LMFDB - Embedded newform 784.2.x.o.373.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			373.8
Character	$\chi$	$=$	784.373
Dual form			784.2.x.o.557.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.262311 - 1.38967i) q^{2} +(-2.91496 - 0.781062i) q^{3} +(-1.86239 - 0.729053i) q^{4} +(0.745506 - 0.199758i) q^{5} +(-1.85005 + 3.84597i) q^{6} +(-1.50167 + 2.39687i) q^{8} +(5.28887 + 3.05353i) q^{9} +O(q^{10})$	\(q+(0.262311 - 1.38967i) q^{2} +(-2.91496 - 0.781062i) q^{3} +(-1.86239 - 0.729053i) q^{4} +(0.745506 - 0.199758i) q^{5} +(-1.85005 + 3.84597i) q^{6} +(-1.50167 + 2.39687i) q^{8} +(5.28887 + 3.05353i) q^{9} +(-0.0820438 - 1.08841i) q^{10} +(-0.333193 + 1.24349i) q^{11} +(4.85935 + 3.57980i) q^{12} +(0.919058 - 0.919058i) q^{13} -2.32914 q^{15} +(2.93696 + 2.71556i) q^{16} +(3.95601 + 6.85200i) q^{17} +(5.63074 - 6.54883i) q^{18} +(-0.478380 - 1.78534i) q^{19} +(-1.53405 - 0.171487i) q^{20} +(1.64065 + 0.789212i) q^{22} +(3.33211 + 1.92380i) q^{23} +(6.24941 - 5.81389i) q^{24} +(-3.81425 + 2.20216i) q^{25} +(-1.03611 - 1.51827i) q^{26} +(-6.63016 - 6.63016i) q^{27} +(5.25154 - 5.25154i) q^{29} +(-0.610960 + 3.23675i) q^{30} +(-2.44642 - 4.23733i) q^{31} +(4.54413 - 3.36910i) q^{32} +(1.94249 - 3.36449i) q^{33} +(10.5598 - 3.70020i) q^{34} +(-7.62373 - 9.54272i) q^{36} +(-1.28190 + 0.343485i) q^{37} +(-2.60652 + 0.196478i) q^{38} +(-3.39686 + 1.96118i) q^{39} +(-0.640710 + 2.08685i) q^{40} +2.84345i q^{41} +(0.585764 + 0.585764i) q^{43} +(1.52711 - 2.07295i) q^{44} +(4.55285 + 1.21993i) q^{45} +(3.54750 - 4.12591i) q^{46} +(2.86095 - 4.95532i) q^{47} +(-6.44012 - 10.2097i) q^{48} +(2.05976 + 5.87821i) q^{50} +(-6.17977 - 23.0632i) q^{51} +(-2.38168 + 1.04160i) q^{52} +(2.54947 - 9.51475i) q^{53} +(-10.9529 + 7.47460i) q^{54} +0.993590i q^{55} +5.57784i q^{57} +(-5.92039 - 8.67547i) q^{58} +(-2.39390 + 8.93417i) q^{59} +(4.33777 + 1.69807i) q^{60} +(1.71139 + 6.38698i) q^{61} +(-6.53023 + 2.28823i) q^{62} +(-3.48998 - 7.19862i) q^{64} +(0.501575 - 0.868753i) q^{65} +(-4.16601 - 3.58197i) q^{66} +(5.94825 + 1.59383i) q^{67} +(-2.37214 - 15.6452i) q^{68} +(-8.21037 - 8.21037i) q^{69} +1.99534i q^{71} +(-15.2611 + 8.09134i) q^{72} +(6.69237 - 3.86384i) q^{73} +(0.141075 + 1.87153i) q^{74} +(12.8384 - 3.44004i) q^{75} +(-0.410678 + 3.67375i) q^{76} +(1.83437 + 5.23497i) q^{78} +(-4.63378 + 8.02594i) q^{79} +(2.73198 + 1.43778i) q^{80} +(4.98751 + 8.63862i) q^{81} +(3.95146 + 0.745866i) q^{82} +(4.78537 - 4.78537i) q^{83} +(4.31797 + 4.31797i) q^{85} +(0.967673 - 0.660369i) q^{86} +(-19.4098 + 11.2063i) q^{87} +(-2.48015 - 2.66594i) q^{88} +(1.84016 + 1.06242i) q^{89} +(2.88957 - 6.00698i) q^{90} +(-4.80313 - 6.01213i) q^{92} +(3.82162 + 14.2625i) q^{93} +(-6.13582 - 5.27563i) q^{94} +(-0.713270 - 1.23542i) q^{95} +(-15.8775 + 6.27155i) q^{96} +9.01961 q^{97} +(-5.55926 + 5.55926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.262311	−	1.38967i	0.185482	−	0.982648i
$2$	0.262311	−	1.38967i	0.185482	−	0.982648i
$3$	−2.91496	−	0.781062i	−1.68295	−	0.450946i	−0.714398	−	0.699740i	$-0.753299\pi$
$3$	−2.91496	−	0.781062i	−1.68295	−	0.450946i	−0.968557	+	0.248794i	$0.919966\pi$
$4$	−1.86239	−	0.729053i	−0.931193	−	0.364526i
$5$	0.745506	−	0.199758i	0.333400	−	0.0893344i	−0.0882353	−	0.996100i	$-0.528123\pi$
$5$	0.745506	−	0.199758i	0.333400	−	0.0893344i	0.421636	+	0.906765i	$0.361456\pi$
$6$	−1.85005	+	3.84597i	−0.755279	+	1.57011i
$7$		0			0
$7$		0			0
$8$	−1.50167	+	2.39687i	−0.530920	+	0.847422i
$9$	5.28887	+	3.05353i	1.76296	+	1.01784i
$10$	−0.0820438	−	1.08841i	−0.0259445	−	0.344185i
$11$	−0.333193	+	1.24349i	−0.100462	+	0.374928i	−0.997791	−	0.0664342i	$-0.978838\pi$
$11$	−0.333193	+	1.24349i	−0.100462	+	0.374928i	0.897329	+	0.441362i	$0.145504\pi$
$12$	4.85935	+	3.57980i	1.40277	+	1.03340i
$13$	0.919058	−	0.919058i	0.254901	−	0.254901i	−0.568076	−	0.822976i	$-0.692312\pi$
$13$	0.919058	−	0.919058i	0.254901	−	0.254901i	0.822976	+	0.568076i	$0.192312\pi$
$14$		0			0
$15$	−2.32914			−0.601383
$16$	2.93696	+	2.71556i	0.734241	+	0.678889i
$17$	3.95601	+	6.85200i	0.959473	+	1.66186i	0.723784	+	0.690026i	$0.242401\pi$
$17$	3.95601	+	6.85200i	0.959473	+	1.66186i	0.235688	+	0.971829i	$0.424266\pi$
$18$	5.63074	−	6.54883i	1.32718	−	1.54357i
$19$	−0.478380	−	1.78534i	−0.109748	−	0.409585i	0.889093	−	0.457727i	$-0.151336\pi$
$19$	−0.478380	−	1.78534i	−0.109748	−	0.409585i	−0.998840	+	0.0481427i	$0.984670\pi$
$20$	−1.53405	−	0.171487i	−0.343025	−	0.0383457i
$21$		0			0
$22$	1.64065	+	0.789212i	0.349788	+	0.168261i
$23$	3.33211	+	1.92380i	0.694793	+	0.401139i	0.805405	−	0.592725i	$-0.201948\pi$
$23$	3.33211	+	1.92380i	0.694793	+	0.401139i	−0.110612	+	0.993864i	$0.535281\pi$
$24$	6.24941	−	5.81389i	1.27566	−	1.18676i
$25$	−3.81425	+	2.20216i	−0.762850	+	0.440432i
$26$	−1.03611	−	1.51827i	−0.203198	−	0.297757i
$27$	−6.63016	−	6.63016i	−1.27598	−	1.27598i
$28$		0			0
$29$	5.25154	−	5.25154i	0.975187	−	0.975187i	−0.0245125	−	0.999700i	$-0.507803\pi$
$29$	5.25154	−	5.25154i	0.975187	−	0.975187i	0.999700	+	0.0245125i	$0.00780335\pi$
$30$	−0.610960	+	3.23675i	−0.111546	+	0.590947i
$31$	−2.44642	−	4.23733i	−0.439391	−	0.761047i	0.558252	−	0.829672i	$-0.311472\pi$
$31$	−2.44642	−	4.23733i	−0.439391	−	0.761047i	−0.997643	+	0.0686244i	$0.978139\pi$
$32$	4.54413	−	3.36910i	0.803297	−	0.595579i
$33$	1.94249	−	3.36449i	0.338144	−	0.585683i
$34$	10.5598	−	3.70020i	1.81098	−	0.634580i
$35$		0			0
$36$	−7.62373	−	9.54272i	−1.27062	−	1.59045i
$37$	−1.28190	+	0.343485i	−0.210743	+	0.0564685i	−0.362646	−	0.931927i	$-0.618127\pi$
$37$	−1.28190	+	0.343485i	−0.210743	+	0.0564685i	0.151903	+	0.988395i	$0.451460\pi$
$38$	−2.60652	+	0.196478i	−0.422834	+	0.0318730i
$39$	−3.39686	+	1.96118i	−0.543933	+	0.314040i
$40$	−0.640710	+	2.08685i	−0.101305	+	0.329960i
$41$			2.84345i			0.444072i	0.975039	+	0.222036i	$0.0712702\pi$
$41$			2.84345i			0.444072i	−0.975039	+	0.222036i	$0.928730\pi$
$42$		0			0
$43$	0.585764	+	0.585764i	0.0893282	+	0.0893282i	0.750359	−	0.661031i	$-0.229881\pi$
$43$	0.585764	+	0.585764i	0.0893282	+	0.0893282i	−0.661031	+	0.750359i	$0.729881\pi$
$44$	1.52711	−	2.07295i	0.230220	−	0.312509i
$45$	4.55285	+	1.21993i	0.678699	+	0.181857i
$46$	3.54750	−	4.12591i	0.523050	−	0.608333i
$47$	2.86095	−	4.95532i	0.417313	−	0.722807i	−0.578355	−	0.815785i	$-0.696305\pi$
$47$	2.86095	−	4.95532i	0.417313	−	0.722807i	0.995668	+	0.0929777i	$0.0296385\pi$
$48$	−6.44012	−	10.2097i	−0.929551	−	1.47364i
$49$		0			0
$50$	2.05976	+	5.87821i	0.291294	+	0.831305i
$51$	−6.17977	−	23.0632i	−0.865341	−	3.22950i
$52$	−2.38168	+	1.04160i	−0.330280	+	0.144444i
$53$	2.54947	−	9.51475i	0.350197	−	1.30695i	−0.536226	−	0.844075i	$-0.680150\pi$
$53$	2.54947	−	9.51475i	0.350197	−	1.30695i	0.886422	−	0.462877i	$-0.153183\pi$
$54$	−10.9529	+	7.47460i	−1.49050	+	1.01716i
$55$			0.993590i			0.133976i
$56$		0			0
$57$			5.57784i			0.738803i
$58$	−5.92039	−	8.67547i	−0.777386	−	1.13914i
$59$	−2.39390	+	8.93417i	−0.311660	+	1.16313i	0.615400	+	0.788215i	$0.288995\pi$
$59$	−2.39390	+	8.93417i	−0.311660	+	1.16313i	−0.927059	+	0.374915i	$0.877672\pi$
$60$	4.33777	+	1.69807i	0.560003	+	0.219220i
$61$	1.71139	+	6.38698i	0.219121	+	0.817769i	0.984675	+	0.174398i	$0.0557980\pi$
$61$	1.71139	+	6.38698i	0.219121	+	0.817769i	−0.765555	+	0.643371i	$0.777535\pi$
$62$	−6.53023	+	2.28823i	−0.829340	+	0.290606i
$63$		0			0
$64$	−3.48998	−	7.19862i	−0.436247	−	0.899827i
$65$	0.501575	−	0.868753i	0.0622127	−	0.107755i
$66$	−4.16601	−	3.58197i	−0.512801	−	0.440910i
$67$	5.94825	+	1.59383i	0.726695	+	0.194717i	0.603157	−	0.797623i	$-0.293909\pi$
$67$	5.94825	+	1.59383i	0.726695	+	0.194717i	0.123538	+	0.992340i	$0.460576\pi$
$68$	−2.37214	−	15.6452i	−0.287664	−	1.89726i
$69$	−8.21037	−	8.21037i	−0.988413	−	0.988413i
$70$		0			0
$71$			1.99534i			0.236803i	0.992966	+	0.118402i	$0.0377770\pi$
$71$			1.99534i			0.236803i	−0.992966	+	0.118402i	$0.962223\pi$
$72$	−15.2611	+	8.09134i	−1.79853	+	0.953574i
$73$	6.69237	−	3.86384i	0.783283	−	0.452229i	−0.0543096	−	0.998524i	$-0.517296\pi$
$73$	6.69237	−	3.86384i	0.783283	−	0.452229i	0.837592	+	0.546296i	$0.183962\pi$
$74$	0.141075	+	1.87153i	0.0163996	+	0.217560i
$75$	12.8384	−	3.44004i	1.48245	−	0.397222i
$76$	−0.410678	+	3.67375i	−0.0471080	+	0.421408i
$77$		0			0
$78$	1.83437	+	5.23497i	0.207701	+	0.592743i
$79$	−4.63378	+	8.02594i	−0.521341	+	0.902989i	0.478351	+	0.878169i	$0.341235\pi$
$79$	−4.63378	+	8.02594i	−0.521341	+	0.902989i	−0.999692	+	0.0248202i	$0.992099\pi$
$80$	2.73198	+	1.43778i	0.305444	+	0.160749i
$81$	4.98751	+	8.63862i	0.554168	+	0.959847i
$82$	3.95146	+	0.745866i	0.436366	+	0.0823672i
$83$	4.78537	−	4.78537i	0.525263	−	0.525263i	−0.393893	−	0.919156i	$-0.628872\pi$
$83$	4.78537	−	4.78537i	0.525263	−	0.525263i	0.919156	+	0.393893i	$0.128872\pi$
$84$		0			0
$85$	4.31797	+	4.31797i	0.468349	+	0.468349i
$86$	0.967673	−	0.660369i	0.104347	−	0.0712094i
$87$	−19.4098	+	11.2063i	−2.08095	+	1.20144i
$88$	−2.48015	−	2.66594i	−0.264385	−	0.284190i
$89$	1.84016	+	1.06242i	0.195057	+	0.112616i	0.594348	−	0.804208i	$-0.297410\pi$
$89$	1.84016	+	1.06242i	0.195057	+	0.112616i	−0.399291	+	0.916824i	$0.630744\pi$
$90$	2.88957	−	6.00698i	0.304588	−	0.633191i
$91$		0			0
$92$	−4.80313	−	6.01213i	−0.500761	−	0.626808i
$93$	3.82162	+	14.2625i	0.396283	+	1.47895i
$94$	−6.13582	−	5.27563i	−0.632861	−	0.544139i
$95$	−0.713270	−	1.23542i	−0.0731800	−	0.126751i
$96$	−15.8775	+	6.27155i	−1.62049	+	0.640088i
$97$	9.01961			0.915802			0.457901	−	0.889003i	$-0.348601\pi$
$97$	9.01961			0.915802			0.457901	+	0.889003i	$0.348601\pi$
$98$		0			0
$99$	−5.55926	+	5.55926i	−0.558727	+	0.558727i
$100$	8.70910	−	1.32048i	0.870910	−	0.132048i
$101$	1.29142	−	4.81966i	0.128501	−	0.479574i	−0.871439	−	0.490504i	$-0.836813\pi$
$101$	1.29142	−	4.81966i	0.128501	−	0.479574i	0.999940	+	0.0109304i	$0.00347933\pi$
$102$	−33.6714	+	2.53813i	−3.33396	+	0.251313i
$103$	10.1524	+	5.86151i	1.00035	+	0.577551i	0.908351	−	0.418208i	$-0.137342\pi$
$103$	10.1524	+	5.86151i	1.00035	+	0.577551i	0.0919971	+	0.995759i	$0.470675\pi$
$104$	0.822742	+	3.58299i	0.0806765	+	0.351341i
$105$		0			0
$106$	−12.5536	−	6.03875i	−1.21932	−	0.586536i
$107$	6.97171	−	1.86807i	0.673981	−	0.180593i	0.0944336	−	0.995531i	$-0.469896\pi$
$107$	6.97171	−	1.86807i	0.673981	−	0.180593i	0.579547	+	0.814938i	$0.303229\pi$
$108$	7.51418	+	17.1817i	0.723052	+	1.65331i
$109$	10.9026	+	2.92133i	1.04428	+	0.279813i	0.739884	−	0.672734i	$-0.234880\pi$
$109$	10.9026	+	2.92133i	1.04428	+	0.279813i	0.304391	+	0.952547i	$0.401547\pi$
$110$	1.38077	+	0.260629i	0.131651	+	0.0248500i
$111$	4.00498			0.380136
$112$		0			0
$113$	9.15066			0.860821			0.430411	−	0.902633i	$-0.358369\pi$
$113$	9.15066			0.860821			0.430411	+	0.902633i	$0.358369\pi$
$114$	7.75137	+	1.46313i	0.725983	+	0.137034i
$115$	2.86840	+	0.768586i	0.267480	+	0.0716710i
$116$	−13.6091	+	5.95175i	−1.26357	+	0.552606i
$117$	7.66715	−	2.05441i	0.708829	−	0.189930i
$118$	11.7876	+	5.67027i	1.08514	+	0.521991i
$119$		0			0
$120$	3.49761	−	5.58266i	0.319286	−	0.509625i
$121$	8.09102	+	4.67135i	0.735547	+	0.424668i
$122$	9.32473	−	0.702894i	0.844222	−	0.0636371i
$123$	2.22091	−	8.28853i	0.200252	−	0.747352i
$124$	1.46695	+	9.67512i	0.131736	+	0.868852i
$125$	−5.13239	+	5.13239i	−0.459055	+	0.459055i
$126$		0			0
$127$	17.4281			1.54649			0.773245	−	0.634108i	$-0.218632\pi$
$127$	17.4281			1.54649			0.773245	+	0.634108i	$0.218632\pi$
$128$	−10.9192	+	2.96165i	−0.965129	+	0.261776i
$129$	−1.24996	−	2.16500i	−0.110053	−	0.190617i
$130$	−1.07571	−	0.924908i	−0.0943464	−	0.0811198i
$131$	−2.71575	−	10.1353i	−0.237276	−	0.885527i	−0.977110	−	0.212737i	$-0.931762\pi$
$131$	−2.71575	−	10.1353i	−0.237276	−	0.885527i	0.739833	−	0.672790i	$-0.234904\pi$
$132$	−6.07056	+	4.84981i	−0.528375	+	0.422121i
$133$		0			0
$134$	3.77520	−	7.84805i	0.326127	−	0.677969i
$135$	−6.26725	−	3.61840i	−0.539399	−	0.311422i
$136$	−22.3640	−	0.807413i	−1.91770	−	0.0692351i
$137$	−5.24143	+	3.02614i	−0.447806	+	0.258541i	−0.706903	−	0.707310i	$-0.749908\pi$
$137$	−5.24143	+	3.02614i	−0.447806	+	0.258541i	0.259097	+	0.965851i	$0.416575\pi$
$138$	−13.5634	+	9.25607i	−1.15459	+	0.787929i
$139$	4.50305	+	4.50305i	0.381944	+	0.381944i	0.871802	−	0.489858i	$-0.162952\pi$
$139$	4.50305	+	4.50305i	0.381944	+	0.381944i	−0.489858	+	0.871802i	$0.662952\pi$
$140$		0			0
$141$	−12.2100	+	12.2100i	−1.02827	+	1.02827i
$142$	2.77287	+	0.523399i	0.232694	+	0.0439227i
$143$	0.836620	+	1.44907i	0.0699616	+	0.121177i
$144$	7.24119	+	23.3303i	0.603432	+	1.94419i
$145$	2.86602	−	4.96409i	0.238010	−	0.412245i
$146$	−3.61400	−	10.3137i	−0.299097	−	0.853571i
$147$		0			0
$148$	2.63782	+	0.294874i	0.216827	+	0.0242385i
$149$	−14.6597	+	3.92804i	−1.20097	+	0.321798i	−0.803211	−	0.595694i	$-0.796877\pi$
$149$	−14.6597	+	3.92804i	−1.20097	+	0.321798i	−0.397754	+	0.917492i	$0.630210\pi$
$150$	−1.41288	−	18.7436i	−0.115361	−	1.53041i
$151$	−12.8763	+	7.43412i	−1.04786	+	0.604980i	−0.922049	−	0.387074i	$-0.873486\pi$
$151$	−12.8763	+	7.43412i	−1.04786	+	0.604980i	−0.125808	+	0.992055i	$0.540152\pi$
$152$	4.99759	+	1.53437i	0.405358	+	0.124454i
$153$			48.3192i			3.90637i
$154$		0			0
$155$	−2.67026	−	2.67026i	−0.214481	−	0.214481i
$156$	7.75607	−	1.17598i	0.620983	−	0.0941538i
$157$	10.9861	+	2.94372i	0.876786	+	0.234934i	0.669020	−	0.743244i	$-0.266714\pi$
$157$	10.9861	+	2.94372i	0.876786	+	0.234934i	0.207766	+	0.978178i	$0.433381\pi$
$158$	9.93795	+	8.54473i	0.790621	+	0.679782i
$159$	−14.8632	+	25.7439i	−1.17873	+	2.04162i
$160$	2.71468	−	3.41941i	0.214614	−	0.270328i
$161$		0			0
$162$	13.3131	−	4.66501i	1.04598	−	0.366518i
$163$	2.61713	+	9.76727i	0.204990	+	0.765032i	0.989453	+	0.144856i	$0.0462720\pi$
$163$	2.61713	+	9.76727i	0.204990	+	0.765032i	−0.784463	+	0.620176i	$0.787061\pi$
$164$	2.07302	−	5.29559i	0.161876	−	0.413516i
$165$	0.776055	−	2.89628i	0.0604158	−	0.225475i
$166$	−5.39485	−	7.90536i	−0.418721	−	0.613575i
$167$			2.61575i			0.202413i	0.994865	+	0.101207i	$0.0322703\pi$
$167$			2.61575i			0.202413i	−0.994865	+	0.101207i	$0.967730\pi$
$168$		0			0
$169$			11.3107i			0.870051i
$170$	7.13322	−	4.86792i	0.547093	−	0.373352i
$171$	2.92150	−	10.9032i	0.223412	−	0.833786i
$172$	−0.663866	−	1.51797i	−0.0506193	−	0.115744i
$173$	−2.64600	−	9.87502i	−0.201172	−	0.750784i	−0.990582	−	0.136918i	$-0.956280\pi$
$173$	−2.64600	−	9.87502i	−0.201172	−	0.750784i	0.789410	−	0.613866i	$-0.210386\pi$
$174$	10.4816	+	29.9129i	0.794612	+	2.26769i
$175$		0			0
$176$	−4.35535	+	2.74729i	−0.328297	+	0.207085i
$177$	13.9563	−	24.1730i	1.04902	−	1.81695i
$178$	1.95911	−	2.27854i	0.146841	−	0.170784i
$179$	−15.0929	−	4.04414i	−1.12810	−	0.302273i	−0.353942	−	0.935267i	$-0.615159\pi$
$179$	−15.0929	−	4.04414i	−1.12810	−	0.302273i	−0.774156	+	0.632994i	$0.781826\pi$
$180$	−7.58977	−	5.59126i	−0.565708	−	0.416748i
$181$	−12.8671	−	12.8671i	−0.956407	−	0.956407i	0.0426817	−	0.999089i	$-0.486410\pi$
$181$	−12.8671	−	12.8671i	−0.956407	−	0.956407i	−0.999089	+	0.0426817i	$0.986410\pi$
$182$		0			0
$183$		−	19.9545i		−	1.47508i
$184$	−9.61482	+	5.09773i	−0.708814	+	0.375810i
$185$	−0.887052	+	0.512140i	−0.0652174	+	0.0376533i
$186$	20.8226	−	1.56960i	1.52679	−	0.115089i
$187$	−9.83854	+	2.63623i	−0.719465	+	0.192780i
$188$	−8.94089	+	7.14293i	−0.652081	+	0.520952i
$189$		0			0
$190$	−1.90393	+	0.667149i	−0.138126	+	0.0484001i
$191$	0.254497	−	0.440801i	0.0184147	−	0.0318952i	−0.856671	−	0.515863i	$-0.827471\pi$
$191$	0.254497	−	0.440801i	0.0184147	−	0.0318952i	0.875086	+	0.483968i	$0.160805\pi$
$192$	4.55058	+	23.7096i	0.328410	+	1.71109i
$193$	−2.41417	−	4.18147i	−0.173776	−	0.300989i	0.765961	−	0.642887i	$-0.222264\pi$
$193$	−2.41417	−	4.18147i	−0.173776	−	0.300989i	−0.939737	+	0.341898i	$0.888930\pi$
$194$	2.36594	−	12.5343i	0.169865	−	0.899911i
$195$	−2.14062	+	2.14062i	−0.153293	+	0.153293i
$196$		0			0
$197$	3.02638	+	3.02638i	0.215621	+	0.215621i	0.806650	−	0.591029i	$-0.201278\pi$
$197$	3.02638	+	3.02638i	0.215621	+	0.215621i	−0.591029	+	0.806650i	$0.701278\pi$
$198$	6.26731	+	9.18382i	0.445398	+	0.652665i
$199$	6.56029	−	3.78758i	0.465046	−	0.268495i	−0.249117	−	0.968473i	$-0.580140\pi$
$199$	6.56029	−	3.78758i	0.465046	−	0.268495i	0.714164	+	0.699979i	$0.246807\pi$
$200$	0.449456	−	12.4492i	0.0317813	−	0.880290i
$201$	−16.0941	−	9.29191i	−1.13519	−	0.655401i
$202$	−6.35900	−	3.05890i	−0.447417	−	0.215224i
$203$		0			0
$204$	−5.30519	+	47.4580i	−0.371438	+	3.32272i
$205$	0.568000	+	2.11981i	0.0396709	+	0.148054i
$206$	10.8087	−	12.5710i	0.753076	−	0.875865i
$207$	11.7487	+	20.3494i	0.816594	+	1.41438i
$208$	5.19500	−	0.203486i	0.360208	−	0.0141092i
$209$	2.37945			0.164590
$210$		0			0
$211$	6.60935	−	6.60935i	0.455006	−	0.455006i	−0.442006	−	0.897012i	$-0.645733\pi$
$211$	6.60935	−	6.60935i	0.455006	−	0.455006i	0.897012	+	0.442006i	$0.145733\pi$
$212$	−11.6849	+	15.8614i	−0.802519	+	1.08937i
$213$	1.55848	−	5.81634i	0.106785	−	0.398529i
$214$	−0.767245	−	10.1784i	−0.0524478	−	0.695783i
$215$	0.553701	+	0.319680i	0.0377621	+	0.0218020i
$216$	25.8479	−	5.93532i	1.75873	−	0.403848i
$217$		0			0
$218$	6.91955	−	14.3847i	0.468651	−	0.974254i
$219$	−22.5259	+	6.03580i	−1.52216	+	0.407862i
$220$	0.724380	−	1.85045i	0.0488377	−	0.124757i
$221$	9.93319	+	2.66159i	0.668179	+	0.179038i
$222$	1.05055	−	5.56561i	0.0705083	−	0.373540i
$223$	20.4381			1.36864			0.684319	−	0.729183i	$-0.260100\pi$
$223$	20.4381			1.36864			0.684319	+	0.729183i	$0.260100\pi$
$224$		0			0
$225$	−26.8974			−1.79316
$226$	2.40032	−	12.7164i	0.159667	−	0.845884i
$227$	11.3952	+	3.05333i	0.756326	+	0.202657i	0.616322	−	0.787494i	$-0.288622\pi$
$227$	11.3952	+	3.05333i	0.756326	+	0.202657i	0.140004	+	0.990151i	$0.455289\pi$
$228$	4.06654	−	10.3881i	0.269313	−	0.687968i
$229$	−13.1330	+	3.51899i	−0.867856	+	0.232541i	−0.665160	−	0.746700i	$-0.731637\pi$
$229$	−13.1330	+	3.51899i	−0.867856	+	0.232541i	−0.202696	+	0.979242i	$0.564970\pi$
$230$	1.82050	−	3.78453i	0.120040	−	0.249545i
$231$		0			0
$232$	4.70118	+	20.4734i	0.308648	+	1.34414i
$233$	−18.6628	−	10.7750i	−1.22264	−	0.705893i	−0.257162	−	0.966368i	$-0.582787\pi$
$233$	−18.6628	−	10.7750i	−1.22264	−	0.705893i	−0.965481	+	0.260475i	$0.916121\pi$
$234$	−0.843779	−	11.1937i	−0.0551595	−	0.731757i
$235$	1.14300	−	4.26572i	0.0745608	−	0.278265i
$236$	10.9719	−	14.8936i	0.714207	−	0.969490i
$237$	19.7760	−	19.7760i	1.28459	−	1.28459i
$238$		0			0
$239$	14.5125			0.938733			0.469366	−	0.883004i	$-0.344482\pi$
$239$	14.5125			0.938733			0.469366	+	0.883004i	$0.344482\pi$
$240$	−6.84061	−	6.32492i	−0.441560	−	0.408272i
$241$	−4.59046	−	7.95090i	−0.295697	−	0.512163i	0.679450	−	0.733722i	$-0.262219\pi$
$241$	−4.59046	−	7.95090i	−0.295697	−	0.512163i	−0.975147	+	0.221560i	$0.928885\pi$
$242$	8.61402	−	10.0185i	0.553730	−	0.644016i
$243$	−0.510685	−	1.90590i	−0.0327604	−	0.122264i
$244$	1.46919	−	13.1427i	0.0940549	−	0.841376i
$245$		0			0
$246$	−10.9358	−	5.26051i	−0.697241	−	0.335398i
$247$	−2.08049	−	1.20117i	−0.132378	−	0.0764287i
$248$	13.8301	+	0.499310i	0.878210	+	0.0317062i
$249$	−17.6868	+	10.2115i	−1.12086	+	0.647128i
$250$	5.78607	+	8.47863i	0.365943	+	0.536236i
$251$	−9.13628	−	9.13628i	−0.576677	−	0.576677i	0.357309	−	0.933986i	$-0.383694\pi$
$251$	−9.13628	−	9.13628i	−0.576677	−	0.576677i	−0.933986	+	0.357309i	$0.883694\pi$
$252$		0			0
$253$	−3.50246	+	3.50246i	−0.220198	+	0.220198i
$254$	4.57157	−	24.2193i	0.286846	−	1.51965i
$255$	−9.21411	−	15.9593i	−0.577010	−	0.999411i
$256$	1.25151	+	15.9510i	0.0782194	+	0.996936i
$257$	−4.85503	+	8.40916i	−0.302849	+	0.524549i	−0.976780	−	0.214245i	$-0.931271\pi$
$257$	−4.85503	+	8.40916i	−0.302849	+	0.524549i	0.673931	+	0.738794i	$0.264604\pi$
$258$	−3.33652	+	1.16914i	−0.207723	+	0.0727873i
$259$		0			0
$260$	−1.56749	+	1.25228i	−0.0972117	+	0.0776630i
$261$	43.8105	−	11.7390i	2.71180	−	0.726625i
$262$	−14.7972	+	1.11540i	−0.914172	+	0.0689098i
$263$	9.24140	−	5.33552i	0.569849	−	0.329002i	−0.187240	−	0.982314i	$-0.559954\pi$
$263$	9.24140	−	5.33552i	0.569849	−	0.329002i	0.757089	+	0.653312i	$0.226621\pi$
$264$	5.14727	+	9.70826i	0.316793	+	0.597502i
$265$		−	7.60258i		−	0.467023i
$266$		0			0
$267$	−4.53418	−	4.53418i	−0.277487	−	0.277487i
$268$	−9.91596	−	7.30492i	−0.605714	−	0.446219i
$269$	−7.31835	−	1.96094i	−0.446207	−	0.119561i	0.0287169	−	0.999588i	$-0.490858\pi$
$269$	−7.31835	−	1.96094i	−0.446207	−	0.119561i	−0.474924	+	0.880027i	$0.657525\pi$
$270$	−6.67236	+	7.76029i	−0.406067	+	0.472276i
$271$	−5.62243	+	9.73834i	−0.341538	+	0.591562i	−0.984719	−	0.174153i	$-0.944281\pi$
$271$	−5.62243	+	9.73834i	−0.341538	+	0.591562i	0.643180	+	0.765715i	$0.277615\pi$
$272$	−6.98836	+	30.8668i	−0.423731	+	1.87158i
$273$		0			0
$274$	2.83047	+	8.07767i	0.170995	+	0.487990i
$275$	−1.46749	−	5.47674i	−0.0884929	−	0.330260i
$276$	9.30509	+	21.2767i	0.560101	+	1.28071i
$277$	5.50691	−	20.5521i	0.330878	−	1.23485i	−0.577391	−	0.816467i	$-0.695929\pi$
$277$	5.50691	−	20.5521i	0.330878	−	1.23485i	0.908269	−	0.418386i	$-0.137404\pi$
$278$	7.43897	−	5.07657i	0.446160	−	0.304472i
$279$		−	29.8809i		−	1.78892i
$280$		0			0
$281$		−	20.0973i		−	1.19891i	−0.800410	−	0.599453i	$-0.795385\pi$
$281$		−	20.0973i		−	1.19891i	0.800410	−	0.599453i	$-0.204615\pi$
$282$	13.7651	+	20.1707i	0.819699	+	1.20115i
$283$	−5.29502	+	19.7613i	−0.314756	+	1.17469i	0.609460	+	0.792816i	$0.291386\pi$
$283$	−5.29502	+	19.7613i	−0.314756	+	1.17469i	−0.924216	+	0.381869i	$0.875281\pi$
$284$	1.45471	−	3.71609i	0.0863210	−	0.220509i
$285$	1.11422	+	4.15831i	0.0660005	+	0.246317i
$286$	2.23319	−	0.782522i	0.132051	−	0.0462715i
$287$		0			0
$288$	34.3210	−	3.94309i	2.02238	−	0.232349i
$289$	−22.8000	+	39.4907i	−1.34117	+	2.32298i
$290$	−6.14668	−	5.28497i	−0.360946	−	0.310344i
$291$	−26.2918	−	7.04487i	−1.54125	−	0.412978i
$292$	−15.2807	+	2.31687i	−0.894237	+	0.135585i
$293$	10.4368	+	10.4368i	0.609726	+	0.609726i	0.942875	−	0.333148i	$-0.108111\pi$
$293$	10.4368	+	10.4368i	0.609726	+	0.609726i	−0.333148	+	0.942875i	$0.608111\pi$
$294$		0			0
$295$			7.13868i			0.415630i
$296$	1.10171	−	3.58835i	0.0640353	−	0.208569i
$297$	10.4537	−	6.03544i	0.606585	−	0.350212i
$298$	1.61331	+	21.4025i	0.0934566	+	1.23981i
$299$	4.83048	−	1.29432i	0.279354	−	0.0748527i
$300$	−26.4181	−	2.95320i	−1.52525	−	0.170503i
$301$		0			0
$302$	6.95342	+	19.8439i	0.400124	+	1.14189i
$303$	−7.52890	+	13.0404i	−0.432524	+	0.749153i
$304$	3.44320	−	6.54254i	0.197481	−	0.375240i
$305$	2.55170	+	4.41967i	0.146110	+	0.253070i
$306$	67.1479	+	12.6746i	3.83859	+	0.724561i
$307$	−4.72698	+	4.72698i	−0.269783	+	0.269783i	−0.829013	−	0.559230i	$-0.811097\pi$
$307$	−4.72698	+	4.72698i	−0.269783	+	0.269783i	0.559230	+	0.829013i	$0.311097\pi$
$308$		0			0
$309$	−25.0157	−	25.0157i	−1.42310	−	1.42310i
$310$	−4.41124	+	3.01036i	−0.250541	+	0.170977i
$311$	4.82684	−	2.78678i	0.273705	−	0.158024i	−0.356865	−	0.934156i	$-0.616154\pi$
$311$	4.82684	−	2.78678i	0.273705	−	0.158024i	0.630570	+	0.776132i	$0.282821\pi$
$312$	0.400273	−	11.0869i	0.0226610	−	0.627671i
$313$	−10.2429	−	5.91372i	−0.578961	−	0.334263i	0.181760	−	0.983343i	$-0.441821\pi$
$313$	−10.2429	−	5.91372i	−0.578961	−	0.334263i	−0.760720	+	0.649080i	$0.775154\pi$
$314$	6.97258	−	14.4949i	0.393485	−	0.817996i
$315$		0			0
$316$	14.4812	−	11.5691i	0.814632	−	0.650814i
$317$	−1.17054	−	4.36851i	−0.0657441	−	0.245360i	0.925231	−	0.379403i	$-0.123871\pi$
$317$	−1.17054	−	4.36851i	−0.0657441	−	0.245360i	−0.990976	+	0.134043i	$0.957204\pi$
$318$	31.8768	+	27.4079i	1.78756	+	1.53696i
$319$	4.78048	+	8.28004i	0.267656	+	0.463593i
$320$	−4.03978	−	4.66946i	−0.225830	−	0.261031i
$321$	−21.7814			−1.21572
$322$		0			0
$323$	10.3407	−	10.3407i	0.575370	−	0.575370i
$324$	−2.99066	−	19.7246i	−0.166148	−	1.09581i
$325$	−1.48161	+	5.52943i	−0.0821848	+	0.306718i
$326$	14.2598	−	1.07490i	0.789779	−	0.0595332i
$327$	−29.4988	−	17.0311i	−1.63129	−	0.941824i
$328$	−6.81537	−	4.26992i	−0.376316	−	0.235767i
$329$		0			0
$330$	−3.82131	−	1.83819i	−0.210356	−	0.101189i
$331$	22.2142	−	5.95228i	1.22100	−	0.327167i	0.409934	−	0.912115i	$-0.365552\pi$
$331$	22.2142	−	5.95228i	1.22100	−	0.327167i	0.811071	+	0.584948i	$0.198885\pi$
$332$	−12.4010	+	5.42342i	−0.680593	+	0.297649i
$333$	−7.82866	−	2.09768i	−0.429008	−	0.114952i
$334$	3.63505	+	0.686141i	0.198901	+	0.0375440i
$335$	4.75284			0.259675
$336$		0			0
$337$	−16.6077			−0.904682			−0.452341	−	0.891845i	$-0.649411\pi$
$337$	−16.6077			−0.904682			−0.452341	+	0.891845i	$0.649411\pi$
$338$	15.7181	+	2.96691i	0.854954	+	0.161379i
$339$	−26.6738	−	7.14723i	−1.44872	−	0.388184i
$340$	−4.89370	−	11.1897i	−0.265398	−	0.606849i
$341$	6.08423	−	1.63026i	0.329479	−	0.0882838i
$342$	−14.3855	−	6.91995i	−0.777879	−	0.374188i
$343$		0			0
$344$	−2.28362	+	0.524376i	−0.123125	+	0.0282725i
$345$	−7.76097	−	4.48080i	−0.417837	−	0.241238i
$346$	−14.4171	+	1.08676i	−0.775070	+	0.0584244i
$347$	−4.00465	+	14.9456i	−0.214981	+	0.802320i	0.771192	+	0.636602i	$0.219661\pi$
$347$	−4.00465	+	14.9456i	−0.214981	+	0.802320i	−0.986173	+	0.165718i	$0.947006\pi$
$348$	44.3186	−	6.71961i	2.37572	−	0.360209i
$349$	−13.7065	+	13.7065i	−0.733694	+	0.733694i	−0.971349	−	0.237656i	$-0.923621\pi$
$349$	−13.7065	+	13.7065i	−0.733694	+	0.733694i	0.237656	+	0.971349i	$0.423621\pi$
$350$		0			0
$351$	−12.1870			−0.650494
$352$	2.67538	+	6.77317i	0.142598	+	0.361011i
$353$	−1.15032	−	1.99241i	−0.0612252	−	0.106045i	0.833788	−	0.552085i	$-0.186167\pi$
$353$	−1.15032	−	1.99241i	−0.0612252	−	0.106045i	−0.895013	+	0.446039i	$0.852834\pi$
$354$	−29.9317	−	25.7355i	−1.59085	−	1.36783i
$355$	0.398584	+	1.48754i	0.0211547	+	0.0789503i
$356$	−2.65253	−	3.32020i	−0.140584	−	0.175970i
$357$		0			0
$358$	−9.57907	+	19.9134i	−0.506270	+	1.05246i
$359$	6.28570	+	3.62905i	0.331747	+	0.191534i	0.656616	−	0.754225i	$-0.271987\pi$
$359$	6.28570	+	3.62905i	0.331747	+	0.191534i	−0.324870	+	0.945759i	$0.605320\pi$
$360$	−9.76090	+	9.08066i	−0.514445	+	0.478593i
$361$	13.4959	−	7.79186i	0.710310	−	0.410098i
$362$	−21.2563	+	14.5059i	−1.11721	+	0.762415i
$363$	−19.9364	−	19.9364i	−1.04639	−	1.04639i
$364$		0			0
$365$	4.21737	−	4.21737i	0.220747	−	0.220747i
$366$	−27.7303	−	5.23428i	−1.44948	−	0.273600i
$367$	13.4406	+	23.2797i	0.701591	+	1.21519i	0.967908	+	0.251306i	$0.0808601\pi$
$367$	13.4406	+	23.2797i	0.701591	+	1.21519i	−0.266316	+	0.963886i	$0.585807\pi$
$368$	4.56211	+	14.6987i	0.237817	+	0.766220i
$369$	−8.68255	+	15.0386i	−0.451995	+	0.782879i
$370$	0.479024	+	1.36705i	0.0249033	+	0.0710697i
$371$		0			0
$372$	3.28077	−	29.3484i	0.170100	−	1.52164i
$373$	1.29586	−	0.347226i	0.0670973	−	0.0179787i	−0.225114	−	0.974332i	$-0.572276\pi$
$373$	1.29586	−	0.347226i	0.0670973	−	0.0179787i	0.292212	+	0.956354i	$0.405609\pi$
$374$	1.08274	+	14.3639i	0.0559873	+	0.742738i
$375$	18.9694	−	10.9520i	0.979578	−	0.565559i
$376$	7.58105	+	14.2986i	0.390963	+	0.737393i
$377$		−	9.65295i		−	0.497152i
$378$		0			0
$379$	−15.3095	−	15.3095i	−0.786396	−	0.786396i	0.194506	−	0.980901i	$-0.437690\pi$
$379$	−15.3095	−	15.3095i	−0.786396	−	0.786396i	−0.980901	+	0.194506i	$0.937690\pi$
$380$	0.427698	+	2.82084i	0.0219404	+	0.144706i
$381$	−50.8021	−	13.6124i	−2.60267	−	0.697384i
$382$	−0.545812	−	0.469294i	−0.0279262	−	0.0240112i
$383$	4.04897	−	7.01302i	0.206893	−	0.358348i	−0.743842	−	0.668356i	$-0.766998\pi$
$383$	4.04897	−	7.01302i	0.206893	−	0.358348i	0.950734	+	0.310008i	$0.100332\pi$
$384$	34.1422	−	0.104547i	1.74231	−	0.00533513i
$385$		0			0
$386$	−6.44415	+	2.25807i	−0.327998	+	0.114933i
$387$	1.30938	+	4.88668i	0.0665596	+	0.248404i
$388$	−16.7980	−	6.57577i	−0.852789	−	0.333834i
$389$	−4.79714	+	17.9032i	−0.243225	+	0.907727i	0.731043	+	0.682332i	$0.239034\pi$
$389$	−4.79714	+	17.9032i	−0.243225	+	0.907727i	−0.974267	+	0.225395i	$0.927633\pi$
$390$	2.41326	+	3.53627i	0.122200	+	0.179066i
$391$			30.4422i			1.53953i
$392$		0			0
$393$			31.6652i			1.59730i
$394$	4.99953	−	3.41183i	0.251873	−	0.171885i
$395$	−1.85127	+	6.90902i	−0.0931473	+	0.347631i
$396$	14.4065	−	6.30050i	0.723953	−	0.316612i
$397$	4.35104	+	16.2383i	0.218372	+	0.814977i	0.984952	+	0.172828i	$0.0552904\pi$
$397$	4.35104	+	16.2383i	0.218372	+	0.814977i	−0.766580	+	0.642149i	$0.778043\pi$
$398$	−3.54267	−	10.1102i	−0.177578	−	0.506778i
$399$		0			0
$400$	−17.1824	−	3.89015i	−0.859120	−	0.194508i
$401$	−2.18786	+	3.78949i	−0.109257	+	0.189238i	−0.915469	−	0.402388i	$-0.868180\pi$
$401$	−2.18786	+	3.78949i	−0.109257	+	0.189238i	0.806213	+	0.591626i	$0.201514\pi$
$402$	−17.1344	+	19.9281i	−0.854585	+	0.993924i
$403$	−6.14276	−	1.64595i	−0.305993	−	0.0819905i
$404$	−5.91891	+	8.03454i	−0.294477	+	0.399734i
$405$	5.44385	+	5.44385i	0.270507	+	0.270507i
$406$		0			0
$407$		−	1.70848i		−	0.0846864i
$408$	64.5595	+	19.8212i	3.19617	+	0.981297i
$409$	0.103105	−	0.0595279i	0.00509823	−	0.00294347i	−0.497449	−	0.867493i	$-0.665730\pi$
$409$	0.103105	−	0.0595279i	0.00509823	−	0.00294347i	0.502547	+	0.864550i	$0.332396\pi$
$410$	3.09483	−	0.233287i	0.152843	−	0.0115212i
$411$	17.6422	−	4.72721i	0.870225	−	0.233176i
$412$	−14.6344	−	18.3180i	−0.720985	−	0.902465i
$413$		0			0
$414$	31.3609	−	10.9890i	1.54130	−	0.540082i
$415$	2.61161	−	4.52344i	0.128199	−	0.222047i
$416$	1.07992	−	7.27273i	0.0529476	−	0.356575i
$417$	−9.60906	−	16.6434i	−0.470558	−	0.815030i
$418$	0.624156	−	3.30666i	0.0305284	−	0.161734i
$419$	−21.5456	+	21.5456i	−1.05257	+	1.05257i	−0.0540333	+	0.998539i	$0.517208\pi$
$419$	−21.5456	+	21.5456i	−1.05257	+	1.05257i	−0.998539	+	0.0540333i	$0.982792\pi$
$420$		0			0
$421$	−0.254915	−	0.254915i	−0.0124238	−	0.0124238i	0.700868	−	0.713291i	$-0.252796\pi$
$421$	−0.254915	−	0.254915i	−0.0124238	−	0.0124238i	−0.713291	+	0.700868i	$0.752796\pi$
$422$	−7.45113	−	10.9185i	−0.362716	−	0.531506i
$423$	30.2624	−	17.4720i	1.47141	−	0.849519i
$424$	18.9772	+	20.3988i	0.921613	+	0.990652i
$425$	−30.1784	−	17.4235i	−1.46387	−	0.845164i
$426$	−7.67400	−	3.69147i	−0.371807	−	0.178852i
$427$		0			0
$428$	−14.3459	−	1.60369i	−0.693437	−	0.0775173i
$429$	−1.30690	−	4.87743i	−0.0630979	−	0.235484i
$430$	0.589492	−	0.685609i	0.0284278	−	0.0330630i
$431$	−12.1470	−	21.0393i	−0.585101	−	1.01343i	−0.994863	−	0.101232i	$-0.967721\pi$
$431$	−12.1470	−	21.0393i	−0.585101	−	1.01343i	0.409762	−	0.912193i	$-0.365612\pi$
$432$	−1.46797	−	37.4771i	−0.0706276	−	1.80312i
$433$	−19.6797			−0.945744			−0.472872	−	0.881131i	$-0.656783\pi$
$433$	−19.6797			−0.945744			−0.472872	+	0.881131i	$0.656783\pi$
$434$		0			0
$435$	−12.2316	+	12.2316i	−0.586461	+	0.586461i
$436$	−18.1750	−	13.3892i	−0.870423	−	0.641226i
$437$	1.84061	−	6.86925i	0.0880483	−	0.328601i
$438$	2.47900	+	32.8869i	0.118451	+	1.57140i
$439$	26.3901	+	15.2363i	1.25953	+	0.727190i	0.972983	−	0.230876i	$-0.0741590\pi$
$439$	26.3901	+	15.2363i	1.25953	+	0.727190i	0.286548	+	0.958066i	$0.407492\pi$
$440$	−2.38151	−	1.49204i	−0.113534	−	0.0711304i
$441$		0			0
$442$	6.30433	−	13.1057i	0.299866	−	0.623376i
$443$	3.77526	−	1.01158i	0.179368	−	0.0480615i	−0.168017	−	0.985784i	$-0.553736\pi$
$443$	3.77526	−	1.01158i	0.179368	−	0.0480615i	0.347385	+	0.937723i	$0.387070\pi$
$444$	−7.45882	−	2.91984i	−0.353980	−	0.138570i
$445$	1.58408	+	0.424452i	0.0750924	+	0.0201209i
$446$	5.36114	−	28.4023i	0.253857	−	1.34489i
$447$	45.8004			2.16628
$448$		0			0
$449$	38.0210			1.79432			0.897161	−	0.441704i	$-0.145626\pi$
$449$	38.0210			1.79432			0.897161	+	0.441704i	$0.145626\pi$
$450$	−7.05549	+	37.3787i	−0.332599	+	1.76205i
$451$	−3.53581	−	0.947417i	−0.166495	−	0.0446121i
$452$	−17.0421	−	6.67131i	−0.801591	−	0.313792i
$453$	43.3404	−	11.6130i	2.03631	−	0.545627i
$454$	7.23222	−	15.0347i	0.339425	−	0.705613i
$455$		0			0
$456$	−13.3694	−	8.37607i	−0.626077	−	0.392245i
$457$	−15.0844	−	8.70896i	−0.705616	−	0.407388i	0.103819	−	0.994596i	$-0.466894\pi$
$457$	−15.0844	−	8.70896i	−0.705616	−	0.407388i	−0.809436	+	0.587208i	$0.800227\pi$
$458$	1.44531	+	19.1737i	0.0675347	+	0.895929i
$459$	19.2009	−	71.6588i	0.896223	−	3.34475i
$460$	−4.78173	−	3.52262i	−0.222949	−	0.164243i
$461$	27.4189	−	27.4189i	1.27703	−	1.27703i	0.334701	−	0.942324i	$-0.391365\pi$
$461$	27.4189	−	27.4189i	1.27703	−	1.27703i	0.942324	−	0.334701i	$-0.108635\pi$
$462$		0			0
$463$	−40.5988			−1.88679			−0.943394	−	0.331674i	$-0.892387\pi$
$463$	−40.5988			−1.88679			−0.943394	+	0.331674i	$0.892387\pi$
$464$	29.6844	−	1.16273i	1.37807	−	0.0539784i
$465$	5.69808	+	9.86936i	0.264242	+	0.457681i
$466$	−19.8692	+	23.1089i	−0.920422	+	1.07050i
$467$	2.38296	+	8.89334i	0.110270	+	0.411535i	0.998890	−	0.0471109i	$-0.0150014\pi$
$467$	2.38296	+	8.89334i	0.110270	+	0.411535i	−0.888619	+	0.458646i	$0.848335\pi$
$468$	−15.7770	−	1.76366i	−0.729291	−	0.0815253i
$469$		0			0
$470$	−5.62813	−	2.70733i	−0.259606	−	0.124880i
$471$	−29.7248	−	17.1616i	−1.36965	−	0.790767i
$472$	−17.8192	−	19.1540i	−0.820195	−	0.881637i
$473$	−0.923566	+	0.533221i	−0.0424656	+	0.0245175i
$474$	−22.2948	−	32.6697i	−1.02403	−	1.50057i
$475$	5.75626	+	5.75626i	0.264115	+	0.264115i
$476$		0			0
$477$	42.5374	−	42.5374i	1.94765	−	1.94765i
$478$	3.80677	−	20.1676i	0.174118	−	0.922444i
$479$	−3.73955	−	6.47710i	−0.170865	−	0.295946i	0.767858	−	0.640620i	$-0.221323\pi$
$479$	−3.73955	−	6.47710i	−0.170865	−	0.295946i	−0.938722	+	0.344674i	$0.887989\pi$
$480$	−10.5839	+	7.84713i	−0.483089	+	0.358171i
$481$	−0.862460	+	1.49383i	−0.0393248	+	0.0681126i
$482$	−12.2533	+	4.29363i	−0.558122	+	0.195569i
$483$		0			0
$484$	−11.6629	−	14.5986i	−0.530134	−	0.663575i
$485$	6.72417	−	1.80174i	0.305329	−	0.0818126i
$486$	−2.78254	+	0.209746i	−0.126218	+	0.00951429i
$487$	17.8451	−	10.3029i	0.808640	−	0.466868i	−0.0378436	−	0.999284i	$-0.512049\pi$
$487$	17.8451	−	10.3029i	0.808640	−	0.466868i	0.846483	+	0.532415i	$0.178716\pi$
$488$	−17.8787	−	5.48916i	−0.809331	−	0.248483i
$489$		−	30.5154i		−	1.37995i
$490$		0			0
$491$	1.13401	+	1.13401i	0.0511771	+	0.0511771i	0.732232	−	0.681055i	$-0.238479\pi$
$491$	1.13401	+	1.13401i	0.0511771	+	0.0511771i	−0.681055	+	0.732232i	$0.738479\pi$
$492$	−10.1790	+	13.8173i	−0.458903	+	0.622932i
$493$	56.7587	+	15.2085i	2.55628	+	0.684954i
$494$	−2.21497	+	2.57612i	−0.0996562	+	0.115905i
$495$	−3.03396	+	5.25497i	−0.136366	+	0.236193i
$496$	4.32165	−	19.0883i	0.194048	−	0.857090i
$497$		0			0
$498$	9.55121	+	27.2575i	0.428000	+	1.22144i
$499$	8.63159	+	32.2136i	0.386403	+	1.44208i	0.835943	+	0.548816i	$0.184921\pi$
$499$	8.63159	+	32.2136i	0.386403	+	1.44208i	−0.449540	+	0.893260i	$0.648412\pi$
$500$	13.3003	−	5.81671i	0.594806	−	0.260131i
$501$	2.04307	−	7.62483i	0.0912775	−	0.340652i
$502$	−15.0930	+	10.2999i	−0.673633	+	0.459707i
$503$		−	20.7931i		−	0.927117i	−0.886066	−	0.463558i	$-0.846572\pi$
$503$		−	20.7931i		−	0.927117i	0.886066	−	0.463558i	$-0.153428\pi$
$504$		0			0
$505$		−	3.85105i		−	0.171370i
$506$	3.94855	+	5.78602i	0.175534	+	0.257220i
$507$	8.83433	−	32.9702i	0.392346	−	1.46426i
$508$	−32.4578	−	12.7060i	−1.44008	−	0.563736i
$509$	10.3474	+	38.6171i	0.458641	+	1.71167i	0.677156	+	0.735839i	$0.263212\pi$
$509$	10.3474	+	38.6171i	0.458641	+	1.71167i	−0.218515	+	0.975834i	$0.570121\pi$
$510$	−24.5952	+	8.61831i	−1.08909	+	0.381625i
$511$		0			0
$512$	22.4949	+	2.44492i	0.994145	+	0.108051i
$513$	−8.66534	+	15.0088i	−0.382584	+	0.662655i
$514$	10.4125	+	8.95273i	0.459274	+	0.394888i
$515$	8.73958	+	2.34176i	0.385112	+	0.103190i
$516$	0.749514	+	4.94335i	0.0329955	+	0.217619i
$517$	5.20866	+	5.20866i	0.229076	+	0.229076i
$518$		0			0
$519$			30.8520i			1.35425i
$520$	1.32909	+	2.50679i	0.0582844	+	0.109930i
$521$	16.0339	−	9.25715i	0.702456	−	0.405563i	−0.105805	−	0.994387i	$-0.533742\pi$
$521$	16.0339	−	9.25715i	0.702456	−	0.405563i	0.808262	+	0.588824i	$0.200409\pi$
$522$	−4.82139	−	63.9615i	−0.211027	−	2.79952i
$523$	−35.2333	+	9.44073i	−1.54064	+	0.412814i	−0.926474	−	0.376360i	$-0.877176\pi$
$523$	−35.2333	+	9.44073i	−1.54064	+	0.412814i	−0.614170	+	0.789174i	$0.710509\pi$
$524$	−2.33141	+	20.8558i	−0.101848	+	0.911090i
$525$		0			0
$526$	−4.99052	−	14.2421i	−0.217597	−	0.620985i
$527$	19.3561	−	33.5258i	0.843167	−	1.46041i
$528$	14.8415	−	4.60645i	0.645893	−	0.200470i
$529$	−4.09802	−	7.09799i	−0.178175	−	0.308608i
$530$	−10.5651	−	1.99424i	−0.458919	−	0.0866242i
$531$	−39.9418	+	39.9418i	−1.73333	+	1.73333i
$532$		0			0
$533$	2.61329	+	2.61329i	0.113194	+	0.113194i
$534$	−7.49040	+	5.11167i	−0.324141	+	0.221204i
$535$	4.82429	−	2.78531i	0.208572	−	0.120419i
$536$	−12.7525	+	11.8638i	−0.550825	+	0.512438i
$537$	40.8366	+	23.5770i	1.76223	+	1.01742i
$538$	−4.64475	+	9.65574i	−0.200250	+	0.416288i
$539$		0			0
$540$	9.03404	+	11.3080i	0.388763	+	0.486619i
$541$	0.613332	+	2.28899i	0.0263692	+	0.0984112i	0.977856	−	0.209277i	$-0.0671112\pi$
$541$	0.613332	+	2.28899i	0.0263692	+	0.0984112i	−0.951487	+	0.307689i	$0.900444\pi$
$542$	12.0583	+	10.3678i	0.517948	+	0.445336i
$543$	27.4572	+	47.5573i	1.17830	+	2.04088i
$544$	41.0617	+	17.8082i	1.76051	+	0.763522i
$545$	8.71148			0.373159
$546$		0			0
$547$	−15.8419	+	15.8419i	−0.677351	+	0.677351i	−0.959400	−	0.282049i	$-0.908986\pi$
$547$	−15.8419	+	15.8419i	−0.677351	+	0.677351i	0.282049	+	0.959400i	$0.408986\pi$
$548$	11.9678	−	1.81456i	0.511239	−	0.0775143i
$549$	−10.4515	+	39.0057i	−0.446061	+	1.66472i
$550$	−7.99582	+	0.602722i	−0.340943	+	0.0257001i
$551$	−11.8880	−	6.86355i	−0.506446	−	0.292397i
$552$	32.0085	−	7.34993i	1.36237	−	0.312834i
$553$		0			0
$554$	−27.1161	−	13.0438i	−1.15205	−	0.554179i
$555$	2.98574	−	0.800026i	0.126737	−	0.0339592i
$556$	−5.10345	−	11.6694i	−0.216435	−	0.494892i
$557$	42.9377	+	11.5051i	1.81933	+	0.487488i	0.996706	−	0.0811008i	$-0.0258436\pi$
$557$	42.9377	+	11.5051i	1.81933	+	0.487488i	0.822622	+	0.568588i	$0.192510\pi$
$558$	−41.5247	−	7.83809i	−1.75788	−	0.331813i
$559$	1.07670			0.0455397
$560$		0			0
$561$	30.7380			1.29776
$562$	−27.9287	−	5.27175i	−1.17810	−	0.222375i
$563$	−5.19184	−	1.39115i	−0.218810	−	0.0586299i	0.147749	−	0.989025i	$-0.452797\pi$
$563$	−5.19184	−	1.39115i	−0.218810	−	0.0586299i	−0.366558	+	0.930395i	$0.619464\pi$
$564$	31.6414	−	13.8380i	1.33234	−	0.582684i
$565$	6.82187	−	1.82791i	0.286998	−	0.0769009i
$566$	26.0728	+	12.5419i	1.09592	+	0.527177i
$567$		0			0
$568$	−4.78257	−	2.99634i	−0.200672	−	0.125724i
$569$	4.37176	+	2.52404i	0.183274	+	0.105813i	0.588830	−	0.808257i	$-0.299589\pi$
$569$	4.37176	+	2.52404i	0.183274	+	0.105813i	−0.405556	+	0.914070i	$0.632922\pi$
$570$	6.07097	−	0.457627i	0.254285	−	0.0191679i
$571$	−9.72141	+	36.2808i	−0.406828	+	1.51830i	0.393830	+	0.919183i	$0.371150\pi$
$571$	−9.72141	+	36.2808i	−0.406828	+	1.51830i	−0.800658	+	0.599121i	$0.795517\pi$
$572$	−0.501662	−	3.30866i	−0.0209755	−	0.138342i
$573$	−1.08614	+	1.08614i	−0.0453742	+	0.0453742i
$574$		0			0
$575$	−16.9460			−0.706697
$576$	3.52317	−	48.7293i	0.146799	−	2.03039i
$577$	−9.36395	−	16.2188i	−0.389826	−	0.675199i	0.602599	−	0.798044i	$-0.294132\pi$
$577$	−9.36395	−	16.2188i	−0.389826	−	0.675199i	−0.992426	+	0.122845i	$0.960798\pi$
$578$	48.8985	+	42.0434i	2.03391	+	1.74877i
$579$	3.77124	+	14.0745i	0.156727	+	0.584914i
$580$	−8.95672	+	7.15558i	−0.371908	+	0.297119i
$581$		0			0
$582$	−16.6867	+	34.6891i	−0.691686	+	1.43791i
$583$	10.9821	+	6.34050i	0.454831	+	0.262597i
$584$	−0.788602	+	21.8430i	−0.0326326	+	0.903868i
$585$	5.30553	−	3.06315i	0.219356	−	0.126646i
$586$	17.2415	−	11.7661i	0.712239	−	0.486053i
$587$	−5.57210	−	5.57210i	−0.229985	−	0.229985i	0.582701	−	0.812686i	$-0.301996\pi$
$587$	−5.57210	−	5.57210i	−0.229985	−	0.229985i	−0.812686	+	0.582701i	$0.801996\pi$
$588$		0			0
$589$	−6.39475	+	6.39475i	−0.263491	+	0.263491i
$590$	9.92043	+	1.87255i	0.408418	+	0.0770918i
$591$	−6.45799	−	11.1856i	−0.265646	−	0.460113i
$592$	−4.69765	−	2.47228i	−0.193072	−	0.101610i
$593$	6.09225	−	10.5521i	0.250179	−	0.433322i	−0.713396	−	0.700761i	$-0.752844\pi$
$593$	6.09225	−	10.5521i	0.250179	−	0.433322i	0.963575	+	0.267439i	$0.0861773\pi$
$594$	−5.64518	−	16.1104i	−0.231624	−	0.661017i
$595$		0			0
$596$	30.1657	+	3.37213i	1.23563	+	0.138128i
$597$	−22.0813	+	5.91667i	−0.903728	+	0.242153i
$598$	−0.531600	−	7.05231i	−0.0217387	−	0.288391i
$599$	16.2977	−	9.40947i	0.665905	−	0.384461i	−0.128618	−	0.991694i	$-0.541054\pi$
$599$	16.2977	−	9.40947i	0.665905	−	0.384461i	0.794523	+	0.607234i	$0.207721\pi$
$600$	−11.0337	+	35.9378i	−0.450450	+	1.46716i
$601$			11.3877i			0.464514i	0.972654	+	0.232257i	$0.0746111\pi$
$601$			11.3877i			0.464514i	−0.972654	+	0.232257i	$0.925389\pi$
$602$		0			0
$603$	26.5927	+	26.5927i	1.08294	+	1.08294i
$604$	29.4005	−	4.45772i	1.19629	−	0.181382i
$605$	6.96504	+	1.86628i	0.283169	+	0.0758750i
$606$	16.1470	+	13.8834i	0.655929	+	0.563973i
$607$	16.9140	−	29.2959i	0.686519	−	1.18909i	−0.286438	−	0.958099i	$-0.592471\pi$
$607$	16.9140	−	29.2959i	0.686519	−	1.18909i	0.972957	−	0.230986i	$-0.0741953\pi$
$608$	−8.18881	−	6.50111i	−0.332100	−	0.263655i
$609$		0			0
$610$	6.81124	−	2.38670i	0.275779	−	0.0966346i
$611$	−1.92484	−	7.18361i	−0.0778708	−	0.290618i
$612$	35.2272	−	89.9889i	1.42398	−	3.63759i
$613$	−0.444885	+	1.66033i	−0.0179687	+	0.0670602i	−0.974328	−	0.225133i	$-0.927718\pi$
$613$	−0.444885	+	1.66033i	−0.0179687	+	0.0670602i	0.956359	+	0.292193i	$0.0943850\pi$
$614$	5.32902	+	7.80890i	0.215062	+	0.315142i
$615$		−	6.62280i		−	0.267057i
$616$		0			0
$617$		−	8.15102i		−	0.328148i	−0.986448	−	0.164074i	$-0.947536\pi$
$617$		−	8.15102i		−	0.328148i	0.986448	−	0.164074i	$-0.0524636\pi$
$618$	−41.3256	+	28.2018i	−1.66236	+	1.13444i
$619$	8.73907	−	32.6147i	0.351253	−	1.31089i	−0.533882	−	0.845559i	$-0.679267\pi$
$619$	8.73907	−	32.6147i	0.351253	−	1.31089i	0.885135	−	0.465335i	$-0.154066\pi$
$620$	3.02630	+	6.91983i	0.121539	+	0.277907i
$621$	−9.33736	−	34.8475i	−0.374695	−	1.39838i
$622$	−2.60658	−	7.43874i	−0.104514	−	0.298266i
$623$		0			0
$624$	−15.3022	−	3.46446i	−0.612576	−	0.138689i
$625$	8.20980	−	14.2198i	0.328392	−	0.568792i
$626$	−10.9050	+	12.6830i	−0.435850	+	0.506915i
$627$	−6.93601	−	1.85850i	−0.276997	−	0.0742212i
$628$	−18.3142	−	13.4918i	−0.730818	−	0.538381i
$629$	−7.42477	−	7.42477i	−0.296045	−	0.296045i
$630$		0			0
$631$			24.8235i			0.988206i	0.869403	+	0.494103i	$0.164504\pi$
$631$			24.8235i			0.988206i	−0.869403	+	0.494103i	$0.835496\pi$
$632$	−12.2787	−	23.1589i	−0.488422	−	0.921211i
$633$	−24.4283	+	14.1037i	−0.970938	+	0.560571i
$634$	−6.37786	+	0.480760i	−0.253297	+	0.0190934i
$635$	12.9927	−	3.48139i	0.515600	−	0.138155i
$636$	46.4497	−	37.1089i	1.84185	−	1.47146i
$637$		0			0
$638$	12.7605	−	4.47137i	0.505194	−	0.177023i
$639$	−6.09283	+	10.5531i	−0.241029	+	0.417474i
$640$	−7.54871	+	4.38912i	−0.298389	+	0.173495i
$641$	−15.4186	−	26.7058i	−0.608998	−	1.05482i	−0.991406	−	0.130822i	$-0.958238\pi$
$641$	−15.4186	−	26.7058i	−0.608998	−	1.05482i	0.382408	−	0.923994i	$-0.375095\pi$
$642$	−5.71349	+	30.2690i	−0.225493	+	1.19462i
$643$	−7.86848	+	7.86848i	−0.310302	+	0.310302i	−0.845027	−	0.534724i	$-0.820416\pi$
$643$	−7.86848	+	7.86848i	−0.310302	+	0.310302i	0.534724	+	0.845027i	$0.320416\pi$
$644$		0			0
$645$	−1.36433	−	1.36433i	−0.0537204	−	0.0537204i
$646$	−11.6577	−	17.0826i	−0.458666	−	0.672107i
$647$	−33.1866	+	19.1603i	−1.30470	+	0.753268i	−0.981206	−	0.192963i	$-0.938190\pi$
$647$	−33.1866	+	19.1603i	−1.30470	+	0.753268i	−0.323492	+	0.946231i	$0.604857\pi$
$648$	−28.1952	−	1.01794i	−1.10761	−	0.0399885i
$649$	−10.3120	−	5.95361i	−0.404780	−	0.233700i
$650$	7.29546	+	3.50938i	0.286152	+	0.137649i
$651$		0			0
$652$	2.24675	−	20.0985i	0.0879894	−	0.787116i
$653$	−3.62018	−	13.5107i	−0.141669	−	0.528714i	−0.999881	−	0.0154198i	$-0.995092\pi$
$653$	−3.62018	−	13.5107i	−0.141669	−	0.528714i	0.858213	−	0.513294i	$-0.171575\pi$
$654$	−31.4056	+	36.5262i	−1.22805	+	1.42829i
$655$	−4.04922	−	7.01345i	−0.158216	−	0.274038i
$656$	−7.72153	+	8.35109i	−0.301475	+	0.326055i
$657$	47.1935			1.84119
$658$		0			0
$659$	−18.0981	+	18.0981i	−0.705003	+	0.705003i	−0.965480	−	0.260477i	$-0.916120\pi$
$659$	−18.0981	+	18.0981i	−0.705003	+	0.705003i	0.260477	+	0.965480i	$0.416120\pi$
$660$	−3.55685	+	4.82820i	−0.138450	+	0.187938i
$661$	−7.80014	+	29.1105i	−0.303390	+	1.13227i	0.630932	+	0.775838i	$0.282673\pi$
$661$	−7.80014	+	29.1105i	−0.303390	+	1.13227i	−0.934322	+	0.356430i	$0.883994\pi$
$662$	−2.44470	−	32.4319i	−0.0950160	−	1.26050i
$663$	−26.8760	−	15.5169i	−1.04378	−	0.602625i
$664$	4.28387	+	18.6560i	0.166246	+	0.723992i
$665$		0			0
$666$	−4.96863	+	10.3290i	−0.192531	+	0.400242i
$667$	27.6016	−	7.39583i	1.06874	−	0.286368i
$668$	1.90702	−	4.87155i	0.0737850	−	0.188486i
$669$	−59.5763	−	15.9634i	−2.30335	−	0.617182i
$670$	1.24672	−	6.60490i	0.0481650	−	0.255169i
$671$	−8.51239			−0.328617
$672$		0			0
$673$	−10.9832			−0.423371			−0.211686	−	0.977338i	$-0.567895\pi$
$673$	−10.9832			−0.423371			−0.211686	+	0.977338i	$0.567895\pi$
$674$	−4.35639	+	23.0793i	−0.167802	+	0.888983i
$675$	39.8898	+	10.6884i	1.53536	+	0.411398i
$676$	8.24607	−	21.0648i	0.317157	−	0.810185i
$677$	−42.5236	+	11.3942i	−1.63431	+	0.437913i	−0.955162	−	0.296084i	$-0.904319\pi$
$677$	−42.5236	+	11.3942i	−1.63431	+	0.437913i	−0.679153	+	0.733997i	$0.737653\pi$
$678$	−16.9291	+	35.1931i	−0.650160	+	1.35158i
$679$		0			0
$680$	−16.8338	+	3.86545i	−0.645546	+	0.148233i
$681$	−30.8317	−	17.8007i	−1.18147	−	0.682125i
$682$	−0.669576	−	8.88273i	−0.0256394	−	0.340137i
$683$	−6.60660	+	24.6562i	−0.252794	+	0.943441i	0.716510	+	0.697577i	$0.245738\pi$
$683$	−6.60660	+	24.6562i	−0.252794	+	0.943441i	−0.969304	+	0.245864i	$0.920928\pi$
$684$	−13.3899	+	18.1760i	−0.511977	+	0.694976i
$685$	−3.30302	+	3.30302i	−0.126202	+	0.126202i
$686$		0			0
$687$	41.0309			1.56543
$688$	0.129692	+	3.31104i	0.00494448	+	0.126232i
$689$	−6.40150	−	11.0877i	−0.243878	−	0.422409i
$690$	−8.26263	+	9.60985i	−0.314553	+	0.365841i
$691$	−11.6155	−	43.3496i	−0.441875	−	1.64910i	−0.724059	−	0.689738i	$-0.757726\pi$
$691$	−11.6155	−	43.3496i	−0.441875	−	1.64910i	0.282184	−	0.959360i	$-0.408941\pi$
$692$	−2.27153	+	20.3202i	−0.0863507	+	0.772457i
$693$		0			0
$694$	19.7190	+	9.48555i	0.748523	+	0.360066i
$695$	4.25657	+	2.45753i	0.161461	+	0.0932195i
$696$	2.28718	−	63.3510i	0.0866952	−	2.40131i
$697$	−19.4833	+	11.2487i	−0.737983	+	0.426074i
$698$	15.4522	+	22.6430i	0.584876	+	0.857049i
$699$	45.9855	+	45.9855i	1.73933	+	1.73933i
$700$		0			0
$701$	−34.8486	+	34.8486i	−1.31621	+	1.31621i	−0.399466	+	0.916748i	$0.630804\pi$
$701$	−34.8486	+	34.8486i	−1.31621	+	1.31621i	−0.916748	+	0.399466i	$0.869196\pi$
$702$	−3.19678	+	16.9360i	−0.120655	+	0.639207i
$703$	1.22647	+	2.12431i	0.0462573	+	0.0801200i
$704$	10.1143	−	1.94123i	0.381196	−	0.0731630i
$705$	−6.66358	+	11.5417i	−0.250965	+	0.434684i
$706$	−3.07054	+	1.07594i	−0.115561	+	0.0404934i
$707$		0			0
$708$	−43.6154	+	34.8446i	−1.63917	+	1.30954i
$709$	33.8583	−	9.07232i	1.27158	−	0.340718i	0.440942	−	0.897536i	$-0.354644\pi$
$709$	33.8583	−	9.07232i	1.27158	−	0.340718i	0.830635	+	0.556818i	$0.187978\pi$
$710$	2.17174	−	0.163705i	0.0815041	−	0.00614374i
$711$	−49.0149	+	28.2988i	−1.83820	+	1.06129i
$712$	−5.30979	+	2.81523i	−0.198993	+	0.105505i
$713$		−	18.8257i		−	0.705027i
$714$		0			0
$715$	0.913167	+	0.913167i	0.0341505	+	0.0341505i
$716$	25.1605	+	18.5353i	0.940291	+	0.692696i
$717$	−42.3033	−	11.3351i	−1.57984	−	0.423318i
$718$	6.69200	−	7.78313i	0.249743	−	0.290464i
$719$	19.3564	−	33.5263i	0.721872	−	1.25032i	−0.238377	−	0.971173i	$-0.576615\pi$
$719$	19.3564	−	33.5263i	0.721872	−	1.25032i	0.960249	−	0.279146i	$-0.0900514\pi$
$720$	10.0588	+	15.9464i	0.374868	+	0.594288i
$721$		0			0
$722$	−7.28802	−	20.7988i	−0.271232	−	0.774051i
$723$	7.17086	+	26.7620i	0.266687	+	0.995290i
$724$	14.5828	+	33.3444i	0.541964	+	1.23924i
$725$	−8.46597	+	31.5954i	−0.314418	+	1.17342i
$726$	−32.9346	+	22.4756i	−1.22232	+	0.834146i
$727$			11.1458i			0.413375i	0.978407	+	0.206688i	$0.0662684\pi$
$727$			11.1458i			0.413375i	−0.978407	+	0.206688i	$0.933732\pi$
$728$		0			0
$729$		−	23.9706i		−	0.887798i
$730$	−4.75451	−	6.96703i	−0.175972	−	0.257861i
$731$	−1.69637	+	6.33094i	−0.0627425	+	0.234158i
$732$	−14.5479	+	37.1630i	−0.537706	+	1.37358i
$733$	−2.45813	−	9.17387i	−0.0907931	−	0.338845i	0.905555	−	0.424229i	$-0.139455\pi$
$733$	−2.45813	−	9.17387i	−0.0907931	−	0.338845i	−0.996348	+	0.0853844i	$0.972788\pi$
$734$	35.8768	−	12.5715i	1.32424	−	0.464021i
$735$		0			0
$736$	21.6230	−	2.48424i	0.797035	−	0.0915701i
$737$	−3.96384	+	6.86557i	−0.146010	+	0.252896i
$738$	18.6212	+	16.0107i	0.685457	+	0.589362i
$739$	31.8880	+	8.54437i	1.17302	+	0.314310i	0.792154	−	0.610321i	$-0.208959\pi$
$739$	31.8880	+	8.54437i	1.17302	+	0.314310i	0.380865	+	0.924630i	$0.375626\pi$
$740$	2.02541	−	0.307094i	0.0744556	−	0.0112890i
$741$	5.12636	+	5.12636i	0.188321	+	0.188321i
$742$		0			0
$743$		−	46.1538i		−	1.69322i	−0.532214	−	0.846610i	$-0.678640\pi$
$743$		−	46.1538i		−	1.69322i	0.532214	−	0.846610i	$-0.321360\pi$
$744$	−39.9241	−	12.2576i	−1.46369	−	0.449385i
$745$	−10.1442	+	5.85676i	−0.371655	+	0.214575i
$746$	−0.142611	−	1.89191i	−0.00522137	−	0.0692677i
$747$	39.9215	−	10.6969i	1.46065	−	0.391380i
$748$	20.2451	+	2.26314i	0.740235	+	0.0827486i
$749$		0			0
$750$	−10.2438	−	29.2342i	−0.374052	−	1.06748i
$751$	−8.69900	+	15.0671i	−0.317431	+	0.549807i	−0.979951	−	0.199237i	$-0.936154\pi$
$751$	−8.69900	+	15.0671i	−0.317431	+	0.549807i	0.662520	+	0.749044i	$0.269487\pi$
$752$	21.8590	−	6.78451i	0.797114	−	0.247405i
$753$	19.4959	+	33.7679i	0.710470	+	1.23057i
$754$	−13.4144	−	2.53207i	−0.488525	−	0.0922127i
$755$	−8.11432	+	8.11432i	−0.295310	+	0.295310i
$756$		0			0
$757$	3.24720	+	3.24720i	0.118021	+	0.118021i	0.763651	−	0.645629i	$-0.223405\pi$
$757$	3.24720	+	3.24720i	0.118021	+	0.118021i	−0.645629	+	0.763651i	$0.723405\pi$
$758$	−25.2910	+	17.2594i	−0.918612	+	0.626888i
$759$	12.9452	−	7.47391i	0.469881	−	0.271286i
$760$	4.03224	+	0.145577i	0.146265	+	0.00528063i
$761$	−7.91882	−	4.57193i	−0.287057	−	0.165732i	0.349557	−	0.936915i	$-0.386332\pi$
$761$	−7.91882	−	4.57193i	−0.287057	−	0.165732i	−0.636614	+	0.771183i	$0.719665\pi$
$762$	−32.2427	+	67.0277i	−1.16803	+	2.42816i
$763$		0			0
$764$	−0.795338	+	0.635400i	−0.0287743	+	0.0229880i
$765$	9.65212	+	36.0222i	0.348973	+	1.30239i
$766$	−8.68372	−	7.46633i	−0.313755	−	0.269770i
$767$	6.01089	+	10.4112i	0.217041	+	0.375925i
$768$	8.81060	−	47.4740i	0.317925	−	1.71307i
$769$	−26.8105			−0.966812			−0.483406	−	0.875396i	$-0.660600\pi$
$769$	−26.8105			−0.966812			−0.483406	+	0.875396i	$0.660600\pi$
$770$		0			0
$771$	20.7203	−	20.7203i	0.746224	−	0.746224i
$772$	1.44761	+	9.54758i	0.0521006	+	0.343625i
$773$	−1.37206	+	5.12058i	−0.0493494	+	0.184175i	−0.986201	−	0.165553i	$-0.947059\pi$
$773$	−1.37206	+	5.12058i	−0.0493494	+	0.184175i	0.936851	+	0.349727i	$0.113726\pi$
$774$	7.13435	−	0.537784i	0.256439	−	0.0193303i
$775$	18.6626	+	10.7748i	0.670379	+	0.387043i
$776$	−13.5445	+	21.6188i	−0.486218	+	0.776071i
$777$		0			0
$778$	23.6212	+	11.3627i	0.846862	+	0.407371i
$779$	5.07651	−	1.36025i	0.181885	−	0.0487359i
$780$	5.54729	−	2.42604i	0.198625	−	0.0868660i
$781$	−2.48119	−	0.664833i	−0.0887840	−	0.0237896i
$782$	42.3047	+	7.98532i	1.51281	+	0.285554i
$783$	−69.6371			−2.48863
$784$		0			0
$785$	8.77824			0.313309
$786$	44.0044	+	8.30614i	1.56958	+	0.296270i
$787$	37.5883	+	10.0718i	1.33988	+	0.359020i	0.856389	−	0.516331i	$-0.172702\pi$
$787$	37.5883	+	10.0718i	1.33988	+	0.359020i	0.483490	+	0.875350i	$0.339369\pi$
$788$	−3.42990	−	7.84268i	−0.122185	−	0.279384i
$789$	−31.1057	+	8.33474i	−1.10739	+	0.296725i
$790$	9.11568	+	4.38497i	0.324321	+	0.156010i
$791$		0			0
$792$	−4.97666	−	21.6730i	−0.176838	−	0.770117i
$793$	7.44287	+	4.29714i	0.264304	+	0.152596i
$794$	23.7073	−	1.78704i	0.841339	−	0.0634198i
$795$	−5.93809	+	22.1612i	−0.210602	+	0.785978i
$796$	−14.9791	+	2.27115i	−0.530921	+	0.0804986i
$797$	−4.08133	+	4.08133i	−0.144568	+	0.144568i	−0.775686	−	0.631118i	$-0.782596\pi$
$797$	−4.08133	+	4.08133i	−0.144568	+	0.144568i	0.631118	+	0.775686i	$0.282596\pi$
$798$		0			0
$799$	45.2718			1.60160
$800$	−9.91317	+	22.8575i	−0.350484	+	0.808135i
$801$	6.48824	+	11.2380i	0.229251	+	0.397074i
$802$	4.69225	+	4.03444i	0.165689	+	0.142461i
$803$	2.57481	+	9.60933i	0.0908631	+	0.339106i
$804$	23.1991	+	29.0385i	0.818168	+	1.02411i
$805$		0			0
$806$	−3.89864	+	8.10469i	−0.137324	+	0.285475i
$807$	19.8011	+	11.4322i	0.697031	+	0.402431i
$808$	9.61280	+	10.3329i	0.338177	+	0.363510i
$809$	−18.4321	+	10.6418i	−0.648037	+	0.374144i	−0.787704	−	0.616054i	$-0.788730\pi$
$809$	−18.4321	+	10.6418i	−0.648037	+	0.374144i	0.139667	+	0.990199i	$0.455397\pi$
$810$	8.99316	−	6.13719i	0.315987	−	0.215639i
$811$	−12.6569	−	12.6569i	−0.444442	−	0.444442i	0.449060	−	0.893502i	$-0.351759\pi$
$811$	−12.6569	−	12.6569i	−0.444442	−	0.444442i	−0.893502	+	0.449060i	$0.851759\pi$
$812$		0			0
$813$	23.9954	−	23.9954i	0.841556	−	0.841556i
$814$	−2.37424	−	0.448154i	−0.0832169	−	0.0157078i
$815$	3.90218	+	6.75877i	0.136687	+	0.236749i
$816$	44.4797	−	84.5173i	1.55710	−	2.95870i
$817$	0.765569	−	1.32600i	0.0267839	−	0.0463910i
$818$	−0.0556787	−	0.158898i	−0.00194676	−	0.00555573i
$819$		0			0
$820$	0.487615	−	4.36200i	0.0170282	−	0.152328i
$821$	−49.6916	+	13.3148i	−1.73425	+	0.464691i	−0.981155	−	0.193222i	$-0.938106\pi$
$821$	−49.6916	+	13.3148i	−1.73425	+	0.464691i	−0.753094	+	0.657912i	$0.771440\pi$
$822$	−1.94154	−	25.7569i	−0.0677190	−	0.898374i
$823$	−21.8000	+	12.5862i	−0.759899	+	0.438728i	−0.829259	−	0.558864i	$-0.811237\pi$
$823$	−21.8000	+	12.5862i	−0.759899	+	0.438728i	0.0693606	+	0.997592i	$0.477904\pi$
$824$	−29.2949	+	15.5320i	−1.02054	+	0.541083i
$825$			17.1107i			0.595718i
$826$		0			0
$827$	−3.76090	−	3.76090i	−0.130779	−	0.130779i	0.638687	−	0.769466i	$-0.279478\pi$
$827$	−3.76090	−	3.76090i	−0.130779	−	0.130779i	−0.769466	+	0.638687i	$0.779478\pi$
$828$	−7.04489	−	46.4639i	−0.244827	−	1.61473i
$829$	−4.47469	−	1.19899i	−0.155412	−	0.0416426i	0.180274	−	0.983616i	$-0.442302\pi$
$829$	−4.47469	−	1.19899i	−0.155412	−	0.0416426i	−0.335686	+	0.941974i	$0.608968\pi$
$830$	−5.60105	−	4.81583i	−0.194415	−	0.167160i
$831$	−32.1048	+	55.6072i	−1.11370	+	1.92899i
$832$	−9.82344	−	3.40846i	−0.340566	−	0.118167i
$833$		0			0
$834$	−25.6494	+	8.98772i	−0.888167	+	0.311219i
$835$	0.522517	+	1.95006i	0.0180825	+	0.0674846i
$836$	−4.43145	−	1.73475i	−0.153265	−	0.0599974i
$837$	−11.8740	+	44.3144i	−0.410426	+	1.53173i
$838$	24.2897	+	35.5930i	0.839075	+	1.22954i
$839$			31.7342i			1.09559i	0.836614	+	0.547793i	$0.184532\pi$
$839$			31.7342i			1.09559i	−0.836614	+	0.547793i	$0.815468\pi$
$840$		0			0
$841$		−	26.1574i		−	0.901979i
$842$	−0.421115	+	0.287381i	−0.0145126	+	0.00990381i
$843$	−15.6973	+	58.5830i	−0.540642	+	2.01771i
$844$	−17.1277	+	7.49059i	−0.589561	+	0.257837i
$845$	2.25939	+	8.43217i	0.0777255	+	0.290075i
$846$	−16.3422	−	46.6380i	−0.561858	−	1.60345i
$847$		0			0
$848$	33.3255	−	21.0213i	1.14440	−	0.721873i
$849$	30.8695	−	53.4676i	1.05944	−	1.83500i
$850$	−32.1291	+	37.3678i	−1.10202	+	1.28170i
$851$	−4.93223	−	1.32159i	−0.169075	−	0.0453035i
$852$	−7.14291	+	9.69605i	−0.244712	+	0.332181i
$853$	−25.3410	−	25.3410i	−0.867661	−	0.867661i	0.124552	−	0.992213i	$-0.460251\pi$
$853$	−25.3410	−	25.3410i	−0.867661	−	0.867661i	−0.992213	+	0.124552i	$0.960251\pi$
$854$		0			0
$855$		−	8.71197i		−	0.297943i
$856$	−5.99170	+	19.5155i	−0.204792	+	0.667027i
$857$	−39.6000	+	22.8631i	−1.35271	+	0.780987i	−0.988628	−	0.150380i	$-0.951950\pi$
$857$	−39.6000	+	22.8631i	−1.35271	+	0.780987i	−0.364082	+	0.931367i	$0.618617\pi$
$858$	−7.12085	+	0.536766i	−0.243102	+	0.0183249i
$859$	−35.5511	+	9.52588i	−1.21299	+	0.325019i	−0.807933	−	0.589274i	$-0.799414\pi$
$859$	−35.5511	+	9.52588i	−1.21299	+	0.325019i	−0.405053	+	0.914293i	$0.632747\pi$
$860$	−0.798142	−	0.999045i	−0.0272164	−	0.0340671i
$861$		0			0
$862$	−32.4240	+	11.3616i	−1.10437	+	0.386977i
$863$	−2.15212	+	3.72758i	−0.0732590	+	0.126888i	−0.900328	−	0.435212i	$-0.856673\pi$
$863$	−2.15212	+	3.72758i	−0.0732590	+	0.126888i	0.827069	+	0.562101i	$0.190007\pi$
$864$	−52.4660	−	7.79066i	−1.78493	−	0.265044i
$865$	−3.94522	−	6.83333i	−0.134142	−	0.232340i
$866$	−5.16219	+	27.3483i	−0.175418	+	0.929333i
$867$	97.3057	−	97.3057i	3.30468	−	3.30468i
$868$		0			0
$869$	−8.43627	−	8.43627i	−0.286181	−	0.286181i
$870$	13.7895	+	20.2064i	0.467506	+	0.685062i
$871$	6.93162	−	4.00197i	0.234869	−	0.135602i
$872$	−23.3741	+	21.7451i	−0.791546	+	0.736383i
$873$	47.7035	+	27.5416i	1.61452	+	0.932143i
$874$	−9.06320	−	4.35973i	−0.306567	−	0.147470i
$875$		0			0
$876$	46.3524	+	5.18159i	1.56610	+	0.175070i
$877$	−14.7923	−	55.2056i	−0.499500	−	1.86416i	−0.503203	−	0.864168i	$-0.667845\pi$
$877$	−14.7923	−	55.2056i	−0.499500	−	1.86416i	0.00370287	−	0.999993i	$-0.498821\pi$
$878$	28.0959	−	32.6770i	0.948192	−	1.10279i
$879$	−22.2712	−	38.5748i	−0.751188	−	1.30110i
$880$	−2.69815	+	2.91814i	−0.0909546	+	0.0983704i
$881$	46.7407			1.57474			0.787368	−	0.616484i	$-0.211443\pi$
$881$	46.7407			1.57474			0.787368	+	0.616484i	$0.211443\pi$
$882$		0			0
$883$	−1.66705	+	1.66705i	−0.0561007	+	0.0561007i	−0.734601	−	0.678500i	$-0.762630\pi$
$883$	−1.66705	+	1.66705i	−0.0561007	+	0.0561007i	0.678500	+	0.734601i	$0.262630\pi$
$884$	−16.5590	−	12.1987i	−0.556939	−	0.410288i
$885$	5.57575	−	20.8090i	0.187427	−	0.699486i
$886$	−0.415471	−	5.51172i	−0.0139580	−	0.185170i
$887$	14.2716	+	8.23972i	0.479194	+	0.276663i	0.720081	−	0.693890i	$-0.244105\pi$
$887$	14.2716	+	8.23972i	0.479194	+	0.276663i	−0.240887	+	0.970553i	$0.577438\pi$
$888$	−6.01416	+	9.59942i	−0.201822	+	0.322135i
$889$		0			0
$890$	1.00537	−	2.09001i	0.0337001	−	0.0700573i
$891$	−12.4039	+	3.32361i	−0.415545	+	0.111345i
$892$	−38.0637	−	14.9005i	−1.27447	−	0.498905i
$893$	−10.2155	−	2.73725i	−0.341850	−	0.0915984i
$894$	12.0139	−	63.6476i	0.401806	−	2.12869i
$895$	−12.0597			−0.403112
$896$		0			0
$897$	−15.0916			−0.503895
$898$	9.97332	−	52.8368i	0.332814	−	1.76319i
$899$	−35.1000	−	9.40503i	−1.17065	−	0.313675i
$900$	50.0934	+	19.6097i	1.66978	+	0.653655i
$901$	75.2808	−	20.1714i	2.50797	−	0.672008i
$902$	−2.24408	+	4.66510i	−0.0747197	+	0.155331i
$903$		0			0
$904$	−13.7413	+	21.9329i	−0.457028	+	0.729479i
$905$	−12.1628	−	7.02222i	−0.404307	−	0.233426i
$906$	−4.76966	−	63.2752i	−0.158461	−	2.10218i
$907$	−1.14578	+	4.27611i	−0.0380450	+	0.141986i	−0.982336	−	0.187126i	$-0.940083\pi$
$907$	−1.14578	+	4.27611i	−0.0380450	+	0.141986i	0.944291	+	0.329112i	$0.106749\pi$
$908$	−18.9962	−	13.9942i	−0.630412	−	0.464414i
$909$	21.5471	−	21.5471i	0.714673	−	0.714673i
$910$		0			0
$911$	−2.42550			−0.0803605			−0.0401802	−	0.999192i	$-0.512793\pi$
$911$	−2.42550			−0.0803605			−0.0401802	+	0.999192i	$0.512793\pi$
$912$	−15.1469	+	16.3819i	−0.501565	+	0.542459i
$913$	4.35613	+	7.54503i	0.144167	+	0.249704i
$914$	−16.0594	+	18.6779i	−0.531198	+	0.617809i
$915$	−3.98607	−	14.8762i	−0.131775	−	0.491792i
$916$	27.0243	+	3.02097i	0.892909	+	0.0998157i
$917$		0			0
$918$	−94.5458	−	45.4799i	−3.12048	−	1.50106i
$919$	35.0592	+	20.2414i	1.15650	+	0.667703i	0.950462	−	0.310842i	$-0.100611\pi$
$919$	35.0592	+	20.2414i	1.15650	+	0.667703i	0.206034	+	0.978545i	$0.433944\pi$
$920$	−6.14959	+	5.72103i	−0.202746	+	0.188617i
$921$	17.4710	−	10.0869i	0.575690	−	0.332375i
$922$	−30.9111	−	45.2956i	−1.01800	−	1.49173i
$923$	1.83383	+	1.83383i	0.0603613	+	0.0603613i
$924$		0			0
$925$	4.13309	−	4.13309i	0.135895	−	0.135895i
$926$	−10.6495	+	56.4191i	−0.349965	+	1.85405i
$927$	35.7966	+	62.0015i	1.17571	+	2.03640i
$928$	6.17074	−	41.5567i	0.202564	−	1.36417i
$929$	13.6726	−	23.6816i	0.448583	−	0.776969i	−0.549711	−	0.835355i	$-0.685262\pi$
$929$	13.6726	−	23.6816i	0.448583	−	0.776969i	0.998294	+	0.0583859i	$0.0185954\pi$
$930$	15.2099	−	5.32963i	0.498751	−	0.174765i
$931$		0			0
$932$	26.9019	+	33.6734i	0.881200	+	1.10301i
$933$	−16.2467	+	4.35329i	−0.531893	+	0.142520i
$934$	12.9839	−	0.978722i	0.424847	−	0.0320248i
$935$	−6.80808	+	3.93065i	−0.222648	+	0.128546i
$936$	−6.58938	+	21.4622i	−0.215381	+	0.701515i
$937$		−	6.30987i		−	0.206135i	−0.994674	−	0.103067i	$-0.967134\pi$
$937$		−	6.30987i		−	0.206135i	0.994674	−	0.103067i	$-0.0328657\pi$
$938$		0			0
$939$	25.2386	+	25.2386i	0.823630	+	0.823630i
$940$	−5.23863	+	7.11111i	−0.170865	+	0.231939i
$941$	−26.3055	−	7.04854i	−0.857535	−	0.229776i	−0.196845	−	0.980435i	$-0.563070\pi$
$941$	−26.3055	−	7.04854i	−0.857535	−	0.229776i	−0.660690	+	0.750659i	$0.729736\pi$
$942$	−31.6462	+	36.8062i	−1.03109	+	1.19921i
$943$	−5.47021	+	9.47467i	−0.178134	+	0.308538i
$944$	−31.2920	+	19.7386i	−1.01847	+	0.642435i
$945$		0			0
$946$	0.498742	+	1.42333i	0.0162155	+	0.0462763i
$947$	−5.93030	−	22.1322i	−0.192709	−	0.719200i	−0.992848	−	0.119385i	$-0.961908\pi$
$947$	−5.93030	−	22.1322i	−0.192709	−	0.719200i	0.800139	−	0.599815i	$-0.204759\pi$
$948$	−51.2484	+	22.4128i	−1.66447	+	0.727935i
$949$	2.59958	−	9.70178i	0.0843860	−	0.314933i
$950$	9.50925	−	6.48939i	0.308521	−	0.210544i
$951$			13.6483i			0.442577i
$952$		0			0
$953$			33.9914i			1.10109i	0.834806	+	0.550545i	$0.185580\pi$
$953$			33.9914i			1.10109i	−0.834806	+	0.550545i	$0.814420\pi$
$954$	−47.9551	−	70.2711i	−1.55260	−	2.27511i
$955$	0.101675	−	0.379457i	0.00329014	−	0.0122790i
$956$	−27.0278	−	10.5803i	−0.874141	−	0.342193i
$957$	−7.46771	−	27.8699i	−0.241397	−	0.900905i
$958$	−9.98197	+	3.49775i	−0.322503	+	0.113007i
$959$		0			0
$960$	8.12866	+	16.7666i	0.262351	+	0.541140i
$961$	3.53001	−	6.11416i	0.113871	−	0.197231i
$962$	1.84970	+	1.59039i	0.0596366	+	0.0512761i
$963$	42.5767	+	11.4084i	1.37201	+	0.367630i
$964$	2.75257	+	18.1543i	0.0886544	+	0.584712i
$965$	−2.63506	−	2.63506i	−0.0848257	−	0.0848257i
$966$		0			0
$967$			50.2769i			1.61680i	0.588635	+	0.808399i	$0.299665\pi$
$967$			50.2769i			1.61680i	−0.588635	+	0.808399i	$0.700335\pi$
$968$	−23.3467	+	12.3783i	−0.750390	+	0.397854i
$969$	−38.2194	+	22.0660i	−1.22778	+	0.708861i
$970$	−0.740002	−	9.81702i	−0.0237600	−	0.315205i
$971$	30.0778	−	8.05932i	0.965243	−	0.258636i	0.258425	−	0.966031i	$-0.416797\pi$
$971$	30.0778	−	8.05932i	0.965243	−	0.258636i	0.706818	+	0.707395i	$0.250130\pi$
$972$	−0.438411	+	3.92184i	−0.0140620	+	0.125793i
$973$		0			0
$974$	−9.63668	−	27.5015i	−0.308779	−	0.881203i
$975$	8.63766	−	14.9609i	0.276626	−	0.479131i
$976$	−12.3179	+	23.4057i	−0.394287	+	0.749198i
$977$	22.6866	+	39.2943i	0.725808	+	1.25714i	0.958640	+	0.284620i	$0.0918674\pi$
$977$	22.6866	+	39.2943i	0.725808	+	1.25714i	−0.232832	+	0.972517i	$0.574799\pi$
$978$	−42.4064	−	8.00451i	−1.35601	−	0.255956i
$979$	−1.93424	+	1.93424i	−0.0618185	+	0.0618185i
$980$		0			0
$981$	48.7418	+	48.7418i	1.55621	+	1.55621i
$982$	1.87337	−	1.27844i	0.0597815	−	0.0407967i
$983$	39.3690	−	22.7297i	1.25568	−	0.724966i	0.283446	−	0.958988i	$-0.408522\pi$
$983$	39.3690	−	22.7297i	1.25568	−	0.724966i	0.972231	+	0.234022i	$0.0751889\pi$
$984$	16.5315	+	17.7699i	0.527004	+	0.566483i
$985$	2.86073	+	1.65164i	0.0911504	+	0.0526257i
$986$	36.0232	−	74.8868i	1.14721	−	2.38488i
$987$		0			0
$988$	2.99896	+	3.75383i	0.0954095	+	0.119425i
$989$	0.824941	+	3.07872i	0.0262316	+	0.0978976i
$990$	6.50685	+	5.59465i	0.206801	+	0.177810i
$991$	−12.9817	−	22.4850i	−0.412379	−	0.714261i	0.582771	−	0.812637i	$-0.301969\pi$
$991$	−12.9817	−	22.4850i	−0.412379	−	0.714261i	−0.995149	+	0.0983759i	$0.968635\pi$
$992$	−25.3929	−	11.0128i	−0.806225	−	0.349655i
$993$	−69.4027			−2.20243
$994$		0			0
$995$	4.13413	−	4.13413i	0.131061	−	0.131061i
$996$	40.3845	−	6.12312i	1.27963	−	0.194018i
$997$	11.7799	−	43.9631i	0.373073	−	1.39233i	−0.483068	−	0.875583i	$-0.660478\pi$
$997$	11.7799	−	43.9631i	0.373073	−	1.39233i	0.856141	−	0.516743i	$-0.172856\pi$
$998$	47.0305	−	3.54514i	1.48872	−	0.112219i
$999$	10.7766	+	6.22186i	0.340956	+	0.196851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.373.8		48
7.2	even	3		784.2.m.k.197.2		24
7.3	odd	6		112.2.w.c.53.11	yes	48
7.4	even	3	inner	784.2.x.o.165.11		48
7.5	odd	6		784.2.m.j.197.2		24
7.6	odd	2		112.2.w.c.37.8	✓	48
16.13	even	4	inner	784.2.x.o.765.11		48
28.3	even	6		448.2.ba.c.305.12		48
28.27	even	2		448.2.ba.c.177.1		48
56.3	even	6		896.2.ba.e.865.1		48
56.13	odd	2		896.2.ba.f.737.1		48
56.27	even	2		896.2.ba.e.737.12		48
56.45	odd	6		896.2.ba.f.865.12		48
112.3	even	12		448.2.ba.c.81.1		48
112.13	odd	4		112.2.w.c.93.11	yes	48
112.27	even	4		896.2.ba.e.289.1		48
112.45	odd	12		112.2.w.c.109.8	yes	48
112.59	even	12		896.2.ba.e.417.12		48
112.61	odd	12		784.2.m.j.589.2		24
112.69	odd	4		896.2.ba.f.289.12		48
112.83	even	4		448.2.ba.c.401.12		48
112.93	even	12		784.2.m.k.589.2		24
112.101	odd	12		896.2.ba.f.417.1		48
112.109	even	12	inner	784.2.x.o.557.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.8	✓	48	7.6	odd	2
112.2.w.c.53.11	yes	48	7.3	odd	6
112.2.w.c.93.11	yes	48	112.13	odd	4
112.2.w.c.109.8	yes	48	112.45	odd	12
448.2.ba.c.81.1		48	112.3	even	12
448.2.ba.c.177.1		48	28.27	even	2
448.2.ba.c.305.12		48	28.3	even	6
448.2.ba.c.401.12		48	112.83	even	4
784.2.m.j.197.2		24	7.5	odd	6
784.2.m.j.589.2		24	112.61	odd	12
784.2.m.k.197.2		24	7.2	even	3
784.2.m.k.589.2		24	112.93	even	12
784.2.x.o.165.11		48	7.4	even	3	inner
784.2.x.o.373.8		48	1.1	even	1	trivial
784.2.x.o.557.8		48	112.109	even	12	inner
784.2.x.o.765.11		48	16.13	even	4	inner
896.2.ba.e.289.1		48	112.27	even	4
896.2.ba.e.417.12		48	112.59	even	12
896.2.ba.e.737.12		48	56.27	even	2
896.2.ba.e.865.1		48	56.3	even	6
896.2.ba.f.289.12		48	112.69	odd	4
896.2.ba.f.417.1		48	112.101	odd	12
896.2.ba.f.737.1		48	56.13	odd	2
896.2.ba.f.865.12		48	56.45	odd	6

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.262311 - 1.38967i) q^{2} +(-2.91496 - 0.781062i) q^{3} +(-1.86239 - 0.729053i) q^{4} +(0.745506 - 0.199758i) q^{5} +(-1.85005 + 3.84597i) q^{6} +(-1.50167 + 2.39687i) q^{8} +(5.28887 + 3.05353i) q^{9} +O(q^{10})\)	\(q+(0.262311 - 1.38967i) q^{2} +(-2.91496 - 0.781062i) q^{3} +(-1.86239 - 0.729053i) q^{4} +(0.745506 - 0.199758i) q^{5} +(-1.85005 + 3.84597i) q^{6} +(-1.50167 + 2.39687i) q^{8} +(5.28887 + 3.05353i) q^{9} +(-0.0820438 - 1.08841i) q^{10} +(-0.333193 + 1.24349i) q^{11} +(4.85935 + 3.57980i) q^{12} +(0.919058 - 0.919058i) q^{13} -2.32914 q^{15} +(2.93696 + 2.71556i) q^{16} +(3.95601 + 6.85200i) q^{17} +(5.63074 - 6.54883i) q^{18} +(-0.478380 - 1.78534i) q^{19} +(-1.53405 - 0.171487i) q^{20} +(1.64065 + 0.789212i) q^{22} +(3.33211 + 1.92380i) q^{23} +(6.24941 - 5.81389i) q^{24} +(-3.81425 + 2.20216i) q^{25} +(-1.03611 - 1.51827i) q^{26} +(-6.63016 - 6.63016i) q^{27} +(5.25154 - 5.25154i) q^{29} +(-0.610960 + 3.23675i) q^{30} +(-2.44642 - 4.23733i) q^{31} +(4.54413 - 3.36910i) q^{32} +(1.94249 - 3.36449i) q^{33} +(10.5598 - 3.70020i) q^{34} +(-7.62373 - 9.54272i) q^{36} +(-1.28190 + 0.343485i) q^{37} +(-2.60652 + 0.196478i) q^{38} +(-3.39686 + 1.96118i) q^{39} +(-0.640710 + 2.08685i) q^{40} +2.84345i q^{41} +(0.585764 + 0.585764i) q^{43} +(1.52711 - 2.07295i) q^{44} +(4.55285 + 1.21993i) q^{45} +(3.54750 - 4.12591i) q^{46} +(2.86095 - 4.95532i) q^{47} +(-6.44012 - 10.2097i) q^{48} +(2.05976 + 5.87821i) q^{50} +(-6.17977 - 23.0632i) q^{51} +(-2.38168 + 1.04160i) q^{52} +(2.54947 - 9.51475i) q^{53} +(-10.9529 + 7.47460i) q^{54} +0.993590i q^{55} +5.57784i q^{57} +(-5.92039 - 8.67547i) q^{58} +(-2.39390 + 8.93417i) q^{59} +(4.33777 + 1.69807i) q^{60} +(1.71139 + 6.38698i) q^{61} +(-6.53023 + 2.28823i) q^{62} +(-3.48998 - 7.19862i) q^{64} +(0.501575 - 0.868753i) q^{65} +(-4.16601 - 3.58197i) q^{66} +(5.94825 + 1.59383i) q^{67} +(-2.37214 - 15.6452i) q^{68} +(-8.21037 - 8.21037i) q^{69} +1.99534i q^{71} +(-15.2611 + 8.09134i) q^{72} +(6.69237 - 3.86384i) q^{73} +(0.141075 + 1.87153i) q^{74} +(12.8384 - 3.44004i) q^{75} +(-0.410678 + 3.67375i) q^{76} +(1.83437 + 5.23497i) q^{78} +(-4.63378 + 8.02594i) q^{79} +(2.73198 + 1.43778i) q^{80} +(4.98751 + 8.63862i) q^{81} +(3.95146 + 0.745866i) q^{82} +(4.78537 - 4.78537i) q^{83} +(4.31797 + 4.31797i) q^{85} +(0.967673 - 0.660369i) q^{86} +(-19.4098 + 11.2063i) q^{87} +(-2.48015 - 2.66594i) q^{88} +(1.84016 + 1.06242i) q^{89} +(2.88957 - 6.00698i) q^{90} +(-4.80313 - 6.01213i) q^{92} +(3.82162 + 14.2625i) q^{93} +(-6.13582 - 5.27563i) q^{94} +(-0.713270 - 1.23542i) q^{95} +(-15.8775 + 6.27155i) q^{96} +9.01961 q^{97} +(-5.55926 + 5.55926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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