LMFDB - Embedded newform 224.2.bd.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	224.37
Dual form			224.2.bd.a.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41418 - 0.00960786i) q^{2} +(-1.76562 + 2.30100i) q^{3} +(1.99982 + 0.0271745i) q^{4} +(2.61963 - 2.01011i) q^{5} +(2.51901 - 3.23706i) q^{6} +(-1.37753 - 2.25885i) q^{7} +(-2.82784 - 0.0576436i) q^{8} +(-1.40073 - 5.22759i) q^{9} +O(q^{10})$	\(q+(-1.41418 - 0.00960786i) q^{2} +(-1.76562 + 2.30100i) q^{3} +(1.99982 + 0.0271745i) q^{4} +(2.61963 - 2.01011i) q^{5} +(2.51901 - 3.23706i) q^{6} +(-1.37753 - 2.25885i) q^{7} +(-2.82784 - 0.0576436i) q^{8} +(-1.40073 - 5.22759i) q^{9} +(-3.72395 + 2.81750i) q^{10} +(3.36958 - 0.443613i) q^{11} +(-3.59344 + 4.55359i) q^{12} +(1.07289 - 0.444407i) q^{13} +(1.92638 + 3.20766i) q^{14} +9.57686i q^{15} +(3.99852 + 0.108688i) q^{16} +(1.96255 - 1.13308i) q^{17} +(1.93066 + 7.40622i) q^{18} +(0.673572 - 5.11629i) q^{19} +(5.29340 - 3.94867i) q^{20} +(7.62981 + 0.818565i) q^{21} +(-4.76946 + 0.594975i) q^{22} +(2.29071 + 8.54904i) q^{23} +(5.12552 - 6.40508i) q^{24} +(1.52781 - 5.70188i) q^{25} +(-1.52153 + 0.618163i) q^{26} +(6.46313 + 2.67711i) q^{27} +(-2.69343 - 4.55472i) q^{28} +(1.58074 + 3.81626i) q^{29} +(0.0920131 - 13.5434i) q^{30} +(-0.413662 - 0.716483i) q^{31} +(-5.65359 - 0.192122i) q^{32} +(-4.92863 + 8.53665i) q^{33} +(-2.78629 + 1.58352i) q^{34} +(-8.14917 - 3.14835i) q^{35} +(-2.65914 - 10.4923i) q^{36} +(0.692315 - 0.531232i) q^{37} +(-1.00171 + 7.22889i) q^{38} +(-0.871740 + 3.25338i) q^{39} +(-7.52377 + 5.53327i) q^{40} +(0.558998 - 0.558998i) q^{41} +(-10.7821 - 1.23090i) q^{42} +(4.35130 - 10.5050i) q^{43} +(6.75059 - 0.795578i) q^{44} +(-14.1774 - 10.8787i) q^{45} +(-3.15734 - 12.1119i) q^{46} +(-1.47692 - 0.852701i) q^{47} +(-7.30996 + 9.00869i) q^{48} +(-3.20480 + 6.22328i) q^{49} +(-2.21539 + 8.04882i) q^{50} +(-0.857903 + 6.51642i) q^{51} +(2.15766 - 0.859576i) q^{52} +(-1.38579 + 0.182443i) q^{53} +(-9.11431 - 3.84802i) q^{54} +(7.93534 - 7.93534i) q^{55} +(3.76523 + 6.46707i) q^{56} +(10.5833 + 10.5833i) q^{57} +(-2.19879 - 5.41206i) q^{58} +(-1.02637 - 7.79609i) q^{59} +(-0.260246 + 19.1520i) q^{60} +(1.84393 + 0.242758i) q^{61} +(0.578108 + 1.01721i) q^{62} +(-9.87879 + 10.3652i) q^{63} +(7.99335 + 0.326014i) q^{64} +(1.91728 - 3.32082i) q^{65} +(7.05200 - 12.0250i) q^{66} +(-1.83529 + 2.39179i) q^{67} +(3.95553 - 2.21262i) q^{68} +(-23.7159 - 9.82343i) q^{69} +(11.4942 + 4.53064i) q^{70} +(9.45424 + 9.45424i) q^{71} +(3.65970 + 14.8635i) q^{72} +(-6.77733 - 1.81598i) q^{73} +(-0.984162 + 0.744606i) q^{74} +(10.4225 + 13.5828i) q^{75} +(1.48605 - 10.2133i) q^{76} +(-5.64376 - 7.00028i) q^{77} +(1.26406 - 4.59249i) q^{78} +(-10.6442 - 6.14541i) q^{79} +(10.6931 - 7.75276i) q^{80} +(-3.51066 + 2.02688i) q^{81} +(-0.795895 + 0.785153i) q^{82} +(6.62223 - 2.74302i) q^{83} +(15.2360 + 1.84431i) q^{84} +(2.86354 - 6.91321i) q^{85} +(-6.25446 + 14.8141i) q^{86} +(-11.5722 - 3.10076i) q^{87} +(-9.55420 + 1.06023i) q^{88} +(-3.05705 + 0.819133i) q^{89} +(19.9450 + 15.5207i) q^{90} +(-2.48179 - 1.81132i) q^{91} +(4.34868 + 17.1588i) q^{92} +(2.37899 + 0.313201i) q^{93} +(2.08044 + 1.22006i) q^{94} +(-8.51981 - 14.7567i) q^{95} +(10.4242 - 12.6697i) q^{96} -6.07384 q^{97} +(4.59197 - 8.77005i) q^{98} +(-7.03890 - 16.9934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−1.41418	−	0.00960786i	−0.999977	−	0.00679378i
$2$	−1.41418	−	0.00960786i	−0.999977	−	0.00679378i
$3$	−1.76562	+	2.30100i	−1.01938	+	1.32848i	−0.0758775	+	0.997117i	$0.524176\pi$
$3$	−1.76562	+	2.30100i	−1.01938	+	1.32848i	−0.943503	+	0.331365i	$0.892491\pi$
$4$	1.99982	+	0.0271745i	0.999908	+	0.0135873i
$5$	2.61963	−	2.01011i	1.17153	−	0.898950i	0.175204	−	0.984532i	$-0.443942\pi$
$5$	2.61963	−	2.01011i	1.17153	−	0.898950i	0.996331	+	0.0855821i	$0.0272750\pi$
$6$	2.51901	−	3.23706i	1.02838	−	1.32153i
$7$	−1.37753	−	2.25885i	−0.520659	−	0.853765i
$7$	−1.37753	−	2.25885i	−0.520659	−	0.853765i
$8$	−2.82784	−	0.0576436i	−0.999792	−	0.0203801i
$9$	−1.40073	−	5.22759i	−0.466910	−	1.74253i
$10$	−3.72395	+	2.81750i	−1.17761	+	0.890970i
$11$	3.36958	−	0.443613i	1.01597	−	0.133754i	0.395891	−	0.918297i	$-0.370436\pi$
$11$	3.36958	−	0.443613i	1.01597	−	0.133754i	0.620075	+	0.784543i	$0.287102\pi$
$12$	−3.59344	+	4.55359i	−1.03734	+	1.31451i
$13$	1.07289	−	0.444407i	0.297567	−	0.123256i	−0.228905	−	0.973449i	$-0.573515\pi$
$13$	1.07289	−	0.444407i	0.297567	−	0.123256i	0.526472	+	0.850192i	$0.323515\pi$
$14$	1.92638	+	3.20766i	0.514846	+	0.857283i
$15$			9.57686i			2.47273i
$16$	3.99852	+	0.108688i	0.999631	+	0.0271720i
$17$	1.96255	−	1.13308i	0.475989	−	0.274812i	−0.242755	−	0.970088i	$-0.578051\pi$
$17$	1.96255	−	1.13308i	0.475989	−	0.274812i	0.718743	+	0.695275i	$0.244718\pi$
$18$	1.93066	+	7.40622i	0.455061	+	1.74566i
$19$	0.673572	−	5.11629i	0.154528	−	1.17376i	−0.721821	−	0.692080i	$-0.756694\pi$
$19$	0.673572	−	5.11629i	0.154528	−	1.17376i	0.876349	−	0.481677i	$-0.159972\pi$
$20$	5.29340	−	3.94867i	1.18364	−	0.882949i
$21$	7.62981	+	0.818565i	1.66496	+	0.178625i
$22$	−4.76946	+	0.594975i	−1.01685	+	0.126849i
$23$	2.29071	+	8.54904i	0.477646	+	1.78260i	0.611111	+	0.791545i	$0.290723\pi$
$23$	2.29071	+	8.54904i	0.477646	+	1.78260i	−0.133465	+	0.991054i	$0.542610\pi$
$24$	5.12552	−	6.40508i	1.04624	−	1.30743i
$25$	1.52781	−	5.70188i	0.305563	−	1.14038i
$26$	−1.52153	+	0.618163i	−0.298398	+	0.121232i
$27$	6.46313	+	2.67711i	1.24383	+	0.515211i
$28$	−2.69343	−	4.55472i	−0.509010	−	0.860760i
$29$	1.58074	+	3.81626i	0.293537	+	0.708661i	1.00000		0.000910563i	$0.000289841\pi$
$29$	1.58074	+	3.81626i	0.293537	+	0.708661i	−0.706463	+	0.707750i	$0.749710\pi$
$30$	0.0920131	−	13.5434i	0.0167992	−	2.47268i
$31$	−0.413662	−	0.716483i	−0.0742958	−	0.128684i	0.826484	−	0.562960i	$-0.190338\pi$
$31$	−0.413662	−	0.716483i	−0.0742958	−	0.128684i	−0.900780	+	0.434276i	$0.857004\pi$
$32$	−5.65359	−	0.192122i	−0.999423	−	0.0339626i
$33$	−4.92863	+	8.53665i	−0.857965	+	1.48604i
$34$	−2.78629	+	1.58352i	−0.477845	+	0.271572i
$35$	−8.14917	−	3.14835i	−1.37746	−	0.532169i
$36$	−2.65914	−	10.4923i	−0.443190	−	1.74871i
$37$	0.692315	−	0.531232i	0.113816	−	0.0873340i	−0.550285	−	0.834977i	$-0.685481\pi$
$37$	0.692315	−	0.531232i	0.113816	−	0.0873340i	0.664101	+	0.747643i	$0.268814\pi$
$38$	−1.00171	+	7.22889i	−0.162499	+	1.17268i
$39$	−0.871740	+	3.25338i	−0.139590	+	0.520957i
$40$	−7.52377	+	5.53327i	−1.18961	+	0.874887i
$41$	0.558998	−	0.558998i	0.0873008	−	0.0873008i	−0.662108	−	0.749409i	$-0.730338\pi$
$41$	0.558998	−	0.558998i	0.0873008	−	0.0873008i	0.749409	+	0.662108i	$0.230338\pi$
$42$	−10.7821	−	1.23090i	−1.66371	−	0.189933i
$43$	4.35130	−	10.5050i	0.663567	−	1.60199i	−0.128605	−	0.991696i	$-0.541050\pi$
$43$	4.35130	−	10.5050i	0.663567	−	1.60199i	0.792172	−	0.610298i	$-0.208950\pi$
$44$	6.75059	−	0.795578i	1.01769	−	0.119938i
$45$	−14.1774	−	10.8787i	−2.11345	−	1.62171i
$46$	−3.15734	−	12.1119i	−0.465524	−	1.78580i
$47$	−1.47692	−	0.852701i	−0.215431	−	0.124379i	0.388402	−	0.921490i	$-0.373027\pi$
$47$	−1.47692	−	0.852701i	−0.215431	−	0.124379i	−0.603833	+	0.797111i	$0.706361\pi$
$48$	−7.30996	+	9.00869i	−1.05510	+	1.30029i
$49$	−3.20480	+	6.22328i	−0.457829	+	0.889040i
$50$	−2.21539	+	8.04882i	−0.313303	+	1.13827i
$51$	−0.857903	+	6.51642i	−0.120130	+	0.912481i
$52$	2.15766	−	0.859576i	0.299214	−	0.119202i
$53$	−1.38579	+	0.182443i	−0.190353	+	0.0250605i	−0.225100	−	0.974336i	$-0.572271\pi$
$53$	−1.38579	+	0.182443i	−0.190353	+	0.0250605i	0.0347468	+	0.999396i	$0.488938\pi$
$54$	−9.11431	−	3.84802i	−1.24030	−	0.523649i
$55$	7.93534	−	7.93534i	1.07000	−	1.07000i
$56$	3.76523	+	6.46707i	0.503151	+	0.864199i
$57$	10.5833	+	10.5833i	1.40179	+	1.40179i
$58$	−2.19879	−	5.41206i	−0.288716	−	0.710639i
$59$	−1.02637	−	7.79609i	−0.133623	−	1.01496i	−0.918530	−	0.395351i	$-0.870623\pi$
$59$	−1.02637	−	7.79609i	−0.133623	−	1.01496i	0.784907	−	0.619613i	$-0.212711\pi$
$60$	−0.260246	+	19.1520i	−0.0335977	+	2.47251i
$61$	1.84393	+	0.242758i	0.236091	+	0.0310820i	0.247643	−	0.968851i	$-0.420344\pi$
$61$	1.84393	+	0.242758i	0.236091	+	0.0310820i	−0.0115520	+	0.999933i	$0.503677\pi$
$62$	0.578108	+	1.01721i	0.0734198	+	0.129186i
$63$	−9.87879	+	10.3652i	−1.24461	+	1.30589i
$64$	7.99335	+	0.326014i	0.999169	+	0.0407517i
$65$	1.91728	−	3.32082i	0.237809	−	0.411897i
$66$	7.05200	−	12.0250i	0.868041	−	1.48018i
$67$	−1.83529	+	2.39179i	−0.224216	+	0.292204i	−0.891892	−	0.452248i	$-0.850622\pi$
$67$	−1.83529	+	2.39179i	−0.224216	+	0.292204i	0.667676	+	0.744452i	$0.267289\pi$
$68$	3.95553	−	2.21262i	0.479679	−	0.268320i
$69$	−23.7159	−	9.82343i	−2.85505	−	1.18260i
$70$	11.4942	+	4.53064i	1.37381	+	0.541515i
$71$	9.45424	+	9.45424i	1.12201	+	1.12201i	0.991439	+	0.130573i	$0.0416818\pi$
$71$	9.45424	+	9.45424i	1.12201	+	1.12201i	0.130573	+	0.991439i	$0.458318\pi$
$72$	3.65970	+	14.8635i	0.431300	+	1.75168i
$73$	−6.77733	−	1.81598i	−0.793227	−	0.212545i	−0.160619	−	0.987017i	$-0.551349\pi$
$73$	−6.77733	−	1.81598i	−0.793227	−	0.212545i	−0.632608	+	0.774472i	$0.718016\pi$
$74$	−0.984162	+	0.744606i	−0.114407	+	0.0865587i
$75$	10.4225	+	13.5828i	1.20349	+	1.56841i
$76$	1.48605	−	10.2133i	0.170462	−	1.17155i
$77$	−5.64376	−	7.00028i	−0.643166	−	0.797756i
$78$	1.26406	−	4.59249i	0.143126	−	0.519997i
$79$	−10.6442	−	6.14541i	−1.19756	−	0.691412i	−0.237550	−	0.971375i	$-0.576345\pi$
$79$	−10.6442	−	6.14541i	−1.19756	−	0.691412i	−0.960011	+	0.279963i	$0.909678\pi$
$80$	10.6931	−	7.75276i	1.19553	−	0.866785i
$81$	−3.51066	+	2.02688i	−0.390073	+	0.225209i
$82$	−0.795895	+	0.785153i	−0.0878918	+	0.0867056i
$83$	6.62223	−	2.74302i	0.726884	−	0.301085i	0.0116133	−	0.999933i	$-0.496303\pi$
$83$	6.62223	−	2.74302i	0.726884	−	0.301085i	0.715271	+	0.698847i	$0.246303\pi$
$84$	15.2360	+	1.84431i	1.66238	+	0.201231i
$85$	2.86354	−	6.91321i	0.310595	−	0.749842i
$86$	−6.25446	+	14.8141i	−0.674436	+	1.59745i
$87$	−11.5722	−	3.10076i	−1.24067	−	0.332436i
$88$	−9.55420	+	1.06023i	−1.01848	+	0.113021i
$89$	−3.05705	+	0.819133i	−0.324046	+	0.0868279i	−0.417175	−	0.908826i	$-0.636980\pi$
$89$	−3.05705	+	0.819133i	−0.324046	+	0.0868279i	0.0931288	+	0.995654i	$0.470313\pi$
$90$	19.9450	+	15.5207i	2.10238	+	1.63603i
$91$	−2.48179	−	1.81132i	−0.260163	−	0.189878i
$92$	4.34868	+	17.1588i	0.453381	+	1.78892i
$93$	2.37899	+	0.313201i	0.246690	+	0.0324774i
$94$	2.08044	+	1.22006i	0.214581	+	0.125840i
$95$	−8.51981	−	14.7567i	−0.874114	−	1.51401i
$96$	10.4242	−	12.6697i	1.06391	−	1.29309i
$97$	−6.07384			−0.616705			−0.308353	−	0.951272i	$-0.599778\pi$
$97$	−6.07384			−0.616705			−0.308353	+	0.951272i	$0.599778\pi$
$98$	4.59197	−	8.77005i	0.463859	−	0.885909i
$99$	−7.03890	−	16.9934i	−0.707436	−	1.70790i
$100$	3.21029	−	11.3612i	0.321029	−	1.13612i
$101$	−0.0897688	−	0.681862i	−0.00893233	−	0.0678478i	0.986398	−	0.164374i	$-0.0525603\pi$
$101$	−0.0897688	−	0.681862i	−0.00893233	−	0.0678478i	−0.995330	+	0.0965259i	$0.969227\pi$
$102$	1.27584	−	9.20715i	0.126327	−	0.911644i
$103$	−13.0494	+	3.49659i	−1.28580	+	0.344529i	−0.836064	−	0.548633i	$-0.815149\pi$
$103$	−13.0494	+	3.49659i	−1.28580	+	0.344529i	−0.449736	+	0.893162i	$0.648482\pi$
$104$	−3.05959	+	1.19487i	−0.300017	+	0.117166i
$105$	21.6327	−	13.1924i	2.11113	−	1.28745i
$106$	1.96151	−	0.244693i	0.190519	−	0.0237667i
$107$	7.09651	+	9.24835i	0.686045	+	0.894072i	0.998437	−	0.0558816i	$-0.0177969\pi$
$107$	7.09651	+	9.24835i	0.686045	+	0.894072i	−0.312392	+	0.949953i	$0.601130\pi$
$108$	12.8523	+	5.52937i	1.23671	+	0.532064i
$109$	14.8990	+	11.4324i	1.42707	+	1.09503i	0.979652	+	0.200704i	$0.0643229\pi$
$109$	14.8990	+	11.4324i	1.42707	+	1.09503i	0.447418	+	0.894325i	$0.352344\pi$
$110$	−11.2982	+	11.1458i	−1.07725	+	1.06271i
$111$			2.53097i			0.240229i
$112$	−5.26259	−	9.18178i	−0.497268	−	0.867597i
$113$			5.14215i			0.483732i	0.970310	+	0.241866i	$0.0777595\pi$
$113$			5.14215i			0.483732i	−0.970310	+	0.241866i	$0.922240\pi$
$114$	−14.8650	−	15.0684i	−1.39224	−	1.41128i
$115$	23.1854	+	17.7908i	2.16205	+	1.65900i
$116$	3.05749	+	7.67476i	0.283881	+	0.712584i
$117$	−3.82601	−	4.98615i	−0.353715	−	0.460970i
$118$	1.37658	+	11.0349i	0.126724	+	1.01585i
$119$	−5.26294	−	2.87226i	−0.482453	−	0.263299i
$120$	0.552045	−	27.0818i	0.0503946	−	2.47222i
$121$	0.532080	−	0.142570i	0.0483709	−	0.0129609i
$122$	−2.60532	−	0.361021i	−0.235875	−	0.0326853i
$123$	0.299276	+	2.27323i	0.0269848	+	0.204970i
$124$	−0.807777	−	1.44407i	−0.0725405	−	0.129682i
$125$	−1.14107	−	2.75479i	−0.102060	−	0.246396i
$126$	14.0700	−	14.5634i	1.25345	−	1.29741i
$127$	1.28194			0.113754			0.0568770	−	0.998381i	$-0.481886\pi$
$127$	1.28194			0.113754			0.0568770	+	0.998381i	$0.481886\pi$
$128$	−11.3009	−	0.537841i	−0.998869	−	0.0475389i
$129$	16.4892	+	28.5601i	1.45179	+	2.51458i
$130$	−2.74328	+	4.67782i	−0.240602	+	0.410272i
$131$	−12.9253	−	1.70165i	−1.12929	−	0.148674i	−0.457355	−	0.889284i	$-0.651203\pi$
$131$	−12.9253	−	1.70165i	−1.12929	−	0.148674i	−0.671935	+	0.740610i	$0.734537\pi$
$132$	−10.0883	+	16.9378i	−0.878077	+	1.47424i
$133$	−12.4848	+	5.52636i	−1.08257	+	0.479196i
$134$	2.61841	−	3.36480i	0.226196	−	0.290674i
$135$	22.3123	−	5.97857i	1.92034	−	0.514553i
$136$	−5.61510	+	3.09104i	−0.481491	+	0.265055i
$137$	−5.47522	−	1.46708i	−0.467780	−	0.125341i	0.0172270	−	0.999852i	$-0.494516\pi$
$137$	−5.47522	−	1.46708i	−0.467780	−	0.125341i	−0.485007	+	0.874510i	$0.661183\pi$
$138$	33.4441	+	14.1200i	2.84695	+	1.20197i
$139$	−4.56535	+	11.0217i	−0.387228	+	0.934852i	0.603296	+	0.797517i	$0.293854\pi$
$139$	−4.56535	+	11.0217i	−0.387228	+	0.934852i	−0.990525	+	0.137335i	$0.956146\pi$
$140$	−16.2113	−	6.51758i	−1.37010	−	0.550836i
$141$	4.56974	−	1.89285i	0.384842	−	0.159407i
$142$	−13.2792	−	13.4608i	−1.11436	−	1.12961i
$143$	3.41805	−	1.97341i	0.285832	−	0.165025i
$144$	−5.03267	−	21.0549i	−0.419389	−	1.75457i
$145$	11.8121	+	6.81971i	0.980940	+	0.566346i
$146$	9.56693	+	2.63324i	0.791765	+	0.217929i
$147$	−8.66130	−	18.3622i	−0.714372	−	1.51449i
$148$	1.39894	−	1.04355i	0.114992	−	0.0857795i
$149$	1.82842	+	2.38284i	0.149790	+	0.195210i	0.862221	−	0.506532i	$-0.169073\pi$
$149$	1.82842	+	2.38284i	0.149790	+	0.195210i	−0.712432	+	0.701742i	$0.752406\pi$
$150$	−14.6088	−	19.3087i	−1.19280	−	1.57655i
$151$	3.83604	+	1.02786i	0.312173	+	0.0836464i	0.411504	−	0.911408i	$-0.365004\pi$
$151$	3.83604	+	1.02786i	0.312173	+	0.0836464i	−0.0993312	+	0.995054i	$0.531670\pi$
$152$	−2.19968	+	14.4292i	−0.178417	+	1.17036i
$153$	−8.67229	−	8.67229i	−0.701113	−	0.701113i
$154$	7.91404	+	9.95388i	0.637732	+	0.802107i
$155$	−2.52385	−	1.04541i	−0.202721	−	0.0839697i
$156$	−1.83173	+	6.48247i	−0.146656	+	0.519013i
$157$	1.80259	−	2.34918i	0.143862	−	0.187485i	−0.715865	−	0.698239i	$-0.753967\pi$
$157$	1.80259	−	2.34918i	0.143862	−	0.187485i	0.859727	+	0.510754i	$0.170634\pi$
$158$	14.9937	+	8.79299i	1.19284	+	0.699532i
$159$	2.02698	−	3.51083i	0.160750	−	0.278427i
$160$	−15.1965	+	10.8611i	−1.20139	+	0.858643i
$161$	16.1555	−	16.9510i	1.27323	−	1.33592i
$162$	4.98418	−	2.83264i	0.391594	−	0.222553i
$163$	11.9219	+	1.56955i	0.933798	+	0.122937i	0.582046	−	0.813156i	$-0.302252\pi$
$163$	11.9219	+	1.56955i	0.933798	+	0.122937i	0.351753	+	0.936093i	$0.385586\pi$
$164$	1.13308	−	1.10270i	0.0884789	−	0.0861065i
$165$	4.24842	+	32.2700i	0.330739	+	2.51221i
$166$	−9.39139	+	3.81550i	−0.728913	+	0.296140i
$167$	4.12786	+	4.12786i	0.319423	+	0.319423i	0.848545	−	0.529122i	$-0.177479\pi$
$167$	4.12786	+	4.12786i	0.319423	+	0.319423i	−0.529122	+	0.848545i	$0.677479\pi$
$168$	−21.5287	−	2.75458i	−1.66097	−	0.212520i
$169$	−8.23879	+	8.23879i	−0.633753	+	0.633753i
$170$	−4.11599	+	9.74901i	−0.315682	+	0.747715i
$171$	−27.6894	+	3.64537i	−2.11746	+	0.278769i
$172$	8.98727	−	20.8898i	0.685273	−	1.59283i
$173$	−1.73705	+	13.1942i	−0.132065	+	1.00313i	0.789183	+	0.614158i	$0.210504\pi$
$173$	−1.73705	+	13.1942i	−0.132065	+	1.00313i	−0.921248	+	0.388976i	$0.872829\pi$
$174$	16.3354	+	4.49622i	1.23838	+	0.340857i
$175$	−14.9843	+	4.40343i	−1.13271	+	0.332868i
$176$	13.5216	−	1.40757i	1.01923	−	0.106099i
$177$	19.7510	+	11.4032i	1.48457	+	0.857120i
$178$	4.33109	−	1.12903i	0.324629	−	0.0846244i
$179$	−16.2932	−	12.5022i	−1.21781	−	0.934462i	−0.218669	−	0.975799i	$-0.570172\pi$
$179$	−16.2932	−	12.5022i	−1.21781	−	0.934462i	−0.999145	+	0.0413371i	$0.986838\pi$
$180$	−28.0567	−	22.1407i	−2.09122	−	1.65027i
$181$	0.194691	−	0.470025i	0.0144713	−	0.0349367i	−0.916479	−	0.400083i	$-0.868981\pi$
$181$	0.194691	−	0.470025i	0.0144713	−	0.0349367i	0.930950	+	0.365147i	$0.118981\pi$
$182$	3.49230	+	2.58538i	0.258867	+	0.191641i
$183$	−3.81427	+	3.81427i	−0.281959	+	0.281959i
$184$	−5.98496	−	24.3074i	−0.441217	−	1.79196i
$185$	0.745773	−	2.78326i	0.0548303	−	0.204630i
$186$	−3.36132	−	0.465779i	−0.246464	−	0.0341526i
$187$	6.11032	−	4.68862i	0.446831	−	0.342866i
$188$	−2.93040	−	1.74538i	−0.213721	−	0.127295i
$189$	−2.85597	−	18.2870i	−0.207741	−	1.33019i
$190$	11.9068	+	20.9506i	0.863808	+	1.51991i
$191$	−11.8280	+	20.4867i	−0.855844	+	1.48237i	0.0200149	+	0.999800i	$0.493629\pi$
$191$	−11.8280	+	20.4867i	−0.855844	+	1.48237i	−0.875859	+	0.482566i	$0.839705\pi$
$192$	−14.8634	+	17.8171i	−1.07267	+	1.28584i
$193$	−1.87686	−	3.25082i	−0.135100	−	0.233999i	0.790536	−	0.612416i	$-0.209802\pi$
$193$	−1.87686	−	3.25082i	−0.135100	−	0.233999i	−0.925635	+	0.378416i	$0.876469\pi$
$194$	8.58952	+	0.0583566i	0.616691	+	0.00418976i
$195$	4.25602	+	10.2749i	0.304780	+	0.735804i
$196$	−6.57813	+	12.3583i	−0.469867	+	0.882737i
$197$	−15.1341	−	6.26874i	−1.07826	−	0.446629i	−0.228360	−	0.973577i	$-0.573336\pi$
$197$	−15.1341	−	6.26874i	−1.07826	−	0.446629i	−0.849898	+	0.526948i	$0.823336\pi$
$198$	9.79100	+	24.0994i	0.695816	+	1.71267i
$199$	3.22379	−	12.0313i	0.228528	−	0.852879i	−0.752432	−	0.658670i	$-0.771119\pi$
$199$	3.22379	−	12.0313i	0.228528	−	0.852879i	0.980960	−	0.194209i	$-0.0622140\pi$
$200$	−4.64909	+	16.0359i	−0.328741	+	1.13391i
$201$	−2.26310	−	8.44599i	−0.159627	−	0.595734i
$202$	0.120398	+	0.965139i	0.00847118	+	0.0679069i
$203$	6.44282	−	8.82768i	0.452197	−	0.619582i
$204$	−1.89273	+	13.0083i	−0.132517	+	0.910764i
$205$	0.340719	−	2.58802i	0.0237968	−	0.180755i
$206$	18.4879	−	4.81943i	1.28811	−	0.335786i
$207$	41.4822	−	23.9498i	2.88322	−	1.66463i
$208$	4.33829	−	1.66036i	0.300806	−	0.115125i
$209$		−	17.5385i		−	1.21317i
$210$	−30.7193	+	18.4487i	−2.11983	+	1.27308i
$211$	−10.8739	+	4.50411i	−0.748588	+	0.310075i	−0.724165	−	0.689626i	$-0.757775\pi$
$211$	−10.8739	+	4.50411i	−0.748588	+	0.310075i	−0.0244229	+	0.999702i	$0.507775\pi$
$212$	−2.77629	+	0.327194i	−0.190676	+	0.0224718i
$213$	−38.4468	+	5.06161i	−2.63433	+	0.346816i
$214$	−9.94689	−	13.1470i	−0.679955	−	0.898712i
$215$	−9.71738	−	36.2658i	−0.662720	−	2.47331i
$216$	−18.1224	−	7.94301i	−1.23307	−	0.540453i
$217$	−1.04859	+	1.92138i	−0.0711832	+	0.130432i
$218$	−20.9601	−	16.3107i	−1.41960	−	1.10470i
$219$	16.1448	−	12.3883i	1.09096	−	0.837124i
$220$	16.0849	−	15.6536i	1.08444	−	1.05536i
$221$	1.60206	−	2.08785i	0.107766	−	0.140444i
$222$	0.0243172	−	3.57925i	0.00163206	−	0.240223i
$223$	−3.28335			−0.219869			−0.109935	−	0.993939i	$-0.535064\pi$
$223$	−3.28335			−0.219869			−0.109935	+	0.993939i	$0.535064\pi$
$224$	7.35403	+	13.0353i	0.491362	+	0.870955i
$225$	−31.9472			−2.12981
$226$	0.0494050	−	7.27193i	0.00328637	−	0.483721i
$227$	6.23703	−	8.12826i	0.413966	−	0.539491i	−0.539104	−	0.842239i	$-0.681237\pi$
$227$	6.23703	−	8.12826i	0.413966	−	0.539491i	0.953071	+	0.302747i	$0.0979039\pi$
$228$	20.8771	+	21.4522i	1.38262	+	1.42071i
$229$	−2.93742	+	2.25396i	−0.194110	+	0.148946i	−0.701244	−	0.712921i	$-0.747372\pi$
$229$	−2.93742	+	2.25396i	−0.194110	+	0.148946i	0.507134	+	0.861867i	$0.330705\pi$
$230$	−32.6174	−	25.3821i	−2.15073	−	1.67365i
$231$	26.0724	−	0.626467i	1.71544	−	0.0412185i
$232$	−4.25011	−	10.8829i	−0.279033	−	0.714496i
$233$	−1.81516	−	6.77428i	−0.118915	−	0.443798i	0.880635	−	0.473796i	$-0.157117\pi$
$233$	−1.81516	−	6.77428i	−0.118915	−	0.443798i	−0.999550	+	0.0299982i	$0.990450\pi$
$234$	5.36276	+	7.08808i	0.350575	+	0.463362i
$235$	−5.58302	+	0.735018i	−0.364196	+	0.0479473i
$236$	−1.84071	−	15.6186i	−0.119820	−	1.01669i
$237$	32.9341	−	13.6417i	2.13930	−	0.886127i
$238$	7.41515	+	4.11245i	0.480653	+	0.266571i
$239$			21.7829i			1.40902i	0.709696	+	0.704508i	$0.248832\pi$
$239$			21.7829i			1.40902i	−0.709696	+	0.704508i	$0.751168\pi$
$240$	−1.04089	+	38.2933i	−0.0671891	+	2.47182i
$241$	−22.9996	+	13.2788i	−1.48153	+	0.855363i	−0.999781	−	0.0209448i	$-0.993333\pi$
$241$	−22.9996	+	13.2788i	−1.48153	+	0.855363i	−0.481752	+	0.876308i	$0.659999\pi$
$242$	−0.753827	+	0.196508i	−0.0484578	+	0.0126320i
$243$	−1.20471	+	9.15066i	−0.0772820	+	0.587015i
$244$	3.68093	+	0.535580i	0.235647	+	0.0342870i
$245$	4.11410	+	22.7447i	0.262840	+	1.45311i
$246$	−0.401390	−	3.21763i	−0.0255917	−	0.205149i
$247$	−1.55104	−	5.78857i	−0.0986905	−	0.368318i
$248$	1.12847	+	2.04994i	0.0716578	+	0.130172i
$249$	−5.38065	+	20.0809i	−0.340985	+	1.27257i
$250$	1.58721	+	3.90673i	0.100384	+	0.247083i
$251$	−14.0102	−	5.80322i	−0.884317	−	0.366296i	−0.106148	−	0.994350i	$-0.533852\pi$
$251$	−14.0102	−	5.80322i	−0.884317	−	0.366296i	−0.778170	+	0.628054i	$0.783852\pi$
$252$	−20.0374	+	20.4601i	−1.26224	+	1.28886i
$253$	11.5112	+	27.7905i	0.723702	+	1.74717i
$254$	−1.81290	−	0.0123167i	−0.113751	−	0.000772820i
$255$	10.8514	+	18.7951i	0.679538	+	1.17699i
$256$	15.9764	+	0.869183i	0.998523	+	0.0543239i
$257$	10.0766	−	17.4531i	0.628558	−	1.08870i	−0.359283	−	0.933229i	$-0.616979\pi$
$257$	10.0766	−	17.4531i	0.628558	−	1.08870i	0.987841	−	0.155466i	$-0.0496880\pi$
$258$	−23.0443	−	40.5476i	−1.43468	−	2.52438i
$259$	−2.15366	−	0.832046i	−0.133822	−	0.0517008i
$260$	3.92444	−	6.58892i	0.243383	−	0.408628i
$261$	17.7356	−	13.6090i	1.09781	−	0.842378i
$262$	18.2624	+	2.53063i	1.12825	+	0.156343i
$263$	1.99620	−	7.44993i	0.123091	−	0.459382i	−0.876673	−	0.481086i	$-0.840242\pi$
$263$	1.99620	−	7.44993i	0.123091	−	0.459382i	0.999764	+	0.0217039i	$0.00690910\pi$
$264$	14.4295	−	23.8562i	0.888073	−	1.46825i
$265$	−3.26353	+	3.26353i	−0.200477	+	0.200477i
$266$	17.7089	−	7.69532i	1.08580	−	0.471830i
$267$	3.51275	−	8.48054i	0.214977	−	0.519000i
$268$	−3.73523	+	4.73327i	−0.228166	+	0.289131i
$269$	17.6100	+	13.5126i	1.07370	+	0.823878i	0.985064	−	0.172186i	$-0.0550830\pi$
$269$	17.6100	+	13.5126i	1.07370	+	0.823878i	0.0886345	+	0.996064i	$0.471750\pi$
$270$	−31.6111	+	8.24040i	−1.92379	+	0.501495i
$271$	1.70866	+	0.986498i	0.103794	+	0.0599255i	0.550998	−	0.834506i	$-0.314247\pi$
$271$	1.70866	+	0.986498i	0.103794	+	0.0599255i	−0.447204	+	0.894432i	$0.647580\pi$
$272$	7.97046	−	4.31734i	0.483280	−	0.261777i
$273$	8.54974	−	2.51251i	0.517454	−	0.152064i
$274$	7.72886	+	2.12732i	0.466917	+	0.128516i
$275$	2.61866	−	19.8907i	0.157911	−	1.19945i
$276$	−47.1604	−	20.2895i	−2.83872	−	1.22128i
$277$	−2.91350	+	0.383570i	−0.175055	+	0.0230465i	−0.217544	−	0.976050i	$-0.569805\pi$
$277$	−2.91350	+	0.383570i	−0.175055	+	0.0230465i	0.0424888	+	0.999097i	$0.486471\pi$
$278$	6.56213	−	15.5429i	0.393570	−	0.932199i
$279$	−3.16605	+	3.16605i	−0.189547	+	0.189547i
$280$	22.8631	+	9.37279i	1.36633	+	0.560131i
$281$	3.36927	+	3.36927i	0.200994	+	0.200994i	0.800426	−	0.599432i	$-0.204607\pi$
$281$	3.36927	+	3.36927i	0.200994	+	0.200994i	−0.599432	+	0.800426i	$0.704607\pi$
$282$	−6.48063	+	2.63293i	−0.385916	+	0.156789i
$283$	3.47979	+	26.4317i	0.206852	+	1.57120i	0.708237	+	0.705974i	$0.249491\pi$
$283$	3.47979	+	26.4317i	0.206852	+	1.57120i	−0.501385	+	0.865224i	$0.667176\pi$
$284$	18.6498	+	19.1637i	1.10666	+	1.13715i
$285$	48.9980	+	6.45071i	2.90239	+	0.382107i
$286$	−4.85270	+	2.75792i	−0.286946	+	0.163079i
$287$	−2.03273	−	0.492654i	−0.119988	−	0.0290804i
$288$	6.91482	+	29.8238i	0.407459	+	1.75738i
$289$	−5.93226	+	10.2750i	−0.348956	+	0.604410i
$290$	−16.6389	−	9.75779i	−0.977069	−	0.572997i
$291$	10.7241	−	13.9759i	0.628657	−	0.819282i
$292$	−13.5041	−	3.81580i	−0.790266	−	0.223303i
$293$	21.2059	+	8.78378i	1.23886	+	0.513154i	0.903359	−	0.428885i	$-0.141093\pi$
$293$	21.2059	+	8.78378i	1.23886	+	0.513154i	0.335504	+	0.942039i	$0.391093\pi$
$294$	12.0722	+	26.0507i	0.704066	+	1.51931i
$295$	−18.3598	−	18.3598i	−1.06895	−	1.06895i
$296$	−1.98838	+	1.46233i	−0.115572	+	0.0849963i
$297$	22.9656	+	6.15362i	1.33260	+	0.357069i
$298$	−2.56282	−	3.38733i	−0.148460	−	0.196223i
$299$	6.25694	+	8.15420i	0.361848	+	0.471570i
$300$	20.4739	+	27.4464i	1.18206	+	1.58462i
$301$	−29.7232	+	4.64201i	−1.71322	+	0.267561i
$302$	−5.41498	−	1.49044i	−0.311597	−	0.0857653i
$303$	1.72746	+	0.997350i	0.0992400	+	0.0572963i
$304$	3.24937	−	20.3844i	0.186364	−	1.16913i
$305$	5.31840	−	3.07058i	0.304531	−	0.175821i
$306$	12.1809	+	12.3475i	0.696333	+	0.705860i
$307$	26.9226	−	11.1517i	1.53655	−	0.636461i	0.555730	−	0.831363i	$-0.312439\pi$
$307$	26.9226	−	11.1517i	1.53655	−	0.636461i	0.980823	+	0.194901i	$0.0624387\pi$
$308$	−11.0963	−	14.1526i	−0.632268	−	0.806421i
$309$	14.9947	−	36.2004i	0.853018	−	2.05937i
$310$	3.55914	+	1.50265i	0.202146	+	0.0853450i
$311$	−5.00588	−	1.34132i	−0.283857	−	0.0760593i	0.114081	−	0.993471i	$-0.463608\pi$
$311$	−5.00588	−	1.34132i	−0.283857	−	0.0760593i	−0.397938	+	0.917412i	$0.630274\pi$
$312$	2.65268	−	9.14978i	0.150178	−	0.518004i
$313$	11.4972	−	3.08065i	0.649858	−	0.174129i	0.0811932	−	0.996698i	$-0.474127\pi$
$313$	11.4972	−	3.08065i	0.649858	−	0.174129i	0.568665	+	0.822570i	$0.307460\pi$
$314$	−2.57175	+	3.30484i	−0.145132	+	0.186503i
$315$	−5.04353	+	47.0105i	−0.284171	+	2.64874i
$316$	−21.1194	−	12.5789i	−1.18806	−	0.707620i
$317$	−10.5940	−	1.39473i	−0.595020	−	0.0783359i	−0.172999	−	0.984922i	$-0.555346\pi$
$317$	−10.5940	−	1.39473i	−0.595020	−	0.0783359i	−0.422021	+	0.906586i	$0.638679\pi$
$318$	−2.90025	+	4.94547i	−0.162638	+	0.277328i
$319$	7.01939	+	12.1579i	0.393010	+	0.680714i
$320$	21.5950	−	15.2135i	1.20720	−	0.850461i
$321$	−33.8102			−1.88710
$322$	−23.0096	+	23.8165i	−1.28228	+	1.32724i
$323$	−4.47525	−	10.8042i	−0.249009	−	0.601162i
$324$	−7.07574	+	3.95798i	−0.393097	+	0.219888i
$325$	−0.894774	−	6.79648i	−0.0496331	−	0.377001i
$326$	−16.8447	−	2.33418i	−0.932942	−	0.129278i
$327$	−52.6120	+	14.0974i	−2.90945	+	0.779586i
$328$	−1.61298	+	1.54853i	−0.0890618	+	0.0855034i
$329$	0.108385	+	4.51077i	0.00597545	+	0.248687i
$330$	−5.69799	−	45.6764i	−0.313664	−	2.51440i
$331$	5.45369	+	7.10739i	0.299762	+	0.390658i	0.918813	−	0.394693i	$-0.129149\pi$
$331$	5.45369	+	7.10739i	0.299762	+	0.390658i	−0.619051	+	0.785351i	$0.712483\pi$
$332$	13.3178	−	5.30557i	0.730908	−	0.291181i
$333$	−3.74681	−	2.87503i	−0.205324	−	0.157551i
$334$	−5.79787	−	5.87719i	−0.317246	−	0.321586i
$335$			9.95476i			0.543887i
$336$	30.4190	+	4.10232i	1.65949	+	0.223800i
$337$		−	7.11474i		−	0.387565i	−0.981045	−	0.193782i	$-0.937924\pi$
$337$		−	7.11474i		−	0.387565i	0.981045	−	0.193782i	$-0.0620756\pi$
$338$	11.7303	−	11.5720i	0.638044	−	0.629433i
$339$	−11.8321	−	9.07907i	−0.642630	−	0.493107i
$340$	5.91442	−	13.7473i	0.320755	−	0.745553i
$341$	−1.71171	−	2.23074i	−0.0926941	−	0.120801i
$342$	39.1928	−	4.88918i	2.11930	−	0.264377i
$343$	18.4722	−	1.33360i	0.997404	−	0.0720078i
$344$	−12.9103	+	29.4556i	−0.696078	+	1.58814i
$345$	−81.8730	+	21.9378i	−4.40789	+	1.18109i
$346$	2.58326	−	18.6423i	0.138877	−	1.00221i
$347$	−2.83848	−	21.5604i	−0.152377	−	1.15742i	−0.881209	−	0.472728i	$-0.843269\pi$
$347$	−2.83848	−	21.5604i	−0.152377	−	1.15742i	0.728831	−	0.684693i	$-0.240064\pi$
$348$	−23.0580	−	6.51541i	−1.23604	−	0.349263i
$349$	4.85008	+	11.7091i	0.259619	+	0.626775i	0.998913	−	0.0466071i	$-0.0148409\pi$
$349$	4.85008	+	11.7091i	0.259619	+	0.626775i	−0.739295	+	0.673382i	$0.764841\pi$
$350$	21.2328	−	6.08328i	1.13494	−	0.325165i
$351$	8.12397			0.433625
$352$	−19.1354	+	1.86064i	−1.01992	+	0.0991724i
$353$	3.95854	+	6.85640i	0.210692	+	0.364929i	0.951931	−	0.306312i	$-0.0990950\pi$
$353$	3.95854	+	6.85640i	0.210692	+	0.364929i	−0.741239	+	0.671241i	$0.765762\pi$
$354$	−27.8219	−	16.3160i	−1.47872	−	0.867186i
$355$	43.7707	+	5.76252i	2.32311	+	0.305843i
$356$	−6.13579	+	1.55504i	−0.325196	+	0.0824170i
$357$	15.9014	−	7.03871i	0.841591	−	0.372528i
$358$	22.9215	+	17.8370i	1.21144	+	0.942714i
$359$	22.7767	−	6.10299i	1.20211	−	0.322103i	0.398446	−	0.917192i	$-0.369550\pi$
$359$	22.7767	−	6.10299i	1.20211	−	0.322103i	0.803660	+	0.595089i	$0.202883\pi$
$360$	39.4645	+	31.5806i	2.07996	+	1.66444i
$361$	−7.37013	−	1.97482i	−0.387902	−	0.103938i
$362$	−0.279844	+	0.662830i	−0.0147083	+	0.0348376i
$363$	−0.611395	+	1.47604i	−0.0320899	+	0.0774720i
$364$	−4.91391	−	3.68975i	−0.257559	−	0.193395i
$365$	−21.4044	+	8.86601i	−1.12036	+	0.464068i
$366$	5.43071	−	5.35742i	0.283868	−	0.280037i
$367$	6.70380	−	3.87044i	0.349936	−	0.202035i	−0.314721	−	0.949184i	$-0.601911\pi$
$367$	6.70380	−	3.87044i	0.349936	−	0.202035i	0.664657	+	0.747149i	$0.268578\pi$
$368$	8.23027	+	34.4325i	0.429033	+	1.79492i
$369$	−3.70522	−	2.13921i	−0.192886	−	0.111363i
$370$	−1.08140	+	3.92887i	−0.0562193	+	0.204252i
$371$	2.32109	+	2.87897i	0.120505	+	0.149469i
$372$	4.74904	+	0.690991i	0.246226	+	0.0358262i
$373$	−13.1177	−	17.0953i	−0.679208	−	0.885161i	0.318828	−	0.947813i	$-0.396711\pi$
$373$	−13.1177	−	17.0953i	−0.679208	−	0.885161i	−0.998035	+	0.0626521i	$0.980044\pi$
$374$	−8.68615	+	6.57184i	−0.449150	+	0.339822i
$375$	8.35345	+	2.23830i	0.431370	+	0.115585i
$376$	4.12735	+	2.49644i	0.212852	+	0.128744i
$377$	3.39194	+	3.39194i	0.174694	+	0.174694i
$378$	3.86316	+	25.8886i	0.198700	+	1.33157i
$379$	15.4541	+	6.40132i	0.793826	+	0.328814i	0.742481	−	0.669867i	$-0.233649\pi$
$379$	15.4541	+	6.40132i	0.793826	+	0.328814i	0.0513454	+	0.998681i	$0.483649\pi$
$380$	−16.6370	−	29.7423i	−0.853462	−	1.52575i
$381$	−2.26342	+	2.94975i	−0.115959	+	0.151120i
$382$	16.9238	−	28.8583i	0.865896	−	1.47652i
$383$	−13.3014	+	23.0387i	−0.679669	+	1.17722i	0.295411	+	0.955370i	$0.404543\pi$
$383$	−13.3014	+	23.0387i	−0.679669	+	1.17722i	−0.975080	+	0.221852i	$0.928790\pi$
$384$	21.1907	−	25.0538i	1.08138	−	1.27852i
$385$	−28.8559	−	6.99355i	−1.47063	−	0.356424i
$386$	2.62299	+	4.61528i	0.133507	+	0.234912i
$387$	−61.0107	−	8.03221i	−3.10135	−	0.408300i
$388$	−12.1466	−	0.165054i	−0.616649	−	0.00837933i
$389$	0.948980	+	7.20822i	0.0481152	+	0.365471i	0.998517	+	0.0544456i	$0.0173392\pi$
$389$	0.948980	+	7.20822i	0.0481152	+	0.365471i	−0.950402	+	0.311026i	$0.899328\pi$
$390$	−5.92007	−	14.5715i	−0.299774	−	0.737858i
$391$	14.1824	+	14.1824i	0.717234	+	0.717234i
$392$	9.42141	−	17.4137i	0.475853	−	0.879525i
$393$	26.7367	−	26.7367i	1.34869	−	1.34869i
$394$	21.3421	+	9.01053i	1.07520	+	0.453944i
$395$	−40.2367	+	5.29727i	−2.02453	+	0.266534i
$396$	−13.6147	−	34.1749i	−0.684165	−	1.71736i
$397$	3.37820	−	25.6599i	0.169547	−	1.28784i	−0.669105	−	0.743168i	$-0.733322\pi$
$397$	3.37820	−	25.6599i	0.169547	−	1.28784i	0.838652	−	0.544668i	$-0.183344\pi$
$398$	−4.67462	+	16.9835i	−0.234317	+	0.851307i
$399$	9.32724	−	38.4849i	0.466946	−	1.92666i
$400$	6.72873	−	22.6331i	0.336436	−	1.13165i
$401$	14.8385	+	8.56703i	0.741001	+	0.427817i	0.822433	−	0.568862i	$-0.192616\pi$
$401$	14.8385	+	8.56703i	0.741001	+	0.427817i	−0.0814324	+	0.996679i	$0.525949\pi$
$402$	3.11928	+	11.9659i	0.155576	+	0.596805i
$403$	−0.762225	−	0.584875i	−0.0379691	−	0.0291347i
$404$	−0.160992	−	1.36604i	−0.00800964	−	0.0679629i
$405$	−5.12237	+	12.3665i	−0.254533	+	0.614496i
$406$	−9.19613	+	12.4220i	−0.456396	+	0.616496i
$407$	2.09715	−	2.09715i	0.103952	−	0.103952i
$408$	2.80164	−	18.3779i	0.138702	−	0.909843i
$409$	9.50210	−	35.4623i	0.469848	−	1.75350i	−0.170444	−	0.985367i	$-0.554520\pi$
$409$	9.50210	−	35.4623i	0.469848	−	1.75350i	0.640293	−	0.768131i	$-0.278813\pi$
$410$	−0.506703	+	3.65665i	−0.0250243	+	0.180589i
$411$	13.0429	−	10.0082i	0.643359	−	0.493667i
$412$	−26.1915	+	6.63792i	−1.29036	+	0.327027i
$413$	−16.1963	+	13.0578i	−0.796969	+	0.642532i
$414$	−58.8935	+	33.4708i	−2.89446	+	1.64500i
$415$	11.8340	−	20.4971i	0.580909	−	1.00616i
$416$	−6.15108	+	2.30637i	−0.301581	+	0.113079i
$417$	−17.3003	−	29.9651i	−0.847201	−	1.46739i
$418$	−0.168508	+	24.8027i	−0.00824199	+	1.21314i
$419$	3.90155	+	9.41917i	0.190603	+	0.460157i	0.990074	−	0.140548i	$-0.0448866\pi$
$419$	3.90155	+	9.41917i	0.190603	+	0.460157i	−0.799471	+	0.600705i	$0.794887\pi$
$420$	43.6199	−	25.7946i	2.12843	−	1.25865i
$421$	1.86479	+	0.772420i	0.0908842	+	0.0376455i	0.427662	−	0.903939i	$-0.359337\pi$
$421$	1.86479	+	0.772420i	0.0908842	+	0.0376455i	−0.336778	+	0.941584i	$0.609337\pi$
$422$	15.4209	−	6.26515i	0.750678	−	0.304983i
$423$	−2.38881	+	8.91515i	−0.116148	+	0.433469i
$424$	3.92931	−	0.436037i	0.190824	−	0.0211759i
$425$	−3.46227	−	12.9214i	−0.167945	−	0.626779i
$426$	54.4193	−	6.78865i	2.63662	−	0.328911i
$427$	−1.99172	−	4.49958i	−0.0963863	−	0.217750i
$428$	13.9404	+	18.6878i	0.673834	+	0.903311i
$429$	−1.49415	+	11.3492i	−0.0721384	+	0.547946i
$430$	13.3937	+	51.3797i	0.645902	+	2.47775i
$431$	−20.8085	+	12.0138i	−1.00231	+	0.578684i	−0.908931	−	0.416946i	$-0.863100\pi$
$431$	−20.8085	+	12.0138i	−1.00231	+	0.578684i	−0.0933793	+	0.995631i	$0.529767\pi$
$432$	25.5520	+	11.4070i	1.22937	+	0.548818i
$433$		−	36.1557i		−	1.73753i	−0.495223	−	0.868766i	$-0.664914\pi$
$433$		−	36.1557i		−	1.73753i	0.495223	−	0.868766i	$-0.335086\pi$
$434$	1.50136	−	2.70710i	0.0720677	−	0.129945i
$435$	−36.5477	+	15.1386i	−1.75233	+	0.725839i
$436$	29.4847	+	23.2676i	1.41206	+	1.11432i
$437$	45.2823	−	5.96153i	2.16615	−	0.285179i
$438$	−22.9506	+	17.3642i	−1.09662	+	0.829693i
$439$	5.88443	+	21.9610i	0.280849	+	1.04814i	0.951820	+	0.306658i	$0.0992108\pi$
$439$	5.88443	+	21.9610i	0.280849	+	1.04814i	−0.670971	+	0.741483i	$0.734123\pi$
$440$	−22.8973	+	21.9824i	−1.09159	+	1.04797i
$441$	37.0218	+	8.03628i	1.76294	+	0.382680i
$442$	−2.28566	+	2.93720i	−0.108718	+	0.139708i
$443$	−4.21481	+	3.23414i	−0.200252	+	0.153659i	−0.704020	−	0.710180i	$-0.748613\pi$
$443$	−4.21481	+	3.23414i	−0.200252	+	0.153659i	0.503768	+	0.863839i	$0.331947\pi$
$444$	−0.0687778	+	5.06147i	−0.00326405	+	0.240207i
$445$	−6.36178	+	8.29084i	−0.301577	+	0.393023i
$446$	4.64325	+	0.0315460i	0.219864	+	0.00149374i
$447$	−8.71119			−0.412025
$448$	−10.2747	−	18.5049i	−0.485434	−	0.874273i
$449$	−4.81471			−0.227220			−0.113610	−	0.993525i	$-0.536241\pi$
$449$	−4.81471			−0.227220			−0.113610	+	0.993525i	$0.536241\pi$
$450$	45.1791	+	0.306944i	2.12976	+	0.0144695i
$451$	1.63561	−	2.13156i	0.0770177	−	0.100371i
$452$	−0.139735	+	10.2833i	−0.00657259	+	0.483688i
$453$	−9.13810	+	7.01191i	−0.429345	+	0.329448i
$454$	−8.89839	+	11.4349i	−0.417622	+	0.536667i
$455$	−10.1423	+	0.243700i	−0.475480	+	0.0114249i
$456$	−29.3178	−	30.5379i	−1.37293	−	1.43007i
$457$	7.07254	+	26.3951i	0.330839	+	1.23471i	0.908310	+	0.418298i	$0.137373\pi$
$457$	7.07254	+	26.3951i	0.330839	+	1.23471i	−0.577470	+	0.816412i	$0.695960\pi$
$458$	4.17570	−	3.15929i	0.195118	−	0.147624i
$459$	15.7176	−	2.06926i	0.733635	−	0.0965849i
$460$	45.8830	+	36.2083i	2.13931	+	1.68822i
$461$	9.84179	−	4.07660i	0.458378	−	0.189866i	−0.141532	−	0.989934i	$-0.545203\pi$
$461$	9.84179	−	4.07660i	0.458378	−	0.189866i	0.599910	+	0.800067i	$0.295203\pi$
$462$	−36.8771	+	0.635439i	−1.71568	+	0.0295633i
$463$			27.0212i			1.25578i	0.778302	+	0.627890i	$0.216081\pi$
$463$			27.0212i			1.25578i	−0.778302	+	0.627890i	$0.783919\pi$
$464$	5.90586	+	15.4312i	0.274173	+	0.716375i
$465$	6.86166	−	3.96158i	0.318202	−	0.183714i
$466$	2.50188	+	9.59749i	0.115897	+	0.444595i
$467$	−4.62799	+	35.1531i	−0.214158	+	1.62669i	0.459870	+	0.887986i	$0.347896\pi$
$467$	−4.62799	+	35.1531i	−0.214158	+	1.62669i	−0.674028	+	0.738705i	$0.735437\pi$
$468$	−7.51582	−	10.0754i	−0.347419	−	0.465734i
$469$	7.93088	+	0.850865i	0.366214	+	0.0392893i
$470$	7.90246	−	0.985808i	0.364513	−	0.0454719i
$471$	2.22277	+	8.29550i	0.102420	+	0.382236i
$472$	2.45303	+	22.1053i	0.112910	+	1.01748i
$473$	10.0019	−	37.3276i	0.459888	−	1.71633i
$474$	−46.7058	+	18.9755i	−2.14527	+	0.871572i
$475$	−28.1434	−	11.6574i	−1.29131	−	0.534877i
$476$	−10.4469	−	5.88700i	−0.478831	−	0.269830i
$477$	2.89486	+	6.98880i	0.132546	+	0.319995i
$478$	0.209287	−	30.8049i	0.00957255	−	1.40898i
$479$	−14.7999	−	25.6342i	−0.676225	−	1.17126i	−0.976109	−	0.217281i	$-0.930281\pi$
$479$	−14.7999	−	25.6342i	−0.676225	−	1.17126i	0.299884	−	0.953976i	$-0.403052\pi$
$480$	1.83992	−	54.1436i	0.0839806	−	2.47131i
$481$	0.506697	−	0.877624i	0.0231034	−	0.0400162i
$482$	32.6531	−	18.5577i	1.48731	−	0.845278i
$483$	10.4797	+	67.1026i	0.476844	+	3.05328i
$484$	1.06794	−	0.270655i	0.0485425	−	0.0123025i
$485$	−15.9112	+	12.2091i	−0.722492	+	0.554387i
$486$	1.79159	−	12.9291i	0.0812683	−	0.586476i
$487$	−0.964086	+	3.59802i	−0.0436869	+	0.163042i	−0.984323	−	0.176375i	$-0.943563\pi$
$487$	−0.964086	+	3.59802i	−0.0436869	+	0.163042i	0.940636	+	0.339417i	$0.110230\pi$
$488$	−5.20035	−	0.792773i	−0.235409	−	0.0358871i
$489$	−24.6611	+	24.6611i	−1.11521	+	1.11521i
$490$	−5.59955	−	32.2047i	−0.252962	−	1.45486i
$491$	1.81367	−	4.37859i	0.0818498	−	0.197603i	−0.877656	−	0.479290i	$-0.840894\pi$
$491$	1.81367	−	4.37859i	0.0818498	−	0.197603i	0.959506	+	0.281687i	$0.0908941\pi$
$492$	0.536723	+	4.55417i	0.0241974	+	0.205318i
$493$	7.42642	+	5.69849i	0.334469	+	0.256647i
$494$	2.13784	+	8.20099i	0.0961860	+	0.368980i
$495$	−52.5980	−	30.3675i	−2.36410	−	1.36492i
$496$	−1.57616	−	2.90983i	−0.0707718	−	0.130655i
$497$	8.33218	−	34.3792i	0.373749	−	1.54212i
$498$	7.80215	−	28.3463i	0.349623	−	1.27023i
$499$	−1.21831	+	9.25400i	−0.0545391	+	0.414266i	0.942297	+	0.334779i	$0.108662\pi$
$499$	−1.21831	+	9.25400i	−0.0545391	+	0.414266i	−0.996836	+	0.0794872i	$0.974672\pi$
$500$	−2.20707	−	5.54007i	−0.0987031	−	0.247760i
$501$	−16.7864	+	2.20997i	−0.749961	+	0.0987343i
$502$	19.7572	+	8.34141i	0.881808	+	0.372296i
$503$	−1.64754	+	1.64754i	−0.0734604	+	0.0734604i	−0.742882	−	0.669422i	$-0.766542\pi$
$503$	−1.64754	+	1.64754i	−0.0734604	+	0.0734604i	0.669422	+	0.742882i	$0.266542\pi$
$504$	28.5331	−	28.7417i	1.27097	−	1.28026i
$505$	−1.60578	−	1.60578i	−0.0714563	−	0.0714563i
$506$	−16.0119	−	39.4114i	−0.711816	−	1.75205i
$507$	−4.41088	−	33.5040i	−0.195894	−	1.48796i
$508$	2.56365	+	0.0348362i	0.113744	+	0.00154561i
$509$	−20.5470	−	2.70507i	−0.910730	−	0.119900i	−0.339421	−	0.940635i	$-0.610231\pi$
$509$	−20.5470	−	2.70507i	−0.910730	−	0.119900i	−0.571310	+	0.820735i	$0.693564\pi$
$510$	−15.1652	−	26.6839i	−0.671526	−	1.18158i
$511$	5.23397	+	17.8106i	0.231537	+	0.787893i
$512$	−22.5851	−	1.38268i	−0.998131	−	0.0611064i
$513$	18.0503	−	31.2640i	0.796939	−	1.38034i
$514$	−14.4178	+	24.5850i	−0.635940	+	1.08440i
$515$	−27.1562	+	35.3906i	−1.19664	+	1.55950i
$516$	32.1992	+	57.5630i	1.41749	+	2.53407i
$517$	−5.35487	−	2.21806i	−0.235507	−	0.0975502i
$518$	3.03767	+	1.19736i	0.133468	+	0.0526088i
$519$	−27.2928	−	27.2928i	−1.19802	−	1.19802i
$520$	−5.61317	+	9.28022i	−0.246154	+	0.406965i
$521$	−38.6319	−	10.3514i	−1.69249	−	0.453503i	−0.721463	−	0.692453i	$-0.756530\pi$
$521$	−38.6319	−	10.3514i	−1.69249	−	0.453503i	−0.971032	+	0.238951i	$0.923197\pi$
$522$	−25.2121	+	19.0752i	−1.10351	+	0.834900i
$523$	−5.99843	−	7.81730i	−0.262293	−	0.341827i	0.643578	−	0.765380i	$-0.277449\pi$
$523$	−5.99843	−	7.81730i	−0.262293	−	0.341827i	−0.905871	+	0.423554i	$0.860783\pi$
$524$	−25.8020	−	3.75422i	−1.12717	−	0.164004i
$525$	16.3243	−	42.2537i	0.712451	−	1.84410i
$526$	−2.89457	+	10.5164i	−0.126209	+	0.458535i
$527$	−1.62367	−	0.937423i	−0.0707280	−	0.0408348i
$528$	−20.6351	+	33.5983i	−0.898027	+	1.46218i
$529$	−47.9202	+	27.6667i	−2.08349	+	1.20290i
$530$	4.64658	−	4.58387i	0.201835	−	0.199111i
$531$	−39.3171	+	16.2857i	−1.70622	+	0.706738i
$532$	−25.1175	+	10.7124i	−1.08898	+	0.464443i
$533$	0.351322	−	0.848167i	0.0152175	−	0.0367382i
$534$	−5.04915	+	11.9593i	−0.218498	+	0.517528i
$535$	37.1805	+	9.96247i	1.60745	+	0.430715i
$536$	5.32777	−	6.65782i	0.230125	−	0.287574i
$537$	57.5353	−	15.4165i	2.48283	−	0.665273i
$538$	−24.7739	−	19.2785i	−1.06808	−	0.831154i
$539$	−8.03811	+	22.3915i	−0.346226	+	0.964471i
$540$	44.7830	−	11.3497i	1.92715	−	0.488413i
$541$	−24.1035	−	3.17328i	−1.03629	−	0.136430i	−0.406862	−	0.913490i	$-0.633377\pi$
$541$	−24.1035	−	3.17328i	−1.03629	−	0.136430i	−0.629427	+	0.777059i	$0.716710\pi$
$542$	−2.40688	−	1.41150i	−0.103384	−	0.0606293i
$543$	0.737778	+	1.27787i	0.0316611	+	0.0548386i
$544$	−11.3132	+	6.02892i	−0.485048	+	0.258488i
$545$	62.0105			2.65624
$546$	−12.1150	+	3.47099i	−0.518475	+	0.148545i
$547$	−10.7474	−	25.9464i	−0.459524	−	1.10939i	−0.968590	−	0.248662i	$-0.920009\pi$
$547$	−10.7474	−	25.9464i	−0.459524	−	1.10939i	0.509066	−	0.860727i	$-0.329991\pi$
$548$	−10.9096	−	3.08268i	−0.466034	−	0.131685i
$549$	−1.31381	−	9.97937i	−0.0560720	−	0.425909i
$550$	−3.89437	+	28.1039i	−0.166056	+	1.19835i
$551$	20.5898	−	5.51702i	0.877156	−	0.235033i
$552$	66.4984	+	29.1461i	2.83036	+	1.24054i
$553$	0.781128	+	32.5091i	0.0332170	+	1.38243i
$554$	4.12391	−	0.514445i	0.175208	−	0.0218567i
$555$	5.08753	+	6.63020i	0.215954	+	0.281436i
$556$	−9.42937	+	21.9174i	−0.399895	+	0.929504i
$557$	−3.80158	−	2.91706i	−0.161078	−	0.123600i	0.525077	−	0.851055i	$-0.324036\pi$
$557$	−3.80158	−	2.91706i	−0.161078	−	0.123600i	−0.686156	+	0.727455i	$0.740703\pi$
$558$	4.50779	−	4.44695i	0.190830	−	0.188254i
$559$		−	13.2045i		−	0.558489i
$560$	−32.2425	−	13.4745i	−1.36249	−	0.569401i
$561$			22.3382i			0.943118i
$562$	−4.73239	−	4.79714i	−0.199624	−	0.202355i
$563$	20.8314	+	15.9845i	0.877940	+	0.673667i	0.946053	−	0.324011i	$-0.105031\pi$
$563$	20.8314	+	15.9845i	0.877940	+	0.673667i	−0.0681136	+	0.997678i	$0.521698\pi$
$564$	9.19008	−	3.66117i	0.386972	−	0.154163i
$565$	10.3363	+	13.4705i	0.434851	+	0.566709i
$566$	−4.66710	−	37.4126i	−0.196173	−	1.57257i
$567$	9.41446	+	5.13795i	0.395370	+	0.215774i
$568$	−26.1901	−	27.2801i	−1.09891	−	1.14465i
$569$	11.8607	−	3.17806i	0.497226	−	0.133231i	−0.00148633	−	0.999999i	$-0.500473\pi$
$569$	11.8607	−	3.17806i	0.497226	−	0.133231i	0.498712	+	0.866768i	$0.333806\pi$
$570$	−69.2300	−	9.59323i	−2.89973	−	0.401816i
$571$	−0.829659	−	6.30189i	−0.0347202	−	0.263726i	−0.999997	−	0.00249634i	$-0.999205\pi$
$571$	−0.829659	−	6.30189i	−0.0347202	−	0.263726i	0.965277	−	0.261230i	$-0.0841279\pi$
$572$	6.88910	−	3.85358i	0.288048	−	0.161126i
$573$	−26.2561	−	63.3879i	−1.09687	−	2.64807i
$574$	2.86991	+	0.716232i	0.119788	+	0.0298949i
$575$	52.2454			2.17878
$576$	−9.49226	−	42.2427i	−0.395511	−	1.76011i
$577$	18.9428	+	32.8098i	0.788598	+	1.36589i	0.926826	+	0.375491i	$0.122526\pi$
$577$	18.9428	+	32.8098i	0.788598	+	1.36589i	−0.138228	+	0.990400i	$0.544141\pi$
$578$	8.48801	−	14.4737i	0.353055	−	0.602026i
$579$	10.7940	+	1.42105i	0.448582	+	0.0590569i
$580$	23.4366	+	13.9591i	0.973154	+	0.579622i
$581$	−15.3184	−	11.1800i	−0.635515	−	0.463826i
$582$	−15.3001	+	19.6614i	−0.634209	+	0.814992i
$583$	−4.58860	+	1.22951i	−0.190040	+	0.0509212i
$584$	19.0605	+	5.52597i	0.788731	+	0.228666i
$585$	−20.0455	−	5.37117i	−0.828778	−	0.222070i
$586$	−29.9046	−	12.6256i	−1.23535	−	0.521559i
$587$	−7.57680	+	18.2920i	−0.312728	+	0.754993i	0.686874	+	0.726777i	$0.258983\pi$
$587$	−7.57680	+	18.2920i	−0.312728	+	0.754993i	−0.999602	+	0.0282158i	$0.991017\pi$
$588$	−16.8220	−	36.9564i	−0.693728	−	1.52405i
$589$	−3.94437	+	1.63381i	−0.162525	+	0.0673199i
$590$	25.7876	+	26.1404i	1.06166	+	1.07618i
$591$	41.1453	−	23.7553i	1.69249	−	0.977161i
$592$	2.82598	−	2.04890i	0.116147	−	0.0842091i
$593$	−36.6933	−	21.1849i	−1.50681	−	0.869959i	−0.999969	−	0.00792205i	$-0.997478\pi$
$593$	−36.6933	−	21.1849i	−1.50681	−	0.869959i	−0.506845	−	0.862037i	$-0.669188\pi$
$594$	−32.4184	−	8.92298i	−1.33014	−	0.366114i
$595$	−19.5605	+	3.05486i	−0.801903	+	0.125237i
$596$	3.59174	+	4.81492i	0.147123	+	0.197227i
$597$	21.9921	+	28.6607i	0.900078	+	1.17300i
$598$	−8.77010	−	11.5916i	−0.358636	−	0.474017i
$599$	−1.06266	−	0.284739i	−0.0434191	−	0.0116341i	0.237044	−	0.971499i	$-0.423821\pi$
$599$	−1.06266	−	0.284739i	−0.0434191	−	0.0116341i	−0.280463	+	0.959865i	$0.590488\pi$
$600$	−28.6902	−	39.0109i	−1.17127	−	1.59261i
$601$	−11.6696	−	11.6696i	−0.476014	−	0.476014i	0.427840	−	0.903854i	$-0.359275\pi$
$601$	−11.6696	−	11.6696i	−0.476014	−	0.476014i	−0.903854	+	0.427840i	$0.859275\pi$
$602$	42.0786	−	6.27907i	1.71500	−	0.255916i
$603$	15.0741	+	6.24388i	0.613864	+	0.254271i
$604$	7.64344	+	2.15978i	0.311007	+	0.0878802i
$605$	1.10727	−	1.44302i	0.0450169	−	0.0586672i
$606$	−2.43336	−	1.42703i	−0.0988485	−	0.0579692i
$607$	16.5505	−	28.6664i	0.671765	−	1.16353i	−0.305638	−	0.952148i	$-0.598870\pi$
$607$	16.5505	−	28.6664i	0.671765	−	1.16353i	0.977403	−	0.211384i	$-0.0677970\pi$
$608$	−4.79105	+	28.7960i	−0.194303	+	1.16783i
$609$	8.93693	+	30.4112i	0.362143	+	1.23233i
$610$	−7.55068	+	4.29125i	−0.305718	+	0.173748i
$611$	−1.96353	−	0.258503i	−0.0794357	−	0.0104579i
$612$	−17.1073	−	17.5786i	−0.691522	−	0.710574i
$613$	−4.85502	−	36.8775i	−0.196092	−	1.48947i	−0.752518	−	0.658572i	$-0.771161\pi$
$613$	−4.85502	−	36.8775i	−0.196092	−	1.48947i	0.556426	−	0.830897i	$-0.312172\pi$
$614$	−38.1806	+	15.5119i	−1.54084	+	0.626007i
$615$	5.35344	+	5.35344i	0.215872	+	0.215872i
$616$	15.5561	+	20.1210i	0.626774	+	0.810698i
$617$	−16.3584	+	16.3584i	−0.658565	+	0.658565i	−0.955040	−	0.296476i	$-0.904189\pi$
$617$	−16.3584	+	16.3584i	−0.658565	+	0.658565i	0.296476	+	0.955040i	$0.404189\pi$
$618$	−21.5530	+	51.0498i	−0.866989	+	2.05353i
$619$	25.8960	−	3.40927i	1.04085	−	0.137030i	0.409325	−	0.912389i	$-0.365764\pi$
$619$	25.8960	−	3.40927i	1.04085	−	0.137030i	0.631521	+	0.775358i	$0.282431\pi$
$620$	−5.01883	−	2.15922i	−0.201561	−	0.0867163i
$621$	−8.08162	+	61.3860i	−0.324304	+	2.46334i
$622$	7.06633	+	1.94497i	0.283334	+	0.0779860i
$623$	6.06148	+	5.77703i	0.242848	+	0.231452i
$624$	−3.83928	+	12.9140i	−0.153694	+	0.516972i
$625$	17.0342	+	9.83472i	0.681369	+	0.393389i
$626$	−16.2887	+	4.24614i	−0.651026	+	0.169710i
$627$	40.3562	+	30.9664i	1.61167	+	1.23668i
$628$	3.66868	−	4.64893i	0.146396	−	0.185513i
$629$	0.756776	−	1.82702i	0.0301746	−	0.0728480i
$630$	7.58414	−	66.4330i	0.302159	−	2.64675i
$631$	18.4986	−	18.4986i	0.736416	−	0.736416i	−0.235466	−	0.971883i	$-0.575662\pi$
$631$	18.4986	−	18.4986i	0.736416	−	0.736416i	0.971883	+	0.235466i	$0.0756617\pi$
$632$	29.7457	+	17.9918i	1.18322	+	0.715675i
$633$	8.83517	−	32.9733i	0.351166	−	1.31057i
$634$	14.9685	+	2.07419i	0.594474	+	0.0823765i
$635$	3.35822	−	2.57685i	0.133267	−	0.102259i
$636$	4.14899	−	6.96593i	0.164518	−	0.276217i
$637$	−0.672744	+	8.10115i	−0.0266551	+	0.320979i
$638$	−9.80987	−	17.2610i	−0.388376	−	0.683368i
$639$	36.1801	−	62.6657i	1.43126	−	2.47902i
$640$	−30.6854	+	21.3072i	−1.21295	+	0.842240i
$641$	4.65760	+	8.06719i	0.183964	+	0.318635i	0.943227	−	0.332149i	$-0.107774\pi$
$641$	4.65760	+	8.06719i	0.183964	+	0.318635i	−0.759263	+	0.650784i	$0.774440\pi$
$642$	47.8137	+	0.324843i	1.88706	+	0.0128205i
$643$	9.24993	+	22.3313i	0.364782	+	0.880661i	0.994587	+	0.103908i	$0.0331347\pi$
$643$	9.24993	+	22.3313i	0.364782	+	0.880661i	−0.629805	+	0.776753i	$0.716865\pi$
$644$	32.7686	−	33.4598i	1.29126	−	1.31850i
$645$	100.605	+	41.6718i	3.96131	+	1.64083i
$646$	6.22500	+	15.3221i	0.244919	+	0.602840i
$647$	1.81036	−	6.75636i	0.0711727	−	0.265620i	−0.921166	−	0.389171i	$-0.872762\pi$
$647$	1.81036	−	6.75636i	0.0711727	−	0.265620i	0.992338	+	0.123551i	$0.0394282\pi$
$648$	10.0444	−	5.52932i	0.394582	−	0.217212i
$649$	−6.91690	−	25.8142i	−0.271512	−	1.01330i
$650$	1.20007	+	9.62005i	0.0470707	+	0.377329i
$651$	−2.56967	−	5.80524i	−0.100713	−	0.227525i
$652$	23.7990	+	3.46279i	0.932042	+	0.135613i
$653$	0.206028	−	1.56494i	0.00806252	−	0.0612409i	−0.986941	−	0.161084i	$-0.948501\pi$
$653$	0.206028	−	1.56494i	0.00806252	−	0.0612409i	0.995003	+	0.0998435i	$0.0318342\pi$
$654$	74.5384	−	19.4307i	2.91468	−	0.759801i
$655$	−37.2801	+	21.5237i	−1.45665	+	0.840999i
$656$	2.29592	−	2.17441i	0.0896407	−	0.0848964i
$657$			37.9728i			1.48146i
$658$	−0.109937	−	6.38009i	−0.00428579	−	0.248722i
$659$	38.2118	−	15.8279i	1.48852	−	0.616566i	0.517527	−	0.855667i	$-0.326853\pi$
$659$	38.2118	−	15.8279i	1.48852	−	0.616566i	0.970995	+	0.239101i	$0.0768526\pi$
$660$	7.61914	+	64.6494i	0.296575	+	2.51648i
$661$	−21.6338	+	2.84815i	−0.841458	+	0.110780i	−0.538920	−	0.842357i	$-0.681167\pi$
$661$	−21.6338	+	2.84815i	−0.841458	+	0.110780i	−0.302538	+	0.953137i	$0.597834\pi$
$662$	−7.64422	−	10.1035i	−0.297101	−	0.392685i
$663$	1.97550	+	7.37268i	0.0767222	+	0.286331i
$664$	−18.8847	+	7.37508i	−0.732869	+	0.286209i
$665$	−21.5970	+	39.5729i	−0.837494	+	1.53457i
$666$	5.27104	+	4.10181i	0.204249	+	0.158942i
$667$	−29.0043	+	22.2558i	−1.12305	+	0.861747i
$668$	8.14278	+	8.36712i	0.315053	+	0.323734i
$669$	5.79714	−	7.55498i	0.224130	−	0.292092i
$670$	0.0956439	−	14.0778i	0.00369505	−	0.543874i
$671$	6.32097			0.244018
$672$	−42.9785	−	6.09368i	−1.65793	−	0.235069i
$673$	23.3493			0.900048			0.450024	−	0.893016i	$-0.351415\pi$
$673$	23.3493			0.900048			0.450024	+	0.893016i	$0.351415\pi$
$674$	−0.0683575	+	10.0615i	−0.00263303	+	0.387556i
$675$	25.1391	−	32.7619i	0.967603	−	1.26100i
$676$	−16.6999	+	16.2522i	−0.642305	+	0.625083i
$677$	−21.6679	+	16.6264i	−0.832765	+	0.639003i	−0.934561	−	0.355802i	$-0.884208\pi$
$677$	−21.6679	+	16.6264i	−0.832765	+	0.639003i	0.101796	+	0.994805i	$0.467541\pi$
$678$	16.6455	+	12.9531i	0.639265	+	0.497462i
$679$	8.36692	+	13.7199i	0.321093	+	0.526522i
$680$	−8.49614	+	19.3844i	−0.325812	+	0.743357i
$681$	7.69089	+	28.7028i	0.294716	+	1.09989i
$682$	2.39923	+	3.17111i	0.0918713	+	0.121428i
$683$	45.3740	−	5.97360i	1.73619	−	0.228574i	0.805042	−	0.593218i	$-0.202143\pi$
$683$	45.3740	−	5.97360i	1.73619	−	0.228574i	0.931147	+	0.364645i	$0.118810\pi$
$684$	−55.4727	+	6.53763i	−2.12105	+	0.249973i
$685$	−17.2921	+	7.16261i	−0.660696	+	0.273669i
$686$	−26.1358	+	1.70848i	−0.997870	+	0.0652300i
$687$		−	10.7386i		−	0.409705i
$688$	18.5405	−	41.5314i	0.706852	−	1.58337i
$689$	−1.40573	+	0.811597i	−0.0535540	+	0.0309194i
$690$	115.994	−	30.2374i	4.41582	−	1.15112i
$691$	4.10224	−	31.1596i	0.156057	−	1.18537i	−0.716760	−	0.697320i	$-0.754376\pi$
$691$	4.10224	−	31.1596i	0.156057	−	1.18537i	0.872817	−	0.488048i	$-0.162291\pi$
$692$	−3.83232	+	26.3387i	−0.145683	+	1.00125i
$693$	−28.6892	+	39.3088i	−1.08981	+	1.49322i
$694$	3.80697	+	30.5175i	0.144511	+	1.15843i
$695$	10.1954	+	38.0498i	0.386734	+	1.44331i
$696$	32.5456	+	9.43551i	1.23364	+	0.357652i
$697$	0.463673	−	1.73045i	0.0175629	−	0.0655455i
$698$	−6.74639	−	16.6054i	−0.255355	−	0.628524i
$699$	18.7925	+	7.78410i	0.710797	+	0.294422i
$700$	−30.0855	+	8.39885i	−1.13713	+	0.317447i
$701$	0.665127	+	1.60576i	0.0251215	+	0.0606487i	0.935942	−	0.352153i	$-0.114550\pi$
$701$	0.665127	+	1.60576i	0.0251215	+	0.0606487i	−0.910821	+	0.412802i	$0.864550\pi$
$702$	−11.4888	−	0.0780540i	−0.433615	−	0.00294596i
$703$	−2.25161	−	3.89991i	−0.0849212	−	0.147088i
$704$	27.0789	−	2.44743i	1.02057	−	0.0922410i
$705$	8.16620	−	14.1443i	0.307557	−	0.532704i
$706$	−5.53222	−	9.73422i	−0.208208	−	0.366352i
$707$	−1.41656	+	1.14206i	−0.0532754	+	0.0429517i
$708$	39.1884	+	23.3411i	1.47279	+	0.877212i
$709$	20.1004	−	15.4236i	0.754885	−	0.579244i	−0.158010	−	0.987437i	$-0.550508\pi$
$709$	20.1004	−	15.4236i	0.754885	−	0.579244i	0.912895	+	0.408194i	$0.133841\pi$
$710$	−61.8444	−	8.56980i	−2.32098	−	0.321619i
$711$	−17.2161	+	64.2514i	−0.645654	+	2.40961i
$712$	8.69205	−	2.14016i	0.325749	−	0.0802058i
$713$	5.17766	−	5.17766i	0.193905	−	0.193905i
$714$	−22.5551	+	9.80123i	−0.844103	+	0.366802i
$715$	4.98725	−	12.0403i	0.186513	−	0.450281i
$716$	−32.2437	−	25.4450i	−1.20501	−	0.950922i
$717$	−50.1223	−	38.4602i	−1.87185	−	1.43632i
$718$	−32.2689	+	8.41189i	−1.20427	+	0.313929i
$719$	39.9966	+	23.0921i	1.49162	+	0.861189i	0.999954	−	0.00959402i	$-0.00305392\pi$
$719$	39.9966	+	23.0921i	1.49162	+	0.861189i	0.491668	+	0.870783i	$0.336387\pi$
$720$	−55.5065	−	45.0398i	−2.06860	−	1.67853i
$721$	25.8743	+	24.6601i	0.963609	+	0.918389i
$722$	10.4037	+	2.86356i	0.387187	+	0.106571i
$723$	10.0539	−	76.3673i	0.373910	−	2.84013i
$724$	0.402118	−	0.934673i	0.0149446	−	0.0347368i
$725$	24.1749	−	3.18269i	0.897834	−	0.118202i
$726$	0.878805	−	2.08151i	0.0326155	−	0.0772522i
$727$	−5.06009	+	5.06009i	−0.187668	+	0.187668i	−0.794687	−	0.607019i	$-0.792365\pi$
$727$	−5.06009	+	5.06009i	−0.187668	+	0.187668i	0.607019	+	0.794687i	$0.292365\pi$
$728$	6.91370	+	5.26518i	0.256239	+	0.195141i
$729$	−27.5279	−	27.5279i	−1.01955	−	1.01955i
$730$	30.3549	−	12.3325i	1.12349	−	0.456446i
$731$	−3.36332	−	25.5469i	−0.124397	−	0.944888i
$732$	−7.73149	+	7.52418i	−0.285764	+	0.278102i
$733$	−18.1131	−	2.38464i	−0.669023	−	0.0880786i	−0.211639	−	0.977348i	$-0.567880\pi$
$733$	−18.1131	−	2.38464i	−0.669023	−	0.0880786i	−0.457384	+	0.889269i	$0.651214\pi$
$734$	−9.51758	+	5.40910i	−0.351300	+	0.199653i
$735$	−59.5995	−	30.6920i	−2.19836	−	1.13209i
$736$	−11.3083	−	48.7729i	−0.416829	−	1.79779i
$737$	−5.12312	+	8.87350i	−0.188712	+	0.326859i
$738$	5.21929	+	3.06083i	0.192125	+	0.112671i
$739$	23.8823	−	31.1240i	0.878525	−	1.14492i	−0.110011	−	0.993930i	$-0.535089\pi$
$739$	23.8823	−	31.1240i	0.878525	−	1.14492i	0.988536	−	0.150985i	$-0.0482446\pi$
$740$	1.56704	−	5.54575i	0.0576056	−	0.203866i
$741$	16.0580	+	6.65146i	0.589907	+	0.244347i
$742$	−3.25477	−	4.09369i	−0.119487	−	0.150284i
$743$	−26.4658	−	26.4658i	−0.970935	−	0.970935i	0.0286546	−	0.999589i	$-0.490878\pi$
$743$	−26.4658	−	26.4658i	−0.970935	−	0.970935i	−0.999589	+	0.0286546i	$0.990878\pi$
$744$	−6.70936	−	1.02281i	−0.245977	−	0.0374982i
$745$	9.57955	+	2.56683i	0.350968	+	0.0940415i
$746$	18.3865	+	24.3019i	0.673178	+	0.889754i
$747$	−23.6153	−	30.7761i	−0.864040	−	1.12604i
$748$	12.3469	−	9.21032i	0.451449	−	0.336763i
$749$	11.1150	−	28.7699i	0.406132	−	1.05123i
$750$	−11.7918	−	3.24562i	−0.430575	−	0.118513i
$751$	−15.8133	−	9.12981i	−0.577035	−	0.333152i	0.182919	−	0.983128i	$-0.441445\pi$
$751$	−15.8133	−	9.12981i	−0.577035	−	0.333152i	−0.759954	+	0.649976i	$0.774779\pi$
$752$	−5.81283	−	3.57007i	−0.211972	−	0.130187i
$753$	38.0899	−	21.9912i	1.38807	−	0.801404i
$754$	−4.76423	−	4.82941i	−0.173503	−	0.175877i
$755$	12.1151	−	5.01825i	0.440915	−	0.182633i
$756$	−5.21447	−	36.6483i	−0.189649	−	1.33289i
$757$	3.15552	−	7.61809i	0.114689	−	0.276884i	−0.856103	−	0.516805i	$-0.827121\pi$
$757$	3.15552	−	7.61809i	0.114689	−	0.276884i	0.970793	+	0.239920i	$0.0771214\pi$
$758$	−21.7935	−	9.20110i	−0.791574	−	0.334199i
$759$	−84.2702	−	22.5801i	−3.05881	−	0.819607i
$760$	23.2420	+	42.2208i	0.843077	+	1.53151i
$761$	−14.8504	+	3.97915i	−0.538327	+	0.144244i	−0.517731	−	0.855544i	$-0.673223\pi$
$761$	−14.8504	+	3.97915i	−0.538327	+	0.144244i	−0.0205959	+	0.999788i	$0.506556\pi$
$762$	3.22923	−	4.14973i	0.116983	−	0.150329i
$763$	5.30023	−	49.4033i	0.191881	−	1.78852i
$764$	−24.2105	+	40.6482i	−0.875907	+	1.47060i
$765$	−40.1505	−	5.28591i	−1.45164	−	0.191112i
$766$	19.0319	−	32.4531i	0.687651	−	1.17258i
$767$	−4.56583	−	7.90824i	−0.164862	−	0.285550i
$768$	−30.2082	+	35.2270i	−1.09004	+	1.27114i
$769$	−16.7630			−0.604491			−0.302245	−	0.953230i	$-0.597736\pi$
$769$	−16.7630			−0.604491			−0.302245	+	0.953230i	$0.597736\pi$
$770$	40.7403	+	10.1674i	1.46818	+	0.366407i
$771$	22.3682	+	54.0017i	0.805572	+	1.94482i
$772$	−3.66504	−	6.55205i	−0.131908	−	0.235813i
$773$	3.00307	+	22.8106i	0.108013	+	0.820440i	0.956604	+	0.291391i	$0.0941180\pi$
$773$	3.00307	+	22.8106i	0.108013	+	0.820440i	−0.848591	+	0.529049i	$0.822549\pi$
$774$	86.2030	+	11.9452i	3.09850	+	0.429361i
$775$	−4.71730	+	1.26400i	−0.169450	+	0.0454041i
$776$	17.1759	+	0.350118i	0.616577	+	0.0125685i
$777$	5.71708	−	3.48649i	0.205099	−	0.125077i
$778$	−1.27277	−	10.2028i	−0.0456312	−	0.365790i
$779$	−2.48347	−	3.23652i	−0.0889795	−	0.115960i
$780$	8.23204	+	20.6637i	0.294754	+	0.739877i
$781$	36.0508	+	27.6628i	1.29000	+	0.989852i
$782$	−19.9202	−	20.1927i	−0.712345	−	0.722090i
$783$			28.8968i			1.03269i
$784$	−13.4909	+	24.5356i	−0.481817	+	0.876272i
$785$		−	9.77738i		−	0.348970i
$786$	−38.0674	+	37.5536i	−1.35782	+	1.33949i
$787$	−12.3350	−	9.46495i	−0.439694	−	0.337389i	0.365074	−	0.930978i	$-0.381044\pi$
$787$	−12.3350	−	9.46495i	−0.439694	−	0.337389i	−0.804768	+	0.593590i	$0.797710\pi$
$788$	−30.0950	−	12.9476i	−1.07209	−	0.461238i
$789$	13.6177	+	17.7470i	0.484804	+	0.631809i
$790$	56.9529	−	7.10470i	2.02629	−	0.252774i
$791$	11.6153	−	7.08348i	0.412994	−	0.251859i
$792$	18.9253	+	48.4604i	0.672482	+	1.72196i
$793$	2.08623	−	0.559003i	0.0740841	−	0.0198508i
$794$	−5.02392	+	36.2553i	−0.178292	+	1.28665i
$795$	−1.74723	−	13.2715i	−0.0619679	−	0.470693i
$796$	6.77393	−	23.9729i	0.240096	−	0.849695i
$797$	0.286281	+	0.691142i	0.0101406	+	0.0244815i	0.928869	−	0.370409i	$-0.120782\pi$
$797$	0.286281	+	0.691142i	0.0101406	+	0.0244815i	−0.918728	+	0.394891i	$0.870782\pi$
$798$	−13.5602	+	54.3351i	−0.480025	+	1.92344i
$799$	−3.86472			−0.136724
$800$	−9.73310	+	31.9426i	−0.344117	+	1.12934i
$801$	8.56419	+	14.8336i	0.302601	+	0.524120i
$802$	−20.9021	−	12.2579i	−0.738077	−	0.432841i
$803$	−23.6424	−	3.11257i	−0.834320	−	0.109840i
$804$	−4.29626	−	16.9519i	−0.151517	−	0.597848i
$805$	8.24803	−	76.8796i	0.290705	−	2.70965i
$806$	1.07230	+	0.834443i	0.0377703	+	0.0293920i
$807$	−62.1850	+	16.6624i	−2.18901	+	0.586545i
$808$	0.214547	+	1.93337i	0.00754773	+	0.0680158i
$809$	45.1936	+	12.1096i	1.58892	+	0.425751i	0.941674	−	0.336528i	$-0.109253\pi$
$809$	45.1936	+	12.1096i	1.58892	+	0.425751i	0.647249	+	0.762278i	$0.275919\pi$
$810$	7.36277	−	17.4392i	0.258701	−	0.612752i
$811$	8.23600	−	19.8835i	0.289205	−	0.698203i	−0.710781	−	0.703413i	$-0.751658\pi$
$811$	8.23600	−	19.8835i	0.289205	−	0.698203i	0.999986	+	0.00521019i	$0.00165846\pi$
$812$	13.1243	−	17.4787i	0.460574	−	0.613381i
$813$	−5.28678	+	2.18986i	−0.185415	+	0.0768016i
$814$	−2.98589	+	2.94560i	−0.104656	+	0.103243i
$815$	34.3861	−	19.8528i	1.20449	−	0.695413i
$816$	−4.13860	+	25.9628i	−0.144880	+	0.908880i
$817$	−50.8156	−	29.3384i	−1.77781	−	1.02642i
$818$	−13.7784	+	50.0588i	−0.481750	+	1.75027i
$819$	−5.99252	+	15.5110i	−0.209395	+	0.541997i
$820$	0.751703	−	5.16630i	0.0262506	−	0.180415i
$821$	−33.7338	−	43.9627i	−1.17732	−	1.53431i	−0.790855	−	0.612003i	$-0.790364\pi$
$821$	−33.7338	−	43.9627i	−1.17732	−	1.53431i	−0.386461	−	0.922306i	$-0.626303\pi$
$822$	−18.5412	+	14.0281i	−0.646698	+	0.489284i
$823$	−14.1369	−	3.78796i	−0.492780	−	0.132040i	0.00386704	−	0.999993i	$-0.498769\pi$
$823$	−14.1369	−	3.78796i	−0.492780	−	0.132040i	−0.496647	+	0.867952i	$0.665436\pi$
$824$	37.1033	−	9.13557i	1.29255	−	0.318253i
$825$	41.1449	+	41.1449i	1.43248	+	1.43248i
$826$	23.0300	−	18.3105i	0.801316	−	0.637103i
$827$	−42.9584	−	17.7940i	−1.49381	−	0.618757i	−0.521668	−	0.853148i	$-0.674690\pi$
$827$	−42.9584	−	17.7940i	−1.49381	−	0.618757i	−0.972142	+	0.234392i	$0.924690\pi$
$828$	83.6076	−	46.7679i	2.90557	−	1.62530i
$829$	0.483335	−	0.629895i	0.0167869	−	0.0218771i	−0.784884	−	0.619642i	$-0.787278\pi$
$829$	0.483335	−	0.629895i	0.0167869	−	0.0218771i	0.801671	+	0.597765i	$0.203944\pi$
$830$	−16.9324	+	28.8729i	−0.587732	+	1.00219i
$831$	4.26154	−	7.38120i	0.147831	−	0.256051i
$832$	8.72090	−	3.20252i	0.302343	−	0.111028i
$833$	0.761879	+	15.8448i	0.0263975	+	0.548990i
$834$	24.1779	+	42.5422i	0.837212	+	1.47312i
$835$	19.1109	+	2.51600i	0.661361	+	0.0870698i
$836$	0.476601	−	35.0738i	0.0164836	−	1.21305i
$837$	−0.755440	−	5.73814i	−0.0261118	−	0.198339i
$838$	−5.42700	−	13.3579i	−0.187473	−	0.461441i
$839$	37.9249	+	37.9249i	1.30931	+	1.30931i	0.921910	+	0.387403i	$0.126628\pi$
$839$	37.9249	+	37.9249i	1.30931	+	1.30931i	0.387403	+	0.921910i	$0.373372\pi$
$840$	−61.9342	+	36.0591i	−2.13693	+	1.24416i
$841$	8.44104	−	8.44104i	0.291070	−	0.291070i
$842$	−2.62973	−	1.11026i	−0.0906263	−	0.0382620i
$843$	−13.7015	+	1.80384i	−0.471906	+	0.0621277i
$844$	−21.8681	+	8.71189i	−0.752732	+	0.299876i
$845$	−5.02168	+	38.1435i	−0.172751	+	1.31218i
$846$	3.46386	−	12.5847i	0.119090	−	0.432670i
$847$	−1.05500	−	1.00549i	−0.0362503	−	0.0345491i
$848$	−5.56095	+	0.578884i	−0.190964	+	0.0198789i
$849$	−66.9632	−	38.6612i	−2.29817	−	1.32685i
$850$	4.77213	+	18.3064i	0.163683	+	0.627906i
$851$	6.12742	+	4.70173i	0.210045	+	0.161173i
$852$	−77.0240	+	9.07752i	−2.63880	+	0.310991i
$853$	−14.8158	+	35.7684i	−0.507282	+	1.22469i	0.438160	+	0.898897i	$0.355630\pi$
$853$	−14.8158	+	35.7684i	−0.507282	+	1.22469i	−0.945442	+	0.325790i	$0.894370\pi$
$854$	2.77343	+	6.38235i	0.0949047	+	0.218400i
$855$	−65.2083	+	65.2083i	−2.23008	+	2.23008i
$856$	−19.5347	−	26.5619i	−0.667682	−	0.907868i
$857$	−6.38238	+	23.8194i	−0.218018	+	0.813654i	0.767064	+	0.641570i	$0.221717\pi$
$857$	−6.38238	+	23.8194i	−0.218018	+	0.813654i	−0.985082	+	0.172084i	$0.944950\pi$
$858$	2.22205	−	16.0355i	0.0758594	−	0.547443i
$859$	5.92970	−	4.55002i	0.202319	−	0.155245i	−0.502633	−	0.864500i	$-0.667635\pi$
$859$	5.92970	−	4.55002i	0.202319	−	0.155245i	0.704952	+	0.709255i	$0.250969\pi$
$860$	−18.4475	−	72.7889i	−0.629053	−	2.48208i
$861$	4.72262	−	3.80747i	0.160946	−	0.129758i
$862$	29.5424	−	16.7898i	1.00622	−	0.571861i
$863$	4.84173	−	8.38613i	0.164815	−	0.285467i	−0.771775	−	0.635896i	$-0.780631\pi$
$863$	4.84173	−	8.38613i	0.164815	−	0.285467i	0.936589	+	0.350429i	$0.113964\pi$
$864$	−36.0255	−	16.3770i	−1.22561	−	0.557157i
$865$	21.9714	+	38.0555i	0.747049	+	1.29393i
$866$	−0.347379	+	51.1307i	−0.0118044	+	1.73749i
$867$	−13.1686	−	31.7918i	−0.447229	−	1.07971i
$868$	−2.14921	+	3.81391i	−0.0729489	+	0.129452i
$869$	−38.5925	−	15.9855i	−1.30916	−	0.542272i
$870$	51.8306	−	21.0575i	1.75722	−	0.713917i
$871$	−0.906138	+	3.38175i	−0.0307033	+	0.114586i
$872$	−41.4731	−	33.1879i	−1.40446	−	1.12389i
$873$	8.50781	+	31.7516i	0.287946	+	1.07463i
$874$	−64.0947	+	7.99562i	−2.16804	+	0.270456i
$875$	−4.65079	+	6.37232i	−0.157225	+	0.215424i
$876$	32.6232	−	24.3356i	1.10223	−	0.822224i
$877$	−0.972259	+	7.38504i	−0.0328309	+	0.249375i	−0.999988	−	0.00480227i	$-0.998471\pi$
$877$	−0.972259	+	7.38504i	−0.0328309	+	0.249375i	0.967158	+	0.254177i	$0.0818047\pi$
$878$	−8.11065	−	31.1134i	−0.273721	−	1.05003i
$879$	−57.6530	+	33.2860i	−1.94459	+	1.12271i
$880$	32.5921	−	30.8672i	1.09868	−	1.04053i
$881$			35.6056i			1.19958i	0.800157	+	0.599791i	$0.204750\pi$
$881$			35.6056i			1.19958i	−0.800157	+	0.599791i	$0.795250\pi$
$882$	−52.2784	−	11.7205i	−1.76030	−	0.394648i
$883$	11.6662	−	4.83231i	0.392600	−	0.162620i	−0.177646	−	0.984094i	$-0.556848\pi$
$883$	11.6662	−	4.83231i	0.392600	−	0.162620i	0.570245	+	0.821474i	$0.306848\pi$
$884$	3.26056	−	4.13177i	0.109665	−	0.138966i
$885$	74.6621	−	9.82945i	2.50974	−	0.330413i
$886$	5.99158	−	4.53317i	0.201291	−	0.152295i
$887$	11.1839	+	41.7387i	0.375517	+	1.40145i	0.852587	+	0.522585i	$0.175032\pi$
$887$	11.1839	+	41.7387i	0.375517	+	1.40145i	−0.477070	+	0.878865i	$0.658301\pi$
$888$	0.145894	−	7.15717i	0.00489589	−	0.240179i
$889$	−1.76592	−	2.89572i	−0.0592270	−	0.0971192i
$890$	9.07637	−	11.6636i	0.304241	−	0.390965i
$891$	−10.9303	+	8.38710i	−0.366178	+	0.280978i
$892$	−6.56609	−	0.0892234i	−0.219849	−	0.00298742i
$893$	−5.35748	+	6.98200i	−0.179281	+	0.233644i
$894$	12.3192	+	0.0836959i	0.412016	+	0.00279921i
$895$	−67.8132			−2.26675
$896$	14.3525	+	26.2680i	0.479483	+	0.877551i
$897$	−29.8102			−0.995333
$898$	6.80887	+	0.0462591i	0.227215	+	0.00154369i
$899$	2.08039	−	2.71122i	0.0693848	−	0.0904241i
$900$	−63.8884	−	0.868149i	−2.12961	−	0.0289383i
$901$	−2.51297	+	1.92827i	−0.0837191	+	0.0642399i
$902$	−2.33352	+	2.99870i	−0.0776979	+	0.0998459i
$903$	41.7986	−	76.5891i	1.39097	−	2.54873i
$904$	0.296412	−	14.5412i	0.00985851	−	0.483632i
$905$	−0.434786	−	1.62264i	−0.0144528	−	0.0539385i
$906$	12.9903	−	9.82831i	0.431574	−	0.326524i
$907$	−23.5474	+	3.10007i	−0.781877	+	0.102936i	−0.510889	−	0.859647i	$-0.670684\pi$
$907$	−23.5474	+	3.10007i	−0.781877	+	0.102936i	−0.270988	+	0.962583i	$0.587350\pi$
$908$	12.6938	−	16.0855i	0.421258	−	0.533817i
$909$	−3.43875	+	1.42438i	−0.114056	+	0.0472437i
$910$	14.3454	−	0.247190i	0.475547	−	0.00819428i
$911$			3.03222i			0.100462i	0.998738	+	0.0502310i	$0.0159958\pi$
$911$			3.03222i			0.100462i	−0.998738	+	0.0502310i	$0.984004\pi$
$912$	41.1673	+	43.4679i	1.36319	+	1.43936i
$913$	21.0973	−	12.1805i	0.698218	−	0.403116i
$914$	−9.74825	−	37.3954i	−0.322444	−	1.23693i
$915$	−2.32486	+	17.6591i	−0.0768576	+	0.583792i
$916$	−5.93555	+	4.42769i	−0.196116	+	0.146295i
$917$	13.9613	+	31.5404i	0.461042	+	1.04156i
$918$	−22.2474	+	2.77530i	−0.734274	+	0.0915985i
$919$	10.5520	+	39.3806i	0.348078	+	1.29905i	0.888974	+	0.457957i	$0.151419\pi$
$919$	10.5520	+	39.3806i	0.348078	+	1.29905i	−0.540896	+	0.841090i	$0.681915\pi$
$920$	−64.5390	−	51.6459i	−2.12779	−	1.70271i
$921$	−21.8750	+	81.6385i	−0.720805	+	2.69008i
$922$	−13.9572	+	5.67049i	−0.459657	+	0.186748i
$923$	14.3449	+	5.94186i	0.472169	+	0.195579i
$924$	52.1569	−	0.544316i	1.71584	−	0.0179067i
$925$	−1.97129	−	4.75912i	−0.0648157	−	0.156479i
$926$	0.259616	−	38.2128i	0.00853150	−	1.25575i
$927$	36.5575	+	63.3194i	1.20070	+	2.07968i
$928$	−8.20370	−	21.8792i	−0.269300	−	0.718221i
$929$	17.3047	−	29.9726i	0.567749	−	0.983370i	−0.429039	−	0.903286i	$-0.641148\pi$
$929$	17.3047	−	29.9726i	0.567749	−	0.983370i	0.996788	−	0.0800843i	$-0.0255190\pi$
$930$	−9.74169	+	5.53646i	−0.319442	+	0.181548i
$931$	29.6814	+	20.5885i	0.972770	+	0.674762i
$932$	−3.44590	−	13.5966i	−0.112874	−	0.445372i
$933$	11.9248	−	9.15025i	0.390402	−	0.299566i
$934$	6.88257	−	49.6684i	0.225204	−	1.62520i
$935$	6.58214	−	24.5649i	0.215259	−	0.803358i
$936$	10.5319	+	14.3206i	0.344247	+	0.468083i
$937$	10.2209	−	10.2209i	0.333903	−	0.333903i	−0.520164	−	0.854066i	$-0.674129\pi$
$937$	10.2209	−	10.2209i	0.333903	−	0.333903i	0.854066	+	0.520164i	$0.174129\pi$
$938$	−11.2075	−	1.27948i	−0.365938	−	0.0417764i
$939$	−13.2110	+	31.8942i	−0.431125	+	1.04083i
$940$	−11.1850	+	1.31818i	−0.364814	+	0.0429945i
$941$	−8.68839	−	6.66684i	−0.283234	−	0.217333i	0.457367	−	0.889278i	$-0.348792\pi$
$941$	−8.68839	−	6.66684i	−0.283234	−	0.217333i	−0.740601	+	0.671945i	$0.765459\pi$
$942$	−3.06370	−	11.7527i	−0.0998207	−	0.382923i
$943$	6.05939	+	3.49839i	0.197321	+	0.113923i
$944$	−3.25664	−	31.2844i	−0.105995	−	1.01822i
$945$	−44.2406	−	42.1645i	−1.43915	−	1.37161i
$946$	−14.5031	+	52.6919i	−0.471538	+	1.71316i
$947$	−5.82788	+	44.2671i	−0.189381	+	1.43849i	0.587696	+	0.809082i	$0.300035\pi$
$947$	−5.82788	+	44.2671i	−0.189381	+	1.43849i	−0.777076	+	0.629407i	$0.783298\pi$
$948$	66.2328	−	26.3860i	2.15114	−	0.856978i
$949$	−8.07839	+	1.06354i	−0.262236	+	0.0345240i
$950$	39.6878	+	16.7560i	1.28764	+	0.543638i
$951$	21.9143	−	21.9143i	0.710619	−	0.710619i
$952$	14.7172	+	8.42565i	0.476987	+	0.273077i
$953$	−16.3004	−	16.3004i	−0.528023	−	0.528023i	0.391959	−	0.919982i	$-0.371797\pi$
$953$	−16.3004	−	16.3004i	−0.528023	−	0.528023i	−0.919982	+	0.391959i	$0.871797\pi$
$954$	−4.02670	−	9.91124i	−0.130369	−	0.320888i
$955$	10.1956	+	77.4433i	0.329922	+	2.50600i
$956$	−0.591939	+	43.5617i	−0.0191447	+	1.40889i
$957$	−40.3689	−	5.31467i	−1.30494	−	0.171799i
$958$	20.6835	+	36.3936i	0.668252	+	1.17582i
$959$	4.22838	+	14.3887i	0.136542	+	0.464634i
$960$	−3.12219	+	76.5512i	−0.100768	+	2.47068i
$961$	15.1578	−	26.2540i	0.488960	−	0.846904i
$962$	−0.724993	+	1.23625i	−0.0233747	+	0.0398583i
$963$	38.4063	−	50.0521i	1.23763	−	1.61291i
$964$	−46.3557	+	25.9302i	−1.49302	+	0.835154i
$965$	−11.4512	−	4.74325i	−0.368628	−	0.152691i
$966$	−14.1755	−	94.9960i	−0.456090	−	3.05644i
$967$	19.2573	+	19.2573i	0.619274	+	0.619274i	0.945345	−	0.326071i	$-0.105725\pi$
$967$	19.2573	+	19.2573i	0.619274	+	0.619274i	−0.326071	+	0.945345i	$0.605725\pi$
$968$	−1.51285	+	0.372495i	−0.0486250	+	0.0119724i
$969$	32.7620	+	8.77856i	1.05247	+	0.282008i
$970$	22.6187	−	17.1130i	0.726242	−	0.549466i
$971$	−34.0440	−	44.3670i	−1.09252	−	1.42380i	−0.896411	−	0.443224i	$-0.853835\pi$
$971$	−34.0440	−	44.3670i	−1.09252	−	1.42380i	−0.196113	−	0.980581i	$-0.562832\pi$
$972$	−2.65786	+	18.2669i	−0.0852508	+	0.585911i
$973$	31.1854	−	4.87036i	0.999757	−	0.156137i
$974$	1.39796	−	5.07898i	0.0447936	−	0.162741i
$975$	17.2185	+	9.94112i	0.551434	+	0.318371i
$976$	7.34663	+	1.17109i	0.235160	+	0.0374856i
$977$	12.2437	−	7.06889i	0.391710	−	0.226154i	−0.291191	−	0.956665i	$-0.594051\pi$
$977$	12.2437	−	7.06889i	0.391710	−	0.226154i	0.682901	+	0.730511i	$0.260718\pi$
$978$	35.1122	−	34.6384i	1.12277	−	1.10761i
$979$	−9.93758	+	4.11628i	−0.317606	+	0.131557i
$980$	7.60936	+	45.5970i	0.243072	+	1.45654i
$981$	38.8946	−	93.8999i	1.24181	−	2.99799i
$982$	−2.60693	+	6.17469i	−0.0831904	+	0.197042i
$983$	−3.68641	−	0.987771i	−0.117578	−	0.0315050i	0.199550	−	0.979888i	$-0.436052\pi$
$983$	−3.68641	−	0.987771i	−0.117578	−	0.0315050i	−0.317128	+	0.948383i	$0.602719\pi$
$984$	−0.715268	−	6.44558i	−0.0228019	−	0.205478i
$985$	−52.2466	+	13.9994i	−1.66471	+	0.446059i
$986$	−10.4475	−	8.13005i	−0.332718	−	0.258914i
$987$	−10.5706	−	7.71490i	−0.336467	−	0.245568i
$988$	−2.94450	−	11.6182i	−0.0936770	−	0.369625i
$989$	99.7750	+	13.1356i	3.17266	+	0.417689i
$990$	74.0913	+	43.4504i	2.35478	+	1.38095i
$991$	−15.8858	−	27.5150i	−0.504628	−	0.874041i	−0.999986	−	0.00535213i	$-0.998296\pi$
$991$	−15.8858	−	27.5150i	−0.504628	−	0.874041i	0.495358	−	0.868689i	$-0.335037\pi$
$992$	2.20102	+	4.13017i	0.0698825	+	0.131133i
$993$	−25.9832			−0.824553
$994$	−12.1135	+	48.5384i	−0.384218	+	1.53954i
$995$	−15.7392	−	37.9979i	−0.498967	−	1.20461i
$996$	−11.3060	+	40.0118i	−0.358244	+	1.26782i
$997$	0.133529	+	1.01425i	0.00422890	+	0.0321217i	0.993429	−	0.114448i	$-0.0365100\pi$
$997$	0.133529	+	1.01425i	0.00422890	+	0.0321217i	−0.989200	+	0.146570i	$0.953177\pi$
$998$	1.81183	−	13.0751i	0.0573523	−	0.413886i
$999$	5.89669	−	1.58001i	0.186563	−	0.0499894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.37.1	✓	240
4.3	odd	2		896.2.bh.a.625.29		240
7.4	even	3	inner	224.2.bd.a.165.21	yes	240
28.11	odd	6		896.2.bh.a.753.2		240
32.13	even	8	inner	224.2.bd.a.205.21	yes	240
32.19	odd	8		896.2.bh.a.401.2		240
224.109	even	24	inner	224.2.bd.a.109.1	yes	240
224.179	odd	24		896.2.bh.a.529.29		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.1	✓	240	1.1	even	1	trivial
224.2.bd.a.109.1	yes	240	224.109	even	24	inner
224.2.bd.a.165.21	yes	240	7.4	even	3	inner
224.2.bd.a.205.21	yes	240	32.13	even	8	inner
896.2.bh.a.401.2		240	32.19	odd	8
896.2.bh.a.529.29		240	224.179	odd	24
896.2.bh.a.625.29		240	4.3	odd	2
896.2.bh.a.753.2		240	28.11	odd	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41418 - 0.00960786i) q^{2} +(-1.76562 + 2.30100i) q^{3} +(1.99982 + 0.0271745i) q^{4} +(2.61963 - 2.01011i) q^{5} +(2.51901 - 3.23706i) q^{6} +(-1.37753 - 2.25885i) q^{7} +(-2.82784 - 0.0576436i) q^{8} +(-1.40073 - 5.22759i) q^{9} +O(q^{10})\)	\(q+(-1.41418 - 0.00960786i) q^{2} +(-1.76562 + 2.30100i) q^{3} +(1.99982 + 0.0271745i) q^{4} +(2.61963 - 2.01011i) q^{5} +(2.51901 - 3.23706i) q^{6} +(-1.37753 - 2.25885i) q^{7} +(-2.82784 - 0.0576436i) q^{8} +(-1.40073 - 5.22759i) q^{9} +(-3.72395 + 2.81750i) q^{10} +(3.36958 - 0.443613i) q^{11} +(-3.59344 + 4.55359i) q^{12} +(1.07289 - 0.444407i) q^{13} +(1.92638 + 3.20766i) q^{14} +9.57686i q^{15} +(3.99852 + 0.108688i) q^{16} +(1.96255 - 1.13308i) q^{17} +(1.93066 + 7.40622i) q^{18} +(0.673572 - 5.11629i) q^{19} +(5.29340 - 3.94867i) q^{20} +(7.62981 + 0.818565i) q^{21} +(-4.76946 + 0.594975i) q^{22} +(2.29071 + 8.54904i) q^{23} +(5.12552 - 6.40508i) q^{24} +(1.52781 - 5.70188i) q^{25} +(-1.52153 + 0.618163i) q^{26} +(6.46313 + 2.67711i) q^{27} +(-2.69343 - 4.55472i) q^{28} +(1.58074 + 3.81626i) q^{29} +(0.0920131 - 13.5434i) q^{30} +(-0.413662 - 0.716483i) q^{31} +(-5.65359 - 0.192122i) q^{32} +(-4.92863 + 8.53665i) q^{33} +(-2.78629 + 1.58352i) q^{34} +(-8.14917 - 3.14835i) q^{35} +(-2.65914 - 10.4923i) q^{36} +(0.692315 - 0.531232i) q^{37} +(-1.00171 + 7.22889i) q^{38} +(-0.871740 + 3.25338i) q^{39} +(-7.52377 + 5.53327i) q^{40} +(0.558998 - 0.558998i) q^{41} +(-10.7821 - 1.23090i) q^{42} +(4.35130 - 10.5050i) q^{43} +(6.75059 - 0.795578i) q^{44} +(-14.1774 - 10.8787i) q^{45} +(-3.15734 - 12.1119i) q^{46} +(-1.47692 - 0.852701i) q^{47} +(-7.30996 + 9.00869i) q^{48} +(-3.20480 + 6.22328i) q^{49} +(-2.21539 + 8.04882i) q^{50} +(-0.857903 + 6.51642i) q^{51} +(2.15766 - 0.859576i) q^{52} +(-1.38579 + 0.182443i) q^{53} +(-9.11431 - 3.84802i) q^{54} +(7.93534 - 7.93534i) q^{55} +(3.76523 + 6.46707i) q^{56} +(10.5833 + 10.5833i) q^{57} +(-2.19879 - 5.41206i) q^{58} +(-1.02637 - 7.79609i) q^{59} +(-0.260246 + 19.1520i) q^{60} +(1.84393 + 0.242758i) q^{61} +(0.578108 + 1.01721i) q^{62} +(-9.87879 + 10.3652i) q^{63} +(7.99335 + 0.326014i) q^{64} +(1.91728 - 3.32082i) q^{65} +(7.05200 - 12.0250i) q^{66} +(-1.83529 + 2.39179i) q^{67} +(3.95553 - 2.21262i) q^{68} +(-23.7159 - 9.82343i) q^{69} +(11.4942 + 4.53064i) q^{70} +(9.45424 + 9.45424i) q^{71} +(3.65970 + 14.8635i) q^{72} +(-6.77733 - 1.81598i) q^{73} +(-0.984162 + 0.744606i) q^{74} +(10.4225 + 13.5828i) q^{75} +(1.48605 - 10.2133i) q^{76} +(-5.64376 - 7.00028i) q^{77} +(1.26406 - 4.59249i) q^{78} +(-10.6442 - 6.14541i) q^{79} +(10.6931 - 7.75276i) q^{80} +(-3.51066 + 2.02688i) q^{81} +(-0.795895 + 0.785153i) q^{82} +(6.62223 - 2.74302i) q^{83} +(15.2360 + 1.84431i) q^{84} +(2.86354 - 6.91321i) q^{85} +(-6.25446 + 14.8141i) q^{86} +(-11.5722 - 3.10076i) q^{87} +(-9.55420 + 1.06023i) q^{88} +(-3.05705 + 0.819133i) q^{89} +(19.9450 + 15.5207i) q^{90} +(-2.48179 - 1.81132i) q^{91} +(4.34868 + 17.1588i) q^{92} +(2.37899 + 0.313201i) q^{93} +(2.08044 + 1.22006i) q^{94} +(-8.51981 - 14.7567i) q^{95} +(10.4242 - 12.6697i) q^{96} -6.07384 q^{97} +(4.59197 - 8.77005i) q^{98} +(-7.03890 - 16.9934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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