LMFDB - Embedded newform 456.2.u.c.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(11,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

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

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

chi := DirichletCharacter("456.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.u (of order $6$, degree $2$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.4857532416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 14x^{5} + 96x^{4} - 82x^{3} - 17x^{2} + 86x + 31 $ x^8 - 2x^7 + x^6 - 14x^5 + 96x^4 - 82x^3 - 17x^2 + 86x + 31
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.2
Root			$-0.479034 + 0.0374240i$ of defining polynomial
Character	$\chi$	$=$	456.11
Dual form			456.2.u.c.83.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.68614 + 0.396143i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.707107 - 1.22474i) q^{5} +(-1.67746 + 1.78498i) q^{6} +4.69042i q^{7} +2.82843 q^{8} +(2.68614 + 1.33591i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.68614 + 0.396143i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.707107 - 1.22474i) q^{5} +(-1.67746 + 1.78498i) q^{6} +4.69042i q^{7} +2.82843 q^{8} +(2.68614 + 1.33591i) q^{9} +(1.00000 + 1.73205i) q^{10} -3.31662i q^{11} +(-1.00000 - 3.31662i) q^{12} +(-5.74456 - 3.31662i) q^{14} +(1.67746 - 1.78498i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(5.74456 + 3.31662i) q^{17} +(-3.53553 + 2.34521i) q^{18} +(-3.50000 - 2.59808i) q^{19} -2.82843 q^{20} +(-1.85808 + 7.90870i) q^{21} +(4.06202 + 2.34521i) q^{22} +(-2.12132 - 3.67423i) q^{23} +(4.76913 + 1.12046i) q^{24} +(1.50000 + 2.59808i) q^{25} +(4.00000 + 3.31662i) q^{27} +(8.12404 - 4.69042i) q^{28} +(3.53553 + 6.12372i) q^{29} +(1.00000 + 3.31662i) q^{30} +4.69042i q^{31} +(-2.82843 - 4.89898i) q^{32} +(1.31386 - 5.59230i) q^{33} +(-8.12404 + 4.69042i) q^{34} +(5.74456 + 3.31662i) q^{35} +(-0.372281 - 5.98844i) q^{36} -4.69042i q^{37} +(5.65685 - 2.44949i) q^{38} +(2.00000 - 3.46410i) q^{40} +(2.87228 + 1.65831i) q^{41} +(-8.37228 - 7.86797i) q^{42} +(-3.00000 + 5.19615i) q^{43} +(-5.74456 + 3.31662i) q^{44} +(3.53553 - 2.34521i) q^{45} +6.00000 q^{46} +(-3.53553 - 6.12372i) q^{47} +(-4.74456 + 5.04868i) q^{48} -15.0000 q^{49} -4.24264 q^{50} +(8.37228 + 7.86797i) q^{51} +(-5.65685 - 9.79796i) q^{53} +(-6.89045 + 2.55377i) q^{54} +(-4.06202 - 2.34521i) q^{55} +13.2665i q^{56} +(-4.87228 - 5.76722i) q^{57} -10.0000 q^{58} +(-2.87228 - 1.65831i) q^{59} +(-4.76913 - 1.12046i) q^{60} +(4.06202 - 2.34521i) q^{61} +(-5.74456 - 3.31662i) q^{62} +(-6.26596 + 12.5991i) q^{63} +8.00000 q^{64} +(5.92010 + 5.56349i) q^{66} +(-2.50000 - 4.33013i) q^{67} -13.2665i q^{68} +(-2.12132 - 7.03562i) q^{69} +(-8.12404 + 4.69042i) q^{70} +(2.82843 - 4.89898i) q^{71} +(7.59755 + 3.77852i) q^{72} +(-0.500000 + 0.866025i) q^{73} +(5.74456 + 3.31662i) q^{74} +(1.50000 + 4.97494i) q^{75} +(-1.00000 + 8.66025i) q^{76} +15.5563 q^{77} +(2.82843 + 4.89898i) q^{80} +(5.43070 + 7.17687i) q^{81} +(-4.06202 + 2.34521i) q^{82} -3.31662i q^{83} +(15.5563 - 4.69042i) q^{84} +(8.12404 - 4.69042i) q^{85} +(-4.24264 - 7.34847i) q^{86} +(3.53553 + 11.7260i) q^{87} -9.38083i q^{88} +(-5.74456 + 3.31662i) q^{89} +(0.372281 + 5.98844i) q^{90} +(-4.24264 + 7.34847i) q^{92} +(-1.85808 + 7.90870i) q^{93} +10.0000 q^{94} +(-5.65685 + 2.44949i) q^{95} +(-2.82843 - 9.38083i) q^{96} +(7.50000 - 12.9904i) q^{97} +(10.6066 - 18.3712i) q^{98} +(4.43070 - 8.90892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 8 q^{4} + 10 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 8 * q^4 + 10 * q^9	$ 8 q + 2 q^{3} - 8 q^{4} + 10 q^{9} + 8 q^{10} - 8 q^{12} - 16 q^{16} - 28 q^{19} + 12 q^{25} + 32 q^{27} + 8 q^{30} + 22 q^{33} + 20 q^{36} + 16 q^{40} - 44 q^{42} - 24 q^{43} + 48 q^{46} + 8 q^{48} - 120 q^{49} + 44 q^{51} - 16 q^{57} - 80 q^{58} + 64 q^{64} - 20 q^{67} - 4 q^{73} + 12 q^{75} - 8 q^{76} - 14 q^{81} - 20 q^{90} + 80 q^{94} + 60 q^{97} - 22 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 8 * q^4 + 10 * q^9 + 8 * q^10 - 8 * q^12 - 16 * q^16 - 28 * q^19 + 12 * q^25 + 32 * q^27 + 8 * q^30 + 22 * q^33 + 20 * q^36 + 16 * q^40 - 44 * q^42 - 24 * q^43 + 48 * q^46 + 8 * q^48 - 120 * q^49 + 44 * q^51 - 16 * q^57 - 80 * q^58 + 64 * q^64 - 20 * q^67 - 4 * q^73 + 12 * q^75 - 8 * q^76 - 14 * q^81 - 20 * q^90 + 80 * q^94 + 60 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i
$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i
$3$	1.68614	+	0.396143i	0.973494	+	0.228714i
$3$	1.68614	+	0.396143i	0.973494	+	0.228714i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	0.707107	−	1.22474i	0.316228	−	0.547723i	−0.663470	−	0.748203i	$-0.730917\pi$
$5$	0.707107	−	1.22474i	0.316228	−	0.547723i	0.979698	+	0.200480i	$0.0642503\pi$
$6$	−1.67746	+	1.78498i	−0.684819	+	0.728714i
$7$			4.69042i			1.77281i	0.462910	+	0.886405i	$0.346805\pi$
$7$			4.69042i			1.77281i	−0.462910	+	0.886405i	$0.653195\pi$
$8$	2.82843			1.00000
$9$	2.68614	+	1.33591i	0.895380	+	0.445302i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$		−	3.31662i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$11$		−	3.31662i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$12$	−1.00000	−	3.31662i	−0.288675	−	0.957427i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−5.74456	−	3.31662i	−1.53530	−	0.886405i
$15$	1.67746	−	1.78498i	0.433117	−	0.460879i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	5.74456	+	3.31662i	1.39326	+	0.804400i	0.993675	−	0.112296i	$-0.0358205\pi$
$17$	5.74456	+	3.31662i	1.39326	+	0.804400i	0.399586	+	0.916696i	$0.369154\pi$
$18$	−3.53553	+	2.34521i	−0.833333	+	0.552771i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$	−2.82843			−0.632456
$21$	−1.85808	+	7.90870i	−0.405466	+	1.72582i
$22$	4.06202	+	2.34521i	0.866025	+	0.500000i
$23$	−2.12132	−	3.67423i	−0.442326	−	0.766131i	0.555536	−	0.831493i	$-0.312513\pi$
$23$	−2.12132	−	3.67423i	−0.442326	−	0.766131i	−0.997862	+	0.0653618i	$0.979180\pi$
$24$	4.76913	+	1.12046i	0.973494	+	0.228714i
$25$	1.50000	+	2.59808i	0.300000	+	0.519615i
$26$		0			0
$27$	4.00000	+	3.31662i	0.769800	+	0.638285i
$28$	8.12404	−	4.69042i	1.53530	−	0.886405i
$29$	3.53553	+	6.12372i	0.656532	+	1.13715i	0.981507	+	0.191425i	$0.0613107\pi$
$29$	3.53553	+	6.12372i	0.656532	+	1.13715i	−0.324975	+	0.945723i	$0.605356\pi$
$30$	1.00000	+	3.31662i	0.182574	+	0.605530i
$31$			4.69042i			0.842424i	0.906962	+	0.421212i	$0.138395\pi$
$31$			4.69042i			0.842424i	−0.906962	+	0.421212i	$0.861605\pi$
$32$	−2.82843	−	4.89898i	−0.500000	−	0.866025i
$33$	1.31386	−	5.59230i	0.228714	−	0.973494i
$34$	−8.12404	+	4.69042i	−1.39326	+	0.804400i
$35$	5.74456	+	3.31662i	0.971008	+	0.560612i
$36$	−0.372281	−	5.98844i	−0.0620469	−	0.998073i
$37$		−	4.69042i		−	0.771100i	−0.922687	−	0.385550i	$-0.874012\pi$
$37$		−	4.69042i		−	0.771100i	0.922687	−	0.385550i	$-0.125988\pi$
$38$	5.65685	−	2.44949i	0.917663	−	0.397360i
$39$		0			0
$40$	2.00000	−	3.46410i	0.316228	−	0.547723i
$41$	2.87228	+	1.65831i	0.448575	+	0.258985i	0.707228	−	0.706985i	$-0.249945\pi$
$41$	2.87228	+	1.65831i	0.448575	+	0.258985i	−0.258653	+	0.965970i	$0.583279\pi$
$42$	−8.37228	−	7.86797i	−1.29187	−	1.21405i
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	−5.74456	+	3.31662i	−0.866025	+	0.500000i
$45$	3.53553	−	2.34521i	0.527046	−	0.349603i
$46$	6.00000			0.884652
$47$	−3.53553	−	6.12372i	−0.515711	−	0.893237i	−0.999834	−	0.0182371i	$-0.994195\pi$
$47$	−3.53553	−	6.12372i	−0.515711	−	0.893237i	0.484123	−	0.875000i	$-0.339139\pi$
$48$	−4.74456	+	5.04868i	−0.684819	+	0.728714i
$49$	−15.0000			−2.14286
$50$	−4.24264			−0.600000
$51$	8.37228	+	7.86797i	1.17235	+	1.10174i
$52$		0			0
$53$	−5.65685	−	9.79796i	−0.777029	−	1.34585i	−0.933647	−	0.358194i	$-0.883393\pi$
$53$	−5.65685	−	9.79796i	−0.777029	−	1.34585i	0.156618	−	0.987659i	$-0.449941\pi$
$54$	−6.89045	+	2.55377i	−0.937671	+	0.347524i
$55$	−4.06202	−	2.34521i	−0.547723	−	0.316228i
$56$			13.2665i			1.77281i
$57$	−4.87228	−	5.76722i	−0.645349	−	0.763888i
$58$	−10.0000			−1.31306
$59$	−2.87228	−	1.65831i	−0.373939	−	0.215894i	0.301239	−	0.953549i	$-0.402600\pi$
$59$	−2.87228	−	1.65831i	−0.373939	−	0.215894i	−0.675178	+	0.737655i	$0.735933\pi$
$60$	−4.76913	−	1.12046i	−0.615692	−	0.144651i
$61$	4.06202	−	2.34521i	0.520088	−	0.300273i	−0.216883	−	0.976198i	$-0.569589\pi$
$61$	4.06202	−	2.34521i	0.520088	−	0.300273i	0.736971	+	0.675925i	$0.236256\pi$
$62$	−5.74456	−	3.31662i	−0.729560	−	0.421212i
$63$	−6.26596	+	12.5991i	−0.789437	+	1.58734i
$64$	8.00000			1.00000
$65$		0			0
$66$	5.92010	+	5.56349i	0.728714	+	0.684819i
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$		−	13.2665i		−	1.60880i
$69$	−2.12132	−	7.03562i	−0.255377	−	0.846990i
$70$	−8.12404	+	4.69042i	−0.971008	+	0.560612i
$71$	2.82843	−	4.89898i	0.335673	−	0.581402i	−0.647941	−	0.761690i	$-0.724370\pi$
$71$	2.82843	−	4.89898i	0.335673	−	0.581402i	0.983614	+	0.180288i	$0.0577031\pi$
$72$	7.59755	+	3.77852i	0.895380	+	0.445302i
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	−0.893801	−	0.448463i	$-0.851972\pi$
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	0.835281	+	0.549823i	$0.185305\pi$
$74$	5.74456	+	3.31662i	0.667792	+	0.385550i
$75$	1.50000	+	4.97494i	0.173205	+	0.574456i
$76$	−1.00000	+	8.66025i	−0.114708	+	0.993399i
$77$	15.5563			1.77281
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	2.82843	+	4.89898i	0.316228	+	0.547723i
$81$	5.43070	+	7.17687i	0.603411	+	0.797430i
$82$	−4.06202	+	2.34521i	−0.448575	+	0.258985i
$83$		−	3.31662i		−	0.364047i	−0.983294	−	0.182023i	$-0.941735\pi$
$83$		−	3.31662i		−	0.364047i	0.983294	−	0.182023i	$-0.0582647\pi$
$84$	15.5563	−	4.69042i	1.69734	−	0.511766i
$85$	8.12404	−	4.69042i	0.881176	−	0.508747i
$86$	−4.24264	−	7.34847i	−0.457496	−	0.792406i
$87$	3.53553	+	11.7260i	0.379049	+	1.25716i
$88$		−	9.38083i		−	1.00000i
$89$	−5.74456	+	3.31662i	−0.608922	+	0.351562i	−0.772544	−	0.634962i	$-0.781016\pi$
$89$	−5.74456	+	3.31662i	−0.608922	+	0.351562i	0.163621	+	0.986523i	$0.447683\pi$
$90$	0.372281	+	5.98844i	0.0392419	+	0.631237i
$91$		0			0
$92$	−4.24264	+	7.34847i	−0.442326	+	0.766131i
$93$	−1.85808	+	7.90870i	−0.192674	+	0.820094i
$94$	10.0000			1.03142
$95$	−5.65685	+	2.44949i	−0.580381	+	0.251312i
$96$	−2.82843	−	9.38083i	−0.288675	−	0.957427i
$97$	7.50000	−	12.9904i	0.761510	−	1.31897i	−0.180563	−	0.983563i	$-0.557792\pi$
$97$	7.50000	−	12.9904i	0.761510	−	1.31897i	0.942072	−	0.335410i	$-0.108875\pi$
$98$	10.6066	−	18.3712i	1.07143	−	1.85577i
$99$	4.43070	−	8.90892i	0.445302	−	0.895380i
$100$	3.00000	−	5.19615i	0.300000	−	0.519615i
$101$	−3.53553	−	6.12372i	−0.351799	−	0.609333i	0.634766	−	0.772704i	$-0.281097\pi$
$101$	−3.53553	−	6.12372i	−0.351799	−	0.609333i	−0.986565	+	0.163371i	$0.947763\pi$
$102$	−15.5563	+	4.69042i	−1.54031	+	0.464420i
$103$		−	9.38083i		−	0.924321i	−0.886796	−	0.462160i	$-0.847074\pi$
$103$		−	9.38083i		−	0.924321i	0.886796	−	0.462160i	$-0.152926\pi$
$104$		0			0
$105$	8.37228	+	7.86797i	0.817051	+	0.767835i
$106$	16.0000			1.55406
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	1.74456	−	10.2448i	0.167871	−	0.985809i
$109$	−8.12404	−	4.69042i	−0.778142	−	0.449260i	0.0576296	−	0.998338i	$-0.481646\pi$
$109$	−8.12404	−	4.69042i	−0.778142	−	0.449260i	−0.835771	+	0.549078i	$0.814979\pi$
$110$	5.74456	−	3.31662i	0.547723	−	0.316228i
$111$	1.85808	−	7.90870i	0.176361	−	0.750661i
$112$	−16.2481	−	9.38083i	−1.53530	−	0.886405i
$113$		−	16.5831i		−	1.56001i	−0.625774	−	0.780005i	$-0.715217\pi$
$113$		−	16.5831i		−	1.56001i	0.625774	−	0.780005i	$-0.284783\pi$
$114$	10.5086	−	1.88926i	0.984221	−	0.176945i
$115$	−6.00000			−0.559503
$116$	7.07107	−	12.2474i	0.656532	−	1.13715i
$117$		0			0
$118$	4.06202	−	2.34521i	0.373939	−	0.215894i
$119$	−15.5563	+	26.9444i	−1.42605	+	2.46999i
$120$	4.74456	−	5.04868i	0.433117	−	0.460879i
$121$		0			0
$122$			6.63325i			0.600546i
$123$	4.18614	+	3.93398i	0.377452	+	0.354715i
$124$	8.12404	−	4.69042i	0.729560	−	0.421212i
$125$	11.3137			1.01193
$126$	−11.0000	−	16.5831i	−0.979958	−	1.47734i
$127$	−16.2481	+	9.38083i	−1.44178	+	0.832414i	−0.997969	−	0.0637043i	$-0.979709\pi$
$127$	−16.2481	+	9.38083i	−1.44178	+	0.832414i	−0.443815	+	0.896119i	$0.646375\pi$
$128$	−5.65685	+	9.79796i	−0.500000	+	0.866025i
$129$	−7.11684	+	7.57301i	−0.626603	+	0.666767i
$130$		0			0
$131$	2.87228	+	1.65831i	0.250952	+	0.144887i	0.620200	−	0.784444i	$-0.287051\pi$
$131$	2.87228	+	1.65831i	0.250952	+	0.144887i	−0.369248	+	0.929331i	$0.620385\pi$
$132$	−11.0000	+	3.31662i	−0.957427	+	0.288675i
$133$	12.1861	−	16.4165i	1.05667	−	1.42349i
$134$	7.07107			0.610847
$135$	6.89045	−	2.55377i	0.593035	−	0.219794i
$136$	16.2481	+	9.38083i	1.39326	+	0.804400i
$137$	−14.3614	+	8.29156i	−1.22698	+	0.708396i	−0.966397	−	0.257056i	$-0.917248\pi$
$137$	−14.3614	+	8.29156i	−1.22698	+	0.708396i	−0.260581	+	0.965452i	$0.583914\pi$
$138$	10.1168	+	2.37686i	0.861203	+	0.202332i
$139$	−7.50000	−	12.9904i	−0.636142	−	1.10183i	−0.986272	−	0.165129i	$-0.947196\pi$
$139$	−7.50000	−	12.9904i	−0.636142	−	1.10183i	0.350130	−	0.936701i	$-0.386137\pi$
$140$		−	13.2665i		−	1.12122i
$141$	−3.53553	−	11.7260i	−0.297746	−	0.987511i
$142$	4.00000	+	6.92820i	0.335673	+	0.581402i
$143$		0			0
$144$	−10.0000	+	6.63325i	−0.833333	+	0.552771i
$145$	10.0000			0.830455
$146$	−0.707107	−	1.22474i	−0.0585206	−	0.101361i
$147$	−25.2921	−	5.94215i	−2.08606	−	0.490100i
$148$	−8.12404	+	4.69042i	−0.667792	+	0.385550i
$149$	3.53553	−	6.12372i	0.289642	−	0.501675i	−0.684082	−	0.729405i	$-0.739797\pi$
$149$	3.53553	−	6.12372i	0.289642	−	0.501675i	0.973724	+	0.227730i	$0.0731303\pi$
$150$	−7.15369	−	1.68069i	−0.584096	−	0.137228i
$151$			4.69042i			0.381701i	0.981619	+	0.190850i	$0.0611245\pi$
$151$			4.69042i			0.381701i	−0.981619	+	0.190850i	$0.938875\pi$
$152$	−9.89949	−	7.34847i	−0.802955	−	0.596040i
$153$	11.0000	+	16.5831i	0.889297	+	1.34067i
$154$	−11.0000	+	19.0526i	−0.886405	+	1.53530i
$155$	5.74456	+	3.31662i	0.461414	+	0.266398i
$156$		0			0
$157$	16.2481	+	9.38083i	1.29674	+	0.748672i	0.979839	−	0.199788i	$-0.0640252\pi$
$157$	16.2481	+	9.38083i	1.29674	+	0.748672i	0.316898	+	0.948459i	$0.397359\pi$
$158$		0			0
$159$	−5.65685	−	18.7617i	−0.448618	−	1.48790i
$160$	−8.00000			−0.632456
$161$	17.2337	−	9.94987i	1.35820	−	0.784160i
$162$	−12.6299	+	1.57641i	−0.992300	+	0.123855i
$163$	15.0000			1.17489			0.587445	−	0.809264i	$-0.300134\pi$
$163$	15.0000			1.17489			0.587445	+	0.809264i	$0.300134\pi$
$164$		−	6.63325i		−	0.517970i
$165$	−5.92010	−	5.56349i	−0.460879	−	0.433117i
$166$	4.06202	+	2.34521i	0.315274	+	0.182023i
$167$	−4.24264	−	7.34847i	−0.328305	−	0.568642i	0.653870	−	0.756607i	$-0.273144\pi$
$167$	−4.24264	−	7.34847i	−0.328305	−	0.568642i	−0.982176	+	0.187965i	$0.939811\pi$
$168$	−5.25544	+	22.3692i	−0.405466	+	1.72582i
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$			13.2665i			1.01749i
$171$	−5.93070	−	11.6545i	−0.453532	−	0.891240i
$172$	12.0000			0.914991
$173$	1.41421	−	2.44949i	0.107521	−	0.186231i	−0.807245	−	0.590217i	$-0.799042\pi$
$173$	1.41421	−	2.44949i	0.107521	−	0.186231i	0.914765	+	0.403986i	$0.132375\pi$
$174$	−16.8614	−	3.96143i	−1.27826	−	0.300316i
$175$	−12.1861	+	7.03562i	−0.921179	+	0.531843i
$176$	11.4891	+	6.63325i	0.866025	+	0.500000i
$177$	−4.18614	−	3.93398i	−0.314650	−	0.295696i
$178$		−	9.38083i		−	0.703123i
$179$			9.94987i			0.743689i	0.928295	+	0.371844i	$0.121274\pi$
$179$			9.94987i			0.743689i	−0.928295	+	0.371844i	$0.878726\pi$
$180$	−7.59755	−	3.77852i	−0.566288	−	0.281634i
$181$	−20.3101	+	11.7260i	−1.50964	+	0.871590i	−0.509701	+	0.860352i	$0.670244\pi$
$181$	−20.3101	+	11.7260i	−1.50964	+	0.871590i	−0.999937	+	0.0112379i	$0.996423\pi$
$182$		0			0
$183$	7.77817	−	2.34521i	0.574979	−	0.173363i
$184$	−6.00000	−	10.3923i	−0.442326	−	0.766131i
$185$	−5.74456	−	3.31662i	−0.422349	−	0.243843i
$186$	−8.37228	−	7.86797i	−0.613885	−	0.576907i
$187$	11.0000	−	19.0526i	0.804400	−	1.39326i
$188$	−7.07107	+	12.2474i	−0.515711	+	0.893237i
$189$	−15.5563	+	18.7617i	−1.13156	+	1.36471i
$190$	1.00000	−	8.66025i	0.0725476	−	0.628281i
$191$	5.65685			0.409316			0.204658	−	0.978834i	$-0.434392\pi$
$191$	5.65685			0.409316			0.204658	+	0.978834i	$0.434392\pi$
$192$	13.4891	+	3.16915i	0.973494	+	0.228714i
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	−0.241257	−	0.970461i	$-0.577560\pi$
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	0.961073	−	0.276296i	$-0.0891071\pi$
$194$	10.6066	+	18.3712i	0.761510	+	1.31897i
$195$		0			0
$196$	15.0000	+	25.9808i	1.07143	+	1.85577i
$197$	12.7279			0.906827			0.453413	−	0.891300i	$-0.350206\pi$
$197$	12.7279			0.906827			0.453413	+	0.891300i	$0.350206\pi$
$198$	7.77817	+	11.7260i	0.552771	+	0.833333i
$199$	8.12404	−	4.69042i	0.575898	−	0.332495i	−0.183604	−	0.983000i	$-0.558776\pi$
$199$	8.12404	−	4.69042i	0.575898	−	0.332495i	0.759501	+	0.650506i	$0.225443\pi$
$200$	4.24264	+	7.34847i	0.300000	+	0.519615i
$201$	−2.50000	−	8.29156i	−0.176336	−	0.584842i
$202$	10.0000			0.703598
$203$	−28.7228	+	16.5831i	−2.01595	+	1.16391i
$204$	5.25544	−	22.3692i	0.367954	−	1.56616i
$205$	4.06202	−	2.34521i	0.283704	−	0.163796i
$206$	11.4891	+	6.63325i	0.800485	+	0.462160i
$207$	−0.789728	−	12.7034i	−0.0548899	−	0.882947i
$208$		0			0
$209$	−8.61684	+	11.6082i	−0.596040	+	0.802955i
$210$	−15.5563	+	4.69042i	−1.07349	+	0.323669i
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	0.447478	+	0.894295i	$0.352322\pi$
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−11.3137	+	19.5959i	−0.777029	+	1.34585i
$213$	6.70982	−	7.13991i	0.459750	−	0.489218i
$214$		0			0
$215$	4.24264	+	7.34847i	0.289346	+	0.501161i
$216$	11.3137	+	9.38083i	0.769800	+	0.638285i
$217$	−22.0000			−1.49346
$218$	11.4891	−	6.63325i	0.778142	−	0.449260i
$219$	−1.18614	+	1.26217i	−0.0801520	+	0.0852895i
$220$			9.38083i			0.632456i
$221$		0			0
$222$	8.37228	+	7.86797i	0.561911	+	0.528063i
$223$	12.1861	+	7.03562i	0.816039	+	0.471140i	0.849049	−	0.528315i	$-0.177176\pi$
$223$	12.1861	+	7.03562i	0.816039	+	0.471140i	−0.0330098	+	0.999455i	$0.510509\pi$
$224$	22.9783	−	13.2665i	1.53530	−	0.886405i
$225$	0.558422	+	8.98266i	0.0372281	+	0.598844i
$226$	20.3101	+	11.7260i	1.35101	+	0.780005i
$227$		−	16.5831i		−	1.10066i	−0.834947	−	0.550330i	$-0.814502\pi$
$227$		−	16.5831i		−	1.10066i	0.834947	−	0.550330i	$-0.185498\pi$
$228$	−5.11684	+	14.2063i	−0.338871	+	0.940833i
$229$			9.38083i			0.619903i	0.950752	+	0.309951i	$0.100313\pi$
$229$			9.38083i			0.619903i	−0.950752	+	0.309951i	$0.899687\pi$
$230$	4.24264	−	7.34847i	0.279751	−	0.484544i
$231$	26.2302	+	6.16255i	1.72582	+	0.405466i
$232$	10.0000	+	17.3205i	0.656532	+	1.13715i
$233$	−14.3614	−	8.29156i	−0.940847	−	0.543198i	−0.0506213	−	0.998718i	$-0.516120\pi$
$233$	−14.3614	−	8.29156i	−0.940847	−	0.543198i	−0.890226	+	0.455520i	$0.849453\pi$
$234$		0			0
$235$	−10.0000			−0.652328
$236$			6.63325i			0.431788i
$237$		0			0
$238$	−22.0000	−	38.1051i	−1.42605	−	2.46999i
$239$	−14.1421			−0.914779			−0.457389	−	0.889267i	$-0.651215\pi$
$239$	−14.1421			−0.914779			−0.457389	+	0.889267i	$0.651215\pi$
$240$	2.82843	+	9.38083i	0.182574	+	0.605530i
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	−0.916159	−	0.400815i	$-0.868727\pi$
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	0.110963	−	0.993825i	$-0.464606\pi$
$242$		0			0
$243$	6.31386	+	14.2525i	0.405034	+	0.914302i
$244$	−8.12404	−	4.69042i	−0.520088	−	0.300273i
$245$	−10.6066	+	18.3712i	−0.677631	+	1.17369i
$246$	−7.77817	+	2.34521i	−0.495918	+	0.149525i
$247$		0			0
$248$			13.2665i			0.842424i
$249$	1.31386	−	5.59230i	0.0832625	−	0.354397i
$250$	−8.00000	+	13.8564i	−0.505964	+	0.876356i
$251$	−14.3614	+	8.29156i	−0.906484	+	0.523359i	−0.879298	−	0.476272i	$-0.841988\pi$
$251$	−14.3614	+	8.29156i	−0.906484	+	0.523359i	−0.0271858	+	0.999630i	$0.508655\pi$
$252$	28.0883	−	1.74615i	1.76939	−	0.109997i
$253$	−12.1861	+	7.03562i	−0.766131	+	0.442326i
$254$		−	26.5330i		−	1.66483i
$255$	15.5563	−	4.69042i	0.974176	−	0.293725i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−8.61684	+	4.97494i	−0.537504	+	0.310328i	−0.744067	−	0.668105i	$-0.767106\pi$
$257$	−8.61684	+	4.97494i	−0.537504	+	0.310328i	0.206563	+	0.978433i	$0.433772\pi$
$258$	−4.24264	−	14.0712i	−0.264135	−	0.876038i
$259$	22.0000			1.36701
$260$		0			0
$261$	1.31621	+	21.1723i	0.0814716	+	1.31053i
$262$	−4.06202	+	2.34521i	−0.250952	+	0.144887i
$263$	−2.12132	+	3.67423i	−0.130806	+	0.226563i	−0.923988	−	0.382422i	$-0.875090\pi$
$263$	−2.12132	+	3.67423i	−0.130806	+	0.226563i	0.793181	+	0.608985i	$0.208423\pi$
$264$	3.71616	−	15.8174i	0.228714	−	0.973494i
$265$	−16.0000			−0.982872
$266$	11.4891	+	26.5330i	0.704443	+	1.62684i
$267$	−11.0000	+	3.31662i	−0.673189	+	0.202974i
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	−5.65685	+	9.79796i	−0.344904	+	0.597392i	−0.985336	−	0.170623i	$-0.945422\pi$
$269$	−5.65685	+	9.79796i	−0.344904	+	0.597392i	0.640432	+	0.768015i	$0.278755\pi$
$270$	−1.74456	+	10.2448i	−0.106171	+	0.623480i
$271$	20.3101	+	11.7260i	1.23375	+	0.712306i	0.967810	−	0.251683i	$-0.0809841\pi$
$271$	20.3101	+	11.7260i	1.23375	+	0.712306i	0.265941	+	0.963989i	$0.414317\pi$
$272$	−22.9783	+	13.2665i	−1.39326	+	0.804400i
$273$		0			0
$274$		−	23.4521i		−	1.41679i
$275$	8.61684	−	4.97494i	0.519615	−	0.300000i
$276$	−10.0647	+	10.7099i	−0.605826	+	0.644658i
$277$			23.4521i			1.40910i	0.709655	+	0.704549i	$0.248851\pi$
$277$			23.4521i			1.40910i	−0.709655	+	0.704549i	$0.751149\pi$
$278$	21.2132			1.27228
$279$	−6.26596	+	12.5991i	−0.375133	+	0.754289i
$280$	16.2481	+	9.38083i	0.971008	+	0.560612i
$281$	−2.87228	+	1.65831i	−0.171346	+	0.0989266i	−0.583220	−	0.812314i	$-0.698208\pi$
$281$	−2.87228	+	1.65831i	−0.171346	+	0.0989266i	0.411874	+	0.911241i	$0.364874\pi$
$282$	16.8614	+	3.96143i	1.00408	+	0.235900i
$283$	−12.5000	+	21.6506i	−0.743048	+	1.28700i	0.208053	+	0.978117i	$0.433287\pi$
$283$	−12.5000	+	21.6506i	−0.743048	+	1.28700i	−0.951101	+	0.308879i	$0.900046\pi$
$284$	−11.3137			−0.671345
$285$	−10.5086	+	1.88926i	−0.622476	+	0.111910i
$286$		0			0
$287$	−7.77817	+	13.4722i	−0.459131	+	0.795238i
$288$	−1.05297	−	16.9379i	−0.0620469	−	0.998073i
$289$	13.5000	+	23.3827i	0.794118	+	1.37545i
$290$	−7.07107	+	12.2474i	−0.415227	+	0.719195i
$291$	17.7921	−	18.9325i	1.04299	−	1.10984i
$292$	2.00000			0.117041
$293$	9.89949			0.578335			0.289167	−	0.957279i	$-0.406622\pi$
$293$	9.89949			0.578335			0.289167	+	0.957279i	$0.406622\pi$
$294$	25.1618	−	26.7746i	1.46747	−	1.56153i
$295$	−4.06202	+	2.34521i	−0.236500	+	0.136543i
$296$		−	13.2665i		−	0.771100i
$297$	11.0000	−	13.2665i	0.638285	−	0.769800i
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$		0			0
$300$	7.11684	−	7.57301i	0.410891	−	0.437228i
$301$	−24.3721	−	14.0712i	−1.40479	−	0.811053i
$302$	−5.74456	−	3.31662i	−0.330562	−	0.190850i
$303$	−3.53553	−	11.7260i	−0.203111	−	0.673643i
$304$	16.0000	−	6.92820i	0.917663	−	0.397360i
$305$		−	6.63325i		−	0.379819i
$306$	−28.0883	+	1.74615i	−1.60570	+	0.0998210i
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	−0.928506	−	0.371318i	$-0.878906\pi$
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	0.785823	+	0.618451i	$0.212239\pi$
$308$	−15.5563	−	26.9444i	−0.886405	−	1.53530i
$309$	3.71616	−	15.8174i	0.211405	−	0.899821i
$310$	−8.12404	+	4.69042i	−0.461414	+	0.266398i
$311$	−7.07107			−0.400963			−0.200482	−	0.979697i	$-0.564251\pi$
$311$	−7.07107			−0.400963			−0.200482	+	0.979697i	$0.564251\pi$
$312$		0			0
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$	−22.9783	+	13.2665i	−1.29674	+	0.748672i
$315$	11.0000	+	16.5831i	0.619780	+	0.934353i
$316$		0			0
$317$	−9.89949	−	17.1464i	−0.556011	−	0.963039i	−0.997824	−	0.0659322i	$-0.978998\pi$
$317$	−9.89949	−	17.1464i	−0.556011	−	0.963039i	0.441813	−	0.897107i	$-0.354335\pi$
$318$	26.9783	+	6.33830i	1.51287	+	0.355434i
$319$	20.3101	−	11.7260i	1.13715	−	0.656532i
$320$	5.65685	−	9.79796i	0.316228	−	0.547723i
$321$		0			0
$322$			28.1425i			1.56832i
$323$	−11.4891	−	26.5330i	−0.639272	−	1.47634i
$324$	7.00000	−	16.5831i	0.388889	−	0.921285i
$325$		0			0
$326$	−10.6066	+	18.3712i	−0.587445	+	1.01749i
$327$	−11.8402	−	11.1270i	−0.654764	−	0.615324i
$328$	8.12404	+	4.69042i	0.448575	+	0.258985i
$329$	28.7228	−	16.5831i	1.58354	−	0.914257i
$330$	11.0000	−	3.31662i	0.605530	−	0.182574i
$331$	−11.0000			−0.604615			−0.302307	−	0.953211i	$-0.597757\pi$
$331$	−11.0000			−0.604615			−0.302307	+	0.953211i	$0.597757\pi$
$332$	−5.74456	+	3.31662i	−0.315274	+	0.182023i
$333$	6.26596	−	12.5991i	0.343373	−	0.690427i
$334$	12.0000			0.656611
$335$	−7.07107			−0.386334
$336$	−23.6804	−	22.2540i	−1.29187	−	1.21405i
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	0.789865	+	0.613280i	$0.210150\pi$
$338$	−9.19239	−	15.9217i	−0.500000	−	0.866025i
$339$	6.56930	−	27.9615i	0.356795	−	1.51866i
$340$	−16.2481	−	9.38083i	−0.881176	−	0.508747i
$341$	15.5563			0.842424
$342$	18.4674	+	0.977359i	0.998602	+	0.0528495i
$343$		−	37.5233i		−	2.02607i
$344$	−8.48528	+	14.6969i	−0.457496	+	0.792406i
$345$	−10.1168	−	2.37686i	−0.544673	−	0.127966i
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	14.3614	+	8.29156i	0.770961	+	0.445114i	0.833217	−	0.552946i	$-0.186496\pi$
$347$	14.3614	+	8.29156i	0.770961	+	0.445114i	−0.0622565	+	0.998060i	$0.519830\pi$
$348$	16.7746	−	17.8498i	0.899211	−	0.956848i
$349$		−	9.38083i		−	0.502144i	−0.967968	−	0.251072i	$-0.919217\pi$
$349$		−	9.38083i		−	0.502144i	0.967968	−	0.251072i	$-0.0807832\pi$
$350$		−	19.8997i		−	1.06369i
$351$		0			0
$352$	−16.2481	+	9.38083i	−0.866025	+	0.500000i
$353$			16.5831i			0.882631i	0.897352	+	0.441315i	$0.145488\pi$
$353$			16.5831i			0.882631i	−0.897352	+	0.441315i	$0.854512\pi$
$354$	7.77817	−	2.34521i	0.413405	−	0.124646i
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$	11.4891	+	6.63325i	0.608922	+	0.351562i
$357$	−36.9040	+	39.2695i	−1.95317	+	2.07836i
$358$	−12.1861	−	7.03562i	−0.644053	−	0.371844i
$359$	12.0208	−	20.8207i	0.634434	−	1.09887i	−0.352200	−	0.935925i	$-0.614566\pi$
$359$	12.0208	−	20.8207i	0.634434	−	1.09887i	0.986635	−	0.162948i	$-0.0521003\pi$
$360$	10.0000	−	6.63325i	0.527046	−	0.349603i
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$		−	33.1662i		−	1.74318i
$363$		0			0
$364$		0			0
$365$	0.707107	+	1.22474i	0.0370117	+	0.0641061i
$366$	−2.62772	+	11.1846i	−0.137353	+	0.584628i
$367$	20.3101	−	11.7260i	1.06018	−	0.612094i	0.134697	−	0.990887i	$-0.456994\pi$
$367$	20.3101	−	11.7260i	1.06018	−	0.612094i	0.925482	+	0.378793i	$0.123661\pi$
$368$	16.9706			0.884652
$369$	5.50000	+	8.29156i	0.286319	+	0.431641i
$370$	8.12404	−	4.69042i	0.422349	−	0.243843i
$371$	45.9565	−	26.5330i	2.38594	−	1.37752i
$372$	15.5563	−	4.69042i	0.806559	−	0.243187i
$373$			9.38083i			0.485721i	0.970061	+	0.242861i	$0.0780857\pi$
$373$			9.38083i			0.485721i	−0.970061	+	0.242861i	$0.921914\pi$
$374$	15.5563	+	26.9444i	0.804400	+	1.39326i
$375$	19.0765	+	4.48185i	0.985106	+	0.231442i
$376$	−10.0000	−	17.3205i	−0.515711	−	0.893237i
$377$		0			0
$378$	−11.9783	−	32.3191i	−0.616095	−	1.66231i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	9.89949	+	7.34847i	0.507833	+	0.376969i
$381$	−31.1127	+	9.38083i	−1.59395	+	0.480595i
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	3.53553	−	6.12372i	0.180657	−	0.312908i	−0.761447	−	0.648227i	$-0.775511\pi$
$383$	3.53553	−	6.12372i	0.180657	−	0.312908i	0.942105	+	0.335319i	$0.108844\pi$
$384$	−13.4196	+	14.2798i	−0.684819	+	0.728714i
$385$	11.0000	−	19.0526i	0.560612	−	0.971008i
$386$	14.1421	+	24.4949i	0.719816	+	1.24676i
$387$	−15.0000	+	9.94987i	−0.762493	+	0.505781i
$388$	−30.0000			−1.52302
$389$	1.41421	+	2.44949i	0.0717035	+	0.124194i	0.899648	−	0.436616i	$-0.143823\pi$
$389$	1.41421	+	2.44949i	0.0717035	+	0.124194i	−0.827945	+	0.560810i	$0.810490\pi$
$390$		0			0
$391$		−	28.1425i		−	1.42323i
$392$	−42.4264			−2.14286
$393$	4.18614	+	3.93398i	0.211163	+	0.198443i
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$		0			0
$396$	−19.8614	+	1.23472i	−0.998073	+	0.0620469i
$397$	4.06202	+	2.34521i	0.203867	+	0.117703i	0.598458	−	0.801154i	$-0.295780\pi$
$397$	4.06202	+	2.34521i	0.203867	+	0.117703i	−0.394591	+	0.918857i	$0.629114\pi$
$398$			13.2665i			0.664990i
$399$	27.0507	−	22.8530i	1.35423	−	1.14408i
$400$	−12.0000			−0.600000
$401$	14.3614	+	8.29156i	0.717174	+	0.414061i	0.813712	−	0.581269i	$-0.197443\pi$
$401$	14.3614	+	8.29156i	0.717174	+	0.414061i	−0.0965374	+	0.995329i	$0.530777\pi$
$402$	11.9228	+	2.80116i	0.594656	+	0.139709i
$403$		0			0
$404$	−7.07107	+	12.2474i	−0.351799	+	0.609333i
$405$	12.6299	−	1.57641i	0.627586	−	0.0783326i
$406$		−	46.9042i		−	2.32781i
$407$	−15.5563			−0.771100
$408$	23.6804	+	22.2540i	1.17235	+	1.10174i
$409$	13.5000	+	23.3827i	0.667532	+	1.15620i	0.978592	+	0.205809i	$0.0659826\pi$
$409$	13.5000	+	23.3827i	0.667532	+	1.15620i	−0.311060	+	0.950390i	$0.600684\pi$
$410$			6.63325i			0.327593i
$411$	−27.5000	+	8.29156i	−1.35647	+	0.408993i
$412$	−16.2481	+	9.38083i	−0.800485	+	0.462160i
$413$	7.77817	−	13.4722i	0.382739	−	0.662923i
$414$	16.1168	+	8.01544i	0.792100	+	0.393938i
$415$	−4.06202	−	2.34521i	−0.199397	−	0.115122i
$416$		0			0
$417$	−7.50000	−	24.8747i	−0.367277	−	1.21812i
$418$	−8.12404	−	18.7617i	−0.397360	−	0.917663i
$419$			26.5330i			1.29622i	0.761546	+	0.648111i	$0.224441\pi$
$419$			26.5330i			1.29622i	−0.761546	+	0.648111i	$0.775559\pi$
$420$	5.25544	−	22.3692i	0.256439	−	1.09150i
$421$	−20.3101	−	11.7260i	−0.989854	−	0.571492i	−0.0846230	−	0.996413i	$-0.526969\pi$
$421$	−20.3101	−	11.7260i	−0.989854	−	0.571492i	−0.905231	+	0.424921i	$0.860302\pi$
$422$	−11.3137	−	19.5959i	−0.550743	−	0.953914i
$423$	−1.31621	−	21.1723i	−0.0639965	−	1.02943i
$424$	−16.0000	−	27.7128i	−0.777029	−	1.34585i
$425$			19.8997i			0.965280i
$426$	4.00000	+	13.2665i	0.193801	+	0.642764i
$427$	11.0000	+	19.0526i	0.532327	+	0.922018i
$428$		0			0
$429$		0			0
$430$	−12.0000			−0.578691
$431$	7.07107	+	12.2474i	0.340601	+	0.589939i	0.984545	−	0.175134i	$-0.0560360\pi$
$431$	7.07107	+	12.2474i	0.340601	+	0.589939i	−0.643943	+	0.765073i	$0.722703\pi$
$432$	−19.4891	+	7.22316i	−0.937671	+	0.347524i
$433$	10.0000	+	17.3205i	0.480569	+	0.832370i	0.999751	−	0.0222931i	$-0.00709671\pi$
$433$	10.0000	+	17.3205i	0.480569	+	0.832370i	−0.519182	+	0.854664i	$0.673763\pi$
$434$	15.5563	−	26.9444i	0.746729	−	1.29337i
$435$	16.8614	+	3.96143i	0.808443	+	0.189936i
$436$			18.7617i			0.898521i
$437$	−2.12132	+	18.3712i	−0.101477	+	0.878812i
$438$	−0.707107	−	2.34521i	−0.0337869	−	0.112058i
$439$	−20.3101	−	11.7260i	−0.969348	−	0.559653i	−0.0703106	−	0.997525i	$-0.522399\pi$
$439$	−20.3101	−	11.7260i	−0.969348	−	0.559653i	−0.899037	+	0.437872i	$0.855732\pi$
$440$	−11.4891	−	6.63325i	−0.547723	−	0.316228i
$441$	−40.2921	−	20.0386i	−1.91867	−	0.954220i
$442$		0			0
$443$	−2.87228	+	1.65831i	−0.136466	+	0.0787888i	−0.566679	−	0.823939i	$-0.691772\pi$
$443$	−2.87228	+	1.65831i	−0.136466	+	0.0787888i	0.430213	+	0.902728i	$0.358439\pi$
$444$	−15.5563	+	4.69042i	−0.738272	+	0.222597i
$445$			9.38083i			0.444694i
$446$	−17.2337	+	9.94987i	−0.816039	+	0.471140i
$447$	8.38728	−	8.92488i	0.396705	−	0.422132i
$448$			37.5233i			1.77281i
$449$			9.94987i			0.469564i	0.972048	+	0.234782i	$0.0754376\pi$
$449$			9.94987i			0.469564i	−0.972048	+	0.234782i	$0.924562\pi$
$450$	−11.3963	−	5.66777i	−0.537228	−	0.267181i
$451$	5.50000	−	9.52628i	0.258985	−	0.448575i
$452$	−28.7228	+	16.5831i	−1.35101	+	0.780005i
$453$	−1.85808	+	7.90870i	−0.0873001	+	0.371583i
$454$	20.3101	+	11.7260i	0.953200	+	0.550330i
$455$		0			0
$456$	−13.7809	−	16.3122i	−0.645349	−	0.763888i
$457$	25.0000			1.16945			0.584725	−	0.811231i	$-0.301202\pi$
$457$	25.0000			1.16945			0.584725	+	0.811231i	$0.301202\pi$
$458$	−11.4891	−	6.63325i	−0.536852	−	0.309951i
$459$	11.9783	+	32.3191i	0.559097	+	1.50852i
$460$	6.00000	+	10.3923i	0.279751	+	0.484544i
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$	−26.0951	+	27.7677i	−1.21405	+	1.29187i
$463$			9.38083i			0.435964i	0.975953	+	0.217982i	$0.0699474\pi$
$463$			9.38083i			0.435964i	−0.975953	+	0.217982i	$0.930053\pi$
$464$	−28.2843			−1.31306
$465$	8.37228	+	7.86797i	0.388255	+	0.364868i
$466$	20.3101	−	11.7260i	0.940847	−	0.543198i
$467$		−	16.5831i		−	0.767375i	−0.923463	−	0.383688i	$-0.874654\pi$
$467$		−	16.5831i		−	0.767375i	0.923463	−	0.383688i	$-0.125346\pi$
$468$		0			0
$469$	20.3101	−	11.7260i	0.937833	−	0.541458i
$470$	7.07107	−	12.2474i	0.326164	−	0.564933i
$471$	23.6804	+	22.2540i	1.09113	+	1.02541i
$472$	−8.12404	−	4.69042i	−0.373939	−	0.215894i
$473$	17.2337	+	9.94987i	0.792406	+	0.457496i
$474$		0			0
$475$	1.50000	−	12.9904i	0.0688247	−	0.596040i
$476$	62.2254			2.85210
$477$	−2.10594	−	33.8757i	−0.0964244	−	1.55106i
$478$	10.0000	−	17.3205i	0.457389	−	0.792222i
$479$	19.7990	+	34.2929i	0.904639	+	1.56688i	0.821401	+	0.570351i	$0.193193\pi$
$479$	19.7990	+	34.2929i	0.904639	+	1.56688i	0.0832378	+	0.996530i	$0.473474\pi$
$480$	−13.4891	−	3.16915i	−0.615692	−	0.144651i
$481$		0			0
$482$	35.3553			1.61039
$483$	33.0000	−	9.94987i	1.50155	−	0.452735i
$484$		0			0
$485$	−10.6066	−	18.3712i	−0.481621	−	0.834192i
$486$	−21.9203	−	2.34521i	−0.994325	−	0.106381i
$487$			4.69042i			0.212543i	0.994337	+	0.106272i	$0.0338913\pi$
$487$			4.69042i			0.212543i	−0.994337	+	0.106272i	$0.966109\pi$
$488$	11.4891	−	6.63325i	0.520088	−	0.300273i
$489$	25.2921	+	5.94215i	1.14375	+	0.268713i
$490$	−15.0000	−	25.9808i	−0.677631	−	1.17369i
$491$	−11.4891	−	6.63325i	−0.518497	−	0.299354i	0.217823	−	0.975988i	$-0.430105\pi$
$491$	−11.4891	−	6.63325i	−0.518497	−	0.299354i	−0.736319	+	0.676634i	$0.763438\pi$
$492$	2.62772	−	11.1846i	0.118467	−	0.504240i
$493$			46.9042i			2.11246i
$494$		0			0
$495$	−7.77817	−	11.7260i	−0.349603	−	0.527046i
$496$	−16.2481	−	9.38083i	−0.729560	−	0.421212i
$497$	22.9783	+	13.2665i	1.03072	+	0.595084i
$498$	5.92010	+	5.56349i	0.265286	+	0.249306i
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	−0.683062	−	0.730361i	$-0.739352\pi$
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	0.974042	+	0.226369i	$0.0726854\pi$
$500$	−11.3137	−	19.5959i	−0.505964	−	0.876356i
$501$	−4.24264	−	14.0712i	−0.189547	−	0.628657i
$502$		−	23.4521i		−	1.04672i
$503$	16.2635	+	28.1691i	0.725152	+	1.25600i	0.958912	+	0.283705i	$0.0915637\pi$
$503$	16.2635	+	28.1691i	0.725152	+	1.25600i	−0.233760	+	0.972294i	$0.575103\pi$
$504$	−17.7228	+	35.6357i	−0.789437	+	1.58734i
$505$	−10.0000			−0.444994
$506$		−	19.8997i		−	0.884652i
$507$	−15.4198	+	16.4082i	−0.684819	+	0.728714i
$508$	32.4962	+	18.7617i	1.44178	+	0.832414i
$509$	8.48528	+	14.6969i	0.376103	+	0.651430i	0.990492	−	0.137574i	$-0.0439304\pi$
$509$	8.48528	+	14.6969i	0.376103	+	0.651430i	−0.614388	+	0.789004i	$0.710597\pi$
$510$	−5.25544	+	22.3692i	−0.232715	+	0.990524i
$511$	−4.06202	−	2.34521i	−0.179693	−	0.103746i
$512$	22.6274			1.00000
$513$	−5.38316	−	22.0005i	−0.237672	−	0.971345i
$514$		−	14.0712i		−	0.620656i
$515$	−11.4891	−	6.63325i	−0.506271	−	0.292296i
$516$	20.2337	+	4.75372i	0.890738	+	0.209271i
$517$	−20.3101	+	11.7260i	−0.893237	+	0.515711i
$518$	−15.5563	+	26.9444i	−0.683507	+	1.18387i
$519$	3.35491	−	3.56995i	0.147264	−	0.156704i
$520$		0			0
$521$		−	16.5831i		−	0.726520i	−0.931688	−	0.363260i	$-0.881664\pi$
$521$		−	16.5831i		−	0.726520i	0.931688	−	0.363260i	$-0.118336\pi$
$522$	−26.8614	−	13.3591i	−1.17569	−	0.584711i
$523$	5.00000	+	8.66025i	0.218635	+	0.378686i	0.954391	−	0.298560i	$-0.0965063\pi$
$523$	5.00000	+	8.66025i	0.218635	+	0.378686i	−0.735756	+	0.677247i	$0.763173\pi$
$524$		−	6.63325i		−	0.289775i
$525$	−23.3345	+	7.03562i	−1.01840	+	0.307060i
$526$	−3.00000	−	5.19615i	−0.130806	−	0.226563i
$527$	−15.5563	+	26.9444i	−0.677645	+	1.17372i
$528$	16.7446	+	15.7359i	0.728714	+	0.684819i
$529$	2.50000	−	4.33013i	0.108696	−	0.188266i
$530$	11.3137	−	19.5959i	0.491436	−	0.851192i
$531$	−5.50000	−	8.29156i	−0.238680	−	0.359823i
$532$	−40.6202	−	4.69042i	−1.76111	−	0.203355i
$533$		0			0
$534$	3.71616	−	15.8174i	0.160814	−	0.684486i
$535$		0			0
$536$	−7.07107	−	12.2474i	−0.305424	−	0.529009i
$537$	−3.94158	+	16.7769i	−0.170092	+	0.723976i
$538$	−8.00000	−	13.8564i	−0.344904	−	0.597392i
$539$			49.7494i			2.14286i
$540$	−11.3137	−	9.38083i	−0.486864	−	0.403687i
$541$	16.2481	−	9.38083i	0.698559	−	0.403313i	−0.108251	−	0.994124i	$-0.534525\pi$
$541$	16.2481	−	9.38083i	0.698559	−	0.403313i	0.806811	+	0.590810i	$0.201192\pi$
$542$	−28.7228	+	16.5831i	−1.23375	+	0.712306i
$543$	−38.8909	+	11.7260i	−1.66897	+	0.503213i
$544$		−	37.5233i		−	1.60880i
$545$	−11.4891	+	6.63325i	−0.492140	+	0.284137i
$546$		0			0
$547$	5.00000	+	8.66025i	0.213785	+	0.370286i	0.952896	−	0.303298i	$-0.0980876\pi$
$547$	5.00000	+	8.66025i	0.213785	+	0.370286i	−0.739111	+	0.673583i	$0.764754\pi$
$548$	28.7228	+	16.5831i	1.22698	+	0.708396i
$549$	14.0441	−	0.873077i	0.599389	−	0.0372620i
$550$			14.0712i			0.600000i
$551$	3.53553	−	30.6186i	0.150619	−	1.30440i
$552$	−6.00000	−	19.8997i	−0.255377	−	0.846990i
$553$		0			0
$554$	−28.7228	−	16.5831i	−1.22032	−	0.704549i
$555$	−8.37228	−	7.86797i	−0.355384	−	0.333977i
$556$	−15.0000	+	25.9808i	−0.636142	+	1.10183i
$557$	−18.3848	−	31.8434i	−0.778988	−	1.34925i	−0.932526	−	0.361104i	$-0.882400\pi$
$557$	−18.3848	−	31.8434i	−0.778988	−	1.34925i	0.153538	−	0.988143i	$-0.450933\pi$
$558$	−11.0000	−	16.5831i	−0.465667	−	0.702020i
$559$		0			0
$560$	−22.9783	+	13.2665i	−0.971008	+	0.560612i
$561$	26.0951	−	27.7677i	1.10174	−	1.17235i
$562$		−	4.69042i		−	0.197853i
$563$		−	16.5831i		−	0.698895i	−0.936956	−	0.349448i	$-0.886369\pi$
$563$		−	16.5831i		−	0.698895i	0.936956	−	0.349448i	$-0.113631\pi$
$564$	−16.7746	+	17.8498i	−0.706336	+	0.751611i
$565$	−20.3101	−	11.7260i	−0.854452	−	0.493318i
$566$	−17.6777	−	30.6186i	−0.743048	−	1.28700i
$567$	−33.6625	+	25.4723i	−1.41369	+	1.06973i
$568$	8.00000	−	13.8564i	0.335673	−	0.581402i
$569$		−	6.63325i		−	0.278080i	−0.990287	−	0.139040i	$-0.955598\pi$
$569$		−	6.63325i		−	0.278080i	0.990287	−	0.139040i	$-0.0444017\pi$
$570$	5.11684	−	14.2063i	0.214321	−	0.595035i
$571$	25.0000			1.04622			0.523109	−	0.852266i	$-0.324772\pi$
$571$	25.0000			1.04622			0.523109	+	0.852266i	$0.324772\pi$
$572$		0			0
$573$	9.53825	+	2.24093i	0.398466	+	0.0936160i
$574$	−11.0000	−	19.0526i	−0.459131	−	0.795238i
$575$	6.36396	−	11.0227i	0.265396	−	0.459679i
$576$	21.4891	+	10.6873i	0.895380	+	0.445302i
$577$	−15.0000			−0.624458			−0.312229	−	0.950007i	$-0.601076\pi$
$577$	−15.0000			−0.624458			−0.312229	+	0.950007i	$0.601076\pi$
$578$	−38.1838			−1.58824
$579$	23.7228	−	25.2434i	0.985886	−	1.04908i
$580$	−10.0000	−	17.3205i	−0.415227	−	0.719195i
$581$	15.5563			0.645386
$582$	10.6066	+	35.1781i	0.439658	+	1.45818i
$583$	−32.4962	+	18.7617i	−1.34585	+	0.777029i
$584$	−1.41421	+	2.44949i	−0.0585206	+	0.101361i
$585$		0			0
$586$	−7.00000	+	12.1244i	−0.289167	+	0.500853i
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	15.0000	+	49.7494i	0.618590	+	2.05163i
$589$	12.1861	−	16.4165i	0.502118	−	0.676428i
$590$		−	6.63325i		−	0.273087i
$591$	21.4611	+	5.04208i	0.882790	+	0.207404i
$592$	16.2481	+	9.38083i	0.667792	+	0.385550i
$593$	14.3614	−	8.29156i	0.589752	−	0.340494i	−0.175247	−	0.984524i	$-0.556072\pi$
$593$	14.3614	−	8.29156i	0.589752	−	0.340494i	0.765000	+	0.644031i	$0.222739\pi$
$594$	8.46990	+	22.8530i	0.347524	+	0.937671i
$595$	22.0000	+	38.1051i	0.901912	+	1.56216i
$596$	−14.1421			−0.579284
$597$	15.5563	−	4.69042i	0.636679	−	0.191966i
$598$		0			0
$599$	−2.12132	−	3.67423i	−0.0866748	−	0.150125i	0.819429	−	0.573181i	$-0.194291\pi$
$599$	−2.12132	−	3.67423i	−0.0866748	−	0.150125i	−0.906104	+	0.423056i	$0.860957\pi$
$600$	4.24264	+	14.0712i	0.173205	+	0.574456i
$601$	1.00000			0.0407909			0.0203954	−	0.999792i	$-0.493507\pi$
$601$	1.00000			0.0407909			0.0203954	+	0.999792i	$0.493507\pi$
$602$	34.4674	−	19.8997i	1.40479	−	0.811053i
$603$	−0.930703	−	14.9711i	−0.0379012	−	0.609670i
$604$	8.12404	−	4.69042i	0.330562	−	0.190850i
$605$		0			0
$606$	16.8614	+	3.96143i	0.684948	+	0.160922i
$607$			4.69042i			0.190378i	0.995459	+	0.0951891i	$0.0303456\pi$
$607$			4.69042i			0.190378i	−0.995459	+	0.0951891i	$0.969654\pi$
$608$	−2.82843	+	24.4949i	−0.114708	+	0.993399i
$609$	−55.0000	+	16.5831i	−2.22871	+	0.671982i
$610$	8.12404	+	4.69042i	0.328933	+	0.189909i
$611$		0			0
$612$	17.7228	−	35.6357i	0.716402	−	1.44049i
$613$	32.4962	+	18.7617i	1.31251	+	0.757776i	0.982511	−	0.186206i	$-0.0596191\pi$
$613$	32.4962	+	18.7617i	1.31251	+	0.757776i	0.329997	+	0.943982i	$0.392952\pi$
$614$	−3.53553	−	6.12372i	−0.142683	−	0.247133i
$615$	7.77817	−	2.34521i	0.313646	−	0.0945679i
$616$	44.0000			1.77281
$617$	8.61684	−	4.97494i	0.346901	−	0.200283i	−0.316418	−	0.948620i	$-0.602480\pi$
$617$	8.61684	−	4.97494i	0.346901	−	0.200283i	0.663320	+	0.748336i	$0.269147\pi$
$618$	16.7446	+	15.7359i	0.673565	+	0.632992i
$619$	−38.0000			−1.52735			−0.763674	−	0.645601i	$-0.776607\pi$
$619$	−38.0000			−1.52735			−0.763674	+	0.645601i	$0.776607\pi$
$620$		−	13.2665i		−	0.532795i
$621$	3.70078	−	21.7326i	0.148507	−	0.872098i
$622$	5.00000	−	8.66025i	0.200482	−	0.347245i
$623$	−15.5563	−	26.9444i	−0.623252	−	1.07950i
$624$		0			0
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	15.5563			0.621757
$627$	−19.1277	+	16.1595i	−0.763888	+	0.645349i
$628$		−	37.5233i		−	1.49734i
$629$	15.5563	−	26.9444i	0.620272	−	1.07434i
$630$	−28.0883	+	1.74615i	−1.11906	+	0.0695684i
$631$	4.06202	−	2.34521i	0.161706	−	0.0933613i	−0.416963	−	0.908923i	$-0.636906\pi$
$631$	4.06202	−	2.34521i	0.161706	−	0.0933613i	0.578669	+	0.815562i	$0.303572\pi$
$632$		0			0
$633$	−18.9783	+	20.1947i	−0.754318	+	0.802667i
$634$	28.0000			1.11202
$635$			26.5330i			1.05293i
$636$	−26.8393	+	28.5596i	−1.06425	+	1.13246i
$637$		0			0
$638$			33.1662i			1.31306i
$639$	14.1421	−	9.38083i	0.559454	−	0.371100i
$640$	8.00000	+	13.8564i	0.316228	+	0.547723i
$641$	−43.0842	−	24.8747i	−1.70172	−	0.982491i	−0.944017	−	0.329896i	$-0.892986\pi$
$641$	−43.0842	−	24.8747i	−1.70172	−	0.982491i	−0.757707	−	0.652595i	$-0.773680\pi$
$642$		0			0
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	0.424555	+	0.905402i	$0.360431\pi$
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	−0.996379	+	0.0850262i	$0.972903\pi$
$644$	−34.4674	−	19.8997i	−1.35820	−	0.784160i
$645$	4.24264	+	14.0712i	0.167054	+	0.554055i
$646$	40.6202	+	4.69042i	1.59818	+	0.184542i
$647$	−8.48528			−0.333591			−0.166795	−	0.985992i	$-0.553342\pi$
$647$	−8.48528			−0.333591			−0.166795	+	0.985992i	$0.553342\pi$
$648$	15.3603	+	20.2993i	0.603411	+	0.797430i
$649$	−5.50000	+	9.52628i	−0.215894	+	0.373939i
$650$		0			0
$651$	−37.0951	−	8.71516i	−1.45387	−	0.341574i
$652$	−15.0000	−	25.9808i	−0.587445	−	1.01749i
$653$	−2.82843			−0.110685			−0.0553425	−	0.998467i	$-0.517625\pi$
$653$	−2.82843			−0.110685			−0.0553425	+	0.998467i	$0.517625\pi$
$654$	22.0000	−	6.63325i	0.860268	−	0.259381i
$655$	4.06202	−	2.34521i	0.158716	−	0.0916349i
$656$	−11.4891	+	6.63325i	−0.448575	+	0.258985i
$657$	−2.50000	+	1.65831i	−0.0975343	+	0.0646969i
$658$			46.9042i			1.82851i
$659$	22.9783	−	13.2665i	0.895106	−	0.516789i	0.0194965	−	0.999810i	$-0.493794\pi$
$659$	22.9783	−	13.2665i	0.895106	−	0.516789i	0.875609	+	0.483020i	$0.160460\pi$
$660$	−3.71616	+	15.8174i	−0.144651	+	0.615692i
$661$	−36.5582	+	21.1069i	−1.42195	+	0.820962i	−0.996465	−	0.0840044i	$-0.973229\pi$
$661$	−36.5582	+	21.1069i	−1.42195	+	0.820962i	−0.425483	+	0.904967i	$0.639896\pi$
$662$	7.77817	−	13.4722i	0.302307	−	0.523612i
$663$		0			0
$664$		−	9.38083i		−	0.364047i
$665$	−11.4891	−	26.5330i	−0.445529	−	1.02891i
$666$	11.0000	+	16.5831i	0.426241	+	0.642583i
$667$	15.0000	−	25.9808i	0.580802	−	1.00598i
$668$	−8.48528	+	14.6969i	−0.328305	+	0.568642i
$669$	17.7603	+	16.6905i	0.686653	+	0.645291i
$670$	5.00000	−	8.66025i	0.193167	−	0.334575i
$671$	−7.77817	−	13.4722i	−0.300273	−	0.520088i
$672$	44.0000	−	13.2665i	1.69734	−	0.511766i
$673$	20.0000			0.770943			0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000			0.770943			0.385472	+	0.922720i	$0.374039\pi$
$674$	−3.53553	−	6.12372i	−0.136184	−	0.235877i
$675$	−2.61684	+	15.3672i	−0.100722	+	0.591485i
$676$	26.0000			1.00000
$677$	−19.7990			−0.760937			−0.380468	−	0.924794i	$-0.624237\pi$
$677$	−19.7990			−0.760937			−0.380468	+	0.924794i	$0.624237\pi$
$678$	29.6005	+	27.8175i	1.13680	+	1.06832i
$679$	60.9303	+	35.1781i	2.33829	+	1.35001i
$680$	22.9783	−	13.2665i	0.881176	−	0.508747i
$681$	6.56930	−	27.9615i	0.251736	−	1.07149i
$682$	−11.0000	+	19.0526i	−0.421212	+	0.729560i
$683$		−	13.2665i		−	0.507628i	−0.967253	−	0.253814i	$-0.918315\pi$
$683$		−	13.2665i		−	0.507628i	0.967253	−	0.253814i	$-0.0816852\pi$
$684$	−14.2554	+	21.9268i	−0.545070	+	0.838390i
$685$			23.4521i			0.896058i
$686$	45.9565	+	26.5330i	1.75463	+	1.01303i
$687$	−3.71616	+	15.8174i	−0.141780	+	0.603472i
$688$	−12.0000	−	20.7846i	−0.457496	−	0.792406i
$689$		0			0
$690$	10.0647	−	10.7099i	0.383158	−	0.407717i
$691$	14.0000			0.532585			0.266293	−	0.963892i	$-0.414201\pi$
$691$	14.0000			0.532585			0.266293	+	0.963892i	$0.414201\pi$
$692$	−5.65685			−0.215041
$693$	41.7865	+	20.7818i	1.58734	+	0.789437i
$694$	−20.3101	+	11.7260i	−0.770961	+	0.445114i
$695$	−21.2132			−0.804663
$696$	10.0000	+	33.1662i	0.379049	+	1.25716i
$697$	11.0000	+	19.0526i	0.416655	+	0.721667i
$698$	11.4891	+	6.63325i	0.434870	+	0.251072i
$699$	−20.9307	−	19.6699i	−0.791672	−	0.743985i
$700$	24.3721	+	14.0712i	0.921179	+	0.531843i
$701$	0.707107	−	1.22474i	0.0267071	−	0.0462580i	−0.852363	−	0.522951i	$-0.824831\pi$
$701$	0.707107	−	1.22474i	0.0267071	−	0.0462580i	0.879070	+	0.476693i	$0.158165\pi$
$702$		0			0
$703$	−12.1861	+	16.4165i	−0.459606	+	0.619158i
$704$		−	26.5330i		−	1.00000i
$705$	−16.8614	−	3.96143i	−0.635037	−	0.149196i
$706$	−20.3101	−	11.7260i	−0.764381	−	0.441315i
$707$	28.7228	−	16.5831i	1.08023	−	0.623673i
$708$	−2.62772	+	11.1846i	−0.0987557	+	0.420343i
$709$	28.4341	−	16.4165i	1.06787	−	0.616533i	0.140269	−	0.990113i	$-0.455203\pi$
$709$	28.4341	−	16.4165i	1.06787	−	0.616533i	0.927598	+	0.373581i	$0.121870\pi$
$710$	11.3137			0.424596
$711$		0			0
$712$	−16.2481	+	9.38083i	−0.608922	+	0.351562i
$713$	17.2337	−	9.94987i	0.645407	−	0.372626i
$714$	−22.0000	−	72.9657i	−0.823329	−	2.73067i
$715$		0			0
$716$	17.2337	−	9.94987i	0.644053	−	0.371844i
$717$	−23.8456	−	5.60232i	−0.890531	−	0.209222i
$718$	17.0000	+	29.4449i	0.634434	+	1.09887i
$719$	19.7990	−	34.2929i	0.738378	−	1.27891i	−0.214848	−	0.976648i	$-0.568926\pi$
$719$	19.7990	−	34.2929i	0.738378	−	1.27891i	0.953225	−	0.302260i	$-0.0977411\pi$
$720$	1.05297	+	16.9379i	0.0392419	+	0.631237i
$721$	44.0000			1.63865
$722$	−26.1630	−	6.12372i	−0.973684	−	0.227901i
$723$	−12.5000	−	41.4578i	−0.464880	−	1.54183i
$724$	40.6202	+	23.4521i	1.50964	+	0.871590i
$725$	−10.6066	+	18.3712i	−0.393919	+	0.682288i
$726$		0			0
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$	−2.00000			−0.0740233
$731$	−34.4674	+	19.8997i	−1.27482	+	0.736019i
$732$	−11.8402	−	11.1270i	−0.437626	−	0.411265i
$733$		−	32.8329i		−	1.21271i	−0.795194	−	0.606356i	$-0.792631\pi$
$733$		−	32.8329i		−	1.21271i	0.795194	−	0.606356i	$-0.207369\pi$
$734$			33.1662i			1.22419i
$735$	−25.1618	+	26.7746i	−0.928109	+	0.987598i
$736$	−12.0000	+	20.7846i	−0.442326	+	0.766131i
$737$	−14.3614	+	8.29156i	−0.529009	+	0.305424i
$738$	−14.0441	+	0.873077i	−0.516972	+	0.0321384i
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	−0.794443	−	0.607339i	$-0.792237\pi$
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	0.923192	+	0.384338i	$0.125570\pi$
$740$			13.2665i			0.487686i
$741$		0			0
$742$			75.0467i			2.75505i
$743$	−12.0208	+	20.8207i	−0.441001	+	0.763836i	−0.997764	−	0.0668353i	$-0.978710\pi$
$743$	−12.0208	+	20.8207i	−0.441001	+	0.763836i	0.556763	+	0.830671i	$0.312043\pi$
$744$	−5.25544	+	22.3692i	−0.192674	+	0.820094i
$745$	−5.00000	−	8.66025i	−0.183186	−	0.317287i
$746$	−11.4891	−	6.63325i	−0.420647	−	0.242861i
$747$	4.43070	−	8.90892i	0.162111	−	0.325960i
$748$	−44.0000			−1.60880
$749$		0			0
$750$	−18.9783	+	20.1947i	−0.692988	+	0.737406i
$751$	−24.3721	+	14.0712i	−0.889351	+	0.513467i	−0.873730	−	0.486411i	$-0.838306\pi$
$751$	−24.3721	+	14.0712i	−0.889351	+	0.513467i	−0.0156209	+	0.999878i	$0.504972\pi$
$752$	28.2843			1.03142
$753$	−27.5000	+	8.29156i	−1.00216	+	0.302161i
$754$		0			0
$755$	5.74456	+	3.31662i	0.209066	+	0.120704i
$756$	48.0525	+	8.18272i	1.74765	+	0.297603i
$757$	16.2481	+	9.38083i	0.590546	+	0.340952i	0.765314	−	0.643658i	$-0.222584\pi$
$757$	16.2481	+	9.38083i	0.590546	+	0.340952i	−0.174767	+	0.984610i	$0.555917\pi$
$758$		0			0
$759$	−23.3345	+	7.03562i	−0.846990	+	0.255377i
$760$	−16.0000	+	6.92820i	−0.580381	+	0.251312i
$761$		−	3.31662i		−	0.120228i	−0.998192	−	0.0601138i	$-0.980854\pi$
$761$		−	3.31662i		−	0.120228i	0.998192	−	0.0601138i	$-0.0191464\pi$
$762$	10.5109	−	44.7384i	0.380769	−	1.62070i
$763$	22.0000	−	38.1051i	0.796453	−	1.37950i
$764$	−5.65685	−	9.79796i	−0.204658	−	0.354478i
$765$	28.0883	−	1.74615i	1.01553	−	0.0631323i
$766$	5.00000	+	8.66025i	0.180657	+	0.312908i
$767$		0			0
$768$	−8.00000	−	26.5330i	−0.288675	−	0.957427i
$769$	12.0000	+	20.7846i	0.432731	+	0.749512i	0.997107	−	0.0760054i	$-0.0242166\pi$
$769$	12.0000	+	20.7846i	0.432731	+	0.749512i	−0.564376	+	0.825518i	$0.690883\pi$
$770$	15.5563	+	26.9444i	0.560612	+	0.971008i
$771$	−16.5000	+	4.97494i	−0.594233	+	0.179168i
$772$	−40.0000			−1.43963
$773$	12.0208	+	20.8207i	0.432359	+	0.748867i	0.997076	−	0.0764173i	$-0.0243481\pi$
$773$	12.0208	+	20.8207i	0.432359	+	0.748867i	−0.564717	+	0.825284i	$0.691015\pi$
$774$	−1.57946	−	25.4068i	−0.0567724	−	0.913228i
$775$	−12.1861	+	7.03562i	−0.437736	+	0.252727i
$776$	21.2132	−	36.7423i	0.761510	−	1.31897i
$777$	37.0951	+	8.71516i	1.33078	+	0.312655i
$778$	−4.00000			−0.143407
$779$	−5.74456	−	13.2665i	−0.205820	−	0.475322i
$780$		0			0
$781$	−16.2481	−	9.38083i	−0.581402	−	0.335673i
$782$	34.4674	+	19.8997i	1.23255	+	0.711614i
$783$	−6.16796	+	36.2209i	−0.220425	+	1.29443i
$784$	30.0000	−	51.9615i	1.07143	−	1.85577i
$785$	22.9783	−	13.2665i	0.820129	−	0.473502i
$786$	−7.77817	+	2.34521i	−0.277438	+	0.0836508i
$787$	−35.0000			−1.24762			−0.623808	−	0.781578i	$-0.714415\pi$
$787$	−35.0000			−1.24762			−0.623808	+	0.781578i	$0.714415\pi$
$788$	−12.7279	−	22.0454i	−0.453413	−	0.785335i
$789$	−5.03237	+	5.35493i	−0.179157	+	0.190641i
$790$		0			0
$791$	77.7817			2.76560
$792$	12.5319	−	25.1982i	0.445302	−	0.895380i
$793$		0			0
$794$	−5.74456	+	3.31662i	−0.203867	+	0.117703i
$795$	−26.9783	−	6.33830i	−0.956820	−	0.224796i
$796$	−16.2481	−	9.38083i	−0.575898	−	0.332495i
$797$	−26.8701			−0.951786			−0.475893	−	0.879503i	$-0.657875\pi$
$797$	−26.8701			−0.951786			−0.475893	+	0.879503i	$0.657875\pi$
$798$	8.86141	+	49.2897i	0.313690	+	1.74484i
$799$		−	46.9042i		−	1.65935i
$800$	8.48528	−	14.6969i	0.300000	−	0.519615i
$801$	−19.8614	+	1.23472i	−0.701768	+	0.0436266i
$802$	−20.3101	+	11.7260i	−0.717174	+	0.414061i
$803$	2.87228	+	1.65831i	0.101361	+	0.0585206i
$804$	−11.8614	+	12.6217i	−0.418320	+	0.445133i
$805$		−	28.1425i		−	0.991893i
$806$		0			0
$807$	−13.4196	+	14.2798i	−0.472394	+	0.502673i
$808$	−10.0000	−	17.3205i	−0.351799	−	0.609333i
$809$			49.7494i			1.74909i	0.484940	+	0.874547i	$0.338841\pi$
$809$			49.7494i			1.74909i	−0.484940	+	0.874547i	$0.661159\pi$
$810$	−7.00000	+	16.5831i	−0.245955	+	0.582672i
$811$	−7.00000	−	12.1244i	−0.245803	−	0.425744i	0.716554	−	0.697532i	$-0.245718\pi$
$811$	−7.00000	−	12.1244i	−0.245803	−	0.425744i	−0.962357	+	0.271788i	$0.912385\pi$
$812$	57.4456	+	33.1662i	2.01595	+	1.16391i
$813$	29.6005	+	27.8175i	1.03813	+	0.975601i
$814$	11.0000	−	19.0526i	0.385550	−	0.667792i
$815$	10.6066	−	18.3712i	0.371533	−	0.643514i
$816$	−44.0000	+	13.2665i	−1.54031	+	0.464420i
$817$	24.0000	−	10.3923i	0.839654	−	0.363581i
$818$	−38.1838			−1.33506
$819$		0			0
$820$	−8.12404	−	4.69042i	−0.283704	−	0.163796i
$821$	−28.2843	−	48.9898i	−0.987128	−	1.70976i	−0.632070	−	0.774911i	$-0.717794\pi$
$821$	−28.2843	−	48.9898i	−0.987128	−	1.70976i	−0.355058	−	0.934844i	$-0.615539\pi$
$822$	9.29039	−	39.5435i	0.324040	−	1.37924i
$823$	−8.12404	+	4.69042i	−0.283186	+	0.163498i	−0.634865	−	0.772623i	$-0.718944\pi$
$823$	−8.12404	+	4.69042i	−0.283186	+	0.163498i	0.351679	+	0.936121i	$0.385611\pi$
$824$		−	26.5330i		−	0.924321i
$825$	16.5000	−	4.97494i	0.574456	−	0.173205i
$826$	11.0000	+	19.0526i	0.382739	+	0.662923i
$827$	14.3614	−	8.29156i	0.499395	−	0.288326i	−0.229069	−	0.973410i	$-0.573568\pi$
$827$	14.3614	−	8.29156i	0.499395	−	0.288326i	0.728464	+	0.685084i	$0.240235\pi$
$828$	−21.2132	+	14.0712i	−0.737210	+	0.489010i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$	5.74456	−	3.31662i	0.199397	−	0.115122i
$831$	−9.29039	+	39.5435i	−0.322280	+	1.37175i
$832$		0			0
$833$	−86.1684	−	49.7494i	−2.98556	−	1.72371i
$834$	35.7684	+	8.40347i	1.23856	+	0.290988i
$835$	−12.0000			−0.415277
$836$	28.7228	+	3.31662i	0.993399	+	0.114708i
$837$	−15.5563	+	18.7617i	−0.537706	+	0.648498i
$838$	−32.4962	−	18.7617i	−1.12256	−	0.648111i
$839$	−4.94975	+	8.57321i	−0.170884	+	0.295980i	−0.938729	−	0.344655i	$-0.887996\pi$
$839$	−4.94975	+	8.57321i	−0.170884	+	0.295980i	0.767845	+	0.640636i	$0.221329\pi$
$840$	23.6804	+	22.2540i	0.817051	+	0.767835i
$841$	−10.5000	+	18.1865i	−0.362069	+	0.627122i
$842$	28.7228	−	16.5831i	0.989854	−	0.571492i
$843$	−5.50000	+	1.65831i	−0.189430	+	0.0571153i
$844$	32.0000			1.10149
$845$	9.19239	+	15.9217i	0.316228	+	0.547723i
$846$	26.8614	+	13.3591i	0.923514	+	0.459294i
$847$		0			0
$848$	45.2548			1.55406
$849$	−29.6535	+	31.5542i	−1.01771	+	1.08294i
$850$	−24.3721	−	14.0712i	−0.835957	−	0.482640i
$851$	−17.2337	+	9.94987i	−0.590763	+	0.341077i
$852$	−19.0765	−	4.48185i	−0.653550	−	0.153546i
$853$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$853$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$854$	−31.1127			−1.06465
$855$	−18.4674	−	0.977359i	−0.631572	−	0.0334250i
$856$		0			0
$857$	−43.0842	−	24.8747i	−1.47173	−	0.849703i	−0.472234	−	0.881473i	$-0.656552\pi$
$857$	−43.0842	−	24.8747i	−1.47173	−	0.849703i	−0.999495	+	0.0317703i	$0.989885\pi$
$858$		0			0
$859$	16.5000	+	28.5788i	0.562973	+	0.975097i	0.997235	+	0.0743110i	$0.0236757\pi$
$859$	16.5000	+	28.5788i	0.562973	+	0.975097i	−0.434262	+	0.900786i	$0.642991\pi$
$860$	8.48528	−	14.6969i	0.289346	−	0.501161i
$861$	−18.4520	+	19.6347i	−0.628843	+	0.669150i
$862$	−20.0000			−0.681203
$863$	−4.24264			−0.144421			−0.0722106	−	0.997389i	$-0.523005\pi$
$863$	−4.24264			−0.144421			−0.0722106	+	0.997389i	$0.523005\pi$
$864$	4.93437	−	28.9767i	0.167871	−	0.985809i
$865$	−2.00000	−	3.46410i	−0.0680020	−	0.117783i
$866$	−28.2843			−0.961139
$867$	13.5000	+	44.7744i	0.458484	+	1.52062i
$868$	22.0000	+	38.1051i	0.746729	+	1.29337i
$869$		0			0
$870$	−16.7746	+	17.8498i	−0.568711	+	0.605164i
$871$		0			0
$872$	−22.9783	−	13.2665i	−0.778142	−	0.449260i
$873$	37.5000	−	24.8747i	1.26918	−	0.841881i
$874$	−21.0000	−	15.5885i	−0.710336	−	0.527287i
$875$			53.0660i			1.79396i
$876$	3.37228	+	0.792287i	0.113939	+	0.0267689i
$877$	4.06202	+	2.34521i	0.137165	+	0.0791920i	0.567012	−	0.823710i	$-0.308099\pi$
$877$	4.06202	+	2.34521i	0.137165	+	0.0791920i	−0.429847	+	0.902902i	$0.641433\pi$
$878$	28.7228	−	16.5831i	0.969348	−	0.559653i
$879$	16.6919	+	3.92162i	0.563005	+	0.132273i
$880$	16.2481	−	9.38083i	0.547723	−	0.316228i
$881$			29.8496i			1.00566i	0.864386	+	0.502830i	$0.167708\pi$
$881$			29.8496i			1.00566i	−0.864386	+	0.502830i	$0.832292\pi$
$882$	53.0330	−	35.1781i	1.78571	−	1.18451i
$883$	−12.5000	−	21.6506i	−0.420658	−	0.728602i	0.575346	−	0.817910i	$-0.304868\pi$
$883$	−12.5000	−	21.6506i	−0.420658	−	0.728602i	−0.996004	+	0.0893086i	$0.971534\pi$
$884$		0			0
$885$	−7.77817	+	2.34521i	−0.261460	+	0.0788333i
$886$		−	4.69042i		−	0.157578i
$887$	−21.2132	−	36.7423i	−0.712270	−	1.23369i	−0.964003	−	0.265891i	$-0.914334\pi$
$887$	−21.2132	−	36.7423i	−0.712270	−	1.23369i	0.251734	−	0.967797i	$-0.418999\pi$
$888$	5.25544	−	22.3692i	0.176361	−	0.750661i
$889$	−44.0000	−	76.2102i	−1.47571	−	2.55601i
$890$	−11.4891	−	6.63325i	−0.385116	−	0.222347i
$891$	23.8030	−	18.0116i	0.797430	−	0.603411i
$892$		−	28.1425i		−	0.942280i
$893$	−3.53553	+	30.6186i	−0.118312	+	1.02461i
$894$	5.00000	+	16.5831i	0.167225	+	0.554623i
$895$	12.1861	+	7.03562i	0.407335	+	0.235175i
$896$	−45.9565	−	26.5330i	−1.53530	−	0.886405i
$897$		0			0
$898$	−12.1861	−	7.03562i	−0.406654	−	0.234782i
$899$	−28.7228	+	16.5831i	−0.957959	+	0.553078i
$900$	15.0000	−	9.94987i	0.500000	−	0.331662i
$901$		−	75.0467i		−	2.50017i
$902$	7.77817	+	13.4722i	0.258985	+	0.448575i
$903$	−35.5206	−	33.3810i	−1.18205	−	1.11085i
$904$		−	46.9042i		−	1.56001i
$905$			33.1662i			1.10248i
$906$	−8.37228	−	7.86797i	−0.278150	−	0.261396i
$907$	1.50000	−	2.59808i	0.0498067	−	0.0862677i	−0.840047	−	0.542513i	$-0.817473\pi$
$907$	1.50000	−	2.59808i	0.0498067	−	0.0862677i	0.889854	+	0.456246i	$0.150806\pi$
$908$	−28.7228	+	16.5831i	−0.953200	+	0.550330i
$909$	−1.31621	−	21.1723i	−0.0436560	−	0.702242i
$910$		0			0
$911$	35.3553			1.17137			0.585687	−	0.810537i	$-0.300825\pi$
$911$	35.3553			1.17137			0.585687	+	0.810537i	$0.300825\pi$
$912$	29.7228	−	5.34363i	0.984221	−	0.176945i
$913$	−11.0000			−0.364047
$914$	−17.6777	+	30.6186i	−0.584725	+	1.01277i
$915$	2.62772	−	11.1846i	0.0868697	−	0.369751i
$916$	16.2481	−	9.38083i	0.536852	−	0.309951i
$917$	−7.77817	+	13.4722i	−0.256858	+	0.444891i
$918$	−48.0525	−	8.18272i	−1.58597	−	0.270070i
$919$			56.2850i			1.85667i	0.371744	+	0.928335i	$0.378760\pi$
$919$			56.2850i			1.85667i	−0.371744	+	0.928335i	$0.621240\pi$
$920$	−16.9706			−0.559503
$921$	−5.93070	+	6.31084i	−0.195423	+	0.207949i
$922$		0			0
$923$		0			0
$924$	−15.5563	−	51.5946i	−0.511766	−	1.69734i
$925$	12.1861	−	7.03562i	0.400675	−	0.231330i
$926$	−11.4891	−	6.63325i	−0.377556	−	0.217982i
$927$	12.5319	−	25.1982i	0.411602	−	0.827619i
$928$	20.0000	−	34.6410i	0.656532	−	1.13715i
$929$	8.61684	+	4.97494i	0.282709	+	0.163222i	0.634649	−	0.772800i	$-0.281145\pi$
$929$	8.61684	+	4.97494i	0.282709	+	0.163222i	−0.351940	+	0.936023i	$0.614478\pi$
$930$	−15.5563	+	4.69042i	−0.510113	+	0.153805i
$931$	52.5000	+	38.9711i	1.72062	+	1.27723i
$932$			33.1662i			1.08640i
$933$	−11.9228	−	2.80116i	−0.390335	−	0.0917058i
$934$	20.3101	+	11.7260i	0.664567	+	0.383688i
$935$	−15.5563	−	26.9444i	−0.508747	−	0.881176i
$936$		0			0
$937$	−3.50000	−	6.06218i	−0.114340	−	0.198043i	0.803176	−	0.595742i	$-0.203142\pi$
$937$	−3.50000	−	6.06218i	−0.114340	−	0.198043i	−0.917516	+	0.397699i	$0.869809\pi$
$938$			33.1662i			1.08292i
$939$	−5.50000	−	18.2414i	−0.179486	−	0.595287i
$940$	10.0000	+	17.3205i	0.326164	+	0.564933i
$941$	21.2132	+	36.7423i	0.691531	+	1.19777i	0.971336	+	0.237710i	$0.0763966\pi$
$941$	21.2132	+	36.7423i	0.691531	+	1.19777i	−0.279806	+	0.960057i	$0.590270\pi$
$942$	−44.0000	+	13.2665i	−1.43360	+	0.432246i
$943$		−	14.0712i		−	0.458223i
$944$	11.4891	−	6.63325i	0.373939	−	0.215894i
$945$	11.9783	+	32.3191i	0.389653	+	1.05134i
$946$	−24.3721	+	14.0712i	−0.792406	+	0.457496i
$947$	−34.4674	−	19.8997i	−1.12004	−	0.646655i	−0.178628	−	0.983917i	$-0.557166\pi$
$947$	−34.4674	−	19.8997i	−1.12004	−	0.646655i	−0.941411	+	0.337262i	$0.890499\pi$
$948$		0			0
$949$		0			0
$950$	14.8492	+	11.0227i	0.481773	+	0.357624i
$951$	−9.89949	−	32.8329i	−0.321013	−	1.06468i
$952$	−44.0000	+	76.2102i	−1.42605	+	2.46999i
$953$	14.3614	+	8.29156i	0.465212	+	0.268590i	0.714233	−	0.699908i	$-0.246776\pi$
$953$	14.3614	+	8.29156i	0.465212	+	0.268590i	−0.249021	+	0.968498i	$0.580109\pi$
$954$	42.9783	+	21.3745i	1.39147	+	0.692026i
$955$	4.00000	−	6.92820i	0.129437	−	0.224191i
$956$	14.1421	+	24.4949i	0.457389	+	0.792222i
$957$	38.8909	−	11.7260i	1.25716	−	0.379049i
$958$	−56.0000			−1.80928
$959$	−38.8909	−	67.3610i	−1.25585	−	2.17520i
$960$	13.4196	−	14.2798i	0.433117	−	0.460879i
$961$	9.00000			0.290323
$962$		0			0
$963$		0			0
$964$	−25.0000	+	43.3013i	−0.805196	+	1.39464i
$965$	−14.1421	−	24.4949i	−0.455251	−	0.788519i
$966$	−11.1485	+	47.4522i	−0.358696	+	1.52675i
$967$	−40.6202	−	23.4521i	−1.30626	−	0.754168i	−0.324788	−	0.945787i	$-0.605293\pi$
$967$	−40.6202	−	23.4521i	−1.30626	−	0.754168i	−0.981469	+	0.191619i	$0.938626\pi$
$968$		0			0
$969$	−8.86141	−	49.2897i	−0.284669	−	1.58341i
$970$	30.0000			0.963242
$971$	−14.3614	−	8.29156i	−0.460879	−	0.266089i	0.251535	−	0.967848i	$-0.419065\pi$
$971$	−14.3614	−	8.29156i	−0.460879	−	0.266089i	−0.712414	+	0.701759i	$0.752398\pi$
$972$	18.3723	−	25.1885i	0.589291	−	0.807921i
$973$	60.9303	−	35.1781i	1.95334	−	1.12776i
$974$	−5.74456	−	3.31662i	−0.184068	−	0.106272i
$975$		0			0
$976$			18.7617i			0.600546i
$977$			16.5831i			0.530541i	0.964174	+	0.265271i	$0.0854613\pi$
$977$			16.5831i			0.530541i	−0.964174	+	0.265271i	$0.914539\pi$
$978$	−25.1618	+	26.7746i	−0.804587	+	0.856159i
$979$	11.0000	+	19.0526i	0.351562	+	0.608922i
$980$	42.4264			1.35526
$981$	−15.5563	−	23.4521i	−0.496676	−	0.748767i
$982$	16.2481	−	9.38083i	0.518497	−	0.299354i
$983$	29.6985	−	51.4393i	0.947235	−	1.64066i	0.196020	−	0.980600i	$-0.437198\pi$
$983$	29.6985	−	51.4393i	0.947235	−	1.64066i	0.751214	−	0.660059i	$-0.229469\pi$
$984$	11.8402	+	11.1270i	0.377452	+	0.354715i
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$	−57.4456	−	33.1662i	−1.82944	−	1.05623i
$987$	55.0000	−	16.5831i	1.75067	−	0.527847i
$988$		0			0
$989$	25.4558			0.809449
$990$	19.8614	−	1.23472i	0.631237	−	0.0392419i
$991$	40.6202	+	23.4521i	1.29034	+	0.744980i	0.978715	−	0.205224i	$-0.0657924\pi$
$991$	40.6202	+	23.4521i	1.29034	+	0.744980i	0.311628	+	0.950204i	$0.399126\pi$
$992$	22.9783	−	13.2665i	0.729560	−	0.421212i
$993$	−18.5475	−	4.35758i	−0.588589	−	0.138284i
$994$	−32.4962	+	18.7617i	−1.03072	+	0.595084i
$995$		−	13.2665i		−	0.420576i
$996$	−11.0000	+	3.31662i	−0.348548	+	0.105091i
$997$	4.06202	−	2.34521i	0.128645	−	0.0742735i	−0.434296	−	0.900770i	$-0.643003\pi$
$997$	4.06202	−	2.34521i	0.128645	−	0.0742735i	0.562942	+	0.826497i	$0.309670\pi$
$998$	9.19239	+	15.9217i	0.290980	+	0.503992i
$999$	15.5563	−	18.7617i	0.492181	−	0.593593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.u.c.11.2	yes	8
3.2	odd	2	inner	456.2.u.c.11.3	yes	8
8.3	odd	2	inner	456.2.u.c.11.4	yes	8
19.7	even	3	inner	456.2.u.c.83.1	yes	8
24.11	even	2	inner	456.2.u.c.11.1	✓	8
57.26	odd	6	inner	456.2.u.c.83.4	yes	8
152.83	odd	6	inner	456.2.u.c.83.3	yes	8
456.83	even	6	inner	456.2.u.c.83.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.u.c.11.1	✓	8	24.11	even	2	inner
456.2.u.c.11.2	yes	8	1.1	even	1	trivial
456.2.u.c.11.3	yes	8	3.2	odd	2	inner
456.2.u.c.11.4	yes	8	8.3	odd	2	inner
456.2.u.c.83.1	yes	8	19.7	even	3	inner
456.2.u.c.83.2	yes	8	456.83	even	6	inner
456.2.u.c.83.3	yes	8	152.83	odd	6	inner
456.2.u.c.83.4	yes	8	57.26	odd	6	inner

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.68614 + 0.396143i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.707107 - 1.22474i) q^{5} +(-1.67746 + 1.78498i) q^{6} +4.69042i q^{7} +2.82843 q^{8} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.68614 + 0.396143i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.707107 - 1.22474i) q^{5} +(-1.67746 + 1.78498i) q^{6} +4.69042i q^{7} +2.82843 q^{8} +(2.68614 + 1.33591i) q^{9} +(1.00000 + 1.73205i) q^{10} -3.31662i q^{11} +(-1.00000 - 3.31662i) q^{12} +(-5.74456 - 3.31662i) q^{14} +(1.67746 - 1.78498i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(5.74456 + 3.31662i) q^{17} +(-3.53553 + 2.34521i) q^{18} +(-3.50000 - 2.59808i) q^{19} -2.82843 q^{20} +(-1.85808 + 7.90870i) q^{21} +(4.06202 + 2.34521i) q^{22} +(-2.12132 - 3.67423i) q^{23} +(4.76913 + 1.12046i) q^{24} +(1.50000 + 2.59808i) q^{25} +(4.00000 + 3.31662i) q^{27} +(8.12404 - 4.69042i) q^{28} +(3.53553 + 6.12372i) q^{29} +(1.00000 + 3.31662i) q^{30} +4.69042i q^{31} +(-2.82843 - 4.89898i) q^{32} +(1.31386 - 5.59230i) q^{33} +(-8.12404 + 4.69042i) q^{34} +(5.74456 + 3.31662i) q^{35} +(-0.372281 - 5.98844i) q^{36} -4.69042i q^{37} +(5.65685 - 2.44949i) q^{38} +(2.00000 - 3.46410i) q^{40} +(2.87228 + 1.65831i) q^{41} +(-8.37228 - 7.86797i) q^{42} +(-3.00000 + 5.19615i) q^{43} +(-5.74456 + 3.31662i) q^{44} +(3.53553 - 2.34521i) q^{45} +6.00000 q^{46} +(-3.53553 - 6.12372i) q^{47} +(-4.74456 + 5.04868i) q^{48} -15.0000 q^{49} -4.24264 q^{50} +(8.37228 + 7.86797i) q^{51} +(-5.65685 - 9.79796i) q^{53} +(-6.89045 + 2.55377i) q^{54} +(-4.06202 - 2.34521i) q^{55} +13.2665i q^{56} +(-4.87228 - 5.76722i) q^{57} -10.0000 q^{58} +(-2.87228 - 1.65831i) q^{59} +(-4.76913 - 1.12046i) q^{60} +(4.06202 - 2.34521i) q^{61} +(-5.74456 - 3.31662i) q^{62} +(-6.26596 + 12.5991i) q^{63} +8.00000 q^{64} +(5.92010 + 5.56349i) q^{66} +(-2.50000 - 4.33013i) q^{67} -13.2665i q^{68} +(-2.12132 - 7.03562i) q^{69} +(-8.12404 + 4.69042i) q^{70} +(2.82843 - 4.89898i) q^{71} +(7.59755 + 3.77852i) q^{72} +(-0.500000 + 0.866025i) q^{73} +(5.74456 + 3.31662i) q^{74} +(1.50000 + 4.97494i) q^{75} +(-1.00000 + 8.66025i) q^{76} +15.5563 q^{77} +(2.82843 + 4.89898i) q^{80} +(5.43070 + 7.17687i) q^{81} +(-4.06202 + 2.34521i) q^{82} -3.31662i q^{83} +(15.5563 - 4.69042i) q^{84} +(8.12404 - 4.69042i) q^{85} +(-4.24264 - 7.34847i) q^{86} +(3.53553 + 11.7260i) q^{87} -9.38083i q^{88} +(-5.74456 + 3.31662i) q^{89} +(0.372281 + 5.98844i) q^{90} +(-4.24264 + 7.34847i) q^{92} +(-1.85808 + 7.90870i) q^{93} +10.0000 q^{94} +(-5.65685 + 2.44949i) q^{95} +(-2.82843 - 9.38083i) q^{96} +(7.50000 - 12.9904i) q^{97} +(10.6066 - 18.3712i) q^{98} +(4.43070 - 8.90892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 8 q^{4} + 10 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 8 * q^4 + 10 * q^9	\( 8 q + 2 q^{3} - 8 q^{4} + 10 q^{9} + 8 q^{10} - 8 q^{12} - 16 q^{16} - 28 q^{19} + 12 q^{25} + 32 q^{27} + 8 q^{30} + 22 q^{33} + 20 q^{36} + 16 q^{40} - 44 q^{42} - 24 q^{43} + 48 q^{46} + 8 q^{48} - 120 q^{49} + 44 q^{51} - 16 q^{57} - 80 q^{58} + 64 q^{64} - 20 q^{67} - 4 q^{73} + 12 q^{75} - 8 q^{76} - 14 q^{81} - 20 q^{90} + 80 q^{94} + 60 q^{97} - 22 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 8 * q^4 + 10 * q^9 + 8 * q^10 - 8 * q^12 - 16 * q^16 - 28 * q^19 + 12 * q^25 + 32 * q^27 + 8 * q^30 + 22 * q^33 + 20 * q^36 + 16 * q^40 - 44 * q^42 - 24 * q^43 + 48 * q^46 + 8 * q^48 - 120 * q^49 + 44 * q^51 - 16 * q^57 - 80 * q^58 + 64 * q^64 - 20 * q^67 - 4 * q^73 + 12 * q^75 - 8 * q^76 - 14 * q^81 - 20 * q^90 + 80 * q^94 + 60 * q^97 - 22 * q^99

Introduction

L-functions

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