LMFDB - Embedded newform 108.3.k.a.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	108.41
Dual form			108.3.k.a.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59609 + 1.50344i) q^{3} +(-0.298552 + 0.355800i) q^{5} +(-10.1488 - 3.69384i) q^{7} +(4.47934 - 7.80612i) q^{9} +O(q^{10})$	\(q+(-2.59609 + 1.50344i) q^{3} +(-0.298552 + 0.355800i) q^{5} +(-10.1488 - 3.69384i) q^{7} +(4.47934 - 7.80612i) q^{9} +(-10.2314 - 12.1933i) q^{11} +(-3.11819 + 17.6841i) q^{13} +(0.240142 - 1.37254i) q^{15} +(-22.6442 - 13.0736i) q^{17} +(1.77864 + 3.08069i) q^{19} +(31.9005 - 5.66850i) q^{21} +(1.41115 + 3.87710i) q^{23} +(4.30374 + 24.4077i) q^{25} +(0.107276 + 26.9998i) q^{27} +(41.0456 - 7.23745i) q^{29} +(-6.62361 + 2.41080i) q^{31} +(44.8934 + 16.2726i) q^{33} +(4.34420 - 2.50812i) q^{35} +(4.92909 - 8.53743i) q^{37} +(-18.4919 - 50.5976i) q^{39} +(-42.8820 - 7.56125i) q^{41} +(-27.2523 + 22.8674i) q^{43} +(1.44010 + 3.92428i) q^{45} +(-5.51742 + 15.1590i) q^{47} +(51.8166 + 43.4793i) q^{49} +(78.4418 - 0.103888i) q^{51} -75.6950i q^{53} +7.39296 q^{55} +(-9.24914 - 5.32367i) q^{57} +(-18.4421 + 21.9784i) q^{59} +(-55.9422 - 20.3613i) q^{61} +(-74.2943 + 62.6764i) q^{63} +(-5.36107 - 6.38908i) q^{65} +(-4.03483 + 22.8827i) q^{67} +(-9.49246 - 7.94372i) q^{69} +(-32.2368 - 18.6119i) q^{71} +(-26.0280 - 45.0817i) q^{73} +(-47.8685 - 56.8942i) q^{75} +(58.7957 + 161.540i) q^{77} +(-20.9619 - 118.881i) q^{79} +(-40.8710 - 69.9325i) q^{81} +(115.091 - 20.2937i) q^{83} +(11.4121 - 4.15365i) q^{85} +(-95.6769 + 80.4987i) q^{87} +(-117.767 + 67.9930i) q^{89} +(96.9682 - 167.954i) q^{91} +(13.5710 - 16.2168i) q^{93} +(-1.62713 - 0.286906i) q^{95} +(-72.3238 + 60.6869i) q^{97} +(-141.012 + 25.2495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.59609	+	1.50344i	−0.865362	+	0.501147i
$3$	−2.59609	+	1.50344i	−0.865362	+	0.501147i
$4$		0			0
$5$	−0.298552	+	0.355800i	−0.0597103	+	0.0711600i	−0.795073	−	0.606514i	$-0.792567\pi$
$5$	−0.298552	+	0.355800i	−0.0597103	+	0.0711600i	0.735363	+	0.677674i	$0.237012\pi$
$6$		0			0
$7$	−10.1488	−	3.69384i	−1.44982	−	0.527692i	−0.507281	−	0.861781i	$-0.669349\pi$
$7$	−10.1488	−	3.69384i	−1.44982	−	0.527692i	−0.942542	+	0.334089i	$0.891571\pi$
$8$		0			0
$9$	4.47934	−	7.80612i	0.497704	−	0.867347i
$10$		0			0
$11$	−10.2314	−	12.1933i	−0.930125	−	1.10848i	−0.993875	−	0.110514i	$-0.964750\pi$
$11$	−10.2314	−	12.1933i	−0.930125	−	1.10848i	0.0637495	−	0.997966i	$-0.479694\pi$
$12$		0			0
$13$	−3.11819	+	17.6841i	−0.239861	+	1.36032i	0.592271	+	0.805739i	$0.298232\pi$
$13$	−3.11819	+	17.6841i	−0.239861	+	1.36032i	−0.832131	+	0.554579i	$0.812879\pi$
$14$		0			0
$15$	0.240142	−	1.37254i	0.0160095	−	0.0915028i
$16$		0			0
$17$	−22.6442	−	13.0736i	−1.33201	−	0.769038i	−0.346405	−	0.938085i	$-0.612598\pi$
$17$	−22.6442	−	13.0736i	−1.33201	−	0.769038i	−0.985608	+	0.169047i	$0.945931\pi$
$18$		0			0
$19$	1.77864	+	3.08069i	0.0936126	+	0.162142i	0.909029	−	0.416733i	$-0.136825\pi$
$19$	1.77864	+	3.08069i	0.0936126	+	0.162142i	−0.815416	+	0.578875i	$0.803492\pi$
$20$		0			0
$21$	31.9005	−	5.66850i	1.51907	−	0.269928i
$22$		0			0
$23$	1.41115	+	3.87710i	0.0613543	+	0.168570i	0.966582	−	0.256357i	$-0.0825222\pi$
$23$	1.41115	+	3.87710i	0.0613543	+	0.168570i	−0.905228	+	0.424926i	$0.860300\pi$
$24$		0			0
$25$	4.30374	+	24.4077i	0.172150	+	0.976310i
$26$		0			0
$27$	0.107276	+	26.9998i	0.00397319	+	0.999992i
$28$		0			0
$29$	41.0456	−	7.23745i	1.41537	−	0.249567i	0.586924	−	0.809642i	$-0.300339\pi$
$29$	41.0456	−	7.23745i	1.41537	−	0.249567i	0.828442	+	0.560075i	$0.189228\pi$
$30$		0			0
$31$	−6.62361	+	2.41080i	−0.213665	+	0.0777677i	−0.446635	−	0.894716i	$-0.647378\pi$
$31$	−6.62361	+	2.41080i	−0.213665	+	0.0777677i	0.232970	+	0.972484i	$0.425156\pi$
$32$		0			0
$33$	44.8934	+	16.2726i	1.36041	+	0.493108i
$34$		0			0
$35$	4.34420	−	2.50812i	0.124120	−	0.0716606i
$36$		0			0
$37$	4.92909	−	8.53743i	0.133219	−	0.230741i	−0.791697	−	0.610914i	$-0.790802\pi$
$37$	4.92909	−	8.53743i	0.133219	−	0.230741i	0.924916	+	0.380173i	$0.124135\pi$
$38$		0			0
$39$	−18.4919	−	50.5976i	−0.474152	−	1.29737i
$40$		0			0
$41$	−42.8820	−	7.56125i	−1.04590	−	0.184421i	−0.375808	−	0.926697i	$-0.622635\pi$
$41$	−42.8820	−	7.56125i	−1.04590	−	0.184421i	−0.670094	+	0.742277i	$0.733746\pi$
$42$		0			0
$43$	−27.2523	+	22.8674i	−0.633773	+	0.531799i	−0.902099	−	0.431529i	$-0.857974\pi$
$43$	−27.2523	+	22.8674i	−0.633773	+	0.531799i	0.268326	+	0.963328i	$0.413530\pi$
$44$		0			0
$45$	1.44010	+	3.92428i	0.0320023	+	0.0872062i
$46$		0			0
$47$	−5.51742	+	15.1590i	−0.117392	+	0.322531i	−0.984447	−	0.175680i	$-0.943788\pi$
$47$	−5.51742	+	15.1590i	−0.117392	+	0.322531i	0.867055	+	0.498212i	$0.166010\pi$
$48$		0			0
$49$	51.8166	+	43.4793i	1.05748	+	0.887332i
$50$		0			0
$51$	78.4418	−	0.103888i	1.53807	−	0.00203703i
$52$		0			0
$53$		−	75.6950i		−	1.42821i	−0.700040	−	0.714104i	$-0.746834\pi$
$53$		−	75.6950i		−	1.42821i	0.700040	−	0.714104i	$-0.253166\pi$
$54$		0			0
$55$	7.39296			0.134417
$56$		0			0
$57$	−9.24914	−	5.32367i	−0.162266	−	0.0933977i
$58$		0			0
$59$	−18.4421	+	21.9784i	−0.312578	+	0.372516i	−0.899345	−	0.437240i	$-0.855956\pi$
$59$	−18.4421	+	21.9784i	−0.312578	+	0.372516i	0.586767	+	0.809756i	$0.300400\pi$
$60$		0			0
$61$	−55.9422	−	20.3613i	−0.917085	−	0.333792i	−0.160007	−	0.987116i	$-0.551152\pi$
$61$	−55.9422	−	20.3613i	−0.917085	−	0.333792i	−0.757078	+	0.653324i	$0.773374\pi$
$62$		0			0
$63$	−74.2943	+	62.6764i	−1.17927	+	0.994864i
$64$		0			0
$65$	−5.36107	−	6.38908i	−0.0824780	−	0.0982935i
$66$		0			0
$67$	−4.03483	+	22.8827i	−0.0602214	+	0.341532i	−1.00000		0.000251397i	$-0.999920\pi$
$67$	−4.03483	+	22.8827i	−0.0602214	+	0.341532i	0.939779	+	0.341784i	$0.111031\pi$
$68$		0			0
$69$	−9.49246	−	7.94372i	−0.137572	−	0.115126i
$70$		0			0
$71$	−32.2368	−	18.6119i	−0.454039	−	0.262139i	0.255496	−	0.966810i	$-0.417761\pi$
$71$	−32.2368	−	18.6119i	−0.454039	−	0.262139i	−0.709534	+	0.704671i	$0.751095\pi$
$72$		0			0
$73$	−26.0280	−	45.0817i	−0.356547	−	0.617558i	0.630834	−	0.775918i	$-0.282713\pi$
$73$	−26.0280	−	45.0817i	−0.356547	−	0.617558i	−0.987382	+	0.158360i	$0.949380\pi$
$74$		0			0
$75$	−47.8685	−	56.8942i	−0.638246	−	0.758590i
$76$		0			0
$77$	58.7957	+	161.540i	0.763580	+	2.09792i
$78$		0			0
$79$	−20.9619	−	118.881i	−0.265341	−	1.50482i	−0.768063	−	0.640374i	$-0.778779\pi$
$79$	−20.9619	−	118.881i	−0.265341	−	1.50482i	0.502722	−	0.864448i	$-0.332332\pi$
$80$		0			0
$81$	−40.8710	−	69.9325i	−0.504581	−	0.863364i
$82$		0			0
$83$	115.091	−	20.2937i	1.38664	−	0.244502i	0.569997	−	0.821647i	$-0.306944\pi$
$83$	115.091	−	20.2937i	1.38664	−	0.244502i	0.816642	+	0.577145i	$0.195833\pi$
$84$		0			0
$85$	11.4121	−	4.15365i	0.134260	−	0.0488665i
$86$		0			0
$87$	−95.6769	+	80.4987i	−1.09974	+	0.925272i
$88$		0			0
$89$	−117.767	+	67.9930i	−1.32323	+	0.763966i	−0.984242	−	0.176826i	$-0.943417\pi$
$89$	−117.767	+	67.9930i	−1.32323	+	0.763966i	−0.338985	+	0.940792i	$0.610084\pi$
$90$		0			0
$91$	96.9682	−	167.954i	1.06558	−	1.84565i
$92$		0			0
$93$	13.5710	−	16.2168i	0.145925	−	0.174375i
$94$		0			0
$95$	−1.62713	−	0.286906i	−0.0171276	−	0.00302006i
$96$		0			0
$97$	−72.3238	+	60.6869i	−0.745606	+	0.625638i	−0.934337	−	0.356391i	$-0.884007\pi$
$97$	−72.3238	+	60.6869i	−0.745606	+	0.625638i	0.188731	+	0.982029i	$0.439563\pi$
$98$		0			0
$99$	−141.012	+	25.2495i	−1.42436	+	0.255046i
$100$		0			0
$101$	52.1346	−	143.239i	0.516184	−	1.41820i	−0.358509	−	0.933526i	$-0.616715\pi$
$101$	52.1346	−	143.239i	0.516184	−	1.41820i	0.874693	−	0.484678i	$-0.161063\pi$
$102$		0			0
$103$	16.6643	+	13.9830i	0.161790	+	0.135758i	0.720088	−	0.693882i	$-0.244101\pi$
$103$	16.6643	+	13.9830i	0.161790	+	0.135758i	−0.558299	+	0.829640i	$0.688546\pi$
$104$		0			0
$105$	−7.50710	+	13.0425i	−0.0714962	+	0.124215i
$106$		0			0
$107$			49.8431i			0.465823i	0.972498	+	0.232912i	$0.0748253\pi$
$107$			49.8431i			0.465823i	−0.972498	+	0.232912i	$0.925175\pi$
$108$		0			0
$109$	171.063			1.56939			0.784695	−	0.619882i	$-0.212820\pi$
$109$	171.063			1.56939			0.784695	+	0.619882i	$0.212820\pi$
$110$		0			0
$111$	0.0391685	+	29.5745i	0.000352869	+	0.266437i
$112$		0			0
$113$	26.1647	−	31.1819i	0.231546	−	0.275946i	−0.637744	−	0.770249i	$-0.720132\pi$
$113$	26.1647	−	31.1819i	0.231546	−	0.275946i	0.869290	+	0.494303i	$0.164577\pi$
$114$		0			0
$115$	−1.80077	−	0.655428i	−0.0156589	−	0.00569937i
$116$		0			0
$117$	124.077	+	103.554i	1.06049	+	0.885078i
$118$		0			0
$119$	181.519	+	216.325i	1.52537	+	1.81786i
$120$		0			0
$121$	−22.9836	+	130.346i	−0.189947	+	1.07724i
$122$		0			0
$123$	122.693	−	44.8408i	0.997506	−	0.364559i
$124$		0			0
$125$	−20.0251	−	11.5615i	−0.160201	−	0.0924920i
$126$		0			0
$127$	−30.8908	−	53.5044i	−0.243235	−	0.421295i	0.718399	−	0.695631i	$-0.244875\pi$
$127$	−30.8908	−	53.5044i	−0.243235	−	0.421295i	−0.961634	+	0.274336i	$0.911542\pi$
$128$		0			0
$129$	36.3695	−	100.338i	0.281934	−	0.777812i
$130$		0			0
$131$	77.3505	+	212.519i	0.590462	+	1.62228i	0.769651	+	0.638465i	$0.220430\pi$
$131$	77.3505	+	212.519i	0.590462	+	1.62228i	−0.179189	+	0.983815i	$0.557347\pi$
$132$		0			0
$133$	−6.67137	−	37.8352i	−0.0501607	−	0.284475i
$134$		0			0
$135$	−9.63855	−	8.02266i	−0.0713967	−	0.0594271i
$136$		0			0
$137$	−149.613	+	26.3808i	−1.09206	+	0.192560i	−0.690544	−	0.723290i	$-0.742629\pi$
$137$	−149.613	+	26.3808i	−1.09206	+	0.192560i	−0.401519	+	0.915851i	$0.631518\pi$
$138$		0			0
$139$	159.710	−	58.1298i	1.14899	−	0.418200i	0.303841	−	0.952723i	$-0.401731\pi$
$139$	159.710	−	58.1298i	1.14899	−	0.418200i	0.845154	+	0.534523i	$0.179509\pi$
$140$		0			0
$141$	−8.46691	−	47.6491i	−0.0600490	−	0.337937i
$142$		0			0
$143$	247.531	−	142.912i	1.73099	−	0.999385i
$144$		0			0
$145$	−9.67915	+	16.7648i	−0.0667528	+	0.115619i
$146$		0			0
$147$	−199.889	−	34.9729i	−1.35979	−	0.237911i
$148$		0			0
$149$	−176.331	−	31.0919i	−1.18343	−	0.208671i	−0.452907	−	0.891558i	$-0.649613\pi$
$149$	−176.331	−	31.0919i	−1.18343	−	0.208671i	−0.730524	+	0.682887i	$0.760724\pi$
$150$		0			0
$151$	92.0549	−	77.2432i	0.609635	−	0.511544i	−0.284891	−	0.958560i	$-0.591958\pi$
$151$	92.0549	−	77.2432i	0.609635	−	0.511544i	0.894526	+	0.447015i	$0.147513\pi$
$152$		0			0
$153$	−203.486	+	118.202i	−1.32997	+	0.772563i
$154$		0			0
$155$	1.11973	−	3.07643i	0.00722405	−	0.0198479i
$156$		0			0
$157$	24.9795	+	20.9603i	0.159105	+	0.133505i	0.718865	−	0.695150i	$-0.244662\pi$
$157$	24.9795	+	20.9603i	0.159105	+	0.133505i	−0.559760	+	0.828655i	$0.689107\pi$
$158$		0			0
$159$	113.803	+	196.511i	0.715741	+	1.23592i
$160$		0			0
$161$		−	44.5603i		−	0.276772i
$162$		0			0
$163$	−219.827			−1.34863			−0.674316	−	0.738443i	$-0.735561\pi$
$163$	−219.827			−1.34863			−0.674316	+	0.738443i	$0.735561\pi$
$164$		0			0
$165$	−19.1928	+	11.1149i	−0.116320	+	0.0673628i
$166$		0			0
$167$	78.0508	−	93.0173i	0.467370	−	0.556990i	−0.479943	−	0.877300i	$-0.659343\pi$
$167$	78.0508	−	93.0173i	0.467370	−	0.556990i	0.947313	+	0.320310i	$0.103787\pi$
$168$		0			0
$169$	−144.197	−	52.4835i	−0.853239	−	0.310553i
$170$		0			0
$171$	32.0154	−	0.0848025i	0.187224	−	0.000495921i
$172$		0			0
$173$	−49.6240	−	59.1396i	−0.286844	−	0.341847i	0.603310	−	0.797506i	$-0.293848\pi$
$173$	−49.6240	−	59.1396i	−0.286844	−	0.341847i	−0.890154	+	0.455659i	$0.849404\pi$
$174$		0			0
$175$	46.4808	−	263.606i	0.265604	−	1.50632i
$176$		0			0
$177$	14.8340	−	84.7845i	0.0838082	−	0.479009i
$178$		0			0
$179$	−128.588	−	74.2402i	−0.718367	−	0.414750i	0.0957841	−	0.995402i	$-0.469464\pi$
$179$	−128.588	−	74.2402i	−0.718367	−	0.414750i	−0.814151	+	0.580653i	$0.802797\pi$
$180$		0			0
$181$	42.2135	+	73.1159i	0.233224	+	0.403955i	0.958755	−	0.284234i	$-0.0917393\pi$
$181$	42.2135	+	73.1159i	0.233224	+	0.403955i	−0.725531	+	0.688189i	$0.758406\pi$
$182$		0			0
$183$	175.843	−	31.2460i	0.960890	−	0.170743i
$184$		0			0
$185$	1.56603	+	4.30263i	0.00846503	+	0.0232575i
$186$		0			0
$187$	72.2709	+	409.869i	0.386475	+	2.19181i
$188$		0			0
$189$	98.6443	−	274.410i	0.521928	−	1.45191i
$190$		0			0
$191$	−1.92568	+	0.339550i	−0.0100821	+	0.00177775i	−0.178687	−	0.983906i	$-0.557185\pi$
$191$	−1.92568	+	0.339550i	−0.0100821	+	0.00177775i	0.168605	+	0.985684i	$0.446074\pi$
$192$		0			0
$193$	−311.970	+	113.548i	−1.61643	+	0.588331i	−0.982697	−	0.185223i	$-0.940699\pi$
$193$	−311.970	+	113.548i	−1.61643	+	0.588331i	−0.633731	+	0.773554i	$0.718477\pi$
$194$		0			0
$195$	23.5234	+	8.52655i	0.120633	+	0.0437259i
$196$		0			0
$197$	−213.145	+	123.059i	−1.08195	+	0.624666i	−0.931423	−	0.363939i	$-0.881432\pi$
$197$	−213.145	+	123.059i	−1.08195	+	0.624666i	−0.150531	+	0.988605i	$0.548098\pi$
$198$		0			0
$199$	−138.226	+	239.415i	−0.694604	+	1.20309i	0.275710	+	0.961241i	$0.411087\pi$
$199$	−138.226	+	239.415i	−0.694604	+	1.20309i	−0.970314	+	0.241849i	$0.922246\pi$
$200$		0			0
$201$	−23.9279	−	65.4716i	−0.119044	−	0.325729i
$202$		0			0
$203$	−443.296	−	78.1650i	−2.18372	−	0.385049i
$204$		0			0
$205$	15.4928	−	13.0000i	0.0755745	−	0.0634145i
$206$		0			0
$207$	36.5861	+	6.35125i	0.176745	+	0.0306824i
$208$		0			0
$209$	19.3658	−	53.2072i	0.0926594	−	0.254580i
$210$		0			0
$211$	−40.7896	−	34.2265i	−0.193316	−	0.162211i	0.540992	−	0.841027i	$-0.318049\pi$
$211$	−40.7896	−	34.2265i	−0.193316	−	0.162211i	−0.734308	+	0.678816i	$0.762493\pi$
$212$		0			0
$213$	111.671	−	0.147898i	0.524279	−	0.000694355i
$214$		0			0
$215$		−	16.5234i		−	0.0768532i
$216$		0			0
$217$	76.1265			0.350813
$218$		0			0
$219$	135.349	+	77.9047i	0.618030	+	0.355729i
$220$		0			0
$221$	301.805	−	359.677i	1.36563	−	1.62750i
$222$		0			0
$223$	101.950	+	37.1068i	0.457175	+	0.166398i	0.560334	−	0.828267i	$-0.310673\pi$
$223$	101.950	+	37.1068i	0.457175	+	0.166398i	−0.103159	+	0.994665i	$0.532895\pi$
$224$		0			0
$225$	209.808	+	75.7350i	0.932479	+	0.336600i
$226$		0			0
$227$	−232.991	−	277.668i	−1.02639	−	1.22321i	−0.974462	−	0.224554i	$-0.927907\pi$
$227$	−232.991	−	277.668i	−1.02639	−	1.22321i	−0.0519295	−	0.998651i	$-0.516537\pi$
$228$		0			0
$229$	−50.2795	+	285.149i	−0.219561	+	1.24519i	0.653252	+	0.757140i	$0.273404\pi$
$229$	−50.2795	+	285.149i	−0.219561	+	1.24519i	−0.872814	+	0.488054i	$0.837707\pi$
$230$		0			0
$231$	−395.504	−	330.976i	−1.71214	−	1.43279i
$232$		0			0
$233$	127.663	+	73.7062i	0.547910	+	0.316336i	0.748279	−	0.663385i	$-0.230881\pi$
$233$	127.663	+	73.7062i	0.547910	+	0.316336i	−0.200369	+	0.979721i	$0.564214\pi$
$234$		0			0
$235$	−3.74633	−	6.48883i	−0.0159418	−	0.0276120i
$236$		0			0
$237$	233.149	+	277.110i	0.983753	+	1.16924i
$238$		0			0
$239$	−4.66249	−	12.8101i	−0.0195083	−	0.0535987i	0.929556	−	0.368680i	$-0.120190\pi$
$239$	−4.66249	−	12.8101i	−0.0195083	−	0.0535987i	−0.949065	+	0.315082i	$0.897968\pi$
$240$		0			0
$241$	−51.5844	−	292.550i	−0.214043	−	1.21390i	−0.882559	−	0.470201i	$-0.844181\pi$
$241$	−51.5844	−	292.550i	−0.214043	−	1.21390i	0.668516	−	0.743698i	$-0.266930\pi$
$242$		0			0
$243$	211.244	+	120.104i	0.869317	+	0.494254i
$244$		0			0
$245$	−30.9398	+	5.45553i	−0.126285	+	0.0222675i
$246$		0			0
$247$	−60.0255	+	21.8475i	−0.243018	+	0.0884514i
$248$		0			0
$249$	−268.276	+	225.717i	−1.07741	+	0.906492i
$250$		0			0
$251$	−0.182848	+	0.105567i	−0.000728476	+	0.000420586i	−0.500364	−	0.865815i	$-0.666801\pi$
$251$	−0.182848	+	0.105567i	−0.000728476	+	0.000420586i	0.499636	+	0.866236i	$0.333467\pi$
$252$		0			0
$253$	32.8366	−	56.8746i	0.129789	−	0.224801i
$254$		0			0
$255$	−23.3820	+	27.9406i	−0.0916939	+	0.109571i
$256$		0			0
$257$	190.970	+	33.6731i	0.743073	+	0.131024i	0.532353	−	0.846523i	$-0.321308\pi$
$257$	190.970	+	33.6731i	0.743073	+	0.131024i	0.210720	+	0.977546i	$0.432419\pi$
$258$		0			0
$259$	−81.5601	+	68.4370i	−0.314904	+	0.264236i
$260$		0			0
$261$	127.361	−	352.826i	0.487973	−	1.35182i
$262$		0			0
$263$	−139.835	+	384.194i	−0.531692	+	1.46081i	0.325363	+	0.945589i	$0.394513\pi$
$263$	−139.835	+	384.194i	−0.531692	+	1.46081i	−0.857056	+	0.515224i	$0.827709\pi$
$264$		0			0
$265$	26.9323	+	22.5989i	0.101631	+	0.0852787i
$266$		0			0
$267$	203.511	−	353.572i	0.762213	−	1.32424i
$268$		0			0
$269$			120.090i			0.446433i	0.974769	+	0.223216i	$0.0716557\pi$
$269$			120.090i			0.446433i	−0.974769	+	0.223216i	$0.928344\pi$
$270$		0			0
$271$	19.0289			0.0702175			0.0351088	−	0.999383i	$-0.488822\pi$
$271$	19.0289			0.0702175			0.0351088	+	0.999383i	$0.488822\pi$
$272$		0			0
$273$	0.770547	+	581.809i	0.00282252	+	2.13117i
$274$		0			0
$275$	253.577	−	302.202i	0.922099	−	1.09891i
$276$		0			0
$277$	299.169	+	108.889i	1.08003	+	0.393099i	0.819919	−	0.572479i	$-0.194018\pi$
$277$	299.169	+	108.889i	1.08003	+	0.393099i	0.260112	+	0.965578i	$0.416240\pi$
$278$		0			0
$279$	−10.8504	+	62.5035i	−0.0388904	+	0.224027i
$280$		0			0
$281$	−154.692	−	184.354i	−0.550504	−	0.656065i	0.417004	−	0.908905i	$-0.363080\pi$
$281$	−154.692	−	184.354i	−0.550504	−	0.656065i	−0.967508	+	0.252839i	$0.918636\pi$
$282$		0			0
$283$	15.5135	−	87.9813i	0.0548179	−	0.310888i	−0.945054	−	0.326915i	$-0.893991\pi$
$283$	15.5135	−	87.9813i	0.0548179	−	0.310888i	0.999872	+	0.0160274i	$0.00510189\pi$
$284$		0			0
$285$	4.65551	−	1.70145i	0.0163351	−	0.00597000i
$286$		0			0
$287$	407.269	+	235.137i	1.41905	+	0.819292i
$288$		0			0
$289$	197.340	+	341.803i	0.682838	+	1.18271i
$290$		0			0
$291$	96.5199	−	266.283i	0.331683	−	0.915062i
$292$		0			0
$293$	106.539	+	292.713i	0.363614	+	0.999022i	0.977741	+	0.209814i	$0.0672860\pi$
$293$	106.539	+	292.713i	0.363614	+	0.999022i	−0.614127	+	0.789207i	$0.710492\pi$
$294$		0			0
$295$	−2.31401	−	13.1234i	−0.00784410	−	0.0444861i
$296$		0			0
$297$	328.118	−	277.553i	1.10478	−	0.934522i
$298$		0			0
$299$	−72.9634	+	12.8654i	−0.244025	+	0.0430282i
$300$		0			0
$301$	361.045	−	131.410i	1.19948	−	0.436577i
$302$		0			0
$303$	80.0047	+	450.241i	0.264042	+	1.48594i
$304$		0			0
$305$	23.9462	−	13.8253i	0.0785120	−	0.0453289i
$306$		0			0
$307$	−296.790	+	514.055i	−0.966743	+	1.67445i	−0.261885	+	0.965099i	$0.584344\pi$
$307$	−296.790	+	514.055i	−0.966743	+	1.67445i	−0.704858	+	0.709348i	$0.748989\pi$
$308$		0			0
$309$	−64.2847	−	11.2474i	−0.208041	−	0.0363992i
$310$		0			0
$311$	−538.372	−	94.9296i	−1.73110	−	0.305240i	−0.782720	−	0.622374i	$-0.786168\pi$
$311$	−538.372	−	94.9296i	−1.73110	−	0.305240i	−0.948381	+	0.317134i	$0.897280\pi$
$312$		0			0
$313$	119.991	−	100.684i	0.383357	−	0.321675i	−0.430662	−	0.902513i	$-0.641720\pi$
$313$	119.991	−	100.684i	0.383357	−	0.321675i	0.814019	+	0.580839i	$0.197275\pi$
$314$		0			0
$315$	−0.119583	−	45.1461i	−0.000379629	−	0.143321i
$316$		0			0
$317$	−14.4734	+	39.7653i	−0.0456574	+	0.125443i	−0.960426	−	0.278536i	$-0.910151\pi$
$317$	−14.4734	+	39.7653i	−0.0456574	+	0.125443i	0.914768	+	0.403979i	$0.132373\pi$
$318$		0			0
$319$	−508.201	−	426.432i	−1.59311	−	1.33678i
$320$		0			0
$321$	−74.9361	−	129.397i	−0.233446	−	0.403106i
$322$		0			0
$323$		−	93.0132i		−	0.287966i
$324$		0			0
$325$	−445.050			−1.36938
$326$		0			0
$327$	−444.096	+	257.184i	−1.35809	+	0.786494i
$328$		0			0
$329$	111.990	−	133.464i	0.340395	−	0.405666i
$330$		0			0
$331$	462.396	+	168.298i	1.39697	+	0.508455i	0.927277	−	0.374376i	$-0.122143\pi$
$331$	462.396	+	168.298i	1.39697	+	0.508455i	0.469691	+	0.882831i	$0.344365\pi$
$332$		0			0
$333$	−44.5652	−	76.7191i	−0.133829	−	0.230388i
$334$		0			0
$335$	−6.93705	−	8.26725i	−0.0207076	−	0.0246784i
$336$		0			0
$337$	113.729	−	644.988i	0.337474	−	1.91391i	−0.0638222	−	0.997961i	$-0.520329\pi$
$337$	113.729	−	644.988i	0.337474	−	1.91391i	0.401296	−	0.915948i	$-0.368560\pi$
$338$		0			0
$339$	−21.0458	+	120.288i	−0.0620820	+	0.354832i
$340$		0			0
$341$	97.1642	+	56.0978i	0.284939	+	0.164510i
$342$		0			0
$343$	−100.666	−	174.359i	−0.293487	−	0.508335i
$344$		0			0
$345$	5.66036	−	1.00581i	0.0164068	−	0.00291538i
$346$		0			0
$347$	−44.4825	−	122.215i	−0.128192	−	0.352204i	0.858948	−	0.512062i	$-0.171118\pi$
$347$	−44.4825	−	122.215i	−0.128192	−	0.352204i	−0.987140	+	0.159859i	$0.948896\pi$
$348$		0			0
$349$	14.3449	+	81.3537i	0.0411027	+	0.233105i	0.998438	−	0.0558751i	$-0.0177949\pi$
$349$	14.3449	+	81.3537i	0.0411027	+	0.233105i	−0.957335	+	0.288980i	$0.906684\pi$
$350$		0			0
$351$	−477.802	−	82.2934i	−1.36126	−	0.234454i
$352$		0			0
$353$	−65.5878	+	11.5649i	−0.185801	+	0.0327618i	−0.265774	−	0.964035i	$-0.585628\pi$
$353$	−65.5878	+	11.5649i	−0.185801	+	0.0327618i	0.0799732	+	0.996797i	$0.474517\pi$
$354$		0			0
$355$	16.2464	−	5.91322i	0.0457646	−	0.0166570i
$356$		0			0
$357$	−796.470	−	288.697i	−2.23101	−	0.808676i
$358$		0			0
$359$	289.619	−	167.211i	0.806737	−	0.465770i	−0.0390844	−	0.999236i	$-0.512444\pi$
$359$	289.619	−	167.211i	0.806737	−	0.465770i	0.845821	+	0.533466i	$0.179111\pi$
$360$		0			0
$361$	174.173	−	301.676i	0.482473	−	0.835668i
$362$		0			0
$363$	−136.300	−	372.945i	−0.375483	−	1.02740i
$364$		0			0
$365$	23.8108	+	4.19848i	0.0652350	+	0.0115027i
$366$		0			0
$367$	312.913	−	262.565i	0.852624	−	0.715437i	−0.107742	−	0.994179i	$-0.534362\pi$
$367$	312.913	−	262.565i	0.852624	−	0.715437i	0.960366	+	0.278742i	$0.0899175\pi$
$368$		0			0
$369$	−251.107	+	300.873i	−0.680507	+	0.815373i
$370$		0			0
$371$	−279.606	+	768.210i	−0.753654	+	2.07065i
$372$		0			0
$373$	−234.819	−	197.037i	−0.629543	−	0.528249i	0.271244	−	0.962511i	$-0.412565\pi$
$373$	−234.819	−	197.037i	−0.629543	−	0.528249i	−0.900787	+	0.434262i	$0.857009\pi$
$374$		0			0
$375$	69.3689	−	0.0918722i	0.184984	−	0.000244993i
$376$		0			0
$377$			748.424i			1.98521i
$378$		0			0
$379$	−98.9004			−0.260951			−0.130475	−	0.991452i	$-0.541650\pi$
$379$	−98.9004			−0.260951			−0.130475	+	0.991452i	$0.541650\pi$
$380$		0			0
$381$	160.636	+	92.4597i	0.421616	+	0.242676i
$382$		0			0
$383$	319.309	−	380.537i	0.833704	−	0.993570i	−0.166268	−	0.986081i	$-0.553172\pi$
$383$	319.309	−	380.537i	0.833704	−	0.993570i	0.999972	−	0.00748907i	$-0.00238387\pi$
$384$		0			0
$385$	−75.0293	−	27.3084i	−0.194881	−	0.0709310i
$386$		0			0
$387$	56.4333	+	315.165i	0.145822	+	0.814380i
$388$		0			0
$389$	305.584	+	364.181i	0.785563	+	0.936197i	0.999171	−	0.0407223i	$-0.0129659\pi$
$389$	305.584	+	364.181i	0.785563	+	0.936197i	−0.213608	+	0.976920i	$0.568521\pi$
$390$		0			0
$391$	18.7335	−	106.243i	0.0479117	−	0.271721i
$392$		0			0
$393$	−520.317	−	435.425i	−1.32396	−	1.10795i
$394$		0			0
$395$	48.5561	+	28.0339i	0.122927	+	0.0709718i
$396$		0			0
$397$	−217.038	−	375.920i	−0.546694	−	0.946902i	−0.998498	−	0.0547849i	$-0.982553\pi$
$397$	−217.038	−	375.920i	−0.546694	−	0.946902i	0.451804	−	0.892117i	$-0.350781\pi$
$398$		0			0
$399$	74.2024	+	88.1935i	0.185971	+	0.221036i
$400$		0			0
$401$	84.0625	+	230.960i	0.209632	+	0.575960i	0.999294	−	0.0375831i	$-0.0119659\pi$
$401$	84.0625	+	230.960i	0.209632	+	0.575960i	−0.789661	+	0.613543i	$0.789744\pi$
$402$		0			0
$403$	−21.9792	−	124.650i	−0.0545389	−	0.309306i
$404$		0			0
$405$	37.0841	+	6.33655i	0.0915657	+	0.0156458i
$406$		0			0
$407$	−154.531	+	27.2479i	−0.379682	+	0.0669482i
$408$		0			0
$409$	−328.561	+	119.587i	−0.803328	+	0.292388i	−0.710865	−	0.703329i	$-0.751696\pi$
$409$	−328.561	+	119.587i	−0.803328	+	0.292388i	−0.0924633	+	0.995716i	$0.529474\pi$
$410$		0			0
$411$	348.746	−	293.420i	0.848530	−	0.713918i
$412$		0			0
$413$	268.349	−	154.932i	0.649756	−	0.375137i
$414$		0			0
$415$	−27.1401	+	47.0081i	−0.0653979	+	0.113272i
$416$		0			0
$417$	−327.227	+	391.025i	−0.784718	+	0.937709i
$418$		0			0
$419$	−271.509	−	47.8743i	−0.647993	−	0.114259i	−0.160015	−	0.987115i	$-0.551154\pi$
$419$	−271.509	−	47.8743i	−0.647993	−	0.114259i	−0.487978	+	0.872856i	$0.662265\pi$
$420$		0			0
$421$	50.0550	−	42.0012i	0.118896	−	0.0997652i	−0.581401	−	0.813617i	$-0.697495\pi$
$421$	50.0550	−	42.0012i	0.118896	−	0.0997652i	0.700297	+	0.713852i	$0.253051\pi$
$422$		0			0
$423$	93.6184	+	110.972i	0.221320	+	0.262345i
$424$		0			0
$425$	221.643	−	608.960i	0.521514	−	1.43285i
$426$		0			0
$427$	492.532	+	413.284i	1.15347	+	0.967877i
$428$		0			0
$429$	−427.752	+	743.160i	−0.997091	+	1.73231i
$430$		0			0
$431$			105.508i			0.244799i	0.992481	+	0.122399i	$0.0390589\pi$
$431$			105.508i			0.244799i	−0.992481	+	0.122399i	$0.960941\pi$
$432$		0			0
$433$	599.181			1.38379			0.691895	−	0.721998i	$-0.256776\pi$
$433$	599.181			1.38379			0.691895	+	0.721998i	$0.256776\pi$
$434$		0			0
$435$	−0.0769143	−	58.0748i	−0.000176815	−	0.133505i
$436$		0			0
$437$	−9.43423	+	11.2433i	−0.0215886	+	0.0257283i
$438$		0			0
$439$	59.8973	+	21.8008i	0.136440	+	0.0496602i	0.409338	−	0.912383i	$-0.365760\pi$
$439$	59.8973	+	21.8008i	0.136440	+	0.0496602i	−0.272897	+	0.962043i	$0.587982\pi$
$440$		0			0
$441$	571.508	−	209.728i	1.29594	−	0.475574i
$442$		0			0
$443$	−85.6046	−	102.020i	−0.193238	−	0.230292i	0.660722	−	0.750631i	$-0.270250\pi$
$443$	−85.6046	−	102.020i	−0.193238	−	0.230292i	−0.853960	+	0.520338i	$0.825806\pi$
$444$		0			0
$445$	10.9677	−	62.2010i	0.0246465	−	0.139777i
$446$		0			0
$447$	504.516	−	184.386i	1.12867	−	0.412496i
$448$		0			0
$449$	−120.484	−	69.5615i	−0.268339	−	0.154925i	0.359794	−	0.933032i	$-0.382847\pi$
$449$	−120.484	−	69.5615i	−0.268339	−	0.154925i	−0.628132	+	0.778106i	$0.716180\pi$
$450$		0			0
$451$	346.545	+	600.234i	0.768393	+	1.33090i
$452$		0			0
$453$	−122.852	+	338.929i	−0.271196	+	0.748188i
$454$		0			0
$455$	30.8079	+	84.6441i	0.0677098	+	0.186031i
$456$		0			0
$457$	−21.0125	−	119.168i	−0.0459792	−	0.260761i	0.953149	−	0.302500i	$-0.0978212\pi$
$457$	−21.0125	−	119.168i	−0.0459792	−	0.260761i	−0.999129	+	0.0417393i	$0.986710\pi$
$458$		0			0
$459$	350.556	−	612.791i	0.763739	−	1.33506i
$460$		0			0
$461$	−266.202	+	46.9386i	−0.577445	+	0.101819i	−0.454740	−	0.890624i	$-0.650268\pi$
$461$	−266.202	+	46.9386i	−0.577445	+	0.101819i	−0.122705	+	0.992443i	$0.539157\pi$
$462$		0			0
$463$	16.9878	−	6.18304i	0.0366906	−	0.0133543i	−0.323610	−	0.946191i	$-0.604896\pi$
$463$	16.9878	−	6.18304i	0.0366906	−	0.0133543i	0.360300	+	0.932836i	$0.382674\pi$
$464$		0			0
$465$	1.71831	+	9.67012i	0.00369529	+	0.0207960i
$466$		0			0
$467$	−439.219	+	253.583i	−0.940511	+	0.543004i	−0.890120	−	0.455725i	$-0.849380\pi$
$467$	−439.219	+	253.583i	−0.940511	+	0.543004i	−0.0503903	+	0.998730i	$0.516047\pi$
$468$		0			0
$469$	125.474	−	217.327i	0.267534	−	0.463383i
$470$		0			0
$471$	−96.3614	−	16.8596i	−0.204589	−	0.0357952i
$472$		0			0
$473$	557.656	+	98.3298i	1.17898	+	0.207885i
$474$		0			0
$475$	−67.5380	+	56.6711i	−0.142185	+	0.119308i
$476$		0			0
$477$	−590.884	−	339.064i	−1.23875	−	0.710825i
$478$		0			0
$479$	210.140	−	577.355i	0.438705	−	1.20533i	−0.501629	−	0.865083i	$-0.667266\pi$
$479$	210.140	−	577.355i	0.438705	−	1.20533i	0.940335	−	0.340251i	$-0.110512\pi$
$480$		0			0
$481$	135.607	+	113.788i	0.281928	+	0.236565i
$482$		0			0
$483$	66.9938	+	115.683i	0.138703	+	0.239508i
$484$		0			0
$485$		−	43.8510i		−	0.0904144i
$486$		0			0
$487$	−218.562			−0.448793			−0.224396	−	0.974498i	$-0.572041\pi$
$487$	−218.562			−0.448793			−0.224396	+	0.974498i	$0.572041\pi$
$488$		0			0
$489$	570.690	−	330.496i	1.16705	−	0.675862i
$490$		0			0
$491$	−128.585	+	153.242i	−0.261885	+	0.312102i	−0.880924	−	0.473258i	$-0.843078\pi$
$491$	−128.585	+	153.242i	−0.261885	+	0.312102i	0.619039	+	0.785360i	$0.287522\pi$
$492$		0			0
$493$	−1024.07	−	372.729i	−2.07721	−	0.756043i
$494$		0			0
$495$	33.1156	−	57.7103i	0.0669001	−	0.116587i
$496$		0			0
$497$	258.414	+	307.965i	0.519947	+	0.619648i
$498$		0			0
$499$	−23.1673	+	131.388i	−0.0464274	+	0.263303i	−0.999182	−	0.0404381i	$-0.987125\pi$
$499$	−23.1673	+	131.388i	−0.0464274	+	0.263303i	0.952755	+	0.303741i	$0.0982358\pi$
$500$		0			0
$501$	−62.7808	+	358.826i	−0.125311	+	0.716219i
$502$		0			0
$503$	156.930	+	90.6037i	0.311989	+	0.180127i	0.647816	−	0.761797i	$-0.275683\pi$
$503$	156.930	+	90.6037i	0.311989	+	0.180127i	−0.335827	+	0.941924i	$0.609016\pi$
$504$		0			0
$505$	35.3994	+	61.3136i	0.0700979	+	0.121413i
$506$		0			0
$507$	453.255	−	80.5401i	0.893993	−	0.158856i
$508$		0			0
$509$	268.953	+	738.941i	0.528394	+	1.45175i	0.860961	+	0.508671i	$0.169863\pi$
$509$	268.953	+	738.941i	0.528394	+	1.45175i	−0.332567	+	0.943080i	$0.607915\pi$
$510$		0			0
$511$	97.6264	+	553.667i	0.191050	+	1.08350i
$512$		0			0
$513$	−82.9872	+	48.3534i	−0.161769	+	0.0942560i
$514$		0			0
$515$	−9.95032	+	1.75451i	−0.0193210	+	0.00340682i
$516$		0			0
$517$	241.288	−	87.8218i	0.466709	−	0.169868i
$518$		0			0
$519$	217.741	+	78.9248i	0.419539	+	0.152071i
$520$		0			0
$521$	−169.525	+	97.8752i	−0.325384	+	0.187860i	−0.653790	−	0.756676i	$-0.726822\pi$
$521$	−169.525	+	97.8752i	−0.325384	+	0.187860i	0.328406	+	0.944537i	$0.393489\pi$
$522$		0			0
$523$	−79.9831	+	138.535i	−0.152931	+	0.264885i	−0.932304	−	0.361676i	$-0.882205\pi$
$523$	−79.9831	+	138.535i	−0.152931	+	0.264885i	0.779373	+	0.626561i	$0.215538\pi$
$524$		0			0
$525$	275.647	+	754.224i	0.525042	+	1.43662i
$526$		0			0
$527$	181.504	+	32.0041i	0.344411	+	0.0607289i
$528$		0			0
$529$	392.197	−	329.092i	0.741393	−	0.622103i
$530$		0			0
$531$	88.9579	+	242.410i	0.167529	+	0.456516i
$532$		0			0
$533$	267.428	−	734.753i	0.501742	−	1.37852i
$534$		0			0
$535$	−17.7342	−	14.8807i	−0.0331480	−	0.0278145i
$536$		0			0
$537$	445.441	−	0.589942i	0.829499	−	0.00109859i
$538$		0			0
$539$		−	1076.67i		−	1.99753i
$540$		0			0
$541$	−34.2145			−0.0632430			−0.0316215	−	0.999500i	$-0.510067\pi$
$541$	−34.2145			−0.0632430			−0.0316215	+	0.999500i	$0.510067\pi$
$542$		0			0
$543$	−219.515	−	126.350i	−0.404264	−	0.232688i
$544$		0			0
$545$	−51.0713	+	60.8644i	−0.0937087	+	0.111678i
$546$		0			0
$547$	281.372	+	102.411i	0.514391	+	0.187223i	0.586155	−	0.810199i	$-0.300641\pi$
$547$	281.372	+	102.411i	0.514391	+	0.187223i	−0.0717647	+	0.997422i	$0.522863\pi$
$548$		0			0
$549$	−409.527	+	345.486i	−0.745950	+	0.629301i
$550$		0			0
$551$	95.3017	+	113.576i	0.172961	+	0.206127i
$552$		0			0
$553$	−226.390	+	1283.92i	−0.409386	+	2.32174i
$554$		0			0
$555$	−10.5343	−	8.81558i	−0.0189807	−	0.0158839i
$556$		0			0
$557$	−686.079	−	396.108i	−1.23174	−	0.711146i	−0.264348	−	0.964427i	$-0.585157\pi$
$557$	−686.079	−	396.108i	−1.23174	−	0.711146i	−0.967393	+	0.253282i	$0.918490\pi$
$558$		0			0
$559$	−319.412	−	553.237i	−0.571398	−	0.989691i
$560$		0			0
$561$	−803.834	−	955.400i	−1.43286	−	1.70303i
$562$		0			0
$563$	−334.881	−	920.079i	−0.594816	−	1.63424i	−0.761450	−	0.648224i	$-0.775512\pi$
$563$	−334.881	−	920.079i	−0.594816	−	1.63424i	0.166634	−	0.986019i	$-0.446710\pi$
$564$		0			0
$565$	3.28300	+	18.6188i	0.00581061	+	0.0329536i
$566$		0			0
$567$	156.470	+	860.699i	0.275962	+	1.51799i
$568$		0			0
$569$	−552.043	+	97.3401i	−0.970199	+	0.171072i	−0.636219	−	0.771508i	$-0.719503\pi$
$569$	−552.043	+	97.3401i	−0.970199	+	0.171072i	−0.333979	+	0.942580i	$0.608392\pi$
$570$		0			0
$571$	−29.2223	+	10.6361i	−0.0511775	+	0.0186271i	−0.367482	−	0.930031i	$-0.619780\pi$
$571$	−29.2223	+	10.6361i	−0.0511775	+	0.0186271i	0.316305	+	0.948658i	$0.397558\pi$
$572$		0			0
$573$	4.48875	−	3.77665i	0.00783377	−	0.00659102i
$574$		0			0
$575$	−88.5581	+	51.1290i	−0.154014	+	0.0889201i
$576$		0			0
$577$	−95.1751	+	164.848i	−0.164948	+	0.285699i	−0.936637	−	0.350302i	$-0.886079\pi$
$577$	−95.1751	+	164.848i	−0.164948	+	0.285699i	0.771689	+	0.636000i	$0.219412\pi$
$578$		0			0
$579$	639.190	−	763.809i	1.10396	−	1.31919i
$580$		0			0
$581$	−1242.99	−	219.173i	−2.13940	−	0.377234i
$582$		0			0
$583$	−922.970	+	774.464i	−1.58314	+	1.32841i
$584$		0			0
$585$	−73.8879	+	13.2303i	−0.126304	+	0.0226160i
$586$		0			0
$587$	−150.974	+	414.798i	−0.257196	+	0.706641i	0.742141	+	0.670244i	$0.233810\pi$
$587$	−150.974	+	414.798i	−0.257196	+	0.706641i	−0.999337	+	0.0363972i	$0.988412\pi$
$588$		0			0
$589$	−19.2079	−	16.1174i	−0.0326111	−	0.0273640i
$590$		0			0
$591$	368.331	−	639.923i	0.623233	−	1.08278i
$592$		0			0
$593$		−	435.642i		−	0.734640i	−0.930095	−	0.367320i	$-0.880275\pi$
$593$		−	435.642i		−	0.734640i	0.930095	−	0.367320i	$-0.119725\pi$
$594$		0			0
$595$	−131.161			−0.220439
$596$		0			0
$597$	−1.09840	−	829.357i	−0.00183987	−	1.38921i
$598$		0			0
$599$	−615.387	+	733.389i	−1.02736	+	1.22436i	−0.0531765	+	0.998585i	$0.516935\pi$
$599$	−615.387	+	733.389i	−1.02736	+	1.22436i	−0.974180	+	0.225771i	$0.927510\pi$
$600$		0			0
$601$	−214.739	−	78.1585i	−0.357302	−	0.130047i	0.157131	−	0.987578i	$-0.449775\pi$
$601$	−214.739	−	78.1585i	−0.357302	−	0.130047i	−0.514433	+	0.857530i	$0.671998\pi$
$602$		0			0
$603$	160.552	+	133.996i	0.266255	+	0.222215i
$604$		0			0
$605$	−39.5154	−	47.0926i	−0.0653147	−	0.0778391i
$606$		0			0
$607$	23.6802	−	134.297i	0.0390118	−	0.221247i	−0.959069	−	0.283173i	$-0.908613\pi$
$607$	23.6802	−	134.297i	0.0390118	−	0.221247i	0.998081	+	0.0619256i	$0.0197241\pi$
$608$		0			0
$609$	1268.35	−	463.545i	2.08268	−	0.761158i
$610$		0			0
$611$	−250.869	−	144.839i	−0.410587	−	0.237053i
$612$		0			0
$613$	−35.5694	−	61.6081i	−0.0580252	−	0.100503i	0.835554	−	0.549409i	$-0.185147\pi$
$613$	−35.5694	−	61.6081i	−0.0580252	−	0.100503i	−0.893579	+	0.448906i	$0.851814\pi$
$614$		0			0
$615$	−20.6759	+	57.0415i	−0.0336194	+	0.0927505i
$616$		0			0
$617$	−348.112	−	956.431i	−0.564201	−	1.55013i	−0.813416	−	0.581682i	$-0.802395\pi$
$617$	−348.112	−	956.431i	−0.564201	−	1.55013i	0.249215	−	0.968448i	$-0.419828\pi$
$618$		0			0
$619$	63.4363	+	359.765i	0.102482	+	0.581204i	0.992196	+	0.124686i	$0.0397924\pi$
$619$	63.4363	+	359.765i	0.102482	+	0.581204i	−0.889714	+	0.456518i	$0.849097\pi$
$620$		0			0
$621$	−104.530	+	38.5167i	−0.168325	+	0.0620236i
$622$		0			0
$623$	1446.35	−	255.030i	2.32158	−	0.409358i
$624$		0			0
$625$	−572.148	+	208.245i	−0.915437	+	0.333192i
$626$		0			0
$627$	29.7184	+	167.246i	0.0473977	+	0.266740i
$628$		0			0
$629$	−223.231	+	128.882i	−0.354898	+	0.204900i
$630$		0			0
$631$	390.214	−	675.871i	0.618406	−	1.07111i	−0.371371	−	0.928485i	$-0.621112\pi$
$631$	390.214	−	675.871i	0.618406	−	1.07111i	0.989777	−	0.142626i	$-0.0455546\pi$
$632$		0			0
$633$	157.351	+	27.5304i	0.248580	+	0.0434919i
$634$		0			0
$635$	28.2594	+	4.98289i	0.0445029	+	0.00784707i
$636$		0			0
$637$	−930.467	+	780.754i	−1.46070	+	1.22567i
$638$		0			0
$639$	−289.686	+	168.275i	−0.453343	+	0.263341i
$640$		0			0
$641$	−96.5071	+	265.151i	−0.150557	+	0.413652i	−0.991927	−	0.126807i	$-0.959527\pi$
$641$	−96.5071	+	265.151i	−0.150557	+	0.413652i	0.841370	+	0.540459i	$0.181749\pi$
$642$		0			0
$643$	−32.0195	−	26.8675i	−0.0497970	−	0.0417846i	0.617549	−	0.786532i	$-0.288126\pi$
$643$	−32.0195	−	26.8675i	−0.0497970	−	0.0417846i	−0.667346	+	0.744747i	$0.732570\pi$
$644$		0			0
$645$	24.8420	+	42.8963i	0.0385147	+	0.0665059i
$646$		0			0
$647$		−	383.618i		−	0.592918i	−0.955046	−	0.296459i	$-0.904194\pi$
$647$		−	383.618i		−	0.592918i	0.955046	−	0.296459i	$-0.0958058\pi$
$648$		0			0
$649$	456.677			0.703663
$650$		0			0
$651$	−197.631	+	114.452i	−0.303581	+	0.175809i
$652$		0			0
$653$	39.3773	−	46.9281i	0.0603022	−	0.0718653i	−0.735050	−	0.678013i	$-0.762841\pi$
$653$	39.3773	−	46.9281i	0.0603022	−	0.0718653i	0.795352	+	0.606147i	$0.207286\pi$
$654$		0			0
$655$	−98.7072	−	35.9265i	−0.150698	−	0.0548496i
$656$		0			0
$657$	−468.502	+	1.24097i	−0.713092	+	0.00188884i
$658$		0			0
$659$	−329.590	−	392.790i	−0.500137	−	0.596040i	0.455629	−	0.890170i	$-0.349415\pi$
$659$	−329.590	−	392.790i	−0.500137	−	0.596040i	−0.955765	+	0.294130i	$0.904970\pi$
$660$		0			0
$661$	−33.1600	+	188.060i	−0.0501664	+	0.284508i	−0.999563	−	0.0295731i	$-0.990585\pi$
$661$	−33.1600	+	188.060i	−0.0501664	+	0.284508i	0.949396	+	0.314081i	$0.101696\pi$
$662$		0			0
$663$	−242.759	+	1387.50i	−0.366153	+	2.09276i
$664$		0			0
$665$	15.4535	+	8.92209i	0.0232384	+	0.0134167i
$666$		0			0
$667$	85.9819	+	148.925i	0.128908	+	0.223276i
$668$		0			0
$669$	−320.459	+	56.9432i	−0.479012	+	0.0851170i
$670$		0			0
$671$	324.095	+	890.443i	0.483003	+	1.32704i
$672$		0			0
$673$	−180.046	−	1021.09i	−0.267527	−	1.51722i	−0.761741	−	0.647882i	$-0.775655\pi$
$673$	−180.046	−	1021.09i	−0.267527	−	1.51722i	0.494214	−	0.869340i	$-0.335456\pi$
$674$		0			0
$675$	−658.542	+	118.819i	−0.975618	+	0.176027i
$676$		0			0
$677$	482.182	−	85.0218i	0.712234	−	0.125586i	0.194220	−	0.980958i	$-0.437782\pi$
$677$	482.182	−	85.0218i	0.712234	−	0.125586i	0.518014	+	0.855372i	$0.326671\pi$
$678$		0			0
$679$	958.165	−	348.743i	1.41114	−	0.513613i
$680$		0			0
$681$	1022.32	+	370.562i	1.50121	+	0.544144i
$682$		0			0
$683$	251.274	−	145.073i	0.367897	−	0.212406i	−0.304642	−	0.952467i	$-0.598537\pi$
$683$	251.274	−	145.073i	0.367897	−	0.212406i	0.672540	+	0.740061i	$0.265204\pi$
$684$		0			0
$685$	35.2808	−	61.1082i	0.0515049	−	0.0892090i
$686$		0			0
$687$	−298.175	−	815.865i	−0.434024	−	1.18758i
$688$		0			0
$689$	1338.60	+	236.031i	1.94282	+	0.342571i
$690$		0			0
$691$	148.698	−	124.773i	0.215193	−	0.180568i	−0.528819	−	0.848735i	$-0.677365\pi$
$691$	148.698	−	124.773i	0.215193	−	0.180568i	0.744012	+	0.668166i	$0.232921\pi$
$692$		0			0
$693$	1524.36	+	264.625i	2.19966	+	0.381855i
$694$		0			0
$695$	−26.9992	+	74.1796i	−0.0388477	+	0.106733i
$696$		0			0
$697$	872.176	+	731.842i	1.25133	+	1.04999i
$698$		0			0
$699$	−442.237	+	0.585699i	−0.632671	+	0.000837910i
$700$		0			0
$701$			294.780i			0.420513i	0.977646	+	0.210257i	$0.0674299\pi$
$701$			294.780i			0.420513i	−0.977646	+	0.210257i	$0.932570\pi$
$702$		0			0
$703$	35.0683			0.0498837
$704$		0			0
$705$	19.4814	+	11.2132i	0.0276331	+	0.0159052i
$706$		0			0
$707$	−1058.20	+	1261.12i	−1.49675	+	1.78376i
$708$		0			0
$709$	916.038	+	333.410i	1.29201	+	0.470255i	0.894387	−	0.447293i	$-0.147612\pi$
$709$	916.038	+	333.410i	1.29201	+	0.470255i	0.397626	+	0.917548i	$0.369834\pi$
$710$		0			0
$711$	−1021.89	−	368.877i	−1.43726	−	0.518814i
$712$		0			0
$713$	−18.6938	−	22.2784i	−0.0262185	−	0.0312460i
$714$		0			0
$715$	−23.0526	+	130.738i	−0.0322415	+	0.182850i
$716$		0			0
$717$	31.3634	+	26.2463i	0.0437426	+	0.0366058i
$718$		0			0
$719$	−574.371	−	331.613i	−0.798848	−	0.461215i	0.0442205	−	0.999022i	$-0.485920\pi$
$719$	−574.371	−	331.613i	−0.798848	−	0.461215i	−0.843068	+	0.537807i	$0.819253\pi$
$720$		0			0
$721$	−117.471	−	203.466i	−0.162928	−	0.282200i
$722$		0			0
$723$	573.748	+	681.930i	0.793566	+	0.943196i
$724$		0			0
$725$	353.300	+	970.683i	0.487310	+	1.33887i
$726$		0			0
$727$	−178.695	−	1013.43i	−0.245797	−	1.39399i	−0.818633	−	0.574316i	$-0.805268\pi$
$727$	−178.695	−	1013.43i	−0.245797	−	1.39399i	0.572836	−	0.819670i	$-0.305843\pi$
$728$		0			0
$729$	−728.977	+	5.79286i	−0.999968	+	0.00794631i
$730$		0			0
$731$	916.066	−	161.527i	1.25317	−	0.220967i
$732$		0			0
$733$	−93.4865	+	34.0263i	−0.127540	+	0.0464206i	−0.405001	−	0.914316i	$-0.632729\pi$
$733$	−93.4865	+	34.0263i	−0.127540	+	0.0464206i	0.277462	+	0.960737i	$0.410507\pi$
$734$		0			0
$735$	72.1205	−	60.6792i	0.0981231	−	0.0825567i
$736$		0			0
$737$	320.297	−	184.923i	0.434595	−	0.250914i
$738$		0			0
$739$	28.7996	−	49.8824i	0.0389710	−	0.0674998i	−0.845882	−	0.533370i	$-0.820925\pi$
$739$	28.7996	−	49.8824i	0.0389710	−	0.0674998i	0.884853	+	0.465870i	$0.154259\pi$
$740$		0			0
$741$	122.985	−	146.963i	0.165972	−	0.198330i
$742$		0			0
$743$	1203.21	+	212.158i	1.61939	+	0.285543i	0.908540	−	0.417798i	$-0.137198\pi$
$743$	1203.21	+	212.158i	1.61939	+	0.285543i	0.710853	+	0.703340i	$0.248309\pi$
$744$		0			0
$745$	63.7064	−	53.4560i	0.0855120	−	0.0717531i
$746$		0			0
$747$	357.117	−	989.317i	0.478068	−	1.32439i
$748$		0			0
$749$	184.113	−	505.845i	0.245811	−	0.675361i
$750$		0			0
$751$	623.699	+	523.346i	0.830492	+	0.696865i	0.955404	−	0.295302i	$-0.0954204\pi$
$751$	623.699	+	523.346i	0.830492	+	0.696865i	−0.124912	+	0.992168i	$0.539865\pi$
$752$		0			0
$753$	0.315974	−	0.548962i	0.000419621	−	0.000729033i
$754$		0			0
$755$			55.8142i			0.0739261i
$756$		0			0
$757$	646.428			0.853933			0.426967	−	0.904267i	$-0.359582\pi$
$757$	646.428			0.853933			0.426967	+	0.904267i	$0.359582\pi$
$758$		0			0
$759$	0.260932	+	197.019i	0.000343785	+	0.259578i
$760$		0			0
$761$	−132.824	+	158.293i	−0.174539	+	0.208007i	−0.846221	−	0.532832i	$-0.821128\pi$
$761$	−132.824	+	158.293i	−0.174539	+	0.208007i	0.671682	+	0.740840i	$0.265572\pi$
$762$		0			0
$763$	−1736.08	−	631.882i	−2.27534	−	0.828154i
$764$		0			0
$765$	18.6946	−	107.690i	0.0244374	−	0.140771i
$766$		0			0
$767$	−331.164	−	394.665i	−0.431765	−	0.514557i
$768$		0			0
$769$	27.9808	−	158.687i	0.0363860	−	0.206355i	−0.961195	−	0.275870i	$-0.911034\pi$
$769$	27.9808	−	158.687i	0.0363860	−	0.206355i	0.997581	+	0.0695149i	$0.0221451\pi$
$770$		0			0
$771$	−546.400	+	199.693i	−0.708689	+	0.259005i
$772$		0			0
$773$	−769.088	−	444.033i	−0.994940	−	0.574429i	−0.0881925	−	0.996103i	$-0.528109\pi$
$773$	−769.088	−	444.033i	−0.994940	−	0.574429i	−0.906747	+	0.421675i	$0.861442\pi$
$774$		0			0
$775$	−87.3485	−	151.292i	−0.112708	−	0.195215i
$776$		0			0
$777$	108.846	−	300.289i	0.140085	−	0.386472i
$778$		0			0
$779$	−52.9777	−	145.555i	−0.0680073	−	0.186848i
$780$		0			0
$781$	102.886	+	583.497i	0.131737	+	0.747116i
$782$		0			0
$783$	199.813	+	1107.45i	0.255189	+	1.41436i
$784$		0			0
$785$	−14.9153	+	2.62997i	−0.0190004	+	0.00335028i
$786$		0			0
$787$	−1121.88	+	408.332i	−1.42552	+	0.518847i	−0.935644	−	0.352945i	$-0.885180\pi$
$787$	−1121.88	+	408.332i	−1.42552	+	0.518847i	−0.489876	+	0.871792i	$0.662958\pi$
$788$		0			0
$789$	−214.588	−	1207.63i	−0.271975	−	1.53059i
$790$		0			0
$791$	−380.720	+	219.809i	−0.481315	+	0.277887i
$792$		0			0
$793$	534.510	−	925.799i	0.674035	−	1.16746i
$794$		0			0
$795$	−103.895	−	18.1776i	−0.130685	−	0.0228649i
$796$		0			0
$797$	477.592	+	84.2124i	0.599237	+	0.105662i	0.465035	−	0.885292i	$-0.346042\pi$
$797$	477.592	+	84.2124i	0.599237	+	0.105662i	0.134202	+	0.990954i	$0.457153\pi$
$798$		0			0
$799$	323.121	−	271.130i	0.404406	−	0.339337i
$800$		0			0
$801$	3.24179	+	1223.87i	0.00404718	+	1.52793i
$802$		0			0
$803$	−283.393	+	778.615i	−0.352917	+	0.969632i
$804$		0			0
$805$	15.8546	+	13.3036i	0.0196951	+	0.0165262i
$806$		0			0
$807$	−180.549	−	311.765i	−0.223728	−	0.386326i
$808$		0			0
$809$			1260.59i			1.55821i	0.626893	+	0.779105i	$0.284326\pi$
$809$			1260.59i			1.55821i	−0.626893	+	0.779105i	$0.715674\pi$
$810$		0			0
$811$	740.450			0.913009			0.456504	−	0.889721i	$-0.349101\pi$
$811$	740.450			0.913009			0.456504	+	0.889721i	$0.349101\pi$
$812$		0			0
$813$	−49.4008	+	28.6089i	−0.0607636	+	0.0351893i
$814$		0			0
$815$	65.6297	−	78.2144i	0.0805272	−	0.0959686i
$816$		0			0
$817$	−118.919	−	43.2831i	−0.145556	−	0.0529780i
$818$		0			0
$819$	−876.714	−	1509.27i	−1.07047	−	1.84282i
$820$		0			0
$821$	600.280	+	715.385i	0.731157	+	0.871359i	0.995664	−	0.0930252i	$-0.0296537\pi$
$821$	600.280	+	715.385i	0.731157	+	0.871359i	−0.264507	+	0.964384i	$0.585209\pi$
$822$		0			0
$823$	−7.57884	+	42.9817i	−0.00920880	+	0.0522257i	−0.989066	−	0.147474i	$-0.952886\pi$
$823$	−7.57884	+	42.9817i	−0.00920880	+	0.0522257i	0.979857	+	0.199700i	$0.0639967\pi$
$824$		0			0
$825$	−203.967	+	1165.78i	−0.247233	+	1.41307i
$826$		0			0
$827$	620.289	+	358.124i	0.750047	+	0.433040i	0.825711	−	0.564093i	$-0.190774\pi$
$827$	620.289	+	358.124i	0.750047	+	0.433040i	−0.0756636	+	0.997133i	$0.524108\pi$
$828$		0			0
$829$	−151.869	−	263.044i	−0.183195	−	0.317303i	0.759772	−	0.650190i	$-0.225311\pi$
$829$	−151.869	−	263.044i	−0.183195	−	0.317303i	−0.942967	+	0.332887i	$0.891977\pi$
$830$		0			0
$831$	−940.376	+	167.098i	−1.13162	+	0.201081i
$832$		0			0
$833$	−604.913	−	1661.99i	−0.726186	−	1.99518i
$834$		0			0
$835$	9.79336	+	55.5409i	0.0117286	+	0.0665161i
$836$		0			0
$837$	−65.8016	−	178.577i	−0.0786160	−	0.213354i
$838$		0			0
$839$	546.700	−	96.3979i	0.651609	−	0.114896i	0.161934	−	0.986802i	$-0.448227\pi$
$839$	546.700	−	96.3979i	0.651609	−	0.114896i	0.489674	+	0.871905i	$0.337116\pi$
$840$		0			0
$841$	842.081	−	306.492i	1.00129	−	0.364438i
$842$		0			0
$843$	678.759	+	246.030i	0.805170	+	0.291851i
$844$		0			0
$845$	61.7240	−	35.6363i	0.0730461	−	0.0421732i
$846$		0			0
$847$	714.734	−	1237.96i	0.843841	−	1.46158i
$848$		0			0
$849$	92.0002	+	251.731i	0.108363	+	0.296503i
$850$		0			0
$851$	40.0562	+	7.06298i	0.0470695	+	0.00829963i
$852$		0			0
$853$	199.807	−	167.658i	0.234241	−	0.196551i	−0.518110	−	0.855314i	$-0.673364\pi$
$853$	199.807	−	167.658i	0.234241	−	0.196551i	0.752351	+	0.658763i	$0.228920\pi$
$854$		0			0
$855$	−9.52807	+	11.4164i	−0.0111439	+	0.0133525i
$856$		0			0
$857$	123.417	−	339.084i	0.144010	−	0.395664i	−0.846627	−	0.532187i	$-0.821370\pi$
$857$	123.417	−	339.084i	0.144010	−	0.395664i	0.990637	+	0.136523i	$0.0435926\pi$
$858$		0			0
$859$	−439.289	−	368.607i	−0.511396	−	0.429112i	0.350224	−	0.936666i	$-0.386105\pi$
$859$	−439.289	−	368.607i	−0.511396	−	0.429112i	−0.861620	+	0.507554i	$0.830550\pi$
$860$		0			0
$861$	−1410.82	+	1.86849i	−1.63858	+	0.00217014i
$862$		0			0
$863$			654.390i			0.758273i	0.925341	+	0.379137i	$0.123779\pi$
$863$			654.390i			0.758273i	−0.925341	+	0.379137i	$0.876221\pi$
$864$		0			0
$865$	35.8572			0.0414534
$866$		0			0
$867$	−1026.19	−	590.662i	−1.18361	−	0.681271i
$868$		0			0
$869$	−1235.08	+	1471.91i	−1.42127	+	1.69380i
$870$		0			0
$871$	−392.079	−	142.705i	−0.450148	−	0.163840i
$872$		0			0
$873$	149.766	+	836.406i	0.171554	+	0.958082i
$874$		0			0
$875$	160.523	+	191.304i	0.183455	+	0.218634i
$876$		0			0
$877$	139.814	−	792.923i	0.159423	−	0.904131i	−0.795208	−	0.606337i	$-0.792638\pi$
$877$	139.814	−	792.923i	0.159423	−	0.904131i	0.954630	−	0.297794i	$-0.0962508\pi$
$878$		0			0
$879$	−716.661	−	599.735i	−0.815314	−	0.682292i
$880$		0			0
$881$	1043.53	+	602.480i	1.18448	+	0.683860i	0.957047	−	0.289934i	$-0.0936334\pi$
$881$	1043.53	+	602.480i	1.18448	+	0.683860i	0.227433	+	0.973794i	$0.426967\pi$
$882$		0			0
$883$	−378.383	−	655.379i	−0.428520	−	0.742219i	0.568222	−	0.822876i	$-0.307632\pi$
$883$	−378.383	−	655.379i	−0.428520	−	0.742219i	−0.996742	+	0.0806566i	$0.974298\pi$
$884$		0			0
$885$	25.7376	+	30.5905i	0.0290820	+	0.0345655i
$886$		0			0
$887$	−209.428	−	575.399i	−0.236108	−	0.648703i	−0.999994	−	0.00335135i	$-0.998933\pi$
$887$	−209.428	−	575.399i	−0.236108	−	0.648703i	0.763886	−	0.645351i	$-0.223289\pi$
$888$		0			0
$889$	115.866	+	657.109i	0.130333	+	0.739155i
$890$		0			0
$891$	−434.540	+	1213.86i	−0.487699	+	1.36235i
$892$		0			0
$893$	−56.5136	+	9.96488i	−0.0632851	+	0.0111589i
$894$		0			0
$895$	64.8047	−	23.5870i	0.0724075	−	0.0263542i
$896$		0			0
$897$	170.077	−	143.096i	0.189606	−	0.159527i
$898$		0			0
$899$	−254.422	+	146.891i	−0.283006	+	0.163393i
$900$		0			0
$901$	−989.610	+	1714.05i	−1.09835	+	1.90239i
$902$		0			0
$903$	−739.738	+	883.960i	−0.819200	+	0.978915i
$904$		0			0
$905$	−38.6175	−	6.80931i	−0.0426713	−	0.00752410i
$906$		0			0
$907$	1232.60	−	1034.27i	1.35898	−	1.14032i	0.382688	−	0.923878i	$-0.374998\pi$
$907$	1232.60	−	1034.27i	1.35898	−	1.14032i	0.976295	−	0.216445i	$-0.0694460\pi$
$908$		0			0
$909$	−884.610	−	1048.58i	−0.973168	−	1.15356i
$910$		0			0
$911$	−471.470	+	1295.35i	−0.517530	+	1.42190i	0.355703	+	0.934599i	$0.384241\pi$
$911$	−471.470	+	1295.35i	−0.517530	+	1.42190i	−0.873233	+	0.487303i	$0.837981\pi$
$912$		0			0
$913$	−1424.99	−	1195.71i	−1.56077	−	1.30964i
$914$		0			0
$915$	−41.3808	+	71.8934i	−0.0452249	+	0.0785720i
$916$		0			0
$917$		−	2442.52i		−	2.66360i
$918$		0			0
$919$	−1619.94			−1.76272			−0.881358	−	0.472449i	$-0.843370\pi$
$919$	−1619.94			−1.76272			−0.881358	+	0.472449i	$0.843370\pi$
$920$		0			0
$921$	−2.35841	−	1780.74i	−0.00256071	−	1.93348i
$922$		0			0
$923$	429.656	−	512.044i	0.465499	−	0.554760i
$924$		0			0
$925$	229.593	+	83.5650i	0.248209	+	0.0903406i
$926$		0			0
$927$	183.798	−	67.4490i	0.198272	−	0.0727606i
$928$		0			0
$929$	63.3425	+	75.4887i	0.0681836	+	0.0812580i	0.799058	−	0.601254i	$-0.205332\pi$
$929$	63.3425	+	75.4887i	0.0681836	+	0.0812580i	−0.730874	+	0.682512i	$0.760888\pi$
$930$		0			0
$931$	−41.7833	+	236.965i	−0.0448800	+	0.254527i
$932$		0			0
$933$	1540.38	−	562.965i	1.65100	−	0.603392i
$934$		0			0
$935$	−167.408	−	96.6529i	−0.179046	−	0.103372i
$936$		0			0
$937$	280.625	+	486.056i	0.299493	+	0.518736i	0.976020	−	0.217681i	$-0.0698493\pi$
$937$	280.625	+	486.056i	0.299493	+	0.518736i	−0.676527	+	0.736417i	$0.736516\pi$
$938$		0			0
$939$	−160.134	+	441.784i	−0.170537	+	0.470483i
$940$		0			0
$941$	−253.931	−	697.670i	−0.269852	−	0.741414i	−0.998407	−	0.0564255i	$-0.982030\pi$
$941$	−253.931	−	697.670i	−0.269852	−	0.741414i	0.728554	−	0.684988i	$-0.240193\pi$
$942$		0			0
$943$	−31.1972	−	176.928i	−0.0330829	−	0.187622i
$944$		0			0
$945$	68.1848	+	117.023i	0.0721532	+	0.123834i
$946$		0			0
$947$	−411.072	+	72.4830i	−0.434078	+	0.0765396i	−0.386417	−	0.922324i	$-0.626288\pi$
$947$	−411.072	+	72.4830i	−0.434078	+	0.0765396i	−0.0476602	+	0.998864i	$0.515176\pi$
$948$		0			0
$949$	878.392	−	319.708i	0.925597	−	0.336890i
$950$		0			0
$951$	−22.2106	−	124.994i	−0.0233550	−	0.131434i
$952$		0			0
$953$	474.227	−	273.795i	0.497615	−	0.287298i	−0.230113	−	0.973164i	$-0.573910\pi$
$953$	474.227	−	273.795i	0.497615	−	0.287298i	0.727728	+	0.685866i	$0.240576\pi$
$954$		0			0
$955$	0.454104	−	0.786531i	0.000475502	−	0.000823593i
$956$		0			0
$957$	1960.45	+	343.004i	2.04854	+	0.358415i
$958$		0			0
$959$	1615.83	+	284.914i	1.68491	+	0.297095i
$960$		0			0
$961$	−698.108	+	585.783i	−0.726440	+	0.609555i
$962$		0			0
$963$	389.081	+	223.264i	0.404030	+	0.231842i
$964$		0			0
$965$	52.7389	−	144.899i	0.0546517	−	0.150154i
$966$		0			0
$967$	−275.438	−	231.120i	−0.284838	−	0.239007i	0.489162	−	0.872193i	$-0.337303\pi$
$967$	−275.438	−	231.120i	−0.284838	−	0.239007i	−0.774000	+	0.633186i	$0.781747\pi$
$968$		0			0
$969$	139.840	+	241.470i	0.144313	+	0.249195i
$970$		0			0
$971$			842.963i			0.868139i	0.900879	+	0.434069i	$0.142923\pi$
$971$			842.963i			0.868139i	−0.900879	+	0.434069i	$0.857077\pi$
$972$		0			0
$973$	−1835.58			−1.88652
$974$		0			0
$975$	1155.39	−	669.105i	1.18501	−	0.686262i
$976$		0			0
$977$	−731.252	+	871.472i	−0.748467	+	0.891988i	−0.997060	−	0.0766199i	$-0.975587\pi$
$977$	−731.252	+	871.472i	−0.748467	+	0.891988i	0.248594	+	0.968608i	$0.420032\pi$
$978$		0			0
$979$	2033.98	+	740.308i	2.07761	+	0.756187i
$980$		0			0
$981$	766.251	−	1335.34i	0.781092	−	1.36120i
$982$		0			0
$983$	−614.192	−	731.965i	−0.624813	−	0.744624i	0.357077	−	0.934075i	$-0.383773\pi$
$983$	−614.192	−	731.965i	−0.624813	−	0.744624i	−0.981890	+	0.189451i	$0.939329\pi$
$984$		0			0
$985$	19.8503	−	112.576i	0.0201526	−	0.114291i
$986$		0			0
$987$	−90.0799	+	514.855i	−0.0912663	+	0.521636i
$988$		0			0
$989$	−127.116	−	73.3905i	−0.128530	−	0.0742068i
$990$		0			0
$991$	734.903	+	1272.89i	0.741577	+	1.28445i	0.951777	+	0.306791i	$0.0992551\pi$
$991$	734.903	+	1272.89i	0.741577	+	1.28445i	−0.210200	+	0.977658i	$0.567412\pi$
$992$		0			0
$993$	−1453.45	+	258.267i	−1.46369	+	0.260088i
$994$		0			0
$995$	−43.9161	−	120.659i	−0.0441368	−	0.121265i
$996$		0			0
$997$	213.101	+	1208.56i	0.213742	+	1.21219i	0.883076	+	0.469230i	$0.155468\pi$
$997$	213.101	+	1208.56i	0.213742	+	1.21219i	−0.669334	+	0.742962i	$0.733420\pi$
$998$		0			0
$999$	231.038	+	132.168i	0.231269	+	0.132301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.41.2	yes	36
3.2	odd	2		324.3.k.a.233.4		36
4.3	odd	2		432.3.bc.b.257.5		36
27.2	odd	18	inner	108.3.k.a.29.2	✓	36
27.5	odd	18		2916.3.c.b.1457.17		36
27.22	even	9		2916.3.c.b.1457.20		36
27.25	even	9		324.3.k.a.89.4		36
108.83	even	18		432.3.bc.b.353.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.2	✓	36	27.2	odd	18	inner
108.3.k.a.41.2	yes	36	1.1	even	1	trivial
324.3.k.a.89.4		36	27.25	even	9
324.3.k.a.233.4		36	3.2	odd	2
432.3.bc.b.257.5		36	4.3	odd	2
432.3.bc.b.353.5		36	108.83	even	18
2916.3.c.b.1457.17		36	27.5	odd	18
2916.3.c.b.1457.20		36	27.22	even	9

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59609 + 1.50344i) q^{3} +(-0.298552 + 0.355800i) q^{5} +(-10.1488 - 3.69384i) q^{7} +(4.47934 - 7.80612i) q^{9} +O(q^{10})\)	\(q+(-2.59609 + 1.50344i) q^{3} +(-0.298552 + 0.355800i) q^{5} +(-10.1488 - 3.69384i) q^{7} +(4.47934 - 7.80612i) q^{9} +(-10.2314 - 12.1933i) q^{11} +(-3.11819 + 17.6841i) q^{13} +(0.240142 - 1.37254i) q^{15} +(-22.6442 - 13.0736i) q^{17} +(1.77864 + 3.08069i) q^{19} +(31.9005 - 5.66850i) q^{21} +(1.41115 + 3.87710i) q^{23} +(4.30374 + 24.4077i) q^{25} +(0.107276 + 26.9998i) q^{27} +(41.0456 - 7.23745i) q^{29} +(-6.62361 + 2.41080i) q^{31} +(44.8934 + 16.2726i) q^{33} +(4.34420 - 2.50812i) q^{35} +(4.92909 - 8.53743i) q^{37} +(-18.4919 - 50.5976i) q^{39} +(-42.8820 - 7.56125i) q^{41} +(-27.2523 + 22.8674i) q^{43} +(1.44010 + 3.92428i) q^{45} +(-5.51742 + 15.1590i) q^{47} +(51.8166 + 43.4793i) q^{49} +(78.4418 - 0.103888i) q^{51} -75.6950i q^{53} +7.39296 q^{55} +(-9.24914 - 5.32367i) q^{57} +(-18.4421 + 21.9784i) q^{59} +(-55.9422 - 20.3613i) q^{61} +(-74.2943 + 62.6764i) q^{63} +(-5.36107 - 6.38908i) q^{65} +(-4.03483 + 22.8827i) q^{67} +(-9.49246 - 7.94372i) q^{69} +(-32.2368 - 18.6119i) q^{71} +(-26.0280 - 45.0817i) q^{73} +(-47.8685 - 56.8942i) q^{75} +(58.7957 + 161.540i) q^{77} +(-20.9619 - 118.881i) q^{79} +(-40.8710 - 69.9325i) q^{81} +(115.091 - 20.2937i) q^{83} +(11.4121 - 4.15365i) q^{85} +(-95.6769 + 80.4987i) q^{87} +(-117.767 + 67.9930i) q^{89} +(96.9682 - 167.954i) q^{91} +(13.5710 - 16.2168i) q^{93} +(-1.62713 - 0.286906i) q^{95} +(-72.3238 + 60.6869i) q^{97} +(-141.012 + 25.2495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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