LMFDB - Embedded newform 684.3.m.a.353.15

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			353.15
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55115 + 2.56787i) q^{3} +5.60337i q^{5} +(-5.05578 + 8.75686i) q^{7} +(-4.18789 - 7.96628i) q^{9} +O(q^{10})$	\(q+(-1.55115 + 2.56787i) q^{3} +5.60337i q^{5} +(-5.05578 + 8.75686i) q^{7} +(-4.18789 - 7.96628i) q^{9} +(-4.84819 - 2.79910i) q^{11} +(-9.41378 + 16.3051i) q^{13} +(-14.3887 - 8.69164i) q^{15} +(1.70269 + 0.983049i) q^{17} +(-12.6901 - 14.1408i) q^{19} +(-14.6442 - 26.5657i) q^{21} +(14.6593 + 8.46356i) q^{23} -6.39771 q^{25} +(26.9524 + 1.60293i) q^{27} +12.2948i q^{29} +(3.88985 + 6.73742i) q^{31} +(14.7080 - 8.10768i) q^{33} +(-49.0679 - 28.3294i) q^{35} +47.4671 q^{37} +(-27.2673 - 49.4650i) q^{39} +36.8133i q^{41} +(-20.2784 - 35.1233i) q^{43} +(44.6380 - 23.4663i) q^{45} -1.53361i q^{47} +(-26.6218 - 46.1103i) q^{49} +(-5.16546 + 2.84743i) q^{51} +(15.7050 - 9.06730i) q^{53} +(15.6844 - 27.1662i) q^{55} +(55.9958 - 10.6521i) q^{57} -25.1714i q^{59} +63.5711 q^{61} +(90.9326 + 3.60298i) q^{63} +(-91.3637 - 52.7488i) q^{65} +(12.0682 - 20.9027i) q^{67} +(-44.4720 + 24.5150i) q^{69} +(-106.323 - 61.3856i) q^{71} +(-10.0030 + 17.3257i) q^{73} +(9.92379 - 16.4285i) q^{75} +(49.0227 - 28.3033i) q^{77} +(5.16465 + 8.94544i) q^{79} +(-45.9232 + 66.7238i) q^{81} +(-39.0802 - 22.5629i) q^{83} +(-5.50839 + 9.54080i) q^{85} +(-31.5714 - 19.0710i) q^{87} +(-141.530 + 81.7125i) q^{89} +(-95.1879 - 164.870i) q^{91} +(-23.3345 - 0.462105i) q^{93} +(79.2359 - 71.1073i) q^{95} +(-90.0648 - 155.997i) q^{97} +(-1.99477 + 50.3443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.55115	+	2.56787i	−0.517049	+	0.855956i
$3$	−1.55115	+	2.56787i	−0.517049	+	0.855956i
$4$		0			0
$5$			5.60337i			1.12067i	0.828265	+	0.560337i	$0.189328\pi$
$5$			5.60337i			1.12067i	−0.828265	+	0.560337i	$0.810672\pi$
$6$		0			0
$7$	−5.05578	+	8.75686i	−0.722254	+	1.25098i	0.237840	+	0.971304i	$0.423560\pi$
$7$	−5.05578	+	8.75686i	−0.722254	+	1.25098i	−0.960094	+	0.279676i	$0.909773\pi$
$8$		0			0
$9$	−4.18789	−	7.96628i	−0.465321	−	0.885142i
$10$		0			0
$11$	−4.84819	−	2.79910i	−0.440744	−	0.254464i	0.263169	−	0.964750i	$-0.415232\pi$
$11$	−4.84819	−	2.79910i	−0.440744	−	0.254464i	−0.703913	+	0.710286i	$0.748566\pi$
$12$		0			0
$13$	−9.41378	+	16.3051i	−0.724137	+	1.25424i	0.235192	+	0.971949i	$0.424428\pi$
$13$	−9.41378	+	16.3051i	−0.724137	+	1.25424i	−0.959328	+	0.282292i	$0.908905\pi$
$14$		0			0
$15$	−14.3887	−	8.69164i	−0.959247	−	0.579443i
$16$		0			0
$17$	1.70269	+	0.983049i	0.100158	+	0.0578264i	0.549242	−	0.835663i	$-0.314916\pi$
$17$	1.70269	+	0.983049i	0.100158	+	0.0578264i	−0.449084	+	0.893489i	$0.648250\pi$
$18$		0			0
$19$	−12.6901	−	14.1408i	−0.667900	−	0.744251i
$19$	−12.6901	−	14.1408i	−0.667900	−	0.744251i
$20$		0			0
$21$	−14.6442	−	26.5657i	−0.697343	−	1.26504i
$22$		0			0
$23$	14.6593	+	8.46356i	0.637361	+	0.367981i	0.783597	−	0.621269i	$-0.213383\pi$
$23$	14.6593	+	8.46356i	0.637361	+	0.367981i	−0.146236	+	0.989250i	$0.546716\pi$
$24$		0			0
$25$	−6.39771			−0.255909
$26$		0			0
$27$	26.9524	+	1.60293i	0.998236	+	0.0593677i
$28$		0			0
$29$			12.2948i			0.423958i	0.977274	+	0.211979i	$0.0679909\pi$
$29$			12.2948i			0.423958i	−0.977274	+	0.211979i	$0.932009\pi$
$30$		0			0
$31$	3.88985	+	6.73742i	0.125479	+	0.217336i	0.921920	−	0.387380i	$-0.126620\pi$
$31$	3.88985	+	6.73742i	0.125479	+	0.217336i	−0.796441	+	0.604716i	$0.793287\pi$
$32$		0			0
$33$	14.7080	−	8.10768i	0.445696	−	0.245687i
$34$		0			0
$35$	−49.0679	−	28.3294i	−1.40194	−	0.809411i
$36$		0			0
$37$	47.4671			1.28290			0.641448	−	0.767167i	$-0.278334\pi$
$37$	47.4671			1.28290			0.641448	+	0.767167i	$0.278334\pi$
$38$		0			0
$39$	−27.2673	−	49.4650i	−0.699161	−	1.26833i
$40$		0			0
$41$			36.8133i			0.897885i	0.893561	+	0.448942i	$0.148199\pi$
$41$			36.8133i			0.897885i	−0.893561	+	0.448942i	$0.851801\pi$
$42$		0			0
$43$	−20.2784	−	35.1233i	−0.471592	−	0.816821i	0.527880	−	0.849319i	$-0.322987\pi$
$43$	−20.2784	−	35.1233i	−0.471592	−	0.816821i	−0.999472	+	0.0324982i	$0.989654\pi$
$44$		0			0
$45$	44.6380	−	23.4663i	0.991955	−	0.521473i
$46$		0			0
$47$		−	1.53361i		−	0.0326299i	−0.999867	−	0.0163150i	$-0.994807\pi$
$47$		−	1.53361i		−	0.0326299i	0.999867	−	0.0163150i	$-0.00519345\pi$
$48$		0			0
$49$	−26.6218	−	46.1103i	−0.543302	−	0.941026i
$50$		0			0
$51$	−5.16546	+	2.84743i	−0.101284	+	0.0558320i
$52$		0			0
$53$	15.7050	−	9.06730i	0.296321	−	0.171081i	−0.344468	−	0.938798i	$-0.611941\pi$
$53$	15.7050	−	9.06730i	0.296321	−	0.171081i	0.640789	+	0.767717i	$0.278607\pi$
$54$		0			0
$55$	15.6844	−	27.1662i	0.285171	−	0.493930i
$56$		0			0
$57$	55.9958	−	10.6521i	0.982383	−	0.186879i
$58$		0			0
$59$		−	25.1714i		−	0.426633i	−0.976983	−	0.213317i	$-0.931573\pi$
$59$		−	25.1714i		−	0.426633i	0.976983	−	0.213317i	$-0.0684266\pi$
$60$		0			0
$61$	63.5711			1.04215			0.521074	−	0.853511i	$-0.325531\pi$
$61$	63.5711			1.04215			0.521074	+	0.853511i	$0.325531\pi$
$62$		0			0
$63$	90.9326	+	3.60298i	1.44338	+	0.0571901i
$64$		0			0
$65$	−91.3637	−	52.7488i	−1.40559	−	0.811520i
$66$		0			0
$67$	12.0682	−	20.9027i	0.180122	−	0.311980i	−0.761800	−	0.647812i	$-0.775684\pi$
$67$	12.0682	−	20.9027i	0.180122	−	0.311980i	0.941922	+	0.335832i	$0.109018\pi$
$68$		0			0
$69$	−44.4720	+	24.5150i	−0.644522	+	0.355289i
$70$		0			0
$71$	−106.323	−	61.3856i	−1.49751	−	0.864586i	−0.497511	−	0.867458i	$-0.665753\pi$
$71$	−106.323	−	61.3856i	−1.49751	−	0.864586i	−0.999996	+	0.00287158i	$0.999086\pi$
$72$		0			0
$73$	−10.0030	+	17.3257i	−0.137028	+	0.237339i	−0.926370	−	0.376614i	$-0.877088\pi$
$73$	−10.0030	+	17.3257i	−0.137028	+	0.237339i	0.789343	+	0.613953i	$0.210422\pi$
$74$		0			0
$75$	9.92379	−	16.4285i	0.132317	−	0.219046i
$76$		0			0
$77$	49.0227	−	28.3033i	0.636659	−	0.367575i
$78$		0			0
$79$	5.16465	+	8.94544i	0.0653753	+	0.113233i	0.896860	−	0.442314i	$-0.145842\pi$
$79$	5.16465	+	8.94544i	0.0653753	+	0.113233i	−0.831485	+	0.555547i	$0.812509\pi$
$80$		0			0
$81$	−45.9232	+	66.7238i	−0.566953	+	0.823750i
$82$		0			0
$83$	−39.0802	−	22.5629i	−0.470845	−	0.271843i	0.245748	−	0.969334i	$-0.420966\pi$
$83$	−39.0802	−	22.5629i	−0.470845	−	0.271843i	−0.716593	+	0.697491i	$0.754300\pi$
$84$		0			0
$85$	−5.50839	+	9.54080i	−0.0648045	+	0.112245i
$86$		0			0
$87$	−31.5714	−	19.0710i	−0.362890	−	0.219207i
$88$		0			0
$89$	−141.530	+	81.7125i	−1.59023	+	0.918118i	−0.596959	+	0.802272i	$0.703625\pi$
$89$	−141.530	+	81.7125i	−1.59023	+	0.918118i	−0.993267	+	0.115846i	$0.963042\pi$
$90$		0			0
$91$	−95.1879	−	164.870i	−1.04602	−	1.81176i
$92$		0			0
$93$	−23.3345	−	0.462105i	−0.250909	−	0.00496887i
$94$		0			0
$95$	79.2359	−	71.1073i	0.834062	−	0.748498i
$96$		0			0
$97$	−90.0648	−	155.997i	−0.928503	−	1.60821i	−0.785829	−	0.618444i	$-0.787763\pi$
$97$	−90.0648	−	155.997i	−0.928503	−	1.60821i	−0.142674	−	0.989770i	$-0.545570\pi$
$98$		0			0
$99$	−1.99477	+	50.3443i	−0.0201492	+	0.508529i
$100$		0			0
$101$			148.940i			1.47466i	0.675534	+	0.737329i	$0.263913\pi$
$101$			148.940i			1.47466i	−0.675534	+	0.737329i	$0.736087\pi$
$102$		0			0
$103$	4.85216	+	8.40418i	0.0471083	+	0.0815940i	0.888618	−	0.458648i	$-0.151666\pi$
$103$	4.85216	+	8.40418i	0.0471083	+	0.0815940i	−0.841510	+	0.540242i	$0.818333\pi$
$104$		0			0
$105$	148.858	−	82.0569i	1.41769	−	0.781494i
$106$		0			0
$107$			166.968i			1.56044i	0.625502	+	0.780222i	$0.284894\pi$
$107$			166.968i			1.56044i	−0.625502	+	0.780222i	$0.715106\pi$
$108$		0			0
$109$	91.3345	−	158.196i	0.837931	−	1.45134i	−0.0536900	−	0.998558i	$-0.517098\pi$
$109$	91.3345	−	158.196i	0.837931	−	1.45134i	0.891621	−	0.452782i	$-0.149568\pi$
$110$		0			0
$111$	−73.6285	+	121.889i	−0.663320	+	1.09810i
$112$		0			0
$113$	143.535	−	82.8699i	1.27022	−	0.733362i	0.295191	−	0.955438i	$-0.404617\pi$
$113$	143.535	−	82.8699i	1.27022	−	0.733362i	0.975029	+	0.222076i	$0.0712834\pi$
$114$		0			0
$115$	−47.4244	+	82.1415i	−0.412386	+	0.714274i
$116$		0			0
$117$	169.315	+	6.70869i	1.44714	+	0.0573392i
$118$		0			0
$119$	−17.2169	+	9.94016i	−0.144679	+	0.0835307i
$120$		0			0
$121$	−44.8301	−	77.6479i	−0.370496	−	0.641718i
$122$		0			0
$123$	−94.5316	−	57.1028i	−0.768550	−	0.464250i
$124$		0			0
$125$			104.235i			0.833883i
$126$		0			0
$127$	−111.040	−	192.328i	−0.874334	−	1.51439i	−0.857471	−	0.514533i	$-0.827965\pi$
$127$	−111.040	−	192.328i	−0.874334	−	1.51439i	−0.0168629	−	0.999858i	$-0.505368\pi$
$128$		0			0
$129$	121.647	+	2.40903i	0.942998	+	0.0186746i
$130$		0			0
$131$		−	135.740i		−	1.03618i	−0.855325	−	0.518092i	$-0.826643\pi$
$131$		−	135.740i		−	1.03618i	0.855325	−	0.518092i	$-0.173357\pi$
$132$		0			0
$133$	187.987	−	39.6329i	1.41344	−	0.297992i
$134$		0			0
$135$	−8.98180	+	151.024i	−0.0665318	+	1.11870i
$136$		0			0
$137$			15.9506i			0.116428i	0.998304	+	0.0582138i	$0.0185405\pi$
$137$			15.9506i			0.116428i	−0.998304	+	0.0582138i	$0.981459\pi$
$138$		0			0
$139$	−93.2674	+	161.544i	−0.670988	+	1.16219i	0.306636	+	0.951827i	$0.400797\pi$
$139$	−93.2674	+	161.544i	−0.670988	+	1.16219i	−0.977624	+	0.210359i	$0.932537\pi$
$140$		0			0
$141$	3.93810	+	2.37885i	0.0279298	+	0.0168713i
$142$		0			0
$143$	91.2795	−	52.7002i	0.638318	−	0.368533i
$144$		0			0
$145$	−68.8922			−0.475119
$146$		0			0
$147$	159.699	+	3.16260i	1.08639	+	0.0215143i
$148$		0			0
$149$			152.829i			1.02570i	0.858479	+	0.512849i	$0.171410\pi$
$149$			152.829i			1.02570i	−0.858479	+	0.512849i	$0.828590\pi$
$150$		0			0
$151$	−95.9784	+	166.239i	−0.635618	+	1.10092i	0.350765	+	0.936463i	$0.385921\pi$
$151$	−95.9784	+	166.239i	−0.635618	+	1.10092i	−0.986384	+	0.164460i	$0.947412\pi$
$152$		0			0
$153$	0.700566	−	17.6810i	0.00457886	−	0.115562i
$154$		0			0
$155$	−37.7523	+	21.7963i	−0.243563	+	0.140621i
$156$		0			0
$157$	46.4968			0.296158			0.148079	−	0.988976i	$-0.452691\pi$
$157$	46.4968			0.296158			0.148079	+	0.988976i	$0.452691\pi$
$158$		0			0
$159$	−1.07717	+	54.3932i	−0.00677468	+	0.342095i
$160$		0			0
$161$	−148.228	+	85.5797i	−0.920674	+	0.531551i
$162$		0			0
$163$	48.7950			0.299356			0.149678	−	0.988735i	$-0.452176\pi$
$163$	48.7950			0.299356			0.149678	+	0.988735i	$0.452176\pi$
$164$		0			0
$165$	45.4303	+	82.4142i	0.275335	+	0.499480i
$166$		0			0
$167$	32.9129	+	19.0023i	0.197083	+	0.113786i	0.595294	−	0.803508i	$-0.297035\pi$
$167$	32.9129	+	19.0023i	0.197083	+	0.113786i	−0.398211	+	0.917294i	$0.630369\pi$
$168$		0			0
$169$	−92.7383	−	160.628i	−0.548748	−	0.950459i
$170$		0			0
$171$	−59.5046	+	160.313i	−0.347980	+	0.937502i
$172$		0			0
$173$	−110.677	+	63.8991i	−0.639749	+	0.369359i	−0.784518	−	0.620106i	$-0.787089\pi$
$173$	−110.677	+	63.8991i	−0.639749	+	0.369359i	0.144769	+	0.989465i	$0.453756\pi$
$174$		0			0
$175$	32.3454	−	56.0239i	0.184831	−	0.320137i
$176$		0			0
$177$	64.6368	+	39.0445i	0.365179	+	0.220590i
$178$		0			0
$179$			46.0254i			0.257125i	0.991701	+	0.128563i	$0.0410363\pi$
$179$			46.0254i			0.257125i	−0.991701	+	0.128563i	$0.958964\pi$
$180$		0			0
$181$	77.9537	+	135.020i	0.430683	+	0.745965i	0.996932	−	0.0782688i	$-0.0249392\pi$
$181$	77.9537	+	135.020i	0.430683	+	0.745965i	−0.566249	+	0.824234i	$0.691606\pi$
$182$		0			0
$183$	−98.6081	+	163.242i	−0.538842	+	0.892033i
$184$		0			0
$185$			265.976i			1.43771i
$186$		0			0
$187$	−5.50331	−	9.53201i	−0.0294295	−	0.0509733i
$188$		0			0
$189$	−150.302	+	227.914i	−0.795248	+	1.20590i
$190$		0			0
$191$	−95.8634	−	55.3467i	−0.501902	−	0.289773i	0.227596	−	0.973756i	$-0.426913\pi$
$191$	−95.8634	−	55.3467i	−0.501902	−	0.289773i	−0.729499	+	0.683982i	$0.760247\pi$
$192$		0			0
$193$	−111.059			−0.575438			−0.287719	−	0.957715i	$-0.592897\pi$
$193$	−111.059			−0.575438			−0.287719	+	0.957715i	$0.592897\pi$
$194$		0			0
$195$	277.170	−	152.789i	1.42139	−	0.783531i
$196$		0			0
$197$			273.143i			1.38651i	0.720691	+	0.693257i	$0.243825\pi$
$197$			273.143i			1.38651i	−0.720691	+	0.693257i	$0.756175\pi$
$198$		0			0
$199$	−47.0505	−	81.4939i	−0.236435	−	0.409517i	0.723254	−	0.690582i	$-0.242646\pi$
$199$	−47.0505	−	81.4939i	−0.236435	−	0.409517i	−0.959689	+	0.281065i	$0.909312\pi$
$200$		0			0
$201$	34.9558	+	63.4125i	0.173909	+	0.315485i
$202$		0			0
$203$	−107.664	−	62.1597i	−0.530364	−	0.306206i
$204$		0			0
$205$	−206.278			−1.00624
$206$		0			0
$207$	6.03152	−	152.225i	0.0291378	−	0.735385i
$208$		0			0
$209$	21.9425	+	104.078i	0.104988	+	0.497981i
$210$		0			0
$211$	57.3158			0.271639			0.135820	−	0.990734i	$-0.456633\pi$
$211$	57.3158			0.271639			0.135820	+	0.990734i	$0.456633\pi$
$212$		0			0
$213$	322.553	−	177.805i	1.51433	−	0.834767i
$214$		0			0
$215$	196.809	−	113.628i	0.915389	−	0.528500i
$216$		0			0
$217$	−78.6649			−0.362511
$218$		0			0
$219$	−28.9740	−	52.5611i	−0.132301	−	0.240005i
$220$		0			0
$221$	−32.0575	+	18.5084i	−0.145057	+	0.0837485i
$222$		0			0
$223$	4.88183	+	8.45557i	0.0218916	+	0.0379174i	0.876764	−	0.480921i	$-0.159698\pi$
$223$	4.88183	+	8.45557i	0.0218916	+	0.0379174i	−0.854872	+	0.518839i	$0.826364\pi$
$224$		0			0
$225$	26.7929	+	50.9660i	0.119080	+	0.226515i
$226$		0			0
$227$	70.3097	+	40.5933i	0.309735	+	0.178825i	0.646808	−	0.762653i	$-0.276104\pi$
$227$	70.3097	+	40.5933i	0.309735	+	0.178825i	−0.337073	+	0.941478i	$0.609437\pi$
$228$		0			0
$229$	91.3522	+	158.227i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$229$	91.3522	+	158.227i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$230$		0			0
$231$	−3.36236	+	169.786i	−0.0145557	+	0.735006i
$232$		0			0
$233$	−143.327	−	82.7501i	−0.615139	−	0.355151i	0.159835	−	0.987144i	$-0.448904\pi$
$233$	−143.327	−	82.7501i	−0.615139	−	0.355151i	−0.774974	+	0.631993i	$0.782237\pi$
$234$		0			0
$235$	8.59336			0.0365675
$236$		0			0
$237$	−30.9818	−	0.613548i	−0.130725	−	0.00258881i
$238$		0			0
$239$	−221.452	+	127.855i	−0.926578	+	0.534960i	−0.885728	−	0.464205i	$-0.846340\pi$
$239$	−221.452	+	127.855i	−0.926578	+	0.534960i	−0.0408500	+	0.999165i	$0.513007\pi$
$240$		0			0
$241$	254.134			1.05450			0.527250	−	0.849710i	$-0.323223\pi$
$241$	254.134			1.05450			0.527250	+	0.849710i	$0.323223\pi$
$242$		0			0
$243$	−100.104	−	221.423i	−0.411951	−	0.911206i
$244$		0			0
$245$	258.373	−	149.172i	1.05458	−	0.608864i
$246$		0			0
$247$	350.029	−	73.7958i	1.41712	−	0.298768i
$248$		0			0
$249$	118.558	−	65.3542i	0.476135	−	0.262467i
$250$		0			0
$251$	49.7549	−	28.7260i	0.198227	−	0.114446i	−0.397601	−	0.917558i	$-0.630157\pi$
$251$	49.7549	−	28.7260i	0.198227	−	0.114446i	0.595828	+	0.803112i	$0.296824\pi$
$252$		0			0
$253$	−47.3807	−	82.0658i	−0.187276	−	0.324371i
$254$		0			0
$255$	−15.9552	−	28.9440i	−0.0625694	−	0.113506i
$256$		0			0
$257$	390.962	+	225.722i	1.52125	+	0.878296i	0.999685	+	0.0250864i	$0.00798609\pi$
$257$	390.962	+	225.722i	1.52125	+	0.878296i	0.521568	+	0.853210i	$0.325347\pi$
$258$		0			0
$259$	−239.983	+	415.663i	−0.926577	+	1.60488i
$260$		0			0
$261$	97.9437	−	51.4892i	0.375263	−	0.197277i
$262$		0			0
$263$	−372.041	+	214.798i	−1.41460	+	0.816722i	−0.995818	−	0.0913629i	$-0.970878\pi$
$263$	−372.041	+	214.798i	−1.41460	+	0.816722i	−0.418786	+	0.908085i	$0.637544\pi$
$264$		0			0
$265$	50.8074	+	88.0010i	0.191726	+	0.332079i
$266$		0			0
$267$	9.70724	−	490.179i	0.0363567	−	1.83588i
$268$		0			0
$269$	−100.097	−	57.7912i	−0.372109	−	0.214837i	0.302270	−	0.953222i	$-0.402255\pi$
$269$	−100.097	−	57.7912i	−0.372109	−	0.214837i	−0.674380	+	0.738385i	$0.735589\pi$
$270$		0			0
$271$	100.230	−	173.603i	0.369851	−	0.640601i	−0.619691	−	0.784846i	$-0.712742\pi$
$271$	100.230	−	173.603i	0.369851	−	0.640601i	0.989542	+	0.144245i	$0.0460754\pi$
$272$		0			0
$273$	571.016	+	11.3081i	2.09163	+	0.0414216i
$274$		0			0
$275$	31.0173	+	17.9079i	0.112790	+	0.0651195i
$276$		0			0
$277$	−58.9086	+	102.033i	−0.212666	+	0.368349i	−0.952548	−	0.304388i	$-0.901548\pi$
$277$	−58.9086	+	102.033i	−0.212666	+	0.368349i	0.739882	+	0.672737i	$0.234881\pi$
$278$		0			0
$279$	37.3819	−	59.2032i	0.133985	−	0.212198i
$280$		0			0
$281$			364.079i			1.29566i	0.761787	+	0.647828i	$0.224322\pi$
$281$			364.079i			1.29566i	−0.761787	+	0.647828i	$0.775678\pi$
$282$		0			0
$283$	−238.948			−0.844340			−0.422170	−	0.906517i	$-0.638731\pi$
$283$	−238.948			−0.844340			−0.422170	+	0.906517i	$0.638731\pi$
$284$		0			0
$285$	59.6875	+	313.765i	0.209430	+	1.10093i
$286$		0			0
$287$	−322.369	−	186.120i	−1.12324	−	0.648501i
$288$		0			0
$289$	−142.567	−	246.934i	−0.493312	−	0.854442i
$290$		0			0
$291$	540.283	+	10.6995i	1.85664	+	0.0367680i
$292$		0			0
$293$	196.017	−	113.171i	0.669000	−	0.386248i	−0.126697	−	0.991941i	$-0.540438\pi$
$293$	196.017	−	113.171i	0.669000	−	0.386248i	0.795698	+	0.605694i	$0.207104\pi$
$294$		0			0
$295$	141.044			0.478117
$296$		0			0
$297$	−126.183	−	83.2138i	−0.424860	−	0.280181i
$298$		0			0
$299$	−275.999	+	159.348i	−0.923073	+	0.532937i
$300$		0			0
$301$	410.093			1.36244
$302$		0			0
$303$	−382.459	−	231.028i	−1.26224	−	0.762470i
$304$		0			0
$305$			356.212i			1.16791i
$306$		0			0
$307$	−37.7716	+	65.4224i	−0.123035	+	0.213102i	−0.920963	−	0.389650i	$-0.872596\pi$
$307$	−37.7716	+	65.4224i	−0.123035	+	0.213102i	0.797928	+	0.602752i	$0.205929\pi$
$308$		0			0
$309$	−29.1072	−	0.576424i	−0.0941981	−	0.00186545i
$310$		0			0
$311$	−271.982	+	157.029i	−0.874539	+	0.504915i	−0.868854	−	0.495068i	$-0.835143\pi$
$311$	−271.982	+	157.029i	−0.874539	+	0.504915i	−0.00568514	+	0.999984i	$0.501810\pi$
$312$		0			0
$313$	−474.866			−1.51714			−0.758571	−	0.651590i	$-0.774102\pi$
$313$	−474.866			−1.51714			−0.758571	+	0.651590i	$0.774102\pi$
$314$		0			0
$315$	−20.1888	+	509.529i	−0.0640915	+	1.61755i
$316$		0			0
$317$		−	525.671i		−	1.65827i	−0.559049	−	0.829135i	$-0.688834\pi$
$317$		−	525.671i		−	1.65827i	0.559049	−	0.829135i	$-0.311166\pi$
$318$		0			0
$319$	34.4144	−	59.6074i	0.107882	−	0.186857i
$320$		0			0
$321$	−428.751	−	258.991i	−1.33567	−	0.806826i
$322$		0			0
$323$	−7.70625	−	36.5524i	−0.0238584	−	0.113165i
$324$		0			0
$325$	60.2266	−	104.316i	0.185313	−	0.320971i
$326$		0			0
$327$	264.553	+	479.920i	0.809031	+	1.46765i
$328$		0			0
$329$	13.4296	+	7.75358i	0.0408194	+	0.0235671i
$330$		0			0
$331$	32.6901	−	56.6210i	0.0987617	−	0.171060i	−0.812411	−	0.583086i	$-0.801845\pi$
$331$	32.6901	−	56.6210i	0.0987617	−	0.171060i	0.911172	+	0.412025i	$0.135178\pi$
$332$		0			0
$333$	−198.787	−	378.137i	−0.596958	−	1.13555i
$334$		0			0
$335$	117.125	+	67.6223i	0.349628	+	0.201858i
$336$		0			0
$337$	154.265			0.457759			0.228880	−	0.973455i	$-0.426494\pi$
$337$	154.265			0.457759			0.228880	+	0.973455i	$0.426494\pi$
$338$		0			0
$339$	−9.84475	+	497.122i	−0.0290405	+	1.46644i
$340$		0			0
$341$		−	43.5524i		−	0.127720i
$342$		0			0
$343$	42.9089			0.125099
$344$		0			0
$345$	−137.366	−	249.193i	−0.398163	−	0.722299i
$346$		0			0
$347$			46.1796i			0.133082i	0.997784	+	0.0665412i	$0.0211964\pi$
$347$			46.1796i			0.133082i	−0.997784	+	0.0665412i	$0.978804\pi$
$348$		0			0
$349$	291.074	−	504.156i	0.834024	−	1.44457i	−0.0607982	−	0.998150i	$-0.519365\pi$
$349$	291.074	−	504.156i	0.834024	−	1.44457i	0.894822	−	0.446422i	$-0.147302\pi$
$350$		0			0
$351$	−279.860	+	424.373i	−0.797321	+	1.20904i
$352$		0			0
$353$	127.757	+	73.7605i	0.361918	+	0.208953i	0.669922	−	0.742432i	$-0.266328\pi$
$353$	127.757	+	73.7605i	0.361918	+	0.208953i	−0.308004	+	0.951385i	$0.599661\pi$
$354$		0			0
$355$	343.966	−	595.767i	0.968918	−	1.67822i
$356$		0			0
$357$	1.18087	−	59.6293i	0.00330775	−	0.167029i
$358$		0			0
$359$	−334.186	−	192.943i	−0.930881	−	0.537445i	−0.0437911	−	0.999041i	$-0.513944\pi$
$359$	−334.186	−	192.943i	−0.930881	−	0.537445i	−0.887090	+	0.461596i	$0.847277\pi$
$360$		0			0
$361$	−38.9227	+	358.896i	−0.107819	+	0.994171i
$362$		0			0
$363$	268.928	+	5.32570i	0.740847	+	0.0146714i
$364$		0			0
$365$	−97.0824	−	56.0505i	−0.265979	−	0.153563i
$366$		0			0
$367$	−8.62992			−0.0235148			−0.0117574	−	0.999931i	$-0.503743\pi$
$367$	−8.62992			−0.0235148			−0.0117574	+	0.999931i	$0.503743\pi$
$368$		0			0
$369$	293.265	−	154.170i	0.794756	−	0.417804i
$370$		0			0
$371$			183.369i			0.494256i
$372$		0			0
$373$	−26.3653	−	45.6661i	−0.0706846	−	0.122429i	0.828517	−	0.559964i	$-0.189185\pi$
$373$	−26.3653	−	45.6661i	−0.0706846	−	0.122429i	−0.899202	+	0.437535i	$0.855852\pi$
$374$		0			0
$375$	−267.663	−	161.684i	−0.713767	−	0.431159i
$376$		0			0
$377$	−200.468	−	115.740i	−0.531746	−	0.307004i
$378$		0			0
$379$	442.574			1.16774			0.583871	−	0.811846i	$-0.301537\pi$
$379$	442.574			1.16774			0.583871	+	0.811846i	$0.301537\pi$
$380$		0			0
$381$	666.112	+	13.1913i	1.74832	+	0.0346229i
$382$		0			0
$383$			306.590i			0.800497i	0.916407	+	0.400249i	$0.131076\pi$
$383$			306.590i			0.800497i	−0.916407	+	0.400249i	$0.868924\pi$
$384$		0			0
$385$	158.594	+	274.692i	0.411932	+	0.713486i
$386$		0			0
$387$	−194.878	+	308.636i	−0.503561	+	0.797509i
$388$		0			0
$389$		−	597.805i		−	1.53677i	−0.639986	−	0.768387i	$-0.721060\pi$
$389$		−	597.805i		−	1.53677i	0.639986	−	0.768387i	$-0.278940\pi$
$390$		0			0
$391$	16.6402	+	28.8217i	0.0425580	+	0.0737127i
$392$		0			0
$393$	348.562	+	210.553i	0.886927	+	0.535757i
$394$		0			0
$395$	−50.1246	+	28.9394i	−0.126898	+	0.0732644i
$396$		0			0
$397$	−322.145	+	557.971i	−0.811447	+	1.40547i	0.100404	+	0.994947i	$0.467987\pi$
$397$	−322.145	+	557.971i	−0.811447	+	1.40547i	−0.911851	+	0.410521i	$0.865347\pi$
$398$		0			0
$399$	−189.824	+	544.202i	−0.475748	+	1.36392i
$400$		0			0
$401$		−	644.375i		−	1.60692i	−0.595359	−	0.803460i	$-0.702990\pi$
$401$		−	644.375i		−	1.60692i	0.595359	−	0.803460i	$-0.297010\pi$
$402$		0			0
$403$	−146.473			−0.363456
$404$		0			0
$405$	−373.878	−	257.325i	−0.923155	−	0.635369i
$406$		0			0
$407$	−230.130	−	132.865i	−0.565429	−	0.326451i
$408$		0			0
$409$	139.081	−	240.895i	0.340050	−	0.588984i	−0.644391	−	0.764696i	$-0.722889\pi$
$409$	139.081	−	240.895i	0.340050	−	0.588984i	0.984442	+	0.175711i	$0.0562226\pi$
$410$		0			0
$411$	−40.9590	−	24.7417i	−0.0996569	−	0.0601988i
$412$		0			0
$413$	220.422	+	127.261i	0.533710	+	0.308138i
$414$		0			0
$415$	126.428	−	218.980i	0.304647	−	0.527664i
$416$		0			0
$417$	−270.152	−	490.076i	−0.647846	−	1.17524i
$418$		0			0
$419$	171.805	−	99.1919i	0.410037	−	0.236735i	−0.280769	−	0.959775i	$-0.590589\pi$
$419$	171.805	−	99.1919i	0.410037	−	0.236735i	0.690806	+	0.723041i	$0.257256\pi$
$420$		0			0
$421$	−353.818	−	612.830i	−0.840422	−	1.45565i	−0.889538	−	0.456861i	$-0.848974\pi$
$421$	−353.818	−	612.830i	−0.840422	−	1.45565i	0.0491163	−	0.998793i	$-0.484359\pi$
$422$		0			0
$423$	−12.2171	+	6.42257i	−0.0288821	+	0.0151834i
$424$		0			0
$425$	−10.8933	−	6.28927i	−0.0256314	−	0.0147983i
$426$		0			0
$427$	−321.401	+	556.683i	−0.752696	+	1.30371i
$428$		0			0
$429$	−6.26066	+	316.139i	−0.0145936	+	0.736922i
$430$		0			0
$431$	−548.645	+	316.760i	−1.27296	+	0.734942i	−0.975543	−	0.219807i	$-0.929457\pi$
$431$	−548.645	+	316.760i	−1.27296	+	0.734942i	−0.297414	+	0.954749i	$0.596124\pi$
$432$		0			0
$433$	159.871	+	276.905i	0.369217	+	0.639503i	0.989443	−	0.144920i	$-0.0462926\pi$
$433$	159.871	+	276.905i	0.369217	+	0.639503i	−0.620226	+	0.784423i	$0.712959\pi$
$434$		0			0
$435$	106.862	−	176.906i	0.245660	−	0.406681i
$436$		0			0
$437$	−66.3469	−	314.697i	−0.151824	−	0.720131i
$438$		0			0
$439$	−295.486	−	511.797i	−0.673089	−	1.16582i	−0.977024	−	0.213131i	$-0.931634\pi$
$439$	−295.486	−	511.797i	−0.673089	−	1.16582i	0.303935	−	0.952693i	$-0.401699\pi$
$440$		0			0
$441$	−255.838	+	405.181i	−0.580132	+	0.918778i
$442$		0			0
$443$		−	665.786i		−	1.50290i	−0.659789	−	0.751451i	$-0.729354\pi$
$443$		−	665.786i		−	1.50290i	0.659789	−	0.751451i	$-0.270646\pi$
$444$		0			0
$445$	−457.865	−	793.045i	−1.02891	−	1.78212i
$446$		0			0
$447$	−392.445	−	237.060i	−0.877952	−	0.530336i
$448$		0			0
$449$			649.827i			1.44728i	0.690180	+	0.723638i	$0.257531\pi$
$449$			649.827i			1.44728i	−0.690180	+	0.723638i	$0.742469\pi$
$450$		0			0
$451$	103.044	−	178.478i	0.228479	−	0.395738i
$452$		0			0
$453$	−278.004	−	504.322i	−0.613696	−	1.11329i
$454$		0			0
$455$	923.829	−	533.373i	2.03039	−	1.17225i
$456$		0			0
$457$	−135.270	+	234.294i	−0.295995	+	0.512678i	−0.975216	−	0.221256i	$-0.928984\pi$
$457$	−135.270	+	234.294i	−0.295995	+	0.512678i	0.679221	+	0.733934i	$0.262318\pi$
$458$		0			0
$459$	44.3158	+	29.2248i	0.0965486	+	0.0636706i
$460$		0			0
$461$	−523.868	+	302.456i	−1.13637	+	0.656086i	−0.945530	−	0.325535i	$-0.894456\pi$
$461$	−523.868	+	302.456i	−1.13637	+	0.656086i	−0.190844	+	0.981620i	$0.561122\pi$
$462$		0			0
$463$	−114.322	−	198.011i	−0.246915	−	0.427669i	0.715753	−	0.698353i	$-0.246084\pi$
$463$	−114.322	−	198.011i	−0.246915	−	0.427669i	−0.962668	+	0.270684i	$0.912750\pi$
$464$		0			0
$465$	2.58935	−	130.752i	0.00556848	−	0.281187i
$466$		0			0
$467$			778.065i			1.66609i	0.553203	+	0.833046i	$0.313405\pi$
$467$			778.065i			1.66609i	−0.553203	+	0.833046i	$0.686595\pi$
$468$		0			0
$469$	122.028	+	211.358i	0.260187	+	0.450657i
$470$		0			0
$471$	−72.1233	+	119.398i	−0.153128	+	0.253498i
$472$		0			0
$473$			227.046i			0.480012i
$474$		0			0
$475$	81.1876	+	90.4686i	0.170921	+	0.190460i
$476$		0			0
$477$	−138.004	−	87.1378i	−0.289316	−	0.182679i
$478$		0			0
$479$		−	54.6238i		−	0.114037i	−0.998373	−	0.0570186i	$-0.981841\pi$
$479$		−	54.6238i		−	0.114037i	0.998373	−	0.0570186i	$-0.0181594\pi$
$480$		0			0
$481$	−446.845	+	773.958i	−0.928992	+	1.60906i
$482$		0			0
$483$	10.1667	−	513.378i	0.0210490	−	1.06289i
$484$		0			0
$485$	874.107	−	504.666i	1.80228	−	1.04055i
$486$		0			0
$487$	−243.924			−0.500871			−0.250436	−	0.968133i	$-0.580574\pi$
$487$	−243.924			−0.500871			−0.250436	+	0.968133i	$0.580574\pi$
$488$		0			0
$489$	−75.6882	+	125.299i	−0.154782	+	0.256235i
$490$		0			0
$491$		−	736.116i		−	1.49922i	−0.661881	−	0.749609i	$-0.730242\pi$
$491$		−	736.116i		−	1.49922i	0.661881	−	0.749609i	$-0.269758\pi$
$492$		0			0
$493$	−12.0864	+	20.9342i	−0.0245160	+	0.0424629i
$494$		0			0
$495$	−282.098	−	11.1774i	−0.569894	−	0.0225806i
$496$		0			0
$497$	1075.09	−	620.704i	2.16316	−	1.24890i
$498$		0			0
$499$	−181.451			−0.363630			−0.181815	−	0.983333i	$-0.558197\pi$
$499$	−181.451			−0.363630			−0.181815	+	0.983333i	$0.558197\pi$
$500$		0			0
$501$	−99.8482	+	55.0407i	−0.199298	+	0.109862i
$502$		0			0
$503$	373.769	−	215.795i	0.743079	−	0.429017i	−0.0801088	−	0.996786i	$-0.525527\pi$
$503$	373.769	−	215.795i	0.743079	−	0.429017i	0.823188	+	0.567769i	$0.192193\pi$
$504$		0			0
$505$	−834.567			−1.65261
$506$		0			0
$507$	556.321	+	11.0171i	1.09728	+	0.0217300i
$508$		0			0
$509$	245.195	+	141.563i	0.481719	+	0.278120i	0.721132	−	0.692797i	$-0.243622\pi$
$509$	245.195	+	141.563i	0.481719	+	0.278120i	−0.239414	+	0.970918i	$0.576955\pi$
$510$		0			0
$511$	−101.146	−	175.190i	−0.197937	−	0.342838i
$512$		0			0
$513$	−319.362	−	401.469i	−0.622537	−	0.782590i
$514$		0			0
$515$	−47.0917	+	27.1884i	−0.0914402	+	0.0527930i
$516$		0			0
$517$	−4.29272	+	7.43521i	−0.00830314	+	0.0143815i
$518$		0			0
$519$	7.59106	−	383.320i	0.0146263	−	0.738573i
$520$		0			0
$521$		−	84.5401i		−	0.162265i	−0.996703	−	0.0811326i	$-0.974146\pi$
$521$		−	84.5401i		−	0.162265i	0.996703	−	0.0811326i	$-0.0258537\pi$
$522$		0			0
$523$	496.389	+	859.771i	0.949119	+	1.64392i	0.747286	+	0.664503i	$0.231357\pi$
$523$	496.389	+	859.771i	0.949119	+	1.64392i	0.201833	+	0.979420i	$0.435310\pi$
$524$		0			0
$525$	93.6895	+	169.960i	0.178456	+	0.323733i
$526$		0			0
$527$			15.2957i			0.0290240i
$528$		0			0
$529$	−121.236	−	209.988i	−0.229180	−	0.396952i
$530$		0			0
$531$	−200.522	+	105.415i	−0.377631	+	0.198521i
$532$		0			0
$533$	−600.246	−	346.552i	−1.12616	−	0.650191i
$534$		0			0
$535$	−935.580			−1.74875
$536$		0			0
$537$	−118.187	−	71.3921i	−0.220088	−	0.132946i
$538$		0			0
$539$			298.068i			0.553002i
$540$		0			0
$541$	343.707	+	595.317i	0.635317	+	1.10040i	0.986448	+	0.164075i	$0.0524640\pi$
$541$	343.707	+	595.317i	0.635317	+	1.10040i	−0.351131	+	0.936326i	$0.614203\pi$
$542$		0			0
$543$	−467.630	−	9.26071i	−0.861198	−	0.0170547i
$544$		0			0
$545$	886.430	+	511.781i	1.62648	+	0.939047i
$546$		0			0
$547$	408.784			0.747320			0.373660	−	0.927566i	$-0.378103\pi$
$547$	408.784			0.747320			0.373660	+	0.927566i	$0.378103\pi$
$548$		0			0
$549$	−266.229	−	506.425i	−0.484934	−	0.922450i
$550$		0			0
$551$	173.858	−	156.022i	0.315531	−	0.283162i
$552$		0			0
$553$	−104.445			−0.188870
$554$		0			0
$555$	−682.991	−	412.568i	−1.23061	−	0.743365i
$556$		0			0
$557$	255.992	−	147.797i	0.459590	−	0.265344i	−0.252282	−	0.967654i	$-0.581181\pi$
$557$	255.992	−	147.797i	0.459590	−	0.265344i	0.711872	+	0.702309i	$0.247848\pi$
$558$		0			0
$559$	763.587			1.36599
$560$		0			0
$561$	33.0134	+	0.653780i	0.0588474	+	0.00116538i
$562$		0			0
$563$	404.587	−	233.589i	0.718628	−	0.414900i	−0.0956197	−	0.995418i	$-0.530483\pi$
$563$	404.587	−	233.589i	0.718628	−	0.414900i	0.814247	+	0.580518i	$0.197150\pi$
$564$		0			0
$565$	464.350	+	804.279i	0.821859	+	1.42350i
$566$		0			0
$567$	−352.113	−	739.484i	−0.621011	−	1.30420i
$568$		0			0
$569$	−968.689	−	559.273i	−1.70244	−	0.982904i	−0.943278	−	0.332003i	$-0.892276\pi$
$569$	−968.689	−	559.273i	−1.70244	−	0.982904i	−0.759162	−	0.650902i	$-0.774391\pi$
$570$		0			0
$571$	154.236	+	267.144i	0.270115	+	0.467853i	0.968891	−	0.247488i	$-0.0796049\pi$
$571$	154.236	+	267.144i	0.270115	+	0.467853i	−0.698776	+	0.715341i	$0.746272\pi$
$572$		0			0
$573$	290.821	−	160.313i	0.507541	−	0.279779i
$574$		0			0
$575$	−93.7861	−	54.1474i	−0.163106	−	0.0941694i
$576$		0			0
$577$	−619.239			−1.07320			−0.536602	−	0.843835i	$-0.680292\pi$
$577$	−619.239			−1.07320			−0.536602	+	0.843835i	$0.680292\pi$
$578$		0			0
$579$	172.270	−	285.186i	0.297529	−	0.492549i
$580$		0			0
$581$	395.161	−	228.146i	0.680140	−	0.392679i
$582$		0			0
$583$	−101.521			−0.174136
$584$		0			0
$585$	−37.5912	+	948.735i	−0.0642585	+	1.62177i
$586$		0			0
$587$	145.340	−	83.9120i	0.247598	−	0.142951i	−0.371066	−	0.928606i	$-0.621008\pi$
$587$	145.340	−	83.9120i	0.247598	−	0.142951i	0.618664	+	0.785656i	$0.287674\pi$
$588$		0			0
$589$	45.9097	−	140.504i	0.0779452	−	0.238547i
$590$		0			0
$591$	−701.395	−	423.685i	−1.18679	−	0.716895i
$592$		0			0
$593$	−182.164	+	105.172i	−0.307191	+	0.177357i	−0.645669	−	0.763618i	$-0.723421\pi$
$593$	−182.164	+	105.172i	−0.307191	+	0.177357i	0.338478	+	0.940974i	$0.390088\pi$
$594$		0			0
$595$	−55.6983	−	96.4724i	−0.0936107	−	0.162138i
$596$		0			0
$597$	282.248	+	5.58949i	0.472777	+	0.00936263i
$598$		0			0
$599$	802.647	+	463.408i	1.33998	+	0.773636i	0.986804	−	0.161921i	$-0.0517691\pi$
$599$	802.647	+	463.408i	1.33998	+	0.773636i	0.353174	+	0.935558i	$0.385102\pi$
$600$		0			0
$601$	41.3839	−	71.6790i	0.0688584	−	0.119266i	−0.829541	−	0.558446i	$-0.811398\pi$
$601$	41.3839	−	71.6790i	0.0688584	−	0.119266i	0.898399	+	0.439180i	$0.144731\pi$
$602$		0			0
$603$	−217.056	−	8.60032i	−0.359961	−	0.0142626i
$604$		0			0
$605$	435.090	−	251.199i	0.719157	−	0.415205i
$606$		0			0
$607$	−95.3438	−	165.140i	−0.157074	−	0.272060i	0.776738	−	0.629823i	$-0.216873\pi$
$607$	−95.3438	−	165.140i	−0.157074	−	0.272060i	−0.933812	+	0.357764i	$0.883539\pi$
$608$		0			0
$609$	326.620	−	180.048i	0.536322	−	0.295645i
$610$		0			0
$611$	25.0057	+	14.4370i	0.0409258	+	0.0236285i
$612$		0			0
$613$	122.066	−	211.425i	0.199129	−	0.344902i	−0.749117	−	0.662438i	$-0.769522\pi$
$613$	122.066	−	211.425i	0.199129	−	0.344902i	0.948246	+	0.317535i	$0.102855\pi$
$614$		0			0
$615$	319.968	−	529.695i	0.520273	−	0.861293i
$616$		0			0
$617$	110.470	+	63.7797i	0.179043	+	0.103371i	0.586843	−	0.809701i	$-0.300371\pi$
$617$	110.470	+	63.7797i	0.179043	+	0.103371i	−0.407800	+	0.913071i	$0.633704\pi$
$618$		0			0
$619$	594.759	−	1030.15i	0.960838	−	1.66422i	0.240433	−	0.970666i	$-0.422711\pi$
$619$	594.759	−	1030.15i	0.960838	−	1.66422i	0.720405	−	0.693554i	$-0.243956\pi$
$620$		0			0
$621$	381.537	+	251.611i	0.614391	+	0.405170i
$622$		0			0
$623$		−	1652.48i		−	2.65246i
$624$		0			0
$625$	−744.012			−1.19042
$626$		0			0
$627$	−301.295	−	105.095i	−0.480534	−	0.167615i
$628$		0			0
$629$	80.8219	+	46.6625i	0.128493	+	0.0741853i
$630$		0			0
$631$	309.854	+	536.683i	0.491052	+	0.850527i	0.999947	−	0.0103016i	$-0.00327917\pi$
$631$	309.854	+	536.683i	0.491052	+	0.850527i	−0.508895	+	0.860829i	$0.669946\pi$
$632$		0			0
$633$	−88.9053	+	147.180i	−0.140451	+	0.232511i
$634$		0			0
$635$	1077.68	−	622.200i	1.69714	−	0.979842i
$636$		0			0
$637$	1002.45			1.57370
$638$		0			0
$639$	−43.7462	+	1104.07i	−0.0684604	+	1.72782i
$640$		0			0
$641$	−426.376	+	246.168i	−0.665173	+	0.384038i	−0.794245	−	0.607597i	$-0.792133\pi$
$641$	−426.376	+	246.168i	−0.665173	+	0.384038i	0.129072	+	0.991635i	$0.458800\pi$
$642$		0			0
$643$	1166.57			1.81426			0.907128	−	0.420855i	$-0.138270\pi$
$643$	1166.57			1.81426			0.907128	+	0.420855i	$0.138270\pi$
$644$		0			0
$645$	−13.4987	+	681.631i	−0.0209282	+	1.05679i
$646$		0			0
$647$			558.344i			0.862974i	0.902119	+	0.431487i	$0.142011\pi$
$647$			558.344i			0.862974i	−0.902119	+	0.431487i	$0.857989\pi$
$648$		0			0
$649$	−70.4573	+	122.036i	−0.108563	+	0.188036i
$650$		0			0
$651$	122.021	−	202.001i	0.187436	−	0.310294i
$652$		0			0
$653$	−819.423	+	473.094i	−1.25486	+	0.724493i	−0.972070	−	0.234690i	$-0.924593\pi$
$653$	−819.423	+	473.094i	−1.25486	+	0.724493i	−0.282788	+	0.959182i	$0.591259\pi$
$654$		0			0
$655$	760.601			1.16122
$656$		0			0
$657$	179.913	+	7.12860i	0.273840	+	0.0108502i
$658$		0			0
$659$		−	516.029i		−	0.783049i	−0.920168	−	0.391525i	$-0.871948\pi$
$659$		−	516.029i		−	0.783049i	0.920168	−	0.391525i	$-0.128052\pi$
$660$		0			0
$661$	−237.002	+	410.499i	−0.358551	+	0.621028i	−0.987719	−	0.156241i	$-0.950062\pi$
$661$	−237.002	+	410.499i	−0.358551	+	0.621028i	0.629168	+	0.777269i	$0.283396\pi$
$662$		0			0
$663$	2.19875	−	111.029i	0.00331637	−	0.167464i
$664$		0			0
$665$	222.078	+	1053.36i	0.333951	+	1.58400i
$666$		0			0
$667$	−104.058	+	180.233i	−0.156008	+	0.270215i
$668$		0			0
$669$	−29.2852	−	0.579949i	−0.0437746	−	0.000866890i
$670$		0			0
$671$	−308.205	−	177.942i	−0.459321	−	0.265189i
$672$		0			0
$673$	180.204	−	312.122i	0.267762	−	0.463777i	−0.700522	−	0.713631i	$-0.747049\pi$
$673$	180.204	−	312.122i	0.267762	−	0.463777i	0.968284	+	0.249854i	$0.0803826\pi$
$674$		0			0
$675$	−172.434	−	10.2551i	−0.255457	−	0.0151927i
$676$		0			0
$677$	633.100	+	365.521i	0.935156	+	0.539912i	0.888438	−	0.458996i	$-0.151791\pi$
$677$	633.100	+	365.521i	0.935156	+	0.539912i	0.0467173	+	0.998908i	$0.485124\pi$
$678$		0			0
$679$	1821.39			2.68246
$680$		0			0
$681$	−213.299	+	117.580i	−0.313214	+	0.172658i
$682$		0			0
$683$		−	222.822i		−	0.326240i	−0.986606	−	0.163120i	$-0.947844\pi$
$683$		−	222.822i		−	0.326240i	0.986606	−	0.163120i	$-0.0521558\pi$
$684$		0			0
$685$	−89.3770			−0.130477
$686$		0			0
$687$	−548.006	−	10.8524i	−0.797679	−	0.0157968i
$688$		0			0
$689$			341.430i			0.495545i
$690$		0			0
$691$	−520.364	+	901.297i	−0.753060	+	1.30434i	0.193273	+	0.981145i	$0.438090\pi$
$691$	−520.364	+	901.297i	−0.753060	+	1.30434i	−0.946333	+	0.323193i	$0.895244\pi$
$692$		0			0
$693$	−430.773	−	271.998i	−0.621607	−	0.392493i
$694$		0			0
$695$	−905.189	−	522.611i	−1.30243	−	0.751959i
$696$		0			0
$697$	−36.1893	+	62.6817i	−0.0519215	+	0.0899306i
$698$		0			0
$699$	434.813	−	239.688i	0.622050	−	0.342901i
$700$		0			0
$701$	1023.92	+	591.162i	1.46066	+	0.843313i	0.999042	−	0.0437659i	$-0.0139356\pi$
$701$	1023.92	+	591.162i	1.46066	+	0.843313i	0.461619	+	0.887079i	$0.347269\pi$
$702$		0			0
$703$	−602.363	−	671.222i	−0.856846	−	0.954797i
$704$		0			0
$705$	−13.3296	+	22.0666i	−0.0189072	+	0.0313002i
$706$		0			0
$707$	−1304.25	−	753.009i	−1.84477	−	1.06508i
$708$		0			0
$709$	−665.458			−0.938587			−0.469294	−	0.883042i	$-0.655491\pi$
$709$	−665.458			−0.938587			−0.469294	+	0.883042i	$0.655491\pi$
$710$		0			0
$711$	49.6329	−	78.6056i	0.0698072	−	0.110556i
$712$		0			0
$713$			131.688i			0.184696i
$714$		0			0
$715$	295.299	+	511.472i	0.413005	+	0.715346i
$716$		0			0
$717$	15.1889	−	766.982i	0.0211840	−	1.06971i
$718$		0			0
$719$	−627.535	−	362.307i	−0.872788	−	0.503904i	−0.00451422	−	0.999990i	$-0.501437\pi$
$719$	−627.535	−	362.307i	−0.872788	−	0.503904i	−0.868274	+	0.496085i	$0.834770\pi$
$720$		0			0
$721$	−98.1257			−0.136097
$722$		0			0
$723$	−394.200	+	652.584i	−0.545228	+	0.902605i
$724$		0			0
$725$		−	78.6585i		−	0.108495i
$726$		0			0
$727$	703.528	+	1218.55i	0.967714	+	1.67613i	0.702140	+	0.712039i	$0.252228\pi$
$727$	703.528	+	1218.55i	0.967714	+	1.67613i	0.265574	+	0.964090i	$0.414439\pi$
$728$		0			0
$729$	723.861	+	86.4055i	0.992951	+	0.118526i
$730$		0			0
$731$		−	79.7388i		−	0.109082i
$732$		0			0
$733$	−86.4814	−	149.790i	−0.117983	−	0.204352i	0.800985	−	0.598684i	$-0.204309\pi$
$733$	−86.4814	−	149.790i	−0.117983	−	0.204352i	−0.918968	+	0.394332i	$0.870976\pi$
$734$		0			0
$735$	−17.7212	+	894.854i	−0.0241105	+	1.21749i
$736$		0			0
$737$	−117.017	+	67.5600i	−0.158775	+	0.0916689i
$738$		0			0
$739$	−66.6721	+	115.480i	−0.0902194	+	0.156265i	−0.907603	−	0.419829i	$-0.862090\pi$
$739$	−66.6721	+	115.480i	−0.0902194	+	0.156265i	0.817384	+	0.576093i	$0.195423\pi$
$740$		0			0
$741$	−353.448	+	1013.30i	−0.476989	+	1.36747i
$742$		0			0
$743$			422.459i			0.568586i	0.958737	+	0.284293i	$0.0917588\pi$
$743$			422.459i			0.568586i	−0.958737	+	0.284293i	$0.908241\pi$
$744$		0			0
$745$	−856.357			−1.14947
$746$		0			0
$747$	−16.0794	+	405.814i	−0.0215253	+	0.543259i
$748$		0			0
$749$	−1462.11	−	844.151i	−1.95209	−	1.12704i
$750$		0			0
$751$	−141.310	+	244.755i	−0.188162	+	0.325906i	−0.944637	−	0.328116i	$-0.893586\pi$
$751$	−141.310	+	244.755i	−0.188162	+	0.325906i	0.756476	+	0.654022i	$0.226920\pi$
$752$		0			0
$753$	−3.41258	+	172.322i	−0.00453198	+	0.228847i
$754$		0			0
$755$	−931.500	−	537.802i	−1.23378	−	0.712321i
$756$		0			0
$757$	82.4999	−	142.894i	0.108983	−	0.188764i	−0.806376	−	0.591404i	$-0.798574\pi$
$757$	82.4999	−	142.894i	0.108983	−	0.188764i	0.915358	+	0.402640i	$0.131907\pi$
$758$		0			0
$759$	284.229	+	5.62872i	0.374478	+	0.00741596i
$760$		0			0
$761$	−1122.72	+	648.202i	−1.47532	+	0.851776i	−0.999613	−	0.0278273i	$-0.991141\pi$
$761$	−1122.72	+	648.202i	−1.47532	+	0.851776i	−0.475707	+	0.879604i	$0.657808\pi$
$762$		0			0
$763$	923.534	+	1599.61i	1.21040	+	2.09647i
$764$		0			0
$765$	99.0732	+	3.92553i	0.129507	+	0.00513141i
$766$		0			0
$767$	410.423	+	236.958i	0.535101	+	0.308941i
$768$		0			0
$769$	−390.911	+	677.077i	−0.508336	+	0.880464i	0.491617	+	0.870812i	$0.336406\pi$
$769$	−390.911	+	677.077i	−0.508336	+	0.880464i	−0.999953	+	0.00965296i	$0.996927\pi$
$770$		0			0
$771$	−1186.06	+	653.811i	−1.53835	+	0.848004i
$772$		0			0
$773$	−722.493	+	417.131i	−0.934661	+	0.539627i	−0.888283	−	0.459297i	$-0.848101\pi$
$773$	−722.493	+	417.131i	−0.934661	+	0.539627i	−0.0463781	+	0.998924i	$0.514768\pi$
$774$		0			0
$775$	−24.8862	−	43.1041i	−0.0321112	−	0.0556182i
$776$		0			0
$777$	−695.119	−	1261.00i	−0.894619	−	1.62291i
$778$		0			0
$779$	520.568	−	467.164i	0.668252	−	0.599697i
$780$		0			0
$781$	343.649	+	595.218i	0.440012	+	0.762123i
$782$		0			0
$783$	−19.7077	+	331.374i	−0.0251694	+	0.423210i
$784$		0			0
$785$			260.538i			0.331896i
$786$		0			0
$787$	282.861	+	489.930i	0.359417	+	0.622529i	0.987864	−	0.155324i	$-0.0496422\pi$
$787$	282.861	+	489.930i	0.359417	+	0.622529i	−0.628446	+	0.777853i	$0.716309\pi$
$788$		0			0
$789$	25.5175	−	1288.53i	0.0323415	−	1.63312i
$790$		0			0
$791$			1675.89i			2.11869i
$792$		0			0
$793$	−598.444	+	1036.54i	−0.754658	+	1.30711i
$794$		0			0
$795$	−304.785	−	6.03580i	−0.383377	−	0.00759220i
$796$		0			0
$797$	−782.624	+	451.848i	−0.981962	+	0.566936i	−0.902862	−	0.429931i	$-0.858538\pi$
$797$	−782.624	+	451.848i	−0.981962	+	0.566936i	−0.0790999	+	0.996867i	$0.525205\pi$
$798$		0			0
$799$	1.50761	−	2.61126i	0.00188687	−	0.00326816i
$800$		0			0
$801$	1243.66	+	785.266i	1.55263	+	0.980357i
$802$		0			0
$803$	96.9929	−	55.9989i	0.120788	−	0.0697371i
$804$		0			0
$805$	−479.535	−	830.578i	−0.595695	−	1.03177i
$806$		0			0
$807$	303.666	−	167.394i	0.376290	−	0.207428i
$808$		0			0
$809$			1325.20i			1.63807i	0.573742	+	0.819036i	$0.305491\pi$
$809$			1325.20i			1.63807i	−0.573742	+	0.819036i	$0.694509\pi$
$810$		0			0
$811$	58.8655	+	101.958i	0.0725838	+	0.125719i	0.900033	−	0.435822i	$-0.143542\pi$
$811$	58.8655	+	101.958i	0.0725838	+	0.125719i	−0.827449	+	0.561541i	$0.810209\pi$
$812$		0			0
$813$	290.318	+	526.660i	0.357095	+	0.647798i
$814$		0			0
$815$			273.416i			0.335480i
$816$		0			0
$817$	−239.335	+	732.471i	−0.292944	+	0.896537i
$818$		0			0
$819$	−914.767	+	1448.75i	−1.11693	+	1.76893i
$820$		0			0
$821$			730.815i			0.890152i	0.895493	+	0.445076i	$0.146823\pi$
$821$			730.815i			0.890152i	−0.895493	+	0.445076i	$0.853177\pi$
$822$		0			0
$823$	314.187	−	544.189i	0.381759	−	0.661226i	−0.609555	−	0.792744i	$-0.708652\pi$
$823$	314.187	−	544.189i	0.381759	−	0.661226i	0.991314	+	0.131518i	$0.0419852\pi$
$824$		0			0
$825$	−94.0974	+	51.8706i	−0.114057	+	0.0628735i
$826$		0			0
$827$	870.300	−	502.468i	1.05236	−	0.607579i	0.129050	−	0.991638i	$-0.458807\pi$
$827$	870.300	−	502.468i	1.05236	−	0.607579i	0.923309	+	0.384059i	$0.125474\pi$
$828$		0			0
$829$	−108.562			−0.130955			−0.0654775	−	0.997854i	$-0.520857\pi$
$829$	−108.562			−0.130955			−0.0654775	+	0.997854i	$0.520857\pi$
$830$		0			0
$831$	−170.631	−	309.537i	−0.205332	−	0.372488i
$832$		0			0
$833$		−	104.682i		−	0.125669i
$834$		0			0
$835$	−106.477	+	184.423i	−0.127517	+	0.220866i
$836$		0			0
$837$	94.0412	+	187.825i	0.112355	+	0.224402i
$838$		0			0
$839$	1238.13	−	714.834i	1.47572	−	0.852007i	0.476095	−	0.879394i	$-0.342052\pi$
$839$	1238.13	−	714.834i	1.47572	−	0.852007i	0.999625	+	0.0273870i	$0.00871866\pi$
$840$		0			0
$841$	689.838			0.820259
$842$		0			0
$843$	−934.907	−	564.740i	−1.10902	−	0.669917i
$844$		0			0
$845$	900.055	−	519.647i	1.06515	−	0.614967i
$846$		0			0
$847$	906.603			1.07037
$848$		0			0
$849$	370.644	−	613.587i	0.436565	−	0.722717i
$850$		0			0
$851$	695.836	+	401.741i	0.817668	+	0.472081i
$852$		0			0
$853$	−611.108	−	1058.47i	−0.716423	−	1.24088i	−0.962408	−	0.271607i	$-0.912445\pi$
$853$	−611.108	−	1058.47i	−0.716423	−	1.24088i	0.245986	−	0.969273i	$-0.420888\pi$
$854$		0			0
$855$	−898.291	−	333.426i	−1.05063	−	0.389972i
$856$		0			0
$857$	987.625	−	570.206i	1.15242	−	0.665351i	0.202945	−	0.979190i	$-0.434949\pi$
$857$	987.625	−	570.206i	1.15242	−	0.665351i	0.949476	+	0.313839i	$0.101615\pi$
$858$		0			0
$859$	−677.078	+	1172.73i	−0.788216	+	1.36523i	0.138843	+	0.990314i	$0.455662\pi$
$859$	−677.078	+	1172.73i	−0.788216	+	1.36523i	−0.927059	+	0.374916i	$0.877672\pi$
$860$		0			0
$861$	977.972	−	539.101i	1.13586	−	0.626134i
$862$		0			0
$863$		−	491.437i		−	0.569451i	−0.958609	−	0.284726i	$-0.908097\pi$
$863$		−	491.437i		−	0.569451i	0.958609	−	0.284726i	$-0.0919025\pi$
$864$		0			0
$865$	−358.050	−	620.161i	−0.413931	−	0.716949i
$866$		0			0
$867$	855.236	+	16.9366i	0.986431	+	0.0195348i
$868$		0			0
$869$		−	57.8256i		−	0.0665426i
$870$		0			0
$871$	227.214	+	393.546i	0.260865	+	0.451832i
$872$		0			0
$873$	−865.532	+	1370.78i	−0.991446	+	1.57019i
$874$		0			0
$875$	−912.775	−	526.991i	−1.04317	−	0.602276i
$876$		0			0
$877$	163.934			0.186926			0.0934631	−	0.995623i	$-0.470206\pi$
$877$	163.934			0.186926			0.0934631	+	0.995623i	$0.470206\pi$
$878$		0			0
$879$	−13.4444	+	678.890i	−0.0152951	+	0.772344i
$880$		0			0
$881$		−	1636.83i		−	1.85792i	−0.370176	−	0.928962i	$-0.620703\pi$
$881$		−	1636.83i		−	1.85792i	0.370176	−	0.928962i	$-0.379297\pi$
$882$		0			0
$883$	29.9320	+	51.8437i	0.0338981	+	0.0587132i	0.882477	−	0.470356i	$-0.155875\pi$
$883$	29.9320	+	51.8437i	0.0338981	+	0.0587132i	−0.848579	+	0.529069i	$0.822541\pi$
$884$		0			0
$885$	−218.781	+	362.183i	−0.247210	+	0.409247i
$886$		0			0
$887$	1347.94	+	778.236i	1.51967	+	0.877380i	0.999731	+	0.0231738i	$0.00737710\pi$
$887$	1347.94	+	778.236i	1.51967	+	0.877380i	0.519935	+	0.854206i	$0.325956\pi$
$888$		0			0
$889$	2245.58			2.52596
$890$		0			0
$891$	409.411	−	194.946i	0.459496	−	0.218794i
$892$		0			0
$893$	−21.6864	+	19.4616i	−0.0242849	+	0.0217935i
$894$		0			0
$895$	−257.897			−0.288153
$896$		0			0
$897$	18.9302	−	955.901i	0.0211039	−	1.06566i
$898$		0			0
$899$	−82.8352	+	47.8249i	−0.0921415	+	0.0531979i
$900$		0			0
$901$	35.6544			0.0395721
$902$		0			0
$903$	−636.115	+	1053.06i	−0.704446	+	1.16618i
$904$		0			0
$905$	−756.565	+	436.803i	−0.835984	+	0.482655i
$906$		0			0
$907$	−39.4731	−	68.3694i	−0.0435205	−	0.0753797i	0.843445	−	0.537216i	$-0.180524\pi$
$907$	−39.4731	−	68.3694i	−0.0435205	−	0.0753797i	−0.886965	+	0.461836i	$0.847191\pi$
$908$		0			0
$909$	1186.50	−	623.745i	1.30528	−	0.686189i
$910$		0			0
$911$	1283.19	+	740.852i	1.40856	+	0.813230i	0.995249	−	0.0973622i	$-0.0310405\pi$
$911$	1283.19	+	740.852i	1.40856	+	0.813230i	0.413306	+	0.910592i	$0.364374\pi$
$912$		0			0
$913$	126.312	+	218.779i	0.138348	+	0.239626i
$914$		0			0
$915$	−914.705	−	552.537i	−0.999678	−	0.603866i
$916$		0			0
$917$	1188.66	+	686.271i	1.29624	+	0.748387i
$918$		0			0
$919$	709.794			0.772355			0.386177	−	0.922425i	$-0.373795\pi$
$919$	709.794			0.772355			0.386177	+	0.922425i	$0.373795\pi$
$920$		0			0
$921$	−109.407	−	198.472i	−0.118791	−	0.215496i
$922$		0			0
$923$	2001.80	−	1155.74i	2.16880	−	1.25216i
$924$		0			0
$925$	−303.681			−0.328304
$926$		0			0
$927$	46.6298	−	73.8494i	0.0503018	−	0.0796649i
$928$		0			0
$929$	88.5290	−	51.1123i	0.0952950	−	0.0550186i	−0.451595	−	0.892223i	$-0.649145\pi$
$929$	88.5290	−	51.1123i	0.0952950	−	0.0550186i	0.546890	+	0.837204i	$0.315812\pi$
$930$		0			0
$931$	−314.202	+	961.596i	−0.337488	+	1.03286i
$932$		0			0
$933$	18.6546	−	941.987i	0.0199942	−	1.00963i
$934$		0			0
$935$	53.4114	−	30.8371i	0.0571245	−	0.0329808i
$936$		0			0
$937$	579.451	+	1003.64i	0.618411	+	1.07112i	0.989776	+	0.142633i	$0.0455567\pi$
$937$	579.451	+	1003.64i	0.618411	+	1.07112i	−0.371364	+	0.928487i	$0.621110\pi$
$938$		0			0
$939$	736.586	−	1219.39i	0.784437	−	1.29861i
$940$		0			0
$941$	−526.142	−	303.768i	−0.559131	−	0.322814i	0.193666	−	0.981068i	$-0.437962\pi$
$941$	−526.142	−	303.768i	−0.559131	−	0.322814i	−0.752797	+	0.658253i	$0.771296\pi$
$942$		0			0
$943$	−311.571	+	539.657i	−0.330404	+	0.572277i
$944$		0			0
$945$	−1277.09	−	842.196i	−1.35141	−	0.891213i
$946$		0			0
$947$	−360.224	+	207.975i	−0.380384	+	0.219615i	−0.677985	−	0.735075i	$-0.737147\pi$
$947$	−360.224	+	207.975i	−0.380384	+	0.219615i	0.297601	+	0.954690i	$0.403813\pi$
$948$		0			0
$949$	−188.332	−	326.201i	−0.198453	−	0.343731i
$950$		0			0
$951$	1349.85	+	815.393i	1.41941	+	0.857406i
$952$		0			0
$953$	964.993	+	557.139i	1.01258	+	0.584616i	0.911947	−	0.410307i	$-0.134579\pi$
$953$	964.993	+	557.139i	1.01258	+	0.584616i	0.100637	+	0.994923i	$0.467912\pi$
$954$		0			0
$955$	310.128	−	537.158i	0.324741	−	0.562469i
$956$		0			0
$957$	99.6823	+	180.831i	0.104161	+	0.188957i
$958$		0			0
$959$	−139.677	−	80.6426i	−0.145649	−	0.0840903i
$960$		0			0
$961$	450.238	−	779.835i	0.468510	−	0.811483i
$962$		0			0
$963$	1330.11	−	699.241i	1.38122	−	0.726107i
$964$		0			0
$965$		−	622.307i		−	0.644878i
$966$		0			0
$967$	−1631.12			−1.68678			−0.843391	−	0.537300i	$-0.819444\pi$
$967$	−1631.12			−1.68678			−0.843391	+	0.537300i	$0.819444\pi$
$968$		0			0
$969$	105.815	+	36.9095i	0.109200	+	0.0380903i
$970$		0			0
$971$	−827.739	−	477.895i	−0.852460	−	0.492168i	0.00901996	−	0.999959i	$-0.497129\pi$
$971$	−827.739	−	477.895i	−0.852460	−	0.492168i	−0.861480	+	0.507791i	$0.830462\pi$
$972$		0			0
$973$	−943.078	−	1633.46i	−0.969248	−	1.67879i
$974$		0			0
$975$	174.448	+	316.463i	0.178921	+	0.324577i
$976$		0			0
$977$	191.615	−	110.629i	0.196126	−	0.113233i	−0.398721	−	0.917072i	$-0.630546\pi$
$977$	191.615	−	110.629i	0.196126	−	0.113233i	0.594847	+	0.803839i	$0.297213\pi$
$978$		0			0
$979$	914.886			0.934511
$980$		0			0
$981$	−1642.73	−	65.0892i	−1.67455	−	0.0663498i
$982$		0			0
$983$	741.557	−	428.138i	0.754382	−	0.435543i	−0.0728931	−	0.997340i	$-0.523223\pi$
$983$	741.557	−	428.138i	0.754382	−	0.435543i	0.827275	+	0.561797i	$0.189890\pi$
$984$		0			0
$985$	−1530.52			−1.55383
$986$		0			0
$987$	−40.7414	+	22.4585i	−0.0412780	+	0.0227543i
$988$		0			0
$989$		−	686.511i		−	0.694147i
$990$		0			0
$991$	−319.105	+	552.707i	−0.322003	+	0.557726i	−0.980901	−	0.194506i	$-0.937690\pi$
$991$	−319.105	+	552.707i	−0.322003	+	0.557726i	0.658898	+	0.752232i	$0.271023\pi$
$992$		0			0
$993$	94.6880	+	171.771i	0.0953555	+	0.172982i
$994$		0			0
$995$	456.640	−	263.641i	0.458935	−	0.264966i
$996$		0			0
$997$	−1176.76			−1.18030			−0.590152	−	0.807292i	$-0.700932\pi$
$997$	−1176.76			−1.18030			−0.590152	+	0.807292i	$0.700932\pi$
$998$		0			0
$999$	1279.35	+	76.0865i	1.28063	+	0.0761626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.15	✓	80
3.2	odd	2		2052.3.m.a.1493.7		80
9.4	even	3		2052.3.be.a.125.34		80
9.5	odd	6		684.3.be.a.581.14	yes	80
19.7	even	3		684.3.be.a.425.14	yes	80
57.26	odd	6		2052.3.be.a.197.34		80
171.121	even	3		2052.3.m.a.881.34		80
171.140	odd	6	inner	684.3.m.a.653.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.15	✓	80	1.1	even	1	trivial
684.3.m.a.653.15	yes	80	171.140	odd	6	inner
684.3.be.a.425.14	yes	80	19.7	even	3
684.3.be.a.581.14	yes	80	9.5	odd	6
2052.3.m.a.881.34		80	171.121	even	3
2052.3.m.a.1493.7		80	3.2	odd	2
2052.3.be.a.125.34		80	9.4	even	3
2052.3.be.a.197.34		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)

\(f(q)\)	\(=\)	\(q+(-1.55115 + 2.56787i) q^{3} +5.60337i q^{5} +(-5.05578 + 8.75686i) q^{7} +(-4.18789 - 7.96628i) q^{9} +O(q^{10})\)	\(q+(-1.55115 + 2.56787i) q^{3} +5.60337i q^{5} +(-5.05578 + 8.75686i) q^{7} +(-4.18789 - 7.96628i) q^{9} +(-4.84819 - 2.79910i) q^{11} +(-9.41378 + 16.3051i) q^{13} +(-14.3887 - 8.69164i) q^{15} +(1.70269 + 0.983049i) q^{17} +(-12.6901 - 14.1408i) q^{19} +(-14.6442 - 26.5657i) q^{21} +(14.6593 + 8.46356i) q^{23} -6.39771 q^{25} +(26.9524 + 1.60293i) q^{27} +12.2948i q^{29} +(3.88985 + 6.73742i) q^{31} +(14.7080 - 8.10768i) q^{33} +(-49.0679 - 28.3294i) q^{35} +47.4671 q^{37} +(-27.2673 - 49.4650i) q^{39} +36.8133i q^{41} +(-20.2784 - 35.1233i) q^{43} +(44.6380 - 23.4663i) q^{45} -1.53361i q^{47} +(-26.6218 - 46.1103i) q^{49} +(-5.16546 + 2.84743i) q^{51} +(15.7050 - 9.06730i) q^{53} +(15.6844 - 27.1662i) q^{55} +(55.9958 - 10.6521i) q^{57} -25.1714i q^{59} +63.5711 q^{61} +(90.9326 + 3.60298i) q^{63} +(-91.3637 - 52.7488i) q^{65} +(12.0682 - 20.9027i) q^{67} +(-44.4720 + 24.5150i) q^{69} +(-106.323 - 61.3856i) q^{71} +(-10.0030 + 17.3257i) q^{73} +(9.92379 - 16.4285i) q^{75} +(49.0227 - 28.3033i) q^{77} +(5.16465 + 8.94544i) q^{79} +(-45.9232 + 66.7238i) q^{81} +(-39.0802 - 22.5629i) q^{83} +(-5.50839 + 9.54080i) q^{85} +(-31.5714 - 19.0710i) q^{87} +(-141.530 + 81.7125i) q^{89} +(-95.1879 - 164.870i) q^{91} +(-23.3345 - 0.462105i) q^{93} +(79.2359 - 71.1073i) q^{95} +(-90.0648 - 155.997i) q^{97} +(-1.99477 + 50.3443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 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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