LMFDB - Embedded newform 847.2.f.n.372.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.n.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.690983 - 2.12663i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-0.854102 - 2.62866i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-0.454915 + 1.40008i) q^{9} +O(q^{10})$	\(q+(0.690983 - 2.12663i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-0.854102 - 2.62866i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-0.454915 + 1.40008i) q^{9} -4.47214 q^{10} -3.70820 q^{12} +(1.00000 - 3.07768i) q^{13} +(-1.80902 + 1.31433i) q^{14} +(-2.00000 - 1.45309i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-1.00000 - 3.07768i) q^{17} +(2.66312 + 1.93487i) q^{18} +(-5.23607 + 3.80423i) q^{19} +(-1.85410 + 5.70634i) q^{20} -1.23607 q^{21} +2.47214 q^{23} +(-0.854102 + 2.62866i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-5.85410 - 4.25325i) q^{26} +(1.70820 + 5.25731i) q^{27} +(0.927051 + 2.85317i) q^{28} +(-6.85410 - 4.97980i) q^{29} +(-4.47214 + 3.24920i) q^{30} +(-0.854102 + 2.62866i) q^{31} -6.70820 q^{32} -7.23607 q^{34} +(-0.618034 + 1.90211i) q^{35} +(3.57295 - 2.59590i) q^{36} +(6.85410 + 4.97980i) q^{37} +(4.47214 + 13.7638i) q^{38} +(-1.23607 - 3.80423i) q^{39} +(3.61803 + 2.62866i) q^{40} +(9.09017 - 6.60440i) q^{41} +(-0.854102 + 2.62866i) q^{42} +8.00000 q^{43} +2.94427 q^{45} +(1.70820 - 5.25731i) q^{46} +(-2.23607 + 1.62460i) q^{47} +(-1.00000 - 0.726543i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.690983 - 2.12663i) q^{50} +(-3.23607 - 2.35114i) q^{51} +(-7.85410 + 5.70634i) q^{52} +(-0.145898 + 0.449028i) q^{53} +12.3607 q^{54} +2.23607 q^{56} +(-2.47214 + 7.60845i) q^{57} +(-15.3262 + 11.1352i) q^{58} +(1.00000 + 0.726543i) q^{59} +(2.29180 + 7.05342i) q^{60} +(-2.23607 - 6.88191i) q^{61} +(5.00000 + 3.63271i) q^{62} +(1.19098 - 0.865300i) q^{63} +(-4.01722 + 12.3637i) q^{64} -6.47214 q^{65} +14.4721 q^{67} +(-3.00000 + 9.23305i) q^{68} +(2.47214 - 1.79611i) q^{69} +(3.61803 + 2.62866i) q^{70} +(-3.23607 - 9.95959i) q^{71} +(-1.01722 - 3.13068i) q^{72} +(0.618034 + 0.449028i) q^{73} +(15.3262 - 11.1352i) q^{74} +(0.381966 - 1.17557i) q^{75} +19.4164 q^{76} -8.94427 q^{78} +(-2.76393 + 8.50651i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(1.95492 + 1.42033i) q^{81} +(-7.76393 - 23.8949i) q^{82} +(-3.52786 - 10.8576i) q^{83} +(3.00000 + 2.17963i) q^{84} +(-5.23607 + 3.80423i) q^{85} +(5.52786 - 17.0130i) q^{86} -10.4721 q^{87} +2.00000 q^{89} +(2.03444 - 6.26137i) q^{90} +(-2.61803 + 1.90211i) q^{91} +(-6.00000 - 4.35926i) q^{92} +(1.05573 + 3.24920i) q^{93} +(1.90983 + 5.87785i) q^{94} +(10.4721 + 7.60845i) q^{95} +(-6.70820 + 4.87380i) q^{96} +(5.38197 - 16.5640i) q^{97} +2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} + 4 q^{3} - 3 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 5 q^{8} - 13 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 + 4 * q^3 - 3 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 5 * q^8 - 13 * q^9	$ 4 q + 5 q^{2} + 4 q^{3} - 3 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 5 q^{8} - 13 q^{9} + 12 q^{12} + 4 q^{13} - 5 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 5 q^{18} - 12 q^{19} + 6 q^{20} + 4 q^{21} - 8 q^{23} + 10 q^{24} + q^{25} - 10 q^{26} - 20 q^{27} - 3 q^{28} - 14 q^{29} + 10 q^{31} - 20 q^{34} + 2 q^{35} + 21 q^{36} + 14 q^{37} + 4 q^{39} + 10 q^{40} + 14 q^{41} + 10 q^{42} + 32 q^{43} - 24 q^{45} - 20 q^{46} - 4 q^{48} - q^{49} - 5 q^{50} - 4 q^{51} - 18 q^{52} - 14 q^{53} - 40 q^{54} + 8 q^{57} - 30 q^{58} + 4 q^{59} + 36 q^{60} + 20 q^{62} + 7 q^{63} + 13 q^{64} - 8 q^{65} + 40 q^{67} - 12 q^{68} - 8 q^{69} + 10 q^{70} - 4 q^{71} + 25 q^{72} - 2 q^{73} + 30 q^{74} + 6 q^{75} + 24 q^{76} - 20 q^{79} - 2 q^{80} + 19 q^{81} - 40 q^{82} - 32 q^{83} + 12 q^{84} - 12 q^{85} + 40 q^{86} - 24 q^{87} + 8 q^{89} - 50 q^{90} - 6 q^{91} - 24 q^{92} + 40 q^{93} + 30 q^{94} + 24 q^{95} + 26 q^{97}+O(q^{100}) $ 4 * q + 5 * q^2 + 4 * q^3 - 3 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 5 * q^8 - 13 * q^9 + 12 * q^12 + 4 * q^13 - 5 * q^14 - 8 * q^15 + q^16 - 4 * q^17 - 5 * q^18 - 12 * q^19 + 6 * q^20 + 4 * q^21 - 8 * q^23 + 10 * q^24 + q^25 - 10 * q^26 - 20 * q^27 - 3 * q^28 - 14 * q^29 + 10 * q^31 - 20 * q^34 + 2 * q^35 + 21 * q^36 + 14 * q^37 + 4 * q^39 + 10 * q^40 + 14 * q^41 + 10 * q^42 + 32 * q^43 - 24 * q^45 - 20 * q^46 - 4 * q^48 - q^49 - 5 * q^50 - 4 * q^51 - 18 * q^52 - 14 * q^53 - 40 * q^54 + 8 * q^57 - 30 * q^58 + 4 * q^59 + 36 * q^60 + 20 * q^62 + 7 * q^63 + 13 * q^64 - 8 * q^65 + 40 * q^67 - 12 * q^68 - 8 * q^69 + 10 * q^70 - 4 * q^71 + 25 * q^72 - 2 * q^73 + 30 * q^74 + 6 * q^75 + 24 * q^76 - 20 * q^79 - 2 * q^80 + 19 * q^81 - 40 * q^82 - 32 * q^83 + 12 * q^84 - 12 * q^85 + 40 * q^86 - 24 * q^87 + 8 * q^89 - 50 * q^90 - 6 * q^91 - 24 * q^92 + 40 * q^93 + 30 * q^94 + 24 * q^95 + 26 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.690983	−	2.12663i	0.488599	−	1.50375i	−0.338101	−	0.941110i	$-0.609785\pi$
$2$	0.690983	−	2.12663i	0.488599	−	1.50375i	0.826700	−	0.562643i	$-0.190215\pi$
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	−0.260418	−	0.965496i	$-0.583860\pi$
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	0.837768	+	0.546027i	$0.183860\pi$
$4$	−2.42705	−	1.76336i	−1.21353	−	0.881678i
$5$	−0.618034	−	1.90211i	−0.276393	−	0.850651i	−0.988847	−	0.148932i	$-0.952416\pi$
$5$	−0.618034	−	1.90211i	−0.276393	−	0.850651i	0.712454	−	0.701719i	$-0.247584\pi$
$6$	−0.854102	−	2.62866i	−0.348686	−	1.07314i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$	−0.454915	+	1.40008i	−0.151638	+	0.466695i
$10$	−4.47214			−1.41421
$11$		0			0
$11$		0			0
$12$	−3.70820			−1.07047
$13$	1.00000	−	3.07768i	0.277350	−	0.853596i	−0.711238	−	0.702951i	$-0.751865\pi$
$13$	1.00000	−	3.07768i	0.277350	−	0.853596i	0.988588	−	0.150644i	$-0.0481349\pi$
$14$	−1.80902	+	1.31433i	−0.483480	+	0.351269i
$15$	−2.00000	−	1.45309i	−0.516398	−	0.375185i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−1.00000	−	3.07768i	−0.242536	−	0.746448i	−0.996032	−	0.0889958i	$-0.971634\pi$
$17$	−1.00000	−	3.07768i	−0.242536	−	0.746448i	0.753496	−	0.657452i	$-0.228366\pi$
$18$	2.66312	+	1.93487i	0.627703	+	0.456053i
$19$	−5.23607	+	3.80423i	−1.20124	+	0.872749i	−0.994406	−	0.105627i	$-0.966315\pi$
$19$	−5.23607	+	3.80423i	−1.20124	+	0.872749i	−0.206831	+	0.978377i	$0.566315\pi$
$20$	−1.85410	+	5.70634i	−0.414590	+	1.27598i
$21$	−1.23607			−0.269732
$22$		0			0
$23$	2.47214			0.515476			0.257738	−	0.966215i	$-0.417023\pi$
$23$	2.47214			0.515476			0.257738	+	0.966215i	$0.417023\pi$
$24$	−0.854102	+	2.62866i	−0.174343	+	0.536572i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	−5.85410	−	4.25325i	−1.14808	−	0.834132i
$27$	1.70820	+	5.25731i	0.328744	+	1.01177i
$28$	0.927051	+	2.85317i	0.175196	+	0.539198i
$29$	−6.85410	−	4.97980i	−1.27277	−	0.924725i	−0.273465	−	0.961882i	$-0.588170\pi$
$29$	−6.85410	−	4.97980i	−1.27277	−	0.924725i	−0.999309	+	0.0371569i	$0.988170\pi$
$30$	−4.47214	+	3.24920i	−0.816497	+	0.593219i
$31$	−0.854102	+	2.62866i	−0.153401	+	0.472120i	−0.997995	−	0.0632866i	$-0.979842\pi$
$31$	−0.854102	+	2.62866i	−0.153401	+	0.472120i	0.844594	+	0.535407i	$0.179842\pi$
$32$	−6.70820			−1.18585
$33$		0			0
$34$	−7.23607			−1.24098
$35$	−0.618034	+	1.90211i	−0.104467	+	0.321516i
$36$	3.57295	−	2.59590i	0.595492	−	0.432650i
$37$	6.85410	+	4.97980i	1.12681	+	0.818674i	0.985227	−	0.171253i	$-0.0547816\pi$
$37$	6.85410	+	4.97980i	1.12681	+	0.818674i	0.141580	+	0.989927i	$0.454782\pi$
$38$	4.47214	+	13.7638i	0.725476	+	2.23279i
$39$	−1.23607	−	3.80423i	−0.197929	−	0.609164i
$40$	3.61803	+	2.62866i	0.572061	+	0.415627i
$41$	9.09017	−	6.60440i	1.41965	−	1.03143i	0.427816	−	0.903866i	$-0.359283\pi$
$41$	9.09017	−	6.60440i	1.41965	−	1.03143i	0.991830	−	0.127567i	$-0.0407169\pi$
$42$	−0.854102	+	2.62866i	−0.131791	+	0.405610i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	2.94427			0.438906
$46$	1.70820	−	5.25731i	0.251861	−	0.775148i
$47$	−2.23607	+	1.62460i	−0.326164	+	0.236972i	−0.738801	−	0.673923i	$-0.764608\pi$
$47$	−2.23607	+	1.62460i	−0.326164	+	0.236972i	0.412637	+	0.910895i	$0.364608\pi$
$48$	−1.00000	−	0.726543i	−0.144338	−	0.104867i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.690983	−	2.12663i	−0.0977198	−	0.300750i
$51$	−3.23607	−	2.35114i	−0.453140	−	0.329226i
$52$	−7.85410	+	5.70634i	−1.08917	+	0.791327i
$53$	−0.145898	+	0.449028i	−0.0200406	+	0.0616787i	−0.960577	−	0.278015i	$-0.910323\pi$
$53$	−0.145898	+	0.449028i	−0.0200406	+	0.0616787i	0.940536	+	0.339694i	$0.110323\pi$
$54$	12.3607			1.68208
$55$		0			0
$56$	2.23607			0.298807
$57$	−2.47214	+	7.60845i	−0.327442	+	1.00776i
$58$	−15.3262	+	11.1352i	−2.01243	+	1.46212i
$59$	1.00000	+	0.726543i	0.130189	+	0.0945878i	0.650974	−	0.759100i	$-0.274361\pi$
$59$	1.00000	+	0.726543i	0.130189	+	0.0945878i	−0.520785	+	0.853688i	$0.674361\pi$
$60$	2.29180	+	7.05342i	0.295870	+	0.910593i
$61$	−2.23607	−	6.88191i	−0.286299	−	0.881138i	−0.986006	−	0.166708i	$-0.946686\pi$
$61$	−2.23607	−	6.88191i	−0.286299	−	0.881138i	0.699707	−	0.714430i	$-0.253314\pi$
$62$	5.00000	+	3.63271i	0.635001	+	0.461355i
$63$	1.19098	−	0.865300i	0.150050	−	0.109018i
$64$	−4.01722	+	12.3637i	−0.502153	+	1.54547i
$65$	−6.47214			−0.802770
$66$		0			0
$67$	14.4721			1.76805			0.884026	−	0.467437i	$-0.154823\pi$
$67$	14.4721			1.76805			0.884026	+	0.467437i	$0.154823\pi$
$68$	−3.00000	+	9.23305i	−0.363803	+	1.11967i
$69$	2.47214	−	1.79611i	0.297610	−	0.216226i
$70$	3.61803	+	2.62866i	0.432438	+	0.314184i
$71$	−3.23607	−	9.95959i	−0.384051	−	1.18199i	−0.937167	−	0.348882i	$-0.886561\pi$
$71$	−3.23607	−	9.95959i	−0.384051	−	1.18199i	0.553116	−	0.833104i	$-0.313439\pi$
$72$	−1.01722	−	3.13068i	−0.119881	−	0.368955i
$73$	0.618034	+	0.449028i	0.0723354	+	0.0525547i	0.623365	−	0.781931i	$-0.285765\pi$
$73$	0.618034	+	0.449028i	0.0723354	+	0.0525547i	−0.551030	+	0.834486i	$0.685765\pi$
$74$	15.3262	−	11.1352i	1.78164	−	1.29444i
$75$	0.381966	−	1.17557i	0.0441056	−	0.135743i
$76$	19.4164			2.22721
$77$		0			0
$78$	−8.94427			−1.01274
$79$	−2.76393	+	8.50651i	−0.310967	+	0.957057i	0.666416	+	0.745580i	$0.267827\pi$
$79$	−2.76393	+	8.50651i	−0.310967	+	0.957057i	−0.977383	+	0.211477i	$0.932173\pi$
$80$	−1.61803	+	1.17557i	−0.180902	+	0.131433i
$81$	1.95492	+	1.42033i	0.217213	+	0.157814i
$82$	−7.76393	−	23.8949i	−0.857383	−	2.63875i
$83$	−3.52786	−	10.8576i	−0.387233	−	1.19178i	−0.934847	−	0.355051i	$-0.884464\pi$
$83$	−3.52786	−	10.8576i	−0.387233	−	1.19178i	0.547614	−	0.836731i	$-0.315536\pi$
$84$	3.00000	+	2.17963i	0.327327	+	0.237817i
$85$	−5.23607	+	3.80423i	−0.567931	+	0.412626i
$86$	5.52786	−	17.0130i	0.596085	−	1.83456i
$87$	−10.4721			−1.12273
$88$		0			0
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	2.03444	−	6.26137i	0.214449	−	0.660006i
$91$	−2.61803	+	1.90211i	−0.274445	+	0.199396i
$92$	−6.00000	−	4.35926i	−0.625543	−	0.454484i
$93$	1.05573	+	3.24920i	0.109474	+	0.336926i
$94$	1.90983	+	5.87785i	0.196984	+	0.606254i
$95$	10.4721	+	7.60845i	1.07442	+	0.780611i
$96$	−6.70820	+	4.87380i	−0.684653	+	0.497430i
$97$	5.38197	−	16.5640i	0.546456	−	1.68182i	−0.171047	−	0.985263i	$-0.554715\pi$
$97$	5.38197	−	16.5640i	0.546456	−	1.68182i	0.717503	−	0.696555i	$-0.245285\pi$
$98$	2.23607			0.225877
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−1.47214	+	4.53077i	−0.146483	+	0.450828i	−0.997199	−	0.0747977i	$-0.976169\pi$
$101$	−1.47214	+	4.53077i	−0.146483	+	0.450828i	0.850716	+	0.525626i	$0.176169\pi$
$102$	−7.23607	+	5.25731i	−0.716477	+	0.520551i
$103$	−6.23607	−	4.53077i	−0.614458	−	0.446430i	0.236523	−	0.971626i	$-0.423992\pi$
$103$	−6.23607	−	4.53077i	−0.614458	−	0.446430i	−0.850981	+	0.525196i	$0.823992\pi$
$104$	2.23607	+	6.88191i	0.219265	+	0.674827i
$105$	0.763932	+	2.35114i	0.0745521	+	0.229448i
$106$	0.854102	+	0.620541i	0.0829577	+	0.0602723i
$107$	3.23607	−	2.35114i	0.312842	−	0.227293i	−0.420273	−	0.907398i	$-0.638066\pi$
$107$	3.23607	−	2.35114i	0.312842	−	0.227293i	0.733115	+	0.680104i	$0.238066\pi$
$108$	5.12461	−	15.7719i	0.493116	−	1.51765i
$109$	−4.47214			−0.428353			−0.214176	−	0.976795i	$-0.568707\pi$
$109$	−4.47214			−0.428353			−0.214176	+	0.976795i	$0.568707\pi$
$110$		0			0
$111$	10.4721			0.993971
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	−1.61803	+	1.17557i	−0.152212	+	0.110588i	−0.661285	−	0.750135i	$-0.729988\pi$
$113$	−1.61803	+	1.17557i	−0.152212	+	0.110588i	0.509073	+	0.860724i	$0.329988\pi$
$114$	14.4721	+	10.5146i	1.35544	+	0.984785i
$115$	−1.52786	−	4.70228i	−0.142474	−	0.438490i
$116$	7.85410	+	24.1724i	0.729235	+	2.24435i
$117$	3.85410	+	2.80017i	0.356312	+	0.258876i
$118$	2.23607	−	1.62460i	0.205847	−	0.149556i
$119$	−1.00000	+	3.07768i	−0.0916698	+	0.282131i
$120$	5.52786			0.504623
$121$		0			0
$122$	−16.1803			−1.46490
$123$	4.29180	−	13.2088i	0.386978	−	1.19100i
$124$	6.70820	−	4.87380i	0.602414	−	0.437680i
$125$	−9.70820	−	7.05342i	−0.868328	−	0.630877i
$126$	−1.01722	−	3.13068i	−0.0906212	−	0.278904i
$127$	0.944272	+	2.90617i	0.0837906	+	0.257881i	0.984171	−	0.177223i	$-0.0567115\pi$
$127$	0.944272	+	2.90617i	0.0837906	+	0.257881i	−0.900380	+	0.435104i	$0.856712\pi$
$128$	12.6631	+	9.20029i	1.11927	+	0.813199i
$129$	8.00000	−	5.81234i	0.704361	−	0.511748i
$130$	−4.47214	+	13.7638i	−0.392232	+	1.20717i
$131$	21.8885			1.91241			0.956205	−	0.292696i	$-0.0945525\pi$
$131$	21.8885			1.91241			0.956205	+	0.292696i	$0.0945525\pi$
$132$		0			0
$133$	6.47214			0.561205
$134$	10.0000	−	30.7768i	0.863868	−	2.65871i
$135$	8.94427	−	6.49839i	0.769800	−	0.559293i
$136$	5.85410	+	4.25325i	0.501985	+	0.364714i
$137$	5.09017	+	15.6659i	0.434883	+	1.33843i	0.893207	+	0.449646i	$0.148450\pi$
$137$	5.09017	+	15.6659i	0.434883	+	1.33843i	−0.458324	+	0.888785i	$0.651550\pi$
$138$	−2.11146	−	6.49839i	−0.179739	−	0.553180i
$139$	1.23607	+	0.898056i	0.104842	+	0.0761721i	0.638971	−	0.769231i	$-0.279360\pi$
$139$	1.23607	+	0.898056i	0.104842	+	0.0761721i	−0.534129	+	0.845403i	$0.679360\pi$
$140$	4.85410	−	3.52671i	0.410246	−	0.298062i
$141$	−1.05573	+	3.24920i	−0.0889083	+	0.273632i
$142$	−23.4164			−1.96506
$143$		0			0
$144$	1.47214			0.122678
$145$	−5.23607	+	16.1150i	−0.434832	+	1.33827i
$146$	1.38197	−	1.00406i	0.114372	−	0.0830964i
$147$	1.00000	+	0.726543i	0.0824786	+	0.0599242i
$148$	−7.85410	−	24.1724i	−0.645603	−	1.98696i
$149$	4.32624	+	13.3148i	0.354419	+	1.09079i	0.956345	+	0.292239i	$0.0944001\pi$
$149$	4.32624	+	13.3148i	0.354419	+	1.09079i	−0.601926	+	0.798552i	$0.705600\pi$
$150$	−2.23607	−	1.62460i	−0.182574	−	0.132648i
$151$	−7.23607	+	5.25731i	−0.588863	+	0.427834i	−0.841908	−	0.539620i	$-0.818568\pi$
$151$	−7.23607	+	5.25731i	−0.588863	+	0.427834i	0.253046	+	0.967454i	$0.418568\pi$
$152$	4.47214	−	13.7638i	0.362738	−	1.11639i
$153$	4.76393			0.385141
$154$		0			0
$155$	5.52786			0.444009
$156$	−3.70820	+	11.4127i	−0.296894	+	0.913746i
$157$	−8.85410	+	6.43288i	−0.706634	+	0.513400i	−0.882086	−	0.471088i	$-0.843861\pi$
$157$	−8.85410	+	6.43288i	−0.706634	+	0.513400i	0.175452	+	0.984488i	$0.443861\pi$
$158$	16.1803	+	11.7557i	1.28724	+	0.935234i
$159$	0.180340	+	0.555029i	0.0143019	+	0.0440167i
$160$	4.14590	+	12.7598i	0.327762	+	1.00875i
$161$	−2.00000	−	1.45309i	−0.157622	−	0.114519i
$162$	4.37132	−	3.17595i	0.343444	−	0.249526i
$163$	−1.05573	+	3.24920i	−0.0826910	+	0.254497i	−0.983851	−	0.178990i	$-0.942717\pi$
$163$	−1.05573	+	3.24920i	−0.0826910	+	0.254497i	0.901160	+	0.433487i	$0.142717\pi$
$164$	−33.7082			−2.63217
$165$		0			0
$166$	−25.5279			−1.98135
$167$	1.52786	−	4.70228i	0.118230	−	0.363874i	−0.874377	−	0.485247i	$-0.838730\pi$
$167$	1.52786	−	4.70228i	0.118230	−	0.363874i	0.992607	+	0.121373i	$0.0387298\pi$
$168$	2.23607	−	1.62460i	0.172516	−	0.125340i
$169$	2.04508	+	1.48584i	0.157314	+	0.114295i
$170$	4.47214	+	13.7638i	0.342997	+	1.05564i
$171$	−2.94427	−	9.06154i	−0.225154	−	0.692953i
$172$	−19.4164	−	14.1068i	−1.48049	−	1.07564i
$173$	10.3262	−	7.50245i	0.785089	−	0.570401i	−0.121413	−	0.992602i	$-0.538742\pi$
$173$	10.3262	−	7.50245i	0.785089	−	0.570401i	0.906502	+	0.422201i	$0.138742\pi$
$174$	−7.23607	+	22.2703i	−0.548565	+	1.68831i
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	1.52786			0.114841
$178$	1.38197	−	4.25325i	0.103583	−	0.318795i
$179$	7.23607	−	5.25731i	0.540849	−	0.392950i	−0.283551	−	0.958957i	$-0.591513\pi$
$179$	7.23607	−	5.25731i	0.540849	−	0.392950i	0.824400	+	0.566007i	$0.191513\pi$
$180$	−7.14590	−	5.19180i	−0.532624	−	0.386974i
$181$	−7.85410	−	24.1724i	−0.583791	−	1.79672i	−0.604073	−	0.796929i	$-0.706456\pi$
$181$	−7.85410	−	24.1724i	−0.583791	−	1.79672i	0.0202821	−	0.999794i	$-0.493544\pi$
$182$	2.23607	+	6.88191i	0.165748	+	0.510121i
$183$	−7.23607	−	5.25731i	−0.534906	−	0.388632i
$184$	−4.47214	+	3.24920i	−0.329690	+	0.239534i
$185$	5.23607	−	16.1150i	0.384963	−	1.18480i
$186$	7.63932			0.560142
$187$		0			0
$188$	8.29180			0.604741
$189$	1.70820	−	5.25731i	0.124254	−	0.382413i
$190$	23.4164	−	17.0130i	1.69880	−	1.23425i
$191$	2.47214	+	1.79611i	0.178877	+	0.129962i	0.673621	−	0.739077i	$-0.264738\pi$
$191$	2.47214	+	1.79611i	0.178877	+	0.129962i	−0.494744	+	0.869039i	$0.664738\pi$
$192$	4.96556	+	15.2824i	0.358358	+	1.10291i
$193$	3.67376	+	11.3067i	0.264443	+	0.813872i	0.991821	+	0.127635i	$0.0407387\pi$
$193$	3.67376	+	11.3067i	0.264443	+	0.813872i	−0.727378	+	0.686237i	$0.759261\pi$
$194$	−31.5066	−	22.8909i	−2.26204	−	1.64347i
$195$	−6.47214	+	4.70228i	−0.463479	+	0.336737i
$196$	0.927051	−	2.85317i	0.0662179	−	0.203798i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	−2.18034			−0.154560			−0.0772801	−	0.997009i	$-0.524624\pi$
$199$	−2.18034			−0.154560			−0.0772801	+	0.997009i	$0.524624\pi$
$200$	−0.690983	+	2.12663i	−0.0488599	+	0.150375i
$201$	14.4721	−	10.5146i	1.02079	−	0.741644i
$202$	8.61803	+	6.26137i	0.606363	+	0.440548i
$203$	2.61803	+	8.05748i	0.183750	+	0.565524i
$204$	3.70820	+	11.4127i	0.259626	+	0.799047i
$205$	−18.1803	−	13.2088i	−1.26977	−	0.922542i
$206$	−13.9443	+	10.1311i	−0.971543	+	0.705868i
$207$	−1.12461	+	3.46120i	−0.0781659	+	0.240570i
$208$	−3.23607			−0.224381
$209$		0			0
$210$	5.52786			0.381459
$211$	−4.29180	+	13.2088i	−0.295459	+	0.909331i	0.687607	+	0.726083i	$0.258661\pi$
$211$	−4.29180	+	13.2088i	−0.295459	+	0.909331i	−0.983067	+	0.183248i	$0.941339\pi$
$212$	1.14590	−	0.832544i	0.0787006	−	0.0571793i
$213$	−10.4721	−	7.60845i	−0.717539	−	0.521323i
$214$	−2.76393	−	8.50651i	−0.188939	−	0.581493i
$215$	−4.94427	−	15.2169i	−0.337197	−	1.03778i
$216$	−10.0000	−	7.26543i	−0.680414	−	0.494350i
$217$	2.23607	−	1.62460i	0.151794	−	0.110285i
$218$	−3.09017	+	9.51057i	−0.209293	+	0.644137i
$219$	0.944272			0.0638080
$220$		0			0
$221$	−10.4721			−0.704432
$222$	7.23607	−	22.2703i	0.485653	−	1.49469i
$223$	8.23607	−	5.98385i	0.551528	−	0.400708i	−0.276821	−	0.960922i	$-0.589281\pi$
$223$	8.23607	−	5.98385i	0.551528	−	0.400708i	0.828348	+	0.560213i	$0.189281\pi$
$224$	5.42705	+	3.94298i	0.362610	+	0.263452i
$225$	0.454915	+	1.40008i	0.0303277	+	0.0933390i
$226$	1.38197	+	4.25325i	0.0919270	+	0.282922i
$227$	−4.76393	−	3.46120i	−0.316193	−	0.229728i	0.418356	−	0.908283i	$-0.362606\pi$
$227$	−4.76393	−	3.46120i	−0.316193	−	0.229728i	−0.734549	+	0.678555i	$0.762606\pi$
$228$	19.4164	−	14.1068i	1.28588	−	0.934249i
$229$	−1.38197	+	4.25325i	−0.0913229	+	0.281063i	−0.986278	−	0.165093i	$-0.947207\pi$
$229$	−1.38197	+	4.25325i	−0.0913229	+	0.281063i	0.894955	+	0.446156i	$0.147207\pi$
$230$	−11.0557			−0.728993
$231$		0			0
$232$	18.9443			1.24375
$233$	2.90983	−	8.95554i	0.190629	−	0.586697i	−0.809371	−	0.587298i	$-0.800192\pi$
$233$	2.90983	−	8.95554i	0.190629	−	0.586697i	1.00000		0.000601692i	$0.000191525\pi$
$234$	8.61803	−	6.26137i	0.563379	−	0.409318i
$235$	4.47214	+	3.24920i	0.291730	+	0.211954i
$236$	−1.14590	−	3.52671i	−0.0745916	−	0.229569i
$237$	3.41641	+	10.5146i	0.221920	+	0.682998i
$238$	5.85410	+	4.25325i	0.379465	+	0.275698i
$239$	8.00000	−	5.81234i	0.517477	−	0.375969i	−0.298176	−	0.954511i	$-0.596378\pi$
$239$	8.00000	−	5.81234i	0.517477	−	0.375969i	0.815653	+	0.578542i	$0.196378\pi$
$240$	−0.763932	+	2.35114i	−0.0493116	+	0.151765i
$241$	−13.1246			−0.845431			−0.422715	−	0.906263i	$-0.638923\pi$
$241$	−13.1246			−0.845431			−0.422715	+	0.906263i	$0.638923\pi$
$242$		0			0
$243$	−13.5967			−0.872232
$244$	−6.70820	+	20.6457i	−0.429449	+	1.32171i
$245$	1.61803	−	1.17557i	0.103372	−	0.0751044i
$246$	−25.1246	−	18.2541i	−1.60189	−	1.16384i
$247$	6.47214	+	19.9192i	0.411812	+	1.26743i
$248$	−1.90983	−	5.87785i	−0.121274	−	0.373244i
$249$	−11.4164	−	8.29451i	−0.723485	−	0.525643i
$250$	−21.7082	+	15.7719i	−1.37295	+	0.997505i
$251$	1.32624	−	4.08174i	0.0837114	−	0.257637i	−0.900436	−	0.434988i	$-0.856753\pi$
$251$	1.32624	−	4.08174i	0.0837114	−	0.257637i	0.984148	+	0.177351i	$0.0567527\pi$
$252$	−4.41641			−0.278208
$253$		0			0
$254$	6.83282			0.428729
$255$	−2.47214	+	7.60845i	−0.154811	+	0.476460i
$256$	7.28115	−	5.29007i	0.455072	−	0.330629i
$257$	4.85410	+	3.52671i	0.302791	+	0.219990i	0.728797	−	0.684730i	$-0.240080\pi$
$257$	4.85410	+	3.52671i	0.302791	+	0.219990i	−0.426006	+	0.904720i	$0.640080\pi$
$258$	−6.83282	−	21.0292i	−0.425393	−	1.30922i
$259$	−2.61803	−	8.05748i	−0.162677	−	0.500667i
$260$	15.7082	+	11.4127i	0.974181	+	0.707784i
$261$	10.0902	−	7.33094i	0.624566	−	0.453774i
$262$	15.1246	−	46.5488i	0.934402	−	2.87579i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	0.944272			0.0580062
$266$	4.47214	−	13.7638i	0.274204	−	0.843914i
$267$	2.00000	−	1.45309i	0.122398	−	0.0889274i
$268$	−35.1246	−	25.5195i	−2.14558	−	1.55885i
$269$	4.14590	+	12.7598i	0.252780	+	0.777976i	0.994259	+	0.107000i	$0.0341246\pi$
$269$	4.14590	+	12.7598i	0.252780	+	0.777976i	−0.741479	+	0.670976i	$0.765875\pi$
$270$	−7.63932	−	23.5114i	−0.464914	−	1.43086i
$271$	8.47214	+	6.15537i	0.514646	+	0.373912i	0.814583	−	0.580047i	$-0.196966\pi$
$271$	8.47214	+	6.15537i	0.514646	+	0.373912i	−0.299937	+	0.953959i	$0.596966\pi$
$272$	−2.61803	+	1.90211i	−0.158742	+	0.115333i
$273$	−1.23607	+	3.80423i	−0.0748102	+	0.230242i
$274$	36.8328			2.22515
$275$		0			0
$276$	−9.16718			−0.551800
$277$	−6.14590	+	18.9151i	−0.369271	+	1.13650i	0.577992	+	0.816043i	$0.303837\pi$
$277$	−6.14590	+	18.9151i	−0.369271	+	1.13650i	−0.947263	+	0.320457i	$0.896163\pi$
$278$	2.76393	−	2.00811i	0.165770	−	0.120439i
$279$	−3.29180	−	2.39163i	−0.197075	−	0.143183i
$280$	−1.38197	−	4.25325i	−0.0825883	−	0.254181i
$281$	−1.09017	−	3.35520i	−0.0650341	−	0.200154i	0.913259	−	0.407379i	$-0.133557\pi$
$281$	−1.09017	−	3.35520i	−0.0650341	−	0.200154i	−0.978293	+	0.207224i	$0.933557\pi$
$282$	6.18034	+	4.49028i	0.368034	+	0.267392i
$283$	−24.1803	+	17.5680i	−1.43737	+	1.04431i	−0.448788	+	0.893638i	$0.648144\pi$
$283$	−24.1803	+	17.5680i	−1.43737	+	1.04431i	−0.988584	+	0.150674i	$0.951856\pi$
$284$	−9.70820	+	29.8788i	−0.576076	+	1.77298i
$285$	16.0000			0.947758
$286$		0			0
$287$	−11.2361			−0.663244
$288$	3.05166	−	9.39205i	0.179821	−	0.553432i
$289$	5.28115	−	3.83698i	0.310656	−	0.225705i
$290$	30.6525	+	22.2703i	1.79998	+	1.30776i
$291$	−6.65248	−	20.4742i	−0.389975	−	1.20022i
$292$	−0.708204	−	2.17963i	−0.0414445	−	0.127553i
$293$	20.3262	+	14.7679i	1.18747	+	0.862749i	0.992995	−	0.118159i	$-0.0376991\pi$
$293$	20.3262	+	14.7679i	1.18747	+	0.862749i	0.194477	+	0.980907i	$0.437699\pi$
$294$	2.23607	−	1.62460i	0.130410	−	0.0947485i
$295$	0.763932	−	2.35114i	0.0444778	−	0.136889i
$296$	−18.9443			−1.10111
$297$		0			0
$298$	31.3050			1.81345
$299$	2.47214	−	7.60845i	0.142967	−	0.440008i
$300$	−3.00000	+	2.17963i	−0.173205	+	0.125841i
$301$	−6.47214	−	4.70228i	−0.373048	−	0.271035i
$302$	6.18034	+	19.0211i	0.355639	+	1.09454i
$303$	1.81966	+	5.60034i	0.104537	+	0.321731i
$304$	5.23607	+	3.80423i	0.300309	+	0.218187i
$305$	−11.7082	+	8.50651i	−0.670410	+	0.487081i
$306$	3.29180	−	10.1311i	0.188179	−	0.579157i
$307$	−8.94427			−0.510477			−0.255238	−	0.966878i	$-0.582154\pi$
$307$	−8.94427			−0.510477			−0.255238	+	0.966878i	$0.582154\pi$
$308$		0			0
$309$	−9.52786			−0.542021
$310$	3.81966	−	11.7557i	0.216942	−	0.667679i
$311$	6.70820	−	4.87380i	0.380387	−	0.276368i	−0.381118	−	0.924527i	$-0.624461\pi$
$311$	6.70820	−	4.87380i	0.380387	−	0.276368i	0.761505	+	0.648159i	$0.224461\pi$
$312$	7.23607	+	5.25731i	0.409662	+	0.297637i
$313$	4.61803	+	14.2128i	0.261027	+	0.803358i	0.992582	+	0.121576i	$0.0387947\pi$
$313$	4.61803	+	14.2128i	0.261027	+	0.803358i	−0.731555	+	0.681782i	$0.761205\pi$
$314$	7.56231	+	23.2744i	0.426766	+	1.31345i
$315$	−2.38197	−	1.73060i	−0.134209	−	0.0975082i
$316$	21.7082	−	15.7719i	1.22118	−	0.887241i
$317$	4.32624	−	13.3148i	0.242986	−	0.747833i	−0.752975	−	0.658049i	$-0.771382\pi$
$317$	4.32624	−	13.3148i	0.242986	−	0.747833i	0.995961	−	0.0897846i	$-0.0286179\pi$
$318$	1.30495			0.0731781
$319$		0			0
$320$	26.0000			1.45344
$321$	1.52786	−	4.70228i	0.0852771	−	0.262456i
$322$	−4.47214	+	3.24920i	−0.249222	+	0.181071i
$323$	16.9443	+	12.3107i	0.942805	+	0.684988i
$324$	−2.24013	−	6.89442i	−0.124452	−	0.383023i
$325$	−1.00000	−	3.07768i	−0.0554700	−	0.170719i
$326$	6.18034	+	4.49028i	0.342297	+	0.248694i
$327$	−4.47214	+	3.24920i	−0.247310	+	0.179681i
$328$	−7.76393	+	23.8949i	−0.428691	+	1.31938i
$329$	2.76393			0.152381
$330$		0			0
$331$	−13.8885			−0.763383			−0.381692	−	0.924290i	$-0.624658\pi$
$331$	−13.8885			−0.763383			−0.381692	+	0.924290i	$0.624658\pi$
$332$	−10.5836	+	32.5729i	−0.580850	+	1.78767i
$333$	−10.0902	+	7.33094i	−0.552938	+	0.401733i
$334$	−8.94427	−	6.49839i	−0.489409	−	0.355576i
$335$	−8.94427	−	27.5276i	−0.488678	−	1.50400i
$336$	0.381966	+	1.17557i	0.0208380	+	0.0641326i
$337$	9.32624	+	6.77591i	0.508033	+	0.369107i	0.812077	−	0.583551i	$-0.198337\pi$
$337$	9.32624	+	6.77591i	0.508033	+	0.369107i	−0.304044	+	0.952658i	$0.598337\pi$
$338$	4.57295	−	3.32244i	0.248736	−	0.180717i
$339$	−0.763932	+	2.35114i	−0.0414911	+	0.127696i
$340$	19.4164			1.05300
$341$		0			0
$342$	−21.3050			−1.15204
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−14.4721	+	10.5146i	−0.780285	+	0.566910i
$345$	−4.94427	−	3.59222i	−0.266191	−	0.193399i
$346$	−8.81966	−	27.1441i	−0.474148	−	1.45928i
$347$	6.47214	+	19.9192i	0.347442	+	1.06932i	0.960263	+	0.279096i	$0.0900348\pi$
$347$	6.47214	+	19.9192i	0.347442	+	1.06932i	−0.612821	+	0.790222i	$0.709965\pi$
$348$	25.4164	+	18.4661i	1.36246	+	0.989887i
$349$	5.85410	−	4.25325i	0.313363	−	0.227671i	−0.419975	−	0.907536i	$-0.637961\pi$
$349$	5.85410	−	4.25325i	0.313363	−	0.227671i	0.733338	+	0.679864i	$0.237961\pi$
$350$	−0.690983	+	2.12663i	−0.0369346	+	0.113673i
$351$	17.8885			0.954820
$352$		0			0
$353$	19.8885			1.05856			0.529280	−	0.848447i	$-0.322462\pi$
$353$	19.8885			1.05856			0.529280	+	0.848447i	$0.322462\pi$
$354$	1.05573	−	3.24920i	0.0561113	−	0.172693i
$355$	−16.9443	+	12.3107i	−0.899309	+	0.653386i
$356$	−4.85410	−	3.52671i	−0.257267	−	0.186915i
$357$	1.23607	+	3.80423i	0.0654197	+	0.201341i
$358$	−6.18034	−	19.0211i	−0.326641	−	1.00530i
$359$	20.1803	+	14.6619i	1.06508	+	0.773824i	0.975021	−	0.222112i	$-0.0712952\pi$
$359$	20.1803	+	14.6619i	1.06508	+	0.773824i	0.0900566	+	0.995937i	$0.471295\pi$
$360$	−5.32624	+	3.86974i	−0.280717	+	0.203953i
$361$	7.07295	−	21.7683i	0.372260	−	1.14570i
$362$	−56.8328			−2.98707
$363$		0			0
$364$	9.70820			0.508848
$365$	0.472136	−	1.45309i	0.0247127	−	0.0760579i
$366$	−16.1803	+	11.7557i	−0.845760	+	0.614481i
$367$	18.7082	+	13.5923i	0.976560	+	0.709513i	0.956937	−	0.290295i	$-0.0937534\pi$
$367$	18.7082	+	13.5923i	0.976560	+	0.709513i	0.0196231	+	0.999807i	$0.493753\pi$
$368$	−0.763932	−	2.35114i	−0.0398227	−	0.122562i
$369$	5.11146	+	15.7314i	0.266092	+	0.818946i
$370$	−30.6525	−	22.2703i	−1.59355	−	1.15778i
$371$	0.381966	−	0.277515i	0.0198307	−	0.0144078i
$372$	3.16718	−	9.74759i	0.164211	−	0.505389i
$373$	6.00000			0.310668			0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$		0			0
$375$	−14.8328			−0.765963
$376$	1.90983	−	5.87785i	0.0984920	−	0.303127i
$377$	−22.1803	+	16.1150i	−1.14235	+	0.829963i
$378$	−10.0000	−	7.26543i	−0.514344	−	0.373693i
$379$	11.5279	+	35.4791i	0.592147	+	1.82244i	0.568446	+	0.822721i	$0.307545\pi$
$379$	11.5279	+	35.4791i	0.592147	+	1.82244i	0.0237009	+	0.999719i	$0.492455\pi$
$380$	−12.0000	−	36.9322i	−0.615587	−	1.89458i
$381$	3.05573	+	2.22012i	0.156550	+	0.113740i
$382$	5.52786	−	4.01623i	0.282830	−	0.205488i
$383$	−1.43769	+	4.42477i	−0.0734627	+	0.226095i	−0.981045	−	0.193779i	$-0.937926\pi$
$383$	−1.43769	+	4.42477i	−0.0734627	+	0.226095i	0.907583	+	0.419874i	$0.137926\pi$
$384$	19.3475			0.987324
$385$		0			0
$386$	26.5836			1.35307
$387$	−3.63932	+	11.2007i	−0.184997	+	0.569362i
$388$	−42.2705	+	30.7113i	−2.14596	+	1.55913i
$389$	−12.8541	−	9.33905i	−0.651729	−	0.473509i	0.212131	−	0.977241i	$-0.431960\pi$
$389$	−12.8541	−	9.33905i	−0.651729	−	0.473509i	−0.863860	+	0.503733i	$0.831960\pi$
$390$	5.52786	+	17.0130i	0.279914	+	0.861488i
$391$	−2.47214	−	7.60845i	−0.125021	−	0.384776i
$392$	−1.80902	−	1.31433i	−0.0913692	−	0.0663836i
$393$	21.8885	−	15.9030i	1.10413	−	0.802198i
$394$	−1.38197	+	4.25325i	−0.0696224	+	0.214276i
$395$	17.8885			0.900070
$396$		0			0
$397$	−35.8885			−1.80119			−0.900597	−	0.434655i	$-0.856870\pi$
$397$	−35.8885			−1.80119			−0.900597	+	0.434655i	$0.856870\pi$
$398$	−1.50658	+	4.63677i	−0.0755179	+	0.232420i
$399$	6.47214	−	4.70228i	0.324012	−	0.235409i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	7.09017	+	21.8213i	0.354066	+	1.08970i	0.956549	+	0.291572i	$0.0941782\pi$
$401$	7.09017	+	21.8213i	0.354066	+	1.08970i	−0.602483	+	0.798132i	$0.705822\pi$
$402$	−12.3607	−	38.0423i	−0.616495	−	1.89738i
$403$	7.23607	+	5.25731i	0.360454	+	0.261885i
$404$	11.5623	−	8.40051i	0.575246	−	0.417941i
$405$	1.49342	−	4.59628i	0.0742087	−	0.228391i
$406$	18.9443			0.940188
$407$		0			0
$408$	8.94427			0.442807
$409$	2.81966	−	8.67802i	0.139423	−	0.429101i	−0.856829	−	0.515601i	$-0.827569\pi$
$409$	2.81966	−	8.67802i	0.139423	−	0.429101i	0.996252	+	0.0865009i	$0.0275685\pi$
$410$	−40.6525	+	29.5358i	−2.00768	+	1.45867i
$411$	16.4721	+	11.9677i	0.812511	+	0.590323i
$412$	7.14590	+	21.9928i	0.352053	+	1.08351i
$413$	−0.381966	−	1.17557i	−0.0187953	−	0.0578460i
$414$	6.58359	+	4.78326i	0.323566	+	0.235084i
$415$	−18.4721	+	13.4208i	−0.906761	+	0.658801i
$416$	−6.70820	+	20.6457i	−0.328897	+	1.01224i
$417$	1.88854			0.0924824
$418$		0			0
$419$	24.6525			1.20435			0.602176	−	0.798363i	$-0.294300\pi$
$419$	24.6525			1.20435			0.602176	+	0.798363i	$0.294300\pi$
$420$	2.29180	−	7.05342i	0.111828	−	0.344172i
$421$	−18.0902	+	13.1433i	−0.881661	+	0.640564i	−0.933690	−	0.358081i	$-0.883431\pi$
$421$	−18.0902	+	13.1433i	−0.881661	+	0.640564i	0.0520294	+	0.998646i	$0.483431\pi$
$422$	25.1246	+	18.2541i	1.22305	+	0.888596i
$423$	−1.25735	−	3.86974i	−0.0611347	−	0.188153i
$424$	−0.326238	−	1.00406i	−0.0158435	−	0.0487613i
$425$	−2.61803	−	1.90211i	−0.126993	−	0.0922660i
$426$	−23.4164	+	17.0130i	−1.13453	+	0.824283i
$427$	−2.23607	+	6.88191i	−0.108211	+	0.333039i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−35.7771			−1.72532
$431$	3.70820	−	11.4127i	0.178618	−	0.549729i	−0.821162	−	0.570695i	$-0.806674\pi$
$431$	3.70820	−	11.4127i	0.178618	−	0.549729i	0.999780	+	0.0209654i	$0.00667397\pi$
$432$	4.47214	−	3.24920i	0.215166	−	0.156327i
$433$	6.85410	+	4.97980i	0.329387	+	0.239314i	0.740171	−	0.672419i	$-0.234745\pi$
$433$	6.85410	+	4.97980i	0.329387	+	0.239314i	−0.410783	+	0.911733i	$0.634745\pi$
$434$	−1.90983	−	5.87785i	−0.0916748	−	0.282146i
$435$	6.47214	+	19.9192i	0.310315	+	0.955052i
$436$	10.8541	+	7.88597i	0.519817	+	0.377669i
$437$	−12.9443	+	9.40456i	−0.619208	+	0.449881i
$438$	0.652476	−	2.00811i	0.0311765	−	0.0959514i
$439$	10.4721			0.499808			0.249904	−	0.968271i	$-0.419601\pi$
$439$	10.4721			0.499808			0.249904	+	0.968271i	$0.419601\pi$
$440$		0			0
$441$	−1.47214			−0.0701017
$442$	−7.23607	+	22.2703i	−0.344185	+	1.05929i
$443$	20.1803	−	14.6619i	0.958797	−	0.696607i	0.00592587	−	0.999982i	$-0.498114\pi$
$443$	20.1803	−	14.6619i	0.958797	−	0.696607i	0.952871	+	0.303376i	$0.0981137\pi$
$444$	−25.4164	−	18.4661i	−1.20621	−	0.876362i
$445$	−1.23607	−	3.80423i	−0.0585952	−	0.180338i
$446$	−7.03444	−	21.6498i	−0.333090	−	1.02515i
$447$	14.0000	+	10.1716i	0.662177	+	0.481100i
$448$	10.5172	−	7.64121i	0.496892	−	0.361013i
$449$	−8.79837	+	27.0786i	−0.415221	+	1.27792i	0.496832	+	0.867847i	$0.334496\pi$
$449$	−8.79837	+	27.0786i	−0.415221	+	1.27792i	−0.912053	+	0.410072i	$0.865504\pi$
$450$	3.29180			0.155177
$451$		0			0
$452$	6.00000			0.282216
$453$	−3.41641	+	10.5146i	−0.160517	+	0.494020i
$454$	−10.6525	+	7.73948i	−0.499945	+	0.363232i
$455$	5.23607	+	3.80423i	0.245471	+	0.178345i
$456$	−5.52786	−	17.0130i	−0.258866	−	0.796707i
$457$	−8.90983	−	27.4216i	−0.416784	−	1.28273i	−0.910645	−	0.413189i	$-0.864415\pi$
$457$	−8.90983	−	27.4216i	−0.416784	−	1.28273i	0.493861	−	0.869541i	$-0.335585\pi$
$458$	8.09017	+	5.87785i	0.378029	+	0.274654i
$459$	14.4721	−	10.5146i	0.675501	−	0.490781i
$460$	−4.58359	+	14.1068i	−0.213711	+	0.657735i
$461$	−12.1803			−0.567295			−0.283647	−	0.958929i	$-0.591545\pi$
$461$	−12.1803			−0.567295			−0.283647	+	0.958929i	$0.591545\pi$
$462$		0			0
$463$	−5.52786			−0.256902			−0.128451	−	0.991716i	$-0.541000\pi$
$463$	−5.52786			−0.256902			−0.128451	+	0.991716i	$0.541000\pi$
$464$	−2.61803	+	8.05748i	−0.121539	+	0.374059i
$465$	5.52786	−	4.01623i	0.256349	−	0.186248i
$466$	−17.0344	−	12.3762i	−0.789105	−	0.573319i
$467$	7.43769	+	22.8909i	0.344175	+	1.05926i	0.962024	+	0.272966i	$0.0880046\pi$
$467$	7.43769	+	22.8909i	0.344175	+	1.05926i	−0.617848	+	0.786297i	$0.711995\pi$
$468$	−4.41641	−	13.5923i	−0.204149	−	0.628305i
$469$	−11.7082	−	8.50651i	−0.540635	−	0.392794i
$470$	10.0000	−	7.26543i	0.461266	−	0.335129i
$471$	−4.18034	+	12.8658i	−0.192620	+	0.592823i
$472$	−2.76393			−0.127220
$473$		0			0
$474$	24.7214			1.13549
$475$	−2.00000	+	6.15537i	−0.0917663	+	0.282428i
$476$	7.85410	−	5.70634i	0.359992	−	0.261550i
$477$	−0.562306	−	0.408539i	−0.0257462	−	0.0187057i
$478$	−6.83282	−	21.0292i	−0.312526	−	0.961855i
$479$	4.18034	+	12.8658i	0.191005	+	0.587852i	1.00000		3.67468e-5i	$1.16969e-5\pi$
$479$	4.18034	+	12.8658i	0.191005	+	0.587852i	−0.808995	+	0.587815i	$0.799988\pi$
$480$	13.4164	+	9.74759i	0.612372	+	0.444915i
$481$	22.1803	−	16.1150i	1.01134	−	0.734779i
$482$	−9.06888	+	27.9112i	−0.413076	+	1.27132i
$483$	−3.05573			−0.139040
$484$		0			0
$485$	−34.8328			−1.58168
$486$	−9.39512	+	28.9152i	−0.426171	+	1.31162i
$487$	29.4164	−	21.3723i	1.33298	−	0.968470i	0.333314	−	0.942816i	$-0.391833\pi$
$487$	29.4164	−	21.3723i	1.33298	−	0.968470i	0.999671	−	0.0256541i	$-0.00816685\pi$
$488$	13.0902	+	9.51057i	0.592564	+	0.430523i
$489$	1.30495	+	4.01623i	0.0590120	+	0.181620i
$490$	−1.38197	−	4.25325i	−0.0624309	−	0.192142i
$491$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$491$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$492$	−33.7082	+	24.4904i	−1.51968	+	1.10411i
$493$	−8.47214	+	26.0746i	−0.381566	+	1.17434i
$494$	46.8328			2.10711
$495$		0			0
$496$	2.76393			0.124104
$497$	−3.23607	+	9.95959i	−0.145157	+	0.446749i
$498$	−25.5279	+	18.5471i	−1.14393	+	0.831114i
$499$	−1.23607	−	0.898056i	−0.0553340	−	0.0402025i	0.559774	−	0.828645i	$-0.310888\pi$
$499$	−1.23607	−	0.898056i	−0.0553340	−	0.0402025i	−0.615108	+	0.788443i	$0.710888\pi$
$500$	11.1246	+	34.2380i	0.497508	+	1.53117i
$501$	−1.88854	−	5.81234i	−0.0843739	−	0.259676i
$502$	−7.76393	−	5.64083i	−0.346521	−	0.251762i
$503$	−18.9443	+	13.7638i	−0.844683	+	0.613698i	−0.923675	−	0.383177i	$-0.874830\pi$
$503$	−18.9443	+	13.7638i	−0.844683	+	0.613698i	0.0789916	+	0.996875i	$0.474830\pi$
$504$	−1.01722	+	3.13068i	−0.0453106	+	0.139452i
$505$	9.52786			0.423984
$506$		0			0
$507$	3.12461			0.138769
$508$	2.83282	−	8.71851i	0.125686	−	0.386821i
$509$	−32.7426	+	23.7889i	−1.45129	+	1.05443i	−0.465765	+	0.884908i	$0.654221\pi$
$509$	−32.7426	+	23.7889i	−1.45129	+	1.05443i	−0.985527	+	0.169517i	$0.945779\pi$
$510$	14.4721	+	10.5146i	0.640837	+	0.465595i
$511$	−0.236068	−	0.726543i	−0.0104430	−	0.0321403i
$512$	3.45492	+	10.6331i	0.152687	+	0.469923i
$513$	−28.9443	−	21.0292i	−1.27792	−	0.928464i
$514$	10.8541	−	7.88597i	0.478754	−	0.347835i
$515$	−4.76393	+	14.6619i	−0.209924	+	0.646079i
$516$	−29.6656			−1.30596
$517$		0			0
$518$	−18.9443			−0.832364
$519$	4.87539	−	15.0049i	0.214006	−	0.658642i
$520$	11.7082	−	8.50651i	0.513439	−	0.373035i
$521$	−24.5623	−	17.8456i	−1.07609	−	0.781828i	−0.0990964	−	0.995078i	$-0.531595\pi$
$521$	−24.5623	−	17.8456i	−1.07609	−	0.781828i	−0.976998	+	0.213250i	$0.931595\pi$
$522$	−8.61803	−	26.5236i	−0.377201	−	1.16091i
$523$	13.5967	+	41.8465i	0.594544	+	1.82982i	0.556982	+	0.830525i	$0.311959\pi$
$523$	13.5967	+	41.8465i	0.594544	+	1.82982i	0.0375627	+	0.999294i	$0.488041\pi$
$524$	−53.1246	−	38.5973i	−2.32076	−	1.68613i
$525$	−1.00000	+	0.726543i	−0.0436436	+	0.0317089i
$526$		0			0
$527$	8.94427			0.389619
$528$		0			0
$529$	−16.8885			−0.734285
$530$	0.652476	−	2.00811i	0.0283417	−	0.0872269i
$531$	−1.47214	+	1.06957i	−0.0638853	+	0.0464154i
$532$	−15.7082	−	11.4127i	−0.681037	−	0.494802i
$533$	−11.2361	−	34.5811i	−0.486688	−	1.49787i
$534$	−1.70820	−	5.25731i	−0.0739212	−	0.227506i
$535$	−6.47214	−	4.70228i	−0.279815	−	0.203297i
$536$	−26.1803	+	19.0211i	−1.13082	+	0.821588i
$537$	3.41641	−	10.5146i	0.147429	−	0.453739i
$538$	30.0000			1.29339
$539$		0			0
$540$	−33.1672			−1.42729
$541$	6.43769	−	19.8132i	0.276778	−	0.851835i	−0.711965	−	0.702215i	$-0.752195\pi$
$541$	6.43769	−	19.8132i	0.276778	−	0.851835i	0.988743	−	0.149621i	$-0.0478053\pi$
$542$	18.9443	−	13.7638i	0.813726	−	0.591207i
$543$	−25.4164	−	18.4661i	−1.09072	−	0.792456i
$544$	6.70820	+	20.6457i	0.287612	+	0.885178i
$545$	2.76393	+	8.50651i	0.118394	+	0.364379i
$546$	7.23607	+	5.25731i	0.309675	+	0.224992i
$547$	−22.6525	+	16.4580i	−0.968550	+	0.703693i	−0.955121	−	0.296217i	$-0.904275\pi$
$547$	−22.6525	+	16.4580i	−0.968550	+	0.703693i	−0.0134293	+	0.999910i	$0.504275\pi$
$548$	15.2705	−	46.9978i	0.652324	−	2.00765i
$549$	10.6525			0.454637
$550$		0			0
$551$	54.8328			2.33596
$552$	−2.11146	+	6.49839i	−0.0898695	+	0.276590i
$553$	7.23607	−	5.25731i	0.307709	−	0.223564i
$554$	35.9787	+	26.1401i	1.52859	+	1.11058i
$555$	−6.47214	−	19.9192i	−0.274727	−	0.845522i
$556$	−1.41641	−	4.35926i	−0.0600691	−	0.184874i
$557$	31.5066	+	22.8909i	1.33498	+	0.969917i	0.999613	+	0.0278285i	$0.00885924\pi$
$557$	31.5066	+	22.8909i	1.33498	+	0.969917i	0.335364	+	0.942089i	$0.391141\pi$
$558$	−7.36068	+	5.34785i	−0.311602	+	0.226392i
$559$	8.00000	−	24.6215i	0.338364	−	1.04138i
$560$	2.00000			0.0845154
$561$		0			0
$562$	−7.88854			−0.332758
$563$	3.88854	−	11.9677i	0.163883	−	0.504379i	−0.835070	−	0.550144i	$-0.814573\pi$
$563$	3.88854	−	11.9677i	0.163883	−	0.504379i	0.998952	+	0.0457655i	$0.0145727\pi$
$564$	8.29180	−	6.02434i	0.349148	−	0.253671i
$565$	3.23607	+	2.35114i	0.136142	+	0.0989132i
$566$	20.6525	+	63.5618i	0.868088	+	2.67170i
$567$	−0.746711	−	2.29814i	−0.0313589	−	0.0965128i
$568$	18.9443	+	13.7638i	0.794884	+	0.577517i
$569$	−6.09017	+	4.42477i	−0.255313	+	0.185496i	−0.708078	−	0.706134i	$-0.750438\pi$
$569$	−6.09017	+	4.42477i	−0.255313	+	0.185496i	0.452765	+	0.891630i	$0.350438\pi$
$570$	11.0557	−	34.0260i	0.463073	−	1.42519i
$571$	−15.0557			−0.630063			−0.315031	−	0.949081i	$-0.602015\pi$
$571$	−15.0557			−0.630063			−0.315031	+	0.949081i	$0.602015\pi$
$572$		0			0
$573$	3.77709			0.157790
$574$	−7.76393	+	23.8949i	−0.324060	+	0.997355i
$575$	2.00000	−	1.45309i	0.0834058	−	0.0605978i
$576$	−15.4828	−	11.2489i	−0.645116	−	0.468704i
$577$	−6.03444	−	18.5721i	−0.251217	−	0.773167i	−0.994551	−	0.104247i	$-0.966757\pi$
$577$	−6.03444	−	18.5721i	−0.251217	−	0.773167i	0.743334	−	0.668920i	$-0.233243\pi$
$578$	−4.51064	−	13.8823i	−0.187618	−	0.577429i
$579$	11.8885	+	8.63753i	0.494071	+	0.358964i
$580$	41.1246	−	29.8788i	1.70761	−	1.24065i
$581$	−3.52786	+	10.8576i	−0.146360	+	0.450451i
$582$	−48.1378			−1.99537
$583$		0			0
$584$	−1.70820			−0.0706860
$585$	2.94427	−	9.06154i	0.121731	−	0.374648i
$586$	45.4508	−	33.0220i	1.87756	−	1.36413i
$587$	−21.9443	−	15.9434i	−0.905737	−	0.658056i	0.0341961	−	0.999415i	$-0.489113\pi$
$587$	−21.9443	−	15.9434i	−0.905737	−	0.658056i	−0.939933	+	0.341359i	$0.889113\pi$
$588$	−1.14590	−	3.52671i	−0.0472560	−	0.145439i
$589$	−5.52786	−	17.0130i	−0.227772	−	0.701009i
$590$	−4.47214	−	3.24920i	−0.184115	−	0.133767i
$591$	−2.00000	+	1.45309i	−0.0822690	+	0.0597719i
$592$	2.61803	−	8.05748i	0.107601	−	0.331160i
$593$	−45.7082			−1.87701			−0.938505	−	0.345264i	$-0.887789\pi$
$593$	−45.7082			−1.87701			−0.938505	+	0.345264i	$0.887789\pi$
$594$		0			0
$595$	6.47214			0.265332
$596$	12.9787	−	39.9444i	0.531629	−	1.63619i
$597$	−2.18034	+	1.58411i	−0.0892354	+	0.0648333i
$598$	−14.4721	−	10.5146i	−0.591810	−	0.429975i
$599$	−7.23607	−	22.2703i	−0.295658	−	0.909941i	−0.983000	−	0.183607i	$-0.941223\pi$
$599$	−7.23607	−	22.2703i	−0.295658	−	0.909941i	0.687342	−	0.726334i	$-0.258777\pi$
$600$	0.854102	+	2.62866i	0.0348686	+	0.107314i
$601$	30.0344	+	21.8213i	1.22513	+	0.890109i	0.996516	−	0.0834076i	$-0.0265803\pi$
$601$	30.0344	+	21.8213i	1.22513	+	0.890109i	0.228615	+	0.973517i	$0.426580\pi$
$602$	−14.4721	+	10.5146i	−0.589840	+	0.428544i
$603$	−6.58359	+	20.2622i	−0.268105	+	0.825141i
$604$	26.8328			1.09181
$605$		0			0
$606$	13.1672			0.534880
$607$	4.00000	−	12.3107i	0.162355	−	0.499677i	−0.836477	−	0.548003i	$-0.815388\pi$
$607$	4.00000	−	12.3107i	0.162355	−	0.499677i	0.998832	+	0.0483253i	$0.0153884\pi$
$608$	35.1246	−	25.5195i	1.42449	−	1.03495i
$609$	8.47214	+	6.15537i	0.343308	+	0.249428i
$610$	10.0000	+	30.7768i	0.404888	+	1.24612i
$611$	2.76393	+	8.50651i	0.111817	+	0.344136i
$612$	−11.5623	−	8.40051i	−0.467379	−	0.339570i
$613$	−12.3820	+	8.99602i	−0.500103	+	0.363346i	−0.809056	−	0.587731i	$-0.800021\pi$
$613$	−12.3820	+	8.99602i	−0.500103	+	0.363346i	0.308953	+	0.951077i	$0.400021\pi$
$614$	−6.18034	+	19.0211i	−0.249418	+	0.767630i
$615$	−27.7771			−1.12008
$616$		0			0
$617$	6.58359			0.265045			0.132523	−	0.991180i	$-0.457692\pi$
$617$	6.58359			0.265045			0.132523	+	0.991180i	$0.457692\pi$
$618$	−6.58359	+	20.2622i	−0.264831	+	0.815066i
$619$	−9.00000	+	6.53888i	−0.361741	+	0.262820i	−0.753778	−	0.657129i	$-0.771770\pi$
$619$	−9.00000	+	6.53888i	−0.361741	+	0.262820i	0.392037	+	0.919949i	$0.371770\pi$
$620$	−13.4164	−	9.74759i	−0.538816	−	0.391473i
$621$	4.22291	+	12.9968i	0.169460	+	0.521543i
$622$	−5.72949	−	17.6336i	−0.229732	−	0.707041i
$623$	−1.61803	−	1.17557i	−0.0648252	−	0.0470982i
$624$	−3.23607	+	2.35114i	−0.129546	+	0.0941210i
$625$	−5.87132	+	18.0701i	−0.234853	+	0.722803i
$626$	33.4164			1.33559
$627$		0			0
$628$	32.8328			1.31017
$629$	8.47214	−	26.0746i	0.337806	−	1.03966i
$630$	−5.32624	+	3.86974i	−0.212202	+	0.154174i
$631$	19.4164	+	14.1068i	0.772955	+	0.561585i	0.902856	−	0.429942i	$-0.141466\pi$
$631$	19.4164	+	14.1068i	0.772955	+	0.561585i	−0.129901	+	0.991527i	$0.541466\pi$
$632$	−6.18034	−	19.0211i	−0.245841	−	0.756620i
$633$	5.30495	+	16.3270i	0.210853	+	0.648938i
$634$	−25.3262	−	18.4006i	−1.00583	−	0.730781i
$635$	4.94427	−	3.59222i	0.196207	−	0.142553i
$636$	0.541020	−	1.66509i	0.0214528	−	0.0660250i
$637$	3.23607			0.128218
$638$		0			0
$639$	15.4164			0.609864
$640$	9.67376	−	29.7728i	0.382389	−	1.17687i
$641$	12.5623	−	9.12705i	0.496181	−	0.360497i	−0.311375	−	0.950287i	$-0.600790\pi$
$641$	12.5623	−	9.12705i	0.496181	−	0.360497i	0.807556	+	0.589790i	$0.200790\pi$
$642$	−8.94427	−	6.49839i	−0.353002	−	0.256471i
$643$	3.43769	+	10.5801i	0.135569	+	0.417240i	0.995678	−	0.0928710i	$-0.0296044\pi$
$643$	3.43769	+	10.5801i	0.135569	+	0.417240i	−0.860109	+	0.510111i	$0.829604\pi$
$644$	2.29180	+	7.05342i	0.0903094	+	0.277944i
$645$	−16.0000	−	11.6247i	−0.629999	−	0.457721i
$646$	37.8885	−	27.5276i	1.49070	−	1.08306i
$647$	11.1459	−	34.3035i	0.438190	−	1.34861i	−0.451591	−	0.892225i	$-0.649143\pi$
$647$	11.1459	−	34.3035i	0.438190	−	1.34861i	0.889782	−	0.456387i	$-0.150857\pi$
$648$	−5.40325			−0.212260
$649$		0			0
$650$	−7.23607			−0.283822
$651$	1.05573	−	3.24920i	0.0413772	−	0.127346i
$652$	8.29180	−	6.02434i	0.324732	−	0.235931i
$653$	−20.2705	−	14.7274i	−0.793246	−	0.576327i	0.115679	−	0.993287i	$-0.463096\pi$
$653$	−20.2705	−	14.7274i	−0.793246	−	0.576327i	−0.908925	+	0.416959i	$0.863096\pi$
$654$	3.81966	+	11.7557i	0.149361	+	0.459684i
$655$	−13.5279	−	41.6345i	−0.528577	−	1.62679i
$656$	−9.09017	−	6.60440i	−0.354912	−	0.257858i
$657$	−0.909830	+	0.661030i	−0.0354959	+	0.0257892i
$658$	1.90983	−	5.87785i	0.0744529	−	0.229143i
$659$	−17.8885			−0.696839			−0.348419	−	0.937339i	$-0.613281\pi$
$659$	−17.8885			−0.696839			−0.348419	+	0.937339i	$0.613281\pi$
$660$		0			0
$661$	−40.8328			−1.58821			−0.794106	−	0.607779i	$-0.792061\pi$
$661$	−40.8328			−1.58821			−0.794106	+	0.607779i	$0.792061\pi$
$662$	−9.59675	+	29.5358i	−0.372988	+	1.14794i
$663$	−10.4721	+	7.60845i	−0.406704	+	0.295488i
$664$	20.6525	+	15.0049i	0.801471	+	0.582303i
$665$	−4.00000	−	12.3107i	−0.155113	−	0.477390i
$666$	8.61803	+	26.5236i	0.333942	+	1.02777i
$667$	−16.9443	−	12.3107i	−0.656085	−	0.476674i
$668$	−12.0000	+	8.71851i	−0.464294	+	0.337329i
$669$	3.88854	−	11.9677i	0.150340	−	0.462698i
$670$	−64.7214			−2.50040
$671$		0			0
$672$	8.29180			0.319863
$673$	−6.61803	+	20.3682i	−0.255106	+	0.785137i	0.738702	+	0.674032i	$0.235439\pi$
$673$	−6.61803	+	20.3682i	−0.255106	+	0.785137i	−0.993809	+	0.111105i	$0.964561\pi$
$674$	20.8541	−	15.1514i	0.803270	−	0.583610i
$675$	4.47214	+	3.24920i	0.172133	+	0.125062i
$676$	−2.34346	−	7.21242i	−0.0901330	−	0.277401i
$677$	−3.00000	−	9.23305i	−0.115299	−	0.354855i	0.876710	−	0.481019i	$-0.159733\pi$
$677$	−3.00000	−	9.23305i	−0.115299	−	0.354855i	−0.992009	+	0.126164i	$0.959733\pi$
$678$	4.47214	+	3.24920i	0.171751	+	0.124785i
$679$	−14.0902	+	10.2371i	−0.540731	+	0.392864i
$680$	4.47214	−	13.7638i	0.171499	−	0.527818i
$681$	−7.27864			−0.278918
$682$		0			0
$683$	−5.88854			−0.225319			−0.112659	−	0.993634i	$-0.535937\pi$
$683$	−5.88854			−0.225319			−0.112659	+	0.993634i	$0.535937\pi$
$684$	−8.83282	+	27.1846i	−0.337731	+	1.03943i
$685$	26.6525	−	19.3642i	1.01834	−	0.739866i
$686$	−1.80902	−	1.31433i	−0.0690686	−	0.0501813i
$687$	1.70820	+	5.25731i	0.0651720	+	0.200579i
$688$	−2.47214	−	7.60845i	−0.0942493	−	0.290070i
$689$	1.23607	+	0.898056i	0.0470904	+	0.0342132i
$690$	−11.0557	+	8.03246i	−0.420884	+	0.305790i
$691$	5.72949	−	17.6336i	0.217960	−	0.670812i	−0.780970	−	0.624568i	$-0.785275\pi$
$691$	5.72949	−	17.6336i	0.217960	−	0.670812i	0.998930	−	0.0462437i	$-0.0147251\pi$
$692$	−38.2918			−1.45564
$693$		0			0
$694$	46.8328			1.77775
$695$	0.944272	−	2.90617i	0.0358183	−	0.110237i
$696$	18.9443	−	13.7638i	0.718081	−	0.521716i
$697$	−29.4164	−	21.3723i	−1.11423	−	0.809533i
$698$	−5.00000	−	15.3884i	−0.189253	−	0.582460i
$699$	−3.59675	−	11.0697i	−0.136041	−	0.418693i
$700$	2.42705	+	1.76336i	0.0917339	+	0.0666486i
$701$	12.5623	−	9.12705i	0.474472	−	0.344724i	−0.324710	−	0.945814i	$-0.605267\pi$
$701$	12.5623	−	9.12705i	0.474472	−	0.344724i	0.799181	+	0.601090i	$0.205267\pi$
$702$	12.3607	−	38.0423i	0.466524	−	1.43581i
$703$	−54.8328			−2.06806
$704$		0			0
$705$	6.83282			0.257339
$706$	13.7426	−	42.2955i	0.517211	−	1.59181i
$707$	3.85410	−	2.80017i	0.144948	−	0.105311i
$708$	−3.70820	−	2.69417i	−0.139363	−	0.101253i
$709$	−4.61803	−	14.2128i	−0.173434	−	0.533775i	0.826125	−	0.563488i	$-0.190541\pi$
$709$	−4.61803	−	14.2128i	−0.173434	−	0.533775i	−0.999558	+	0.0297129i	$0.990541\pi$
$710$	14.4721	+	44.5407i	0.543130	+	1.67158i
$711$	−10.6525	−	7.73948i	−0.399499	−	0.290253i
$712$	−3.61803	+	2.62866i	−0.135592	+	0.0985130i
$713$	−2.11146	+	6.49839i	−0.0790747	+	0.243367i
$714$	8.94427			0.334731
$715$		0			0
$716$	−26.8328			−1.00279
$717$	3.77709	−	11.6247i	0.141058	−	0.434132i
$718$	45.1246	−	32.7849i	1.68404	−	1.22352i
$719$	41.6525	+	30.2623i	1.55338	+	1.12859i	0.941189	+	0.337879i	$0.109710\pi$
$719$	41.6525	+	30.2623i	1.55338	+	1.12859i	0.612186	+	0.790714i	$0.290290\pi$
$720$	−0.909830	−	2.80017i	−0.0339074	−	0.104356i
$721$	2.38197	+	7.33094i	0.0887090	+	0.273018i
$722$	−41.4058	−	30.0830i	−1.54096	−	1.11958i
$723$	−13.1246	+	9.53559i	−0.488110	+	0.354632i
$724$	−23.5623	+	72.5173i	−0.875686	+	2.69509i
$725$	−8.47214			−0.314647
$726$		0			0
$727$	25.0132			0.927687			0.463843	−	0.885917i	$-0.346470\pi$
$727$	25.0132			0.927687			0.463843	+	0.885917i	$0.346470\pi$
$728$	2.23607	−	6.88191i	0.0828742	−	0.255061i
$729$	−19.4615	+	14.1396i	−0.720796	+	0.523689i
$730$	−2.76393	−	2.00811i	−0.102298	−	0.0743236i
$731$	−8.00000	−	24.6215i	−0.295891	−	0.910658i
$732$	8.29180	+	25.5195i	0.306474	+	0.943229i
$733$	−7.09017	−	5.15131i	−0.261881	−	0.190268i	0.449095	−	0.893484i	$-0.351747\pi$
$733$	−7.09017	−	5.15131i	−0.261881	−	0.190268i	−0.710976	+	0.703216i	$0.751747\pi$
$734$	41.8328	−	30.3933i	1.54408	−	1.12184i
$735$	0.763932	−	2.35114i	0.0281781	−	0.0867231i
$736$	−16.5836			−0.611279
$737$		0			0
$738$	36.9868			1.36150
$739$	7.70820	−	23.7234i	0.283551	−	0.872680i	−0.703278	−	0.710915i	$-0.748281\pi$
$739$	7.70820	−	23.7234i	0.283551	−	0.872680i	0.986829	−	0.161765i	$-0.0517187\pi$
$740$	−41.1246	+	29.8788i	−1.51177	+	1.09837i
$741$	20.9443	+	15.2169i	0.769407	+	0.559007i
$742$	−0.326238	−	1.00406i	−0.0119766	−	0.0368601i
$743$	0.583592	+	1.79611i	0.0214099	+	0.0658930i	0.961191	−	0.275885i	$-0.0889709\pi$
$743$	0.583592	+	1.79611i	0.0214099	+	0.0658930i	−0.939781	+	0.341778i	$0.888971\pi$
$744$	−6.18034	−	4.49028i	−0.226582	−	0.164622i
$745$	22.6525	−	16.4580i	0.829923	−	0.602974i
$746$	4.14590	−	12.7598i	0.151792	−	0.467168i
$747$	16.8065			0.614918
$748$		0			0
$749$	−4.00000			−0.146157
$750$	−10.2492	+	31.5439i	−0.374249	+	1.15182i
$751$	−23.8885	+	17.3560i	−0.871705	+	0.633331i	−0.931044	−	0.364907i	$-0.881101\pi$
$751$	−23.8885	+	17.3560i	−0.871705	+	0.633331i	0.0593387	+	0.998238i	$0.481101\pi$
$752$	2.23607	+	1.62460i	0.0815410	+	0.0592430i
$753$	−1.63932	−	5.04531i	−0.0597402	−	0.183861i
$754$	18.9443	+	58.3045i	0.689910	+	2.12332i
$755$	14.4721	+	10.5146i	0.526695	+	0.382666i
$756$	−13.4164	+	9.74759i	−0.487950	+	0.354516i
$757$	4.90983	−	15.1109i	0.178451	−	0.549215i	−0.821323	−	0.570463i	$-0.806764\pi$
$757$	4.90983	−	15.1109i	0.178451	−	0.549215i	0.999774	+	0.0212477i	$0.00676386\pi$
$758$	83.4164			3.02982
$759$		0			0
$760$	−28.9443			−1.04992
$761$	−9.76393	+	30.0503i	−0.353942	+	1.08932i	0.602678	+	0.797984i	$0.294100\pi$
$761$	−9.76393	+	30.0503i	−0.353942	+	1.08932i	−0.956620	+	0.291338i	$0.905900\pi$
$762$	6.83282	−	4.96433i	0.247527	−	0.179839i
$763$	3.61803	+	2.62866i	0.130982	+	0.0951637i
$764$	−2.83282	−	8.71851i	−0.102488	−	0.315425i
$765$	−2.94427	−	9.06154i	−0.106450	−	0.327621i
$766$	8.41641	+	6.11488i	0.304097	+	0.220940i
$767$	3.23607	−	2.35114i	0.116848	−	0.0848948i
$768$	3.43769	−	10.5801i	0.124047	−	0.381778i
$769$	18.2918			0.659619			0.329810	−	0.944047i	$-0.393015\pi$
$769$	18.2918			0.659619			0.329810	+	0.944047i	$0.393015\pi$
$770$		0			0
$771$	7.41641			0.267095
$772$	11.0213	−	33.9200i	0.396665	−	1.22081i
$773$	31.0344	−	22.5478i	1.11623	−	0.810990i	0.132598	−	0.991170i	$-0.457668\pi$
$773$	31.0344	−	22.5478i	1.11623	−	0.810990i	0.983634	+	0.180180i	$0.0576682\pi$
$774$	21.3050	+	15.4790i	0.765791	+	0.556379i
$775$	0.854102	+	2.62866i	0.0306802	+	0.0944241i
$776$	12.0344	+	37.0382i	0.432011	+	1.32959i
$777$	−8.47214	−	6.15537i	−0.303936	−	0.220823i
$778$	−28.7426	+	20.8828i	−1.03047	+	0.748683i
$779$	−22.4721	+	69.1621i	−0.805148	+	2.47799i
$780$	24.0000			0.859338
$781$		0			0
$782$	−17.8885			−0.639693
$783$	14.4721	−	44.5407i	0.517192	−	1.59175i
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	17.7082	+	12.8658i	0.632033	+	0.459199i
$786$	−18.6950	−	57.5374i	−0.666830	−	2.05229i
$787$	−13.4164	−	41.2915i	−0.478243	−	1.47188i	−0.841533	−	0.540205i	$-0.818347\pi$
$787$	−13.4164	−	41.2915i	−0.478243	−	1.47188i	0.363290	−	0.931676i	$-0.381653\pi$
$788$	4.85410	+	3.52671i	0.172920	+	0.125634i
$789$		0			0
$790$	12.3607	−	38.0423i	0.439773	−	1.35348i
$791$	2.00000			0.0711118
$792$		0			0
$793$	−23.4164			−0.831541
$794$	−24.7984	+	76.3215i	−0.880061	+	2.70855i
$795$	0.944272	−	0.686054i	0.0334899	−	0.0243318i
$796$	5.29180	+	3.84471i	0.187563	+	0.136272i
$797$	−4.61803	−	14.2128i	−0.163579	−	0.503445i	0.835350	−	0.549719i	$-0.185265\pi$
$797$	−4.61803	−	14.2128i	−0.163579	−	0.503445i	−0.998929	+	0.0462742i	$0.985265\pi$
$798$	−5.52786	−	17.0130i	−0.195684	−	0.602254i
$799$	7.23607	+	5.25731i	0.255994	+	0.185990i
$800$	−5.42705	+	3.94298i	−0.191875	+	0.139406i
$801$	−0.909830	+	2.80017i	−0.0321473	+	0.0989391i
$802$	51.3050			1.81164
$803$		0			0
$804$	−53.6656			−1.89264
$805$	−1.52786	+	4.70228i	−0.0538501	+	0.165734i
$806$	16.1803	−	11.7557i	0.569928	−	0.414077i
$807$	13.4164	+	9.74759i	0.472280	+	0.343131i
$808$	−3.29180	−	10.1311i	−0.115805	−	0.356411i
$809$	6.50658	+	20.0252i	0.228759	+	0.704048i	0.997888	+	0.0649547i	$0.0206903\pi$
$809$	6.50658	+	20.0252i	0.228759	+	0.704048i	−0.769129	+	0.639093i	$0.779310\pi$
$810$	−8.74265	−	6.35190i	−0.307185	−	0.223183i
$811$	28.1803	−	20.4742i	0.989546	−	0.718947i	0.0297241	−	0.999558i	$-0.490537\pi$
$811$	28.1803	−	20.4742i	0.989546	−	0.718947i	0.959822	+	0.280611i	$0.0905371\pi$
$812$	7.85410	−	24.1724i	0.275625	−	0.848286i
$813$	12.9443			0.453975
$814$		0			0
$815$	6.83282			0.239343
$816$	−1.23607	+	3.80423i	−0.0432710	+	0.133175i
$817$	−41.8885	+	30.4338i	−1.46549	+	1.06474i
$818$	−16.5066	−	11.9927i	−0.577139	−	0.419316i
$819$	−1.47214	−	4.53077i	−0.0514406	−	0.158318i
$820$	20.8328	+	64.1168i	0.727513	+	2.23906i
$821$	−36.2705	−	26.3521i	−1.26585	−	0.919694i	−0.266820	−	0.963746i	$-0.585973\pi$
$821$	−36.2705	−	26.3521i	−1.26585	−	0.919694i	−0.999029	+	0.0440528i	$0.985973\pi$
$822$	36.8328	−	26.7606i	1.28469	−	0.933383i
$823$	−4.36068	+	13.4208i	−0.152004	+	0.467819i	−0.997845	−	0.0656153i	$-0.979099\pi$
$823$	−4.36068	+	13.4208i	−0.152004	+	0.467819i	0.845841	+	0.533435i	$0.179099\pi$
$824$	17.2361			0.600447
$825$		0			0
$826$	−2.76393			−0.0961695
$827$	−4.00000	+	12.3107i	−0.139094	+	0.428086i	−0.996204	−	0.0870462i	$-0.972257\pi$
$827$	−4.00000	+	12.3107i	−0.139094	+	0.428086i	0.857111	+	0.515132i	$0.172257\pi$
$828$	8.83282	−	6.41742i	0.306962	−	0.223021i
$829$	−29.7984	−	21.6498i	−1.03494	−	0.751928i	−0.0656488	−	0.997843i	$-0.520912\pi$
$829$	−29.7984	−	21.6498i	−1.03494	−	0.751928i	−0.969291	+	0.245915i	$0.920912\pi$
$830$	15.7771	+	48.5569i	0.547631	+	1.68543i
$831$	7.59675	+	23.3804i	0.263528	+	0.811057i
$832$	34.0344	+	24.7275i	1.17993	+	0.857271i
$833$	2.61803	−	1.90211i	0.0907095	−	0.0659043i
$834$	1.30495	−	4.01623i	0.0451868	−	0.139071i
$835$	−9.88854			−0.342207
$836$		0			0
$837$	−15.2786			−0.528107
$838$	17.0344	−	52.4266i	0.588445	−	1.81105i
$839$	−35.6525	+	25.9030i	−1.23086	+	0.894272i	−0.996954	−	0.0779870i	$-0.975151\pi$
$839$	−35.6525	+	25.9030i	−1.23086	+	0.894272i	−0.233906	+	0.972259i	$0.575151\pi$
$840$	−4.47214	−	3.24920i	−0.154303	−	0.112108i
$841$	13.2188	+	40.6834i	0.455822	+	1.40288i
$842$	15.4508	+	47.5528i	0.532471	+	1.63878i
$843$	−3.52786	−	2.56314i	−0.121506	−	0.0882793i
$844$	33.7082	−	24.4904i	1.16028	−	0.842996i
$845$	1.56231	−	4.80828i	0.0537450	−	0.165410i
$846$	−9.09830			−0.312806
$847$		0			0
$848$	0.472136			0.0162132
$849$	−11.4164	+	35.1361i	−0.391810	+	1.20587i
$850$	−5.85410	+	4.25325i	−0.200794	+	0.145885i
$851$	16.9443	+	12.3107i	0.580842	+	0.422007i
$852$	12.0000	+	36.9322i	0.411113	+	1.26528i
$853$	−9.47214	−	29.1522i	−0.324320	−	0.998154i	−0.971747	−	0.236026i	$-0.924155\pi$
$853$	−9.47214	−	29.1522i	−0.324320	−	0.998154i	0.647427	−	0.762128i	$-0.275845\pi$
$854$	13.0902	+	9.51057i	0.447936	+	0.325445i
$855$	−15.4164	+	11.2007i	−0.527230	+	0.383055i
$856$	−2.76393	+	8.50651i	−0.0944693	+	0.290746i
$857$	15.2361			0.520454			0.260227	−	0.965547i	$-0.416203\pi$
$857$	15.2361			0.520454			0.260227	+	0.965547i	$0.416203\pi$
$858$		0			0
$859$	−26.5410			−0.905568			−0.452784	−	0.891620i	$-0.649569\pi$
$859$	−26.5410			−0.905568			−0.452784	+	0.891620i	$0.649569\pi$
$860$	−14.8328	+	45.6507i	−0.505795	+	1.55668i
$861$	−11.2361	+	8.16348i	−0.382924	+	0.278211i
$862$	−21.7082	−	15.7719i	−0.739384	−	0.537194i
$863$	−0.944272	−	2.90617i	−0.0321434	−	0.0989272i	0.933698	−	0.358062i	$-0.116562\pi$
$863$	−0.944272	−	2.90617i	−0.0321434	−	0.0989272i	−0.965841	+	0.259135i	$0.916562\pi$
$864$	−11.4590	−	35.2671i	−0.389842	−	1.19981i
$865$	−20.6525	−	15.0049i	−0.702205	−	0.510182i
$866$	15.3262	−	11.1352i	0.520807	−	0.378388i
$867$	2.49342	−	7.67396i	0.0846811	−	0.260621i
$868$	−8.29180			−0.281442
$869$		0			0
$870$	46.8328			1.58778
$871$	14.4721	−	44.5407i	0.490370	−	1.50920i
$872$	8.09017	−	5.87785i	0.273968	−	0.199049i
$873$	20.7426	+	15.0704i	0.702032	+	0.510056i
$874$	11.0557	+	34.0260i	0.373966	+	1.15095i
$875$	3.70820	+	11.4127i	0.125360	+	0.385819i
$876$	−2.29180	−	1.66509i	−0.0774326	−	0.0562581i
$877$	−11.7984	+	8.57202i	−0.398403	+	0.289457i	−0.768890	−	0.639381i	$-0.779191\pi$
$877$	−11.7984	+	8.57202i	−0.398403	+	0.289457i	0.370487	+	0.928838i	$0.379191\pi$
$878$	7.23607	−	22.2703i	0.244205	−	0.751587i
$879$	31.0557			1.04748
$880$		0			0
$881$	2.58359			0.0870434			0.0435217	−	0.999052i	$-0.486142\pi$
$881$	2.58359			0.0870434			0.0435217	+	0.999052i	$0.486142\pi$
$882$	−1.01722	+	3.13068i	−0.0342516	+	0.105416i
$883$	7.23607	−	5.25731i	0.243513	−	0.176923i	−0.459334	−	0.888264i	$-0.651912\pi$
$883$	7.23607	−	5.25731i	0.243513	−	0.176923i	0.702847	+	0.711341i	$0.251912\pi$
$884$	25.4164	+	18.4661i	0.854846	+	0.621082i
$885$	−0.944272	−	2.90617i	−0.0317414	−	0.0976898i
$886$	−17.2361	−	53.0472i	−0.579057	−	1.78215i
$887$	3.52786	+	2.56314i	0.118454	+	0.0860619i	0.645435	−	0.763815i	$-0.276676\pi$
$887$	3.52786	+	2.56314i	0.118454	+	0.0860619i	−0.526981	+	0.849877i	$0.676676\pi$
$888$	−18.9443	+	13.7638i	−0.635728	+	0.461884i
$889$	0.944272	−	2.90617i	0.0316699	−	0.0974698i
$890$	−8.94427			−0.299813
$891$		0			0
$892$	−30.5410			−1.02259
$893$	5.52786	−	17.0130i	0.184983	−	0.569319i
$894$	31.3050	−	22.7444i	1.04699	−	0.760686i
$895$	−14.4721	−	10.5146i	−0.483750	−	0.351465i
$896$	−4.83688	−	14.8864i	−0.161589	−	0.497319i
$897$	−3.05573	−	9.40456i	−0.102028	−	0.314009i
$898$	51.5066	+	37.4217i	1.71880	+	1.24878i
$899$	18.9443	−	13.7638i	0.631827	−	0.459049i
$900$	1.36475	−	4.20025i	0.0454915	−	0.140008i
$901$	1.52786			0.0509005
$902$		0			0
$903$	−9.88854			−0.329070
$904$	1.38197	−	4.25325i	0.0459635	−	0.141461i
$905$	−41.1246	+	29.8788i	−1.36703	+	0.993204i
$906$	20.0000	+	14.5309i	0.664455	+	0.482755i
$907$	6.94427	+	21.3723i	0.230581	+	0.709655i	0.997677	+	0.0681225i	$0.0217009\pi$
$907$	6.94427	+	21.3723i	0.230581	+	0.709655i	−0.767096	+	0.641532i	$0.778299\pi$
$908$	5.45898	+	16.8010i	0.181163	+	0.557561i
$909$	−5.67376	−	4.12223i	−0.188187	−	0.136726i
$910$	11.7082	−	8.50651i	0.388123	−	0.281988i
$911$	13.1246	−	40.3934i	0.434838	−	1.33829i	−0.458415	−	0.888738i	$-0.651583\pi$
$911$	13.1246	−	40.3934i	0.434838	−	1.33829i	0.893253	−	0.449555i	$-0.148417\pi$
$912$	8.00000			0.264906
$913$		0			0
$914$	−64.4721			−2.13255
$915$	−5.52786	+	17.0130i	−0.182746	+	0.562433i
$916$	10.8541	−	7.88597i	0.358630	−	0.260560i
$917$	−17.7082	−	12.8658i	−0.584776	−	0.424865i
$918$	−12.3607	−	38.0423i	−0.407963	−	1.25558i
$919$	12.9443	+	39.8384i	0.426992	+	1.31415i	0.901074	+	0.433666i	$0.142780\pi$
$919$	12.9443	+	39.8384i	0.426992	+	1.31415i	−0.474082	+	0.880481i	$0.657220\pi$
$920$	8.94427	+	6.49839i	0.294884	+	0.214246i
$921$	−8.94427	+	6.49839i	−0.294724	+	0.214129i
$922$	−8.41641	+	25.9030i	−0.277180	+	0.853071i
$923$	−33.8885			−1.11546
$924$		0			0
$925$	8.47214			0.278562
$926$	−3.81966	+	11.7557i	−0.125522	+	0.386316i
$927$	9.18034	−	6.66991i	0.301522	−	0.219068i
$928$	45.9787	+	33.4055i	1.50933	+	1.09659i
$929$	−16.1459	−	49.6920i	−0.529730	−	1.63034i	−0.754769	−	0.655991i	$-0.772251\pi$
$929$	−16.1459	−	49.6920i	−0.529730	−	1.63034i	0.225039	−	0.974350i	$-0.427749\pi$
$930$	−4.72136	−	14.5309i	−0.154819	−	0.476485i
$931$	−5.23607	−	3.80423i	−0.171605	−	0.124678i
$932$	−22.8541	+	16.6045i	−0.748611	+	0.543898i
$933$	3.16718	−	9.74759i	0.103689	−	0.319122i
$934$	53.8197			1.76103
$935$		0			0
$936$	−10.6525			−0.348187
$937$	−3.29180	+	10.1311i	−0.107538	+	0.330969i	−0.990318	−	0.138819i	$-0.955669\pi$
$937$	−3.29180	+	10.1311i	−0.107538	+	0.330969i	0.882780	+	0.469788i	$0.155669\pi$
$938$	−26.1803	+	19.0211i	−0.854818	+	0.621062i
$939$	14.9443	+	10.8576i	0.487688	+	0.354326i
$940$	−5.12461	−	15.7719i	−0.167146	−	0.514424i
$941$	2.34752	+	7.22494i	0.0765271	+	0.235526i	0.982001	−	0.188876i	$-0.0604844\pi$
$941$	2.34752	+	7.22494i	0.0765271	+	0.235526i	−0.905474	+	0.424402i	$0.860484\pi$
$942$	24.4721	+	17.7800i	0.797345	+	0.579305i
$943$	22.4721	−	16.3270i	0.731793	−	0.531679i
$944$	0.381966	−	1.17557i	0.0124319	−	0.0382616i
$945$	−11.0557			−0.359643
$946$		0			0
$947$	−5.16718			−0.167911			−0.0839555	−	0.996470i	$-0.526755\pi$
$947$	−5.16718			−0.167911			−0.0839555	+	0.996470i	$0.526755\pi$
$948$	10.2492	−	31.5439i	0.332879	−	1.02450i
$949$	2.00000	−	1.45309i	0.0649227	−	0.0471691i
$950$	11.7082	+	8.50651i	0.379864	+	0.275988i
$951$	−5.34752	−	16.4580i	−0.173405	−	0.533687i
$952$	−2.23607	−	6.88191i	−0.0724714	−	0.223044i
$953$	−18.5623	−	13.4863i	−0.601292	−	0.436864i	0.245045	−	0.969512i	$-0.421197\pi$
$953$	−18.5623	−	13.4863i	−0.601292	−	0.436864i	−0.846337	+	0.532647i	$0.821197\pi$
$954$	−1.25735	+	0.913521i	−0.0407083	+	0.0295763i
$955$	1.88854	−	5.81234i	0.0611118	−	0.188083i
$956$	−29.6656			−0.959455
$957$		0			0
$958$	30.2492			0.977308
$959$	5.09017	−	15.6659i	0.164370	−	0.505879i
$960$	26.0000	−	18.8901i	0.839146	−	0.609676i
$961$	18.8992	+	13.7311i	0.609651	+	0.442938i
$962$	−18.9443	−	58.3045i	−0.610788	−	1.87981i
$963$	1.81966	+	5.60034i	0.0586377	+	0.180468i
$964$	31.8541	+	23.1434i	1.02595	+	0.745397i
$965$	19.2361	−	13.9758i	0.619231	−	0.449898i
$966$	−2.11146	+	6.49839i	−0.0679350	+	0.209082i
$967$	−13.8885			−0.446625			−0.223313	−	0.974747i	$-0.571687\pi$
$967$	−13.8885			−0.446625			−0.223313	+	0.974747i	$0.571687\pi$
$968$		0			0
$969$	25.8885			0.831660
$970$	−24.0689	+	74.0764i	−0.772805	+	2.37845i
$971$	−9.00000	+	6.53888i	−0.288824	+	0.209843i	−0.722757	−	0.691102i	$-0.757125\pi$
$971$	−9.00000	+	6.53888i	−0.288824	+	0.209843i	0.433933	+	0.900945i	$0.357125\pi$
$972$	33.0000	+	23.9759i	1.05848	+	0.769027i
$973$	−0.472136	−	1.45309i	−0.0151360	−	0.0465838i
$974$	−25.1246	−	77.3256i	−0.805044	−	2.47767i
$975$	−3.23607	−	2.35114i	−0.103637	−	0.0752968i
$976$	−5.85410	+	4.25325i	−0.187385	+	0.136143i
$977$	7.09017	−	21.8213i	0.226835	−	0.698125i	−0.771266	−	0.636513i	$-0.780376\pi$
$977$	7.09017	−	21.8213i	0.226835	−	0.698125i	0.998100	−	0.0616117i	$-0.0196240\pi$
$978$	9.44272			0.301945
$979$		0			0
$980$	−6.00000			−0.191663
$981$	2.03444	−	6.26137i	0.0649547	−	0.199910i
$982$		0			0
$983$	−17.6525	−	12.8253i	−0.563027	−	0.409063i	0.269539	−	0.962990i	$-0.413129\pi$
$983$	−17.6525	−	12.8253i	−0.563027	−	0.409063i	−0.832565	+	0.553927i	$0.813129\pi$
$984$	9.59675	+	29.5358i	0.305933	+	0.941565i
$985$	1.23607	+	3.80423i	0.0393844	+	0.121213i
$986$	49.5967	+	36.0341i	1.57948	+	1.14756i
$987$	2.76393	−	2.00811i	0.0879769	−	0.0639190i
$988$	19.4164	−	59.7576i	0.617718	−	1.90114i
$989$	19.7771			0.628875
$990$		0			0
$991$	54.2492			1.72328			0.861642	−	0.507517i	$-0.169437\pi$
$991$	54.2492			1.72328			0.861642	+	0.507517i	$0.169437\pi$
$992$	5.72949	−	17.6336i	0.181911	−	0.559866i
$993$	−13.8885	+	10.0906i	−0.440740	+	0.320216i
$994$	18.9443	+	13.7638i	0.600876	+	0.436562i
$995$	1.34752	+	4.14725i	0.0427194	+	0.131477i
$996$	13.0820	+	40.2624i	0.414520	+	1.27576i
$997$	−1.09017	−	0.792055i	−0.0345260	−	0.0250846i	0.570388	−	0.821375i	$-0.306793\pi$
$997$	−1.09017	−	0.792055i	−0.0345260	−	0.0250846i	−0.604914	+	0.796290i	$0.706793\pi$
$998$	−2.76393	+	2.00811i	−0.0874907	+	0.0635657i
$999$	−14.4721	+	44.5407i	−0.457878	+	1.40920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.n.372.1		4
11.2	odd	10		847.2.f.m.729.1		4
11.3	even	5		847.2.f.a.323.1		4
11.4	even	5		77.2.a.d.1.2	✓	2
11.5	even	5	inner	847.2.f.n.148.1		4
11.6	odd	10		847.2.f.b.148.1		4
11.7	odd	10		847.2.a.f.1.1		2
11.8	odd	10		847.2.f.m.323.1		4
11.9	even	5		847.2.f.a.729.1		4
11.10	odd	2		847.2.f.b.372.1		4
33.26	odd	10		693.2.a.h.1.1		2
33.29	even	10		7623.2.a.bl.1.2		2
44.15	odd	10		1232.2.a.m.1.2		2
55.4	even	10		1925.2.a.r.1.1		2
55.37	odd	20		1925.2.b.h.1849.3		4
55.48	odd	20		1925.2.b.h.1849.2		4
77.4	even	15		539.2.e.i.177.1		4
77.26	odd	30		539.2.e.j.67.1		4
77.37	even	15		539.2.e.i.67.1		4
77.48	odd	10		539.2.a.f.1.2		2
77.59	odd	30		539.2.e.j.177.1		4
77.62	even	10		5929.2.a.m.1.1		2
88.37	even	10		4928.2.a.bm.1.2		2
88.59	odd	10		4928.2.a.bv.1.1		2
231.125	even	10		4851.2.a.y.1.1		2
308.279	even	10		8624.2.a.ce.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.d.1.2	✓	2	11.4	even	5
539.2.a.f.1.2		2	77.48	odd	10
539.2.e.i.67.1		4	77.37	even	15
539.2.e.i.177.1		4	77.4	even	15
539.2.e.j.67.1		4	77.26	odd	30
539.2.e.j.177.1		4	77.59	odd	30
693.2.a.h.1.1		2	33.26	odd	10
847.2.a.f.1.1		2	11.7	odd	10
847.2.f.a.323.1		4	11.3	even	5
847.2.f.a.729.1		4	11.9	even	5
847.2.f.b.148.1		4	11.6	odd	10
847.2.f.b.372.1		4	11.10	odd	2
847.2.f.m.323.1		4	11.8	odd	10
847.2.f.m.729.1		4	11.2	odd	10
847.2.f.n.148.1		4	11.5	even	5	inner
847.2.f.n.372.1		4	1.1	even	1	trivial
1232.2.a.m.1.2		2	44.15	odd	10
1925.2.a.r.1.1		2	55.4	even	10
1925.2.b.h.1849.2		4	55.48	odd	20
1925.2.b.h.1849.3		4	55.37	odd	20
4851.2.a.y.1.1		2	231.125	even	10
4928.2.a.bm.1.2		2	88.37	even	10
4928.2.a.bv.1.1		2	88.59	odd	10
5929.2.a.m.1.1		2	77.62	even	10
7623.2.a.bl.1.2		2	33.29	even	10
8624.2.a.ce.1.1		2	308.279	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.690983 - 2.12663i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-0.854102 - 2.62866i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-0.454915 + 1.40008i) q^{9} +O(q^{10})\)	\(q+(0.690983 - 2.12663i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(-0.854102 - 2.62866i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-0.454915 + 1.40008i) q^{9} -4.47214 q^{10} -3.70820 q^{12} +(1.00000 - 3.07768i) q^{13} +(-1.80902 + 1.31433i) q^{14} +(-2.00000 - 1.45309i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-1.00000 - 3.07768i) q^{17} +(2.66312 + 1.93487i) q^{18} +(-5.23607 + 3.80423i) q^{19} +(-1.85410 + 5.70634i) q^{20} -1.23607 q^{21} +2.47214 q^{23} +(-0.854102 + 2.62866i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-5.85410 - 4.25325i) q^{26} +(1.70820 + 5.25731i) q^{27} +(0.927051 + 2.85317i) q^{28} +(-6.85410 - 4.97980i) q^{29} +(-4.47214 + 3.24920i) q^{30} +(-0.854102 + 2.62866i) q^{31} -6.70820 q^{32} -7.23607 q^{34} +(-0.618034 + 1.90211i) q^{35} +(3.57295 - 2.59590i) q^{36} +(6.85410 + 4.97980i) q^{37} +(4.47214 + 13.7638i) q^{38} +(-1.23607 - 3.80423i) q^{39} +(3.61803 + 2.62866i) q^{40} +(9.09017 - 6.60440i) q^{41} +(-0.854102 + 2.62866i) q^{42} +8.00000 q^{43} +2.94427 q^{45} +(1.70820 - 5.25731i) q^{46} +(-2.23607 + 1.62460i) q^{47} +(-1.00000 - 0.726543i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.690983 - 2.12663i) q^{50} +(-3.23607 - 2.35114i) q^{51} +(-7.85410 + 5.70634i) q^{52} +(-0.145898 + 0.449028i) q^{53} +12.3607 q^{54} +2.23607 q^{56} +(-2.47214 + 7.60845i) q^{57} +(-15.3262 + 11.1352i) q^{58} +(1.00000 + 0.726543i) q^{59} +(2.29180 + 7.05342i) q^{60} +(-2.23607 - 6.88191i) q^{61} +(5.00000 + 3.63271i) q^{62} +(1.19098 - 0.865300i) q^{63} +(-4.01722 + 12.3637i) q^{64} -6.47214 q^{65} +14.4721 q^{67} +(-3.00000 + 9.23305i) q^{68} +(2.47214 - 1.79611i) q^{69} +(3.61803 + 2.62866i) q^{70} +(-3.23607 - 9.95959i) q^{71} +(-1.01722 - 3.13068i) q^{72} +(0.618034 + 0.449028i) q^{73} +(15.3262 - 11.1352i) q^{74} +(0.381966 - 1.17557i) q^{75} +19.4164 q^{76} -8.94427 q^{78} +(-2.76393 + 8.50651i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(1.95492 + 1.42033i) q^{81} +(-7.76393 - 23.8949i) q^{82} +(-3.52786 - 10.8576i) q^{83} +(3.00000 + 2.17963i) q^{84} +(-5.23607 + 3.80423i) q^{85} +(5.52786 - 17.0130i) q^{86} -10.4721 q^{87} +2.00000 q^{89} +(2.03444 - 6.26137i) q^{90} +(-2.61803 + 1.90211i) q^{91} +(-6.00000 - 4.35926i) q^{92} +(1.05573 + 3.24920i) q^{93} +(1.90983 + 5.87785i) q^{94} +(10.4721 + 7.60845i) q^{95} +(-6.70820 + 4.87380i) q^{96} +(5.38197 - 16.5640i) q^{97} +2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} + 4 q^{3} - 3 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 5 q^{8} - 13 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 + 4 * q^3 - 3 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 5 * q^8 - 13 * q^9	\( 4 q + 5 q^{2} + 4 q^{3} - 3 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 5 q^{8} - 13 q^{9} + 12 q^{12} + 4 q^{13} - 5 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 5 q^{18} - 12 q^{19} + 6 q^{20} + 4 q^{21} - 8 q^{23} + 10 q^{24} + q^{25} - 10 q^{26} - 20 q^{27} - 3 q^{28} - 14 q^{29} + 10 q^{31} - 20 q^{34} + 2 q^{35} + 21 q^{36} + 14 q^{37} + 4 q^{39} + 10 q^{40} + 14 q^{41} + 10 q^{42} + 32 q^{43} - 24 q^{45} - 20 q^{46} - 4 q^{48} - q^{49} - 5 q^{50} - 4 q^{51} - 18 q^{52} - 14 q^{53} - 40 q^{54} + 8 q^{57} - 30 q^{58} + 4 q^{59} + 36 q^{60} + 20 q^{62} + 7 q^{63} + 13 q^{64} - 8 q^{65} + 40 q^{67} - 12 q^{68} - 8 q^{69} + 10 q^{70} - 4 q^{71} + 25 q^{72} - 2 q^{73} + 30 q^{74} + 6 q^{75} + 24 q^{76} - 20 q^{79} - 2 q^{80} + 19 q^{81} - 40 q^{82} - 32 q^{83} + 12 q^{84} - 12 q^{85} + 40 q^{86} - 24 q^{87} + 8 q^{89} - 50 q^{90} - 6 q^{91} - 24 q^{92} + 40 q^{93} + 30 q^{94} + 24 q^{95} + 26 q^{97}+O(q^{100}) \) 4 * q + 5 * q^2 + 4 * q^3 - 3 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 5 * q^8 - 13 * q^9 + 12 * q^12 + 4 * q^13 - 5 * q^14 - 8 * q^15 + q^16 - 4 * q^17 - 5 * q^18 - 12 * q^19 + 6 * q^20 + 4 * q^21 - 8 * q^23 + 10 * q^24 + q^25 - 10 * q^26 - 20 * q^27 - 3 * q^28 - 14 * q^29 + 10 * q^31 - 20 * q^34 + 2 * q^35 + 21 * q^36 + 14 * q^37 + 4 * q^39 + 10 * q^40 + 14 * q^41 + 10 * q^42 + 32 * q^43 - 24 * q^45 - 20 * q^46 - 4 * q^48 - q^49 - 5 * q^50 - 4 * q^51 - 18 * q^52 - 14 * q^53 - 40 * q^54 + 8 * q^57 - 30 * q^58 + 4 * q^59 + 36 * q^60 + 20 * q^62 + 7 * q^63 + 13 * q^64 - 8 * q^65 + 40 * q^67 - 12 * q^68 - 8 * q^69 + 10 * q^70 - 4 * q^71 + 25 * q^72 - 2 * q^73 + 30 * q^74 + 6 * q^75 + 24 * q^76 - 20 * q^79 - 2 * q^80 + 19 * q^81 - 40 * q^82 - 32 * q^83 + 12 * q^84 - 12 * q^85 + 40 * q^86 - 24 * q^87 + 8 * q^89 - 50 * q^90 - 6 * q^91 - 24 * q^92 + 40 * q^93 + 30 * q^94 + 24 * q^95 + 26 * q^97

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