LMFDB - Embedded newform 784.2.x.o.373.3

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			373.3
Character	$\chi$	$=$	784.373
Dual form			784.2.x.o.557.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25281 + 0.656100i) q^{2} +(-1.95279 - 0.523249i) q^{3} +(1.13907 - 1.64394i) q^{4} +(-0.959072 + 0.256983i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} +(0.941530 + 0.543593i) q^{9} +O(q^{10})$	\(q+(-1.25281 + 0.656100i) q^{2} +(-1.95279 - 0.523249i) q^{3} +(1.13907 - 1.64394i) q^{4} +(-0.959072 + 0.256983i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} +(0.941530 + 0.543593i) q^{9} +(1.03293 - 0.951197i) q^{10} +(-0.505816 + 1.88773i) q^{11} +(-3.08455 + 2.61425i) q^{12} +(2.10314 - 2.10314i) q^{13} +2.00733 q^{15} +(-1.40505 - 3.74511i) q^{16} +(-2.83885 - 4.91704i) q^{17} +(-1.53621 - 0.0632809i) q^{18} +(0.165210 + 0.616573i) q^{19} +(-0.669984 + 1.86937i) q^{20} +(-0.604848 - 2.69683i) q^{22} +(-5.92691 - 3.42190i) q^{23} +(2.14914 - 5.29893i) q^{24} +(-3.47635 + 2.00707i) q^{25} +(-1.25497 + 4.01471i) q^{26} +(2.73445 + 2.73445i) q^{27} +(-0.207295 + 0.207295i) q^{29} +(-2.51481 + 1.31701i) q^{30} +(3.94693 + 6.83628i) q^{31} +(4.21743 + 3.77005i) q^{32} +(1.97551 - 3.42168i) q^{33} +(6.78261 + 4.29755i) q^{34} +(1.96610 - 0.928627i) q^{36} +(9.60533 - 2.57374i) q^{37} +(-0.611510 - 0.664054i) q^{38} +(-5.20747 + 3.00653i) q^{39} +(-0.387132 - 2.78155i) q^{40} -2.40202i q^{41} +(3.65586 + 3.65586i) q^{43} +(2.52715 + 2.98178i) q^{44} +(-1.04269 - 0.279388i) q^{45} +(9.67040 + 0.398352i) q^{46} +(0.144593 - 0.250442i) q^{47} +(0.784155 + 8.04861i) q^{48} +(3.03837 - 4.79531i) q^{50} +(2.97086 + 11.0874i) q^{51} +(-1.06181 - 5.85305i) q^{52} +(-2.04376 + 7.62740i) q^{53} +(-5.21982 - 1.63168i) q^{54} -1.94045i q^{55} -1.29048i q^{57} +(0.123695 - 0.395707i) q^{58} +(-3.60507 + 13.4543i) q^{59} +(2.28649 - 3.29993i) q^{60} +(0.969174 + 3.61701i) q^{61} +(-9.43003 - 5.97498i) q^{62} +(-7.75717 - 1.95611i) q^{64} +(-1.47659 + 2.55754i) q^{65} +(-0.229973 + 5.58284i) q^{66} +(10.0468 + 2.69202i) q^{67} +(-11.3169 - 0.933941i) q^{68} +(9.78352 + 9.78352i) q^{69} +11.5947i q^{71} +(-1.85387 + 2.45335i) q^{72} +(0.310772 - 0.179424i) q^{73} +(-10.3450 + 9.52646i) q^{74} +(7.83878 - 2.10040i) q^{75} +(1.20179 + 0.430722i) q^{76} +(4.55138 - 7.18323i) q^{78} +(-3.84953 + 6.66758i) q^{79} +(2.30997 + 3.23075i) q^{80} +(-5.53979 - 9.59520i) q^{81} +(1.57596 + 3.00927i) q^{82} +(0.424001 - 0.424001i) q^{83} +(3.98626 + 3.98626i) q^{85} +(-6.97871 - 2.18149i) q^{86} +(0.513270 - 0.296337i) q^{87} +(-5.12238 - 2.07754i) q^{88} +(15.2323 + 8.79437i) q^{89} +(1.48960 - 0.334088i) q^{90} +(-12.3765 + 5.84569i) q^{92} +(-4.13045 - 15.4150i) q^{93} +(-0.0168324 + 0.408623i) q^{94} +(-0.316897 - 0.548881i) q^{95} +(-6.26308 - 9.56889i) q^{96} -12.2678 q^{97} +(-1.50240 + 1.50240i) 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 $

$2$	−1.25281	+	0.656100i	−0.885871	+	0.463932i
$2$	−1.25281	+	0.656100i	−0.885871	+	0.463932i
$3$	−1.95279	−	0.523249i	−1.12744	−	0.302098i	−0.353552	−	0.935415i	$-0.615026\pi$
$3$	−1.95279	−	0.523249i	−1.12744	−	0.302098i	−0.773893	+	0.633317i	$0.781693\pi$
$4$	1.13907	−	1.64394i	0.569533	−	0.821968i
$5$	−0.959072	+	0.256983i	−0.428910	+	0.114926i	−0.466814	−	0.884355i	$-0.654598\pi$
$5$	−0.959072	+	0.256983i	−0.428910	+	0.114926i	0.0379045	+	0.999281i	$0.487932\pi$
$6$	2.78978	−	0.625694i	1.13892	−	0.255439i
$7$		0			0
$7$		0			0
$8$	−0.348448	+	2.80688i	−0.123195	+	0.992382i
$9$	0.941530	+	0.543593i	0.313843	+	0.181198i
$10$	1.03293	−	0.951197i	0.326641	−	0.300795i
$11$	−0.505816	+	1.88773i	−0.152509	+	0.569172i	0.846797	+	0.531917i	$0.178528\pi$
$11$	−0.505816	+	1.88773i	−0.152509	+	0.569172i	−0.999306	+	0.0372551i	$0.988139\pi$
$12$	−3.08455	+	2.61425i	−0.890432	+	0.754669i
$13$	2.10314	−	2.10314i	0.583307	−	0.583307i	−0.352504	−	0.935810i	$-0.614670\pi$
$13$	2.10314	−	2.10314i	0.583307	−	0.583307i	0.935810	+	0.352504i	$0.114670\pi$
$14$		0			0
$15$	2.00733			0.518291
$16$	−1.40505	−	3.74511i	−0.351264	−	0.936277i
$17$	−2.83885	−	4.91704i	−0.688523	−	1.19256i	−0.972316	−	0.233672i	$-0.924926\pi$
$17$	−2.83885	−	4.91704i	−0.688523	−	1.19256i	0.283792	−	0.958886i	$-0.408407\pi$
$18$	−1.53621	−	0.0632809i	−0.362088	−	0.0149155i
$19$	0.165210	+	0.616573i	0.0379018	+	0.141451i	0.982284	−	0.187399i	$-0.0600056\pi$
$19$	0.165210	+	0.616573i	0.0379018	+	0.141451i	−0.944382	+	0.328850i	$0.893339\pi$
$20$	−0.669984	+	1.86937i	−0.149813	+	0.418005i
$21$		0			0
$22$	−0.604848	−	2.69683i	−0.128954	−	0.574967i
$23$	−5.92691	−	3.42190i	−1.23585	−	0.713516i	−0.267604	−	0.963529i	$-0.586232\pi$
$23$	−5.92691	−	3.42190i	−1.23585	−	0.713516i	−0.968243	+	0.250013i	$0.919565\pi$
$24$	2.14914	−	5.29893i	0.438692	−	1.08164i
$25$	−3.47635	+	2.00707i	−0.695270	+	0.401414i
$26$	−1.25497	+	4.01471i	−0.246119	+	0.787349i
$27$	2.73445	+	2.73445i	0.526245	+	0.526245i
$28$		0			0
$29$	−0.207295	+	0.207295i	−0.0384937	+	0.0384937i	−0.726092	−	0.687598i	$-0.758665\pi$
$29$	−0.207295	+	0.207295i	−0.0384937	+	0.0384937i	0.687598	+	0.726092i	$0.258665\pi$
$30$	−2.51481	+	1.31701i	−0.459139	+	0.240452i
$31$	3.94693	+	6.83628i	0.708889	+	1.22783i	0.965270	+	0.261255i	$0.0841365\pi$
$31$	3.94693	+	6.83628i	0.708889	+	1.22783i	−0.256381	+	0.966576i	$0.582530\pi$
$32$	4.21743	+	3.77005i	0.745543	+	0.666457i
$33$	1.97551	−	3.42168i	0.343891	−	0.595637i
$34$	6.78261	+	4.29755i	1.16321	+	0.737023i
$35$		0			0
$36$	1.96610	−	0.928627i	0.327683	−	0.154771i
$37$	9.60533	−	2.57374i	1.57911	−	0.423120i	0.640457	−	0.767994i	$-0.278745\pi$
$37$	9.60533	−	2.57374i	1.57911	−	0.423120i	0.938649	+	0.344873i	$0.112078\pi$
$38$	−0.611510	−	0.664054i	−0.0992000	−	0.107724i
$39$	−5.20747	+	3.00653i	−0.833862	+	0.481430i
$40$	−0.387132	−	2.78155i	−0.0612110	−	0.439801i
$41$		−	2.40202i		−	0.375132i	−0.982252	−	0.187566i	$-0.939940\pi$
$41$		−	2.40202i		−	0.375132i	0.982252	−	0.187566i	$-0.0600599\pi$
$42$		0			0
$43$	3.65586	+	3.65586i	0.557514	+	0.557514i	0.928599	−	0.371085i	$-0.121014\pi$
$43$	3.65586	+	3.65586i	0.557514	+	0.557514i	−0.371085	+	0.928599i	$0.621014\pi$
$44$	2.52715	+	2.98178i	0.380982	+	0.449520i
$45$	−1.04269	−	0.279388i	−0.155435	−	0.0416486i
$46$	9.67040	+	0.398352i	1.42582	+	0.0587338i
$47$	0.144593	−	0.250442i	0.0210910	−	0.0365307i	−0.855287	−	0.518154i	$-0.826619\pi$
$47$	0.144593	−	0.250442i	0.0210910	−	0.0365307i	0.876378	+	0.481623i	$0.159953\pi$
$48$	0.784155	+	8.04861i	0.113183	+	1.16172i
$49$		0			0
$50$	3.03837	−	4.79531i	0.429690	−	0.678159i
$51$	2.97086	+	11.0874i	0.416003	+	1.55254i
$52$	−1.06181	−	5.85305i	−0.147247	−	0.811672i
$53$	−2.04376	+	7.62740i	−0.280732	+	1.04770i	0.671171	+	0.741303i	$0.265792\pi$
$53$	−2.04376	+	7.62740i	−0.280732	+	1.04770i	−0.951902	+	0.306402i	$0.900875\pi$
$54$	−5.21982	−	1.63168i	−0.710328	−	0.222043i
$55$		−	1.94045i		−	0.261651i
$56$		0			0
$57$		−	1.29048i		−	0.170929i
$58$	0.123695	−	0.395707i	0.0162419	−	0.0519589i
$59$	−3.60507	+	13.4543i	−0.469340	+	1.75160i	0.172744	+	0.984967i	$0.444737\pi$
$59$	−3.60507	+	13.4543i	−0.469340	+	1.75160i	−0.642084	+	0.766634i	$0.721930\pi$
$60$	2.28649	−	3.29993i	0.295184	−	0.426019i
$61$	0.969174	+	3.61701i	0.124090	+	0.463110i	0.999806	−	0.0197171i	$-0.00627654\pi$
$61$	0.969174	+	3.61701i	0.124090	+	0.463110i	−0.875716	+	0.482827i	$0.839610\pi$
$62$	−9.43003	−	5.97498i	−1.19761	−	0.758823i
$63$		0			0
$64$	−7.75717	−	1.95611i	−0.969646	−	0.244513i
$65$	−1.47659	+	2.55754i	−0.183149	+	0.317223i
$66$	−0.229973	+	5.58284i	−0.0283078	+	0.687200i
$67$	10.0468	+	2.69202i	1.22741	+	0.328883i	0.813570	−	0.581467i	$-0.197521\pi$
$67$	10.0468	+	2.69202i	1.22741	+	0.328883i	0.413838	+	0.910350i	$0.364188\pi$
$68$	−11.3169	−	0.933941i	−1.37238	−	0.113257i
$69$	9.78352	+	9.78352i	1.17780	+	1.17780i
$70$		0			0
$71$			11.5947i			1.37603i	0.725695	+	0.688017i	$0.241518\pi$
$71$			11.5947i			1.37603i	−0.725695	+	0.688017i	$0.758482\pi$
$72$	−1.85387	+	2.45335i	−0.218481	+	0.289130i
$73$	0.310772	−	0.179424i	0.0363731	−	0.0210000i	−0.481703	−	0.876334i	$-0.659982\pi$
$73$	0.310772	−	0.179424i	0.0363731	−	0.0210000i	0.518076	+	0.855334i	$0.326648\pi$
$74$	−10.3450	+	9.52646i	−1.20258	+	1.10743i
$75$	7.83878	−	2.10040i	0.905145	−	0.242533i
$76$	1.20179	+	0.430722i	0.137855	+	0.0494073i
$77$		0			0
$78$	4.55138	−	7.18323i	0.515342	−	0.813341i
$79$	−3.84953	+	6.66758i	−0.433106	+	0.750161i	−0.997139	−	0.0755910i	$-0.975916\pi$
$79$	−3.84953	+	6.66758i	−0.433106	+	0.750161i	0.564033	+	0.825752i	$0.309249\pi$
$80$	2.30997	+	3.23075i	0.258263	+	0.361209i
$81$	−5.53979	−	9.59520i	−0.615532	−	1.06613i
$82$	1.57596	+	3.00927i	0.174036	+	0.332318i
$83$	0.424001	−	0.424001i	0.0465402	−	0.0465402i	−0.683454	−	0.729994i	$-0.739523\pi$
$83$	0.424001	−	0.424001i	0.0465402	−	0.0465402i	0.729994	+	0.683454i	$0.239523\pi$
$84$		0			0
$85$	3.98626	+	3.98626i	0.432371	+	0.432371i
$86$	−6.97871	−	2.18149i	−0.752534	−	0.235236i
$87$	0.513270	−	0.296337i	0.0550283	−	0.0317706i
$88$	−5.12238	−	2.07754i	−0.546048	−	0.221467i
$89$	15.2323	+	8.79437i	1.61462	+	0.932201i	0.988280	+	0.152652i	$0.0487813\pi$
$89$	15.2323	+	8.79437i	1.61462	+	0.932201i	0.626340	+	0.779550i	$0.284552\pi$
$90$	1.48960	−	0.334088i	0.157017	−	0.0352160i
$91$		0			0
$92$	−12.3765	+	5.84569i	−1.29034	+	0.609455i
$93$	−4.13045	−	15.4150i	−0.428308	−	1.59847i
$94$	−0.0168324	+	0.408623i	−0.00173613	+	0.0421462i
$95$	−0.316897	−	0.548881i	−0.0325129	−	0.0563140i
$96$	−6.26308	−	9.56889i	−0.639223	−	0.976621i
$97$	−12.2678			−1.24560			−0.622802	−	0.782379i	$-0.714006\pi$
$97$	−12.2678			−1.24560			−0.622802	+	0.782379i	$0.714006\pi$
$98$		0			0
$99$	−1.50240	+	1.50240i	−0.150997	+	0.150997i
$100$	−0.660296	+	8.00108i	−0.0660296	+	0.800108i
$101$	0.313118	−	1.16857i	0.0311564	−	0.116277i	−0.948596	−	0.316488i	$-0.897496\pi$
$101$	0.313118	−	1.16857i	0.0311564	−	0.116277i	0.979753	+	0.200211i	$0.0641628\pi$
$102$	−10.9963	−	11.9412i	−1.08880	−	1.18236i
$103$	−5.06181	−	2.92244i	−0.498755	−	0.287956i	0.229444	−	0.973322i	$-0.426309\pi$
$103$	−5.06181	−	2.92244i	−0.498755	−	0.287956i	−0.728199	+	0.685365i	$0.759643\pi$
$104$	5.17043	+	6.63611i	0.507003	+	0.650724i
$105$		0			0
$106$	−2.44390	−	10.8966i	−0.237372	−	1.05837i
$107$	3.62492	−	0.971295i	0.350435	−	0.0938987i	−0.0793079	−	0.996850i	$-0.525271\pi$
$107$	3.62492	−	0.971295i	0.350435	−	0.0938987i	0.429742	+	0.902952i	$0.358604\pi$
$108$	7.60999	−	1.38054i	0.732271	−	0.132843i
$109$	9.67656	+	2.59283i	0.926846	+	0.248348i	0.690509	−	0.723323i	$-0.257386\pi$
$109$	9.67656	+	2.59283i	0.926846	+	0.248348i	0.236337	+	0.971671i	$0.424053\pi$
$110$	1.27313	+	2.43102i	0.121388	+	0.231789i
$111$	−20.1039			−1.90818
$112$		0			0
$113$	5.07461			0.477379			0.238689	−	0.971096i	$-0.423282\pi$
$113$	5.07461			0.477379			0.238689	+	0.971096i	$0.423282\pi$
$114$	0.846686	+	1.61673i	0.0792994	+	0.151421i
$115$	6.56370	+	1.75874i	0.612069	+	0.164003i
$116$	0.104657	+	0.576902i	0.00971714	+	0.0535640i
$117$	3.12342	−	0.836919i	0.288761	−	0.0773732i
$118$	−4.31089	−	19.2210i	−0.396850	−	1.76943i
$119$		0			0
$120$	−0.699452	+	5.63435i	−0.0638509	+	0.514343i
$121$	6.21861	+	3.59031i	0.565328	+	0.326392i
$122$	−3.58731	−	3.89555i	−0.324780	−	0.352686i
$123$	−1.25685	+	4.69064i	−0.113327	+	0.422941i
$124$	15.7342	+	1.29848i	1.41297	+	0.116607i
$125$	6.32873	−	6.32873i	0.566059	−	0.566059i
$126$		0			0
$127$	−11.1710			−0.991270			−0.495635	−	0.868531i	$-0.665065\pi$
$127$	−11.1710			−0.991270			−0.495635	+	0.868531i	$0.665065\pi$
$128$	11.0017	−	2.63884i	0.972418	−	0.233243i
$129$	−5.22621	−	9.05207i	−0.460142	−	0.796990i
$130$	0.171894	−	4.17290i	0.0150761	−	0.365987i
$131$	3.26332	+	12.1789i	0.285118	+	1.06407i	0.948753	+	0.316017i	$0.102346\pi$
$131$	3.26332	+	12.1789i	0.285118	+	1.06407i	−0.663636	+	0.748056i	$0.730988\pi$
$132$	−3.37478	−	7.14512i	−0.293737	−	0.621903i
$133$		0			0
$134$	−14.3529	+	3.21909i	−1.23990	+	0.278087i
$135$	−3.32524	−	1.91983i	−0.286191	−	0.165233i
$136$	14.7907	−	6.25499i	1.26830	−	0.536361i
$137$	14.0325	−	8.10166i	1.19888	−	0.692172i	0.238572	−	0.971125i	$-0.423321\pi$
$137$	14.0325	−	8.10166i	1.19888	−	0.692172i	0.960305	+	0.278953i	$0.0899874\pi$
$138$	−18.6758	−	5.83793i	−1.58979	−	0.496957i
$139$	−10.5018	−	10.5018i	−0.890748	−	0.890748i	0.103846	−	0.994593i	$-0.466885\pi$
$139$	−10.5018	−	10.5018i	−0.890748	−	0.890748i	−0.994593	+	0.103846i	$0.966885\pi$
$140$		0			0
$141$	−0.413403	+	0.413403i	−0.0348148	+	0.0348148i
$142$	−7.60725	−	14.5259i	−0.638386	−	1.21899i
$143$	2.90636	+	5.03397i	0.243042	+	0.420961i
$144$	0.712912	−	4.28991i	0.0594093	−	0.357492i
$145$	0.145539	−	0.252082i	0.0120864	−	0.0209342i
$146$	−0.271618	+	0.428682i	−0.0224793	+	0.0354780i
$147$		0			0
$148$	6.71005	−	18.7222i	0.551562	−	1.53896i
$149$	−9.61931	+	2.57749i	−0.788045	+	0.211156i	−0.630329	−	0.776328i	$-0.717080\pi$
$149$	−9.61931	+	2.57749i	−0.788045	+	0.211156i	−0.157716	+	0.987484i	$0.550413\pi$
$150$	−8.44244	+	7.77442i	−0.689322	+	0.634779i
$151$	8.97638	−	5.18252i	0.730487	−	0.421747i	−0.0881130	−	0.996110i	$-0.528084\pi$
$151$	8.97638	−	5.18252i	0.730487	−	0.421747i	0.818600	+	0.574363i	$0.194750\pi$
$152$	−1.78821	+	0.248882i	−0.145043	+	0.0201870i
$153$		−	6.17272i		−	0.499035i
$154$		0			0
$155$	−5.54219	−	5.54219i	−0.445159	−	0.445159i
$156$	−0.989104	+	11.9854i	−0.0791917	+	0.959599i
$157$	−3.98512	−	1.06781i	−0.318047	−	0.0852205i	0.0962637	−	0.995356i	$-0.469311\pi$
$157$	−3.98512	−	1.06781i	−0.318047	−	0.0852205i	−0.414311	+	0.910135i	$0.635977\pi$
$158$	0.448133	−	10.8789i	0.0356515	−	0.865477i
$159$	7.98206	−	13.8253i	0.633019	−	1.09642i
$160$	−5.01366	−	2.53195i	−0.396364	−	0.200168i
$161$		0			0
$162$	13.2357	+	8.38631i	1.03990	+	0.658891i
$163$	2.13899	+	7.98280i	0.167538	+	0.625261i	0.997703	+	0.0677429i	$0.0215797\pi$
$163$	2.13899	+	7.98280i	0.167538	+	0.625261i	−0.830165	+	0.557518i	$0.811754\pi$
$164$	−3.94876	−	2.73606i	−0.308347	−	0.213650i
$165$	−1.01534	+	3.78930i	−0.0790442	+	0.294997i
$166$	−0.253006	+	0.809380i	−0.0196371	+	0.0628201i
$167$			8.92669i			0.690768i	0.938462	+	0.345384i	$0.112251\pi$
$167$			8.92669i			0.690768i	−0.938462	+	0.345384i	$0.887749\pi$
$168$		0			0
$169$			4.15359i			0.319507i
$170$	−7.60941	−	2.37864i	−0.583615	−	0.182434i
$171$	−0.179614	+	0.670329i	−0.0137354	+	0.0512613i
$172$	10.1743	−	1.84573i	0.775781	−	0.140736i
$173$	−1.41044	−	5.26383i	−0.107234	−	0.400202i	0.891355	−	0.453305i	$-0.149755\pi$
$173$	−1.41044	−	5.26383i	−0.107234	−	0.400202i	−0.998589	+	0.0531037i	$0.983089\pi$
$174$	−0.448604	+	0.708010i	−0.0340086	+	0.0536741i
$175$		0			0
$176$	7.78045	−	0.758029i	0.586473	−	0.0571386i
$177$	14.0799	−	24.3871i	1.05831	−	1.83305i
$178$	−24.8532	−	1.02377i	−1.86282	−	0.0767351i
$179$	−9.42440	−	2.52526i	−0.704413	−	0.188747i	−0.111207	−	0.993797i	$-0.535472\pi$
$179$	−9.42440	−	2.52526i	−0.704413	−	0.188747i	−0.593206	+	0.805050i	$0.702138\pi$
$180$	−1.64699	+	1.39587i	−0.122759	+	0.104042i
$181$	8.42976	+	8.42976i	0.626579	+	0.626579i	0.947206	−	0.320627i	$-0.103894\pi$
$181$	8.42976	+	8.42976i	0.626579	+	0.626579i	−0.320627	+	0.947206i	$0.603894\pi$
$182$		0			0
$183$		−	7.57038i		−	0.559619i
$184$	11.6701	−	15.4438i	0.860331	−	1.13853i
$185$	−8.55080	+	4.93680i	−0.628667	+	0.362961i
$186$	15.2885	+	16.6021i	1.12101	+	1.21733i
$187$	10.7180	−	2.87187i	0.783776	−	0.210012i
$188$	−0.247010	−	0.522971i	−0.0180150	−	0.0381416i
$189$		0			0
$190$	0.757132	+	0.479728i	0.0549282	+	0.0348032i
$191$	2.46522	−	4.26989i	0.178377	−	0.308958i	−0.762948	−	0.646460i	$-0.776249\pi$
$191$	2.46522	−	4.26989i	0.178377	−	0.308958i	0.941325	+	0.337502i	$0.109582\pi$
$192$	14.1246	+	7.87880i	1.01936	+	0.568603i
$193$	−10.9543	−	18.9735i	−0.788510	−	1.36574i	−0.926880	−	0.375358i	$-0.877520\pi$
$193$	−10.9543	−	18.9735i	−0.788510	−	1.36574i	0.138370	−	0.990381i	$-0.455814\pi$
$194$	15.3692	−	8.04889i	1.10344	−	0.577877i
$195$	4.22171	−	4.22171i	0.302323	−	0.302323i
$196$		0			0
$197$	7.61984	+	7.61984i	0.542891	+	0.542891i	0.924375	−	0.381484i	$-0.124587\pi$
$197$	7.61984	+	7.61984i	0.542891	+	0.542891i	−0.381484	+	0.924375i	$0.624587\pi$
$198$	0.896496	−	2.86794i	0.0637112	−	0.203816i
$199$	3.09710	−	1.78811i	0.219547	−	0.126756i	−0.386193	−	0.922418i	$-0.626210\pi$
$199$	3.09710	−	1.78811i	0.219547	−	0.126756i	0.605741	+	0.795662i	$0.292877\pi$
$200$	−4.42228	−	10.4571i	−0.312703	−	0.739426i
$201$	−18.2106	−	10.5139i	−1.28448	−	0.741595i
$202$	0.374422	+	1.66944i	0.0263443	+	0.117461i
$203$		0			0
$204$	21.6110	+	7.74537i	1.51307	+	0.542285i
$205$	0.617276	+	2.30371i	0.0431125	+	0.160898i
$206$	8.25890	+	0.340208i	0.575425	+	0.0237034i
$207$	−3.72024	−	6.44365i	−0.258575	−	0.447865i
$208$	−10.8315	−	4.92146i	−0.751031	−	0.341242i
$209$	−1.24749			−0.0862906
$210$		0			0
$211$	7.33737	−	7.33737i	0.505126	−	0.505126i	−0.407901	−	0.913026i	$-0.633739\pi$
$211$	7.33737	−	7.33737i	0.505126	−	0.505126i	0.913026	+	0.407901i	$0.133739\pi$
$212$	10.2110	+	12.0479i	0.701294	+	0.827455i
$213$	6.06690	−	22.6420i	0.415697	−	1.55140i
$214$	−3.90407	+	3.59516i	−0.266877	+	0.245760i
$215$	−4.44573	−	2.56674i	−0.303196	−	0.175050i
$216$	−8.62809	+	6.72246i	−0.587067	+	0.457406i
$217$		0			0
$218$	−13.8240	+	3.10047i	−0.936283	+	0.209990i
$219$	−0.700757	+	0.187767i	−0.0473528	+	0.0126881i
$220$	−3.18998	−	2.21031i	−0.215069	−	0.149019i
$221$	−16.3117	−	4.37072i	−1.09725	−	0.294006i
$222$	25.1864	−	13.1902i	1.69040	−	0.885266i
$223$	−4.26037			−0.285295			−0.142648	−	0.989774i	$-0.545562\pi$
$223$	−4.26037			−0.285295			−0.142648	+	0.989774i	$0.545562\pi$
$224$		0			0
$225$	−4.36411			−0.290941
$226$	−6.35752	+	3.32945i	−0.422896	+	0.221471i
$227$	4.67340	+	1.25223i	0.310184	+	0.0831136i	0.410553	−	0.911837i	$-0.365336\pi$
$227$	4.67340	+	1.25223i	0.310184	+	0.0831136i	−0.100369	+	0.994950i	$0.532002\pi$
$228$	−2.12147	−	1.46995i	−0.140498	−	0.0973497i
$229$	−18.9490	+	5.07737i	−1.25218	+	0.335522i	−0.823180	−	0.567781i	$-0.807802\pi$
$229$	−18.9490	+	5.07737i	−1.25218	+	0.335522i	−0.429005	+	0.903302i	$0.641136\pi$
$230$	−9.37698	+	2.10308i	−0.618300	+	0.138673i
$231$		0			0
$232$	−0.509620	−	0.654083i	−0.0334582	−	0.0429427i
$233$	4.38681	+	2.53273i	0.287390	+	0.165925i	0.636764	−	0.771059i	$-0.280273\pi$
$233$	4.38681	+	2.53273i	0.287390	+	0.165925i	−0.349374	+	0.936983i	$0.613606\pi$
$234$	−3.36395	+	3.09778i	−0.219909	+	0.202508i
$235$	−0.0743155	+	0.277349i	−0.00484781	+	0.0180923i
$236$	18.0116	+	21.2519i	1.17246	+	1.38338i
$237$	11.0061	−	11.0061i	0.714925	−	0.714925i
$238$		0			0
$239$	−9.32494			−0.603181			−0.301590	−	0.953438i	$-0.597517\pi$
$239$	−9.32494			−0.603181			−0.301590	+	0.953438i	$0.597517\pi$
$240$	−2.82041	−	7.51768i	−0.182057	−	0.485264i
$241$	12.8663	+	22.2850i	0.828789	+	1.43550i	0.898989	+	0.437971i	$0.144303\pi$
$241$	12.8663	+	22.2850i	0.828789	+	1.43550i	−0.0702006	+	0.997533i	$0.522364\pi$
$242$	−10.1463	−	0.417957i	−0.652231	−	0.0268673i
$243$	2.79475	+	10.4301i	0.179283	+	0.669093i
$244$	7.05008	+	2.52675i	0.451335	+	0.161759i
$245$		0			0
$246$	−1.50293	−	6.70110i	−0.0958232	−	0.427247i
$247$	1.64420	+	0.949280i	0.104618	+	0.0604012i
$248$	−20.5639	+	8.69646i	−1.30581	+	0.552226i
$249$	−1.04984	+	0.606128i	−0.0665312	+	0.0384118i
$250$	−3.77642	+	12.0810i	−0.238842	+	0.764068i
$251$	3.64372	+	3.64372i	0.229990	+	0.229990i	0.812688	−	0.582699i	$-0.198003\pi$
$251$	3.64372	+	3.64372i	0.229990	+	0.229990i	−0.582699	+	0.812688i	$0.698003\pi$
$252$		0			0
$253$	9.45755	−	9.45755i	0.594591	−	0.594591i
$254$	13.9952	−	7.32932i	0.878137	−	0.459882i
$255$	−5.69853	−	9.87014i	−0.356856	−	0.618092i
$256$	−12.0516	+	10.5242i	−0.753228	+	0.657760i
$257$	−1.87774	+	3.25234i	−0.117130	+	0.202875i	−0.918629	−	0.395121i	$-0.870703\pi$
$257$	−1.87774	+	3.25234i	−0.117130	+	0.202875i	0.801499	+	0.597996i	$0.204036\pi$
$258$	12.4865	+	7.91160i	0.777376	+	0.492555i
$259$		0			0
$260$	2.52249	+	5.34063i	0.156438	+	0.331212i
$261$	−0.307858	+	0.0824903i	−0.0190559	+	0.00510602i
$262$	−12.0789	−	13.1168i	−0.746235	−	0.810356i
$263$	−16.3252	+	9.42534i	−1.00665	+	0.581191i	−0.910210	−	0.414147i	$-0.864080\pi$
$263$	−16.3252	+	9.42534i	−1.00665	+	0.581191i	−0.0964430	+	0.995339i	$0.530747\pi$
$264$	8.91588	+	6.73729i	0.548734	+	0.414651i
$265$		−	7.84044i		−	0.481634i
$266$		0			0
$267$	−25.1439	−	25.1439i	−1.53878	−	1.53878i
$268$	15.8695	−	13.4499i	0.969381	−	0.821581i
$269$	−16.5643	−	4.43839i	−1.00994	−	0.270614i	−0.284338	−	0.958724i	$-0.591774\pi$
$269$	−16.5643	−	4.43839i	−1.00994	−	0.270614i	−0.725606	+	0.688111i	$0.758440\pi$
$270$	5.42549	+	0.223492i	0.330185	+	0.0136013i
$271$	2.65608	−	4.60046i	0.161345	−	0.279458i	−0.774006	−	0.633178i	$-0.781750\pi$
$271$	2.65608	−	4.60046i	0.161345	−	0.279458i	0.935351	+	0.353720i	$0.115083\pi$
$272$	−14.4261	+	17.5405i	−0.874711	+	1.06355i
$273$		0			0
$274$	−12.2646	+	19.3566i	−0.740929	+	1.16937i
$275$	−2.03042	−	7.57761i	−0.122439	−	0.456947i
$276$	27.2276	−	4.93940i	1.63891	−	0.297317i
$277$	−3.93434	+	14.6832i	−0.236392	+	0.882226i	0.741125	+	0.671367i	$0.234293\pi$
$277$	−3.93434	+	14.6832i	−0.236392	+	0.882226i	−0.977517	+	0.210859i	$0.932374\pi$
$278$	20.0469	+	6.26651i	1.20233	+	0.375840i
$279$			8.58208i			0.513795i
$280$		0			0
$281$		−	3.15786i		−	0.188382i	−0.995554	−	0.0941910i	$-0.969974\pi$
$281$		−	3.15786i		−	0.188382i	0.995554	−	0.0941910i	$-0.0300264\pi$
$282$	0.246682	−	0.789148i	0.0146897	−	0.0469931i
$283$	3.65368	−	13.6357i	0.217189	−	0.810559i	−0.768196	−	0.640215i	$-0.778845\pi$
$283$	3.65368	−	13.6357i	0.217189	−	0.810559i	0.985385	−	0.170344i	$-0.0544879\pi$
$284$	19.0609	+	13.2071i	1.13106	+	0.783697i
$285$	0.331632	+	1.23767i	0.0196442	+	0.0733131i
$286$	−6.94390	−	4.39974i	−0.410602	−	0.260162i
$287$		0			0
$288$	1.92146	+	5.84218i	0.113223	+	0.344254i
$289$	−7.61819	+	13.1951i	−0.448129	+	0.776182i
$290$	−0.0169426	+	0.411299i	−0.000994903	+	0.0241523i
$291$	23.9564	+	6.41911i	1.40435	+	0.376295i
$292$	0.0590279	−	0.715266i	0.00345435	−	0.0418578i
$293$	10.9335	+	10.9335i	0.638743	+	0.638743i	0.950245	−	0.311502i	$-0.100832\pi$
$293$	10.9335	+	10.9335i	0.638743	+	0.638743i	−0.311502	+	0.950245i	$0.600832\pi$
$294$		0			0
$295$		−	13.8301i		−	0.805219i
$296$	3.87722	+	27.8578i	0.225359	+	1.61920i
$297$	−6.54503	+	3.77878i	−0.379781	+	0.219267i
$298$	10.3601	−	9.54033i	0.600144	−	0.552656i
$299$	−19.6619	+	5.26839i	−1.13708	+	0.304679i
$300$	5.47598	−	15.2789i	0.316156	−	0.882131i
$301$		0			0
$302$	−7.84545	+	12.3821i	−0.451455	+	0.712510i
$303$	−1.22291	+	2.11814i	−0.0702543	+	0.121684i
$304$	2.07700	−	1.48505i	0.119124	−	0.0851733i
$305$	−1.85902	−	3.21991i	−0.106447	−	0.184371i
$306$	4.04992	+	7.73325i	0.231518	+	0.442080i
$307$	14.7735	−	14.7735i	0.843170	−	0.843170i	−0.146100	−	0.989270i	$-0.546672\pi$
$307$	14.7735	−	14.7735i	0.843170	−	0.843170i	0.989270	+	0.146100i	$0.0466721\pi$
$308$		0			0
$309$	8.35550	+	8.35550i	0.475328	+	0.475328i
$310$	10.5795	+	3.30708i	0.600877	+	0.187830i
$311$	7.56549	−	4.36794i	0.429000	−	0.247683i	−0.269921	−	0.962883i	$-0.586998\pi$
$311$	7.56549	−	4.36794i	0.429000	−	0.247683i	0.698920	+	0.715199i	$0.253664\pi$
$312$	−6.62444	−	15.6644i	−0.375035	−	0.886820i
$313$	−3.56615	−	2.05892i	−0.201571	−	0.116377i	0.395817	−	0.918329i	$-0.370461\pi$
$313$	−3.56615	−	2.05892i	−0.201571	−	0.116377i	−0.597388	+	0.801952i	$0.703795\pi$
$314$	5.69319	−	1.27687i	0.321285	−	0.0720581i
$315$		0			0
$316$	6.57621	+	13.9232i	0.369940	+	0.783241i
$317$	6.32257	+	23.5962i	0.355111	+	1.32529i	0.880345	+	0.474335i	$0.157311\pi$
$317$	6.32257	+	23.5962i	0.355111	+	1.32529i	−0.525234	+	0.850958i	$0.676022\pi$
$318$	−0.929211	+	22.5576i	−0.0521076	+	1.26496i
$319$	−0.286463	−	0.496169i	−0.0160389	−	0.0277801i
$320$	7.94237	−	0.117410i	0.443992	−	0.00656340i
$321$	−7.58695			−0.423462
$322$		0			0
$323$	2.56271	−	2.56271i	0.142593	−	0.142593i
$324$	−22.0841	−	1.82251i	−1.22689	−	0.101250i
$325$	−3.09010	+	11.5324i	−0.171408	+	0.639703i
$326$	−7.91726	−	8.59755i	−0.438496	−	0.476174i
$327$	−17.5396	−	10.1265i	−0.969943	−	0.559997i
$328$	6.74218	+	0.836979i	0.372274	+	0.0462144i
$329$		0			0
$330$	−1.21413	−	5.41344i	−0.0668357	−	0.298000i
$331$	−7.05503	+	1.89039i	−0.387780	+	0.103905i	−0.447441	−	0.894313i	$-0.647665\pi$
$331$	−7.05503	+	1.89039i	−0.387780	+	0.103905i	0.0596615	+	0.998219i	$0.480998\pi$
$332$	−0.214065	−	1.18000i	−0.0117484	−	0.0647607i
$333$	10.4428	+	2.79813i	0.572260	+	0.153337i
$334$	−5.85680	−	11.1834i	−0.320470	−	0.611931i
$335$	−10.3274			−0.564245
$336$		0			0
$337$	−9.53985			−0.519669			−0.259834	−	0.965653i	$-0.583668\pi$
$337$	−9.53985			−0.519669			−0.259834	+	0.965653i	$0.583668\pi$
$338$	−2.72517	−	5.20366i	−0.148230	−	0.283042i
$339$	−9.90965	−	2.65528i	−0.538218	−	0.144215i
$340$	11.0938	−	2.01254i	0.601644	−	0.109145i
$341$	−14.9015	+	3.99283i	−0.806959	+	0.216224i
$342$	−0.214780	−	0.957639i	−0.0116140	−	0.0517832i
$343$		0			0
$344$	−11.5355	+	8.98769i	−0.621950	+	0.484584i
$345$	−11.8973	−	6.86890i	−0.640528	−	0.369809i
$346$	5.22061	+	5.66919i	0.280662	+	0.304778i
$347$	2.36483	−	8.82567i	0.126951	−	0.473787i	−0.872951	−	0.487808i	$-0.837797\pi$
$347$	2.36483	−	8.82567i	0.126951	−	0.473787i	0.999902	+	0.0140212i	$0.00446323\pi$
$348$	0.0974903	−	1.18133i	0.00522603	−	0.0633260i
$349$	−24.4862	+	24.4862i	−1.31072	+	1.31072i	−0.389831	+	0.920887i	$0.627467\pi$
$349$	−24.4862	+	24.4862i	−1.31072	+	1.31072i	−0.920887	+	0.389831i	$0.872533\pi$
$350$		0			0
$351$	11.5019			0.613925
$352$	−9.25008	+	6.05441i	−0.493031	+	0.322701i
$353$	−13.0352	−	22.5776i	−0.693793	−	1.20168i	−0.970586	−	0.240755i	$-0.922605\pi$
$353$	−13.0352	−	22.5776i	−0.693793	−	1.20168i	0.276793	−	0.960930i	$-0.410728\pi$
$354$	−1.63907	+	39.7902i	−0.0871159	+	2.11483i
$355$	−2.97963	−	11.1201i	−0.158142	−	0.590194i
$356$	31.8080	−	15.0236i	1.68582	−	0.796247i
$357$		0			0
$358$	13.4638	−	3.01967i	0.711584	−	0.159595i
$359$	−3.01740	−	1.74210i	−0.159252	−	0.0919443i	0.418256	−	0.908329i	$-0.362642\pi$
$359$	−3.01740	−	1.74210i	−0.159252	−	0.0919443i	−0.577508	+	0.816385i	$0.695975\pi$
$360$	1.14753	−	2.82935i	0.0604802	−	0.149120i
$361$	16.1016	−	9.29627i	0.847453	−	0.489277i
$362$	−16.0916	−	5.03013i	−0.845758	−	0.264378i
$363$	−10.2650	−	10.2650i	−0.538773	−	0.538773i
$364$		0			0
$365$	−0.251944	+	0.251944i	−0.0131873	+	0.0131873i
$366$	4.96692	+	9.48425i	0.259625	+	0.495750i
$367$	12.2280	+	21.1796i	0.638298	+	1.10556i	0.985806	+	0.167888i	$0.0536946\pi$
$367$	12.2280	+	21.1796i	0.638298	+	1.10556i	−0.347508	+	0.937677i	$0.612972\pi$
$368$	−4.48776	+	27.0049i	−0.233941	+	1.40773i
$369$	1.30572	−	2.26157i	0.0679730	−	0.117733i
$370$	7.47349	−	11.7951i	0.388528	−	0.613196i
$371$		0			0
$372$	−30.0462	−	10.7686i	−1.55782	−	0.558324i
$373$	−35.4993	+	9.51200i	−1.83808	+	0.492513i	−0.998697	−	0.0510246i	$-0.983751\pi$
$373$	−35.4993	+	9.51200i	−1.83808	+	0.492513i	−0.839385	+	0.543537i	$0.817085\pi$
$374$	−11.5434	+	10.6300i	−0.596893	+	0.549663i
$375$	−15.6702	+	9.04719i	−0.809206	+	0.467195i
$376$	0.652577	+	0.493120i	0.0336541	+	0.0254307i
$377$			0.871940i			0.0449072i
$378$		0			0
$379$	18.5183	+	18.5183i	0.951222	+	0.951222i	0.998864	−	0.0476420i	$-0.0151707\pi$
$379$	18.5183	+	18.5183i	0.951222	+	0.951222i	−0.0476420	+	0.998864i	$0.515171\pi$
$380$	−1.26329	−	0.104254i	−0.0648056	−	0.00534813i
$381$	21.8147	+	5.84524i	1.11760	+	0.299461i
$382$	−0.286982	+	6.96679i	−0.0146833	+	0.356452i
$383$	−7.89785	+	13.6795i	−0.403562	+	0.698989i	−0.994153	−	0.107982i	$-0.965561\pi$
$383$	−7.89785	+	13.6795i	−0.403562	+	0.698989i	0.590591	+	0.806971i	$0.298895\pi$
$384$	−22.8647	−	0.603494i	−1.16681	−	0.0307969i
$385$		0			0
$386$	26.1722	+	16.5830i	1.33213	+	0.844053i
$387$	1.45480	+	5.42940i	0.0739519	+	0.275992i
$388$	−13.9738	+	20.1675i	−0.709414	+	1.02385i
$389$	1.47562	−	5.50707i	0.0748167	−	0.279220i	−0.918375	−	0.395711i	$-0.870498\pi$
$389$	1.47562	−	5.50707i	0.0748167	−	0.279220i	0.993192	+	0.116492i	$0.0371648\pi$
$390$	−2.51914	+	8.05886i	−0.127561	+	0.408076i
$391$			38.8572i			1.96509i
$392$		0			0
$393$		−	25.4903i		−	1.28582i
$394$	−14.5456	−	4.54684i	−0.732797	−	0.229067i
$395$	1.97852	−	7.38395i	0.0995503	−	0.371527i
$396$	0.758514	+	4.18117i	0.0381168	+	0.210112i
$397$	−0.260427	−	0.971927i	−0.0130705	−	0.0487796i	0.959083	−	0.283126i	$-0.0913716\pi$
$397$	−0.260427	−	0.971927i	−0.0130705	−	0.0487796i	−0.972153	+	0.234347i	$0.924705\pi$
$398$	−2.70690	+	4.27216i	−0.135684	+	0.214144i
$399$		0			0
$400$	12.4012	+	10.1993i	0.620058	+	0.509963i
$401$	8.70318	−	15.0744i	0.434616	−	0.752777i	−0.562648	−	0.826697i	$-0.690217\pi$
$401$	8.70318	−	15.0744i	0.434616	−	0.752777i	0.997264	+	0.0739192i	$0.0235507\pi$
$402$	29.7127	+	1.22395i	1.48193	+	0.0610451i
$403$	22.6786	+	6.07671i	1.12970	+	0.302703i
$404$	−1.56440	−	1.84583i	−0.0778317	−	0.0918334i
$405$	7.77886	+	7.77886i	0.386535	+	0.386535i
$406$		0			0
$407$			19.4341i			0.963313i
$408$	−32.1562	+	4.47546i	−1.59197	+	0.221568i
$409$	33.0605	−	19.0875i	1.63474	−	0.943815i	0.652131	−	0.758106i	$-0.273875\pi$
$409$	33.0605	−	19.0875i	1.63474	−	0.943815i	0.982605	−	0.185709i	$-0.0594582\pi$
$410$	−2.28479	−	2.48111i	−0.112838	−	0.122533i
$411$	−31.6417	+	8.47837i	−1.56077	+	0.418207i
$412$	−10.5700	+	4.99245i	−0.520749	+	0.245960i
$413$		0			0
$414$	8.88843	+	5.63182i	0.436843	+	0.276789i
$415$	−0.297687	+	0.515608i	−0.0146129	+	0.0253102i
$416$	16.7988	−	0.940897i	0.823629	−	0.0461312i
$417$	15.0127	+	26.0028i	0.735176	+	1.27336i
$418$	1.56287	−	0.818477i	0.0764423	−	0.0400330i
$419$	27.0004	−	27.0004i	1.31905	−	1.31905i	0.404529	−	0.914525i	$-0.367435\pi$
$419$	27.0004	−	27.0004i	1.31905	−	1.31905i	0.914525	−	0.404529i	$-0.132565\pi$
$420$		0			0
$421$	−19.1472	−	19.1472i	−0.933175	−	0.933175i	0.0647277	−	0.997903i	$-0.479382\pi$
$421$	−19.1472	−	19.1472i	−0.933175	−	0.933175i	−0.997903	+	0.0647277i	$0.979382\pi$
$422$	−4.37829	+	14.0064i	−0.213132	+	0.681820i
$423$	0.272276	−	0.157199i	0.0132385	−	0.00764327i
$424$	−20.6971	−	8.39434i	−1.00514	−	0.407665i
$425$	19.7377	+	11.3956i	0.957419	+	0.552766i
$426$	7.25471	+	32.3466i	0.351492	+	1.56720i
$427$		0			0
$428$	2.53228	−	7.06551i	0.122402	−	0.341524i
$429$	−3.04150	−	11.3510i	−0.146845	−	0.548033i
$430$	7.25369	+	0.298801i	0.349804	+	0.0144094i
$431$	−0.628555	−	1.08869i	−0.0302764	−	0.0524403i	0.850490	−	0.525991i	$-0.176305\pi$
$431$	−0.628555	−	1.08869i	−0.0302764	−	0.0524403i	−0.880767	+	0.473551i	$0.842972\pi$
$432$	6.39876	−	14.0829i	0.307860	−	0.677562i
$433$	9.16885			0.440627			0.220313	−	0.975429i	$-0.429292\pi$
$433$	9.16885			0.440627			0.220313	+	0.975429i	$0.429292\pi$
$434$		0			0
$435$	−0.416110	+	0.416110i	−0.0199509	+	0.0199509i
$436$	15.2847	−	12.9542i	0.732004	−	0.620396i
$437$	1.13067	−	4.21971i	0.0540871	−	0.201856i
$438$	0.754721	−	0.695003i	0.0360620	−	0.0332085i
$439$	6.89864	+	3.98293i	0.329254	+	0.190095i	0.655510	−	0.755187i	$-0.272454\pi$
$439$	6.89864	+	3.98293i	0.329254	+	0.190095i	−0.326256	+	0.945282i	$0.605787\pi$
$440$	5.44663	+	0.676148i	0.259658	+	0.0322341i
$441$		0			0
$442$	23.3032	−	5.22645i	1.10842	−	0.248597i
$443$	−24.1691	+	6.47610i	−1.14831	+	0.307689i	−0.782288	−	0.622918i	$-0.785947\pi$
$443$	−24.1691	+	6.47610i	−1.14831	+	0.307689i	−0.366022	+	0.930606i	$0.619281\pi$
$444$	−22.8997	+	33.0496i	−1.08677	+	1.56846i
$445$	−16.8689	−	4.52000i	−0.799661	−	0.214269i
$446$	5.33743	−	2.79522i	0.252735	−	0.132358i
$447$	20.1332			0.952267
$448$		0			0
$449$	−8.33038			−0.393135			−0.196567	−	0.980490i	$-0.562979\pi$
$449$	−8.33038			−0.393135			−0.196567	+	0.980490i	$0.562979\pi$
$450$	5.46741	−	2.86329i	0.257736	−	0.134977i
$451$	4.53436	+	1.21498i	0.213515	+	0.0572111i
$452$	5.78031	−	8.34233i	0.271883	−	0.392390i
$453$	−20.2407	+	5.42349i	−0.950993	+	0.254818i
$454$	−6.67647	+	1.49740i	−0.313342	+	0.0702766i
$455$		0			0
$456$	3.62224	+	0.449667i	0.169627	+	0.0210576i
$457$	−12.5338	−	7.23641i	−0.586308	−	0.338505i	0.177328	−	0.984152i	$-0.443255\pi$
$457$	−12.5338	−	7.23641i	−0.586308	−	0.338505i	−0.763636	+	0.645647i	$0.776588\pi$
$458$	20.4082	−	18.7934i	0.953614	−	0.878158i
$459$	5.68270	−	21.2081i	0.265246	−	0.989910i
$460$	10.3678	−	8.78699i	0.483399	−	0.409696i
$461$	4.23021	−	4.23021i	0.197020	−	0.197020i	−0.601701	−	0.798721i	$-0.705510\pi$
$461$	4.23021	−	4.23021i	0.197020	−	0.197020i	0.798721	+	0.601701i	$0.205510\pi$
$462$		0			0
$463$	−25.1987			−1.17108			−0.585542	−	0.810642i	$-0.699118\pi$
$463$	−25.1987			−1.17108			−0.585542	+	0.810642i	$0.699118\pi$
$464$	1.06760	+	0.485080i	0.0495621	+	0.0225193i
$465$	7.92280	+	13.7227i	0.367411	+	0.636374i
$466$	−7.15757	−	0.294841i	−0.331568	−	0.0136582i
$467$	−3.97667	−	14.8411i	−0.184018	−	0.686766i	−0.994839	−	0.101470i	$-0.967645\pi$
$467$	−3.97667	−	14.8411i	−0.184018	−	0.686766i	0.810820	−	0.585295i	$-0.199021\pi$
$468$	2.18195	−	6.08802i	0.100860	−	0.281419i
$469$		0			0
$470$	−0.0888655	−	0.396224i	−0.00409906	−	0.0182765i
$471$	7.22338	+	4.17042i	0.332836	+	0.192163i
$472$	−36.5085	−	14.8071i	−1.68044	−	0.681554i
$473$	−8.75047	+	5.05209i	−0.402347	+	0.232295i
$474$	−6.56747	+	21.0097i	−0.301654	+	0.965008i
$475$	−1.81183	−	1.81183i	−0.0831326	−	0.0831326i
$476$		0			0
$477$	−6.07046	+	6.07046i	−0.277947	+	0.277947i
$478$	11.6824	−	6.11809i	0.534340	−	0.279835i
$479$	−10.4147	−	18.0387i	−0.475859	−	0.824211i	0.523759	−	0.851867i	$-0.324529\pi$
$479$	−10.4147	−	18.0387i	−0.475859	−	0.824211i	−0.999618	+	0.0276553i	$0.991196\pi$
$480$	8.46579	+	7.56775i	0.386409	+	0.345419i
$481$	14.7884	−	25.6143i	0.674294	−	1.16791i
$482$	−30.7402	−	19.4773i	−1.40018	−	0.887169i
$483$		0			0
$484$	12.9857	−	6.13339i	0.590257	−	0.278790i
$485$	11.7657	−	3.15261i	0.534252	−	0.143152i
$486$	−10.3445	−	11.2333i	−0.469236	−	0.509555i
$487$	−0.192631	+	0.111216i	−0.00872895	+	0.00503966i	−0.504358	−	0.863495i	$-0.668271\pi$
$487$	−0.192631	+	0.111216i	−0.00872895	+	0.00503966i	0.495629	+	0.868534i	$0.334938\pi$
$488$	−10.4902	+	1.46002i	−0.474870	+	0.0660918i
$489$		−	16.7080i		−	0.755561i
$490$		0			0
$491$	18.1586	+	18.1586i	0.819486	+	0.819486i	0.986033	−	0.166547i	$-0.0532618\pi$
$491$	18.1586	+	18.1586i	0.819486	+	0.819486i	−0.166547	+	0.986033i	$0.553262\pi$
$492$	6.27947	+	7.40914i	0.283101	+	0.334030i
$493$	1.60776	+	0.430797i	0.0724097	+	0.0194021i
$494$	−2.68269	−	0.110508i	−0.120700	−	0.00497199i
$495$	1.05482	−	1.82700i	0.0474105	−	0.0821173i
$496$	20.0569	−	24.3870i	0.900583	−	1.09501i
$497$		0			0
$498$	0.917575	−	1.44816i	0.0411175	−	0.0648938i
$499$	0.908747	+	3.39149i	0.0406811	+	0.151824i	0.983279	−	0.182107i	$-0.0582916\pi$
$499$	0.908747	+	3.39149i	0.0406811	+	0.151824i	−0.942598	+	0.333930i	$0.891625\pi$
$500$	−3.19519	−	17.6129i	−0.142893	−	0.787672i
$501$	4.67088	−	17.4320i	0.208680	−	0.778802i
$502$	−6.95553	−	2.17425i	−0.310441	−	0.0970414i
$503$			7.65278i			0.341220i	0.985339	+	0.170610i	$0.0545739\pi$
$503$			7.65278i			0.341220i	−0.985339	+	0.170610i	$0.945426\pi$
$504$		0			0
$505$			1.20121i			0.0534532i
$506$	−5.64342	+	18.0536i	−0.250881	+	0.802581i
$507$	2.17336	−	8.11109i	0.0965223	−	0.360226i
$508$	−12.7246	+	18.3645i	−0.564561	+	0.814792i
$509$	8.27238	+	30.8730i	0.366667	+	1.36842i	0.865147	+	0.501519i	$0.167225\pi$
$509$	8.27238	+	30.8730i	0.366667	+	1.36842i	−0.498480	+	0.866901i	$0.666108\pi$
$510$	13.6150	+	8.62661i	0.602881	+	0.381993i
$511$		0			0
$512$	8.19353	−	21.0918i	0.362106	−	0.932137i
$513$	−1.23423	+	2.13775i	−0.0544925	+	0.0943838i
$514$	0.218592	−	5.30655i	0.00964169	−	0.234062i
$515$	5.60566	+	1.50203i	0.247015	+	0.0661874i
$516$	−20.8340	−	1.71935i	−0.917167	−	0.0756900i
$517$	0.399629	+	0.399629i	0.0175757	+	0.0175757i
$518$		0			0
$519$			11.0172i			0.483600i
$520$	−6.66418	−	5.03579i	−0.292244	−	0.220834i
$521$	−2.39816	+	1.38458i	−0.105065	+	0.0606595i	−0.551612	−	0.834101i	$-0.685987\pi$
$521$	−2.39816	+	1.38458i	−0.105065	+	0.0606595i	0.446547	+	0.894760i	$0.352654\pi$
$522$	0.331566	−	0.305330i	0.0145122	−	0.0133639i
$523$	21.3583	−	5.72293i	0.933932	−	0.250246i	0.240401	−	0.970674i	$-0.422721\pi$
$523$	21.3583	−	5.72293i	0.933932	−	0.250246i	0.693530	+	0.720427i	$0.256054\pi$
$524$	23.7384	+	8.50786i	1.03702	+	0.371668i
$525$		0			0
$526$	14.2684	−	22.5191i	0.622131	−	0.981879i
$527$	22.4095	−	38.8144i	0.976173	−	1.69078i
$528$	−15.5902	−	2.59084i	−0.678478	−	0.112752i
$529$	11.9189	+	20.6441i	0.518211	+	0.897568i
$530$	5.14411	+	9.82258i	0.223446	+	0.426666i
$531$	−10.7079	+	10.7079i	−0.464685	+	0.464685i
$532$		0			0
$533$	−5.05178	−	5.05178i	−0.218817	−	0.218817i
$534$	47.9974	+	15.0036i	2.07705	+	0.649270i
$535$	−3.22696	+	1.86308i	−0.139513	+	0.0805481i
$536$	−11.0570	+	27.2621i	−0.477588	+	1.17754i
$537$	17.0826	+	9.86262i	0.737167	+	0.425603i
$538$	23.6640	−	5.30737i	1.02023	−	0.228817i
$539$		0			0
$540$	−6.94375	+	3.27967i	−0.298811	+	0.141135i
$541$	8.64497	+	32.2635i	0.371676	+	1.38711i	0.858141	+	0.513414i	$0.171619\pi$
$541$	8.64497	+	32.2635i	0.371676	+	1.38711i	−0.486465	+	0.873700i	$0.661714\pi$
$542$	−0.309200	+	7.50615i	−0.0132813	+	0.322417i
$543$	−12.0507	−	20.8724i	−0.517145	−	0.895721i
$544$	6.56483	−	31.4399i	0.281465	−	1.34797i
$545$	−9.94683			−0.426075
$546$		0			0
$547$	3.45137	−	3.45137i	0.147570	−	0.147570i	−0.629462	−	0.777032i	$-0.716724\pi$
$547$	3.45137	−	3.45137i	0.147570	−	0.147570i	0.777032	+	0.629462i	$0.216724\pi$
$548$	2.66533	−	32.2969i	0.113857	−	1.37965i
$549$	−1.05367	+	3.93236i	−0.0449696	+	0.167829i
$550$	7.51539	+	8.16116i	0.320457	+	0.347993i
$551$	−0.162059	−	0.0935651i	−0.00690396	−	0.00398601i
$552$	−30.8702	+	24.0521i	−1.31392	+	1.02373i
$553$		0			0
$554$	−4.70464	−	20.9765i	−0.199881	−	0.891208i
$555$	19.2811	−	5.16636i	0.818437	−	0.219300i
$556$	−29.2264	+	5.30202i	−1.23948	+	0.224856i
$557$	21.3055	+	5.70879i	0.902742	+	0.241889i	0.680194	−	0.733032i	$-0.261896\pi$
$557$	21.3055	+	5.70879i	0.902742	+	0.241889i	0.222549	+	0.974922i	$0.428562\pi$
$558$	−5.63070	−	10.7517i	−0.238366	−	0.455156i
$559$	15.3776			0.650403
$560$		0			0
$561$	−22.4327			−0.947109
$562$	2.07187	+	3.95620i	0.0873965	+	0.166882i
$563$	−26.6690	−	7.14593i	−1.12396	−	0.301165i	−0.351477	−	0.936196i	$-0.614321\pi$
$563$	−26.6690	−	7.14593i	−1.12396	−	0.301165i	−0.772486	+	0.635031i	$0.780987\pi$
$564$	0.208714	+	1.15050i	0.00878846	+	0.0484448i
$565$	−4.86691	+	1.30408i	−0.204752	+	0.0548633i
$566$	4.36902	+	19.4801i	0.183644	+	0.818811i
$567$		0			0
$568$	−32.5448	−	4.04014i	−1.36555	−	0.169521i
$569$	30.3657	+	17.5317i	1.27300	+	0.734965i	0.975551	−	0.219773i	$-0.0705318\pi$
$569$	30.3657	+	17.5317i	1.27300	+	0.734965i	0.297446	+	0.954739i	$0.403865\pi$
$570$	−1.22750	−	1.33298i	−0.0514145	−	0.0558323i
$571$	−0.334280	+	1.24755i	−0.0139892	+	0.0522083i	−0.972568	−	0.232620i	$-0.925270\pi$
$571$	−0.334280	+	1.24755i	−0.0139892	+	0.0522083i	0.958578	+	0.284829i	$0.0919367\pi$
$572$	11.5861	+	0.956149i	0.484437	+	0.0399786i
$573$	−7.04827	+	7.04827i	−0.294446	+	0.294446i
$574$		0			0
$575$	27.4720			1.14566
$576$	−6.24028	−	6.05847i	−0.260012	−	0.252436i
$577$	7.66470	+	13.2757i	0.319086	+	0.552673i	0.980298	−	0.197527i	$-0.0632909\pi$
$577$	7.66470	+	13.2757i	0.319086	+	0.552673i	−0.661212	+	0.750199i	$0.729958\pi$
$578$	0.886852	−	21.5292i	0.0368882	−	0.895498i
$579$	11.4637	+	42.7830i	0.476414	+	1.77800i
$580$	−0.248627	−	0.526395i	−0.0103237	−	0.0218574i
$581$		0			0
$582$	−34.2244	+	7.67588i	−1.41865	+	0.318176i
$583$	−13.3647	−	7.71612i	−0.553510	−	0.319569i
$584$	0.395335	+	0.934821i	0.0163591	+	0.0386832i
$585$	−2.78051	+	1.60533i	−0.114960	+	0.0663722i
$586$	−20.8711	−	6.52415i	−0.862177	−	0.269510i
$587$	27.8270	+	27.8270i	1.14854	+	1.14854i	0.986840	+	0.161702i	$0.0516982\pi$
$587$	27.8270	+	27.8270i	1.14854	+	1.14854i	0.161702	+	0.986840i	$0.448302\pi$
$588$		0			0
$589$	−3.56299	+	3.56299i	−0.146810	+	0.146810i
$590$	9.07391	+	17.3265i	0.373567	+	0.713320i
$591$	−10.8929	−	18.8670i	−0.448074	−	0.776087i
$592$	−23.1349	−	32.3567i	−0.950840	−	1.32985i
$593$	8.89810	−	15.4120i	0.365401	−	0.632894i	−0.623439	−	0.781872i	$-0.714265\pi$
$593$	8.89810	−	15.4120i	0.365401	−	0.632894i	0.988840	+	0.148978i	$0.0475984\pi$
$594$	5.72043	−	9.02828i	0.234712	−	0.370435i
$595$		0			0
$596$	−6.71981	+	18.7495i	−0.275254	+	0.768008i
$597$	−6.98361	+	1.87125i	−0.285820	+	0.0765853i
$598$	21.1760	−	19.5004i	0.865952	−	0.797432i
$599$	−16.6221	+	9.59676i	−0.679159	+	0.392113i	−0.799538	−	0.600615i	$-0.794922\pi$
$599$	−16.6221	+	9.59676i	−0.679159	+	0.392113i	0.120379	+	0.992728i	$0.461589\pi$
$600$	3.16415	+	22.7344i	0.129176	+	0.928128i
$601$			26.9530i			1.09944i	0.835351	+	0.549718i	$0.185265\pi$
$601$			26.9530i			1.09944i	−0.835351	+	0.549718i	$0.814735\pi$
$602$		0			0
$603$	7.99597	+	7.99597i	0.325621	+	0.325621i
$604$	1.70497	−	20.6598i	0.0693742	−	0.840637i
$605$	−6.88674	−	1.84530i	−0.279986	−	0.0750219i
$606$	0.142362	−	3.45598i	0.00578305	−	0.140390i
$607$	−14.7276	+	25.5089i	−0.597773	+	1.03537i	0.395376	+	0.918519i	$0.370614\pi$
$607$	−14.7276	+	25.5089i	−0.597773	+	1.03537i	−0.993149	+	0.116854i	$0.962719\pi$
$608$	−1.62775	+	3.22320i	−0.0660140	+	0.130718i
$609$		0			0
$610$	4.44157	+	2.81424i	0.179834	+	0.113945i
$611$	−0.222616	−	0.830813i	−0.00900607	−	0.0336111i
$612$	−10.1476	−	7.03114i	−0.410191	−	0.284217i
$613$	−6.46001	+	24.1091i	−0.260917	+	0.973756i	0.703785	+	0.710413i	$0.251492\pi$
$613$	−6.46001	+	24.1091i	−0.260917	+	0.973756i	−0.964702	+	0.263343i	$0.915175\pi$
$614$	−8.81552	+	28.2013i	−0.355766	+	1.13811i
$615$		−	4.82165i		−	0.194428i
$616$		0			0
$617$			10.8407i			0.436431i	0.975901	+	0.218216i	$0.0700236\pi$
$617$			10.8407i			0.436431i	−0.975901	+	0.218216i	$0.929976\pi$
$618$	−15.9499	−	4.98582i	−0.641599	−	0.200559i
$619$	−5.19721	+	19.3962i	−0.208893	+	0.779601i	0.779334	+	0.626609i	$0.215558\pi$
$619$	−5.19721	+	19.3962i	−0.208893	+	0.779601i	−0.988227	+	0.152992i	$0.951109\pi$
$620$	−15.4239	+	2.79808i	−0.619440	+	0.112374i
$621$	−6.84982	−	25.5639i	−0.274874	−	1.02584i
$622$	−6.61232	+	10.4359i	−0.265130	+	0.418442i
$623$		0			0
$624$	18.5766	+	15.2782i	0.743657	+	0.611616i
$625$	5.59202	−	9.68566i	0.223681	−	0.387426i
$626$	5.81857	+	0.239684i	0.232557	+	0.00957969i
$627$	2.43609	+	0.652747i	0.0972879	+	0.0260682i
$628$	−6.29473	+	5.33498i	−0.251187	+	0.212889i
$629$	−39.9233	−	39.9233i	−1.59185	−	1.59185i
$630$		0			0
$631$		−	5.71697i		−	0.227589i	−0.993504	−	0.113794i	$-0.963699\pi$
$631$		−	5.71697i		−	0.227589i	0.993504	−	0.113794i	$-0.0363005\pi$
$632$	−17.3737	−	13.1285i	−0.691090	−	0.522223i
$633$	−18.1676	+	10.4891i	−0.722099	+	0.416904i
$634$	−23.4024	−	25.4133i	−0.929429	−	1.00929i
$635$	10.7138	−	2.87076i	0.425166	−	0.113923i
$636$	−13.6359	−	28.8700i	−0.540698	−	1.14477i
$637$		0			0
$638$	0.684421	+	0.433657i	0.0270965	+	0.0171687i
$639$	−6.30277	+	10.9167i	−0.249334	+	0.431859i
$640$	−9.87325	+	5.35808i	−0.390274	+	0.211797i
$641$	−14.8475	−	25.7166i	−0.586441	−	1.01575i	−0.994694	−	0.102877i	$-0.967195\pi$
$641$	−14.8475	−	25.7166i	−0.586441	−	1.01575i	0.408253	−	0.912869i	$-0.366138\pi$
$642$	9.50501	−	4.97779i	0.375133	−	0.196458i
$643$	−3.53512	+	3.53512i	−0.139412	+	0.139412i	−0.773368	−	0.633957i	$-0.781430\pi$
$643$	−3.53512	+	3.53512i	−0.139412	+	0.139412i	0.633957	+	0.773368i	$0.281430\pi$
$644$		0			0
$645$	7.33854	+	7.33854i	0.288955	+	0.288955i
$646$	−1.52919	+	4.89197i	−0.0601653	+	0.192472i
$647$	−12.7788	+	7.37782i	−0.502385	+	0.290052i	−0.729698	−	0.683770i	$-0.760339\pi$
$647$	−12.7788	+	7.37782i	−0.502385	+	0.290052i	0.227313	+	0.973822i	$0.427006\pi$
$648$	28.8629	−	12.2061i	1.13384	−	0.479501i
$649$	−23.5746	−	13.6108i	−0.925384	−	0.534270i
$650$	−3.69510	−	16.4753i	−0.144934	−	0.646216i
$651$		0			0
$652$	15.5597	+	5.57659i	0.609364	+	0.218396i
$653$	−2.56350	−	9.56710i	−0.100317	−	0.374390i	0.897455	−	0.441107i	$-0.145414\pi$
$653$	−2.56350	−	9.56710i	−0.100317	−	0.374390i	−0.997772	+	0.0667174i	$0.978747\pi$
$654$	28.6178	+	1.17885i	1.11904	+	0.0460967i
$655$	−6.25952	−	10.8418i	−0.244580	−	0.423624i
$656$	−8.99581	+	3.37496i	−0.351227	+	0.131770i
$657$	0.390135			0.0152206
$658$		0			0
$659$	5.68205	−	5.68205i	0.221341	−	0.221341i	−0.587722	−	0.809063i	$-0.699975\pi$
$659$	5.68205	−	5.68205i	0.221341	−	0.221341i	0.809063	+	0.587722i	$0.199975\pi$
$660$	5.07283	+	5.98542i	0.197460	+	0.232982i
$661$	2.48266	−	9.26542i	0.0965643	−	0.360383i	−0.900688	−	0.434467i	$-0.856937\pi$
$661$	2.48266	−	9.26542i	0.0965643	−	0.360383i	0.997252	+	0.0740843i	$0.0236034\pi$
$662$	7.59833	−	6.99710i	0.295317	−	0.271950i
$663$	29.5665	+	17.0702i	1.14827	+	0.662952i
$664$	1.04238	+	1.33786i	0.0404521	+	0.0519192i
$665$		0			0
$666$	−14.9187	+	3.34597i	−0.578086	+	0.129654i
$667$	1.93796	−	0.519275i	0.0750381	−	0.0201064i
$668$	14.6749	+	10.1681i	0.567789	+	0.393415i
$669$	8.31961	+	2.22923i	0.321655	+	0.0861871i
$670$	12.9382	−	6.77579i	0.499848	−	0.261771i
$671$	−7.31815			−0.282514
$672$		0			0
$673$	3.24280			0.125001			0.0625004	−	0.998045i	$-0.480093\pi$
$673$	3.24280			0.125001			0.0625004	+	0.998045i	$0.480093\pi$
$674$	11.9516	−	6.25909i	0.460359	−	0.241091i
$675$	−14.9941	−	4.01767i	−0.577125	−	0.154640i
$676$	6.82823	+	4.73121i	0.262624	+	0.181970i
$677$	32.3879	−	8.67832i	1.24477	−	0.333535i	0.424455	−	0.905449i	$-0.360466\pi$
$677$	32.3879	−	8.67832i	1.24477	−	0.333535i	0.820314	+	0.571914i	$0.193799\pi$
$678$	14.1570	−	3.17515i	0.543698	−	0.121941i
$679$		0			0
$680$	−12.5780	+	9.79995i	−0.482343	+	0.375811i
$681$	−8.47094	−	4.89070i	−0.324607	−	0.187412i
$682$	16.0490	−	14.7791i	0.614548	−	0.565921i
$683$	4.81432	−	17.9673i	0.184215	−	0.687499i	−0.810583	−	0.585624i	$-0.800849\pi$
$683$	4.81432	−	17.9673i	0.184215	−	0.687499i	0.994797	−	0.101874i	$-0.0324840\pi$
$684$	0.897385	+	1.05882i	0.0343124	+	0.0404851i
$685$	−11.3762	+	11.3762i	−0.434662	+	0.434662i
$686$		0			0
$687$	39.6602			1.51313
$688$	8.55491	−	18.8283i	0.326153	−	0.717822i
$689$	11.7432	+	20.3398i	0.447380	+	0.774886i
$690$	19.4117	+	0.799625i	0.738992	+	0.0304412i
$691$	−5.60826	−	20.9303i	−0.213348	−	0.796227i	−0.986741	−	0.162300i	$-0.948109\pi$
$691$	−5.60826	−	20.9303i	−0.213348	−	0.796227i	0.773393	−	0.633927i	$-0.218558\pi$
$692$	−10.2600	−	3.67718i	−0.390026	−	0.139786i
$693$		0			0
$694$	2.82783	+	12.6085i	0.107343	+	0.478611i
$695$	12.7707	+	7.37317i	0.484421	+	0.279680i
$696$	0.652934	+	1.54395i	0.0247494	+	0.0585231i
$697$	−11.8108	+	6.81898i	−0.447367	+	0.258287i
$698$	14.6112	−	46.7420i	0.553042	−	1.76921i
$699$	−7.24128	−	7.24128i	−0.273891	−	0.273891i
$700$		0			0
$701$	4.96023	−	4.96023i	0.187345	−	0.187345i	−0.607202	−	0.794547i	$-0.707708\pi$
$701$	4.96023	−	4.96023i	0.187345	−	0.187345i	0.794547	+	0.607202i	$0.207708\pi$
$702$	−14.4097	+	7.54638i	−0.543858	+	0.284820i
$703$	3.17380	+	5.49718i	0.119702	+	0.207330i
$704$	7.61630	−	13.6540i	0.287050	−	0.514605i
$705$	0.290246	−	0.502720i	0.0109313	−	0.0189335i
$706$	31.1438	+	19.7331i	1.17211	+	0.742664i
$707$		0			0
$708$	−24.0529	−	50.9250i	−0.903963	−	1.91388i
$709$	13.9774	−	3.74523i	0.524932	−	0.140655i	0.0133851	−	0.999910i	$-0.495739\pi$
$709$	13.9774	−	3.74523i	0.524932	−	0.140655i	0.511547	+	0.859255i	$0.329073\pi$
$710$	11.0288	+	11.9765i	0.413904	+	0.449469i
$711$	−7.24889	+	4.18515i	−0.271855	+	0.156955i
$712$	−29.9924	+	39.6909i	−1.12401	+	1.48748i
$713$		−	54.0240i		−	2.02321i
$714$		0			0
$715$	−4.08105	−	4.08105i	−0.152623	−	0.152623i
$716$	−14.8864	+	12.6167i	−0.556331	+	0.471507i
$717$	18.2097	+	4.87927i	0.680053	+	0.182220i
$718$	4.92322	+	0.202802i	0.183733	+	0.00756849i
$719$	16.5646	−	28.6908i	0.617756	−	1.06998i	−0.372138	−	0.928177i	$-0.621375\pi$
$719$	16.5646	−	28.6908i	0.617756	−	1.06998i	0.989894	−	0.141808i	$-0.0452914\pi$
$720$	0.418698	+	4.29753i	0.0156039	+	0.160160i
$721$		0			0
$722$	−14.0730	+	22.2107i	−0.523742	+	0.826598i
$723$	−13.4645	−	50.2502i	−0.500751	−	1.86883i
$724$	23.4600	−	4.25593i	0.871885	−	0.158170i
$725$	0.304573	−	1.13668i	0.0113116	−	0.0422154i
$726$	19.5950	+	6.12524i	0.727238	+	0.227329i
$727$		−	23.5496i		−	0.873406i	−0.899606	−	0.436703i	$-0.856146\pi$
$727$		−	23.5496i		−	0.873406i	0.899606	−	0.436703i	$-0.143854\pi$
$728$		0			0
$729$			11.4085i			0.422538i
$730$	0.150338	−	0.480938i	0.00556424	−	0.0178003i
$731$	7.59756	−	28.3545i	0.281006	−	1.04873i
$732$	−12.4452	−	8.62317i	−0.459989	−	0.318721i
$733$	−0.462947	−	1.72774i	−0.0170993	−	0.0638156i	0.956849	−	0.290586i	$-0.0938501\pi$
$733$	−0.462947	−	1.72774i	−0.0170993	−	0.0638156i	−0.973948	+	0.226770i	$0.927183\pi$
$734$	−29.2153	−	18.5112i	−1.07836	−	0.683260i
$735$		0			0
$736$	−12.0956	−	36.7764i	−0.445849	−	1.35560i
$737$	−10.1636	+	17.6039i	−0.374382	+	0.648448i
$738$	−0.152002	+	3.69000i	−0.00559526	+	0.135831i
$739$	−22.6228	−	6.06175i	−0.832192	−	0.222985i	−0.182522	−	0.983202i	$-0.558426\pi$
$739$	−22.6228	−	6.06175i	−0.832192	−	0.222985i	−0.649670	+	0.760217i	$0.725093\pi$
$740$	−1.62413	+	19.6803i	−0.0597044	+	0.723463i
$741$	−2.71407	−	2.71407i	−0.0997039	−	0.0997039i
$742$		0			0
$743$		−	13.9219i		−	0.510747i	−0.966843	−	0.255373i	$-0.917802\pi$
$743$		−	13.9219i		−	0.510747i	0.966843	−	0.255373i	$-0.0821984\pi$
$744$	44.7075	−	6.22233i	1.63905	−	0.228122i
$745$	8.56324	−	4.94399i	0.313733	−	0.181134i
$746$	38.2330	−	35.2078i	1.39981	−	1.28905i
$747$	0.629693	−	0.168726i	0.0230393	−	0.00617336i
$748$	7.48732	−	20.8909i	0.273763	−	0.763848i
$749$		0			0
$750$	13.6959	−	21.6156i	0.500104	−	0.789291i
$751$	4.53854	−	7.86098i	0.165614	−	0.286851i	−0.771259	−	0.636521i	$-0.780373\pi$
$751$	4.53854	−	7.86098i	0.165614	−	0.286851i	0.936873	+	0.349670i	$0.113706\pi$
$752$	−1.14109	−	0.189630i	−0.0416113	−	0.00691511i
$753$	−5.20885	−	9.02200i	−0.189821	−	0.328780i
$754$	−0.572080	−	1.09238i	−0.0208339	−	0.0397820i
$755$	−7.27718	+	7.27718i	−0.264844	+	0.264844i
$756$		0			0
$757$	−1.14043	−	1.14043i	−0.0414496	−	0.0414496i	0.686078	−	0.727528i	$-0.259331\pi$
$757$	−1.14043	−	1.14043i	−0.0414496	−	0.0414496i	−0.727528	+	0.686078i	$0.759331\pi$
$758$	−35.3498	−	11.0501i	−1.28396	−	0.401357i
$759$	−23.4173	+	13.5200i	−0.849994	+	0.490744i
$760$	1.65107	−	0.698235i	0.0598905	−	0.0253276i
$761$	7.60476	+	4.39061i	0.275672	+	0.159159i	0.631463	−	0.775406i	$-0.282455\pi$
$761$	7.60476	+	4.39061i	0.275672	+	0.159159i	−0.355790	+	0.934566i	$0.615788\pi$
$762$	−31.1648	+	6.98966i	−1.12898	+	0.253209i
$763$		0			0
$764$	−4.21137	−	8.91635i	−0.152362	−	0.322582i
$765$	1.58628	+	5.92008i	0.0573521	+	0.214041i
$766$	0.919408	−	22.3196i	0.0332196	−	0.806439i
$767$	20.7143	+	35.8783i	0.747951	+	1.29549i
$768$	29.0411	−	14.2455i	1.04793	−	0.514039i
$769$	−29.8204			−1.07535			−0.537676	−	0.843152i	$-0.680697\pi$
$769$	−29.8204			−1.07535			−0.537676	+	0.843152i	$0.680697\pi$
$770$		0			0
$771$	5.36862	−	5.36862i	0.193346	−	0.193346i
$772$	−43.6689	−	3.60381i	−1.57168	−	0.129704i
$773$	−11.9365	+	44.5476i	−0.429326	+	1.60227i	0.324965	+	0.945726i	$0.394648\pi$
$773$	−11.9365	+	44.5476i	−0.429326	+	1.60227i	−0.754291	+	0.656540i	$0.772019\pi$
$774$	−5.38482	−	5.84752i	−0.193553	−	0.210185i
$775$	−27.4418	−	15.8435i	−0.985738	−	0.569116i
$776$	4.27469	−	34.4342i	0.153452	−	1.23612i
$777$		0			0
$778$	1.76452	+	7.86746i	0.0632611	+	0.282062i
$779$	1.48102	−	0.396838i	0.0530630	−	0.0142182i
$780$	−2.13141	−	11.7490i	−0.0763168	−	0.420683i
$781$	−21.8876	−	5.86476i	−0.783199	−	0.209858i
$782$	−25.4942	−	48.6806i	−0.911669	−	1.74082i
$783$	−1.13367			−0.0405142
$784$		0			0
$785$	4.09643			0.146208
$786$	16.7242	+	31.9345i	0.596532	+	1.13907i
$787$	25.3091	+	6.78154i	0.902170	+	0.241736i	0.679948	−	0.733260i	$-0.262002\pi$
$787$	25.3091	+	6.78154i	0.902170	+	0.241736i	0.222222	+	0.974996i	$0.428669\pi$
$788$	21.2061	−	3.84703i	0.755434	−	0.137045i
$789$	36.8115	−	9.86360i	1.31052	−	0.351153i
$790$	2.36589	+	10.5488i	0.0841746	+	0.375309i
$791$		0			0
$792$	−3.69354	−	4.74056i	−0.131244	−	0.168448i
$793$	9.64539	+	5.56877i	0.342518	+	0.197753i
$794$	0.963946	+	1.04677i	0.0342092	+	0.0371486i
$795$	−4.10250	+	15.3107i	−0.145501	+	0.543016i
$796$	0.588261	−	7.12820i	0.0208504	−	0.252653i
$797$	16.7419	−	16.7419i	0.593028	−	0.593028i	−0.345420	−	0.938448i	$-0.612264\pi$
$797$	16.7419	−	16.7419i	0.593028	−	0.593028i	0.938448	+	0.345420i	$0.112264\pi$
$798$		0			0
$799$	−1.64191			−0.0580866
$800$	−22.2280	−	4.64134i	−0.785879	−	0.164096i
$801$	9.56111	+	16.5603i	0.337825	+	0.585130i
$802$	−1.01316	+	24.5955i	−0.0357759	+	0.868496i
$803$	0.181511	+	0.677409i	0.00640540	+	0.0239053i
$804$	−38.0274	+	17.9611i	−1.34112	+	0.633439i
$805$		0			0
$806$	−32.3989	+	7.26645i	−1.14120	+	0.255950i
$807$	30.0243	+	17.3345i	1.05690	+	0.610204i
$808$	3.17094	+	1.28607i	0.111553	+	0.0452439i
$809$	30.7720	−	17.7662i	1.08189	−	0.624628i	0.150482	−	0.988613i	$-0.451917\pi$
$809$	30.7720	−	17.7662i	1.08189	−	0.624628i	0.931405	+	0.363985i	$0.118584\pi$
$810$	−14.8491	−	4.64173i	−0.521746	−	0.163094i
$811$	−29.5602	−	29.5602i	−1.03800	−	1.03800i	−0.999249	−	0.0387507i	$-0.987662\pi$
$811$	−29.5602	−	29.5602i	−1.03800	−	1.03800i	−0.0387507	−	0.999249i	$-0.512338\pi$
$812$		0			0
$813$	−7.59395	+	7.59395i	−0.266331	+	0.266331i
$814$	−12.7507	−	24.3472i	−0.446912	−	0.853370i
$815$	−4.10288	−	7.10640i	−0.143718	−	0.248926i
$816$	37.3492	−	26.7045i	1.30748	−	0.934846i
$817$	−1.65012	+	2.85809i	−0.0577304	+	0.0999920i
$818$	−28.8952	+	45.6040i	−1.01030	+	1.59451i
$819$		0			0
$820$	4.49027	+	1.60931i	0.156807	+	0.0561996i
$821$	−7.63653	+	2.04620i	−0.266517	+	0.0714129i	−0.389602	−	0.920983i	$-0.627388\pi$
$821$	−7.63653	+	2.04620i	−0.266517	+	0.0714129i	0.123086	+	0.992396i	$0.460721\pi$
$822$	34.0784	−	31.3819i	1.18862	−	1.09457i
$823$	43.2107	−	24.9477i	1.50623	−	0.869623i	0.506258	−	0.862382i	$-0.331028\pi$
$823$	43.2107	−	24.9477i	1.50623	−	0.869623i	0.999974	−	0.00724096i	$-0.00230489\pi$
$824$	9.96672	−	13.1896i	0.347207	−	0.459481i
$825$			15.8599i			0.552171i
$826$		0			0
$827$	−8.11672	−	8.11672i	−0.282246	−	0.282246i	0.551758	−	0.834004i	$-0.313957\pi$
$827$	−8.11672	−	8.11672i	−0.282246	−	0.282246i	−0.834004	+	0.551758i	$0.813957\pi$
$828$	−14.8306	−	1.22390i	−0.515397	−	0.0425336i
$829$	−6.87035	−	1.84091i	−0.238617	−	0.0639373i	0.137528	−	0.990498i	$-0.456084\pi$
$829$	−6.87035	−	1.84091i	−0.238617	−	0.0639373i	−0.376146	+	0.926561i	$0.622751\pi$
$830$	0.0346544	−	0.841271i	0.00120287	−	0.0292010i
$831$	15.3659	−	26.6145i	0.533037	−	0.923248i
$832$	−20.4284	+	12.2005i	−0.708227	+	0.422975i
$833$		0			0
$834$	−35.8685	−	22.7267i	−1.24202	−	0.786962i
$835$	−2.29400	−	8.56133i	−0.0793872	−	0.296277i
$836$	−1.42097	+	2.05079i	−0.0491454	+	0.0709281i
$837$	−7.90079	+	29.4861i	−0.273091	+	1.01919i
$838$	−16.1114	+	51.5413i	−0.556559	+	1.78046i
$839$			3.57060i			0.123271i	0.998099	+	0.0616354i	$0.0196316\pi$
$839$			3.57060i			0.123271i	−0.998099	+	0.0616354i	$0.980368\pi$
$840$		0			0
$841$			28.9141i			0.997036i
$842$	36.5502	+	11.4253i	1.25960	+	0.393742i
$843$	−1.65235	+	6.16664i	−0.0569098	+	0.212390i
$844$	−3.70442	−	20.4199i	−0.127511	−	0.702883i
$845$	−1.06740	−	3.98359i	−0.0367197	−	0.137040i
$846$	−0.237973	+	0.375581i	−0.00818167	+	0.0129127i
$847$		0			0
$848$	31.4370	−	3.06283i	1.07955	−	0.105178i
$849$	−14.2697	+	24.7159i	−0.489736	+	0.848248i
$850$	−32.2042	−	1.32658i	−1.10460	−	0.0455015i
$851$	−65.7370	−	17.6142i	−2.25344	−	0.603806i
$852$	−30.3113	−	35.7643i	−1.03845	−	1.22526i
$853$	−13.8958	−	13.8958i	−0.475784	−	0.475784i	0.427996	−	0.903780i	$-0.359220\pi$
$853$	−13.8958	−	13.8958i	−0.475784	−	0.475784i	−0.903780	+	0.427996i	$0.859220\pi$
$854$		0			0
$855$		−	0.689051i		−	0.0235650i
$856$	1.46321	+	10.5132i	0.0500116	+	0.359333i
$857$	−34.8241	+	20.1057i	−1.18957	+	0.686798i	−0.958209	−	0.286070i	$-0.907651\pi$
$857$	−34.8241	+	20.1057i	−1.18957	+	0.686798i	−0.231360	+	0.972868i	$0.574318\pi$
$858$	11.2578	+	12.2252i	0.384336	+	0.417360i
$859$	25.0429	−	6.71022i	0.854452	−	0.228950i	0.195099	−	0.980784i	$-0.437497\pi$
$859$	25.0429	−	6.71022i	0.854452	−	0.228950i	0.659353	+	0.751834i	$0.270830\pi$
$860$	−9.28354	+	4.38480i	−0.316566	+	0.149521i
$861$		0			0
$862$	1.50175	+	0.951526i	0.0511497	+	0.0324091i
$863$	−8.22908	+	14.2532i	−0.280121	+	0.485184i	−0.971414	−	0.237390i	$-0.923708\pi$
$863$	−8.22908	+	14.2532i	−0.280121	+	0.485184i	0.691293	+	0.722574i	$0.257041\pi$
$864$	1.22333	+	21.8414i	0.0416185	+	0.743059i
$865$	2.70543	+	4.68593i	0.0919872	+	0.159327i
$866$	−11.4868	+	6.01568i	−0.390338	+	0.204421i
$867$	21.7811	−	21.7811i	0.739724	−	0.739724i
$868$		0			0
$869$	−10.6394	−	10.6394i	−0.360918	−	0.360918i
$870$	0.248297	−	0.794316i	0.00841806	−	0.0269298i
$871$	26.7915	−	15.4681i	0.907795	−	0.524116i
$872$	−10.6495	+	26.2575i	−0.360639	+	0.889191i
$873$	−11.5505	−	6.66868i	−0.390925	−	0.225700i
$874$	1.35204	+	6.02832i	0.0457333	+	0.203911i
$875$		0			0
$876$	−0.489531	+	1.36588i	−0.0165397	+	0.0461488i
$877$	5.90884	+	22.0521i	0.199527	+	0.744646i	0.991048	+	0.133504i	$0.0426228\pi$
$877$	5.90884	+	22.0521i	0.199527	+	0.744646i	−0.791521	+	0.611142i	$0.790710\pi$
$878$	−11.2559	−	0.463663i	−0.379868	−	0.0156479i
$879$	−15.6299	−	27.0718i	−0.527185	−	0.913111i
$880$	−7.26721	+	2.72644i	−0.244978	+	0.0919084i
$881$	−5.29761			−0.178481			−0.0892405	−	0.996010i	$-0.528444\pi$
$881$	−5.29761			−0.178481			−0.0892405	+	0.996010i	$0.528444\pi$
$882$		0			0
$883$	−30.7426	+	30.7426i	−1.03457	+	1.03457i	−0.0351900	+	0.999381i	$0.511204\pi$
$883$	−30.7426	+	30.7426i	−1.03457	+	1.03457i	−0.999381	+	0.0351900i	$0.988796\pi$
$884$	−25.7654	+	21.8369i	−0.866583	+	0.734456i
$885$	−7.23658	+	27.0073i	−0.243255	+	0.907840i
$886$	26.0304	−	23.9707i	0.874507	−	0.805310i
$887$	−5.04199	−	2.91100i	−0.169294	−	0.0977417i	0.412959	−	0.910750i	$-0.364495\pi$
$887$	−5.04199	−	2.91100i	−0.169294	−	0.0977417i	−0.582253	+	0.813008i	$0.697829\pi$
$888$	7.00518	−	56.4293i	0.235078	−	1.89364i
$889$		0			0
$890$	24.0991	−	5.40496i	0.807802	−	0.181175i
$891$	20.9153	−	5.60423i	0.700688	−	0.187749i
$892$	−4.85284	+	7.00377i	−0.162485	+	0.234504i
$893$	0.178304	+	0.0477763i	0.00596671	+	0.00159877i
$894$	−25.2231	+	13.2094i	−0.843585	+	0.441788i
$895$	9.68763			0.323822
$896$		0			0
$897$	41.1522			1.37403
$898$	10.4364	−	5.46556i	0.348267	−	0.182388i
$899$	−2.23530	−	0.598947i	−0.0745514	−	0.0199760i
$900$	−4.97102	+	7.17433i	−0.165701	+	0.239144i
$901$	43.3062	−	11.6039i	1.44274	−	0.386581i
$902$	−6.47784	+	1.45285i	−0.215688	+	0.0483748i
$903$		0			0
$904$	−1.76824	+	14.2438i	−0.0588107	+	0.473742i
$905$	−10.2510	−	5.91844i	−0.340756	−	0.196736i
$906$	21.7995	−	20.0746i	0.724239	−	0.666932i
$907$	−5.44791	+	20.3319i	−0.180895	+	0.675108i	0.814577	+	0.580055i	$0.196969\pi$
$907$	−5.44791	+	20.3319i	−0.180895	+	0.675108i	−0.995472	+	0.0950536i	$0.969698\pi$
$908$	7.38190	−	6.25639i	0.244977	−	0.207626i
$909$	0.930037	−	0.930037i	0.0308474	−	0.0308474i
$910$		0			0
$911$	−46.3231			−1.53475			−0.767376	−	0.641197i	$-0.778438\pi$
$911$	−46.3231			−1.53475			−0.767376	+	0.641197i	$0.778438\pi$
$912$	−4.83300	+	1.81320i	−0.160037	+	0.0600411i
$913$	0.585933	+	1.01487i	0.0193916	+	0.0335872i
$914$	20.4503	+	0.842408i	0.676437	+	0.0278644i
$915$	1.94546	+	7.26054i	0.0643148	+	0.240026i
$916$	−13.2373	+	36.9344i	−0.437373	+	1.22035i
$917$		0			0
$918$	6.79529	+	30.2982i	0.224278	+	0.999988i
$919$	12.8775	+	7.43484i	0.424790	+	0.245253i	0.697125	−	0.716950i	$-0.254462\pi$
$919$	12.8775	+	7.43484i	0.424790	+	0.245253i	−0.272335	+	0.962203i	$0.587796\pi$
$920$	−7.22368	+	17.8107i	−0.238158	+	0.587202i
$921$	−36.5799	+	21.1194i	−1.20535	+	0.695908i
$922$	−2.52421	+	8.07508i	−0.0831304	+	0.265939i
$923$	24.3852	+	24.3852i	0.802649	+	0.802649i
$924$		0			0
$925$	−28.2258	+	28.2258i	−0.928058	+	0.928058i
$926$	31.5692	−	16.5329i	1.03743	−	0.543304i
$927$	−3.17723	−	5.50313i	−0.104354	−	0.180746i
$928$	−1.65576	+	0.0927388i	−0.0543531	+	0.00304430i
$929$	−25.8504	+	44.7742i	−0.848124	+	1.46899i	0.0347569	+	0.999396i	$0.488934\pi$
$929$	−25.8504	+	44.7742i	−0.848124	+	1.46899i	−0.882881	+	0.469598i	$0.844399\pi$
$930$	−18.9292	−	11.9938i	−0.620713	−	0.393291i
$931$		0			0
$932$	9.16052	−	4.32670i	0.300063	−	0.141726i
$933$	−17.0593	+	4.57104i	−0.558498	+	0.149649i
$934$	14.7193	+	15.9840i	0.481629	+	0.523013i
$935$	−9.54129	+	5.50867i	−0.312034	+	0.180153i
$936$	1.26078	+	9.05870i	0.0412099	+	0.296093i
$937$			50.1408i			1.63803i	0.573773	+	0.819014i	$0.305479\pi$
$937$			50.1408i			1.63803i	−0.573773	+	0.819014i	$0.694521\pi$
$938$		0			0
$939$	5.88663	+	5.88663i	0.192103	+	0.192103i
$940$	0.371294	+	0.438089i	0.0121103	+	0.0142889i
$941$	43.3123	+	11.6055i	1.41194	+	0.378328i	0.882617	−	0.470093i	$-0.155780\pi$
$941$	43.3123	+	11.6055i	1.41194	+	0.378328i	0.529322	+	0.848421i	$0.322446\pi$
$942$	−11.7857	−	0.485489i	−0.384000	−	0.0158181i
$943$	−8.21947	+	14.2365i	−0.267663	+	0.463606i
$944$	55.4531	−	5.40265i	1.80485	−	0.175841i
$945$		0			0
$946$	7.64801	−	12.0705i	0.248658	−	0.392445i
$947$	0.427149	+	1.59414i	0.0138805	+	0.0518027i	0.972519	−	0.232825i	$-0.0747968\pi$
$947$	0.427149	+	1.59414i	0.0138805	+	0.0518027i	−0.958638	+	0.284627i	$0.908130\pi$
$948$	−5.55666	−	30.6301i	−0.180472	−	0.994819i
$949$	0.276243	−	1.03095i	0.00896723	−	0.0334661i
$950$	3.45863	+	1.08114i	0.112213	+	0.0350768i
$951$		−	49.3867i		−	1.60147i
$952$		0			0
$953$		−	40.9510i		−	1.32653i	−0.748384	−	0.663266i	$-0.769170\pi$
$953$		−	40.9510i		−	1.32653i	0.748384	−	0.663266i	$-0.230830\pi$
$954$	3.62231	−	11.5880i	0.117277	−	0.375174i
$955$	−1.26704	+	4.72865i	−0.0410003	+	0.153015i
$956$	−10.6217	+	15.3296i	−0.343531	+	0.495795i
$957$	0.299783	+	1.11881i	0.00969062	+	0.0361659i
$958$	24.8828	+	15.7661i	0.803927	+	0.509378i
$959$		0			0
$960$	−15.5712	−	3.92656i	−0.502559	−	0.126729i
$961$	−15.6564	+	27.1177i	−0.505046	+	0.874766i
$962$	−1.72156	+	41.7926i	−0.0555052	+	1.34745i
$963$	3.94096	+	1.05598i	0.126996	+	0.0340284i
$964$	51.2907	+	4.23281i	1.65196	+	0.136329i
$965$	15.3818	+	15.3818i	0.495159	+	0.495159i
$966$		0			0
$967$			14.6315i			0.470518i	0.971933	+	0.235259i	$0.0755938\pi$
$967$			14.6315i			0.470518i	−0.971933	+	0.235259i	$0.924406\pi$
$968$	−12.2444	+	16.2039i	−0.393551	+	0.520811i
$969$	−6.34536	+	3.66350i	−0.203842	+	0.117688i
$970$	−12.6717	+	11.6691i	−0.406865	+	0.374672i
$971$	23.5944	−	6.32211i	0.757181	−	0.202886i	0.140480	−	0.990084i	$-0.455135\pi$
$971$	23.5944	−	6.32211i	0.757181	−	0.202886i	0.616701	+	0.787197i	$0.288469\pi$
$972$	20.3299	+	7.28623i	0.652081	+	0.233706i
$973$		0			0
$974$	0.168362	−	0.265717i	0.00539466	−	0.00851413i
$975$	12.0686	−	20.9035i	0.386506	−	0.669448i
$976$	12.1843	−	8.71175i	0.390011	−	0.278856i
$977$	2.85781	+	4.94988i	0.0914295	+	0.158361i	0.908113	−	0.418725i	$-0.137523\pi$
$977$	2.85781	+	4.94988i	0.0914295	+	0.158361i	−0.816683	+	0.577086i	$0.804190\pi$
$978$	10.9621	+	20.9319i	0.350529	+	0.669329i
$979$	−24.3061	+	24.3061i	−0.776827	+	0.776827i
$980$		0			0
$981$	7.70133	+	7.70133i	0.245885	+	0.245885i
$982$	−34.6631	−	10.8354i	−1.10614	−	0.345772i
$983$	−18.6714	+	10.7799i	−0.595525	+	0.343827i	−0.767279	−	0.641313i	$-0.778390\pi$
$983$	−18.6714	+	10.7799i	−0.595525	+	0.343827i	0.171754	+	0.985140i	$0.445057\pi$
$984$	−12.7281	−	5.16228i	−0.405758	−	0.164568i
$985$	−9.26615	−	5.34981i	−0.295244	−	0.170459i
$986$	−2.29686	+	0.515141i	−0.0731469	+	0.0164054i
$987$		0			0
$988$	3.43341	−	1.62167i	0.109231	−	0.0515921i
$989$	−9.15796	−	34.1780i	−0.291206	−	1.08680i
$990$	−0.122794	+	2.98094i	−0.00390264	+	0.0947406i
$991$	17.3811	+	30.1049i	0.552128	+	0.956314i	0.998121	+	0.0612772i	$0.0195174\pi$
$991$	17.3811	+	30.1049i	0.552128	+	0.956314i	−0.445993	+	0.895037i	$0.647149\pi$
$992$	−9.12724	+	43.7116i	−0.289790	+	1.38785i
$993$	14.7661			0.468590
$994$		0			0
$995$	−2.51082	+	2.51082i	−0.0795985	+	0.0795985i
$996$	−0.199407	+	2.41630i	−0.00631845	+	0.0765633i
$997$	−1.32792	+	4.95586i	−0.0420556	+	0.156954i	−0.983760	−	0.179487i	$-0.942556\pi$
$997$	−1.32792	+	4.95586i	−0.0420556	+	0.156954i	0.941705	+	0.336440i	$0.109223\pi$
$998$	−3.36364	−	3.65266i	−0.106474	−	0.115623i
$999$	33.3031	+	19.2275i	1.05366	+	0.608332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.373.3		48
7.2	even	3		784.2.m.k.197.10		24
7.3	odd	6		112.2.w.c.53.7	yes	48
7.4	even	3	inner	784.2.x.o.165.7		48
7.5	odd	6		784.2.m.j.197.10		24
7.6	odd	2		112.2.w.c.37.3	✓	48
16.13	even	4	inner	784.2.x.o.765.7		48
28.3	even	6		448.2.ba.c.305.10		48
28.27	even	2		448.2.ba.c.177.3		48
56.3	even	6		896.2.ba.e.865.3		48
56.13	odd	2		896.2.ba.f.737.3		48
56.27	even	2		896.2.ba.e.737.10		48
56.45	odd	6		896.2.ba.f.865.10		48
112.3	even	12		448.2.ba.c.81.3		48
112.13	odd	4		112.2.w.c.93.7	yes	48
112.27	even	4		896.2.ba.e.289.3		48
112.45	odd	12		112.2.w.c.109.3	yes	48
112.59	even	12		896.2.ba.e.417.10		48
112.61	odd	12		784.2.m.j.589.10		24
112.69	odd	4		896.2.ba.f.289.10		48
112.83	even	4		448.2.ba.c.401.10		48
112.93	even	12		784.2.m.k.589.10		24
112.101	odd	12		896.2.ba.f.417.3		48
112.109	even	12	inner	784.2.x.o.557.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.3	✓	48	7.6	odd	2
112.2.w.c.53.7	yes	48	7.3	odd	6
112.2.w.c.93.7	yes	48	112.13	odd	4
112.2.w.c.109.3	yes	48	112.45	odd	12
448.2.ba.c.81.3		48	112.3	even	12
448.2.ba.c.177.3		48	28.27	even	2
448.2.ba.c.305.10		48	28.3	even	6
448.2.ba.c.401.10		48	112.83	even	4
784.2.m.j.197.10		24	7.5	odd	6
784.2.m.j.589.10		24	112.61	odd	12
784.2.m.k.197.10		24	7.2	even	3
784.2.m.k.589.10		24	112.93	even	12
784.2.x.o.165.7		48	7.4	even	3	inner
784.2.x.o.373.3		48	1.1	even	1	trivial
784.2.x.o.557.3		48	112.109	even	12	inner
784.2.x.o.765.7		48	16.13	even	4	inner
896.2.ba.e.289.3		48	112.27	even	4
896.2.ba.e.417.10		48	112.59	even	12
896.2.ba.e.737.10		48	56.27	even	2
896.2.ba.e.865.3		48	56.3	even	6
896.2.ba.f.289.10		48	112.69	odd	4
896.2.ba.f.417.3		48	112.101	odd	12
896.2.ba.f.737.3		48	56.13	odd	2
896.2.ba.f.865.10		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)

\(f(q)\)	\(=\)	\(q+(-1.25281 + 0.656100i) q^{2} +(-1.95279 - 0.523249i) q^{3} +(1.13907 - 1.64394i) q^{4} +(-0.959072 + 0.256983i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} +(0.941530 + 0.543593i) q^{9} +O(q^{10})\)	\(q+(-1.25281 + 0.656100i) q^{2} +(-1.95279 - 0.523249i) q^{3} +(1.13907 - 1.64394i) q^{4} +(-0.959072 + 0.256983i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} +(0.941530 + 0.543593i) q^{9} +(1.03293 - 0.951197i) q^{10} +(-0.505816 + 1.88773i) q^{11} +(-3.08455 + 2.61425i) q^{12} +(2.10314 - 2.10314i) q^{13} +2.00733 q^{15} +(-1.40505 - 3.74511i) q^{16} +(-2.83885 - 4.91704i) q^{17} +(-1.53621 - 0.0632809i) q^{18} +(0.165210 + 0.616573i) q^{19} +(-0.669984 + 1.86937i) q^{20} +(-0.604848 - 2.69683i) q^{22} +(-5.92691 - 3.42190i) q^{23} +(2.14914 - 5.29893i) q^{24} +(-3.47635 + 2.00707i) q^{25} +(-1.25497 + 4.01471i) q^{26} +(2.73445 + 2.73445i) q^{27} +(-0.207295 + 0.207295i) q^{29} +(-2.51481 + 1.31701i) q^{30} +(3.94693 + 6.83628i) q^{31} +(4.21743 + 3.77005i) q^{32} +(1.97551 - 3.42168i) q^{33} +(6.78261 + 4.29755i) q^{34} +(1.96610 - 0.928627i) q^{36} +(9.60533 - 2.57374i) q^{37} +(-0.611510 - 0.664054i) q^{38} +(-5.20747 + 3.00653i) q^{39} +(-0.387132 - 2.78155i) q^{40} -2.40202i q^{41} +(3.65586 + 3.65586i) q^{43} +(2.52715 + 2.98178i) q^{44} +(-1.04269 - 0.279388i) q^{45} +(9.67040 + 0.398352i) q^{46} +(0.144593 - 0.250442i) q^{47} +(0.784155 + 8.04861i) q^{48} +(3.03837 - 4.79531i) q^{50} +(2.97086 + 11.0874i) q^{51} +(-1.06181 - 5.85305i) q^{52} +(-2.04376 + 7.62740i) q^{53} +(-5.21982 - 1.63168i) q^{54} -1.94045i q^{55} -1.29048i q^{57} +(0.123695 - 0.395707i) q^{58} +(-3.60507 + 13.4543i) q^{59} +(2.28649 - 3.29993i) q^{60} +(0.969174 + 3.61701i) q^{61} +(-9.43003 - 5.97498i) q^{62} +(-7.75717 - 1.95611i) q^{64} +(-1.47659 + 2.55754i) q^{65} +(-0.229973 + 5.58284i) q^{66} +(10.0468 + 2.69202i) q^{67} +(-11.3169 - 0.933941i) q^{68} +(9.78352 + 9.78352i) q^{69} +11.5947i q^{71} +(-1.85387 + 2.45335i) q^{72} +(0.310772 - 0.179424i) q^{73} +(-10.3450 + 9.52646i) q^{74} +(7.83878 - 2.10040i) q^{75} +(1.20179 + 0.430722i) q^{76} +(4.55138 - 7.18323i) q^{78} +(-3.84953 + 6.66758i) q^{79} +(2.30997 + 3.23075i) q^{80} +(-5.53979 - 9.59520i) q^{81} +(1.57596 + 3.00927i) q^{82} +(0.424001 - 0.424001i) q^{83} +(3.98626 + 3.98626i) q^{85} +(-6.97871 - 2.18149i) q^{86} +(0.513270 - 0.296337i) q^{87} +(-5.12238 - 2.07754i) q^{88} +(15.2323 + 8.79437i) q^{89} +(1.48960 - 0.334088i) q^{90} +(-12.3765 + 5.84569i) q^{92} +(-4.13045 - 15.4150i) q^{93} +(-0.0168324 + 0.408623i) q^{94} +(-0.316897 - 0.548881i) q^{95} +(-6.26308 - 9.56889i) q^{96} -12.2678 q^{97} +(-1.50240 + 1.50240i) 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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