LMFDB - Embedded newform 684.3.bl.a.373.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(373,684)]

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, 5]))

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

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

chi := DirichletCharacter("684.373");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.bl (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			373.7
Character	$\chi$	$=$	684.373
Dual form			684.3.bl.a.673.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70298 - 1.30149i) q^{3} -2.67889 q^{5} +(3.94899 + 6.83985i) q^{7} +(5.61225 + 7.03581i) q^{9} +O(q^{10})$	\(q+(-2.70298 - 1.30149i) q^{3} -2.67889 q^{5} +(3.94899 + 6.83985i) q^{7} +(5.61225 + 7.03581i) q^{9} +(-4.28360 - 7.41940i) q^{11} +(7.82016 - 4.51497i) q^{13} +(7.24101 + 3.48655i) q^{15} +(-5.47035 - 9.47493i) q^{17} +(12.2593 + 14.5158i) q^{19} +(-1.77207 - 23.6276i) q^{21} +(-15.3722 - 26.6254i) q^{23} -17.8235 q^{25} +(-6.01282 - 26.3220i) q^{27} +38.4214i q^{29} +(-4.68676 - 2.70590i) q^{31} +(1.92222 + 25.6296i) q^{33} +(-10.5789 - 18.3232i) q^{35} +5.16539i q^{37} +(-27.0139 + 2.02605i) q^{39} -0.196918i q^{41} +(-28.7847 + 49.8566i) q^{43} +(-15.0346 - 18.8482i) q^{45} -52.4170 q^{47} +(-6.68907 + 11.5858i) q^{49} +(2.45477 + 32.7302i) q^{51} +(47.6183 + 27.4924i) q^{53} +(11.4753 + 19.8758i) q^{55} +(-14.2445 - 55.1914i) q^{57} +39.8572i q^{59} -42.8444 q^{61} +(-25.9612 + 66.1714i) q^{63} +(-20.9494 + 12.0951i) q^{65} +(-81.0911 + 46.8180i) q^{67} +(6.89812 + 91.9747i) q^{69} +(-96.9215 + 55.9577i) q^{71} +(59.8200 + 103.611i) q^{73} +(48.1767 + 23.1971i) q^{75} +(33.8318 - 58.5983i) q^{77} +(-19.6941 - 11.3704i) q^{79} +(-18.0052 + 78.9735i) q^{81} +(4.68953 + 8.12250i) q^{83} +(14.6545 + 25.3823i) q^{85} +(50.0050 - 103.852i) q^{87} +(-127.411 - 73.5609i) q^{89} +(61.7635 + 35.6592i) q^{91} +(9.14654 + 13.4138i) q^{93} +(-32.8414 - 38.8864i) q^{95} +(-106.286 - 61.3644i) q^{97} +(28.1609 - 71.7781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−2.70298	−	1.30149i	−0.900995	−	0.433830i
$3$	−2.70298	−	1.30149i	−0.900995	−	0.433830i
$4$		0			0
$5$	−2.67889			−0.535779			−0.267889	−	0.963450i	$-0.586326\pi$
$5$	−2.67889			−0.535779			−0.267889	+	0.963450i	$0.586326\pi$
$6$		0			0
$7$	3.94899	+	6.83985i	0.564142	+	0.977122i	0.997129	+	0.0757220i	$0.0241262\pi$
$7$	3.94899	+	6.83985i	0.564142	+	0.977122i	−0.432987	+	0.901400i	$0.642541\pi$
$8$		0			0
$9$	5.61225	+	7.03581i	0.623584	+	0.781756i
$10$		0			0
$11$	−4.28360	−	7.41940i	−0.389418	−	0.674491i	0.602954	−	0.797776i	$-0.293990\pi$
$11$	−4.28360	−	7.41940i	−0.389418	−	0.674491i	−0.992371	+	0.123285i	$0.960657\pi$
$12$		0			0
$13$	7.82016	−	4.51497i	0.601550	−	0.347305i	−0.168101	−	0.985770i	$-0.553763\pi$
$13$	7.82016	−	4.51497i	0.601550	−	0.347305i	0.769651	+	0.638464i	$0.220430\pi$
$14$		0			0
$15$	7.24101	+	3.48655i	0.482734	+	0.232437i
$16$		0			0
$17$	−5.47035	−	9.47493i	−0.321785	−	0.557349i	0.659071	−	0.752081i	$-0.270950\pi$
$17$	−5.47035	−	9.47493i	−0.321785	−	0.557349i	−0.980856	+	0.194732i	$0.937616\pi$
$18$		0			0
$19$	12.2593	+	14.5158i	0.645226	+	0.763992i
$19$	12.2593	+	14.5158i	0.645226	+	0.763992i
$20$		0			0
$21$	−1.77207	−	23.6276i	−0.0843844	−	1.12512i
$22$		0			0
$23$	−15.3722	−	26.6254i	−0.668356	−	1.15763i	−0.978364	−	0.206892i	$-0.933665\pi$
$23$	−15.3722	−	26.6254i	−0.668356	−	1.15763i	0.310008	−	0.950734i	$-0.399668\pi$
$24$		0			0
$25$	−17.8235			−0.712941
$26$		0			0
$27$	−6.01282	−	26.3220i	−0.222697	−	0.974888i
$28$		0			0
$29$			38.4214i			1.32487i	0.749117	+	0.662437i	$0.230478\pi$
$29$			38.4214i			1.32487i	−0.749117	+	0.662437i	$0.769522\pi$
$30$		0			0
$31$	−4.68676	−	2.70590i	−0.151186	−	0.0872872i	0.422499	−	0.906364i	$-0.361153\pi$
$31$	−4.68676	−	2.70590i	−0.151186	−	0.0872872i	−0.573685	+	0.819076i	$0.694486\pi$
$32$		0			0
$33$	1.92222	+	25.6296i	0.0582492	+	0.776654i
$34$		0			0
$35$	−10.5789	−	18.3232i	−0.302255	−	0.523521i
$36$		0			0
$37$			5.16539i			0.139605i	0.997561	+	0.0698026i	$0.0222369\pi$
$37$			5.16539i			0.139605i	−0.997561	+	0.0698026i	$0.977763\pi$
$38$		0			0
$39$	−27.0139	+	2.02605i	−0.692665	+	0.0519500i
$40$		0			0
$41$		−	0.196918i		−	0.00480287i	−0.999997	−	0.00240144i	$-0.999236\pi$
$41$		−	0.196918i		−	0.00480287i	0.999997	−	0.00240144i	$-0.000764402\pi$
$42$		0			0
$43$	−28.7847	+	49.8566i	−0.669412	+	1.15946i	0.308656	+	0.951174i	$0.400121\pi$
$43$	−28.7847	+	49.8566i	−0.669412	+	1.15946i	−0.978069	+	0.208283i	$0.933213\pi$
$44$		0			0
$45$	−15.0346	−	18.8482i	−0.334103	−	0.418848i
$46$		0			0
$47$	−52.4170			−1.11526			−0.557628	−	0.830091i	$-0.688288\pi$
$47$	−52.4170			−1.11526			−0.557628	+	0.830091i	$0.688288\pi$
$48$		0			0
$49$	−6.68907	+	11.5858i	−0.136512	+	0.236445i
$50$		0			0
$51$	2.45477	+	32.7302i	0.0481327	+	0.641768i
$52$		0			0
$53$	47.6183	+	27.4924i	0.898458	+	0.518725i	0.876700	−	0.481038i	$-0.159740\pi$
$53$	47.6183	+	27.4924i	0.898458	+	0.518725i	0.0217584	+	0.999763i	$0.493074\pi$
$54$		0			0
$55$	11.4753	+	19.8758i	0.208642	+	0.361378i
$56$		0			0
$57$	−14.2445	−	55.1914i	−0.249903	−	0.968271i
$58$		0			0
$59$			39.8572i			0.675545i	0.941228	+	0.337773i	$0.109673\pi$
$59$			39.8572i			0.675545i	−0.941228	+	0.337773i	$0.890327\pi$
$60$		0			0
$61$	−42.8444			−0.702367			−0.351184	−	0.936307i	$-0.614221\pi$
$61$	−42.8444			−0.702367			−0.351184	+	0.936307i	$0.614221\pi$
$62$		0			0
$63$	−25.9612	+	66.1714i	−0.412082	+	1.05034i
$64$		0			0
$65$	−20.9494	+	12.0951i	−0.322298	+	0.186079i
$66$		0			0
$67$	−81.0911	+	46.8180i	−1.21031	+	0.698775i	−0.962828	−	0.270116i	$-0.912938\pi$
$67$	−81.0911	+	46.8180i	−1.21031	+	0.698775i	−0.247487	+	0.968891i	$0.579605\pi$
$68$		0			0
$69$	6.89812	+	91.9747i	0.0999727	+	1.33297i
$70$		0			0
$71$	−96.9215	+	55.9577i	−1.36509	+	0.788136i	−0.990296	−	0.138972i	$-0.955620\pi$
$71$	−96.9215	+	55.9577i	−1.36509	+	0.788136i	−0.374795	+	0.927108i	$0.622287\pi$
$72$		0			0
$73$	59.8200	+	103.611i	0.819451	+	1.41933i	0.906087	+	0.423092i	$0.139055\pi$
$73$	59.8200	+	103.611i	0.819451	+	1.41933i	−0.0866355	+	0.996240i	$0.527612\pi$
$74$		0			0
$75$	48.1767	+	23.1971i	0.642356	+	0.309295i
$76$		0			0
$77$	33.8318	−	58.5983i	0.439374	−	0.761017i
$78$		0			0
$79$	−19.6941	−	11.3704i	−0.249292	−	0.143929i	0.370148	−	0.928973i	$-0.379307\pi$
$79$	−19.6941	−	11.3704i	−0.249292	−	0.143929i	−0.619440	+	0.785044i	$0.712640\pi$
$80$		0			0
$81$	−18.0052	+	78.9735i	−0.222286	+	0.974981i
$82$		0			0
$83$	4.68953	+	8.12250i	0.0565003	+	0.0978615i	0.892892	−	0.450271i	$-0.148672\pi$
$83$	4.68953	+	8.12250i	0.0565003	+	0.0978615i	−0.836392	+	0.548132i	$0.815339\pi$
$84$		0			0
$85$	14.6545	+	25.3823i	0.172406	+	0.298616i
$86$		0			0
$87$	50.0050	−	103.852i	0.574770	−	1.19371i
$88$		0			0
$89$	−127.411	−	73.5609i	−1.43159	−	0.826527i	−0.434344	−	0.900747i	$-0.643020\pi$
$89$	−127.411	−	73.5609i	−1.43159	−	0.826527i	−0.997242	+	0.0742203i	$0.976353\pi$
$90$		0			0
$91$	61.7635	+	35.6592i	0.678719	+	0.391859i
$92$		0			0
$93$	9.14654	+	13.4138i	0.0983499	+	0.144234i
$94$		0			0
$95$	−32.8414	−	38.8864i	−0.345698	−	0.409330i
$96$		0			0
$97$	−106.286	−	61.3644i	−1.09573	−	0.632623i	−0.160637	−	0.987014i	$-0.551355\pi$
$97$	−106.286	−	61.3644i	−1.09573	−	0.632623i	−0.935097	+	0.354391i	$0.884688\pi$
$98$		0			0
$99$	28.1609	−	71.7781i	0.284453	−	0.725032i
$100$		0			0
$101$	27.7876			0.275124			0.137562	−	0.990493i	$-0.456073\pi$
$101$	27.7876			0.275124			0.137562	+	0.990493i	$0.456073\pi$
$102$		0			0
$103$	−149.064	−	86.0622i	−1.44722	−	0.835555i	−0.448909	−	0.893577i	$-0.648187\pi$
$103$	−149.064	−	86.0622i	−1.44722	−	0.835555i	−0.998315	+	0.0580219i	$0.981521\pi$
$104$		0			0
$105$	4.74719	+	63.2958i	0.0452114	+	0.602817i
$106$		0			0
$107$		−	114.895i		−	1.07378i	−0.843651	−	0.536892i	$-0.819598\pi$
$107$		−	114.895i		−	1.07378i	0.843651	−	0.536892i	$-0.180402\pi$
$108$		0			0
$109$	−42.3676	+	24.4610i	−0.388694	+	0.224412i	−0.681594	−	0.731731i	$-0.738713\pi$
$109$	−42.3676	+	24.4610i	−0.388694	+	0.224412i	0.292900	+	0.956143i	$0.405380\pi$
$110$		0			0
$111$	6.72270	−	13.9620i	0.0605649	−	0.125784i
$112$		0			0
$113$	72.4213	+	41.8125i	0.640897	+	0.370022i	0.784960	−	0.619547i	$-0.212683\pi$
$113$	72.4213	+	41.8125i	0.640897	+	0.370022i	−0.144063	+	0.989569i	$0.546017\pi$
$114$		0			0
$115$	41.1804	+	71.3266i	0.358091	+	0.620231i
$116$		0			0
$117$	75.6552	+	29.6820i	0.646625	+	0.253692i
$118$		0			0
$119$	43.2047	−	74.8328i	0.363065	−	0.628847i
$120$		0			0
$121$	23.8016	−	41.2256i	0.196708	−	0.340708i
$122$		0			0
$123$	−0.256286	+	0.532266i	−0.00208363	+	0.00432737i
$124$		0			0
$125$	114.720			0.917757
$126$		0			0
$127$	−162.862	−	94.0285i	−1.28238	−	0.740382i	−0.305096	−	0.952322i	$-0.598689\pi$
$127$	−162.862	−	94.0285i	−1.28238	−	0.740382i	−0.977283	+	0.211940i	$0.932022\pi$
$128$		0			0
$129$	142.693	−	97.2987i	1.10614	−	0.754253i
$130$		0			0
$131$	−181.093			−1.38239			−0.691197	−	0.722667i	$-0.742916\pi$
$131$	−181.093			−1.38239			−0.691197	+	0.722667i	$0.742916\pi$
$132$		0			0
$133$	−50.8744	+	141.175i	−0.382514	+	1.06146i
$134$		0			0
$135$	16.1077	+	70.5138i	0.119316	+	0.522324i
$136$		0			0
$137$	110.306			0.805154			0.402577	−	0.915386i	$-0.368115\pi$
$137$	110.306			0.805154			0.402577	+	0.915386i	$0.368115\pi$
$138$		0			0
$139$	82.7302	+	143.293i	0.595181	+	1.03088i	0.993521	+	0.113646i	$0.0362530\pi$
$139$	82.7302	+	143.293i	0.595181	+	1.03088i	−0.398340	+	0.917238i	$0.630414\pi$
$140$		0			0
$141$	141.682	+	68.2202i	1.00484	+	0.483831i
$142$		0			0
$143$	−66.9968	−	38.6806i	−0.468509	−	0.270494i
$144$		0			0
$145$		−	102.927i		−	0.709840i
$146$		0			0
$147$	33.1593	−	22.6105i	0.225573	−	0.153813i
$148$		0			0
$149$	−132.226			−0.887420			−0.443710	−	0.896170i	$-0.646338\pi$
$149$	−132.226			−0.887420			−0.443710	+	0.896170i	$0.646338\pi$
$150$		0			0
$151$	−14.1937	+	8.19471i	−0.0939977	+	0.0542696i	−0.546262	−	0.837614i	$-0.683950\pi$
$151$	−14.1937	+	8.19471i	−0.0939977	+	0.0542696i	0.452264	+	0.891884i	$0.350616\pi$
$152$		0			0
$153$	35.9628	−	91.6640i	0.235051	−	0.599111i
$154$		0			0
$155$	12.5553	+	7.24883i	0.0810022	+	0.0467666i
$156$		0			0
$157$	228.144			1.45315			0.726573	−	0.687090i	$-0.241112\pi$
$157$	228.144			1.45315			0.726573	+	0.687090i	$0.241112\pi$
$158$		0			0
$159$	−92.9304	−	136.286i	−0.584468	−	0.857146i
$160$		0			0
$161$	121.409	−	210.287i	0.754094	−	1.30613i
$162$		0			0
$163$	158.988			0.975387			0.487693	−	0.873015i	$-0.337838\pi$
$163$	158.988			0.975387			0.487693	+	0.873015i	$0.337838\pi$
$164$		0			0
$165$	−5.14943	−	68.6589i	−0.0312087	−	0.416115i
$166$		0			0
$167$	−241.516	+	139.439i	−1.44620	+	0.834965i	−0.998252	−	0.0590943i	$-0.981179\pi$
$167$	−241.516	+	139.439i	−1.44620	+	0.834965i	−0.447949	+	0.894059i	$0.647845\pi$
$168$		0			0
$169$	−43.7301	+	75.7428i	−0.258758	+	0.448182i
$170$		0			0
$171$	−33.3284	+	167.721i	−0.194903	+	0.980823i
$172$		0			0
$173$	−36.0092	−	20.7899i	−0.208146	−	0.120173i	0.392304	−	0.919836i	$-0.371678\pi$
$173$	−36.0092	−	20.7899i	−0.208146	−	0.120173i	−0.600449	+	0.799663i	$0.705012\pi$
$174$		0			0
$175$	−70.3850	−	121.910i	−0.402200	−	0.696630i
$176$		0			0
$177$	51.8736	−	107.733i	0.293071	−	0.608663i
$178$		0			0
$179$		−	28.2132i		−	0.157616i	−0.996890	−	0.0788079i	$-0.974889\pi$
$179$		−	28.2132i		−	0.157616i	0.996890	−	0.0788079i	$-0.0251114\pi$
$180$		0			0
$181$	231.069	+	133.408i	1.27663	+	0.737061i	0.976227	−	0.216753i	$-0.0695465\pi$
$181$	231.069	+	133.408i	1.27663	+	0.737061i	0.300400	+	0.953813i	$0.402880\pi$
$182$		0			0
$183$	115.808	+	55.7615i	0.632829	+	0.304708i
$184$		0			0
$185$		−	13.8375i		−	0.0747975i
$186$		0			0
$187$	−46.8655	+	81.1735i	−0.250618	+	0.434083i
$188$		0			0
$189$	156.294	−	145.072i	0.826952	−	0.767577i
$190$		0			0
$191$	−115.225	−	199.576i	−0.603274	−	1.04490i	−0.992322	−	0.123684i	$-0.960529\pi$
$191$	−115.225	−	199.576i	−0.603274	−	1.04490i	0.389048	−	0.921218i	$-0.372804\pi$
$192$		0			0
$193$			83.7003i			0.433680i	0.976207	+	0.216840i	$0.0695751\pi$
$193$			83.7003i			0.433680i	−0.976207	+	0.216840i	$0.930425\pi$
$194$		0			0
$195$	72.3675	−	5.42757i	0.371115	−	0.0278337i
$196$		0			0
$197$	−11.8579			−0.0601923			−0.0300961	−	0.999547i	$-0.509581\pi$
$197$	−11.8579			−0.0601923			−0.0300961	+	0.999547i	$0.509581\pi$
$198$		0			0
$199$	−71.2816	+	123.463i	−0.358199	+	0.620419i	−0.987660	−	0.156613i	$-0.949942\pi$
$199$	−71.2816	+	123.463i	−0.358199	+	0.620419i	0.629461	+	0.777032i	$0.283276\pi$
$200$		0			0
$201$	280.121	−	21.0091i	1.39364	−	0.104523i
$202$		0			0
$203$	−262.797	+	151.726i	−1.29456	+	0.747417i
$204$		0			0
$205$			0.527522i			0.00257328i
$206$		0			0
$207$	101.059	−	257.584i	0.488206	−	1.24437i
$208$		0			0
$209$	55.1850	−	153.137i	0.264043	−	0.732711i
$210$		0			0
$211$		−	85.3653i		−	0.404575i	−0.979326	−	0.202288i	$-0.935162\pi$
$211$		−	85.3653i		−	0.404575i	0.979326	−	0.202288i	$-0.0648376\pi$
$212$		0			0
$213$	334.806	−	25.1105i	1.57186	−	0.117890i
$214$		0			0
$215$	77.1112	−	133.561i	0.358657	−	0.621212i
$216$		0			0
$217$		−	42.7424i		−	0.196969i
$218$		0			0
$219$	−26.8436	−	357.915i	−0.122574	−	1.63431i
$220$		0			0
$221$	−85.5580	−	49.3969i	−0.387140	−	0.223516i
$222$		0			0
$223$	11.4352	+	6.60211i	0.0512789	+	0.0296059i	0.525420	−	0.850843i	$-0.323908\pi$
$223$	11.4352	+	6.60211i	0.0512789	+	0.0296059i	−0.474141	+	0.880449i	$0.657241\pi$
$224$		0			0
$225$	−100.030	−	125.403i	−0.444579	−	0.557346i
$226$		0			0
$227$	302.960	−	174.914i	1.33462	−	0.770545i	0.348619	−	0.937264i	$-0.386651\pi$
$227$	302.960	−	174.914i	1.33462	−	0.770545i	0.986004	+	0.166719i	$0.0533172\pi$
$228$		0			0
$229$	−86.8786	+	150.478i	−0.379383	+	0.657110i	−0.990973	−	0.134065i	$-0.957197\pi$
$229$	−86.8786	+	150.478i	−0.379383	+	0.657110i	0.611590	+	0.791175i	$0.290530\pi$
$230$		0			0
$231$	−167.712	+	114.359i	−0.726025	+	0.495060i
$232$		0			0
$233$	85.4215	+	147.954i	0.366616	+	0.634997i	0.989034	−	0.147687i	$-0.0471830\pi$
$233$	85.4215	+	147.954i	0.366616	+	0.634997i	−0.622418	+	0.782685i	$0.713850\pi$
$234$		0			0
$235$	140.420			0.597530
$236$		0			0
$237$	38.4344	+	56.3657i	0.162171	+	0.237830i
$238$		0			0
$239$	60.5709	−	104.912i	0.253435	−	0.438962i	−0.711034	−	0.703157i	$-0.751773\pi$
$239$	60.5709	−	104.912i	0.253435	−	0.438962i	0.964469	+	0.264195i	$0.0851064\pi$
$240$		0			0
$241$			147.754i			0.613086i	0.951857	+	0.306543i	$0.0991723\pi$
$241$			147.754i			0.613086i	−0.951857	+	0.306543i	$0.900828\pi$
$242$		0			0
$243$	151.451	−	190.031i	0.623255	−	0.782019i
$244$		0			0
$245$	17.9193	−	31.0372i	0.0731400	−	0.126682i
$246$		0			0
$247$	161.408	+	58.1658i	0.653474	+	0.235489i
$248$		0			0
$249$	−2.10438	−	28.0584i	−0.00845133	−	0.112684i
$250$		0			0
$251$	42.2197	−	73.1266i	0.168206	−	0.291341i	−0.769583	−	0.638547i	$-0.779536\pi$
$251$	42.2197	−	73.1266i	0.168206	−	0.291341i	0.937789	+	0.347205i	$0.112869\pi$
$252$		0			0
$253$	−131.696	+	228.105i	−0.520539	+	0.901600i
$254$		0			0
$255$	−6.57606	−	87.6807i	−0.0257885	−	0.343846i
$256$		0			0
$257$	−121.335	+	70.0525i	−0.472119	+	0.272578i	−0.717126	−	0.696943i	$-0.754543\pi$
$257$	−121.335	+	70.0525i	−0.472119	+	0.272578i	0.245007	+	0.969521i	$0.421210\pi$
$258$		0			0
$259$	−35.3305	+	20.3981i	−0.136411	+	0.0787571i
$260$		0			0
$261$	−270.325	+	215.631i	−1.03573	+	0.826171i
$262$		0			0
$263$	62.0378	−	107.453i	0.235885	−	0.408565i	−0.723644	−	0.690173i	$-0.757534\pi$
$263$	62.0378	−	107.453i	0.235885	−	0.408565i	0.959530	+	0.281608i	$0.0908678\pi$
$264$		0			0
$265$	−127.564	−	73.6493i	−0.481375	−	0.277922i
$266$		0			0
$267$	248.652	+	364.658i	0.931280	+	1.36576i
$268$		0			0
$269$	−49.9138	+	28.8177i	−0.185553	+	0.107129i	−0.589899	−	0.807477i	$-0.700833\pi$
$269$	−49.9138	+	28.8177i	−0.185553	+	0.107129i	0.404346	+	0.914606i	$0.367499\pi$
$270$		0			0
$271$	−32.3322	−	56.0009i	−0.119307	−	0.206646i	0.800186	−	0.599751i	$-0.204734\pi$
$271$	−32.3322	−	56.0009i	−0.119307	−	0.206646i	−0.919493	+	0.393106i	$0.871401\pi$
$272$		0			0
$273$	−120.536	−	176.771i	−0.441523	−	0.647511i
$274$		0			0
$275$	76.3488	+	132.240i	0.277632	+	0.480873i
$276$		0			0
$277$	94.5582	+	163.780i	0.341365	+	0.591262i	0.984687	−	0.174334i	$-0.0557773\pi$
$277$	94.5582	+	163.780i	0.341365	+	0.591262i	−0.643321	+	0.765596i	$0.722444\pi$
$278$		0			0
$279$	−7.26509	−	48.1614i	−0.0260397	−	0.172621i
$280$		0			0
$281$		−	58.4471i		−	0.207997i	−0.994577	−	0.103998i	$-0.966836\pi$
$281$		−	58.4471i		−	0.207997i	0.994577	−	0.103998i	$-0.0331637\pi$
$282$		0			0
$283$	25.9265			0.0916131			0.0458066	−	0.998950i	$-0.485414\pi$
$283$	25.9265			0.0916131			0.0458066	+	0.998950i	$0.485414\pi$
$284$		0			0
$285$	38.1595	+	147.852i	0.133893	+	0.518779i
$286$		0			0
$287$	1.34689	−	0.777627i	0.00469299	−	0.00270950i
$288$		0			0
$289$	84.6505	−	146.619i	0.292908	−	0.507332i
$290$		0			0
$291$	207.425	+	304.197i	0.712801	+	1.04535i
$292$		0			0
$293$	43.1821	+	24.9312i	0.147379	+	0.0850894i	0.571876	−	0.820340i	$-0.306216\pi$
$293$	43.1821	+	24.9312i	0.147379	+	0.0850894i	−0.424497	+	0.905429i	$0.639549\pi$
$294$		0			0
$295$		−	106.773i		−	0.361943i
$296$		0			0
$297$	−169.537	+	157.364i	−0.570831	+	0.529846i
$298$		0			0
$299$	−240.426	−	138.810i	−0.804099	−	0.464247i
$300$		0			0
$301$	−454.683			−1.51057
$302$		0			0
$303$	−75.1094	−	36.1652i	−0.247886	−	0.119357i
$304$		0			0
$305$	114.776			0.376313
$306$		0			0
$307$	−264.700	+	152.825i	−0.862215	+	0.497800i	−0.864753	−	0.502197i	$-0.832525\pi$
$307$	−264.700	+	152.825i	−0.862215	+	0.497800i	0.00253851	+	0.999997i	$0.499192\pi$
$308$		0			0
$309$	290.909	+	426.630i	0.941453	+	1.38068i
$310$		0			0
$311$	−169.216	+	293.091i	−0.544104	+	0.942415i	0.454559	+	0.890717i	$0.349797\pi$
$311$	−169.216	+	293.091i	−0.544104	+	0.942415i	−0.998663	+	0.0516988i	$0.983536\pi$
$312$		0			0
$313$	531.978			1.69961			0.849805	−	0.527097i	$-0.176719\pi$
$313$	531.978			1.69961			0.849805	+	0.527097i	$0.176719\pi$
$314$		0			0
$315$	69.5472	−	177.266i	0.220785	−	0.562749i
$316$		0			0
$317$		−	402.604i		−	1.27005i	−0.772493	−	0.635023i	$-0.780991\pi$
$317$		−	402.604i		−	1.27005i	0.772493	−	0.635023i	$-0.219009\pi$
$318$		0			0
$319$	285.064	−	164.582i	0.893617	−	0.515930i
$320$		0			0
$321$	−149.534	+	310.559i	−0.465839	+	0.967473i
$322$		0			0
$323$	70.4738	−	195.563i	0.218185	−	0.605457i
$324$		0			0
$325$	−139.383	+	80.4727i	−0.428870	+	0.247608i
$326$		0			0
$327$	146.355	−	10.9766i	0.447568	−	0.0335677i
$328$		0			0
$329$	−206.994	−	358.525i	−0.629162	−	1.08974i
$330$		0			0
$331$	−139.693	+	80.6518i	−0.422033	+	0.243661i	−0.695947	−	0.718093i	$-0.745015\pi$
$331$	−139.693	+	80.6518i	−0.422033	+	0.243661i	0.273914	+	0.961754i	$0.411682\pi$
$332$		0			0
$333$	−36.3427	+	28.9895i	−0.109137	+	0.0870556i
$334$		0			0
$335$	217.234	−	125.420i	0.648461	−	0.374389i
$336$		0			0
$337$			166.654i			0.494523i	0.968949	+	0.247261i	$0.0795306\pi$
$337$			166.654i			0.494523i	−0.968949	+	0.247261i	$0.920469\pi$
$338$		0			0
$339$	−141.335	−	207.274i	−0.416918	−	0.611428i
$340$		0			0
$341$			46.3640i			0.135965i
$342$		0			0
$343$	281.341			0.820236
$344$		0			0
$345$	−18.4793	−	246.391i	−0.0535633	−	0.714176i
$346$		0			0
$347$	−15.3552			−0.0442513			−0.0221257	−	0.999755i	$-0.507043\pi$
$347$	−15.3552			−0.0442513			−0.0221257	+	0.999755i	$0.507043\pi$
$348$		0			0
$349$	−89.3968	−	154.840i	−0.256151	−	0.443667i	0.709056	−	0.705152i	$-0.249121\pi$
$349$	−89.3968	−	154.840i	−0.256151	−	0.443667i	−0.965208	+	0.261485i	$0.915788\pi$
$350$		0			0
$351$	−165.864	−	178.694i	−0.472547	−	0.509100i
$352$		0			0
$353$	−183.358	−	317.585i	−0.519428	−	0.899675i	−0.999745	−	0.0225805i	$-0.992812\pi$
$353$	−183.358	−	317.585i	−0.519428	−	0.899675i	0.480317	−	0.877095i	$-0.340522\pi$
$354$		0			0
$355$	259.642	−	149.905i	0.731387	−	0.422267i
$356$		0			0
$357$	−214.176	+	146.041i	−0.599932	+	0.409080i
$358$		0			0
$359$	170.933	+	296.065i	0.476138	+	0.824695i	0.999626	−	0.0273381i	$-0.00870306\pi$
$359$	170.933	+	296.065i	0.476138	+	0.824695i	−0.523489	+	0.852033i	$0.675370\pi$
$360$		0			0
$361$	−60.4192	+	355.908i	−0.167366	+	0.985895i
$362$		0			0
$363$	−117.990	+	80.4547i	−0.325042	+	0.221638i
$364$		0			0
$365$	−160.251	−	277.563i	−0.439045	−	0.760448i
$366$		0			0
$367$	−21.3626			−0.0582086			−0.0291043	−	0.999576i	$-0.509265\pi$
$367$	−21.3626			−0.0582086			−0.0291043	+	0.999576i	$0.509265\pi$
$368$		0			0
$369$	1.38548	−	1.10515i	0.00375468	−	0.00299500i
$370$		0			0
$371$			434.269i			1.17054i
$372$		0			0
$373$	−565.547	−	326.519i	−1.51621	−	0.875386i	−0.999819	−	0.0190347i	$-0.993941\pi$
$373$	−565.547	−	326.519i	−1.51621	−	0.875386i	−0.516394	−	0.856351i	$-0.672726\pi$
$374$		0			0
$375$	−310.086	−	149.306i	−0.826895	−	0.398150i
$376$		0			0
$377$	173.471	+	300.461i	0.460136	+	0.796979i
$378$		0			0
$379$		−	580.854i		−	1.53260i	−0.642486	−	0.766298i	$-0.722097\pi$
$379$		−	580.854i		−	1.53260i	0.642486	−	0.766298i	$-0.277903\pi$
$380$		0			0
$381$	317.837	+	466.121i	0.834218	+	1.22341i
$382$		0			0
$383$			569.539i			1.48705i	0.668710	+	0.743523i	$0.266847\pi$
$383$			569.539i			1.48705i	−0.668710	+	0.743523i	$0.733153\pi$
$384$		0			0
$385$	−90.6317	+	156.979i	−0.235407	+	0.407737i
$386$		0			0
$387$	−512.329	+	77.2842i	−1.32385	+	0.199701i
$388$		0			0
$389$	488.007			1.25452			0.627259	−	0.778811i	$-0.284177\pi$
$389$	488.007			1.25452			0.627259	+	0.778811i	$0.284177\pi$
$390$		0			0
$391$	−168.182	+	291.300i	−0.430134	+	0.745014i
$392$		0			0
$393$	489.493	+	235.691i	1.24553	+	0.599723i
$394$		0			0
$395$	52.7584	+	30.4601i	0.133566	+	0.0771141i
$396$		0			0
$397$	113.279	+	196.205i	0.285337	+	0.494218i	0.972691	−	0.232104i	$-0.0745611\pi$
$397$	113.279	+	196.205i	0.285337	+	0.494218i	−0.687354	+	0.726323i	$0.741228\pi$
$398$		0			0
$399$	321.250	−	315.381i	0.805138	−	0.790428i
$400$		0			0
$401$		−	280.797i		−	0.700243i	−0.936704	−	0.350121i	$-0.886140\pi$
$401$		−	280.797i		−	0.700243i	0.936704	−	0.350121i	$-0.113860\pi$
$402$		0			0
$403$	−48.8683			−0.121261
$404$		0			0
$405$	48.2340	−	211.562i	0.119096	−	0.522374i
$406$		0			0
$407$	38.3242	−	22.1265i	0.0941625	−	0.0543648i
$408$		0			0
$409$	−23.3718	+	13.4937i	−0.0571439	+	0.0329920i	−0.528300	−	0.849058i	$-0.677170\pi$
$409$	−23.3718	+	13.4937i	−0.0571439	+	0.0329920i	0.471156	+	0.882050i	$0.343837\pi$
$410$		0			0
$411$	−298.156	−	143.562i	−0.725439	−	0.349299i
$412$		0			0
$413$	−272.617	+	157.396i	−0.660090	+	0.381103i
$414$		0			0
$415$	−12.5627	−	21.7593i	−0.0302717	−	0.0524321i
$416$		0			0
$417$	−37.1244	−	494.991i	−0.0890273	−	1.18703i
$418$		0			0
$419$	−313.564	+	543.108i	−0.748362	+	1.29620i	0.200246	+	0.979746i	$0.435826\pi$
$419$	−313.564	+	543.108i	−0.748362	+	1.29620i	−0.948608	+	0.316455i	$0.897507\pi$
$420$		0			0
$421$	−268.763	−	155.170i	−0.638392	−	0.368576i	0.145603	−	0.989343i	$-0.453488\pi$
$421$	−268.763	−	155.170i	−0.638392	−	0.368576i	−0.783995	+	0.620767i	$0.786821\pi$
$422$		0			0
$423$	−294.178	−	368.796i	−0.695456	−	0.871858i
$424$		0			0
$425$	97.5010	+	168.877i	0.229414	+	0.397357i
$426$		0			0
$427$	−169.192	−	293.049i	−0.396235	−	0.686299i
$428$		0			0
$429$	130.749	+	191.749i	0.304776	+	0.446966i
$430$		0			0
$431$	99.2968	+	57.3290i	0.230387	+	0.133014i	0.610751	−	0.791823i	$-0.290868\pi$
$431$	99.2968	+	57.3290i	0.230387	+	0.133014i	−0.380364	+	0.924837i	$0.624201\pi$
$432$		0			0
$433$	198.843	+	114.802i	0.459222	+	0.265132i	0.711717	−	0.702466i	$-0.247918\pi$
$433$	198.843	+	114.802i	0.459222	+	0.265132i	−0.252495	+	0.967598i	$0.581251\pi$
$434$		0			0
$435$	−133.958	+	278.210i	−0.307949	+	0.639562i
$436$		0			0
$437$	198.038	−	549.549i	0.453176	−	1.25755i
$438$		0			0
$439$	457.999	+	264.426i	1.04328	+	0.602336i	0.920760	−	0.390130i	$-0.127570\pi$
$439$	457.999	+	264.426i	1.04328	+	0.602336i	0.122517	+	0.992466i	$0.460903\pi$
$440$		0			0
$441$	−119.056	+	17.9595i	−0.269969	+	0.0407245i
$442$		0			0
$443$	−733.345			−1.65541			−0.827703	−	0.561166i	$-0.810353\pi$
$443$	−733.345			−1.65541			−0.827703	+	0.561166i	$0.810353\pi$
$444$		0			0
$445$	341.321	+	197.062i	0.767013	+	0.442835i
$446$		0			0
$447$	357.404	+	172.090i	0.799561	+	0.384989i
$448$		0			0
$449$			379.685i			0.845623i	0.906218	+	0.422811i	$0.138957\pi$
$449$			379.685i			0.845623i	−0.906218	+	0.422811i	$0.861043\pi$
$450$		0			0
$451$	−1.46101	+	0.843516i	−0.00323950	+	0.00187032i
$452$		0			0
$453$	49.0306	−	3.67730i	0.108235	−	0.00811766i
$454$		0			0
$455$	−165.458	−	95.5271i	−0.363643	−	0.209950i
$456$		0			0
$457$	−429.940	−	744.678i	−0.940788	−	1.62949i	−0.763973	−	0.645248i	$-0.776754\pi$
$457$	−429.940	−	744.678i	−0.940788	−	1.62949i	−0.176815	−	0.984244i	$-0.556579\pi$
$458$		0			0
$459$	−216.506	+	200.961i	−0.471692	+	0.437824i
$460$		0			0
$461$	31.1568	−	53.9652i	0.0675853	−	0.117061i	−0.830253	−	0.557387i	$-0.811804\pi$
$461$	31.1568	−	53.9652i	0.0675853	−	0.117061i	0.897838	+	0.440326i	$0.145137\pi$
$462$		0			0
$463$	253.463	−	439.011i	0.547436	−	0.948188i	−0.451013	−	0.892517i	$-0.648937\pi$
$463$	253.463	−	439.011i	0.547436	−	0.948188i	0.998449	−	0.0556702i	$-0.0177295\pi$
$464$		0			0
$465$	−24.5026	−	35.9341i	−0.0526938	−	0.0772776i
$466$		0			0
$467$	721.660			1.54531			0.772655	−	0.634826i	$-0.218928\pi$
$467$	721.660			1.54531			0.772655	+	0.634826i	$0.218928\pi$
$468$		0			0
$469$	−640.456	−	369.767i	−1.36558	−	0.788417i
$470$		0			0
$471$	−616.669	−	296.927i	−1.30928	−	0.630417i
$472$		0			0
$473$	493.209			1.04272
$474$		0			0
$475$	−218.504	−	258.723i	−0.460008	−	0.544681i
$476$		0			0
$477$	73.8145	+	489.327i	0.154747	+	1.02584i
$478$		0			0
$479$	52.3233			0.109234			0.0546172	−	0.998507i	$-0.482606\pi$
$479$	52.3233			0.109234			0.0546172	+	0.998507i	$0.482606\pi$
$480$		0			0
$481$	23.3216	+	40.3942i	0.0484856	+	0.0839796i
$482$		0			0
$483$	−601.853	+	410.390i	−1.24607	+	0.849668i
$484$		0			0
$485$	284.730	+	164.389i	0.587071	+	0.338946i
$486$		0			0
$487$		−	409.665i		−	0.841201i	−0.907246	−	0.420601i	$-0.861819\pi$
$487$		−	409.665i		−	0.841201i	0.907246	−	0.420601i	$-0.138181\pi$
$488$		0			0
$489$	−429.742	−	206.921i	−0.878818	−	0.423152i
$490$		0			0
$491$	−636.795			−1.29694			−0.648468	−	0.761242i	$-0.724590\pi$
$491$	−636.795			−1.29694			−0.648468	+	0.761242i	$0.724590\pi$
$492$		0			0
$493$	364.040	−	210.178i	0.738417	−	0.426325i
$494$		0			0
$495$	−75.4400	+	192.286i	−0.152404	+	0.388457i
$496$		0			0
$497$	−765.484	−	441.953i	−1.54021	−	0.889241i
$498$		0			0
$499$	215.208			0.431279			0.215639	−	0.976473i	$-0.430816\pi$
$499$	215.208			0.431279			0.215639	+	0.976473i	$0.430816\pi$
$500$		0			0
$501$	834.292	−	62.5720i	1.66525	−	0.124894i
$502$		0			0
$503$	−59.6655	+	103.344i	−0.118619	+	0.205455i	−0.919221	−	0.393743i	$-0.871180\pi$
$503$	−59.6655	+	103.344i	−0.118619	+	0.205455i	0.800601	+	0.599197i	$0.204513\pi$
$504$		0			0
$505$	−74.4399			−0.147406
$506$		0			0
$507$	216.780	−	147.817i	0.427574	−	0.291553i
$508$		0			0
$509$	−608.603	+	351.377i	−1.19568	+	0.690329i	−0.959590	−	0.281402i	$-0.909201\pi$
$509$	−608.603	+	351.377i	−1.19568	+	0.690329i	−0.236094	+	0.971730i	$0.575867\pi$
$510$		0			0
$511$	−472.457	+	818.320i	−0.924573	+	1.60141i
$512$		0			0
$513$	308.373	−	409.970i	0.601116	−	0.799162i
$514$		0			0
$515$	399.327	+	230.552i	0.775392	+	0.447673i
$516$		0			0
$517$	224.533	+	388.903i	0.434300	+	0.752230i
$518$		0			0
$519$	70.2746	+	103.061i	0.135404	+	0.198575i
$520$		0			0
$521$			881.609i			1.69215i	0.533066	+	0.846074i	$0.321040\pi$
$521$			881.609i			1.69215i	−0.533066	+	0.846074i	$0.678960\pi$
$522$		0			0
$523$	670.142	+	386.907i	1.28134	+	0.739783i	0.977094	−	0.212810i	$-0.0682615\pi$
$523$	670.142	+	386.907i	1.28134	+	0.739783i	0.304248	+	0.952593i	$0.401595\pi$
$524$		0			0
$525$	31.5846	+	421.127i	0.0601611	+	0.802147i
$526$		0			0
$527$			59.2090i			0.112351i
$528$		0			0
$529$	−208.108	+	360.453i	−0.393398	+	0.681386i
$530$		0			0
$531$	−280.427	+	223.689i	−0.528112	+	0.421259i
$532$		0			0
$533$	−0.889078	−	1.53993i	−0.00166806	−	0.00288917i
$534$		0			0
$535$			307.791i			0.575310i
$536$		0			0
$537$	−36.7192	+	76.2599i	−0.0683784	+	0.142011i
$538$		0			0
$539$	114.613			0.212640
$540$		0			0
$541$	−246.112	+	426.278i	−0.454920	+	0.787944i	−0.998684	−	0.0512943i	$-0.983665\pi$
$541$	−246.112	+	426.278i	−0.454920	+	0.787944i	0.543764	+	0.839238i	$0.316999\pi$
$542$		0			0
$543$	−450.948	−	661.334i	−0.830475	−	1.21793i
$544$		0			0
$545$	113.498	−	65.5283i	0.208254	−	0.120235i
$546$		0			0
$547$		−	531.808i		−	0.972227i	−0.873896	−	0.486114i	$-0.838414\pi$
$547$		−	531.808i		−	0.972227i	0.873896	−	0.486114i	$-0.161586\pi$
$548$		0			0
$549$	−240.454	−	301.445i	−0.437985	−	0.549080i
$550$		0			0
$551$	−557.718	+	471.019i	−1.01219	+	0.854844i
$552$		0			0
$553$		−	179.606i		−	0.324786i
$554$		0			0
$555$	−18.0094	+	37.4027i	−0.0324494	+	0.0673922i
$556$		0			0
$557$	−172.254	+	298.352i	−0.309253	+	0.535642i	−0.978199	−	0.207669i	$-0.933412\pi$
$557$	−172.254	+	298.352i	−0.309253	+	0.535642i	0.668946	+	0.743311i	$0.266746\pi$
$558$		0			0
$559$			519.849i			0.929962i
$560$		0			0
$561$	232.323	−	158.416i	0.414123	−	0.282381i
$562$		0			0
$563$	751.453	+	433.851i	1.33473	+	0.770606i	0.986020	−	0.166625i	$-0.0532869\pi$
$563$	751.453	+	433.851i	1.33473	+	0.770606i	0.348709	+	0.937231i	$0.386620\pi$
$564$		0			0
$565$	−194.009	−	112.011i	−0.343379	−	0.198250i
$566$		0			0
$567$	−611.270	+	188.713i	−1.07808	+	0.332827i
$568$		0			0
$569$	29.8460	−	17.2316i	0.0524534	−	0.0302840i	−0.473544	−	0.880770i	$-0.657025\pi$
$569$	29.8460	−	17.2316i	0.0524534	−	0.0302840i	0.525997	+	0.850486i	$0.323692\pi$
$570$		0			0
$571$	−250.214	+	433.383i	−0.438203	+	0.758990i	−0.997551	−	0.0699428i	$-0.977718\pi$
$571$	−250.214	+	433.383i	−0.438203	+	0.758990i	0.559348	+	0.828933i	$0.311052\pi$
$572$		0			0
$573$	51.7063	+	689.416i	0.0902379	+	1.20317i
$574$		0			0
$575$	273.986	+	474.558i	0.476498	+	0.825319i
$576$		0			0
$577$	−780.995			−1.35354			−0.676772	−	0.736193i	$-0.736622\pi$
$577$	−780.995			−1.35354			−0.676772	+	0.736193i	$0.736622\pi$
$578$		0			0
$579$	108.935	−	226.241i	0.188143	−	0.390744i
$580$		0			0
$581$	−37.0378	+	64.1514i	−0.0637484	+	0.110415i
$582$		0			0
$583$		−	471.066i		−	0.808003i
$584$		0			0
$585$	−202.672	−	79.5148i	−0.346448	−	0.135923i
$586$		0			0
$587$	−159.696	+	276.602i	−0.272055	+	0.471212i	−0.969388	−	0.245535i	$-0.921036\pi$
$587$	−159.696	+	276.602i	−0.272055	+	0.471212i	0.697333	+	0.716747i	$0.254370\pi$
$588$		0			0
$589$	−18.1780	−	101.205i	−0.0308624	−	0.171825i
$590$		0			0
$591$	32.0517	+	15.4329i	0.0542330	+	0.0261132i
$592$		0			0
$593$	154.888	−	268.273i	0.261193	−	0.452400i	−0.705366	−	0.708843i	$-0.749217\pi$
$593$	154.888	−	268.273i	0.261193	−	0.452400i	0.966559	+	0.256443i	$0.0825507\pi$
$594$		0			0
$595$	−115.741	+	200.469i	−0.194523	+	0.336923i
$596$		0			0
$597$	353.359	−	240.947i	0.591892	−	0.403597i
$598$		0			0
$599$	−569.818	+	328.985i	−0.951282	+	0.549223i	−0.893479	−	0.449105i	$-0.851743\pi$
$599$	−569.818	+	328.985i	−0.951282	+	0.549223i	−0.0578031	+	0.998328i	$0.518410\pi$
$600$		0			0
$601$	757.787	−	437.508i	1.26088	−	0.727967i	0.287632	−	0.957741i	$-0.407132\pi$
$601$	757.787	−	437.508i	1.26088	−	0.727967i	0.973244	+	0.229774i	$0.0737986\pi$
$602$		0			0
$603$	−784.506	−	307.787i	−1.30100	−	0.510426i
$604$		0			0
$605$	−63.7620	+	110.439i	−0.105392	+	0.182544i
$606$		0			0
$607$	−340.767	−	196.742i	−0.561396	−	0.324122i	0.192310	−	0.981334i	$-0.438402\pi$
$607$	−340.767	−	196.742i	−0.561396	−	0.324122i	−0.753706	+	0.657212i	$0.771736\pi$
$608$		0			0
$609$	907.804	−	68.0855i	1.49065	−	0.111799i
$610$		0			0
$611$	−409.909	+	236.661i	−0.670883	+	0.387334i
$612$		0			0
$613$	−581.450	−	1007.10i	−0.948533	−	1.64291i	−0.748519	−	0.663114i	$-0.769235\pi$
$613$	−581.450	−	1007.10i	−0.948533	−	1.64291i	−0.200014	−	0.979793i	$-0.564099\pi$
$614$		0			0
$615$	0.686564	−	1.42588i	0.00111636	−	0.00231851i
$616$		0			0
$617$	175.255	+	303.550i	0.284043	+	0.491978i	0.972377	−	0.233417i	$-0.0749907\pi$
$617$	175.255	+	303.550i	0.284043	+	0.491978i	−0.688333	+	0.725395i	$0.741657\pi$
$618$		0			0
$619$	367.778	+	637.010i	0.594148	+	1.02909i	0.993666	+	0.112370i	$0.0358440\pi$
$619$	367.778	+	637.010i	0.594148	+	1.02909i	−0.399518	+	0.916725i	$0.630823\pi$
$620$		0			0
$621$	−608.403	+	564.720i	−0.979714	+	0.909371i
$622$		0			0
$623$		−	1161.97i		−	1.86511i
$624$		0			0
$625$	138.266			0.221226
$626$		0			0
$627$	−348.470	+	342.103i	−0.555773	+	0.545620i
$628$		0			0
$629$	48.9417	−	28.2565i	0.0778088	−	0.0449229i
$630$		0			0
$631$	−108.316	+	187.610i	−0.171658	+	0.297321i	−0.939000	−	0.343918i	$-0.888246\pi$
$631$	−108.316	+	187.610i	−0.171658	+	0.297321i	0.767341	+	0.641239i	$0.221579\pi$
$632$		0			0
$633$	−111.102	+	230.741i	−0.175517	+	0.364520i
$634$		0			0
$635$	436.290	+	251.892i	0.687071	+	0.396681i
$636$		0			0
$637$			120.804i			0.189645i
$638$		0			0
$639$	−937.656	−	367.872i	−1.46738	−	0.575700i
$640$		0			0
$641$	−63.9111	−	36.8991i	−0.0997053	−	0.0575649i	0.449318	−	0.893372i	$-0.351667\pi$
$641$	−63.9111	−	36.8991i	−0.0997053	−	0.0575649i	−0.549024	+	0.835807i	$0.685000\pi$
$642$		0			0
$643$	1156.13			1.79803			0.899016	−	0.437916i	$-0.144283\pi$
$643$	1156.13			1.79803			0.899016	+	0.437916i	$0.144283\pi$
$644$		0			0
$645$	−382.258	+	260.653i	−0.592648	+	0.404113i
$646$		0			0
$647$	616.353			0.952632			0.476316	−	0.879274i	$-0.341972\pi$
$647$	616.353			0.952632			0.476316	+	0.879274i	$0.341972\pi$
$648$		0			0
$649$	295.716	−	170.732i	0.455649	−	0.263069i
$650$		0			0
$651$	−55.6287	+	115.532i	−0.0854511	+	0.177468i
$652$		0			0
$653$	43.0169	−	74.5074i	0.0658758	−	0.114100i	−0.831206	−	0.555964i	$-0.812349\pi$
$653$	43.0169	−	74.5074i	0.0658758	−	0.114100i	0.897082	+	0.441864i	$0.145683\pi$
$654$		0			0
$655$	485.130			0.740657
$656$		0			0
$657$	−393.264	+	1002.37i	−0.598575	+	1.52568i
$658$		0			0
$659$		−	122.094i		−	0.185271i	−0.995700	−	0.0926356i	$-0.970471\pi$
$659$		−	122.094i		−	0.185271i	0.995700	−	0.0926356i	$-0.0295292\pi$
$660$		0			0
$661$	−49.8532	+	28.7828i	−0.0754209	+	0.0435443i	−0.537236	−	0.843432i	$-0.680532\pi$
$661$	−49.8532	+	28.7828i	−0.0754209	+	0.0435443i	0.461815	+	0.886976i	$0.347198\pi$
$662$		0			0
$663$	166.972	+	244.872i	0.251844	+	0.369339i
$664$		0			0
$665$	136.287	−	378.192i	0.204943	−	0.568710i
$666$		0			0
$667$	1022.98	−	590.620i	1.53371	−	0.885487i
$668$		0			0
$669$	−22.3166	−	32.7282i	−0.0333581	−	0.0489210i
$670$		0			0
$671$	183.528	+	317.880i	0.273514	+	0.473741i
$672$		0			0
$673$	702.761	−	405.739i	1.04422	−	0.602882i	0.123195	−	0.992382i	$-0.460686\pi$
$673$	702.761	−	405.739i	1.04422	−	0.602882i	0.921026	+	0.389501i	$0.127352\pi$
$674$		0			0
$675$	107.170	+	469.150i	0.158770	+	0.695038i
$676$		0			0
$677$	72.6816	−	41.9627i	0.107358	−	0.0619834i	−0.445359	−	0.895352i	$-0.646924\pi$
$677$	72.6816	−	41.9627i	0.107358	−	0.0619834i	0.552718	+	0.833369i	$0.313591\pi$
$678$		0			0
$679$		−	969.310i		−	1.42756i
$680$		0			0
$681$	−1046.54	+	78.4909i	−1.53677	+	0.115258i
$682$		0			0
$683$		−	1065.59i		−	1.56017i	−0.625675	−	0.780084i	$-0.715176\pi$
$683$		−	1065.59i		−	1.56017i	0.625675	−	0.780084i	$-0.284824\pi$
$684$		0			0
$685$	−295.498			−0.431384
$686$		0			0
$687$	430.677	−	293.669i	0.626896	−	0.427465i
$688$		0			0
$689$	496.510			0.720624
$690$		0			0
$691$	−290.460	−	503.092i	−0.420348	−	0.728064i	0.575626	−	0.817713i	$-0.304759\pi$
$691$	−290.460	−	503.092i	−0.420348	−	0.728064i	−0.995973	+	0.0896497i	$0.971425\pi$
$692$		0			0
$693$	602.159	−	90.8350i	0.868916	−	0.131075i
$694$		0			0
$695$	−221.625	−	383.866i	−0.318885	−	0.552326i
$696$		0			0
$697$	−1.86578	+	1.07721i	−0.00267688	+	0.00154549i
$698$		0			0
$699$	−38.3321	−	511.094i	−0.0548385	−	0.731178i
$700$		0			0
$701$	341.550	+	591.583i	0.487233	+	0.843913i	0.999892	−	0.0146796i	$-0.00467282\pi$
$701$	341.550	+	591.583i	0.487233	+	0.843913i	−0.512659	+	0.858592i	$0.671339\pi$
$702$		0			0
$703$	−74.9800	+	63.3241i	−0.106657	+	0.0900770i
$704$		0			0
$705$	−379.552	−	182.755i	−0.538372	−	0.259226i
$706$		0			0
$707$	109.733	+	190.063i	0.155209	+	0.268830i
$708$		0			0
$709$	355.358			0.501210			0.250605	−	0.968089i	$-0.419371\pi$
$709$	355.358			0.501210			0.250605	+	0.968089i	$0.419371\pi$
$710$		0			0
$711$	−30.5284	−	202.377i	−0.0429373	−	0.284638i
$712$		0			0
$713$			166.382i			0.233356i
$714$		0			0
$715$	179.477	+	103.621i	0.251017	+	0.144925i
$716$		0			0
$717$	−300.264	+	204.743i	−0.418778	+	0.285555i
$718$		0			0
$719$	610.091	+	1056.71i	0.848528	+	1.46969i	0.882522	+	0.470271i	$0.155844\pi$
$719$	610.091	+	1056.71i	0.848528	+	1.46969i	−0.0339943	+	0.999422i	$0.510823\pi$
$720$		0			0
$721$		−	1359.44i		−	1.88549i
$722$		0			0
$723$	192.300	−	399.376i	0.265975	−	0.552387i
$724$		0			0
$725$		−	684.804i		−	0.944558i
$726$		0			0
$727$	722.833	−	1251.98i	0.994269	−	1.72212i	0.404546	−	0.914518i	$-0.367429\pi$
$727$	722.833	−	1251.98i	0.994269	−	1.72212i	0.589722	−	0.807606i	$-0.299237\pi$
$728$		0			0
$729$	−656.692	+	316.538i	−0.900812	+	0.434209i
$730$		0			0
$731$	629.850			0.861628
$732$		0			0
$733$	228.185	−	395.227i	0.311302	−	0.539192i	−0.667342	−	0.744751i	$-0.732568\pi$
$733$	228.185	−	395.227i	0.311302	−	0.539192i	0.978645	+	0.205560i	$0.0659015\pi$
$734$		0			0
$735$	−88.8301	+	60.5712i	−0.120857	+	0.0824098i
$736$		0			0
$737$	694.723	+	401.098i	0.942636	+	0.544231i
$738$		0			0
$739$	−525.271	−	909.796i	−0.710786	−	1.23112i	−0.964563	−	0.263854i	$-0.915006\pi$
$739$	−525.271	−	909.796i	−0.710786	−	1.23112i	0.253777	−	0.967263i	$-0.418327\pi$
$740$		0			0
$741$	−360.582	−	367.292i	−0.486615	−	0.495671i
$742$		0			0
$743$		−	907.544i		−	1.22146i	−0.791839	−	0.610729i	$-0.790876\pi$
$743$		−	907.544i		−	1.22146i	0.791839	−	0.610729i	$-0.209124\pi$
$744$		0			0
$745$	354.218			0.475461
$746$		0			0
$747$	−30.8295	+	78.5802i	−0.0412711	+	0.105194i
$748$		0			0
$749$	785.864	−	453.719i	1.04922	−	0.605766i
$750$		0			0
$751$	−468.416	+	270.440i	−0.623724	+	0.360107i	−0.778317	−	0.627871i	$-0.783926\pi$
$751$	−468.416	+	270.440i	−0.623724	+	0.360107i	0.154594	+	0.987978i	$0.450593\pi$
$752$		0			0
$753$	−209.293	+	142.712i	−0.277945	+	0.189524i
$754$		0			0
$755$	38.0233	−	21.9528i	0.0503620	−	0.0290765i
$756$		0			0
$757$	−337.788	−	585.066i	−0.446219	−	0.772874i	0.551917	−	0.833899i	$-0.313896\pi$
$757$	−337.788	−	585.066i	−0.446219	−	0.772874i	−0.998136	+	0.0610249i	$0.980563\pi$
$758$		0			0
$759$	652.849	−	445.163i	0.860144	−	0.586512i
$760$		0			0
$761$	644.819	−	1116.86i	0.847331	−	1.46762i	−0.0362499	−	0.999343i	$-0.511541\pi$
$761$	644.819	−	1116.86i	0.847331	−	1.46762i	0.883581	−	0.468278i	$-0.155125\pi$
$762$		0			0
$763$	−334.619	−	193.192i	−0.438557	−	0.253201i
$764$		0			0
$765$	−96.3404	+	245.558i	−0.125935	+	0.320991i
$766$		0			0
$767$	179.954	+	311.689i	0.234620	+	0.406374i
$768$		0			0
$769$	−140.979	−	244.183i	−0.183328	−	0.317533i	0.759684	−	0.650293i	$-0.225354\pi$
$769$	−140.979	−	244.183i	−0.183328	−	0.317533i	−0.943012	+	0.332759i	$0.892020\pi$
$770$		0			0
$771$	419.138	−	31.4354i	0.543629	−	0.0407722i
$772$		0			0
$773$	70.8563	+	40.9089i	0.0916640	+	0.0529222i	0.545131	−	0.838351i	$-0.316480\pi$
$773$	70.8563	+	40.9089i	0.0916640	+	0.0529222i	−0.453467	+	0.891273i	$0.649813\pi$
$774$		0			0
$775$	83.5346	+	48.2287i	0.107787	+	0.0622306i
$776$		0			0
$777$	122.046	−	9.15345i	0.157073	−	0.0117805i
$778$		0			0
$779$	2.85843	−	2.41407i	0.00366936	−	0.00309894i
$780$		0			0
$781$	830.345	+	479.400i	1.06318	+	0.613828i
$782$		0			0
$783$	1011.33	−	231.021i	1.29160	−	0.295046i
$784$		0			0
$785$	−611.173			−0.778564
$786$		0			0
$787$	−246.928	−	142.564i	−0.313758	−	0.181148i	0.334849	−	0.942272i	$-0.391315\pi$
$787$	−246.928	−	142.564i	−0.313758	−	0.181148i	−0.648607	+	0.761124i	$0.724648\pi$
$788$		0			0
$789$	−307.535	+	209.701i	−0.389779	+	0.265781i
$790$		0			0
$791$			660.469i			0.834979i
$792$		0			0
$793$	−335.050	+	193.441i	−0.422509	+	0.243936i
$794$		0			0
$795$	248.951	+	365.096i	0.313145	+	0.459241i
$796$		0			0
$797$	1337.76	+	772.354i	1.67849	+	0.969077i	0.962625	+	0.270839i	$0.0873011\pi$
$797$	1337.76	+	772.354i	1.67849	+	0.969077i	0.715866	+	0.698238i	$0.246032\pi$
$798$		0			0
$799$	286.740	+	496.647i	0.358873	+	0.621586i
$800$		0			0
$801$	−197.504	−	1309.28i	−0.246572	−	1.63456i
$802$		0			0
$803$	512.489	−	887.657i	0.638218	−	1.10543i
$804$		0			0
$805$	−325.242	+	563.336i	−0.404028	+	0.699797i
$806$		0			0
$807$	172.422	−	12.9317i	0.213658	−	0.0160244i
$808$		0			0
$809$	−814.325			−1.00658			−0.503291	−	0.864117i	$-0.667878\pi$
$809$	−814.325			−1.00658			−0.503291	+	0.864117i	$0.667878\pi$
$810$		0			0
$811$	127.960	+	73.8776i	0.157780	+	0.0910944i	0.576811	−	0.816877i	$-0.304297\pi$
$811$	127.960	+	73.8776i	0.157780	+	0.0910944i	−0.419031	+	0.907972i	$0.637630\pi$
$812$		0			0
$813$	14.5088	+	193.450i	0.0178459	+	0.237945i
$814$		0			0
$815$	−425.912			−0.522591
$816$		0			0
$817$	−1076.59	+	193.373i	−1.31774	+	0.236686i
$818$		0			0
$819$	95.7413	+	634.684i	0.116900	+	0.774950i
$820$		0			0
$821$	1356.63			1.65241			0.826204	−	0.563371i	$-0.190496\pi$
$821$	1356.63			1.65241			0.826204	+	0.563371i	$0.190496\pi$
$822$		0			0
$823$	741.409	+	1284.16i	0.900862	+	1.56034i	0.826378	+	0.563116i	$0.190398\pi$
$823$	741.409	+	1284.16i	0.900862	+	1.56034i	0.0744842	+	0.997222i	$0.476269\pi$
$824$		0			0
$825$	−34.2608	−	456.810i	−0.0415282	−	0.553709i
$826$		0			0
$827$	525.877	+	303.615i	0.635885	+	0.367128i	0.783028	−	0.621987i	$-0.213674\pi$
$827$	525.877	+	303.615i	0.635885	+	0.367128i	−0.147143	+	0.989115i	$0.547008\pi$
$828$		0			0
$829$			441.338i			0.532374i	0.963921	+	0.266187i	$0.0857638\pi$
$829$			441.338i			0.532374i	−0.963921	+	0.266187i	$0.914236\pi$
$830$		0			0
$831$	−42.4321	−	565.760i	−0.0510615	−	0.680818i
$832$		0			0
$833$	146.366			0.175710
$834$		0			0
$835$	646.995	−	373.543i	0.774844	−	0.447356i
$836$		0			0
$837$	−43.0441	+	139.635i	−0.0514266	+	0.166828i
$838$		0			0
$839$	777.305	+	448.777i	0.926466	+	0.534895i	0.885692	−	0.464273i	$-0.153684\pi$
$839$	777.305	+	448.777i	0.926466	+	0.534895i	0.0407738	+	0.999168i	$0.487018\pi$
$840$		0			0
$841$	−635.202			−0.755294
$842$		0			0
$843$	−76.0682	+	157.982i	−0.0902352	+	0.187404i
$844$		0			0
$845$	117.148	−	202.907i	0.138637	−	0.240126i
$846$		0			0
$847$	375.970			0.443884
$848$		0			0
$849$	−70.0790	−	33.7431i	−0.0825430	−	0.0397445i
$850$		0			0
$851$	137.531	−	79.4034i	0.161611	−	0.0933059i
$852$		0			0
$853$	98.9535	−	171.393i	0.116006	−	0.200929i	−0.802175	−	0.597089i	$-0.796324\pi$
$853$	98.9535	−	171.393i	0.116006	−	0.200929i	0.918182	+	0.396160i	$0.129657\pi$
$854$		0			0
$855$	89.2831	−	449.306i	0.104425	−	0.525504i
$856$		0			0
$857$	−327.858	−	189.289i	−0.382564	−	0.220874i	0.296369	−	0.955073i	$-0.404224\pi$
$857$	−327.858	−	189.289i	−0.382564	−	0.220874i	−0.678933	+	0.734200i	$0.737557\pi$
$858$		0			0
$859$	−145.890	−	252.689i	−0.169837	−	0.294167i	0.768525	−	0.639819i	$-0.220991\pi$
$859$	−145.890	−	252.689i	−0.169837	−	0.294167i	−0.938363	+	0.345653i	$0.887658\pi$
$860$		0			0
$861$	−4.65269	+	0.348953i	−0.00540383	+	0.000405288i
$862$		0			0
$863$			884.191i			1.02456i	0.858820	+	0.512278i	$0.171198\pi$
$863$			884.191i			1.02456i	−0.858820	+	0.512278i	$0.828802\pi$
$864$		0			0
$865$	96.4649	+	55.6941i	0.111520	+	0.0643862i
$866$		0			0
$867$	−419.632	+	286.137i	−0.484005	+	0.330031i
$868$		0			0
$869$			194.825i			0.224194i
$870$		0			0
$871$	−422.763	+	732.247i	−0.485377	+	0.840697i
$872$		0			0
$873$	−164.757	−	1092.20i	−0.188726	−	1.25109i
$874$		0			0
$875$	453.027	+	784.666i	0.517745	+	0.896761i
$876$		0			0
$877$			909.336i			1.03687i	0.855117	+	0.518436i	$0.173485\pi$
$877$			909.336i			1.03687i	−0.855117	+	0.518436i	$0.826515\pi$
$878$		0			0
$879$	−84.2729	−	123.590i	−0.0958736	−	0.140603i
$880$		0			0
$881$	−909.618			−1.03248			−0.516242	−	0.856443i	$-0.672669\pi$
$881$	−909.618			−1.03248			−0.516242	+	0.856443i	$0.672669\pi$
$882$		0			0
$883$	659.262	−	1141.88i	0.746616	−	1.29318i	−0.202820	−	0.979216i	$-0.565011\pi$
$883$	659.262	−	1141.88i	0.746616	−	1.29318i	0.949436	−	0.313961i	$-0.101656\pi$
$884$		0			0
$885$	−138.964	+	288.606i	−0.157021	+	0.326109i
$886$		0			0
$887$	−583.618	+	336.952i	−0.657969	+	0.379878i	−0.791503	−	0.611166i	$-0.790701\pi$
$887$	−583.618	+	336.952i	−0.657969	+	0.379878i	0.133534	+	0.991044i	$0.457367\pi$
$888$		0			0
$889$		−	1485.27i		−	1.67072i
$890$		0			0
$891$	663.063	−	204.703i	0.744179	−	0.229745i
$892$		0			0
$893$	−642.596	−	760.877i	−0.719592	−	0.852046i
$894$		0			0
$895$			75.5802i			0.0844472i
$896$		0			0
$897$	469.208	+	688.112i	0.523085	+	0.767126i
$898$		0			0
$899$	103.965	−	180.072i	0.115645	−	0.200302i
$900$		0			0
$901$		−	601.573i		−	0.667672i
$902$		0			0
$903$	1229.00	+	591.764i	1.36102	+	0.655331i
$904$		0			0
$905$	−619.010	−	357.386i	−0.683989	−	0.394901i
$906$		0			0
$907$	−930.927	−	537.471i	−1.02638	−	0.592581i	−0.110435	−	0.993883i	$-0.535224\pi$
$907$	−930.927	−	537.471i	−1.02638	−	0.592581i	−0.915946	+	0.401302i	$0.868558\pi$
$908$		0			0
$909$	155.951	+	195.508i	0.171563	+	0.215080i
$910$		0			0
$911$	−420.259	+	242.637i	−0.461316	+	0.266341i	−0.712598	−	0.701573i	$-0.752481\pi$
$911$	−420.259	+	242.637i	−0.461316	+	0.266341i	0.251281	+	0.967914i	$0.419148\pi$
$912$		0			0
$913$	40.1761	−	69.5870i	0.0440045	−	0.0762180i
$914$		0			0
$915$	−310.237	−	149.379i	−0.339057	−	0.163256i
$916$		0			0
$917$	−715.137	−	1238.65i	−0.779866	−	1.35077i
$918$		0			0
$919$	1213.32			1.32026			0.660129	−	0.751153i	$-0.270502\pi$
$919$	1213.32			1.32026			0.660129	+	0.751153i	$0.270502\pi$
$920$		0			0
$921$	914.379	−	68.5786i	0.992812	−	0.0744610i
$922$		0			0
$923$	−505.294	+	875.195i	−0.547448	+	0.948207i
$924$		0			0
$925$		−	92.0656i		−	0.0995303i
$926$		0			0
$927$	−231.069	−	1531.79i	−0.249265	−	1.65242i
$928$		0			0
$929$	219.672	−	380.483i	0.236461	−	0.409562i	−0.723235	−	0.690601i	$-0.757346\pi$
$929$	219.672	−	380.483i	0.236461	−	0.409562i	0.959696	+	0.281040i	$0.0906792\pi$
$930$		0			0
$931$	−250.181	+	44.9364i	−0.268723	+	0.0482668i
$932$		0			0
$933$	838.844	−	571.988i	0.899082	−	0.613063i
$934$		0			0
$935$	125.548	−	217.455i	0.134276	−	0.232572i
$936$		0			0
$937$	602.042	−	1042.77i	0.642521	−	1.11288i	−0.342347	−	0.939574i	$-0.611222\pi$
$937$	602.042	−	1042.77i	0.642521	−	1.11288i	0.984868	−	0.173305i	$-0.0554447\pi$
$938$		0			0
$939$	−1437.93	−	692.363i	−1.53134	−	0.737341i
$940$		0			0
$941$	−1388.46	+	801.627i	−1.47551	+	0.851889i	−0.999619	−	0.0276131i	$-0.991209\pi$
$941$	−1388.46	+	801.627i	−1.47551	+	0.851889i	−0.475896	+	0.879502i	$0.657876\pi$
$942$		0			0
$943$	−5.24302	+	3.02706i	−0.00555993	+	0.00321003i
$944$		0			0
$945$	−418.695	+	388.633i	−0.443063	+	0.411251i
$946$		0			0
$947$	261.919	−	453.656i	0.276577	−	0.479046i	−0.693955	−	0.720019i	$-0.744133\pi$
$947$	261.919	−	453.656i	0.276577	−	0.479046i	0.970532	+	0.240973i	$0.0774665\pi$
$948$		0			0
$949$	935.603	+	540.171i	0.985883	+	0.569200i
$950$		0			0
$951$	−523.985	+	1088.23i	−0.550983	+	1.14430i
$952$		0			0
$953$	632.378	−	365.104i	0.663566	−	0.383110i	−0.130068	−	0.991505i	$-0.541520\pi$
$953$	632.378	−	365.104i	0.663566	−	0.383110i	0.793634	+	0.608395i	$0.208186\pi$
$954$		0			0
$955$	308.676	+	534.643i	0.323221	+	0.559836i
$956$		0			0
$957$	−984.724	+	73.8544i	−1.02897	+	0.0771729i
$958$		0			0
$959$	435.598	+	754.477i	0.454221	+	0.786733i
$960$		0			0
$961$	−465.856	−	806.887i	−0.484762	−	0.839632i
$962$		0			0
$963$	808.378	−	644.819i	0.839437	−	0.669594i
$964$		0			0
$965$		−	224.224i		−	0.232357i
$966$		0			0
$967$	394.403			0.407863			0.203931	−	0.978985i	$-0.434628\pi$
$967$	394.403			0.407863			0.203931	+	0.978985i	$0.434628\pi$
$968$		0			0
$969$	−445.012	+	436.882i	−0.459249	+	0.450859i
$970$		0			0
$971$	−162.445	+	93.7875i	−0.167296	+	0.0965886i	−0.581310	−	0.813682i	$-0.697460\pi$
$971$	−162.445	+	93.7875i	−0.167296	+	0.0965886i	0.414014	+	0.910271i	$0.364126\pi$
$972$		0			0
$973$	−653.401	+	1131.72i	−0.671533	+	1.16313i
$974$		0			0
$975$	481.484	−	36.1114i	0.493830	−	0.0370373i
$976$		0			0
$977$	−577.746	−	333.562i	−0.591347	−	0.341415i	0.174283	−	0.984696i	$-0.444239\pi$
$977$	−577.746	−	333.562i	−0.591347	−	0.341415i	−0.765630	+	0.643281i	$0.777573\pi$
$978$		0			0
$979$			1260.42i			1.28746i
$980$		0			0
$981$	−409.880	−	160.809i	−0.417819	−	0.163924i
$982$		0			0
$983$	−1184.54	−	683.896i	−1.20503	−	0.695723i	−0.243359	−	0.969936i	$-0.578249\pi$
$983$	−1184.54	−	683.896i	−1.20503	−	0.695723i	−0.961669	+	0.274213i	$0.911583\pi$
$984$		0			0
$985$	31.7660			0.0322498
$986$		0			0
$987$	92.8868	+	1238.49i	0.0941102	+	1.25480i
$988$		0			0
$989$	1769.94			1.78962
$990$		0			0
$991$	377.503	−	217.952i	0.380932	−	0.219931i	−0.297292	−	0.954787i	$-0.596083\pi$
$991$	377.503	−	217.952i	0.380932	−	0.219931i	0.678224	+	0.734856i	$0.262750\pi$
$992$		0			0
$993$	482.555	−	36.1917i	0.485957	−	0.0364469i
$994$		0			0
$995$	190.956	−	330.745i	0.191915	−	0.332407i
$996$		0			0
$997$	−448.551			−0.449901			−0.224951	−	0.974370i	$-0.572222\pi$
$997$	−448.551			−0.449901			−0.224951	+	0.974370i	$0.572222\pi$
$998$		0			0
$999$	135.963	−	31.0586i	0.136099	−	0.0310897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.bl.a.373.7	yes	80
3.2	odd	2		2052.3.bl.a.145.25		80
9.2	odd	6		2052.3.s.a.829.16		80
9.7	even	3		684.3.s.a.601.20	yes	80
19.8	odd	6		684.3.s.a.445.20	✓	80
57.8	even	6		2052.3.s.a.901.16		80
171.65	even	6		2052.3.bl.a.1585.25		80
171.160	odd	6	inner	684.3.bl.a.673.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.20	✓	80	19.8	odd	6
684.3.s.a.601.20	yes	80	9.7	even	3
684.3.bl.a.373.7	yes	80	1.1	even	1	trivial
684.3.bl.a.673.7	yes	80	171.160	odd	6	inner
2052.3.s.a.829.16		80	9.2	odd	6
2052.3.s.a.901.16		80	57.8	even	6
2052.3.bl.a.145.25		80	3.2	odd	2
2052.3.bl.a.1585.25		80	171.65	even	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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70298 - 1.30149i) q^{3} -2.67889 q^{5} +(3.94899 + 6.83985i) q^{7} +(5.61225 + 7.03581i) q^{9} +O(q^{10})\)	\(q+(-2.70298 - 1.30149i) q^{3} -2.67889 q^{5} +(3.94899 + 6.83985i) q^{7} +(5.61225 + 7.03581i) q^{9} +(-4.28360 - 7.41940i) q^{11} +(7.82016 - 4.51497i) q^{13} +(7.24101 + 3.48655i) q^{15} +(-5.47035 - 9.47493i) q^{17} +(12.2593 + 14.5158i) q^{19} +(-1.77207 - 23.6276i) q^{21} +(-15.3722 - 26.6254i) q^{23} -17.8235 q^{25} +(-6.01282 - 26.3220i) q^{27} +38.4214i q^{29} +(-4.68676 - 2.70590i) q^{31} +(1.92222 + 25.6296i) q^{33} +(-10.5789 - 18.3232i) q^{35} +5.16539i q^{37} +(-27.0139 + 2.02605i) q^{39} -0.196918i q^{41} +(-28.7847 + 49.8566i) q^{43} +(-15.0346 - 18.8482i) q^{45} -52.4170 q^{47} +(-6.68907 + 11.5858i) q^{49} +(2.45477 + 32.7302i) q^{51} +(47.6183 + 27.4924i) q^{53} +(11.4753 + 19.8758i) q^{55} +(-14.2445 - 55.1914i) q^{57} +39.8572i q^{59} -42.8444 q^{61} +(-25.9612 + 66.1714i) q^{63} +(-20.9494 + 12.0951i) q^{65} +(-81.0911 + 46.8180i) q^{67} +(6.89812 + 91.9747i) q^{69} +(-96.9215 + 55.9577i) q^{71} +(59.8200 + 103.611i) q^{73} +(48.1767 + 23.1971i) q^{75} +(33.8318 - 58.5983i) q^{77} +(-19.6941 - 11.3704i) q^{79} +(-18.0052 + 78.9735i) q^{81} +(4.68953 + 8.12250i) q^{83} +(14.6545 + 25.3823i) q^{85} +(50.0050 - 103.852i) q^{87} +(-127.411 - 73.5609i) q^{89} +(61.7635 + 35.6592i) q^{91} +(9.14654 + 13.4138i) q^{93} +(-32.8414 - 38.8864i) q^{95} +(-106.286 - 61.3644i) q^{97} +(28.1609 - 71.7781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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