LMFDB - Embedded newform 324.3.d.h.163.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.d (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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.389136420864.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 $ x^8 + 5x^6 + 24x^4 + 80*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.8
Root			$-1.52274 + 1.29664i$ of defining polynomial
Character	$\chi$	$=$	324.163
Dual form			324.3.d.h.163.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52274 + 1.29664i) q^{2} +(0.637459 + 3.94888i) q^{4} -7.82300 q^{5} -12.3894i q^{7} +(-4.14959 + 6.83966i) q^{8} +O(q^{10})$	\(q+(1.52274 + 1.29664i) q^{2} +(0.637459 + 3.94888i) q^{4} -7.82300 q^{5} -12.3894i q^{7} +(-4.14959 + 6.83966i) q^{8} +(-11.9124 - 10.1436i) q^{10} -11.0860i q^{11} +3.54983 q^{13} +(16.0646 - 18.8659i) q^{14} +(-15.1873 + 5.03449i) q^{16} -8.77534 q^{17} -19.2016i q^{19} +(-4.98684 - 30.8921i) q^{20} +(14.3746 - 16.8811i) q^{22} -0.712936i q^{23} +36.1993 q^{25} +(5.40547 + 4.60285i) q^{26} +(48.9244 - 7.89776i) q^{28} -18.2153 q^{29} +11.1546i q^{31} +(-29.6542 - 12.0262i) q^{32} +(-13.3625 - 11.3784i) q^{34} +96.9226i q^{35} -35.5498 q^{37} +(24.8975 - 29.2390i) q^{38} +(32.4622 - 53.5067i) q^{40} +12.1819 q^{41} -66.2897i q^{43} +(43.7774 - 7.06689i) q^{44} +(0.924421 - 1.08561i) q^{46} +41.4924i q^{47} -104.498 q^{49} +(55.1221 + 46.9374i) q^{50} +(2.26287 + 14.0179i) q^{52} -74.7659 q^{53} +86.7261i q^{55} +(84.7396 + 51.4111i) q^{56} +(-27.7371 - 23.6187i) q^{58} +20.7462i q^{59} +48.8488 q^{61} +(-14.4635 + 16.9855i) q^{62} +(-29.5619 - 56.7635i) q^{64} -27.7704 q^{65} -8.04699i q^{67} +(-5.59392 - 34.6528i) q^{68} +(-125.674 + 147.588i) q^{70} -87.9754i q^{71} +62.0997 q^{73} +(-54.1331 - 46.0953i) q^{74} +(75.8248 - 12.2402i) q^{76} -137.350 q^{77} -9.91976i q^{79} +(118.810 - 39.3848i) q^{80} +(18.5498 + 15.7955i) q^{82} +22.1721i q^{83} +68.6495 q^{85} +(85.9537 - 100.942i) q^{86} +(75.8248 + 46.0025i) q^{88} +106.231 q^{89} -43.9805i q^{91} +(2.81530 - 0.454467i) q^{92} +(-53.8007 + 63.1821i) q^{94} +150.214i q^{95} +131.100 q^{97} +(-159.124 - 135.497i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{4}+O(q^{10}) $ 8 * q - 10 * q^4	$ 8 q - 10 q^{4} - 50 q^{10} - 32 q^{13} - 46 q^{16} - 36 q^{22} + 48 q^{25} + 180 q^{28} - 122 q^{34} - 224 q^{37} + 154 q^{40} - 204 q^{46} - 232 q^{49} + 154 q^{52} - 86 q^{58} - 32 q^{61} - 10 q^{64} - 492 q^{70} + 376 q^{73} + 516 q^{76} + 88 q^{82} + 368 q^{85} + 516 q^{88} - 672 q^{94} + 928 q^{97}+O(q^{100}) $ 8 * q - 10 * q^4 - 50 * q^10 - 32 * q^13 - 46 * q^16 - 36 * q^22 + 48 * q^25 + 180 * q^28 - 122 * q^34 - 224 * q^37 + 154 * q^40 - 204 * q^46 - 232 * q^49 + 154 * q^52 - 86 * q^58 - 32 * q^61 - 10 * q^64 - 492 * q^70 + 376 * q^73 + 516 * q^76 + 88 * q^82 + 368 * q^85 + 516 * q^88 - 672 * q^94 + 928 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.52274	+	1.29664i	0.761369	+	0.648319i
$2$	1.52274	+	1.29664i	0.761369	+	0.648319i
$3$		0			0
$3$		0			0
$4$	0.637459	+	3.94888i	0.159365	+	0.987220i
$5$	−7.82300			−1.56460			−0.782300	−	0.622902i	$-0.785954\pi$
$5$	−7.82300			−1.56460			−0.782300	+	0.622902i	$0.785954\pi$
$6$		0			0
$7$		−	12.3894i		−	1.76992i	−0.465666	−	0.884960i	$-0.654185\pi$
$7$		−	12.3894i		−	1.76992i	0.465666	−	0.884960i	$-0.345815\pi$
$8$	−4.14959	+	6.83966i	−0.518698	+	0.854957i
$9$		0			0
$10$	−11.9124	−	10.1436i	−1.19124	−	1.01436i
$11$		−	11.0860i		−	1.00782i	−0.863756	−	0.503911i	$-0.831894\pi$
$11$		−	11.0860i		−	1.00782i	0.863756	−	0.503911i	$-0.168106\pi$
$12$		0			0
$13$	3.54983			0.273064			0.136532	−	0.990636i	$-0.456404\pi$
$13$	3.54983			0.273064			0.136532	+	0.990636i	$0.456404\pi$
$14$	16.0646	−	18.8659i	1.14747	−	1.34756i
$15$		0			0
$16$	−15.1873	+	5.03449i	−0.949206	+	0.314656i
$17$	−8.77534			−0.516197			−0.258098	−	0.966119i	$-0.583096\pi$
$17$	−8.77534			−0.516197			−0.258098	+	0.966119i	$0.583096\pi$
$18$		0			0
$19$		−	19.2016i		−	1.01061i	−0.862941	−	0.505305i	$-0.831380\pi$
$19$		−	19.2016i		−	1.01061i	0.862941	−	0.505305i	$-0.168620\pi$
$20$	−4.98684	−	30.8921i	−0.249342	−	1.54460i
$21$		0			0
$22$	14.3746	−	16.8811i	0.653390	−	0.767324i
$23$		−	0.712936i		−	0.0309972i	−0.999880	−	0.0154986i	$-0.995066\pi$
$23$		−	0.712936i		−	0.0309972i	0.999880	−	0.0154986i	$-0.00493356\pi$
$24$		0			0
$25$	36.1993			1.44797
$26$	5.40547	+	4.60285i	0.207903	+	0.177033i
$27$		0			0
$28$	48.9244	−	7.89776i	1.74730	−	0.282063i
$29$	−18.2153			−0.628114			−0.314057	−	0.949404i	$-0.601688\pi$
$29$	−18.2153			−0.628114			−0.314057	+	0.949404i	$0.601688\pi$
$30$		0			0
$31$			11.1546i			0.359826i	0.983683	+	0.179913i	$0.0575816\pi$
$31$			11.1546i			0.359826i	−0.983683	+	0.179913i	$0.942418\pi$
$32$	−29.6542	−	12.0262i	−0.926693	−	0.375819i
$33$		0			0
$34$	−13.3625	−	11.3784i	−0.393016	−	0.334660i
$35$			96.9226i			2.76922i
$36$		0			0
$37$	−35.5498			−0.960806			−0.480403	−	0.877048i	$-0.659510\pi$
$37$	−35.5498			−0.960806			−0.480403	+	0.877048i	$0.659510\pi$
$38$	24.8975	−	29.2390i	0.655198	−	0.769447i
$39$		0			0
$40$	32.4622	−	53.5067i	0.811555	−	1.33767i
$41$	12.1819			0.297120			0.148560	−	0.988903i	$-0.452536\pi$
$41$	12.1819			0.297120			0.148560	+	0.988903i	$0.452536\pi$
$42$		0			0
$43$		−	66.2897i		−	1.54162i	−0.637065	−	0.770810i	$-0.719852\pi$
$43$		−	66.2897i		−	1.54162i	0.637065	−	0.770810i	$-0.280148\pi$
$44$	43.7774	−	7.06689i	0.994942	−	0.160611i
$45$		0			0
$46$	0.924421	−	1.08561i	0.0200961	−	0.0236003i
$47$			41.4924i			0.882818i	0.897306	+	0.441409i	$0.145521\pi$
$47$			41.4924i			0.882818i	−0.897306	+	0.441409i	$0.854479\pi$
$48$		0			0
$49$	−104.498			−2.13262
$50$	55.1221	+	46.9374i	1.10244	+	0.938749i
$51$		0			0
$52$	2.26287	+	14.0179i	0.0435168	+	0.269574i
$53$	−74.7659			−1.41068			−0.705339	−	0.708870i	$-0.749205\pi$
$53$	−74.7659			−1.41068			−0.705339	+	0.708870i	$0.749205\pi$
$54$		0			0
$55$			86.7261i			1.57684i
$56$	84.7396	+	51.4111i	1.51321	+	0.918055i
$57$		0			0
$58$	−27.7371	−	23.6187i	−0.478226	−	0.407218i
$59$			20.7462i			0.351631i	0.984423	+	0.175815i	$0.0562562\pi$
$59$			20.7462i			0.351631i	−0.984423	+	0.175815i	$0.943744\pi$
$60$		0			0
$61$	48.8488			0.800801			0.400400	−	0.916340i	$-0.368871\pi$
$61$	48.8488			0.800801			0.400400	+	0.916340i	$0.368871\pi$
$62$	−14.4635	+	16.9855i	−0.233282	+	0.273960i
$63$		0			0
$64$	−29.5619	−	56.7635i	−0.461904	−	0.886930i
$65$	−27.7704			−0.427236
$66$		0			0
$67$		−	8.04699i		−	0.120104i	−0.998195	−	0.0600521i	$-0.980873\pi$
$67$		−	8.04699i		−	0.120104i	0.998195	−	0.0600521i	$-0.0191267\pi$
$68$	−5.59392	−	34.6528i	−0.0822635	−	0.509599i
$69$		0			0
$70$	−125.674	+	147.588i	−1.79534	+	2.10840i
$71$		−	87.9754i		−	1.23909i	−0.784961	−	0.619545i	$-0.787317\pi$
$71$		−	87.9754i		−	1.23909i	0.784961	−	0.619545i	$-0.212683\pi$
$72$		0			0
$73$	62.0997			0.850680			0.425340	−	0.905034i	$-0.360154\pi$
$73$	62.0997			0.850680			0.425340	+	0.905034i	$0.360154\pi$
$74$	−54.1331	−	46.0953i	−0.731528	−	0.622909i
$75$		0			0
$76$	75.8248	−	12.2402i	0.997694	−	0.161055i
$77$	−137.350			−1.78377
$78$		0			0
$79$		−	9.91976i		−	0.125567i	−0.998027	−	0.0627833i	$-0.980002\pi$
$79$		−	9.91976i		−	0.125567i	0.998027	−	0.0627833i	$-0.0199977\pi$
$80$	118.810	−	39.3848i	1.48513	−	0.492311i
$81$		0			0
$82$	18.5498	+	15.7955i	0.226217	+	0.192628i
$83$			22.1721i			0.267134i	0.991040	+	0.133567i	$0.0426431\pi$
$83$			22.1721i			0.267134i	−0.991040	+	0.133567i	$0.957357\pi$
$84$		0			0
$85$	68.6495			0.807641
$86$	85.9537	−	100.942i	0.999462	−	1.17374i
$87$		0			0
$88$	75.8248	+	46.0025i	0.861645	+	0.522755i
$89$	106.231			1.19360			0.596801	−	0.802389i	$-0.296438\pi$
$89$	106.231			1.19360			0.596801	+	0.802389i	$0.296438\pi$
$90$		0			0
$91$		−	43.9805i		−	0.483302i
$92$	2.81530	−	0.454467i	0.0306011	−	0.00493986i
$93$		0			0
$94$	−53.8007	+	63.1821i	−0.572347	+	0.672150i
$95$			150.214i			1.58120i
$96$		0			0
$97$	131.100			1.35154			0.675771	−	0.737111i	$-0.263811\pi$
$97$	131.100			1.35154			0.675771	+	0.737111i	$0.263811\pi$
$98$	−159.124	−	135.497i	−1.62371	−	1.38262i
$99$		0			0
$100$	23.0756	+	142.947i	0.230756	+	1.42947i
$101$	−45.8389			−0.453851			−0.226925	−	0.973912i	$-0.572867\pi$
$101$	−45.8389			−0.453851			−0.226925	+	0.973912i	$0.572867\pi$
$102$		0			0
$103$			200.701i			1.94855i	0.225359	+	0.974276i	$0.427644\pi$
$103$			200.701i			1.94855i	−0.225359	+	0.974276i	$0.572356\pi$
$104$	−14.7303	+	24.2797i	−0.141638	+	0.233458i
$105$		0			0
$106$	−113.849	−	96.9443i	−1.07405	−	0.914569i
$107$		−	90.1142i		−	0.842189i	−0.907017	−	0.421094i	$-0.861646\pi$
$107$		−	90.1142i		−	0.842189i	0.907017	−	0.421094i	$-0.138354\pi$
$108$		0			0
$109$	−183.447			−1.68300			−0.841499	−	0.540258i	$-0.818327\pi$
$109$	−183.447			−1.68300			−0.841499	+	0.540258i	$0.818327\pi$
$110$	−112.452	+	132.061i	−1.02229	+	1.20056i
$111$		0			0
$112$	62.3746	+	188.162i	0.556916	+	1.68002i
$113$	88.2195			0.780704			0.390352	−	0.920666i	$-0.372353\pi$
$113$	88.2195			0.780704			0.390352	+	0.920666i	$0.372353\pi$
$114$		0			0
$115$			5.57730i			0.0484983i
$116$	−11.6115	−	71.9300i	−0.100099	−	0.620087i
$117$		0			0
$118$	−26.9003	+	31.5910i	−0.227969	+	0.267721i
$119$			108.722i			0.913627i
$120$		0			0
$121$	−1.90033			−0.0157052
$122$	74.3840	+	63.3393i	0.609705	+	0.519174i
$123$		0			0
$124$	−44.0482	+	7.11060i	−0.355227	+	0.0573435i
$125$	−87.6124			−0.700899
$126$		0			0
$127$		−	37.1683i		−	0.292664i	−0.989236	−	0.146332i	$-0.953253\pi$
$127$		−	37.1683i		−	0.292664i	0.989236	−	0.146332i	$-0.0467468\pi$
$128$	28.5867	−	124.767i	0.223334	−	0.974742i
$129$		0			0
$130$	−42.2870	−	36.0081i	−0.325284	−	0.276985i
$131$		−	117.669i		−	0.898235i	−0.893473	−	0.449118i	$-0.851738\pi$
$131$		−	117.669i		−	0.898235i	0.893473	−	0.449118i	$-0.148262\pi$
$132$		0			0
$133$	−237.897			−1.78870
$134$	10.4340	−	12.2534i	0.0778659	−	0.0914436i
$135$		0			0
$136$	36.4140	−	60.0203i	0.267750	−	0.441326i
$137$	36.9485			0.269697			0.134849	−	0.990866i	$-0.456945\pi$
$137$	36.9485			0.269697			0.134849	+	0.990866i	$0.456945\pi$
$138$		0			0
$139$			16.0940i			0.115784i	0.998323	+	0.0578920i	$0.0184379\pi$
$139$			16.0940i			0.115784i	−0.998323	+	0.0578920i	$0.981562\pi$
$140$	−382.736	+	61.7842i	−2.73383	+	0.441315i
$141$		0			0
$142$	114.072	−	133.963i	0.803326	−	0.943404i
$143$		−	39.3536i		−	0.275200i
$144$		0			0
$145$	142.498			0.982747
$146$	94.5615	+	80.5208i	0.647681	+	0.551512i
$147$		0			0
$148$	−22.6615	−	140.382i	−0.153119	−	0.948527i
$149$	8.28335			0.0555930			0.0277965	−	0.999614i	$-0.491151\pi$
$149$	8.28335			0.0555930			0.0277965	+	0.999614i	$0.491151\pi$
$150$		0			0
$151$			209.386i			1.38666i	0.720620	+	0.693330i	$0.243857\pi$
$151$			209.386i			1.38666i	−0.720620	+	0.693330i	$0.756143\pi$
$152$	131.332	+	79.6786i	0.864028	+	0.524202i
$153$		0			0
$154$	−209.148	−	178.093i	−1.35810	−	1.15645i
$155$		−	87.2625i		−	0.562984i
$156$		0			0
$157$	−38.4502			−0.244906			−0.122453	−	0.992474i	$-0.539076\pi$
$157$	−38.4502			−0.244906			−0.122453	+	0.992474i	$0.539076\pi$
$158$	12.8623	−	15.1052i	0.0814072	−	0.0956025i
$159$		0			0
$160$	231.985	+	94.0811i	1.44990	+	0.588007i
$161$	−8.83289			−0.0548626
$162$		0			0
$163$			266.353i			1.63406i	0.576592	+	0.817032i	$0.304382\pi$
$163$			266.353i			1.63406i	−0.576592	+	0.817032i	$0.695618\pi$
$164$	7.76546	+	48.1048i	0.0473503	+	0.293322i
$165$		0			0
$166$	−28.7492	+	33.7623i	−0.173188	+	0.203387i
$167$		−	296.863i		−	1.77763i	−0.458271	−	0.888813i	$-0.651531\pi$
$167$		−	296.863i		−	1.77763i	0.458271	−	0.888813i	$-0.348469\pi$
$168$		0			0
$169$	−156.399			−0.925436
$170$	104.535	+	89.0136i	0.614913	+	0.523609i
$171$		0			0
$172$	261.770	−	42.2569i	1.52192	−	0.245680i
$173$	169.537			0.979981			0.489990	−	0.871728i	$-0.337000\pi$
$173$	169.537			0.979981			0.489990	+	0.871728i	$0.337000\pi$
$174$		0			0
$175$		−	448.490i		−	2.56280i
$176$	55.8126	+	168.367i	0.317117	+	0.956631i
$177$		0			0
$178$	161.761	+	137.743i	0.908771	+	0.773835i
$179$		−	15.0427i		−	0.0840375i	−0.999117	−	0.0420188i	$-0.986621\pi$
$179$		−	15.0427i		−	0.0840375i	0.999117	−	0.0420188i	$-0.0133789\pi$
$180$		0			0
$181$	99.1960			0.548044			0.274022	−	0.961723i	$-0.411646\pi$
$181$	99.1960			0.548044			0.274022	+	0.961723i	$0.411646\pi$
$182$	57.0268	−	66.9707i	0.313334	−	0.367971i
$183$		0			0
$184$	4.87624	+	2.95839i	0.0265013	+	0.0160782i
$185$	278.106			1.50328
$186$		0			0
$187$			97.2838i			0.520234i
$188$	−163.849	+	26.4497i	−0.871535	+	0.140690i
$189$		0			0
$190$	−194.773	+	228.737i	−1.02512	+	1.20388i
$191$		−	271.840i		−	1.42324i	−0.702563	−	0.711622i	$-0.747961\pi$
$191$		−	271.840i		−	1.42324i	0.702563	−	0.711622i	$-0.252039\pi$
$192$		0			0
$193$	145.900			0.755960			0.377980	−	0.925814i	$-0.376619\pi$
$193$	145.900			0.755960			0.377980	+	0.925814i	$0.376619\pi$
$194$	199.630	+	169.989i	1.02902	+	0.876231i
$195$		0			0
$196$	−66.6134	−	412.651i	−0.339864	−	2.10536i
$197$	187.202			0.950266			0.475133	−	0.879914i	$-0.342400\pi$
$197$	187.202			0.950266			0.475133	+	0.879914i	$0.342400\pi$
$198$		0			0
$199$		−	338.220i		−	1.69960i	−0.527109	−	0.849798i	$-0.676724\pi$
$199$		−	338.220i		−	1.69960i	0.527109	−	0.849798i	$-0.323276\pi$
$200$	−150.212	+	247.591i	−0.751061	+	1.23796i
$201$		0			0
$202$	−69.8007	−	59.4365i	−0.345548	−	0.294240i
$203$			225.678i			1.11171i
$204$		0			0
$205$	−95.2990			−0.464873
$206$	−260.236	+	305.615i	−1.26328	+	1.48357i
$207$		0			0
$208$	−53.9124	+	17.8716i	−0.259194	+	0.0859213i
$209$	−212.870			−1.01851
$210$		0			0
$211$		−	118.317i		−	0.560745i	−0.959891	−	0.280372i	$-0.909542\pi$
$211$		−	118.317i		−	0.560745i	0.959891	−	0.280372i	$-0.0904580\pi$
$212$	−47.6602	−	295.242i	−0.224812	−	1.39265i
$213$		0			0
$214$	116.846	−	137.220i	0.546007	−	0.641216i
$215$			518.584i			2.41202i
$216$		0			0
$217$	138.199			0.636863
$218$	−279.341	−	237.864i	−1.28138	−	1.09112i
$219$		0			0
$220$	−342.471	+	55.2843i	−1.55669	+	0.251292i
$221$	−31.1510			−0.140955
$222$		0			0
$223$		−	245.278i		−	1.09990i	−0.835197	−	0.549951i	$-0.814646\pi$
$223$		−	245.278i		−	1.09990i	0.835197	−	0.549951i	$-0.185354\pi$
$224$	−148.998	+	367.399i	−0.665170	+	1.64017i
$225$		0			0
$226$	134.335	+	114.389i	0.594403	+	0.506145i
$227$			31.8323i			0.140230i	0.997539	+	0.0701151i	$0.0223367\pi$
$227$			31.8323i			0.140230i	−0.997539	+	0.0701151i	$0.977663\pi$
$228$		0			0
$229$	143.344			0.625956			0.312978	−	0.949760i	$-0.398673\pi$
$229$	143.344			0.625956			0.312978	+	0.949760i	$0.398673\pi$
$230$	−7.23174	+	8.49277i	−0.0314424	+	0.0369251i
$231$		0			0
$232$	75.5860	−	124.586i	0.325802	−	0.537011i
$233$	329.147			1.41265			0.706324	−	0.707888i	$-0.250352\pi$
$233$	329.147			1.41265			0.706324	+	0.707888i	$0.250352\pi$
$234$		0			0
$235$		−	324.595i		−	1.38126i
$236$	−81.9243	+	13.2249i	−0.347137	+	0.0560375i
$237$		0			0
$238$	−140.973	+	165.554i	−0.592322	+	0.695607i
$239$			87.2625i			0.365115i	0.983195	+	0.182557i	$0.0584376\pi$
$239$			87.2625i			0.365115i	−0.983195	+	0.182557i	$0.941562\pi$
$240$		0			0
$241$	179.199			0.743566			0.371783	−	0.928320i	$-0.378747\pi$
$241$	179.199			0.743566			0.371783	+	0.928320i	$0.378747\pi$
$242$	−2.89371	−	2.46404i	−0.0119575	−	0.0101820i
$243$		0			0
$244$	31.1391	+	192.898i	0.127619	+	0.790566i
$245$	817.491			3.33670
$246$		0			0
$247$		−	68.1625i		−	0.275961i
$248$	−76.2937	−	46.2870i	−0.307636	−	0.186641i
$249$		0			0
$250$	−133.411	−	113.602i	−0.533643	−	0.454406i
$251$		−	410.968i		−	1.63732i	−0.574278	−	0.818660i	$-0.694717\pi$
$251$		−	410.968i		−	1.63732i	0.574278	−	0.818660i	$-0.305283\pi$
$252$		0			0
$253$	−7.90364			−0.0312397
$254$	48.1939	−	56.5976i	0.189740	−	0.222825i
$255$		0			0
$256$	205.308	−	152.921i	0.801983	−	0.597346i
$257$	−198.777			−0.773453			−0.386726	−	0.922195i	$-0.626394\pi$
$257$	−198.777			−0.773453			−0.386726	+	0.922195i	$0.626394\pi$
$258$		0			0
$259$			440.443i			1.70055i
$260$	−17.7025	−	109.662i	−0.0680864	−	0.421776i
$261$		0			0
$262$	152.574	−	179.179i	0.582343	−	0.683888i
$263$		−	310.409i		−	1.18026i	−0.807307	−	0.590132i	$-0.799076\pi$
$263$		−	310.409i		−	1.18026i	0.807307	−	0.590132i	$-0.200924\pi$
$264$		0			0
$265$	584.894			2.20715
$266$	−362.255	−	308.466i	−1.36186	−	1.15965i
$267$		0			0
$268$	31.7766	−	5.12962i	0.118569	−	0.0191404i
$269$	−199.384			−0.741206			−0.370603	−	0.928791i	$-0.620849\pi$
$269$	−199.384			−0.741206			−0.370603	+	0.928791i	$0.620849\pi$
$270$		0			0
$271$		−	68.1625i		−	0.251522i	−0.992061	−	0.125761i	$-0.959863\pi$
$271$		−	68.1625i		−	0.251522i	0.992061	−	0.125761i	$-0.0401372\pi$
$272$	133.274	−	44.1794i	0.489977	−	0.162424i
$273$		0			0
$274$	56.2629	+	47.9088i	0.205339	+	0.174850i
$275$		−	401.307i		−	1.45930i
$276$		0			0
$277$	−292.199			−1.05487			−0.527436	−	0.849595i	$-0.676846\pi$
$277$	−292.199			−1.05487			−0.527436	+	0.849595i	$0.676846\pi$
$278$	−20.8681	+	24.5069i	−0.0750650	+	0.0881543i
$279$		0			0
$280$	−662.918	−	402.189i	−2.36756	−	1.43639i
$281$	−468.632			−1.66773			−0.833865	−	0.551969i	$-0.813877\pi$
$281$	−468.632			−1.66773			−0.833865	+	0.551969i	$0.813877\pi$
$282$		0			0
$283$			13.6243i			0.0481424i	0.999710	+	0.0240712i	$0.00766283\pi$
$283$			13.6243i			0.0481424i	−0.999710	+	0.0240712i	$0.992337\pi$
$284$	347.404	−	56.0807i	1.22325	−	0.197467i
$285$		0			0
$286$	51.0274	−	59.9252i	0.178417	−	0.209529i
$287$		−	150.927i		−	0.525878i
$288$		0			0
$289$	−211.993			−0.733541
$290$	216.988	+	184.769i	0.748233	+	0.637134i
$291$		0			0
$292$	39.5860	+	245.224i	0.135568	+	0.839809i
$293$	33.7462			0.115175			0.0575874	−	0.998340i	$-0.481659\pi$
$293$	33.7462			0.115175			0.0575874	+	0.998340i	$0.481659\pi$
$294$		0			0
$295$		−	162.298i		−	0.550161i
$296$	147.517	−	243.149i	0.498369	−	0.821449i
$297$		0			0
$298$	12.6134	+	10.7405i	0.0423267	+	0.0360420i
$299$		−	2.53081i		−	0.00846423i
$300$		0			0
$301$	−821.292			−2.72855
$302$	−271.498	+	318.839i	−0.898998	+	1.05576i
$303$		0			0
$304$	96.6703	+	291.620i	0.317994	+	0.959277i
$305$	−382.145			−1.25293
$306$		0			0
$307$			141.264i			0.460144i	0.973174	+	0.230072i	$0.0738962\pi$
$307$			141.264i			0.460144i	−0.973174	+	0.230072i	$0.926104\pi$
$308$	−87.5549	−	542.378i	−0.284269	−	1.76097i
$309$		0			0
$310$	113.148	−	132.878i	0.364993	−	0.428638i
$311$		−	397.672i		−	1.27869i	−0.768921	−	0.639343i	$-0.779206\pi$
$311$		−	397.672i		−	1.27869i	0.768921	−	0.639343i	$-0.220794\pi$
$312$		0			0
$313$	−478.389			−1.52840			−0.764199	−	0.644980i	$-0.776866\pi$
$313$	−478.389			−1.52840			−0.764199	+	0.644980i	$0.776866\pi$
$314$	−58.5495	−	49.8560i	−0.186463	−	0.158777i
$315$		0			0
$316$	39.1719	−	6.32344i	0.123962	−	0.0200109i
$317$	−223.455			−0.704904			−0.352452	−	0.935830i	$-0.614652\pi$
$317$	−223.455			−0.704904			−0.352452	+	0.935830i	$0.614652\pi$
$318$		0			0
$319$			201.936i			0.633027i
$320$	231.263	+	444.061i	0.722696	+	1.38769i
$321$		0			0
$322$	−13.4502	−	11.4531i	−0.0417707	−	0.0355685i
$323$			168.500i			0.521673i
$324$		0			0
$325$	128.502			0.395390
$326$	−345.363	+	405.585i	−1.05940	+	1.24413i
$327$		0			0
$328$	−50.5498	+	83.3200i	−0.154115	+	0.254025i
$329$	514.068			1.56252
$330$		0			0
$331$		−	325.233i		−	0.982578i	−0.870997	−	0.491289i	$-0.836526\pi$
$331$		−	325.233i		−	0.982578i	0.870997	−	0.491289i	$-0.163474\pi$
$332$	−87.5549	+	14.1338i	−0.263720	+	0.0425716i
$333$		0			0
$334$	384.924	−	452.045i	1.15247	−	1.35343i
$335$			62.9516i			0.187915i
$336$		0			0
$337$	257.698			0.764682			0.382341	−	0.924021i	$-0.375118\pi$
$337$	257.698			0.764682			0.382341	+	0.924021i	$0.375118\pi$
$338$	−238.154	−	202.793i	−0.704598	−	0.599978i
$339$		0			0
$340$	43.7612	+	271.089i	0.128709	+	0.797319i
$341$	123.660			0.362640
$342$		0			0
$343$			687.594i			2.00465i
$344$	453.399	+	275.075i	1.31802	+	0.799636i
$345$		0			0
$346$	258.160	+	219.828i	0.746127	+	0.635340i
$347$			435.991i			1.25646i	0.778028	+	0.628230i	$0.216220\pi$
$347$			435.991i			1.25646i	−0.778028	+	0.628230i	$0.783780\pi$
$348$		0			0
$349$	361.492			1.03579			0.517896	−	0.855443i	$-0.326715\pi$
$349$	361.492			1.03579			0.517896	+	0.855443i	$0.326715\pi$
$350$	581.529	−	682.932i	1.66151	−	1.95123i
$351$		0			0
$352$	−133.323	+	328.747i	−0.378759	+	0.933942i
$353$	−503.100			−1.42521			−0.712607	−	0.701564i	$-0.752486\pi$
$353$	−503.100			−1.42521			−0.712607	+	0.701564i	$0.752486\pi$
$354$		0			0
$355$			688.232i			1.93868i
$356$	67.7176	+	419.492i	0.190218	+	1.17835i
$357$		0			0
$358$	19.5050	−	22.9061i	0.0544831	−	0.0639836i
$359$		−	221.008i		−	0.615621i	−0.951448	−	0.307810i	$-0.900404\pi$
$359$		−	221.008i		−	0.615621i	0.951448	−	0.307810i	$-0.0995963\pi$
$360$		0			0
$361$	−7.70099			−0.0213324
$362$	151.050	+	128.621i	0.417264	+	0.355308i
$363$		0			0
$364$	173.674	−	28.0357i	0.477125	−	0.0770212i
$365$	−485.806			−1.33097
$366$		0			0
$367$			336.944i			0.918103i	0.888410	+	0.459051i	$0.151811\pi$
$367$			336.944i			0.918103i	−0.888410	+	0.459051i	$0.848189\pi$
$368$	3.58927	+	10.8276i	0.00975346	+	0.0294228i
$369$		0			0
$370$	423.483	+	360.603i	1.14455	+	0.974604i
$371$			926.308i			2.49679i
$372$		0			0
$373$	−457.189			−1.22571			−0.612854	−	0.790196i	$-0.709979\pi$
$373$	−457.189			−1.22571			−0.612854	+	0.790196i	$0.709979\pi$
$374$	−126.142	+	148.138i	−0.337278	+	0.396090i
$375$		0			0
$376$	−283.794	−	172.176i	−0.754771	−	0.457916i
$377$	−64.6613			−0.171515
$378$		0			0
$379$			74.3367i			0.196139i	0.995180	+	0.0980695i	$0.0312667\pi$
$379$			74.3367i			0.196139i	−0.995180	+	0.0980695i	$0.968733\pi$
$380$	−593.177	+	95.7552i	−1.56099	+	0.251987i
$381$		0			0
$382$	352.478	−	413.940i	0.922716	−	1.08361i
$383$			570.058i			1.48840i	0.667956	+	0.744201i	$0.267169\pi$
$383$			570.058i			1.48840i	−0.667956	+	0.744201i	$0.732831\pi$
$384$		0			0
$385$	1074.49			2.79088
$386$	222.168	+	189.180i	0.575564	+	0.490103i
$387$		0			0
$388$	83.5706	+	517.697i	0.215388	+	1.33427i
$389$	635.720			1.63424			0.817121	−	0.576466i	$-0.195569\pi$
$389$	635.720			1.63424			0.817121	+	0.576466i	$0.195569\pi$
$390$		0			0
$391$			6.25626i			0.0160007i
$392$	433.625	−	714.733i	1.10619	−	1.82330i
$393$		0			0
$394$	285.060	+	242.734i	0.723503	+	0.616076i
$395$			77.6023i			0.196462i
$396$		0			0
$397$	−482.849			−1.21624			−0.608122	−	0.793844i	$-0.708077\pi$
$397$	−482.849			−1.21624			−0.608122	+	0.793844i	$0.708077\pi$
$398$	438.548	−	515.020i	1.10188	−	1.29402i
$399$		0			0
$400$	−549.770	+	182.245i	−1.37442	+	0.455613i
$401$	−157.208			−0.392040			−0.196020	−	0.980600i	$-0.562802\pi$
$401$	−157.208			−0.392040			−0.196020	+	0.980600i	$0.562802\pi$
$402$		0			0
$403$			39.5970i			0.0982556i
$404$	−29.2204	−	181.012i	−0.0723278	−	0.448051i
$405$		0			0
$406$	−292.622	+	343.648i	−0.720744	+	0.846423i
$407$			394.107i			0.968322i
$408$		0			0
$409$	301.302			0.736680			0.368340	−	0.929691i	$-0.379926\pi$
$409$	301.302			0.736680			0.368340	+	0.929691i	$0.379926\pi$
$410$	−145.115	−	123.568i	−0.353940	−	0.301386i
$411$		0			0
$412$	−792.543	+	127.938i	−1.92365	+	0.310530i
$413$	257.034			0.622358
$414$		0			0
$415$		−	173.452i		−	0.417957i
$416$	−105.267	−	42.6911i	−0.253047	−	0.102623i
$417$		0			0
$418$	−324.145	−	276.015i	−0.775465	−	0.660323i
$419$			484.292i			1.15583i	0.816097	+	0.577914i	$0.196133\pi$
$419$			484.292i			1.15583i	−0.816097	+	0.577914i	$0.803867\pi$
$420$		0			0
$421$	−5.15116			−0.0122355			−0.00611777	−	0.999981i	$-0.501947\pi$
$421$	−5.15116			−0.0122355			−0.00611777	+	0.999981i	$0.501947\pi$
$422$	153.415	−	180.166i	0.363542	−	0.426934i
$423$		0			0
$424$	310.248	−	511.373i	0.731716	−	1.20607i
$425$	−317.662			−0.747439
$426$		0			0
$427$		−	605.210i		−	1.41735i
$428$	355.850	−	57.4441i	0.831426	−	0.134215i
$429$		0			0
$430$	−672.416	+	789.668i	−1.56376	+	1.83644i
$431$		−	317.539i		−	0.736748i	−0.929678	−	0.368374i	$-0.879915\pi$
$431$		−	317.539i		−	0.736748i	0.929678	−	0.368374i	$-0.120085\pi$
$432$		0			0
$433$	190.203			0.439267			0.219634	−	0.975582i	$-0.429514\pi$
$433$	190.203			0.439267			0.219634	+	0.975582i	$0.429514\pi$
$434$	210.441	+	179.195i	0.484888	+	0.412891i
$435$		0			0
$436$	−116.940	−	724.409i	−0.268210	−	1.66149i
$437$	−13.6895			−0.0313261
$438$		0			0
$439$		−	116.485i		−	0.265343i	−0.991160	−	0.132671i	$-0.957645\pi$
$439$		−	116.485i		−	0.265343i	0.991160	−	0.132671i	$-0.0423555\pi$
$440$	−593.177	−	359.877i	−1.34813	−	0.817903i
$441$		0			0
$442$	−47.4348	−	40.3916i	−0.107319	−	0.0913837i
$443$		−	490.638i		−	1.10753i	−0.832672	−	0.553767i	$-0.813190\pi$
$443$		−	490.638i		−	1.10753i	0.832672	−	0.553767i	$-0.186810\pi$
$444$		0			0
$445$	−831.042			−1.86751
$446$	318.037	−	373.494i	0.713088	−	0.837431i
$447$		0			0
$448$	−703.268	+	366.255i	−1.56980	+	0.817534i
$449$	155.936			0.347297			0.173649	−	0.984808i	$-0.444444\pi$
$449$	155.936			0.347297			0.173649	+	0.984808i	$0.444444\pi$
$450$		0			0
$451$		−	135.049i		−	0.299444i
$452$	56.2363	+	348.368i	0.124417	+	0.770726i
$453$		0			0
$454$	−41.2749	+	48.4722i	−0.0909139	+	0.106767i
$455$			344.059i			0.756174i
$456$		0			0
$457$	122.498			0.268049			0.134024	−	0.990978i	$-0.457210\pi$
$457$	122.498			0.268049			0.134024	+	0.990978i	$0.457210\pi$
$458$	218.275	+	185.865i	0.476583	+	0.405819i
$459$		0			0
$460$	−22.0241	+	3.55530i	−0.0478785	+	0.00772891i
$461$	469.443			1.01832			0.509158	−	0.860673i	$-0.329957\pi$
$461$	469.443			1.01832			0.509158	+	0.860673i	$0.329957\pi$
$462$		0			0
$463$			382.838i			0.826864i	0.910535	+	0.413432i	$0.135670\pi$
$463$			382.838i			0.826864i	−0.910535	+	0.413432i	$0.864330\pi$
$464$	276.641	−	91.7048i	0.596209	−	0.197640i
$465$		0			0
$466$	501.205	+	426.785i	1.07555	+	0.915847i
$467$			253.232i			0.542253i	0.962544	+	0.271127i	$0.0873962\pi$
$467$			253.232i			0.542253i	−0.962544	+	0.271127i	$0.912604\pi$
$468$		0			0
$469$	−99.6977			−0.212575
$470$	420.883	−	494.273i	0.895495	−	1.05165i
$471$		0			0
$472$	−141.897	−	86.0882i	−0.300629	−	0.182390i
$473$	−734.890			−1.55368
$474$		0			0
$475$		−	695.085i		−	1.46334i
$476$	−429.329	+	69.3055i	−0.901951	+	0.145600i
$477$		0			0
$478$	−113.148	+	132.878i	−0.236711	+	0.277987i
$479$			826.926i			1.72636i	0.504898	+	0.863179i	$0.331530\pi$
$479$			826.926i			1.72636i	−0.504898	+	0.863179i	$0.668470\pi$
$480$		0			0
$481$	−126.196			−0.262362
$482$	272.874	+	232.357i	0.566128	+	0.482068i
$483$		0			0
$484$	−1.21138	−	7.50418i	−0.00250286	−	0.0155045i
$485$	−1025.59			−2.11462
$486$		0			0
$487$			320.932i			0.658997i	0.944156	+	0.329499i	$0.106880\pi$
$487$			320.932i			0.658997i	−0.944156	+	0.329499i	$0.893120\pi$
$488$	−202.702	+	334.109i	−0.415374	+	0.684650i
$489$		0			0
$490$	1244.82	+	1059.99i	2.54046	+	2.16324i
$491$		−	561.895i		−	1.14439i	−0.820118	−	0.572194i	$-0.806092\pi$
$491$		−	561.895i		−	1.14439i	0.820118	−	0.572194i	$-0.193908\pi$
$492$		0			0
$493$	159.846			0.324230
$494$	88.3821	−	103.794i	0.178911	−	0.210108i
$495$		0			0
$496$	−56.1578	−	169.408i	−0.113221	−	0.341549i
$497$	−1089.97			−2.19309
$498$		0			0
$499$			30.3562i			0.0608341i	0.999537	+	0.0304170i	$0.00968353\pi$
$499$			30.3562i			0.0608341i	−0.999537	+	0.0304170i	$0.990316\pi$
$500$	−55.8493	−	345.971i	−0.111699	−	0.691942i
$501$		0			0
$502$	532.876	−	625.796i	1.06151	−	1.24660i
$503$			12.8329i			0.0255126i	0.999919	+	0.0127563i	$0.00406057\pi$
$503$			12.8329i			0.0255126i	−0.999919	+	0.0127563i	$0.995939\pi$
$504$		0			0
$505$	358.598			0.710095
$506$	−12.0352	−	10.2482i	−0.0237849	−	0.0202533i
$507$		0			0
$508$	146.773	−	23.6933i	0.288924	−	0.0466403i
$509$	−757.539			−1.48829			−0.744145	−	0.668019i	$-0.767143\pi$
$509$	−757.539			−1.48829			−0.744145	+	0.668019i	$0.767143\pi$
$510$		0			0
$511$		−	769.380i		−	1.50564i
$512$	510.913	+	33.3518i	0.997876	+	0.0651403i
$513$		0			0
$514$	−302.686	−	257.742i	−0.588883	−	0.501444i
$515$		−	1570.08i		−	3.04870i
$516$		0			0
$517$	459.987			0.889723
$518$	−571.095	+	670.679i	−1.10250	+	1.29475i
$519$		0			0
$520$	115.235	−	189.940i	0.221607	−	0.365269i
$521$	495.775			0.951584			0.475792	−	0.879558i	$-0.342162\pi$
$521$	495.775			0.951584			0.475792	+	0.879558i	$0.342162\pi$
$522$		0			0
$523$			359.891i			0.688128i	0.938946	+	0.344064i	$0.111804\pi$
$523$			359.891i			0.688128i	−0.938946	+	0.344064i	$0.888196\pi$
$524$	464.660	−	75.0090i	0.886756	−	0.143147i
$525$		0			0
$526$	402.488	−	472.672i	0.765187	−	0.898615i
$527$		−	97.8855i		−	0.185741i
$528$		0			0
$529$	528.492			0.999039
$530$	890.640	+	758.396i	1.68045	+	1.43093i
$531$		0			0
$532$	−151.650	−	939.427i	−0.285055	−	1.76584i
$533$	43.2437			0.0811327
$534$		0			0
$535$			704.964i			1.31769i
$536$	55.0386	+	33.3917i	0.102684	+	0.0622979i
$537$		0			0
$538$	−303.610	−	258.529i	−0.564331	−	0.480538i
$539$			1158.47i			2.14930i
$540$		0			0
$541$	−292.354			−0.540395			−0.270198	−	0.962805i	$-0.587089\pi$
$541$	−292.354			−0.540395			−0.270198	+	0.962805i	$0.587089\pi$
$542$	88.3821	−	103.794i	0.163067	−	0.191501i
$543$		0			0
$544$	260.226	+	105.534i	0.478356	+	0.193997i
$545$	1435.10			2.63322
$546$		0			0
$547$		−	587.202i		−	1.07350i	−0.843743	−	0.536748i	$-0.819653\pi$
$547$		−	587.202i		−	1.07350i	0.843743	−	0.536748i	$-0.180347\pi$
$548$	23.5531	+	145.905i	0.0429802	+	0.266250i
$549$		0			0
$550$	520.350	−	611.086i	0.946092	−	1.11107i
$551$			349.763i			0.634778i
$552$		0			0
$553$	−122.900			−0.222243
$554$	−444.943	−	378.877i	−0.803146	−	0.683893i
$555$		0			0
$556$	−63.5531	+	10.2592i	−0.114304	+	0.0184519i
$557$	−523.617			−0.940067			−0.470034	−	0.882649i	$-0.655758\pi$
$557$	−523.617			−0.940067			−0.470034	+	0.882649i	$0.655758\pi$
$558$		0			0
$559$		−	235.317i		−	0.420961i
$560$	−487.956	−	1471.99i	−0.871351	−	2.62856i
$561$		0			0
$562$	−713.603	−	607.646i	−1.26976	−	1.08122i
$563$		−	869.773i		−	1.54489i	−0.635082	−	0.772445i	$-0.719034\pi$
$563$		−	869.773i		−	1.54489i	0.635082	−	0.772445i	$-0.280966\pi$
$564$		0			0
$565$	−690.141			−1.22149
$566$	−17.6658	+	20.7462i	−0.0312116	+	0.0366541i
$567$		0			0
$568$	601.722	+	365.061i	1.05937	+	0.642714i
$569$	−258.024			−0.453469			−0.226734	−	0.973957i	$-0.572805\pi$
$569$	−258.024			−0.453469			−0.226734	+	0.973957i	$0.572805\pi$
$570$		0			0
$571$		−	82.9395i		−	0.145253i	−0.997359	−	0.0726266i	$-0.976862\pi$
$571$		−	82.9395i		−	0.145253i	0.997359	−	0.0726266i	$-0.0231381\pi$
$572$	155.403	−	25.0863i	0.271683	−	0.0438572i
$573$		0			0
$574$	195.698	−	229.822i	0.340937	−	0.400387i
$575$		−	25.8078i		−	0.0448832i
$576$		0			0
$577$	−167.694			−0.290631			−0.145316	−	0.989385i	$-0.546420\pi$
$577$	−167.694			−0.290631			−0.145316	+	0.989385i	$0.546420\pi$
$578$	−322.810	−	274.879i	−0.558495	−	0.475569i
$579$		0			0
$580$	90.8368	+	562.709i	0.156615	+	0.970187i
$581$	274.700			0.472805
$582$		0			0
$583$			828.858i			1.42171i
$584$	−257.688	+	424.741i	−0.441246	+	0.727296i
$585$		0			0
$586$	51.3866	+	43.7566i	0.0876905	+	0.0746700i
$587$			518.976i			0.884116i	0.896986	+	0.442058i	$0.145752\pi$
$587$			518.976i			0.884116i	−0.896986	+	0.442058i	$0.854248\pi$
$588$		0			0
$589$	214.186			0.363644
$590$	210.441	−	247.137i	0.356680	−	0.418876i
$591$		0			0
$592$	539.906	−	178.975i	0.912003	−	0.302323i
$593$	−865.433			−1.45941			−0.729707	−	0.683760i	$-0.760344\pi$
$593$	−865.433			−1.45941			−0.729707	+	0.683760i	$0.760344\pi$
$594$		0			0
$595$		−	850.529i		−	1.42946i
$596$	5.28029	+	32.7100i	0.00885955	+	0.0548825i
$597$		0			0
$598$	3.28154	−	3.85375i	0.00548752	−	0.00644440i
$599$		−	43.7023i		−	0.0729587i	−0.999334	−	0.0364794i	$-0.988386\pi$
$599$		−	43.7023i		−	0.0729587i	0.999334	−	0.0364794i	$-0.0116143\pi$
$600$		0			0
$601$	−142.100			−0.236439			−0.118219	−	0.992988i	$-0.537719\pi$
$601$	−142.100			−0.236439			−0.118219	+	0.992988i	$0.537719\pi$
$602$	−1250.61	−	1064.92i	−2.07743	−	1.76897i
$603$		0			0
$604$	−826.839	+	133.475i	−1.36894	+	0.220985i
$605$	14.8663			0.0245724
$606$		0			0
$607$		−	114.057i		−	0.187902i	−0.995577	−	0.0939512i	$-0.970050\pi$
$607$		−	114.057i		−	0.187902i	0.995577	−	0.0939512i	$-0.0299498\pi$
$608$	−230.922	+	569.407i	−0.379807	+	0.936525i
$609$		0			0
$610$	−581.906	−	495.503i	−0.953944	−	0.812300i
$611$			147.291i			0.241066i
$612$		0			0
$613$	−515.196			−0.840450			−0.420225	−	0.907420i	$-0.638049\pi$
$613$	−515.196			−0.840450			−0.420225	+	0.907420i	$0.638049\pi$
$614$	−183.169	+	215.108i	−0.298320	+	0.350339i
$615$		0			0
$616$	569.945	−	939.427i	0.925236	−	1.52504i
$617$	573.706			0.929831			0.464916	−	0.885355i	$-0.346085\pi$
$617$	573.706			0.929831			0.464916	+	0.885355i	$0.346085\pi$
$618$		0			0
$619$			650.466i			1.05083i	0.850845	+	0.525417i	$0.176091\pi$
$619$			650.466i			1.05083i	−0.850845	+	0.525417i	$0.823909\pi$
$620$	344.589	−	55.6262i	0.555789	−	0.0897197i
$621$		0			0
$622$	515.636	−	605.550i	0.828997	−	0.973552i
$623$		−	1316.14i		−	2.11258i
$624$		0			0
$625$	−219.591			−0.351346
$626$	−728.460	−	620.297i	−1.16367	−	0.990890i
$627$		0			0
$628$	−24.5104	−	151.835i	−0.0390293	−	0.241776i
$629$	311.962			0.495965
$630$		0			0
$631$		−	915.625i		−	1.45107i	−0.688185	−	0.725535i	$-0.741592\pi$
$631$		−	915.625i		−	1.45107i	0.688185	−	0.725535i	$-0.258408\pi$
$632$	67.8478	+	41.1629i	0.107354	+	0.0651312i
$633$		0			0
$634$	−340.263	−	289.740i	−0.536692	−	0.457003i
$635$			290.768i			0.457902i
$636$		0			0
$637$	−370.952			−0.582342
$638$	−261.837	+	307.495i	−0.410404	+	0.481967i
$639$		0			0
$640$	−223.634	+	976.052i	−0.349428	+	1.52508i
$641$	1005.85			1.56919			0.784594	−	0.620010i	$-0.212871\pi$
$641$	1005.85			1.56919			0.784594	+	0.620010i	$0.212871\pi$
$642$		0			0
$643$		−	645.527i		−	1.00393i	−0.864888	−	0.501965i	$-0.832611\pi$
$643$		−	645.527i		−	1.00393i	0.864888	−	0.501965i	$-0.167389\pi$
$644$	−5.63060	−	34.8800i	−0.00874317	−	0.0541615i
$645$		0			0
$646$	−218.484	+	256.582i	−0.338211	+	0.397186i
$647$			469.962i			0.726372i	0.931717	+	0.363186i	$0.118311\pi$
$647$			469.962i			0.726372i	−0.931717	+	0.363186i	$0.881689\pi$
$648$		0			0
$649$	229.993			0.354381
$650$	195.674	+	166.620i	0.301037	+	0.256339i
$651$		0			0
$652$	−1051.79	+	169.789i	−1.61318	+	0.260412i
$653$	−727.398			−1.11393			−0.556966	−	0.830535i	$-0.688035\pi$
$653$	−727.398			−1.11393			−0.556966	+	0.830535i	$0.688035\pi$
$654$		0			0
$655$			920.523i			1.40538i
$656$	−185.010	+	61.3297i	−0.282028	+	0.0934904i
$657$		0			0
$658$	782.791	+	666.560i	1.18965	+	1.01301i
$659$			265.744i			0.403254i	0.979462	+	0.201627i	$0.0646228\pi$
$659$			265.744i			0.403254i	−0.979462	+	0.201627i	$0.935377\pi$
$660$		0			0
$661$	642.251			0.971635			0.485818	−	0.874060i	$-0.338522\pi$
$661$	642.251			0.971635			0.485818	+	0.874060i	$0.338522\pi$
$662$	421.710	−	495.245i	0.637024	−	0.748104i
$663$		0			0
$664$	−151.650	−	92.0050i	−0.228388	−	0.138562i
$665$	1861.07			2.79860
$666$		0			0
$667$			12.9864i			0.0194698i
$668$	1172.28	−	189.238i	1.75491	−	0.283291i
$669$		0			0
$670$	−81.6254	+	95.8587i	−0.121829	+	0.143073i
$671$		−	541.540i		−	0.807065i
$672$		0			0
$673$	486.106			0.722298			0.361149	−	0.932508i	$-0.382385\pi$
$673$	486.106			0.722298			0.361149	+	0.932508i	$0.382385\pi$
$674$	392.406	+	334.141i	0.582205	+	0.495758i
$675$		0			0
$676$	−99.6977	−	617.599i	−0.147482	−	0.913609i
$677$	1074.27			1.58681			0.793404	−	0.608696i	$-0.208307\pi$
$677$	1074.27			1.58681			0.793404	+	0.608696i	$0.208307\pi$
$678$		0			0
$679$		−	1624.25i		−	2.39212i
$680$	−284.867	+	469.539i	−0.418922	+	0.690499i
$681$		0			0
$682$	188.302	+	160.343i	0.276103	+	0.235107i
$683$		−	545.105i		−	0.798104i	−0.916928	−	0.399052i	$-0.869339\pi$
$683$		−	545.105i		−	0.798104i	0.916928	−	0.399052i	$-0.130661\pi$
$684$		0			0
$685$	−289.048			−0.421968
$686$	−891.560	+	1047.02i	−1.29965	+	1.52627i
$687$		0			0
$688$	333.735	+	1006.76i	0.485080	+	1.46332i
$689$	−265.407			−0.385205
$690$		0			0
$691$		−	1246.91i		−	1.80450i	−0.431213	−	0.902250i	$-0.641914\pi$
$691$		−	1246.91i		−	1.80450i	0.431213	−	0.902250i	$-0.358086\pi$
$692$	108.073	+	669.480i	0.156174	+	0.967457i
$693$		0			0
$694$	−565.323	+	663.900i	−0.814587	+	0.956629i
$695$		−	125.903i		−	0.181156i
$696$		0			0
$697$	−106.900			−0.153372
$698$	550.457	+	468.724i	0.788620	+	0.671524i
$699$		0			0
$700$	1771.03	−	285.894i	2.53005	−	0.408419i
$701$	474.890			0.677446			0.338723	−	0.940886i	$-0.390005\pi$
$701$	474.890			0.677446			0.338723	+	0.940886i	$0.390005\pi$
$702$		0			0
$703$			682.613i			0.971000i
$704$	−629.283	+	327.724i	−0.893867	+	0.465517i
$705$		0			0
$706$	−766.090	−	652.339i	−1.08511	−	0.923993i
$707$			567.919i			0.803280i
$708$		0			0
$709$	−882.636			−1.24490			−0.622452	−	0.782658i	$-0.713863\pi$
$709$	−882.636			−1.24490			−0.622452	+	0.782658i	$0.713863\pi$
$710$	−892.387	+	1048.00i	−1.25688	+	1.47605i
$711$		0			0
$712$	−440.813	+	726.581i	−0.619119	+	1.02048i
$713$	7.95252			0.0111536
$714$		0			0
$715$			307.863i			0.430578i
$716$	59.4019	−	9.58911i	0.0829635	−	0.0133926i
$717$		0			0
$718$	286.567	−	336.537i	0.399119	−	0.468715i
$719$		−	193.132i		−	0.268612i	−0.990940	−	0.134306i	$-0.957119\pi$
$719$		−	193.132i		−	0.268612i	0.990940	−	0.134306i	$-0.0428806\pi$
$720$		0			0
$721$	2486.57			3.44878
$722$	−11.7266	−	9.98540i	−0.0162418	−	0.0138302i
$723$		0			0
$724$	63.2334	+	391.713i	0.0873389	+	0.541040i
$725$	−659.382			−0.909492
$726$		0			0
$727$		−	362.957i		−	0.499254i	−0.968342	−	0.249627i	$-0.919692\pi$
$727$		−	362.957i		−	0.499254i	0.968342	−	0.249627i	$-0.0803079\pi$
$728$	300.811	+	182.501i	0.413203	+	0.250688i
$729$		0			0
$730$	−739.755	−	629.914i	−1.01336	−	0.862896i
$731$			581.715i			0.795779i
$732$		0			0
$733$	454.193			0.619635			0.309818	−	0.950796i	$-0.399732\pi$
$733$	454.193			0.619635			0.309818	+	0.950796i	$0.399732\pi$
$734$	−436.894	+	513.077i	−0.595223	+	0.699015i
$735$		0			0
$736$	−8.57392	+	21.1415i	−0.0116494	+	0.0287249i
$737$	−89.2092			−0.121044
$738$		0			0
$739$			999.841i			1.35296i	0.736459	+	0.676482i	$0.236496\pi$
$739$			999.841i			1.35296i	−0.736459	+	0.676482i	$0.763504\pi$
$740$	177.281	+	1098.21i	0.239569	+	1.48407i
$741$		0			0
$742$	−1201.09	+	1410.52i	−1.61871	+	1.90098i
$743$			1325.41i			1.78386i	0.452177	+	0.891928i	$0.350648\pi$
$743$			1325.41i			1.78386i	−0.452177	+	0.891928i	$0.649352\pi$
$744$		0			0
$745$	−64.8007			−0.0869808
$746$	−696.179	−	592.809i	−0.933216	−	0.794650i
$747$		0			0
$748$	−384.162	+	62.0144i	−0.513586	+	0.0829070i
$749$	−1116.47			−1.49061
$750$		0			0
$751$			361.846i			0.481818i	0.970548	+	0.240909i	$0.0774456\pi$
$751$			361.846i			0.481818i	−0.970548	+	0.240909i	$0.922554\pi$
$752$	−208.893	−	630.158i	−0.277784	−	0.837976i
$753$		0			0
$754$	−98.4622	−	83.8423i	−0.130586	−	0.111197i
$755$		−	1638.02i		−	2.16957i
$756$		0			0
$757$	99.1960			0.131038			0.0655192	−	0.997851i	$-0.479130\pi$
$757$	99.1960			0.131038			0.0655192	+	0.997851i	$0.479130\pi$
$758$	−96.3878	+	113.195i	−0.127161	+	0.149334i
$759$		0			0
$760$	−1027.41	−	623.326i	−1.35186	−	0.820166i
$761$	1395.54			1.83383			0.916915	−	0.399084i	$-0.130672\pi$
$761$	1395.54			1.83383			0.916915	+	0.399084i	$0.130672\pi$
$762$		0			0
$763$			2272.80i			2.97877i
$764$	1073.46	−	173.286i	1.40505	−	0.226815i
$765$		0			0
$766$	−739.159	+	868.048i	−0.964959	+	1.13322i
$767$			73.6456i			0.0960178i
$768$		0			0
$769$	481.900			0.626658			0.313329	−	0.949645i	$-0.398556\pi$
$769$	481.900			0.626658			0.313329	+	0.949645i	$0.398556\pi$
$770$	1636.16	+	1393.22i	2.12489	+	1.80938i
$771$		0			0
$772$	93.0054	+	576.143i	0.120473	+	0.746299i
$773$	−1026.09			−1.32741			−0.663707	−	0.747993i	$-0.731018\pi$
$773$	−1026.09			−1.32741			−0.663707	+	0.747993i	$0.731018\pi$
$774$		0			0
$775$			403.789i			0.521018i
$776$	−544.009	+	896.677i	−0.701043	+	1.15551i
$777$		0			0
$778$	968.035	+	824.299i	1.24426	+	1.05951i
$779$		−	233.912i		−	0.300272i
$780$		0			0
$781$	−975.299			−1.24878
$782$	−8.11211	+	9.52664i	−0.0103735	+	0.0121824i
$783$		0			0
$784$	1587.05	−	526.096i	2.02429	−	0.671041i
$785$	300.796			0.383179
$786$		0			0
$787$		−	680.905i		−	0.865190i	−0.901588	−	0.432595i	$-0.857598\pi$
$787$		−	680.905i		−	0.865190i	0.901588	−	0.432595i	$-0.142402\pi$
$788$	119.334	+	739.240i	0.151439	+	0.938122i
$789$		0			0
$790$	−100.622	+	118.168i	−0.127370	+	0.149580i
$791$		−	1092.99i		−	1.38178i
$792$		0			0
$793$	173.405			0.218670
$794$	−735.252	−	626.080i	−0.926010	−	0.788514i
$795$		0			0
$796$	1335.59	−	215.601i	1.67787	−	0.270855i
$797$	196.035			0.245967			0.122983	−	0.992409i	$-0.460754\pi$
$797$	196.035			0.245967			0.122983	+	0.992409i	$0.460754\pi$
$798$		0			0
$799$		−	364.110i		−	0.455707i
$800$	−1073.46	−	435.341i	−1.34183	−	0.544176i
$801$		0			0
$802$	−239.387	−	203.842i	−0.298487	−	0.254167i
$803$		−	688.440i		−	0.857334i
$804$		0			0
$805$	69.0997			0.0858381
$806$	−51.3430	+	60.2958i	−0.0637010	+	0.0748087i
$807$		0			0
$808$	190.213	−	313.523i	0.235412	−	0.388023i
$809$	579.944			0.716865			0.358432	−	0.933556i	$-0.383311\pi$
$809$	579.944			0.716865			0.358432	+	0.933556i	$0.383311\pi$
$810$		0			0
$811$		−	527.766i		−	0.650759i	−0.945583	−	0.325380i	$-0.894508\pi$
$811$		−	527.766i		−	0.650759i	0.945583	−	0.325380i	$-0.105492\pi$
$812$	−891.173	+	143.860i	−1.09750	+	0.177168i
$813$		0			0
$814$	−511.014	+	600.121i	−0.627782	+	0.737250i
$815$		−	2083.68i		−	2.55666i
$816$		0			0
$817$	−1272.87			−1.55798
$818$	458.804	+	390.680i	0.560885	+	0.477604i
$819$		0			0
$820$	−60.7492	−	376.324i	−0.0740844	−	0.458932i
$821$	649.499			0.791107			0.395554	−	0.918443i	$-0.370553\pi$
$821$	649.499			0.791107			0.395554	+	0.918443i	$0.370553\pi$
$822$		0			0
$823$			268.740i			0.326537i	0.986582	+	0.163269i	$0.0522037\pi$
$823$			268.740i			0.326537i	−0.986582	+	0.163269i	$0.947796\pi$
$824$	−1372.73	−	832.825i	−1.66593	−	1.01071i
$825$		0			0
$826$	391.395	+	333.280i	0.473844	+	0.403487i
$827$		−	799.300i		−	0.966505i	−0.875481	−	0.483253i	$-0.839455\pi$
$827$		−	799.300i		−	0.966505i	0.875481	−	0.483253i	$-0.160545\pi$
$828$		0			0
$829$	−1149.38			−1.38647			−0.693234	−	0.720712i	$-0.743815\pi$
$829$	−1149.38			−1.38647			−0.693234	+	0.720712i	$0.743815\pi$
$830$	224.905	−	264.122i	0.270970	−	0.318220i
$831$		0			0
$832$	−104.940	−	201.501i	−0.126130	−	0.242189i
$833$	917.009			1.10085
$834$		0			0
$835$			2322.36i			2.78127i
$836$	−135.696	−	840.596i	−0.162315	−	1.00550i
$837$		0			0
$838$	−627.952	+	737.450i	−0.749346	+	0.880012i
$839$		−	177.448i		−	0.211499i	−0.994393	−	0.105750i	$-0.966276\pi$
$839$		−	177.448i		−	0.211499i	0.994393	−	0.105750i	$-0.0337242\pi$
$840$		0			0
$841$	−509.203			−0.605473
$842$	−7.84386	−	6.67919i	−0.00931575	−	0.00793253i
$843$		0			0
$844$	467.220	−	75.4223i	0.553578	−	0.0893629i
$845$	1223.51			1.44794
$846$		0			0
$847$			23.5440i			0.0277970i
$848$	1135.49	−	376.408i	1.33902	−	0.443878i
$849$		0			0
$850$	−483.715	−	411.892i	−0.569077	−	0.484579i
$851$			25.3448i			0.0297823i
$852$		0			0
$853$	1101.00			1.29073			0.645367	−	0.763872i	$-0.276704\pi$
$853$	1101.00			1.29073			0.645367	+	0.763872i	$0.276704\pi$
$854$	784.738	−	921.576i	0.918897	−	1.07913i
$855$		0			0
$856$	616.350	+	373.937i	0.720036	+	0.436842i
$857$	−826.459			−0.964363			−0.482181	−	0.876071i	$-0.660155\pi$
$857$	−826.459			−0.964363			−0.482181	+	0.876071i	$0.660155\pi$
$858$		0			0
$859$			1191.77i			1.38740i	0.720265	+	0.693699i	$0.244020\pi$
$859$			1191.77i			1.38740i	−0.720265	+	0.693699i	$0.755980\pi$
$860$	−2047.83	+	330.576i	−2.38119	+	0.384391i
$861$		0			0
$862$	411.733	−	483.528i	0.477648	−	0.560937i
$863$			1491.45i			1.72821i	0.503311	+	0.864106i	$0.332115\pi$
$863$			1491.45i			1.72821i	−0.503311	+	0.864106i	$0.667885\pi$
$864$		0			0
$865$	−1326.29			−1.53328
$866$	289.629	+	246.624i	0.334444	+	0.284785i
$867$		0			0
$868$	88.0964	+	545.732i	0.101493	+	0.628724i
$869$	−109.971			−0.126549
$870$		0			0
$871$		−	28.5655i		−	0.0327962i
$872$	761.228	−	1254.71i	0.872968	−	1.43889i
$873$		0			0
$874$	−20.8455	−	17.7503i	−0.0238507	−	0.0203093i
$875$			1085.47i			1.24054i
$876$		0			0
$877$	810.540			0.924219			0.462109	−	0.886823i	$-0.347093\pi$
$877$	810.540			0.924219			0.462109	+	0.886823i	$0.347093\pi$
$878$	151.039	−	177.377i	0.172027	−	0.202024i
$879$		0			0
$880$	−436.622	−	1317.13i	−0.496161	−	1.49674i
$881$	251.884			0.285907			0.142953	−	0.989729i	$-0.454340\pi$
$881$	251.884			0.285907			0.142953	+	0.989729i	$0.454340\pi$
$882$		0			0
$883$		−	1150.98i		−	1.30349i	−0.758437	−	0.651746i	$-0.774037\pi$
$883$		−	1150.98i		−	1.30349i	0.758437	−	0.651746i	$-0.225963\pi$
$884$	−19.8575	−	123.012i	−0.0224632	−	0.139153i
$885$		0			0
$886$	636.179	−	747.112i	0.718036	−	0.843242i
$887$			168.892i			0.190409i	0.995458	+	0.0952043i	$0.0303504\pi$
$887$			168.892i			0.190409i	−0.995458	+	0.0952043i	$0.969650\pi$
$888$		0			0
$889$	−460.495			−0.517992
$890$	−1265.46	−	1077.56i	−1.42186	−	1.21074i
$891$		0			0
$892$	968.574	−	156.355i	1.08585	−	0.175286i
$893$	796.720			0.892184
$894$		0			0
$895$			117.679i			0.131485i
$896$	−1545.79	−	354.174i	−1.72522	−	0.395283i
$897$		0			0
$898$	237.450	+	202.193i	0.264421	+	0.225159i
$899$		−	203.184i		−	0.226012i
$900$		0			0
$901$	656.096			0.728187
$902$	175.110	−	205.644i	0.194135	−	0.227987i
$903$		0			0
$904$	−366.074	+	603.391i	−0.404950	+	0.667468i
$905$	−776.011			−0.857470
$906$		0			0
$907$		−	471.993i		−	0.520389i	−0.965556	−	0.260194i	$-0.916213\pi$
$907$		−	471.993i		−	0.520389i	0.965556	−	0.260194i	$-0.0837867\pi$
$908$	−125.702	+	20.2917i	−0.138438	+	0.0223477i
$909$		0			0
$910$	−446.120	+	523.912i	−0.490242	+	0.575727i
$911$		−	190.281i		−	0.208870i	−0.994532	−	0.104435i	$-0.966697\pi$
$911$		−	190.281i		−	0.208870i	0.994532	−	0.104435i	$-0.0333034\pi$
$912$		0			0
$913$	245.801			0.269223
$914$	186.533	+	158.836i	0.204084	+	0.173781i
$915$		0			0
$916$	91.3758	+	566.048i	0.0997552	+	0.617956i
$917$	−1457.85			−1.58981
$918$		0			0
$919$		−	1046.89i		−	1.13916i	−0.821936	−	0.569580i	$-0.807106\pi$
$919$		−	1046.89i		−	1.13916i	0.821936	−	0.569580i	$-0.192894\pi$
$920$	−38.1468	−	23.1435i	−0.0414640	−	0.0251560i
$921$		0			0
$922$	714.839	+	608.698i	0.775313	+	0.660193i
$923$		−	312.298i		−	0.338351i
$924$		0			0
$925$	−1286.88			−1.39122
$926$	−496.402	+	582.962i	−0.536072	+	0.629548i
$927$		0			0
$928$	540.160	+	219.061i	0.582069	+	0.236057i
$929$	691.664			0.744525			0.372262	−	0.928127i	$-0.378582\pi$
$929$	691.664			0.744525			0.372262	+	0.928127i	$0.378582\pi$
$930$		0			0
$931$			2006.53i			2.15525i
$932$	209.818	+	1299.76i	0.225126	+	1.39459i
$933$		0			0
$934$	−328.350	+	385.606i	−0.351553	+	0.412854i
$935$		−	761.051i		−	0.813959i
$936$		0			0
$937$	−1413.88			−1.50894			−0.754472	−	0.656332i	$-0.772107\pi$
$937$	−1413.88			−1.50894			−0.754472	+	0.656332i	$0.772107\pi$
$938$	−151.813	−	129.272i	−0.161848	−	0.137816i
$939$		0			0
$940$	1281.79	−	206.916i	1.36360	−	0.220123i
$941$	1122.49			1.19287			0.596433	−	0.802663i	$-0.296584\pi$
$941$	1122.49			1.19287			0.596433	+	0.802663i	$0.296584\pi$
$942$		0			0
$943$		−	8.68492i		−	0.00920988i
$944$	−104.447	−	315.079i	−0.110643	−	0.333770i
$945$		0			0
$946$	−1119.04	−	952.887i	−1.18292	−	1.00728i
$947$			1649.89i			1.74223i	0.491076	+	0.871116i	$0.336604\pi$
$947$			1649.89i			1.74223i	−0.491076	+	0.871116i	$0.663396\pi$
$948$		0			0
$949$	220.444			0.232290
$950$	901.273	−	1058.43i	0.948709	−	1.11414i
$951$		0			0
$952$	−743.619	−	451.150i	−0.781112	−	0.473897i
$953$	−828.887			−0.869766			−0.434883	−	0.900487i	$-0.643210\pi$
$953$	−828.887			−0.869766			−0.434883	+	0.900487i	$0.643210\pi$
$954$		0			0
$955$			2126.60i			2.22681i
$956$	−344.589	+	55.6262i	−0.360449	+	0.0581864i
$957$		0			0
$958$	−1072.22	+	1259.19i	−1.11923	+	1.31440i
$959$		−	457.771i		−	0.477343i
$960$		0			0
$961$	836.575			0.870525
$962$	−192.163	−	163.631i	−0.199754	−	0.170094i
$963$		0			0
$964$	114.232	+	707.637i	0.118498	+	0.734063i
$965$	−1141.38			−1.18278
$966$		0			0
$967$		−	1404.95i		−	1.45289i	−0.687224	−	0.726446i	$-0.741171\pi$
$967$		−	1404.95i		−	1.45289i	0.687224	−	0.726446i	$-0.258829\pi$
$968$	7.88559	−	12.9976i	0.00814627	−	0.0134273i
$969$		0			0
$970$	−1561.71	−	1329.82i	−1.61001	−	1.37095i
$971$			331.476i			0.341376i	0.985325	+	0.170688i	$0.0545991\pi$
$971$			331.476i			0.341376i	−0.985325	+	0.170688i	$0.945401\pi$
$972$		0			0
$973$	199.395			0.204928
$974$	−416.132	+	488.695i	−0.427241	+	0.501740i
$975$		0			0
$976$	−741.882	+	245.929i	−0.760125	+	0.251977i
$977$	−1117.09			−1.14339			−0.571695	−	0.820466i	$-0.693714\pi$
$977$	−1117.09			−1.14339			−0.571695	+	0.820466i	$0.693714\pi$
$978$		0			0
$979$		−	1177.68i		−	1.20294i
$980$	521.116	+	3228.17i	0.531751	+	3.29405i
$981$		0			0
$982$	728.574	−	855.618i	0.741929	−	0.871301i
$983$		−	1391.92i		−	1.41599i	−0.706216	−	0.707997i	$-0.749599\pi$
$983$		−	1391.92i		−	1.41599i	0.706216	−	0.707997i	$-0.250401\pi$
$984$		0			0
$985$	−1464.49			−1.48679
$986$	243.403	+	207.262i	0.246859	+	0.210205i
$987$		0			0
$988$	269.165	−	43.4507i	0.272435	−	0.0439785i
$989$	−47.2603			−0.0477860
$990$		0			0
$991$		−	226.715i		−	0.228773i	−0.993436	−	0.114387i	$-0.963510\pi$
$991$		−	226.715i		−	0.228773i	0.993436	−	0.114387i	$-0.0364903\pi$
$992$	134.148	−	330.781i	0.135229	−	0.333448i
$993$		0			0
$994$	−1659.73	−	1413.29i	−1.66975	−	1.42182i
$995$			2645.89i			2.65919i
$996$		0			0
$997$	1279.74			1.28359			0.641793	−	0.766878i	$-0.278191\pi$
$997$	1279.74			1.28359			0.641793	+	0.766878i	$0.278191\pi$
$998$	−39.3610	+	46.2245i	−0.0394399	+	0.0463171i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.d.h.163.8	yes	8
3.2	odd	2	inner	324.3.d.h.163.1	✓	8
4.3	odd	2	inner	324.3.d.h.163.7	yes	8
9.2	odd	6		324.3.f.s.271.4		16
9.4	even	3		324.3.f.s.55.2		16
9.5	odd	6		324.3.f.s.55.7		16
9.7	even	3		324.3.f.s.271.5		16
12.11	even	2	inner	324.3.d.h.163.2	yes	8
36.7	odd	6		324.3.f.s.271.2		16
36.11	even	6		324.3.f.s.271.7		16
36.23	even	6		324.3.f.s.55.4		16
36.31	odd	6		324.3.f.s.55.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.h.163.1	✓	8	3.2	odd	2	inner
324.3.d.h.163.2	yes	8	12.11	even	2	inner
324.3.d.h.163.7	yes	8	4.3	odd	2	inner
324.3.d.h.163.8	yes	8	1.1	even	1	trivial
324.3.f.s.55.2		16	9.4	even	3
324.3.f.s.55.4		16	36.23	even	6
324.3.f.s.55.5		16	36.31	odd	6
324.3.f.s.55.7		16	9.5	odd	6
324.3.f.s.271.2		16	36.7	odd	6
324.3.f.s.271.4		16	9.2	odd	6
324.3.f.s.271.5		16	9.7	even	3
324.3.f.s.271.7		16	36.11	even	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52274 + 1.29664i) q^{2} +(0.637459 + 3.94888i) q^{4} -7.82300 q^{5} -12.3894i q^{7} +(-4.14959 + 6.83966i) q^{8} +O(q^{10})\)	\(q+(1.52274 + 1.29664i) q^{2} +(0.637459 + 3.94888i) q^{4} -7.82300 q^{5} -12.3894i q^{7} +(-4.14959 + 6.83966i) q^{8} +(-11.9124 - 10.1436i) q^{10} -11.0860i q^{11} +3.54983 q^{13} +(16.0646 - 18.8659i) q^{14} +(-15.1873 + 5.03449i) q^{16} -8.77534 q^{17} -19.2016i q^{19} +(-4.98684 - 30.8921i) q^{20} +(14.3746 - 16.8811i) q^{22} -0.712936i q^{23} +36.1993 q^{25} +(5.40547 + 4.60285i) q^{26} +(48.9244 - 7.89776i) q^{28} -18.2153 q^{29} +11.1546i q^{31} +(-29.6542 - 12.0262i) q^{32} +(-13.3625 - 11.3784i) q^{34} +96.9226i q^{35} -35.5498 q^{37} +(24.8975 - 29.2390i) q^{38} +(32.4622 - 53.5067i) q^{40} +12.1819 q^{41} -66.2897i q^{43} +(43.7774 - 7.06689i) q^{44} +(0.924421 - 1.08561i) q^{46} +41.4924i q^{47} -104.498 q^{49} +(55.1221 + 46.9374i) q^{50} +(2.26287 + 14.0179i) q^{52} -74.7659 q^{53} +86.7261i q^{55} +(84.7396 + 51.4111i) q^{56} +(-27.7371 - 23.6187i) q^{58} +20.7462i q^{59} +48.8488 q^{61} +(-14.4635 + 16.9855i) q^{62} +(-29.5619 - 56.7635i) q^{64} -27.7704 q^{65} -8.04699i q^{67} +(-5.59392 - 34.6528i) q^{68} +(-125.674 + 147.588i) q^{70} -87.9754i q^{71} +62.0997 q^{73} +(-54.1331 - 46.0953i) q^{74} +(75.8248 - 12.2402i) q^{76} -137.350 q^{77} -9.91976i q^{79} +(118.810 - 39.3848i) q^{80} +(18.5498 + 15.7955i) q^{82} +22.1721i q^{83} +68.6495 q^{85} +(85.9537 - 100.942i) q^{86} +(75.8248 + 46.0025i) q^{88} +106.231 q^{89} -43.9805i q^{91} +(2.81530 - 0.454467i) q^{92} +(-53.8007 + 63.1821i) q^{94} +150.214i q^{95} +131.100 q^{97} +(-159.124 - 135.497i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{4}+O(q^{10}) \) 8 * q - 10 * q^4	\( 8 q - 10 q^{4} - 50 q^{10} - 32 q^{13} - 46 q^{16} - 36 q^{22} + 48 q^{25} + 180 q^{28} - 122 q^{34} - 224 q^{37} + 154 q^{40} - 204 q^{46} - 232 q^{49} + 154 q^{52} - 86 q^{58} - 32 q^{61} - 10 q^{64} - 492 q^{70} + 376 q^{73} + 516 q^{76} + 88 q^{82} + 368 q^{85} + 516 q^{88} - 672 q^{94} + 928 q^{97}+O(q^{100}) \) 8 * q - 10 * q^4 - 50 * q^10 - 32 * q^13 - 46 * q^16 - 36 * q^22 + 48 * q^25 + 180 * q^28 - 122 * q^34 - 224 * q^37 + 154 * q^40 - 204 * q^46 - 232 * q^49 + 154 * q^52 - 86 * q^58 - 32 * q^61 - 10 * q^64 - 492 * q^70 + 376 * q^73 + 516 * q^76 + 88 * q^82 + 368 * q^85 + 516 * q^88 - 672 * q^94 + 928 * q^97

Introduction

L-functions

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