LMFDB - Embedded newform 684.3.g.a.343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.1
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	684.343
Dual form			684.3.g.a.343.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} -6.54983 q^{5} +1.31342i q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} -6.54983 q^{5} +1.31342i q^{7} -8.00000 q^{8} +(-6.54983 + 11.3446i) q^{10} -4.30136i q^{11} +0.824752 q^{13} +(2.27492 + 1.31342i) q^{14} +(-8.00000 + 13.8564i) q^{16} -0.274917 q^{17} -4.35890i q^{19} +(13.0997 + 22.6893i) q^{20} +(-7.45017 - 4.30136i) q^{22} +33.5578i q^{23} +17.9003 q^{25} +(0.824752 - 1.42851i) q^{26} +(4.54983 - 2.62685i) q^{28} +33.3746 q^{29} +48.7276i q^{31} +(16.0000 + 27.7128i) q^{32} +(-0.274917 + 0.476171i) q^{34} -8.60271i q^{35} -36.1993 q^{37} +(-7.54983 - 4.35890i) q^{38} +52.3987 q^{40} +68.7492 q^{41} +55.6558i q^{43} +(-14.9003 + 8.60271i) q^{44} +(58.1238 + 33.5578i) q^{46} -24.1336i q^{47} +47.2749 q^{49} +(17.9003 - 31.0043i) q^{50} +(-1.64950 - 2.85702i) q^{52} -25.9244 q^{53} +28.1732i q^{55} -10.5074i q^{56} +(33.3746 - 57.8065i) q^{58} +46.2317i q^{59} -47.0997 q^{61} +(84.3987 + 48.7276i) q^{62} +64.0000 q^{64} -5.40199 q^{65} -112.625i q^{67} +(0.549834 + 0.952341i) q^{68} +(-14.9003 - 8.60271i) q^{70} -70.4645i q^{71} -58.0756 q^{73} +(-36.1993 + 62.6991i) q^{74} +(-15.0997 + 8.71780i) q^{76} +5.64950 q^{77} +113.478i q^{79} +(52.3987 - 90.7572i) q^{80} +(68.7492 - 119.077i) q^{82} +148.579i q^{83} +1.80066 q^{85} +(96.3987 + 55.6558i) q^{86} +34.4108i q^{88} -57.8488 q^{89} +1.08325i q^{91} +(116.248 - 67.1155i) q^{92} +(-41.8007 - 24.1336i) q^{94} +28.5501i q^{95} -117.698 q^{97} +(47.2749 - 81.8826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 32 q^{8} + 4 q^{10} - 42 q^{13} - 6 q^{14} - 32 q^{16} + 14 q^{17} - 8 q^{20} - 60 q^{22} + 132 q^{25} - 42 q^{26} - 12 q^{28} + 58 q^{29} + 64 q^{32} + 14 q^{34} - 24 q^{37} - 32 q^{40} + 124 q^{41} - 120 q^{44} + 6 q^{46} + 174 q^{49} + 132 q^{50} + 84 q^{52} + 2 q^{53} + 58 q^{58} - 128 q^{61} + 96 q^{62} + 256 q^{64} - 384 q^{65} - 28 q^{68} - 120 q^{70} - 338 q^{73} - 24 q^{74} - 68 q^{77} - 32 q^{80} + 124 q^{82} + 128 q^{85} + 144 q^{86} - 20 q^{89} + 12 q^{92} - 288 q^{94} - 48 q^{97} + 174 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 32 * q^8 + 4 * q^10 - 42 * q^13 - 6 * q^14 - 32 * q^16 + 14 * q^17 - 8 * q^20 - 60 * q^22 + 132 * q^25 - 42 * q^26 - 12 * q^28 + 58 * q^29 + 64 * q^32 + 14 * q^34 - 24 * q^37 - 32 * q^40 + 124 * q^41 - 120 * q^44 + 6 * q^46 + 174 * q^49 + 132 * q^50 + 84 * q^52 + 2 * q^53 + 58 * q^58 - 128 * q^61 + 96 * q^62 + 256 * q^64 - 384 * q^65 - 28 * q^68 - 120 * q^70 - 338 * q^73 - 24 * q^74 - 68 * q^77 - 32 * q^80 + 124 * q^82 + 128 * q^85 + 144 * q^86 - 20 * q^89 + 12 * q^92 - 288 * q^94 - 48 * q^97 + 174 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.00000	−	1.73205i	0.500000	−	0.866025i
$2$	1.00000	−	1.73205i	0.500000	−	0.866025i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	−6.54983			−1.30997			−0.654983	−	0.755643i	$-0.727324\pi$
$5$	−6.54983			−1.30997			−0.654983	+	0.755643i	$0.727324\pi$
$6$		0			0
$7$			1.31342i			0.187632i	0.995590	+	0.0938160i	$0.0299065\pi$
$7$			1.31342i			0.187632i	−0.995590	+	0.0938160i	$0.970093\pi$
$8$	−8.00000			−1.00000
$9$		0			0
$10$	−6.54983	+	11.3446i	−0.654983	+	1.13446i
$11$		−	4.30136i		−	0.391032i	−0.980700	−	0.195516i	$-0.937362\pi$
$11$		−	4.30136i		−	0.391032i	0.980700	−	0.195516i	$-0.0626382\pi$
$12$		0			0
$13$	0.824752			0.0634424			0.0317212	−	0.999497i	$-0.489901\pi$
$13$	0.824752			0.0634424			0.0317212	+	0.999497i	$0.489901\pi$
$14$	2.27492	+	1.31342i	0.162494	+	0.0938160i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$	−0.274917			−0.0161716			−0.00808580	−	0.999967i	$-0.502574\pi$
$17$	−0.274917			−0.0161716			−0.00808580	+	0.999967i	$0.502574\pi$
$18$		0			0
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	13.0997	+	22.6893i	0.654983	+	1.13446i
$21$		0			0
$22$	−7.45017	−	4.30136i	−0.338644	−	0.195516i
$23$			33.5578i			1.45903i	0.683963	+	0.729517i	$0.260255\pi$
$23$			33.5578i			1.45903i	−0.683963	+	0.729517i	$0.739745\pi$
$24$		0			0
$25$	17.9003			0.716013
$26$	0.824752	−	1.42851i	0.0317212	−	0.0549428i
$27$		0			0
$28$	4.54983	−	2.62685i	0.162494	−	0.0938160i
$29$	33.3746			1.15085			0.575424	−	0.817855i	$-0.304837\pi$
$29$	33.3746			1.15085			0.575424	+	0.817855i	$0.304837\pi$
$30$		0			0
$31$			48.7276i			1.57186i	0.618317	+	0.785929i	$0.287815\pi$
$31$			48.7276i			1.57186i	−0.618317	+	0.785929i	$0.712185\pi$
$32$	16.0000	+	27.7128i	0.500000	+	0.866025i
$33$		0			0
$34$	−0.274917	+	0.476171i	−0.00808580	+	0.0140050i
$35$		−	8.60271i		−	0.245792i
$36$		0			0
$37$	−36.1993			−0.978360			−0.489180	−	0.872183i	$-0.662704\pi$
$37$	−36.1993			−0.978360			−0.489180	+	0.872183i	$0.662704\pi$
$38$	−7.54983	−	4.35890i	−0.198680	−	0.114708i
$39$		0			0
$40$	52.3987			1.30997
$41$	68.7492			1.67681			0.838405	−	0.545048i	$-0.183489\pi$
$41$	68.7492			1.67681			0.838405	+	0.545048i	$0.183489\pi$
$42$		0			0
$43$			55.6558i			1.29432i	0.762354	+	0.647160i	$0.224044\pi$
$43$			55.6558i			1.29432i	−0.762354	+	0.647160i	$0.775956\pi$
$44$	−14.9003	+	8.60271i	−0.338644	+	0.195516i
$45$		0			0
$46$	58.1238	+	33.5578i	1.26356	+	0.729517i
$47$		−	24.1336i		−	0.513481i	−0.966480	−	0.256741i	$-0.917351\pi$
$47$		−	24.1336i		−	0.513481i	0.966480	−	0.256741i	$-0.0826486\pi$
$48$		0			0
$49$	47.2749			0.964794
$50$	17.9003	−	31.0043i	0.358007	−	0.620086i
$51$		0			0
$52$	−1.64950	−	2.85702i	−0.0317212	−	0.0549428i
$53$	−25.9244			−0.489140			−0.244570	−	0.969632i	$-0.578647\pi$
$53$	−25.9244			−0.489140			−0.244570	+	0.969632i	$0.578647\pi$
$54$		0			0
$55$			28.1732i			0.512239i
$56$		−	10.5074i		−	0.187632i
$57$		0			0
$58$	33.3746	−	57.8065i	0.575424	−	0.996663i
$59$			46.2317i			0.783587i	0.920053	+	0.391794i	$0.128145\pi$
$59$			46.2317i			0.783587i	−0.920053	+	0.391794i	$0.871855\pi$
$60$		0			0
$61$	−47.0997			−0.772126			−0.386063	−	0.922472i	$-0.626165\pi$
$61$	−47.0997			−0.772126			−0.386063	+	0.922472i	$0.626165\pi$
$62$	84.3987	+	48.7276i	1.36127	+	0.785929i
$63$		0			0
$64$	64.0000			1.00000
$65$	−5.40199			−0.0831075
$66$		0			0
$67$		−	112.625i		−	1.68097i	−0.541834	−	0.840485i	$-0.682270\pi$
$67$		−	112.625i		−	1.68097i	0.541834	−	0.840485i	$-0.317730\pi$
$68$	0.549834	+	0.952341i	0.00808580	+	0.0140050i
$69$		0			0
$70$	−14.9003	−	8.60271i	−0.212862	−	0.122896i
$71$		−	70.4645i		−	0.992458i	−0.868192	−	0.496229i	$-0.834718\pi$
$71$		−	70.4645i		−	0.992458i	0.868192	−	0.496229i	$-0.165282\pi$
$72$		0			0
$73$	−58.0756			−0.795556			−0.397778	−	0.917482i	$-0.630219\pi$
$73$	−58.0756			−0.795556			−0.397778	+	0.917482i	$0.630219\pi$
$74$	−36.1993	+	62.6991i	−0.489180	+	0.847285i
$75$		0			0
$76$	−15.0997	+	8.71780i	−0.198680	+	0.114708i
$77$	5.64950			0.0733702
$78$		0			0
$79$			113.478i			1.43643i	0.695820	+	0.718216i	$0.255041\pi$
$79$			113.478i			1.43643i	−0.695820	+	0.718216i	$0.744959\pi$
$80$	52.3987	−	90.7572i	0.654983	−	1.13446i
$81$		0			0
$82$	68.7492	−	119.077i	0.838405	−	1.45216i
$83$			148.579i			1.79011i	0.445952	+	0.895057i	$0.352865\pi$
$83$			148.579i			1.79011i	−0.445952	+	0.895057i	$0.647135\pi$
$84$		0			0
$85$	1.80066			0.0211843
$86$	96.3987	+	55.6558i	1.12091	+	0.647160i
$87$		0			0
$88$			34.4108i			0.391032i
$89$	−57.8488			−0.649987			−0.324993	−	0.945716i	$-0.605362\pi$
$89$	−57.8488			−0.649987			−0.324993	+	0.945716i	$0.605362\pi$
$90$		0			0
$91$			1.08325i			0.0119038i
$92$	116.248	−	67.1155i	1.26356	−	0.729517i
$93$		0			0
$94$	−41.8007	−	24.1336i	−0.444688	−	0.256741i
$95$			28.5501i			0.300527i
$96$		0			0
$97$	−117.698			−1.21338			−0.606689	−	0.794939i	$-0.707503\pi$
$97$	−117.698			−1.21338			−0.606689	+	0.794939i	$0.707503\pi$
$98$	47.2749	−	81.8826i	0.482397	−	0.835536i
$99$		0			0
$100$	−35.8007	−	62.0086i	−0.358007	−	0.620086i
$101$	−173.299			−1.71583			−0.857916	−	0.513790i	$-0.828241\pi$
$101$	−173.299			−1.71583			−0.857916	+	0.513790i	$0.828241\pi$
$102$		0			0
$103$			1.18252i			0.0114807i	0.999984	+	0.00574037i	$0.00182723\pi$
$103$			1.18252i			0.0114807i	−0.999984	+	0.00574037i	$0.998173\pi$
$104$	−6.59801			−0.0634424
$105$		0			0
$106$	−25.9244	+	44.9024i	−0.244570	+	0.423608i
$107$			92.7928i			0.867222i	0.901100	+	0.433611i	$0.142761\pi$
$107$			92.7928i			0.867222i	−0.901100	+	0.433611i	$0.857239\pi$
$108$		0			0
$109$	−44.8248			−0.411236			−0.205618	−	0.978632i	$-0.565920\pi$
$109$	−44.8248			−0.411236			−0.205618	+	0.978632i	$0.565920\pi$
$110$	48.7974	+	28.1732i	0.443612	+	0.256120i
$111$		0			0
$112$	−18.1993	−	10.5074i	−0.162494	−	0.0938160i
$113$	−65.6977			−0.581395			−0.290698	−	0.956815i	$-0.593887\pi$
$113$	−65.6977			−0.581395			−0.290698	+	0.956815i	$0.593887\pi$
$114$		0			0
$115$		−	219.798i		−	1.91129i
$116$	−66.7492	−	115.613i	−0.575424	−	0.996663i
$117$		0			0
$118$	80.0756	+	46.2317i	0.678607	+	0.391794i
$119$		−	0.361083i		−	0.00303431i
$120$		0			0
$121$	102.498			0.847094
$122$	−47.0997	+	81.5790i	−0.386063	+	0.668680i
$123$		0			0
$124$	168.797	−	97.4552i	1.36127	−	0.785929i
$125$	46.5017			0.372013
$126$		0			0
$127$			93.9076i			0.739430i	0.929145	+	0.369715i	$0.120545\pi$
$127$			93.9076i			0.739430i	−0.929145	+	0.369715i	$0.879455\pi$
$128$	64.0000	−	110.851i	0.500000	−	0.866025i
$129$		0			0
$130$	−5.40199	+	9.35652i	−0.0415537	+	0.0719732i
$131$		−	9.81687i		−	0.0749379i	−0.999298	−	0.0374690i	$-0.988070\pi$
$131$		−	9.81687i		−	0.0749379i	0.999298	−	0.0374690i	$-0.0119295\pi$
$132$		0			0
$133$	5.72508			0.0430457
$134$	−195.072	−	112.625i	−1.45576	−	0.840485i
$135$		0			0
$136$	2.19934			0.0161716
$137$	−63.9726			−0.466953			−0.233477	−	0.972362i	$-0.575010\pi$
$137$	−63.9726			−0.466953			−0.233477	+	0.972362i	$0.575010\pi$
$138$		0			0
$139$			18.8799i			0.135827i	0.997691	+	0.0679134i	$0.0216342\pi$
$139$			18.8799i			0.135827i	−0.997691	+	0.0679134i	$0.978366\pi$
$140$	−29.8007	+	17.2054i	−0.212862	+	0.122896i
$141$		0			0
$142$	−122.048	−	70.4645i	−0.859494	−	0.496229i
$143$		−	3.54755i		−	0.0248080i
$144$		0			0
$145$	−218.598			−1.50757
$146$	−58.0756	+	100.590i	−0.397778	+	0.688972i
$147$		0			0
$148$	72.3987	+	125.398i	0.489180	+	0.847285i
$149$	78.9485			0.529856			0.264928	−	0.964268i	$-0.414652\pi$
$149$	78.9485			0.529856			0.264928	+	0.964268i	$0.414652\pi$
$150$		0			0
$151$			192.744i			1.27645i	0.769850	+	0.638225i	$0.220331\pi$
$151$			192.744i			1.27645i	−0.769850	+	0.638225i	$0.779669\pi$
$152$			34.8712i			0.229416i
$153$		0			0
$154$	5.64950	−	9.78523i	0.0366851	−	0.0635404i
$155$		−	319.158i		−	2.05908i
$156$		0			0
$157$	7.00331			0.0446071			0.0223035	−	0.999751i	$-0.492900\pi$
$157$	7.00331			0.0446071			0.0223035	+	0.999751i	$0.492900\pi$
$158$	196.550	+	113.478i	1.24399	+	0.718216i
$159$		0			0
$160$	−104.797	−	181.514i	−0.654983	−	1.13446i
$161$	−44.0756			−0.273761
$162$		0			0
$163$		−	12.6423i		−	0.0775598i	−0.999248	−	0.0387799i	$-0.987653\pi$
$163$		−	12.6423i		−	0.0775598i	0.999248	−	0.0387799i	$-0.0123471\pi$
$164$	−137.498	−	238.154i	−0.838405	−	1.45216i
$165$		0			0
$166$	257.347	+	148.579i	1.55028	+	0.895057i
$167$			112.296i			0.672429i	0.941786	+	0.336214i	$0.109147\pi$
$167$			112.296i			0.672429i	−0.941786	+	0.336214i	$0.890853\pi$
$168$		0			0
$169$	−168.320			−0.995975
$170$	1.80066	−	3.11884i	0.0105921	−	0.0183461i
$171$		0			0
$172$	192.797	−	111.312i	1.12091	−	0.647160i
$173$	−39.8970			−0.230619			−0.115309	−	0.993330i	$-0.536786\pi$
$173$	−39.8970			−0.230619			−0.115309	+	0.993330i	$0.536786\pi$
$174$		0			0
$175$			23.5107i			0.134347i
$176$	59.6013	+	34.4108i	0.338644	+	0.195516i
$177$		0			0
$178$	−57.8488	+	100.197i	−0.324993	+	0.562905i
$179$		−	141.159i		−	0.788599i	−0.918982	−	0.394300i	$-0.870987\pi$
$179$		−	141.159i		−	0.788599i	0.918982	−	0.394300i	$-0.129013\pi$
$180$		0			0
$181$	142.000			0.784530			0.392265	−	0.919852i	$-0.371692\pi$
$181$	142.000			0.784530			0.392265	+	0.919852i	$0.371692\pi$
$182$	1.87624	+	1.08325i	0.0103090	+	0.00595192i
$183$		0			0
$184$		−	268.462i		−	1.45903i
$185$	237.100			1.28162
$186$		0			0
$187$			1.18252i			0.00632362i
$188$	−83.6013	+	48.2672i	−0.444688	+	0.256741i
$189$		0			0
$190$	49.4502	+	28.5501i	0.260264	+	0.150264i
$191$			315.416i			1.65139i	0.564115	+	0.825696i	$0.309217\pi$
$191$			315.416i			1.65139i	−0.564115	+	0.825696i	$0.690783\pi$
$192$		0			0
$193$	44.1993			0.229012			0.114506	−	0.993423i	$-0.463471\pi$
$193$	44.1993			0.229012			0.114506	+	0.993423i	$0.463471\pi$
$194$	−117.698	+	203.858i	−0.606689	+	1.05082i
$195$		0			0
$196$	−94.5498	−	163.765i	−0.482397	−	0.835536i
$197$	317.547			1.61191			0.805956	−	0.591976i	$-0.201652\pi$
$197$	317.547			1.61191			0.805956	+	0.591976i	$0.201652\pi$
$198$		0			0
$199$			344.835i			1.73284i	0.499317	+	0.866419i	$0.333584\pi$
$199$			344.835i			1.73284i	−0.499317	+	0.866419i	$0.666416\pi$
$200$	−143.203			−0.716013
$201$		0			0
$202$	−173.299	+	300.163i	−0.857916	+	1.48595i
$203$			43.8350i			0.215936i
$204$		0			0
$205$	−450.296			−2.19656
$206$	2.04818	+	1.18252i	0.00994262	+	0.00574037i
$207$		0			0
$208$	−6.59801	+	11.4281i	−0.0317212	+	0.0549428i
$209$	−18.7492			−0.0897090
$210$		0			0
$211$		−	325.725i		−	1.54372i	−0.635793	−	0.771860i	$-0.719327\pi$
$211$		−	325.725i		−	1.54372i	0.635793	−	0.771860i	$-0.280673\pi$
$212$	51.8488	+	89.8048i	0.244570	+	0.423608i
$213$		0			0
$214$	160.722	+	92.7928i	0.751036	+	0.433611i
$215$		−	364.536i		−	1.69552i
$216$		0			0
$217$	−64.0000			−0.294931
$218$	−44.8248	+	77.6387i	−0.205618	+	0.356141i
$219$		0			0
$220$	97.5947	−	56.3463i	0.443612	−	0.256120i
$221$	−0.226738			−0.00102597
$222$		0			0
$223$		−	300.246i		−	1.34640i	−0.739463	−	0.673198i	$-0.764920\pi$
$223$		−	300.246i		−	1.34640i	0.739463	−	0.673198i	$-0.235080\pi$
$224$	−36.3987	+	21.0148i	−0.162494	+	0.0938160i
$225$		0			0
$226$	−65.6977	+	113.792i	−0.290698	+	0.503503i
$227$		−	177.376i		−	0.781390i	−0.920520	−	0.390695i	$-0.872235\pi$
$227$		−	177.376i		−	0.781390i	0.920520	−	0.390695i	$-0.127765\pi$
$228$		0			0
$229$	38.3987			0.167680			0.0838399	−	0.996479i	$-0.473282\pi$
$229$	38.3987			0.167680			0.0838399	+	0.996479i	$0.473282\pi$
$230$	−380.701	−	219.798i	−1.65522	−	0.955643i
$231$		0			0
$232$	−266.997			−1.15085
$233$	−374.399			−1.60686			−0.803431	−	0.595398i	$-0.796994\pi$
$233$	−374.399			−1.60686			−0.803431	+	0.595398i	$0.796994\pi$
$234$		0			0
$235$			158.071i			0.672644i
$236$	160.151	−	92.4633i	0.678607	−	0.391794i
$237$		0			0
$238$	−0.625414	−	0.361083i	−0.00262779	−	0.00151716i
$239$			17.3363i			0.0725369i	0.999342	+	0.0362685i	$0.0115471\pi$
$239$			17.3363i			0.0725369i	−0.999342	+	0.0362685i	$0.988453\pi$
$240$		0			0
$241$	346.646			1.43837			0.719183	−	0.694821i	$-0.244516\pi$
$241$	346.646			1.43837			0.719183	+	0.694821i	$0.244516\pi$
$242$	102.498	−	177.532i	0.423547	−	0.733605i
$243$		0			0
$244$	94.1993	+	163.158i	0.386063	+	0.668680i
$245$	−309.643			−1.26385
$246$		0			0
$247$		−	3.59501i		−	0.0145547i
$248$		−	389.821i		−	1.57186i
$249$		0			0
$250$	46.5017	−	80.5432i	0.186007	−	0.322173i
$251$			231.258i			0.921345i	0.887570	+	0.460672i	$0.152392\pi$
$251$			231.258i			0.921345i	−0.887570	+	0.460672i	$0.847608\pi$
$252$		0			0
$253$	144.344			0.570529
$254$	162.653	+	93.9076i	0.640365	+	0.369715i
$255$		0			0
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$	−169.849			−0.660890			−0.330445	−	0.943825i	$-0.607199\pi$
$257$	−169.849			−0.660890			−0.330445	+	0.943825i	$0.607199\pi$
$258$		0			0
$259$		−	47.5451i		−	0.183572i
$260$	10.8040	+	18.7130i	0.0415537	+	0.0719732i
$261$		0			0
$262$	−17.0033	−	9.81687i	−0.0648981	−	0.0374690i
$263$		−	90.0666i		−	0.342459i	−0.985231	−	0.171229i	$-0.945226\pi$
$263$		−	90.0666i		−	0.342459i	0.985231	−	0.171229i	$-0.0547739\pi$
$264$		0			0
$265$	169.801			0.640757
$266$	5.72508	−	9.91613i	0.0215229	−	0.0372787i
$267$		0			0
$268$	−390.145	+	225.250i	−1.45576	+	0.840485i
$269$	−435.993			−1.62079			−0.810397	−	0.585882i	$-0.800748\pi$
$269$	−435.993			−1.62079			−0.810397	+	0.585882i	$0.800748\pi$
$270$		0			0
$271$			353.438i			1.30420i	0.758134	+	0.652099i	$0.226111\pi$
$271$			353.438i			1.30420i	−0.758134	+	0.652099i	$0.773889\pi$
$272$	2.19934	−	3.80936i	0.00808580	−	0.0140050i
$273$		0			0
$274$	−63.9726	+	110.804i	−0.233477	+	0.404393i
$275$		−	76.9957i		−	0.279984i
$276$		0			0
$277$	−227.045			−0.819657			−0.409828	−	0.912163i	$-0.634411\pi$
$277$	−227.045			−0.819657			−0.409828	+	0.912163i	$0.634411\pi$
$278$	32.7010	+	18.8799i	0.117629	+	0.0679134i
$279$		0			0
$280$			68.8217i			0.245792i
$281$	−114.646			−0.407994			−0.203997	−	0.978972i	$-0.565393\pi$
$281$	−114.646			−0.407994			−0.203997	+	0.978972i	$0.565393\pi$
$282$		0			0
$283$			101.296i			0.357937i	0.983855	+	0.178969i	$0.0572760\pi$
$283$			101.296i			0.357937i	−0.983855	+	0.178969i	$0.942724\pi$
$284$	−244.096	+	140.929i	−0.859494	+	0.496229i
$285$		0			0
$286$	−6.14454	−	3.54755i	−0.0214844	−	0.0124040i
$287$			90.2968i			0.314623i
$288$		0			0
$289$	−288.924			−0.999738
$290$	−218.598	+	378.623i	−0.753786	+	1.30560i
$291$		0			0
$292$	116.151	+	201.180i	0.397778	+	0.688972i
$293$	−272.069			−0.928563			−0.464281	−	0.885688i	$-0.653687\pi$
$293$	−272.069			−0.928563			−0.464281	+	0.885688i	$0.653687\pi$
$294$		0			0
$295$		−	302.810i		−	1.02647i
$296$	289.595			0.978360
$297$		0			0
$298$	78.9485	−	136.743i	0.264928	−	0.458869i
$299$			27.6768i			0.0925646i
$300$		0			0
$301$	−73.0997			−0.242856
$302$	333.842	+	192.744i	1.10544	+	0.638225i
$303$		0			0
$304$	60.3987	+	34.8712i	0.198680	+	0.114708i
$305$	308.495			1.01146
$306$		0			0
$307$		−	131.176i		−	0.427282i	−0.976912	−	0.213641i	$-0.931468\pi$
$307$		−	131.176i		−	0.427282i	0.976912	−	0.213641i	$-0.0685322\pi$
$308$	−11.2990	−	19.5705i	−0.0366851	−	0.0635404i
$309$		0			0
$310$	−552.797	−	319.158i	−1.78322	−	1.02954i
$311$			486.423i			1.56406i	0.623240	+	0.782030i	$0.285816\pi$
$311$			486.423i			1.56406i	−0.623240	+	0.782030i	$0.714184\pi$
$312$		0			0
$313$	308.027			0.984113			0.492057	−	0.870563i	$-0.336245\pi$
$313$	308.027			0.984113			0.492057	+	0.870563i	$0.336245\pi$
$314$	7.00331	−	12.1301i	0.0223035	−	0.0386309i
$315$		0			0
$316$	393.100	−	226.956i	1.24399	−	0.718216i
$317$	219.918			0.693747			0.346873	−	0.937912i	$-0.387243\pi$
$317$	219.918			0.693747			0.346873	+	0.937912i	$0.387243\pi$
$318$		0			0
$319$		−	143.556i		−	0.450019i
$320$	−419.189			−1.30997
$321$		0			0
$322$	−44.0756	+	76.3411i	−0.136881	+	0.237084i
$323$			1.19834i			0.00371002i
$324$		0			0
$325$	14.7633			0.0454256
$326$	−21.8970	−	12.6423i	−0.0671688	−	0.0387799i
$327$		0			0
$328$	−549.993			−1.67681
$329$	31.6977			0.0963455
$330$		0			0
$331$		−	107.110i		−	0.323594i	−0.986824	−	0.161797i	$-0.948271\pi$
$331$		−	107.110i		−	0.323594i	0.986824	−	0.161797i	$-0.0517289\pi$
$332$	514.694	−	297.159i	1.55028	−	0.895057i
$333$		0			0
$334$	194.502	+	112.296i	0.582340	+	0.336214i
$335$			737.675i			2.20202i
$336$		0			0
$337$	425.849			1.26365			0.631823	−	0.775113i	$-0.282307\pi$
$337$	425.849			1.26365			0.631823	+	0.775113i	$0.282307\pi$
$338$	−168.320	+	291.538i	−0.497988	+	0.862540i
$339$		0			0
$340$	−3.60132	−	6.23768i	−0.0105921	−	0.0183461i
$341$	209.595			0.614647
$342$		0			0
$343$			126.450i			0.368658i
$344$		−	445.246i		−	1.29432i
$345$		0			0
$346$	−39.8970	+	69.1037i	−0.115309	+	0.199722i
$347$		−	633.427i		−	1.82544i	−0.408587	−	0.912719i	$-0.633978\pi$
$347$		−	633.427i		−	1.82544i	0.408587	−	0.912719i	$-0.366022\pi$
$348$		0			0
$349$	−223.292			−0.639806			−0.319903	−	0.947450i	$-0.603650\pi$
$349$	−223.292			−0.639806			−0.319903	+	0.947450i	$0.603650\pi$
$350$	40.7218	+	23.5107i	0.116348	+	0.0671735i
$351$		0			0
$352$	119.203	−	68.8217i	0.338644	−	0.195516i
$353$	−122.323			−0.346524			−0.173262	−	0.984876i	$-0.555431\pi$
$353$	−122.323			−0.346524			−0.173262	+	0.984876i	$0.555431\pi$
$354$		0			0
$355$			461.531i			1.30009i
$356$	115.698	+	200.394i	0.324993	+	0.562905i
$357$		0			0
$358$	−244.495	−	141.159i	−0.682947	−	0.394300i
$359$		−	535.214i		−	1.49085i	−0.666592	−	0.745423i	$-0.732247\pi$
$359$		−	535.214i		−	1.49085i	0.666592	−	0.745423i	$-0.267753\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	142.000	−	245.951i	0.392265	−	0.679423i
$363$		0			0
$364$	3.75248	−	2.16650i	0.0103090	−	0.00595192i
$365$	380.385			1.04215
$366$		0			0
$367$			100.177i			0.272962i	0.990643	+	0.136481i	$0.0435792\pi$
$367$			100.177i			0.272962i	−0.990643	+	0.136481i	$0.956421\pi$
$368$	−464.990	−	268.462i	−1.26356	−	0.729517i
$369$		0			0
$370$	237.100	−	410.669i	0.640810	−	1.10992i
$371$		−	34.0498i		−	0.0917783i
$372$		0			0
$373$	191.767			0.514120			0.257060	−	0.966395i	$-0.417246\pi$
$373$	191.767			0.514120			0.257060	+	0.966395i	$0.417246\pi$
$374$	2.04818	+	1.18252i	0.00547641	+	0.00316181i
$375$		0			0
$376$			193.069i			0.513481i
$377$	27.5257			0.0730126
$378$		0			0
$379$		−	108.292i		−	0.285731i	−0.989742	−	0.142865i	$-0.954368\pi$
$379$		−	108.292i		−	0.285731i	0.989742	−	0.142865i	$-0.0456316\pi$
$380$	98.9003	−	57.1001i	0.260264	−	0.150264i
$381$		0			0
$382$	546.316	+	315.416i	1.43015	+	0.825696i
$383$			173.571i			0.453187i	0.973989	+	0.226593i	$0.0727588\pi$
$383$			173.571i			0.453187i	−0.973989	+	0.226593i	$0.927241\pi$
$384$		0			0
$385$	−37.0033			−0.0961125
$386$	44.1993	−	76.5555i	0.114506	−	0.198330i
$387$		0			0
$388$	235.395	+	407.717i	0.606689	+	1.05082i
$389$	541.890			1.39303			0.696517	−	0.717540i	$-0.254732\pi$
$389$	541.890			1.39303			0.696517	+	0.717540i	$0.254732\pi$
$390$		0			0
$391$		−	9.22561i		−	0.0235949i
$392$	−378.199			−0.964794
$393$		0			0
$394$	317.547	−	550.007i	0.805956	−	1.39596i
$395$		−	743.263i		−	1.88168i
$396$		0			0
$397$	443.444			1.11699			0.558493	−	0.829509i	$-0.311380\pi$
$397$	443.444			1.11699			0.558493	+	0.829509i	$0.311380\pi$
$398$	597.272	+	344.835i	1.50068	+	0.866419i
$399$		0			0
$400$	−143.203	+	248.034i	−0.358007	+	0.620086i
$401$	287.141			0.716063			0.358031	−	0.933710i	$-0.383448\pi$
$401$	287.141			0.716063			0.358031	+	0.933710i	$0.383448\pi$
$402$		0			0
$403$			40.1882i			0.0997225i
$404$	346.598	+	600.325i	0.857916	+	1.48595i
$405$		0			0
$406$	75.9244	+	43.8350i	0.187006	+	0.107968i
$407$			155.706i			0.382571i
$408$		0			0
$409$	−258.248			−0.631412			−0.315706	−	0.948857i	$-0.602241\pi$
$409$	−258.248			−0.631412			−0.315706	+	0.948857i	$0.602241\pi$
$410$	−450.296	+	779.935i	−1.09828	+	1.90228i
$411$		0			0
$412$	4.09636	−	2.36503i	0.00994262	−	0.00574037i
$413$	−60.7218			−0.147026
$414$		0			0
$415$		−	973.171i		−	2.34499i
$416$	13.1960	+	22.8562i	0.0317212	+	0.0549428i
$417$		0			0
$418$	−18.7492	+	32.4745i	−0.0448545	+	0.0776902i
$419$		−	421.176i		−	1.00519i	−0.864521	−	0.502597i	$-0.832378\pi$
$419$		−	421.176i		−	1.00519i	0.864521	−	0.502597i	$-0.167622\pi$
$420$		0			0
$421$	513.815			1.22046			0.610231	−	0.792223i	$-0.291076\pi$
$421$	513.815			1.22046			0.610231	+	0.792223i	$0.291076\pi$
$422$	−564.172	−	325.725i	−1.33690	−	0.771860i
$423$		0			0
$424$	207.395			0.489140
$425$	−4.92111			−0.0115791
$426$		0			0
$427$		−	61.8618i		−	0.144876i
$428$	321.444	−	185.586i	0.751036	−	0.433611i
$429$		0			0
$430$	−631.395	−	364.536i	−1.46836	−	0.847759i
$431$			170.808i			0.396307i	0.980171	+	0.198154i	$0.0634945\pi$
$431$			170.808i			0.396307i	−0.980171	+	0.198154i	$0.936506\pi$
$432$		0			0
$433$	277.299			0.640413			0.320207	−	0.947348i	$-0.396248\pi$
$433$	277.299			0.640413			0.320207	+	0.947348i	$0.396248\pi$
$434$	−64.0000	+	110.851i	−0.147465	+	0.255418i
$435$		0			0
$436$	89.6495	+	155.277i	0.205618	+	0.356141i
$437$	146.275			0.334725
$438$		0			0
$439$		−	233.654i		−	0.532242i	−0.963940	−	0.266121i	$-0.914258\pi$
$439$		−	233.654i		−	0.532242i	0.963940	−	0.266121i	$-0.0857421\pi$
$440$		−	225.385i		−	0.512239i
$441$		0			0
$442$	−0.226738	+	0.392722i	−0.000512983	+	0.000888512i
$443$		−	571.430i		−	1.28991i	−0.764221	−	0.644955i	$-0.776876\pi$
$443$		−	571.430i		−	1.28991i	0.764221	−	0.644955i	$-0.223124\pi$
$444$		0			0
$445$	378.900			0.851461
$446$	−520.042	−	300.246i	−1.16601	−	0.673198i
$447$		0			0
$448$			84.0591i			0.187632i
$449$	230.990			0.514454			0.257227	−	0.966351i	$-0.417191\pi$
$449$	230.990			0.514454			0.257227	+	0.966351i	$0.417191\pi$
$450$		0			0
$451$		−	295.715i		−	0.655686i
$452$	131.395	+	227.583i	0.290698	+	0.503503i
$453$		0			0
$454$	−307.223	−	177.376i	−0.676704	−	0.390695i
$455$		−	7.09510i		−	0.0155936i
$456$		0			0
$457$	−412.275			−0.902133			−0.451067	−	0.892490i	$-0.648956\pi$
$457$	−412.275			−0.902133			−0.451067	+	0.892490i	$0.648956\pi$
$458$	38.3987	−	66.5085i	0.0838399	−	0.145215i
$459$		0			0
$460$	−761.402	+	439.596i	−1.65522	+	0.955643i
$461$	89.2575			0.193617			0.0968085	−	0.995303i	$-0.469137\pi$
$461$	89.2575			0.193617			0.0968085	+	0.995303i	$0.469137\pi$
$462$		0			0
$463$			70.9565i			0.153254i	0.997060	+	0.0766269i	$0.0244150\pi$
$463$			70.9565i			0.153254i	−0.997060	+	0.0766269i	$0.975585\pi$
$464$	−266.997	+	462.452i	−0.575424	+	0.996663i
$465$		0			0
$466$	−374.399	+	648.478i	−0.803431	+	1.39158i
$467$			592.508i			1.26875i	0.773024	+	0.634377i	$0.218743\pi$
$467$			592.508i			1.26875i	−0.773024	+	0.634377i	$0.781257\pi$
$468$		0			0
$469$	147.924			0.315404
$470$	273.787	+	158.071i	0.582526	+	0.336322i
$471$		0			0
$472$		−	369.853i		−	0.783587i
$473$	239.395			0.506121
$474$		0			0
$475$		−	78.0257i		−	0.164265i
$476$	−1.25083	+	0.722166i	−0.00262779	+	0.00151716i
$477$		0			0
$478$	30.0274	+	17.3363i	0.0628188	+	0.0362685i
$479$			697.257i			1.45565i	0.685762	+	0.727826i	$0.259469\pi$
$479$			697.257i			1.45565i	−0.685762	+	0.727826i	$0.740531\pi$
$480$		0			0
$481$	−29.8555			−0.0620696
$482$	346.646	−	600.409i	0.719183	−	1.24566i
$483$		0			0
$484$	−204.997	−	355.065i	−0.423547	−	0.733605i
$485$	770.900			1.58949
$486$		0			0
$487$			241.869i			0.496650i	0.968677	+	0.248325i	$0.0798801\pi$
$487$			241.869i			0.496650i	−0.968677	+	0.248325i	$0.920120\pi$
$488$	376.797			0.772126
$489$		0			0
$490$	−309.643	+	536.317i	−0.631924	+	1.09452i
$491$		−	195.601i		−	0.398373i	−0.979962	−	0.199186i	$-0.936170\pi$
$491$		−	195.601i		−	0.398373i	0.979962	−	0.199186i	$-0.0638299\pi$
$492$		0			0
$493$	−9.17525			−0.0186111
$494$	−6.22674	−	3.59501i	−0.0126047	−	0.00727735i
$495$		0			0
$496$	−675.189	−	389.821i	−1.36127	−	0.785929i
$497$	92.5498			0.186217
$498$		0			0
$499$		−	237.233i		−	0.475418i	−0.971336	−	0.237709i	$-0.923604\pi$
$499$		−	237.233i		−	0.475418i	0.971336	−	0.237709i	$-0.0763964\pi$
$500$	−93.0033	−	161.086i	−0.186007	−	0.322173i
$501$		0			0
$502$	400.550	+	231.258i	0.797908	+	0.460672i
$503$			162.472i			0.323006i	0.986872	+	0.161503i	$0.0516341\pi$
$503$			162.472i			0.323006i	−0.986872	+	0.161503i	$0.948366\pi$
$504$		0			0
$505$	1135.08			2.24768
$506$	144.344	−	250.011i	0.285265	−	0.494093i
$507$		0			0
$508$	325.306	−	187.815i	0.640365	−	0.369715i
$509$	−55.7043			−0.109439			−0.0547194	−	0.998502i	$-0.517426\pi$
$509$	−55.7043			−0.109439			−0.0547194	+	0.998502i	$0.517426\pi$
$510$		0			0
$511$		−	76.2779i		−	0.149272i
$512$	−512.000			−1.00000
$513$		0			0
$514$	−169.849	+	294.187i	−0.330445	+	0.572348i
$515$		−	7.74529i		−	0.0150394i
$516$		0			0
$517$	−103.807			−0.200788
$518$	−82.3505	−	47.5451i	−0.158978	−	0.0917859i
$519$		0			0
$520$	43.2159			0.0831075
$521$	15.4435			0.0296421			0.0148211	−	0.999890i	$-0.495282\pi$
$521$	15.4435			0.0296421			0.0148211	+	0.999890i	$0.495282\pi$
$522$		0			0
$523$			388.246i			0.742343i	0.928564	+	0.371172i	$0.121044\pi$
$523$			388.246i			0.742343i	−0.928564	+	0.371172i	$0.878956\pi$
$524$	−34.0066	+	19.6337i	−0.0648981	+	0.0374690i
$525$		0			0
$526$	−156.000	−	90.0666i	−0.296578	−	0.171229i
$527$		−	13.3961i		−	0.0254195i
$528$		0			0
$529$	−597.124			−1.12878
$530$	169.801	−	294.103i	0.320379	−	0.554912i
$531$		0			0
$532$	−11.4502	−	19.8323i	−0.0215229	−	0.0372787i
$533$	56.7010			0.106381
$534$		0			0
$535$		−	607.777i		−	1.13603i
$536$			901.000i			1.68097i
$537$		0			0
$538$	−435.993	+	755.163i	−0.810397	+	1.40365i
$539$		−	203.346i		−	0.377266i
$540$		0			0
$541$	630.894			1.16616			0.583081	−	0.812414i	$-0.301847\pi$
$541$	630.894			1.16616			0.583081	+	0.812414i	$0.301847\pi$
$542$	612.172	+	353.438i	1.12947	+	0.652099i
$543$		0			0
$544$	−4.39868	−	7.61873i	−0.00808580	−	0.0140050i
$545$	293.595			0.538706
$546$		0			0
$547$		−	746.969i		−	1.36557i	−0.730618	−	0.682787i	$-0.760768\pi$
$547$		−	746.969i		−	1.36557i	0.730618	−	0.682787i	$-0.239232\pi$
$548$	127.945	+	221.608i	0.233477	+	0.404393i
$549$		0			0
$550$	−133.360	−	76.9957i	−0.242474	−	0.139992i
$551$		−	145.476i		−	0.264023i
$552$		0			0
$553$	−149.045			−0.269521
$554$	−227.045	+	393.253i	−0.409828	+	0.709843i
$555$		0			0
$556$	65.4020	−	37.7599i	0.117629	−	0.0679134i
$557$	−320.145			−0.574766			−0.287383	−	0.957816i	$-0.592785\pi$
$557$	−320.145			−0.574766			−0.287383	+	0.957816i	$0.592785\pi$
$558$		0			0
$559$			45.9022i			0.0821149i
$560$	119.203	+	68.8217i	0.212862	+	0.122896i
$561$		0			0
$562$	−114.646	+	198.573i	−0.203997	+	0.353333i
$563$			532.885i			0.946509i	0.880926	+	0.473255i	$0.156921\pi$
$563$			532.885i			0.946509i	−0.880926	+	0.473255i	$0.843079\pi$
$564$		0			0
$565$	430.309			0.761609
$566$	175.450	+	101.296i	0.309983	+	0.178969i
$567$		0			0
$568$			563.716i			0.992458i
$569$	212.749			0.373900			0.186950	−	0.982369i	$-0.440140\pi$
$569$	212.749			0.373900			0.186950	+	0.982369i	$0.440140\pi$
$570$		0			0
$571$			544.439i			0.953484i	0.879043	+	0.476742i	$0.158182\pi$
$571$			544.439i			0.953484i	−0.879043	+	0.476742i	$0.841818\pi$
$572$	−12.2891	+	7.09510i	−0.0214844	+	0.0124040i
$573$		0			0
$574$	156.399	+	90.2968i	0.272472	+	0.157312i
$575$			600.695i			1.04469i
$576$		0			0
$577$	1094.65			1.89715			0.948573	−	0.316557i	$-0.102527\pi$
$577$	1094.65			1.89715			0.948573	+	0.316557i	$0.102527\pi$
$578$	−288.924	+	500.432i	−0.499869	+	0.865799i
$579$		0			0
$580$	437.196	+	757.246i	0.753786	+	1.30560i
$581$	−195.148			−0.335883
$582$		0			0
$583$			111.510i			0.191270i
$584$	464.605			0.795556
$585$		0			0
$586$	−272.069	+	471.237i	−0.464281	+	0.804159i
$587$			334.292i			0.569492i	0.958603	+	0.284746i	$0.0919092\pi$
$587$			334.292i			0.569492i	−0.958603	+	0.284746i	$0.908091\pi$
$588$		0			0
$589$	212.399			0.360609
$590$	−524.482	−	302.810i	−0.888952	−	0.513237i
$591$		0			0
$592$	289.595	−	501.593i	0.489180	−	0.847285i
$593$	−834.385			−1.40706			−0.703529	−	0.710667i	$-0.748393\pi$
$593$	−834.385			−1.40706			−0.703529	+	0.710667i	$0.748393\pi$
$594$		0			0
$595$			2.36503i			0.00397485i
$596$	−157.897	−	273.486i	−0.264928	−	0.458869i
$597$		0			0
$598$	47.9377	+	27.6768i	0.0801633	+	0.0462823i
$599$		−	619.602i		−	1.03439i	−0.855866	−	0.517197i	$-0.826975\pi$
$599$		−	619.602i		−	1.03439i	0.855866	−	0.517197i	$-0.173025\pi$
$600$		0			0
$601$	245.450			0.408403			0.204201	−	0.978929i	$-0.434540\pi$
$601$	245.450			0.408403			0.204201	+	0.978929i	$0.434540\pi$
$602$	−73.0997	+	126.612i	−0.121428	+	0.210320i
$603$		0			0
$604$	667.684	−	385.488i	1.10544	−	0.638225i
$605$	−671.347			−1.10966
$606$		0			0
$607$			827.250i			1.36285i	0.731888	+	0.681425i	$0.238639\pi$
$607$			827.250i			1.36285i	−0.731888	+	0.681425i	$0.761361\pi$
$608$	120.797	−	69.7424i	0.198680	−	0.114708i
$609$		0			0
$610$	308.495	−	534.329i	0.505730	−	0.875949i
$611$		−	19.9042i		−	0.0325765i
$612$		0			0
$613$	−909.093			−1.48302			−0.741511	−	0.670940i	$-0.765891\pi$
$613$	−909.093			−1.48302			−0.741511	+	0.670940i	$0.765891\pi$
$614$	−227.203	−	131.176i	−0.370037	−	0.213641i
$615$		0			0
$616$	−45.1960			−0.0733702
$617$	809.382			1.31180			0.655901	−	0.754847i	$-0.272289\pi$
$617$	809.382			1.31180			0.655901	+	0.754847i	$0.272289\pi$
$618$		0			0
$619$			484.085i			0.782044i	0.920381	+	0.391022i	$0.127878\pi$
$619$			484.085i			0.782044i	−0.920381	+	0.391022i	$0.872122\pi$
$620$	−1105.59	+	638.315i	−1.78322	+	1.02954i
$621$		0			0
$622$	842.509	+	486.423i	1.35452	+	0.782030i
$623$		−	75.9801i		−	0.121958i
$624$		0			0
$625$	−752.086			−1.20334
$626$	308.027	−	533.519i	0.492057	−	0.852267i
$627$		0			0
$628$	−14.0066	−	24.2602i	−0.0223035	−	0.0386309i
$629$	9.95182			0.0158217
$630$		0			0
$631$			427.350i			0.677259i	0.940920	+	0.338630i	$0.109963\pi$
$631$			427.350i			0.677259i	−0.940920	+	0.338630i	$0.890037\pi$
$632$		−	907.825i		−	1.43643i
$633$		0			0
$634$	219.918	−	380.909i	0.346873	−	0.600803i
$635$		−	615.080i		−	0.968629i
$636$		0			0
$637$	38.9901			0.0612089
$638$	−248.646	−	143.556i	−0.389728	−	0.225009i
$639$		0			0
$640$	−419.189	+	726.057i	−0.654983	+	1.13446i
$641$	120.804			0.188462			0.0942309	−	0.995550i	$-0.469961\pi$
$641$	120.804			0.188462			0.0942309	+	0.995550i	$0.469961\pi$
$642$		0			0
$643$			220.163i			0.342400i	0.985236	+	0.171200i	$0.0547644\pi$
$643$			220.163i			0.342400i	−0.985236	+	0.171200i	$0.945236\pi$
$644$	88.1512	+	152.682i	0.136881	+	0.237084i
$645$		0			0
$646$	2.07558	+	1.19834i	0.00321297	+	0.00185501i
$647$			143.362i			0.221579i	0.993844	+	0.110790i	$0.0353380\pi$
$647$			143.362i			0.221579i	−0.993844	+	0.110790i	$0.964662\pi$
$648$		0			0
$649$	198.859			0.306408
$650$	14.7633	−	25.5708i	0.0227128	−	0.0393397i
$651$		0			0
$652$	−43.7940	+	25.2845i	−0.0671688	+	0.0387799i
$653$	494.042			0.756572			0.378286	−	0.925689i	$-0.376514\pi$
$653$	494.042			0.756572			0.378286	+	0.925689i	$0.376514\pi$
$654$		0			0
$655$			64.2988i			0.0981662i
$656$	−549.993	+	952.616i	−0.838405	+	1.45216i
$657$		0			0
$658$	31.6977	−	54.9020i	0.0481728	−	0.0834377i
$659$			1213.13i			1.84087i	0.390901	+	0.920433i	$0.372164\pi$
$659$			1213.13i			1.84087i	−0.390901	+	0.920433i	$0.627836\pi$
$660$		0			0
$661$	−761.718			−1.15237			−0.576186	−	0.817318i	$-0.695460\pi$
$661$	−761.718			−1.15237			−0.576186	+	0.817318i	$0.695460\pi$
$662$	−185.519	−	107.110i	−0.280240	−	0.161797i
$663$		0			0
$664$		−	1188.64i		−	1.79011i
$665$	−37.4983			−0.0563885
$666$		0			0
$667$			1119.98i			1.67913i
$668$	389.003	−	224.591i	0.582340	−	0.336214i
$669$		0			0
$670$	1277.69	+	737.675i	1.90700	+	1.10101i
$671$			202.592i			0.301926i
$672$		0			0
$673$	−825.836			−1.22710			−0.613548	−	0.789657i	$-0.710258\pi$
$673$	−825.836			−1.22710			−0.613548	+	0.789657i	$0.710258\pi$
$674$	425.849	−	737.592i	0.631823	−	1.09435i
$675$		0			0
$676$	336.640	+	583.077i	0.497988	+	0.862540i
$677$	−303.767			−0.448695			−0.224348	−	0.974509i	$-0.572025\pi$
$677$	−303.767			−0.448695			−0.224348	+	0.974509i	$0.572025\pi$
$678$		0			0
$679$		−	154.587i		−	0.227669i
$680$	−14.4053			−0.0211843
$681$		0			0
$682$	209.595	−	363.029i	0.307324	−	0.532300i
$683$			314.197i			0.460026i	0.973188	+	0.230013i	$0.0738768\pi$
$683$			314.197i			0.460026i	−0.973188	+	0.230013i	$0.926123\pi$
$684$		0			0
$685$	419.010			0.611693
$686$	219.017	+	126.450i	0.319267	+	0.184329i
$687$		0			0
$688$	−771.189	−	445.246i	−1.12091	−	0.647160i
$689$	−21.3812			−0.0310322
$690$		0			0
$691$		−	731.469i		−	1.05857i	−0.848445	−	0.529283i	$-0.822461\pi$
$691$		−	731.469i		−	1.05857i	0.848445	−	0.529283i	$-0.177539\pi$
$692$	79.7940	+	138.207i	0.115309	+	0.199722i
$693$		0			0
$694$	−1097.13	−	633.427i	−1.58088	−	0.912719i
$695$		−	123.660i		−	0.177929i
$696$		0			0
$697$	−18.9003			−0.0271167
$698$	−223.292	+	386.754i	−0.319903	+	0.554088i
$699$		0			0
$700$	81.4435	−	47.0215i	0.116348	−	0.0671735i
$701$	−103.952			−0.148291			−0.0741454	−	0.997247i	$-0.523623\pi$
$701$	−103.952			−0.148291			−0.0741454	+	0.997247i	$0.523623\pi$
$702$		0			0
$703$			157.789i			0.224451i
$704$		−	275.287i		−	0.391032i
$705$		0			0
$706$	−122.323	+	211.870i	−0.173262	+	0.300099i
$707$		−	227.615i		−	0.321945i
$708$		0			0
$709$	−899.086			−1.26810			−0.634052	−	0.773290i	$-0.718610\pi$
$709$	−899.086			−1.26810			−0.634052	+	0.773290i	$0.718610\pi$
$710$	799.395	+	461.531i	1.12591	+	0.650044i
$711$		0			0
$712$	462.791			0.649987
$713$	−1635.19			−2.29339
$714$		0			0
$715$			23.2359i			0.0324977i
$716$	−488.990	+	282.319i	−0.682947	+	0.394300i
$717$		0			0
$718$	−927.017	−	535.214i	−1.29111	−	0.745423i
$719$		−	601.472i		−	0.836539i	−0.908323	−	0.418270i	$-0.862637\pi$
$719$		−	601.472i		−	0.836539i	0.908323	−	0.418270i	$-0.137363\pi$
$720$		0			0
$721$	−1.55315			−0.00215415
$722$	−19.0000	+	32.9090i	−0.0263158	+	0.0455803i
$723$		0			0
$724$	−284.000	−	491.902i	−0.392265	−	0.679423i
$725$	597.416			0.824022
$726$		0			0
$727$		−	863.895i		−	1.18830i	−0.804354	−	0.594151i	$-0.797488\pi$
$727$		−	863.895i		−	1.18830i	0.804354	−	0.594151i	$-0.202512\pi$
$728$		−	8.66599i		−	0.0119038i
$729$		0			0
$730$	380.385	−	658.847i	0.521076	−	0.902530i
$731$		−	15.3007i		−	0.0209312i
$732$		0			0
$733$	−979.238			−1.33593			−0.667966	−	0.744192i	$-0.732835\pi$
$733$	−979.238			−1.33593			−0.667966	+	0.744192i	$0.732835\pi$
$734$	173.512	+	100.177i	0.236392	+	0.136481i
$735$		0			0
$736$	−929.980	+	536.924i	−1.26356	+	0.729517i
$737$	−484.440			−0.657314
$738$		0			0
$739$		−	944.578i		−	1.27818i	−0.769130	−	0.639092i	$-0.779310\pi$
$739$		−	944.578i		−	1.27818i	0.769130	−	0.639092i	$-0.220690\pi$
$740$	−474.199	−	821.337i	−0.640810	−	1.10992i
$741$		0			0
$742$	−58.9759	−	34.0498i	−0.0794824	−	0.0458892i
$743$		−	443.278i		−	0.596606i	−0.954471	−	0.298303i	$-0.903579\pi$
$743$		−	443.278i		−	0.596606i	0.954471	−	0.298303i	$-0.0964206\pi$
$744$		0			0
$745$	−517.100			−0.694094
$746$	191.767	−	332.150i	0.257060	−	0.445241i
$747$		0			0
$748$	4.09636	−	2.36503i	0.00547641	−	0.00316181i
$749$	−121.876			−0.162719
$750$		0			0
$751$		−	42.6165i		−	0.0567463i	−0.999597	−	0.0283732i	$-0.990967\pi$
$751$		−	42.6165i		−	0.0567463i	0.999597	−	0.0283732i	$-0.00903267\pi$
$752$	334.405	+	193.069i	0.444688	+	0.256741i
$753$		0			0
$754$	27.5257	−	47.6760i	0.0365063	−	0.0632308i
$755$		−	1262.44i		−	1.67211i
$756$		0			0
$757$	−166.000			−0.219287			−0.109643	−	0.993971i	$-0.534971\pi$
$757$	−166.000			−0.219287			−0.109643	+	0.993971i	$0.534971\pi$
$758$	−187.567	−	108.292i	−0.247450	−	0.142865i
$759$		0			0
$760$		−	228.401i		−	0.300527i
$761$	1009.71			1.32681			0.663407	−	0.748259i	$-0.269110\pi$
$761$	1009.71			1.32681			0.663407	+	0.748259i	$0.269110\pi$
$762$		0			0
$763$		−	58.8739i		−	0.0771611i
$764$	1092.63	−	630.832i	1.43015	−	0.825696i
$765$		0			0
$766$	300.633	+	173.571i	0.392471	+	0.226593i
$767$			38.1296i			0.0497127i
$768$		0			0
$769$	157.512			0.204828			0.102414	−	0.994742i	$-0.467343\pi$
$769$	157.512			0.204828			0.102414	+	0.994742i	$0.467343\pi$
$770$	−37.0033	+	64.0916i	−0.0480562	+	0.0832359i
$771$		0			0
$772$	−88.3987	−	153.111i	−0.114506	−	0.198330i
$773$	−1048.26			−1.35610			−0.678048	−	0.735018i	$-0.737174\pi$
$773$	−1048.26			−1.35610			−0.678048	+	0.735018i	$0.737174\pi$
$774$		0			0
$775$			872.240i			1.12547i
$776$	941.581			1.21338
$777$		0			0
$778$	541.890	−	938.582i	0.696517	−	1.20640i
$779$		−	299.671i		−	0.384686i
$780$		0			0
$781$	−303.093			−0.388083
$782$	−15.9792	−	9.22561i	−0.0204338	−	0.0117975i
$783$		0			0
$784$	−378.199	+	655.060i	−0.482397	+	0.835536i
$785$	−45.8705			−0.0584338
$786$		0			0
$787$			146.774i			0.186498i	0.995643	+	0.0932491i	$0.0297253\pi$
$787$			146.774i			0.186498i	−0.995643	+	0.0932491i	$0.970275\pi$
$788$	−635.093	−	1100.01i	−0.805956	−	1.39596i
$789$		0			0
$790$	−1287.37	−	743.263i	−1.62958	−	0.940839i
$791$		−	86.2889i		−	0.109088i
$792$		0			0
$793$	−38.8455			−0.0489855
$794$	443.444	−	768.067i	0.558493	−	0.967338i
$795$		0			0
$796$	1194.54	−	689.670i	1.50068	−	0.866419i
$797$	−523.217			−0.656483			−0.328241	−	0.944594i	$-0.606456\pi$
$797$	−523.217			−0.656483			−0.328241	+	0.944594i	$0.606456\pi$
$798$		0			0
$799$			6.63475i			0.00830382i
$800$	286.405	+	496.069i	0.358007	+	0.620086i
$801$		0			0
$802$	287.141	−	497.343i	0.358031	−	0.620129i
$803$			249.804i			0.311088i
$804$		0			0
$805$	288.688			0.358618
$806$	69.6079	+	40.1882i	0.0863622	+	0.0498612i
$807$		0			0
$808$	1386.39			1.71583
$809$	−487.821			−0.602993			−0.301497	−	0.953467i	$-0.597486\pi$
$809$	−487.821			−0.602993			−0.301497	+	0.953467i	$0.597486\pi$
$810$		0			0
$811$			362.501i			0.446980i	0.974706	+	0.223490i	$0.0717450\pi$
$811$			362.501i			0.446980i	−0.974706	+	0.223490i	$0.928255\pi$
$812$	151.849	−	87.6700i	0.187006	−	0.107968i
$813$		0			0
$814$	269.691	+	155.706i	0.331316	+	0.191285i
$815$			82.8046i			0.101601i
$816$		0			0
$817$	242.598			0.296938
$818$	−258.248	+	447.298i	−0.315706	+	0.546819i
$819$		0			0
$820$	900.591	+	1559.87i	1.09828	+	1.90228i
$821$	−1260.35			−1.53514			−0.767570	−	0.640965i	$-0.778534\pi$
$821$	−1260.35			−1.53514			−0.767570	+	0.640965i	$0.778534\pi$
$822$		0			0
$823$		−	436.179i		−	0.529987i	−0.964250	−	0.264993i	$-0.914630\pi$
$823$		−	436.179i		−	0.529987i	0.964250	−	0.264993i	$-0.0853698\pi$
$824$		−	9.46013i		−	0.0114807i
$825$		0			0
$826$	−60.7218	+	105.173i	−0.0735130	+	0.127328i
$827$			51.0250i			0.0616989i	0.999524	+	0.0308495i	$0.00982125\pi$
$827$			51.0250i			0.0616989i	−0.999524	+	0.0308495i	$0.990179\pi$
$828$		0			0
$829$	−153.416			−0.185062			−0.0925308	−	0.995710i	$-0.529496\pi$
$829$	−153.416			−0.185062			−0.0925308	+	0.995710i	$0.529496\pi$
$830$	−1685.58	−	973.171i	−2.03082	−	1.17250i
$831$		0			0
$832$	52.7841			0.0634424
$833$	−12.9967			−0.0156023
$834$		0			0
$835$		−	735.517i		−	0.880859i
$836$	37.4983	+	64.9490i	0.0448545	+	0.0776902i
$837$		0			0
$838$	−729.498	−	421.176i	−0.870523	−	0.502597i
$839$		−	687.106i		−	0.818959i	−0.912319	−	0.409479i	$-0.865710\pi$
$839$		−	687.106i		−	0.818959i	0.912319	−	0.409479i	$-0.134290\pi$
$840$		0			0
$841$	272.863			0.324451
$842$	513.815	−	889.953i	0.610231	−	1.05695i
$843$		0			0
$844$	−1128.34	+	651.450i	−1.33690	+	0.771860i
$845$	1102.47			1.30469
$846$		0			0
$847$			134.624i			0.158942i
$848$	207.395	−	359.219i	0.244570	−	0.423608i
$849$		0			0
$850$	−4.92111	+	8.52361i	−0.00578954	+	0.0100278i
$851$		−	1214.77i		−	1.42746i
$852$		0			0
$853$	1116.89			1.30936			0.654682	−	0.755905i	$-0.272803\pi$
$853$	1116.89			1.30936			0.654682	+	0.755905i	$0.272803\pi$
$854$	−107.148	−	61.8618i	−0.125466	−	0.0724378i
$855$		0			0
$856$		−	742.342i		−	0.867222i
$857$	−1526.94			−1.78172			−0.890861	−	0.454277i	$-0.849898\pi$
$857$	−1526.94			−1.78172			−0.890861	+	0.454277i	$0.849898\pi$
$858$		0			0
$859$		−	487.641i		−	0.567685i	−0.958871	−	0.283842i	$-0.908391\pi$
$859$		−	487.641i		−	0.567685i	0.958871	−	0.283842i	$-0.0916093\pi$
$860$	−1262.79	+	729.073i	−1.46836	+	0.847759i
$861$		0			0
$862$	295.849	+	170.808i	0.343212	+	0.198154i
$863$			1657.13i			1.92019i	0.279669	+	0.960097i	$0.409775\pi$
$863$			1657.13i			1.92019i	−0.279669	+	0.960097i	$0.590225\pi$
$864$		0			0
$865$	261.319			0.302103
$866$	277.299	−	480.296i	0.320207	−	0.554614i
$867$		0			0
$868$	128.000	+	221.703i	0.147465	+	0.255418i
$869$	488.110			0.561691
$870$		0			0
$871$		−	92.8877i		−	0.106645i
$872$	358.598			0.411236
$873$		0			0
$874$	146.275	−	253.356i	0.167363	−	0.289881i
$875$			61.0764i			0.0698016i
$876$		0			0
$877$	−349.429			−0.398437			−0.199219	−	0.979955i	$-0.563840\pi$
$877$	−349.429			−0.398437			−0.199219	+	0.979955i	$0.563840\pi$
$878$	−404.701	−	233.654i	−0.460935	−	0.266121i
$879$		0			0
$880$	−390.379	−	225.385i	−0.443612	−	0.256120i
$881$	101.890			0.115653			0.0578266	−	0.998327i	$-0.481583\pi$
$881$	101.890			0.115653			0.0578266	+	0.998327i	$0.481583\pi$
$882$		0			0
$883$		−	1012.41i		−	1.14655i	−0.819362	−	0.573277i	$-0.805672\pi$
$883$		−	1012.41i		−	1.14655i	0.819362	−	0.573277i	$-0.194328\pi$
$884$	0.453477	+	0.785445i	0.000512983	+	0.000888512i
$885$		0			0
$886$	−989.746	−	571.430i	−1.11709	−	0.644955i
$887$			984.067i			1.10943i	0.832040	+	0.554716i	$0.187173\pi$
$887$			984.067i			1.10943i	−0.832040	+	0.554716i	$0.812827\pi$
$888$		0			0
$889$	−123.341			−0.138741
$890$	378.900	−	656.275i	0.425731	−	0.737387i
$891$		0			0
$892$	−1040.08	+	600.492i	−1.16601	+	0.673198i
$893$	−105.196			−0.117801
$894$		0			0
$895$			924.570i			1.03304i
$896$	145.595	+	84.0591i	0.162494	+	0.0938160i
$897$		0			0
$898$	230.990	−	400.087i	0.257227	−	0.445531i
$899$			1626.26i			1.80897i
$900$		0			0
$901$	7.12707			0.00791018
$902$	−512.193	−	295.715i	−0.567841	−	0.327843i
$903$		0			0
$904$	525.581			0.581395
$905$	−930.076			−1.02771
$906$		0			0
$907$			1497.68i			1.65124i	0.564223	+	0.825622i	$0.309176\pi$
$907$			1497.68i			1.65124i	−0.564223	+	0.825622i	$0.690824\pi$
$908$	−614.447	+	354.751i	−0.676704	+	0.390695i
$909$		0			0
$910$	−12.2891	−	7.09510i	−0.0135045	−	0.00779681i
$911$		−	550.384i		−	0.604153i	−0.953284	−	0.302077i	$-0.902320\pi$
$911$		−	550.384i		−	0.604153i	0.953284	−	0.302077i	$-0.0976798\pi$
$912$		0			0
$913$	639.093			0.699992
$914$	−412.275	+	714.081i	−0.451067	+	0.781270i
$915$		0			0
$916$	−76.7974	−	133.017i	−0.0838399	−	0.145215i
$917$	12.8937			0.0140608
$918$		0			0
$919$		−	706.483i		−	0.768751i	−0.923177	−	0.384376i	$-0.874417\pi$
$919$		−	706.483i		−	0.768751i	0.923177	−	0.384376i	$-0.125583\pi$
$920$			1758.38i			1.91129i
$921$		0			0
$922$	89.2575	−	154.598i	0.0968085	−	0.167677i
$923$		−	58.1158i		−	0.0629640i
$924$		0			0
$925$	−647.980			−0.700519
$926$	122.900	+	70.9565i	0.132722	+	0.0766269i
$927$		0			0
$928$	533.993	+	924.904i	0.575424	+	0.996663i
$929$	−145.609			−0.156737			−0.0783686	−	0.996924i	$-0.524971\pi$
$929$	−145.609			−0.156737			−0.0783686	+	0.996924i	$0.524971\pi$
$930$		0			0
$931$		−	206.067i		−	0.221339i
$932$	748.797	+	1296.96i	0.803431	+	1.39158i
$933$		0			0
$934$	1026.25	+	592.508i	1.09877	+	0.634377i
$935$		−	7.74529i		−	0.00828373i
$936$		0			0
$937$	−909.953			−0.971134			−0.485567	−	0.874199i	$-0.661387\pi$
$937$	−909.953			−0.971134			−0.485567	+	0.874199i	$0.661387\pi$
$938$	147.924	−	256.213i	0.157702	−	0.273148i
$939$		0			0
$940$	547.575	−	316.142i	0.582526	−	0.336322i
$941$	248.963			0.264572			0.132286	−	0.991212i	$-0.457768\pi$
$941$	248.963			0.264572			0.132286	+	0.991212i	$0.457768\pi$
$942$		0			0
$943$			2307.07i			2.44652i
$944$	−640.605	−	369.853i	−0.678607	−	0.391794i
$945$		0			0
$946$	239.395	−	414.645i	0.253061	−	0.438314i
$947$		−	1304.57i		−	1.37759i	−0.724958	−	0.688793i	$-0.758141\pi$
$947$		−	1304.57i		−	1.37759i	0.724958	−	0.688793i	$-0.241859\pi$
$948$		0			0
$949$	−47.8979			−0.0504720
$950$	−135.145	−	78.0257i	−0.142257	−	0.0821324i
$951$		0			0
$952$			2.88866i			0.00303431i
$953$	710.605			0.745650			0.372825	−	0.927902i	$-0.378389\pi$
$953$	710.605			0.745650			0.372825	+	0.927902i	$0.378389\pi$
$954$		0			0
$955$		−	2065.92i		−	2.16327i
$956$	60.0548	−	34.6727i	0.0628188	−	0.0362685i
$957$		0			0
$958$	1207.68	+	697.257i	1.26063	+	0.727826i
$959$		−	84.0232i		−	0.0876154i
$960$		0			0
$961$	−1413.38			−1.47074
$962$	−29.8555	+	51.7112i	−0.0310348	+	0.0537538i
$963$		0			0
$964$	−693.292	−	1200.82i	−0.719183	−	1.24566i
$965$	−289.498			−0.299998
$966$		0			0
$967$			692.924i			0.716571i	0.933612	+	0.358285i	$0.116639\pi$
$967$			692.924i			0.716571i	−0.933612	+	0.358285i	$0.883361\pi$
$968$	−819.987			−0.847094
$969$		0			0
$970$	770.900	−	1335.24i	0.794743	−	1.37653i
$971$			1042.10i			1.07322i	0.843831	+	0.536610i	$0.180295\pi$
$971$			1042.10i			1.07322i	−0.843831	+	0.536610i	$0.819705\pi$
$972$		0			0
$973$	−24.7974			−0.0254855
$974$	418.929	+	241.869i	0.430112	+	0.248325i
$975$		0			0
$976$	376.797	−	652.632i	0.386063	−	0.668680i
$977$	1488.13			1.52316			0.761582	−	0.648069i	$-0.224423\pi$
$977$	1488.13			1.52316			0.761582	+	0.648069i	$0.224423\pi$
$978$		0			0
$979$			248.828i			0.254166i
$980$	619.286	+	1072.63i	0.631924	+	1.09452i
$981$		0			0
$982$	−338.791	−	195.601i	−0.345001	−	0.199186i
$983$		−	988.210i		−	1.00530i	−0.864490	−	0.502650i	$-0.832358\pi$
$983$		−	988.210i		−	1.00530i	0.864490	−	0.502650i	$-0.167642\pi$
$984$		0			0
$985$	−2079.88			−2.11155
$986$	−9.17525	+	15.8920i	−0.00930553	+	0.0161176i
$987$		0			0
$988$	−12.4535	+	7.19002i	−0.0126047	+	0.00727735i
$989$	−1867.68			−1.88846
$990$		0			0
$991$		−	692.694i		−	0.698985i	−0.936939	−	0.349492i	$-0.886354\pi$
$991$		−	692.694i		−	0.698985i	0.936939	−	0.349492i	$-0.113646\pi$
$992$	−1350.38	+	779.642i	−1.36127	+	0.785929i
$993$		0			0
$994$	92.5498	−	160.301i	0.0931085	−	0.161269i
$995$		−	2258.61i		−	2.26996i
$996$		0			0
$997$	−1405.22			−1.40945			−0.704723	−	0.709483i	$-0.748929\pi$
$997$	−1405.22			−1.40945			−0.704723	+	0.709483i	$0.748929\pi$
$998$	−410.900	−	237.233i	−0.411724	−	0.237709i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.a.343.1		4
3.2	odd	2		76.3.b.a.39.3	yes	4
4.3	odd	2	inner	684.3.g.a.343.3		4
12.11	even	2		76.3.b.a.39.2	✓	4
24.5	odd	2		1216.3.d.a.191.3		4
24.11	even	2		1216.3.d.a.191.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.a.39.2	✓	4	12.11	even	2
76.3.b.a.39.3	yes	4	3.2	odd	2
684.3.g.a.343.1		4	1.1	even	1	trivial
684.3.g.a.343.3		4	4.3	odd	2	inner
1216.3.d.a.191.2		4	24.11	even	2
1216.3.d.a.191.3		4	24.5	odd	2

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} -6.54983 q^{5} +1.31342i q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} -6.54983 q^{5} +1.31342i q^{7} -8.00000 q^{8} +(-6.54983 + 11.3446i) q^{10} -4.30136i q^{11} +0.824752 q^{13} +(2.27492 + 1.31342i) q^{14} +(-8.00000 + 13.8564i) q^{16} -0.274917 q^{17} -4.35890i q^{19} +(13.0997 + 22.6893i) q^{20} +(-7.45017 - 4.30136i) q^{22} +33.5578i q^{23} +17.9003 q^{25} +(0.824752 - 1.42851i) q^{26} +(4.54983 - 2.62685i) q^{28} +33.3746 q^{29} +48.7276i q^{31} +(16.0000 + 27.7128i) q^{32} +(-0.274917 + 0.476171i) q^{34} -8.60271i q^{35} -36.1993 q^{37} +(-7.54983 - 4.35890i) q^{38} +52.3987 q^{40} +68.7492 q^{41} +55.6558i q^{43} +(-14.9003 + 8.60271i) q^{44} +(58.1238 + 33.5578i) q^{46} -24.1336i q^{47} +47.2749 q^{49} +(17.9003 - 31.0043i) q^{50} +(-1.64950 - 2.85702i) q^{52} -25.9244 q^{53} +28.1732i q^{55} -10.5074i q^{56} +(33.3746 - 57.8065i) q^{58} +46.2317i q^{59} -47.0997 q^{61} +(84.3987 + 48.7276i) q^{62} +64.0000 q^{64} -5.40199 q^{65} -112.625i q^{67} +(0.549834 + 0.952341i) q^{68} +(-14.9003 - 8.60271i) q^{70} -70.4645i q^{71} -58.0756 q^{73} +(-36.1993 + 62.6991i) q^{74} +(-15.0997 + 8.71780i) q^{76} +5.64950 q^{77} +113.478i q^{79} +(52.3987 - 90.7572i) q^{80} +(68.7492 - 119.077i) q^{82} +148.579i q^{83} +1.80066 q^{85} +(96.3987 + 55.6558i) q^{86} +34.4108i q^{88} -57.8488 q^{89} +1.08325i q^{91} +(116.248 - 67.1155i) q^{92} +(-41.8007 - 24.1336i) q^{94} +28.5501i q^{95} -117.698 q^{97} +(47.2749 - 81.8826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 32 q^{8} + 4 q^{10} - 42 q^{13} - 6 q^{14} - 32 q^{16} + 14 q^{17} - 8 q^{20} - 60 q^{22} + 132 q^{25} - 42 q^{26} - 12 q^{28} + 58 q^{29} + 64 q^{32} + 14 q^{34} - 24 q^{37} - 32 q^{40} + 124 q^{41} - 120 q^{44} + 6 q^{46} + 174 q^{49} + 132 q^{50} + 84 q^{52} + 2 q^{53} + 58 q^{58} - 128 q^{61} + 96 q^{62} + 256 q^{64} - 384 q^{65} - 28 q^{68} - 120 q^{70} - 338 q^{73} - 24 q^{74} - 68 q^{77} - 32 q^{80} + 124 q^{82} + 128 q^{85} + 144 q^{86} - 20 q^{89} + 12 q^{92} - 288 q^{94} - 48 q^{97} + 174 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 32 * q^8 + 4 * q^10 - 42 * q^13 - 6 * q^14 - 32 * q^16 + 14 * q^17 - 8 * q^20 - 60 * q^22 + 132 * q^25 - 42 * q^26 - 12 * q^28 + 58 * q^29 + 64 * q^32 + 14 * q^34 - 24 * q^37 - 32 * q^40 + 124 * q^41 - 120 * q^44 + 6 * q^46 + 174 * q^49 + 132 * q^50 + 84 * q^52 + 2 * q^53 + 58 * q^58 - 128 * q^61 + 96 * q^62 + 256 * q^64 - 384 * q^65 - 28 * q^68 - 120 * q^70 - 338 * q^73 - 24 * q^74 - 68 * q^77 - 32 * q^80 + 124 * q^82 + 128 * q^85 + 144 * q^86 - 20 * q^89 + 12 * q^92 - 288 * q^94 - 48 * q^97 + 174 * q^98

Introduction

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