LMFDB - Embedded newform 585.2.w.b.577.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(73,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	585.577
Dual form			585.2.w.b.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} -2.00000i q^{7} +3.00000 q^{8} +(-1.00000 + 2.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(3.00000 + 2.00000i) q^{13} +2.00000i q^{14} -1.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} +(-5.00000 - 5.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(-1.00000 - 1.00000i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +2.00000i q^{28} +(5.00000 - 5.00000i) q^{31} -5.00000 q^{32} +(1.00000 - 1.00000i) q^{34} +(-4.00000 - 2.00000i) q^{35} +(5.00000 + 5.00000i) q^{38} +(3.00000 - 6.00000i) q^{40} +(7.00000 - 7.00000i) q^{41} +(-1.00000 - 1.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(3.00000 + 3.00000i) q^{46} -6.00000i q^{47} +3.00000 q^{49} +(3.00000 + 4.00000i) q^{50} +(-3.00000 - 2.00000i) q^{52} +(-5.00000 + 5.00000i) q^{53} +(3.00000 - 1.00000i) q^{55} -6.00000i q^{56} +(7.00000 - 7.00000i) q^{59} -14.0000 q^{61} +(-5.00000 + 5.00000i) q^{62} +7.00000 q^{64} +(7.00000 - 4.00000i) q^{65} -4.00000 q^{67} +(1.00000 - 1.00000i) q^{68} +(4.00000 + 2.00000i) q^{70} +(-1.00000 + 1.00000i) q^{71} -10.0000 q^{73} +(5.00000 + 5.00000i) q^{76} +(2.00000 - 2.00000i) q^{77} -2.00000i q^{79} +(-1.00000 + 2.00000i) q^{80} +(-7.00000 + 7.00000i) q^{82} +6.00000i q^{83} +(1.00000 + 3.00000i) q^{85} +(1.00000 + 1.00000i) q^{86} +(3.00000 + 3.00000i) q^{88} +(-5.00000 + 5.00000i) q^{89} +(4.00000 - 6.00000i) q^{91} +(3.00000 + 3.00000i) q^{92} +6.00000i q^{94} +(-15.0000 + 5.00000i) q^{95} +2.00000 q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 6 q^{8} - 2 q^{10} + 2 q^{11} + 6 q^{13} - 2 q^{16} - 2 q^{17} - 10 q^{19} - 2 q^{20} - 2 q^{22} - 6 q^{23} - 6 q^{25} - 6 q^{26} + 10 q^{31} - 10 q^{32} + 2 q^{34} - 8 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 6 * q^8 - 2 * q^10 + 2 * q^11 + 6 * q^13 - 2 * q^16 - 2 * q^17 - 10 * q^19 - 2 * q^20 - 2 * q^22 - 6 * q^23 - 6 * q^25 - 6 * q^26 + 10 * q^31 - 10 * q^32 + 2 * q^34 - 8 * q^35 + 10 * q^38 + 6 * q^40 + 14 * q^41 - 2 * q^43 - 2 * q^44 + 6 * q^46 + 6 * q^49 + 6 * q^50 - 6 * q^52 - 10 * q^53 + 6 * q^55 + 14 * q^59 - 28 * q^61 - 10 * q^62 + 14 * q^64 + 14 * q^65 - 8 * q^67 + 2 * q^68 + 8 * q^70 - 2 * q^71 - 20 * q^73 + 10 * q^76 + 4 * q^77 - 2 * q^80 - 14 * q^82 + 2 * q^85 + 2 * q^86 + 6 * q^88 - 10 * q^89 + 8 * q^91 + 6 * q^92 - 30 * q^95 + 4 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$		0			0
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$		0			0
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$			2.00000i			0.534522i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$		0			0
$19$	−5.00000	−	5.00000i	−1.14708	−	1.14708i	−0.987124	−	0.159954i	$-0.948865\pi$
$19$	−5.00000	−	5.00000i	−1.14708	−	1.14708i	−0.159954	−	0.987124i	$-0.551135\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$		0			0
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	0.321400	−	0.946943i	$-0.395847\pi$
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	−0.946943	+	0.321400i	$0.895847\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	−3.00000	−	2.00000i	−0.588348	−	0.392232i
$27$		0			0
$28$			2.00000i			0.377964i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	−0.0972349	−	0.995261i	$-0.531000\pi$
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	0.995261	+	0.0972349i	$0.0309998\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	1.00000	−	1.00000i	0.171499	−	0.171499i
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	5.00000	+	5.00000i	0.811107	+	0.811107i
$39$		0			0
$40$	3.00000	−	6.00000i	0.474342	−	0.948683i
$41$	7.00000	−	7.00000i	1.09322	−	1.09322i	0.0980332	−	0.995183i	$-0.468745\pi$
$41$	7.00000	−	7.00000i	1.09322	−	1.09322i	0.995183	−	0.0980332i	$-0.0312551\pi$
$42$		0			0
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	0.626734	−	0.779233i	$-0.284391\pi$
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	−0.779233	+	0.626734i	$0.784391\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$		0			0
$46$	3.00000	+	3.00000i	0.442326	+	0.442326i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$	3.00000	+	4.00000i	0.424264	+	0.565685i
$51$		0			0
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$	−5.00000	+	5.00000i	−0.686803	+	0.686803i	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−5.00000	+	5.00000i	−0.686803	+	0.686803i	0.274721	+	0.961524i	$0.411414\pi$
$54$		0			0
$55$	3.00000	−	1.00000i	0.404520	−	0.134840i
$56$		−	6.00000i		−	0.801784i
$57$		0			0
$58$		0			0
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	−0.0850540	−	0.996376i	$-0.527106\pi$
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	0.996376	+	0.0850540i	$0.0271063\pi$
$60$		0			0
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$	−5.00000	+	5.00000i	−0.635001	+	0.635001i
$63$		0			0
$64$	7.00000			0.875000
$65$	7.00000	−	4.00000i	0.868243	−	0.496139i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	1.00000	−	1.00000i	0.121268	−	0.121268i
$69$		0			0
$70$	4.00000	+	2.00000i	0.478091	+	0.239046i
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	−0.763952	−	0.645273i	$-0.776743\pi$
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	0.645273	+	0.763952i	$0.276743\pi$
$72$		0			0
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$		0			0
$75$		0			0
$76$	5.00000	+	5.00000i	0.573539	+	0.573539i
$77$	2.00000	−	2.00000i	0.227921	−	0.227921i
$78$		0			0
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$		0			0
$82$	−7.00000	+	7.00000i	−0.773021	+	0.773021i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	1.00000	+	3.00000i	0.108465	+	0.325396i
$86$	1.00000	+	1.00000i	0.107833	+	0.107833i
$87$		0			0
$88$	3.00000	+	3.00000i	0.319801	+	0.319801i
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	−0.920572	−	0.390573i	$-0.872277\pi$
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	0.390573	+	0.920572i	$0.372277\pi$
$90$		0			0
$91$	4.00000	−	6.00000i	0.419314	−	0.628971i
$92$	3.00000	+	3.00000i	0.312772	+	0.312772i
$93$		0			0
$94$			6.00000i			0.618853i
$95$	−15.0000	+	5.00000i	−1.53897	+	0.512989i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		−	12.0000i		−	1.19404i	−0.802225	−	0.597022i	$-0.796350\pi$
$101$		−	12.0000i		−	1.19404i	0.802225	−	0.597022i	$-0.203650\pi$
$102$		0			0
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	0.962172	−	0.272442i	$-0.0878312\pi$
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	−0.272442	+	0.962172i	$0.587831\pi$
$104$	9.00000	+	6.00000i	0.882523	+	0.588348i
$105$		0			0
$106$	5.00000	−	5.00000i	0.485643	−	0.485643i
$107$	−7.00000	−	7.00000i	−0.676716	−	0.676716i	0.282540	−	0.959256i	$-0.408823\pi$
$107$	−7.00000	−	7.00000i	−0.676716	−	0.676716i	−0.959256	+	0.282540i	$0.908823\pi$
$108$		0			0
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	0.991575	−	0.129532i	$-0.0413474\pi$
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	−0.129532	+	0.991575i	$0.541347\pi$
$110$	−3.00000	+	1.00000i	−0.286039	+	0.0953463i
$111$		0			0
$112$			2.00000i			0.188982i
$113$	−5.00000	+	5.00000i	−0.470360	+	0.470360i	−0.902031	−	0.431671i	$-0.857924\pi$
$113$	−5.00000	+	5.00000i	−0.470360	+	0.470360i	0.431671	+	0.902031i	$0.357924\pi$
$114$		0			0
$115$	−9.00000	+	3.00000i	−0.839254	+	0.279751i
$116$		0			0
$117$		0			0
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	2.00000	+	2.00000i	0.183340	+	0.183340i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$	14.0000			1.26750
$123$		0			0
$124$	−5.00000	+	5.00000i	−0.449013	+	0.449013i
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$		0			0
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	−0.184257	−	0.982878i	$-0.558988\pi$
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	0.982878	+	0.184257i	$0.0589879\pi$
$128$	3.00000			0.265165
$129$		0			0
$130$	−7.00000	+	4.00000i	−0.613941	+	0.350823i
$131$	20.0000			1.74741			0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000			1.74741			0.873704	+	0.486458i	$0.161711\pi$
$132$		0			0
$133$	−10.0000	+	10.0000i	−0.867110	+	0.867110i
$134$	4.00000			0.345547
$135$		0			0
$136$	−3.00000	+	3.00000i	−0.257248	+	0.257248i
$137$			16.0000i			1.36697i	0.729964	+	0.683486i	$0.239537\pi$
$137$			16.0000i			1.36697i	−0.729964	+	0.683486i	$0.760463\pi$
$138$		0			0
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$	4.00000	+	2.00000i	0.338062	+	0.169031i
$141$		0			0
$142$	1.00000	−	1.00000i	0.0839181	−	0.0839181i
$143$	1.00000	+	5.00000i	0.0836242	+	0.418121i
$144$		0			0
$145$		0			0
$146$	10.0000			0.827606
$147$		0			0
$148$		0			0
$149$	3.00000	+	3.00000i	0.245770	+	0.245770i	0.819232	−	0.573462i	$-0.194400\pi$
$149$	3.00000	+	3.00000i	0.245770	+	0.245770i	−0.573462	+	0.819232i	$0.694400\pi$
$150$		0			0
$151$	7.00000	+	7.00000i	0.569652	+	0.569652i	0.932031	−	0.362379i	$-0.118035\pi$
$151$	7.00000	+	7.00000i	0.569652	+	0.569652i	−0.362379	+	0.932031i	$0.618035\pi$
$152$	−15.0000	−	15.0000i	−1.21666	−	1.21666i
$153$		0			0
$154$	−2.00000	+	2.00000i	−0.161165	+	0.161165i
$155$	−5.00000	−	15.0000i	−0.401610	−	1.20483i
$156$		0			0
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.999268	+	0.0382445i	$0.0121766\pi$
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.0382445	+	0.999268i	$0.487823\pi$
$158$			2.00000i			0.159111i
$159$		0			0
$160$	−5.00000	+	10.0000i	−0.395285	+	0.790569i
$161$	−6.00000	+	6.00000i	−0.472866	+	0.472866i
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−7.00000	+	7.00000i	−0.546608	+	0.546608i
$165$		0			0
$166$		−	6.00000i		−	0.465690i
$167$			18.0000i			1.39288i	0.717614	+	0.696441i	$0.245234\pi$
$167$			18.0000i			1.39288i	−0.717614	+	0.696441i	$0.754766\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$	−1.00000	−	3.00000i	−0.0766965	−	0.230089i
$171$		0			0
$172$	1.00000	+	1.00000i	0.0762493	+	0.0762493i
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	−0.152057	+	0.988372i	$0.548590\pi$
$174$		0			0
$175$	−8.00000	+	6.00000i	−0.604743	+	0.453557i
$176$	−1.00000	−	1.00000i	−0.0753778	−	0.0753778i
$177$		0			0
$178$	5.00000	−	5.00000i	0.374766	−	0.374766i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$		0			0
$181$		−	8.00000i		−	0.594635i	−0.954779	−	0.297318i	$-0.903908\pi$
$181$		−	8.00000i		−	0.594635i	0.954779	−	0.297318i	$-0.0960920\pi$
$182$	−4.00000	+	6.00000i	−0.296500	+	0.444750i
$183$		0			0
$184$	−9.00000	−	9.00000i	−0.663489	−	0.663489i
$185$		0			0
$186$		0			0
$187$	−2.00000			−0.146254
$188$			6.00000i			0.437595i
$189$		0			0
$190$	15.0000	−	5.00000i	1.08821	−	0.362738i
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	18.0000			1.29567			0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000			1.29567			0.647834	+	0.761781i	$0.275675\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	−9.00000	−	12.0000i	−0.636396	−	0.848528i
$201$		0			0
$202$			12.0000i			0.844317i
$203$		0			0
$204$		0			0
$205$	−7.00000	−	21.0000i	−0.488901	−	1.46670i
$206$	−7.00000	−	7.00000i	−0.487713	−	0.487713i
$207$		0			0
$208$	−3.00000	−	2.00000i	−0.208013	−	0.138675i
$209$		−	10.0000i		−	0.691714i
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	5.00000	−	5.00000i	0.343401	−	0.343401i
$213$		0			0
$214$	7.00000	+	7.00000i	0.478510	+	0.478510i
$215$	−3.00000	+	1.00000i	−0.204598	+	0.0681994i
$216$		0			0
$217$	−10.0000	−	10.0000i	−0.678844	−	0.678844i
$218$	−9.00000	−	9.00000i	−0.609557	−	0.609557i
$219$		0			0
$220$	−3.00000	+	1.00000i	−0.202260	+	0.0674200i
$221$	−5.00000	+	1.00000i	−0.336336	+	0.0672673i
$222$		0			0
$223$		−	2.00000i		−	0.133930i	−0.997755	−	0.0669650i	$-0.978668\pi$
$223$		−	2.00000i		−	0.133930i	0.997755	−	0.0669650i	$-0.0213316\pi$
$224$			10.0000i			0.668153i
$225$		0			0
$226$	5.00000	−	5.00000i	0.332595	−	0.332595i
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$		0			0
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	−0.799248	−	0.601002i	$-0.794768\pi$
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	0.601002	+	0.799248i	$0.294768\pi$
$230$	9.00000	−	3.00000i	0.593442	−	0.197814i
$231$		0			0
$232$		0			0
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	0.673592	−	0.739104i	$-0.264751\pi$
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	−0.739104	+	0.673592i	$0.764751\pi$
$234$		0			0
$235$	−12.0000	−	6.00000i	−0.782794	−	0.391397i
$236$	−7.00000	+	7.00000i	−0.455661	+	0.455661i
$237$		0			0
$238$	−2.00000	−	2.00000i	−0.129641	−	0.129641i
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	0.603391	−	0.797445i	$-0.293816\pi$
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	−0.797445	+	0.603391i	$0.793816\pi$
$240$		0			0
$241$	17.0000	+	17.0000i	1.09507	+	1.09507i	0.994979	+	0.100088i	$0.0319123\pi$
$241$	17.0000	+	17.0000i	1.09507	+	1.09507i	0.100088	+	0.994979i	$0.468088\pi$
$242$			9.00000i			0.578542i
$243$		0			0
$244$	14.0000			0.896258
$245$	3.00000	−	6.00000i	0.191663	−	0.383326i
$246$		0			0
$247$	−5.00000	−	25.0000i	−0.318142	−	1.59071i
$248$	15.0000	−	15.0000i	0.952501	−	0.952501i
$249$		0			0
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$		−	2.00000i		−	0.126239i	−0.998006	−	0.0631194i	$-0.979895\pi$
$251$		−	2.00000i		−	0.126239i	0.998006	−	0.0631194i	$-0.0201049\pi$
$252$		0			0
$253$		−	6.00000i		−	0.377217i
$254$	−9.00000	+	9.00000i	−0.564710	+	0.564710i
$255$		0			0
$256$	−17.0000			−1.06250
$257$	11.0000	−	11.0000i	0.686161	−	0.686161i	−0.275220	−	0.961381i	$-0.588751\pi$
$257$	11.0000	−	11.0000i	0.686161	−	0.686161i	0.961381	+	0.275220i	$0.0887507\pi$
$258$		0			0
$259$		0			0
$260$	−7.00000	+	4.00000i	−0.434122	+	0.248069i
$261$		0			0
$262$	−20.0000			−1.23560
$263$	−1.00000	+	1.00000i	−0.0616626	+	0.0616626i	−0.737266	−	0.675603i	$-0.763883\pi$
$263$	−1.00000	+	1.00000i	−0.0616626	+	0.0616626i	0.675603	+	0.737266i	$0.263883\pi$
$264$		0			0
$265$	5.00000	+	15.0000i	0.307148	+	0.921443i
$266$	10.0000	−	10.0000i	0.613139	−	0.613139i
$267$		0			0
$268$	4.00000			0.244339
$269$		−	12.0000i		−	0.731653i	−0.930683	−	0.365826i	$-0.880786\pi$
$269$		−	12.0000i		−	0.731653i	0.930683	−	0.365826i	$-0.119214\pi$
$270$		0			0
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	0.378777	−	0.925488i	$-0.376345\pi$
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	−0.925488	+	0.378777i	$0.876345\pi$
$272$	1.00000	−	1.00000i	0.0606339	−	0.0606339i
$273$		0			0
$274$		−	16.0000i		−	0.966595i
$275$	1.00000	−	7.00000i	0.0603023	−	0.422116i
$276$		0			0
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	−0.995545	−	0.0942828i	$-0.969944\pi$
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	0.0942828	+	0.995545i	$0.469944\pi$
$278$			14.0000i			0.839664i
$279$		0			0
$280$	−12.0000	−	6.00000i	−0.717137	−	0.358569i
$281$	−1.00000	−	1.00000i	−0.0596550	−	0.0596550i	0.676650	−	0.736305i	$-0.263431\pi$
$281$	−1.00000	−	1.00000i	−0.0596550	−	0.0596550i	−0.736305	+	0.676650i	$0.763431\pi$
$282$		0			0
$283$	−9.00000	−	9.00000i	−0.534994	−	0.534994i	0.387060	−	0.922055i	$-0.373491\pi$
$283$	−9.00000	−	9.00000i	−0.534994	−	0.534994i	−0.922055	+	0.387060i	$0.873491\pi$
$284$	1.00000	−	1.00000i	0.0593391	−	0.0593391i
$285$		0			0
$286$	−1.00000	−	5.00000i	−0.0591312	−	0.295656i
$287$	−14.0000	−	14.0000i	−0.826394	−	0.826394i
$288$		0			0
$289$			15.0000i			0.882353i
$290$		0			0
$291$		0			0
$292$	10.0000			0.585206
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	−7.00000	−	21.0000i	−0.407556	−	1.22267i
$296$		0			0
$297$		0			0
$298$	−3.00000	−	3.00000i	−0.173785	−	0.173785i
$299$	−3.00000	−	15.0000i	−0.173494	−	0.867472i
$300$		0			0
$301$	−2.00000	+	2.00000i	−0.115278	+	0.115278i
$302$	−7.00000	−	7.00000i	−0.402805	−	0.402805i
$303$		0			0
$304$	5.00000	+	5.00000i	0.286770	+	0.286770i
$305$	−14.0000	+	28.0000i	−0.801638	+	1.60328i
$306$		0			0
$307$			18.0000i			1.02731i	0.857996	+	0.513657i	$0.171710\pi$
$307$			18.0000i			1.02731i	−0.857996	+	0.513657i	$0.828290\pi$
$308$	−2.00000	+	2.00000i	−0.113961	+	0.113961i
$309$		0			0
$310$	5.00000	+	15.0000i	0.283981	+	0.851943i
$311$		−	6.00000i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$311$		−	6.00000i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$	−13.0000	−	13.0000i	−0.733632	−	0.733632i
$315$		0			0
$316$			2.00000i			0.112509i
$317$	14.0000			0.786318			0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000			0.786318			0.393159	+	0.919470i	$0.371382\pi$
$318$		0			0
$319$		0			0
$320$	7.00000	−	14.0000i	0.391312	−	0.782624i
$321$		0			0
$322$	6.00000	−	6.00000i	0.334367	−	0.334367i
$323$	10.0000			0.556415
$324$		0			0
$325$	−1.00000	−	18.0000i	−0.0554700	−	0.998460i
$326$	−4.00000			−0.221540
$327$		0			0
$328$	21.0000	−	21.0000i	1.15953	−	1.15953i
$329$	−12.0000			−0.661581
$330$		0			0
$331$	−3.00000	+	3.00000i	−0.164895	+	0.164895i	−0.784731	−	0.619836i	$-0.787199\pi$
$331$	−3.00000	+	3.00000i	−0.164895	+	0.164895i	0.619836	+	0.784731i	$0.287199\pi$
$332$		−	6.00000i		−	0.329293i
$333$		0			0
$334$		−	18.0000i		−	0.984916i
$335$	−4.00000	+	8.00000i	−0.218543	+	0.437087i
$336$		0			0
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	−0.257992	−	0.966147i	$-0.583061\pi$
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	0.966147	+	0.257992i	$0.0830608\pi$
$338$	−5.00000	−	12.0000i	−0.271964	−	0.652714i
$339$		0			0
$340$	−1.00000	−	3.00000i	−0.0542326	−	0.162698i
$341$	10.0000			0.541530
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$	−3.00000	−	3.00000i	−0.161749	−	0.161749i
$345$		0			0
$346$	−11.0000	−	11.0000i	−0.591364	−	0.591364i
$347$	−3.00000	−	3.00000i	−0.161048	−	0.161048i	0.621983	−	0.783031i	$-0.286327\pi$
$347$	−3.00000	−	3.00000i	−0.161048	−	0.161048i	−0.783031	+	0.621983i	$0.786327\pi$
$348$		0			0
$349$	9.00000	−	9.00000i	0.481759	−	0.481759i	−0.423934	−	0.905693i	$-0.639351\pi$
$349$	9.00000	−	9.00000i	0.481759	−	0.481759i	0.905693	+	0.423934i	$0.139351\pi$
$350$	8.00000	−	6.00000i	0.427618	−	0.320713i
$351$		0			0
$352$	−5.00000	−	5.00000i	−0.266501	−	0.266501i
$353$		−	12.0000i		−	0.638696i	−0.947638	−	0.319348i	$-0.896536\pi$
$353$		−	12.0000i		−	0.638696i	0.947638	−	0.319348i	$-0.103464\pi$
$354$		0			0
$355$	1.00000	+	3.00000i	0.0530745	+	0.159223i
$356$	5.00000	−	5.00000i	0.264999	−	0.264999i
$357$		0			0
$358$	−20.0000			−1.05703
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	−0.733003	−	0.680225i	$-0.761882\pi$
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	0.680225	+	0.733003i	$0.261882\pi$
$360$		0			0
$361$			31.0000i			1.63158i
$362$			8.00000i			0.420471i
$363$		0			0
$364$	−4.00000	+	6.00000i	−0.209657	+	0.314485i
$365$	−10.0000	+	20.0000i	−0.523424	+	1.04685i
$366$		0			0
$367$	−1.00000	−	1.00000i	−0.0521996	−	0.0521996i	0.680525	−	0.732725i	$-0.261752\pi$
$367$	−1.00000	−	1.00000i	−0.0521996	−	0.0521996i	−0.732725	+	0.680525i	$0.761752\pi$
$368$	3.00000	+	3.00000i	0.156386	+	0.156386i
$369$		0			0
$370$		0			0
$371$	10.0000	+	10.0000i	0.519174	+	0.519174i
$372$		0			0
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	−0.979263	−	0.202593i	$-0.935063\pi$
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	0.202593	+	0.979263i	$0.435063\pi$
$374$	2.00000			0.103418
$375$		0			0
$376$		−	18.0000i		−	0.928279i
$377$		0			0
$378$		0			0
$379$	−1.00000	−	1.00000i	−0.0513665	−	0.0513665i	0.680957	−	0.732323i	$-0.261564\pi$
$379$	−1.00000	−	1.00000i	−0.0513665	−	0.0513665i	−0.732323	+	0.680957i	$0.761564\pi$
$380$	15.0000	−	5.00000i	0.769484	−	0.256495i
$381$		0			0
$382$	8.00000			0.409316
$383$		−	30.0000i		−	1.53293i	−0.642287	−	0.766464i	$-0.722014\pi$
$383$		−	30.0000i		−	1.53293i	0.642287	−	0.766464i	$-0.277986\pi$
$384$		0			0
$385$	−2.00000	−	6.00000i	−0.101929	−	0.305788i
$386$	−18.0000			−0.916176
$387$		0			0
$388$	−2.00000			−0.101535
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	9.00000			0.454569
$393$		0			0
$394$	6.00000			0.302276
$395$	−4.00000	−	2.00000i	−0.201262	−	0.100631i
$396$		0			0
$397$			16.0000i			0.803017i	0.915855	+	0.401508i	$0.131514\pi$
$397$			16.0000i			0.803017i	−0.915855	+	0.401508i	$0.868486\pi$
$398$	8.00000			0.401004
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	11.0000	+	11.0000i	0.549314	+	0.549314i	0.926242	−	0.376929i	$-0.123020\pi$
$401$	11.0000	+	11.0000i	0.549314	+	0.549314i	−0.376929	+	0.926242i	$0.623020\pi$
$402$		0			0
$403$	25.0000	−	5.00000i	1.24534	−	0.249068i
$404$			12.0000i			0.597022i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−7.00000	−	7.00000i	−0.346128	−	0.346128i	0.512537	−	0.858665i	$-0.328706\pi$
$409$	−7.00000	−	7.00000i	−0.346128	−	0.346128i	−0.858665	+	0.512537i	$0.828706\pi$
$410$	7.00000	+	21.0000i	0.345705	+	1.03712i
$411$		0			0
$412$	−7.00000	−	7.00000i	−0.344865	−	0.344865i
$413$	−14.0000	−	14.0000i	−0.688895	−	0.688895i
$414$		0			0
$415$	12.0000	+	6.00000i	0.589057	+	0.294528i
$416$	−15.0000	−	10.0000i	−0.735436	−	0.490290i
$417$		0			0
$418$			10.0000i			0.489116i
$419$			38.0000i			1.85642i	0.372055	+	0.928211i	$0.378653\pi$
$419$			38.0000i			1.85642i	−0.372055	+	0.928211i	$0.621347\pi$
$420$		0			0
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	−0.922383	−	0.386276i	$-0.873761\pi$
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	0.386276	+	0.922383i	$0.373761\pi$
$422$	−4.00000			−0.194717
$423$		0			0
$424$	−15.0000	+	15.0000i	−0.728464	+	0.728464i
$425$	7.00000	+	1.00000i	0.339550	+	0.0485071i
$426$		0			0
$427$			28.0000i			1.35501i
$428$	7.00000	+	7.00000i	0.338358	+	0.338358i
$429$		0			0
$430$	3.00000	−	1.00000i	0.144673	−	0.0482243i
$431$	−13.0000	+	13.0000i	−0.626188	+	0.626188i	−0.947107	−	0.320919i	$-0.896008\pi$
$431$	−13.0000	+	13.0000i	−0.626188	+	0.626188i	0.320919	+	0.947107i	$0.396008\pi$
$432$		0			0
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	0.985668	−	0.168700i	$-0.0539568\pi$
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	−0.168700	+	0.985668i	$0.553957\pi$
$434$	10.0000	+	10.0000i	0.480015	+	0.480015i
$435$		0			0
$436$	−9.00000	−	9.00000i	−0.431022	−	0.431022i
$437$			30.0000i			1.43509i
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	9.00000	−	3.00000i	0.429058	−	0.143019i
$441$		0			0
$442$	5.00000	−	1.00000i	0.237826	−	0.0475651i
$443$	−25.0000	+	25.0000i	−1.18779	+	1.18779i	−0.210108	+	0.977678i	$0.567381\pi$
$443$	−25.0000	+	25.0000i	−1.18779	+	1.18779i	−0.977678	+	0.210108i	$0.932619\pi$
$444$		0			0
$445$	5.00000	+	15.0000i	0.237023	+	0.711068i
$446$			2.00000i			0.0947027i
$447$		0			0
$448$		−	14.0000i		−	0.661438i
$449$	3.00000	−	3.00000i	0.141579	−	0.141579i	−0.632765	−	0.774344i	$-0.718080\pi$
$449$	3.00000	−	3.00000i	0.141579	−	0.141579i	0.774344	+	0.632765i	$0.218080\pi$
$450$		0			0
$451$	14.0000			0.659234
$452$	5.00000	−	5.00000i	0.235180	−	0.235180i
$453$		0			0
$454$	−12.0000			−0.563188
$455$	−8.00000	−	14.0000i	−0.375046	−	0.656330i
$456$		0			0
$457$	2.00000			0.0935561			0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000			0.0935561			0.0467780	+	0.998905i	$0.485105\pi$
$458$	3.00000	−	3.00000i	0.140181	−	0.140181i
$459$		0			0
$460$	9.00000	−	3.00000i	0.419627	−	0.139876i
$461$	−17.0000	+	17.0000i	−0.791769	+	0.791769i	−0.981782	−	0.190013i	$-0.939147\pi$
$461$	−17.0000	+	17.0000i	−0.791769	+	0.791769i	0.190013	+	0.981782i	$0.439147\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$		0			0
$465$		0			0
$466$	1.00000	+	1.00000i	0.0463241	+	0.0463241i
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	−0.883985	−	0.467515i	$-0.845149\pi$
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	0.467515	+	0.883985i	$0.345149\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$	12.0000	+	6.00000i	0.553519	+	0.276759i
$471$		0			0
$472$	21.0000	−	21.0000i	0.966603	−	0.966603i
$473$		−	2.00000i		−	0.0919601i
$474$		0			0
$475$	−5.00000	+	35.0000i	−0.229416	+	1.60591i
$476$	−2.00000	−	2.00000i	−0.0916698	−	0.0916698i
$477$		0			0
$478$	3.00000	+	3.00000i	0.137217	+	0.137217i
$479$	7.00000	−	7.00000i	0.319838	−	0.319838i	−0.528867	−	0.848705i	$-0.677383\pi$
$479$	7.00000	−	7.00000i	0.319838	−	0.319838i	0.848705	+	0.528867i	$0.177383\pi$
$480$		0			0
$481$		0			0
$482$	−17.0000	−	17.0000i	−0.774329	−	0.774329i
$483$		0			0
$484$			9.00000i			0.409091i
$485$	2.00000	−	4.00000i	0.0908153	−	0.181631i
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	−42.0000			−1.90125
$489$		0			0
$490$	−3.00000	+	6.00000i	−0.135526	+	0.271052i
$491$			22.0000i			0.992846i	0.868081	+	0.496423i	$0.165354\pi$
$491$			22.0000i			0.992846i	−0.868081	+	0.496423i	$0.834646\pi$
$492$		0			0
$493$		0			0
$494$	5.00000	+	25.0000i	0.224961	+	1.12480i
$495$		0			0
$496$	−5.00000	+	5.00000i	−0.224507	+	0.224507i
$497$	2.00000	+	2.00000i	0.0897123	+	0.0897123i
$498$		0			0
$499$	3.00000	+	3.00000i	0.134298	+	0.134298i	0.771060	−	0.636762i	$-0.219727\pi$
$499$	3.00000	+	3.00000i	0.134298	+	0.134298i	−0.636762	+	0.771060i	$0.719727\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$		0			0
$502$			2.00000i			0.0892644i
$503$	3.00000	−	3.00000i	0.133763	−	0.133763i	−0.637055	−	0.770818i	$-0.719848\pi$
$503$	3.00000	−	3.00000i	0.133763	−	0.133763i	0.770818	+	0.637055i	$0.219848\pi$
$504$		0			0
$505$	−24.0000	−	12.0000i	−1.06799	−	0.533993i
$506$			6.00000i			0.266733i
$507$		0			0
$508$	−9.00000	+	9.00000i	−0.399310	+	0.399310i
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	0.357643	−	0.933858i	$-0.383580\pi$
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	−0.933858	+	0.357643i	$0.883580\pi$
$510$		0			0
$511$			20.0000i			0.884748i
$512$	11.0000			0.486136
$513$		0			0
$514$	−11.0000	+	11.0000i	−0.485189	+	0.485189i
$515$	21.0000	−	7.00000i	0.925371	−	0.308457i
$516$		0			0
$517$	6.00000	−	6.00000i	0.263880	−	0.263880i
$518$		0			0
$519$		0			0
$520$	21.0000	−	12.0000i	0.920911	−	0.526235i
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$		0			0
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	−0.482405	−	0.875948i	$-0.660237\pi$
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	0.875948	+	0.482405i	$0.160237\pi$
$524$	−20.0000			−0.873704
$525$		0			0
$526$	1.00000	−	1.00000i	0.0436021	−	0.0436021i
$527$			10.0000i			0.435607i
$528$		0			0
$529$		−	5.00000i		−	0.217391i
$530$	−5.00000	−	15.0000i	−0.217186	−	0.651558i
$531$		0			0
$532$	10.0000	−	10.0000i	0.433555	−	0.433555i
$533$	35.0000	−	7.00000i	1.51602	−	0.303204i
$534$		0			0
$535$	−21.0000	+	7.00000i	−0.907909	+	0.302636i
$536$	−12.0000			−0.518321
$537$		0			0
$538$			12.0000i			0.517357i
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$		0			0
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	0.873595	−	0.486654i	$-0.161783\pi$
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	−0.486654	+	0.873595i	$0.661783\pi$
$542$	9.00000	+	9.00000i	0.386583	+	0.386583i
$543$		0			0
$544$	5.00000	−	5.00000i	0.214373	−	0.214373i
$545$	27.0000	−	9.00000i	1.15655	−	0.385518i
$546$		0			0
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	0.488020	−	0.872832i	$-0.337719\pi$
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	−0.872832	+	0.488020i	$0.837719\pi$
$548$		−	16.0000i		−	0.683486i
$549$		0			0
$550$	−1.00000	+	7.00000i	−0.0426401	+	0.298481i
$551$		0			0
$552$		0			0
$553$	−4.00000			−0.170097
$554$	15.0000	−	15.0000i	0.637289	−	0.637289i
$555$		0			0
$556$			14.0000i			0.593732i
$557$		−	24.0000i		−	1.01691i	−0.861088	−	0.508456i	$-0.830216\pi$
$557$		−	24.0000i		−	1.01691i	0.861088	−	0.508456i	$-0.169784\pi$
$558$		0			0
$559$	−1.00000	−	5.00000i	−0.0422955	−	0.211477i
$560$	4.00000	+	2.00000i	0.169031	+	0.0845154i
$561$		0			0
$562$	1.00000	+	1.00000i	0.0421825	+	0.0421825i
$563$	−15.0000	−	15.0000i	−0.632175	−	0.632175i	0.316438	−	0.948613i	$-0.397513\pi$
$563$	−15.0000	−	15.0000i	−0.632175	−	0.632175i	−0.948613	+	0.316438i	$0.897513\pi$
$564$		0			0
$565$	5.00000	+	15.0000i	0.210352	+	0.631055i
$566$	9.00000	+	9.00000i	0.378298	+	0.378298i
$567$		0			0
$568$	−3.00000	+	3.00000i	−0.125877	+	0.125877i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$		−	6.00000i		−	0.251092i	−0.992088	−	0.125546i	$-0.959932\pi$
$571$		−	6.00000i		−	0.251092i	0.992088	−	0.125546i	$-0.0400683\pi$
$572$	−1.00000	−	5.00000i	−0.0418121	−	0.209061i
$573$		0			0
$574$	14.0000	+	14.0000i	0.584349	+	0.584349i
$575$	−3.00000	+	21.0000i	−0.125109	+	0.875761i
$576$		0			0
$577$	46.0000			1.91501			0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000			1.91501			0.957503	+	0.288425i	$0.0931316\pi$
$578$		−	15.0000i		−	0.623918i
$579$		0			0
$580$		0			0
$581$	12.0000			0.497844
$582$		0			0
$583$	−10.0000			−0.414158
$584$	−30.0000			−1.24141
$585$		0			0
$586$	−6.00000			−0.247858
$587$	4.00000			0.165098			0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000			0.165098			0.0825488	+	0.996587i	$0.473694\pi$
$588$		0			0
$589$	−50.0000			−2.06021
$590$	7.00000	+	21.0000i	0.288185	+	0.864556i
$591$		0			0
$592$		0			0
$593$	−10.0000			−0.410651			−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000			−0.410651			−0.205325	+	0.978694i	$0.565825\pi$
$594$		0			0
$595$	6.00000	−	2.00000i	0.245976	−	0.0819920i
$596$	−3.00000	−	3.00000i	−0.122885	−	0.122885i
$597$		0			0
$598$	3.00000	+	15.0000i	0.122679	+	0.613396i
$599$		−	30.0000i		−	1.22577i	−0.790173	−	0.612883i	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$		0			0
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$	2.00000	−	2.00000i	0.0815139	−	0.0815139i
$603$		0			0
$604$	−7.00000	−	7.00000i	−0.284826	−	0.284826i
$605$	−18.0000	−	9.00000i	−0.731804	−	0.365902i
$606$		0			0
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	0.392218	−	0.919872i	$-0.371708\pi$
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	−0.919872	+	0.392218i	$0.871708\pi$
$608$	25.0000	+	25.0000i	1.01388	+	1.01388i
$609$		0			0
$610$	14.0000	−	28.0000i	0.566843	−	1.13369i
$611$	12.0000	−	18.0000i	0.485468	−	0.728202i
$612$		0			0
$613$			20.0000i			0.807792i	0.914805	+	0.403896i	$0.132344\pi$
$613$			20.0000i			0.807792i	−0.914805	+	0.403896i	$0.867656\pi$
$614$		−	18.0000i		−	0.726421i
$615$		0			0
$616$	6.00000	−	6.00000i	0.241747	−	0.241747i
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$		0			0
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.00484658	−	0.999988i	$-0.498457\pi$
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.999988	−	0.00484658i	$-0.00154272\pi$
$620$	5.00000	+	15.0000i	0.200805	+	0.602414i
$621$		0			0
$622$			6.00000i			0.240578i
$623$	10.0000	+	10.0000i	0.400642	+	0.400642i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−9.00000	+	9.00000i	−0.359712	+	0.359712i
$627$		0			0
$628$	−13.0000	−	13.0000i	−0.518756	−	0.518756i
$629$		0			0
$630$		0			0
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	0.891306	−	0.453403i	$-0.149790\pi$
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	−0.453403	+	0.891306i	$0.649790\pi$
$632$		−	6.00000i		−	0.238667i
$633$		0			0
$634$	−14.0000			−0.556011
$635$	−9.00000	−	27.0000i	−0.357154	−	1.07146i
$636$		0			0
$637$	9.00000	+	6.00000i	0.356593	+	0.237729i
$638$		0			0
$639$		0			0
$640$	3.00000	−	6.00000i	0.118585	−	0.237171i
$641$			24.0000i			0.947943i	0.880540	+	0.473972i	$0.157180\pi$
$641$			24.0000i			0.947943i	−0.880540	+	0.473972i	$0.842820\pi$
$642$		0			0
$643$			34.0000i			1.34083i	0.741987	+	0.670415i	$0.233884\pi$
$643$			34.0000i			1.34083i	−0.741987	+	0.670415i	$0.766116\pi$
$644$	6.00000	−	6.00000i	0.236433	−	0.236433i
$645$		0			0
$646$	−10.0000			−0.393445
$647$	−1.00000	+	1.00000i	−0.0393141	+	0.0393141i	−0.726491	−	0.687176i	$-0.758850\pi$
$647$	−1.00000	+	1.00000i	−0.0393141	+	0.0393141i	0.687176	+	0.726491i	$0.258850\pi$
$648$		0			0
$649$	14.0000			0.549548
$650$	1.00000	+	18.0000i	0.0392232	+	0.706018i
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−13.0000	+	13.0000i	−0.508729	+	0.508729i	−0.914136	−	0.405407i	$-0.867130\pi$
$653$	−13.0000	+	13.0000i	−0.508729	+	0.508729i	0.405407	+	0.914136i	$0.367130\pi$
$654$		0			0
$655$	20.0000	−	40.0000i	0.781465	−	1.56293i
$656$	−7.00000	+	7.00000i	−0.273304	+	0.273304i
$657$		0			0
$658$	12.0000			0.467809
$659$		−	26.0000i		−	1.01282i	−0.862294	−	0.506408i	$-0.830973\pi$
$659$		−	26.0000i		−	1.01282i	0.862294	−	0.506408i	$-0.169027\pi$
$660$		0			0
$661$	17.0000	+	17.0000i	0.661223	+	0.661223i	0.955668	−	0.294445i	$-0.0951348\pi$
$661$	17.0000	+	17.0000i	0.661223	+	0.661223i	−0.294445	+	0.955668i	$0.595135\pi$
$662$	3.00000	−	3.00000i	0.116598	−	0.116598i
$663$		0			0
$664$			18.0000i			0.698535i
$665$	10.0000	+	30.0000i	0.387783	+	1.16335i
$666$		0			0
$667$		0			0
$668$		−	18.0000i		−	0.696441i
$669$		0			0
$670$	4.00000	−	8.00000i	0.154533	−	0.309067i
$671$	−14.0000	−	14.0000i	−0.540464	−	0.540464i
$672$		0			0
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	0.356202	−	0.934409i	$-0.384072\pi$
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	−0.934409	+	0.356202i	$0.884072\pi$
$674$	−13.0000	+	13.0000i	−0.500741	+	0.500741i
$675$		0			0
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$	23.0000	+	23.0000i	0.883962	+	0.883962i	0.993935	−	0.109973i	$-0.0350764\pi$
$677$	23.0000	+	23.0000i	0.883962	+	0.883962i	−0.109973	+	0.993935i	$0.535076\pi$
$678$		0			0
$679$		−	4.00000i		−	0.153506i
$680$	3.00000	+	9.00000i	0.115045	+	0.345134i
$681$		0			0
$682$	−10.0000			−0.382920
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$	32.0000	+	16.0000i	1.22266	+	0.611329i
$686$			20.0000i			0.763604i
$687$		0			0
$688$	1.00000	+	1.00000i	0.0381246	+	0.0381246i
$689$	−25.0000	+	5.00000i	−0.952424	+	0.190485i
$690$		0			0
$691$	−3.00000	+	3.00000i	−0.114125	+	0.114125i	−0.761863	−	0.647738i	$-0.775715\pi$
$691$	−3.00000	+	3.00000i	−0.114125	+	0.114125i	0.647738	+	0.761863i	$0.275715\pi$
$692$	−11.0000	−	11.0000i	−0.418157	−	0.418157i
$693$		0			0
$694$	3.00000	+	3.00000i	0.113878	+	0.113878i
$695$	−28.0000	−	14.0000i	−1.06210	−	0.531050i
$696$		0			0
$697$			14.0000i			0.530288i
$698$	−9.00000	+	9.00000i	−0.340655	+	0.340655i
$699$		0			0
$700$	8.00000	−	6.00000i	0.302372	−	0.226779i
$701$		−	12.0000i		−	0.453234i	−0.973984	−	0.226617i	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$		0			0
$703$		0			0
$704$	7.00000	+	7.00000i	0.263822	+	0.263822i
$705$		0			0
$706$			12.0000i			0.451626i
$707$	−24.0000			−0.902613
$708$		0			0
$709$	29.0000	−	29.0000i	1.08912	−	1.08912i	0.0934984	−	0.995619i	$-0.470195\pi$
$709$	29.0000	−	29.0000i	1.08912	−	1.08912i	0.995619	−	0.0934984i	$-0.0298050\pi$
$710$	−1.00000	−	3.00000i	−0.0375293	−	0.112588i
$711$		0			0
$712$	−15.0000	+	15.0000i	−0.562149	+	0.562149i
$713$	−30.0000			−1.12351
$714$		0			0
$715$	11.0000	+	3.00000i	0.411377	+	0.112194i
$716$	−20.0000			−0.747435
$717$		0			0
$718$	1.00000	−	1.00000i	0.0373197	−	0.0373197i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$		0			0
$721$	14.0000	−	14.0000i	0.521387	−	0.521387i
$722$		−	31.0000i		−	1.15370i
$723$		0			0
$724$			8.00000i			0.297318i
$725$		0			0
$726$		0			0
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.368418	+	0.929660i	$0.620100\pi$
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.929660	+	0.368418i	$0.879900\pi$
$728$	12.0000	−	18.0000i	0.444750	−	0.667124i
$729$		0			0
$730$	10.0000	−	20.0000i	0.370117	−	0.740233i
$731$	2.00000			0.0739727
$732$		0			0
$733$			4.00000i			0.147743i	0.997268	+	0.0738717i	$0.0235355\pi$
$733$			4.00000i			0.147743i	−0.997268	+	0.0738717i	$0.976464\pi$
$734$	1.00000	+	1.00000i	0.0369107	+	0.0369107i
$735$		0			0
$736$	15.0000	+	15.0000i	0.552907	+	0.552907i
$737$	−4.00000	−	4.00000i	−0.147342	−	0.147342i
$738$		0			0
$739$	−3.00000	+	3.00000i	−0.110357	+	0.110357i	−0.760129	−	0.649772i	$-0.774864\pi$
$739$	−3.00000	+	3.00000i	−0.110357	+	0.110357i	0.649772	+	0.760129i	$0.274864\pi$
$740$		0			0
$741$		0			0
$742$	−10.0000	−	10.0000i	−0.367112	−	0.367112i
$743$			34.0000i			1.24734i	0.781688	+	0.623670i	$0.214359\pi$
$743$			34.0000i			1.24734i	−0.781688	+	0.623670i	$0.785641\pi$
$744$		0			0
$745$	9.00000	−	3.00000i	0.329734	−	0.109911i
$746$	15.0000	−	15.0000i	0.549189	−	0.549189i
$747$		0			0
$748$	2.00000			0.0731272
$749$	−14.0000	+	14.0000i	−0.511549	+	0.511549i
$750$		0			0
$751$		−	50.0000i		−	1.82453i	−0.409605	−	0.912263i	$-0.634333\pi$
$751$		−	50.0000i		−	1.82453i	0.409605	−	0.912263i	$-0.365667\pi$
$752$			6.00000i			0.218797i
$753$		0			0
$754$		0			0
$755$	21.0000	−	7.00000i	0.764268	−	0.254756i
$756$		0			0
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.327111	−	0.944986i	$-0.606075\pi$
$758$	1.00000	+	1.00000i	0.0363216	+	0.0363216i
$759$		0			0
$760$	−45.0000	+	15.0000i	−1.63232	+	0.544107i
$761$	7.00000	+	7.00000i	0.253750	+	0.253750i	0.822506	−	0.568756i	$-0.192575\pi$
$761$	7.00000	+	7.00000i	0.253750	+	0.253750i	−0.568756	+	0.822506i	$0.692575\pi$
$762$		0			0
$763$	18.0000	−	18.0000i	0.651644	−	0.651644i
$764$	8.00000			0.289430
$765$		0			0
$766$			30.0000i			1.08394i
$767$	35.0000	−	7.00000i	1.26378	−	0.252755i
$768$		0			0
$769$	−15.0000	−	15.0000i	−0.540914	−	0.540914i	0.382883	−	0.923797i	$-0.374931\pi$
$769$	−15.0000	−	15.0000i	−0.540914	−	0.540914i	−0.923797	+	0.382883i	$0.874931\pi$
$770$	2.00000	+	6.00000i	0.0720750	+	0.216225i
$771$		0			0
$772$	−18.0000			−0.647834
$773$		−	32.0000i		−	1.15096i	−0.817816	−	0.575480i	$-0.804815\pi$
$773$		−	32.0000i		−	1.15096i	0.817816	−	0.575480i	$-0.195185\pi$
$774$		0			0
$775$	−35.0000	−	5.00000i	−1.25724	−	0.179605i
$776$	6.00000			0.215387
$777$		0			0
$778$	−18.0000			−0.645331
$779$	−70.0000			−2.50801
$780$		0			0
$781$	−2.00000			−0.0715656
$782$	−6.00000			−0.214560
$783$		0			0
$784$	−3.00000			−0.107143
$785$	39.0000	−	13.0000i	1.39197	−	0.463990i
$786$		0			0
$787$		−	22.0000i		−	0.784215i	−0.919919	−	0.392108i	$-0.871746\pi$
$787$		−	22.0000i		−	0.784215i	0.919919	−	0.392108i	$-0.128254\pi$
$788$	6.00000			0.213741
$789$		0			0
$790$	4.00000	+	2.00000i	0.142314	+	0.0711568i
$791$	10.0000	+	10.0000i	0.355559	+	0.355559i
$792$		0			0
$793$	−42.0000	−	28.0000i	−1.49146	−	0.994309i
$794$		−	16.0000i		−	0.567819i
$795$		0			0
$796$	8.00000			0.283552
$797$	−17.0000	+	17.0000i	−0.602171	+	0.602171i	−0.940888	−	0.338717i	$-0.890007\pi$
$797$	−17.0000	+	17.0000i	−0.602171	+	0.602171i	0.338717	+	0.940888i	$0.390007\pi$
$798$		0			0
$799$	6.00000	+	6.00000i	0.212265	+	0.212265i
$800$	15.0000	+	20.0000i	0.530330	+	0.707107i
$801$		0			0
$802$	−11.0000	−	11.0000i	−0.388424	−	0.388424i
$803$	−10.0000	−	10.0000i	−0.352892	−	0.352892i
$804$		0			0
$805$	6.00000	+	18.0000i	0.211472	+	0.634417i
$806$	−25.0000	+	5.00000i	−0.880587	+	0.176117i
$807$		0			0
$808$		−	36.0000i		−	1.26648i
$809$		−	28.0000i		−	0.984428i	−0.870474	−	0.492214i	$-0.836188\pi$
$809$		−	28.0000i		−	0.984428i	0.870474	−	0.492214i	$-0.163812\pi$
$810$		0			0
$811$	−27.0000	+	27.0000i	−0.948098	+	0.948098i	−0.998718	−	0.0506198i	$-0.983880\pi$
$811$	−27.0000	+	27.0000i	−0.948098	+	0.948098i	0.0506198	+	0.998718i	$0.483880\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4.00000	−	8.00000i	0.140114	−	0.280228i
$816$		0			0
$817$			10.0000i			0.349856i
$818$	7.00000	+	7.00000i	0.244749	+	0.244749i
$819$		0			0
$820$	7.00000	+	21.0000i	0.244451	+	0.733352i
$821$	−9.00000	+	9.00000i	−0.314102	+	0.314102i	−0.846496	−	0.532394i	$-0.821292\pi$
$821$	−9.00000	+	9.00000i	−0.314102	+	0.314102i	0.532394	+	0.846496i	$0.321292\pi$
$822$		0			0
$823$	−9.00000	−	9.00000i	−0.313720	−	0.313720i	0.532629	−	0.846349i	$-0.321204\pi$
$823$	−9.00000	−	9.00000i	−0.313720	−	0.313720i	−0.846349	+	0.532629i	$0.821204\pi$
$824$	21.0000	+	21.0000i	0.731570	+	0.731570i
$825$		0			0
$826$	14.0000	+	14.0000i	0.487122	+	0.487122i
$827$			46.0000i			1.59958i	0.600282	+	0.799788i	$0.295055\pi$
$827$			46.0000i			1.59958i	−0.600282	+	0.799788i	$0.704945\pi$
$828$		0			0
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	−12.0000	−	6.00000i	−0.416526	−	0.208263i
$831$		0			0
$832$	21.0000	+	14.0000i	0.728044	+	0.485363i
$833$	−3.00000	+	3.00000i	−0.103944	+	0.103944i
$834$		0			0
$835$	36.0000	+	18.0000i	1.24583	+	0.622916i
$836$			10.0000i			0.345857i
$837$		0			0
$838$		−	38.0000i		−	1.31269i
$839$	35.0000	−	35.0000i	1.20833	−	1.20833i	0.236768	−	0.971566i	$-0.423912\pi$
$839$	35.0000	−	35.0000i	1.20833	−	1.20833i	0.971566	−	0.236768i	$-0.0760881\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	11.0000	−	11.0000i	0.379085	−	0.379085i
$843$		0			0
$844$	−4.00000			−0.137686
$845$	29.0000	+	2.00000i	0.997630	+	0.0688021i
$846$		0			0
$847$	−18.0000			−0.618487
$848$	5.00000	−	5.00000i	0.171701	−	0.171701i
$849$		0			0
$850$	−7.00000	−	1.00000i	−0.240098	−	0.0342997i
$851$		0			0
$852$		0			0
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$		−	28.0000i		−	0.958140i
$855$		0			0
$856$	−21.0000	−	21.0000i	−0.717765	−	0.717765i
$857$	3.00000	−	3.00000i	0.102478	−	0.102478i	−0.654009	−	0.756487i	$-0.726914\pi$
$857$	3.00000	−	3.00000i	0.102478	−	0.102478i	0.756487	+	0.654009i	$0.226914\pi$
$858$		0			0
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	3.00000	−	1.00000i	0.102299	−	0.0340997i
$861$		0			0
$862$	13.0000	−	13.0000i	0.442782	−	0.442782i
$863$		−	30.0000i		−	1.02121i	−0.859815	−	0.510606i	$-0.829421\pi$
$863$		−	30.0000i		−	1.02121i	0.859815	−	0.510606i	$-0.170579\pi$
$864$		0			0
$865$	33.0000	−	11.0000i	1.12203	−	0.374011i
$866$	−17.0000	−	17.0000i	−0.577684	−	0.577684i
$867$		0			0
$868$	10.0000	+	10.0000i	0.339422	+	0.339422i
$869$	2.00000	−	2.00000i	0.0678454	−	0.0678454i
$870$		0			0
$871$	−12.0000	−	8.00000i	−0.406604	−	0.271070i
$872$	27.0000	+	27.0000i	0.914335	+	0.914335i
$873$		0			0
$874$		−	30.0000i		−	1.01477i
$875$	4.00000	+	22.0000i	0.135225	+	0.743736i
$876$		0			0
$877$	38.0000			1.28317			0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000			1.28317			0.641584	+	0.767052i	$0.278277\pi$
$878$		0			0
$879$		0			0
$880$	−3.00000	+	1.00000i	−0.101130	+	0.0337100i
$881$			52.0000i			1.75192i	0.482380	+	0.875962i	$0.339773\pi$
$881$			52.0000i			1.75192i	−0.482380	+	0.875962i	$0.660227\pi$
$882$		0			0
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.919601	+	0.392853i	$0.128512\pi$
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.392853	+	0.919601i	$0.371488\pi$
$884$	5.00000	−	1.00000i	0.168168	−	0.0336336i
$885$		0			0
$886$	25.0000	−	25.0000i	0.839891	−	0.839891i
$887$	1.00000	+	1.00000i	0.0335767	+	0.0335767i	0.723696	−	0.690119i	$-0.242442\pi$
$887$	1.00000	+	1.00000i	0.0335767	+	0.0335767i	−0.690119	+	0.723696i	$0.742442\pi$
$888$		0			0
$889$	−18.0000	−	18.0000i	−0.603701	−	0.603701i
$890$	−5.00000	−	15.0000i	−0.167600	−	0.502801i
$891$		0			0
$892$			2.00000i			0.0669650i
$893$	−30.0000	+	30.0000i	−1.00391	+	1.00391i
$894$		0			0
$895$	20.0000	−	40.0000i	0.668526	−	1.33705i
$896$		−	6.00000i		−	0.200446i
$897$		0			0
$898$	−3.00000	+	3.00000i	−0.100111	+	0.100111i
$899$		0			0
$900$		0			0
$901$		−	10.0000i		−	0.333148i
$902$	−14.0000			−0.466149
$903$		0			0
$904$	−15.0000	+	15.0000i	−0.498893	+	0.498893i
$905$	−16.0000	−	8.00000i	−0.531858	−	0.265929i
$906$		0			0
$907$	−39.0000	+	39.0000i	−1.29497	+	1.29497i	−0.363303	+	0.931671i	$0.618351\pi$
$907$	−39.0000	+	39.0000i	−1.29497	+	1.29497i	−0.931671	+	0.363303i	$0.881649\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$	8.00000	+	14.0000i	0.265197	+	0.464095i
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		0			0
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$	−2.00000			−0.0661541
$915$		0			0
$916$	3.00000	−	3.00000i	0.0991228	−	0.0991228i
$917$		−	40.0000i		−	1.32092i
$918$		0			0
$919$		−	10.0000i		−	0.329870i	−0.986304	−	0.164935i	$-0.947259\pi$
$919$		−	10.0000i		−	0.329870i	0.986304	−	0.164935i	$-0.0527414\pi$
$920$	−27.0000	+	9.00000i	−0.890164	+	0.296721i
$921$		0			0
$922$	17.0000	−	17.0000i	0.559865	−	0.559865i
$923$	−5.00000	+	1.00000i	−0.164577	+	0.0329154i
$924$		0			0
$925$		0			0
$926$	24.0000			0.788689
$927$		0			0
$928$		0			0
$929$	19.0000	+	19.0000i	0.623370	+	0.623370i	0.946392	−	0.323022i	$-0.104699\pi$
$929$	19.0000	+	19.0000i	0.623370	+	0.623370i	−0.323022	+	0.946392i	$0.604699\pi$
$930$		0			0
$931$	−15.0000	−	15.0000i	−0.491605	−	0.491605i
$932$	1.00000	+	1.00000i	0.0327561	+	0.0327561i
$933$		0			0
$934$	9.00000	−	9.00000i	0.294489	−	0.294489i
$935$	−2.00000	+	4.00000i	−0.0654070	+	0.130814i
$936$		0			0
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	0.583461	−	0.812141i	$-0.301698\pi$
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	−0.812141	+	0.583461i	$0.801698\pi$
$938$		−	8.00000i		−	0.261209i
$939$		0			0
$940$	12.0000	+	6.00000i	0.391397	+	0.195698i
$941$	−21.0000	+	21.0000i	−0.684580	+	0.684580i	−0.961029	−	0.276448i	$-0.910843\pi$
$941$	−21.0000	+	21.0000i	−0.684580	+	0.684580i	0.276448	+	0.961029i	$0.410843\pi$
$942$		0			0
$943$	−42.0000			−1.36771
$944$	−7.00000	+	7.00000i	−0.227831	+	0.227831i
$945$		0			0
$946$			2.00000i			0.0650256i
$947$		−	18.0000i		−	0.584921i	−0.956278	−	0.292461i	$-0.905526\pi$
$947$		−	18.0000i		−	0.584921i	0.956278	−	0.292461i	$-0.0944741\pi$
$948$		0			0
$949$	−30.0000	−	20.0000i	−0.973841	−	0.649227i
$950$	5.00000	−	35.0000i	0.162221	−	1.13555i
$951$		0			0
$952$	6.00000	+	6.00000i	0.194461	+	0.194461i
$953$	−13.0000	−	13.0000i	−0.421111	−	0.421111i	0.464475	−	0.885586i	$-0.346243\pi$
$953$	−13.0000	−	13.0000i	−0.421111	−	0.421111i	−0.885586	+	0.464475i	$0.846243\pi$
$954$		0			0
$955$	−8.00000	+	16.0000i	−0.258874	+	0.517748i
$956$	3.00000	+	3.00000i	0.0970269	+	0.0970269i
$957$		0			0
$958$	−7.00000	+	7.00000i	−0.226160	+	0.226160i
$959$	32.0000			1.03333
$960$		0			0
$961$		−	19.0000i		−	0.612903i
$962$		0			0
$963$		0			0
$964$	−17.0000	−	17.0000i	−0.547533	−	0.547533i
$965$	18.0000	−	36.0000i	0.579441	−	1.15888i
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$		−	27.0000i		−	0.867813i
$969$		0			0
$970$	−2.00000	+	4.00000i	−0.0642161	+	0.128432i
$971$	60.0000			1.92549			0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000			1.92549			0.962746	+	0.270408i	$0.0871586\pi$
$972$		0			0
$973$	−28.0000			−0.897639
$974$	−16.0000			−0.512673
$975$		0			0
$976$	14.0000			0.448129
$977$	−62.0000			−1.98356			−0.991778	−	0.127971i	$-0.959153\pi$
$977$	−62.0000			−1.98356			−0.991778	+	0.127971i	$0.959153\pi$
$978$		0			0
$979$	−10.0000			−0.319601
$980$	−3.00000	+	6.00000i	−0.0958315	+	0.191663i
$981$		0			0
$982$		−	22.0000i		−	0.702048i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$		0			0
$985$	−6.00000	+	12.0000i	−0.191176	+	0.382352i
$986$		0			0
$987$		0			0
$988$	5.00000	+	25.0000i	0.159071	+	0.795356i
$989$			6.00000i			0.190789i
$990$		0			0
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$	−25.0000	+	25.0000i	−0.793751	+	0.793751i
$993$		0			0
$994$	−2.00000	−	2.00000i	−0.0634361	−	0.0634361i
$995$	−8.00000	+	16.0000i	−0.253617	+	0.507234i
$996$		0			0
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	0.835112	−	0.550079i	$-0.185403\pi$
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	−0.550079	+	0.835112i	$0.685403\pi$
$998$	−3.00000	−	3.00000i	−0.0949633	−	0.0949633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.w.b.577.1		2
3.2	odd	2		65.2.k.a.57.1	yes	2
5.3	odd	4		585.2.n.c.343.1		2
12.11	even	2		1040.2.bg.a.577.1		2
13.8	odd	4		585.2.n.c.307.1		2
15.2	even	4		325.2.f.a.18.1		2
15.8	even	4		65.2.f.a.18.1	✓	2
15.14	odd	2		325.2.k.a.57.1		2
39.2	even	12		845.2.t.b.657.1		4
39.5	even	4		845.2.f.a.437.1		2
39.8	even	4		65.2.f.a.47.1	yes	2
39.11	even	12		845.2.t.a.657.1		4
39.17	odd	6		845.2.o.b.587.1		4
39.20	even	12		845.2.t.a.427.1		4
39.23	odd	6		845.2.o.b.357.1		4
39.29	odd	6		845.2.o.a.357.1		4
39.32	even	12		845.2.t.b.427.1		4
39.35	odd	6		845.2.o.a.587.1		4
39.38	odd	2		845.2.k.a.577.1		2
60.23	odd	4		1040.2.cd.b.993.1		2
65.8	even	4	inner	585.2.w.b.73.1		2
156.47	odd	4		1040.2.cd.b.177.1		2
195.8	odd	4		65.2.k.a.8.1	yes	2
195.23	even	12		845.2.t.b.188.1		4
195.38	even	4		845.2.f.a.408.1		2
195.47	odd	4		325.2.k.a.268.1		2
195.68	even	12		845.2.t.a.188.1		4
195.83	odd	4		845.2.k.a.268.1		2
195.98	odd	12		845.2.o.a.258.1		4
195.113	even	12		845.2.t.a.418.1		4
195.128	odd	12		845.2.o.a.488.1		4
195.158	odd	12		845.2.o.b.488.1		4
195.164	even	4		325.2.f.a.307.1		2
195.173	even	12		845.2.t.b.418.1		4
195.188	odd	12		845.2.o.b.258.1		4
780.203	even	4		1040.2.bg.a.593.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	15.8	even	4
65.2.f.a.47.1	yes	2	39.8	even	4
65.2.k.a.8.1	yes	2	195.8	odd	4
65.2.k.a.57.1	yes	2	3.2	odd	2
325.2.f.a.18.1		2	15.2	even	4
325.2.f.a.307.1		2	195.164	even	4
325.2.k.a.57.1		2	15.14	odd	2
325.2.k.a.268.1		2	195.47	odd	4
585.2.n.c.307.1		2	13.8	odd	4
585.2.n.c.343.1		2	5.3	odd	4
585.2.w.b.73.1		2	65.8	even	4	inner
585.2.w.b.577.1		2	1.1	even	1	trivial
845.2.f.a.408.1		2	195.38	even	4
845.2.f.a.437.1		2	39.5	even	4
845.2.k.a.268.1		2	195.83	odd	4
845.2.k.a.577.1		2	39.38	odd	2
845.2.o.a.258.1		4	195.98	odd	12
845.2.o.a.357.1		4	39.29	odd	6
845.2.o.a.488.1		4	195.128	odd	12
845.2.o.a.587.1		4	39.35	odd	6
845.2.o.b.258.1		4	195.188	odd	12
845.2.o.b.357.1		4	39.23	odd	6
845.2.o.b.488.1		4	195.158	odd	12
845.2.o.b.587.1		4	39.17	odd	6
845.2.t.a.188.1		4	195.68	even	12
845.2.t.a.418.1		4	195.113	even	12
845.2.t.a.427.1		4	39.20	even	12
845.2.t.a.657.1		4	39.11	even	12
845.2.t.b.188.1		4	195.23	even	12
845.2.t.b.418.1		4	195.173	even	12
845.2.t.b.427.1		4	39.32	even	12
845.2.t.b.657.1		4	39.2	even	12
1040.2.bg.a.577.1		2	12.11	even	2
1040.2.bg.a.593.1		2	780.203	even	4
1040.2.cd.b.177.1		2	156.47	odd	4
1040.2.cd.b.993.1		2	60.23	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} -2.00000i q^{7} +3.00000 q^{8} +(-1.00000 + 2.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(3.00000 + 2.00000i) q^{13} +2.00000i q^{14} -1.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} +(-5.00000 - 5.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(-1.00000 - 1.00000i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +2.00000i q^{28} +(5.00000 - 5.00000i) q^{31} -5.00000 q^{32} +(1.00000 - 1.00000i) q^{34} +(-4.00000 - 2.00000i) q^{35} +(5.00000 + 5.00000i) q^{38} +(3.00000 - 6.00000i) q^{40} +(7.00000 - 7.00000i) q^{41} +(-1.00000 - 1.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(3.00000 + 3.00000i) q^{46} -6.00000i q^{47} +3.00000 q^{49} +(3.00000 + 4.00000i) q^{50} +(-3.00000 - 2.00000i) q^{52} +(-5.00000 + 5.00000i) q^{53} +(3.00000 - 1.00000i) q^{55} -6.00000i q^{56} +(7.00000 - 7.00000i) q^{59} -14.0000 q^{61} +(-5.00000 + 5.00000i) q^{62} +7.00000 q^{64} +(7.00000 - 4.00000i) q^{65} -4.00000 q^{67} +(1.00000 - 1.00000i) q^{68} +(4.00000 + 2.00000i) q^{70} +(-1.00000 + 1.00000i) q^{71} -10.0000 q^{73} +(5.00000 + 5.00000i) q^{76} +(2.00000 - 2.00000i) q^{77} -2.00000i q^{79} +(-1.00000 + 2.00000i) q^{80} +(-7.00000 + 7.00000i) q^{82} +6.00000i q^{83} +(1.00000 + 3.00000i) q^{85} +(1.00000 + 1.00000i) q^{86} +(3.00000 + 3.00000i) q^{88} +(-5.00000 + 5.00000i) q^{89} +(4.00000 - 6.00000i) q^{91} +(3.00000 + 3.00000i) q^{92} +6.00000i q^{94} +(-15.0000 + 5.00000i) q^{95} +2.00000 q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 6 q^{8} - 2 q^{10} + 2 q^{11} + 6 q^{13} - 2 q^{16} - 2 q^{17} - 10 q^{19} - 2 q^{20} - 2 q^{22} - 6 q^{23} - 6 q^{25} - 6 q^{26} + 10 q^{31} - 10 q^{32} + 2 q^{34} - 8 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 6 * q^8 - 2 * q^10 + 2 * q^11 + 6 * q^13 - 2 * q^16 - 2 * q^17 - 10 * q^19 - 2 * q^20 - 2 * q^22 - 6 * q^23 - 6 * q^25 - 6 * q^26 + 10 * q^31 - 10 * q^32 + 2 * q^34 - 8 * q^35 + 10 * q^38 + 6 * q^40 + 14 * q^41 - 2 * q^43 - 2 * q^44 + 6 * q^46 + 6 * q^49 + 6 * q^50 - 6 * q^52 - 10 * q^53 + 6 * q^55 + 14 * q^59 - 28 * q^61 - 10 * q^62 + 14 * q^64 + 14 * q^65 - 8 * q^67 + 2 * q^68 + 8 * q^70 - 2 * q^71 - 20 * q^73 + 10 * q^76 + 4 * q^77 - 2 * q^80 - 14 * q^82 + 2 * q^85 + 2 * q^86 + 6 * q^88 - 10 * q^89 + 8 * q^91 + 6 * q^92 - 30 * q^95 + 4 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more