LMFDB - Embedded newform 108.3.k.a.29.2

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			29.2
Character	$\chi$	$=$	108.29
Dual form			108.3.k.a.41.2

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

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	0.735363	−	0.677674i	$-0.237012\pi$
$5$	−0.298552	−	0.355800i	−0.0597103	−	0.0711600i	−0.795073	+	0.606514i	$0.792567\pi$
$6$		0			0
$7$	−10.1488	+	3.69384i	−1.44982	+	0.527692i	−0.942542	−	0.334089i	$-0.891571\pi$
$7$	−10.1488	+	3.69384i	−1.44982	+	0.527692i	−0.507281	+	0.861781i	$0.669349\pi$
$8$		0			0
$9$	4.47934	+	7.80612i	0.497704	+	0.867347i
$10$		0			0
$11$	−10.2314	+	12.1933i	−0.930125	+	1.10848i	0.0637495	+	0.997966i	$0.479694\pi$
$11$	−10.2314	+	12.1933i	−0.930125	+	1.10848i	−0.993875	+	0.110514i	$0.964750\pi$
$12$		0			0
$13$	−3.11819	−	17.6841i	−0.239861	−	1.36032i	−0.832131	−	0.554579i	$-0.812879\pi$
$13$	−3.11819	−	17.6841i	−0.239861	−	1.36032i	0.592271	−	0.805739i	$-0.298232\pi$
$14$		0			0
$15$	0.240142	+	1.37254i	0.0160095	+	0.0915028i
$16$		0			0
$17$	−22.6442	+	13.0736i	−1.33201	+	0.769038i	−0.985608	−	0.169047i	$-0.945931\pi$
$17$	−22.6442	+	13.0736i	−1.33201	+	0.769038i	−0.346405	+	0.938085i	$0.612598\pi$
$18$		0			0
$19$	1.77864	−	3.08069i	0.0936126	−	0.162142i	−0.815416	−	0.578875i	$-0.803492\pi$
$19$	1.77864	−	3.08069i	0.0936126	−	0.162142i	0.909029	+	0.416733i	$0.136825\pi$
$20$		0			0
$21$	31.9005	+	5.66850i	1.51907	+	0.269928i
$22$		0			0
$23$	1.41115	−	3.87710i	0.0613543	−	0.168570i	−0.905228	−	0.424926i	$-0.860300\pi$
$23$	1.41115	−	3.87710i	0.0613543	−	0.168570i	0.966582	+	0.256357i	$0.0825222\pi$
$24$		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	0.828442	−	0.560075i	$-0.189228\pi$
$29$	41.0456	+	7.23745i	1.41537	+	0.249567i	0.586924	+	0.809642i	$0.300339\pi$
$30$		0			0
$31$	−6.62361	−	2.41080i	−0.213665	−	0.0777677i	0.232970	−	0.972484i	$-0.425156\pi$
$31$	−6.62361	−	2.41080i	−0.213665	−	0.0777677i	−0.446635	+	0.894716i	$0.647378\pi$
$32$		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	0.924916	−	0.380173i	$-0.124135\pi$
$37$	4.92909	+	8.53743i	0.133219	+	0.230741i	−0.791697	+	0.610914i	$0.790802\pi$
$38$		0			0
$39$	−18.4919	+	50.5976i	−0.474152	+	1.29737i
$40$		0			0
$41$	−42.8820	+	7.56125i	−1.04590	+	0.184421i	−0.670094	−	0.742277i	$-0.733746\pi$
$41$	−42.8820	+	7.56125i	−1.04590	+	0.184421i	−0.375808	+	0.926697i	$0.622635\pi$
$42$		0			0
$43$	−27.2523	−	22.8674i	−0.633773	−	0.531799i	0.268326	−	0.963328i	$-0.413530\pi$
$43$	−27.2523	−	22.8674i	−0.633773	−	0.531799i	−0.902099	+	0.431529i	$0.857974\pi$
$44$		0			0
$45$	1.44010	−	3.92428i	0.0320023	−	0.0872062i
$46$		0			0
$47$	−5.51742	−	15.1590i	−0.117392	−	0.322531i	0.867055	−	0.498212i	$-0.166010\pi$
$47$	−5.51742	−	15.1590i	−0.117392	−	0.322531i	−0.984447	+	0.175680i	$0.943788\pi$
$48$		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	$0.253166\pi$
$53$			75.6950i			1.42821i	−0.700040	+	0.714104i	$0.746834\pi$
$54$		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	0.586767	−	0.809756i	$-0.300400\pi$
$59$	−18.4421	−	21.9784i	−0.312578	−	0.372516i	−0.899345	+	0.437240i	$0.855956\pi$
$60$		0			0
$61$	−55.9422	+	20.3613i	−0.917085	+	0.333792i	−0.757078	−	0.653324i	$-0.773374\pi$
$61$	−55.9422	+	20.3613i	−0.917085	+	0.333792i	−0.160007	+	0.987116i	$0.551152\pi$
$62$		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	0.939779	−	0.341784i	$-0.111031\pi$
$67$	−4.03483	−	22.8827i	−0.0602214	−	0.341532i	−1.00000		0.000251397i	$0.999920\pi$
$68$		0			0
$69$	−9.49246	+	7.94372i	−0.137572	+	0.115126i
$70$		0			0
$71$	−32.2368	+	18.6119i	−0.454039	+	0.262139i	−0.709534	−	0.704671i	$-0.751095\pi$
$71$	−32.2368	+	18.6119i	−0.454039	+	0.262139i	0.255496	+	0.966810i	$0.417761\pi$
$72$		0			0
$73$	−26.0280	+	45.0817i	−0.356547	+	0.617558i	−0.987382	−	0.158360i	$-0.949380\pi$
$73$	−26.0280	+	45.0817i	−0.356547	+	0.617558i	0.630834	+	0.775918i	$0.282713\pi$
$74$		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	0.502722	+	0.864448i	$0.332332\pi$
$79$	−20.9619	+	118.881i	−0.265341	+	1.50482i	−0.768063	+	0.640374i	$0.778779\pi$
$80$		0			0
$81$	−40.8710	+	69.9325i	−0.504581	+	0.863364i
$82$		0			0
$83$	115.091	+	20.2937i	1.38664	+	0.244502i	0.816642	−	0.577145i	$-0.195833\pi$
$83$	115.091	+	20.2937i	1.38664	+	0.244502i	0.569997	+	0.821647i	$0.306944\pi$
$84$		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	−0.338985	−	0.940792i	$-0.610084\pi$
$89$	−117.767	−	67.9930i	−1.32323	−	0.763966i	−0.984242	+	0.176826i	$0.943417\pi$
$90$		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	0.188731	−	0.982029i	$-0.439563\pi$
$97$	−72.3238	−	60.6869i	−0.745606	−	0.625638i	−0.934337	+	0.356391i	$0.884007\pi$
$98$		0			0
$99$	−141.012	−	25.2495i	−1.42436	−	0.255046i
$100$		0			0
$101$	52.1346	+	143.239i	0.516184	+	1.41820i	0.874693	+	0.484678i	$0.161063\pi$
$101$	52.1346	+	143.239i	0.516184	+	1.41820i	−0.358509	+	0.933526i	$0.616715\pi$
$102$		0			0
$103$	16.6643	−	13.9830i	0.161790	−	0.135758i	−0.558299	−	0.829640i	$-0.688546\pi$
$103$	16.6643	−	13.9830i	0.161790	−	0.135758i	0.720088	+	0.693882i	$0.244101\pi$
$104$		0			0
$105$	−7.50710	−	13.0425i	−0.0714962	−	0.124215i
$106$		0			0
$107$		−	49.8431i		−	0.465823i	−0.972498	−	0.232912i	$-0.925175\pi$
$107$		−	49.8431i		−	0.465823i	0.972498	−	0.232912i	$-0.0748253\pi$
$108$		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	0.869290	−	0.494303i	$-0.164577\pi$
$113$	26.1647	+	31.1819i	0.231546	+	0.275946i	−0.637744	+	0.770249i	$0.720132\pi$
$114$		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	−0.961634	−	0.274336i	$-0.911542\pi$
$127$	−30.8908	+	53.5044i	−0.243235	+	0.421295i	0.718399	+	0.695631i	$0.244875\pi$
$128$		0			0
$129$	36.3695	+	100.338i	0.281934	+	0.777812i
$130$		0			0
$131$	77.3505	−	212.519i	0.590462	−	1.62228i	−0.179189	−	0.983815i	$-0.557347\pi$
$131$	77.3505	−	212.519i	0.590462	−	1.62228i	0.769651	−	0.638465i	$-0.220430\pi$
$132$		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	−0.401519	−	0.915851i	$-0.631518\pi$
$137$	−149.613	−	26.3808i	−1.09206	−	0.192560i	−0.690544	+	0.723290i	$0.742629\pi$
$138$		0			0
$139$	159.710	+	58.1298i	1.14899	+	0.418200i	0.845154	−	0.534523i	$-0.179509\pi$
$139$	159.710	+	58.1298i	1.14899	+	0.418200i	0.303841	+	0.952723i	$0.401731\pi$
$140$		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	−0.730524	−	0.682887i	$-0.760724\pi$
$149$	−176.331	+	31.0919i	−1.18343	+	0.208671i	−0.452907	+	0.891558i	$0.649613\pi$
$150$		0			0
$151$	92.0549	+	77.2432i	0.609635	+	0.511544i	0.894526	−	0.447015i	$-0.147513\pi$
$151$	92.0549	+	77.2432i	0.609635	+	0.511544i	−0.284891	+	0.958560i	$0.591958\pi$
$152$		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	−0.559760	−	0.828655i	$-0.689107\pi$
$157$	24.9795	−	20.9603i	0.159105	−	0.133505i	0.718865	+	0.695150i	$0.244662\pi$
$158$		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	0.947313	−	0.320310i	$-0.103787\pi$
$167$	78.0508	+	93.0173i	0.467370	+	0.556990i	−0.479943	+	0.877300i	$0.659343\pi$
$168$		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	−0.890154	−	0.455659i	$-0.849404\pi$
$173$	−49.6240	+	59.1396i	−0.286844	+	0.341847i	0.603310	+	0.797506i	$0.293848\pi$
$174$		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	−0.814151	−	0.580653i	$-0.802797\pi$
$179$	−128.588	+	74.2402i	−0.718367	+	0.414750i	0.0957841	+	0.995402i	$0.469464\pi$
$180$		0			0
$181$	42.2135	−	73.1159i	0.233224	−	0.403955i	−0.725531	−	0.688189i	$-0.758406\pi$
$181$	42.2135	−	73.1159i	0.233224	−	0.403955i	0.958755	+	0.284234i	$0.0917393\pi$
$182$		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	0.168605	−	0.985684i	$-0.446074\pi$
$191$	−1.92568	−	0.339550i	−0.0100821	−	0.00177775i	−0.178687	+	0.983906i	$0.557185\pi$
$192$		0			0
$193$	−311.970	−	113.548i	−1.61643	−	0.588331i	−0.633731	−	0.773554i	$-0.718477\pi$
$193$	−311.970	−	113.548i	−1.61643	−	0.588331i	−0.982697	+	0.185223i	$0.940699\pi$
$194$		0			0
$195$	23.5234	−	8.52655i	0.120633	−	0.0437259i
$196$		0			0
$197$	−213.145	−	123.059i	−1.08195	−	0.624666i	−0.150531	−	0.988605i	$-0.548098\pi$
$197$	−213.145	−	123.059i	−1.08195	−	0.624666i	−0.931423	+	0.363939i	$0.881432\pi$
$198$		0			0
$199$	−138.226	−	239.415i	−0.694604	−	1.20309i	−0.970314	−	0.241849i	$-0.922246\pi$
$199$	−138.226	−	239.415i	−0.694604	−	1.20309i	0.275710	−	0.961241i	$-0.411087\pi$
$200$		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	−0.734308	−	0.678816i	$-0.762493\pi$
$211$	−40.7896	+	34.2265i	−0.193316	+	0.162211i	0.540992	+	0.841027i	$0.318049\pi$
$212$		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	−0.103159	−	0.994665i	$-0.532895\pi$
$223$	101.950	−	37.1068i	0.457175	−	0.166398i	0.560334	+	0.828267i	$0.310673\pi$
$224$		0			0
$225$	209.808	−	75.7350i	0.932479	−	0.336600i
$226$		0			0
$227$	−232.991	+	277.668i	−1.02639	+	1.22321i	−0.0519295	+	0.998651i	$0.516537\pi$
$227$	−232.991	+	277.668i	−1.02639	+	1.22321i	−0.974462	+	0.224554i	$0.927907\pi$
$228$		0			0
$229$	−50.2795	−	285.149i	−0.219561	−	1.24519i	−0.872814	−	0.488054i	$-0.837707\pi$
$229$	−50.2795	−	285.149i	−0.219561	−	1.24519i	0.653252	−	0.757140i	$-0.273404\pi$
$230$		0			0
$231$	−395.504	+	330.976i	−1.71214	+	1.43279i
$232$		0			0
$233$	127.663	−	73.7062i	0.547910	−	0.316336i	−0.200369	−	0.979721i	$-0.564214\pi$
$233$	127.663	−	73.7062i	0.547910	−	0.316336i	0.748279	+	0.663385i	$0.230881\pi$
$234$		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	−0.949065	−	0.315082i	$-0.897968\pi$
$239$	−4.66249	+	12.8101i	−0.0195083	+	0.0535987i	0.929556	+	0.368680i	$0.120190\pi$
$240$		0			0
$241$	−51.5844	+	292.550i	−0.214043	+	1.21390i	0.668516	+	0.743698i	$0.266930\pi$
$241$	−51.5844	+	292.550i	−0.214043	+	1.21390i	−0.882559	+	0.470201i	$0.844181\pi$
$242$		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	0.499636	−	0.866236i	$-0.333467\pi$
$251$	−0.182848	−	0.105567i	−0.000728476	−	0.000420586i	−0.500364	+	0.865815i	$0.666801\pi$
$252$		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	0.210720	−	0.977546i	$-0.432419\pi$
$257$	190.970	−	33.6731i	0.743073	−	0.131024i	0.532353	+	0.846523i	$0.321308\pi$
$258$		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	−0.857056	−	0.515224i	$-0.827709\pi$
$263$	−139.835	−	384.194i	−0.531692	−	1.46081i	0.325363	−	0.945589i	$-0.394513\pi$
$264$		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	$-0.928344\pi$
$269$		−	120.090i		−	0.446433i	0.974769	−	0.223216i	$-0.0716557\pi$
$270$		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	0.260112	−	0.965578i	$-0.416240\pi$
$277$	299.169	−	108.889i	1.08003	−	0.393099i	0.819919	+	0.572479i	$0.194018\pi$
$278$		0			0
$279$	−10.8504	−	62.5035i	−0.0388904	−	0.224027i
$280$		0			0
$281$	−154.692	+	184.354i	−0.550504	+	0.656065i	−0.967508	−	0.252839i	$-0.918636\pi$
$281$	−154.692	+	184.354i	−0.550504	+	0.656065i	0.417004	+	0.908905i	$0.363080\pi$
$282$		0			0
$283$	15.5135	+	87.9813i	0.0548179	+	0.310888i	0.999872	−	0.0160274i	$-0.00510189\pi$
$283$	15.5135	+	87.9813i	0.0548179	+	0.310888i	−0.945054	+	0.326915i	$0.893991\pi$
$284$		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	−0.614127	−	0.789207i	$-0.710492\pi$
$293$	106.539	−	292.713i	0.363614	−	0.999022i	0.977741	−	0.209814i	$-0.0672860\pi$
$294$		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	−0.704858	−	0.709348i	$-0.748989\pi$
$307$	−296.790	−	514.055i	−0.966743	−	1.67445i	−0.261885	−	0.965099i	$-0.584344\pi$
$308$		0			0
$309$	−64.2847	+	11.2474i	−0.208041	+	0.0363992i
$310$		0			0
$311$	−538.372	+	94.9296i	−1.73110	+	0.305240i	−0.948381	−	0.317134i	$-0.897280\pi$
$311$	−538.372	+	94.9296i	−1.73110	+	0.305240i	−0.782720	+	0.622374i	$0.786168\pi$
$312$		0			0
$313$	119.991	+	100.684i	0.383357	+	0.321675i	0.814019	−	0.580839i	$-0.197275\pi$
$313$	119.991	+	100.684i	0.383357	+	0.321675i	−0.430662	+	0.902513i	$0.641720\pi$
$314$		0			0
$315$	−0.119583	+	45.1461i	−0.000379629	+	0.143321i
$316$		0			0
$317$	−14.4734	−	39.7653i	−0.0456574	−	0.125443i	0.914768	−	0.403979i	$-0.132373\pi$
$317$	−14.4734	−	39.7653i	−0.0456574	−	0.125443i	−0.960426	+	0.278536i	$0.910151\pi$
$318$		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	0.469691	−	0.882831i	$-0.344365\pi$
$331$	462.396	−	168.298i	1.39697	−	0.508455i	0.927277	+	0.374376i	$0.122143\pi$
$332$		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	0.401296	+	0.915948i	$0.368560\pi$
$337$	113.729	+	644.988i	0.337474	+	1.91391i	−0.0638222	+	0.997961i	$0.520329\pi$
$338$		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	−0.987140	−	0.159859i	$-0.948896\pi$
$347$	−44.4825	+	122.215i	−0.128192	+	0.352204i	0.858948	+	0.512062i	$0.171118\pi$
$348$		0			0
$349$	14.3449	−	81.3537i	0.0411027	−	0.233105i	−0.957335	−	0.288980i	$-0.906684\pi$
$349$	14.3449	−	81.3537i	0.0411027	−	0.233105i	0.998438	+	0.0558751i	$0.0177949\pi$
$350$		0			0
$351$	−477.802	+	82.2934i	−1.36126	+	0.234454i
$352$		0			0
$353$	−65.5878	−	11.5649i	−0.185801	−	0.0327618i	0.0799732	−	0.996797i	$-0.474517\pi$
$353$	−65.5878	−	11.5649i	−0.185801	−	0.0327618i	−0.265774	+	0.964035i	$0.585628\pi$
$354$		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	0.845821	−	0.533466i	$-0.179111\pi$
$359$	289.619	+	167.211i	0.806737	+	0.465770i	−0.0390844	+	0.999236i	$0.512444\pi$
$360$		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	0.960366	−	0.278742i	$-0.0899175\pi$
$367$	312.913	+	262.565i	0.852624	+	0.715437i	−0.107742	+	0.994179i	$0.534362\pi$
$368$		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	−0.900787	−	0.434262i	$-0.857009\pi$
$373$	−234.819	+	197.037i	−0.629543	+	0.528249i	0.271244	+	0.962511i	$0.412565\pi$
$374$		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	0.999972	+	0.00748907i	$0.00238387\pi$
$383$	319.309	+	380.537i	0.833704	+	0.993570i	−0.166268	+	0.986081i	$0.553172\pi$
$384$		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	−0.213608	−	0.976920i	$-0.568521\pi$
$389$	305.584	−	364.181i	0.785563	−	0.936197i	0.999171	+	0.0407223i	$0.0129659\pi$
$390$		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	0.451804	+	0.892117i	$0.350781\pi$
$397$	−217.038	+	375.920i	−0.546694	+	0.946902i	−0.998498	+	0.0547849i	$0.982553\pi$
$398$		0			0
$399$	74.2024	−	88.1935i	0.185971	−	0.221036i
$400$		0			0
$401$	84.0625	−	230.960i	0.209632	−	0.575960i	−0.789661	−	0.613543i	$-0.789744\pi$
$401$	84.0625	−	230.960i	0.209632	−	0.575960i	0.999294	+	0.0375831i	$0.0119659\pi$
$402$		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	−0.0924633	−	0.995716i	$-0.529474\pi$
$409$	−328.561	−	119.587i	−0.803328	−	0.292388i	−0.710865	+	0.703329i	$0.751696\pi$
$410$		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	−0.487978	−	0.872856i	$-0.662265\pi$
$419$	−271.509	+	47.8743i	−0.647993	+	0.114259i	−0.160015	+	0.987115i	$0.551154\pi$
$420$		0			0
$421$	50.0550	+	42.0012i	0.118896	+	0.0997652i	0.700297	−	0.713852i	$-0.253051\pi$
$421$	50.0550	+	42.0012i	0.118896	+	0.0997652i	−0.581401	+	0.813617i	$0.697495\pi$
$422$		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	$-0.960941\pi$
$431$		−	105.508i		−	0.244799i	0.992481	−	0.122399i	$-0.0390589\pi$
$432$		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	−0.272897	−	0.962043i	$-0.587982\pi$
$439$	59.8973	−	21.8008i	0.136440	−	0.0496602i	0.409338	+	0.912383i	$0.365760\pi$
$440$		0			0
$441$	571.508	+	209.728i	1.29594	+	0.475574i
$442$		0			0
$443$	−85.6046	+	102.020i	−0.193238	+	0.230292i	−0.853960	−	0.520338i	$-0.825806\pi$
$443$	−85.6046	+	102.020i	−0.193238	+	0.230292i	0.660722	+	0.750631i	$0.270250\pi$
$444$		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	−0.628132	−	0.778106i	$-0.716180\pi$
$449$	−120.484	+	69.5615i	−0.268339	+	0.154925i	0.359794	+	0.933032i	$0.382847\pi$
$450$		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	−0.999129	−	0.0417393i	$-0.986710\pi$
$457$	−21.0125	+	119.168i	−0.0459792	+	0.260761i	0.953149	+	0.302500i	$0.0978212\pi$
$458$		0			0
$459$	350.556	+	612.791i	0.763739	+	1.33506i
$460$		0			0
$461$	−266.202	−	46.9386i	−0.577445	−	0.101819i	−0.122705	−	0.992443i	$-0.539157\pi$
$461$	−266.202	−	46.9386i	−0.577445	−	0.101819i	−0.454740	+	0.890624i	$0.650268\pi$
$462$		0			0
$463$	16.9878	+	6.18304i	0.0366906	+	0.0133543i	0.360300	−	0.932836i	$-0.382674\pi$
$463$	16.9878	+	6.18304i	0.0366906	+	0.0133543i	−0.323610	+	0.946191i	$0.604896\pi$
$464$		0			0
$465$	1.71831	−	9.67012i	0.00369529	−	0.0207960i
$466$		0			0
$467$	−439.219	−	253.583i	−0.940511	−	0.543004i	−0.0503903	−	0.998730i	$-0.516047\pi$
$467$	−439.219	−	253.583i	−0.940511	−	0.543004i	−0.890120	+	0.455725i	$0.849380\pi$
$468$		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	0.940335	+	0.340251i	$0.110512\pi$
$479$	210.140	+	577.355i	0.438705	+	1.20533i	−0.501629	+	0.865083i	$0.667266\pi$
$480$		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	0.619039	−	0.785360i	$-0.287522\pi$
$491$	−128.585	−	153.242i	−0.261885	−	0.312102i	−0.880924	+	0.473258i	$0.843078\pi$
$492$		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	0.952755	−	0.303741i	$-0.0982358\pi$
$499$	−23.1673	−	131.388i	−0.0464274	−	0.263303i	−0.999182	+	0.0404381i	$0.987125\pi$
$500$		0			0
$501$	−62.7808	−	358.826i	−0.125311	−	0.716219i
$502$		0			0
$503$	156.930	−	90.6037i	0.311989	−	0.180127i	−0.335827	−	0.941924i	$-0.609016\pi$
$503$	156.930	−	90.6037i	0.311989	−	0.180127i	0.647816	+	0.761797i	$0.275683\pi$
$504$		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	−0.332567	−	0.943080i	$-0.607915\pi$
$509$	268.953	−	738.941i	0.528394	−	1.45175i	0.860961	−	0.508671i	$-0.169863\pi$
$510$		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	0.328406	−	0.944537i	$-0.393489\pi$
$521$	−169.525	−	97.8752i	−0.325384	−	0.187860i	−0.653790	+	0.756676i	$0.726822\pi$
$522$		0			0
$523$	−79.9831	−	138.535i	−0.152931	−	0.264885i	0.779373	−	0.626561i	$-0.215538\pi$
$523$	−79.9831	−	138.535i	−0.152931	−	0.264885i	−0.932304	+	0.361676i	$0.882205\pi$
$524$		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	−0.0717647	−	0.997422i	$-0.522863\pi$
$547$	281.372	−	102.411i	0.514391	−	0.187223i	0.586155	+	0.810199i	$0.300641\pi$
$548$		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	−0.967393	−	0.253282i	$-0.918490\pi$
$557$	−686.079	+	396.108i	−1.23174	+	0.711146i	−0.264348	+	0.964427i	$0.585157\pi$
$558$		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	0.166634	+	0.986019i	$0.446710\pi$
$563$	−334.881	+	920.079i	−0.594816	+	1.63424i	−0.761450	+	0.648224i	$0.775512\pi$
$564$		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	−0.333979	−	0.942580i	$-0.608392\pi$
$569$	−552.043	−	97.3401i	−0.970199	−	0.171072i	−0.636219	+	0.771508i	$0.719503\pi$
$570$		0			0
$571$	−29.2223	−	10.6361i	−0.0511775	−	0.0186271i	0.316305	−	0.948658i	$-0.397558\pi$
$571$	−29.2223	−	10.6361i	−0.0511775	−	0.0186271i	−0.367482	+	0.930031i	$0.619780\pi$
$572$		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	0.771689	−	0.636000i	$-0.219412\pi$
$577$	−95.1751	−	164.848i	−0.164948	−	0.285699i	−0.936637	+	0.350302i	$0.886079\pi$
$578$		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	−0.999337	−	0.0363972i	$-0.988412\pi$
$587$	−150.974	−	414.798i	−0.257196	−	0.706641i	0.742141	−	0.670244i	$-0.233810\pi$
$588$		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	$0.119725\pi$
$593$			435.642i			0.734640i	−0.930095	+	0.367320i	$0.880275\pi$
$594$		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	−0.974180	−	0.225771i	$-0.927510\pi$
$599$	−615.387	−	733.389i	−1.02736	−	1.22436i	−0.0531765	−	0.998585i	$-0.516935\pi$
$600$		0			0
$601$	−214.739	+	78.1585i	−0.357302	+	0.130047i	−0.514433	−	0.857530i	$-0.671998\pi$
$601$	−214.739	+	78.1585i	−0.357302	+	0.130047i	0.157131	+	0.987578i	$0.449775\pi$
$602$		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	0.998081	−	0.0619256i	$-0.0197241\pi$
$607$	23.6802	+	134.297i	0.0390118	+	0.221247i	−0.959069	+	0.283173i	$0.908613\pi$
$608$		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	−0.893579	−	0.448906i	$-0.851814\pi$
$613$	−35.5694	+	61.6081i	−0.0580252	+	0.100503i	0.835554	+	0.549409i	$0.185147\pi$
$614$		0			0
$615$	−20.6759	−	57.0415i	−0.0336194	−	0.0927505i
$616$		0			0
$617$	−348.112	+	956.431i	−0.564201	+	1.55013i	0.249215	+	0.968448i	$0.419828\pi$
$617$	−348.112	+	956.431i	−0.564201	+	1.55013i	−0.813416	+	0.581682i	$0.802395\pi$
$618$		0			0
$619$	63.4363	−	359.765i	0.102482	−	0.581204i	−0.889714	−	0.456518i	$-0.849097\pi$
$619$	63.4363	−	359.765i	0.102482	−	0.581204i	0.992196	−	0.124686i	$-0.0397924\pi$
$620$		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	0.989777	+	0.142626i	$0.0455546\pi$
$631$	390.214	+	675.871i	0.618406	+	1.07111i	−0.371371	+	0.928485i	$0.621112\pi$
$632$		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	0.841370	−	0.540459i	$-0.181749\pi$
$641$	−96.5071	−	265.151i	−0.150557	−	0.413652i	−0.991927	+	0.126807i	$0.959527\pi$
$642$		0			0
$643$	−32.0195	+	26.8675i	−0.0497970	+	0.0417846i	−0.667346	−	0.744747i	$-0.732570\pi$
$643$	−32.0195	+	26.8675i	−0.0497970	+	0.0417846i	0.617549	+	0.786532i	$0.288126\pi$
$644$		0			0
$645$	24.8420	−	42.8963i	0.0385147	−	0.0665059i
$646$		0			0
$647$			383.618i			0.592918i	0.955046	+	0.296459i	$0.0958058\pi$
$647$			383.618i			0.592918i	−0.955046	+	0.296459i	$0.904194\pi$
$648$		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	0.795352	−	0.606147i	$-0.207286\pi$
$653$	39.3773	+	46.9281i	0.0603022	+	0.0718653i	−0.735050	+	0.678013i	$0.762841\pi$
$654$		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	−0.955765	−	0.294130i	$-0.904970\pi$
$659$	−329.590	+	392.790i	−0.500137	+	0.596040i	0.455629	+	0.890170i	$0.349415\pi$
$660$		0			0
$661$	−33.1600	−	188.060i	−0.0501664	−	0.284508i	0.949396	−	0.314081i	$-0.101696\pi$
$661$	−33.1600	−	188.060i	−0.0501664	−	0.284508i	−0.999563	+	0.0295731i	$0.990585\pi$
$662$		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	0.494214	+	0.869340i	$0.335456\pi$
$673$	−180.046	+	1021.09i	−0.267527	+	1.51722i	−0.761741	+	0.647882i	$0.775655\pi$
$674$		0			0
$675$	−658.542	−	118.819i	−0.975618	−	0.176027i
$676$		0			0
$677$	482.182	+	85.0218i	0.712234	+	0.125586i	0.518014	−	0.855372i	$-0.326671\pi$
$677$	482.182	+	85.0218i	0.712234	+	0.125586i	0.194220	+	0.980958i	$0.437782\pi$
$678$		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	0.672540	−	0.740061i	$-0.265204\pi$
$683$	251.274	+	145.073i	0.367897	+	0.212406i	−0.304642	+	0.952467i	$0.598537\pi$
$684$		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	0.744012	−	0.668166i	$-0.232921\pi$
$691$	148.698	+	124.773i	0.215193	+	0.180568i	−0.528819	+	0.848735i	$0.677365\pi$
$692$		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	$-0.932570\pi$
$701$		−	294.780i		−	0.420513i	0.977646	−	0.210257i	$-0.0674299\pi$
$702$		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	0.397626	−	0.917548i	$-0.369834\pi$
$709$	916.038	−	333.410i	1.29201	−	0.470255i	0.894387	+	0.447293i	$0.147612\pi$
$710$		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	−0.843068	−	0.537807i	$-0.819253\pi$
$719$	−574.371	+	331.613i	−0.798848	+	0.461215i	0.0442205	+	0.999022i	$0.485920\pi$
$720$		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	0.572836	+	0.819670i	$0.305843\pi$
$727$	−178.695	+	1013.43i	−0.245797	+	1.39399i	−0.818633	+	0.574316i	$0.805268\pi$
$728$		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	0.277462	−	0.960737i	$-0.410507\pi$
$733$	−93.4865	−	34.0263i	−0.127540	−	0.0464206i	−0.405001	+	0.914316i	$0.632729\pi$
$734$		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	0.884853	−	0.465870i	$-0.154259\pi$
$739$	28.7996	+	49.8824i	0.0389710	+	0.0674998i	−0.845882	+	0.533370i	$0.820925\pi$
$740$		0			0
$741$	122.985	+	146.963i	0.165972	+	0.198330i
$742$		0			0
$743$	1203.21	−	212.158i	1.61939	−	0.285543i	0.710853	−	0.703340i	$-0.248309\pi$
$743$	1203.21	−	212.158i	1.61939	−	0.285543i	0.908540	+	0.417798i	$0.137198\pi$
$744$		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	−0.124912	−	0.992168i	$-0.539865\pi$
$751$	623.699	−	523.346i	0.830492	−	0.696865i	0.955404	+	0.295302i	$0.0954204\pi$
$752$		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	0.671682	−	0.740840i	$-0.265572\pi$
$761$	−132.824	−	158.293i	−0.174539	−	0.208007i	−0.846221	+	0.532832i	$0.821128\pi$
$762$		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	0.997581	−	0.0695149i	$-0.0221451\pi$
$769$	27.9808	+	158.687i	0.0363860	+	0.206355i	−0.961195	+	0.275870i	$0.911034\pi$
$770$		0			0
$771$	−546.400	−	199.693i	−0.708689	−	0.259005i
$772$		0			0
$773$	−769.088	+	444.033i	−0.994940	+	0.574429i	−0.906747	−	0.421675i	$-0.861442\pi$
$773$	−769.088	+	444.033i	−0.994940	+	0.574429i	−0.0881925	+	0.996103i	$0.528109\pi$
$774$		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	−0.489876	−	0.871792i	$-0.662958\pi$
$787$	−1121.88	−	408.332i	−1.42552	−	0.518847i	−0.935644	+	0.352945i	$0.885180\pi$
$788$		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	0.134202	−	0.990954i	$-0.457153\pi$
$797$	477.592	−	84.2124i	0.599237	−	0.105662i	0.465035	+	0.885292i	$0.346042\pi$
$798$		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	$-0.715674\pi$
$809$		−	1260.59i		−	1.55821i	0.626893	−	0.779105i	$-0.284326\pi$
$810$		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	−0.264507	−	0.964384i	$-0.585209\pi$
$821$	600.280	−	715.385i	0.731157	−	0.871359i	0.995664	+	0.0930252i	$0.0296537\pi$
$822$		0			0
$823$	−7.57884	−	42.9817i	−0.00920880	−	0.0522257i	0.979857	−	0.199700i	$-0.0639967\pi$
$823$	−7.57884	−	42.9817i	−0.00920880	−	0.0522257i	−0.989066	+	0.147474i	$0.952886\pi$
$824$		0			0
$825$	−203.967	−	1165.78i	−0.247233	−	1.41307i
$826$		0			0
$827$	620.289	−	358.124i	0.750047	−	0.433040i	−0.0756636	−	0.997133i	$-0.524108\pi$
$827$	620.289	−	358.124i	0.750047	−	0.433040i	0.825711	+	0.564093i	$0.190774\pi$
$828$		0			0
$829$	−151.869	+	263.044i	−0.183195	+	0.317303i	−0.942967	−	0.332887i	$-0.891977\pi$
$829$	−151.869	+	263.044i	−0.183195	+	0.317303i	0.759772	+	0.650190i	$0.225311\pi$
$830$		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	0.489674	−	0.871905i	$-0.337116\pi$
$839$	546.700	+	96.3979i	0.651609	+	0.114896i	0.161934	+	0.986802i	$0.448227\pi$
$840$		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	0.752351	−	0.658763i	$-0.228920\pi$
$853$	199.807	+	167.658i	0.234241	+	0.196551i	−0.518110	+	0.855314i	$0.673364\pi$
$854$		0			0
$855$	−9.52807	−	11.4164i	−0.0111439	−	0.0133525i
$856$		0			0
$857$	123.417	+	339.084i	0.144010	+	0.395664i	0.990637	−	0.136523i	$-0.0435926\pi$
$857$	123.417	+	339.084i	0.144010	+	0.395664i	−0.846627	+	0.532187i	$0.821370\pi$
$858$		0			0
$859$	−439.289	+	368.607i	−0.511396	+	0.429112i	−0.861620	−	0.507554i	$-0.830550\pi$
$859$	−439.289	+	368.607i	−0.511396	+	0.429112i	0.350224	+	0.936666i	$0.386105\pi$
$860$		0			0
$861$	−1410.82	−	1.86849i	−1.63858	−	0.00217014i
$862$		0			0
$863$		−	654.390i		−	0.758273i	−0.925341	−	0.379137i	$-0.876221\pi$
$863$		−	654.390i		−	0.758273i	0.925341	−	0.379137i	$-0.123779\pi$
$864$		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	0.954630	+	0.297794i	$0.0962508\pi$
$877$	139.814	+	792.923i	0.159423	+	0.904131i	−0.795208	+	0.606337i	$0.792638\pi$
$878$		0			0
$879$	−716.661	+	599.735i	−0.815314	+	0.682292i
$880$		0			0
$881$	1043.53	−	602.480i	1.18448	−	0.683860i	0.227433	−	0.973794i	$-0.426967\pi$
$881$	1043.53	−	602.480i	1.18448	−	0.683860i	0.957047	+	0.289934i	$0.0936334\pi$
$882$		0			0
$883$	−378.383	+	655.379i	−0.428520	+	0.742219i	−0.996742	−	0.0806566i	$-0.974298\pi$
$883$	−378.383	+	655.379i	−0.428520	+	0.742219i	0.568222	+	0.822876i	$0.307632\pi$
$884$		0			0
$885$	25.7376	−	30.5905i	0.0290820	−	0.0345655i
$886$		0			0
$887$	−209.428	+	575.399i	−0.236108	+	0.648703i	0.763886	+	0.645351i	$0.223289\pi$
$887$	−209.428	+	575.399i	−0.236108	+	0.648703i	−0.999994	+	0.00335135i	$0.998933\pi$
$888$		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	0.976295	+	0.216445i	$0.0694460\pi$
$907$	1232.60	+	1034.27i	1.35898	+	1.14032i	0.382688	+	0.923878i	$0.374998\pi$
$908$		0			0
$909$	−884.610	+	1048.58i	−0.973168	+	1.15356i
$910$		0			0
$911$	−471.470	−	1295.35i	−0.517530	−	1.42190i	−0.873233	−	0.487303i	$-0.837981\pi$
$911$	−471.470	−	1295.35i	−0.517530	−	1.42190i	0.355703	−	0.934599i	$-0.384241\pi$
$912$		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	−0.730874	−	0.682512i	$-0.760888\pi$
$929$	63.3425	−	75.4887i	0.0681836	−	0.0812580i	0.799058	+	0.601254i	$0.205332\pi$
$930$		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	−0.676527	−	0.736417i	$-0.736516\pi$
$937$	280.625	−	486.056i	0.299493	−	0.518736i	0.976020	+	0.217681i	$0.0698493\pi$
$938$		0			0
$939$	−160.134	−	441.784i	−0.170537	−	0.470483i
$940$		0			0
$941$	−253.931	+	697.670i	−0.269852	+	0.741414i	0.728554	+	0.684988i	$0.240193\pi$
$941$	−253.931	+	697.670i	−0.269852	+	0.741414i	−0.998407	+	0.0564255i	$0.982030\pi$
$942$		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	−0.0476602	−	0.998864i	$-0.515176\pi$
$947$	−411.072	−	72.4830i	−0.434078	−	0.0765396i	−0.386417	+	0.922324i	$0.626288\pi$
$948$		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	0.727728	−	0.685866i	$-0.240576\pi$
$953$	474.227	+	273.795i	0.497615	+	0.287298i	−0.230113	+	0.973164i	$0.573910\pi$
$954$		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	−0.774000	−	0.633186i	$-0.781747\pi$
$967$	−275.438	+	231.120i	−0.284838	+	0.239007i	0.489162	+	0.872193i	$0.337303\pi$
$968$		0			0
$969$	139.840	−	241.470i	0.144313	−	0.249195i
$970$		0			0
$971$		−	842.963i		−	0.868139i	−0.900879	−	0.434069i	$-0.857077\pi$
$971$		−	842.963i		−	0.868139i	0.900879	−	0.434069i	$-0.142923\pi$
$972$		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	0.248594	−	0.968608i	$-0.420032\pi$
$977$	−731.252	−	871.472i	−0.748467	−	0.891988i	−0.997060	+	0.0766199i	$0.975587\pi$
$978$		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	−0.981890	−	0.189451i	$-0.939329\pi$
$983$	−614.192	+	731.965i	−0.624813	+	0.744624i	0.357077	+	0.934075i	$0.383773\pi$
$984$		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	−0.210200	−	0.977658i	$-0.567412\pi$
$991$	734.903	−	1272.89i	0.741577	−	1.28445i	0.951777	−	0.306791i	$-0.0992551\pi$
$992$		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	−0.669334	−	0.742962i	$-0.733420\pi$
$997$	213.101	−	1208.56i	0.213742	−	1.21219i	0.883076	−	0.469230i	$-0.155468\pi$
$998$		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.29.2	✓	36
3.2	odd	2		324.3.k.a.89.4		36
4.3	odd	2		432.3.bc.b.353.5		36
27.11	odd	18		2916.3.c.b.1457.20		36
27.13	even	9		324.3.k.a.233.4		36
27.14	odd	18	inner	108.3.k.a.41.2	yes	36
27.16	even	9		2916.3.c.b.1457.17		36
108.95	even	18		432.3.bc.b.257.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.2	✓	36	1.1	even	1	trivial
108.3.k.a.41.2	yes	36	27.14	odd	18	inner
324.3.k.a.89.4		36	3.2	odd	2
324.3.k.a.233.4		36	27.13	even	9
432.3.bc.b.257.5		36	108.95	even	18
432.3.bc.b.353.5		36	4.3	odd	2
2916.3.c.b.1457.17		36	27.16	even	9
2916.3.c.b.1457.20		36	27.11	odd	18

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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