LMFDB - Embedded newform 224.2.bd.a.109.1

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			109.1
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.1

$q$-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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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	−0.943503	−	0.331365i	$-0.892491\pi$
$3$	−1.76562	−	2.30100i	−1.01938	−	1.32848i	−0.0758775	−	0.997117i	$-0.524176\pi$
$4$	1.99982	−	0.0271745i	0.999908	−	0.0135873i
$5$	2.61963	+	2.01011i	1.17153	+	0.898950i	0.996331	−	0.0855821i	$-0.0272750\pi$
$5$	2.61963	+	2.01011i	1.17153	+	0.898950i	0.175204	+	0.984532i	$0.443942\pi$
$6$	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	0.620075	−	0.784543i	$-0.287102\pi$
$11$	3.36958	+	0.443613i	1.01597	+	0.133754i	0.395891	+	0.918297i	$0.370436\pi$
$12$	−3.59344	−	4.55359i	−1.03734	−	1.31451i
$13$	1.07289	+	0.444407i	0.297567	+	0.123256i	0.526472	−	0.850192i	$-0.323515\pi$
$13$	1.07289	+	0.444407i	0.297567	+	0.123256i	−0.228905	+	0.973449i	$0.573515\pi$
$14$	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	0.718743	−	0.695275i	$-0.244718\pi$
$17$	1.96255	+	1.13308i	0.475989	+	0.274812i	−0.242755	+	0.970088i	$0.578051\pi$
$18$	1.93066	−	7.40622i	0.455061	−	1.74566i
$19$	0.673572	+	5.11629i	0.154528	+	1.17376i	0.876349	+	0.481677i	$0.159972\pi$
$19$	0.673572	+	5.11629i	0.154528	+	1.17376i	−0.721821	+	0.692080i	$0.756694\pi$
$20$	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	−0.133465	−	0.991054i	$-0.542610\pi$
$23$	2.29071	−	8.54904i	0.477646	−	1.78260i	0.611111	−	0.791545i	$-0.290723\pi$
$24$	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	−0.706463	−	0.707750i	$-0.749710\pi$
$29$	1.58074	−	3.81626i	0.293537	−	0.708661i	1.00000		0.000910563i	$-0.000289841\pi$
$30$	0.0920131	+	13.5434i	0.0167992	+	2.47268i
$31$	−0.413662	+	0.716483i	−0.0742958	+	0.128684i	−0.900780	−	0.434276i	$-0.857004\pi$
$31$	−0.413662	+	0.716483i	−0.0742958	+	0.128684i	0.826484	+	0.562960i	$0.190338\pi$
$32$	−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	0.664101	−	0.747643i	$-0.268814\pi$
$37$	0.692315	+	0.531232i	0.113816	+	0.0873340i	−0.550285	+	0.834977i	$0.685481\pi$
$38$	−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	0.749409	−	0.662108i	$-0.230338\pi$
$41$	0.558998	+	0.558998i	0.0873008	+	0.0873008i	−0.662108	+	0.749409i	$0.730338\pi$
$42$	−10.7821	+	1.23090i	−1.66371	+	0.189933i
$43$	4.35130	+	10.5050i	0.663567	+	1.60199i	0.792172	+	0.610298i	$0.208950\pi$
$43$	4.35130	+	10.5050i	0.663567	+	1.60199i	−0.128605	+	0.991696i	$0.541050\pi$
$44$	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	−0.603833	−	0.797111i	$-0.706361\pi$
$47$	−1.47692	+	0.852701i	−0.215431	+	0.124379i	0.388402	+	0.921490i	$0.373027\pi$
$48$	−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	0.0347468	−	0.999396i	$-0.488938\pi$
$53$	−1.38579	−	0.182443i	−0.190353	−	0.0250605i	−0.225100	+	0.974336i	$0.572271\pi$
$54$	−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	0.784907	+	0.619613i	$0.212711\pi$
$59$	−1.02637	+	7.79609i	−0.133623	+	1.01496i	−0.918530	+	0.395351i	$0.870623\pi$
$60$	−0.260246	−	19.1520i	−0.0335977	−	2.47251i
$61$	1.84393	−	0.242758i	0.236091	−	0.0310820i	−0.0115520	−	0.999933i	$-0.503677\pi$
$61$	1.84393	−	0.242758i	0.236091	−	0.0310820i	0.247643	+	0.968851i	$0.420344\pi$
$62$	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	0.667676	−	0.744452i	$-0.267289\pi$
$67$	−1.83529	−	2.39179i	−0.224216	−	0.292204i	−0.891892	+	0.452248i	$0.850622\pi$
$68$	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	0.130573	−	0.991439i	$-0.458318\pi$
$71$	9.45424	−	9.45424i	1.12201	−	1.12201i	0.991439	−	0.130573i	$-0.0416818\pi$
$72$	3.65970	−	14.8635i	0.431300	−	1.75168i
$73$	−6.77733	+	1.81598i	−0.793227	+	0.212545i	−0.632608	−	0.774472i	$-0.718016\pi$
$73$	−6.77733	+	1.81598i	−0.793227	+	0.212545i	−0.160619	+	0.987017i	$0.551349\pi$
$74$	−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	−0.960011	−	0.279963i	$-0.909678\pi$
$79$	−10.6442	+	6.14541i	−1.19756	+	0.691412i	−0.237550	+	0.971375i	$0.576345\pi$
$80$	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	0.715271	−	0.698847i	$-0.246303\pi$
$83$	6.62223	+	2.74302i	0.726884	+	0.301085i	0.0116133	+	0.999933i	$0.496303\pi$
$84$	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	0.0931288	−	0.995654i	$-0.470313\pi$
$89$	−3.05705	−	0.819133i	−0.324046	−	0.0868279i	−0.417175	+	0.908826i	$0.636980\pi$
$90$	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	−0.995330	−	0.0965259i	$-0.969227\pi$
$101$	−0.0897688	+	0.681862i	−0.00893233	+	0.0678478i	0.986398	+	0.164374i	$0.0525603\pi$
$102$	1.27584	+	9.20715i	0.126327	+	0.911644i
$103$	−13.0494	−	3.49659i	−1.28580	−	0.344529i	−0.449736	−	0.893162i	$-0.648482\pi$
$103$	−13.0494	−	3.49659i	−1.28580	−	0.344529i	−0.836064	+	0.548633i	$0.815149\pi$
$104$	−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	−0.312392	−	0.949953i	$-0.601130\pi$
$107$	7.09651	−	9.24835i	0.686045	−	0.894072i	0.998437	+	0.0558816i	$0.0177969\pi$
$108$	12.8523	−	5.52937i	1.23671	−	0.532064i
$109$	14.8990	−	11.4324i	1.42707	−	1.09503i	0.447418	−	0.894325i	$-0.352344\pi$
$109$	14.8990	−	11.4324i	1.42707	−	1.09503i	0.979652	−	0.200704i	$-0.0643229\pi$
$110$	−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	$-0.922240\pi$
$113$		−	5.14215i		−	0.483732i	0.970310	−	0.241866i	$-0.0777595\pi$
$114$	−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	−0.671935	−	0.740610i	$-0.734537\pi$
$131$	−12.9253	+	1.70165i	−1.12929	+	0.148674i	−0.457355	+	0.889284i	$0.651203\pi$
$132$	−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	−0.485007	−	0.874510i	$-0.661183\pi$
$137$	−5.47522	+	1.46708i	−0.467780	+	0.125341i	0.0172270	+	0.999852i	$0.494516\pi$
$138$	33.4441	−	14.1200i	2.84695	−	1.20197i
$139$	−4.56535	−	11.0217i	−0.387228	−	0.934852i	−0.990525	−	0.137335i	$-0.956146\pi$
$139$	−4.56535	−	11.0217i	−0.387228	−	0.934852i	0.603296	−	0.797517i	$-0.293854\pi$
$140$	−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	−0.712432	−	0.701742i	$-0.752406\pi$
$149$	1.82842	−	2.38284i	0.149790	−	0.195210i	0.862221	+	0.506532i	$0.169073\pi$
$150$	−14.6088	+	19.3087i	−1.19280	+	1.57655i
$151$	3.83604	−	1.02786i	0.312173	−	0.0836464i	−0.0993312	−	0.995054i	$-0.531670\pi$
$151$	3.83604	−	1.02786i	0.312173	−	0.0836464i	0.411504	+	0.911408i	$0.365004\pi$
$152$	−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	0.859727	−	0.510754i	$-0.170634\pi$
$157$	1.80259	+	2.34918i	0.143862	+	0.187485i	−0.715865	+	0.698239i	$0.753967\pi$
$158$	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	0.351753	−	0.936093i	$-0.385586\pi$
$163$	11.9219	−	1.56955i	0.933798	−	0.122937i	0.582046	+	0.813156i	$0.302252\pi$
$164$	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	−0.529122	−	0.848545i	$-0.677479\pi$
$167$	4.12786	−	4.12786i	0.319423	−	0.319423i	0.848545	+	0.529122i	$0.177479\pi$
$168$	−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	−0.921248	−	0.388976i	$-0.872829\pi$
$173$	−1.73705	−	13.1942i	−0.132065	−	1.00313i	0.789183	−	0.614158i	$-0.210504\pi$
$174$	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	−0.999145	−	0.0413371i	$-0.986838\pi$
$179$	−16.2932	+	12.5022i	−1.21781	+	0.934462i	−0.218669	+	0.975799i	$0.570172\pi$
$180$	−28.0567	+	22.1407i	−2.09122	+	1.65027i
$181$	0.194691	+	0.470025i	0.0144713	+	0.0349367i	0.930950	−	0.365147i	$-0.118981\pi$
$181$	0.194691	+	0.470025i	0.0144713	+	0.0349367i	−0.916479	+	0.400083i	$0.868981\pi$
$182$	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	−0.875859	−	0.482566i	$-0.839705\pi$
$191$	−11.8280	−	20.4867i	−0.855844	−	1.48237i	0.0200149	−	0.999800i	$-0.493629\pi$
$192$	−14.8634	−	17.8171i	−1.07267	−	1.28584i
$193$	−1.87686	+	3.25082i	−0.135100	+	0.233999i	−0.925635	−	0.378416i	$-0.876469\pi$
$193$	−1.87686	+	3.25082i	−0.135100	+	0.233999i	0.790536	+	0.612416i	$0.209802\pi$
$194$	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	−0.849898	−	0.526948i	$-0.823336\pi$
$197$	−15.1341	+	6.26874i	−1.07826	+	0.446629i	−0.228360	+	0.973577i	$0.573336\pi$
$198$	9.79100	−	24.0994i	0.695816	−	1.71267i
$199$	3.22379	+	12.0313i	0.228528	+	0.852879i	0.980960	+	0.194209i	$0.0622140\pi$
$199$	3.22379	+	12.0313i	0.228528	+	0.852879i	−0.752432	+	0.658670i	$0.771119\pi$
$200$	−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	−0.0244229	−	0.999702i	$-0.507775\pi$
$211$	−10.8739	−	4.50411i	−0.748588	−	0.310075i	−0.724165	+	0.689626i	$0.757775\pi$
$212$	−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	0.953071	−	0.302747i	$-0.0979039\pi$
$227$	6.23703	+	8.12826i	0.413966	+	0.539491i	−0.539104	+	0.842239i	$0.681237\pi$
$228$	20.8771	−	21.4522i	1.38262	−	1.42071i
$229$	−2.93742	−	2.25396i	−0.194110	−	0.148946i	0.507134	−	0.861867i	$-0.330705\pi$
$229$	−2.93742	−	2.25396i	−0.194110	−	0.148946i	−0.701244	+	0.712921i	$0.747372\pi$
$230$	−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	−0.999550	−	0.0299982i	$-0.990450\pi$
$233$	−1.81516	+	6.77428i	−0.118915	+	0.443798i	0.880635	+	0.473796i	$0.157117\pi$
$234$	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	$-0.751168\pi$
$239$		−	21.7829i		−	1.40902i	0.709696	−	0.704508i	$-0.248832\pi$
$240$	−1.04089	−	38.2933i	−0.0671891	−	2.47182i
$241$	−22.9996	−	13.2788i	−1.48153	−	0.855363i	−0.481752	−	0.876308i	$-0.659999\pi$
$241$	−22.9996	−	13.2788i	−1.48153	−	0.855363i	−0.999781	+	0.0209448i	$0.993333\pi$
$242$	−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	−0.778170	−	0.628054i	$-0.783852\pi$
$251$	−14.0102	+	5.80322i	−0.884317	+	0.366296i	−0.106148	+	0.994350i	$0.533852\pi$
$252$	−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	0.987841	+	0.155466i	$0.0496880\pi$
$257$	10.0766	+	17.4531i	0.628558	+	1.08870i	−0.359283	+	0.933229i	$0.616979\pi$
$258$	−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	0.999764	−	0.0217039i	$-0.00690910\pi$
$263$	1.99620	+	7.44993i	0.123091	+	0.459382i	−0.876673	+	0.481086i	$0.840242\pi$
$264$	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	0.0886345	−	0.996064i	$-0.471750\pi$
$269$	17.6100	−	13.5126i	1.07370	−	0.823878i	0.985064	+	0.172186i	$0.0550830\pi$
$270$	−31.6111	−	8.24040i	−1.92379	−	0.501495i
$271$	1.70866	−	0.986498i	0.103794	−	0.0599255i	−0.447204	−	0.894432i	$-0.647580\pi$
$271$	1.70866	−	0.986498i	0.103794	−	0.0599255i	0.550998	+	0.834506i	$0.314247\pi$
$272$	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	0.0424888	−	0.999097i	$-0.486471\pi$
$277$	−2.91350	−	0.383570i	−0.175055	−	0.0230465i	−0.217544	+	0.976050i	$0.569805\pi$
$278$	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	−0.599432	−	0.800426i	$-0.704607\pi$
$281$	3.36927	−	3.36927i	0.200994	−	0.200994i	0.800426	+	0.599432i	$0.204607\pi$
$282$	−6.48063	−	2.63293i	−0.385916	−	0.156789i
$283$	3.47979	−	26.4317i	0.206852	−	1.57120i	−0.501385	−	0.865224i	$-0.667176\pi$
$283$	3.47979	−	26.4317i	0.206852	−	1.57120i	0.708237	−	0.705974i	$-0.249491\pi$
$284$	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	0.335504	−	0.942039i	$-0.391093\pi$
$293$	21.2059	−	8.78378i	1.23886	−	0.513154i	0.903359	+	0.428885i	$0.141093\pi$
$294$	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	0.980823	−	0.194901i	$-0.0624387\pi$
$307$	26.9226	+	11.1517i	1.53655	+	0.636461i	0.555730	+	0.831363i	$0.312439\pi$
$308$	−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	−0.397938	−	0.917412i	$-0.630274\pi$
$311$	−5.00588	+	1.34132i	−0.283857	+	0.0760593i	0.114081	+	0.993471i	$0.463608\pi$
$312$	2.65268	+	9.14978i	0.150178	+	0.518004i
$313$	11.4972	+	3.08065i	0.649858	+	0.174129i	0.568665	−	0.822570i	$-0.307460\pi$
$313$	11.4972	+	3.08065i	0.649858	+	0.174129i	0.0811932	+	0.996698i	$0.474127\pi$
$314$	−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	−0.422021	−	0.906586i	$-0.638679\pi$
$317$	−10.5940	+	1.39473i	−0.595020	+	0.0783359i	−0.172999	+	0.984922i	$0.555346\pi$
$318$	−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	−0.619051	−	0.785351i	$-0.712483\pi$
$331$	5.45369	−	7.10739i	0.299762	−	0.390658i	0.918813	+	0.394693i	$0.129149\pi$
$332$	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	$0.0620756\pi$
$337$			7.11474i			0.387565i	−0.981045	+	0.193782i	$0.937924\pi$
$338$	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	0.728831	+	0.684693i	$0.240064\pi$
$347$	−2.83848	+	21.5604i	−0.152377	+	1.15742i	−0.881209	+	0.472728i	$0.843269\pi$
$348$	−23.0580	+	6.51541i	−1.23604	+	0.349263i
$349$	4.85008	−	11.7091i	0.259619	−	0.626775i	−0.739295	−	0.673382i	$-0.764841\pi$
$349$	4.85008	−	11.7091i	0.259619	−	0.626775i	0.998913	+	0.0466071i	$0.0148409\pi$
$350$	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	−0.741239	−	0.671241i	$-0.765762\pi$
$353$	3.95854	−	6.85640i	0.210692	−	0.364929i	0.951931	+	0.306312i	$0.0990950\pi$
$354$	−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	0.803660	−	0.595089i	$-0.202883\pi$
$359$	22.7767	+	6.10299i	1.20211	+	0.322103i	0.398446	+	0.917192i	$0.369550\pi$
$360$	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	0.664657	−	0.747149i	$-0.268578\pi$
$367$	6.70380	+	3.87044i	0.349936	+	0.202035i	−0.314721	+	0.949184i	$0.601911\pi$
$368$	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	−0.998035	−	0.0626521i	$-0.980044\pi$
$373$	−13.1177	+	17.0953i	−0.679208	+	0.885161i	0.318828	+	0.947813i	$0.396711\pi$
$374$	−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	0.0513454	−	0.998681i	$-0.483649\pi$
$379$	15.4541	−	6.40132i	0.793826	−	0.328814i	0.742481	+	0.669867i	$0.233649\pi$
$380$	−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	−0.975080	−	0.221852i	$-0.928790\pi$
$383$	−13.3014	−	23.0387i	−0.679669	−	1.17722i	0.295411	−	0.955370i	$-0.404543\pi$
$384$	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	−0.950402	−	0.311026i	$-0.899328\pi$
$389$	0.948980	−	7.20822i	0.0481152	−	0.365471i	0.998517	−	0.0544456i	$-0.0173392\pi$
$390$	−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	0.838652	+	0.544668i	$0.183344\pi$
$397$	3.37820	+	25.6599i	0.169547	+	1.28784i	−0.669105	+	0.743168i	$0.733322\pi$
$398$	−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	−0.0814324	−	0.996679i	$-0.525949\pi$
$401$	14.8385	−	8.56703i	0.741001	−	0.427817i	0.822433	+	0.568862i	$0.192616\pi$
$402$	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	0.640293	+	0.768131i	$0.278813\pi$
$409$	9.50210	+	35.4623i	0.469848	+	1.75350i	−0.170444	+	0.985367i	$0.554520\pi$
$410$	−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	−0.799471	−	0.600705i	$-0.794887\pi$
$419$	3.90155	−	9.41917i	0.190603	−	0.460157i	0.990074	+	0.140548i	$0.0448866\pi$
$420$	43.6199	+	25.7946i	2.12843	+	1.25865i
$421$	1.86479	−	0.772420i	0.0908842	−	0.0376455i	−0.336778	−	0.941584i	$-0.609337\pi$
$421$	1.86479	−	0.772420i	0.0908842	−	0.0376455i	0.427662	+	0.903939i	$0.359337\pi$
$422$	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	−0.0933793	−	0.995631i	$-0.529767\pi$
$431$	−20.8085	−	12.0138i	−1.00231	−	0.578684i	−0.908931	+	0.416946i	$0.863100\pi$
$432$	25.5520	−	11.4070i	1.22937	−	0.548818i
$433$			36.1557i			1.73753i	0.495223	+	0.868766i	$0.335086\pi$
$433$			36.1557i			1.73753i	−0.495223	+	0.868766i	$0.664914\pi$
$434$	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	−0.670971	−	0.741483i	$-0.734123\pi$
$439$	5.88443	−	21.9610i	0.280849	−	1.04814i	0.951820	−	0.306658i	$-0.0992108\pi$
$440$	−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	0.503768	−	0.863839i	$-0.331947\pi$
$443$	−4.21481	−	3.23414i	−0.200252	−	0.153659i	−0.704020	+	0.710180i	$0.748613\pi$
$444$	−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	−0.577470	−	0.816412i	$-0.695960\pi$
$457$	7.07254	−	26.3951i	0.330839	−	1.23471i	0.908310	−	0.418298i	$-0.137373\pi$
$458$	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	0.599910	−	0.800067i	$-0.295203\pi$
$461$	9.84179	+	4.07660i	0.458378	+	0.189866i	−0.141532	+	0.989934i	$0.545203\pi$
$462$	−36.8771	−	0.635439i	−1.71568	−	0.0295633i
$463$		−	27.0212i		−	1.25578i	−0.778302	−	0.627890i	$-0.783919\pi$
$463$		−	27.0212i		−	1.25578i	0.778302	−	0.627890i	$-0.216081\pi$
$464$	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	−0.674028	−	0.738705i	$-0.735437\pi$
$467$	−4.62799	−	35.1531i	−0.214158	−	1.62669i	0.459870	−	0.887986i	$-0.347896\pi$
$468$	−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	0.299884	+	0.953976i	$0.403052\pi$
$479$	−14.7999	+	25.6342i	−0.676225	+	1.17126i	−0.976109	+	0.217281i	$0.930281\pi$
$480$	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	0.940636	−	0.339417i	$-0.110230\pi$
$487$	−0.964086	−	3.59802i	−0.0436869	−	0.163042i	−0.984323	+	0.176375i	$0.943563\pi$
$488$	−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	0.959506	−	0.281687i	$-0.0908941\pi$
$491$	1.81367	+	4.37859i	0.0818498	+	0.197603i	−0.877656	+	0.479290i	$0.840894\pi$
$492$	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	−0.996836	−	0.0794872i	$-0.974672\pi$
$499$	−1.21831	−	9.25400i	−0.0545391	−	0.414266i	0.942297	−	0.334779i	$-0.108662\pi$
$500$	−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	0.669422	−	0.742882i	$-0.266542\pi$
$503$	−1.64754	−	1.64754i	−0.0734604	−	0.0734604i	−0.742882	+	0.669422i	$0.766542\pi$
$504$	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	−0.571310	−	0.820735i	$-0.693564\pi$
$509$	−20.5470	+	2.70507i	−0.910730	+	0.119900i	−0.339421	+	0.940635i	$0.610231\pi$
$510$	−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	−0.971032	−	0.238951i	$-0.923197\pi$
$521$	−38.6319	+	10.3514i	−1.69249	+	0.453503i	−0.721463	+	0.692453i	$0.756530\pi$
$522$	−25.2121	−	19.0752i	−1.10351	−	0.834900i
$523$	−5.99843	+	7.81730i	−0.262293	+	0.341827i	−0.905871	−	0.423554i	$-0.860783\pi$
$523$	−5.99843	+	7.81730i	−0.262293	+	0.341827i	0.643578	+	0.765380i	$0.277449\pi$
$524$	−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	−0.629427	−	0.777059i	$-0.716710\pi$
$541$	−24.1035	+	3.17328i	−1.03629	+	0.136430i	−0.406862	+	0.913490i	$0.633377\pi$
$542$	−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	0.509066	+	0.860727i	$0.329991\pi$
$547$	−10.7474	+	25.9464i	−0.459524	+	1.10939i	−0.968590	+	0.248662i	$0.920009\pi$
$548$	−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	−0.686156	−	0.727455i	$-0.740703\pi$
$557$	−3.80158	+	2.91706i	−0.161078	+	0.123600i	0.525077	+	0.851055i	$0.324036\pi$
$558$	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	−0.0681136	−	0.997678i	$-0.521698\pi$
$563$	20.8314	−	15.9845i	0.877940	−	0.673667i	0.946053	+	0.324011i	$0.105031\pi$
$564$	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	0.498712	−	0.866768i	$-0.333806\pi$
$569$	11.8607	+	3.17806i	0.497226	+	0.133231i	−0.00148633	+	0.999999i	$0.500473\pi$
$570$	−69.2300	+	9.59323i	−2.89973	+	0.401816i
$571$	−0.829659	+	6.30189i	−0.0347202	+	0.263726i	0.965277	+	0.261230i	$0.0841279\pi$
$571$	−0.829659	+	6.30189i	−0.0347202	+	0.263726i	−0.999997	+	0.00249634i	$0.999205\pi$
$572$	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	−0.138228	−	0.990400i	$-0.544141\pi$
$577$	18.9428	−	32.8098i	0.788598	−	1.36589i	0.926826	−	0.375491i	$-0.122526\pi$
$578$	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	−0.999602	−	0.0282158i	$-0.991017\pi$
$587$	−7.57680	−	18.2920i	−0.312728	−	0.754993i	0.686874	−	0.726777i	$-0.258983\pi$
$588$	−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	−0.506845	+	0.862037i	$0.669188\pi$
$593$	−36.6933	+	21.1849i	−1.50681	+	0.869959i	−0.999969	+	0.00792205i	$0.997478\pi$
$594$	−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	−0.280463	−	0.959865i	$-0.590488\pi$
$599$	−1.06266	+	0.284739i	−0.0434191	+	0.0116341i	0.237044	+	0.971499i	$0.423821\pi$
$600$	−28.6902	+	39.0109i	−1.17127	+	1.59261i
$601$	−11.6696	+	11.6696i	−0.476014	+	0.476014i	−0.903854	−	0.427840i	$-0.859275\pi$
$601$	−11.6696	+	11.6696i	−0.476014	+	0.476014i	0.427840	+	0.903854i	$0.359275\pi$
$602$	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	0.977403	+	0.211384i	$0.0677970\pi$
$607$	16.5505	+	28.6664i	0.671765	+	1.16353i	−0.305638	+	0.952148i	$0.598870\pi$
$608$	−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	0.556426	+	0.830897i	$0.312172\pi$
$613$	−4.85502	+	36.8775i	−0.196092	+	1.48947i	−0.752518	+	0.658572i	$0.771161\pi$
$614$	−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	0.296476	−	0.955040i	$-0.404189\pi$
$617$	−16.3584	−	16.3584i	−0.658565	−	0.658565i	−0.955040	+	0.296476i	$0.904189\pi$
$618$	−21.5530	−	51.0498i	−0.866989	−	2.05353i
$619$	25.8960	+	3.40927i	1.04085	+	0.137030i	0.631521	−	0.775358i	$-0.282431\pi$
$619$	25.8960	+	3.40927i	1.04085	+	0.137030i	0.409325	+	0.912389i	$0.365764\pi$
$620$	−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	0.971883	−	0.235466i	$-0.0756617\pi$
$631$	18.4986	+	18.4986i	0.736416	+	0.736416i	−0.235466	+	0.971883i	$0.575662\pi$
$632$	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	−0.759263	−	0.650784i	$-0.774440\pi$
$641$	4.65760	−	8.06719i	0.183964	−	0.318635i	0.943227	+	0.332149i	$0.107774\pi$
$642$	47.8137	−	0.324843i	1.88706	−	0.0128205i
$643$	9.24993	−	22.3313i	0.364782	−	0.880661i	−0.629805	−	0.776753i	$-0.716865\pi$
$643$	9.24993	−	22.3313i	0.364782	−	0.880661i	0.994587	−	0.103908i	$-0.0331347\pi$
$644$	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	0.992338	−	0.123551i	$-0.0394282\pi$
$647$	1.81036	+	6.75636i	0.0711727	+	0.265620i	−0.921166	+	0.389171i	$0.872762\pi$
$648$	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	0.995003	−	0.0998435i	$-0.0318342\pi$
$653$	0.206028	+	1.56494i	0.00806252	+	0.0612409i	−0.986941	+	0.161084i	$0.948501\pi$
$654$	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	0.970995	−	0.239101i	$-0.0768526\pi$
$659$	38.2118	+	15.8279i	1.48852	+	0.616566i	0.517527	+	0.855667i	$0.326853\pi$
$660$	7.61914	−	64.6494i	0.296575	−	2.51648i
$661$	−21.6338	−	2.84815i	−0.841458	−	0.110780i	−0.302538	−	0.953137i	$-0.597834\pi$
$661$	−21.6338	−	2.84815i	−0.841458	−	0.110780i	−0.538920	+	0.842357i	$0.681167\pi$
$662$	−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	0.101796	−	0.994805i	$-0.467541\pi$
$677$	−21.6679	−	16.6264i	−0.832765	−	0.639003i	−0.934561	+	0.355802i	$0.884208\pi$
$678$	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	0.931147	−	0.364645i	$-0.118810\pi$
$683$	45.3740	+	5.97360i	1.73619	+	0.228574i	0.805042	+	0.593218i	$0.202143\pi$
$684$	−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	0.872817	+	0.488048i	$0.162291\pi$
$691$	4.10224	+	31.1596i	0.156057	+	1.18537i	−0.716760	+	0.697320i	$0.754376\pi$
$692$	−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	−0.910821	−	0.412802i	$-0.864550\pi$
$701$	0.665127	−	1.60576i	0.0251215	−	0.0606487i	0.935942	+	0.352153i	$0.114550\pi$
$702$	−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	0.912895	−	0.408194i	$-0.133841\pi$
$709$	20.1004	+	15.4236i	0.754885	+	0.579244i	−0.158010	+	0.987437i	$0.550508\pi$
$710$	−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	0.491668	−	0.870783i	$-0.336387\pi$
$719$	39.9966	−	23.0921i	1.49162	−	0.861189i	0.999954	+	0.00959402i	$0.00305392\pi$
$720$	−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	0.607019	−	0.794687i	$-0.292365\pi$
$727$	−5.06009	−	5.06009i	−0.187668	−	0.187668i	−0.794687	+	0.607019i	$0.792365\pi$
$728$	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	−0.457384	−	0.889269i	$-0.651214\pi$
$733$	−18.1131	+	2.38464i	−0.669023	+	0.0880786i	−0.211639	+	0.977348i	$0.567880\pi$
$734$	−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	0.988536	+	0.150985i	$0.0482446\pi$
$739$	23.8823	+	31.1240i	0.878525	+	1.14492i	−0.110011	+	0.993930i	$0.535089\pi$
$740$	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	−0.999589	−	0.0286546i	$-0.990878\pi$
$743$	−26.4658	+	26.4658i	−0.970935	+	0.970935i	0.0286546	+	0.999589i	$0.490878\pi$
$744$	−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	−0.759954	−	0.649976i	$-0.774779\pi$
$751$	−15.8133	+	9.12981i	−0.577035	+	0.333152i	0.182919	+	0.983128i	$0.441445\pi$
$752$	−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	0.970793	−	0.239920i	$-0.0771214\pi$
$757$	3.15552	+	7.61809i	0.114689	+	0.276884i	−0.856103	+	0.516805i	$0.827121\pi$
$758$	−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	−0.0205959	−	0.999788i	$-0.506556\pi$
$761$	−14.8504	−	3.97915i	−0.538327	−	0.144244i	−0.517731	+	0.855544i	$0.673223\pi$
$762$	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	−0.848591	−	0.529049i	$-0.822549\pi$
$773$	3.00307	−	22.8106i	0.108013	−	0.820440i	0.956604	−	0.291391i	$-0.0941180\pi$
$774$	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	−0.804768	−	0.593590i	$-0.797710\pi$
$787$	−12.3350	+	9.46495i	−0.439694	+	0.337389i	0.365074	+	0.930978i	$0.381044\pi$
$788$	−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	−0.918728	−	0.394891i	$-0.870782\pi$
$797$	0.286281	−	0.691142i	0.0101406	−	0.0244815i	0.928869	+	0.370409i	$0.120782\pi$
$798$	−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	0.647249	−	0.762278i	$-0.275919\pi$
$809$	45.1936	−	12.1096i	1.58892	−	0.425751i	0.941674	+	0.336528i	$0.109253\pi$
$810$	7.36277	+	17.4392i	0.258701	+	0.612752i
$811$	8.23600	+	19.8835i	0.289205	+	0.698203i	0.999986	−	0.00521019i	$-0.00165846\pi$
$811$	8.23600	+	19.8835i	0.289205	+	0.698203i	−0.710781	+	0.703413i	$0.751658\pi$
$812$	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	−0.386461	+	0.922306i	$0.626303\pi$
$821$	−33.7338	+	43.9627i	−1.17732	+	1.53431i	−0.790855	+	0.612003i	$0.790364\pi$
$822$	−18.5412	−	14.0281i	−0.646698	−	0.489284i
$823$	−14.1369	+	3.78796i	−0.492780	+	0.132040i	−0.496647	−	0.867952i	$-0.665436\pi$
$823$	−14.1369	+	3.78796i	−0.492780	+	0.132040i	0.00386704	+	0.999993i	$0.498769\pi$
$824$	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	−0.972142	−	0.234392i	$-0.924690\pi$
$827$	−42.9584	+	17.7940i	−1.49381	+	0.618757i	−0.521668	+	0.853148i	$0.674690\pi$
$828$	83.6076	+	46.7679i	2.90557	+	1.62530i
$829$	0.483335	+	0.629895i	0.0167869	+	0.0218771i	0.801671	−	0.597765i	$-0.203944\pi$
$829$	0.483335	+	0.629895i	0.0167869	+	0.0218771i	−0.784884	+	0.619642i	$0.787278\pi$
$830$	−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	0.387403	−	0.921910i	$-0.373372\pi$
$839$	37.9249	−	37.9249i	1.30931	−	1.30931i	0.921910	−	0.387403i	$-0.126628\pi$
$840$	−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	−0.945442	−	0.325790i	$-0.894370\pi$
$853$	−14.8158	−	35.7684i	−0.507282	−	1.22469i	0.438160	−	0.898897i	$-0.355630\pi$
$854$	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	−0.985082	−	0.172084i	$-0.944950\pi$
$857$	−6.38238	−	23.8194i	−0.218018	−	0.813654i	0.767064	−	0.641570i	$-0.221717\pi$
$858$	2.22205	+	16.0355i	0.0758594	+	0.547443i
$859$	5.92970	+	4.55002i	0.202319	+	0.155245i	0.704952	−	0.709255i	$-0.250969\pi$
$859$	5.92970	+	4.55002i	0.202319	+	0.155245i	−0.502633	+	0.864500i	$0.667635\pi$
$860$	−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	0.936589	−	0.350429i	$-0.113964\pi$
$863$	4.84173	+	8.38613i	0.164815	+	0.285467i	−0.771775	+	0.635896i	$0.780631\pi$
$864$	−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	0.967158	−	0.254177i	$-0.0818047\pi$
$877$	−0.972259	−	7.38504i	−0.0328309	−	0.249375i	−0.999988	+	0.00480227i	$0.998471\pi$
$878$	−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	$-0.795250\pi$
$881$		−	35.6056i		−	1.19958i	0.800157	−	0.599791i	$-0.204750\pi$
$882$	−52.2784	+	11.7205i	−1.76030	+	0.394648i
$883$	11.6662	+	4.83231i	0.392600	+	0.162620i	0.570245	−	0.821474i	$-0.306848\pi$
$883$	11.6662	+	4.83231i	0.392600	+	0.162620i	−0.177646	+	0.984094i	$0.556848\pi$
$884$	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	−0.477070	−	0.878865i	$-0.658301\pi$
$887$	11.1839	−	41.7387i	0.375517	−	1.40145i	0.852587	−	0.522585i	$-0.175032\pi$
$888$	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	−0.270988	−	0.962583i	$-0.587350\pi$
$907$	−23.5474	−	3.10007i	−0.781877	−	0.102936i	−0.510889	+	0.859647i	$0.670684\pi$
$908$	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	$-0.984004\pi$
$911$		−	3.03222i		−	0.100462i	0.998738	−	0.0502310i	$-0.0159958\pi$
$912$	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	−0.540896	−	0.841090i	$-0.681915\pi$
$919$	10.5520	−	39.3806i	0.348078	−	1.29905i	0.888974	−	0.457957i	$-0.151419\pi$
$920$	−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	0.996788	+	0.0800843i	$0.0255190\pi$
$929$	17.3047	+	29.9726i	0.567749	+	0.983370i	−0.429039	+	0.903286i	$0.641148\pi$
$930$	−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	0.854066	−	0.520164i	$-0.174129\pi$
$937$	10.2209	+	10.2209i	0.333903	+	0.333903i	−0.520164	+	0.854066i	$0.674129\pi$
$938$	−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	−0.740601	−	0.671945i	$-0.765459\pi$
$941$	−8.68839	+	6.66684i	−0.283234	+	0.217333i	0.457367	+	0.889278i	$0.348792\pi$
$942$	−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	−0.777076	−	0.629407i	$-0.783298\pi$
$947$	−5.82788	−	44.2671i	−0.189381	−	1.43849i	0.587696	−	0.809082i	$-0.300035\pi$
$948$	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	−0.919982	−	0.391959i	$-0.871797\pi$
$953$	−16.3004	+	16.3004i	−0.528023	+	0.528023i	0.391959	+	0.919982i	$0.371797\pi$
$954$	−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	−0.326071	−	0.945345i	$-0.605725\pi$
$967$	19.2573	−	19.2573i	0.619274	−	0.619274i	0.945345	+	0.326071i	$0.105725\pi$
$968$	−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	−0.196113	+	0.980581i	$0.562832\pi$
$971$	−34.0440	+	44.3670i	−1.09252	+	1.42380i	−0.896411	+	0.443224i	$0.853835\pi$
$972$	−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	0.682901	−	0.730511i	$-0.260718\pi$
$977$	12.2437	+	7.06889i	0.391710	+	0.226154i	−0.291191	+	0.956665i	$0.594051\pi$
$978$	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	−0.317128	−	0.948383i	$-0.602719\pi$
$983$	−3.68641	+	0.987771i	−0.117578	+	0.0315050i	0.199550	+	0.979888i	$0.436052\pi$
$984$	−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	0.495358	+	0.868689i	$0.335037\pi$
$991$	−15.8858	+	27.5150i	−0.504628	+	0.874041i	−0.999986	+	0.00535213i	$0.998296\pi$
$992$	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	−0.989200	−	0.146570i	$-0.953177\pi$
$997$	0.133529	−	1.01425i	0.00422890	−	0.0321217i	0.993429	+	0.114448i	$0.0365100\pi$
$998$	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.109.1	yes	240
4.3	odd	2		896.2.bh.a.529.29		240
7.2	even	3	inner	224.2.bd.a.205.21	yes	240
28.23	odd	6		896.2.bh.a.401.2		240
32.5	even	8	inner	224.2.bd.a.165.21	yes	240
32.27	odd	8		896.2.bh.a.753.2		240
224.37	even	24	inner	224.2.bd.a.37.1	✓	240
224.219	odd	24		896.2.bh.a.625.29		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.1	✓	240	224.37	even	24	inner
224.2.bd.a.109.1	yes	240	1.1	even	1	trivial
224.2.bd.a.165.21	yes	240	32.5	even	8	inner
224.2.bd.a.205.21	yes	240	7.2	even	3	inner
896.2.bh.a.401.2		240	28.23	odd	6
896.2.bh.a.529.29		240	4.3	odd	2
896.2.bh.a.625.29		240	224.219	odd	24
896.2.bh.a.753.2		240	32.27	odd	8

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

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