.81485	−	14.2372i	−0.191462	−	0.714546i	0.801692	−	0.597737i	$-0.203933\pi$
$398$	8.94113	−	12.7693i	0.448178	−	0.640065i
$399$	0.0619661	−	0.231261i	0.00310218	−	0.0115775i
$400$	2.74120	+	4.18160i	0.137060	+	0.209080i
$401$	−15.0426	+	15.0426i	−0.751192	+	0.751192i	−0.974702	−	0.223510i	$-0.928249\pi$
$401$	−15.0426	+	15.0426i	−0.751192	+	0.751192i	0.223510	+	0.974702i	$0.428249\pi$
$402$	8.02992	−	2.92265i	0.400496	−	0.145769i
$403$	−8.23525	−	11.7612i	−0.410227	−	0.585865i
$404$	−4.61721	+	5.50257i	−0.229715	+	0.273763i
$405$	0.400036	+	14.1169i	0.0198779	+	0.701472i
$406$			15.7802i			0.783159i
$407$	1.67171	−	3.62818i	0.0828635	−	0.179842i
$408$	−0.534797	+	0.534797i	−0.0264764	+	0.0264764i
$409$	−28.0850	−	2.45712i	−1.38871	−	0.121497i	−0.631860	−	0.775082i	$-0.717708\pi$
$409$	−28.0850	−	2.45712i	−1.38871	−	0.121497i	−0.756853	+	0.653586i	$0.773264\pi$
$410$	−3.28834	−	15.9867i	−0.162399	−	0.789526i
$411$	−8.18620	−	1.44345i	−0.403796	−	0.0712000i
$412$	−2.89098	−	7.94290i	−0.142428	−	0.391319i
$413$	17.5417			0.863171
$414$	−0.126719	−	0.348159i	−0.00622792	−	0.0171111i
$415$	−5.24763	+	3.90053i	−0.257596	+	0.191470i
$416$	0.291091	+	1.65086i	0.0142719	+	0.0809401i
$417$	−2.17371	+	0.582443i	−0.106447	+	0.0285224i
$418$	−0.0212094	+	0.0791544i	−0.00103738	+	0.00387157i
$419$	−2.09940	−	2.50197i	−0.102562	−	0.122229i	0.712322	−	0.701853i	$-0.247644\pi$
$419$	−2.09940	−	2.50197i	−0.102562	−	0.122229i	−0.814884	+	0.579624i	$0.803199\pi$
$420$	3.20725	−	2.84985i	0.156498	−	0.139058i
$421$	−7.81342	−	29.1601i	−0.380803	−	1.42118i	−0.844678	−	0.535275i	$-0.820208\pi$
$421$	−7.81342	−	29.1601i	−0.380803	−	1.42118i	0.463875	−	0.885901i	$-0.346459\pi$
$422$	−14.3595	−	5.22642i	−0.699008	−	0.254418i
$423$	−21.9549	+	10.2377i	−1.06748	+	0.497776i
$424$	4.88544	+	3.42082i	0.237258	+	0.166130i
$425$	−6.07619	−	3.06313i	−0.294738	−	0.148584i
$426$	−0.407873	−	4.66201i	−0.0197615	−	0.225875i
$427$	3.34519	+	18.9715i	0.161885	+	0.918095i
$428$	7.27575	+	15.6029i	0.351687	+	0.754195i
$429$	0.554495	−	0.258565i	0.0267713	−	0.0124836i
$430$	2.27491	+	5.73899i	0.109706	+	0.276758i
$431$	−14.2685	−	20.3776i	−0.687292	−	0.981554i	−0.999502	−	0.0315414i	$-0.989958\pi$
$431$	−14.2685	−	20.3776i	−0.687292	−	0.981554i	0.312211	−	0.950013i	$-0.398930\pi$
$432$	−0.275655	+	3.15076i	−0.0132625	+	0.151591i
$433$	35.7575	+	9.58120i	1.71840	+	0.460443i	0.977458	−	0.211129i	$-0.0677139\pi$
$433$	35.7575	+	9.58120i	1.71840	+	0.460443i	0.740939	+	0.671572i	$0.234381\pi$
$434$	14.7858	−	25.6098i	0.709742	−	1.22931i
$435$	−2.69934	+	4.99716i	−0.129424	+	0.239596i
$436$	−11.4310	−	3.06292i	−0.547444	−	0.146687i
$437$	0.00726005	−	0.0155692i	0.000347295	−	0.000744777i
$438$			8.46974i			0.404700i
$439$	29.7661	+	13.8801i	1.42066	+	0.662463i	0.972801	−	0.231643i	$-0.0744101\pi$
$439$	29.7661	+	13.8801i	1.42066	+	0.662463i	0.447856	+	0.894106i	$0.352188\pi$
$440$	−1.09776	+	0.975429i	−0.0523335	+	0.0465017i
$441$	10.1440	+	8.51183i	0.483048	+	0.405325i
$442$	−1.46643	−	1.74762i	−0.0697508	−	0.0831257i
$443$	16.6370	+	16.6370i	0.790450	+	0.790450i	0.981567	−	0.191118i	$-0.0612112\pi$
$443$	16.6370	+	16.6370i	0.790450	+	0.790450i	−0.191118	+	0.981567i	$0.561211\pi$
$444$	2.91978	−	1.70357i	0.138567	−	0.0808479i
$445$	1.90351	−	0.221024i	0.0902348	−	0.0104775i
$446$	−0.831182	+	9.50045i	−0.0393576	+	0.449859i
$447$	3.96158	−	0.346594i	0.187377	−	0.0163933i
$448$	−2.82822	+	1.98034i	−0.133621	+	0.0935623i
$449$	10.6204	−	22.7755i	0.501207	−	1.07484i	−0.479172	−	0.877721i	$-0.659063\pi$
$449$	10.6204	−	22.7755i	0.501207	−	1.07484i	0.980379	−	0.197122i	$-0.0631594\pi$
$450$	−13.0978	+	3.08324i	−0.617435	+	0.145345i
$451$	4.50454	−	1.63952i	0.212110	−	0.0772018i
$452$	−6.48903	+	3.74644i	−0.305218	+	0.176218i
$453$	−2.42288	−	1.69652i	−0.113837	−	0.0797093i
$454$	−0.794782	−	0.458867i	−0.0373010	−	0.0215357i
$455$	7.72039	+	10.3867i	0.361937	+	0.486937i
$456$	−0.0531206	+	0.0445735i	−0.00248760	+	0.00208734i
$457$	11.0243	+	1.94389i	0.515697	+	0.0909313i	0.425439	−	0.904987i	$-0.360120\pi$
$457$	11.0243	+	1.94389i	0.515697	+	0.0909313i	0.0902580	+	0.995918i	$0.471231\pi$
$458$	8.92449	+	5.15256i	0.417014	+	0.240763i
$459$	−1.81908	−	3.90104i	−0.0849075	−	0.182085i
$460$	0.262138	−	0.161415i	0.0122222	−	0.00752599i
$461$	−19.6471	+	28.0589i	−0.915055	+	1.30683i	0.0364931	+	0.999334i	$0.488381\pi$
$461$	−19.6471	+	28.0589i	−0.915055	+	1.30683i	−0.951548	+	0.307500i	$0.900508\pi$
$462$	0.965308	+	0.809989i	0.0449102	+	0.0376841i
$463$	23.5455	+	19.7570i	1.09425	+	0.918187i	0.997025	−	0.0770750i	$-0.0245581\pi$
$463$	23.5455	+	19.7570i	1.09425	+	0.918187i	0.0972275	+	0.995262i	$0.469003\pi$
$464$	2.62153	−	3.74394i	0.121702	−	0.173808i
$465$	9.06305	−	5.58068i	0.420289	−	0.258798i
$466$	2.13065	+	4.56919i	0.0987004	+	0.211664i
$467$	20.6870	+	11.9437i	0.957281	+	0.552686i	0.895335	−	0.445393i	$-0.146936\pi$
$467$	20.6870	+	11.9437i	0.957281	+	0.552686i	0.0619459	+	0.998080i	$0.480269\pi$
$468$	−4.44272	−	0.783372i	−0.205365	−	0.0362114i
$469$	−40.6685	+	34.1249i	−1.87790	+	1.57574i
$470$	−12.0074	−	16.1543i	−0.553860	−	0.745142i
$471$	0.885361	+	0.511163i	0.0407953	+	0.0235532i
$472$	−4.16186	−	2.91416i	−0.191565	−	0.134135i
$473$	−1.57023	+	0.906576i	−0.0721995	+	0.0416844i
$474$	−4.05015	+	1.47413i	−0.186030	+	0.0677092i
$475$	−0.530506	−	0.328334i	−0.0243413	−	0.0150650i
$476$	1.98578	−	4.25852i	0.0910180	−	0.195189i
$477$	−13.1475	+	9.20596i	−0.601981	+	0.421512i
$478$	6.01348	−	0.526111i	0.275050	−	0.0240638i
$479$	0.878131	−	10.0371i	0.0401228	−	0.458606i	−0.949384	−	0.314118i	$-0.898291\pi$
$479$	0.878131	−	10.0371i	0.0401228	−	0.458606i	0.989507	−	0.144487i	$-0.0461533\pi$
$480$	−1.23437	+	0.143328i	−0.0563412	+	0.00654201i
$481$	4.35150	+	9.22156i	0.198411	+	0.420467i
$482$	6.80427	+	6.80427i	0.309926	+	0.309926i
$483$	−0.169801	−	0.202360i	−0.00772619	−	0.00920772i
$484$	8.09609	+	6.79343i	0.368004	+	0.308792i
$485$	28.8039	−	25.5941i	1.30792	−	1.16217i
$486$	−11.7805	−	5.49332i	−0.534372	−	0.249182i
$487$		−	26.8835i		−	1.21821i	−0.793090	−	0.609104i	$-0.791529\pi$
$487$		−	26.8835i		−	1.21821i	0.793090	−	0.609104i	$-0.208471\pi$
$488$	2.35803	−	5.05681i	0.106743	−	0.228911i
$489$	−7.48193	−	2.00478i	−0.338344	−	0.0906591i
$490$	−5.22927	+	9.68068i	−0.236234	+	0.437329i
$491$	8.01643	−	13.8849i	0.361776	−	0.626615i	−0.626477	−	0.779440i	$-0.715504\pi$
$491$	8.01643	−	13.8849i	0.361776	−	0.626615i	0.988253	+	0.152825i	$0.0488370\pi$
$492$	3.91819	+	1.04988i	0.176646	+	0.0473321i
$493$	−0.542118	+	6.19643i	−0.0244158	+	0.279073i
$494$	−0.119974	−	0.171341i	−0.00539791	−	0.00770901i
$495$	−1.45631	−	3.67388i	−0.0654564	−	0.165129i
$496$	−7.76252	+	3.61972i	−0.348547	+	0.162530i
$497$	12.2873	+	26.3502i	0.551161	+	1.18197i
$498$	−0.282184	−	1.60035i	−0.0126450	−	0.0717132i
$499$	1.47502	+	16.8595i	0.0660308	+	0.754736i	0.954968	+	0.296708i	$0.0958886\pi$
$499$	1.47502	+	16.8595i	0.0660308	+	0.754736i	−0.888938	+	0.458028i	$0.848556\pi$
$500$	−4.70193	−	10.1436i	−0.210277	−	0.453634i
$501$	−2.12828	−	1.49024i	−0.0950844	−	0.0665788i
$502$	21.2409	−	9.90479i	0.948027	−	0.442072i
$503$	12.8495	+	4.67684i	0.572931	+	0.208530i	0.612206	−	0.790698i	$-0.290282\pi$
$503$	12.8495	+	4.67684i	0.572931	+	0.208530i	−0.0392743	+	0.999228i	$0.512505\pi$
$504$	−2.40483	−	8.97494i	−0.107119	−	0.399775i
$505$	12.0067	−	10.6688i	0.534293	−	0.474754i
$506$	0.0581183	+	0.0692627i	0.00258367	+	0.00307910i
$507$	1.46567	−	5.46997i	0.0650929	−	0.242930i
$508$	10.2824	−	2.75515i	0.456206	−	0.122240i
$509$	−5.57883	−	31.6391i	−0.247277	−	1.40238i	−0.815143	−	0.579259i	$-0.803342\pi$
$509$	−5.57883	−	31.6391i	−0.247277	−	1.40238i	0.567866	−	0.823121i	$-0.307769\pi$
$510$	1.35730	−	1.00887i	0.0601022	−	0.0446735i
$511$	−17.9970	−	49.4464i	−0.796141	−	2.18738i
$512$	1.00000			0.0441942
$513$	−0.134977	−	0.370847i	−0.00595940	−	0.0163733i
$514$	2.37403	+	0.418606i	0.104714	+	0.0184639i
$515$	3.80801	+	18.5131i	0.167801	+	0.815787i
$516$	−1.52847	−	0.133723i	−0.0672869	−	0.00588684i
$517$	4.18018	−	4.18018i	0.183844	−	0.183844i
$518$	−13.4258	+	16.1496i	−0.589897	+	0.709572i
$519$			8.57155i			0.376249i
$520$	−0.106177	−	3.74688i	−0.00465617	−	0.164311i
$521$	15.6198	−	18.6149i	0.684315	−	0.815535i	−0.306340	−	0.951922i	$-0.599105\pi$
$521$	15.6198	−	18.6149i	0.684315	−	0.815535i	0.990656	+	0.136387i	$0.0435490\pi$
$522$	7.05495	+	10.0755i	0.308787	+	0.440993i
$523$	−19.2963	+	7.02328i	−0.843769	+	0.307107i	−0.727497	−	0.686111i	$-0.759316\pi$
$523$	−19.2963	+	7.02328i	−0.843769	+	0.307107i	−0.116272	+	0.993217i	$0.537094\pi$
$524$	−4.85702	+	4.85702i	−0.212180	+	0.212180i
$525$	−8.02346	+	5.25969i	−0.350173	+	0.229552i
$526$	0.762661	−	2.84629i	0.0332536	−	0.124104i
$527$	6.68578	−	9.54828i	0.291237	−	0.415929i
$528$	−0.0944624	−	0.352539i	−0.00411095	−	0.0153423i
$529$	11.4905	+	19.9022i	0.499588	+	0.865312i
$530$	−9.69327	−	9.15905i	−0.421049	−	0.397844i
$531$	11.2002	−	7.84247i	0.486048	−	0.340334i
$532$	0.215406	−	0.373094i	0.00933903	−	0.0161757i
$533$	−4.18487	+	11.4978i	−0.181267	+	0.498027i
$534$	−0.162892	+	0.447542i	−0.00704902	+	0.0193670i
$535$	−11.0128	−	36.8870i	−0.476123	−	1.59477i
$536$	15.3179	−	1.34014i	0.661633	−	0.0578854i
$537$	0.790589	−	0.942188i	0.0341165	−	0.0406584i
$538$	16.9482	−	2.98842i	0.730689	−	0.128840i
$539$	−3.03666	−	1.10525i	−0.130798	−	0.0476066i
$540$	1.63619	−	6.88035i	0.0704103	−	0.296083i
$541$	36.5920	−	9.80481i	1.57322	−	0.421542i	0.636398	−	0.771361i	$-0.280424\pi$
$541$	36.5920	−	9.80481i	1.57322	−	0.421542i	0.936817	+	0.349819i	$0.113757\pi$
$542$	1.89873	−	10.7682i	0.0815573	−	0.462535i
$543$	−7.11395	−	0.622390i	−0.305289	−	0.0267093i
$544$	−1.17859	+	0.680462i	−0.0505318	+	0.0291746i
$545$	24.2899	+	10.4995i	1.04047	+	0.449750i
$546$	−3.16759	+	0.558532i	−0.135560	+	0.0239030i
$547$	−4.04166	−	7.00036i	−0.172809	−	0.299314i	0.766592	−	0.642135i	$-0.221951\pi$
$547$	−4.04166	−	7.00036i	−0.172809	−	0.299314i	−0.939401	+	0.342821i	$0.888618\pi$
$548$	−13.5562	−	6.32134i	−0.579090	−	0.270034i
$549$	10.6176	+	10.6176i	0.453147	+	0.453147i
$550$	2.74622	−	1.80025i	0.117099	−	0.0767631i
$551$	−0.0990314	+	0.561635i	−0.00421888	+	0.0239265i
$552$	0.00666836	+	0.0762196i	0.000283824	+	0.00324412i
$553$	20.5125	−	17.2120i	0.872279	−	0.731929i
$554$	12.0763			0.513071
$555$	−7.01412	+	2.81752i	−0.297733	+	0.119597i
$556$	−4.04937			−0.171731
$557$	−19.0089	+	15.9504i	−0.805432	+	0.675838i	−0.949513	−	0.313728i	$-0.898422\pi$
$557$	−19.0089	+	15.9504i	−0.805432	+	0.675838i	0.144080	+	0.989566i	$0.453978\pi$
$558$	−2.00891	−	22.9620i	−0.0850441	−	0.972059i
$559$	0.803656	−	4.55776i	0.0339910	−	0.192773i
$560$	6.90173	−	3.45962i	0.291651	−	0.146196i
$561$	0.351222	+	0.351222i	0.0148286	+	0.0148286i
$562$	15.9294	+	7.42802i	0.671943	+	0.313332i
$563$	−15.5635	−	26.9568i	−0.655923	−	1.13609i	−0.981662	−	0.190632i	$-0.938946\pi$
$563$	−15.5635	−	26.9568i	−0.655923	−	1.13609i	0.325738	−	0.945460i	$-0.394387\pi$
$564$	4.92650	−	0.868675i	0.207443	−	0.0365778i
$565$	15.5755	−	6.17408i	0.655268	−	0.259746i
$566$	15.6716	−	9.04801i	0.658727	−	0.380316i
$567$	21.7230	+	1.90052i	0.912281	+	0.0798142i
$568$	1.46228	−	8.29298i	0.0613558	−	0.347966i
$569$	34.1575	−	9.15247i	1.43196	−	0.383691i	0.542247	−	0.840219i	$-0.317574\pi$
$569$	34.1575	−	9.15247i	1.43196	−	0.383691i	0.889709	+	0.456528i	$0.150907\pi$
$570$	0.132034	−	0.0813016i	0.00553030	−	0.00340535i
$571$	−26.0017	−	9.46386i	−1.08814	−	0.396050i	−0.265208	−	0.964191i	$-0.585441\pi$
$571$	−26.0017	−	9.46386i	−1.08814	−	0.396050i	−0.822931	+	0.568141i	$0.807663\pi$
$572$	1.08418	−	0.191171i	0.0453320	−	0.00799326i
$573$	6.83929	−	8.15075i	0.285715	−	0.340502i
$574$	−25.1052	+	2.19642i	−1.04787	+	0.0916770i
$575$	−0.632486	+	0.271690i	−0.0263765	+	0.0113303i
$576$	−0.920429	+	2.52886i	−0.0383512	+	0.105369i
$577$	5.37329	−	14.7630i	0.223693	−	0.614591i	−0.776180	−	0.630511i	$-0.782845\pi$
$577$	5.37329	−	14.7630i	0.223693	−	0.614591i	0.999873	+	0.0159198i	$0.00506763\pi$
$578$	−7.57394	+	13.1185i	−0.315035	+	0.545656i
$579$	3.31175	−	2.31891i	0.137632	−	0.0963706i
$580$	−7.01900	+	7.42840i	−0.291448	+	0.308448i
$581$	5.04790	+	8.74322i	0.209422	+	0.362730i
$582$	2.47859	+	9.25021i	0.102741	+	0.383433i
$583$	2.24659	−	3.20846i	0.0930441	−	0.132881i
$584$	−3.94454	+	14.7212i	−0.163226	+	0.609168i
$585$	9.57305	+	3.18023i	0.395797	+	0.131486i
$586$	−2.94580	+	2.94580i	−0.121690	+	0.121690i
$587$	17.3006	−	6.29691i	0.714073	−	0.259901i	0.0406656	−	0.999173i	$-0.487052\pi$
$587$	17.3006	−	6.29691i	0.714073	−	0.259901i	0.673408	+	0.739271i	$0.264830\pi$
$588$	−1.56848	−	2.24002i	−0.0646829	−	0.0923768i
$589$	0.686962	−	0.818690i	0.0283058	−	0.0337335i
$590$	8.25761	+	7.80250i	0.339960	+	0.321224i
$591$		−	3.34195i		−	0.137470i
$592$	5.86824	−	1.60117i	0.241183	−	0.0658076i
$593$	20.0059	−	20.0059i	0.821545	−	0.821545i	−0.164784	−	0.986330i	$-0.552693\pi$
$593$	20.0059	−	20.0059i	0.821545	−	0.821545i	0.986330	+	0.164784i	$0.0526928\pi$
$594$	2.06922	+	0.181034i	0.0849013	+	0.00742790i
$595$	−5.78020	+	8.77386i	−0.236965	+	0.359693i
$596$	7.04703	+	1.24258i	0.288658	+	0.0508981i
$597$	−2.96294	−	8.14061i	−0.121265	−	0.333173i
$598$	−0.230787			−0.00943758
$599$	10.5315	+	28.9351i	0.430306	+	1.18226i	0.945625	+	0.325259i	$0.105451\pi$
$599$	10.5315	+	28.9351i	0.430306	+	1.18226i	−0.515319	+	0.856999i	$0.672326\pi$
$600$	2.77739	+	0.0850332i	0.113386	+	0.00347147i
$601$	−1.15417	−	6.54564i	−0.0470797	−	0.267002i	0.952177	−	0.305546i	$-0.0988391\pi$
$601$	−1.15417	−	6.54564i	−0.0470797	−	0.267002i	−0.999257	+	0.0385441i	$0.987728\pi$
$602$	9.20733	−	2.46710i	0.375263	−	0.100551i
$603$	−10.7100	+	39.9703i	−0.436146	+	1.62772i
$604$	−3.42109	−	4.07709i	−0.139202	−	0.165894i
$605$	−15.6973	−	17.6659i	−0.638185	−	0.718219i
$606$	1.03319	+	3.85590i	0.0419703	+	0.156635i
$607$	−30.1055	−	10.9575i	−1.22194	−	0.444751i	−0.351113	−	0.936333i	$-0.614197\pi$
$607$	−30.1055	−	10.9575i	−1.22194	−	0.444751i	−0.870831	+	0.491582i	$0.836419\pi$
$608$	−0.113087	+	0.0527336i	−0.00458630	+	0.00213863i
$609$	7.18369	+	5.03007i	0.291098	+	0.203829i
$610$	−6.86375	+	10.4186i	−0.277905	+	0.421837i
$611$	1.31514	+	15.0321i	0.0532048	+	0.608134i
$612$	−0.635979	−	3.60682i	−0.0257079	−	0.145797i
$613$	0.717133	+	1.53790i	0.0289647	+	0.0621151i	0.920258	−	0.391313i	$-0.127979\pi$
$613$	0.717133	+	1.53790i	0.0289647	+	0.0621151i	−0.891293	+	0.453428i	$0.850201\pi$
$614$	27.1689	−	12.6691i	1.09645	−	0.511282i
$615$	−8.32586	−	3.59892i	−0.335731	−	0.145123i
$616$	1.30057	+	1.85740i	0.0524014	+	0.0748369i
$617$	2.62692	−	30.0258i	0.105756	−	1.20879i	−0.739024	−	0.673680i	$-0.764713\pi$
$617$	2.62692	−	30.0258i	0.105756	−	1.20879i	0.844779	−	0.535115i	$-0.179732\pi$
$618$	−4.53740	−	1.21579i	−0.182521	−	0.0489064i
$619$	−6.97481	+	12.0807i	−0.280341	+	0.485565i	−0.971469	−	0.237168i	$-0.923781\pi$
$619$	−6.97481	+	12.0807i	−0.280341	+	0.485565i	0.691128	+	0.722733i	$0.257114\pi$
$620$	18.3515	−	5.47890i	0.737013	−	0.220038i
$621$	−0.420598	−	0.112699i	−0.0168780	−	0.00452245i
$622$	−14.1999	+	30.4518i	−0.569364	+	1.22100i
$623$		−	2.95887i		−	0.118545i
$624$	0.844315	+	0.393711i	0.0337997	+	0.0157610i
$625$	7.09734	+	23.9714i	0.283894	+	0.958856i
$626$	14.5393	+	12.1999i	0.581108	+	0.487608i
$627$	0.0292731	+	0.0348864i	0.00116906	+	0.00139323i
$628$	1.30078	+	1.30078i	0.0519068	+	0.0519068i
$629$	−5.82674	+	5.88024i	−0.232327	+	0.234461i
$630$	2.39634	+	20.6378i	0.0954726	+	0.822232i
$631$	−0.434125	+	4.96207i	−0.0172823	+	0.197537i	0.982645	+	0.185495i	$0.0593888\pi$
$631$	−0.434125	+	4.96207i	−0.0172823	+	0.197537i	−0.999927	+	0.0120422i	$0.996167\pi$
$632$	−7.72608	+	0.675945i	−0.307327	+	0.0268876i
$633$	−6.95645	+	4.87096i	−0.276494	+	0.193603i
$634$	−3.69677	+	7.92776i	−0.146818	+	0.314851i
$635$	−23.6443	+	2.74543i	−0.938295	+	0.108949i
$636$	3.11455	−	1.13360i	0.123500	−	0.0449503i
$637$	7.14342	−	4.12426i	0.283033	−	0.163409i
$638$	−2.45879	−	1.72166i	−0.0973444	−	0.0681613i
$639$	19.6259	+	11.3310i	0.776387	+	0.448247i
$640$	−2.21221	−	0.325756i	−0.0874454	−	0.0128767i
$641$	−11.7529	+	9.86185i	−0.464211	+	0.389520i	−0.844678	−	0.535275i	$-0.820208\pi$
$641$	−11.7529	+	9.86185i	−0.464211	+	0.389520i	0.380466	+	0.924795i	$0.375763\pi$
$642$	9.42218	+	1.66138i	0.371864	+	0.0655696i
$643$	−11.9442	−	6.89599i	−0.471034	−	0.271951i	0.245639	−	0.969361i	$-0.421002\pi$
$643$	−11.9442	−	6.89599i	−0.471034	−	0.271951i	−0.716672	+	0.697410i	$0.754336\pi$
$644$	−0.200886	−	0.430801i	−0.00791602	−	0.0169760i
$645$	3.33773	+	0.793732i	0.131423	+	0.0312532i
$646$	0.0974011	−	0.139103i	0.00383219	−	0.00547294i
$647$	1.92979	+	1.61928i	0.0758677	+	0.0636606i	0.679933	−	0.733274i	$-0.262009\pi$
$647$	1.92979	+	1.61928i	0.0758677	+	0.0636606i	−0.604065	+	0.796935i	$0.706453\pi$
$648$	−4.83817	−	4.05971i	−0.190061	−	0.159480i
$649$	−1.91385	+	2.73325i	−0.0751250	+	0.107290i
$650$	−0.985684	+	8.32348i	−0.0386617	+	0.326474i
$651$	−6.94535	−	14.8943i	−0.272210	−	0.583755i
$652$	−12.0706	−	6.96899i	−0.472723	−	0.272927i
$653$	19.4962	+	3.43771i	0.762945	+	0.134528i	0.541564	−	0.840660i	$-0.317832\pi$
$653$	19.4962	+	3.43771i	0.762945	+	0.134528i	0.221381	+	0.975187i	$0.428944\pi$
$654$	−5.03806	+	4.22743i	−0.197004	+	0.165306i
$655$	12.3270	−	9.16255i	0.481654	−	0.358010i
$656$	6.32124	+	3.64957i	0.246803	+	0.142492i
$657$	−33.5972	−	23.5250i	−1.31075	−	0.917798i
$658$	−26.9151	+	15.5395i	−1.04926	+	0.605791i
$659$	3.54502	−	1.29028i	0.138094	−	0.0502622i	−0.272048	−	0.962284i	$-0.587701\pi$
$659$	3.54502	−	1.29028i	0.138094	−	0.0502622i	0.410143	+	0.912021i	$0.365479\pi$
$660$	0.0941292	+	0.810662i	0.00366397	+	0.0315550i
$661$	−7.38842	+	15.8445i	−0.287376	+	0.616280i	−0.996005	−	0.0893016i	$-0.971537\pi$
$661$	−7.38842	+	15.8445i	−0.287376	+	0.616280i	0.708628	+	0.705582i	$0.249314\pi$
$662$	−13.7832	+	9.65111i	−0.535700	+	0.375101i
$663$	−1.26301	+	0.110499i	−0.0490513	+	0.00429143i
$664$	0.254852	−	2.91297i	0.00989018	−	0.113045i
$665$	−0.598061	+	0.755193i	−0.0231918	+	0.0292851i
$666$	−1.35218	+	16.3137i	−0.0523958	+	0.632144i
$667$	0.444940	+	0.444940i	0.0172281	+	0.0172281i
$668$	−3.00511	−	3.58136i	−0.116271	−	0.138567i
$669$	4.05998	+	3.40673i	0.156968	+	0.131712i
$670$	−34.3230	−	2.02523i	−1.32601	−	0.0782414i
$671$	−3.32101	−	1.54861i	−0.128206	−	0.0597835i
$672$			1.91875i			0.0740175i
$673$	−6.27635	+	13.4597i	−0.241936	+	0.518833i	−0.989355	−	0.145519i	$-0.953515\pi$
$673$	−6.27635	+	13.4597i	−0.241936	+	0.518833i	0.747420	+	0.664352i	$0.231292\pi$
$674$	33.2562	+	8.91097i	1.28098	+	0.343238i
$675$	−5.86091	+	14.6878i	−0.225587	+	0.565333i
$676$	5.09496	−	8.82474i	0.195960	−	0.339413i
$677$	24.9598	+	6.68796i	0.959283	+	0.257039i	0.704297	−	0.709905i	$-0.251262\pi$
$677$	24.9598	+	6.68796i	0.959283	+	0.257039i	0.254986	+	0.966945i	$0.417929\pi$
$678$	−0.362924	+	4.14824i	−0.0139380	+	0.159312i
$679$	−34.1254	−	48.7361i	−1.30961	−	1.87032i
$680$	2.82897	−	1.12139i	0.108486	−	0.0430034i
$681$	−0.462235	+	0.215544i	−0.0177129	+	0.00825966i
$682$	2.37721	+	5.09795i	0.0910281	+	0.195210i
$683$	0.115887	+	0.657229i	0.00443430	+	0.0251482i	0.986945	−	0.161060i	$-0.0514912\pi$
$683$	0.115887	+	0.657229i	0.00443430	+	0.0251482i	−0.982510	+	0.186208i	$0.940380\pi$
$684$	−0.0292667	−	0.334520i	−0.00111904	−	0.0127907i
$685$	27.9299	+	18.4001i	1.06715	+	0.703034i
$686$	−5.88104	−	4.11795i	−0.224539	−	0.157224i
$687$	5.19037	−	2.42031i	0.198025	−	0.0923406i
$688$	−2.59434	−	0.944263i	−0.0989083	−	0.0359997i
$689$	2.58758	+	9.65699i	0.0985790	+	0.367902i
$690$	0.0100772	−	0.170786i	0.000383634	−	0.00650172i
$691$	−13.1759	−	15.7024i	−0.501234	−	0.597348i	0.454803	−	0.890592i	$-0.349710\pi$
$691$	−13.1759	−	15.7024i	−0.501234	−	0.597348i	−0.956038	+	0.293244i	$0.905265\pi$
$692$	−3.99195	+	14.8982i	−0.151751	+	0.566344i
$693$	−5.89419	+	1.57934i	−0.223902	+	0.0599943i
$694$	2.30370	+	13.0649i	0.0874473	+	0.495938i
$695$	8.95806	+	1.31911i	0.339799	+	0.0500366i
$696$	−0.868732	−	2.38682i	−0.0329292	−	0.0904722i
$697$	−9.93357			−0.376261
$698$	−6.00947	−	16.5109i	−0.227462	−	0.624946i
$699$	2.75921	+	0.486523i	0.104363	+	0.0184020i
$700$	−16.3951	+	5.40514i	−0.619676	+	0.204295i
$701$	46.7599	+	4.09096i	1.76610	+	0.154513i	0.923391	−	0.383861i	$-0.125406\pi$
$701$	46.7599	+	4.09096i	1.76610	+	0.154513i	0.842706	+	0.538374i	$0.180961\pi$
$702$	−3.74899	+	3.74899i	−0.141497	+	0.141497i
$703$	−0.579189	+	0.490525i	−0.0218445	+	0.0185005i
$704$		−	0.656739i		−	0.0247518i
$705$	−11.1814	+	0.316854i	−0.421118	+	0.0119334i
$706$	−21.7095	+	25.8723i	−0.817047	+	0.973719i
$707$	−14.2250	−	20.3154i	−0.534986	−	0.764039i
$708$	−2.65325	+	0.965705i	−0.0997154	+	0.0362934i
$709$	26.3597	−	26.3597i	0.989959	−	0.989959i	−0.00999127	−	0.999950i	$-0.503180\pi$
$709$	26.3597	−	26.3597i	0.989959	−	0.989959i	0.999950	+	0.00999127i	$0.00318037\pi$
$710$	−5.93636	+	17.8695i	−0.222788	+	0.670630i
$711$	5.40195	−	20.1603i	0.202589	−	0.756072i
$712$	−0.491551	+	0.702008i	−0.0184217	+	0.0263089i
$713$	−0.305194	−	1.13900i	−0.0114296	−	0.0426558i
$714$	−1.30564	−	2.26143i	−0.0488623	−	0.0846319i
$715$	−2.46072	+	0.0697306i	−0.0920257	+	0.00260778i
$716$	1.81292	−	1.26942i	0.0677519	−	0.0474404i
$717$	1.67734	−	2.90524i	0.0626415	−	0.108498i
$718$	12.4820	−	34.2939i	0.465823	−	1.27984i
$719$	7.82976	−	21.5121i	0.292001	−	0.802266i	−0.703773	−	0.710425i	$-0.748503\pi$
$719$	7.82976	−	21.5121i	0.292001	−	0.802266i	0.995774	−	0.0918408i	$-0.0292751\pi$
$720$	2.85998	−	5.29454i	0.106585	−	0.197316i
$721$	29.0728	−	2.54354i	1.08273	−	0.0947263i
$722$	−12.2030	+	14.5429i	−0.454147	+	0.541231i
$723$	5.26645	−	0.928618i	0.195861	−	0.0345357i
$724$	−12.0749	−	4.39489i	−0.448759	−	0.163335i
$725$	17.9474	−	14.1467i	0.666548	−	0.525396i
$726$	5.67329	−	1.52015i	0.210556	−	0.0564182i
$727$	2.35531	−	13.3576i	0.0873535	−	0.495406i	−0.909470	−	0.415769i	$-0.863513\pi$
$727$	2.35531	−	13.3576i	0.0873535	−	0.495406i	0.996824	−	0.0796377i	$-0.0253763\pi$
$728$	−5.76570	−	0.504433i	−0.213691	−	0.0186955i
$729$	10.1530	−	5.86185i	0.376038	−	0.217105i
$730$	13.5217	−	31.2815i	0.500460	−	1.15778i
$731$	3.70021	−	0.652447i	0.136857	−	0.0241316i
$732$	−1.55039	−	2.68536i	−0.0573041	−	0.0992537i
$733$	13.1948	+	6.15285i	0.487362	+	0.227261i	0.650737	−	0.759303i	$-0.274460\pi$
$733$	13.1948	+	6.15285i	0.487362	+	0.227261i	−0.163374	+	0.986564i	$0.552238\pi$
$734$	7.39735	+	7.39735i	0.273041	+	0.273041i
$735$	2.74010	+	5.46634i	0.101070	+	0.201629i
$736$	−0.0239069	+	0.135583i	−0.000881219	+	0.00499764i
$737$	−0.880125	−	10.0599i	−0.0324198	−	0.370560i
$738$	−15.0475	+	12.6263i	−0.553906	+	0.464782i
$739$	−50.1213			−1.84374			−0.921871	−	0.387496i	$-0.873340\pi$
$739$	−50.1213			−1.84374			−0.921871	+	0.387496i	$0.873340\pi$
$740$	−13.5034	+	1.63050i	−0.496394	+	0.0599385i
$741$	−0.116243			−0.00427030
$742$	−15.7740	+	13.2360i	−0.579082	+	0.485907i
$743$	−1.73315	−	19.8100i	−0.0635831	−	0.726759i	−0.959347	−	0.282229i	$-0.908926\pi$
$743$	−1.73315	−	19.8100i	−0.0635831	−	0.726759i	0.895764	−	0.444530i	$-0.146629\pi$
$744$	−0.826546	+	4.68758i	−0.0303027	+	0.171855i
$745$	−15.1847	−	5.04447i	−0.556326	−	0.184815i
$746$	−5.51390	−	5.51390i	−0.201878	−	0.201878i
$747$	7.13192	+	3.32567i	0.260943	+	0.121680i
$748$	0.446886	+	0.774029i	0.0163398	+	0.0283013i
$749$	−58.5369	+	10.3216i	−2.13889	+	0.377144i
$750$	−6.11647	−	1.09286i	−0.223342	−	0.0399058i
$751$	−42.3977	+	24.4783i	−1.54711	+	0.893227i	−0.548754	+	0.835984i	$0.684898\pi$
$751$	−42.3977	+	24.4783i	−1.54711	+	0.893227i	−0.998360	+	0.0572430i	$0.981769\pi$
$752$	8.96729	+	0.784536i	0.327003	+	0.0286091i
$753$	2.26171	−	12.8268i	0.0824214	−	0.467435i
$754$	7.40059	−	1.98298i	0.269514	−	0.0722160i
$755$	6.24003	+	10.1338i	0.227098	+	0.368808i
$756$	−10.2614	−	3.73483i	−0.373202	−	0.135835i
$757$	−17.9294	+	3.16143i	−0.651654	+	0.114904i	−0.489696	−	0.871893i	$-0.662892\pi$
$757$	−17.9294	+	3.16143i	−0.651654	+	0.114904i	−0.161958	+	0.986798i	$0.551781\pi$
$758$	−7.18573	+	8.56362i	−0.260998	+	0.311045i
$759$	0.0500564	−	0.00437937i	0.00181693	−	0.000158961i
$760$	0.267352	−	0.0798188i	0.00969787	−	0.00289533i
$761$	−8.84775	+	24.3090i	−0.320731	+	0.881201i	0.669631	+	0.742694i	$0.266452\pi$
$761$	−8.84775	+	24.3090i	−0.320731	+	0.881201i	−0.990362	+	0.138507i	$0.955770\pi$
$762$	2.02335	−	5.55911i	0.0732983	−	0.201385i
$763$	20.4295	−	35.3849i	0.739598	−	1.28102i
$764$	15.6833	−	10.9816i	0.567402	−	0.397299i
$765$	0.231977	+	8.18622i	0.00838713	+	0.295973i
$766$	−4.72006	−	8.17539i	−0.170543	−	0.295389i
$767$	−2.20434	−	8.22670i	−0.0795940	−	0.297049i
$768$	0.318758	−	0.455234i	0.0115022	−	0.0164268i
$769$	−13.9778	+	52.1659i	−0.504053	+	1.88115i	−0.0321834	+	0.999482i	$0.510246\pi$
$769$	−13.9778	+	52.1659i	−0.504053	+	1.88115i	−0.471869	+	0.881669i	$0.656421\pi$
$770$	−2.27207	−	4.53264i	−0.0818797	−	0.163345i
$771$	0.947307	−	0.947307i	0.0341164	−	0.0341164i
$772$	6.83610	−	2.48814i	0.246037	−	0.0895500i
$773$	−25.9464	−	37.0552i	−0.933226	−	1.33278i	−0.942986	−	0.332832i	$-0.891996\pi$
$773$	−25.9464	−	37.0552i	−0.933226	−	1.33278i	0.00976061	−	0.999952i	$-0.496893\pi$
$774$	4.77581	−	5.69159i	0.171663	−	0.204580i
$775$	−42.3822	+	6.14238i	−1.52241	+	0.220641i
$776$			17.2321i			0.618595i
$777$	3.07224	+	11.2597i	0.110216	+	0.403940i
$778$	−4.72629	+	4.72629i	−0.169446	+	0.169446i
$779$	−0.907307	−	0.0793791i	−0.0325077	−	0.00284405i
$780$	−1.73955	−	1.14601i	−0.0622859	−	0.0410338i
$781$	−5.44632	−	0.960334i	−0.194885	−	0.0343634i
$782$	−0.0640823	−	0.176065i	−0.00229158	−	0.00629606i
$783$	14.4555			0.516599
$784$	−1.68294	−	4.62384i	−0.0601050	−	0.165137i
$785$	−2.45387	−	3.30134i	−0.0875823	−	0.117830i
$786$	0.662865	+	3.75929i	0.0236436	+	0.134090i
$787$	−42.0648	+	11.2712i	−1.49945	+	0.401776i	−0.912916	−	0.408148i	$-0.866175\pi$
$787$	−42.0648	+	11.2712i	−1.49945	+	0.401776i	−0.586534	+	0.809925i	$0.699508\pi$
$788$	1.55642	−	5.80863i	0.0554451	−	0.206924i
$789$	−1.05262	−	1.25447i	−0.0374744	−	0.0446602i
$790$	17.3119	+	1.02149i	0.615931	+	0.0363429i
$791$	−6.69567	−	24.9886i	−0.238071	−	0.888492i
$792$	1.66080	+	0.604482i	0.0590140	+	0.0214793i
$793$	8.47687	−	3.95283i	0.301023	−	0.140369i
$794$	−12.0739	−	8.45421i	−0.428485	−	0.300029i
$795$	−7.25932	+	1.49319i	−0.257462	+	0.0529578i
$796$	−1.35862	−	15.5291i	−0.0481549	−	0.550413i
$797$	5.64663	+	32.0236i	0.200014	+	1.13433i	0.905095	+	0.425208i	$0.139799\pi$
$797$	5.64663	+	32.0236i	0.200014	+	1.13433i	−0.705082	+	0.709126i	$0.749090\pi$
$798$	−0.101183	−	0.216987i	−0.00358183	−	0.00768125i
$799$	−11.1026	+	5.17725i	−0.392783	+	0.183158i
$800$	4.78777	+	1.44128i	0.169273	+	0.0509571i
$801$	−1.32284	−	1.88921i	−0.0467403	−	0.0667520i
$802$	−1.85410	+	21.1925i	−0.0654707	+	0.748334i
$803$	9.66800	+	2.59053i	0.341176	+	0.0914179i
$804$	4.27263	−	7.40042i	0.150684	−	0.260993i
$805$	0.304066	+	1.01846i	0.0107169	+	0.0358961i
$806$	−13.8685	−	3.71605i	−0.488497	−	0.130892i
$807$	4.04195	−	8.66798i	0.142283	−	0.305127i
$808$			7.18310i			0.252701i
$809$	−37.2037	−	17.3484i	−1.30801	−	0.609937i	−0.361431	−	0.932399i	$-0.617712\pi$
$809$	−37.2037	−	17.3484i	−1.30801	−	0.609937i	−0.946582	+	0.322462i	$0.895490\pi$
$810$	9.38058	+	10.5570i	0.329600	+	0.370935i
$811$	5.24564	+	4.40161i	0.184199	+	0.154562i	0.730225	−	0.683207i	$-0.239415\pi$
$811$	5.24564	+	4.40161i	0.184199	+	0.154562i	−0.546025	+	0.837769i	$0.683860\pi$
$812$	10.1433	+	12.0883i	0.355961	+	0.424218i
$813$	−4.29683	−	4.29683i	−0.150696	−	0.150696i
$814$	−1.05155	−	3.85390i	−0.0368568	−	0.135079i
$815$	24.4326	+	19.3490i	0.855837	+	0.677765i
$816$	−0.0659174	+	0.753439i	−0.00230757	+	0.0263756i
$817$	0.343182	−	0.0300245i	0.0120064	−	0.00105042i
$818$	−23.0937	+	16.1704i	−0.807454	+	0.565385i
$819$	6.58256	−	14.1163i	0.230013	−	0.493265i
$820$	−12.7950	−	10.1328i	−0.446822	−	0.353853i
$821$	−27.1130	+	9.86832i	−0.946250	+	0.344407i	−0.768631	−	0.639693i	$-0.779062\pi$
$821$	−27.1130	+	9.86832i	−0.946250	+	0.344407i	−0.177619	+	0.984099i	$0.556839\pi$
$822$	−7.19882	+	4.15624i	−0.251088	+	0.144966i
$823$	41.0913	+	28.7725i	1.43235	+	1.00294i	0.994593	+	0.103853i	$0.0331173\pi$
$823$	41.0913	+	28.7725i	1.43235	+	1.00294i	0.437761	+	0.899091i	$0.355772\pi$
$824$	−7.32022	−	4.22633i	−0.255012	−	0.147231i
$825$	0.0558446	−	1.82402i	0.00194426	−	0.0635042i
$826$	13.4377	−	11.2756i	0.467558	−	0.392328i
$827$	−28.7564	−	5.07053i	−0.999959	−	0.176320i	−0.350375	−	0.936610i	$-0.613946\pi$
$827$	−28.7564	−	5.07053i	−0.999959	−	0.176320i	−0.649584	+	0.760290i	$0.725057\pi$
$828$	−0.320865	−	0.185251i	−0.0111508	−	0.00643793i
$829$	18.0511	+	38.7107i	0.626941	+	1.34448i	0.921326	+	0.388791i	$0.127107\pi$
$829$	18.0511	+	38.7107i	0.626941	+	1.34448i	−0.294385	+	0.955687i	$0.595115\pi$
$830$	−1.51271	+	6.36109i	−0.0525068	+	0.220797i
$831$	3.84941	−	5.49752i	0.133534	−	0.190707i
$832$	1.28414	+	1.07752i	0.0445196	+	0.0373564i
$833$	5.12985	+	4.30445i	0.177739	+	0.149140i
$834$	−1.29077	+	1.84341i	−0.0446957	+	0.0638321i
$835$	5.48130	+	8.90165i	0.189688	+	0.308054i
$836$	0.0346322	+	0.0742689i	0.00119778	+	0.00256865i
$837$	−23.4600	−	13.5446i	−0.810896	−	0.468171i
$838$	−3.21647	−	0.567150i	−0.111111	−	0.0195919i
$839$	15.8495	−	13.2993i	0.547184	−	0.459142i	−0.326802	−	0.945093i	$-0.605971\pi$
$839$	15.8495	−	13.2993i	0.547184	−	0.459142i	0.873986	+	0.485951i	$0.161527\pi$
$840$	0.625046	−	4.24469i	0.0215661	−	0.146456i
$841$	7.02390	+	4.05525i	0.242204	+	0.139836i
$842$	−24.7292	−	17.3156i	−0.852224	−	0.596733i
$843$	8.45913	−	4.88388i	0.291348	−	0.168210i
$844$	−14.3595	+	5.22642i	−0.494273	+	0.179901i
$845$	−14.1459	+	17.8625i	−0.486632	+	0.614488i
$846$	−10.2377	+	21.9549i	−0.351981	+	0.754825i
$847$	−29.8906	+	20.9296i	−1.02705	+	0.719150i
$848$	5.94132	−	0.519799i	0.204026	−	0.0178500i
$849$	0.876494	−	10.0184i	0.0300812	−	0.343830i
$850$	−6.62357	+	1.55920i	−0.227187	+	0.0534802i
$851$	0.0767991	+	0.833911i	0.00263264	+	0.0285861i
$852$	−3.30913	−	3.30913i	−0.113369	−	0.113369i
$853$	−3.97503	−	4.73726i	−0.136103	−	0.162201i	0.693688	−	0.720276i	$-0.255985\pi$
$853$	−3.97503	−	4.73726i	−0.136103	−	0.162201i	−0.829791	+	0.558075i	$0.811540\pi$
$854$	14.7572	+	12.3828i	0.504981	+	0.423729i
$855$	−0.0442279	+	0.749562i	−0.00151256	+	0.0256345i
$856$	15.6029	+	7.27575i	0.533296	+	0.248680i
$857$		−	26.7830i		−	0.914890i	−0.889238	−	0.457445i	$-0.848765\pi$
$857$		−	26.7830i		−	0.914890i	0.889238	−	0.457445i	$-0.151235\pi$
$858$	0.258565	−	0.554495i	0.00882727	−	0.0189301i
$859$	−52.0493	−	13.9466i	−1.77590	−	0.475850i	−0.786072	−	0.618135i	$-0.787889\pi$
$859$	−52.0493	−	13.9466i	−1.77590	−	0.475850i	−0.989826	+	0.142284i	$0.954555\pi$
$860$	5.43163	+	2.93403i	0.185217	+	0.100050i
$861$	−7.00262	+	12.1289i	−0.238649	+	0.413352i
$862$	−24.0288	−	6.43850i	−0.818424	−	0.219296i
$863$	−0.234301	+	2.67808i	−0.00797571	+	0.0911628i	−0.999139	−	0.0414831i	$-0.986792\pi$
$863$	−0.234301	+	2.67808i	−0.00797571	+	0.0911628i	0.991163	+	0.132646i	$0.0423473\pi$
$864$	1.81410	+	2.59081i	0.0617170	+	0.0881411i
$865$	13.6842	−	31.6575i	0.465278	−	1.07639i
$866$	33.5505	−	15.6449i	1.14009	−	0.531635i
$867$	3.55771	+	7.62953i	0.120826	+	0.259113i
$868$	−5.13506	−	29.1224i	−0.174295	−	0.988478i
$869$	0.443919	+	5.07402i	0.0150589	+	0.172124i
$870$	1.14430	+	5.56315i	0.0387953	+	0.188608i
$871$	21.1144	+	14.7845i	0.715434	+	0.500952i
$872$	−10.7254	+	5.00135i	−0.363209	+	0.169367i
$873$	−43.5775	−	15.8609i	−1.47487	−	0.536810i
$874$	−0.00444619	−	0.0165934i	−0.000150394	−	0.000561280i
$875$	38.0302	−	6.61651i	1.28566	−	0.223679i
$876$	5.44424	+	6.48820i	0.183944	+	0.219216i
$877$	−0.0602456	+	0.224840i	−0.00203435	+	0.00759230i	−0.966936	−	0.255021i	$-0.917918\pi$
$877$	−0.0602456	+	0.224840i	−0.00203435	+	0.00759230i	0.964901	+	0.262613i	$0.0845843\pi$
$878$	31.7241	−	8.50045i	1.07064	−	0.286876i
$879$	0.402030	+	2.28003i	0.0135601	+	0.0769034i
$880$	−0.213937	+	1.45285i	−0.00721181	+	0.0489754i
$881$	18.5013	+	50.8320i	0.623326	+	1.71257i	0.698697	+	0.715418i	$0.253763\pi$
$881$	18.5013	+	50.8320i	0.623326	+	1.71257i	−0.0753716	+	0.997156i	$0.524014\pi$
$882$	13.2421			0.445883
$883$	16.2504	+	44.6477i	0.546871	+	1.50252i	0.837912	+	0.545805i	$0.183776\pi$
$883$	16.2504	+	44.6477i	0.546871	+	1.50252i	−0.291041	+	0.956710i	$0.594002\pi$
$884$	−2.24669	−	0.396153i	−0.0755645	−	0.0133241i
$885$	6.18415	−	1.27203i	0.207878	−	0.0427588i
$886$	23.4388	+	2.05063i	0.787442	+	0.0688922i
$887$	−19.4967	+	19.4967i	−0.654633	+	0.654633i	−0.954105	−	0.299472i	$-0.903190\pi$
$887$	−19.4967	+	19.4967i	−0.654633	+	0.654633i	0.299472	+	0.954105i	$0.403190\pi$
$888$	1.14165	−	3.18181i	0.0383111	−	0.106775i
$889$			36.7535i			1.23267i
$890$	1.31610	−	1.39286i	0.0441157	−	0.0466889i
$891$	−2.66617	+	3.17741i	−0.0893200	+	0.106447i
$892$	5.47005	+	7.81204i	0.183151	+	0.261567i
$893$	−1.05546	+	0.384156i	−0.0353196	+	0.0128553i
$894$	2.81196	−	2.81196i	0.0940461	−	0.0940461i
$895$	−4.42408	+	2.21765i	−0.147881	+	0.0741280i
$896$	−0.893604	+	3.33498i	−0.0298532	+	0.111414i
$897$	−0.0735653	+	0.105062i	−0.00245627	+	0.00350792i
$898$	−6.50412	−	24.2737i	−0.217045	−	0.810024i
$899$	19.5731	+	33.9017i	0.652801	+	1.13068i
$900$	−8.05161	+	10.7810i	−0.268387	+	0.359366i
$901$	−6.64871	+	4.65548i	−0.221501	+	0.155096i
$902$	2.39681	−	4.15140i	0.0798052	−	0.138227i
$903$	1.81181	−	4.97790i	0.0602932	−	0.165654i
$904$	−2.56272	+	7.04101i	−0.0852347	+	0.234180i
$905$	25.2805	+	13.6559i	0.840353	+	0.453938i
$906$	−2.94653	+	0.257788i	−0.0978919	+	0.00856443i
$907$	20.6607	−	24.6225i	0.686028	−	0.817577i	−0.304841	−	0.952403i	$-0.598603\pi$
$907$	20.6607	−	24.6225i	0.686028	−	0.817577i	0.990869	+	0.134826i	$0.0430477\pi$
$908$	−0.903792	+	0.159363i	−0.0299934	+	0.00528865i
$909$	−18.1650	−	6.61153i	−0.602496	−	0.219291i
$910$	12.5906	+	2.99413i	0.417375	+	0.0992543i
$911$	5.99345	−	1.60594i	0.198572	−	0.0532072i	−0.158162	−	0.987413i	$-0.550557\pi$
$911$	5.99345	−	1.60594i	0.198572	−	0.0532072i	0.356734	+	0.934206i	$0.383890\pi$
$912$	−0.0120415	+	0.0682905i	−0.000398733	+	0.00226132i
$913$	−1.91306	−	0.167371i	−0.0633131	−	0.00553918i
$914$	9.69464	−	5.59720i	0.320670	−	0.185139i
$915$	2.55502	+	6.44563i	0.0844664	+	0.213086i
$916$	10.1486	−	1.78946i	0.335318	−	0.0591256i
$917$	−11.8578	−	20.5383i	−0.391578	−	0.678234i
$918$	−3.90104	−	1.81908i	−0.128753	−	0.0600387i
$919$	16.4720	+	16.4720i	0.543361	+	0.543361i	0.924513	−	0.381151i	$-0.124472\pi$
$919$	16.4720	+	16.4720i	0.543361	+	0.543361i	−0.381151	+	0.924513i	$0.624472\pi$
$920$	0.0970540	−	0.292150i	0.00319978	−	0.00963189i
$921$	2.89292	−	16.4066i	0.0953250	−	0.540615i
$922$	2.98540	+	34.1233i	0.0983189	+	1.12379i
$923$	10.8136	−	9.07372i	0.355935	−	0.298665i
$924$	1.26012			0.0414549
$925$	30.4035	+	0.791798i	0.999661	+	0.0260342i
$926$	30.7365			1.01006
$927$	17.4255	−	14.6218i	0.572330	−	0.480242i
$928$	−0.398346	−	4.55311i	−0.0130763	−	0.149463i
$929$	2.87730	−	16.3180i	0.0944012	−	0.535376i	−0.900528	−	0.434798i	$-0.856820\pi$
$929$	2.87730	−	16.3180i	0.0944012	−	0.535376i	0.994929	−	0.100578i	$-0.0320691\pi$
$930$	3.35550	−	10.1007i	0.110031	−	0.331214i
$931$	0.434151	+	0.434151i	0.0142287	+	0.0142287i
$932$	4.56919	+	2.13065i	0.149669	+	0.0697917i
$933$	9.33635	+	16.1710i	0.305658	+	0.529416i
$934$	23.5244	−	4.14799i	0.769742	−	0.135726i
$935$	−0.736461	−	1.85789i	−0.0240849	−	0.0607596i
$936$	−3.90686	+	2.25563i	−0.127700	+	0.0737275i
$937$	−18.1228	−	1.58554i	−0.592046	−	0.0517973i	−0.212804	−	0.977095i	$-0.568260\pi$
$937$	−18.1228	−	1.58554i	−0.592046	−	0.0517973i	−0.379242	+	0.925298i	$0.623815\pi$
$938$	−9.21880	+	52.2824i	−0.301004	+	1.70708i
$939$	10.1884	−	2.72996i	0.332484	−	0.0890889i
$940$	−19.5820	−	4.65671i	−0.638694	−	0.151885i
$941$	44.7730	+	16.2961i	1.45956	+	0.531236i	0.945244	−	0.326365i	$-0.105824\pi$
$941$	44.7730	+	16.2961i	1.45956	+	0.531236i	0.514316	+	0.857601i	$0.328046\pi$
$942$	1.00679	−	0.177525i	0.0328031	−	0.00578408i
$943$	−0.645939	+	0.769800i	−0.0210347	+	0.0250681i
$944$	−5.06136	+	0.442811i	−0.164733	+	0.0144123i
$945$	21.4837	+	11.6049i	0.698864	+	0.377509i
$946$	−0.620134	+	1.70380i	−0.0201623	+	0.0553955i
$947$	17.8191	−	48.9577i	0.579044	−	1.59091i	−0.210751	−	0.977540i	$-0.567591\pi$
$947$	17.8191	−	48.9577i	0.579044	−	1.59091i	0.789795	−	0.613371i	$-0.210187\pi$
$948$	−2.15504	+	3.73264i	−0.0699925	+	0.121230i
$949$	−20.9278	+	14.6538i	−0.679345	+	0.475682i
$950$	−0.617440	+	0.0894846i	−0.0200324	+	0.00290326i
$951$	2.43061	+	4.20993i	0.0788178	+	0.136516i
$952$	−1.21613	−	4.53865i	−0.0394149	−	0.147098i
$953$	20.1471	−	28.7731i	0.652629	−	0.932051i	−0.347355	−	0.937734i	$-0.612920\pi$
$953$	20.1471	−	28.7731i	0.652629	−	0.932051i	0.999984	+	0.00568288i	$0.00180893\pi$
$954$	−4.15407	+	15.5032i	−0.134493	+	0.501935i
$955$	−38.2721	+	19.1846i	−1.23846	+	0.620800i
$956$	4.26841	−	4.26841i	0.138050	−	0.138050i
$957$	−1.56752	+	0.570530i	−0.0506707	+	0.0184426i
$958$	−5.77902	−	8.25330i	−0.186712	−	0.266652i
$959$	33.1953	−	39.5607i	1.07193	−	1.27748i
$960$	−0.853456	+	0.903237i	−0.0275452	+	0.0291518i
$961$		−	42.3590i		−	1.36642i
$962$	9.26094	+	4.26704i	0.298585	+	0.137575i
$963$	−32.7607	+	32.7607i	−1.05570	+	1.05570i
$964$	9.58607	+	0.838673i	0.308747	+	0.0270118i
$965$	−15.9334	+	3.27738i	−0.512915	+	0.105503i
$966$	−0.260149	−	0.0458714i	−0.00837017	−	0.00147589i
$967$	6.99735	+	19.2251i	0.225020	+	0.618236i	0.999904	−	0.0138668i	$-0.00441407\pi$
$967$	6.99735	+	19.2251i	0.225020	+	0.618236i	−0.774884	+	0.632103i	$0.782192\pi$
$968$	10.5687			0.339691
$969$	−0.0322771	−	0.0886806i	−0.00103689	−	0.00284883i
$970$	5.61346	−	38.1210i	0.180237	−	1.22399i
$971$	−10.4087	−	59.0306i	−0.334031	−	1.89438i	−0.436597	−	0.899657i	$-0.643816\pi$
$971$	−10.4087	−	59.0306i	−0.334031	−	1.89438i	0.102566	−	0.994726i	$-0.467295\pi$
$972$	−12.5554	+	3.36421i	−0.402714	+	0.107907i
$973$	3.61853	−	13.5045i	0.116005	−	0.432936i
$974$	−17.2804	−	20.5940i	−0.553699	−	0.659873i
$975$	3.47493	+	3.10189i	0.111287	+	0.0993401i
$976$	−1.44410	−	5.38946i	−0.0462245	−	0.172512i
$977$	2.40853	+	0.876633i	0.0770557	+	0.0280460i	0.380260	−	0.924879i	$-0.375834\pi$
$977$	2.40853	+	0.876633i	0.0770557	+	0.0280460i	−0.303205	+	0.952925i	$0.598057\pi$
$978$	−7.02013	+	3.27354i	−0.224479	+	0.104676i
$979$	0.461036	+	0.322821i	0.0147348	+	0.0103174i
$980$	2.21677	+	10.7771i	0.0708123	+	0.344263i
$981$	−2.77571	−	31.7265i	−0.0886215	−	1.01295i
$982$	−2.78408	−	15.7893i	−0.0888435	−	0.503856i
$983$	−19.7457	−	42.3448i	−0.629790	−	1.35059i	−0.919355	−	0.393430i	$-0.871288\pi$
$983$	−19.7457	−	42.3448i	−0.629790	−	1.35059i	0.289565	−	0.957158i	$-0.406489\pi$
$984$	3.67635	−	1.71431i	0.117198	−	0.0546503i
$985$	−5.33533	+	12.3429i	−0.169998	+	0.393278i
$986$	3.56771	+	5.09521i	0.113619	+	0.162265i
$987$	−1.50533	+	17.2060i	−0.0479152	+	0.547673i
$988$	−0.202042	−	0.0541370i	−0.00642781	−	0.00172233i
$989$	0.190048	−	0.329173i	0.00604318	−	0.0104671i
$990$	−3.47713	−	1.87826i	−0.110510	−	0.0596950i
$991$	31.8420	+	8.53205i	1.01150	+	0.271029i	0.726254	−	0.687426i	$-0.241260\pi$
$991$	31.8420	+	8.53205i	1.01150	+	0.271029i	0.285241	+	0.958456i	$0.407926\pi$
$992$	−3.61972	+	7.76252i	−0.114926	+	0.246460i
$993$			9.35095i			0.296744i
$994$	26.3502	+	12.2873i	0.835777	+	0.389729i
$995$	−2.05314	+	34.7962i	−0.0650890	+	1.10311i
$996$	−1.24485	−	1.04455i	−0.0394445	−	0.0330979i
$997$	10.7469	+	12.8077i	0.340358	+	0.405623i	0.908888	−	0.417039i	$-0.136932\pi$
$997$	10.7469	+	12.8077i	0.340358	+	0.405623i	−0.568530	+	0.822662i	$0.692488\pi$
$998$	11.9670	+	11.9670i	0.378809	+	0.378809i
$999$	14.7939	+	12.2988i	0.468059	+	0.389117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.ba.a.257.5	yes	108
5.3	odd	4		370.2.bd.a.183.5	yes	108
37.18	odd	36		370.2.bd.a.277.5	yes	108
185.18	even	36	inner	370.2.ba.a.203.5	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.ba.a.203.5	✓	108	185.18	even	36	inner
370.2.ba.a.257.5	yes	108	1.1	even	1	trivial
370.2.bd.a.183.5	yes	108	5.3	odd	4
370.2.bd.a.277.5	yes	108	37.18	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)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.0484358 - 0.553623i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.704954 + 2.12204i) q^{5} +(-0.392966 - 0.392966i) q^{6} +(3.12914 + 1.45914i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.65027 - 0.467314i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.0484358 - 0.553623i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.704954 + 2.12204i) q^{5} +(-0.392966 - 0.392966i) q^{6} +(3.12914 + 1.45914i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.65027 - 0.467314i) q^{9} +(0.823993 + 2.07871i) q^{10} +(-0.568753 + 0.328369i) q^{11} +(-0.553623 - 0.0484358i) q^{12} +(0.291091 - 1.65086i) q^{13} +(3.33498 - 0.893604i) q^{14} +(1.20895 + 0.287497i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.34025 - 0.236322i) q^{17} +(1.72984 - 2.06154i) q^{18} +(0.124303 - 0.0108751i) q^{19} +(1.96738 + 1.06273i) q^{20} +(0.656252 - 1.80304i) q^{21} +(-0.224618 + 0.617133i) q^{22} +(0.0688371 - 0.119229i) q^{23} +(-0.455234 + 0.318758i) q^{24} +(-4.00608 - 2.99188i) q^{25} +(-0.838164 - 1.45174i) q^{26} +(-0.818591 - 3.05502i) q^{27} +(1.98034 - 2.82822i) q^{28} +(-1.18293 + 4.41477i) q^{29} +(1.11091 - 0.556866i) q^{30} +(6.05636 - 6.05636i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.209341 + 0.298970i) q^{33} +(0.874785 - 1.04253i) q^{34} +(-5.30225 + 5.61152i) q^{35} -2.69116i q^{36} +(-4.96671 + 3.51166i) q^{37} +(0.0882315 - 0.0882315i) q^{38} +(-0.928054 - 0.0811942i) q^{39} +(2.19021 - 0.450510i) q^{40} +(-7.18825 - 1.26748i) q^{41} +(-0.656252 - 1.80304i) q^{42} +2.76084 q^{43} +(0.224618 + 0.617133i) q^{44} +(-0.876661 + 5.95341i) q^{45} +(-0.0239069 - 0.135583i) q^{46} +(-8.69482 + 2.32977i) q^{47} +(-0.143836 + 0.536802i) q^{48} +(3.16289 + 3.76939i) q^{49} +(-4.99198 + 0.283147i) q^{50} +(-0.195749 - 0.730546i) q^{51} +(-1.57523 - 0.573338i) q^{52} +(-5.40524 + 2.52050i) q^{53} +(-2.59081 - 1.81410i) q^{54} +(-0.295868 - 1.43840i) q^{55} +(-0.300916 - 3.43948i) q^{56} +(-0.0120415 - 0.0682905i) q^{57} +(1.93158 + 4.14228i) q^{58} +(4.60467 - 2.14719i) q^{59} +(0.493062 - 1.14066i) q^{60} +(3.20031 + 4.57052i) q^{61} +(0.746488 - 8.53240i) q^{62} +(8.97494 + 2.40483i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.29798 + 1.78149i) q^{65} +(0.352539 + 0.0944624i) q^{66} +(-6.49836 + 13.9358i) q^{67} -1.36092i q^{68} +(-0.0693423 - 0.0323349i) q^{69} +(-0.454744 + 7.70689i) q^{70} +(6.45079 + 5.41286i) q^{71} +(-1.72984 - 2.06154i) q^{72} +(-10.7767 - 10.7767i) q^{73} +(-1.54747 + 5.88263i) q^{74} +(-1.46234 + 2.36277i) q^{75} +(0.0108751 - 0.124303i) q^{76} +(-2.25884 + 0.197623i) q^{77} +(-0.763121 + 0.534343i) q^{78} +(3.27766 - 7.02896i) q^{79} +(1.38822 - 1.75295i) q^{80} +(5.93489 - 2.16012i) q^{81} +(-6.32124 + 3.64957i) q^{82} +(2.39528 + 1.67719i) q^{83} +(-1.66169 - 0.959376i) q^{84} +(-0.443330 + 3.01065i) q^{85} +(2.11493 - 1.77463i) q^{86} +(2.50141 + 0.441067i) q^{87} +(0.568753 + 0.328369i) q^{88} +(-0.362181 - 0.776700i) q^{89} +(3.15521 + 5.12408i) q^{90} +(3.31970 - 4.74102i) q^{91} +(-0.105465 - 0.0884953i) q^{92} +(-3.64629 - 3.05960i) q^{93} +(-5.16307 + 7.37363i) q^{94} +(-0.0645507 + 0.271443i) q^{95} +(0.234865 + 0.503670i) q^{96} +(-14.9234 - 8.61604i) q^{97} +(4.84583 + 0.854451i) q^{98} +(-1.35390 + 1.13605i) 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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