LMFDB - Embedded newform 684.3.s.a.445.20

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			445.20
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.224370 - 2.99160i) q^{3} +(1.33945 + 2.31999i) q^{5} +(3.94899 + 6.83985i) q^{7} +(-8.89932 + 1.34245i) q^{9} +O(q^{10})$	\(q+(-0.224370 - 2.99160i) q^{3} +(1.33945 + 2.31999i) q^{5} +(3.94899 + 6.83985i) q^{7} +(-8.89932 + 1.34245i) q^{9} +(-4.28360 - 7.41940i) q^{11} -9.02994i q^{13} +(6.63995 - 4.52762i) q^{15} +(-5.47035 + 9.47493i) q^{17} +(12.2593 - 14.5158i) q^{19} +(19.5761 - 13.3485i) q^{21} +30.7444 q^{23} +(8.91176 - 15.4356i) q^{25} +(6.01282 + 26.3220i) q^{27} +(33.2739 + 19.2107i) q^{29} +(4.68676 + 2.70590i) q^{31} +(-21.2348 + 14.4795i) q^{33} +(-10.5789 + 18.3232i) q^{35} -5.16539i q^{37} +(-27.0139 + 2.02605i) q^{39} +(0.170536 - 0.0984589i) q^{41} +57.5695 q^{43} +(-15.0346 - 18.8482i) q^{45} +(26.2085 - 45.3945i) q^{47} +(-6.68907 + 11.5858i) q^{49} +(29.5726 + 14.2392i) q^{51} +(47.6183 - 27.4924i) q^{53} +(11.4753 - 19.8758i) q^{55} +(-46.1762 - 33.4180i) q^{57} +(-34.5173 + 19.9286i) q^{59} +(21.4222 - 37.1043i) q^{61} +(-44.3255 - 55.5687i) q^{63} +(20.9494 - 12.0951i) q^{65} +93.6359i q^{67} +(-6.89812 - 91.9747i) q^{69} +(-96.9215 - 55.9577i) q^{71} +(59.8200 - 103.611i) q^{73} +(-48.1767 - 23.1971i) q^{75} +(33.8318 - 58.5983i) q^{77} -22.7408i q^{79} +(77.3956 - 23.8938i) q^{81} +(4.68953 + 8.12250i) q^{83} -29.3090 q^{85} +(50.0050 - 103.852i) q^{87} +(-127.411 + 73.5609i) q^{89} +(61.7635 - 35.6592i) q^{91} +(7.04340 - 14.6280i) q^{93} +(50.0973 + 8.99825i) q^{95} -122.729i q^{97} +(48.0813 + 60.2771i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.224370	−	2.99160i	−0.0747901	−	0.997199i
$3$	−0.224370	−	2.99160i	−0.0747901	−	0.997199i
$4$		0			0
$5$	1.33945	+	2.31999i	0.267889	+	0.463998i	0.968317	−	0.249726i	$-0.0803405\pi$
$5$	1.33945	+	2.31999i	0.267889	+	0.463998i	−0.700427	+	0.713724i	$0.747007\pi$
$6$		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
$9$	−8.89932	+	1.34245i	−0.988813	+	0.149161i
$10$		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
$13$		−	9.02994i		−	0.694611i	−0.937752	−	0.347305i	$-0.887097\pi$
$13$		−	9.02994i		−	0.694611i	0.937752	−	0.347305i	$-0.112903\pi$
$14$		0			0
$15$	6.63995	−	4.52762i	0.442663	−	0.301842i
$16$		0			0
$17$	−5.47035	+	9.47493i	−0.321785	+	0.557349i	−0.980856	−	0.194732i	$-0.937616\pi$
$17$	−5.47035	+	9.47493i	−0.321785	+	0.557349i	0.659071	+	0.752081i	$0.270950\pi$
$18$		0			0
$19$	12.2593	−	14.5158i	0.645226	−	0.763992i
$19$	12.2593	−	14.5158i	0.645226	−	0.763992i
$20$		0			0
$21$	19.5761	−	13.3485i	0.932193	−	0.635641i
$22$		0			0
$23$	30.7444			1.33671			0.668356	−	0.743842i	$-0.266998\pi$
$23$	30.7444			1.33671			0.668356	+	0.743842i	$0.266998\pi$
$24$		0			0
$25$	8.91176	−	15.4356i	0.356471	−	0.617425i
$26$		0			0
$27$	6.01282	+	26.3220i	0.222697	+	0.974888i
$28$		0			0
$29$	33.2739	+	19.2107i	1.14738	+	0.662437i	0.948246	−	0.317536i	$-0.102855\pi$
$29$	33.2739	+	19.2107i	1.14738	+	0.662437i	0.199129	+	0.979973i	$0.436189\pi$
$30$		0			0
$31$	4.68676	+	2.70590i	0.151186	+	0.0872872i	0.573685	−	0.819076i	$-0.305514\pi$
$31$	4.68676	+	2.70590i	0.151186	+	0.0872872i	−0.422499	+	0.906364i	$0.638847\pi$
$32$		0			0
$33$	−21.2348	+	14.4795i	−0.643478	+	0.438772i
$34$		0			0
$35$	−10.5789	+	18.3232i	−0.302255	+	0.523521i
$36$		0			0
$37$		−	5.16539i		−	0.139605i	−0.997561	−	0.0698026i	$-0.977763\pi$
$37$		−	5.16539i		−	0.139605i	0.997561	−	0.0698026i	$-0.0222369\pi$
$38$		0			0
$39$	−27.0139	+	2.02605i	−0.692665	+	0.0519500i
$40$		0			0
$41$	0.170536	−	0.0984589i	0.00415941	−	0.00240144i	−0.497919	−	0.867224i	$-0.665902\pi$
$41$	0.170536	−	0.0984589i	0.00415941	−	0.00240144i	0.502078	+	0.864822i	$0.332569\pi$
$42$		0			0
$43$	57.5695			1.33882			0.669412	−	0.742891i	$-0.266546\pi$
$43$	57.5695			1.33882			0.669412	+	0.742891i	$0.266546\pi$
$44$		0			0
$45$	−15.0346	−	18.8482i	−0.334103	−	0.418848i
$46$		0			0
$47$	26.2085	−	45.3945i	0.557628	−	0.965840i	−0.440066	−	0.897965i	$-0.645045\pi$
$47$	26.2085	−	45.3945i	0.557628	−	0.965840i	0.997694	−	0.0678744i	$-0.0216217\pi$
$48$		0			0
$49$	−6.68907	+	11.5858i	−0.136512	+	0.236445i
$50$		0			0
$51$	29.5726	+	14.2392i	0.579854	+	0.279200i
$52$		0			0
$53$	47.6183	−	27.4924i	0.898458	−	0.518725i	0.0217584	−	0.999763i	$-0.493074\pi$
$53$	47.6183	−	27.4924i	0.898458	−	0.518725i	0.876700	+	0.481038i	$0.159740\pi$
$54$		0			0
$55$	11.4753	−	19.8758i	0.208642	−	0.361378i
$56$		0			0
$57$	−46.1762	−	33.4180i	−0.810108	−	0.586280i
$58$		0			0
$59$	−34.5173	+	19.9286i	−0.585039	+	0.337773i	−0.763133	−	0.646241i	$-0.776340\pi$
$59$	−34.5173	+	19.9286i	−0.585039	+	0.337773i	0.178094	+	0.984013i	$0.443007\pi$
$60$		0			0
$61$	21.4222	−	37.1043i	0.351184	−	0.608268i	−0.635273	−	0.772287i	$-0.719113\pi$
$61$	21.4222	−	37.1043i	0.351184	−	0.608268i	0.986457	+	0.164019i	$0.0524460\pi$
$62$		0			0
$63$	−44.3255	−	55.5687i	−0.703579	−	0.882043i
$64$		0			0
$65$	20.9494	−	12.0951i	0.322298	−	0.186079i
$66$		0			0
$67$			93.6359i			1.39755i	0.715341	+	0.698775i	$0.246271\pi$
$67$			93.6359i			1.39755i	−0.715341	+	0.698775i	$0.753729\pi$
$68$		0			0
$69$	−6.89812	−	91.9747i	−0.0999727	−	1.33297i
$70$		0			0
$71$	−96.9215	−	55.9577i	−1.36509	−	0.788136i	−0.374795	−	0.927108i	$-0.622287\pi$
$71$	−96.9215	−	55.9577i	−1.36509	−	0.788136i	−0.990296	+	0.138972i	$0.955620\pi$
$72$		0			0
$73$	59.8200	−	103.611i	0.819451	−	1.41933i	−0.0866355	−	0.996240i	$-0.527612\pi$
$73$	59.8200	−	103.611i	0.819451	−	1.41933i	0.906087	−	0.423092i	$-0.139055\pi$
$74$		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
$79$		−	22.7408i		−	0.287858i	−0.989588	−	0.143929i	$-0.954026\pi$
$79$		−	22.7408i		−	0.287858i	0.989588	−	0.143929i	$-0.0459737\pi$
$80$		0			0
$81$	77.3956	−	23.8938i	0.955502	−	0.294985i
$82$		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
$85$	−29.3090			−0.344812
$86$		0			0
$87$	50.0050	−	103.852i	0.574770	−	1.19371i
$88$		0			0
$89$	−127.411	+	73.5609i	−1.43159	+	0.826527i	−0.997242	−	0.0742203i	$-0.976353\pi$
$89$	−127.411	+	73.5609i	−1.43159	+	0.826527i	−0.434344	+	0.900747i	$0.643020\pi$
$90$		0			0
$91$	61.7635	−	35.6592i	0.678719	−	0.391859i
$92$		0			0
$93$	7.04340	−	14.6280i	0.0757355	−	0.157291i
$94$		0			0
$95$	50.0973	+	8.99825i	0.527340	+	0.0947185i
$96$		0			0
$97$		−	122.729i		−	1.26525i	−0.774460	−	0.632623i	$-0.781978\pi$
$97$		−	122.729i		−	1.26525i	0.774460	−	0.632623i	$-0.218022\pi$
$98$		0			0
$99$	48.0813	+	60.2771i	0.485669	+	0.608860i
$100$		0			0
$101$	−13.8938	+	24.0647i	−0.137562	+	0.238265i	−0.926573	−	0.376114i	$-0.877260\pi$
$101$	−13.8938	+	24.0647i	−0.137562	+	0.238265i	0.789011	+	0.614379i	$0.210593\pi$
$102$		0			0
$103$	149.064	+	86.0622i	1.44722	+	0.835555i	0.998315	−	0.0580219i	$-0.0184793\pi$
$103$	149.064	+	86.0622i	1.44722	+	0.835555i	0.448909	+	0.893577i	$0.351813\pi$
$104$		0			0
$105$	57.1894	+	27.5367i	0.544661	+	0.262254i
$106$		0			0
$107$			114.895i			1.07378i	0.843651	+	0.536892i	$0.180402\pi$
$107$			114.895i			1.07378i	−0.843651	+	0.536892i	$0.819598\pi$
$108$		0			0
$109$	−42.3676	−	24.4610i	−0.388694	−	0.224412i	0.292900	−	0.956143i	$-0.405380\pi$
$109$	−42.3676	−	24.4610i	−0.388694	−	0.224412i	−0.681594	+	0.731731i	$0.738713\pi$
$110$		0			0
$111$	−15.4528	+	1.15896i	−0.139214	+	0.0104411i
$112$		0			0
$113$	−72.4213	−	41.8125i	−0.640897	−	0.370022i	0.144063	−	0.989569i	$-0.453983\pi$
$113$	−72.4213	−	41.8125i	−0.640897	−	0.370022i	−0.784960	+	0.619547i	$0.787317\pi$
$114$		0			0
$115$	41.1804	+	71.3266i	0.358091	+	0.620231i
$116$		0			0
$117$	12.1223	+	80.3603i	0.103609	+	0.686840i
$118$		0			0
$119$	−86.4095			−0.726130
$120$		0			0
$121$	23.8016	−	41.2256i	0.196708	−	0.340708i
$122$		0			0
$123$	−0.332813	−	0.488084i	−0.00270579	−	0.00396816i
$124$		0			0
$125$	114.720			0.917757
$126$		0			0
$127$	−162.862	+	94.0285i	−1.28238	+	0.740382i	−0.977283	−	0.211940i	$-0.932022\pi$
$127$	−162.862	+	94.0285i	−1.28238	+	0.740382i	−0.305096	+	0.952322i	$0.598689\pi$
$128$		0			0
$129$	−12.9169	−	172.225i	−0.100131	−	1.33508i
$130$		0			0
$131$	90.5467	+	156.832i	0.691197	+	1.19719i	0.971446	+	0.237260i	$0.0762494\pi$
$131$	90.5467	+	156.832i	0.691197	+	1.19719i	−0.280250	+	0.959927i	$0.590417\pi$
$132$		0			0
$133$	147.698	+	26.5289i	1.11051	+	0.199465i
$134$		0			0
$135$	−53.0129	+	49.2066i	−0.392688	+	0.364493i
$136$		0			0
$137$	−55.1530	+	95.5279i	−0.402577	+	0.697284i	−0.994036	−	0.109051i	$-0.965219\pi$
$137$	−55.1530	+	95.5279i	−0.402577	+	0.697284i	0.591459	+	0.806335i	$0.298552\pi$
$138$		0			0
$139$	−165.460			−1.19036			−0.595181	−	0.803592i	$-0.702920\pi$
$139$	−165.460			−1.19036			−0.595181	+	0.803592i	$0.702920\pi$
$140$		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
$147$	36.1609	+	17.4115i	0.245993	+	0.118446i
$148$		0			0
$149$	66.1128	+	114.511i	0.443710	+	0.768528i	0.997961	−	0.0638211i	$-0.0203287\pi$
$149$	66.1128	+	114.511i	0.443710	+	0.768528i	−0.554251	+	0.832349i	$0.686995\pi$
$150$		0			0
$151$	14.1937	−	8.19471i	0.0939977	−	0.0542696i	−0.452264	−	0.891884i	$-0.649384\pi$
$151$	14.1937	−	8.19471i	0.0939977	−	0.0542696i	0.546262	+	0.837614i	$0.316050\pi$
$152$		0			0
$153$	35.9628	−	91.6640i	0.235051	−	0.599111i
$154$		0			0
$155$			14.4977i			0.0935332i
$156$		0			0
$157$	−114.072	−	197.578i	−0.726573	−	1.25846i	−0.958323	−	0.285685i	$-0.907779\pi$
$157$	−114.072	−	197.578i	−0.726573	−	1.25846i	0.231751	−	0.972775i	$-0.425555\pi$
$158$		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
$165$	−62.0351	−	29.8699i	−0.375970	−	0.181030i
$166$		0			0
$167$			278.878i			1.66993i	0.550303	+	0.834965i	$0.314512\pi$
$167$			278.878i			1.66993i	−0.550303	+	0.834965i	$0.685488\pi$
$168$		0			0
$169$	87.4602			0.517516
$170$		0			0
$171$	−89.6126	+	145.639i	−0.524050	+	0.851687i
$172$		0			0
$173$		−	41.5799i		−	0.240346i	−0.992753	−	0.120173i	$-0.961655\pi$
$173$		−	41.5799i		−	0.240346i	0.992753	−	0.120173i	$-0.0383450\pi$
$174$		0			0
$175$	140.770			0.804400
$176$		0			0
$177$	67.3630	+	98.7905i	0.380582	+	0.558139i
$178$		0			0
$179$			28.2132i			0.157616i	0.996890	+	0.0788079i	$0.0251114\pi$
$179$			28.2132i			0.157616i	−0.996890	+	0.0788079i	$0.974889\pi$
$180$		0			0
$181$	231.069	−	133.408i	1.27663	−	0.737061i	0.300400	−	0.953813i	$-0.402880\pi$
$181$	231.069	−	133.408i	1.27663	−	0.737061i	0.976227	+	0.216753i	$0.0695465\pi$
$182$		0			0
$183$	−115.808	−	55.7615i	−0.632829	−	0.304708i
$184$		0			0
$185$	11.9837	−	6.91877i	0.0647766	−	0.0373988i
$186$		0			0
$187$	93.7311			0.501236
$188$		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
$193$	−72.4866	+	41.8502i	−0.375578	+	0.216840i	−0.675893	−	0.737000i	$-0.736242\pi$
$193$	−72.4866	+	41.8502i	−0.375578	+	0.216840i	0.300314	+	0.953840i	$0.402908\pi$
$194$		0			0
$195$	−40.8842	−	59.9583i	−0.209662	−	0.307478i
$196$		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	0.629461	−	0.777032i	$-0.283276\pi$
$199$	−71.2816	−	123.463i	−0.358199	−	0.620419i	−0.987660	+	0.156613i	$0.949942\pi$
$200$		0			0
$201$	280.121	−	21.0091i	1.39364	−	0.104523i
$202$		0			0
$203$			303.451i			1.49483i
$204$		0			0
$205$	0.456847	+	0.263761i	0.00222852	+	0.00128664i
$206$		0			0
$207$	−273.604	+	41.2728i	−1.32176	+	0.199386i
$208$		0			0
$209$	−160.213	−	28.7767i	−0.766568	−	0.137688i
$210$		0			0
$211$	73.9286	−	42.6827i	0.350372	−	0.202288i	−0.314477	−	0.949265i	$-0.601829\pi$
$211$	73.9286	−	42.6827i	0.350372	−	0.202288i	0.664849	+	0.746978i	$0.268496\pi$
$212$		0			0
$213$	−145.657	+	302.505i	−0.683833	+	1.42021i
$214$		0			0
$215$	77.1112	+	133.561i	0.358657	+	0.621212i
$216$		0			0
$217$			42.7424i			0.196969i
$218$		0			0
$219$	−323.385	−	155.710i	−1.47664	−	0.711004i
$220$		0			0
$221$	85.5580	+	49.3969i	0.387140	+	0.223516i
$222$		0			0
$223$			13.2042i			0.0592117i	0.999562	+	0.0296059i	$0.00942522\pi$
$223$			13.2042i			0.0592117i	−0.999562	+	0.0296059i	$0.990575\pi$
$224$		0			0
$225$	−58.5870	+	149.330i	−0.260387	+	0.663690i
$226$		0			0
$227$	−302.960	+	174.914i	−1.33462	+	0.770545i	−0.986004	−	0.166719i	$-0.946683\pi$
$227$	−302.960	+	174.914i	−1.33462	+	0.770545i	−0.348619	+	0.937264i	$0.613349\pi$
$228$		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
$231$	−182.893	−	88.0633i	−0.791747	−	0.381226i
$232$		0			0
$233$	85.4215	−	147.954i	0.366616	−	0.634997i	−0.622418	−	0.782685i	$-0.713850\pi$
$233$	85.4215	−	147.954i	0.366616	−	0.634997i	0.989034	+	0.147687i	$0.0471830\pi$
$234$		0			0
$235$	140.420			0.597530
$236$		0			0
$237$	−68.0313	+	5.10236i	−0.287052	+	0.0215289i
$238$		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
$241$	127.958	+	73.8769i	0.530948	+	0.306543i	0.741402	−	0.671061i	$-0.234161\pi$
$241$	127.958	+	73.8769i	0.530948	+	0.306543i	−0.210454	+	0.977604i	$0.567494\pi$
$242$		0			0
$243$	−88.8459	−	226.176i	−0.365621	−	0.930764i
$244$		0			0
$245$	−35.8386			−0.146280
$246$		0			0
$247$	−131.077	−	110.701i	−0.530677	−	0.448181i
$248$		0			0
$249$	23.2471	−	15.8516i	0.0933617	−	0.0636612i
$250$		0			0
$251$	42.2197	+	73.1266i	0.168206	+	0.291341i	0.937789	−	0.347205i	$-0.112869\pi$
$251$	42.2197	+	73.1266i	0.168206	+	0.291341i	−0.769583	+	0.638547i	$0.779536\pi$
$252$		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
$257$			140.105i			0.545156i	0.962134	+	0.272578i	$0.0878762\pi$
$257$			140.105i			0.545156i	−0.962134	+	0.272578i	$0.912124\pi$
$258$		0			0
$259$	35.3305	−	20.3981i	0.136411	−	0.0787571i
$260$		0			0
$261$	−321.904	−	126.293i	−1.23335	−	0.483883i
$262$		0			0
$263$	−124.076			−0.471770			−0.235885	−	0.971781i	$-0.575799\pi$
$263$	−124.076			−0.471770			−0.235885	+	0.971781i	$0.575799\pi$
$264$		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	0.404346	−	0.914606i	$-0.367499\pi$
$269$	−49.9138	−	28.8177i	−0.185553	−	0.107129i	−0.589899	+	0.807477i	$0.700833\pi$
$270$		0			0
$271$	−32.3322	+	56.0009i	−0.119307	+	0.206646i	−0.919493	−	0.393106i	$-0.871401\pi$
$271$	−32.3322	+	56.0009i	−0.119307	+	0.206646i	0.800186	+	0.599751i	$0.204734\pi$
$272$		0			0
$273$	−120.536	−	176.771i	−0.441523	−	0.647511i
$274$		0			0
$275$	−152.698			−0.555264
$276$		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
$279$	−45.3415	−	17.7889i	−0.162514	−	0.0637596i
$280$		0			0
$281$	−50.6167	−	29.2236i	−0.180131	−	0.103998i	0.407223	−	0.913329i	$-0.366497\pi$
$281$	−50.6167	−	29.2236i	−0.180131	−	0.103998i	−0.587354	+	0.809330i	$0.699830\pi$
$282$		0			0
$283$	−12.9633	−	22.4530i	−0.0458066	−	0.0793393i	0.842213	−	0.539145i	$-0.181252\pi$
$283$	−12.9633	−	22.4530i	−0.0458066	−	0.0793393i	−0.888020	+	0.459806i	$0.847919\pi$
$284$		0			0
$285$	15.6788	−	151.890i	0.0550134	−	0.532947i
$286$		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
$291$	−367.155	+	27.5367i	−1.26170	+	0.0946278i
$292$		0			0
$293$	−43.1821	−	24.9312i	−0.147379	−	0.0850894i	0.424497	−	0.905429i	$-0.360451\pi$
$293$	−43.1821	−	24.9312i	−0.147379	−	0.0850894i	−0.571876	+	0.820340i	$0.693784\pi$
$294$		0			0
$295$	−92.4682	−	53.3865i	−0.313452	−	0.180971i
$296$		0			0
$297$	169.537	−	157.364i	0.570831	−	0.529846i
$298$		0			0
$299$		−	277.620i		−	0.928494i
$300$		0			0
$301$	227.341	+	393.767i	0.755287	+	1.30820i
$302$		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	0.00253851	−	0.999997i	$-0.499192\pi$
$307$	−264.700	−	152.825i	−0.862215	−	0.497800i	−0.864753	+	0.502197i	$0.832525\pi$
$308$		0			0
$309$	224.018	−	465.250i	0.724977	−	1.50566i
$310$		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
$313$	−265.989	+	460.707i	−0.849805	+	1.47191i	0.0315766	+	0.999501i	$0.489947\pi$
$313$	−265.989	+	460.707i	−0.849805	+	1.47191i	−0.881382	+	0.472404i	$0.843386\pi$
$314$		0			0
$315$	69.5472	−	177.266i	0.220785	−	0.562749i
$316$		0			0
$317$	−348.666	−	201.302i	−1.09989	−	0.635023i	−0.163699	−	0.986510i	$-0.552343\pi$
$317$	−348.666	−	201.302i	−1.09989	−	0.635023i	−0.936193	+	0.351488i	$0.885676\pi$
$318$		0			0
$319$		−	329.163i		−	1.03186i
$320$		0			0
$321$	343.719	−	25.7790i	1.07078	−	0.0803084i
$322$		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
$327$	−63.6713	+	132.235i	−0.194713	+	0.404389i
$328$		0			0
$329$	413.989			1.25832
$330$		0			0
$331$	139.693	−	80.6518i	0.422033	−	0.243661i	−0.273914	−	0.961754i	$-0.588318\pi$
$331$	139.693	−	80.6518i	0.422033	−	0.243661i	0.695947	+	0.718093i	$0.254985\pi$
$332$		0			0
$333$	6.93429	+	45.9685i	0.0208237	+	0.138043i
$334$		0			0
$335$	−217.234	+	125.420i	−0.648461	+	0.374389i
$336$		0			0
$337$	−144.327	+	83.3271i	−0.428269	+	0.247261i	−0.698609	−	0.715504i	$-0.746197\pi$
$337$	−144.327	+	83.3271i	−0.428269	+	0.247261i	0.270340	+	0.962765i	$0.412864\pi$
$338$		0			0
$339$	−108.837	+	226.037i	−0.321053	+	0.666776i
$340$		0			0
$341$		−	46.3640i		−	0.135965i
$342$		0			0
$343$	281.341			0.820236
$344$		0			0
$345$	204.141	−	139.199i	0.591713	−	0.403475i
$346$		0			0
$347$	7.67760	+	13.2980i	0.0221257	+	0.0383228i	0.876876	−	0.480716i	$-0.159623\pi$
$347$	7.67760	+	13.2980i	0.0221257	+	0.0383228i	−0.854751	+	0.519039i	$0.826290\pi$
$348$		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
$351$	237.686	−	54.2954i	0.677167	−	0.154688i
$352$		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
$355$		−	299.809i		−	0.844533i
$356$		0			0
$357$	19.3877	+	258.502i	0.0543073	+	0.724096i
$358$		0			0
$359$	170.933	−	296.065i	0.476138	−	0.824695i	−0.523489	−	0.852033i	$-0.675370\pi$
$359$	170.933	−	296.065i	0.476138	−	0.824695i	0.999626	+	0.0273381i	$0.00870306\pi$
$360$		0			0
$361$	−60.4192	−	355.908i	−0.167366	−	0.985895i
$362$		0			0
$363$	−128.671	−	61.9551i	−0.354465	−	0.170675i
$364$		0			0
$365$	320.503			0.878089
$366$		0			0
$367$	10.6813	−	18.5005i	0.0291043	−	0.0504101i	−0.851106	−	0.524993i	$-0.824068\pi$
$367$	10.6813	−	18.5005i	0.0291043	−	0.0504101i	0.880211	+	0.474583i	$0.157401\pi$
$368$		0			0
$369$	−1.38548	+	1.10515i	−0.00375468	+	0.00299500i
$370$		0			0
$371$	376.088	+	217.135i	1.01372	+	0.585269i
$372$		0			0
$373$	565.547	+	326.519i	1.51621	+	0.875386i	0.999819	+	0.0190347i	$0.00605930\pi$
$373$	565.547	+	326.519i	1.51621	+	0.875386i	0.516394	+	0.856351i	$0.327274\pi$
$374$		0			0
$375$	−25.7397	−	343.195i	−0.0686392	−	0.915187i
$376$		0			0
$377$	173.471	−	300.461i	0.460136	−	0.796979i
$378$		0			0
$379$			580.854i			1.53260i	0.642486	+	0.766298i	$0.277903\pi$
$379$			580.854i			1.53260i	−0.642486	+	0.766298i	$0.722097\pi$
$380$		0			0
$381$	317.837	+	466.121i	0.834218	+	1.22341i
$382$		0			0
$383$	−493.235	+	284.769i	−1.28782	+	0.743523i	−0.978265	−	0.207359i	$-0.933513\pi$
$383$	−493.235	+	284.769i	−1.28782	+	0.743523i	−0.309555	+	0.950882i	$0.600180\pi$
$384$		0			0
$385$	181.263			0.470814
$386$		0			0
$387$	−512.329	+	77.2842i	−1.32385	+	0.199701i
$388$		0			0
$389$	−244.004	+	422.627i	−0.627259	+	1.08644i	0.360841	+	0.932627i	$0.382490\pi$
$389$	−244.004	+	422.627i	−0.627259	+	1.08644i	−0.988099	+	0.153816i	$0.950844\pi$
$390$		0			0
$391$	−168.182	+	291.300i	−0.430134	+	0.745014i
$392$		0			0
$393$	448.861	−	306.068i	1.14214	−	0.778798i
$394$		0			0
$395$	52.7584	−	30.4601i	0.133566	−	0.0771141i
$396$		0			0
$397$	113.279	−	196.205i	0.285337	−	0.494218i	−0.687354	−	0.726323i	$-0.741228\pi$
$397$	113.279	−	196.205i	0.285337	−	0.494218i	0.972691	+	0.232104i	$0.0745611\pi$
$398$		0			0
$399$	46.2247	−	447.806i	0.115851	−	1.12232i
$400$		0			0
$401$	243.178	−	140.399i	0.606428	−	0.350121i	−0.165138	−	0.986270i	$-0.552807\pi$
$401$	243.178	−	140.399i	0.606428	−	0.350121i	0.771566	+	0.636149i	$0.219474\pi$
$402$		0			0
$403$	24.4341	−	42.3212i	0.0606306	−	0.105015i
$404$		0			0
$405$	159.101	+	147.553i	0.392841	+	0.364328i
$406$		0			0
$407$	−38.3242	+	22.1265i	−0.0941625	+	0.0543648i
$408$		0			0
$409$			26.9875i			0.0659841i	0.999456	+	0.0329920i	$0.0105036\pi$
$409$			26.9875i			0.0659841i	−0.999456	+	0.0329920i	$0.989496\pi$
$410$		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
$421$		−	310.341i		−	0.737152i	−0.929598	−	0.368576i	$-0.879845\pi$
$421$		−	310.341i		−	0.737152i	0.929598	−	0.368576i	$-0.120155\pi$
$422$		0			0
$423$	−172.298	+	439.163i	−0.407324	+	1.03821i
$424$		0			0
$425$	97.5010	+	168.877i	0.229414	+	0.397357i
$426$		0			0
$427$	338.384			0.792469
$428$		0			0
$429$	130.749	+	191.749i	0.304776	+	0.446966i
$430$		0			0
$431$	99.2968	−	57.3290i	0.230387	−	0.133014i	−0.380364	−	0.924837i	$-0.624201\pi$
$431$	99.2968	−	57.3290i	0.230387	−	0.133014i	0.610751	+	0.791823i	$0.290868\pi$
$432$		0			0
$433$	198.843	−	114.802i	0.459222	−	0.265132i	−0.252495	−	0.967598i	$-0.581251\pi$
$433$	198.843	−	114.802i	0.459222	−	0.265132i	0.711717	+	0.702466i	$0.247918\pi$
$434$		0			0
$435$	307.916	−	23.0937i	0.707852	−	0.0530890i
$436$		0			0
$437$	376.904	−	446.280i	0.862481	−	1.02124i
$438$		0			0
$439$			528.851i			1.20467i	0.798243	+	0.602336i	$0.205763\pi$
$439$			528.851i			1.20467i	−0.798243	+	0.602336i	$0.794237\pi$
$440$		0			0
$441$	43.9748	−	112.086i	0.0997160	−	0.254162i
$442$		0			0
$443$	366.673	−	635.095i	0.827703	−	1.43362i	−0.0721324	−	0.997395i	$-0.522980\pi$
$443$	366.673	−	635.095i	0.827703	−	1.43362i	0.899836	−	0.436229i	$-0.143686\pi$
$444$		0			0
$445$	−341.321	−	197.062i	−0.767013	−	0.442835i
$446$		0			0
$447$	327.736	−	223.476i	0.733191	−	0.499946i
$448$		0			0
$449$		−	379.685i		−	0.845623i	−0.906218	−	0.422811i	$-0.861043\pi$
$449$		−	379.685i		−	0.845623i	0.906218	−	0.422811i	$-0.138957\pi$
$450$		0			0
$451$	−1.46101	−	0.843516i	−0.00323950	−	0.00187032i
$452$		0			0
$453$	−27.6999	−	40.6231i	−0.0611477	−	0.0896756i
$454$		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
$459$	−282.291	−	87.0194i	−0.615013	−	0.189585i
$460$		0			0
$461$	−62.3136			−0.135171			−0.0675853	−	0.997713i	$-0.521529\pi$
$461$	−62.3136			−0.135171			−0.0675853	+	0.997713i	$0.521529\pi$
$462$		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
$465$	43.3711	−	3.25284i	0.0932713	−	0.00699536i
$466$		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
$471$	−565.480	+	385.588i	−1.20060	+	0.818658i
$472$		0			0
$473$	−246.604	−	427.131i	−0.521362	−	0.903026i
$474$		0			0
$475$	−114.809	−	318.592i	−0.241703	−	0.670719i
$476$		0			0
$477$	−386.863	+	308.589i	−0.811033	+	0.646937i
$478$		0			0
$479$	−26.1617	+	45.3133i	−0.0546172	+	0.0945998i	−0.892041	−	0.451954i	$-0.850727\pi$
$479$	−26.1617	+	45.3133i	−0.0546172	+	0.0945998i	0.837424	+	0.546554i	$0.184061\pi$
$480$		0			0
$481$	−46.6432			−0.0969713
$482$		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	$0.138181\pi$
$487$			409.665i			0.841201i	−0.907246	+	0.420601i	$0.861819\pi$
$488$		0			0
$489$	−35.6722	−	475.628i	−0.0729493	−	0.972655i
$490$		0			0
$491$	318.398	+	551.481i	0.648468	+	1.12318i	0.983489	+	0.180969i	$0.0579232\pi$
$491$	318.398	+	551.481i	0.648468	+	1.12318i	−0.335021	+	0.942211i	$0.608743\pi$
$492$		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
$497$		−	883.905i		−	1.77848i
$498$		0			0
$499$	−107.604	−	186.376i	−0.215639	−	0.373498i	0.737831	−	0.674986i	$-0.235850\pi$
$499$	−107.604	−	186.376i	−0.215639	−	0.373498i	−0.953470	+	0.301487i	$0.902517\pi$
$500$		0			0
$501$	834.292	−	62.5720i	1.66525	−	0.124894i
$502$		0			0
$503$	−59.6655	−	103.344i	−0.118619	−	0.205455i	0.800601	−	0.599197i	$-0.204513\pi$
$503$	−59.6655	−	103.344i	−0.118619	−	0.205455i	−0.919221	+	0.393743i	$0.871180\pi$
$504$		0			0
$505$	−74.4399			−0.147406
$506$		0			0
$507$	−19.6235	−	261.646i	−0.0387051	−	0.516067i
$508$		0			0
$509$			702.755i			1.38066i	0.723496	+	0.690329i	$0.242534\pi$
$509$			702.755i			1.38066i	−0.723496	+	0.690329i	$0.757466\pi$
$510$		0			0
$511$	944.914			1.84915
$512$		0			0
$513$	455.798	+	235.408i	0.888496	+	0.458885i
$514$		0			0
$515$			461.103i			0.895346i
$516$		0			0
$517$	−449.067			−0.868601
$518$		0			0
$519$	−124.390	+	9.32929i	−0.239673	+	0.0179755i
$520$		0			0
$521$		−	881.609i		−	1.69215i	−0.533066	−	0.846074i	$-0.678960\pi$
$521$		−	881.609i		−	1.69215i	0.533066	−	0.846074i	$-0.321040\pi$
$522$		0			0
$523$	670.142	−	386.907i	1.28134	−	0.739783i	0.304248	−	0.952593i	$-0.401595\pi$
$523$	670.142	−	386.907i	1.28134	−	0.739783i	0.977094	+	0.212810i	$0.0682615\pi$
$524$		0			0
$525$	−31.5846	−	421.127i	−0.0601611	−	0.802147i
$526$		0			0
$527$	−51.2765	+	29.6045i	−0.0972988	+	0.0561755i
$528$		0			0
$529$	416.215			0.786796
$530$		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
$535$	−266.555	+	153.896i	−0.498233	+	0.287655i
$536$		0			0
$537$	84.4026	−	6.33021i	0.157174	−	0.0117881i
$538$		0			0
$539$	114.613			0.212640
$540$		0			0
$541$	−246.112	−	426.278i	−0.454920	−	0.787944i	0.543764	−	0.839238i	$-0.316999\pi$
$541$	−246.112	−	426.278i	−0.454920	−	0.787944i	−0.998684	+	0.0512943i	$0.983665\pi$
$542$		0			0
$543$	−450.948	−	661.334i	−0.830475	−	1.21793i
$544$		0			0
$545$		−	131.057i		−	0.240471i
$546$		0			0
$547$	−460.560	−	265.904i	−0.841974	−	0.486114i	0.0159610	−	0.999873i	$-0.494919\pi$
$547$	−460.560	−	265.904i	−0.841974	−	0.486114i	−0.857935	+	0.513759i	$0.828253\pi$
$548$		0			0
$549$	−140.832	+	358.962i	−0.256525	+	0.653846i
$550$		0			0
$551$	686.774	−	247.489i	1.24641	−	0.449163i
$552$		0			0
$553$	155.544	−	89.8032i	0.281273	−	0.162393i
$554$		0			0
$555$	−23.3870	−	34.2979i	−0.0421387	−	0.0617981i
$556$		0			0
$557$	−172.254	−	298.352i	−0.309253	−	0.535642i	0.668946	−	0.743311i	$-0.266746\pi$
$557$	−172.254	−	298.352i	−0.309253	−	0.535642i	−0.978199	+	0.207669i	$0.933412\pi$
$558$		0			0
$559$		−	519.849i		−	0.929962i
$560$		0			0
$561$	−21.0305	−	280.406i	−0.0374875	−	0.499832i
$562$		0			0
$563$	−751.453	−	433.851i	−1.33473	−	0.770606i	−0.348709	−	0.937231i	$-0.613380\pi$
$563$	−751.453	−	433.851i	−1.33473	−	0.770606i	−0.986020	+	0.166625i	$0.946713\pi$
$564$		0			0
$565$		−	224.022i		−	0.396500i
$566$		0			0
$567$	469.065	+	435.019i	0.827275	+	0.767228i
$568$		0			0
$569$	−29.8460	+	17.2316i	−0.0524534	+	0.0302840i	−0.525997	−	0.850486i	$-0.676308\pi$
$569$	−29.8460	+	17.2316i	−0.0524534	+	0.0302840i	0.473544	+	0.880770i	$0.342975\pi$
$570$		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
$573$	−571.199	+	389.487i	−0.996856	+	0.679733i
$574$		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
$579$	141.463	+	207.461i	0.244322	+	0.358309i
$580$		0			0
$581$	−37.0378	+	64.1514i	−0.0637484	+	0.110415i
$582$		0			0
$583$	−407.955	−	235.533i	−0.699751	−	0.404001i
$584$		0			0
$585$	−170.198	+	135.762i	−0.290937	+	0.232071i
$586$		0			0
$587$	319.392			0.544109			0.272055	−	0.962282i	$-0.412297\pi$
$587$	319.392			0.544109			0.272055	+	0.962282i	$0.412297\pi$
$588$		0			0
$589$	96.7349	−	34.8598i	0.164236	−	0.0591847i
$590$		0			0
$591$	2.66056	+	35.4740i	0.00450179	+	0.0600237i
$592$		0			0
$593$	154.888	+	268.273i	0.261193	+	0.452400i	0.966559	−	0.256443i	$-0.0825507\pi$
$593$	154.888	+	268.273i	0.261193	+	0.452400i	−0.705366	+	0.708843i	$0.749217\pi$
$594$		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
$599$			657.969i			1.09845i	0.835676	+	0.549223i	$0.185076\pi$
$599$			657.969i			1.09845i	−0.835676	+	0.549223i	$0.814924\pi$
$600$		0			0
$601$	−757.787	+	437.508i	−1.26088	+	0.727967i	−0.973244	−	0.229774i	$-0.926201\pi$
$601$	−757.787	+	437.508i	−1.26088	+	0.727967i	−0.287632	+	0.957741i	$0.592868\pi$
$602$		0			0
$603$	−125.702	−	833.295i	−0.208460	−	1.38192i
$604$		0			0
$605$	127.524			0.210784
$606$		0			0
$607$	340.767	+	196.742i	0.561396	+	0.324122i	0.753706	−	0.657212i	$-0.228264\pi$
$607$	340.767	+	196.742i	0.561396	+	0.324122i	−0.192310	+	0.981334i	$0.561598\pi$
$608$		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	−0.200014	+	0.979793i	$0.564099\pi$
$613$	−581.450	+	1007.10i	−0.948533	+	1.64291i	−0.748519	+	0.663114i	$0.769235\pi$
$614$		0			0
$615$	0.686564	−	1.42588i	0.00111636	−	0.00231851i
$616$		0			0
$617$	−350.510			−0.568087			−0.284043	−	0.958811i	$-0.591676\pi$
$617$	−350.510			−0.568087			−0.284043	+	0.958811i	$0.591676\pi$
$618$		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
$621$	184.860	+	809.252i	0.297681	+	1.30314i
$622$		0			0
$623$	−1006.29	−	580.983i	−1.61523	−	0.932556i
$624$		0			0
$625$	−69.1332	−	119.742i	−0.110613	−	0.191588i
$626$		0			0
$627$	−50.1414	+	485.749i	−0.0799703	+	0.774719i
$628$		0			0
$629$	48.9417	+	28.2565i	0.0778088	+	0.0449229i
$630$		0			0
$631$	−108.316	−	187.610i	−0.171658	−	0.297321i	0.767341	−	0.641239i	$-0.221579\pi$
$631$	−108.316	−	187.610i	−0.171658	−	0.297321i	−0.939000	+	0.343918i	$0.888246\pi$
$632$		0			0
$633$	−144.277	−	211.588i	−0.227925	−	0.334262i
$634$		0			0
$635$	−436.290	−	251.892i	−0.687071	−	0.396681i
$636$		0			0
$637$	104.619	+	60.4019i	0.164237	+	0.0948224i
$638$		0			0
$639$	937.656	+	367.872i	1.46738	+	0.575700i
$640$		0			0
$641$		−	73.7982i		−	0.115130i	−0.998342	−	0.0575649i	$-0.981666\pi$
$641$		−	73.7982i		−	0.115130i	0.998342	−	0.0575649i	$-0.0183336\pi$
$642$		0			0
$643$	−578.067	−	1001.24i	−0.899016	−	1.55714i	−0.828754	−	0.559613i	$-0.810950\pi$
$643$	−578.067	−	1001.24i	−0.899016	−	1.55714i	−0.0702619	−	0.997529i	$-0.522384\pi$
$644$		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
$651$	127.868	−	9.59011i	0.196418	−	0.0147314i
$652$		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
$655$	−242.565	+	420.135i	−0.370328	+	0.641428i
$656$		0			0
$657$	−393.264	+	1002.37i	−0.598575	+	1.52568i
$658$		0			0
$659$	−105.736	−	61.0468i	−0.160449	−	0.0926356i	0.417625	−	0.908619i	$-0.362862\pi$
$659$	−105.736	−	61.0468i	−0.160449	−	0.0926356i	−0.578075	+	0.815984i	$0.696196\pi$
$660$		0			0
$661$			57.5656i			0.0870886i	0.999051	+	0.0435443i	$0.0138650\pi$
$661$			57.5656i			0.0870886i	−0.999051	+	0.0435443i	$0.986135\pi$
$662$		0			0
$663$	128.579	−	267.038i	0.193935	−	0.402773i
$664$		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
$669$	39.5017	−	2.96263i	0.0590459	−	0.00442845i
$670$		0			0
$671$	−367.056			−0.547029
$672$		0			0
$673$	−702.761	+	405.739i	−1.04422	+	0.602882i	−0.921026	−	0.389501i	$-0.872648\pi$
$673$	−702.761	+	405.739i	−1.04422	+	0.602882i	−0.123195	+	0.992382i	$0.539314\pi$
$674$		0			0
$675$	459.881	+	141.764i	0.681305	+	0.210020i
$676$		0			0
$677$	−72.6816	+	41.9627i	−0.107358	+	0.0619834i	−0.552718	−	0.833369i	$-0.686409\pi$
$677$	−72.6816	+	41.9627i	−0.107358	+	0.0619834i	0.445359	+	0.895352i	$0.353076\pi$
$678$		0			0
$679$	839.447	−	484.655i	1.23630	−	0.713778i
$680$		0			0
$681$	591.247	+	867.088i	0.868204	+	1.27326i
$682$		0			0
$683$			1065.59i			1.56017i	0.625675	+	0.780084i	$0.284824\pi$
$683$			1065.59i			1.56017i	−0.625675	+	0.780084i	$0.715176\pi$
$684$		0			0
$685$	−295.498			−0.431384
$686$		0			0
$687$	469.663	+	226.143i	0.683644	+	0.329175i
$688$		0			0
$689$	−248.255	−	429.990i	−0.360312	−	0.624078i
$690$		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
$693$	−222.414	+	566.903i	−0.320944	+	0.818041i
$694$		0			0
$695$	−221.625	−	383.866i	−0.318885	−	0.552326i
$696$		0			0
$697$			2.15442i			0.00309099i
$698$		0			0
$699$	−461.786	−	222.350i	−0.660638	−	0.318098i
$700$		0			0
$701$	341.550	−	591.583i	0.487233	−	0.843913i	−0.512659	−	0.858592i	$-0.671339\pi$
$701$	341.550	−	591.583i	0.487233	−	0.843913i	0.999892	+	0.0146796i	$0.00467282\pi$
$702$		0			0
$703$	−74.9800	−	63.3241i	−0.106657	−	0.0900770i
$704$		0			0
$705$	−31.5060	−	420.079i	−0.0446894	−	0.595857i
$706$		0			0
$707$	−219.466			−0.310418
$708$		0			0
$709$	−177.679	+	307.749i	−0.250605	+	0.434060i	−0.963693	−	0.267015i	$-0.913963\pi$
$709$	−177.679	+	307.749i	−0.250605	+	0.434060i	0.713088	+	0.701075i	$0.247296\pi$
$710$		0			0
$711$	30.5284	+	202.377i	0.0429373	+	0.284638i
$712$		0			0
$713$	144.091	+	83.1912i	0.202092	+	0.116678i
$714$		0			0
$715$	−179.477	−	103.621i	−0.251017	−	0.144925i
$716$		0			0
$717$	−327.444	−	157.665i	−0.456687	−	0.219895i
$718$		0			0
$719$	610.091	−	1056.71i	0.848528	−	1.46969i	−0.0339943	−	0.999422i	$-0.510823\pi$
$719$	610.091	−	1056.71i	0.848528	−	1.46969i	0.882522	−	0.470271i	$-0.155844\pi$
$720$		0			0
$721$			1359.44i			1.88549i
$722$		0			0
$723$	192.300	−	399.376i	0.265975	−	0.552387i
$724$		0			0
$725$	593.058	−	342.402i	0.818011	−	0.472279i
$726$		0			0
$727$	−1445.67			−1.98854			−0.994269	−	0.106912i	$-0.965904\pi$
$727$	−1445.67			−1.98854			−0.994269	+	0.106912i	$0.965904\pi$
$728$		0			0
$729$	−656.692	+	316.538i	−0.900812	+	0.434209i
$730$		0			0
$731$	−314.925	+	545.466i	−0.430814	+	0.746192i
$732$		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
$735$	8.04112	+	107.215i	0.0109403	+	0.145870i
$736$		0			0
$737$	694.723	−	401.098i	0.942636	−	0.544231i
$738$		0			0
$739$	−525.271	+	909.796i	−0.710786	+	1.23112i	0.253777	+	0.967263i	$0.418327\pi$
$739$	−525.271	+	909.796i	−0.710786	+	1.23112i	−0.964563	+	0.263854i	$0.915006\pi$
$740$		0			0
$741$	−301.762	+	416.968i	−0.407236	+	0.562710i
$742$		0			0
$743$	785.956	−	453.772i	1.05781	−	0.610729i	0.132987	−	0.991118i	$-0.457543\pi$
$743$	785.956	−	453.772i	1.05781	−	0.610729i	0.924827	+	0.380388i	$0.124210\pi$
$744$		0			0
$745$	−177.109	+	306.762i	−0.237730	+	0.411761i
$746$		0			0
$747$	−52.6377	−	65.9892i	−0.0704654	−	0.0883390i
$748$		0			0
$749$	−785.864	+	453.719i	−1.04922	+	0.605766i
$750$		0			0
$751$			540.881i			0.720214i	0.932911	+	0.360107i	$0.117260\pi$
$751$			540.881i			0.720214i	−0.932911	+	0.360107i	$0.882740\pi$
$752$		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	−0.998136	−	0.0610249i	$-0.980563\pi$
$757$	−337.788	+	585.066i	−0.446219	+	0.772874i	0.551917	+	0.833899i	$0.313896\pi$
$758$		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
$763$		−	386.384i		−	0.506402i
$764$		0			0
$765$	260.830	−	39.3459i	0.340954	−	0.0514325i
$766$		0			0
$767$	179.954	+	311.689i	0.234620	+	0.406374i
$768$		0			0
$769$	281.959			0.366656			0.183328	−	0.983052i	$-0.441313\pi$
$769$	281.959			0.366656			0.183328	+	0.983052i	$0.441313\pi$
$770$		0			0
$771$	419.138	−	31.4354i	0.543629	−	0.0407722i
$772$		0			0
$773$	70.8563	−	40.9089i	0.0916640	−	0.0529222i	−0.453467	−	0.891273i	$-0.649813\pi$
$773$	70.8563	−	40.9089i	0.0916640	−	0.0529222i	0.545131	+	0.838351i	$0.316480\pi$
$774$		0			0
$775$	83.5346	−	48.2287i	0.107787	−	0.0622306i
$776$		0			0
$777$	−68.9500	−	101.118i	−0.0887388	−	0.130139i
$778$		0			0
$779$	0.661436	−	3.68251i	0.000849084	−	0.00472723i
$780$		0			0
$781$			958.800i			1.22766i
$782$		0			0
$783$	−305.593	+	991.344i	−0.390285	+	1.26608i
$784$		0			0
$785$	305.586	−	529.291i	0.389282	−	0.674256i
$786$		0			0
$787$	246.928	+	142.564i	0.313758	+	0.181148i	0.648607	−	0.761124i	$-0.275352\pi$
$787$	246.928	+	142.564i	0.313758	+	0.181148i	−0.334849	+	0.942272i	$0.608685\pi$
$788$		0			0
$789$	27.8389	+	371.184i	0.0352837	+	0.470449i
$790$		0			0
$791$		−	660.469i		−	0.834979i
$792$		0			0
$793$	−335.050	−	193.441i	−0.422509	−	0.243936i
$794$		0			0
$795$	191.707	−	398.146i	0.241141	−	0.500812i
$796$		0			0
$797$	−1337.76	−	772.354i	−1.67849	−	0.969077i	−0.962625	−	0.270839i	$-0.912699\pi$
$797$	−1337.76	−	772.354i	−1.67849	−	0.969077i	−0.715866	−	0.698238i	$-0.753968\pi$
$798$		0			0
$799$	286.740	+	496.647i	0.358873	+	0.621586i
$800$		0			0
$801$	1035.12	−	825.685i	1.29229	−	1.03082i
$802$		0			0
$803$	−1024.98			−1.27644
$804$		0			0
$805$	−325.242	+	563.336i	−0.404028	+	0.699797i
$806$		0			0
$807$	−75.0119	+	155.788i	−0.0929516	+	0.193046i
$808$		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	−0.419031	−	0.907972i	$-0.637630\pi$
$811$	127.960	−	73.8776i	0.157780	−	0.0910944i	0.576811	+	0.816877i	$0.304297\pi$
$812$		0			0
$813$	174.787	+	84.1599i	0.214990	+	0.103518i
$814$		0			0
$815$	212.956	+	368.851i	0.261296	+	0.452577i
$816$		0			0
$817$	705.761	−	835.669i	0.863845	−	1.02285i
$818$		0			0
$819$	−501.782	+	400.256i	−0.612676	+	0.488714i
$820$		0			0
$821$	−678.314	+	1174.87i	−0.826204	+	1.43103i	0.0747912	+	0.997199i	$0.476171\pi$
$821$	−678.314	+	1174.87i	−0.826204	+	1.43103i	−0.900995	+	0.433829i	$0.857162\pi$
$822$		0			0
$823$	−1482.82			−1.80172			−0.900862	−	0.434106i	$-0.857064\pi$
$823$	−1482.82			−1.80172			−0.900862	+	0.434106i	$0.857064\pi$
$824$		0			0
$825$	34.2608	+	456.810i	0.0415282	+	0.553709i
$826$		0			0
$827$	525.877	−	303.615i	0.635885	−	0.367128i	−0.147143	−	0.989115i	$-0.547008\pi$
$827$	525.877	−	303.615i	0.635885	−	0.367128i	0.783028	+	0.621987i	$0.213674\pi$
$828$		0			0
$829$		−	441.338i		−	0.532374i	−0.963921	−	0.266187i	$-0.914236\pi$
$829$		−	441.338i		−	0.532374i	0.963921	−	0.266187i	$-0.0857638\pi$
$830$		0			0
$831$	468.747	−	319.627i	0.564075	−	0.384630i
$832$		0			0
$833$	−73.1831	−	126.757i	−0.0878549	−	0.152169i
$834$		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
$839$			897.554i			1.06979i	0.844918	+	0.534895i	$0.179649\pi$
$839$			897.554i			1.06979i	−0.844918	+	0.534895i	$0.820351\pi$
$840$		0			0
$841$	317.601	+	550.101i	0.377647	+	0.654103i
$842$		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
$849$	−64.2618	+	43.8186i	−0.0756912	+	0.0516121i
$850$		0			0
$851$		−	158.807i		−	0.186612i
$852$		0			0
$853$	−197.907			−0.232013			−0.116006	−	0.993248i	$-0.537009\pi$
$853$	−197.907			−0.232013			−0.116006	+	0.993248i	$0.537009\pi$
$854$		0			0
$855$	−457.911	−	12.8251i	−0.535569	−	0.0150002i
$856$		0			0
$857$		−	378.577i		−	0.441747i	−0.975302	−	0.220874i	$-0.929109\pi$
$857$		−	378.577i		−	0.441747i	0.975302	−	0.220874i	$-0.0708908\pi$
$858$		0			0
$859$	291.780			0.339675			0.169837	−	0.985472i	$-0.445676\pi$
$859$	291.780			0.339675			0.169837	+	0.985472i	$0.445676\pi$
$860$		0			0
$861$	2.02415	−	4.20383i	0.00235092	−	0.00488250i
$862$		0			0
$863$		−	884.191i		−	1.02456i	−0.858820	−	0.512278i	$-0.828802\pi$
$863$		−	884.191i		−	1.02456i	0.858820	−	0.512278i	$-0.171198\pi$
$864$		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
$869$	−168.723	+	97.4123i	−0.194158	+	0.112097i
$870$		0			0
$871$	845.526			0.970754
$872$		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
$877$	−787.508	+	454.668i	−0.897957	+	0.518436i	−0.876537	−	0.481335i	$-0.840152\pi$
$877$	−787.508	+	454.668i	−0.897957	+	0.518436i	−0.0214201	+	0.999771i	$0.506819\pi$
$878$		0			0
$879$	−64.8953	+	134.777i	−0.0738286	+	0.153330i
$880$		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	0.949436	+	0.313961i	$0.101656\pi$
$883$	659.262	+	1141.88i	0.746616	+	1.29318i	−0.202820	+	0.979216i	$0.565011\pi$
$884$		0			0
$885$	−138.964	+	288.606i	−0.157021	+	0.326109i
$886$		0			0
$887$			673.904i			0.759757i	0.925036	+	0.379878i	$0.124034\pi$
$887$			673.904i			0.759757i	−0.925036	+	0.379878i	$0.875966\pi$
$888$		0			0
$889$	−1286.28	−	742.636i	−1.44689	−	0.835361i
$890$		0			0
$891$	−508.809	−	471.878i	−0.571054	−	0.529605i
$892$		0			0
$893$	−337.641	−	936.943i	−0.378097	−	1.04921i
$894$		0			0
$895$	−65.4544	+	37.7901i	−0.0731334	+	0.0422236i
$896$		0			0
$897$	−830.526	+	62.2896i	−0.925893	+	0.0694421i
$898$		0			0
$899$	103.965	+	180.072i	0.115645	+	0.200302i
$900$		0			0
$901$			601.573i			0.667672i
$902$		0			0
$903$	1126.98	−	768.463i	1.24804	−	0.851012i
$904$		0			0
$905$	619.010	+	357.386i	0.683989	+	0.394901i
$906$		0			0
$907$		−	1074.94i		−	1.18516i	−0.805511	−	0.592581i	$-0.798109\pi$
$907$		−	1074.94i		−	1.18516i	0.805511	−	0.592581i	$-0.201891\pi$
$908$		0			0
$909$	91.3394	−	232.811i	0.100483	−	0.256118i
$910$		0			0
$911$	420.259	−	242.637i	0.461316	−	0.266341i	−0.251281	−	0.967914i	$-0.580852\pi$
$911$	420.259	−	242.637i	0.461316	−	0.266341i	0.712598	+	0.701573i	$0.247519\pi$
$912$		0			0
$913$	40.1761	−	69.5870i	0.0440045	−	0.0762180i
$914$		0			0
$915$	−25.7522	−	343.362i	−0.0281445	−	0.375260i
$916$		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
$921$	−397.799	+	826.165i	−0.431921	+	0.897031i
$922$		0			0
$923$	−505.294	+	875.195i	−0.547448	+	0.948207i
$924$		0			0
$925$	−79.7311	−	46.0328i	−0.0861958	−	0.0497652i
$926$		0			0
$927$	−1442.10	−	565.783i	−1.55567	−	0.610338i
$928$		0			0
$929$	−439.344			−0.472921			−0.236461	−	0.971641i	$-0.575987\pi$
$929$	−439.344			−0.472921			−0.236461	+	0.971641i	$0.575987\pi$
$930$		0			0
$931$	86.1744	+	239.131i	0.0925612	+	0.256854i
$932$		0			0
$933$	914.778	+	440.466i	0.980470	+	0.472097i
$934$		0			0
$935$	125.548	+	217.455i	0.134276	+	0.232572i
$936$		0			0
$937$	602.042	+	1042.77i	0.642521	+	1.11288i	0.984868	+	0.173305i	$0.0554447\pi$
$937$	602.042	+	1042.77i	0.642521	+	1.11288i	−0.342347	+	0.939574i	$0.611222\pi$
$938$		0			0
$939$	1437.93	+	692.363i	1.53134	+	0.737341i
$940$		0			0
$941$			1603.25i			1.70378i	0.523723	+	0.851889i	$0.324543\pi$
$941$			1603.25i			1.70378i	−0.523723	+	0.851889i	$0.675457\pi$
$942$		0			0
$943$	5.24302	−	3.02706i	0.00555993	−	0.00321003i
$944$		0			0
$945$	−545.913	−	168.284i	−0.577686	−	0.178078i
$946$		0			0
$947$	−523.837			−0.553154			−0.276577	−	0.960992i	$-0.589200\pi$
$947$	−523.837			−0.553154			−0.276577	+	0.960992i	$0.589200\pi$
$948$		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	0.793634	−	0.608395i	$-0.208186\pi$
$953$	632.378	+	365.104i	0.663566	+	0.383110i	−0.130068	+	0.991505i	$0.541520\pi$
$954$		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
$959$	−871.195			−0.908442
$960$		0			0
$961$	−465.856	−	806.887i	−0.484762	−	0.839632i
$962$		0			0
$963$	−154.241	−	1022.49i	−0.160167	−	1.06177i
$964$		0			0
$965$	−194.184	−	112.112i	−0.201227	−	0.116178i
$966$		0			0
$967$	−197.202	−	341.563i	−0.203931	−	0.353219i	0.745860	−	0.666102i	$-0.232039\pi$
$967$	−197.202	−	341.563i	−0.203931	−	0.353219i	−0.949792	+	0.312883i	$0.898705\pi$
$968$		0			0
$969$	569.233	−	254.708i	0.587443	−	0.262856i
$970$		0			0
$971$	−162.445	−	93.7875i	−0.167296	−	0.0965886i	0.414014	−	0.910271i	$-0.364126\pi$
$971$	−162.445	−	93.7875i	−0.167296	−	0.0965886i	−0.581310	+	0.813682i	$0.697460\pi$
$972$		0			0
$973$	−653.401	−	1131.72i	−0.671533	−	1.16313i
$974$		0			0
$975$	−209.469	+	435.033i	−0.214840	+	0.446188i
$976$		0			0
$977$	577.746	+	333.562i	0.591347	+	0.341415i	0.765630	−	0.643281i	$-0.222427\pi$
$977$	577.746	+	333.562i	0.591347	+	0.341415i	−0.174283	+	0.984696i	$0.555761\pi$
$978$		0			0
$979$	1091.56	+	630.210i	1.11497	+	0.643728i
$980$		0			0
$981$	409.880	+	160.809i	0.417819	+	0.163924i
$982$		0			0
$983$		−	1367.79i		−	1.39145i	−0.718310	−	0.695723i	$-0.755084\pi$
$983$		−	1367.79i		−	1.39145i	0.718310	−	0.695723i	$-0.244916\pi$
$984$		0			0
$985$	−15.8830	−	27.5102i	−0.0161249	−	0.0279291i
$986$		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	0.678224	−	0.734856i	$-0.262750\pi$
$991$	377.503	+	217.952i	0.380932	+	0.219931i	−0.297292	+	0.954787i	$0.596083\pi$
$992$		0			0
$993$	−272.621	−	399.809i	−0.274543	−	0.402628i
$994$		0			0
$995$	190.956	−	330.745i	0.191915	−	0.332407i
$996$		0			0
$997$	224.276	−	388.457i	0.224951	−	0.389626i	−0.731354	−	0.681998i	$-0.761111\pi$
$997$	224.276	−	388.457i	0.224951	−	0.389626i	0.956305	+	0.292372i	$0.0944446\pi$
$998$		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.s.a.445.20	✓	80
3.2	odd	2		2052.3.s.a.901.16		80
9.2	odd	6		2052.3.bl.a.1585.25		80
9.7	even	3		684.3.bl.a.673.7	yes	80
19.12	odd	6		684.3.bl.a.373.7	yes	80
57.50	even	6		2052.3.bl.a.145.25		80
171.88	odd	6	inner	684.3.s.a.601.20	yes	80
171.164	even	6		2052.3.s.a.829.16		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.20	✓	80	1.1	even	1	trivial
684.3.s.a.601.20	yes	80	171.88	odd	6	inner
684.3.bl.a.373.7	yes	80	19.12	odd	6
684.3.bl.a.673.7	yes	80	9.7	even	3
2052.3.s.a.829.16		80	171.164	even	6
2052.3.s.a.901.16		80	3.2	odd	2
2052.3.bl.a.145.25		80	57.50	even	6
2052.3.bl.a.1585.25		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)

\(f(q)\)	\(=\)	\(q+(-0.224370 - 2.99160i) q^{3} +(1.33945 + 2.31999i) q^{5} +(3.94899 + 6.83985i) q^{7} +(-8.89932 + 1.34245i) q^{9} +O(q^{10})\)	\(q+(-0.224370 - 2.99160i) q^{3} +(1.33945 + 2.31999i) q^{5} +(3.94899 + 6.83985i) q^{7} +(-8.89932 + 1.34245i) q^{9} +(-4.28360 - 7.41940i) q^{11} -9.02994i q^{13} +(6.63995 - 4.52762i) q^{15} +(-5.47035 + 9.47493i) q^{17} +(12.2593 - 14.5158i) q^{19} +(19.5761 - 13.3485i) q^{21} +30.7444 q^{23} +(8.91176 - 15.4356i) q^{25} +(6.01282 + 26.3220i) q^{27} +(33.2739 + 19.2107i) q^{29} +(4.68676 + 2.70590i) q^{31} +(-21.2348 + 14.4795i) q^{33} +(-10.5789 + 18.3232i) q^{35} -5.16539i q^{37} +(-27.0139 + 2.02605i) q^{39} +(0.170536 - 0.0984589i) q^{41} +57.5695 q^{43} +(-15.0346 - 18.8482i) q^{45} +(26.2085 - 45.3945i) q^{47} +(-6.68907 + 11.5858i) q^{49} +(29.5726 + 14.2392i) q^{51} +(47.6183 - 27.4924i) q^{53} +(11.4753 - 19.8758i) q^{55} +(-46.1762 - 33.4180i) q^{57} +(-34.5173 + 19.9286i) q^{59} +(21.4222 - 37.1043i) q^{61} +(-44.3255 - 55.5687i) q^{63} +(20.9494 - 12.0951i) q^{65} +93.6359i q^{67} +(-6.89812 - 91.9747i) q^{69} +(-96.9215 - 55.9577i) q^{71} +(59.8200 - 103.611i) q^{73} +(-48.1767 - 23.1971i) q^{75} +(33.8318 - 58.5983i) q^{77} -22.7408i q^{79} +(77.3956 - 23.8938i) q^{81} +(4.68953 + 8.12250i) q^{83} -29.3090 q^{85} +(50.0050 - 103.852i) q^{87} +(-127.411 + 73.5609i) q^{89} +(61.7635 - 35.6592i) q^{91} +(7.04340 - 14.6280i) q^{93} +(50.0973 + 8.99825i) q^{95} -122.729i q^{97} +(48.0813 + 60.2771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 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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