LMFDB - Embedded newform 468.2.k.a.61.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,2,Mod(61,468)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(468, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("468.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.k (of order $3$, degree $2$, 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:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.12
Character	$\chi$	$=$	468.61
Dual form			468.2.k.a.445.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36018 + 1.07234i) q^{3} +(1.62465 + 2.81398i) q^{5} +4.02812 q^{7} +(0.700171 + 2.91715i) q^{9} +O(q^{10})$	\(q+(1.36018 + 1.07234i) q^{3} +(1.62465 + 2.81398i) q^{5} +4.02812 q^{7} +(0.700171 + 2.91715i) q^{9} +(-2.72160 - 4.71395i) q^{11} +(-1.08718 + 3.43774i) q^{13} +(-0.807727 + 5.56969i) q^{15} +(-3.51592 - 6.08975i) q^{17} +(-3.02788 - 5.24444i) q^{19} +(5.47896 + 4.31952i) q^{21} +0.705898 q^{23} +(-2.77897 + 4.81332i) q^{25} +(-2.17582 + 4.71867i) q^{27} +(-1.32512 - 2.29517i) q^{29} +(2.87494 + 4.97955i) q^{31} +(1.35310 - 9.33031i) q^{33} +(6.54428 + 11.3350i) q^{35} +(0.965424 - 1.67216i) q^{37} +(-5.16519 + 3.51010i) q^{39} -4.07703 q^{41} +5.42909 q^{43} +(-7.07126 + 6.70961i) q^{45} +(1.62139 - 2.80833i) q^{47} +9.22575 q^{49} +(1.74801 - 12.0534i) q^{51} -0.0982107 q^{53} +(8.84330 - 15.3170i) q^{55} +(1.50537 - 10.3803i) q^{57} +(-3.47707 + 6.02246i) q^{59} -7.95204 q^{61} +(2.82037 + 11.7506i) q^{63} +(-11.4400 + 2.52581i) q^{65} -0.0908569 q^{67} +(0.960148 + 0.756964i) q^{69} +(2.62645 + 4.54914i) q^{71} +4.40666 q^{73} +(-8.94142 + 3.56697i) q^{75} +(-10.9629 - 18.9884i) q^{77} +(2.93814 - 5.08901i) q^{79} +(-8.01952 + 4.08500i) q^{81} +(-3.26489 + 5.65496i) q^{83} +(11.4243 - 19.7874i) q^{85} +(0.658808 - 4.54282i) q^{87} +(-3.12352 + 5.41009i) q^{89} +(-4.37930 + 13.8476i) q^{91} +(-1.42934 + 9.85600i) q^{93} +(9.83849 - 17.0408i) q^{95} +16.7145 q^{97} +(11.8457 - 11.2399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 28 * q - 4 * q^7 - 2 * q^9	$ 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43} - 38 q^{45} + 11 q^{47} + 24 q^{49} + 5 q^{51} + 52 q^{53} - q^{57} - 8 q^{59} + 14 q^{61} - 21 q^{63} + 38 q^{65} + 14 q^{67} - 21 q^{69} - 12 q^{71} + 14 q^{73} - 14 q^{75} - 28 q^{77} + 5 q^{79} + 10 q^{81} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 11 q^{89} - q^{91} - 9 q^{93} + 28 q^{95} + 50 q^{97} - 29 q^{99}+O(q^{100}) $ 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	1.36018	+	1.07234i	0.785299	+	0.619116i
$3$	1.36018	+	1.07234i	0.785299	+	0.619116i
$4$		0			0
$5$	1.62465	+	2.81398i	0.726565	+	1.25845i	0.958326	+	0.285675i	$0.0922179\pi$
$5$	1.62465	+	2.81398i	0.726565	+	1.25845i	−0.231761	+	0.972773i	$0.574449\pi$
$6$		0			0
$7$	4.02812			1.52249			0.761243	−	0.648467i	$-0.224589\pi$
$7$	4.02812			1.52249			0.761243	+	0.648467i	$0.224589\pi$
$8$		0			0
$9$	0.700171	+	2.91715i	0.233390	+	0.972383i
$10$		0			0
$11$	−2.72160	−	4.71395i	−0.820594	−	1.42131i	−0.905240	−	0.424900i	$-0.860309\pi$
$11$	−2.72160	−	4.71395i	−0.820594	−	1.42131i	0.0846462	−	0.996411i	$-0.473024\pi$
$12$		0			0
$13$	−1.08718	+	3.43774i	−0.301530	+	0.953457i
$13$	−1.08718	+	3.43774i	−0.301530	+	0.953457i
$14$		0			0
$15$	−0.807727	+	5.56969i	−0.208554	+	1.43809i
$16$		0			0
$17$	−3.51592	−	6.08975i	−0.852736	−	1.47698i	−0.878730	−	0.477320i	$-0.841608\pi$
$17$	−3.51592	−	6.08975i	−0.852736	−	1.47698i	0.0259935	−	0.999662i	$-0.491725\pi$
$18$		0			0
$19$	−3.02788	−	5.24444i	−0.694643	−	1.20316i	−0.970301	−	0.241901i	$-0.922229\pi$
$19$	−3.02788	−	5.24444i	−0.694643	−	1.20316i	0.275658	−	0.961256i	$-0.411104\pi$
$20$		0			0
$21$	5.47896	+	4.31952i	1.19561	+	0.942596i
$22$		0			0
$23$	0.705898			0.147190			0.0735950	−	0.997288i	$-0.476553\pi$
$23$	0.705898			0.147190			0.0735950	+	0.997288i	$0.476553\pi$
$24$		0			0
$25$	−2.77897	+	4.81332i	−0.555794	+	0.962664i
$26$		0			0
$27$	−2.17582	+	4.71867i	−0.418737	+	0.908108i
$28$		0			0
$29$	−1.32512	−	2.29517i	−0.246068	−	0.426202i	0.716363	−	0.697727i	$-0.245805\pi$
$29$	−1.32512	−	2.29517i	−0.246068	−	0.426202i	−0.962431	+	0.271525i	$0.912472\pi$
$30$		0			0
$31$	2.87494	+	4.97955i	0.516355	+	0.894353i	0.999820	+	0.0189895i	$0.00604491\pi$
$31$	2.87494	+	4.97955i	0.516355	+	0.894353i	−0.483464	+	0.875364i	$0.660622\pi$
$32$		0			0
$33$	1.35310	−	9.33031i	0.235544	−	1.62420i
$34$		0			0
$35$	6.54428	+	11.3350i	1.10619	+	1.91597i
$36$		0			0
$37$	0.965424	−	1.67216i	0.158715	−	0.274902i	−0.775691	−	0.631113i	$-0.782598\pi$
$37$	0.965424	−	1.67216i	0.158715	−	0.274902i	0.934405	+	0.356211i	$0.115932\pi$
$38$		0			0
$39$	−5.16519	+	3.51010i	−0.827092	+	0.562067i
$40$		0			0
$41$	−4.07703			−0.636725			−0.318363	−	0.947969i	$-0.603133\pi$
$41$	−4.07703			−0.636725			−0.318363	+	0.947969i	$0.603133\pi$
$42$		0			0
$43$	5.42909			0.827929			0.413965	−	0.910293i	$-0.364144\pi$
$43$	5.42909			0.827929			0.413965	+	0.910293i	$0.364144\pi$
$44$		0			0
$45$	−7.07126	+	6.70961i	−1.05412	+	1.00021i
$46$		0			0
$47$	1.62139	−	2.80833i	0.236504	−	0.409637i	−0.723205	−	0.690634i	$-0.757332\pi$
$47$	1.62139	−	2.80833i	0.236504	−	0.409637i	0.959709	+	0.280997i	$0.0906651\pi$
$48$		0			0
$49$	9.22575			1.31796
$50$		0			0
$51$	1.74801	−	12.0534i	0.244771	−	1.68782i
$52$		0			0
$53$	−0.0982107			−0.0134903			−0.00674514	−	0.999977i	$-0.502147\pi$
$53$	−0.0982107			−0.0134903			−0.00674514	+	0.999977i	$0.502147\pi$
$54$		0			0
$55$	8.84330	−	15.3170i	1.19243	−	2.06535i
$56$		0			0
$57$	1.50537	−	10.3803i	0.199391	−	1.37490i
$58$		0			0
$59$	−3.47707	+	6.02246i	−0.452676	+	0.784058i	−0.998551	−	0.0538087i	$-0.982864\pi$
$59$	−3.47707	+	6.02246i	−0.452676	+	0.784058i	0.545875	+	0.837866i	$0.316197\pi$
$60$		0			0
$61$	−7.95204			−1.01815			−0.509077	−	0.860721i	$-0.670013\pi$
$61$	−7.95204			−1.01815			−0.509077	+	0.860721i	$0.670013\pi$
$62$		0			0
$63$	2.82037	+	11.7506i	0.355333	+	1.48044i
$64$		0			0
$65$	−11.4400	+	2.52581i	−1.41896	+	0.313288i
$66$		0			0
$67$	−0.0908569			−0.0110999			−0.00554997	−	0.999985i	$-0.501767\pi$
$67$	−0.0908569			−0.0110999			−0.00554997	+	0.999985i	$0.501767\pi$
$68$		0			0
$69$	0.960148	+	0.756964i	0.115588	+	0.0911277i
$70$		0			0
$71$	2.62645	+	4.54914i	0.311702	+	0.539883i	0.978731	−	0.205148i	$-0.0657677\pi$
$71$	2.62645	+	4.54914i	0.311702	+	0.539883i	−0.667029	+	0.745032i	$0.732434\pi$
$72$		0			0
$73$	4.40666			0.515761			0.257880	−	0.966177i	$-0.416976\pi$
$73$	4.40666			0.515761			0.257880	+	0.966177i	$0.416976\pi$
$74$		0			0
$75$	−8.94142	+	3.56697i	−1.03247	+	0.411878i
$76$		0			0
$77$	−10.9629	−	18.9884i	−1.24934	−	2.16393i
$78$		0			0
$79$	2.93814	−	5.08901i	0.330567	−	0.572559i	−0.652056	−	0.758171i	$-0.726093\pi$
$79$	2.93814	−	5.08901i	0.330567	−	0.572559i	0.982623	+	0.185612i	$0.0594267\pi$
$80$		0			0
$81$	−8.01952	+	4.08500i	−0.891058	+	0.453889i
$82$		0			0
$83$	−3.26489	+	5.65496i	−0.358368	+	0.620712i	−0.987688	−	0.156434i	$-0.950000\pi$
$83$	−3.26489	+	5.65496i	−0.358368	+	0.620712i	0.629320	+	0.777146i	$0.283333\pi$
$84$		0			0
$85$	11.4243	−	19.7874i	1.23914	−	2.14625i
$86$		0			0
$87$	0.658808	−	4.54282i	0.0706317	−	0.487041i
$88$		0			0
$89$	−3.12352	+	5.41009i	−0.331092	+	0.573469i	−0.982726	−	0.185065i	$-0.940751\pi$
$89$	−3.12352	+	5.41009i	−0.331092	+	0.573469i	0.651634	+	0.758534i	$0.274084\pi$
$90$		0			0
$91$	−4.37930	+	13.8476i	−0.459076	+	1.45162i
$92$		0			0
$93$	−1.42934	+	9.85600i	−0.148215	+	1.02202i
$94$		0			0
$95$	9.83849	−	17.0408i	1.00941	−	1.74834i
$96$		0			0
$97$	16.7145			1.69710			0.848552	−	0.529112i	$-0.177475\pi$
$97$	16.7145			1.69710			0.848552	+	0.529112i	$0.177475\pi$
$98$		0			0
$99$	11.8457	−	11.2399i	1.19054	−	1.12965i
$100$		0			0
$101$	−1.97434	−	3.41965i	−0.196454	−	0.340268i	0.750922	−	0.660391i	$-0.229609\pi$
$101$	−1.97434	−	3.41965i	−0.196454	−	0.340268i	−0.947376	+	0.320122i	$0.896276\pi$
$102$		0			0
$103$	1.89833	+	3.28800i	0.187048	+	0.323976i	0.944265	−	0.329187i	$-0.106775\pi$
$103$	1.89833	+	3.28800i	0.187048	+	0.323976i	−0.757217	+	0.653164i	$0.773441\pi$
$104$		0			0
$105$	−3.25362	+	22.4354i	−0.317521	+	2.18947i
$106$		0			0
$107$	4.36995	−	7.56898i	0.422459	−	0.731720i	−0.573720	−	0.819051i	$-0.694500\pi$
$107$	4.36995	−	7.56898i	0.422459	−	0.731720i	0.996179	+	0.0873308i	$0.0278337\pi$
$108$		0			0
$109$	−16.8174			−1.61082			−0.805408	−	0.592721i	$-0.798054\pi$
$109$	−16.8174			−1.61082			−0.805408	+	0.592721i	$0.798054\pi$
$110$		0			0
$111$	3.10628	−	1.23918i	0.294835	−	0.117617i
$112$		0			0
$113$	−1.03438	+	1.79160i	−0.0973064	+	0.168540i	−0.910569	−	0.413357i	$-0.864356\pi$
$113$	−1.03438	+	1.79160i	−0.0973064	+	0.168540i	0.813262	+	0.581897i	$0.197689\pi$
$114$		0			0
$115$	1.14684	+	1.98638i	0.106943	+	0.185231i
$116$		0			0
$117$	−10.7896	−	0.764473i	−0.997499	−	0.0706756i
$118$		0			0
$119$	−14.1625	−	24.5303i	−1.29828	−	2.24868i
$120$		0			0
$121$	−9.31425	+	16.1327i	−0.846750	+	1.46661i
$122$		0			0
$123$	−5.54549	−	4.37196i	−0.500020	−	0.394207i
$124$		0			0
$125$	−1.81293			−0.162153
$126$		0			0
$127$	−3.99454	+	6.91874i	−0.354458	+	0.613939i	−0.987025	−	0.160566i	$-0.948668\pi$
$127$	−3.99454	+	6.91874i	−0.354458	+	0.613939i	0.632567	+	0.774506i	$0.282001\pi$
$128$		0			0
$129$	7.38454	+	5.82184i	0.650172	+	0.512584i
$130$		0			0
$131$	−7.71565	−	13.3639i	−0.674120	−	1.16761i	−0.976725	−	0.214494i	$-0.931190\pi$
$131$	−7.71565	−	13.3639i	−0.674120	−	1.16761i	0.302606	−	0.953116i	$-0.402144\pi$
$132$		0			0
$133$	−12.1967	−	21.1252i	−1.05758	−	1.83179i
$134$		0			0
$135$	−16.8132	+	1.54347i	−1.44705	+	0.132841i
$136$		0			0
$137$	−3.16054			−0.270023			−0.135012	−	0.990844i	$-0.543107\pi$
$137$	−3.16054			−0.270023			−0.135012	+	0.990844i	$0.543107\pi$
$138$		0			0
$139$	9.57578	−	16.5857i	0.812207	−	1.40678i	−0.0991091	−	0.995077i	$-0.531599\pi$
$139$	9.57578	−	16.5857i	0.812207	−	1.40678i	0.911316	−	0.411707i	$-0.135067\pi$
$140$		0			0
$141$	5.21686	−	2.08115i	0.439339	−	0.175264i
$142$		0			0
$143$	19.1642	−	4.23122i	1.60259	−	0.353833i
$144$		0			0
$145$	4.30570	−	7.45769i	0.357569	−	0.619327i
$146$		0			0
$147$	12.5487	+	9.89315i	1.03500	+	0.815973i
$148$		0			0
$149$	−7.98355	+	13.8279i	−0.654038	+	1.13283i	0.328096	+	0.944644i	$0.393593\pi$
$149$	−7.98355	+	13.8279i	−0.654038	+	1.13283i	−0.982134	+	0.188182i	$0.939740\pi$
$150$		0			0
$151$	−5.36881	+	9.29905i	−0.436908	+	0.756746i	−0.997449	−	0.0713802i	$-0.977260\pi$
$151$	−5.36881	+	9.29905i	−0.436908	+	0.756746i	0.560542	+	0.828126i	$0.310593\pi$
$152$		0			0
$153$	15.3030	−	14.5203i	1.23717	−	1.17390i
$154$		0			0
$155$	−9.34155	+	16.1800i	−0.750332	+	1.29961i
$156$		0			0
$157$	−8.93916	−	15.4831i	−0.713423	−	1.23568i	−0.963565	−	0.267476i	$-0.913811\pi$
$157$	−8.93916	−	15.4831i	−0.713423	−	1.23568i	0.250142	−	0.968209i	$-0.419523\pi$
$158$		0			0
$159$	−0.133584	−	0.105315i	−0.0105939	−	0.00835205i
$160$		0			0
$161$	2.84344			0.224095
$162$		0			0
$163$	4.38749	+	7.59936i	0.343655	+	0.595228i	0.985108	−	0.171934i	$-0.0550016\pi$
$163$	4.38749	+	7.59936i	0.343655	+	0.595228i	−0.641453	+	0.767162i	$0.721668\pi$
$164$		0			0
$165$	28.4536	−	11.3509i	2.21511	−	0.883665i
$166$		0			0
$167$	21.7081			1.67982			0.839912	−	0.542723i	$-0.182607\pi$
$167$	21.7081			1.67982			0.839912	+	0.542723i	$0.182607\pi$
$168$		0			0
$169$	−10.6361	−	7.47490i	−0.818159	−	0.574992i
$170$		0			0
$171$	13.1788	−	12.5048i	1.00781	−	0.956264i
$172$		0			0
$173$	1.80542			0.137264			0.0686318	−	0.997642i	$-0.478137\pi$
$173$	1.80542			0.137264			0.0686318	+	0.997642i	$0.478137\pi$
$174$		0			0
$175$	−11.1940	+	19.3886i	−0.846189	+	1.46564i
$176$		0			0
$177$	−11.1876	+	4.46302i	−0.840909	+	0.335461i
$178$		0			0
$179$	−0.722888	+	1.25208i	−0.0540312	+	0.0935847i	−0.891776	−	0.452477i	$-0.850540\pi$
$179$	−0.722888	+	1.25208i	−0.0540312	+	0.0935847i	0.837745	+	0.546062i	$0.183874\pi$
$180$		0			0
$181$	14.4828			1.07650			0.538250	−	0.842785i	$-0.319086\pi$
$181$	14.4828			1.07650			0.538250	+	0.842785i	$0.319086\pi$
$182$		0			0
$183$	−10.8162	−	8.52729i	−0.799556	−	0.630356i
$184$		0			0
$185$	6.27390			0.461266
$186$		0			0
$187$	−19.1379	+	33.1478i	−1.39950	+	2.42401i
$188$		0			0
$189$	−8.76447	+	19.0073i	−0.637521	+	1.38258i
$190$		0			0
$191$	18.0109			1.30322			0.651611	−	0.758553i	$-0.274094\pi$
$191$	18.0109			1.30322			0.651611	+	0.758553i	$0.274094\pi$
$192$		0			0
$193$	−12.4334			−0.894973			−0.447487	−	0.894291i	$-0.647681\pi$
$193$	−12.4334			−0.894973			−0.447487	+	0.894291i	$0.647681\pi$
$194$		0			0
$195$	−18.2690	−	8.83202i	−1.30827	−	0.632474i
$196$		0			0
$197$	−10.2982	+	17.8369i	−0.733713	+	1.27083i	0.221572	+	0.975144i	$0.428881\pi$
$197$	−10.2982	+	17.8369i	−0.733713	+	1.27083i	−0.955286	+	0.295685i	$0.904452\pi$
$198$		0			0
$199$	−2.70264	−	4.68111i	−0.191585	−	0.331835i	0.754191	−	0.656656i	$-0.228029\pi$
$199$	−2.70264	−	4.68111i	−0.191585	−	0.331835i	−0.945776	+	0.324820i	$0.894696\pi$
$200$		0			0
$201$	−0.123582	−	0.0974296i	−0.00871677	−	0.00687215i
$202$		0			0
$203$	−5.33773	−	9.24521i	−0.374635	−	0.648887i
$204$		0			0
$205$	−6.62374	−	11.4727i	−0.462622	−	0.801285i
$206$		0			0
$207$	0.494249	+	2.05921i	0.0343527	+	0.143125i
$208$		0			0
$209$	−16.4814	+	28.5466i	−1.14004	+	1.97461i
$210$		0			0
$211$	−8.39324			−0.577814			−0.288907	−	0.957357i	$-0.593292\pi$
$211$	−8.39324			−0.577814			−0.288907	+	0.957357i	$0.593292\pi$
$212$		0			0
$213$	−1.30579	+	9.00408i	−0.0894713	+	0.616950i
$214$		0			0
$215$	8.82038	+	15.2773i	0.601545	+	1.04191i
$216$		0			0
$217$	11.5806	+	20.0582i	0.786144	+	1.36164i
$218$		0			0
$219$	5.99385	+	4.72544i	0.405027	+	0.319316i
$220$		0			0
$221$	24.7574	−	5.46613i	1.66536	−	0.367692i
$222$		0			0
$223$	10.7663	+	18.6477i	0.720964	+	1.24875i	0.960614	+	0.277886i	$0.0896339\pi$
$223$	10.7663	+	18.6477i	0.720964	+	1.24875i	−0.239650	+	0.970859i	$0.577033\pi$
$224$		0			0
$225$	−15.9869	−	4.73653i	−1.06580	−	0.315769i
$226$		0			0
$227$	4.16383			0.276363			0.138181	−	0.990407i	$-0.455874\pi$
$227$	4.16383			0.276363			0.138181	+	0.990407i	$0.455874\pi$
$228$		0			0
$229$	1.09865	+	1.90291i	0.0726005	+	0.125748i	0.900040	−	0.435807i	$-0.143537\pi$
$229$	1.09865	+	1.90291i	0.0726005	+	0.125748i	−0.827440	+	0.561554i	$0.810204\pi$
$230$		0			0
$231$	5.45045	−	37.5836i	0.358613	−	2.47282i
$232$		0			0
$233$	10.4375			0.683786			0.341893	−	0.939739i	$-0.388932\pi$
$233$	10.4375			0.683786			0.341893	+	0.939739i	$0.388932\pi$
$234$		0			0
$235$	10.5368			0.687342
$236$		0			0
$237$	9.45356	−	3.77128i	0.614074	−	0.244971i
$238$		0			0
$239$	4.61001	+	7.98476i	0.298197	+	0.516491i	0.975723	−	0.219007i	$-0.0702816\pi$
$239$	4.61001	+	7.98476i	0.298197	+	0.516491i	−0.677527	+	0.735498i	$0.736948\pi$
$240$		0			0
$241$	27.3211			1.75991			0.879954	−	0.475058i	$-0.157573\pi$
$241$	27.3211			1.75991			0.879954	+	0.475058i	$0.157573\pi$
$242$		0			0
$243$	−15.2885	−	3.04333i	−0.980758	−	0.195229i
$244$		0			0
$245$	14.9886	+	25.9610i	0.957587	+	1.65859i
$246$		0			0
$247$	21.3209	−	4.70738i	1.35661	−	0.299524i
$248$		0			0
$249$	−10.5049	+	4.19067i	−0.665719	+	0.265573i
$250$		0			0
$251$	9.33769	+	16.1734i	0.589390	+	1.02085i	0.994312	+	0.106502i	$0.0339652\pi$
$251$	9.33769	+	16.1734i	0.589390	+	1.02085i	−0.404923	+	0.914351i	$0.632702\pi$
$252$		0			0
$253$	−1.92118	−	3.32757i	−0.120783	−	0.209203i
$254$		0			0
$255$	36.7579	−	14.6637i	2.30187	−	0.918278i
$256$		0			0
$257$	−14.5721			−0.908983			−0.454491	−	0.890751i	$-0.650179\pi$
$257$	−14.5721			−0.908983			−0.454491	+	0.890751i	$0.650179\pi$
$258$		0			0
$259$	3.88884	−	6.73567i	0.241641	−	0.418534i
$260$		0			0
$261$	5.76754	−	5.47257i	0.357002	−	0.338744i
$262$		0			0
$263$	−11.7110	−	20.2841i	−0.722132	−	1.25077i	−0.960143	−	0.279508i	$-0.909829\pi$
$263$	−11.7110	−	20.2841i	−0.722132	−	1.25077i	0.238011	−	0.971262i	$-0.423505\pi$
$264$		0			0
$265$	−0.159558	−	0.276362i	−0.00980156	−	0.0169768i
$266$		0			0
$267$	−10.0500	+	4.00922i	−0.615051	+	0.245360i
$268$		0			0
$269$	2.43575	+	4.21884i	0.148510	+	0.257227i	0.930677	−	0.365842i	$-0.119219\pi$
$269$	2.43575	+	4.21884i	0.148510	+	0.257227i	−0.782167	+	0.623069i	$0.785886\pi$
$270$		0			0
$271$	7.35182	−	12.7337i	0.446592	−	0.773519i	−0.551570	−	0.834129i	$-0.685971\pi$
$271$	7.35182	−	12.7337i	0.446592	−	0.773519i	0.998162	+	0.0606094i	$0.0193044\pi$
$272$		0			0
$273$	−20.8060	+	14.1391i	−1.25924	+	0.855739i
$274$		0			0
$275$	30.2530			1.82433
$276$		0			0
$277$	−11.7453			−0.705709			−0.352855	−	0.935678i	$-0.614789\pi$
$277$	−11.7453			−0.705709			−0.352855	+	0.935678i	$0.614789\pi$
$278$		0			0
$279$	−12.5131	+	11.8732i	−0.749142	+	0.710828i
$280$		0			0
$281$	1.46853	−	2.54357i	0.0876052	−	0.151737i	−0.818893	−	0.573946i	$-0.805412\pi$
$281$	1.46853	−	2.54357i	0.0876052	−	0.151737i	0.906498	+	0.422209i	$0.138745\pi$
$282$		0			0
$283$	−13.4171			−0.797564			−0.398782	−	0.917046i	$-0.630567\pi$
$283$	−13.4171			−0.797564			−0.398782	+	0.917046i	$0.630567\pi$
$284$		0			0
$285$	31.6556	−	12.6283i	1.87512	−	0.748034i
$286$		0			0
$287$	−16.4228			−0.969405
$288$		0			0
$289$	−16.2234	+	28.0997i	−0.954318	+	1.65293i
$290$		0			0
$291$	22.7348	+	17.9237i	1.33274	+	1.05070i
$292$		0			0
$293$	2.80259	−	4.85422i	0.163729	−	0.283587i	−0.772474	−	0.635046i	$-0.780981\pi$
$293$	2.80259	−	4.85422i	0.163729	−	0.283587i	0.936203	+	0.351459i	$0.114314\pi$
$294$		0			0
$295$	−22.5961			−1.31559
$296$		0			0
$297$	28.1653	−	2.58561i	1.63432	−	0.150032i
$298$		0			0
$299$	−0.767441	+	2.42669i	−0.0443822	+	0.140339i
$300$		0			0
$301$	21.8690			1.26051
$302$		0			0
$303$	0.981582	−	6.76850i	0.0563904	−	0.388840i
$304$		0			0
$305$	−12.9193	−	22.3768i	−0.739755	−	1.28129i
$306$		0			0
$307$	−18.2337			−1.04065			−0.520327	−	0.853967i	$-0.674190\pi$
$307$	−18.2337			−1.04065			−0.520327	+	0.853967i	$0.674190\pi$
$308$		0			0
$309$	−0.943792	+	6.50792i	−0.0536904	+	0.370223i
$310$		0			0
$311$	8.07146	+	13.9802i	0.457691	+	0.792743i	0.998838	−	0.0481840i	$-0.0153434\pi$
$311$	8.07146	+	13.9802i	0.457691	+	0.792743i	−0.541148	+	0.840927i	$0.682010\pi$
$312$		0			0
$313$	9.71308	−	16.8235i	0.549016	−	0.950923i	−0.449327	−	0.893368i	$-0.648336\pi$
$313$	9.71308	−	16.8235i	0.549016	−	0.950923i	0.998342	−	0.0575555i	$-0.0183306\pi$
$314$		0			0
$315$	−28.4839	+	27.0271i	−1.60488	+	1.52280i
$316$		0			0
$317$	−7.10482	+	12.3059i	−0.399047	+	0.691169i	−0.993609	−	0.112881i	$-0.963992\pi$
$317$	−7.10482	+	12.3059i	−0.399047	+	0.691169i	0.594562	+	0.804050i	$0.297325\pi$
$318$		0			0
$319$	−7.21288	+	12.4931i	−0.403844	+	0.699478i
$320$		0			0
$321$	14.0604	−	5.60908i	0.784777	−	0.313068i
$322$		0			0
$323$	−21.2916	+	36.8781i	−1.18469	+	2.05195i
$324$		0			0
$325$	−13.5257	−	14.7863i	−0.750270	−	0.820198i
$326$		0			0
$327$	−22.8747	−	18.0340i	−1.26497	−	0.997283i
$328$		0			0
$329$	6.53115	−	11.3123i	0.360074	−	0.623666i
$330$		0			0
$331$	−7.90919			−0.434728			−0.217364	−	0.976091i	$-0.569746\pi$
$331$	−7.90919			−0.434728			−0.217364	+	0.976091i	$0.569746\pi$
$332$		0			0
$333$	5.55391	+	1.64549i	0.304353	+	0.0901721i
$334$		0			0
$335$	−0.147611	−	0.255669i	−0.00806483	−	0.0139687i
$336$		0			0
$337$	−13.4689	−	23.3289i	−0.733699	−	1.27080i	−0.955292	−	0.295665i	$-0.904459\pi$
$337$	−13.4689	−	23.3289i	−0.733699	−	1.27080i	0.221593	−	0.975139i	$-0.428874\pi$
$338$		0			0
$339$	−3.32815	+	1.32769i	−0.180760	+	0.0721101i
$340$		0			0
$341$	15.6489	−	27.1047i	0.847436	−	1.46780i
$342$		0			0
$343$	8.96558			0.484096
$344$		0			0
$345$	−0.570173	+	3.93163i	−0.0306971	+	0.211672i
$346$		0			0
$347$	2.65856	−	4.60476i	0.142719	−	0.247196i	−0.785801	−	0.618480i	$-0.787749\pi$
$347$	2.65856	−	4.60476i	0.142719	−	0.247196i	0.928520	+	0.371284i	$0.121082\pi$
$348$		0			0
$349$	13.8453	+	23.9808i	0.741122	+	1.28366i	0.951985	+	0.306145i	$0.0990392\pi$
$349$	13.8453	+	23.9808i	0.741122	+	1.28366i	−0.210863	+	0.977516i	$0.567627\pi$
$350$		0			0
$351$	−13.8560	−	12.6100i	−0.739579	−	0.673070i
$352$		0			0
$353$	3.58010	+	6.20091i	0.190549	+	0.330041i	0.945432	−	0.325818i	$-0.105640\pi$
$353$	3.58010	+	6.20091i	0.190549	+	0.330041i	−0.754883	+	0.655859i	$0.772306\pi$
$354$		0			0
$355$	−8.53411	+	14.7815i	−0.452943	+	0.784521i
$356$		0			0
$357$	7.04120	−	48.5526i	0.372660	−	2.56968i
$358$		0			0
$359$	−32.7676			−1.72941			−0.864703	−	0.502284i	$-0.832493\pi$
$359$	−32.7676			−1.72941			−0.864703	+	0.502284i	$0.832493\pi$
$360$		0			0
$361$	−8.83611	+	15.3046i	−0.465058	+	0.805505i
$362$		0			0
$363$	−29.9688	+	11.9554i	−1.57296	+	0.627494i
$364$		0			0
$365$	7.15928	+	12.4002i	0.374734	+	0.649058i
$366$		0			0
$367$	−7.37685	−	12.7771i	−0.385068	−	0.666958i	0.606710	−	0.794923i	$-0.292489\pi$
$367$	−7.37685	−	12.7771i	−0.385068	−	0.666958i	−0.991779	+	0.127965i	$0.959155\pi$
$368$		0			0
$369$	−2.85462	−	11.8933i	−0.148605	−	0.619141i
$370$		0			0
$371$	−0.395604			−0.0205388
$372$		0			0
$373$	−11.4458	+	19.8247i	−0.592642	+	1.02649i	0.401233	+	0.915976i	$0.368582\pi$
$373$	−11.4458	+	19.8247i	−0.592642	+	1.02649i	−0.993875	+	0.110510i	$0.964752\pi$
$374$		0			0
$375$	−2.46591	−	1.94408i	−0.127339	−	0.100392i
$376$		0			0
$377$	9.33083	−	2.06013i	0.480562	−	0.106102i
$378$		0			0
$379$	−11.7486	+	20.3491i	−0.603483	+	1.04526i	0.388807	+	0.921319i	$0.372887\pi$
$379$	−11.7486	+	20.3491i	−0.603483	+	1.04526i	−0.992289	+	0.123943i	$0.960446\pi$
$380$		0			0
$381$	−12.8525	+	5.12722i	−0.658455	+	0.262675i
$382$		0			0
$383$	1.43764	−	2.49007i	0.0734601	−	0.127237i	−0.826955	−	0.562267i	$-0.809929\pi$
$383$	1.43764	−	2.49007i	0.0734601	−	0.127237i	0.900416	+	0.435031i	$0.143262\pi$
$384$		0			0
$385$	35.6219	−	61.6989i	1.81546	−	3.14447i
$386$		0			0
$387$	3.80129	+	15.8375i	0.193231	+	0.805064i
$388$		0			0
$389$	8.62393	−	14.9371i	0.437251	−	0.757341i	−0.560226	−	0.828340i	$-0.689286\pi$
$389$	8.62393	−	14.9371i	0.437251	−	0.757341i	0.997476	+	0.0709995i	$0.0226189\pi$
$390$		0			0
$391$	−2.48188	−	4.29875i	−0.125514	−	0.217397i
$392$		0			0
$393$	3.83599	−	26.4511i	0.193500	−	1.33428i
$394$		0			0
$395$	19.0938			0.960714
$396$		0			0
$397$	1.34311	+	2.32633i	0.0674086	+	0.116755i	0.897760	−	0.440485i	$-0.145194\pi$
$397$	1.34311	+	2.32633i	0.0674086	+	0.116755i	−0.830351	+	0.557240i	$0.811860\pi$
$398$		0			0
$399$	6.06382	−	41.8131i	0.303571	−	2.09327i
$400$		0			0
$401$	12.0183			0.600168			0.300084	−	0.953913i	$-0.402985\pi$
$401$	12.0183			0.600168			0.300084	+	0.953913i	$0.402985\pi$
$402$		0			0
$403$	−20.2440	+	4.46962i	−1.00842	+	0.222648i
$404$		0			0
$405$	−24.5240	−	15.9300i	−1.21861	−	0.791570i
$406$		0			0
$407$	−10.5100			−0.520962
$408$		0			0
$409$	−3.11465	+	5.39473i	−0.154009	+	0.266752i	−0.932698	−	0.360659i	$-0.882552\pi$
$409$	−3.11465	+	5.39473i	−0.154009	+	0.266752i	0.778689	+	0.627411i	$0.215885\pi$
$410$		0			0
$411$	−4.29890	−	3.38917i	−0.212049	−	0.167176i
$412$		0			0
$413$	−14.0061	+	24.2592i	−0.689193	+	1.19372i
$414$		0			0
$415$	−21.2172			−1.04151
$416$		0			0
$417$	30.8103	−	12.2911i	1.50879	−	0.601896i
$418$		0			0
$419$	−3.65128			−0.178377			−0.0891883	−	0.996015i	$-0.528427\pi$
$419$	−3.65128			−0.178377			−0.0891883	+	0.996015i	$0.528427\pi$
$420$		0			0
$421$	−0.290663	+	0.503443i	−0.0141661	+	0.0245363i	−0.873022	−	0.487682i	$-0.837843\pi$
$421$	−0.290663	+	0.503443i	−0.0141661	+	0.0245363i	0.858855	+	0.512218i	$0.171176\pi$
$422$		0			0
$423$	9.32756	+	2.76353i	0.453522	+	0.134367i
$424$		0			0
$425$	39.0826			1.89578
$426$		0			0
$427$	−32.0318			−1.55013
$428$		0			0
$429$	30.6041	+	14.7954i	1.47758	+	0.714326i
$430$		0			0
$431$	18.4032	−	31.8752i	0.886450	−	1.53538i	0.0424070	−	0.999100i	$-0.486497\pi$
$431$	18.4032	−	31.8752i	0.886450	−	1.53538i	0.844043	−	0.536276i	$-0.180169\pi$
$432$		0			0
$433$	−9.01403	−	15.6128i	−0.433187	−	0.750301i	0.563959	−	0.825803i	$-0.309278\pi$
$433$	−9.01403	−	15.6128i	−0.433187	−	0.750301i	−0.997146	+	0.0755015i	$0.975944\pi$
$434$		0			0
$435$	13.8537	−	5.52661i	0.664234	−	0.264981i
$436$		0			0
$437$	−2.13738	−	3.70204i	−0.102245	−	0.177093i
$438$		0			0
$439$	−7.60936	−	13.1798i	−0.363175	−	0.629037i	0.625307	−	0.780379i	$-0.284974\pi$
$439$	−7.60936	−	13.1798i	−0.363175	−	0.629037i	−0.988481	+	0.151342i	$0.951641\pi$
$440$		0			0
$441$	6.45960	+	26.9129i	0.307600	+	1.28157i
$442$		0			0
$443$	6.86666	−	11.8934i	0.326245	−	0.565073i	−0.655519	−	0.755179i	$-0.727550\pi$
$443$	6.86666	−	11.8934i	0.326245	−	0.565073i	0.981763	+	0.190106i	$0.0608833\pi$
$444$		0			0
$445$	−20.2985			−0.962241
$446$		0			0
$447$	−25.6873	+	10.2473i	−1.21497	+	0.484683i
$448$		0			0
$449$	−13.7788	−	23.8656i	−0.650261	−	1.12629i	−0.983059	−	0.183287i	$-0.941326\pi$
$449$	−13.7788	−	23.8656i	−0.650261	−	1.12629i	0.332798	−	0.942998i	$-0.392007\pi$
$450$		0			0
$451$	11.0961	+	19.2189i	0.522493	+	0.904984i
$452$		0			0
$453$	−17.2743	+	6.89117i	−0.811617	+	0.323776i
$454$		0			0
$455$	−46.0817	+	10.1743i	−2.16034	+	0.476977i
$456$		0			0
$457$	14.0293	+	24.2995i	0.656264	+	1.13668i	0.981575	+	0.191076i	$0.0611977\pi$
$457$	14.0293	+	24.2995i	0.656264	+	1.13668i	−0.325311	+	0.945607i	$0.605469\pi$
$458$		0			0
$459$	36.3855	−	3.34024i	1.69833	−	0.155909i
$460$		0			0
$461$	−2.69132			−0.125347			−0.0626737	−	0.998034i	$-0.519963\pi$
$461$	−2.69132			−0.125347			−0.0626737	+	0.998034i	$0.519963\pi$
$462$		0			0
$463$	−2.13932	−	3.70542i	−0.0994228	−	0.172205i	0.812023	−	0.583625i	$-0.198366\pi$
$463$	−2.13932	−	3.70542i	−0.0994228	−	0.172205i	−0.911446	+	0.411420i	$0.865033\pi$
$464$		0			0
$465$	−30.0567	+	11.9904i	−1.39385	+	0.556042i
$466$		0			0
$467$	23.7286			1.09803			0.549014	−	0.835813i	$-0.315004\pi$
$467$	23.7286			1.09803			0.549014	+	0.835813i	$0.315004\pi$
$468$		0			0
$469$	−0.365983			−0.0168995
$470$		0			0
$471$	4.44429	−	30.6456i	0.204782	−	1.41207i
$472$		0			0
$473$	−14.7758	−	25.5925i	−0.679394	−	1.17674i
$474$		0			0
$475$	33.6576			1.54432
$476$		0			0
$477$	−0.0687642	−	0.286495i	−0.00314850	−	0.0131177i
$478$		0			0
$479$	−14.1800	−	24.5605i	−0.647902	−	1.12220i	−0.983623	−	0.180237i	$-0.942313\pi$
$479$	−14.1800	−	24.5605i	−0.647902	−	1.12220i	0.335721	−	0.941961i	$-0.391020\pi$
$480$		0			0
$481$	4.69886	+	5.13682i	0.214250	+	0.234219i
$482$		0			0
$483$	3.86759	+	3.04914i	0.175981	+	0.138741i
$484$		0			0
$485$	27.1553	+	47.0343i	1.23306	+	2.13572i
$486$		0			0
$487$	−18.4267	−	31.9159i	−0.834992	−	1.44625i	−0.894037	−	0.447993i	$-0.852139\pi$
$487$	−18.4267	−	31.9159i	−0.834992	−	1.44625i	0.0590452	−	0.998255i	$-0.481194\pi$
$488$		0			0
$489$	−2.18133	+	15.0414i	−0.0986432	+	0.680195i
$490$		0			0
$491$	16.3370			0.737277			0.368638	−	0.929573i	$-0.379824\pi$
$491$	16.3370			0.737277			0.368638	+	0.929573i	$0.379824\pi$
$492$		0			0
$493$	−9.31801	+	16.1393i	−0.419662	+	0.726876i
$494$		0			0
$495$	50.8739	+	15.0727i	2.28661	+	0.677467i
$496$		0			0
$497$	10.5796	+	18.3245i	0.474562	+	0.821965i
$498$		0			0
$499$	7.02133	+	12.1613i	0.314318	+	0.544415i	0.979292	−	0.202452i	$-0.0648909\pi$
$499$	7.02133	+	12.1613i	0.314318	+	0.544415i	−0.664974	+	0.746866i	$0.731558\pi$
$500$		0			0
$501$	29.5269	+	23.2785i	1.31916	+	1.04001i
$502$		0			0
$503$	5.29736	+	9.17530i	0.236198	+	0.409107i	0.959620	−	0.281299i	$-0.0907653\pi$
$503$	5.29736	+	9.17530i	0.236198	+	0.409107i	−0.723422	+	0.690406i	$0.757432\pi$
$504$		0			0
$505$	6.41522	−	11.1115i	0.285473	−	0.494454i
$506$		0			0
$507$	−6.45131	−	21.5727i	−0.286513	−	0.958076i
$508$		0			0
$509$	2.10992			0.0935206			0.0467603	−	0.998906i	$-0.485110\pi$
$509$	2.10992			0.0935206			0.0467603	+	0.998906i	$0.485110\pi$
$510$		0			0
$511$	17.7506			0.785239
$512$		0			0
$513$	31.3349	−	2.87658i	1.38347	−	0.127004i
$514$		0			0
$515$	−6.16823	+	10.6837i	−0.271805	+	0.470780i
$516$		0			0
$517$	−17.6511			−0.776295
$518$		0			0
$519$	2.45569	+	1.93603i	0.107793	+	0.0849821i
$520$		0			0
$521$	1.56756			0.0686761			0.0343380	−	0.999410i	$-0.489068\pi$
$521$	1.56756			0.0686761			0.0343380	+	0.999410i	$0.489068\pi$
$522$		0			0
$523$	5.77964	−	10.0106i	0.252726	−	0.437734i	−0.711549	−	0.702636i	$-0.752006\pi$
$523$	5.77964	−	10.0106i	0.252726	−	0.437734i	0.964275	+	0.264902i	$0.0853395\pi$
$524$		0			0
$525$	−36.0171	+	14.3682i	−1.57192	+	0.627079i
$526$		0			0
$527$	20.2162	−	35.0154i	0.880629	−	1.52529i
$528$		0			0
$529$	−22.5017			−0.978335
$530$		0			0
$531$	−20.0030	−	5.92638i	−0.868055	−	0.257183i
$532$		0			0
$533$	4.43248	−	14.0158i	0.191992	−	0.607090i
$534$		0			0
$535$	28.3985			1.22778
$536$		0			0
$537$	−2.32591	+	0.927868i	−0.100370	+	0.0400405i
$538$		0			0
$539$	−25.1088	−	43.4898i	−1.08151	−	1.87324i
$540$		0			0
$541$	0.625513			0.0268929			0.0134465	−	0.999910i	$-0.495720\pi$
$541$	0.625513			0.0268929			0.0134465	+	0.999910i	$0.495720\pi$
$542$		0			0
$543$	19.6992	+	15.5305i	0.845374	+	0.666478i
$544$		0			0
$545$	−27.3224	−	47.3238i	−1.17036	−	2.02713i
$546$		0			0
$547$	−13.9938	+	24.2381i	−0.598334	+	1.03634i	0.394733	+	0.918796i	$0.370837\pi$
$547$	−13.9938	+	24.2381i	−0.598334	+	1.03634i	−0.993067	+	0.117549i	$0.962496\pi$
$548$		0			0
$549$	−5.56778	−	23.1973i	−0.237627	−	0.990036i
$550$		0			0
$551$	−8.02458	+	13.8990i	−0.341859	+	0.592117i
$552$		0			0
$553$	11.8352	−	20.4992i	0.503284	−	0.871713i
$554$		0			0
$555$	8.53363	+	6.72776i	0.362232	+	0.285578i
$556$		0			0
$557$	−2.38269	+	4.12695i	−0.100958	+	0.174864i	−0.912080	−	0.410013i	$-0.865524\pi$
$557$	−2.38269	+	4.12695i	−0.100958	+	0.174864i	0.811122	+	0.584878i	$0.198857\pi$
$558$		0			0
$559$	−5.90242	+	18.6638i	−0.249646	+	0.789394i
$560$		0			0
$561$	−61.5767	+	24.5646i	−2.59977	+	1.03712i
$562$		0			0
$563$	−15.2728	+	26.4532i	−0.643670	+	1.11487i	0.340937	+	0.940086i	$0.389256\pi$
$563$	−15.2728	+	26.4532i	−0.643670	+	1.11487i	−0.984607	+	0.174783i	$0.944077\pi$
$564$		0			0
$565$	−6.72203			−0.282798
$566$		0			0
$567$	−32.3036	+	16.4549i	−1.35662	+	0.691040i
$568$		0			0
$569$	5.32035	+	9.21512i	0.223041	+	0.386318i	0.955730	−	0.294246i	$-0.0950684\pi$
$569$	5.32035	+	9.21512i	0.223041	+	0.386318i	−0.732689	+	0.680563i	$0.761735\pi$
$570$		0			0
$571$	−5.02689	−	8.70682i	−0.210369	−	0.364369i	0.741461	−	0.670996i	$-0.234133\pi$
$571$	−5.02689	−	8.70682i	−0.210369	−	0.364369i	−0.951830	+	0.306626i	$0.900800\pi$
$572$		0			0
$573$	24.4980	+	19.3138i	1.02342	+	0.806846i
$574$		0			0
$575$	−1.96167	+	3.39772i	−0.0818074	+	0.141695i
$576$		0			0
$577$	12.1464			0.505661			0.252831	−	0.967511i	$-0.418638\pi$
$577$	12.1464			0.505661			0.252831	+	0.967511i	$0.418638\pi$
$578$		0			0
$579$	−16.9116	−	13.3328i	−0.702822	−	0.554092i
$580$		0			0
$581$	−13.1514	+	22.7788i	−0.545611	+	0.945025i
$582$		0			0
$583$	0.267290	+	0.462961i	0.0110700	+	0.0191739i
$584$		0			0
$585$	−15.3781	−	31.6037i	−0.635807	−	1.30665i
$586$		0			0
$587$	−9.29123	−	16.0929i	−0.383490	−	0.664224i	0.608068	−	0.793885i	$-0.291945\pi$
$587$	−9.29123	−	16.0929i	−0.383490	−	0.664224i	−0.991558	+	0.129660i	$0.958611\pi$
$588$		0			0
$589$	17.4100	−	30.1550i	0.717365	−	1.24251i
$590$		0			0
$591$	−33.1346	+	13.2183i	−1.36298	+	0.543727i
$592$		0			0
$593$	−43.4076			−1.78253			−0.891267	−	0.453478i	$-0.850183\pi$
$593$	−43.4076			−1.78253			−0.891267	+	0.453478i	$0.850183\pi$
$594$		0			0
$595$	46.0184	−	79.7061i	1.88657	−	3.26763i
$596$		0			0
$597$	1.34367	−	9.26530i	0.0549929	−	0.379204i
$598$		0			0
$599$	20.6511	+	35.7688i	0.843781	+	1.46147i	0.886676	+	0.462392i	$0.153009\pi$
$599$	20.6511	+	35.7688i	0.843781	+	1.46147i	−0.0428945	+	0.999080i	$0.513658\pi$
$600$		0			0
$601$	21.6234	+	37.4528i	0.882036	+	1.52773i	0.849073	+	0.528275i	$0.177161\pi$
$601$	21.6234	+	37.4528i	0.882036	+	1.52773i	0.0329627	+	0.999457i	$0.489506\pi$
$602$		0			0
$603$	−0.0636153	−	0.265043i	−0.00259062	−	0.0107934i
$604$		0			0
$605$	−60.5295			−2.46088
$606$		0			0
$607$	0.715469	−	1.23923i	0.0290400	−	0.0502988i	−0.851140	−	0.524939i	$-0.824088\pi$
$607$	0.715469	−	1.23923i	0.0290400	−	0.0502988i	0.880180	+	0.474640i	$0.157422\pi$
$608$		0			0
$609$	2.65376	−	18.2990i	0.107536	−	0.741513i
$610$		0			0
$611$	7.89155	+	8.62708i	0.319258	+	0.349014i
$612$		0			0
$613$	13.8456	−	23.9813i	0.559219	−	0.968596i	−0.438342	−	0.898808i	$-0.644434\pi$
$613$	13.8456	−	23.9813i	0.559219	−	0.968596i	0.997562	−	0.0697884i	$-0.0222324\pi$
$614$		0			0
$615$	3.29313	−	22.7078i	0.132792	−	0.915666i
$616$		0			0
$617$	−19.1736	+	33.2096i	−0.771900	+	1.33697i	0.164621	+	0.986357i	$0.447360\pi$
$617$	−19.1736	+	33.2096i	−0.771900	+	1.33697i	−0.936521	+	0.350613i	$0.885973\pi$
$618$		0			0
$619$	16.5499	−	28.6652i	0.665196	−	1.15215i	−0.314036	−	0.949411i	$-0.601681\pi$
$619$	16.5499	−	28.6652i	0.665196	−	1.15215i	0.979232	−	0.202742i	$-0.0649853\pi$
$620$		0			0
$621$	−1.53591	+	3.33090i	−0.0616339	+	0.133664i
$622$		0			0
$623$	−12.5819	+	21.7925i	−0.504084	+	0.873098i
$624$		0			0
$625$	10.9495	+	18.9651i	0.437979	+	0.758603i
$626$		0			0
$627$	−53.0293	+	21.1548i	−2.11778	+	0.844841i
$628$		0			0
$629$	−13.5774			−0.541367
$630$		0			0
$631$	12.0434	+	20.8597i	0.479439	+	0.830412i	0.999722	−	0.0235818i	$-0.00750702\pi$
$631$	12.0434	+	20.8597i	0.479439	+	0.830412i	−0.520283	+	0.853994i	$0.674174\pi$
$632$		0			0
$633$	−11.4163	−	9.00041i	−0.453757	−	0.357734i
$634$		0			0
$635$	−25.9589			−1.03015
$636$		0			0
$637$	−10.0301	+	31.7157i	−0.397406	+	1.25662i
$638$		0			0
$639$	−11.4316	+	10.8469i	−0.452225	+	0.429097i
$640$		0			0
$641$	−2.65545			−0.104884			−0.0524419	−	0.998624i	$-0.516700\pi$
$641$	−2.65545			−0.104884			−0.0524419	+	0.998624i	$0.516700\pi$
$642$		0			0
$643$	11.3475	−	19.6544i	0.447500	−	0.775092i	−0.550723	−	0.834688i	$-0.685648\pi$
$643$	11.3475	−	19.6544i	0.447500	−	0.775092i	0.998223	+	0.0595958i	$0.0189812\pi$
$644$		0			0
$645$	−4.38523	+	30.2384i	−0.172668	+	1.19063i
$646$		0			0
$647$	−1.50565	+	2.60785i	−0.0591930	+	0.102525i	−0.894103	−	0.447861i	$-0.852186\pi$
$647$	−1.50565	+	2.60785i	−0.0591930	+	0.102525i	0.834910	+	0.550386i	$0.185519\pi$
$648$		0			0
$649$	37.8528			1.48585
$650$		0			0
$651$	−5.75754	+	39.7011i	−0.225656	+	1.55601i
$652$		0			0
$653$	−34.4444			−1.34791			−0.673957	−	0.738770i	$-0.735407\pi$
$653$	−34.4444			−1.34791			−0.673957	+	0.738770i	$0.735407\pi$
$654$		0			0
$655$	25.0705	−	43.4233i	0.979584	−	1.69669i
$656$		0			0
$657$	3.08542	+	12.8549i	0.120374	+	0.501517i
$658$		0			0
$659$	49.7199			1.93681			0.968406	−	0.249380i	$-0.0802270\pi$
$659$	49.7199			1.93681			0.968406	+	0.249380i	$0.0802270\pi$
$660$		0			0
$661$	2.92718			0.113854			0.0569271	−	0.998378i	$-0.481870\pi$
$661$	2.92718			0.113854			0.0569271	+	0.998378i	$0.481870\pi$
$662$		0			0
$663$	39.5361	+	19.1135i	1.53545	+	0.742306i
$664$		0			0
$665$	39.6306	−	68.6422i	1.53681	−	2.66183i
$666$		0			0
$667$	−0.935397	−	1.62016i	−0.0362187	−	0.0627327i
$668$		0			0
$669$	−5.35268	+	36.9094i	−0.206946	+	1.42700i
$670$		0			0
$671$	21.6423	+	37.4855i	0.835491	+	1.44711i
$672$		0			0
$673$	22.1916	+	38.4370i	0.855425	+	1.48164i	0.876250	+	0.481856i	$0.160037\pi$
$673$	22.1916	+	38.4370i	0.855425	+	1.48164i	−0.0208257	+	0.999783i	$0.506630\pi$
$674$		0			0
$675$	−16.6659	−	23.5860i	−0.641471	−	0.907824i
$676$		0			0
$677$	−16.3241	+	28.2742i	−0.627388	+	1.08667i	0.360686	+	0.932687i	$0.382543\pi$
$677$	−16.3241	+	28.2742i	−0.627388	+	1.08667i	−0.988074	+	0.153980i	$0.950791\pi$
$678$		0			0
$679$	67.3282			2.58382
$680$		0			0
$681$	5.66355	+	4.46504i	0.217028	+	0.171101i
$682$		0			0
$683$	−11.0403	−	19.1223i	−0.422443	−	0.731694i	0.573734	−	0.819041i	$-0.305494\pi$
$683$	−11.0403	−	19.1223i	−0.422443	−	0.731694i	−0.996178	+	0.0873478i	$0.972161\pi$
$684$		0			0
$685$	−5.13477	−	8.89368i	−0.196189	−	0.339810i
$686$		0			0
$687$	−0.546214	+	3.76642i	−0.0208394	+	0.143698i
$688$		0			0
$689$	0.106773	−	0.337622i	0.00406773	−	0.0128624i
$690$		0			0
$691$	2.16761	+	3.75441i	0.0824597	+	0.142824i	0.904306	−	0.426885i	$-0.140389\pi$
$691$	2.16761	+	3.75441i	0.0824597	+	0.142824i	−0.821846	+	0.569709i	$0.807056\pi$
$692$		0			0
$693$	47.7160	−	45.2756i	1.81258	−	1.71988i
$694$		0			0
$695$	62.2291			2.36049
$696$		0			0
$697$	14.3345	+	24.8281i	0.542958	+	0.940431i
$698$		0			0
$699$	14.1969	+	11.1926i	0.536976	+	0.423343i
$700$		0			0
$701$	35.4162			1.33765			0.668826	−	0.743419i	$-0.266797\pi$
$701$	35.4162			1.33765			0.668826	+	0.743419i	$0.266797\pi$
$702$		0			0
$703$	−11.6927			−0.441000
$704$		0			0
$705$	14.3319	+	11.2990i	0.539769	+	0.425545i
$706$		0			0
$707$	−7.95287	−	13.7748i	−0.299098	−	0.518054i
$708$		0			0
$709$	−40.5386			−1.52246			−0.761230	−	0.648483i	$-0.775404\pi$
$709$	−40.5386			−1.52246			−0.761230	+	0.648483i	$0.775404\pi$
$710$		0			0
$711$	16.9026	+	5.00783i	0.633898	+	0.187808i
$712$		0			0
$713$	2.02942	+	3.51506i	0.0760023	+	0.131640i
$714$		0			0
$715$	43.0417	+	47.0534i	1.60967	+	1.75970i
$716$		0			0
$717$	−2.29196	+	15.8042i	−0.0855947	+	0.590219i
$718$		0			0
$719$	0.807119	+	1.39797i	0.0301005	+	0.0521355i	0.880683	−	0.473706i	$-0.157084\pi$
$719$	0.807119	+	1.39797i	0.0301005	+	0.0521355i	−0.850583	+	0.525841i	$0.823751\pi$
$720$		0			0
$721$	7.64669	+	13.2445i	0.284778	+	0.493249i
$722$		0			0
$723$	37.1616	+	29.2976i	1.38206	+	1.08959i
$724$		0			0
$725$	14.7298			0.547053
$726$		0			0
$727$	15.9573	−	27.6388i	0.591823	−	1.02507i	−0.402164	−	0.915568i	$-0.631742\pi$
$727$	15.9573	−	27.6388i	0.591823	−	1.02507i	0.993987	−	0.109499i	$-0.0349247\pi$
$728$		0			0
$729$	−17.5316	−	20.5339i	−0.649319	−	0.760516i
$730$		0			0
$731$	−19.0883	−	33.0618i	−0.706005	−	1.22284i
$732$		0			0
$733$	12.2816	+	21.2723i	0.453630	+	0.785710i	0.998608	−	0.0527400i	$-0.0167955\pi$
$733$	12.2816	+	21.2723i	0.453630	+	0.785710i	−0.544978	+	0.838450i	$0.683462\pi$
$734$		0			0
$735$	−7.45189	+	51.3845i	−0.274867	+	1.89535i
$736$		0			0
$737$	0.247276	+	0.428295i	0.00910855	+	0.0157765i
$738$		0			0
$739$	−24.5720	+	42.5599i	−0.903895	+	1.56559i	−0.0815009	+	0.996673i	$0.525971\pi$
$739$	−24.5720	+	42.5599i	−0.903895	+	1.56559i	−0.822394	+	0.568918i	$0.807362\pi$
$740$		0			0
$741$	34.0481	+	16.4604i	1.25079	+	0.604686i
$742$		0			0
$743$	−4.29312			−0.157499			−0.0787496	−	0.996894i	$-0.525093\pi$
$743$	−4.29312			−0.157499			−0.0787496	+	0.996894i	$0.525093\pi$
$744$		0			0
$745$	−51.8819			−1.90080
$746$		0			0
$747$	−18.7823	−	5.56474i	−0.687210	−	0.203603i
$748$		0			0
$749$	17.6027	−	30.4887i	0.643188	−	1.11403i
$750$		0			0
$751$	−20.9211			−0.763421			−0.381711	−	0.924282i	$-0.624665\pi$
$751$	−20.9211			−0.763421			−0.381711	+	0.924282i	$0.624665\pi$
$752$		0			0
$753$	−4.64242	+	32.0118i	−0.169179	+	1.16658i
$754$		0			0
$755$	−34.8897			−1.26977
$756$		0			0
$757$	−12.0256	+	20.8289i	−0.437077	+	0.757040i	−0.997463	−	0.0711917i	$-0.977320\pi$
$757$	−12.0256	+	20.8289i	−0.437077	+	0.757040i	0.560385	+	0.828232i	$0.310653\pi$
$758$		0			0
$759$	0.955151	−	6.58625i	0.0346698	−	0.239066i
$760$		0			0
$761$	6.95555	−	12.0474i	0.252138	−	0.436717i	−0.711976	−	0.702204i	$-0.752199\pi$
$761$	6.95555	−	12.0474i	0.252138	−	0.436717i	0.964114	+	0.265487i	$0.0855328\pi$
$762$		0			0
$763$	−67.7426			−2.45245
$764$		0			0
$765$	65.7218	+	19.4718i	2.37618	+	0.704003i
$766$		0			0
$767$	−16.9234	−	18.5008i	−0.611069	−	0.668024i
$768$		0			0
$769$	−25.5903			−0.922808			−0.461404	−	0.887190i	$-0.652654\pi$
$769$	−25.5903			−0.922808			−0.461404	+	0.887190i	$0.652654\pi$
$770$		0			0
$771$	−19.8207	−	15.6263i	−0.713823	−	0.562766i
$772$		0			0
$773$	15.7133	+	27.2162i	0.565168	+	0.978899i	0.997034	+	0.0769618i	$0.0245219\pi$
$773$	15.7133	+	27.2162i	0.565168	+	0.978899i	−0.431866	+	0.901938i	$0.642145\pi$
$774$		0			0
$775$	−31.9576			−1.14795
$776$		0			0
$777$	12.5125	−	4.99155i	0.448882	−	0.179071i
$778$		0			0
$779$	12.3448	+	21.3817i	0.442297	+	0.766080i
$780$		0			0
$781$	14.2963	−	24.7619i	0.511561	−	0.886050i
$782$		0			0
$783$	13.7133	−	1.25890i	0.490075	−	0.0449895i
$784$		0			0
$785$	29.0460	−	50.3092i	1.03670	−	1.79561i
$786$		0			0
$787$	8.09761	−	14.0255i	0.288648	−	0.499954i	−0.684839	−	0.728694i	$-0.740127\pi$
$787$	8.09761	−	14.0255i	0.288648	−	0.499954i	0.973487	+	0.228741i	$0.0734608\pi$
$788$		0			0
$789$	5.82237	−	40.1482i	0.207282	−	1.42931i
$790$		0			0
$791$	−4.16661	+	7.21678i	−0.148148	+	0.256599i
$792$		0			0
$793$	8.64532	−	27.3370i	0.307004	−	0.970766i
$794$		0			0
$795$	0.0793274	−	0.547003i	0.00281345	−	0.0194002i
$796$		0			0
$797$	−27.0121	+	46.7864i	−0.956819	+	1.65726i	−0.226670	+	0.973972i	$0.572784\pi$
$797$	−27.0121	+	46.7864i	−0.956819	+	1.65726i	−0.730149	+	0.683288i	$0.760549\pi$
$798$		0			0
$799$	−22.8027			−0.806702
$800$		0			0
$801$	−17.9691	−	5.32378i	−0.634905	−	0.188107i
$802$		0			0
$803$	−11.9932	−	20.7728i	−0.423230	−	0.733056i
$804$		0			0
$805$	4.61960	+	8.00138i	0.162819	+	0.282012i
$806$		0			0
$807$	−1.21098	+	8.35034i	−0.0426286	+	0.293946i
$808$		0			0
$809$	−23.0258	+	39.8818i	−0.809542	+	1.40217i	0.103639	+	0.994615i	$0.466951\pi$
$809$	−23.0258	+	39.8818i	−0.809542	+	1.40217i	−0.913181	+	0.407553i	$0.866382\pi$
$810$		0			0
$811$	19.0000			0.667180			0.333590	−	0.942718i	$-0.391740\pi$
$811$	19.0000			0.667180			0.333590	+	0.942718i	$0.391740\pi$
$812$		0			0
$813$	23.6547	−	9.43649i	0.829606	−	0.330952i
$814$		0			0
$815$	−14.2563	+	24.6926i	−0.499376	+	0.864944i
$816$		0			0
$817$	−16.4386	−	28.4726i	−0.575115	−	0.996129i
$818$		0			0
$819$	−43.4618	−	3.07939i	−1.51868	−	0.107603i
$820$		0			0
$821$	−12.4001	−	21.4776i	−0.432767	−	0.749575i	0.564343	−	0.825540i	$-0.309129\pi$
$821$	−12.4001	−	21.4776i	−0.432767	−	0.749575i	−0.997110	+	0.0759655i	$0.975796\pi$
$822$		0			0
$823$	8.54471	−	14.7999i	0.297850	−	0.515891i	−0.677794	−	0.735252i	$-0.737064\pi$
$823$	8.54471	−	14.7999i	0.297850	−	0.515891i	0.975644	+	0.219361i	$0.0703972\pi$
$824$		0			0
$825$	41.1495	+	32.4416i	1.43264	+	1.12947i
$826$		0			0
$827$	37.9512			1.31969			0.659846	−	0.751401i	$-0.270622\pi$
$827$	37.9512			1.31969			0.659846	+	0.751401i	$0.270622\pi$
$828$		0			0
$829$	11.7837	−	20.4099i	0.409263	−	0.708865i	−0.585544	−	0.810640i	$-0.699119\pi$
$829$	11.7837	−	20.4099i	0.409263	−	0.708865i	0.994807	+	0.101776i	$0.0324525\pi$
$830$		0			0
$831$	−15.9758	−	12.5950i	−0.554193	−	0.436916i
$832$		0			0
$833$	−32.4370	−	56.1825i	−1.12388	−	1.94661i
$834$		0			0
$835$	35.2681	+	61.0861i	1.22050	+	2.11397i
$836$		0			0
$837$	−29.7522	+	2.73129i	−1.02839	+	0.0944072i
$838$		0			0
$839$	29.0685			1.00356			0.501778	−	0.864996i	$-0.332679\pi$
$839$	29.0685			1.00356			0.501778	+	0.864996i	$0.332679\pi$
$840$		0			0
$841$	10.9881	−	19.0320i	0.378901	−	0.656276i
$842$		0			0
$843$	4.72504	−	1.88494i	0.162739	−	0.0649209i
$844$		0			0
$845$	3.75430	−	42.0737i	0.129152	−	1.44738i
$846$		0			0
$847$	−37.5189	+	64.9846i	−1.28916	+	2.23290i
$848$		0			0
$849$	−18.2497	−	14.3877i	−0.626327	−	0.493785i
$850$		0			0
$851$	0.681491	−	1.18038i	0.0233612	−	0.0404628i
$852$		0			0
$853$	13.6037	−	23.5624i	0.465783	−	0.806760i	−0.533453	−	0.845830i	$-0.679106\pi$
$853$	13.6037	−	23.5624i	0.465783	−	0.806760i	0.999237	+	0.0390692i	$0.0124393\pi$
$854$		0			0
$855$	56.5991	+	16.7689i	1.93565	+	0.573484i
$856$		0			0
$857$	−17.1683	+	29.7363i	−0.586457	+	1.01577i	0.408235	+	0.912877i	$0.366144\pi$
$857$	−17.1683	+	29.7363i	−0.586457	+	1.01577i	−0.994692	+	0.102896i	$0.967189\pi$
$858$		0			0
$859$	−24.9768	−	43.2610i	−0.852196	−	1.47605i	−0.879222	−	0.476412i	$-0.841937\pi$
$859$	−24.9768	−	43.2610i	−0.852196	−	1.47605i	0.0270262	−	0.999635i	$-0.491396\pi$
$860$		0			0
$861$	−22.3379	−	17.6108i	−0.761273	−	0.600174i
$862$		0			0
$863$	8.06797			0.274637			0.137318	−	0.990527i	$-0.456152\pi$
$863$	8.06797			0.274637			0.137318	+	0.990527i	$0.456152\pi$
$864$		0			0
$865$	2.93318	+	5.08041i	0.0997309	+	0.172739i
$866$		0			0
$867$	−52.1992	+	20.8237i	−1.77278	+	0.707209i
$868$		0			0
$869$	−31.9858			−1.08505
$870$		0			0
$871$	0.0987781	−	0.312342i	0.00334697	−	0.0105833i
$872$		0			0
$873$	11.7030	+	48.7588i	0.396088	+	1.65024i
$874$		0			0
$875$	−7.30270			−0.246876
$876$		0			0
$877$	12.1463	−	21.0381i	0.410153	−	0.710406i	−0.584753	−	0.811211i	$-0.698809\pi$
$877$	12.1463	−	21.0381i	0.410153	−	0.710406i	0.994906	+	0.100805i	$0.0321420\pi$
$878$		0			0
$879$	9.01740	−	3.59728i	0.304149	−	0.121333i
$880$		0			0
$881$	22.8199	−	39.5252i	0.768822	−	1.33164i	−0.169379	−	0.985551i	$-0.554176\pi$
$881$	22.8199	−	39.5252i	0.768822	−	1.33164i	0.938202	−	0.346089i	$-0.112490\pi$
$882$		0			0
$883$	31.7238			1.06759			0.533796	−	0.845613i	$-0.320765\pi$
$883$	31.7238			1.06759			0.533796	+	0.845613i	$0.320765\pi$
$884$		0			0
$885$	−30.7347	−	24.2307i	−1.03314	−	0.814506i
$886$		0			0
$887$	26.4579			0.888370			0.444185	−	0.895935i	$-0.353493\pi$
$887$	26.4579			0.888370			0.444185	+	0.895935i	$0.353493\pi$
$888$		0			0
$889$	−16.0905	+	27.8695i	−0.539657	+	0.934714i
$890$		0			0
$891$	41.0825	+	26.6859i	1.37631	+	0.894011i
$892$		0			0
$893$	−19.6375			−0.657143
$894$		0			0
$895$	−4.69776			−0.157029
$896$		0			0
$897$	−3.64610	+	2.47778i	−0.121740	+	0.0827306i
$898$		0			0
$899$	7.61927	−	13.1970i	0.254117	−	0.440143i
$900$		0			0
$901$	0.345301	+	0.598079i	0.0115036	+	0.0199249i
$902$		0			0
$903$	29.7458	+	23.4511i	0.989878	+	0.780403i
$904$		0			0
$905$	23.5295	+	40.7543i	0.782147	+	1.35472i
$906$		0			0
$907$	−14.1210	−	24.4583i	−0.468880	−	0.812124i	0.530487	−	0.847693i	$-0.322009\pi$
$907$	−14.1210	−	24.4583i	−0.468880	−	0.812124i	−0.999367	+	0.0355691i	$0.988676\pi$
$908$		0			0
$909$	8.59327	−	8.15378i	0.285021	−	0.270444i
$910$		0			0
$911$	−6.73518	+	11.6657i	−0.223146	+	0.386501i	−0.955762	−	0.294142i	$-0.904966\pi$
$911$	−6.73518	+	11.6657i	−0.223146	+	0.386501i	0.732615	+	0.680643i	$0.238299\pi$
$912$		0			0
$913$	35.5429			1.17630
$914$		0			0
$915$	6.42308	−	44.2904i	0.212340	−	1.46419i
$916$		0			0
$917$	−31.0796	−	53.8314i	−1.02634	−	1.77767i
$918$		0			0
$919$	−0.668978	−	1.15870i	−0.0220675	−	0.0382221i	0.854781	−	0.518989i	$-0.173692\pi$
$919$	−0.668978	−	1.15870i	−0.0220675	−	0.0382221i	−0.876848	+	0.480767i	$0.840358\pi$
$920$		0			0
$921$	−24.8011	−	19.5528i	−0.817225	−	0.644285i
$922$		0			0
$923$	−18.4942	+	4.08328i	−0.608743	+	0.134403i
$924$		0			0
$925$	5.36577	+	9.29379i	0.176426	+	0.305578i
$926$		0			0
$927$	−8.26243	+	7.83986i	−0.271374	+	0.257495i
$928$		0			0
$929$	35.6255			1.16884			0.584418	−	0.811453i	$-0.301323\pi$
$929$	35.6255			1.16884			0.584418	+	0.811453i	$0.301323\pi$
$930$		0			0
$931$	−27.9345	−	48.3839i	−0.915515	−	1.58572i
$932$		0			0
$933$	−4.01289	+	27.6709i	−0.131376	+	0.905905i
$934$		0			0
$935$	−124.369			−4.06731
$936$		0			0
$937$	−4.94466			−0.161535			−0.0807674	−	0.996733i	$-0.525737\pi$
$937$	−4.94466			−0.161535			−0.0807674	+	0.996733i	$0.525737\pi$
$938$		0			0
$939$	31.2521	−	12.4673i	1.01987	−	0.406855i
$940$		0			0
$941$	21.5001	+	37.2393i	0.700884	+	1.21397i	0.968156	+	0.250346i	$0.0805445\pi$
$941$	21.5001	+	37.2393i	0.700884	+	1.21397i	−0.267272	+	0.963621i	$0.586122\pi$
$942$		0			0
$943$	−2.87797			−0.0937195
$944$		0			0
$945$	−67.7254	+	6.21728i	−2.20311	+	0.202248i
$946$		0			0
$947$	7.05397	+	12.2178i	0.229223	+	0.397026i	0.957578	−	0.288174i	$-0.0930481\pi$
$947$	7.05397	+	12.2178i	0.229223	+	0.397026i	−0.728355	+	0.685200i	$0.759715\pi$
$948$		0			0
$949$	−4.79085	+	15.1489i	−0.155518	+	0.491756i
$950$		0			0
$951$	−22.8600	+	9.11945i	−0.741285	+	0.295718i
$952$		0			0
$953$	−12.1851	−	21.1053i	−0.394716	−	0.683668i	0.598349	−	0.801235i	$-0.295824\pi$
$953$	−12.1851	−	21.1053i	−0.394716	−	0.683668i	−0.993065	+	0.117568i	$0.962490\pi$
$954$		0			0
$955$	29.2614	+	50.6822i	0.946876	+	1.64004i
$956$		0			0
$957$	−23.2076	+	9.25815i	−0.750196	+	0.299273i
$958$		0			0
$959$	−12.7310			−0.411106
$960$		0			0
$961$	−1.03061	+	1.78507i	−0.0332455	+	0.0575828i
$962$		0			0
$963$	25.1395	+	7.44822i	0.810110	+	0.240016i
$964$		0			0
$965$	−20.1999	−	34.9872i	−0.650257	−	1.12628i
$966$		0			0
$967$	11.6255	+	20.1359i	0.373850	+	0.647527i	0.990154	−	0.139981i	$-0.0447043\pi$
$967$	11.6255	+	20.1359i	0.373850	+	0.647527i	−0.616304	+	0.787508i	$0.711371\pi$
$968$		0			0
$969$	−68.5062	+	27.3289i	−2.20074	+	0.877932i
$970$		0			0
$971$	−9.46186	−	16.3884i	−0.303646	−	0.525930i	0.673313	−	0.739357i	$-0.264871\pi$
$971$	−9.46186	−	16.3884i	−0.303646	−	0.525930i	−0.976959	+	0.213428i	$0.931537\pi$
$972$		0			0
$973$	38.5724	−	66.8093i	1.23657	−	2.14181i
$974$		0			0
$975$	−2.54135	−	34.6162i	−0.0813882	−	1.10861i
$976$		0			0
$977$	−4.51953			−0.144592			−0.0722962	−	0.997383i	$-0.523033\pi$
$977$	−4.51953			−0.144592			−0.0722962	+	0.997383i	$0.523033\pi$
$978$		0			0
$979$	34.0039			1.08677
$980$		0			0
$981$	−11.7751	−	49.0589i	−0.375949	−	1.56633i
$982$		0			0
$983$	−2.16165	+	3.74408i	−0.0689459	+	0.119418i	−0.898438	−	0.439101i	$-0.855297\pi$
$983$	−2.16165	+	3.74408i	−0.0689459	+	0.119418i	0.829492	+	0.558519i	$0.188630\pi$
$984$		0			0
$985$	−66.9236			−2.13236
$986$		0			0
$987$	21.0142	−	8.38311i	0.668888	−	0.266837i
$988$		0			0
$989$	3.83239			0.121863
$990$		0			0
$991$	19.8927	−	34.4552i	0.631912	−	1.09450i	−0.355248	−	0.934772i	$-0.615604\pi$
$991$	19.8927	−	34.4552i	0.631912	−	1.09450i	0.987160	−	0.159732i	$-0.0510630\pi$
$992$		0			0
$993$	−10.7579	−	8.48134i	−0.341392	−	0.269147i
$994$		0			0
$995$	8.78169	−	15.2103i	0.278398	−	0.482200i
$996$		0			0
$997$	21.7154			0.687735			0.343867	−	0.939018i	$-0.388263\pi$
$997$	21.7154			0.687735			0.343867	+	0.939018i	$0.388263\pi$
$998$		0			0
$999$	5.78979	+	8.19384i	0.183181	+	0.259242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.k.a.61.12	yes	28
3.2	odd	2		1404.2.k.a.1153.3		28
9.4	even	3		468.2.j.a.373.2	yes	28
9.5	odd	6		1404.2.j.a.685.3		28
13.3	even	3		468.2.j.a.133.2	✓	28
39.29	odd	6		1404.2.j.a.289.3		28
117.68	odd	6		1404.2.k.a.1225.3		28
117.94	even	3	inner	468.2.k.a.445.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.2	✓	28	13.3	even	3
468.2.j.a.373.2	yes	28	9.4	even	3
468.2.k.a.61.12	yes	28	1.1	even	1	trivial
468.2.k.a.445.12	yes	28	117.94	even	3	inner
1404.2.j.a.289.3		28	39.29	odd	6
1404.2.j.a.685.3		28	9.5	odd	6
1404.2.k.a.1153.3		28	3.2	odd	2
1404.2.k.a.1225.3		28	117.68	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36018 + 1.07234i) q^{3} +(1.62465 + 2.81398i) q^{5} +4.02812 q^{7} +(0.700171 + 2.91715i) q^{9} +O(q^{10})\)	\(q+(1.36018 + 1.07234i) q^{3} +(1.62465 + 2.81398i) q^{5} +4.02812 q^{7} +(0.700171 + 2.91715i) q^{9} +(-2.72160 - 4.71395i) q^{11} +(-1.08718 + 3.43774i) q^{13} +(-0.807727 + 5.56969i) q^{15} +(-3.51592 - 6.08975i) q^{17} +(-3.02788 - 5.24444i) q^{19} +(5.47896 + 4.31952i) q^{21} +0.705898 q^{23} +(-2.77897 + 4.81332i) q^{25} +(-2.17582 + 4.71867i) q^{27} +(-1.32512 - 2.29517i) q^{29} +(2.87494 + 4.97955i) q^{31} +(1.35310 - 9.33031i) q^{33} +(6.54428 + 11.3350i) q^{35} +(0.965424 - 1.67216i) q^{37} +(-5.16519 + 3.51010i) q^{39} -4.07703 q^{41} +5.42909 q^{43} +(-7.07126 + 6.70961i) q^{45} +(1.62139 - 2.80833i) q^{47} +9.22575 q^{49} +(1.74801 - 12.0534i) q^{51} -0.0982107 q^{53} +(8.84330 - 15.3170i) q^{55} +(1.50537 - 10.3803i) q^{57} +(-3.47707 + 6.02246i) q^{59} -7.95204 q^{61} +(2.82037 + 11.7506i) q^{63} +(-11.4400 + 2.52581i) q^{65} -0.0908569 q^{67} +(0.960148 + 0.756964i) q^{69} +(2.62645 + 4.54914i) q^{71} +4.40666 q^{73} +(-8.94142 + 3.56697i) q^{75} +(-10.9629 - 18.9884i) q^{77} +(2.93814 - 5.08901i) q^{79} +(-8.01952 + 4.08500i) q^{81} +(-3.26489 + 5.65496i) q^{83} +(11.4243 - 19.7874i) q^{85} +(0.658808 - 4.54282i) q^{87} +(-3.12352 + 5.41009i) q^{89} +(-4.37930 + 13.8476i) q^{91} +(-1.42934 + 9.85600i) q^{93} +(9.83849 - 17.0408i) q^{95} +16.7145 q^{97} +(11.8457 - 11.2399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 28 * q - 4 * q^7 - 2 * q^9	\( 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43} - 38 q^{45} + 11 q^{47} + 24 q^{49} + 5 q^{51} + 52 q^{53} - q^{57} - 8 q^{59} + 14 q^{61} - 21 q^{63} + 38 q^{65} + 14 q^{67} - 21 q^{69} - 12 q^{71} + 14 q^{73} - 14 q^{75} - 28 q^{77} + 5 q^{79} + 10 q^{81} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 11 q^{89} - q^{91} - 9 q^{93} + 28 q^{95} + 50 q^{97} - 29 q^{99}+O(q^{100}) \) 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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