LMFDB - Embedded newform 1338.2.e.g.1075.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(931,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.931"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-12,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 24 x^{10} + x^{9} + 237 x^{8} + 22 x^{7} + 1386 x^{6} + 2016 x^{5} + 2360 x^{4} + \cdots + 16 $ x^12 - 3x^11 + 24x^10 + x^9 + 237x^8 + 22x^7 + 1386x^6 + 2016x^5 + 2360x^4 + 1336x^3 + 568x^2 + 112x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1075.4
Root			$-0.123027 - 0.213090i$ of defining polynomial
Character	$\chi$	$=$	1338.1075
Dual form			1338.2.e.g.931.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.623027 + 1.07912i) q^{5} +(-0.500000 - 0.866025i) q^{6} +4.88222 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.623027 - 1.07912i) q^{10} +(-1.38368 + 2.39661i) q^{11} +(0.500000 + 0.866025i) q^{12} -3.00000 q^{13} -4.88222 q^{14} -1.24605 q^{15} +1.00000 q^{16} +3.18130 q^{17} +(0.500000 - 0.866025i) q^{18} +(1.69092 + 2.92876i) q^{19} +(-0.623027 + 1.07912i) q^{20} +(2.44111 + 4.22812i) q^{21} +(1.38368 - 2.39661i) q^{22} +(-2.41644 - 4.18539i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.72367 + 2.98549i) q^{25} +3.00000 q^{26} -1.00000 q^{27} +4.88222 q^{28} +(-3.74459 + 6.48582i) q^{29} +1.24605 q^{30} +(4.28157 + 7.41590i) q^{31} -1.00000 q^{32} -2.76736 q^{33} -3.18130 q^{34} +(-3.04175 + 5.26847i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.02505 - 3.50749i) q^{37} +(-1.69092 - 2.92876i) q^{38} +(-1.50000 - 2.59808i) q^{39} +(0.623027 - 1.07912i) q^{40} -4.21396 q^{41} +(-2.44111 - 4.22812i) q^{42} +(-4.40644 - 7.63218i) q^{43} +(-1.38368 + 2.39661i) q^{44} +(-0.623027 - 1.07912i) q^{45} +(2.41644 + 4.18539i) q^{46} +(5.19763 - 9.00256i) q^{47} +(0.500000 + 0.866025i) q^{48} +16.8360 q^{49} +(-1.72367 - 2.98549i) q^{50} +(1.59065 + 2.75509i) q^{51} -3.00000 q^{52} +(-4.24085 + 7.34536i) q^{53} +1.00000 q^{54} +(-1.72414 - 2.98630i) q^{55} -4.88222 q^{56} +(-1.69092 + 2.92876i) q^{57} +(3.74459 - 6.48582i) q^{58} +5.05893 q^{59} -1.24605 q^{60} +(-3.81808 - 6.61311i) q^{61} +(-4.28157 - 7.41590i) q^{62} +(-2.44111 + 4.22812i) q^{63} +1.00000 q^{64} +(1.86908 - 3.23735i) q^{65} +2.76736 q^{66} +(4.40039 + 7.62169i) q^{67} +3.18130 q^{68} +(2.41644 - 4.18539i) q^{69} +(3.04175 - 5.26847i) q^{70} +(0.203212 + 0.351974i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-6.67525 + 11.5619i) q^{73} +(-2.02505 + 3.50749i) q^{74} +(-1.72367 + 2.98549i) q^{75} +(1.69092 + 2.92876i) q^{76} +(-6.75543 + 11.7008i) q^{77} +(1.50000 + 2.59808i) q^{78} +(3.20176 - 5.54561i) q^{79} +(-0.623027 + 1.07912i) q^{80} +(-0.500000 - 0.866025i) q^{81} +4.21396 q^{82} +(-3.82066 + 6.61757i) q^{83} +(2.44111 + 4.22812i) q^{84} +(-1.98204 + 3.43299i) q^{85} +(4.40644 + 7.63218i) q^{86} -7.48918 q^{87} +(1.38368 - 2.39661i) q^{88} +(5.53176 + 9.58129i) q^{89} +(0.623027 + 1.07912i) q^{90} -14.6466 q^{91} +(-2.41644 - 4.18539i) q^{92} +(-4.28157 + 7.41590i) q^{93} +(-5.19763 + 9.00256i) q^{94} -4.21396 q^{95} +(-0.500000 - 0.866025i) q^{96} +(6.38892 - 11.0659i) q^{97} -16.8360 q^{98} +(-1.38368 - 2.39661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 6 q^{3} + 12 q^{4} - 3 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + 6 q^{12} - 36 q^{13} + 2 q^{14} - 6 q^{15} + 12 q^{16} + 6 q^{18} + 4 q^{19} - 3 q^{20} - q^{21}+ \cdots + 3 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 + 6 * q^3 + 12 * q^4 - 3 * q^5 - 6 * q^6 - 2 * q^7 - 12 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 + 6 * q^12 - 36 * q^13 + 2 * q^14 - 6 * q^15 + 12 * q^16 + 6 * q^18 + 4 * q^19 - 3 * q^20 - q^21 - 3 * q^22 + 4 * q^23 - 6 * q^24 - 9 * q^25 + 36 * q^26 - 12 * q^27 - 2 * q^28 + 5 * q^29 + 6 * q^30 + 16 * q^31 - 12 * q^32 + 6 * q^33 + 19 * q^35 - 6 * q^36 - q^37 - 4 * q^38 - 18 * q^39 + 3 * q^40 - 8 * q^41 + q^42 - 26 * q^43 + 3 * q^44 - 3 * q^45 - 4 * q^46 + 22 * q^47 + 6 * q^48 + 26 * q^49 + 9 * q^50 - 36 * q^52 + 4 * q^53 + 12 * q^54 + 4 * q^55 + 2 * q^56 - 4 * q^57 - 5 * q^58 - 2 * q^59 - 6 * q^60 - 20 * q^61 - 16 * q^62 + q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 + 3 * q^67 - 4 * q^69 - 19 * q^70 - 20 * q^71 + 6 * q^72 - 19 * q^73 + q^74 + 9 * q^75 + 4 * q^76 - 2 * q^77 + 18 * q^78 - 7 * q^79 - 3 * q^80 - 6 * q^81 + 8 * q^82 - q^83 - q^84 + 3 * q^85 + 26 * q^86 + 10 * q^87 - 3 * q^88 + 17 * q^89 + 3 * q^90 + 6 * q^91 + 4 * q^92 - 16 * q^93 - 22 * q^94 - 8 * q^95 - 6 * q^96 - 8 * q^97 - 26 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$.

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	−0.623027	+	1.07912i	−0.278626	+	0.482595i	−0.971044	−	0.238902i	$-0.923212\pi$
$5$	−0.623027	+	1.07912i	−0.278626	+	0.482595i	0.692417	+	0.721497i	$0.256546\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	4.88222			1.84530			0.922652	−	0.385634i	$-0.126017\pi$
$7$	4.88222			1.84530			0.922652	+	0.385634i	$0.126017\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.623027	−	1.07912i	0.197019	−	0.341246i
$11$	−1.38368	+	2.39661i	−0.417196	+	0.722604i	−0.995656	−	0.0931063i	$-0.970320\pi$
$11$	−1.38368	+	2.39661i	−0.417196	+	0.722604i	0.578460	+	0.815710i	$0.303654\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.00000			−0.832050			−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000			−0.832050			−0.416025	+	0.909353i	$0.636577\pi$
$14$	−4.88222			−1.30483
$15$	−1.24605			−0.321730
$16$	1.00000			0.250000
$17$	3.18130			0.771579			0.385789	−	0.922587i	$-0.373929\pi$
$17$	3.18130			0.771579			0.385789	+	0.922587i	$0.373929\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	1.69092	+	2.92876i	0.387923	+	0.671903i	0.992170	−	0.124894i	$-0.0398592\pi$
$19$	1.69092	+	2.92876i	0.387923	+	0.671903i	−0.604247	+	0.796797i	$0.706526\pi$
$20$	−0.623027	+	1.07912i	−0.139313	+	0.241297i
$21$	2.44111	+	4.22812i	0.532693	+	0.922652i
$22$	1.38368	−	2.39661i	0.295002	−	0.510958i
$23$	−2.41644	−	4.18539i	−0.503862	−	0.872714i	−0.999990	−	0.00446494i	$-0.998579\pi$
$23$	−2.41644	−	4.18539i	−0.503862	−	0.872714i	0.496128	−	0.868249i	$-0.334755\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	1.72367	+	2.98549i	0.344735	+	0.597098i
$26$	3.00000			0.588348
$27$	−1.00000			−0.192450
$28$	4.88222			0.922652
$29$	−3.74459	+	6.48582i	−0.695353	+	1.20439i	0.274709	+	0.961527i	$0.411418\pi$
$29$	−3.74459	+	6.48582i	−0.695353	+	1.20439i	−0.970062	+	0.242859i	$0.921915\pi$
$30$	1.24605			0.227497
$31$	4.28157	+	7.41590i	0.768993	+	1.33193i	0.938110	+	0.346338i	$0.112575\pi$
$31$	4.28157	+	7.41590i	0.768993	+	1.33193i	−0.169117	+	0.985596i	$0.554092\pi$
$32$	−1.00000			−0.176777
$33$	−2.76736			−0.481736
$34$	−3.18130			−0.545589
$35$	−3.04175	+	5.26847i	−0.514150	+	0.890534i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.02505	−	3.50749i	0.332916	−	0.576627i	−0.650166	−	0.759792i	$-0.725301\pi$
$37$	2.02505	−	3.50749i	0.332916	−	0.576627i	0.983082	+	0.183165i	$0.0586341\pi$
$38$	−1.69092	−	2.92876i	−0.274303	−	0.475107i
$39$	−1.50000	−	2.59808i	−0.240192	−	0.416025i
$40$	0.623027	−	1.07912i	0.0985093	−	0.170623i
$41$	−4.21396			−0.658109			−0.329055	−	0.944311i	$-0.606730\pi$
$41$	−4.21396			−0.658109			−0.329055	+	0.944311i	$0.606730\pi$
$42$	−2.44111	−	4.22812i	−0.376671	−	0.652414i
$43$	−4.40644	−	7.63218i	−0.671976	−	1.16390i	−0.977343	−	0.211662i	$-0.932113\pi$
$43$	−4.40644	−	7.63218i	−0.671976	−	1.16390i	0.305367	−	0.952235i	$-0.401221\pi$
$44$	−1.38368	+	2.39661i	−0.208598	+	0.361302i
$45$	−0.623027	−	1.07912i	−0.0928754	−	0.160865i
$46$	2.41644	+	4.18539i	0.356284	+	0.617102i
$47$	5.19763	−	9.00256i	0.758152	−	1.31316i	−0.185640	−	0.982618i	$-0.559436\pi$
$47$	5.19763	−	9.00256i	0.758152	−	1.31316i	0.943792	−	0.330540i	$-0.107231\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	16.8360			2.40515
$50$	−1.72367	−	2.98549i	−0.243764	−	0.422212i
$51$	1.59065	+	2.75509i	0.222736	+	0.385789i
$52$	−3.00000			−0.416025
$53$	−4.24085	+	7.34536i	−0.582525	+	1.00896i	0.412654	+	0.910888i	$0.364602\pi$
$53$	−4.24085	+	7.34536i	−0.582525	+	1.00896i	−0.995179	+	0.0980754i	$0.968731\pi$
$54$	1.00000			0.136083
$55$	−1.72414	−	2.98630i	−0.232483	−	0.402673i
$56$	−4.88222			−0.652414
$57$	−1.69092	+	2.92876i	−0.223968	+	0.387923i
$58$	3.74459	−	6.48582i	0.491689	−	0.851630i
$59$	5.05893			0.658617			0.329309	−	0.944222i	$-0.393184\pi$
$59$	5.05893			0.658617			0.329309	+	0.944222i	$0.393184\pi$
$60$	−1.24605			−0.160865
$61$	−3.81808	−	6.61311i	−0.488855	−	0.846722i	0.511063	−	0.859543i	$-0.329252\pi$
$61$	−3.81808	−	6.61311i	−0.488855	−	0.846722i	−0.999918	+	0.0128216i	$0.995919\pi$
$62$	−4.28157	−	7.41590i	−0.543760	−	0.941820i
$63$	−2.44111	+	4.22812i	−0.307551	+	0.532693i
$64$	1.00000			0.125000
$65$	1.86908	−	3.23735i	0.231831	−	0.401543i
$66$	2.76736			0.340639
$67$	4.40039	+	7.62169i	0.537593	+	0.931138i	0.999033	+	0.0439667i	$0.0139996\pi$
$67$	4.40039	+	7.62169i	0.537593	+	0.931138i	−0.461440	+	0.887171i	$0.652667\pi$
$68$	3.18130			0.385789
$69$	2.41644	−	4.18539i	0.290905	−	0.503862i
$70$	3.04175	−	5.26847i	0.363559	−	0.629703i
$71$	0.203212	+	0.351974i	0.0241168	+	0.0417716i	0.877832	−	0.478969i	$-0.158989\pi$
$71$	0.203212	+	0.351974i	0.0241168	+	0.0417716i	−0.853715	+	0.520740i	$0.825656\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−6.67525	+	11.5619i	−0.781279	+	1.35321i	0.149919	+	0.988698i	$0.452099\pi$
$73$	−6.67525	+	11.5619i	−0.781279	+	1.35321i	−0.931197	+	0.364516i	$0.881235\pi$
$74$	−2.02505	+	3.50749i	−0.235407	+	0.407737i
$75$	−1.72367	+	2.98549i	−0.199033	+	0.344735i
$76$	1.69092	+	2.92876i	0.193962	+	0.335952i
$77$	−6.75543	+	11.7008i	−0.769853	+	1.33342i
$78$	1.50000	+	2.59808i	0.169842	+	0.294174i
$79$	3.20176	−	5.54561i	0.360226	−	0.623930i	−0.627772	−	0.778398i	$-0.716033\pi$
$79$	3.20176	−	5.54561i	0.360226	−	0.623930i	0.987998	+	0.154467i	$0.0493661\pi$
$80$	−0.623027	+	1.07912i	−0.0696566	+	0.120649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.21396			0.465354
$83$	−3.82066	+	6.61757i	−0.419371	+	0.726373i	−0.995876	−	0.0907211i	$-0.971083\pi$
$83$	−3.82066	+	6.61757i	−0.419371	+	0.726373i	0.576505	+	0.817094i	$0.304416\pi$
$84$	2.44111	+	4.22812i	0.266347	+	0.461326i
$85$	−1.98204	+	3.43299i	−0.214982	+	0.372360i
$86$	4.40644	+	7.63218i	0.475159	+	0.822999i
$87$	−7.48918			−0.802924
$88$	1.38368	−	2.39661i	0.147501	−	0.255479i
$89$	5.53176	+	9.58129i	0.586365	+	1.01561i	0.994704	+	0.102784i	$0.0327750\pi$
$89$	5.53176	+	9.58129i	0.586365	+	1.01561i	−0.408339	+	0.912831i	$0.633892\pi$
$90$	0.623027	+	1.07912i	0.0656729	+	0.113749i
$91$	−14.6466			−1.53539
$92$	−2.41644	−	4.18539i	−0.251931	−	0.436357i
$93$	−4.28157	+	7.41590i	−0.443978	+	0.768993i
$94$	−5.19763	+	9.00256i	−0.536094	+	0.928543i
$95$	−4.21396			−0.432343
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	6.38892	−	11.0659i	0.648697	−	1.12358i	−0.334737	−	0.942311i	$-0.608648\pi$
$97$	6.38892	−	11.0659i	0.648697	−	1.12358i	0.983434	−	0.181265i	$-0.0580191\pi$
$98$	−16.8360			−1.70070
$99$	−1.38368	−	2.39661i	−0.139065	−	0.240868i
$100$	1.72367	+	2.98549i	0.172367	+	0.298549i
$101$	2.18092	+	3.77747i	0.217010	+	0.375872i	0.953892	−	0.300149i	$-0.0970363\pi$
$101$	2.18092	+	3.77747i	0.217010	+	0.375872i	−0.736883	+	0.676021i	$0.763703\pi$
$102$	−1.59065	−	2.75509i	−0.157498	−	0.272794i
$103$	−16.8443			−1.65972			−0.829859	−	0.557973i	$-0.811579\pi$
$103$	−16.8443			−1.65972			−0.829859	+	0.557973i	$0.811579\pi$
$104$	3.00000			0.294174
$105$	−6.08351			−0.593690
$106$	4.24085	−	7.34536i	0.411908	−	0.713445i
$107$	3.59836	−	6.23253i	0.347866	−	0.602522i	−0.638004	−	0.770033i	$-0.720240\pi$
$107$	3.59836	−	6.23253i	0.347866	−	0.602522i	0.985870	+	0.167511i	$0.0535730\pi$
$108$	−1.00000			−0.0962250
$109$	−4.42315	+	7.66111i	−0.423660	+	0.733801i	−0.996294	−	0.0860098i	$-0.972588\pi$
$109$	−4.42315	+	7.66111i	−0.423660	+	0.733801i	0.572634	+	0.819811i	$0.305922\pi$
$110$	1.72414	+	2.98630i	0.164391	+	0.284733i
$111$	4.05010			0.384418
$112$	4.88222			0.461326
$113$	3.60698	+	6.24747i	0.339316	+	0.587712i	0.984304	−	0.176480i	$-0.0564711\pi$
$113$	3.60698	+	6.24747i	0.339316	+	0.587712i	−0.644988	+	0.764192i	$0.723138\pi$
$114$	1.69092	−	2.92876i	0.158369	−	0.274303i
$115$	6.02202			0.561557
$116$	−3.74459	+	6.48582i	−0.347676	+	0.602193i
$117$	1.50000	−	2.59808i	0.138675	−	0.240192i
$118$	−5.05893			−0.465713
$119$	15.5318			1.42380
$120$	1.24605			0.113749
$121$	1.67085	+	2.89400i	0.151896	+	0.263091i
$122$	3.81808	+	6.61311i	0.345673	+	0.598723i
$123$	−2.10698	−	3.64939i	−0.189980	−	0.329055i
$124$	4.28157	+	7.41590i	0.384496	+	0.665967i
$125$	−10.5259			−0.941461
$126$	2.44111	−	4.22812i	0.217471	−	0.376671i
$127$	5.06083	+	8.76561i	0.449076	+	0.777822i	0.998326	−	0.0578359i	$-0.0184200\pi$
$127$	5.06083	+	8.76561i	0.449076	+	0.777822i	−0.549250	+	0.835658i	$0.685087\pi$
$128$	−1.00000			−0.0883883
$129$	4.40644	−	7.63218i	0.387965	−	0.671976i
$130$	−1.86908	+	3.23735i	−0.163929	+	0.283934i
$131$	6.99378	+	12.1136i	0.611049	+	1.05837i	0.991064	+	0.133388i	$0.0425857\pi$
$131$	6.99378	+	12.1136i	0.611049	+	1.05837i	−0.380014	+	0.924981i	$0.624081\pi$
$132$	−2.76736			−0.240868
$133$	8.25543	+	14.2988i	0.715837	+	1.23987i
$134$	−4.40039	−	7.62169i	−0.380136	−	0.658414i
$135$	0.623027	−	1.07912i	0.0536217	−	0.0928754i
$136$	−3.18130			−0.272794
$137$	−4.46387	−	7.73164i	−0.381374	−	0.660559i	0.609885	−	0.792490i	$-0.291216\pi$
$137$	−4.46387	−	7.73164i	−0.381374	−	0.660559i	−0.991259	+	0.131931i	$0.957882\pi$
$138$	−2.41644	+	4.18539i	−0.205701	+	0.356284i
$139$	−9.00782	−	15.6020i	−0.764033	−	1.32334i	−0.940756	−	0.339084i	$-0.889883\pi$
$139$	−9.00782	−	15.6020i	−0.764033	−	1.32334i	0.176723	−	0.984261i	$-0.443450\pi$
$140$	−3.04175	+	5.26847i	−0.257075	+	0.445267i
$141$	10.3953			0.875438
$142$	−0.203212	−	0.351974i	−0.0170532	−	0.0295370i
$143$	4.15104	−	7.18982i	0.347128	−	0.601243i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−4.66596	−	8.08168i	−0.387487	−	0.671147i
$146$	6.67525	−	11.5619i	0.552447	−	0.956867i
$147$	8.41801	+	14.5804i	0.694306	+	1.20257i
$148$	2.02505	−	3.50749i	0.166458	−	0.288314i
$149$	−4.71183	+	8.16114i	−0.386009	+	0.668586i	−0.991909	−	0.126954i	$-0.959480\pi$
$149$	−4.71183	+	8.16114i	−0.386009	+	0.668586i	0.605900	+	0.795541i	$0.292813\pi$
$150$	1.72367	−	2.98549i	0.140737	−	0.243764i
$151$	−6.15334	+	10.6579i	−0.500751	+	0.867327i	0.499248	+	0.866459i	$0.333610\pi$
$151$	−6.15334	+	10.6579i	−0.500751	+	0.867327i	−1.00000		0.000867766i	$0.999724\pi$
$152$	−1.69092	−	2.92876i	−0.137152	−	0.237554i
$153$	−1.59065	+	2.75509i	−0.128596	+	0.222736i
$154$	6.75543	−	11.7008i	0.544368	−	0.942873i
$155$	−10.6701			−0.857046
$156$	−1.50000	−	2.59808i	−0.120096	−	0.208013i
$157$	5.51207			0.439911			0.219956	−	0.975510i	$-0.429409\pi$
$157$	5.51207			0.439911			0.219956	+	0.975510i	$0.429409\pi$
$158$	−3.20176	+	5.54561i	−0.254719	+	0.441185i
$159$	−8.48170			−0.672642
$160$	0.623027	−	1.07912i	0.0492546	−	0.0853115i
$161$	−11.7976	−	20.4340i	−0.929778	−	1.61042i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−6.41300			−0.502305			−0.251152	−	0.967948i	$-0.580810\pi$
$163$	−6.41300			−0.502305			−0.251152	+	0.967948i	$0.580810\pi$
$164$	−4.21396			−0.329055
$165$	1.72414	−	2.98630i	0.134224	−	0.232483i
$166$	3.82066	−	6.61757i	0.296540	−	0.513623i
$167$	11.0406			0.854349			0.427175	−	0.904169i	$-0.359509\pi$
$167$	11.0406			0.854349			0.427175	+	0.904169i	$0.359509\pi$
$168$	−2.44111	−	4.22812i	−0.188336	−	0.326207i
$169$	−4.00000			−0.307692
$170$	1.98204	−	3.43299i	0.152015	−	0.263298i
$171$	−3.38184			−0.258616
$172$	−4.40644	−	7.63218i	−0.335988	−	0.581948i
$173$	−1.70992	−	2.96167i	−0.130003	−	0.225172i	0.793675	−	0.608343i	$-0.208165\pi$
$173$	−1.70992	−	2.96167i	−0.130003	−	0.225172i	−0.923677	+	0.383171i	$0.874832\pi$
$174$	7.48918			0.567753
$175$	8.41535	+	14.5758i	0.636140	+	1.10183i
$176$	−1.38368	+	2.39661i	−0.104299	+	0.180651i
$177$	2.52947	+	4.38117i	0.190126	+	0.329309i
$178$	−5.53176	−	9.58129i	−0.414623	−	0.718148i
$179$	7.74315	−	13.4115i	0.578750	−	1.00242i	−0.416873	−	0.908965i	$-0.636874\pi$
$179$	7.74315	−	13.4115i	0.578750	−	1.00242i	0.995623	−	0.0934595i	$-0.0297926\pi$
$180$	−0.623027	−	1.07912i	−0.0464377	−	0.0804325i
$181$	−7.97023	−	13.8049i	−0.592423	−	1.02611i	−0.993905	−	0.110240i	$-0.964838\pi$
$181$	−7.97023	−	13.8049i	−0.592423	−	1.02611i	0.401482	−	0.915867i	$-0.368495\pi$
$182$	14.6466			1.08568
$183$	3.81808	−	6.61311i	0.282241	−	0.488855i
$184$	2.41644	+	4.18539i	0.178142	+	0.308551i
$185$	2.52332	+	4.37052i	0.185518	+	0.321327i
$186$	4.28157	−	7.41590i	0.313940	−	0.543760i
$187$	−4.40191	+	7.62433i	−0.321899	+	0.557546i
$188$	5.19763	−	9.00256i	0.379076	−	0.656579i
$189$	−4.88222			−0.355129
$190$	4.21396			0.305712
$191$	−9.41194			−0.681024			−0.340512	−	0.940240i	$-0.610600\pi$
$191$	−9.41194			−0.681024			−0.340512	+	0.940240i	$0.610600\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	23.9432			1.72347			0.861735	−	0.507358i	$-0.169378\pi$
$193$	23.9432			1.72347			0.861735	+	0.507358i	$0.169378\pi$
$194$	−6.38892	+	11.0659i	−0.458698	+	0.794488i
$195$	3.73816			0.267696
$196$	16.8360			1.20257
$197$	5.90311			0.420580			0.210290	−	0.977639i	$-0.432559\pi$
$197$	5.90311			0.420580			0.210290	+	0.977639i	$0.432559\pi$
$198$	1.38368	+	2.39661i	0.0983340	+	0.170319i
$199$	4.12432	+	7.14353i	0.292365	+	0.506392i	0.974369	−	0.224957i	$-0.0722243\pi$
$199$	4.12432	+	7.14353i	0.292365	+	0.506392i	−0.682003	+	0.731349i	$0.738891\pi$
$200$	−1.72367	−	2.98549i	−0.121882	−	0.211106i
$201$	−4.40039	+	7.62169i	−0.310379	+	0.537593i
$202$	−2.18092	−	3.77747i	−0.153449	−	0.265782i
$203$	−18.2819	+	31.6652i	−1.28314	+	2.22246i
$204$	1.59065	+	2.75509i	0.111368	+	0.192895i
$205$	2.62541	−	4.54734i	0.183367	−	0.317600i
$206$	16.8443			1.17360
$207$	4.83287			0.335908
$208$	−3.00000			−0.208013
$209$	−9.35877			−0.647360
$210$	6.08351			0.419802
$211$	2.82616	+	4.89506i	0.194561	+	0.336990i	0.946757	−	0.321950i	$-0.104338\pi$
$211$	2.82616	+	4.89506i	0.194561	+	0.336990i	−0.752195	+	0.658940i	$0.771005\pi$
$212$	−4.24085	+	7.34536i	−0.291263	+	0.504482i
$213$	−0.203212	+	0.351974i	−0.0139239	+	0.0241168i
$214$	−3.59836	+	6.23253i	−0.245979	+	0.426047i
$215$	10.9813			0.748921
$216$	1.00000			0.0680414
$217$	20.9035	+	36.2060i	1.41903	+	2.45782i
$218$	4.42315	−	7.66111i	0.299573	−	0.518876i
$219$	−13.3505			−0.902143
$220$	−1.72414	−	2.98630i	−0.116242	−	0.201337i
$221$	−9.54390			−0.641992
$222$	−4.05010			−0.271825
$223$	12.5404	−	8.10792i	0.839767	−	0.542946i
$223$	12.5404	−	8.10792i	0.839767	−	0.542946i
$224$	−4.88222			−0.326207
$225$	−3.44735			−0.229823
$226$	−3.60698	−	6.24747i	−0.239933	−	0.415575i
$227$	−8.40101			−0.557595			−0.278797	−	0.960350i	$-0.589936\pi$
$227$	−8.40101			−0.557595			−0.278797	+	0.960350i	$0.589936\pi$
$228$	−1.69092	+	2.92876i	−0.111984	+	0.193962i
$229$	−8.44423	−	14.6258i	−0.558010	−	0.966502i	−0.997662	−	0.0683342i	$-0.978232\pi$
$229$	−8.44423	−	14.6258i	−0.558010	−	0.966502i	0.439652	−	0.898168i	$-0.355102\pi$
$230$	−6.02202			−0.397080
$231$	−13.5109			−0.888950
$232$	3.74459	−	6.48582i	0.245844	−	0.425815i
$233$	10.1970	−	17.6617i	0.668027	−	1.15706i	−0.310428	−	0.950597i	$-0.600472\pi$
$233$	10.1970	−	17.6617i	0.668027	−	1.15706i	0.978455	−	0.206460i	$-0.0661944\pi$
$234$	−1.50000	+	2.59808i	−0.0980581	+	0.169842i
$235$	6.47653	+	11.2177i	0.422482	+	0.731761i
$236$	5.05893			0.329309
$237$	6.40352			0.415954
$238$	−15.5318			−1.00678
$239$	11.6854			0.755863			0.377931	−	0.925834i	$-0.376636\pi$
$239$	11.6854			0.755863			0.377931	+	0.925834i	$0.376636\pi$
$240$	−1.24605			−0.0804325
$241$	9.75564	−	16.8973i	0.628416	−	1.08845i	−0.359454	−	0.933163i	$-0.617037\pi$
$241$	9.75564	−	16.8973i	0.628416	−	1.08845i	0.987870	−	0.155286i	$-0.0496298\pi$
$242$	−1.67085	−	2.89400i	−0.107406	−	0.186033i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.81808	−	6.61311i	−0.244428	−	0.423361i
$245$	−10.4893	+	18.1680i	−0.670137	+	1.16071i
$246$	2.10698	+	3.64939i	0.134336	+	0.232677i
$247$	−5.07276	−	8.78627i	−0.322772	−	0.559057i
$248$	−4.28157	−	7.41590i	−0.271880	−	0.470910i
$249$	−7.64131			−0.484248
$250$	10.5259			0.665714
$251$	11.2266			0.708616			0.354308	−	0.935129i	$-0.384716\pi$
$251$	11.2266			0.708616			0.354308	+	0.935129i	$0.384716\pi$
$252$	−2.44111	+	4.22812i	−0.153775	+	0.266347i
$253$	13.3743			0.840836
$254$	−5.06083	−	8.76561i	−0.317544	−	0.550003i
$255$	−3.96407			−0.248240
$256$	1.00000			0.0625000
$257$	−12.6258			−0.787573			−0.393787	−	0.919202i	$-0.628835\pi$
$257$	−12.6258			−0.787573			−0.393787	+	0.919202i	$0.628835\pi$
$258$	−4.40644	+	7.63218i	−0.274333	+	0.475159i
$259$	9.88673	−	17.1243i	0.614331	−	1.06405i
$260$	1.86908	−	3.23735i	0.115916	−	0.200772i
$261$	−3.74459	−	6.48582i	−0.231784	−	0.401462i
$262$	−6.99378	−	12.1136i	−0.432077	−	0.748380i
$263$	−5.74019	+	9.94231i	−0.353955	+	0.613069i	−0.986939	−	0.161097i	$-0.948497\pi$
$263$	−5.74019	+	9.94231i	−0.353955	+	0.613069i	0.632983	+	0.774166i	$0.281830\pi$
$264$	2.76736			0.170319
$265$	−5.28433	−	9.15273i	−0.324614	−	0.562248i
$266$	−8.25543	−	14.2988i	−0.506173	−	0.876717i
$267$	−5.53176	+	9.58129i	−0.338538	+	0.586365i
$268$	4.40039	+	7.62169i	0.268796	+	0.465569i
$269$	3.07902	+	5.33302i	0.187731	+	0.325160i	0.944493	−	0.328530i	$-0.106553\pi$
$269$	3.07902	+	5.33302i	0.187731	+	0.325160i	−0.756762	+	0.653690i	$0.773220\pi$
$270$	−0.623027	+	1.07912i	−0.0379162	+	0.0656729i
$271$	−2.19448	−	3.80094i	−0.133305	−	0.230891i	0.791644	−	0.610983i	$-0.209226\pi$
$271$	−2.19448	−	3.80094i	−0.133305	−	0.230891i	−0.924949	+	0.380092i	$0.875892\pi$
$272$	3.18130			0.192895
$273$	−7.32332	−	12.6844i	−0.443228	−	0.767693i
$274$	4.46387	+	7.73164i	0.269672	+	0.467086i
$275$	−9.54006			−0.575287
$276$	2.41644	−	4.18539i	0.145452	−	0.251931i
$277$	11.7233			0.704385			0.352193	−	0.935928i	$-0.385436\pi$
$277$	11.7233			0.704385			0.352193	+	0.935928i	$0.385436\pi$
$278$	9.00782	+	15.6020i	0.540253	+	0.935746i
$279$	−8.56314			−0.512662
$280$	3.04175	−	5.26847i	0.181780	−	0.314851i
$281$	9.68346	−	16.7722i	0.577667	−	1.00055i	−0.418080	−	0.908410i	$-0.637297\pi$
$281$	9.68346	−	16.7722i	0.577667	−	1.00055i	0.995746	−	0.0921377i	$-0.0293700\pi$
$282$	−10.3953			−0.619028
$283$	8.42194			0.500632			0.250316	−	0.968164i	$-0.419465\pi$
$283$	8.42194			0.500632			0.250316	+	0.968164i	$0.419465\pi$
$284$	0.203212	+	0.351974i	0.0120584	+	0.0208858i
$285$	−2.10698	−	3.64939i	−0.124807	−	0.216171i
$286$	−4.15104	+	7.18982i	−0.245456	+	0.425143i
$287$	−20.5734			−1.21441
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−6.87933			−0.404666
$290$	4.66596	+	8.08168i	0.273995	+	0.474573i
$291$	12.7778			0.749051
$292$	−6.67525	+	11.5619i	−0.390639	+	0.676607i
$293$	8.87537	−	15.3726i	0.518505	−	0.898077i	−0.481264	−	0.876576i	$-0.659822\pi$
$293$	8.87537	−	15.3726i	0.518505	−	0.898077i	0.999769	−	0.0215011i	$-0.00684453\pi$
$294$	−8.41801	−	14.5804i	−0.490949	−	0.850348i
$295$	−3.15186	+	5.45917i	−0.183508	+	0.317845i
$296$	−2.02505	+	3.50749i	−0.117704	+	0.203869i
$297$	1.38368	−	2.39661i	0.0802893	−	0.139065i
$298$	4.71183	−	8.16114i	0.272949	−	0.472762i
$299$	7.24931	+	12.5562i	0.419238	+	0.726142i
$300$	−1.72367	+	2.98549i	−0.0995163	+	0.172367i
$301$	−21.5132	−	37.2619i	−1.24000	−	2.14774i
$302$	6.15334	−	10.6579i	0.354085	−	0.613293i
$303$	−2.18092	+	3.77747i	−0.125291	+	0.217010i
$304$	1.69092	+	2.92876i	0.0969809	+	0.167976i
$305$	9.51507			0.544832
$306$	1.59065	−	2.75509i	0.0909314	−	0.157498i
$307$	1.66585	+	2.88534i	0.0950753	+	0.164675i	0.909640	−	0.415397i	$-0.136357\pi$
$307$	1.66585	+	2.88534i	0.0950753	+	0.164675i	−0.814565	+	0.580073i	$0.803024\pi$
$308$	−6.75543	+	11.7008i	−0.384926	+	0.666712i
$309$	−8.42215	−	14.5876i	−0.479119	−	0.829859i
$310$	10.6701			0.606023
$311$	12.5452	−	21.7288i	0.711370	−	1.23213i	−0.252972	−	0.967473i	$-0.581408\pi$
$311$	12.5452	−	21.7288i	0.711370	−	1.23213i	0.964343	−	0.264656i	$-0.0852585\pi$
$312$	1.50000	+	2.59808i	0.0849208	+	0.147087i
$313$	−9.37104	−	16.2311i	−0.529682	−	0.917437i	−0.999401	−	0.0346204i	$-0.988978\pi$
$313$	−9.37104	−	16.2311i	−0.529682	−	0.917437i	0.469718	−	0.882816i	$-0.344356\pi$
$314$	−5.51207			−0.311064
$315$	−3.04175	−	5.26847i	−0.171383	−	0.296845i
$316$	3.20176	−	5.54561i	0.180113	−	0.311965i
$317$	6.60177	−	11.4346i	0.370792	−	0.642231i	−0.618895	−	0.785474i	$-0.712419\pi$
$317$	6.60177	−	11.4346i	0.370792	−	0.642231i	0.989688	+	0.143242i	$0.0457528\pi$
$318$	8.48170			0.475630
$319$	−10.3626	−	17.9486i	−0.580196	−	1.00493i
$320$	−0.623027	+	1.07912i	−0.0348283	+	0.0603244i
$321$	7.19671			0.401681
$322$	11.7976	+	20.4340i	0.657452	+	1.13874i
$323$	5.37932	+	9.31726i	0.299313	+	0.518426i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−5.17102	−	8.95647i	−0.286837	−	0.496816i
$326$	6.41300			0.355183
$327$	−8.84629			−0.489201
$328$	4.21396			0.232677
$329$	25.3759	−	43.9524i	1.39902	−	2.42318i
$330$	−1.72414	+	2.98630i	−0.0949110	+	0.164391i
$331$	18.6644			1.02589			0.512945	−	0.858422i	$-0.328555\pi$
$331$	18.6644			1.02589			0.512945	+	0.858422i	$0.328555\pi$
$332$	−3.82066	+	6.61757i	−0.209686	+	0.363186i
$333$	2.02505	+	3.50749i	0.110972	+	0.192209i
$334$	−11.0406			−0.604116
$335$	−10.9662			−0.599150
$336$	2.44111	+	4.22812i	0.133173	+	0.230663i
$337$	10.5044	−	18.1942i	0.572213	−	0.991102i	−0.424125	−	0.905604i	$-0.639418\pi$
$337$	10.5044	−	18.1942i	0.572213	−	0.991102i	0.996338	−	0.0854988i	$-0.0272484\pi$
$338$	4.00000			0.217571
$339$	−3.60698	+	6.24747i	−0.195904	+	0.339316i
$340$	−1.98204	+	3.43299i	−0.107491	+	0.186180i
$341$	−23.6973			−1.28328
$342$	3.38184			0.182869
$343$	48.0216			2.59292
$344$	4.40644	+	7.63218i	0.237579	+	0.411499i
$345$	3.01101	+	5.21523i	0.162107	+	0.280778i
$346$	1.70992	+	2.96167i	0.0919259	+	0.159220i
$347$	2.85499	+	4.94499i	0.153264	+	0.265461i	0.932426	−	0.361362i	$-0.117688\pi$
$347$	2.85499	+	4.94499i	0.153264	+	0.265461i	−0.779162	+	0.626823i	$0.784355\pi$
$348$	−7.48918			−0.401462
$349$	−4.40103	+	7.62280i	−0.235581	+	0.408039i	−0.959442	−	0.281908i	$-0.909033\pi$
$349$	−4.40103	+	7.62280i	−0.235581	+	0.408039i	0.723860	+	0.689947i	$0.242366\pi$
$350$	−8.41535	−	14.5758i	−0.449819	−	0.779110i
$351$	3.00000			0.160128
$352$	1.38368	−	2.39661i	0.0737505	−	0.127740i
$353$	17.8038	−	30.8371i	0.947601	−	1.64129i	0.197145	−	0.980374i	$-0.436833\pi$
$353$	17.8038	−	30.8371i	0.947601	−	1.64129i	0.750457	−	0.660919i	$-0.229834\pi$
$354$	−2.52947	−	4.38117i	−0.134440	−	0.232856i
$355$	−0.506427			−0.0268783
$356$	5.53176	+	9.58129i	0.293183	+	0.507807i
$357$	7.76590	+	13.4509i	0.411015	+	0.711899i
$358$	−7.74315	+	13.4115i	−0.409238	+	0.708821i
$359$	−20.2968			−1.07122			−0.535612	−	0.844464i	$-0.679919\pi$
$359$	−20.2968			−1.07122			−0.535612	+	0.844464i	$0.679919\pi$
$360$	0.623027	+	1.07912i	0.0328364	+	0.0568744i
$361$	3.78159	−	6.54990i	0.199031	−	0.344731i
$362$	7.97023	+	13.8049i	0.418906	+	0.725567i
$363$	−1.67085	+	2.89400i	−0.0876969	+	0.151896i
$364$	−14.6466			−0.767693
$365$	−8.31772	−	14.4067i	−0.435370	−	0.754082i
$366$	−3.81808	+	6.61311i	−0.199574	+	0.345673i
$367$	−8.83865	+	15.3090i	−0.461374	+	0.799123i	−0.999030	−	0.0440413i	$-0.985977\pi$
$367$	−8.83865	+	15.3090i	−0.461374	+	0.799123i	0.537656	+	0.843164i	$0.319310\pi$
$368$	−2.41644	−	4.18539i	−0.125965	−	0.218179i
$369$	2.10698	−	3.64939i	0.109685	−	0.189980i
$370$	−2.52332	−	4.37052i	−0.131181	−	0.227213i
$371$	−20.7047	+	35.8617i	−1.07494	+	1.86184i
$372$	−4.28157	+	7.41590i	−0.221989	+	0.384496i
$373$	6.82214	−	11.8163i	0.353237	−	0.611825i	−0.633577	−	0.773679i	$-0.718414\pi$
$373$	6.82214	−	11.8163i	0.353237	−	0.611825i	0.986815	+	0.161855i	$0.0517476\pi$
$374$	4.40191	−	7.62433i	0.227617	−	0.394245i
$375$	−5.26293	−	9.11566i	−0.271776	−	0.470731i
$376$	−5.19763	+	9.00256i	−0.268047	+	0.464271i
$377$	11.2338	−	19.4575i	0.578568	−	1.00211i
$378$	4.88222			0.251114
$379$	14.3484	+	24.8521i	0.737026	+	1.27657i	0.953829	+	0.300352i	$0.0971040\pi$
$379$	14.3484	+	24.8521i	0.737026	+	1.27657i	−0.216802	+	0.976216i	$0.569563\pi$
$380$	−4.21396			−0.216171
$381$	−5.06083	+	8.76561i	−0.259274	+	0.449076i
$382$	9.41194			0.481557
$383$	10.8721	−	18.8310i	0.555537	−	0.962218i	−0.442325	−	0.896855i	$-0.645846\pi$
$383$	10.8721	−	18.8310i	0.555537	−	0.962218i	0.997862	−	0.0653630i	$-0.0208205\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−8.41764	−	14.5798i	−0.429003	−	0.743054i
$386$	−23.9432			−1.21868
$387$	8.81288			0.447984
$388$	6.38892	−	11.0659i	0.324349	−	0.561788i
$389$	16.9985	−	29.4422i	0.861856	−	1.49278i	−0.00827900	−	0.999966i	$-0.502635\pi$
$389$	16.9985	−	29.4422i	0.861856	−	1.49278i	0.870135	−	0.492813i	$-0.164031\pi$
$390$	−3.73816			−0.189289
$391$	−7.68741	−	13.3150i	−0.388769	−	0.673368i
$392$	−16.8360			−0.850348
$393$	−6.99378	+	12.1136i	−0.352790	+	0.611049i
$394$	−5.90311			−0.297395
$395$	3.98957	+	6.91014i	0.200737	+	0.347687i
$396$	−1.38368	−	2.39661i	−0.0695326	−	0.120434i
$397$	1.75896			0.0882795			0.0441397	−	0.999025i	$-0.485945\pi$
$397$	1.75896			0.0882795			0.0441397	+	0.999025i	$0.485945\pi$
$398$	−4.12432	−	7.14353i	−0.206734	−	0.358073i
$399$	−8.25543	+	14.2988i	−0.413289	+	0.715837i
$400$	1.72367	+	2.98549i	0.0861837	+	0.149275i
$401$	15.5324	+	26.9029i	0.775651	+	1.34347i	0.934428	+	0.356152i	$0.115912\pi$
$401$	15.5324	+	26.9029i	0.775651	+	1.34347i	−0.158777	+	0.987314i	$0.550755\pi$
$402$	4.40039	−	7.62169i	0.219471	−	0.380136i
$403$	−12.8447	−	22.2477i	−0.639840	−	1.10824i
$404$	2.18092	+	3.77747i	0.108505	+	0.187936i
$405$	1.24605			0.0619170
$406$	18.2819	−	31.6652i	0.907315	−	1.57152i
$407$	5.60405	+	9.70649i	0.277782	+	0.481133i
$408$	−1.59065	−	2.75509i	−0.0787489	−	0.136397i
$409$	−5.65041	+	9.78680i	−0.279395	+	0.483926i	−0.971234	−	0.238125i	$-0.923467\pi$
$409$	−5.65041	+	9.78680i	−0.279395	+	0.483926i	0.691840	+	0.722051i	$0.256800\pi$
$410$	−2.62541	+	4.54734i	−0.129660	+	0.224577i
$411$	4.46387	−	7.73164i	0.220186	−	0.381374i
$412$	−16.8443			−0.829859
$413$	24.6988			1.21535
$414$	−4.83287			−0.237523
$415$	−4.76075	−	8.24585i	−0.233696	−	0.404773i
$416$	3.00000			0.147087
$417$	9.00782	−	15.6020i	0.441115	−	0.764033i
$418$	9.35877			0.457753
$419$	−19.0801			−0.932122			−0.466061	−	0.884753i	$-0.654327\pi$
$419$	−19.0801			−0.932122			−0.466061	+	0.884753i	$0.654327\pi$
$420$	−6.08351			−0.296845
$421$	−2.06701	−	3.58017i	−0.100740	−	0.174487i	0.811250	−	0.584700i	$-0.198788\pi$
$421$	−2.06701	−	3.58017i	−0.100740	−	0.174487i	−0.911990	+	0.410213i	$0.865454\pi$
$422$	−2.82616	−	4.89506i	−0.137575	−	0.238288i
$423$	5.19763	+	9.00256i	0.252717	+	0.437719i
$424$	4.24085	−	7.34536i	0.205954	−	0.356722i
$425$	5.48352	+	9.49774i	0.265990	+	0.460708i
$426$	0.203212	−	0.351974i	0.00984566	−	0.0170532i
$427$	−18.6407	−	32.2866i	−0.902086	−	1.56246i
$428$	3.59836	−	6.23253i	0.173933	−	0.301261i
$429$	8.30209			0.400829
$430$	−10.9813			−0.529567
$431$	−7.28927			−0.351112			−0.175556	−	0.984469i	$-0.556172\pi$
$431$	−7.28927			−0.351112			−0.175556	+	0.984469i	$0.556172\pi$
$432$	−1.00000			−0.0481125
$433$	−36.6254			−1.76011			−0.880053	−	0.474876i	$-0.842493\pi$
$433$	−36.6254			−1.76011			−0.880053	+	0.474876i	$0.842493\pi$
$434$	−20.9035	−	36.2060i	−1.00340	−	1.73794i
$435$	4.66596	−	8.08168i	0.223716	−	0.387487i
$436$	−4.42315	+	7.66111i	−0.211830	+	0.366901i
$437$	8.17200	−	14.1543i	0.390920	−	0.677093i
$438$	13.3505			0.637911
$439$	33.5039			1.59906			0.799528	−	0.600629i	$-0.205083\pi$
$439$	33.5039			1.59906			0.799528	+	0.600629i	$0.205083\pi$
$440$	1.72414	+	2.98630i	0.0821953	+	0.142366i
$441$	−8.41801	+	14.5804i	−0.400858	+	0.694306i
$442$	9.54390			0.453957
$443$	−15.4109	−	26.6925i	−0.732194	−	1.26820i	−0.955943	−	0.293551i	$-0.905163\pi$
$443$	−15.4109	−	26.6925i	−0.732194	−	1.26820i	0.223749	−	0.974647i	$-0.428170\pi$
$444$	4.05010			0.192209
$445$	−13.7857			−0.653507
$446$	−12.5404	+	8.10792i	−0.593805	+	0.383921i
$447$	−9.42367			−0.445724
$448$	4.88222			0.230663
$449$	4.41598	+	7.64871i	0.208403	+	0.360965i	0.951212	−	0.308539i	$-0.0998401\pi$
$449$	4.41598	+	7.64871i	0.208403	+	0.360965i	−0.742809	+	0.669504i	$0.766507\pi$
$450$	3.44735			0.162510
$451$	5.83077	−	10.0992i	0.274560	−	0.475553i
$452$	3.60698	+	6.24747i	0.169658	+	0.293856i
$453$	−12.3067			−0.578218
$454$	8.40101			0.394279
$455$	9.12526	−	15.8054i	0.427799	−	0.740969i
$456$	1.69092	−	2.92876i	0.0791845	−	0.137152i
$457$	14.6510	−	25.3762i	0.685343	−	1.18705i	−0.287986	−	0.957635i	$-0.592986\pi$
$457$	14.6510	−	25.3762i	0.685343	−	1.18705i	0.973329	−	0.229414i	$-0.0736809\pi$
$458$	8.44423	+	14.6258i	0.394573	+	0.683420i
$459$	−3.18130			−0.148490
$460$	6.02202			0.280778
$461$	38.0014			1.76990			0.884950	−	0.465685i	$-0.154192\pi$
$461$	38.0014			1.76990			0.884950	+	0.465685i	$0.154192\pi$
$462$	13.5109			0.628582
$463$	−28.4100			−1.32033			−0.660163	−	0.751122i	$-0.729513\pi$
$463$	−28.4100			−1.32033			−0.660163	+	0.751122i	$0.729513\pi$
$464$	−3.74459	+	6.48582i	−0.173838	+	0.301097i
$465$	−5.33507	−	9.24061i	−0.247408	−	0.428523i
$466$	−10.1970	+	17.6617i	−0.472367	+	0.818163i
$467$	0.284899	+	0.493460i	0.0131836	+	0.0228346i	0.872542	−	0.488539i	$-0.162470\pi$
$467$	0.284899	+	0.493460i	0.0131836	+	0.0228346i	−0.859358	+	0.511374i	$0.829137\pi$
$468$	1.50000	−	2.59808i	0.0693375	−	0.120096i
$469$	21.4836	+	37.2107i	0.992022	+	1.71823i
$470$	−6.47653	−	11.2177i	−0.298740	−	0.517433i
$471$	2.75604	+	4.77359i	0.126991	+	0.219956i
$472$	−5.05893			−0.232856
$473$	24.3884			1.12138
$474$	−6.40352			−0.294124
$475$	−5.82919	+	10.0964i	−0.267461	+	0.463257i
$476$	15.5318			0.711899
$477$	−4.24085	−	7.34536i	−0.194175	−	0.336321i
$478$	−11.6854			−0.534476
$479$	−11.6056			−0.530274			−0.265137	−	0.964211i	$-0.585417\pi$
$479$	−11.6056			−0.530274			−0.265137	+	0.964211i	$0.585417\pi$
$480$	1.24605			0.0568744
$481$	−6.07515	+	10.5225i	−0.277003	+	0.479783i
$482$	−9.75564	+	16.8973i	−0.444357	+	0.769649i
$483$	11.7976	−	20.4340i	0.536808	−	0.929778i
$484$	1.67085	+	2.89400i	0.0759478	+	0.131545i
$485$	7.96095	+	13.7888i	0.361488	+	0.626116i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−14.7108			−0.666612			−0.333306	−	0.942819i	$-0.608164\pi$
$487$	−14.7108			−0.666612			−0.333306	+	0.942819i	$0.608164\pi$
$488$	3.81808	+	6.61311i	0.172836	+	0.299361i
$489$	−3.20650	−	5.55382i	−0.145003	−	0.251152i
$490$	10.4893	−	18.1680i	0.473859	−	0.820747i
$491$	−9.29629	−	16.1016i	−0.419535	−	0.726657i	0.576357	−	0.817198i	$-0.304474\pi$
$491$	−9.29629	−	16.1016i	−0.419535	−	0.726657i	−0.995893	+	0.0905411i	$0.971140\pi$
$492$	−2.10698	−	3.64939i	−0.0949899	−	0.164527i
$493$	−11.9127	+	20.6333i	−0.536519	+	0.929279i
$494$	5.07276	+	8.78627i	0.228234	+	0.395313i
$495$	3.44829			0.154989
$496$	4.28157	+	7.41590i	0.192248	+	0.332984i
$497$	0.992125	+	1.71841i	0.0445029	+	0.0770813i
$498$	7.64131			0.342415
$499$	−16.8916	+	29.2571i	−0.756171	+	1.30973i	0.188619	+	0.982050i	$0.439599\pi$
$499$	−16.8916	+	29.2571i	−0.756171	+	1.30973i	−0.944790	+	0.327676i	$0.893735\pi$
$500$	−10.5259			−0.470731
$501$	5.52031	+	9.56146i	0.246629	+	0.427175i
$502$	−11.2266			−0.501067
$503$	16.2272	−	28.1064i	0.723536	−	1.25320i	−0.236037	−	0.971744i	$-0.575849\pi$
$503$	16.2272	−	28.1064i	0.723536	−	1.25320i	0.959574	−	0.281458i	$-0.0908180\pi$
$504$	2.44111	−	4.22812i	0.108736	−	0.188336i
$505$	−5.43510			−0.241859
$506$	−13.3743			−0.594561
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$	5.06083	+	8.76561i	0.224538	+	0.388911i
$509$	18.1935	−	31.5121i	0.806413	−	1.39675i	−0.108921	−	0.994050i	$-0.534739\pi$
$509$	18.1935	−	31.5121i	0.806413	−	1.39675i	0.915333	−	0.402697i	$-0.131927\pi$
$510$	3.96407			0.175532
$511$	−32.5900	+	56.4475i	−1.44170	+	2.49709i
$512$	−1.00000			−0.0441942
$513$	−1.69092	−	2.92876i	−0.0746559	−	0.129308i
$514$	12.6258			0.556898
$515$	10.4945	−	18.1769i	0.462441	−	0.800971i
$516$	4.40644	−	7.63218i	0.193983	−	0.335988i
$517$	14.3837	+	24.9133i	0.632595	+	1.09569i
$518$	−9.88673	+	17.1243i	−0.434398	+	0.752399i
$519$	1.70992	−	2.96167i	0.0750572	−	0.130003i
$520$	−1.86908	+	3.23735i	−0.0819647	+	0.141967i
$521$	−9.10685	+	15.7735i	−0.398978	+	0.691050i	−0.993600	−	0.112955i	$-0.963968\pi$
$521$	−9.10685	+	15.7735i	−0.398978	+	0.691050i	0.594622	+	0.804005i	$0.297302\pi$
$522$	3.74459	+	6.48582i	0.163896	+	0.283877i
$523$	−16.1248	+	27.9290i	−0.705090	+	1.22125i	0.261570	+	0.965185i	$0.415760\pi$
$523$	−16.1248	+	27.9290i	−0.705090	+	1.22125i	−0.966659	+	0.256066i	$0.917573\pi$
$524$	6.99378	+	12.1136i	0.305525	+	0.529184i
$525$	−8.41535	+	14.5758i	−0.367276	+	0.636140i
$526$	5.74019	−	9.94231i	0.250284	−	0.433505i
$527$	13.6210	+	23.5922i	0.593338	+	1.02769i
$528$	−2.76736			−0.120434
$529$	−0.178327	+	0.308872i	−0.00775336	+	0.0134292i
$530$	5.28433	+	9.15273i	0.229537	+	0.397569i
$531$	−2.52947	+	4.38117i	−0.109770	+	0.190126i
$532$	8.25543	+	14.2988i	0.357918	+	0.619933i
$533$	12.6419			0.547580
$534$	5.53176	−	9.58129i	0.239383	−	0.414623i
$535$	4.48375	+	7.76608i	0.193849	+	0.335757i
$536$	−4.40039	−	7.62169i	−0.190068	−	0.329207i
$537$	15.4863			0.668283
$538$	−3.07902	−	5.33302i	−0.132746	−	0.229923i
$539$	−23.2957	+	40.3493i	−1.00342	+	1.73797i
$540$	0.623027	−	1.07912i	0.0268108	−	0.0464377i
$541$	−28.1647			−1.21089			−0.605447	−	0.795886i	$-0.707006\pi$
$541$	−28.1647			−1.21089			−0.605447	+	0.795886i	$0.707006\pi$
$542$	2.19448	+	3.80094i	0.0942608	+	0.163264i
$543$	7.97023	−	13.8049i	0.342035	−	0.592423i
$544$	−3.18130			−0.136397
$545$	−5.51148	−	9.54617i	−0.236086	−	0.408913i
$546$	7.32332	+	12.6844i	0.313409	+	0.542841i
$547$	10.4734	+	18.1405i	0.447810	+	0.775630i	0.998243	−	0.0592490i	$-0.0188706\pi$
$547$	10.4734	+	18.1405i	0.447810	+	0.775630i	−0.550433	+	0.834879i	$0.685537\pi$
$548$	−4.46387	−	7.73164i	−0.190687	−	0.330279i
$549$	7.63616			0.325903
$550$	9.54006			0.406790
$551$	−25.3272			−1.07897
$552$	−2.41644	+	4.18539i	−0.102850	+	0.178142i
$553$	15.6317	−	27.0749i	0.664727	−	1.15134i
$554$	−11.7233			−0.498076
$555$	−2.52332	+	4.37052i	−0.107109	+	0.185518i
$556$	−9.00782	−	15.6020i	−0.382017	−	0.661672i
$557$	−7.17929			−0.304196			−0.152098	−	0.988365i	$-0.548603\pi$
$557$	−7.17929			−0.304196			−0.152098	+	0.988365i	$0.548603\pi$
$558$	8.56314			0.362507
$559$	13.2193	+	22.8965i	0.559118	+	0.968420i
$560$	−3.04175	+	5.26847i	−0.128538	+	0.222634i
$561$	−8.80381			−0.371697
$562$	−9.68346	+	16.7722i	−0.408472	+	0.707494i
$563$	−6.72175	+	11.6424i	−0.283288	+	0.490669i	−0.972193	−	0.234183i	$-0.924759\pi$
$563$	−6.72175	+	11.6424i	−0.283288	+	0.490669i	0.688904	+	0.724852i	$0.258092\pi$
$564$	10.3953			0.437719
$565$	−8.98898			−0.378169
$566$	−8.42194			−0.354001
$567$	−2.44111	−	4.22812i	−0.102517	−	0.177564i
$568$	−0.203212	−	0.351974i	−0.00852659	−	0.0147685i
$569$	5.23889	+	9.07402i	0.219626	+	0.380403i	0.954694	−	0.297591i	$-0.0961831\pi$
$569$	5.23889	+	9.07402i	0.219626	+	0.380403i	−0.735068	+	0.677994i	$0.762850\pi$
$570$	2.10698	+	3.64939i	0.0882516	+	0.152856i
$571$	−12.4930			−0.522816			−0.261408	−	0.965228i	$-0.584187\pi$
$571$	−12.4930			−0.522816			−0.261408	+	0.965228i	$0.584187\pi$
$572$	4.15104	−	7.18982i	0.173564	−	0.300621i
$573$	−4.70597	−	8.15098i	−0.196595	−	0.340512i
$574$	20.5734			0.858719
$575$	8.33029	−	14.4285i	0.347397	−	0.601710i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	0.0735342	+	0.127365i	0.00306127	+	0.00530227i	0.867552	−	0.497347i	$-0.165692\pi$
$577$	0.0735342	+	0.127365i	0.00306127	+	0.00530227i	−0.864491	+	0.502649i	$0.832359\pi$
$578$	6.87933			0.286142
$579$	11.9716	+	20.7354i	0.497523	+	0.861735i
$580$	−4.66596	−	8.08168i	−0.193744	−	0.335574i
$581$	−18.6533	+	32.3084i	−0.773868	+	1.34038i
$582$	−12.7778			−0.529659
$583$	−11.7360	−	20.3273i	−0.486054	−	0.841870i
$584$	6.67525	−	11.5619i	0.276224	−	0.478433i
$585$	1.86908	+	3.23735i	0.0772770	+	0.133848i
$586$	−8.87537	+	15.3726i	−0.366638	+	0.635036i
$587$	35.1185			1.44950			0.724748	−	0.689014i	$-0.241956\pi$
$587$	35.1185			1.44950			0.724748	+	0.689014i	$0.241956\pi$
$588$	8.41801	+	14.5804i	0.347153	+	0.601287i
$589$	−14.4796	+	25.0794i	−0.596620	+	1.03338i
$590$	3.15186	−	5.45917i	0.129760	−	0.224751i
$591$	2.95156	+	5.11225i	0.121411	+	0.210290i
$592$	2.02505	−	3.50749i	0.0832290	−	0.144157i
$593$	11.3424	+	19.6457i	0.465778	+	0.806752i	0.999236	−	0.0390749i	$-0.0124411\pi$
$593$	11.3424	+	19.6457i	0.465778	+	0.806752i	−0.533458	+	0.845827i	$0.679108\pi$
$594$	−1.38368	+	2.39661i	−0.0567731	+	0.0983340i
$595$	−9.67673	+	16.7606i	−0.396707	+	0.687117i
$596$	−4.71183	+	8.16114i	−0.193004	+	0.334293i
$597$	−4.12432	+	7.14353i	−0.168797	+	0.292365i
$598$	−7.24931	−	12.5562i	−0.296446	−	0.513460i
$599$	0.675004	−	1.16914i	0.0275799	−	0.0477698i	−0.851906	−	0.523695i	$-0.824553\pi$
$599$	0.675004	−	1.16914i	0.0275799	−	0.0477698i	0.879486	+	0.475925i	$0.157887\pi$
$600$	1.72367	−	2.98549i	0.0703687	−	0.121882i
$601$	−19.0899			−0.778694			−0.389347	−	0.921091i	$-0.627299\pi$
$601$	−19.0899			−0.778694			−0.389347	+	0.921091i	$0.627299\pi$
$602$	21.5132	+	37.2619i	0.876812	+	1.51868i
$603$	−8.80077			−0.358395
$604$	−6.15334	+	10.6579i	−0.250376	+	0.433663i
$605$	−4.16394			−0.169288
$606$	2.18092	−	3.77747i	0.0885939	−	0.153449i
$607$	14.1640	+	24.5327i	0.574897	+	0.995751i	0.996053	+	0.0887628i	$0.0282913\pi$
$607$	14.1640	+	24.5327i	0.574897	+	0.995751i	−0.421156	+	0.906988i	$0.638375\pi$
$608$	−1.69092	−	2.92876i	−0.0685758	−	0.118777i
$609$	−36.5638			−1.48164
$610$	−9.51507			−0.385254
$611$	−15.5929	+	27.0077i	−0.630821	+	1.09261i
$612$	−1.59065	+	2.75509i	−0.0642982	+	0.111368i
$613$	−21.3895			−0.863913			−0.431956	−	0.901895i	$-0.642177\pi$
$613$	−21.3895			−0.863913			−0.431956	+	0.901895i	$0.642177\pi$
$614$	−1.66585	−	2.88534i	−0.0672284	−	0.116443i
$615$	5.25082			0.211733
$616$	6.75543	−	11.7008i	0.272184	−	0.471437i
$617$	−44.0231			−1.77230			−0.886152	−	0.463394i	$-0.846631\pi$
$617$	−44.0231			−1.77230			−0.886152	+	0.463394i	$0.846631\pi$
$618$	8.42215	+	14.5876i	0.338788	+	0.586799i
$619$	19.9515	+	34.5570i	0.801917	+	1.38896i	0.918353	+	0.395763i	$0.129520\pi$
$619$	19.9515	+	34.5570i	0.801917	+	1.38896i	−0.116435	+	0.993198i	$0.537147\pi$
$620$	−10.6701			−0.428523
$621$	2.41644	+	4.18539i	0.0969682	+	0.167954i
$622$	−12.5452	+	21.7288i	−0.503015	+	0.871247i
$623$	27.0072	+	46.7779i	1.08202	+	1.87412i
$624$	−1.50000	−	2.59808i	−0.0600481	−	0.104006i
$625$	−2.06047	+	3.56884i	−0.0824188	+	0.142754i
$626$	9.37104	+	16.2311i	0.374542	+	0.648726i
$627$	−4.67939	−	8.10494i	−0.186877	−	0.323680i
$628$	5.51207			0.219956
$629$	6.44229	−	11.1584i	0.256871	−	0.444913i
$630$	3.04175	+	5.26847i	0.121186	+	0.209901i
$631$	−10.7072	−	18.5455i	−0.426249	−	0.738285i	0.570287	−	0.821445i	$-0.306832\pi$
$631$	−10.7072	−	18.5455i	−0.426249	−	0.738285i	−0.996536	+	0.0831607i	$0.973499\pi$
$632$	−3.20176	+	5.54561i	−0.127359	+	0.220593i
$633$	−2.82616	+	4.89506i	−0.112330	+	0.194561i
$634$	−6.60177	+	11.4346i	−0.262190	+	0.454126i
$635$	−12.6121			−0.500497
$636$	−8.48170			−0.336321
$637$	−50.5081			−2.00120
$638$	10.3626	+	17.9486i	0.410261	+	0.710592i
$639$	−0.406424			−0.0160779
$640$	0.623027	−	1.07912i	0.0246273	−	0.0426558i
$641$	45.4557			1.79539			0.897697	−	0.440614i	$-0.145239\pi$
$641$	45.4557			1.79539			0.897697	+	0.440614i	$0.145239\pi$
$642$	−7.19671			−0.284032
$643$	5.14357			0.202843			0.101421	−	0.994844i	$-0.467661\pi$
$643$	5.14357			0.202843			0.101421	+	0.994844i	$0.467661\pi$
$644$	−11.7976	−	20.4340i	−0.464889	−	0.805212i
$645$	5.49067	+	9.51011i	0.216195	+	0.374460i
$646$	−5.37932	−	9.31726i	−0.211647	−	0.366583i
$647$	9.41281	−	16.3035i	0.370056	−	0.640956i	−0.619518	−	0.784983i	$-0.712672\pi$
$647$	9.41281	−	16.3035i	0.370056	−	0.640956i	0.989574	+	0.144027i	$0.0460052\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−6.99995	+	12.1243i	−0.274772	+	0.475920i
$650$	5.17102	+	8.95647i	0.202824	+	0.351302i
$651$	−20.9035	+	36.2060i	−0.819275	+	1.41903i
$652$	−6.41300			−0.251152
$653$	42.9359			1.68021			0.840106	−	0.542423i	$-0.182493\pi$
$653$	42.9359			1.68021			0.840106	+	0.542423i	$0.182493\pi$
$654$	8.84629			0.345917
$655$	−17.4293			−0.681018
$656$	−4.21396			−0.164527
$657$	−6.67525	−	11.5619i	−0.260426	−	0.451071i
$658$	−25.3759	+	43.9524i	−0.989257	+	1.71344i
$659$	19.8904	−	34.4513i	0.774822	−	1.34203i	−0.160073	−	0.987105i	$-0.551173\pi$
$659$	19.8904	−	34.4513i	0.774822	−	1.34203i	0.934895	−	0.354926i	$-0.115494\pi$
$660$	1.72414	−	2.98630i	0.0671122	−	0.116242i
$661$	0.821365			0.0319474			0.0159737	−	0.999872i	$-0.494915\pi$
$661$	0.821365			0.0319474			0.0159737	+	0.999872i	$0.494915\pi$
$662$	−18.6644			−0.725413
$663$	−4.77195	−	8.26526i	−0.185327	−	0.320996i
$664$	3.82066	−	6.61757i	0.148270	−	0.256811i
$665$	−20.5734			−0.797804
$666$	−2.02505	−	3.50749i	−0.0784691	−	0.135912i
$667$	36.1942			1.40145
$668$	11.0406			0.427175
$669$	13.2919	+	6.80635i	0.513893	+	0.263149i
$670$	10.9662			0.423663
$671$	21.1320			0.815793
$672$	−2.44111	−	4.22812i	−0.0941678	−	0.163103i
$673$	33.1305			1.27709			0.638543	−	0.769586i	$-0.279538\pi$
$673$	33.1305			1.27709			0.638543	+	0.769586i	$0.279538\pi$
$674$	−10.5044	+	18.1942i	−0.404616	+	0.700815i
$675$	−1.72367	−	2.98549i	−0.0663442	−	0.114912i
$676$	−4.00000			−0.153846
$677$	−11.5084			−0.442306			−0.221153	−	0.975239i	$-0.570982\pi$
$677$	−11.5084			−0.442306			−0.221153	+	0.975239i	$0.570982\pi$
$678$	3.60698	−	6.24747i	0.138525	−	0.239933i
$679$	31.1921	−	54.0263i	1.19704	−	2.07334i
$680$	1.98204	−	3.43299i	0.0760077	−	0.131649i
$681$	−4.20050	−	7.27549i	−0.160964	−	0.278797i
$682$	23.6973			0.907417
$683$	26.7142			1.02219			0.511095	−	0.859524i	$-0.329240\pi$
$683$	26.7142			1.02219			0.511095	+	0.859524i	$0.329240\pi$
$684$	−3.38184			−0.129308
$685$	11.1244			0.425043
$686$	−48.0216			−1.83347
$687$	8.44423	−	14.6258i	0.322167	−	0.558010i
$688$	−4.40644	−	7.63218i	−0.167994	−	0.290974i
$689$	12.7225	−	22.0361i	0.484690	−	0.839508i
$690$	−3.01101	−	5.21523i	−0.114627	−	0.198540i
$691$	18.3257	−	31.7410i	0.697142	−	1.20749i	−0.272311	−	0.962209i	$-0.587788\pi$
$691$	18.3257	−	31.7410i	0.697142	−	1.20749i	0.969453	−	0.245277i	$-0.0788788\pi$
$692$	−1.70992	−	2.96167i	−0.0650014	−	0.112586i
$693$	−6.75543	−	11.7008i	−0.256618	−	0.444475i
$694$	−2.85499	−	4.94499i	−0.108374	−	0.187709i
$695$	22.4485			0.851519
$696$	7.48918			0.283877
$697$	−13.4059			−0.507783
$698$	4.40103	−	7.62280i	0.166581	−	0.288527i
$699$	20.3940			0.771371
$700$	8.41535	+	14.5758i	0.318070	+	0.550914i
$701$	−36.6709			−1.38504			−0.692520	−	0.721399i	$-0.743499\pi$
$701$	−36.6709			−1.38504			−0.692520	+	0.721399i	$0.743499\pi$
$702$	−3.00000			−0.113228
$703$	13.6968			0.516584
$704$	−1.38368	+	2.39661i	−0.0521495	+	0.0903255i
$705$	−6.47653	+	11.2177i	−0.243920	+	0.422482i
$706$	−17.8038	+	30.8371i	−0.670055	+	1.16057i
$707$	10.6477	+	18.4424i	0.400449	+	0.693599i
$708$	2.52947	+	4.38117i	0.0950632	+	0.164654i
$709$	21.8465	−	37.8392i	0.820462	−	1.42108i	−0.0848765	−	0.996391i	$-0.527050\pi$
$709$	21.8465	−	37.8392i	0.820462	−	1.42108i	0.905339	−	0.424691i	$-0.139617\pi$
$710$	0.506427			0.0190059
$711$	3.20176	+	5.54561i	0.120075	+	0.207977i
$712$	−5.53176	−	9.58129i	−0.207311	−	0.359074i
$713$	20.6923	−	35.8401i	0.774932	−	1.34222i
$714$	−7.76590	−	13.4509i	−0.290631	−	0.503388i
$715$	5.17243	+	8.95891i	0.193438	+	0.335044i
$716$	7.74315	−	13.4115i	0.289375	−	0.501212i
$717$	5.84268	+	10.1198i	0.218199	+	0.377931i
$718$	20.2968			0.757470
$719$	16.0347	+	27.7728i	0.597992	+	1.03575i	0.993117	+	0.117125i	$0.0373678\pi$
$719$	16.0347	+	27.7728i	0.597992	+	1.03575i	−0.395125	+	0.918627i	$0.629299\pi$
$720$	−0.623027	−	1.07912i	−0.0232189	−	0.0402162i
$721$	−82.2375			−3.06268
$722$	−3.78159	+	6.54990i	−0.140736	+	0.243762i
$723$	19.5113			0.725632
$724$	−7.97023	−	13.8049i	−0.296211	−	0.513053i
$725$	−25.8178			−0.958849
$726$	1.67085	−	2.89400i	0.0620111	−	0.107406i
$727$	−13.9384	+	24.1421i	−0.516947	+	0.895379i	0.482859	+	0.875698i	$0.339598\pi$
$727$	−13.9384	+	24.1421i	−0.516947	+	0.895379i	−0.999806	+	0.0196810i	$0.993735\pi$
$728$	14.6466			0.542841
$729$	1.00000			0.0370370
$730$	8.31772	+	14.4067i	0.307853	+	0.533217i
$731$	−14.0182	−	24.2803i	−0.518482	−	0.898038i
$732$	3.81808	−	6.61311i	0.141120	−	0.244428i
$733$	17.4517			0.644595			0.322297	−	0.946638i	$-0.395545\pi$
$733$	17.4517			0.644595			0.322297	+	0.946638i	$0.395545\pi$
$734$	8.83865	−	15.3090i	0.326241	−	0.565065i
$735$	−20.9786			−0.773808
$736$	2.41644	+	4.18539i	0.0890710	+	0.154276i
$737$	−24.3549			−0.897126
$738$	−2.10698	+	3.64939i	−0.0775589	+	0.134336i
$739$	5.98056	−	10.3586i	0.219998	−	0.381048i	−0.734809	−	0.678274i	$-0.762728\pi$
$739$	5.98056	−	10.3586i	0.219998	−	0.381048i	0.954807	+	0.297226i	$0.0960615\pi$
$740$	2.52332	+	4.37052i	0.0927592	+	0.160664i
$741$	5.07276	−	8.78627i	0.186352	−	0.322772i
$742$	20.7047	−	35.8617i	0.760095	−	1.31652i
$743$	−9.24199	+	16.0076i	−0.339056	+	0.587262i	−0.984255	−	0.176752i	$-0.943441\pi$
$743$	−9.24199	+	16.0076i	−0.339056	+	0.587262i	0.645200	+	0.764014i	$0.276774\pi$
$744$	4.28157	−	7.41590i	0.156970	−	0.271880i
$745$	−5.87120	−	10.1692i	−0.215104	−	0.372572i
$746$	−6.82214	+	11.8163i	−0.249776	+	0.432625i
$747$	−3.82066	−	6.61757i	−0.139790	−	0.242124i
$748$	−4.40191	+	7.62433i	−0.160950	+	0.278773i
$749$	17.5679	−	30.4286i	0.641919	−	1.11184i
$750$	5.26293	+	9.11566i	0.192175	+	0.332857i
$751$	−19.0018			−0.693387			−0.346694	−	0.937978i	$-0.612696\pi$
$751$	−19.0018			−0.693387			−0.346694	+	0.937978i	$0.612696\pi$
$752$	5.19763	−	9.00256i	0.189538	−	0.328289i
$753$	5.61329	+	9.72251i	0.204560	+	0.354308i
$754$	−11.2338	+	19.4575i	−0.409110	+	0.708599i
$755$	−7.66739	−	13.2803i	−0.279045	−	0.483320i
$756$	−4.88222			−0.177564
$757$	−5.26647	+	9.12179i	−0.191413	+	0.331537i	−0.945719	−	0.324986i	$-0.894640\pi$
$757$	−5.26647	+	9.12179i	−0.191413	+	0.331537i	0.754306	+	0.656523i	$0.227974\pi$
$758$	−14.3484	−	24.8521i	−0.521156	−	0.902669i
$759$	6.68716	+	11.5825i	0.242728	+	0.420418i
$760$	4.21396			0.152856
$761$	20.6953	+	35.8453i	0.750203	+	1.29939i	0.947724	+	0.319091i	$0.103378\pi$
$761$	20.6953	+	35.8453i	0.750203	+	1.29939i	−0.197521	+	0.980299i	$0.563289\pi$
$762$	5.06083	−	8.76561i	0.183334	−	0.317544i
$763$	−21.5947	+	37.4032i	−0.781782	+	1.35409i
$764$	−9.41194			−0.340512
$765$	−1.98204	−	3.43299i	−0.0716607	−	0.124120i
$766$	−10.8721	+	18.8310i	−0.392824	+	0.680391i
$767$	−15.1768			−0.548003
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−11.5466	−	19.9993i	−0.416382	−	0.721195i	0.579190	−	0.815192i	$-0.303369\pi$
$769$	−11.5466	−	19.9993i	−0.416382	−	0.721195i	−0.995572	+	0.0939975i	$0.970035\pi$
$770$	8.41764	+	14.5798i	0.303351	+	0.525419i
$771$	−6.31288	−	10.9342i	−0.227353	−	0.393787i
$772$	23.9432			0.861735
$773$	13.6231			0.489989			0.244995	−	0.969524i	$-0.421214\pi$
$773$	13.6231			0.489989			0.244995	+	0.969524i	$0.421214\pi$
$774$	−8.81288			−0.316772
$775$	−14.7601	+	25.5652i	−0.530197	+	0.918328i
$776$	−6.38892	+	11.0659i	−0.229349	+	0.397244i
$777$	19.7735			0.709369
$778$	−16.9985	+	29.4422i	−0.609424	+	1.05555i
$779$	−7.12546	−	12.3417i	−0.255296	−	0.442186i
$780$	3.73816			0.133848
$781$	−1.12472			−0.0402458
$782$	7.68741	+	13.3150i	0.274901	+	0.476143i
$783$	3.74459	−	6.48582i	0.133821	−	0.231784i
$784$	16.8360			0.601287
$785$	−3.43417	+	5.94816i	−0.122571	+	0.212299i
$786$	6.99378	−	12.1136i	0.249460	−	0.432077i
$787$	15.0414			0.536168			0.268084	−	0.963395i	$-0.413609\pi$
$787$	15.0414			0.536168			0.268084	+	0.963395i	$0.413609\pi$
$788$	5.90311			0.210290
$789$	−11.4804			−0.408713
$790$	−3.98957	−	6.91014i	−0.141943	−	0.245852i
$791$	17.6100	+	30.5015i	0.626141	+	1.08451i
$792$	1.38368	+	2.39661i	0.0491670	+	0.0851597i
$793$	11.4542	+	19.8393i	0.406752	+	0.704515i
$794$	−1.75896			−0.0624230
$795$	5.28433	−	9.15273i	0.187416	−	0.324614i
$796$	4.12432	+	7.14353i	0.146183	+	0.253196i
$797$	28.4692			1.00843			0.504216	−	0.863578i	$-0.331782\pi$
$797$	28.4692			1.00843			0.504216	+	0.863578i	$0.331782\pi$
$798$	8.25543	−	14.2988i	0.292239	−	0.506173i
$799$	16.5352	−	28.6398i	0.584974	−	1.01320i
$800$	−1.72367	−	2.98549i	−0.0609411	−	0.105553i
$801$	−11.0635			−0.390910
$802$	−15.5324	−	26.9029i	−0.548468	−	0.949974i
$803$	−18.4728	−	31.9959i	−0.651892	−	1.12911i
$804$	−4.40039	+	7.62169i	−0.155190	+	0.268796i
$805$	29.4008			1.03624
$806$	12.8447	+	22.2477i	0.452436	+	0.783641i
$807$	−3.07902	+	5.33302i	−0.108387	+	0.187731i
$808$	−2.18092	−	3.77747i	−0.0767246	−	0.132891i
$809$	−15.1895	+	26.3090i	−0.534035	+	0.924976i	0.465174	+	0.885219i	$0.345992\pi$
$809$	−15.1895	+	26.3090i	−0.534035	+	0.924976i	−0.999209	+	0.0397572i	$0.987342\pi$
$810$	−1.24605			−0.0437819
$811$	−9.05881	−	15.6903i	−0.318098	−	0.550962i	0.661993	−	0.749510i	$-0.269711\pi$
$811$	−9.05881	−	15.6903i	−0.318098	−	0.550962i	−0.980091	+	0.198548i	$0.936377\pi$
$812$	−18.2819	+	31.6652i	−0.641569	+	1.11123i
$813$	2.19448	−	3.80094i	0.0769636	−	0.133305i
$814$	−5.60405	−	9.70649i	−0.196422	−	0.340212i
$815$	3.99547	−	6.92036i	0.139955	−	0.242410i
$816$	1.59065	+	2.75509i	0.0556839	+	0.0964473i
$817$	14.9019	−	25.8108i	0.521350	−	0.903005i
$818$	5.65041	−	9.78680i	0.197562	−	0.342187i
$819$	7.32332	−	12.6844i	0.255898	−	0.443228i
$820$	2.62541	−	4.54734i	0.0916833	−	0.158800i
$821$	−25.7731	−	44.6404i	−0.899489	−	1.55796i	−0.828149	−	0.560508i	$-0.810606\pi$
$821$	−25.7731	−	44.6404i	−0.899489	−	1.55796i	−0.0713396	−	0.997452i	$-0.522727\pi$
$822$	−4.46387	+	7.73164i	−0.155695	+	0.269672i
$823$	21.9021	−	37.9356i	0.763461	−	1.32235i	−0.177596	−	0.984104i	$-0.556832\pi$
$823$	21.9021	−	37.9356i	0.763461	−	1.32235i	0.941056	−	0.338250i	$-0.109835\pi$
$824$	16.8443			0.586799
$825$	−4.77003	−	8.26194i	−0.166071	−	0.287644i
$826$	−24.6988			−0.859382
$827$	−4.79109	+	8.29842i	−0.166603	+	0.288564i	−0.937223	−	0.348730i	$-0.886613\pi$
$827$	−4.79109	+	8.29842i	−0.166603	+	0.288564i	0.770621	+	0.637294i	$0.219946\pi$
$828$	4.83287			0.167954
$829$	2.58676	−	4.48040i	0.0898419	−	0.155611i	−0.817602	−	0.575783i	$-0.804697\pi$
$829$	2.58676	−	4.48040i	0.0898419	−	0.155611i	0.907444	+	0.420173i	$0.138031\pi$
$830$	4.76075	+	8.24585i	0.165248	+	0.286218i
$831$	5.86165	+	10.1527i	0.203339	+	0.352193i
$832$	−3.00000			−0.104006
$833$	53.5605			1.85576
$834$	−9.00782	+	15.6020i	−0.311915	+	0.540253i
$835$	−6.87861	+	11.9141i	−0.238044	+	0.412305i
$836$	−9.35877			−0.323680
$837$	−4.28157	−	7.41590i	−0.147993	−	0.256331i
$838$	19.0801			0.659109
$839$	−10.0471	+	17.4021i	−0.346865	+	0.600788i	−0.985691	−	0.168563i	$-0.946087\pi$
$839$	−10.0471	+	17.4021i	−0.346865	+	0.600788i	0.638825	+	0.769352i	$0.279421\pi$
$840$	6.08351			0.209901
$841$	−13.5439	−	23.4587i	−0.467031	−	0.808921i
$842$	2.06701	+	3.58017i	0.0712339	+	0.123381i
$843$	19.3669			0.667032
$844$	2.82616	+	4.89506i	0.0972806	+	0.168495i
$845$	2.49211	−	4.31646i	0.0857312	−	0.148491i
$846$	−5.19763	−	9.00256i	−0.178698	−	0.309514i
$847$	8.15745	+	14.1291i	0.280293	+	0.485482i
$848$	−4.24085	+	7.34536i	−0.145631	+	0.252241i
$849$	4.21097	+	7.29361i	0.144520	+	0.250316i
$850$	−5.48352	−	9.49774i	−0.188083	−	0.325770i
$851$	−19.5736			−0.670975
$852$	−0.203212	+	0.351974i	−0.00696193	+	0.0120584i
$853$	−15.7336	−	27.2513i	−0.538707	−	0.933068i	−0.998974	−	0.0452876i	$-0.985580\pi$
$853$	−15.7336	−	27.2513i	−0.538707	−	0.933068i	0.460267	−	0.887781i	$-0.347754\pi$
$854$	18.6407	+	32.2866i	0.637871	+	1.10483i
$855$	2.10698	−	3.64939i	0.0720571	−	0.124807i
$856$	−3.59836	+	6.23253i	−0.122989	+	0.213024i
$857$	−6.39355	+	11.0740i	−0.218400	+	0.378279i	−0.954319	−	0.298790i	$-0.903417\pi$
$857$	−6.39355	+	11.0740i	−0.218400	+	0.378279i	0.735919	+	0.677069i	$0.236750\pi$
$858$	−8.30209			−0.283429
$859$	−37.5587			−1.28148			−0.640742	−	0.767756i	$-0.721373\pi$
$859$	−37.5587			−1.28148			−0.640742	+	0.767756i	$0.721373\pi$
$860$	10.9813			0.374460
$861$	−10.2867	−	17.8171i	−0.350570	−	0.607206i
$862$	7.28927			0.248274
$863$	−12.5577	+	21.7506i	−0.427469	+	0.740398i	−0.996647	−	0.0818162i	$-0.973928\pi$
$863$	−12.5577	+	21.7506i	−0.427469	+	0.740398i	0.569179	+	0.822214i	$0.307261\pi$
$864$	1.00000			0.0340207
$865$	4.26131			0.144889
$866$	36.6254			1.24458
$867$	−3.43966	−	5.95767i	−0.116817	−	0.202333i
$868$	20.9035	+	36.2060i	0.709513	+	1.22891i
$869$	8.86044	+	15.3467i	0.300570	+	0.520602i
$870$	−4.66596	+	8.08168i	−0.158191	+	0.273995i
$871$	−13.2012	−	22.8651i	−0.447304	−	0.774754i
$872$	4.42315	−	7.66111i	0.149787	−	0.259438i
$873$	6.38892	+	11.0659i	0.216232	+	0.374525i
$874$	−8.17200	+	14.1543i	−0.276422	+	0.478777i
$875$	−51.3895			−1.73728
$876$	−13.3505			−0.451071
$877$	−41.0285			−1.38543			−0.692717	−	0.721210i	$-0.743586\pi$
$877$	−41.0285			−1.38543			−0.692717	+	0.721210i	$0.743586\pi$
$878$	−33.5039			−1.13070
$879$	17.7507			0.598718
$880$	−1.72414	−	2.98630i	−0.0581209	−	0.100668i
$881$	7.57504	−	13.1204i	0.255210	−	0.442036i	−0.709743	−	0.704461i	$-0.751189\pi$
$881$	7.57504	−	13.1204i	0.255210	−	0.442036i	0.964952	+	0.262425i	$0.0845222\pi$
$882$	8.41801	−	14.5804i	0.283449	−	0.490949i
$883$	9.10401	−	15.7686i	0.306374	−	0.530656i	−0.671192	−	0.741284i	$-0.734217\pi$
$883$	9.10401	−	15.7686i	0.306374	−	0.530656i	0.977566	+	0.210628i	$0.0675507\pi$
$884$	−9.54390			−0.320996
$885$	−6.30371			−0.211897
$886$	15.4109	+	26.6925i	0.517740	+	0.896751i
$887$	−3.80669	+	6.59338i	−0.127816	+	0.221384i	−0.922830	−	0.385207i	$-0.874130\pi$
$887$	−3.80669	+	6.59338i	−0.127816	+	0.221384i	0.795014	+	0.606591i	$0.207463\pi$
$888$	−4.05010			−0.135912
$889$	24.7080	+	42.7956i	0.828681	+	1.43532i
$890$	13.7857			0.462099
$891$	2.76736			0.0927102
$892$	12.5404	−	8.10792i	0.419884	−	0.271473i
$893$	35.1551			1.17642
$894$	9.42367			0.315175
$895$	9.64838	+	16.7115i	0.322510	+	0.558603i
$896$	−4.88222			−0.163103
$897$	−7.24931	+	12.5562i	−0.242047	+	0.419238i
$898$	−4.41598	−	7.64871i	−0.147363	−	0.255241i
$899$	−64.1309			−2.13888
$900$	−3.44735			−0.114912
$901$	−13.4914	+	23.3678i	−0.449464	+	0.778495i
$902$	−5.83077	+	10.0992i	−0.194144	+	0.336266i
$903$	21.5132	−	37.2619i	0.715914	−	1.24000i
$904$	−3.60698	−	6.24747i	−0.119966	−	0.207788i
$905$	19.8627			0.660258
$906$	12.3067			0.408862
$907$	14.4827			0.480890			0.240445	−	0.970663i	$-0.422707\pi$
$907$	14.4827			0.480890			0.240445	+	0.970663i	$0.422707\pi$
$908$	−8.40101			−0.278797
$909$	−4.36185			−0.144673
$910$	−9.12526	+	15.8054i	−0.302500	+	0.523945i
$911$	5.69280	+	9.86022i	0.188611	+	0.326684i	0.944787	−	0.327684i	$-0.106268\pi$
$911$	5.69280	+	9.86022i	0.188611	+	0.326684i	−0.756176	+	0.654368i	$0.772935\pi$
$912$	−1.69092	+	2.92876i	−0.0559919	+	0.0969809i
$913$	−10.5731	−	18.3132i	−0.349920	−	0.606079i
$914$	−14.6510	+	25.3762i	−0.484610	+	0.839370i
$915$	4.75754	+	8.24030i	0.157279	+	0.272416i
$916$	−8.44423	−	14.6258i	−0.279005	−	0.483251i
$917$	34.1451	+	59.1411i	1.12757	+	1.95301i
$918$	3.18130			0.104999
$919$	1.87167			0.0617406			0.0308703	−	0.999523i	$-0.490172\pi$
$919$	1.87167			0.0617406			0.0308703	+	0.999523i	$0.490172\pi$
$920$	−6.02202			−0.198540
$921$	−1.66585	+	2.88534i	−0.0548918	+	0.0950753i
$922$	−38.0014			−1.25151
$923$	−0.609636	−	1.05592i	−0.0200664	−	0.0347561i
$924$	−13.5109			−0.444475
$925$	13.9621			0.459071
$926$	28.4100			0.933612
$927$	8.42215	−	14.5876i	0.276620	−	0.479119i
$928$	3.74459	−	6.48582i	0.122922	−	0.212907i
$929$	−14.7446	+	25.5384i	−0.483754	+	0.837887i	−0.999826	−	0.0186583i	$-0.994061\pi$
$929$	−14.7446	+	25.5384i	−0.483754	+	0.837887i	0.516072	+	0.856546i	$0.327394\pi$
$930$	5.33507	+	9.24061i	0.174944	+	0.303012i
$931$	28.4684	+	49.3087i	0.933013	+	1.61603i
$932$	10.1970	−	17.6617i	0.334014	−	0.578529i
$933$	25.0903			0.821420
$934$	−0.284899	−	0.493460i	−0.00932218	−	0.0161465i
$935$	−5.48502	−	9.50033i	−0.179379	−	0.310694i
$936$	−1.50000	+	2.59808i	−0.0490290	+	0.0849208i
$937$	24.6688	+	42.7277i	0.805896	+	1.39585i	0.915685	+	0.401897i	$0.131649\pi$
$937$	24.6688	+	42.7277i	0.805896	+	1.39585i	−0.109789	+	0.993955i	$0.535018\pi$
$938$	−21.4836	−	37.2107i	−0.701466	−	1.21497i
$939$	9.37104	−	16.2311i	0.305812	−	0.529682i
$940$	6.47653	+	11.2177i	0.211241	+	0.365880i
$941$	−25.3326			−0.825818			−0.412909	−	0.910772i	$-0.635487\pi$
$941$	−25.3326			−0.825818			−0.412909	+	0.910772i	$0.635487\pi$
$942$	−2.75604	−	4.77359i	−0.0897965	−	0.155532i
$943$	10.1828	+	17.6370i	0.331596	+	0.574341i
$944$	5.05893			0.164654
$945$	3.04175	−	5.26847i	0.0989483	−	0.171383i
$946$	−24.3884			−0.792937
$947$	−14.3170	−	24.7978i	−0.465240	−	0.805820i	0.533972	−	0.845502i	$-0.320699\pi$
$947$	−14.3170	−	24.7978i	−0.465240	−	0.805820i	−0.999212	+	0.0396825i	$0.987365\pi$
$948$	6.40352			0.207977
$949$	20.0257	−	34.6856i	0.650063	−	1.12594i
$950$	5.82919	−	10.0964i	0.189124	−	0.327572i
$951$	13.2035			0.428154
$952$	−15.5318			−0.503388
$953$	3.23696	+	5.60658i	0.104855	+	0.181615i	0.913679	−	0.406436i	$-0.133229\pi$
$953$	3.23696	+	5.60658i	0.104855	+	0.181615i	−0.808824	+	0.588051i	$0.799895\pi$
$954$	4.24085	+	7.34536i	0.137303	+	0.237815i
$955$	5.86390	−	10.1566i	0.189751	−	0.328659i
$956$	11.6854			0.377931
$957$	10.3626	−	17.9486i	0.334976	−	0.580196i
$958$	11.6056			0.374960
$959$	−21.7936	−	37.7475i	−0.703751	−	1.21893i
$960$	−1.24605			−0.0402162
$961$	−21.1637	+	36.6566i	−0.682699	+	1.18247i
$962$	6.07515	−	10.5225i	0.195871	−	0.339258i
$963$	3.59836	+	6.23253i	0.115955	+	0.200841i
$964$	9.75564	−	16.8973i	0.314208	−	0.544224i
$965$	−14.9173	+	25.8375i	−0.480204	+	0.831738i
$966$	−11.7976	+	20.4340i	−0.379580	+	0.657452i
$967$	14.4693	−	25.0615i	0.465300	−	0.805923i	−0.533915	−	0.845538i	$-0.679280\pi$
$967$	14.4693	−	25.0615i	0.465300	−	0.805923i	0.999215	+	0.0396151i	$0.0126132\pi$
$968$	−1.67085	−	2.89400i	−0.0537032	−	0.0930166i
$969$	−5.37932	+	9.31726i	−0.172809	+	0.299313i
$970$	−7.96095	−	13.7888i	−0.255611	−	0.442731i
$971$	−22.3255	+	38.6689i	−0.716460	+	1.24095i	0.245933	+	0.969287i	$0.420906\pi$
$971$	−22.3255	+	38.6689i	−0.716460	+	1.24095i	−0.962394	+	0.271659i	$0.912428\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−43.9781	−	76.1723i	−1.40987	−	2.44197i
$974$	14.7108			0.471366
$975$	5.17102	−	8.95647i	0.165605	−	0.286837i
$976$	−3.81808	−	6.61311i	−0.122214	−	0.211680i
$977$	26.6893	−	46.2273i	0.853868	−	1.47894i	−0.0238240	−	0.999716i	$-0.507584\pi$
$977$	26.6893	−	46.2273i	0.853868	−	1.47894i	0.877692	−	0.479226i	$-0.159083\pi$
$978$	3.20650	+	5.55382i	0.102533	+	0.177592i
$979$	−30.6168			−0.978516
$980$	−10.4893	+	18.1680i	−0.335069	+	0.580356i
$981$	−4.42315	−	7.66111i	−0.141220	−	0.244600i
$982$	9.29629	+	16.1016i	0.296656	+	0.513824i
$983$	−4.51117			−0.143884			−0.0719420	−	0.997409i	$-0.522920\pi$
$983$	−4.51117			−0.143884			−0.0719420	+	0.997409i	$0.522920\pi$
$984$	2.10698	+	3.64939i	0.0671680	+	0.116338i
$985$	−3.67780	+	6.37014i	−0.117185	+	0.202970i
$986$	11.9127	−	20.6333i	0.379376	−	0.657099i
$987$	50.7519			1.61545
$988$	−5.07276	−	8.78627i	−0.161386	−	0.279529i
$989$	−21.2958	+	36.8853i	−0.677166	+	1.17289i
$990$	−3.44829			−0.109594
$991$	−18.0859	−	31.3257i	−0.574517	−	0.995093i	−0.996094	−	0.0883004i	$-0.971856\pi$
$991$	−18.0859	−	31.3257i	−0.574517	−	0.995093i	0.421577	−	0.906793i	$-0.361477\pi$
$992$	−4.28157	−	7.41590i	−0.135940	−	0.235455i
$993$	9.33221	+	16.1639i	0.296149	+	0.512945i
$994$	−0.992125	−	1.71841i	−0.0314683	−	0.0545047i
$995$	−10.2783			−0.325843
$996$	−7.64131			−0.242124
$997$	−26.5844			−0.841937			−0.420968	−	0.907075i	$-0.638310\pi$
$997$	−26.5844			−0.841937			−0.420968	+	0.907075i	$0.638310\pi$
$998$	16.8916	−	29.2571i	0.534694	−	0.926116i
$999$	−2.02505	+	3.50749i	−0.0640697	+	0.110972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.g.1075.4	yes	12
223.39	even	3	inner	1338.2.e.g.931.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.g.931.4	✓	12	223.39	even	3	inner
1338.2.e.g.1075.4	yes	12	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.623027 + 1.07912i) q^{5} +(-0.500000 - 0.866025i) q^{6} +4.88222 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.623027 - 1.07912i) q^{10} +(-1.38368 + 2.39661i) q^{11} +(0.500000 + 0.866025i) q^{12} -3.00000 q^{13} -4.88222 q^{14} -1.24605 q^{15} +1.00000 q^{16} +3.18130 q^{17} +(0.500000 - 0.866025i) q^{18} +(1.69092 + 2.92876i) q^{19} +(-0.623027 + 1.07912i) q^{20} +(2.44111 + 4.22812i) q^{21} +(1.38368 - 2.39661i) q^{22} +(-2.41644 - 4.18539i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.72367 + 2.98549i) q^{25} +3.00000 q^{26} -1.00000 q^{27} +4.88222 q^{28} +(-3.74459 + 6.48582i) q^{29} +1.24605 q^{30} +(4.28157 + 7.41590i) q^{31} -1.00000 q^{32} -2.76736 q^{33} -3.18130 q^{34} +(-3.04175 + 5.26847i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.02505 - 3.50749i) q^{37} +(-1.69092 - 2.92876i) q^{38} +(-1.50000 - 2.59808i) q^{39} +(0.623027 - 1.07912i) q^{40} -4.21396 q^{41} +(-2.44111 - 4.22812i) q^{42} +(-4.40644 - 7.63218i) q^{43} +(-1.38368 + 2.39661i) q^{44} +(-0.623027 - 1.07912i) q^{45} +(2.41644 + 4.18539i) q^{46} +(5.19763 - 9.00256i) q^{47} +(0.500000 + 0.866025i) q^{48} +16.8360 q^{49} +(-1.72367 - 2.98549i) q^{50} +(1.59065 + 2.75509i) q^{51} -3.00000 q^{52} +(-4.24085 + 7.34536i) q^{53} +1.00000 q^{54} +(-1.72414 - 2.98630i) q^{55} -4.88222 q^{56} +(-1.69092 + 2.92876i) q^{57} +(3.74459 - 6.48582i) q^{58} +5.05893 q^{59} -1.24605 q^{60} +(-3.81808 - 6.61311i) q^{61} +(-4.28157 - 7.41590i) q^{62} +(-2.44111 + 4.22812i) q^{63} +1.00000 q^{64} +(1.86908 - 3.23735i) q^{65} +2.76736 q^{66} +(4.40039 + 7.62169i) q^{67} +3.18130 q^{68} +(2.41644 - 4.18539i) q^{69} +(3.04175 - 5.26847i) q^{70} +(0.203212 + 0.351974i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-6.67525 + 11.5619i) q^{73} +(-2.02505 + 3.50749i) q^{74} +(-1.72367 + 2.98549i) q^{75} +(1.69092 + 2.92876i) q^{76} +(-6.75543 + 11.7008i) q^{77} +(1.50000 + 2.59808i) q^{78} +(3.20176 - 5.54561i) q^{79} +(-0.623027 + 1.07912i) q^{80} +(-0.500000 - 0.866025i) q^{81} +4.21396 q^{82} +(-3.82066 + 6.61757i) q^{83} +(2.44111 + 4.22812i) q^{84} +(-1.98204 + 3.43299i) q^{85} +(4.40644 + 7.63218i) q^{86} -7.48918 q^{87} +(1.38368 - 2.39661i) q^{88} +(5.53176 + 9.58129i) q^{89} +(0.623027 + 1.07912i) q^{90} -14.6466 q^{91} +(-2.41644 - 4.18539i) q^{92} +(-4.28157 + 7.41590i) q^{93} +(-5.19763 + 9.00256i) q^{94} -4.21396 q^{95} +(-0.500000 - 0.866025i) q^{96} +(6.38892 - 11.0659i) q^{97} -16.8360 q^{98} +(-1.38368 - 2.39661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 6 q^{3} + 12 q^{4} - 3 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + 6 q^{12} - 36 q^{13} + 2 q^{14} - 6 q^{15} + 12 q^{16} + 6 q^{18} + 4 q^{19} - 3 q^{20} - q^{21}+ \cdots + 3 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 6 * q^3 + 12 * q^4 - 3 * q^5 - 6 * q^6 - 2 * q^7 - 12 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 + 6 * q^12 - 36 * q^13 + 2 * q^14 - 6 * q^15 + 12 * q^16 + 6 * q^18 + 4 * q^19 - 3 * q^20 - q^21 - 3 * q^22 + 4 * q^23 - 6 * q^24 - 9 * q^25 + 36 * q^26 - 12 * q^27 - 2 * q^28 + 5 * q^29 + 6 * q^30 + 16 * q^31 - 12 * q^32 + 6 * q^33 + 19 * q^35 - 6 * q^36 - q^37 - 4 * q^38 - 18 * q^39 + 3 * q^40 - 8 * q^41 + q^42 - 26 * q^43 + 3 * q^44 - 3 * q^45 - 4 * q^46 + 22 * q^47 + 6 * q^48 + 26 * q^49 + 9 * q^50 - 36 * q^52 + 4 * q^53 + 12 * q^54 + 4 * q^55 + 2 * q^56 - 4 * q^57 - 5 * q^58 - 2 * q^59 - 6 * q^60 - 20 * q^61 - 16 * q^62 + q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 + 3 * q^67 - 4 * q^69 - 19 * q^70 - 20 * q^71 + 6 * q^72 - 19 * q^73 + q^74 + 9 * q^75 + 4 * q^76 - 2 * q^77 + 18 * q^78 - 7 * q^79 - 3 * q^80 - 6 * q^81 + 8 * q^82 - q^83 - q^84 + 3 * q^85 + 26 * q^86 + 10 * q^87 - 3 * q^88 + 17 * q^89 + 3 * q^90 + 6 * q^91 + 4 * q^92 - 16 * q^93 - 22 * q^94 - 8 * q^95 - 6 * q^96 - 8 * q^97 - 26 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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