LMFDB - Embedded newform 684.3.m.a.353.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.6
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.74110 - 1.21916i) q^{3} -1.38038i q^{5} +(-1.29258 + 2.23881i) q^{7} +(6.02728 + 6.68370i) q^{9} +O(q^{10})$	\(q+(-2.74110 - 1.21916i) q^{3} -1.38038i q^{5} +(-1.29258 + 2.23881i) q^{7} +(6.02728 + 6.68370i) q^{9} +(-3.36484 - 1.94269i) q^{11} +(-1.06693 + 1.84798i) q^{13} +(-1.68291 + 3.78377i) q^{15} +(-10.4602 - 6.03918i) q^{17} +(18.7458 + 3.09785i) q^{19} +(6.27255 - 4.56093i) q^{21} +(8.68045 + 5.01166i) q^{23} +23.0945 q^{25} +(-8.37286 - 25.6690i) q^{27} +55.1072i q^{29} +(-4.94828 - 8.57068i) q^{31} +(6.85492 + 9.42741i) q^{33} +(3.09041 + 1.78425i) q^{35} -7.98205 q^{37} +(5.17756 - 3.76474i) q^{39} -46.5218i q^{41} +(-35.4681 - 61.4325i) q^{43} +(9.22606 - 8.31995i) q^{45} -63.5847i q^{47} +(21.1585 + 36.6476i) q^{49} +(21.3096 + 29.3067i) q^{51} +(87.4751 - 50.5037i) q^{53} +(-2.68166 + 4.64477i) q^{55} +(-47.6072 - 31.3457i) q^{57} -65.8518i q^{59} +83.3834 q^{61} +(-22.7542 + 4.85472i) q^{63} +(2.55092 + 1.47277i) q^{65} +(51.4627 - 89.1360i) q^{67} +(-17.6840 - 24.3204i) q^{69} +(-96.3301 - 55.6162i) q^{71} +(31.7504 - 54.9933i) q^{73} +(-63.3045 - 28.1560i) q^{75} +(8.69862 - 5.02215i) q^{77} +(46.1044 + 79.8551i) q^{79} +(-8.34378 + 80.5691i) q^{81} +(86.6071 + 50.0027i) q^{83} +(-8.33637 + 14.4390i) q^{85} +(67.1847 - 151.055i) q^{87} +(-22.4872 + 12.9830i) q^{89} +(-2.75818 - 4.77731i) q^{91} +(3.11469 + 29.5259i) q^{93} +(4.27621 - 25.8763i) q^{95} +(47.1806 + 81.7192i) q^{97} +(-7.29647 - 34.1988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.74110	−	1.21916i	−0.913701	−	0.406388i
$3$	−2.74110	−	1.21916i	−0.913701	−	0.406388i
$4$		0			0
$5$		−	1.38038i		−	0.276076i	−0.990427	−	0.138038i	$-0.955920\pi$
$5$		−	1.38038i		−	0.276076i	0.990427	−	0.138038i	$-0.0440797\pi$
$6$		0			0
$7$	−1.29258	+	2.23881i	−0.184654	+	0.319829i	−0.943460	−	0.331487i	$-0.892450\pi$
$7$	−1.29258	+	2.23881i	−0.184654	+	0.319829i	0.758806	+	0.651317i	$0.225783\pi$
$8$		0			0
$9$	6.02728	+	6.68370i	0.669698	+	0.742634i
$10$		0			0
$11$	−3.36484	−	1.94269i	−0.305895	−	0.176608i	0.339193	−	0.940717i	$-0.389846\pi$
$11$	−3.36484	−	1.94269i	−0.305895	−	0.176608i	−0.645088	+	0.764108i	$0.723179\pi$
$12$		0			0
$13$	−1.06693	+	1.84798i	−0.0820717	+	0.142152i	−0.904140	−	0.427237i	$-0.859487\pi$
$13$	−1.06693	+	1.84798i	−0.0820717	+	0.142152i	0.822068	+	0.569389i	$0.192820\pi$
$14$		0			0
$15$	−1.68291	+	3.78377i	−0.112194	+	0.252251i
$16$		0			0
$17$	−10.4602	−	6.03918i	−0.615304	−	0.355246i	0.159734	−	0.987160i	$-0.448936\pi$
$17$	−10.4602	−	6.03918i	−0.615304	−	0.355246i	−0.775038	+	0.631914i	$0.782270\pi$
$18$		0			0
$19$	18.7458	+	3.09785i	0.986619	+	0.163045i
$19$	18.7458	+	3.09785i	0.986619	+	0.163045i
$20$		0			0
$21$	6.27255	−	4.56093i	0.298693	−	0.217187i
$22$		0			0
$23$	8.68045	+	5.01166i	0.377411	+	0.217898i	0.676691	−	0.736267i	$-0.263413\pi$
$23$	8.68045	+	5.01166i	0.377411	+	0.217898i	−0.299280	+	0.954165i	$0.596747\pi$
$24$		0			0
$25$	23.0945			0.923782
$26$		0			0
$27$	−8.37286	−	25.6690i	−0.310106	−	0.950702i
$28$		0			0
$29$			55.1072i			1.90025i	0.311870	+	0.950125i	$0.399045\pi$
$29$			55.1072i			1.90025i	−0.311870	+	0.950125i	$0.600955\pi$
$30$		0			0
$31$	−4.94828	−	8.57068i	−0.159622	−	0.276473i	0.775110	−	0.631826i	$-0.217694\pi$
$31$	−4.94828	−	8.57068i	−0.159622	−	0.276473i	−0.934732	+	0.355352i	$0.884361\pi$
$32$		0			0
$33$	6.85492	+	9.42741i	0.207725	+	0.285679i
$34$		0			0
$35$	3.09041	+	1.78425i	0.0882973	+	0.0509785i
$36$		0			0
$37$	−7.98205			−0.215731			−0.107866	−	0.994165i	$-0.534402\pi$
$37$	−7.98205			−0.215731			−0.107866	+	0.994165i	$0.534402\pi$
$38$		0			0
$39$	5.17756	−	3.76474i	0.132758	−	0.0965318i
$40$		0			0
$41$		−	46.5218i		−	1.13468i	−0.823484	−	0.567339i	$-0.807973\pi$
$41$		−	46.5218i		−	1.13468i	0.823484	−	0.567339i	$-0.192027\pi$
$42$		0			0
$43$	−35.4681	−	61.4325i	−0.824839	−	1.42866i	−0.902043	−	0.431647i	$-0.857933\pi$
$43$	−35.4681	−	61.4325i	−0.824839	−	1.42866i	0.0772040	−	0.997015i	$-0.475401\pi$
$44$		0			0
$45$	9.22606	−	8.31995i	0.205024	−	0.184888i
$46$		0			0
$47$		−	63.5847i		−	1.35287i	−0.736504	−	0.676433i	$-0.763525\pi$
$47$		−	63.5847i		−	1.35287i	0.736504	−	0.676433i	$-0.236475\pi$
$48$		0			0
$49$	21.1585	+	36.6476i	0.431806	+	0.747910i
$50$		0			0
$51$	21.3096	+	29.3067i	0.417836	+	0.574640i
$52$		0			0
$53$	87.4751	−	50.5037i	1.65047	−	0.952901i	0.673596	−	0.739100i	$-0.264749\pi$
$53$	87.4751	−	50.5037i	1.65047	−	0.952901i	0.976877	−	0.213801i	$-0.0685843\pi$
$54$		0			0
$55$	−2.68166	+	4.64477i	−0.0487574	+	0.0844503i
$56$		0			0
$57$	−47.6072	−	31.3457i	−0.835215	−	0.549924i
$58$		0			0
$59$		−	65.8518i		−	1.11613i	−0.829797	−	0.558066i	$-0.811544\pi$
$59$		−	65.8518i		−	1.11613i	0.829797	−	0.558066i	$-0.188456\pi$
$60$		0			0
$61$	83.3834			1.36694			0.683471	−	0.729978i	$-0.260470\pi$
$61$	83.3834			1.36694			0.683471	+	0.729978i	$0.260470\pi$
$62$		0			0
$63$	−22.7542	+	4.85472i	−0.361178	+	0.0770591i
$64$		0			0
$65$	2.55092	+	1.47277i	0.0392449	+	0.0226580i
$66$		0			0
$67$	51.4627	−	89.1360i	0.768100	−	1.33039i	−0.170492	−	0.985359i	$-0.554536\pi$
$67$	51.4627	−	89.1360i	0.768100	−	1.33039i	0.938592	−	0.345029i	$-0.112131\pi$
$68$		0			0
$69$	−17.6840	−	24.3204i	−0.256289	−	0.352469i
$70$		0			0
$71$	−96.3301	−	55.6162i	−1.35676	−	0.783327i	−0.367576	−	0.929993i	$-0.619812\pi$
$71$	−96.3301	−	55.6162i	−1.35676	−	0.783327i	−0.989186	+	0.146666i	$0.953146\pi$
$72$		0			0
$73$	31.7504	−	54.9933i	0.434937	−	0.753333i	−0.562353	−	0.826897i	$-0.690104\pi$
$73$	31.7504	−	54.9933i	0.434937	−	0.753333i	0.997291	+	0.0735638i	$0.0234372\pi$
$74$		0			0
$75$	−63.3045	−	28.1560i	−0.844060	−	0.375414i
$76$		0			0
$77$	8.69862	−	5.02215i	0.112969	−	0.0652228i
$78$		0			0
$79$	46.1044	+	79.8551i	0.583600	+	1.01082i	0.995048	+	0.0993912i	$0.0316895\pi$
$79$	46.1044	+	79.8551i	0.583600	+	1.01082i	−0.411449	+	0.911433i	$0.634977\pi$
$80$		0			0
$81$	−8.34378	+	80.5691i	−0.103010	+	0.994680i
$82$		0			0
$83$	86.6071	+	50.0027i	1.04346	+	0.602442i	0.920811	−	0.390009i	$-0.127528\pi$
$83$	86.6071	+	50.0027i	1.04346	+	0.602442i	0.122648	+	0.992450i	$0.460861\pi$
$84$		0			0
$85$	−8.33637	+	14.4390i	−0.0980750	+	0.169871i
$86$		0			0
$87$	67.1847	−	151.055i	0.772238	−	1.73626i
$88$		0			0
$89$	−22.4872	+	12.9830i	−0.252665	+	0.145876i	−0.620984	−	0.783823i	$-0.713267\pi$
$89$	−22.4872	+	12.9830i	−0.252665	+	0.145876i	0.368319	+	0.929700i	$0.379934\pi$
$90$		0			0
$91$	−2.75818	−	4.77731i	−0.0303097	−	0.0524979i
$92$		0			0
$93$	3.11469	+	29.5259i	0.0334913	+	0.317482i
$94$		0			0
$95$	4.27621	−	25.8763i	0.0450128	−	0.272382i
$96$		0			0
$97$	47.1806	+	81.7192i	0.486398	+	0.842466i	0.999878	−	0.0156355i	$-0.00497712\pi$
$97$	47.1806	+	81.7192i	0.486398	+	0.842466i	−0.513480	+	0.858102i	$0.671644\pi$
$98$		0			0
$99$	−7.29647	−	34.1988i	−0.0737017	−	0.345442i
$100$		0			0
$101$		−	121.912i		−	1.20705i	−0.797346	−	0.603523i	$-0.793763\pi$
$101$		−	121.912i		−	1.20705i	0.797346	−	0.603523i	$-0.206237\pi$
$102$		0			0
$103$	48.8611	+	84.6299i	0.474380	+	0.821649i	0.999570	−	0.0293355i	$-0.00933911\pi$
$103$	48.8611	+	84.6299i	0.474380	+	0.821649i	−0.525190	+	0.850985i	$0.676006\pi$
$104$		0			0
$105$	−6.29583	−	8.65851i	−0.0599603	−	0.0824620i
$106$		0			0
$107$		−	47.3728i		−	0.442736i	−0.975190	−	0.221368i	$-0.928948\pi$
$107$		−	47.3728i		−	0.442736i	0.975190	−	0.221368i	$-0.0710523\pi$
$108$		0			0
$109$	3.40177	−	5.89204i	0.0312089	−	0.0540554i	−0.849999	−	0.526784i	$-0.823398\pi$
$109$	3.40177	−	5.89204i	0.0312089	−	0.0540554i	0.881208	+	0.472729i	$0.156731\pi$
$110$		0			0
$111$	21.8796	+	9.73143i	0.197114	+	0.0876705i
$112$		0			0
$113$	28.1324	−	16.2423i	0.248960	−	0.143737i	−0.370328	−	0.928901i	$-0.620755\pi$
$113$	28.1324	−	16.2423i	0.248960	−	0.143737i	0.619288	+	0.785164i	$0.287421\pi$
$114$		0			0
$115$	6.91800	−	11.9823i	0.0601565	−	0.104194i
$116$		0			0
$117$	−18.7821	+	4.00724i	−0.160530	+	0.0342499i
$118$		0			0
$119$	27.0411	−	15.6122i	0.227236	−	0.131195i
$120$		0			0
$121$	−52.9519	−	91.7154i	−0.437619	−	0.757978i
$122$		0			0
$123$	−56.7177	+	127.521i	−0.461120	+	1.03676i
$124$		0			0
$125$		−	66.3888i		−	0.531111i
$126$		0			0
$127$	1.47267	+	2.55073i	0.0115958	+	0.0200845i	0.871765	−	0.489924i	$-0.162976\pi$
$127$	1.47267	+	2.55073i	0.0115958	+	0.0200845i	−0.860169	+	0.510009i	$0.829642\pi$
$128$		0			0
$129$	22.3253	+	211.634i	0.173065	+	1.64057i
$130$		0			0
$131$		−	135.584i		−	1.03499i	−0.855685	−	0.517496i	$-0.826864\pi$
$131$		−	135.584i		−	1.03499i	0.855685	−	0.517496i	$-0.173136\pi$
$132$		0			0
$133$	−31.1658	+	37.9639i	−0.234329	+	0.285443i
$134$		0			0
$135$	−35.4329	+	11.5577i	−0.262466	+	0.0856129i
$136$		0			0
$137$			216.977i			1.58377i	0.610668	+	0.791887i	$0.290901\pi$
$137$			216.977i			1.58377i	−0.610668	+	0.791887i	$0.709099\pi$
$138$		0			0
$139$	4.74973	−	8.22677i	0.0341707	−	0.0591854i	−0.848434	−	0.529301i	$-0.822454\pi$
$139$	4.74973	−	8.22677i	0.0341707	−	0.0591854i	0.882605	+	0.470115i	$0.155788\pi$
$140$		0			0
$141$	−77.5202	+	174.292i	−0.549788	+	1.23611i
$142$		0			0
$143$	7.18012	−	4.14544i	0.0502106	−	0.0289891i
$144$		0			0
$145$	76.0690			0.524614
$146$		0			0
$147$	−13.3182	−	126.250i	−0.0905999	−	0.858847i
$148$		0			0
$149$		−	153.517i		−	1.03032i	−0.857095	−	0.515158i	$-0.827733\pi$
$149$		−	153.517i		−	1.03032i	0.857095	−	0.515158i	$-0.172267\pi$
$150$		0			0
$151$	−100.480	+	174.036i	−0.665430	+	1.15256i	0.313739	+	0.949509i	$0.398418\pi$
$151$	−100.480	+	174.036i	−0.665430	+	1.15256i	−0.979169	+	0.203049i	$0.934915\pi$
$152$		0			0
$153$	−22.6823	−	106.312i	−0.148250	−	0.694853i
$154$		0			0
$155$	−11.8308	+	6.83052i	−0.0763277	+	0.0440678i
$156$		0			0
$157$	212.710			1.35484			0.677420	−	0.735597i	$-0.263098\pi$
$157$	212.710			1.35484			0.677420	+	0.735597i	$0.263098\pi$
$158$		0			0
$159$	−301.350	+	31.7895i	−1.89529	+	0.199934i
$160$		0			0
$161$	−22.4403	+	12.9559i	−0.139381	+	0.0804714i
$162$		0			0
$163$	−107.459			−0.659256			−0.329628	−	0.944111i	$-0.606923\pi$
$163$	−107.459			−0.659256			−0.329628	+	0.944111i	$0.606923\pi$
$164$		0			0
$165$	13.0134	−	9.46240i	0.0788692	−	0.0573479i
$166$		0			0
$167$	−164.004	−	94.6877i	−0.982060	−	0.566992i	−0.0791684	−	0.996861i	$-0.525226\pi$
$167$	−164.004	−	94.6877i	−0.982060	−	0.566992i	−0.902891	+	0.429869i	$0.858560\pi$
$168$		0			0
$169$	82.2233	+	142.415i	0.486528	+	0.842692i
$170$		0			0
$171$	92.2808	+	143.963i	0.539654	+	0.841887i
$172$		0			0
$173$	−46.0473	+	26.5854i	−0.266170	+	0.153673i	−0.627146	−	0.778902i	$-0.715777\pi$
$173$	−46.0473	+	26.5854i	−0.266170	+	0.153673i	0.360976	+	0.932575i	$0.382444\pi$
$174$		0			0
$175$	−29.8514	+	51.7042i	−0.170580	+	0.295453i
$176$		0			0
$177$	−80.2841	+	180.506i	−0.453582	+	1.01981i
$178$		0			0
$179$			109.214i			0.610133i	0.952331	+	0.305067i	$0.0986788\pi$
$179$			109.214i			0.610133i	−0.952331	+	0.305067i	$0.901321\pi$
$180$		0			0
$181$	168.086	+	291.133i	0.928649	+	1.60847i	0.785584	+	0.618755i	$0.212363\pi$
$181$	168.086	+	291.133i	0.928649	+	1.60847i	0.143065	+	0.989713i	$0.454304\pi$
$182$		0			0
$183$	−228.563	−	101.658i	−1.24898	−	0.555508i
$184$		0			0
$185$			11.0183i			0.0595582i
$186$		0			0
$187$	23.4645	+	40.6418i	0.125479	+	0.217336i
$188$		0			0
$189$	68.2904	+	14.4338i	0.361325	+	0.0763695i
$190$		0			0
$191$	90.3104	+	52.1407i	0.472829	+	0.272988i	0.717423	−	0.696637i	$-0.245321\pi$
$191$	90.3104	+	52.1407i	0.472829	+	0.272988i	−0.244594	+	0.969626i	$0.578655\pi$
$192$		0			0
$193$	48.2822			0.250167			0.125083	−	0.992146i	$-0.460080\pi$
$193$	48.2822			0.250167			0.125083	+	0.992146i	$0.460080\pi$
$194$		0			0
$195$	−5.19677	−	7.14701i	−0.0266501	−	0.0366513i
$196$		0			0
$197$		−	29.3092i		−	0.148778i	−0.997229	−	0.0743888i	$-0.976299\pi$
$197$		−	29.3092i		−	0.148778i	0.997229	−	0.0743888i	$-0.0237006\pi$
$198$		0			0
$199$	−197.010	−	341.232i	−0.990002	−	1.71473i	−0.617156	−	0.786841i	$-0.711715\pi$
$199$	−197.010	−	341.232i	−0.990002	−	1.71473i	−0.372846	−	0.927893i	$-0.621618\pi$
$200$		0			0
$201$	−249.736	+	181.589i	−1.24247	+	0.903430i
$202$		0			0
$203$	−123.374	−	71.2302i	−0.607756	−	0.350888i
$204$		0			0
$205$	−64.2179			−0.313258
$206$		0			0
$207$	18.8231	+	88.2242i	0.0909326	+	0.426204i
$208$		0			0
$209$	−57.0584	−	46.8410i	−0.273006	−	0.224120i
$210$		0			0
$211$	256.343			1.21490			0.607449	−	0.794359i	$-0.292193\pi$
$211$	256.343			1.21490			0.607449	+	0.794359i	$0.292193\pi$
$212$		0			0
$213$	196.245	+	269.892i	0.921340	+	1.26710i
$214$		0			0
$215$	−84.8003	+	48.9594i	−0.394420	+	0.227718i
$216$		0			0
$217$	25.5841			0.117899
$218$		0			0
$219$	−154.077	+	112.033i	−0.703548	+	0.511568i
$220$		0			0
$221$	22.3206	−	12.8868i	0.100998	−	0.0583113i
$222$		0			0
$223$	105.037	+	181.929i	0.471018	+	0.815827i	0.999450	−	0.0331482i	$-0.0105533\pi$
$223$	105.037	+	181.929i	0.471018	+	0.815827i	−0.528432	+	0.848975i	$0.677220\pi$
$224$		0			0
$225$	139.197	+	154.357i	0.618655	+	0.686032i
$226$		0			0
$227$	24.1547	+	13.9457i	0.106408	+	0.0614348i	0.552260	−	0.833672i	$-0.313766\pi$
$227$	24.1547	+	13.9457i	0.106408	+	0.0614348i	−0.445851	+	0.895107i	$0.647099\pi$
$228$		0			0
$229$	162.855	+	282.073i	0.711158	+	1.23176i	0.964423	+	0.264364i	$0.0851622\pi$
$229$	162.855	+	282.073i	0.711158	+	1.23176i	−0.253265	+	0.967397i	$0.581505\pi$
$230$		0			0
$231$	−29.9666	+	3.16119i	−0.129726	+	0.0136848i
$232$		0			0
$233$	−70.2877	−	40.5806i	−0.301664	−	0.174166i	0.341526	−	0.939872i	$-0.389056\pi$
$233$	−70.2877	−	40.5806i	−0.301664	−	0.174166i	−0.643190	+	0.765706i	$0.722390\pi$
$234$		0			0
$235$	−87.7712			−0.373494
$236$		0			0
$237$	−29.0203	−	275.100i	−0.122449	−	1.16076i
$238$		0			0
$239$	−46.0884	+	26.6092i	−0.192839	+	0.111335i	−0.593311	−	0.804973i	$-0.702179\pi$
$239$	−46.0884	+	26.6092i	−0.192839	+	0.111335i	0.400472	+	0.916309i	$0.368846\pi$
$240$		0			0
$241$	−206.272			−0.855898			−0.427949	−	0.903803i	$-0.640764\pi$
$241$	−206.272			−0.855898			−0.427949	+	0.903803i	$0.640764\pi$
$242$		0			0
$243$	121.098	−	210.676i	0.498346	−	0.866978i
$244$		0			0
$245$	50.5877	−	29.2068i	0.206480	−	0.119211i
$246$		0			0
$247$	−25.7252	+	31.3366i	−0.104151	+	0.126869i
$248$		0			0
$249$	−176.438	−	242.651i	−0.708585	−	0.974501i
$250$		0			0
$251$	250.206	−	144.457i	0.996839	−	0.575525i	0.0895272	−	0.995984i	$-0.471464\pi$
$251$	250.206	−	144.457i	0.996839	−	0.575525i	0.907311	+	0.420459i	$0.138131\pi$
$252$		0			0
$253$	−19.4722	−	33.7269i	−0.0769653	−	0.133308i
$254$		0			0
$255$	40.4544	−	29.4154i	0.158645	−	0.115355i
$256$		0			0
$257$	−390.508	−	225.460i	−1.51949	−	0.877275i	−0.999736	−	0.0229561i	$-0.992692\pi$
$257$	−390.508	−	225.460i	−1.51949	−	0.877275i	−0.519749	−	0.854319i	$-0.673974\pi$
$258$		0			0
$259$	10.3174	−	17.8703i	0.0398355	−	0.0689971i
$260$		0			0
$261$	−368.320	+	332.147i	−1.41119	+	1.27259i
$262$		0			0
$263$	267.296	−	154.324i	1.01634	−	0.586782i	0.103296	−	0.994651i	$-0.467061\pi$
$263$	267.296	−	154.324i	1.01634	−	0.586782i	0.913041	+	0.407869i	$0.133728\pi$
$264$		0			0
$265$	−69.7144	−	120.749i	−0.263073	−	0.455656i
$266$		0			0
$267$	77.4681	−	8.17213i	0.290143	−	0.0306072i
$268$		0			0
$269$	38.1781	+	22.0421i	0.141926	+	0.0819410i	0.569282	−	0.822143i	$-0.307221\pi$
$269$	38.1781	+	22.0421i	0.141926	+	0.0819410i	−0.427356	+	0.904084i	$0.640555\pi$
$270$		0			0
$271$	−118.444	+	205.151i	−0.437062	+	0.757013i	−0.997461	−	0.0712090i	$-0.977314\pi$
$271$	−118.444	+	205.151i	−0.437062	+	0.757013i	0.560400	+	0.828222i	$0.310648\pi$
$272$		0			0
$273$	1.73613	+	16.4578i	0.00635946	+	0.0602848i
$274$		0			0
$275$	−77.7095	−	44.8656i	−0.282580	−	0.163148i
$276$		0			0
$277$	135.627	−	234.912i	0.489627	−	0.848059i	−0.510301	−	0.859996i	$-0.670466\pi$
$277$	135.627	−	234.912i	0.489627	−	0.848059i	0.999929	+	0.0119362i	$0.00379949\pi$
$278$		0			0
$279$	27.4592	−	84.7307i	0.0984200	−	0.303694i
$280$		0			0
$281$			169.501i			0.603205i	0.953434	+	0.301603i	$0.0975216\pi$
$281$			169.501i			0.603205i	−0.953434	+	0.301603i	$0.902478\pi$
$282$		0			0
$283$	295.153			1.04295			0.521473	−	0.853268i	$-0.325383\pi$
$283$	295.153			1.04295			0.521473	+	0.853268i	$0.325383\pi$
$284$		0			0
$285$	−43.2690	+	65.7161i	−0.151821	+	0.230583i
$286$		0			0
$287$	104.153	+	60.1330i	0.362904	+	0.209523i
$288$		0			0
$289$	−71.5566	−	123.940i	−0.247601	−	0.428857i
$290$		0			0
$291$	−29.6978	−	281.522i	−0.102054	−	0.967428i
$292$		0			0
$293$	−57.8582	+	33.4045i	−0.197468	+	0.114008i	−0.595474	−	0.803375i	$-0.703036\pi$
$293$	−57.8582	+	33.4045i	−0.197468	+	0.114008i	0.398006	+	0.917383i	$0.369702\pi$
$294$		0			0
$295$	−90.9006			−0.308137
$296$		0			0
$297$	−21.6935	+	102.638i	−0.0730422	+	0.345582i
$298$		0			0
$299$	−18.5229	+	10.6942i	−0.0619495	+	0.0357666i
$300$		0			0
$301$	183.381			0.609238
$302$		0			0
$303$	−148.630	+	334.172i	−0.490529	+	1.10288i
$304$		0			0
$305$		−	115.101i		−	0.377380i
$306$		0			0
$307$	43.5778	−	75.4790i	0.141947	−	0.245860i	−0.786283	−	0.617867i	$-0.787997\pi$
$307$	43.5778	−	75.4790i	0.141947	−	0.245860i	0.928230	+	0.372007i	$0.121330\pi$
$308$		0			0
$309$	−30.7556	−	291.549i	−0.0995325	−	0.943524i
$310$		0			0
$311$	−35.1333	+	20.2842i	−0.112969	+	0.0652226i	−0.555420	−	0.831570i	$-0.687442\pi$
$311$	−35.1333	+	20.2842i	−0.112969	+	0.0652226i	0.442451	+	0.896793i	$0.354109\pi$
$312$		0			0
$313$	567.186			1.81210			0.906048	−	0.423174i	$-0.139084\pi$
$313$	567.186			1.81210			0.906048	+	0.423174i	$0.139084\pi$
$314$		0			0
$315$	6.70137	+	31.4095i	0.0212742	+	0.0997127i
$316$		0			0
$317$			356.558i			1.12479i	0.826869	+	0.562395i	$0.190120\pi$
$317$			356.558i			1.12479i	−0.826869	+	0.562395i	$0.809880\pi$
$318$		0			0
$319$	107.056	−	185.427i	0.335600	−	0.581277i
$320$		0			0
$321$	−57.7552	+	129.854i	−0.179923	+	0.404529i
$322$		0			0
$323$	−177.375	−	145.613i	−0.549149	−	0.450814i
$324$		0			0
$325$	−24.6403	+	42.6783i	−0.0758163	+	0.131318i
$326$		0			0
$327$	−16.5080	+	12.0034i	−0.0504831	+	0.0367075i
$328$		0			0
$329$	142.354	+	82.1880i	0.432686	+	0.249812i
$330$		0			0
$331$	−253.094	+	438.371i	−0.764633	+	1.32438i	0.175807	+	0.984425i	$0.443747\pi$
$331$	−253.094	+	438.371i	−0.764633	+	1.32438i	−0.940440	+	0.339959i	$0.889587\pi$
$332$		0			0
$333$	−48.1101	−	53.3497i	−0.144475	−	0.160209i
$334$		0			0
$335$	−123.042	−	71.0381i	−0.367289	−	0.212054i
$336$		0			0
$337$	−316.034			−0.937785			−0.468893	−	0.883255i	$-0.655347\pi$
$337$	−316.034			−0.937785			−0.468893	+	0.883255i	$0.655347\pi$
$338$		0			0
$339$	−96.9158	+	10.2237i	−0.285887	+	0.0301583i
$340$		0			0
$341$			38.4520i			0.112762i
$342$		0			0
$343$	−236.068			−0.688245
$344$		0			0
$345$	−33.5714	+	24.4106i	−0.0973083	+	0.0707554i
$346$		0			0
$347$		−	376.424i		−	1.08479i	−0.840122	−	0.542397i	$-0.817517\pi$
$347$		−	376.424i		−	1.08479i	0.840122	−	0.542397i	$-0.182483\pi$
$348$		0			0
$349$	−142.119	+	246.158i	−0.407219	+	0.705324i	−0.994577	−	0.104003i	$-0.966835\pi$
$349$	−142.119	+	246.158i	−0.407219	+	0.705324i	0.587358	+	0.809327i	$0.300168\pi$
$350$		0			0
$351$	56.3690	+	11.9141i	0.160595	+	0.0339434i
$352$		0			0
$353$	−34.1350	−	19.7079i	−0.0966998	−	0.0558296i	0.450870	−	0.892589i	$-0.351114\pi$
$353$	−34.1350	−	19.7079i	−0.0966998	−	0.0558296i	−0.547570	+	0.836760i	$0.684447\pi$
$354$		0			0
$355$	−76.7716	+	132.972i	−0.216258	+	0.374570i
$356$		0			0
$357$	−93.1562	+	9.82707i	−0.260942	+	0.0275268i
$358$		0			0
$359$	321.444	+	185.586i	0.895388	+	0.516953i	0.875701	−	0.482854i	$-0.160400\pi$
$359$	321.444	+	185.586i	0.895388	+	0.516953i	0.0196870	+	0.999806i	$0.493733\pi$
$360$		0			0
$361$	341.807	+	116.143i	0.946833	+	0.321726i
$362$		0			0
$363$	33.3305	+	315.958i	0.0918196	+	0.870408i
$364$		0			0
$365$	−75.9118	−	43.8277i	−0.207977	−	0.120076i
$366$		0			0
$367$	−47.6536			−0.129846			−0.0649231	−	0.997890i	$-0.520680\pi$
$367$	−47.6536			−0.129846			−0.0649231	+	0.997890i	$0.520680\pi$
$368$		0			0
$369$	310.938	−	280.400i	0.842651	−	0.759892i
$370$		0			0
$371$			261.120i			0.703826i
$372$		0			0
$373$	−147.919	−	256.203i	−0.396565	−	0.686870i	0.596735	−	0.802439i	$-0.296464\pi$
$373$	−147.919	−	256.203i	−0.396565	−	0.686870i	−0.993300	+	0.115568i	$0.963131\pi$
$374$		0			0
$375$	−80.9388	+	181.979i	−0.215837	+	0.485276i
$376$		0			0
$377$	−101.837	−	58.7957i	−0.270125	−	0.155957i
$378$		0			0
$379$	579.474			1.52895			0.764477	−	0.644651i	$-0.222997\pi$
$379$	579.474			1.52895			0.764477	+	0.644651i	$0.222997\pi$
$380$		0			0
$381$	−0.926969	−	8.78725i	−0.00243299	−	0.0230636i
$382$		0			0
$383$		−	468.952i		−	1.22442i	−0.790696	−	0.612209i	$-0.790281\pi$
$383$		−	468.952i		−	1.22442i	0.790696	−	0.612209i	$-0.209719\pi$
$384$		0			0
$385$	−6.93249	−	12.0074i	−0.0180065	−	0.0311881i
$386$		0			0
$387$	196.821	−	607.329i	0.508580	−	1.56933i
$388$		0			0
$389$		−	154.607i		−	0.397448i	−0.980056	−	0.198724i	$-0.936320\pi$
$389$		−	154.607i		−	0.397448i	0.980056	−	0.198724i	$-0.0636797\pi$
$390$		0			0
$391$	−60.5326	−	104.846i	−0.154815	−	0.268147i
$392$		0			0
$393$	−165.299	+	371.650i	−0.420608	+	0.945673i
$394$		0			0
$395$	110.230	−	63.6416i	0.279065	−	0.161118i
$396$		0			0
$397$	−44.0284	+	76.2595i	−0.110903	+	0.192089i	−0.916135	−	0.400871i	$-0.868708\pi$
$397$	−44.0284	+	76.2595i	−0.110903	+	0.192089i	0.805232	+	0.592960i	$0.202041\pi$
$398$		0			0
$399$	131.713	−	66.0667i	0.330107	−	0.165581i
$400$		0			0
$401$			306.269i			0.763764i	0.924211	+	0.381882i	$0.124724\pi$
$401$			306.269i			0.763764i	−0.924211	+	0.381882i	$0.875276\pi$
$402$		0			0
$403$	21.1179			0.0524018
$404$		0			0
$405$	111.216	+	11.5176i	0.274608	+	0.0284385i
$406$		0			0
$407$	26.8583	+	15.5067i	0.0659910	+	0.0380999i
$408$		0			0
$409$	−163.455	+	283.112i	−0.399645	+	0.692205i	−0.993682	−	0.112232i	$-0.964200\pi$
$409$	−163.455	+	283.112i	−0.399645	+	0.692205i	0.594037	+	0.804438i	$0.297533\pi$
$410$		0			0
$411$	264.530	−	594.756i	0.643626	−	1.44709i
$412$		0			0
$413$	147.429	+	85.1184i	0.356972	+	0.206098i
$414$		0			0
$415$	69.0227	−	119.551i	0.166320	−	0.288074i
$416$		0			0
$417$	−23.0493	+	16.7597i	−0.0552740	+	0.0401912i
$418$		0			0
$419$	254.321	−	146.832i	0.606972	−	0.350435i	−0.164807	−	0.986326i	$-0.552700\pi$
$419$	254.321	−	146.832i	0.606972	−	0.350435i	0.771779	+	0.635890i	$0.219367\pi$
$420$		0			0
$421$	−197.347	−	341.815i	−0.468758	−	0.811912i	0.530605	−	0.847619i	$-0.321965\pi$
$421$	−197.347	−	341.815i	−0.468758	−	0.811912i	−0.999362	+	0.0357074i	$0.988632\pi$
$422$		0			0
$423$	424.981	−	383.243i	1.00468	−	0.906012i
$424$		0			0
$425$	−241.573	−	139.472i	−0.568407	−	0.328170i
$426$		0			0
$427$	−107.779	+	186.679i	−0.252411	+	0.437188i
$428$		0			0
$429$	−24.7354	+	2.60934i	−0.0576583	+	0.00608239i
$430$		0			0
$431$	117.009	−	67.5553i	0.271483	−	0.156741i	−0.358078	−	0.933692i	$-0.616568\pi$
$431$	117.009	−	67.5553i	0.271483	−	0.156741i	0.629561	+	0.776951i	$0.283235\pi$
$432$		0			0
$433$	34.2521	+	59.3264i	0.0791042	+	0.137012i	0.902864	−	0.429927i	$-0.141461\pi$
$433$	34.2521	+	59.3264i	0.0791042	+	0.137012i	−0.823760	+	0.566939i	$0.808127\pi$
$434$		0			0
$435$	−208.513	−	92.7406i	−0.479340	−	0.213197i
$436$		0			0
$437$	147.196	+	120.838i	0.336833	+	0.276517i
$438$		0			0
$439$	−215.098	−	372.560i	−0.489972	−	0.848656i	0.509962	−	0.860197i	$-0.329660\pi$
$439$	−215.098	−	372.560i	−0.489972	−	0.848656i	−0.999933	+	0.0115413i	$0.996326\pi$
$440$		0			0
$441$	−117.413	+	362.302i	−0.266244	+	0.821548i
$442$		0			0
$443$			572.815i			1.29304i	0.762899	+	0.646518i	$0.223775\pi$
$443$			572.815i			1.29304i	−0.762899	+	0.646518i	$0.776225\pi$
$444$		0			0
$445$	17.9215	+	31.0409i	0.0402730	+	0.0697549i
$446$		0			0
$447$	−187.162	+	420.806i	−0.418708	+	0.941401i
$448$		0			0
$449$		−	852.506i		−	1.89868i	−0.314254	−	0.949339i	$-0.601754\pi$
$449$		−	852.506i		−	1.89868i	0.314254	−	0.949339i	$-0.398246\pi$
$450$		0			0
$451$	−90.3776	+	156.539i	−0.200394	+	0.347092i
$452$		0			0
$453$	487.604	−	354.550i	1.07639	−	0.782671i
$454$		0			0
$455$	−6.59451	+	3.80734i	−0.0144934	+	0.00836778i
$456$		0			0
$457$	405.072	−	701.605i	0.886371	−	1.53524i	0.0422374	−	0.999108i	$-0.486551\pi$
$457$	405.072	−	701.605i	0.886371	−	1.53524i	0.844134	−	0.536132i	$-0.180115\pi$
$458$		0			0
$459$	−67.4379	+	319.067i	−0.146923	+	0.695135i
$460$		0			0
$461$	−248.798	+	143.644i	−0.539693	+	0.311592i	−0.744954	−	0.667115i	$-0.767529\pi$
$461$	−248.798	+	143.644i	−0.539693	+	0.311592i	0.205262	+	0.978707i	$0.434195\pi$
$462$		0			0
$463$	−171.102	−	296.358i	−0.369552	−	0.640082i	0.619944	−	0.784646i	$-0.287155\pi$
$463$	−171.102	−	296.358i	−0.369552	−	0.640082i	−0.989495	+	0.144564i	$0.953822\pi$
$464$		0			0
$465$	40.7569	−	4.29946i	0.0876493	−	0.00924615i
$466$		0			0
$467$			356.059i			0.762438i	0.924485	+	0.381219i	$0.124496\pi$
$467$			356.059i			0.762438i	−0.924485	+	0.381219i	$0.875504\pi$
$468$		0			0
$469$	133.039	+	230.430i	0.283665	+	0.491322i
$470$		0			0
$471$	−583.059	−	259.328i	−1.23792	−	0.550590i
$472$		0			0
$473$			275.614i			0.582694i
$474$		0			0
$475$	432.925	+	71.5434i	0.911420	+	0.150618i
$476$		0			0
$477$	864.789	+	280.257i	1.81297	+	0.587541i
$478$		0			0
$479$			539.154i			1.12558i	0.826599	+	0.562791i	$0.190273\pi$
$479$			539.154i			1.12558i	−0.826599	+	0.562791i	$0.809727\pi$
$480$		0			0
$481$	8.51631	−	14.7507i	0.0177054	−	0.0306667i
$482$		0			0
$483$	77.3064	−	8.15507i	0.160055	−	0.0168842i
$484$		0			0
$485$	112.804	−	65.1273i	0.232585	−	0.134283i
$486$		0			0
$487$	−370.126			−0.760013			−0.380007	−	0.924984i	$-0.624078\pi$
$487$	−370.126			−0.760013			−0.380007	+	0.924984i	$0.624078\pi$
$488$		0			0
$489$	294.555	+	131.010i	0.602362	+	0.267913i
$490$		0			0
$491$			394.591i			0.803647i	0.915717	+	0.401824i	$0.131624\pi$
$491$			394.591i			0.803647i	−0.915717	+	0.401824i	$0.868376\pi$
$492$		0			0
$493$	332.803	−	576.431i	0.675056	−	1.16923i
$494$		0			0
$495$	−47.2073	+	10.0719i	−0.0953684	+	0.0203473i
$496$		0			0
$497$	249.028	−	143.776i	0.501062	−	0.289288i
$498$		0			0
$499$	−172.786			−0.346265			−0.173132	−	0.984899i	$-0.555389\pi$
$499$	−172.786			−0.346265			−0.173132	+	0.984899i	$0.555389\pi$
$500$		0			0
$501$	334.112	+	459.496i	0.666890	+	0.917159i
$502$		0			0
$503$	708.414	−	409.003i	1.40838	−	0.813127i	0.413145	−	0.910665i	$-0.364430\pi$
$503$	708.414	−	409.003i	1.40838	−	0.813127i	0.995232	+	0.0975384i	$0.0310969\pi$
$504$		0			0
$505$	−168.284			−0.333237
$506$		0			0
$507$	−51.7554	−	490.618i	−0.102082	−	0.967688i
$508$		0			0
$509$	−477.624	−	275.756i	−0.938357	−	0.541761i	−0.0489124	−	0.998803i	$-0.515576\pi$
$509$	−477.624	−	275.756i	−0.938357	−	0.541761i	−0.889445	+	0.457042i	$0.848909\pi$
$510$		0			0
$511$	82.0796	+	142.166i	0.160625	+	0.278211i
$512$		0			0
$513$	−77.4371	−	507.122i	−0.150949	−	0.988541i
$514$		0			0
$515$	116.822	−	67.4469i	0.226838	−	0.130965i
$516$		0			0
$517$	−123.526	+	213.953i	−0.238928	+	0.413835i
$518$		0			0
$519$	158.632	−	16.7342i	0.305650	−	0.0322431i
$520$		0			0
$521$			127.205i			0.244156i	0.992521	+	0.122078i	$0.0389557\pi$
$521$			127.205i			0.244156i	−0.992521	+	0.122078i	$0.961044\pi$
$522$		0			0
$523$	−433.805	−	751.373i	−0.829456	−	1.43666i	−0.898466	−	0.439043i	$-0.855317\pi$
$523$	−433.805	−	751.373i	−0.829456	−	1.43666i	0.0690101	−	0.997616i	$-0.478016\pi$
$524$		0			0
$525$	144.862	−	105.333i	0.275927	−	0.200634i
$526$		0			0
$527$			119.534i			0.226820i
$528$		0			0
$529$	−214.267	−	371.121i	−0.405041	−	0.701551i
$530$		0			0
$531$	440.134	−	396.907i	0.828877	−	0.747471i
$532$		0			0
$533$	85.9714	+	49.6356i	0.161297	+	0.0931250i
$534$		0			0
$535$	−65.3925			−0.122229
$536$		0			0
$537$	133.150	−	299.366i	0.247951	−	0.557479i
$538$		0			0
$539$		−	164.418i		−	0.305042i
$540$		0			0
$541$	−36.4501	−	63.1335i	−0.0673755	−	0.116698i	0.830370	−	0.557213i	$-0.188129\pi$
$541$	−36.4501	−	63.1335i	−0.0673755	−	0.116698i	−0.897745	+	0.440515i	$0.854796\pi$
$542$		0			0
$543$	−105.801	−	1002.95i	−0.194846	−	1.84705i
$544$		0			0
$545$	−8.13326	−	4.69574i	−0.0149234	−	0.00861604i
$546$		0			0
$547$	−658.030			−1.20298			−0.601490	−	0.798880i	$-0.705426\pi$
$547$	−658.030			−1.20298			−0.601490	+	0.798880i	$0.705426\pi$
$548$		0			0
$549$	502.575	+	557.310i	0.915438	+	1.01514i
$550$		0			0
$551$	−170.714	+	1033.03i	−0.309826	+	1.87482i
$552$		0			0
$553$	−238.373			−0.431055
$554$		0			0
$555$	13.4331	−	30.2022i	0.0242037	−	0.0544184i
$556$		0			0
$557$	593.928	−	342.904i	1.06630	−	0.615627i	0.139130	−	0.990274i	$-0.455569\pi$
$557$	593.928	−	342.904i	1.06630	−	0.615627i	0.927168	+	0.374647i	$0.122236\pi$
$558$		0			0
$559$	151.368			0.270784
$560$		0			0
$561$	−14.7697	−	140.010i	−0.0263275	−	0.249573i
$562$		0			0
$563$	−13.7786	+	7.95507i	−0.0244735	+	0.0141298i	−0.512187	−	0.858874i	$-0.671164\pi$
$563$	−13.7786	+	7.95507i	−0.0244735	+	0.0141298i	0.487713	+	0.873004i	$0.337831\pi$
$564$		0			0
$565$	−22.4205	−	38.8335i	−0.0396823	−	0.0687318i
$566$		0			0
$567$	−169.594	−	122.822i	−0.299107	−	0.216617i
$568$		0			0
$569$	−493.461	−	284.900i	−0.867243	−	0.500703i	−0.000812088	−	1.00000i	$-0.500258\pi$
$569$	−493.461	−	284.900i	−0.867243	−	0.500703i	−0.866431	+	0.499297i	$0.833592\pi$
$570$		0			0
$571$	−374.309	−	648.322i	−0.655532	−	1.13542i	−0.981760	−	0.190124i	$-0.939111\pi$
$571$	−374.309	−	648.322i	−0.655532	−	1.13542i	0.326228	−	0.945291i	$-0.394222\pi$
$572$		0			0
$573$	−183.982	−	253.026i	−0.321085	−	0.441582i
$574$		0			0
$575$	200.471	+	115.742i	0.348645	+	0.201290i
$576$		0			0
$577$	20.3633			0.0352917			0.0176458	−	0.999844i	$-0.494383\pi$
$577$	20.3633			0.0352917			0.0176458	+	0.999844i	$0.494383\pi$
$578$		0			0
$579$	−132.346	−	58.8638i	−0.228577	−	0.101665i
$580$		0			0
$581$	−223.892	+	129.264i	−0.385357	+	0.222486i
$582$		0			0
$583$	−392.453			−0.673161
$584$		0			0
$585$	5.53152	+	25.9264i	0.00945559	+	0.0443186i
$586$		0			0
$587$	233.846	−	135.011i	0.398374	−	0.230002i	−0.287408	−	0.957808i	$-0.592794\pi$
$587$	233.846	−	135.011i	0.398374	−	0.230002i	0.685782	+	0.727807i	$0.259460\pi$
$588$		0			0
$589$	−66.2086	−	175.993i	−0.112409	−	0.298799i
$590$		0			0
$591$	−35.7327	+	80.3395i	−0.0604614	+	0.135938i
$592$		0			0
$593$	586.198	−	338.441i	0.988529	−	0.570728i	0.0836948	−	0.996491i	$-0.473328\pi$
$593$	586.198	−	338.441i	0.988529	−	0.570728i	0.904834	+	0.425764i	$0.139995\pi$
$594$		0			0
$595$	−21.5508	−	37.3270i	−0.0362198	−	0.0627345i
$596$		0			0
$597$	124.008	+	1175.54i	0.207719	+	1.96908i
$598$		0			0
$599$	−313.642	−	181.081i	−0.523609	−	0.302306i	0.214801	−	0.976658i	$-0.431090\pi$
$599$	−313.642	−	181.081i	−0.523609	−	0.302306i	−0.738410	+	0.674352i	$0.764423\pi$
$600$		0			0
$601$	60.0000	−	103.923i	0.0998335	−	0.172917i	−0.811782	−	0.583960i	$-0.801502\pi$
$601$	60.0000	−	103.923i	0.0998335	−	0.172917i	0.911616	+	0.411044i	$0.134836\pi$
$602$		0			0
$603$	905.939	−	193.286i	1.50239	−	0.320541i
$604$		0			0
$605$	−126.602	+	73.0938i	−0.209260	+	0.120816i
$606$		0			0
$607$	46.0757	+	79.8054i	0.0759072	+	0.131475i	0.901480	−	0.432820i	$-0.142481\pi$
$607$	46.0757	+	79.8054i	0.0759072	+	0.131475i	−0.825573	+	0.564295i	$0.809148\pi$
$608$		0			0
$609$	251.341	+	345.663i	0.412710	+	0.567591i
$610$		0			0
$611$	117.503	+	67.8406i	0.192313	+	0.111032i
$612$		0			0
$613$	398.866	−	690.857i	0.650679	−	1.12701i	−0.332279	−	0.943181i	$-0.607818\pi$
$613$	398.866	−	690.857i	0.650679	−	1.12701i	0.982958	−	0.183828i	$-0.0588490\pi$
$614$		0			0
$615$	176.028	+	78.2921i	0.286224	+	0.127304i
$616$		0			0
$617$	−657.673	−	379.708i	−1.06592	−	0.615409i	−0.138856	−	0.990313i	$-0.544343\pi$
$617$	−657.673	−	379.708i	−1.06592	−	0.615409i	−0.927064	+	0.374903i	$0.877676\pi$
$618$		0			0
$619$	199.138	−	344.918i	0.321710	−	0.557218i	−0.659131	−	0.752028i	$-0.729076\pi$
$619$	199.138	−	344.918i	0.321710	−	0.557218i	0.980841	+	0.194810i	$0.0624092\pi$
$620$		0			0
$621$	55.9638	−	264.780i	0.0901189	−	0.426377i
$622$		0			0
$623$		−	67.1260i		−	0.107746i
$624$		0			0
$625$	485.722			0.777155
$626$		0			0
$627$	99.2959	+	197.959i	0.158367	+	0.315725i
$628$		0			0
$629$	83.4936	+	48.2050i	0.132740	+	0.0766376i
$630$		0			0
$631$	606.658	+	1050.76i	0.961424	+	1.66524i	0.718930	+	0.695082i	$0.244632\pi$
$631$	606.658	+	1050.76i	0.961424	+	1.66524i	0.242493	+	0.970153i	$0.422035\pi$
$632$		0			0
$633$	−702.663	−	312.524i	−1.11005	−	0.493720i
$634$		0			0
$635$	3.52099	−	2.03284i	0.00554486	−	0.00320133i
$636$		0			0
$637$	−90.2987			−0.141756
$638$		0			0
$639$	−208.886	−	979.057i	−0.326896	−	1.53217i
$640$		0			0
$641$	−947.005	+	546.753i	−1.47739	+	0.852970i	−0.999674	−	0.0255464i	$-0.991867\pi$
$641$	−947.005	+	546.753i	−1.47739	+	0.852970i	−0.477713	+	0.878516i	$0.658534\pi$
$642$		0			0
$643$	−411.742			−0.640344			−0.320172	−	0.947359i	$-0.603741\pi$
$643$	−411.742			−0.640344			−0.320172	+	0.947359i	$0.603741\pi$
$644$		0			0
$645$	292.136	−	30.8175i	0.452924	−	0.0477790i
$646$		0			0
$647$		−	173.973i		−	0.268892i	−0.990921	−	0.134446i	$-0.957074\pi$
$647$		−	173.973i		−	0.268892i	0.990921	−	0.134446i	$-0.0429255\pi$
$648$		0			0
$649$	−127.930	+	221.581i	−0.197118	+	0.341419i
$650$		0			0
$651$	−70.1286	−	31.1912i	−0.107724	−	0.0479128i
$652$		0			0
$653$	−703.393	+	406.104i	−1.07717	+	0.621905i	−0.930132	−	0.367226i	$-0.880308\pi$
$653$	−703.393	+	406.104i	−1.07717	+	0.621905i	−0.147039	+	0.989131i	$0.546974\pi$
$654$		0			0
$655$	−187.158			−0.285737
$656$		0			0
$657$	558.928	−	119.250i	0.850727	−	0.181507i
$658$		0			0
$659$			521.567i			0.791452i	0.918369	+	0.395726i	$0.129507\pi$
$659$			521.567i			0.791452i	−0.918369	+	0.395726i	$0.870493\pi$
$660$		0			0
$661$	192.672	−	333.718i	0.291486	−	0.504869i	−0.682675	−	0.730722i	$-0.739184\pi$
$661$	192.672	−	333.718i	0.291486	−	0.504869i	0.974161	+	0.225853i	$0.0725170\pi$
$662$		0			0
$663$	−76.8941	+	8.11157i	−0.115979	+	0.0122347i
$664$		0			0
$665$	52.4047	+	43.0207i	0.0788040	+	0.0646927i
$666$		0			0
$667$	−276.179	+	478.356i	−0.414061	+	0.717175i
$668$		0			0
$669$	−66.1154	−	626.745i	−0.0988273	−	0.936838i
$670$		0			0
$671$	−280.572	−	161.988i	−0.418140	−	0.241413i
$672$		0			0
$673$	−77.0773	+	133.502i	−0.114528	+	0.198368i	−0.917591	−	0.397526i	$-0.869869\pi$
$673$	−77.0773	+	133.502i	−0.114528	+	0.198368i	0.803063	+	0.595894i	$0.203202\pi$
$674$		0			0
$675$	−193.367	−	592.813i	−0.286470	−	0.878241i
$676$		0			0
$677$	477.529	+	275.702i	0.705360	+	0.407240i	0.809341	−	0.587339i	$-0.199825\pi$
$677$	477.529	+	275.702i	0.705360	+	0.407240i	−0.103980	+	0.994579i	$0.533158\pi$
$678$		0			0
$679$	−243.938			−0.359261
$680$		0			0
$681$	−49.2083	−	67.6750i	−0.0722589	−	0.0993760i
$682$		0			0
$683$			447.782i			0.655610i	0.944745	+	0.327805i	$0.106309\pi$
$683$			447.782i			0.655610i	−0.944745	+	0.327805i	$0.893691\pi$
$684$		0			0
$685$	299.511			0.437242
$686$		0			0
$687$	−102.509	−	971.739i	−0.149212	−	1.41447i
$688$		0			0
$689$			215.536i			0.312825i
$690$		0			0
$691$	−161.242	+	279.280i	−0.233346	+	0.404167i	−0.958791	−	0.284113i	$-0.908301\pi$
$691$	−161.242	+	279.280i	−0.233346	+	0.404167i	0.725445	+	0.688280i	$0.241634\pi$
$692$		0			0
$693$	85.9956	+	27.8691i	0.124092	+	0.0402151i
$694$		0			0
$695$	−11.3561	−	6.55644i	−0.0163397	−	0.00943372i
$696$		0			0
$697$	−280.954	+	486.626i	−0.403090	+	0.698172i
$698$		0			0
$699$	143.191	+	196.928i	0.204852	+	0.281728i
$700$		0			0
$701$	705.633	+	407.397i	1.00661	+	0.581166i	0.910197	−	0.414175i	$-0.135930\pi$
$701$	705.633	+	407.397i	1.00661	+	0.581166i	0.0964122	+	0.995341i	$0.469263\pi$
$702$		0			0
$703$	−149.630	−	24.7272i	−0.212844	−	0.0351738i
$704$		0			0
$705$	240.590	+	107.007i	0.341262	+	0.151784i
$706$		0			0
$707$	272.936	+	157.580i	0.386049	+	0.222885i
$708$		0			0
$709$	−366.557			−0.517006			−0.258503	−	0.966010i	$-0.583229\pi$
$709$	−366.557			−0.517006			−0.258503	+	0.966010i	$0.583229\pi$
$710$		0			0
$711$	−255.844	+	789.457i	−0.359837	+	1.11035i
$712$		0			0
$713$		−	99.1964i		−	0.139125i
$714$		0			0
$715$	−5.72229	−	9.91130i	−0.00800321	−	0.0138620i
$716$		0			0
$717$	158.774	−	16.7491i	0.221442	−	0.0233600i
$718$		0			0
$719$	669.724	+	386.666i	0.931466	+	0.537782i	0.887275	−	0.461241i	$-0.152596\pi$
$719$	669.724	+	386.666i	0.931466	+	0.537782i	0.0441914	+	0.999023i	$0.485929\pi$
$720$		0			0
$721$	−252.627			−0.350384
$722$		0			0
$723$	565.411	+	251.479i	0.782035	+	0.347827i
$724$		0			0
$725$			1272.68i			1.75542i
$726$		0			0
$727$	−352.852	−	611.157i	−0.485353	−	0.840656i	0.514505	−	0.857487i	$-0.327976\pi$
$727$	−352.852	−	611.157i	−0.485353	−	0.840656i	−0.999858	+	0.0168312i	$0.994642\pi$
$728$		0			0
$729$	−588.790	+	429.845i	−0.807668	+	0.589637i
$730$		0			0
$731$			856.792i			1.17208i
$732$		0			0
$733$	−110.559	−	191.494i	−0.150831	−	0.261247i	0.780702	−	0.624903i	$-0.214862\pi$
$733$	−110.559	−	191.494i	−0.150831	−	0.261247i	−0.931533	+	0.363657i	$0.881528\pi$
$734$		0			0
$735$	−174.274	+	18.3842i	−0.237107	+	0.0250125i
$736$		0			0
$737$	−346.328	+	199.952i	−0.469916	+	0.271306i
$738$		0			0
$739$	−567.567	+	983.056i	−0.768021	+	1.33025i	0.170614	+	0.985338i	$0.445425\pi$
$739$	−567.567	+	983.056i	−0.768021	+	1.33025i	−0.938635	+	0.344913i	$0.887908\pi$
$740$		0			0
$741$	108.720	−	54.5336i	0.146720	−	0.0735946i
$742$		0			0
$743$			1201.79i			1.61748i	0.588164	+	0.808741i	$0.299851\pi$
$743$			1201.79i			1.61748i	−0.588164	+	0.808741i	$0.700149\pi$
$744$		0			0
$745$	−211.912			−0.284446
$746$		0			0
$747$	187.803	+	880.236i	0.251409	+	1.17836i
$748$		0			0
$749$	106.058	+	61.2329i	0.141600	+	0.0817529i
$750$		0			0
$751$	−608.799	+	1054.47i	−0.810652	+	1.40409i	0.101757	+	0.994809i	$0.467554\pi$
$751$	−608.799	+	1054.47i	−0.810652	+	1.40409i	−0.912409	+	0.409280i	$0.865780\pi$
$752$		0			0
$753$	−861.958	+	90.9281i	−1.14470	+	0.120755i
$754$		0			0
$755$	240.236	+	138.701i	0.318194	+	0.183709i
$756$		0			0
$757$	264.301	−	457.783i	0.349143	−	0.604733i	−0.636955	−	0.770901i	$-0.719806\pi$
$757$	264.301	−	457.783i	0.349143	−	0.604733i	0.986097	+	0.166168i	$0.0531396\pi$
$758$		0			0
$759$	12.2568	+	116.189i	0.0161486	+	0.153081i
$760$		0			0
$761$	−816.105	+	471.178i	−1.07241	+	0.619157i	−0.928839	−	0.370483i	$-0.879192\pi$
$761$	−816.105	+	471.178i	−1.07241	+	0.619157i	−0.143572	+	0.989640i	$0.545859\pi$
$762$		0			0
$763$	8.79409	+	15.2318i	0.0115257	+	0.0199630i
$764$		0			0
$765$	−146.752	+	31.3102i	−0.191832	+	0.0409283i
$766$		0			0
$767$	121.693	+	70.2594i	0.158661	+	0.0916028i
$768$		0			0
$769$	−32.7211	+	56.6746i	−0.0425502	+	0.0736991i	−0.886516	−	0.462698i	$-0.846882\pi$
$769$	−32.7211	+	56.6746i	−0.0425502	+	0.0736991i	0.843966	+	0.536397i	$0.180215\pi$
$770$		0			0
$771$	795.549	+	1094.10i	1.03184	+	1.41907i
$772$		0			0
$773$	153.219	−	88.4613i	0.198214	−	0.114439i	−0.397608	−	0.917555i	$-0.630160\pi$
$773$	153.219	−	88.4613i	0.198214	−	0.114439i	0.595822	+	0.803116i	$0.296826\pi$
$774$		0			0
$775$	−114.278	−	197.936i	−0.147456	−	0.255401i
$776$		0			0
$777$	−50.0678	+	36.4056i	−0.0644373	+	0.0468541i
$778$		0			0
$779$	144.118	−	872.087i	0.185003	−	1.11950i
$780$		0			0
$781$	216.091	+	374.280i	0.276684	+	0.479231i
$782$		0			0
$783$	1414.55	−	461.405i	1.80657	−	0.589279i
$784$		0			0
$785$		−	293.621i		−	0.374039i
$786$		0			0
$787$	−184.323	−	319.258i	−0.234210	−	0.405664i	0.724833	−	0.688925i	$-0.241917\pi$
$787$	−184.323	−	319.258i	−0.234210	−	0.405664i	−0.959043	+	0.283261i	$0.908584\pi$
$788$		0			0
$789$	−920.833	+	97.1389i	−1.16709	+	0.123116i
$790$		0			0
$791$			83.9774i			0.106166i
$792$		0			0
$793$	−88.9645	+	154.091i	−0.112187	+	0.194314i
$794$		0			0
$795$	43.8817	+	415.978i	0.0551971	+	0.523243i
$796$		0			0
$797$	−172.117	+	99.3717i	−0.215956	+	0.124682i	−0.604076	−	0.796926i	$-0.706458\pi$
$797$	−172.117	+	99.3717i	−0.215956	+	0.124682i	0.388120	+	0.921609i	$0.373124\pi$
$798$		0			0
$799$	−384.000	+	665.107i	−0.480600	+	0.832424i
$800$		0			0
$801$	−222.311	−	72.0457i	−0.277542	−	0.0899447i
$802$		0			0
$803$	−213.670	+	123.363i	−0.266090	+	0.153627i
$804$		0			0
$805$	17.8841	+	30.9761i	0.0222162	+	0.0384797i
$806$		0			0
$807$	−77.7770	−	106.965i	−0.0963780	−	0.132546i
$808$		0			0
$809$		−	163.606i		−	0.202233i	−0.994875	−	0.101116i	$-0.967759\pi$
$809$		−	163.606i		−	0.202233i	0.994875	−	0.101116i	$-0.0322415\pi$
$810$		0			0
$811$	−583.715	−	1011.02i	−0.719747	−	1.24664i	−0.961100	−	0.276201i	$-0.910924\pi$
$811$	−583.715	−	1011.02i	−0.719747	−	1.24664i	0.241352	−	0.970438i	$-0.422409\pi$
$812$		0			0
$813$	574.779	−	417.936i	0.706985	−	0.514067i
$814$		0			0
$815$			148.334i			0.182005i
$816$		0			0
$817$	−474.567	−	1261.47i	−0.580865	−	1.54403i
$818$		0			0
$819$	15.3058	−	47.2290i	0.0186884	−	0.0576667i
$820$		0			0
$821$		−	635.471i		−	0.774021i	−0.922075	−	0.387010i	$-0.873508\pi$
$821$		−	635.471i		−	0.774021i	0.922075	−	0.387010i	$-0.126492\pi$
$822$		0			0
$823$	−395.809	+	685.562i	−0.480935	+	0.833003i	−0.999761	−	0.0218766i	$-0.993036\pi$
$823$	−395.809	+	685.562i	−0.480935	+	0.833003i	0.518826	+	0.854880i	$0.326369\pi$
$824$		0			0
$825$	158.311	+	217.722i	0.191892	+	0.263905i
$826$		0			0
$827$	−1202.33	+	694.165i	−1.45384	+	0.839377i	−0.998697	−	0.0510395i	$-0.983747\pi$
$827$	−1202.33	+	694.165i	−1.45384	+	0.839377i	−0.455147	+	0.890416i	$0.650413\pi$
$828$		0			0
$829$	1284.57			1.54954			0.774769	−	0.632245i	$-0.217866\pi$
$829$	1284.57			1.54954			0.774769	+	0.632245i	$0.217866\pi$
$830$		0			0
$831$	−658.164	+	478.568i	−0.792014	+	0.575894i
$832$		0			0
$833$		−	511.120i		−	0.613589i
$834$		0			0
$835$	−130.705	+	226.388i	−0.156533	+	0.271123i
$836$		0			0
$837$	−178.569	+	198.778i	−0.213344	+	0.237489i
$838$		0			0
$839$	−466.494	+	269.330i	−0.556011	+	0.321013i	−0.751543	−	0.659684i	$-0.770690\pi$
$839$	−466.494	+	269.330i	−0.556011	+	0.321013i	0.195532	+	0.980697i	$0.437357\pi$
$840$		0			0
$841$	−2195.81			−2.61095
$842$		0			0
$843$	206.649	−	464.619i	0.245135	−	0.551149i
$844$		0			0
$845$	196.587	−	113.500i	0.232647	−	0.134319i
$846$		0			0
$847$	273.777			0.323232
$848$		0			0
$849$	−809.046	−	359.840i	−0.952940	−	0.423840i
$850$		0			0
$851$	−69.2878	−	40.0033i	−0.0814193	−	0.0470074i
$852$		0			0
$853$	545.119	+	944.173i	0.639060	+	1.10689i	0.985639	+	0.168864i	$0.0540100\pi$
$853$	545.119	+	944.173i	0.639060	+	1.10689i	−0.346579	+	0.938021i	$0.612657\pi$
$854$		0			0
$855$	198.723	−	127.383i	0.232425	−	0.148986i
$856$		0			0
$857$	−341.259	+	197.026i	−0.398202	+	0.229902i	−0.685708	−	0.727877i	$-0.740507\pi$
$857$	−341.259	+	197.026i	−0.398202	+	0.229902i	0.287506	+	0.957779i	$0.407174\pi$
$858$		0			0
$859$	473.520	−	820.161i	0.551246	−	0.954786i	−0.446939	−	0.894564i	$-0.647486\pi$
$859$	473.520	−	820.161i	0.551246	−	0.954786i	0.998185	−	0.0602217i	$-0.0191808\pi$
$860$		0			0
$861$	−212.183	−	291.811i	−0.246438	−	0.338920i
$862$		0			0
$863$			676.247i			0.783600i	0.920050	+	0.391800i	$0.128147\pi$
$863$			676.247i			0.783600i	−0.920050	+	0.391800i	$0.871853\pi$
$864$		0			0
$865$	36.6980	+	63.5629i	0.0424255	+	0.0734831i
$866$		0			0
$867$	45.0412	+	426.971i	0.0519507	+	0.492469i
$868$		0			0
$869$		−	358.266i		−	0.412274i
$870$		0			0
$871$	109.814	+	190.204i	0.126079	+	0.218374i
$872$		0			0
$873$	−261.816	+	807.886i	−0.299904	+	0.925414i
$874$		0			0
$875$	148.632	+	85.8125i	0.169865	+	0.0980715i
$876$		0			0
$877$	1088.29			1.24093			0.620464	−	0.784235i	$-0.286944\pi$
$877$	1088.29			1.24093			0.620464	+	0.784235i	$0.286944\pi$
$878$		0			0
$879$	199.321	−	21.0264i	0.226759	−	0.0239208i
$880$		0			0
$881$			1090.35i			1.23763i	0.785537	+	0.618814i	$0.212387\pi$
$881$			1090.35i			1.23763i	−0.785537	+	0.618814i	$0.787613\pi$
$882$		0			0
$883$	−240.315	−	416.237i	−0.272157	−	0.471390i	0.697257	−	0.716821i	$-0.254404\pi$
$883$	−240.315	−	416.237i	−0.272157	−	0.471390i	−0.969414	+	0.245432i	$0.921070\pi$
$884$		0			0
$885$	249.168	+	110.823i	0.281545	+	0.125223i
$886$		0			0
$887$	937.624	+	541.338i	1.05707	+	0.610302i	0.924621	−	0.380888i	$-0.124382\pi$
$887$	937.624	+	541.338i	1.05707	+	0.610302i	0.132452	+	0.991189i	$0.457715\pi$
$888$		0			0
$889$	−7.61413			−0.00856483
$890$		0			0
$891$	184.597	−	254.893i	0.207179	−	0.286075i
$892$		0			0
$893$	196.976	−	1191.94i	0.220578	−	1.33476i
$894$		0			0
$895$	150.757			0.168443
$896$		0			0
$897$	63.8111	−	6.73145i	0.0711384	−	0.00750441i
$898$		0			0
$899$	472.306	−	272.686i	0.525369	−	0.303322i
$900$		0			0
$901$	−1220.00			−1.35406
$902$		0			0
$903$	−502.665	−	223.571i	−0.556661	−	0.247587i
$904$		0			0
$905$	401.874	−	232.022i	0.444060	−	0.256378i
$906$		0			0
$907$	461.575	+	799.471i	0.508903	+	0.881445i	0.999947	+	0.0103107i	$0.00328206\pi$
$907$	461.575	+	799.471i	0.508903	+	0.881445i	−0.491044	+	0.871135i	$0.663385\pi$
$908$		0			0
$909$	814.821	−	734.795i	0.896393	−	0.808356i
$910$		0			0
$911$	717.632	+	414.325i	0.787740	+	0.454802i	0.839166	−	0.543875i	$-0.183043\pi$
$911$	717.632	+	414.325i	0.787740	+	0.454802i	−0.0514260	+	0.998677i	$0.516377\pi$
$912$		0			0
$913$	−194.280	−	336.502i	−0.212793	−	0.368568i
$914$		0			0
$915$	−140.327	+	315.503i	−0.153363	+	0.344812i
$916$		0			0
$917$	303.546	+	175.253i	0.331021	+	0.191115i
$918$		0			0
$919$	99.4111			0.108173			0.0540865	−	0.998536i	$-0.482775\pi$
$919$	99.4111			0.108173			0.0540865	+	0.998536i	$0.482775\pi$
$920$		0			0
$921$	−211.473	+	153.767i	−0.229612	+	0.166957i
$922$		0			0
$923$	205.555	−	118.677i	0.222704	−	0.128578i
$924$		0			0
$925$	−184.342			−0.199289
$926$		0			0
$927$	−271.142	+	836.661i	−0.292494	+	0.902547i
$928$		0			0
$929$	−672.497	+	388.266i	−0.723893	+	0.417940i	−0.816184	−	0.577792i	$-0.803914\pi$
$929$	−672.497	+	388.266i	−0.723893	+	0.417940i	0.0922906	+	0.995732i	$0.470581\pi$
$930$		0			0
$931$	283.103	+	752.533i	0.304085	+	0.808306i
$932$		0			0
$933$	121.034	−	12.7679i	0.129725	−	0.0136848i
$934$		0			0
$935$	56.1012	−	32.3900i	0.0600012	−	0.0346417i
$936$		0			0
$937$	−67.4595	−	116.843i	−0.0719952	−	0.124699i	0.827780	−	0.561052i	$-0.189603\pi$
$937$	−67.4595	−	116.843i	−0.0719952	−	0.124699i	−0.899776	+	0.436353i	$0.856270\pi$
$938$		0			0
$939$	−1554.72	−	691.493i	−1.65571	−	0.736414i
$940$		0			0
$941$	−1033.41	−	596.637i	−1.09820	−	0.634046i	−0.162452	−	0.986716i	$-0.551940\pi$
$941$	−1033.41	−	596.637i	−1.09820	−	0.634046i	−0.935747	+	0.352671i	$0.885274\pi$
$942$		0			0
$943$	233.152	−	403.830i	0.247245	−	0.428240i
$944$		0			0
$945$	19.9242	−	94.2667i	0.0210838	−	0.0997531i
$946$		0			0
$947$	−1181.43	+	682.096i	−1.24754	+	0.720270i	−0.970619	−	0.240621i	$-0.922649\pi$
$947$	−1181.43	+	682.096i	−1.24754	+	0.720270i	−0.276926	+	0.960891i	$0.589316\pi$
$948$		0			0
$949$	67.7511	+	117.348i	0.0713921	+	0.123655i
$950$		0			0
$951$	434.703	−	977.362i	0.457101	−	1.02772i
$952$		0			0
$953$	−1201.81	−	693.865i	−1.26108	−	0.728085i	−0.287796	−	0.957692i	$-0.592923\pi$
$953$	−1201.81	−	693.865i	−1.26108	−	0.728085i	−0.973283	+	0.229607i	$0.926256\pi$
$954$		0			0
$955$	71.9741	−	124.663i	0.0753656	−	0.130537i
$956$		0			0
$957$	−519.519	+	377.756i	−0.542862	+	0.394729i
$958$		0			0
$959$	−485.769	−	280.459i	−0.506537	−	0.292449i
$960$		0			0
$961$	431.529	−	747.430i	0.449042	−	0.777763i
$962$		0			0
$963$	316.626	−	285.529i	0.328791	−	0.296500i
$964$		0			0
$965$		−	66.6478i		−	0.0690651i
$966$		0			0
$967$	1102.31			1.13993			0.569963	−	0.821671i	$-0.306958\pi$
$967$	1102.31			1.13993			0.569963	+	0.821671i	$0.306958\pi$
$968$		0			0
$969$	308.678	+	615.390i	0.318553	+	0.635077i
$970$		0			0
$971$	866.098	+	500.042i	0.891965	+	0.514976i	0.874585	−	0.484873i	$-0.161134\pi$
$971$	866.098	+	500.042i	0.891965	+	0.514976i	0.0173804	+	0.999849i	$0.494467\pi$
$972$		0			0
$973$	12.2788	+	21.2674i	0.0126195	+	0.0218576i
$974$		0			0
$975$	119.573	−	86.9449i	0.122639	−	0.0891743i
$976$		0			0
$977$	−1494.39	+	862.786i	−1.52957	+	0.883097i	−0.530190	+	0.847879i	$0.677879\pi$
$977$	−1494.39	+	862.786i	−1.52957	+	0.883097i	−0.999380	+	0.0352187i	$0.988787\pi$
$978$		0			0
$979$	100.888			0.103052
$980$		0			0
$981$	59.8841	−	12.7765i	0.0610439	−	0.0130240i
$982$		0			0
$983$	888.716	−	513.101i	0.904086	−	0.521974i	0.0255622	−	0.999673i	$-0.491862\pi$
$983$	888.716	−	513.101i	0.904086	−	0.521974i	0.878524	+	0.477699i	$0.158529\pi$
$984$		0			0
$985$	−40.4578			−0.0410740
$986$		0			0
$987$	−290.006	−	398.838i	−0.293825	−	0.404092i
$988$		0			0
$989$		−	711.015i		−	0.718924i
$990$		0			0
$991$	−96.7075	+	167.502i	−0.0975858	+	0.169024i	−0.910685	−	0.413102i	$-0.864445\pi$
$991$	−96.7075	+	167.502i	−0.0975858	+	0.169024i	0.813099	+	0.582125i	$0.197779\pi$
$992$		0			0
$993$	1228.20	−	893.057i	1.23686	−	0.899353i
$994$		0			0
$995$	−471.030	+	271.949i	−0.473397	+	0.273316i
$996$		0			0
$997$	−44.6895			−0.0448240			−0.0224120	−	0.999749i	$-0.507135\pi$
$997$	−44.6895			−0.0448240			−0.0224120	+	0.999749i	$0.507135\pi$
$998$		0			0
$999$	66.8326	+	204.891i	0.0668995	+	0.205096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.6	✓	80
3.2	odd	2		2052.3.m.a.1493.24		80
9.4	even	3		2052.3.be.a.125.17		80
9.5	odd	6		684.3.be.a.581.33	yes	80
19.7	even	3		684.3.be.a.425.33	yes	80
57.26	odd	6		2052.3.be.a.197.17		80
171.121	even	3		2052.3.m.a.881.17		80
171.140	odd	6	inner	684.3.m.a.653.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.6	✓	80	1.1	even	1	trivial
684.3.m.a.653.6	yes	80	171.140	odd	6	inner
684.3.be.a.425.33	yes	80	19.7	even	3
684.3.be.a.581.33	yes	80	9.5	odd	6
2052.3.m.a.881.17		80	171.121	even	3
2052.3.m.a.1493.24		80	3.2	odd	2
2052.3.be.a.125.17		80	9.4	even	3
2052.3.be.a.197.17		80	57.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.74110 - 1.21916i) q^{3} -1.38038i q^{5} +(-1.29258 + 2.23881i) q^{7} +(6.02728 + 6.68370i) q^{9} +O(q^{10})\)	\(q+(-2.74110 - 1.21916i) q^{3} -1.38038i q^{5} +(-1.29258 + 2.23881i) q^{7} +(6.02728 + 6.68370i) q^{9} +(-3.36484 - 1.94269i) q^{11} +(-1.06693 + 1.84798i) q^{13} +(-1.68291 + 3.78377i) q^{15} +(-10.4602 - 6.03918i) q^{17} +(18.7458 + 3.09785i) q^{19} +(6.27255 - 4.56093i) q^{21} +(8.68045 + 5.01166i) q^{23} +23.0945 q^{25} +(-8.37286 - 25.6690i) q^{27} +55.1072i q^{29} +(-4.94828 - 8.57068i) q^{31} +(6.85492 + 9.42741i) q^{33} +(3.09041 + 1.78425i) q^{35} -7.98205 q^{37} +(5.17756 - 3.76474i) q^{39} -46.5218i q^{41} +(-35.4681 - 61.4325i) q^{43} +(9.22606 - 8.31995i) q^{45} -63.5847i q^{47} +(21.1585 + 36.6476i) q^{49} +(21.3096 + 29.3067i) q^{51} +(87.4751 - 50.5037i) q^{53} +(-2.68166 + 4.64477i) q^{55} +(-47.6072 - 31.3457i) q^{57} -65.8518i q^{59} +83.3834 q^{61} +(-22.7542 + 4.85472i) q^{63} +(2.55092 + 1.47277i) q^{65} +(51.4627 - 89.1360i) q^{67} +(-17.6840 - 24.3204i) q^{69} +(-96.3301 - 55.6162i) q^{71} +(31.7504 - 54.9933i) q^{73} +(-63.3045 - 28.1560i) q^{75} +(8.69862 - 5.02215i) q^{77} +(46.1044 + 79.8551i) q^{79} +(-8.34378 + 80.5691i) q^{81} +(86.6071 + 50.0027i) q^{83} +(-8.33637 + 14.4390i) q^{85} +(67.1847 - 151.055i) q^{87} +(-22.4872 + 12.9830i) q^{89} +(-2.75818 - 4.77731i) q^{91} +(3.11469 + 29.5259i) q^{93} +(4.27621 - 25.8763i) q^{95} +(47.1806 + 81.7192i) q^{97} +(-7.29647 - 34.1988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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