LMFDB - Embedded newform 374.2.g.d.103.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [374,2,Mod(69,374)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(374, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("374.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$374 = 2 \cdot 11 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	374.g (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,5] 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:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1$ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			103.1
Root			$1.69513 + 1.23158i$ of defining polynomial
Character	$\chi$	$=$	374.103
Dual form			374.2.g.d.69.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.856664 + 2.63654i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.570387 - 0.414410i) q^{5} +(2.24278 - 1.62947i) q^{6} +(-1.44244 - 4.43939i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-3.79042 - 2.75390i) q^{9} -0.705037 q^{10} +(0.309017 - 3.30220i) q^{11} -2.77222 q^{12} +(0.389313 + 0.282852i) q^{13} +(-1.44244 + 4.43939i) q^{14} +(0.603980 + 1.85886i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(1.44781 + 4.45591i) q^{18} +(1.45113 - 4.46612i) q^{19} +(0.570387 + 0.414410i) q^{20} +12.9403 q^{21} +(-2.19098 + 2.48990i) q^{22} +8.70693 q^{23} +(2.24278 + 1.62947i) q^{24} +(-1.39148 + 4.28253i) q^{25} +(-0.148704 - 0.457664i) q^{26} +(3.77957 - 2.74602i) q^{27} +(3.77637 - 2.74369i) q^{28} +(-2.91837 - 8.98180i) q^{29} +(0.603980 - 1.85886i) q^{30} +(-3.19513 - 2.32140i) q^{31} +1.00000 q^{32} +(8.44165 + 3.64361i) q^{33} +1.00000 q^{34} +(-2.66248 - 1.93440i) q^{35} +(1.44781 - 4.45591i) q^{36} +(1.17081 + 3.60337i) q^{37} +(-3.79911 + 2.76021i) q^{38} +(-1.07926 + 0.784129i) q^{39} +(-0.217868 - 0.670530i) q^{40} +(-1.16485 + 3.58505i) q^{41} +(-10.4689 - 7.60613i) q^{42} +3.21870 q^{43} +(3.23607 - 0.726543i) q^{44} -3.30325 q^{45} +(-7.04405 - 5.11780i) q^{46} +(3.36791 - 10.3654i) q^{47} +(-0.856664 - 2.63654i) q^{48} +(-11.9644 + 8.69264i) q^{49} +(3.64294 - 2.64675i) q^{50} +(-0.856664 - 2.63654i) q^{51} +(-0.148704 + 0.457664i) q^{52} +(-2.17437 - 1.57977i) q^{53} -4.67180 q^{54} +(-1.19221 - 2.01159i) q^{55} -4.66785 q^{56} +(10.5320 + 7.65193i) q^{57} +(-2.91837 + 8.98180i) q^{58} +(-1.00746 - 3.10065i) q^{59} +(-1.58124 + 1.14884i) q^{60} +(5.49226 - 3.99036i) q^{61} +(1.22043 + 3.75610i) q^{62} +(-6.75817 + 20.7995i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.339276 q^{65} +(-4.68778 - 7.90962i) q^{66} -15.0249 q^{67} +(-0.809017 - 0.587785i) q^{68} +(-7.45891 + 22.9562i) q^{69} +(1.01698 + 3.12993i) q^{70} +(10.8271 - 7.86637i) q^{71} +(-3.79042 + 2.75390i) q^{72} +(1.54631 + 4.75905i) q^{73} +(1.17081 - 3.60337i) q^{74} +(-10.0990 - 7.33739i) q^{75} +4.69596 q^{76} +(-15.1055 + 3.39139i) q^{77} +1.33404 q^{78} +(-4.39544 - 3.19347i) q^{79} +(-0.217868 + 0.670530i) q^{80} +(-0.341271 - 1.05032i) q^{81} +(3.04963 - 2.21568i) q^{82} +(2.19162 - 1.59231i) q^{83} +(3.99878 + 12.3070i) q^{84} +(-0.217868 + 0.670530i) q^{85} +(-2.60398 - 1.89190i) q^{86} +26.1809 q^{87} +(-3.04508 - 1.31433i) q^{88} +2.81526 q^{89} +(2.67239 + 1.94160i) q^{90} +(0.694129 - 2.13631i) q^{91} +(2.69059 + 8.28078i) q^{92} +(8.85761 - 6.43543i) q^{93} +(-8.81731 + 6.40615i) q^{94} +(-1.02310 - 3.14878i) q^{95} +(-0.856664 + 2.63654i) q^{96} +(11.1963 + 8.13460i) q^{97} +14.7888 q^{98} +(-10.2652 + 11.6657i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 2 q^{2} + 5 q^{3} - 2 q^{4} + 3 q^{5} - 2 q^{7} - 2 q^{8} - 5 q^{9} - 12 q^{10} - 2 q^{11} - 10 q^{12} + 14 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + 6 q^{19} + 3 q^{20} + 24 q^{21} - 22 q^{22}+ \cdots - 25 q^{99}+O(q^{100})$ 8 * q - 2 * q^2 + 5 * q^3 - 2 * q^4 + 3 * q^5 - 2 * q^7 - 2 * q^8 - 5 * q^9 - 12 * q^10 - 2 * q^11 - 10 * q^12 + 14 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + 6 * q^19 + 3 * q^20 + 24 * q^21 - 22 * q^22 + 12 * q^23 - 3 * q^25 - 11 * q^26 + 20 * q^27 + 3 * q^28 - 6 * q^29 - 6 * q^30 - 15 * q^31 + 8 * q^32 - 10 * q^33 + 8 * q^34 + 12 * q^35 + 23 * q^37 - 9 * q^38 + 12 * q^39 + 3 * q^40 - 14 * q^41 - 31 * q^42 + 8 * q^44 + 10 * q^45 + 2 * q^46 + 34 * q^47 + 5 * q^48 - 24 * q^49 + 7 * q^50 + 5 * q^51 - 11 * q^52 - 5 * q^53 - 10 * q^54 - 27 * q^55 - 2 * q^56 + 28 * q^57 - 6 * q^58 + q^59 + 4 * q^60 + 8 * q^61 + 20 * q^62 - 40 * q^63 - 2 * q^64 - 14 * q^65 - 25 * q^66 - 30 * q^67 - 2 * q^68 - q^69 - 18 * q^70 + q^71 - 5 * q^72 + 3 * q^73 + 23 * q^74 - 17 * q^75 + 6 * q^76 - 12 * q^77 - 18 * q^78 - 35 * q^79 + 3 * q^80 + 13 * q^81 + 21 * q^82 + 24 * q^83 + 19 * q^84 + 3 * q^85 - 10 * q^86 + 52 * q^87 - 2 * q^88 - 4 * q^89 + 5 * q^90 + 36 * q^91 - 8 * q^92 + 27 * q^93 - 36 * q^94 + 29 * q^95 + 5 * q^96 + 15 * q^97 + 46 * q^98 - 25 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$ .

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.856664	+	2.63654i	−0.494595	+	1.52221i	0.322991	+	0.946402i	$0.395311\pi$
$3$	−0.856664	+	2.63654i	−0.494595	+	1.52221i	−0.817587	+	0.575806i	$0.804689\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.570387	−	0.414410i	0.255085	−	0.185330i	−0.452893	−	0.891565i	$-0.649608\pi$
$5$	0.570387	−	0.414410i	0.255085	−	0.185330i	0.707977	+	0.706235i	$0.249608\pi$
$6$	2.24278	−	1.62947i	0.915609	−	0.665229i
$7$	−1.44244	−	4.43939i	−0.545193	−	1.67793i	−0.720531	−	0.693422i	$-0.756102\pi$
$7$	−1.44244	−	4.43939i	−0.545193	−	1.67793i	0.175339	−	0.984508i	$-0.443898\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−3.79042	−	2.75390i	−1.26347	−	0.917968i
$10$	−0.705037			−0.222952
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$	−2.77222			−0.800272
$13$	0.389313	+	0.282852i	0.107976	+	0.0784491i	0.640463	−	0.767989i	$-0.278742\pi$
$13$	0.389313	+	0.282852i	0.107976	+	0.0784491i	−0.532487	+	0.846438i	$0.678742\pi$
$14$	−1.44244	+	4.43939i	−0.385509	+	1.18648i
$15$	0.603980	+	1.85886i	0.155947	+	0.479955i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$18$	1.44781	+	4.45591i	0.341253	+	1.05027i
$19$	1.45113	−	4.46612i	0.332912	−	1.02460i	−0.634829	−	0.772652i	$-0.718930\pi$
$19$	1.45113	−	4.46612i	0.332912	−	1.02460i	0.967741	−	0.251946i	$-0.0810704\pi$
$20$	0.570387	+	0.414410i	0.127542	+	0.0926650i
$21$	12.9403			2.82381
$22$	−2.19098	+	2.48990i	−0.467119	+	0.530848i
$23$	8.70693			1.81552			0.907760	−	0.419490i	$-0.137791\pi$
$23$	8.70693			1.81552			0.907760	+	0.419490i	$0.137791\pi$
$24$	2.24278	+	1.62947i	0.457805	+	0.332615i
$25$	−1.39148	+	4.28253i	−0.278296	+	0.856507i
$26$	−0.148704	−	0.457664i	−0.0291633	−	0.0897554i
$27$	3.77957	−	2.74602i	0.727378	−	0.528471i
$28$	3.77637	−	2.74369i	0.713667	−	0.518509i
$29$	−2.91837	−	8.98180i	−0.541927	−	1.66788i	−0.728187	−	0.685379i	$-0.759637\pi$
$29$	−2.91837	−	8.98180i	−0.541927	−	1.66788i	0.186260	−	0.982500i	$-0.440363\pi$
$30$	0.603980	−	1.85886i	0.110271	−	0.339380i
$31$	−3.19513	−	2.32140i	−0.573862	−	0.416935i	0.262644	−	0.964893i	$-0.415405\pi$
$31$	−3.19513	−	2.32140i	−0.573862	−	0.416935i	−0.836506	+	0.547958i	$0.815405\pi$
$32$	1.00000			0.176777
$33$	8.44165	+	3.64361i	1.46950	+	0.634271i
$34$	1.00000			0.171499
$35$	−2.66248	−	1.93440i	−0.450041	−	0.326974i
$36$	1.44781	−	4.45591i	0.241302	−	0.742651i
$37$	1.17081	+	3.60337i	0.192479	+	0.592390i	0.999997	+	0.00254646i	$0.000810565\pi$
$37$	1.17081	+	3.60337i	0.192479	+	0.592390i	−0.807518	+	0.589843i	$0.799189\pi$
$38$	−3.79911	+	2.76021i	−0.616297	+	0.447766i
$39$	−1.07926	+	0.784129i	−0.172820	+	0.125561i
$40$	−0.217868	−	0.670530i	−0.0344480	−	0.106020i
$41$	−1.16485	+	3.58505i	−0.181920	+	0.559891i	−0.999882	−	0.0153813i	$-0.995104\pi$
$41$	−1.16485	+	3.58505i	−0.181920	+	0.559891i	0.817962	+	0.575272i	$0.195104\pi$
$42$	−10.4689	−	7.60613i	−1.61539	−	1.17365i
$43$	3.21870			0.490847			0.245423	−	0.969416i	$-0.421073\pi$
$43$	3.21870			0.490847			0.245423	+	0.969416i	$0.421073\pi$
$44$	3.23607	−	0.726543i	0.487856	−	0.109530i
$45$	−3.30325			−0.492420
$46$	−7.04405	−	5.11780i	−1.03859	−	0.754579i
$47$	3.36791	−	10.3654i	0.491260	−	1.51194i	−0.331444	−	0.943475i	$-0.607536\pi$
$47$	3.36791	−	10.3654i	0.491260	−	1.51194i	0.822704	−	0.568469i	$-0.192464\pi$
$48$	−0.856664	−	2.63654i	−0.123649	−	0.380552i
$49$	−11.9644	+	8.69264i	−1.70920	+	1.24181i
$50$	3.64294	−	2.64675i	0.515190	−	0.374307i
$51$	−0.856664	−	2.63654i	−0.119957	−	0.369190i
$52$	−0.148704	+	0.457664i	−0.0206216	+	0.0634666i
$53$	−2.17437	−	1.57977i	−0.298672	−	0.216998i	0.428348	−	0.903614i	$-0.359096\pi$
$53$	−2.17437	−	1.57977i	−0.298672	−	0.216998i	−0.727021	+	0.686616i	$0.759096\pi$
$54$	−4.67180			−0.635752
$55$	−1.19221	−	2.01159i	−0.160757	−	0.271243i
$56$	−4.66785			−0.623767
$57$	10.5320	+	7.65193i	1.39499	+	1.01352i
$58$	−2.91837	+	8.98180i	−0.383200	+	1.17937i
$59$	−1.00746	−	3.10065i	−0.131161	−	0.403671i	0.863813	−	0.503813i	$-0.168070\pi$
$59$	−1.00746	−	3.10065i	−0.131161	−	0.403671i	−0.994973	+	0.100143i	$0.968070\pi$
$60$	−1.58124	+	1.14884i	−0.204137	+	0.148314i
$61$	5.49226	−	3.99036i	0.703212	−	0.510913i	−0.177765	−	0.984073i	$-0.556887\pi$
$61$	5.49226	−	3.99036i	0.703212	−	0.510913i	0.880977	+	0.473160i	$0.156887\pi$
$62$	1.22043	+	3.75610i	0.154995	+	0.477025i
$63$	−6.75817	+	20.7995i	−0.851449	+	2.62049i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.339276			0.0420820
$66$	−4.68778	−	7.90962i	−0.577026	−	0.973607i
$67$	−15.0249			−1.83558			−0.917790	−	0.397066i	$-0.870028\pi$
$67$	−15.0249			−1.83558			−0.917790	+	0.397066i	$0.870028\pi$
$68$	−0.809017	−	0.587785i	−0.0981077	−	0.0712794i
$69$	−7.45891	+	22.9562i	−0.897947	+	2.76360i
$70$	1.01698	+	3.12993i	0.121552	+	0.374099i
$71$	10.8271	−	7.86637i	1.28494	−	0.933566i	0.285253	−	0.958452i	$-0.407922\pi$
$71$	10.8271	−	7.86637i	1.28494	−	0.933566i	0.999690	+	0.0248861i	$0.00792230\pi$
$72$	−3.79042	+	2.75390i	−0.446706	+	0.324551i
$73$	1.54631	+	4.75905i	0.180982	+	0.557004i	0.999856	−	0.0169686i	$-0.00540152\pi$
$73$	1.54631	+	4.75905i	0.180982	+	0.557004i	−0.818874	+	0.573973i	$0.805402\pi$
$74$	1.17081	−	3.60337i	0.136103	−	0.418883i
$75$	−10.0990	−	7.33739i	−1.16614	−	0.847248i
$76$	4.69596			0.538663
$77$	−15.1055	+	3.39139i	−1.72143	+	0.386485i
$78$	1.33404			0.151050
$79$	−4.39544	−	3.19347i	−0.494525	−	0.359294i	0.312397	−	0.949952i	$-0.398868\pi$
$79$	−4.39544	−	3.19347i	−0.494525	−	0.359294i	−0.806922	+	0.590658i	$0.798868\pi$
$80$	−0.217868	+	0.670530i	−0.0243584	+	0.0749675i
$81$	−0.341271	−	1.05032i	−0.0379190	−	0.116703i
$82$	3.04963	−	2.21568i	0.336775	−	0.244681i
$83$	2.19162	−	1.59231i	0.240562	−	0.174778i	−0.460972	−	0.887415i	$-0.652499\pi$
$83$	2.19162	−	1.59231i	0.240562	−	0.174778i	0.701534	+	0.712636i	$0.252499\pi$
$84$	3.99878	+	12.3070i	0.436302	+	1.34280i
$85$	−0.217868	+	0.670530i	−0.0236312	+	0.0727292i
$86$	−2.60398	−	1.89190i	−0.280794	−	0.204009i
$87$	26.1809			2.80689
$88$	−3.04508	−	1.31433i	−0.324607	−	0.140108i
$89$	2.81526			0.298417			0.149208	−	0.988806i	$-0.452327\pi$
$89$	2.81526			0.298417			0.149208	+	0.988806i	$0.452327\pi$
$90$	2.67239	+	1.94160i	0.281694	+	0.204663i
$91$	0.694129	−	2.13631i	0.0727644	−	0.223946i
$92$	2.69059	+	8.28078i	0.280513	+	0.863331i
$93$	8.85761	−	6.43543i	0.918491	−	0.667323i
$94$	−8.81731	+	6.40615i	−0.909436	+	0.660744i
$95$	−1.02310	−	3.14878i	−0.104968	−	0.323058i
$96$	−0.856664	+	2.63654i	−0.0874329	+	0.269091i
$97$	11.1963	+	8.13460i	1.13681	+	0.825944i	0.986672	−	0.162721i	$-0.0520270\pi$
$97$	11.1963	+	8.13460i	1.13681	+	0.825944i	0.150142	+	0.988665i	$0.452027\pi$
$98$	14.7888			1.49389
$99$	−10.2652	+	11.6657i	−1.03170	+	1.17245i
$100$	−4.50292			−0.450292
$101$	−0.247504	−	0.179823i	−0.0246276	−	0.0178930i	0.575403	−	0.817870i	$-0.304845\pi$
$101$	−0.247504	−	0.179823i	−0.0246276	−	0.0178930i	−0.600031	+	0.799977i	$0.704845\pi$
$102$	−0.856664	+	2.63654i	−0.0848224	+	0.261056i
$103$	2.48385	+	7.64451i	0.244741	+	0.753236i	0.995679	+	0.0928627i	$0.0296018\pi$
$103$	2.48385	+	7.64451i	0.244741	+	0.753236i	−0.750938	+	0.660373i	$0.770398\pi$
$104$	0.389313	−	0.282852i	0.0381752	−	0.0277359i
$105$	7.38099	−	5.36260i	0.720311	−	0.523336i
$106$	0.830534	+	2.55612i	0.0806686	+	0.248272i
$107$	−0.990731	+	3.04916i	−0.0957775	+	0.294773i	−0.987456	−	0.157897i	$-0.949529\pi$
$107$	−0.990731	+	3.04916i	−0.0957775	+	0.294773i	0.891678	+	0.452670i	$0.149529\pi$
$108$	3.77957	+	2.74602i	0.363689	+	0.264236i
$109$	−8.71845			−0.835076			−0.417538	−	0.908659i	$-0.637107\pi$
$109$	−8.71845			−0.835076			−0.417538	+	0.908659i	$0.637107\pi$
$110$	−0.217868	+	2.32817i	−0.0207729	+	0.221982i
$111$	−10.5034			−0.996940
$112$	3.77637	+	2.74369i	0.356833	+	0.259255i
$113$	0.737802	−	2.27072i	0.0694066	−	0.213612i	−0.910337	−	0.413868i	$-0.864178\pi$
$113$	0.737802	−	2.27072i	0.0694066	−	0.213612i	0.979744	+	0.200256i	$0.0641775\pi$
$114$	−4.02286	−	12.3811i	−0.376775	−	1.15959i
$115$	4.96632	−	3.60824i	0.463111	−	0.336470i
$116$	7.64038	−	5.55106i	0.709391	−	0.515403i
$117$	−0.696712	−	2.14426i	−0.0644110	−	0.198237i
$118$	−1.00746	+	3.10065i	−0.0927445	+	0.285438i
$119$	3.77637	+	2.74369i	0.346179	+	0.251514i
$120$	1.95452			0.178422
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	−6.78880			−0.614629
$123$	−8.45424	−	6.14237i	−0.762293	−	0.553838i
$124$	1.22043	−	3.75610i	0.109598	−	0.337308i
$125$	2.07039	+	6.37200i	0.185181	+	0.569929i
$126$	17.6931	−	12.8548i	1.57623	−	1.14520i
$127$	−9.20105	+	6.68495i	−0.816461	+	0.593193i	−0.915697	−	0.401870i	$-0.868360\pi$
$127$	−9.20105	+	6.68495i	−0.816461	+	0.593193i	0.0992357	+	0.995064i	$0.468360\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−2.75734	+	8.48622i	−0.242770	+	0.747170i
$130$	−0.274480	−	0.199421i	−0.0240735	−	0.0174904i
$131$	−1.59633			−0.139472			−0.0697359	−	0.997565i	$-0.522216\pi$
$131$	−1.59633			−0.139472			−0.0697359	+	0.997565i	$0.522216\pi$
$132$	−0.856664	+	9.15443i	−0.0745630	+	0.796791i
$133$	−21.9200			−1.90071
$134$	12.1554	+	8.83140i	1.05006	+	0.762917i
$135$	1.01784	−	3.13259i	0.0876016	−	0.269610i
$136$	0.309017	+	0.951057i	0.0264980	+	0.0815524i
$137$	5.23351	−	3.80236i	0.447129	−	0.324858i	−0.341332	−	0.939943i	$-0.610878\pi$
$137$	5.23351	−	3.80236i	0.447129	−	0.324858i	0.788461	+	0.615085i	$0.210878\pi$
$138$	19.5277	−	14.1877i	1.66231	−	1.20774i
$139$	−2.93901	−	9.04534i	−0.249284	−	0.767216i	−0.994902	−	0.100843i	$-0.967846\pi$
$139$	−2.93901	−	9.04534i	−0.249284	−	0.767216i	0.745619	−	0.666373i	$-0.232154\pi$
$140$	1.01698	−	3.12993i	0.0859502	−	0.264528i
$141$	24.4435	+	17.7593i	2.05852	+	1.49560i
$142$	−13.3831			−1.12308
$143$	1.05434	−	1.19818i	0.0881682	−	0.100197i
$144$	4.68522			0.390435
$145$	−5.38675	−	3.91370i	−0.447345	−	0.325015i
$146$	1.54631	−	4.75905i	0.127973	−	0.393861i
$147$	−12.6690	−	38.9913i	−1.04492	−	3.21595i
$148$	−3.06521	+	2.22700i	−0.251958	+	0.183059i
$149$	−5.35544	+	3.89096i	−0.438735	+	0.318760i	−0.785132	−	0.619328i	$-0.787405\pi$
$149$	−5.35544	+	3.89096i	−0.438735	+	0.318760i	0.346397	+	0.938088i	$0.387405\pi$
$150$	3.85749	+	11.8721i	0.314963	+	0.969356i
$151$	−6.80372	+	20.9397i	−0.553679	+	1.70405i	0.145728	+	0.989325i	$0.453448\pi$
$151$	−6.80372	+	20.9397i	−0.553679	+	1.70405i	−0.699407	+	0.714724i	$0.746552\pi$
$152$	−3.79911	−	2.76021i	−0.308148	−	0.223883i
$153$	4.68522			0.378778
$154$	14.2140	+	6.13508i	1.14540	+	0.494379i
$155$	−2.78447			−0.223654
$156$	−1.07926	−	0.784129i	−0.0864101	−	0.0627806i
$157$	−3.59202	+	11.0551i	−0.286674	+	0.882293i	0.699217	+	0.714909i	$0.253532\pi$
$157$	−3.59202	+	11.0551i	−0.286674	+	0.882293i	−0.985892	+	0.167384i	$0.946468\pi$
$158$	1.67891	+	5.16715i	0.133567	+	0.411076i
$159$	6.02783	−	4.37947i	0.478038	−	0.347315i
$160$	0.570387	−	0.414410i	0.0450931	−	0.0327620i
$161$	−12.5593	−	38.6534i	−0.989808	−	3.04632i
$162$	−0.341271	+	1.05032i	−0.0268128	+	0.0825212i
$163$	−7.43790	−	5.40395i	−0.582582	−	0.423270i	0.257072	−	0.966392i	$-0.417242\pi$
$163$	−7.43790	−	5.40395i	−0.582582	−	0.423270i	−0.839654	+	0.543122i	$0.817242\pi$
$164$	−3.76954			−0.294352
$165$	6.32496	−	1.42004i	0.492397	−	0.110550i
$166$	−2.70899			−0.210259
$167$	17.7484	+	12.8950i	1.37341	+	0.997843i	0.997462	+	0.0712041i	$0.0226842\pi$
$167$	17.7484	+	12.8950i	1.37341	+	0.997843i	0.375952	+	0.926639i	$0.377316\pi$
$168$	3.99878	−	12.3070i	0.308512	−	0.949503i
$169$	−3.94566	−	12.1435i	−0.303512	−	0.934115i
$170$	0.570387	−	0.414410i	0.0437467	−	0.0317838i
$171$	−17.7997	+	12.9322i	−1.36117	+	0.988951i
$172$	0.994632	+	3.06116i	0.0758400	+	0.233411i
$173$	4.46357	−	13.7374i	0.339359	−	1.04444i	−0.625176	−	0.780484i	$-0.714973\pi$
$173$	4.46357	−	13.7374i	0.339359	−	1.04444i	0.964535	−	0.263955i	$-0.0850271\pi$
$174$	−21.1808	−	15.3888i	−1.60571	−	1.16662i
$175$	21.0190			1.58888
$176$	1.69098	+	2.85317i	0.127463	+	0.215066i
$177$	9.03805			0.679342
$178$	−2.27759	−	1.65477i	−0.170713	−	0.124030i
$179$	2.03067	−	6.24976i	0.151779	−	0.467129i	−0.846041	−	0.533118i	$-0.821020\pi$
$179$	2.03067	−	6.24976i	0.151779	−	0.467129i	0.997820	+	0.0659889i	$0.0210202\pi$
$180$	−1.02076	−	3.14158i	−0.0760831	−	0.234160i
$181$	11.9957	−	8.71539i	0.891634	−	0.647810i	−0.0446698	−	0.999002i	$-0.514224\pi$
$181$	11.9957	−	8.71539i	0.891634	−	0.647810i	0.936303	+	0.351192i	$0.114224\pi$
$182$	−1.81725	+	1.32031i	−0.134704	+	0.0978680i
$183$	5.81572	+	17.8990i	0.429911	+	1.32313i
$184$	2.69059	−	8.28078i	0.198353	−	0.610467i
$185$	2.16108	+	1.57012i	0.158886	+	0.115438i
$186$	−10.9486			−0.802791
$187$	1.69098	+	2.85317i	0.123657	+	0.208644i
$188$	10.8988			0.794876
$189$	−17.6425	−	12.8180i	−1.28330	−	0.932372i
$190$	−1.02310	+	3.14878i	−0.0742235	+	0.228437i
$191$	1.96857	+	6.05865i	0.142441	+	0.438388i	0.996673	−	0.0815036i	$-0.0259722\pi$
$191$	1.96857	+	6.05865i	0.142441	+	0.438388i	−0.854232	+	0.519892i	$0.825972\pi$
$192$	2.24278	−	1.62947i	0.161858	−	0.117597i
$193$	11.4436	−	8.31429i	0.823731	−	0.598475i	−0.0940480	−	0.995568i	$-0.529981\pi$
$193$	11.4436	−	8.31429i	0.823731	−	0.598475i	0.917779	+	0.397092i	$0.129981\pi$
$194$	−4.27661	−	13.1621i	−0.307043	−	0.944981i
$195$	−0.290645	+	0.894514i	−0.0208135	+	0.0640575i
$196$	−11.9644	−	8.69264i	−0.854600	−	0.620903i
$197$	−6.40484			−0.456326			−0.228163	−	0.973623i	$-0.573272\pi$
$197$	−6.40484			−0.456326			−0.228163	+	0.973623i	$0.573272\pi$
$198$	15.1617	−	3.40401i	1.07749	−	0.241913i
$199$	6.58329			0.466677			0.233339	−	0.972396i	$-0.425035\pi$
$199$	6.58329			0.466677			0.233339	+	0.972396i	$0.425035\pi$
$200$	3.64294	+	2.64675i	0.257595	+	0.187154i
$201$	12.8713	−	39.6137i	0.907869	−	2.79413i
$202$	0.0945383	+	0.290959i	0.00665169	+	0.0204718i
$203$	−35.6641	+	25.9115i	−2.50313	+	1.81863i
$204$	2.24278	−	1.62947i	0.157026	−	0.114086i
$205$	0.821265	+	2.52759i	0.0573596	+	0.176535i
$206$	2.48385	−	7.64451i	0.173058	−	0.532618i
$207$	−33.0029	−	23.9780i	−2.29386	−	1.66659i
$208$	−0.481217			−0.0333664
$209$	−14.2996	−	6.17203i	−0.989123	−	0.426928i
$210$	−9.12340			−0.629575
$211$	0.404706	+	0.294036i	0.0278611	+	0.0202423i	0.601629	−	0.798776i	$-0.294519\pi$
$211$	0.404706	+	0.294036i	0.0278611	+	0.0202423i	−0.573768	+	0.819018i	$0.694519\pi$
$212$	0.830534	−	2.55612i	0.0570413	−	0.175555i
$213$	11.4648	+	35.2850i	0.785554	+	2.41769i
$214$	2.59377	−	1.88448i	0.177306	−	0.128820i
$215$	1.83590	−	1.33386i	0.125208	−	0.0909686i
$216$	−1.44367	−	4.44315i	−0.0982291	−	0.302318i
$217$	−5.69678	+	17.5329i	−0.386723	+	1.19021i
$218$	7.05338	+	5.12458i	0.477715	+	0.347080i
$219$	−13.8721			−0.937389
$220$	1.54472	−	1.75547i	0.104145	−	0.118354i
$221$	−0.481217			−0.0323702
$222$	8.49744	+	6.17375i	0.570311	+	0.414355i
$223$	−0.612061	+	1.88373i	−0.0409866	+	0.126144i	−0.969456	−	0.245265i	$-0.921125\pi$
$223$	−0.612061	+	1.88373i	−0.0409866	+	0.126144i	0.928469	+	0.371409i	$0.121125\pi$
$224$	−1.44244	−	4.43939i	−0.0963774	−	0.296619i
$225$	17.0680	−	12.4006i	1.13787	−	0.826708i
$226$	−1.93159	+	1.40338i	−0.128488	+	0.0933517i
$227$	5.73006	+	17.6353i	0.380317	+	1.17050i	0.939821	+	0.341669i	$0.110992\pi$
$227$	5.73006	+	17.6353i	0.380317	+	1.17050i	−0.559503	+	0.828828i	$0.689008\pi$
$228$	−4.02286	+	12.3811i	−0.266420	+	0.819957i
$229$	17.9550	+	13.0451i	1.18650	+	0.862042i	0.992890	−	0.119037i	$-0.0379808\pi$
$229$	17.9550	+	13.0451i	1.18650	+	0.862042i	0.193609	+	0.981079i	$0.437981\pi$
$230$	−6.13871			−0.404774
$231$	3.99878	−	42.7315i	0.263100	−	2.81152i
$232$	−9.44403			−0.620031
$233$	14.2187	+	10.3305i	0.931496	+	0.676771i	0.946359	−	0.323118i	$-0.104731\pi$
$233$	14.2187	+	10.3305i	0.931496	+	0.676771i	−0.0148630	+	0.999890i	$0.504731\pi$
$234$	−0.696712	+	2.14426i	−0.0455455	+	0.140175i
$235$	−2.37450	−	7.30797i	−0.154895	−	0.476719i
$236$	2.63757	−	1.91631i	0.171691	−	0.124741i
$237$	12.1851	−	8.85302i	0.791509	−	0.575065i
$238$	−1.44244	−	4.43939i	−0.0934998	−	0.287763i
$239$	−1.64509	+	5.06307i	−0.106412	+	0.327503i	−0.990059	−	0.140651i	$-0.955081\pi$
$239$	−1.64509	+	5.06307i	−0.106412	+	0.327503i	0.883647	+	0.468153i	$0.155081\pi$
$240$	−1.58124	−	1.14884i	−0.102069	−	0.0741572i
$241$	10.6659			0.687050			0.343525	−	0.939143i	$-0.388379\pi$
$241$	10.6659			0.687050			0.343525	+	0.939143i	$0.388379\pi$
$242$	7.54508	+	8.00448i	0.485016	+	0.514547i
$243$	17.0770			1.09549
$244$	5.49226	+	3.99036i	0.351606	+	0.255457i
$245$	−3.22201	+	9.91634i	−0.205847	+	0.633532i
$246$	3.22923	+	9.93856i	0.205888	+	0.633659i
$247$	1.82820	−	1.32826i	0.116325	−	0.0845153i
$248$	−3.19513	+	2.32140i	−0.202891	+	0.147409i
$249$	2.32070	+	7.14237i	0.147068	+	0.452629i
$250$	2.07039	−	6.37200i	0.130943	−	0.403000i
$251$	−4.60038	−	3.34237i	−0.290374	−	0.210969i	0.433056	−	0.901367i	$-0.357435\pi$
$251$	−4.60038	−	3.34237i	−0.290374	−	0.210969i	−0.723429	+	0.690398i	$0.757435\pi$
$252$	−21.8699			−1.37767
$253$	2.69059	−	28.7520i	0.169156	−	1.80762i
$254$	11.3731			0.713613
$255$	−1.58124	−	1.14884i	−0.0990211	−	0.0719430i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	8.16429	+	25.1271i	0.509274	+	1.56738i	0.793464	+	0.608617i	$0.208275\pi$
$257$	8.16429	+	25.1271i	0.509274	+	1.56738i	−0.284190	+	0.958768i	$0.591725\pi$
$258$	7.21881	−	5.24477i	0.449424	−	0.326525i
$259$	14.3079	−	10.3953i	0.889051	−	0.645933i
$260$	0.104842	+	0.322670i	0.00650202	+	0.0200112i
$261$	−13.6732	+	42.0817i	−0.846349	+	2.60479i
$262$	1.29146	+	0.938298i	0.0797865	+	0.0579683i
$263$	−26.1687			−1.61363			−0.806816	−	0.590803i	$-0.798811\pi$
$263$	−26.1687			−1.61363			−0.806816	+	0.590803i	$0.798811\pi$
$264$	6.07389	−	6.90255i	0.373822	−	0.424823i
$265$	−1.89490			−0.116403
$266$	17.7337	+	12.8843i	1.08732	+	0.789985i
$267$	−2.41173	+	7.42254i	−0.147595	+	0.454252i
$268$	−4.64294	−	14.2895i	−0.283613	−	0.872870i
$269$	14.5801	−	10.5931i	0.888965	−	0.645871i	−0.0466427	−	0.998912i	$-0.514852\pi$
$269$	14.5801	−	10.5931i	0.888965	−	0.645871i	0.935608	+	0.353041i	$0.114852\pi$
$270$	−2.66474	+	1.93604i	−0.162171	+	0.117824i
$271$	3.33829	+	10.2742i	0.202787	+	0.624114i	0.999797	+	0.0201478i	$0.00641368\pi$
$271$	3.33829	+	10.2742i	0.202787	+	0.624114i	−0.797010	+	0.603966i	$0.793586\pi$
$272$	0.309017	−	0.951057i	0.0187369	−	0.0576663i
$273$	5.03783	+	3.66020i	0.304903	+	0.221525i
$274$	−6.46897			−0.390805
$275$	13.7118	+	5.91832i	0.826852	+	0.356888i
$276$	−24.1375			−1.45291
$277$	−1.83892	−	1.33605i	−0.110490	−	0.0802755i	0.531168	−	0.847266i	$-0.321753\pi$
$277$	−1.83892	−	1.33605i	−0.110490	−	0.0802755i	−0.641658	+	0.766991i	$0.721753\pi$
$278$	−2.93901	+	9.04534i	−0.176270	+	0.542504i
$279$	5.71798	+	17.5981i	0.342327	+	1.05357i
$280$	−2.66248	+	1.93440i	−0.159114	+	0.115603i
$281$	11.1237	−	8.08182i	0.663583	−	0.482121i	−0.204288	−	0.978911i	$-0.565488\pi$
$281$	11.1237	−	8.08182i	0.663583	−	0.482121i	0.867871	+	0.496790i	$0.165488\pi$
$282$	−9.33660	−	28.7351i	−0.555987	−	1.71115i
$283$	−1.17416	+	3.61368i	−0.0697964	+	0.214811i	−0.979870	−	0.199634i	$-0.936025\pi$
$283$	−1.17416	+	3.61368i	−0.0697964	+	0.214811i	0.910074	+	0.414446i	$0.136025\pi$
$284$	10.8271	+	7.86637i	0.642472	+	0.466783i
$285$	9.17834			0.543678
$286$	−1.55725	+	0.349625i	−0.0920822	+	0.0206737i
$287$	17.5957			1.03864
$288$	−3.79042	−	2.75390i	−0.223353	−	0.162275i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	2.05756	+	6.33251i	0.120824	+	0.371858i
$291$	−31.0387	+	22.5509i	−1.81952	+	1.32196i
$292$	−4.04829	+	2.94125i	−0.236908	+	0.172124i
$293$	7.20883	+	22.1865i	0.421144	+	1.29615i	0.906638	+	0.421909i	$0.138640\pi$
$293$	7.20883	+	22.1865i	0.421144	+	1.29615i	−0.485494	+	0.874240i	$0.661360\pi$
$294$	−12.6690	+	38.9913i	−0.738873	+	2.27402i
$295$	−1.85959	−	1.35107i	−0.108269	−	0.0786623i
$296$	3.78880			0.220220
$297$	−7.89994	−	13.3295i	−0.458401	−	0.773453i
$298$	6.61969			0.383468
$299$	3.38972	+	2.46277i	0.196032	+	0.142426i
$300$	3.85749	−	11.8721i	0.222712	−	0.685438i
$301$	−4.64279	−	14.2890i	−0.267606	−	0.823606i
$302$	17.8124	−	12.9414i	1.02499	−	0.744697i
$303$	0.686137	−	0.498508i	0.0394176	−	0.0286385i
$304$	1.45113	+	4.46612i	0.0832280	+	0.256150i
$305$	1.47907	−	4.55210i	0.0846911	−	0.260652i
$306$	−3.79042	−	2.75390i	−0.216684	−	0.157430i
$307$	3.13272			0.178794			0.0893968	−	0.995996i	$-0.471506\pi$
$307$	3.13272			0.178794			0.0893968	+	0.995996i	$0.471506\pi$
$308$	−7.89325	−	13.3182i	−0.449760	−	0.758873i
$309$	−22.2829			−1.26763
$310$	2.25268	+	1.63667i	0.127944	+	0.0929567i
$311$	3.33894	−	10.2762i	0.189334	−	0.582710i	−0.810662	−	0.585514i	$-0.800893\pi$
$311$	3.33894	−	10.2762i	0.189334	−	0.582710i	0.999996	+	0.00280416i	$0.000892593\pi$
$312$	0.412241	+	1.26875i	0.0233386	+	0.0718287i
$313$	4.90278	−	3.56208i	0.277122	−	0.201341i	−0.440539	−	0.897733i	$-0.645213\pi$
$313$	4.90278	−	3.56208i	0.277122	−	0.201341i	0.717661	+	0.696393i	$0.245213\pi$
$314$	9.40403	−	6.83243i	0.530700	−	0.385576i
$315$	4.76476	+	14.6644i	0.268464	+	0.826247i
$316$	1.67891	−	5.16715i	0.0944459	−	0.290675i
$317$	18.3926	+	13.3630i	1.03303	+	0.750540i	0.968913	−	0.247402i	$-0.0795769\pi$
$317$	18.3926	+	13.3630i	1.03303	+	0.750540i	0.0641172	+	0.997942i	$0.479577\pi$
$318$	−7.45081			−0.417821
$319$	−30.5615	+	6.86149i	−1.71112	+	0.384170i
$320$	−0.705037			−0.0394128
$321$	−7.19050	−	5.22420i	−0.401334	−	0.291587i
$322$	−12.5593	+	38.6534i	−0.699900	+	2.15407i
$323$	1.45113	+	4.46612i	0.0807430	+	0.248502i
$324$	0.893458	−	0.649135i	0.0496366	−	0.0360631i
$325$	−1.75304	+	1.27366i	−0.0972414	+	0.0706500i
$326$	2.84103	+	8.74378i	0.157350	+	0.484273i
$327$	7.46878	−	22.9866i	0.413025	−	1.27116i
$328$	3.04963	+	2.21568i	0.168387	+	0.122341i
$329$	−50.8739			−2.80477
$330$	−5.95168	−	2.56888i	−0.327629	−	0.141412i
$331$	21.7409			1.19499			0.597493	−	0.801874i	$-0.296163\pi$
$331$	21.7409			1.19499			0.597493	+	0.801874i	$0.296163\pi$
$332$	2.19162	+	1.59231i	0.120281	+	0.0873892i
$333$	5.48548	−	16.8826i	0.300602	−	0.925159i
$334$	−6.77929	−	20.8645i	−0.370946	−	1.14166i
$335$	−8.56999	+	6.22646i	−0.468229	+	0.340188i
$336$	−10.4689	+	7.60613i	−0.571127	+	0.414948i
$337$	−2.74180	−	8.43838i	−0.149355	−	0.459668i	0.848190	−	0.529692i	$-0.177692\pi$
$337$	−2.74180	−	8.43838i	−0.149355	−	0.459668i	−0.997545	+	0.0700239i	$0.977692\pi$
$338$	−3.94566	+	12.1435i	−0.214616	+	0.660519i
$339$	5.35480	+	3.89049i	0.290833	+	0.211302i
$340$	−0.705037			−0.0382360
$341$	−8.65306	+	9.83359i	−0.468589	+	0.532519i
$342$	22.0016			1.18971
$343$	29.4134	+	21.3701i	1.58817	+	1.15388i
$344$	0.994632	−	3.06116i	0.0536270	−	0.165047i
$345$	5.25881	+	16.1849i	0.283125	+	0.871368i
$346$	−11.6858	+	8.49021i	−0.628231	+	0.456436i
$347$	0.981405	−	0.713033i	0.0526846	−	0.0382776i	−0.561131	−	0.827727i	$-0.689634\pi$
$347$	0.981405	−	0.713033i	0.0526846	−	0.0382776i	0.613816	+	0.789449i	$0.289634\pi$
$348$	8.09036	+	24.8996i	0.433689	+	1.33476i
$349$	−0.819925	+	2.52347i	−0.0438896	+	0.135078i	−0.970600	−	0.240698i	$-0.922624\pi$
$349$	−0.819925	+	2.52347i	−0.0438896	+	0.135078i	0.926711	+	0.375776i	$0.122624\pi$
$350$	−17.0047	−	12.3546i	−0.908939	−	0.660383i
$351$	2.24815			0.119997
$352$	0.309017	−	3.30220i	0.0164707	−	0.176008i
$353$	−28.9598			−1.54138			−0.770688	−	0.637213i	$-0.780087\pi$
$353$	−28.9598			−1.54138			−0.770688	+	0.637213i	$0.780087\pi$
$354$	−7.31194	−	5.31244i	−0.388625	−	0.282353i
$355$	2.91575	−	8.97375i	0.154752	−	0.476277i
$356$	0.869962	+	2.67747i	0.0461079	+	0.141906i
$357$	−10.4689	+	7.60613i	−0.554075	+	0.402559i
$358$	−5.31636	+	3.86256i	−0.280979	+	0.204143i
$359$	−9.23406	−	28.4195i	−0.487355	−	1.49992i	−0.828541	−	0.559928i	$-0.810829\pi$
$359$	−9.23406	−	28.4195i	−0.487355	−	1.49992i	0.341186	−	0.939996i	$-0.389171\pi$
$360$	−1.02076	+	3.14158i	−0.0537989	+	0.165576i
$361$	−2.46912	−	1.79392i	−0.129954	−	0.0944170i
$362$	−14.8275			−0.779316
$363$	14.6405	−	26.7501i	0.768429	−	1.40401i
$364$	2.24625			0.117735
$365$	2.85419	+	2.07369i	0.149395	+	0.108542i
$366$	5.81572	−	17.8990i	0.303993	−	0.935594i
$367$	0.415442	+	1.27860i	0.0216859	+	0.0667424i	0.961314	−	0.275456i	$-0.0888287\pi$
$367$	0.415442	+	1.27860i	0.0216859	+	0.0667424i	−0.939628	+	0.342198i	$0.888829\pi$
$368$	−7.04405	+	5.11780i	−0.367197	+	0.266784i
$369$	14.2882	−	10.3810i	0.743812	−	0.540411i
$370$	−0.825461	−	2.54051i	−0.0429137	−	0.132075i
$371$	−3.87681	+	11.9316i	−0.201274	+	0.619457i
$372$	8.85761	+	6.43543i	0.459246	+	0.333661i
$373$	3.05773			0.158323			0.0791616	−	0.996862i	$-0.474776\pi$
$373$	3.05773			0.158323			0.0791616	+	0.996862i	$0.474776\pi$
$374$	0.309017	−	3.30220i	0.0159789	−	0.170753i
$375$	−18.5737			−0.959139
$376$	−8.81731	−	6.40615i	−0.454718	−	0.330372i
$377$	1.40437	−	4.32220i	0.0723286	−	0.222604i
$378$	6.73882	+	20.7400i	0.346607	+	1.06675i
$379$	−11.6322	+	8.45128i	−0.597505	+	0.434113i	−0.844992	−	0.534778i	$-0.820395\pi$
$379$	−11.6322	+	8.45128i	−0.597505	+	0.434113i	0.247487	+	0.968891i	$0.420395\pi$
$380$	2.67851	−	1.94605i	0.137405	−	0.0998304i
$381$	−9.74294	−	29.9857i	−0.499146	−	1.53621i
$382$	1.96857	−	6.05865i	0.100721	−	0.309987i
$383$	0.166381	+	0.120883i	0.00850168	+	0.00617683i	0.592028	−	0.805917i	$-0.298327\pi$
$383$	0.166381	+	0.120883i	0.00850168	+	0.00617683i	−0.583526	+	0.812094i	$0.698327\pi$
$384$	−2.77222			−0.141469
$385$	−7.21054	+	8.19427i	−0.367483	+	0.417619i
$386$	−14.1451			−0.719967
$387$	−12.2002	−	8.86398i	−0.620172	−	0.450581i
$388$	−4.27661	+	13.1621i	−0.217112	+	0.668202i
$389$	1.11960	+	3.44576i	0.0567658	+	0.174707i	0.975419	−	0.220357i	$-0.0707223\pi$
$389$	1.11960	+	3.44576i	0.0567658	+	0.174707i	−0.918653	+	0.395064i	$0.870722\pi$
$390$	0.760919	−	0.552840i	0.0385306	−	0.0279942i
$391$	−7.04405	+	5.11780i	−0.356233	+	0.258818i
$392$	4.56999	+	14.0650i	0.230819	+	0.710389i
$393$	1.36752	−	4.20878i	0.0689821	−	0.212305i
$394$	5.18162	+	3.76467i	0.261046	+	0.189661i
$395$	−3.83051			−0.192734
$396$	−14.2669	−	6.15791i	−0.716938	−	0.309447i
$397$	−20.5376			−1.03075			−0.515377	−	0.856964i	$-0.672348\pi$
$397$	−20.5376			−1.03075			−0.515377	+	0.856964i	$0.672348\pi$
$398$	−5.32599	−	3.86956i	−0.266968	−	0.193964i
$399$	18.7781	−	57.7930i	0.940080	−	2.89327i
$400$	−1.39148	−	4.28253i	−0.0695740	−	0.214127i
$401$	−25.9623	+	18.8627i	−1.29649	+	0.941959i	−0.999915	−	0.0130492i	$-0.995846\pi$
$401$	−25.9623	+	18.8627i	−1.29649	+	0.941959i	−0.296580	+	0.955008i	$0.595846\pi$
$402$	−33.6974	+	24.4826i	−1.68067	+	1.22108i
$403$	−0.587292	−	1.80750i	−0.0292551	−	0.0900379i
$404$	0.0945383	−	0.290959i	0.00470346	−	0.0144757i
$405$	−0.629921	−	0.457664i	−0.0313010	−	0.0227415i
$406$	44.0833			2.18782
$407$	12.2608	−	2.75273i	0.607747	−	0.136448i
$408$	−2.77222			−0.137245
$409$	18.9669	+	13.7802i	0.937851	+	0.681389i	0.947902	−	0.318561i	$-0.103199\pi$
$409$	18.9669	+	13.7802i	0.937851	+	0.681389i	−0.0100513	+	0.999949i	$0.503199\pi$
$410$	0.821265	−	2.52759i	0.0405594	−	0.124829i
$411$	5.54173	+	17.0557i	0.273354	+	0.841296i
$412$	−6.50281	+	4.72457i	−0.320370	+	0.232763i
$413$	−12.3118	+	8.94504i	−0.605824	+	0.440157i
$414$	12.6060	+	38.7973i	0.619551	+	1.90678i
$415$	0.590204	−	1.81646i	0.0289720	−	0.0891666i
$416$	0.389313	+	0.282852i	0.0190876	+	0.0138680i
$417$	26.3662			1.29116
$418$	7.94078	+	13.3984i	0.388396	+	0.655335i
$419$	6.91451			0.337796			0.168898	−	0.985634i	$-0.445979\pi$
$419$	6.91451			0.337796			0.168898	+	0.985634i	$0.445979\pi$
$420$	7.38099	+	5.36260i	0.360155	+	0.261668i
$421$	−11.7457	+	36.1494i	−0.572449	+	1.76182i	0.0722584	+	0.997386i	$0.476979\pi$
$421$	−11.7457	+	36.1494i	−0.572449	+	1.76182i	−0.644707	+	0.764430i	$0.723021\pi$
$422$	−0.154584	−	0.475760i	−0.00752503	−	0.0231597i
$423$	−41.3110	+	30.0142i	−2.00861	+	1.45934i
$424$	−2.17437	+	1.57977i	−0.105597	+	0.0767204i
$425$	−1.39148	−	4.28253i	−0.0674967	−	0.207733i
$426$	11.4648	−	35.2850i	0.555471	−	1.70956i
$427$	−25.6370	−	18.6264i	−1.24066	−	0.901394i
$428$	−3.20607			−0.154971
$429$	2.25584	+	3.80624i	0.108913	+	0.183767i
$430$	−2.26930			−0.109435
$431$	28.6366	+	20.8057i	1.37937	+	1.00217i	0.996938	+	0.0781924i	$0.0249148\pi$
$431$	28.6366	+	20.8057i	1.37937	+	1.00217i	0.382436	+	0.923982i	$0.375085\pi$
$432$	−1.44367	+	4.44315i	−0.0694585	+	0.213771i
$433$	−5.58341	−	17.1840i	−0.268321	−	0.825808i	−0.990910	−	0.134530i	$-0.957048\pi$
$433$	−5.58341	−	17.1840i	−0.268321	−	0.825808i	0.722588	−	0.691279i	$-0.242952\pi$
$434$	14.9144	−	10.8359i	0.715913	−	0.520141i
$435$	14.9333	−	10.8497i	0.715996	−	0.520201i
$436$	−2.69415	−	8.29174i	−0.129026	−	0.397102i
$437$	12.6349	−	38.8862i	0.604408	−	1.86018i
$438$	11.2228	+	8.15381i	0.536244	+	0.389604i
$439$	−6.32568			−0.301908			−0.150954	−	0.988541i	$-0.548235\pi$
$439$	−6.32568			−0.301908			−0.150954	+	0.988541i	$0.548235\pi$
$440$	−2.28155	+	0.512239i	−0.108769	+	0.0244201i
$441$	69.2888			3.29947
$442$	0.389313	+	0.282852i	0.0185177	+	0.0134539i
$443$	−3.94857	+	12.1524i	−0.187602	+	0.577380i	−0.999983	−	0.00574651i	$-0.998171\pi$
$443$	−3.94857	+	12.1524i	−0.187602	+	0.577380i	0.812381	+	0.583127i	$0.198171\pi$
$444$	−3.24573	−	9.98934i	−0.154036	−	0.474073i
$445$	1.60579	−	1.16667i	0.0761216	−	0.0553056i
$446$	1.60240	−	1.16421i	0.0758757	−	0.0551269i
$447$	−5.67085	−	17.4531i	−0.268222	−	0.825502i
$448$	−1.44244	+	4.43939i	−0.0681491	+	0.209741i
$449$	−9.95111	−	7.22991i	−0.469622	−	0.341200i	0.327672	−	0.944792i	$-0.393736\pi$
$449$	−9.95111	−	7.22991i	−0.469622	−	0.341200i	−0.797294	+	0.603591i	$0.793736\pi$
$450$	−21.0972			−0.994531
$451$	11.4786	+	4.95442i	0.540505	+	0.233294i
$452$	2.38758			0.112302
$453$	−49.3799	−	35.8766i	−2.32007	−	1.68563i
$454$	5.73006	−	17.6353i	0.268925	−	0.827666i
$455$	−0.489386	−	1.50618i	−0.0229428	−	0.0706106i
$456$	10.5320	−	7.65193i	0.493205	−	0.358334i
$457$	15.0376	−	10.9255i	0.703432	−	0.511073i	−0.177616	−	0.984100i	$-0.556839\pi$
$457$	15.0376	−	10.9255i	0.703432	−	0.511073i	0.881048	+	0.473027i	$0.156839\pi$
$458$	−6.85819	−	21.1073i	−0.320462	−	0.986281i
$459$	−1.44367	+	4.44315i	−0.0673846	+	0.207389i
$460$	4.96632	+	3.60824i	0.231556	+	0.168235i
$461$	−22.1581			−1.03201			−0.516004	−	0.856586i	$-0.672581\pi$
$461$	−22.1581			−1.03201			−0.516004	+	0.856586i	$0.672581\pi$
$462$	−28.3520	+	32.2201i	−1.31905	+	1.49901i
$463$	27.5868			1.28207			0.641034	−	0.767512i	$-0.278506\pi$
$463$	27.5868			1.28207			0.641034	+	0.767512i	$0.278506\pi$
$464$	7.64038	+	5.55106i	0.354696	+	0.257702i
$465$	2.38536	−	7.34137i	0.110618	−	0.340448i
$466$	−5.43105	−	16.7150i	−0.251588	−	0.774309i
$467$	4.11255	−	2.98794i	0.190306	−	0.138265i	−0.488553	−	0.872534i	$-0.662475\pi$
$467$	4.11255	−	2.98794i	0.190306	−	0.138265i	0.678859	+	0.734269i	$0.262475\pi$
$468$	1.82402	−	1.32522i	0.0843151	−	0.0612585i
$469$	21.6725	+	66.7012i	1.00075	+	3.07998i
$470$	−2.37450	+	7.30797i	−0.109528	+	0.337091i
$471$	−26.0701	−	18.9410i	−1.20125	−	0.872756i
$472$	−3.26022			−0.150064
$473$	0.994632	−	10.6288i	0.0457332	−	0.488711i
$474$	−15.0616			−0.691804
$475$	17.1071	+	12.4290i	0.784927	+	0.570283i
$476$	−1.44244	+	4.43939i	−0.0661143	+	0.203479i
$477$	3.89124	+	11.9760i	0.178167	+	0.548343i
$478$	4.30691	−	3.12915i	0.196993	−	0.143124i
$479$	7.53005	−	5.47090i	0.344057	−	0.249972i	−0.402315	−	0.915501i	$-0.631794\pi$
$479$	7.53005	−	5.47090i	0.344057	−	0.249972i	0.746372	+	0.665529i	$0.231794\pi$
$480$	0.603980	+	1.85886i	0.0275678	+	0.0848449i
$481$	−0.563411	+	1.73400i	−0.0256893	+	0.0790637i
$482$	−8.62889	−	6.26925i	−0.393035	−	0.285557i
$483$	112.670			5.12668
$484$	−1.39919	−	10.9106i	−0.0635994	−	0.495939i
$485$	9.75730			0.443056
$486$	−13.8156	−	10.0376i	−0.626687	−	0.455315i
$487$	4.20881	−	12.9534i	0.190719	−	0.586974i	−0.809281	−	0.587422i	$-0.800143\pi$
$487$	4.20881	−	12.9534i	0.190719	−	0.586974i	1.00000		0.000448561i	$0.000142781\pi$
$488$	−2.09786	−	6.45654i	−0.0949655	−	0.292274i
$489$	20.6195	−	14.9810i	0.932447	−	0.677463i
$490$	8.43534	−	6.12863i	0.381070	−	0.276863i
$491$	−8.73354	−	26.8791i	−0.394139	−	1.21304i	−0.929630	−	0.368495i	$-0.879873\pi$
$491$	−8.73354	−	26.8791i	−0.394139	−	1.21304i	0.535491	−	0.844541i	$-0.320127\pi$
$492$	3.22923	−	9.93856i	0.145585	−	0.448065i
$493$	7.64038	+	5.55106i	0.344105	+	0.250007i
$494$	−2.25977			−0.101672
$495$	−1.02076	+	10.9080i	−0.0458798	+	0.490278i
$496$	3.94940			0.177333
$497$	−50.5394	−	36.7190i	−2.26700	−	1.64707i
$498$	2.32070	−	7.14237i	0.103993	−	0.320057i
$499$	−1.75944	−	5.41499i	−0.0787632	−	0.242408i	0.903920	−	0.427701i	$-0.140677\pi$
$499$	−1.75944	−	5.41499i	−0.0787632	−	0.242408i	−0.982683	+	0.185293i	$0.940677\pi$
$500$	−5.42034	+	3.93811i	−0.242405	+	0.176118i
$501$	−49.2026	+	35.7478i	−2.19821	+	1.59709i
$502$	1.75719	+	5.40808i	0.0784272	+	0.241374i
$503$	7.99228	−	24.5977i	0.356358	−	1.09676i	−0.598860	−	0.800854i	$-0.704379\pi$
$503$	7.99228	−	24.5977i	0.356358	−	1.09676i	0.955218	−	0.295904i	$-0.0956207\pi$
$504$	17.6931	+	12.8548i	0.788114	+	0.572598i
$505$	−0.215694			−0.00959824
$506$	−19.0767	+	21.6794i	−0.848064	+	0.963765i
$507$	35.3969			1.57203
$508$	−9.20105	−	6.68495i	−0.408230	−	0.296597i
$509$	11.4749	−	35.3161i	0.508616	−	1.56536i	−0.285988	−	0.958233i	$-0.592322\pi$
$509$	11.4749	−	35.3161i	0.508616	−	1.56536i	0.794605	−	0.607127i	$-0.207678\pi$
$510$	0.603980	+	1.85886i	0.0267447	+	0.0823117i
$511$	18.8968	−	13.7293i	0.835945	−	0.607349i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−6.77940	−	20.8648i	−0.299318	−	0.921205i
$514$	8.16429	−	25.1271i	0.360111	−	1.10831i
$515$	4.58472	+	3.33099i	0.202027	+	0.146781i
$516$	−8.92294			−0.392811
$517$	−33.1877	−	14.3246i	−1.45960	−	0.629995i
$518$	−17.6856			−0.777059
$519$	32.3956	+	23.5367i	1.42201	+	1.03315i
$520$	0.104842	−	0.322670i	0.00459762	−	0.0141500i
$521$	9.01381	+	27.7417i	0.394902	+	1.21538i	0.929038	+	0.369985i	$0.120637\pi$
$521$	9.01381	+	27.7417i	0.394902	+	1.21538i	−0.534135	+	0.845399i	$0.679363\pi$
$522$	35.7969	−	26.0079i	1.56679	−	1.13834i
$523$	4.45903	−	3.23967i	0.194980	−	0.141661i	−0.486012	−	0.873952i	$-0.661549\pi$
$523$	4.45903	−	3.23967i	0.194980	−	0.141661i	0.680992	+	0.732291i	$0.261549\pi$
$524$	−0.493293	−	1.51820i	−0.0215496	−	0.0663228i
$525$	−18.0062	+	55.4173i	−0.785854	+	2.41861i
$526$	21.1709	+	15.3816i	0.923096	+	0.670669i
$527$	3.94940			0.172038
$528$	−8.97110	+	2.01414i	−0.390417	+	0.0876541i
$529$	52.8106			2.29611
$530$	1.53301	+	1.11380i	0.0665897	+	0.0483802i
$531$	−4.72019	+	14.5272i	−0.204839	+	0.630429i
$532$	−6.77366	−	20.8472i	−0.293675	−	0.903839i
$533$	−1.46753	+	1.06622i	−0.0635658	+	0.0461833i
$534$	6.31399	−	4.58738i	0.273233	−	0.198515i
$535$	0.698502	+	2.14977i	0.0301989	+	0.0929426i
$536$	−4.64294	+	14.2895i	−0.200545	+	0.617213i
$537$	14.7381	+	10.7079i	0.635998	+	0.462080i
$538$	−18.0220			−0.776984
$539$	25.0076	+	42.1950i	1.07715	+	1.81747i
$540$	3.29380			0.141742
$541$	23.4338	+	17.0257i	1.00750	+	0.731991i	0.963683	−	0.267049i	$-0.0860485\pi$
$541$	23.4338	+	17.0257i	1.00750	+	0.731991i	0.0438158	+	0.999040i	$0.486049\pi$
$542$	3.33829	−	10.2742i	0.143392	−	0.441315i
$543$	12.7022	+	39.0933i	0.545103	+	1.67765i
$544$	−0.809017	+	0.587785i	−0.0346863	+	0.0252011i
$545$	−4.97289	+	3.61302i	−0.213015	+	0.154765i
$546$	−1.92428	−	5.92232i	−0.0823515	−	0.253452i
$547$	7.11645	−	21.9022i	0.304277	−	0.936470i	−0.675668	−	0.737206i	$-0.736145\pi$
$547$	7.11645	−	21.9022i	0.304277	−	0.936470i	0.979946	−	0.199264i	$-0.0638551\pi$
$548$	5.23351	+	3.80236i	0.223564	+	0.162429i
$549$	−31.8070			−1.35749
$550$	−7.61437	−	12.8476i	−0.324678	−	0.547824i
$551$	−44.3487			−1.88932
$552$	19.5277	+	14.1877i	0.831153	+	0.603868i
$553$	−7.83688	+	24.1194i	−0.333258	+	1.02566i
$554$	0.702403	+	2.16177i	0.0298422	+	0.0918450i
$555$	−5.99101	+	4.35272i	−0.254304	+	0.184763i
$556$	7.69443	−	5.59033i	0.326316	−	0.237083i
$557$	−7.76188	−	23.8886i	−0.328881	−	1.01219i	−0.969658	−	0.244466i	$-0.921387\pi$
$557$	−7.76188	−	23.8886i	−0.328881	−	1.01219i	0.640776	−	0.767727i	$-0.278613\pi$
$558$	5.71798	−	17.5981i	0.242062	−	0.744989i
$559$	1.25308	+	0.910415i	0.0529996	+	0.0385065i
$560$	3.29101			0.139070
$561$	−8.97110	+	2.01414i	−0.378760	+	0.0850370i
$562$	−13.7496			−0.579993
$563$	6.74878	+	4.90328i	0.284427	+	0.206649i	0.720846	−	0.693095i	$-0.243753\pi$
$563$	6.74878	+	4.90328i	0.284427	+	0.206649i	−0.436419	+	0.899744i	$0.643753\pi$
$564$	−9.33660	+	28.7351i	−0.393142	+	1.20997i
$565$	−0.520178	−	1.60094i	−0.0218841	−	0.0673522i
$566$	3.07398	−	2.23338i	0.129209	−	0.0938759i
$567$	−4.17053	+	3.03006i	−0.175146	+	0.127251i
$568$	−4.13559	−	12.7281i	−0.173526	−	0.534057i
$569$	9.29086	−	28.5943i	0.389493	−	1.19874i	−0.543675	−	0.839296i	$-0.682967\pi$
$569$	9.29086	−	28.5943i	0.389493	−	1.19874i	0.933168	−	0.359441i	$-0.117033\pi$
$570$	−7.42543	−	5.39489i	−0.311017	−	0.225967i
$571$	−45.7789			−1.91579			−0.957893	−	0.287126i	$-0.907300\pi$
$571$	−45.7789			−1.91579			−0.957893	+	0.287126i	$0.907300\pi$
$572$	1.46535	+	0.632477i	0.0612692	+	0.0264452i
$573$	−17.6603			−0.737769
$574$	−14.2352	−	10.3425i	−0.594165	−	0.431686i
$575$	−12.1155	+	37.2877i	−0.505252	+	1.55500i
$576$	1.44781	+	4.45591i	0.0603255	+	0.185663i
$577$	−15.1102	+	10.9782i	−0.629046	+	0.457029i	−0.856070	−	0.516861i	$-0.827101\pi$
$577$	−15.1102	+	10.9782i	−0.629046	+	0.457029i	0.227024	+	0.973889i	$0.427101\pi$
$578$	−0.809017	+	0.587785i	−0.0336507	+	0.0244486i
$579$	12.1176	+	37.2942i	0.503590	+	1.54989i
$580$	2.05756	−	6.33251i	0.0854353	−	0.262943i
$581$	−10.2302	−	7.43265i	−0.424419	−	0.308358i
$582$	38.3659			1.59032
$583$	−5.88863	+	6.69201i	−0.243882	+	0.277155i
$584$	5.00396			0.207065
$585$	−1.28600	−	0.934333i	−0.0531695	−	0.0386299i
$586$	7.20883	−	22.1865i	0.297794	−	0.916516i
$587$	−5.90243	−	18.1658i	−0.243619	−	0.749783i	−0.995860	−	0.0908952i	$-0.971027\pi$
$587$	−5.90243	−	18.1658i	−0.243619	−	0.749783i	0.752241	−	0.658888i	$-0.228973\pi$
$588$	33.1680	−	24.0979i	1.36782	−	0.993782i
$589$	−15.0042	+	10.9012i	−0.618237	+	0.449175i
$590$	0.710299	+	2.18608i	0.0292425	+	0.0899993i
$591$	5.48679	−	16.8866i	0.225697	−	0.694623i
$592$	−3.06521	−	2.22700i	−0.125979	−	0.0915293i
$593$	36.8682			1.51399			0.756997	−	0.653418i	$-0.226666\pi$
$593$	36.8682			1.51399			0.756997	+	0.653418i	$0.226666\pi$
$594$	−1.44367	+	15.4272i	−0.0592344	+	0.632987i
$595$	3.29101			0.134918
$596$	−5.35544	−	3.89096i	−0.219367	−	0.159380i
$597$	−5.63967	+	17.3571i	−0.230816	+	0.710379i
$598$	−1.29476	−	3.98485i	−0.0529465	−	0.162953i
$599$	10.9389	−	7.94758i	0.446951	−	0.324729i	−0.341439	−	0.939904i	$-0.610914\pi$
$599$	10.9389	−	7.94758i	0.446951	−	0.324729i	0.788391	+	0.615174i	$0.210914\pi$
$600$	−10.0990	+	7.33739i	−0.412292	+	0.299547i
$601$	0.0626008	+	0.192666i	0.00255354	+	0.00785899i	0.952325	−	0.305085i	$-0.0986848\pi$
$601$	0.0626008	+	0.192666i	0.00255354	+	0.00785899i	−0.949772	+	0.312944i	$0.898685\pi$
$602$	−4.64279	+	14.2890i	−0.189226	+	0.582378i
$603$	56.9506	+	41.3770i	2.31921	+	1.68500i
$604$	−22.0173			−0.895871
$605$	−7.01108	+	3.31528i	−0.285041	+	0.134785i
$606$	−0.848113			−0.0344522
$607$	−27.8641	−	20.2445i	−1.13097	−	0.821698i	−0.145134	−	0.989412i	$-0.546361\pi$
$607$	−27.8641	−	20.2445i	−1.13097	−	0.821698i	−0.985836	+	0.167714i	$0.946361\pi$
$608$	1.45113	−	4.46612i	0.0588511	−	0.181125i
$609$	−37.7646	−	116.227i	−1.53030	−	4.70977i
$610$	−3.87225	+	2.81335i	−0.156783	+	0.113909i
$611$	4.24304	−	3.08275i	0.171655	−	0.124715i
$612$	1.44781	+	4.45591i	0.0585244	+	0.180119i
$613$	1.87196	−	5.76131i	0.0756079	−	0.232697i	−0.906109	−	0.423045i	$-0.860961\pi$
$613$	1.87196	−	5.76131i	0.0756079	−	0.232697i	0.981717	+	0.190347i	$0.0609614\pi$
$614$	−2.53442	−	1.84136i	−0.102281	−	0.0743114i
$615$	−7.36765			−0.297092
$616$	−1.44244	+	15.4142i	−0.0581177	+	0.621054i
$617$	2.67400			0.107651			0.0538255	−	0.998550i	$-0.482859\pi$
$617$	2.67400			0.107651			0.0538255	+	0.998550i	$0.482859\pi$
$618$	18.0272	+	13.0975i	0.725161	+	0.526861i
$619$	−1.86669	+	5.74508i	−0.0750286	+	0.230914i	−0.981537	−	0.191274i	$-0.938738\pi$
$619$	−1.86669	+	5.74508i	−0.0750286	+	0.230914i	0.906508	+	0.422189i	$0.138738\pi$
$620$	−0.860449	−	2.64819i	−0.0345565	−	0.106354i
$621$	32.9084	−	23.9094i	1.32057	−	0.959450i
$622$	−8.74146	+	6.35104i	−0.350501	+	0.254654i
$623$	−4.06085	−	12.4980i	−0.162695	−	0.500723i
$624$	0.412241	−	1.26875i	0.0165029	−	0.0507906i
$625$	−14.3932	−	10.4572i	−0.575726	−	0.418290i
$626$	−6.06017			−0.242213
$627$	28.5227	−	32.4141i	1.13909	−	1.29449i
$628$	−11.6240			−0.463849
$629$	−3.06521	−	2.22700i	−0.122218	−	0.0887964i
$630$	4.76476	−	14.6644i	0.189833	−	0.584245i
$631$	11.5539	+	35.5592i	0.459953	+	1.41559i	0.865221	+	0.501391i	$0.167178\pi$
$631$	11.5539	+	35.5592i	0.459953	+	1.41559i	−0.405268	+	0.914198i	$0.632822\pi$
$632$	−4.39544	+	3.19347i	−0.174841	+	0.127029i
$633$	−1.12194	+	0.815134i	−0.0445929	+	0.0323987i
$634$	−7.02534	−	21.6218i	−0.279012	−	0.858710i
$635$	−2.47784	+	7.62602i	−0.0983302	+	0.302629i
$636$	6.02783	+	4.37947i	0.239019	+	0.173657i
$637$	−7.11662			−0.281971
$638$	28.7579	+	12.4125i	1.13853	+	0.491417i
$639$	−62.7026			−2.48048
$640$	0.570387	+	0.414410i	0.0225465	+	0.0163810i
$641$	−8.89580	+	27.3784i	−0.351363	+	1.08138i	0.606726	+	0.794911i	$0.292483\pi$
$641$	−8.89580	+	27.3784i	−0.351363	+	1.08138i	−0.958088	+	0.286472i	$0.907517\pi$
$642$	2.74653	+	8.45294i	0.108397	+	0.333611i
$643$	20.6494	−	15.0027i	0.814333	−	0.591648i	−0.100751	−	0.994912i	$-0.532124\pi$
$643$	20.6494	−	15.0027i	0.814333	−	0.591648i	0.915084	+	0.403264i	$0.132124\pi$
$644$	32.8806	−	23.8891i	1.29568	−	0.941363i
$645$	1.94403	+	5.98310i	0.0765460	+	0.235584i
$646$	1.45113	−	4.46612i	0.0570940	−	0.175717i
$647$	0.565902	+	0.411152i	0.0222479	+	0.0161641i	0.598854	−	0.800858i	$-0.295623\pi$
$647$	0.565902	+	0.411152i	0.0222479	+	0.0161641i	−0.576606	+	0.817023i	$0.695623\pi$
$648$	−1.10437			−0.0433839
$649$	−10.5503	+	2.36869i	−0.414135	+	0.0929791i
$650$	2.16688			0.0849921
$651$	−41.3460	−	30.0396i	−1.62048	−	1.17734i
$652$	2.84103	−	8.74378i	0.111263	−	0.342433i
$653$	0.124604	+	0.383491i	0.00487612	+	0.0150072i	0.953465	−	0.301504i	$-0.0974886\pi$
$653$	0.124604	+	0.383491i	0.00487612	+	0.0150072i	−0.948589	+	0.316511i	$0.897489\pi$
$654$	−19.5535	+	14.2065i	−0.764604	+	0.555517i
$655$	−0.910525	+	0.661535i	−0.0355771	+	0.0258483i
$656$	−1.16485	−	3.58505i	−0.0454799	−	0.139973i
$657$	7.24479	−	22.2972i	0.282646	−	0.869896i
$658$	41.1579	+	29.9029i	1.60450	+	1.16574i
$659$	−32.9229			−1.28249			−0.641247	−	0.767335i	$-0.721582\pi$
$659$	−32.9229			−1.28249			−0.641247	+	0.767335i	$0.721582\pi$
$660$	3.30506	+	5.57658i	0.128649	+	0.217068i
$661$	35.9974			1.40014			0.700068	−	0.714076i	$-0.253153\pi$
$661$	35.9974			1.40014			0.700068	+	0.714076i	$0.253153\pi$
$662$	−17.5887	−	12.7790i	−0.683606	−	0.496669i
$663$	0.412241	−	1.26875i	0.0160101	−	0.0492741i
$664$	−0.837125	−	2.57641i	−0.0324868	−	0.0999840i
$665$	−12.5029	+	9.08388i	−0.484841	+	0.352258i
$666$	−14.3612	+	10.4340i	−0.556484	+	0.404309i
$667$	−25.4100	−	78.2039i	−0.983879	−	3.02807i
$668$	−6.77929	+	20.8645i	−0.262299	+	0.807272i
$669$	−4.44220	−	3.22745i	−0.171745	−	0.124780i
$670$	10.5931			0.409247
$671$	−11.4798	−	19.3696i	−0.443171	−	0.747756i
$672$	12.9403			0.499183
$673$	−1.72769	−	1.25524i	−0.0665974	−	0.0483859i	0.553988	−	0.832524i	$-0.313105\pi$
$673$	−1.72769	−	1.25524i	−0.0665974	−	0.0483859i	−0.620586	+	0.784138i	$0.713105\pi$
$674$	−2.74180	+	8.43838i	−0.105610	+	0.325034i
$675$	6.50072	+	20.0072i	0.250213	+	0.770076i
$676$	10.3299	−	7.50510i	0.397303	−	0.288658i
$677$	−9.31390	+	6.76694i	−0.357962	+	0.260075i	−0.752202	−	0.658933i	$-0.771008\pi$
$677$	−9.31390	+	6.76694i	−0.357962	+	0.260075i	0.394239	+	0.919008i	$0.371008\pi$
$678$	−2.04535	−	6.29495i	−0.0785513	−	0.241756i
$679$	19.9626	−	61.4385i	0.766093	−	2.35779i
$680$	0.570387	+	0.414410i	0.0218733	+	0.0158919i
$681$	−51.4050			−1.96984
$682$	12.7805	−	2.86940i	0.489391	−	0.109875i
$683$	10.6786			0.408605			0.204302	−	0.978908i	$-0.434507\pi$
$683$	10.6786			0.408605			0.204302	+	0.978908i	$0.434507\pi$
$684$	−17.7997	−	12.9322i	−0.680587	−	0.494475i
$685$	1.40938	−	4.33764i	0.0538498	−	0.165733i
$686$	−11.2349	−	34.5775i	−0.428951	−	1.32018i
$687$	−49.7752	+	36.1638i	−1.89904	+	1.37974i
$688$	−2.60398	+	1.89190i	−0.0992758	+	0.0721281i
$689$	−0.399667	−	1.23005i	−0.0152261	−	0.0468611i
$690$	5.25881	−	16.1849i	0.200199	−	0.616150i
$691$	−36.0830	−	26.2158i	−1.37266	−	0.997297i	−0.997524	−	0.0703274i	$-0.977596\pi$
$691$	−36.0830	−	26.2158i	−1.37266	−	0.997297i	−0.375137	−	0.926969i	$-0.622404\pi$
$692$	14.4444			0.549094
$693$	66.5957	+	28.7442i	2.52976	+	1.09190i
$694$	−1.21308			−0.0460480
$695$	−5.42486	−	3.94139i	−0.205777	−	0.149505i
$696$	8.09036	−	24.8996i	0.306664	−	0.943816i
$697$	−1.16485	−	3.58505i	−0.0441220	−	0.135793i
$698$	2.14659	−	1.55959i	0.0812497	−	0.0590314i
$699$	−39.4173	+	28.6383i	−1.49090	+	1.08320i
$700$	6.49522	+	19.9902i	0.245496	+	0.755559i
$701$	−5.69040	+	17.5132i	−0.214923	+	0.661466i	0.784236	+	0.620463i	$0.213055\pi$
$701$	−5.69040	+	17.5132i	−0.214923	+	0.661466i	−0.999159	+	0.0410031i	$0.986945\pi$
$702$	−1.81879	−	1.32143i	−0.0686459	−	0.0498742i
$703$	17.7921			0.671040
$704$	−2.19098	+	2.48990i	−0.0825758	+	0.0938416i
$705$	21.3019			0.802276
$706$	23.4290	+	17.0221i	0.881761	+	0.640637i
$707$	−0.441290	+	1.35815i	−0.0165964	+	0.0510786i
$708$	2.79291	+	8.59570i	0.104964	+	0.323046i
$709$	6.00022	−	4.35941i	0.225343	−	0.163721i	−0.469386	−	0.882993i	$-0.655525\pi$
$709$	6.00022	−	4.35941i	0.225343	−	0.163721i	0.694728	+	0.719272i	$0.255525\pi$
$710$	−7.63353	+	5.54608i	−0.286481	+	0.208141i
$711$	7.86605	+	24.2092i	0.295000	+	0.907916i
$712$	0.869962	−	2.67747i	0.0326032	−	0.100342i
$713$	−27.8197	−	20.2122i	−1.04186	−	0.756954i
$714$	12.9403			0.484279
$715$	0.104842	−	1.12036i	0.00392087	−	0.0418989i
$716$	6.57139			0.245584
$717$	−11.9397	−	8.67470i	−0.445896	−	0.323963i
$718$	−9.23406	+	28.4195i	−0.344612	+	1.06061i
$719$	1.28332	+	3.94965i	0.0478598	+	0.147297i	0.972130	−	0.234440i	$-0.0753258\pi$
$719$	1.28332	+	3.94965i	0.0478598	+	0.147297i	−0.924271	+	0.381738i	$0.875326\pi$
$720$	2.67239	−	1.94160i	0.0995940	−	0.0723593i
$721$	30.3541	−	22.0536i	1.13045	−	0.821317i
$722$	0.943121	+	2.90263i	0.0350993	+	0.108025i
$723$	−9.13708	+	28.1211i	−0.339812	+	1.04583i
$724$	11.9957	+	8.71539i	0.445817	+	0.323905i
$725$	42.5257			1.57937
$726$	−27.5677	+	13.0358i	−1.02313	+	0.483803i
$727$	45.3600			1.68231			0.841155	−	0.540794i	$-0.181876\pi$
$727$	45.3600			1.68231			0.841155	+	0.540794i	$0.181876\pi$
$728$	−1.81725	−	1.32031i	−0.0673518	−	0.0489340i
$729$	−13.6054	+	41.8732i	−0.503905	+	1.55086i
$730$	−1.09020	−	3.35530i	−0.0403503	−	0.124185i
$731$	−2.60398	+	1.89190i	−0.0963117	+	0.0699745i
$732$	−15.2258	+	11.0622i	−0.562760	+	0.408869i
$733$	−9.44283	−	29.0621i	−0.348779	−	1.07343i	−0.959529	−	0.281608i	$-0.909132\pi$
$733$	−9.44283	−	29.0621i	−0.348779	−	1.07343i	0.610750	−	0.791823i	$-0.290868\pi$
$734$	0.415442	−	1.27860i	0.0153343	−	0.0471940i
$735$	−23.3846	−	16.9899i	−0.862556	−	0.626683i
$736$	8.70693			0.320942
$737$	−4.64294	+	49.6151i	−0.171025	+	1.82760i
$738$	−17.6611			−0.650116
$739$	17.8765	+	12.9880i	0.657597	+	0.477772i	0.865850	−	0.500303i	$-0.166778\pi$
$739$	17.8765	+	12.9880i	0.657597	+	0.477772i	−0.208254	+	0.978075i	$0.566778\pi$
$740$	−0.825461	+	2.54051i	−0.0303445	+	0.0933909i
$741$	1.93587	+	5.95798i	0.0711158	+	0.218872i
$742$	10.1496	−	7.37413i	0.372604	−	0.270713i
$743$	−35.8077	+	26.0158i	−1.31366	+	0.954428i	−0.313670	+	0.949532i	$0.601559\pi$
$743$	−35.8077	+	26.0158i	−1.31366	+	0.954428i	−0.999988	+	0.00489639i	$0.998441\pi$
$744$	−3.38331	−	10.4127i	−0.124038	−	0.381750i
$745$	−1.44222	+	4.43870i	−0.0528389	+	0.162621i
$746$	−2.47375	−	1.79729i	−0.0905706	−	0.0658034i
$747$	−12.6922			−0.464384
$748$	−2.19098	+	2.48990i	−0.0801103	+	0.0910397i
$749$	14.9655			0.546826
$750$	15.0264	+	10.9173i	0.548687	+	0.398644i
$751$	−8.52656	+	26.2421i	−0.311139	+	0.957586i	0.666176	+	0.745794i	$0.267930\pi$
$751$	−8.52656	+	26.2421i	−0.311139	+	0.957586i	−0.977315	+	0.211792i	$0.932070\pi$
$752$	3.36791	+	10.3654i	0.122815	+	0.377986i
$753$	12.7533	−	9.26581i	0.464756	−	0.337665i
$754$	−3.67668	+	2.67126i	−0.133897	+	0.0972817i
$755$	4.79688	+	14.7633i	0.174576	+	0.537290i
$756$	6.73882	−	20.7400i	0.245088	−	0.754305i
$757$	−24.3027	−	17.6569i	−0.883296	−	0.641752i	0.0508255	−	0.998708i	$-0.483815\pi$
$757$	−24.3027	−	17.6569i	−0.883296	−	0.641752i	−0.934121	+	0.356956i	$0.883815\pi$
$758$	14.3782			0.522239
$759$	73.5009	+	31.7246i	2.66791	+	1.15153i
$760$	−3.31082			−0.120096
$761$	36.2586	+	26.3434i	1.31437	+	0.954949i	0.999984	+	0.00565507i	$0.00180008\pi$
$761$	36.2586	+	26.3434i	1.31437	+	0.954949i	0.314390	+	0.949294i	$0.398200\pi$
$762$	−9.74294	+	29.9857i	−0.352950	+	1.08627i
$763$	12.5759	+	38.7046i	0.455277	+	1.40120i
$764$	−5.15379	+	3.74445i	−0.186458	+	0.135469i
$765$	2.67239	−	1.94160i	0.0966204	−	0.0701988i
$766$	−0.0635519	−	0.195593i	−0.00229622	−	0.00706705i
$767$	0.484808	−	1.49209i	0.0175054	−	0.0538761i
$768$	2.24278	+	1.62947i	0.0809292	+	0.0587985i
$769$	16.0802			0.579868			0.289934	−	0.957047i	$-0.406367\pi$
$769$	16.0802			0.579868			0.289934	+	0.957047i	$0.406367\pi$
$770$	10.6499	−	2.39106i	0.383796	−	0.0861677i
$771$	−73.2426			−2.63777
$772$	11.4436	+	8.31429i	0.411865	+	0.299238i
$773$	−2.30486	+	7.09363i	−0.0829001	+	0.255140i	−0.983912	−	0.178654i	$-0.942826\pi$
$773$	−2.30486	+	7.09363i	−0.0829001	+	0.255140i	0.901012	+	0.433795i	$0.142826\pi$
$774$	4.66007	+	14.3422i	0.167503	+	0.515520i
$775$	14.3874	−	10.4531i	0.516811	−	0.375485i
$776$	11.1963	−	8.13460i	0.401924	−	0.292015i
$777$	15.1506	+	46.6287i	0.543524	+	1.67280i
$778$	1.11960	−	3.44576i	0.0401395	−	0.123537i
$779$	14.3209	+	10.4047i	0.513100	+	0.372789i
$780$	−0.940548			−0.0336770
$781$	−22.6305	−	38.1842i	−0.809784	−	1.36634i
$782$	8.70693			0.311359
$783$	−35.6944	−	25.9335i	−1.27561	−	0.926787i
$784$	4.56999	−	14.0650i	0.163214	−	0.502321i
$785$	2.53251	+	7.79426i	0.0903891	+	0.278189i
$786$	−3.58021	+	2.60117i	−0.127702	+	0.0927807i
$787$	16.6222	−	12.0767i	0.592517	−	0.430489i	−0.250698	−	0.968065i	$-0.580660\pi$
$787$	16.6222	−	12.0767i	0.592517	−	0.430489i	0.843215	+	0.537577i	$0.180660\pi$
$788$	−1.97920	−	6.09136i	−0.0705062	−	0.216996i
$789$	22.4178	−	68.9948i	0.798094	−	2.45628i
$790$	3.09895	+	2.25152i	0.110256	+	0.0801053i
$791$	−11.1449			−0.396265
$792$	7.92263	+	13.3677i	0.281518	+	0.475001i
$793$	3.26689			0.116011
$794$	16.6153	+	12.0717i	0.589655	+	0.428409i
$795$	1.62330	−	4.99599i	0.0575724	−	0.177190i
$796$	2.03435	+	6.26108i	0.0721056	+	0.221918i
$797$	−17.5500	+	12.7508i	−0.621652	+	0.451656i	−0.853498	−	0.521096i	$-0.825523\pi$
$797$	−17.5500	+	12.7508i	−0.621652	+	0.451656i	0.231846	+	0.972752i	$0.425523\pi$
$798$	−49.1617	+	35.7180i	−1.74030	+	1.26440i
$799$	3.36791	+	10.3654i	0.119148	+	0.366700i
$800$	−1.39148	+	4.28253i	−0.0491962	+	0.151410i
$801$	−10.6710	−	7.75295i	−0.377042	−	0.273937i
$802$	32.0912			1.13318
$803$	16.1931	−	3.63559i	0.571444	−	0.128297i
$804$	41.6523			1.46896
$805$	−23.1820	−	16.8427i	−0.817059	−	0.593628i
$806$	−0.587292	+	1.80750i	−0.0206865	+	0.0636664i
$807$	15.4388	+	47.5158i	0.543472	+	1.67263i
$808$	−0.247504	+	0.179823i	−0.00870718	+	0.00632613i
$809$	10.9261	−	7.93826i	0.384140	−	0.279094i	−0.378910	−	0.925434i	$-0.623701\pi$
$809$	10.9261	−	7.93826i	0.384140	−	0.279094i	0.763050	+	0.646339i	$0.223701\pi$
$810$	0.240608	+	0.740517i	0.00845412	+	0.0260191i
$811$	12.5703	−	38.6875i	0.441404	−	1.35850i	−0.444976	−	0.895543i	$-0.646788\pi$
$811$	12.5703	−	38.6875i	0.441404	−	1.35850i	0.886380	−	0.462959i	$-0.153212\pi$
$812$	−35.6641	−	25.9115i	−1.25157	−	0.909316i
$813$	−29.9482			−1.05033
$814$	−11.5372	−	4.97973i	−0.404380	−	0.174539i
$815$	−6.48194			−0.227052
$816$	2.24278	+	1.62947i	0.0785128	+	0.0570429i
$817$	4.67075	−	14.3751i	0.163409	−	0.502920i
$818$	−7.24470	−	22.2969i	−0.253305	−	0.779592i
$819$	−8.51423	+	6.18595i	−0.297511	+	0.216154i
$820$	−2.15010	+	1.56214i	−0.0750847	+	0.0545522i
$821$	−16.3411	−	50.2928i	−0.570309	−	1.75523i	−0.651624	−	0.758542i	$-0.725912\pi$
$821$	−16.3411	−	50.2928i	−0.570309	−	1.75523i	0.0813149	−	0.996688i	$-0.474088\pi$
$822$	5.54173	−	17.0557i	0.193290	−	0.594886i
$823$	−20.2400	−	14.7052i	−0.705523	−	0.512593i	0.176203	−	0.984354i	$-0.443618\pi$
$823$	−20.2400	−	14.7052i	−0.705523	−	0.512593i	−0.881726	+	0.471761i	$0.843618\pi$
$824$	8.03791			0.280014
$825$	−27.3503	+	31.0817i	−0.952214	+	1.08212i
$826$	15.2182			0.529509
$827$	−3.93873	−	2.86166i	−0.136963	−	0.0995095i	0.517194	−	0.855868i	$-0.326977\pi$
$827$	−3.93873	−	2.86166i	−0.136963	−	0.0995095i	−0.654157	+	0.756359i	$0.726977\pi$
$828$	12.6060	−	38.7973i	0.438089	−	1.34830i
$829$	7.27391	+	22.3868i	0.252633	+	0.777526i	0.994287	+	0.106742i	$0.0340420\pi$
$829$	7.27391	+	22.3868i	0.252633	+	0.777526i	−0.741653	+	0.670783i	$0.765958\pi$
$830$	−1.54517	+	1.12264i	−0.0536338	+	0.0389672i
$831$	5.09788	−	3.70383i	0.176844	−	0.128484i
$832$	−0.148704	−	0.457664i	−0.00515539	−	0.0158667i
$833$	4.56999	−	14.0650i	0.158341	−	0.487323i
$834$	−21.3307	−	15.4976i	−0.738621	−	0.536639i
$835$	15.4673			0.535267
$836$	1.45113	−	15.5070i	0.0501884	−	0.536320i
$837$	−18.4508			−0.637753
$838$	−5.59395	−	4.06425i	−0.193240	−	0.140397i
$839$	−1.11468	+	3.43064i	−0.0384831	+	0.118439i	−0.968453	−	0.249198i	$-0.919833\pi$
$839$	−1.11468	+	3.43064i	−0.0384831	+	0.118439i	0.929969	+	0.367637i	$0.119833\pi$
$840$	−2.81929	−	8.67687i	−0.0972746	−	0.299380i
$841$	−48.6945	+	35.3786i	−1.67912	+	1.21995i
$842$	30.7505	−	22.3416i	1.05973	−	0.769942i
$843$	11.7788	+	36.2514i	0.405683	+	1.24857i
$844$	−0.154584	+	0.475760i	−0.00532100	+	0.0163764i
$845$	−7.28295	−	5.29137i	−0.250541	−	0.182029i
$846$	51.0632			1.75559
$847$	6.53119	+	50.9293i	0.224414	+	1.74995i
$848$	2.68767			0.0922948
$849$	−8.52177	−	6.19143i	−0.292466	−	0.212489i
$850$	−1.39148	+	4.28253i	−0.0477274	+	0.146890i
$851$	10.1941	+	31.3743i	0.349450	+	1.07550i
$852$	−30.0152	+	21.8073i	−1.02830	+	0.747107i
$853$	19.3166	−	14.0343i	0.661386	−	0.480525i	−0.205744	−	0.978606i	$-0.565962\pi$
$853$	19.3166	−	14.0343i	0.661386	−	0.480525i	0.867131	+	0.498080i	$0.165962\pi$
$854$	9.79247	+	30.1381i	0.335092	+	1.03131i
$855$	−4.79345	+	14.7527i	−0.163933	+	0.504533i
$856$	2.59377	+	1.88448i	0.0886531	+	0.0644102i
$857$	50.5004			1.72506			0.862530	−	0.506006i	$-0.168879\pi$
$857$	50.5004			1.72506			0.862530	+	0.506006i	$0.168879\pi$
$858$	0.412241	−	4.40527i	0.0140737	−	0.150393i
$859$	−42.2968			−1.44315			−0.721575	−	0.692337i	$-0.756581\pi$
$859$	−42.2968			−1.44315			−0.721575	+	0.692337i	$0.756581\pi$
$860$	1.83590	+	1.33386i	0.0626038	+	0.0454843i
$861$	−15.0736	+	46.3917i	−0.513706	+	1.58102i
$862$	−10.9382	−	33.6643i	−0.372556	−	1.14661i
$863$	−3.03521	+	2.20521i	−0.103320	+	0.0750662i	−0.638246	−	0.769833i	$-0.720340\pi$
$863$	−3.03521	+	2.20521i	−0.103320	+	0.0750662i	0.534926	+	0.844899i	$0.320340\pi$
$864$	3.77957	−	2.74602i	0.128584	−	0.0934214i
$865$	−3.14698	−	9.68541i	−0.107001	−	0.329314i
$866$	−5.58341	+	17.1840i	−0.189732	+	0.583935i
$867$	2.24278	+	1.62947i	0.0761686	+	0.0553398i
$868$	−18.4352			−0.625731
$869$	−11.9037	+	13.5278i	−0.403807	+	0.458898i
$870$	−18.4585			−0.625803
$871$	−5.84937	−	4.24982i	−0.198198	−	0.144000i
$872$	−2.69415	+	8.29174i	−0.0912354	+	0.280794i
$873$	−20.0369	−	61.6671i	−0.678145	−	2.08712i
$874$	−33.0786	+	24.0330i	−1.11890	+	0.812928i
$875$	25.3013	−	18.3825i	0.855341	−	0.621442i
$876$	−4.28671	−	13.1931i	−0.144834	−	0.445755i
$877$	−2.59569	+	7.98871i	−0.0876502	+	0.269760i	−0.985269	−	0.171014i	$-0.945296\pi$
$877$	−2.59569	+	7.98871i	−0.0876502	+	0.269760i	0.897618	+	0.440773i	$0.145296\pi$
$878$	5.11758	+	3.71814i	0.172710	+	0.125481i
$879$	−64.6712			−2.18130
$880$	2.14690	+	0.926650i	0.0723719	+	0.0312374i
$881$	−11.2447			−0.378842			−0.189421	−	0.981896i	$-0.560661\pi$
$881$	−11.2447			−0.378842			−0.189421	+	0.981896i	$0.560661\pi$
$882$	−56.0558	−	40.7269i	−1.88750	−	1.37135i
$883$	−11.0747	+	34.0844i	−0.372693	+	1.14703i	0.572329	+	0.820024i	$0.306040\pi$
$883$	−11.0747	+	34.0844i	−0.372693	+	1.14703i	−0.945022	+	0.327007i	$0.893960\pi$
$884$	−0.148704	−	0.457664i	−0.00500146	−	0.0153929i
$885$	5.15519	−	3.74546i	0.173290	−	0.125902i
$886$	10.3375	−	7.51062i	0.347295	−	0.252324i
$887$	5.77899	+	17.7859i	0.194039	+	0.597192i	0.999986	+	0.00520437i	$0.00165661\pi$
$887$	5.77899	+	17.7859i	0.194039	+	0.597192i	−0.805947	+	0.591988i	$0.798343\pi$
$888$	−3.24573	+	9.98934i	−0.108920	+	0.335220i
$889$	42.9491	+	31.2043i	1.44047	+	1.04656i
$890$	−1.98486			−0.0665327
$891$	−3.57383	+	0.802375i	−0.119728	+	0.0268806i
$892$	−1.98067			−0.0663178
$893$	−41.4057	−	30.0830i	−1.38559	−	1.00669i
$894$	−5.67085	+	17.4531i	−0.189662	+	0.583718i
$895$	−1.43170	−	4.40631i	−0.0478564	−	0.147287i
$896$	3.77637	−	2.74369i	0.126160	−	0.0916603i
$897$	−9.39705	+	6.82736i	−0.313758	+	0.227959i
$898$	3.80099	+	11.6982i	0.126841	+	0.390375i
$899$	−11.5258	+	35.4727i	−0.384406	+	1.18308i
$900$	17.0680	+	12.4006i	0.568933	+	0.413354i
$901$	2.68767			0.0895391
$902$	−6.37424	−	10.7551i	−0.212239	−	0.358107i
$903$	41.6509			1.38606
$904$	−1.93159	−	1.40338i	−0.0642438	−	0.0466758i
$905$	3.23045	−	9.94229i	0.107384	−	0.330493i
$906$	18.8614	+	58.0495i	0.626629	+	1.92857i
$907$	22.6661	−	16.4679i	0.752615	−	0.546807i	−0.144021	−	0.989575i	$-0.546003\pi$
$907$	22.6661	−	16.4679i	0.752615	−	0.546807i	0.896636	+	0.442768i	$0.146003\pi$
$908$	−15.0015	+	10.8992i	−0.497842	+	0.361703i
$909$	0.442933	+	1.36321i	0.0146911	+	0.0452147i
$910$	−0.489386	+	1.50618i	−0.0162230	+	0.0499293i
$911$	14.5948	+	10.6037i	0.483547	+	0.351318i	0.802697	−	0.596386i	$-0.203397\pi$
$911$	14.5948	+	10.6037i	0.483547	+	0.351318i	−0.319150	+	0.947704i	$0.603397\pi$
$912$	−13.0182			−0.431077
$913$	−4.58086	−	7.72922i	−0.151604	−	0.255800i
$914$	−18.5876			−0.614822
$915$	10.7347	+	7.79924i	0.354879	+	0.257835i
$916$	−6.85819	+	21.1073i	−0.226601	+	0.697406i
$917$	2.30261	+	7.08672i	0.0760390	+	0.234024i
$918$	3.77957	−	2.74602i	0.124744	−	0.0906321i
$919$	31.0343	−	22.5477i	1.02373	−	0.743780i	0.0566823	−	0.998392i	$-0.481948\pi$
$919$	31.0343	−	22.5477i	1.02373	−	0.743780i	0.967043	+	0.254612i	$0.0819478\pi$
$920$	−1.89696	−	5.83826i	−0.0625411	−	0.192482i
$921$	−2.68369	+	8.25953i	−0.0884304	+	0.272161i
$922$	17.9263	+	13.0242i	0.590372	+	0.428930i
$923$	6.44016			0.211980
$924$	41.8757	−	9.40169i	1.37761	−	0.309293i
$925$	−17.0607			−0.560952
$926$	−22.3182	−	16.2151i	−0.733422	−	0.532862i
$927$	11.6374	−	35.8162i	0.382222	−	1.17636i
$928$	−2.91837	−	8.98180i	−0.0958000	−	0.294842i
$929$	−2.67885	+	1.94630i	−0.0878903	+	0.0638560i	−0.630863	−	0.775895i	$-0.717299\pi$
$929$	−2.67885	+	1.94630i	−0.0878903	+	0.0638560i	0.542972	+	0.839751i	$0.317299\pi$
$930$	−6.24494	+	4.53722i	−0.204780	+	0.148781i
$931$	21.4605	+	66.0486i	0.703339	+	2.16465i
$932$	−5.43105	+	16.7150i	−0.177900	+	0.547519i
$933$	24.2333	+	17.6065i	0.793362	+	0.576411i
$934$	−5.08339			−0.166334
$935$	2.14690	+	0.926650i	0.0702111	+	0.0303047i
$936$	−2.25461			−0.0736941
$937$	−36.3856	−	26.4357i	−1.18866	−	0.863615i	−0.195542	−	0.980695i	$-0.562647\pi$
$937$	−36.3856	−	26.4357i	−1.18866	−	0.863615i	−0.993122	+	0.117080i	$0.962647\pi$
$938$	21.6725	−	66.7012i	0.707634	−	2.17787i
$939$	5.19153	+	15.9779i	0.169419	+	0.521419i
$940$	6.21653	−	4.51657i	0.202761	−	0.147314i
$941$	29.0367	−	21.0964i	0.946568	−	0.687722i	−0.00342450	−	0.999994i	$-0.501090\pi$
$941$	29.0367	−	21.0964i	0.946568	−	0.687722i	0.949993	+	0.312272i	$0.101090\pi$
$942$	9.95788	+	30.6472i	0.324445	+	0.998540i
$943$	−10.1423	+	31.2148i	−0.330278	+	1.01649i
$944$	2.63757	+	1.91631i	0.0858457	+	0.0623705i
$945$	−15.3749			−0.500147
$946$	−7.05211	+	8.01423i	−0.229284	+	0.260565i
$947$	−25.1189			−0.816255			−0.408127	−	0.912925i	$-0.633818\pi$
$947$	−25.1189			−0.816255			−0.408127	+	0.912925i	$0.633818\pi$
$948$	12.1851	+	8.85302i	0.395755	+	0.287533i
$949$	−0.744109	+	2.29013i	−0.0241548	+	0.0743409i
$950$	−6.53433	−	20.1106i	−0.212002	−	0.652474i
$951$	−50.9883	+	37.0452i	−1.65341	+	1.20127i
$952$	3.77637	−	2.74369i	0.122393	−	0.0889236i
$953$	3.38154	+	10.4073i	0.109539	+	0.337126i	0.990769	−	0.135562i	$-0.0432840\pi$
$953$	3.38154	+	10.4073i	0.109539	+	0.337126i	−0.881230	+	0.472687i	$0.843284\pi$
$954$	3.89124	−	11.9760i	0.125983	−	0.387737i
$955$	3.63362	+	2.63998i	0.117581	+	0.0854276i
$956$	−5.32363			−0.172178
$957$	8.09036	−	86.4547i	0.261524	−	2.79468i
$958$	−9.30766			−0.300717
$959$	−24.4292	−	17.7489i	−0.788860	−	0.573141i
$960$	0.603980	−	1.85886i	0.0194934	−	0.0599944i
$961$	−4.75956	−	14.6484i	−0.153534	−	0.472530i
$962$	1.47503	−	1.07167i	0.0475569	−	0.0345521i
$963$	12.1524	−	8.82921i	0.391604	−	0.284517i
$964$	3.29594	+	10.1439i	0.106155	+	0.326712i
$965$	3.08177	−	9.48472i	0.0992058	−	0.305324i
$966$	−91.1522	−	66.2260i	−2.93278	−	2.13079i
$967$	21.6521			0.696286			0.348143	−	0.937442i	$-0.386812\pi$
$967$	21.6521			0.696286			0.348143	+	0.937442i	$0.386812\pi$
$968$	−5.28115	+	9.64932i	−0.169743	+	0.310141i
$969$	−13.0182			−0.418206
$970$	−7.89382	−	5.73520i	−0.253455	−	0.184146i
$971$	−11.9182	+	36.6803i	−0.382472	+	1.17713i	0.555826	+	0.831299i	$0.312402\pi$
$971$	−11.9182	+	36.6803i	−0.382472	+	1.17713i	−0.938298	+	0.345829i	$0.887598\pi$
$972$	5.27708	+	16.2412i	0.169262	+	0.520936i
$973$	−35.9164	+	26.0948i	−1.15143	+	0.836561i
$974$	−11.0188	+	8.00563i	−0.353065	+	0.256517i
$975$	−1.85629	−	5.71307i	−0.0594489	−	0.182965i
$976$	−2.09786	+	6.45654i	−0.0671507	+	0.206669i
$977$	40.8260	+	29.6618i	1.30614	+	0.948965i	0.999995	−	0.00302042i	$-0.000961431\pi$
$977$	40.8260	+	29.6618i	1.30614	+	0.948965i	0.306143	+	0.951986i	$0.400961\pi$
$978$	−25.4871			−0.814989
$979$	0.869962	−	9.29654i	0.0278041	−	0.297119i
$980$	−10.4267			−0.333067
$981$	33.0466	+	24.0098i	1.05510	+	0.766573i
$982$	−8.73354	+	26.8791i	−0.278699	+	0.857746i
$983$	−7.07113	−	21.7627i	−0.225534	−	0.694122i	−0.998237	−	0.0593546i	$-0.981096\pi$
$983$	−7.07113	−	21.7627i	−0.225534	−	0.694122i	0.772703	−	0.634768i	$-0.218904\pi$
$984$	−8.45424	+	6.14237i	−0.269511	+	0.195811i
$985$	−3.65324	+	2.65423i	−0.116402	+	0.0845709i
$986$	−2.91837	−	8.98180i	−0.0929397	−	0.286039i
$987$	43.5818	−	134.131i	1.38723	−	4.26944i
$988$	1.82820	+	1.32826i	0.0581626	+	0.0422576i
$989$	28.0249			0.891141
$990$	7.23737	−	8.22477i	0.230019	−	0.261400i
$991$	62.1043			1.97281			0.986404	−	0.164339i	$-0.0525491\pi$
$991$	62.1043			1.97281			0.986404	+	0.164339i	$0.0525491\pi$
$992$	−3.19513	−	2.32140i	−0.101445	−	0.0737044i
$993$	−18.6246	+	57.3207i	−0.591035	+	1.81902i
$994$	19.3043	+	59.4126i	0.612296	+	1.88445i
$995$	3.75502	−	2.72818i	0.119042	−	0.0864892i
$996$	−6.07567	+	4.41423i	−0.192515	+	0.139870i
$997$	12.7655	+	39.2881i	0.404287	+	1.24427i	0.921490	+	0.388403i	$0.126973\pi$
$997$	12.7655	+	39.2881i	0.404287	+	1.24427i	−0.517203	+	0.855863i	$0.673027\pi$
$998$	−1.75944	+	5.41499i	−0.0556940	+	0.171408i
$999$	14.3201	+	10.4041i	0.453066	+	0.329172i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.g.d.103.1	yes	8
11.3	even	5	inner	374.2.g.d.69.1	✓	8
11.5	even	5		4114.2.a.z.1.1		4
11.6	odd	10		4114.2.a.u.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.d.69.1	✓	8	11.3	even	5	inner
374.2.g.d.103.1	yes	8	1.1	even	1	trivial
4114.2.a.u.1.1		4	11.6	odd	10
4114.2.a.z.1.1		4	11.5	even	5

Overview	Random
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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

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	374.2.g.d.103.1

Level	$374$
Weight	$2$
Character	374.103
Analytic conductor	$2.986$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$