LMFDB - Embedded newform 684.3.m.a.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.1
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.99548 - 0.164631i) q^{3} +2.57048i q^{5} +(1.88687 - 3.26816i) q^{7} +(8.94579 + 0.986299i) q^{9} +O(q^{10})$	\(q+(-2.99548 - 0.164631i) q^{3} +2.57048i q^{5} +(1.88687 - 3.26816i) q^{7} +(8.94579 + 0.986299i) q^{9} +(4.03231 + 2.32806i) q^{11} +(-7.34051 + 12.7141i) q^{13} +(0.423182 - 7.69983i) q^{15} +(-18.4395 - 10.6461i) q^{17} +(-0.913280 - 18.9780i) q^{19} +(-6.19012 + 9.47905i) q^{21} +(33.7978 + 19.5132i) q^{23} +18.3926 q^{25} +(-26.6346 - 4.42719i) q^{27} -19.0894i q^{29} +(-6.93319 - 12.0086i) q^{31} +(-11.6954 - 7.63749i) q^{33} +(8.40073 + 4.85017i) q^{35} -39.9245 q^{37} +(24.0815 - 36.8764i) q^{39} +44.3840i q^{41} +(26.6826 + 46.2157i) q^{43} +(-2.53526 + 22.9950i) q^{45} +82.5135i q^{47} +(17.3794 + 30.1021i) q^{49} +(53.4825 + 34.9258i) q^{51} +(-6.91394 + 3.99177i) q^{53} +(-5.98423 + 10.3650i) q^{55} +(-0.388668 + 56.9987i) q^{57} +75.4608i q^{59} -69.1471 q^{61} +(20.1029 - 27.3752i) q^{63} +(-32.6814 - 18.8686i) q^{65} +(-43.2174 + 74.8548i) q^{67} +(-98.0281 - 64.0155i) q^{69} +(82.8003 + 47.8048i) q^{71} +(-34.0198 + 58.9240i) q^{73} +(-55.0947 - 3.02800i) q^{75} +(15.2169 - 8.78549i) q^{77} +(-41.8231 - 72.4397i) q^{79} +(79.0544 + 17.6465i) q^{81} +(50.6159 + 29.2231i) q^{83} +(27.3655 - 47.3984i) q^{85} +(-3.14272 + 57.1820i) q^{87} +(6.58995 - 3.80471i) q^{89} +(27.7012 + 47.9798i) q^{91} +(18.7912 + 37.1130i) q^{93} +(48.7827 - 2.34757i) q^{95} +(24.7763 + 42.9139i) q^{97} +(33.7761 + 24.8034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.99548	−	0.164631i	−0.998493	−	0.0548771i
$3$	−2.99548	−	0.164631i	−0.998493	−	0.0548771i
$4$		0			0
$5$			2.57048i			0.514096i	0.966399	+	0.257048i	$0.0827499\pi$
$5$			2.57048i			0.514096i	−0.966399	+	0.257048i	$0.917250\pi$
$6$		0			0
$7$	1.88687	−	3.26816i	0.269553	−	0.466879i	−0.699194	−	0.714932i	$-0.746457\pi$
$7$	1.88687	−	3.26816i	0.269553	−	0.466879i	0.968746	+	0.248053i	$0.0797908\pi$
$8$		0			0
$9$	8.94579	+	0.986299i	0.993977	+	0.109589i
$10$		0			0
$11$	4.03231	+	2.32806i	0.366574	+	0.211642i	0.671961	−	0.740587i	$-0.265452\pi$
$11$	4.03231	+	2.32806i	0.366574	+	0.211642i	−0.305387	+	0.952228i	$0.598786\pi$
$12$		0			0
$13$	−7.34051	+	12.7141i	−0.564654	+	0.978010i	0.432427	+	0.901669i	$0.357657\pi$
$13$	−7.34051	+	12.7141i	−0.564654	+	0.978010i	−0.997082	+	0.0763412i	$0.975676\pi$
$14$		0			0
$15$	0.423182	−	7.69983i	0.0282121	−	0.513322i
$16$		0			0
$17$	−18.4395	−	10.6461i	−1.08468	−	0.626238i	−0.152523	−	0.988300i	$-0.548740\pi$
$17$	−18.4395	−	10.6461i	−1.08468	−	0.626238i	−0.932154	+	0.362062i	$0.882073\pi$
$18$		0			0
$19$	−0.913280	−	18.9780i	−0.0480673	−	0.998844i
$19$	−0.913280	−	18.9780i	−0.0480673	−	0.998844i
$20$		0			0
$21$	−6.19012	+	9.47905i	−0.294768	+	0.451384i
$22$		0			0
$23$	33.7978	+	19.5132i	1.46947	+	0.848399i	0.999414	−	0.0342378i	$-0.0109004\pi$
$23$	33.7978	+	19.5132i	1.46947	+	0.848399i	0.470056	+	0.882637i	$0.344234\pi$
$24$		0			0
$25$	18.3926			0.735705
$26$		0			0
$27$	−26.6346	−	4.42719i	−0.986465	−	0.163970i
$28$		0			0
$29$		−	19.0894i		−	0.658256i	−0.944285	−	0.329128i	$-0.893245\pi$
$29$		−	19.0894i		−	0.658256i	0.944285	−	0.329128i	$-0.106755\pi$
$30$		0			0
$31$	−6.93319	−	12.0086i	−0.223651	−	0.387375i	0.732263	−	0.681022i	$-0.238464\pi$
$31$	−6.93319	−	12.0086i	−0.223651	−	0.387375i	−0.955914	+	0.293647i	$0.905131\pi$
$32$		0			0
$33$	−11.6954	−	7.63749i	−0.354407	−	0.231439i
$34$		0			0
$35$	8.40073	+	4.85017i	0.240021	+	0.138576i
$36$		0			0
$37$	−39.9245			−1.07904			−0.539521	−	0.841972i	$-0.681395\pi$
$37$	−39.9245			−1.07904			−0.539521	+	0.841972i	$0.681395\pi$
$38$		0			0
$39$	24.0815	−	36.8764i	0.617474	−	0.945550i
$40$		0			0
$41$			44.3840i			1.08254i	0.840850	+	0.541269i	$0.182056\pi$
$41$			44.3840i			1.08254i	−0.840850	+	0.541269i	$0.817944\pi$
$42$		0			0
$43$	26.6826	+	46.2157i	0.620527	+	1.07478i	0.989388	+	0.145299i	$0.0464144\pi$
$43$	26.6826	+	46.2157i	0.620527	+	1.07478i	−0.368861	+	0.929484i	$0.620252\pi$
$44$		0			0
$45$	−2.53526	+	22.9950i	−0.0563392	+	0.511000i
$46$		0			0
$47$			82.5135i			1.75561i	0.479022	+	0.877803i	$0.340991\pi$
$47$			82.5135i			1.75561i	−0.479022	+	0.877803i	$0.659009\pi$
$48$		0			0
$49$	17.3794	+	30.1021i	0.354682	+	0.614328i
$50$		0			0
$51$	53.4825	+	34.9258i	1.04868	+	0.684819i
$52$		0			0
$53$	−6.91394	+	3.99177i	−0.130452	+	0.0753163i	−0.563806	−	0.825907i	$-0.690663\pi$
$53$	−6.91394	+	3.99177i	−0.130452	+	0.0753163i	0.433354	+	0.901224i	$0.357330\pi$
$54$		0			0
$55$	−5.98423	+	10.3650i	−0.108804	+	0.188454i
$56$		0			0
$57$	−0.388668	+	56.9987i	−0.00681873	+	0.999977i
$58$		0			0
$59$			75.4608i			1.27900i	0.768792	+	0.639499i	$0.220858\pi$
$59$			75.4608i			1.27900i	−0.768792	+	0.639499i	$0.779142\pi$
$60$		0			0
$61$	−69.1471			−1.13356			−0.566780	−	0.823869i	$-0.691811\pi$
$61$	−69.1471			−1.13356			−0.566780	+	0.823869i	$0.691811\pi$
$62$		0			0
$63$	20.1029	−	27.3752i	0.319094	−	0.434527i
$64$		0			0
$65$	−32.6814	−	18.8686i	−0.502791	−	0.290287i
$66$		0			0
$67$	−43.2174	+	74.8548i	−0.645036	+	1.11724i	0.339257	+	0.940694i	$0.389824\pi$
$67$	−43.2174	+	74.8548i	−0.645036	+	1.11724i	−0.984293	+	0.176542i	$0.943509\pi$
$68$		0			0
$69$	−98.0281	−	64.0155i	−1.42070	−	0.927761i
$70$		0			0
$71$	82.8003	+	47.8048i	1.16620	+	0.673307i	0.952782	−	0.303654i	$-0.0982066\pi$
$71$	82.8003	+	47.8048i	1.16620	+	0.673307i	0.213419	+	0.976961i	$0.431540\pi$
$72$		0			0
$73$	−34.0198	+	58.9240i	−0.466025	+	0.807178i	−0.999247	−	0.0387968i	$-0.987647\pi$
$73$	−34.0198	+	58.9240i	−0.466025	+	0.807178i	0.533223	+	0.845975i	$0.320981\pi$
$74$		0			0
$75$	−55.0947	−	3.02800i	−0.734596	−	0.0403733i
$76$		0			0
$77$	15.2169	−	8.78549i	0.197622	−	0.114097i
$78$		0			0
$79$	−41.8231	−	72.4397i	−0.529406	−	0.916958i	−0.999412	−	0.0342946i	$-0.989082\pi$
$79$	−41.8231	−	72.4397i	−0.529406	−	0.916958i	0.470006	−	0.882663i	$-0.344252\pi$
$80$		0			0
$81$	79.0544	+	17.6465i	0.975981	+	0.217857i
$82$		0			0
$83$	50.6159	+	29.2231i	0.609830	+	0.352086i	0.772899	−	0.634529i	$-0.218806\pi$
$83$	50.6159	+	29.2231i	0.609830	+	0.352086i	−0.163069	+	0.986615i	$0.552139\pi$
$84$		0			0
$85$	27.3655	−	47.3984i	0.321947	−	0.557628i
$86$		0			0
$87$	−3.14272	+	57.1820i	−0.0361232	+	0.657264i
$88$		0			0
$89$	6.58995	−	3.80471i	0.0740444	−	0.0427495i	−0.462521	−	0.886608i	$-0.653055\pi$
$89$	6.58995	−	3.80471i	0.0740444	−	0.0427495i	0.536565	+	0.843859i	$0.319722\pi$
$90$		0			0
$91$	27.7012	+	47.9798i	0.304408	+	0.527251i
$92$		0			0
$93$	18.7912	+	37.1130i	0.202056	+	0.399065i
$94$		0			0
$95$	48.7827	−	2.34757i	0.513502	−	0.0247112i
$96$		0			0
$97$	24.7763	+	42.9139i	0.255426	+	0.442411i	0.965011	−	0.262209i	$-0.0844509\pi$
$97$	24.7763	+	42.9139i	0.255426	+	0.442411i	−0.709585	+	0.704620i	$0.751118\pi$
$98$		0			0
$99$	33.7761	+	24.8034i	0.341173	+	0.250539i
$100$		0			0
$101$			3.51995i			0.0348510i	0.999848	+	0.0174255i	$0.00554698\pi$
$101$			3.51995i			0.0348510i	−0.999848	+	0.0174255i	$0.994453\pi$
$102$		0			0
$103$	90.8919	+	157.429i	0.882446	+	1.52844i	0.848614	+	0.529013i	$0.177438\pi$
$103$	90.8919	+	157.429i	0.882446	+	1.52844i	0.0338323	+	0.999428i	$0.489229\pi$
$104$		0			0
$105$	−24.3657	−	15.9116i	−0.232055	−	0.151539i
$106$		0			0
$107$		−	199.358i		−	1.86316i	−0.363533	−	0.931581i	$-0.618430\pi$
$107$		−	199.358i		−	1.86316i	0.363533	−	0.931581i	$-0.381570\pi$
$108$		0			0
$109$	−23.4475	+	40.6122i	−0.215114	+	0.372589i	−0.953308	−	0.302000i	$-0.902346\pi$
$109$	−23.4475	+	40.6122i	−0.215114	+	0.372589i	0.738194	+	0.674589i	$0.235679\pi$
$110$		0			0
$111$	119.593	+	6.57282i	1.07742	+	0.0592146i
$112$		0			0
$113$	127.706	−	73.7309i	1.13014	−	0.652486i	0.186169	−	0.982518i	$-0.440393\pi$
$113$	127.706	−	73.7309i	1.13014	−	0.652486i	0.943970	+	0.330032i	$0.107059\pi$
$114$		0			0
$115$	−50.1583	+	86.8766i	−0.436159	+	0.755449i
$116$		0			0
$117$	−78.2066	+	106.498i	−0.668432	+	0.910240i
$118$		0			0
$119$	−69.5859	+	40.1754i	−0.584756	+	0.337609i
$120$		0			0
$121$	−49.6603	−	86.0142i	−0.410416	−	0.710861i
$122$		0			0
$123$	7.30700	−	132.951i	0.0594065	−	1.08091i
$124$		0			0
$125$			111.540i			0.892320i
$126$		0			0
$127$	−45.2320	−	78.3441i	−0.356158	−	0.616883i	0.631158	−	0.775654i	$-0.282580\pi$
$127$	−45.2320	−	78.3441i	−0.356158	−	0.616883i	−0.987315	+	0.158771i	$0.949247\pi$
$128$		0			0
$129$	−72.3188	−	142.831i	−0.560610	−	1.10722i
$130$		0			0
$131$		−	111.963i		−	0.854679i	−0.904091	−	0.427340i	$-0.859451\pi$
$131$		−	111.963i		−	0.854679i	0.904091	−	0.427340i	$-0.140549\pi$
$132$		0			0
$133$	−63.7464	−	32.8244i	−0.479296	−	0.246800i
$134$		0			0
$135$	11.3800	−	68.4637i	0.0842965	−	0.507138i
$136$		0			0
$137$			220.658i			1.61064i	0.592841	+	0.805320i	$0.298006\pi$
$137$			220.658i			1.61064i	−0.592841	+	0.805320i	$0.701994\pi$
$138$		0			0
$139$	−66.7761	+	115.660i	−0.480403	+	0.832083i	−0.999747	−	0.0224822i	$-0.992843\pi$
$139$	−66.7761	+	115.660i	−0.480403	+	0.832083i	0.519344	+	0.854565i	$0.326176\pi$
$140$		0			0
$141$	13.5843	−	247.167i	0.0963425	−	1.75296i
$142$		0			0
$143$	−59.1985	+	34.1782i	−0.413975	+	0.239009i
$144$		0			0
$145$	49.0690			0.338407
$146$		0			0
$147$	−47.1040	−	93.0313i	−0.320435	−	0.632866i
$148$		0			0
$149$		−	46.9985i		−	0.315426i	−0.987485	−	0.157713i	$-0.949588\pi$
$149$		−	46.9985i		−	0.315426i	0.987485	−	0.157713i	$-0.0504121\pi$
$150$		0			0
$151$	−76.4722	+	132.454i	−0.506438	+	0.877177i	0.493534	+	0.869727i	$0.335705\pi$
$151$	−76.4722	+	132.454i	−0.506438	+	0.877177i	−0.999972	+	0.00745046i	$0.997628\pi$
$152$		0			0
$153$	−154.456	−	113.424i	−1.00952	−	0.741335i
$154$		0			0
$155$	30.8680	−	17.8216i	0.199148	−	0.114978i
$156$		0			0
$157$	−147.645			−0.940415			−0.470207	−	0.882556i	$-0.655821\pi$
$157$	−147.645			−0.940415			−0.470207	+	0.882556i	$0.655821\pi$
$158$		0			0
$159$	21.3677	−	10.8190i	0.134388	−	0.0680440i
$160$		0			0
$161$	127.544	−	73.6376i	0.792200	−	0.457377i
$162$		0			0
$163$	221.993			1.36192			0.680959	−	0.732322i	$-0.261563\pi$
$163$	221.993			1.36192			0.680959	+	0.732322i	$0.261563\pi$
$164$		0			0
$165$	19.6320	−	30.0629i	0.118982	−	0.182200i
$166$		0			0
$167$	211.568	+	122.149i	1.26688	+	0.731432i	0.974396	−	0.224840i	$-0.0721858\pi$
$167$	211.568	+	122.149i	1.26688	+	0.731432i	0.292481	+	0.956271i	$0.405519\pi$
$168$		0			0
$169$	−23.2661	−	40.2980i	−0.137669	−	0.238450i
$170$		0			0
$171$	10.5480	−	170.674i	0.0616843	−	0.998096i
$172$		0			0
$173$	−50.9284	+	29.4035i	−0.294384	+	0.169963i	−0.639917	−	0.768444i	$-0.721031\pi$
$173$	−50.9284	+	29.4035i	−0.294384	+	0.169963i	0.345533	+	0.938406i	$0.387698\pi$
$174$		0			0
$175$	34.7045	−	60.1099i	0.198311	−	0.343485i
$176$		0			0
$177$	12.4232	−	226.041i	0.0701876	−	1.27707i
$178$		0			0
$179$			240.380i			1.34291i	0.741047	+	0.671453i	$0.234329\pi$
$179$			240.380i			1.34291i	−0.741047	+	0.671453i	$0.765671\pi$
$180$		0			0
$181$	−171.845	−	297.644i	−0.949418	−	1.64444i	−0.746654	−	0.665212i	$-0.768341\pi$
$181$	−171.845	−	297.644i	−0.949418	−	1.64444i	−0.202764	−	0.979228i	$-0.564992\pi$
$182$		0			0
$183$	207.129	+	11.3838i	1.13185	+	0.0622064i
$184$		0			0
$185$		−	102.625i		−	0.554731i
$186$		0			0
$187$	−49.5693	−	85.8565i	−0.265076	−	0.459126i
$188$		0			0
$189$	−64.7247	+	78.6923i	−0.342459	+	0.416362i
$190$		0			0
$191$	−161.191	−	93.0639i	−0.843934	−	0.487246i	0.0146654	−	0.999892i	$-0.495332\pi$
$191$	−161.191	−	93.0639i	−0.843934	−	0.487246i	−0.858600	+	0.512647i	$0.828665\pi$
$192$		0			0
$193$	−228.043			−1.18157			−0.590784	−	0.806830i	$-0.701181\pi$
$193$	−228.043			−1.18157			−0.590784	+	0.806830i	$0.701181\pi$
$194$		0			0
$195$	94.7902	+	61.9010i	0.486104	+	0.317441i
$196$		0			0
$197$		−	118.336i		−	0.600690i	−0.953831	−	0.300345i	$-0.902898\pi$
$197$		−	118.336i		−	0.600690i	0.953831	−	0.300345i	$-0.0971019\pi$
$198$		0			0
$199$	−138.028	−	239.071i	−0.693606	−	1.20136i	−0.970648	−	0.240503i	$-0.922687\pi$
$199$	−138.028	−	239.071i	−0.693606	−	1.20136i	0.277042	−	0.960858i	$-0.410646\pi$
$200$		0			0
$201$	141.780	−	217.111i	0.705375	−	1.08015i
$202$		0			0
$203$	−62.3872	−	36.0193i	−0.307326	−	0.177435i
$204$		0			0
$205$	−114.088			−0.556529
$206$		0			0
$207$	283.102	+	207.896i	1.36764	+	1.00433i
$208$		0			0
$209$	40.4993	−	78.6516i	0.193777	−	0.376323i
$210$		0			0
$211$	−168.040			−0.796399			−0.398200	−	0.917299i	$-0.630365\pi$
$211$	−168.040			−0.796399			−0.398200	+	0.917299i	$0.630365\pi$
$212$		0			0
$213$	−240.157	−	156.830i	−1.12750	−	0.736290i
$214$		0			0
$215$	−118.797	+	68.5872i	−0.552542	+	0.319010i
$216$		0			0
$217$	−52.3281			−0.241143
$218$		0			0
$219$	111.606	−	170.905i	0.509618	−	0.780388i
$220$		0			0
$221$	270.711	−	156.295i	1.22493	−	0.707216i
$222$		0			0
$223$	−72.3681	−	125.345i	−0.324520	−	0.562086i	0.656895	−	0.753982i	$-0.271870\pi$
$223$	−72.3681	−	125.345i	−0.324520	−	0.562086i	−0.981415	+	0.191896i	$0.938536\pi$
$224$		0			0
$225$	164.537	+	18.1406i	0.731274	+	0.0806250i
$226$		0			0
$227$	211.093	+	121.874i	0.929924	+	0.536892i	0.886787	−	0.462178i	$-0.152932\pi$
$227$	211.093	+	121.874i	0.929924	+	0.536892i	0.0431362	+	0.999069i	$0.486265\pi$
$228$		0			0
$229$	221.657	+	383.921i	0.967935	+	1.67651i	0.701515	+	0.712655i	$0.252508\pi$
$229$	221.657	+	383.921i	0.967935	+	1.67651i	0.266420	+	0.963857i	$0.414159\pi$
$230$		0			0
$231$	−47.0283	+	23.8116i	−0.203586	+	0.103080i
$232$		0			0
$233$	175.338	+	101.231i	0.752522	+	0.434469i	0.826605	−	0.562783i	$-0.190269\pi$
$233$	175.338	+	101.231i	0.752522	+	0.434469i	−0.0740822	+	0.997252i	$0.523603\pi$
$234$		0			0
$235$	−212.099			−0.902551
$236$		0			0
$237$	113.354	+	223.877i	0.478288	+	0.944628i
$238$		0			0
$239$	319.721	−	184.591i	1.33774	−	0.772347i	0.351271	−	0.936274i	$-0.385749\pi$
$239$	319.721	−	184.591i	1.33774	−	0.772347i	0.986472	+	0.163927i	$0.0524162\pi$
$240$		0			0
$241$	−294.746			−1.22301			−0.611507	−	0.791239i	$-0.709436\pi$
$241$	−294.746			−1.22301			−0.611507	+	0.791239i	$0.709436\pi$
$242$		0			0
$243$	−233.901	−	65.8744i	−0.962555	−	0.271088i
$244$		0			0
$245$	−77.3768	+	44.6735i	−0.315824	+	0.182341i
$246$		0			0
$247$	247.993	+	127.697i	1.00402	+	0.516991i
$248$		0			0
$249$	−146.808	−	95.8701i	−0.589590	−	0.385021i
$250$		0			0
$251$	−215.739	+	124.557i	−0.859520	+	0.496244i	−0.863851	−	0.503747i	$-0.831954\pi$
$251$	−215.739	+	124.557i	−0.859520	+	0.496244i	0.00433178	+	0.999991i	$0.498621\pi$
$252$		0			0
$253$	90.8556	+	157.366i	0.359113	+	0.622002i
$254$		0			0
$255$	−89.7760	+	137.476i	−0.352063	+	0.539121i
$256$		0			0
$257$	106.370	+	61.4130i	0.413892	+	0.238961i	0.692461	−	0.721455i	$-0.256527\pi$
$257$	106.370	+	61.4130i	0.413892	+	0.238961i	−0.278568	+	0.960416i	$0.589860\pi$
$258$		0			0
$259$	−75.3324	+	130.480i	−0.290859	+	0.503782i
$260$		0			0
$261$	18.8279	−	170.770i	0.0721375	−	0.654292i
$262$		0			0
$263$	235.132	−	135.754i	0.894038	−	0.516173i	0.0187769	−	0.999824i	$-0.494023\pi$
$263$	235.132	−	135.754i	0.894038	−	0.516173i	0.875261	+	0.483651i	$0.160689\pi$
$264$		0			0
$265$	−10.2608	−	17.7722i	−0.0387199	−	0.0670647i
$266$		0			0
$267$	−20.3664	+	10.3120i	−0.0762788	+	0.0386218i
$268$		0			0
$269$	147.379	+	85.0895i	0.547879	+	0.316318i	0.748266	−	0.663399i	$-0.230887\pi$
$269$	147.379	+	85.0895i	0.547879	+	0.316318i	−0.200387	+	0.979717i	$0.564220\pi$
$270$		0			0
$271$	258.791	−	448.239i	0.954948	−	1.65402i	0.220460	−	0.975396i	$-0.429244\pi$
$271$	258.791	−	448.239i	0.954948	−	1.65402i	0.734488	−	0.678622i	$-0.237423\pi$
$272$		0			0
$273$	−75.0793	−	148.283i	−0.275016	−	0.543161i
$274$		0			0
$275$	74.1648	+	42.8191i	0.269690	+	0.155706i
$276$		0			0
$277$	−95.4014	+	165.240i	−0.344409	+	0.596535i	−0.985246	−	0.171142i	$-0.945254\pi$
$277$	−95.4014	+	165.240i	−0.344409	+	0.596535i	0.640837	+	0.767677i	$0.278588\pi$
$278$		0			0
$279$	−50.1788	−	114.265i	−0.179852	−	0.409552i
$280$		0			0
$281$		−	180.921i		−	0.643846i	−0.946766	−	0.321923i	$-0.895671\pi$
$281$		−	180.921i		−	0.643846i	0.946766	−	0.321923i	$-0.104329\pi$
$282$		0			0
$283$	371.862			1.31400			0.656999	−	0.753891i	$-0.271825\pi$
$283$	371.862			1.31400			0.656999	+	0.753891i	$0.271825\pi$
$284$		0			0
$285$	−146.514	−	0.999063i	−0.514084	−	0.00350548i
$286$		0			0
$287$	145.054	+	83.7469i	0.505414	+	0.291801i
$288$		0			0
$289$	82.1769	+	142.335i	0.284349	+	0.492507i
$290$		0			0
$291$	−67.1521	−	132.627i	−0.230763	−	0.455762i
$292$		0			0
$293$	−191.619	+	110.631i	−0.653989	+	0.377581i	−0.789983	−	0.613129i	$-0.789911\pi$
$293$	−191.619	+	110.631i	−0.653989	+	0.377581i	0.135994	+	0.990710i	$0.456577\pi$
$294$		0			0
$295$	−193.971			−0.657528
$296$		0			0
$297$	−97.0922	−	79.8586i	−0.326910	−	0.268884i
$298$		0			0
$299$	−496.186	+	286.473i	−1.65948	+	0.958104i
$300$		0			0
$301$	201.387			0.669059
$302$		0			0
$303$	0.579493	−	10.5439i	0.00191252	−	0.0347985i
$304$		0			0
$305$		−	177.741i		−	0.582759i
$306$		0			0
$307$	0.624919	−	1.08239i	0.00203557	−	0.00352570i	−0.865006	−	0.501762i	$-0.832685\pi$
$307$	0.624919	−	1.08239i	0.00203557	−	0.00352570i	0.867041	+	0.498236i	$0.166019\pi$
$308$		0			0
$309$	−246.347	−	486.540i	−0.797240	−	1.57456i
$310$		0			0
$311$	113.120	−	65.3101i	0.363731	−	0.210000i	−0.306985	−	0.951714i	$-0.599320\pi$
$311$	113.120	−	65.3101i	0.363731	−	0.210000i	0.670716	+	0.741714i	$0.265987\pi$
$312$		0			0
$313$	441.296			1.40989			0.704946	−	0.709261i	$-0.250971\pi$
$313$	441.296			1.40989			0.704946	+	0.709261i	$0.250971\pi$
$314$		0			0
$315$	70.3675	+	51.6742i	0.223389	+	0.164045i
$316$		0			0
$317$			46.7649i			0.147523i	0.997276	+	0.0737617i	$0.0235004\pi$
$317$			46.7649i			0.147523i	−0.997276	+	0.0737617i	$0.976500\pi$
$318$		0			0
$319$	44.4413	−	76.9746i	0.139314	−	0.241300i
$320$		0			0
$321$	−32.8206	+	597.174i	−0.102245	+	1.86036i
$322$		0			0
$323$	−185.201	+	359.668i	−0.573377	+	1.11352i
$324$		0			0
$325$	−135.011	+	233.846i	−0.415419	+	0.719527i
$326$		0			0
$327$	76.9224	−	117.793i	0.235237	−	0.360222i
$328$		0			0
$329$	269.667	+	155.692i	0.819656	+	0.473229i
$330$		0			0
$331$	26.5228	−	45.9388i	0.0801293	−	0.138788i	−0.823176	−	0.567786i	$-0.807800\pi$
$331$	26.5228	−	45.9388i	0.0801293	−	0.138788i	0.903305	+	0.428998i	$0.141133\pi$
$332$		0			0
$333$	−357.157	−	39.3775i	−1.07254	−	0.118251i
$334$		0			0
$335$	−192.413	−	111.090i	−0.574367	−	0.331611i
$336$		0			0
$337$	−305.345			−0.906067			−0.453034	−	0.891493i	$-0.649658\pi$
$337$	−305.345			−0.906067			−0.453034	+	0.891493i	$0.649658\pi$
$338$		0			0
$339$	−394.678	+	199.835i	−1.16424	+	0.589484i
$340$		0			0
$341$		−	64.5634i		−	0.189336i
$342$		0			0
$343$	316.084			0.921529
$344$		0			0
$345$	164.551	−	251.980i	0.476958	−	0.730376i
$346$		0			0
$347$		−	48.8001i		−	0.140634i	−0.997525	−	0.0703171i	$-0.977599\pi$
$347$		−	48.8001i		−	0.140634i	0.997525	−	0.0703171i	$-0.0224011\pi$
$348$		0			0
$349$	201.500	−	349.009i	0.577364	−	1.00002i	−0.418416	−	0.908256i	$-0.637415\pi$
$349$	201.500	−	349.009i	0.577364	−	1.00002i	0.995780	−	0.0917689i	$-0.0292521\pi$
$350$		0			0
$351$	251.799	−	306.137i	0.717376	−	0.872186i
$352$		0			0
$353$	−311.647	−	179.930i	−0.882854	−	0.509716i	−0.0112555	−	0.999937i	$-0.503583\pi$
$353$	−311.647	−	179.930i	−0.882854	−	0.509716i	−0.871598	+	0.490221i	$0.836916\pi$
$354$		0			0
$355$	−122.881	+	212.837i	−0.346145	+	0.599540i
$356$		0			0
$357$	215.057	−	108.889i	0.602401	−	0.305010i
$358$		0			0
$359$	80.8127	+	46.6572i	0.225105	+	0.129964i	0.608312	−	0.793698i	$-0.291847\pi$
$359$	80.8127	+	46.6572i	0.225105	+	0.129964i	−0.383207	+	0.923663i	$0.625180\pi$
$360$		0			0
$361$	−359.332	+	34.6645i	−0.995379	+	0.0960236i
$362$		0			0
$363$	134.596	+	265.829i	0.370787	+	0.732312i
$364$		0			0
$365$	−151.463	−	87.4473i	−0.414967	−	0.239582i
$366$		0			0
$367$	−595.581			−1.62284			−0.811418	−	0.584466i	$-0.801304\pi$
$367$	−595.581			−1.62284			−0.811418	+	0.584466i	$0.801304\pi$
$368$		0			0
$369$	−43.7759	+	397.050i	−0.118634	+	1.07602i
$370$		0			0
$371$			30.1278i			0.0812069i
$372$		0			0
$373$	−94.7517	−	164.115i	−0.254026	−	0.439986i	0.710605	−	0.703592i	$-0.248422\pi$
$373$	−94.7517	−	164.115i	−0.254026	−	0.439986i	−0.964631	+	0.263606i	$0.915088\pi$
$374$		0			0
$375$	18.3630	−	334.116i	0.0489679	−	0.890975i
$376$		0			0
$377$	242.706	+	140.126i	0.643781	+	0.371687i
$378$		0			0
$379$	289.779			0.764589			0.382294	−	0.924041i	$-0.375134\pi$
$379$	289.779			0.764589			0.382294	+	0.924041i	$0.375134\pi$
$380$		0			0
$381$	122.594	+	242.125i	0.321768	+	0.635498i
$382$		0			0
$383$		−	231.194i		−	0.603640i	−0.953365	−	0.301820i	$-0.902406\pi$
$383$		−	231.194i		−	0.603640i	0.953365	−	0.301820i	$-0.0975941\pi$
$384$		0			0
$385$	22.5829	+	39.1148i	0.0586570	+	0.101597i
$386$		0			0
$387$	193.115	+	439.753i	0.499005	+	1.13631i
$388$		0			0
$389$			257.248i			0.661306i	0.943752	+	0.330653i	$0.107269\pi$
$389$			257.248i			0.661306i	−0.943752	+	0.330653i	$0.892731\pi$
$390$		0			0
$391$	−415.477	−	719.627i	−1.06260	−	1.84048i
$392$		0			0
$393$	−18.4326	+	335.383i	−0.0469023	+	0.853391i
$394$		0			0
$395$	186.205	−	107.505i	0.471405	−	0.272166i
$396$		0			0
$397$	−294.646	+	510.342i	−0.742181	+	1.28550i	0.209319	+	0.977847i	$0.432875\pi$
$397$	−294.646	+	510.342i	−0.742181	+	1.28550i	−0.951500	+	0.307648i	$0.900458\pi$
$398$		0			0
$399$	185.547	+	108.819i	0.465030	+	0.272730i
$400$		0			0
$401$			90.3287i			0.225259i	0.993637	+	0.112629i	$0.0359272\pi$
$401$			90.3287i			0.225259i	−0.993637	+	0.112629i	$0.964073\pi$
$402$		0			0
$403$	203.572			0.505142
$404$		0			0
$405$	−45.3599	+	203.208i	−0.112000	+	0.501748i
$406$		0			0
$407$	−160.988	−	92.9466i	−0.395548	−	0.228370i
$408$		0			0
$409$	103.648	−	179.523i	0.253417	−	0.438932i	−0.711047	−	0.703144i	$-0.751779\pi$
$409$	103.648	−	179.523i	0.253417	−	0.438932i	0.964464	+	0.264213i	$0.0851121\pi$
$410$		0			0
$411$	36.3271	−	660.975i	0.0883872	−	1.60821i
$412$		0			0
$413$	246.618	+	142.385i	0.597137	+	0.344757i
$414$		0			0
$415$	−75.1174	+	130.107i	−0.181006	+	0.313511i
$416$		0			0
$417$	219.068	−	335.462i	0.525342	−	0.804466i
$418$		0			0
$419$	247.987	−	143.175i	0.591854	−	0.341707i	−0.173976	−	0.984750i	$-0.555662\pi$
$419$	247.987	−	143.175i	0.591854	−	0.341707i	0.765830	+	0.643043i	$0.222328\pi$
$420$		0			0
$421$	81.9214	+	141.892i	0.194588	+	0.337036i	0.946765	−	0.321925i	$-0.104330\pi$
$421$	81.9214	+	141.892i	0.194588	+	0.337036i	−0.752178	+	0.658960i	$0.770996\pi$
$422$		0			0
$423$	−81.3830	+	738.149i	−0.192395	+	1.74503i
$424$		0			0
$425$	−339.151	−	195.809i	−0.798002	−	0.460727i
$426$		0			0
$427$	−130.472	+	225.984i	−0.305554	+	0.529235i
$428$		0			0
$429$	182.955	−	92.6343i	0.426467	−	0.215931i
$430$		0			0
$431$	−295.277	+	170.478i	−0.685098	+	0.395541i	−0.801773	−	0.597629i	$-0.796110\pi$
$431$	−295.277	+	170.478i	−0.685098	+	0.395541i	0.116675	+	0.993170i	$0.462776\pi$
$432$		0			0
$433$	110.714	+	191.763i	0.255691	+	0.442871i	0.965083	−	0.261944i	$-0.0843636\pi$
$433$	110.714	+	191.763i	0.255691	+	0.442871i	−0.709392	+	0.704814i	$0.751030\pi$
$434$		0			0
$435$	−146.985	−	8.07830i	−0.337897	−	0.0185708i
$436$		0			0
$437$	339.455	−	659.237i	0.776785	−	1.50855i
$438$		0			0
$439$	173.106	+	299.828i	0.394318	+	0.682979i	0.993014	−	0.117998i	$-0.0376476\pi$
$439$	173.106	+	299.828i	0.394318	+	0.682979i	−0.598696	+	0.800976i	$0.704314\pi$
$440$		0			0
$441$	125.783	+	286.428i	0.285223	+	0.649497i
$442$		0			0
$443$		−	142.676i		−	0.322069i	−0.986949	−	0.161034i	$-0.948517\pi$
$443$		−	142.676i		−	0.322069i	0.986949	−	0.161034i	$-0.0514830\pi$
$444$		0			0
$445$	9.77993	+	16.9393i	0.0219774	+	0.0380659i
$446$		0			0
$447$	−7.73741	+	140.783i	−0.0173096	+	0.314951i
$448$		0			0
$449$			292.698i			0.651888i	0.945389	+	0.325944i	$0.105682\pi$
$449$			292.698i			0.651888i	−0.945389	+	0.325944i	$0.894318\pi$
$450$		0			0
$451$	−103.329	+	178.970i	−0.229110	+	0.396830i
$452$		0			0
$453$	250.877	−	384.173i	0.553812	−	0.848063i
$454$		0			0
$455$	−123.331	+	71.2053i	−0.271058	+	0.156495i
$456$		0			0
$457$	188.802	−	327.015i	0.413133	−	0.715568i	−0.582097	−	0.813119i	$-0.697768\pi$
$457$	188.802	−	327.015i	0.413133	−	0.715568i	0.995230	+	0.0975513i	$0.0311010\pi$
$458$		0			0
$459$	443.996	+	365.188i	0.967312	+	0.795617i
$460$		0			0
$461$	80.3090	−	46.3664i	0.174206	−	0.100578i	−0.410362	−	0.911923i	$-0.634598\pi$
$461$	80.3090	−	46.3664i	0.174206	−	0.100578i	0.584568	+	0.811345i	$0.301264\pi$
$462$		0			0
$463$	44.6401	+	77.3189i	0.0964149	+	0.166995i	0.910198	−	0.414173i	$-0.135929\pi$
$463$	44.6401	+	77.3189i	0.0964149	+	0.166995i	−0.813783	+	0.581168i	$0.802596\pi$
$464$		0			0
$465$	−95.3984	+	48.3025i	−0.205158	+	0.103876i
$466$		0			0
$467$		−	282.015i		−	0.603886i	−0.953326	−	0.301943i	$-0.902365\pi$
$467$		−	282.015i		−	0.603886i	0.953326	−	0.301943i	$-0.0976352\pi$
$468$		0			0
$469$	163.091	+	282.483i	0.347743	+	0.602308i
$470$		0			0
$471$	442.268	+	24.3070i	0.938998	+	0.0516072i
$472$		0			0
$473$			248.475i			0.525317i
$474$		0			0
$475$	−16.7976	−	349.056i	−0.0353634	−	0.734855i
$476$		0			0
$477$	−65.7878	+	28.8903i	−0.137920	+	0.0605667i
$478$		0			0
$479$			0.997746i			0.00208298i	0.999999	+	0.00104149i	$0.000331516\pi$
$479$			0.997746i			0.00208298i	−0.999999	+	0.00104149i	$0.999668\pi$
$480$		0			0
$481$	293.066	−	507.606i	0.609285	−	1.05531i
$482$		0			0
$483$	−394.179	+	199.582i	−0.816105	+	0.413214i
$484$		0			0
$485$	−110.309	+	63.6871i	−0.227442	+	0.131314i
$486$		0			0
$487$	623.243			1.27976			0.639880	−	0.768475i	$-0.278984\pi$
$487$	623.243			1.27976			0.639880	+	0.768475i	$0.278984\pi$
$488$		0			0
$489$	−664.974	−	36.5469i	−1.35987	−	0.0747381i
$490$		0			0
$491$			692.249i			1.40988i	0.709269	+	0.704938i	$0.249025\pi$
$491$			692.249i			1.40988i	−0.709269	+	0.704938i	$0.750975\pi$
$492$		0			0
$493$	−203.227	+	352.000i	−0.412225	+	0.713995i
$494$		0			0
$495$	−63.7567	+	86.8208i	−0.128801	+	0.175396i
$496$		0			0
$497$	312.467	−	180.403i	0.628706	−	0.362984i
$498$		0			0
$499$	167.342			0.335354			0.167677	−	0.985842i	$-0.446373\pi$
$499$	167.342			0.335354			0.167677	+	0.985842i	$0.446373\pi$
$500$		0			0
$501$	−613.639	−	400.726i	−1.22483	−	0.799852i
$502$		0			0
$503$	−303.931	+	175.475i	−0.604237	+	0.348856i	−0.770707	−	0.637190i	$-0.780097\pi$
$503$	−303.931	+	175.475i	−0.604237	+	0.348856i	0.166470	+	0.986047i	$0.446763\pi$
$504$		0			0
$505$	−9.04796			−0.0179168
$506$		0			0
$507$	63.0587	+	124.542i	0.124376	+	0.245645i
$508$		0			0
$509$	−713.576	−	411.984i	−1.40192	−	0.809398i	−0.407329	−	0.913282i	$-0.633540\pi$
$509$	−713.576	−	411.984i	−1.40192	−	0.809398i	−0.994589	+	0.103884i	$0.966873\pi$
$510$		0			0
$511$	128.382	+	222.364i	0.251237	+	0.435154i
$512$		0			0
$513$	−59.6947	+	509.515i	−0.116364	+	0.993207i
$514$		0			0
$515$	−404.669	+	233.636i	−0.785766	+	0.453662i
$516$		0			0
$517$	−192.096	+	332.720i	−0.371559	+	0.643560i
$518$		0			0
$519$	157.396	−	79.6932i	0.303267	−	0.153552i
$520$		0			0
$521$			487.488i			0.935678i	0.883814	+	0.467839i	$0.154967\pi$
$521$			487.488i			0.935678i	−0.883814	+	0.467839i	$0.845033\pi$
$522$		0			0
$523$	−333.089	−	576.927i	−0.636881	−	1.10311i	−0.986113	−	0.166074i	$-0.946891\pi$
$523$	−333.089	−	576.927i	−0.636881	−	1.10311i	0.349232	−	0.937036i	$-0.386442\pi$
$524$		0			0
$525$	−113.853	+	174.345i	−0.216862	+	0.332085i
$526$		0			0
$527$			295.244i			0.560236i
$528$		0			0
$529$	497.028	+	860.877i	0.939561	+	1.62737i
$530$		0			0
$531$	−74.4269	+	675.057i	−0.140164	+	1.27129i
$532$		0			0
$533$	−564.304	−	325.801i	−1.05873	−	0.611260i
$534$		0			0
$535$	512.447			0.957845
$536$		0			0
$537$	39.5741	−	720.054i	0.0736947	−	1.34088i
$538$		0			0
$539$			161.841i			0.300262i
$540$		0			0
$541$	181.232	+	313.902i	0.334994	+	0.580226i	0.983484	−	0.180997i	$-0.0579325\pi$
$541$	181.232	+	313.902i	0.334994	+	0.580226i	−0.648490	+	0.761223i	$0.724599\pi$
$542$		0			0
$543$	465.756	+	919.876i	0.857745	+	1.69406i
$544$		0			0
$545$	−104.393	−	60.2712i	−0.191547	−	0.110589i
$546$		0			0
$547$	533.652			0.975598			0.487799	−	0.872956i	$-0.337800\pi$
$547$	533.652			0.975598			0.487799	+	0.872956i	$0.337800\pi$
$548$		0			0
$549$	−618.576	−	68.1997i	−1.12673	−	0.124225i
$550$		0			0
$551$	−362.280	+	17.4340i	−0.657495	+	0.0316406i
$552$		0			0
$553$	−315.659			−0.570812
$554$		0			0
$555$	−16.8953	+	307.412i	−0.0304420	+	0.553895i
$556$		0			0
$557$	−187.203	+	108.082i	−0.336091	+	0.194042i	−0.658542	−	0.752544i	$-0.728827\pi$
$557$	−187.203	+	108.082i	−0.336091	+	0.194042i	0.322451	+	0.946586i	$0.395493\pi$
$558$		0			0
$559$	−783.456			−1.40153
$560$		0			0
$561$	134.349	+	265.342i	0.239481	+	0.472980i
$562$		0			0
$563$	950.756	−	548.919i	1.68873	−	0.974990i	0.733242	−	0.679967i	$-0.238006\pi$
$563$	950.756	−	548.919i	1.68873	−	0.974990i	0.955490	−	0.295023i	$-0.0953272\pi$
$564$		0			0
$565$	189.524	+	328.265i	0.335441	+	0.581000i
$566$		0			0
$567$	206.837	−	225.066i	0.364792	−	0.396941i
$568$		0			0
$569$	−290.590	−	167.772i	−0.510703	−	0.294854i	0.222420	−	0.974951i	$-0.428604\pi$
$569$	−290.590	−	167.772i	−0.510703	−	0.294854i	−0.733122	+	0.680097i	$0.761938\pi$
$570$		0			0
$571$	−50.4122	−	87.3166i	−0.0882876	−	0.152919i	0.818500	−	0.574507i	$-0.194806\pi$
$571$	−50.4122	−	87.3166i	−0.0882876	−	0.152919i	−0.906787	+	0.421588i	$0.861473\pi$
$572$		0			0
$573$	467.524	+	305.308i	0.815924	+	0.532824i
$574$		0			0
$575$	621.630	+	358.898i	1.08110	+	0.624171i
$576$		0			0
$577$	336.540			0.583258			0.291629	−	0.956532i	$-0.405803\pi$
$577$	336.540			0.583258			0.291629	+	0.956532i	$0.405803\pi$
$578$		0			0
$579$	683.097	+	37.5429i	1.17979	+	0.0648410i
$580$		0			0
$581$	191.011	−	110.280i	0.328763	−	0.189811i
$582$		0			0
$583$	−37.1722			−0.0637603
$584$		0			0
$585$	−273.751	−	201.029i	−0.467951	−	0.343639i
$586$		0			0
$587$	−967.910	+	558.823i	−1.64891	+	0.951999i	−0.671405	+	0.741091i	$0.734309\pi$
$587$	−967.910	+	558.823i	−1.64891	+	0.951999i	−0.977506	+	0.210908i	$0.932358\pi$
$588$		0			0
$589$	−221.568	+	142.546i	−0.376177	+	0.242013i
$590$		0			0
$591$	−19.4818	+	354.473i	−0.0329641	+	0.599785i
$592$		0			0
$593$	531.741	−	307.001i	0.896697	−	0.517708i	0.0205697	−	0.999788i	$-0.493452\pi$
$593$	531.741	−	307.001i	0.896697	−	0.517708i	0.876127	+	0.482080i	$0.160119\pi$
$594$		0			0
$595$	−103.270	−	178.869i	−0.173563	−	0.300621i
$596$		0			0
$597$	374.100	+	738.856i	0.626634	+	1.23761i
$598$		0			0
$599$	−641.225	−	370.211i	−1.07049	−	0.618049i	−0.142176	−	0.989841i	$-0.545410\pi$
$599$	−641.225	−	370.211i	−1.07049	−	0.618049i	−0.928316	+	0.371792i	$0.878743\pi$
$600$		0			0
$601$	508.111	−	880.074i	0.845443	−	1.46435i	−0.0397934	−	0.999208i	$-0.512670\pi$
$601$	508.111	−	880.074i	0.845443	−	1.46435i	0.885236	−	0.465142i	$-0.153997\pi$
$602$		0			0
$603$	−460.444	+	627.010i	−0.763588	+	1.03982i
$604$		0			0
$605$	221.098	−	127.651i	0.365451	−	0.210993i
$606$		0			0
$607$	−335.064	−	580.348i	−0.552000	−	0.956092i	−0.998130	−	0.0611236i	$-0.980532\pi$
$607$	−335.064	−	580.348i	−0.552000	−	0.956092i	0.446131	−	0.894968i	$-0.352802\pi$
$608$		0			0
$609$	180.950	+	118.166i	0.297126	+	0.194033i
$610$		0			0
$611$	−1049.09	−	605.691i	−1.71700	−	0.991310i
$612$		0			0
$613$	−32.1036	+	55.6051i	−0.0523713	+	0.0907097i	−0.891023	−	0.453959i	$-0.850011\pi$
$613$	−32.1036	+	55.6051i	−0.0523713	+	0.0907097i	0.838651	+	0.544669i	$0.183345\pi$
$614$		0			0
$615$	341.749	+	18.7825i	0.555690	+	0.0305407i
$616$		0			0
$617$	−857.474	−	495.063i	−1.38975	−	0.802371i	−0.396461	−	0.918052i	$-0.629762\pi$
$617$	−857.474	−	495.063i	−1.38975	−	0.802371i	−0.993286	+	0.115681i	$0.963095\pi$
$618$		0			0
$619$	407.935	−	706.564i	0.659023	−	1.14146i	−0.321846	−	0.946792i	$-0.604303\pi$
$619$	407.935	−	706.564i	0.659023	−	1.14146i	0.980869	−	0.194669i	$-0.0623633\pi$
$620$		0			0
$621$	−813.801	−	669.354i	−1.31047	−	1.07787i
$622$		0			0
$623$		−	28.7160i		−	0.0460930i
$624$		0			0
$625$	173.104			0.276967
$626$		0			0
$627$	−134.263	+	228.932i	−0.214136	+	0.365122i
$628$		0			0
$629$	736.189	+	425.039i	1.17041	+	0.675737i
$630$		0			0
$631$	243.562	+	421.861i	0.385993	+	0.668559i	0.991906	−	0.126971i	$-0.0405256\pi$
$631$	243.562	+	421.861i	0.385993	+	0.668559i	−0.605913	+	0.795531i	$0.707192\pi$
$632$		0			0
$633$	503.361	+	27.6647i	0.795199	+	0.0437041i
$634$		0			0
$635$	201.382	−	116.268i	0.317137	−	0.183099i
$636$		0			0
$637$	−510.296			−0.801092
$638$		0			0
$639$	693.565	+	509.318i	1.08539	+	0.797054i
$640$		0			0
$641$	828.405	−	478.280i	1.29236	−	0.746147i	0.313291	−	0.949657i	$-0.398568\pi$
$641$	828.405	−	478.280i	1.29236	−	0.746147i	0.979073	+	0.203510i	$0.0652351\pi$
$642$		0			0
$643$	266.582			0.414591			0.207295	−	0.978278i	$-0.433534\pi$
$643$	266.582			0.414591			0.207295	+	0.978278i	$0.433534\pi$
$644$		0			0
$645$	367.144	−	185.894i	0.569216	−	0.288208i
$646$		0			0
$647$			1127.22i			1.74223i	0.491080	+	0.871114i	$0.336602\pi$
$647$			1127.22i			1.74223i	−0.491080	+	0.871114i	$0.663398\pi$
$648$		0			0
$649$	−175.677	+	304.282i	−0.270689	+	0.468847i
$650$		0			0
$651$	156.748	+	8.61484i	0.240780	+	0.0132332i
$652$		0			0
$653$	−1019.58	+	588.653i	−1.56137	+	0.901459i	−0.564254	+	0.825601i	$0.690836\pi$
$653$	−1019.58	+	588.653i	−1.56137	+	0.901459i	−0.997119	+	0.0758579i	$0.975830\pi$
$654$		0			0
$655$	287.799			0.439388
$656$		0			0
$657$	−362.451	+	493.568i	−0.551675	+	0.751246i
$658$		0			0
$659$		−	516.136i		−	0.783211i	−0.920133	−	0.391605i	$-0.871920\pi$
$659$		−	516.136i		−	0.783211i	0.920133	−	0.391605i	$-0.128080\pi$
$660$		0			0
$661$	29.6738	−	51.3965i	0.0448923	−	0.0777557i	−0.842706	−	0.538374i	$-0.819039\pi$
$661$	29.6738	−	51.3965i	0.0448923	−	0.0777557i	0.887598	+	0.460618i	$0.152372\pi$
$662$		0			0
$663$	−836.639	+	423.611i	−1.26190	+	0.638930i
$664$		0			0
$665$	84.3744	−	163.859i	0.126879	−	0.246405i
$666$		0			0
$667$	372.495	−	645.181i	0.558464	−	0.967288i
$668$		0			0
$669$	196.141	+	387.383i	0.293186	+	0.579048i
$670$		0			0
$671$	−278.823	−	160.979i	−0.415533	−	0.239908i
$672$		0			0
$673$	−236.746	+	410.056i	−0.351777	+	0.609296i	−0.986561	−	0.163394i	$-0.947756\pi$
$673$	−236.746	+	410.056i	−0.351777	+	0.609296i	0.634784	+	0.772690i	$0.281089\pi$
$674$		0			0
$675$	−489.879	−	81.4277i	−0.725747	−	0.120634i
$676$		0			0
$677$	625.734	+	361.268i	0.924275	+	0.533631i	0.884996	−	0.465598i	$-0.154161\pi$
$677$	625.734	+	361.268i	0.924275	+	0.533631i	0.0392788	+	0.999228i	$0.487494\pi$
$678$		0			0
$679$	186.999			0.275404
$680$		0			0
$681$	−612.259	−	399.825i	−0.899059	−	0.587114i
$682$		0			0
$683$			501.462i			0.734205i	0.930180	+	0.367103i	$0.119650\pi$
$683$			501.462i			0.734205i	−0.930180	+	0.367103i	$0.880350\pi$
$684$		0			0
$685$	−567.196			−0.828024
$686$		0			0
$687$	−600.764	−	1186.52i	−0.874474	−	1.72710i
$688$		0			0
$689$		−	117.206i		−	0.170111i
$690$		0			0
$691$	333.572	−	577.764i	0.482738	−	0.836127i	−0.517065	−	0.855946i	$-0.672976\pi$
$691$	333.572	−	577.764i	0.482738	−	0.836127i	0.999804	+	0.0198188i	$0.00630893\pi$
$692$		0			0
$693$	144.792	−	63.5847i	0.208936	−	0.0917528i
$694$		0			0
$695$	−297.301	−	171.647i	−0.427771	−	0.246974i
$696$		0			0
$697$	472.515	−	818.420i	0.677927	−	1.17420i
$698$		0			0
$699$	−508.555	−	332.102i	−0.727546	−	0.475111i
$700$		0			0
$701$	368.320	+	212.650i	0.525421	+	0.303352i	0.739150	−	0.673541i	$-0.235228\pi$
$701$	368.320	+	212.650i	0.525421	+	0.303352i	−0.213729	+	0.976893i	$0.568561\pi$
$702$		0			0
$703$	36.4623	+	757.689i	0.0518666	+	1.07779i
$704$		0			0
$705$	635.339	+	34.9182i	0.901191	+	0.0495293i
$706$		0			0
$707$	11.5037	+	6.64168i	0.0162712	+	0.00939418i
$708$		0			0
$709$	280.942			0.396251			0.198125	−	0.980177i	$-0.436515\pi$
$709$	280.942			0.396251			0.198125	+	0.980177i	$0.436515\pi$
$710$		0			0
$711$	−302.693	−	689.280i	−0.425729	−	0.969452i
$712$		0			0
$713$		−	541.154i		−	0.758982i
$714$		0			0
$715$	−87.8546	−	152.169i	−0.122873	−	0.212823i
$716$		0			0
$717$	−988.106	+	500.302i	−1.37811	+	0.697771i
$718$		0			0
$719$	−178.192	−	102.879i	−0.247834	−	0.143087i	0.370938	−	0.928658i	$-0.379036\pi$
$719$	−178.192	−	102.879i	−0.247834	−	0.143087i	−0.618772	+	0.785571i	$0.712369\pi$
$720$		0			0
$721$	686.005			0.951463
$722$		0			0
$723$	882.906	+	48.5244i	1.22117	+	0.0671154i
$724$		0			0
$725$		−	351.105i		−	0.484282i
$726$		0			0
$727$	−400.262	−	693.275i	−0.550567	−	0.953611i	−0.998234	−	0.0594099i	$-0.981078\pi$
$727$	−400.262	−	693.275i	−0.550567	−	0.953611i	0.447666	−	0.894201i	$-0.352255\pi$
$728$		0			0
$729$	689.800	+	235.833i	0.946228	+	0.323502i
$730$		0			0
$731$		−	1136.26i		−	1.55439i
$732$		0			0
$733$	80.9641	+	140.234i	0.110456	+	0.191315i	0.915954	−	0.401283i	$-0.131436\pi$
$733$	80.9641	+	140.234i	0.110456	+	0.191315i	−0.805498	+	0.592598i	$0.798102\pi$
$734$		0			0
$735$	239.135	−	121.080i	0.325354	−	0.164735i
$736$		0			0
$737$	−348.533	+	201.225i	−0.472907	+	0.273033i
$738$		0			0
$739$	314.576	−	544.862i	0.425678	−	0.737296i	−0.570806	−	0.821085i	$-0.693369\pi$
$739$	314.576	−	544.862i	0.425678	−	0.737296i	0.996483	+	0.0837895i	$0.0267023\pi$
$740$		0			0
$741$	−721.835	−	423.341i	−0.974137	−	0.571310i
$742$		0			0
$743$		−	722.376i		−	0.972242i	−0.873891	−	0.486121i	$-0.838411\pi$
$743$		−	722.376i		−	0.972242i	0.873891	−	0.486121i	$-0.161589\pi$
$744$		0			0
$745$	120.809			0.162159
$746$		0			0
$747$	423.977	+	311.346i	0.567572	+	0.416795i
$748$		0			0
$749$	−651.534	−	376.163i	−0.869872	−	0.502221i
$750$		0			0
$751$	386.294	−	669.082i	0.514373	−	0.890921i	−0.485487	−	0.874244i	$-0.661358\pi$
$751$	386.294	−	669.082i	0.514373	−	0.890921i	0.999861	−	0.0166773i	$-0.00530880\pi$
$752$		0			0
$753$	666.749	−	337.591i	0.885457	−	0.448328i
$754$		0			0
$755$	−340.470	−	196.570i	−0.450954	−	0.260358i
$756$		0			0
$757$	358.590	−	621.097i	0.473699	−	0.820471i	−0.525847	−	0.850579i	$-0.676252\pi$
$757$	358.590	−	621.097i	0.473699	−	0.820471i	0.999547	+	0.0301078i	$0.00958505\pi$
$758$		0			0
$759$	−246.249	−	486.346i	−0.324438	−	0.640772i
$760$		0			0
$761$	697.740	−	402.841i	0.916873	−	0.529357i	0.0342369	−	0.999414i	$-0.489100\pi$
$761$	697.740	−	402.841i	0.916873	−	0.529357i	0.882636	+	0.470057i	$0.155767\pi$
$762$		0			0
$763$	88.4846	+	153.260i	0.115969	+	0.200865i
$764$		0			0
$765$	291.555	−	397.026i	0.381118	−	0.518988i
$766$		0			0
$767$	−959.419	−	553.921i	−1.25087	−	0.722191i
$768$		0			0
$769$	−121.352	+	210.188i	−0.157805	+	0.273326i	−0.934077	−	0.357072i	$-0.883775\pi$
$769$	−121.352	+	210.188i	−0.157805	+	0.273326i	0.776272	+	0.630398i	$0.217108\pi$
$770$		0			0
$771$	−308.520	−	201.473i	−0.400155	−	0.261314i
$772$		0			0
$773$	174.409	−	100.695i	0.225626	−	0.130265i	−0.382927	−	0.923779i	$-0.625084\pi$
$773$	174.409	−	100.695i	0.225626	−	0.130265i	0.608552	+	0.793514i	$0.291750\pi$
$774$		0			0
$775$	−127.519	−	220.870i	−0.164541	−	0.284994i
$776$		0			0
$777$	247.138	−	378.447i	0.318066	−	0.487061i
$778$		0			0
$779$	842.322	−	40.5350i	1.08129	−	0.0520347i
$780$		0			0
$781$	222.585	+	385.528i	0.285000	+	0.493634i
$782$		0			0
$783$	−84.5126	+	508.439i	−0.107934	+	0.649347i
$784$		0			0
$785$		−	379.519i		−	0.483464i
$786$		0			0
$787$	−208.339	−	360.853i	−0.264725	−	0.458518i	0.702766	−	0.711421i	$-0.251948\pi$
$787$	−208.339	−	360.853i	−0.264725	−	0.458518i	−0.967492	+	0.252903i	$0.918615\pi$
$788$		0			0
$789$	−726.682	+	367.937i	−0.921017	+	0.466333i
$790$		0			0
$791$		−	556.483i		−	0.703518i
$792$		0			0
$793$	507.575	−	879.145i	0.640069	−	1.10863i
$794$		0			0
$795$	27.8100	+	54.9254i	0.0349812	+	0.0690885i
$796$		0			0
$797$	−330.486	+	190.806i	−0.414663	+	0.239406i	−0.692791	−	0.721138i	$-0.743619\pi$
$797$	−330.486	+	190.806i	−0.414663	+	0.239406i	0.278128	+	0.960544i	$0.410286\pi$
$798$		0			0
$799$	878.443	−	1521.51i	1.09943	−	1.90427i
$800$		0			0
$801$	62.7049	−	27.5365i	0.0782833	−	0.0343776i
$802$		0			0
$803$	−274.357	+	158.400i	−0.341665	+	0.197260i
$804$		0			0
$805$	189.284	+	327.850i	0.235136	+	0.407267i
$806$		0			0
$807$	−427.463	−	279.147i	−0.529694	−	0.345907i
$808$		0			0
$809$		−	215.326i		−	0.266163i	−0.991105	−	0.133082i	$-0.957513\pi$
$809$		−	215.326i		−	0.266163i	0.991105	−	0.133082i	$-0.0424872\pi$
$810$		0			0
$811$	−23.8247	−	41.2657i	−0.0293770	−	0.0508824i	0.850963	−	0.525225i	$-0.176019\pi$
$811$	−23.8247	−	41.2657i	−0.0293770	−	0.0508824i	−0.880340	+	0.474343i	$0.842686\pi$
$812$		0			0
$813$	−848.997	+	1300.09i	−1.04428	+	1.59912i
$814$		0			0
$815$			570.628i			0.700157i
$816$		0			0
$817$	852.714	−	548.592i	1.04371	−	0.671471i
$818$		0			0
$819$	200.486	+	456.539i	0.244794	+	0.557435i
$820$		0			0
$821$			459.035i			0.559117i	0.960129	+	0.279558i	$0.0901881\pi$
$821$			459.035i			0.559117i	−0.960129	+	0.279558i	$0.909812\pi$
$822$		0			0
$823$	−197.591	+	342.238i	−0.240086	+	0.415842i	−0.960739	−	0.277455i	$-0.910509\pi$
$823$	−197.591	+	342.238i	−0.240086	+	0.415842i	0.720652	+	0.693297i	$0.243842\pi$
$824$		0			0
$825$	−215.110	−	140.474i	−0.260739	−	0.170271i
$826$		0			0
$827$	−631.849	+	364.798i	−0.764026	+	0.441110i	−0.830739	−	0.556662i	$-0.812082\pi$
$827$	−631.849	+	364.798i	−0.764026	+	0.441110i	0.0667136	+	0.997772i	$0.478749\pi$
$828$		0			0
$829$	−237.513			−0.286505			−0.143253	−	0.989686i	$-0.545756\pi$
$829$	−237.513			−0.286505			−0.143253	+	0.989686i	$0.545756\pi$
$830$		0			0
$831$	312.977	−	479.267i	0.376627	−	0.576736i
$832$		0			0
$833$		−	740.090i		−	0.888463i
$834$		0			0
$835$	−313.982	+	543.833i	−0.376026	+	0.651297i
$836$		0			0
$837$	131.498	+	350.539i	0.157106	+	0.418804i
$838$		0			0
$839$	152.351	−	87.9601i	0.181587	−	0.104839i	−0.406451	−	0.913673i	$-0.633234\pi$
$839$	152.351	−	87.9601i	0.181587	−	0.104839i	0.588038	+	0.808833i	$0.299901\pi$
$840$		0			0
$841$	476.594			0.566699
$842$		0			0
$843$	−29.7852	+	541.945i	−0.0353324	+	0.642876i
$844$		0			0
$845$	103.585	−	59.8050i	0.122586	−	0.0707751i
$846$		0			0
$847$	−374.810			−0.442515
$848$		0			0
$849$	−1113.90	−	61.2200i	−1.31202	−	0.0721084i
$850$		0			0
$851$	−1349.36	−	779.054i	−1.58562	−	0.915457i
$852$		0			0
$853$	629.542	+	1090.40i	0.738032	+	1.27831i	0.953380	+	0.301772i	$0.0975782\pi$
$853$	629.542	+	1090.40i	0.738032	+	1.27831i	−0.215348	+	0.976537i	$0.569088\pi$
$854$		0			0
$855$	438.715	+	27.1135i	0.513117	+	0.0317117i
$856$		0			0
$857$	−551.154	+	318.209i	−0.643120	+	0.371305i	−0.785815	−	0.618461i	$-0.787756\pi$
$857$	−551.154	+	318.209i	−0.643120	+	0.371305i	0.142695	+	0.989767i	$0.454423\pi$
$858$		0			0
$859$	−498.140	+	862.804i	−0.579907	+	1.00443i	0.415582	+	0.909556i	$0.363578\pi$
$859$	−498.140	+	862.804i	−0.579907	+	1.00443i	−0.995489	+	0.0948729i	$0.969756\pi$
$860$		0			0
$861$	−420.719	−	274.743i	−0.488640	−	0.319097i
$862$		0			0
$863$			309.627i			0.358780i	0.983778	+	0.179390i	$0.0574123\pi$
$863$			309.627i			0.358780i	−0.983778	+	0.179390i	$0.942588\pi$
$864$		0			0
$865$	−75.5812	−	130.911i	−0.0873771	−	0.151342i
$866$		0			0
$867$	−222.727	−	439.889i	−0.256893	−	0.507369i
$868$		0			0
$869$		−	389.466i		−	0.448177i
$870$		0			0
$871$	−634.476	−	1098.94i	−0.728445	−	1.26170i
$872$		0			0
$873$	179.318	+	408.336i	0.205405	+	0.467738i
$874$		0			0
$875$	364.530	+	210.461i	0.416606	+	0.240527i
$876$		0			0
$877$	69.5709			0.0793283			0.0396641	−	0.999213i	$-0.487371\pi$
$877$	69.5709			0.0793283			0.0396641	+	0.999213i	$0.487371\pi$
$878$		0			0
$879$	592.203	−	299.847i	0.673724	−	0.341123i
$880$		0			0
$881$		−	901.073i		−	1.02278i	−0.859348	−	0.511392i	$-0.829130\pi$
$881$		−	901.073i		−	1.02278i	0.859348	−	0.511392i	$-0.170870\pi$
$882$		0			0
$883$	−512.605	−	887.858i	−0.580527	−	1.00550i	−0.995417	−	0.0956300i	$-0.969513\pi$
$883$	−512.605	−	887.858i	−0.580527	−	1.00550i	0.414890	−	0.909871i	$-0.363820\pi$
$884$		0			0
$885$	581.035	+	31.9336i	0.656537	+	0.0360832i
$886$		0			0
$887$	474.356	+	273.870i	0.534787	+	0.308759i	0.742964	−	0.669332i	$-0.233420\pi$
$887$	474.356	+	273.870i	0.534787	+	0.308759i	−0.208177	+	0.978091i	$0.566753\pi$
$888$		0			0
$889$	−341.388			−0.384013
$890$		0			0
$891$	277.690	+	255.199i	0.311661	+	0.286419i
$892$		0			0
$893$	1565.94	−	75.3579i	1.75358	−	0.0843873i
$894$		0			0
$895$	−617.893			−0.690383
$896$		0			0
$897$	1533.48	−	776.437i	1.70956	−	0.865593i
$898$		0			0
$899$	−229.238	+	132.351i	−0.254992	+	0.147220i
$900$		0			0
$901$	169.986			0.188664
$902$		0			0
$903$	−603.250	−	33.1545i	−0.668051	−	0.0367160i
$904$		0			0
$905$	765.088	−	441.724i	0.845401	−	0.488092i
$906$		0			0
$907$	303.350	+	525.418i	0.334454	+	0.579292i	0.983380	−	0.181560i	$-0.0581147\pi$
$907$	303.350	+	525.418i	0.334454	+	0.579292i	−0.648926	+	0.760852i	$0.724781\pi$
$908$		0			0
$909$	−3.47172	+	31.4887i	−0.00381927	+	0.0346411i
$910$		0			0
$911$	−656.737	−	379.167i	−0.720897	−	0.416210i	0.0941856	−	0.995555i	$-0.469975\pi$
$911$	−656.737	−	379.167i	−0.720897	−	0.416210i	−0.815083	+	0.579344i	$0.803309\pi$
$912$		0			0
$913$	136.066	+	235.673i	0.149032	+	0.258131i
$914$		0			0
$915$	−29.2618	+	532.421i	−0.0319801	+	0.581881i
$916$		0			0
$917$	−365.912	−	211.260i	−0.399032	−	0.230381i
$918$		0			0
$919$	−521.132			−0.567064			−0.283532	−	0.958963i	$-0.591506\pi$
$919$	−521.132			−0.567064			−0.283532	+	0.958963i	$0.591506\pi$
$920$		0			0
$921$	−2.05013	+	3.13940i	−0.00222598	+	0.00340868i
$922$		0			0
$923$	−1215.59	+	701.823i	−1.31700	+	0.760371i
$924$		0			0
$925$	−734.317			−0.793856
$926$		0			0
$927$	657.828	+	1497.98i	0.709631	+	1.61594i
$928$		0			0
$929$	850.723	−	491.165i	0.915741	−	0.528703i	0.0334669	−	0.999440i	$-0.489345\pi$
$929$	850.723	−	491.165i	0.915741	−	0.528703i	0.882274	+	0.470737i	$0.156012\pi$
$930$		0			0
$931$	555.406	−	357.319i	0.596569	−	0.383802i
$932$		0			0
$933$	−349.602	+	177.012i	−0.374707	+	0.189723i
$934$		0			0
$935$	220.692	−	127.417i	0.236035	−	0.136275i
$936$		0			0
$937$	588.699	+	1019.66i	0.628280	+	1.08821i	0.987897	+	0.155113i	$0.0495742\pi$
$937$	588.699	+	1019.66i	0.628280	+	1.08821i	−0.359616	+	0.933100i	$0.617092\pi$
$938$		0			0
$939$	−1321.89	−	72.6512i	−1.40777	−	0.0773708i
$940$		0			0
$941$	114.154	+	65.9069i	0.121311	+	0.0700392i	0.559428	−	0.828879i	$-0.311021\pi$
$941$	114.154	+	65.9069i	0.121311	+	0.0700392i	−0.438116	+	0.898918i	$0.644354\pi$
$942$		0			0
$943$	−866.074	+	1500.08i	−0.918424	+	1.59076i
$944$		0			0
$945$	−202.277	−	166.374i	−0.214050	−	0.176057i
$946$		0			0
$947$	22.1450	−	12.7854i	0.0233844	−	0.0135010i	−0.488262	−	0.872697i	$-0.662369\pi$
$947$	22.1450	−	12.7854i	0.0233844	−	0.0135010i	0.511647	+	0.859196i	$0.329036\pi$
$948$		0			0
$949$	−499.445	−	865.064i	−0.526286	−	0.911553i
$950$		0			0
$951$	7.69897	−	140.083i	0.00809565	−	0.147301i
$952$		0			0
$953$	518.708	+	299.476i	0.544290	+	0.314246i	0.746816	−	0.665031i	$-0.231582\pi$
$953$	518.708	+	299.476i	0.544290	+	0.314246i	−0.202526	+	0.979277i	$0.564915\pi$
$954$		0			0
$955$	239.219	−	414.340i	0.250491	−	0.433863i
$956$		0			0
$957$	−145.795	+	223.259i	−0.152346	+	0.233291i
$958$		0			0
$959$	721.143	+	416.352i	0.751974	+	0.434152i
$960$		0			0
$961$	384.362	−	665.734i	0.399960	−	0.692752i
$962$		0			0
$963$	196.627	−	1783.42i	0.204182	−	1.85194i
$964$		0			0
$965$		−	586.179i		−	0.607440i
$966$		0			0
$967$	−936.634			−0.968598			−0.484299	−	0.874902i	$-0.660925\pi$
$967$	−936.634			−0.968598			−0.484299	+	0.874902i	$0.660925\pi$
$968$		0			0
$969$	613.978	−	1046.89i	0.633620	−	1.08038i
$970$		0			0
$971$	47.9921	+	27.7083i	0.0494254	+	0.0285358i	0.524509	−	0.851405i	$-0.324249\pi$
$971$	47.9921	+	27.7083i	0.0494254	+	0.0285358i	−0.475084	+	0.879941i	$0.657582\pi$
$972$		0			0
$973$	251.996	+	436.469i	0.258988	+	0.448581i
$974$		0			0
$975$	442.922	−	678.254i	0.454278	−	0.695646i
$976$		0			0
$977$	−709.666	+	409.726i	−0.726373	+	0.419371i	−0.817094	−	0.576505i	$-0.804416\pi$
$977$	−709.666	+	409.726i	−0.726373	+	0.419371i	0.0907210	+	0.995876i	$0.471083\pi$
$978$		0			0
$979$	35.4303			0.0361903
$980$		0			0
$981$	−249.812	+	340.182i	−0.254650	+	0.346771i
$982$		0			0
$983$	−1009.88	+	583.057i	−1.02735	+	0.593140i	−0.916224	−	0.400667i	$-0.868779\pi$
$983$	−1009.88	+	583.057i	−1.02735	+	0.593140i	−0.111125	+	0.993806i	$0.535445\pi$
$984$		0			0
$985$	304.181			0.308813
$986$		0			0
$987$	−782.150	−	510.768i	−0.792452	−	0.517496i
$988$		0			0
$989$			2082.65i			2.10582i
$990$		0			0
$991$	575.897	−	997.483i	0.581127	−	1.00654i	−0.414219	−	0.910177i	$-0.635945\pi$
$991$	575.897	−	997.483i	0.581127	−	1.00654i	0.995346	−	0.0963646i	$-0.0307215\pi$
$992$		0			0
$993$	−87.0114	+	133.242i	−0.0876248	+	0.134182i
$994$		0			0
$995$	614.527	−	354.798i	0.617615	−	0.356580i
$996$		0			0
$997$	226.996			0.227679			0.113839	−	0.993499i	$-0.463685\pi$
$997$	226.996			0.227679			0.113839	+	0.993499i	$0.463685\pi$
$998$		0			0
$999$	1063.37	+	176.754i	1.06444	+	0.176931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.1	✓	80
3.2	odd	2		2052.3.m.a.1493.15		80
9.4	even	3		2052.3.be.a.125.26		80
9.5	odd	6		684.3.be.a.581.27	yes	80
19.7	even	3		684.3.be.a.425.27	yes	80
57.26	odd	6		2052.3.be.a.197.26		80
171.121	even	3		2052.3.m.a.881.26		80
171.140	odd	6	inner	684.3.m.a.653.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.1	✓	80	1.1	even	1	trivial
684.3.m.a.653.1	yes	80	171.140	odd	6	inner
684.3.be.a.425.27	yes	80	19.7	even	3
684.3.be.a.581.27	yes	80	9.5	odd	6
2052.3.m.a.881.26		80	171.121	even	3
2052.3.m.a.1493.15		80	3.2	odd	2
2052.3.be.a.125.26		80	9.4	even	3
2052.3.be.a.197.26		80	57.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.99548 - 0.164631i) q^{3} +2.57048i q^{5} +(1.88687 - 3.26816i) q^{7} +(8.94579 + 0.986299i) q^{9} +O(q^{10})\)	\(q+(-2.99548 - 0.164631i) q^{3} +2.57048i q^{5} +(1.88687 - 3.26816i) q^{7} +(8.94579 + 0.986299i) q^{9} +(4.03231 + 2.32806i) q^{11} +(-7.34051 + 12.7141i) q^{13} +(0.423182 - 7.69983i) q^{15} +(-18.4395 - 10.6461i) q^{17} +(-0.913280 - 18.9780i) q^{19} +(-6.19012 + 9.47905i) q^{21} +(33.7978 + 19.5132i) q^{23} +18.3926 q^{25} +(-26.6346 - 4.42719i) q^{27} -19.0894i q^{29} +(-6.93319 - 12.0086i) q^{31} +(-11.6954 - 7.63749i) q^{33} +(8.40073 + 4.85017i) q^{35} -39.9245 q^{37} +(24.0815 - 36.8764i) q^{39} +44.3840i q^{41} +(26.6826 + 46.2157i) q^{43} +(-2.53526 + 22.9950i) q^{45} +82.5135i q^{47} +(17.3794 + 30.1021i) q^{49} +(53.4825 + 34.9258i) q^{51} +(-6.91394 + 3.99177i) q^{53} +(-5.98423 + 10.3650i) q^{55} +(-0.388668 + 56.9987i) q^{57} +75.4608i q^{59} -69.1471 q^{61} +(20.1029 - 27.3752i) q^{63} +(-32.6814 - 18.8686i) q^{65} +(-43.2174 + 74.8548i) q^{67} +(-98.0281 - 64.0155i) q^{69} +(82.8003 + 47.8048i) q^{71} +(-34.0198 + 58.9240i) q^{73} +(-55.0947 - 3.02800i) q^{75} +(15.2169 - 8.78549i) q^{77} +(-41.8231 - 72.4397i) q^{79} +(79.0544 + 17.6465i) q^{81} +(50.6159 + 29.2231i) q^{83} +(27.3655 - 47.3984i) q^{85} +(-3.14272 + 57.1820i) q^{87} +(6.58995 - 3.80471i) q^{89} +(27.7012 + 47.9798i) q^{91} +(18.7912 + 37.1130i) q^{93} +(48.7827 - 2.34757i) q^{95} +(24.7763 + 42.9139i) q^{97} +(33.7761 + 24.8034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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