LMFDB - Embedded newform 847.2.f.a.148.1

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			148.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	847.148
Dual form			847.2.f.a.372.1

$q$-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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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	−0.826700	−	0.562643i	$-0.809785\pi$
$2$	−0.690983	−	2.12663i	−0.488599	−	1.50375i	0.338101	−	0.941110i	$-0.390215\pi$
$3$	−2.61803	−	1.90211i	−1.51152	−	1.09819i	−0.965496	−	0.260418i	$-0.916140\pi$
$3$	−2.61803	−	1.90211i	−1.51152	−	1.09819i	−0.546027	−	0.837768i	$-0.683860\pi$
$4$	−2.42705	+	1.76336i	−1.21353	+	0.881678i
$5$	−0.618034	+	1.90211i	−0.276393	+	0.850651i	0.712454	+	0.701719i	$0.247584\pi$
$5$	−0.618034	+	1.90211i	−0.276393	+	0.850651i	−0.988847	+	0.148932i	$0.952416\pi$
$6$	−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	$-0.154833\pi$
$13$	−0.381966	−	1.17557i	−0.105938	−	0.326045i	−0.989950	+	0.141421i	$0.954833\pi$
$14$	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	$-0.852106\pi$
$17$	0.381966	−	1.17557i	0.0926404	−	0.285118i	0.986632	+	0.162967i	$0.0521064\pi$
$18$	13.5172	−	9.82084i	3.18604	−	2.31479i
$19$	2.00000	+	1.45309i	0.458831	+	0.333361i	0.793073	−	0.609127i	$-0.208480\pi$
$19$	2.00000	+	1.45309i	0.458831	+	0.333361i	−0.334241	+	0.942488i	$0.608480\pi$
$20$	−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	$-0.686042\pi$
$29$	0.381966	−	0.277515i	0.0709293	−	0.0515332i	0.622685	+	0.782473i	$0.286042\pi$
$30$	−11.7082	−	8.50651i	−2.13762	−	1.55307i
$31$	−2.23607	−	6.88191i	−0.401610	−	1.23603i	−0.923693	−	0.383133i	$-0.874845\pi$
$31$	−2.23607	−	6.88191i	−0.401610	−	1.23603i	0.522083	−	0.852894i	$-0.325155\pi$
$32$	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	−0.618740	−	0.785596i	$-0.712356\pi$
$37$	−0.381966	+	0.277515i	−0.0627948	+	0.0456231i	0.555945	+	0.831219i	$0.312356\pi$
$38$	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	$-0.122877\pi$
$41$	5.47214	+	3.97574i	0.854604	+	0.620906i	−0.0718076	+	0.997419i	$0.522877\pi$
$42$	−2.23607	−	6.88191i	−0.345033	−	1.06190i
$43$	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
$45$	−14.9443			−2.22776
$46$	4.47214	+	13.7638i	0.659380	+	2.02936i
$47$	−5.85410	−	4.25325i	−0.853909	−	0.620401i	0.0723124	−	0.997382i	$-0.476962\pi$
$47$	−5.85410	−	4.25325i	−0.853909	−	0.620401i	−0.926221	+	0.376981i	$0.876962\pi$
$48$	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	0.953285	+	0.302072i	$0.0976782\pi$
$53$	2.61803	+	8.05748i	0.359615	+	1.10678i	−0.593671	+	0.804708i	$0.702322\pi$
$54$	−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	−0.745016	−	0.667047i	$-0.767558\pi$
$59$	−2.61803	+	1.90211i	−0.340839	+	0.247634i	0.404177	+	0.914681i	$0.367558\pi$
$60$	−6.00000	+	18.4661i	−0.774597	+	2.38396i
$61$	−0.854102	+	2.62866i	−0.109357	+	0.336565i	−0.990728	−	0.135859i	$-0.956621\pi$
$61$	−0.854102	+	2.62866i	−0.109357	+	0.336565i	0.881372	+	0.472423i	$0.156621\pi$
$62$	−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	−0.975156	−	0.221520i	$-0.928898\pi$
$71$	−0.472136	+	1.45309i	−0.0560322	+	0.172449i	0.919124	+	0.393969i	$0.128898\pi$
$72$	−5.16312	+	15.8904i	−0.608479	+	1.87271i
$73$	4.23607	−	3.07768i	0.495794	−	0.360216i	−0.311614	−	0.950209i	$-0.600870\pi$
$73$	4.23607	−	3.07768i	0.495794	−	0.360216i	0.807408	+	0.589993i	$0.200870\pi$
$74$	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	0.977383	+	0.211477i	$0.0678274\pi$
$79$	2.76393	+	8.50651i	0.310967	+	0.957057i	−0.666416	+	0.745580i	$0.732173\pi$
$80$	−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	−0.245504	−	0.969396i	$-0.578953\pi$
$83$	4.76393	−	14.6619i	0.522909	−	1.60935i	0.768413	−	0.639954i	$-0.221047\pi$
$84$	−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	−0.983070	−	0.183228i	$-0.941345\pi$
$97$	−2.90983	−	8.95554i	−0.295448	−	0.909297i	0.687622	−	0.726069i	$-0.258655\pi$
$98$	−2.23607			−0.225877
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−2.85410	−	8.78402i	−0.283994	−	0.874043i	−0.986698	−	0.162561i	$-0.948024\pi$
$101$	−2.85410	−	8.78402i	−0.283994	−	0.874043i	0.702705	−	0.711482i	$-0.251976\pi$
$102$	7.23607	+	5.25731i	0.716477	+	0.520551i
$103$	4.61803	−	3.35520i	0.455028	−	0.330597i	−0.336549	−	0.941666i	$-0.609260\pi$
$103$	4.61803	−	3.35520i	0.455028	−	0.330597i	0.791578	+	0.611068i	$0.209260\pi$
$104$	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	$-0.238066\pi$
$107$	3.23607	+	2.35114i	0.312842	+	0.227293i	−0.420273	+	0.907398i	$0.638066\pi$
$108$	13.4164	+	41.2915i	1.29099	+	3.97327i
$109$	4.47214			0.428353			0.214176	−	0.976795i	$-0.431293\pi$
$109$	4.47214			0.428353			0.214176	+	0.976795i	$0.431293\pi$
$110$		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	0.509073	−	0.860724i	$-0.329988\pi$
$113$	−1.61803	−	1.17557i	−0.152212	−	0.110588i	−0.661285	+	0.750135i	$0.729988\pi$
$114$	−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	−0.0642104	−	0.997936i	$-0.520453\pi$
$127$	6.47214	−	19.9192i	0.574309	−	1.76754i	0.638520	−	0.769606i	$-0.279547\pi$
$128$	−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	$-0.707517\pi$
$131$	−13.8885			−1.21345			−0.606724	+	0.794913i	$0.707517\pi$
$132$		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	−0.801169	−	0.598439i	$-0.795788\pi$
$137$	2.32624	−	7.15942i	0.198744	−	0.611671i	0.999912	−	0.0132321i	$-0.00421203\pi$
$138$	14.4721	−	44.5407i	1.23195	−	3.79155i
$139$	8.47214	−	6.15537i	0.718597	−	0.522091i	−0.167339	−	0.985899i	$-0.553517\pi$
$139$	8.47214	−	6.15537i	0.718597	−	0.522091i	0.885936	+	0.463808i	$0.153517\pi$
$140$	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	−0.601926	−	0.798552i	$-0.705600\pi$
$149$	4.32624	−	13.3148i	0.354419	−	1.09079i	0.956345	−	0.292239i	$-0.0944001\pi$
$150$	−5.85410	+	4.25325i	−0.477985	+	0.347277i
$151$	7.23607	+	5.25731i	0.588863	+	0.427834i	0.841908	−	0.539620i	$-0.181432\pi$
$151$	7.23607	+	5.25731i	0.588863	+	0.427834i	−0.253046	+	0.967454i	$0.581432\pi$
$152$	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	0.788951	−	0.614456i	$-0.210624\pi$
$157$	5.61803	+	4.08174i	0.448368	+	0.325758i	−0.340583	+	0.940214i	$0.610624\pi$
$158$	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	0.662625	+	0.748951i	$0.269442\pi$
$163$	7.23607	+	22.2703i	0.566773	+	1.74435i	−0.0958527	+	0.995396i	$0.530558\pi$
$164$	−20.2918			−1.58452
$165$		0			0
$166$	−34.4721			−2.67556
$167$	−4.00000	−	12.3107i	−0.309529	−	0.952633i	−0.977948	−	0.208848i	$-0.933029\pi$
$167$	−4.00000	−	12.3107i	−0.309529	−	0.952633i	0.668419	−	0.743785i	$-0.266971\pi$
$168$	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	$-0.0725772\pi$
$173$	13.9443	+	10.1311i	1.06016	+	0.770254i	0.0860448	+	0.996291i	$0.472577\pi$
$174$	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	0.283551	−	0.958957i	$-0.408487\pi$
$179$	−7.23607	−	5.25731i	−0.540849	−	0.392950i	−0.824400	+	0.566007i	$0.808487\pi$
$180$	36.2705	−	26.3521i	2.70344	−	1.96417i
$181$	0.437694	−	1.34708i	0.0325335	−	0.100128i	−0.933471	−	0.358653i	$-0.883236\pi$
$181$	0.437694	−	1.34708i	0.0325335	−	0.100128i	0.966005	+	0.258525i	$0.0832363\pi$
$182$	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	0.229457	−	0.973319i	$-0.426305\pi$
$191$	16.9443	−	12.3107i	1.22604	−	0.890773i	0.996587	+	0.0825453i	$0.0263049\pi$
$192$	−13.0000	+	40.0099i	−0.938194	+	2.88746i
$193$	−7.38197	+	22.7194i	−0.531366	+	1.63537i	0.220008	+	0.975498i	$0.429392\pi$
$193$	−7.38197	+	22.7194i	−0.531366	+	1.63537i	−0.751374	+	0.659877i	$0.770608\pi$
$194$	−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	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		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	0.858165	+	0.513373i	$0.171604\pi$
$211$	6.76393	+	20.8172i	0.465648	+	1.43312i	−0.392517	+	0.919745i	$0.628396\pi$
$212$	−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	0.206743	−	0.978395i	$-0.433714\pi$
$223$	−9.85410	−	7.15942i	−0.659879	−	0.479431i	−0.866622	+	0.498965i	$0.833714\pi$
$224$	−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	0.727728	−	0.685866i	$-0.240576\pi$
$227$	24.1803	−	17.5680i	1.60491	−	1.16603i	0.877177	−	0.480166i	$-0.159424\pi$
$228$	19.4164	+	14.1068i	1.28588	+	0.934249i
$229$	1.38197	+	4.25325i	0.0913229	+	0.281063i	0.986278	−	0.165093i	$-0.0527925\pi$
$229$	1.38197	+	4.25325i	0.0913229	+	0.281063i	−0.894955	+	0.446156i	$0.852793\pi$
$230$	−28.9443			−1.90853
$231$		0			0
$232$	1.05573			0.0693119
$233$	−5.38197	−	16.5640i	−0.352584	−	1.08514i	−0.957397	−	0.288775i	$-0.906752\pi$
$233$	−5.38197	−	16.5640i	−0.352584	−	1.08514i	0.604813	−	0.796368i	$-0.293248\pi$
$234$	−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	−0.998758	−	0.0498191i	$-0.984136\pi$
$239$	−20.9443	−	15.2169i	−1.35477	−	0.984300i	−0.356014	−	0.934481i	$-0.615864\pi$
$240$	2.00000	+	6.15537i	0.129099	+	0.397327i
$241$	27.1246			1.74725			0.873625	−	0.486600i	$-0.161763\pi$
$241$	27.1246			1.74725			0.873625	+	0.486600i	$0.161763\pi$
$242$		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	0.961370	+	0.275258i	$0.0887634\pi$
$251$	5.47214	+	16.8415i	0.345398	+	1.06303i	−0.615972	+	0.787768i	$0.711237\pi$
$252$	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	−0.426006	−	0.904720i	$-0.640080\pi$
$257$	4.85410	−	3.52671i	0.302791	−	0.219990i	0.728797	+	0.684730i	$0.240080\pi$
$258$	−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	0.741479	+	0.670976i	$0.234125\pi$
$269$	−4.14590	+	12.7598i	−0.252780	+	0.777976i	−0.994259	+	0.107000i	$0.965875\pi$
$270$	20.0000	−	61.5537i	1.21716	−	3.74604i
$271$	1.23607	−	0.898056i	0.0750858	−	0.0545530i	−0.549609	−	0.835422i	$-0.685223\pi$
$271$	1.23607	−	0.898056i	0.0750858	−	0.0545530i	0.624695	+	0.780869i	$0.285223\pi$
$272$	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	0.983220	+	0.182422i	$0.0583936\pi$
$277$	4.90983	+	15.1109i	0.295003	+	0.907926i	−0.688217	+	0.725505i	$0.741606\pi$
$278$	−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	0.767839	+	0.640643i	$0.221332\pi$
$281$	−3.85410	+	11.8617i	−0.229916	+	0.707610i	−0.997755	+	0.0669669i	$0.978668\pi$
$282$	42.3607	−	30.7768i	2.52254	−	1.83273i
$283$	4.76393	+	3.46120i	0.283186	+	0.205747i	0.720306	−	0.693656i	$-0.244001\pi$
$283$	4.76393	+	3.46120i	0.283186	+	0.205747i	−0.437120	+	0.899403i	$0.644001\pi$
$284$	−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	$-0.845658\pi$
$293$	−12.2361	+	8.89002i	−0.714839	+	0.519361i	0.169892	+	0.985463i	$0.445658\pi$
$294$	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	$-0.417846\pi$
$307$	8.94427			0.510477			0.255238	+	0.966878i	$0.417846\pi$
$308$		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	0.961198	−	0.275859i	$-0.0889623\pi$
$311$	17.5623	+	12.7598i	0.995867	+	0.723540i	0.0346689	+	0.999399i	$0.488962\pi$
$312$	−7.23607	+	5.25731i	−0.409662	+	0.297637i
$313$	−0.909830	+	2.80017i	−0.0514266	+	0.158275i	−0.973472	−	0.228808i	$-0.926517\pi$
$313$	−0.909830	+	2.80017i	−0.0514266	+	0.158275i	0.922045	+	0.387083i	$0.126517\pi$
$314$	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	0.995961	+	0.0897846i	$0.0286179\pi$
$317$	4.32624	+	13.3148i	0.242986	+	0.747833i	−0.752975	+	0.658049i	$0.771382\pi$
$318$	−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	$-0.511725\pi$
$337$	16.5623	−	12.0332i	0.902206	−	0.655491i	0.939032	+	0.343830i	$0.111725\pi$
$338$	−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	$-0.873863\pi$
$347$	0.944272	−	2.90617i	0.0506912	−	0.156011i	0.973198	+	0.229970i	$0.0738628\pi$
$348$	3.70820	−	2.69417i	0.198781	−	0.144423i
$349$	2.23607	+	1.62460i	0.119694	+	0.0869628i	0.646022	−	0.763319i	$-0.276432\pi$
$349$	2.23607	+	1.62460i	0.119694	+	0.0869628i	−0.526328	+	0.850282i	$0.676432\pi$
$350$	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	$-0.640385\pi$
$359$	5.70820	−	4.14725i	0.301267	−	0.218884i	0.728140	+	0.685428i	$0.240385\pi$
$360$	−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	−0.887398	−	0.461004i	$-0.847489\pi$
$367$	−13.8541	+	10.0656i	−0.723178	+	0.525420i	0.164220	+	0.986424i	$0.447489\pi$
$368$	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	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$		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	0.521976	+	0.852960i	$0.325195\pi$
$379$	−7.81966	+	24.0664i	−0.401669	+	1.23621i	−0.923645	+	0.383250i	$0.874805\pi$
$380$	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	0.906919	+	0.421306i	$0.138428\pi$
$383$	8.23607	+	25.3480i	0.420843	+	1.29522i	−0.486075	+	0.873917i	$0.661572\pi$
$384$	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	−0.0997035	−	0.995017i	$-0.531789\pi$
$389$	16.0902	−	11.6902i	0.815804	−	0.592716i	0.915508	+	0.402301i	$0.131789\pi$
$390$	−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	−0.904439	−	0.426602i	$-0.859710\pi$
$401$	1.56231	−	4.80828i	0.0780178	−	0.240114i	0.982457	+	0.186488i	$0.0597105\pi$
$402$	−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	−0.845172	−	0.534494i	$-0.820502\pi$
$409$	−9.61803	−	29.6013i	−0.475581	−	1.46369i	0.369591	−	0.929194i	$-0.379498\pi$
$410$	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	0.933690	−	0.358081i	$-0.116569\pi$
$421$	18.0902	+	13.1433i	0.881661	+	0.640564i	−0.0520294	+	0.998646i	$0.516569\pi$
$422$	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	$-0.00667397\pi$
$431$	3.70820	+	11.4127i	0.178618	+	0.549729i	−0.821162	+	0.570695i	$0.806674\pi$
$432$	11.7082	+	8.50651i	0.563311	+	0.409270i
$433$	−0.381966	+	0.277515i	−0.0183561	+	0.0133365i	−0.596925	−	0.802297i	$-0.703611\pi$
$433$	−0.381966	+	0.277515i	−0.0183561	+	0.0133365i	0.578569	+	0.815633i	$0.303611\pi$
$434$	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	$-0.488392\pi$
$439$	1.52786			0.0729210			0.0364605	+	0.999335i	$0.488392\pi$
$440$		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	0.715072	−	0.699051i	$-0.246394\pi$
$443$	5.70820	+	4.14725i	0.271205	+	0.197042i	−0.443867	+	0.896093i	$0.646394\pi$
$444$	−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	−0.986464	−	0.163980i	$-0.947567\pi$
$449$	−6.03444	−	18.5721i	−0.284783	−	0.876472i	0.701681	−	0.712492i	$-0.252433\pi$
$450$	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	−0.594712	−	0.803939i	$-0.702734\pi$
$457$	7.67376	−	23.6174i	0.358963	−	1.10478i	0.953676	−	0.300837i	$-0.0972661\pi$
$458$	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	$-0.423812\pi$
$461$	10.1803			0.474146			0.237073	+	0.971492i	$0.423812\pi$
$462$		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	0.341640	+	0.939831i	$0.389018\pi$
$467$	−10.5279	+	32.4014i	−0.487171	+	1.49936i	−0.828811	+	0.559529i	$0.810982\pi$
$468$	−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	−0.657509	−	0.753447i	$-0.728390\pi$
$479$	6.94427	−	21.3723i	0.317292	−	0.976524i	0.974801	−	0.223077i	$-0.0716102\pi$
$480$	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	0.423892	−	0.905713i	$-0.360664\pi$
$487$	−6.76393	−	4.91428i	−0.306503	−	0.222687i	−0.730395	+	0.683025i	$0.760664\pi$
$488$	−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	$-0.700000\pi$
$491$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$492$	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	−0.761042	−	0.648702i	$-0.775312\pi$
$499$	−8.47214	+	6.15537i	−0.379265	+	0.275552i	0.381777	+	0.924254i	$0.375312\pi$
$500$	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	$-0.275732\pi$
$503$	2.76393	+	2.00811i	0.123238	+	0.0895374i	−0.524459	+	0.851436i	$0.675732\pi$
$504$	−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	−0.144783	−	0.989463i	$-0.546248\pi$
$509$	−25.5066	−	18.5316i	−1.13056	−	0.821399i	−0.985776	+	0.168064i	$0.946248\pi$
$510$	−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	−0.303447	−	0.952848i	$-0.598138\pi$
$521$	11.6180	−	8.44100i	0.508995	−	0.369807i	0.812442	+	0.583042i	$0.198138\pi$
$522$	2.43769	−	7.50245i	0.106695	−	0.328373i
$523$	13.5967	−	41.8465i	0.594544	−	1.82982i	0.0375627	−	0.999294i	$-0.488041\pi$
$523$	13.5967	−	41.8465i	0.594544	−	1.82982i	0.556982	−	0.830525i	$-0.311959\pi$
$524$	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	−0.891845	−	0.452340i	$-0.850589\pi$
$541$	−10.1459	−	31.2259i	−0.436206	−	1.34250i	0.455639	−	0.890165i	$-0.349411\pi$
$542$	−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	$-0.504275\pi$
$547$	−22.6525	−	16.4580i	−0.968550	−	0.703693i	−0.955121	+	0.296217i	$0.904275\pi$
$548$	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	$-0.552820\pi$
$557$	17.0344	−	12.3762i	0.721772	−	0.524398i	0.886950	+	0.461865i	$0.152820\pi$
$558$	−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	0.786282	+	0.617868i	$0.212003\pi$
$563$	12.1803	+	37.4872i	0.513340	+	1.57990i	−0.272942	+	0.962031i	$0.587997\pi$
$564$	−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	$-0.412214\pi$
$569$	−13.3262	−	9.68208i	−0.558665	−	0.405894i	−0.830970	+	0.556317i	$0.812214\pi$
$570$	−11.0557	−	34.0260i	−0.463073	−	1.42519i
$571$	−32.9443			−1.37867			−0.689337	−	0.724440i	$-0.742098\pi$
$571$	−32.9443			−1.37867			−0.689337	+	0.724440i	$0.742098\pi$
$572$		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	0.582894	+	0.812548i	$0.301920\pi$
$577$	−8.79837	+	27.0786i	−0.366281	+	1.12730i	−0.949175	+	0.314749i	$0.898080\pi$
$578$	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	−0.346687	−	0.937981i	$-0.612693\pi$
$587$	10.6180	−	7.71445i	0.438253	−	0.318410i	0.784940	+	0.619571i	$0.212693\pi$
$588$	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	$-0.730731\pi$
$593$	−32.2918			−1.32607			−0.663033	+	0.748591i	$0.730731\pi$
$594$		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	−0.927169	−	0.374643i	$-0.877765\pi$
$599$	1.05573	−	3.24920i	0.0431359	−	0.132759i	0.970305	+	0.241884i	$0.0777654\pi$
$600$	2.23607	−	6.88191i	0.0912871	−	0.280953i
$601$	−2.52786	+	1.83660i	−0.103114	+	0.0749165i	−0.638147	−	0.769914i	$-0.720299\pi$
$601$	−2.52786	+	1.83660i	−0.103114	+	0.0749165i	0.535034	+	0.844831i	$0.320299\pi$
$602$	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	$-0.131993\pi$
$607$	−1.52786	−	4.70228i	−0.0620141	−	0.190860i	−0.977264	+	0.212028i	$0.931993\pi$
$608$	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	0.946610	+	0.322381i	$0.104483\pi$
$613$	38.2705	+	27.8052i	1.54573	+	1.12304i	0.599121	+	0.800658i	$0.295517\pi$
$614$	−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	0.950107	−	0.311924i	$-0.100973\pi$
$619$	23.5623	+	17.1190i	0.947049	+	0.688071i	−0.00305805	+	0.999995i	$0.500973\pi$
$620$	−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	−0.129901	−	0.991527i	$-0.541466\pi$
$631$	19.4164	−	14.1068i	0.772955	−	0.561585i	0.902856	+	0.429942i	$0.141466\pi$
$632$	−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	0.905575	−	0.424186i	$-0.139440\pi$
$641$	19.7984	+	14.3844i	0.781989	+	0.568148i	−0.123586	+	0.992334i	$0.539440\pi$
$642$	−23.4164	+	17.0130i	−0.924172	+	0.671450i
$643$	−9.00000	+	27.6992i	−0.354925	+	1.09235i	0.601127	+	0.799153i	$0.294718\pi$
$643$	−9.00000	+	27.6992i	−0.354925	+	1.09235i	−0.956053	+	0.293195i	$0.905282\pi$
$644$	−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	−0.990961	−	0.134151i	$-0.957169\pi$
$647$	−6.81966	−	20.9888i	−0.268109	−	0.825153i	0.722852	−	0.691002i	$-0.242831\pi$
$648$	−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	−0.361114	+	0.932522i	$0.617603\pi$
$653$	−34.7426	+	25.2420i	−1.35958	+	0.987796i	−0.998471	+	0.0552743i	$0.982397\pi$
$654$	−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	$-0.386719\pi$
$659$	17.8885			0.696839			0.348419	+	0.937339i	$0.386719\pi$
$660$		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	$-0.0667098\pi$
$673$	1.67376	+	5.15131i	0.0645188	+	0.198568i	−0.913601	+	0.406613i	$0.866710\pi$
$674$	−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	$-0.877298\pi$
$677$	1.14590	−	3.52671i	0.0440404	−	0.135543i	0.970659	+	0.240460i	$0.0772983\pi$
$678$	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	−0.650609	−	0.759413i	$-0.725486\pi$
$691$	−15.0000	−	46.1653i	−0.570627	−	1.75621i	0.0799823	−	0.996796i	$-0.474514\pi$
$692$	−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	$-0.147078\pi$
$701$	19.7984	+	14.3844i	0.747774	+	0.543290i	−0.147362	+	0.989083i	$0.547078\pi$
$702$	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	−0.932517	−	0.361126i	$-0.882393\pi$
$709$	0.909830	−	2.80017i	0.0341694	−	0.105163i	0.966687	+	0.255963i	$0.0823926\pi$
$710$	−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	−0.964270	−	0.264920i	$-0.914655\pi$
$719$	−27.0902	+	19.6822i	−1.01029	+	0.734021i	−0.0460224	+	0.998940i	$0.514655\pi$
$720$	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	$-0.778605\pi$
$733$	−10.7082	+	7.77997i	−0.395517	+	0.287360i	0.372196	+	0.928154i	$0.378605\pi$
$734$	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	$-0.0585746\pi$
$739$	2.18034	+	6.71040i	0.0802051	+	0.246846i	−0.902911	+	0.429827i	$0.858575\pi$
$740$	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	0.552884	+	0.833258i	$0.313527\pi$
$743$	−10.4721	+	32.2299i	−0.384185	+	1.18240i	−0.937069	+	0.349143i	$0.886473\pi$
$744$	−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	−0.149231	−	0.988802i	$-0.547680\pi$
$751$	−31.1246	−	22.6134i	−1.13575	−	0.825173i	−0.986522	+	0.163629i	$0.947680\pi$
$752$	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	−0.998452	−	0.0556139i	$-0.982288\pi$
$757$	−6.14590	−	18.9151i	−0.223376	−	0.687482i	0.775076	−	0.631868i	$-0.217712\pi$
$758$	56.5836			2.05521
$759$		0			0
$760$	−11.0557			−0.401033
$761$	5.43769	+	16.7355i	0.197116	+	0.606661i	0.999945	+	0.0104523i	$0.00332712\pi$
$761$	5.43769	+	16.7355i	0.197116	+	0.606661i	−0.802829	+	0.596209i	$0.796673\pi$
$762$	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	$-0.306279\pi$
$769$	31.7082			1.14343			0.571714	+	0.820453i	$0.306279\pi$
$770$		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	0.491385	−	0.870943i	$-0.336491\pi$
$773$	−5.14590	−	3.73871i	−0.185085	−	0.134472i	−0.676470	+	0.736471i	$0.736491\pi$
$774$	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	$-0.995510\pi$
$787$	−5.12461	+	15.7719i	−0.182673	+	0.562209i	0.817228	+	0.576315i	$0.195510\pi$
$788$	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	−0.933649	−	0.358190i	$-0.883394\pi$
$797$	0.909830	−	2.80017i	0.0322278	−	0.0991871i	0.965877	+	0.259003i	$0.0833940\pi$
$798$	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	−0.481685	−	0.876344i	$-0.659975\pi$
$809$	12.0344	−	37.0382i	0.423108	−	1.30219i	0.904794	−	0.425850i	$-0.140025\pi$
$810$	−88.3394	+	64.1823i	−3.10393	+	2.25514i
$811$	−15.2361	−	11.0697i	−0.535011	−	0.388708i	0.287218	−	0.957865i	$-0.407270\pi$
$811$	−15.2361	−	11.0697i	−0.535011	−	0.388708i	−0.822229	+	0.569157i	$0.807270\pi$
$812$	−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	$-0.650741\pi$
$821$	7.14590	−	5.19180i	0.249394	−	0.181195i	0.705458	+	0.708752i	$0.250741\pi$
$822$	44.0689	+	32.0179i	1.53708	+	1.11675i
$823$	−15.4164	−	47.4468i	−0.537382	−	1.65389i	−0.738445	−	0.674314i	$-0.764439\pi$
$823$	−15.4164	−	47.4468i	−0.537382	−	1.65389i	0.201063	−	0.979578i	$-0.435561\pi$
$824$	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	$-0.0726028\pi$
$827$	1.52786	+	4.70228i	0.0531290	+	0.163514i	−0.920971	+	0.389630i	$0.872603\pi$
$828$	117.374	+	85.2771i	4.07902	+	2.96358i
$829$	13.6180	−	9.89408i	0.472974	−	0.343636i	−0.325625	−	0.945499i	$-0.605575\pi$
$829$	13.6180	−	9.89408i	0.472974	−	0.343636i	0.798599	+	0.601863i	$0.205575\pi$
$830$	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	0.766663	−	0.642050i	$-0.221916\pi$
$839$	11.3820	+	8.26948i	0.392949	+	0.285494i	−0.373714	+	0.927544i	$0.621916\pi$
$840$	−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	$-0.896444\pi$
$853$	0.201626	−	0.620541i	0.00690355	−	0.0212469i	0.954449	+	0.298374i	$0.0964443\pi$
$854$	−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	$-0.441146\pi$
$857$	10.7639			0.367689			0.183844	+	0.982955i	$0.441146\pi$
$858$		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	0.778419	+	0.627744i	$0.216022\pi$
$863$	−6.47214	+	19.9192i	−0.220314	+	0.678057i	−0.998734	+	0.0503125i	$0.983978\pi$
$864$	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	$-0.546490\pi$
$877$	−33.5066	−	24.3440i	−1.13144	−	0.822037i	−0.985903	+	0.167316i	$0.946490\pi$
$878$	−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	0.459334	−	0.888264i	$-0.348088\pi$
$883$	−7.23607	−	5.25731i	−0.243513	−	0.176923i	−0.702847	+	0.711341i	$0.748088\pi$
$884$	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	$-0.936975\pi$
$887$	−32.6525	+	23.7234i	−1.09636	+	0.796554i	−0.115900	+	0.993261i	$0.536975\pi$
$888$	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	−0.857357	−	0.514723i	$-0.827895\pi$
$907$	4.18034	−	12.8658i	0.138806	−	0.427201i	0.996163	+	0.0875221i	$0.0278948\pi$
$908$	−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	0.962506	+	0.271259i	$0.0874401\pi$
$911$	10.3607	+	31.8869i	0.343265	+	1.05646i	−0.619242	+	0.785200i	$0.712560\pi$
$912$	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	$-0.867860\pi$
$919$	1.88854	−	5.81234i	0.0622973	−	0.191731i	0.977361	+	0.211577i	$0.0678600\pi$
$920$	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	−0.699569	−	0.714565i	$-0.746624\pi$
$929$	8.72949	−	26.8666i	0.286405	−	0.881465i	0.985974	−	0.166899i	$-0.0533755\pi$
$930$	−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	0.999552	+	0.0299298i	$0.00952837\pi$
$937$	6.38197	+	19.6417i	0.208490	+	0.641665i	−0.791062	+	0.611736i	$0.790472\pi$
$938$	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	0.489563	+	0.871968i	$0.337156\pi$
$941$	−12.8541	+	39.5609i	−0.419032	+	1.28965i	−0.908595	+	0.417679i	$0.862844\pi$
$942$	−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	$-0.726094\pi$
$953$	−4.09017	+	2.97168i	−0.132494	+	0.0962622i	0.519565	+	0.854431i	$0.326094\pi$
$954$	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	$-0.385521\pi$
$967$	21.8885			0.703888			0.351944	+	0.936021i	$0.385521\pi$
$968$		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	0.897727	−	0.440552i	$-0.145217\pi$
$971$	23.5623	+	17.1190i	0.756150	+	0.549375i	−0.141577	+	0.989927i	$0.545217\pi$
$972$	−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	0.972933	−	0.231089i	$-0.0742290\pi$
$977$	1.56231	+	4.80828i	0.0499826	+	0.153831i	−0.922950	+	0.384920i	$0.874229\pi$
$978$	−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	−0.987121	−	0.159975i	$-0.948859\pi$
$983$	−35.7426	+	25.9686i	−1.14001	+	0.828268i	−0.152892	+	0.988243i	$0.548859\pi$
$984$	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	$-0.872973\pi$
$997$	−26.4164	+	19.1926i	−0.836616	+	0.607837i	0.0848073	+	0.996397i	$0.472973\pi$
$998$	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.a.148.1		4
11.2	odd	10		847.2.f.m.372.1		4
11.3	even	5		77.2.a.d.1.1	✓	2
11.4	even	5		847.2.f.n.729.1		4
11.5	even	5		847.2.f.n.323.1		4
11.6	odd	10		847.2.f.b.323.1		4
11.7	odd	10		847.2.f.b.729.1		4
11.8	odd	10		847.2.a.f.1.2		2
11.9	even	5	inner	847.2.f.a.372.1		4
11.10	odd	2		847.2.f.m.148.1		4
33.8	even	10		7623.2.a.bl.1.1		2
33.14	odd	10		693.2.a.h.1.2		2
44.3	odd	10		1232.2.a.m.1.1		2
55.3	odd	20		1925.2.b.h.1849.4		4
55.14	even	10		1925.2.a.r.1.2		2
55.47	odd	20		1925.2.b.h.1849.1		4
77.3	odd	30		539.2.e.j.177.2		4
77.25	even	15		539.2.e.i.177.2		4
77.41	even	10		5929.2.a.m.1.2		2
77.47	odd	30		539.2.e.j.67.2		4
77.58	even	15		539.2.e.i.67.2		4
77.69	odd	10		539.2.a.f.1.1		2
88.3	odd	10		4928.2.a.bv.1.2		2
88.69	even	10		4928.2.a.bm.1.1		2
231.146	even	10		4851.2.a.y.1.2		2
308.223	even	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	11.3	even	5
539.2.a.f.1.1		2	77.69	odd	10
539.2.e.i.67.2		4	77.58	even	15
539.2.e.i.177.2		4	77.25	even	15
539.2.e.j.67.2		4	77.47	odd	30
539.2.e.j.177.2		4	77.3	odd	30
693.2.a.h.1.2		2	33.14	odd	10
847.2.a.f.1.2		2	11.8	odd	10
847.2.f.a.148.1		4	1.1	even	1	trivial
847.2.f.a.372.1		4	11.9	even	5	inner
847.2.f.b.323.1		4	11.6	odd	10
847.2.f.b.729.1		4	11.7	odd	10
847.2.f.m.148.1		4	11.10	odd	2
847.2.f.m.372.1		4	11.2	odd	10
847.2.f.n.323.1		4	11.5	even	5
847.2.f.n.729.1		4	11.4	even	5
1232.2.a.m.1.1		2	44.3	odd	10
1925.2.a.r.1.2		2	55.14	even	10
1925.2.b.h.1849.1		4	55.47	odd	20
1925.2.b.h.1849.4		4	55.3	odd	20
4851.2.a.y.1.2		2	231.146	even	10
4928.2.a.bm.1.1		2	88.69	even	10
4928.2.a.bv.1.2		2	88.3	odd	10
5929.2.a.m.1.2		2	77.41	even	10
7623.2.a.bl.1.1		2	33.8	even	10
8624.2.a.ce.1.2		2	308.223	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)

\(f(q)\)	\(=\)	\(q+(-0.690983 - 2.12663i) q^{2} +(-2.61803 - 1.90211i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.618034 + 1.90211i) q^{5} +(-2.23607 + 6.88191i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(1.80902 + 1.31433i) q^{8} +(2.30902 + 7.10642i) q^{9} +O(q^{10})\)	\(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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more