LMFDB - Embedded newform 110.2.j.b.69.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,2,Mod(9,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 10 x^{13} - 109 x^{12} + 280 x^{11} - 198 x^{10} - 1168 x^{9} + \cdots + 390625 $ x^16 - 4x^15 + 8x^14 + 10x^13 - 109x^12 + 280x^11 - 198x^10 - 1168x^9 + 4281x^8 - 5840x^7 - 4950x^6 + 35000x^5 - 68125x^4 + 31250x^3 + 125000x^2 - 312500*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.3
Root			$0.147217 - 2.23122i$ of defining polynomial
Character	$\chi$	$=$	110.69
Dual form			110.2.j.b.59.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 + 0.809017i) q^{2} +(1.53884 - 0.500000i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.07652 - 0.829496i) q^{5} +(1.30902 + 0.951057i) q^{6} +(3.59321 + 1.16751i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 + 0.224514i) q^{9} +(-0.549472 - 2.16751i) q^{10} +(-2.64861 - 1.99621i) q^{11} +1.61803i q^{12} +(-1.82151 - 2.50710i) q^{13} +(1.16751 + 3.59321i) q^{14} +(-3.61018 - 0.238203i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.93806 + 2.66751i) q^{17} +(-0.363271 - 0.118034i) q^{18} +(-0.400863 - 1.23373i) q^{19} +(1.43058 - 1.71856i) q^{20} +6.11314 q^{21} +(0.0581575 - 3.31611i) q^{22} -0.556884i q^{23} +(-1.30902 + 0.951057i) q^{24} +(3.62387 + 3.44493i) q^{25} +(0.957626 - 2.94727i) q^{26} +(-3.21644 + 4.42705i) q^{27} +(-2.22073 + 3.05657i) q^{28} +(2.95763 - 9.10264i) q^{29} +(-1.92930 - 3.06071i) q^{30} +(-4.32760 + 3.14419i) q^{31} -1.00000i q^{32} +(-5.07390 - 1.74755i) q^{33} -3.29722 q^{34} +(-6.49294 - 5.40490i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(7.52785 + 2.44595i) q^{37} +(0.762486 - 1.04947i) q^{38} +(-4.05657 - 2.94727i) q^{39} +(2.23122 + 0.147217i) q^{40} +(1.94312 + 5.98030i) q^{41} +(3.59321 + 4.94563i) q^{42} -3.61803i q^{43} +(2.71698 - 1.90211i) q^{44} +(0.827913 - 0.209880i) q^{45} +(0.450528 - 0.327328i) q^{46} +(5.08740 - 1.65300i) q^{47} +(-1.53884 - 0.500000i) q^{48} +(5.88499 + 4.27570i) q^{49} +(-0.656948 + 4.95665i) q^{50} +(-1.64861 + 5.07390i) q^{51} +(2.94727 - 0.957626i) q^{52} +(6.47398 + 8.91067i) q^{53} -5.47214 q^{54} +(3.84404 + 6.34219i) q^{55} -3.77813 q^{56} +(-1.23373 - 1.69808i) q^{57} +(9.10264 - 2.95763i) q^{58} +(-1.63693 + 5.03795i) q^{59} +(1.34215 - 3.35988i) q^{60} +(-1.98801 - 1.44437i) q^{61} +(-5.08740 - 1.65300i) q^{62} +(-1.37249 + 0.445947i) q^{63} +(0.809017 - 0.587785i) q^{64} +(1.70278 + 6.71698i) q^{65} +(-1.56856 - 5.13205i) q^{66} +9.21247i q^{67} +(-1.93806 - 2.66751i) q^{68} +(-0.278442 - 0.856956i) q^{69} +(0.556206 - 8.42982i) q^{70} +(-8.81173 - 6.40210i) q^{71} +(0.224514 - 0.309017i) q^{72} +(3.22994 + 1.04947i) q^{73} +(2.44595 + 7.52785i) q^{74} +(7.29903 + 3.48927i) q^{75} +1.29722 q^{76} +(-7.18643 - 10.2651i) q^{77} -5.01420i q^{78} +(13.2383 - 9.61817i) q^{79} +(1.19237 + 1.89162i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(-3.69603 + 5.08714i) q^{82} +(-0.108199 + 0.148923i) q^{83} +(-1.88906 + 5.81394i) q^{84} +(6.23710 - 3.93152i) q^{85} +(2.92705 - 2.12663i) q^{86} -15.4863i q^{87} +(3.13584 + 1.08005i) q^{88} -6.09017 q^{89} +(0.656431 + 0.546432i) q^{90} +(-3.61803 - 11.1352i) q^{91} +(0.529628 + 0.172087i) q^{92} +(-5.08740 + 7.00220i) q^{93} +(4.32760 + 3.14419i) q^{94} +(-0.190973 + 2.89437i) q^{95} +(-0.500000 - 1.53884i) q^{96} +(-7.26384 - 9.99782i) q^{97} +7.27425i q^{98} +(1.26664 + 0.0222142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 20 q^{11} - 12 q^{14} + 2 q^{15} - 4 q^{16} - 16 q^{19} + 6 q^{20} - 16 q^{21} - 12 q^{24} - 16 q^{26} + 16 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{34}+ \cdots - 20 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 6 * q^5 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 20 * q^11 - 12 * q^14 + 2 * q^15 - 4 * q^16 - 16 * q^19 + 6 * q^20 - 16 * q^21 - 12 * q^24 - 16 * q^26 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^34 - 48 * q^35 + 16 * q^36 - 8 * q^39 - 4 * q^40 + 40 * q^41 - 4 * q^45 + 20 * q^46 + 84 * q^49 + 4 * q^50 - 4 * q^51 - 16 * q^54 + 32 * q^55 - 8 * q^56 + 8 * q^60 + 20 * q^61 + 4 * q^64 + 72 * q^65 - 20 * q^66 + 36 * q^70 - 56 * q^71 + 4 * q^74 + 32 * q^75 - 24 * q^76 + 36 * q^79 + 4 * q^80 - 56 * q^81 - 4 * q^84 - 54 * q^85 + 20 * q^86 - 8 * q^89 - 4 * q^90 - 40 * q^91 + 4 * q^94 - 50 * q^95 - 8 * q^96 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	1.53884	−	0.500000i	0.888451	−	0.288675i	0.170989	−	0.985273i	$-0.445304\pi$
$3$	1.53884	−	0.500000i	0.888451	−	0.288675i	0.717462	+	0.696598i	$0.245304\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−2.07652	−	0.829496i	−0.928648	−	0.370962i
$5$	−2.07652	−	0.829496i	−0.928648	−	0.370962i
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	3.59321	+	1.16751i	1.35811	+	0.441276i	0.895411	−	0.445241i	$-0.146882\pi$
$7$	3.59321	+	1.16751i	1.35811	+	0.441276i	0.462696	+	0.886517i	$0.346882\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.309017	+	0.224514i	−0.103006	+	0.0748380i
$10$	−0.549472	−	2.16751i	−0.173758	−	0.685425i
$11$	−2.64861	−	1.99621i	−0.798586	−	0.601881i
$11$	−2.64861	−	1.99621i	−0.798586	−	0.601881i
$12$			1.61803i			0.467086i
$13$	−1.82151	−	2.50710i	−0.505197	−	0.695344i	0.477903	−	0.878412i	$-0.341397\pi$
$13$	−1.82151	−	2.50710i	−0.505197	−	0.695344i	−0.983100	+	0.183069i	$0.941397\pi$
$14$	1.16751	+	3.59321i	0.312029	+	0.960327i
$15$	−3.61018	−	0.238203i	−0.932146	−	0.0615037i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.93806	+	2.66751i	−0.470048	+	0.646965i	−0.976554	−	0.215271i	$-0.930937\pi$
$17$	−1.93806	+	2.66751i	−0.470048	+	0.646965i	0.506507	+	0.862236i	$0.330937\pi$
$18$	−0.363271	−	0.118034i	−0.0856239	−	0.0278209i
$19$	−0.400863	−	1.23373i	−0.0919642	−	0.283037i	0.894486	−	0.447095i	$-0.147541\pi$
$19$	−0.400863	−	1.23373i	−0.0919642	−	0.283037i	−0.986451	+	0.164058i	$0.947541\pi$
$20$	1.43058	−	1.71856i	0.319887	−	0.384282i
$21$	6.11314			1.33400
$22$	0.0581575	−	3.31611i	0.0123992	−	0.706998i
$23$		−	0.556884i		−	0.116118i	−0.998313	−	0.0580591i	$-0.981509\pi$
$23$		−	0.556884i		−	0.116118i	0.998313	−	0.0580591i	$-0.0184912\pi$
$24$	−1.30902	+	0.951057i	−0.267202	+	0.194134i
$25$	3.62387	+	3.44493i	0.724775	+	0.688986i
$26$	0.957626	−	2.94727i	0.187806	−	0.578007i
$27$	−3.21644	+	4.42705i	−0.619004	+	0.851986i
$28$	−2.22073	+	3.05657i	−0.419678	+	0.577637i
$29$	2.95763	−	9.10264i	0.549217	−	1.69032i	−0.161528	−	0.986868i	$-0.551642\pi$
$29$	2.95763	−	9.10264i	0.549217	−	1.69032i	0.710746	−	0.703449i	$-0.248358\pi$
$30$	−1.92930	−	3.06071i	−0.352241	−	0.558807i
$31$	−4.32760	+	3.14419i	−0.777260	+	0.564712i	−0.904155	−	0.427204i	$-0.859499\pi$
$31$	−4.32760	+	3.14419i	−0.777260	+	0.564712i	0.126896	+	0.991916i	$0.459499\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.07390	−	1.74755i	−0.883252	−	0.304210i
$34$	−3.29722			−0.565468
$35$	−6.49294	−	5.40490i	−1.09751	−	0.913596i
$36$	−0.118034	−	0.363271i	−0.0196723	−	0.0605452i
$37$	7.52785	+	2.44595i	1.23757	+	0.402111i	0.853452	−	0.521172i	$-0.174505\pi$
$37$	7.52785	+	2.44595i	1.23757	+	0.402111i	0.384120	+	0.923283i	$0.374505\pi$
$38$	0.762486	−	1.04947i	0.123692	−	0.170247i
$39$	−4.05657	−	2.94727i	−0.649571	−	0.471941i
$40$	2.23122	+	0.147217i	0.352786	+	0.0232771i
$41$	1.94312	+	5.98030i	0.303464	+	0.933966i	0.980246	+	0.197782i	$0.0633739\pi$
$41$	1.94312	+	5.98030i	0.303464	+	0.933966i	−0.676782	+	0.736183i	$0.736626\pi$
$42$	3.59321	+	4.94563i	0.554445	+	0.763128i
$43$		−	3.61803i		−	0.551745i	−0.961194	−	0.275873i	$-0.911033\pi$
$43$		−	3.61803i		−	0.551745i	0.961194	−	0.275873i	$-0.0889668\pi$
$44$	2.71698	−	1.90211i	0.409600	−	0.286754i
$45$	0.827913	−	0.209880i	0.123418	−	0.0312870i
$46$	0.450528	−	0.327328i	0.0664268	−	0.0482619i
$47$	5.08740	−	1.65300i	0.742073	−	0.241114i	0.0865064	−	0.996251i	$-0.472430\pi$
$47$	5.08740	−	1.65300i	0.742073	−	0.241114i	0.655567	+	0.755137i	$0.272430\pi$
$48$	−1.53884	−	0.500000i	−0.222113	−	0.0721688i
$49$	5.88499	+	4.27570i	0.840713	+	0.610814i
$50$	−0.656948	+	4.95665i	−0.0929065	+	0.700977i
$51$	−1.64861	+	5.07390i	−0.230851	+	0.710488i
$52$	2.94727	−	0.957626i	0.408713	−	0.132799i
$53$	6.47398	+	8.91067i	0.889270	+	1.22397i	0.973766	+	0.227551i	$0.0730719\pi$
$53$	6.47398	+	8.91067i	0.889270	+	1.22397i	−0.0844964	+	0.996424i	$0.526928\pi$
$54$	−5.47214			−0.744663
$55$	3.84404	+	6.34219i	0.518330	+	0.855181i
$56$	−3.77813			−0.504874
$57$	−1.23373	−	1.69808i	−0.163411	−	0.224916i
$58$	9.10264	−	2.95763i	1.19523	−	0.388355i
$59$	−1.63693	+	5.03795i	−0.213110	+	0.655886i	0.786172	+	0.618008i	$0.212060\pi$
$59$	−1.63693	+	5.03795i	−0.213110	+	0.655886i	−0.999282	+	0.0378782i	$0.987940\pi$
$60$	1.34215	−	3.35988i	0.173271	−	0.433759i
$61$	−1.98801	−	1.44437i	−0.254538	−	0.184933i	0.453197	−	0.891410i	$-0.350283\pi$
$61$	−1.98801	−	1.44437i	−0.254538	−	0.184933i	−0.707736	+	0.706477i	$0.750283\pi$
$62$	−5.08740	−	1.65300i	−0.646100	−	0.209931i
$63$	−1.37249	+	0.445947i	−0.172917	+	0.0561841i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	1.70278	+	6.71698i	0.211204	+	0.833139i
$66$	−1.56856	−	5.13205i	−0.193077	−	0.631712i
$67$			9.21247i			1.12548i	0.826633	+	0.562741i	$0.190253\pi$
$67$			9.21247i			1.12548i	−0.826633	+	0.562741i	$0.809747\pi$
$68$	−1.93806	−	2.66751i	−0.235024	−	0.323483i
$69$	−0.278442	−	0.856956i	−0.0335205	−	0.103165i
$70$	0.556206	−	8.42982i	0.0664794	−	1.00756i
$71$	−8.81173	−	6.40210i	−1.04576	−	0.759789i	−0.0743582	−	0.997232i	$-0.523691\pi$
$71$	−8.81173	−	6.40210i	−1.04576	−	0.759789i	−0.971402	+	0.237443i	$0.923691\pi$
$72$	0.224514	−	0.309017i	0.0264592	−	0.0364180i
$73$	3.22994	+	1.04947i	0.378036	+	0.122831i	0.491871	−	0.870668i	$-0.336313\pi$
$73$	3.22994	+	1.04947i	0.378036	+	0.122831i	−0.113834	+	0.993500i	$0.536313\pi$
$74$	2.44595	+	7.52785i	0.284336	+	0.875095i
$75$	7.29903	+	3.48927i	0.842820	+	0.402906i
$76$	1.29722			0.148801
$77$	−7.18643	−	10.2651i	−0.818969	−	1.16982i
$78$		−	5.01420i		−	0.567746i
$79$	13.2383	−	9.61817i	1.48942	−	1.08213i	0.515057	−	0.857156i	$-0.327771\pi$
$79$	13.2383	−	9.61817i	1.48942	−	1.08213i	0.974365	−	0.224972i	$-0.0722291\pi$
$80$	1.19237	+	1.89162i	0.133312	+	0.211490i
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$	−3.69603	+	5.08714i	−0.408158	+	0.561781i
$83$	−0.108199	+	0.148923i	−0.0118764	+	0.0163464i	−0.814914	−	0.579582i	$-0.803216\pi$
$83$	−0.108199	+	0.148923i	−0.0118764	+	0.0163464i	0.803038	+	0.595928i	$0.203216\pi$
$84$	−1.88906	+	5.81394i	−0.206114	+	0.634353i
$85$	6.23710	−	3.93152i	0.676508	−	0.426433i
$86$	2.92705	−	2.12663i	0.315632	−	0.229320i
$87$		−	15.4863i		−	1.66031i
$88$	3.13584	+	1.08005i	0.334282	+	0.115133i
$89$	−6.09017			−0.645557			−0.322778	−	0.946475i	$-0.604617\pi$
$89$	−6.09017			−0.645557			−0.322778	+	0.946475i	$0.604617\pi$
$90$	0.656431	+	0.546432i	0.0691939	+	0.0575990i
$91$	−3.61803	−	11.1352i	−0.379273	−	1.16728i
$92$	0.529628	+	0.172087i	0.0552175	+	0.0179413i
$93$	−5.08740	+	7.00220i	−0.527539	+	0.726095i
$94$	4.32760	+	3.14419i	0.446358	+	0.324298i
$95$	−0.190973	+	2.89437i	−0.0195934	+	0.296957i
$96$	−0.500000	−	1.53884i	−0.0510310	−	0.157057i
$97$	−7.26384	−	9.99782i	−0.737531	−	1.01512i	−0.998757	−	0.0498467i	$-0.984127\pi$
$97$	−7.26384	−	9.99782i	−0.737531	−	1.01512i	0.261226	−	0.965278i	$-0.415873\pi$
$98$			7.27425i			0.734810i
$99$	1.26664	+	0.0222142i	0.127302	+	0.00223261i
$100$	−4.39616	+	2.38197i	−0.439616	+	0.238197i
$101$	7.29264	−	5.29841i	0.725645	−	0.527212i	−0.162538	−	0.986702i	$-0.551968\pi$
$101$	7.29264	−	5.29841i	0.725645	−	0.527212i	0.888183	+	0.459491i	$0.151968\pi$
$102$	−5.07390	+	1.64861i	−0.502391	+	0.163237i
$103$	−10.8743	−	3.53329i	−1.07148	−	0.348145i	−0.280416	−	0.959878i	$-0.590473\pi$
$103$	−10.8743	−	3.53329i	−1.07148	−	0.348145i	−0.791064	+	0.611733i	$0.790473\pi$
$104$	2.50710	+	1.82151i	0.245841	+	0.178614i
$105$	−12.6941	−	5.07082i	−1.23881	−	0.494862i
$106$	−3.40357	+	10.4751i	−0.330584	+	1.01743i
$107$	−14.6031	+	4.74484i	−1.41174	+	0.458701i	−0.912967	−	0.408033i	$-0.866215\pi$
$107$	−14.6031	+	4.74484i	−1.41174	+	0.458701i	−0.498770	+	0.866734i	$0.666215\pi$
$108$	−3.21644	−	4.42705i	−0.309502	−	0.425993i
$109$	−2.42892			−0.232648			−0.116324	−	0.993211i	$-0.537111\pi$
$109$	−2.42892			−0.232648			−0.116324	+	0.993211i	$0.537111\pi$
$110$	−2.87147	+	6.83774i	−0.273784	+	0.651953i
$111$	12.8071			1.21560
$112$	−2.22073	−	3.05657i	−0.209839	−	0.288819i
$113$	7.97113	−	2.58998i	0.749860	−	0.243644i	0.0909393	−	0.995856i	$-0.471013\pi$
$113$	7.97113	−	2.58998i	0.749860	−	0.243644i	0.658921	+	0.752212i	$0.271013\pi$
$114$	0.648609	−	1.99621i	0.0607478	−	0.186963i
$115$	−0.461933	+	1.15638i	−0.0430754	+	0.107833i
$116$	7.74317	+	5.62574i	0.718935	+	0.522337i
$117$	1.12576	+	0.365781i	0.104076	+	0.0338164i
$118$	−5.03795	+	1.63693i	−0.463781	+	0.150692i
$119$	−10.0782	+	7.32222i	−0.923865	+	0.671227i
$120$	3.50710	−	0.889064i	0.320153	−	0.0811601i
$121$	3.03026	+	10.5744i	0.275478	+	0.961307i
$122$		−	2.45731i		−	0.222475i
$123$	5.98030	+	8.23117i	0.539225	+	0.742180i
$124$	−1.65300	−	5.08740i	−0.148443	−	0.456862i
$125$	−4.66749	−	10.1595i	−0.417473	−	0.908689i
$126$	−1.16751	−	0.848243i	−0.104010	−	0.0755675i
$127$	4.08713	−	5.62545i	0.362674	−	0.499178i	−0.588217	−	0.808703i	$-0.700170\pi$
$127$	4.08713	−	5.62545i	0.362674	−	0.499178i	0.950891	+	0.309525i	$0.100170\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−1.80902	−	5.56758i	−0.159275	−	0.490198i
$130$	−4.43328	+	5.32572i	−0.388824	+	0.467097i
$131$	−5.61741			−0.490795			−0.245398	−	0.969423i	$-0.578918\pi$
$131$	−5.61741			−0.490795			−0.245398	+	0.969423i	$0.578918\pi$
$132$	3.22994	−	4.28554i	0.281130	−	0.373008i
$133$		−	4.90106i		−	0.424976i
$134$	−7.45305	+	5.41495i	−0.643845	+	0.467781i
$135$	10.3512	−	6.52484i	0.890892	−	0.561569i
$136$	1.01890	−	3.13584i	0.0873697	−	0.268896i
$137$	4.51887	−	6.21969i	0.386073	−	0.531384i	−0.571108	−	0.820875i	$-0.693486\pi$
$137$	4.51887	−	6.21969i	0.386073	−	0.531384i	0.957181	+	0.289491i	$0.0934861\pi$
$138$	0.529628	−	0.728970i	0.0450849	−	0.0620541i
$139$	−0.297218	+	0.914744i	−0.0252097	+	0.0775876i	−0.962870	−	0.269966i	$-0.912988\pi$
$139$	−0.297218	+	0.914744i	−0.0252097	+	0.0775876i	0.937660	+	0.347554i	$0.112988\pi$
$140$	7.14680	−	4.50494i	0.604015	−	0.380737i
$141$	7.00220	−	5.08740i	0.589692	−	0.428436i
$142$		−	10.8919i		−	0.914028i
$143$	−0.180227	+	10.2765i	−0.0150713	+	0.859360i
$144$	0.381966			0.0318305
$145$	−13.6922	+	16.4485i	−1.13707	+	1.36597i
$146$	1.04947	+	3.22994i	0.0868549	+	0.267312i
$147$	11.1939	+	3.63712i	0.923259	+	0.299985i
$148$	−4.65247	+	6.40357i	−0.382431	+	0.526371i
$149$	−7.11314	−	5.16800i	−0.582731	−	0.423379i	0.256977	−	0.966418i	$-0.417274\pi$
$149$	−7.11314	−	5.16800i	−0.582731	−	0.423379i	−0.839708	+	0.543039i	$0.817274\pi$
$150$	1.46739	+	7.95598i	0.119812	+	0.649603i
$151$	−2.76194	−	8.50038i	−0.224764	−	0.691751i	−0.998316	−	0.0580184i	$-0.981522\pi$
$151$	−2.76194	−	8.50038i	−0.224764	−	0.691751i	0.773552	−	0.633733i	$-0.218478\pi$
$152$	0.762486	+	1.04947i	0.0618458	+	0.0851234i
$153$		−	1.25943i		−	0.101819i
$154$	4.08056	−	11.8476i	0.328820	−	0.954707i
$155$	11.5944	−	2.93924i	0.931288	−	0.236085i
$156$	4.05657	−	2.94727i	0.324785	−	0.235970i
$157$	−16.7776	+	5.45137i	−1.33900	+	0.435067i	−0.888977	−	0.457952i	$-0.848583\pi$
$157$	−16.7776	+	5.45137i	−1.33900	+	0.435067i	−0.450020	+	0.893018i	$0.648583\pi$
$158$	15.5625	+	5.05657i	1.23809	+	0.402279i
$159$	14.4178	+	10.4751i	1.14340	+	0.830731i
$160$	−0.829496	+	2.07652i	−0.0655774	+	0.164163i
$161$	0.650165	−	2.00100i	0.0512402	−	0.157701i
$162$	−7.33094	+	2.38197i	−0.575973	+	0.187145i
$163$	−0.102445	−	0.141003i	−0.00802409	−	0.0110442i	0.804986	−	0.593294i	$-0.202173\pi$
$163$	−0.102445	−	0.141003i	−0.00802409	−	0.0110442i	−0.813010	+	0.582249i	$0.802173\pi$
$164$	−6.28806			−0.491015
$165$	9.08646	+	7.83761i	0.707380	+	0.610157i
$166$	−0.184079			−0.0142873
$167$	3.22478	+	4.43854i	0.249541	+	0.343464i	0.915351	−	0.402658i	$-0.131914\pi$
$167$	3.22478	+	4.43854i	0.249541	+	0.343464i	−0.665809	+	0.746122i	$0.731914\pi$
$168$	−5.81394	+	1.88906i	−0.448555	+	0.145744i
$169$	1.04959	−	3.23031i	0.0807378	−	0.248485i
$170$	6.84674	+	2.73503i	0.525121	+	0.209767i
$171$	0.400863	+	0.291244i	0.0306547	+	0.0222720i
$172$	3.44095	+	1.11803i	0.262370	+	0.0852493i
$173$	22.8216	−	7.41518i	1.73509	−	0.563766i	0.740922	−	0.671591i	$-0.234389\pi$
$173$	22.8216	−	7.41518i	1.73509	−	0.563766i	0.994170	+	0.107825i	$0.0343887\pi$
$174$	12.5287	−	9.10264i	0.949799	−	0.690069i
$175$	8.99937	+	16.6093i	0.680289	+	1.25554i
$176$	0.969425	+	3.17178i	0.0730731	+	0.239082i
$177$			8.57108i			0.644242i
$178$	−3.57971	−	4.92705i	−0.268311	−	0.369298i
$179$	0.0658512	+	0.202669i	0.00492195	+	0.0151482i	0.953487	−	0.301433i	$-0.0974650\pi$
$179$	0.0658512	+	0.202669i	0.00492195	+	0.0151482i	−0.948565	+	0.316581i	$0.897465\pi$
$180$	−0.0562321	+	0.852249i	−0.00419129	+	0.0635229i
$181$	−0.839906	−	0.610228i	−0.0624297	−	0.0453579i	0.556133	−	0.831094i	$-0.312285\pi$
$181$	−0.839906	−	0.610228i	−0.0624297	−	0.0453579i	−0.618562	+	0.785736i	$0.712285\pi$
$182$	6.88191	−	9.47214i	0.510121	−	0.702121i
$183$	−3.78141	−	1.22866i	−0.279530	−	0.0908249i
$184$	0.172087	+	0.529628i	0.0126864	+	0.0390447i
$185$	−13.6028	−	11.3234i	−1.00010	−	0.832512i
$186$	−8.65520			−0.634630
$187$	10.4581	−	3.19641i	0.764769	−	0.233744i
$188$			5.34921i			0.390131i
$189$	−16.7260	+	12.1521i	−1.21663	+	0.883937i
$190$	−2.45385	+	1.54677i	−0.178021	+	0.112215i
$191$	−5.54206	+	17.0567i	−0.401009	+	1.23418i	0.523172	+	0.852227i	$0.324748\pi$
$191$	−5.54206	+	17.0567i	−0.401009	+	1.23418i	−0.924182	+	0.381953i	$0.875252\pi$
$192$	0.951057	−	1.30902i	0.0686366	−	0.0944702i
$193$	−5.30174	+	7.29722i	−0.381628	+	0.525265i	−0.956015	−	0.293318i	$-0.905240\pi$
$193$	−5.30174	+	7.29722i	−0.381628	+	0.525265i	0.574387	+	0.818584i	$0.305240\pi$
$194$	3.81883	−	11.7531i	0.274176	−	0.843826i
$195$	5.97880	+	9.48497i	0.428151	+	0.679233i
$196$	−5.88499	+	4.27570i	−0.420357	+	0.305407i
$197$			3.68422i			0.262490i	0.991350	+	0.131245i	$0.0418974\pi$
$197$			3.68422i			0.262490i	−0.991350	+	0.131245i	$0.958103\pi$
$198$	0.726543	+	1.03779i	0.0516331	+	0.0737527i
$199$	4.23544			0.300242			0.150121	−	0.988668i	$-0.452034\pi$
$199$	4.23544			0.300242			0.150121	+	0.988668i	$0.452034\pi$
$200$	−4.51105	−	2.15649i	−0.318979	−	0.152487i
$201$	4.60624	+	14.1765i	0.324899	+	0.999936i
$202$	8.57301	+	2.78554i	0.603195	+	0.195990i
$203$	21.2548	−	29.2547i	1.49179	−	2.05328i
$204$	−4.31611	−	3.13584i	−0.302188	−	0.219553i
$205$	0.925712	−	14.0300i	0.0646545	−	0.979899i
$206$	−3.53329	−	10.8743i	−0.246176	−	0.757651i
$207$	0.125028	+	0.172087i	0.00869006	+	0.0119608i
$208$			3.09894i			0.214873i
$209$	−1.40106	+	4.06787i	−0.0969131	+	0.281380i
$210$	−3.35900	−	13.2503i	−0.231793	−	0.914355i
$211$	11.0596	−	8.03527i	0.761374	−	0.553171i	−0.137958	−	0.990438i	$-0.544054\pi$
$211$	11.0596	−	8.03527i	0.761374	−	0.553171i	0.899331	+	0.437268i	$0.144054\pi$
$212$	−10.4751	+	3.40357i	−0.719434	+	0.233758i
$213$	−16.7609	−	5.44595i	−1.14844	−	0.373150i
$214$	−12.4222	−	9.02522i	−0.849161	−	0.616952i
$215$	−3.00114	+	7.51292i	−0.204676	+	0.512377i
$216$	1.69098	−	5.20431i	0.115057	−	0.354108i
$217$	−19.2208	+	6.24523i	−1.30480	+	0.423954i
$218$	−1.42768	−	1.96504i	−0.0966949	−	0.133089i
$219$	5.49511			0.371325
$220$	−7.21965	+	1.69605i	−0.486749	+	0.114348i
$221$	10.2179			0.687330
$222$	7.52785	+	10.3612i	0.505236	+	0.695398i
$223$	−22.7988	+	7.40777i	−1.52672	+	0.496061i	−0.947675	−	0.319236i	$-0.896574\pi$
$223$	−22.7988	+	7.40777i	−1.52672	+	0.496061i	−0.579043	+	0.815297i	$0.696574\pi$
$224$	1.16751	−	3.59321i	0.0780073	−	0.240082i
$225$	−1.89327	−	0.250932i	−0.126218	−	0.0167288i
$226$	6.78064	+	4.92643i	0.451042	+	0.327701i
$227$	−19.6911	−	6.39803i	−1.30695	−	0.424652i	−0.428953	−	0.903327i	$-0.641117\pi$
$227$	−19.6911	−	6.39803i	−1.30695	−	0.424652i	−0.877992	+	0.478675i	$0.841117\pi$
$228$	1.99621	−	0.648609i	0.132202	−	0.0429552i
$229$	−13.2199	+	9.60481i	−0.873594	+	0.634704i	−0.931549	−	0.363616i	$-0.881542\pi$
$229$	−13.2199	+	9.60481i	−0.873594	+	0.634704i	0.0579546	+	0.998319i	$0.481542\pi$
$230$	−1.20705	+	0.305992i	−0.0795904	+	0.0201765i
$231$	−16.1913	−	12.2031i	−1.06531	−	0.802907i
$232$			9.57108i			0.628372i
$233$	−0.282302	−	0.388556i	−0.0184942	−	0.0254551i	0.799670	−	0.600440i	$-0.205008\pi$
$233$	−0.282302	−	0.388556i	−0.0184942	−	0.0254551i	−0.818164	+	0.574985i	$0.805008\pi$
$234$	0.365781	+	1.12576i	0.0239118	+	0.0735930i
$235$	−11.9352	−	0.787497i	−0.778569	−	0.0513706i
$236$	−4.28554	−	3.11363i	−0.278965	−	0.202680i
$237$	15.5625	−	21.4200i	1.01089	−	1.39138i
$238$	−11.8476	−	3.84952i	−0.767966	−	0.249527i
$239$	−0.348754	−	1.07335i	−0.0225590	−	0.0694295i	0.939143	−	0.343526i	$-0.111621\pi$
$239$	−0.348754	−	1.07335i	−0.0225590	−	0.0694295i	−0.961702	+	0.274096i	$0.911621\pi$
$240$	2.78069	+	2.31472i	0.179493	+	0.149415i
$241$	−12.7220			−0.819497			−0.409748	−	0.912199i	$-0.634384\pi$
$241$	−12.7220			−0.819497			−0.409748	+	0.912199i	$0.634384\pi$
$242$	−6.77371	+	8.66700i	−0.435431	+	0.557136i
$243$		−	3.94427i		−	0.253025i
$244$	1.98801	−	1.44437i	0.127269	−	0.0924664i
$245$	−8.67363	−	13.7601i	−0.554138	−	0.879104i
$246$	−3.14403	+	9.67632i	−0.200456	+	0.616940i
$247$	−2.36290	+	3.25225i	−0.150348	+	0.206936i
$248$	3.14419	−	4.32760i	0.199656	−	0.274803i
$249$	−0.0920396	+	0.283269i	−0.00583277	+	0.0179514i
$250$	5.47569	−	9.74766i	0.346313	−	0.616496i
$251$	2.29722	−	1.66903i	0.144999	−	0.105348i	−0.512921	−	0.858436i	$-0.671437\pi$
$251$	2.29722	−	1.66903i	0.144999	−	0.105348i	0.657920	+	0.753088i	$0.271437\pi$
$252$		−	1.44312i		−	0.0909078i
$253$	−1.11166	+	1.47497i	−0.0698894	+	0.0927304i
$254$	6.95343			0.436297
$255$	7.63215	−	9.16854i	0.477944	−	0.574156i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	29.3315	+	9.53038i	1.82965	+	0.594489i	0.999307	+	0.0372347i	$0.0118549\pi$
$257$	29.3315	+	9.53038i	1.82965	+	0.594489i	0.830342	+	0.557254i	$0.188145\pi$
$258$	3.44095	−	4.73607i	0.214224	−	0.294855i
$259$	24.1935	+	17.5776i	1.50331	+	1.09222i
$260$	−6.91441	−	0.456219i	−0.428814	−	0.0282935i
$261$	1.12971	+	3.47690i	0.0699275	+	0.215215i
$262$	−3.30183	−	4.54458i	−0.203988	−	0.280765i
$263$			27.7069i			1.70848i	0.519876	+	0.854242i	$0.325978\pi$
$263$			27.7069i			1.70848i	−0.519876	+	0.854242i	$0.674022\pi$
$264$	5.36559	+	0.0941007i	0.330229	+	0.00579150i
$265$	−6.05199	−	23.8733i	−0.371771	−	1.46653i
$266$	3.96504	−	2.88077i	0.243112	−	0.176631i
$267$	−9.37181	+	3.04508i	−0.573545	+	0.186356i
$268$	−8.76158	−	2.84681i	−0.535199	−	0.173897i
$269$	10.3224	+	7.49966i	0.629367	+	0.457262i	0.856181	−	0.516676i	$-0.172831\pi$
$269$	10.3224	+	7.49966i	0.629367	+	0.457262i	−0.226814	+	0.973938i	$0.572831\pi$
$270$	11.3630	+	4.53911i	0.691530	+	0.276242i
$271$	1.76218	−	5.42344i	0.107045	−	0.329450i	−0.883160	−	0.469072i	$-0.844589\pi$
$271$	1.76218	−	5.42344i	0.107045	−	0.329450i	0.990205	+	0.139621i	$0.0445885\pi$
$272$	3.13584	−	1.01890i	0.190138	−	0.0617797i
$273$	−11.1352	−	15.3262i	−0.673931	−	0.927586i
$274$	7.68796			0.464447
$275$	−2.72141	−	16.3583i	−0.164107	−	0.986443i
$276$	0.901057			0.0542372
$277$	18.6489	+	25.6680i	1.12050	+	1.54224i	0.804957	+	0.593333i	$0.202188\pi$
$277$	18.6489	+	25.6680i	1.12050	+	1.54224i	0.315548	+	0.948910i	$0.397812\pi$
$278$	−0.914744	+	0.297218i	−0.0548627	+	0.0178260i
$279$	0.631388	−	1.94321i	0.0378002	−	0.116337i
$280$	7.84536	+	3.13394i	0.468850	+	0.187289i
$281$	1.56805	+	1.13926i	0.0935423	+	0.0679624i	0.633573	−	0.773683i	$-0.281588\pi$
$281$	1.56805	+	1.13926i	0.0935423	+	0.0679624i	−0.540031	+	0.841645i	$0.681588\pi$
$282$	8.23158	+	2.67460i	0.490184	+	0.159270i
$283$	4.67528	−	1.51909i	0.277917	−	0.0903006i	−0.166742	−	0.986000i	$-0.553325\pi$
$283$	4.67528	−	1.51909i	0.277917	−	0.0903006i	0.444659	+	0.895700i	$0.353325\pi$
$284$	8.81173	−	6.40210i	0.522880	−	0.379894i
$285$	1.15331	+	4.54947i	0.0683162	+	0.269487i
$286$	−8.41976	+	5.89454i	−0.497871	+	0.348551i
$287$			23.7571i			1.40234i
$288$	0.224514	+	0.309017i	0.0132296	+	0.0182090i
$289$	1.89376	+	5.82841i	0.111398	+	0.342848i
$290$	−21.3552	−	1.40903i	−1.25402	−	0.0827411i
$291$	−16.1768	−	11.7531i	−0.948301	−	0.688981i
$292$	−1.99621	+	2.74755i	−0.116820	+	0.160788i
$293$	0.179488	+	0.0583193i	0.0104858	+	0.00340705i	0.314255	−	0.949339i	$-0.398245\pi$
$293$	0.179488	+	0.0583193i	0.0104858	+	0.00340705i	−0.303769	+	0.952746i	$0.598245\pi$
$294$	3.63712	+	11.1939i	0.212121	+	0.652843i
$295$	7.57808	−	9.10359i	0.441213	−	0.530031i
$296$	−7.91525			−0.460065
$297$	17.3564	−	5.30482i	1.00712	−	0.307817i
$298$		−	8.79232i		−	0.509326i
$299$	−1.39616	+	1.01437i	−0.0807421	+	0.0586626i
$300$	−5.57401	+	5.86355i	−0.321816	+	0.338532i
$301$	4.22408	−	13.0004i	0.243472	−	0.749329i
$302$	5.25353	−	7.23086i	0.302306	−	0.416089i
$303$	8.57301	−	11.7997i	0.492507	−	0.677877i
$304$	−0.400863	+	1.23373i	−0.0229910	+	0.0707592i
$305$	2.93004	+	4.64831i	0.167773	+	0.266162i
$306$	1.01890	−	0.740272i	0.0582464	−	0.0423185i
$307$		−	12.3820i		−	0.706676i	−0.935496	−	0.353338i	$-0.885047\pi$
$307$		−	12.3820i		−	0.706676i	0.935496	−	0.353338i	$-0.114953\pi$
$308$	11.9834	−	3.66261i	0.682818	−	0.208697i
$309$	−18.5005			−1.05246
$310$	9.19293	+	7.65246i	0.522123	+	0.434630i
$311$	−6.52587	−	20.0846i	−0.370048	−	1.13889i	−0.946759	−	0.321943i	$-0.895664\pi$
$311$	−6.52587	−	20.0846i	−0.370048	−	1.13889i	0.576711	−	0.816949i	$-0.304336\pi$
$312$	4.76878	+	1.54947i	0.269979	+	0.0877216i
$313$	−9.74502	+	13.4129i	−0.550821	+	0.758140i	−0.990123	−	0.140199i	$-0.955226\pi$
$313$	−9.74502	+	13.4129i	−0.550821	+	0.758140i	0.439302	+	0.898339i	$0.355226\pi$
$314$	−14.2719	−	10.3691i	−0.805408	−	0.585163i
$315$	3.21991	+	0.212452i	0.181421	+	0.0119703i
$316$	5.05657	+	15.5625i	0.284454	+	0.875460i
$317$	11.5424	+	15.8867i	0.648283	+	0.892285i	0.999023	−	0.0441877i	$-0.0140699\pi$
$317$	11.5424	+	15.8867i	0.648283	+	0.892285i	−0.350740	+	0.936473i	$0.614070\pi$
$318$			17.8213i			0.999371i
$319$	−26.0044	+	18.2053i	−1.45597	+	1.01930i
$320$	−2.16751	+	0.549472i	−0.121167	+	0.0307164i
$321$	−20.0995	+	14.6031i	−1.12184	+	0.815067i
$322$	2.00100	−	0.650165i	0.111511	−	0.0362323i
$323$	4.06787	+	1.32173i	0.226342	+	0.0735431i
$324$	−6.23607	−	4.53077i	−0.346448	−	0.251709i
$325$	2.03584	−	15.3604i	0.112928	−	0.852041i
$326$	0.0538584	−	0.165759i	0.00298294	−	0.00918055i
$327$	−3.73772	+	1.21446i	−0.206697	+	0.0671598i
$328$	−3.69603	−	5.08714i	−0.204079	−	0.280891i
$329$	20.2100			1.11421
$330$	−0.999867	+	11.9579i	−0.0550409	+	0.658262i
$331$	−23.4826			−1.29072			−0.645360	−	0.763879i	$-0.723293\pi$
$331$	−23.4826			−1.29072			−0.645360	+	0.763879i	$0.723293\pi$
$332$	−0.108199	−	0.148923i	−0.00593820	−	0.00817322i
$333$	−2.87538	+	0.934269i	−0.157570	+	0.0511976i
$334$	−1.69537	+	5.21781i	−0.0927665	+	0.285506i
$335$	7.64171	−	19.1299i	0.417511	−	1.04518i
$336$	−4.94563	−	3.59321i	−0.269806	−	0.196026i
$337$	12.1974	+	3.96317i	0.664434	+	0.215888i	0.621768	−	0.783202i	$-0.286415\pi$
$337$	12.1974	+	3.96317i	0.664434	+	0.215888i	0.0426660	+	0.999089i	$0.486415\pi$
$338$	3.23031	−	1.04959i	0.175706	−	0.0570903i
$339$	10.9713	−	7.97113i	0.595880	−	0.432932i
$340$	1.81173	+	7.14674i	0.0982548	+	0.387586i
$341$	17.7386	+	0.311096i	0.960598	+	0.0168468i
$342$			0.495493i			0.0267932i
$343$	0.609033	+	0.838262i	0.0328847	+	0.0452619i
$344$	1.11803	+	3.44095i	0.0602804	+	0.185524i
$345$	−0.132651	+	2.01045i	−0.00714170	+	0.108239i
$346$	19.4132	+	14.1045i	1.04366	+	0.758263i
$347$	12.1634	−	16.7415i	0.652966	−	0.898730i	−0.346257	−	0.938140i	$-0.612548\pi$
$347$	12.1634	−	16.7415i	0.652966	−	0.898730i	0.999223	+	0.0394093i	$0.0125476\pi$
$348$	14.7284	+	4.78554i	0.789524	+	0.256532i
$349$	−6.71104	−	20.6544i	−0.359233	−	1.10561i	−0.953514	−	0.301349i	$-0.902563\pi$
$349$	−6.71104	−	20.6544i	−0.359233	−	1.10561i	0.594280	−	0.804258i	$-0.297437\pi$
$350$	−8.14748	+	17.0433i	−0.435501	+	0.911004i
$351$	16.9578			0.905143
$352$	−1.99621	+	2.64861i	−0.106399	+	0.141171i
$353$			0.260293i			0.0138540i	0.999976	+	0.00692701i	$0.00220495\pi$
$353$			0.260293i			0.0138540i	−0.999976	+	0.00692701i	$0.997795\pi$
$354$	−6.93415	+	5.03795i	−0.368546	+	0.267764i
$355$	12.9872	+	20.6034i	0.689290	+	1.09351i
$356$	1.88197	−	5.79210i	0.0997440	−	0.306980i
$357$	−11.8476	+	16.3068i	−0.627042	+	0.863049i
$358$	−0.125256	+	0.172401i	−0.00662000	+	0.00911165i
$359$	−2.54070	+	7.81947i	−0.134093	+	0.412696i	−0.995448	−	0.0953081i	$-0.969616\pi$
$359$	−2.54070	+	7.81947i	−0.134093	+	0.412696i	0.861355	+	0.508004i	$0.169616\pi$
$360$	−0.722536	+	0.455447i	−0.0380810	+	0.0240041i
$361$	14.0099	−	10.1788i	0.737365	−	0.535727i
$362$		−	1.03818i		−	0.0545656i
$363$	9.95028	+	14.7572i	0.522254	+	0.774550i
$364$	11.7082			0.613677
$365$	−5.83651	−	4.85847i	−0.305497	−	0.254304i
$366$	−1.22866	−	3.78141i	−0.0642229	−	0.197658i
$367$	6.86029	+	2.22904i	0.358104	+	0.116355i	0.482543	−	0.875872i	$-0.339713\pi$
$367$	6.86029	+	2.22904i	0.358104	+	0.116355i	−0.124439	+	0.992227i	$0.539713\pi$
$368$	−0.327328	+	0.450528i	−0.0170632	+	0.0234854i
$369$	−1.94312	−	1.41176i	−0.101155	−	0.0734931i
$370$	1.16526	−	17.6606i	0.0605792	−	0.918133i
$371$	12.8591	+	39.5764i	0.667613	+	2.05470i
$372$	−5.08740	−	7.00220i	−0.263769	−	0.363047i
$373$		−	29.9629i		−	1.55142i	−0.631090	−	0.775709i	$-0.717392\pi$
$373$		−	29.9629i		−	1.55142i	0.631090	−	0.775709i	$-0.282608\pi$
$374$	8.73304	+	6.58195i	0.451575	+	0.340345i
$375$	−12.2623	−	13.3000i	−0.633220	−	0.686812i
$376$	−4.32760	+	3.14419i	−0.223179	+	0.162149i
$377$	−28.2086	+	9.16552i	−1.45281	+	0.472048i
$378$	−19.6626	−	6.38875i	−1.01133	−	0.328602i
$379$	−29.6962	−	21.5756i	−1.52539	−	1.10826i	−0.958732	−	0.284312i	$-0.908235\pi$
$379$	−29.6962	−	21.5756i	−1.52539	−	1.10826i	−0.566661	−	0.823951i	$-0.691765\pi$
$380$	−2.69370	−	1.07604i	−0.138184	−	0.0551996i
$381$	3.47672	−	10.7002i	0.178118	−	0.548190i
$382$	−17.0567	+	5.54206i	−0.872697	+	0.283556i
$383$	−3.79013	−	5.21666i	−0.193666	−	0.266559i	0.701130	−	0.713034i	$-0.252679\pi$
$383$	−3.79013	−	5.21666i	−0.193666	−	0.266559i	−0.894796	+	0.446475i	$0.852679\pi$
$384$	1.61803			0.0825700
$385$	6.40791	+	27.2768i	0.326577	+	1.39015i
$386$	−9.01986			−0.459099
$387$	0.812299	+	1.11803i	0.0412915	+	0.0568329i
$388$	11.7531	−	3.81883i	0.596675	−	0.193872i
$389$	8.83792	−	27.2003i	0.448100	−	1.37911i	−0.430948	−	0.902377i	$-0.641821\pi$
$389$	8.83792	−	27.2003i	0.448100	−	1.37911i	0.879048	−	0.476734i	$-0.158179\pi$
$390$	−4.15925	+	10.4121i	−0.210612	+	0.527236i
$391$	1.48549	+	1.07927i	0.0751245	+	0.0545811i
$392$	−6.91822	−	2.24787i	−0.349423	−	0.113534i
$393$	−8.64430	+	2.80870i	−0.436047	+	0.141680i
$394$	−2.98060	+	2.16553i	−0.150160	+	0.109098i
$395$	−35.4678	+	8.99123i	−1.78458	+	0.452398i
$396$	−0.412541	+	1.19778i	−0.0207310	+	0.0601909i
$397$		−	24.5049i		−	1.22987i	−0.788579	−	0.614934i	$-0.789183\pi$
$397$		−	24.5049i		−	1.22987i	0.788579	−	0.614934i	$-0.210817\pi$
$398$	2.48953	+	3.42654i	0.124789	+	0.171757i
$399$	−2.45053	−	7.54195i	−0.122680	−	0.377570i
$400$	−0.906896	−	4.91707i	−0.0453448	−	0.245853i
$401$	24.8467	+	18.0522i	1.24079	+	0.901483i	0.997650	−	0.0685091i	$-0.0218242\pi$
$401$	24.8467	+	18.0522i	1.24079	+	0.901483i	0.243135	+	0.969992i	$0.421824\pi$
$402$	−8.76158	+	12.0593i	−0.436988	+	0.601462i
$403$	15.7656	+	5.12254i	0.785338	+	0.255172i
$404$	2.78554	+	8.57301i	0.138586	+	0.426523i
$405$	11.0272	−	13.2470i	0.547945	−	0.658249i
$406$	36.1608			1.79463
$407$	−15.0557	−	21.5056i	−0.746284	−	1.06599i
$408$		−	5.33501i		−	0.264122i
$409$	17.6836	−	12.8479i	0.874397	−	0.635287i	−0.0573660	−	0.998353i	$-0.518270\pi$
$409$	17.6836	−	12.8479i	0.874397	−	0.635287i	0.931763	+	0.363066i	$0.118270\pi$
$410$	11.8946	−	7.49772i	0.587434	−	0.370286i
$411$	3.84398	−	11.8306i	0.189609	−	0.583558i
$412$	6.72071	−	9.25026i	0.331106	−	0.455728i
$413$	−11.7637	+	16.1913i	−0.578853	+	0.796723i
$414$	−0.0657312	+	0.202300i	−0.00323051	+	0.00994249i
$415$	0.348209	−	0.219491i	0.0170929	−	0.0107744i
$416$	−2.50710	+	1.82151i	−0.122921	+	0.0893070i
$417$			1.55626i			0.0762102i
$418$	−4.11450	+	1.25756i	−0.201247	+	0.0615091i
$419$	−4.17764			−0.204091			−0.102046	−	0.994780i	$-0.532539\pi$
$419$	−4.17764			−0.204091			−0.102046	+	0.994780i	$0.532539\pi$
$420$	8.74532	−	10.5058i	0.426728	−	0.512630i
$421$	3.92266	+	12.0727i	0.191179	+	0.588388i	1.00000		0.000333393i	$0.000106122\pi$
$421$	3.92266	+	12.0727i	0.191179	+	0.588388i	−0.808821	+	0.588055i	$0.799894\pi$
$422$	13.0013	+	4.22439i	0.632895	+	0.205640i
$423$	−1.20097	+	1.65300i	−0.0583932	+	0.0803714i
$424$	−8.91067	−	6.47398i	−0.432740	−	0.314404i
$425$	−16.2126	+	2.99023i	−0.786429	+	0.145048i
$426$	−5.44595	−	16.7609i	−0.263857	−	0.812068i
$427$	−5.45702	−	7.51095i	−0.264084	−	0.363480i
$428$		−	15.3546i		−	0.742194i
$429$	4.86089	+	15.9039i	0.234686	+	0.767850i
$430$	−7.84211	+	1.98801i	−0.378180	+	0.0958702i
$431$	0.591217	−	0.429545i	0.0284779	−	0.0206904i	−0.573455	−	0.819237i	$-0.694397\pi$
$431$	0.591217	−	0.429545i	0.0284779	−	0.0206904i	0.601933	+	0.798546i	$0.294397\pi$
$432$	5.20431	−	1.69098i	0.250393	−	0.0813575i
$433$	5.36947	+	1.74465i	0.258040	+	0.0838424i	0.435180	−	0.900343i	$-0.356685\pi$
$433$	5.36947	+	1.74465i	0.258040	+	0.0838424i	−0.177140	+	0.984186i	$0.556685\pi$
$434$	−16.3502	−	11.8791i	−0.784836	−	0.570217i
$435$	−12.8458	+	32.1577i	−0.615911	+	1.54184i
$436$	0.750578	−	2.31004i	0.0359462	−	0.110631i
$437$	−0.687043	+	0.223234i	−0.0328657	+	0.0106787i
$438$	3.22994	+	4.44563i	0.154333	+	0.212421i
$439$	−13.7074			−0.654220			−0.327110	−	0.944986i	$-0.606075\pi$
$439$	−13.7074			−0.654220			−0.327110	+	0.944986i	$0.606075\pi$
$440$	−5.61574	−	4.84391i	−0.267720	−	0.230924i
$441$	−2.77852			−0.132310
$442$	6.00593	+	8.26645i	0.285673	+	0.393195i
$443$	−13.3561	+	4.33967i	−0.634568	+	0.206184i	−0.608598	−	0.793479i	$-0.708268\pi$
$443$	−13.3561	+	4.33967i	−0.634568	+	0.206184i	−0.0259707	+	0.999663i	$0.508268\pi$
$444$	−3.95763	+	12.1803i	−0.187821	+	0.578052i
$445$	12.6464	+	5.05177i	0.599495	+	0.239477i
$446$	−19.3938	−	14.0904i	−0.918322	−	0.667200i
$447$	−13.5300	−	4.39616i	−0.639947	−	0.207931i
$448$	3.59321	−	1.16751i	0.169763	−	0.0551595i
$449$	7.81141	−	5.67532i	0.368643	−	0.267835i	−0.388005	−	0.921657i	$-0.626836\pi$
$449$	7.81141	−	5.67532i	0.368643	−	0.267835i	0.756648	+	0.653822i	$0.226836\pi$
$450$	−0.909830	−	1.67918i	−0.0428898	−	0.0791575i
$451$	6.79140	−	19.7183i	0.319794	−	0.928501i
$452$			8.38134i			0.394225i
$453$	−8.50038	−	11.6998i	−0.399383	−	0.549703i
$454$	−6.39803	−	19.6911i	−0.300274	−	0.924150i
$455$	−1.72365	+	26.1235i	−0.0808061	+	1.22469i
$456$	1.69808	+	1.23373i	0.0795199	+	0.0577746i
$457$	0.604702	−	0.832300i	0.0282867	−	0.0389334i	−0.794639	−	0.607082i	$-0.792340\pi$
$457$	0.604702	−	0.832300i	0.0282867	−	0.0389334i	0.822926	+	0.568148i	$0.192340\pi$
$458$	−15.5409	−	5.04955i	−0.726179	−	0.235950i
$459$	−5.57554	−	17.1597i	−0.260244	−	0.800948i
$460$	−0.957038	−	0.796665i	−0.0446221	−	0.0371447i
$461$	−8.05882			−0.375336			−0.187668	−	0.982232i	$-0.560093\pi$
$461$	−8.05882			−0.375336			−0.187668	+	0.982232i	$0.560093\pi$
$462$	0.355525	−	20.2719i	0.0165405	−	0.943133i
$463$		−	7.46633i		−	0.346990i	−0.984835	−	0.173495i	$-0.944494\pi$
$463$		−	7.46633i		−	0.346990i	0.984835	−	0.173495i	$-0.0555060\pi$
$464$	−7.74317	+	5.62574i	−0.359467	+	0.261168i
$465$	16.3724	−	10.3202i	0.759251	−	0.478590i
$466$	0.148415	−	0.456775i	0.00687520	−	0.0211597i
$467$	−6.57694	+	9.05238i	−0.304344	+	0.418894i	−0.933607	−	0.358299i	$-0.883357\pi$
$467$	−6.57694	+	9.05238i	−0.304344	+	0.418894i	0.629263	+	0.777193i	$0.283357\pi$
$468$	−0.695756	+	0.957626i	−0.0321613	+	0.0442663i
$469$	−10.7556	+	33.1024i	−0.496648	+	1.52853i
$470$	−6.37826	−	10.1187i	−0.294207	−	0.466740i
$471$	−23.0924	+	16.7776i	−1.06404	+	0.773071i
$472$		−	5.29722i		−	0.243824i
$473$	−7.22237	+	9.58276i	−0.332085	+	0.440616i
$474$	26.4765			1.21611
$475$	2.79743	−	5.85182i	0.128355	−	0.268500i
$476$	−3.84952	−	11.8476i	−0.176443	−	0.543034i
$477$	−4.00114	−	1.30005i	−0.183200	−	0.0595252i
$478$	0.663369	−	0.913049i	0.0303418	−	0.0417619i
$479$	21.6571	+	15.7348i	0.989536	+	0.718940i	0.959819	−	0.280618i	$-0.0905395\pi$
$479$	21.6571	+	15.7348i	0.989536	+	0.718940i	0.0297167	+	0.999558i	$0.490539\pi$
$480$	−0.238203	+	3.61018i	−0.0108724	+	0.164782i
$481$	−7.57985	−	23.3284i	−0.345612	−	1.06368i
$482$	−7.47781	−	10.2923i	−0.340605	−	0.468802i
$483$		−	3.40431i		−	0.154901i
$484$	−10.9932	−	0.385714i	−0.499693	−	0.0175324i
$485$	6.79036	+	26.7860i	0.308334	+	1.21629i
$486$	3.19098	−	2.31838i	0.144746	−	0.105164i
$487$	17.4787	−	5.67918i	0.792037	−	0.257348i	0.115066	−	0.993358i	$-0.463292\pi$
$487$	17.4787	−	5.67918i	0.792037	−	0.257348i	0.676971	+	0.736009i	$0.263292\pi$
$488$	2.33704	+	0.759351i	0.105793	+	0.0343742i
$489$	−0.228148	−	0.165759i	−0.0103172	−	0.00749589i
$490$	6.03396	−	15.1051i	0.272587	−	0.682380i
$491$	−8.02923	+	24.7114i	−0.362354	+	1.11521i	0.589268	+	0.807938i	$0.299416\pi$
$491$	−8.02923	+	24.7114i	−0.362354	+	1.11521i	−0.951622	+	0.307273i	$0.900584\pi$
$492$	−9.67632	+	3.14403i	−0.436242	+	0.141744i
$493$	18.5493	+	25.5309i	0.835418	+	1.14985i
$494$	−4.02001			−0.180869
$495$	−2.61178	−	1.09680i	−0.117391	−	0.0492977i
$496$	5.34921			0.240186
$497$	−24.1879	−	33.2918i	−1.08498	−	1.49334i
$498$	−0.283269	+	0.0920396i	−0.0126936	+	0.00412439i
$499$	−5.24736	+	16.1497i	−0.234904	+	0.722960i	0.762230	+	0.647306i	$0.224104\pi$
$499$	−5.24736	+	16.1497i	−0.234904	+	0.722960i	−0.997134	+	0.0756541i	$0.975896\pi$
$500$	11.1046	−	1.29960i	0.496611	−	0.0581200i
$501$	7.18170	+	5.21781i	0.320855	+	0.233115i
$502$	2.70054	+	0.877459i	0.120531	+	0.0391629i
$503$	12.7362	−	4.13825i	0.567880	−	0.184515i	−0.0109840	−	0.999940i	$-0.503496\pi$
$503$	12.7362	−	4.13825i	0.567880	−	0.184515i	0.578864	+	0.815424i	$0.303496\pi$
$504$	1.16751	−	0.848243i	0.0520048	−	0.0377837i
$505$	−19.5383	+	4.95305i	−0.869444	+	0.220408i
$506$	−1.84669	−	0.0323869i	−0.0820954	−	0.00143977i
$507$		−	5.49573i		−	0.244074i
$508$	4.08713	+	5.62545i	0.181337	+	0.249589i
$509$	6.18963	+	19.0497i	0.274351	+	0.844365i	0.989390	+	0.145281i	$0.0464086\pi$
$509$	6.18963	+	19.0497i	0.274351	+	0.844365i	−0.715040	+	0.699084i	$0.753591\pi$
$510$	11.9036	+	0.785407i	0.527099	+	0.0347784i
$511$	10.3806	+	7.54195i	0.459211	+	0.333636i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	6.75113	+	2.19357i	0.298070	+	0.0968487i
$514$	9.53038	+	29.3315i	0.420367	+	1.29376i
$515$	19.6499	+	16.3572i	0.865880	+	0.720783i
$516$	5.85410			0.257712
$517$	−16.7743	−	5.77739i	−0.737731	−	0.254090i
$518$			29.9048i			1.31394i
$519$	31.4112	−	22.8216i	1.37880	−	1.00176i
$520$	−3.69510	−	5.86204i	−0.162041	−	0.257067i
$521$	0.718847	−	2.21238i	0.0314933	−	0.0969263i	−0.934074	−	0.357079i	$-0.883773\pi$
$521$	0.718847	−	2.21238i	0.0314933	−	0.0969263i	0.965568	+	0.260152i	$0.0837728\pi$
$522$	−2.14884	+	2.95763i	−0.0940522	+	0.129452i
$523$	−11.2376	+	15.4672i	−0.491386	+	0.676335i	−0.980643	−	0.195805i	$-0.937268\pi$
$523$	−11.2376	+	15.4672i	−0.491386	+	0.676335i	0.489257	+	0.872140i	$0.337268\pi$
$524$	1.73587	−	5.34247i	0.0758320	−	0.233387i
$525$	22.1532	+	21.0593i	0.966847	+	0.919105i
$526$	−22.4154	+	16.2857i	−0.977358	+	0.710092i
$527$		−	17.6375i		−	0.768302i
$528$	3.07768	+	4.39616i	0.133939	+	0.191318i
$529$	22.6899			0.986517
$530$	15.7567	−	18.9286i	0.684426	−	0.822204i
$531$	−0.625252	−	1.92433i	−0.0271336	−	0.0835087i
$532$	4.66118	+	1.51451i	0.202088	+	0.0656623i
$533$	11.4538	−	15.7648i	0.496118	−	0.682848i
$534$	−7.97214	−	5.79210i	−0.344988	−	0.250648i
$535$	34.2595	+	2.26047i	1.48117	+	0.0977286i
$536$	−2.84681	−	8.76158i	−0.122963	−	0.378443i
$537$	0.202669	+	0.278950i	0.00874581	+	0.0120376i
$538$			12.7592i			0.550087i
$539$	−7.05184	−	23.0723i	−0.303744	−	0.993796i
$540$	3.00678	+	11.8609i	0.129391	+	0.510411i
$541$	−24.1108	+	17.5175i	−1.03660	+	0.753136i	−0.969619	−	0.244618i	$-0.921337\pi$
$541$	−24.1108	+	17.5175i	−1.03660	+	0.753136i	−0.0669831	+	0.997754i	$0.521337\pi$
$542$	5.42344	−	1.76218i	0.232957	−	0.0756922i
$543$	−1.59760	−	0.519091i	−0.0685594	−	0.0222763i
$544$	2.66751	+	1.93806i	0.114368	+	0.0830935i
$545$	5.04370	+	2.01478i	0.216049	+	0.0863037i
$546$	5.85410	−	18.0171i	0.250532	−	0.771060i
$547$	18.0221	−	5.85573i	0.770569	−	0.250373i	0.102760	−	0.994706i	$-0.467233\pi$
$547$	18.0221	−	5.85573i	0.770569	−	0.250373i	0.667808	+	0.744333i	$0.267233\pi$
$548$	4.51887	+	6.21969i	0.193036	+	0.265692i
$549$	0.938610			0.0400589
$550$	11.6345	−	11.8168i	0.496098	−	0.503871i
$551$	−12.4158			−0.528930
$552$	0.529628	+	0.728970i	0.0225425	+	0.0310270i
$553$	58.7972	−	19.1044i	2.50031	−	0.812400i
$554$	−9.80432	+	30.1746i	−0.416545	+	1.28200i
$555$	−26.5943	−	10.6235i	−1.12887	−	0.450941i
$556$	−0.778128	−	0.565343i	−0.0330000	−	0.0239759i
$557$	−6.35647	−	2.06534i	−0.269332	−	0.0875114i	0.171237	−	0.985230i	$-0.445224\pi$
$557$	−6.35647	−	2.06534i	−0.269332	−	0.0875114i	−0.440570	+	0.897718i	$0.645224\pi$
$558$	1.94321	−	0.631388i	0.0822628	−	0.0267288i
$559$	−9.07077	+	6.59030i	−0.383652	+	0.278740i
$560$	2.07597	+	8.18911i	0.0877259	+	0.346053i
$561$	14.4951	−	10.1478i	0.611984	−	0.428440i
$562$			1.93822i			0.0817589i
$563$	−5.59814	−	7.70518i	−0.235933	−	0.324735i	0.674589	−	0.738193i	$-0.264321\pi$
$563$	−5.59814	−	7.70518i	−0.235933	−	0.324735i	−0.910523	+	0.413459i	$0.864321\pi$
$564$	2.67460	+	8.23158i	0.112621	+	0.346612i
$565$	−18.7006	−	1.23388i	−0.786739	−	0.0519097i
$566$	3.97703	+	2.88948i	0.167167	+	0.121454i
$567$	−17.1178	+	23.5607i	−0.718881	+	0.989455i
$568$	10.3588	+	3.36578i	0.434646	+	0.141225i
$569$	−8.67150	−	26.6881i	−0.363528	−	1.11883i	−0.950897	−	0.309506i	$-0.899836\pi$
$569$	−8.67150	−	26.6881i	−0.363528	−	1.11883i	0.587369	−	0.809319i	$-0.300164\pi$
$570$	−3.00270	+	3.60716i	−0.125769	+	0.151087i
$571$	−1.61429			−0.0675561			−0.0337781	−	0.999429i	$-0.510754\pi$
$571$	−1.61429			−0.0675561			−0.0337781	+	0.999429i	$0.510754\pi$
$572$	−9.71779	−	3.34700i	−0.406321	−	0.139945i
$573$			29.0186i			1.21227i
$574$	−19.2199	+	13.9641i	−0.802222	+	0.582849i
$575$	1.91843	−	2.01808i	0.0800039	−	0.0841596i
$576$	−0.118034	+	0.363271i	−0.00491808	+	0.0151363i
$577$	1.92182	−	2.64516i	0.0800066	−	0.110120i	−0.767138	−	0.641482i	$-0.778320\pi$
$577$	1.92182	−	2.64516i	0.0800066	−	0.110120i	0.847145	+	0.531363i	$0.178320\pi$
$578$	−3.60215	+	4.95794i	−0.149830	+	0.206223i
$579$	−4.50993	+	13.8801i	−0.187426	+	0.576839i
$580$	−11.4123	−	18.1049i	−0.473871	−	0.751764i
$581$	−0.562651	+	0.408790i	−0.0233427	+	0.0169595i
$582$		−	19.9956i		−	0.828846i
$583$	0.640558	−	36.5243i	0.0265292	−	1.51268i
$584$	−3.39616			−0.140534
$585$	−2.03424	−	1.69336i	−0.0841056	−	0.0700119i
$586$	0.0583193	+	0.179488i	0.00240915	+	0.00741459i
$587$	3.33276	+	1.08288i	0.137558	+	0.0446952i	0.376987	−	0.926219i	$-0.376960\pi$
$587$	3.33276	+	1.08288i	0.137558	+	0.0446952i	−0.239429	+	0.970914i	$0.576960\pi$
$588$	−6.91822	+	9.52212i	−0.285303	+	0.392685i
$589$	5.61384	+	4.07869i	0.231314	+	0.168060i
$590$	11.8192	+	0.779843i	0.486590	+	0.0321056i
$591$	1.84211	+	5.66943i	0.0757742	+	0.233209i
$592$	−4.65247	−	6.40357i	−0.191215	−	0.263185i
$593$			27.6283i			1.13456i	0.823526	+	0.567278i	$0.192004\pi$
$593$			27.6283i			1.13456i	−0.823526	+	0.567278i	$0.807996\pi$
$594$	14.4935	+	10.9236i	0.594678	+	0.448199i
$595$	27.0013	−	6.84494i	1.10695	−	0.280615i
$596$	7.11314	−	5.16800i	0.291366	−	0.211689i
$597$	6.51767	−	2.11772i	0.266751	−	0.0866725i
$598$	−1.64129	−	0.533286i	−0.0671172	−	0.0218077i
$599$	−6.43434	−	4.67482i	−0.262900	−	0.191008i	0.448524	−	0.893771i	$-0.351950\pi$
$599$	−6.43434	−	4.67482i	−0.262900	−	0.191008i	−0.711425	+	0.702762i	$0.751950\pi$
$600$	−8.02003	−	1.06296i	−0.327417	−	0.0433953i
$601$	2.01909	−	6.21412i	0.0823604	−	0.253479i	−0.901394	−	0.433000i	$-0.857455\pi$
$601$	2.01909	−	6.21412i	0.0823604	−	0.253479i	0.983754	+	0.179521i	$0.0574548\pi$
$602$	13.0004	−	4.22408i	0.529855	−	0.172160i
$603$	−2.06833	−	2.84681i	−0.0842288	−	0.115931i
$604$	8.93783			0.363675
$605$	2.47901	−	24.4715i	0.100786	−	0.994908i
$606$	14.5853			0.592486
$607$	4.92460	+	6.77813i	0.199883	+	0.275116i	0.897178	−	0.441668i	$-0.145613\pi$
$607$	4.92460	+	6.77813i	0.199883	+	0.275116i	−0.697295	+	0.716784i	$0.745613\pi$
$608$	−1.23373	+	0.400863i	−0.0500343	+	0.0162571i
$609$	18.0804	−	55.6457i	0.732654	−	2.25488i
$610$	−2.03833	+	5.10266i	−0.0825296	+	0.206601i
$611$	−13.4110	−	9.74365i	−0.542550	−	0.394186i
$612$	1.19778	+	0.389184i	0.0484176	+	0.0157318i
$613$	−17.0358	+	5.53528i	−0.688071	+	0.223568i	−0.632125	−	0.774866i	$-0.717817\pi$
$613$	−17.0358	+	5.53528i	−0.688071	+	0.223568i	−0.0559453	+	0.998434i	$0.517817\pi$
$614$	10.0172	−	7.27794i	0.404262	−	0.293714i
$615$	−5.59048	−	22.0528i	−0.225430	−	0.889256i
$616$	10.0068	+	7.54195i	0.403185	+	0.303874i
$617$			21.3999i			0.861529i	0.902464	+	0.430765i	$0.141756\pi$
$617$			21.3999i			0.861529i	−0.902464	+	0.430765i	$0.858244\pi$
$618$	−10.8743	−	14.9672i	−0.437430	−	0.602071i
$619$	1.82954	+	5.63076i	0.0735356	+	0.226319i	0.981068	−	0.193662i	$-0.0620366\pi$
$619$	1.82954	+	5.63076i	0.0735356	+	0.226319i	−0.907533	+	0.419981i	$0.862037\pi$
$620$	−0.787497	+	11.9352i	−0.0316266	+	0.479331i
$621$	2.46535	+	1.79118i	0.0989312	+	0.0718777i
$622$	12.4130	−	17.0850i	0.497714	−	0.685045i
$623$	−21.8833	−	7.11031i	−0.876735	−	0.284868i
$624$	1.54947	+	4.76878i	0.0620285	+	0.190904i
$625$	1.26491	+	24.9680i	0.0505964	+	0.998719i
$626$	−16.5792			−0.662639
$627$	−0.122069	+	6.96034i	−0.00487497	+	0.277969i
$628$		−	17.6410i		−	0.703953i
$629$	−21.1140	+	15.3402i	−0.841870	+	0.611654i
$630$	1.72074	+	2.72983i	0.0685557	+	0.108759i
$631$	5.62521	−	17.3126i	0.223936	−	0.689204i	−0.774462	−	0.632620i	$-0.781979\pi$
$631$	5.62521	−	17.3126i	0.223936	−	0.689204i	0.998398	−	0.0565834i	$-0.0180207\pi$
$632$	−9.61817	+	13.2383i	−0.382590	+	0.526590i
$633$	13.0013	−	17.8948i	0.516757	−	0.711254i
$634$	−6.06817	+	18.6759i	−0.240998	+	0.741716i
$635$	−13.1533	+	8.29110i	−0.521972	+	0.329022i
$636$	−14.4178	+	10.4751i	−0.571702	+	0.415366i
$637$		−	22.5425i		−	0.893166i
$638$	−30.0134	−	10.3372i	−1.18824	−	0.409254i
$639$	4.16033			0.164580
$640$	−1.71856	−	1.43058i	−0.0679320	−	0.0565485i
$641$	5.44931	+	16.7712i	0.215235	+	0.662424i	0.999137	+	0.0415398i	$0.0132263\pi$
$641$	5.44931	+	16.7712i	0.215235	+	0.662424i	−0.783902	+	0.620884i	$0.786774\pi$
$642$	−23.6283	−	7.67731i	−0.932536	−	0.302999i
$643$	−25.8329	+	35.5559i	−1.01875	+	1.40219i	−0.105673	+	0.994401i	$0.533700\pi$
$643$	−25.8329	+	35.5559i	−1.01875	+	1.40219i	−0.913077	+	0.407788i	$0.866300\pi$
$644$	1.70215	+	1.23669i	0.0670742	+	0.0487323i
$645$	−0.861826	+	13.0618i	−0.0339344	+	0.514307i
$646$	1.32173	+	4.06787i	0.0520028	+	0.160048i
$647$	0.291613	+	0.401371i	0.0114645	+	0.0157795i	0.814711	−	0.579868i	$-0.196896\pi$
$647$	0.291613	+	0.401371i	0.0114645	+	0.0157795i	−0.803246	+	0.595647i	$0.796896\pi$
$648$		−	7.70820i		−	0.302807i
$649$	14.3924	−	10.0759i	0.564952	−	0.395514i
$650$	13.6235	−	7.38158i	0.534356	−	0.289529i
$651$	−26.4552	+	19.2208i	−1.03686	+	0.753324i
$652$	0.165759	−	0.0538584i	0.00649163	−	0.00210926i
$653$	17.2685	+	5.61086i	0.675767	+	0.219570i	0.626741	−	0.779228i	$-0.284388\pi$
$653$	17.2685	+	5.61086i	0.675767	+	0.219570i	0.0490258	+	0.998798i	$0.484388\pi$
$654$	−3.17950	−	2.31004i	−0.124328	−	0.0903297i
$655$	11.6647	+	4.65962i	0.455776	+	0.182066i
$656$	1.94312	−	5.98030i	0.0758659	−	0.233491i
$657$	−1.23373	+	0.400863i	−0.0481323	+	0.0156391i
$658$	11.8791	+	16.3502i	0.463097	+	0.637398i
$659$	14.4974			0.564739			0.282370	−	0.959306i	$-0.408880\pi$
$659$	14.4974			0.564739			0.282370	+	0.959306i	$0.408880\pi$
$660$	−10.2619	+	6.21979i	−0.399443	+	0.242105i
$661$	−11.6178			−0.451880			−0.225940	−	0.974141i	$-0.572545\pi$
$661$	−11.6178			−0.451880			−0.225940	+	0.974141i	$0.572545\pi$
$662$	−13.8027	−	18.9978i	−0.536458	−	0.738371i
$663$	15.7237	−	5.10895i	0.610659	−	0.198415i
$664$	0.0568836	−	0.175070i	0.00220751	−	0.00679402i
$665$	−4.06541	+	10.1771i	−0.157650	+	0.394653i
$666$	−2.44595	−	1.77708i	−0.0947785	−	0.0688606i
$667$	−5.06911	−	1.64705i	−0.196277	−	0.0637742i
$668$	−5.21781	+	1.69537i	−0.201883	+	0.0655958i
$669$	−31.3798	+	22.7988i	−1.21321	+	0.881451i
$670$	19.9681	−	5.06199i	0.771434	−	0.195562i
$671$	2.38218	+	7.79406i	0.0919630	+	0.300886i
$672$		−	6.11314i		−	0.235819i
$673$	−20.9418	−	28.8239i	−0.807246	−	1.11108i	−0.991743	−	0.128245i	$-0.959066\pi$
$673$	−20.9418	−	28.8239i	−0.807246	−	1.11108i	0.184497	−	0.982833i	$-0.440934\pi$
$674$	3.96317	+	12.1974i	0.152656	+	0.469825i
$675$	−26.9069	+	4.96266i	−1.03565	+	0.191013i
$676$	2.74787	+	1.99644i	0.105687	+	0.0767862i
$677$	−14.4064	+	19.8288i	−0.553684	+	0.762081i	−0.990506	−	0.137467i	$-0.956104\pi$
$677$	−14.4064	+	19.8288i	−0.553684	+	0.762081i	0.436822	+	0.899548i	$0.356104\pi$
$678$	12.8976	+	4.19067i	0.495328	+	0.160942i
$679$	−14.4280	−	44.4049i	−0.553696	−	1.70410i
$680$	−4.71693	+	5.66647i	−0.180886	+	0.217299i
$681$	−33.5005			−1.28374
$682$	10.1748	+	14.5337i	0.389613	+	0.556523i
$683$		−	25.5212i		−	0.976540i	−0.872693	−	0.488270i	$-0.837628\pi$
$683$		−	25.5212i		−	0.976540i	0.872693	−	0.488270i	$-0.162372\pi$
$684$	−0.400863	+	0.291244i	−0.0153274	+	0.0111360i
$685$	−14.5427	+	9.16693i	−0.555649	+	0.350250i
$686$	−0.320187	+	0.985436i	−0.0122248	+	0.0376241i
$687$	−15.5409	+	21.3902i	−0.592922	+	0.816088i
$688$	−2.12663	+	2.92705i	−0.0810769	+	0.111593i
$689$	10.5475	−	32.4618i	0.401827	−	1.23670i
$690$	−1.70446	+	1.07440i	−0.0648877	+	0.0409016i
$691$	36.7992	−	26.7362i	1.39991	−	1.01709i	0.405215	−	0.914222i	$-0.367197\pi$
$691$	36.7992	−	26.7362i	1.39991	−	1.01709i	0.994695	−	0.102872i	$-0.0328032\pi$
$692$			23.9960i			0.912192i
$693$	4.52538	+	1.55863i	0.171905	+	0.0592076i
$694$	20.6936			0.785519
$695$	1.37596	−	1.65294i	0.0521930	−	0.0626997i
$696$	4.78554	+	14.7284i	0.181395	+	0.558278i
$697$	−19.7183	−	6.40688i	−0.746886	−	0.242678i
$698$	12.7651	−	17.5697i	0.483168	−	0.665024i
$699$	−0.628696	−	0.456775i	−0.0237795	−	0.0172768i
$700$	−18.5773	+	3.42637i	−0.702156	+	0.129505i
$701$	−9.00678	−	27.7200i	−0.340182	−	1.04697i	−0.964113	−	0.265492i	$-0.914466\pi$
$701$	−9.00678	−	27.7200i	−0.340182	−	1.04697i	0.623932	−	0.781479i	$-0.285534\pi$
$702$	9.96757	+	13.7192i	0.376202	+	0.517797i
$703$		−	10.2678i		−	0.387258i
$704$	−3.31611	−	0.0581575i	−0.124981	−	0.00219189i
$705$	−18.7602	+	4.75579i	−0.706550	+	0.179113i
$706$	−0.210582	+	0.152997i	−0.00792535	+	0.00575810i
$707$	32.3899	−	10.5241i	1.21815	−	0.395800i
$708$	−8.15158	−	2.64861i	−0.306355	−	0.0995408i
$709$	25.0122	+	18.1724i	0.939353	+	0.682480i	0.948265	−	0.317480i	$-0.102837\pi$
$709$	25.0122	+	18.1724i	0.939353	+	0.682480i	−0.00891175	+	0.999960i	$0.502837\pi$
$710$	−9.03478	+	22.6172i	−0.339069	+	0.848810i
$711$	−1.93144	+	5.94435i	−0.0724346	+	0.222931i
$712$	5.79210	−	1.88197i	0.217068	−	0.0705297i
$713$	1.75095	+	2.40997i	0.0655734	+	0.0902541i
$714$	−20.1564			−0.754333
$715$	8.89852	−	21.1898i	0.332786	−	0.792452i
$716$	−0.213099			−0.00796388
$717$	−1.07335	−	1.47734i	−0.0400851	−	0.0551725i
$718$	−7.81947	+	2.54070i	−0.291820	+	0.0948180i
$719$	5.42235	−	16.6883i	0.202220	−	0.622368i	−0.797597	−	0.603191i	$-0.793896\pi$
$719$	5.42235	−	16.6883i	0.202220	−	0.622368i	0.999816	−	0.0191765i	$-0.00610444\pi$
$720$	−0.793160	−	0.316839i	−0.0295593	−	0.0118079i
$721$	−34.9487	−	25.3917i	−1.30156	−	0.945636i
$722$	16.4697	+	5.35132i	0.612937	+	0.199155i
$723$	−19.5772	+	6.36101i	−0.728083	+	0.236568i
$724$	0.839906	−	0.610228i	0.0312149	−	0.0226789i
$725$	42.0760	−	22.7980i	1.56266	−	0.846696i
$726$	−6.09017	+	16.7240i	−0.226027	+	0.620686i
$727$			16.7731i			0.622080i	0.950397	+	0.311040i	$0.100677\pi$
$727$			16.7731i			0.622080i	−0.950397	+	0.311040i	$0.899323\pi$
$728$	6.88191	+	9.47214i	0.255061	+	0.351061i
$729$	−9.11803	−	28.0624i	−0.337705	−	1.03935i
$730$	0.499974	−	7.57757i	0.0185049	−	0.280459i
$731$	9.65113	+	7.01195i	0.356960	+	0.259346i
$732$	2.33704	−	3.21666i	0.0863796	−	0.118891i
$733$	−8.79812	−	2.85868i	−0.324966	−	0.105588i	0.141991	−	0.989868i	$-0.454650\pi$
$733$	−8.79812	−	2.85868i	−0.324966	−	0.105588i	−0.466957	+	0.884280i	$0.654650\pi$
$734$	2.22904	+	6.86029i	0.0822755	+	0.253218i
$735$	−20.2274	−	16.8379i	−0.746100	−	0.621074i
$736$	−0.556884			−0.0205270
$737$	18.3901	−	24.4002i	0.677407	−	0.898794i
$738$		−	2.40182i		−	0.0884124i
$739$	6.06468	−	4.40625i	0.223093	−	0.162087i	−0.470625	−	0.882333i	$-0.655971\pi$
$739$	6.06468	−	4.40625i	0.223093	−	0.162087i	0.693718	+	0.720247i	$0.255971\pi$
$740$	14.9727	−	9.43795i	0.550407	−	0.346946i
$741$	−2.01000	+	6.18615i	−0.0738393	+	0.227254i
$742$	−24.4595	+	33.6657i	−0.897938	+	1.23591i
$743$	−3.82251	+	5.26124i	−0.140234	+	0.193016i	−0.873357	−	0.487080i	$-0.838062\pi$
$743$	−3.82251	+	5.26124i	−0.140234	+	0.193016i	0.733123	+	0.680096i	$0.238062\pi$
$744$	2.67460	−	8.23158i	0.0980557	−	0.301784i
$745$	10.4837	+	16.6318i	0.384095	+	0.609341i
$746$	24.2405	−	17.6117i	0.887507	−	0.644811i
$747$		−	0.0703120i		−	0.00257258i
$748$	−0.191758	+	10.9340i	−0.00701136	+	0.399785i
$749$	−58.0118			−2.11970
$750$	3.55239	−	17.7379i	0.129715	−	0.647698i
$751$	6.27064	+	19.2991i	0.228819	+	0.704232i	0.997881	+	0.0650587i	$0.0207235\pi$
$751$	6.27064	+	19.2991i	0.228819	+	0.704232i	−0.769062	+	0.639174i	$0.779277\pi$
$752$	−5.08740	−	1.65300i	−0.185518	−	0.0602786i
$753$	2.70054	−	3.71698i	0.0984132	−	0.135454i
$754$	−23.9956	−	17.4338i	−0.873869	−	0.634903i
$755$	−1.31581	+	19.9422i	−0.0478871	+	0.725772i
$756$	−6.38875	−	19.6626i	−0.232357	−	0.715120i
$757$	10.8452	+	14.9271i	0.394174	+	0.542534i	0.959270	−	0.282492i	$-0.0911609\pi$
$757$	10.8452	+	14.9271i	0.394174	+	0.542534i	−0.565096	+	0.825025i	$0.691161\pi$
$758$		−	36.7066i		−	1.33324i
$759$	−0.973183	+	2.82557i	−0.0353243	+	0.102562i
$760$	−0.712785	−	2.81173i	−0.0258554	−	0.101992i
$761$	11.0383	−	8.01981i	0.400139	−	0.290718i	−0.369459	−	0.929247i	$-0.620457\pi$
$761$	11.0383	−	8.01981i	0.400139	−	0.290718i	0.769598	+	0.638529i	$0.220457\pi$
$762$	10.7002	−	3.47672i	0.387629	−	0.125948i
$763$	−8.72763	−	2.83578i	−0.315961	−	0.102662i
$764$	−14.5093	−	10.5416i	−0.524928	−	0.381383i
$765$	−1.04469	+	2.61522i	−0.0377708	+	0.0945536i
$766$	1.99259	−	6.13256i	0.0719951	−	0.221578i
$767$	15.6123	−	5.07275i	0.563729	−	0.183167i
$768$	0.951057	+	1.30902i	0.0343183	+	0.0472351i
$769$	6.77400			0.244277			0.122138	−	0.992513i	$-0.461025\pi$
$769$	6.77400			0.244277			0.122138	+	0.992513i	$0.461025\pi$
$770$	−18.3009	+	21.2170i	−0.659519	+	0.764607i
$771$	49.9017			1.79717
$772$	−5.30174	−	7.29722i	−0.190814	−	0.262633i
$773$	−17.8559	+	5.80173i	−0.642231	+	0.208674i	−0.611986	−	0.790869i	$-0.709629\pi$
$773$	−17.8559	+	5.80173i	−0.642231	+	0.208674i	−0.0302456	+	0.999542i	$0.509629\pi$
$774$	−0.427051	+	1.31433i	−0.0153500	+	0.0472425i
$775$	−26.5142	−	3.51415i	−0.952417	−	0.126232i
$776$	9.99782	+	7.26384i	0.358901	+	0.260757i
$777$	46.0188	+	14.9524i	1.65092	+	0.536415i
$778$	27.2003	−	8.83792i	0.975178	−	0.316855i
$779$	6.59914	−	4.79455i	0.236439	−	0.171783i
$780$	−10.8683	+	2.75516i	−0.389147	+	0.0986505i
$781$	10.5589	+	34.5467i	0.377826	+	1.23618i
$782$			1.83617i			0.0656612i
$783$	30.7848	+	42.3717i	1.10016	+	1.51424i
$784$	−2.24787	−	6.91822i	−0.0802810	−	0.247079i
$785$	39.3609	+	2.59706i	1.40485	+	0.0926932i
$786$	−7.35328	−	5.34247i	−0.262283	−	0.190560i
$787$	−16.1285	+	22.1990i	−0.574921	+	0.791310i	−0.993127	−	0.117042i	$-0.962659\pi$
$787$	−16.1285	+	22.1990i	−0.574921	+	0.791310i	0.418206	+	0.908352i	$0.362659\pi$
$788$	−3.50390	−	1.13849i	−0.124821	−	0.0405569i
$789$	13.8535	+	42.6366i	0.493197	+	1.51790i
$790$	−28.1215	−	23.4091i	−1.00052	−	0.832859i
$791$	31.6658			1.12590
$792$	−1.21151	+	0.370287i	−0.0430493	+	0.0131576i
$793$			7.61507i			0.270419i
$794$	19.8249	−	14.4036i	0.703560	−	0.511166i
$795$	−21.2497	−	33.7113i	−0.753650	−	1.19562i
$796$	−1.30882	+	4.02814i	−0.0463900	+	0.142774i
$797$	31.6667	−	43.5855i	1.12169	−	1.54388i	0.318732	−	0.947845i	$-0.396743\pi$
$797$	31.6667	−	43.5855i	1.12169	−	1.54388i	0.802960	−	0.596032i	$-0.203257\pi$
$798$	4.66118	−	6.41557i	0.165004	−	0.227109i
$799$	−5.45029	+	16.7743i	−0.192817	+	0.593431i
$800$	3.44493	−	3.62387i	0.121797	−	0.128123i
$801$	1.88197	−	1.36733i	0.0664960	−	0.0483122i
$802$			30.7122i			1.08449i
$803$	−6.45988	−	9.22729i	−0.227964	−	0.325624i
$804$	−14.9061			−0.525697
$805$	−3.00990	+	3.61581i	−0.106085	+	0.127441i
$806$	5.12254	+	15.7656i	0.180434	+	0.555318i
$807$	19.6344	+	6.37959i	0.691162	+	0.224572i
$808$	−5.29841	+	7.29264i	−0.186397	+	0.256554i
$809$	26.1612	+	19.0073i	0.919781	+	0.668260i	0.943469	−	0.331460i	$-0.107541\pi$
$809$	26.1612	+	19.0073i	0.919781	+	0.668260i	−0.0236888	+	0.999719i	$0.507541\pi$
$810$	17.1987	+	1.13478i	0.604300	+	0.0398722i
$811$	14.1920	+	43.6785i	0.498349	+	1.53376i	0.811671	+	0.584114i	$0.198558\pi$
$811$	14.1920	+	43.6785i	0.498349	+	1.53376i	−0.313322	+	0.949647i	$0.601442\pi$
$812$	21.2548	+	29.2547i	0.745896	+	1.02664i
$813$		−	9.22691i		−	0.323602i
$814$	8.54884	−	24.8210i	0.299637	−	0.869975i
$815$	0.0957671	+	0.377773i	0.00335458	+	0.0132328i
$816$	4.31611	−	3.13584i	0.151094	−	0.109776i
$817$	−4.46367	+	1.45033i	−0.156164	+	0.0507408i
$818$	20.7883	+	6.75453i	0.726846	+	0.236167i
$819$	3.61803	+	2.62866i	0.126424	+	0.0918527i
$820$	13.0573	+	5.21592i	0.455980	+	0.182148i
$821$	8.78690	−	27.0433i	0.306665	−	0.943818i	−0.672386	−	0.740201i	$-0.734730\pi$
$821$	8.78690	−	27.0433i	0.306665	−	0.943818i	0.979051	−	0.203617i	$-0.0652697\pi$
$822$	11.8306	−	3.84398i	0.412638	−	0.134074i
$823$	6.09146	+	8.38417i	0.212335	+	0.292254i	0.901878	−	0.431991i	$-0.142189\pi$
$823$	6.09146	+	8.38417i	0.212335	+	0.292254i	−0.689543	+	0.724245i	$0.742189\pi$
$824$	11.4340			0.398321
$825$	−12.3670	−	23.8121i	−0.430562	−	0.829032i
$826$	−20.0136			−0.696361
$827$	11.5254	+	15.8634i	0.400779	+	0.551625i	0.960939	−	0.276760i	$-0.0892605\pi$
$827$	11.5254	+	15.8634i	0.400779	+	0.551625i	−0.560161	+	0.828384i	$0.689261\pi$
$828$	−0.202300	+	0.0657312i	−0.00703040	+	0.00228432i
$829$	−15.4118	+	47.4327i	−0.535275	+	1.64741i	0.207780	+	0.978176i	$0.433376\pi$
$829$	−15.4118	+	47.4327i	−0.535275	+	1.64741i	−0.743054	+	0.669231i	$0.766624\pi$
$830$	0.382244	+	0.152693i	0.0132679	+	0.00530005i
$831$	41.5317	+	30.1746i	1.44072	+	1.04674i
$832$	−2.94727	−	0.957626i	−0.102178	−	0.0331997i
$833$	−22.8109	+	7.41171i	−0.790350	+	0.256800i
$834$	−1.25904	+	0.914744i	−0.0435969	+	0.0316750i
$835$	−3.01458	−	11.8917i	−0.104324	−	0.411528i
$836$	−3.43582	−	2.58953i	−0.118830	−	0.0895606i
$837$		−	29.2716i		−	1.01177i
$838$	−2.45556	−	3.37978i	−0.0848258	−	0.116753i
$839$	3.25249	+	10.0101i	0.112289	+	0.345589i	0.991372	−	0.131080i	$-0.0418443\pi$
$839$	3.25249	+	10.0101i	0.112289	+	0.345589i	−0.879083	+	0.476668i	$0.841844\pi$
$840$	13.6397	+	0.899961i	0.470616	+	0.0310516i
$841$	−50.6490	−	36.7986i	−1.74652	−	1.26892i
$842$	−7.46135	+	10.2697i	−0.257135	+	0.353916i
$843$	2.98262	+	0.969111i	0.102727	+	0.0333779i
$844$	4.22439	+	13.0013i	0.145409	+	0.447524i
$845$	−4.85903	+	5.83717i	−0.167156	+	0.200805i
$846$	−2.04322			−0.0702472
$847$	−1.45728	+	41.5338i	−0.0500726	+	1.42712i
$848$		−	11.0142i		−	0.378229i
$849$	6.43497	−	4.67528i	0.220848	−	0.160455i
$850$	−11.9487	−	11.3587i	−0.409837	−	0.389600i
$851$	1.36211	−	4.19214i	0.0466925	−	0.143705i
$852$	10.3588	−	14.2577i	0.354887	−	0.488460i
$853$	−9.24016	+	12.7180i	−0.316377	+	0.435456i	−0.937357	−	0.348371i	$-0.886735\pi$
$853$	−9.24016	+	12.7180i	−0.316377	+	0.435456i	0.620980	+	0.783827i	$0.286735\pi$
$854$	2.86893	−	8.82965i	0.0981726	−	0.302144i
$855$	−0.590814	−	0.937287i	−0.0202054	−	0.0320545i
$856$	12.4222	−	9.02522i	0.424581	−	0.308476i
$857$			37.8967i			1.29453i	0.762267	+	0.647263i	$0.224086\pi$
$857$			37.8967i			1.29453i	−0.762267	+	0.647263i	$0.775914\pi$
$858$	−10.0094	+	13.2806i	−0.341716	+	0.453394i
$859$	−20.5913			−0.702567			−0.351283	−	0.936269i	$-0.614255\pi$
$859$	−20.5913			−0.702567			−0.351283	+	0.936269i	$0.614255\pi$
$860$	−6.21781	−	5.17588i	−0.212025	−	0.176496i
$861$	11.8785	+	36.5584i	0.404820	+	1.24591i
$862$	0.695018	+	0.225825i	0.0236724	+	0.00769163i
$863$	−5.05094	+	6.95203i	−0.171936	+	0.236650i	−0.886285	−	0.463140i	$-0.846723\pi$
$863$	−5.05094	+	6.95203i	−0.171936	+	0.236650i	0.714349	+	0.699789i	$0.246723\pi$
$864$	4.42705	+	3.21644i	0.150611	+	0.109426i
$865$	−53.5403	−	3.53263i	−1.82043	−	0.120113i
$866$	1.74465	+	5.36947i	0.0592855	+	0.182462i
$867$	5.82841	+	8.02212i	0.197943	+	0.272445i
$868$		−	20.2100i		−	0.685972i
$869$	−54.2629	−	0.951654i	−1.84074	−	0.0322826i
$870$	−33.5667	+	8.50930i	−1.13802	+	0.288492i
$871$	23.0966	−	16.7806i	0.782597	−	0.568590i
$872$	2.31004	−	0.750578i	0.0782279	−	0.0254178i
$873$	4.48930	+	1.45866i	0.151940	+	0.0493682i
$874$	−0.584434	−	0.424616i	−0.0197688	−	0.0143628i
$875$	−4.91006	−	41.9544i	−0.165990	−	1.41832i
$876$	−1.69808	+	5.22616i	−0.0573728	+	0.176575i
$877$	−42.9395	+	13.9519i	−1.44996	+	0.471122i	−0.924989	−	0.379995i	$-0.875926\pi$
$877$	−42.9395	+	13.9519i	−1.44996	+	0.471122i	−0.524976	+	0.851117i	$0.675926\pi$
$878$	−8.05702	−	11.0895i	−0.271911	−	0.374254i
$879$	0.305364			0.0102997
$880$	0.617952	−	7.39041i	0.0208312	−	0.249131i
$881$	−38.4847			−1.29658			−0.648291	−	0.761393i	$-0.724516\pi$
$881$	−38.4847			−1.29658			−0.648291	+	0.761393i	$0.724516\pi$
$882$	−1.63317	−	2.24787i	−0.0549917	−	0.0756896i
$883$	37.3951	−	12.1504i	1.25845	−	0.408894i	0.397505	−	0.917600i	$-0.369876\pi$
$883$	37.3951	−	12.1504i	1.25845	−	0.408894i	0.860940	+	0.508706i	$0.169876\pi$
$884$	−3.15750	+	9.71779i	−0.106198	+	0.326845i
$885$	7.10968	−	17.7980i	0.238989	−	0.598274i
$886$	−11.3614	−	8.25454i	−0.381693	−	0.277317i
$887$	7.46016	+	2.42395i	0.250488	+	0.0813883i	0.431570	−	0.902080i	$-0.357960\pi$
$887$	7.46016	+	2.42395i	0.250488	+	0.0813883i	−0.181082	+	0.983468i	$0.557960\pi$
$888$	−12.1803	+	3.95763i	−0.408745	+	0.132809i
$889$	21.2537	−	15.4417i	0.712825	−	0.517897i
$890$	3.34638	+	13.2005i	0.112171	+	0.442481i
$891$	20.9430	−	14.6619i	0.701617	−	0.491191i
$892$		−	23.9720i		−	0.802643i
$893$	−4.07869	−	5.61384i	−0.136488	−	0.187860i
$894$	−4.39616	−	13.5300i	−0.147030	−	0.452511i
$895$	0.0313719	−	0.475470i	0.00104865	−	0.0158932i
$896$	3.05657	+	2.22073i	0.102113	+	0.0741893i
$897$	−1.64129	+	2.25904i	−0.0548010	+	0.0754271i
$898$	9.18287	+	2.98369i	0.306436	+	0.0995672i
$899$	15.8210	+	48.6919i	0.527658	+	1.62397i
$900$	0.823704	−	1.72307i	0.0274568	−	0.0574356i
$901$	−36.3162			−1.20987
$902$	19.9444	−	6.09580i	0.664075	−	0.202968i
$903$		−	22.1175i		−	0.736026i
$904$	−6.78064	+	4.92643i	−0.225521	+	0.163851i
$905$	1.23790	+	1.96385i	0.0411492	+	0.0652805i
$906$	4.46892	−	13.7539i	0.148470	−	0.456943i
$907$	26.0762	−	35.8908i	0.865845	−	1.19173i	−0.114299	−	0.993446i	$-0.536462\pi$
$907$	26.0762	−	35.8908i	0.865845	−	1.19173i	0.980144	−	0.198287i	$-0.0635379\pi$
$908$	12.1698	−	16.7503i	0.403868	−	0.555877i
$909$	−1.06398	+	3.27460i	−0.0352900	+	0.108612i
$910$	−22.1475	+	13.9606i	−0.734183	+	0.462788i
$911$	−11.2063	+	8.14186i	−0.371282	+	0.269752i	−0.757742	−	0.652554i	$-0.773698\pi$
$911$	−11.2063	+	8.14186i	−0.371282	+	0.269752i	0.386460	+	0.922306i	$0.373698\pi$
$912$			2.09894i			0.0695030i
$913$	0.583860	−	0.178451i	0.0193229	−	0.00590587i
$914$	1.02878			0.0340290
$915$	6.83302	+	5.68800i	0.225893	+	0.188039i
$916$	−5.04955	−	15.5409i	−0.166842	−	0.513486i
$917$	−20.1845	−	6.55835i	−0.666552	−	0.216576i
$918$	10.6053	−	14.5970i	0.350027	−	0.481771i
$919$	−12.3286	−	8.95726i	−0.406684	−	0.295473i	0.365574	−	0.930782i	$-0.380873\pi$
$919$	−12.3286	−	8.95726i	−0.406684	−	0.295473i	−0.772258	+	0.635309i	$0.780873\pi$
$920$	0.0819830	−	1.24253i	0.00270290	−	0.0409649i
$921$	−6.19098	−	19.0539i	−0.204000	−	0.627847i
$922$	−4.73685	−	6.51972i	−0.156000	−	0.214716i
$923$			33.7534i			1.11101i
$924$	16.6093	−	11.6279i	0.546405	−	0.382529i
$925$	18.8539	+	34.7967i	0.619911	+	1.14411i
$926$	6.04038	−	4.38860i	0.198499	−	0.144218i
$927$	4.15363	−	1.34960i	0.136423	−	0.0443265i
$928$	−9.10264	−	2.95763i	−0.298809	−	0.0970888i
$929$	30.6793	+	22.2898i	1.00656	+	0.731306i	0.963484	−	0.267766i	$-0.0862855\pi$
$929$	30.6793	+	22.2898i	1.00656	+	0.731306i	0.0430721	+	0.999072i	$0.486285\pi$
$930$	17.9727	+	7.17945i	0.589348	+	0.235424i
$931$	2.91597	−	8.97444i	0.0955672	−	0.294126i
$932$	0.456775	−	0.148415i	0.0149621	−	0.00486150i
$933$	−20.0846	−	27.6440i	−0.657540	−	0.905025i
$934$	−11.1894			−0.366127
$935$	−24.3678	−	2.03752i	−0.796912	−	0.0666341i
$936$	−1.18369			−0.0386902
$937$	−3.21963	−	4.43144i	−0.105181	−	0.144769i	0.753182	−	0.657812i	$-0.228518\pi$
$937$	−3.21963	−	4.43144i	−0.105181	−	0.144769i	−0.858363	+	0.513043i	$0.828518\pi$
$938$	−33.1024	+	10.7556i	−1.08083	+	0.351183i
$939$	−8.28961	+	25.5128i	−0.270521	+	0.832579i
$940$	4.43715	−	11.1077i	0.144724	−	0.362294i
$941$	−37.5713	−	27.2971i	−1.22479	−	0.889861i	−0.228301	−	0.973591i	$-0.573317\pi$
$941$	−37.5713	−	27.2971i	−1.22479	−	0.889861i	−0.996489	+	0.0837293i	$0.973317\pi$
$942$	−27.1467	−	8.82050i	−0.884488	−	0.287387i
$943$	3.33033	−	1.08209i	0.108450	−	0.0352377i
$944$	4.28554	−	3.11363i	0.139482	−	0.101340i
$945$	44.8119	−	11.3600i	1.45773	−	0.369541i
$946$	−11.9978	−	0.210416i	−0.390083	−	0.00684120i
$947$			22.7220i			0.738366i	0.929357	+	0.369183i	$0.120362\pi$
$947$			22.7220i			0.738366i	−0.929357	+	0.369183i	$0.879638\pi$
$948$	15.5625	+	21.4200i	0.505447	+	0.695688i
$949$	−3.25225	−	10.0094i	−0.105573	−	0.324919i
$950$	6.37851	−	1.17644i	0.206946	−	0.0381688i
$951$	25.7052	+	18.6759i	0.833548	+	0.605608i
$952$	7.32222	−	10.0782i	0.237315	−	0.326636i
$953$	−34.2554	−	11.1302i	−1.10964	−	0.360544i	−0.303835	−	0.952725i	$-0.598267\pi$
$953$	−34.2554	−	11.1302i	−1.10964	−	0.360544i	−0.805805	+	0.592181i	$0.798267\pi$
$954$	−1.30005	−	4.00114i	−0.0420907	−	0.129542i
$955$	25.6567	−	30.8215i	0.830230	−	0.997360i
$956$	1.12859			0.0365012
$957$	−30.9140	+	41.0172i	−0.999309	+	1.32590i
$958$			26.7696i			0.864886i
$959$	23.4988	−	17.0729i	0.758815	−	0.551311i
$960$	−3.06071	+	1.92930i	−0.0987841	+	0.0622680i
$961$	−0.737310	+	2.26921i	−0.0237842	+	0.0732002i
$962$	14.4177	−	19.8443i	0.464846	−	0.639806i
$963$	3.44733	−	4.74484i	0.111089	−	0.152900i
$964$	3.93132	−	12.0994i	0.126619	−	0.389694i
$965$	17.0622	−	10.7551i	0.549251	−	0.346217i
$966$	2.75414	−	2.00100i	0.0886131	−	0.0643812i
$967$			23.8349i			0.766479i	0.923649	+	0.383240i	$0.125192\pi$
$967$			23.8349i			0.766479i	−0.923649	+	0.383240i	$0.874808\pi$
$968$	−6.14961	−	9.12043i	−0.197656	−	0.293142i
$969$	6.92067			0.222324
$970$	−17.6790	+	21.2379i	−0.567640	+	0.681909i
$971$	−10.9297	−	33.6381i	−0.350750	−	1.07950i	−0.958433	−	0.285319i	$-0.907901\pi$
$971$	−10.9297	−	33.6381i	−0.350750	−	1.07950i	0.607682	−	0.794180i	$-0.292099\pi$
$972$	3.75123	+	1.21885i	0.120321	+	0.0390945i
$973$	−2.13594	+	2.93987i	−0.0684750	+	0.0942478i
$974$	14.8683	+	10.8025i	0.476411	+	0.346133i
$975$	−4.54735	−	24.6551i	−0.145632	−	0.789596i
$976$	0.759351	+	2.33704i	0.0243062	+	0.0748069i
$977$	−6.63066	−	9.12632i	−0.212134	−	0.291977i	0.689669	−	0.724124i	$-0.257756\pi$
$977$	−6.63066	−	9.12632i	−0.212134	−	0.291977i	−0.901803	+	0.432148i	$0.857756\pi$
$978$		−	0.282006i		−	0.00901757i
$979$	16.1305	+	12.1573i	0.515532	+	0.388548i
$980$	15.7670	−	3.99699i	0.503658	−	0.127679i
$981$	0.750578	−	0.545327i	0.0239641	−	0.0174109i
$982$	−24.7114	+	8.02923i	−0.788573	+	0.256223i
$983$	−8.14486	−	2.64643i	−0.259781	−	0.0844079i	0.176231	−	0.984349i	$-0.443609\pi$
$983$	−8.14486	−	2.64643i	−0.259781	−	0.0844079i	−0.436012	+	0.899941i	$0.643609\pi$
$984$	−8.23117	−	5.98030i	−0.262400	−	0.190645i
$985$	3.05604	−	7.65035i	0.0973737	−	0.243761i
$986$	−9.75194	+	30.0134i	−0.310565	+	0.955821i
$987$	31.1000	−	10.1050i	0.989923	−	0.321645i
$988$	−2.36290	−	3.25225i	−0.0751739	−	0.103468i
$989$	−2.01482			−0.0640677
$990$	−0.647835	−	2.75766i	−0.0205896	−	0.0876443i
$991$	−15.9978			−0.508185			−0.254093	−	0.967180i	$-0.581777\pi$
$991$	−15.9978			−0.508185			−0.254093	+	0.967180i	$0.581777\pi$
$992$	3.14419	+	4.32760i	0.0998280	+	0.137401i
$993$	−36.1360	+	11.7413i	−1.14674	+	0.372599i
$994$	12.7163	−	39.1369i	0.403338	−	1.24135i
$995$	−8.79498	−	3.51328i	−0.278820	−	0.111378i
$996$	−0.240963	−	0.175070i	−0.00763520	−	0.00554730i
$997$	27.0137	+	8.77729i	0.855533	+	0.277979i	0.703762	−	0.710436i	$-0.251502\pi$
$997$	27.0137	+	8.77729i	0.855533	+	0.277979i	0.151771	+	0.988416i	$0.451502\pi$
$998$	−16.1497	+	5.24736i	−0.511210	+	0.166102i
$999$	−35.0412	+	25.4589i	−1.10866	+	0.805485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.j.b.69.3	yes	16
3.2	odd	2		990.2.ba.h.289.2		16
4.3	odd	2		880.2.cd.b.289.1		16
5.2	odd	4		550.2.h.j.201.1		8
5.3	odd	4		550.2.h.n.201.2		8
5.4	even	2	inner	110.2.j.b.69.1	yes	16
11.2	odd	10		1210.2.b.l.969.6		8
11.4	even	5	inner	110.2.j.b.59.1	✓	16
11.9	even	5		1210.2.b.k.969.2		8
15.14	odd	2		990.2.ba.h.289.4		16
20.19	odd	2		880.2.cd.b.289.3		16
33.26	odd	10		990.2.ba.h.829.4		16
44.15	odd	10		880.2.cd.b.609.3		16
55.2	even	20		6050.2.a.da.1.2		4
55.4	even	10	inner	110.2.j.b.59.3	yes	16
55.9	even	10		1210.2.b.k.969.8		8
55.13	even	20		6050.2.a.dl.1.3		4
55.24	odd	10		1210.2.b.l.969.4		8
55.37	odd	20		550.2.h.j.301.1		8
55.42	odd	20		6050.2.a.di.1.1		4
55.48	odd	20		550.2.h.n.301.2		8
55.53	odd	20		6050.2.a.dd.1.4		4
165.59	odd	10		990.2.ba.h.829.2		16
220.59	odd	10		880.2.cd.b.609.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.1	✓	16	11.4	even	5	inner
110.2.j.b.59.3	yes	16	55.4	even	10	inner
110.2.j.b.69.1	yes	16	5.4	even	2	inner
110.2.j.b.69.3	yes	16	1.1	even	1	trivial
550.2.h.j.201.1		8	5.2	odd	4
550.2.h.j.301.1		8	55.37	odd	20
550.2.h.n.201.2		8	5.3	odd	4
550.2.h.n.301.2		8	55.48	odd	20
880.2.cd.b.289.1		16	4.3	odd	2
880.2.cd.b.289.3		16	20.19	odd	2
880.2.cd.b.609.1		16	220.59	odd	10
880.2.cd.b.609.3		16	44.15	odd	10
990.2.ba.h.289.2		16	3.2	odd	2
990.2.ba.h.289.4		16	15.14	odd	2
990.2.ba.h.829.2		16	165.59	odd	10
990.2.ba.h.829.4		16	33.26	odd	10
1210.2.b.k.969.2		8	11.9	even	5
1210.2.b.k.969.8		8	55.9	even	10
1210.2.b.l.969.4		8	55.24	odd	10
1210.2.b.l.969.6		8	11.2	odd	10
6050.2.a.da.1.2		4	55.2	even	20
6050.2.a.dd.1.4		4	55.53	odd	20
6050.2.a.di.1.1		4	55.42	odd	20
6050.2.a.dl.1.3		4	55.13	even	20

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(1.53884 - 0.500000i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.07652 - 0.829496i) q^{5} +(1.30902 + 0.951057i) q^{6} +(3.59321 + 1.16751i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 + 0.224514i) q^{9} +(-0.549472 - 2.16751i) q^{10} +(-2.64861 - 1.99621i) q^{11} +1.61803i q^{12} +(-1.82151 - 2.50710i) q^{13} +(1.16751 + 3.59321i) q^{14} +(-3.61018 - 0.238203i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.93806 + 2.66751i) q^{17} +(-0.363271 - 0.118034i) q^{18} +(-0.400863 - 1.23373i) q^{19} +(1.43058 - 1.71856i) q^{20} +6.11314 q^{21} +(0.0581575 - 3.31611i) q^{22} -0.556884i q^{23} +(-1.30902 + 0.951057i) q^{24} +(3.62387 + 3.44493i) q^{25} +(0.957626 - 2.94727i) q^{26} +(-3.21644 + 4.42705i) q^{27} +(-2.22073 + 3.05657i) q^{28} +(2.95763 - 9.10264i) q^{29} +(-1.92930 - 3.06071i) q^{30} +(-4.32760 + 3.14419i) q^{31} -1.00000i q^{32} +(-5.07390 - 1.74755i) q^{33} -3.29722 q^{34} +(-6.49294 - 5.40490i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(7.52785 + 2.44595i) q^{37} +(0.762486 - 1.04947i) q^{38} +(-4.05657 - 2.94727i) q^{39} +(2.23122 + 0.147217i) q^{40} +(1.94312 + 5.98030i) q^{41} +(3.59321 + 4.94563i) q^{42} -3.61803i q^{43} +(2.71698 - 1.90211i) q^{44} +(0.827913 - 0.209880i) q^{45} +(0.450528 - 0.327328i) q^{46} +(5.08740 - 1.65300i) q^{47} +(-1.53884 - 0.500000i) q^{48} +(5.88499 + 4.27570i) q^{49} +(-0.656948 + 4.95665i) q^{50} +(-1.64861 + 5.07390i) q^{51} +(2.94727 - 0.957626i) q^{52} +(6.47398 + 8.91067i) q^{53} -5.47214 q^{54} +(3.84404 + 6.34219i) q^{55} -3.77813 q^{56} +(-1.23373 - 1.69808i) q^{57} +(9.10264 - 2.95763i) q^{58} +(-1.63693 + 5.03795i) q^{59} +(1.34215 - 3.35988i) q^{60} +(-1.98801 - 1.44437i) q^{61} +(-5.08740 - 1.65300i) q^{62} +(-1.37249 + 0.445947i) q^{63} +(0.809017 - 0.587785i) q^{64} +(1.70278 + 6.71698i) q^{65} +(-1.56856 - 5.13205i) q^{66} +9.21247i q^{67} +(-1.93806 - 2.66751i) q^{68} +(-0.278442 - 0.856956i) q^{69} +(0.556206 - 8.42982i) q^{70} +(-8.81173 - 6.40210i) q^{71} +(0.224514 - 0.309017i) q^{72} +(3.22994 + 1.04947i) q^{73} +(2.44595 + 7.52785i) q^{74} +(7.29903 + 3.48927i) q^{75} +1.29722 q^{76} +(-7.18643 - 10.2651i) q^{77} -5.01420i q^{78} +(13.2383 - 9.61817i) q^{79} +(1.19237 + 1.89162i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(-3.69603 + 5.08714i) q^{82} +(-0.108199 + 0.148923i) q^{83} +(-1.88906 + 5.81394i) q^{84} +(6.23710 - 3.93152i) q^{85} +(2.92705 - 2.12663i) q^{86} -15.4863i q^{87} +(3.13584 + 1.08005i) q^{88} -6.09017 q^{89} +(0.656431 + 0.546432i) q^{90} +(-3.61803 - 11.1352i) q^{91} +(0.529628 + 0.172087i) q^{92} +(-5.08740 + 7.00220i) q^{93} +(4.32760 + 3.14419i) q^{94} +(-0.190973 + 2.89437i) q^{95} +(-0.500000 - 1.53884i) q^{96} +(-7.26384 - 9.99782i) q^{97} +7.27425i q^{98} +(1.26664 + 0.0222142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 20 q^{11} - 12 q^{14} + 2 q^{15} - 4 q^{16} - 16 q^{19} + 6 q^{20} - 16 q^{21} - 12 q^{24} - 16 q^{26} + 16 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{34}+ \cdots - 20 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 6 * q^5 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 20 * q^11 - 12 * q^14 + 2 * q^15 - 4 * q^16 - 16 * q^19 + 6 * q^20 - 16 * q^21 - 12 * q^24 - 16 * q^26 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^34 - 48 * q^35 + 16 * q^36 - 8 * q^39 - 4 * q^40 + 40 * q^41 - 4 * q^45 + 20 * q^46 + 84 * q^49 + 4 * q^50 - 4 * q^51 - 16 * q^54 + 32 * q^55 - 8 * q^56 + 8 * q^60 + 20 * q^61 + 4 * q^64 + 72 * q^65 - 20 * q^66 + 36 * q^70 - 56 * q^71 + 4 * q^74 + 32 * q^75 - 24 * q^76 + 36 * q^79 + 4 * q^80 - 56 * q^81 - 4 * q^84 - 54 * q^85 + 20 * q^86 - 8 * q^89 - 4 * q^90 - 40 * q^91 + 4 * q^94 - 50 * q^95 - 8 * q^96 - 20 * q^99

Introduction

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