LMFDB - Embedded newform 684.3.s.a.445.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (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			445.21
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0763560 + 2.99903i) q^{3} +(-3.93735 - 6.81968i) q^{5} +(2.97107 + 5.14604i) q^{7} +(-8.98834 - 0.457987i) q^{9} +O(q^{10})$	\(q+(-0.0763560 + 2.99903i) q^{3} +(-3.93735 - 6.81968i) q^{5} +(2.97107 + 5.14604i) q^{7} +(-8.98834 - 0.457987i) q^{9} +(2.93551 + 5.08444i) q^{11} -10.1683i q^{13} +(20.7531 - 11.2875i) q^{15} +(-2.78184 + 4.81829i) q^{17} +(-11.6693 - 14.9942i) q^{19} +(-15.6600 + 8.51739i) q^{21} +45.5995 q^{23} +(-18.5054 + 32.0523i) q^{25} +(2.05983 - 26.9213i) q^{27} +(34.1266 + 19.7030i) q^{29} +(18.3346 + 10.5855i) q^{31} +(-15.4725 + 8.41544i) q^{33} +(23.3963 - 40.5235i) q^{35} +32.9592i q^{37} +(30.4950 + 0.776411i) q^{39} +(43.7963 - 25.2858i) q^{41} -24.1061 q^{43} +(32.2669 + 63.1009i) q^{45} +(29.6984 - 51.4391i) q^{47} +(6.84550 - 11.8568i) q^{49} +(-14.2378 - 8.71073i) q^{51} +(-9.43881 + 5.44950i) q^{53} +(23.1162 - 40.0384i) q^{55} +(45.8591 - 33.8518i) q^{57} +(31.2938 - 18.0675i) q^{59} +(-8.22190 + 14.2407i) q^{61} +(-24.3482 - 47.6151i) q^{63} +(-69.3446 + 40.0361i) q^{65} +122.714i q^{67} +(-3.48180 + 136.754i) q^{69} +(111.397 + 64.3151i) q^{71} +(35.7968 - 62.0019i) q^{73} +(-94.7127 - 57.9456i) q^{75} +(-17.4432 + 30.2125i) q^{77} -30.6165i q^{79} +(80.5805 + 8.23309i) q^{81} +(61.1539 + 105.922i) q^{83} +43.8123 q^{85} +(-61.6955 + 100.842i) q^{87} +(51.6517 - 29.8211i) q^{89} +(52.3265 - 30.2107i) q^{91} +(-33.1461 + 54.1777i) q^{93} +(-56.3096 + 138.619i) q^{95} +91.8294i q^{97} +(-24.0567 - 47.0451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0763560	+	2.99903i	−0.0254520	+	0.999676i
$3$	−0.0763560	+	2.99903i	−0.0254520	+	0.999676i
$4$		0			0
$5$	−3.93735	−	6.81968i	−0.787469	−	1.36394i	−0.927513	−	0.373792i	$-0.878058\pi$
$5$	−3.93735	−	6.81968i	−0.787469	−	1.36394i	0.140043	−	0.990145i	$-0.455276\pi$
$6$		0			0
$7$	2.97107	+	5.14604i	0.424438	+	0.735149i	0.996368	−	0.0851540i	$-0.0271382\pi$
$7$	2.97107	+	5.14604i	0.424438	+	0.735149i	−0.571929	+	0.820303i	$0.693805\pi$
$8$		0			0
$9$	−8.98834	−	0.457987i	−0.998704	−	0.0508875i
$10$		0			0
$11$	2.93551	+	5.08444i	0.266864	+	0.462222i	0.968050	−	0.250756i	$-0.0806792\pi$
$11$	2.93551	+	5.08444i	0.266864	+	0.462222i	−0.701186	+	0.712978i	$0.747346\pi$
$12$		0			0
$13$		−	10.1683i		−	0.782177i	−0.920353	−	0.391089i	$-0.872099\pi$
$13$		−	10.1683i		−	0.782177i	0.920353	−	0.391089i	$-0.127901\pi$
$14$		0			0
$15$	20.7531	−	11.2875i	1.38354	−	0.752499i
$16$		0			0
$17$	−2.78184	+	4.81829i	−0.163638	+	0.283429i	−0.936171	−	0.351546i	$-0.885656\pi$
$17$	−2.78184	+	4.81829i	−0.163638	+	0.283429i	0.772533	+	0.634975i	$0.218989\pi$
$18$		0			0
$19$	−11.6693	−	14.9942i	−0.614176	−	0.789169i
$19$	−11.6693	−	14.9942i	−0.614176	−	0.789169i
$20$		0			0
$21$	−15.6600	+	8.51739i	−0.745713	+	0.405590i
$22$		0			0
$23$	45.5995			1.98259			0.991294	−	0.131665i	$-0.0420322\pi$
$23$	45.5995			1.98259			0.991294	+	0.131665i	$0.0420322\pi$
$24$		0			0
$25$	−18.5054	+	32.0523i	−0.740216	+	1.28209i
$26$		0			0
$27$	2.05983	−	26.9213i	0.0762900	−	0.997086i
$28$		0			0
$29$	34.1266	+	19.7030i	1.17678	+	0.679413i	0.955267	−	0.295745i	$-0.0955679\pi$
$29$	34.1266	+	19.7030i	1.17678	+	0.679413i	0.221511	+	0.975158i	$0.428901\pi$
$30$		0			0
$31$	18.3346	+	10.5855i	0.591438	+	0.341467i	0.765666	−	0.643238i	$-0.222410\pi$
$31$	18.3346	+	10.5855i	0.591438	+	0.341467i	−0.174228	+	0.984705i	$0.555743\pi$
$32$		0			0
$33$	−15.4725	+	8.41544i	−0.468865	+	0.255013i
$34$		0			0
$35$	23.3963	−	40.5235i	0.668464	−	1.15781i
$36$		0			0
$37$			32.9592i			0.890789i	0.895334	+	0.445394i	$0.146937\pi$
$37$			32.9592i			0.890789i	−0.895334	+	0.445394i	$0.853063\pi$
$38$		0			0
$39$	30.4950	+	0.776411i	0.781924	+	0.0199080i
$40$		0			0
$41$	43.7963	−	25.2858i	1.06820	−	0.616727i	0.140513	−	0.990079i	$-0.455125\pi$
$41$	43.7963	−	25.2858i	1.06820	−	0.616727i	0.927690	+	0.373352i	$0.121791\pi$
$42$		0			0
$43$	−24.1061			−0.560606			−0.280303	−	0.959912i	$-0.590435\pi$
$43$	−24.1061			−0.560606			−0.280303	+	0.959912i	$0.590435\pi$
$44$		0			0
$45$	32.2669	+	63.1009i	0.717042	+	1.40224i
$46$		0			0
$47$	29.6984	−	51.4391i	0.631880	−	1.09445i	−0.355287	−	0.934757i	$-0.615617\pi$
$47$	29.6984	−	51.4391i	0.631880	−	1.09445i	0.987167	−	0.159691i	$-0.0510499\pi$
$48$		0			0
$49$	6.84550	−	11.8568i	0.139704	−	0.241975i
$50$		0			0
$51$	−14.2378	−	8.71073i	−0.279172	−	0.170799i
$52$		0			0
$53$	−9.43881	+	5.44950i	−0.178091	+	0.102821i	−0.586395	−	0.810025i	$-0.699453\pi$
$53$	−9.43881	+	5.44950i	−0.178091	+	0.102821i	0.408305	+	0.912846i	$0.366120\pi$
$54$		0			0
$55$	23.1162	−	40.0384i	0.420295	−	0.727972i
$56$		0			0
$57$	45.8591	−	33.8518i	0.804546	−	0.593891i
$58$		0			0
$59$	31.2938	−	18.0675i	0.530403	−	0.306229i	−0.210777	−	0.977534i	$-0.567599\pi$
$59$	31.2938	−	18.0675i	0.530403	−	0.306229i	0.741181	+	0.671306i	$0.234266\pi$
$60$		0			0
$61$	−8.22190	+	14.2407i	−0.134785	+	0.233455i	−0.925515	−	0.378710i	$-0.876368\pi$
$61$	−8.22190	+	14.2407i	−0.134785	+	0.233455i	0.790730	+	0.612165i	$0.209701\pi$
$62$		0			0
$63$	−24.3482	−	47.6151i	−0.386479	−	0.755795i
$64$		0			0
$65$	−69.3446	+	40.0361i	−1.06684	+	0.615941i
$66$		0			0
$67$			122.714i			1.83156i	0.401683	+	0.915779i	$0.368425\pi$
$67$			122.714i			1.83156i	−0.401683	+	0.915779i	$0.631575\pi$
$68$		0			0
$69$	−3.48180	+	136.754i	−0.0504608	+	1.98195i
$70$		0			0
$71$	111.397	+	64.3151i	1.56897	+	0.905847i	0.996289	+	0.0860708i	$0.0274311\pi$
$71$	111.397	+	64.3151i	1.56897	+	0.905847i	0.572684	+	0.819776i	$0.305902\pi$
$72$		0			0
$73$	35.7968	−	62.0019i	0.490368	−	0.849342i	−0.509571	−	0.860429i	$-0.670196\pi$
$73$	35.7968	−	62.0019i	0.490368	−	0.849342i	0.999939	+	0.0110870i	$0.00352918\pi$
$74$		0			0
$75$	−94.7127	−	57.9456i	−1.26284	−	0.772608i
$76$		0			0
$77$	−17.4432	+	30.2125i	−0.226535	+	0.392370i
$78$		0			0
$79$		−	30.6165i		−	0.387551i	−0.981046	−	0.193775i	$-0.937927\pi$
$79$		−	30.6165i		−	0.387551i	0.981046	−	0.193775i	$-0.0620733\pi$
$80$		0			0
$81$	80.5805	+	8.23309i	0.994821	+	0.101643i
$82$		0			0
$83$	61.1539	+	105.922i	0.736794	+	1.27616i	0.953932	+	0.300023i	$0.0969945\pi$
$83$	61.1539	+	105.922i	0.736794	+	1.27616i	−0.217138	+	0.976141i	$0.569672\pi$
$84$		0			0
$85$	43.8123			0.515439
$86$		0			0
$87$	−61.6955	+	100.842i	−0.709144	+	1.15910i
$88$		0			0
$89$	51.6517	−	29.8211i	0.580356	−	0.335069i	−0.180919	−	0.983498i	$-0.557907\pi$
$89$	51.6517	−	29.8211i	0.580356	−	0.335069i	0.761275	+	0.648429i	$0.224574\pi$
$90$		0			0
$91$	52.3265	−	30.2107i	0.575017	−	0.331986i
$92$		0			0
$93$	−33.1461	+	54.1777i	−0.356410	+	0.582555i
$94$		0			0
$95$	−56.3096	+	138.619i	−0.592732	+	1.45914i
$96$		0			0
$97$			91.8294i			0.946695i	0.880876	+	0.473347i	$0.156954\pi$
$97$			91.8294i			0.946695i	−0.880876	+	0.473347i	$0.843046\pi$
$98$		0			0
$99$	−24.0567	−	47.0451i	−0.242997	−	0.475203i
$100$		0			0
$101$	−10.6133	+	18.3828i	−0.105082	+	0.182008i	−0.913772	−	0.406228i	$-0.866844\pi$
$101$	−10.6133	+	18.3828i	−0.105082	+	0.182008i	0.808690	+	0.588236i	$0.200177\pi$
$102$		0			0
$103$	7.07481	+	4.08464i	0.0686875	+	0.0396567i	0.533950	−	0.845516i	$-0.320707\pi$
$103$	7.07481	+	4.08464i	0.0686875	+	0.0396567i	−0.465263	+	0.885173i	$0.654040\pi$
$104$		0			0
$105$	119.745	+	73.2602i	1.14043	+	0.697717i
$106$		0			0
$107$		−	28.0913i		−	0.262536i	−0.991347	−	0.131268i	$-0.958095\pi$
$107$		−	28.0913i		−	0.262536i	0.991347	−	0.131268i	$-0.0419048\pi$
$108$		0			0
$109$	−115.785	−	66.8483i	−1.06225	−	0.613288i	−0.136193	−	0.990682i	$-0.543487\pi$
$109$	−115.785	−	66.8483i	−1.06225	−	0.613288i	−0.926052	+	0.377395i	$0.876820\pi$
$110$		0			0
$111$	−98.8455	−	2.51663i	−0.890500	−	0.0226723i
$112$		0			0
$113$	2.57918	+	1.48909i	0.0228246	+	0.0131778i	0.511369	−	0.859361i	$-0.329139\pi$
$113$	2.57918	+	1.48909i	0.0228246	+	0.0131778i	−0.488544	+	0.872539i	$0.662472\pi$
$114$		0			0
$115$	−179.541	−	310.974i	−1.56123	−	2.70413i
$116$		0			0
$117$	−4.65696	+	91.3962i	−0.0398030	+	0.781164i
$118$		0			0
$119$	−33.0602			−0.277817
$120$		0			0
$121$	43.2656	−	74.9382i	0.357567	−	0.619324i
$122$		0			0
$123$	72.4888	+	133.277i	0.589340	+	1.08355i
$124$		0			0
$125$	94.5813			0.756651
$126$		0			0
$127$	−83.0708	+	47.9610i	−0.654101	+	0.377645i	−0.790026	−	0.613074i	$-0.789933\pi$
$127$	−83.0708	+	47.9610i	−0.654101	+	0.377645i	0.135925	+	0.990719i	$0.456599\pi$
$128$		0			0
$129$	1.84064	−	72.2947i	0.0142685	−	0.560424i
$130$		0			0
$131$	−101.532	−	175.859i	−0.775057	−	1.34244i	−0.934763	−	0.355273i	$-0.884388\pi$
$131$	−101.532	−	175.859i	−0.775057	−	1.34244i	0.159706	−	0.987165i	$-0.448945\pi$
$132$		0			0
$133$	42.4904	−	104.600i	0.319477	−	0.786464i
$134$		0			0
$135$	−191.705	+	91.9512i	−1.42004	+	0.681120i
$136$		0			0
$137$	−67.1829	+	116.364i	−0.490386	+	0.849374i	−0.999939	−	0.0110654i	$-0.996478\pi$
$137$	−67.1829	+	116.364i	−0.490386	+	0.849374i	0.509552	+	0.860440i	$0.329811\pi$
$138$		0			0
$139$	181.947			1.30897			0.654485	−	0.756075i	$-0.272885\pi$
$139$	181.947			1.30897			0.654485	+	0.756075i	$0.272885\pi$
$140$		0			0
$141$	152.000	+	92.9939i	1.07801	+	0.659532i
$142$		0			0
$143$	51.7002	−	29.8491i	0.361540	−	0.208735i
$144$		0			0
$145$		−	310.310i		−	2.14007i
$146$		0			0
$147$	35.0361	+	21.4352i	0.238341	+	0.145818i
$148$		0			0
$149$	−95.9040	−	166.111i	−0.643651	−	1.11484i	−0.984611	−	0.174758i	$-0.944086\pi$
$149$	−95.9040	−	166.111i	−0.643651	−	1.11484i	0.340961	−	0.940078i	$-0.389248\pi$
$150$		0			0
$151$	95.6299	−	55.2120i	0.633311	−	0.365642i	−0.148722	−	0.988879i	$-0.547516\pi$
$151$	95.6299	−	55.2120i	0.633311	−	0.365642i	0.782033	+	0.623237i	$0.214183\pi$
$152$		0			0
$153$	27.2109	−	42.0344i	0.177849	−	0.274735i
$154$		0			0
$155$		−	166.715i		−	1.07558i
$156$		0			0
$157$	13.2059	+	22.8732i	0.0841138	+	0.145689i	0.905013	−	0.425383i	$-0.139861\pi$
$157$	13.2059	+	22.8732i	0.0841138	+	0.145689i	−0.820899	+	0.571073i	$0.806527\pi$
$158$		0			0
$159$	−15.6225	−	28.7233i	−0.0982546	−	0.180650i
$160$		0			0
$161$	135.479	+	234.657i	0.841487	+	1.45750i
$162$		0			0
$163$	−86.6847			−0.531808			−0.265904	−	0.964000i	$-0.585670\pi$
$163$	−86.6847			−0.531808			−0.265904	+	0.964000i	$0.585670\pi$
$164$		0			0
$165$	118.311	+	72.3833i	0.717038	+	0.438687i
$166$		0			0
$167$		−	262.722i		−	1.57318i	−0.617473	−	0.786592i	$-0.711844\pi$
$167$		−	262.722i		−	1.57318i	0.617473	−	0.786592i	$-0.288156\pi$
$168$		0			0
$169$	65.6056			0.388199
$170$		0			0
$171$	98.0208	+	140.118i	0.573221	+	0.819401i
$172$		0			0
$173$		−	298.824i		−	1.72730i	−0.504088	−	0.863652i	$-0.668171\pi$
$173$		−	298.824i		−	1.72730i	0.504088	−	0.863652i	$-0.331829\pi$
$174$		0			0
$175$	−219.923			−1.25670
$176$		0			0
$177$	51.7954	+	95.2306i	0.292630	+	0.538026i
$178$		0			0
$179$			29.5036i			0.164825i	0.996598	+	0.0824124i	$0.0262625\pi$
$179$			29.5036i			0.164825i	−0.996598	+	0.0824124i	$0.973738\pi$
$180$		0			0
$181$	−158.150	+	91.3082i	−0.873759	+	0.504465i	−0.868596	−	0.495522i	$-0.834977\pi$
$181$	−158.150	+	91.3082i	−0.873759	+	0.504465i	−0.00516334	+	0.999987i	$0.501644\pi$
$182$		0			0
$183$	−42.0806	−	25.7451i	−0.229949	−	0.140683i
$184$		0			0
$185$	224.771	−	129.772i	1.21498	−	0.701469i
$186$		0			0
$187$	−32.6644			−0.174676
$188$		0			0
$189$	144.658	−	69.3851i	0.765387	−	0.367117i
$190$		0			0
$191$	70.1739	+	121.545i	0.367403	+	0.636360i	0.989159	−	0.146851i	$-0.0469138\pi$
$191$	70.1739	+	121.545i	0.367403	+	0.636360i	−0.621756	+	0.783211i	$0.713580\pi$
$192$		0			0
$193$	288.160	−	166.369i	1.49306	−	0.862018i	0.493091	−	0.869978i	$-0.335867\pi$
$193$	288.160	−	166.369i	1.49306	−	0.862018i	0.999968	+	0.00795994i	$0.00253376\pi$
$194$		0			0
$195$	−114.775	−	211.024i	−0.588588	−	1.08217i
$196$		0			0
$197$	−52.4559			−0.266274			−0.133137	−	0.991098i	$-0.542505\pi$
$197$	−52.4559			−0.266274			−0.133137	+	0.991098i	$0.542505\pi$
$198$		0			0
$199$	−108.793	−	188.435i	−0.546698	−	0.946909i	−0.998498	−	0.0547893i	$-0.982551\pi$
$199$	−108.793	−	188.435i	−0.546698	−	0.946909i	0.451800	−	0.892119i	$-0.350782\pi$
$200$		0			0
$201$	−368.024	−	9.36997i	−1.83096	−	0.0466168i
$202$		0			0
$203$			234.156i			1.15348i
$204$		0			0
$205$	−344.883	−	199.118i	−1.68235	−	0.971308i
$206$		0			0
$207$	−409.864	−	20.8840i	−1.98002	−	0.100889i
$208$		0			0
$209$	41.9818	−	103.348i	0.200870	−	0.494487i
$210$		0			0
$211$	−297.418	+	171.714i	−1.40956	+	0.813811i	−0.995346	−	0.0963679i	$-0.969277\pi$
$211$	−297.418	+	171.714i	−1.40956	+	0.813811i	−0.414216	+	0.910179i	$0.635944\pi$
$212$		0			0
$213$	−201.389	+	329.172i	−0.945487	+	1.54541i
$214$		0			0
$215$	94.9139	+	164.396i	0.441460	+	0.764631i
$216$		0			0
$217$			125.801i			0.579727i
$218$		0			0
$219$	183.212	+	112.090i	0.836586	+	0.511826i
$220$		0			0
$221$	48.9939	+	28.2866i	0.221692	+	0.127994i
$222$		0			0
$223$		−	71.7449i		−	0.321726i	−0.986977	−	0.160863i	$-0.948572\pi$
$223$		−	71.7449i		−	0.321726i	0.986977	−	0.160863i	$-0.0514277\pi$
$224$		0			0
$225$	181.012	−	279.622i	0.804499	−	1.24276i
$226$		0			0
$227$	226.307	−	130.659i	0.996949	−	0.575589i	0.0896049	−	0.995977i	$-0.471440\pi$
$227$	226.307	−	130.659i	0.996949	−	0.575589i	0.907344	+	0.420389i	$0.138106\pi$
$228$		0			0
$229$	7.31766	−	12.6746i	0.0319548	−	0.0553474i	−0.849606	−	0.527418i	$-0.823160\pi$
$229$	7.31766	−	12.6746i	0.0319548	−	0.0553474i	0.881561	+	0.472071i	$0.156493\pi$
$230$		0			0
$231$	−89.2761	−	54.6195i	−0.386477	−	0.236448i
$232$		0			0
$233$	−51.4515	+	89.1166i	−0.220822	+	0.382475i	−0.955058	−	0.296420i	$-0.904207\pi$
$233$	−51.4515	+	89.1166i	−0.220822	+	0.382475i	0.734236	+	0.678894i	$0.237541\pi$
$234$		0			0
$235$	−467.731			−1.99035
$236$		0			0
$237$	91.8198	+	2.33775i	0.387425	+	0.00986394i
$238$		0			0
$239$	60.9446	−	105.559i	0.254998	−	0.441670i	−0.709897	−	0.704306i	$-0.751258\pi$
$239$	60.9446	−	105.559i	0.254998	−	0.441670i	0.964895	+	0.262636i	$0.0845917\pi$
$240$		0			0
$241$	−162.771	−	93.9756i	−0.675397	−	0.389940i	0.122722	−	0.992441i	$-0.460838\pi$
$241$	−162.771	−	93.9756i	−0.675397	−	0.389940i	−0.798118	+	0.602501i	$0.794171\pi$
$242$		0			0
$243$	−30.8441	+	241.035i	−0.126930	+	0.991912i
$244$		0			0
$245$	−107.812			−0.440051
$246$		0			0
$247$	−152.466	+	118.657i	−0.617270	+	0.480394i
$248$		0			0
$249$	−322.331	+	175.314i	−1.29450	+	0.704074i
$250$		0			0
$251$	−12.6291	−	21.8742i	−0.0503150	−	0.0871482i	0.839771	−	0.542941i	$-0.182689\pi$
$251$	−12.6291	−	21.8742i	−0.0503150	−	0.0871482i	−0.890086	+	0.455793i	$0.849356\pi$
$252$		0			0
$253$	133.858	+	231.848i	0.529082	+	0.916397i
$254$		0			0
$255$	−3.34533	+	131.394i	−0.0131189	+	0.515272i
$256$		0			0
$257$			198.021i			0.770511i	0.922810	+	0.385256i	$0.125887\pi$
$257$			198.021i			0.770511i	−0.922810	+	0.385256i	$0.874113\pi$
$258$		0			0
$259$	−169.609	+	97.9240i	−0.654862	+	0.378085i
$260$		0			0
$261$	−297.717	−	192.727i	−1.14068	−	0.738416i
$262$		0			0
$263$	−162.907			−0.619418			−0.309709	−	0.950831i	$-0.600232\pi$
$263$	−162.907			−0.619418			−0.309709	+	0.950831i	$0.600232\pi$
$264$		0			0
$265$	74.3277	+	42.9131i	0.280482	+	0.161936i
$266$		0			0
$267$	85.4905	+	157.182i	0.320189	+	0.588696i
$268$		0			0
$269$	341.865	+	197.376i	1.27088	+	0.733740i	0.975153	−	0.221534i	$-0.0711063\pi$
$269$	341.865	+	197.376i	1.27088	+	0.733740i	0.295722	+	0.955274i	$0.404440\pi$
$270$		0			0
$271$	−179.436	+	310.792i	−0.662125	+	1.14683i	0.317931	+	0.948114i	$0.397012\pi$
$271$	−179.436	+	310.792i	−0.662125	+	1.14683i	−0.980056	+	0.198721i	$0.936321\pi$
$272$		0			0
$273$	86.6074	+	159.235i	0.317243	+	0.583280i
$274$		0			0
$275$	−217.291			−0.790148
$276$		0			0
$277$	54.4726	+	94.3494i	0.196652	+	0.340611i	0.947441	−	0.319931i	$-0.103660\pi$
$277$	54.4726	+	94.3494i	0.196652	+	0.340611i	−0.750789	+	0.660542i	$0.770326\pi$
$278$		0			0
$279$	−159.949	−	103.543i	−0.573295	−	0.371121i
$280$		0			0
$281$	−381.622	−	220.330i	−1.35809	−	0.784091i	−0.368720	−	0.929541i	$-0.620204\pi$
$281$	−381.622	−	220.330i	−1.35809	−	0.784091i	−0.989366	+	0.145449i	$0.953537\pi$
$282$		0			0
$283$	−21.8750	−	37.8886i	−0.0772969	−	0.133882i	0.824786	−	0.565445i	$-0.191296\pi$
$283$	−21.8750	−	37.8886i	−0.0772969	−	0.133882i	−0.902083	+	0.431563i	$0.857962\pi$
$284$		0			0
$285$	−411.422	−	179.458i	−1.44358	−	0.629678i
$286$		0			0
$287$	260.244	+	150.252i	0.906773	+	0.523525i
$288$		0			0
$289$	129.023	+	223.474i	0.446445	+	0.773266i
$290$		0			0
$291$	−275.399	−	7.01172i	−0.946388	−	0.0240953i
$292$		0			0
$293$	−15.3446	−	8.85919i	−0.0523706	−	0.0302362i	0.473586	−	0.880748i	$-0.342959\pi$
$293$	−15.3446	−	8.85919i	−0.0523706	−	0.0302362i	−0.525957	+	0.850511i	$0.676293\pi$
$294$		0			0
$295$	−246.429	−	142.276i	−0.835353	−	0.482291i
$296$		0			0
$297$	142.927	−	68.5546i	0.481234	−	0.230823i
$298$		0			0
$299$		−	463.670i		−	1.55074i
$300$		0			0
$301$	−71.6208	−	124.051i	−0.237943	−	0.412129i
$302$		0			0
$303$	−54.3201	−	33.2332i	−0.179274	−	0.109681i
$304$		0			0
$305$	129.490			0.424557
$306$		0			0
$307$	−124.766	−	72.0337i	−0.406404	−	0.234638i	0.282839	−	0.959167i	$-0.408724\pi$
$307$	−124.766	−	72.0337i	−0.406404	−	0.234638i	−0.689244	+	0.724530i	$0.742057\pi$
$308$		0			0
$309$	−12.7902	+	20.9057i	−0.0413921	+	0.0676559i
$310$		0			0
$311$	−100.334	+	173.784i	−0.322617	+	0.558790i	−0.981027	−	0.193870i	$-0.937896\pi$
$311$	−100.334	+	173.784i	−0.322617	+	0.558790i	0.658410	+	0.752660i	$0.271229\pi$
$312$		0			0
$313$	173.486	−	300.486i	0.554267	−	0.960019i	−0.443693	−	0.896179i	$-0.646332\pi$
$313$	173.486	−	300.486i	0.554267	−	0.960019i	0.997960	−	0.0638403i	$-0.0203348\pi$
$314$		0			0
$315$	−228.853	+	353.524i	−0.726517	+	1.12230i
$316$		0			0
$317$	31.0236	+	17.9115i	0.0978662	+	0.0565031i	0.548134	−	0.836390i	$-0.315338\pi$
$317$	31.0236	+	17.9115i	0.0978662	+	0.0565031i	−0.450268	+	0.892893i	$0.648672\pi$
$318$		0			0
$319$			231.353i			0.725244i
$320$		0			0
$321$	84.2467	+	2.14494i	0.262451	+	0.00668206i
$322$		0			0
$323$	104.709	−	14.5147i	0.324176	−	0.0449373i
$324$		0			0
$325$	325.917	+	188.169i	1.00282	+	0.578980i
$326$		0			0
$327$	209.321	−	342.137i	0.640125	−	1.04629i
$328$		0			0
$329$	352.944			1.07278
$330$		0			0
$331$	524.816	−	303.003i	1.58555	−	0.915416i	0.591519	−	0.806291i	$-0.298529\pi$
$331$	524.816	−	303.003i	1.58555	−	0.915416i	0.994028	−	0.109125i	$-0.0348048\pi$
$332$		0			0
$333$	15.0949	−	296.248i	0.0453300	−	0.889635i
$334$		0			0
$335$	836.873	−	483.169i	2.49813	−	1.44230i
$336$		0			0
$337$	304.419	−	175.756i	0.903319	−	0.521532i	0.0250436	−	0.999686i	$-0.492028\pi$
$337$	304.419	−	175.756i	0.903319	−	0.521532i	0.878276	+	0.478155i	$0.158694\pi$
$338$		0			0
$339$	−4.66276	+	7.62134i	−0.0137545	+	0.0224818i
$340$		0			0
$341$			124.295i			0.364501i
$342$		0			0
$343$	372.519			1.08606
$344$		0			0
$345$	946.330	−	514.704i	2.74299	−	1.49190i
$346$		0			0
$347$	168.248	+	291.414i	0.484865	+	0.839810i	0.999849	−	0.0173894i	$-0.00553551\pi$
$347$	168.248	+	291.414i	0.484865	+	0.839810i	−0.514984	+	0.857200i	$0.672202\pi$
$348$		0			0
$349$	147.329	+	255.181i	0.422146	+	0.731178i	0.996149	−	0.0876751i	$-0.0279437\pi$
$349$	147.329	+	255.181i	0.422146	+	0.731178i	−0.574003	+	0.818853i	$0.694610\pi$
$350$		0			0
$351$	−273.744	−	20.9450i	−0.779898	−	0.0596723i
$352$		0			0
$353$	147.760	+	255.928i	0.418584	+	0.725009i	0.995797	−	0.0915844i	$-0.0291931\pi$
$353$	147.760	+	255.928i	0.418584	+	0.725009i	−0.577213	+	0.816594i	$0.695860\pi$
$354$		0			0
$355$		−	1012.92i		−	2.85331i
$356$		0			0
$357$	2.52434	−	99.1484i	0.00707098	−	0.277727i
$358$		0			0
$359$	−36.1082	+	62.5412i	−0.100580	+	0.174210i	−0.911924	−	0.410360i	$-0.865403\pi$
$359$	−36.1082	+	62.5412i	−0.100580	+	0.174210i	0.811344	+	0.584569i	$0.198736\pi$
$360$		0			0
$361$	−88.6530	+	349.945i	−0.245576	+	0.969377i
$362$		0			0
$363$	221.438	+	135.477i	0.610023	+	0.373214i
$364$		0			0
$365$	−563.778			−1.54460
$366$		0			0
$367$	−325.528	+	563.832i	−0.886998	+	1.53633i	−0.0435924	+	0.999049i	$0.513880\pi$
$367$	−325.528	+	563.832i	−0.886998	+	1.53633i	−0.843406	+	0.537277i	$0.819453\pi$
$368$		0			0
$369$	−405.237	+	207.219i	−1.09820	+	0.561570i
$370$		0			0
$371$	−56.0867	−	32.3817i	−0.151177	−	0.0872821i
$372$		0			0
$373$	−25.4034	−	14.6667i	−0.0681057	−	0.0393209i	0.465560	−	0.885016i	$-0.345853\pi$
$373$	−25.4034	−	14.6667i	−0.0681057	−	0.0393209i	−0.533666	+	0.845695i	$0.679186\pi$
$374$		0			0
$375$	−7.22185	+	283.652i	−0.0192583	+	0.756406i
$376$		0			0
$377$	200.346	−	347.009i	0.531421	−	0.920449i
$378$		0			0
$379$		−	680.418i		−	1.79530i	−0.440712	−	0.897648i	$-0.645274\pi$
$379$		−	680.418i		−	1.79530i	0.440712	−	0.897648i	$-0.354726\pi$
$380$		0			0
$381$	−137.493	−	252.794i	−0.360875	−	0.663501i
$382$		0			0
$383$	133.912	−	77.3144i	0.349641	−	0.201865i	−0.314886	−	0.949129i	$-0.601966\pi$
$383$	133.912	−	77.3144i	0.349641	−	0.201865i	0.664527	+	0.747264i	$0.268633\pi$
$384$		0			0
$385$	274.719			0.713557
$386$		0			0
$387$	216.673	+	11.0403i	0.559880	+	0.0285278i
$388$		0			0
$389$	−233.091	+	403.726i	−0.599207	+	1.03786i	0.393732	+	0.919225i	$0.371184\pi$
$389$	−233.091	+	403.726i	−0.599207	+	1.03786i	−0.992938	+	0.118631i	$0.962149\pi$
$390$		0			0
$391$	−126.851	+	219.712i	−0.324426	+	0.561923i
$392$		0			0
$393$	535.160	−	291.071i	1.36173	−	0.740638i
$394$		0			0
$395$	−208.795	+	120.548i	−0.528595	+	0.305184i
$396$		0			0
$397$	−185.889	+	321.969i	−0.468233	+	0.811004i	−0.999341	−	0.0363003i	$-0.988443\pi$
$397$	−185.889	+	321.969i	−0.468233	+	0.811004i	0.531107	+	0.847304i	$0.321776\pi$
$398$		0			0
$399$	310.453	+	135.417i	0.778078	+	0.339391i
$400$		0			0
$401$	−378.810	+	218.706i	−0.944662	+	0.545401i	−0.891419	−	0.453180i	$-0.850289\pi$
$401$	−378.810	+	218.706i	−0.944662	+	0.545401i	−0.0532436	+	0.998582i	$0.516956\pi$
$402$		0			0
$403$	107.636	−	186.432i	0.267088	−	0.462609i
$404$		0			0
$405$	−261.126	−	581.950i	−0.644756	−	1.43691i
$406$		0			0
$407$	−167.579	+	96.7519i	−0.411742	+	0.237720i
$408$		0			0
$409$			281.030i			0.687115i	0.939132	+	0.343558i	$0.111632\pi$
$409$			281.030i			0.687115i	−0.939132	+	0.343558i	$0.888368\pi$
$410$		0			0
$411$	−343.850	−	210.369i	−0.836618	−	0.511846i
$412$		0			0
$413$	185.952	+	107.359i	0.450247	+	0.259950i
$414$		0			0
$415$	481.568	−	834.100i	1.16041	−	2.00988i
$416$		0			0
$417$	−13.8927	+	545.664i	−0.0333159	+	1.30855i
$418$		0			0
$419$	−308.348	+	534.075i	−0.735914	+	1.27464i	0.218406	+	0.975858i	$0.429914\pi$
$419$	−308.348	+	534.075i	−0.735914	+	1.27464i	−0.954321	+	0.298783i	$0.903419\pi$
$420$		0			0
$421$		−	231.305i		−	0.549418i	−0.961527	−	0.274709i	$-0.911418\pi$
$421$		−	231.305i		−	0.549418i	0.961527	−	0.274709i	$-0.0885816\pi$
$422$		0			0
$423$	−290.498	+	448.751i	−0.686755	+	1.06088i
$424$		0			0
$425$	−102.958	−	178.329i	−0.242255	−	0.419597i
$426$		0			0
$427$	−97.7113			−0.228832
$428$		0			0
$429$	85.5707	+	157.329i	0.199466	+	0.366735i
$430$		0			0
$431$	229.645	−	132.586i	0.532819	−	0.307623i	−0.209344	−	0.977842i	$-0.567133\pi$
$431$	229.645	−	132.586i	0.532819	−	0.307623i	0.742164	+	0.670219i	$0.233800\pi$
$432$		0			0
$433$	−273.676	+	158.007i	−0.632047	+	0.364913i	−0.781545	−	0.623849i	$-0.785568\pi$
$433$	−273.676	+	158.007i	−0.632047	+	0.364913i	0.149497	+	0.988762i	$0.452234\pi$
$434$		0			0
$435$	930.628	+	23.6940i	2.13937	+	0.0544690i
$436$		0			0
$437$	−532.117	−	683.729i	−1.21766	−	1.56460i
$438$		0			0
$439$			327.989i			0.747128i	0.927604	+	0.373564i	$0.121864\pi$
$439$			327.989i			0.747128i	−0.927604	+	0.373564i	$0.878136\pi$
$440$		0			0
$441$	−66.9600	+	103.437i	−0.151837	+	0.234552i
$442$		0			0
$443$	245.844	−	425.814i	0.554952	−	0.961205i	−0.442955	−	0.896544i	$-0.646070\pi$
$443$	245.844	−	425.814i	0.554952	−	0.961205i	0.997907	−	0.0646616i	$-0.0205968\pi$
$444$		0			0
$445$	−406.741	−	234.832i	−0.914025	−	0.527713i
$446$		0			0
$447$	505.493	−	274.935i	1.13086	−	0.615067i
$448$		0			0
$449$			270.439i			0.602315i	0.953574	+	0.301157i	$0.0973730\pi$
$449$			270.439i			0.602315i	−0.953574	+	0.301157i	$0.902627\pi$
$450$		0			0
$451$	257.129	+	148.453i	0.570130	+	0.329165i
$452$		0			0
$453$	158.280	+	291.013i	0.349405	+	0.642412i
$454$		0			0
$455$	−412.055	−	237.900i	−0.905616	−	0.522858i
$456$		0			0
$457$	419.072	+	725.854i	0.917007	+	1.58830i	0.803936	+	0.594716i	$0.202735\pi$
$457$	419.072	+	725.854i	0.917007	+	1.58830i	0.113071	+	0.993587i	$0.463931\pi$
$458$		0			0
$459$	123.985	+	84.8157i	0.270119	+	0.184784i
$460$		0			0
$461$	472.893			1.02580			0.512899	−	0.858449i	$-0.328572\pi$
$461$	472.893			1.02580			0.512899	+	0.858449i	$0.328572\pi$
$462$		0			0
$463$	−380.427	+	658.918i	−0.821656	+	1.42315i	0.0827930	+	0.996567i	$0.473616\pi$
$463$	−380.427	+	658.918i	−0.821656	+	1.42315i	−0.904449	+	0.426583i	$0.859717\pi$
$464$		0			0
$465$	499.982	+	12.7297i	1.07523	+	0.0273756i
$466$		0			0
$467$	−428.831			−0.918268			−0.459134	−	0.888367i	$-0.651840\pi$
$467$	−428.831			−0.918268			−0.459134	+	0.888367i	$0.651840\pi$
$468$		0			0
$469$	−631.493	+	364.593i	−1.34647	+	0.777383i
$470$		0			0
$471$	−69.6058	+	37.8582i	−0.147783	+	0.0803784i
$472$		0			0
$473$	−70.7635	−	122.566i	−0.149606	−	0.259125i
$474$		0			0
$475$	696.545	−	96.5552i	1.46641	−	0.203274i
$476$		0			0
$477$	87.3350	−	44.6591i	0.183092	−	0.0936249i
$478$		0			0
$479$	−273.315	+	473.396i	−0.570596	+	0.988301i	0.425909	+	0.904766i	$0.359954\pi$
$479$	−273.315	+	473.396i	−0.570596	+	0.988301i	−0.996505	+	0.0835350i	$0.973379\pi$
$480$		0			0
$481$	335.139			0.696755
$482$		0			0
$483$	−714.088	+	388.389i	−1.47844	+	0.804118i
$484$		0			0
$485$	626.248	−	361.564i	1.29123	−	0.745493i
$486$		0			0
$487$		−	22.0584i		−	0.0452945i	−0.999744	−	0.0226472i	$-0.992791\pi$
$487$		−	22.0584i		−	0.0452945i	0.999744	−	0.0226472i	$-0.00720946\pi$
$488$		0			0
$489$	6.61889	−	259.970i	0.0135356	−	0.531635i
$490$		0			0
$491$	−457.746	−	792.840i	−0.932274	−	1.61475i	−0.779425	−	0.626496i	$-0.784489\pi$
$491$	−457.746	−	792.840i	−0.932274	−	1.61475i	−0.152849	−	0.988250i	$-0.548845\pi$
$492$		0			0
$493$	−189.869	+	109.621i	−0.385131	+	0.222355i
$494$		0			0
$495$	−226.113	+	349.292i	−0.456795	+	0.705641i
$496$		0			0
$497$			764.339i			1.53790i
$498$		0			0
$499$	−410.616	−	711.208i	−0.822878	−	1.42527i	−0.903530	−	0.428524i	$-0.859034\pi$
$499$	−410.616	−	711.208i	−0.822878	−	1.42527i	0.0806527	−	0.996742i	$-0.474300\pi$
$500$		0			0
$501$	787.910	+	20.0604i	1.57267	+	0.0400407i
$502$		0			0
$503$	227.039	+	393.244i	0.451371	+	0.781797i	0.998471	−	0.0552698i	$-0.0176019\pi$
$503$	227.039	+	393.244i	0.451371	+	0.781797i	−0.547101	+	0.837067i	$0.684269\pi$
$504$		0			0
$505$	167.153			0.330996
$506$		0			0
$507$	−5.00937	+	196.753i	−0.00988042	+	0.388073i
$508$		0			0
$509$			342.757i			0.673393i	0.941613	+	0.336696i	$0.109310\pi$
$509$			342.757i			0.673393i	−0.941613	+	0.336696i	$0.890690\pi$
$510$		0			0
$511$	425.419			0.832523
$512$		0			0
$513$	−427.701	+	283.268i	−0.833725	+	0.552180i
$514$		0			0
$515$		−	64.3307i		−	0.124914i
$516$		0			0
$517$	348.719			0.674505
$518$		0			0
$519$	896.180	+	22.8170i	1.72674	+	0.0439633i
$520$		0			0
$521$		−	346.949i		−	0.665929i	−0.942939	−	0.332965i	$-0.891951\pi$
$521$		−	346.949i		−	0.665929i	0.942939	−	0.332965i	$-0.108049\pi$
$522$		0			0
$523$	652.430	−	376.681i	1.24748	−	0.720231i	0.276871	−	0.960907i	$-0.410703\pi$
$523$	652.430	−	376.681i	1.24748	−	0.720231i	0.970605	+	0.240676i	$0.0773693\pi$
$524$		0			0
$525$	16.7924	−	659.556i	0.0319856	−	1.25630i
$526$		0			0
$527$	−102.008	+	58.8942i	−0.193563	+	0.111754i
$528$		0			0
$529$	1550.32			2.93066
$530$		0			0
$531$	−289.554	+	148.065i	−0.545299	+	0.278841i
$532$		0			0
$533$	−257.114	−	445.334i	−0.482390	−	0.835524i
$534$		0			0
$535$	−191.574	+	110.605i	−0.358082	+	0.206739i
$536$		0			0
$537$	−88.4822	−	2.25278i	−0.164771	−	0.00419512i
$538$		0			0
$539$	80.3800			0.149128
$540$		0			0
$541$	131.685	+	228.086i	0.243411	+	0.421600i	0.961684	−	0.274162i	$-0.0884003\pi$
$541$	131.685	+	228.086i	0.243411	+	0.421600i	−0.718273	+	0.695762i	$0.755067\pi$
$542$		0			0
$543$	−261.760	−	481.269i	−0.482063	−	0.886315i
$544$		0			0
$545$			1052.82i			1.93178i
$546$		0			0
$547$	−112.904	−	65.1853i	−0.206406	−	0.119169i	0.393234	−	0.919439i	$-0.371356\pi$
$547$	−112.904	−	65.1853i	−0.206406	−	0.119169i	−0.599640	+	0.800270i	$0.704690\pi$
$548$		0			0
$549$	80.4233	−	124.235i	0.146490	−	0.226293i
$550$		0			0
$551$	−102.804	−	741.622i	−0.186577	−	1.34596i
$552$		0			0
$553$	157.554	−	90.9638i	0.284908	−	0.164491i
$554$		0			0
$555$	372.027	+	684.004i	0.670318	+	1.23244i
$556$		0			0
$557$	85.9690	+	148.903i	0.154343	+	0.267330i	0.932820	−	0.360344i	$-0.117341\pi$
$557$	85.9690	+	148.903i	0.154343	+	0.267330i	−0.778477	+	0.627674i	$0.784007\pi$
$558$		0			0
$559$			245.118i			0.438493i
$560$		0			0
$561$	2.49413	−	97.9616i	0.00444586	−	0.174620i
$562$		0			0
$563$	327.977	+	189.358i	0.582553	+	0.336337i	0.762147	−	0.647404i	$-0.224145\pi$
$563$	327.977	+	189.358i	0.582553	+	0.336337i	−0.179595	+	0.983741i	$0.557479\pi$
$564$		0			0
$565$		−	23.4523i		−	0.0415084i
$566$		0			0
$567$	197.042	+	439.132i	0.347517	+	0.774483i
$568$		0			0
$569$	279.072	−	161.122i	0.490460	−	0.283167i	−0.234305	−	0.972163i	$-0.575282\pi$
$569$	279.072	−	161.122i	0.490460	−	0.283167i	0.724765	+	0.688996i	$0.241948\pi$
$570$		0			0
$571$	24.9340	−	43.1869i	0.0436672	−	0.0756339i	−0.843366	−	0.537340i	$-0.819429\pi$
$571$	24.9340	−	43.1869i	0.0436672	−	0.0756339i	0.887033	+	0.461706i	$0.152763\pi$
$572$		0			0
$573$	−369.874	+	201.173i	−0.645505	+	0.351087i
$574$		0			0
$575$	−843.838	+	1461.57i	−1.46754	+	2.54186i
$576$		0			0
$577$	−219.364			−0.380181			−0.190090	−	0.981767i	$-0.560878\pi$
$577$	−219.364			−0.380181			−0.190090	+	0.981767i	$0.560878\pi$
$578$		0			0
$579$	476.944	+	876.904i	0.823737	+	1.51452i
$580$		0			0
$581$	−363.385	+	629.401i	−0.625447	+	1.08331i
$582$		0			0
$583$	−55.4153	−	31.9941i	−0.0950520	−	0.0548783i
$584$		0			0
$585$	641.629	−	328.100i	1.09680	−	0.560854i
$586$		0			0
$587$	708.395			1.20681			0.603403	−	0.797437i	$-0.293811\pi$
$587$	708.395			1.20681			0.603403	+	0.797437i	$0.293811\pi$
$588$		0			0
$589$	−55.2316	−	398.438i	−0.0937718	−	0.676465i
$590$		0			0
$591$	4.00532	−	157.317i	0.00677720	−	0.266187i
$592$		0			0
$593$	−461.768	−	799.805i	−0.778698	−	1.34874i	−0.932693	−	0.360672i	$-0.882547\pi$
$593$	−461.768	−	799.805i	−0.778698	−	1.34874i	0.153995	−	0.988072i	$-0.450786\pi$
$594$		0			0
$595$	130.169	+	225.460i	0.218772	+	0.378924i
$596$		0			0
$597$	573.428	−	311.885i	0.960516	−	0.522420i
$598$		0			0
$599$			174.459i			0.291250i	0.989340	+	0.145625i	$0.0465193\pi$
$599$			174.459i			0.291250i	−0.989340	+	0.145625i	$0.953481\pi$
$600$		0			0
$601$	−749.076	+	432.479i	−1.24638	+	0.719599i	−0.970386	−	0.241559i	$-0.922341\pi$
$601$	−749.076	+	432.479i	−1.24638	+	0.719599i	−0.275997	+	0.961159i	$0.589008\pi$
$602$		0			0
$603$	56.2016	−	1103.00i	0.0932033	−	1.82918i
$604$		0			0
$605$	−681.407			−1.12629
$606$		0			0
$607$	78.0604	+	45.0682i	0.128600	+	0.0742475i	0.562920	−	0.826511i	$-0.309678\pi$
$607$	78.0604	+	45.0682i	0.128600	+	0.0742475i	−0.434320	+	0.900759i	$0.643011\pi$
$608$		0			0
$609$	−702.239	−	17.8792i	−1.15310	−	0.0293582i
$610$		0			0
$611$	−523.048	−	301.982i	−0.856053	−	0.494243i
$612$		0			0
$613$	−272.257	+	471.563i	−0.444139	+	0.769271i	−0.997992	−	0.0633433i	$-0.979824\pi$
$613$	−272.257	+	471.563i	−0.444139	+	0.769271i	0.553853	+	0.832615i	$0.313157\pi$
$614$		0			0
$615$	623.495	−	1019.11i	1.01381	−	1.65709i
$616$		0			0
$617$	−1044.52			−1.69291			−0.846453	−	0.532463i	$-0.821267\pi$
$617$	−1044.52			−1.69291			−0.846453	+	0.532463i	$0.821267\pi$
$618$		0			0
$619$	−234.817	−	406.714i	−0.379348	−	0.657051i	0.611619	−	0.791152i	$-0.290518\pi$
$619$	−234.817	−	406.714i	−0.379348	−	0.657051i	−0.990968	+	0.134102i	$0.957185\pi$
$620$		0			0
$621$	93.9273	−	1227.60i	0.151252	−	1.97681i
$622$		0			0
$623$	306.921	+	177.201i	0.492651	+	0.284432i
$624$		0			0
$625$	90.2354	+	156.292i	0.144377	+	0.250068i
$626$		0			0
$627$	306.737	+	133.796i	0.489214	+	0.213391i
$628$		0			0
$629$	−158.807	−	91.6872i	−0.252475	−	0.145767i
$630$		0			0
$631$	−357.598	−	619.379i	−0.566717	−	0.981582i	−0.996888	−	0.0788350i	$-0.974880\pi$
$631$	−357.598	−	619.379i	−0.566717	−	0.981582i	0.430171	−	0.902748i	$-0.358453\pi$
$632$		0			0
$633$	−492.266	−	905.075i	−0.777671	−	1.42982i
$634$		0			0
$635$	654.157	+	377.678i	1.03017	+	0.594768i
$636$		0			0
$637$	−120.563	−	69.6072i	−0.189267	−	0.109273i
$638$		0			0
$639$	−971.819	−	629.105i	−1.52084	−	0.984514i
$640$		0			0
$641$		−	926.859i		−	1.44596i	−0.690870	−	0.722979i	$-0.742772\pi$
$641$		−	926.859i		−	1.44596i	0.690870	−	0.722979i	$-0.257228\pi$
$642$		0			0
$643$	487.865	+	845.006i	0.758732	+	1.31416i	0.943498	+	0.331379i	$0.107514\pi$
$643$	487.865	+	845.006i	0.758732	+	1.31416i	−0.184766	+	0.982783i	$0.559153\pi$
$644$		0			0
$645$	−500.275	+	272.097i	−0.775620	+	0.421856i
$646$		0			0
$647$	709.164			1.09608			0.548040	−	0.836452i	$-0.315374\pi$
$647$	709.164			1.09608			0.548040	+	0.836452i	$0.315374\pi$
$648$		0			0
$649$	183.726	+	106.074i	0.283091	+	0.163443i
$650$		0			0
$651$	−377.280	−	9.60563i	−0.579539	−	0.0147552i
$652$		0			0
$653$	230.160	−	398.649i	0.352466	−	0.610489i	−0.634215	−	0.773157i	$-0.718677\pi$
$653$	230.160	−	398.649i	0.352466	−	0.610489i	0.986681	+	0.162668i	$0.0520099\pi$
$654$		0			0
$655$	−799.537	+	1384.84i	−1.22067	+	2.11426i
$656$		0			0
$657$	−350.150	+	540.900i	−0.532953	+	0.823288i
$658$		0			0
$659$	51.4876	+	29.7264i	0.0781300	+	0.0451083i	0.538556	−	0.842590i	$-0.318970\pi$
$659$	51.4876	+	29.7264i	0.0781300	+	0.0451083i	−0.460426	+	0.887698i	$0.652303\pi$
$660$		0			0
$661$			766.157i			1.15909i	0.814941	+	0.579544i	$0.196769\pi$
$661$			766.157i			1.15909i	−0.814941	+	0.579544i	$0.803231\pi$
$662$		0			0
$663$	−88.5733	+	144.774i	−0.133595	+	0.218362i
$664$		0			0
$665$	−880.637	+	122.074i	−1.32427	+	0.183570i
$666$		0			0
$667$	1556.16	+	898.447i	2.33307	+	1.34700i
$668$		0			0
$669$	215.165	+	5.47815i	0.321622	+	0.00818857i
$670$		0			0
$671$	−96.5417			−0.143877
$672$		0			0
$673$	235.641	−	136.048i	0.350136	−	0.202151i	−0.314609	−	0.949221i	$-0.601873\pi$
$673$	235.641	−	136.048i	0.350136	−	0.202151i	0.664745	+	0.747070i	$0.268540\pi$
$674$		0			0
$675$	824.772	+	564.212i	1.22188	+	0.835869i
$676$		0			0
$677$	−156.365	+	90.2772i	−0.230967	+	0.133349i	−0.611018	−	0.791617i	$-0.709240\pi$
$677$	−156.365	+	90.2772i	−0.230967	+	0.133349i	0.380051	+	0.924966i	$0.375906\pi$
$678$		0			0
$679$	−472.558	+	272.831i	−0.695962	+	0.401814i
$680$		0			0
$681$	374.569	+	688.679i	0.550028	+	1.01128i
$682$		0			0
$683$			581.525i			0.851427i	0.904858	+	0.425714i	$0.139977\pi$
$683$			581.525i			0.851427i	−0.904858	+	0.425714i	$0.860023\pi$
$684$		0			0
$685$	1058.09			1.54466
$686$		0			0
$687$	37.4526	+	22.9136i	0.0545162	+	0.0333532i
$688$		0			0
$689$	55.4122	+	95.9767i	0.0804240	+	0.139299i
$690$		0			0
$691$	−533.790	−	924.552i	−0.772489	−	1.33799i	−0.936195	−	0.351482i	$-0.885678\pi$
$691$	−533.790	−	924.552i	−0.772489	−	1.33799i	0.163705	−	0.986509i	$-0.447655\pi$
$692$		0			0
$693$	170.622	−	263.571i	0.246208	−	0.380334i
$694$		0			0
$695$	−716.388	−	1240.82i	−1.03077	−	1.78535i
$696$		0			0
$697$			281.365i			0.403679i
$698$		0			0
$699$	−263.334	−	161.109i	−0.376730	−	0.230485i
$700$		0			0
$701$	155.364	−	269.099i	0.221632	−	0.383878i	−0.733671	−	0.679504i	$-0.762195\pi$
$701$	155.364	−	269.099i	0.221632	−	0.383878i	0.955304	+	0.295626i	$0.0955282\pi$
$702$		0			0
$703$	494.197	−	384.612i	0.702983	−	0.547101i
$704$		0			0
$705$	35.7141	−	1402.74i	0.0506582	−	1.98970i
$706$		0			0
$707$	−126.131			−0.178404
$708$		0			0
$709$	−480.517	+	832.280i	−0.677739	+	1.17388i	0.297921	+	0.954591i	$0.403707\pi$
$709$	−480.517	+	832.280i	−0.677739	+	1.17388i	−0.975660	+	0.219289i	$0.929626\pi$
$710$		0			0
$711$	−14.0220	+	275.192i	−0.0197215	+	0.387049i
$712$		0			0
$713$	836.048	+	482.693i	1.17258	+	0.676988i
$714$		0			0
$715$	−407.123	−	235.053i	−0.569403	−	0.328745i
$716$		0			0
$717$	311.921	+	190.835i	0.435037	+	0.266157i
$718$		0			0
$719$	103.698	−	179.611i	0.144226	−	0.249807i	−0.784858	−	0.619676i	$-0.787264\pi$
$719$	103.698	−	179.611i	0.144226	−	0.249807i	0.929084	+	0.369869i	$0.120597\pi$
$720$		0			0
$721$			48.5430i			0.0673274i
$722$		0			0
$723$	294.264	−	480.978i	0.407004	−	0.665253i
$724$		0			0
$725$	−1263.05	+	729.223i	−1.74214	+	1.00582i
$726$		0			0
$727$	−559.005			−0.768921			−0.384460	−	0.923141i	$-0.625612\pi$
$727$	−559.005			−0.768921			−0.384460	+	0.923141i	$0.625612\pi$
$728$		0			0
$729$	−720.514	−	110.907i	−0.988360	−	0.152135i
$730$		0			0
$731$	67.0592	−	116.150i	0.0917363	−	0.158892i
$732$		0			0
$733$	−474.704	+	822.211i	−0.647618	+	1.12171i	0.336072	+	0.941836i	$0.390901\pi$
$733$	−474.704	+	822.211i	−0.647618	+	1.12171i	−0.983690	+	0.179871i	$0.942432\pi$
$734$		0			0
$735$	8.23213	−	323.333i	0.0112002	−	0.439908i
$736$		0			0
$737$	−623.934	+	360.229i	−0.846586	+	0.488777i
$738$		0			0
$739$	216.376	−	374.774i	0.292796	−	0.507137i	−0.681674	−	0.731656i	$-0.738748\pi$
$739$	216.376	−	374.774i	0.292796	−	0.507137i	0.974470	+	0.224519i	$0.0720811\pi$
$740$		0			0
$741$	−344.215	−	466.309i	−0.464528	−	0.629297i
$742$		0			0
$743$	1268.36	−	732.288i	1.70708	−	0.985583i	0.768945	−	0.639315i	$-0.220782\pi$
$743$	1268.36	−	732.288i	1.70708	−	0.985583i	0.938136	−	0.346268i	$-0.112551\pi$
$744$		0			0
$745$	−755.214	+	1308.07i	−1.01371	+	1.75580i
$746$		0			0
$747$	−501.161	−	980.067i	−0.670898	−	1.31200i
$748$		0			0
$749$	144.559	−	83.4613i	0.193003	−	0.111430i
$750$		0			0
$751$		−	374.822i		−	0.499097i	−0.968362	−	0.249549i	$-0.919718\pi$
$751$		−	374.822i		−	0.499097i	0.968362	−	0.249549i	$-0.0802823\pi$
$752$		0			0
$753$	66.5656	−	36.2047i	0.0884006	−	0.0480806i
$754$		0			0
$755$	−753.056	−	434.777i	−0.997426	−	0.575864i
$756$		0			0
$757$	744.294	−	1289.15i	0.983215	−	1.70298i	0.333600	−	0.942715i	$-0.391737\pi$
$757$	744.294	−	1289.15i	0.983215	−	1.70298i	0.649615	−	0.760263i	$-0.274930\pi$
$758$		0			0
$759$	−705.540	+	383.740i	−0.929566	+	0.505586i
$760$		0			0
$761$	−380.900	+	659.738i	−0.500526	+	0.866936i	0.499474	+	0.866329i	$0.333527\pi$
$761$	−380.900	+	659.738i	−0.500526	+	0.866936i	−1.00000		0.000607148i	$0.999807\pi$
$762$		0			0
$763$		−	794.444i		−	1.04121i
$764$		0			0
$765$	−393.800	−	20.0655i	−0.514771	−	0.0262294i
$766$		0			0
$767$	−183.716	−	318.205i	−0.239525	−	0.414870i
$768$		0			0
$769$	338.282			0.439899			0.219949	−	0.975511i	$-0.429411\pi$
$769$	338.282			0.439899			0.219949	+	0.975511i	$0.429411\pi$
$770$		0			0
$771$	−593.872	−	15.1201i	−0.770262	−	0.0196110i
$772$		0			0
$773$	119.263	−	68.8563i	0.154285	−	0.0890767i	−0.420870	−	0.907121i	$-0.638275\pi$
$773$	119.263	−	68.8563i	0.154285	−	0.0890767i	0.575155	+	0.818044i	$0.304942\pi$
$774$		0			0
$775$	−678.577	+	391.777i	−0.875584	+	0.505518i
$776$		0			0
$777$	−280.726	−	516.140i	−0.361295	−	0.664273i
$778$		0			0
$779$	−890.215	−	361.623i	−1.14277	−	0.464214i
$780$		0			0
$781$			755.190i			0.966952i
$782$		0			0
$783$	600.725	−	878.147i	0.767209	−	1.12152i
$784$		0			0
$785$	103.992	−	180.120i	0.132474	−	0.229452i
$786$		0			0
$787$	−463.682	−	267.707i	−0.589177	−	0.340161i	0.175595	−	0.984462i	$-0.443815\pi$
$787$	−463.682	−	267.707i	−0.589177	−	0.340161i	−0.764772	+	0.644301i	$0.777148\pi$
$788$		0			0
$789$	12.4389	−	488.562i	0.0157654	−	0.619217i
$790$		0			0
$791$			17.6968i			0.0223726i
$792$		0			0
$793$	144.804	+	83.6028i	0.182603	+	0.105426i
$794$		0			0
$795$	−134.373	+	219.634i	−0.169023	+	0.276269i
$796$		0			0
$797$	−652.486	−	376.713i	−0.818678	−	0.472664i	0.0312825	−	0.999511i	$-0.490041\pi$
$797$	−652.486	−	376.713i	−0.818678	−	0.472664i	−0.849960	+	0.526847i	$0.823374\pi$
$798$		0			0
$799$	165.232	+	286.191i	0.206799	+	0.358186i
$800$		0			0
$801$	−477.921	+	244.387i	−0.596655	+	0.305102i
$802$		0			0
$803$	420.327			0.523446
$804$		0			0
$805$	1066.86	−	1847.85i	1.32529	−	2.29547i
$806$		0			0
$807$	−618.040	+	1010.19i	−0.765849	+	1.25179i
$808$		0			0
$809$	1183.21			1.46256			0.731279	−	0.682078i	$-0.238924\pi$
$809$	1183.21			1.46256			0.731279	+	0.682078i	$0.238924\pi$
$810$		0			0
$811$	−457.899	+	264.368i	−0.564610	+	0.325978i	−0.754994	−	0.655732i	$-0.772360\pi$
$811$	−457.899	+	264.368i	−0.564610	+	0.325978i	0.190384	+	0.981710i	$0.439027\pi$
$812$		0			0
$813$	−918.374	−	561.864i	−1.12961	−	0.691100i
$814$		0			0
$815$	341.308	+	591.162i	0.418782	+	0.725352i
$816$		0			0
$817$	281.302	+	361.451i	0.344311	+	0.442413i
$818$		0			0
$819$	−484.165	+	247.579i	−0.591166	+	0.302295i
$820$		0			0
$821$	−262.124	+	454.013i	−0.319275	+	0.553000i	−0.980337	−	0.197331i	$-0.936773\pi$
$821$	−262.124	+	454.013i	−0.319275	+	0.553000i	0.661062	+	0.750331i	$0.270106\pi$
$822$		0			0
$823$	903.782			1.09816			0.549078	−	0.835771i	$-0.314979\pi$
$823$	903.782			1.09816			0.549078	+	0.835771i	$0.314979\pi$
$824$		0			0
$825$	16.5914	−	651.661i	0.0201108	−	0.789892i
$826$		0			0
$827$	−269.472	+	155.580i	−0.325843	+	0.188126i	−0.653994	−	0.756500i	$-0.726908\pi$
$827$	−269.472	+	155.580i	−0.325843	+	0.188126i	0.328151	+	0.944625i	$0.393575\pi$
$828$		0			0
$829$		−	243.583i		−	0.293827i	−0.989149	−	0.146914i	$-0.953066\pi$
$829$		−	243.583i		−	0.293827i	0.989149	−	0.146914i	$-0.0469339\pi$
$830$		0			0
$831$	−287.116	+	156.161i	−0.345506	+	0.187919i
$832$		0			0
$833$	38.0862	+	65.9673i	0.0457217	+	0.0791924i
$834$		0			0
$835$	−1791.68	+	1034.43i	−2.14572	+	1.23883i
$836$		0			0
$837$	322.741	−	471.787i	0.385593	−	0.563664i
$838$		0			0
$839$		−	740.595i		−	0.882712i	−0.897332	−	0.441356i	$-0.854498\pi$
$839$		−	740.595i		−	0.882712i	0.897332	−	0.441356i	$-0.145502\pi$
$840$		0			0
$841$	355.914	+	616.462i	0.423204	+	0.733011i
$842$		0			0
$843$	689.914	−	1127.67i	0.818403	−	1.33769i
$844$		0			0
$845$	−258.312	−	447.409i	−0.305694	−	0.529478i
$846$		0			0
$847$	514.180			0.607061
$848$		0			0
$849$	115.299	−	62.7108i	0.135806	−	0.0738643i
$850$		0			0
$851$			1502.92i			1.76607i
$852$		0			0
$853$	251.119			0.294395			0.147198	−	0.989107i	$-0.452975\pi$
$853$	251.119			0.294395			0.147198	+	0.989107i	$0.452975\pi$
$854$		0			0
$855$	569.615	−	1220.16i	0.666217	−	1.42709i
$856$		0			0
$857$		−	984.602i		−	1.14889i	−0.818542	−	0.574447i	$-0.805217\pi$
$857$		−	984.602i		−	1.14889i	0.818542	−	0.574447i	$-0.194783\pi$
$858$		0			0
$859$	865.547			1.00762			0.503811	−	0.863814i	$-0.331931\pi$
$859$	865.547			1.00762			0.503811	+	0.863814i	$0.331931\pi$
$860$		0			0
$861$	−470.481	+	769.006i	−0.546435	+	0.893154i
$862$		0			0
$863$			809.822i			0.938380i	0.883097	+	0.469190i	$0.155454\pi$
$863$			809.822i			0.938380i	−0.883097	+	0.469190i	$0.844546\pi$
$864$		0			0
$865$	−2037.88	+	1176.57i	−2.35593	+	1.36020i
$866$		0			0
$867$	−680.056	+	369.879i	−0.784379	+	0.426620i
$868$		0			0
$869$	155.668	−	89.8750i	0.179135	−	0.103423i
$870$		0			0
$871$	1247.80			1.43260
$872$		0			0
$873$	42.0567	−	825.394i	0.0481749	−	0.945468i
$874$		0			0
$875$	281.008	+	486.720i	0.321152	+	0.556251i
$876$		0			0
$877$	−122.144	+	70.5197i	−0.139274	+	0.0804101i	−0.568018	−	0.823016i	$-0.692290\pi$
$877$	−122.144	+	70.5197i	−0.139274	+	0.0804101i	0.428744	+	0.903426i	$0.358956\pi$
$878$		0			0
$879$	27.7406	−	45.3423i	0.0315593	−	0.0515840i
$880$		0			0
$881$	−1590.79			−1.80567			−0.902833	−	0.429991i	$-0.858517\pi$
$881$	−1590.79			−1.80567			−0.902833	+	0.429991i	$0.858517\pi$
$882$		0			0
$883$	−323.546	−	560.398i	−0.366417	−	0.634652i	0.622586	−	0.782552i	$-0.286082\pi$
$883$	−323.546	−	560.398i	−0.366417	−	0.634652i	−0.989002	+	0.147899i	$0.952749\pi$
$884$		0			0
$885$	445.506	−	728.184i	0.503396	−	0.822807i
$886$		0			0
$887$		−	466.256i		−	0.525655i	−0.964843	−	0.262828i	$-0.915345\pi$
$887$		−	466.256i		−	0.525655i	0.964843	−	0.262828i	$-0.0846550\pi$
$888$		0			0
$889$	−493.618	−	284.991i	−0.555251	−	0.320574i
$890$		0			0
$891$	194.684	+	433.875i	0.218500	+	0.486953i
$892$		0			0
$893$	−1117.85	+	154.956i	−1.25179	+	0.173523i
$894$		0			0
$895$	201.205	−	116.166i	0.224811	−	0.129794i
$896$		0			0
$897$	1390.56	+	35.4040i	1.55023	+	0.0394693i
$898$		0			0
$899$	417.131	+	722.491i	0.463994	+	0.803661i
$900$		0			0
$901$		−	60.6386i		−	0.0673014i
$902$		0			0
$903$	377.500	−	205.321i	0.418051	−	0.227376i
$904$		0			0
$905$	1245.39	+	719.024i	1.37612	+	0.794501i
$906$		0			0
$907$		−	48.3295i		−	0.0532850i	−0.999645	−	0.0266425i	$-0.991518\pi$
$907$		−	48.3295i		−	0.0532850i	0.999645	−	0.0266425i	$-0.00848157\pi$
$908$		0			0
$909$	103.815	−	160.370i	0.114208	−	0.176425i
$910$		0			0
$911$	−820.395	+	473.655i	−0.900543	+	0.519929i	−0.877376	−	0.479803i	$-0.840708\pi$
$911$	−820.395	+	473.655i	−0.900543	+	0.519929i	−0.0231666	+	0.999732i	$0.507375\pi$
$912$		0			0
$913$	−359.035	+	621.867i	−0.393248	+	0.681125i
$914$		0			0
$915$	−9.88732	+	388.344i	−0.0108058	+	0.424419i
$916$		0			0
$917$	603.320	−	1044.98i	0.657928	−	1.13956i
$918$		0			0
$919$	−227.469			−0.247518			−0.123759	−	0.992312i	$-0.539495\pi$
$919$	−227.469			−0.247518			−0.123759	+	0.992312i	$0.539495\pi$
$920$		0			0
$921$	225.558	−	368.677i	0.244905	−	0.400300i
$922$		0			0
$923$	653.976	−	1132.72i	0.708533	−	1.22722i
$924$		0			0
$925$	−1056.42	−	609.923i	−1.14207	−	0.659376i
$926$		0			0
$927$	−61.7201	−	39.9544i	−0.0665805	−	0.0431007i
$928$		0			0
$929$	−342.447			−0.368619			−0.184310	−	0.982868i	$-0.559005\pi$
$929$	−342.447			−0.368619			−0.184310	+	0.982868i	$0.559005\pi$
$930$		0			0
$931$	−257.665	+	35.7176i	−0.276762	+	0.0383648i
$932$		0			0
$933$	−513.521	−	314.174i	−0.550397	−	0.336735i
$934$		0			0
$935$	128.611	+	222.761i	0.137552	+	0.238247i
$936$		0			0
$937$	−190.923	−	330.688i	−0.203760	−	0.352922i	0.745977	−	0.665972i	$-0.231983\pi$
$937$	−190.923	−	330.688i	−0.203760	−	0.352922i	−0.949737	+	0.313049i	$0.898649\pi$
$938$		0			0
$939$	887.919	+	543.232i	0.945601	+	0.578522i
$940$		0			0
$941$		−	411.762i		−	0.437580i	−0.975772	−	0.218790i	$-0.929789\pi$
$941$		−	411.762i		−	0.437580i	0.975772	−	0.218790i	$-0.0702109\pi$
$942$		0			0
$943$	1997.09	−	1153.02i	2.11781	−	1.22272i
$944$		0			0
$945$	−1042.75	−	713.329i	−1.10344	−	0.754846i
$946$		0			0
$947$	1099.68			1.16123			0.580614	−	0.814179i	$-0.302812\pi$
$947$	1099.68			1.16123			0.580614	+	0.814179i	$0.302812\pi$
$948$		0			0
$949$	−630.455	−	363.993i	−0.664336	−	0.383554i
$950$		0			0
$951$	−56.0858	+	91.6729i	−0.0589757	+	0.0963964i
$952$		0			0
$953$	311.556	+	179.877i	0.326921	+	0.188748i	0.654473	−	0.756085i	$-0.272890\pi$
$953$	311.556	+	179.877i	0.326921	+	0.188748i	−0.327552	+	0.944833i	$0.606224\pi$
$954$		0			0
$955$	552.598	−	957.128i	0.578637	−	1.00223i
$956$		0			0
$957$	−693.833	−	17.6652i	−0.725009	−	0.0184589i
$958$		0			0
$959$	−798.420			−0.832555
$960$		0			0
$961$	−256.396	−	444.090i	−0.266801	−	0.462112i
$962$		0			0
$963$	−12.8655	+	252.494i	−0.0133598	+	0.262196i
$964$		0			0
$965$	−2269.17	−	1310.11i	−2.35148	−	1.35763i
$966$		0			0
$967$	171.720	+	297.428i	0.177580	+	0.307578i	0.941051	−	0.338264i	$-0.109840\pi$
$967$	171.720	+	297.428i	0.177580	+	0.307578i	−0.763471	+	0.645842i	$0.776506\pi$
$968$		0			0
$969$	35.5350	+	315.133i	0.0366718	+	0.325214i
$970$		0			0
$971$	657.424	+	379.564i	0.677059	+	0.390900i	0.798746	−	0.601668i	$-0.205497\pi$
$971$	657.424	+	379.564i	0.677059	+	0.390900i	−0.121687	+	0.992569i	$0.538830\pi$
$972$		0			0
$973$	540.577	+	936.306i	0.555577	+	0.962288i
$974$		0			0
$975$	−589.209	+	963.068i	−0.604316	+	0.987762i
$976$		0			0
$977$	−984.799	−	568.574i	−1.00798	−	0.581959i	−0.0973823	−	0.995247i	$-0.531047\pi$
$977$	−984.799	−	568.574i	−1.00798	−	0.581959i	−0.910600	+	0.413288i	$0.864380\pi$
$978$		0			0
$979$	303.248	+	175.080i	0.309752	+	0.178836i
$980$		0			0
$981$	1010.10	+	653.884i	1.02966	+	0.666548i
$982$		0			0
$983$		−	1248.06i		−	1.26964i	−0.772659	−	0.634821i	$-0.781074\pi$
$983$		−	1248.06i		−	1.26964i	0.772659	−	0.634821i	$-0.218926\pi$
$984$		0			0
$985$	206.537	+	357.733i	0.209682	+	0.363181i
$986$		0			0
$987$	−26.9494	+	1058.49i	−0.0273043	+	1.07243i
$988$		0			0
$989$	−1099.23			−1.11145
$990$		0			0
$991$	−657.089	−	379.370i	−0.663056	−	0.382816i	0.130384	−	0.991464i	$-0.458379\pi$
$991$	−657.089	−	379.370i	−0.663056	−	0.382816i	−0.793441	+	0.608648i	$0.791712\pi$
$992$		0			0
$993$	868.641	+	1597.07i	0.874764	+	1.60833i
$994$		0			0
$995$	−856.711	+	1483.87i	−0.861016	+	1.49132i
$996$		0			0
$997$	722.576	−	1251.54i	0.724750	−	1.25530i	−0.234327	−	0.972158i	$-0.575289\pi$
$997$	722.576	−	1251.54i	0.724750	−	1.25530i	0.959077	−	0.283146i	$-0.0913781\pi$
$998$		0			0
$999$	887.305	+	67.8903i	0.888193	+	0.0679583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.21	✓	80
3.2	odd	2		2052.3.s.a.901.37		80
9.2	odd	6		2052.3.bl.a.1585.4		80
9.7	even	3		684.3.bl.a.673.34	yes	80
19.12	odd	6		684.3.bl.a.373.34	yes	80
57.50	even	6		2052.3.bl.a.145.4		80
171.88	odd	6	inner	684.3.s.a.601.21	yes	80
171.164	even	6		2052.3.s.a.829.37		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.21	✓	80	1.1	even	1	trivial
684.3.s.a.601.21	yes	80	171.88	odd	6	inner
684.3.bl.a.373.34	yes	80	19.12	odd	6
684.3.bl.a.673.34	yes	80	9.7	even	3
2052.3.s.a.829.37		80	171.164	even	6
2052.3.s.a.901.37		80	3.2	odd	2
2052.3.bl.a.145.4		80	57.50	even	6
2052.3.bl.a.1585.4		80	9.2	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0763560 + 2.99903i) q^{3} +(-3.93735 - 6.81968i) q^{5} +(2.97107 + 5.14604i) q^{7} +(-8.98834 - 0.457987i) q^{9} +O(q^{10})\)	\(q+(-0.0763560 + 2.99903i) q^{3} +(-3.93735 - 6.81968i) q^{5} +(2.97107 + 5.14604i) q^{7} +(-8.98834 - 0.457987i) q^{9} +(2.93551 + 5.08444i) q^{11} -10.1683i q^{13} +(20.7531 - 11.2875i) q^{15} +(-2.78184 + 4.81829i) q^{17} +(-11.6693 - 14.9942i) q^{19} +(-15.6600 + 8.51739i) q^{21} +45.5995 q^{23} +(-18.5054 + 32.0523i) q^{25} +(2.05983 - 26.9213i) q^{27} +(34.1266 + 19.7030i) q^{29} +(18.3346 + 10.5855i) q^{31} +(-15.4725 + 8.41544i) q^{33} +(23.3963 - 40.5235i) q^{35} +32.9592i q^{37} +(30.4950 + 0.776411i) q^{39} +(43.7963 - 25.2858i) q^{41} -24.1061 q^{43} +(32.2669 + 63.1009i) q^{45} +(29.6984 - 51.4391i) q^{47} +(6.84550 - 11.8568i) q^{49} +(-14.2378 - 8.71073i) q^{51} +(-9.43881 + 5.44950i) q^{53} +(23.1162 - 40.0384i) q^{55} +(45.8591 - 33.8518i) q^{57} +(31.2938 - 18.0675i) q^{59} +(-8.22190 + 14.2407i) q^{61} +(-24.3482 - 47.6151i) q^{63} +(-69.3446 + 40.0361i) q^{65} +122.714i q^{67} +(-3.48180 + 136.754i) q^{69} +(111.397 + 64.3151i) q^{71} +(35.7968 - 62.0019i) q^{73} +(-94.7127 - 57.9456i) q^{75} +(-17.4432 + 30.2125i) q^{77} -30.6165i q^{79} +(80.5805 + 8.23309i) q^{81} +(61.1539 + 105.922i) q^{83} +43.8123 q^{85} +(-61.6955 + 100.842i) q^{87} +(51.6517 - 29.8211i) q^{89} +(52.3265 - 30.2107i) q^{91} +(-33.1461 + 54.1777i) q^{93} +(-56.3096 + 138.619i) q^{95} +91.8294i q^{97} +(-24.0567 - 47.0451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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