LMFDB - Embedded newform 847.2.f.y.323.4

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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.4
Character	$\chi$	$=$	847.323
Dual form			847.2.f.y.729.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0973732 - 0.0707458i) q^{2} +(0.855309 - 2.63237i) q^{3} +(-0.613557 - 1.88834i) q^{4} +(2.27214 - 1.65081i) q^{5} +(-0.269513 + 0.195813i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.148234 + 0.456218i) q^{8} +(-3.77078 - 2.73963i) q^{9} +O(q^{10})$	\(q+(-0.0973732 - 0.0707458i) q^{2} +(0.855309 - 2.63237i) q^{3} +(-0.613557 - 1.88834i) q^{4} +(2.27214 - 1.65081i) q^{5} +(-0.269513 + 0.195813i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.148234 + 0.456218i) q^{8} +(-3.77078 - 2.73963i) q^{9} -0.338034 q^{10} -5.49558 q^{12} +(-0.873475 - 0.634617i) q^{13} +(0.0371933 - 0.114469i) q^{14} +(-2.40216 - 7.39308i) q^{15} +(-3.16592 + 2.30017i) q^{16} +(-5.62937 + 4.08998i) q^{17} +(0.173355 + 0.533533i) q^{18} +(2.33126 - 7.17488i) q^{19} +(-4.51137 - 3.27771i) q^{20} +2.76784 q^{21} +4.82552 q^{23} +(1.07415 + 0.780415i) q^{24} +(0.892384 - 2.74647i) q^{25} +(0.0401566 + 0.123589i) q^{26} +(-3.71922 + 2.70217i) q^{27} +(1.60631 - 1.16706i) q^{28} +(0.379245 + 1.16720i) q^{29} +(-0.289124 + 0.889831i) q^{30} +(6.53207 + 4.74583i) q^{31} +1.43040 q^{32} +0.837498 q^{34} +(2.27214 + 1.65081i) q^{35} +(-2.85975 + 8.80141i) q^{36} +(0.474419 + 1.46011i) q^{37} +(-0.734595 + 0.533714i) q^{38} +(-2.41764 + 1.75652i) q^{39} +(0.416320 + 1.28130i) q^{40} +(2.87381 - 8.84469i) q^{41} +(-0.269513 - 0.195813i) q^{42} -5.23402 q^{43} -13.0904 q^{45} +(-0.469876 - 0.341385i) q^{46} +(-0.585237 + 1.80117i) q^{47} +(3.34707 + 10.3012i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.281196 + 0.204301i) q^{50} +(5.95149 + 18.3168i) q^{51} +(-0.662442 + 2.03879i) q^{52} +(3.09491 + 2.24858i) q^{53} +0.553319 q^{54} -0.479696 q^{56} +(-16.8930 - 12.2735i) q^{57} +(0.0456459 - 0.140484i) q^{58} +(-2.05913 - 6.33736i) q^{59} +(-12.4868 + 9.07216i) q^{60} +(7.92798 - 5.76001i) q^{61} +(-0.300302 - 0.924233i) q^{62} +(1.44031 - 4.43281i) q^{63} +(6.19256 + 4.49915i) q^{64} -3.03229 q^{65} -2.06100 q^{67} +(11.1772 + 8.12070i) q^{68} +(4.12731 - 12.7026i) q^{69} +(-0.104458 - 0.321489i) q^{70} +(-10.1299 + 7.35977i) q^{71} +(1.80883 - 1.31419i) q^{72} +(0.793272 + 2.44144i) q^{73} +(0.0571011 - 0.175739i) q^{74} +(-6.46648 - 4.69817i) q^{75} -14.9789 q^{76} +0.359679 q^{78} +(12.4009 + 9.00978i) q^{79} +(-3.39627 + 10.4527i) q^{80} +(-0.388893 - 1.19689i) q^{81} +(-0.905557 + 0.657925i) q^{82} +(-1.65527 + 1.20262i) q^{83} +(-1.69823 - 5.22661i) q^{84} +(-6.03897 + 18.5860i) q^{85} +(0.509654 + 0.370285i) q^{86} +3.39687 q^{87} +4.76119 q^{89} +(1.27465 + 0.926087i) q^{90} +(0.333638 - 1.02683i) q^{91} +(-2.96073 - 9.11220i) q^{92} +(18.0797 - 13.1357i) q^{93} +(0.184412 - 0.133983i) q^{94} +(-6.54740 - 20.1508i) q^{95} +(1.22343 - 3.76533i) q^{96} +(-7.37429 - 5.35773i) q^{97} +0.120360 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.0973732	−	0.0707458i	−0.0688532	−	0.0500248i	0.552826	−	0.833297i	$-0.313549\pi$
$2$	−0.0973732	−	0.0707458i	−0.0688532	−	0.0500248i	−0.621679	+	0.783272i	$0.713549\pi$
$3$	0.855309	−	2.63237i	0.493813	−	1.51980i	−0.324985	−	0.945719i	$-0.605359\pi$
$3$	0.855309	−	2.63237i	0.493813	−	1.51980i	0.818798	−	0.574081i	$-0.194641\pi$
$4$	−0.613557	−	1.88834i	−0.306779	−	0.944168i
$5$	2.27214	−	1.65081i	1.01613	−	0.738265i	0.0506472	−	0.998717i	$-0.483872\pi$
$5$	2.27214	−	1.65081i	1.01613	−	0.738265i	0.965487	+	0.260452i	$0.0838716\pi$
$6$	−0.269513	+	0.195813i	−0.110028	+	0.0799403i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.148234	+	0.456218i	−0.0524087	+	0.161297i
$9$	−3.77078	−	2.73963i	−1.25693	−	0.913210i
$10$	−0.338034			−0.106896
$11$		0			0
$11$		0			0
$12$	−5.49558			−1.58644
$13$	−0.873475	−	0.634617i	−0.242258	−	0.176011i	0.460030	−	0.887903i	$-0.347838\pi$
$13$	−0.873475	−	0.634617i	−0.242258	−	0.176011i	−0.702289	+	0.711892i	$0.747838\pi$
$14$	0.0371933	−	0.114469i	0.00994031	−	0.0305931i
$15$	−2.40216	−	7.39308i	−0.620235	−	1.90889i
$16$	−3.16592	+	2.30017i	−0.791480	+	0.575044i
$17$	−5.62937	+	4.08998i	−1.36532	+	0.991965i	−0.367237	+	0.930128i	$0.619696\pi$
$17$	−5.62937	+	4.08998i	−1.36532	+	0.991965i	−0.998086	+	0.0618375i	$0.980304\pi$
$18$	0.173355	+	0.533533i	0.0408603	+	0.125755i
$19$	2.33126	−	7.17488i	0.534828	−	1.64603i	−0.209194	−	0.977874i	$-0.567084\pi$
$19$	2.33126	−	7.17488i	0.534828	−	1.64603i	0.744021	−	0.668156i	$-0.232916\pi$
$20$	−4.51137	−	3.27771i	−1.00877	−	0.732917i
$21$	2.76784			0.603992
$22$		0			0
$23$	4.82552			1.00619			0.503095	−	0.864231i	$-0.332194\pi$
$23$	4.82552			1.00619			0.503095	+	0.864231i	$0.332194\pi$
$24$	1.07415	+	0.780415i	0.219260	+	0.159302i
$25$	0.892384	−	2.74647i	0.178477	−	0.549295i
$26$	0.0401566	+	0.123589i	0.00787536	+	0.0242379i
$27$	−3.71922	+	2.70217i	−0.715764	+	0.520033i
$28$	1.60631	−	1.16706i	0.303565	−	0.220553i
$29$	0.379245	+	1.16720i	0.0704241	+	0.216743i	0.980074	−	0.198633i	$-0.0636501\pi$
$29$	0.379245	+	1.16720i	0.0704241	+	0.216743i	−0.909650	+	0.415376i	$0.863650\pi$
$30$	−0.289124	+	0.889831i	−0.0527865	+	0.162460i
$31$	6.53207	+	4.74583i	1.17319	+	0.852376i	0.991388	−	0.130958i	$-0.0418054\pi$
$31$	6.53207	+	4.74583i	1.17319	+	0.852376i	0.181807	+	0.983334i	$0.441805\pi$
$32$	1.43040			0.252861
$33$		0			0
$34$	0.837498			0.143630
$35$	2.27214	+	1.65081i	0.384063	+	0.279038i
$36$	−2.85975	+	8.80141i	−0.476625	+	1.46690i
$37$	0.474419	+	1.46011i	0.0779941	+	0.240041i	0.982450	−	0.186526i	$-0.0597228\pi$
$37$	0.474419	+	1.46011i	0.0779941	+	0.240041i	−0.904456	+	0.426567i	$0.859723\pi$
$38$	−0.734595	+	0.533714i	−0.119167	+	0.0865799i
$39$	−2.41764	+	1.75652i	−0.387132	+	0.281268i
$40$	0.416320	+	1.28130i	0.0658259	+	0.202591i
$41$	2.87381	−	8.84469i	0.448814	−	1.38131i	−0.429432	−	0.903099i	$-0.641286\pi$
$41$	2.87381	−	8.84469i	0.448814	−	1.38131i	0.878246	−	0.478209i	$-0.158714\pi$
$42$	−0.269513	−	0.195813i	−0.0415868	−	0.0302146i
$43$	−5.23402			−0.798181			−0.399091	−	0.916912i	$-0.630674\pi$
$43$	−5.23402			−0.798181			−0.399091	+	0.916912i	$0.630674\pi$
$44$		0			0
$45$	−13.0904			−1.95140
$46$	−0.469876	−	0.341385i	−0.0692795	−	0.0503345i
$47$	−0.585237	+	1.80117i	−0.0853655	+	0.262728i	−0.984623	−	0.174691i	$-0.944107\pi$
$47$	−0.585237	+	1.80117i	−0.0853655	+	0.262728i	0.899258	+	0.437419i	$0.144107\pi$
$48$	3.34707	+	10.3012i	0.483109	+	1.48686i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−0.281196	+	0.204301i	−0.0397671	+	0.0288925i
$51$	5.95149	+	18.3168i	0.833375	+	2.56486i
$52$	−0.662442	+	2.03879i	−0.0918642	+	0.282729i
$53$	3.09491	+	2.24858i	0.425119	+	0.308867i	0.779694	−	0.626161i	$-0.215375\pi$
$53$	3.09491	+	2.24858i	0.425119	+	0.308867i	−0.354575	+	0.935027i	$0.615375\pi$
$54$	0.553319			0.0752972
$55$		0			0
$56$	−0.479696			−0.0641021
$57$	−16.8930	−	12.2735i	−2.23753	−	1.62566i
$58$	0.0456459	−	0.140484i	0.00599360	−	0.0184464i
$59$	−2.05913	−	6.33736i	−0.268076	−	0.825053i	−0.990969	−	0.134093i	$-0.957188\pi$
$59$	−2.05913	−	6.33736i	−0.268076	−	0.825053i	0.722893	−	0.690960i	$-0.242812\pi$
$60$	−12.4868	+	9.07216i	−1.61203	+	1.17121i
$61$	7.92798	−	5.76001i	1.01507	−	0.737494i	0.0498066	−	0.998759i	$-0.484139\pi$
$61$	7.92798	−	5.76001i	1.01507	−	0.737494i	0.965267	+	0.261265i	$0.0841395\pi$
$62$	−0.300302	−	0.924233i	−0.0381383	−	0.117378i
$63$	1.44031	−	4.43281i	0.181462	−	0.558482i
$64$	6.19256	+	4.49915i	0.774069	+	0.562394i
$65$	−3.03229			−0.376110
$66$		0			0
$67$	−2.06100			−0.251792			−0.125896	−	0.992043i	$-0.540181\pi$
$67$	−2.06100			−0.251792			−0.125896	+	0.992043i	$0.540181\pi$
$68$	11.1772	+	8.12070i	1.35543	+	0.984780i
$69$	4.12731	−	12.7026i	0.496870	−	1.52921i
$70$	−0.104458	−	0.321489i	−0.0124851	−	0.0384253i
$71$	−10.1299	+	7.35977i	−1.20219	+	0.873444i	−0.994499	−	0.104749i	$-0.966596\pi$
$71$	−10.1299	+	7.35977i	−1.20219	+	0.873444i	−0.207694	+	0.978194i	$0.566596\pi$
$72$	1.80883	−	1.31419i	0.213172	−	0.154879i
$73$	0.793272	+	2.44144i	0.0928454	+	0.285749i	0.986686	−	0.162636i	$-0.0519995\pi$
$73$	0.793272	+	2.44144i	0.0928454	+	0.285749i	−0.893841	+	0.448385i	$0.852000\pi$
$74$	0.0571011	−	0.175739i	0.00663786	−	0.0204292i
$75$	−6.46648	−	4.69817i	−0.746685	−	0.542498i
$76$	−14.9789			−1.71820
$77$		0			0
$78$	0.359679			0.0407257
$79$	12.4009	+	9.00978i	1.39521	+	1.01368i	0.995271	+	0.0971373i	$0.0309686\pi$
$79$	12.4009	+	9.00978i	1.39521	+	1.01368i	0.399939	+	0.916542i	$0.369031\pi$
$80$	−3.39627	+	10.4527i	−0.379715	+	1.16864i
$81$	−0.388893	−	1.19689i	−0.0432103	−	0.132988i
$82$	−0.905557	+	0.657925i	−0.100002	+	0.0726557i
$83$	−1.65527	+	1.20262i	−0.181689	+	0.132005i	−0.674912	−	0.737898i	$-0.735819\pi$
$83$	−1.65527	+	1.20262i	−0.181689	+	0.132005i	0.493223	+	0.869903i	$0.335819\pi$
$84$	−1.69823	−	5.22661i	−0.185292	−	0.570270i
$85$	−6.03897	+	18.5860i	−0.655018	+	2.01594i
$86$	0.509654	+	0.370285i	0.0549574	+	0.0399289i
$87$	3.39687			0.364183
$88$		0			0
$89$	4.76119			0.504685			0.252342	−	0.967638i	$-0.418799\pi$
$89$	4.76119			0.504685			0.252342	+	0.967638i	$0.418799\pi$
$90$	1.27465	+	0.926087i	0.134360	+	0.0976182i
$91$	0.333638	−	1.02683i	0.0349747	−	0.107641i
$92$	−2.96073	−	9.11220i	−0.308678	−	0.950013i
$93$	18.0797	−	13.1357i	1.87478	−	1.36211i
$94$	0.184412	−	0.133983i	0.0190206	−	0.0138193i
$95$	−6.54740	−	20.1508i	−0.671749	−	2.06743i
$96$	1.22343	−	3.76533i	0.124866	−	0.384298i
$97$	−7.37429	−	5.35773i	−0.748745	−	0.543995i	0.146692	−	0.989182i	$-0.453137\pi$
$97$	−7.37429	−	5.35773i	−0.748745	−	0.543995i	−0.895438	+	0.445187i	$0.853137\pi$
$98$	0.120360			0.0121582
$99$		0			0
$100$	−5.73379			−0.573379
$101$	3.83786	+	2.78837i	0.381881	+	0.277453i	0.762120	−	0.647435i	$-0.224158\pi$
$101$	3.83786	+	2.78837i	0.381881	+	0.277453i	−0.380239	+	0.924888i	$0.624158\pi$
$102$	0.716320	−	2.20461i	0.0709263	−	0.218289i
$103$	0.108434	+	0.333726i	0.0106843	+	0.0328830i	0.956257	−	0.292529i	$-0.0944969\pi$
$103$	0.108434	+	0.333726i	0.0106843	+	0.0328830i	−0.945572	+	0.325412i	$0.894497\pi$
$104$	0.419002	−	0.304423i	0.0410866	−	0.0298511i
$105$	6.28893	−	4.56918i	0.613737	−	0.445906i
$106$	−0.142284	−	0.437904i	−0.0138198	−	0.0425330i
$107$	0.787293	−	2.42304i	0.0761105	−	0.234244i	−0.905762	−	0.423787i	$-0.860701\pi$
$107$	0.787293	−	2.42304i	0.0761105	−	0.234244i	0.981872	+	0.189543i	$0.0607006\pi$
$108$	7.38455	+	5.36519i	0.710579	+	0.516266i
$109$	−3.81522			−0.365432			−0.182716	−	0.983166i	$-0.558489\pi$
$109$	−3.81522			−0.365432			−0.182716	+	0.983166i	$0.558489\pi$
$110$		0			0
$111$	4.24933			0.403329
$112$	−3.16592	−	2.30017i	−0.299151	−	0.217346i
$113$	0.715276	−	2.20139i	0.0672875	−	0.207090i	−0.911759	−	0.410725i	$-0.865276\pi$
$113$	0.715276	−	2.20139i	0.0672875	−	0.207090i	0.979047	+	0.203635i	$0.0652757\pi$
$114$	0.776629	+	2.39022i	0.0727379	+	0.223864i
$115$	10.9643	−	7.96602i	1.02242	−	0.742835i
$116$	1.97137	−	1.43228i	0.183037	−	0.132984i
$117$	1.55506	+	4.78599i	0.143766	+	0.442465i
$118$	−0.247837	+	0.762763i	−0.0228152	+	0.0702181i
$119$	−5.62937	−	4.08998i	−0.516044	−	0.374928i
$120$	3.72894			0.340404
$121$		0			0
$122$	−1.17947			−0.106784
$123$	−20.8245	−	15.1299i	−1.87768	−	1.36422i
$124$	4.95392	−	15.2466i	0.444875	−	1.36918i
$125$	1.83313	+	5.64179i	0.163960	+	0.504617i
$126$	−0.453850	+	0.329741i	−0.0404322	+	0.0293757i
$127$	−7.96594	+	5.78759i	−0.706863	+	0.513566i	−0.882160	−	0.470950i	$-0.843911\pi$
$127$	−7.96594	+	5.78759i	−0.706863	+	0.513566i	0.175297	+	0.984516i	$0.443911\pi$
$128$	−1.16873	−	3.59697i	−0.103302	−	0.317930i
$129$	−4.47671	+	13.7779i	−0.394152	+	1.21308i
$130$	0.295264	+	0.214522i	0.0258964	+	0.0188148i
$131$	16.3782			1.43097			0.715484	−	0.698629i	$-0.246206\pi$
$131$	16.3782			1.43097			0.715484	+	0.698629i	$0.246206\pi$
$132$		0			0
$133$	7.54411			0.654158
$134$	0.200687	+	0.145807i	0.0173367	+	0.0125958i
$135$	−3.98983	+	12.2794i	−0.343390	+	1.05685i
$136$	−1.03146	−	3.17449i	−0.0884466	−	0.272211i
$137$	11.4995	−	8.35487i	0.982468	−	0.713805i	0.0242094	−	0.999707i	$-0.492293\pi$
$137$	11.4995	−	8.35487i	0.982468	−	0.713805i	0.958259	+	0.285902i	$0.0922931\pi$
$138$	−1.30054	+	0.944899i	−0.110710	+	0.0804352i
$139$	−2.83660	−	8.73015i	−0.240597	−	0.740481i	−0.996330	−	0.0856009i	$-0.972719\pi$
$139$	−2.83660	−	8.73015i	−0.240597	−	0.740481i	0.755733	−	0.654880i	$-0.227281\pi$
$140$	1.72319	−	5.30344i	0.145636	−	0.448222i
$141$	4.24080	+	3.08112i	0.357140	+	0.259477i
$142$	1.50705			0.126469
$143$		0			0
$144$	18.2396			1.51997
$145$	2.78852	+	2.02598i	0.231574	+	0.168248i
$146$	0.0954781	−	0.293851i	0.00790182	−	0.0243193i
$147$	0.855309	+	2.63237i	0.0705447	+	0.217114i
$148$	2.46610	−	1.79173i	0.202712	−	0.147279i
$149$	−9.40077	+	6.83006i	−0.770141	+	0.559540i	−0.902004	−	0.431728i	$-0.857904\pi$
$149$	−9.40077	+	6.83006i	−0.770141	+	0.559540i	0.131863	+	0.991268i	$0.457904\pi$
$150$	0.297286	+	0.914952i	0.0242733	+	0.0747055i
$151$	5.53604	−	17.0382i	0.450517	−	1.38655i	−0.425802	−	0.904816i	$-0.640008\pi$
$151$	5.53604	−	17.0382i	0.450517	−	1.38655i	0.876319	−	0.481732i	$-0.159992\pi$
$152$	2.92774	+	2.12713i	0.237471	+	0.172533i
$153$	32.4321			2.62198
$154$		0			0
$155$	22.6763			1.82140
$156$	4.80025	+	3.48759i	0.384328	+	0.279231i
$157$	2.29539	−	7.06450i	0.183192	−	0.563808i	−0.816720	−	0.577034i	$-0.804210\pi$
$157$	2.29539	−	7.06450i	0.183192	−	0.563808i	0.999913	+	0.0132257i	$0.00421001\pi$
$158$	−0.570111	−	1.75462i	−0.0453556	−	0.139590i
$159$	8.56622	−	6.22372i	0.679345	−	0.493573i
$160$	3.25006	−	2.36131i	0.256940	−	0.186678i
$161$	1.49117	+	4.58934i	0.117520	+	0.361691i
$162$	−0.0468071	+	0.144057i	−0.00367751	+	0.0113182i
$163$	−6.35318	−	4.61585i	−0.497619	−	0.361542i	0.310488	−	0.950577i	$-0.399508\pi$
$163$	−6.35318	−	4.61585i	−0.497619	−	0.361542i	−0.808107	+	0.589036i	$0.799508\pi$
$164$	−18.4650			−1.44187
$165$		0			0
$166$	0.246259			0.0191134
$167$	4.37078	+	3.17556i	0.338221	+	0.245732i	0.743911	−	0.668279i	$-0.232969\pi$
$167$	4.37078	+	3.17556i	0.338221	+	0.245732i	−0.405690	+	0.914011i	$0.632969\pi$
$168$	−0.410289	+	1.26274i	−0.0316544	+	0.0974224i
$169$	−3.65700	−	11.2551i	−0.281308	−	0.865776i
$170$	1.90292	−	1.38255i	0.145947	−	0.106037i
$171$	−28.4472	+	20.6681i	−2.17541	+	1.58053i
$172$	3.21137	+	9.88359i	0.244865	+	0.753617i
$173$	−6.09416	+	18.7559i	−0.463331	+	1.42599i	0.397739	+	0.917499i	$0.369795\pi$
$173$	−6.09416	+	18.7559i	−0.463331	+	1.42599i	−0.861070	+	0.508487i	$0.830205\pi$
$174$	−0.330764	−	0.240314i	−0.0250751	−	0.0182182i
$175$	2.88781			0.218298
$176$		0			0
$177$	−18.4435			−1.38630
$178$	−0.463612	−	0.336834i	−0.0347492	−	0.0252468i
$179$	−7.20911	+	22.1873i	−0.538834	+	1.65836i	0.196382	+	0.980527i	$0.437081\pi$
$179$	−7.20911	+	22.1873i	−0.538834	+	1.65836i	−0.735216	+	0.677833i	$0.762919\pi$
$180$	8.03169	+	24.7190i	0.598646	+	1.84244i
$181$	−2.49582	+	1.81332i	−0.185513	+	0.134783i	−0.676666	−	0.736291i	$-0.736576\pi$
$181$	−2.49582	+	1.81332i	−0.185513	+	0.134783i	0.491153	+	0.871073i	$0.336576\pi$
$182$	−0.105131	+	0.0763824i	−0.00779285	+	0.00566184i
$183$	−8.38162	−	25.7960i	−0.619588	−	1.90689i
$184$	−0.715307	+	2.20149i	−0.0527331	+	0.162296i
$185$	3.48832	+	2.53441i	0.256466	+	0.186334i
$186$	−2.68978			−0.197224
$187$		0			0
$188$	3.76030			0.274248
$189$	−3.71922	−	2.70217i	−0.270533	−	0.196554i
$190$	−0.788045	+	2.42535i	−0.0571708	+	0.175954i
$191$	3.88480	+	11.9562i	0.281094	+	0.865119i	0.987542	+	0.157354i	$0.0502964\pi$
$191$	3.88480	+	11.9562i	0.281094	+	0.865119i	−0.706448	+	0.707765i	$0.749704\pi$
$192$	17.1400	−	12.4529i	1.23697	−	0.898713i
$193$	16.7212	−	12.1487i	1.20362	−	0.874479i	0.208982	−	0.977920i	$-0.432985\pi$
$193$	16.7212	−	12.1487i	1.20362	−	0.874479i	0.994636	+	0.103440i	$0.0329850\pi$
$194$	0.339021	+	1.04340i	0.0243403	+	0.0749117i
$195$	−2.59355	+	7.98212i	−0.185728	+	0.571612i
$196$	1.60631	+	1.16706i	0.114737	+	0.0833611i
$197$	6.27954			0.447399			0.223699	−	0.974658i	$-0.428187\pi$
$197$	6.27954			0.447399			0.223699	+	0.974658i	$0.428187\pi$
$198$		0			0
$199$	−6.86896			−0.486927			−0.243464	−	0.969910i	$-0.578284\pi$
$199$	−6.86896			−0.486927			−0.243464	+	0.969910i	$0.578284\pi$
$200$	1.12071	+	0.814243i	0.0792461	+	0.0575757i
$201$	−1.76280	+	5.42533i	−0.124338	+	0.382673i
$202$	−0.176439	−	0.543024i	−0.0124142	−	0.0382070i
$203$	−0.992877	+	0.721367i	−0.0696863	+	0.0506301i
$204$	30.9367	−	22.4768i	2.16600	−	1.57369i
$205$	−8.07118	−	24.8405i	−0.563716	−	1.73494i
$206$	0.0130511	−	0.0401673i	0.000909316	−	0.00279859i
$207$	−18.1960	−	13.2201i	−1.26471	−	0.918863i
$208$	4.22508			0.292957
$209$		0			0
$210$	−0.935623			−0.0645641
$211$	−8.29939	−	6.02986i	−0.571354	−	0.415113i	0.264243	−	0.964456i	$-0.414878\pi$
$211$	−8.29939	−	6.02986i	−0.571354	−	0.415113i	−0.835597	+	0.549343i	$0.814878\pi$
$212$	2.34718	−	7.22387i	0.161205	−	0.496137i
$213$	10.7095	+	32.9604i	0.733802	+	2.25841i
$214$	−0.248081	+	0.180241i	−0.0169585	+	0.0123211i
$215$	−11.8925	+	8.64038i	−0.811059	+	0.589269i
$216$	−0.681463	−	2.09733i	−0.0463677	−	0.142705i
$217$	−2.49503	+	7.67891i	−0.169374	+	0.521279i
$218$	0.371500	+	0.269910i	0.0251611	+	0.0182806i
$219$	7.10527			0.480130
$220$		0			0
$221$	7.51268			0.505358
$222$	−0.413771	−	0.300622i	−0.0277705	−	0.0201765i
$223$	−4.17855	+	12.8603i	−0.279817	+	0.861187i	0.708088	+	0.706124i	$0.249558\pi$
$223$	−4.17855	+	12.8603i	−0.279817	+	0.861187i	−0.987905	+	0.155063i	$0.950442\pi$
$224$	0.442016	+	1.36039i	0.0295335	+	0.0908947i
$225$	−10.8893	+	7.91154i	−0.725953	+	0.527436i
$226$	−0.225388	+	0.163754i	−0.0149926	+	0.0108927i
$227$	4.19535	+	12.9120i	0.278455	+	0.856997i	0.988284	+	0.152623i	$0.0487721\pi$
$227$	4.19535	+	12.9120i	0.278455	+	0.856997i	−0.709829	+	0.704374i	$0.751228\pi$
$228$	−12.8116	+	39.4301i	−0.848471	+	2.61133i
$229$	1.17547	+	0.854026i	0.0776770	+	0.0564356i	0.625946	−	0.779866i	$-0.284713\pi$
$229$	1.17547	+	0.854026i	0.0776770	+	0.0564356i	−0.548269	+	0.836302i	$0.684713\pi$
$230$	−1.63119			−0.107557
$231$		0			0
$232$	−0.588713			−0.0386509
$233$	−6.63707	−	4.82211i	−0.434809	−	0.315907i	0.348760	−	0.937212i	$-0.386603\pi$
$233$	−6.63707	−	4.82211i	−0.434809	−	0.315907i	−0.783569	+	0.621305i	$0.786603\pi$
$234$	0.187167	−	0.576042i	0.0122355	−	0.0376570i
$235$	1.64365	+	5.05864i	0.107220	+	0.329989i
$236$	−10.7037	+	7.77666i	−0.696749	+	0.506218i
$237$	34.3237	−	24.9376i	2.22956	−	1.61987i
$238$	0.258801	+	0.796508i	0.0167756	+	0.0516300i
$239$	3.20869	−	9.87533i	0.207553	−	0.638782i	−0.792046	−	0.610461i	$-0.790984\pi$
$239$	3.20869	−	9.87533i	0.207553	−	0.638782i	0.999599	−	0.0283205i	$-0.00901589\pi$
$240$	24.6104	+	17.8805i	1.58860	+	1.15418i
$241$	−8.20445			−0.528495			−0.264248	−	0.964455i	$-0.585124\pi$
$241$	−8.20445			−0.528495			−0.264248	+	0.964455i	$0.585124\pi$
$242$		0			0
$243$	−17.2749			−1.10818
$244$	−15.7411	−	11.4366i	−1.00772	−	0.732152i
$245$	−0.867882	+	2.67107i	−0.0554470	+	0.170648i
$246$	0.957373	+	2.94649i	0.0610399	+	0.187861i
$247$	−6.58959	+	4.78762i	−0.419286	+	0.304629i
$248$	−3.13341	+	2.27655i	−0.198972	+	0.144561i
$249$	1.74998	+	5.38589i	0.110901	+	0.341317i
$250$	0.220635	−	0.679045i	0.0139542	−	0.0429466i
$251$	13.3044	+	9.66623i	0.839768	+	0.610127i	0.922306	−	0.386461i	$-0.126302\pi$
$251$	13.3044	+	9.66623i	0.839768	+	0.610127i	−0.0825377	+	0.996588i	$0.526302\pi$
$252$	−9.25435			−0.582969
$253$		0			0
$254$	1.18512			0.0743608
$255$	43.7602	+	31.7936i	2.74037	+	1.99099i
$256$	4.59002	−	14.1266i	0.286876	−	0.882915i
$257$	−3.72179	−	11.4545i	−0.232159	−	0.714511i	−0.997486	−	0.0708695i	$-0.977423\pi$
$257$	−3.72179	−	11.4545i	−0.232159	−	0.714511i	0.765327	−	0.643642i	$-0.222577\pi$
$258$	1.41064	−	1.02489i	0.0878226	−	0.0638068i
$259$	−1.24205	+	0.902399i	−0.0771770	+	0.0560724i
$260$	1.86049	+	5.72599i	0.115382	+	0.355111i
$261$	1.76764	−	5.44023i	0.109414	−	0.336742i
$262$	−1.59479	−	1.15869i	−0.0985268	−	0.0715839i
$263$	1.87602			0.115681			0.0578403	−	0.998326i	$-0.481579\pi$
$263$	1.87602			0.115681			0.0578403	+	0.998326i	$0.481579\pi$
$264$		0			0
$265$	10.7441			0.660003
$266$	−0.734595	−	0.533714i	−0.0450409	−	0.0327241i
$267$	4.07229	−	12.5332i	0.249220	−	0.767021i
$268$	1.26454	+	3.89187i	0.0772443	+	0.237734i
$269$	11.3497	−	8.24603i	0.692003	−	0.502769i	−0.185315	−	0.982679i	$-0.559331\pi$
$269$	11.3497	−	8.24603i	0.692003	−	0.502769i	0.877318	+	0.479910i	$0.159331\pi$
$270$	1.25722	−	0.913424i	0.0765120	−	0.0555892i
$271$	0.418185	+	1.28704i	0.0254029	+	0.0781822i	0.962954	−	0.269665i	$-0.0869129\pi$
$271$	0.418185	+	1.28704i	0.0254029	+	0.0781822i	−0.937551	+	0.347847i	$0.886913\pi$
$272$	8.41447	−	25.8971i	0.510202	−	1.57024i
$273$	−2.41764	−	1.75652i	−0.146322	−	0.106309i
$274$	−1.71081			−0.103354
$275$		0			0
$276$	−26.5190			−1.59626
$277$	10.8275	+	7.86663i	0.650561	+	0.472660i	0.863462	−	0.504413i	$-0.168291\pi$
$277$	10.8275	+	7.86663i	0.650561	+	0.472660i	−0.212901	+	0.977074i	$0.568291\pi$
$278$	−0.341412	+	1.05076i	−0.0204766	+	0.0630204i
$279$	−11.6292	−	35.7909i	−0.696220	−	2.14275i
$280$	−1.08994	+	0.791887i	−0.0651363	+	0.0473243i
$281$	−1.87600	+	1.36300i	−0.111913	+	0.0813096i	−0.642334	−	0.766425i	$-0.722034\pi$
$281$	−1.87600	+	1.36300i	−0.111913	+	0.0813096i	0.530421	+	0.847734i	$0.322034\pi$
$282$	−0.194964	−	0.600037i	−0.0116099	−	0.0357317i
$283$	−6.88116	+	21.1780i	−0.409042	+	1.25890i	0.508430	+	0.861103i	$0.330226\pi$
$283$	−6.88116	+	21.1780i	−0.409042	+	1.25890i	−0.917472	+	0.397800i	$0.869774\pi$
$284$	20.1130	+	14.6129i	1.19349	+	0.867118i
$285$	−58.6445			−3.47380
$286$		0			0
$287$	9.29986			0.548953
$288$	−5.39370	−	3.91875i	−0.317827	−	0.230915i
$289$	9.70861	−	29.8800i	0.571095	−	1.75765i
$290$	−0.128198	−	0.394552i	−0.00752803	−	0.0231689i
$291$	−20.4108	+	14.8293i	−1.19650	+	0.869312i
$292$	4.12354	−	2.99593i	0.241312	−	0.175323i
$293$	−0.753942	−	2.32039i	−0.0440457	−	0.135559i	0.926615	−	0.376011i	$-0.122704\pi$
$293$	−0.753942	−	2.32039i	−0.0440457	−	0.135559i	−0.970661	+	0.240452i	$0.922704\pi$
$294$	0.102945	−	0.316832i	0.00600387	−	0.0184780i
$295$	−15.1404	−	11.0002i	−0.881509	−	0.640454i
$296$	−0.736455			−0.0428056
$297$		0			0
$298$	1.39858			0.0810176
$299$	−4.21497	−	3.06235i	−0.243758	−	0.177101i
$300$	−4.90417	+	15.0935i	−0.283142	+	0.871422i
$301$	−1.61740	−	4.97785i	−0.0932255	−	0.286919i
$302$	−1.74444	+	1.26741i	−0.100381	+	0.0729313i
$303$	10.6226	−	7.71775i	0.610251	−	0.443373i
$304$	9.12290	+	28.0774i	0.523234	+	1.61035i
$305$	8.50483	−	26.1752i	0.486985	−	1.49879i
$306$	−3.15802	−	2.29444i	−0.180532	−	0.131164i
$307$	−8.89055			−0.507410			−0.253705	−	0.967282i	$-0.581649\pi$
$307$	−8.89055			−0.507410			−0.253705	+	0.967282i	$0.581649\pi$
$308$		0			0
$309$	0.971237			0.0552517
$310$	−2.20806	−	1.60425i	−0.125409	−	0.0911153i
$311$	−3.65713	+	11.2555i	−0.207377	+	0.638240i	0.792231	+	0.610222i	$0.208920\pi$
$311$	−3.65713	+	11.2555i	−0.207377	+	0.638240i	−0.999607	+	0.0280183i	$0.991080\pi$
$312$	−0.442978	−	1.36335i	−0.0250787	−	0.0771843i
$313$	23.8988	−	17.3635i	1.35084	−	0.981443i	0.351872	−	0.936048i	$-0.385545\pi$
$313$	23.8988	−	17.3635i	1.35084	−	0.981443i	0.998969	−	0.0453948i	$-0.0144546\pi$
$314$	−0.723293	+	0.525503i	−0.0408178	+	0.0296559i
$315$	−4.04514	−	12.4497i	−0.227918	−	0.701459i
$316$	9.40482	−	28.9451i	0.529063	−	1.62829i
$317$	20.3504	+	14.7854i	1.14299	+	0.830433i	0.987533	−	0.157409i	$-0.0503141\pi$
$317$	20.3504	+	14.7854i	1.14299	+	0.830433i	0.155460	+	0.987842i	$0.450314\pi$
$318$	−1.27442			−0.0714660
$319$		0			0
$320$	21.4976			1.20175
$321$	−5.70496	−	4.14490i	−0.318420	−	0.231346i
$322$	0.179477	−	0.552373i	0.0100018	−	0.0307825i
$323$	16.2216	+	49.9248i	0.902592	+	2.77789i
$324$	−2.02152	+	1.46872i	−0.112307	+	0.0815956i
$325$	−2.52243	+	1.83265i	−0.139919	+	0.101657i
$326$	0.292077	+	0.898921i	0.0161767	+	0.0497866i
$327$	−3.26319	+	10.0431i	−0.180455	+	0.555383i
$328$	3.60911	+	2.62217i	0.199280	+	0.144785i
$329$	−1.89387			−0.104412
$330$		0			0
$331$	−9.46333			−0.520152			−0.260076	−	0.965588i	$-0.583748\pi$
$331$	−9.46333			−0.520152			−0.260076	+	0.965588i	$0.583748\pi$
$332$	3.28656	+	2.38782i	0.180373	+	0.131049i
$333$	2.21124	−	6.80549i	0.121175	−	0.372939i
$334$	−0.200940	−	0.618429i	−0.0109949	−	0.0338389i
$335$	−4.68290	+	3.40233i	−0.255854	+	0.185889i
$336$	−8.76276	+	6.36651i	−0.478047	+	0.347322i
$337$	−5.32277	−	16.3818i	−0.289950	−	0.892373i	−0.984871	−	0.173288i	$-0.944561\pi$
$337$	−5.32277	−	16.3818i	−0.289950	−	0.892373i	0.694922	−	0.719086i	$-0.255439\pi$
$338$	−0.440156	+	1.35466i	−0.0239413	+	0.0736839i
$339$	−5.18310	−	3.76574i	−0.281508	−	0.204527i
$340$	38.8019			2.10433
$341$		0			0
$342$	4.23217			0.228850
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	0.775861	−	2.38786i	0.0418316	−	0.128745i
$345$	−11.5917	−	35.6755i	−0.624074	−	1.92070i
$346$	1.92031	−	1.39519i	0.103236	−	0.0750057i
$347$	7.06664	−	5.13421i	0.379357	−	0.275619i	−0.381723	−	0.924277i	$-0.624669\pi$
$347$	7.06664	−	5.13421i	0.379357	−	0.275619i	0.761080	+	0.648658i	$0.224669\pi$
$348$	−2.08417	−	6.41443i	−0.111723	−	0.343849i
$349$	−9.26589	+	28.5175i	−0.495992	+	1.52651i	0.319413	+	0.947616i	$0.396514\pi$
$349$	−9.26589	+	28.5175i	−0.495992	+	1.52651i	−0.815405	+	0.578891i	$0.803486\pi$
$350$	−0.281196	−	0.204301i	−0.0150305	−	0.0109203i
$351$	4.96348			0.264931
$352$		0			0
$353$	7.31999			0.389604			0.194802	−	0.980843i	$-0.437594\pi$
$353$	7.31999			0.389604			0.194802	+	0.980843i	$0.437594\pi$
$354$	1.79590	+	1.30480i	0.0954510	+	0.0693492i
$355$	−10.8669	+	33.4449i	−0.576756	+	1.77507i
$356$	−2.92126	−	8.99072i	−0.154827	−	0.476507i
$357$	−15.5812	+	11.3204i	−0.824644	+	0.599139i
$358$	2.27163	−	1.65044i	0.120060	−	0.0872284i
$359$	1.53580	+	4.72671i	0.0810565	+	0.249466i	0.983370	−	0.181615i	$-0.0581323\pi$
$359$	1.53580	+	4.72671i	0.0810565	+	0.249466i	−0.902313	+	0.431081i	$0.858132\pi$
$360$	1.94044	−	5.97206i	0.102270	−	0.314755i
$361$	−30.6728	−	22.2851i	−1.61436	−	1.17290i
$362$	0.371311			0.0195156
$363$		0			0
$364$	−2.14371			−0.112361
$365$	5.83278	+	4.23776i	0.305302	+	0.221815i
$366$	−1.00881	+	3.10480i	−0.0527314	+	0.162291i
$367$	−4.38935	−	13.5090i	−0.229122	−	0.705165i	−0.997847	−	0.0655858i	$-0.979108\pi$
$367$	−4.38935	−	13.5090i	−0.229122	−	0.705165i	0.768725	−	0.639580i	$-0.220892\pi$
$368$	−15.2772	+	11.0995i	−0.796379	+	0.578603i
$369$	−35.0677	+	25.4782i	−1.82555	+	1.32634i
$370$	−0.160370	−	0.493567i	−0.00833723	−	0.0256593i
$371$	−1.18215	+	3.63829i	−0.0613742	+	0.188890i
$372$	−35.8975	−	26.0811i	−1.86120	−	1.35224i
$373$	8.97781			0.464853			0.232427	−	0.972614i	$-0.425333\pi$
$373$	8.97781			0.464853			0.232427	+	0.972614i	$0.425333\pi$
$374$		0			0
$375$	16.4192			0.847883
$376$	−0.734975	−	0.533991i	−0.0379035	−	0.0275385i
$377$	0.409461	−	1.26019i	0.0210883	−	0.0649032i
$378$	0.170985	+	0.526238i	0.00879452	+	0.0270667i
$379$	−8.72895	+	6.34195i	−0.448376	+	0.325764i	−0.788954	−	0.614452i	$-0.789377\pi$
$379$	−8.72895	+	6.34195i	−0.448376	+	0.325764i	0.340578	+	0.940216i	$0.389377\pi$
$380$	−34.0343	+	24.7274i	−1.74592	+	1.26849i
$381$	8.42175	+	25.9195i	0.431459	+	1.32790i
$382$	0.467574	−	1.43905i	0.0239232	−	0.0736280i
$383$	19.0200	+	13.8188i	0.971875	+	0.706109i	0.955878	−	0.293763i	$-0.0949077\pi$
$383$	19.0200	+	13.8188i	0.971875	+	0.706109i	0.0159972	+	0.999872i	$0.494908\pi$
$384$	−10.4682			−0.534202
$385$		0			0
$386$	−2.48766			−0.126619
$387$	19.7363	+	14.3393i	1.00325	+	0.728907i
$388$	−5.59265	+	17.2124i	−0.283924	+	0.873827i
$389$	−3.66944	−	11.2934i	−0.186048	−	0.572596i	0.813917	−	0.580981i	$-0.197331\pi$
$389$	−3.66944	−	11.2934i	−0.186048	−	0.572596i	−0.999965	+	0.00838486i	$0.997331\pi$
$390$	0.817243	−	0.593762i	0.0413827	−	0.0300663i
$391$	−27.1646	+	19.7363i	−1.37377	+	0.998106i
$392$	−0.148234	−	0.456218i	−0.00748696	−	0.0230425i
$393$	14.0084	−	43.1134i	0.706631	−	2.17479i
$394$	−0.611459	−	0.444251i	−0.0308048	−	0.0223810i
$395$	43.0501			2.16608
$396$		0			0
$397$	−23.7264			−1.19079			−0.595397	−	0.803431i	$-0.703005\pi$
$397$	−23.7264			−1.19079			−0.595397	+	0.803431i	$0.703005\pi$
$398$	0.668852	+	0.485950i	0.0335265	+	0.0243585i
$399$	6.45255	−	19.8589i	0.323032	−	0.994189i
$400$	3.49216	+	10.7478i	0.174608	+	0.537388i
$401$	3.07524	−	2.23430i	0.153570	−	0.111575i	−0.508347	−	0.861153i	$-0.669743\pi$
$401$	3.07524	−	2.23430i	0.153570	−	0.111575i	0.661917	+	0.749577i	$0.269743\pi$
$402$	0.555468	−	0.403571i	0.0277042	−	0.0201283i
$403$	−2.69382	−	8.29072i	−0.134189	−	0.412990i
$404$	2.91062	−	8.95798i	0.144809	−	0.445676i
$405$	−2.85946	−	2.07752i	−0.142088	−	0.103233i
$406$	0.147713			0.00733089
$407$		0			0
$408$	−9.23866			−0.457382
$409$	4.84028	+	3.51667i	0.239336	+	0.173888i	0.700988	−	0.713174i	$-0.252743\pi$
$409$	4.84028	+	3.51667i	0.239336	+	0.173888i	−0.461651	+	0.887062i	$0.652743\pi$
$410$	−0.971446	+	2.98980i	−0.0479763	+	0.147656i
$411$	−12.1575	−	37.4170i	−0.599686	−	1.84564i
$412$	0.563657	−	0.409521i	0.0277694	−	0.0201756i
$413$	5.39088	−	3.91670i	0.265268	−	0.192728i
$414$	0.836530	+	2.57457i	0.0411132	+	0.126533i
$415$	−1.77571	+	5.46506i	−0.0871660	+	0.268269i
$416$	−1.24941	−	0.907752i	−0.0612576	−	0.0445062i
$417$	−25.4072			−1.24419
$418$		0			0
$419$	−4.16889			−0.203664			−0.101832	−	0.994802i	$-0.532470\pi$
$419$	−4.16889			−0.203664			−0.101832	+	0.994802i	$0.532470\pi$
$420$	−12.4868	−	9.07216i	−0.609291	−	0.442676i
$421$	7.24814	−	22.3075i	0.353253	−	1.08720i	−0.603763	−	0.797164i	$-0.706333\pi$
$421$	7.24814	−	22.3075i	0.353253	−	1.08720i	0.957016	−	0.290036i	$-0.0936674\pi$
$422$	0.381551	+	1.17429i	0.0185736	+	0.0571637i
$423$	7.14134	−	5.18849i	0.347224	−	0.252273i
$424$	−1.48462	+	1.07864i	−0.0720993	+	0.0523832i
$425$	6.20946	+	19.1108i	0.301203	+	0.927008i
$426$	1.28899	−	3.96711i	0.0624519	−	0.192207i
$427$	7.92798	+	5.76001i	0.383662	+	0.278747i
$428$	−5.05856			−0.244515
$429$		0			0
$430$	1.76928			0.0853221
$431$	−30.1545	−	21.9085i	−1.45249	−	1.05530i	−0.985241	−	0.171171i	$-0.945245\pi$
$431$	−30.1545	−	21.9085i	−1.45249	−	1.05530i	−0.467250	−	0.884125i	$-0.654755\pi$
$432$	5.55928	−	17.1097i	0.267471	−	0.823191i
$433$	−7.04136	−	21.6711i	−0.338386	−	1.04145i	−0.965030	−	0.262139i	$-0.915572\pi$
$433$	−7.04136	−	21.6711i	−0.338386	−	1.04145i	0.626644	−	0.779306i	$-0.284428\pi$
$434$	0.786200	−	0.571207i	0.0377388	−	0.0274188i
$435$	7.71818	−	5.60758i	0.370058	−	0.268863i
$436$	2.34085	+	7.20441i	0.112107	+	0.345029i
$437$	11.2495	−	34.6225i	0.538138	−	1.65622i
$438$	−0.691863	−	0.502668i	−0.0330585	−	0.0240184i
$439$	−1.42974			−0.0682379			−0.0341189	−	0.999418i	$-0.510863\pi$
$439$	−1.42974			−0.0682379			−0.0341189	+	0.999418i	$0.510863\pi$
$440$		0			0
$441$	4.66094			0.221949
$442$	−0.731534	−	0.531490i	−0.0347955	−	0.0252804i
$443$	−8.16736	+	25.1365i	−0.388043	+	1.19427i	0.546206	+	0.837651i	$0.316072\pi$
$443$	−8.16736	+	25.1365i	−0.388043	+	1.19427i	−0.934249	+	0.356622i	$0.883928\pi$
$444$	−2.60721	−	8.02417i	−0.123733	−	0.380810i
$445$	10.8181	−	7.85982i	0.512828	−	0.372591i
$446$	1.31669	−	0.956630i	0.0623470	−	0.0452978i
$447$	9.93869	+	30.5881i	0.470084	+	1.44677i
$448$	−2.36535	+	7.27979i	−0.111752	+	0.343938i
$449$	−11.3966	−	8.28012i	−0.537839	−	0.390763i	0.285443	−	0.958396i	$-0.407859\pi$
$449$	−11.3966	−	8.28012i	−0.537839	−	0.390763i	−0.823282	+	0.567633i	$0.807859\pi$
$450$	1.62003			0.0763691
$451$		0			0
$452$	−4.59583			−0.216170
$453$	−40.1158	−	29.1458i	−1.88481	−	1.36939i
$454$	0.504952	−	1.55408i	0.0236986	−	0.0729367i
$455$	−0.937030	−	2.88388i	−0.0439286	−	0.135198i
$456$	8.10350	−	5.88754i	0.379481	−	0.275709i
$457$	−23.8521	+	17.3296i	−1.11576	+	0.810645i	−0.983560	−	0.180579i	$-0.942203\pi$
$457$	−23.8521	+	17.3296i	−1.11576	+	0.810645i	−0.132196	+	0.991224i	$0.542203\pi$
$458$	−0.0540402	−	0.166319i	−0.00252513	−	0.00777156i
$459$	9.88504	−	30.4230i	0.461394	−	1.42002i
$460$	−21.7697	−	15.8166i	−1.01502	−	0.737454i
$461$	31.7282			1.47773			0.738866	−	0.673853i	$-0.235362\pi$
$461$	31.7282			1.47773			0.738866	+	0.673853i	$0.235362\pi$
$462$		0			0
$463$	−12.7839			−0.594117			−0.297059	−	0.954859i	$-0.596006\pi$
$463$	−12.7839			−0.594117			−0.297059	+	0.954859i	$0.596006\pi$
$464$	−3.88542	−	2.82292i	−0.180376	−	0.131051i
$465$	19.3952	−	59.6924i	0.899432	−	2.76817i
$466$	0.305129	+	0.939089i	0.0141348	+	0.0435025i
$467$	−23.9281	+	17.3848i	−1.10726	+	0.804472i	−0.982230	−	0.187681i	$-0.939903\pi$
$467$	−23.9281	+	17.3848i	−1.10726	+	0.804472i	−0.125030	+	0.992153i	$0.539903\pi$
$468$	8.08344	−	5.87296i	0.373657	−	0.271478i
$469$	−0.636885	−	1.96013i	−0.0294086	−	0.0905105i
$470$	0.197830	−	0.608857i	0.00912521	−	0.0280845i
$471$	−16.6331	−	12.0847i	−0.766413	−	0.556832i
$472$	3.19645			0.147129
$473$		0			0
$474$	−5.10644			−0.234546
$475$	−17.6252	−	12.8055i	−0.808702	−	0.587556i
$476$	−4.26931	+	13.1396i	−0.195683	+	0.602251i
$477$	−5.50993	−	16.9578i	−0.252282	−	0.776445i
$478$	−1.01108	+	0.734591i	−0.0462456	+	0.0335994i
$479$	23.1034	−	16.7856i	1.05562	−	0.766955i	0.0823493	−	0.996604i	$-0.473758\pi$
$479$	23.1034	−	16.7856i	1.05562	−	0.766955i	0.973274	+	0.229649i	$0.0737577\pi$
$480$	−3.43604	−	10.5750i	−0.156833	−	0.482682i
$481$	0.512218	−	1.57645i	0.0233551	−	0.0718797i
$482$	0.798894	+	0.580430i	0.0363886	+	0.0264379i
$483$	13.3563			0.607731
$484$		0			0
$485$	−25.6000			−1.16244
$486$	1.68211	+	1.22213i	0.0763021	+	0.0554367i
$487$	0.327026	−	1.00648i	0.0148190	−	0.0456081i	−0.943374	−	0.331732i	$-0.892367\pi$
$487$	0.327026	−	1.00648i	0.0148190	−	0.0456081i	0.958193	+	0.286124i	$0.0923670\pi$
$488$	1.45262	+	4.47072i	0.0657572	+	0.202380i
$489$	−17.5846	+	12.7759i	−0.795202	+	0.577748i
$490$	0.273475	−	0.198691i	0.0123543	−	0.00897596i
$491$	5.70102	+	17.5459i	0.257283	+	0.791837i	0.993371	+	0.114951i	$0.0366710\pi$
$491$	5.70102	+	17.5459i	0.257283	+	0.791837i	−0.736088	+	0.676886i	$0.763329\pi$
$492$	−15.7933	+	48.6067i	−0.712016	+	2.19136i
$493$	−6.90872	−	5.01948i	−0.311153	−	0.226066i
$494$	0.980354			0.0441082
$495$		0			0
$496$	−31.5962			−1.41871
$497$	−10.1299	−	7.35977i	−0.454386	−	0.330131i
$498$	0.210628	−	0.648246i	0.00943846	−	0.0290486i
$499$	9.80490	+	30.1764i	0.438927	+	1.35088i	0.889008	+	0.457892i	$0.151395\pi$
$499$	9.80490	+	30.1764i	0.438927	+	1.35088i	−0.450081	+	0.892988i	$0.648605\pi$
$500$	9.52886	−	6.92312i	0.426144	−	0.309611i
$501$	12.0976	−	8.78944i	0.540482	−	0.392683i
$502$	−0.611650	−	1.88246i	−0.0272993	−	0.0840185i
$503$	−8.97024	+	27.6076i	−0.399963	+	1.23096i	0.525065	+	0.851062i	$0.324041\pi$
$503$	−8.97024	+	27.6076i	−0.399963	+	1.23096i	−0.925028	+	0.379898i	$0.875959\pi$
$504$	1.80883	+	1.31419i	0.0805715	+	0.0585386i
$505$	13.3232			0.592876
$506$		0			0
$507$	−32.7555			−1.45472
$508$	15.8165	+	11.4913i	0.701743	+	0.509846i
$509$	0.892536	−	2.74694i	0.0395610	−	0.121756i	−0.929326	−	0.369261i	$-0.879611\pi$
$509$	0.892536	−	2.74694i	0.0395610	−	0.121756i	0.968887	+	0.247505i	$0.0796107\pi$
$510$	−2.01180	−	6.19169i	−0.0890842	−	0.274173i
$511$	−2.07681	+	1.50889i	−0.0918728	+	0.0667495i
$512$	−7.56587	+	5.49693i	−0.334367	+	0.242932i
$513$	10.7173	+	32.9844i	0.473179	+	1.45630i
$514$	−0.447954	+	1.37866i	−0.0197584	+	0.0608101i
$515$	0.797297	+	0.579270i	0.0351331	+	0.0255257i
$516$	28.7640			1.26626
$517$		0			0
$518$	0.184783			0.00811890
$519$	44.1601	+	32.0842i	1.93841	+	1.40834i
$520$	0.449489	−	1.38339i	0.0197114	−	0.0606655i
$521$	9.78683	+	30.1208i	0.428769	+	1.31961i	0.899339	+	0.437252i	$0.144048\pi$
$521$	9.78683	+	30.1208i	0.428769	+	1.31961i	−0.470570	+	0.882362i	$0.655952\pi$
$522$	−0.556994	+	0.404680i	−0.0243790	+	0.0177123i
$523$	12.9751	−	9.42693i	0.567359	−	0.412211i	−0.266786	−	0.963756i	$-0.585962\pi$
$523$	12.9751	−	9.42693i	0.567359	−	0.412211i	0.834145	+	0.551545i	$0.185962\pi$
$524$	−10.0489	−	30.9275i	−0.438990	−	1.35107i
$525$	2.46997	−	7.60180i	0.107799	−	0.331770i
$526$	−0.182674	−	0.132721i	−0.00796498	−	0.00578690i
$527$	−56.1818			−2.44732
$528$		0			0
$529$	0.285644			0.0124193
$530$	−1.04618	−	0.760097i	−0.0454433	−	0.0330165i
$531$	−9.59748	+	29.5380i	−0.416495	+	1.28184i
$532$	−4.62875	−	14.2458i	−0.200682	−	0.617635i
$533$	−8.12319	+	5.90184i	−0.351854	+	0.255637i
$534$	−1.28320	+	0.932302i	−0.0555297	+	0.0403447i
$535$	−2.21113	−	6.80517i	−0.0955956	−	0.294213i
$536$	0.305511	−	0.940267i	0.0131961	−	0.0406134i
$537$	52.2393	+	37.9541i	2.25429	+	1.63784i
$538$	−1.68853			−0.0727976
$539$		0			0
$540$	25.6357			1.10318
$541$	−10.9983	−	7.99073i	−0.472854	−	0.343549i	0.325699	−	0.945474i	$-0.394401\pi$
$541$	−10.9983	−	7.99073i	−0.472854	−	0.343549i	−0.798553	+	0.601925i	$0.794401\pi$
$542$	0.0503327	−	0.154908i	0.00216198	−	0.00665388i
$543$	2.63863	+	8.12087i	0.113235	+	0.348500i
$544$	−8.05222	+	5.85028i	−0.345236	+	0.250829i
$545$	−8.66873	+	6.29820i	−0.371327	+	0.269785i
$546$	0.111147	+	0.342075i	0.00475665	+	0.0146395i
$547$	−2.72703	+	8.39294i	−0.116599	+	0.358856i	−0.992277	−	0.124040i	$-0.960415\pi$
$547$	−2.72703	+	8.39294i	−0.116599	+	0.358856i	0.875678	+	0.482896i	$0.160415\pi$
$548$	−22.8324	−	16.5887i	−0.975352	−	0.708635i
$549$	−45.6749			−1.94936
$550$		0			0
$551$	9.25862			0.394430
$552$	5.18333	+	3.76591i	0.220617	+	0.160288i
$553$	−4.73672	+	14.5781i	−0.201426	+	0.619925i
$554$	−0.497777	−	1.53200i	−0.0211485	−	0.0650884i
$555$	9.65510	−	7.01484i	0.409836	−	0.297764i
$556$	−14.7450	+	10.7129i	−0.625329	+	0.454328i
$557$	10.5041	+	32.3284i	0.445074	+	1.36980i	0.882403	+	0.470495i	$0.155925\pi$
$557$	10.5041	+	32.3284i	0.445074	+	1.36980i	−0.437329	+	0.899302i	$0.644075\pi$
$558$	−1.39969	+	4.30779i	−0.0592534	+	0.182363i
$559$	4.57179	+	3.32160i	0.193366	+	0.140489i
$560$	−10.9906			−0.464437
$561$		0			0
$562$	0.279099			0.0117731
$563$	16.3628	+	11.8883i	0.689611	+	0.501032i	0.876532	−	0.481343i	$-0.159851\pi$
$563$	16.3628	+	11.8883i	0.689611	+	0.501032i	−0.186921	+	0.982375i	$0.559851\pi$
$564$	3.21622	−	9.89850i	0.135427	−	0.416802i
$565$	−2.00887	−	6.18267i	−0.0845138	−	0.260107i
$566$	2.16830	−	1.57536i	0.0911403	−	0.0662173i
$567$	1.01813	−	0.739718i	0.0427576	−	0.0310652i
$568$	−1.85607	−	5.71239i	−0.0778789	−	0.239687i
$569$	8.94078	−	27.5169i	0.374817	−	1.15357i	−0.568785	−	0.822486i	$-0.692586\pi$
$569$	8.94078	−	27.5169i	0.374817	−	1.15357i	0.943602	−	0.331082i	$-0.107414\pi$
$570$	5.71041	+	4.14885i	0.239183	+	0.173776i
$571$	−7.51312			−0.314414			−0.157207	−	0.987566i	$-0.550249\pi$
$571$	−7.51312			−0.314414			−0.157207	+	0.987566i	$0.550249\pi$
$572$		0			0
$573$	34.7958			1.45362
$574$	−0.905557	−	0.657925i	−0.0377972	−	0.0274613i
$575$	4.30622	−	13.2532i	0.179582	−	0.552695i
$576$	−11.0247	−	33.9306i	−0.459364	−	1.41378i
$577$	−27.8098	+	20.2050i	−1.15774	+	0.841145i	−0.989490	−	0.144600i	$-0.953810\pi$
$577$	−27.8098	+	20.2050i	−1.15774	+	0.841145i	−0.168247	+	0.985745i	$0.553810\pi$
$578$	−3.05924	+	2.22267i	−0.127248	+	0.0924509i
$579$	−17.6780	−	54.4072i	−0.734672	−	2.26109i
$580$	2.11481	−	6.50872i	0.0878127	−	0.270260i
$581$	−1.65527	−	1.20262i	−0.0686721	−	0.0498932i
$582$	3.03658			0.125870
$583$		0			0
$584$	−1.23142			−0.0509565
$585$	11.4341	+	8.30736i	0.472742	+	0.343467i
$586$	−0.0907443	+	0.279282i	−0.00374861	+	0.0115370i
$587$	12.9908	+	39.9816i	0.536188	+	1.65022i	0.741067	+	0.671431i	$0.234320\pi$
$587$	12.9908	+	39.9816i	0.536188	+	1.65022i	−0.204879	+	0.978787i	$0.565680\pi$
$588$	4.44602	−	3.23022i	0.183351	−	0.133212i
$589$	49.2787	−	35.8031i	2.03049	−	1.47524i
$590$	0.696056	+	2.14224i	0.0286562	+	0.0881946i
$591$	5.37095	−	16.5301i	0.220931	−	0.679957i
$592$	−4.86049	−	3.53135i	−0.199765	−	0.145138i
$593$	29.2867			1.20266			0.601331	−	0.799000i	$-0.294637\pi$
$593$	29.2867			1.20266			0.601331	+	0.799000i	$0.294637\pi$
$594$		0			0
$595$	−19.5425			−0.801165
$596$	18.6654	+	13.5612i	0.764563	+	0.555487i
$597$	−5.87508	+	18.0817i	−0.240451	+	0.740033i
$598$	0.193776	+	0.596383i	0.00792411	+	0.0243879i
$599$	12.2628	−	8.90947i	0.501046	−	0.364031i	−0.308370	−	0.951266i	$-0.599784\pi$
$599$	12.2628	−	8.90947i	0.501046	−	0.364031i	0.809416	+	0.587235i	$0.199784\pi$
$600$	3.10194	−	2.25369i	0.126636	−	0.0920067i
$601$	9.84944	+	30.3135i	0.401767	+	1.23651i	0.923565	+	0.383443i	$0.125262\pi$
$601$	9.84944	+	30.3135i	0.401767	+	1.23651i	−0.521798	+	0.853069i	$0.674738\pi$
$602$	−0.194670	+	0.599134i	−0.00793417	+	0.0244189i
$603$	7.77159	+	5.64639i	0.316483	+	0.229939i
$604$	−35.5705			−1.44734
$605$		0			0
$606$	−1.58035			−0.0641974
$607$	16.2987	+	11.8417i	0.661545	+	0.480640i	0.867184	−	0.497987i	$-0.165927\pi$
$607$	16.2987	+	11.8417i	0.661545	+	0.480640i	−0.205639	+	0.978628i	$0.565927\pi$
$608$	3.33462	−	10.2629i	0.135237	−	0.416216i
$609$	1.04969	+	3.23061i	0.0425356	+	0.130911i
$610$	−2.67993	+	1.94708i	−0.108507	+	0.0788350i
$611$	1.65424	−	1.20188i	0.0669235	−	0.0486228i
$612$	−19.8990	−	61.2427i	−0.804368	−	2.47559i
$613$	−1.20248	+	3.70086i	−0.0485678	+	0.149476i	−0.972399	−	0.233323i	$-0.925040\pi$
$613$	−1.20248	+	3.70086i	−0.0485678	+	0.149476i	0.923831	+	0.382800i	$0.125040\pi$
$614$	0.865701	+	0.628969i	0.0349368	+	0.0253831i
$615$	−72.2929			−2.91513
$616$		0			0
$617$	28.6122			1.15189			0.575943	−	0.817490i	$-0.304635\pi$
$617$	28.6122			1.15189			0.575943	+	0.817490i	$0.304635\pi$
$618$	−0.0945724	−	0.0687109i	−0.00380426	−	0.00276396i
$619$	−8.08222	+	24.8745i	−0.324852	+	0.999791i	0.646656	+	0.762782i	$0.276167\pi$
$619$	−8.08222	+	24.8745i	−0.324852	+	0.999791i	−0.971507	+	0.237009i	$0.923833\pi$
$620$	−13.9132	−	42.8204i	−0.558767	−	1.71971i
$621$	−17.9472	+	13.0394i	−0.720194	+	0.523252i
$622$	1.15238	−	0.837256i	0.0462064	−	0.0335709i
$623$	1.47129	+	4.52816i	0.0589459	+	0.181417i
$624$	3.61375	−	11.1220i	0.144666	−	0.445236i
$625$	25.1601	+	18.2799i	1.00640	+	0.731195i
$626$	−3.55550			−0.142106
$627$		0			0
$628$	−14.7485			−0.588529
$629$	−8.64251	−	6.27915i	−0.344599	−	0.250366i
$630$	−0.486873	+	1.49844i	−0.0193975	+	0.0596993i
$631$	−1.75606	−	5.40459i	−0.0699075	−	0.215153i	0.909999	−	0.414610i	$-0.136082\pi$
$631$	−1.75606	−	5.40459i	−0.0699075	−	0.215153i	−0.979907	+	0.199457i	$0.936082\pi$
$632$	−5.94866	+	4.32195i	−0.236625	+	0.171918i
$633$	−22.9714	+	16.6897i	−0.913031	+	0.663356i
$634$	−0.935578	−	2.87941i	−0.0371565	−	0.114356i
$635$	−8.54555	+	26.3005i	−0.339120	+	1.04370i
$636$	−17.0083	−	12.3573i	−0.674424	−	0.489998i
$637$	1.07967			0.0427782
$638$		0			0
$639$	58.3605			2.30870
$640$	−8.59342	−	6.24349i	−0.339685	−	0.246795i
$641$	−6.40569	+	19.7147i	−0.253009	+	0.778683i	0.741206	+	0.671278i	$0.234254\pi$
$641$	−6.40569	+	19.7147i	−0.253009	+	0.778683i	−0.994215	+	0.107405i	$0.965746\pi$
$642$	0.262276	+	0.807204i	0.0103512	+	0.0318578i
$643$	−17.2123	+	12.5055i	−0.678789	+	0.493169i	−0.872956	−	0.487800i	$-0.837800\pi$
$643$	−17.2123	+	12.5055i	−0.678789	+	0.493169i	0.194167	+	0.980969i	$0.437800\pi$
$644$	7.75130	−	5.63165i	0.305444	−	0.221918i
$645$	12.5730	+	38.6956i	0.495060	+	1.52364i
$646$	1.95243	−	6.00895i	0.0768172	−	0.236419i
$647$	13.9732	+	10.1521i	0.549341	+	0.399120i	0.827543	−	0.561403i	$-0.189738\pi$
$647$	13.9732	+	10.1521i	0.549341	+	0.399120i	−0.278201	+	0.960523i	$0.589738\pi$
$648$	0.603690			0.0237152
$649$		0			0
$650$	0.375270			0.0147193
$651$	18.0797	+	13.1357i	0.708600	+	0.514828i
$652$	−4.81824	+	14.8290i	−0.188697	+	0.580749i
$653$	12.6940	+	39.0682i	0.496756	+	1.52886i	0.814202	+	0.580582i	$0.197175\pi$
$653$	12.6940	+	39.0682i	0.496756	+	1.52886i	−0.317446	+	0.948276i	$0.602825\pi$
$654$	1.02825	−	0.747069i	0.0402078	−	0.0292127i
$655$	37.2136	−	27.0372i	1.45405	−	1.05643i
$656$	11.2461	+	34.6118i	0.439085	+	1.35137i
$657$	3.69739	−	11.3794i	0.144249	−	0.443952i
$658$	0.184412	+	0.133983i	0.00718912	+	0.00522320i
$659$	6.00410			0.233887			0.116943	−	0.993139i	$-0.462690\pi$
$659$	6.00410			0.233887			0.116943	+	0.993139i	$0.462690\pi$
$660$		0			0
$661$	−1.83502			−0.0713739			−0.0356870	−	0.999363i	$-0.511362\pi$
$661$	−1.83502			−0.0713739			−0.0356870	+	0.999363i	$0.511362\pi$
$662$	0.921475	+	0.669491i	0.0358141	+	0.0260205i
$663$	6.42567	−	19.7762i	0.249552	−	0.768043i
$664$	−0.303291	−	0.933433i	−0.0117700	−	0.0362242i
$665$	17.1413	−	12.4539i	0.664712	−	0.482941i
$666$	−0.696775	+	0.506237i	−0.0269995	+	0.0196163i
$667$	1.83006	+	5.63233i	0.0708600	+	0.218085i
$668$	3.31480	−	10.2019i	0.128253	−	0.394723i
$669$	30.2790	+	21.9990i	1.17066	+	0.850531i
$670$	0.696689			0.0269154
$671$		0			0
$672$	3.95910			0.152726
$673$	−35.9530	−	26.1214i	−1.38589	−	1.00690i	−0.996303	−	0.0859135i	$-0.972619\pi$
$673$	−35.9530	−	26.1214i	−1.38589	−	1.00690i	−0.389583	−	0.920991i	$-0.627381\pi$
$674$	−0.640648	+	1.97171i	−0.0246768	+	0.0759475i
$675$	4.10247	+	12.6261i	0.157904	+	0.485979i
$676$	−19.0096	+	13.8113i	−0.731139	+	0.531203i
$677$	−12.5779	+	9.13838i	−0.483408	+	0.351216i	−0.802644	−	0.596459i	$-0.796574\pi$
$677$	−12.5779	+	9.13838i	−0.483408	+	0.351216i	0.319236	+	0.947675i	$0.396574\pi$
$678$	0.238285	+	0.733365i	0.00915127	+	0.0281647i
$679$	2.81673	−	8.66899i	0.108096	−	0.332685i
$680$	−7.58410	−	5.51017i	−0.290837	−	0.211305i
$681$	37.5774			1.43997
$682$		0			0
$683$	−36.8979			−1.41186			−0.705930	−	0.708282i	$-0.749471\pi$
$683$	−36.8979			−1.41186			−0.705930	+	0.708282i	$0.749471\pi$
$684$	56.4822	+	41.0367i	2.15965	+	1.56908i
$685$	12.3362	−	37.9670i	0.471343	−	1.45064i
$686$	0.0371933	+	0.114469i	0.00142004	+	0.00437045i
$687$	3.25350	−	2.36381i	0.124129	−	0.0901849i
$688$	16.5705	−	12.0392i	0.631744	−	0.458989i
$689$	−1.27634	−	3.92816i	−0.0486246	−	0.149651i
$690$	−1.39517	+	4.29390i	−0.0531133	+	0.163466i
$691$	15.1064	+	10.9755i	0.574676	+	0.417527i	0.836801	−	0.547507i	$-0.184423\pi$
$691$	15.1064	+	10.9755i	0.574676	+	0.417527i	−0.262125	+	0.965034i	$0.584423\pi$
$692$	39.1566			1.48851
$693$		0			0
$694$	−1.05133			−0.0399078
$695$	−20.8570	−	15.1535i	−0.791150	−	0.574804i
$696$	−0.503532	+	1.54971i	−0.0190863	+	0.0587417i
$697$	19.9968	+	61.5439i	0.757433	+	2.33114i
$698$	2.91974	−	2.12132i	0.110514	−	0.0802930i
$699$	−18.3703	+	13.3468i	−0.694830	+	0.504824i
$700$	−1.77184	−	5.45316i	−0.0669693	−	0.206110i
$701$	−8.07548	+	24.8538i	−0.305007	+	0.938714i	0.674668	+	0.738121i	$0.264287\pi$
$701$	−8.07548	+	24.8538i	−0.305007	+	0.938714i	−0.979675	+	0.200593i	$0.935713\pi$
$702$	−0.483310	−	0.351145i	−0.0182414	−	0.0132531i
$703$	11.5821			0.436828
$704$		0			0
$705$	14.7221			0.554465
$706$	−0.712771	−	0.517858i	−0.0268255	−	0.0194899i
$707$	−1.46593	+	4.51167i	−0.0551320	+	0.169679i
$708$	11.3161	+	34.8275i	0.425286	+	1.30890i
$709$	13.3042	−	9.66609i	0.499651	−	0.363017i	−0.309233	−	0.950986i	$-0.600072\pi$
$709$	13.3042	−	9.66609i	0.499651	−	0.363017i	0.808884	+	0.587969i	$0.200072\pi$
$710$	3.42423	−	2.48785i	0.128509	−	0.0933674i
$711$	−22.0776	−	67.9477i	−0.827973	−	2.54824i
$712$	−0.705771	+	2.17214i	−0.0264499	+	0.0814044i
$713$	31.5206	+	22.9011i	1.18046	+	0.857653i
$714$	2.31806			0.0867513
$715$		0			0
$716$	46.3204			1.73107
$717$	−23.2511	−	16.8929i	−0.868329	−	0.630878i
$718$	0.184849	−	0.568907i	0.00689850	−	0.0212314i
$719$	−2.88904	−	8.89155i	−0.107743	−	0.331599i	0.882621	−	0.470084i	$-0.155777\pi$
$719$	−2.88904	−	8.89155i	−0.107743	−	0.331599i	−0.990364	+	0.138486i	$0.955777\pi$
$720$	41.4430	−	30.1101i	1.54449	−	1.12214i
$721$	−0.283885	+	0.206254i	−0.0105724	+	0.00768131i
$722$	1.41013	+	4.33994i	0.0524797	+	0.161516i
$723$	−7.01735	+	21.5972i	−0.260978	+	0.803207i
$724$	4.95548	+	3.60037i	0.184169	+	0.133807i
$725$	3.54411			0.131625
$726$		0			0
$727$	27.7523			1.02928			0.514638	−	0.857408i	$-0.327927\pi$
$727$	27.7523			1.02928			0.514638	+	0.857408i	$0.327927\pi$
$728$	0.419002	+	0.304423i	0.0155293	+	0.0112827i
$729$	−13.6087	+	41.8833i	−0.504026	+	1.55123i
$730$	−0.268153	−	0.825289i	−0.00992478	−	0.0305453i
$731$	29.4643	−	21.4070i	1.08977	−	0.791768i
$732$	−43.5689	+	31.6546i	−1.61035	+	1.16999i
$733$	0.450021	+	1.38502i	0.0166219	+	0.0511569i	0.959023	−	0.283327i	$-0.0914381\pi$
$733$	0.450021	+	1.38502i	0.0166219	+	0.0511569i	−0.942402	+	0.334484i	$0.891438\pi$
$734$	−0.528302	+	1.62594i	−0.0195000	+	0.0600147i
$735$	6.28893	+	4.56918i	0.231971	+	0.168537i
$736$	6.90240			0.254426
$737$		0			0
$738$	5.21712			0.192045
$739$	22.3261	+	16.2209i	0.821280	+	0.596695i	0.917079	−	0.398706i	$-0.130541\pi$
$739$	22.3261	+	16.2209i	0.821280	+	0.596695i	−0.0957991	+	0.995401i	$0.530541\pi$
$740$	2.64554	−	8.14212i	0.0972518	−	0.299310i
$741$	6.96665	+	21.4412i	0.255926	+	0.787661i
$742$	0.372503	−	0.270639i	0.0136750	−	0.00993548i
$743$	−22.6341	+	16.4446i	−0.830365	+	0.603296i	−0.919663	−	0.392709i	$-0.871538\pi$
$743$	−22.6341	+	16.4446i	−0.830365	+	0.603296i	0.0892975	+	0.996005i	$0.471538\pi$
$744$	3.31270	+	10.1955i	0.121450	+	0.373784i
$745$	−10.0848	+	31.0378i	−0.369478	+	1.13714i
$746$	−0.874198	−	0.635142i	−0.0320067	−	0.0232542i
$747$	9.53638			0.348918
$748$		0			0
$749$	2.54774			0.0930922
$750$	−1.59879	−	1.16159i	−0.0583795	−	0.0424152i
$751$	10.5361	−	32.4269i	0.384469	−	1.18328i	−0.552395	−	0.833582i	$-0.686286\pi$
$751$	10.5361	−	32.4269i	0.384469	−	1.18328i	0.936864	−	0.349693i	$-0.113714\pi$
$752$	−2.29020	−	7.04851i	−0.0835150	−	0.257033i
$753$	36.8245	−	26.7546i	1.34196	−	0.974991i
$754$	−0.129024	+	0.0937413i	−0.00469877	+	0.00341386i
$755$	−15.5481	−	47.8522i	−0.565854	−	1.74152i
$756$	−2.82065	+	8.68106i	−0.102586	+	0.315727i
$757$	32.1689	+	23.3721i	1.16920	+	0.849472i	0.990913	−	0.134507i	$-0.0429451\pi$
$757$	32.1689	+	23.3721i	1.16920	+	0.849472i	0.178285	+	0.983979i	$0.442945\pi$
$758$	1.29863			0.0471684
$759$		0			0
$760$	10.1637			0.368677
$761$	3.09381	+	2.24778i	0.112150	+	0.0814820i	0.642447	−	0.766330i	$-0.277919\pi$
$761$	3.09381	+	2.24778i	0.112150	+	0.0814820i	−0.530296	+	0.847812i	$0.677919\pi$
$762$	1.01364	−	3.11967i	0.0367203	−	0.113014i
$763$	−1.17897	−	3.62849i	−0.0426815	−	0.131360i
$764$	20.1937	−	14.6716i	0.730584	−	0.530800i
$765$	73.6905	−	53.5393i	2.66428	−	1.93572i
$766$	−0.874413	−	2.69117i	−0.0315938	−	0.0972358i
$767$	−2.22319	+	6.84228i	−0.0802748	+	0.247060i
$768$	−33.2607	−	24.1653i	−1.20019	−	0.871990i
$769$	−19.6583			−0.708897			−0.354449	−	0.935075i	$-0.615331\pi$
$769$	−19.6583			−0.708897			−0.354449	+	0.935075i	$0.615331\pi$
$770$		0			0
$771$	−33.3358			−1.20056
$772$	−33.2001	−	24.1213i	−1.19490	−	0.868145i
$773$	−5.43764	+	16.7353i	−0.195578	+	0.601928i	0.804391	+	0.594100i	$0.202492\pi$
$773$	−5.43764	+	16.7353i	−0.195578	+	0.601928i	−0.999969	+	0.00782804i	$0.997508\pi$
$774$	−0.907346	−	2.79252i	−0.0326139	−	0.100375i
$775$	18.8634	−	13.7051i	0.677594	−	0.492301i
$776$	3.53742	−	2.57008i	0.126986	−	0.0922606i
$777$	1.31312	+	4.04136i	0.0471078	+	0.144983i
$778$	−0.441653	+	1.35927i	−0.0158340	+	0.0487321i
$779$	−56.7600	−	41.2385i	−2.03364	−	1.47752i
$780$	16.6642			0.596675
$781$		0			0
$782$	4.04136			0.144519
$783$	−4.56446	−	3.31627i	−0.163120	−	0.118514i
$784$	1.20927	−	3.72176i	0.0431883	−	0.132920i
$785$	−6.44667	−	19.8408i	−0.230092	−	0.708149i
$786$	−4.41414	+	3.20706i	−0.157447	+	0.114392i
$787$	43.7651	−	31.7972i	1.56006	−	1.13345i	0.624098	−	0.781346i	$-0.285467\pi$
$787$	43.7651	−	31.7972i	1.56006	−	1.13345i	0.935961	−	0.352103i	$-0.114533\pi$
$788$	−3.85286	−	11.8579i	−0.137252	−	0.422419i
$789$	1.60458	−	4.93839i	0.0571246	−	0.175811i
$790$	−4.19192	−	3.04561i	−0.149142	−	0.108358i
$791$	2.31468			0.0823006
$792$		0			0
$793$	−10.5803			−0.375717
$794$	2.31032	+	1.67854i	0.0819901	+	0.0595693i
$795$	9.18950	−	28.2824i	0.325918	−	1.00307i
$796$	4.21450	+	12.9709i	0.149379	+	0.459741i
$797$	−29.5489	+	21.4685i	−1.04667	+	0.760454i	−0.971577	−	0.236722i	$-0.923927\pi$
$797$	−29.5489	+	21.4685i	−1.04667	+	0.760454i	−0.0750976	+	0.997176i	$0.523927\pi$
$798$	−2.03324	+	1.47724i	−0.0719759	+	0.0522936i
$799$	−4.07224	−	12.5331i	−0.144066	−	0.443388i
$800$	1.27646	−	3.92854i	0.0451297	−	0.138895i
$801$	−17.9534	−	13.0439i	−0.634351	−	0.460883i
$802$	−0.457513			−0.0161554
$803$		0			0
$804$	11.3264			0.399452
$805$	10.9643	+	7.96602i	0.386440	+	0.280765i
$806$	−0.324228	+	0.997871i	−0.0114204	+	0.0351485i
$807$	−11.9991	−	36.9295i	−0.422389	−	1.29998i
$808$	−1.84100	+	1.33757i	−0.0647663	+	0.0470555i
$809$	−37.9716	+	27.5880i	−1.33501	+	0.969941i	−0.335397	+	0.942077i	$0.608870\pi$
$809$	−37.9716	+	27.5880i	−1.33501	+	0.969941i	−0.999612	+	0.0278638i	$0.991130\pi$
$810$	0.131459	+	0.404589i	0.00461900	+	0.0142158i
$811$	−3.91262	+	12.0418i	−0.137391	+	0.422845i	−0.995954	−	0.0898623i	$-0.971357\pi$
$811$	−3.91262	+	12.0418i	−0.137391	+	0.422845i	0.858564	+	0.512707i	$0.171357\pi$
$812$	1.97137	+	1.43228i	0.0691815	+	0.0502633i
$813$	3.74565			0.131366
$814$		0			0
$815$	−22.0552			−0.772561
$816$	−60.9737	−	44.3000i	−2.13451	−	1.55081i
$817$	−12.2019	+	37.5535i	−0.426889	+	1.31383i
$818$	−0.222524	−	0.684858i	−0.00778037	−	0.0239455i
$819$	−4.07121	+	2.95791i	−0.142260	+	0.103358i
$820$	−41.9551	+	30.4822i	−1.46514	+	1.06448i
$821$	−15.2326	−	46.8812i	−0.531622	−	1.63616i	−0.750837	−	0.660488i	$-0.770349\pi$
$821$	−15.2326	−	46.8812i	−0.531622	−	1.63616i	0.219214	−	0.975677i	$-0.429651\pi$
$822$	−1.46328	+	4.50350i	−0.0510376	+	0.157078i
$823$	−15.5541	−	11.3007i	−0.542182	−	0.393918i	0.282713	−	0.959205i	$-0.408766\pi$
$823$	−15.5541	−	11.3007i	−0.542182	−	0.393918i	−0.824895	+	0.565287i	$0.808766\pi$
$824$	−0.168326			−0.00586390
$825$		0			0
$826$	−0.802017			−0.0279057
$827$	−35.3070	−	25.6521i	−1.22775	−	0.892010i	−0.231027	−	0.972947i	$-0.574208\pi$
$827$	−35.3070	−	25.6521i	−1.22775	−	0.892010i	−0.996719	+	0.0809378i	$0.974208\pi$
$828$	−13.7998	+	42.4714i	−0.479576	+	1.47598i
$829$	−11.3432	−	34.9106i	−0.393964	−	1.21250i	−0.929765	−	0.368153i	$-0.879990\pi$
$829$	−11.3432	−	34.9106i	−0.393964	−	1.21250i	0.535801	−	0.844344i	$-0.320010\pi$
$830$	0.559536	−	0.406527i	0.0194218	−	0.0141108i
$831$	29.9688	−	21.7736i	1.03960	−	0.755317i
$832$	−2.55380	−	7.85980i	−0.0885372	−	0.272489i
$833$	2.15023	−	6.61772i	0.0745010	−	0.229290i
$834$	2.47398	+	1.79745i	0.0856668	+	0.0622406i
$835$	15.1733			0.525094
$836$		0			0
$837$	−37.1182			−1.28299
$838$	0.405939	+	0.294932i	0.0140229	+	0.0101882i
$839$	12.5011	−	38.4745i	0.431587	−	1.32829i	−0.464957	−	0.885333i	$-0.653930\pi$
$839$	12.5011	−	38.4745i	0.431587	−	1.32829i	0.896544	−	0.442955i	$-0.146070\pi$
$840$	1.15231	+	3.54643i	0.0397583	+	0.122364i
$841$	22.2430	−	16.1605i	0.766999	−	0.557257i
$842$	−2.28393	+	1.65938i	−0.0787096	+	0.0571859i
$843$	1.98335	+	6.10413i	0.0683102	+	0.210237i
$844$	−6.29425	+	19.3717i	−0.216657	+	0.666802i
$845$	−26.8893	−	19.5362i	−0.925018	−	0.672065i
$846$	−1.06244			−0.0365274
$847$		0			0
$848$	−14.9704			−0.514085
$849$	49.8629	+	36.2275i	1.71129	+	1.24333i
$850$	0.747370	−	2.30017i	0.0256346	−	0.0788951i
$851$	2.28932	+	7.04580i	0.0784769	+	0.241527i
$852$	55.6695	−	40.4462i	1.90720	−	1.38567i
$853$	−20.6258	+	14.9855i	−0.706213	+	0.513094i	−0.881950	−	0.471344i	$-0.843769\pi$
$853$	−20.6258	+	14.9855i	−0.706213	+	0.513094i	0.175737	+	0.984437i	$0.443769\pi$
$854$	−0.364476	−	1.12174i	−0.0124721	−	0.0383852i
$855$	−30.5170	+	93.9217i	−1.04366	+	3.21206i
$856$	0.988731	+	0.718355i	0.0337941	+	0.0245529i
$857$	49.4756			1.69005			0.845027	−	0.534723i	$-0.179584\pi$
$857$	49.4756			1.69005			0.845027	+	0.534723i	$0.179584\pi$
$858$		0			0
$859$	21.6779			0.739641			0.369821	−	0.929103i	$-0.379419\pi$
$859$	21.6779			0.739641			0.369821	+	0.929103i	$0.379419\pi$
$860$	23.6126	+	17.1556i	0.805184	+	0.585001i
$861$	7.95426	−	24.4807i	0.271080	−	0.834299i
$862$	1.38630	+	4.26661i	0.0472177	+	0.145321i
$863$	−11.0349	+	8.01730i	−0.375631	+	0.272912i	−0.759542	−	0.650458i	$-0.774577\pi$
$863$	−11.0349	+	8.01730i	−0.375631	+	0.272912i	0.383911	+	0.923370i	$0.374577\pi$
$864$	−5.31995	+	3.86517i	−0.180988	+	0.131496i
$865$	17.1156	+	52.6764i	0.581948	+	1.79105i
$866$	−0.847497	+	2.60833i	−0.0287991	+	0.0886346i
$867$	−70.3515	−	51.1133i	−2.38926	−	1.73590i
$868$	16.0312			0.544135
$869$		0			0
$870$	−1.14826			−0.0389295
$871$	1.80024	+	1.30795i	0.0609986	+	0.0443181i
$872$	0.565546	−	1.74057i	0.0191518	−	0.0589432i
$873$	13.1286	+	40.4056i	0.444335	+	1.36752i
$874$	−3.54480	+	2.57545i	−0.119905	+	0.0871158i
$875$	−4.79919	+	3.48682i	−0.162242	+	0.117876i
$876$	−4.35949	−	13.4171i	−0.147294	−	0.453323i
$877$	9.00137	−	27.7034i	0.303955	−	0.935476i	−0.676111	−	0.736800i	$-0.736336\pi$
$877$	9.00137	−	27.7034i	0.303955	−	0.935476i	0.980065	−	0.198676i	$-0.0636641\pi$
$878$	0.139219	+	0.101148i	0.00469840	+	0.00341359i
$879$	−6.75299			−0.227773
$880$		0			0
$881$	−48.8256			−1.64498			−0.822488	−	0.568783i	$-0.807414\pi$
$881$	−48.8256			−1.64498			−0.822488	+	0.568783i	$0.807414\pi$
$882$	−0.453850	−	0.329741i	−0.0152819	−	0.0111030i
$883$	−7.48227	+	23.0281i	−0.251799	+	0.774956i	0.742645	+	0.669685i	$0.233571\pi$
$883$	−7.48227	+	23.0281i	−0.251799	+	0.774956i	−0.994444	+	0.105271i	$0.966429\pi$
$884$	−4.60946	−	14.1865i	−0.155033	−	0.477142i
$885$	−41.9062	+	30.4467i	−1.40866	+	1.02345i
$886$	2.57359	−	1.86982i	0.0864613	−	0.0628178i
$887$	2.05419	+	6.32214i	0.0689729	+	0.212277i	0.979602	−	0.200948i	$-0.0644023\pi$
$887$	2.05419	+	6.32214i	0.0689729	+	0.212277i	−0.910629	+	0.413225i	$0.864402\pi$
$888$	−0.629897	+	1.93862i	−0.0211380	+	0.0650559i
$889$	−7.96594	−	5.78759i	−0.267169	−	0.194110i
$890$	−1.60944			−0.0539486
$891$		0			0
$892$	26.8483			0.898947
$893$	11.5589	+	8.39800i	0.386803	+	0.281028i
$894$	1.19622	−	3.68158i	0.0400076	−	0.123131i
$895$	20.2470	+	62.3137i	0.676781	+	2.08292i
$896$	3.05976	−	2.22305i	0.102220	−	0.0742668i
$897$	−11.6664	+	8.47611i	−0.389528	+	0.283009i
$898$	0.523941	+	1.61252i	0.0174841	+	0.0538106i
$899$	−3.06206	+	9.42405i	−0.102125	+	0.314310i
$900$	21.6209	+	15.7085i	0.720695	+	0.523616i
$901$	−26.6191			−0.886809
$902$		0			0
$903$	−14.4869			−0.482095
$904$	0.898287	+	0.652643i	0.0298766	+	0.0217066i
$905$	−2.67742	+	8.24025i	−0.0890004	+	0.273915i
$906$	1.84426	+	5.67605i	0.0612714	+	0.188574i
$907$	6.77799	−	4.92450i	0.225060	−	0.163515i	−0.469542	−	0.882910i	$-0.655581\pi$
$907$	6.77799	−	4.92450i	0.225060	−	0.163515i	0.694601	+	0.719395i	$0.255581\pi$
$908$	21.8080	−	15.8445i	0.723725	−	0.525817i
$909$	−6.83261	−	21.0286i	−0.226623	−	0.697475i
$910$	−0.112781	+	0.347104i	−0.00373865	+	0.0115064i
$911$	15.1988	+	11.0426i	0.503559	+	0.365857i	0.810375	−	0.585912i	$-0.199263\pi$
$911$	15.1988	+	11.0426i	0.503559	+	0.365857i	−0.306816	+	0.951769i	$0.599263\pi$
$912$	81.7130			2.70579
$913$		0			0
$914$	3.54856			0.117376
$915$	−61.6285	−	44.7757i	−2.03738	−	1.48024i
$916$	0.891472	−	2.74367i	0.0294551	−	0.0906534i
$917$	5.06113	+	15.5766i	0.167133	+	0.514384i
$918$	−3.11484	+	2.26306i	−0.102805	+	0.0746922i
$919$	−14.5655	+	10.5824i	−0.480470	+	0.349082i	−0.801508	−	0.597984i	$-0.795968\pi$
$919$	−14.5655	+	10.5824i	−0.480470	+	0.349082i	0.321038	+	0.947066i	$0.395968\pi$
$920$	2.00896	+	6.18294i	0.0662334	+	0.203845i
$921$	−7.60417	+	23.4032i	−0.250566	+	0.771163i
$922$	−3.08948	−	2.24464i	−0.101747	−	0.0739232i
$923$	13.5188			0.444977
$924$		0			0
$925$	4.43353			0.145773
$926$	1.24481	+	0.904405i	0.0409069	+	0.0297206i
$927$	0.505405	−	1.55548i	0.0165997	−	0.0510886i
$928$	0.542471	+	1.66955i	0.0178075	+	0.0548058i
$929$	8.18928	−	5.94986i	0.268682	−	0.195209i	−0.445284	−	0.895389i	$-0.646897\pi$
$929$	8.18928	−	5.94986i	0.268682	−	0.195209i	0.713966	+	0.700181i	$0.246897\pi$
$930$	−6.11156	+	4.44031i	−0.200406	+	0.145603i
$931$	2.33126	+	7.17488i	0.0764039	+	0.235147i
$932$	−5.03354	+	15.4917i	−0.164879	+	0.507446i
$933$	26.5006	+	19.2538i	0.867592	+	0.630343i
$934$	3.55986			0.116482
$935$		0			0
$936$	−2.41397			−0.0789031
$937$	22.8234	+	16.5822i	0.745608	+	0.541716i	0.894462	−	0.447143i	$-0.147559\pi$
$937$	22.8234	+	16.5822i	0.745608	+	0.541716i	−0.148854	+	0.988859i	$0.547559\pi$
$938$	−0.0766554	+	0.235921i	−0.00250289	+	0.00770310i
$939$	−25.2663	−	77.7617i	−0.824535	−	2.53766i
$940$	8.54394	−	6.20753i	0.278672	−	0.202467i
$941$	16.3018	−	11.8439i	0.531423	−	0.386101i	−0.289467	−	0.957188i	$-0.593478\pi$
$941$	16.3018	−	11.8439i	0.531423	−	0.386101i	0.820890	+	0.571087i	$0.193478\pi$
$942$	0.764680	+	2.35344i	0.0249146	+	0.0766794i
$943$	13.8676	−	42.6802i	0.451593	−	1.38986i
$944$	21.0961	+	15.3272i	0.686619	+	0.498858i
$945$	−12.9114			−0.420007
$946$		0			0
$947$	0.125141			0.00406653			0.00203326	−	0.999998i	$-0.499353\pi$
$947$	0.125141			0.00406653			0.00203326	+	0.999998i	$0.499353\pi$
$948$	−68.1501	−	49.5140i	−2.21341	−	1.60814i
$949$	0.856475	−	2.63596i	0.0278024	−	0.0855669i
$950$	0.810292	+	2.49382i	0.0262894	+	0.0809103i
$951$	56.3267	−	40.9237i	1.82652	−	1.32704i
$952$	2.70039	−	1.96195i	0.0875200	−	0.0635870i
$953$	−9.06949	−	27.9130i	−0.293790	−	0.904192i	−0.983625	−	0.180226i	$-0.942317\pi$
$953$	−9.06949	−	27.9130i	−0.293790	−	0.904192i	0.689836	−	0.723966i	$-0.257683\pi$
$954$	−0.663174	+	2.04104i	−0.0214711	+	0.0660811i
$955$	28.5642	+	20.7531i	0.924316	+	0.671555i
$956$	−20.6166			−0.666790
$957$		0			0
$958$	−3.43717			−0.111050
$959$	11.4995	+	8.35487i	0.371338	+	0.269793i
$960$	18.3871	−	56.5898i	0.593442	−	1.82643i
$961$	10.5656	+	32.5174i	0.340824	+	1.04895i
$962$	−0.161403	+	0.117266i	−0.00520385	+	0.00378082i
$963$	−9.60694	+	6.97985i	−0.309579	+	0.224923i
$964$	5.03390	+	15.4928i	0.162131	+	0.498988i
$965$	17.9378	−	55.2070i	0.577440	−	1.77718i
$966$	−1.30054	−	0.944899i	−0.0418443	−	0.0304016i
$967$	−51.9463			−1.67048			−0.835240	−	0.549885i	$-0.814672\pi$
$967$	−51.9463			−1.67048			−0.835240	+	0.549885i	$0.814672\pi$
$968$		0			0
$969$	145.295			4.66756
$970$	2.49276	+	1.81109i	0.0800376	+	0.0581507i
$971$	−7.72746	+	23.7827i	−0.247986	+	0.763222i	0.747145	+	0.664661i	$0.231424\pi$
$971$	−7.72746	+	23.7827i	−0.247986	+	0.763222i	−0.995131	+	0.0985614i	$0.968576\pi$
$972$	10.5991	+	32.6208i	0.339968	+	1.04631i
$973$	7.42631	−	5.39553i	0.238076	−	0.172973i
$974$	−0.103048	+	0.0748688i	−0.00330187	+	0.00239895i
$975$	2.66677	+	8.20747i	0.0854049	+	0.262849i
$976$	−11.8503	+	36.4715i	−0.379319	+	1.16742i
$977$	14.0896	+	10.2367i	0.450765	+	0.327500i	0.789898	−	0.613239i	$-0.210134\pi$
$977$	14.0896	+	10.2367i	0.450765	+	0.327500i	−0.339133	+	0.940738i	$0.610134\pi$
$978$	2.61611			0.0836540
$979$		0			0
$980$	5.57636			0.178130
$981$	14.3863	+	10.4523i	0.459320	+	0.333716i
$982$	0.686174	−	2.11183i	0.0218967	−	0.0673911i
$983$	−13.0822	−	40.2629i	−0.417258	−	1.28419i	−0.910216	−	0.414135i	$-0.864084\pi$
$983$	−13.0822	−	40.2629i	−0.417258	−	1.28419i	0.492958	−	0.870053i	$-0.335916\pi$
$984$	9.98943	−	7.25775i	0.318452	−	0.231369i
$985$	14.2680	−	10.3663i	0.454617	−	0.330298i
$986$	0.317617	+	0.977525i	0.0101150	+	0.0311308i
$987$	−1.61984	+	4.98536i	−0.0515601	+	0.158686i
$988$	13.0837	+	9.50588i	0.416249	+	0.302422i
$989$	−25.2569			−0.803122
$990$		0			0
$991$	55.6263			1.76703			0.883513	−	0.468406i	$-0.155172\pi$
$991$	55.6263			1.76703			0.883513	+	0.468406i	$0.155172\pi$
$992$	9.34345	+	6.78841i	0.296655	+	0.215532i
$993$	−8.09408	+	24.9110i	−0.256858	+	0.790527i
$994$	0.465704	+	1.43329i	0.0147712	+	0.0454612i
$995$	−15.6073	+	11.3393i	−0.494784	+	0.359481i
$996$	9.09666	−	6.60911i	0.288239	−	0.209418i
$997$	−5.07614	−	15.6228i	−0.160763	−	0.494778i	0.837936	−	0.545768i	$-0.183762\pi$
$997$	−5.07614	−	15.6228i	−0.160763	−	0.494778i	−0.998699	+	0.0509905i	$0.983762\pi$
$998$	1.18012	−	3.63202i	0.0373559	−	0.114970i
$999$	−5.70994	−	4.14851i	−0.180654	−	0.131253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.y.323.4		24
11.2	odd	10		847.2.f.z.148.4		24
11.3	even	5	inner	847.2.f.y.729.4		24
11.4	even	5	inner	847.2.f.y.372.3		24
11.5	even	5		847.2.a.n.1.3	yes	6
11.6	odd	10		847.2.a.m.1.4	✓	6
11.7	odd	10		847.2.f.z.372.4		24
11.8	odd	10		847.2.f.z.729.3		24
11.9	even	5	inner	847.2.f.y.148.3		24
11.10	odd	2		847.2.f.z.323.3		24
33.5	odd	10		7623.2.a.cp.1.4		6
33.17	even	10		7623.2.a.cs.1.3		6
77.6	even	10		5929.2.a.bj.1.4		6
77.27	odd	10		5929.2.a.bm.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.4	✓	6	11.6	odd	10
847.2.a.n.1.3	yes	6	11.5	even	5
847.2.f.y.148.3		24	11.9	even	5	inner
847.2.f.y.323.4		24	1.1	even	1	trivial
847.2.f.y.372.3		24	11.4	even	5	inner
847.2.f.y.729.4		24	11.3	even	5	inner
847.2.f.z.148.4		24	11.2	odd	10
847.2.f.z.323.3		24	11.10	odd	2
847.2.f.z.372.4		24	11.7	odd	10
847.2.f.z.729.3		24	11.8	odd	10
5929.2.a.bj.1.4		6	77.6	even	10
5929.2.a.bm.1.3		6	77.27	odd	10
7623.2.a.cp.1.4		6	33.5	odd	10
7623.2.a.cs.1.3		6	33.17	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)

\(f(q)\)	\(=\)	\(q+(-0.0973732 - 0.0707458i) q^{2} +(0.855309 - 2.63237i) q^{3} +(-0.613557 - 1.88834i) q^{4} +(2.27214 - 1.65081i) q^{5} +(-0.269513 + 0.195813i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.148234 + 0.456218i) q^{8} +(-3.77078 - 2.73963i) q^{9} +O(q^{10})\)	\(q+(-0.0973732 - 0.0707458i) q^{2} +(0.855309 - 2.63237i) q^{3} +(-0.613557 - 1.88834i) q^{4} +(2.27214 - 1.65081i) q^{5} +(-0.269513 + 0.195813i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.148234 + 0.456218i) q^{8} +(-3.77078 - 2.73963i) q^{9} -0.338034 q^{10} -5.49558 q^{12} +(-0.873475 - 0.634617i) q^{13} +(0.0371933 - 0.114469i) q^{14} +(-2.40216 - 7.39308i) q^{15} +(-3.16592 + 2.30017i) q^{16} +(-5.62937 + 4.08998i) q^{17} +(0.173355 + 0.533533i) q^{18} +(2.33126 - 7.17488i) q^{19} +(-4.51137 - 3.27771i) q^{20} +2.76784 q^{21} +4.82552 q^{23} +(1.07415 + 0.780415i) q^{24} +(0.892384 - 2.74647i) q^{25} +(0.0401566 + 0.123589i) q^{26} +(-3.71922 + 2.70217i) q^{27} +(1.60631 - 1.16706i) q^{28} +(0.379245 + 1.16720i) q^{29} +(-0.289124 + 0.889831i) q^{30} +(6.53207 + 4.74583i) q^{31} +1.43040 q^{32} +0.837498 q^{34} +(2.27214 + 1.65081i) q^{35} +(-2.85975 + 8.80141i) q^{36} +(0.474419 + 1.46011i) q^{37} +(-0.734595 + 0.533714i) q^{38} +(-2.41764 + 1.75652i) q^{39} +(0.416320 + 1.28130i) q^{40} +(2.87381 - 8.84469i) q^{41} +(-0.269513 - 0.195813i) q^{42} -5.23402 q^{43} -13.0904 q^{45} +(-0.469876 - 0.341385i) q^{46} +(-0.585237 + 1.80117i) q^{47} +(3.34707 + 10.3012i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.281196 + 0.204301i) q^{50} +(5.95149 + 18.3168i) q^{51} +(-0.662442 + 2.03879i) q^{52} +(3.09491 + 2.24858i) q^{53} +0.553319 q^{54} -0.479696 q^{56} +(-16.8930 - 12.2735i) q^{57} +(0.0456459 - 0.140484i) q^{58} +(-2.05913 - 6.33736i) q^{59} +(-12.4868 + 9.07216i) q^{60} +(7.92798 - 5.76001i) q^{61} +(-0.300302 - 0.924233i) q^{62} +(1.44031 - 4.43281i) q^{63} +(6.19256 + 4.49915i) q^{64} -3.03229 q^{65} -2.06100 q^{67} +(11.1772 + 8.12070i) q^{68} +(4.12731 - 12.7026i) q^{69} +(-0.104458 - 0.321489i) q^{70} +(-10.1299 + 7.35977i) q^{71} +(1.80883 - 1.31419i) q^{72} +(0.793272 + 2.44144i) q^{73} +(0.0571011 - 0.175739i) q^{74} +(-6.46648 - 4.69817i) q^{75} -14.9789 q^{76} +0.359679 q^{78} +(12.4009 + 9.00978i) q^{79} +(-3.39627 + 10.4527i) q^{80} +(-0.388893 - 1.19689i) q^{81} +(-0.905557 + 0.657925i) q^{82} +(-1.65527 + 1.20262i) q^{83} +(-1.69823 - 5.22661i) q^{84} +(-6.03897 + 18.5860i) q^{85} +(0.509654 + 0.370285i) q^{86} +3.39687 q^{87} +4.76119 q^{89} +(1.27465 + 0.926087i) q^{90} +(0.333638 - 1.02683i) q^{91} +(-2.96073 - 9.11220i) q^{92} +(18.0797 - 13.1357i) q^{93} +(0.184412 - 0.133983i) q^{94} +(-6.54740 - 20.1508i) q^{95} +(1.22343 - 3.76533i) q^{96} +(-7.37429 - 5.35773i) q^{97} +0.120360 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

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