LMFDB - Embedded newform 684.3.m.a.353.10

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			353.10
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11779 - 2.12485i) q^{3} +8.55202i q^{5} +(-5.68709 + 9.85033i) q^{7} +(-0.0299448 + 8.99995i) q^{9} +O(q^{10})$	\(q+(-2.11779 - 2.12485i) q^{3} +8.55202i q^{5} +(-5.68709 + 9.85033i) q^{7} +(-0.0299448 + 8.99995i) q^{9} +(12.9413 + 7.47166i) q^{11} +(-0.847351 + 1.46766i) q^{13} +(18.1717 - 18.1114i) q^{15} +(-22.9277 - 13.2373i) q^{17} +(1.22562 + 18.9604i) q^{19} +(32.9745 - 8.77672i) q^{21} +(-2.95885 - 1.70829i) q^{23} -48.1370 q^{25} +(19.1869 - 18.9964i) q^{27} -11.0579i q^{29} +(-18.4894 - 32.0245i) q^{31} +(-11.5308 - 43.3216i) q^{33} +(-84.2401 - 48.6361i) q^{35} +55.7350 q^{37} +(4.91305 - 1.30769i) q^{39} -45.0347i q^{41} +(12.0594 + 20.8875i) q^{43} +(-76.9677 - 0.256089i) q^{45} +88.7028i q^{47} +(-40.1859 - 69.6041i) q^{49} +(20.4288 + 76.7517i) q^{51} +(-49.9793 + 28.8555i) q^{53} +(-63.8977 + 110.674i) q^{55} +(37.6924 - 42.7584i) q^{57} -23.5787i q^{59} +32.3568 q^{61} +(-88.4821 - 51.4785i) q^{63} +(-12.5514 - 7.24656i) q^{65} +(-28.6083 + 49.5510i) q^{67} +(2.63636 + 9.90491i) q^{69} +(51.0876 + 29.4954i) q^{71} +(39.1711 - 67.8463i) q^{73} +(101.944 + 102.284i) q^{75} +(-147.197 + 84.9839i) q^{77} +(26.4100 + 45.7434i) q^{79} +(-80.9982 - 0.539004i) q^{81} +(-60.4098 - 34.8776i) q^{83} +(113.206 - 196.078i) q^{85} +(-23.4963 + 23.4182i) q^{87} +(-9.10392 + 5.25615i) q^{89} +(-9.63792 - 16.6934i) q^{91} +(-28.8906 + 107.108i) q^{93} +(-162.150 + 10.4815i) q^{95} +(-41.4092 - 71.7229i) q^{97} +(-67.6321 + 116.247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.11779	−	2.12485i	−0.705929	−	0.708282i
$3$	−2.11779	−	2.12485i	−0.705929	−	0.708282i
$4$		0			0
$5$			8.55202i			1.71040i	0.518296	+	0.855202i	$0.326567\pi$
$5$			8.55202i			1.71040i	−0.518296	+	0.855202i	$0.673433\pi$
$6$		0			0
$7$	−5.68709	+	9.85033i	−0.812441	+	1.40719i	0.0987097	+	0.995116i	$0.468528\pi$
$7$	−5.68709	+	9.85033i	−0.812441	+	1.40719i	−0.911151	+	0.412073i	$0.864805\pi$
$8$		0			0
$9$	−0.0299448	+	8.99995i	−0.00332720	+	0.999994i
$10$		0			0
$11$	12.9413	+	7.47166i	1.17648	+	0.679242i	0.955198	−	0.295968i	$-0.0956422\pi$
$11$	12.9413	+	7.47166i	1.17648	+	0.679242i	0.221283	+	0.975210i	$0.428976\pi$
$12$		0			0
$13$	−0.847351	+	1.46766i	−0.0651809	+	0.112897i	−0.896774	−	0.442488i	$-0.854096\pi$
$13$	−0.847351	+	1.46766i	−0.0651809	+	0.112897i	0.831593	+	0.555385i	$0.187429\pi$
$14$		0			0
$15$	18.1717	−	18.1114i	1.21145	−	1.20742i
$16$		0			0
$17$	−22.9277	−	13.2373i	−1.34869	−	0.778666i	−0.360625	−	0.932711i	$-0.617436\pi$
$17$	−22.9277	−	13.2373i	−1.34869	−	0.778666i	−0.988064	+	0.154045i	$0.950770\pi$
$18$		0			0
$19$	1.22562	+	18.9604i	0.0645064	+	0.997917i
$19$	1.22562	+	18.9604i	0.0645064	+	0.997917i
$20$		0			0
$21$	32.9745	−	8.77672i	1.57021	−	0.417939i
$22$		0			0
$23$	−2.95885	−	1.70829i	−0.128646	−	0.0742736i	0.434296	−	0.900770i	$-0.356997\pi$
$23$	−2.95885	−	1.70829i	−0.128646	−	0.0742736i	−0.562942	+	0.826497i	$0.690330\pi$
$24$		0			0
$25$	−48.1370			−1.92548
$26$		0			0
$27$	19.1869	−	18.9964i	0.710627	−	0.703569i
$28$		0			0
$29$		−	11.0579i		−	0.381306i	−0.981658	−	0.190653i	$-0.938940\pi$
$29$		−	11.0579i		−	0.381306i	0.981658	−	0.190653i	$-0.0610605\pi$
$30$		0			0
$31$	−18.4894	−	32.0245i	−0.596431	−	1.03305i	−0.993343	−	0.115192i	$-0.963252\pi$
$31$	−18.4894	−	32.0245i	−0.596431	−	1.03305i	0.396912	−	0.917857i	$-0.370082\pi$
$32$		0			0
$33$	−11.5308	−	43.3216i	−0.349418	−	1.31278i
$34$		0			0
$35$	−84.2401	−	48.6361i	−2.40686	−	1.38960i
$36$		0			0
$37$	55.7350			1.50635			0.753176	−	0.657819i	$-0.228521\pi$
$37$	55.7350			1.50635			0.753176	+	0.657819i	$0.228521\pi$
$38$		0			0
$39$	4.91305	−	1.30769i	0.125976	−	0.0335306i
$40$		0			0
$41$		−	45.0347i		−	1.09841i	−0.835688	−	0.549204i	$-0.814931\pi$
$41$		−	45.0347i		−	1.09841i	0.835688	−	0.549204i	$-0.185069\pi$
$42$		0			0
$43$	12.0594	+	20.8875i	0.280451	+	0.485755i	0.971496	−	0.237057i	$-0.0761827\pi$
$43$	12.0594	+	20.8875i	0.280451	+	0.485755i	−0.691045	+	0.722812i	$0.742849\pi$
$44$		0			0
$45$	−76.9677	−	0.256089i	−1.71039	−	0.00569086i
$46$		0			0
$47$			88.7028i			1.88729i	0.330954	+	0.943647i	$0.392629\pi$
$47$			88.7028i			1.88729i	−0.330954	+	0.943647i	$0.607371\pi$
$48$		0			0
$49$	−40.1859	−	69.6041i	−0.820121	−	1.42049i
$50$		0			0
$51$	20.4288	+	76.7517i	0.400564	+	1.50493i
$52$		0			0
$53$	−49.9793	+	28.8555i	−0.943005	+	0.544444i	−0.890901	−	0.454197i	$-0.849926\pi$
$53$	−49.9793	+	28.8555i	−0.943005	+	0.544444i	−0.0521040	+	0.998642i	$0.516593\pi$
$54$		0			0
$55$	−63.8977	+	110.674i	−1.16178	+	2.01226i
$56$		0			0
$57$	37.6924	−	42.7584i	0.661270	−	0.750148i
$58$		0			0
$59$		−	23.5787i		−	0.399640i	−0.979833	−	0.199820i	$-0.935964\pi$
$59$		−	23.5787i		−	0.399640i	0.979833	−	0.199820i	$-0.0640357\pi$
$60$		0			0
$61$	32.3568			0.530439			0.265220	−	0.964188i	$-0.414556\pi$
$61$	32.3568			0.530439			0.265220	+	0.964188i	$0.414556\pi$
$62$		0			0
$63$	−88.4821	−	51.4785i	−1.40448	−	0.817119i
$64$		0			0
$65$	−12.5514	−	7.24656i	−0.193099	−	0.111486i
$66$		0			0
$67$	−28.6083	+	49.5510i	−0.426989	+	0.739567i	−0.996604	−	0.0823446i	$-0.973759\pi$
$67$	−28.6083	+	49.5510i	−0.426989	+	0.739567i	0.569615	+	0.821912i	$0.307093\pi$
$68$		0			0
$69$	2.63636	+	9.90491i	0.0382081	+	0.143549i
$70$		0			0
$71$	51.0876	+	29.4954i	0.719543	+	0.415429i	0.814585	−	0.580045i	$-0.196965\pi$
$71$	51.0876	+	29.4954i	0.719543	+	0.415429i	−0.0950412	+	0.995473i	$0.530298\pi$
$72$		0			0
$73$	39.1711	−	67.8463i	0.536590	−	0.929401i	−0.462495	−	0.886622i	$-0.653046\pi$
$73$	39.1711	−	67.8463i	0.536590	−	0.929401i	0.999085	−	0.0427787i	$-0.0136210\pi$
$74$		0			0
$75$	101.944	+	102.284i	1.35925	+	1.36378i
$76$		0			0
$77$	−147.197	+	84.9839i	−1.91164	+	1.10369i
$78$		0			0
$79$	26.4100	+	45.7434i	0.334303	+	0.579030i	0.983351	−	0.181718i	$-0.0581657\pi$
$79$	26.4100	+	45.7434i	0.334303	+	0.579030i	−0.649047	+	0.760748i	$0.724832\pi$
$80$		0			0
$81$	−80.9982	−	0.539004i	−0.999978	−	0.00665437i
$82$		0			0
$83$	−60.4098	−	34.8776i	−0.727828	−	0.420212i	0.0897988	−	0.995960i	$-0.471378\pi$
$83$	−60.4098	−	34.8776i	−0.727828	−	0.420212i	−0.817627	+	0.575748i	$0.804711\pi$
$84$		0			0
$85$	113.206	−	196.078i	1.33183	−	2.30680i
$86$		0			0
$87$	−23.4963	+	23.4182i	−0.270072	+	0.269175i
$88$		0			0
$89$	−9.10392	+	5.25615i	−0.102291	+	0.0590579i	−0.550273	−	0.834985i	$-0.685476\pi$
$89$	−9.10392	+	5.25615i	−0.102291	+	0.0590579i	0.447982	+	0.894043i	$0.352143\pi$
$90$		0			0
$91$	−9.63792	−	16.6934i	−0.105911	−	0.183444i
$92$		0			0
$93$	−28.8906	+	107.108i	−0.310652	+	1.15170i
$94$		0			0
$95$	−162.150	+	10.4815i	−1.70684	+	0.110332i
$96$		0			0
$97$	−41.4092	−	71.7229i	−0.426899	−	0.739412i	0.569696	−	0.821855i	$-0.307061\pi$
$97$	−41.4092	−	71.7229i	−0.426899	−	0.739412i	−0.996596	+	0.0824438i	$0.973728\pi$
$98$		0			0
$99$	−67.6321	+	116.247i	−0.683152	+	1.17421i
$100$		0			0
$101$			60.8711i			0.602684i	0.953516	+	0.301342i	$0.0974346\pi$
$101$			60.8711i			0.602684i	−0.953516	+	0.301342i	$0.902565\pi$
$102$		0			0
$103$	−63.9370	−	110.742i	−0.620747	−	1.07517i	−0.989347	−	0.145578i	$-0.953496\pi$
$103$	−63.9370	−	110.742i	−0.620747	−	1.07517i	0.368599	−	0.929588i	$-0.379837\pi$
$104$		0			0
$105$	75.0586	+	281.998i	0.714844	+	2.68570i
$106$		0			0
$107$			7.27245i			0.0679668i	0.999422	+	0.0339834i	$0.0108193\pi$
$107$			7.27245i			0.0679668i	−0.999422	+	0.0339834i	$0.989181\pi$
$108$		0			0
$109$	57.9610	−	100.391i	0.531752	−	0.921022i	−0.467561	−	0.883961i	$-0.654867\pi$
$109$	57.9610	−	100.391i	0.531752	−	0.921022i	0.999313	−	0.0370607i	$-0.0117995\pi$
$110$		0			0
$111$	−118.035	−	118.428i	−1.06338	−	1.06692i
$112$		0			0
$113$	−162.932	+	94.0691i	−1.44188	+	0.832469i	−0.997975	−	0.0636047i	$-0.979740\pi$
$113$	−162.932	+	94.0691i	−1.44188	+	0.832469i	−0.443904	+	0.896074i	$0.646407\pi$
$114$		0			0
$115$	14.6093	−	25.3041i	0.127038	−	0.220036i
$116$		0			0
$117$	−13.1835	−	7.67007i	−0.112679	−	0.0655561i
$118$		0			0
$119$	260.784	−	150.564i	2.19146	−	1.26524i
$120$		0			0
$121$	51.1513	+	88.5967i	0.422738	+	0.732204i
$122$		0			0
$123$	−95.6919	+	95.3740i	−0.777983	+	0.775399i
$124$		0			0
$125$		−	197.868i		−	1.58294i
$126$		0			0
$127$	52.5288	+	90.9825i	0.413612	+	0.716398i	0.995282	−	0.0970277i	$-0.0309336\pi$
$127$	52.5288	+	90.9825i	0.413612	+	0.716398i	−0.581669	+	0.813425i	$0.697600\pi$
$128$		0			0
$129$	18.8434	−	69.8596i	0.146073	−	0.541547i
$130$		0			0
$131$		−	31.2636i		−	0.238654i	−0.992855	−	0.119327i	$-0.961926\pi$
$131$		−	31.2636i		−	0.238654i	0.992855	−	0.119327i	$-0.0380736\pi$
$132$		0			0
$133$	−193.737	−	95.7569i	−1.45667	−	0.719976i
$134$		0			0
$135$	162.457	+	164.087i	1.20339	+	1.21546i
$136$		0			0
$137$			46.3064i			0.338003i	0.985616	+	0.169001i	$0.0540543\pi$
$137$			46.3064i			0.338003i	−0.985616	+	0.169001i	$0.945946\pi$
$138$		0			0
$139$	7.87782	−	13.6448i	0.0566749	−	0.0981639i	−0.836296	−	0.548278i	$-0.815283\pi$
$139$	7.87782	−	13.6448i	0.0566749	−	0.0981639i	0.892971	+	0.450114i	$0.148617\pi$
$140$		0			0
$141$	188.480	−	187.854i	1.33674	−	1.33230i
$142$		0			0
$143$	−21.9316	+	12.6622i	−0.153368	+	0.0885471i
$144$		0			0
$145$	94.5670			0.652186
$146$		0			0
$147$	−62.7927	+	232.796i	−0.427161	+	1.58364i
$148$		0			0
$149$		−	259.890i		−	1.74423i	−0.489305	−	0.872113i	$-0.662749\pi$
$149$		−	259.890i		−	1.74423i	0.489305	−	0.872113i	$-0.337251\pi$
$150$		0			0
$151$	55.7981	−	96.6452i	0.369524	−	0.640035i	−0.619967	−	0.784628i	$-0.712854\pi$
$151$	55.7981	−	96.6452i	0.369524	−	0.640035i	0.989491	+	0.144593i	$0.0461874\pi$
$152$		0			0
$153$	119.822	−	205.952i	0.783149	−	1.34609i
$154$		0			0
$155$	273.874	−	158.121i	1.76693	−	1.02014i
$156$		0			0
$157$	69.6329			0.443522			0.221761	−	0.975101i	$-0.428820\pi$
$157$	69.6329			0.443522			0.221761	+	0.975101i	$0.428820\pi$
$158$		0			0
$159$	167.159	+	45.0883i	1.05132	+	0.283574i
$160$		0			0
$161$	33.6545	−	19.4304i	0.209034	−	0.120686i
$162$		0			0
$163$	−201.458			−1.23594			−0.617969	−	0.786203i	$-0.712044\pi$
$163$	−201.458			−1.23594			−0.617969	+	0.786203i	$0.712044\pi$
$164$		0			0
$165$	370.487	−	98.6115i	2.24538	−	0.597645i
$166$		0			0
$167$	87.5324	+	50.5369i	0.524146	+	0.302616i	0.738629	−	0.674112i	$-0.235473\pi$
$167$	87.5324	+	50.5369i	0.524146	+	0.302616i	−0.214483	+	0.976728i	$0.568807\pi$
$168$		0			0
$169$	83.0640	+	143.871i	0.491503	+	0.851308i
$170$		0			0
$171$	−170.680	+	10.4628i	−0.998126	+	0.0611858i
$172$		0			0
$173$	−135.808	+	78.4086i	−0.785016	+	0.453229i	−0.838205	−	0.545355i	$-0.816395\pi$
$173$	−135.808	+	78.4086i	−0.785016	+	0.453229i	0.0531893	+	0.998584i	$0.483061\pi$
$174$		0			0
$175$	273.759	−	474.165i	1.56434	−	2.70951i
$176$		0			0
$177$	−50.1012	+	49.9348i	−0.283058	+	0.282117i
$178$		0			0
$179$			211.533i			1.18175i	0.806764	+	0.590874i	$0.201217\pi$
$179$			211.533i			1.18175i	−0.806764	+	0.590874i	$0.798783\pi$
$180$		0			0
$181$	−149.964	−	259.745i	−0.828529	−	1.43505i	−0.899192	−	0.437554i	$-0.855845\pi$
$181$	−149.964	−	259.745i	−0.828529	−	1.43505i	0.0706634	−	0.997500i	$-0.477488\pi$
$182$		0			0
$183$	−68.5248	−	68.7532i	−0.374453	−	0.375701i
$184$		0			0
$185$			476.647i			2.57647i
$186$		0			0
$187$	−197.809	−	342.616i	−1.05780	−	1.83217i
$188$		0			0
$189$	78.0026	+	297.031i	0.412712	+	1.57160i
$190$		0			0
$191$	−2.94629	−	1.70104i	−0.0154256	−	0.00890598i	0.492267	−	0.870444i	$-0.336168\pi$
$191$	−2.94629	−	1.70104i	−0.0154256	−	0.00890598i	−0.507693	+	0.861538i	$0.669502\pi$
$192$		0			0
$193$	−117.968			−0.611233			−0.305617	−	0.952155i	$-0.598863\pi$
$193$	−117.968			−0.611233			−0.305617	+	0.952155i	$0.598863\pi$
$194$		0			0
$195$	11.1834	+	42.0165i	0.0573508	+	0.215469i
$196$		0			0
$197$			211.815i			1.07520i	0.843200	+	0.537600i	$0.180669\pi$
$197$			211.815i			1.07520i	−0.843200	+	0.537600i	$0.819331\pi$
$198$		0			0
$199$	17.4240	+	30.1792i	0.0875576	+	0.151654i	0.906478	−	0.422253i	$-0.138760\pi$
$199$	17.4240	+	30.1792i	0.0875576	+	0.151654i	−0.818921	+	0.573907i	$0.805427\pi$
$200$		0			0
$201$	165.875	−	44.1503i	0.825247	−	0.219653i
$202$		0			0
$203$	108.924	+	62.8870i	0.536569	+	0.309788i
$204$		0			0
$205$	385.138			1.87872
$206$		0			0
$207$	15.4632	−	26.5784i	0.0747012	−	0.128398i
$208$		0			0
$209$	−125.805	+	254.530i	−0.601936	+	1.21785i
$210$		0			0
$211$	221.862			1.05148			0.525740	−	0.850645i	$-0.323788\pi$
$211$	221.862			1.05148			0.525740	+	0.850645i	$0.323788\pi$
$212$		0			0
$213$	−45.5194	−	171.018i	−0.213706	−	0.802903i
$214$		0			0
$215$	−178.630	+	103.132i	−0.830837	+	0.479684i
$216$		0			0
$217$	420.602			1.93826
$218$		0			0
$219$	−227.119	+	60.4515i	−1.03707	+	0.276034i
$220$		0			0
$221$	38.8556	−	22.4333i	0.175817	−	0.101508i
$222$		0			0
$223$	159.876	+	276.914i	0.716934	+	1.24177i	0.962209	+	0.272312i	$0.0877884\pi$
$223$	159.876	+	276.914i	0.716934	+	1.24177i	−0.245275	+	0.969454i	$0.578878\pi$
$224$		0			0
$225$	1.44145	−	433.230i	0.00640646	−	1.92547i
$226$		0			0
$227$	−150.571	−	86.9322i	−0.663308	−	0.382961i	0.130228	−	0.991484i	$-0.458429\pi$
$227$	−150.571	−	86.9322i	−0.663308	−	0.382961i	−0.793536	+	0.608523i	$0.791762\pi$
$228$		0			0
$229$	156.869	+	271.705i	0.685017	+	1.18648i	0.973432	+	0.228978i	$0.0735384\pi$
$229$	156.869	+	271.705i	0.685017	+	1.18648i	−0.288415	+	0.957506i	$0.593128\pi$
$230$		0			0
$231$	492.309	+	132.792i	2.13121	+	0.574857i
$232$		0			0
$233$	−41.0716	−	23.7127i	−0.176273	−	0.101771i	0.409268	−	0.912414i	$-0.365784\pi$
$233$	−41.0716	−	23.7127i	−0.176273	−	0.101771i	−0.585540	+	0.810643i	$0.699118\pi$
$234$		0			0
$235$	−758.588			−3.22803
$236$		0			0
$237$	41.2670	−	152.992i	0.174122	−	0.645536i
$238$		0			0
$239$	−15.4509	+	8.92060i	−0.0646483	+	0.0373247i	−0.531976	−	0.846760i	$-0.678550\pi$
$239$	−15.4509	+	8.92060i	−0.0646483	+	0.0373247i	0.467327	+	0.884084i	$0.345217\pi$
$240$		0			0
$241$	248.187			1.02982			0.514912	−	0.857243i	$-0.327825\pi$
$241$	248.187			1.02982			0.514912	+	0.857243i	$0.327825\pi$
$242$		0			0
$243$	170.392	+	173.250i	0.701201	+	0.712964i
$244$		0			0
$245$	595.255	−	343.671i	2.42961	−	1.40274i
$246$		0			0
$247$	−28.8659	−	14.2674i	−0.116866	−	0.0577626i
$248$		0			0
$249$	53.8256	+	202.225i	0.216167	+	0.812148i
$250$		0			0
$251$	−172.100	+	99.3621i	−0.685658	+	0.395865i	−0.801984	−	0.597346i	$-0.796222\pi$
$251$	−172.100	+	99.3621i	−0.685658	+	0.395865i	0.116325	+	0.993211i	$0.462889\pi$
$252$		0			0
$253$	−25.5276	−	44.2150i	−0.100899	−	0.174763i
$254$		0			0
$255$	−656.382	+	174.707i	−2.57405	+	0.685126i
$256$		0			0
$257$	−279.705	−	161.488i	−1.08835	−	0.628357i	−0.155210	−	0.987881i	$-0.549605\pi$
$257$	−279.705	−	161.488i	−1.08835	−	0.628357i	−0.933135	+	0.359525i	$0.882939\pi$
$258$		0			0
$259$	−316.970	+	549.008i	−1.22382	+	2.11972i
$260$		0			0
$261$	99.5202	+	0.331126i	0.381304	+	0.00126868i
$262$		0			0
$263$	−281.674	+	162.624i	−1.07100	+	0.618343i	−0.928455	−	0.371445i	$-0.878863\pi$
$263$	−281.674	+	162.624i	−1.07100	+	0.618343i	−0.142547	+	0.989788i	$0.545529\pi$
$264$		0			0
$265$	−246.773	−	427.423i	−0.931219	−	1.61292i
$266$		0			0
$267$	30.4487	+	8.21301i	0.114040	+	0.0307604i
$268$		0			0
$269$	−341.263	−	197.028i	−1.26864	−	0.732448i	−0.293907	−	0.955834i	$-0.594956\pi$
$269$	−341.263	−	197.028i	−1.26864	−	0.732448i	−0.974730	+	0.223386i	$0.928289\pi$
$270$		0			0
$271$	31.9450	−	55.3304i	0.117878	−	0.204171i	−0.801048	−	0.598600i	$-0.795724\pi$
$271$	31.9450	−	55.3304i	0.117878	−	0.204171i	0.918927	+	0.394428i	$0.129057\pi$
$272$		0			0
$273$	−15.0598	+	55.8321i	−0.0551640	+	0.204513i
$274$		0			0
$275$	−622.954	−	359.663i	−2.26529	−	1.30787i
$276$		0			0
$277$	−99.8043	+	172.866i	−0.360304	+	0.624066i	−0.988011	−	0.154385i	$-0.950661\pi$
$277$	−99.8043	+	172.866i	−0.360304	+	0.624066i	0.627706	+	0.778450i	$0.283994\pi$
$278$		0			0
$279$	288.773	−	165.444i	1.03503	−	0.592990i
$280$		0			0
$281$			388.747i			1.38344i	0.722166	+	0.691720i	$0.243147\pi$
$281$			388.747i			1.38344i	−0.722166	+	0.691720i	$0.756853\pi$
$282$		0			0
$283$	431.751			1.52562			0.762811	−	0.646621i	$-0.223819\pi$
$283$	431.751			1.52562			0.762811	+	0.646621i	$0.223819\pi$
$284$		0			0
$285$	365.671	+	322.346i	1.28306	+	1.13104i
$286$		0			0
$287$	443.607	+	256.116i	1.54567	+	0.892392i
$288$		0			0
$289$	205.953	+	356.721i	0.712640	+	1.23433i
$290$		0			0
$291$	−64.7042	+	239.882i	−0.222351	+	0.824338i
$292$		0			0
$293$	329.972	−	190.510i	1.12618	−	0.650203i	0.183212	−	0.983073i	$-0.441350\pi$
$293$	329.972	−	190.510i	1.12618	−	0.650203i	0.942973	+	0.332870i	$0.108017\pi$
$294$		0			0
$295$	201.646			0.683545
$296$		0			0
$297$	390.238	−	102.479i	1.31393	−	0.345048i
$298$		0			0
$299$	5.01437	−	2.89505i	0.0167705	−	0.00968244i
$300$		0			0
$301$	−274.331			−0.911399
$302$		0			0
$303$	129.342	−	128.912i	0.426870	−	0.425452i
$304$		0			0
$305$			276.716i			0.907265i
$306$		0			0
$307$	−201.382	+	348.804i	−0.655968	+	1.13617i	0.325682	+	0.945479i	$0.394406\pi$
$307$	−201.382	+	348.804i	−0.655968	+	1.13617i	−0.981650	+	0.190690i	$0.938927\pi$
$308$		0			0
$309$	−99.9050	+	370.385i	−0.323317	+	1.19866i
$310$		0			0
$311$	−6.94866	+	4.01181i	−0.0223430	+	0.0128997i	−0.511130	−	0.859503i	$-0.670773\pi$
$311$	−6.94866	+	4.01181i	−0.0223430	+	0.0128997i	0.488787	+	0.872403i	$0.337440\pi$
$312$		0			0
$313$	481.944			1.53976			0.769879	−	0.638190i	$-0.220317\pi$
$313$	481.944			1.53976			0.769879	+	0.638190i	$0.220317\pi$
$314$		0			0
$315$	440.245	−	756.701i	1.39760	−	2.40222i
$316$		0			0
$317$			5.80886i			0.0183245i	0.999958	+	0.00916225i	$0.00291647\pi$
$317$			5.80886i			0.0183245i	−0.999958	+	0.00916225i	$0.997084\pi$
$318$		0			0
$319$	82.6206	−	143.103i	0.258999	−	0.448599i
$320$		0			0
$321$	15.4528	−	15.4015i	0.0481397	−	0.0479798i
$322$		0			0
$323$	222.884	−	450.943i	0.690045	−	1.39611i
$324$		0			0
$325$	40.7889	−	70.6485i	0.125504	−	0.217380i
$326$		0			0
$327$	−336.065	+	89.4495i	−1.02772	+	0.273546i
$328$		0			0
$329$	−873.751	−	504.461i	−2.65578	−	1.53331i
$330$		0			0
$331$	190.031	−	329.143i	0.574110	−	0.994388i	−0.422027	−	0.906583i	$-0.638681\pi$
$331$	190.031	−	329.143i	0.574110	−	0.994388i	0.996138	−	0.0878052i	$-0.0279853\pi$
$332$		0			0
$333$	−1.66898	+	501.612i	−0.00501194	+	1.50634i
$334$		0			0
$335$	−423.761	−	244.659i	−1.26496	−	0.730324i
$336$		0			0
$337$	−91.0767			−0.270257			−0.135129	−	0.990828i	$-0.543145\pi$
$337$	−91.0767			−0.270257			−0.135129	+	0.990828i	$0.543145\pi$
$338$		0			0
$339$	544.939	+	146.988i	1.60749	+	0.433593i
$340$		0			0
$341$		−	552.585i		−	1.62048i
$342$		0			0
$343$	356.829			1.04032
$344$		0			0
$345$	−84.7069	+	22.5462i	−0.245527	+	0.0653512i
$346$		0			0
$347$			515.909i			1.48677i	0.668863	+	0.743385i	$0.266781\pi$
$347$			515.909i			1.48677i	−0.668863	+	0.743385i	$0.733219\pi$
$348$		0			0
$349$	−83.2922	+	144.266i	−0.238660	+	0.413371i	−0.960330	−	0.278866i	$-0.910041\pi$
$349$	−83.2922	+	144.266i	−0.238660	+	0.413371i	0.721670	+	0.692237i	$0.243375\pi$
$350$		0			0
$351$	11.6220	+	44.2564i	0.0331112	+	0.126087i
$352$		0			0
$353$	−323.433	−	186.734i	−0.916241	−	0.528992i	−0.0338071	−	0.999428i	$-0.510763\pi$
$353$	−323.433	−	186.734i	−0.916241	−	0.528992i	−0.882434	+	0.470436i	$0.844097\pi$
$354$		0			0
$355$	−252.245	+	436.902i	−0.710550	+	1.23071i
$356$		0			0
$357$	−872.209	−	235.264i	−2.44316	−	0.659002i
$358$		0			0
$359$	−425.053	−	245.405i	−1.18399	−	0.683578i	−0.227058	−	0.973881i	$-0.572911\pi$
$359$	−425.053	−	245.405i	−1.18399	−	0.683578i	−0.956935	+	0.290303i	$0.906244\pi$
$360$		0			0
$361$	−357.996	+	46.4766i	−0.991678	+	0.128744i
$362$		0			0
$363$	79.9267	−	296.318i	0.220184	−	0.816302i
$364$		0			0
$365$	580.222	+	334.991i	1.58965	+	0.917785i
$366$		0			0
$367$	582.904			1.58829			0.794147	−	0.607726i	$-0.207918\pi$
$367$	582.904			1.58829			0.794147	+	0.607726i	$0.207918\pi$
$368$		0			0
$369$	405.310	+	1.34856i	1.09840	+	0.00365463i
$370$		0			0
$371$		−	656.416i		−	1.76932i
$372$		0			0
$373$	−230.863	−	399.867i	−0.618936	−	1.07203i	−0.989680	−	0.143293i	$-0.954231\pi$
$373$	−230.863	−	399.867i	−0.618936	−	1.07203i	0.370744	−	0.928735i	$-0.379103\pi$
$374$		0			0
$375$	−420.439	+	419.042i	−1.12117	+	1.11745i
$376$		0			0
$377$	16.2291	+	9.36989i	0.0430481	+	0.0248538i
$378$		0			0
$379$	117.960			0.311240			0.155620	−	0.987817i	$-0.450262\pi$
$379$	117.960			0.311240			0.155620	+	0.987817i	$0.450262\pi$
$380$		0			0
$381$	82.0790	−	304.297i	0.215430	−	0.798680i
$382$		0			0
$383$		−	532.359i		−	1.38997i	−0.719024	−	0.694986i	$-0.755411\pi$
$383$		−	532.359i		−	1.38997i	0.719024	−	0.694986i	$-0.244589\pi$
$384$		0			0
$385$	−726.784	−	1258.83i	−1.88775	−	3.26968i
$386$		0			0
$387$	−188.347	+	107.908i	−0.486686	+	0.278833i
$388$		0			0
$389$		−	204.479i		−	0.525653i	−0.964843	−	0.262826i	$-0.915345\pi$
$389$		−	204.479i		−	0.525653i	0.964843	−	0.262826i	$-0.0846546\pi$
$390$		0			0
$391$	45.2264	+	78.3345i	0.115669	+	0.200344i
$392$		0			0
$393$	−66.4304	+	66.2097i	−0.169034	+	0.168473i
$394$		0			0
$395$	−391.198	+	225.858i	−0.990375	+	0.571793i
$396$		0			0
$397$	139.246	−	241.180i	0.350745	−	0.607508i	−0.635635	−	0.771989i	$-0.719262\pi$
$397$	139.246	−	241.180i	0.350745	−	0.607508i	0.986380	+	0.164482i	$0.0525952\pi$
$398$		0			0
$399$	206.825	+	614.453i	0.518357	+	1.53998i
$400$		0			0
$401$			792.290i			1.97579i	0.155139	+	0.987893i	$0.450417\pi$
$401$			792.290i			1.97579i	−0.155139	+	0.987893i	$0.549583\pi$
$402$		0			0
$403$	62.6679			0.155504
$404$		0			0
$405$	4.60957	−	692.698i	0.0113817	−	1.71037i
$406$		0			0
$407$	721.283	+	416.433i	1.77219	+	1.02318i
$408$		0			0
$409$	−340.011	+	588.917i	−0.831324	+	1.43989i	0.0656652	+	0.997842i	$0.479083\pi$
$409$	−340.011	+	588.917i	−0.831324	+	1.43989i	−0.896989	+	0.442053i	$0.854250\pi$
$410$		0			0
$411$	98.3940	−	98.0672i	0.239401	−	0.238606i
$412$		0			0
$413$	232.258	+	134.094i	0.562369	+	0.324684i
$414$		0			0
$415$	298.274	−	516.625i	0.718732	−	1.24488i
$416$		0			0
$417$	−45.6766	+	12.1576i	−0.109536	+	0.0291549i
$418$		0			0
$419$	−53.3836	+	30.8210i	−0.127407	+	0.0735586i	−0.562349	−	0.826900i	$-0.690102\pi$
$419$	−53.3836	+	30.8210i	−0.127407	+	0.0735586i	0.434942	+	0.900459i	$0.356769\pi$
$420$		0			0
$421$	223.104	+	386.427i	0.529938	+	0.917880i	0.999390	+	0.0349216i	$0.0111182\pi$
$421$	223.104	+	386.427i	0.529938	+	0.917880i	−0.469452	+	0.882958i	$0.655549\pi$
$422$		0			0
$423$	−798.321	−	2.65619i	−1.88728	−	0.00627941i
$424$		0			0
$425$	1103.67	+	637.204i	2.59687	+	1.49930i
$426$		0			0
$427$	−184.016	+	318.725i	−0.430951	+	0.746428i
$428$		0			0
$429$	73.3519	+	19.7854i	0.170983	+	0.0461199i
$430$		0			0
$431$	−43.4486	+	25.0851i	−0.100809	+	0.0582020i	−0.549557	−	0.835456i	$-0.685203\pi$
$431$	−43.4486	+	25.0851i	−0.100809	+	0.0582020i	0.448748	+	0.893658i	$0.351870\pi$
$432$		0			0
$433$	−281.978	−	488.400i	−0.651219	−	1.12794i	−0.982827	−	0.184527i	$-0.940925\pi$
$433$	−281.978	−	488.400i	−0.651219	−	1.12794i	0.331609	−	0.943417i	$-0.392409\pi$
$434$		0			0
$435$	−200.273	−	200.940i	−0.460398	−	0.461932i
$436$		0			0
$437$	28.7635	−	58.1948i	0.0658205	−	0.133169i
$438$		0			0
$439$	208.341	+	360.857i	0.474581	+	0.821998i	0.999576	−	0.0291067i	$-0.00926627\pi$
$439$	208.341	+	360.857i	0.474581	+	0.821998i	−0.524995	+	0.851105i	$0.675933\pi$
$440$		0			0
$441$	627.637	−	359.587i	1.42321	−	0.815390i
$442$		0			0
$443$			331.474i			0.748249i	0.927378	+	0.374125i	$0.122057\pi$
$443$			331.474i			0.748249i	−0.927378	+	0.374125i	$0.877943\pi$
$444$		0			0
$445$	−44.9507	−	77.8568i	−0.101013	−	0.174959i
$446$		0			0
$447$	−552.226	+	550.391i	−1.23540	+	1.23130i
$448$		0			0
$449$		−	482.323i		−	1.07422i	−0.843513	−	0.537108i	$-0.819517\pi$
$449$		−	482.323i		−	1.07422i	0.843513	−	0.537108i	$-0.180483\pi$
$450$		0			0
$451$	336.484	−	582.807i	0.746084	−	1.29226i
$452$		0			0
$453$	−323.525	+	86.1116i	−0.714183	+	0.190092i
$454$		0			0
$455$	142.762	−	82.4237i	0.313763	−	0.181151i
$456$		0			0
$457$	−164.410	+	284.767i	−0.359760	+	0.623122i	−0.987921	−	0.154961i	$-0.950475\pi$
$457$	−164.410	+	284.767i	−0.359760	+	0.623122i	0.628161	+	0.778084i	$0.283808\pi$
$458$		0			0
$459$	−691.373	+	181.560i	−1.50626	+	0.395554i
$460$		0			0
$461$	−84.5382	+	48.8081i	−0.183380	+	0.105874i	−0.588880	−	0.808221i	$-0.700431\pi$
$461$	−84.5382	+	48.8081i	−0.183380	+	0.105874i	0.405500	+	0.914095i	$0.367098\pi$
$462$		0			0
$463$	460.726	+	798.001i	0.995089	+	1.72354i	0.583270	+	0.812278i	$0.301773\pi$
$463$	460.726	+	798.001i	0.995089	+	1.72354i	0.411818	+	0.911266i	$0.364894\pi$
$464$		0			0
$465$	−915.991	−	247.073i	−1.96987	−	0.531340i
$466$		0			0
$467$		−	483.678i		−	1.03571i	−0.855467	−	0.517857i	$-0.826730\pi$
$467$		−	483.678i		−	1.03571i	0.855467	−	0.517857i	$-0.173270\pi$
$468$		0			0
$469$	−325.396	−	563.602i	−0.693808	−	1.20171i
$470$		0			0
$471$	−147.468	−	147.959i	−0.313095	−	0.314139i
$472$		0			0
$473$			360.414i			0.761976i
$474$		0			0
$475$	−58.9977	−	912.698i	−0.124206	−	1.92147i
$476$		0			0
$477$	−258.202	−	450.675i	−0.541304	−	0.944811i
$478$		0			0
$479$			722.222i			1.50777i	0.657006	+	0.753886i	$0.271823\pi$
$479$			722.222i			1.50777i	−0.657006	+	0.753886i	$0.728177\pi$
$480$		0			0
$481$	−47.2271	+	81.7998i	−0.0981853	+	0.170062i
$482$		0			0
$483$	−112.560	−	30.3611i	−0.233043	−	0.0628594i
$484$		0			0
$485$	613.376	−	354.133i	1.26469	−	0.730170i
$486$		0			0
$487$	−461.951			−0.948564			−0.474282	−	0.880373i	$-0.657292\pi$
$487$	−461.951			−0.948564			−0.474282	+	0.880373i	$0.657292\pi$
$488$		0			0
$489$	426.645	+	428.067i	0.872485	+	0.875393i
$490$		0			0
$491$			372.061i			0.757761i	0.925446	+	0.378881i	$0.123691\pi$
$491$			372.061i			0.757761i	−0.925446	+	0.378881i	$0.876309\pi$
$492$		0			0
$493$	−146.376	+	253.531i	−0.296910	+	0.514262i
$494$		0			0
$495$	−994.148	−	578.391i	−2.00838	−	1.16847i
$496$		0			0
$497$	−581.079	+	335.486i	−1.16917	+	0.675022i
$498$		0			0
$499$	−500.410			−1.00283			−0.501413	−	0.865208i	$-0.667186\pi$
$499$	−500.410			−1.00283			−0.501413	+	0.865208i	$0.667186\pi$
$500$		0			0
$501$	−77.9920	−	293.019i	−0.155673	−	0.584869i
$502$		0			0
$503$	−427.105	+	246.589i	−0.849115	+	0.490237i	−0.860352	−	0.509700i	$-0.829756\pi$
$503$	−427.105	+	246.589i	−0.849115	+	0.490237i	0.0112372	+	0.999937i	$0.496423\pi$
$504$		0			0
$505$	−520.571			−1.03083
$506$		0			0
$507$	129.792	−	481.187i	0.256000	−	0.949086i
$508$		0			0
$509$	−236.316	−	136.437i	−0.464275	−	0.268049i	0.249565	−	0.968358i	$-0.419712\pi$
$509$	−236.316	−	136.437i	−0.464275	−	0.268049i	−0.713840	+	0.700309i	$0.753046\pi$
$510$		0			0
$511$	445.538	+	771.695i	0.871895	+	1.51017i
$512$		0			0
$513$	383.695	+	340.510i	0.747944	+	0.663762i
$514$		0			0
$515$	947.068	−	546.790i	1.83897	−	1.06173i
$516$		0			0
$517$	−662.757	+	1147.93i	−1.28193	+	2.22036i
$518$		0			0
$519$	454.218	+	122.518i	0.875180	+	0.236065i
$520$		0			0
$521$			355.563i			0.682463i	0.939979	+	0.341231i	$0.110844\pi$
$521$			355.563i			0.682463i	−0.939979	+	0.341231i	$0.889156\pi$
$522$		0			0
$523$	−13.8818	−	24.0441i	−0.0265427	−	0.0459734i	0.852449	−	0.522811i	$-0.175116\pi$
$523$	−13.8818	−	24.0441i	−0.0265427	−	0.0459734i	−0.878992	+	0.476837i	$0.841783\pi$
$524$		0			0
$525$	−1587.29	+	422.484i	−3.02341	+	0.804732i
$526$		0			0
$527$			978.998i			1.85768i
$528$		0			0
$529$	−258.663	−	448.018i	−0.488967	−	0.846915i
$530$		0			0
$531$	212.207	+	0.706061i	0.399637	+	0.00132968i
$532$		0			0
$533$	66.0955	+	38.1602i	0.124006	+	0.0715952i
$534$		0			0
$535$	−62.1941			−0.116251
$536$		0			0
$537$	449.475	−	447.982i	0.837011	−	0.834230i
$538$		0			0
$539$		−	1201.02i		−	2.22824i
$540$		0			0
$541$	312.904	+	541.966i	0.578381	+	1.00178i	0.995665	+	0.0930090i	$0.0296485\pi$
$541$	312.904	+	541.966i	0.578381	+	1.00178i	−0.417284	+	0.908776i	$0.637018\pi$
$542$		0			0
$543$	−234.326	+	868.734i	−0.431540	+	1.59988i
$544$		0			0
$545$	858.548	+	495.683i	1.57532	+	0.909510i
$546$		0			0
$547$	−799.520			−1.46165			−0.730823	−	0.682567i	$-0.760863\pi$
$547$	−799.520			−1.46165			−0.730823	+	0.682567i	$0.760863\pi$
$548$		0			0
$549$	−0.968918	+	291.209i	−0.00176488	+	0.530436i
$550$		0			0
$551$	209.662	−	13.5528i	0.380511	−	0.0245967i
$552$		0			0
$553$	−600.783			−1.08641
$554$		0			0
$555$	1012.80	−	1009.44i	1.82487	−	1.81881i
$556$		0			0
$557$	418.721	−	241.749i	0.751744	−	0.434019i	−0.0745799	−	0.997215i	$-0.523762\pi$
$557$	418.721	−	241.749i	0.751744	−	0.434019i	0.826324	+	0.563196i	$0.190428\pi$
$558$		0			0
$559$	−40.8741			−0.0731201
$560$		0			0
$561$	−309.088	+	1145.90i	−0.550959	+	2.04261i
$562$		0			0
$563$	−487.316	+	281.352i	−0.865571	+	0.499738i	−0.865874	−	0.500262i	$-0.833237\pi$
$563$	−487.316	+	281.352i	−0.865571	+	0.499738i	0.000302975		1.00000i	$0.499904\pi$
$564$		0			0
$565$	−804.480	−	1393.40i	−1.42386	−	2.46620i
$566$		0			0
$567$	465.953	−	794.793i	0.821787	−	1.40175i
$568$		0			0
$569$	104.072	+	60.0860i	0.182903	+	0.105599i	0.588656	−	0.808384i	$-0.299657\pi$
$569$	104.072	+	60.0860i	0.182903	+	0.105599i	−0.405753	+	0.913983i	$0.632991\pi$
$570$		0			0
$571$	−29.2018	−	50.5790i	−0.0511415	−	0.0885797i	0.839321	−	0.543636i	$-0.182953\pi$
$571$	−29.2018	−	50.5790i	−0.0511415	−	0.0885797i	−0.890463	+	0.455056i	$0.849619\pi$
$572$		0			0
$573$	2.62517	+	9.86286i	0.00458144	+	0.0172127i
$574$		0			0
$575$	142.430	+	82.2321i	0.247705	+	0.143012i
$576$		0			0
$577$	−370.132			−0.641477			−0.320739	−	0.947168i	$-0.603931\pi$
$577$	−370.132			−0.641477			−0.320739	+	0.947168i	$0.603931\pi$
$578$		0			0
$579$	249.831	+	250.664i	0.431488	+	0.432926i
$580$		0			0
$581$	687.111	−	396.704i	1.18264	−	0.682795i
$582$		0			0
$583$	−862.395			−1.47924
$584$		0			0
$585$	65.5945	−	112.745i	0.112127	−	0.192727i
$586$		0			0
$587$	621.065	−	358.572i	1.05803	−	0.610855i	0.133145	−	0.991097i	$-0.457492\pi$
$587$	621.065	−	358.572i	1.05803	−	0.610855i	0.924887	+	0.380241i	$0.124159\pi$
$588$		0			0
$589$	584.537	−	389.816i	0.992424	−	0.661827i
$590$		0			0
$591$	450.073	−	448.578i	0.761546	−	0.759016i
$592$		0			0
$593$	242.517	−	140.017i	0.408966	−	0.236116i	−0.281380	−	0.959597i	$-0.590792\pi$
$593$	242.517	−	140.017i	0.408966	−	0.236116i	0.690345	+	0.723480i	$0.257459\pi$
$594$		0			0
$595$	1287.62	+	2230.23i	2.16407	+	3.74828i
$596$		0			0
$597$	27.2259	−	100.936i	0.0456045	−	0.169073i
$598$		0			0
$599$	−264.415	−	152.660i	−0.441428	−	0.254859i	0.262775	−	0.964857i	$-0.415362\pi$
$599$	−264.415	−	152.660i	−0.441428	−	0.254859i	−0.704203	+	0.709999i	$0.748696\pi$
$600$		0			0
$601$	−88.1717	+	152.718i	−0.146708	+	0.254106i	−0.930009	−	0.367537i	$-0.880201\pi$
$601$	−88.1717	+	152.718i	−0.146708	+	0.254106i	0.783301	+	0.621643i	$0.213535\pi$
$602$		0			0
$603$	−445.100	−	258.957i	−0.738143	−	0.429448i
$604$		0			0
$605$	−757.680	+	437.447i	−1.25236	+	0.723053i
$606$		0			0
$607$	−180.879	−	313.292i	−0.297989	−	0.516132i	0.677687	−	0.735351i	$-0.262983\pi$
$607$	−180.879	−	313.292i	−0.297989	−	0.516132i	−0.975676	+	0.219219i	$0.929649\pi$
$608$		0			0
$609$	−97.0517	−	364.627i	−0.159362	−	0.598731i
$610$		0			0
$611$	−130.185	−	75.1624i	−0.213069	−	0.123015i
$612$		0			0
$613$	−27.3251	+	47.3285i	−0.0445760	+	0.0772080i	−0.887453	−	0.460899i	$-0.847527\pi$
$613$	−27.3251	+	47.3285i	−0.0445760	+	0.0772080i	0.842877	+	0.538107i	$0.180860\pi$
$614$		0			0
$615$	−815.640	−	818.358i	−1.32624	−	1.33066i
$616$		0			0
$617$	346.644	+	200.135i	0.561822	+	0.324368i	0.753876	−	0.657016i	$-0.228182\pi$
$617$	346.644	+	200.135i	0.561822	+	0.324368i	−0.192054	+	0.981384i	$0.561515\pi$
$618$		0			0
$619$	−379.887	+	657.984i	−0.613711	+	1.06298i	0.376898	+	0.926255i	$0.376991\pi$
$619$	−379.887	+	657.984i	−0.613711	+	1.06298i	−0.990609	+	0.136724i	$0.956343\pi$
$620$		0			0
$621$	−89.2226	+	23.4305i	−0.143676	+	0.0377303i
$622$		0			0
$623$		−	119.569i		−	0.191924i
$624$		0			0
$625$	488.744			0.781990
$626$		0			0
$627$	807.265	−	271.725i	1.28750	−	0.433373i
$628$		0			0
$629$	−1277.88	−	737.782i	−2.03160	−	1.17294i
$630$		0			0
$631$	−360.320	−	624.093i	−0.571030	−	0.989053i	−0.996461	−	0.0840620i	$-0.973211\pi$
$631$	−360.320	−	624.093i	−0.571030	−	0.989053i	0.425430	−	0.904991i	$-0.360123\pi$
$632$		0			0
$633$	−469.858	−	471.423i	−0.742271	−	0.744745i
$634$		0			0
$635$	−778.084	+	449.227i	−1.22533	+	0.707444i
$636$		0			0
$637$	136.206			0.213825
$638$		0			0
$639$	−266.987	+	458.902i	−0.417820	+	0.718157i
$640$		0			0
$641$	953.036	−	550.236i	1.48680	−	0.858402i	0.486909	−	0.873453i	$-0.338124\pi$
$641$	953.036	−	550.236i	1.48680	−	0.858402i	0.999887	+	0.0150504i	$0.00479087\pi$
$642$		0			0
$643$	993.537			1.54516			0.772579	−	0.634919i	$-0.218966\pi$
$643$	993.537			1.54516			0.772579	+	0.634919i	$0.218966\pi$
$644$		0			0
$645$	597.440	+	161.149i	0.926264	+	0.249844i
$646$		0			0
$647$		−	137.029i		−	0.211792i	−0.994377	−	0.105896i	$-0.966229\pi$
$647$		−	137.029i		−	0.211792i	0.994377	−	0.105896i	$-0.0337710\pi$
$648$		0			0
$649$	176.172	−	305.139i	0.271452	−	0.470168i
$650$		0			0
$651$	−890.747	−	893.716i	−1.36827	−	1.37284i
$652$		0			0
$653$	−747.785	+	431.734i	−1.14515	+	0.661155i	−0.947702	−	0.319158i	$-0.896600\pi$
$653$	−747.785	+	431.734i	−1.14515	+	0.661155i	−0.197452	+	0.980313i	$0.563267\pi$
$654$		0			0
$655$	267.367			0.408194
$656$		0			0
$657$	609.440	+	354.569i	0.927610	+	0.539679i
$658$		0			0
$659$			666.363i			1.01117i	0.862776	+	0.505587i	$0.168724\pi$
$659$			666.363i			1.01117i	−0.862776	+	0.505587i	$0.831276\pi$
$660$		0			0
$661$	−192.637	+	333.657i	−0.291433	+	0.504776i	−0.974149	−	0.225907i	$-0.927465\pi$
$661$	−192.637	+	333.657i	−0.291433	+	0.504776i	0.682716	+	0.730684i	$0.260799\pi$
$662$		0			0
$663$	−129.955	−	35.0532i	−0.196011	−	0.0528707i
$664$		0			0
$665$	818.914	−	1656.84i	1.23145	−	2.49149i
$666$		0			0
$667$	−18.8901	+	32.7186i	−0.0283209	+	0.0490533i
$668$		0			0
$669$	249.815	−	926.157i	0.373416	−	1.38439i
$670$		0			0
$671$	418.739	+	241.759i	0.624051	+	0.360296i
$672$		0			0
$673$	−536.452	+	929.163i	−0.797106	+	1.38063i	0.124387	+	0.992234i	$0.460304\pi$
$673$	−536.452	+	929.163i	−0.797106	+	1.38063i	−0.921493	+	0.388395i	$0.873030\pi$
$674$		0			0
$675$	−923.601	+	914.427i	−1.36830	+	1.35471i
$676$		0			0
$677$	331.840	+	191.588i	0.490162	+	0.282995i	0.724642	−	0.689126i	$-0.242005\pi$
$677$	331.840	+	191.588i	0.490162	+	0.282995i	−0.234479	+	0.972121i	$0.575339\pi$
$678$		0			0
$679$	941.992			1.38732
$680$		0			0
$681$	134.160	+	504.044i	0.197004	+	0.740153i
$682$		0			0
$683$		−	951.204i		−	1.39269i	−0.717710	−	0.696343i	$-0.754809\pi$
$683$		−	951.204i		−	1.39269i	0.717710	−	0.696343i	$-0.245191\pi$
$684$		0			0
$685$	−396.013			−0.578121
$686$		0			0
$687$	245.116	−	908.735i	0.356792	−	1.32276i
$688$		0			0
$689$		−	97.8031i		−	0.141949i
$690$		0			0
$691$	−324.517	+	562.080i	−0.469634	+	0.813430i	−0.999397	−	0.0347159i	$-0.988947\pi$
$691$	−324.517	+	562.080i	−0.469634	+	0.813430i	0.529763	+	0.848145i	$0.322281\pi$
$692$		0			0
$693$	−760.444	−	1327.31i	−1.09732	−	1.91530i
$694$		0			0
$695$	116.690	+	67.3712i	0.167900	+	0.0969370i
$696$		0			0
$697$	−596.139	+	1032.54i	−0.855293	+	1.48141i
$698$		0			0
$699$	36.5951	+	137.489i	0.0523535	+	0.196694i
$700$		0			0
$701$	−96.5605	−	55.7493i	−0.137747	−	0.0795282i	0.429543	−	0.903046i	$-0.358675\pi$
$701$	−96.5605	−	55.7493i	−0.137747	−	0.0795282i	−0.567290	+	0.823518i	$0.692008\pi$
$702$		0			0
$703$	68.3101	+	1056.76i	0.0971693	+	1.50321i
$704$		0			0
$705$	1606.53	+	1611.88i	2.27876	+	2.28636i
$706$		0			0
$707$	−599.600	−	346.179i	−0.848091	−	0.489645i
$708$		0			0
$709$	134.935			0.190317			0.0951587	−	0.995462i	$-0.469664\pi$
$709$	134.935			0.190317			0.0951587	+	0.995462i	$0.469664\pi$
$710$		0			0
$711$	−412.479	+	236.319i	−0.580139	+	0.332375i
$712$		0			0
$713$			126.341i			0.177196i
$714$		0			0
$715$	−108.288	−	187.560i	−0.151451	−	0.262321i
$716$		0			0
$717$	51.6767	+	13.9389i	0.0720735	+	0.0194406i
$718$		0			0
$719$	1049.29	+	605.806i	1.45937	+	0.842568i	0.998980	−	0.0451490i	$-0.0143762\pi$
$719$	1049.29	+	605.806i	1.45937	+	0.842568i	0.460390	+	0.887717i	$0.347710\pi$
$720$		0			0
$721$	1454.46			2.01728
$722$		0			0
$723$	−525.609	−	527.360i	−0.726983	−	0.729406i
$724$		0			0
$725$			532.292i			0.734196i
$726$		0			0
$727$	−420.993	−	729.182i	−0.579083	−	1.00300i	−0.995585	−	0.0938662i	$-0.970077\pi$
$727$	−420.993	−	729.182i	−0.579083	−	1.00300i	0.416502	−	0.909135i	$-0.363256\pi$
$728$		0			0
$729$	7.27648	−	728.964i	0.00998146	−	0.999950i
$730$		0			0
$731$		−	638.536i		−	0.873510i
$732$		0			0
$733$	−240.487	−	416.537i	−0.328087	−	0.568263i	0.654046	−	0.756455i	$-0.273070\pi$
$733$	−240.487	−	416.537i	−0.328087	−	0.568263i	−0.982132	+	0.188193i	$0.939737\pi$
$734$		0			0
$735$	−1990.87	−	537.004i	−2.70867	−	0.730618i
$736$		0			0
$737$	−740.456	+	427.503i	−1.00469	+	0.580058i
$738$		0			0
$739$	−456.243	+	790.237i	−0.617380	+	1.06933i	0.372582	+	0.927999i	$0.378472\pi$
$739$	−456.243	+	790.237i	−0.617380	+	1.06933i	−0.989962	+	0.141334i	$0.954861\pi$
$740$		0			0
$741$	30.8159	+	91.5508i	0.0415870	+	0.123550i
$742$		0			0
$743$		−	1221.65i		−	1.64422i	−0.569332	−	0.822108i	$-0.692798\pi$
$743$		−	1221.65i		−	1.64422i	0.569332	−	0.822108i	$-0.307202\pi$
$744$		0			0
$745$	2222.58			2.98333
$746$		0			0
$747$	315.706	−	542.640i	0.422631	−	0.726426i
$748$		0			0
$749$	−71.6360	−	41.3591i	−0.0956422	−	0.0552191i
$750$		0			0
$751$	−159.165	+	275.682i	−0.211938	+	0.367087i	−0.952321	−	0.305098i	$-0.901311\pi$
$751$	−159.165	+	275.682i	−0.211938	+	0.367087i	0.740383	+	0.672185i	$0.234644\pi$
$752$		0			0
$753$	575.601	+	155.259i	0.764411	+	0.206187i
$754$		0			0
$755$	826.512	+	477.187i	1.09472	+	0.632035i
$756$		0			0
$757$	162.381	−	281.252i	0.214506	−	0.371535i	−0.738614	−	0.674129i	$-0.764519\pi$
$757$	162.381	−	281.252i	0.214506	−	0.371535i	0.953120	+	0.302594i	$0.0978525\pi$
$758$		0			0
$759$	−39.8882	+	147.880i	−0.0525536	+	0.194836i
$760$		0			0
$761$	380.041	−	219.417i	0.499397	−	0.288327i	−0.229068	−	0.973410i	$-0.573568\pi$
$761$	380.041	−	219.417i	0.499397	−	0.288327i	0.728464	+	0.685084i	$0.240234\pi$
$762$		0			0
$763$	659.258	+	1141.87i	0.864034	+	1.49655i
$764$		0			0
$765$	1761.30	+	1024.72i	2.30236	+	1.33950i
$766$		0			0
$767$	34.6055	+	19.9795i	0.0451179	+	0.0260488i
$768$		0			0
$769$	411.909	−	713.448i	0.535643	−	0.927761i	−0.463489	−	0.886103i	$-0.653403\pi$
$769$	411.909	−	713.448i	0.535643	−	0.927761i	0.999132	−	0.0416581i	$-0.0132640\pi$
$770$		0			0
$771$	249.219	+	936.326i	0.323241	+	1.21443i
$772$		0			0
$773$	−269.588	+	155.647i	−0.348756	+	0.201354i	−0.664137	−	0.747611i	$-0.731201\pi$
$773$	−269.588	+	155.647i	−0.348756	+	0.201354i	0.315381	+	0.948965i	$0.397868\pi$
$774$		0			0
$775$	890.022	+	1541.56i	1.14842	+	1.98911i
$776$		0			0
$777$	1837.83	−	489.170i	2.36529	−	0.629563i
$778$		0			0
$779$	853.878	−	55.1955i	1.09612	−	0.0708543i
$780$		0			0
$781$	440.759	+	763.418i	0.564353	+	0.977488i
$782$		0			0
$783$	−210.059	−	212.166i	−0.268275	−	0.270966i
$784$		0			0
$785$			595.502i			0.758601i
$786$		0			0
$787$	405.386	+	702.149i	0.515103	+	0.892184i	0.999846	+	0.0175280i	$0.00557962\pi$
$787$	405.386	+	702.149i	0.515103	+	0.892184i	−0.484743	+	0.874656i	$0.661087\pi$
$788$		0			0
$789$	942.077	+	254.109i	1.19401	+	0.322065i
$790$		0			0
$791$		−	2139.92i		−	2.70533i
$792$		0			0
$793$	−27.4176	+	47.4886i	−0.0345745	+	0.0598847i
$794$		0			0
$795$	−385.596	+	1429.55i	−0.485027	+	1.79817i
$796$		0			0
$797$	−1228.55	+	709.305i	−1.54147	+	0.889968i	−0.542724	+	0.839911i	$0.682607\pi$
$797$	−1228.55	+	709.305i	−1.54147	+	0.889968i	−0.998746	+	0.0500570i	$0.984060\pi$
$798$		0			0
$799$	1174.19	−	2033.75i	1.46957	−	2.54537i
$800$		0			0
$801$	−47.0325	−	82.0922i	−0.0587172	−	0.102487i
$802$		0			0
$803$	1013.85	−	585.345i	1.26258	−	0.728948i
$804$		0			0
$805$	166.169	+	287.814i	0.206422	+	0.357533i
$806$		0			0
$807$	304.068	+	1142.40i	0.376788	+	1.41561i
$808$		0			0
$809$			158.566i			0.196002i	0.995186	+	0.0980012i	$0.0312449\pi$
$809$			158.566i			0.196002i	−0.995186	+	0.0980012i	$0.968755\pi$
$810$		0			0
$811$	283.176	+	490.475i	0.349169	+	0.604779i	0.986102	−	0.166141i	$-0.0531305\pi$
$811$	283.176	+	490.475i	0.349169	+	0.604779i	−0.636933	+	0.770919i	$0.719797\pi$
$812$		0			0
$813$	−185.222	+	49.2998i	−0.227825	+	0.0606394i
$814$		0			0
$815$		−	1722.87i		−	2.11395i
$816$		0			0
$817$	−381.255	+	254.251i	−0.466653	+	0.311201i
$818$		0			0
$819$	150.528	−	86.2409i	0.183795	−	0.105300i
$820$		0			0
$821$		−	584.175i		−	0.711541i	−0.934573	−	0.355770i	$-0.884218\pi$
$821$		−	584.175i		−	0.711541i	0.934573	−	0.355770i	$-0.115782\pi$
$822$		0			0
$823$	222.553	−	385.473i	0.270417	−	0.468376i	−0.698552	−	0.715559i	$-0.746172\pi$
$823$	222.553	−	385.473i	0.270417	−	0.468376i	0.968969	+	0.247184i	$0.0795052\pi$
$824$		0			0
$825$	555.057	+	2085.37i	0.672797	+	2.52772i
$826$		0			0
$827$	724.099	−	418.059i	0.875573	−	0.505512i	0.00637661	−	0.999980i	$-0.497970\pi$
$827$	724.099	−	418.059i	0.875573	−	0.505512i	0.869196	+	0.494468i	$0.164637\pi$
$828$		0			0
$829$	−445.954			−0.537942			−0.268971	−	0.963148i	$-0.586684\pi$
$829$	−445.954			−0.537942			−0.268971	+	0.963148i	$0.586684\pi$
$830$		0			0
$831$	578.678	−	154.025i	0.696364	−	0.185349i
$832$		0			0
$833$			2127.82i			2.55440i
$834$		0			0
$835$	−432.192	+	748.578i	−0.517595	+	0.896501i
$836$		0			0
$837$	−963.103	−	263.221i	−1.15066	−	0.314482i
$838$		0			0
$839$	−187.587	+	108.303i	−0.223583	+	0.129086i	−0.607608	−	0.794237i	$-0.707871\pi$
$839$	−187.587	+	108.303i	−0.223583	+	0.129086i	0.384025	+	0.923323i	$0.374538\pi$
$840$		0			0
$841$	718.724			0.854606
$842$		0			0
$843$	826.027	−	823.283i	0.979866	−	0.976611i
$844$		0			0
$845$	−1230.39	+	710.365i	−1.45608	+	0.840668i
$846$		0			0
$847$	−1163.61			−1.37380
$848$		0			0
$849$	−914.358	−	917.405i	−1.07698	−	1.08057i
$850$		0			0
$851$	−164.912	−	95.2118i	−0.193786	−	0.111882i
$852$		0			0
$853$	237.775	+	411.839i	0.278752	+	0.482812i	0.971075	−	0.238776i	$-0.0767461\pi$
$853$	237.775	+	411.839i	0.278752	+	0.482812i	−0.692323	+	0.721588i	$0.743413\pi$
$854$		0			0
$855$	−89.4777	−	1459.65i	−0.104652	−	1.70720i
$856$		0			0
$857$	−450.201	+	259.924i	−0.525322	+	0.303295i	−0.739109	−	0.673585i	$-0.764753\pi$
$857$	−450.201	+	259.924i	−0.525322	+	0.303295i	0.213787	+	0.976880i	$0.431420\pi$
$858$		0			0
$859$	217.791	−	377.224i	0.253540	−	0.439144i	−0.710958	−	0.703234i	$-0.751738\pi$
$859$	217.791	−	377.224i	0.253540	−	0.439144i	0.964498	+	0.264091i	$0.0850718\pi$
$860$		0			0
$861$	−395.257	−	1485.00i	−0.459067	−	1.72473i
$862$		0			0
$863$			817.640i			0.947440i	0.880676	+	0.473720i	$0.157089\pi$
$863$			817.640i			0.947440i	−0.880676	+	0.473720i	$0.842911\pi$
$864$		0			0
$865$	−670.552	−	1161.43i	−0.775204	−	1.34269i
$866$		0			0
$867$	321.813	−	1193.08i	0.371180	−	1.37610i
$868$		0			0
$869$			789.305i			0.908291i
$870$		0			0
$871$	−48.4825	−	83.9742i	−0.0556631	−	0.0964113i
$872$		0			0
$873$	646.743	−	370.533i	0.740828	−	0.424437i
$874$		0			0
$875$	1949.06	+	1125.29i	2.22750	+	1.28605i
$876$		0			0
$877$	−414.657			−0.472813			−0.236406	−	0.971654i	$-0.575970\pi$
$877$	−414.657			−0.472813			−0.236406	+	0.971654i	$0.575970\pi$
$878$		0			0
$879$	−1103.61	−	297.681i	−1.25553	−	0.338659i
$880$		0			0
$881$			1325.14i			1.50413i	0.659091	+	0.752064i	$0.270941\pi$
$881$			1325.14i			1.50413i	−0.659091	+	0.752064i	$0.729059\pi$
$882$		0			0
$883$	−368.791	−	638.765i	−0.417657	−	0.723403i	0.578046	−	0.816004i	$-0.303815\pi$
$883$	−368.791	−	638.765i	−0.417657	−	0.723403i	−0.995703	+	0.0926007i	$0.970482\pi$
$884$		0			0
$885$	−427.043	−	428.466i	−0.482534	−	0.484143i
$886$		0			0
$887$	1077.35	+	622.009i	1.21460	+	0.701251i	0.963758	−	0.266777i	$-0.0859588\pi$
$887$	1077.35	+	622.009i	1.21460	+	0.701251i	0.250843	+	0.968028i	$0.419292\pi$
$888$		0			0
$889$	−1194.94			−1.34414
$890$		0			0
$891$	−1044.19	−	612.166i	−1.17193	−	0.687055i
$892$		0			0
$893$	−1681.84	+	108.716i	−1.88336	+	0.121743i
$894$		0			0
$895$	−1809.03			−2.02126
$896$		0			0
$897$	−16.7709	−	4.52367i	−0.0186967	−	0.00504311i
$898$		0			0
$899$	−354.123	+	204.453i	−0.393907	+	0.227422i
$900$		0			0
$901$	1527.88			1.69576
$902$		0			0
$903$	580.975	+	582.912i	0.643384	+	0.645528i
$904$		0			0
$905$	2221.34	−	1282.49i	2.45452	−	1.41712i
$906$		0			0
$907$	−227.093	−	393.336i	−0.250378	−	0.433667i	0.713252	−	0.700908i	$-0.247222\pi$
$907$	−227.093	−	393.336i	−0.250378	−	0.433667i	−0.963630	+	0.267240i	$0.913888\pi$
$908$		0			0
$909$	−547.837	−	1.82277i	−0.602681	−	0.00200525i
$910$		0			0
$911$	−272.556	−	157.360i	−0.299183	−	0.172733i	0.342893	−	0.939375i	$-0.388593\pi$
$911$	−272.556	−	157.360i	−0.299183	−	0.172733i	−0.642076	+	0.766641i	$0.721927\pi$
$912$		0			0
$913$	−521.187	−	902.722i	−0.570851	−	0.988743i
$914$		0			0
$915$	587.978	−	586.025i	0.642599	−	0.640465i
$916$		0			0
$917$	307.957	+	177.799i	0.335831	+	0.193892i
$918$		0			0
$919$	1676.31			1.82406			0.912031	−	0.410122i	$-0.134514\pi$
$919$	1676.31			1.82406			0.912031	+	0.410122i	$0.134514\pi$
$920$		0			0
$921$	1167.64	−	310.787i	1.26780	−	0.337445i
$922$		0			0
$923$	−86.5782	+	49.9860i	−0.0938009	+	0.0541560i
$924$		0			0
$925$	−2682.92			−2.90045
$926$		0			0
$927$	998.588	−	572.114i	1.07723	−	0.617167i
$928$		0			0
$929$	120.834	−	69.7635i	0.130069	−	0.0750952i	−0.433554	−	0.901128i	$-0.642741\pi$
$929$	120.834	−	69.7635i	0.130069	−	0.0750952i	0.563623	+	0.826032i	$0.309407\pi$
$930$		0			0
$931$	1270.47	−	847.251i	1.36463	−	0.910044i
$932$		0			0
$933$	23.2403	+	6.26867i	0.0249092	+	0.00671883i
$934$		0			0
$935$	2930.06	−	1691.67i	3.13375	−	1.80927i
$936$		0			0
$937$	259.743	+	449.888i	0.277207	+	0.480137i	0.970690	−	0.240337i	$-0.0772578\pi$
$937$	259.743	+	449.888i	0.277207	+	0.480137i	−0.693482	+	0.720474i	$0.743924\pi$
$938$		0			0
$939$	−1020.66	−	1024.06i	−1.08696	−	1.09058i
$940$		0			0
$941$	509.957	+	294.424i	0.541931	+	0.312884i	0.745861	−	0.666101i	$-0.232038\pi$
$941$	509.957	+	294.424i	0.541931	+	0.312884i	−0.203930	+	0.978985i	$0.565372\pi$
$942$		0			0
$943$	−76.9325	+	133.251i	−0.0815827	+	0.141305i
$944$		0			0
$945$	−2540.22	+	667.079i	−2.68806	+	0.705904i
$946$		0			0
$947$	605.601	−	349.644i	0.639494	−	0.369212i	−0.144926	−	0.989443i	$-0.546294\pi$
$947$	605.601	−	349.644i	0.639494	−	0.369212i	0.784420	+	0.620230i	$0.212961\pi$
$948$		0			0
$949$	66.3833	+	114.979i	0.0699508	+	0.121158i
$950$		0			0
$951$	12.3429	−	12.3019i	0.0129789	−	0.0129358i
$952$		0			0
$953$	−481.604	−	278.054i	−0.505356	−	0.291767i	0.225567	−	0.974228i	$-0.427577\pi$
$953$	−481.604	−	278.054i	−0.505356	−	0.291767i	−0.730922	+	0.682461i	$0.760910\pi$
$954$		0			0
$955$	14.5473	−	25.1967i	0.0152328	−	0.0263840i
$956$		0			0
$957$	−479.045	+	127.506i	−0.500569	+	0.133235i
$958$		0			0
$959$	−456.133	−	263.349i	−0.475634	−	0.274608i
$960$		0			0
$961$	−203.213	+	351.975i	−0.211460	+	0.366259i
$962$		0			0
$963$	−65.4517	−	0.217772i	−0.0679665	−	0.000226139i
$964$		0			0
$965$		−	1008.86i		−	1.04546i
$966$		0			0
$967$	1410.44			1.45857			0.729284	−	0.684211i	$-0.239853\pi$
$967$	1410.44			1.45857			0.729284	+	0.684211i	$0.239853\pi$
$968$		0			0
$969$	−1430.21	+	481.407i	−1.47596	+	0.496808i
$970$		0			0
$971$	−511.215	−	295.150i	−0.526483	−	0.303965i	0.213100	−	0.977030i	$-0.431644\pi$
$971$	−511.215	−	295.150i	−0.526483	−	0.303965i	−0.739583	+	0.673065i	$0.764977\pi$
$972$		0			0
$973$	89.6037	+	155.198i	0.0920901	+	0.159505i
$974$		0			0
$975$	−236.499	+	62.9483i	−0.242564	+	0.0645624i
$976$		0			0
$977$	451.299	−	260.557i	0.461923	−	0.266691i	−0.250930	−	0.968005i	$-0.580736\pi$
$977$	451.299	−	260.557i	0.461923	−	0.266691i	0.712852	+	0.701314i	$0.247403\pi$
$978$		0			0
$979$	−157.089			−0.160458
$980$		0			0
$981$	901.782	+	524.652i	0.919247	+	0.534814i
$982$		0			0
$983$	−346.513	+	200.059i	−0.352505	+	0.203519i	−0.665788	−	0.746141i	$-0.731905\pi$
$983$	−346.513	+	200.059i	−0.352505	+	0.203519i	0.313283	+	0.949660i	$0.398571\pi$
$984$		0			0
$985$	−1811.44			−1.83903
$986$		0			0
$987$	778.519	+	2924.93i	0.788773	+	2.96345i
$988$		0			0
$989$		−	82.4039i		−	0.0833204i
$990$		0			0
$991$	265.562	−	459.968i	0.267974	−	0.464145i	−0.700364	−	0.713786i	$-0.746979\pi$
$991$	265.562	−	459.968i	0.267974	−	0.464145i	0.968339	+	0.249641i	$0.0803125\pi$
$992$		0			0
$993$	−1101.82	+	293.269i	−1.10959	+	0.295336i
$994$		0			0
$995$	−258.093	+	149.010i	−0.259390	+	0.149759i
$996$		0			0
$997$	−928.012			−0.930804			−0.465402	−	0.885099i	$-0.654090\pi$
$997$	−928.012			−0.930804			−0.465402	+	0.885099i	$0.654090\pi$
$998$		0			0
$999$	1069.38	−	1058.76i	1.07045	−	1.05982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.10	✓	80
3.2	odd	2		2052.3.m.a.1493.5		80
9.4	even	3		2052.3.be.a.125.36		80
9.5	odd	6		684.3.be.a.581.36	yes	80
19.7	even	3		684.3.be.a.425.36	yes	80
57.26	odd	6		2052.3.be.a.197.36		80
171.121	even	3		2052.3.m.a.881.36		80
171.140	odd	6	inner	684.3.m.a.653.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.10	✓	80	1.1	even	1	trivial
684.3.m.a.653.10	yes	80	171.140	odd	6	inner
684.3.be.a.425.36	yes	80	19.7	even	3
684.3.be.a.581.36	yes	80	9.5	odd	6
2052.3.m.a.881.36		80	171.121	even	3
2052.3.m.a.1493.5		80	3.2	odd	2
2052.3.be.a.125.36		80	9.4	even	3
2052.3.be.a.197.36		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)

\(f(q)\)	\(=\)	\(q+(-2.11779 - 2.12485i) q^{3} +8.55202i q^{5} +(-5.68709 + 9.85033i) q^{7} +(-0.0299448 + 8.99995i) q^{9} +O(q^{10})\)	\(q+(-2.11779 - 2.12485i) q^{3} +8.55202i q^{5} +(-5.68709 + 9.85033i) q^{7} +(-0.0299448 + 8.99995i) q^{9} +(12.9413 + 7.47166i) q^{11} +(-0.847351 + 1.46766i) q^{13} +(18.1717 - 18.1114i) q^{15} +(-22.9277 - 13.2373i) q^{17} +(1.22562 + 18.9604i) q^{19} +(32.9745 - 8.77672i) q^{21} +(-2.95885 - 1.70829i) q^{23} -48.1370 q^{25} +(19.1869 - 18.9964i) q^{27} -11.0579i q^{29} +(-18.4894 - 32.0245i) q^{31} +(-11.5308 - 43.3216i) q^{33} +(-84.2401 - 48.6361i) q^{35} +55.7350 q^{37} +(4.91305 - 1.30769i) q^{39} -45.0347i q^{41} +(12.0594 + 20.8875i) q^{43} +(-76.9677 - 0.256089i) q^{45} +88.7028i q^{47} +(-40.1859 - 69.6041i) q^{49} +(20.4288 + 76.7517i) q^{51} +(-49.9793 + 28.8555i) q^{53} +(-63.8977 + 110.674i) q^{55} +(37.6924 - 42.7584i) q^{57} -23.5787i q^{59} +32.3568 q^{61} +(-88.4821 - 51.4785i) q^{63} +(-12.5514 - 7.24656i) q^{65} +(-28.6083 + 49.5510i) q^{67} +(2.63636 + 9.90491i) q^{69} +(51.0876 + 29.4954i) q^{71} +(39.1711 - 67.8463i) q^{73} +(101.944 + 102.284i) q^{75} +(-147.197 + 84.9839i) q^{77} +(26.4100 + 45.7434i) q^{79} +(-80.9982 - 0.539004i) q^{81} +(-60.4098 - 34.8776i) q^{83} +(113.206 - 196.078i) q^{85} +(-23.4963 + 23.4182i) q^{87} +(-9.10392 + 5.25615i) q^{89} +(-9.63792 - 16.6934i) q^{91} +(-28.8906 + 107.108i) q^{93} +(-162.150 + 10.4815i) q^{95} +(-41.4092 - 71.7229i) q^{97} +(-67.6321 + 116.247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 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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