LMFDB - Embedded newform 847.2.f.m.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.m.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.690983 - 2.12663i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(2.23607 + 6.88191i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(2.30902 - 7.10642i) q^{9} +O(q^{10})$	\(q+(0.690983 - 2.12663i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(2.23607 + 6.88191i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(2.30902 - 7.10642i) q^{9} -4.47214 q^{10} +9.70820 q^{12} +(0.381966 - 1.17557i) q^{13} +(1.80902 - 1.31433i) q^{14} +(5.23607 + 3.80423i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.381966 - 1.17557i) q^{17} +(-13.5172 - 9.82084i) q^{18} +(-2.00000 + 1.45309i) q^{19} +(-1.85410 + 5.70634i) q^{20} -3.23607 q^{21} -6.47214 q^{23} +(2.23607 - 6.88191i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-2.23607 - 1.62460i) q^{26} +(4.47214 + 13.7638i) q^{27} +(-0.927051 - 2.85317i) q^{28} +(-0.381966 - 0.277515i) q^{29} +(11.7082 - 8.50651i) q^{30} +(-2.23607 + 6.88191i) q^{31} -6.70820 q^{32} -2.76393 q^{34} +(0.618034 - 1.90211i) q^{35} +(-18.1353 + 13.1760i) q^{36} +(-0.381966 - 0.277515i) q^{37} +(1.70820 + 5.25731i) q^{38} +(1.23607 + 3.80423i) q^{39} +(3.61803 + 2.62866i) q^{40} +(-5.47214 + 3.97574i) q^{41} +(-2.23607 + 6.88191i) q^{42} -8.00000 q^{43} -14.9443 q^{45} +(-4.47214 + 13.7638i) q^{46} +(-5.85410 + 4.25325i) q^{47} +(2.61803 + 1.90211i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.690983 - 2.12663i) q^{50} +(3.23607 + 2.35114i) q^{51} +(-3.00000 + 2.17963i) q^{52} +(2.61803 - 8.05748i) q^{53} +32.3607 q^{54} -2.23607 q^{56} +(2.47214 - 7.60845i) q^{57} +(-0.854102 + 0.620541i) q^{58} +(-2.61803 - 1.90211i) q^{59} +(-6.00000 - 18.4661i) q^{60} +(0.854102 + 2.62866i) q^{61} +(13.0902 + 9.51057i) q^{62} +(6.04508 - 4.39201i) q^{63} +(-4.01722 + 12.3637i) q^{64} -2.47214 q^{65} +5.52786 q^{67} +(-1.14590 + 3.52671i) q^{68} +(16.9443 - 12.3107i) q^{69} +(-3.61803 - 2.62866i) q^{70} +(-0.472136 - 1.45309i) q^{71} +(5.16312 + 15.8904i) q^{72} +(-4.23607 - 3.07768i) q^{73} +(-0.854102 + 0.620541i) q^{74} +(-1.00000 + 3.07768i) q^{75} +7.41641 q^{76} +8.94427 q^{78} +(-2.76393 + 8.50651i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(-19.7533 - 14.3516i) q^{81} +(4.67376 + 14.3844i) q^{82} +(-4.76393 - 14.6619i) q^{83} +(7.85410 + 5.70634i) q^{84} +(-2.00000 + 1.45309i) q^{85} +(-5.52786 + 17.0130i) q^{86} +1.52786 q^{87} +2.00000 q^{89} +(-10.3262 + 31.7809i) q^{90} +(1.00000 - 0.726543i) q^{91} +(15.7082 + 11.4127i) q^{92} +(-7.23607 - 22.2703i) q^{93} +(5.00000 + 15.3884i) q^{94} +(4.00000 + 2.90617i) q^{95} +(17.5623 - 12.7598i) q^{96} +(-2.90983 + 8.95554i) q^{97} +2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} + q^{7} - 5 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 - 6 * q^3 - 3 * q^4 + 2 * q^5 + q^7 - 5 * q^8 + 7 * q^9	$ 4 q + 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} + q^{7} - 5 q^{8} + 7 q^{9} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 12 q^{15} + q^{16} - 6 q^{17} - 25 q^{18} - 8 q^{19} + 6 q^{20} - 4 q^{21} - 8 q^{23} + q^{25} + 3 q^{28} - 6 q^{29} + 20 q^{30} - 20 q^{34} - 2 q^{35} - 39 q^{36} - 6 q^{37} - 20 q^{38} - 4 q^{39} + 10 q^{40} - 4 q^{41} - 32 q^{43} - 24 q^{45} - 10 q^{47} + 6 q^{48} - q^{49} - 5 q^{50} + 4 q^{51} - 12 q^{52} + 6 q^{53} + 40 q^{54} - 8 q^{57} + 10 q^{58} - 6 q^{59} - 24 q^{60} - 10 q^{61} + 30 q^{62} + 13 q^{63} + 13 q^{64} + 8 q^{65} + 40 q^{67} - 18 q^{68} + 32 q^{69} - 10 q^{70} + 16 q^{71} + 5 q^{72} - 8 q^{73} + 10 q^{74} - 4 q^{75} - 24 q^{76} - 20 q^{79} - 2 q^{80} - 41 q^{81} + 50 q^{82} - 28 q^{83} + 18 q^{84} - 8 q^{85} - 40 q^{86} + 24 q^{87} + 8 q^{89} - 10 q^{90} + 4 q^{91} + 36 q^{92} - 20 q^{93} + 20 q^{94} + 16 q^{95} + 30 q^{96} - 34 q^{97}+O(q^{100}) $ 4 * q + 5 * q^2 - 6 * q^3 - 3 * q^4 + 2 * q^5 + q^7 - 5 * q^8 + 7 * q^9 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 12 * q^15 + q^16 - 6 * q^17 - 25 * q^18 - 8 * q^19 + 6 * q^20 - 4 * q^21 - 8 * q^23 + q^25 + 3 * q^28 - 6 * q^29 + 20 * q^30 - 20 * q^34 - 2 * q^35 - 39 * q^36 - 6 * q^37 - 20 * q^38 - 4 * q^39 + 10 * q^40 - 4 * q^41 - 32 * q^43 - 24 * q^45 - 10 * q^47 + 6 * q^48 - q^49 - 5 * q^50 + 4 * q^51 - 12 * q^52 + 6 * q^53 + 40 * q^54 - 8 * q^57 + 10 * q^58 - 6 * q^59 - 24 * q^60 - 10 * q^61 + 30 * q^62 + 13 * q^63 + 13 * q^64 + 8 * q^65 + 40 * q^67 - 18 * q^68 + 32 * q^69 - 10 * q^70 + 16 * q^71 + 5 * q^72 - 8 * q^73 + 10 * q^74 - 4 * q^75 - 24 * q^76 - 20 * q^79 - 2 * q^80 - 41 * q^81 + 50 * q^82 - 28 * q^83 + 18 * q^84 - 8 * q^85 - 40 * q^86 + 24 * q^87 + 8 * q^89 - 10 * q^90 + 4 * q^91 + 36 * q^92 - 20 * q^93 + 20 * q^94 + 16 * q^95 + 30 * q^96 - 34 * 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	$-0.190215\pi$
$3$	−2.61803	+	1.90211i	−1.51152	+	1.09819i	−0.546027	+	0.837768i	$0.683860\pi$
$3$	−2.61803	+	1.90211i	−1.51152	+	1.09819i	−0.965496	+	0.260418i	$0.916140\pi$
$4$	−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	$-0.247584\pi$
$6$	2.23607	+	6.88191i	0.912871	+	2.80953i
$7$	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
$9$	2.30902	−	7.10642i	0.769672	−	2.36881i
$10$	−4.47214			−1.41421
$11$		0			0
$11$		0			0
$12$	9.70820			2.80252
$13$	0.381966	−	1.17557i	0.105938	−	0.326045i	−0.884011	−	0.467466i	$-0.845167\pi$
$13$	0.381966	−	1.17557i	0.105938	−	0.326045i	0.989950	+	0.141421i	$0.0451671\pi$
$14$	1.80902	−	1.31433i	0.483480	−	0.351269i
$15$	5.23607	+	3.80423i	1.35195	+	0.982247i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.381966	−	1.17557i	−0.0926404	−	0.285118i	0.893991	−	0.448085i	$-0.147894\pi$
$17$	−0.381966	−	1.17557i	−0.0926404	−	0.285118i	−0.986632	+	0.162967i	$0.947894\pi$
$18$	−13.5172	−	9.82084i	−3.18604	−	2.31479i
$19$	−2.00000	+	1.45309i	−0.458831	+	0.333361i	−0.793073	−	0.609127i	$-0.791520\pi$
$19$	−2.00000	+	1.45309i	−0.458831	+	0.333361i	0.334241	+	0.942488i	$0.391520\pi$
$20$	−1.85410	+	5.70634i	−0.414590	+	1.27598i
$21$	−3.23607			−0.706168
$22$		0			0
$23$	−6.47214			−1.34953			−0.674767	−	0.738031i	$-0.735756\pi$
$23$	−6.47214			−1.34953			−0.674767	+	0.738031i	$0.735756\pi$
$24$	2.23607	−	6.88191i	0.456435	−	1.40476i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	−2.23607	−	1.62460i	−0.438529	−	0.318610i
$27$	4.47214	+	13.7638i	0.860663	+	2.64885i
$28$	−0.927051	−	2.85317i	−0.175196	−	0.539198i
$29$	−0.381966	−	0.277515i	−0.0709293	−	0.0515332i	0.551756	−	0.834006i	$-0.313958\pi$
$29$	−0.381966	−	0.277515i	−0.0709293	−	0.0515332i	−0.622685	+	0.782473i	$0.713958\pi$
$30$	11.7082	−	8.50651i	2.13762	−	1.55307i
$31$	−2.23607	+	6.88191i	−0.401610	+	1.23603i	0.522083	+	0.852894i	$0.325155\pi$
$31$	−2.23607	+	6.88191i	−0.401610	+	1.23603i	−0.923693	+	0.383133i	$0.874845\pi$
$32$	−6.70820			−1.18585
$33$		0			0
$34$	−2.76393			−0.474010
$35$	0.618034	−	1.90211i	0.104467	−	0.321516i
$36$	−18.1353	+	13.1760i	−3.02254	+	2.19601i
$37$	−0.381966	−	0.277515i	−0.0627948	−	0.0456231i	0.555945	−	0.831219i	$-0.312356\pi$
$37$	−0.381966	−	0.277515i	−0.0627948	−	0.0456231i	−0.618740	+	0.785596i	$0.712356\pi$
$38$	1.70820	+	5.25731i	0.277107	+	0.852848i
$39$	1.23607	+	3.80423i	0.197929	+	0.609164i
$40$	3.61803	+	2.62866i	0.572061	+	0.415627i
$41$	−5.47214	+	3.97574i	−0.854604	+	0.620906i	−0.926412	−	0.376512i	$-0.877123\pi$
$41$	−5.47214	+	3.97574i	−0.854604	+	0.620906i	0.0718076	+	0.997419i	$0.477123\pi$
$42$	−2.23607	+	6.88191i	−0.345033	+	1.06190i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	−14.9443			−2.22776
$46$	−4.47214	+	13.7638i	−0.659380	+	2.02936i
$47$	−5.85410	+	4.25325i	−0.853909	+	0.620401i	−0.926221	−	0.376981i	$-0.876962\pi$
$47$	−5.85410	+	4.25325i	−0.853909	+	0.620401i	0.0723124	+	0.997382i	$0.476962\pi$
$48$	2.61803	+	1.90211i	0.377881	+	0.274546i
$49$	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
$52$	−3.00000	+	2.17963i	−0.416025	+	0.302260i
$53$	2.61803	−	8.05748i	0.359615	−	1.10678i	−0.593671	−	0.804708i	$-0.702322\pi$
$53$	2.61803	−	8.05748i	0.359615	−	1.10678i	0.953285	−	0.302072i	$-0.0976782\pi$
$54$	32.3607			4.40373
$55$		0			0
$56$	−2.23607			−0.298807
$57$	2.47214	−	7.60845i	0.327442	−	1.00776i
$58$	−0.854102	+	0.620541i	−0.112149	+	0.0814811i
$59$	−2.61803	−	1.90211i	−0.340839	−	0.247634i	0.404177	−	0.914681i	$-0.367558\pi$
$59$	−2.61803	−	1.90211i	−0.340839	−	0.247634i	−0.745016	+	0.667047i	$0.767558\pi$
$60$	−6.00000	−	18.4661i	−0.774597	−	2.38396i
$61$	0.854102	+	2.62866i	0.109357	+	0.336565i	0.990728	−	0.135859i	$-0.0433793\pi$
$61$	0.854102	+	2.62866i	0.109357	+	0.336565i	−0.881372	+	0.472423i	$0.843379\pi$
$62$	13.0902	+	9.51057i	1.66245	+	1.20784i
$63$	6.04508	−	4.39201i	0.761609	−	0.553341i
$64$	−4.01722	+	12.3637i	−0.502153	+	1.54547i
$65$	−2.47214			−0.306631
$66$		0			0
$67$	5.52786			0.675336			0.337668	−	0.941265i	$-0.390362\pi$
$67$	5.52786			0.675336			0.337668	+	0.941265i	$0.390362\pi$
$68$	−1.14590	+	3.52671i	−0.138961	+	0.427677i
$69$	16.9443	−	12.3107i	2.03985	−	1.48204i
$70$	−3.61803	−	2.62866i	−0.432438	−	0.314184i
$71$	−0.472136	−	1.45309i	−0.0560322	−	0.172449i	0.919124	−	0.393969i	$-0.128898\pi$
$71$	−0.472136	−	1.45309i	−0.0560322	−	0.172449i	−0.975156	+	0.221520i	$0.928898\pi$
$72$	5.16312	+	15.8904i	0.608479	+	1.87271i
$73$	−4.23607	−	3.07768i	−0.495794	−	0.360216i	0.311614	−	0.950209i	$-0.399130\pi$
$73$	−4.23607	−	3.07768i	−0.495794	−	0.360216i	−0.807408	+	0.589993i	$0.799130\pi$
$74$	−0.854102	+	0.620541i	−0.0992873	+	0.0721365i
$75$	−1.00000	+	3.07768i	−0.115470	+	0.355380i
$76$	7.41641			0.850720
$77$		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
$81$	−19.7533	−	14.3516i	−2.19481	−	1.59462i
$82$	4.67376	+	14.3844i	0.516131	+	1.58849i
$83$	−4.76393	−	14.6619i	−0.522909	−	1.60935i	−0.768413	−	0.639954i	$-0.778953\pi$
$83$	−4.76393	−	14.6619i	−0.522909	−	1.60935i	0.245504	−	0.969396i	$-0.421047\pi$
$84$	7.85410	+	5.70634i	0.856953	+	0.622613i
$85$	−2.00000	+	1.45309i	−0.216930	+	0.157609i
$86$	−5.52786	+	17.0130i	−0.596085	+	1.83456i
$87$	1.52786			0.163804
$88$		0			0
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	−10.3262	+	31.7809i	−1.08848	+	3.35000i
$91$	1.00000	−	0.726543i	0.104828	−	0.0761624i
$92$	15.7082	+	11.4127i	1.63769	+	1.18985i
$93$	−7.23607	−	22.2703i	−0.750345	−	2.30933i
$94$	5.00000	+	15.3884i	0.515711	+	1.58719i
$95$	4.00000	+	2.90617i	0.410391	+	0.298167i
$96$	17.5623	−	12.7598i	1.79245	−	1.30229i
$97$	−2.90983	+	8.95554i	−0.295448	+	0.909297i	0.687622	+	0.726069i	$0.258655\pi$
$97$	−2.90983	+	8.95554i	−0.295448	+	0.909297i	−0.983070	+	0.183228i	$0.941345\pi$
$98$	2.23607			0.225877
$99$		0			0
$100$	−3.00000			−0.300000
$101$	2.85410	−	8.78402i	0.283994	−	0.874043i	−0.702705	−	0.711482i	$-0.748024\pi$
$101$	2.85410	−	8.78402i	0.283994	−	0.874043i	0.986698	−	0.162561i	$-0.0519755\pi$
$102$	7.23607	−	5.25731i	0.716477	−	0.520551i
$103$	4.61803	+	3.35520i	0.455028	+	0.330597i	0.791578	−	0.611068i	$-0.209260\pi$
$103$	4.61803	+	3.35520i	0.455028	+	0.330597i	−0.336549	+	0.941666i	$0.609260\pi$
$104$	0.854102	+	2.62866i	0.0837516	+	0.257761i
$105$	2.00000	+	6.15537i	0.195180	+	0.600702i
$106$	−15.3262	−	11.1352i	−1.48862	−	1.08154i
$107$	−3.23607	+	2.35114i	−0.312842	+	0.227293i	−0.733115	−	0.680104i	$-0.761934\pi$
$107$	−3.23607	+	2.35114i	−0.312842	+	0.227293i	0.420273	+	0.907398i	$0.361934\pi$
$108$	13.4164	−	41.2915i	1.29099	−	3.97327i
$109$	−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
$111$	1.52786			0.145018
$112$	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
$115$	4.00000	+	12.3107i	0.373002	+	1.14798i
$116$	0.437694	+	1.34708i	0.0406389	+	0.125074i
$117$	−7.47214	−	5.42882i	−0.690799	−	0.501895i
$118$	−5.85410	+	4.25325i	−0.538914	+	0.391544i
$119$	0.381966	−	1.17557i	0.0350148	−	0.107764i
$120$	−14.4721			−1.32112
$121$		0			0
$122$	6.18034			0.559542
$123$	6.76393	−	20.8172i	0.609883	−	1.87703i
$124$	17.5623	−	12.7598i	1.57714	−	1.14586i
$125$	−9.70820	−	7.05342i	−0.868328	−	0.630877i
$126$	−5.16312	−	15.8904i	−0.459967	−	1.41563i
$127$	−6.47214	−	19.9192i	−0.574309	−	1.76754i	−0.638520	−	0.769606i	$-0.720453\pi$
$127$	−6.47214	−	19.9192i	−0.574309	−	1.76754i	0.0642104	−	0.997936i	$-0.479547\pi$
$128$	12.6631	+	9.20029i	1.11927	+	0.813199i
$129$	20.9443	−	15.2169i	1.84404	−	1.33977i
$130$	−1.70820	+	5.25731i	−0.149819	+	0.461097i
$131$	13.8885			1.21345			0.606724	−	0.794913i	$-0.292483\pi$
$131$	13.8885			1.21345			0.606724	+	0.794913i	$0.292483\pi$
$132$		0			0
$133$	−2.47214			−0.214361
$134$	3.81966	−	11.7557i	0.329968	−	1.01554i
$135$	23.4164	−	17.0130i	2.01536	−	1.46425i
$136$	2.23607	+	1.62460i	0.191741	+	0.139308i
$137$	2.32624	+	7.15942i	0.198744	+	0.611671i	0.999912	+	0.0132321i	$0.00421203\pi$
$137$	2.32624	+	7.15942i	0.198744	+	0.611671i	−0.801169	+	0.598439i	$0.795788\pi$
$138$	−14.4721	−	44.5407i	−1.23195	−	3.79155i
$139$	−8.47214	−	6.15537i	−0.718597	−	0.522091i	0.167339	−	0.985899i	$-0.446483\pi$
$139$	−8.47214	−	6.15537i	−0.718597	−	0.522091i	−0.885936	+	0.463808i	$0.846483\pi$
$140$	−4.85410	+	3.52671i	−0.410246	+	0.298062i
$141$	7.23607	−	22.2703i	0.609387	−	1.87550i
$142$	−3.41641			−0.286699
$143$		0			0
$144$	−7.47214			−0.622678
$145$	−0.291796	+	0.898056i	−0.0242323	+	0.0745795i
$146$	−9.47214	+	6.88191i	−0.783920	+	0.569551i
$147$	−2.61803	−	1.90211i	−0.215932	−	0.156884i
$148$	0.437694	+	1.34708i	0.0359782	+	0.110730i
$149$	−4.32624	−	13.3148i	−0.354419	−	1.09079i	−0.956345	−	0.292239i	$-0.905600\pi$
$149$	−4.32624	−	13.3148i	−0.354419	−	1.09079i	0.601926	−	0.798552i	$-0.294400\pi$
$150$	5.85410	+	4.25325i	0.477985	+	0.347277i
$151$	−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	$0.418568\pi$
$152$	1.70820	−	5.25731i	0.138554	−	0.426424i
$153$	−9.23607			−0.746692
$154$		0			0
$155$	14.4721			1.16243
$156$	3.70820	−	11.4127i	0.296894	−	0.913746i
$157$	5.61803	−	4.08174i	0.448368	−	0.325758i	−0.340583	−	0.940214i	$-0.610624\pi$
$157$	5.61803	−	4.08174i	0.448368	−	0.325758i	0.788951	+	0.614456i	$0.210624\pi$
$158$	16.1803	+	11.7557i	1.28724	+	0.935234i
$159$	8.47214	+	26.0746i	0.671884	+	2.06785i
$160$	4.14590	+	12.7598i	0.327762	+	1.00875i
$161$	−5.23607	−	3.80423i	−0.412660	−	0.299815i
$162$	−44.1697	+	32.0912i	−3.47030	+	2.52132i
$163$	7.23607	−	22.2703i	0.566773	−	1.74435i	−0.0958527	−	0.995396i	$-0.530558\pi$
$163$	7.23607	−	22.2703i	0.566773	−	1.74435i	0.662625	−	0.748951i	$-0.269442\pi$
$164$	20.2918			1.58452
$165$		0			0
$166$	−34.4721			−2.67556
$167$	4.00000	−	12.3107i	0.309529	−	0.952633i	−0.668419	−	0.743785i	$-0.733029\pi$
$167$	4.00000	−	12.3107i	0.309529	−	0.952633i	0.977948	−	0.208848i	$-0.0669714\pi$
$168$	5.85410	−	4.25325i	0.451654	−	0.328146i
$169$	9.28115	+	6.74315i	0.713935	+	0.518704i
$170$	1.70820	+	5.25731i	0.131013	+	0.403217i
$171$	5.70820	+	17.5680i	0.436517	+	1.34346i
$172$	19.4164	+	14.1068i	1.48049	+	1.07564i
$173$	−13.9443	+	10.1311i	−1.06016	+	0.770254i	−0.974119	−	0.226038i	$-0.927423\pi$
$173$	−13.9443	+	10.1311i	−1.06016	+	0.770254i	−0.0860448	+	0.996291i	$0.527423\pi$
$174$	1.05573	−	3.24920i	0.0800345	−	0.246321i
$175$	1.00000			0.0755929
$176$		0			0
$177$	10.4721			0.787134
$178$	1.38197	−	4.25325i	0.103583	−	0.318795i
$179$	−7.23607	+	5.25731i	−0.540849	+	0.392950i	−0.824400	−	0.566007i	$-0.808487\pi$
$179$	−7.23607	+	5.25731i	−0.540849	+	0.392950i	0.283551	+	0.958957i	$0.408487\pi$
$180$	36.2705	+	26.3521i	2.70344	+	1.96417i
$181$	0.437694	+	1.34708i	0.0325335	+	0.100128i	0.966005	−	0.258525i	$-0.0832363\pi$
$181$	0.437694	+	1.34708i	0.0325335	+	0.100128i	−0.933471	+	0.358653i	$0.883236\pi$
$182$	−0.854102	−	2.62866i	−0.0633102	−	0.194849i
$183$	−7.23607	−	5.25731i	−0.534906	−	0.388632i
$184$	11.7082	−	8.50651i	0.863140	−	0.627108i
$185$	−0.291796	+	0.898056i	−0.0214533	+	0.0660264i
$186$	−52.3607			−3.83927
$187$		0			0
$188$	21.7082			1.58323
$189$	−4.47214	+	13.7638i	−0.325300	+	1.00117i
$190$	8.94427	−	6.49839i	0.648886	−	0.471443i
$191$	16.9443	+	12.3107i	1.22604	+	0.890773i	0.996587	−	0.0825453i	$-0.0263049\pi$
$191$	16.9443	+	12.3107i	1.22604	+	0.890773i	0.229457	+	0.973319i	$0.426305\pi$
$192$	−13.0000	−	40.0099i	−0.938194	−	2.88746i
$193$	7.38197	+	22.7194i	0.531366	+	1.63537i	0.751374	+	0.659877i	$0.229392\pi$
$193$	7.38197	+	22.7194i	0.531366	+	1.63537i	−0.220008	+	0.975498i	$0.570608\pi$
$194$	17.0344	+	12.3762i	1.22300	+	0.888563i
$195$	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	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	20.1803			1.43055			0.715273	−	0.698845i	$-0.246302\pi$
$199$	20.1803			1.43055			0.715273	+	0.698845i	$0.246302\pi$
$200$	−0.690983	+	2.12663i	−0.0488599	+	0.150375i
$201$	−14.4721	+	10.5146i	−1.02079	+	0.741644i
$202$	−16.7082	−	12.1392i	−1.17559	−	0.854113i
$203$	−0.145898	−	0.449028i	−0.0102400	−	0.0315156i
$204$	−3.70820	−	11.4127i	−0.259626	−	0.799047i
$205$	10.9443	+	7.95148i	0.764381	+	0.555355i
$206$	10.3262	−	7.50245i	0.719463	−	0.522721i
$207$	−14.9443	+	45.9937i	−1.03870	+	3.19679i
$208$	−1.23607			−0.0857059
$209$		0			0
$210$	14.4721			0.998672
$211$	−6.76393	+	20.8172i	−0.465648	+	1.43312i	0.392517	+	0.919745i	$0.371604\pi$
$211$	−6.76393	+	20.8172i	−0.465648	+	1.43312i	−0.858165	+	0.513373i	$0.828396\pi$
$212$	−20.5623	+	14.9394i	−1.41222	+	1.02604i
$213$	4.00000	+	2.90617i	0.274075	+	0.199127i
$214$	2.76393	+	8.50651i	0.188939	+	0.581493i
$215$	4.94427	+	15.2169i	0.337197	+	1.03778i
$216$	−26.1803	−	19.0211i	−1.78135	−	1.29422i
$217$	−5.85410	+	4.25325i	−0.397402	+	0.288730i
$218$	−3.09017	+	9.51057i	−0.209293	+	0.644137i
$219$	16.9443			1.14499
$220$		0			0
$221$	−1.52786			−0.102775
$222$	1.05573	−	3.24920i	0.0708558	−	0.218072i
$223$	−9.85410	+	7.15942i	−0.659879	+	0.479431i	−0.866622	−	0.498965i	$-0.833714\pi$
$223$	−9.85410	+	7.15942i	−0.659879	+	0.479431i	0.206743	+	0.978395i	$0.433714\pi$
$224$	−5.42705	−	3.94298i	−0.362610	−	0.263452i
$225$	−2.30902	−	7.10642i	−0.153934	−	0.473762i
$226$	1.38197	+	4.25325i	0.0919270	+	0.282922i
$227$	−24.1803	−	17.5680i	−1.60491	−	1.16603i	−0.877177	−	0.480166i	$-0.840576\pi$
$227$	−24.1803	−	17.5680i	−1.60491	−	1.16603i	−0.727728	−	0.685866i	$-0.759424\pi$
$228$	−19.4164	+	14.1068i	−1.28588	+	0.934249i
$229$	1.38197	−	4.25325i	0.0913229	−	0.281063i	−0.894955	−	0.446156i	$-0.852793\pi$
$229$	1.38197	−	4.25325i	0.0913229	−	0.281063i	0.986278	+	0.165093i	$0.0527925\pi$
$230$	28.9443			1.90853
$231$		0			0
$232$	1.05573			0.0693119
$233$	5.38197	−	16.5640i	0.352584	−	1.08514i	−0.604813	−	0.796368i	$-0.706752\pi$
$233$	5.38197	−	16.5640i	0.352584	−	1.08514i	0.957397	−	0.288775i	$-0.0932480\pi$
$234$	−16.7082	+	12.1392i	−1.09225	+	0.793566i
$235$	11.7082	+	8.50651i	0.763759	+	0.554903i
$236$	3.00000	+	9.23305i	0.195283	+	0.601020i
$237$	−8.94427	−	27.5276i	−0.580993	−	1.78811i
$238$	−2.23607	−	1.62460i	−0.144943	−	0.105307i
$239$	20.9443	−	15.2169i	1.35477	−	0.984300i	0.356014	−	0.934481i	$-0.384136\pi$
$239$	20.9443	−	15.2169i	1.35477	−	0.984300i	0.998758	−	0.0498191i	$-0.0158645\pi$
$240$	2.00000	−	6.15537i	0.129099	−	0.397327i
$241$	−27.1246			−1.74725			−0.873625	−	0.486600i	$-0.838237\pi$
$241$	−27.1246			−1.74725			−0.873625	+	0.486600i	$0.838237\pi$
$242$		0			0
$243$	35.5967			2.28353
$244$	2.56231	−	7.88597i	0.164035	−	0.504847i
$245$	1.61803	−	1.17557i	0.103372	−	0.0751044i
$246$	−39.5967	−	28.7687i	−2.52460	−	1.83423i
$247$	0.944272	+	2.90617i	0.0600826	+	0.184915i
$248$	−5.00000	−	15.3884i	−0.317500	−	0.977166i
$249$	40.3607	+	29.3238i	2.55775	+	1.85832i
$250$	−21.7082	+	15.7719i	−1.37295	+	0.997505i
$251$	5.47214	−	16.8415i	0.345398	−	1.06303i	−0.615972	−	0.787768i	$-0.711237\pi$
$251$	5.47214	−	16.8415i	0.345398	−	1.06303i	0.961370	−	0.275258i	$-0.0887634\pi$
$252$	−22.4164			−1.41210
$253$		0			0
$254$	−46.8328			−2.93855
$255$	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	$0.640080\pi$
$258$	−17.8885	−	55.0553i	−1.11369	−	3.42759i
$259$	−0.145898	−	0.449028i	−0.00906566	−	0.0279012i
$260$	6.00000	+	4.35926i	0.372104	+	0.270350i
$261$	−2.85410	+	2.07363i	−0.176664	+	0.128354i
$262$	9.59675	−	29.5358i	0.592889	−	1.82472i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	−16.9443			−1.04088
$266$	−1.70820	+	5.25731i	−0.104737	+	0.322346i
$267$	−5.23607	+	3.80423i	−0.320442	+	0.232815i
$268$	−13.4164	−	9.74759i	−0.819538	−	0.595429i
$269$	−4.14590	−	12.7598i	−0.252780	−	0.777976i	−0.994259	−	0.107000i	$-0.965875\pi$
$269$	−4.14590	−	12.7598i	−0.252780	−	0.777976i	0.741479	−	0.670976i	$-0.234125\pi$
$270$	−20.0000	−	61.5537i	−1.21716	−	3.74604i
$271$	−1.23607	−	0.898056i	−0.0750858	−	0.0545530i	0.549609	−	0.835422i	$-0.314777\pi$
$271$	−1.23607	−	0.898056i	−0.0750858	−	0.0545530i	−0.624695	+	0.780869i	$0.714777\pi$
$272$	−1.00000	+	0.726543i	−0.0606339	+	0.0440531i
$273$	−1.23607	+	3.80423i	−0.0748102	+	0.230242i
$274$	16.8328			1.01691
$275$		0			0
$276$	−62.8328			−3.78209
$277$	−4.90983	+	15.1109i	−0.295003	+	0.907926i	0.688217	+	0.725505i	$0.258394\pi$
$277$	−4.90983	+	15.1109i	−0.295003	+	0.907926i	−0.983220	+	0.182422i	$0.941606\pi$
$278$	−18.9443	+	13.7638i	−1.13620	+	0.825499i
$279$	43.7426	+	31.7809i	2.61880	+	1.90267i
$280$	1.38197	+	4.25325i	0.0825883	+	0.254181i
$281$	3.85410	+	11.8617i	0.229916	+	0.707610i	0.997755	+	0.0669669i	$0.0213322\pi$
$281$	3.85410	+	11.8617i	0.229916	+	0.707610i	−0.767839	+	0.640643i	$0.778668\pi$
$282$	−42.3607	−	30.7768i	−2.52254	−	1.83273i
$283$	−4.76393	+	3.46120i	−0.283186	+	0.205747i	−0.720306	−	0.693656i	$-0.755999\pi$
$283$	−4.76393	+	3.46120i	−0.283186	+	0.205747i	0.437120	+	0.899403i	$0.355999\pi$
$284$	−1.41641	+	4.35926i	−0.0840483	+	0.258674i
$285$	−16.0000			−0.947758
$286$		0			0
$287$	−6.76393			−0.399262
$288$	−15.4894	+	47.6713i	−0.912719	+	2.80906i
$289$	12.5172	−	9.09429i	0.736307	−	0.534958i
$290$	1.70820	+	1.24108i	0.100309	+	0.0728789i
$291$	−9.41641	−	28.9807i	−0.552000	−	1.69888i
$292$	4.85410	+	14.9394i	0.284065	+	0.874262i
$293$	12.2361	+	8.89002i	0.714839	+	0.519361i	0.884731	−	0.466102i	$-0.154342\pi$
$293$	12.2361	+	8.89002i	0.714839	+	0.519361i	−0.169892	+	0.985463i	$0.554342\pi$
$294$	−5.85410	+	4.25325i	−0.341418	+	0.248055i
$295$	−2.00000	+	6.15537i	−0.116445	+	0.358379i
$296$	1.05573			0.0613629
$297$		0			0
$298$	−31.3050			−1.81345
$299$	−2.47214	+	7.60845i	−0.142967	+	0.440008i
$300$	7.85410	−	5.70634i	0.453457	−	0.329456i
$301$	−6.47214	−	4.70228i	−0.373048	−	0.271035i
$302$	6.18034	+	19.0211i	0.355639	+	1.09454i
$303$	9.23607	+	28.4257i	0.530598	+	1.63301i
$304$	2.00000	+	1.45309i	0.114708	+	0.0833401i
$305$	4.47214	−	3.24920i	0.256074	−	0.186048i
$306$	−6.38197	+	19.6417i	−0.364833	+	1.12284i
$307$	−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
$309$	−18.4721			−1.05084
$310$	10.0000	−	30.7768i	0.567962	−	1.74801i
$311$	17.5623	−	12.7598i	0.995867	−	0.723540i	0.0346689	−	0.999399i	$-0.488962\pi$
$311$	17.5623	−	12.7598i	0.995867	−	0.723540i	0.961198	+	0.275859i	$0.0889623\pi$
$312$	−7.23607	−	5.25731i	−0.409662	−	0.297637i
$313$	−0.909830	−	2.80017i	−0.0514266	−	0.158275i	0.922045	−	0.387083i	$-0.126517\pi$
$313$	−0.909830	−	2.80017i	−0.0514266	−	0.158275i	−0.973472	+	0.228808i	$0.926517\pi$
$314$	−4.79837	−	14.7679i	−0.270788	−	0.833399i
$315$	−12.0902	−	8.78402i	−0.681204	−	0.494924i
$316$	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	$-0.0286179\pi$
$318$	61.3050			3.43781
$319$		0			0
$320$	26.0000			1.45344
$321$	4.00000	−	12.3107i	0.223258	−	0.687118i
$322$	−11.7082	+	8.50651i	−0.652473	+	0.474049i
$323$	2.47214	+	1.79611i	0.137553	+	0.0999383i
$324$	22.6353	+	69.6642i	1.25751	+	3.87023i
$325$	−0.381966	−	1.17557i	−0.0211877	−	0.0652089i
$326$	−42.3607	−	30.7768i	−2.34614	−	1.70457i
$327$	11.7082	−	8.50651i	0.647465	−	0.470411i
$328$	4.67376	−	14.3844i	0.258065	−	0.794243i
$329$	−7.23607			−0.398937
$330$		0			0
$331$	21.8885			1.20310			0.601552	−	0.798834i	$-0.294549\pi$
$331$	21.8885			1.20310			0.601552	+	0.798834i	$0.294549\pi$
$332$	−14.2918	+	43.9856i	−0.784364	+	2.41402i
$333$	−2.85410	+	2.07363i	−0.156404	+	0.113634i
$334$	−23.4164	−	17.0130i	−1.28129	−	0.930911i
$335$	−3.41641	−	10.5146i	−0.186658	−	0.574475i
$336$	1.00000	+	3.07768i	0.0545545	+	0.167901i
$337$	−16.5623	−	12.0332i	−0.902206	−	0.655491i	0.0368254	−	0.999322i	$-0.488275\pi$
$337$	−16.5623	−	12.0332i	−0.902206	−	0.655491i	−0.939032	+	0.343830i	$0.888275\pi$
$338$	20.7533	−	15.0781i	1.12883	−	0.820143i
$339$	2.00000	−	6.15537i	0.108625	−	0.334314i
$340$	7.41641			0.402211
$341$		0			0
$342$	41.3050			2.23352
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	14.4721	−	10.5146i	0.780285	−	0.566910i
$345$	−33.8885	−	24.6215i	−1.82450	−	1.32558i
$346$	11.9098	+	36.6547i	0.640276	+	1.97057i
$347$	−0.944272	−	2.90617i	−0.0506912	−	0.156011i	0.922507	−	0.385982i	$-0.126137\pi$
$347$	−0.944272	−	2.90617i	−0.0506912	−	0.156011i	−0.973198	+	0.229970i	$0.926137\pi$
$348$	−3.70820	−	2.69417i	−0.198781	−	0.144423i
$349$	−2.23607	+	1.62460i	−0.119694	+	0.0869628i	−0.646022	−	0.763319i	$-0.723568\pi$
$349$	−2.23607	+	1.62460i	−0.119694	+	0.0869628i	0.526328	+	0.850282i	$0.323568\pi$
$350$	0.690983	−	2.12663i	0.0369346	−	0.113673i
$351$	17.8885			0.954820
$352$		0			0
$353$	−15.8885			−0.845662			−0.422831	−	0.906209i	$-0.638964\pi$
$353$	−15.8885			−0.845662			−0.422831	+	0.906209i	$0.638964\pi$
$354$	7.23607	−	22.2703i	0.384593	−	1.18365i
$355$	−2.47214	+	1.79611i	−0.131207	+	0.0953277i
$356$	−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
$359$	−5.70820	−	4.14725i	−0.301267	−	0.218884i	0.426873	−	0.904312i	$-0.359615\pi$
$359$	−5.70820	−	4.14725i	−0.301267	−	0.218884i	−0.728140	+	0.685428i	$0.759615\pi$
$360$	27.0344	−	19.6417i	1.42484	−	1.03521i
$361$	−3.98278	+	12.2577i	−0.209620	+	0.645144i
$362$	3.16718			0.166464
$363$		0			0
$364$	−3.70820			−0.194363
$365$	−3.23607	+	9.95959i	−0.169384	+	0.521309i
$366$	−16.1803	+	11.7557i	−0.845760	+	0.614481i
$367$	−13.8541	−	10.0656i	−0.723178	−	0.525420i	0.164220	−	0.986424i	$-0.447489\pi$
$367$	−13.8541	−	10.0656i	−0.723178	−	0.525420i	−0.887398	+	0.461004i	$0.847489\pi$
$368$	2.00000	+	6.15537i	0.104257	+	0.320871i
$369$	15.6180	+	48.0674i	0.813042	+	2.50229i
$370$	1.70820	+	1.24108i	0.0888053	+	0.0645208i
$371$	6.85410	−	4.97980i	0.355847	−	0.258538i
$372$	−21.7082	+	66.8110i	−1.12552	+	3.46399i
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		0			0
$375$	38.8328			2.00532
$376$	5.00000	−	15.3884i	0.257855	−	0.793597i
$377$	−0.472136	+	0.343027i	−0.0243162	+	0.0176668i
$378$	26.1803	+	19.0211i	1.34657	+	0.978341i
$379$	−7.81966	−	24.0664i	−0.401669	−	1.23621i	−0.923645	−	0.383250i	$-0.874805\pi$
$379$	−7.81966	−	24.0664i	−0.401669	−	1.23621i	0.521976	−	0.852960i	$-0.325195\pi$
$380$	−4.58359	−	14.1068i	−0.235133	−	0.723666i
$381$	54.8328	+	39.8384i	2.80917	+	2.04098i
$382$	37.8885	−	27.5276i	1.93855	−	1.40844i
$383$	8.23607	−	25.3480i	0.420843	−	1.29522i	−0.486075	−	0.873917i	$-0.661572\pi$
$383$	8.23607	−	25.3480i	0.420843	−	1.29522i	0.906919	−	0.421306i	$-0.138428\pi$
$384$	−50.6525			−2.58485
$385$		0			0
$386$	53.4164			2.71882
$387$	−18.4721	+	56.8514i	−0.938991	+	2.88992i
$388$	22.8541	−	16.6045i	1.16024	−	0.842965i
$389$	16.0902	+	11.6902i	0.815804	+	0.592716i	0.915508	−	0.402301i	$-0.131789\pi$
$389$	16.0902	+	11.6902i	0.815804	+	0.592716i	−0.0997035	+	0.995017i	$0.531789\pi$
$390$	−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
$393$	−36.3607	+	26.4176i	−1.83415	+	1.33259i
$394$	1.38197	−	4.25325i	0.0696224	−	0.214276i
$395$	17.8885			0.900070
$396$		0			0
$397$	−0.111456			−0.00559383			−0.00279691	−	0.999996i	$-0.500890\pi$
$397$	−0.111456			−0.00559383			−0.00279691	+	0.999996i	$0.500890\pi$
$398$	13.9443	−	42.9161i	0.698963	−	2.15119i
$399$	6.47214	−	4.70228i	0.324012	−	0.235409i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	1.56231	+	4.80828i	0.0780178	+	0.240114i	0.982457	−	0.186488i	$-0.0597105\pi$
$401$	1.56231	+	4.80828i	0.0780178	+	0.240114i	−0.904439	+	0.426602i	$0.859710\pi$
$402$	12.3607	+	38.0423i	0.616495	+	1.89738i
$403$	7.23607	+	5.25731i	0.360454	+	0.261885i
$404$	−22.4164	+	16.2865i	−1.11526	+	0.810282i
$405$	−15.0902	+	46.4428i	−0.749837	+	2.30776i
$406$	−1.05573			−0.0523949
$407$		0			0
$408$	−8.94427			−0.442807
$409$	9.61803	−	29.6013i	0.475581	−	1.46369i	−0.369591	−	0.929194i	$-0.620502\pi$
$409$	9.61803	−	29.6013i	0.475581	−	1.46369i	0.845172	−	0.534494i	$-0.179498\pi$
$410$	24.4721	−	17.7800i	1.20859	−	0.878094i
$411$	−19.7082	−	14.3188i	−0.972134	−	0.706297i
$412$	−5.29180	−	16.2865i	−0.260708	−	0.802377i
$413$	−1.00000	−	3.07768i	−0.0492068	−	0.151443i
$414$	87.4853	+	63.5618i	4.29967	+	3.12389i
$415$	−24.9443	+	18.1231i	−1.22447	+	0.889627i
$416$	−2.56231	+	7.88597i	−0.125627	+	0.386641i
$417$	33.8885			1.65953
$418$		0			0
$419$	−6.65248			−0.324995			−0.162497	−	0.986709i	$-0.551955\pi$
$419$	−6.65248			−0.324995			−0.162497	+	0.986709i	$0.551955\pi$
$420$	6.00000	−	18.4661i	0.292770	−	0.901053i
$421$	18.0902	−	13.1433i	0.881661	−	0.640564i	−0.0520294	−	0.998646i	$-0.516569\pi$
$421$	18.0902	−	13.1433i	0.881661	−	0.640564i	0.933690	+	0.358081i	$0.116569\pi$
$422$	39.5967	+	28.7687i	1.92754	+	1.40044i
$423$	16.7082	+	51.4226i	0.812381	+	2.50025i
$424$	5.85410	+	18.0171i	0.284300	+	0.874986i
$425$	−1.00000	−	0.726543i	−0.0485071	−	0.0352425i
$426$	8.94427	−	6.49839i	0.433351	−	0.314848i
$427$	−0.854102	+	2.62866i	−0.0413329	+	0.127210i
$428$	12.0000			0.580042
$429$		0			0
$430$	35.7771			1.72532
$431$	−3.70820	+	11.4127i	−0.178618	+	0.549729i	−0.999780	−	0.0209654i	$-0.993326\pi$
$431$	−3.70820	+	11.4127i	−0.178618	+	0.549729i	0.821162	+	0.570695i	$0.193326\pi$
$432$	11.7082	−	8.50651i	0.563311	−	0.409270i
$433$	−0.381966	−	0.277515i	−0.0183561	−	0.0133365i	0.578569	−	0.815633i	$-0.303611\pi$
$433$	−0.381966	−	0.277515i	−0.0183561	−	0.0133365i	−0.596925	+	0.802297i	$0.703611\pi$
$434$	5.00000	+	15.3884i	0.240008	+	0.738668i
$435$	−0.944272	−	2.90617i	−0.0452744	−	0.139340i
$436$	10.8541	+	7.88597i	0.519817	+	0.377669i
$437$	12.9443	−	9.40456i	0.619208	−	0.449881i
$438$	11.7082	−	36.0341i	0.559440	−	1.72178i
$439$	−1.52786			−0.0729210			−0.0364605	−	0.999335i	$-0.511608\pi$
$439$	−1.52786			−0.0729210			−0.0364605	+	0.999335i	$0.511608\pi$
$440$		0			0
$441$	7.47214			0.355816
$442$	−1.05573	+	3.24920i	−0.0502159	+	0.154549i
$443$	5.70820	−	4.14725i	0.271205	−	0.197042i	−0.443867	−	0.896093i	$-0.646394\pi$
$443$	5.70820	−	4.14725i	0.271205	−	0.197042i	0.715072	+	0.699051i	$0.246394\pi$
$444$	−3.70820	−	2.69417i	−0.175984	−	0.127860i
$445$	−1.23607	−	3.80423i	−0.0585952	−	0.180338i
$446$	8.41641	+	25.9030i	0.398528	+	1.22654i
$447$	36.6525	+	26.6296i	1.73360	+	1.25954i
$448$	−10.5172	+	7.64121i	−0.496892	+	0.361013i
$449$	−6.03444	+	18.5721i	−0.284783	+	0.876472i	0.701681	+	0.712492i	$0.252433\pi$
$449$	−6.03444	+	18.5721i	−0.284783	+	0.876472i	−0.986464	+	0.163980i	$0.947567\pi$
$450$	−16.7082			−0.787632
$451$		0			0
$452$	6.00000			0.282216
$453$	8.94427	−	27.5276i	0.420239	−	1.29336i
$454$	−54.0689	+	39.2833i	−2.53758	+	1.84366i
$455$	−2.00000	−	1.45309i	−0.0937614	−	0.0681217i
$456$	5.52786	+	17.0130i	0.258866	+	0.796707i
$457$	−7.67376	−	23.6174i	−0.358963	−	1.10478i	−0.953676	−	0.300837i	$-0.902734\pi$
$457$	−7.67376	−	23.6174i	−0.358963	−	1.10478i	0.594712	−	0.803939i	$-0.297266\pi$
$458$	−8.09017	−	5.87785i	−0.378029	−	0.274654i
$459$	14.4721	−	10.5146i	0.675501	−	0.490781i
$460$	12.0000	−	36.9322i	0.559503	−	1.72197i
$461$	−10.1803			−0.474146			−0.237073	−	0.971492i	$-0.576188\pi$
$461$	−10.1803			−0.474146			−0.237073	+	0.971492i	$0.576188\pi$
$462$		0			0
$463$	−14.4721			−0.672577			−0.336289	−	0.941759i	$-0.609172\pi$
$463$	−14.4721			−0.672577			−0.336289	+	0.941759i	$0.609172\pi$
$464$	−0.145898	+	0.449028i	−0.00677315	+	0.0208456i
$465$	−37.8885	+	27.5276i	−1.75704	+	1.27656i
$466$	−31.5066	−	22.8909i	−1.45951	−	1.06040i
$467$	−10.5279	−	32.4014i	−0.487171	−	1.49936i	−0.828811	−	0.559529i	$-0.810982\pi$
$467$	−10.5279	−	32.4014i	−0.487171	−	1.49936i	0.341640	−	0.939831i	$-0.389018\pi$
$468$	8.56231	+	26.3521i	0.395793	+	1.21812i
$469$	4.47214	+	3.24920i	0.206504	+	0.150034i
$470$	26.1803	−	19.0211i	1.20761	−	0.877379i
$471$	−6.94427	+	21.3723i	−0.319975	+	0.984782i
$472$	7.23607			0.333067
$473$		0			0
$474$	−64.7214			−2.97275
$475$	−0.763932	+	2.35114i	−0.0350516	+	0.107878i
$476$	−3.00000	+	2.17963i	−0.137505	+	0.0999031i
$477$	−51.2148	−	37.2097i	−2.34496	−	1.70372i
$478$	−17.8885	−	55.0553i	−0.818203	−	2.51817i
$479$	−6.94427	−	21.3723i	−0.317292	−	0.976524i	−0.974801	−	0.223077i	$-0.928390\pi$
$479$	−6.94427	−	21.3723i	−0.317292	−	0.976524i	0.657509	−	0.753447i	$-0.271610\pi$
$480$	−35.1246	−	25.5195i	−1.60321	−	1.16480i
$481$	−0.472136	+	0.343027i	−0.0215275	+	0.0156407i
$482$	−18.7426	+	57.6839i	−0.853704	+	2.62743i
$483$	20.9443			0.952997
$484$		0			0
$485$	18.8328			0.855154
$486$	24.5967	−	75.7010i	1.11573	−	3.43387i
$487$	−6.76393	+	4.91428i	−0.306503	+	0.222687i	−0.730395	−	0.683025i	$-0.760664\pi$
$487$	−6.76393	+	4.91428i	−0.306503	+	0.222687i	0.423892	+	0.905713i	$0.360664\pi$
$488$	−5.00000	−	3.63271i	−0.226339	−	0.164445i
$489$	23.4164	+	72.0683i	1.05893	+	3.25904i
$490$	−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	$0.700000\pi$
$492$	−53.1246	+	38.5973i	−2.39504	+	1.74010i
$493$	−0.180340	+	0.555029i	−0.00812210	+	0.0249973i
$494$	6.83282			0.307423
$495$		0			0
$496$	7.23607			0.324909
$497$	0.472136	−	1.45309i	0.0211782	−	0.0651798i
$498$	90.2492	−	65.5699i	4.04416	−	2.93826i
$499$	−8.47214	−	6.15537i	−0.379265	−	0.275552i	0.381777	−	0.924254i	$-0.375312\pi$
$499$	−8.47214	−	6.15537i	−0.379265	−	0.275552i	−0.761042	+	0.648702i	$0.775312\pi$
$500$	11.1246	+	34.2380i	0.497508	+	1.53117i
$501$	12.9443	+	39.8384i	0.578307	+	1.77985i
$502$	−32.0344	−	23.2744i	−1.42977	−	1.03879i
$503$	−2.76393	+	2.00811i	−0.123238	+	0.0895374i	−0.647697	−	0.761898i	$-0.724268\pi$
$503$	−2.76393	+	2.00811i	−0.123238	+	0.0895374i	0.524459	+	0.851436i	$0.324268\pi$
$504$	−5.16312	+	15.8904i	−0.229984	+	0.707817i
$505$	−18.4721			−0.821999
$506$		0			0
$507$	−37.1246			−1.64876
$508$	−19.4164	+	59.7576i	−0.861464	+	2.65131i
$509$	−25.5066	+	18.5316i	−1.13056	+	0.821399i	−0.985776	−	0.168064i	$-0.946248\pi$
$509$	−25.5066	+	18.5316i	−1.13056	+	0.821399i	−0.144783	+	0.989463i	$0.546248\pi$
$510$	−14.4721	−	10.5146i	−0.640837	−	0.465595i
$511$	−1.61803	−	4.97980i	−0.0715776	−	0.220293i
$512$	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
$515$	3.52786	−	10.8576i	0.155456	−	0.478445i
$516$	−77.6656			−3.41904
$517$		0			0
$518$	−1.05573			−0.0463860
$519$	17.2361	−	53.0472i	0.756579	−	2.32851i
$520$	4.47214	−	3.24920i	0.196116	−	0.142487i
$521$	11.6180	+	8.44100i	0.508995	+	0.369807i	0.812442	−	0.583042i	$-0.198138\pi$
$521$	11.6180	+	8.44100i	0.508995	+	0.369807i	−0.303447	+	0.952848i	$0.598138\pi$
$522$	2.43769	+	7.50245i	0.106695	+	0.328373i
$523$	−13.5967	−	41.8465i	−0.594544	−	1.82982i	−0.556982	−	0.830525i	$-0.688041\pi$
$523$	−13.5967	−	41.8465i	−0.594544	−	1.82982i	−0.0375627	−	0.999294i	$-0.511959\pi$
$524$	−33.7082	−	24.4904i	−1.47255	−	1.06987i
$525$	−2.61803	+	1.90211i	−0.114260	+	0.0830150i
$526$		0			0
$527$	8.94427			0.389619
$528$		0			0
$529$	18.8885			0.821241
$530$	−11.7082	+	36.0341i	−0.508572	+	1.56522i
$531$	−19.5623	+	14.2128i	−0.848932	+	0.616785i
$532$	6.00000	+	4.35926i	0.260133	+	0.188998i
$533$	2.58359	+	7.95148i	0.111908	+	0.344417i
$534$	4.47214	+	13.7638i	0.193528	+	0.595619i
$535$	6.47214	+	4.70228i	0.279815	+	0.203297i
$536$	−10.0000	+	7.26543i	−0.431934	+	0.313819i
$537$	8.94427	−	27.5276i	0.385974	−	1.18791i
$538$	−30.0000			−1.29339
$539$		0			0
$540$	−86.8328			−3.73669
$541$	10.1459	−	31.2259i	0.436206	−	1.34250i	−0.455639	−	0.890165i	$-0.650589\pi$
$541$	10.1459	−	31.2259i	0.436206	−	1.34250i	0.891845	−	0.452340i	$-0.149411\pi$
$542$	−2.76393	+	2.00811i	−0.118721	+	0.0862559i
$543$	−3.70820	−	2.69417i	−0.159134	−	0.115618i
$544$	2.56231	+	7.88597i	0.109858	+	0.338108i
$545$	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	0.0134293	−	0.999910i	$-0.495725\pi$
$547$	22.6525	−	16.4580i	0.968550	−	0.703693i	0.955121	+	0.296217i	$0.0957252\pi$
$548$	6.97871	−	21.4783i	0.298116	−	0.917506i
$549$	20.6525			0.881426
$550$		0			0
$551$	1.16718			0.0497237
$552$	−14.4721	+	44.5407i	−0.615975	+	1.89578i
$553$	−7.23607	+	5.25731i	−0.307709	+	0.223564i
$554$	28.7426	+	20.8828i	1.22116	+	0.887223i
$555$	−0.944272	−	2.90617i	−0.0400821	−	0.123360i
$556$	9.70820	+	29.8788i	0.411720	+	1.26714i
$557$	−17.0344	−	12.3762i	−0.721772	−	0.524398i	0.165178	−	0.986264i	$-0.447180\pi$
$557$	−17.0344	−	12.3762i	−0.721772	−	0.524398i	−0.886950	+	0.461865i	$0.847180\pi$
$558$	97.8115	−	71.0642i	4.14069	−	3.00839i
$559$	−3.05573	+	9.40456i	−0.129244	+	0.397771i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	27.8885			1.17641
$563$	−12.1803	+	37.4872i	−0.513340	+	1.57990i	0.272942	+	0.962031i	$0.412003\pi$
$563$	−12.1803	+	37.4872i	−0.513340	+	1.57990i	−0.786282	+	0.617868i	$0.787997\pi$
$564$	−56.8328	+	41.2915i	−2.39309	+	1.73868i
$565$	3.23607	+	2.35114i	0.136142	+	0.0989132i
$566$	4.06888	+	12.5227i	0.171028	+	0.526370i
$567$	−7.54508	−	23.2214i	−0.316864	−	0.975206i
$568$	2.76393	+	2.00811i	0.115972	+	0.0842586i
$569$	13.3262	−	9.68208i	0.558665	−	0.405894i	−0.272305	−	0.962211i	$-0.587786\pi$
$569$	13.3262	−	9.68208i	0.558665	−	0.405894i	0.830970	+	0.556317i	$0.187786\pi$
$570$	−11.0557	+	34.0260i	−0.463073	+	1.42519i
$571$	32.9443			1.37867			0.689337	−	0.724440i	$-0.257902\pi$
$571$	32.9443			1.37867			0.689337	+	0.724440i	$0.257902\pi$
$572$		0			0
$573$	−67.7771			−2.83143
$574$	−4.67376	+	14.3844i	−0.195079	+	0.600392i
$575$	−5.23607	+	3.80423i	−0.218359	+	0.158647i
$576$	78.5861	+	57.0961i	3.27442	+	2.37901i
$577$	−8.79837	−	27.0786i	−0.366281	−	1.12730i	−0.949175	−	0.314749i	$-0.898080\pi$
$577$	−8.79837	−	27.0786i	−0.366281	−	1.12730i	0.582894	−	0.812548i	$-0.301920\pi$
$578$	−10.6910	−	32.9035i	−0.444686	−	1.36860i
$579$	−62.5410	−	45.4387i	−2.59912	−	1.88837i
$580$	2.29180	−	1.66509i	0.0951617	−	0.0691390i
$581$	4.76393	−	14.6619i	0.197641	−	0.608277i
$582$	−68.1378			−2.82440
$583$		0			0
$584$	11.7082			0.484489
$585$	−5.70820	+	17.5680i	−0.236005	+	0.726349i
$586$	27.3607	−	19.8787i	1.13026	−	0.821181i
$587$	10.6180	+	7.71445i	0.438253	+	0.318410i	0.784940	−	0.619571i	$-0.212693\pi$
$587$	10.6180	+	7.71445i	0.438253	+	0.318410i	−0.346687	+	0.937981i	$0.612693\pi$
$588$	3.00000	+	9.23305i	0.123718	+	0.380765i
$589$	−5.52786	−	17.0130i	−0.227772	−	0.701009i
$590$	11.7082	+	8.50651i	0.482019	+	0.350207i
$591$	−5.23607	+	3.80423i	−0.215383	+	0.156485i
$592$	−0.145898	+	0.449028i	−0.00599637	+	0.0184549i
$593$	32.2918			1.32607			0.663033	−	0.748591i	$-0.269269\pi$
$593$	32.2918			1.32607			0.663033	+	0.748591i	$0.269269\pi$
$594$		0			0
$595$	−2.47214			−0.101348
$596$	−12.9787	+	39.9444i	−0.531629	+	1.63619i
$597$	−52.8328	+	38.3853i	−2.16230	+	1.57101i
$598$	14.4721	+	10.5146i	0.591810	+	0.429975i
$599$	1.05573	+	3.24920i	0.0431359	+	0.132759i	0.970305	−	0.241884i	$-0.0777654\pi$
$599$	1.05573	+	3.24920i	0.0431359	+	0.132759i	−0.927169	+	0.374643i	$0.877765\pi$
$600$	−2.23607	−	6.88191i	−0.0912871	−	0.280953i
$601$	2.52786	+	1.83660i	0.103114	+	0.0749165i	0.638147	−	0.769914i	$-0.279701\pi$
$601$	2.52786	+	1.83660i	0.103114	+	0.0749165i	−0.535034	+	0.844831i	$0.679701\pi$
$602$	−14.4721	+	10.5146i	−0.589840	+	0.428544i
$603$	12.7639	−	39.2833i	0.519787	−	1.59974i
$604$	26.8328			1.09181
$605$		0			0
$606$	66.8328			2.71490
$607$	1.52786	−	4.70228i	0.0620141	−	0.190860i	−0.915250	−	0.402887i	$-0.868007\pi$
$607$	1.52786	−	4.70228i	0.0620141	−	0.190860i	0.977264	+	0.212028i	$0.0680067\pi$
$608$	13.4164	−	9.74759i	0.544107	−	0.395317i
$609$	1.23607	+	0.898056i	0.0500880	+	0.0363911i
$610$	−3.81966	−	11.7557i	−0.154654	−	0.475975i
$611$	2.76393	+	8.50651i	0.111817	+	0.344136i
$612$	22.4164	+	16.2865i	0.906130	+	0.658342i
$613$	−38.2705	+	27.8052i	−1.54573	+	1.12304i	−0.599121	+	0.800658i	$0.704483\pi$
$613$	−38.2705	+	27.8052i	−1.54573	+	1.12304i	−0.946610	+	0.322381i	$0.895517\pi$
$614$	−6.18034	+	19.0211i	−0.249418	+	0.767630i
$615$	−43.7771			−1.76526
$616$		0			0
$617$	33.4164			1.34529			0.672647	−	0.739964i	$-0.265157\pi$
$617$	33.4164			1.34529			0.672647	+	0.739964i	$0.265157\pi$
$618$	−12.7639	+	39.2833i	−0.513441	+	1.58021i
$619$	23.5623	−	17.1190i	0.947049	−	0.688071i	−0.00305805	−	0.999995i	$-0.500973\pi$
$619$	23.5623	−	17.1190i	0.947049	−	0.688071i	0.950107	+	0.311924i	$0.100973\pi$
$620$	−35.1246	−	25.5195i	−1.41064	−	1.02489i
$621$	−28.9443	−	89.0813i	−1.16149	−	3.57471i
$622$	−15.0000	−	46.1653i	−0.601445	−	1.85106i
$623$	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
$626$	−6.58359			−0.263133
$627$		0			0
$628$	−20.8328			−0.831320
$629$	−0.180340	+	0.555029i	−0.00719062	+	0.0221305i
$630$	−27.0344	+	19.6417i	−1.07708	+	0.782543i
$631$	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
$633$	−21.8885	−	67.3660i	−0.869992	−	2.67756i
$634$	−25.3262	−	18.4006i	−1.00583	−	0.730781i
$635$	−33.8885	+	24.6215i	−1.34483	+	0.977073i
$636$	25.4164	−	78.2237i	1.00783	−	3.10177i
$637$	1.23607			0.0489748
$638$		0			0
$639$	−11.4164			−0.451626
$640$	9.67376	−	29.7728i	0.382389	−	1.17687i
$641$	19.7984	−	14.3844i	0.781989	−	0.568148i	−0.123586	−	0.992334i	$-0.539440\pi$
$641$	19.7984	−	14.3844i	0.781989	−	0.568148i	0.905575	+	0.424186i	$0.139440\pi$
$642$	−23.4164	−	17.0130i	−0.924172	−	0.671450i
$643$	−9.00000	−	27.6992i	−0.354925	−	1.09235i	−0.956053	−	0.293195i	$-0.905282\pi$
$643$	−9.00000	−	27.6992i	−0.354925	−	1.09235i	0.601127	−	0.799153i	$-0.294718\pi$
$644$	6.00000	+	18.4661i	0.236433	+	0.727666i
$645$	−41.8885	−	30.4338i	−1.64936	−	1.19833i
$646$	5.52786	−	4.01623i	0.217491	−	0.158016i
$647$	−6.81966	+	20.9888i	−0.268109	+	0.825153i	0.722852	+	0.691002i	$0.242831\pi$
$647$	−6.81966	+	20.9888i	−0.268109	+	0.825153i	−0.990961	+	0.134151i	$0.957169\pi$
$648$	54.5967			2.14476
$649$		0			0
$650$	−2.76393			−0.108410
$651$	7.23607	−	22.2703i	0.283604	−	0.872843i
$652$	−56.8328	+	41.2915i	−2.22574	+	1.61710i
$653$	−34.7426	−	25.2420i	−1.35958	−	0.987796i	−0.998471	−	0.0552743i	$-0.982397\pi$
$653$	−34.7426	−	25.2420i	−1.35958	−	0.987796i	−0.361114	−	0.932522i	$-0.617603\pi$
$654$	−10.0000	−	30.7768i	−0.391031	−	1.20347i
$655$	−8.58359	−	26.4176i	−0.335389	−	1.03222i
$656$	5.47214	+	3.97574i	0.213651	+	0.155227i
$657$	−31.6525	+	22.9969i	−1.23488	+	0.897193i
$658$	−5.00000	+	15.3884i	−0.194920	+	0.599903i
$659$	−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
$661$	12.8328			0.499139			0.249569	−	0.968357i	$-0.419711\pi$
$661$	12.8328			0.499139			0.249569	+	0.968357i	$0.419711\pi$
$662$	15.1246	−	46.5488i	0.587835	−	1.80917i
$663$	4.00000	−	2.90617i	0.155347	−	0.112866i
$664$	27.8885	+	20.2622i	1.08229	+	0.786326i
$665$	1.52786	+	4.70228i	0.0592480	+	0.182347i
$666$	2.43769	+	7.50245i	0.0944587	+	0.290714i
$667$	2.47214	+	1.79611i	0.0957215	+	0.0695457i
$668$	−31.4164	+	22.8254i	−1.21554	+	0.883140i
$669$	12.1803	−	37.4872i	0.470919	−	1.44934i
$670$	−24.7214			−0.955069
$671$		0			0
$672$	21.7082			0.837412
$673$	−1.67376	+	5.15131i	−0.0645188	+	0.198568i	−0.978119	−	0.208044i	$-0.933290\pi$
$673$	−1.67376	+	5.15131i	−0.0645188	+	0.198568i	0.913601	+	0.406613i	$0.133290\pi$
$674$	−37.0344	+	26.9071i	−1.42651	+	1.03642i
$675$	11.7082	+	8.50651i	0.450649	+	0.327416i
$676$	−10.6353	−	32.7319i	−0.409048	−	1.25892i
$677$	−1.14590	−	3.52671i	−0.0440404	−	0.135543i	0.926619	−	0.376003i	$-0.122702\pi$
$677$	−1.14590	−	3.52671i	−0.0440404	−	0.135543i	−0.970659	+	0.240460i	$0.922702\pi$
$678$	−11.7082	−	8.50651i	−0.449651	−	0.326690i
$679$	−7.61803	+	5.53483i	−0.292353	+	0.212407i
$680$	1.70820	−	5.25731i	0.0655066	−	0.201609i
$681$	96.7214			3.70637
$682$		0			0
$683$	29.8885			1.14365			0.571827	−	0.820374i	$-0.306235\pi$
$683$	29.8885			1.14365			0.571827	+	0.820374i	$0.306235\pi$
$684$	17.1246	−	52.7041i	0.654776	−	2.01519i
$685$	12.1803	−	8.84953i	0.465387	−	0.338123i
$686$	1.80902	+	1.31433i	0.0690686	+	0.0501813i
$687$	4.47214	+	13.7638i	0.170623	+	0.525122i
$688$	2.47214	+	7.60845i	0.0942493	+	0.290070i
$689$	−8.47214	−	6.15537i	−0.322763	−	0.234501i
$690$	−75.7771	+	55.0553i	−2.88478	+	2.09592i
$691$	−15.0000	+	46.1653i	−0.570627	+	1.75621i	0.0799823	+	0.996796i	$0.474514\pi$
$691$	−15.0000	+	46.1653i	−0.570627	+	1.75621i	−0.650609	+	0.759413i	$0.725486\pi$
$692$	51.7082			1.96565
$693$		0			0
$694$	−6.83282			−0.259370
$695$	−6.47214	+	19.9192i	−0.245502	+	0.755578i
$696$	−2.76393	+	2.00811i	−0.104767	+	0.0761174i
$697$	6.76393	+	4.91428i	0.256202	+	0.186142i
$698$	1.90983	+	5.87785i	0.0722881	+	0.222480i
$699$	17.4164	+	53.6022i	0.658749	+	2.02742i
$700$	−2.42705	−	1.76336i	−0.0917339	−	0.0666486i
$701$	−19.7984	+	14.3844i	−0.747774	+	0.543290i	−0.895136	−	0.445793i	$-0.852922\pi$
$701$	−19.7984	+	14.3844i	−0.747774	+	0.543290i	0.147362	+	0.989083i	$0.452922\pi$
$702$	12.3607	−	38.0423i	0.466524	−	1.43581i
$703$	1.16718			0.0440212
$704$		0			0
$705$	−46.8328			−1.76383
$706$	−10.9787	+	33.7890i	−0.413189	+	1.27167i
$707$	7.47214	−	5.42882i	0.281019	−	0.204172i
$708$	−25.4164	−	18.4661i	−0.955207	−	0.693999i
$709$	0.909830	+	2.80017i	0.0341694	+	0.105163i	0.966687	−	0.255963i	$-0.0823926\pi$
$709$	0.909830	+	2.80017i	0.0341694	+	0.105163i	−0.932517	+	0.361126i	$0.882393\pi$
$710$	2.11146	+	6.49839i	0.0792415	+	0.243880i
$711$	54.0689	+	39.2833i	2.02774	+	1.47324i
$712$	−3.61803	+	2.62866i	−0.135592	+	0.0985130i
$713$	14.4721	−	44.5407i	0.541986	−	1.66806i
$714$	8.94427			0.334731
$715$		0			0
$716$	26.8328			1.00279
$717$	−25.8885	+	79.6767i	−0.966825	+	2.97558i
$718$	−12.7639	+	9.27354i	−0.476346	+	0.346085i
$719$	−27.0902	−	19.6822i	−1.01029	−	0.734021i	−0.0460224	−	0.998940i	$-0.514655\pi$
$719$	−27.0902	−	19.6822i	−1.01029	−	0.734021i	−0.964270	+	0.264920i	$0.914655\pi$
$720$	4.61803	+	14.2128i	0.172104	+	0.529682i
$721$	1.76393	+	5.42882i	0.0656923	+	0.202180i
$722$	23.3156	+	16.9398i	0.867717	+	0.630433i
$723$	71.0132	−	51.5941i	2.64101	−	1.91880i
$724$	1.31308	−	4.04125i	0.0488003	−	0.150192i
$725$	−0.472136			−0.0175347
$726$		0			0
$727$	−51.0132			−1.89197			−0.945987	−	0.324206i	$-0.894903\pi$
$727$	−51.0132			−1.89197			−0.945987	+	0.324206i	$0.894903\pi$
$728$	−0.854102	+	2.62866i	−0.0316551	+	0.0974245i
$729$	−33.9336	+	24.6542i	−1.25680	+	0.913119i
$730$	18.9443	+	13.7638i	0.701159	+	0.509422i
$731$	3.05573	+	9.40456i	0.113020	+	0.347840i
$732$	8.29180	+	25.5195i	0.306474	+	0.943229i
$733$	10.7082	+	7.77997i	0.395517	+	0.287360i	0.767712	−	0.640795i	$-0.221395\pi$
$733$	10.7082	+	7.77997i	0.395517	+	0.287360i	−0.372196	+	0.928154i	$0.621395\pi$
$734$	−30.9787	+	22.5074i	−1.14345	+	0.830762i
$735$	−2.00000	+	6.15537i	−0.0737711	+	0.227044i
$736$	43.4164			1.60035
$737$		0			0
$738$	113.013			4.16007
$739$	−2.18034	+	6.71040i	−0.0802051	+	0.246846i	−0.983116	−	0.182981i	$-0.941425\pi$
$739$	−2.18034	+	6.71040i	−0.0802051	+	0.246846i	0.902911	+	0.429827i	$0.141425\pi$
$740$	2.29180	−	1.66509i	0.0842481	−	0.0612098i
$741$	−8.00000	−	5.81234i	−0.293887	−	0.213522i
$742$	−5.85410	−	18.0171i	−0.214911	−	0.661428i
$743$	10.4721	+	32.2299i	0.384185	+	1.18240i	0.937069	+	0.349143i	$0.113527\pi$
$743$	10.4721	+	32.2299i	0.384185	+	1.18240i	−0.552884	+	0.833258i	$0.686473\pi$
$744$	42.3607	+	30.7768i	1.55302	+	1.12833i
$745$	−22.6525	+	16.4580i	−0.829923	+	0.602974i
$746$	−4.14590	+	12.7598i	−0.151792	+	0.467168i
$747$	−115.193			−4.21471
$748$		0			0
$749$	−4.00000			−0.146157
$750$	26.8328	−	82.5829i	0.979796	−	3.01550i
$751$	−31.1246	+	22.6134i	−1.13575	+	0.825173i	−0.986522	−	0.163629i	$-0.947680\pi$
$751$	−31.1246	+	22.6134i	−1.13575	+	0.825173i	−0.149231	+	0.988802i	$0.547680\pi$
$752$	5.85410	+	4.25325i	0.213477	+	0.155100i
$753$	17.7082	+	54.5002i	0.645323	+	1.98610i
$754$	0.403252	+	1.24108i	0.0146856	+	0.0451976i
$755$	14.4721	+	10.5146i	0.526695	+	0.382666i
$756$	35.1246	−	25.5195i	1.27747	−	0.928136i
$757$	−6.14590	+	18.9151i	−0.223376	+	0.687482i	0.775076	+	0.631868i	$0.217712\pi$
$757$	−6.14590	+	18.9151i	−0.223376	+	0.687482i	−0.998452	+	0.0556139i	$0.982288\pi$
$758$	−56.5836			−2.05521
$759$		0			0
$760$	−11.0557			−0.401033
$761$	−5.43769	+	16.7355i	−0.197116	+	0.606661i	0.802829	+	0.596209i	$0.203327\pi$
$761$	−5.43769	+	16.7355i	−0.197116	+	0.606661i	−0.999945	+	0.0104523i	$0.996673\pi$
$762$	122.610	−	89.0813i	4.44169	−	3.22708i
$763$	−3.61803	−	2.62866i	−0.130982	−	0.0951637i
$764$	−19.4164	−	59.7576i	−0.702461	−	2.16195i
$765$	5.70820	+	17.5680i	0.206381	+	0.635174i
$766$	−48.2148	−	35.0301i	−1.74207	−	1.26569i
$767$	−3.23607	+	2.35114i	−0.116848	+	0.0848948i
$768$	−9.00000	+	27.6992i	−0.324760	+	0.999507i
$769$	−31.7082			−1.14343			−0.571714	−	0.820453i	$-0.693721\pi$
$769$	−31.7082			−1.14343			−0.571714	+	0.820453i	$0.693721\pi$
$770$		0			0
$771$	−19.4164			−0.699265
$772$	22.1459	−	68.1581i	0.797048	−	2.45306i
$773$	−5.14590	+	3.73871i	−0.185085	+	0.134472i	−0.676470	−	0.736471i	$-0.736491\pi$
$773$	−5.14590	+	3.73871i	−0.185085	+	0.134472i	0.491385	+	0.870943i	$0.336491\pi$
$774$	108.138	+	78.5667i	3.88693	+	2.82402i
$775$	2.23607	+	6.88191i	0.0803219	+	0.247205i
$776$	−6.50658	−	20.0252i	−0.233573	−	0.718862i
$777$	1.23607	+	0.898056i	0.0443437	+	0.0322176i
$778$	35.9787	−	26.1401i	1.28990	−	0.937167i
$779$	5.16718	−	15.9030i	0.185134	−	0.569783i
$780$	−24.0000			−0.859338
$781$		0			0
$782$	17.8885			0.639693
$783$	2.11146	−	6.49839i	0.0754573	−	0.232234i
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	−11.2361	−	8.16348i	−0.401032	−	0.291367i
$786$	31.0557	+	95.5797i	1.10772	+	3.40922i
$787$	5.12461	+	15.7719i	0.182673	+	0.562209i	0.999901	−	0.0141060i	$-0.00449024\pi$
$787$	5.12461	+	15.7719i	0.182673	+	0.562209i	−0.817228	+	0.576315i	$0.804490\pi$
$788$	−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
$793$	3.41641			0.121320
$794$	−0.0770143	+	0.237026i	−0.00273314	+	0.00841173i
$795$	44.3607	−	32.2299i	1.57331	−	1.14308i
$796$	−48.9787	−	35.5851i	−1.73600	−	1.26128i
$797$	0.909830	+	2.80017i	0.0322278	+	0.0991871i	0.965877	−	0.259003i	$-0.0833940\pi$
$797$	0.909830	+	2.80017i	0.0322278	+	0.0991871i	−0.933649	+	0.358190i	$0.883394\pi$
$798$	−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
$801$	4.61803	−	14.2128i	0.163170	−	0.502186i
$802$	11.3050			0.399192
$803$		0			0
$804$	53.6656			1.89264
$805$	−4.00000	+	12.3107i	−0.140981	+	0.433896i
$806$	16.1803	−	11.7557i	0.569928	−	0.414077i
$807$	35.1246	+	25.5195i	1.23644	+	0.898330i
$808$	6.38197	+	19.6417i	0.224517	+	0.690992i
$809$	−12.0344	−	37.0382i	−0.423108	−	1.30219i	−0.904794	−	0.425850i	$-0.859975\pi$
$809$	−12.0344	−	37.0382i	−0.423108	−	1.30219i	0.481685	−	0.876344i	$-0.340025\pi$
$810$	88.3394	+	64.1823i	3.10393	+	2.25514i
$811$	15.2361	−	11.0697i	0.535011	−	0.388708i	−0.287218	−	0.957865i	$-0.592730\pi$
$811$	15.2361	−	11.0697i	0.535011	−	0.388708i	0.822229	+	0.569157i	$0.192730\pi$
$812$	−0.437694	+	1.34708i	−0.0153601	+	0.0472734i
$813$	4.94427			0.173403
$814$		0			0
$815$	−46.8328			−1.64048
$816$	1.23607	−	3.80423i	0.0432710	−	0.133175i
$817$	16.0000	−	11.6247i	0.559769	−	0.406696i
$818$	−56.3050	−	40.9079i	−1.96866	−	1.43031i
$819$	−2.85410	−	8.78402i	−0.0997304	−	0.306939i
$820$	−12.5410	−	38.5973i	−0.437951	−	1.34788i
$821$	−7.14590	−	5.19180i	−0.249394	−	0.181195i	0.456064	−	0.889947i	$-0.349259\pi$
$821$	−7.14590	−	5.19180i	−0.249394	−	0.181195i	−0.705458	+	0.708752i	$0.749259\pi$
$822$	−44.0689	+	32.0179i	−1.53708	+	1.11675i
$823$	−15.4164	+	47.4468i	−0.537382	+	1.65389i	0.201063	+	0.979578i	$0.435561\pi$
$823$	−15.4164	+	47.4468i	−0.537382	+	1.65389i	−0.738445	+	0.674314i	$0.764439\pi$
$824$	−12.7639			−0.444653
$825$		0			0
$826$	−7.23607			−0.251775
$827$	−1.52786	+	4.70228i	−0.0531290	+	0.163514i	−0.974100	−	0.226116i	$-0.927397\pi$
$827$	−1.52786	+	4.70228i	−0.0531290	+	0.163514i	0.920971	+	0.389630i	$0.127397\pi$
$828$	117.374	−	85.2771i	4.07902	−	2.96358i
$829$	13.6180	+	9.89408i	0.472974	+	0.343636i	0.798599	−	0.601863i	$-0.205575\pi$
$829$	13.6180	+	9.89408i	0.472974	+	0.343636i	−0.325625	+	0.945499i	$0.605575\pi$
$830$	21.3050	+	65.5699i	0.739506	+	2.27596i
$831$	−15.8885	−	48.8999i	−0.551167	−	1.69632i
$832$	13.0000	+	9.44505i	0.450694	+	0.327448i
$833$	1.00000	−	0.726543i	0.0346479	−	0.0251732i
$834$	23.4164	−	72.0683i	0.810844	−	2.49552i
$835$	−25.8885			−0.895910
$836$		0			0
$837$	−104.721			−3.61970
$838$	−4.59675	+	14.1473i	−0.158792	+	0.488712i
$839$	11.3820	−	8.26948i	0.392949	−	0.285494i	−0.373714	−	0.927544i	$-0.621916\pi$
$839$	11.3820	−	8.26948i	0.392949	−	0.285494i	0.766663	+	0.642050i	$0.221916\pi$
$840$	−11.7082	−	8.50651i	−0.403971	−	0.293502i
$841$	−8.89261	−	27.3686i	−0.306642	−	0.943746i
$842$	−15.4508	−	47.5528i	−0.532471	−	1.63878i
$843$	−32.6525	−	23.7234i	−1.12461	−	0.817078i
$844$	53.1246	−	38.5973i	1.82862	−	1.32857i
$845$	7.09017	−	21.8213i	0.243909	−	0.750676i
$846$	120.902			4.15669
$847$		0			0
$848$	−8.47214			−0.290934
$849$	5.88854	−	18.1231i	0.202094	−	0.621982i
$850$	−2.23607	+	1.62460i	−0.0766965	+	0.0557233i
$851$	2.47214	+	1.79611i	0.0847437	+	0.0615699i
$852$	−4.58359	−	14.1068i	−0.157031	−	0.483293i
$853$	−0.201626	−	0.620541i	−0.00690355	−	0.0212469i	0.947545	−	0.319621i	$-0.103556\pi$
$853$	−0.201626	−	0.620541i	−0.00690355	−	0.0212469i	−0.954449	+	0.298374i	$0.903556\pi$
$854$	5.00000	+	3.63271i	0.171096	+	0.124309i
$855$	29.8885	−	21.7153i	1.02217	−	0.742648i
$856$	2.76393	−	8.50651i	0.0944693	−	0.290746i
$857$	−10.7639			−0.367689			−0.183844	−	0.982955i	$-0.558854\pi$
$857$	−10.7639			−0.367689			−0.183844	+	0.982955i	$0.558854\pi$
$858$		0			0
$859$	40.5410			1.38324			0.691621	−	0.722261i	$-0.256897\pi$
$859$	40.5410			1.38324			0.691621	+	0.722261i	$0.256897\pi$
$860$	14.8328	−	45.6507i	0.505795	−	1.55668i
$861$	17.7082	−	12.8658i	0.603494	−	0.438464i
$862$	21.7082	+	15.7719i	0.739384	+	0.537194i
$863$	−6.47214	−	19.9192i	−0.220314	−	0.678057i	−0.998734	−	0.0503125i	$-0.983978\pi$
$863$	−6.47214	−	19.9192i	−0.220314	−	0.678057i	0.778419	−	0.627744i	$-0.216022\pi$
$864$	−30.0000	−	92.3305i	−1.02062	−	3.14115i
$865$	27.8885	+	20.2622i	0.948239	+	0.688936i
$866$	−0.854102	+	0.620541i	−0.0290236	+	0.0210869i
$867$	−15.4721	+	47.6183i	−0.525461	+	1.61720i
$868$	21.7082			0.736824
$869$		0			0
$870$	−6.83282			−0.231654
$871$	2.11146	−	6.49839i	0.0715440	−	0.220190i
$872$	8.09017	−	5.87785i	0.273968	−	0.199049i
$873$	56.9230	+	41.3570i	1.92655	+	1.39972i
$874$	−11.0557	−	34.0260i	−0.373966	−	1.15095i
$875$	−3.70820	−	11.4127i	−0.125360	−	0.385819i
$876$	−41.1246	−	29.8788i	−1.38947	−	1.00951i
$877$	33.5066	−	24.3440i	1.13144	−	0.822037i	0.145533	−	0.989353i	$-0.453510\pi$
$877$	33.5066	−	24.3440i	1.13144	−	0.822037i	0.985903	+	0.167316i	$0.0535101\pi$
$878$	−1.05573	+	3.24920i	−0.0356291	+	0.109655i
$879$	−48.9443			−1.65085
$880$		0			0
$881$	29.4164			0.991064			0.495532	−	0.868590i	$-0.334973\pi$
$881$	29.4164			0.991064			0.495532	+	0.868590i	$0.334973\pi$
$882$	5.16312	−	15.8904i	0.173851	−	0.535059i
$883$	−7.23607	+	5.25731i	−0.243513	+	0.176923i	−0.702847	−	0.711341i	$-0.748088\pi$
$883$	−7.23607	+	5.25731i	−0.243513	+	0.176923i	0.459334	+	0.888264i	$0.348088\pi$
$884$	3.70820	+	2.69417i	0.124720	+	0.0906147i
$885$	−6.47214	−	19.9192i	−0.217558	−	0.669576i
$886$	−4.87539	−	15.0049i	−0.163792	−	0.504100i
$887$	32.6525	+	23.7234i	1.09636	+	0.796554i	0.980462	−	0.196707i	$-0.0630246\pi$
$887$	32.6525	+	23.7234i	1.09636	+	0.796554i	0.115900	+	0.993261i	$0.463025\pi$
$888$	−2.76393	+	2.00811i	−0.0927515	+	0.0673879i
$889$	6.47214	−	19.9192i	0.217068	−	0.668068i
$890$	−8.94427			−0.299813
$891$		0			0
$892$	36.5410			1.22348
$893$	5.52786	−	17.0130i	0.184983	−	0.569319i
$894$	81.9574	−	59.5456i	2.74107	−	1.99150i
$895$	14.4721	+	10.5146i	0.483750	+	0.351465i
$896$	4.83688	+	14.8864i	0.161589	+	0.497319i
$897$	−8.00000	−	24.6215i	−0.267112	−	0.822087i
$898$	35.3262	+	25.6660i	1.17885	+	0.856486i
$899$	2.76393	−	2.00811i	0.0921823	−	0.0669744i
$900$	−6.92705	+	21.3193i	−0.230902	+	0.710642i
$901$	−10.4721			−0.348877
$902$		0			0
$903$	25.8885			0.861517
$904$	1.38197	−	4.25325i	0.0459635	−	0.141461i
$905$	2.29180	−	1.66509i	0.0761819	−	0.0553494i
$906$	−52.3607	−	38.0423i	−1.73957	−	1.26387i
$907$	4.18034	+	12.8658i	0.138806	+	0.427201i	0.996163	−	0.0875221i	$-0.0278948\pi$
$907$	4.18034	+	12.8658i	0.138806	+	0.427201i	−0.857357	+	0.514723i	$0.827895\pi$
$908$	27.7082	+	85.2771i	0.919529	+	2.83002i
$909$	−55.8328	−	40.5649i	−1.85186	−	1.34545i
$910$	−4.47214	+	3.24920i	−0.148250	+	0.107710i
$911$	10.3607	−	31.8869i	0.343265	−	1.05646i	−0.619242	−	0.785200i	$-0.712560\pi$
$911$	10.3607	−	31.8869i	0.343265	−	1.05646i	0.962506	−	0.271259i	$-0.0874401\pi$
$912$	−8.00000			−0.264906
$913$		0			0
$914$	−55.5279			−1.83670
$915$	−5.52786	+	17.0130i	−0.182746	+	0.562433i
$916$	−10.8541	+	7.88597i	−0.358630	+	0.260560i
$917$	11.2361	+	8.16348i	0.371048	+	0.269582i
$918$	−12.3607	−	38.0423i	−0.407963	−	1.25558i
$919$	−1.88854	−	5.81234i	−0.0622973	−	0.191731i	0.915064	−	0.403309i	$-0.132140\pi$
$919$	−1.88854	−	5.81234i	−0.0622973	−	0.191731i	−0.977361	+	0.211577i	$0.932140\pi$
$920$	−23.4164	−	17.0130i	−0.772016	−	0.560903i
$921$	23.4164	−	17.0130i	0.771597	−	0.560598i
$922$	−7.03444	+	21.6498i	−0.231667	+	0.712998i
$923$	−1.88854			−0.0621622
$924$		0			0
$925$	−0.472136			−0.0155237
$926$	−10.0000	+	30.7768i	−0.328620	+	1.01139i
$927$	34.5066	−	25.0705i	1.13334	−	0.823423i
$928$	2.56231	+	1.86162i	0.0841118	+	0.0611108i
$929$	8.72949	+	26.8666i	0.286405	+	0.881465i	0.985974	+	0.166899i	$0.0533755\pi$
$929$	8.72949	+	26.8666i	0.286405	+	0.881465i	−0.699569	+	0.714565i	$0.746624\pi$
$930$	32.3607	+	99.5959i	1.06115	+	3.26588i
$931$	−2.00000	−	1.45309i	−0.0655474	−	0.0476229i
$932$	−42.2705	+	30.7113i	−1.38462	+	1.00598i
$933$	−21.7082	+	66.8110i	−0.710695	+	2.18729i
$934$	−76.1803			−2.49270
$935$		0			0
$936$	20.6525			0.675047
$937$	−6.38197	+	19.6417i	−0.208490	+	0.641665i	0.791062	+	0.611736i	$0.209528\pi$
$937$	−6.38197	+	19.6417i	−0.208490	+	0.641665i	−0.999552	+	0.0299298i	$0.990472\pi$
$938$	10.0000	−	7.26543i	0.326512	−	0.237225i
$939$	7.70820	+	5.60034i	0.251548	+	0.182760i
$940$	−13.4164	−	41.2915i	−0.437595	−	1.34678i
$941$	12.8541	+	39.5609i	0.419032	+	1.28965i	0.908595	+	0.417679i	$0.137156\pi$
$941$	12.8541	+	39.5609i	0.419032	+	1.28965i	−0.489563	+	0.871968i	$0.662844\pi$
$942$	40.6525	+	29.5358i	1.32453	+	0.962327i
$943$	35.4164	−	25.7315i	1.15332	−	0.837934i
$944$	−1.00000	+	3.07768i	−0.0325472	+	0.100170i
$945$	28.9443			0.941557
$946$		0			0
$947$	−58.8328			−1.91181			−0.955905	−	0.293677i	$-0.905121\pi$
$947$	−58.8328			−1.91181			−0.955905	+	0.293677i	$0.905121\pi$
$948$	−26.8328	+	82.5829i	−0.871489	+	2.68217i
$949$	−5.23607	+	3.80423i	−0.169970	+	0.123490i
$950$	4.47214	+	3.24920i	0.145095	+	0.105418i
$951$	14.0000	+	43.0876i	0.453981	+	1.39721i
$952$	0.854102	+	2.62866i	0.0276816	+	0.0851952i
$953$	4.09017	+	2.97168i	0.132494	+	0.0962622i	0.652058	−	0.758169i	$-0.273906\pi$
$953$	4.09017	+	2.97168i	0.132494	+	0.0962622i	−0.519565	+	0.854431i	$0.673906\pi$
$954$	−114.520	+	83.2035i	−3.70771	+	2.69381i
$955$	12.9443	−	39.8384i	0.418867	−	1.28914i
$956$	−77.6656			−2.51189
$957$		0			0
$958$	−50.2492			−1.62348
$959$	−2.32624	+	7.15942i	−0.0751181	+	0.231190i
$960$	−68.0689	+	49.4549i	−2.19691	+	1.59615i
$961$	−17.2812	−	12.5555i	−0.557457	−	0.405016i
$962$	0.403252	+	1.24108i	0.0130014	+	0.0400141i
$963$	9.23607	+	28.4257i	0.297628	+	0.916005i
$964$	65.8328	+	47.8303i	2.12033	+	1.54051i
$965$	38.6525	−	28.0827i	1.24427	−	0.904013i
$966$	14.4721	−	44.5407i	0.465633	−	1.43307i
$967$	−21.8885			−0.703888			−0.351944	−	0.936021i	$-0.614479\pi$
$967$	−21.8885			−0.703888			−0.351944	+	0.936021i	$0.614479\pi$
$968$		0			0
$969$	−9.88854			−0.317666
$970$	13.0132	−	40.0504i	0.417827	−	1.28594i
$971$	23.5623	−	17.1190i	0.756150	−	0.549375i	−0.141577	−	0.989927i	$-0.545217\pi$
$971$	23.5623	−	17.1190i	0.756150	−	0.549375i	0.897727	+	0.440552i	$0.145217\pi$
$972$	−86.3951	−	62.7697i	−2.77112	−	2.01334i
$973$	−3.23607	−	9.95959i	−0.103744	−	0.319290i
$974$	5.77709	+	17.7800i	0.185110	+	0.569709i
$975$	3.23607	+	2.35114i	0.103637	+	0.0752968i
$976$	2.23607	−	1.62460i	0.0715748	−	0.0520021i
$977$	1.56231	−	4.80828i	0.0499826	−	0.153831i	−0.922950	−	0.384920i	$-0.874229\pi$
$977$	1.56231	−	4.80828i	0.0499826	−	0.153831i	0.972933	+	0.231089i	$0.0742290\pi$
$978$	169.443			5.41818
$979$		0			0
$980$	−6.00000			−0.191663
$981$	−10.3262	+	31.7809i	−0.329691	+	1.01469i
$982$		0			0
$983$	−35.7426	−	25.9686i	−1.14001	−	0.828268i	−0.152892	−	0.988243i	$-0.548859\pi$
$983$	−35.7426	−	25.9686i	−1.14001	−	0.828268i	−0.987121	+	0.159975i	$0.948859\pi$
$984$	15.1246	+	46.5488i	0.482155	+	1.48392i
$985$	−1.23607	−	3.80423i	−0.0393844	−	0.121213i
$986$	1.05573	+	0.767031i	0.0336212	+	0.0244273i
$987$	18.9443	−	13.7638i	0.603003	−	0.438107i
$988$	2.83282	−	8.71851i	0.0901239	−	0.277373i
$989$	51.7771			1.64642
$990$		0			0
$991$	−26.2492			−0.833834			−0.416917	−	0.908945i	$-0.636889\pi$
$991$	−26.2492			−0.833834			−0.416917	+	0.908945i	$0.636889\pi$
$992$	15.0000	−	46.1653i	0.476250	−	1.46575i
$993$	−57.3050	+	41.6345i	−1.81852	+	1.32123i
$994$	−2.76393	−	2.00811i	−0.0876666	−	0.0636935i
$995$	−12.4721	−	38.3853i	−0.395393	−	1.21690i
$996$	−46.2492	−	142.340i	−1.46546	−	4.51023i
$997$	26.4164	+	19.1926i	0.836616	+	0.607837i	0.921423	−	0.388560i	$-0.127027\pi$
$997$	26.4164	+	19.1926i	0.836616	+	0.607837i	−0.0848073	+	0.996397i	$0.527027\pi$
$998$	−18.9443	+	13.7638i	−0.599670	+	0.435686i
$999$	2.11146	−	6.49839i	0.0668035	−	0.205600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.m.372.1		4
11.2	odd	10		847.2.f.n.729.1		4
11.3	even	5		847.2.f.b.323.1		4
11.4	even	5		847.2.a.f.1.2		2
11.5	even	5	inner	847.2.f.m.148.1		4
11.6	odd	10		847.2.f.a.148.1		4
11.7	odd	10		77.2.a.d.1.1	✓	2
11.8	odd	10		847.2.f.n.323.1		4
11.9	even	5		847.2.f.b.729.1		4
11.10	odd	2		847.2.f.a.372.1		4
33.26	odd	10		7623.2.a.bl.1.1		2
33.29	even	10		693.2.a.h.1.2		2
44.7	even	10		1232.2.a.m.1.1		2
55.7	even	20		1925.2.b.h.1849.1		4
55.18	even	20		1925.2.b.h.1849.4		4
55.29	odd	10		1925.2.a.r.1.2		2
77.18	odd	30		539.2.e.i.177.2		4
77.40	even	30		539.2.e.j.67.2		4
77.48	odd	10		5929.2.a.m.1.2		2
77.51	odd	30		539.2.e.i.67.2		4
77.62	even	10		539.2.a.f.1.1		2
77.73	even	30		539.2.e.j.177.2		4
88.29	odd	10		4928.2.a.bm.1.1		2
88.51	even	10		4928.2.a.bv.1.2		2
231.62	odd	10		4851.2.a.y.1.2		2
308.139	odd	10		8624.2.a.ce.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.d.1.1	✓	2	11.7	odd	10
539.2.a.f.1.1		2	77.62	even	10
539.2.e.i.67.2		4	77.51	odd	30
539.2.e.i.177.2		4	77.18	odd	30
539.2.e.j.67.2		4	77.40	even	30
539.2.e.j.177.2		4	77.73	even	30
693.2.a.h.1.2		2	33.29	even	10
847.2.a.f.1.2		2	11.4	even	5
847.2.f.a.148.1		4	11.6	odd	10
847.2.f.a.372.1		4	11.10	odd	2
847.2.f.b.323.1		4	11.3	even	5
847.2.f.b.729.1		4	11.9	even	5
847.2.f.m.148.1		4	11.5	even	5	inner
847.2.f.m.372.1		4	1.1	even	1	trivial
847.2.f.n.323.1		4	11.8	odd	10
847.2.f.n.729.1		4	11.2	odd	10
1232.2.a.m.1.1		2	44.7	even	10
1925.2.a.r.1.2		2	55.29	odd	10
1925.2.b.h.1849.1		4	55.7	even	20
1925.2.b.h.1849.4		4	55.18	even	20
4851.2.a.y.1.2		2	231.62	odd	10
4928.2.a.bm.1.1		2	88.29	odd	10
4928.2.a.bv.1.2		2	88.51	even	10
5929.2.a.m.1.2		2	77.48	odd	10
7623.2.a.bl.1.1		2	33.26	odd	10
8624.2.a.ce.1.2		2	308.139	odd	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)

\(f(q)\)	\(=\)	\(q+(0.690983 - 2.12663i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(2.23607 + 6.88191i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(2.30902 - 7.10642i) q^{9} +O(q^{10})\)	\(q+(0.690983 - 2.12663i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-0.618034 - 1.90211i) q^{5} +(2.23607 + 6.88191i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(2.30902 - 7.10642i) q^{9} -4.47214 q^{10} +9.70820 q^{12} +(0.381966 - 1.17557i) q^{13} +(1.80902 - 1.31433i) q^{14} +(5.23607 + 3.80423i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.381966 - 1.17557i) q^{17} +(-13.5172 - 9.82084i) q^{18} +(-2.00000 + 1.45309i) q^{19} +(-1.85410 + 5.70634i) q^{20} -3.23607 q^{21} -6.47214 q^{23} +(2.23607 - 6.88191i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-2.23607 - 1.62460i) q^{26} +(4.47214 + 13.7638i) q^{27} +(-0.927051 - 2.85317i) q^{28} +(-0.381966 - 0.277515i) q^{29} +(11.7082 - 8.50651i) q^{30} +(-2.23607 + 6.88191i) q^{31} -6.70820 q^{32} -2.76393 q^{34} +(0.618034 - 1.90211i) q^{35} +(-18.1353 + 13.1760i) q^{36} +(-0.381966 - 0.277515i) q^{37} +(1.70820 + 5.25731i) q^{38} +(1.23607 + 3.80423i) q^{39} +(3.61803 + 2.62866i) q^{40} +(-5.47214 + 3.97574i) q^{41} +(-2.23607 + 6.88191i) q^{42} -8.00000 q^{43} -14.9443 q^{45} +(-4.47214 + 13.7638i) q^{46} +(-5.85410 + 4.25325i) q^{47} +(2.61803 + 1.90211i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.690983 - 2.12663i) q^{50} +(3.23607 + 2.35114i) q^{51} +(-3.00000 + 2.17963i) q^{52} +(2.61803 - 8.05748i) q^{53} +32.3607 q^{54} -2.23607 q^{56} +(2.47214 - 7.60845i) q^{57} +(-0.854102 + 0.620541i) q^{58} +(-2.61803 - 1.90211i) q^{59} +(-6.00000 - 18.4661i) q^{60} +(0.854102 + 2.62866i) q^{61} +(13.0902 + 9.51057i) q^{62} +(6.04508 - 4.39201i) q^{63} +(-4.01722 + 12.3637i) q^{64} -2.47214 q^{65} +5.52786 q^{67} +(-1.14590 + 3.52671i) q^{68} +(16.9443 - 12.3107i) q^{69} +(-3.61803 - 2.62866i) q^{70} +(-0.472136 - 1.45309i) q^{71} +(5.16312 + 15.8904i) q^{72} +(-4.23607 - 3.07768i) q^{73} +(-0.854102 + 0.620541i) q^{74} +(-1.00000 + 3.07768i) q^{75} +7.41641 q^{76} +8.94427 q^{78} +(-2.76393 + 8.50651i) q^{79} +(-1.61803 + 1.17557i) q^{80} +(-19.7533 - 14.3516i) q^{81} +(4.67376 + 14.3844i) q^{82} +(-4.76393 - 14.6619i) q^{83} +(7.85410 + 5.70634i) q^{84} +(-2.00000 + 1.45309i) q^{85} +(-5.52786 + 17.0130i) q^{86} +1.52786 q^{87} +2.00000 q^{89} +(-10.3262 + 31.7809i) q^{90} +(1.00000 - 0.726543i) q^{91} +(15.7082 + 11.4127i) q^{92} +(-7.23607 - 22.2703i) q^{93} +(5.00000 + 15.3884i) q^{94} +(4.00000 + 2.90617i) q^{95} +(17.5623 - 12.7598i) q^{96} +(-2.90983 + 8.95554i) q^{97} +2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} + q^{7} - 5 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 - 6 * q^3 - 3 * q^4 + 2 * q^5 + q^7 - 5 * q^8 + 7 * q^9	\( 4 q + 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} + q^{7} - 5 q^{8} + 7 q^{9} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 12 q^{15} + q^{16} - 6 q^{17} - 25 q^{18} - 8 q^{19} + 6 q^{20} - 4 q^{21} - 8 q^{23} + q^{25} + 3 q^{28} - 6 q^{29} + 20 q^{30} - 20 q^{34} - 2 q^{35} - 39 q^{36} - 6 q^{37} - 20 q^{38} - 4 q^{39} + 10 q^{40} - 4 q^{41} - 32 q^{43} - 24 q^{45} - 10 q^{47} + 6 q^{48} - q^{49} - 5 q^{50} + 4 q^{51} - 12 q^{52} + 6 q^{53} + 40 q^{54} - 8 q^{57} + 10 q^{58} - 6 q^{59} - 24 q^{60} - 10 q^{61} + 30 q^{62} + 13 q^{63} + 13 q^{64} + 8 q^{65} + 40 q^{67} - 18 q^{68} + 32 q^{69} - 10 q^{70} + 16 q^{71} + 5 q^{72} - 8 q^{73} + 10 q^{74} - 4 q^{75} - 24 q^{76} - 20 q^{79} - 2 q^{80} - 41 q^{81} + 50 q^{82} - 28 q^{83} + 18 q^{84} - 8 q^{85} - 40 q^{86} + 24 q^{87} + 8 q^{89} - 10 q^{90} + 4 q^{91} + 36 q^{92} - 20 q^{93} + 20 q^{94} + 16 q^{95} + 30 q^{96} - 34 q^{97}+O(q^{100}) \) 4 * q + 5 * q^2 - 6 * q^3 - 3 * q^4 + 2 * q^5 + q^7 - 5 * q^8 + 7 * q^9 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 12 * q^15 + q^16 - 6 * q^17 - 25 * q^18 - 8 * q^19 + 6 * q^20 - 4 * q^21 - 8 * q^23 + q^25 + 3 * q^28 - 6 * q^29 + 20 * q^30 - 20 * q^34 - 2 * q^35 - 39 * q^36 - 6 * q^37 - 20 * q^38 - 4 * q^39 + 10 * q^40 - 4 * q^41 - 32 * q^43 - 24 * q^45 - 10 * q^47 + 6 * q^48 - q^49 - 5 * q^50 + 4 * q^51 - 12 * q^52 + 6 * q^53 + 40 * q^54 - 8 * q^57 + 10 * q^58 - 6 * q^59 - 24 * q^60 - 10 * q^61 + 30 * q^62 + 13 * q^63 + 13 * q^64 + 8 * q^65 + 40 * q^67 - 18 * q^68 + 32 * q^69 - 10 * q^70 + 16 * q^71 + 5 * q^72 - 8 * q^73 + 10 * q^74 - 4 * q^75 - 24 * q^76 - 20 * q^79 - 2 * q^80 - 41 * q^81 + 50 * q^82 - 28 * q^83 + 18 * q^84 - 8 * q^85 - 40 * q^86 + 24 * q^87 + 8 * q^89 - 10 * q^90 + 4 * q^91 + 36 * q^92 - 20 * q^93 + 20 * q^94 + 16 * q^95 + 30 * q^96 - 34 * q^97

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