LMFDB - Embedded newform 108.3.k.a.41.6

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			41.6
Character	$\chi$	$=$	108.41
Dual form			108.3.k.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.88785 - 0.812609i) q^{3} +(0.980262 - 1.16823i) q^{5} +(3.23920 + 1.17897i) q^{7} +(7.67933 - 4.69338i) q^{9} +O(q^{10})$	\(q+(2.88785 - 0.812609i) q^{3} +(0.980262 - 1.16823i) q^{5} +(3.23920 + 1.17897i) q^{7} +(7.67933 - 4.69338i) q^{9} +(-3.21124 - 3.82701i) q^{11} +(-0.778815 + 4.41688i) q^{13} +(1.88153 - 4.17024i) q^{15} +(-3.57252 - 2.06259i) q^{17} +(6.75637 + 11.7024i) q^{19} +(10.3124 + 0.772492i) q^{21} +(-5.79885 - 15.9322i) q^{23} +(3.93735 + 22.3298i) q^{25} +(18.3629 - 19.7941i) q^{27} +(-47.1200 + 8.30853i) q^{29} +(-14.3439 + 5.22075i) q^{31} +(-12.3834 - 8.44233i) q^{33} +(4.55258 - 2.62843i) q^{35} +(-32.3836 + 56.0901i) q^{37} +(1.34010 + 13.3882i) q^{39} +(-55.4020 - 9.76887i) q^{41} +(22.7258 - 19.0692i) q^{43} +(2.04481 - 13.5720i) q^{45} +(-7.04255 + 19.3493i) q^{47} +(-28.4337 - 23.8587i) q^{49} +(-11.9930 - 3.05340i) q^{51} +19.8596i q^{53} -7.61868 q^{55} +(29.0208 + 28.3044i) q^{57} +(63.6903 - 75.9031i) q^{59} +(77.5488 + 28.2255i) q^{61} +(30.4083 - 6.14908i) q^{63} +(4.39650 + 5.23954i) q^{65} +(11.2495 - 63.7992i) q^{67} +(-29.6928 - 41.2976i) q^{69} +(109.778 + 63.3803i) q^{71} +(18.0346 + 31.2369i) q^{73} +(29.5159 + 61.2857i) q^{75} +(-5.88991 - 16.1824i) q^{77} +(-14.4798 - 82.1188i) q^{79} +(36.9443 - 72.0841i) q^{81} +(-16.5506 + 2.91831i) q^{83} +(-5.91159 + 2.15164i) q^{85} +(-129.324 + 62.2839i) q^{87} +(66.0425 - 38.1296i) q^{89} +(-7.73012 + 13.3890i) q^{91} +(-37.1806 + 26.7327i) q^{93} +(20.2941 + 3.57840i) q^{95} +(82.1613 - 68.9415i) q^{97} +(-42.6218 - 14.3173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.88785	−	0.812609i	0.962616	−	0.270870i
$3$	2.88785	−	0.812609i	0.962616	−	0.270870i
$4$		0			0
$5$	0.980262	−	1.16823i	0.196052	−	0.233646i	−0.659058	−	0.752092i	$-0.729045\pi$
$5$	0.980262	−	1.16823i	0.196052	−	0.233646i	0.855110	+	0.518446i	$0.173489\pi$
$6$		0			0
$7$	3.23920	+	1.17897i	0.462743	+	0.168425i	0.562862	−	0.826551i	$-0.309700\pi$
$7$	3.23920	+	1.17897i	0.462743	+	0.168425i	−0.100119	+	0.994975i	$0.531922\pi$
$8$		0			0
$9$	7.67933	−	4.69338i	0.853259	−	0.521487i
$10$		0			0
$11$	−3.21124	−	3.82701i	−0.291931	−	0.347910i	0.600067	−	0.799950i	$-0.295141\pi$
$11$	−3.21124	−	3.82701i	−0.291931	−	0.347910i	−0.891997	+	0.452040i	$0.850696\pi$
$12$		0			0
$13$	−0.778815	+	4.41688i	−0.0599089	+	0.339760i	−0.999999	−	0.00116503i	$-0.999629\pi$
$13$	−0.778815	+	4.41688i	−0.0599089	+	0.339760i	0.940090	+	0.340925i	$0.110740\pi$
$14$		0			0
$15$	1.88153	−	4.17024i	0.125436	−	0.278016i
$16$		0			0
$17$	−3.57252	−	2.06259i	−0.210148	−	0.121329i	0.391232	−	0.920292i	$-0.372049\pi$
$17$	−3.57252	−	2.06259i	−0.210148	−	0.121329i	−0.601380	+	0.798963i	$0.705382\pi$
$18$		0			0
$19$	6.75637	+	11.7024i	0.355599	+	0.615915i	0.987220	−	0.159362i	$-0.0509437\pi$
$19$	6.75637	+	11.7024i	0.355599	+	0.615915i	−0.631622	+	0.775277i	$0.717610\pi$
$20$		0			0
$21$	10.3124	+	0.772492i	0.491065	+	0.0367853i
$22$		0			0
$23$	−5.79885	−	15.9322i	−0.252124	−	0.692705i	−0.999596	−	0.0284118i	$-0.990955\pi$
$23$	−5.79885	−	15.9322i	−0.252124	−	0.692705i	0.747472	−	0.664293i	$-0.231267\pi$
$24$		0			0
$25$	3.93735	+	22.3298i	0.157494	+	0.893194i
$26$		0			0
$27$	18.3629	−	19.7941i	0.680106	−	0.733114i
$28$		0			0
$29$	−47.1200	+	8.30853i	−1.62483	+	0.286501i	−0.910562	−	0.413373i	$-0.864351\pi$
$29$	−47.1200	+	8.30853i	−1.62483	+	0.286501i	−0.714267	+	0.699874i	$0.753240\pi$
$30$		0			0
$31$	−14.3439	+	5.22075i	−0.462706	+	0.168411i	−0.562845	−	0.826562i	$-0.690293\pi$
$31$	−14.3439	+	5.22075i	−0.462706	+	0.168411i	0.100139	+	0.994973i	$0.468071\pi$
$32$		0			0
$33$	−12.3834	−	8.44233i	−0.375255	−	0.255828i
$34$		0			0
$35$	4.55258	−	2.62843i	0.130074	−	0.0750981i
$36$		0			0
$37$	−32.3836	+	56.0901i	−0.875233	+	1.51595i	−0.0187185	+	0.999825i	$0.505959\pi$
$37$	−32.3836	+	56.0901i	−0.875233	+	1.51595i	−0.856514	+	0.516123i	$0.827375\pi$
$38$		0			0
$39$	1.34010	+	13.3882i	0.0343614	+	0.343286i
$40$		0			0
$41$	−55.4020	−	9.76887i	−1.35127	−	0.238265i	−0.549297	−	0.835627i	$-0.685104\pi$
$41$	−55.4020	−	9.76887i	−1.35127	−	0.238265i	−0.801972	+	0.597362i	$0.796216\pi$
$42$		0			0
$43$	22.7258	−	19.0692i	0.528507	−	0.443470i	−0.339079	−	0.940758i	$-0.610115\pi$
$43$	22.7258	−	19.0692i	0.528507	−	0.443470i	0.867585	+	0.497288i	$0.165671\pi$
$44$		0			0
$45$	2.04481	−	13.5720i	0.0454402	−	0.301600i
$46$		0			0
$47$	−7.04255	+	19.3493i	−0.149842	+	0.411686i	−0.991791	−	0.127870i	$-0.959186\pi$
$47$	−7.04255	+	19.3493i	−0.149842	+	0.411686i	0.841949	+	0.539557i	$0.181408\pi$
$48$		0			0
$49$	−28.4337	−	23.8587i	−0.580280	−	0.486913i
$50$		0			0
$51$	−11.9930	−	3.05340i	−0.235156	−	0.0598706i
$52$		0			0
$53$			19.8596i			0.374710i	0.982292	+	0.187355i	$0.0599915\pi$
$53$			19.8596i			0.374710i	−0.982292	+	0.187355i	$0.940009\pi$
$54$		0			0
$55$	−7.61868			−0.138522
$56$		0			0
$57$	29.0208	+	28.3044i	0.509138	+	0.496569i
$58$		0			0
$59$	63.6903	−	75.9031i	1.07950	−	1.28649i	0.123746	−	0.992314i	$-0.460509\pi$
$59$	63.6903	−	75.9031i	1.07950	−	1.28649i	0.955750	−	0.294179i	$-0.0950463\pi$
$60$		0			0
$61$	77.5488	+	28.2255i	1.27129	+	0.462713i	0.887543	−	0.460725i	$-0.152411\pi$
$61$	77.5488	+	28.2255i	1.27129	+	0.462713i	0.383749	+	0.923437i	$0.374633\pi$
$62$		0			0
$63$	30.4083	−	6.14908i	0.482671	−	0.0976044i
$64$		0			0
$65$	4.39650	+	5.23954i	0.0676384	+	0.0806083i
$66$		0			0
$67$	11.2495	−	63.7992i	0.167903	−	0.952226i	−0.778117	−	0.628119i	$-0.783825\pi$
$67$	11.2495	−	63.7992i	0.167903	−	0.952226i	0.946020	−	0.324107i	$-0.105064\pi$
$68$		0			0
$69$	−29.6928	−	41.2976i	−0.430331	−	0.598516i
$70$		0			0
$71$	109.778	+	63.3803i	1.54617	+	0.892680i	0.998429	+	0.0560292i	$0.0178440\pi$
$71$	109.778	+	63.3803i	1.54617	+	0.892680i	0.547737	+	0.836650i	$0.315489\pi$
$72$		0			0
$73$	18.0346	+	31.2369i	0.247049	+	0.427902i	0.962706	−	0.270550i	$-0.0872057\pi$
$73$	18.0346	+	31.2369i	0.247049	+	0.427902i	−0.715656	+	0.698453i	$0.753872\pi$
$74$		0			0
$75$	29.5159	+	61.2857i	0.393545	+	0.817142i
$76$		0			0
$77$	−5.88991	−	16.1824i	−0.0764924	−	0.210161i
$78$		0			0
$79$	−14.4798	−	82.1188i	−0.183288	−	1.03948i	−0.928135	−	0.372243i	$-0.878589\pi$
$79$	−14.4798	−	82.1188i	−0.183288	−	1.03948i	0.744847	−	0.667235i	$-0.232522\pi$
$80$		0			0
$81$	36.9443	−	72.0841i	0.456103	−	0.889927i
$82$		0			0
$83$	−16.5506	+	2.91831i	−0.199404	+	0.0351604i	−0.272458	−	0.962168i	$-0.587837\pi$
$83$	−16.5506	+	2.91831i	−0.199404	+	0.0351604i	0.0730538	+	0.997328i	$0.476726\pi$
$84$		0			0
$85$	−5.91159	+	2.15164i	−0.0695481	+	0.0253135i
$86$		0			0
$87$	−129.324	+	62.2839i	−1.48648	+	0.715907i
$88$		0			0
$89$	66.0425	−	38.1296i	0.742050	−	0.428423i	−0.0807640	−	0.996733i	$-0.525736\pi$
$89$	66.0425	−	38.1296i	0.742050	−	0.428423i	0.822814	+	0.568310i	$0.192403\pi$
$90$		0			0
$91$	−7.73012	+	13.3890i	−0.0849464	+	0.147132i
$92$		0			0
$93$	−37.1806	+	26.7327i	−0.399791	+	0.287448i
$94$		0			0
$95$	20.2941	+	3.57840i	0.213622	+	0.0376674i
$96$		0			0
$97$	82.1613	−	68.9415i	0.847023	−	0.710737i	−0.112109	−	0.993696i	$-0.535761\pi$
$97$	82.1613	−	68.9415i	0.847023	−	0.710737i	0.959132	+	0.282959i	$0.0913161\pi$
$98$		0			0
$99$	−42.6218	−	14.3173i	−0.430523	−	0.144619i
$100$		0			0
$101$	−38.6196	+	106.106i	−0.382372	+	1.05056i	0.587982	+	0.808874i	$0.299922\pi$
$101$	−38.6196	+	106.106i	−0.382372	+	1.05056i	−0.970355	+	0.241685i	$0.922300\pi$
$102$		0			0
$103$	−110.992	−	93.1334i	−1.07759	−	0.904208i	−0.0818743	−	0.996643i	$-0.526091\pi$
$103$	−110.992	−	93.1334i	−1.07759	−	0.904208i	−0.995719	+	0.0924347i	$0.970535\pi$
$104$		0			0
$105$	11.0113	−	11.2900i	0.104869	−	0.107524i
$106$		0			0
$107$			90.9102i			0.849628i	0.905281	+	0.424814i	$0.139661\pi$
$107$			90.9102i			0.849628i	−0.905281	+	0.424814i	$0.860339\pi$
$108$		0			0
$109$	−44.2294			−0.405774			−0.202887	−	0.979202i	$-0.565032\pi$
$109$	−44.2294			−0.405774			−0.202887	+	0.979202i	$0.565032\pi$
$110$		0			0
$111$	−47.9397	+	188.295i	−0.431889	+	1.69635i
$112$		0			0
$113$	92.3757	−	110.089i	0.817484	−	0.974240i	−0.182476	−	0.983210i	$-0.558411\pi$
$113$	92.3757	−	110.089i	0.817484	−	0.974240i	0.999960	+	0.00897066i	$0.00285549\pi$
$114$		0			0
$115$	−24.2969	−	8.84335i	−0.211277	−	0.0768987i
$116$		0			0
$117$	14.7493	+	37.5740i	0.126063	+	0.321145i
$118$		0			0
$119$	−9.14036	−	10.8931i	−0.0768098	−	0.0915383i
$120$		0			0
$121$	16.6775	−	94.5829i	0.137831	−	0.781677i
$122$		0			0
$123$	−167.931	+	16.8091i	−1.36529	+	0.136660i
$124$		0			0
$125$	62.9637	+	36.3521i	0.503709	+	0.290817i
$126$		0			0
$127$	−18.8346	−	32.6225i	−0.148304	−	0.256870i	0.782297	−	0.622906i	$-0.214048\pi$
$127$	−18.8346	−	32.6225i	−0.148304	−	0.256870i	−0.930601	+	0.366036i	$0.880715\pi$
$128$		0			0
$129$	50.1328	−	73.5361i	0.388626	−	0.570047i
$130$		0			0
$131$	52.3965	+	143.958i	0.399973	+	1.09892i	0.962297	+	0.272001i	$0.0876853\pi$
$131$	52.3965	+	143.958i	0.399973	+	1.09892i	−0.562324	+	0.826917i	$0.690093\pi$
$132$		0			0
$133$	8.08846	+	45.8720i	0.0608155	+	0.344902i
$134$		0			0
$135$	−5.12362	−	40.8555i	−0.0379527	−	0.302633i
$136$		0			0
$137$	−58.4666	+	10.3092i	−0.426764	+	0.0752499i	−0.382905	−	0.923788i	$-0.625076\pi$
$137$	−58.4666	+	10.3092i	−0.426764	+	0.0752499i	−0.0438588	+	0.999038i	$0.513965\pi$
$138$		0			0
$139$	−56.3970	+	20.5268i	−0.405734	+	0.147675i	−0.536822	−	0.843696i	$-0.680375\pi$
$139$	−56.3970	+	20.5268i	−0.405734	+	0.147675i	0.131088	+	0.991371i	$0.458153\pi$
$140$		0			0
$141$	−4.61445	+	61.6006i	−0.0327266	+	0.436883i
$142$		0			0
$143$	19.4044	−	11.2031i	0.135695	−	0.0783436i
$144$		0			0
$145$	−36.4837	+	63.1916i	−0.251612	+	0.435804i
$146$		0			0
$147$	−101.500	−	45.7949i	−0.690477	−	0.311530i
$148$		0			0
$149$	−264.707	−	46.6751i	−1.77656	−	0.313255i	−0.813304	−	0.581839i	$-0.802333\pi$
$149$	−264.707	−	46.6751i	−1.77656	−	0.313255i	−0.963256	+	0.268584i	$0.913444\pi$
$150$		0			0
$151$	9.35126	−	7.84664i	0.0619289	−	0.0519645i	−0.611298	−	0.791401i	$-0.709352\pi$
$151$	9.35126	−	7.84664i	0.0619289	−	0.0519645i	0.673227	+	0.739436i	$0.264908\pi$
$152$		0			0
$153$	−37.1151	+	0.927838i	−0.242582	+	0.00606430i
$154$		0			0
$155$	−7.96173	+	21.8747i	−0.0513660	+	0.141127i
$156$		0			0
$157$	−34.5963	−	29.0297i	−0.220359	−	0.184903i	0.525925	−	0.850531i	$-0.323719\pi$
$157$	−34.5963	−	29.0297i	−0.220359	−	0.184903i	−0.746284	+	0.665628i	$0.768164\pi$
$158$		0			0
$159$	16.1381	+	57.3516i	0.101498	+	0.360702i
$160$		0			0
$161$		−	58.4443i		−	0.363008i
$162$		0			0
$163$	5.88721			0.0361178			0.0180589	−	0.999837i	$-0.494251\pi$
$163$	5.88721			0.0361178			0.0180589	+	0.999837i	$0.494251\pi$
$164$		0			0
$165$	−22.0016	+	6.19101i	−0.133343	+	0.0375213i
$166$		0			0
$167$	143.168	−	170.621i	0.857294	−	1.02168i	−0.142198	−	0.989838i	$-0.545417\pi$
$167$	143.168	−	170.621i	0.857294	−	1.02168i	0.999493	−	0.0318455i	$-0.0101384\pi$
$168$		0			0
$169$	139.906	+	50.9215i	0.827845	+	0.301311i
$170$		0			0
$171$	106.808	+	58.1563i	0.624609	+	0.340095i
$172$		0			0
$173$	16.4944	+	19.6573i	0.0953434	+	0.113626i	0.811607	−	0.584204i	$-0.198593\pi$
$173$	16.4944	+	19.6573i	0.0953434	+	0.113626i	−0.716263	+	0.697830i	$0.754149\pi$
$174$		0			0
$175$	−13.5724	+	76.9729i	−0.0775566	+	0.439845i
$176$		0			0
$177$	122.248	−	270.952i	0.690668	−	1.53080i
$178$		0			0
$179$	−67.7828	−	39.1344i	−0.378675	−	0.218628i	0.298567	−	0.954389i	$-0.403492\pi$
$179$	−67.7828	−	39.1344i	−0.378675	−	0.218628i	−0.677242	+	0.735761i	$0.736825\pi$
$180$		0			0
$181$	72.1634	+	124.991i	0.398693	+	0.690557i	0.993565	−	0.113264i	$-0.0361306\pi$
$181$	72.1634	+	124.991i	0.398693	+	0.690557i	−0.594872	+	0.803821i	$0.702797\pi$
$182$		0			0
$183$	246.885	+	18.4940i	1.34910	+	0.101060i
$184$		0			0
$185$	33.7817	+	92.8145i	0.182604	+	0.501700i
$186$		0			0
$187$	3.57865	+	20.2955i	0.0191372	+	0.108532i
$188$		0			0
$189$	82.8177	−	42.4676i	0.438189	−	0.224697i
$190$		0			0
$191$	109.649	−	19.3342i	0.574081	−	0.101226i	0.120932	−	0.992661i	$-0.461412\pi$
$191$	109.649	−	19.3342i	0.574081	−	0.101226i	0.453149	+	0.891435i	$0.350301\pi$
$192$		0			0
$193$	90.9049	−	33.0867i	0.471010	−	0.171434i	−0.0955998	−	0.995420i	$-0.530477\pi$
$193$	90.9049	−	33.0867i	0.471010	−	0.171434i	0.566610	+	0.823986i	$0.308255\pi$
$194$		0			0
$195$	16.9541	+	11.5584i	0.0869441	+	0.0592737i
$196$		0			0
$197$	12.0311	−	6.94615i	0.0610715	−	0.0352596i	−0.469153	−	0.883117i	$-0.655441\pi$
$197$	12.0311	−	6.94615i	0.0610715	−	0.0352596i	0.530225	+	0.847857i	$0.322108\pi$
$198$		0			0
$199$	77.7745	−	134.709i	0.390827	−	0.676932i	−0.601732	−	0.798698i	$-0.705522\pi$
$199$	77.7745	−	134.709i	0.390827	−	0.676932i	0.992559	+	0.121766i	$0.0388558\pi$
$200$		0			0
$201$	−19.3569	−	193.384i	−0.0963028	−	0.962108i
$202$		0			0
$203$	−162.427	−	28.6402i	−0.800132	−	0.141085i
$204$		0			0
$205$	−65.7208	+	55.1463i	−0.320589	+	0.269006i
$206$		0			0
$207$	−119.307	−	95.1325i	−0.576363	−	0.459577i
$208$		0			0
$209$	23.0888	−	63.4358i	0.110473	−	0.303521i
$210$		0			0
$211$	285.417	+	239.493i	1.35269	+	1.13504i	0.978167	+	0.207821i	$0.0666370\pi$
$211$	285.417	+	239.493i	1.35269	+	1.13504i	0.374520	+	0.927219i	$0.377807\pi$
$212$		0			0
$213$	368.525	+	93.8261i	1.73016	+	0.440498i
$214$		0			0
$215$		−	45.2418i		−	0.210427i
$216$		0			0
$217$	−52.6179			−0.242479
$218$		0			0
$219$	77.4646	+	75.5522i	0.353719	+	0.344987i
$220$		0			0
$221$	11.8926	−	14.1730i	0.0538125	−	0.0641313i
$222$		0			0
$223$	−256.023	−	93.1848i	−1.14809	−	0.417869i	−0.303259	−	0.952908i	$-0.598075\pi$
$223$	−256.023	−	93.1848i	−1.14809	−	0.417869i	−0.844827	+	0.535039i	$0.820297\pi$
$224$		0			0
$225$	135.039	+	152.999i	0.600172	+	0.679995i
$226$		0			0
$227$	−186.342	−	222.073i	−0.820888	−	0.978296i	0.179097	−	0.983831i	$-0.442682\pi$
$227$	−186.342	−	222.073i	−0.820888	−	0.978296i	−0.999985	+	0.00553531i	$0.998238\pi$
$228$		0			0
$229$	−24.8927	+	141.173i	−0.108702	+	0.616478i	0.880975	+	0.473162i	$0.156888\pi$
$229$	−24.8927	+	141.173i	−0.108702	+	0.616478i	−0.989677	+	0.143316i	$0.954224\pi$
$230$		0			0
$231$	−30.1591	−	41.9461i	−0.130559	−	0.181585i
$232$		0			0
$233$	−244.086	−	140.923i	−1.04758	−	0.604819i	−0.125607	−	0.992080i	$-0.540088\pi$
$233$	−244.086	−	140.923i	−1.04758	−	0.604819i	−0.921970	+	0.387261i	$0.873421\pi$
$234$		0			0
$235$	15.7009	+	27.1947i	0.0668122	+	0.115722i
$236$		0			0
$237$	−108.546	−	225.380i	−0.457999	−	0.950971i
$238$		0			0
$239$	132.471	+	363.961i	0.554271	+	1.52285i	0.827823	+	0.560990i	$0.189579\pi$
$239$	132.471	+	363.961i	0.554271	+	1.52285i	−0.273551	+	0.961857i	$0.588198\pi$
$240$		0			0
$241$	33.2184	+	188.391i	0.137836	+	0.781705i	0.972843	+	0.231466i	$0.0743522\pi$
$241$	33.2184	+	188.391i	0.137836	+	0.781705i	−0.835007	+	0.550239i	$0.814537\pi$
$242$		0			0
$243$	48.1135	−	238.189i	0.197998	−	0.980202i
$244$		0			0
$245$	−55.7450	+	9.82935i	−0.227531	+	0.0401198i
$246$		0			0
$247$	−56.9500	+	20.7281i	−0.230567	+	0.0839195i
$248$		0			0
$249$	−45.4240	+	21.8768i	−0.182426	+	0.0878585i
$250$		0			0
$251$	−377.425	+	217.906i	−1.50368	+	0.868153i	−0.503693	+	0.863882i	$0.668026\pi$
$251$	−377.425	+	217.906i	−1.50368	+	0.868153i	−0.999991	+	0.00427006i	$0.998641\pi$
$252$		0			0
$253$	−42.3512	+	73.3543i	−0.167396	+	0.289938i
$254$		0			0
$255$	−15.3233	+	11.0174i	−0.0600915	+	0.0432056i
$256$		0			0
$257$	−412.498	−	72.7345i	−1.60505	−	0.283014i	−0.701880	−	0.712295i	$-0.747656\pi$
$257$	−412.498	−	72.7345i	−1.60505	−	0.283014i	−0.903171	+	0.429281i	$0.858767\pi$
$258$		0			0
$259$	−171.026	+	143.508i	−0.660331	+	0.554084i
$260$		0			0
$261$	−322.855	+	284.956i	−1.23699	+	1.09179i
$262$		0			0
$263$	113.154	−	310.887i	0.430242	−	1.18208i	−0.515423	−	0.856936i	$-0.672365\pi$
$263$	113.154	−	310.887i	0.430242	−	1.18208i	0.945665	−	0.325144i	$-0.105413\pi$
$264$		0			0
$265$	23.2006	+	19.4676i	0.0875496	+	0.0734628i
$266$		0			0
$267$	159.736	−	163.779i	0.598263	−	0.613406i
$268$		0			0
$269$		−	136.569i		−	0.507690i	−0.967245	−	0.253845i	$-0.918305\pi$
$269$		−	136.569i		−	0.507690i	0.967245	−	0.253845i	$-0.0816953\pi$
$270$		0			0
$271$	170.355			0.628615			0.314307	−	0.949321i	$-0.398228\pi$
$271$	170.355			0.628615			0.314307	+	0.949321i	$0.398228\pi$
$272$		0			0
$273$	−11.4434	+	44.9469i	−0.0419173	+	0.164641i
$274$		0			0
$275$	72.8127	−	86.7748i	0.264773	−	0.315545i
$276$		0			0
$277$	−125.607	−	45.7173i	−0.453456	−	0.165044i	0.105188	−	0.994452i	$-0.466456\pi$
$277$	−125.607	−	45.7173i	−0.453456	−	0.165044i	−0.558643	+	0.829408i	$0.688678\pi$
$278$		0			0
$279$	−85.6486	+	107.413i	−0.306984	+	0.384994i
$280$		0			0
$281$	291.841	+	347.803i	1.03858	+	1.23773i	0.970764	+	0.240034i	$0.0771587\pi$
$281$	291.841	+	347.803i	1.03858	+	1.23773i	0.0678161	+	0.997698i	$0.478397\pi$
$282$		0			0
$283$	−67.6428	+	383.621i	−0.239020	+	1.35555i	0.594959	+	0.803756i	$0.297168\pi$
$283$	−67.6428	+	383.621i	−0.239020	+	1.35555i	−0.833979	+	0.551796i	$0.813943\pi$
$284$		0			0
$285$	61.5141	−	6.15730i	0.215839	−	0.0216045i
$286$		0			0
$287$	−167.941	−	96.9608i	−0.585161	−	0.337843i
$288$		0			0
$289$	−135.991	−	235.544i	−0.470559	−	0.815031i
$290$		0			0
$291$	181.247	−	265.857i	0.622841	−	0.913600i
$292$		0			0
$293$	116.307	+	319.550i	0.396951	+	1.09061i	0.963762	+	0.266765i	$0.0859548\pi$
$293$	116.307	+	319.550i	0.396951	+	1.09061i	−0.566811	+	0.823848i	$0.691823\pi$
$294$		0			0
$295$	−26.2392	−	148.810i	−0.0889465	−	0.504440i
$296$		0			0
$297$	−134.720	−	6.71133i	−0.453601	−	0.0225971i
$298$		0			0
$299$	74.8869	−	13.2046i	0.250458	−	0.0441625i
$300$		0			0
$301$	96.0954	−	34.9759i	0.319254	−	0.116199i
$302$		0			0
$303$	−25.3045	+	337.802i	−0.0835132	+	1.11486i
$304$		0			0
$305$	108.992	−	62.9266i	0.357351	−	0.206317i
$306$		0			0
$307$	232.919	−	403.428i	0.758695	−	1.31410i	−0.184822	−	0.982772i	$-0.559171\pi$
$307$	232.919	−	403.428i	0.758695	−	1.31410i	0.943516	−	0.331326i	$-0.107496\pi$
$308$		0			0
$309$	−396.209	−	178.762i	−1.28223	−	0.578518i
$310$		0			0
$311$	82.0156	+	14.4616i	0.263716	+	0.0465002i	0.303942	−	0.952690i	$-0.401697\pi$
$311$	82.0156	+	14.4616i	0.263716	+	0.0465002i	−0.0402268	+	0.999191i	$0.512808\pi$
$312$		0			0
$313$	−213.260	+	178.947i	−0.681343	+	0.571714i	−0.916398	−	0.400268i	$-0.868917\pi$
$313$	−213.260	+	178.947i	−0.681343	+	0.571714i	0.235056	+	0.971982i	$0.424473\pi$
$314$		0			0
$315$	22.6245	−	41.5516i	0.0718240	−	0.131910i
$316$		0			0
$317$	56.6181	−	155.557i	0.178606	−	0.490716i	−0.817792	−	0.575513i	$-0.804802\pi$
$317$	56.6181	−	155.557i	0.178606	−	0.490716i	0.996398	+	0.0847979i	$0.0270245\pi$
$318$		0			0
$319$	183.110	+	153.648i	0.574014	+	0.481655i
$320$		0			0
$321$	73.8744	+	262.535i	0.230138	+	0.817866i
$322$		0			0
$323$		−	55.7426i		−	0.172578i
$324$		0			0
$325$	−101.695			−0.312907
$326$		0			0
$327$	−127.728	+	35.9412i	−0.390605	+	0.109912i
$328$		0			0
$329$	−45.6245	+	54.3732i	−0.138676	+	0.165268i
$330$		0			0
$331$	−10.7745	−	3.92161i	−0.0325515	−	0.0118478i	0.325693	−	0.945476i	$-0.394402\pi$
$331$	−10.7745	−	3.92161i	−0.0325515	−	0.0118478i	−0.358245	+	0.933628i	$0.616625\pi$
$332$		0			0
$333$	14.5675	+	582.723i	0.0437461	+	1.74992i
$334$		0			0
$335$	−63.5047	−	75.6819i	−0.189566	−	0.225916i
$336$		0			0
$337$	70.1777	−	397.997i	0.208242	−	1.18100i	−0.684013	−	0.729470i	$-0.739767\pi$
$337$	70.1777	−	397.997i	0.208242	−	1.18100i	0.892255	−	0.451531i	$-0.149122\pi$
$338$		0			0
$339$	177.308	−	392.986i	0.523032	−	1.15925i
$340$		0			0
$341$	66.0415	+	38.1291i	0.193670	+	0.111815i
$342$		0			0
$343$	−148.427	−	257.084i	−0.432733	−	0.749515i
$344$		0			0
$345$	−77.3519	−	5.79437i	−0.224208	−	0.0167953i
$346$		0			0
$347$	182.542	+	501.529i	0.526057	+	1.44533i	0.863676	+	0.504047i	$0.168156\pi$
$347$	182.542	+	501.529i	0.526057	+	1.44533i	−0.337620	+	0.941283i	$0.609622\pi$
$348$		0			0
$349$	−40.5969	−	230.237i	−0.116324	−	0.659704i	−0.986086	−	0.166234i	$-0.946839\pi$
$349$	−40.5969	−	230.237i	−0.116324	−	0.659704i	0.869763	−	0.493470i	$-0.164272\pi$
$350$		0			0
$351$	73.1268	+	96.5225i	0.208338	+	0.274993i
$352$		0			0
$353$	486.656	−	85.8106i	1.37863	−	0.243090i	0.565297	−	0.824888i	$-0.308762\pi$
$353$	486.656	−	85.8106i	1.37863	−	0.243090i	0.813333	+	0.581798i	$0.197651\pi$
$354$		0			0
$355$	181.654	−	66.1166i	0.511701	−	0.186244i
$356$		0			0
$357$	−35.2478	−	24.0300i	−0.0987333	−	0.0673108i
$358$		0			0
$359$	46.1066	−	26.6196i	0.128431	−	0.0741494i	−0.434408	−	0.900716i	$-0.643042\pi$
$359$	46.1066	−	26.6196i	0.128431	−	0.0741494i	0.562839	+	0.826567i	$0.309709\pi$
$360$		0			0
$361$	89.2028	−	154.504i	0.247099	−	0.427988i
$362$		0			0
$363$	−28.6967	−	286.693i	−0.0790544	−	0.789789i
$364$		0			0
$365$	54.1705	+	9.55172i	0.148412	+	0.0261691i
$366$		0			0
$367$	−51.6382	+	43.3296i	−0.140704	+	0.118064i	−0.710423	−	0.703775i	$-0.751496\pi$
$367$	−51.6382	+	43.3296i	−0.140704	+	0.118064i	0.569719	+	0.821839i	$0.307052\pi$
$368$		0			0
$369$	−471.300	+	185.004i	−1.27724	+	0.501367i
$370$		0			0
$371$	−23.4140	+	64.3293i	−0.0631104	+	0.173394i
$372$		0			0
$373$	−138.334	−	116.076i	−0.370868	−	0.311195i	0.438237	−	0.898860i	$-0.355603\pi$
$373$	−138.334	−	116.076i	−0.370868	−	0.311195i	−0.809105	+	0.587664i	$0.800048\pi$
$374$		0			0
$375$	211.370	+	53.8145i	0.563652	+	0.143505i
$376$		0			0
$377$		−	214.594i		−	0.569216i
$378$		0			0
$379$	609.218			1.60743			0.803717	−	0.595011i	$-0.202852\pi$
$379$	609.218			1.60743			0.803717	+	0.595011i	$0.202852\pi$
$380$		0			0
$381$	−80.9007	−	78.9036i	−0.212338	−	0.207096i
$382$		0			0
$383$	220.984	−	263.359i	0.576983	−	0.687622i	−0.396065	−	0.918222i	$-0.629625\pi$
$383$	220.984	−	263.359i	0.576983	−	0.687622i	0.973048	+	0.230601i	$0.0740691\pi$
$384$		0			0
$385$	−24.6785	−	8.98222i	−0.0640999	−	0.0233304i
$386$		0			0
$387$	85.0199	−	253.099i	0.219690	−	0.654004i
$388$		0			0
$389$	314.120	+	374.354i	0.807507	+	0.962349i	0.999820	−	0.0189843i	$-0.00604325\pi$
$389$	314.120	+	374.354i	0.807507	+	0.962349i	−0.192313	+	0.981334i	$0.561599\pi$
$390$		0			0
$391$	−12.1452	+	68.8788i	−0.0310619	+	0.176161i
$392$		0			0
$393$	268.295	+	373.152i	0.682684	+	0.949495i
$394$		0			0
$395$	−110.128	−	63.5822i	−0.278804	−	0.160968i
$396$		0			0
$397$	−185.104	−	320.610i	−0.466258	−	0.807582i	0.533000	−	0.846115i	$-0.321065\pi$
$397$	−185.104	−	320.610i	−0.466258	−	0.807582i	−0.999257	+	0.0385336i	$0.987731\pi$
$398$		0			0
$399$	60.6342	+	125.898i	0.151965	+	0.315535i
$400$		0			0
$401$	182.815	+	502.279i	0.455897	+	1.25257i	0.928514	+	0.371298i	$0.121087\pi$
$401$	182.815	+	502.279i	0.455897	+	1.25257i	−0.472617	+	0.881268i	$0.656691\pi$
$402$		0			0
$403$	−11.8882	−	67.4213i	−0.0294992	−	0.167298i
$404$		0			0
$405$	−47.9957	−	113.821i	−0.118508	−	0.281039i
$406$		0			0
$407$	318.649	−	56.1863i	0.782920	−	0.138050i
$408$		0			0
$409$	137.720	−	50.1258i	0.336723	−	0.122557i	−0.168125	−	0.985766i	$-0.553771\pi$
$409$	137.720	−	50.1258i	0.336723	−	0.122557i	0.504847	+	0.863209i	$0.331549\pi$
$410$		0			0
$411$	−160.465	+	77.2820i	−0.390427	+	0.188034i
$412$		0			0
$413$	295.793	−	170.776i	0.716207	−	0.413502i
$414$		0			0
$415$	−12.8146	+	22.1956i	−0.0308786	+	0.0534833i
$416$		0			0
$417$	−146.186	+	105.107i	−0.350565	+	0.252055i
$418$		0			0
$419$	−197.145	−	34.7619i	−0.470512	−	0.0829640i	−0.0666354	−	0.997777i	$-0.521226\pi$
$419$	−197.145	−	34.7619i	−0.470512	−	0.0829640i	−0.403877	+	0.914813i	$0.632338\pi$
$420$		0			0
$421$	337.985	−	283.603i	0.802815	−	0.673641i	−0.146067	−	0.989275i	$-0.546661\pi$
$421$	337.985	−	283.603i	0.802815	−	0.673641i	0.948881	+	0.315633i	$0.102217\pi$
$422$		0			0
$423$	36.7313	+	181.643i	0.0868353	+	0.429416i
$424$		0			0
$425$	31.9911	−	87.8950i	0.0752733	−	0.206812i
$426$		0			0
$427$	217.919	+	182.856i	0.510349	+	0.428234i
$428$		0			0
$429$	46.9332	−	48.1211i	0.109401	−	0.112170i
$430$		0			0
$431$			474.920i			1.10190i	0.834537	+	0.550951i	$0.185735\pi$
$431$			474.920i			1.10190i	−0.834537	+	0.550951i	$0.814265\pi$
$432$		0			0
$433$	−540.928			−1.24926			−0.624628	−	0.780922i	$-0.714749\pi$
$433$	−540.928			−1.24926			−0.624628	+	0.780922i	$0.714749\pi$
$434$		0			0
$435$	−54.0093	+	212.135i	−0.124159	+	0.487666i
$436$		0			0
$437$	147.266	−	175.504i	0.336992	−	0.401612i
$438$		0			0
$439$	−615.853	−	224.152i	−1.40285	−	0.510597i	−0.473831	−	0.880616i	$-0.657129\pi$
$439$	−615.853	−	224.152i	−1.40285	−	0.510597i	−0.929024	+	0.370019i	$0.879351\pi$
$440$		0			0
$441$	−330.330	−	49.7688i	−0.749048	−	0.112855i
$442$		0			0
$443$	−461.210	−	549.649i	−1.04111	−	1.24074i	−0.969957	−	0.243277i	$-0.921777\pi$
$443$	−461.210	−	549.649i	−1.04111	−	1.24074i	−0.0711502	−	0.997466i	$-0.522667\pi$
$444$		0			0
$445$	20.1947	−	114.530i	0.0453814	−	0.257371i
$446$		0			0
$447$	−802.363	+	80.3131i	−1.79500	+	0.179671i
$448$		0			0
$449$	118.270	+	68.2833i	0.263408	+	0.152079i	0.625888	−	0.779913i	$-0.284737\pi$
$449$	118.270	+	68.2833i	0.263408	+	0.152079i	−0.362480	+	0.931991i	$0.618070\pi$
$450$		0			0
$451$	140.524	+	243.394i	0.311582	+	0.539676i
$452$		0			0
$453$	20.6288	−	30.2588i	0.0455381	−	0.0667965i
$454$		0			0
$455$	8.06386	+	22.1553i	0.0177228	+	0.0486929i
$456$		0			0
$457$	43.5634	+	247.060i	0.0953247	+	0.540613i	0.994647	+	0.103327i	$0.0329490\pi$
$457$	43.5634	+	247.060i	0.0953247	+	0.540613i	−0.899323	+	0.437286i	$0.855940\pi$
$458$		0			0
$459$	−106.429	+	32.8395i	−0.231871	+	0.0715458i
$460$		0			0
$461$	−227.426	+	40.1013i	−0.493331	+	0.0869876i	−0.414779	−	0.909922i	$-0.636141\pi$
$461$	−227.426	+	40.1013i	−0.493331	+	0.0869876i	−0.0785527	+	0.996910i	$0.525030\pi$
$462$		0			0
$463$	−418.337	+	152.262i	−0.903535	+	0.328860i	−0.751669	−	0.659541i	$-0.770751\pi$
$463$	−418.337	+	152.262i	−0.903535	+	0.328860i	−0.151867	+	0.988401i	$0.548528\pi$
$464$		0			0
$465$	−5.21672	+	69.6405i	−0.0112188	+	0.149765i
$466$		0			0
$467$	−515.922	+	297.868i	−1.10476	+	0.637833i	−0.937467	−	0.348075i	$-0.886836\pi$
$467$	−515.922	+	297.868i	−1.10476	+	0.637833i	−0.167292	+	0.985907i	$0.553502\pi$
$468$		0			0
$469$	111.657	−	193.395i	0.238074	−	0.412357i
$470$		0			0
$471$	−123.499	−	55.7202i	−0.262205	−	0.118302i
$472$		0			0
$473$	−145.956	−	25.7360i	−0.308575	−	0.0544100i
$474$		0			0
$475$	−234.710	+	196.945i	−0.494127	+	0.414622i
$476$		0			0
$477$	93.2088	+	152.509i	0.195406	+	0.319725i
$478$		0			0
$479$	−112.035	+	307.814i	−0.233894	+	0.642618i	−1.00000		9.59229e-5i	$-0.999969\pi$
$479$	−112.035	+	307.814i	−0.233894	+	0.642618i	0.766106	+	0.642714i	$0.222192\pi$
$480$		0			0
$481$	−222.522	−	186.718i	−0.462624	−	0.388188i
$482$		0			0
$483$	−47.4924	−	168.778i	−0.0983279	−	0.349437i
$484$		0			0
$485$		−	163.564i		−	0.337245i
$486$		0			0
$487$	−39.4271			−0.0809592			−0.0404796	−	0.999180i	$-0.512889\pi$
$487$	−39.4271			−0.0809592			−0.0404796	+	0.999180i	$0.512889\pi$
$488$		0			0
$489$	17.0014	−	4.78400i	0.0347676	−	0.00978322i
$490$		0			0
$491$	−209.908	+	250.158i	−0.427510	+	0.509487i	−0.936202	−	0.351462i	$-0.885685\pi$
$491$	−209.908	+	250.158i	−0.427510	+	0.509487i	0.508692	+	0.860949i	$0.330129\pi$
$492$		0			0
$493$	185.474	+	67.5071i	0.376216	+	0.136931i
$494$		0			0
$495$	−58.5064	+	35.7574i	−0.118195	+	0.0722371i
$496$		0			0
$497$	280.869	+	334.726i	0.565128	+	0.673494i
$498$		0			0
$499$	−77.0969	+	437.238i	−0.154503	+	0.876229i	0.804736	+	0.593633i	$0.202307\pi$
$499$	−77.0969	+	437.238i	−0.154503	+	0.876229i	−0.959239	+	0.282596i	$0.908804\pi$
$500$		0			0
$501$	274.800	−	609.068i	0.548502	−	1.21570i
$502$		0			0
$503$	−248.594	−	143.526i	−0.494223	−	0.285340i	0.232102	−	0.972692i	$-0.425440\pi$
$503$	−248.594	−	143.526i	−0.494223	−	0.285340i	−0.726325	+	0.687352i	$0.758773\pi$
$504$		0			0
$505$	86.0996	+	149.129i	0.170494	+	0.295305i
$506$		0			0
$507$	445.406	+	33.3650i	0.878513	+	0.0658087i
$508$		0			0
$509$	−278.163	−	764.247i	−0.546489	−	1.50147i	−0.838418	−	0.545027i	$-0.816519\pi$
$509$	−278.163	−	764.247i	−0.546489	−	1.50147i	0.291929	−	0.956440i	$-0.405703\pi$
$510$		0			0
$511$	21.5903	+	122.445i	0.0422511	+	0.239618i
$512$		0			0
$513$	355.704	+	81.1532i	0.693380	+	0.158193i
$514$		0			0
$515$	−217.603	+	38.3692i	−0.422530	+	0.0745034i
$516$		0			0
$517$	96.6650	−	35.1832i	0.186973	−	0.0680526i
$518$		0			0
$519$	63.6070	+	43.3637i	0.122557	+	0.0835524i
$520$		0			0
$521$	−17.1141	+	9.88086i	−0.0328486	+	0.0189652i	−0.516334	−	0.856387i	$-0.672704\pi$
$521$	−17.1141	+	9.88086i	−0.0328486	+	0.0189652i	0.483486	+	0.875352i	$0.339370\pi$
$522$		0			0
$523$	−342.155	+	592.630i	−0.654216	+	1.13313i	0.327874	+	0.944721i	$0.393668\pi$
$523$	−342.155	+	592.630i	−0.654216	+	1.13313i	−0.982090	+	0.188413i	$0.939666\pi$
$524$		0			0
$525$	23.3538	+	233.315i	0.0444835	+	0.444410i
$526$		0			0
$527$	62.0121	+	10.9344i	0.117670	+	0.0207484i
$528$		0			0
$529$	185.029	−	155.258i	0.349771	−	0.293493i
$530$		0			0
$531$	132.857	−	881.808i	0.250201	−	1.66066i
$532$		0			0
$533$	86.2959	−	237.096i	0.161906	−	0.444833i
$534$		0			0
$535$	106.204	+	89.1159i	0.198512	+	0.166572i
$536$		0			0
$537$	−227.548	−	57.9334i	−0.423738	−	0.107883i
$538$		0			0
$539$			185.432i			0.344030i
$540$		0			0
$541$	283.876			0.524724			0.262362	−	0.964970i	$-0.415499\pi$
$541$	283.876			0.524724			0.262362	+	0.964970i	$0.415499\pi$
$542$		0			0
$543$	309.966	+	302.314i	0.570839	+	0.556747i
$544$		0			0
$545$	−43.3564	+	51.6702i	−0.0795531	+	0.0948077i
$546$		0			0
$547$	681.270	+	247.962i	1.24547	+	0.453312i	0.878867	−	0.477067i	$-0.158300\pi$
$547$	681.270	+	247.962i	1.24547	+	0.453312i	0.366598	+	0.930379i	$0.380522\pi$
$548$		0			0
$549$	727.996	−	147.213i	1.32604	−	0.268148i
$550$		0			0
$551$	−415.590	−	495.281i	−0.754247	−	0.898877i
$552$		0			0
$553$	49.9130	−	283.071i	0.0902585	−	0.511882i
$554$		0			0
$555$	172.978	+	240.583i	0.311673	+	0.433483i
$556$		0			0
$557$	637.275	+	367.931i	1.14412	+	0.660558i	0.947448	−	0.319911i	$-0.103653\pi$
$557$	637.275	+	367.931i	1.14412	+	0.660558i	0.196672	+	0.980469i	$0.436986\pi$
$558$		0			0
$559$	66.5272	+	115.228i	0.119011	+	0.206133i
$560$		0			0
$561$	26.8269	+	55.7024i	0.0478198	+	0.0992912i
$562$		0			0
$563$	−264.958	−	727.966i	−0.470618	−	1.29301i	−0.917256	−	0.398298i	$-0.869601\pi$
$563$	−264.958	−	727.966i	−0.470618	−	1.29301i	0.446638	−	0.894715i	$-0.352621\pi$
$564$		0			0
$565$	−38.0571	−	215.832i	−0.0673576	−	0.382004i
$566$		0			0
$567$	204.655	−	189.938i	0.360944	−	0.334989i
$568$		0			0
$569$	−649.361	+	114.500i	−1.14123	+	0.201230i	−0.712144	−	0.702033i	$-0.752276\pi$
$569$	−649.361	+	114.500i	−1.14123	+	0.201230i	−0.429087	+	0.903263i	$0.641165\pi$
$570$		0			0
$571$	96.2986	−	35.0498i	0.168649	−	0.0613832i	−0.256316	−	0.966593i	$-0.582509\pi$
$571$	96.2986	−	35.0498i	0.168649	−	0.0613832i	0.424965	+	0.905210i	$0.360286\pi$
$572$		0			0
$573$	300.940	−	144.936i	0.525200	−	0.252943i
$574$		0			0
$575$	332.932	−	192.218i	0.579012	−	0.334292i
$576$		0			0
$577$	−474.467	+	821.801i	−0.822300	+	1.42426i	0.0816661	+	0.996660i	$0.473976\pi$
$577$	−474.467	+	821.801i	−0.822300	+	1.42426i	−0.903966	+	0.427605i	$0.859357\pi$
$578$		0			0
$579$	235.633	−	169.419i	0.406966	−	0.292607i
$580$		0			0
$581$	−57.0512	−	10.0597i	−0.0981948	−	0.0173144i
$582$		0			0
$583$	76.0029	−	63.7740i	0.130365	−	0.109389i
$584$		0			0
$585$	58.3533	+	19.6017i	0.0997492	+	0.0335073i
$586$		0			0
$587$	−286.142	+	786.168i	−0.487465	+	1.33930i	0.415504	+	0.909591i	$0.363605\pi$
$587$	−286.142	+	786.168i	−0.487465	+	1.33930i	−0.902968	+	0.429707i	$0.858617\pi$
$588$		0			0
$589$	−158.008	−	132.584i	−0.268265	−	0.225101i
$590$		0			0
$591$	29.0994	−	29.8360i	0.0492376	−	0.0504839i
$592$		0			0
$593$		−	485.118i		−	0.818075i	−0.912518	−	0.409037i	$-0.865865\pi$
$593$		−	485.118i		−	0.818075i	0.912518	−	0.409037i	$-0.134135\pi$
$594$		0			0
$595$	−21.6856			−0.0364463
$596$		0			0
$597$	115.135	−	452.221i	0.192856	−	0.757488i
$598$		0			0
$599$	190.110	−	226.565i	0.317380	−	0.378238i	−0.583643	−	0.812010i	$-0.698373\pi$
$599$	190.110	−	226.565i	0.317380	−	0.378238i	0.901023	+	0.433772i	$0.142818\pi$
$600$		0			0
$601$	642.355	+	233.798i	1.06881	+	0.389015i	0.815732	−	0.578431i	$-0.196335\pi$
$601$	642.355	+	233.798i	1.06881	+	0.389015i	0.253079	+	0.967446i	$0.418557\pi$
$602$		0			0
$603$	−213.045	−	542.733i	−0.353308	−	0.900055i
$604$		0			0
$605$	−94.1463	−	112.199i	−0.155614	−	0.185453i
$606$		0			0
$607$	27.7719	−	157.502i	0.0457527	−	0.259476i	−0.953348	−	0.301873i	$-0.902388\pi$
$607$	27.7719	−	157.502i	0.0457527	−	0.259476i	0.999101	+	0.0423966i	$0.0134993\pi$
$608$		0			0
$609$	−492.337	+	49.2808i	−0.808436	+	0.0809209i
$610$		0			0
$611$	−79.9785	−	46.1756i	−0.130898	−	0.0755739i
$612$		0			0
$613$	370.587	+	641.875i	0.604546	+	1.04711i	0.992123	+	0.125268i	$0.0399790\pi$
$613$	370.587	+	641.875i	0.604546	+	1.04711i	−0.387577	+	0.921838i	$0.626688\pi$
$614$		0			0
$615$	−144.979	+	212.659i	−0.235739	+	0.345788i
$616$		0			0
$617$	−33.9467	−	93.2678i	−0.0550189	−	0.151163i	0.909139	−	0.416494i	$-0.136741\pi$
$617$	−33.9467	−	93.2678i	−0.0550189	−	0.151163i	−0.964158	+	0.265330i	$0.914519\pi$
$618$		0			0
$619$	67.3069	+	381.716i	0.108735	+	0.616666i	0.989663	+	0.143415i	$0.0458085\pi$
$619$	67.3069	+	381.716i	0.108735	+	0.616666i	−0.880928	+	0.473251i	$0.843080\pi$
$620$		0			0
$621$	−421.847	−	177.778i	−0.679302	−	0.286277i
$622$		0			0
$623$	258.879	−	45.6473i	0.415536	−	0.0732701i
$624$		0			0
$625$	−428.484	+	155.955i	−0.685574	+	0.249529i
$626$		0			0
$627$	15.1283	−	201.955i	0.0241281	−	0.322098i
$628$		0			0
$629$	231.382	−	133.589i	0.367857	−	0.212382i
$630$		0			0
$631$	116.257	−	201.363i	0.184243	−	0.319118i	−0.759078	−	0.650999i	$-0.774350\pi$
$631$	116.257	−	201.363i	0.184243	−	0.319118i	0.943321	+	0.331882i	$0.107683\pi$
$632$		0			0
$633$	1018.86	+	459.688i	1.60957	+	0.726205i
$634$		0			0
$635$	−56.5734	−	9.97542i	−0.0890920	−	0.0157093i
$636$		0			0
$637$	127.526	−	107.007i	0.200198	−	0.167986i
$638$		0			0
$639$	1140.49	−	28.5110i	1.78480	−	0.0446181i
$640$		0			0
$641$	−23.5131	+	64.6018i	−0.0366819	+	0.100783i	−0.956681	−	0.291137i	$-0.905967\pi$
$641$	−23.5131	+	64.6018i	−0.0366819	+	0.100783i	0.920000	+	0.391919i	$0.128189\pi$
$642$		0			0
$643$	−659.704	−	553.557i	−1.02598	−	0.860898i	−0.0356111	−	0.999366i	$-0.511338\pi$
$643$	−659.704	−	553.557i	−1.02598	−	0.860898i	−0.990367	+	0.138468i	$0.955782\pi$
$644$		0			0
$645$	−36.7639	−	130.651i	−0.0569982	−	0.202560i
$646$		0			0
$647$			175.249i			0.270864i	0.990787	+	0.135432i	$0.0432422\pi$
$647$			175.249i			0.270864i	−0.990787	+	0.135432i	$0.956758\pi$
$648$		0			0
$649$	−495.006			−0.762722
$650$		0			0
$651$	−151.952	+	42.7577i	−0.233414	+	0.0656801i
$652$		0			0
$653$	231.306	−	275.659i	0.354220	−	0.422143i	−0.559282	−	0.828978i	$-0.688923\pi$
$653$	231.306	−	275.659i	0.354220	−	0.422143i	0.913502	+	0.406835i	$0.133367\pi$
$654$		0			0
$655$	219.539	+	79.9056i	0.335174	+	0.121993i
$656$		0			0
$657$	285.100	+	155.235i	0.433943	+	0.236279i
$658$		0			0
$659$	−19.8517	−	23.6583i	−0.0301240	−	0.0359004i	0.750772	−	0.660561i	$-0.229682\pi$
$659$	−19.8517	−	23.6583i	−0.0301240	−	0.0359004i	−0.780896	+	0.624661i	$0.785237\pi$
$660$		0			0
$661$	39.3517	−	223.174i	0.0595335	−	0.337631i	−0.940464	−	0.339894i	$-0.889609\pi$
$661$	39.3517	−	223.174i	0.0595335	−	0.337631i	0.999997	+	0.00226216i	$0.000720070\pi$
$662$		0			0
$663$	22.8268	−	50.5935i	0.0344296	−	0.0763100i
$664$		0			0
$665$	61.5179	+	35.5174i	0.0925081	+	0.0534096i
$666$		0			0
$667$	405.615	+	702.546i	0.608119	+	1.05329i
$668$		0			0
$669$	−815.079	−	61.0569i	−1.21835	−	0.0912660i
$670$		0			0
$671$	−141.009	−	387.418i	−0.210147	−	0.577375i
$672$		0			0
$673$	101.271	+	574.339i	0.150478	+	0.853401i	0.962805	+	0.270199i	$0.0870894\pi$
$673$	101.271	+	574.339i	0.150478	+	0.853401i	−0.812327	+	0.583202i	$0.801799\pi$
$674$		0			0
$675$	514.300	+	332.104i	0.761925	+	0.492006i
$676$		0			0
$677$	−1292.96	+	227.984i	−1.90984	+	0.336756i	−0.997375	−	0.0724045i	$-0.976933\pi$
$677$	−1292.96	+	227.984i	−1.90984	+	0.336756i	−0.912462	+	0.409160i	$0.865822\pi$
$678$		0			0
$679$	347.417	−	126.449i	0.511660	−	0.186229i
$680$		0			0
$681$	−718.585	−	489.891i	−1.05519	−	0.719370i
$682$		0			0
$683$	201.799	−	116.509i	0.295460	−	0.170584i	−0.344941	−	0.938624i	$-0.612101\pi$
$683$	201.799	−	116.509i	0.295460	−	0.170584i	0.640402	+	0.768040i	$0.278768\pi$
$684$		0			0
$685$	−45.2690	+	78.4083i	−0.0660862	+	0.114465i
$686$		0			0
$687$	42.8325	+	427.916i	0.0623471	+	0.622876i
$688$		0			0
$689$	−87.7176	−	15.4670i	−0.127312	−	0.0224485i
$690$		0			0
$691$	641.761	−	538.502i	0.928743	−	0.779308i	−0.0468483	−	0.998902i	$-0.514918\pi$
$691$	641.761	−	538.502i	0.928743	−	0.779308i	0.975591	+	0.219594i	$0.0704733\pi$
$692$		0			0
$693$	−121.181	−	96.6265i	−0.174864	−	0.139432i
$694$		0			0
$695$	−31.3038	+	86.0064i	−0.0450414	+	0.123750i
$696$		0			0
$697$	177.776	+	149.171i	0.255058	+	0.214019i
$698$		0			0
$699$	−819.397	−	208.618i	−1.17224	−	0.298452i
$700$		0			0
$701$			855.750i			1.22076i	0.792111	+	0.610378i	$0.208982\pi$
$701$			855.750i			1.22076i	−0.792111	+	0.610378i	$0.791018\pi$
$702$		0			0
$703$	−875.183			−1.24493
$704$		0			0
$705$	67.4403	+	65.7755i	0.0956600	+	0.0932985i
$706$		0			0
$707$	−250.193	+	298.169i	−0.353880	+	0.421738i
$708$		0			0
$709$	−115.321	−	41.9735i	−0.162653	−	0.0592010i	0.259410	−	0.965767i	$-0.416472\pi$
$709$	−115.321	−	41.9735i	−0.162653	−	0.0592010i	−0.422064	+	0.906566i	$0.638694\pi$
$710$		0			0
$711$	−496.610	−	562.659i	−0.698466	−	0.791362i
$712$		0			0
$713$	166.356	+	198.255i	0.233319	+	0.278058i
$714$		0			0
$715$	5.93355	−	33.6508i	0.00829867	−	0.0470641i
$716$		0			0
$717$	678.313	+	943.416i	0.946043	+	1.31578i
$718$		0			0
$719$	675.931	+	390.249i	0.940099	+	0.542766i	0.889991	−	0.455978i	$-0.150710\pi$
$719$	675.931	+	390.249i	0.940099	+	0.542766i	0.0501075	+	0.998744i	$0.484044\pi$
$720$		0			0
$721$	−249.724	−	432.535i	−0.346358	−	0.599909i
$722$		0			0
$723$	249.018	+	517.051i	0.344423	+	0.715146i
$724$		0			0
$725$	−371.057	−	1019.47i	−0.511802	−	1.40616i
$726$		0			0
$727$	−136.489	−	774.066i	−0.187742	−	1.06474i	−0.922381	−	0.386281i	$-0.873759\pi$
$727$	−136.489	−	774.066i	−0.187742	−	1.06474i	0.734639	−	0.678458i	$-0.237352\pi$
$728$		0			0
$729$	−54.6101	−	726.952i	−0.0749109	−	0.997190i
$730$		0			0
$731$	−120.520	+	21.2510i	−0.164870	+	0.0290711i
$732$		0			0
$733$	−1059.68	+	385.691i	−1.44567	+	0.526181i	−0.941379	−	0.337352i	$-0.890469\pi$
$733$	−1059.68	+	385.691i	−1.44567	+	0.526181i	−0.504292	+	0.863533i	$0.668247\pi$
$734$		0			0
$735$	−152.996	+	73.6846i	−0.208157	+	0.100251i
$736$		0			0
$737$	−280.285	+	161.822i	−0.380305	+	0.219569i
$738$		0			0
$739$	57.1510	−	98.9885i	0.0773357	−	0.133949i	−0.824764	−	0.565477i	$-0.808692\pi$
$739$	57.1510	−	98.9885i	0.0773357	−	0.133949i	0.902100	+	0.431528i	$0.142025\pi$
$740$		0			0
$741$	−147.619	+	106.138i	−0.199216	+	0.143236i
$742$		0			0
$743$	1136.32	+	200.363i	1.52936	+	0.269668i	0.874105	−	0.485738i	$-0.161449\pi$
$743$	1136.32	+	200.363i	1.52936	+	0.269668i	0.655258	+	0.755405i	$0.272560\pi$
$744$		0			0
$745$	−314.010	+	263.486i	−0.421490	+	0.353672i
$746$		0			0
$747$	−113.401	+	100.089i	−0.151808	+	0.133988i
$748$		0			0
$749$	−107.181	+	294.477i	−0.143098	+	0.393160i
$750$		0			0
$751$	−747.335	−	627.088i	−0.995120	−	0.835004i	−0.00881873	−	0.999961i	$-0.502807\pi$
$751$	−747.335	−	627.088i	−0.995120	−	0.835004i	−0.986301	+	0.164957i	$0.947252\pi$
$752$		0			0
$753$	−912.873	+	935.979i	−1.21231	+	1.24300i
$754$		0			0
$755$		−	18.6162i		−	0.0246572i
$756$		0			0
$757$	886.690			1.17132			0.585661	−	0.810556i	$-0.300835\pi$
$757$	886.690			1.17132			0.585661	+	0.810556i	$0.300835\pi$
$758$		0			0
$759$	−62.6953	+	246.251i	−0.0826025	+	0.324442i
$760$		0			0
$761$	−553.370	+	659.480i	−0.727161	+	0.866597i	−0.995306	−	0.0967819i	$-0.969145\pi$
$761$	−553.370	+	659.480i	−0.727161	+	0.866597i	0.268145	+	0.963379i	$0.413590\pi$
$762$		0			0
$763$	−143.268	−	52.1453i	−0.187769	−	0.0683424i
$764$		0			0
$765$	−35.2986	+	44.2685i	−0.0461420	+	0.0578674i
$766$		0			0
$767$	285.652	+	340.427i	0.372428	+	0.443842i
$768$		0			0
$769$	44.1099	−	250.159i	0.0573600	−	0.325305i	−0.942603	−	0.333916i	$-0.891630\pi$
$769$	44.1099	−	250.159i	0.0573600	−	0.325305i	0.999963	+	0.00861097i	$0.00274099\pi$
$770$		0			0
$771$	−1250.34	+	125.153i	−1.62171	+	0.162326i
$772$		0			0
$773$	45.5630	+	26.3058i	0.0589430	+	0.0340308i	0.529182	−	0.848508i	$-0.322499\pi$
$773$	45.5630	+	26.3058i	0.0589430	+	0.0340308i	−0.470239	+	0.882539i	$0.655832\pi$
$774$		0			0
$775$	−173.056	−	299.741i	−0.223297	−	0.386763i
$776$		0			0
$777$	−377.281	+	553.405i	−0.485561	+	0.712233i
$778$		0			0
$779$	−259.998	−	714.338i	−0.333758	−	0.916993i
$780$		0			0
$781$	−109.966	−	623.649i	−0.140802	−	0.798527i
$782$		0			0
$783$	−700.799	+	1085.27i	−0.895018	+	1.38604i
$784$		0			0
$785$	−67.8269	+	11.9597i	−0.0864037	+	0.0152353i
$786$		0			0
$787$	−4.75688	+	1.73136i	−0.00604433	+	0.00219995i	−0.345041	−	0.938588i	$-0.612135\pi$
$787$	−4.75688	+	1.73136i	−0.00604433	+	0.00219995i	0.338996	+	0.940788i	$0.389913\pi$
$788$		0			0
$789$	74.1410	−	989.744i	0.0939683	−	1.25443i
$790$		0			0
$791$	429.016	−	247.692i	0.542371	−	0.313138i
$792$		0			0
$793$	−185.065	+	320.542i	−0.233373	+	0.404214i
$794$		0			0
$795$	82.8195	+	37.3666i	0.104175	+	0.0470020i
$796$		0			0
$797$	1014.91	+	178.956i	1.27342	+	0.224538i	0.769182	−	0.639030i	$-0.220664\pi$
$797$	1014.91	+	178.956i	1.27342	+	0.224538i	0.504234	+	0.863567i	$0.331775\pi$
$798$		0			0
$799$	65.0693	−	54.5996i	0.0814385	−	0.0683350i
$800$		0			0
$801$	328.205	−	602.773i	0.409744	−	0.752525i
$802$		0			0
$803$	61.6302	−	169.328i	0.0767499	−	0.210869i
$804$		0			0
$805$	−68.2765	−	57.2908i	−0.0848155	−	0.0711686i
$806$		0			0
$807$	−110.977	−	394.389i	−0.137518	−	0.488710i
$808$		0			0
$809$			369.548i			0.456796i	0.973568	+	0.228398i	$0.0733488\pi$
$809$			369.548i			0.456796i	−0.973568	+	0.228398i	$0.926651\pi$
$810$		0			0
$811$	−366.571			−0.451998			−0.225999	−	0.974127i	$-0.572565\pi$
$811$	−366.571			−0.451998			−0.225999	+	0.974127i	$0.572565\pi$
$812$		0			0
$813$	491.958	−	138.432i	0.605115	−	0.170273i
$814$		0			0
$815$	5.77101	−	6.87762i	0.00708099	−	0.00843880i
$816$		0			0
$817$	376.699	+	137.107i	0.461076	+	0.167818i
$818$		0			0
$819$	3.47732	+	139.099i	0.00424581	+	0.169840i
$820$		0			0
$821$	146.181	+	174.211i	0.178052	+	0.212194i	0.847688	−	0.530496i	$-0.177994\pi$
$821$	146.181	+	174.211i	0.178052	+	0.212194i	−0.669636	+	0.742690i	$0.733550\pi$
$822$		0			0
$823$	246.238	−	1396.48i	0.299195	−	1.69682i	−0.350448	−	0.936582i	$-0.613970\pi$
$823$	246.238	−	1396.48i	0.299195	−	1.69682i	0.649643	−	0.760239i	$-0.274918\pi$
$824$		0			0
$825$	139.758	−	309.761i	0.169404	−	0.375467i
$826$		0			0
$827$	946.493	+	546.458i	1.14449	+	0.660771i	0.947538	−	0.319642i	$-0.103563\pi$
$827$	946.493	+	546.458i	1.14449	+	0.660771i	0.196951	+	0.980413i	$0.436896\pi$
$828$		0			0
$829$	195.763	+	339.072i	0.236144	+	0.409013i	0.959604	−	0.281353i	$-0.0907831\pi$
$829$	195.763	+	339.072i	0.236144	+	0.409013i	−0.723461	+	0.690365i	$0.757450\pi$
$830$		0			0
$831$	−399.885	−	29.9551i	−0.481209	−	0.0360470i
$832$		0			0
$833$	52.3691	+	143.883i	0.0628681	+	0.172729i
$834$		0			0
$835$	−58.9826	−	334.507i	−0.0706379	−	0.400607i
$836$		0			0
$837$	−160.055	+	379.792i	−0.191225	+	0.453754i
$838$		0			0
$839$	875.233	−	154.327i	1.04319	−	0.183942i	0.374300	−	0.927308i	$-0.377883\pi$
$839$	875.233	−	154.327i	1.04319	−	0.183942i	0.668885	+	0.743366i	$0.266772\pi$
$840$		0			0
$841$	1360.98	−	495.358i	1.61829	−	0.589010i
$842$		0			0
$843$	1125.42	+	767.249i	1.33502	+	0.910141i
$844$		0			0
$845$	196.632	−	113.526i	0.232701	−	0.134350i
$846$		0			0
$847$	165.532	−	286.711i	0.195434	−	0.338501i
$848$		0			0
$849$	116.392	+	1162.81i	0.137093	+	1.36962i
$850$		0			0
$851$	1081.43	+	190.685i	1.27077	+	0.224071i
$852$		0			0
$853$	586.494	−	492.127i	0.687566	−	0.576936i	−0.230640	−	0.973039i	$-0.574082\pi$
$853$	586.494	−	492.127i	0.687566	−	0.576936i	0.918206	+	0.396103i	$0.129638\pi$
$854$		0			0
$855$	172.640	−	67.7683i	0.201918	−	0.0792611i
$856$		0			0
$857$	329.168	−	904.381i	0.384093	−	1.05529i	−0.585523	−	0.810656i	$-0.699111\pi$
$857$	329.168	−	904.381i	0.384093	−	1.05529i	0.969616	−	0.244632i	$-0.0786670\pi$
$858$		0			0
$859$	398.533	+	334.409i	0.463950	+	0.389300i	0.844582	−	0.535427i	$-0.179849\pi$
$859$	398.533	+	334.409i	0.463950	+	0.389300i	−0.380632	+	0.924727i	$0.624294\pi$
$860$		0			0
$861$	−563.780	−	143.538i	−0.654796	−	0.166711i
$862$		0			0
$863$		−	384.728i		−	0.445803i	−0.974841	−	0.222901i	$-0.928447\pi$
$863$		−	384.728i		−	0.445803i	0.974841	−	0.222901i	$-0.0715528\pi$
$864$		0			0
$865$	39.1331			0.0452406
$866$		0			0
$867$	−584.128	−	569.708i	−0.673734	−	0.657102i
$868$		0			0
$869$	−267.771	+	319.117i	−0.308137	+	0.367223i
$870$		0			0
$871$	273.032	+	99.3755i	0.313470	+	0.114094i
$872$		0			0
$873$	307.375	−	915.039i	0.352091	−	1.04815i
$874$		0			0
$875$	161.094	+	191.984i	0.184107	+	0.219410i
$876$		0			0
$877$	−219.693	+	1245.94i	−0.250505	+	1.42069i	0.556847	+	0.830615i	$0.312011\pi$
$877$	−219.693	+	1245.94i	−0.250505	+	1.42069i	−0.807352	+	0.590070i	$0.799100\pi$
$878$		0			0
$879$	595.545	+	828.299i	0.677525	+	0.942320i
$880$		0			0
$881$	−664.884	−	383.871i	−0.754692	−	0.435722i	0.0726947	−	0.997354i	$-0.476840\pi$
$881$	−664.884	−	383.871i	−0.754692	−	0.435722i	−0.827387	+	0.561633i	$0.810173\pi$
$882$		0			0
$883$	−499.788	−	865.659i	−0.566012	−	0.980361i	−0.996955	−	0.0779818i	$-0.975152\pi$
$883$	−499.788	−	865.659i	−0.566012	−	0.980361i	0.430943	−	0.902379i	$-0.358181\pi$
$884$		0			0
$885$	−196.699	−	408.418i	−0.222259	−	0.461490i
$886$		0			0
$887$	−16.8056	−	46.1731i	−0.0189466	−	0.0520553i	0.929859	−	0.367917i	$-0.119929\pi$
$887$	−16.8056	−	46.1731i	−0.0189466	−	0.0520553i	−0.948805	+	0.315861i	$0.897707\pi$
$888$		0			0
$889$	−22.5480	−	127.876i	−0.0253634	−	0.143843i
$890$		0			0
$891$	−394.503	+	90.0930i	−0.442765	+	0.101114i
$892$		0			0
$893$	−274.015	+	48.3162i	−0.306847	+	0.0541054i
$894$		0			0
$895$	−112.163	+	40.8240i	−0.125322	+	0.0456134i
$896$		0			0
$897$	205.532	−	98.9866i	0.229132	−	0.110353i
$898$		0			0
$899$	632.508	−	365.179i	0.703568	−	0.406205i
$900$		0			0
$901$	40.9624	−	70.9489i	0.0454632	−	0.0787446i
$902$		0			0
$903$	249.087	−	179.093i	0.275844	−	0.198331i
$904$		0			0
$905$	216.757	+	38.2201i	0.239511	+	0.0422322i
$906$		0			0
$907$	295.716	−	248.135i	0.326037	−	0.273578i	−0.465046	−	0.885287i	$-0.653962\pi$
$907$	295.716	−	248.135i	0.326037	−	0.273578i	0.791083	+	0.611709i	$0.209518\pi$
$908$		0			0
$909$	201.425	+	996.084i	0.221590	+	1.09580i
$910$		0			0
$911$	−248.878	+	683.786i	−0.273192	+	0.750588i	0.724901	+	0.688853i	$0.241886\pi$
$911$	−248.878	+	683.786i	−0.273192	+	0.750588i	−0.998093	+	0.0617350i	$0.980337\pi$
$912$		0			0
$913$	64.3162	+	53.9677i	0.0704449	+	0.0591103i
$914$		0			0
$915$	263.618	−	270.290i	0.288107	−	0.295399i
$916$		0			0
$917$			528.084i			0.575882i
$918$		0			0
$919$	407.999			0.443960			0.221980	−	0.975051i	$-0.428748\pi$
$919$	407.999			0.443960			0.221980	+	0.975051i	$0.428748\pi$
$920$		0			0
$921$	344.806	−	1354.31i	0.374383	−	1.47048i
$922$		0			0
$923$	−365.440	+	435.514i	−0.395926	+	0.471846i
$924$		0			0
$925$	−1379.99	−	502.275i	−1.49188	−	0.543000i
$926$		0			0
$927$	−1289.46	−	194.274i	−1.39100	−	0.209573i
$928$		0			0
$929$	308.671	+	367.860i	0.332261	+	0.395974i	0.906148	−	0.422961i	$-0.139009\pi$
$929$	308.671	+	367.860i	0.332261	+	0.395974i	−0.573886	+	0.818935i	$0.694565\pi$
$930$		0			0
$931$	87.0951	−	493.941i	0.0935501	−	0.530549i
$932$		0			0
$933$	248.600	−	24.8838i	0.266452	−	0.0266707i
$934$		0			0
$935$	27.2179	+	15.7143i	0.0291100	+	0.0168067i
$936$		0			0
$937$	83.9651	+	145.432i	0.0896105	+	0.155210i	0.907347	−	0.420383i	$-0.138104\pi$
$937$	83.9651	+	145.432i	0.0896105	+	0.155210i	−0.817736	+	0.575593i	$0.804771\pi$
$938$		0			0
$939$	−470.450	+	690.068i	−0.501011	+	0.734896i
$940$		0			0
$941$	−400.997	−	1101.73i	−0.426140	−	1.17081i	−0.948137	−	0.317862i	$-0.897035\pi$
$941$	−400.997	−	1101.73i	−0.426140	−	1.17081i	0.521997	−	0.852947i	$-0.325187\pi$
$942$		0			0
$943$	165.628	+	939.325i	0.175640	+	0.996103i
$944$		0			0
$945$	31.5710	−	138.380i	0.0334085	−	0.146433i
$946$		0			0
$947$	1224.52	−	215.916i	1.29305	−	0.228000i	0.515539	−	0.856866i	$-0.327592\pi$
$947$	1224.52	−	215.916i	1.29305	−	0.228000i	0.777514	+	0.628866i	$0.216481\pi$
$948$		0			0
$949$	−152.015	+	55.3290i	−0.160185	+	0.0583024i
$950$		0			0
$951$	37.0975	−	495.233i	0.0390090	−	0.520750i
$952$		0			0
$953$	−964.422	+	556.809i	−1.01198	+	0.584270i	−0.911772	−	0.410696i	$-0.865286\pi$
$953$	−964.422	+	556.809i	−1.01198	+	0.584270i	−0.100213	+	0.994966i	$0.531952\pi$
$954$		0			0
$955$	84.8984	−	147.048i	0.0888989	−	0.153977i
$956$		0			0
$957$	653.651	+	294.915i	0.683021	+	0.308166i
$958$		0			0
$959$	−201.539	−	35.5368i	−0.210156	−	0.0370561i
$960$		0			0
$961$	−557.678	+	467.947i	−0.580310	+	0.486938i
$962$		0			0
$963$	426.676	+	698.130i	0.443070	+	0.724953i
$964$		0			0
$965$	50.4578	−	138.632i	0.0522879	−	0.143660i
$966$		0			0
$967$	−327.682	−	274.958i	−0.338864	−	0.284341i	0.457436	−	0.889243i	$-0.348768\pi$
$967$	−327.682	−	274.958i	−0.338864	−	0.284341i	−0.796300	+	0.604902i	$0.793212\pi$
$968$		0			0
$969$	−45.2970	−	160.976i	−0.0467461	−	0.166126i
$970$		0			0
$971$		−	713.622i		−	0.734935i	−0.930036	−	0.367467i	$-0.880225\pi$
$971$		−	713.622i		−	0.734935i	0.930036	−	0.367467i	$-0.119775\pi$
$972$		0			0
$973$	−206.882			−0.212623
$974$		0			0
$975$	−293.679	+	82.6380i	−0.301209	+	0.0847570i
$976$		0			0
$977$	−841.747	+	1003.15i	−0.861563	+	1.02677i	0.137778	+	0.990463i	$0.456004\pi$
$977$	−841.747	+	1003.15i	−0.861563	+	1.02677i	−0.999341	+	0.0363074i	$0.988440\pi$
$978$		0			0
$979$	−358.001	−	130.302i	−0.365680	−	0.133097i
$980$		0			0
$981$	−339.652	+	207.585i	−0.346231	+	0.211606i
$982$		0			0
$983$	−845.714	−	1007.88i	−0.860340	−	1.02531i	−0.999386	−	0.0350269i	$-0.988848\pi$
$983$	−845.714	−	1007.88i	−0.860340	−	1.02531i	0.139047	−	0.990286i	$-0.455596\pi$
$984$		0			0
$985$	3.67891	−	20.8641i	0.00373493	−	0.0211819i
$986$		0			0
$987$	−87.5725	+	194.096i	−0.0887260	+	0.196653i
$988$		0			0
$989$	−435.598	−	251.492i	−0.440443	−	0.254290i
$990$		0			0
$991$	−92.3556	−	159.965i	−0.0931944	−	0.161417i	0.815659	−	0.578533i	$-0.196374\pi$
$991$	−92.3556	−	159.965i	−0.0931944	−	0.161417i	−0.908854	+	0.417115i	$0.863041\pi$
$992$		0			0
$993$	−34.3019	−	2.56953i	−0.0345437	−	0.00258765i
$994$		0			0
$995$	−81.1323	−	222.909i	−0.0815400	−	0.224029i
$996$		0			0
$997$	180.998	+	1026.49i	0.181543	+	1.02958i	0.930317	+	0.366755i	$0.119531\pi$
$997$	180.998	+	1026.49i	0.181543	+	1.02958i	−0.748775	+	0.662825i	$0.769358\pi$
$998$		0			0
$999$	515.594	+	1670.98i	0.516111	+	1.67265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.41.6	yes	36
3.2	odd	2		324.3.k.a.233.3		36
4.3	odd	2		432.3.bc.b.257.1		36
27.2	odd	18	inner	108.3.k.a.29.6	✓	36
27.5	odd	18		2916.3.c.b.1457.21		36
27.22	even	9		2916.3.c.b.1457.16		36
27.25	even	9		324.3.k.a.89.3		36
108.83	even	18		432.3.bc.b.353.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.6	✓	36	27.2	odd	18	inner
108.3.k.a.41.6	yes	36	1.1	even	1	trivial
324.3.k.a.89.3		36	27.25	even	9
324.3.k.a.233.3		36	3.2	odd	2
432.3.bc.b.257.1		36	4.3	odd	2
432.3.bc.b.353.1		36	108.83	even	18
2916.3.c.b.1457.16		36	27.22	even	9
2916.3.c.b.1457.21		36	27.5	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)

\(f(q)\)	\(=\)	\(q+(2.88785 - 0.812609i) q^{3} +(0.980262 - 1.16823i) q^{5} +(3.23920 + 1.17897i) q^{7} +(7.67933 - 4.69338i) q^{9} +O(q^{10})\)	\(q+(2.88785 - 0.812609i) q^{3} +(0.980262 - 1.16823i) q^{5} +(3.23920 + 1.17897i) q^{7} +(7.67933 - 4.69338i) q^{9} +(-3.21124 - 3.82701i) q^{11} +(-0.778815 + 4.41688i) q^{13} +(1.88153 - 4.17024i) q^{15} +(-3.57252 - 2.06259i) q^{17} +(6.75637 + 11.7024i) q^{19} +(10.3124 + 0.772492i) q^{21} +(-5.79885 - 15.9322i) q^{23} +(3.93735 + 22.3298i) q^{25} +(18.3629 - 19.7941i) q^{27} +(-47.1200 + 8.30853i) q^{29} +(-14.3439 + 5.22075i) q^{31} +(-12.3834 - 8.44233i) q^{33} +(4.55258 - 2.62843i) q^{35} +(-32.3836 + 56.0901i) q^{37} +(1.34010 + 13.3882i) q^{39} +(-55.4020 - 9.76887i) q^{41} +(22.7258 - 19.0692i) q^{43} +(2.04481 - 13.5720i) q^{45} +(-7.04255 + 19.3493i) q^{47} +(-28.4337 - 23.8587i) q^{49} +(-11.9930 - 3.05340i) q^{51} +19.8596i q^{53} -7.61868 q^{55} +(29.0208 + 28.3044i) q^{57} +(63.6903 - 75.9031i) q^{59} +(77.5488 + 28.2255i) q^{61} +(30.4083 - 6.14908i) q^{63} +(4.39650 + 5.23954i) q^{65} +(11.2495 - 63.7992i) q^{67} +(-29.6928 - 41.2976i) q^{69} +(109.778 + 63.3803i) q^{71} +(18.0346 + 31.2369i) q^{73} +(29.5159 + 61.2857i) q^{75} +(-5.88991 - 16.1824i) q^{77} +(-14.4798 - 82.1188i) q^{79} +(36.9443 - 72.0841i) q^{81} +(-16.5506 + 2.91831i) q^{83} +(-5.91159 + 2.15164i) q^{85} +(-129.324 + 62.2839i) q^{87} +(66.0425 - 38.1296i) q^{89} +(-7.73012 + 13.3890i) q^{91} +(-37.1806 + 26.7327i) q^{93} +(20.2941 + 3.57840i) q^{95} +(82.1613 - 68.9415i) q^{97} +(-42.6218 - 14.3173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 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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